Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [112,13,Mod(17,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("112.17");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.s (of order \(6\), degree \(2\), 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: | \(102.367307535\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} - 2204556 x^{14} - 87623088 x^{13} + 1948666431190 x^{12} + 195028079162640 x^{11} + \cdots + 24\!\cdots\!25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{62}\cdot 3^{11}\cdot 7^{7} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 33.7 | ||
Root | \(-496.819 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 112.33 |
Dual form | 112.13.s.c.17.7 |
$q$-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 \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(85\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 745.979 | − | 430.691i | 1.02329 | − | 0.590797i | 0.108235 | − | 0.994125i | \(-0.465480\pi\) |
0.915055 | + | 0.403328i | \(0.132147\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7532.28 | − | 4348.76i | −0.482066 | − | 0.278321i | 0.239211 | − | 0.970968i | \(-0.423111\pi\) |
−0.721277 | + | 0.692647i | \(0.756445\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 93774.2 | + | 71047.1i | 0.797067 | + | 0.603891i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 105269. | − | 182331.i | 0.198082 | − | 0.343089i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −257922. | − | 446735.i | −0.145590 | − | 0.252170i | 0.784003 | − | 0.620758i | \(-0.213175\pi\) |
−0.929593 | + | 0.368587i | \(0.879842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.74786e6i | 0.569292i | 0.958633 | + | 0.284646i | \(0.0918760\pi\) | ||||
−0.958633 | + | 0.284646i | \(0.908124\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.49190e6 | −0.657725 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.50579e6 | − | 3.17877e6i | 0.228100 | − | 0.131694i | −0.381595 | − | 0.924330i | \(-0.624625\pi\) |
0.609695 | + | 0.792636i | \(0.291292\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.71736e7 | − | 3.87827e7i | −1.42783 | − | 0.824359i | −0.430882 | − | 0.902408i | \(-0.641797\pi\) |
−0.996949 | + | 0.0780497i | \(0.975131\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00553e8 | + | 1.26120e7i | 1.17241 | + | 0.147051i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.20289e7 | + | 9.01168e7i | −0.351462 | + | 0.608750i | −0.986506 | − | 0.163726i | \(-0.947649\pi\) |
0.635044 | + | 0.772476i | \(0.280982\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.42468e7 | − | 1.45920e8i | −0.345075 | − | 0.597687i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.76420e8i | 0.713488i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.41564e8 | −0.237994 | −0.118997 | − | 0.992895i | \(-0.537968\pi\) | ||||
−0.118997 | + | 0.992895i | \(0.537968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.99677e8 | − | 4.03959e8i | 0.788365 | − | 0.455163i | −0.0510215 | − | 0.998698i | \(-0.516248\pi\) |
0.839387 | + | 0.543535i | \(0.182914\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.84809e8 | − | 2.22170e8i | −0.297963 | − | 0.172029i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.97366e8 | − | 9.42949e8i | −0.216164 | − | 0.512956i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.86759e9 | − | 3.23475e9i | 0.727898 | − | 1.26076i | −0.229873 | − | 0.973221i | \(-0.573831\pi\) |
0.957770 | − | 0.287535i | \(-0.0928357\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.18348e9 | + | 2.04985e9i | 0.336336 | + | 0.582551i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.75235e9i | − | 1.00047i | −0.865889 | − | 0.500236i | \(-0.833246\pi\) | ||
0.865889 | − | 0.500236i | \(-0.166754\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.94118e9 | −1.41444 | −0.707219 | − | 0.706994i | \(-0.750051\pi\) | ||||
−0.707219 | + | 0.706994i | \(0.750051\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.58583e9 | + | 9.15581e8i | −0.190977 | + | 0.110261i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.79163e10 | − | 1.03440e10i | −1.66211 | − | 0.959621i | −0.971705 | − | 0.236199i | \(-0.924098\pi\) |
−0.690407 | − | 0.723421i | \(-0.742568\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.74590e9 | + | 1.33248e10i | 0.270632 | + | 0.962683i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.73814e9 | − | 4.74259e9i | 0.155609 | − | 0.269522i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.17271e10 | − | 2.03119e10i | −0.529097 | − | 0.916423i | −0.999424 | − | 0.0339308i | \(-0.989197\pi\) |
0.470327 | − | 0.882492i | \(-0.344136\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.48657e9i | 0.162083i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.68134e10 | −1.94811 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.83475e9 | − | 1.05929e9i | 0.0434976 | − | 0.0251133i | −0.478094 | − | 0.878309i | \(-0.658672\pi\) |
0.521591 | + | 0.853196i | \(0.325339\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.28376e9 | − | 4.20528e9i | −0.141376 | − | 0.0816237i | 0.427643 | − | 0.903947i | \(-0.359344\pi\) |
−0.569020 | + | 0.822324i | \(0.692677\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.28256e10 | − | 9.61890e9i | 0.365073 | − | 0.153845i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.19498e10 | − | 2.06977e10i | 0.158446 | − | 0.274436i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.27239e10 | − | 5.66794e10i | −0.361756 | − | 0.626580i | 0.626494 | − | 0.779426i | \(-0.284489\pi\) |
−0.988250 | + | 0.152846i | \(0.951156\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.96336e10i | 0.830570i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.46780e11 | 1.92646 | 0.963229 | − | 0.268683i | \(-0.0865885\pi\) | ||||
0.963229 | + | 0.268683i | \(0.0865885\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.87210e10 | − | 5.12231e10i | 0.586259 | − | 0.338477i | −0.177358 | − | 0.984146i | \(-0.556755\pi\) |
0.763617 | + | 0.645670i | \(0.223422\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.25693e11 | − | 7.25687e10i | −0.706224 | − | 0.407738i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.55276e9 | − | 6.02168e10i | 0.0362378 | − | 0.288917i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.38548e11 | + | 2.39973e11i | −0.569952 | + | 0.987187i | 0.426618 | + | 0.904432i | \(0.359705\pi\) |
−0.996570 | + | 0.0827544i | \(0.973628\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.74996e11 | + | 3.03102e11i | 0.619609 | + | 1.07319i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 8.18271e10i | − | 0.250281i | −0.992139 | − | 0.125141i | \(-0.960062\pi\) | ||
0.992139 | − | 0.125141i | \(-0.0399382\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.52949e10 | −0.146613 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.05604e11 | + | 6.09705e10i | −0.243537 | + | 0.140606i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.69496e10 | − | 2.71064e10i | −0.0944695 | − | 0.0545420i | 0.452021 | − | 0.892007i | \(-0.350703\pi\) |
−0.546491 | + | 0.837465i | \(0.684037\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.95228e11 | + | 2.57679e11i | −0.343790 | + | 0.453764i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.47963e11 | − | 6.02689e11i | 0.537818 | − | 0.931528i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.37314e11 | + | 5.84244e11i | 0.458873 | + | 0.794791i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.42738e11i | 0.411465i | 0.978608 | + | 0.205732i | \(0.0659576\pi\) | ||||
−0.978608 | + | 0.205732i | \(0.934042\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.08605e11 | −0.115356 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.47590e12 | + | 8.52112e11i | −1.39037 | + | 0.802728i | −0.993356 | − | 0.115086i | \(-0.963286\pi\) |
−0.397010 | + | 0.917814i | \(0.629952\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.13530e12 | − | 6.55464e11i | −0.950793 | − | 0.548941i | −0.0574658 | − | 0.998347i | \(-0.518302\pi\) |
−0.893327 | + | 0.449407i | \(0.851635\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.02546e11 | − | 5.32278e11i | −0.524251 | − | 0.397194i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.01708e12 | + | 1.76164e12i | −0.677727 | + | 1.17386i | 0.297937 | + | 0.954585i | \(0.403701\pi\) |
