Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,9,Mod(319,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.319");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(156.433386263\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 4826x^{6} + 8748877x^{4} + 7060845096x^{2} + 2140819627716 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{11} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.8 | ||
Root | \(-1.73205 + 33.5532i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.319 |
Dual form | 384.9.b.b.319.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 46.7654 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1205.32i | 1.92851i | 0.264973 | + | 0.964256i | \(0.414637\pi\) | ||||
−0.264973 | + | 0.964256i | \(0.585363\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1133.44i | − 0.472069i | −0.971745 | − | 0.236034i | \(-0.924152\pi\) | ||||
0.971745 | − | 0.236034i | \(-0.0758478\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2187.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 20623.5 | 1.40861 | 0.704306 | − | 0.709897i | \(-0.251259\pi\) | ||||
0.704306 | + | 0.709897i | \(0.251259\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 25759.2i | 0.901901i | 0.892549 | + | 0.450950i | \(0.148915\pi\) | ||||
−0.892549 | + | 0.450950i | \(0.851085\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 56367.2i | 1.11343i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2473.09 | 0.0296104 | 0.0148052 | − | 0.999890i | \(-0.495287\pi\) | ||||
0.0148052 | + | 0.999890i | \(0.495287\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −206001. | −1.58072 | −0.790361 | − | 0.612642i | \(-0.790107\pi\) | ||||
−0.790361 | + | 0.612642i | \(0.790107\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 53005.6i | − 0.272549i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 223202.i | 0.797603i | 0.917037 | + | 0.398802i | \(0.130574\pi\) | ||||
−0.917037 | + | 0.398802i | \(0.869426\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.06217e6 | −2.71916 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 102276. | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 202690.i | − 0.286577i | −0.989681 | − | 0.143288i | \(-0.954232\pi\) | ||||
0.989681 | − | 0.143288i | \(-0.0457676\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.16928e6i | 1.26611i | 0.774106 | + | 0.633056i | \(0.218200\pi\) | ||||
−0.774106 | + | 0.633056i | \(0.781800\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 964465. | 0.813262 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.36615e6 | 0.910390 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.62267e6i | − 1.39939i | −0.714444 | − | 0.699693i | \(-0.753320\pi\) | ||||
0.714444 | − | 0.699693i | \(-0.246680\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.20464e6i | 0.520713i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.46741e6 | 0.519298 | 0.259649 | − | 0.965703i | \(-0.416393\pi\) | ||||
0.259649 | + | 0.965703i | \(0.416393\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00580e6 | −1.46420 | −0.732099 | − | 0.681198i | \(-0.761459\pi\) | ||||
−0.732099 | + | 0.681198i | \(0.761459\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.63603e6i | 0.642837i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.93618e6i | 1.42144i | 0.703474 | + | 0.710721i | \(0.251631\pi\) | ||||
−0.703474 | + | 0.710721i | \(0.748369\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.48012e6 | 0.777151 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 115655. | 0.0170956 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.16384e6i | 0.147500i | 0.997277 | + | 0.0737498i | \(0.0234966\pi\) | ||||
−0.997277 | + | 0.0737498i | \(0.976503\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.48579e7i | 2.71652i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.63372e6 | −0.912630 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.03352e7 | 1.67819 | 0.839095 | − | 0.543986i | \(-0.183085\pi\) | ||||
0.839095 | + | 0.543986i | \(0.183085\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.06867e6i | 0.221631i | 0.993841 | + | 0.110816i | \(0.0353463\pi\) | ||||
−0.993841 | + | 0.110816i | \(0.964654\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 2.47883e6i | − 0.157356i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.10481e7 | −1.73933 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.74270e6 | −0.185731 | −0.0928657 | − | 0.995679i | \(-0.529603\pi\) | ||||
−0.0928657 | + | 0.995679i | \(0.529603\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.04381e7i | 0.460496i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.03025e7i | 1.19246i | 0.802812 | + | 0.596232i | \(0.203336\pi\) | ||||
−0.802812 | + | 0.596232i | \(0.796664\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.81452e7 | −0.638954 | −0.319477 | − | 0.947594i | \(-0.603507\pi\) | ||||
−0.319477 | + | 0.947594i | \(0.603507\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.96728e7 | −1.56991 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.33754e7i | − 0.664961i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 6.18230e7i | − 1.58724i | −0.608416 | − | 0.793618i | \(-0.708195\pi\) | ||||
0.608416 | − | 0.793618i | \(-0.291805\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.78297e6 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.39301e6 | −0.176850 | −0.0884250 | − | 0.996083i | \(-0.528183\pi\) | ||||
−0.0884250 | + | 0.996083i | \(0.528183\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.98087e6i | 0.0571040i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 9.47888e6i | − 0.165455i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.73301e7 | 0.276212 | 0.138106 | − | 0.990417i | \(-0.455899\pi\) | ||||
0.138106 | + | 0.990417i | \(0.455899\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.91964e7 | 0.425759 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.46819e7i | 0.730991i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 2.48297e8i | − 3.04844i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.34674e8 | −1.52124 | −0.760620 | − | 0.649197i | \(-0.775105\pi\) | ||||
−0.760620 | + | 0.649197i | \(0.775105\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.51035e7 | 0.469537 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.35048e8i | − 1.29778i | −0.760882 | − | 0.648890i | \(-0.775233\pi\) | ||||
0.760882 | − | 0.648890i | \(-0.224767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.71582e7i | 0.596692i | 0.954458 | + | 0.298346i | \(0.0964349\pi\) | ||||
−0.954458 | + | 0.298346i | \(0.903565\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.38887e7 | 0.525614 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.14494e7 | −0.545084 | −0.272542 | − | 0.962144i | \(-0.587864\pi\) | ||||
