Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,6,Mod(99,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.99");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(39.2940358542\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-11}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 5) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.2 | ||
Root | \(0.500000 - 1.65831i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.99 |
Dual form | 245.6.b.a.99.1 |
$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.63325i | 1.17260i | 0.810093 | + | 0.586302i | \(0.199417\pi\) | ||||
−0.810093 | + | 0.586302i | \(0.800583\pi\) | |||||||
\(3\) | 19.8997i | 1.27657i | 0.769800 | + | 0.638285i | \(0.220356\pi\) | ||||
−0.769800 | + | 0.638285i | \(0.779644\pi\) | |||||||
\(4\) | −12.0000 | −0.375000 | ||||||||
\(5\) | 45.0000 | − | 33.1662i | 0.804984 | − | 0.593296i | ||||
\(6\) | −132.000 | −1.49691 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 132.665i | 0.732877i | ||||||||
\(9\) | −153.000 | −0.629630 | ||||||||
\(10\) | 220.000 | + | 298.496i | 0.695701 | + | 0.943928i | ||||
\(11\) | 252.000 | 0.627941 | 0.313970 | − | 0.949433i | \(-0.398341\pi\) | ||||
0.313970 | + | 0.949433i | \(0.398341\pi\) | |||||||
\(12\) | − | 238.797i | − | 0.478714i | ||||||
\(13\) | 119.398i | 0.195948i | 0.995189 | + | 0.0979739i | \(0.0312362\pi\) | ||||
−0.995189 | + | 0.0979739i | \(0.968764\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 660.000 | + | 895.489i | 0.757383 | + | 1.02762i | ||||
\(16\) | −1264.00 | −1.23438 | ||||||||
\(17\) | 689.858i | 0.578945i | 0.957186 | + | 0.289473i | \(0.0934799\pi\) | ||||
−0.957186 | + | 0.289473i | \(0.906520\pi\) | |||||||
\(18\) | − | 1014.89i | − | 0.738306i | ||||||
\(19\) | 220.000 | 0.139810 | 0.0699051 | − | 0.997554i | \(-0.477730\pi\) | ||||
0.0699051 | + | 0.997554i | \(0.477730\pi\) | |||||||
\(20\) | −540.000 | + | 397.995i | −0.301869 | + | 0.222486i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1671.58i | 0.736326i | ||||||||
\(23\) | 2434.40i | 0.959561i | 0.877388 | + | 0.479781i | \(0.159284\pi\) | ||||
−0.877388 | + | 0.479781i | \(0.840716\pi\) | |||||||
\(24\) | −2640.00 | −0.935569 | ||||||||
\(25\) | 925.000 | − | 2984.96i | 0.296000 | − | 0.955188i | ||||
\(26\) | −792.000 | −0.229769 | ||||||||
\(27\) | 1790.98i | 0.472804i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6930.00 | −1.53016 | −0.765082 | − | 0.643932i | \(-0.777302\pi\) | ||||
−0.765082 | + | 0.643932i | \(0.777302\pi\) | |||||||
\(30\) | −5940.00 | + | 4377.94i | −1.20499 | + | 0.888111i | ||||
\(31\) | −6752.00 | −1.26191 | −0.630955 | − | 0.775820i | \(-0.717337\pi\) | ||||
−0.630955 | + | 0.775820i | \(0.717337\pi\) | |||||||
\(32\) | − | 4139.15i | − | 0.714556i | ||||||
\(33\) | 5014.74i | 0.801610i | ||||||||
\(34\) | −4576.00 | −0.678873 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1836.00 | 0.236111 | ||||||||
\(37\) | 13969.6i | 1.67757i | 0.544464 | + | 0.838785i | \(0.316733\pi\) | ||||
−0.544464 | + | 0.838785i | \(0.683267\pi\) | |||||||
\(38\) | 1459.31i | 0.163942i | ||||||||
\(39\) | −2376.00 | −0.250141 | ||||||||
\(40\) | 4400.00 | + | 5969.92i | 0.434813 | + | 0.589955i | ||||
\(41\) | 198.000 | 0.0183952 | 0.00919762 | − | 0.999958i | \(-0.497072\pi\) | ||||
0.00919762 | + | 0.999958i | \(0.497072\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 417.895i | − | 0.0344664i | −0.999851 | − | 0.0172332i | \(-0.994514\pi\) | ||
0.999851 | − | 0.0172332i | \(-0.00548577\pi\) | |||||||
\(44\) | −3024.00 | −0.235478 | ||||||||
\(45\) | −6885.00 | + | 5074.44i | −0.506842 | + | 0.373557i | ||||
\(46\) | −16148.0 | −1.12519 | ||||||||
\(47\) | 10540.2i | 0.695994i | 0.937496 | + | 0.347997i | \(0.113138\pi\) | ||||
−0.937496 | + | 0.347997i | \(0.886862\pi\) | |||||||
\(48\) | − | 25153.3i | − | 1.57577i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 19800.0 | + | 6135.76i | 1.12006 | + | 0.347091i | ||||
\(51\) | −13728.0 | −0.739064 | ||||||||
\(52\) | − | 1432.78i | − | 0.0734804i | ||||||
\(53\) | − | 5823.99i | − | 0.284794i | −0.989810 | − | 0.142397i | \(-0.954519\pi\) | ||
0.989810 | − | 0.142397i | \(-0.0454810\pi\) | |||||||
\(54\) | −11880.0 | −0.554411 | ||||||||
\(55\) | 11340.0 | − | 8357.89i | 0.505483 | − | 0.372555i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4377.94i | 0.178477i | ||||||||
\(58\) | − | 45968.4i | − | 1.79428i | ||||||
\(59\) | 24660.0 | 0.922281 | 0.461140 | − | 0.887327i | \(-0.347440\pi\) | ||||
0.461140 | + | 0.887327i | \(0.347440\pi\) | |||||||
\(60\) | −7920.00 | − | 10745.9i | −0.284019 | − | 0.385357i | ||||
\(61\) | 5698.00 | 0.196064 | 0.0980320 | − | 0.995183i | \(-0.468745\pi\) | ||||
0.0980320 | + | 0.995183i | \(0.468745\pi\) | |||||||
\(62\) | − | 44787.7i | − | 1.47972i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12992.0 | −0.396484 | ||||||||
\(65\) | 3960.00 | + | 5372.93i | 0.116255 | + | 0.157735i | ||||
\(66\) | −33264.0 | −0.939971 | ||||||||
\(67\) | − | 43640.1i | − | 1.18768i | −0.804583 | − | 0.593840i | \(-0.797611\pi\) | ||
0.804583 | − | 0.593840i | \(-0.202389\pi\) | |||||||
\(68\) | − | 8278.30i | − | 0.217104i | ||||||
\(69\) | −48444.0 | −1.22495 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 53352.0 | 1.25604 | 0.628022 | − | 0.778196i | \(-0.283865\pi\) | ||||
0.628022 | + | 0.778196i | \(0.283865\pi\) | |||||||
\(72\) | − | 20297.7i | − | 0.461441i | ||||||
\(73\) | − | 70922.7i | − | 1.55768i | −0.627223 | − | 0.778840i | \(-0.715808\pi\) | ||
0.627223 | − | 0.778840i | \(-0.284192\pi\) | |||||||
\(74\) | −92664.0 | −1.96712 | ||||||||
\(75\) | 59400.0 | + | 18407.3i | 1.21936 | + | 0.377865i | ||||
\(76\) | −2640.00 | −0.0524288 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 15760.6i | − | 0.293316i | ||||||
\(79\) | 51920.0 | 0.935981 | 0.467990 | − | 0.883734i | \(-0.344978\pi\) | ||||
0.467990 | + | 0.883734i | \(0.344978\pi\) | |||||||
\(80\) | −56880.0 | + | 41922.1i | −0.993653 | + | 0.732350i | ||||
\(81\) | −72819.0 | −1.23320 | ||||||||
\(82\) | 1313.38i | 0.0215703i | ||||||||
\(83\) | 61841.8i | 0.985342i | 0.870216 | + | 0.492671i | \(0.163979\pi\) | ||||
−0.870216 | + | 0.492671i | \(0.836021\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22880.0 | + | 31043.6i | 0.343486 | + | 0.466042i | ||||
\(86\) | 2772.00 | 0.0404154 | ||||||||
\(87\) | − | 137905.i | − | 1.95336i | ||||||
\(88\) | 33431.6i | 0.460204i | ||||||||
\(89\) | 9990.00 | 0.133687 | 0.0668437 | − | 0.997763i | \(-0.478707\pi\) | ||||
0.0668437 | + | 0.997763i | \(0.478707\pi\) | |||||||
\(90\) | −33660.0 | − | 45669.9i | −0.438034 | − | 0.594325i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 29212.8i | − | 0.359836i | ||||||
\(93\) | − | 134363.i | − | 1.61092i | ||||||
\(94\) | −69916.0 | −0.816125 | ||||||||
\(95\) | 9900.00 | − | 7296.57i | 0.112545 | − | 0.0829488i | ||||
\(96\) | 82368.0 | 0.912180 | ||||||||
\(97\) | 101250.i | 1.09261i | 0.837586 | + | 0.546305i | \(0.183966\pi\) | ||||
−0.837586 | + | 0.546305i | \(0.816034\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −38556.0 | −0.395370 | ||||||||
\(100\) | −11100.0 | + | 35819.5i | −0.111000 | + | 0.358195i | ||||
\(101\) | 109098. | 1.06418 | 0.532088 | − | 0.846689i | \(-0.321408\pi\) | ||||
0.532088 | + | 0.846689i | \(0.321408\pi\) | |||||||
\(102\) | − | 91061.3i | − | 0.866629i | ||||||
\(103\) | − | 70624.2i | − | 0.655935i | −0.944689 | − | 0.327967i | \(-0.893636\pi\) | ||
0.944689 | − | 0.327967i | \(-0.106364\pi\) | |||||||
\(104\) | −15840.0 | −0.143606 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 38632.0 | 0.333951 | ||||||||
\(107\) | 97117.4i | 0.820045i | 0.912075 | + | 0.410022i | \(0.134479\pi\) | ||||
−0.912075 | + | 0.410022i | \(0.865521\pi\) | |||||||
\(108\) | − | 21491.7i | − | 0.177301i | ||||||
\(109\) | −21010.0 | −0.169379 | −0.0846895 | − | 0.996407i | \(-0.526990\pi\) | ||||
−0.0846895 | + | 0.996407i | \(0.526990\pi\) | |||||||
\(110\) | 55440.0 | + | 75221.1i | 0.436859 | + | 0.592731i | ||||
\(111\) | −277992. | −2.14153 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 105018.i | 0.773688i | 0.922145 | + | 0.386844i | \(0.126435\pi\) | ||||
