Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,6,Mod(505,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.505");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(109.702532752\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 7 x^{17} + 17616 x^{16} - 456301 x^{15} + 216301789 x^{14} - 6076762674 x^{13} + \cdots + 55\!\cdots\!41 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{7}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 577.3 | ||
Root | \(-30.6056 + 54.7425i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 684.577 |
Dual form | 684.6.k.f.505.3 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −31.6056 | − | 54.7425i | −0.565378 | − | 0.979263i | −0.997014 | − | 0.0772156i | \(-0.975397\pi\) |
0.431637 | − | 0.902048i | \(-0.357936\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −80.2775 | −0.619225 | −0.309613 | − | 0.950863i | \(-0.600199\pi\) | ||||
−0.309613 | + | 0.950863i | \(0.600199\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 475.169 | 1.18404 | 0.592020 | − | 0.805923i | \(-0.298331\pi\) | ||||
0.592020 | + | 0.805923i | \(0.298331\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −337.473 | + | 584.520i | −0.553835 | + | 0.959270i | 0.444158 | + | 0.895948i | \(0.353503\pi\) |
−0.997993 | + | 0.0633218i | \(0.979831\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −866.499 | − | 1500.82i | −0.727186 | − | 1.25952i | −0.958068 | − | 0.286542i | \(-0.907494\pi\) |
0.230881 | − | 0.972982i | \(-0.425839\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −574.366 | + | 1464.99i | −0.365010 | + | 0.931004i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2424.72 | − | 4199.73i | 0.955743 | − | 1.65540i | 0.223085 | − | 0.974799i | \(-0.428387\pi\) |
0.732658 | − | 0.680597i | \(-0.238279\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −435.326 | + | 754.007i | −0.139304 | + | 0.241282i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2394.08 | + | 4146.67i | −0.528620 | + | 0.915597i | 0.470823 | + | 0.882228i | \(0.343957\pi\) |
−0.999443 | + | 0.0333693i | \(0.989376\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −127.218 | −0.0237764 | −0.0118882 | − | 0.999929i | \(-0.503784\pi\) | ||||
−0.0118882 | + | 0.999929i | \(0.503784\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2537.22 | + | 4394.59i | 0.350096 | + | 0.606384i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −13949.4 | −1.67514 | −0.837570 | − | 0.546331i | \(-0.816024\pi\) | ||||
−0.837570 | + | 0.546331i | \(0.816024\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7883.24 | − | 13654.2i | −0.732394 | − | 1.26854i | −0.955857 | − | 0.293831i | \(-0.905070\pi\) |
0.223463 | − | 0.974712i | \(-0.428264\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 964.112 | + | 1669.89i | 0.0795163 | + | 0.137726i | 0.903041 | − | 0.429554i | \(-0.141329\pi\) |
−0.823525 | + | 0.567280i | \(0.807996\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8099.51 | + | 14028.8i | −0.534828 | + | 0.926349i | 0.464344 | + | 0.885655i | \(0.346290\pi\) |
−0.999172 | + | 0.0406941i | \(0.987043\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10362.5 | −0.616560 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8925.98 | + | 15460.3i | −0.436482 | + | 0.756009i | −0.997415 | − | 0.0718520i | \(-0.977109\pi\) |
0.560933 | + | 0.827861i | \(0.310442\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15018.0 | − | 26011.9i | −0.669430 | − | 1.15949i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8424.75 | − | 14592.1i | −0.315084 | − | 0.545742i | 0.664371 | − | 0.747403i | \(-0.268699\pi\) |
−0.979455 | + | 0.201661i | \(0.935366\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11641.7 | − | 20164.0i | 0.400583 | − | 0.693830i | −0.593214 | − | 0.805045i | \(-0.702141\pi\) |
0.993796 | + | 0.111215i | \(0.0354743\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 42664.1 | 1.25250 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13618.4 | − | 23587.8i | 0.370630 | − | 0.641950i | −0.619033 | − | 0.785365i | \(-0.712475\pi\) |
0.989663 | + | 0.143415i | \(0.0458085\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 37449.3 | + | 64864.1i | 0.881654 | + | 1.52707i | 0.849501 | + | 0.527586i | \(0.176903\pi\) |
0.0321524 | + | 0.999483i | \(0.489764\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 34900.9 | + | 60450.1i | 0.766530 | + | 1.32767i | 0.939434 | + | 0.342731i | \(0.111352\pi\) |
−0.172903 | + | 0.984939i | \(0.555315\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −38145.4 | −0.733188 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11408.5 | + | 19760.1i | 0.205665 | + | 0.356222i | 0.950344 | − | 0.311200i | \(-0.100731\pi\) |
−0.744680 | + | 0.667422i | \(0.767398\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 58008.8 | 0.924270 | 0.462135 | − | 0.886810i | \(-0.347084\pi\) | ||||
0.462135 | + | 0.886810i | \(0.347084\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −54772.4 | + | 94868.6i | −0.822270 | + | 1.42421i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8203.84 | + | 14209.5i | −0.109785 | + | 0.190153i | −0.915683 | − | 0.401901i | \(-0.868349\pi\) |
0.805898 | + | 0.592054i | \(0.201683\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 27091.5 | − | 46923.8i | 0.342948 | − | 0.594004i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 98350.5 | − | 14859.7i | 1.11807 | − | 0.168928i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 65710.8 | + | 113814.i | 0.709100 | + | 1.22820i | 0.965191 | + | 0.261544i | \(0.0842318\pi\) |
−0.256092 | + | 0.966653i | \(0.582435\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 46068.0 | − | 79792.2i | 0.449362 | − | 0.778318i | −0.548983 | − | 0.835834i | \(-0.684985\pi\) |
0.998345 | + | 0.0575159i | \(0.0183180\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 149801. | 1.39130 | 0.695651 | − | 0.718380i | \(-0.255116\pi\) | ||||
