Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,10,Mod(1,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.a (trivial) |
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: | yes |
Analytic conductor: | \(13.9059675764\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{14}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 14 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.74166\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −22.4499 | −0.992157 | −0.496078 | − | 0.868278i | \(-0.665227\pi\) | ||||
−0.496078 | + | 0.868278i | \(0.665227\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.00000 | −0.0156250 | ||||||||
\(5\) | 493.899 | 0.353405 | 0.176703 | − | 0.984264i | \(-0.443457\pi\) | ||||
0.176703 | + | 0.984264i | \(0.443457\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −763.000 | −0.120111 | −0.0600556 | − | 0.998195i | \(-0.519128\pi\) | ||||
−0.0600556 | + | 0.998195i | \(0.519128\pi\) | |||||||
\(8\) | 11674.0 | 1.00766 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −11088.0 | −0.350633 | ||||||||
\(11\) | 56888.2 | 1.17153 | 0.585767 | − | 0.810480i | \(-0.300793\pi\) | ||||
0.585767 | + | 0.810480i | \(0.300793\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −73015.0 | −0.709034 | −0.354517 | − | 0.935050i | \(-0.615355\pi\) | ||||
−0.354517 | + | 0.935050i | \(0.615355\pi\) | |||||||
\(14\) | 17129.3 | 0.119169 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −257984. | −0.984131 | ||||||||
\(17\) | −168240. | −0.488550 | −0.244275 | − | 0.969706i | \(-0.578550\pi\) | ||||
−0.244275 | + | 0.969706i | \(0.578550\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −598129. | −1.05294 | −0.526470 | − | 0.850194i | \(-0.676485\pi\) | ||||
−0.526470 | + | 0.850194i | \(0.676485\pi\) | |||||||
\(20\) | −3951.19 | −0.00552196 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.27714e6 | −1.16235 | ||||||||
\(23\) | −2.40039e6 | −1.78857 | −0.894287 | − | 0.447493i | \(-0.852317\pi\) | ||||
−0.894287 | + | 0.447493i | \(0.852317\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.70919e6 | −0.875105 | ||||||||
\(26\) | 1.63918e6 | 0.703473 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6104.00 | 0.00187674 | ||||||||
\(29\) | 4.65378e6 | 1.22184 | 0.610921 | − | 0.791691i | \(-0.290799\pi\) | ||||
0.610921 | + | 0.791691i | \(0.290799\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.82410e6 | −0.354749 | −0.177374 | − | 0.984143i | \(-0.556760\pi\) | ||||
−0.177374 | + | 0.984143i | \(0.556760\pi\) | |||||||
\(32\) | −185347. | −0.0312471 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.77698e6 | 0.484718 | ||||||||
\(35\) | −376845. | −0.0424479 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.42722e7 | 1.25194 | 0.625968 | − | 0.779848i | \(-0.284704\pi\) | ||||
0.625968 | + | 0.779848i | \(0.284704\pi\) | |||||||
\(38\) | 1.34280e7 | 1.04468 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.76576e6 | 0.356112 | ||||||||
\(41\) | −2.98243e7 | −1.64833 | −0.824163 | − | 0.566353i | \(-0.808354\pi\) | ||||
−0.824163 | + | 0.566353i | \(0.808354\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.75690e6 | 0.346003 | 0.173002 | − | 0.984922i | \(-0.444653\pi\) | ||||
0.173002 | + | 0.984922i | \(0.444653\pi\) | |||||||
\(44\) | −455105. | −0.0183052 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.38887e7 | 1.77455 | ||||||||
\(47\) | −3.09903e7 | −0.926372 | −0.463186 | − | 0.886261i | \(-0.653294\pi\) | ||||
−0.463186 | + | 0.886261i | \(0.653294\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.97714e7 | −0.985573 | ||||||||
\(50\) | 3.83712e7 | 0.868241 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 584120. | 0.0110787 | ||||||||
\(53\) | −9.90123e6 | −0.172365 | −0.0861823 | − | 0.996279i | \(-0.527467\pi\) | ||||
−0.0861823 | + | 0.996279i | \(0.527467\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.80970e7 | 0.414026 | ||||||||
\(56\) | −8.90724e6 | −0.121031 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.04477e8 | −1.21226 | ||||||||
\(59\) | 1.25210e8 | 1.34525 | 0.672627 | − | 0.739982i | \(-0.265166\pi\) | ||||
0.672627 | + | 0.739982i | \(0.265166\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.52766e8 | −1.41268 | −0.706340 | − | 0.707873i | \(-0.749655\pi\) | ||||
−0.706340 | + | 0.707873i | \(0.749655\pi\) | |||||||
\(62\) | 4.09509e7 | 0.351966 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.36249e8 | 1.01513 | ||||||||
\(65\) | −3.60620e7 | −0.250576 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.20752e8 | −1.94461 | −0.972306 | − | 0.233712i | \(-0.924913\pi\) | ||||
−0.972306 | + | 0.233712i | \(0.924913\pi\) | |||||||
\(68\) | 1.34592e6 | 0.00763359 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.46014e6 | 0.0421150 | ||||||||
\(71\) | −1.09152e8 | −0.509763 | −0.254881 | − | 0.966972i | \(-0.582036\pi\) | ||||
−0.254881 | + | 0.966972i | \(0.582036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.64640e7 | 0.273926 | 0.136963 | − | 0.990576i | \(-0.456266\pi\) | ||||
0.136963 | + | 0.990576i | \(0.456266\pi\) | |||||||
\(74\) | −3.20410e8 | −1.24212 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.78503e6 | 0.0164522 | ||||||||
\(77\) | −4.34057e7 | −0.140714 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.15357e8 | −0.333214 | −0.166607 | − | 0.986023i | \(-0.553281\pi\) | ||||
−0.166607 | + | 0.986023i | \(0.553281\pi\) | |||||||
\(80\) | −1.27418e8 | −0.347797 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.69554e8 | 1.63540 | ||||||||
\(83\) | 6.14639e8 | 1.42157 | 0.710785 | − | 0.703409i | \(-0.248340\pi\) | ||||
0.710785 | + | 0.703409i | \(0.248340\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.30935e7 | −0.172656 | ||||||||
\(86\) | −1.74142e8 | −0.343290 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.64111e8 | 1.18051 | ||||||||
\(89\) | 3.37797e8 | 0.570691 | 0.285345 | − | 0.958425i | \(-0.407892\pi\) | ||||
0.285345 | + | 0.958425i | \(0.407892\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.57104e7 | 0.0851629 | ||||||||
\(92\) | 1.92031e7 | 0.0279465 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.95731e8 | 0.919106 | ||||||||
\(95\) | −2.95415e8 | −0.372114 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.35307e8 | −0.269874 | −0.134937 | − | 0.990854i | \(-0.543083\pi\) | ||||
−0.134937 | + | 0.990854i | \(0.543083\pi\) | |||||||
\(98\) | 8.92867e8 | 0.977843 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.36735e7 | 0.0136735 | ||||||||
\(101\) | 9.16170e8 | 0.876052 | 0.438026 | − | 0.898962i | \(-0.355678\pi\) | ||||
0.438026 | + | 0.898962i | \(0.355678\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.00799e8 | 0.0882451 | 0.0441225 | − | 0.999026i | \(-0.485951\pi\) | ||||
0.0441225 | + | 0.999026i | \(0.485951\pi\) | |||||||
\(104\) | −8.52375e8 | −0.714465 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.22282e8 | 0.171013 | ||||||||
\(107\) | −1.50887e9 | −1.11282 | −0.556411 | − | 0.830907i | \(-0.687822\pi\) | ||||