−0.922145 | + | 0.386844i | \(0.873565\pi\) | |||||||
\(114\) | −29040.0 | −0.209283 | ||||||||
\(115\) | 80740.0 | + | 109548.i | 0.569304 | + | 0.772432i | ||||
\(116\) | 83160.0 | 0.573812 | ||||||||
\(117\) | − | 18268.0i | − | 0.123375i | ||||||
\(118\) | 163576.i | 1.08147i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −118800. | + | 87558.9i | −0.753119 | + | 0.555069i | ||||
\(121\) | −97547.0 | −0.605690 | ||||||||
\(122\) | 37796.3i | 0.229905i | ||||||||
\(123\) | 3940.15i | 0.0234828i | ||||||||
\(124\) | 81024.0 | 0.473216 | ||||||||
\(125\) | −57375.0 | − | 165002.i | −0.328434 | − | 0.944527i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 87220.6i | − | 0.479855i | −0.970791 | − | 0.239927i | \(-0.922876\pi\) | ||
0.970791 | − | 0.239927i | \(-0.0771236\pi\) | |||||||
\(128\) | − | 218632.i | − | 1.17947i | ||||||
\(129\) | 8316.00 | 0.0439987 | ||||||||
\(130\) | −35640.0 | + | 26267.7i | −0.184961 | + | 0.136321i | ||||
\(131\) | −192852. | −0.981852 | −0.490926 | − | 0.871201i | \(-0.663341\pi\) | ||||
−0.490926 | + | 0.871201i | \(0.663341\pi\) | |||||||
\(132\) | − | 60176.8i | − | 0.300604i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 289476. | 1.39268 | ||||||||
\(135\) | 59400.0 | + | 80594.0i | 0.280512 | + | 0.380599i | ||||
\(136\) | −91520.0 | −0.424296 | ||||||||
\(137\) | − | 143570.i | − | 0.653525i | −0.945106 | − | 0.326763i | \(-0.894042\pi\) | ||
0.945106 | − | 0.326763i | \(-0.105958\pi\) | |||||||
\(138\) | − | 321341.i | − | 1.43638i | ||||||
\(139\) | 318340. | 1.39751 | 0.698754 | − | 0.715362i | \(-0.253738\pi\) | ||||
0.698754 | + | 0.715362i | \(0.253738\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −209748. | −0.888485 | ||||||||
\(142\) | 353897.i | 1.47284i | ||||||||
\(143\) | 30088.4i | 0.123044i | ||||||||
\(144\) | 193392. | 0.777199 | ||||||||
\(145\) | −311850. | + | 229842.i | −1.23176 | + | 0.907841i | ||||
\(146\) | 470448. | 1.82654 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 167635.i | − | 0.629088i | ||||||
\(149\) | 84150.0 | 0.310519 | 0.155260 | − | 0.987874i | \(-0.450379\pi\) | ||||
0.155260 | + | 0.987874i | \(0.450379\pi\) | |||||||
\(150\) | −122100. | + | 394015.i | −0.443085 | + | 1.42983i | ||||
\(151\) | −155848. | −0.556236 | −0.278118 | − | 0.960547i | \(-0.589711\pi\) | ||||
−0.278118 | + | 0.960547i | \(0.589711\pi\) | |||||||
\(152\) | 29186.3i | 0.102464i | ||||||||
\(153\) | − | 105548.i | − | 0.364521i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −303840. | + | 223939.i | −1.01582 | + | 0.748686i | ||||
\(156\) | 28512.0 | 0.0938029 | ||||||||
\(157\) | − | 356643.i | − | 1.15474i | −0.816482 | − | 0.577371i | \(-0.804079\pi\) | ||
0.816482 | − | 0.577371i | \(-0.195921\pi\) | |||||||
\(158\) | 344398.i | 1.09753i | ||||||||
\(159\) | 115896. | 0.363560 | ||||||||
\(160\) | −137280. | − | 186262.i | −0.423943 | − | 0.575206i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 483027.i | − | 1.44605i | ||||||
\(163\) | − | 144890.i | − | 0.427139i | −0.976928 | − | 0.213570i | \(-0.931491\pi\) | ||
0.976928 | − | 0.213570i | \(-0.0685090\pi\) | |||||||
\(164\) | −2376.00 | −0.00689822 | ||||||||
\(165\) | 166320. | + | 225663.i | 0.475592 | + | 0.645284i | ||||
\(166\) | −410212. | −1.15542 | ||||||||
\(167\) | 18102.1i | 0.0502272i | 0.999685 | + | 0.0251136i | \(0.00799474\pi\) | ||||
−0.999685 | + | 0.0251136i | \(0.992005\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 357037. | 0.961604 | ||||||||
\(170\) | −205920. | + | 151769.i | −0.546482 | + | 0.402773i | ||||
\(171\) | −33660.0 | −0.0880286 | ||||||||
\(172\) | 5014.74i | 0.0129249i | ||||||||
\(173\) | 492572.i | 1.25128i | 0.780112 | + | 0.625640i | \(0.215162\pi\) | ||||
−0.780112 | + | 0.625640i | \(0.784838\pi\) | |||||||
\(174\) | 914760. | 2.29052 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −318528. | −0.775115 | ||||||||
\(177\) | 490728.i | 1.17736i | ||||||||
\(178\) | 66266.2i | 0.156762i | ||||||||
\(179\) | 444420. | 1.03672 | 0.518359 | − | 0.855163i | \(-0.326543\pi\) | ||||
0.518359 | + | 0.855163i | \(0.326543\pi\) | |||||||
\(180\) | 82620.0 | − | 60893.2i | 0.190066 | − | 0.140084i | ||||
\(181\) | −156902. | −0.355985 | −0.177993 | − | 0.984032i | \(-0.556960\pi\) | ||||
−0.177993 | + | 0.984032i | \(0.556960\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 113389.i | 0.250289i | ||||||||
\(184\) | −322960. | −0.703241 | ||||||||
\(185\) | 463320. | + | 628633.i | 0.995295 | + | 1.35042i | ||||
\(186\) | 891264. | 1.88897 | ||||||||
\(187\) | 173844.i | 0.363543i | ||||||||
\(188\) | − | 126483.i | − | 0.260998i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 48400.0 | + | 65669.2i | 0.0972661 | + | 0.131971i | ||||
\(191\) | 332352. | 0.659196 | 0.329598 | − | 0.944121i | \(-0.393087\pi\) | ||||
0.329598 | + | 0.944121i | \(0.393087\pi\) | |||||||
\(192\) | − | 258538.i | − | 0.506140i | ||||||
\(193\) | 786120.i | 1.51913i | 0.650430 | + | 0.759566i | \(0.274589\pi\) | ||||
−0.650430 | + | 0.759566i | \(0.725411\pi\) | |||||||
\(194\) | −671616. | −1.28120 | ||||||||
\(195\) | −106920. | + | 78803.0i | −0.201360 | + | 0.148408i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 59606.4i | 0.109428i | 0.998502 | + | 0.0547138i | \(0.0174247\pi\) | ||||
−0.998502 | + | 0.0547138i | \(0.982575\pi\) | |||||||
\(198\) | − | 255752.i | − | 0.463613i | ||||||
\(199\) | 395800. | 0.708505 | 0.354253 | − | 0.935150i | \(-0.384735\pi\) | ||||
0.354253 | + | 0.935150i | \(0.384735\pi\) | |||||||
\(200\) | 396000. | + | 122715.i | 0.700036 | + | 0.216932i | ||||
\(201\) | 868428. | 1.51616 | ||||||||
\(202\) | 723674.i | 1.24786i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 164736. | 0.277149 | ||||||||
\(205\) | 8910.00 | − | 6566.92i | 0.0148079 | − | 0.0109138i | ||||
\(206\) | 468468. | 0.769151 | ||||||||
\(207\) | − | 372464.i | − | 0.604168i | ||||||
\(208\) | − | 150920.i | − | 0.241873i | ||||||
\(209\) | 55440.0 | 0.0877925 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −251548. | −0.388969 | −0.194484 | − | 0.980906i | \(-0.562303\pi\) | ||||
−0.194484 | + | 0.980906i | \(0.562303\pi\) | |||||||
\(212\) | 69887.9i | 0.106798i | ||||||||
\(213\) | 1.06169e6i | 1.60343i | ||||||||
\(214\) | −644204. | −0.961588 | ||||||||
\(215\) | −13860.0 | − | 18805.3i | −0.0204488 | − | 0.0277449i | ||||
\(216\) | −237600. | −0.346507 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 139365.i | − | 0.198615i | ||||||
\(219\) | 1.41134e6 | 1.98849 | ||||||||
\(220\) | −136080. | + | 100295.i | −0.189556 | + | 0.139708i | ||||
\(221\) | −82368.0 | −0.113443 | ||||||||
\(222\) | − | 1.84399e6i | − | 2.51117i | ||||||
\(223\) | 288765.i | 0.388851i | 0.980917 | + | 0.194425i | \(0.0622842\pi\) | ||||
−0.980917 | + | 0.194425i | \(0.937716\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −141525. | + | 456699.i | −0.186370 | + | 0.601415i | ||||
\(226\) | −696608. | −0.907230 | ||||||||
\(227\) | − | 1.16414e6i | − | 1.49948i | −0.661731 | − | 0.749741i | \(-0.730178\pi\) | ||
0.661731 | − | 0.749741i | \(-0.269822\pi\) | |||||||
\(228\) | − | 52535.3i | − | 0.0669290i | ||||||
\(229\) | −547670. | −0.690129 | −0.345064 | − | 0.938579i | \(-0.612143\pi\) | ||||
−0.345064 | + | 0.938579i | \(0.612143\pi\) | |||||||
\(230\) | −726660. | + | 535569.i | −0.905757 | + | 0.667568i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 919368.i | − | 1.12142i | ||||||
\(233\) | 48104.3i | 0.0580489i | 0.999579 | + | 0.0290245i | \(0.00924007\pi\) | ||||
−0.999579 | + | 0.0290245i | \(0.990760\pi\) | |||||||
\(234\) | 121176. | 0.144669 | ||||||||
\(235\) | 349580. | + | 474311.i | 0.412930 | + | 0.560264i | ||||
\(236\) | −295920. | −0.345855 | ||||||||
\(237\) | 1.03319e6i | 1.19484i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.00584e6 | −1.13903 | −0.569514 | − | 0.821982i | \(-0.692868\pi\) | ||||
−0.569514 | + | 0.821982i | \(0.692868\pi\) | |||||||
\(240\) | −834240. | − | 1.13190e6i | −0.934895 | − | 1.26847i | ||||
