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.j.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 | \(-0.766642\pi\) | ||||
−0.743092 | + | 0.669189i | \(0.766642\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 420.629i | − | 0.690305i | −0.938547 | − | 0.345152i | \(-0.887827\pi\) | ||
0.938547 | − | 0.345152i | \(-0.112173\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 238.281 | − | 109.963i | 0.273439 | − | 0.126188i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 974.149i | 0.817529i | 0.912640 | + | 0.408764i | \(0.134040\pi\) | ||||
−0.912640 | + | 0.408764i | \(0.865960\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −380.528 | −0.241825 | −0.120913 | − | 0.992663i | \(-0.538582\pi\) | ||||
−0.120913 | + | 0.992663i | \(0.538582\pi\) | |||||||
\(20\) | 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 | \(-0.609957\pi\) | ||||
−0.338609 | + | 0.940927i | \(0.609957\pi\) | |||||||
\(32\) | 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 | \(-0.966376\pi\) | ||
0.994426 | − | 0.105437i | \(-0.0336241\pi\) | |||||||
\(38\) | 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 | \(0.305460\pi\) | ||||
−0.573823 | + | 0.818979i | \(0.694540\pi\) | |||||||
\(54\) | 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 | \(-0.517308\pi\) | ||||
−0.0543492 | + | 0.998522i | \(0.517308\pi\) | |||||||
\(60\) | 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 | \(-0.907012\pi\) | ||||
−0.957633 | + | 0.287992i | \(0.907012\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 55127.9i | − | 1.21078i | −0.795930 | − | 0.605388i | \(-0.793018\pi\) | ||
0.795930 | − | 0.605388i | \(-0.206982\pi\) | |||||||
\(74\) | 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 | \(-0.547317\pi\) | ||||
−0.148103 | + | 0.988972i | \(0.547317\pi\) | |||||||
\(80\) | 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 | \(0.110379\pi\) | ||||
−0.940477 | + | 0.339858i | \(0.889621\pi\) | |||||||
\(98\) | 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 | \(0.208418\pi\) | ||||
−0.793191 | + | 0.608973i | \(0.791582\pi\) | |||||||
\(114\) | 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 | \(-0.139775\pi\) | ||||
0.905128 | + | 0.425140i | \(0.139775\pi\) | |||||||
\(132\) | 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 | \(-0.822132\pi\) | ||
0.847898 | − | 0.530160i | \(-0.177868\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −62526.2 | −0.274489 | −0.137245 | − | 0.990537i | \(-0.543825\pi\) | ||||
−0.137245 | + | 0.990537i | \(0.543825\pi\) | |||||||
\(140\) | 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 | \(-0.700179\pi\) | ||||
−0.588240 | + | 0.808686i | \(0.700179\pi\) | |||||||
\(152\) | 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 | \(0.224858\pi\) | ||||
−0.760696 | + | 0.649108i | \(0.775142\pi\) | |||||||
\(158\) | 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 | \(-0.986512\pi\) | ||
0.999102 | − | 0.0423607i | \(-0.0134879\pi\) | |||||||
\(174\) | 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 | \(-0.619650\pi\) | ||||
−0.367103 | + | 0.930180i | \(0.619650\pi\) | |||||||
\(180\) | 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 | \(-0.336940\pi\) | ||||
0.490155 | + | 0.871635i | \(0.336940\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 62426.1i | 0.120635i | 0.998179 | + | 0.0603175i | \(0.0192113\pi\) | ||||
−0.998179 | + | 0.0603175i | \(0.980789\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −46253.5 | − | 100228.i | −0.0871080 | − | 0.188756i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 513844.i | − | 0.943334i | −0.881777 | − | 0.471667i | \(-0.843652\pi\) | ||
