Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(1889,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.1889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.k (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} - 45 x^{12} + 306 x^{11} - 378 x^{10} + 1704 x^{9} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1889.6 | ||
Root | \(0.924776 + 0.247793i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.1889 |
Dual form | 3024.2.k.l.1889.5 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.22223 | −0.546599 | −0.273299 | − | 0.961929i | \(-0.588115\pi\) | ||||
−0.273299 | + | 0.961929i | \(0.588115\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.48321 | + | 2.19091i | 0.560601 | + | 0.828086i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.31156i | − | 0.998472i | −0.866466 | − | 0.499236i | \(-0.833614\pi\) | ||
0.866466 | − | 0.499236i | \(-0.166386\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.60032i | − | 0.443848i | −0.975064 | − | 0.221924i | \(-0.928766\pi\) | ||
0.975064 | − | 0.221924i | \(-0.0712337\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.11387 | 1.48283 | 0.741416 | − | 0.671046i | \(-0.234155\pi\) | ||||
0.741416 | + | 0.671046i | \(0.234155\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.35397i | − | 0.310621i | −0.987866 | − | 0.155311i | \(-0.950362\pi\) | ||
0.987866 | − | 0.155311i | \(-0.0496378\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.11697i | − | 0.232904i | −0.993196 | − | 0.116452i | \(-0.962848\pi\) | ||
0.993196 | − | 0.116452i | \(-0.0371521\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.50615 | −0.701230 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 9.39495i | − | 1.74460i | −0.488973 | − | 0.872299i | \(-0.662628\pi\) | ||
0.488973 | − | 0.872299i | \(-0.337372\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.00177i | 1.25756i | 0.777585 | + | 0.628778i | \(0.216445\pi\) | ||||
−0.777585 | + | 0.628778i | \(0.783555\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.81283 | − | 2.67780i | −0.306424 | − | 0.452631i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.7065 | −1.92454 | −0.962269 | − | 0.272101i | \(-0.912282\pi\) | ||||
−0.962269 | + | 0.272101i | \(0.912282\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.86752 | −0.916353 | −0.458177 | − | 0.888861i | \(-0.651497\pi\) | ||||
−0.458177 | + | 0.888861i | \(0.651497\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.58954 | 1.30989 | 0.654946 | − | 0.755676i | \(-0.272691\pi\) | ||||
0.654946 | + | 0.755676i | \(0.272691\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.15959 | 0.460873 | 0.230437 | − | 0.973087i | \(-0.425985\pi\) | ||||
0.230437 | + | 0.973087i | \(0.425985\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.60018 | + | 6.49916i | −0.371454 | + | 0.928451i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 0.539730i | − | 0.0741376i | −0.999313 | − | 0.0370688i | \(-0.988198\pi\) | ||
0.999313 | − | 0.0370688i | \(-0.0118021\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.04749i | 0.545764i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.87004 | 0.894403 | 0.447202 | − | 0.894433i | \(-0.352421\pi\) | ||||
0.447202 | + | 0.894433i | \(0.352421\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.40968i | − | 0.948712i | −0.880333 | − | 0.474356i | \(-0.842681\pi\) | ||
0.880333 | − | 0.474356i | \(-0.157319\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.95596i | 0.242607i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.74008 | 0.701263 | 0.350631 | − | 0.936514i | \(-0.385967\pi\) | ||||
0.350631 | + | 0.936514i | \(0.385967\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.81587i | − | 0.571539i | −0.958298 | − | 0.285769i | \(-0.907751\pi\) | ||
0.958298 | − | 0.285769i | \(-0.0922491\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 14.5107i | − | 1.69834i | −0.528116 | − | 0.849172i | \(-0.677102\pi\) | ||
0.528116 | − | 0.849172i | \(-0.322898\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.25533 | − | 4.91174i | 0.826821 | − | 0.559744i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.15055 | −0.129447 | −0.0647234 | − | 0.997903i | \(-0.520617\pi\) | ||||
−0.0647234 | + | 0.997903i | \(0.520617\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.27794 | 0.798858 | 0.399429 | − | 0.916764i | \(-0.369208\pi\) | ||||
0.399429 | + | 0.916764i | \(0.369208\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.47257 | −0.810514 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.4545 | 1.21417 | 0.607085 | − | 0.794637i | \(-0.292339\pi\) | ||||
0.607085 | + | 0.794637i | \(0.292339\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.50615 | − | 2.37360i | 0.367544 | − | 0.248821i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.65486i | 0.169785i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.04749i | − | 0.410961i | −0.978661 | − | 0.205480i | \(-0.934124\pi\) | ||
0.978661 | − | 0.205480i | \(-0.0658756\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.62565 | −0.360766 | −0.180383 | − | 0.983596i | \(-0.557734\pi\) | ||||
−0.180383 | + | 0.983596i | \(0.557734\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 6.68185i | − | 0.658383i | −0.944263 | − | 0.329191i | \(-0.893224\pi\) | ||
