Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,7,Mod(22,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.22");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.d (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: | \(15.8737317698\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.18 | ||
Character | \(\chi\) | \(=\) | 69.22 |
Dual form | 69.7.d.a.22.17 |
$q$-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 \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.36312 | 0.795390 | 0.397695 | − | 0.917518i | \(-0.369810\pi\) | ||||
0.397695 | + | 0.917518i | \(0.369810\pi\) | |||||||
\(3\) | 15.5885 | 0.577350 | ||||||||
\(4\) | −23.5107 | −0.367354 | ||||||||
\(5\) | 60.2242i | 0.481793i | 0.970551 | + | 0.240897i | \(0.0774415\pi\) | ||||
−0.970551 | + | 0.240897i | \(0.922559\pi\) | |||||||
\(6\) | 99.1913 | 0.459219 | ||||||||
\(7\) | 233.613i | 0.681087i | 0.940229 | + | 0.340544i | \(0.110611\pi\) | ||||
−0.940229 | + | 0.340544i | \(0.889389\pi\) | |||||||
\(8\) | −556.841 | −1.08758 | ||||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | 383.214i | 0.383214i | ||||||||
\(11\) | 1397.49i | 1.04995i | 0.851116 | + | 0.524977i | \(0.175926\pi\) | ||||
−0.851116 | + | 0.524977i | \(0.824074\pi\) | |||||||
\(12\) | −366.495 | −0.212092 | ||||||||
\(13\) | −1285.15 | −0.584955 | −0.292477 | − | 0.956272i | \(-0.594480\pi\) | ||||
−0.292477 | + | 0.956272i | \(0.594480\pi\) | |||||||
\(14\) | 1486.51i | 0.541730i | ||||||||
\(15\) | 938.802i | 0.278163i | ||||||||
\(16\) | −2038.57 | −0.497697 | ||||||||
\(17\) | 2821.93i | 0.574379i | 0.957874 | + | 0.287190i | \(0.0927210\pi\) | ||||
−0.957874 | + | 0.287190i | \(0.907279\pi\) | |||||||
\(18\) | 1546.24 | 0.265130 | ||||||||
\(19\) | 10185.1i | 1.48493i | 0.669884 | + | 0.742466i | \(0.266344\pi\) | ||||
−0.669884 | + | 0.742466i | \(0.733656\pi\) | |||||||
\(20\) | − | 1415.91i | − | 0.176989i | ||||||
\(21\) | 3641.66i | 0.393226i | ||||||||
\(22\) | 8892.40i | 0.835123i | ||||||||
\(23\) | −3980.90 | − | 11497.3i | −0.327188 | − | 0.944959i | ||||
\(24\) | −8680.29 | −0.627915 | ||||||||
\(25\) | 11998.1 | 0.767875 | ||||||||
\(26\) | −8177.54 | −0.465267 | ||||||||
\(27\) | 3788.00 | 0.192450 | ||||||||
\(28\) | − | 5492.39i | − | 0.250200i | ||||||
\(29\) | 5523.92 | 0.226492 | 0.113246 | − | 0.993567i | \(-0.463875\pi\) | ||||
0.113246 | + | 0.993567i | \(0.463875\pi\) | |||||||
\(30\) | 5973.71i | 0.221249i | ||||||||
\(31\) | −27306.5 | −0.916603 | −0.458301 | − | 0.888797i | \(-0.651542\pi\) | ||||
−0.458301 | + | 0.888797i | \(0.651542\pi\) | |||||||
\(32\) | 22666.2 | 0.691717 | ||||||||
\(33\) | 21784.7i | 0.606191i | ||||||||
\(34\) | 17956.3i | 0.456856i | ||||||||
\(35\) | −14069.1 | −0.328143 | ||||||||
\(36\) | −5713.09 | −0.122451 | ||||||||
\(37\) | 39765.7i | 0.785060i | 0.919739 | + | 0.392530i | \(0.128400\pi\) | ||||
−0.919739 | + | 0.392530i | \(0.871600\pi\) | |||||||
\(38\) | 64809.3i | 1.18110i | ||||||||
\(39\) | −20033.4 | −0.337724 | ||||||||
\(40\) | − | 33535.3i | − | 0.523989i | ||||||
\(41\) | −18455.9 | −0.267784 | −0.133892 | − | 0.990996i | \(-0.542748\pi\) | ||||
−0.133892 | + | 0.990996i | \(0.542748\pi\) | |||||||
\(42\) | 23172.4i | 0.312768i | ||||||||
\(43\) | − | 30920.7i | − | 0.388906i | −0.980912 | − | 0.194453i | \(-0.937707\pi\) | ||
0.980912 | − | 0.194453i | \(-0.0622931\pi\) | |||||||
\(44\) | − | 32855.9i | − | 0.385705i | ||||||
\(45\) | 14634.5i | 0.160598i | ||||||||
\(46\) | −25330.9 | − | 73158.9i | −0.260242 | − | 0.751612i | ||||
\(47\) | 62793.6 | 0.604814 | 0.302407 | − | 0.953179i | \(-0.402210\pi\) | ||||
0.302407 | + | 0.953179i | \(0.402210\pi\) | |||||||
\(48\) | −31778.1 | −0.287345 | ||||||||
\(49\) | 63074.0 | 0.536120 | ||||||||
\(50\) | 76345.1 | 0.610761 | ||||||||
\(51\) | 43989.5i | 0.331618i | ||||||||
\(52\) | 30214.6 | 0.214885 | ||||||||
\(53\) | − | 56165.6i | − | 0.377262i | −0.982048 | − | 0.188631i | \(-0.939595\pi\) | ||
0.982048 | − | 0.188631i | \(-0.0604050\pi\) | |||||||
\(54\) | 24103.5 | 0.153073 | ||||||||
\(55\) | −84162.6 | −0.505861 | ||||||||
\(56\) | − | 130085.i | − | 0.740737i | ||||||
\(57\) | 158771.i | 0.857326i | ||||||||
\(58\) | 35149.4 | 0.180150 | ||||||||
\(59\) | −159966. | −0.778880 | −0.389440 | − | 0.921052i | \(-0.627331\pi\) | ||||
−0.389440 | + | 0.921052i | \(0.627331\pi\) | |||||||
\(60\) | − | 22071.8i | − | 0.102184i | ||||||
\(61\) | − | 333535.i | − | 1.46944i | −0.678372 | − | 0.734719i | \(-0.737314\pi\) | ||
0.678372 | − | 0.734719i | \(-0.262686\pi\) | |||||||
\(62\) | −173755. | −0.729057 | ||||||||
\(63\) | 56767.9i | 0.227029i | ||||||||
\(64\) | 274696. | 1.04788 | ||||||||
\(65\) | − | 77396.8i | − | 0.281827i | ||||||
\(66\) | 138619.i | 0.482159i | ||||||||
\(67\) | − | 244298.i | − | 0.812260i | −0.913815 | − | 0.406130i | \(-0.866878\pi\) | ||