−0.272542 | + | 0.962144i | \(0.587864\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.49238e8i | 1.76566i | 0.469690 | + | 0.882831i | \(0.344366\pi\) | ||||
−0.469690 | + | 0.882831i | \(0.655634\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 1.22650e8i | − 0.807936i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.58091e7 | 0.158292 | 0.0791460 | − | 0.996863i | \(-0.474781\pi\) | ||||
0.0791460 | + | 0.996863i | \(0.474781\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.69030e8 | −1.53819 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.63353e7i | 0.300634i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 2.80309e6i | − 0.0139782i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.10969e8 | 0.984185 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.86240e7 | 0.299817 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 8.09428e8i | − 3.31542i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1.05318e8i | − 0.404844i | −0.979298 | − | 0.202422i | \(-0.935119\pi\) | ||||
0.979298 | − | 0.202422i | \(-0.0648812\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.34098e8 | −0.845356 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.28724e8 | −0.437093 | −0.218547 | − | 0.975826i | \(-0.570132\pi\) | ||||
−0.218547 | + | 0.975826i | \(0.570132\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.33489e8i | 0.746209i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.23275e8i | 0.371142i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.20872e8 | −0.910855 | −0.455428 | − | 0.890273i | \(-0.650514\pi\) | ||||
−0.455428 | + | 0.890273i | \(0.650514\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.98209e8 | 0.530964 | 0.265482 | − | 0.964116i | \(-0.414469\pi\) | ||||
0.265482 | + | 0.964116i | \(0.414469\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.24373e8i | 0.820670i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.31244e8i | 1.27043i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.44306e8 | 0.552666 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.09515e8 | 0.448688 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 2.17324e8i | − 0.440922i | −0.975396 | − | 0.220461i | \(-0.929244\pi\) | ||||
0.975396 | − | 0.220461i | \(-0.0707562\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.92507e8i | 0.947338i | 0.880703 | + | 0.473669i | \(0.157071\pi\) | ||||
−0.880703 | + | 0.473669i | \(0.842929\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.40865e6 | 0.00987014 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.40936e9 | −2.44171 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.14935e8i | 1.17671i | 0.808604 | + | 0.588353i | \(0.200223\pi\) | ||||
−0.808604 | + | 0.588353i | \(0.799777\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.44276e7i | 0.0851590i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.52985e8 | 0.376523 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.75590e8 | −1.24037 | −0.620184 | − | 0.784457i | \(-0.712942\pi\) | ||||
−0.620184 | + | 0.784457i | \(0.712942\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.16249e9i | 1.56839i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.17630e8i | 0.408372i | 0.978932 | + | 0.204186i | \(0.0654548\pi\) | ||||
−0.978932 | + | 0.204186i | \(0.934545\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.52195e8 | 0.186575 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.50525e8 | −0.526907 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.05364e9i | − 1.17627i | −0.808762 | − | 0.588136i | \(-0.799862\pi\) | ||||
0.808762 | − | 0.588136i | \(-0.200138\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.20390e9i | 1.28363i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.50984e8 | 0.968903 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.57916e8 | −0.543446 | −0.271723 | − | 0.962375i | \(-0.587594\pi\) | ||||
−0.271723 | + | 0.962375i | \(0.587594\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 6.12888e8i | − 0.571041i | −0.958373 | − | 0.285520i | \(-0.907834\pi\) | ||||
0.958373 | − | 0.285520i | \(-0.0921664\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.43508e8i | 0.127959i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.16116e9 | 2.69873 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.10038e7 | 0.0417096 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1.15923e8i | − 0.0908496i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.36504e9i | 1.02568i | 0.858485 | + | 0.512839i | \(0.171406\pi\) | ||||
−0.858485 | + | 0.512839i | \(0.828594\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.89607e8 | −0.569091 | −0.284546 | − | 0.958663i | \(-0.591843\pi\) | ||||
−0.284546 | + | 0.958663i | \(0.591843\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.45197e9 | −1.00420 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.90708e9i | − 1.26620i | −0.774068 | − | 0.633102i | \(-0.781781\pi\) | ||||
0.774068 | − | 0.633102i | \(-0.218219\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 2.00160e9i | − 1.27634i | −0.769896 | − | 0.638170i | \(-0.779692\pi\) | ||||
0.769896 | − | 0.638170i | \(-0.220308\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.75029e8 | −0.107232 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.29736e8 | −0.135284 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.76870e9i | 1.00147i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.88143e8i | 0.265868i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.24846e9 | −2.22662 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.30961e9 | −1.66973 | −0.834867 | − | 0.550451i | \(-0.814456\pi\) | ||||
−0.834867 | + | 0.550451i | \(0.814456\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.41711e9i | 0.688470i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 6.03360e9i | − 2.82372i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.32531e9 | 0.597692 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.48565e8 | −0.368900 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.37048e7i | 0.0267057i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2.94041e9i | − 1.18902i | −0.804089 | − | 0.594510i | \(-0.797346\pi\) | ||||
0.804089 | − | 0.594510i | \(-0.202654\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.32297e9 | −0.906386 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.84361e9 | −0.694331 | −0.347165 | − | 0.937804i | \(-0.612856\pi\) | ||||
−0.347165 | + | 0.937804i | \(0.612856\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 3.87979e9i | − 1.41080i | −0.708808 | − | 0.705402i | \(-0.750767\pi\) | ||||