\(241\) | −895202. | −0.992838 | −0.496419 | − | 0.868083i | \(-0.665352\pi\) | ||||
−0.496419 | + | 0.868083i | \(0.665352\pi\) | |||||||
\(242\) | − | 647054.i | − | 0.710235i | ||||||
\(243\) | − | 1.01387e6i | − | 1.10146i | ||||||
\(244\) | −68376.0 | −0.0735240 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −26136.0 | −0.0275360 | ||||||||
\(247\) | 26267.7i | 0.0273955i | ||||||||
\(248\) | − | 895754.i | − | 0.924825i | ||||||
\(249\) | −1.23064e6 | −1.25786 | ||||||||
\(250\) | 1.09450e6 | − | 380583.i | 1.10756 | − | 0.385123i | ||||
\(251\) | −558252. | −0.559301 | −0.279651 | − | 0.960102i | \(-0.590219\pi\) | ||||
−0.279651 | + | 0.960102i | \(0.590219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 613469.i | 0.602548i | ||||||||
\(254\) | 578556. | 0.562680 | ||||||||
\(255\) | −617760. | + | 455306.i | −0.594935 | + | 0.438483i | ||||
\(256\) | 1.03450e6 | 0.986572 | ||||||||
\(257\) | 787924.i | 0.744135i | 0.928206 | + | 0.372067i | \(0.121351\pi\) | ||||
−0.928206 | + | 0.372067i | \(0.878649\pi\) | |||||||
\(258\) | 55162.1i | 0.0515931i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −47520.0 | − | 64475.2i | −0.0435956 | − | 0.0591506i | ||||
\(261\) | 1.06029e6 | 0.963437 | ||||||||
\(262\) | − | 1.27924e6i | − | 1.15132i | ||||||
\(263\) | − | 1.63173e6i | − | 1.45465i | −0.686291 | − | 0.727327i | \(-0.740762\pi\) | ||
0.686291 | − | 0.727327i | \(-0.259238\pi\) | |||||||
\(264\) | −665280. | −0.587482 | ||||||||
\(265\) | −193160. | − | 262080.i | −0.168967 | − | 0.229255i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 198798.i | 0.170661i | ||||||||
\(268\) | 523682.i | 0.445380i | ||||||||
\(269\) | 1.73637e6 | 1.46306 | 0.731529 | − | 0.681810i | \(-0.238807\pi\) | ||||
0.731529 | + | 0.681810i | \(0.238807\pi\) | |||||||
\(270\) | −534600. | + | 394015.i | −0.446292 | + | 0.328930i | ||||
\(271\) | 1.72005e6 | 1.42271 | 0.711357 | − | 0.702831i | \(-0.248081\pi\) | ||||
0.711357 | + | 0.702831i | \(0.248081\pi\) | |||||||
\(272\) | − | 871980.i | − | 0.714635i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 952336. | 0.766326 | ||||||||
\(275\) | 233100. | − | 752211.i | 0.185871 | − | 0.599802i | ||||
\(276\) | 581328. | 0.459355 | ||||||||
\(277\) | 1.27243e6i | 0.996402i | 0.867062 | + | 0.498201i | \(0.166006\pi\) | ||||
−0.867062 | + | 0.498201i | \(0.833994\pi\) | |||||||
\(278\) | 2.11163e6i | 1.63872i | ||||||||
\(279\) | 1.03306e6 | 0.794536 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.46500e6 | 1.10681 | 0.553404 | − | 0.832913i | \(-0.313329\pi\) | ||||
0.553404 | + | 0.832913i | \(0.313329\pi\) | |||||||
\(282\) | − | 1.39131e6i | − | 1.04184i | ||||||
\(283\) | 1.65051e6i | 1.22504i | 0.790455 | + | 0.612521i | \(0.209844\pi\) | ||||
−0.790455 | + | 0.612521i | \(0.790156\pi\) | |||||||
\(284\) | −640224. | −0.471016 | ||||||||
\(285\) | 145200. | + | 197008.i | 0.105890 | + | 0.143672i | ||||
\(286\) | −199584. | −0.144281 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 633290.i | 0.449905i | ||||||||
\(289\) | 943953. | 0.664823 | ||||||||
\(290\) | −1.52460e6 | − | 2.06858e6i | −1.06454 | − | 1.44437i | ||||
\(291\) | −2.01485e6 | −1.39479 | ||||||||
\(292\) | 851072.i | 0.584130i | ||||||||
\(293\) | − | 2.38772e6i | − | 1.62485i | −0.583064 | − | 0.812426i | \(-0.698146\pi\) | ||
0.583064 | − | 0.812426i | \(-0.301854\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.10970e6 | − | 817880.i | 0.742422 | − | 0.547185i | ||||
\(296\) | −1.85328e6 | −1.22945 | ||||||||
\(297\) | 451326.i | 0.296893i | ||||||||
\(298\) | 558188.i | 0.364116i | ||||||||
\(299\) | −290664. | −0.188024 | ||||||||
\(300\) | −712800. | − | 220887.i | −0.457261 | − | 0.141699i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 1.03378e6i | − | 0.652244i | ||||||
\(303\) | 2.17102e6i | 1.35849i | ||||||||
\(304\) | −278080. | −0.172578 | ||||||||
\(305\) | 256410. | − | 188981.i | 0.157828 | − | 0.116324i | ||||
\(306\) | 700128. | 0.427439 | ||||||||
\(307\) | − | 928264.i | − | 0.562115i | −0.959691 | − | 0.281058i | \(-0.909315\pi\) | ||
0.959691 | − | 0.281058i | \(-0.0906852\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.40540e6 | 0.837346 | ||||||||
\(310\) | −1.48544e6 | − | 2.01545e6i | −0.877912 | − | 1.19115i | ||||
\(311\) | −568152. | −0.333092 | −0.166546 | − | 0.986034i | \(-0.553261\pi\) | ||||
−0.166546 | + | 0.986034i | \(0.553261\pi\) | |||||||
\(312\) | − | 315212.i | − | 0.183323i | ||||||
\(313\) | 1.72244e6i | 0.993766i | 0.867818 | + | 0.496883i | \(0.165522\pi\) | ||||
−0.867818 | + | 0.496883i | \(0.834478\pi\) | |||||||
\(314\) | 2.36570e6 | 1.35405 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −623040. | −0.350993 | ||||||||
\(317\) | 131643.i | 0.0735785i | 0.999323 | + | 0.0367893i | \(0.0117130\pi\) | ||||
−0.999323 | + | 0.0367893i | \(0.988287\pi\) | |||||||
\(318\) | 768767.i | 0.426311i | ||||||||
\(319\) | −1.74636e6 | −0.960853 | ||||||||
\(320\) | −584640. | + | 430896.i | −0.319164 | + | 0.235233i | ||||
\(321\) | −1.93261e6 | −1.04684 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 151769.i | 0.0809424i | ||||||||
\(324\) | 873828. | 0.462449 | ||||||||
\(325\) | 356400. | + | 110444.i | 0.187167 | + | 0.0580006i | ||||
\(326\) | 961092. | 0.500865 | ||||||||
\(327\) | − | 418094.i | − | 0.216224i | ||||||
\(328\) | 26267.7i | 0.0134815i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.49688e6 | + | 1.10324e6i | −0.756662 | + | 0.557681i | ||||
\(331\) | −1.58055e6 | −0.792935 | −0.396468 | − | 0.918049i | \(-0.629764\pi\) | ||||
−0.396468 | + | 0.918049i | \(0.629764\pi\) | |||||||
\(332\) | − | 742101.i | − | 0.369503i | ||||||
\(333\) | − | 2.13735e6i | − | 1.05625i | ||||||
\(334\) | −120076. | −0.0588966 | ||||||||
\(335\) | −1.44738e6 | − | 1.96381e6i | −0.704645 | − | 0.956063i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.22885e6i | 0.589419i | 0.955587 | + | 0.294709i | \(0.0952228\pi\) | ||||
−0.955587 | + | 0.294709i | \(0.904777\pi\) | |||||||
\(338\) | 2.36832e6i | 1.12758i | ||||||||
\(339\) | −2.08982e6 | −0.987667 | ||||||||
\(340\) | −274560. | − | 372523.i | −0.128807 | − | 0.174766i | ||||
\(341\) | −1.70150e6 | −0.792405 | ||||||||
\(342\) | − | 223275.i | − | 0.103223i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 55440.0 | 0.0252596 | ||||||||
\(345\) | −2.17998e6 | + | 1.60671e6i | −0.986063 | + | 0.726756i | ||||
\(346\) | −3.26735e6 | −1.46726 | ||||||||
\(347\) | − | 3.84224e6i | − | 1.71301i | −0.516137 | − | 0.856506i | \(-0.672630\pi\) | ||
0.516137 | − | 0.856506i | \(-0.327370\pi\) | |||||||
\(348\) | 1.65486e6i | 0.732511i | ||||||||
\(349\) | 1.59445e6 | 0.700725 | 0.350362 | − | 0.936614i | \(-0.386058\pi\) | ||||
0.350362 | + | 0.936614i | \(0.386058\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −213840. | −0.0926448 | ||||||||
\(352\) | − | 1.04307e6i | − | 0.448699i | ||||||
\(353\) | 295365.i | 0.126160i | 0.998008 | + | 0.0630802i | \(0.0200924\pi\) | ||||
−0.998008 | + | 0.0630802i | \(0.979908\pi\) | |||||||
\(354\) | −3.25512e6 | −1.38057 | ||||||||
\(355\) | 2.40084e6 | − | 1.76949e6i | 1.01110 | − | 0.745206i | ||||
\(356\) | −119880. | −0.0501328 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.94795e6i | 1.21566i | ||||||||
\(359\) | 1.10484e6 | 0.452442 | 0.226221 | − | 0.974076i | \(-0.427363\pi\) | ||||
0.226221 | + | 0.974076i | \(0.427363\pi\) | |||||||
\(360\) | −673200. | − | 913398.i | −0.273771 | − | 0.371453i | ||||
\(361\) | −2.42770e6 | −0.980453 | ||||||||
\(362\) | − | 1.04077e6i | − | 0.417430i | ||||||
\(363\) | − | 1.94116e6i | − | 0.773206i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.35224e6 | − | 3.19152e6i | −0.924165 | − | 1.25391i | ||||
\(366\) | −752136. | −0.293490 | ||||||||
\(367\) | 1.83760e6i | 0.712174i | 0.934453 | + | 0.356087i | \(0.115889\pi\) | ||||
−0.934453 | + | 0.356087i | \(0.884111\pi\) | |||||||
\(368\) | − | 3.07708e6i | − | 1.18446i | ||||||
\(369\) | −30294.0 | −0.0115822 | ||||||||
\(370\) | −4.16988e6 | + | 3.07332e6i | −1.58350 | + | 1.16709i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.61236e6i | 0.604093i | ||||||||