0.913815 | − | 0.406130i | \(-0.133122\pi\) | |||||||
\(68\) | − | 66345.4i | − | 0.211001i | ||||||
\(69\) | −62056.1 | − | 179225.i | −0.188902 | − | 0.545572i | ||||
\(70\) | −89523.7 | −0.261002 | ||||||||
\(71\) | 437275. | 1.22174 | 0.610871 | − | 0.791731i | \(-0.290820\pi\) | ||||
0.610871 | + | 0.791731i | \(0.290820\pi\) | |||||||
\(72\) | −135312. | −0.362527 | ||||||||
\(73\) | 494935. | 1.27227 | 0.636135 | − | 0.771578i | \(-0.280532\pi\) | ||||
0.636135 | + | 0.771578i | \(0.280532\pi\) | |||||||
\(74\) | 253034.i | 0.624429i | ||||||||
\(75\) | 187031. | 0.443333 | ||||||||
\(76\) | − | 239459.i | − | 0.545496i | ||||||
\(77\) | −326471. | −0.715110 | ||||||||
\(78\) | −127475. | −0.268622 | ||||||||
\(79\) | − | 571913.i | − | 1.15998i | −0.814625 | − | 0.579988i | \(-0.803057\pi\) | ||
0.814625 | − | 0.579988i | \(-0.196943\pi\) | |||||||
\(80\) | − | 122771.i | − | 0.239787i | ||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | −117437. | −0.212993 | ||||||||
\(83\) | 720923.i | 1.26082i | 0.776261 | + | 0.630412i | \(0.217114\pi\) | ||||
−0.776261 | + | 0.630412i | \(0.782886\pi\) | |||||||
\(84\) | − | 85617.9i | − | 0.144453i | ||||||
\(85\) | −169948. | −0.276732 | ||||||||
\(86\) | − | 196752.i | − | 0.309332i | ||||||
\(87\) | 86109.4 | 0.130765 | ||||||||
\(88\) | − | 778179.i | − | 1.14191i | ||||||
\(89\) | 785492.i | 1.11422i | 0.830438 | + | 0.557111i | \(0.188090\pi\) | ||||
−0.830438 | + | 0.557111i | \(0.811910\pi\) | |||||||
\(90\) | 93120.9i | 0.127738i | ||||||||
\(91\) | − | 300226.i | − | 0.398405i | ||||||
\(92\) | 93593.5 | + | 270310.i | 0.120194 | + | 0.347135i | ||||
\(93\) | −425666. | −0.529201 | ||||||||
\(94\) | 399563. | 0.481063 | ||||||||
\(95\) | −613392. | −0.715430 | ||||||||
\(96\) | 353331. | 0.399363 | ||||||||
\(97\) | − | 274434.i | − | 0.300692i | −0.988633 | − | 0.150346i | \(-0.951961\pi\) | ||
0.988633 | − | 0.150346i | \(-0.0480388\pi\) | |||||||
\(98\) | 401348. | 0.426425 | ||||||||
\(99\) | 339590.i | 0.349985i | ||||||||
\(100\) | −282082. | −0.282082 | ||||||||
\(101\) | −999436. | −0.970043 | −0.485021 | − | 0.874502i | \(-0.661188\pi\) | ||||
−0.485021 | + | 0.874502i | \(0.661188\pi\) | |||||||
\(102\) | 279910.i | 0.263766i | ||||||||
\(103\) | 359691.i | 0.329168i | 0.986363 | + | 0.164584i | \(0.0526282\pi\) | ||||
−0.986363 | + | 0.164584i | \(0.947372\pi\) | |||||||
\(104\) | 715622. | 0.636185 | ||||||||
\(105\) | −219316. | −0.189454 | ||||||||
\(106\) | − | 357389.i | − | 0.300070i | ||||||
\(107\) | 2.15412e6i | 1.75841i | 0.476447 | + | 0.879203i | \(0.341924\pi\) | ||||
−0.476447 | + | 0.879203i | \(0.658076\pi\) | |||||||
\(108\) | −89058.3 | −0.0706973 | ||||||||
\(109\) | 1.90465e6i | 1.47074i | 0.677668 | + | 0.735368i | \(0.262991\pi\) | ||||
−0.677668 | + | 0.735368i | \(0.737009\pi\) | |||||||
\(110\) | −535537. | −0.402357 | ||||||||
\(111\) | 619885.i | 0.453255i | ||||||||
\(112\) | − | 476235.i | − | 0.338975i | ||||||
\(113\) | 2.60669e6i | 1.80657i | 0.429041 | + | 0.903285i | \(0.358851\pi\) | ||||
−0.429041 | + | 0.903285i | \(0.641149\pi\) | |||||||
\(114\) | 1.01028e6i | 0.681909i | ||||||||
\(115\) | 692416. | − | 239746.i | 0.455275 | − | 0.157637i | ||||
\(116\) | −129871. | −0.0832028 | ||||||||
\(117\) | −312290. | −0.194985 | ||||||||
\(118\) | −1.01788e6 | −0.619514 | ||||||||
\(119\) | −659238. | −0.391202 | ||||||||
\(120\) | − | 522763.i | − | 0.302525i | ||||||
\(121\) | −181415. | −0.102404 | ||||||||
\(122\) | − | 2.12232e6i | − | 1.16878i | ||||||
\(123\) | −287700. | −0.154605 | ||||||||
\(124\) | 641994. | 0.336718 | ||||||||
\(125\) | 1.66357e6i | 0.851750i | ||||||||
\(126\) | 361221.i | 0.180577i | ||||||||
\(127\) | 1.00672e6 | 0.491473 | 0.245736 | − | 0.969337i | \(-0.420970\pi\) | ||||
0.245736 | + | 0.969337i | \(0.420970\pi\) | |||||||
\(128\) | 297289. | 0.141758 | ||||||||
\(129\) | − | 482007.i | − | 0.224535i | ||||||
\(130\) | − | 492485.i | − | 0.224163i | ||||||
\(131\) | −1.48663e6 | −0.661284 | −0.330642 | − | 0.943756i | \(-0.607265\pi\) | ||||
−0.330642 | + | 0.943756i | \(0.607265\pi\) | |||||||
\(132\) | − | 512173.i | − | 0.222687i | ||||||
\(133\) | −2.37938e6 | −1.01137 | ||||||||
\(134\) | − | 1.55450e6i | − | 0.646064i | ||||||
\(135\) | 228129.i | 0.0927212i | ||||||||
\(136\) | − | 1.57136e6i | − | 0.624684i | ||||||
\(137\) | − | 933505.i | − | 0.363041i | −0.983387 | − | 0.181520i | \(-0.941898\pi\) | ||
0.983387 | − | 0.181520i | \(-0.0581018\pi\) | |||||||
\(138\) | −394870. | − | 1.14043e6i | −0.150251 | − | 0.433943i | ||||
\(139\) | 2.57479e6 | 0.958734 | 0.479367 | − | 0.877615i | \(-0.340866\pi\) | ||||
0.479367 | + | 0.877615i | \(0.340866\pi\) | |||||||
\(140\) | 330775. | 0.120545 | ||||||||
\(141\) | 978855. | 0.349189 | ||||||||
\(142\) | 2.78243e6 | 0.971761 | ||||||||
\(143\) | − | 1.79598e6i | − | 0.614176i | ||||||
