Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(73,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.73");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.z (of order \(6\), degree \(2\), 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: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + \cdots + 45\!\cdots\!96 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{10}\cdot 7^{4} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.5 | ||
Root | \(-72.3408 - 125.298i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.145 |
Dual form | 252.9.z.d.73.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 225.043 | + | 129.928i | 0.360068 | + | 0.207885i | 0.669111 | − | 0.743163i | \(-0.266675\pi\) |
−0.309042 | + | 0.951048i | \(0.600009\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 597.275 | − | 2325.52i | 0.248761 | − | 0.968565i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9723.49 | − | 16841.6i | −0.664127 | − | 1.15030i | −0.979521 | − | 0.201341i | \(-0.935470\pi\) |
0.315394 | − | 0.948961i | \(-0.397863\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 46381.7i | − | 1.62395i | −0.583690 | − | 0.811976i | \(-0.698392\pi\) | ||
0.583690 | − | 0.811976i | \(-0.301608\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 105886. | − | 61133.6i | 1.26778 | − | 0.731955i | 0.293215 | − | 0.956047i | \(-0.405275\pi\) |
0.974568 | + | 0.224092i | \(0.0719416\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 18446.7 | + | 10650.2i | 0.141548 | + | 0.0817230i | 0.569102 | − | 0.822267i | \(-0.307291\pi\) |
−0.427553 | + | 0.903990i | \(0.640624\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −152199. | + | 263616.i | −0.543876 | + | 0.942020i | 0.454801 | + | 0.890593i | \(0.349710\pi\) |
−0.998677 | + | 0.0514271i | \(0.983623\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −161550. | − | 279812.i | −0.413567 | − | 0.716320i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −88119.4 | −0.124589 | −0.0622945 | − | 0.998058i | \(-0.519842\pi\) | ||||
−0.0622945 | + | 0.998058i | \(0.519842\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.54998e6 | + | 894884.i | −1.67834 | + | 0.968991i | −0.715624 | + | 0.698486i | \(0.753857\pi\) |
−0.962718 | + | 0.270505i | \(0.912809\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 436564. | − | 445739.i | 0.290921 | − | 0.297036i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 755092. | − | 1.30786e6i | 0.402896 | − | 0.697836i | −0.591178 | − | 0.806541i | \(-0.701337\pi\) |
0.994074 | + | 0.108705i | \(0.0346703\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 188022.i | 0.0665385i | 0.999446 | + | 0.0332692i | \(0.0105919\pi\) | ||||
−0.999446 | + | 0.0332692i | \(0.989408\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −123402. | −0.0360953 | −0.0180476 | − | 0.999837i | \(-0.505745\pi\) | ||||
−0.0180476 | + | 0.999837i | \(0.505745\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.58909e6 | + | 3.22686e6i | 1.14538 | + | 0.661285i | 0.947757 | − | 0.318993i | \(-0.103345\pi\) |
0.197623 | + | 0.980278i | \(0.436678\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.05133e6 | − | 2.77796e6i | −0.876236 | − | 0.481882i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.88508e6 | + | 1.19253e7i | 0.872580 | + | 1.51135i | 0.859318 | + | 0.511441i | \(0.170888\pi\) |
0.0132616 | + | 0.999912i | \(0.495779\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.05343e6i | − | 0.552250i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00305e7 | + | 5.79109e6i | −0.827776 | + | 0.477917i | −0.853090 | − | 0.521763i | \(-0.825275\pi\) |
0.0253148 | + | 0.999680i | \(0.491941\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.92663e7 | − | 1.11234e7i | −1.39149 | − | 0.803375i | −0.398007 | − | 0.917383i | \(-0.630298\pi\) |
−0.993480 | + | 0.114007i | \(0.963631\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.02630e6 | − | 1.04379e7i | 0.337596 | − | 0.584734i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.75873e6 | + | 9.97442e6i | 0.285777 | + | 0.494981i | 0.972797 | − | 0.231658i | \(-0.0744149\pi\) |
−0.687020 | + | 0.726638i | \(0.741082\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.11345e7 | 1.22520 | 0.612602 | − | 0.790392i | \(-0.290123\pi\) | ||||
0.612602 | + | 0.790392i | \(0.290123\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.08437e7 | + | 6.26059e6i | −0.381843 | + | 0.220457i | −0.678620 | − | 0.734490i | \(-0.737422\pi\) |
0.296777 | + | 0.954947i | \(0.404088\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.49731e7 | + | 1.25532e7i | −1.27935 | + | 0.357100i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.13222e7 | − | 3.69312e7i | 0.547424 | − | 0.948167i | −0.451026 | − | 0.892511i | \(-0.648942\pi\) |
0.998450 | − | 0.0556558i | \(-0.0177249\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.19982e7i | − | 1.51708i | −0.651625 | − | 0.758541i | \(-0.725912\pi\) | ||
0.651625 | − | 0.758541i | \(-0.274088\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.17720e7 | 0.608651 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.37683e7 | − | 2.52696e7i | −0.697589 | − | 0.402753i | 0.108860 | − | 0.994057i | \(-0.465280\pi\) |
−0.806449 | + | 0.591304i | \(0.798613\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.07862e8 | − | 2.77026e7i | −1.57290 | − | 0.403976i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.76753e6 | + | 4.79351e6i | 0.0339781 | + | 0.0588517i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.16642e8i | 1.31755i | 0.752339 | + | 0.658776i | \(0.228925\pi\) | ||||
−0.752339 | + | 0.658776i | \(0.771075\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.23786e7 | + | 5.33348e7i | −0.887740 | + | 0.512537i | −0.873203 | − | 0.487357i | \(-0.837961\pi\) |
−0.0145374 | + | 0.999894i | \(0.504628\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.77725e8 | + | 1.02609e8i | 1.57906 | + | 0.911671i | 0.994991 | + | 0.0999675i | \(0.0318739\pi\) |
