Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [200,6,Mod(49,200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("200.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 200.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0767639626\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 200.49 |
Dual form | 200.6.c.c.49.2 |
$q$-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 \(\left(\mathbb{Z}/200\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 8.00000i | − 0.513200i | −0.966518 | − | 0.256600i | \(-0.917398\pi\) | ||||
0.966518 | − | 0.256600i | \(-0.0826023\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 108.000i | 0.833065i | 0.909121 | + | 0.416532i | \(0.136755\pi\) | ||||
−0.909121 | + | 0.416532i | \(0.863245\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 179.000 | 0.736626 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −604.000 | −1.50506 | −0.752532 | − | 0.658555i | \(-0.771168\pi\) | ||||
−0.752532 | + | 0.658555i | \(0.771168\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 306.000i | − 0.502184i | −0.967963 | − | 0.251092i | \(-0.919210\pi\) | ||||
0.967963 | − | 0.251092i | \(-0.0807897\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 930.000i | − 0.780478i | −0.920714 | − | 0.390239i | \(-0.872392\pi\) | ||||
0.920714 | − | 0.390239i | \(-0.127608\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1324.00 | 0.841403 | 0.420701 | − | 0.907199i | \(-0.361784\pi\) | ||||
0.420701 | + | 0.907199i | \(0.361784\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 864.000 | 0.427529 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 852.000i | − 0.335830i | −0.985801 | − | 0.167915i | \(-0.946297\pi\) | ||||
0.985801 | − | 0.167915i | \(-0.0537035\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 3376.00i | − 0.891237i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5902.00 | −1.30318 | −0.651590 | − | 0.758572i | \(-0.725898\pi\) | ||||
−0.651590 | + | 0.758572i | \(0.725898\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3320.00 | −0.620489 | −0.310244 | − | 0.950657i | \(-0.600411\pi\) | ||||
−0.310244 | + | 0.950657i | \(0.600411\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4832.00i | 0.772400i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 10774.0i | − 1.29382i | −0.762568 | − | 0.646908i | \(-0.776062\pi\) | ||||
0.762568 | − | 0.646908i | \(-0.223938\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2448.00 | −0.257721 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17958.0 | −1.66839 | −0.834196 | − | 0.551467i | \(-0.814068\pi\) | ||||
−0.834196 | + | 0.551467i | \(0.814068\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9264.00i | 0.764060i | 0.924150 | + | 0.382030i | \(0.124775\pi\) | ||||
−0.924150 | + | 0.382030i | \(0.875225\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9796.00i | 0.646851i | 0.946254 | + | 0.323425i | \(0.104834\pi\) | ||||
−0.946254 | + | 0.323425i | \(0.895166\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5143.00 | 0.306003 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7440.00 | −0.400541 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 31434.0i | − 1.53713i | −0.639773 | − | 0.768564i | \(-0.720972\pi\) | ||||
0.639773 | − | 0.768564i | \(-0.279028\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 10592.0i | − 0.431808i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −33228.0 | −1.24272 | −0.621361 | − | 0.783524i | \(-0.713420\pi\) | ||||
−0.621361 | + | 0.783524i | \(0.713420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −40210.0 | −1.38360 | −0.691798 | − | 0.722091i | \(-0.743181\pi\) | ||||
−0.691798 | + | 0.722091i | \(0.743181\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 19332.0i | 0.613657i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 58864.0i | − 1.60200i | −0.598664 | − | 0.801000i | \(-0.704301\pi\) | ||||
0.598664 | − | 0.801000i | \(-0.295699\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6816.00 | −0.172348 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −55312.0 | −1.30219 | −0.651094 | − | 0.758997i | \(-0.725690\pi\) | ||||
−0.651094 | + | 0.758997i | \(0.725690\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 27258.0i | 0.598669i | 0.954148 | + | 0.299335i | \(0.0967647\pi\) | ||||
−0.954148 | + | 0.299335i | \(0.903235\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 65232.0i | − 1.25382i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −31456.0 | −0.567069 | −0.283534 | − | 0.958962i | \(-0.591507\pi\) | ||||
−0.283534 | + | 0.958962i | \(0.591507\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16489.0 | 0.279243 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 24552.0i | 0.391194i | 0.980684 | + | 0.195597i | \(0.0626644\pi\) | ||||
−0.980684 | + | 0.195597i | \(0.937336\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 47216.0i | 0.668792i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 90854.0 | 1.21582 | 0.607910 | − | 0.794006i | \(-0.292008\pi\) | ||||
0.607910 | + | 0.794006i | \(0.292008\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 33048.0 | 0.418352 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 26560.0i | 0.318435i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 154706.i | − 1.66947i | −0.550654 | − | 0.834733i | \(-0.685622\pi\) | ||||
0.550654 | − | 0.834733i | \(-0.314378\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −108116. | −1.10867 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −72714.0 | −0.709275 | −0.354637 | − | 0.935004i | \(-0.615396\pi\) | ||||
−0.354637 | + | 0.935004i | \(0.615396\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 129396.i | − 1.20179i | −0.799329 | − | 0.600894i | \(-0.794811\pi\) | ||||
0.799329 | − | 0.600894i | \(-0.205189\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 206680.i | 1.74518i | 0.488458 | + | 0.872588i | \(0.337560\pi\) | ||||
