Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,6,Mod(47,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("160.47");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.o (of order \(4\), degree \(2\), 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: | \(25.6614111701\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.11 | ||
Character | \(\chi\) | \(=\) | 160.47 |
Dual form | 160.6.o.a.143.11 |
$q$-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 \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −4.45554 | + | 4.45554i | −0.285823 | + | 0.285823i | −0.835426 | − | 0.549603i | \(-0.814779\pi\) |
0.549603 | + | 0.835426i | \(0.314779\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 49.9881 | + | 25.0237i | 0.894215 | + | 0.447638i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 169.279 | − | 169.279i | 1.30574 | − | 1.30574i | 0.381287 | − | 0.924457i | \(-0.375481\pi\) |
0.924457 | − | 0.381287i | \(-0.124519\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 203.296i | 0.836610i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 207.026 | 0.515874 | 0.257937 | − | 0.966162i | \(-0.416957\pi\) | ||||
0.257937 | + | 0.966162i | \(0.416957\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −249.136 | − | 249.136i | −0.408864 | − | 0.408864i | 0.472478 | − | 0.881342i | \(-0.343360\pi\) |
−0.881342 | + | 0.472478i | \(0.843360\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −334.219 | + | 111.230i | −0.383533 | + | 0.127642i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −424.145 | − | 424.145i | −0.355952 | − | 0.355952i | 0.506366 | − | 0.862318i | \(-0.330988\pi\) |
−0.862318 | + | 0.506366i | \(0.830988\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2282.02i | − | 1.45022i | −0.688631 | − | 0.725112i | \(-0.741788\pi\) | ||
0.688631 | − | 0.725112i | \(-0.258212\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1508.46i | 0.746424i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −351.205 | − | 351.205i | −0.138433 | − | 0.138433i | 0.634494 | − | 0.772928i | \(-0.281208\pi\) |
−0.772928 | + | 0.634494i | \(0.781208\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1872.62 | + | 2501.78i | 0.599240 | + | 0.800569i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1988.49 | − | 1988.49i | −0.524946 | − | 0.524946i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7256.22 | 1.60219 | 0.801097 | − | 0.598534i | \(-0.204250\pi\) | ||||
0.801097 | + | 0.598534i | \(0.204250\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7244.36i | 1.35393i | 0.736016 | + | 0.676964i | \(0.236705\pi\) | ||||
−0.736016 | + | 0.676964i | \(0.763295\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −922.415 | + | 922.415i | −0.147449 | + | 0.147449i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12697.9 | − | 4225.95i | 1.75212 | − | 0.583114i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 266.347 | − | 266.347i | 0.0319848 | − | 0.0319848i | −0.690933 | − | 0.722918i | \(-0.742800\pi\) |
0.722918 | + | 0.690933i | \(0.242800\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2220.08 | 0.233726 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16812.6 | 1.56198 | 0.780990 | − | 0.624543i | \(-0.214715\pi\) | ||||
0.780990 | + | 0.624543i | \(0.214715\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4601.16 | − | 4601.16i | 0.379486 | − | 0.379486i | −0.491431 | − | 0.870917i | \(-0.663526\pi\) |
0.870917 | + | 0.491431i | \(0.163526\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5087.23 | + | 10162.4i | −0.374499 | + | 0.748109i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5614.39 | − | 5614.39i | 0.370730 | − | 0.370730i | −0.497013 | − | 0.867743i | \(-0.665570\pi\) |
0.867743 | + | 0.497013i | \(0.165570\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 40503.7i | − | 2.40993i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3779.59 | 0.203479 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 937.132 | + | 937.132i | 0.0458259 | + | 0.0458259i | 0.729648 | − | 0.683822i | \(-0.239684\pi\) |
−0.683822 | + | 0.729648i | \(0.739684\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10348.9 | + | 5180.57i | 0.461302 | + | 0.230925i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10167.6 | + | 10167.6i | 0.414508 | + | 0.414508i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 16983.7i | 0.635189i | 0.948227 | + | 0.317595i | \(0.102875\pi\) | ||||
−0.948227 | + | 0.317595i | \(0.897125\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 27237.2i | 0.937212i | 0.883407 | + | 0.468606i | \(0.155244\pi\) | ||||
−0.883407 | + | 0.468606i | \(0.844756\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 34413.8 | + | 34413.8i | 1.09240 | + | 1.09240i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6219.54 | − | 18688.2i | −0.182589 | − | 0.548635i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7571.99 | + | 7571.99i | 0.206074 | + | 0.206074i | 0.802596 | − | 0.596523i | \(-0.203451\pi\) |
−0.596523 | + | 0.802596i | \(0.703451\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3129.62 | 0.0791350 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 17125.0i | − | 0.403167i | −0.979471 | − | 0.201583i | \(-0.935391\pi\) | ||
0.979471 | − | 0.201583i | \(-0.0646087\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15977.8 | − | 15977.8i | 0.350922 | − | 0.350922i | −0.509530 | − | 0.860453i | \(-0.670181\pi\) |
0.860453 | + | 0.509530i | \(0.170181\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −19490.4 | − | 2803.23i | −0.400098 | − | 0.0575447i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 35045.2 | − | 35045.2i | 0.673599 | − | 0.673599i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −72486.1 | −1.30673 | −0.653367 | − | 0.757041i | \(-0.726644\pi\) | ||||
−0.653367 | + | 0.757041i | \(0.726644\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −31681.3 | −0.536526 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 58657.5 | − | 58657.5i | 0.934606 | − | 0.934606i | −0.0633833 | − | 0.997989i | \(-0.520189\pi\) |
0.997989 | + | 0.0633833i | \(0.0201891\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10588.5 | − | 31815.9i | −0.158960 | − | 0.477636i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −32330.4 | + | 32330.4i | −0.457944 | + | 0.457944i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 34335.8i | 0.459486i | 0.973251 | + | 0.229743i | \(0.0737886\pi\) | ||||
−0.973251 | + | 0.229743i | \(0.926211\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −84347.1 | −1.06774 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −32277.6 | − | 32277.6i | −0.386984 | − | 0.386984i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 57104.6 | − | 114074.i | 0.649176 | − | 1.29681i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 62650.0 | + | 62650.0i | 0.676070 | + | 0.676070i | 0.959109 | − | 0.283039i | \(-0.0913425\pi\) |
−0.283039 | + | 0.959109i | \(0.591342\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 42087.6i | 0.431585i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 79446.8i | 0.774948i | 0.921881 | + | 0.387474i | \(0.126652\pi\) | ||||
−0.921881 | + | 0.387474i | \(0.873348\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15635.6 | + | 15635.6i | 0.145219 | + | 0.145219i | 0.775978 | − | 0.630760i | \(-0.217257\pi\) |
−0.630760 | + | 0.775978i | \(0.717257\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −37747.3 | + | 75405.1i | −0.334128 | + | 0.667463i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18399.8 | + | 18399.8i | 0.155365 | + | 0.155365i | 0.780509 | − | 0.625144i | \(-0.214960\pi\) |
−0.625144 | + | 0.780509i | \(0.714960\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −30952.5 | −0.249534 | −0.124767 | − | 0.992186i | \(-0.539818\pi\) | ||||