0.695651 | + | 0.718380i | \(0.255116\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −62370.7 | −0.526649 | −0.263324 | − | 0.964707i | \(-0.584819\pi\) | ||||
−0.263324 | + | 0.964707i | \(0.584819\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −27370.0 | − | 47406.1i | −0.220652 | − | 0.382180i | 0.734354 | − | 0.678767i | \(-0.237485\pi\) |
−0.955006 | + | 0.296586i | \(0.904152\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 84395.3 | 0.621759 | 0.310879 | − | 0.950449i | \(-0.399376\pi\) | ||||
0.310879 | + | 0.950449i | \(0.399376\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −306538. | −2.16142 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 69560.4 | + | 120482.i | 0.450292 | + | 0.779929i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 64734.8 | 0.401952 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −142500. | −0.815717 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 59200.7 | − | 102539.i | 0.325700 | − | 0.564128i | −0.655954 | − | 0.754801i | \(-0.727734\pi\) |
0.981654 | + | 0.190672i | \(0.0610668\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 37228.3 | + | 64481.4i | 0.189538 | + | 0.328289i | 0.945096 | − | 0.326792i | \(-0.105968\pi\) |
−0.755559 | + | 0.655081i | \(0.772634\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 46108.6 | − | 117606.i | 0.226023 | − | 0.576501i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 70227.1 | − | 121637.i | 0.319671 | − | 0.553686i | −0.660748 | − | 0.750607i | \(-0.729761\pi\) |
0.980419 | + | 0.196921i | \(0.0630943\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −112322. | + | 194548.i | −0.493093 | + | 0.854061i | −0.999968 | − | 0.00795774i | \(-0.997467\pi\) |
0.506876 | + | 0.862019i | \(0.330800\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −160357. | + | 277746.i | −0.655763 | + | 1.13581i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 302665. | 1.19548 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 146994. | + | 254601.i | 0.542417 | + | 0.939494i | 0.998765 | + | 0.0496923i | \(0.0158241\pi\) |
−0.456347 | + | 0.889802i | \(0.650843\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 366703. | 1.30880 | 0.654398 | − | 0.756150i | \(-0.272922\pi\) | ||||
0.654398 | + | 0.756150i | \(0.272922\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4020.81 | + | 6964.26i | 0.0134426 | + | 0.0232833i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14338.2 | + | 24834.5i | 0.0464243 | + | 0.0804093i | 0.888304 | − | 0.459256i | \(-0.151884\pi\) |
−0.841880 | + | 0.539666i | \(0.818551\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −194650. | + | 337144.i | −0.591820 | + | 1.02506i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12767.3 | 0.0376383 | 0.0188192 | − | 0.999823i | \(-0.494009\pi\) | ||||
0.0188192 | + | 0.999823i | \(0.494009\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 121547. | − | 210526.i | 0.337252 | − | 0.584138i | −0.646663 | − | 0.762776i | \(-0.723836\pi\) |
0.983915 | + | 0.178638i | \(0.0571692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −42129.2 | − | 72969.8i | −0.113466 | − | 0.196529i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 213672. | + | 370091.i | 0.542792 | + | 0.940143i | 0.998742 | + | 0.0501376i | \(0.0159660\pi\) |
−0.455951 | + | 0.890005i | \(0.650701\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 34946.9 | − | 60529.7i | 0.0862607 | − | 0.149408i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −41174.1 | −0.0960488 | −0.0480244 | − | 0.998846i | \(-0.515293\pi\) | ||||
−0.0480244 | + | 0.998846i | \(0.515293\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −241411. | + | 418136.i | −0.547723 | + | 0.948684i | 0.450707 | + | 0.892672i | \(0.351172\pi\) |
−0.998430 | + | 0.0560122i | \(0.982161\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 440879. | + | 763624.i | 0.947087 | + | 1.64040i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −411734. | − | 713144.i | −0.861018 | − | 1.49133i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −218201. | −0.432786 | −0.216393 | − | 0.976306i | \(-0.569429\pi\) | ||||
−0.216393 | + | 0.976306i | \(0.569429\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 357570. | + | 619329.i | 0.690983 | + | 1.19682i | 0.971516 | + | 0.236973i | \(0.0761554\pi\) |
−0.280533 | + | 0.959844i | \(0.590511\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17740.5 | −0.0325686 | −0.0162843 | − | 0.999867i | \(-0.505184\pi\) | ||||
−0.0162843 | + | 0.999867i | \(0.505184\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −290101. | + | 502469.i | −0.519297 | + | 0.899449i | 0.480451 | + | 0.877021i | \(0.340473\pi\) |
−0.999748 | + | 0.0224275i | \(0.992861\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 192191. | − | 332884.i | 0.327335 | − | 0.566961i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −498309. | + | 863096.i | −0.828159 | + | 1.43441i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −272921. | + | 696119.i | −0.432186 | + | 1.10235i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 418159. | + | 724272.i | 0.646599 | + | 1.11994i | 0.983930 | + | 0.178556i | \(0.0571427\pi\) |
−0.337330 | + | 0.941386i | \(0.609524\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 60942.6 | − | 105556.i | 0.0899135 | − | 0.155735i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10212.8 | 0.0147229 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.16968e6 | 1.61096 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 349535. | + | 605413.i | 0.470684 | + | 0.815248i | 0.999438 | − | 0.0335271i | \(-0.0106740\pi\) |
−0.528754 | + | 0.848775i | \(0.677341\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −813403. | −1.04771 | −0.523855 | − | 0.851808i | \(-0.675507\pi\) | ||||
−0.523855 | + | 0.851808i | \(0.675507\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.18902e6 | −1.49830 | −0.749151 | − | 0.662399i | \(-0.769538\pi\) | ||||