\(144\) | −495372. | −0.165899 | ||||||||
\(145\) | 332673.i | 0.109122i | ||||||||
\(146\) | 3.14933e6 | 1.01195 | ||||||||
\(147\) | 983227. | 0.309529 | ||||||||
\(148\) | − | 934917.i | − | 0.288395i | ||||||
\(149\) | − | 665234.i | − | 0.201102i | −0.994932 | − | 0.100551i | \(-0.967940\pi\) | ||
0.994932 | − | 0.100551i | \(-0.0320605\pi\) | |||||||
\(150\) | 1.19010e6 | 0.352623 | ||||||||
\(151\) | −385234. | −0.111891 | −0.0559453 | − | 0.998434i | \(-0.517817\pi\) | ||||
−0.0559453 | + | 0.998434i | \(0.517817\pi\) | |||||||
\(152\) | − | 5.67151e6i | − | 1.61498i | ||||||
\(153\) | 685728.i | 0.191460i | ||||||||
\(154\) | −2.07738e6 | −0.568792 | ||||||||
\(155\) | − | 1.64451e6i | − | 0.441613i | ||||||
\(156\) | 470999. | 0.124064 | ||||||||
\(157\) | − | 2.55515e6i | − | 0.660263i | −0.943935 | − | 0.330132i | \(-0.892907\pi\) | ||
0.943935 | − | 0.330132i | \(-0.107093\pi\) | |||||||
\(158\) | − | 3.63916e6i | − | 0.922634i | ||||||
\(159\) | − | 875535.i | − | 0.217812i | ||||||
\(160\) | 1.36505e6i | 0.333265i | ||||||||
\(161\) | 2.68592e6 | − | 929989.i | 0.643599 | − | 0.222844i | ||||
\(162\) | 375736. | 0.0883767 | ||||||||
\(163\) | −4.76008e6 | −1.09914 | −0.549568 | − | 0.835449i | \(-0.685208\pi\) | ||||
−0.549568 | + | 0.835449i | \(0.685208\pi\) | |||||||
\(164\) | 433911. | 0.0983715 | ||||||||
\(165\) | −1.31197e6 | −0.292059 | ||||||||
\(166\) | 4.58732e6i | 1.00285i | ||||||||
\(167\) | 3.47396e6 | 0.745892 | 0.372946 | − | 0.927853i | \(-0.378348\pi\) | ||||
0.372946 | + | 0.927853i | \(0.378348\pi\) | |||||||
\(168\) | − | 2.02783e6i | − | 0.427665i | ||||||
\(169\) | −3.17521e6 | −0.657828 | ||||||||
\(170\) | −1.08140e6 | −0.220110 | ||||||||
\(171\) | 2.47499e6i | 0.494977i | ||||||||
\(172\) | 726967.i | 0.142866i | ||||||||
\(173\) | 3.58125e6 | 0.691666 | 0.345833 | − | 0.938296i | \(-0.387596\pi\) | ||||
0.345833 | + | 0.938296i | \(0.387596\pi\) | |||||||
\(174\) | 547925. | 0.104009 | ||||||||
\(175\) | 2.80290e6i | 0.522990i | ||||||||
\(176\) | − | 2.84887e6i | − | 0.522559i | ||||||
\(177\) | −2.49362e6 | −0.449687 | ||||||||
\(178\) | 4.99818e6i | 0.886242i | ||||||||
\(179\) | −1.81514e6 | −0.316483 | −0.158241 | − | 0.987400i | \(-0.550582\pi\) | ||||
−0.158241 | + | 0.987400i | \(0.550582\pi\) | |||||||
\(180\) | − | 344066.i | − | 0.0589962i | ||||||
\(181\) | 5.36160e6i | 0.904188i | 0.891970 | + | 0.452094i | \(0.149323\pi\) | ||||
−0.891970 | + | 0.452094i | \(0.850677\pi\) | |||||||
\(182\) | − | 1.91038e6i | − | 0.316888i | ||||||
\(183\) | − | 5.19929e6i | − | 0.848380i | ||||||
\(184\) | 2.21673e6 | + | 6.40218e6i | 0.355843 | + | 1.02772i | ||||
\(185\) | −2.39485e6 | −0.378237 | ||||||||
\(186\) | −2.70857e6 | −0.420921 | ||||||||
\(187\) | −3.94361e6 | −0.603072 | ||||||||
\(188\) | −1.47632e6 | −0.222181 | ||||||||
\(189\) | 884924.i | 0.131075i | ||||||||
\(190\) | −3.90309e6 | −0.569046 | ||||||||
\(191\) | 6.26268e6i | 0.898794i | 0.893332 | + | 0.449397i | \(0.148361\pi\) | ||||
−0.893332 | + | 0.449397i | \(0.851639\pi\) | |||||||
\(192\) | 4.28209e6 | 0.604995 | ||||||||
\(193\) | 1.28599e7 | 1.78882 | 0.894408 | − | 0.447252i | \(-0.147597\pi\) | ||||
0.894408 | + | 0.447252i | \(0.147597\pi\) | |||||||
\(194\) | − | 1.74626e6i | − | 0.239168i | ||||||
\(195\) | − | 1.20650e6i | − | 0.162713i | ||||||
\(196\) | −1.48291e6 | −0.196946 | ||||||||
\(197\) | 9.53336e6 | 1.24694 | 0.623472 | − | 0.781845i | \(-0.285721\pi\) | ||||
0.623472 | + | 0.781845i | \(0.285721\pi\) | |||||||
\(198\) | 2.16085e6i | 0.278374i | ||||||||
\(199\) | − | 1.75998e6i | − | 0.223331i | −0.993746 | − | 0.111665i | \(-0.964382\pi\) | ||
0.993746 | − | 0.111665i | \(-0.0356185\pi\) | |||||||
\(200\) | −6.68101e6 | −0.835126 | ||||||||
\(201\) | − | 3.80823e6i | − | 0.468959i | ||||||
\(202\) | −6.35954e6 | −0.771563 | ||||||||
\(203\) | 1.29046e6i | 0.154261i | ||||||||
\(204\) | − | 1.03422e6i | − | 0.121821i | ||||||
\(205\) | − | 1.11149e6i | − | 0.129017i | ||||||
\(206\) | 2.28876e6i | 0.261817i | ||||||||
\(207\) | −967358. | − | 2.79385e6i | −0.109063 | − | 0.314986i | ||||
\(208\) | 2.61985e6 | 0.291130 | ||||||||
\(209\) | −1.42336e7 | −1.55911 | ||||||||
\(210\) | −1.39554e6 | −0.150690 | ||||||||
\(211\) | −1.02042e6 | −0.108626 | −0.0543128 | − | 0.998524i | \(-0.517297\pi\) | ||||
−0.0543128 | + | 0.998524i | \(0.517297\pi\) | |||||||
\(212\) | 1.32049e6i | 0.138589i | ||||||||
\(213\) | 6.81644e6 | 0.705372 | ||||||||
\(214\) | 1.37069e7i | 1.39862i | ||||||||
\(215\) | 1.86218e6 | 0.187372 | ||||||||
\(216\) | −2.10931e6 | −0.209305 | ||||||||
\(217\) | − | 6.37915e6i | − | 0.624286i | ||||||
\(218\) | 1.21195e7i | 1.16981i | ||||||||
\(219\) | 7.71527e6 | 0.734545 | ||||||||
\(220\) | 1.97872e6 | 0.185830 | ||||||||
\(221\) | − | 3.62659e6i | − | 0.335986i | ||||||
\(222\) | 3.94441e6i | 0.360515i | ||||||||