−0.975664 | + | 0.219271i | \(0.929632\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.09731e12 | − | 1.90060e12i | −0.654290 | − | 1.13326i | −0.982071 | − | 0.188510i | \(-0.939634\pi\) |
0.327781 | − | 0.944754i | \(-0.393699\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 3.21741e12i | − | 1.72016i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.33384e11 | −0.112098 | −0.0560492 | − | 0.998428i | \(-0.517850\pi\) | ||||
−0.0560492 | + | 0.998428i | \(0.517850\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.83793e11 | − | 4.52523e11i | 0.338855 | − | 0.195638i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.01022e11 | + | 2.89265e11i | 0.195318 | + | 0.112767i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.42143e11 | + | 9.30842e10i | 0.261340 | + | 0.0327789i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.43617e12 | − | 2.48751e12i | 0.457607 | − | 0.792598i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.04679e12 | − | 3.54515e12i | −0.591076 | − | 1.02377i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.58890e12i | 0.940808i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.43716e12 | −1.29583 | −0.647917 | − | 0.761711i | \(-0.724360\pi\) | ||||
−0.647917 | + | 0.761711i | \(0.724360\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.66993e12 | + | 3.85089e12i | −1.44738 | + | 0.835646i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.18347e12 | − | 4.14738e12i | −1.42137 | − | 0.820627i | −0.424953 | − | 0.905216i | \(-0.639709\pi\) |
−0.996416 | + | 0.0845881i | \(0.973043\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.54375e12 | − | 8.40930e12i | −0.640255 | − | 1.51932i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.20209e12 | − | 2.08207e12i | 0.198579 | − | 0.343948i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.43911e12 | − | 2.49260e12i | −0.217655 | − | 0.376990i | 0.736435 | − | 0.676508i | \(-0.236508\pi\) |
−0.954091 | + | 0.299518i | \(0.903174\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.39529e12i | 1.02534i | 0.858587 | + | 0.512669i | \(0.171343\pi\) | ||||
−0.858587 | + | 0.512669i | \(0.828657\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.78202e13 | −2.26776 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.22757e12 | − | 7.08735e11i | 0.143558 | − | 0.0828835i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.06630e12 | + | 6.15630e11i | 0.114729 | + | 0.0662387i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.53322e12 | + | 8.32667e12i | 0.845685 | + | 0.825216i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.78126e11 | + | 1.69416e12i | −0.0893876 | + | 0.154824i | −0.907252 | − | 0.420587i | \(-0.861824\pi\) |
0.817865 | + | 0.575410i | \(0.195158\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.20437e12 | − | 1.24783e13i | −0.607763 | − | 1.05268i | −0.991608 | − | 0.129279i | \(-0.958734\pi\) |
0.383845 | − | 0.923397i | \(-0.374600\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.33850e12i | − | 0.104345i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.02689e12 | −0.506725 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.59678e13 | − | 9.21899e12i | 1.06622 | − | 0.615582i | 0.139073 | − | 0.990282i | \(-0.455588\pi\) |
0.927146 | + | 0.374701i | \(0.122255\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.74963e13 | − | 1.01015e13i | −1.08284 | − | 0.625178i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.12815e13 | + | 4.75412e12i | −0.647757 | + | 0.272970i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.38586e13 | + | 2.40039e13i | −0.738916 | + | 1.27984i | 0.214069 | + | 0.976819i | \(0.431328\pi\) |
−0.952984 | + | 0.303021i | \(0.902005\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.93233e12 | + | 3.34689e12i | 0.0957584 | + | 0.165858i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.19940e12i | − | 0.0552923i | −0.999618 | − | 0.0276461i | \(-0.991199\pi\) | ||
0.999618 | − | 0.0276461i | \(-0.00880116\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.57473e13 | 0.675907 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.41426e13 | + | 8.16523e12i | −0.565656 | + | 0.326582i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.84029e12 | + | 2.21719e12i | 0.143248 | + | 0.0827041i | 0.569911 | − | 0.821706i | \(-0.306978\pi\) |
−0.426663 | + | 0.904411i | \(0.640311\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.46701e12 | − | 1.96690e13i | 0.0858899 | − | 0.684784i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.12456e11 | − | 1.58042e12i | 0.0296738 | − | 0.0513964i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.21016e13 | + | 3.82811e13i | 0.671902 | + | 1.16377i | 0.977364 | + | 0.211564i | \(0.0678557\pi\) |
−0.305462 | + | 0.952204i | \(0.598811\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.41993e12i | 0.0403828i | 0.999796 | + | 0.0201914i | \(0.00642756\pi\) | ||||
−0.999796 | + | 0.0201914i | \(0.993572\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.24471e12 | −0.192892 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.81344e13 | + | 1.62434e13i | −0.701789 | + | 0.405178i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.84013e12 | − | 1.63975e12i | −0.0664185 | − | 0.0383467i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.96388e13 | + | 2.59211e13i | −0.430869 | + | 0.568698i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.94428e13 | − | 5.09965e13i | 0.606428 | − | 1.05036i | −0.385396 | − | 0.922751i | \(-0.625935\pi\) |
0.991824 | − | 0.127613i | \(-0.0407316\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.84219e13 | − | 4.92282e13i | −0.549933 | − | 0.952512i | −0.998279 | − | 0.0586517i | \(-0.981320\pi\) |
0.448345 | − | 0.893860i | \(-0.352013\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 2.05867e13i | − | 0.374437i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.01766e13 | −0.858428 | −0.429214 | − | 0.903203i | \(-0.641209\pi\) | ||||
−0.429214 | + | 0.903203i | \(0.641209\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.71256e13 | − | 1.56610e13i | 0.436778 | − | 0.252174i | −0.265452 | − | 0.964124i | \(-0.585521\pi\) |
0.702230 | + | 0.711950i | \(0.252188\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.88226e13 | − | 2.81878e13i | −0.740363 | − | 0.427449i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.32751e13 | − | 1.00577e13i | −0.189697 | − | 0.143722i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.06668e13 | + | 3.57960e13i | −0.278452 | + | 0.482294i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.09541e13 | + | 1.89730e13i | 0.139237 | + | 0.241165i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00117e13i | 0.480075i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.26653e14 | −1.43523 | −0.717616 | − | 0.696438i | \(-0.754767\pi\) | ||||
−0.717616 | + | 0.696438i | \(0.754767\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.84092e14 | − | 1.06286e14i | 1.97133 | − | 1.13815i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.73475e13 | + | 3.88831e13i | 0.681853 | + | 0.393668i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.43117e13 | + | 1.18292e13i | 0.903249 | + | 0.113291i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.41227e13 | − | 7.64227e13i | 0.399942 | − | 0.692720i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.73482e12 | + | 1.51292e13i | 0.0749723 | + | 0.129856i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.65375e13i | − | 0.703680i | −0.936060 | − | 0.351840i | \(-0.885556\pi\) | ||
0.936060 | − | 0.351840i | \(-0.114444\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.54743e13 | −0.273413 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.42952e14 | + | 8.25335e13i | −1.04481 | + | 0.603220i | −0.921191 | − | 0.389111i | \(-0.872782\pi\) |
−0.123616 | + | 0.992330i | \(0.539449\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.41450e13 | − | 4.85811e13i | −0.583466 | − | 0.336864i | 0.179044 | − | 0.983841i | \(-0.442700\pi\) |
−0.762510 | + | 0.646977i | \(0.776033\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.03006e13 | − | 4.81734e13i | −0.133610 | − | 0.317055i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.12110e13 | + | 3.67385e13i | −0.132564 | + | 0.229607i | −0.924664 | − | 0.380784i | \(-0.875654\pi\) |