0.584070 | + | 0.811703i | \(0.301459\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.90703e7 | + | 1.54274e8i | −0.679513 | + | 1.17695i | 0.295615 | + | 0.955307i | \(0.404476\pi\) |
−0.975128 | + | 0.221644i | \(0.928858\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.48168e7 | − | 9.49454e7i | −0.388336 | − | 0.672617i | 0.603890 | − | 0.797068i | \(-0.293617\pi\) |
−0.992226 | + | 0.124450i | \(0.960283\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.74592e8 | −1.68413 | −0.842063 | − | 0.539379i | \(-0.818659\pi\) | ||||
−0.842063 | + | 0.539379i | \(0.818659\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.85024e7 | + | 3.95499e7i | −0.391665 | + | 0.226128i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.89243e7 | − | 2.82755e8i | −0.393571 | − | 1.41001i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.19129e7 | + | 1.41877e8i | −0.382130 | + | 0.661868i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.85466e8i | − | 0.759669i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.97605e7 | −0.152840 | −0.0764199 | − | 0.997076i | \(-0.524349\pi\) | ||||
−0.0764199 | + | 0.997076i | \(0.524349\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.31807e7 | − | 1.91569e7i | −0.112668 | − | 0.0650490i | 0.442607 | − | 0.896716i | \(-0.354054\pi\) |
−0.555275 | + | 0.831667i | \(0.687387\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.57851e7 | − | 3.65372e7i | 0.114366 | − | 0.116769i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.07018e8 | − | 3.58565e8i | −0.587659 | − | 1.01786i | −0.994538 | − | 0.104374i | \(-0.966716\pi\) |
0.406879 | − | 0.913482i | \(-0.366617\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.15646e8i | − | 0.577674i | −0.957378 | − | 0.288837i | \(-0.906731\pi\) | ||
0.957378 | − | 0.288837i | \(-0.0932686\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.81141e8 | + | 4.50992e8i | −1.86804 | + | 1.07851i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.98306e7 | − | 1.14492e7i | −0.0448605 | − | 0.0259002i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.59668e8 | − | 4.49759e8i | 0.526834 | − | 0.912503i | −0.472677 | − | 0.881236i | \(-0.656712\pi\) |
0.999511 | − | 0.0312676i | \(-0.00995442\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.65131e8 | − | 2.86015e8i | −0.317630 | − | 0.550151i | 0.662363 | − | 0.749183i | \(-0.269554\pi\) |
−0.979993 | + | 0.199032i | \(0.936220\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.65083e8 | −0.805757 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.58909e8 | + | 1.49481e8i | −0.426137 | + | 0.246030i | −0.697700 | − | 0.716390i | \(-0.745793\pi\) |
0.271563 | + | 0.962421i | \(0.412460\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.22141e8 | + | 5.11393e8i | 0.777113 | + | 0.761117i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.92142e8 | − | 5.06004e8i | 0.413850 | − | 0.716810i | −0.581457 | − | 0.813577i | \(-0.697517\pi\) |
0.995307 | + | 0.0967676i | \(0.0308504\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.46657e8i | 0.959965i | 0.877278 | + | 0.479983i | \(0.159357\pi\) | ||||
−0.877278 | + | 0.479983i | \(0.840643\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.33553e9 | −1.63722 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.08205e8 | − | 5.24352e8i | −1.01391 | − | 0.585381i | −0.101576 | − | 0.994828i | \(-0.532388\pi\) |
−0.912334 | + | 0.409447i | \(0.865722\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.47200e8 | + | 2.08563e8i | −0.796681 | + | 0.222374i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.24237e8 | + | 2.15185e8i | 0.121015 | + | 0.209604i | 0.920168 | − | 0.391523i | \(-0.128052\pi\) |
−0.799153 | + | 0.601127i | \(0.794718\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.91957e8i | 0.458366i | 0.973383 | + | 0.229183i | \(0.0736055\pi\) | ||||
−0.973383 | + | 0.229183i | \(0.926394\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.39856e8 | − | 1.96216e8i | 0.290140 | − | 0.167512i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.05917e9 | − | 1.18886e9i | −1.68394 | − | 0.972222i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.53669e8 | + | 1.65180e9i | −0.716579 | + | 1.24115i | 0.245768 | + | 0.969329i | \(0.420960\pi\) |
−0.962347 | + | 0.271823i | \(0.912374\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.70293e8 | − | 8.14571e8i | −0.338953 | − | 0.587083i | 0.645283 | − | 0.763943i | \(-0.276739\pi\) |
−0.984236 | + | 0.176860i | \(0.943406\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.22807e9 | −0.815379 | −0.407689 | − | 0.913121i | \(-0.633665\pi\) | ||||
−0.407689 | + | 0.913121i | \(0.633665\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.98896e7 | − | 5.76713e7i | 0.0636954 | − | 0.0367745i | −0.467814 | − | 0.883827i | \(-0.654958\pi\) |
0.531509 | + | 0.847052i | \(0.321625\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.26315e7 | + | 2.04924e8i | −0.0309929 | + | 0.120672i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.44294e7 | + | 4.23129e7i | −0.0138324 | + | 0.0239584i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4.14229e8i | − | 0.217098i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.33973e9 | 1.18042 | 0.590209 | − | 0.807250i | \(-0.299045\pi\) | ||||
0.590209 | + | 0.807250i | \(0.299045\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.77708e7 | − | 1.60335e7i | −0.0129968 | − | 0.00750368i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.15531e9 | + | 4.13902e9i | 0.521025 | + | 1.86663i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.83548e9 | − | 4.91120e9i | −1.18866 | − | 2.05882i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.14133e9i | − | 0.461523i | −0.973010 | − | 0.230762i | \(-0.925878\pi\) | ||
0.973010 | − | 0.230762i | \(-0.0741218\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.82252e8 | − | 1.05223e8i | 0.0686387 | − | 0.0396285i | −0.465288 | − | 0.885159i | \(-0.654049\pi\) |
0.533927 | + | 0.845531i | \(0.320716\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.18730e9 | − | 1.84019e9i | −1.15899 | − | 0.669146i | −0.207932 | − | 0.978143i | \(-0.566673\pi\) |