\(223\) | −5.16861e6 | −0.466078 | −0.233039 | − | 0.972467i | \(-0.574867\pi\) | ||||
−0.233039 | + | 0.972467i | \(0.574867\pi\) | |||||||
\(224\) | 5.29511e6i | 0.471119i | ||||||||
\(225\) | 2.91553e6 | 0.255958 | ||||||||
\(226\) | 1.65867e7i | 1.43693i | ||||||||
\(227\) | − | 7.01786e6i | − | 0.599967i | −0.953944 | − | 0.299983i | \(-0.903019\pi\) | ||
0.953944 | − | 0.299983i | \(-0.0969812\pi\) | |||||||
\(228\) | − | 3.73280e6i | − | 0.314942i | ||||||
\(229\) | − | 1.15614e7i | − | 0.962731i | −0.876520 | − | 0.481366i | \(-0.840141\pi\) | ||
0.876520 | − | 0.481366i | \(-0.159859\pi\) | |||||||
\(230\) | 4.40593e6 | − | 1.52553e6i | 0.362121 | − | 0.125383i | ||||
\(231\) | −5.08919e6 | −0.412869 | ||||||||
\(232\) | −3.07594e6 | −0.246328 | ||||||||
\(233\) | −1.34263e7 | −1.06143 | −0.530713 | − | 0.847552i | \(-0.678076\pi\) | ||||
−0.530713 | + | 0.847552i | \(0.678076\pi\) | |||||||
\(234\) | −1.98714e6 | −0.155089 | ||||||||
\(235\) | 3.78169e6i | 0.291395i | ||||||||
\(236\) | 3.76090e6 | 0.286125 | ||||||||
\(237\) | − | 8.91525e6i | − | 0.669712i | ||||||
\(238\) | −4.19481e6 | −0.311159 | ||||||||
\(239\) | 7.65228e6 | 0.560528 | 0.280264 | − | 0.959923i | \(-0.409578\pi\) | ||||
0.280264 | + | 0.959923i | \(0.409578\pi\) | |||||||
\(240\) | − | 1.91381e6i | − | 0.138441i | ||||||
\(241\) | − | 9.36770e6i | − | 0.669240i | −0.942353 | − | 0.334620i | \(-0.891392\pi\) | ||
0.942353 | − | 0.334620i | \(-0.108608\pi\) | |||||||
\(242\) | −1.15436e6 | −0.0814510 | ||||||||
\(243\) | 920483. | 0.0641500 | ||||||||
\(244\) | 7.84162e6i | 0.539804i | ||||||||
\(245\) | 3.79858e6i | 0.258299i | ||||||||
\(246\) | −1.83067e6 | −0.122971 | ||||||||
\(247\) | − | 1.30894e7i | − | 0.868618i | ||||||
\(248\) | 1.52054e7 | 0.996879 | ||||||||
\(249\) | 1.12381e7i | 0.727937i | ||||||||
\(250\) | 1.05855e7i | 0.677474i | ||||||||
\(251\) | − | 109973.i | − | 0.00695448i | −0.999994 | − | 0.00347724i | \(-0.998893\pi\) | ||
0.999994 | − | 0.00347724i | \(-0.00110684\pi\) | |||||||
\(252\) | − | 1.33465e6i | − | 0.0834000i | ||||||
\(253\) | 1.60674e7 | − | 5.56326e6i | 0.992164 | − | 0.343533i | ||||
\(254\) | 6.40591e6 | 0.390913 | ||||||||
\(255\) | −2.64923e6 | −0.159771 | ||||||||
\(256\) | −1.56889e7 | −0.935129 | ||||||||
\(257\) | 5.24170e6 | 0.308797 | 0.154398 | − | 0.988009i | \(-0.450656\pi\) | ||||
0.154398 | + | 0.988009i | \(0.450656\pi\) | |||||||
\(258\) | − | 3.06707e6i | − | 0.178593i | ||||||
\(259\) | −9.28977e6 | −0.534694 | ||||||||
\(260\) | 1.81965e6i | 0.103530i | ||||||||
\(261\) | 1.34231e6 | 0.0754974 | ||||||||
\(262\) | −9.45959e6 | −0.525979 | ||||||||
\(263\) | 2.01529e7i | 1.10782i | 0.832576 | + | 0.553911i | \(0.186865\pi\) | ||||
−0.832576 | + | 0.553911i | \(0.813135\pi\) | |||||||
\(264\) | − | 1.21306e7i | − | 0.659282i | ||||||
\(265\) | 3.38253e6 | 0.181762 | ||||||||
\(266\) | −1.51403e7 | −0.804432 | ||||||||
\(267\) | 1.22446e7i | 0.643297i | ||||||||
\(268\) | 5.74360e6i | 0.298387i | ||||||||
\(269\) | −3.23774e7 | −1.66336 | −0.831678 | − | 0.555258i | \(-0.812620\pi\) | ||||
−0.831678 | + | 0.555258i | \(0.812620\pi\) | |||||||
\(270\) | 1.45161e6i | 0.0737495i | ||||||||
\(271\) | 1.93637e7 | 0.972929 | 0.486465 | − | 0.873700i | \(-0.338286\pi\) | ||||
0.486465 | + | 0.873700i | \(0.338286\pi\) | |||||||
\(272\) | − | 5.75268e6i | − | 0.285867i | ||||||
\(273\) | − | 4.68007e6i | − | 0.230019i | ||||||
\(274\) | − | 5.94001e6i | − | 0.288759i | ||||||
\(275\) | 1.67671e7i | 0.806234i | ||||||||
\(276\) | 1.45898e6 | + | 4.21371e6i | 0.0693940 | + | 0.200418i | ||||
\(277\) | 3.05629e7 | 1.43799 | 0.718994 | − | 0.695016i | \(-0.244603\pi\) | ||||
0.718994 | + | 0.695016i | \(0.244603\pi\) | |||||||
\(278\) | 1.63837e7 | 0.762568 | ||||||||
\(279\) | −6.63548e6 | −0.305534 | ||||||||
\(280\) | 7.83427e6 | 0.356882 | ||||||||
\(281\) | − | 1.20980e7i | − | 0.545249i | −0.962120 | − | 0.272625i | \(-0.912108\pi\) | ||
0.962120 | − | 0.272625i | \(-0.0878917\pi\) | |||||||
\(282\) | 6.22857e6 | 0.277742 | ||||||||
\(283\) | − | 3.45135e7i | − | 1.52275i | −0.648310 | − | 0.761377i | \(-0.724524\pi\) | ||
0.648310 | − | 0.761377i | \(-0.275476\pi\) | |||||||
\(284\) | −1.02806e7 | −0.448812 | ||||||||
\(285\) | −9.56183e6 | −0.413054 | ||||||||
\(286\) | − | 1.14280e7i | − | 0.488509i | ||||||
\(287\) | − | 4.31154e6i | − | 0.182384i | ||||||
\(288\) | 5.50788e6 | 0.230572 | ||||||||
\(289\) | 1.61743e7 | 0.670088 | ||||||||
\(290\) | 2.11684e6i | 0.0867949i | ||||||||
\(291\) | − | 4.27800e6i | − | 0.173605i | ||||||
\(292\) | −1.16362e7 | −0.467373 | ||||||||
\(293\) | − | 3.33872e7i | − | 1.32733i | −0.748032 | − | 0.663663i | \(-0.769001\pi\) | ||
0.748032 | − | 0.663663i | \(-0.230999\pi\) | |||||||
\(294\) | 6.25639e6 | 0.246197 | ||||||||
\(295\) | − | 9.63379e6i | − | 0.375259i | ||||||
\(296\) | − | 2.21432e7i | − | 0.853816i | ||||||