0.944263 | − | 0.329191i | \(-0.106776\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 15.7563i | − | 1.52322i | −0.648036 | − | 0.761610i | \(-0.724409\pi\) | ||
0.648036 | − | 0.761610i | \(-0.275591\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.77367 | 0.744582 | 0.372291 | − | 0.928116i | \(-0.378572\pi\) | ||||
0.372291 | + | 0.928116i | \(0.378572\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.111204i | 0.0104612i | 0.999986 | + | 0.00523058i | \(0.00166495\pi\) | ||||
−0.999986 | + | 0.00523058i | \(0.998335\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.36519i | 0.127305i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.06815 | + | 13.3949i | 0.831276 | + | 1.22791i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.0335804 | 0.00305277 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.3965 | 0.929890 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.11697 | 0.187851 | 0.0939253 | − | 0.995579i | \(-0.470059\pi\) | ||||
0.0939253 | + | 0.995579i | \(0.470059\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.38434 | 0.470432 | 0.235216 | − | 0.971943i | \(-0.424420\pi\) | ||||
0.235216 | + | 0.971943i | \(0.424420\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.96642 | − | 2.00822i | 0.257221 | − | 0.174134i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 10.2108i | − | 0.872369i | −0.899857 | − | 0.436184i | \(-0.856330\pi\) | ||
0.899857 | − | 0.436184i | \(-0.143670\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.9151i | 1.77400i | 0.461774 | + | 0.886998i | \(0.347213\pi\) | ||||
−0.461774 | + | 0.886998i | \(0.652787\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.29954 | −0.443170 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.4828i | 0.953595i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 12.1274i | − | 0.993518i | −0.867889 | − | 0.496759i | \(-0.834523\pi\) | ||
0.867889 | − | 0.496759i | \(-0.165477\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.2837 | 1.16239 | 0.581197 | − | 0.813763i | \(-0.302584\pi\) | ||||
0.581197 | + | 0.813763i | \(0.302584\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 8.55779i | − | 0.687378i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 7.36716i | − | 0.587964i | −0.955811 | − | 0.293982i | \(-0.905019\pi\) | ||
0.955811 | − | 0.293982i | \(-0.0949805\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.44718 | − | 1.65670i | 0.192865 | − | 0.130566i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.57724 | −0.280191 | −0.140095 | − | 0.990138i | \(-0.544741\pi\) | ||||
−0.140095 | + | 0.990138i | \(0.544741\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.9964 | −1.23784 | −0.618918 | − | 0.785456i | \(-0.712429\pi\) | ||||
−0.618918 | + | 0.785456i | \(0.712429\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4390 | 0.802999 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.07012 | −0.461502 | −0.230751 | − | 0.973013i | \(-0.574118\pi\) | ||||
−0.230751 | + | 0.973013i | \(0.574118\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.20035 | − | 7.68166i | −0.393110 | − | 0.580679i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 17.8004i | − | 1.33046i | −0.746638 | − | 0.665230i | \(-0.768333\pi\) | ||
0.746638 | − | 0.665230i | \(-0.231667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.6983i | 0.795197i | 0.917559 | + | 0.397599i | \(0.130156\pi\) | ||||
−0.917559 | + | 0.397599i | \(0.869844\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.3081 | 1.05195 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 20.2464i | − | 1.48057i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 12.6903i | − | 0.918236i | −0.888375 | − | 0.459118i | \(-0.848165\pi\) | ||
0.888375 | − | 0.459118i | \(-0.151835\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.69890 | −0.626161 | −0.313080 | − | 0.949727i | \(-0.601361\pi\) | ||||
−0.313080 | + | 0.949727i | \(0.601361\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.62128i | 0.471747i | 0.971784 | + | 0.235873i | \(0.0757951\pi\) | ||||
−0.971784 | + | 0.235873i | \(0.924205\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.6802i | 1.39509i | 0.716541 | + | 0.697545i | \(0.245724\pi\) | ||||
−0.716541 | + | 0.697545i | \(0.754276\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.5835 | − | 13.9347i | 1.44468 | − | 0.978022i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.17147 | 0.500877 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.48374 | −0.310147 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.4390 | −0.787492 | −0.393746 | − | 0.919219i | \(-0.628821\pi\) | ||||
−0.393746 | + | 0.919219i | \(0.628821\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.4984 | −0.715985 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.3403 | + | 10.3851i | −1.04136 | + | 0.704987i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 9.78413i | − | 0.658152i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 17.8616i | − | 1.19610i | −0.801458 | − | 0.598051i | \(-0.795942\pi\) | ||
0.801458 | − | 0.598051i | \(-0.204058\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.7215 | 1.70719 | 0.853597 | − | 0.520934i | \(-0.174416\pi\) | ||||