−0.124767 | + | 0.992186i | \(0.539818\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2373.45i | 0.0182840i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −125022. | + | 125022.i | −0.921068 | + | 0.921068i | −0.997105 | − | 0.0760370i | \(-0.975773\pi\) |
0.0760370 | + | 0.997105i | \(0.475773\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8767.62 | − | 26344.5i | −0.0618211 | − | 0.185757i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 50648.5 | − | 50648.5i | 0.342060 | − | 0.342060i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −143598. | −0.929565 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −118191. | −0.733874 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −74909.4 | + | 74909.4i | −0.446451 | + | 0.446451i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 31005.1 | + | 171919.i | 0.177484 | + | 0.984124i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5560.02 | − | 5560.02i | 0.0305892 | − | 0.0305892i | −0.691647 | − | 0.722236i | \(-0.743114\pi\) |
0.722236 | + | 0.691647i | \(0.243114\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 41001.3i | 0.216932i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −207693. | −1.05741 | −0.528705 | − | 0.848805i | \(-0.677322\pi\) | ||||
−0.528705 | + | 0.848805i | \(0.677322\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −386298. | − | 386298.i | −1.89362 | − | 1.89362i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −49641.5 | − | 149161.i | −0.234429 | − | 0.704400i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −254454. | − | 254454.i | −1.15827 | − | 1.15827i | −0.984848 | − | 0.173418i | \(-0.944519\pi\) |
−0.173418 | − | 0.984848i | \(-0.555481\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 145526.i | − | 0.638856i | −0.947610 | − | 0.319428i | \(-0.896509\pi\) | ||
0.947610 | − | 0.319428i | \(-0.103491\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 50030.3i | 0.211927i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −51577.8 | − | 51577.8i | −0.210922 | − | 0.210922i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 362725. | + | 181578.i | 1.43271 | + | 0.717203i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 180466. | + | 180466.i | 0.688815 | + | 0.688815i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 209820. | 0.774252 | 0.387126 | − | 0.922027i | \(-0.373468\pi\) | ||||
0.387126 | + | 0.922027i | \(0.373468\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 91400.1i | 0.326215i | 0.986608 | + | 0.163108i | \(0.0521518\pi\) | ||||
−0.986608 | + | 0.163108i | \(0.947848\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 86227.0 | − | 86227.0i | 0.297793 | − | 0.297793i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −181281. | + | 362132.i | −0.606070 | + | 1.21070i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 239586. | − | 239586.i | 0.775734 | − | 0.775734i | −0.203368 | − | 0.979102i | \(-0.565189\pi\) |
0.979102 | + | 0.203368i | \(0.0651888\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8350.87 | −0.0261962 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −118903. | −0.361517 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −235878. | + | 235878.i | −0.695375 | + | 0.695375i | −0.963409 | − | 0.268034i | \(-0.913626\pi\) |
0.268034 | + | 0.963409i | \(0.413626\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −69192.0 | + | 23027.5i | −0.197855 | + | 0.0658472i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 28120.6 | − | 28120.6i | 0.0780249 | − | 0.0780249i | −0.667017 | − | 0.745042i | \(-0.732429\pi\) |
0.745042 | + | 0.667017i | \(0.232429\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 247155.i | − | 0.665660i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 463926. | 1.21327 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 65641.2 | + | 65641.2i | 0.166748 | + | 0.166748i | 0.785548 | − | 0.618800i | \(-0.212381\pi\) |
−0.618800 | + | 0.785548i | \(0.712381\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 740495. | + | 106503.i | 1.82779 | + | 0.262885i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −75671.8 | − | 75671.8i | −0.181552 | − | 0.181552i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 377529.i | − | 0.880679i | −0.897831 | − | 0.440340i | \(-0.854858\pi\) | ||
0.897831 | − | 0.440340i | \(-0.145142\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 523723.i | 1.18824i | 0.804376 | + | 0.594121i | \(0.202500\pi\) | ||||
−0.804376 | + | 0.594121i | \(0.797500\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −121357. | − | 121357.i | −0.267877 | − | 0.267877i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19979.2 | − | 6649.20i | 0.0429190 | − | 0.0142837i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −87809.1 | − | 87809.1i | −0.183626 | − | 0.183626i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −673220. | −1.37089 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 601520.i | 1.19307i | 0.802586 | + | 0.596536i | \(0.203457\pi\) | ||||
−0.802586 | + | 0.596536i | \(0.796543\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 423362. | − | 423362.i | 0.818123 | − | 0.818123i | −0.167713 | − | 0.985836i | \(-0.553638\pi\) |
0.985836 | + | 0.167713i | \(0.0536381\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 110977. | + | 55554.6i | 0.209001 | + | 0.104625i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −164947. | + | 164947.i | −0.302815 | + | 0.302815i | −0.842114 | − | 0.539299i | \(-0.818689\pi\) |
0.539299 | + | 0.842114i | \(0.318689\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −609467. | −1.09098 | −0.545491 | − | 0.838117i | \(-0.683657\pi\) | ||||
−0.545491 | + | 0.838117i | \(0.683657\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −67474.7 | −0.117801 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.22832e6 | − | 1.22832e6i | 2.09205 | − | 2.09205i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 840431. | + | 420715.i | 1.39675 | + | 0.699202i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 71398.7 | − | 71398.7i | 0.115815 | − | 0.115815i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 472437.i | − | 0.748133i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −582093. | −0.900090 | −0.450045 | − | 0.893006i | \(-0.648592\pi\) | ||||
−0.450045 | + | 0.893006i | \(0.648592\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 76301.2 | + | 76301.2i | 0.115234 | + | 0.115234i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 345141. | − | 114865.i | 0.509215 | − | 0.169470i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.22632e6 | + | 1.22632e6i | 1.76788 | + | 1.76788i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 142380.i | 0.200604i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 211340.i | 0.291072i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27105.9 | + | 27105.9i | 0.0365007 | + | 0.0365007i | 0.725122 | − | 0.688621i | \(-0.241784\pi\) |
−0.688621 | + | 0.725122i | \(0.741784\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −508602. | + | 380698.i | −0.669764 | + | 0.501330i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23392.5 | + | 23392.5i | 0.0301309 | + | 0.0301309i | 0.722012 | − | 0.691881i | \(-0.243218\pi\) |
−0.691881 | + | 0.722012i | \(0.743218\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 637450. | 0.803262 | 0.401631 | − | 0.915801i | \(-0.368443\pi\) | ||||
0.401631 | + | 0.915801i | \(0.368443\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 312291.i | 0.385061i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 401694. | − | 401694.i | 0.484737 | − | 0.484737i | −0.421904 | − | 0.906641i | \(-0.638638\pi\) |