−0.488458 | + | 0.872588i | \(0.662440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 70146.0 | 0.565505 | 0.282753 | − | 0.959193i | \(-0.408752\pi\) | ||||
0.282753 | + | 0.959193i | \(0.408752\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −86192.0 | −0.663987 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 151854.i | − 1.11874i | −0.828917 | − | 0.559371i | \(-0.811043\pi\) | ||||
0.828917 | − | 0.559371i | \(-0.188957\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 54774.0i | − 0.369922i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 100440. | 0.650189 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 203765. | 1.26522 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 143664.i | 0.856220i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 336596.i | 1.85182i | 0.377740 | + | 0.925912i | \(0.376701\pi\) | ||||
−0.377740 | + | 0.925912i | \(0.623299\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 74112.0 | 0.392116 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 275308. | 1.40165 | 0.700827 | − | 0.713332i | \(-0.252815\pi\) | ||||
0.700827 | + | 0.713332i | \(0.252815\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 142992.i | 0.700943i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 228502.i | 1.04013i | 0.854126 | + | 0.520066i | \(0.174093\pi\) | ||||
−0.854126 | + | 0.520066i | \(0.825907\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −224284. | −0.984603 | −0.492302 | − | 0.870425i | \(-0.663844\pi\) | ||||
−0.492302 | + | 0.870425i | \(0.663844\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 78368.0 | 0.331964 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 184824.i | 0.755820i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 41144.0i | − 0.157041i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 183802. | 0.678242 | 0.339121 | − | 0.940743i | \(-0.389870\pi\) | ||||
0.339121 | + | 0.940743i | \(0.389870\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 296032. | 1.05657 | 0.528283 | − | 0.849069i | \(-0.322836\pi\) | ||||
0.528283 | + | 0.849069i | \(0.322836\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 166470.i | − 0.574920i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 134766.i | − 0.436346i | −0.975910 | − | 0.218173i | \(-0.929990\pi\) | ||||
0.975910 | − | 0.218173i | \(-0.0700097\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −251472. | −0.788854 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 92016.0 | 0.279768 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 60248.0i | − 0.177613i | −0.996049 | − | 0.0888063i | \(-0.971695\pi\) | ||||
0.996049 | − | 0.0888063i | \(-0.0283052\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 62012.0i | 0.172062i | 0.996292 | + | 0.0860309i | \(0.0274184\pi\) | ||||
−0.996292 | + | 0.0860309i | \(0.972582\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 277657. | 0.747811 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 236996. | 0.619799 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 591682.i | − 1.50305i | −0.659705 | − | 0.751524i | \(-0.729319\pi\) | ||||
0.659705 | − | 0.751524i | \(-0.270681\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 265824.i | 0.637766i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 241404. | 0.563134 | 0.281567 | − | 0.959542i | \(-0.409146\pi\) | ||||
0.281567 | + | 0.959542i | \(0.409146\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 187622. | 0.425684 | 0.212842 | − | 0.977087i | \(-0.431728\pi\) | ||||
0.212842 | + | 0.977087i | \(0.431728\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 321680.i | 0.710062i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 561720.i | 1.17467i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 364608. | 0.742458 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 37560.0 | 0.0744976 | 0.0372488 | − | 0.999306i | \(-0.488141\pi\) | ||||
0.0372488 | + | 0.999306i | \(0.488141\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 164434.i | 0.317759i | 0.987298 | + | 0.158880i | \(0.0507882\pi\) | ||||
−0.987298 | + | 0.158880i | \(0.949212\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 360518.i | − 0.661853i | −0.943657 | − | 0.330926i | \(-0.892639\pi\) | ||||
0.943657 | − | 0.330926i | \(-0.107361\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 654168. | 1.17100 | 0.585500 | − | 0.810673i | \(-0.300898\pi\) | ||||
0.585500 | + | 0.810673i | \(0.300898\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −470912. | −0.822147 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 637416.i | − 1.08563i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 152508.i | − 0.247381i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −799696. | −1.26637 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −693156. | −1.07183 | −0.535914 | − | 0.844273i | \(-0.680033\pi\) | ||||
−0.535914 | + | 0.844273i | \(0.680033\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 442496.i | 0.668283i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 358560.i | − 0.516907i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 218064. | 0.307237 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −284580. | −0.391944 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 494756.i | 0.666237i | 0.942885 | + | 0.333119i | \(0.108101\pi\) | ||||
−0.942885 | + | 0.333119i | \(0.891899\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 907088.i | − 1.16838i | −0.811616 | − | 0.584191i | \(-0.801412\pi\) | ||||
0.811616 | − | 0.584191i | \(-0.198588\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.08949e6 | −1.37289 | −0.686446 | − | 0.727181i | \(-0.740830\pi\) | ||||