−0.749151 | + | 0.662399i | \(0.769538\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 106736. | + | 184872.i | 0.128801 | + | 0.223091i | 0.923212 | − | 0.384290i | \(-0.125554\pi\) |
−0.794411 | + | 0.607381i | \(0.792220\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.02396e6 | 1.20952 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 965775. | 1.09366 | 0.546829 | − | 0.837245i | \(-0.315835\pi\) | ||||
0.546829 | + | 0.837245i | \(0.315835\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 391235. | − | 677639.i | 0.433906 | − | 0.751547i | −0.563300 | − | 0.826252i | \(-0.690468\pi\) |
0.997206 | + | 0.0747059i | \(0.0238018\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 327514. | + | 567270.i | 0.348590 | + | 0.603775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −662485. | − | 830123.i | −0.690929 | − | 0.865765i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 448780. | − | 777310.i | 0.449624 | − | 0.778771i | −0.548738 | − | 0.835995i | \(-0.684891\pi\) |
0.998361 | + | 0.0572236i | \(0.0182248\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.15215e6 | − | 1.99558e6i | 1.13164 | − | 1.96006i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 552328. | − | 956660.i | 0.521632 | − | 0.903493i | −0.478051 | − | 0.878332i | \(-0.658657\pi\) |
0.999683 | − | 0.0251612i | \(-0.00800989\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.11982e6 | 1.03729 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 306009. | + | 530023.i | 0.272800 | + | 0.472504i | 0.969578 | − | 0.244783i | \(-0.0787169\pi\) |
−0.696778 | + | 0.717287i | \(0.745384\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.12844e6 | 0.987109 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 248820. | + | 430969.i | 0.209655 | + | 0.363133i | 0.951606 | − | 0.307321i | \(-0.0994326\pi\) |
−0.741951 | + | 0.670454i | \(0.766099\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 724980. | + | 1.25570e6i | 0.599657 | + | 1.03864i | 0.992871 | + | 0.119190i | \(0.0380297\pi\) |
−0.393214 | + | 0.919447i | \(0.628637\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −206853. | + | 358281.i | −0.164942 | + | 0.285688i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −87028.2 | −0.0681492 | −0.0340746 | − | 0.999419i | \(-0.510848\pi\) | ||||
−0.0340746 | + | 0.999419i | \(0.510848\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −949563. | + | 1.64469e6i | −0.717394 | + | 1.24256i | 0.244635 | + | 0.969615i | \(0.421332\pi\) |
−0.962029 | + | 0.272948i | \(0.912001\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −727473. | − | 1.26002e6i | −0.539946 | − | 0.935214i | −0.998906 | − | 0.0467574i | \(-0.985111\pi\) |
0.458960 | − | 0.888457i | \(-0.348222\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 632846. | + | 1.09612e6i | 0.453517 | + | 0.785514i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −791713. | + | 1.37129e6i | −0.557600 | + | 0.965792i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −795288. | −0.541197 | −0.270598 | − | 0.962692i | \(-0.587222\pi\) | ||||
−0.270598 | + | 0.962692i | \(0.587222\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −532538. | + | 922383.i | −0.356283 | + | 0.617101i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.63655e6 | + | 2.83459e6i | 1.05865 | + | 1.83363i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −77396.5 | − | 134055.i | −0.0492385 | − | 0.0852836i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.47177e6 | −0.905923 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 964887. | + | 1.67123e6i | 0.584293 | + | 1.01202i | 0.994963 | + | 0.100241i | \(0.0319613\pi\) |
−0.410670 | + | 0.911784i | \(0.634705\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.42463e6 | −0.835220 | −0.417610 | − | 0.908626i | \(-0.637132\pi\) | ||||
−0.417610 | + | 0.908626i | \(0.637132\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.12004e6 | − | 1.93997e6i | 0.646209 | − | 1.11927i | −0.337812 | − | 0.941214i | \(-0.609687\pi\) |
0.984021 | − | 0.178053i | \(-0.0569800\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 278493. | − | 482363.i | 0.155656 | − | 0.269604i | −0.777642 | − | 0.628708i | \(-0.783584\pi\) |
0.933298 | + | 0.359104i | \(0.116918\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.13759e6 | + | 1.97037e6i | −0.625908 | + | 1.08410i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.69638e6 | − | 407395.i | 1.43805 | − | 0.217275i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −293821. | − | 508913.i | −0.154303 | − | 0.267261i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 650208. | − | 1.12619e6i | 0.331179 | − | 0.573619i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.85079e6 | −0.928511 | −0.464256 | − | 0.885701i | \(-0.653678\pi\) | ||||
−0.464256 | + | 0.885701i | \(0.653678\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.72168e6 | −0.838184 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.16626e6 | + | 2.02003e6i | 0.559399 | + | 0.968907i | 0.997547 | + | 0.0700041i | \(0.0223013\pi\) |
−0.438148 | + | 0.898903i | \(0.644365\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −60450.3 | −0.0281522 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.18110e6 | 1.00101 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.33391e6 | − | 2.31041e6i | −0.594708 | − | 1.03006i | −0.993588 | − | 0.113062i | \(-0.963934\pi\) |
0.398880 | − | 0.917003i | \(-0.369399\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.33528e6 | −1.02630 | −0.513152 | − | 0.858298i | \(-0.671522\pi\) | ||||
−0.513152 | + | 0.858298i | \(0.671522\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.57168e6 | 1.09845 | 0.549225 | − | 0.835675i | \(-0.314923\pi\) | ||||
0.549225 | + | 0.835675i | \(0.314923\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.36722e6 | − | 4.10014e6i | 0.996935 | − | 1.72674i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.06014e6 | + | 3.56826e6i | 0.843645 | + | 1.46124i | 0.886793 | + | 0.462168i | \(0.152928\pi\) |