−0.556411 | + | 0.830907i | \(0.687822\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.26733e9 | −1.53849 | −0.769247 | − | 0.638951i | \(-0.779369\pi\) | ||||
−0.769247 | + | 0.638951i | \(0.779369\pi\) | |||||||
\(110\) | −6.30776e8 | −0.410779 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.96842e8 | 0.118205 | ||||||||
\(113\) | −1.15962e9 | −0.669054 | −0.334527 | − | 0.942386i | \(-0.608577\pi\) | ||||
−0.334527 | + | 0.942386i | \(0.608577\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.18555e9 | −0.632092 | ||||||||
\(116\) | −3.72303e7 | −0.0190913 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.81095e9 | −1.33470 | ||||||||
\(119\) | 1.28367e8 | 0.0586803 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.78315e8 | 0.372491 | ||||||||
\(122\) | 3.42960e9 | 1.40160 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.45928e7 | 0.00554295 | ||||||||
\(125\) | −1.80881e9 | −0.662672 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.61195e9 | −0.890938 | −0.445469 | − | 0.895297i | \(-0.646963\pi\) | ||||
−0.445469 | + | 0.895297i | \(0.646963\pi\) | |||||||
\(128\) | −2.96388e9 | −0.975924 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.09590e8 | 0.248611 | ||||||||
\(131\) | 3.26886e9 | 0.969786 | 0.484893 | − | 0.874574i | \(-0.338859\pi\) | ||||
0.484893 | + | 0.874574i | \(0.338859\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.56372e8 | 0.126470 | ||||||||
\(134\) | 7.20087e9 | 1.92936 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.96403e9 | −0.492292 | ||||||||
\(137\) | 5.66884e7 | 0.0137484 | 0.00687419 | − | 0.999976i | \(-0.497812\pi\) | ||||
0.00687419 | + | 0.999976i | \(0.497812\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.79897e9 | 1.54482 | 0.772408 | − | 0.635127i | \(-0.219052\pi\) | ||||
0.772408 | + | 0.635127i | \(0.219052\pi\) | |||||||
\(140\) | 3.01476e6 | 0.000663249 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.45045e9 | 0.505764 | ||||||||
\(143\) | −4.15369e9 | −0.830657 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.29850e9 | 0.431805 | ||||||||
\(146\) | −1.49211e9 | −0.271778 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.14177e8 | −0.0195615 | ||||||||
\(149\) | −1.45949e9 | −0.242585 | −0.121292 | − | 0.992617i | \(-0.538704\pi\) | ||||
−0.121292 | + | 0.992617i | \(0.538704\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.95922e9 | 0.776277 | 0.388139 | − | 0.921601i | \(-0.373118\pi\) | ||||
0.388139 | + | 0.921601i | \(0.373118\pi\) | |||||||
\(152\) | −6.98254e9 | −1.06100 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9.74455e8 | 0.139611 | ||||||||
\(155\) | −9.00921e8 | −0.125370 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.69095e9 | 0.747543 | 0.373772 | − | 0.927521i | \(-0.378064\pi\) | ||||
0.373772 | + | 0.927521i | \(0.378064\pi\) | |||||||
\(158\) | 2.58977e9 | 0.330601 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.15425e7 | −0.0110429 | ||||||||
\(161\) | 1.83150e9 | 0.214828 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.88882e9 | 0.875322 | 0.437661 | − | 0.899140i | \(-0.355807\pi\) | ||||
0.437661 | + | 0.899140i | \(0.355807\pi\) | |||||||
\(164\) | 2.38594e8 | 0.0257551 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.37986e10 | −1.41042 | ||||||||
\(167\) | −9.25008e9 | −0.920283 | −0.460142 | − | 0.887846i | \(-0.652201\pi\) | ||||
−0.460142 | + | 0.887846i | \(0.652201\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.27331e9 | −0.497271 | ||||||||
\(170\) | 1.86544e9 | 0.171302 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.20552e7 | −0.00540630 | ||||||||
\(173\) | 1.85425e10 | 1.57384 | 0.786922 | − | 0.617052i | \(-0.211673\pi\) | ||||
0.786922 | + | 0.617052i | \(0.211673\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.30411e9 | 0.105110 | ||||||||
\(176\) | −1.46762e10 | −1.15294 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.58352e9 | −0.566215 | ||||||||
\(179\) | 1.83931e10 | 1.33911 | 0.669555 | − | 0.742762i | \(-0.266485\pi\) | ||||
0.669555 | + | 0.742762i | \(0.266485\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.17014e9 | 0.0810375 | 0.0405187 | − | 0.999179i | \(-0.487099\pi\) | ||||
0.0405187 | + | 0.999179i | \(0.487099\pi\) | |||||||
\(182\) | −1.25070e9 | −0.0844949 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.80221e10 | −1.80227 | ||||||||
\(185\) | 7.04901e9 | 0.442441 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.57086e9 | −0.572353 | ||||||||
\(188\) | 2.47922e8 | 0.0144746 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.63205e9 | 0.369196 | ||||||||
\(191\) | 1.03749e10 | 0.564073 | 0.282036 | − | 0.959404i | \(-0.408990\pi\) | ||||
0.282036 | + | 0.959404i | \(0.408990\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.17395e10 | −0.609037 | −0.304518 | − | 0.952506i | \(-0.598496\pi\) | ||||
−0.304518 | + | 0.952506i | \(0.598496\pi\) | |||||||
\(194\) | 5.28263e9 | 0.267758 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.18172e8 | 0.0153996 | ||||||||
\(197\) | −2.61163e10 | −1.23542 | −0.617708 | − | 0.786408i | \(-0.711938\pi\) | ||||
−0.617708 | + | 0.786408i | \(0.711938\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.31315e10 | 1.04560 | 0.522800 | − | 0.852455i | \(-0.324887\pi\) | ||||
0.522800 | + | 0.852455i | \(0.324887\pi\) | |||||||
\(200\) | −1.99530e10 | −0.881807 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.05680e10 | −0.869181 | ||||||||
\(203\) | −3.55084e9 | −0.146757 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.47302e10 | −0.582527 | ||||||||
\(206\) | −2.26294e9 | −0.0875530 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.88367e10 | 0.697782 | ||||||||
\(209\) | −3.40265e10 | −1.23355 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.57907e10 | 0.895759 | 0.447880 | − | 0.894094i | \(-0.352179\pi\) | ||||
0.447880 | + | 0.894094i | \(0.352179\pi\) | |||||||
\(212\) | 7.92099e7 | 0.00269320 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.38741e10 | 1.10409 | ||||||||
\(215\) | 3.83113e9 | 0.122279 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.39179e9 | 0.0426093 | ||||||||
\(218\) | 5.09015e10 | 1.52643 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.24776e8 | −0.00646916 | ||||||||
\(221\) | 1.22840e10 | 0.346398 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00337e9 | −0.0271699 | −0.0135850 | − | 0.999908i | \(-0.504324\pi\) | ||||
−0.0135850 | + | 0.999908i | \(0.504324\pi\) | |||||||
\(224\) | 1.41420e8 | 0.00375313 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.60333e10 | 0.663806 | ||||||||
\(227\) | −5.27911e10 | −1.31961 | −0.659803 | − | 0.751438i | \(-0.729360\pi\) | ||||
−0.659803 | + | 0.751438i | \(0.729360\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.10909e10 | 0.747091 | 0.373546 | − | 0.927612i | \(-0.378142\pi\) | ||||
0.373546 | + | 0.927612i | \(0.378142\pi\) | |||||||
\(230\) | 2.66156e10 | 0.627134 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.43281e10 | 1.23120 | ||||||||