0.906641 | + | 0.421904i | \(0.138638\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 421146. | − | 140160.i | 0.497465 | − | 0.165559i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 322965. | − | 322965.i | 0.373495 | − | 0.373495i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 797896. | 0.903548 | 0.451774 | − | 0.892132i | \(-0.350791\pi\) | ||||
0.451774 | + | 0.892132i | \(0.350791\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −313970. | −0.348214 | −0.174107 | − | 0.984727i | \(-0.555704\pi\) | ||||
−0.174107 | + | 0.984727i | \(0.555704\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 624361. | − | 624361.i | 0.678298 | − | 0.678298i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.01356e6 | − | 2.02471e6i | 1.07878 | − | 2.15500i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −568534. | + | 568534.i | −0.592944 | + | 0.592944i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 522703.i | 0.534264i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −972796. | −0.974624 | −0.487312 | − | 0.873228i | \(-0.662023\pi\) | ||||
−0.487312 | + | 0.873228i | \(0.662023\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −72708.6 | − | 72708.6i | −0.0714142 | − | 0.0714142i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 188935. | + | 94579.5i | 0.181954 | + | 0.0910849i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −736633. | − | 736633.i | −0.695694 | − | 0.695694i | 0.267785 | − | 0.963479i | \(-0.413708\pi\) |
−0.963479 | + | 0.267785i | \(0.913708\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 90174.1i | − | 0.0835280i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.47516e6i | 1.34041i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.10841e6 | − | 1.10841e6i | −0.988125 | − | 0.988125i | 0.0118057 | − | 0.999930i | \(-0.496242\pi\) |
−0.999930 | + | 0.0118057i | \(0.996242\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23394.9 | + | 70296.0i | 0.0204648 | + | 0.0614916i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −152985. | − | 152985.i | −0.131332 | − | 0.131332i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.08719e6 | −1.75866 | −0.879328 | − | 0.476216i | \(-0.842008\pi\) | ||||
−0.879328 | + | 0.476216i | \(0.842008\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 869347.i | 0.719068i | 0.933132 | + | 0.359534i | \(0.117064\pi\) | ||||
−0.933132 | + | 0.359534i | \(0.882936\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 375812. | − | 375812.i | 0.305186 | − | 0.305186i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 387682. | + | 517934.i | 0.309132 | + | 0.412993i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.39022e6 | + | 1.39022e6i | −1.08864 | + | 1.08864i | −0.0929676 | + | 0.995669i | \(0.529635\pi\) |
−0.995669 | + | 0.0929676i | \(0.970365\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.47275e6 | −1.13271 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −620023. | −0.468427 | −0.234214 | − | 0.972185i | \(-0.575252\pi\) | ||||
−0.234214 | + | 0.972185i | \(0.575252\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.76320e6 | + | 1.76320e6i | −1.30869 | + | 1.30869i | −0.386327 | + | 0.922362i | \(0.626256\pi\) |
−0.922362 | + | 0.386327i | \(0.873744\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 253829. | + | 762693.i | 0.185109 | + | 0.556209i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.84602e6 | − | 2.84602e6i | 2.03955 | − | 2.03955i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.06006e6i | − | 0.746596i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −558280. | −0.386473 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −729494. | − | 729494.i | −0.496424 | − | 0.496424i | 0.413899 | − | 0.910323i | \(-0.364167\pi\) |
−0.910323 | + | 0.413899i | \(0.864167\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −424997. | + | 848985.i | −0.284335 | + | 0.567996i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −411670. | − | 411670.i | −0.270806 | − | 0.270806i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 174996.i | 0.113201i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1.55776e6i | − | 0.991023i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −353979. | − | 353979.i | −0.221498 | − | 0.221498i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −681577. | + | 1.36154e6i | −0.419532 | + | 0.838069i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 907649. | + | 907649.i | 0.549632 | + | 0.549632i | 0.926334 | − | 0.376702i | \(-0.122942\pi\) |
−0.376702 | + | 0.926334i | \(0.622942\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −139331. | −0.0830138 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.31610e6i | 0.771594i | 0.922584 | + | 0.385797i | \(0.126073\pi\) | ||||
−0.922584 | + | 0.385797i | \(0.873927\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −896253. | + | 896253.i | −0.517094 | + | 0.517094i | −0.916691 | − | 0.399597i | \(-0.869150\pi\) |
0.399597 | + | 0.916691i | \(0.369150\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 859119. | + | 2.58144e6i | 0.487839 | + | 1.46584i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.81983e6 | − | 1.81983e6i | 1.01715 | − | 1.01715i | 0.0172954 | − | 0.999850i | \(-0.494494\pi\) |
0.999850 | − | 0.0172954i | \(-0.00550557\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.50223e6 | 0.826530 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −163963. | −0.0888141 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −967906. | + | 967906.i | −0.516210 | + | 0.516210i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 156745. | − | 1.08982e6i | 0.0823164 | − | 0.572332i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 137910. | − | 137910.i | 0.0713225 | − | 0.0713225i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 1.90080e6i | − | 0.968157i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −979058. | −0.491178 | −0.245589 | − | 0.969374i | \(-0.578981\pi\) | ||||
−0.245589 | + | 0.969374i | \(0.578981\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 54147.4 | + | 54147.4i | 0.0267588 | + | 0.0267588i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 189030. | + | 567989.i | 0.0920277 | + | 0.276521i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.59947e6 | + | 2.59947e6i | 1.24684 | + | 1.24684i | 0.957108 | + | 0.289731i | \(0.0935659\pi\) |
0.289731 | + | 0.957108i | \(0.406434\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 1.11409e6i | − | 0.526525i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.49977e6i | 0.698457i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.01136e6 | − | 4.01136e6i | −1.84101 | − | 1.84101i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 156444. | + | 78314.8i | 0.0707637 | + | 0.0354239i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.85742e6 | − | 1.85742e6i | −0.828107 | − | 0.828107i | 0.159148 | − | 0.987255i | \(-0.449125\pi\) |
−0.987255 | + | 0.159148i | \(0.949125\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.47861e6 | −1.52877 | −0.764385 | − | 0.644760i | \(-0.776957\pi\) | ||||
−0.764385 | + | 0.644760i | \(0.776957\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 990812.i | 0.429263i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −846494. | + | 846494.i | −0.361566 | + | 0.361566i | −0.864389 | − | 0.502823i | \(-0.832295\pi\) |
0.502823 | + | 0.864389i | \(0.332295\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 428532. | − | 856047.i | 0.180473 | − | 0.360518i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 639805. | − | 639805.i | 0.265691 | − | 0.265691i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.26831e6 | −0.928892 | −0.464446 | − | 0.885601i | \(-0.653747\pi\) | ||||
−0.464446 | + | 0.885601i | \(0.653747\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.73151e6 | −1.10315 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 526606. | − | 526606.i | 0.209758 | − | 0.209758i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.19853e6 | − | 398877.i | 0.470886 | − | 0.156714i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −936339. | + | 936339.i | −0.362884 | + | 0.362884i | −0.864874 | − | 0.501990i | \(-0.832602\pi\) |