0.792100 | + | 0.610391i | \(0.208988\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.99669e13 | + | 1.55827e14i | 0.534165 | + | 0.925201i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.38686e14i | 1.34690i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.49165e13 | 0.294656 | 0.147328 | − | 0.989088i | \(-0.452933\pi\) | ||||
0.147328 | + | 0.989088i | \(0.452933\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.63730e14 | − | 1.52264e14i | 1.34604 | − | 0.777134i | 0.358351 | − | 0.933587i | \(-0.383339\pi\) |
0.987685 | + | 0.156453i | \(0.0500059\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.33867e14 | + | 7.72879e13i | 0.650181 | + | 0.375382i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.97311e13 | − | 1.16656e14i | 0.137472 | − | 0.539399i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.06570e14 | − | 1.84584e14i | 0.469301 | − | 0.812853i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.52422e13 | − | 6.10413e13i | −0.147866 | − | 0.256111i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.75080e14i | 1.49996i | 0.661458 | + | 0.749982i | \(0.269938\pi\) | ||||
−0.661458 | + | 0.749982i | \(0.730062\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.36777e13 | 0.204678 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.12488e13 | + | 2.38150e13i | −0.150027 | + | 0.0866183i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.15923e14 | + | 1.24663e14i | 0.749378 | + | 0.432653i | 0.825469 | − | 0.564447i | \(-0.190911\pi\) |
−0.0760913 | + | 0.997101i | \(0.524244\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.04951e14 | − | 1.70650e14i | 1.34154 | − | 0.565336i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.49023e13 | + | 2.58116e13i | −0.0471424 | + | 0.0816530i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.94573e14 | + | 5.10216e14i | 0.890141 | + | 1.54177i | 0.839705 | + | 0.543042i | \(0.182728\pi\) |
0.0504357 | + | 0.998727i | \(0.483939\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.03994e14i | 0.589035i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.66979e13 | −0.128893 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.77909e14 | − | 1.60451e14i | 0.733482 | − | 0.423476i | −0.0862129 | − | 0.996277i | \(-0.527477\pi\) |
0.819694 | + | 0.572801i | \(0.194143\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.39461e13 | − | 4.84663e13i | −0.211926 | − | 0.122356i | 0.390280 | − | 0.920696i | \(-0.372378\pi\) |
−0.602206 | + | 0.798340i | \(0.705712\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.46560e13 | + | 2.76306e14i | −0.0837148 | + | 0.667442i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.34583e13 | + | 7.52719e13i | −0.100479 | + | 0.174035i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.88703e14 | + | 5.00048e14i | 0.639106 | + | 1.10696i | 0.985629 | + | 0.168923i | \(0.0540288\pi\) |
−0.346523 | + | 0.938041i | \(0.612638\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 1.70097e14i | − | 0.360639i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.01179e14 | 1.01802 | 0.509009 | − | 0.860761i | \(-0.330012\pi\) | ||||
0.509009 | + | 0.860761i | \(0.330012\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.28775e14 | − | 4.20758e14i | 1.41865 | − | 0.819057i | 0.422468 | − | 0.906378i | \(-0.361164\pi\) |
0.996180 | + | 0.0873212i | \(0.0278306\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.03257e14 | + | 2.90556e14i | 0.939120 | + | 0.542201i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.37641e14 | − | 4.45647e14i | 0.604176 | − | 0.797444i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.71102e14 | + | 4.69562e14i | −0.465313 | + | 0.805947i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.47614e14 | + | 2.55676e14i | 0.243092 | + | 0.421048i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 9.39106e14i | − | 1.48426i | −0.670258 | − | 0.742128i | \(-0.733817\pi\) | ||
0.670258 | − | 0.742128i | \(-0.266183\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.84265e13 | −0.0279583 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.23486e14 | − | 7.12949e13i | 0.179920 | − | 0.103877i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.47629e14 | − | 1.42968e14i | −0.346556 | − | 0.200084i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.38452e14 | − | 6.35245e14i | −1.12740 | − | 0.854166i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.33994e14 | + | 1.27131e15i | −0.948499 | + | 1.64285i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.65756e13 | + | 6.33507e13i | 0.0454351 | + | 0.0786960i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.66830e14i | − | 0.796498i | −0.917277 | − | 0.398249i | \(-0.869618\pi\) | ||
0.917277 | − | 0.398249i | \(-0.130382\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.12921e15 | −1.29725 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.70814e14 | − | 1.56355e14i | 0.299302 | − | 0.172802i | −0.342827 | − | 0.939398i | \(-0.611385\pi\) |
0.642129 | + | 0.766596i | \(0.278051\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.09440e14 | − | 1.20920e14i | −0.222738 | − | 0.128598i | 0.384479 | − | 0.923134i | \(-0.374381\pi\) |
−0.607217 | + | 0.794536i | \(0.707714\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.13759e14 | − | 2.68110e13i | −0.218807 | − | 0.0274442i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.62099e13 | − | 1.14679e14i | 0.0652480 | − | 0.113013i | −0.831556 | − | 0.555441i | \(-0.812549\pi\) |
0.896804 | + | 0.442428i | \(0.145883\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.65126e13 | + | 6.32417e13i | 0.0346497 | + | 0.0600150i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.75220e15i | 1.60160i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.93125e14 | −0.434252 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.00968e14 | − | 2.31499e14i | 0.340259 | − | 0.196448i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.63714e15 | − | 9.45203e14i | −1.33906 | − | 0.773106i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.45173e14 | − | 2.24289e15i | −0.745309 | − | 1.76862i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.14852e14 | − | 7.18544e14i | 0.315446 | − | 0.546368i | −0.664086 | − | 0.747656i | \(-0.731179\pi\) |
0.979532 | + | 0.201288i | \(0.0645126\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.93198e14 | − | 6.81039e14i | −0.288367 | − | 0.499467i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.69234e14i | 0.402737i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.75664e14 | −0.188192 | −0.0940958 | − | 0.995563i | \(-0.529996\pi\) | ||||
−0.0940958 | + | 0.995563i | \(0.529996\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.74099e14 | + | 1.00516e14i | −0.114709 | + | 0.0662274i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.60925e14 | − | 2.08380e14i | −0.229557 | − | 0.132535i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.95418e14 | + | 1.51565e15i | −0.365643 | + | 0.930755i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.89795e14 | − | 6.75146e14i | 0.231165 | − | 0.400390i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.45392e12 | + | 1.11785e13i | 0.00369698 | + | 0.00640335i | 0.867868 | − | 0.496795i | \(-0.165490\pi\) |
−0.864171 | + | 0.503198i | \(0.832157\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.51191e14i | 0.415717i | 0.978159 | + | 0.207858i | \(0.0666493\pi\) | ||||
−0.978159 | + | 0.207858i | \(0.933351\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.59564e14 | −0.406183 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.28243e14 | − | 5.35921e14i | 0.479748 | − | 0.276983i | −0.240563 | − | 0.970633i | \(-0.577332\pi\) |
0.720312 | + | 0.693651i | \(0.243999\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.85881e15 | − | 1.07319e15i | −0.928679 | − | 0.536173i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.93714e14 | − | 2.50196e14i | 0.286792 | − | 0.120857i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.15290e14 | + | 1.58533e15i | −0.427555 | + | 0.740547i | −0.996655 | − | 0.0817210i | \(-0.973958\pi\) |