0.853597 | + | 0.520934i | \(0.174416\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.0232i | 0.992760i | 0.868105 | + | 0.496380i | \(0.165338\pi\) | ||||
−0.868105 | + | 0.496380i | \(0.834662\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3.03542i | − | 0.198857i | −0.995045 | − | 0.0994284i | \(-0.968299\pi\) | ||
0.995045 | − | 0.0994284i | \(-0.0317014\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.86175 | −0.251913 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.90110i | 0.446395i | 0.974773 | + | 0.223197i | \(0.0716494\pi\) | ||||
−0.974773 | + | 0.223197i | \(0.928351\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 26.6819i | − | 1.71874i | −0.511358 | − | 0.859368i | \(-0.670857\pi\) | ||
0.511358 | − | 0.859368i | \(-0.329143\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.17802 | − | 7.94348i | 0.203036 | − | 0.507490i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.16677 | −0.137869 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.3729 | −1.22281 | −0.611405 | − | 0.791318i | \(-0.709395\pi\) | ||||
−0.611405 | + | 0.791318i | \(0.709395\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.69890 | −0.232548 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.1363 | −1.13131 | −0.565656 | − | 0.824641i | \(-0.691377\pi\) | ||||
−0.565656 | + | 0.824641i | \(0.691377\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.3632 | − | 25.6479i | −1.07890 | − | 1.59368i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.4072i | 0.765063i | 0.923942 | + | 0.382532i | \(0.124948\pi\) | ||||
−0.923942 | + | 0.382532i | \(0.875052\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.659675i | 0.0405235i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.80468 | 0.536831 | 0.268416 | − | 0.963303i | \(-0.413500\pi\) | ||||
0.268416 | + | 0.963303i | \(0.413500\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3.81237i | − | 0.231585i | −0.993273 | − | 0.115792i | \(-0.963059\pi\) | ||
0.993273 | − | 0.115792i | \(-0.0369408\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.6108i | 0.700159i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.5722 | 1.53648 | 0.768242 | − | 0.640160i | \(-0.221132\pi\) | ||||
0.768242 | + | 0.640160i | \(0.221132\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 31.5683i | − | 1.88320i | −0.336728 | − | 0.941602i | \(-0.609320\pi\) | ||
0.336728 | − | 0.941602i | \(-0.390680\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.3214i | 0.613546i | 0.951783 | + | 0.306773i | \(0.0992493\pi\) | ||||
−0.951783 | + | 0.306773i | \(0.900751\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.70277 | − | 12.8552i | −0.513708 | − | 0.758819i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20.3794 | 1.19879 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.7722 | −1.03826 | −0.519130 | − | 0.854695i | \(-0.673744\pi\) | ||||
−0.519130 | + | 0.854695i | \(0.673744\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.39678 | −0.488880 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.78750 | −0.103374 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.7401 | + | 18.8189i | 0.734326 | + | 1.08470i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.05634i | 0.518565i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5.38163i | − | 0.307146i | −0.988137 | − | 0.153573i | \(-0.950922\pi\) | ||
0.988137 | − | 0.153573i | \(-0.0490780\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.7118 | 1.51469 | 0.757343 | − | 0.653018i | \(-0.226497\pi\) | ||||
0.757343 | + | 0.653018i | \(0.226497\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.2579i | 1.08852i | 0.838917 | + | 0.544259i | \(0.183189\pi\) | ||||
−0.838917 | + | 0.544259i | \(0.816811\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.56571i | 0.368767i | 0.982854 | + | 0.184383i | \(0.0590288\pi\) | ||||
−0.982854 | + | 0.184383i | \(0.940971\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −31.1119 | −1.74193 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8.27798i | − | 0.460599i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.61095i | 0.311239i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.68633 | + | 6.92238i | 0.258366 | + | 0.381643i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.27614 | 0.399933 | 0.199966 | − | 0.979803i | \(-0.435917\pi\) | ||||
0.199966 | + | 0.979803i | \(0.435917\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.01571 | −0.383309 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.04588 | 0.165920 | 0.0829598 | − | 0.996553i | \(-0.473563\pi\) | ||||
0.0829598 | + | 0.996553i | \(0.473563\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.1868 | 1.25563 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0957 | + | 3.94286i | −0.977075 | + | 0.212894i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 11.8675i | − | 0.637082i | −0.947909 | − | 0.318541i | \(-0.896807\pi\) | ||
0.947909 | − | 0.318541i | \(-0.103193\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 22.6968i | − | 1.21493i | −0.794346 | − | 0.607466i | \(-0.792186\pi\) | ||
0.794346 | − | 0.607466i | \(-0.207814\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.7139 | 0.570245 | 0.285123 | − | 0.958491i | \(-0.407966\pi\) | ||||