\(297\) | 5.29368e6i | 0.202064i | ||||||||
\(298\) | − | 4.23296e6i | − | 0.159954i | ||||||
\(299\) | 5.11603e6 | + | 1.47757e7i | 0.191390 | + | 0.552758i | ||||
\(300\) | −4.39722e6 | −0.162860 | ||||||||
\(301\) | 7.22348e6 | 0.264879 | ||||||||
\(302\) | −2.45129e6 | −0.0889968 | ||||||||
\(303\) | −1.55797e7 | −0.560055 | ||||||||
\(304\) | − | 2.07631e7i | − | 0.739046i | ||||||
\(305\) | 2.00868e7 | 0.707965 | ||||||||
\(306\) | 4.36337e6i | 0.152285i | ||||||||
\(307\) | −5.47778e7 | −1.89317 | −0.946585 | − | 0.322455i | \(-0.895492\pi\) | ||||
−0.946585 | + | 0.322455i | \(0.895492\pi\) | |||||||
\(308\) | 7.67556e6 | 0.262699 | ||||||||
\(309\) | 5.60703e6i | 0.190045i | ||||||||
\(310\) | − | 1.04642e7i | − | 0.351255i | ||||||
\(311\) | 2.86189e7 | 0.951418 | 0.475709 | − | 0.879603i | \(-0.342192\pi\) | ||||
0.475709 | + | 0.879603i | \(0.342192\pi\) | |||||||
\(312\) | 1.11554e7 | 0.367302 | ||||||||
\(313\) | − | 3.59059e7i | − | 1.17094i | −0.810695 | − | 0.585468i | \(-0.800911\pi\) | ||
0.810695 | − | 0.585468i | \(-0.199089\pi\) | |||||||
\(314\) | − | 1.62587e7i | − | 0.525167i | ||||||
\(315\) | −3.41880e6 | −0.109381 | ||||||||
\(316\) | 1.34461e7i | 0.426122i | ||||||||
\(317\) | 3.22286e7 | 1.01173 | 0.505865 | − | 0.862613i | \(-0.331174\pi\) | ||||
0.505865 | + | 0.862613i | \(0.331174\pi\) | |||||||
\(318\) | − | 5.57114e6i | − | 0.173246i | ||||||
\(319\) | 7.71962e6i | 0.237806i | ||||||||
\(320\) | 1.65433e7i | 0.504862i | ||||||||
\(321\) | 3.35795e7i | 1.01522i | ||||||||
\(322\) | 1.70908e7 | − | 5.91763e6i | 0.511913 | − | 0.177248i | ||||
\(323\) | −2.87417e7 | −0.852914 | ||||||||
\(324\) | −1.38828e6 | −0.0408171 | ||||||||
\(325\) | −1.54192e7 | −0.449172 | ||||||||
\(326\) | −3.02890e7 | −0.874242 | ||||||||
\(327\) | 2.96905e7i | 0.849130i | ||||||||
\(328\) | 1.02770e7 | 0.291237 | ||||||||
\(329\) | 1.46694e7i | 0.411931i | ||||||||
\(330\) | −8.34820e6 | −0.232301 | ||||||||
\(331\) | 3.35391e7 | 0.924842 | 0.462421 | − | 0.886661i | \(-0.346981\pi\) | ||||
0.462421 | + | 0.886661i | \(0.346981\pi\) | |||||||
\(332\) | − | 1.69494e7i | − | 0.463169i | ||||||
\(333\) | 9.66306e6i | 0.261687i | ||||||||
\(334\) | 2.21053e7 | 0.593275 | ||||||||
\(335\) | 1.47126e7 | 0.391341 | ||||||||
\(336\) | − | 7.42377e6i | − | 0.195707i | ||||||
\(337\) | − | 5.76754e7i | − | 1.50696i | −0.657472 | − | 0.753479i | \(-0.728374\pi\) | ||
0.657472 | − | 0.753479i | \(-0.271626\pi\) | |||||||
\(338\) | −2.02043e7 | −0.523230 | ||||||||
\(339\) | 4.06343e7i | 1.04302i | ||||||||
\(340\) | 3.99559e6 | 0.101659 | ||||||||
\(341\) | − | 3.81606e7i | − | 0.962391i | ||||||
\(342\) | 1.57487e7i | 0.393700i | ||||||||
\(343\) | 4.22192e7i | 1.04623i | ||||||||
\(344\) | 1.72179e7i | 0.422966i | ||||||||
\(345\) | 1.07937e7 | − | 3.73727e6i | 0.262853 | − | 0.0910118i | ||||
\(346\) | 2.27879e7 | 0.550144 | ||||||||
\(347\) | −2.70139e7 | −0.646545 | −0.323272 | − | 0.946306i | \(-0.604783\pi\) | ||||
−0.323272 | + | 0.946306i | \(0.604783\pi\) | |||||||
\(348\) | −2.02449e6 | −0.0480372 | ||||||||
\(349\) | 3.28000e6 | 0.0771609 | 0.0385804 | − | 0.999255i | \(-0.487716\pi\) | ||||
0.0385804 | + | 0.999255i | \(0.487716\pi\) | |||||||
\(350\) | 1.78352e7i | 0.415981i | ||||||||
\(351\) | −4.86812e6 | −0.112575 | ||||||||
\(352\) | 3.16757e7i | 0.726271i | ||||||||
\(353\) | −4.41288e7 | −1.00323 | −0.501613 | − | 0.865092i | \(-0.667260\pi\) | ||||
−0.501613 | + | 0.865092i | \(0.667260\pi\) | |||||||
\(354\) | −1.58672e7 | −0.357676 | ||||||||
\(355\) | 2.63345e7i | 0.588627i | ||||||||
\(356\) | − | 1.84674e7i | − | 0.409314i | ||||||
\(357\) | −1.02765e7 | −0.225861 | ||||||||
\(358\) | −1.15499e7 | −0.251728 | ||||||||
\(359\) | 3.84523e7i | 0.831073i | 0.909576 | + | 0.415537i | \(0.136406\pi\) | ||||
−0.909576 | + | 0.415537i | \(0.863594\pi\) | |||||||
\(360\) | − | 8.14907e6i | − | 0.174663i | ||||||
\(361\) | −5.66913e7 | −1.20502 | ||||||||
\(362\) | 3.41165e7i | 0.719182i | ||||||||
\(363\) | −2.82797e6 | −0.0591229 | ||||||||
\(364\) | 7.05852e6i | 0.146356i | ||||||||
\(365\) | 2.98070e7i | 0.612971i | ||||||||
\(366\) | − | 3.30837e7i | − | 0.674794i | ||||||
\(367\) | 1.90097e7i | 0.384571i | 0.981339 | + | 0.192286i | \(0.0615900\pi\) | ||||
−0.981339 | + | 0.192286i | \(0.938410\pi\) | |||||||
\(368\) | 8.11533e6 | + | 2.34380e7i | 0.162841 | + | 0.470303i | ||||
\(369\) | −4.48479e6 | −0.0892613 | ||||||||
\(370\) | −1.52387e7 | −0.300846 | ||||||||
\(371\) | 1.31210e7 | 0.256948 | ||||||||
\(372\) | 1.00077e7 | 0.194404 | ||||||||
\(373\) | − | 6.82339e7i | − | 1.31484i | −0.753523 | − | 0.657421i | \(-0.771647\pi\) | ||
0.753523 | − | 0.657421i | \(-0.228353\pi\) | |||||||
\(374\) | −2.50937e7 | −0.479678 | ||||||||
\(375\) | 2.59326e7i | 0.491758i | ||||||||
\(376\) | −3.49660e7 | −0.657783 | ||||||||