0.569100 | + | 0.822268i | \(0.307292\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.90154e15 | + | 3.29356e15i | 0.859135 | + | 1.48806i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 2.47418e15i | − | 1.08141i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.91029e14 | −0.376821 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.74439e15 | − | 1.00713e15i | 0.713917 | − | 0.412180i | −0.0985926 | − | 0.995128i | \(-0.531434\pi\) |
0.812510 | + | 0.582948i | \(0.198101\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.66502e14 | − | 5.00275e14i | −0.343251 | − | 0.198176i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.43406e14 | − | 2.73791e15i | 0.131693 | − | 1.04997i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.67420e14 | − | 1.67562e15i | 0.359221 | − | 0.622189i | −0.628610 | − | 0.777721i | \(-0.716376\pi\) |
0.987831 | + | 0.155531i | \(0.0497090\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.54571e15 | + | 2.67724e15i | 0.555827 | + | 0.962720i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.89000e14i | − | 0.135488i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.16588e15 | −0.730802 | −0.365401 | − | 0.930850i | \(-0.619068\pi\) | ||||
−0.365401 | + | 0.930850i | \(0.619068\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.05600e15 | + | 2.34174e15i | −1.32602 | + | 0.765575i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.61537e15 | + | 2.66469e15i | 1.46222 | + | 0.844215i | 0.999114 | − | 0.0420855i | \(-0.0134002\pi\) |
0.463110 | + | 0.886301i | \(0.346734\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.18758e14 | + | 4.20725e14i | −0.0978807 | + | 0.129191i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.41230e14 | + | 1.63026e15i | −0.280175 | + | 0.485278i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.08260e15 | − | 1.87512e15i | −0.312444 | − | 0.541168i | 0.666447 | − | 0.745552i | \(-0.267814\pi\) |
−0.978891 | + | 0.204384i | \(0.934481\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.61552e14i | 0.185141i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.14496e15 | −1.93930 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.08717e15 | − | 1.20503e15i | 0.549509 | − | 0.317259i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.75072e14 | − | 4.47488e14i | −0.197970 | − | 0.114298i | 0.397738 | − | 0.917499i | \(-0.369795\pi\) |
−0.595708 | + | 0.803201i | \(0.703128\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.26537e15 | − | 4.74690e15i | −1.55278 | − | 1.17645i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.82791e15 | + | 6.63014e15i | −0.920653 | + | 1.59462i | −0.122245 | + | 0.992500i | \(0.539009\pi\) |
−0.798408 | + | 0.602117i | \(0.794324\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.11002e15 | + | 1.92262e15i | 0.259121 | + | 0.448810i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 3.04406e15i | − | 0.689801i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.92677e15 | −0.423900 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.13235e15 | − | 1.80846e15i | 0.669160 | − | 0.386340i | −0.126598 | − | 0.991954i | \(-0.540406\pi\) |
0.795758 | + | 0.605614i | \(0.207073\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.14708e15 | − | 1.23962e15i | −0.445449 | − | 0.257180i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.47312e14 | + | 3.10194e13i | 0.0498362 | + | 0.00625076i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.55847e14 | + | 6.16345e14i | −0.0696586 | + | 0.120652i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.18509e15 | + | 5.51673e15i | 0.605766 | + | 1.04922i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.64888e15i | 0.674335i | 0.941445 | + | 0.337168i | \(0.109469\pi\) | ||||
−0.941445 | + | 0.337168i | \(0.890531\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.29475e15 | 0.591739 | 0.295870 | − | 0.955228i | \(-0.404391\pi\) | ||||
0.295870 | + | 0.955228i | \(0.404391\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.77206e15 | + | 2.17780e15i | −0.658470 | + | 0.380168i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.27691e14 | − | 5.35602e14i | −0.157423 | − | 0.0908885i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.84255e14 | − | 9.11837e14i | −0.0633947 | − | 0.150435i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.10492e14 | − | 1.05740e15i | 0.0979346 | − | 0.169628i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.72907e15 | − | 8.19099e15i | −0.737755 | − | 1.27783i | −0.953504 | − | 0.301381i | \(-0.902553\pi\) |
0.215749 | − | 0.976449i | \(-0.430781\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.38135e15i | − | 1.42344i | −0.702465 | − | 0.711718i | \(-0.747917\pi\) | ||
0.702465 | − | 0.711718i | \(-0.252083\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.06059e15 | 0.156535 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.98994e15 | − | 4.03564e15i | 1.00366 | − | 0.579461i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.10191e14 | + | 1.79089e14i | 0.0433353 | + | 0.0250196i | 0.521511 | − | 0.853244i | \(-0.325369\pi\) |
−0.478176 | + | 0.878264i | \(0.658702\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.82385e15 | + | 7.19692e14i | 0.383893 | + | 0.0978396i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.44826e15 | − | 2.50846e15i | 0.191613 | − | 0.331883i | −0.754172 | − | 0.656677i | \(-0.771962\pi\) |
0.945785 | + | 0.324794i | \(0.105295\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.35758e14 | + | 4.08345e14i | 0.0303604 | + | 0.0525857i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.68508e15i | 0.211240i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.51822e15 | 0.673474 | 0.336737 | − | 0.941599i | \(-0.390677\pi\) | ||||
0.336737 | + | 0.941599i | \(0.390677\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.12304e15 | + | 1.22574e15i | −0.252289 | + | 0.145659i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.07486e16 | − | 6.20571e15i | −1.24384 | − | 0.718129i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.59109e15 | − | 1.09191e15i | 0.292021 | − | 0.123060i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.58011e15 | + | 6.20094e15i | −0.393006 | + | 0.680707i | −0.992845 | − | 0.119414i | \(-0.961898\pi\) |
0.599838 | + | 0.800121i | \(0.295232\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.78676e14 | + | 1.52191e15i | 0.0939620 | + | 0.162747i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 7.56470e15i | − | 0.788108i | −0.919087 | − | 0.394054i | \(-0.871072\pi\) | ||
0.919087 | − | 0.394054i | \(-0.128928\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.69921e15 | 0.477022 | 0.238511 | − | 0.971140i | \(-0.423341\pi\) | ||||
0.238511 | + | 0.971140i | \(0.423341\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.24191e15 | + | 3.02642e15i | −0.518527 | + | 0.299372i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.24885e16 | + | 7.21026e15i | 1.20395 | + | 0.695103i | 0.961432 | − | 0.275043i | \(-0.0886919\pi\) |
0.242522 | + | 0.970146i | \(0.422025\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.58256e14 | − | 7.64000e15i | 0.0900419 | − | 0.717888i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.94108e15 | − | 1.37543e16i | 0.727368 | − | 1.25984i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.30613e15 | + | 3.99433e15i | 0.205929 | + | 0.356679i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.30693e16i | 1.13786i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.93800e15 | −0.419219 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.75512e15 | − | 5.05477e15i | 0.724851 | − | 0.418493i | −0.0916844 | − | 0.995788i | \(-0.529225\pi\) |
0.816536 | + | 0.577295i | \(0.195892\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.88866e15 | + | 5.13187e15i | 0.717738 | + | 0.414386i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.36821e15 | + | 8.40532e15i | −0.501574 | + | 0.662020i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.49049e15 | − | 2.58160e15i | 0.114519 | − | 0.198353i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.21346e15 | − | 5.56587e15i | −0.240879 | − | 0.417215i | 0.720086 | − | 0.693885i | \(-0.244102\pi\) |