\(233\) | 3.41332e10 | 0.758710 | 0.379355 | − | 0.925251i | \(-0.376146\pi\) | ||||
0.379355 | + | 0.925251i | \(0.376146\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.53061e10 | −0.327385 | ||||||||
\(236\) | −1.00168e9 | −0.0210196 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.88183e9 | −0.0582200 | ||||||||
\(239\) | 9.02670e10 | 1.78953 | 0.894764 | − | 0.446539i | \(-0.147344\pi\) | ||||
0.894764 | + | 0.446539i | \(0.147344\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.73393e10 | −1.47681 | −0.738403 | − | 0.674360i | \(-0.764420\pi\) | ||||
−0.738403 | + | 0.674360i | \(0.764420\pi\) | |||||||
\(242\) | −1.97181e10 | −0.369570 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.22213e9 | 0.0220731 | ||||||||
\(245\) | −1.96431e10 | −0.348307 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.36724e10 | 0.746570 | ||||||||
\(248\) | −2.12945e10 | −0.357466 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.06077e10 | 0.657474 | ||||||||
\(251\) | −4.53113e10 | −0.720568 | −0.360284 | − | 0.932843i | \(-0.617320\pi\) | ||||
−0.360284 | + | 0.932843i | \(0.617320\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.36554e11 | −2.09538 | ||||||||
\(254\) | 5.86380e10 | 0.883950 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.22043e9 | −0.0468635 | ||||||||
\(257\) | −1.35887e11 | −1.94303 | −0.971514 | − | 0.236984i | \(-0.923841\pi\) | ||||
−0.971514 | + | 0.236984i | \(0.923841\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.08897e10 | −0.150372 | ||||||||
\(260\) | 2.88496e8 | 0.00391525 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.33858e10 | −0.962179 | ||||||||
\(263\) | −4.81731e10 | −0.620875 | −0.310437 | − | 0.950594i | \(-0.600475\pi\) | ||||
−0.310437 | + | 0.950594i | \(0.600475\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.89021e9 | −0.0609145 | ||||||||
\(266\) | −1.02455e10 | −0.125478 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.56602e9 | 0.0303846 | ||||||||
\(269\) | 1.33744e11 | 1.55736 | 0.778682 | − | 0.627418i | \(-0.215888\pi\) | ||||
0.778682 | + | 0.627418i | \(0.215888\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.03388e10 | −0.792197 | −0.396098 | − | 0.918208i | \(-0.629636\pi\) | ||||
−0.396098 | + | 0.918208i | \(0.629636\pi\) | |||||||
\(272\) | 4.34032e10 | 0.480797 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.27265e9 | −0.0136406 | ||||||||
\(275\) | −9.72326e10 | −1.02521 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.34327e11 | −1.37090 | −0.685449 | − | 0.728121i | \(-0.740394\pi\) | ||||
−0.685449 | + | 0.728121i | \(0.740394\pi\) | |||||||
\(278\) | −1.52637e11 | −1.53270 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.39927e9 | −0.0427730 | ||||||||
\(281\) | 1.15851e11 | 1.10847 | 0.554233 | − | 0.832362i | \(-0.313012\pi\) | ||||
0.554233 | + | 0.832362i | \(0.313012\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.40288e11 | 1.30011 | 0.650055 | − | 0.759887i | \(-0.274746\pi\) | ||||
0.650055 | + | 0.759887i | \(0.274746\pi\) | |||||||
\(284\) | 8.73214e8 | 0.00796504 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.32501e10 | 0.824142 | ||||||||
\(287\) | 2.27559e10 | 0.197982 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.02832e10 | −0.761319 | ||||||||
\(290\) | −5.16012e10 | −0.428419 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.31712e8 | −0.00428010 | ||||||||
\(293\) | 1.59942e11 | 1.26782 | 0.633910 | − | 0.773407i | \(-0.281449\pi\) | ||||
0.633910 | + | 0.773407i | \(0.281449\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.18409e10 | 0.475420 | ||||||||
\(296\) | 1.66613e11 | 1.26153 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.27655e10 | 0.240682 | ||||||||
\(299\) | 1.75265e11 | 1.26816 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.91852e9 | −0.0415589 | ||||||||
\(302\) | −1.11334e11 | −0.770189 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.54308e11 | 1.03623 | ||||||||
\(305\) | −7.54512e10 | −0.499249 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.98532e11 | 1.27558 | 0.637791 | − | 0.770210i | \(-0.279849\pi\) | ||||
0.637791 | + | 0.770210i | \(0.279849\pi\) | |||||||
\(308\) | 3.47245e8 | 0.00219866 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.02256e10 | 0.124387 | ||||||||
\(311\) | 2.24811e10 | 0.136269 | 0.0681344 | − | 0.997676i | \(-0.478295\pi\) | ||||
0.0681344 | + | 0.997676i | \(0.478295\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.95978e10 | −0.350978 | −0.175489 | − | 0.984481i | \(-0.556151\pi\) | ||||
−0.175489 | + | 0.984481i | \(0.556151\pi\) | |||||||
\(314\) | −1.27761e11 | −0.741680 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.22860e8 | 0.00520647 | ||||||||
\(317\) | −3.02644e11 | −1.68332 | −0.841658 | − | 0.540012i | \(-0.818420\pi\) | ||||
−0.841658 | + | 0.540012i | \(0.818420\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.64745e11 | 1.43143 | ||||||||
\(320\) | 6.72931e10 | 0.358753 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.11171e10 | −0.213143 | ||||||||
\(323\) | 1.00629e11 | 0.514414 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.24796e11 | 0.620479 | ||||||||
\(326\) | −1.77104e11 | −0.868456 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.48168e11 | −1.66095 | ||||||||
\(329\) | 2.36456e10 | 0.111268 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.50482e10 | 0.206277 | 0.103139 | − | 0.994667i | \(-0.467111\pi\) | ||||
0.103139 | + | 0.994667i | \(0.467111\pi\) | |||||||
\(332\) | −4.91711e9 | −0.0222120 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.07664e11 | 0.913065 | ||||||||
\(335\) | −1.58419e11 | −0.687236 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.02480e11 | −0.432818 | −0.216409 | − | 0.976303i | \(-0.569435\pi\) | ||||
−0.216409 | + | 0.976303i | \(0.569435\pi\) | |||||||
\(338\) | 1.18385e11 | 0.493371 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.64748e8 | 0.00269775 | ||||||||
\(341\) | −1.03770e11 | −0.415600 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.11354e10 | 0.238490 | ||||||||
\(344\) | 9.05539e10 | 0.348654 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.16279e11 | −1.56150 | ||||||||
\(347\) | 1.90947e11 | 0.707017 | 0.353509 | − | 0.935431i | \(-0.384988\pi\) | ||||
0.353509 | + | 0.935431i | \(0.384988\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.17959e11 | −0.786431 | −0.393216 | − | 0.919446i | \(-0.628637\pi\) | ||||
−0.393216 | + | 0.919446i | \(0.628637\pi\) | |||||||
\(350\) | −2.92772e10 | −0.104285 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.05440e10 | −0.0366071 | ||||||||
\(353\) | 3.13329e11 | 1.07403 | 0.537013 | − | 0.843574i | \(-0.319553\pi\) | ||||
0.537013 | + | 0.843574i | \(0.319553\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.39099e10 | −0.180153 | ||||||||
\(356\) | −2.70238e9 | −0.00891704 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.12924e11 | −1.32861 | ||||||||
\(359\) | −2.37983e11 | −0.756173 | −0.378087 | − | 0.925770i | \(-0.623418\pi\) | ||||
