Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [90,6,Mod(19,90)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(90, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("90.19");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 90 = 2 \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 90.c (of order \(2\), degree \(1\), 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: | \(14.4345437832\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.1 | ||
Root | \(-2.17945 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 90.19 |
Dual form | 90.6.c.d.19.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/90\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | −43.5890 | + | 35.0000i | −0.779744 | + | 0.626099i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.4356i | 0.134491i | 0.997736 | + | 0.0672453i | \(0.0214210\pi\) | ||||
−0.997736 | + | 0.0672453i | \(0.978579\pi\) | |||||||
\(8\) | 64.0000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 140.000 | + | 174.356i | 0.442719 | + | 0.551362i | ||||
\(11\) | 645.117 | 1.60752 | 0.803761 | − | 0.594953i | \(-0.202829\pi\) | ||||
0.803761 | + | 0.594953i | \(0.202829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1098.44i | − | 1.80268i | −0.433111 | − | 0.901341i | \(-0.642584\pi\) | ||
0.433111 | − | 0.901341i | \(-0.357416\pi\) | |||||||
\(14\) | 69.7424 | 0.0950992 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 1166.00i | 0.978535i | 0.872134 | + | 0.489267i | \(0.162736\pi\) | ||||
−0.872134 | + | 0.489267i | \(0.837264\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2244.00 | 1.42606 | 0.713032 | − | 0.701132i | \(-0.247322\pi\) | ||||
0.713032 | + | 0.701132i | \(0.247322\pi\) | |||||||
\(20\) | 697.424 | − | 560.000i | 0.389872 | − | 0.313050i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 2580.47i | − | 1.13669i | ||||||
\(23\) | − | 500.000i | − | 0.197084i | −0.995133 | − | 0.0985418i | \(-0.968582\pi\) | ||
0.995133 | − | 0.0985418i | \(-0.0314178\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 675.000 | − | 3051.23i | 0.216000 | − | 0.976393i | ||||
\(26\) | −4393.77 | −1.27469 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 278.970i | − | 0.0672453i | ||||||
\(29\) | 470.761 | 0.103945 | 0.0519727 | − | 0.998649i | \(-0.483449\pi\) | ||||
0.0519727 | + | 0.998649i | \(0.483449\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3856.00 | 0.720664 | 0.360332 | − | 0.932824i | \(-0.382663\pi\) | ||||
0.360332 | + | 0.932824i | \(0.382663\pi\) | |||||||
\(32\) | − | 1024.00i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4664.00 | 0.691929 | ||||||||
\(35\) | −610.246 | − | 760.000i | −0.0842044 | − | 0.104868i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6991.67i | − | 0.839609i | −0.907615 | − | 0.419804i | \(-0.862099\pi\) | ||
0.907615 | − | 0.419804i | \(-0.137901\pi\) | |||||||
\(38\) | − | 8976.00i | − | 1.00838i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2240.00 | − | 2789.70i | −0.221359 | − | 0.275681i | ||||
\(41\) | 9589.58 | 0.890922 | 0.445461 | − | 0.895301i | \(-0.353040\pi\) | ||||
0.445461 | + | 0.895301i | \(0.353040\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5300.42i | − | 0.437159i | −0.975819 | − | 0.218579i | \(-0.929858\pi\) | ||
0.975819 | − | 0.218579i | \(-0.0701423\pi\) | |||||||
\(44\) | −10321.9 | −0.803761 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2000.00 | −0.139359 | ||||||||
\(47\) | 19900.0i | 1.31404i | 0.753873 | + | 0.657020i | \(0.228183\pi\) | ||||
−0.753873 | + | 0.657020i | \(0.771817\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16503.0 | 0.981912 | ||||||||
\(50\) | −12204.9 | − | 2700.00i | −0.690414 | − | 0.152735i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 17575.1i | 0.901341i | ||||||||
\(53\) | − | 1146.00i | − | 0.0560396i | −0.999607 | − | 0.0280198i | \(-0.991080\pi\) | ||
0.999607 | − | 0.0280198i | \(-0.00892015\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −28120.0 | + | 22579.1i | −1.25345 | + | 1.00647i | ||||
\(56\) | −1115.88 | −0.0475496 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 1883.04i | − | 0.0735005i | ||||||
\(59\) | 37364.5 | 1.39743 | 0.698713 | − | 0.715402i | \(-0.253756\pi\) | ||||
0.698713 | + | 0.715402i | \(0.253756\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −38158.0 | −1.31299 | −0.656494 | − | 0.754331i | \(-0.727961\pi\) | ||||
−0.656494 | + | 0.754331i | \(0.727961\pi\) | |||||||
\(62\) | − | 15424.0i | − | 0.509586i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 38445.5 | + | 47880.0i | 1.12866 | + | 1.40563i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 36231.2i | 0.986042i | 0.870017 | + | 0.493021i | \(0.164107\pi\) | ||||
−0.870017 | + | 0.493021i | \(0.835893\pi\) | |||||||
\(68\) | − | 18656.0i | − | 0.489267i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3040.00 | + | 2440.98i | −0.0741530 | + | 0.0595415i | ||||
\(71\) | −16633.6 | −0.391597 | −0.195798 | − | 0.980644i | \(-0.562730\pi\) | ||||
−0.195798 | + | 0.980644i | \(0.562730\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 69393.7i | 1.52410i | 0.647520 | + | 0.762049i | \(0.275806\pi\) | ||||
−0.647520 | + | 0.762049i | \(0.724194\pi\) | |||||||
\(74\) | −27966.7 | −0.593693 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −35904.0 | −0.713032 | ||||||||
\(77\) | 11248.0i | 0.216196i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 20664.0 | 0.372517 | 0.186259 | − | 0.982501i | \(-0.440364\pi\) | ||||
0.186259 | + | 0.982501i | \(0.440364\pi\) | |||||||
\(80\) | −11158.8 | + | 8960.00i | −0.194936 | + | 0.156525i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 38358.3i | − | 0.629977i | ||||||
\(83\) | − | 96968.0i | − | 1.54502i | −0.635005 | − | 0.772508i | \(-0.719002\pi\) | ||
0.635005 | − | 0.772508i | \(-0.280998\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −40810.0 | − | 50824.8i | −0.612660 | − | 0.763006i | ||||
\(86\) | −21201.7 | −0.309118 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 41287.5i | 0.568345i | ||||||||
\(89\) | −59699.5 | −0.798906 | −0.399453 | − | 0.916754i | \(-0.630800\pi\) | ||||
−0.399453 | + | 0.916754i | \(0.630800\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19152.0 | 0.242444 | ||||||||
\(92\) | 8000.00i | 0.0985418i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 79600.0 | 0.929166 | ||||||||
\(95\) | −97813.7 | + | 78540.0i | −1.11196 | + | 0.892857i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 5823.49i | − | 0.0628426i | −0.999506 | − | 0.0314213i | \(-0.989997\pi\) | ||
0.999506 | − | 0.0314213i | \(-0.0100034\pi\) | |||||||
\(98\) | − | 66012.0i | − | 0.694317i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −10800.0 | + | 48819.7i | −0.108000 | + | 0.488197i | ||||
\(101\) | 102922. | 1.00394 | 0.501968 | − | 0.864886i | \(-0.332609\pi\) | ||||
0.501968 | + | 0.864886i | \(0.332609\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 178558.i | − | 1.65839i | −0.558961 | − | 0.829194i | \(-0.688800\pi\) | ||
0.558961 | − | 0.829194i | \(-0.311200\pi\) | |||||||
\(104\) | 70300.3 | 0.637344 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4584.00 | −0.0396260 | ||||||||
\(107\) | − | 7512.00i | − | 0.0634302i | −0.999497 | − | 0.0317151i | \(-0.989903\pi\) | ||
0.999497 | − | 0.0317151i | \(-0.0100969\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 58238.0 | 0.469505 | 0.234752 | − | 0.972055i | \(-0.424572\pi\) | ||||
0.234752 | + | 0.972055i | \(0.424572\pi\) | |||||||