0.708808 | − | 0.705402i | \(-0.249233\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 1.09316e9i | − 0.383915i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.75956e9 | −1.27560 | −0.637799 | − | 0.770203i | \(-0.720155\pi\) | ||||
−0.637799 | + | 0.770203i | \(0.720155\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.36032e9 | −2.74127 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 2.89118e9i | − 0.916392i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.01650e9i | 0.311541i | 0.987793 | + | 0.155770i | \(0.0497860\pi\) | ||||
−0.987793 | + | 0.155770i | \(0.950214\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.04339e9 | 0.605735 | 0.302868 | − | 0.953033i | \(-0.402056\pi\) | ||||
0.302868 | + | 0.953033i | \(0.402056\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.23677e8 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.39998e9i | 1.49875i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 5.30642e9i | − 1.42565i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.92502e8 | −0.102104 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.92562e9 | 0.737093 | 0.368547 | − | 0.929609i | \(-0.379855\pi\) | ||||
0.368547 | + | 0.929609i | \(0.379855\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.60320e9i | 1.12351i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.39401e8i | 0.0329690i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.47836e9 | 1.94348 | 0.971739 | − | 0.236059i | \(-0.0758559\pi\) | ||||
0.971739 | + | 0.236059i | \(0.0758559\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.97264e9 | −0.660606 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 4.43283e8i | − 0.0955255i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.09637e9i | 1.48325i | 0.670817 | + | 0.741623i | \(0.265944\pi\) | ||||
−0.670817 | + | 0.741623i | \(0.734056\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.40280e9 | −0.284455 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.10450e8 | 0.159471 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.19620e8i | 0.137434i | 0.997636 | + | 0.0687170i | \(0.0218906\pi\) | ||||
−0.997636 | + | 0.0687170i | \(0.978109\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.70234e9i | 0.501029i | 0.968113 | + | 0.250514i | \(0.0805997\pi\) | ||||
−0.968113 | + | 0.250514i | \(0.919400\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.36538e9 | 0.245812 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.19057e10 | −3.83024 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 6.00431e9i | − 1.01987i | −0.860213 | − | 0.509934i | \(-0.829670\pi\) | ||||
0.860213 | − | 0.509934i | \(-0.170330\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.55722e9i | 0.422038i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.33314e9 | −1.33654 | −0.668272 | − | 0.743917i | \(-0.732966\pi\) | ||||
−0.668272 | + | 0.743917i | \(0.732966\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.01898e9 | −0.314765 | −0.157382 | − | 0.987538i | \(-0.550306\pi\) | ||||
−0.157382 | + | 0.987538i | \(0.550306\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 1.16117e10i | − 1.76002i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1.66322e9i | − 0.245144i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.96964e9 | −0.999123 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.29810e9 | −0.878289 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.22776e10i | 1.66588i | 0.553362 | + | 0.832941i | \(0.313345\pi\) | ||||
−0.553362 | + | 0.832941i | \(0.686655\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.45104e10i | 3.23641i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.10928e9 | 0.271087 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.74950e9 | −0.719359 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.67376e9i | 0.691202i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 6.31555e9i | − 0.749274i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.69873e9 | −0.427418 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.15941e9 | 0.468251 | 0.234125 | − | 0.972206i | \(-0.424777\pi\) | ||||
0.234125 | + | 0.972206i | \(0.424777\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.14068e9i | 0.344500i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.21765e9i | 0.343951i | 0.985101 | + | 0.171976i | \(0.0550151\pi\) | ||||
−0.985101 | + | 0.171976i | \(0.944985\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.39012e9 | −0.561592 | −0.280796 | − | 0.959767i | \(-0.590598\pi\) | ||||
−0.280796 | + | 0.959767i | \(0.590598\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.98778e9 | 0.303463 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.15002e10i | 1.13886i | 0.822041 | + | 0.569428i | \(0.192835\pi\) | ||||
−0.822041 | + | 0.569428i | \(0.807165\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 4.18018e9i | − 0.403675i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.34136e9 | −0.314704 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.09460e8 | −0.0468058 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 2.73607e10i | − 2.45241i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.16557e10i | 1.01941i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.86172e9 | 0.671018 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.39319e9 | 0.532606 | 0.266303 | − | 0.963889i | \(-0.414198\pi\) | ||||
0.266303 | + | 0.963889i | \(0.414198\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 5.73579e9i | − 0.466462i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 4.51115e9i | − 0.358185i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.36857e10 | 1.83640 | 0.918198 | − | 0.396122i | \(-0.129644\pi\) | ||||
0.918198 | + | 0.396122i | \(0.129644\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.20697e9 | 0.0913899 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.41147e10i | 1.78346i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.16120e10i | − 0.838937i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.25813e10 | −0.888073 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.00975e10 | −1.38619 | −0.693096 | − | 0.720845i | \(-0.743754\pi\) | ||||
−0.693096 | + | 0.720845i | \(0.743754\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 1.88548e9i | − 0.127093i | −0.997979 | − | 0.0635464i | \(-0.979759\pi\) | ||||
0.997979 | − | 0.0635464i | \(-0.0202411\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.63454e9i | 0.173571i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.45724e10 | −0.938496 | −0.469248 | − | 0.883066i | \(-0.655475\pi\) | ||||
−0.469248 | + | 0.883066i | \(0.655475\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.65242e10 | −2.29968 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 1.31088e8i | − 0.00807029i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.57991e10i | 0.951163i | 0.879672 | + | 0.475581i | \(0.157762\pi\) | ||||