−0.960965 | + | 0.276670i | \(0.910769\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.38752e16i | 1.74620i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.05122e16 | −0.750244 | −0.375122 | − | 0.926975i | \(-0.622399\pi\) | ||||
−0.375122 | + | 0.926975i | \(0.622399\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.79424e14 | + | 4.50000e14i | −0.0542865 | + | 0.0313423i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.18043e14 | + | 4.72298e14i | 0.0556090 | + | 0.0321059i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.31416e16 | + | 1.75330e16i | 1.53552 | + | 1.16337i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.95068e14 | + | 3.37868e14i | −0.0126352 | + | 0.0218849i | −0.872274 | − | 0.489018i | \(-0.837355\pi\) |
0.859639 | + | 0.510903i | \(0.170689\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.16570e14 | − | 8.94725e14i | −0.0326665 | − | 0.0565800i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.10468e16i | 0.682070i | 0.940051 | + | 0.341035i | \(0.110777\pi\) | ||||
−0.940051 | + | 0.341035i | \(0.889223\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.48225e16 | 0.893664 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.17472e16 | − | 6.78224e15i | 0.691649 | − | 0.399324i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.97600e15 | + | 1.14085e15i | 0.113627 | + | 0.0656024i | 0.555736 | − | 0.831359i | \(-0.312436\pi\) |
−0.442110 | + | 0.896961i | \(0.645770\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.19590e16 | + | 1.49997e15i | 0.671691 | + | 0.0842476i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.07203e16 | − | 1.85681e16i | 0.588170 | − | 1.01874i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.70091e15 | + | 9.87427e15i | 0.305563 | + | 0.529251i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.06718e16i | 0.558846i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.81970e15 | 0.195445 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.36143e16 | + | 1.36337e16i | −1.18073 | + | 0.681693i | −0.956183 | − | 0.292771i | \(-0.905423\pi\) |
−0.224544 | + | 0.974464i | \(0.572089\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.67291e15 | + | 5.00731e15i | 0.423794 | + | 0.244678i | 0.696699 | − | 0.717363i | \(-0.254651\pi\) |
−0.272905 | + | 0.962041i | \(0.587985\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.63093e15 | − | 1.57352e16i | −0.316678 | − | 0.751477i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.56818e15 | − | 4.44822e15i | 0.119884 | − | 0.207646i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.54329e15 | + | 9.60126e15i | 0.252949 | + | 0.438121i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 4.46043e14i | − | 0.0198980i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.30588e16 | 0.569561 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.53219e16 | − | 8.84612e15i | 0.653418 | − | 0.377251i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.29747e16 | + | 1.90379e16i | 1.37510 | + | 0.793915i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.98649e15 | − | 5.11018e15i | 0.203358 | − | 0.208403i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.03051e16 | − | 3.51694e16i | 0.809880 | − | 1.40275i | −0.103067 | − | 0.994674i | \(-0.532866\pi\) |
0.912947 | − | 0.408079i | \(-0.133801\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.11553e14 | + | 1.05924e15i | 0.0238580 | + | 0.0413233i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.90878e16i | 0.728411i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.98211e16 | 1.48658 | 0.743291 | − | 0.668968i | \(-0.233264\pi\) | ||||
0.743291 | + | 0.668968i | \(0.233264\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.53351e15 | + | 8.85372e14i | −0.0560083 | + | 0.0323364i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.50938e15 | + | 5.49025e15i | 0.339815 | + | 0.196192i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.00416e16 | + | 1.26598e16i | −1.05044 | + | 0.442665i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.39918e16 | + | 2.42344e16i | −0.478756 | + | 0.829230i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.37991e16 | − | 2.39007e16i | −0.462081 | − | 0.800348i | 0.536983 | − | 0.843593i | \(-0.319564\pi\) |
−0.999065 | + | 0.0432447i | \(0.986230\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.45691e16i | − | 0.805228i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.82491e15 | −0.0906206 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.01324e16 | + | 2.89439e16i | −1.57423 | + | 0.908882i | −0.578587 | + | 0.815620i | \(0.696396\pi\) |
−0.995642 | + | 0.0932613i | \(0.970271\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.75791e15 | + | 1.01493e15i | 0.0540389 | + | 0.0311993i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.12442e15 | + | 4.08561e16i | −0.154222 | + | 1.22958i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.77987e15 | − | 4.81487e15i | 0.0819125 | − | 0.141877i | −0.822159 | − | 0.569258i | \(-0.807231\pi\) |
0.904071 | + | 0.427381i | \(0.140564\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.02171e16 | − | 1.76965e16i | −0.294788 | − | 0.510588i | 0.680147 | − | 0.733075i | \(-0.261916\pi\) |
−0.974936 | + | 0.222487i | \(0.928582\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 5.07231e16i | − | 1.43310i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.75331e16 | 0.485122 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.56461e14 | − | 2.05803e14i | 0.00965956 | − | 0.00557695i | −0.495162 | − | 0.868800i | \(-0.664891\pi\) |
0.504822 | + | 0.863223i | \(0.331558\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.24043e16 | − | 2.44822e16i | −1.12548 | − | 0.649798i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.81358e15 | − | 7.67327e15i | 0.151143 | − | 0.199491i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.04936e15 | + | 1.04778e16i | −0.154063 | + | 0.266845i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.51589e15 | − | 4.35765e15i | −0.0627706 | − | 0.108722i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 4.40809e16i | − | 1.07751i | −0.842462 | − | 0.538756i | \(-0.818894\pi\) | ||
0.842462 | − | 0.538756i | \(-0.181106\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.26664e16 | −1.50087 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.74307e16 | + | 2.16106e16i | −0.878421 | + | 0.507157i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.84620e16 | + | 2.22061e16i | 0.884513 | + | 0.510674i | 0.872144 | − | 0.489250i | \(-0.162729\pi\) |
0.0123689 | + | 0.999924i | \(0.496063\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.18523e15 | − | 3.92854e15i | −0.116860 | − | 0.0885380i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.34901e16 | − | 2.33655e16i | 0.297967 | − | 0.516095i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.03286e16 | − | 6.98511e16i | −0.873075 | − | 1.51221i | −0.858799 | − | 0.512313i | \(-0.828789\pi\) |
−0.0142767 | − | 0.999898i | \(-0.504545\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.23496e16i | 1.11088i | 0.831557 | + | 0.555439i | \(0.187450\pi\) | ||||
−0.831557 | + | 0.555439i | \(0.812550\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.37792e16 | −0.286630 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.16352e16 | + | 1.24911e16i | −0.441193 | + | 0.254723i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.93747e16 | − | 1.11860e16i | −0.387350 | − | 0.223636i | 0.293662 | − | 0.955909i | \(-0.405126\pi\) |
−0.681011 | + | 0.732273i | \(0.738459\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.42347e16 | − | 1.78540e15i | −0.279026 | − | 0.0349972i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.84238e16 | − | 4.92314e16i | 0.546304 | − | 0.946227i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.91851e16 | − | 5.05500e16i | −0.550045 | − | 0.952705i | −0.998271 | − | 0.0587849i | \(-0.981277\pi\) |
0.448226 | − | 0.893920i | \(-0.352056\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.56041e16i | 0.658036i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.98026e16 | −0.358931 | −0.179466 | − | 0.983764i | \(-0.557437\pi\) | ||||
−0.179466 | + | 0.983764i | \(0.557437\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.60595e16 | + | 9.27195e15i | −0.285488 | + | 0.164827i | −0.635905 | − | 0.771767i | \(-0.719373\pi\) |