\(377\) | −7.09904e6 | −0.132488 | ||||||||
\(378\) | 5.63088e6i | 0.104256i | ||||||||
\(379\) | 5.18792e7i | 0.952961i | 0.879185 | + | 0.476481i | \(0.158088\pi\) | ||||
−0.879185 | + | 0.476481i | \(0.841912\pi\) | |||||||
\(380\) | 1.44212e7 | 0.262816 | ||||||||
\(381\) | 1.56933e7 | 0.283752 | ||||||||
\(382\) | 3.98502e7i | 0.714892i | ||||||||
\(383\) | 1.02080e8i | 1.81696i | 0.417931 | + | 0.908479i | \(0.362755\pi\) | ||||
−0.417931 | + | 0.908479i | \(0.637245\pi\) | |||||||
\(384\) | 4.63427e6 | 0.0818442 | ||||||||
\(385\) | − | 1.96615e7i | − | 0.344535i | ||||||
\(386\) | 8.18291e7 | 1.42281 | ||||||||
\(387\) | − | 7.51374e6i | − | 0.129635i | ||||||
\(388\) | 6.45212e6i | 0.110461i | ||||||||
\(389\) | 2.97488e7i | 0.505383i | 0.967547 | + | 0.252691i | \(0.0813157\pi\) | ||||
−0.967547 | + | 0.252691i | \(0.918684\pi\) | |||||||
\(390\) | − | 7.67709e6i | − | 0.129420i | ||||||
\(391\) | 3.24446e7 | − | 1.12338e7i | 0.542765 | − | 0.187930i | ||||
\(392\) | −3.51222e7 | −0.583074 | ||||||||
\(393\) | −2.31742e7 | −0.381793 | ||||||||
\(394\) | 6.06619e7 | 0.991808 | ||||||||
\(395\) | 3.44430e7 | 0.558869 | ||||||||
\(396\) | − | 7.98398e6i | − | 0.128568i | ||||||
\(397\) | −5.08435e6 | −0.0812576 | −0.0406288 | − | 0.999174i | \(-0.512936\pi\) | ||||
−0.0406288 | + | 0.999174i | \(0.512936\pi\) | |||||||
\(398\) | − | 1.11990e7i | − | 0.177635i | ||||||
\(399\) | −3.70909e7 | −0.583913 | ||||||||
\(400\) | −2.44588e7 | −0.382169 | ||||||||
\(401\) | − | 8.46941e7i | − | 1.31347i | −0.754122 | − | 0.656735i | \(-0.771937\pi\) | ||
0.754122 | − | 0.656735i | \(-0.228063\pi\) | |||||||
\(402\) | − | 2.42322e7i | − | 0.373005i | ||||||
\(403\) | 3.50928e7 | 0.536171 | ||||||||
\(404\) | 2.34974e7 | 0.356349 | ||||||||
\(405\) | 3.55618e6i | 0.0535326i | ||||||||
\(406\) | 8.21134e6i | 0.122698i | ||||||||
\(407\) | −5.55721e7 | −0.824277 | ||||||||
\(408\) | − | 2.44952e7i | − | 0.360661i | ||||||
\(409\) | 1.01530e7 | 0.148397 | 0.0741985 | − | 0.997243i | \(-0.476360\pi\) | ||||
0.0741985 | + | 0.997243i | \(0.476360\pi\) | |||||||
\(410\) | − | 7.07257e6i | − | 0.102618i | ||||||
\(411\) | − | 1.45519e7i | − | 0.209602i | ||||||
\(412\) | − | 8.45657e6i | − | 0.120921i | ||||||
\(413\) | − | 3.73700e7i | − | 0.530485i | ||||||
\(414\) | −6.15542e6 | − | 1.77776e7i | −0.0867474 | − | 0.250537i | ||||
\(415\) | −4.34170e7 | −0.607456 | ||||||||
\(416\) | −2.91293e7 | −0.404623 | ||||||||
\(417\) | 4.01371e7 | 0.553525 | ||||||||
\(418\) | −9.05703e7 | −1.24010 | ||||||||
\(419\) | 2.98259e7i | 0.405464i | 0.979234 | + | 0.202732i | \(0.0649820\pi\) | ||||
−0.979234 | + | 0.202732i | \(0.935018\pi\) | |||||||
\(420\) | 5.15627e6 | 0.0695965 | ||||||||
\(421\) | − | 8.63872e7i | − | 1.15772i | −0.815427 | − | 0.578860i | \(-0.803498\pi\) | ||
0.815427 | − | 0.578860i | \(-0.196502\pi\) | |||||||
\(422\) | −6.49306e6 | −0.0863997 | ||||||||
\(423\) | 1.52588e7 | 0.201605 | ||||||||
\(424\) | 3.12753e7i | 0.410303i | ||||||||
\(425\) | 3.38576e7i | 0.441052i | ||||||||
\(426\) | 4.33738e7 | 0.561047 | ||||||||
\(427\) | 7.79179e7 | 1.00082 | ||||||||
\(428\) | − | 5.06449e7i | − | 0.645958i | ||||||
\(429\) | − | 2.79965e7i | − | 0.354594i | ||||||
\(430\) | 1.18492e7 | 0.149034 | ||||||||
\(431\) | − | 4.07286e7i | − | 0.508707i | −0.967111 | − | 0.254353i | \(-0.918137\pi\) | ||
0.967111 | − | 0.254353i | \(-0.0818626\pi\) | |||||||
\(432\) | −7.72208e6 | −0.0957818 | ||||||||
\(433\) | 1.05183e8i | 1.29563i | 0.761798 | + | 0.647814i | \(0.224317\pi\) | ||||
−0.761798 | + | 0.647814i | \(0.775683\pi\) | |||||||
\(434\) | − | 4.05913e7i | − | 0.496551i | ||||||
\(435\) | 5.18586e6i | 0.0630019i | ||||||||
\(436\) | − | 4.47795e7i | − | 0.540281i | ||||||
\(437\) | 1.17102e8 | − | 4.05460e7i | 1.40320 | − | 0.485852i | ||||
\(438\) | 4.90932e7 | 0.584250 | ||||||||
\(439\) | −5.25897e7 | −0.621594 | −0.310797 | − | 0.950476i | \(-0.600596\pi\) | ||||
−0.310797 | + | 0.950476i | \(0.600596\pi\) | |||||||
\(440\) | 4.68652e7 | 0.550164 | ||||||||
\(441\) | 1.53270e7 | 0.178707 | ||||||||
\(442\) | − | 2.30764e7i | − | 0.267240i | ||||||
\(443\) | −1.46092e8 | −1.68041 | −0.840207 | − | 0.542266i | \(-0.817566\pi\) | ||||
−0.840207 | + | 0.542266i | \(0.817566\pi\) | |||||||
\(444\) | − | 1.45739e7i | − | 0.166505i | ||||||
\(445\) | −4.73056e7 | −0.536825 | ||||||||
\(446\) | −3.28885e7 | −0.370714 | ||||||||
\(447\) | − | 1.03700e7i | − | 0.116106i | ||||||
\(448\) | 6.41725e7i | 0.713699i | ||||||||
\(449\) | 3.09669e7 | 0.342104 | 0.171052 | − | 0.985262i | \(-0.445283\pi\) | ||||
0.171052 | + | 0.985262i | \(0.445283\pi\) | |||||||
\(450\) | 1.85519e7 | 0.203587 | ||||||||
\(451\) | − | 2.57920e7i | − | 0.281161i | ||||||
\(452\) | − | 6.12851e7i | − | 0.663651i | ||||||
\(453\) | −6.00520e6 | −0.0646001 | ||||||||
\(454\) | − | 4.46555e7i | − | 0.477208i | ||||||