−0.879672 | + | 0.475581i | \(0.842238\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.54529e10 | 1.49868 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.86604e9 | 0.568220 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 2.18707e10i | − 1.23223i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 3.24057e9i | − 0.178631i | −0.996003 | − | 0.0893156i | \(-0.971532\pi\) | ||||
0.996003 | − | 0.0893156i | \(-0.0284680\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.20923e9 | 0.173099 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.31914e9 | 0.0696300 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 2.27941e10i | − 1.17757i | −0.808288 | − | 0.588787i | \(-0.799606\pi\) | ||||
0.808288 | − | 0.588787i | \(-0.200394\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 3.78532e10i | − 1.91416i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.22113e9 | 0.258464 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.83101e10 | 1.37210 | 0.686049 | − | 0.727556i | \(-0.259344\pi\) | ||||
0.686049 | + | 0.727556i | \(0.259344\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 4.92523e9i | − 0.233737i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 3.54736e10i | − 1.64858i | −0.566169 | − | 0.824289i | \(-0.691575\pi\) | ||||
0.566169 | − | 0.824289i | \(-0.308425\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.81748e10 | 1.28239 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.09477e10 | −0.488066 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.40513e10i | 0.613646i | 0.951767 | + | 0.306823i | \(0.0992659\pi\) | ||||
−0.951767 | + | 0.306823i | \(0.900734\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.51999e8i | 0.0236174i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.01982e9 | −0.252356 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.45165e10 | 3.06100 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.82104e10i | 1.53822i | 0.639115 | + | 0.769111i | \(0.279301\pi\) | ||||
−0.639115 | + | 0.769111i | \(0.720699\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.09192e10i | 0.430824i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.13716e10 | 0.826530 | 0.413265 | − | 0.910611i | \(-0.364388\pi\) | ||||
0.413265 | + | 0.910611i | \(0.364388\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.01197e10 | −1.14191 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.76501e9i | 0.214279i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 5.40887e10i | − 1.97119i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.90485e10 | −0.680717 | −0.340359 | − | 0.940296i | \(-0.610548\pi\) | ||||
−0.340359 | + | 0.940296i | \(0.610548\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.50057e10 | −0.525882 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2.30487e10i | − 0.792220i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 1.01163e10i | − 0.341057i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.26933e9 | 0.306552 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.04260e9 | 0.0987163 | 0.0493582 | − | 0.998781i | \(-0.484282\pi\) | ||||
0.0493582 | + | 0.998781i | \(0.484282\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.68586e10i | 1.17330i | 0.809839 | + | 0.586652i | \(0.199554\pi\) | ||||
−0.809839 | + | 0.586652i | \(0.800446\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.51694e10i | 0.473814i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.62685e9 | −0.0805154 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.47814e9 | 0.104625 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.48438e10i | 0.733482i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.30543e10i | 1.53749i | 0.639557 | + | 0.768744i | \(0.279118\pi\) | ||||
−0.639557 | + | 0.768744i | \(0.720882\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.82756e10 | −0.804379 | −0.402190 | − | 0.915556i | \(-0.631751\pi\) | ||||
−0.402190 | + | 0.915556i | \(0.631751\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.14251e10 | 0.319082 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 4.59799e10i | − 1.26079i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 6.30601e10i | − 1.69784i | −0.528522 | − | 0.848920i | \(-0.677254\pi\) | ||||
0.528522 | − | 0.848920i | \(-0.322746\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.79803e9 | 0.259050 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.71295e10 | 0.964060 | 0.482030 | − | 0.876155i | \(-0.339900\pi\) | ||||
0.482030 | + | 0.876155i | \(0.339900\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.08883e10i | 0.532677i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 1.01632e10i | − 0.254566i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.04464e10 | −0.749118 | −0.374559 | − | 0.927203i | \(-0.622206\pi\) | ||||
−0.374559 | + | 0.927203i | \(0.622206\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.02631e10 | 0.731488 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.30323e10i | 0.546946i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.51910e10i | 0.821081i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.91731e10 | 0.668832 | 0.334416 | − | 0.942425i | \(-0.391461\pi\) | ||||
0.334416 | + | 0.942425i | \(0.391461\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.52938e8 | 0.00569853 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 2.33681e10i | − 0.517392i | −0.965959 | − | 0.258696i | \(-0.916707\pi\) | ||||
0.965959 | − | 0.258696i | \(-0.0832929\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.43080e10i | 1.83461i | 0.398181 | + | 0.917307i | \(0.369642\pi\) | ||||
−0.398181 | + | 0.917307i | \(0.630358\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.59092e10 | −1.40972 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.98604e9 | −0.167905 | −0.0839526 | − | 0.996470i | \(-0.526754\pi\) | ||||
−0.0839526 | + | 0.996470i | \(0.526754\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.24211e9i | 0.0876780i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.34342e10i | 0.679371i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.03237e11 | −2.06249 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.18808e11 | 4.29823 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.54533e9i | 0.0491666i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.14200e10i | 0.976765i | 0.872630 | + | 0.488382i | \(0.162413\pi\) | ||||
−0.872630 | + | 0.488382i | \(0.837587\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.75580e10 | 1.26211 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.18310e10 | 0.217386 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 1.62326e11i | − 2.93373i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.06516e10i | 1.07827i | 0.842220 | + | 0.539134i | \(0.181248\pi\) | ||||