0.350417 | + | 0.936594i | \(0.386040\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.49101e16 | − | 1.43818e16i | −0.434336 | − | 0.250764i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.47683e15 | − | 5.87751e15i | −0.0423612 | − | 0.100523i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.96079e15 | + | 8.59235e15i | −0.0832283 | + | 0.144156i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.72327e16 | + | 2.98479e16i | 0.283627 | + | 0.491256i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 2.37465e16i | − | 0.383439i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.12464e16 | −0.178171 | −0.0890855 | − | 0.996024i | \(-0.528394\pi\) | ||||
−0.0890855 | + | 0.996024i | \(0.528394\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.44808e16 | + | 5.45485e16i | −1.46866 | + | 0.847931i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.09542e16 | + | 2.36449e16i | 0.624678 | + | 0.360658i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.66146e16 | + | 1.02932e16i | −0.548048 | + | 0.154069i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.59783e16 | − | 4.49957e16i | 0.381597 | − | 0.660946i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.17347e16 | − | 3.76457e16i | −0.313333 | − | 0.542709i | 0.665749 | − | 0.746176i | \(-0.268112\pi\) |
−0.979082 | + | 0.203467i | \(0.934779\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 3.56902e16i | − | 0.504990i | −0.967598 | − | 0.252495i | \(-0.918749\pi\) | ||
0.967598 | − | 0.252495i | \(-0.0812512\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.69864e16 | 0.930311 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.83324e16 | + | 5.09987e16i | −1.20419 | + | 0.695238i | −0.961484 | − | 0.274862i | \(-0.911368\pi\) |
−0.242704 | + | 0.970100i | \(0.578034\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.46446e14 | − | 5.46431e14i | −0.0126657 | − | 0.00731252i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.54493e16 | − | 3.17949e16i | 0.991218 | − | 0.417707i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.37945e16 | + | 2.38927e16i | −0.177921 | + | 0.308168i | −0.941168 | − | 0.337939i | \(-0.890270\pi\) |
0.763247 | + | 0.646106i | \(0.223604\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.60720e16 | + | 6.24785e16i | 0.456796 | + | 0.791193i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 2.15688e16i | − | 0.268185i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.60974e16 | −1.05118 | −0.525590 | − | 0.850738i | \(-0.676156\pi\) | ||||
−0.525590 | + | 0.850738i | \(0.676156\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.10364e16 | − | 6.37188e15i | 0.132318 | − | 0.0763939i | −0.432380 | − | 0.901692i | \(-0.642326\pi\) |
0.564698 | + | 0.825298i | \(0.308993\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.30320e16 | + | 7.52402e15i | 0.153437 | + | 0.0885868i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.87758e15 | + | 7.87522e16i | −0.114214 | + | 0.910610i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.36544e15 | − | 1.27573e16i | 0.0836458 | − | 0.144879i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.72709e16 | − | 6.45551e16i | −0.415732 | − | 0.720069i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.33854e15i | 0.0475345i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.37493e17 | 1.47976 | 0.739879 | − | 0.672740i | \(-0.234883\pi\) | ||||
0.739879 | + | 0.672740i | \(0.234883\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.03351e16 | − | 2.32875e16i | 0.426443 | − | 0.246207i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.86231e16 | − | 1.65256e16i | −0.297293 | − | 0.171642i | 0.343933 | − | 0.938994i | \(-0.388241\pi\) |
−0.641226 | + | 0.767352i | \(0.721574\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.43506e16 | + | 3.21400e16i | −0.248480 | + | 0.327965i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.10929e16 | + | 1.23137e17i | −0.712761 | + | 1.23454i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.98041e16 | − | 3.43017e16i | −0.195088 | − | 0.337903i | 0.751841 | − | 0.659344i | \(-0.229166\pi\) |
−0.946929 | + | 0.321441i | \(0.895833\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.50333e16i | 0.242312i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.36938e16 | −0.796073 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.58144e16 | − | 3.22245e16i | 0.521712 | − | 0.301211i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.34564e16 | + | 3.66366e16i | 0.582918 | + | 0.336548i | 0.762292 | − | 0.647233i | \(-0.224074\pi\) |
−0.179374 | + | 0.983781i | \(0.557407\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.01843e16 | − | 7.71607e15i | −0.0919461 | − | 0.0696622i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.21604e16 | − | 5.57034e16i | 0.285373 | − | 0.494280i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.51066e16 | − | 2.61654e16i | −0.131756 | − | 0.228208i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.65415e16i | 0.313273i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.17411e16 | −0.183220 | −0.0916101 | − | 0.995795i | \(-0.529201\pi\) | ||||
−0.0916101 | + | 0.995795i | \(0.529201\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.50905e17 | + | 1.44860e17i | −2.07863 | + | 1.20010i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.34227e17 | + | 7.74958e16i | 1.09321 | + | 0.631166i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.98942e17 | − | 2.49525e16i | −1.59297 | − | 0.199801i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.03734e17 | − | 1.79673e17i | 0.816665 | − | 1.41450i | −0.0914619 | − | 0.995809i | \(-0.529154\pi\) |
0.908126 | − | 0.418696i | \(-0.137513\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.91697e16 | + | 5.05234e16i | 0.225795 | + | 0.391088i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.40702e16i | 0.639889i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.23285e16 | −0.0922728 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.09665e16 | − | 2.36520e16i | 0.301519 | − | 0.174082i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.07457e17 | + | 1.19775e17i | 1.50160 | + | 0.866950i | 0.999998 | + | 0.00185138i | \(0.000589312\pi\) |
0.501602 | + | 0.865098i | \(0.332744\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.98926e16 | − | 1.42125e17i | −0.426346 | − | 1.01172i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.31158e17 | − | 2.27172e17i | 0.918257 | − | 1.59047i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.19263e16 | + | 2.06570e16i | 0.0821257 | + | 0.142246i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 5.15434e16i | − | 0.349113i | −0.984647 | − | 0.174557i | \(-0.944151\pi\) | ||
0.984647 | − | 0.174557i | \(-0.0558492\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.28512e16 | −0.352119 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.92283e16 | + | 2.84220e16i | −0.322634 | + | 0.186273i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.01615e17 | − | 5.86675e16i | −0.655140 | − | 0.378245i | 0.135283 | − | 0.990807i | \(-0.456806\pi\) |
−0.790423 | + | 0.612562i | \(0.790139\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.80639e16 | − | 9.98278e16i | −0.178001 | − | 0.633180i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.68804e16 | + | 2.92378e16i | −0.105337 | + | 0.182448i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.17864e15 | + | 8.96968e15i | 0.0317943 | + | 0.0550694i | 0.881485 | − | 0.472213i | \(-0.156545\pi\) |
−0.849690 | + | 0.527282i | \(0.823211\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 1.83594e17i | − | 1.10905i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.76902e17 | 1.64586 | 0.822929 | − | 0.568144i | \(-0.192338\pi\) | ||||
0.822929 | + | 0.568144i | \(0.192338\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.47350e16 | − | 8.50728e15i | 0.0861814 | − | 0.0497569i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.49196e16 | − | 8.61386e15i | −0.0858687 | − | 0.0495763i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.20536e17 | + | 9.29356e16i | −1.24907 | + | 0.526370i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.83851e15 | − | 4.91644e15i | 0.0158216 | − | 0.0274038i | −0.858006 | − | 0.513639i | \(-0.828297\pi\) |