−0.686446 | + | 0.727181i | \(0.740830\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −521856. | −0.643459 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 499706.i | 0.603010i | 0.953465 | + | 0.301505i | \(0.0974891\pi\) | ||||
−0.953465 | + | 0.301505i | \(0.902511\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 251648.i | 0.291020i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.62038e6 | −1.83495 | −0.917473 | − | 0.397799i | \(-0.869774\pi\) | ||||
−0.917473 | + | 0.397799i | \(0.869774\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00122e6 | 1.11042 | 0.555208 | − | 0.831711i | \(-0.312638\pi\) | ||||
0.555208 | + | 0.831711i | \(0.312638\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 952280.i | − 1.03454i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 405144.i | − 0.422539i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 196416. | 0.200761 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 368980. | 0.369674 | 0.184837 | − | 0.982769i | \(-0.440824\pi\) | ||||
0.184837 | + | 0.982769i | \(0.440824\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 514608.i | 0.505447i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 279010.i | − 0.263504i | −0.991283 | − | 0.131752i | \(-0.957940\pi\) | ||||
0.991283 | − | 0.131752i | \(-0.0420602\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.16359e6 | 1.07783 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.05646e6 | −0.959955 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 811740.i | 0.723648i | 0.932246 | + | 0.361824i | \(0.117846\pi\) | ||||
−0.932246 | + | 0.361824i | \(0.882154\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 726832.i | − 0.623959i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −353214. | −0.297617 | −0.148808 | − | 0.988866i | \(-0.547544\pi\) | ||||
−0.148808 | + | 0.988866i | \(0.547544\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.71622e6 | −1.41954 | −0.709772 | − | 0.704432i | \(-0.751202\pi\) | ||||
−0.709772 | + | 0.704432i | \(0.751202\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 264384.i | − 0.214698i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 245882.i | 0.192543i | 0.995355 | + | 0.0962714i | \(0.0306917\pi\) | ||||
−0.995355 | + | 0.0962714i | \(0.969308\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −594280. | −0.457068 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.67618e6 | −1.26635 | −0.633177 | − | 0.774007i | \(-0.718250\pi\) | ||||
−0.633177 | + | 0.774007i | \(0.718250\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1.25882e6i | − 0.934321i | −0.884173 | − | 0.467161i | \(-0.845277\pi\) | ||||
0.884173 | − | 0.467161i | \(-0.154723\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1.93946e6i | − 1.38988i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 554957. | 0.390854 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.23765e6 | −0.856771 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 719158.i | 0.489390i | 0.969600 | + | 0.244695i | \(0.0786879\pi\) | ||||
−0.969600 | + | 0.244695i | \(0.921312\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.03910e6i | 1.34137i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −260712. | −0.168649 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00051e6 | −0.636511 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 581712.i | 0.364000i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.86013e6i | − 1.12641i | −0.826317 | − | 0.563206i | \(-0.809568\pi\) | ||||
0.826317 | − | 0.563206i | \(-0.190432\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.03517e6 | −0.616758 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 278384. | 0.163209 | 0.0816043 | − | 0.996665i | \(-0.473996\pi\) | ||||
0.0816043 | + | 0.996665i | \(0.473996\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 474182.i | − 0.273580i | −0.990600 | − | 0.136790i | \(-0.956321\pi\) | ||||
0.990600 | − | 0.136790i | \(-0.0436785\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.83738e6i | 1.02695i | 0.858104 | + | 0.513476i | \(0.171643\pi\) | ||||
−0.858104 | + | 0.513476i | \(0.828357\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.56481e6 | 1.96137 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.65344e6 | 0.895624 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.23132e6i | − 0.656696i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 561168.i | − 0.290217i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.05797e6 | −0.538868 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.99743e6 | 1.50376 | 0.751880 | − | 0.659299i | \(-0.229147\pi\) | ||||
0.751880 | + | 0.659299i | \(0.229147\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 1.92855e6i | − 0.953058i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 1.87531e6i | − 0.899496i | −0.893155 | − | 0.449748i | \(-0.851514\pi\) | ||||
0.893155 | − | 0.449748i | \(-0.148486\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.21483e6 | −0.574139 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00528e6 | 0.933876 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.37060e6i | 1.08799i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 180312.i | − 0.0803898i | −0.999192 | − | 0.0401949i | \(-0.987202\pi\) | ||||
0.999192 | − | 0.0401949i | \(-0.0127979\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 87058.0 | 0.0382600 | 0.0191300 | − | 0.999817i | \(-0.493910\pi\) | ||||
0.0191300 | + | 0.999817i | \(0.493910\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.03306e6 | −0.447565 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.65901e6i | 1.13575i | 0.823114 | + | 0.567876i | \(0.192235\pi\) | ||||
−0.823114 | + | 0.567876i | \(0.807765\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 803520.i | − 0.333677i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.14937e6 | 0.880186 | 0.440093 | − | 0.897952i | \(-0.354945\pi\) | ||||