0.501990 | + | 0.864874i | \(0.332602\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.41794e6i | 1.30677i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 317273. | 0.119674 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 529380. | + | 529380.i | 0.197013 | + | 0.197013i | 0.798718 | − | 0.601705i | \(-0.205512\pi\) |
−0.601705 | + | 0.798718i | \(0.705512\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −904139. | − | 627850.i | −0.332015 | − | 0.230557i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.80779e6 | − | 1.80779e6i | −0.655080 | − | 0.655080i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.76855e6i | − | 0.632439i | −0.948686 | − | 0.316220i | \(-0.897586\pi\) | ||
0.948686 | − | 0.316220i | \(-0.102414\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 49545.9i | 0.0174862i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.62315e6 | + | 2.62315e6i | 0.913746 | + | 0.913746i | 0.996565 | − | 0.0828182i | \(-0.0263921\pi\) |
−0.0828182 | + | 0.996565i | \(0.526392\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.62880e6 | − | 874881.i | 0.903871 | − | 0.300814i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 935398. | + | 935398.i | 0.317482 | + | 0.317482i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.62506e6 | 0.879561 | 0.439780 | − | 0.898105i | \(-0.355056\pi\) | ||||
0.439780 | + | 0.898105i | \(0.355056\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 297923.i | 0.0985514i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 925386. | − | 925386.i | 0.302233 | − | 0.302233i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.62344e6 | − | 1.81387e6i | −1.16850 | − | 0.584944i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.09332e6 | + | 1.09332e6i | −0.348153 | + | 0.348153i | −0.859421 | − | 0.511268i | \(-0.829176\pi\) |
0.511268 | + | 0.859421i | \(0.329176\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.44233e6 | 1.08248 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.31952e6 | −1.03089 | −0.515447 | − | 0.856922i | \(-0.672374\pi\) | ||||
−0.515447 | + | 0.856922i | \(0.672374\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.80483e6 | − | 1.80483e6i | 0.553573 | − | 0.553573i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.58369e6 | − | 792786.i | −0.479770 | − | 0.240170i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 55140.9 | − | 55140.9i | 0.0165001 | − | 0.0165001i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.60316e6i | 1.06506i | 0.846410 | + | 0.532531i | \(0.178759\pi\) | ||||
−0.846410 | + | 0.532531i | \(0.821241\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.26747e6 | 0.662119 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.87499e6 | + | 2.87499e6i | 0.829395 | + | 0.829395i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.40001e6 | − | 1.46435e6i | 1.25410 | − | 0.417373i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 648397. | + | 648397.i | 0.182600 | + | 0.182600i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.60065e6i | − | 0.445410i | −0.974886 | − | 0.222705i | \(-0.928511\pi\) | ||
0.974886 | − | 0.222705i | \(-0.0714887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 387801.i | 0.106636i | 0.998578 | + | 0.0533180i | \(0.0169797\pi\) | ||||
−0.998578 | + | 0.0533180i | \(0.983020\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.14138e6 | + | 1.14138e6i | 0.310156 | + | 0.310156i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 266853. | − | 1.85538e6i | 0.0716637 | − | 0.498265i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.61069e6 | + | 4.61069e6i | 1.22376 | + | 1.22376i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 459614. | 0.120573 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 2.12752e6i | − | 0.551673i | −0.961205 | − | 0.275836i | \(-0.911045\pi\) | ||
0.961205 | − | 0.275836i | \(-0.0889548\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.65162e6 | − | 4.65162e6i | 1.19230 | − | 1.19230i | 0.215877 | − | 0.976420i | \(-0.430739\pi\) |
0.976420 | − | 0.215877i | \(-0.0692612\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.42516e6 | + | 807108.i | −0.614494 | + | 0.204507i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −801456. | + | 801456.i | −0.200760 | + | 0.200760i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.59779e6 | −1.13864 | −0.569321 | − | 0.822115i | \(-0.692794\pi\) | ||||
−0.569321 | + | 0.822115i | \(0.692794\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.23426e6 | 2.01617 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.69307e6 | − | 1.69307e6i | 0.409889 | − | 0.409889i | −0.471811 | − | 0.881700i | \(-0.656400\pi\) |
0.881700 | + | 0.471811i | \(0.156400\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −859211. | + | 1.71638e6i | −0.205684 | + | 0.410879i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −934865. | + | 934865.i | −0.221299 | + | 0.221299i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3.17626e6i | − | 0.743533i | −0.928326 | − | 0.371766i | \(-0.878752\pi\) | ||
0.928326 | − | 0.371766i | \(-0.121248\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.48065e6 | 0.805785 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −407237. | − | 407237.i | −0.0932399 | − | 0.0932399i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.21635e6 | − | 2.11068e6i | −0.954792 | − | 0.477963i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.52765e6 | − | 1.52765e6i | −0.342163 | − | 0.342163i | 0.515017 | − | 0.857180i | \(-0.327786\pi\) |
−0.857180 | + | 0.515017i | \(0.827786\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.68682e6i | 0.373711i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.42900e6i | − | 0.532323i | −0.963928 | − | 0.266161i | \(-0.914245\pi\) | ||
0.963928 | − | 0.266161i | \(-0.0857554\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.98030e6 | + | 5.98030e6i | 1.29649 | + | 1.29649i | 0.930693 | + | 0.365801i | \(0.119205\pi\) |
0.365801 | + | 0.930693i | \(0.380795\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −805790. | − | 2.42120e6i | −0.172818 | − | 0.519276i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.69887e6 | − | 3.69887e6i | −0.784833 | − | 0.784833i | 0.195809 | − | 0.980642i | \(-0.437267\pi\) |
−0.980642 | + | 0.195809i | \(0.937267\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.56356e6 | 0.538159 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.13498e6i | 0.443446i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 952560. | − | 952560.i | 0.195767 | − | 0.195767i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.70911e6 | − | 4.27336e6i | 1.16100 | − | 0.869032i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −190515. | + | 190515.i | −0.0383384 | + | 0.0383384i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.88773e6 | 1.17249 | 0.586245 | − | 0.810134i | \(-0.300606\pi\) | ||||
0.586245 | + | 0.810134i | \(0.300606\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −132714. | −0.0261549 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 529779. | − | 529779.i | 0.103330 | − | 0.103330i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.56402e6 | + | 4.69949e6i | 0.301917 | + | 0.907186i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.54087e6 | + | 4.54087e6i | −0.867594 | + | 0.867594i | −0.992206 | − | 0.124612i | \(-0.960232\pi\) |
0.124612 | + | 0.992206i | \(0.460232\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 2.10193e6i | − | 0.397509i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.71881e6 | −0.508951 | −0.254475 | − | 0.967079i | \(-0.581903\pi\) | ||||