\(455\) | 1.80809e7 | 0.191949 | ||||||||
\(456\) | − | 8.84101e7i | − | 0.932410i | ||||||
\(457\) | − | 3.64508e7i | − | 0.381908i | −0.981599 | − | 0.190954i | \(-0.938842\pi\) | ||
0.981599 | − | 0.190954i | \(-0.0611581\pi\) | |||||||
\(458\) | − | 7.35668e7i | − | 0.765747i | ||||||
\(459\) | 1.06894e7i | 0.110539i | ||||||||
\(460\) | −1.62792e7 | + | 5.63659e6i | −0.167247 | + | 0.0579086i | ||||
\(461\) | 3.26518e7 | 0.333276 | 0.166638 | − | 0.986018i | \(-0.446709\pi\) | ||||
0.166638 | + | 0.986018i | \(0.446709\pi\) | |||||||
\(462\) | −3.23831e7 | −0.328392 | ||||||||
\(463\) | 1.67599e8 | 1.68860 | 0.844302 | − | 0.535868i | \(-0.180016\pi\) | ||||
0.844302 | + | 0.535868i | \(0.180016\pi\) | |||||||
\(464\) | −1.12609e7 | −0.112724 | ||||||||
\(465\) | − | 2.56354e7i | − | 0.254965i | ||||||
\(466\) | −8.54334e7 | −0.844248 | ||||||||
\(467\) | − | 3.58074e7i | − | 0.351578i | −0.984428 | − | 0.175789i | \(-0.943752\pi\) | ||
0.984428 | − | 0.175789i | \(-0.0562477\pi\) | |||||||
\(468\) | 7.34215e6 | 0.0716285 | ||||||||
\(469\) | 5.70711e7 | 0.553220 | ||||||||
\(470\) | 2.40634e7i | 0.231773i | ||||||||
\(471\) | − | 3.98308e7i | − | 0.381203i | ||||||
\(472\) | 8.90754e7 | 0.847094 | ||||||||
\(473\) | 4.32114e7 | 0.408333 | ||||||||
\(474\) | − | 5.67288e7i | − | 0.532683i | ||||||
\(475\) | 1.22202e8i | 1.14024i | ||||||||
\(476\) | 1.54991e7 | 0.143710 | ||||||||
\(477\) | − | 1.36482e7i | − | 0.125754i | ||||||
\(478\) | 4.86924e7 | 0.445838 | ||||||||
\(479\) | 4.01741e7i | 0.365544i | 0.983155 | + | 0.182772i | \(0.0585070\pi\) | ||||
−0.983155 | + | 0.182772i | \(0.941493\pi\) | |||||||
\(480\) | 2.12791e7i | 0.192410i | ||||||||
\(481\) | − | 5.11047e7i | − | 0.459225i | ||||||
\(482\) | − | 5.96078e7i | − | 0.532307i | ||||||
\(483\) | 4.18694e7 | − | 1.44971e7i | 0.371582 | − | 0.128659i | ||||
\(484\) | 4.26518e6 | 0.0376185 | ||||||||
\(485\) | 1.65275e7 | 0.144872 | ||||||||
\(486\) | 5.85715e6 | 0.0510243 | ||||||||
\(487\) | −1.60417e8 | −1.38888 | −0.694439 | − | 0.719552i | \(-0.744347\pi\) | ||||
−0.694439 | + | 0.719552i | \(0.744347\pi\) | |||||||
\(488\) | 1.85726e8i | 1.59813i | ||||||||
\(489\) | −7.42023e7 | −0.634586 | ||||||||
\(490\) | 2.41708e7i | 0.205449i | ||||||||
\(491\) | −7.40765e7 | −0.625800 | −0.312900 | − | 0.949786i | \(-0.601301\pi\) | ||||
−0.312900 | + | 0.949786i | \(0.601301\pi\) | |||||||
\(492\) | 6.76401e6 | 0.0567948 | ||||||||
\(493\) | 1.55881e7i | 0.130092i | ||||||||
\(494\) | − | 8.32894e7i | − | 0.690890i | ||||||
\(495\) | −2.04515e7 | −0.168620 | ||||||||
\(496\) | 5.56661e7 | 0.456190 | ||||||||
\(497\) | 1.02153e8i | 0.832112i | ||||||||
\(498\) | 7.15092e7i | 0.578994i | ||||||||
\(499\) | −1.97181e8 | −1.58695 | −0.793474 | − | 0.608604i | \(-0.791730\pi\) | ||||
−0.793474 | + | 0.608604i | \(0.791730\pi\) | |||||||
\(500\) | − | 3.91117e7i | − | 0.312894i | ||||||
\(501\) | 5.41537e7 | 0.430641 | ||||||||
\(502\) | − | 699772.i | − | 0.00553153i | ||||||
\(503\) | − | 6.73802e6i | − | 0.0529454i | −0.999650 | − | 0.0264727i | \(-0.991572\pi\) | ||
0.999650 | − | 0.0264727i | \(-0.00842750\pi\) | |||||||
\(504\) | − | 3.16107e7i | − | 0.246912i | ||||||
\(505\) | − | 6.01902e7i | − | 0.467360i | ||||||
\(506\) | 1.02239e8 | − | 3.53997e7i | 0.789158 | − | 0.273242i | ||||
\(507\) | −4.94966e7 | −0.379797 | ||||||||
\(508\) | −2.36688e7 | −0.180544 | ||||||||
\(509\) | 2.39743e7 | 0.181799 | 0.0908997 | − | 0.995860i | \(-0.471026\pi\) | ||||
0.0908997 | + | 0.995860i | \(0.471026\pi\) | |||||||
\(510\) | −1.68574e7 | −0.127081 | ||||||||
\(511\) | 1.15623e8i | 0.866526i | ||||||||
\(512\) | −1.18857e8 | −0.885551 | ||||||||
\(513\) | 3.85813e7i | 0.285775i | ||||||||
\(514\) | 3.33536e7 | 0.245614 | ||||||||
\(515\) | −2.16621e7 | −0.158591 | ||||||||
\(516\) | 1.13323e7i | 0.0824838i | ||||||||
\(517\) | 8.77533e7i | 0.635027i | ||||||||
\(518\) | −5.91119e7 | −0.425291 | ||||||||
\(519\) | 5.58262e7 | 0.399334 | ||||||||
\(520\) | 4.30977e7i | 0.306510i | ||||||||
\(521\) | − | 1.14966e8i | − | 0.812933i | −0.913666 | − | 0.406467i | \(-0.866761\pi\) | ||
0.913666 | − | 0.406467i | \(-0.133239\pi\) | |||||||
\(522\) | 8.54130e6 | 0.0600499 | ||||||||
\(523\) | 2.70926e8i | 1.89385i | 0.321456 | + | 0.946925i | \(0.395828\pi\) | ||||
−0.321456 | + | 0.946925i | \(0.604172\pi\) | |||||||
\(524\) | 3.49516e7 | 0.242926 | ||||||||
\(525\) | 4.36929e7i | 0.301948i | ||||||||
\(526\) | 1.28235e8i | 0.881152i | ||||||||
\(527\) | − | 7.70570e7i | − | 0.526478i | ||||||
\(528\) | − | 4.44096e7i | − | 0.301700i | ||||||
\(529\) | −1.16341e8 | + | 9.15393e7i | −0.785896 | + | 0.618359i | ||||
\(530\) | 2.15234e7 | 0.144572 | ||||||||
\(531\) | −3.88716e7 | −0.259627 | ||||||||
\(532\) | 5.59408e7 | 0.371530 | ||||||||
\(533\) | 2.37186e7 | 0.156641 | ||||||||
\(534\) | 7.79140e7i | 0.511672i | ||||||||
