Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(129,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.129");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 41x^{6} + 460x^{4} + 969x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{31}\cdot 5^{3} \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.5 | ||
Root | \(-3.98753i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.129 |
Dual form | 320.6.c.i.129.4 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.69449i | 0.301152i | 0.988598 | + | 0.150576i | \(0.0481128\pi\) | ||||
−0.988598 | + | 0.150576i | \(0.951887\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −23.4238 | + | 50.7575i | −0.419017 | + | 0.907978i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.2635i | 0.0791678i | 0.999216 | + | 0.0395839i | \(0.0126032\pi\) | ||||
−0.999216 | + | 0.0395839i | \(0.987397\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 220.962 | 0.909308 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 596.423 | 1.48618 | 0.743092 | − | 0.669189i | \(-0.233358\pi\) | ||||
0.743092 | + | 0.669189i | \(0.233358\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 420.629i | 0.690305i | 0.938547 | + | 0.345152i | \(0.112173\pi\) | ||||
−0.938547 | + | 0.345152i | \(0.887827\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −238.281 | − | 109.963i | −0.273439 | − | 0.126188i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 974.149i | − | 0.817529i | −0.912640 | − | 0.408764i | \(-0.865960\pi\) | ||
0.912640 | − | 0.408764i | \(-0.134040\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 380.528 | 0.241825 | 0.120913 | − | 0.992663i | \(-0.461418\pi\) | ||||
0.120913 | + | 0.992663i | \(0.461418\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −48.1817 | −0.0238415 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3543.51i | − | 1.39673i | −0.715740 | − | 0.698367i | \(-0.753910\pi\) | ||
0.715740 | − | 0.698367i | \(-0.246090\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2027.65 | − | 2377.87i | −0.648849 | − | 0.760917i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2178.06i | 0.574991i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5440.89 | 1.20136 | 0.600682 | − | 0.799488i | \(-0.294896\pi\) | ||||
0.600682 | + | 0.799488i | \(0.294896\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3623.54 | 0.677219 | 0.338609 | − | 0.940927i | \(-0.390043\pi\) | ||||
0.338609 | + | 0.940927i | \(0.390043\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2799.90i | 0.447567i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −520.948 | − | 240.409i | −0.0718827 | − | 0.0331727i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1756.01i | 0.210874i | 0.994426 | + | 0.105437i | \(0.0336241\pi\) | ||||
−0.994426 | + | 0.105437i | \(0.966376\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1974.64 | −0.207886 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 263.984 | 0.0245255 | 0.0122628 | − | 0.999925i | \(-0.496097\pi\) | ||||
0.0122628 | + | 0.999925i | \(0.496097\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 14410.5i | 1.18853i | 0.804271 | + | 0.594263i | \(0.202556\pi\) | ||||
−0.804271 | + | 0.594263i | \(0.797444\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5175.76 | + | 11215.5i | −0.381015 | + | 0.825632i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 23464.8i | 1.54943i | 0.632308 | + | 0.774717i | \(0.282108\pi\) | ||||
−0.632308 | + | 0.774717i | \(0.717892\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16701.7 | 0.993732 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4573.13 | 0.246200 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 33496.0i | − | 1.63796i | −0.573823 | − | 0.818979i | \(-0.694540\pi\) | ||
0.573823 | − | 0.818979i | \(-0.305460\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13970.5 | + | 30273.0i | −0.622737 | + | 1.34942i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1786.38i | 0.0728261i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2906.38 | 0.108698 | 0.0543492 | − | 0.998522i | \(-0.482692\pi\) | ||||
0.0543492 | + | 0.998522i | \(0.482692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −29431.9 | −1.01273 | −0.506366 | − | 0.862319i | \(-0.669011\pi\) | ||||
−0.506366 | + | 0.862319i | \(0.669011\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2267.83i | 0.0719879i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −21350.1 | − | 9852.72i | −0.626782 | − | 0.289250i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7163.34i | − | 0.194952i | −0.995238 | − | 0.0974762i | \(-0.968923\pi\) | ||
0.995238 | − | 0.0974762i | \(-0.0310770\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16635.0 | 0.420629 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 81353.2 | 1.91527 | 0.957633 | − | 0.287992i | \(-0.0929878\pi\) | ||||
0.957633 | + | 0.287992i | \(0.0929878\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 55127.9i | 1.21078i | 0.795930 | + | 0.605388i | \(0.206982\pi\) | ||||
−0.795930 | + | 0.605388i | \(0.793018\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11162.9 | − | 9518.80i | 0.229151 | − | 0.195402i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6121.36i | 0.117658i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16430.9 | 0.296205 | 0.148103 | − | 0.988972i | \(-0.452683\pi\) | ||||
0.148103 | + | 0.988972i | \(0.452683\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 43468.8 | 0.736148 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 116869.i | 1.86210i | 0.364891 | + | 0.931050i | \(0.381106\pi\) | ||||
−0.364891 | + | 0.931050i | \(0.618894\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 49445.4 | + | 22818.2i | 0.742299 | + | 0.342559i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 25542.2i | 0.361793i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −99364.0 | −1.32970 | −0.664851 | − | 0.746976i | \(-0.731505\pi\) | ||||
−0.664851 | + | 0.746976i | \(0.731505\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4317.11 | −0.0546499 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 17010.7i | 0.203946i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8913.39 | + | 19314.6i | −0.101329 | + | 0.219572i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 62987.8i | − | 0.679715i | −0.940477 | − | 0.339858i | \(-0.889621\pi\) | ||
0.940477 | − | 0.339858i | \(-0.110379\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 131787. | 1.35140 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −40702.1 | −0.397021 | −0.198510 | − | 0.980099i | \(-0.563610\pi\) | ||||
−0.198510 | + | 0.980099i | \(0.563610\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 108113.i | 1.00412i | 0.864834 | + | 0.502058i | \(0.167424\pi\) | ||||
−0.864834 | + | 0.502058i | \(0.832576\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1128.60 | − | 2445.58i | 0.00999000 | − | 0.0216476i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 198380.i | 1.67509i | 0.546367 | + | 0.837546i | \(0.316010\pi\) | ||||
−0.546367 | + | 0.837546i | \(0.683990\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −89150.3 | −0.718715 | −0.359357 | − | 0.933200i | \(-0.617004\pi\) | ||||