−0.842220 | + | 0.539134i | \(0.818752\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.09473e10 | −0.716126 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.27344e10 | 1.25145 | 0.625726 | − | 0.780043i | \(-0.284803\pi\) | ||||
0.625726 | + | 0.780043i | \(0.284803\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 5.01271e8i | − 0.00848565i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.43642e10i | 0.905508i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.43460e10 | 0.562925 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.93007e10 | −0.956439 | −0.478220 | − | 0.878240i | \(-0.658718\pi\) | ||||
−0.478220 | + | 0.878240i | \(0.658718\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.48541e10i | 0.235774i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.07478e10i | 0.167899i | 0.996470 | + | 0.0839495i | \(0.0267535\pi\) | ||||
−0.996470 | + | 0.0839495i | \(0.973247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.62776e11 | 2.50279 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.11746e9 | 0.107719 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.30363e9i | 0.0194215i | 0.999953 | + | 0.00971074i | \(0.00309107\pi\) | ||||
−0.999953 | + | 0.00971074i | \(0.996909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.05664e10i | 0.301630i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.10690e10 | −0.304210 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.09471e10 | −1.15073 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.43048e11i | 2.00226i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 4.92739e10i | − 0.679121i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.82717e10 | 0.519429 | 0.259715 | − | 0.965685i | \(-0.416371\pi\) | ||||
0.259715 | + | 0.965685i | \(0.416371\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.70009e10 | 0.227229 | 0.113615 | − | 0.993525i | \(-0.463757\pi\) | ||||
0.113615 | + | 0.993525i | \(0.463757\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.63010e10i | 0.741104i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.89174e9i | 0.0374901i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.84918e10 | 0.363829 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.44731e10 | 0.559396 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.77993e10i | 0.468355i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 8.61193e10i | − 1.05120i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.60911e10 | −0.313759 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.23957e10 | 1.09470 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 1.28391e11i | − 1.49881i | −0.662111 | − | 0.749406i | \(-0.730339\pi\) | ||||
0.662111 | − | 0.749406i | \(-0.269661\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 2.86619e10i | − 0.329690i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.00411e11 | −3.40510 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.72133e10 | 0.974167 | 0.487083 | − | 0.873356i | \(-0.338061\pi\) | ||||
0.487083 | + | 0.873356i | \(0.338061\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.71118e9i | 0.0738771i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.17544e10i | 0.452998i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.00725e10 | −0.749285 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.47833e11 | 1.55811 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 3.76332e10i | − 0.390977i | −0.980706 | − | 0.195488i | \(-0.937371\pi\) | ||||
0.980706 | − | 0.195488i | \(-0.0626292\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 1.28945e11i | − 1.32056i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.38521e9 | 0.0240810 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.92375e10 | 0.788674 | 0.394337 | − | 0.918966i | \(-0.370974\pi\) | ||||
0.394337 | + | 0.918966i | \(0.370974\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.11082e10i | 0.305268i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 5.42119e9i | − 0.0524521i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.50563e11 | 1.43638 | 0.718191 | − | 0.695846i | \(-0.244970\pi\) | ||||
0.718191 | + | 0.695846i | \(0.244970\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.89532e10 | −0.366437 | −0.183218 | − | 0.983072i | \(-0.558652\pi\) | ||||
−0.183218 | + | 0.983072i | \(0.558652\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.38365e10i | 0.592176i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 2.37079e11i | − 2.16881i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.76797e10 | −0.700817 | −0.350408 | − | 0.936597i | \(-0.613957\pi\) | ||||
−0.350408 | + | 0.936597i | \(0.613957\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.69263e10 | −0.328565 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.51294e9i | 0.0834854i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.40025e10i | 0.207770i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.79021e10 | −0.579775 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.18050e11 | 0.994293 | 0.497146 | − | 0.867667i | \(-0.334381\pi\) | ||||
0.497146 | + | 0.867667i | \(0.334381\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 2.40873e11i | − 2.00137i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 8.91853e10i | − 0.731044i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.28434e10 | −0.103863 | −0.0519317 | − | 0.998651i | \(-0.516538\pi\) | ||||
−0.0519317 | + | 0.998651i | \(0.516538\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.37862e9 | 0.0269570 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 9.36058e10i | − 0.736895i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 4.09653e10i | − 0.318206i | −0.987262 | − | 0.159103i | \(-0.949140\pi\) | ||||
0.987262 | − | 0.159103i | \(-0.0508602\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.68532e10 | 0.665714 | 0.332857 | − | 0.942977i | \(-0.391987\pi\) | ||||
0.332857 | + | 0.942977i | \(0.391987\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.18527e9 | −0.0619105 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.54285e11i | 1.89801i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 1.20813e11i | − 0.889934i | −0.895547 | − | 0.444967i | \(-0.853215\pi\) | ||||
0.895547 | − | 0.444967i | \(-0.146785\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.07437e10 | −0.0781061 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.78670e11 | −1.28200 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.16441e11i | 0.824636i | 0.911040 | + | 0.412318i | \(0.135281\pi\) | ||||