\(373\) | 2.93350e6i | 1.09173i | 0.837874 | + | 0.545864i | \(0.183798\pi\) | ||||
−0.837874 | + | 0.545864i | \(0.816202\pi\) | |||||||
\(374\) | −1.15315e6 | −0.426292 | ||||||||
\(375\) | 3.28350e6 | − | 1.14175e6i | 1.20575 | − | 0.419268i | ||||
\(376\) | −1.39832e6 | −0.510078 | ||||||||
\(377\) | − | 827432.i | − | 0.299832i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.09342e6 | 1.82143 | 0.910713 | − | 0.413040i | \(-0.135533\pi\) | ||||
0.910713 | + | 0.413040i | \(0.135533\pi\) | |||||||
\(380\) | −118800. | + | 87558.9i | −0.0422044 | + | 0.0311058i | ||||
\(381\) | 1.73567e6 | 0.612568 | ||||||||
\(382\) | 2.20457e6i | 0.772976i | ||||||||
\(383\) | − | 3.17485e6i | − | 1.10593i | −0.833205 | − | 0.552964i | \(-0.813497\pi\) | ||
0.833205 | − | 0.552964i | \(-0.186503\pi\) | |||||||
\(384\) | 4.35072e6 | 1.50568 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.21453e6 | −1.78134 | ||||||||
\(387\) | 63937.9i | 0.0217011i | ||||||||
\(388\) | − | 1.21500e6i | − | 0.409729i | ||||||
\(389\) | 1.79991e6 | 0.603083 | 0.301541 | − | 0.953453i | \(-0.402499\pi\) | ||||
0.301541 | + | 0.953453i | \(0.402499\pi\) | |||||||
\(390\) | −522720. | − | 709227.i | −0.174023 | − | 0.236115i | ||||
\(391\) | −1.67939e6 | −0.555533 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 3.83771e6i | − | 1.25340i | ||||||
\(394\) | −395384. | −0.128315 | ||||||||
\(395\) | 2.33640e6 | − | 1.72199e6i | 0.753450 | − | 0.555314i | ||||
\(396\) | 462672. | 0.148264 | ||||||||
\(397\) | 4.90405e6i | 1.56163i | 0.624760 | + | 0.780817i | \(0.285197\pi\) | ||||
−0.624760 | + | 0.780817i | \(0.714803\pi\) | |||||||
\(398\) | 2.62544e6i | 0.830796i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.16920e6 | + | 3.77299e6i | −0.365375 | + | 1.17906i | ||||
\(401\) | −642798. | −0.199624 | −0.0998122 | − | 0.995006i | \(-0.531824\pi\) | ||||
−0.0998122 | + | 0.995006i | \(0.531824\pi\) | |||||||
\(402\) | 5.76050e6i | 1.77785i | ||||||||
\(403\) | − | 806179.i | − | 0.247268i | ||||||
\(404\) | −1.30918e6 | −0.399066 | ||||||||
\(405\) | −3.27686e6 | + | 2.41513e6i | −0.992704 | + | 0.731650i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.52035e6i | 1.05341i | ||||||||
\(408\) | − | 1.82123e6i | − | 0.541643i | ||||||
\(409\) | 2.05711e6 | 0.608064 | 0.304032 | − | 0.952662i | \(-0.401667\pi\) | ||||
0.304032 | + | 0.952662i | \(0.401667\pi\) | |||||||
\(410\) | 43560.0 | + | 59102.3i | 0.0127976 | + | 0.0173638i | ||||
\(411\) | 2.85701e6 | 0.834271 | ||||||||
\(412\) | 847490.i | 0.245975i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.47064e6 | 0.708450 | ||||||||
\(415\) | 2.05106e6 | + | 2.78288e6i | 0.584599 | + | 0.793185i | ||||
\(416\) | 494208. | 0.140016 | ||||||||
\(417\) | 6.33489e6i | 1.78402i | ||||||||
\(418\) | 367747.i | 0.102946i | ||||||||
\(419\) | 2.93742e6 | 0.817393 | 0.408697 | − | 0.912670i | \(-0.365983\pi\) | ||||
0.408697 | + | 0.912670i | \(0.365983\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.71770e6 | 0.747303 | 0.373651 | − | 0.927569i | \(-0.378106\pi\) | ||||
0.373651 | + | 0.927569i | \(0.378106\pi\) | |||||||
\(422\) | − | 1.66858e6i | − | 0.456106i | ||||||
\(423\) | − | 1.61266e6i | − | 0.438219i | ||||||
\(424\) | 772640. | 0.208719 | ||||||||
\(425\) | 2.05920e6 | + | 638119.i | 0.553001 | + | 0.171368i | ||||
\(426\) | −7.04246e6 | −1.88019 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 1.16541e6i | − | 0.307517i | ||||||
\(429\) | −598752. | −0.157074 | ||||||||
\(430\) | 124740. | − | 91936.8i | 0.0325338 | − | 0.0239783i | ||||
\(431\) | 4.99435e6 | 1.29505 | 0.647524 | − | 0.762045i | \(-0.275804\pi\) | ||||
0.647524 | + | 0.762045i | \(0.275804\pi\) | |||||||
\(432\) | − | 2.26380e6i | − | 0.583617i | ||||||
\(433\) | 2.08183e6i | 0.533612i | 0.963750 | + | 0.266806i | \(0.0859684\pi\) | ||||
−0.963750 | + | 0.266806i | \(0.914032\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.57380e6 | − | 6.20574e6i | −1.15892 | − | 1.57243i | ||||
\(436\) | 252120. | 0.0635172 | ||||||||
\(437\) | 535569.i | 0.134156i | ||||||||
\(438\) | 9.36180e6i | 2.33171i | ||||||||
\(439\) | 4.70404e6 | 1.16496 | 0.582478 | − | 0.812846i | \(-0.302083\pi\) | ||||
0.582478 | + | 0.812846i | \(0.302083\pi\) | |||||||
\(440\) | 1.10880e6 | + | 1.50442e6i | 0.273037 | + | 0.370457i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 546368.i | − | 0.133024i | ||||||
\(443\) | − | 5.70103e6i | − | 1.38021i | −0.723711 | − | 0.690103i | \(-0.757565\pi\) | ||
0.723711 | − | 0.690103i | \(-0.242435\pi\) | |||||||
\(444\) | 3.33590e6 | 0.803075 | ||||||||
\(445\) | 449550. | − | 331331.i | 0.107616 | − | 0.0793162i | ||||
\(446\) | −1.91545e6 | −0.455968 | ||||||||
\(447\) | 1.67456e6i | 0.396399i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.20325e6 | 1.45212 | 0.726062 | − | 0.687630i | \(-0.241349\pi\) | ||||
0.726062 | + | 0.687630i | \(0.241349\pi\) | |||||||
\(450\) | −3.02940e6 | − | 938771.i | −0.705221 | − | 0.218539i | ||||
\(451\) | 49896.0 | 0.0115511 | ||||||||
\(452\) | − | 1.26021e6i | − | 0.290133i | ||||||
\(453\) | − | 3.10134e6i | − | 0.710074i | ||||||
\(454\) | 7.72204e6 | 1.75830 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −580800. | −0.130802 | ||||||||
\(457\) | − | 2.15371e6i | − | 0.482388i | −0.970477 | − | 0.241194i | \(-0.922461\pi\) | ||
0.970477 | − | 0.241194i | \(-0.0775391\pi\) | |||||||
\(458\) | − | 3.63283e6i | − | 0.809248i | ||||||
\(459\) | −1.23552e6 | −0.273727 | ||||||||
\(460\) | −968880. | − | 1.31458e6i | −0.213489 | − | 0.289662i | ||||
\(461\) | 3.85130e6 | 0.844024 | 0.422012 | − | 0.906590i | \(-0.361324\pi\) | ||||
0.422012 | + | 0.906590i | \(0.361324\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.08213e6i | − | 0.451394i | −0.974198 | − | 0.225697i | \(-0.927534\pi\) | ||
0.974198 | − | 0.225697i | \(-0.0724659\pi\) | |||||||
\(464\) | 8.75952e6 | 1.88880 | ||||||||
\(465\) | −4.45632e6 | − | 6.04634e6i | −0.955749 | − | 1.29676i | ||||
\(466\) | −319088. | −0.0680684 | ||||||||
\(467\) | − | 1.30822e6i | − | 0.277579i | −0.990322 | − | 0.138790i | \(-0.955679\pi\) | ||
0.990322 | − | 0.138790i | \(-0.0443212\pi\) | |||||||
\(468\) | 219216.i | 0.0462655i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.14622e6 | + | 2.31885e6i | −0.656968 | + | 0.484204i | ||||
\(471\) | 7.09711e6 | 1.47411 | ||||||||
\(472\) | 3.27152e6i | 0.675919i | ||||||||
\(473\) | − | 105309.i | − | 0.0216429i | ||||||
\(474\) | −6.85344e6 | −1.40108 | ||||||||
\(475\) | 203500. | − | 656692.i | 0.0413838 | − | 0.133545i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 891071.i | 0.179315i | ||||||||
\(478\) | − | 6.67199e6i | − | 1.33563i | ||||||
\(479\) | 6.76368e6 | 1.34693 | 0.673464 | − | 0.739220i | \(-0.264806\pi\) | ||||
0.673464 | + | 0.739220i | \(0.264806\pi\) | |||||||
\(480\) | 3.70656e6 | − | 2.73184e6i | 0.734291 | − | 0.541193i | ||||
\(481\) | −1.66795e6 | −0.328716 | ||||||||
\(482\) | − | 5.93810e6i | − | 1.16421i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.17056e6 | 0.227134 | ||||||||
\(485\) | 3.35808e6 | + | 4.55625e6i | 0.648241 | + | 0.879534i | ||||
\(486\) | 6.72527e6 | 1.29157 | ||||||||
\(487\) | 6.67193e6i | 1.27476i | 0.770549 | + | 0.637381i | \(0.219982\pi\) | ||||
−0.770549 | + | 0.637381i | \(0.780018\pi\) | |||||||
\(488\) | 755925.i | 0.143691i | ||||||||
\(489\) | 2.88328e6 | 0.545273 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.87575e6 | −1.28711 | −0.643556 | − | 0.765399i | \(-0.722542\pi\) | ||||
−0.643556 | + | 0.765399i | \(0.722542\pi\) | |||||||
\(492\) | − | 47281.8i | − | 0.00880605i | ||||||
\(493\) | − | 4.78072e6i | − | 0.885881i | ||||||
\(494\) | −174240. | −0.0321241 | ||||||||
\(495\) | −1.73502e6 | + | 1.27876e6i | −0.318267 | + | 0.234572i | ||||
\(496\) | 8.53453e6 | 1.55767 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 8.16312e6i | − | 1.47497i | ||||||
\(499\) | 6.94010e6 | 1.24771 | 0.623856 | − | 0.781539i | \(-0.285565\pi\) | ||||
0.623856 | + | 0.781539i | \(0.285565\pi\) | |||||||
\(500\) | 688500. | + | 1.98002e6i | 0.123163 | + | 0.354198i | ||||
\(501\) | −360228. | −0.0641185 | ||||||||