−0.254475 | + | 0.967079i | \(0.581903\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.07768e6 | − | 3.07768e6i | −0.570305 | − | 0.570305i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.05319e6 | + | 2.10388e6i | −0.193194 | + | 0.385930i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.89890e6 | − | 2.89890e6i | −0.526433 | − | 0.526433i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.02884e7i | 1.84967i | 0.380366 | + | 0.924836i | \(0.375798\pi\) | ||||
−0.380366 | + | 0.924836i | \(0.624202\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 250585.i | 0.0446027i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.13863e6 | + | 2.13863e6i | 0.376891 | + | 0.376891i | 0.869979 | − | 0.493088i | \(-0.164132\pi\) |
−0.493088 | + | 0.869979i | \(0.664132\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.98805e6 | + | 3.97139e6i | −0.346897 | + | 0.692970i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.10121e6 | + | 1.10121e6i | 0.190261 | + | 0.190261i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.79654e6 | 1.33385 | 0.666926 | − | 0.745124i | \(-0.267610\pi\) | ||||
0.666926 | + | 0.745124i | \(0.267610\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 5.40943e6i | − | 0.916430i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.53778e6 | + | 4.53778e6i | −0.761289 | + | 0.761289i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 390334. | + | 1.17286e6i | 0.0648513 | + | 0.194862i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.16233e6 | − | 1.16233e6i | 0.191250 | − | 0.191250i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −584934. | −0.0953210 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.36971e6 | 1.51228 | 0.756139 | − | 0.654411i | \(-0.227083\pi\) | ||||
0.756139 | + | 0.654411i | \(0.227083\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.04052e6 | + | 5.04052e6i | −0.805789 | + | 0.805789i | −0.983994 | − | 0.178204i | \(-0.942971\pi\) |
0.178204 | + | 0.983994i | \(0.442971\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.77383e6 | + | 2.82478e6i | −0.597564 | + | 0.447287i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.07266e6 | − | 3.07266e6i | 0.481934 | − | 0.481934i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 6.18965e6i | − | 0.961672i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.45273e6 | −0.531406 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.18864e6 | − | 4.18864e6i | −0.638638 | − | 0.638638i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 459340. | + | 1.38021e6i | 0.0693825 | + | 0.208478i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.68210e6 | + | 1.68210e6i | 0.251719 | + | 0.251719i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 8.38534e6i | − | 1.24322i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.33336e6i | 0.783443i | 0.920084 | + | 0.391721i | \(0.128120\pi\) | ||||
−0.920084 | + | 0.391721i | \(0.871880\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.33347e6 | − | 2.33347e6i | −0.339627 | − | 0.339627i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.54726e6 | − | 774546.i | −0.223137 | − | 0.111701i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.38265e6 | − | 4.38265e6i | −0.626280 | − | 0.626280i | 0.320850 | − | 0.947130i | \(-0.396031\pi\) |
−0.947130 | + | 0.320850i | \(0.896031\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.53722e6 | −0.784081 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.65588e7i | − | 2.32354i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.22704e7 | + | 1.22704e7i | −1.70626 | + | 1.70626i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −59392.5 | + | 118644.i | −0.00818463 | + | 0.0163498i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 803306. | − | 803306.i | 0.109709 | − | 0.109709i | −0.650121 | − | 0.759830i | \(-0.725282\pi\) |
0.759830 | + | 0.650121i | \(0.225282\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.29263e6 | −0.310316 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 782474. | 0.104969 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −804076. | + | 804076.i | −0.106912 | + | 0.106912i | −0.758539 | − | 0.651627i | \(-0.774087\pi\) |
0.651627 | + | 0.758539i | \(0.274087\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.37816e6 | + | 3.12111e6i | −1.23594 | + | 0.411327i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.36299e6 | + | 5.36299e6i | −0.700566 | + | 0.700566i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.92427e6i | 0.508134i | 0.967187 | + | 0.254067i | \(0.0817683\pi\) | ||||
−0.967187 | + | 0.254067i | \(0.918232\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.25466e7 | 1.61040 | 0.805201 | − | 0.593002i | \(-0.202057\pi\) | ||||
0.805201 | + | 0.593002i | \(0.202057\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.68010e6 | − | 2.68010e6i | −0.341008 | − | 0.341008i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 220962. | − | 1.53631e6i | 0.0278707 | − | 0.193780i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.21454e6 | − | 1.21454e6i | −0.151870 | − | 0.151870i | 0.627083 | − | 0.778953i | \(-0.284249\pi\) |
−0.778953 | + | 0.627083i | \(0.784249\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.77262e6i | 0.467677i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1.98590e7i | − | 2.44071i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 194011. | + | 194011.i | 0.0236404 | + | 0.0236404i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.79924e6 | − | 1.26441e6i | 0.458994 | − | 0.152756i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.81043e6 | − | 6.81043e6i | −0.815791 | − | 0.815791i | 0.169704 | − | 0.985495i | \(-0.445719\pi\) |
−0.985495 | + | 0.169704i | \(0.945719\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.65318e7 | 1.96350 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 1.46985e6i | − | 0.173103i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.21457e6 | + | 6.21457e6i | −0.725729 | + | 0.725729i | −0.969766 | − | 0.244037i | \(-0.921528\pi\) |
0.244037 | + | 0.969766i | \(0.421528\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.17817e6 | − | 3.59335e6i | −0.831230 | − | 0.416109i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.71551e6 | − | 2.71551e6i | 0.311828 | − | 0.311828i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.64825e6 | −0.757078 | −0.378539 | − | 0.925585i | \(-0.623573\pi\) | ||||
−0.378539 | + | 0.925585i | \(0.623573\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.82874e6 | −0.884109 | −0.442055 | − | 0.896988i | \(-0.645750\pi\) | ||||
−0.442055 | + | 0.896988i | \(0.645750\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.53936e6 | + | 1.53936e6i | −0.172403 | + | 0.172403i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.90815e6 | − | 2.95758e6i | −0.656241 | − | 0.328510i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 76234.2 | − | 76234.2i | 0.00839804 | − | 0.00839804i | −0.702895 | − | 0.711293i | \(-0.748110\pi\) |
0.711293 | + | 0.702895i | \(0.248110\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.09457e7i | 1.19592i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.79750e6 | −0.303156 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.22892e6 | + | 9.22892e6i | 0.991973 | + | 0.991973i | 0.999968 | − | 0.00799526i | \(-0.00254500\pi\) |
−0.00799526 | + | 0.999968i | \(0.502545\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.61909e6 | + | 1.87007e6i | −0.599071 | + | 0.199374i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −60556.8 | − | 60556.8i | −0.00640398 | − | 0.00640398i | 0.703898 | − | 0.710302i | \(-0.251441\pi\) |
−0.710302 | + | 0.703898i | \(0.751441\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.44485e7i | 1.51564i | 0.652466 | + | 0.757818i | \(0.273734\pi\) | ||||