−0.951063 | + | 0.308997i | \(0.900007\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.42196e8 | + | 2.46291e8i | −0.0482464 | + | 0.0835652i | −0.889140 | − | 0.457635i | \(-0.848697\pi\) |
0.840894 | + | 0.541200i | \(0.182030\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.38522e8 | + | 1.45236e9i | 0.274943 | + | 0.476216i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.62607e9 | −0.804850 | −0.402425 | − | 0.915453i | \(-0.631833\pi\) | ||||
−0.402425 | + | 0.915453i | \(0.631833\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.05781e8 | − | 1.18808e8i | 0.0610011 | − | 0.0352190i | −0.469189 | − | 0.883098i | \(-0.655454\pi\) |
0.530190 | + | 0.847879i | \(0.322120\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.75828e8 | − | 1.28147e9i | −0.215328 | − | 0.355667i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.93976e8 | − | 8.55591e8i | 0.132714 | − | 0.229868i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 3.49203e9i | − | 0.879797i | −0.898047 | − | 0.439899i | \(-0.855014\pi\) | ||
0.898047 | − | 0.439899i | \(-0.144986\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.91961e9 | 1.44481 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.36384e9 | + | 1.94211e9i | 0.771086 | + | 0.445187i | 0.833262 | − | 0.552879i | \(-0.186471\pi\) |
−0.0621759 | + | 0.998065i | \(0.519804\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.59046e9 | − | 2.53714e9i | −0.575675 | − | 0.563825i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.40863e8 | + | 1.62962e9i | 0.196654 | + | 0.340615i | 0.947442 | − | 0.319929i | \(-0.103659\pi\) |
−0.750787 | + | 0.660544i | \(0.770326\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.57827e9i | 0.725587i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.78854e9 | + | 1.60997e9i | −0.532559 | + | 0.307473i | −0.742058 | − | 0.670336i | \(-0.766150\pi\) |
0.209499 | + | 0.977809i | \(0.432817\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.42388e9 | + | 2.55413e9i | 0.820212 | + | 0.473550i | 0.850490 | − | 0.525992i | \(-0.176306\pi\) |
−0.0302773 | + | 0.999542i | \(0.509639\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.14165e9 | + | 5.44150e9i | −0.549323 | + | 0.951455i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.20091e9 | + | 9.00825e9i | 0.883406 | + | 1.53010i | 0.847529 | + | 0.530749i | \(0.178089\pi\) |
0.0358772 | + | 0.999356i | \(0.488577\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.79146e9 | 1.57044 | 0.785222 | − | 0.619215i | \(-0.212549\pi\) | ||||
0.785222 | + | 0.619215i | \(0.212549\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.03261e8 | + | 5.21498e8i | −0.140821 | + | 0.0813031i | −0.568755 | − | 0.822507i | \(-0.692575\pi\) |
0.427934 | + | 0.903810i | \(0.359242\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.37249e8 | + | 1.12301e8i | 0.0644468 | + | 0.0165522i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.98675e9 | − | 6.90526e9i | 0.571515 | − | 0.989893i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 2.83834e9i | − | 0.385118i | −0.981285 | − | 0.192559i | \(-0.938321\pi\) | ||
0.981285 | − | 0.192559i | \(-0.0616787\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.00971e9 | −0.397408 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.22270e10 | + | 7.05924e9i | 1.52980 | + | 0.883228i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.37052e7 | + | 2.86975e8i | −0.00897909 | + | 0.0349606i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.89049e9 | − | 5.00648e9i | −0.334020 | − | 0.578540i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.01655e10i | − | 1.14439i | −0.820116 | − | 0.572197i | \(-0.806091\pi\) | ||
0.820116 | − | 0.572197i | \(-0.193909\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.35774e9 | − | 5.40269e9i | 1.00030 | − | 0.577522i | 0.0919614 | − | 0.995763i | \(-0.470686\pi\) |
0.908336 | + | 0.418240i | \(0.137353\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.81261e9 | − | 4.51061e9i | −0.813989 | − | 0.469957i | 0.0343502 | − | 0.999410i | \(-0.489064\pi\) |
−0.848339 | + | 0.529453i | \(0.822397\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.10486e9 | + | 3.64573e9i | −0.208443 | + | 0.361034i | −0.951224 | − | 0.308500i | \(-0.900173\pi\) |
0.742781 | + | 0.669534i | \(0.233506\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.56828e8 | + | 1.48407e9i | 0.0827429 | + | 0.143315i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.60435e9 | 0.239270 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.29782e10 | + | 7.49295e9i | −1.16327 | + | 0.671614i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.08424e10 | − | 1.10702e10i | 0.925424 | − | 0.944873i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.98155e9 | − | 1.03603e10i | 0.498312 | − | 0.863102i | −0.501686 | − | 0.865050i | \(-0.667287\pi\) |
0.999998 | + | 0.00194777i | \(0.000619995\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.99289e9i | 0.237636i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.47484e9 | 0.657070 | 0.328535 | − | 0.944492i | \(-0.393445\pi\) | ||||
0.328535 | + | 0.944492i | \(0.393445\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.01425e10 | + | 1.74028e10i | 2.22927 | + | 1.28707i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.47723e9 | + | 1.00878e10i | −0.684708 | + | 0.728818i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.92809e9 | + | 1.37319e10i | 0.546828 | + | 0.947134i | 0.998489 | + | 0.0549447i | \(0.0174983\pi\) |
−0.451661 | + | 0.892190i | \(0.649168\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.90260e9i | 0.532682i | 0.963879 | + | 0.266341i | \(0.0858148\pi\) | ||||
−0.963879 | + | 0.266341i | \(0.914185\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.28745e9 | + | 4.78476e9i | −0.533731 | + | 0.308150i | −0.742534 | − | 0.669808i | \(-0.766376\pi\) |