0.881777 | − | 0.471667i | \(-0.156348\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 29132.1 | 0.0521481 | 0.0260741 | − | 0.999660i | \(-0.491699\pi\) | ||||
0.0260741 | + | 0.999660i | \(0.491699\pi\) | |||||||
\(200\) | 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 | \(-0.417867\pi\) | ||||
0.255173 | + | 0.966895i | \(0.417867\pi\) | |||||||
\(212\) | 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 | \(-0.926647\pi\) | ||
0.973565 | − | 0.228410i | \(-0.0733526\pi\) | |||||||
\(234\) | 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 | \(-0.519089\pi\) | ||||
−0.0599351 | + | 0.998202i | \(0.519089\pi\) | |||||||
\(240\) | 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 | \(-0.606575\pi\) | ||||
−0.328595 | + | 0.944471i | \(0.606575\pi\) | |||||||
\(252\) | 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 | \(0.154284\pi\) | ||||
−0.884816 | + | 0.465941i | \(0.845716\pi\) | |||||||
\(258\) | 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 | \(-0.353153\pi\) | ||||
0.445143 | + | 0.895459i | \(0.353153\pi\) | |||||||
\(272\) | 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 | \(-0.921933\pi\) | ||
0.970076 | − | 0.242802i | \(-0.0780666\pi\) | |||||||
\(278\) | 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 | \(-0.936122\pi\) | ||
0.979931 | − | 0.199336i | \(-0.0638784\pi\) | |||||||
\(294\) | 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 | \(-0.278469\pi\) | ||||
0.641123 | + | 0.767438i | \(0.278469\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2.76800e6i | − | 1.59700i | −0.601993 | − | 0.798501i | \(-0.705626\pi\) | ||
0.601993 | − | 0.798501i | \(-0.294374\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 115110. | − | 53121.2i | 0.0653635 | − | 0.0301642i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.71952e6i | 0.961077i | 0.876974 | + | 0.480538i | \(0.159559\pi\) | ||||
−0.876974 | + | 0.480538i | \(0.840441\pi\) | |||||||
\(318\) | 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 | \(-0.398684\pi\) | ||||
0.312948 | + | 0.949770i | \(0.398684\pi\) | |||||||
\(332\) | 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 | \(0.156207\pi\) | ||||
−0.881985 | + | 0.471278i | \(0.843793\pi\) | |||||||
\(338\) | 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 | \(0.224326\pi\) | ||||
−0.761779 | + | 0.647837i | \(0.775674\pi\) | |||||||
\(354\) | 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 | \(-0.685196\pi\) | ||||
−0.549538 | + | 0.835469i | \(0.685196\pi\) | |||||||
\(360\) | 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 | \(-0.720387\pi\) | ||
0.638361 | − | 0.769737i | \(-0.279613\pi\) | |||||||
\(374\) | 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 | \(-0.756117\pi\) | ||||
−0.720565 | + | 0.693387i | \(0.756117\pi\) | |||||||
\(380\) | 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 | \(-0.922837\pi\) | ||
0.970761 | − | 0.240047i | \(-0.0771630\pi\) | |||||||
\(398\) | 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 | \(-0.767684\pi\) | ||||
−0.745280 | + | 0.666752i | \(0.767684\pi\) | |||||||
\(420\) | 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 | \(-0.779537\pi\) | ||||
−0.769586 | + | 0.638543i | \(0.779537\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.72633e6i | 0.698810i | 0.936972 | + | 0.349405i | \(0.113616\pi\) | ||||
−0.936972 | + | 0.349405i | \(0.886384\pi\) | |||||||
\(434\) | 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 | \(-0.790707\pi\) | ||||
−0.791515 | + | 0.611150i | \(0.790707\pi\) | |||||||
\(440\) | 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 | \(0.0539130\pi\) | ||||
−0.985691 | + | 0.168564i | \(0.946087\pi\) | |||||||