\(110\) | 90316.4 | + | 112480.i | 0.711680 | + | 0.886326i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4463.51i | 0.0336226i | ||||||||
\(113\) | − | 217314.i | − | 1.60100i | −0.599332 | − | 0.800500i | \(-0.704567\pi\) | ||
0.599332 | − | 0.800500i | \(-0.295433\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17500.0 | + | 21794.5i | 0.123394 | + | 0.153675i | ||||
\(116\) | −7532.18 | −0.0519727 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 149458.i | − | 0.988130i | ||||||
\(119\) | −20329.9 | −0.131604 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 255125. | 1.58413 | ||||||||
\(122\) | 152632.i | 0.928423i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −61696.0 | −0.360332 | ||||||||
\(125\) | 77370.5 | + | 156625.i | 0.442894 | + | 0.896574i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 212348.i | − | 1.16826i | −0.811660 | − | 0.584129i | \(-0.801436\pi\) | ||
0.811660 | − | 0.584129i | \(-0.198564\pi\) | |||||||
\(128\) | 16384.0i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 191520. | − | 153782.i | 0.993930 | − | 0.798081i | ||||
\(131\) | −279266. | −1.42180 | −0.710902 | − | 0.703291i | \(-0.751713\pi\) | ||||
−0.710902 | + | 0.703291i | \(0.751713\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 39125.5i | 0.191792i | ||||||||
\(134\) | 144925. | 0.697237 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −74624.0 | −0.345964 | ||||||||
\(137\) | 337914.i | 1.53817i | 0.639146 | + | 0.769086i | \(0.279288\pi\) | ||||
−0.639146 | + | 0.769086i | \(0.720712\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −92620.0 | −0.406600 | −0.203300 | − | 0.979116i | \(-0.565167\pi\) | ||||
−0.203300 | + | 0.979116i | \(0.565167\pi\) | |||||||
\(140\) | 9763.93 | + | 12160.0i | 0.0421022 | + | 0.0524341i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 66534.2i | 0.276901i | ||||||||
\(143\) | − | 708624.i | − | 2.89785i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20520.0 | + | 16476.6i | −0.0810508 | + | 0.0650802i | ||||
\(146\) | 277575. | 1.07770 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 111867.i | 0.419804i | ||||||||
\(149\) | −29588.2 | −0.109182 | −0.0545912 | − | 0.998509i | \(-0.517386\pi\) | ||||
−0.0545912 | + | 0.998509i | \(0.517386\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 40384.0 | 0.144134 | 0.0720671 | − | 0.997400i | \(-0.477040\pi\) | ||||
0.0720671 | + | 0.997400i | \(0.477040\pi\) | |||||||
\(152\) | 143616.i | 0.504190i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 44992.0 | 0.152874 | ||||||||
\(155\) | −168079. | + | 134960.i | −0.561933 | + | 0.451207i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 81476.5i | 0.263805i | 0.991263 | + | 0.131903i | \(0.0421086\pi\) | ||||
−0.991263 | + | 0.131903i | \(0.957891\pi\) | |||||||
\(158\) | − | 82656.0i | − | 0.263410i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 35840.0 | + | 44635.1i | 0.110680 | + | 0.137840i | ||||
\(161\) | 8717.80 | 0.0265059 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 458382.i | 1.35132i | 0.737213 | + | 0.675660i | \(0.236141\pi\) | ||||
−0.737213 | + | 0.675660i | \(0.763859\pi\) | |||||||
\(164\) | −153433. | −0.445461 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −387872. | −1.09249 | ||||||||
\(167\) | − | 194436.i | − | 0.539493i | −0.962931 | − | 0.269746i | \(-0.913060\pi\) | ||
0.962931 | − | 0.269746i | \(-0.0869398\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −835283. | −2.24966 | ||||||||
\(170\) | −203299. | + | 163240.i | −0.539527 | + | 0.433216i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 84806.7i | 0.218579i | ||||||||
\(173\) | − | 322222.i | − | 0.818540i | −0.912413 | − | 0.409270i | \(-0.865783\pi\) | ||
0.912413 | − | 0.409270i | \(-0.134217\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 53200.0 | + | 11769.0i | 0.131316 | + | 0.0290500i | ||||
\(176\) | 165150. | 0.401880 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 238798.i | 0.564912i | ||||||||
\(179\) | −430258. | −1.00368 | −0.501842 | − | 0.864960i | \(-0.667344\pi\) | ||||
−0.501842 | + | 0.864960i | \(0.667344\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 242522. | 0.550243 | 0.275122 | − | 0.961409i | \(-0.411282\pi\) | ||||
0.275122 | + | 0.961409i | \(0.411282\pi\) | |||||||
\(182\) | − | 76608.0i | − | 0.171433i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 32000.0 | 0.0696796 | ||||||||
\(185\) | 244709. | + | 304760.i | 0.525678 | + | 0.654679i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 752206.i | 1.57302i | ||||||||
\(188\) | − | 318400.i | − | 0.657020i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 314160. | + | 391255.i | 0.631345 | + | 0.786277i | ||||
\(191\) | −290930. | −0.577040 | −0.288520 | − | 0.957474i | \(-0.593163\pi\) | ||||
−0.288520 | + | 0.957474i | \(0.593163\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 723054.i | − | 1.39726i | −0.715483 | − | 0.698631i | \(-0.753793\pi\) | ||
0.715483 | − | 0.698631i | \(-0.246207\pi\) | |||||||
\(194\) | −23294.0 | −0.0444364 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −264048. | −0.490956 | ||||||||
\(197\) | 599638.i | 1.10084i | 0.834888 | + | 0.550419i | \(0.185532\pi\) | ||||
−0.834888 | + | 0.550419i | \(0.814468\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −650184. | −1.16387 | −0.581934 | − | 0.813236i | \(-0.697704\pi\) | ||||
−0.581934 | + | 0.813236i | \(0.697704\pi\) | |||||||
\(200\) | 195279. | + | 43200.0i | 0.345207 | + | 0.0763675i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 411689.i | − | 0.709890i | ||||||
\(203\) | 8208.00i | 0.0139797i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −418000. | + | 335635.i | −0.694691 | + | 0.557806i | ||||
\(206\) | −714232. | −1.17266 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 281201.i | − | 0.450670i | ||||||
\(209\) | 1.44764e6 | 2.29243 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 986316. | 1.52514 | 0.762570 | − | 0.646905i | \(-0.223937\pi\) | ||||
0.762570 | + | 0.646905i | \(0.223937\pi\) | |||||||
\(212\) | 18336.0i | 0.0280198i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −30048.0 | −0.0448519 | ||||||||
\(215\) | 185515. | + | 231040.i | 0.273705 | + | 0.340872i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 67231.7i | 0.0969225i | ||||||||
\(218\) | − | 232952.i | − | 0.331990i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 449920. | − | 361266.i | 0.626727 | − | 0.503234i | ||||
\(221\) | 1.28078e6 | 1.76399 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 694407.i | 0.935087i | 0.883970 | + | 0.467544i | \(0.154861\pi\) | ||||
−0.883970 | + | 0.467544i | \(0.845139\pi\) | |||||||
\(224\) | 17854.1 | 0.0237748 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −869256. | −1.13208 | ||||||||
\(227\) | − | 435400.i | − | 0.560820i | −0.959880 | − | 0.280410i | \(-0.909530\pi\) | ||
0.959880 | − | 0.280410i | \(-0.0904705\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.16123e6 | 1.46328 | 0.731641 | − | 0.681690i | \(-0.238755\pi\) | ||||
0.731641 | + | 0.681690i | \(0.238755\pi\) | |||||||
\(230\) | 87178.0 | − | 70000.0i | 0.108664 | − | 0.0872526i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 30128.7i | 0.0367503i | ||||||||
\(233\) | 1.21303e6i | 1.46380i | 0.681409 | + | 0.731902i | \(0.261367\pi\) | ||||
−0.681409 | + | 0.731902i | \(0.738633\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −696500. | − | 867421.i | −0.822719 | − | 1.02461i | ||||
\(236\) | −597832. | −0.698713 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 81319.6i | 0.0930578i | ||||||||