\(502\) | − | 3.70302e6i | − | 0.655839i | ||||||
\(503\) | − | 921007.i | − | 0.162309i | −0.996702 | − | 0.0811546i | \(-0.974139\pi\) | ||
0.996702 | − | 0.0811546i | \(-0.0258607\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.90941e6 | − | 3.61837e6i | 0.856645 | − | 0.631371i | ||||
\(506\) | −4.06930e6 | −0.706550 | ||||||||
\(507\) | 7.10495e6i | 1.22755i | ||||||||
\(508\) | 1.04665e6i | 0.179946i | ||||||||
\(509\) | −4.97979e6 | −0.851955 | −0.425977 | − | 0.904734i | \(-0.640070\pi\) | ||||
−0.425977 | + | 0.904734i | \(0.640070\pi\) | |||||||
\(510\) | −3.02016e6 | − | 4.09776e6i | −0.514167 | − | 0.697623i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 134151.i | − | 0.0226161i | ||||||
\(513\) | 394015.i | 0.0661027i | ||||||||
\(514\) | −5.22650e6 | −0.872575 | ||||||||
\(515\) | −2.34234e6 | − | 3.17809e6i | −0.389163 | − | 0.528017i | ||||
\(516\) | −99792.0 | −0.0164995 | ||||||||
\(517\) | 2.65614e6i | 0.437043i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.80206e6 | −1.59735 | ||||||||
\(520\) | −712800. | + | 525353.i | −0.115600 | + | 0.0852007i | ||||
\(521\) | 147798. | 0.0238547 | 0.0119274 | − | 0.999929i | \(-0.496203\pi\) | ||||
0.0119274 | + | 0.999929i | \(0.496203\pi\) | |||||||
\(522\) | 7.03317e6i | 1.12973i | ||||||||
\(523\) | − | 1.23884e7i | − | 1.98043i | −0.139543 | − | 0.990216i | \(-0.544563\pi\) | ||
0.139543 | − | 0.990216i | \(-0.455437\pi\) | |||||||
\(524\) | 2.31422e6 | 0.368194 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.08237e7 | 1.70573 | ||||||||
\(527\) | − | 4.65792e6i | − | 0.730576i | ||||||
\(528\) | − | 6.33863e6i | − | 0.989488i | ||||||
\(529\) | 510027. | 0.0792417 | ||||||||
\(530\) | 1.73844e6 | − | 1.28128e6i | 0.268825 | − | 0.198132i | ||||
\(531\) | −3.77298e6 | −0.580695 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23640.9i | 0.00360451i | ||||||||
\(534\) | −1.31868e6 | −0.200118 | ||||||||
\(535\) | 3.22102e6 | + | 4.37028e6i | 0.486529 | + | 0.660123i | ||||
\(536\) | 5.78952e6 | 0.870423 | ||||||||
\(537\) | 8.84385e6i | 1.32344i | ||||||||
\(538\) | 1.15178e7i | 1.71559i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −712800. | − | 967128.i | −0.105192 | − | 0.142725i | ||||
\(541\) | −9.99810e6 | −1.46867 | −0.734335 | − | 0.678787i | \(-0.762506\pi\) | ||||
−0.734335 | + | 0.678787i | \(0.762506\pi\) | |||||||
\(542\) | 1.14095e7i | 1.66828i | ||||||||
\(543\) | − | 3.12231e6i | − | 0.454440i | ||||||
\(544\) | 2.85542e6 | 0.413688 | ||||||||
\(545\) | −945450. | + | 696823.i | −0.136348 | + | 0.100492i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.18580e7i | 1.69451i | 0.531189 | + | 0.847253i | \(0.321745\pi\) | ||||
−0.531189 | + | 0.847253i | \(0.678255\pi\) | |||||||
\(548\) | 1.72284e6i | 0.245072i | ||||||||
\(549\) | −871794. | −0.123448 | ||||||||
\(550\) | 4.98960e6 | + | 1.54621e6i | 0.703330 | + | 0.217953i | ||||
\(551\) | −1.52460e6 | −0.213933 | ||||||||
\(552\) | − | 6.42682e6i | − | 0.897736i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8.44034e6 | −1.16838 | ||||||||
\(555\) | −1.25096e7 | + | 9.21995e6i | −1.72390 | + | 1.27056i | ||||
\(556\) | −3.82008e6 | −0.524065 | ||||||||
\(557\) | 904550.i | 0.123536i | 0.998091 | + | 0.0617681i | \(0.0196739\pi\) | ||||
−0.998091 | + | 0.0617681i | \(0.980326\pi\) | |||||||
\(558\) | 6.85252e6i | 0.931676i | ||||||||
\(559\) | 49896.0 | 0.00675361 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.45946e6 | −0.464088 | ||||||||
\(562\) | 9.71772e6i | 1.29785i | ||||||||
\(563\) | 8.68719e6i | 1.15507i | 0.816366 | + | 0.577535i | \(0.195985\pi\) | ||||
−0.816366 | + | 0.577535i | \(0.804015\pi\) | |||||||
\(564\) | 2.51698e6 | 0.333182 | ||||||||
\(565\) | 3.48304e6 | + | 4.72579e6i | 0.459026 | + | 0.622807i | ||||
\(566\) | −1.09482e7 | −1.43649 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.07794e6i | 0.920526i | ||||||||
\(569\) | −2.27007e6 | −0.293940 | −0.146970 | − | 0.989141i | \(-0.546952\pi\) | ||||
−0.146970 | + | 0.989141i | \(0.546952\pi\) | |||||||
\(570\) | −1.30680e6 | + | 963148.i | −0.168470 | + | 0.124167i | ||||
\(571\) | 1.43807e7 | 1.84582 | 0.922908 | − | 0.385021i | \(-0.125806\pi\) | ||||
0.922908 | + | 0.385021i | \(0.125806\pi\) | |||||||
\(572\) | − | 361061.i | − | 0.0461414i | ||||||
\(573\) | 6.61372e6i | 0.841510i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.26660e6 | + | 2.25182e6i | 0.916562 | + | 0.284030i | ||||
\(576\) | 1.98778e6 | 0.249638 | ||||||||
\(577\) | − | 5.63943e6i | − | 0.705173i | −0.935779 | − | 0.352586i | \(-0.885302\pi\) | ||
0.935779 | − | 0.352586i | \(-0.114698\pi\) | |||||||
\(578\) | 6.26148e6i | 0.779574i | ||||||||
\(579\) | −1.56436e7 | −1.93928 | ||||||||
\(580\) | 3.74220e6 | − | 2.75811e6i | 0.461910 | − | 0.340440i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 1.33650e7i | − | 1.63554i | ||||||
\(583\) | − | 1.46765e6i | − | 0.178834i | ||||||
\(584\) | 9.40896e6 | 1.14159 | ||||||||
\(585\) | −605880. | − | 822059.i | −0.0731976 | − | 0.0993146i | ||||
\(586\) | 1.58383e7 | 1.90531 | ||||||||
\(587\) | − | 1.28473e6i | − | 0.153893i | −0.997035 | − | 0.0769464i | \(-0.975483\pi\) | ||
0.997035 | − | 0.0769464i | \(-0.0245170\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.48544e6 | −0.176428 | ||||||||
\(590\) | 5.42520e6 | + | 7.36092e6i | 0.641632 | + | 0.870566i | ||||
\(591\) | −1.18615e6 | −0.139692 | ||||||||
\(592\) | − | 1.76576e7i | − | 2.07075i | ||||||
\(593\) | − | 7.00943e6i | − | 0.818552i | −0.912411 | − | 0.409276i | \(-0.865781\pi\) | ||
0.912411 | − | 0.409276i | \(-0.134219\pi\) | |||||||
\(594\) | −2.99376e6 | −0.348138 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.00980e6 | −0.116445 | ||||||||
\(597\) | 7.87632e6i | 0.904456i | ||||||||
\(598\) | − | 1.92805e6i | − | 0.220478i | ||||||
\(599\) | −8.80020e6 | −1.00213 | −0.501067 | − | 0.865409i | \(-0.667059\pi\) | ||||
−0.501067 | + | 0.865409i | \(0.667059\pi\) | |||||||
\(600\) | −2.44200e6 | + | 7.88030e6i | −0.276928 | + | 0.893644i | ||||
\(601\) | 1.07670e7 | 1.21593 | 0.607965 | − | 0.793964i | \(-0.291986\pi\) | ||||
0.607965 | + | 0.793964i | \(0.291986\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.67694e6i | 0.747798i | ||||||||
\(604\) | 1.87018e6 | 0.208588 | ||||||||
\(605\) | −4.38962e6 | + | 3.23527e6i | −0.487571 | + | 0.359353i | ||||
\(606\) | −1.44009e7 | −1.59298 | ||||||||
\(607\) | 1.51219e7i | 1.66584i | 0.553391 | + | 0.832921i | \(0.313333\pi\) | ||||
−0.553391 | + | 0.832921i | \(0.686667\pi\) | |||||||
\(608\) | − | 910613.i | − | 0.0999021i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.25356e6 | + | 1.70083e6i | 0.136402 | + | 0.185070i | ||||
\(611\) | −1.25849e6 | −0.136379 | ||||||||
\(612\) | 1.26658e6i | 0.136695i | ||||||||
\(613\) | − | 8.31622e6i | − | 0.893871i | −0.894566 | − | 0.446936i | \(-0.852515\pi\) | ||
0.894566 | − | 0.446936i | \(-0.147485\pi\) | |||||||
\(614\) | 6.15740e6 | 0.659139 | ||||||||
\(615\) | 130680. | + | 177307.i | 0.0139323 | + | 0.0189033i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.21083e7i | 1.28047i | 0.768178 | + | 0.640237i | \(0.221164\pi\) | ||||
−0.768178 | + | 0.640237i | \(0.778836\pi\) | |||||||
\(618\) | 9.32240e6i | 0.981875i | ||||||||
\(619\) | −9.73238e6 | −1.02092 | −0.510461 | − | 0.859901i | \(-0.670525\pi\) | ||||
−0.510461 | + | 0.859901i | \(0.670525\pi\) | |||||||
\(620\) | 3.64608e6 | − | 2.68726e6i | 0.380932 | − | 0.280757i | ||||
\(621\) | −4.35996e6 | −0.453684 | ||||||||
\(622\) | − | 3.76869e6i | − | 0.390584i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.00326e6 | 0.308768 | ||||||||
\(625\) | −8.05437e6 | − | 5.52218e6i | −0.824768 | − | 0.565471i | ||||
\(626\) | −1.14254e7 | −1.16529 | ||||||||
\(627\) | 1.10324e6i | 0.112073i | ||||||||
\(628\) | 4.27972e6i | 0.433028i | ||||||||
\(629\) | −9.63706e6 | −0.971220 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.60145e6 | −0.859999 | −0.430000 | − | 0.902829i | \(-0.641486\pi\) | ||||
−0.430000 | + | 0.902829i | \(0.641486\pi\) | |||||||
\(632\) | 6.88797e6i | 0.685959i | ||||||||
\(633\) | − | 5.00574e6i | − | 0.496546i | ||||||