\(458\) | 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 | \(-0.740600\pi\) | ||||
−0.685920 | + | 0.727677i | \(0.740600\pi\) | |||||||
\(480\) | 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 | \(-0.289908\pi\) | ||||
0.613137 | + | 0.789977i | \(0.289908\pi\) | |||||||
\(492\) | 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 | \(-0.621581\pi\) | ||||
−0.372738 | + | 0.927936i | \(0.621581\pi\) | |||||||
\(500\) | 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 | \(0.105668\pi\) | ||||
−0.945404 | + | 0.325902i | \(0.894332\pi\) | |||||||
\(558\) | 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 | \(-0.330856\pi\) | ||||
0.506725 | + | 0.862108i | \(0.330856\pi\) | |||||||
\(572\) | 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 | \(0.318371\pi\) | ||||
−0.540141 | + | 0.841575i | \(0.681629\pi\) | |||||||
\(578\) | 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 | \(0.0257044\pi\) | ||||
−0.996741 | + | 0.0806649i | \(0.974296\pi\) | |||||||
\(594\) | 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 | \(-0.621261\pi\) | ||||
−0.371806 | + | 0.928310i | \(0.621261\pi\) | |||||||
\(600\) | 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 | \(0.101014\pi\) | ||||
−0.950067 | + | 0.312046i | \(0.898986\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 62902.4 | − | 29028.4i | 0.00670624 | − | 0.00309482i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.80508e6i | − | 0.719648i | −0.933020 | − | 0.359824i | \(-0.882837\pi\) | ||
0.933020 | − | 0.359824i | \(-0.117163\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 852530. | 0.0894299 | 0.0447150 | − | 0.999000i | \(-0.485762\pi\) | ||||
0.0447150 | + | 0.999000i | \(0.485762\pi\) | |||||||
\(620\) | 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 | \(-0.368801\pi\) | ||||
0.400603 | + | 0.916252i | \(0.368801\pi\) | |||||||
\(632\) | 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 | \(-0.983159\pi\) | ||
0.998601 | − | 0.0528836i | \(-0.0168412\pi\) | |||||||
\(654\) | 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 | \(-0.741037\pi\) | ||||
−0.686919 | + | 0.726734i | \(0.741037\pi\) | |||||||
\(660\) | 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 | \(-0.979132\pi\) | ||
0.997852 | − | 0.0655129i | \(-0.0208683\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.17914e6 | − | 4.41636e6i | −0.437520 | − | 0.373083i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.16833e7i | 0.979702i | 0.871806 | + | 0.489851i | \(0.162949\pi\) | ||||
−0.871806 | + | 0.489851i | \(0.837051\pi\) | |||||||
\(678\) | 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 | \(-0.370945\pi\) | ||||
0.394422 | + | 0.918930i | \(0.370945\pi\) | |||||||
\(692\) | 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 | \(-0.360091\pi\) | ||||
0.425522 | + | 0.904948i | \(0.360091\pi\) | |||||||
\(720\) | 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 | \(-0.844794\pi\) | ||
0.883463 | − | 0.468501i | \(-0.155206\pi\) | |||||||
\(734\) | 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 | \(-0.381899\pi\) | ||||
0.362571 | + | 0.931956i | \(0.381899\pi\) | |||||||
\(740\) | 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 | \(-0.416003\pi\) | ||||
0.260832 | + | 0.965384i | \(0.416003\pi\) | |||||||
\(752\) | 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 | \(0.112229\pi\) | ||||
−0.938485 | + | 0.345319i | \(0.887771\pi\) | |||||||
\(758\) | 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 | \(-0.963876\pi\) | ||
0.993567 | − | 0.113244i | \(-0.0361240\pi\) | |||||||
\(774\) | 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 | \(-0.830014\pi\) | ||