\(239\) | −1.40053e6 | −1.58598 | −0.792991 | − | 0.609234i | \(-0.791477\pi\) | ||||
−0.792991 | + | 0.609234i | \(0.791477\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 471490. | 0.522914 | 0.261457 | − | 0.965215i | \(-0.415797\pi\) | ||||
0.261457 | + | 0.965215i | \(0.415797\pi\) | |||||||
\(242\) | − | 1.02050e6i | − | 1.12015i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 610528. | 0.656494 | ||||||||
\(245\) | −719349. | + | 577605.i | −0.765640 | + | 0.614774i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.46491e6i | − | 2.57074i | ||||||
\(248\) | 246784.i | 0.254793i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 626500. | − | 309482.i | 0.633973 | − | 0.313174i | ||||
\(251\) | 601371. | 0.602502 | 0.301251 | − | 0.953545i | \(-0.402596\pi\) | ||||
0.301251 | + | 0.953545i | \(0.402596\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 322559.i | − | 0.316816i | ||||||
\(254\) | −849392. | −0.826084 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | − | 124206.i | − | 0.117303i | −0.998279 | − | 0.0586516i | \(-0.981320\pi\) | ||
0.998279 | − | 0.0586516i | \(-0.0186801\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 121904. | 0.112919 | ||||||||
\(260\) | −615128. | − | 766080.i | −0.564329 | − | 0.702815i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.11706e6i | 1.00537i | ||||||||
\(263\) | − | 429956.i | − | 0.383296i | −0.981464 | − | 0.191648i | \(-0.938617\pi\) | ||
0.981464 | − | 0.191648i | \(-0.0613832\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 40110.0 | + | 49953.0i | 0.0350863 | + | 0.0436965i | ||||
\(266\) | 156502. | 0.135617 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 579699.i | − | 0.493021i | ||||||
\(269\) | 1.43755e6 | 1.21127 | 0.605636 | − | 0.795742i | \(-0.292919\pi\) | ||||
0.605636 | + | 0.795742i | \(0.292919\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.54473e6 | 1.27770 | 0.638850 | − | 0.769331i | \(-0.279411\pi\) | ||||
0.638850 | + | 0.769331i | \(0.279411\pi\) | |||||||
\(272\) | 298496.i | 0.244634i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.35166e6 | 1.08765 | ||||||||
\(275\) | 435454. | − | 1.96840e6i | 0.347225 | − | 1.56957i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 211128.i | 0.165328i | 0.996577 | + | 0.0826639i | \(0.0263428\pi\) | ||||
−0.996577 | + | 0.0826639i | \(0.973657\pi\) | |||||||
\(278\) | 370480.i | 0.287510i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 48640.0 | − | 39055.7i | 0.0370765 | − | 0.0297707i | ||||
\(281\) | −1.29051e6 | −0.974982 | −0.487491 | − | 0.873128i | \(-0.662088\pi\) | ||||
−0.487491 | + | 0.873128i | \(0.662088\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.69959e6i | − | 1.26147i | −0.775998 | − | 0.630736i | \(-0.782753\pi\) | ||
0.775998 | − | 0.630736i | \(-0.217247\pi\) | |||||||
\(284\) | 266137. | 0.195798 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.83450e6 | −2.04909 | ||||||||
\(287\) | 167200.i | 0.119821i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 60301.0 | 0.0424698 | ||||||||
\(290\) | 65906.6 | + | 82080.0i | 0.0460186 | + | 0.0573116i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 1.11030e6i | − | 0.762049i | ||||||
\(293\) | 2.49148e6i | 1.69546i | 0.530424 | + | 0.847732i | \(0.322033\pi\) | ||||
−0.530424 | + | 0.847732i | \(0.677967\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.62868e6 | + | 1.30776e6i | −1.08963 | + | 0.874927i | ||||
\(296\) | 447467. | 0.296846 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 118353.i | 0.0772037i | ||||||||
\(299\) | −549221. | −0.355279 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 92416.0 | 0.0587937 | ||||||||
\(302\) | − | 161536.i | − | 0.101918i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 574464. | 0.356516 | ||||||||
\(305\) | 1.66327e6 | − | 1.33553e6i | 1.02379 | − | 0.822061i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.16791e6i | 1.91834i | 0.282822 | + | 0.959172i | \(0.408729\pi\) | ||||
−0.282822 | + | 0.959172i | \(0.591271\pi\) | |||||||
\(308\) | − | 179968.i | − | 0.108098i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 539840. | + | 672317.i | 0.319052 | + | 0.397347i | ||||
\(311\) | −2.23653e6 | −1.31122 | −0.655608 | − | 0.755101i | \(-0.727588\pi\) | ||||
−0.655608 | + | 0.755101i | \(0.727588\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.37351e6i | 1.36940i | 0.728826 | + | 0.684699i | \(0.240066\pi\) | ||||
−0.728826 | + | 0.684699i | \(0.759934\pi\) | |||||||
\(314\) | 325906. | 0.186538 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −330624. | −0.186259 | ||||||||
\(317\) | − | 987502.i | − | 0.551937i | −0.961167 | − | 0.275969i | \(-0.911001\pi\) | ||
0.961167 | − | 0.275969i | \(-0.0889986\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 303696. | 0.167095 | ||||||||
\(320\) | 178541. | − | 143360.i | 0.0974679 | − | 0.0782624i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 34871.2i | − | 0.0187425i | ||||||
\(323\) | 2.61650e6i | 1.39545i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.35160e6 | − | 741449.i | −1.76013 | − | 0.389379i | ||||
\(326\) | 1.83353e6 | 0.955528 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 613733.i | 0.314989i | ||||||||
\(329\) | −346968. | −0.176726 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −918644. | −0.460869 | −0.230434 | − | 0.973088i | \(-0.574015\pi\) | ||||
−0.230434 | + | 0.973088i | \(0.574015\pi\) | |||||||
\(332\) | 1.55149e6i | 0.772508i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −777744. | −0.381479 | ||||||||
\(335\) | −1.26809e6 | − | 1.57928e6i | −0.617360 | − | 0.768860i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 355547.i | 0.170538i | 0.996358 | + | 0.0852691i | \(0.0271750\pi\) | ||||
−0.996358 | + | 0.0852691i | \(0.972825\pi\) | |||||||
\(338\) | 3.34113e6i | 1.59075i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 652960. | + | 813196.i | 0.306330 | + | 0.381503i | ||||
\(341\) | 2.48757e6 | 1.15848 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 580780.i | 0.266548i | ||||||||
\(344\) | 339227. | 0.154559 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.28889e6 | −0.578795 | ||||||||
\(347\) | − | 1.85760e6i | − | 0.828187i | −0.910234 | − | 0.414094i | \(-0.864099\pi\) | ||
0.910234 | − | 0.414094i | \(-0.135901\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −950578. | −0.417757 | −0.208879 | − | 0.977942i | \(-0.566981\pi\) | ||||
−0.208879 | + | 0.977942i | \(0.566981\pi\) | |||||||
\(350\) | 47076.1 | − | 212800.i | 0.0205414 | − | 0.0928542i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 660600.i | − | 0.284172i | ||||||
\(353\) | 767570.i | 0.327855i | 0.986472 | + | 0.163927i | \(0.0524162\pi\) | ||||
−0.986472 | + | 0.163927i | \(0.947584\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 725040. | − | 582175.i | 0.305345 | − | 0.245178i | ||||
\(356\) | 955192. | 0.399453 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.72103e6i | 0.709711i | ||||||||
\(359\) | −160896. | −0.0658883 | −0.0329441 | − | 0.999457i | \(-0.510488\pi\) | ||||
−0.0329441 | + | 0.999457i | \(0.510488\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.55944e6 | 1.03366 | ||||||||
\(362\) | − | 970088.i | − | 0.389081i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −306432. | −0.121222 | ||||||||
\(365\) | −2.42878e6 | − | 3.02480e6i | −0.954236 | − | 1.18841i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 202131.i | 0.0783371i | 0.999233 | + | 0.0391685i | \(0.0124709\pi\) | ||||
−0.999233 | + | 0.0391685i | \(0.987529\pi\) | |||||||