−0.359357 | + | 0.933200i | \(0.617004\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8243.56 | −0.0635049 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 165319.i | − | 1.21795i | −0.793191 | − | 0.608973i | \(-0.791582\pi\) | ||
0.793191 | − | 0.608973i | \(-0.208418\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 179860. | + | 83002.3i | 1.26820 | + | 0.585255i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 92943.0i | 0.627700i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9998.14 | 0.0647220 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 194669. | 1.20874 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1239.27i | 0.00738591i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 168190. | − | 47220.2i | 0.962775 | − | 0.270304i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 137238.i | 0.755031i | 0.926003 | + | 0.377516i | \(0.123222\pi\) | ||||
−0.926003 | + | 0.377516i | \(0.876778\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −67650.1 | −0.357927 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −355564. | −1.81026 | −0.905128 | − | 0.425140i | \(-0.860225\pi\) | ||||
−0.905128 | + | 0.425140i | \(0.860225\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3905.53i | 0.0191448i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −110553. | − | 51018.4i | −0.522080 | − | 0.240931i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 232937.i | 1.06032i | 0.847898 | + | 0.530160i | \(0.177868\pi\) | ||||
−0.847898 | + | 0.530160i | \(0.822132\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 62526.2 | 0.274489 | 0.137245 | − | 0.990537i | \(-0.456175\pi\) | ||||
0.137245 | + | 0.990537i | \(0.456175\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −110155. | −0.466614 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 250873.i | 1.02592i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −127446. | + | 276166.i | −0.503392 | + | 1.09081i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 78405.8i | 0.299264i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 267151. | 0.985804 | 0.492902 | − | 0.870085i | \(-0.335936\pi\) | ||||
0.492902 | + | 0.870085i | \(0.335936\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 329630. | 1.17648 | 0.588240 | − | 0.808686i | \(-0.299821\pi\) | ||||
0.588240 | + | 0.808686i | \(0.299821\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 215250.i | − | 0.743385i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −84877.0 | + | 183922.i | −0.283766 | + | 0.614900i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 400955.i | − | 1.29822i | −0.760696 | − | 0.649108i | \(-0.775142\pi\) | ||
0.760696 | − | 0.649108i | \(-0.224858\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 157246. | 0.493274 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 36368.6 | 0.110576 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 511411.i | − | 1.50765i | −0.657074 | − | 0.753826i | \(-0.728206\pi\) | ||
0.657074 | − | 0.753826i | \(-0.271794\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −142116. | − | 65584.2i | −0.406381 | − | 0.187538i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 63650.1i | − | 0.176607i | −0.996094 | − | 0.0883035i | \(-0.971855\pi\) | ||
0.996094 | − | 0.0883035i | \(-0.0281445\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 194364. | 0.523479 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 84082.0 | 0.219894 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 33351.0i | 0.0847214i | 0.999102 | + | 0.0423607i | \(0.0134879\pi\) | ||||
−0.999102 | + | 0.0423607i | \(0.986512\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 24405.1 | − | 20810.7i | 0.0602401 | − | 0.0513680i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13644.0i | 0.0327347i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 314739. | 0.734207 | 0.367103 | − | 0.930180i | \(-0.380350\pi\) | ||||
0.367103 | + | 0.930180i | \(0.380350\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −415818. | −0.943425 | −0.471712 | − | 0.881753i | \(-0.656364\pi\) | ||||
−0.471712 | + | 0.881753i | \(0.656364\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 138168.i | − | 0.304986i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −89130.7 | − | 41132.3i | −0.191469 | − | 0.0883596i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 581005.i | − | 1.21500i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −22354.5 | −0.0455208 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −494250. | −0.980310 | −0.490155 | − | 0.871635i | \(-0.663060\pi\) | ||||
−0.490155 | + | 0.871635i | \(0.663060\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 62426.1i | − | 0.120635i | −0.998179 | − | 0.0603175i | \(-0.980789\pi\) | ||
0.998179 | − | 0.0603175i | \(-0.0192113\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 46253.5 | − | 100228.i | 0.0871080 | − | 0.188756i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 513844.i | 0.943334i | 0.881777 | + | 0.471667i | \(0.156348\pi\) | ||||
−0.881777 | + | 0.471667i | \(0.843652\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −29132.1 | −0.0521481 | −0.0260741 | − | 0.999660i | \(-0.508301\pi\) | ||||
−0.0260741 | + | 0.999660i | \(0.508301\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 33628.2 | 0.0587102 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 55842.3i | 0.0951094i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6183.51 | + | 13399.2i | −0.0102766 | + | 0.0222687i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 782980.i | − | 1.27006i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 226955. | 0.359397 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −330044. | −0.510347 | −0.255173 | − | 0.966895i | \(-0.582133\pi\) | ||||
−0.255173 | + | 0.966895i | \(0.582133\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 381912.i | 0.576785i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −731443. | − | 337549.i | −1.07916 | − | 0.498013i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 37190.1i | 0.0536139i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −258797. | −0.364627 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 409756. | 0.564344 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 930113.i | − | 1.25249i | −0.779627 | − | 0.626244i | \(-0.784591\pi\) | ||
0.779627 | − | 0.626244i | \(-0.215409\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −448034. | − | 525417.i | −0.590004 | − | 0.691908i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 37009.2i | 0.0476699i | 0.999716 | + | 0.0238350i | \(0.00758762\pi\) | ||||
−0.999716 | + | 0.0238350i | \(0.992412\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 506969. | 0.638841 | 0.319421 | − | 0.947613i | \(-0.396512\pi\) | ||||
0.319421 | + | 0.947613i | \(0.396512\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −28736.7 | −0.0354329 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 378560.i | 0.456819i | 0.973565 | + | 0.228410i | \(0.0733526\pi\) | ||||
−0.973565 | + | 0.228410i | \(0.926647\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.19102e6 | − | 549635.i | −1.40685 | − | 0.649239i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 77134.5i | 0.0892026i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 105854. | 0.119870 | 0.0599351 | − | 0.998202i | \(-0.480911\pi\) | ||||