0.440093 | + | 0.897952i | \(0.354945\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −723123. | −0.292041 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.63012e6i | − 0.649311i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.08258e6i | 1.19467i | 0.801991 | + | 0.597337i | \(0.203774\pi\) | ||||
−0.801991 | + | 0.597337i | \(0.796226\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.21448e6 | −1.22898 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.39487e6 | 1.28053 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.28727e6i | 0.851227i | 0.904905 | + | 0.425613i | \(0.139942\pi\) | ||||
−0.904905 | + | 0.425613i | \(0.860058\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.80601e6i | 0.654436i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.30154e6 | 0.465435 | 0.232718 | − | 0.972544i | \(-0.425238\pi\) | ||||
0.232718 | + | 0.972544i | \(0.425238\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.69277e6 | 0.950356 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 2.03276e6i | − 0.708093i | −0.935228 | − | 0.354046i | \(-0.884806\pi\) | ||||
0.935228 | − | 0.354046i | \(-0.115194\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.65826e6i | 0.562826i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −94230.0 | −0.0315730 | −0.0157865 | − | 0.999875i | \(-0.505025\pi\) | ||||
−0.0157865 | + | 0.999875i | \(0.505025\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −792360. | −0.262108 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 2.20246e6i | − 0.719329i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.55551e6i | 1.76908i | 0.466465 | + | 0.884540i | \(0.345527\pi\) | ||||
−0.466465 | + | 0.884540i | \(0.654473\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.14394e6 | 0.359724 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −784814. | −0.243728 | −0.121864 | − | 0.992547i | \(-0.538887\pi\) | ||||
−0.121864 | + | 0.992547i | \(0.538887\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.01592e6i | 0.311600i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.50750e6i | 1.94728i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.59401e6 | 1.35795 | 0.678974 | − | 0.734162i | \(-0.262425\pi\) | ||||
0.678974 | + | 0.734162i | \(0.262425\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.82802e6 | 0.533796 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 3.58862e6i | − 1.03527i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.79427e6i | 0.505299i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.41301e6 | −0.393198 | −0.196599 | − | 0.980484i | \(-0.562990\pi\) | ||||
−0.196599 | + | 0.980484i | \(0.562990\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.94556e6 | 1.63489 | 0.817443 | − | 0.576010i | \(-0.195391\pi\) | ||||
0.817443 | + | 0.576010i | \(0.195391\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.75348e6i | 0.476487i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 4.34268e6i | − 1.15263i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.47859e6 | 0.387887 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.48114e6 | −1.68058 | −0.840289 | − | 0.542139i | \(-0.817615\pi\) | ||||
−0.840289 | + | 0.542139i | \(0.817615\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.05597e6i | 1.03962i | 0.854282 | + | 0.519810i | \(0.173997\pi\) | ||||
−0.854282 | + | 0.519810i | \(0.826003\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1.12805e6i | − 0.282569i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.21450e6 | 0.300772 | 0.150386 | − | 0.988627i | \(-0.451948\pi\) | ||||
0.150386 | + | 0.988627i | \(0.451948\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 920597. | 0.225410 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 5.53154e6i | − 1.33917i | −0.742734 | − | 0.669586i | \(-0.766472\pi\) | ||||
0.742734 | − | 0.669586i | \(-0.233528\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 1.47042e6i | − 0.348074i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.20111e6 | −0.515258 | −0.257629 | − | 0.966244i | \(-0.582941\pi\) | ||||
−0.257629 | + | 0.966244i | \(0.582941\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.08466e7 | 2.51104 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 2.36826e6i | − 0.542229i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 3.29835e6i | − 0.738764i | −0.929278 | − | 0.369382i | \(-0.879569\pi\) | ||||
0.929278 | − | 0.369382i | \(-0.120431\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.13968e6 | −0.695591 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.94266e6 | −0.864046 | −0.432023 | − | 0.901863i | \(-0.642200\pi\) | ||||
−0.432023 | + | 0.901863i | \(0.642200\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.82040e6i | 1.91221i | 0.293021 | + | 0.956106i | \(0.405339\pi\) | ||||
−0.293021 | + | 0.956106i | \(0.594661\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.28709e6i | 0.273096i | 0.990633 | + | 0.136548i | \(0.0436009\pi\) | ||||
−0.990633 | + | 0.136548i | \(0.956399\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.35731e6 | 1.33457 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.07813e6 | −0.223933 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 5.59546e6i | − 1.14996i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 5.62669e6i | − 1.13229i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.51179e6 | −1.29677 | −0.648383 | − | 0.761314i | \(-0.724555\pi\) | ||||
−0.648383 | + | 0.761314i | \(0.724555\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.29684e6 | −0.649734 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 736128.i | − 0.143577i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.79523e6i | 1.10726i | 0.832764 | + | 0.553628i | \(0.186757\pi\) | ||||