−0.378087 | + | 0.925770i | \(0.623418\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.50706e10 | 0.108683 | ||||||||
\(362\) | −2.62697e10 | −0.0804019 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.45684e8 | −0.00133067 | ||||||||
\(365\) | 3.28265e10 | 0.0968069 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.25345e11 | 0.936153 | 0.468077 | − | 0.883688i | \(-0.344947\pi\) | ||||
0.468077 | + | 0.883688i | \(0.344947\pi\) | |||||||
\(368\) | 6.19263e11 | 1.76019 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.58250e11 | −0.438971 | ||||||||
\(371\) | 7.55464e9 | 0.0207029 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.13899e11 | −1.37464 | −0.687319 | − | 0.726356i | \(-0.741212\pi\) | ||||
−0.687319 | + | 0.726356i | \(0.741212\pi\) | |||||||
\(374\) | 2.14865e11 | 0.567863 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.61780e11 | −0.933467 | ||||||||
\(377\) | −3.39796e11 | −0.866328 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.49235e11 | 1.61631 | 0.808156 | − | 0.588968i | \(-0.200466\pi\) | ||||
0.808156 | + | 0.588968i | \(0.200466\pi\) | |||||||
\(380\) | 2.36332e9 | 0.00581429 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.32917e11 | −0.559649 | ||||||||
\(383\) | −5.68193e11 | −1.34928 | −0.674638 | − | 0.738148i | \(-0.735700\pi\) | ||||
−0.674638 | + | 0.738148i | \(0.735700\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.14380e10 | −0.0497292 | ||||||||
\(386\) | 2.63552e11 | 0.604260 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.88245e9 | 0.00421679 | ||||||||
\(389\) | 1.85758e11 | 0.411315 | 0.205657 | − | 0.978624i | \(-0.434067\pi\) | ||||
0.205657 | + | 0.978624i | \(0.434067\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.03842e11 | 0.873808 | ||||||||
\(392\) | −4.64291e11 | −0.993122 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.86309e11 | 1.22573 | ||||||||
\(395\) | −5.69749e10 | −0.117760 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.00165e11 | −0.606461 | −0.303230 | − | 0.952917i | \(-0.598065\pi\) | ||||
−0.303230 | + | 0.952917i | \(0.598065\pi\) | |||||||
\(398\) | −5.19302e11 | −1.03740 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.40943e11 | 0.861218 | ||||||||
\(401\) | −6.13010e11 | −1.18391 | −0.591954 | − | 0.805972i | \(-0.701643\pi\) | ||||
−0.591954 | + | 0.805972i | \(0.701643\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.33187e11 | 0.251529 | ||||||||
\(404\) | −7.32936e9 | −0.0136883 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.97161e10 | 0.145606 | ||||||||
\(407\) | 8.11918e11 | 1.46669 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.78447e11 | 0.315322 | 0.157661 | − | 0.987493i | \(-0.449605\pi\) | ||||
0.157661 | + | 0.987493i | \(0.449605\pi\) | |||||||
\(410\) | 3.30692e11 | 0.577958 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.06395e8 | −0.00137883 | ||||||||
\(413\) | −9.55350e10 | −0.161580 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.03569e11 | 0.502391 | ||||||||
\(416\) | 1.35331e10 | 0.0221553 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.63892e11 | 1.22388 | ||||||||
\(419\) | −1.13405e11 | −0.179751 | −0.0898753 | − | 0.995953i | \(-0.528647\pi\) | ||||
−0.0898753 | + | 0.995953i | \(0.528647\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.70461e11 | 0.264457 | 0.132229 | − | 0.991219i | \(-0.457787\pi\) | ||||
0.132229 | + | 0.991219i | \(0.457787\pi\) | |||||||
\(422\) | −5.78999e11 | −0.888734 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.15587e11 | −0.173685 | ||||||||
\(425\) | 2.87554e11 | 0.427532 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.16561e11 | 0.169679 | ||||||||
\(428\) | 1.20710e10 | 0.0173878 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.60086e10 | −0.121320 | ||||||||
\(431\) | 6.06017e11 | 0.845936 | 0.422968 | − | 0.906145i | \(-0.360988\pi\) | ||||
0.422968 | + | 0.906145i | \(0.360988\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.94608e11 | −1.22303 | −0.611515 | − | 0.791233i | \(-0.709440\pi\) | ||||
−0.611515 | + | 0.791233i | \(0.709440\pi\) | |||||||
\(434\) | −3.12456e10 | −0.0422751 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.81387e10 | 0.0240390 | ||||||||
\(437\) | 1.43574e12 | 1.88326 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.16164e11 | 1.04879 | 0.524393 | − | 0.851476i | \(-0.324292\pi\) | ||||
0.524393 | + | 0.851476i | \(0.324292\pi\) | |||||||
\(440\) | 3.28003e11 | 0.417197 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.75776e11 | −0.343681 | ||||||||
\(443\) | −2.55777e11 | −0.315533 | −0.157767 | − | 0.987476i | \(-0.550429\pi\) | ||||
−0.157767 | + | 0.987476i | \(0.550429\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.66838e11 | 0.201685 | ||||||||
\(446\) | 2.25256e10 | 0.0269568 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.03958e11 | −0.121929 | ||||||||
\(449\) | 2.65080e11 | 0.307800 | 0.153900 | − | 0.988086i | \(-0.450817\pi\) | ||||
0.153900 | + | 0.988086i | \(0.450817\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.69665e12 | −1.93107 | ||||||||
\(452\) | 9.27693e9 | 0.0104540 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.18516e12 | 1.30926 | ||||||||
\(455\) | 2.75153e10 | 0.0300970 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.25565e12 | −1.34662 | −0.673312 | − | 0.739358i | \(-0.735129\pi\) | ||||
−0.673312 | + | 0.739358i | \(0.735129\pi\) | |||||||
\(458\) | −6.97989e11 | −0.741232 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.48441e9 | 0.00987643 | ||||||||
\(461\) | −1.49720e12 | −1.54393 | −0.771963 | − | 0.635667i | \(-0.780725\pi\) | ||||
−0.771963 | + | 0.635667i | \(0.780725\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.88248e12 | −1.90377 | −0.951886 | − | 0.306453i | \(-0.900858\pi\) | ||||
−0.951886 | + | 0.306453i | \(0.900858\pi\) | |||||||
\(464\) | −1.20060e12 | −1.20245 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.66289e11 | −0.752759 | ||||||||
\(467\) | −1.43018e11 | −0.139145 | −0.0695723 | − | 0.997577i | \(-0.522163\pi\) | ||||
−0.0695723 | + | 0.997577i | \(0.522163\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.44734e11 | 0.233570 | ||||||||
\(470\) | 3.43621e11 | 0.324817 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.46170e12 | 1.35556 | ||||||||
\(473\) | 4.41276e11 | 0.405355 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.02232e12 | 0.921433 | ||||||||
\(476\) | −1.02694e9 | −0.000916879 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.02649e12 | −1.77549 | ||||||||
\(479\) | −3.78756e11 | −0.328738 | −0.164369 | − | 0.986399i | \(-0.552559\pi\) | ||||
−0.164369 | + | 0.986399i | \(0.552559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.04208e12 | −0.887666 | ||||||||
\(482\) | 1.73626e12 | 1.46522 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.02652e9 | −0.00582018 | ||||||||
\(485\) | −1.16218e11 | −0.0953750 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.66599e9 | 0.00778692 | 0.00389346 | − | 0.999992i | \(-0.498761\pi\) | ||||