0.0599351 | + | 0.998202i | \(0.480911\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.14897e6 | −1.27429 | −0.637144 | − | 0.770745i | \(-0.719884\pi\) | ||||
−0.637144 | + | 0.770745i | \(0.719884\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 733333.i | 0.796683i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −391216. | + | 847735.i | −0.416391 | + | 0.902288i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 160061.i | 0.166933i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −548639. | −0.560775 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 655956. | 0.657189 | 0.328595 | − | 0.944471i | \(-0.393425\pi\) | ||||
0.328595 | + | 0.944471i | \(0.393425\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.11343e6i | − | 2.07580i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −107120. | + | 232121.i | −0.103162 | + | 0.223544i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 986720.i | − | 0.931883i | −0.884816 | − | 0.465941i | \(-0.845716\pi\) | ||
0.884816 | − | 0.465941i | \(-0.154284\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18022.7 | −0.0166944 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.20223e6 | 1.09241 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 865331.i | − | 0.771424i | −0.922619 | − | 0.385712i | \(-0.873956\pi\) | ||
0.922619 | − | 0.385712i | \(-0.126044\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.70017e6 | + | 784602.i | 1.48723 | + | 0.686333i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 466463.i | − | 0.400442i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.75595e6 | −1.47956 | −0.739780 | − | 0.672849i | \(-0.765070\pi\) | ||||
−0.739780 | + | 0.672849i | \(0.765070\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.07635e6 | −0.890287 | −0.445143 | − | 0.895459i | \(-0.646847\pi\) | ||||
−0.445143 | + | 0.895459i | \(0.646847\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 20266.6i | − | 0.0164579i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.20934e6 | − | 1.41821e6i | −0.964310 | − | 1.13086i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 620129.i | 0.485605i | 0.970076 | + | 0.242802i | \(0.0780666\pi\) | ||||
−0.970076 | + | 0.242802i | \(0.921933\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 800664. | 0.615800 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 884924. | 0.668560 | 0.334280 | − | 0.942474i | \(-0.391507\pi\) | ||||
0.334280 | + | 0.942474i | \(0.391507\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.06088e6i | − | 0.787408i | −0.919237 | − | 0.393704i | \(-0.871194\pi\) | ||
0.919237 | − | 0.393704i | \(-0.128806\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −90672.4 | − | 41843.8i | −0.0661246 | − | 0.0305154i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2709.39i | 0.00194163i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 470891. | 0.331646 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 295696. | 0.204697 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 585847.i | 0.398672i | 0.979931 | + | 0.199336i | \(0.0638784\pi\) | ||||
−0.979931 | + | 0.199336i | \(0.936122\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −68078.5 | + | 147521.i | −0.0455465 | + | 0.0986958i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.29905e6i | 0.854543i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.49050e6 | 0.964172 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −147902. | −0.0940931 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 191076.i | − | 0.119563i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 689407. | − | 1.49389e6i | 0.424352 | − | 0.919539i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.33467e6i | − | 1.41377i | −0.707328 | − | 0.706886i | \(-0.750099\pi\) | ||
0.707328 | − | 0.706886i | \(-0.249901\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −507534. | −0.302391 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.18712e6 | −1.28225 | −0.641123 | − | 0.767438i | \(-0.721531\pi\) | ||||
−0.641123 | + | 0.767438i | \(0.721531\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.76800e6i | 1.59700i | 0.601993 | + | 0.798501i | \(0.294374\pi\) | ||||
−0.601993 | + | 0.798501i | \(0.705626\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −115110. | − | 53121.2i | −0.0653635 | − | 0.0301642i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.71952e6i | − | 0.961077i | −0.876974 | − | 0.480538i | \(-0.840441\pi\) | ||
0.876974 | − | 0.480538i | \(-0.159559\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.24507e6 | 1.78545 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −931293. | −0.504457 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 370691.i | − | 0.197699i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00020e6 | − | 852891.i | 0.525265 | − | 0.447904i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 418515.i | − | 0.216442i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −240830. | −0.122665 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.24759e6 | −0.625895 | −0.312948 | − | 0.949770i | \(-0.601316\pi\) | ||||
−0.312948 | + | 0.949770i | \(0.601316\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 388011.i | 0.191749i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 363593. | + | 167792.i | 0.177013 | + | 0.0816884i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.96509e6i | − | 0.942556i | −0.881985 | − | 0.471278i | \(-0.843793\pi\) | ||
0.881985 | − | 0.471278i | \(-0.156207\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 776090. | 0.366786 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.16116e6 | 1.00647 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343915.i | 0.157839i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −389653. | + | 844349.i | −0.176251 | + | 0.381922i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.27623e6i | 1.46067i | 0.683091 | + | 0.730333i | \(0.260635\pi\) | ||||
−0.683091 | + | 0.730333i | \(0.739365\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 101966. | 0.0448117 | 0.0224058 | − | 0.999749i | \(-0.492867\pi\) | ||||
0.0224058 | + | 0.999749i | \(0.492867\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −916157. | −0.396919 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 3.03342e6i | − | 1.29567i | −0.761779 | − | 0.647837i | \(-0.775674\pi\) | ||
0.761779 | − | 0.647837i | \(-0.224326\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.90560e6 | + | 4.12929e6i | −0.802529 | + | 1.73902i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 46936.2i | 0.0194911i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.68388e6 | 1.09908 | 0.549538 | − | 0.835469i | \(-0.314804\pi\) | ||||
0.549538 | + | 0.835469i | \(0.314804\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.33130e6 | −0.941520 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 913874.i | 0.364015i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.79815e6 | − | 1.29130e6i | −1.09936 | − | 0.507336i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.17487e6i | 0.455329i | 0.973740 | + | 0.227664i | \(0.0731089\pi\) | ||||