−0.832764 | + | 0.553628i | \(0.813243\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −481984. | −0.0911508 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 990276. | 0.185376 | 0.0926878 | − | 0.995695i | \(-0.470454\pi\) | ||||
0.0926878 | + | 0.995695i | \(0.470454\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.48886e6i | 1.01710i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 5.97370e6i | − 1.08481i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.91500e6 | −0.524067 | −0.262033 | − | 0.965059i | \(-0.584393\pi\) | ||||
−0.262033 | + | 0.965059i | \(0.584393\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 496096. | 0.0883022 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.47872e6i | 0.436824i | 0.975857 | + | 0.218412i | \(0.0700877\pi\) | ||||
−0.975857 | + | 0.218412i | \(0.929912\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 2.22126e6i | − 0.383777i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.75807e6 | 1.15619 | 0.578093 | − | 0.815971i | \(-0.303797\pi\) | ||||
0.578093 | + | 0.815971i | \(0.303797\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.94386e6 | −0.498730 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 4.46982e6i | − 0.749889i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 5.91678e6i | − 0.973552i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.73346e6 | −0.771365 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.33903e6 | −1.02312 | −0.511562 | − | 0.859246i | \(-0.670933\pi\) | ||||
−0.511562 | + | 0.859246i | \(0.670933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 231920.i | 0.0370752i | 0.999828 | + | 0.0185376i | \(0.00590105\pi\) | ||||
−0.999828 | + | 0.0185376i | \(0.994099\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.08760e6i | 0.484278i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.71044e6 | 0.887218 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.94781e6 | −0.915421 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.49515e6i | 0.837841i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 1.93123e6i | − 0.289001i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.10637e6 | −0.460555 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.44440e6 | −1.38733 | −0.693667 | − | 0.720295i | \(-0.744006\pi\) | ||||
−0.693667 | + | 0.720295i | \(0.744006\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 1.50098e6i | − 0.218461i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3.10162e6i | − 0.443220i | −0.975135 | − | 0.221610i | \(-0.928869\pi\) | ||||
0.975135 | − | 0.221610i | \(-0.0711312\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.19759e6 | −1.01919 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.81425e6 | −1.09650 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 3.39725e6i | − 0.472405i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.22330e6i | 0.167068i | 0.996505 | + | 0.0835342i | \(0.0266208\pi\) | ||||
−0.996505 | + | 0.0835342i | \(0.973379\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.83478e6 | 0.383699 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.49376e6 | 0.602841 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.40896e7i | − 1.87339i | −0.350151 | − | 0.936693i | \(-0.613870\pi\) | ||||
0.350151 | − | 0.936693i | \(-0.386130\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.78081e6i | 0.232627i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.48468e6 | −0.192244 | −0.0961220 | − | 0.995370i | \(-0.530644\pi\) | ||||
−0.0961220 | + | 0.995370i | \(0.530644\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.86470e6 | −0.367696 | −0.183848 | − | 0.982955i | \(-0.558855\pi\) | ||||
−0.183848 | + | 0.982955i | \(0.558855\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 300480.i | − 0.0382322i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 4.21728e6i | − 0.527343i | −0.964613 | − | 0.263671i | \(-0.915067\pi\) | ||||
0.964613 | − | 0.263671i | \(-0.0849335\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.31547e6 | 0.163074 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.65162e6 | −0.325889 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.89861e7i | 2.31348i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.01047e6i | 0.240826i | 0.992724 | + | 0.120413i | \(0.0384218\pi\) | ||||
−0.992724 | + | 0.120413i | \(0.961578\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.39568e6 | −0.522081 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.88414e6 | −0.339663 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.33691e6i | 0.856795i | 0.903590 | + | 0.428397i | \(0.140922\pi\) | ||||
−0.903590 | + | 0.428397i | \(0.859078\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 5.23334e6i | − 0.600957i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.14884e6 | −0.130826 | −0.0654128 | − | 0.997858i | \(-0.520836\pi\) | ||||
−0.0654128 | + | 0.997858i | \(0.520836\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.16409e7 | 1.31462 | 0.657312 | − | 0.753618i | \(-0.271693\pi\) | ||||
0.657312 | + | 0.753618i | \(0.271693\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.05367e7i | − 1.18007i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 155540.i | 0.0171345i | 0.999963 | + | 0.00856723i | \(0.00272707\pi\) | ||||
−0.999963 | + | 0.00856723i | \(0.997273\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.09933e6 | −0.557147 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.99758e6 | 0.324838 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.18137e7i | − 1.26980i | −0.772595 | − | 0.634899i | \(-0.781042\pi\) | ||||
0.772595 | − | 0.634899i | \(-0.218958\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 6.42252e6i | − 0.679192i | −0.940571 | − | 0.339596i | \(-0.889710\pi\) | ||||
0.940571 | − | 0.339596i | \(-0.110290\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.85252e6 | −0.404128 | −0.202064 | − | 0.979372i | \(-0.564765\pi\) | ||||