0.208804 | + | 0.977958i | \(0.433043\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.00658e9 | + | 4.04525e9i | 0.441157 | + | 0.254702i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.12021e9 | + | 8.86847e9i | −0.308255 | + | 0.533914i | −0.977981 | − | 0.208695i | \(-0.933078\pi\) |
0.669726 | + | 0.742609i | \(0.266412\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.26493e9 | − | 1.43153e10i | −0.486643 | − | 0.842890i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.25371e9 | −0.183319 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.80339e10 | − | 1.61854e10i | 1.54532 | − | 0.892193i | 0.546834 | − | 0.837241i | \(-0.315833\pi\) |
0.998489 | − | 0.0549514i | \(-0.0175004\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.18449e10 | − | 8.88873e9i | 1.68091 | − | 0.469185i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.25975e10 | − | 2.18195e10i | 0.650803 | − | 1.12722i | −0.332126 | − | 0.943235i | \(-0.607766\pi\) |
0.982928 | − | 0.183988i | \(-0.0589008\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.08713e9i | 0.202327i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.03658e9 | −0.292573 | −0.146287 | − | 0.989242i | \(-0.546732\pi\) | ||||
−0.146287 | + | 0.989242i | \(0.546732\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.57427e9 | + | 5.52771e9i | 0.444949 | + | 0.256892i | 0.705695 | − | 0.708516i | \(-0.250635\pi\) |
−0.260745 | + | 0.965408i | \(0.583968\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.17519e10 | − | 3.01829e9i | −0.534890 | − | 0.137378i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.58412e10 | − | 2.74378e10i | −0.691814 | − | 1.19826i | −0.971243 | − | 0.238091i | \(-0.923478\pi\) |
0.279428 | − | 0.960167i | \(-0.409855\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.72178e10i | 1.59237i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.59682e9 | − | 5.54072e9i | 0.394220 | − | 0.227603i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.81623e10 | − | 1.04860e10i | −0.731155 | − | 0.422132i | 0.0876897 | − | 0.996148i | \(-0.472052\pi\) |
−0.818844 | + | 0.574015i | \(0.805385\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.84375e9 | − | 1.01217e10i | 0.226003 | − | 0.391449i | −0.730617 | − | 0.682788i | \(-0.760767\pi\) |
0.956620 | + | 0.291339i | \(0.0941007\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.15062e10 | + | 7.18909e10i | 1.57360 | + | 2.72555i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.93685e10 | −1.07030 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.98804e10 | − | 1.72515e10i | 1.06781 | − | 0.616499i | 0.140226 | − | 0.990119i | \(-0.455217\pi\) |
0.927582 | + | 0.373620i | \(0.121884\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.47637e9 | + | 2.67849e10i | 0.256975 | + | 0.920642i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.35461e9 | − | 1.62027e10i | 0.315379 | − | 0.546253i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.71261e10i | − | 0.555652i | −0.960631 | − | 0.277826i | \(-0.910386\pi\) | ||
0.960631 | − | 0.277826i | \(-0.0896139\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.64524e10 | 1.16037 | 0.580187 | − | 0.814484i | \(-0.302980\pi\) | ||||
0.580187 | + | 0.814484i | \(0.302980\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.42119e10 | − | 1.97522e10i | −1.04863 | − | 0.605425i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.73750e10 | + | 3.81605e10i | −1.12427 | + | 1.14790i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.09904e10 | − | 1.90360e10i | −0.318497 | − | 0.551654i | 0.661677 | − | 0.749789i | \(-0.269845\pi\) |
−0.980175 | + | 0.198135i | \(0.936512\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.35544e10i | 0.385593i | 0.981239 | + | 0.192796i | \(0.0617557\pi\) | ||||
−0.981239 | + | 0.192796i | \(0.938244\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.61514e9 | + | 3.24190e9i | −0.153969 | + | 0.0888943i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.13004e10 | − | 2.38448e10i | −1.11198 | − | 0.642001i | −0.172637 | − | 0.984986i | \(-0.555229\pi\) |
−0.939341 | + | 0.342985i | \(0.888562\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.20913e9 | + | 1.59507e10i | −0.239113 | + | 0.414156i | −0.960460 | − | 0.278418i | \(-0.910190\pi\) |
0.721347 | + | 0.692574i | \(0.243523\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.56648e9 | − | 1.13735e10i | −0.167453 | − | 0.290037i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.72530e10 | −1.16264 | −0.581319 | − | 0.813676i | \(-0.697463\pi\) | ||||
−0.581319 | + | 0.813676i | \(0.697463\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.16658e9 | − | 1.82823e9i | 0.0765393 | − | 0.0441900i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.06741e10 | − | 2.02486e10i | −0.482372 | − | 0.472443i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.30524e9 | − | 1.61172e10i | 0.213335 | − | 0.369508i | −0.739421 | − | 0.673243i | \(-0.764901\pi\) |
0.952756 | + | 0.303736i | \(0.0982340\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 9.20893e9i | − | 0.203895i | −0.994790 | − | 0.101947i | \(-0.967493\pi\) | ||
0.994790 | − | 0.101947i | \(-0.0325073\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.42010e10 | −0.309025 | −0.154513 | − | 0.987991i | \(-0.549381\pi\) | ||||
−0.154513 | + | 0.987991i | \(0.549381\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.95507e10 | + | 1.70611e10i | 0.621299 | + | 0.358707i | 0.777374 | − | 0.629038i | \(-0.216551\pi\) |
−0.156076 | + | 0.987745i | \(0.549884\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.66353e10 | − | 7.43460e9i | 0.550511 | − | 0.153662i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.19990e9 | + | 2.07829e9i | 0.0239718 | + | 0.0415204i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6.88216e9i | − | 0.135192i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.59507e9 | + | 4.38502e9i | −0.144275 | + | 0.0832970i | −0.570400 | − | 0.821367i | \(-0.693212\pi\) |