\(634\) | −873224. | −0.0862785 | ||||||||
\(635\) | −2.89278e6 | − | 3.92493e6i | −0.284696 | − | 0.386276i | ||||
\(636\) | −1.39075e6 | −0.136335 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 1.15840e7i | − | 1.12670i | ||||||
\(639\) | −8.16286e6 | −0.790842 | ||||||||
\(640\) | −7.25120e6 | − | 9.83844e6i | −0.699777 | − | 0.949459i | ||||
\(641\) | −6.42440e6 | −0.617572 | −0.308786 | − | 0.951132i | \(-0.599923\pi\) | ||||
−0.308786 | + | 0.951132i | \(0.599923\pi\) | |||||||
\(642\) | − | 1.28195e7i | − | 1.22753i | ||||||
\(643\) | − | 3.64721e6i | − | 0.347883i | −0.984756 | − | 0.173941i | \(-0.944350\pi\) | ||
0.984756 | − | 0.173941i | \(-0.0556503\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 374220. | − | 275811.i | 0.0354183 | − | 0.0261043i | ||||
\(646\) | −1.00672e6 | −0.0949134 | ||||||||
\(647\) | − | 3.78036e6i | − | 0.355036i | −0.984118 | − | 0.177518i | \(-0.943193\pi\) | ||
0.984118 | − | 0.177518i | \(-0.0568068\pi\) | |||||||
\(648\) | − | 9.66053e6i | − | 0.903782i | ||||||
\(649\) | 6.21432e6 | 0.579138 | ||||||||
\(650\) | −732600. | + | 2.36409e6i | −0.0680117 | + | 0.219473i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.73868e6i | 0.160177i | ||||||||
\(653\) | − | 1.66957e7i | − | 1.53223i | −0.642706 | − | 0.766113i | \(-0.722188\pi\) | ||
0.642706 | − | 0.766113i | \(-0.277812\pi\) | |||||||
\(654\) | 2.77332e6 | 0.253545 | ||||||||
\(655\) | −8.67834e6 | + | 6.39618e6i | −0.790375 | + | 0.582529i | ||||
\(656\) | −250272. | −0.0227066 | ||||||||
\(657\) | 1.08512e7i | 0.980761i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.22166e6 | −0.109581 | −0.0547907 | − | 0.998498i | \(-0.517449\pi\) | ||||
−0.0547907 | + | 0.998498i | \(0.517449\pi\) | |||||||
\(660\) | −1.99584e6 | − | 2.70796e6i | −0.178347 | − | 0.241981i | ||||
\(661\) | −1.62789e7 | −1.44918 | −0.724589 | − | 0.689182i | \(-0.757970\pi\) | ||||
−0.724589 | + | 0.689182i | \(0.757970\pi\) | |||||||
\(662\) | − | 1.04842e7i | − | 0.929799i | ||||||
\(663\) | − | 1.63910e6i | − | 0.144818i | ||||||
\(664\) | −8.20424e6 | −0.722135 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.41776e7 | 1.23856 | ||||||||
\(667\) | − | 1.68704e7i | − | 1.46829i | ||||||
\(668\) | − | 217226.i | − | 0.0188352i | ||||||
\(669\) | −5.74636e6 | −0.496395 | ||||||||
\(670\) | 1.30264e7 | − | 9.60083e6i | 1.12108 | − | 0.826270i | ||||
\(671\) | 1.43590e6 | 0.123117 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.43928e7i | 1.22492i | 0.790503 | + | 0.612459i | \(0.209819\pi\) | ||||
−0.790503 | + | 0.612459i | \(0.790181\pi\) | |||||||
\(674\) | −8.15126e6 | −0.691155 | ||||||||
\(675\) | 5.34600e6 | + | 1.65665e6i | 0.451616 | + | 0.139950i | ||||
\(676\) | −4.28444e6 | −0.360602 | ||||||||
\(677\) | − | 2.62429e6i | − | 0.220059i | −0.993928 | − | 0.110030i | \(-0.964905\pi\) | ||
0.993928 | − | 0.110030i | \(-0.0350946\pi\) | |||||||
\(678\) | − | 1.38623e7i | − | 1.15814i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.11840e6 | + | 3.03538e6i | −0.341552 | + | 0.251733i | ||||
\(681\) | 2.31661e7 | 1.91419 | ||||||||
\(682\) | − | 1.12865e7i | − | 0.929177i | ||||||
\(683\) | 1.03039e7i | 0.845184i | 0.906320 | + | 0.422592i | \(0.138880\pi\) | ||||
−0.906320 | + | 0.422592i | \(0.861120\pi\) | |||||||
\(684\) | 403920. | 0.0330107 | ||||||||
\(685\) | −4.76168e6 | − | 6.46065e6i | −0.387734 | − | 0.526078i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1.08985e7i | − | 0.880998i | ||||||
\(688\) | 528219.i | 0.0425444i | ||||||||
\(689\) | 695376. | 0.0558048 | ||||||||
\(690\) | −1.06577e7 | − | 1.44604e7i | −0.852197 | − | 1.15626i | ||||
\(691\) | −4.50285e6 | −0.358751 | −0.179375 | − | 0.983781i | \(-0.557408\pi\) | ||||
−0.179375 | + | 0.983781i | \(0.557408\pi\) | |||||||
\(692\) | − | 5.91086e6i | − | 0.469230i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.54865e7 | 2.00868 | ||||||||
\(695\) | 1.43253e7 | − | 1.05581e7i | 1.12497 | − | 0.829136i | ||||
\(696\) | 1.82952e7 | 1.43157 | ||||||||
\(697\) | 136592.i | 0.0106498i | ||||||||
\(698\) | 1.05764e7i | 0.821672i | ||||||||
\(699\) | −957264. | −0.0741035 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.88090e6 | −0.375150 | −0.187575 | − | 0.982250i | \(-0.560063\pi\) | ||||
−0.187575 | + | 0.982250i | \(0.560063\pi\) | |||||||
\(702\) | − | 1.41845e6i | − | 0.108636i | ||||||
\(703\) | 3.07332e6i | 0.234541i | ||||||||
\(704\) | −3.27398e6 | −0.248969 | ||||||||
\(705\) | −9.43866e6 | + | 6.95655e6i | −0.715217 | + | 0.527134i | ||||
\(706\) | −1.95923e6 | −0.147936 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 5.88873e6i | − | 0.441508i | ||||||
\(709\) | −9.96961e6 | −0.744839 | −0.372420 | − | 0.928064i | \(-0.621472\pi\) | ||||
−0.372420 | + | 0.928064i | \(0.621472\pi\) | |||||||
\(710\) | 1.17374e7 | + | 1.59254e7i | 0.873831 | + | 1.18561i | ||||
\(711\) | −7.94376e6 | −0.589321 | ||||||||
\(712\) | 1.32532e6i | 0.0979765i | ||||||||
\(713\) | − | 1.64371e7i | − | 1.21088i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 997920. | + | 1.35398e6i | 0.0730013 | + | 0.0990482i | ||||
\(716\) | −5.33304e6 | −0.388770 | ||||||||
\(717\) | − | 2.00160e7i | − | 1.45405i | ||||||
\(718\) | 7.32868e6i | 0.530536i | ||||||||
\(719\) | 1.19167e7 | 0.859675 | 0.429838 | − | 0.902906i | \(-0.358571\pi\) | ||||
0.429838 | + | 0.902906i | \(0.358571\pi\) | |||||||
\(720\) | 8.70264e6 | − | 6.41409e6i | 0.625633 | − | 0.461109i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 1.61035e7i | − | 1.14968i | ||||||
\(723\) | − | 1.78143e7i | − | 1.26743i | ||||||
\(724\) | 1.88282e6 | 0.133494 | ||||||||
\(725\) | −6.41025e6 | + | 2.06858e7i | −0.452929 | + | 1.46160i | ||||
\(726\) | 1.28762e7 | 0.906664 | ||||||||
\(727\) | 1.38269e6i | 0.0970264i | 0.998823 | + | 0.0485132i | \(0.0154483\pi\) | ||||
−0.998823 | + | 0.0485132i | \(0.984552\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.48079e6 | 0.172890 | ||||||||
\(730\) | 2.11702e7 | − | 1.56030e7i | 1.47034 | − | 1.08368i | ||||
\(731\) | 288288. | 0.0199541 | ||||||||
\(732\) | − | 1.36067e6i | − | 0.0938585i | ||||||
\(733\) | 6.09661e6i | 0.419110i | 0.977797 | + | 0.209555i | \(0.0672016\pi\) | ||||
−0.977797 | + | 0.209555i | \(0.932798\pi\) | |||||||
\(734\) | −1.21893e7 | −0.835099 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00764e7 | 0.685660 | ||||||||
\(737\) | − | 1.09973e7i | − | 0.745793i | ||||||
\(738\) | − | 200948.i | − | 0.0135813i | ||||||
\(739\) | 6.16946e6 | 0.415562 | 0.207781 | − | 0.978175i | \(-0.433376\pi\) | ||||
0.207781 | + | 0.978175i | \(0.433376\pi\) | |||||||
\(740\) | −5.55984e6 | − | 7.54360e6i | −0.373236 | − | 0.506406i | ||||
\(741\) | −522720. | −0.0349723 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.57574e7i | − | 1.04716i | −0.851978 | − | 0.523578i | \(-0.824597\pi\) | ||
0.851978 | − | 0.523578i | \(-0.175403\pi\) | |||||||
\(744\) | 1.78253e7 | 1.18060 | ||||||||
\(745\) | 3.78675e6 | − | 2.79094e6i | 0.249963 | − | 0.184230i | ||||
\(746\) | −1.94586e7 | −1.28016 | ||||||||
\(747\) | − | 9.46179e6i | − | 0.620400i | ||||||
\(748\) | − | 2.08613e6i | − | 0.136329i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 7.57350e6 | + | 2.17803e7i | 0.491636 | + | 1.41387i | ||||
\(751\) | −1.51816e7 | −0.982243 | −0.491122 | − | 0.871091i | \(-0.663413\pi\) | ||||
−0.491122 | + | 0.871091i | \(0.663413\pi\) | |||||||
\(752\) | − | 1.33229e7i | − | 0.859118i | ||||||
\(753\) | − | 1.11091e7i | − | 0.713987i | ||||||
\(754\) | 5.48856e6 | 0.351585 | ||||||||
\(755\) | −7.01316e6 | + | 5.16889e6i | −0.447761 | + | 0.330012i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 652274.i | − | 0.0413705i | −0.999786 | − | 0.0206852i | \(-0.993415\pi\) | ||
0.999786 | − | 0.0206852i | \(-0.00658478\pi\) | |||||||
\(758\) | 3.37859e7i | 2.13581i | ||||||||
\(759\) | −1.22079e7 | −0.769194 | ||||||||
\(760\) | 968000. | + | 1.31338e6i | 0.0607913 | + | 0.0824817i | ||||
\(761\) | −4.51420e6 | −0.282566 | −0.141283 | − | 0.989969i | \(-0.545123\pi\) | ||||
−0.141283 | + | 0.989969i | \(0.545123\pi\) | |||||||