−0.0431473 | + | 0.999069i | \(0.513738\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.81631e6 | − | 1.68288e6i | −0.733536 | − | 0.679651i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.20613e6 | − | 3.82112e6i | 0.866759 | − | 1.50127i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.76851e6 | + | 3.06315e6i | −0.685398 | + | 1.18714i | 0.287914 | + | 0.957656i | \(0.407038\pi\) |
−0.973312 | + | 0.229487i | \(0.926295\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 716555. | − | 1.24111e6i | 0.270281 | − | 0.468140i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.14142e6 | −1.16910 | −0.584552 | − | 0.811356i | \(-0.698730\pi\) | ||||
−0.584552 | + | 0.811356i | \(0.698730\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.61587e6 | − | 2.79878e6i | −0.585537 | − | 1.01418i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.24166e6 | 0.444021 | 0.222011 | − | 0.975044i | \(-0.428738\pi\) | ||||
0.222011 | + | 0.975044i | \(0.428738\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.41220e6 | − | 2.44600e6i | −0.491924 | − | 0.852038i | 0.508032 | − | 0.861338i | \(-0.330373\pi\) |
−0.999957 | + | 0.00929990i | \(0.997040\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.20561e6 | + | 2.08817e6i | 0.414528 | + | 0.717984i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.26664e6 | + | 3.92593e6i | −0.759465 | + | 1.31543i | 0.183658 | + | 0.982990i | \(0.441206\pi\) |
−0.943124 | + | 0.332442i | \(0.892127\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.40405e6 | −2.78001 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 721143. | − | 1.24906e6i | 0.232557 | − | 0.402800i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 968813. | + | 1.67803e6i | 0.308506 | + | 0.534348i | 0.978036 | − | 0.208437i | \(-0.0668377\pi\) |
−0.669530 | + | 0.742785i | \(0.733504\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.21857e6 | − | 3.84268e6i | −0.688990 | − | 1.19336i | −0.972165 | − | 0.234297i | \(-0.924721\pi\) |
0.283176 | − | 0.959068i | \(-0.408612\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 42932.8 | − | 74361.7i | 0.0131682 | − | 0.0228080i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.62832e6 | −1.98343 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.20721e6 | − | 5.55506e6i | 0.948025 | − | 1.64203i | 0.198446 | − | 0.980112i | \(-0.436411\pi\) |
0.749579 | − | 0.661915i | \(-0.230256\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 676317. | + | 1.17142e6i | 0.195108 | + | 0.337937i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.83340e6 | − | 3.17555e6i | −0.522562 | − | 0.905103i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.16492e6 | −0.602429 | −0.301215 | − | 0.953556i | \(-0.597392\pi\) | ||||
−0.301215 | + | 0.953556i | \(0.597392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.39931e6 | + | 5.88777e6i | 0.934727 | + | 1.61900i | 0.775119 | + | 0.631815i | \(0.217690\pi\) |
0.159608 | + | 0.987180i | \(0.448977\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.50884e6 | 0.405201 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −934567. | + | 1.61872e6i | −0.248051 | + | 0.429637i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −101699. | + | 176148.i | −0.0263708 | + | 0.0456756i | −0.878910 | − | 0.476988i | \(-0.841728\pi\) |
0.852539 | + | 0.522664i | \(0.175062\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 487850. | − | 844981.i | 0.125045 | − | 0.216584i | −0.796705 | − | 0.604368i | \(-0.793426\pi\) |
0.921751 | + | 0.387783i | \(0.126759\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.75990e6 | + | 5.96437e6i | 1.19232 | + | 1.49404i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.96789e6 | − | 3.40848e6i | −0.487348 | − | 0.844111i | 0.512546 | − | 0.858660i | \(-0.328702\pi\) |
−0.999894 | + | 0.0145483i | \(0.995369\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.39091e6 | + | 2.40913e6i | −0.336737 | + | 0.583246i | −0.983817 | − | 0.179176i | \(-0.942657\pi\) |
0.647080 | + | 0.762422i | \(0.275990\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.03715e6 | 0.248279 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.91764e6 | −1.61936 | −0.809678 | − | 0.586875i | \(-0.800358\pi\) | ||||
−0.809678 | + | 0.586875i | \(0.800358\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.74587e6 | − | 6.48804e6i | −0.867184 | − | 1.50201i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.42497e6 | −0.775582 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.44928e6 | 1.44451 | 0.722256 | − | 0.691626i | \(-0.243105\pi\) | ||||
0.722256 | + | 0.691626i | \(0.243105\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −610341. | − | 1.05714e6i | −0.133758 | − | 0.231676i | 0.791364 | − | 0.611345i | \(-0.209371\pi\) |
−0.925122 | + | 0.379669i | \(0.876038\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 847245. | 0.183678 | 0.0918388 | − | 0.995774i | \(-0.470726\pi\) | ||||
0.0918388 | + | 0.995774i | \(0.470726\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 76212.7 | 0.0161709 | 0.00808547 | − | 0.999967i | \(-0.497426\pi\) | ||||
0.00808547 | + | 0.999967i | \(0.497426\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.09325e6 | + | 1.89357e6i | −0.229503 | + | 0.397512i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 458116. | + | 793481.i | 0.0941505 | + | 0.163074i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −854578. | − | 1.07082e6i | −0.173787 | − | 0.217763i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.33045e6 | − | 2.30441e6i | 0.264947 | − | 0.458902i | −0.702602 | − | 0.711583i | \(-0.747979\pi\) |
0.967550 | + | 0.252680i | \(0.0813121\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.70754e6 | − | 8.15370e6i | 0.927750 | − | 1.60691i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.15366e6 | − | 7.19434e6i | 0.801819 | − | 1.38879i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.81426e6 | 1.11089 | 0.555446 | − | 0.831552i | \(-0.312547\pi\) | ||||