0.426125 | + | 0.904664i | \(0.359878\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.06607e10 | − | 3.50225e10i | −1.13325 | − | 0.654284i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.51551e10 | + | 2.62494e10i | −0.273900 | + | 0.474408i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.41038e9 | − | 1.11031e10i | −0.113964 | − | 0.197392i | 0.803401 | − | 0.595438i | \(-0.203022\pi\) |
−0.917365 | + | 0.398047i | \(0.869688\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.34320e10 | −1.09140 | −0.545698 | − | 0.837982i | \(-0.683735\pi\) | ||||
−0.545698 | + | 0.837982i | \(0.683735\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.33065e9 | + | 5.38705e9i | −0.157952 | + | 0.0911934i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.85958e10 | − | 7.24040e10i | 0.304783 | − | 1.18669i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.36380e10 | + | 5.82628e10i | −0.542536 | + | 0.939700i | 0.456222 | + | 0.889866i | \(0.349202\pi\) |
−0.998758 | + | 0.0498336i | \(0.984131\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.04697e11i | − | 1.63554i | −0.575542 | − | 0.817772i | \(-0.695209\pi\) | ||
0.575542 | − | 0.817772i | \(-0.304791\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.77188e10 | −0.426196 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.94469e10 | + | 2.85482e10i | 0.736662 | + | 0.425312i | 0.820854 | − | 0.571137i | \(-0.193498\pi\) |
−0.0841923 | + | 0.996450i | \(0.526831\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.08251e9 | + | 2.89565e10i | 0.118539 | + | 0.424680i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.66637e10 | + | 4.61830e10i | 0.379046 | + | 0.656527i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.25505e11i | − | 1.75671i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.48609e10 | + | 4.32210e10i | −1.01602 | + | 0.586602i | −0.912950 | − | 0.408072i | \(-0.866201\pi\) |
−0.103074 | + | 0.994674i | \(0.532868\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.27623e10 | + | 7.36833e9i | 0.170578 | + | 0.0984832i | 0.582858 | − | 0.812574i | \(-0.301934\pi\) |
−0.412280 | + | 0.911057i | \(0.635268\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.09415e11 | + | 1.89512e11i | −1.41852 | + | 2.45694i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.17338e9 | − | 1.24247e10i | −0.0916012 | − | 0.158658i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.72077e9 | 0.108055 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.00892e10 | + | 2.31455e10i | −0.489342 | + | 0.282522i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.33136e9 | + | 1.12084e11i | 0.0276220 | + | 1.32797i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.99660e10 | + | 1.03864e11i | −0.700029 | + | 1.21249i | 0.268427 | + | 0.963300i | \(0.413496\pi\) |
−0.968456 | + | 0.249185i | \(0.919837\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 2.84890e10i | − | 0.322917i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.72241e10 | −0.862588 | −0.431294 | − | 0.902211i | \(-0.641943\pi\) | ||||
−0.431294 | + | 0.902211i | \(0.641943\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.62551e9 | − | 9.38491e8i | −0.0176354 | − | 0.0101818i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.31491e10 | − | 7.16434e10i | −0.782183 | − | 0.766083i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.89933e10 | − | 1.54141e11i | −0.924564 | − | 1.60139i | −0.792262 | − | 0.610182i | \(-0.791096\pi\) |
−0.132302 | − | 0.991209i | \(-0.542237\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.72362e9i | 0.0586170i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.36022e11 | − | 7.85323e10i | 1.35386 | − | 0.781654i | 0.365076 | − | 0.930978i | \(-0.381043\pi\) |
0.988788 | + | 0.149323i | \(0.0477096\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.17950e10 | − | 3.56774e10i | −0.606400 | − | 0.350105i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.78668e8 | − | 4.82667e8i | 0.00265851 | − | 0.00460467i | −0.864693 | − | 0.502301i | \(-0.832487\pi\) |
0.867352 | + | 0.497696i | \(0.165820\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.85718e10 | + | 3.21672e10i | 0.174706 | + | 0.302600i | 0.940060 | − | 0.341010i | \(-0.110769\pi\) |
−0.765353 | + | 0.643610i | \(0.777436\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.83506e10 | 0.899716 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.46036e10 | − | 1.99784e10i | 0.312189 | − | 0.180243i | −0.335716 | − | 0.941963i | \(-0.608978\pi\) |
0.647906 | + | 0.761721i | \(0.275645\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.67434e11 | − | 4.30027e10i | −1.46939 | − | 0.377391i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.33894e11 | − | 2.31911e11i | 1.15901 | − | 2.00746i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.12252e11i | 0.945460i | 0.881207 | + | 0.472730i | \(0.156731\pi\) | ||||
−0.881207 | + | 0.472730i | \(0.843269\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.81229e10 | −0.316756 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.84487e10 | − | 2.79719e10i | −0.391799 | − | 0.226205i | 0.291140 | − | 0.956680i | \(-0.405965\pi\) |
−0.682939 | + | 0.730475i | \(0.739299\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.89766e10 | − | 7.38865e10i | 0.151409 | − | 0.589518i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.46361e10 | − | 2.53505e10i | −0.113689 | − | 0.196916i | 0.803566 | − | 0.595216i | \(-0.202933\pi\) |
−0.917255 | + | 0.398300i | \(0.869600\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.04406e10i | − | 0.233322i | −0.993172 | − | 0.116661i | \(-0.962781\pi\) | ||
0.993172 | − | 0.116661i | \(-0.0372191\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.68678e10 | + | 2.12856e10i | −0.275186 | + | 0.158879i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.87228e11 | + | 1.08096e11i | 1.37917 | + | 0.796262i | 0.992059 | − | 0.125772i | \(-0.0401409\pi\) |
0.387107 | + | 0.922035i | \(0.373474\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.49667e11 | − | 2.59232e11i | 1.07390 | − | 1.86004i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.15010e10 | + | 5.45613e10i | 0.223091 | + | 0.386405i | 0.955745 | − | 0.294196i | \(-0.0950519\pi\) |