−0.652466 | + | 0.757818i | \(0.726266\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.39674e6i | 0.145340i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.81233e6 | + | 5.81233e6i | 0.599971 | + | 0.599971i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.75218e6 | + | 9.36979e6i | −0.281823 | + | 0.959466i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.10497e6 | + | 2.10497e6i | 0.213834 | + | 0.213834i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −225940. | −0.0227702 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 998279.i | − | 0.0998110i | −0.998754 | − | 0.0499055i | \(-0.984108\pi\) | ||
0.998754 | − | 0.0499055i | \(-0.0158920\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.59354e6 | − | 2.59354e6i | 0.257267 | − | 0.257267i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 417068. | − | 138803.i | 0.0410461 | − | 0.0136604i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00910e7 | + | 1.00910e7i | −0.985335 | + | 0.985335i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.48145e6 | 0.337293 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.95063e6 | 0.668158 | 0.334079 | − | 0.942545i | \(-0.391575\pi\) | ||||
0.334079 | + | 0.942545i | \(0.391575\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.82012e6 | − | 2.82012e6i | 0.268993 | − | 0.268993i | −0.559702 | − | 0.828694i | \(-0.689084\pi\) |
0.828694 | + | 0.559702i | \(0.189084\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.02601e6 | + | 2.04958e6i | −0.0971071 | + | 0.193984i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.26200e6 | + | 5.26200e6i | −0.494186 | + | 0.494186i | −0.909622 | − | 0.415437i | \(-0.863629\pi\) |
0.415437 | + | 0.909622i | \(0.363629\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.51608e6i | 0.327678i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.09278e7 | −1.01060 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.68361e6 | − | 1.68361e6i | −0.154511 | − | 0.154511i | 0.625618 | − | 0.780129i | \(-0.284847\pi\) |
−0.780129 | + | 0.625618i | \(0.784847\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.03822e7 | − | 5.19726e6i | −0.945552 | − | 0.473338i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.24824e6 | + | 3.24824e6i | 0.293585 | + | 0.293585i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.34724e6i | 0.569339i | 0.958626 | + | 0.284670i | \(0.0918839\pi\) | ||||
−0.958626 | + | 0.284670i | \(0.908116\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 3.70354e6i | − | 0.329696i | −0.986319 | − | 0.164848i | \(-0.947287\pi\) | ||
0.986319 | − | 0.164848i | \(-0.0527133\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −941634. | − | 941634.i | −0.0831952 | − | 0.0831952i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.64368e6 | − | 2.89769e7i | −0.845646 | − | 2.54096i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.54842e6 | − | 2.54842e6i | −0.221797 | − | 0.221797i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −241543. | −0.0208655 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.63882e6i | 0.483483i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.25751e7 | − | 1.25751e7i | 1.07022 | − | 1.07022i | 0.0728820 | − | 0.997341i | \(-0.476780\pi\) |
0.997341 | − | 0.0728820i | \(-0.0232197\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.25107e6 | − | 8.69847e6i | 0.105687 | − | 0.734824i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.12742e6 | + | 1.12742e6i | −0.0945397 | + | 0.0945397i | −0.752795 | − | 0.658255i | \(-0.771295\pi\) |
0.658255 | + | 0.752795i | \(0.271295\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.12106e7 | 1.76555 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −208453. | −0.0172242 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.77294e6 | + | 6.77294e6i | −0.555553 | + | 0.555553i | −0.928038 | − | 0.372485i | \(-0.878506\pi\) |
0.372485 | + | 0.928038i | \(0.378506\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.35229e6 | − | 1.90871e7i | −0.517254 | − | 1.55422i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.84019e6 | + | 2.84019e6i | −0.229591 | + | 0.229591i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 466947.i | − | 0.0374731i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.88767e7 | 1.50394 | 0.751969 | − | 0.659198i | \(-0.229104\pi\) | ||||
0.751969 | + | 0.659198i | \(0.229104\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.12455e6 | + | 7.12455e6i | 0.563540 | + | 0.563540i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.64160e6 | − | 7.27457e6i | 0.285977 | − | 0.571275i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.13098e6 | − | 7.13098e6i | −0.555991 | − | 0.555991i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.57953e6i | 0.277098i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 4.36760e6i | − | 0.335697i | −0.985813 | − | 0.167849i | \(-0.946318\pi\) | ||
0.985813 | − | 0.167849i | \(-0.0536820\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −607810. | − | 607810.i | −0.0463852 | − | 0.0463852i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.25195e6 | + | 2.50092e6i | −0.0948664 | + | 0.189508i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.34487e7 | + | 1.34487e7i | 1.01188 | + | 1.01188i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.34469e7 | −1.75174 | −0.875871 | − | 0.482545i | \(-0.839713\pi\) | ||||
−0.875871 | + | 0.482545i | \(0.839713\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1.47362e7i | − | 1.09323i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.54426e6 | − | 2.54426e6i | 0.187429 | − | 0.187429i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.28761e6 | − | 3.86894e6i | −0.0941929 | − | 0.283027i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.55506e6 | + | 3.55506e6i | −0.258255 | + | 0.258255i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.10054e6 | −0.223674 | −0.111837 | − | 0.993727i | \(-0.535673\pi\) | ||||
−0.111837 | + | 0.993727i | \(0.535673\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.29357e6 | 0.379237 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.39891e6 | − | 1.39891e6i | 0.0995276 | − | 0.0995276i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.35882e7 | + | 1.81535e7i | 0.960099 | + | 1.28267i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.31022e7 | − | 1.31022e7i | 0.919406 | − | 0.919406i | −0.0775805 | − | 0.996986i | \(-0.524719\pi\) |
0.996986 | + | 0.0775805i | \(0.0247195\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 2.13483e6i | − | 0.148780i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.90311e6 | −0.270158 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.58810e7 | + | 1.58810e7i | 1.09174 | + | 1.09174i | 0.995343 | + | 0.0963958i | \(0.0307315\pi\) |
0.0963958 | + | 0.995343i | \(0.469269\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.50523e6 | + | 1.35371e7i | 0.307609 | + | 0.924289i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.56760e6 | + | 1.56760e6i | 0.106308 | + | 0.106308i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.89695e7i | − | 1.27774i | −0.769313 | − | 0.638872i | \(-0.779401\pi\) | ||
0.769313 | − | 0.638872i | \(-0.220599\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 5.06626e6i | − | 0.338955i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.76147e7 | + | 1.76147e7i | 1.17058 | + | 1.17058i | 0.982071 | + | 0.188512i | \(0.0603663\pi\) |
0.188512 | + | 0.982071i | \(0.439634\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.04885e7 | + | 5.25049e6i | 0.692347 | + | 0.346585i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.19249e7 | + | 1.19249e7i | 0.781901 | + | 0.781901i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.22941e6 | 0.405735 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.68412e6i | 0.303060i | 0.988453 | + | 0.151530i | \(0.0484200\pi\) | ||||