−0.202064 | + | 0.979372i | \(0.564765\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.87635e6 | −0.299304 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.81223e6i | 1.01286i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.39757e6i | 0.649899i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.00198e7 | −1.00980 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.75136e6 | −0.675022 | −0.337511 | − | 0.941322i | \(-0.609585\pi\) | ||||
−0.337511 | + | 0.941322i | \(0.609585\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.54525e6i | 0.550062i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.57376e6i | − 0.153670i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.90085e6 | −0.959224 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.35493e6 | −0.707022 | −0.353511 | − | 0.935430i | \(-0.615012\pi\) | ||||
−0.353511 | + | 0.935430i | \(0.615012\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.59694e7i | 1.52322i | 0.648036 | + | 0.761610i | \(0.275591\pi\) | ||||
−0.648036 | + | 0.761610i | \(0.724409\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 1.72667e7i | − 1.62162i | −0.585311 | − | 0.810809i | \(-0.699028\pi\) | ||||
0.585311 | − | 0.810809i | \(-0.300972\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.00697e7 | 1.87038 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.86848e6 | −0.265277 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 1.36251e6i | − 0.125043i | −0.998044 | − | 0.0625213i | \(-0.980086\pi\) | ||||
0.998044 | − | 0.0625213i | \(-0.0199141\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.87918e6i | 0.440995i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.81808e6 | 0.790971 | 0.395485 | − | 0.918472i | \(-0.370576\pi\) | ||||
0.395485 | + | 0.918472i | \(0.370576\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.52035e6 | −0.135344 | −0.0676720 | − | 0.997708i | \(-0.521557\pi\) | ||||
−0.0676720 | + | 0.997708i | \(0.521557\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.27664e6i | 0.201146i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.02850e6i | 0.437647i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.95805e6 | 0.341913 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.42868e7 | 2.08240 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 315086.i | − 0.0268158i | −0.999910 | − | 0.0134079i | \(-0.995732\pi\) | ||||
0.999910 | − | 0.0134079i | \(-0.00426800\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.74092e6i | 0.145985i | 0.997332 | + | 0.0729924i | \(0.0232549\pi\) | ||||
−0.997332 | + | 0.0729924i | \(0.976745\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.67082e7 | 1.39077 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.25670e6 | −0.599614 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.98935e7i | − 1.63177i | −0.578214 | − | 0.815885i | \(-0.696250\pi\) | ||||
0.578214 | − | 0.815885i | \(-0.303750\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.71595e6i | 0.704568i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.61880e6 | −0.771921 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.01519e7 | 1.60554 | 0.802770 | − | 0.596289i | \(-0.203359\pi\) | ||||
0.802770 | + | 0.596289i | \(0.203359\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.16765e7i | − 0.923593i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.67009e7i | 1.30214i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.99765e6 | 0.309465 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.10766e6 | 0.623161 | 0.311581 | − | 0.950220i | \(-0.399142\pi\) | ||||
0.311581 | + | 0.950220i | \(0.399142\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1.42648e7i | − 1.08862i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 7.85311e6i | − 0.590872i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.35613e7 | 1.01317 | 0.506587 | − | 0.862189i | \(-0.330907\pi\) | ||||
0.506587 | + | 0.862189i | \(0.330907\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.63062e6 | −0.417717 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.82864e6i | 0.208379i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.29631e7i | 0.941695i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.28314e6 | −0.308987 | −0.154493 | − | 0.987994i | \(-0.549375\pi\) | ||||
−0.154493 | + | 0.987994i | \(0.549375\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.39748e7 | 1.00117 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 8.00974e6i | − 0.569866i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1.12084e7i | − 0.786515i | −0.919428 | − | 0.393258i | \(-0.871348\pi\) | ||||
0.919428 | − | 0.393258i | \(-0.128652\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.61141e6 | −0.251686 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.61552e6 | 0.596332 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.70549e6i | 0.323478i | 0.986834 | + | 0.161739i | \(0.0517102\pi\) | ||||
−0.986834 | + | 0.161739i | \(0.948290\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.55539e7i | 2.41112i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.31099e7 | 1.55663 | 0.778317 | − | 0.627872i | \(-0.216074\pi\) | ||||
0.778317 | + | 0.627872i | \(0.216074\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.24115e6 | −0.216847 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.75294e6i | 0.382312i | 0.981560 | + | 0.191156i | \(0.0612236\pi\) | ||||
−0.981560 | + | 0.191156i | \(0.938776\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.39481e6i | 0.288163i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.23214e7 | −1.45384 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.92424e7 | −1.24497 | −0.622485 | − | 0.782632i | \(-0.713877\pi\) | ||||
−0.622485 | + | 0.782632i | \(0.713877\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 2.95184e6i | − 0.189717i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 4.49210e6i | − 0.284911i | −0.989801 | − | 0.142456i | \(-0.954500\pi\) | ||||