0.00389346 | + | 0.999992i | \(0.498761\pi\) | |||||||
\(488\) | −1.78339e12 | −1.42350 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.40986e11 | 0.345575 | ||||||||
\(491\) | 6.90819e11 | 0.536411 | 0.268205 | − | 0.963362i | \(-0.413569\pi\) | ||||
0.268205 | + | 0.963362i | \(0.413569\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.82952e11 | −0.596931 | ||||||||
\(494\) | −9.80443e11 | −0.740715 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.70589e11 | 0.349119 | ||||||||
\(497\) | 8.32828e10 | 0.0612282 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.97646e11 | 0.575914 | 0.287957 | − | 0.957643i | \(-0.407024\pi\) | ||||
0.287957 | + | 0.957643i | \(0.407024\pi\) | |||||||
\(500\) | 1.44705e10 | 0.0103542 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.01724e12 | 0.714916 | ||||||||
\(503\) | −4.71233e11 | −0.328231 | −0.164116 | − | 0.986441i | \(-0.552477\pi\) | ||||
−0.164116 | + | 0.986441i | \(0.552477\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.52495e11 | 0.309601 | ||||||||
\(506\) | 3.06563e12 | 2.07894 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.08956e10 | 0.0139209 | ||||||||
\(509\) | −2.09988e12 | −1.38664 | −0.693320 | − | 0.720630i | \(-0.743853\pi\) | ||||
−0.693320 | + | 0.720630i | \(0.743853\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.07120e10 | −0.0329016 | ||||||||
\(512\) | 1.58981e12 | 1.02242 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.05066e12 | 1.92779 | ||||||||
\(515\) | 4.97847e10 | 0.0311863 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.76298e12 | −1.08528 | ||||||||
\(518\) | 2.44472e11 | 0.149192 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.20987e11 | −0.252495 | ||||||||
\(521\) | 2.49095e12 | 1.48114 | 0.740569 | − | 0.671980i | \(-0.234556\pi\) | ||||
0.740569 | + | 0.671980i | \(0.234556\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.27462e11 | 0.542049 | 0.271024 | − | 0.962572i | \(-0.412638\pi\) | ||||
0.271024 | + | 0.962572i | \(0.412638\pi\) | |||||||
\(524\) | −2.61509e10 | −0.0151529 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.08148e12 | 0.616005 | ||||||||
\(527\) | 3.06886e11 | 0.173312 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.96073e12 | 2.19900 | ||||||||
\(530\) | 1.09785e11 | 0.0604368 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.65098e9 | −0.00197609 | ||||||||
\(533\) | 2.17762e12 | 1.16872 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.45230e11 | −0.393277 | ||||||||
\(536\) | −3.74445e12 | −1.95951 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.00255e12 | −1.54515 | ||||||||
\(539\) | −2.26252e12 | −1.15463 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.99506e12 | 1.00131 | 0.500655 | − | 0.865647i | \(-0.333093\pi\) | ||||
0.500655 | + | 0.865647i | \(0.333093\pi\) | |||||||
\(542\) | 1.57910e12 | 0.785984 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.11827e10 | 0.0152658 | ||||||||
\(545\) | −1.11983e12 | −0.543712 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.49828e11 | −0.0715567 | −0.0357784 | − | 0.999360i | \(-0.511391\pi\) | ||||
−0.0357784 | + | 0.999360i | \(0.511391\pi\) | |||||||
\(548\) | −4.53507e8 | −0.000214818 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.18287e12 | 1.01717 | ||||||||
\(551\) | −2.78356e12 | −1.28653 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.80177e10 | 0.0400228 | ||||||||
\(554\) | 3.01564e12 | 1.36015 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.43918e10 | −0.0241378 | ||||||||
\(557\) | −6.75741e11 | −0.297462 | −0.148731 | − | 0.988878i | \(-0.547519\pi\) | ||||
−0.148731 | + | 0.988878i | \(0.547519\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.66370e11 | −0.245328 | ||||||||
\(560\) | 9.72199e10 | 0.0417743 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.60086e12 | −1.09977 | ||||||||
\(563\) | −1.25366e12 | −0.525885 | −0.262943 | − | 0.964811i | \(-0.584693\pi\) | ||||
−0.262943 | + | 0.964811i | \(0.584693\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.72733e11 | −0.236447 | ||||||||
\(566\) | −3.14945e12 | −1.28991 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.27423e12 | −0.513667 | ||||||||
\(569\) | −3.15164e12 | −1.26047 | −0.630233 | − | 0.776406i | \(-0.717041\pi\) | ||||
−0.630233 | + | 0.776406i | \(0.717041\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.23310e12 | −1.66647 | −0.833233 | − | 0.552923i | \(-0.813513\pi\) | ||||
−0.833233 | + | 0.552923i | \(0.813513\pi\) | |||||||
\(572\) | 3.32295e10 | 0.0129790 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.10870e11 | −0.196429 | ||||||||
\(575\) | 4.10273e12 | 1.56519 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.23367e12 | 1.59011 | 0.795053 | − | 0.606540i | \(-0.207443\pi\) | ||||
0.795053 | + | 0.606540i | \(0.207443\pi\) | |||||||
\(578\) | 2.02685e12 | 0.755348 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.83880e10 | −0.00674696 | ||||||||
\(581\) | −4.68969e11 | −0.170747 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.63263e11 | −0.201931 | ||||||||
\(584\) | 7.75899e11 | 0.276024 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.59068e12 | −1.25788 | ||||||||
\(587\) | 1.39753e12 | 0.485837 | 0.242919 | − | 0.970047i | \(-0.421895\pi\) | ||||
0.242919 | + | 0.970047i | \(0.421895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.09105e12 | 0.373529 | ||||||||
\(590\) | −1.38833e12 | −0.471691 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.68199e12 | −1.23207 | ||||||||
\(593\) | −6.32131e11 | −0.209923 | −0.104962 | − | 0.994476i | \(-0.533472\pi\) | ||||
−0.104962 | + | 0.994476i | \(0.533472\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.34003e10 | 0.0207379 | ||||||||
\(596\) | 1.16759e10 | 0.00379039 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.93468e12 | −1.25821 | ||||||||
\(599\) | 5.15452e12 | 1.63594 | 0.817970 | − | 0.575261i | \(-0.195100\pi\) | ||||
0.817970 | + | 0.575261i | \(0.195100\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.37044e11 | −0.230440 | −0.115220 | − | 0.993340i | \(-0.536757\pi\) | ||||
−0.115220 | + | 0.993340i | \(0.536757\pi\) | |||||||
\(602\) | 1.32870e11 | 0.0412329 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.96737e10 | −0.0121293 | ||||||||
\(605\) | 4.33799e11 | 0.131640 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.87389e12 | 0.560267 | 0.280134 | − | 0.959961i | \(-0.409621\pi\) | ||||
0.280134 | + | 0.959961i | \(0.409621\pi\) | |||||||
\(608\) | 1.10861e11 | 0.0329013 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.69387e12 | 0.495333 | ||||||||
\(611\) | 2.26276e12 | 0.656829 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.62540e12 | −0.464931 | −0.232465 | − | 0.972605i | \(-0.574679\pi\) | ||||
−0.232465 | + | 0.972605i | \(0.574679\pi\) | |||||||
\(614\) | −4.45703e12 | −1.26558 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.06716e11 | −0.141792 | ||||||||