0.555446 | + | 0.831552i | \(0.312547\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.27968e6 | − | 3.94853e6i | −0.426747 | − | 0.739148i | 0.569834 | − | 0.821760i | \(-0.307007\pi\) |
−0.996582 | + | 0.0826113i | \(0.973674\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.29787e6 | 1.53762 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.00634e6 | − | 5.20713e6i | −0.545942 | − | 0.945600i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.38613e6 | + | 5.86495e6i | 0.608769 | + | 1.05442i | 0.991444 | + | 0.130536i | \(0.0416697\pi\) |
−0.382675 | + | 0.923883i | \(0.624997\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.62169e6 | + | 4.54089e6i | −0.462020 | + | 0.800242i | −0.999062 | − | 0.0433140i | \(-0.986208\pi\) |
0.537042 | + | 0.843556i | \(0.319542\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.82403e6 | −1.01624 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.68578e6 | − | 8.11601e6i | 0.801655 | − | 1.38851i | −0.116872 | − | 0.993147i | \(-0.537287\pi\) |
0.918526 | − | 0.395360i | \(-0.129380\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.80175e6 | − | 4.85278e6i | −0.474655 | − | 0.822126i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.73455e6 | − | 8.20047e6i | −0.786611 | − | 1.36245i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.84864e6 | + | 6.66604e6i | −0.633258 | + | 1.09683i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −244496. | −0.0394619 | −0.0197309 | − | 0.999805i | \(-0.506281\pi\) | ||||
−0.0197309 | + | 0.999805i | \(0.506281\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.04939e6 | + | 3.54964e6i | −0.327619 | + | 0.567453i | −0.982039 | − | 0.188678i | \(-0.939580\pi\) |
0.654420 | + | 0.756131i | \(0.272913\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 110235. | + | 190932.i | 0.0172899 | + | 0.0299469i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.54032e6 | − | 1.47923e7i | −1.32689 | − | 2.29824i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.06415e7 | 1.62250 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.97126e6 | + | 3.41433e6i | 0.297756 | + | 0.515728i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.92395e6 | −0.730032 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 227501. | − | 394043.i | 0.0334187 | − | 0.0578829i | −0.848832 | − | 0.528662i | \(-0.822694\pi\) |
0.882251 | + | 0.470779i | \(0.156027\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.73009e6 | + | 2.99660e6i | −0.249503 | + | 0.432153i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.19066e6 | + | 7.25843e6i | −0.598844 | + | 1.03723i | 0.394148 | + | 0.919047i | \(0.371040\pi\) |
−0.992992 | + | 0.118182i | \(0.962293\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.69976e6 | − | 5.88901e6i | −0.659473 | − | 0.826349i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −915844. | − | 1.58629e6i | −0.127353 | − | 0.220582i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.14702e6 | − | 3.71874e6i | 0.293222 | − | 0.507876i | −0.681347 | − | 0.731960i | \(-0.738606\pi\) |
0.974570 | + | 0.224084i | \(0.0719390\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.30145e6 | −0.176156 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.43360e6 | 0.722465 | 0.361232 | − | 0.932476i | \(-0.382356\pi\) | ||||
0.361232 | + | 0.932476i | \(0.382356\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.66736e6 | − | 4.62001e6i | −0.351529 | − | 0.608866i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.53732e6 | −0.587514 | −0.293757 | − | 0.955880i | \(-0.594906\pi\) | ||||
−0.293757 | + | 0.955880i | \(0.594906\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.75132e6 | −0.224789 | −0.112395 | − | 0.993664i | \(-0.535852\pi\) | ||||
−0.112395 | + | 0.993664i | \(0.535852\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.11108e6 | + | 3.65650e6i | 0.266278 | + | 0.461208i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.69353e6 | 0.336808 | 0.168404 | − | 0.985718i | \(-0.446139\pi\) | ||||
0.168404 | + | 0.985718i | \(0.446139\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.65680e6 | −0.572331 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.24135e6 | + | 7.34624e6i | −0.516812 | + | 0.895145i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.95802e6 | − | 3.39138e6i | −0.234542 | − | 0.406239i | 0.724597 | − | 0.689172i | \(-0.242026\pi\) |
−0.959140 | + | 0.282934i | \(0.908692\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 73069.9 | − | 186374.i | 0.00867862 | − | 0.0221359i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.66866e6 | − | 9.81841e6i | 0.661978 | − | 1.14658i | −0.318117 | − | 0.948051i | \(-0.603050\pi\) |
0.980095 | − | 0.198528i | \(-0.0636162\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.39699e6 | − | 7.61581e6i | 0.509170 | − | 0.881909i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.86543e6 | + | 6.69512e6i | −0.440180 | + | 0.762414i | −0.997702 | − | 0.0677475i | \(-0.978419\pi\) |
0.557522 | + | 0.830162i | \(0.311752\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.87953e6 | −0.776913 | −0.388457 | − | 0.921467i | \(-0.626992\pi\) | ||||
−0.388457 | + | 0.921467i | \(0.626992\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.04598e6 | − | 3.54374e6i | −0.227255 | − | 0.393617i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.19598e7 | 1.31750 | 0.658750 | − | 0.752362i | \(-0.271085\pi\) | ||||
0.658750 | + | 0.752362i | \(0.271085\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.46673e6 | − | 9.46865e6i | −0.592413 | − | 1.02609i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.49181e6 | + | 2.58389e6i | 0.160347 | + | 0.277730i | 0.934993 | − | 0.354666i | \(-0.115405\pi\) |