−0.988453 | + | 0.151530i | \(0.951580\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.33433e6 | − | 4.33433e6i | 0.278570 | − | 0.278570i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.28717e6 | + | 4.56892e6i | −0.146026 | + | 0.291706i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.09156e6 | − | 9.09156e6i | 0.576632 | − | 0.576632i | −0.357342 | − | 0.933974i | \(-0.616317\pi\) |
0.933974 | + | 0.357342i | \(0.116317\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 647913. | 0.0408237 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.93887e6 | −0.309148 | −0.154574 | − | 0.987981i | \(-0.549400\pi\) | ||||
−0.154574 | + | 0.987981i | \(0.549400\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.23960e6 | + | 5.23960e6i | −0.325827 | + | 0.325827i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.46805e6 | − | 2.15260e6i | 0.399595 | − | 0.132987i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.23127e6 | − | 4.23127e6i | 0.259706 | − | 0.259706i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.04569e6i | 0.0637656i | 0.999492 | + | 0.0318828i | \(0.0101503\pi\) | ||||
−0.999492 | + | 0.0318828i | \(0.989850\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.56420e6 | 0.397691 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.05820e6 | + | 4.05820e6i | 0.244278 | + | 0.244278i | 0.818617 | − | 0.574339i | \(-0.194741\pi\) |
−0.574339 | + | 0.818617i | \(0.694741\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.81238e7 | + | 1.35660e7i | −1.08391 | + | 0.811328i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 401775. | + | 401775.i | 0.0238743 | + | 0.0238743i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 3.83667e7i | − | 2.26522i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 3.54532e6i | − | 0.207983i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.44289e7 | − | 1.44289e7i | −0.841065 | − | 0.841065i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.79718e7 | − | 5.98113e6i | 1.04092 | − | 0.346425i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.09025e7 | − | 1.09025e7i | −0.627464 | − | 0.627464i | 0.319966 | − | 0.947429i | \(-0.396329\pi\) |
−0.947429 | + | 0.319966i | \(0.896329\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.87716e6 | 0.564858 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.23273e7i | 2.40536i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.78578e6 | − | 6.78578e6i | 0.383192 | − | 0.383192i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −417444. | − | 208970.i | −0.0234251 | − | 0.0117264i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.70728e7 | + | 1.70728e7i | −0.952049 | + | 0.952049i | −0.998902 | − | 0.0468526i | \(-0.985081\pi\) |
0.0468526 | + | 0.998902i | \(0.485081\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.76262e6 | −0.263924 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.98034e6 | −0.384411 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.30783e6 | − | 3.30783e6i | 0.181032 | − | 0.181032i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.94375e6 | − | 2.97540e6i | −0.323274 | − | 0.161829i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.29957e6 | − | 9.29957e6i | 0.502665 | − | 0.502665i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.78529e7i | 0.959040i | 0.877531 | + | 0.479520i | \(0.159189\pi\) | ||||
−0.877531 | + | 0.479520i | \(0.840811\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.39804e7 | 1.28028 | 0.640139 | − | 0.768259i | \(-0.278877\pi\) | ||||
0.640139 | + | 0.768259i | \(0.278877\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.87341e6 | − | 3.87341e6i | −0.205526 | − | 0.205526i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.76937e7 | + | 5.88856e6i | −0.933091 | + | 0.310538i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.04999e7 | − | 1.04999e7i | −0.550340 | − | 0.550340i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 1.71475e7i | − | 0.893285i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.28789e7i | 0.666841i | 0.942778 | + | 0.333421i | \(0.108203\pi\) | ||||
−0.942778 | + | 0.333421i | \(0.891797\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.48554e7 | − | 1.48554e7i | −0.764515 | − | 0.764515i | 0.212620 | − | 0.977135i | \(-0.431800\pi\) |
−0.977135 | + | 0.212620i | \(0.931800\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.03501e6 | − | 580341.i | −0.206400 | − | 0.0296858i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.43004e7 | − | 1.43004e7i | −0.727084 | − | 0.727084i | 0.242954 | − | 0.970038i | \(-0.421884\pi\) |
−0.970038 | + | 0.242954i | \(0.921884\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.83120e6 | −0.0925443 | −0.0462722 | − | 0.998929i | \(-0.514734\pi\) | ||||
−0.0462722 | + | 0.998929i | \(0.514734\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1.23883e7i | − | 0.622316i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.71794e7 | + | 1.71794e7i | −0.857821 | + | 0.857821i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.10938e6 | − | 702013.i | 0.104698 | − | 0.0348441i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.44054e7 | − | 1.44054e7i | 0.710739 | − | 0.710739i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.93770e7 | 1.44080 | 0.720398 | − | 0.693561i | \(-0.243959\pi\) | ||||
0.720398 | + | 0.693561i | \(0.243959\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.21415e7 | 1.56703 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.76254e6 | − | 2.76254e6i | 0.133887 | − | 0.133887i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.18474e6 | − | 1.23548e7i | 0.297975 | − | 0.595243i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.00073e7 | + | 2.00073e7i | −0.958251 | + | 0.958251i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 1.57121e7i | − | 0.748108i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −187085. | −0.00885555 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.76720e6 | + | 6.76720e6i | 0.318446 | + | 0.318446i | 0.848170 | − | 0.529724i | \(-0.177704\pi\) |
−0.529724 | + | 0.848170i | \(0.677704\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.31908e7 | + | 1.16092e7i | 1.08493 | + | 0.543107i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.35330e7 | + | 2.35330e7i | 1.09452 | + | 1.09452i | 0.995039 | + | 0.0994857i | \(0.0317198\pi\) |
0.0994857 | + | 0.995039i | \(0.468280\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.12302e7i | 0.981681i | 0.871250 | + | 0.490840i | \(0.163310\pi\) | ||||
−0.871250 | + | 0.490840i | \(0.836690\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.53612e7i | 1.16590i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.84791e7 | − | 1.84791e7i | −0.844605 | − | 0.844605i | 0.144849 | − | 0.989454i | \(-0.453730\pi\) |
−0.989454 | + | 0.144849i | \(0.953730\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.63869e6 | + | 4.92387e6i | 0.0744658 | + | 0.223751i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.72314e6 | + | 4.72314e6i | 0.213395 | + | 0.213395i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.50065e7 | −0.674110 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 3.77292e6i | − | 0.168512i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.27365e7 | + | 1.27365e7i | −0.565607 | + | 0.565607i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.43508e7 | + | 2.38538e7i | 1.51676 | + | 1.05327i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.31623e7 | − | 2.31623e7i | 1.01691 | − | 1.01691i | 0.0170541 | − | 0.999855i | \(-0.494571\pi\) |
0.999855 | − | 0.0170541i | \(-0.00542874\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.50059e6 | 0.283779 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.17232e7 | −1.37701 | −0.688505 | − | 0.725232i | \(-0.741733\pi\) | ||||