0.873828 | + | 0.486236i | \(0.161630\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.61543e17 | + | 2.79801e17i | 0.886175 | + | 1.53490i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.25320e17i | 0.676612i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.87044e16 | 0.311957 | 0.155979 | − | 0.987760i | \(-0.450147\pi\) | ||||
0.155979 | + | 0.987760i | \(0.450147\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.00424e16 | − | 2.31185e16i | 0.209445 | − | 0.120923i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.47143e17 | − | 8.49529e16i | −0.757585 | − | 0.437392i | 0.0708433 | − | 0.997487i | \(-0.477431\pi\) |
−0.828428 | + | 0.560096i | \(0.810764\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.21326e16 | − | 2.56188e17i | 0.162854 | − | 1.29841i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.82084e15 | + | 1.00820e16i | −0.0290414 | + | 0.0503011i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.91079e15 | + | 5.04164e15i | 0.0142968 | + | 0.0247628i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.95491e17i | 0.945298i | 0.881251 | + | 0.472649i | \(0.156702\pi\) | ||||
−0.881251 | + | 0.472649i | \(0.843298\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.14766e17 | 1.02244 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.12824e17 | + | 6.51389e16i | −0.528840 | + | 0.305326i | −0.740544 | − | 0.672008i | \(-0.765432\pi\) |
0.211704 | + | 0.977334i | \(0.432099\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.17891e17 | − | 6.80645e16i | −0.544090 | − | 0.314131i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.28588e17 | − | 3.01710e17i | 1.03879 | − | 1.37108i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.84309e17 | + | 3.19232e17i | −0.824748 | + | 1.42851i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.36500e16 | − | 1.10245e17i | −0.280474 | − | 0.485795i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 3.91312e16i | − | 0.169806i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.60365e17 | −0.685317 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.17760e17 | − | 6.79890e16i | 0.495622 | − | 0.286148i | −0.231282 | − | 0.972887i | \(-0.574292\pi\) |
0.726904 | + | 0.686739i | \(0.240959\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.39491e17 | + | 2.53740e17i | 1.82175 | + | 1.05179i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.18853e16 | − | 1.65812e16i | −0.0893500 | − | 0.0676952i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.15555e16 | − | 2.00148e16i | 0.0464677 | − | 0.0804844i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.78582e16 | + | 1.52175e17i | 0.348000 | + | 0.602754i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.42818e16i | 0.289823i | 0.989445 | + | 0.144911i | \(0.0462897\pi\) | ||||
−0.989445 | + | 0.144911i | \(0.953710\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.31524e17 | −0.505505 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.88468e15 | + | 5.70692e15i | −0.0374255 | + | 0.0216076i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.57663e16 | − | 2.64232e16i | −0.170707 | − | 0.0985580i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.05650e17 | + | 1.32513e16i | 0.388235 | + | 0.0486948i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.38210e17 | − | 2.39386e17i | 0.500376 | − | 0.866677i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.62235e16 | + | 1.49343e17i | 0.307563 | + | 0.532715i | 0.977829 | − | 0.209406i | \(-0.0671531\pi\) |
−0.670265 | + | 0.742121i | \(0.733820\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.05781e16i | 0.318345i | 0.987251 | + | 0.159172i | \(0.0508826\pi\) | ||||
−0.987251 | + | 0.159172i | \(0.949117\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.34960e16 | −0.289150 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.08774e17 | − | 1.20536e17i | 0.712412 | − | 0.411311i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.00611e17 | + | 3.46763e17i | 2.01958 | + | 1.16600i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.64314e16 | + | 6.27217e16i | 0.0875825 | + | 0.207833i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.90373e17 | − | 5.02941e17i | 0.948195 | − | 1.64232i | 0.198971 | − | 0.980005i | \(-0.436240\pi\) |
0.749224 | − | 0.662316i | \(-0.230426\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.00951e16 | + | 1.56049e17i | 0.289936 | + | 0.502184i | 0.973794 | − | 0.227431i | \(-0.0730326\pi\) |
−0.683858 | + | 0.729615i | \(0.739699\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.48684e16i | 0.237451i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.77617e17 | −1.18037 | −0.590185 | − | 0.807268i | \(-0.700945\pi\) | ||||
−0.590185 | + | 0.807268i | \(0.700945\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.20459e16 | + | 3.00487e16i | −0.160346 | + | 0.0925760i | −0.578026 | − | 0.816018i | \(-0.696177\pi\) |
0.417680 | + | 0.908594i | \(0.362843\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.30733e17 | + | 2.48684e17i | 1.30798 | + | 0.755164i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.29805e16 | + | 6.14561e16i | 0.188511 | + | 0.183948i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.21590e15 | + | 9.03420e15i | −0.0153890 | + | 0.0266545i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.11662e17 | + | 1.93405e17i | 0.324753 | + | 0.562489i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.04585e17i | 0.586546i | 0.956029 | + | 0.293273i | \(0.0947444\pi\) | ||||
−0.956029 | + | 0.293273i | \(0.905256\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.33774e17 | −0.943359 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.73869e17 | − | 2.15853e17i | 1.04173 | − | 0.601442i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.18613e17 | − | 6.84814e16i | −0.325832 | − | 0.188119i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.11406e17 | − | 1.31229e17i | 0.843386 | − | 0.355410i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.62434e17 | − | 6.27753e17i | 0.967793 | − | 1.67627i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.94337e17 | + | 3.36602e17i | 0.511656 | + | 0.886215i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.22323e17i | 1.35595i | 0.735083 | + | 0.677977i | \(0.237143\pi\) | ||||
−0.735083 | + | 0.677977i | \(0.762857\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.42035e17 | 0.363578 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.73203e17 | + | 1.57734e17i | −0.689605 | + | 0.398144i | −0.803464 | − | 0.595353i | \(-0.797012\pi\) |
0.113859 | + | 0.993497i | \(0.463679\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.29262e17 | + | 2.47835e17i | 1.06847 | + | 0.616883i | 0.927764 | − | 0.373168i | \(-0.121728\pi\) |
0.140709 | + | 0.990051i | \(0.455062\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.99365e16 | − | 4.77862e17i | 0.147120 | − | 1.17296i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.43524e17 | + | 2.48591e17i | −0.347424 | + | 0.601755i | −0.985791 | − | 0.167976i | \(-0.946277\pi\) |
0.638367 | + | 0.769732i | \(0.279610\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.92841e16 | − | 3.34010e16i | −0.0460366 | − | 0.0797377i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.67045e17i | 1.09962i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.42939e17 | 0.331919 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.55747e17 | − | 8.99208e16i | 0.356707 | − | 0.205945i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.24920e16 | + | 3.60798e16i | 0.141169 | + | 0.0815039i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.54981e17 | + | 3.36546e17i | −0.568145 | + | 0.749887i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.90465e17 | + | 3.29896e17i | −0.418619 | + | 0.725069i | −0.995801 | − | 0.0915468i | \(-0.970819\pi\) |
0.577182 | + | 0.816615i | \(0.304152\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.04465e17 | − | 7.00553e17i | −0.876894 | − | 1.51883i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 4.35093e17i | − | 0.930522i | −0.885174 | − | 0.465261i | \(-0.845961\pi\) | ||