−0.973740 | + | 0.227664i | \(0.926891\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 58330.5 | 0.0223013 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 343784. | 0.129674 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.13661e6i | 1.53947i | 0.638361 | + | 0.769737i | \(0.279613\pi\) | ||||
−0.638361 | + | 0.769737i | \(0.720387\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 221675. | + | 789566.i | 0.0814025 | + | 0.289941i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.28860e6i | 0.829308i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.02996e6 | 1.44113 | 0.720565 | − | 0.693387i | \(-0.243883\pi\) | ||||
0.720565 | + | 0.693387i | \(0.243883\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −644262. | −0.227379 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.29187e6i | 1.14669i | 0.819314 | + | 0.573345i | \(0.194355\pi\) | ||||
−0.819314 | + | 0.573345i | \(0.805645\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −310705. | − | 143385.i | −0.106831 | − | 0.0493007i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.18418e6i | 1.08074i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.23387e6 | 1.08355 | 0.541774 | − | 0.840524i | \(-0.317753\pi\) | ||||
0.541774 | + | 0.840524i | \(0.317753\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.45190e6 | −1.14187 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 1.66919e6i | − | 0.545161i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −384872. | + | 833990.i | −0.124115 | + | 0.268948i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.50766e6i | 0.480095i | 0.970761 | + | 0.240047i | \(0.0771630\pi\) | ||||
−0.970761 | + | 0.240047i | \(0.922837\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18334.5 | −0.00576549 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −132613. | −0.0411837 | −0.0205918 | − | 0.999788i | \(-0.506555\pi\) | ||||
−0.0205918 | + | 0.999788i | \(0.506555\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.52417e6i | 0.467487i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.01820e6 | + | 2.20637e6i | −0.308459 | + | 0.668407i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.04732e6i | 0.313397i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.30354e6 | 1.27209 | 0.636044 | − | 0.771653i | \(-0.280570\pi\) | ||||
0.636044 | + | 0.771653i | \(0.280570\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.09352e6 | −0.319317 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29829.6i | 0.00860541i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.93197e6 | − | 2.73751e6i | −1.69075 | − | 0.780252i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 293529.i | 0.0826628i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.35654e6 | 1.49056 | 0.745280 | − | 0.666752i | \(-0.232316\pi\) | ||||
0.745280 | + | 0.666752i | \(0.232316\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.95420e6 | −0.812335 | −0.406167 | − | 0.913799i | \(-0.633135\pi\) | ||||
−0.406167 | + | 0.913799i | \(0.633135\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.18483e6i | 1.40891i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.31640e6 | + | 1.97524e6i | −0.622071 | + | 0.530453i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 302074.i | − | 0.0801758i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.17772e6 | −0.308958 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.93581e6 | 1.53917 | 0.769586 | − | 0.638543i | \(-0.220463\pi\) | ||||
0.769586 | + | 0.638543i | \(0.220463\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.72633e6i | − | 0.698810i | −0.936972 | − | 0.349405i | \(-0.886384\pi\) | ||
0.936972 | − | 0.349405i | \(-0.113616\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.29646e6 | − | 598294.i | −0.328500 | − | 0.151597i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.34840e6i | − | 0.337766i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.39220e6 | 1.58303 | 0.791515 | − | 0.611150i | \(-0.209293\pi\) | ||||
0.791515 | + | 0.611150i | \(0.209293\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.69043e6 | 0.903609 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 990808.i | − | 0.239872i | −0.992782 | − | 0.119936i | \(-0.961731\pi\) | ||
0.992782 | − | 0.119936i | \(-0.0382690\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.32748e6 | − | 5.04347e6i | 0.557168 | − | 1.20734i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.25414e6i | 0.296877i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.79185e6 | −1.12173 | −0.560864 | − | 0.827908i | \(-0.689531\pi\) | ||||
−0.560864 | + | 0.827908i | \(0.689531\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 157446. | 0.0364495 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.54745e6i | 0.354299i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 101123. | − | 219126.i | 0.0228993 | − | 0.0496210i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1.50517e6i | − | 0.337128i | −0.985691 | − | 0.168564i | \(-0.946087\pi\) | ||
0.985691 | − | 0.168564i | \(-0.0539130\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.12176e6 | 0.470072 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.28168e6 | −0.280883 | −0.140442 | − | 0.990089i | \(-0.544852\pi\) | ||||
−0.140442 | + | 0.990089i | \(0.544852\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 700105.i | − | 0.151779i | −0.997116 | − | 0.0758893i | \(-0.975820\pi\) | ||
0.997116 | − | 0.0758893i | \(-0.0241796\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −863420. | − | 398454.i | −0.185178 | − | 0.0854567i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.89776e6i | 0.402669i | 0.979523 | + | 0.201334i | \(0.0645278\pi\) | ||||
−0.979523 | + | 0.201334i | \(0.935472\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 73520.6 | 0.0154340 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.88228e6 | 0.390960 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.59478e6i | 1.76637i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −771578. | − | 904843.i | −0.156908 | − | 0.184009i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 7.40133e6i | − | 1.48941i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.88878e6 | 1.37184 | 0.685920 | − | 0.727677i | \(-0.259400\pi\) | ||||
0.685920 | + | 0.727677i | \(0.259400\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −738628. | −0.145567 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 170732.i | 0.0333003i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.19710e6 | + | 1.47541e6i | 0.617167 | + | 0.284812i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.31559e6i | 0.633488i | 0.948511 | + | 0.316744i | \(0.102590\pi\) | ||||
−0.948511 | + | 0.316744i | \(0.897410\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.40081e6 | 0.454032 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.55075e6 | −1.22627 | −0.613137 | − | 0.789977i | \(-0.710092\pi\) | ||||