\(368\) | − | 128000.i | − | 0.0492709i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.21904e6 | − | 978834.i | 0.462928 | − | 0.371711i | ||||
\(371\) | 19981.2 | 0.00753679 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.48933e6i | 0.554267i | 0.960831 | + | 0.277134i | \(0.0893845\pi\) | ||||
−0.960831 | + | 0.277134i | \(0.910616\pi\) | |||||||
\(374\) | 3.00883e6 | 1.11229 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.27360e6 | −0.464583 | ||||||||
\(377\) | − | 517104.i | − | 0.187381i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.69222e6 | −0.962748 | −0.481374 | − | 0.876515i | \(-0.659862\pi\) | ||||
−0.481374 | + | 0.876515i | \(0.659862\pi\) | |||||||
\(380\) | 1.56502e6 | − | 1.25664e6i | 0.555982 | − | 0.446428i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.16372e6i | 0.408029i | ||||||||
\(383\) | 565100.i | 0.196847i | 0.995145 | + | 0.0984234i | \(0.0313799\pi\) | ||||
−0.995145 | + | 0.0984234i | \(0.968620\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −393680. | − | 490289.i | −0.135360 | − | 0.168578i | ||||
\(386\) | −2.89222e6 | −0.988013 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 93175.8i | 0.0314213i | ||||||||
\(389\) | −5.46587e6 | −1.83141 | −0.915704 | − | 0.401853i | \(-0.868366\pi\) | ||||
−0.915704 | + | 0.401853i | \(0.868366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 583000. | 0.192853 | ||||||||
\(392\) | 1.05619e6i | 0.347158i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.39855e6 | 0.778410 | ||||||||
\(395\) | −900723. | + | 723240.i | −0.290468 | + | 0.233233i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.00762e6i | − | 1.27618i | −0.769963 | − | 0.638088i | \(-0.779726\pi\) | ||
0.769963 | − | 0.638088i | \(-0.220274\pi\) | |||||||
\(398\) | 2.60074e6i | 0.822979i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 172800. | − | 781115.i | 0.0540000 | − | 0.244098i | ||||
\(401\) | −3.92967e6 | −1.22038 | −0.610190 | − | 0.792255i | \(-0.708907\pi\) | ||||
−0.610190 | + | 0.792255i | \(0.708907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4.23559e6i | − | 1.29913i | ||||||
\(404\) | −1.64676e6 | −0.501968 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 32832.0 | 0.00988513 | ||||||||
\(407\) | − | 4.51045e6i | − | 1.34969i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.15028e6 | 0.340013 | 0.170007 | − | 0.985443i | \(-0.445621\pi\) | ||||
0.170007 | + | 0.985443i | \(0.445621\pi\) | |||||||
\(410\) | 1.34254e6 | + | 1.67200e6i | 0.394428 | + | 0.491221i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.85693e6i | 0.829194i | ||||||||
\(413\) | 651472.i | 0.187941i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.39388e6 | + | 4.22674e6i | 0.967334 | + | 1.20472i | ||||
\(416\) | −1.12481e6 | −0.318672 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 5.79057e6i | − | 1.62099i | ||||||
\(419\) | 4.95898e6 | 1.37993 | 0.689965 | − | 0.723842i | \(-0.257626\pi\) | ||||
0.689965 | + | 0.723842i | \(0.257626\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.89077e6 | 0.794893 | 0.397447 | − | 0.917625i | \(-0.369896\pi\) | ||||
0.397447 | + | 0.917625i | \(0.369896\pi\) | |||||||
\(422\) | − | 3.94526e6i | − | 1.07844i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 73344.0 | 0.0198130 | ||||||||
\(425\) | 3.55773e6 | + | 787050.i | 0.955435 | + | 0.211364i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 665307.i | − | 0.176585i | ||||||
\(428\) | 120192.i | 0.0317151i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 924160. | − | 742059.i | 0.241033 | − | 0.193538i | ||||
\(431\) | 1.98417e6 | 0.514501 | 0.257250 | − | 0.966345i | \(-0.417184\pi\) | ||||
0.257250 | + | 0.966345i | \(0.417184\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.75622e6i | − | 0.962789i | −0.876504 | − | 0.481395i | \(-0.840130\pi\) | ||
0.876504 | − | 0.481395i | \(-0.159870\pi\) | |||||||
\(434\) | 268927. | 0.0685345 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −931808. | −0.234752 | ||||||||
\(437\) | − | 1.12200e6i | − | 0.281054i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.94897e6 | −0.482662 | −0.241331 | − | 0.970443i | \(-0.577584\pi\) | ||||
−0.241331 | + | 0.970443i | \(0.577584\pi\) | |||||||
\(440\) | −1.44506e6 | − | 1.79968e6i | −0.355840 | − | 0.443163i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 5.12314e6i | − | 1.24733i | ||||||
\(443\) | 5.74198e6i | 1.39012i | 0.718952 | + | 0.695060i | \(0.244622\pi\) | ||||
−0.718952 | + | 0.695060i | \(0.755378\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.60224e6 | − | 2.08948e6i | 0.622942 | − | 0.500194i | ||||
\(446\) | 2.77763e6 | 0.661207 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 71416.2i | − | 0.0168113i | ||||||
\(449\) | 538655. | 0.126094 | 0.0630471 | − | 0.998011i | \(-0.479918\pi\) | ||||
0.0630471 | + | 0.998011i | \(0.479918\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.18640e6 | 1.43218 | ||||||||
\(452\) | 3.47702e6i | 0.800500i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.74160e6 | −0.396560 | ||||||||
\(455\) | −834816. | + | 670320.i | −0.189044 | + | 0.151794i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1.55459e6i | − | 0.348198i | −0.984728 | − | 0.174099i | \(-0.944299\pi\) | ||
0.984728 | − | 0.174099i | \(-0.0557013\pi\) | |||||||
\(458\) | − | 4.64490e6i | − | 1.03470i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −280000. | − | 348712.i | −0.0616969 | − | 0.0768373i | ||||
\(461\) | 4.22445e6 | 0.925802 | 0.462901 | − | 0.886410i | \(-0.346809\pi\) | ||||
0.462901 | + | 0.886410i | \(0.346809\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.77347e6i | 1.03486i | 0.855726 | + | 0.517430i | \(0.173111\pi\) | ||||
−0.855726 | + | 0.517430i | \(0.826889\pi\) | |||||||
\(464\) | 120515. | 0.0259864 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.85214e6 | 1.03507 | ||||||||
\(467\) | 9.11683e6i | 1.93442i | 0.253970 | + | 0.967212i | \(0.418264\pi\) | ||||
−0.253970 | + | 0.967212i | \(0.581736\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −631712. | −0.132613 | ||||||||
\(470\) | −3.46968e6 | + | 2.78600e6i | −0.724511 | + | 0.581750i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.39133e6i | 0.494065i | ||||||||
\(473\) | − | 3.41939e6i | − | 0.702742i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.51470e6 | − | 6.84696e6i | 0.308030 | − | 1.39240i | ||||
\(476\) | 325278. | 0.0658018 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.60213e6i | 1.12146i | ||||||||
\(479\) | 4.22182e6 | 0.840739 | 0.420369 | − | 0.907353i | \(-0.361901\pi\) | ||||
0.420369 | + | 0.907353i | \(0.361901\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.67995e6 | −1.51355 | ||||||||
\(482\) | − | 1.88596e6i | − | 0.369756i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.08200e6 | −0.792063 | ||||||||
\(485\) | 203822. | + | 253840.i | 0.0393457 | + | 0.0490011i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 501465.i | − | 0.0958117i | −0.998852 | − | 0.0479058i | \(-0.984745\pi\) | ||
0.998852 | − | 0.0479058i | \(-0.0152547\pi\) | |||||||
\(488\) | − | 2.44211e6i | − | 0.464212i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.31042e6 | + | 2.87740e6i | 0.434711 | + | 0.541389i | ||||
\(491\) | 2.61435e6 | 0.489395 | 0.244697 | − | 0.969600i | \(-0.421311\pi\) | ||||
0.244697 | + | 0.969600i | \(0.421311\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 548907.i | 0.101714i | ||||||||
\(494\) | −9.85962e6 | −1.81779 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 987136. | 0.180166 | ||||||||