0.989801 | − | 0.142456i | \(-0.0454999\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.11686e6 | 0.259395 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.33500e6 | 0.459133 | 0.229567 | − | 0.973293i | \(-0.426269\pi\) | ||||
0.229567 | + | 0.973293i | \(0.426269\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.57577e6i | 0.471102i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.01678e7i | 0.624076i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.85526e6 | 0.357051 | 0.178526 | − | 0.983935i | \(-0.442867\pi\) | ||||
0.178526 | + | 0.983935i | \(0.442867\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.23208e6 | −0.135230 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.34558e7i | 0.809952i | 0.914327 | + | 0.404976i | \(0.132720\pi\) | ||||
−0.914327 | + | 0.404976i | \(0.867280\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 9.30874e6i | − 0.553144i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.37764e7 | −1.40379 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.34084e7 | 1.95988 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.99252e7i | 1.16144i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.00706e7i | − 0.579587i | −0.957089 | − | 0.289794i | \(-0.906413\pi\) | ||||
0.957089 | − | 0.289794i | \(-0.0935867\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.49392e6 | 0.371377 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.64002e7 | 0.931985 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.23043e7i | 0.694820i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.18844e7i | 0.662723i | 0.943504 | + | 0.331362i | \(0.107508\pi\) | ||||
−0.943504 | + | 0.331362i | \(0.892492\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.11028e6 | 0.504853 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.62629e7 | 0.895604 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.64638e7i | − 0.901036i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.82571e6i | 0.152737i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.06053e7 | −0.569705 | −0.284852 | − | 0.958571i | \(-0.591945\pi\) | ||||
−0.284852 | + | 0.958571i | \(0.591945\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.38944e6 | −0.0741799 | −0.0370900 | − | 0.999312i | \(-0.511809\pi\) | ||||
−0.0370900 | + | 0.999312i | \(0.511809\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.37297e7i | 0.728510i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.22655e7i | 0.642882i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.91559e6 | 0.308169 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.12661e7 | −0.583334 | −0.291667 | − | 0.956520i | \(-0.594210\pi\) | ||||
−0.291667 | + | 0.956520i | \(0.594210\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 2.77093e7i | − 1.42602i | −0.701152 | − | 0.713011i | \(-0.747331\pi\) | ||||
0.701152 | − | 0.713011i | \(-0.252669\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1.23662e7i | − 0.628740i | −0.949300 | − | 0.314370i | \(-0.898207\pi\) | ||||
0.949300 | − | 0.314370i | \(-0.101793\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.23182e7 | −0.622530 | −0.311265 | − | 0.950323i | \(-0.600753\pi\) | ||||
−0.311265 | + | 0.950323i | \(0.600753\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.96706e6 | 0.0988130 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 4.78299e6i | − 0.238829i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.12083e7i | 0.553002i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.17277e7 | 0.575183 | 0.287592 | − | 0.957753i | \(-0.407145\pi\) | ||||
0.287592 | + | 0.957753i | \(0.407145\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.43225e7 | 0.698277 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.34095e7i | 0.649894i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.20066e7i | 1.05401i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.00705e7 | −0.479494 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.17945e6 | −0.434503 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.57059e7i | 0.739077i | 0.929215 | + | 0.369538i | \(0.120484\pi\) | ||||
−0.929215 | + | 0.369538i | \(0.879516\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 2.52390e7i | − 1.17387i | −0.809634 | − | 0.586935i | \(-0.800334\pi\) | ||||
0.809634 | − | 0.586935i | \(-0.199666\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.66248e6 | −0.169353 | −0.0846763 | − | 0.996409i | \(-0.526986\pi\) | ||||
−0.0846763 | + | 0.996409i | \(0.526986\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.55157e7 | −0.713286 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 4.17938e7i | − 1.91023i | −0.296243 | − | 0.955113i | \(-0.595734\pi\) | ||||
0.296243 | − | 0.955113i | \(-0.404266\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 4.43966e6i | − 0.200586i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.89994e7 | 0.853475 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.80124e7 | −0.804500 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 2.76924e7i | − 1.22977i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1.08990e7i | − 0.478505i | −0.970957 | − | 0.239253i | \(-0.923098\pi\) | ||||
0.970957 | − | 0.239253i | \(-0.0769024\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.75326e6 | 0.251155 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.04336e7 | −1.32103 | −0.660517 | − | 0.750811i | \(-0.729663\pi\) | ||||
−0.660517 | + | 0.750811i | \(0.729663\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.09028e6i | 0.262867i | 0.991325 | + | 0.131433i | \(0.0419579\pi\) | ||||
−0.991325 | + | 0.131433i | \(0.958042\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 2.77908e7i | − 1.18602i | −0.805195 | − | 0.593010i | \(-0.797940\pi\) | ||||