−0.688505 | + | 0.725232i | \(0.741733\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −991053. | + | 991053.i | −0.0427755 | + | 0.0427755i | −0.728171 | − | 0.685395i | \(-0.759629\pi\) |
0.685395 | + | 0.728171i | \(0.259629\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.88910e6 | − | 5.67628e6i | −0.0810768 | − | 0.243616i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.16096e7 | − | 2.16096e7i | 0.922228 | − | 0.922228i | −0.0749584 | − | 0.997187i | \(-0.523882\pi\) |
0.997187 | + | 0.0749584i | \(0.0238824\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.88239e6i | − | 0.0798832i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.55887e6 | −0.276780 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.28121e7 | − | 1.28121e7i | −0.537641 | − | 0.537641i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.44719e6 | − | 1.88720e7i | 0.394226 | − | 0.787516i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −779702. | − | 779702.i | −0.0323555 | − | 0.0323555i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.25666e7i | 2.16926i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 794959.i | − | 0.0326237i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.94066e6 | + | 6.94066e6i | 0.283258 | + | 0.283258i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.31055e7 | + | 2.61799e7i | −0.531903 | + | 1.06254i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.16848e7 | − | 3.16848e7i | −1.27889 | − | 1.27889i | −0.941289 | − | 0.337601i | \(-0.890385\pi\) |
−0.337601 | − | 0.941289i | \(-0.609615\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.61512e7 | −0.648330 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.77379e7i | − | 0.708121i | −0.935223 | − | 0.354060i | \(-0.884801\pi\) | ||
0.935223 | − | 0.354060i | \(-0.115199\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.21436e7 | − | 1.21436e7i | 0.482139 | − | 0.482139i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.02959e6 | − | 9.10319e6i | −0.119628 | − | 0.359452i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.51581e7 | + | 3.51581e7i | −1.38071 | + | 1.38071i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.13742e6 | 0.122542 | 0.0612708 | − | 0.998121i | \(-0.480485\pi\) | ||||
0.0612708 | + | 0.998121i | \(0.480485\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.08815e6 | −0.314195 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.26646e6 | + | 4.26646e6i | −0.164840 | + | 0.164840i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.16511e6 | + | 167574.i | 0.0447727 | + | 0.00643949i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.17867e6 | + | 3.17867e6i | −0.121491 | + | 0.121491i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 3.33387e7i | − | 1.26739i | −0.773584 | − | 0.633694i | \(-0.781538\pi\) | ||
0.773584 | − | 0.633694i | \(-0.218462\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.24303e7 | −3.49494 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.86395e6 | − | 5.86395e6i | −0.220539 | − | 0.220539i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.19210e6 | − | 6.58672e6i | −0.0820033 | − | 0.246400i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.71957e6 | − | 8.71957e6i | −0.324449 | − | 0.324449i | 0.526022 | − | 0.850471i | \(-0.323683\pi\) |
−0.850471 | + | 0.526022i | \(0.823683\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 7.98659e6i | − | 0.295595i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3.11580e7i | − | 1.14708i | −0.819176 | − | 0.573542i | \(-0.805569\pi\) | ||
0.819176 | − | 0.573542i | \(-0.194431\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.90468e6 | − | 5.90468e6i | −0.216230 | − | 0.216230i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.36530e7 | − | 1.68465e7i | −1.22587 | − | 0.613663i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.99596e7 | + | 2.99596e7i | 1.08558 | + | 1.08558i | 0.995978 | + | 0.0895993i | \(0.0285586\pi\) |
0.0895993 | + | 0.995978i | \(0.471441\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.96133e6 | −0.286959 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.62167e7i | 0.581448i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.16784e7 | − | 1.16784e7i | 0.416534 | − | 0.416534i | −0.467473 | − | 0.884007i | \(-0.654835\pi\) |
0.884007 | + | 0.467473i | \(0.154835\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.50523e7 | + | 3.00689e7i | −0.534065 | + | 1.06686i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.69324e6 | + | 6.69324e6i | −0.236242 | + | 0.236242i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.61475e7 | −3.02480 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.38516e7 | −0.833123 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.74062e6 | + | 3.74062e6i | −0.129980 | + | 0.129980i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.17572e7 | − | 1.05690e7i | 1.09780 | − | 0.365355i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.11322e6 | + | 6.11322e6i | −0.210234 | + | 0.210234i | −0.804367 | − | 0.594133i | \(-0.797495\pi\) |
0.594133 | + | 0.804367i | \(0.297495\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 8.62509e6i | − | 0.295090i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.60288e7 | 1.22631 | 0.613157 | − | 0.789961i | \(-0.289899\pi\) | ||||
0.613157 | + | 0.789961i | \(0.289899\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.46345e7 | − | 2.46345e7i | −0.834183 | − | 0.834183i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.15737e6 | + | 5.55414e6i | 0.140058 | + | 0.187114i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.67594e7 | + | 2.67594e7i | 0.896892 | + | 0.896892i | 0.995160 | − | 0.0982680i | \(-0.0313303\pi\) |
−0.0982680 | + | 0.995160i | \(0.531330\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.10841e6i | 0.237037i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 6.29252e6i | − | 0.208762i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.14544e7 | − | 1.14544e7i | −0.378084 | − | 0.378084i | 0.492326 | − | 0.870411i | \(-0.336147\pi\) |
−0.870411 | + | 0.492326i | \(0.836147\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.23730e7 | + | 4.11779e6i | −0.406334 | + | 0.135230i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.46908e6 | + | 8.46908e6i | 0.276722 | + | 0.276722i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.23190e6 | −0.105067 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.84941e7i | 1.56857i | 0.620399 | + | 0.784286i | \(0.286971\pi\) | ||||
−0.620399 | + | 0.784286i | \(0.713029\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.36224e6 | − | 4.36224e6i | 0.140390 | − | 0.140390i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.04661e7 | − | 1.52511e7i | −0.975572 | − | 0.488365i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.47473e6 | − | 8.47473e6i | 0.270015 | − | 0.270015i | −0.559091 | − | 0.829106i | \(-0.688850\pi\) |
0.829106 | + | 0.559091i | \(0.188850\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.05926e6 | −0.0335806 |
(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 | 160.6.o.a.47.11 | 56 | ||
4.3 | odd | 2 | 40.6.k.a.27.13 | yes | 56 | ||
5.3 | odd | 4 | inner | 160.6.o.a.143.12 | 56 | ||
8.3 | odd | 2 | inner | 160.6.o.a.47.12 | 56 | ||
8.5 | even | 2 | 40.6.k.a.27.27 | yes | 56 | ||
20.3 | even | 4 | 40.6.k.a.3.27 | yes | 56 | ||
40.3 | even | 4 | inner | 160.6.o.a.143.11 | 56 | ||
40.13 | odd | 4 | 40.6.k.a.3.13 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.k.a.3.13 | ✓ | 56 | 40.13 | odd | 4 | ||
40.6.k.a.3.27 | yes | 56 | 20.3 | even | 4 | ||
40.6.k.a.27.13 | yes | 56 | 4.3 | odd | 2 | ||
40.6.k.a.27.27 | yes | 56 | 8.5 | even | 2 | ||
160.6.o.a.47.11 | 56 | 1.1 | even | 1 | trivial | ||
160.6.o.a.47.12 | 56 | 8.3 | odd | 2 | inner | ||
160.6.o.a.143.11 | 56 | 40.3 | even | 4 | inner | ||
160.6.o.a.143.12 | 56 | 5.3 | odd | 4 | inner |