\(497\) | − | 290016.i | − | 0.0526661i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.68240e6 | −1.02160 | −0.510799 | − | 0.859700i | \(-0.670650\pi\) | ||||
−0.510799 | + | 0.859700i | \(0.670650\pi\) | |||||||
\(500\) | −1.23793e6 | − | 2.50600e6i | −0.221447 | − | 0.448287i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 2.40548e6i | − | 0.426033i | ||||||
\(503\) | − | 3.36030e6i | − | 0.592186i | −0.955159 | − | 0.296093i | \(-0.904316\pi\) | ||
0.955159 | − | 0.296093i | \(-0.0956838\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.48628e6 | + | 3.60228e6i | −0.782813 | + | 0.628564i | ||||
\(506\) | −1.29023e6 | −0.224023 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.39757e6i | 0.584129i | ||||||||
\(509\) | −5.60242e6 | −0.958476 | −0.479238 | − | 0.877685i | \(-0.659087\pi\) | ||||
−0.479238 | + | 0.877685i | \(0.659087\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.20992e6 | −0.204977 | ||||||||
\(512\) | − | 262144.i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −496824. | −0.0829459 | ||||||||
\(515\) | 6.24953e6 | + | 7.78316e6i | 1.03832 | + | 1.29312i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.28378e7i | 2.11235i | ||||||||
\(518\) | − | 487616.i | − | 0.0798461i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.06432e6 | + | 2.46051e6i | −0.496965 | + | 0.399041i | ||||
\(521\) | −8.49019e6 | −1.37032 | −0.685162 | − | 0.728391i | \(-0.740269\pi\) | ||||
−0.685162 | + | 0.728391i | \(0.740269\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.31350e6i | 0.529703i | 0.964289 | + | 0.264851i | \(0.0853229\pi\) | ||||
−0.964289 | + | 0.264851i | \(0.914677\pi\) | |||||||
\(524\) | 4.46826e6 | 0.710902 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.71982e6 | −0.271031 | ||||||||
\(527\) | 4.49610e6i | 0.705195i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.18634e6 | 0.961158 | ||||||||
\(530\) | 199812. | − | 160440.i | 0.0308981 | − | 0.0248098i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 626008.i | − | 0.0958960i | ||||||
\(533\) | − | 1.05336e7i | − | 1.60605i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 262920. | + | 327440.i | 0.0397136 | + | 0.0494593i | ||||
\(536\) | −2.31879e6 | −0.348618 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 5.75019e6i | − | 0.856498i | ||||||
\(539\) | 1.06464e7 | 1.57845 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.76958e6 | −0.700627 | −0.350314 | − | 0.936632i | \(-0.613925\pi\) | ||||
−0.350314 | + | 0.936632i | \(0.613925\pi\) | |||||||
\(542\) | − | 6.17891e6i | − | 0.903470i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.19398e6 | 0.172982 | ||||||||
\(545\) | −2.53854e6 | + | 2.03833e6i | −0.366093 | + | 0.293957i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.10402e6i | − | 0.157765i | −0.996884 | − | 0.0788823i | \(-0.974865\pi\) | ||
0.996884 | − | 0.0788823i | \(-0.0251351\pi\) | |||||||
\(548\) | − | 5.40662e6i | − | 0.769086i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.87360e6 | − | 1.74182e6i | −1.10986 | − | 0.245525i | ||||
\(551\) | 1.05639e6 | 0.148233 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 360289.i | 0.0501001i | ||||||||
\(554\) | 844511. | 0.116904 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.48192e6 | 0.203300 | ||||||||
\(557\) | 5.14466e6i | 0.702617i | 0.936260 | + | 0.351308i | \(0.114263\pi\) | ||||
−0.936260 | + | 0.351308i | \(0.885737\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.82221e6 | −0.788058 | ||||||||
\(560\) | −156223. | − | 194560.i | −0.0210511 | − | 0.0262170i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.16205e6i | 0.689416i | ||||||||
\(563\) | − | 9.51894e6i | − | 1.26566i | −0.774290 | − | 0.632831i | \(-0.781893\pi\) | ||
0.774290 | − | 0.632831i | \(-0.218107\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.60599e6 | + | 9.47250e6i | 1.00239 | + | 1.24837i | ||||
\(566\) | −6.79835e6 | −0.891995 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 1.06455e6i | − | 0.138450i | ||||||
\(569\) | −1.29027e6 | −0.167070 | −0.0835352 | − | 0.996505i | \(-0.526621\pi\) | ||||
−0.0835352 | + | 0.996505i | \(0.526621\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.11726e7 | −1.43405 | −0.717024 | − | 0.697048i | \(-0.754496\pi\) | ||||
−0.717024 | + | 0.697048i | \(0.754496\pi\) | |||||||
\(572\) | 1.13380e7i | 1.44892i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 668800. | 0.0847260 | ||||||||
\(575\) | −1.52561e6 | − | 337500.i | −0.192431 | − | 0.0425701i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 129791.i | 0.0162294i | 0.999967 | + | 0.00811472i | \(0.00258302\pi\) | ||||
−0.999967 | + | 0.00811472i | \(0.997417\pi\) | |||||||
\(578\) | − | 241204.i | − | 0.0300307i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 328320. | − | 263626.i | 0.0405254 | − | 0.0325401i | ||||
\(581\) | 1.69069e6 | 0.207790 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 739304.i | − | 0.0900848i | ||||||
\(584\) | −4.44119e6 | −0.538850 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.96593e6 | 1.19887 | ||||||||
\(587\) | 9.30142e6i | 1.11418i | 0.830453 | + | 0.557088i | \(0.188081\pi\) | ||||
−0.830453 | + | 0.557088i | \(0.811919\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.65286e6 | 1.02771 | ||||||||
\(590\) | 5.23103e6 | + | 6.51472e6i | 0.618667 | + | 0.770488i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 1.78987e6i | − | 0.209902i | ||||||
\(593\) | − | 6.91802e6i | − | 0.807876i | −0.914786 | − | 0.403938i | \(-0.867641\pi\) | ||
0.914786 | − | 0.403938i | \(-0.132359\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 886160. | − | 711547.i | 0.102617 | − | 0.0823969i | ||||
\(596\) | 473411. | 0.0545912 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.19689e6i | 0.251220i | ||||||||
\(599\) | −1.57759e7 | −1.79650 | −0.898252 | − | 0.439481i | \(-0.855162\pi\) | ||||
−0.898252 | + | 0.439481i | \(0.855162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.95761e6 | −0.785731 | −0.392866 | − | 0.919596i | \(-0.628516\pi\) | ||||
−0.392866 | + | 0.919596i | \(0.628516\pi\) | |||||||
\(602\) | − | 369664.i | − | 0.0415734i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −646144. | −0.0720671 | ||||||||
\(605\) | −1.11206e7 | + | 8.92938e6i | −1.23521 | + | 0.991819i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.13874e6i | − | 0.676251i | −0.941101 | − | 0.338125i | \(-0.890207\pi\) | ||
0.941101 | − | 0.338125i | \(-0.109793\pi\) | |||||||
\(608\) | − | 2.29786e6i | − | 0.252095i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.34212e6 | − | 6.65307e6i | −0.581285 | − | 0.723932i | ||||
\(611\) | 2.18590e7 | 2.36879 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 5.89321e6i | − | 0.633433i | −0.948520 | − | 0.316717i | \(-0.897420\pi\) | ||
0.948520 | − | 0.316717i | \(-0.102580\pi\) | |||||||
\(614\) | 1.26716e7 | 1.35647 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −719872. | −0.0764370 | ||||||||
\(617\) | − | 9.14737e6i | − | 0.967349i | −0.875248 | − | 0.483675i | \(-0.839302\pi\) | ||
0.875248 | − | 0.483675i | \(-0.160698\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.23318e7 | 1.29360 | 0.646799 | − | 0.762661i | \(-0.276107\pi\) | ||||
0.646799 | + | 0.762661i | \(0.276107\pi\) | |||||||
\(620\) | 2.68927e6 | − | 2.15936e6i | 0.280967 | − | 0.225603i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.94613e6i | 0.927170i | ||||||||
\(623\) | − | 1.04090e6i | − | 0.107445i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.85438e6 | − | 4.11916e6i | −0.906688 | − | 0.421802i | ||||