0.285123 | + | 0.958491i | \(0.407966\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.88611i | 0.312402i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 37.1531i | 1.96087i | 0.196855 | + | 0.980433i | \(0.436927\pi\) | ||||
−0.196855 | + | 0.980433i | \(0.563073\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.1668 | 0.903514 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.7354i | 0.928313i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.0454i | 1.09856i | 0.835639 | + | 0.549280i | \(0.185098\pi\) | ||||
−0.835639 | + | 0.549280i | \(0.814902\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.18250 | − | 0.800532i | 0.0613923 | − | 0.0415616i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.928141 | −0.0480573 | −0.0240287 | − | 0.999711i | \(-0.507649\pi\) | ||||
−0.0240287 | + | 0.999711i | \(0.507649\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.0349 | −0.774336 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.2625 | −0.938080 | −0.469040 | − | 0.883177i | \(-0.655400\pi\) | ||||
−0.469040 | + | 0.883177i | \(0.655400\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.4262 | −0.992633 | −0.496317 | − | 0.868142i | \(-0.665315\pi\) | ||||
−0.496317 | + | 0.868142i | \(0.665315\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.86769 | + | 6.00328i | −0.451939 | + | 0.305955i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 37.1137i | 1.88174i | 0.338765 | + | 0.940871i | \(0.389991\pi\) | ||||
−0.338765 | + | 0.940871i | \(0.610009\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 6.82900i | − | 0.345357i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.40624 | 0.0707554 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.2726i | 1.82047i | 0.414092 | + | 0.910235i | \(0.364099\pi\) | ||||
−0.414092 | + | 0.910235i | \(0.635901\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 5.67798i | − | 0.283545i | −0.989899 | − | 0.141772i | \(-0.954720\pi\) | ||
0.989899 | − | 0.141772i | \(-0.0452801\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.2051 | 0.558163 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 38.7668i | 1.92160i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.9255i | 1.28194i | 0.767568 | + | 0.640968i | \(0.221467\pi\) | ||||
−0.767568 | + | 0.640968i | \(0.778533\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.1897 | + | 15.0516i | 0.501403 | + | 0.740643i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.89533 | −0.436655 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.09103 | 0.395273 | 0.197636 | − | 0.980275i | \(-0.436673\pi\) | ||||
0.197636 | + | 0.980275i | \(0.436673\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.08732 | 0.345415 | 0.172707 | − | 0.984973i | \(-0.444749\pi\) | ||||
0.172707 | + | 0.984973i | \(0.444749\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.4361 | −1.03981 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.2339 | − | 10.9901i | 0.785615 | − | 0.531848i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.1791i | 0.731150i | 0.930782 | + | 0.365575i | \(0.119128\pi\) | ||||
−0.930782 | + | 0.365575i | \(0.880872\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 17.5583i | − | 0.843800i | −0.906642 | − | 0.421900i | \(-0.861363\pi\) | ||
0.906642 | − | 0.421900i | \(-0.138637\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.51234 | −0.0723449 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 40.2321i | − | 1.92017i | −0.279700 | − | 0.960087i | \(-0.590235\pi\) | ||
0.279700 | − | 0.960087i | \(-0.409765\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 22.0440i | − | 1.04734i | −0.851920 | − | 0.523672i | \(-0.824562\pi\) | ||
0.851920 | − | 0.523672i | \(-0.175438\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.0000 | −0.663664 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.6910i | 1.58998i | 0.606625 | + | 0.794988i | \(0.292523\pi\) | ||||
−0.606625 | + | 0.794988i | \(0.707477\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.4306i | 0.914953i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.28533 | + | 2.90110i | −0.200899 | + | 0.136005i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.92814 | 0.183751 | 0.0918753 | − | 0.995771i | \(-0.470714\pi\) | ||||
0.0918753 | + | 0.995771i | \(0.470714\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.1525 | −1.59064 | −0.795320 | − | 0.606190i | \(-0.792697\pi\) | ||||
−0.795320 | + | 0.606190i | \(0.792697\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.43036 | 0.159422 | 0.0797112 | − | 0.996818i | \(-0.474600\pi\) | ||||
0.0797112 | + | 0.996818i | \(0.474600\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.1436 | 1.25606 | 0.628028 | − | 0.778191i | \(-0.283862\pi\) | ||||
0.628028 | + | 0.778191i | \(0.283862\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.51375 | + | 12.5760i | 0.393128 | + | 0.580706i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 28.4448i | − | 1.30789i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.74721i | 0.217817i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.3877 | −1.47983 | −0.739915 | − | 0.672700i | \(-0.765134\pi\) | ||||
−0.739915 | + | 0.672700i | \(0.765134\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.7341i | 0.854202i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.94697i | 0.224631i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.3257 | 1.10230 | 0.551151 | − | 0.834405i | \(-0.314189\pi\) | ||||