−0.911040 | + | 0.412318i | \(0.864719\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.27139e10i | 0.578200i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.81037e10 | −0.331923 | −0.165962 | − | 0.986132i | \(-0.553073\pi\) | ||||
−0.165962 | + | 0.986132i | \(0.553073\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.05490e11 | 1.39968 | 0.699838 | − | 0.714301i | \(-0.253255\pi\) | ||||
0.699838 | + | 0.714301i | \(0.253255\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.28282e10i | 0.153499i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1.96426e10i | − 0.130391i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.60709e11 | 3.67466 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.98681e11 | −1.28554 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 6.48612e9i | − 0.0414364i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.45214e11i | 1.54678i | 0.633932 | + | 0.773389i | \(0.281440\pi\) | ||||
−0.633932 | + | 0.773389i | \(0.718560\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.54775e11 | −0.964022 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.26942e11 | 0.780746 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.15404e11i | 0.700913i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.62716e10i | 0.397488i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.07017e10 | 0.359558 | 0.179779 | − | 0.983707i | \(-0.442462\pi\) | ||||
0.179779 | + | 0.983707i | \(0.442462\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.52262e10 | −0.440074 | −0.220037 | − | 0.975492i | \(-0.570618\pi\) | ||||
−0.220037 | + | 0.975492i | \(0.570618\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 2.82163e11i | − 1.63028i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 3.65466e10i | − 0.208559i | −0.994548 | − | 0.104280i | \(-0.966746\pi\) | ||||
0.994548 | − | 0.104280i | \(-0.0332537\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.19383e11 | 2.36392 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.19785e10 | 0.345078 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.44063e11i | 1.34230i | 0.741322 | + | 0.671150i | \(0.234199\pi\) | ||||
−0.741322 | + | 0.671150i | \(0.765801\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 1.55154e11i | − 0.842940i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.96835e10 | −0.212985 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.68123e11 | 0.891427 | 0.445714 | − | 0.895176i | \(-0.352950\pi\) | ||||
0.445714 | + | 0.895176i | \(0.352950\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 5.28700e10i | − 0.276951i | −0.990366 | − | 0.138476i | \(-0.955780\pi\) | ||||
0.990366 | − | 0.138476i | \(-0.0442203\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.97918e9i | 0.0154185i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.81429e11 | −1.43907 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.52409e10 | 0.228574 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 1.37509e11i | − 0.686480i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.32866e10i | 0.312192i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.17550e11 | 1.06047 | 0.530237 | − | 0.847850i | \(-0.322103\pi\) | ||||
0.530237 | + | 0.847850i | \(0.322103\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.08634e11 | −0.523302 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.10635e11i | 0.526668i | 0.964705 | + | 0.263334i | \(0.0848222\pi\) | ||||
−0.964705 | + | 0.263334i | \(0.915178\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.52645e11i | 0.718130i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.62172e10 | −0.400872 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.80246e10 | −0.450456 | −0.225228 | − | 0.974306i | \(-0.572313\pi\) | ||||
−0.225228 | + | 0.974306i | \(0.572313\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 3.86753e11i | − 1.75659i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 1.81440e11i | − 0.814528i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.99797e10 | −0.133030 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.42053e11 | −1.06169 | −0.530846 | − | 0.847468i | \(-0.678126\pi\) | ||||
−0.530846 | + | 0.847468i | \(0.678126\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 5.11220e10i | − 0.221654i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.38906e11i | 1.02397i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.62904e9 | 0.0153766 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.75817e11 | −0.736467 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.51496e10i | 0.269798i | 0.990859 | + | 0.134899i | \(0.0430711\pi\) | ||||
−0.990859 | + | 0.134899i | \(0.956929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.40274e11i | 2.21204i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.90973e11 | −1.58267 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.53068e11 | −0.612641 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.77744e11i | 0.703412i | 0.936111 | + | 0.351706i | \(0.114398\pi\) | ||||
−0.936111 | + | 0.351706i | \(0.885602\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 1.35207e11i | − 0.529079i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.60986e11 | −1.00986 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.40319e11 | −2.45003 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.75369e10i | 0.179868i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.48867e11i | 1.67958i | 0.542908 | + | 0.839792i | \(0.317323\pi\) | ||||
−0.542908 | + | 0.839792i | \(0.682677\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.61196e10 | 0.281680 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.55598e10 | 0.349721 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.15292e11i | 0.779247i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.46455e11i | 0.524284i | 0.965029 | + | 0.262142i | \(0.0844289\pi\) | ||||
−0.965029 | + | 0.262142i | \(0.915571\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.04604e10 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.23798e10 | −0.0433555 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.76979e11i | − 0.613063i | −0.951861 | − | 0.306531i | \(-0.900832\pi\) | ||||
0.951861 | − | 0.306531i | \(-0.0991684\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.52532e11i | 0.865301i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.71874e10 | −0.261623 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.79399e10 | −0.127209 | −0.0636046 | − | 0.997975i | \(-0.520260\pi\) | ||||
−0.0636046 | + | 0.997975i | \(0.520260\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 2.48157e11i | − 0.823102i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 4.78465e11i | − 1.56998i | −0.619507 | − | 0.784991i | \(-0.712667\pi\) | ||||