\(626\) | 9.49403e6 | 0.968311 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 1.30362e6i | − | 0.131903i | ||||||
\(629\) | 8.15229e6 | 0.821586 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.87452e6 | 0.687336 | 0.343668 | − | 0.939091i | \(-0.388331\pi\) | ||||
0.343668 | + | 0.939091i | \(0.388331\pi\) | |||||||
\(632\) | 1.32250e6i | 0.131705i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.95001e6 | −0.390279 | ||||||||
\(635\) | 7.43218e6 | + | 9.25604e6i | 0.731446 | + | 0.910942i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.81276e7i | − | 1.77007i | ||||||
\(638\) | − | 1.21478e6i | − | 0.118154i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −573440. | − | 714162.i | −0.0553399 | − | 0.0689202i | ||||
\(641\) | −9.05120e6 | −0.870084 | −0.435042 | − | 0.900410i | \(-0.643266\pi\) | ||||
−0.435042 | + | 0.900410i | \(0.643266\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.76840e6i | 0.836359i | 0.908364 | + | 0.418179i | \(0.137332\pi\) | ||||
−0.908364 | + | 0.418179i | \(0.862668\pi\) | |||||||
\(644\) | −139485. | −0.0132529 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.04660e7 | 0.986734 | ||||||||
\(647\) | 1.49567e6i | 0.140467i | 0.997531 | + | 0.0702335i | \(0.0223744\pi\) | ||||
−0.997531 | + | 0.0702335i | \(0.977626\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.41045e7 | 2.24639 | ||||||||
\(650\) | −2.96579e6 | + | 1.34064e7i | −0.275333 | + | 1.24460i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 7.33411e6i | − | 0.675660i | ||||||
\(653\) | − | 1.17639e7i | − | 1.07962i | −0.841788 | − | 0.539809i | \(-0.818497\pi\) | ||
0.841788 | − | 0.539809i | \(-0.181503\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.21729e7 | − | 9.77431e6i | 1.10864 | − | 0.890190i | ||||
\(656\) | 2.45493e6 | 0.222731 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.38787e6i | 0.124964i | ||||||||
\(659\) | −3.36184e6 | −0.301553 | −0.150777 | − | 0.988568i | \(-0.548177\pi\) | ||||
−0.150777 | + | 0.988568i | \(0.548177\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.28140e7 | −1.14072 | −0.570361 | − | 0.821394i | \(-0.693197\pi\) | ||||
−0.570361 | + | 0.821394i | \(0.693197\pi\) | |||||||
\(662\) | 3.67458e6i | 0.325883i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.20595e6 | 0.546246 | ||||||||
\(665\) | −1.36939e6 | − | 1.70544e6i | −0.120081 | − | 0.149549i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 235381.i | − | 0.0204859i | ||||||
\(668\) | 3.11098e6i | 0.269746i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.31712e6 | + | 5.07236e6i | −0.543666 | + | 0.436539i | ||||
\(671\) | −2.46164e7 | −2.11066 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.07843e7i | − | 0.917813i | −0.888485 | − | 0.458907i | \(-0.848241\pi\) | ||
0.888485 | − | 0.458907i | \(-0.151759\pi\) | |||||||
\(674\) | 1.42219e6 | 0.120589 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.33645e7 | 1.12483 | ||||||||
\(677\) | − | 1.72031e7i | − | 1.44257i | −0.692640 | − | 0.721283i | \(-0.743553\pi\) | ||
0.692640 | − | 0.721283i | \(-0.256447\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 101536. | 0.00845173 | ||||||||
\(680\) | 3.25278e6 | − | 2.61184e6i | 0.269763 | − | 0.216608i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 9.95029e6i | − | 0.819171i | ||||||
\(683\) | − | 5.61037e6i | − | 0.460193i | −0.973168 | − | 0.230096i | \(-0.926096\pi\) | ||
0.973168 | − | 0.230096i | \(-0.0739041\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.18270e7 | − | 1.47293e7i | −0.963048 | − | 1.19938i | ||||
\(686\) | 2.32312e6 | 0.188478 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 1.35691e6i | − | 0.109290i | ||||||
\(689\) | −1.25882e6 | −0.101022 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.89064e6 | −0.309974 | −0.154987 | − | 0.987916i | \(-0.549534\pi\) | ||||
−0.154987 | + | 0.987916i | \(0.549534\pi\) | |||||||
\(692\) | 5.15555e6i | 0.409270i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.43040e6 | −0.585617 | ||||||||
\(695\) | 4.03721e6 | − | 3.24170e6i | 0.317044 | − | 0.254572i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.11814e7i | 0.871798i | ||||||||
\(698\) | 3.80231e6i | 0.295399i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −851200. | − | 188304.i | −0.0656578 | − | 0.0145250i | ||||
\(701\) | −2.02753e7 | −1.55838 | −0.779190 | − | 0.626788i | \(-0.784369\pi\) | ||||
−0.779190 | + | 0.626788i | \(0.784369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.56893e7i | − | 1.19734i | ||||||
\(704\) | −2.64240e6 | −0.200940 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.07028e6 | 0.231828 | ||||||||
\(707\) | 1.79451e6i | 0.135020i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.60535e6 | 0.119938 | 0.0599688 | − | 0.998200i | \(-0.480900\pi\) | ||||
0.0599688 | + | 0.998200i | \(0.480900\pi\) | |||||||
\(710\) | −2.32870e6 | − | 2.90016e6i | −0.173367 | − | 0.215912i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 3.82077e6i | − | 0.282456i | ||||||
\(713\) | − | 1.92800e6i | − | 0.142031i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.48018e7 | + | 3.08882e7i | 1.81434 | + | 2.25958i | ||||
\(716\) | 6.88413e6 | 0.501842 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 643583.i | 0.0465901i | ||||||||
\(719\) | −1.04392e7 | −0.753090 | −0.376545 | − | 0.926398i | \(-0.622888\pi\) | ||||
−0.376545 | + | 0.926398i | \(0.622888\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.11326e6 | 0.223037 | ||||||||
\(722\) | − | 1.02377e7i | − | 0.730906i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.88035e6 | −0.275122 | ||||||||
\(725\) | 317764. | − | 1.43640e6i | 0.0224522 | − | 0.101492i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.36879e7i | 1.66223i | 0.556102 | + | 0.831114i | \(0.312297\pi\) | ||||
−0.556102 | + | 0.831114i | \(0.687703\pi\) | |||||||
\(728\) | 1.22573e6i | 0.0857167i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.20992e7 | + | 9.71511e6i | −0.840329 | + | 0.674747i | ||||
\(731\) | 6.18029e6 | 0.427775 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.14116e7i | 0.784487i | 0.919861 | + | 0.392244i | \(0.128301\pi\) | ||||
−0.919861 | + | 0.392244i | \(0.871699\pi\) | |||||||
\(734\) | 808523. | 0.0553927 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −512000. | −0.0348398 | ||||||||
\(737\) | 2.33733e7i | 1.58508i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.57126e7 | −1.73195 | −0.865975 | − | 0.500088i | \(-0.833301\pi\) | ||||
−0.865975 | + | 0.500088i | \(0.833301\pi\) | |||||||
\(740\) | −3.91534e6 | − | 4.87616e6i | −0.262839 | − | 0.327340i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 79924.8i | − | 0.00532932i | ||||||
\(743\) | − | 7.87830e6i | − | 0.523553i | −0.965129 | − | 0.261776i | \(-0.915692\pi\) | ||
0.965129 | − | 0.261776i | \(-0.0843083\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.28972e6 | − | 1.03559e6i | 0.0851343 | − | 0.0683590i | ||||
\(746\) | 5.95732e6 | 0.391926 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1.20353e7i | − | 0.786508i | ||||||
\(749\) | 130976. | 0.00853076 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.69649e7 | −1.74461 | −0.872306 | − | 0.488961i | \(-0.837376\pi\) | ||||
−0.872306 | + | 0.488961i | \(0.837376\pi\) | |||||||
\(752\) | 5.09440e6i | 0.328510i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.06842e6 | −0.132498 | ||||||||
\(755\) | −1.76030e6 | + | 1.41344e6i | −0.112388 | + | 0.0902423i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.92135e6i | 0.248712i | 0.992238 | + | 0.124356i | \(0.0396864\pi\) | ||||