\(762\) | 1.15131e7i | 0.718300i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.98822e6 | −0.247199 | ||||||||
\(765\) | −3.50064e6 | − | 4.74967e6i | −0.216269 | − | 0.293434i | ||||
\(766\) | 2.10596e7 | 1.29681 | ||||||||
\(767\) | 2.94437e6i | 0.180719i | ||||||||
\(768\) | 2.05862e7i | 1.25943i | ||||||||
\(769\) | 1.20799e7 | 0.736625 | 0.368312 | − | 0.929702i | \(-0.379936\pi\) | ||||
0.368312 | + | 0.929702i | \(0.379936\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.56795e7 | −0.949939 | ||||||||
\(772\) | − | 9.43344e6i | − | 0.569674i | ||||||
\(773\) | 1.04245e7i | 0.627492i | 0.949507 | + | 0.313746i | \(0.101584\pi\) | ||||
−0.949507 | + | 0.313746i | \(0.898416\pi\) | |||||||
\(774\) | −424116. | −0.0254467 | ||||||||
\(775\) | −6.24560e6 | + | 2.01545e7i | −0.373525 | + | 1.20536i | ||||
\(776\) | −1.34323e7 | −0.800750 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.19393e7i | 0.707177i | ||||||||
\(779\) | 43560.0 | 0.00257184 | ||||||||
\(780\) | 1.28304e6 | − | 945636.i | 0.0755099 | − | 0.0556529i | ||||
\(781\) | 1.34447e7 | 0.788721 | ||||||||
\(782\) | − | 1.11398e7i | − | 0.651421i | ||||||
\(783\) | − | 1.24115e7i | − | 0.723467i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.18285e7 | − | 1.60489e7i | −0.685104 | − | 0.929549i | ||||
\(786\) | 2.54565e7 | 1.46974 | ||||||||
\(787\) | − | 3.45366e7i | − | 1.98766i | −0.110913 | − | 0.993830i | \(-0.535378\pi\) | ||
0.110913 | − | 0.993830i | \(-0.464622\pi\) | |||||||
\(788\) | − | 715277.i | − | 0.0410354i | ||||||
\(789\) | 3.24711e7 | 1.85697 | ||||||||
\(790\) | 1.14224e7 | + | 1.54979e7i | 0.651163 | + | 0.883498i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 5.11503e6i | − | 0.289758i | ||||||
\(793\) | 680333.i | 0.0384183i | ||||||||
\(794\) | −3.25298e7 | −1.83118 | ||||||||
\(795\) | 5.21532e6 | − | 3.84384e6i | 0.292660 | − | 0.215698i | ||||
\(796\) | −4.74960e6 | −0.265689 | ||||||||
\(797\) | 2.09287e7i | 1.16707i | 0.812089 | + | 0.583533i | \(0.198330\pi\) | ||||
−0.812089 | + | 0.583533i | \(0.801670\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.27126e6 | −0.402942 | ||||||||
\(800\) | −1.23552e7 | − | 3.82871e6i | −0.682535 | − | 0.211508i | ||||
\(801\) | −1.52847e6 | −0.0841735 | ||||||||
\(802\) | − | 4.26384e6i | − | 0.234080i | ||||||
\(803\) | − | 1.78725e7i | − | 0.978131i | ||||||
\(804\) | −1.04211e7 | −0.568558 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.34758e6 | 0.289948 | ||||||||
\(807\) | 3.45533e7i | 1.86770i | ||||||||
\(808\) | 1.44735e7i | 0.779910i | ||||||||
\(809\) | 2.48797e7 | 1.33651 | 0.668257 | − | 0.743930i | \(-0.267041\pi\) | ||||
0.668257 | + | 0.743930i | \(0.267041\pi\) | |||||||
\(810\) | −1.60202e7 | − | 2.17362e7i | −0.857936 | − | 1.16405i | ||||
\(811\) | 3.95415e6 | 0.211106 | 0.105553 | − | 0.994414i | \(-0.466339\pi\) | ||||
0.105553 | + | 0.994414i | \(0.466339\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.42285e7i | 1.81619i | ||||||||
\(814\) | −2.33513e7 | −1.23524 | ||||||||
\(815\) | −4.80546e6 | − | 6.52005e6i | −0.253420 | − | 0.343841i | ||||
\(816\) | 1.73522e7 | 0.912282 | ||||||||
\(817\) | − | 91936.8i | − | 0.00481875i | ||||||
\(818\) | 1.36453e7i | 0.713018i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −106920. | + | 78803.0i | −0.00555296 | + | 0.00409268i | ||||
\(821\) | −3.43550e6 | −0.177882 | −0.0889410 | − | 0.996037i | \(-0.528348\pi\) | ||||
−0.0889410 | + | 0.996037i | \(0.528348\pi\) | |||||||
\(822\) | 1.89512e7i | 0.978269i | ||||||||
\(823\) | − | 3.94833e6i | − | 0.203195i | −0.994826 | − | 0.101598i | \(-0.967605\pi\) | ||
0.994826 | − | 0.101598i | \(-0.0323954\pi\) | |||||||
\(824\) | 9.36936e6 | 0.480720 | ||||||||
\(825\) | 1.49688e7 | + | 4.63863e6i | 0.765688 | + | 0.237277i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 3.38176e7i | − | 1.71941i | −0.510791 | − | 0.859705i | \(-0.670647\pi\) | ||
0.510791 | − | 0.859705i | \(-0.329353\pi\) | |||||||
\(828\) | 4.46956e6i | 0.226563i | ||||||||
\(829\) | −1.52015e7 | −0.768244 | −0.384122 | − | 0.923282i | \(-0.625496\pi\) | ||||
−0.384122 | + | 0.923282i | \(0.625496\pi\) | |||||||
\(830\) | −1.84595e7 | + | 1.36052e7i | −0.930091 | + | 0.685503i | ||||
\(831\) | −2.53210e7 | −1.27198 | ||||||||
\(832\) | − | 1.55123e6i | − | 0.0776903i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.20209e7 | −2.09194 | ||||||||
\(835\) | 600380. | + | 814596.i | 0.0297996 | + | 0.0404321i | ||||
\(836\) | −665280. | −0.0329222 | ||||||||
\(837\) | − | 1.20927e7i | − | 0.596635i | ||||||
\(838\) | 1.94846e7i | 0.958478i | ||||||||
\(839\) | −2.89012e7 | −1.41746 | −0.708729 | − | 0.705481i | \(-0.750731\pi\) | ||||
−0.708729 | + | 0.705481i | \(0.750731\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.75138e7 | 1.34140 | ||||||||
\(842\) | 1.80272e7i | 0.876290i | ||||||||
\(843\) | 2.91532e7i | 1.41292i | ||||||||
\(844\) | 3.01858e6 | 0.145863 | ||||||||
\(845\) | 1.60667e7 | − | 1.18416e7i | 0.774077 | − | 0.570516i | ||||
\(846\) | 1.06971e7 | 0.513857 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.36153e6i | 0.351543i | ||||||||
\(849\) | −3.28446e7 | −1.56385 | ||||||||
\(850\) | −4.23280e6 | + | 1.36592e7i | −0.200946 | + | 0.648452i | ||||
\(851\) | −3.40077e7 | −1.60973 | ||||||||
\(852\) | − | 1.27403e7i | − | 0.601285i | ||||||
\(853\) | 2.02107e7i | 0.951062i | 0.879699 | + | 0.475531i | \(0.157744\pi\) | ||||
−0.879699 | + | 0.475531i | \(0.842256\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.51470e6 | + | 1.11638e6i | −0.0708617 | + | 0.0522270i | ||||
\(856\) | −1.28841e7 | −0.600992 | ||||||||
\(857\) | − | 1.70522e7i | − | 0.793101i | −0.918013 | − | 0.396550i | \(-0.870207\pi\) | ||
0.918013 | − | 0.396550i | \(-0.129793\pi\) | |||||||
\(858\) | − | 3.97167e6i | − | 0.184185i | ||||||
\(859\) | −1.95505e7 | −0.904015 | −0.452008 | − | 0.892014i | \(-0.649292\pi\) | ||||
−0.452008 | + | 0.892014i | \(0.649292\pi\) | |||||||
\(860\) | 166320. | + | 225663.i | 0.00766829 | + | 0.0104043i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.31288e7i | 1.51858i | ||||||||
\(863\) | 2.70896e7i | 1.23816i | 0.785330 | + | 0.619078i | \(0.212493\pi\) | ||||
−0.785330 | + | 0.619078i | \(0.787507\pi\) | |||||||
\(864\) | 7.41312e6 | 0.337844 | ||||||||
\(865\) | 1.63368e7 | + | 2.21657e7i | 0.742379 | + | 1.00726i | ||||
\(866\) | −1.38093e7 | −0.625716 | ||||||||
\(867\) | 1.87844e7i | 0.848692i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.30838e7 | 0.587741 | ||||||||
\(870\) | 4.11642e7 | − | 3.03392e7i | 1.84383 | − | 1.35896i | ||||
\(871\) | 5.21057e6 | 0.232723 | ||||||||
\(872\) | − | 2.78729e6i | − | 0.124134i | ||||||
\(873\) | − | 1.54912e7i | − | 0.687940i | ||||||
\(874\) | −3.55256e6 | −0.157312 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.69361e7 | −0.745682 | ||||||||
\(877\) | 1.98285e6i | 0.0870545i | 0.999052 | + | 0.0435272i | \(0.0138595\pi\) | ||||
−0.999052 | + | 0.0435272i | \(0.986140\pi\) | |||||||
\(878\) | 3.12031e7i | 1.36603i | ||||||||
\(879\) | 4.75150e7 | 2.07424 | ||||||||
\(880\) | −1.43338e7 | + | 1.05644e7i | −0.623955 | + | 0.459872i | ||||
\(881\) | 4.22840e7 | 1.83542 | 0.917712 | − | 0.397247i | \(-0.130034\pi\) | ||||
0.917712 | + | 0.397247i | \(0.130034\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 134502.i | 0.00580535i | 0.999996 | + | 0.00290267i | \(0.000923951\pi\) | ||||
−0.999996 | + | 0.00290267i | \(0.999076\pi\) | |||||||
\(884\) | 988416. | 0.0425411 | ||||||||
\(885\) | 1.62756e7 | + | 2.20828e7i | 0.698520 | + | 0.947753i | ||||
\(886\) | 3.78164e7 | 1.61844 | ||||||||
\(887\) | − | 3.87668e6i | − | 0.165444i | −0.996573 | − | 0.0827219i | \(-0.973639\pi\) | ||
0.996573 | − | 0.0827219i | \(-0.0263613\pi\) | |||||||
\(888\) | − | 3.68798e7i | − | 1.56948i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.19780e6 | + | 2.98198e6i | 0.0930065 | + | 0.126191i | ||||
\(891\) | −1.83504e7 | −0.774374 | ||||||||
\(892\) | − | 3.46518e6i | − | 0.145819i | ||||||
\(893\) | 2.31885e6i | 0.0973070i | ||||||||
\(894\) | −1.11078e7 | −0.464819 | ||||||||