−0.774646 | + | 0.632395i | \(0.782072\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.62649e6 | − | 4.54922e6i | 0.277756 | − | 0.481087i | −0.693071 | − | 0.720869i | \(-0.743743\pi\) |
0.970827 | + | 0.239782i | \(0.0770761\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.09695e7 | −1.15069 | −0.575346 | − | 0.817910i | \(-0.695133\pi\) | ||||
−0.575346 | + | 0.817910i | \(0.695133\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 658583. | − | 1.14070e6i | 0.0679815 | − | 0.117747i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.86419e6 | + | 1.01571e7i | 0.600493 | + | 1.04008i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.20871e7 | + | 2.09355e7i | 1.21814 | + | 2.10988i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.73436e6 | + | 6.46811e6i | −0.373373 | + | 0.646701i | −0.990082 | − | 0.140490i | \(-0.955132\pi\) |
0.616709 | + | 0.787191i | \(0.288466\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.48429e6 | −0.736573 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.49707e6 | − | 6.05710e6i | 0.341473 | − | 0.591448i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.26419e6 | + | 1.43140e7i | 0.794430 | + | 1.37599i | 0.923201 | + | 0.384318i | \(0.125563\pi\) |
−0.128771 | + | 0.991674i | \(0.541103\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.29383e6 | − | 1.09012e7i | −0.600326 | − | 1.03980i | −0.992771 | − | 0.120020i | \(-0.961704\pi\) |
0.392445 | − | 0.919775i | \(-0.371629\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.21912e7 | −1.14494 | −0.572472 | − | 0.819924i | \(-0.694015\pi\) | ||||
−0.572472 | + | 0.819924i | \(0.694015\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.00318e6 | − | 6.93371e6i | −0.373073 | − | 0.646181i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.52249e6 | 0.690365 | 0.345182 | − | 0.938536i | \(-0.387817\pi\) | ||||
0.345182 | + | 0.938536i | \(0.387817\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.35325e6 | − | 4.07594e6i | 0.214321 | − | 0.371214i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.02028e6 | + | 1.38915e7i | −0.719409 | + | 1.24605i | 0.241825 | + | 0.970320i | \(0.422254\pi\) |
−0.961234 | + | 0.275733i | \(0.911079\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.26368e6 | − | 1.08490e7i | 0.557604 | − | 0.965798i | −0.440092 | − | 0.897953i | \(-0.645054\pi\) |
0.997696 | − | 0.0678454i | \(-0.0216125\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.89533e6 | + | 1.19290e6i | −0.692335 | + | 0.104605i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.16099e7 | + | 2.01090e7i | 1.01045 | + | 1.75015i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.53178e6 | − | 9.58133e6i | 0.474306 | − | 0.821523i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.50054e6 | −0.638344 | −0.319172 | − | 0.947697i | \(-0.603405\pi\) | ||||
−0.319172 | + | 0.947697i | \(0.603405\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.19677e7 | −1.00355 | −0.501777 | − | 0.864997i | \(-0.667320\pi\) | ||||
−0.501777 | + | 0.864997i | \(0.667320\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.27510e6 | − | 9.13673e6i | −0.439092 | − | 0.760530i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.11577e6 | −0.665699 | −0.332850 | − | 0.942980i | \(-0.608010\pi\) | ||||
−0.332850 | + | 0.942980i | \(0.608010\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.87827e6 | −0.722939 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.02455e6 | − | 1.04348e7i | −0.483478 | − | 0.837408i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.23034e7 | −0.980235 | −0.490117 | − | 0.871657i | \(-0.663046\pi\) | ||||
−0.490117 | + | 0.871657i | \(0.663046\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.42000e7 | 1.11513 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.36616e7 | + | 2.36626e7i | −1.06517 | + | 1.84494i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.04732e6 | + | 1.22063e7i | 0.541663 | + | 0.938188i | 0.998809 | + | 0.0487959i | \(0.0155384\pi\) |
−0.457146 | + | 0.889392i | \(0.651128\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.01205e6 | − | 2.04358e7i | 0.611442 | − | 1.55956i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.69823e6 | + | 6.40552e6i | −0.278256 | + | 0.481954i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.13108e6 | + | 3.69113e6i | −0.159215 | + | 0.275768i | −0.934586 | − | 0.355738i | \(-0.884230\pi\) |
0.775371 | + | 0.631506i | \(0.217563\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −308469. | + | 534283.i | −0.0227241 | + | 0.0393593i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.02727e7 | 1.48302 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.85763e6 | − | 1.18778e7i | −0.494711 | − | 0.856865i | 0.505270 | − | 0.862961i | \(-0.331393\pi\) |
−0.999981 | + | 0.00609644i | \(0.998059\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.20256e7 | −0.861529 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.08441e6 | − | 3.61031e6i | −0.147278 | − | 0.255093i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.05919e7 | − | 1.83457e7i | −0.743256 | − | 1.28736i | −0.951005 | − | 0.309175i | \(-0.899947\pi\) |
0.207749 | − | 0.978182i | \(-0.433386\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.67080e6 | − | 2.89392e6i | 0.115646 | − | 0.200305i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.01308e6 | 0.413368 | 0.206684 | − | 0.978408i | \(-0.433733\pi\) | ||||
0.206684 | + | 0.978408i | \(0.433733\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.47107e6 | − | 1.12082e7i | 0.438841 | − | 0.760095i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.41424e6 | − | 1.45739e7i | −0.566766 | − | 0.981667i | −0.996883 | − | 0.0788942i | \(-0.974861\pi\) |
0.430117 | − | 0.902773i | \(-0.358472\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.01935e6 | + | 3.49762e6i | 0.134196 | + | 0.232434i | 0.925290 | − | 0.379260i | \(-0.123821\pi\) |