−0.992238 | + | 0.124356i | \(0.960314\pi\) | |||||||
\(758\) | 1.07689e7i | 0.680765i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.02656e6 | − | 6.26008e6i | −0.315673 | − | 0.393139i | ||||
\(761\) | 2.84849e7 | 1.78301 | 0.891504 | − | 0.453013i | \(-0.149651\pi\) | ||||
0.891504 | + | 0.453013i | \(0.149651\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.01541e6i | 0.0631440i | ||||||||
\(764\) | 4.65489e6 | 0.288520 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.26040e6 | 0.139192 | ||||||||
\(767\) | − | 4.10427e7i | − | 2.51911i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.18935e6 | 0.316444 | 0.158222 | − | 0.987404i | \(-0.449424\pi\) | ||||
0.158222 | + | 0.987404i | \(0.449424\pi\) | |||||||
\(770\) | −1.96116e6 | + | 1.57472e6i | −0.119202 | + | 0.0957142i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.15689e7i | 0.698631i | ||||||||
\(773\) | 1.88767e7i | 1.13626i | 0.822939 | + | 0.568130i | \(0.192333\pi\) | ||||
−0.822939 | + | 0.568130i | \(0.807667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.60280e6 | − | 1.17655e7i | 0.155663 | − | 0.703651i | ||||
\(776\) | 372703. | 0.0222182 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.18635e7i | 1.29500i | ||||||||
\(779\) | 2.15190e7 | 1.27051 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.07306e7 | −0.629501 | ||||||||
\(782\) | − | 2.33200e6i | − | 0.136368i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.22477e6 | 0.245478 | ||||||||
\(785\) | −2.85168e6 | − | 3.55148e6i | −0.165168 | − | 0.205700i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.73159e7i | − | 0.996570i | −0.867013 | − | 0.498285i | \(-0.833963\pi\) | ||
0.867013 | − | 0.498285i | \(-0.166037\pi\) | |||||||
\(788\) | − | 9.59421e6i | − | 0.550419i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.89296e6 | + | 3.60289e6i | 0.164921 | + | 0.205392i | ||||
\(791\) | 3.78900e6 | 0.215319 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.19144e7i | 2.36690i | ||||||||
\(794\) | −1.60305e7 | −0.902393 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.04029e7 | 0.581934 | ||||||||
\(797\) | 2.62525e7i | 1.46394i | 0.681335 | + | 0.731972i | \(0.261400\pi\) | ||||
−0.681335 | + | 0.731972i | \(0.738600\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.32034e7 | −1.28583 | ||||||||
\(800\) | −3.12446e6 | − | 691200.i | −0.172604 | − | 0.0381838i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.57187e7i | 0.862939i | ||||||||
\(803\) | 4.47670e7i | 2.45002i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −380000. | + | 305123.i | −0.0206678 | + | 0.0165953i | ||||
\(806\) | −1.69424e7 | −0.918622 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.58703e6i | 0.354945i | ||||||||
\(809\) | 3.02992e6 | 0.162765 | 0.0813824 | − | 0.996683i | \(-0.474067\pi\) | ||||
0.0813824 | + | 0.996683i | \(0.474067\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.81951e6 | 0.524249 | 0.262124 | − | 0.965034i | \(-0.415577\pi\) | ||||
0.262124 | + | 0.965034i | \(0.415577\pi\) | |||||||
\(812\) | − | 131328.i | − | 0.00698984i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.80418e7 | −0.954374 | ||||||||
\(815\) | −1.60434e7 | − | 1.99804e7i | −0.846060 | − | 1.05368i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.18941e7i | − | 0.623416i | ||||||
\(818\) | − | 4.60113e6i | − | 0.240426i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.68800e6 | − | 5.37016e6i | 0.347345 | − | 0.278903i | ||||
\(821\) | 5.80196e6 | 0.300411 | 0.150206 | − | 0.988655i | \(-0.452006\pi\) | ||||
0.150206 | + | 0.988655i | \(0.452006\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.31473e7i | − | 0.676606i | −0.941037 | − | 0.338303i | \(-0.890147\pi\) | ||
0.941037 | − | 0.338303i | \(-0.109853\pi\) | |||||||
\(824\) | 1.14277e7 | 0.586329 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.60589e6 | 0.132894 | ||||||||
\(827\) | 2.77989e7i | 1.41340i | 0.707515 | + | 0.706698i | \(0.249816\pi\) | ||||
−0.707515 | + | 0.706698i | \(0.750184\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.08971e7 | 0.550714 | 0.275357 | − | 0.961342i | \(-0.411204\pi\) | ||||
0.275357 | + | 0.961342i | \(0.411204\pi\) | |||||||
\(830\) | 1.69069e7 | − | 1.35755e7i | 0.851863 | − | 0.684008i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.49922e6i | 0.225335i | ||||||||
\(833\) | 1.92425e7i | 0.960835i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.80526e6 | + | 8.47527e6i | 0.337776 | + | 0.420666i | ||||
\(836\) | −2.31623e7 | −1.14621 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 1.98359e7i | − | 0.975758i | ||||||
\(839\) | −1.13976e7 | −0.558995 | −0.279497 | − | 0.960146i | \(-0.590168\pi\) | ||||
−0.279497 | + | 0.960146i | \(0.590168\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.02895e7 | −0.989195 | ||||||||
\(842\) | − | 1.15631e7i | − | 0.562075i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.57811e7 | −0.762570 | ||||||||
\(845\) | 3.64091e7 | − | 2.92349e7i | 1.75416 | − | 1.40851i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.44826e6i | 0.213050i | ||||||||
\(848\) | − | 293376.i | − | 0.0140099i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.14820e6 | − | 1.42309e7i | 0.149457 | − | 0.675594i | ||||
\(851\) | −3.49584e6 | −0.165473 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.97544e6i | 0.234131i | 0.993124 | + | 0.117065i | \(0.0373487\pi\) | ||||
−0.993124 | + | 0.117065i | \(0.962651\pi\) | |||||||
\(854\) | −2.66123e6 | −0.124864 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 480768. | 0.0224260 | ||||||||
\(857\) | − | 2.38632e7i | − | 1.10988i | −0.831889 | − | 0.554942i | \(-0.812741\pi\) | ||
0.831889 | − | 0.554942i | \(-0.187259\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.49286e7 | −0.690298 | −0.345149 | − | 0.938548i | \(-0.612172\pi\) | ||||
−0.345149 | + | 0.938548i | \(0.612172\pi\) | |||||||
\(860\) | −2.96824e6 | − | 3.69664e6i | −0.136852 | − | 0.170436i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 7.93668e6i | − | 0.363807i | ||||||
\(863\) | − | 9.90376e6i | − | 0.452661i | −0.974051 | − | 0.226330i | \(-0.927327\pi\) | ||
0.974051 | − | 0.226330i | \(-0.0726729\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.12778e7 | + | 1.40453e7i | 0.512487 | + | 0.638251i | ||||
\(866\) | −1.50249e7 | −0.680795 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 1.07571e6i | − | 0.0484612i | ||||||
\(869\) | 1.33307e7 | 0.598830 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.97979e7 | 1.77752 | ||||||||
\(872\) | 3.72723e6i | 0.165995i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.48800e6 | −0.198735 | ||||||||
\(875\) | −2.73085e6 | + | 1.34900e6i | −0.120581 | + | 0.0595651i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.84422e6i | 0.168775i | 0.996433 | + | 0.0843877i | \(0.0268934\pi\) | ||||
−0.996433 | + | 0.0843877i | \(0.973107\pi\) | |||||||
\(878\) | 7.79587e6i | 0.341294i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7.19872e6 | + | 5.78025e6i | −0.313364 | + | 0.251617i | ||||
\(881\) | 2.94025e7 | 1.27627 | 0.638137 | − | 0.769922i | \(-0.279705\pi\) | ||||
0.638137 | + | 0.769922i | \(0.279705\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 6.24156e6i | − | 0.269396i | −0.990887 | − | 0.134698i | \(-0.956994\pi\) | ||
0.990887 | − | 0.134698i | \(-0.0430065\pi\) | |||||||
\(884\) | −2.04925e7 | −0.881993 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.29679e7 | 0.982963 | ||||||||