0.805195 | − | 0.593010i | \(-0.202060\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.63524e7 | −1.54269 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.95936e6 | −0.420278 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.29699e7i | 0.544262i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.08570e6i | 0.0865506i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.95946e7 | 0.808608 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.92336e7 | −1.19969 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.00410e6i | 0.326658i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 3.71510e7i | − 1.49952i | −0.661709 | − | 0.749761i | \(-0.730169\pi\) | ||||
0.661709 | − | 0.749761i | \(-0.269831\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.30158e7 | −0.522470 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.85959e6 | −0.313765 | −0.156882 | − | 0.987617i | \(-0.550144\pi\) | ||||
−0.156882 | + | 0.987617i | \(0.550144\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 1.48294e7i | − 0.588772i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.97333e7i | 1.16767i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.62693e7 | 0.635448 | 0.317724 | − | 0.948183i | \(-0.397081\pi\) | ||||
0.317724 | + | 0.948183i | \(0.397081\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.48810e7 | −0.578074 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.69255e7i | 0.653938i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 2.31619e7i | − 0.885268i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.69365e7 | 1.40416 | 0.702079 | − | 0.712099i | \(-0.252255\pi\) | ||||
0.702079 | + | 0.712099i | \(0.252255\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.80933e6 | 0.257472 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 2.22707e6i | − 0.0837587i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 4.89705e6i | − 0.182216i | −0.995841 | − | 0.0911078i | \(-0.970959\pi\) | ||||
0.995841 | − | 0.0911078i | \(-0.0290408\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.79346e6 | −0.140401 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.83943e6 | −0.251794 | −0.125897 | − | 0.992043i | \(-0.540181\pi\) | ||||
−0.125897 | + | 0.992043i | \(0.540181\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.53002e7i | 0.560297i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.03790e7i | − 0.376082i | −0.982161 | − | 0.188041i | \(-0.939786\pi\) | ||||
0.982161 | − | 0.188041i | \(-0.0602137\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.34095e6 | 0.300642 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.46990e7 | 0.527032 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.59587e7i | 0.925873i | 0.886391 | + | 0.462937i | \(0.153204\pi\) | ||||
−0.886391 | + | 0.462937i | \(0.846796\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 2.85185e7i | − 1.00658i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.46782e7 | −0.866497 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.76068e7 | −0.614994 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.69957e7i | 1.28554i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.92120e7i | 1.34851i | 0.738501 | + | 0.674253i | \(0.235534\pi\) | ||||
−0.738501 | + | 0.674253i | \(0.764466\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.85056e6 | −0.337017 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.06876e7 | −0.363774 | −0.181887 | − | 0.983319i | \(-0.558221\pi\) | ||||
−0.181887 | + | 0.983319i | \(0.558221\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2.42227e7i | − 0.820238i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 2.77266e7i | − 0.929308i | −0.885492 | − | 0.464654i | \(-0.846179\pi\) | ||||
0.885492 | − | 0.464654i | \(-0.153821\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.48758e7 | −1.82989 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.25561e7 | 0.416566 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 9.49272e6i | − 0.313334i | −0.987652 | − | 0.156667i | \(-0.949925\pi\) | ||||
0.987652 | − | 0.156667i | \(-0.0500749\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.46374e6i | 0.276547i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.89293e6 | 0.256595 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.03243e7 | −0.657403 | −0.328702 | − | 0.944434i | \(-0.606611\pi\) | ||||
−0.328702 | + | 0.944434i | \(0.606611\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 2.39794e7i | − 0.771730i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 4.70508e7i | − 1.49909i | −0.661951 | − | 0.749547i | \(-0.730271\pi\) | ||||
0.661951 | − | 0.749547i | \(-0.269729\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.63730e7 | −1.15310 |
(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 | 200.6.c.c.49.1 | 2 | ||
4.3 | odd | 2 | 400.6.c.h.49.2 | 2 | |||
5.2 | odd | 4 | 40.6.a.b.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 200.6.a.c.1.1 | 1 | |||
5.4 | even | 2 | inner | 200.6.c.c.49.2 | 2 | ||
15.2 | even | 4 | 360.6.a.b.1.1 | 1 | |||
20.3 | even | 4 | 400.6.a.f.1.1 | 1 | |||
20.7 | even | 4 | 80.6.a.f.1.1 | 1 | |||
20.19 | odd | 2 | 400.6.c.h.49.1 | 2 | |||
40.27 | even | 4 | 320.6.a.e.1.1 | 1 | |||
40.37 | odd | 4 | 320.6.a.l.1.1 | 1 | |||
60.47 | odd | 4 | 720.6.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.a.b.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
80.6.a.f.1.1 | 1 | 20.7 | even | 4 | |||
200.6.a.c.1.1 | 1 | 5.3 | odd | 4 | |||
200.6.c.c.49.1 | 2 | 1.1 | even | 1 | trivial | ||
200.6.c.c.49.2 | 2 | 5.4 | even | 2 | inner | ||
320.6.a.e.1.1 | 1 | 40.27 | even | 4 | |||
320.6.a.l.1.1 | 1 | 40.37 | odd | 4 | |||
360.6.a.b.1.1 | 1 | 15.2 | even | 4 | |||
400.6.a.f.1.1 | 1 | 20.3 | even | 4 | |||
400.6.c.h.49.1 | 2 | 20.19 | odd | 2 | |||
400.6.c.h.49.2 | 2 | 4.3 | odd | 2 | |||
720.6.a.h.1.1 | 1 | 60.47 | odd | 4 |