0.551151 | + | 0.834405i | \(0.314189\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 34.4906i | − | 1.55654i | −0.627930 | − | 0.778270i | \(-0.716097\pi\) | ||
0.627930 | − | 0.778270i | \(-0.283903\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 57.4395i | − | 2.58694i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.5511 | − | 7.14295i | 0.473283 | − | 0.320405i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0285 | −0.628003 | −0.314002 | − | 0.949422i | \(-0.601670\pi\) | ||||
−0.314002 | + | 0.949422i | \(0.601670\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.1573 | −1.65676 | −0.828382 | − | 0.560164i | \(-0.810738\pi\) | ||||
−0.828382 | + | 0.560164i | \(0.810738\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.43139 | 0.197194 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.9141 | 0.749703 | 0.374852 | − | 0.927085i | \(-0.377694\pi\) | ||||
0.374852 | + | 0.927085i | \(0.377694\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.7915 | − | 21.5223i | 1.40638 | − | 0.952093i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.16677i | 0.359871i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 10.4632i | − | 0.460169i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.5989 | 0.946267 | 0.473133 | − | 0.880991i | \(-0.343123\pi\) | ||||
0.473133 | + | 0.880991i | \(0.343123\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 3.24610i | − | 0.141942i | −0.997478 | − | 0.0709710i | \(-0.977390\pi\) | ||
0.997478 | − | 0.0709710i | \(-0.0226098\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 42.8080i | 1.86474i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.7524 | 0.945756 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.38989i | 0.406721i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.2579i | 0.832590i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.5223 | + | 8.61064i | 0.927033 | + | 0.370887i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.7267 | −1.40703 | −0.703514 | − | 0.710681i | \(-0.748387\pi\) | ||||
−0.703514 | + | 0.710681i | \(0.748387\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.50122 | −0.406988 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.1830 | 0.820206 | 0.410103 | − | 0.912039i | \(-0.365493\pi\) | ||||
0.410103 | + | 0.912039i | \(0.365493\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.7204 | −0.541909 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.70650 | − | 2.52075i | −0.0725679 | − | 0.107193i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 26.1751i | − | 1.10908i | −0.832158 | − | 0.554538i | \(-0.812895\pi\) | ||
0.832158 | − | 0.554538i | \(-0.187105\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 13.7460i | − | 0.581393i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.7130 | −1.16797 | −0.583983 | − | 0.811766i | \(-0.698506\pi\) | ||||
−0.583983 | + | 0.811766i | \(0.698506\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 0.135917i | − | 0.00571805i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.7661i | 1.08017i | 0.841611 | + | 0.540085i | \(0.181608\pi\) | ||||
−0.841611 | + | 0.540085i | \(0.818392\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.5895 | −1.28013 | −0.640066 | − | 0.768320i | \(-0.721093\pi\) | ||||
−0.640066 | + | 0.768320i | \(0.721093\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.91626i | 0.163319i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 32.4033i | − | 1.34897i | −0.738289 | − | 0.674484i | \(-0.764366\pi\) | ||
0.738289 | − | 0.674484i | \(-0.235634\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.7947 | + | 15.9453i | 0.447840 | + | 0.661523i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.78735 | −0.0740243 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.1925 | −0.874709 | −0.437354 | − | 0.899289i | \(-0.644084\pi\) | ||||
−0.437354 | + | 0.899289i | \(0.644084\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.48017 | 0.390624 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −46.5951 | −1.91343 | −0.956715 | − | 0.291027i | \(-0.906003\pi\) | ||||
−0.956715 | + | 0.291027i | \(0.906003\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.0834 | − | 16.3717i | −0.454375 | − | 0.671175i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.6412i | 0.598222i | 0.954218 | + | 0.299111i | \(0.0966902\pi\) | ||||
−0.954218 | + | 0.299111i | \(0.903310\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.1517i | 0.454885i | 0.973791 | + | 0.227443i | \(0.0730364\pi\) | ||||
−0.973791 | + | 0.227443i | \(0.926964\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.0410431 | −0.00166864 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.7259i | 0.597708i | 0.954299 | + | 0.298854i | \(0.0966043\pi\) | ||||
−0.954299 | + | 0.298854i | \(0.903396\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 5.05634i | − | 0.204558i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −40.7589 | −1.64623 | −0.823117 | − | 0.567871i | \(-0.807767\pi\) | ||||
−0.823117 | + | 0.567871i | \(0.807767\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.2549i | 1.13750i | 0.822511 | + | 0.568749i | \(0.192572\pi\) | ||||