−0.613137 | + | 0.789977i | \(0.710092\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.30024e6i | − | 0.982150i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.08694e6 | + | 6.68917e6i | −0.566259 | + | 1.22704i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 834966.i | 0.151627i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.14654e6 | 0.745477 | 0.372738 | − | 0.927936i | \(-0.378419\pi\) | ||||
0.372738 | + | 0.927936i | \(0.378419\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 298805. | 0.0531855 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 386446.i | − | 0.0681035i | −0.999420 | − | 0.0340517i | \(-0.989159\pi\) | ||
0.999420 | − | 0.0340517i | \(-0.0108411\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 953396. | − | 2.06594e6i | 0.166358 | − | 0.360486i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 912440.i | 0.157647i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.04725e6 | 0.521331 | 0.260665 | − | 0.965429i | \(-0.416058\pi\) | ||||
0.260665 | + | 0.965429i | \(0.416058\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −565802. | −0.0958545 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 828813.i | 0.139048i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.48753e6 | − | 2.53241e6i | −0.911715 | − | 0.420742i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.39950e7i | 2.30274i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −156566. | −0.0255140 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.88552e6 | 1.43413 | 0.717065 | − | 0.697007i | \(-0.245485\pi\) | ||||
0.717065 | + | 0.697007i | \(0.245485\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.92458e6i | 0.787254i | 0.919270 | + | 0.393627i | \(0.128780\pi\) | ||||
−0.919270 | + | 0.393627i | \(0.871220\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 97695.8 | + | 114570.i | 0.0154696 | + | 0.0181414i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 3.52987e6i | − | 0.553646i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.12010e6 | −0.950866 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 642200. | 0.0988403 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 111040.i | 0.0169301i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.00693e7 | − | 4.64681e6i | −1.52095 | − | 0.701892i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.47754e6i | 0.221108i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.96126e6 | 1.47687 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.45948e6 | −0.801970 | −0.400985 | − | 0.916085i | \(-0.631332\pi\) | ||||
−0.400985 | + | 0.916085i | \(0.631332\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1.95205e6i | − | 0.284114i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.08824e6 | − | 4.52505e6i | 0.301154 | − | 0.652577i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 9.70824e6i | − | 1.38731i | −0.720309 | − | 0.693653i | \(-0.756000\pi\) | ||
0.720309 | − | 0.693653i | \(-0.244000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.50334e6 | −0.920885 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.07041e6 | 0.290521 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 168637.i | 0.0234499i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 193095. | − | 418423.i | 0.0266097 | − | 0.0576611i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 4.77260e6i | − | 0.651804i | −0.945404 | − | 0.325902i | \(-0.894332\pi\) | ||
0.945404 | − | 0.325902i | \(-0.105668\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.06149e6 | −0.820446 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.72752e6 | 0.365899 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.16768e6i | 0.288220i | 0.989562 | + | 0.144110i | \(0.0460319\pi\) | ||||
−0.989562 | + | 0.144110i | \(0.953968\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.39121e6 | + | 3.87240e6i | 1.10587 | + | 0.510340i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 446140.i | 0.0582792i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.17864e6 | −0.541070 | −0.270535 | − | 0.962710i | \(-0.587201\pi\) | ||||
−0.270535 | + | 0.962710i | \(0.587201\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.89574e6 | −1.01345 | −0.506725 | − | 0.862108i | \(-0.669144\pi\) | ||||
−0.506725 | + | 0.862108i | \(0.669144\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 2.32025e6i | − | 0.295222i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.42598e6 | + | 7.18501e6i | −1.06280 | + | 0.906270i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.34605e7i | − | 1.68315i | −0.540141 | − | 0.841575i | \(-0.681629\pi\) | ||
0.540141 | − | 0.841575i | \(-0.318371\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 293059. | 0.0363294 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.19948e6 | −0.147418 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.99778e7i | − | 2.43431i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.71756e6 | − | 2.17707e6i | −0.569938 | − | 0.263017i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.43350e6i | 0.171713i | 0.996308 | + | 0.0858564i | \(0.0273626\pi\) | ||||
−0.996308 | + | 0.0858564i | \(0.972637\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.37886e6 | 0.163769 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.41223e6 | −0.284087 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.38150e6i | − | 0.161330i | −0.996741 | − | 0.0806649i | \(-0.974296\pi\) | ||
0.996741 | − | 0.0806649i | \(-0.0257044\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −234194. | + | 507481.i | −0.0271196 | + | 0.0587661i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 136760.i | − | 0.0157045i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.53001e6 | 0.743612 | 0.371806 | − | 0.928310i | \(-0.378739\pi\) | ||||
0.371806 | + | 0.928310i | \(0.378739\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.81467e6 | −0.430795 | −0.215398 | − | 0.976526i | \(-0.569105\pi\) | ||||
−0.215398 | + | 0.976526i | \(0.569105\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.58282e6i | − | 0.177272i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.55989e6 | + | 9.88094e6i | −0.506484 | + | 1.09751i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.06018e7i | − | 1.16791i | −0.811787 | − | 0.583954i | \(-0.801505\pi\) | ||
0.811787 | − | 0.583954i | \(-0.198495\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −262151. | −0.0286424 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.87000e6 | −1.06958 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 5.80630e6i | − | 0.624091i | −0.950067 | − | 0.312046i | \(-0.898986\pi\) | ||
0.950067 | − | 0.312046i | \(-0.101014\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −62902.4 | − | 29028.4i | −0.00670624 | − | 0.00309482i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.80508e6i | 0.719648i | 0.933020 | + | 0.359824i | \(0.117163\pi\) | ||||
−0.933020 | + | 0.359824i | \(0.882837\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −852530. | −0.0894299 | −0.0447150 | − | 0.999000i | \(-0.514238\pi\) | ||||
−0.0447150 | + | 0.999000i | \(0.514238\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.71798e6 | 0.803110 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1.01982e6i | − | 0.105270i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.54286e6 | + | 9.64298e6i | −0.157989 | + | 0.987441i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.06544e6i | 0.108233i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.71061e6 | 0.172395 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.01341e6 | −0.801205 | −0.400603 | − | 0.916252i | \(-0.631199\pi\) | ||||