\(617\) | 4.48555e12 | 1.24604 | 0.623021 | − | 0.782205i | \(-0.285905\pi\) | ||||
0.623021 | + | 0.782205i | \(0.285905\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.64489e12 | 0.724102 | 0.362051 | − | 0.932158i | \(-0.382077\pi\) | ||||
0.362051 | + | 0.932158i | \(0.382077\pi\) | |||||||
\(620\) | 7.20737e9 | 0.00195891 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.04700e11 | −0.135200 | ||||||||
\(623\) | −2.57739e11 | −0.0685463 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.44489e12 | 0.640913 | ||||||||
\(626\) | 1.33797e12 | 0.348226 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.55276e10 | −0.0116804 | ||||||||
\(629\) | −2.40115e12 | −0.611633 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.53561e12 | −0.636723 | −0.318361 | − | 0.947969i | \(-0.603133\pi\) | ||||
−0.318361 | + | 0.947969i | \(0.603133\pi\) | |||||||
\(632\) | −1.34668e12 | −0.335767 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.79434e12 | 1.67011 | ||||||||
\(635\) | −1.29004e12 | −0.314862 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.90391e12 | 0.698805 | ||||||||
\(638\) | −5.94351e12 | −1.42020 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.46386e12 | −0.344897 | ||||||||
\(641\) | 7.11969e11 | 0.166571 | 0.0832856 | − | 0.996526i | \(-0.473459\pi\) | ||||
0.0832856 | + | 0.996526i | \(0.473459\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.97690e11 | −0.137888 | −0.0689441 | − | 0.997621i | \(-0.521963\pi\) | ||||
−0.0689441 | + | 0.997621i | \(0.521963\pi\) | |||||||
\(644\) | −1.46520e10 | −0.00335668 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.25912e12 | −0.510379 | ||||||||
\(647\) | −3.90064e12 | −0.875119 | −0.437559 | − | 0.899189i | \(-0.644157\pi\) | ||||
−0.437559 | + | 0.899189i | \(0.644157\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.12295e12 | 1.57601 | ||||||||
\(650\) | −2.80167e12 | −0.615612 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.31106e10 | −0.0136769 | ||||||||
\(653\) | −2.73627e11 | −0.0588912 | −0.0294456 | − | 0.999566i | \(-0.509374\pi\) | ||||
−0.0294456 | + | 0.999566i | \(0.509374\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.61449e12 | 0.342727 | ||||||||
\(656\) | 7.69419e12 | 1.62217 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.30843e11 | −0.110395 | ||||||||
\(659\) | 1.93239e12 | 0.399126 | 0.199563 | − | 0.979885i | \(-0.436048\pi\) | ||||
0.199563 | + | 0.979885i | \(0.436048\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.99819e12 | 1.83336 | 0.916682 | − | 0.399617i | \(-0.130857\pi\) | ||||
0.916682 | + | 0.399617i | \(0.130857\pi\) | |||||||
\(662\) | −1.01133e12 | −0.204660 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.17528e12 | 1.43246 | ||||||||
\(665\) | 2.25402e11 | 0.0446951 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.11709e13 | −2.18536 | ||||||||
\(668\) | 7.40007e10 | 0.0143794 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.55650e12 | 0.681846 | ||||||||
\(671\) | −8.69060e12 | −1.65500 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.80149e12 | −0.714309 | −0.357155 | − | 0.934045i | \(-0.616253\pi\) | ||||
−0.357155 | + | 0.934045i | \(0.616253\pi\) | |||||||
\(674\) | 2.30068e12 | 0.429424 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.21865e10 | 0.00776986 | ||||||||
\(677\) | 2.51015e12 | 0.459252 | 0.229626 | − | 0.973279i | \(-0.426250\pi\) | ||||
0.229626 | + | 0.973279i | \(0.426250\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.79539e11 | 0.0324149 | ||||||||
\(680\) | −9.70031e11 | −0.173978 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.32962e12 | 0.412341 | ||||||||
\(683\) | 1.00278e12 | 0.176325 | 0.0881623 | − | 0.996106i | \(-0.471901\pi\) | ||||
0.0881623 | + | 0.996106i | \(0.471901\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.79983e10 | 0.00485875 | ||||||||
\(686\) | −1.37249e12 | −0.236619 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.00116e12 | −0.340513 | ||||||||
\(689\) | 7.22939e11 | 0.122212 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.14248e12 | 0.190632 | 0.0953161 | − | 0.995447i | \(-0.469614\pi\) | ||||
0.0953161 | + | 0.995447i | \(0.469614\pi\) | |||||||
\(692\) | −1.48340e11 | −0.0245913 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.28675e12 | −0.701472 | ||||||||
\(695\) | 3.35801e12 | 0.545946 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.01764e12 | 0.805289 | ||||||||
\(698\) | 4.89317e12 | 0.780263 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.04329e10 | −0.00164234 | ||||||||
\(701\) | 5.29555e12 | 0.828285 | 0.414143 | − | 0.910212i | \(-0.364081\pi\) | ||||
0.414143 | + | 0.910212i | \(0.364081\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.53660e12 | −1.31821 | ||||||||
\(704\) | 7.75095e12 | 1.18926 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.03422e12 | −1.06560 | ||||||||
\(707\) | −6.99037e11 | −0.105224 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.01497e13 | −1.50849 | −0.754246 | − | 0.656592i | \(-0.771998\pi\) | ||||
−0.754246 | + | 0.656592i | \(0.771998\pi\) | |||||||
\(710\) | 1.21027e12 | 0.178740 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.94343e12 | 0.575062 | ||||||||
\(713\) | 4.37856e12 | 0.634495 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.05150e12 | −0.293559 | ||||||||
\(716\) | −1.47145e11 | −0.0209236 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.34271e12 | 0.750242 | ||||||||
\(719\) | −5.75277e12 | −0.802780 | −0.401390 | − | 0.915907i | \(-0.631473\pi\) | ||||
−0.401390 | + | 0.915907i | \(0.631473\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.69100e10 | −0.0105992 | ||||||||
\(722\) | −7.87333e11 | −0.107830 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.36116e9 | −0.00126621 | ||||||||
\(725\) | −7.95420e12 | −1.06924 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.10169e13 | −1.46270 | −0.731351 | − | 0.682001i | \(-0.761110\pi\) | ||||
−0.731351 | + | 0.682001i | \(0.761110\pi\) | |||||||
\(728\) | 6.50362e11 | 0.0858152 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.36953e11 | −0.0960476 | ||||||||
\(731\) | −1.30502e12 | −0.169040 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.75672e12 | −0.224768 | −0.112384 | − | 0.993665i | \(-0.535849\pi\) | ||||
−0.112384 | + | 0.993665i | \(0.535849\pi\) | |||||||
\(734\) | −7.30398e12 | −0.928811 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.44905e11 | 0.0558878 | ||||||||
\(737\) | −1.82470e13 | −2.27818 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.52901e12 | −0.558603 | −0.279301 | − | 0.960204i | \(-0.590103\pi\) | ||||
−0.279301 | + | 0.960204i | \(0.590103\pi\) | |||||||
\(740\) | −5.63921e10 | −0.00691314 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.69601e11 | −0.0205405 | ||||||||
\(743\) | 2.25595e12 | 0.271569 | 0.135784 | − | 0.990738i | \(-0.456645\pi\) | ||||
0.135784 | + | 0.990738i | \(0.456645\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.20841e11 | −0.0857307 | ||||||||