−0.822511 | + | 0.568749i | \(0.807428\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.538166i | 0.0216307i | 0.999942 | + | 0.0108154i | \(0.00344270\pi\) | ||||
−0.999942 | + | 0.0108154i | \(0.996557\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.9894 | + | 25.0957i | 0.680664 | + | 1.00544i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.82383 | 0.192953 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −71.5721 | −2.85377 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.1416 | 0.642586 | 0.321293 | − | 0.946980i | \(-0.395883\pi\) | ||||
0.321293 | + | 0.946980i | \(0.395883\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.58743 | −0.102679 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.4007 | + | 4.16111i | 0.412091 | + | 0.164869i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.5205i | 0.534029i | 0.963692 | + | 0.267015i | \(0.0860372\pi\) | ||||
−0.963692 | + | 0.267015i | \(0.913963\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.1685i | 1.15029i | 0.818051 | + | 0.575146i | \(0.195055\pi\) | ||||
−0.818051 | + | 0.575146i | \(0.804945\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.3787 | 1.15499 | 0.577497 | − | 0.816393i | \(-0.304030\pi\) | ||||
0.577497 | + | 0.816393i | \(0.304030\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 22.7505i | − | 0.893037i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 15.8726i | − | 0.621142i | −0.950550 | − | 0.310571i | \(-0.899480\pi\) | ||
0.950550 | − | 0.310571i | \(-0.100520\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.58091 | −0.257137 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 3.06603i | − | 0.119436i | −0.998215 | − | 0.0597178i | \(-0.980980\pi\) | ||
0.998215 | − | 0.0597178i | \(-0.0190201\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 43.3592i | − | 1.68648i | −0.537540 | − | 0.843239i | \(-0.680646\pi\) | ||
0.537540 | − | 0.843239i | \(-0.319354\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.62565 | + | 2.45451i | −0.140597 | + | 0.0951817i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.4939 | −0.406324 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.5376 | −0.947263 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.8733 | −0.650417 | −0.325209 | − | 0.945642i | \(-0.605435\pi\) | ||||
−0.325209 | + | 0.945642i | \(0.605435\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.77260 | −0.183426 | −0.0917130 | − | 0.995785i | \(-0.529234\pi\) | ||||
−0.0917130 | + | 0.995785i | \(0.529234\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.86769 | − | 6.00328i | 0.340311 | − | 0.230385i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.9097i | 0.532241i | 0.963940 | + | 0.266120i | \(0.0857419\pi\) | ||||
−0.963940 | + | 0.266120i | \(0.914258\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.4800i | 0.476836i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.863738 | −0.0329058 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.0116i | 0.647151i | 0.946202 | + | 0.323575i | \(0.104885\pi\) | ||||
−0.946202 | + | 0.323575i | \(0.895115\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 25.5631i | − | 0.969664i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −35.8733 | −1.35880 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.5779i | − | 0.814988i | −0.913208 | − | 0.407494i | \(-0.866403\pi\) | ||
0.913208 | − | 0.407494i | \(-0.133597\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.8502i | 0.597802i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.37760 | − | 7.94348i | −0.202246 | − | 0.298745i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.1542 | −0.418906 | −0.209453 | − | 0.977819i | \(-0.567168\pi\) | ||||
−0.209453 | + | 0.977819i | \(0.567168\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.82076 | 0.292890 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.47727 | 0.242236 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.5141 | −0.653166 | −0.326583 | − | 0.945168i | \(-0.605897\pi\) | ||||
−0.326583 | + | 0.945168i | \(0.605897\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.6393 | − | 9.91059i | 0.545198 | − | 0.369090i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.9401i | 1.22336i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.2920i | 0.678411i | 0.940712 | + | 0.339206i | \(0.110158\pi\) | ||||
−0.940712 | + | 0.339206i | \(0.889842\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 52.5153 | 1.94235 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.9149i | 0.883315i | 0.897184 | + | 0.441658i | \(0.145609\pi\) | ||||
−0.897184 | + | 0.441658i | \(0.854391\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 19.0086i | − | 0.700192i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.6989 | 0.651065 | 0.325532 | − | 0.945531i | \(-0.394456\pi\) | ||||
0.325532 | + | 0.945531i | \(0.394456\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.1300i | 0.775184i | 0.921831 | + | 0.387592i | \(0.126693\pi\) | ||||
−0.921831 | + | 0.387592i | \(0.873307\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.8225i | 0.543056i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 34.5207 | − | 23.3699i | 1.26136 | − | 0.853918i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 51.6928 | 1.88630 | 0.943149 | − | 0.332370i | \(-0.107848\pi\) | ||||