0.885174 | − | 0.465261i | \(-0.154039\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.33662e17 | −1.54786 | −0.773931 | − | 0.633270i | \(-0.781712\pi\) | ||||
−0.773931 | + | 0.633270i | \(0.781712\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.37458e16 | + | 7.93612e15i | −0.0286094 | + | 0.0165177i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.12834e17 | − | 2.96085e17i | −1.05302 | − | 0.607959i | −0.129524 | − | 0.991576i | \(-0.541345\pi\) |
−0.923492 | + | 0.383617i | \(0.874678\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.09865e17 | − | 3.86295e17i | −1.03287 | − | 0.782543i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.02707e16 | − | 1.56353e17i | 0.180418 | − | 0.312494i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.02333e17 | + | 1.38968e18i | 1.58214 | + | 2.74035i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3.84459e17i | − | 0.748018i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.46301e17 | −0.472837 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.90493e16 | + | 5.71862e16i | −0.187626 | + | 0.108326i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.29134e17 | − | 7.45555e16i | −0.241375 | − | 0.139358i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.99061e17 | − | 1.12766e17i | −1.65830 | − | 0.207994i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.17496e15 | − | 1.06953e16i | 0.0112394 | − | 0.0194672i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.30494e16 | − | 2.26022e16i | −0.0234394 | − | 0.0405982i | 0.854068 | − | 0.520162i | \(-0.174128\pi\) |
−0.877507 | + | 0.479564i | \(0.840795\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.58804e17i | 0.636025i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.22736e17 | −0.564595 | −0.282297 | − | 0.959327i | \(-0.591096\pi\) | ||||
−0.282297 | + | 0.959327i | \(0.591096\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.65550e16 | + | 2.11050e16i | −0.0631135 | + | 0.0364386i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.45692e16 | + | 3.15055e16i | 0.0929867 | + | 0.0536859i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.78965e17 | − | 8.99282e17i | −0.637357 | − | 1.51245i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.47547e17 | − | 6.01969e17i | 0.576926 | − | 0.999266i | −0.418903 | − | 0.908031i | \(-0.637585\pi\) |
0.995829 | − | 0.0912348i | \(-0.0290814\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.87198e17 | − | 4.97441e17i | −0.470569 | − | 0.815049i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.78117e17i | 1.09672i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.29353e17 | −1.00472 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.39023e17 | + | 1.38000e17i | −0.376671 | + | 0.217471i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.55576e17 | − | 1.47557e17i | −0.397581 | − | 0.229544i | 0.287858 | − | 0.957673i | \(-0.407057\pi\) |
−0.685440 | + | 0.728129i | \(0.740390\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.65145e17 | − | 1.04035e18i | 0.407179 | − | 1.59765i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.34681e17 | − | 2.33275e17i | 0.204182 | − | 0.353653i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.42618e16 | + | 2.47021e16i | 0.0213454 | + | 0.0369713i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 6.78231e17i | − | 1.00217i | −0.865399 | − | 0.501083i | \(-0.832935\pi\) | ||
0.865399 | − | 0.501083i | \(-0.167065\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.08317e17 | −0.303901 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.12976e17 | + | 4.69372e17i | −1.17095 | + | 0.676051i | −0.953905 | − | 0.300109i | \(-0.902977\pi\) |
−0.217050 | + | 0.976160i | \(0.569644\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.28266e17 | + | 2.47260e17i | 0.609037 | + | 0.351628i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.60650e17 | − | 1.09840e17i | 0.365988 | − | 0.154230i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.28673e17 | − | 7.42484e17i | 0.594328 | − | 1.02941i | −0.399313 | − | 0.916815i | \(-0.630751\pi\) |
0.993641 | − | 0.112592i | \(-0.0359153\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.40754e17 | + | 2.43793e17i | 0.192692 | + | 0.333752i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1.14064e17i | − | 0.154193i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.08071e17 | −1.07868 | −0.539339 | − | 0.842088i | \(-0.681326\pi\) | ||||
−0.539339 | + | 0.842088i | \(0.681326\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.43543e17 | + | 2.56080e17i | −0.584677 | + | 0.337563i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.44753e16 | + | 3.14513e16i | 0.0709133 | + | 0.0409418i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.21415e16 | − | 3.35986e17i | 0.0541749 | − | 0.431926i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.74661e16 | + | 1.16855e17i | −0.0856536 | + | 0.148356i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.14135e17 | + | 3.70893e17i | 0.268491 | + | 0.465041i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.94401e17i | 0.612232i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.31160e17 | −0.527326 | −0.263663 | − | 0.964615i | \(-0.584931\pi\) | ||||
−0.263663 | + | 0.964615i | \(0.584931\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.67861e17 | + | 2.12384e17i | −0.444366 | + | 0.256555i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.24945e17 | + | 1.29872e17i | 0.268387 | + | 0.154953i | 0.628154 | − | 0.778089i | \(-0.283811\pi\) |
−0.359767 | + | 0.933042i | \(0.617144\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.25414e17 | + | 6.93488e17i | −0.619192 | + | 0.817263i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.99409e17 | − | 3.45386e17i | 0.232122 | − | 0.402047i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.71442e17 | − | 1.16297e18i | −0.772042 | − | 1.33722i | −0.936442 | − | 0.350822i | \(-0.885902\pi\) |
0.164400 | − | 0.986394i | \(-0.447431\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.79654e16i | 0.0317632i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.62051e17 | −0.518413 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.08952e17 | + | 3.51578e17i | −0.674935 | + | 0.389674i | −0.797944 | − | 0.602732i | \(-0.794079\pi\) |
0.123009 | + | 0.992406i | \(0.460746\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.77944e17 | + | 2.18206e17i | 0.413819 | + | 0.238919i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.67107e18 | − | 1.26607e18i | −1.80756 | − | 1.36948i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.65200e17 | − | 8.05750e17i | 0.497121 | − | 0.861039i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.22531e17 | + | 7.31845e17i | 0.446084 | + | 0.772640i | 0.998127 | − | 0.0611757i | \(-0.0194850\pi\) |
−0.552043 | + | 0.833815i | \(0.686152\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 7.14692e17i | − | 0.745458i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.72424e17 | −0.280741 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.30531e18 | − | 7.53621e17i | 1.32905 | − | 0.767330i | 0.343901 | − | 0.939006i | \(-0.388252\pi\) |
0.985153 | + | 0.171676i | \(0.0549182\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.94151e17 | + | 5.16238e17i | 0.899534 | + | 0.519346i |
(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 | 112.13.s.c.33.7 | 16 | ||
4.3 | odd | 2 | 14.13.d.a.5.1 | yes | 16 | ||
7.3 | odd | 6 | inner | 112.13.s.c.17.7 | 16 | ||
12.11 | even | 2 | 126.13.n.a.19.7 | 16 | |||
28.3 | even | 6 | 14.13.d.a.3.1 | ✓ | 16 | ||
28.11 | odd | 6 | 98.13.d.a.31.4 | 16 | |||
28.19 | even | 6 | 98.13.b.c.97.15 | 16 | |||
28.23 | odd | 6 | 98.13.b.c.97.10 | 16 | |||
28.27 | even | 2 | 98.13.d.a.19.4 | 16 | |||
84.59 | odd | 6 | 126.13.n.a.73.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.13.d.a.3.1 | ✓ | 16 | 28.3 | even | 6 | ||
14.13.d.a.5.1 | yes | 16 | 4.3 | odd | 2 | ||
98.13.b.c.97.10 | 16 | 28.23 | odd | 6 | |||
98.13.b.c.97.15 | 16 | 28.19 | even | 6 | |||
98.13.d.a.19.4 | 16 | 28.27 | even | 2 | |||
98.13.d.a.31.4 | 16 | 28.11 | odd | 6 | |||
112.13.s.c.17.7 | 16 | 7.3 | odd | 6 | inner | ||
112.13.s.c.33.7 | 16 | 1.1 | even | 1 | trivial | ||
126.13.n.a.19.7 | 16 | 12.11 | even | 2 | |||
126.13.n.a.73.7 | 16 | 84.59 | odd | 6 |