−0.400603 | + | 0.916252i | \(0.631199\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1.54939e6i | − | 0.153692i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.96586e6 | − | 3.21463e6i | −0.685552 | − | 0.316371i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.02521e6i | 0.685978i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.79760e7 | 1.74157 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.68737e6 | −0.354464 | −0.177232 | − | 0.984169i | \(-0.556714\pi\) | ||||
−0.177232 | + | 0.984169i | \(0.556714\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 9.97031e6i | − | 0.951001i | −0.879715 | − | 0.475501i | \(-0.842267\pi\) | ||
0.879715 | − | 0.475501i | \(-0.157733\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.58462e6 | − | 3.43375e6i | 0.149977 | − | 0.324990i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.73097e6i | 0.162566i | 0.996691 | + | 0.0812830i | \(0.0259018\pi\) | ||||
−0.996691 | + | 0.0812830i | \(0.974098\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.73343e6 | 0.161546 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −174588. | −0.0161459 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.15248e6i | 0.105767i | 0.998601 | + | 0.0528836i | \(0.0168412\pi\) | ||||
−0.998601 | + | 0.0528836i | \(0.983159\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.32865e6 | − | 1.80476e7i | 0.758528 | − | 1.64367i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.21811e7i | 1.10097i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.53161e7 | 1.37384 | 0.686919 | − | 0.726734i | \(-0.258963\pi\) | ||||
0.686919 | + | 0.726734i | \(0.258963\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.69450e6 | −0.150848 | −0.0754238 | − | 0.997152i | \(-0.524031\pi\) | ||||
−0.0754238 | + | 0.997152i | \(0.524031\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.92359e6i | 0.169953i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −198235. | − | 91482.2i | −0.0173831 | − | 0.00802199i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.92798e7i | − | 1.67799i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.36641e6 | 0.377189 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.75539e7 | −1.50511 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.53955e6i | 0.131026i | 0.997852 | + | 0.0655129i | \(0.0208683\pi\) | ||||
−0.997852 | + | 0.0655129i | \(0.979132\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.17914e6 | − | 4.41636e6i | 0.437520 | − | 0.373083i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.16833e7i | − | 0.979702i | −0.871806 | − | 0.489851i | \(-0.837051\pi\) | ||
0.871806 | − | 0.489851i | \(-0.162949\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 646473. | 0.0538116 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −173739. | −0.0143559 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1.49762e7i | − | 1.22843i | −0.789139 | − | 0.614215i | \(-0.789473\pi\) | ||
0.789139 | − | 0.614215i | \(-0.210527\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.18233e7 | − | 5.45626e6i | −0.962747 | − | 0.444292i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.37996e6i | 0.192388i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.40894e7 | 1.13069 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.90115e6 | −0.788843 | −0.394422 | − | 0.918930i | \(-0.629055\pi\) | ||||
−0.394422 | + | 0.918930i | \(0.629055\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.35259e6i | 0.106987i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.46460e6 | + | 3.17368e6i | −0.115016 | + | 0.249230i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 257160.i | − | 0.0200503i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.77714e6 | −0.137572 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.48933e7 | −1.14471 | −0.572357 | − | 0.820005i | \(-0.693971\pi\) | ||||
−0.572357 | + | 0.820005i | \(0.693971\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 668209.i | 0.0509946i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.58026e6 | − | 5.59122e6i | 0.195519 | − | 0.423676i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 417744.i | − | 0.0314313i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.63694e6 | 0.271719 | 0.135860 | − | 0.990728i | \(-0.456620\pi\) | ||||
0.135860 | + | 0.990728i | \(0.456620\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.63059e6 | 0.269342 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.28400e7i | − | 0.945894i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.27337e7 | − | 5.87639e6i | −0.931514 | − | 0.429878i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 496929.i | 0.0360991i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.17971e7 | −0.851044 | −0.425522 | − | 0.904948i | \(-0.639909\pi\) | ||||
−0.425522 | + | 0.904948i | \(0.639909\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.10961e6 | −0.0794936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 5.39384e6i | − | 0.383754i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.10322e7 | − | 1.29377e7i | −0.779505 | − | 0.914139i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 7.53381e6i | − | 0.528663i | −0.964432 | − | 0.264331i | \(-0.914849\pi\) | ||
0.964432 | − | 0.264331i | \(-0.0851513\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.12030e6 | 0.496226 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.40380e7 | 0.971655 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.36302e7i | 0.937003i | 0.883463 | + | 0.468501i | \(0.155206\pi\) | ||||
−0.883463 | + | 0.468501i | \(0.844794\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.97968e6 | − | 1.83656e6i | −0.271725 | − | 0.125397i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 4.27238e6i | − | 0.289735i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.07655e7 | −0.725141 | −0.362571 | − | 0.931956i | \(-0.618101\pi\) | ||||
−0.362571 | + | 0.931956i | \(0.618101\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −751405. | −0.0502722 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.53921e7i | 1.68743i | 0.536788 | + | 0.843717i | \(0.319637\pi\) | ||||
−0.536788 | + | 0.843717i | \(0.680363\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.25768e6 | + | 1.35599e7i | −0.413069 | + | 0.895089i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.58235e7i | 1.69322i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.03607e6 | −0.132613 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.06289e6 | −0.521664 | −0.260832 | − | 0.965384i | \(-0.583997\pi\) | ||||
−0.260832 | + | 0.965384i | \(0.583997\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.07938e6i | 0.197914i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.72118e6 | + | 1.67312e7i | −0.492965 | + | 1.06822i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.08891e7i | − | 0.690639i | −0.938485 | − | 0.345319i | \(-0.887771\pi\) | ||