0.943149 | + | 0.332370i | \(0.107848\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.4580 | −0.635363 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.0248524 | −0.000903274 | −0.000451637 | − | 1.00000i | \(-0.500144\pi\) | ||||
−0.000451637 | 1.00000i | \(0.500144\pi\) | ||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.930657 | −0.0337363 | −0.0168682 | − | 0.999858i | \(-0.505370\pi\) | ||||
−0.0168682 | + | 0.999858i | \(0.505370\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.5300 | + | 17.0314i | 0.417413 | + | 0.616578i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 10.9942i | − | 0.396979i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.6327i | 0.491609i | 0.969319 | + | 0.245805i | \(0.0790521\pi\) | ||||
−0.969319 | + | 0.245805i | \(0.920948\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.8294 | −0.425472 | −0.212736 | − | 0.977110i | \(-0.568238\pi\) | ||||
−0.212736 | + | 0.977110i | \(0.568238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 24.5493i | − | 0.881836i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.94443i | 0.284639i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.9480 | −0.570666 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.00438i | 0.321380i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.6561i | 0.985834i | 0.870076 | + | 0.492917i | \(0.164069\pi\) | ||||
−0.870076 | + | 0.492917i | \(0.835931\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.243637 | + | 0.164938i | −0.00866274 | + | 0.00586453i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.8578 | −0.421084 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.974413 | −0.0345155 | −0.0172577 | − | 0.999851i | \(-0.505494\pi\) | ||||
−0.0172577 | + | 0.999851i | \(0.505494\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.3173 | 0.683398 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −48.0529 | −1.69575 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.99102 | + | 2.02487i | −0.105419 | + | 0.0713672i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.4715i | 0.719741i | 0.933002 | + | 0.359871i | \(0.117179\pi\) | ||||
−0.933002 | + | 0.359871i | \(0.882821\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.6484i | 1.46247i | 0.682123 | + | 0.731237i | \(0.261057\pi\) | ||||
−0.682123 | + | 0.731237i | \(0.738943\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.37221 | 0.153152 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 11.6299i | − | 0.406880i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43.2166i | 1.50827i | 0.656720 | + | 0.754135i | \(0.271943\pi\) | ||||
−0.656720 | + | 0.754135i | \(0.728057\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.16172 | 0.319357 | 0.159679 | − | 0.987169i | \(-0.448954\pi\) | ||||
0.159679 | + | 0.987169i | \(0.448954\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.7458i | 0.443217i | 0.975136 | + | 0.221608i | \(0.0711306\pi\) | ||||
−0.975136 | + | 0.221608i | \(0.928869\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 3.92018i | − | 0.136154i | −0.997680 | − | 0.0680768i | \(-0.978314\pi\) | ||
0.997680 | − | 0.0680768i | \(-0.0216863\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.8972 | + | 39.7350i | −0.550804 | + | 1.37674i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.5513 | 0.676599 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −53.2940 | −1.83991 | −0.919957 | − | 0.392019i | \(-0.871777\pi\) | ||||
−0.919957 | + | 0.392019i | \(0.871777\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −59.2650 | −2.04362 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.7589 | −0.438918 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.0498068 | + | 0.0735717i | 0.00171138 | + | 0.00252795i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.0758i | 0.448232i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 27.2338i | − | 0.932468i | −0.884661 | − | 0.466234i | \(-0.845610\pi\) | ||
0.884661 | − | 0.466234i | \(-0.154390\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46.0202 | 1.57202 | 0.786010 | − | 0.618214i | \(-0.212143\pi\) | ||||
0.786010 | + | 0.618214i | \(0.212143\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 41.6542i | − | 1.42122i | −0.703584 | − | 0.710612i | \(-0.748418\pi\) | ||
0.703584 | − | 0.710612i | \(-0.251582\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.2375i | 1.40374i | 0.712305 | + | 0.701871i | \(0.247651\pi\) | ||||
−0.712305 | + | 0.701871i | \(0.752349\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.41909 | 0.252257 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.81011i | 0.129249i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 9.18595i | − | 0.311254i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.4202 | + | 22.7778i | 0.521297 | + | 0.770029i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.1469 | 0.443938 | 0.221969 | − | 0.975054i | \(-0.428752\pi\) | ||||
0.221969 | + | 0.975054i | \(0.428752\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.9485 | −0.773154 | −0.386577 | − | 0.922257i | \(-0.626343\pi\) | ||||
−0.386577 | + | 0.922257i | \(0.626343\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.1693 | 1.55372 | 0.776861 | − | 0.629673i | \(-0.216811\pi\) | ||||