\(887\) | − | 1.67076e7i | − | 0.713025i | −0.934291 | − | 0.356512i | \(-0.883966\pi\) | ||
0.934291 | − | 0.356512i | \(-0.116034\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.70242e6 | 0.157120 | ||||||||
\(890\) | −8.35793e6 | − | 1.04090e7i | −0.353691 | − | 0.440486i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 1.11105e7i | − | 0.467544i | ||||||
\(893\) | 4.46556e7i | 1.87390i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.87545e7 | − | 1.50590e7i | 0.782615 | − | 0.628405i | ||||
\(896\) | −285665. | −0.0118874 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 2.15462e6i | − | 0.0891621i | ||||||
\(899\) | 1.81525e6 | 0.0749098 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.33624e6 | 0.0548367 | ||||||||
\(902\) | − | 2.47456e7i | − | 1.01270i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.39081e7 | 0.566039 | ||||||||
\(905\) | −1.05713e7 | + | 8.48827e6i | −0.429049 | + | 0.344507i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 7.14197e6i | − | 0.288270i | −0.989558 | − | 0.144135i | \(-0.953960\pi\) | ||
0.989558 | − | 0.144135i | \(-0.0460400\pi\) | |||||||
\(908\) | 6.96640e6i | 0.280410i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.68128e6 | + | 3.33927e6i | 0.107334 | + | 0.133674i | ||||
\(911\) | −3.51083e7 | −1.40157 | −0.700784 | − | 0.713374i | \(-0.747166\pi\) | ||||
−0.700784 | + | 0.713374i | \(0.747166\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 6.25557e7i | − | 2.48365i | ||||||
\(914\) | −6.21837e6 | −0.246213 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.85796e7 | −0.731641 | ||||||||
\(917\) | − | 4.86917e6i | − | 0.191219i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.66789e7 | −1.04203 | −0.521014 | − | 0.853548i | \(-0.674446\pi\) | ||||
−0.521014 | + | 0.853548i | \(0.674446\pi\) | |||||||
\(920\) | −1.39485e6 | + | 1.12000e6i | −0.0543322 | + | 0.0436263i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 1.68978e7i | − | 0.654641i | ||||||
\(923\) | 1.82710e7i | 0.705925i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.13332e7 | − | 4.71938e6i | −0.819788 | − | 0.181355i | ||||
\(926\) | 1.90939e7 | 0.731756 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 482059.i | − | 0.0183751i | ||||||
\(929\) | −6.04426e6 | −0.229776 | −0.114888 | − | 0.993378i | \(-0.536651\pi\) | ||||
−0.114888 | + | 0.993378i | \(0.536651\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.70327e7 | 1.40027 | ||||||||
\(932\) | − | 1.94085e7i | − | 0.731902i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.64673e7 | 1.36784 | ||||||||
\(935\) | −2.63272e7 | − | 3.27879e7i | −0.984864 | − | 1.22655i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.60422e6i | − | 0.134110i | −0.997749 | − | 0.0670551i | \(-0.978640\pi\) | ||
0.997749 | − | 0.0670551i | \(-0.0213603\pi\) | |||||||
\(938\) | 2.52685e6i | 0.0937718i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.11440e7 | + | 1.38787e7i | 0.411359 | + | 0.512307i | ||||
\(941\) | 1.30244e7 | 0.479495 | 0.239747 | − | 0.970835i | \(-0.422935\pi\) | ||||
0.239747 | + | 0.970835i | \(0.422935\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.79479e6i | − | 0.175586i | ||||||
\(944\) | 9.56531e6 | 0.349357 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.36776e7 | −0.496914 | ||||||||
\(947\) | − | 3.17698e7i | − | 1.15117i | −0.817742 | − | 0.575585i | \(-0.804774\pi\) | ||
0.817742 | − | 0.575585i | \(-0.195226\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.62250e7 | 2.74746 | ||||||||
\(950\) | −2.73878e7 | − | 6.05880e6i | −0.984575 | − | 0.217810i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 1.30111e6i | − | 0.0465289i | ||||||
\(953\) | 2.25254e7i | 0.803417i | 0.915768 | + | 0.401708i | \(0.131583\pi\) | ||||
−0.915768 | + | 0.401708i | \(0.868417\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.26814e7 | − | 1.01826e7i | 0.449943 | − | 0.361284i | ||||
\(956\) | 2.24085e7 | 0.792991 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 1.68873e7i | − | 0.594492i | ||||||
\(959\) | −5.89173e6 | −0.206869 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.37604e7 | −0.480643 | ||||||||
\(962\) | 3.07198e7i | 1.07024i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.54384e6 | −0.261457 | ||||||||
\(965\) | 2.53069e7 | + | 3.15172e7i | 0.874824 | + | 1.08951i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 169805.i | − | 0.00583963i | −0.999996 | − | 0.00291981i | \(-0.999071\pi\) | ||
0.999996 | − | 0.00291981i | \(-0.000929407\pi\) | |||||||
\(968\) | 1.63280e7i | 0.560073i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.01536e6 | − | 815288.i | 0.0346490 | − | 0.0278216i | ||||
\(971\) | 164296. | 0.00559214 | 0.00279607 | − | 0.999996i | \(-0.499110\pi\) | ||||
0.00279607 | + | 0.999996i | \(0.499110\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.61488e6i | − | 0.0546839i | ||||||
\(974\) | −2.00586e6 | −0.0677491 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.76845e6 | −0.328247 | ||||||||
\(977\) | 2.00989e7i | 0.673653i | 0.941567 | + | 0.336827i | \(0.109354\pi\) | ||||
−0.941567 | + | 0.336827i | \(0.890646\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.85132e7 | −1.28426 | ||||||||
\(980\) | 1.15096e7 | − | 9.24168e6i | 0.382820 | − | 0.307387i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 1.04574e7i | − | 0.346054i | ||||||
\(983\) | − | 1.39716e7i | − | 0.461172i | −0.973052 | − | 0.230586i | \(-0.925936\pi\) | ||
0.973052 | − | 0.230586i | \(-0.0740644\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.09873e7 | − | 2.61376e7i | −0.689234 | − | 0.858372i | ||||
\(986\) | 2.19563e6 | 0.0719228 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.94385e7i | 1.28537i | ||||||||
\(989\) | −2.65021e6 | −0.0861568 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 140392. | 0.00454107 | 0.00227054 | − | 0.999997i | \(-0.499277\pi\) | ||||
0.00227054 | + | 0.999997i | \(0.499277\pi\) | |||||||
\(992\) | − | 3.94854e6i | − | 0.127397i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.16006e6 | −0.0372405 | ||||||||
\(995\) | 2.83409e7 | − | 2.27564e7i | 0.907518 | − | 0.728696i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.79809e7i | 0.572894i | 0.958096 | + | 0.286447i | \(0.0924742\pi\) | ||||
−0.958096 | + | 0.286447i | \(0.907526\pi\) | |||||||
\(998\) | 2.27296e7i | 0.722379i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 90.6.c.d.19.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 90.6.c.d.19.4 | yes | 4 | |
4.3 | odd | 2 | 720.6.f.j.289.2 | 4 | |||
5.2 | odd | 4 | 450.6.a.be.1.1 | 2 | |||
5.3 | odd | 4 | 450.6.a.z.1.2 | 2 | |||
5.4 | even | 2 | inner | 90.6.c.d.19.3 | yes | 4 | |
12.11 | even | 2 | 720.6.f.j.289.3 | 4 | |||
15.2 | even | 4 | 450.6.a.z.1.1 | 2 | |||
15.8 | even | 4 | 450.6.a.be.1.2 | 2 | |||
15.14 | odd | 2 | inner | 90.6.c.d.19.2 | yes | 4 | |
20.19 | odd | 2 | 720.6.f.j.289.1 | 4 | |||
60.59 | even | 2 | 720.6.f.j.289.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.6.c.d.19.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
90.6.c.d.19.2 | yes | 4 | 15.14 | odd | 2 | inner | |
90.6.c.d.19.3 | yes | 4 | 5.4 | even | 2 | inner | |
90.6.c.d.19.4 | yes | 4 | 3.2 | odd | 2 | inner | |
450.6.a.z.1.1 | 2 | 15.2 | even | 4 | |||
450.6.a.z.1.2 | 2 | 5.3 | odd | 4 | |||
450.6.a.be.1.1 | 2 | 5.2 | odd | 4 | |||
450.6.a.be.1.2 | 2 | 15.8 | even | 4 | |||
720.6.f.j.289.1 | 4 | 20.19 | odd | 2 | |||
720.6.f.j.289.2 | 4 | 4.3 | odd | 2 | |||
720.6.f.j.289.3 | 4 | 12.11 | even | 2 | |||
720.6.f.j.289.4 | 4 | 60.59 | even | 2 |