0.938485 | − | 0.345319i | \(-0.112229\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.92147e6 | 0.625132 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.07800e7 | −0.674773 | −0.337387 | − | 0.941366i | \(-0.609543\pi\) | ||||
−0.337387 | + | 0.941366i | \(0.609543\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 914990.i | − | 0.0568991i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.09255e7 | + | 5.04196e6i | 0.674978 | + | 0.311491i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.22251e6i | 0.0750350i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.24398e6 | 0.502714 | 0.251357 | − | 0.967894i | \(-0.419123\pi\) | ||||
0.251357 | + | 0.967894i | \(0.419123\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.63215e6 | 0.280638 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.76264e6i | 0.226487i | 0.993567 | + | 0.113244i | \(0.0361240\pi\) | ||||
−0.993567 | + | 0.113244i | \(0.963876\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.34729e6 | − | 8.61629e6i | −0.439413 | − | 0.515307i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 84607.5i | − | 0.00502755i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 100453. | 0.00593090 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.85209e7 | 2.84644 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.18506e7i | 0.690774i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.03515e7 | + | 9.39189e6i | 1.17875 | + | 0.543975i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.14314e7i | − | 0.657906i | −0.944346 | − | 0.328953i | \(-0.893304\pi\) | ||
0.944346 | − | 0.328953i | \(-0.106696\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.06229e6 | 0.232315 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.69675e6 | 0.0964221 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1.23799e7i | − | 0.699094i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.68330e6 | + | 7.98144e6i | −0.206690 | + | 0.447882i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.82556e7i | 1.01801i | 0.860765 | + | 0.509003i | \(0.169986\pi\) | ||||
−0.860765 | + | 0.509003i | \(0.830014\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.28583e7 | 1.26671 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.19557e7 | −1.20911 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.28795e7i | 1.79944i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −851890. | + | 1.84598e6i | −0.0463334 | + | 0.100401i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 8.24331e6i | − | 0.445572i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.82214e7 | −1.51603 | −0.758014 | − | 0.652238i | \(-0.773830\pi\) | ||||
−0.758014 | + | 0.652238i | \(0.773830\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.56400e7 | 1.36888 | 0.684441 | − | 0.729068i | \(-0.260046\pi\) | ||||
0.684441 | + | 0.729068i | \(0.260046\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 5.05291e6i | − | 0.268111i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.59580e7 | + | 1.19792e7i | 1.36892 | + | 0.631732i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.48360e6i | 0.287416i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −953916. | −0.0496936 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.20567e6 | 0.217759 | 0.108880 | − | 0.994055i | \(-0.465274\pi\) | ||||
0.108880 | + | 0.994055i | \(0.465274\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 9.80010e6i | − | 0.504349i | −0.967682 | − | 0.252174i | \(-0.918854\pi\) | ||
0.967682 | − | 0.252174i | \(-0.0811457\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.65779e6 | − | 5.67723e6i | 0.340561 | − | 0.290404i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.45973e7i | 1.25061i | 0.780379 | + | 0.625306i | \(0.215026\pi\) | ||||
−0.780379 | + | 0.625306i | \(0.784974\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.33070e7 | −1.68325 | −0.841627 | − | 0.540060i | \(-0.818402\pi\) | ||||
−0.841627 | + | 0.540060i | \(0.818402\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.91119e6 | −0.146241 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.62699e7i | − | 0.812405i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.23072e6 | + | 1.49092e6i | 0.160355 | + | 0.0740013i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.89230e6i | 0.389395i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.31345e7 | −1.13463 | −0.567315 | − | 0.823501i | \(-0.692018\pi\) | ||||
−0.567315 | + | 0.823501i | \(0.692018\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.09212e6 | 0.443277 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.15427e6i | 0.201338i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.55274e6 | + | 9.86544e6i | −0.219347 | + | 0.475308i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.99798e6i | 0.0956936i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.98028e6 | 0.237129 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.22243e6 | 0.294534 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.59506e7i | − | 0.750592i | −0.926905 | − | 0.375296i | \(-0.877541\pi\) | ||
0.926905 | − | 0.375296i | \(-0.122459\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.96952e6 | + | 4.26780e6i | −0.0921392 | + | 0.199659i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.04392e7i | − | 0.485529i | −0.970085 | − | 0.242764i | \(-0.921946\pi\) | ||
0.970085 | − | 0.242764i | \(-0.0780542\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.94442e6 | −0.228630 | −0.114315 | − | 0.993445i | \(-0.536467\pi\) | ||||
−0.114315 | + | 0.993445i | \(0.536467\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12719.2 | −0.000584726 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 7.28636e6i | − | 0.333030i | −0.986039 | − | 0.166515i | \(-0.946749\pi\) | ||
0.986039 | − | 0.166515i | \(-0.0532515\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.69281e6 | − | 781205.i | −0.0769252 | − | 0.0354997i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.21059e6i | 0.0998759i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.79974e6 | 0.440215 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.01311e6 | 0.134577 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1.39179e7i | − | 0.618070i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 484642. | + | 1.72621e6i | 0.0213994 | + | 0.0762208i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 6.14124e6i | − | 0.269623i | −0.990871 | − | 0.134812i | \(-0.956957\pi\) | ||
0.990871 | − | 0.134812i | \(-0.0430429\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.75025e6 | −0.120061 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.64342e6 | 0.375185 | 0.187593 | − | 0.982247i | \(-0.439932\pi\) | ||||
0.187593 | + | 0.982247i | \(0.439932\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 3.13575e7i | − | 1.35344i | −0.736240 | − | 0.676720i | \(-0.763401\pi\) | ||
0.736240 | − | 0.676720i | \(-0.236599\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −692535. | − | 319594.i | −0.0297224 | − | 0.0137164i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.41228e7i | 1.02948i | 0.857346 | + | 0.514741i | \(0.172112\pi\) | ||||