−0.732654 | + | 0.680601i | \(0.761719\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.31396e11 | −1.59667 | −0.798336 | − | 0.602213i | \(-0.794286\pi\) | ||||
−0.798336 | + | 0.602213i | \(0.794286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.62110e10 | + | 4.97739e10i | −0.587219 | + | 0.339031i | −0.763997 | − | 0.645220i | \(-0.776766\pi\) |
0.176778 | + | 0.984251i | \(0.443432\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.49068e10 | + | 8.66913e10i | −0.563625 | + | 0.575471i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.90080e10 | + | 6.75639e10i | −0.255643 | + | 0.442787i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.84646e11i | − | 1.17961i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.88355e10 | −0.244969 | −0.122485 | − | 0.992470i | \(-0.539086\pi\) | ||||
−0.122485 | + | 0.992470i | \(0.539086\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.94780e9 | − | 5.16602e9i | −0.0550328 | − | 0.0317732i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.28846e11 | + | 2.34289e11i | −0.782554 | + | 1.42297i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.01203e11 | + | 1.75289e11i | 0.599462 | + | 1.03830i | 0.992901 | + | 0.118948i | \(0.0379521\pi\) |
−0.393439 | + | 0.919351i | \(0.628715\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.46591e11i | 0.857558i | 0.903409 | + | 0.428779i | \(0.141056\pi\) | ||||
−0.903409 | + | 0.428779i | \(0.858944\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.40431e11 | + | 1.38813e11i | −1.37206 | + | 0.792158i | −0.991187 | − | 0.132470i | \(-0.957709\pi\) |
−0.380871 | + | 0.924628i | \(0.624376\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.95062e11 | + | 1.12619e11i | 1.09950 | + | 0.634795i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.35533e11 | − | 2.34750e11i | 0.745406 | − | 1.29108i | −0.204598 | − | 0.978846i | \(-0.565589\pi\) |
0.950005 | − | 0.312236i | \(-0.101078\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.97805e9 | − | 8.62224e9i | −0.0270455 | − | 0.0468441i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.76828e10 | −0.464914 | −0.232457 | − | 0.972607i | \(-0.574676\pi\) | ||||
−0.232457 | + | 0.972607i | \(0.574676\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.77894e10 | + | 2.18177e10i | −0.197954 | + | 0.114289i | −0.595701 | − | 0.803206i | \(-0.703126\pi\) |
0.397747 | + | 0.917495i | \(0.369792\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.28004e10 | − | 3.57292e9i | 0.0654541 | − | 0.0182699i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.34117e10 | − | 2.32297e10i | 0.0677609 | − | 0.117365i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.32633e11i | 2.13417i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.88626e11 | 0.919480 | 0.459740 | − | 0.888054i | \(-0.347943\pi\) | ||||
0.459740 | + | 0.888054i | \(0.347943\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.41068e10 | − | 1.96916e10i | −0.162363 | − | 0.0937401i | 0.416617 | − | 0.909082i | \(-0.363216\pi\) |
−0.578980 | + | 0.815342i | \(0.696549\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.71253e11 | + | 6.96673e10i | 1.27613 | + | 0.327755i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.05360e11 | + | 1.82490e11i | 0.484167 | + | 0.838601i | 0.999835 | − | 0.0181874i | \(-0.00578954\pi\) |
−0.515668 | + | 0.856788i | \(0.672456\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1.07590e11i | − | 0.488663i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.53116e11 | − | 3.19342e11i | 2.45437 | − | 1.41703i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.03078e10 | − | 1.74982e10i | −0.132936 | − | 0.0767505i | 0.432057 | − | 0.901846i | \(-0.357788\pi\) |
−0.564993 | + | 0.825096i | \(0.691121\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.80186e10 | − | 4.85296e10i | 0.120090 | − | 0.208002i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.14944e10 | + | 1.99090e10i | 0.0487031 | + | 0.0843563i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.58032e10 | −0.355330 | −0.177665 | − | 0.984091i | \(-0.556854\pi\) | ||||
−0.177665 | + | 0.984091i | \(0.556854\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.78580e10 | − | 1.60838e10i | 0.114059 | − | 0.0658517i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.88559e10 | + | 2.46684e11i | 0.275590 | + | 0.987333i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.74057e10 | − | 1.68712e11i | 0.385478 | − | 0.667668i | −0.606357 | − | 0.795192i | \(-0.707370\pi\) |
0.991835 | + | 0.127525i | \(0.0407032\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 5.44801e11i | − | 2.10804i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.34387e11 | −0.896827 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.89871e11 | + | 1.67357e11i | 1.08465 | + | 0.626222i | 0.932147 | − | 0.362081i | \(-0.117934\pi\) |
0.152502 | + | 0.988303i | \(0.451267\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.44771e11 | − | 3.52017e11i | 1.27582 | − | 1.30263i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.42357e10 | + | 2.46569e10i | 0.0515259 | + | 0.0892455i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 9.86180e10i | − | 0.353035i | −0.984297 | − | 0.176518i | \(-0.943517\pi\) | ||
0.984297 | − | 0.176518i | \(-0.0564833\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.30667e10 | + | 7.54404e9i | −0.0457609 | + | 0.0264201i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.61192e11 | + | 1.50799e11i | 0.904782 | + | 0.522376i | 0.878749 | − | 0.477285i | \(-0.158379\pi\) |
0.0260337 | + | 0.999661i | \(0.491712\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.11990e11 | − | 1.93972e11i | 0.379585 | − | 0.657460i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.82846e11 | − | 3.16698e11i | −0.613065 | − | 1.06186i | −0.990721 | − | 0.135914i | \(-0.956603\pi\) |
0.377655 | − | 0.925946i | \(-0.376730\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.52082e11 | 1.15528 | 0.577642 | − | 0.816290i | \(-0.303973\pi\) | ||||