\(895\) | 1.99989e7 | − | 1.47397e7i | 0.834543 | − | 0.615081i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 5.78414e6i | − | 0.240026i | ||||||
\(898\) | 4.11477e7i | 1.70277i | ||||||||
\(899\) | 4.67914e7 | 1.93093 | ||||||||
\(900\) | 1.69830e6 | − | 5.48039e6i | 0.0698889 | − | 0.225530i | ||||
\(901\) | 4.01773e6 | 0.164880 | ||||||||
\(902\) | 330973.i | 0.0135449i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.39322e7 | −0.567019 | ||||||||
\(905\) | −7.06059e6 | + | 5.20385e6i | −0.286563 | + | 0.211205i | ||||
\(906\) | 2.05719e7 | 0.832635 | ||||||||
\(907\) | − | 2.87363e7i | − | 1.15988i | −0.814660 | − | 0.579939i | \(-0.803076\pi\) | ||
0.814660 | − | 0.579939i | \(-0.196924\pi\) | |||||||
\(908\) | 1.39697e7i | 0.562306i | ||||||||
\(909\) | −1.66920e7 | −0.670037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.87675e6 | 0.0749223 | 0.0374611 | − | 0.999298i | \(-0.488073\pi\) | ||||
0.0374611 | + | 0.999298i | \(0.488073\pi\) | |||||||
\(912\) | − | 5.53372e6i | − | 0.220308i | ||||||
\(913\) | 1.55841e7i | 0.618736i | ||||||||
\(914\) | 1.42861e7 | 0.565650 | ||||||||
\(915\) | 3.76068e6 | + | 5.10249e6i | 0.148496 | + | 0.201479i | ||||
\(916\) | 6.57204e6 | 0.258798 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 8.19551e6i | − | 0.320974i | ||||||
\(919\) | −6.76852e6 | −0.264366 | −0.132183 | − | 0.991225i | \(-0.542199\pi\) | ||||
−0.132183 | + | 0.991225i | \(0.542199\pi\) | |||||||
\(920\) | −1.45332e7 | + | 1.07114e7i | −0.566098 | + | 0.417230i | ||||
\(921\) | 1.84722e7 | 0.717579 | ||||||||
\(922\) | 2.55466e7i | 0.989706i | ||||||||
\(923\) | 6.37015e6i | 0.246119i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.16988e7 | + | 1.29219e7i | 1.60239 | + | 0.496560i | ||||
\(926\) | 1.38113e7 | 0.529306 | ||||||||
\(927\) | 1.08055e7i | 0.412996i | ||||||||
\(928\) | 2.86843e7i | 1.09339i | ||||||||
\(929\) | −1.15356e7 | −0.438530 | −0.219265 | − | 0.975665i | \(-0.570366\pi\) | ||||
−0.219265 | + | 0.975665i | \(0.570366\pi\) | |||||||
\(930\) | 4.01069e7 | − | 2.95599e7i | 1.52059 | − | 1.12072i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 577252.i | − | 0.0217684i | ||||||
\(933\) | − | 1.13061e7i | − | 0.425214i | ||||||
\(934\) | 8.67772e6 | 0.325491 | ||||||||
\(935\) | 5.76576e6 | + | 7.82299e6i | 0.215689 | + | 0.292647i | ||||
\(936\) | 2.42352e6 | 0.0904184 | ||||||||
\(937\) | − | 3.92632e7i | − | 1.46096i | −0.682936 | − | 0.730478i | \(-0.739297\pi\) | ||
0.682936 | − | 0.730478i | \(-0.260703\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.42762e7 | −1.26861 | ||||||||
\(940\) | −4.19496e6 | − | 5.69173e6i | −0.154849 | − | 0.210099i | ||||
\(941\) | −2.94919e7 | −1.08575 | −0.542874 | − | 0.839814i | \(-0.682664\pi\) | ||||
−0.542874 | + | 0.839814i | \(0.682664\pi\) | |||||||
\(942\) | 4.70769e7i | 1.72855i | ||||||||
\(943\) | 482012.i | 0.0176514i | ||||||||
\(944\) | −3.11702e7 | −1.13844 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 698544. | 0.0253785 | ||||||||
\(947\) | 2.09628e7i | 0.759581i | 0.925072 | + | 0.379791i | \(0.124004\pi\) | ||||
−0.925072 | + | 0.379791i | \(0.875996\pi\) | |||||||
\(948\) | − | 1.23983e7i | − | 0.448067i | ||||||
\(949\) | 8.46806e6 | 0.305224 | ||||||||
\(950\) | 4.35600e6 | + | 1.34987e6i | 0.156595 | + | 0.0485268i | ||||
\(951\) | −2.61967e6 | −0.0939281 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.64122e7i | − | 0.585375i | −0.956208 | − | 0.292687i | \(-0.905451\pi\) | ||
0.956208 | − | 0.292687i | \(-0.0945495\pi\) | |||||||
\(954\) | −5.91070e6 | −0.210265 | ||||||||
\(955\) | 1.49558e7 | − | 1.10229e7i | 0.530643 | − | 0.391099i | ||||
\(956\) | 1.20701e7 | 0.427135 | ||||||||
\(957\) | − | 3.47521e7i | − | 1.22660i | ||||||
\(958\) | 4.48652e7i | 1.57941i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −8.57472e6 | − | 1.16342e7i | −0.300291 | − | 0.407435i | ||||
\(961\) | 1.69604e7 | 0.592416 | ||||||||
\(962\) | − | 1.10639e7i | − | 0.385454i | ||||||
\(963\) | − | 1.48590e7i | − | 0.516325i | ||||||
\(964\) | 1.07424e7 | 0.372314 | ||||||||
\(965\) | 2.60726e7 | + | 3.53754e7i | 0.901295 | + | 1.22288i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.71911e7i | − | 1.62291i | −0.584416 | − | 0.811454i | \(-0.698676\pi\) | ||
0.584416 | − | 0.811454i | \(-0.301324\pi\) | |||||||
\(968\) | − | 1.29411e7i | − | 0.443897i | ||||||
\(969\) | −3.02016e6 | −0.103329 | ||||||||
\(970\) | −3.02227e7 | + | 2.22750e7i | −1.03135 | + | 0.760130i | ||||
\(971\) | −3.84771e7 | −1.30965 | −0.654823 | − | 0.755783i | \(-0.727257\pi\) | ||||
−0.654823 | + | 0.755783i | \(0.727257\pi\) | |||||||
\(972\) | 1.21665e7i | 0.413046i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.42566e7 | −1.49479 | ||||||||
\(975\) | −2.19780e6 | + | 7.09227e6i | −0.0740417 | + | 0.238932i | ||||
\(976\) | −7.20227e6 | −0.242016 | ||||||||
\(977\) | 2.70184e7i | 0.905572i | 0.891619 | + | 0.452786i | \(0.149570\pi\) | ||||
−0.891619 | + | 0.452786i | \(0.850430\pi\) | |||||||
\(978\) | 1.91255e7i | 0.639389i | ||||||||
\(979\) | 2.51748e6 | 0.0839478 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.21453e6 | 0.106646 | ||||||||
\(982\) | − | 4.56086e7i | − | 1.50927i | ||||||
\(983\) | − | 2.88475e7i | − | 0.952192i | −0.879393 | − | 0.476096i | \(-0.842051\pi\) | ||
0.879393 | − | 0.476096i | \(-0.157949\pi\) | |||||||
\(984\) | −522720. | −0.0172100 | ||||||||
\(985\) | 1.97692e6 | + | 2.68229e6i | 0.0649230 | + | 0.0880876i | ||||
\(986\) | 3.17117e7 | 1.03879 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 315212.i | − | 0.0102733i | ||||||
\(989\) | 1.01732e6 | 0.0330726 | ||||||||
\(990\) | −8.48232e6 | − | 1.15088e7i | −0.275060 | − | 0.373201i | ||||
\(991\) | −5.21596e7 | −1.68714 | −0.843569 | − | 0.537021i | \(-0.819550\pi\) | ||||
−0.843569 | + | 0.537021i | \(0.819550\pi\) | |||||||
\(992\) | 2.79475e7i | 0.901704i | ||||||||
\(993\) | − | 3.14525e7i | − | 1.01224i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.78110e7 | − | 1.31272e7i | 0.570336 | − | 0.420353i | ||||
\(996\) | 1.47676e7 | 0.471696 | ||||||||
\(997\) | 9.78148e6i | 0.311650i | 0.987785 | + | 0.155825i | \(0.0498036\pi\) | ||||
−0.987785 | + | 0.155825i | \(0.950196\pi\) | |||||||
\(998\) | 4.60354e7i | 1.46307i | ||||||||
\(999\) | −2.50193e7 | −0.793161 |
(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 | 245.6.b.a.99.2 | 2 | ||
5.4 | even | 2 | inner | 245.6.b.a.99.1 | 2 | ||
7.6 | odd | 2 | 5.6.b.a.4.2 | yes | 2 | ||
21.20 | even | 2 | 45.6.b.b.19.1 | 2 | |||
28.27 | even | 2 | 80.6.c.a.49.2 | 2 | |||
35.13 | even | 4 | 25.6.a.c.1.2 | 2 | |||
35.27 | even | 4 | 25.6.a.c.1.1 | 2 | |||
35.34 | odd | 2 | 5.6.b.a.4.1 | ✓ | 2 | ||
56.13 | odd | 2 | 320.6.c.f.129.2 | 2 | |||
56.27 | even | 2 | 320.6.c.g.129.1 | 2 | |||
84.83 | odd | 2 | 720.6.f.f.289.1 | 2 | |||
105.62 | odd | 4 | 225.6.a.n.1.2 | 2 | |||
105.83 | odd | 4 | 225.6.a.n.1.1 | 2 | |||
105.104 | even | 2 | 45.6.b.b.19.2 | 2 | |||
140.27 | odd | 4 | 400.6.a.t.1.2 | 2 | |||
140.83 | odd | 4 | 400.6.a.t.1.1 | 2 | |||
140.139 | even | 2 | 80.6.c.a.49.1 | 2 | |||
280.69 | odd | 2 | 320.6.c.f.129.1 | 2 | |||
280.139 | even | 2 | 320.6.c.g.129.2 | 2 | |||
420.419 | odd | 2 | 720.6.f.f.289.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.6.b.a.4.1 | ✓ | 2 | 35.34 | odd | 2 | ||
5.6.b.a.4.2 | yes | 2 | 7.6 | odd | 2 | ||
25.6.a.c.1.1 | 2 | 35.27 | even | 4 | |||
25.6.a.c.1.2 | 2 | 35.13 | even | 4 | |||
45.6.b.b.19.1 | 2 | 21.20 | even | 2 | |||
45.6.b.b.19.2 | 2 | 105.104 | even | 2 | |||
80.6.c.a.49.1 | 2 | 140.139 | even | 2 | |||
80.6.c.a.49.2 | 2 | 28.27 | even | 2 | |||
225.6.a.n.1.1 | 2 | 105.83 | odd | 4 | |||
225.6.a.n.1.2 | 2 | 105.62 | odd | 4 | |||
245.6.b.a.99.1 | 2 | 5.4 | even | 2 | inner | ||
245.6.b.a.99.2 | 2 | 1.1 | even | 1 | trivial | ||
320.6.c.f.129.1 | 2 | 280.69 | odd | 2 | |||
320.6.c.f.129.2 | 2 | 56.13 | odd | 2 | |||
320.6.c.g.129.1 | 2 | 56.27 | even | 2 | |||
320.6.c.g.129.2 | 2 | 280.139 | even | 2 | |||
400.6.a.t.1.1 | 2 | 140.83 | odd | 4 | |||
400.6.a.t.1.2 | 2 | 140.27 | odd | 4 | |||
720.6.f.f.289.1 | 2 | 84.83 | odd | 2 | |||
720.6.f.f.289.2 | 2 | 420.419 | odd | 2 |