\(746\) | 1.15370e13 | 1.36386 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.65669e10 | 0.00894301 | ||||||||
\(749\) | 1.15127e12 | 0.133662 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.29242e12 | −1.06598 | −0.532990 | − | 0.846122i | \(-0.678932\pi\) | ||||
−0.532990 | + | 0.846122i | \(0.678932\pi\) | |||||||
\(752\) | 7.99500e12 | 0.911671 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.62840e12 | 0.859533 | ||||||||
\(755\) | 2.44935e12 | 0.274340 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.28505e12 | 0.806308 | 0.403154 | − | 0.915132i | \(-0.367914\pi\) | ||||
0.403154 | + | 0.915132i | \(0.367914\pi\) | |||||||
\(758\) | −1.45753e13 | −1.60364 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.44867e12 | −0.374965 | ||||||||
\(761\) | −2.78674e12 | −0.301207 | −0.150604 | − | 0.988594i | \(-0.548122\pi\) | ||||
−0.150604 | + | 0.988594i | \(0.548122\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.72998e12 | 0.184790 | ||||||||
\(764\) | −8.29995e10 | −0.00881364 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.27559e13 | 1.33869 | ||||||||
\(767\) | −9.14219e12 | −0.953830 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.63000e12 | 0.477433 | 0.238716 | − | 0.971089i | \(-0.423273\pi\) | ||||
0.238716 | + | 0.971089i | \(0.423273\pi\) | |||||||
\(770\) | 4.81282e11 | 0.0493391 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.39164e10 | 0.00951620 | ||||||||
\(773\) | 8.49811e12 | 0.856080 | 0.428040 | − | 0.903760i | \(-0.359204\pi\) | ||||
0.428040 | + | 0.903760i | \(0.359204\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.11773e12 | 0.310442 | ||||||||
\(776\) | −2.74697e12 | −0.271941 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.17026e12 | −0.408089 | ||||||||
\(779\) | 1.78388e13 | 1.73559 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.20944e12 | −0.597204 | ||||||||
\(782\) | −9.06623e12 | −0.866954 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.02604e13 | 0.969933 | ||||||||
\(785\) | 2.81075e12 | 0.264186 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.57079e12 | 0.331801 | 0.165900 | − | 0.986143i | \(-0.446947\pi\) | ||||
0.165900 | + | 0.986143i | \(0.446947\pi\) | |||||||
\(788\) | 2.08930e11 | 0.0193034 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.27908e12 | 0.116836 | ||||||||
\(791\) | 8.84787e11 | 0.0803608 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.11542e13 | 1.00164 | ||||||||
\(794\) | 6.73868e12 | 0.601704 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.85052e11 | −0.0163375 | ||||||||
\(797\) | 9.06883e12 | 0.796139 | 0.398070 | − | 0.917355i | \(-0.369680\pi\) | ||||
0.398070 | + | 0.917355i | \(0.369680\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.21381e12 | 0.452579 | ||||||||
\(800\) | 3.16793e11 | 0.0273445 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.37620e13 | 1.17462 | ||||||||
\(803\) | 3.78101e12 | 0.320914 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.04576e11 | 0.0759213 | ||||||||
\(806\) | −2.99003e12 | −0.249556 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.06953e13 | 0.882762 | ||||||||
\(809\) | 1.10403e13 | 0.906173 | 0.453087 | − | 0.891467i | \(-0.350323\pi\) | ||||
0.453087 | + | 0.891467i | \(0.350323\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.04507e12 | −0.0848302 | −0.0424151 | − | 0.999100i | \(-0.513505\pi\) | ||||
−0.0424151 | + | 0.999100i | \(0.513505\pi\) | |||||||
\(812\) | 2.84067e10 | 0.00229308 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.82275e13 | −1.45518 | ||||||||
\(815\) | 3.89628e12 | 0.309343 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.63963e12 | −0.364321 | ||||||||
\(818\) | −4.00612e12 | −0.312849 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.17841e11 | 0.00910198 | ||||||||
\(821\) | −1.04318e13 | −0.801340 | −0.400670 | − | 0.916223i | \(-0.631223\pi\) | ||||
−0.400670 | + | 0.916223i | \(0.631223\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.03298e12 | 0.534367 | 0.267184 | − | 0.963646i | \(-0.413907\pi\) | ||||
0.267184 | + | 0.963646i | \(0.413907\pi\) | |||||||
\(824\) | 1.17673e12 | 0.0889210 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.14476e12 | 0.160313 | ||||||||
\(827\) | −1.69223e13 | −1.25801 | −0.629006 | − | 0.777400i | \(-0.716538\pi\) | ||||
−0.629006 | + | 0.777400i | \(0.716538\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.27155e12 | 0.167042 | 0.0835212 | − | 0.996506i | \(-0.473383\pi\) | ||||
0.0835212 | + | 0.996506i | \(0.473383\pi\) | |||||||
\(830\) | −6.81511e12 | −0.498450 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9.94821e12 | −0.719764 | ||||||||
\(833\) | 6.69114e12 | 0.481502 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.56860e12 | −0.325233 | ||||||||
\(836\) | 2.72212e11 | 0.0192743 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.54594e12 | 0.178341 | ||||||||
\(839\) | 1.79457e13 | 1.25035 | 0.625175 | − | 0.780484i | \(-0.285027\pi\) | ||||
0.625175 | + | 0.780484i | \(0.285027\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.15056e12 | 0.492899 | ||||||||
\(842\) | −3.82684e12 | −0.262383 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.06325e11 | −0.0139962 | ||||||||
\(845\) | −2.60448e12 | −0.175738 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.70154e11 | −0.0447404 | ||||||||
\(848\) | 2.55436e12 | 0.169629 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.45557e12 | −0.424179 | ||||||||
\(851\) | −3.42588e13 | −2.23918 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.20102e13 | −1.42349 | −0.711744 | − | 0.702439i | \(-0.752095\pi\) | ||||
−0.711744 | + | 0.702439i | \(0.752095\pi\) | |||||||
\(854\) | −2.61678e12 | −0.168348 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.76145e13 | −1.12135 | ||||||||
\(857\) | −2.34048e13 | −1.48215 | −0.741074 | − | 0.671424i | \(-0.765683\pi\) | ||||
−0.741074 | + | 0.671424i | \(0.765683\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.26808e10 | 0.00267463 | 0.00133732 | − | 0.999999i | \(-0.499574\pi\) | ||||
0.00133732 | + | 0.999999i | \(0.499574\pi\) | |||||||
\(860\) | −3.06490e10 | −0.00191062 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.36051e13 | −0.839301 | ||||||||
\(863\) | 3.10119e13 | 1.90318 | 0.951590 | − | 0.307370i | \(-0.0994490\pi\) | ||||
0.951590 | + | 0.307370i | \(0.0994490\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.15814e12 | 0.556205 | ||||||||
\(866\) | 2.00839e13 | 1.21344 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.11343e10 | −0.000665770 0 | ||||||||
\(869\) | −6.56247e12 | −0.390372 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.34197e13 | 1.37880 | ||||||||
\(872\) | −2.64688e13 | −1.55028 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.22324e13 | −1.86849 | ||||||||
\(875\) | 1.38012e12 | 0.0795943 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.64046e13 | −0.936416 | −0.468208 | − | 0.883618i | \(-0.655100\pi\) | ||||
−0.468208 | + | 0.883618i | \(0.655100\pi\) | |||||||