0.577642 | + | 0.816290i | \(0.303973\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.16873e11 | − | 6.74766e10i | 0.379392 | − | 0.219042i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.05569e11 | + | 2.99279e11i | 0.970917 | + | 0.950932i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.44039e11 | + | 2.49484e11i | −0.452816 | + | 0.784300i | −0.998560 | − | 0.0536517i | \(-0.982914\pi\) |
0.545744 | + | 0.837952i | \(0.316247\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 8.58209e10i | − | 0.264122i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.34615e11 | −1.62801 | −0.814006 | − | 0.580857i | \(-0.802718\pi\) | ||||
−0.814006 | + | 0.580857i | \(0.802718\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.20516e10 | − | 1.27315e10i | −0.0657507 | − | 0.0379612i | 0.466764 | − | 0.884382i | \(-0.345420\pi\) |
−0.532515 | + | 0.846421i | \(0.678753\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.53539e11 | + | 7.07692e10i | −0.748076 | + | 0.208807i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.68601e11 | + | 4.65230e11i | 0.776114 | + | 1.34427i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.61134e11i | − | 0.460768i | −0.973100 | − | 0.230384i | \(-0.926002\pi\) | ||
0.973100 | − | 0.230384i | \(-0.0739982\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.00134e11 | − | 1.15547e11i | 0.560535 | − | 0.323625i | −0.192825 | − | 0.981233i | \(-0.561765\pi\) |
0.753360 | + | 0.657608i | \(0.228432\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.00799e11 | + | 2.89136e11i | 1.38821 | + | 0.801486i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.00247e9 | + | 3.46839e9i | −0.00543772 | + | 0.00941841i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.02736e11 | − | 5.24353e11i | −0.813691 | − | 1.40935i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.76875e10 | −0.204585 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.19226e9 | − | 4.72980e9i | 0.0213553 | − | 0.0123295i | −0.489284 | − | 0.872124i | \(-0.662742\pi\) |
0.510640 | + | 0.859795i | \(0.329409\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.64007e11 | + | 6.38571e11i | −0.418945 | + | 1.63119i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.15923e11 | + | 8.93604e11i | −1.30464 | + | 2.25971i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.06562e11i | 0.264100i | 0.991243 | + | 0.132050i | \(0.0421559\pi\) | ||||
−0.991243 | + | 0.132050i | \(0.957844\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.89079e11 | 1.93612 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.10876e11 | + | 1.21750e11i | 0.507184 | + | 0.292823i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.10594e10 | + | 1.82926e11i | 0.121588 | + | 0.435604i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.71049e11 | + | 2.96266e11i | 0.399326 | + | 0.691652i | 0.993643 | − | 0.112578i | \(-0.0359110\pi\) |
−0.594317 | + | 0.804231i | \(0.702578\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.89997e11i | − | 0.670362i | −0.942154 | − | 0.335181i | \(-0.891203\pi\) | ||
0.942154 | − | 0.335181i | \(-0.108797\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.31489e11 | − | 7.59150e10i | 0.298029 | − | 0.172067i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.27637e9 | − | 1.31426e9i | −0.00510923 | − | 0.00294981i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.60897e11 | − | 6.25091e11i | 0.794347 | − | 1.37585i | −0.128906 | − | 0.991657i | \(-0.541147\pi\) |
0.923253 | − | 0.384193i | \(-0.125520\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.88089e10 | − | 1.36501e11i | −0.171781 | − | 0.297534i | 0.767261 | − | 0.641335i | \(-0.221619\pi\) |
−0.939043 | + | 0.343801i | \(0.888286\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.81570e11 | 1.45710 | 0.728549 | − | 0.684994i | \(-0.240195\pi\) | ||||
0.728549 | + | 0.684994i | \(0.240195\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.06194e11 | − | 2.34516e11i | 0.860034 | − | 0.496541i | −0.00398941 | − | 0.999992i | \(-0.501270\pi\) |
0.864024 | + | 0.503451i | \(0.167937\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.04693e11 | + | 1.46578e10i | −1.46359 | + | 0.0304430i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.70120e10 | + | 1.68030e11i | −0.199563 | + | 0.345653i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 9.20167e11i | − | 1.85703i | −0.371294 | − | 0.928515i | \(-0.621086\pi\) | ||
0.371294 | − | 0.928515i | \(-0.378914\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.92481e11 | −0.984478 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.00552e11 | − | 1.73524e11i | −0.589512 | − | 0.340355i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.81015e11 | + | 2.75230e11i | 0.546004 | + | 0.534765i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.29848e11 | + | 3.98108e11i | 0.438251 | + | 0.759072i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 5.25940e11i | − | 0.993437i | −0.867912 | − | 0.496718i | \(-0.834538\pi\) | ||
0.867912 | − | 0.496718i | \(-0.165462\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.85568e10 | + | 3.38078e10i | −0.108556 | + | 0.0626748i | −0.553295 | − | 0.832985i | \(-0.686630\pi\) |
0.444739 | + | 0.895660i | \(0.353296\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.39418e11 | − | 1.38228e11i | −0.439728 | − | 0.253877i | 0.263754 | − | 0.964590i | \(-0.415039\pi\) |
−0.703482 | + | 0.710713i | \(0.748373\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.25121e11 | + | 3.89921e11i | −0.405857 | + | 0.702964i | −0.994421 | − | 0.105486i | \(-0.966360\pi\) |
0.588564 | + | 0.808450i | \(0.299693\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.36256e11 | − | 2.36003e11i | −0.243384 | − | 0.421554i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.29305e11 | −1.45424 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.62631e11 | − | 2.67100e11i | 0.803825 | − | 0.464089i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.31306e11 | − | 1.10774e11i | −0.735789 | − | 0.188976i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.03817e10 | + | 1.56546e11i | −0.152786 | + | 0.264632i | −0.932250 | − | 0.361814i | \(-0.882158\pi\) |