0.776861 | + | 0.629673i | \(0.216811\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.9382 | −0.938072 | −0.469036 | − | 0.883179i | \(-0.655399\pi\) | ||||
−0.469036 | + | 0.883179i | \(0.655399\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.13991 | + | 4.63809i | 0.105309 | + | 0.155556i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 4.27798i | − | 0.143157i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.7562i | 0.727228i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 65.7813 | 2.19393 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 3.29984i | − | 0.109934i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 13.0758i | − | 0.434654i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.91661 | 0.163253 | 0.0816267 | − | 0.996663i | \(-0.473988\pi\) | ||||
0.0816267 | + | 0.996663i | \(0.473988\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.1936i | 1.06662i | 0.845920 | + | 0.533310i | \(0.179052\pi\) | ||||
−0.845920 | + | 0.533310i | \(0.820948\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 24.1013i | − | 0.797637i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.98610 | + | 11.7966i | 0.263724 | + | 0.389558i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.2289 | −1.09612 | −0.548060 | − | 0.836439i | \(-0.684633\pi\) | ||||
−0.548060 | + | 0.836439i | \(0.684633\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.70692 | −0.253676 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 41.0448 | 1.34954 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.26452 | −0.0414875 | −0.0207437 | − | 0.999785i | \(-0.506603\pi\) | ||||
−0.0207437 | + | 0.999785i | \(0.506603\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.79965 | + | 3.52055i | 0.288397 | + | 0.115381i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.7458i | 0.809276i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 26.1127i | − | 0.853065i | −0.904472 | − | 0.426533i | \(-0.859735\pi\) | ||
0.904472 | − | 0.426533i | \(-0.140265\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.25105 | −0.0407830 | −0.0203915 | − | 0.999792i | \(-0.506491\pi\) | ||||
−0.0203915 | + | 0.999792i | \(0.506491\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.55383i | 0.213422i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 44.5809i | − | 1.44868i | −0.689440 | − | 0.724342i | \(-0.742143\pi\) | ||
0.689440 | − | 0.724342i | \(-0.257857\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.2216 | −0.753806 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 35.2115i | − | 1.14061i | −0.821432 | − | 0.570307i | \(-0.806824\pi\) | ||
0.821432 | − | 0.570307i | \(-0.193176\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.5105i | 0.501907i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.3710 | − | 15.1448i | 0.722397 | − | 0.489051i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.0249 | −0.581447 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.6321 | 0.342259 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.7600 | −1.47154 | −0.735771 | − | 0.677230i | \(-0.763180\pi\) | ||||
−0.735771 | + | 0.677230i | \(0.763180\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.45116 | 0.110753 | 0.0553766 | − | 0.998466i | \(-0.482364\pi\) | ||||
0.0553766 | + | 0.998466i | \(0.482364\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −45.8231 | + | 31.0215i | −1.46902 | + | 0.994503i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 51.2902i | 1.64092i | 0.571704 | + | 0.820460i | \(0.306282\pi\) | ||||
−0.571704 | + | 0.820460i | \(0.693718\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 37.9321i | − | 1.21232i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.3484 | −0.967964 | −0.483982 | − | 0.875078i | \(-0.660810\pi\) | ||||
−0.483982 | + | 0.875078i | \(0.660810\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 8.09274i | − | 0.257856i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 9.59423i | − | 0.305079i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.11407 | 0.225986 | 0.112993 | − | 0.993596i | \(-0.463956\pi\) | ||||
0.112993 | + | 0.993596i | \(0.463956\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 24.0537i | − | 0.762555i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.2710i | 0.895353i | 0.894196 | + | 0.447676i | \(0.147748\pi\) | ||||
−0.894196 | + | 0.447676i | \(0.852252\pi\) | |||||||
\(998\) | 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 | 3024.2.k.l.1889.6 | 16 | ||
3.2 | odd | 2 | inner | 3024.2.k.l.1889.12 | 16 | ||
4.3 | odd | 2 | 1512.2.k.b.377.5 | ✓ | 16 | ||
7.6 | odd | 2 | inner | 3024.2.k.l.1889.11 | 16 | ||
12.11 | even | 2 | 1512.2.k.b.377.11 | yes | 16 | ||
21.20 | even | 2 | inner | 3024.2.k.l.1889.5 | 16 | ||
28.27 | even | 2 | 1512.2.k.b.377.12 | yes | 16 | ||
84.83 | odd | 2 | 1512.2.k.b.377.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.k.b.377.5 | ✓ | 16 | 4.3 | odd | 2 | ||
1512.2.k.b.377.6 | yes | 16 | 84.83 | odd | 2 | ||
1512.2.k.b.377.11 | yes | 16 | 12.11 | even | 2 | ||
1512.2.k.b.377.12 | yes | 16 | 28.27 | even | 2 | ||
3024.2.k.l.1889.5 | 16 | 21.20 | even | 2 | inner | ||
3024.2.k.l.1889.6 | 16 | 1.1 | even | 1 | trivial | ||
3024.2.k.l.1889.11 | 16 | 7.6 | odd | 2 | inner | ||
3024.2.k.l.1889.12 | 16 | 3.2 | odd | 2 | inner |