0.619507 | − | 0.784991i | \(-0.287333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.61944e11 | 0.850323 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.83555e10 | −0.0589500 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.09833e10i | 0.257317i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.44597e10i | 0.171205i | 0.996329 | + | 0.0856023i | \(0.0272814\pi\) | ||||
−0.996329 | + | 0.0856023i | \(0.972719\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.36818e11 | 0.425561 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.93629e11 | −1.82695 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 4.87219e11i | − 1.48368i | −0.670575 | − | 0.741841i | \(-0.733953\pi\) | ||||
0.670575 | − | 0.741841i | \(-0.266047\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.15270e11i | 0.648660i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.82246e11 | 0.841567 | 0.420783 | − | 0.907161i | \(-0.361755\pi\) | ||||
0.420783 | + | 0.907161i | \(0.361755\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.82495e11 | 0.833514 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.51916e9i | 0.0190347i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.23819e11i | 1.51356i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.56182e10 | −0.0446607 | −0.0223303 | − | 0.999751i | \(-0.507109\pi\) | ||||
−0.0223303 | + | 0.999751i | \(0.507109\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.96494e11 | 1.12207 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.70943e11i | 0.758856i | 0.925221 | + | 0.379428i | \(0.123879\pi\) | ||||
−0.925221 | + | 0.379428i | \(0.876121\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1.24198e12i | − 3.44276i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.39016e11 | −0.381401 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.02288e11 | −0.820865 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.24943e11i | 1.67972i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 2.07303e10i | − 0.0551517i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.61725e11 | −2.26929 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.02095e11 | −0.787488 | −0.393744 | − | 0.919220i | \(-0.628820\pi\) | ||||
−0.393744 | + | 0.919220i | \(0.628820\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.31864e11i | 0.856353i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 2.92530e10i | − 0.0747246i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.90465e10 | −0.199889 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.56026e10 | −0.164230 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 3.70077e11i | − 0.917189i | −0.888646 | − | 0.458595i | \(-0.848353\pi\) | ||||
0.888646 | − | 0.458595i | \(-0.151647\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.71538e10i | 0.0420895i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.79010e10 | 0.0920705 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.74216e11 | −0.900037 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.04928e11i | 0.726130i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.36533e10i | 0.0793476i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.12768e9 | −0.0189746 | −0.00948730 | − | 0.999955i | \(-0.503020\pi\) | ||||
−0.00948730 | + | 0.999955i | \(0.503020\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.82470e11 | −1.11529 | −0.557643 | − | 0.830081i | \(-0.688294\pi\) | ||||
−0.557643 | + | 0.830081i | \(0.688294\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.26376e11i | 0.289269i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1.05537e12i | − 2.39206i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.03120e12 | 2.31449 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.38525e10 | 0.141920 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 3.20753e10i | − 0.0705989i | −0.999377 | − | 0.0352995i | \(-0.988762\pi\) | ||||
0.999377 | − | 0.0352995i | \(-0.0112385\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.03986e10i | 0.197044i | 0.995135 | + | 0.0985218i | \(0.0314114\pi\) | ||||
−0.995135 | + | 0.0985218i | \(0.968589\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.02443e12 | −2.21139 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.40230e11 | −1.79629 | −0.898144 | − | 0.439701i | \(-0.855084\pi\) | ||||
−0.898144 | + | 0.439701i | \(0.855084\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1.29286e11i | − 0.273737i | −0.990589 | − | 0.136868i | \(-0.956296\pi\) | ||||
0.990589 | − | 0.136868i | \(-0.0437038\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 2.80794e11i | − 0.588821i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.10798e10 | 0.0230118 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.82846e11 | −0.787551 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.19589e11i | 0.243664i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 6.65798e11i | − 1.34368i | −0.740698 | − | 0.671838i | \(-0.765505\pi\) | ||||
0.740698 | − | 0.671838i | \(-0.234495\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.59163e11 | 0.917874 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.89702e11 | −0.771654 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.83444e11i | 0.359812i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 2.39120e11i | − 0.464603i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.44183e10 | −0.181730 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.85386e11 | 1.11615 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.81152e11i | − 0.531062i | −0.964102 | − | 0.265531i | \(-0.914453\pi\) | ||||
0.964102 | − | 0.265531i | \(-0.0855473\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 5.43026e11i | − 1.01615i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.53826e11 | −1.39749 | −0.698744 | − | 0.715372i | \(-0.746257\pi\) | ||||
−0.698744 | + | 0.715372i | \(0.746257\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.75148e11 | −0.321687 | −0.160843 | − | 0.986980i | \(-0.551421\pi\) | ||||
−0.160843 | + | 0.986980i | \(0.551421\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 7.77810e10i | − 0.141534i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 2.00425e11i | − 0.361334i | −0.983544 | − | 0.180667i | \(-0.942174\pi\) | ||||
0.983544 | − | 0.180667i | \(-0.0578257\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.26997e12 | 2.26845 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.25938e11 | −0.576844 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.27501e12i | − 2.23580i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 9.64088e10i | − 0.167511i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.94533e11 | −0.507080 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.17435e11 | −1.56510 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 3.29390e11i | − 0.556816i | −0.960463 | − | 0.278408i | \(-0.910193\pi\) | ||||