0.779465 | + | 0.626446i | \(0.215491\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.07020e11i | 0.343644i | 0.985128 | + | 0.171822i | \(0.0549655\pi\) | ||||
−0.985128 | + | 0.171822i | \(0.945035\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.01138e11 | −0.166369 | −0.0831845 | − | 0.996534i | \(-0.526509\pi\) | ||||
−0.0831845 | + | 0.996534i | \(0.526509\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.35333e11 | + | 7.81346e10i | 0.218630 | + | 0.126226i | 0.605316 | − | 0.795985i | \(-0.293047\pi\) |
−0.386686 | + | 0.922212i | \(0.626380\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.37479e10 | + | 9.24640e10i | −0.0380206 | + | 0.148035i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.87336e10 | + | 1.19050e11i | 0.108084 | + | 0.187208i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.45676e10i | 0.100629i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.36584e11 | − | 7.88566e10i | 0.209103 | − | 0.120726i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.45807e12 | + | 8.41819e11i | 2.21248 | + | 1.27738i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.39192e10 | + | 1.10711e11i | −0.0952877 | + | 0.165043i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.32401e11 | + | 1.09535e12i | 0.934466 | + | 1.61854i | 0.775584 | + | 0.631245i | \(0.217456\pi\) |
0.158882 | + | 0.987298i | \(0.449211\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.10755e12 | −1.60801 | −0.804005 | − | 0.594623i | \(-0.797301\pi\) | ||||
−0.804005 | + | 0.594623i | \(0.797301\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.21256e12 | + | 7.00074e11i | −1.74510 | + | 1.00754i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.43679e10 | + | 6.57207e10i | −0.0910316 | + | 0.0929447i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.08017e10 | − | 5.33501e10i | 0.0431830 | − | 0.0747951i | −0.843626 | − | 0.536931i | \(-0.819583\pi\) |
0.886809 | + | 0.462136i | \(0.152917\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.44407e12i | − | 1.98967i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.87940e11 | −0.666498 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.05667e11 | − | 1.76477e11i | −0.410379 | − | 0.236933i | 0.280573 | − | 0.959833i | \(-0.409475\pi\) |
−0.690953 | + | 0.722900i | \(0.742809\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.35946e10 | − | 1.05042e11i | −0.0846489 | − | 0.139818i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.08934e11 | − | 5.35090e11i | −0.404222 | − | 0.700132i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.00546e12i | − | 1.30439i | −0.758051 | − | 0.652195i | \(-0.773848\pi\) | ||
0.758051 | − | 0.652195i | \(-0.226152\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.52508e11 | − | 8.80503e10i | 0.194506 | − | 0.112298i | −0.399584 | − | 0.916696i | \(-0.630846\pi\) |
0.594090 | + | 0.804398i | \(0.297512\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.95655e10 | − | 2.86167e10i | −0.0626806 | − | 0.0361886i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.75622e11 | − | 4.77392e11i | 0.342700 | − | 0.593574i | −0.642233 | − | 0.766510i | \(-0.721992\pi\) |
0.984933 | + | 0.172935i | \(0.0553251\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.90377e11 | + | 5.02947e11i | 0.358012 | + | 0.620094i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.34459e11 | −1.01166 | −0.505829 | − | 0.862634i | \(-0.668813\pi\) | ||||
−0.505829 | + | 0.862634i | \(0.668813\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.29232e11 | + | 2.47817e11i | −0.516035 | + | 0.297933i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.57499e11 | + | 2.67263e11i | −1.13205 | + | 0.315983i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.17519e12 | − | 2.03549e12i | 1.37789 | − | 2.38657i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 2.44418e11i | − | 0.281853i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.68610e11 | −0.879022 | −0.439511 | − | 0.898237i | \(-0.644848\pi\) | ||||
−0.439511 | + | 0.898237i | \(0.644848\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.08759e11 | − | 2.35997e11i | −0.459823 | − | 0.265479i | 0.252147 | − | 0.967689i | \(-0.418863\pi\) |
−0.711970 | + | 0.702210i | \(0.752197\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.01491e11 | − | 1.28800e11i | −0.559515 | − | 0.143703i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.48912e11 | − | 1.29715e12i | −0.821964 | − | 1.42368i | −0.904218 | − | 0.427071i | \(-0.859545\pi\) |
0.0822542 | − | 0.996611i | \(-0.473788\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.82835e11i | 1.06992i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.25935e11 | + | 3.03649e11i | −0.563272 | + | 0.325205i | −0.754458 | − | 0.656349i | \(-0.772100\pi\) |
0.191186 | + | 0.981554i | \(0.438767\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.76369e11 | − | 1.59562e11i | −0.293592 | − | 0.169505i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.87817e10 | − | 3.25309e10i | 0.0196313 | − | 0.0340025i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.64617e11 | − | 8.04740e11i | −0.481726 | − | 0.834374i | 0.518054 | − | 0.855348i | \(-0.326657\pi\) |
−0.999780 | + | 0.0209739i | \(0.993323\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.99725e10 | 0.0305796 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.58181e12 | − | 9.13259e11i | 1.60094 | − | 0.924300i | 0.609635 | − | 0.792682i | \(-0.291316\pi\) |
0.991301 | − | 0.131618i | \(-0.0420172\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.9.z.d.145.5 | 12 | ||
3.2 | odd | 2 | 84.9.m.b.61.2 | ✓ | 12 | ||
7.3 | odd | 6 | inner | 252.9.z.d.73.5 | 12 | ||
21.17 | even | 6 | 84.9.m.b.73.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.9.m.b.61.2 | ✓ | 12 | 3.2 | odd | 2 | ||
84.9.m.b.73.2 | yes | 12 | 21.17 | even | 6 | ||
252.9.z.d.73.5 | 12 | 7.3 | odd | 6 | inner | ||
252.9.z.d.145.5 | 12 | 1.1 | even | 1 | trivial |