−0.791094 | + | 0.611695i | \(0.790488\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.29165e6 | − | 1.60936e7i | 0.613341 | − | 1.06234i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.00696e6 | 0.326114 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −351347. | + | 608550.i | −0.0227319 | + | 0.0393728i | −0.877168 | − | 0.480184i | \(-0.840570\pi\) |
0.854436 | + | 0.519557i | \(0.173903\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.15899e7 | − | 2.00742e7i | −0.739964 | − | 1.28166i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.19882e7 | + | 2.07642e7i | 0.760354 | + | 1.31697i | 0.942668 | + | 0.333731i | \(0.108308\pi\) |
−0.182314 | + | 0.983240i | \(0.558359\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.29063e7 | 0.807869 | 0.403934 | − | 0.914788i | \(-0.367642\pi\) | ||||
0.403934 | + | 0.914788i | \(0.367642\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.19719e6 | + | 3.80565e6i | 0.136633 | + | 0.236656i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.13725e7 | 0.698019 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.05367e7 | + | 1.82501e7i | −0.642524 | + | 1.11288i | 0.342343 | + | 0.939575i | \(0.388779\pi\) |
−0.984867 | + | 0.173310i | \(0.944554\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.35234e6 | + | 7.53848e6i | −0.261984 | + | 0.453769i | −0.966769 | − | 0.255652i | \(-0.917710\pi\) |
0.704785 | + | 0.709421i | \(0.251043\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 55381.5 | − | 95923.6i | 0.00331215 | − | 0.00573682i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.45311e7 | − | 3.70640e6i | 1.44835 | − | 0.218831i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.77948e7 | + | 3.08214e7i | 1.04391 | + | 1.80811i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 906334. | − | 1.56982e6i | 0.0524946 | − | 0.0909232i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.69329e6 | −0.155005 | −0.0775026 | − | 0.996992i | \(-0.524695\pi\) | ||||
−0.0775026 | + | 0.996992i | \(0.524695\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.77504e6 | −0.385009 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.85752e6 | + | 1.36096e7i | 0.443713 | + | 0.768534i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.67101e6 | 0.260474 | 0.130237 | − | 0.991483i | \(-0.458426\pi\) | ||||
0.130237 | + | 0.991483i | \(0.458426\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.80729e7 | 1.55568 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.65838e7 | + | 2.87240e7i | 0.907603 | + | 1.57201i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.46081e7 | 1.33841 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.82792e7 | 0.981941 | 0.490970 | − | 0.871176i | \(-0.336642\pi\) | ||||
0.490970 | + | 0.871176i | \(0.336642\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.38560e6 | + | 1.62563e7i | −0.501083 | + | 0.867902i | 0.498916 | + | 0.866650i | \(0.333732\pi\) |
−0.999999 | + | 0.00125119i | \(0.999602\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −403518. | − | 698914.i | −0.0212799 | − | 0.0368578i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.00013e6 | + | 453289.i | −0.157248 | + | 0.0237585i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.00143e6 | + | 8.66273e6i | −0.258962 | + | 0.448536i | −0.965964 | − | 0.258676i | \(-0.916714\pi\) |
0.707002 | + | 0.707212i | \(0.250047\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.31371e6 | + | 9.20361e6i | −0.273463 | + | 0.473651i | −0.969746 | − | 0.244116i | \(-0.921502\pi\) |
0.696283 | + | 0.717767i | \(0.254836\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.74700e6 | − | 4.75795e6i | 0.139668 | − | 0.241911i | −0.787703 | − | 0.616055i | \(-0.788730\pi\) |
0.927371 | + | 0.374144i | \(0.122063\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.66282e6 | 0.336722 | 0.168361 | − | 0.985725i | \(-0.446153\pi\) | ||||
0.168361 | + | 0.985725i | \(0.446153\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.97912e6 | + | 1.55523e7i | 0.448354 | + | 0.776572i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.53663e7 | −0.762699 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.62638e6 | + | 6.28107e6i | 0.177856 | + | 0.308055i | 0.941146 | − | 0.338001i | \(-0.109751\pi\) |
−0.763290 | + | 0.646056i | \(0.776417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.20767e6 | − | 2.09174e6i | −0.0588786 | − | 0.101981i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.66303e6 | + | 4.61251e6i | −0.128302 | + | 0.222226i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.19674e6 | −0.248899 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.38233e7 | + | 5.85837e7i | −1.60100 | + | 2.77302i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.39644e7 | + | 2.41871e7i | 0.657130 | + | 1.13818i | 0.981355 | + | 0.192202i | \(0.0615630\pi\) |
−0.324225 | + | 0.945980i | \(0.605104\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.35275e6 | + | 2.34304e6i | 0.0629169 | + | 0.108975i | 0.895768 | − | 0.444522i | \(-0.146626\pi\) |
−0.832851 | + | 0.553497i | \(0.813293\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.45030e7 | − | 2.51199e7i | 0.670616 | − | 1.16154i | −0.307114 | − | 0.951673i | \(-0.599363\pi\) |
0.977730 | − | 0.209868i | \(-0.0673034\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.44738e6 | 0.386096 | 0.193048 | − | 0.981189i | \(-0.438163\pi\) | ||||
0.193048 | + | 0.981189i | \(0.438163\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.35065e7 | − | 2.33939e7i | 0.613765 | − | 1.06307i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.42096e6 | + | 9.38937e6i | 0.243515 | + | 0.421781i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.19171e6 | + | 1.59205e7i | 0.410536 | + | 0.711068i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.14395e7 | 0.505113 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.25597e7 | − | 2.17540e7i | −0.551416 | − | 0.955080i | −0.998173 | − | 0.0604245i | \(-0.980755\pi\) |