−0.857346 | + | 0.514741i | \(0.827888\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.40854e6 | −0.0597742 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.59258e7 | 1.09405 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.92902e6i | 0.374693i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.37238e6 | + | 1.59754e7i | −0.307645 | + | 0.666644i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.99715e6i | 0.290362i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.97153e7 | 0.813587 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.26301e7 | −1.33908 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 694324.i | − | 0.0283363i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.74003e6 | − | 2.11059e7i | 0.395311 | − | 0.856609i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.78230e7i | − | 0.719389i | −0.933070 | − | 0.359694i | \(-0.882881\pi\) | ||
0.933070 | − | 0.359694i | \(-0.117119\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.99361e6 | −0.361014 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.55925e7 | 1.02169 | 0.510843 | − | 0.859674i | \(-0.329333\pi\) | ||||
0.510843 | + | 0.859674i | \(0.329333\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.97032e7i | 2.76742i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.01307e6 | + | 3.23641e6i | 0.276921 | + | 0.127794i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 3.64932e6i | − | 0.143314i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.28071e6 | 0.128138 | 0.0640691 | − | 0.997945i | \(-0.479592\pi\) | ||||
0.0640691 | + | 0.997945i | \(0.479592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.09601e7 | 0.425760 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.42195e7i | 1.32212i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.17555e6 | − | 3.56058e6i | 0.160457 | − | 0.136825i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.38888e7i | 0.913050i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.34815e7 | −0.512506 | −0.256253 | − | 0.966610i | \(-0.582488\pi\) | ||||
−0.256253 | + | 0.966610i | \(0.582488\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.35544e6 | 0.240310 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 1.02674e7i | − | 0.386151i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.94904e7 | + | 1.36093e7i | 1.10319 | + | 0.509105i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.85534e7i | − | 1.06245i | −0.847231 | − | 0.531225i | \(-0.821732\pi\) | ||
0.847231 | − | 0.531225i | \(-0.178268\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.29944e7 | −0.480940 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.61677e7 | 0.963366 | 0.481683 | − | 0.876346i | \(-0.340026\pi\) | ||||
0.481683 | + | 0.876346i | \(0.340026\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 935431.i | − | 0.0342557i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 523626. | − | 1.13466e6i | 0.0190740 | − | 0.0413319i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.17031e7i | 0.786404i | 0.919452 | + | 0.393202i | \(0.128633\pi\) | ||||
−0.919452 | + | 0.393202i | \(0.871367\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.31884e7 | −0.835805 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.07225e6 | 0.289430 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.46596e7i | 1.23621i | 0.786096 | + | 0.618104i | \(0.212099\pi\) | ||||
−0.786096 | + | 0.618104i | \(0.787901\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.15772e7 | − | 2.50869e7i | 0.410767 | − | 0.890100i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.52340e7i | 0.537691i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.39074e6 | −0.0839432 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.54991e7 | −0.541375 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.38344e7i | 1.52317i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.16860e6 | + | 1.46225e6i | 0.109534 | + | 0.0505481i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.00486e7i | 1.37728i | 0.725104 | + | 0.688639i | \(0.241791\pi\) | ||||
−0.725104 | + | 0.688639i | \(0.758209\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.74020e6 | 0.0595375 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.42657e7 | −0.825933 | −0.412967 | − | 0.910746i | \(-0.635507\pi\) | ||||
−0.412967 | + | 0.910746i | \(0.635507\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 641735.i | 0.0217307i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.00389e6 | + | 4.69543e6i | 0.134887 | + | 0.158184i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.73026e7i | 1.92060i | 0.278963 | + | 0.960302i | \(0.410009\pi\) | ||||
−0.278963 | + | 0.960302i | \(0.589991\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.92630e7 | −1.97618 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.96988e7 | −0.653533 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.13971e6i | 0.301682i | 0.988558 | + | 0.150841i | \(0.0481981\pi\) | ||||
−0.988558 | + | 0.150841i | \(0.951802\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.60814e7 | − | 1.20362e7i | −0.856527 | − | 0.395273i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 1.13058e6i | − | 0.0369408i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.10638e7 | 1.66006 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.80365e6 | −0.0906858 | −0.0453429 | − | 0.998971i | \(-0.514438\pi\) | ||||
−0.0453429 | + | 0.998971i | \(0.514438\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 5.85680e6i | − | 0.188489i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 682383. | − | 1.47867e6i | 0.0218510 | − | 0.0473494i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 4.72423e7i | − | 1.50520i | −0.658481 | − | 0.752598i | \(-0.728801\pi\) | ||
0.658481 | − | 0.752598i | \(-0.271199\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.82470e6 | −0.121250 |
(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 | 320.6.c.i.129.5 | 8 | ||
4.3 | odd | 2 | 320.6.c.j.129.4 | 8 | |||
5.4 | even | 2 | inner | 320.6.c.i.129.4 | 8 | ||
8.3 | odd | 2 | 40.6.c.a.9.5 | yes | 8 | ||
8.5 | even | 2 | 80.6.c.d.49.4 | 8 | |||
20.19 | odd | 2 | 320.6.c.j.129.5 | 8 | |||
24.5 | odd | 2 | 720.6.f.n.289.4 | 8 | |||
24.11 | even | 2 | 360.6.f.b.289.4 | 8 | |||
40.3 | even | 4 | 200.6.a.j.1.2 | 4 | |||
40.13 | odd | 4 | 400.6.a.ba.1.3 | 4 | |||
40.19 | odd | 2 | 40.6.c.a.9.4 | ✓ | 8 | ||
40.27 | even | 4 | 200.6.a.k.1.3 | 4 | |||
40.29 | even | 2 | 80.6.c.d.49.5 | 8 | |||
40.37 | odd | 4 | 400.6.a.z.1.2 | 4 | |||
120.29 | odd | 2 | 720.6.f.n.289.3 | 8 | |||
120.59 | even | 2 | 360.6.f.b.289.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.c.a.9.4 | ✓ | 8 | 40.19 | odd | 2 | ||
40.6.c.a.9.5 | yes | 8 | 8.3 | odd | 2 | ||
80.6.c.d.49.4 | 8 | 8.5 | even | 2 | |||
80.6.c.d.49.5 | 8 | 40.29 | even | 2 | |||
200.6.a.j.1.2 | 4 | 40.3 | even | 4 | |||
200.6.a.k.1.3 | 4 | 40.27 | even | 4 | |||
320.6.c.i.129.4 | 8 | 5.4 | even | 2 | inner | ||
320.6.c.i.129.5 | 8 | 1.1 | even | 1 | trivial | ||
320.6.c.j.129.4 | 8 | 4.3 | odd | 2 | |||
320.6.c.j.129.5 | 8 | 20.19 | odd | 2 | |||
360.6.f.b.289.3 | 8 | 120.59 | even | 2 | |||
360.6.f.b.289.4 | 8 | 24.11 | even | 2 | |||
400.6.a.z.1.2 | 4 | 40.37 | odd | 4 | |||
400.6.a.ba.1.3 | 4 | 40.13 | odd | 4 | |||
720.6.f.n.289.3 | 8 | 120.29 | odd | 2 | |||
720.6.f.n.289.4 | 8 | 24.5 | odd | 2 |