0.960463 | − | 0.278408i | \(-0.0898068\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.74168e11i | 0.961797i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.87218e11 | −1.47274 | −0.736371 | − | 0.676578i | \(-0.763462\pi\) | ||||
−0.736371 | + | 0.676578i | \(0.763462\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.69085e11 | 1.42962 | 0.714808 | − | 0.699321i | \(-0.246514\pi\) | ||||
0.714808 | + | 0.699321i | \(0.246514\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.14624e12i | 1.86854i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.19260e12i | 1.92663i | 0.268364 | + | 0.963317i | \(0.413517\pi\) | ||||
−0.268364 | + | 0.963317i | \(0.586483\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.19371e11 | −0.191114 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.86414e10 | 0.156512 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.42886e12i | − 2.24690i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 6.72467e11i | − 1.04804i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.68878e11 | −0.415322 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.37002e11 | 0.362838 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.87829e9i | 0.00436753i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.65336e11i | 0.399066i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.38726e11 | 1.10126 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.06869e11 | 0.748974 | 0.374487 | − | 0.927232i | \(-0.377819\pi\) | ||||
0.374487 | + | 0.927232i | \(0.377819\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 2.95349e11i | − 0.432594i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.36648e11i | 0.924327i | 0.886795 | + | 0.462164i | \(0.152927\pi\) | ||||
−0.886795 | + | 0.462164i | \(0.847073\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.73093e11 | −0.249113 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.72972e11 | −0.246770 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.45900e11i | 0.206338i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.02943e12i | 1.44322i | 0.692299 | + | 0.721611i | \(0.256598\pi\) | ||||
−0.692299 | + | 0.721611i | \(0.743402\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.94516e11 | 0.270345 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.80568e11 | −1.07548 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.78573e12i | 3.80515i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.46875e11i | 0.198897i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.00103e11 | −1.20845 | −0.604226 | − | 0.796813i | \(-0.706518\pi\) | ||||
−0.604226 | + | 0.796813i | \(0.706518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.22911e11 | −1.22846 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.50475e11i | 0.198580i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.14758e10i | 0.0804374i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.42921e11 | −0.185412 | −0.0927060 | − | 0.995694i | \(-0.529552\pi\) | ||||
−0.0927060 | + | 0.995694i | \(0.529552\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.52071e11 | −0.324235 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 2.35339e11i | − 0.300148i | −0.988675 | − | 0.150074i | \(-0.952049\pi\) | ||||
0.988675 | − | 0.150074i | \(-0.0479511\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.27529e11i | 0.414193i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.39725e11 | 0.175205 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.13889e11 | 0.887628 | 0.443814 | − | 0.896119i | \(-0.353625\pi\) | ||||
0.443814 | + | 0.896119i | \(0.353625\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 4.67405e11i | − 0.576273i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.37811e11i | 0.657518i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.16680e11 | 1.11134 | 0.555669 | − | 0.831403i | \(-0.312462\pi\) | ||||
0.555669 | + | 0.831403i | \(0.312462\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.64531e12 | −1.97803 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1.95487e11i | − 0.233062i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.63688e11i | 0.429986i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.14329e11 | −0.603042 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.56260e11 | −0.181695 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 9.51729e11i | − 1.09750i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.25148e12i | 1.43126i | 0.698480 | + | 0.715630i | \(0.253860\pi\) | ||||
−0.698480 | + | 0.715630i | \(0.746140\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.38251e10 | −0.0270234 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.49155e12 | 1.67788 | 0.838938 | − | 0.544227i | \(-0.183177\pi\) | ||||
0.838938 | + | 0.544227i | \(0.183177\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2.24658e11i | − 0.250651i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 1.27953e12i | − 1.41590i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.16356e12 | 1.27705 | 0.638527 | − | 0.769600i | \(-0.279544\pi\) | ||||
0.638527 | + | 0.769600i | \(0.279544\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.57408e11 | 0.389075 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.45083e11i | 0.588554i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.21391e12i | 1.30008i | 0.759898 | + | 0.650042i | \(0.225249\pi\) | ||||
−0.759898 | + | 0.650042i | \(0.774751\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.29864e12 | 2.44189 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.67656e11 | 0.387412 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1.11731e12i | − 1.16785i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.61795e10i | 0.0271436i | 0.999908 | + | 0.0135718i | \(0.00432017\pi\) | ||||
−0.999908 | + | 0.0135718i | \(0.995680\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.98980e11 | 0.307500 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.41257e12 | 2.46143 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.49208e12i | 1.51012i | 0.655653 | + | 0.755062i | \(0.272393\pi\) | ||||
−0.655653 | + | 0.755062i | \(0.727607\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 2.68236e11i | − 0.269312i |
(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 | 384.9.b.b.319.8 | yes | 8 | |
4.3 | odd | 2 | inner | 384.9.b.b.319.4 | yes | 8 | |
8.3 | odd | 2 | inner | 384.9.b.b.319.5 | yes | 8 | |
8.5 | even | 2 | inner | 384.9.b.b.319.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.9.b.b.319.1 | ✓ | 8 | 8.5 | even | 2 | inner | |
384.9.b.b.319.4 | yes | 8 | 4.3 | odd | 2 | inner | |
384.9.b.b.319.5 | yes | 8 | 8.3 | odd | 2 | inner | |
384.9.b.b.319.8 | yes | 8 | 1.1 | even | 1 | trivial |