0.446757 | − | 0.894655i | \(-0.352579\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.95758e7 | 0.849728 | 0.424864 | − | 0.905257i | \(-0.360322\pi\) | ||||
0.424864 | + | 0.905257i | \(0.360322\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.40024e6 | + | 2.42528e6i | −0.0604366 | + | 0.104679i | −0.894661 | − | 0.446746i | \(-0.852583\pi\) |
0.834224 | + | 0.551426i | \(0.185916\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.11985e7 | + | 3.67169e7i | −0.904682 | + | 1.56696i | −0.0833393 | + | 0.996521i | \(0.526559\pi\) |
−0.821343 | + | 0.570435i | \(0.806775\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.75248e6 | + | 8.23154e6i | −0.201681 | + | 0.349322i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.59000e7 | − | 1.99234e7i | −0.667217 | − | 0.836053i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.30133e6 | + | 2.25397e6i | 0.0543039 | + | 0.0940571i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 304571. | − | 527533.i | 0.0125687 | − | 0.0217696i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.09374e7 | 1.26962 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.05198e7 | 1.23868 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.00865e7 | + | 1.74703e7i | 0.407118 | + | 0.705149i | 0.994565 | − | 0.104113i | \(-0.0332004\pi\) |
−0.587447 | + | 0.809262i | \(0.699867\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.89915e7 | 1.55659 | 0.778294 | − | 0.627900i | \(-0.216085\pi\) | ||||
0.778294 | + | 0.627900i | \(0.216085\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.75640e7 | 1.09437 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.98860e6 | − | 5.17640e6i | −0.117366 | − | 0.203285i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.96447e6 | 0.389193 | 0.194597 | − | 0.980883i | \(-0.437660\pi\) | ||||
0.194597 | + | 0.980883i | \(0.437660\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.05525e7 | −1.95316 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.07253e6 | − | 1.05179e7i | 0.233354 | − | 0.404181i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.00913e6 | − | 1.04081e7i | −0.228440 | − | 0.395670i | 0.728906 | − | 0.684614i | \(-0.240029\pi\) |
−0.957346 | + | 0.288944i | \(0.906696\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.95188e6 | − | 1.51810e7i | 0.225050 | − | 0.574020i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.60262e7 | + | 4.50786e7i | −0.973601 | + | 1.68633i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.90689e7 | − | 3.30284e7i | 0.709541 | − | 1.22896i | −0.255486 | − | 0.966813i | \(-0.582236\pi\) |
0.965027 | − | 0.262149i | \(-0.0844311\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.78331e6 | + | 1.52131e7i | −0.323358 | + | 0.560073i | −0.981179 | − | 0.193102i | \(-0.938145\pi\) |
0.657820 | + | 0.753175i | \(0.271479\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.64584e7 | −2.79992 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.41786e7 | − | 4.18786e7i | −0.876106 | − | 1.51746i | −0.855580 | − | 0.517671i | \(-0.826799\pi\) |
−0.0205267 | − | 0.999789i | \(-0.506534\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.71124e7 | −1.69812 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.89643e7 | + | 3.28471e7i | 0.676402 | + | 1.17156i | 0.976057 | + | 0.217514i | \(0.0697949\pi\) |
−0.299656 | + | 0.954047i | \(0.596872\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.89637e6 | + | 1.19449e7i | 0.244688 | + | 0.423812i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.63765e6 | + | 9.76470e6i | −0.197948 | + | 0.342856i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.86130e7 | −0.999435 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.26024e7 | − | 3.91485e7i | 0.781333 | − | 1.35331i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.31734e6 | − | 1.44061e7i | −0.286034 | − | 0.495426i | 0.686825 | − | 0.726823i | \(-0.259004\pi\) |
−0.972859 | + | 0.231397i | \(0.925670\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.41242e7 | + | 2.44638e7i | 0.480746 | + | 0.832677i | 0.999756 | − | 0.0220914i | \(-0.00703248\pi\) |
−0.519010 | + | 0.854768i | \(0.673699\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.01694e6 | − | 1.56178e7i | 0.305335 | − | 0.528856i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.01881e7 | 1.01181 | 0.505906 | − | 0.862589i | \(-0.331158\pi\) | ||||
0.505906 | + | 0.862589i | \(0.331158\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.89821e6 | + | 6.75190e6i | −0.129990 | + | 0.225149i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2321.02 | + | 4020.12i | 7.66117e−5 | + | 0.000132695i | 0.866064 | − | 0.499934i | \(-0.166642\pi\) |
−0.865987 | + | 0.500066i | \(0.833309\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 560698. | + | 971158.i | 0.0184136 | + | 0.0318933i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.35079e6 | 0.303989 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.56708e7 | + | 2.71426e7i | 0.506882 | + | 0.877945i | 0.999968 | + | 0.00796469i | \(0.00253527\pi\) |
−0.493087 | + | 0.869980i | \(0.664131\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.66752e7 | 1.17440 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.11856e7 | + | 1.93740e7i | −0.356387 | + | 0.617280i | −0.987354 | − | 0.158529i | \(-0.949325\pi\) |
0.630968 | + | 0.775809i | \(0.282658\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 684.6.k.f.577.3 | 18 | ||
3.2 | odd | 2 | 76.6.e.a.45.4 | ✓ | 18 | ||
12.11 | even | 2 | 304.6.i.d.273.6 | 18 | |||
19.11 | even | 3 | inner | 684.6.k.f.505.3 | 18 | ||
57.11 | odd | 6 | 76.6.e.a.49.4 | yes | 18 | ||
228.11 | even | 6 | 304.6.i.d.49.6 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.e.a.45.4 | ✓ | 18 | 3.2 | odd | 2 | ||
76.6.e.a.49.4 | yes | 18 | 57.11 | odd | 6 | ||
304.6.i.d.49.6 | 18 | 228.11 | even | 6 | |||
304.6.i.d.273.6 | 18 | 12.11 | even | 2 | |||
684.6.k.f.505.3 | 18 | 19.11 | even | 3 | inner | ||
684.6.k.f.577.3 | 18 | 1.1 | even | 1 | trivial |