0.860765 | − | 0.509003i | \(-0.169986\pi\) | |||||||
\(798\) | 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 | \(-0.739954\pi\) | ||||
−0.684441 | + | 0.729068i | \(0.739954\pi\) | |||||||
\(812\) | 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 | \(-0.307982\pi\) | ||||
0.567315 | + | 0.823501i | \(0.307982\pi\) | |||||||
\(840\) | 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 | \(0.122459\pi\) | ||||
−0.926905 | + | 0.375296i | \(0.877541\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.96952e6 | + | 4.26780e6i | 0.0921392 | + | 0.199659i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.04392e7i | 0.485529i | 0.970085 | + | 0.242764i | \(0.0780542\pi\) | ||||
−0.970085 | + | 0.242764i | \(0.921946\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.94442e6 | 0.228630 | 0.114315 | − | 0.993445i | \(-0.463533\pi\) | ||||
0.114315 | + | 0.993445i | \(0.463533\pi\) | |||||||
\(860\) | 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 | \(0.0430429\pi\) | ||||
−0.990871 | + | 0.134812i | \(0.956957\pi\) | |||||||
\(878\) | 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 | \(-0.670667\pi\) | ||||
−0.510843 | + | 0.859674i | \(0.670667\pi\) | |||||||
\(912\) | 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 | \(-0.520408\pi\) | ||||
−0.0640691 | + | 0.997945i | \(0.520408\pi\) | |||||||
\(920\) | 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 | \(0.178268\pi\) | ||||
−0.847231 | + | 0.531225i | \(0.821732\pi\) | |||||||
\(938\) | 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 | \(-0.787901\pi\) | ||
0.786096 | − | 0.618104i | \(-0.212099\pi\) | |||||||
\(954\) | 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 | \(-0.364493\pi\) | ||||
0.412967 | + | 0.910746i | \(0.364493\pi\) | |||||||
\(972\) | 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 | \(-0.589991\pi\) | ||
0.278963 | − | 0.960302i | \(-0.410009\pi\) | |||||||
\(978\) | 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 | \(-0.485562\pi\) | ||||
0.0453429 | + | 0.998971i | \(0.485562\pi\) | |||||||
\(992\) | 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 | \(0.271199\pi\) | ||||
−0.658481 | + | 0.752598i | \(0.728801\pi\) | |||||||
\(998\) | 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.j.129.5 | 8 | ||
4.3 | odd | 2 | 320.6.c.i.129.4 | 8 | |||
5.4 | even | 2 | inner | 320.6.c.j.129.4 | 8 | ||
8.3 | odd | 2 | 80.6.c.d.49.5 | 8 | |||
8.5 | even | 2 | 40.6.c.a.9.4 | ✓ | 8 | ||
20.19 | odd | 2 | 320.6.c.i.129.5 | 8 | |||
24.5 | odd | 2 | 360.6.f.b.289.3 | 8 | |||
24.11 | even | 2 | 720.6.f.n.289.3 | 8 | |||
40.3 | even | 4 | 400.6.a.z.1.2 | 4 | |||
40.13 | odd | 4 | 200.6.a.k.1.3 | 4 | |||
40.19 | odd | 2 | 80.6.c.d.49.4 | 8 | |||
40.27 | even | 4 | 400.6.a.ba.1.3 | 4 | |||
40.29 | even | 2 | 40.6.c.a.9.5 | yes | 8 | ||
40.37 | odd | 4 | 200.6.a.j.1.2 | 4 | |||
120.29 | odd | 2 | 360.6.f.b.289.4 | 8 | |||
120.59 | even | 2 | 720.6.f.n.289.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.c.a.9.4 | ✓ | 8 | 8.5 | even | 2 | ||
40.6.c.a.9.5 | yes | 8 | 40.29 | even | 2 | ||
80.6.c.d.49.4 | 8 | 40.19 | odd | 2 | |||
80.6.c.d.49.5 | 8 | 8.3 | odd | 2 | |||
200.6.a.j.1.2 | 4 | 40.37 | odd | 4 | |||
200.6.a.k.1.3 | 4 | 40.13 | odd | 4 | |||
320.6.c.i.129.4 | 8 | 4.3 | odd | 2 | |||
320.6.c.i.129.5 | 8 | 20.19 | odd | 2 | |||
320.6.c.j.129.4 | 8 | 5.4 | even | 2 | inner | ||
320.6.c.j.129.5 | 8 | 1.1 | even | 1 | trivial | ||
360.6.f.b.289.3 | 8 | 24.5 | odd | 2 | |||
360.6.f.b.289.4 | 8 | 120.29 | odd | 2 | |||
400.6.a.z.1.2 | 4 | 40.3 | even | 4 | |||
400.6.a.ba.1.3 | 4 | 40.27 | even | 4 | |||
720.6.f.n.289.3 | 8 | 24.11 | even | 2 | |||
720.6.f.n.289.4 | 8 | 120.59 | even | 2 |