\(878\) | −1.83228e13 | −1.04056 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7.24857e12 | −0.407456 | ||||||||
\(881\) | 2.25741e13 | 1.26246 | 0.631231 | − | 0.775595i | \(-0.282550\pi\) | ||||
0.631231 | + | 0.775595i | \(0.282550\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.75871e12 | −0.429503 | −0.214752 | − | 0.976669i | \(-0.568894\pi\) | ||||
−0.214752 | + | 0.976669i | \(0.568894\pi\) | |||||||
\(884\) | −9.82723e10 | −0.00541247 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.74219e12 | 0.313058 | ||||||||
\(887\) | 4.44036e12 | 0.240858 | 0.120429 | − | 0.992722i | \(-0.461573\pi\) | ||||
0.120429 | + | 0.992722i | \(0.461573\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.99291e12 | 0.107012 | ||||||||
\(890\) | −3.74549e12 | −0.200103 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.02694e9 | 0.000424530 0 | ||||||||
\(893\) | 1.85362e13 | 0.975414 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.08433e12 | 0.473249 | ||||||||
\(896\) | 2.26144e12 | 0.117219 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.95104e12 | −0.305386 | ||||||||
\(899\) | −8.48897e12 | −0.433447 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.66578e12 | 0.0842087 | ||||||||
\(902\) | 3.80897e13 | 1.91592 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.35373e13 | −0.674178 | ||||||||
\(905\) | 5.77933e11 | 0.0286391 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.71069e13 | 0.839342 | 0.419671 | − | 0.907676i | \(-0.362145\pi\) | ||||
0.419671 | + | 0.907676i | \(0.362145\pi\) | |||||||
\(908\) | 4.22329e11 | 0.0206189 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.17717e11 | −0.0298609 | ||||||||
\(911\) | −1.88236e13 | −0.905460 | −0.452730 | − | 0.891648i | \(-0.649550\pi\) | ||||
−0.452730 | + | 0.891648i | \(0.649550\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.49657e13 | 1.66542 | ||||||||
\(914\) | 2.81893e13 | 1.33606 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.48727e11 | −0.0116733 | ||||||||
\(917\) | −2.49414e12 | −0.116482 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.20992e13 | −1.94695 | −0.973473 | − | 0.228800i | \(-0.926520\pi\) | ||||
−0.973473 | + | 0.228800i | \(0.926520\pi\) | |||||||
\(920\) | −1.38401e13 | −0.636933 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.36121e13 | 1.53182 | ||||||||
\(923\) | 7.96971e12 | 0.361439 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.43938e13 | −1.09558 | ||||||||
\(926\) | 4.22615e13 | 1.88884 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.62564e11 | −0.0381791 | ||||||||
\(929\) | −1.23689e13 | −0.544831 | −0.272415 | − | 0.962180i | \(-0.587823\pi\) | ||||
−0.272415 | + | 0.962180i | \(0.587823\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.37885e13 | 1.03775 | ||||||||
\(932\) | −2.73066e11 | −0.0118548 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.21076e12 | 0.138053 | ||||||||
\(935\) | −4.72703e12 | −0.202272 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.10110e13 | 0.890467 | 0.445234 | − | 0.895414i | \(-0.353121\pi\) | ||||
0.445234 | + | 0.895414i | \(0.353121\pi\) | |||||||
\(938\) | −5.49426e12 | −0.231738 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.22449e11 | 0.00511539 | ||||||||
\(941\) | −1.49975e13 | −0.623543 | −0.311771 | − | 0.950157i | \(-0.600922\pi\) | ||||
−0.311771 | + | 0.950157i | \(0.600922\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.15900e13 | 2.94815 | ||||||||
\(944\) | −3.23021e13 | −1.32391 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.90662e12 | −0.402175 | ||||||||
\(947\) | −1.30832e12 | −0.0528615 | −0.0264307 | − | 0.999651i | \(-0.508414\pi\) | ||||
−0.0264307 | + | 0.999651i | \(0.508414\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.85287e12 | −0.194223 | ||||||||
\(950\) | −2.29509e13 | −0.914206 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.49855e12 | 0.0591297 | ||||||||
\(953\) | −4.18691e13 | −1.64428 | −0.822140 | − | 0.569285i | \(-0.807220\pi\) | ||||
−0.822140 | + | 0.569285i | \(0.807220\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.12417e12 | 0.199346 | ||||||||
\(956\) | −7.22136e11 | −0.0279614 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.50306e12 | 0.326160 | ||||||||
\(959\) | −4.32532e10 | −0.00165133 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.31123e13 | −0.874153 | ||||||||
\(962\) | 2.33947e13 | 0.880703 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.18714e11 | 0.0230751 | ||||||||
\(965\) | −5.79815e12 | −0.215237 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.10706e12 | −0.0407148 | −0.0203574 | − | 0.999793i | \(-0.506480\pi\) | ||||
−0.0203574 | + | 0.999793i | \(0.506480\pi\) | |||||||
\(968\) | 1.02534e13 | 0.375344 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.60908e12 | 0.0946270 | ||||||||
\(971\) | 2.21624e13 | 0.800075 | 0.400038 | − | 0.916499i | \(-0.368997\pi\) | ||||
0.400038 | + | 0.916499i | \(0.368997\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.18762e12 | −0.185550 | ||||||||
\(974\) | −2.17001e11 | −0.00772585 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.94113e13 | 1.39026 | ||||||||
\(977\) | 2.19683e13 | 0.771384 | 0.385692 | − | 0.922628i | \(-0.373963\pi\) | ||||
0.385692 | + | 0.922628i | \(0.373963\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.92166e13 | 0.668583 | ||||||||
\(980\) | 1.57145e11 | 0.00544229 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.55088e13 | −0.532204 | ||||||||
\(983\) | −4.07229e13 | −1.39107 | −0.695533 | − | 0.718494i | \(-0.744832\pi\) | ||||
−0.695533 | + | 0.718494i | \(0.744832\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.28988e13 | −0.436602 | ||||||||
\(986\) | 1.75772e13 | 0.592249 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.49379e11 | −0.0116652 | ||||||||
\(989\) | −1.86196e13 | −0.618853 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.69138e13 | 0.557070 | 0.278535 | − | 0.960426i | \(-0.410151\pi\) | ||||
0.278535 | + | 0.960426i | \(0.410151\pi\) | |||||||
\(992\) | 3.38091e11 | 0.0110849 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.86969e12 | −0.0607480 | ||||||||
\(995\) | 1.14246e13 | 0.369521 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.00661e13 | −1.28425 | −0.642125 | − | 0.766600i | \(-0.721947\pi\) | ||||
−0.642125 | + | 0.766600i | \(0.721947\pi\) | |||||||
\(998\) | −1.79071e13 | −0.571397 | ||||||||
\(999\) | 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 | 27.10.a.a.1.1 | ✓ | 2 | |
3.2 | odd | 2 | inner | 27.10.a.a.1.2 | yes | 2 | |
9.2 | odd | 6 | 81.10.c.f.28.1 | 4 | |||
9.4 | even | 3 | 81.10.c.f.55.2 | 4 | |||
9.5 | odd | 6 | 81.10.c.f.55.1 | 4 | |||
9.7 | even | 3 | 81.10.c.f.28.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.10.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
27.10.a.a.1.2 | yes | 2 | 3.2 | odd | 2 | inner | |
81.10.c.f.28.1 | 4 | 9.2 | odd | 6 | |||
81.10.c.f.28.2 | 4 | 9.7 | even | 3 | |||
81.10.c.f.55.1 | 4 | 9.5 | odd | 6 | |||
81.10.c.f.55.2 | 4 | 9.4 | even | 3 |