\(535\) | −1.29730e8 | −0.847188 | ||||||||
\(536\) | 1.36035e8i | 0.883398i | ||||||||
\(537\) | −2.82952e7 | −0.182722 | ||||||||
\(538\) | −2.06021e8 | −1.32302 | ||||||||
\(539\) | 8.81453e7i | 0.562902i | ||||||||
\(540\) | − | 5.36346e6i | − | 0.0340615i | ||||||
\(541\) | 1.43573e8 | 0.906739 | 0.453370 | − | 0.891323i | \(-0.350222\pi\) | ||||
0.453370 | + | 0.891323i | \(0.350222\pi\) | |||||||
\(542\) | 1.23214e8 | 0.773859 | ||||||||
\(543\) | 8.35790e7i | 0.522033i | ||||||||
\(544\) | 6.39623e7i | 0.397308i | ||||||||
\(545\) | −1.14706e8 | −0.708591 | ||||||||
\(546\) | − | 2.97798e7i | − | 0.182955i | ||||||
\(547\) | 2.07872e8 | 1.27009 | 0.635045 | − | 0.772475i | \(-0.280982\pi\) | ||||
0.635045 | + | 0.772475i | \(0.280982\pi\) | |||||||
\(548\) | 2.19473e7i | 0.133364i | ||||||||
\(549\) | − | 8.10489e7i | − | 0.489813i | ||||||
\(550\) | 1.06691e8i | 0.641271i | ||||||||
\(551\) | 5.62619e7i | 0.336325i | ||||||||
\(552\) | 3.45554e7 | + | 9.98001e7i | 0.205446 | + | 0.593354i | ||||
\(553\) | 1.33606e8 | 0.790044 | ||||||||
\(554\) | 1.94475e8 | 1.14376 | ||||||||
\(555\) | −3.73321e7 | −0.218375 | ||||||||
\(556\) | −6.05351e7 | −0.352195 | ||||||||
\(557\) | − | 2.03427e8i | − | 1.17718i | −0.808431 | − | 0.588591i | \(-0.799683\pi\) | ||
0.808431 | − | 0.588591i | \(-0.200317\pi\) | |||||||
\(558\) | −4.22224e7 | −0.243019 | ||||||||
\(559\) | 3.97376e7i | 0.227492i | ||||||||
\(560\) | 2.86809e7 | 0.163316 | ||||||||
\(561\) | −6.14748e7 | −0.348184 | ||||||||
\(562\) | − | 7.69812e7i | − | 0.433686i | ||||||
\(563\) | − | 4.02092e7i | − | 0.225320i | −0.993634 | − | 0.112660i | \(-0.964063\pi\) | ||
0.993634 | − | 0.112660i | \(-0.0359371\pi\) | |||||||
\(564\) | −2.30135e7 | −0.128276 | ||||||||
\(565\) | −1.56986e8 | −0.870393 | ||||||||
\(566\) | − | 2.19614e8i | − | 1.21118i | ||||||
\(567\) | 1.37946e7i | 0.0756763i | ||||||||
\(568\) | −2.43492e8 | −1.32874 | ||||||||
\(569\) | 2.17982e8i | 1.18327i | 0.806205 | + | 0.591636i | \(0.201518\pi\) | ||||
−0.806205 | + | 0.591636i | \(0.798482\pi\) | |||||||
\(570\) | −6.08431e7 | −0.328539 | ||||||||
\(571\) | − | 1.53635e8i | − | 0.825243i | −0.910903 | − | 0.412621i | \(-0.864613\pi\) | ||
0.910903 | − | 0.412621i | \(-0.135387\pi\) | |||||||
\(572\) | 4.22246e7i | 0.225620i | ||||||||
\(573\) | 9.76256e7i | 0.518919i | ||||||||
\(574\) | − | 2.74349e7i | − | 0.145067i | ||||||
\(575\) | −4.77630e7 | − | 1.37945e8i | −0.251240 | − | 0.725611i | ||||
\(576\) | 6.67511e7 | 0.349294 | ||||||||
\(577\) | 4.00536e7 | 0.208504 | 0.104252 | − | 0.994551i | \(-0.466755\pi\) | ||||
0.104252 | + | 0.994551i | \(0.466755\pi\) | |||||||
\(578\) | 1.02919e8 | 0.532982 | ||||||||
\(579\) | 2.00466e8 | 1.03277 | ||||||||
\(580\) | − | 7.82137e6i | − | 0.0400866i | ||||||
\(581\) | −1.68417e8 | −0.858731 | ||||||||
\(582\) | − | 2.72214e7i | − | 0.138084i | ||||||
\(583\) | 7.84908e7 | 0.396108 | ||||||||
\(584\) | −2.75600e8 | −1.38370 | ||||||||
\(585\) | − | 1.88074e7i | − | 0.0939424i | ||||||
\(586\) | − | 2.12447e8i | − | 1.05574i | ||||||
\(587\) | −1.79154e8 | −0.885750 | −0.442875 | − | 0.896583i | \(-0.646042\pi\) | ||||
−0.442875 | + | 0.896583i | \(0.646042\pi\) | |||||||
\(588\) | −2.31163e7 | −0.113707 | ||||||||
\(589\) | − | 2.78121e8i | − | 1.36109i | ||||||
\(590\) | − | 6.13010e7i | − | 0.298477i | ||||||
\(591\) | 1.48610e8 | 0.719924 | ||||||||
\(592\) | − | 8.10649e7i | − | 0.390722i | ||||||
\(593\) | 3.94002e8 | 1.88944 | 0.944722 | − | 0.327872i | \(-0.106331\pi\) | ||||
0.944722 | + | 0.327872i | \(0.106331\pi\) | |||||||
\(594\) | 3.36843e7i | 0.160720i | ||||||||
\(595\) | − | 3.97021e7i | − | 0.188479i | ||||||
\(596\) | 1.56401e7i | 0.0738755i | ||||||||
\(597\) | − | 2.74354e7i | − | 0.128940i | ||||||
\(598\) | 3.25539e7 | + | 9.40198e7i | 0.152230 | + | 0.439659i | ||||
\(599\) | 3.26132e8 | 1.51745 | 0.758723 | − | 0.651413i | \(-0.225823\pi\) | ||||
0.758723 | + | 0.651413i | \(0.225823\pi\) | |||||||
\(600\) | −1.04147e8 | −0.482160 | ||||||||
\(601\) | 3.34444e8 | 1.54064 | 0.770318 | − | 0.637659i | \(-0.220097\pi\) | ||||
0.770318 | + | 0.637659i | \(0.220097\pi\) | |||||||
\(602\) | 4.59639e7 | 0.210682 | ||||||||
\(603\) | − | 5.93644e7i | − | 0.270753i | ||||||
\(604\) | 9.05711e6 | 0.0411035 | ||||||||
\(605\) | − | 1.09255e7i | − | 0.0493375i | ||||||
\(606\) | −9.91353e7 | −0.445462 | ||||||||
\(607\) | −2.70163e8 | −1.20798 | −0.603991 | − | 0.796991i | \(-0.706424\pi\) | ||||
−0.603991 | + | 0.796991i | \(0.706424\pi\) | |||||||
\(608\) | 2.30858e8i | 1.02715i | ||||||||
\(609\) | 2.01163e7i | 0.0890626i | ||||||||
\(610\) | 1.27815e8 | 0.563109 | ||||||||
\(611\) | −8.06989e7 | −0.353789 | ||||||||
\(612\) | − | 1.61219e7i | − | 0.0703335i | ||||||
\(613\) | − | 1.66910e8i | − | 0.724606i | −0.932060 | − | 0.362303i | \(-0.881991\pi\) | ||
0.932060 | − | 0.362303i | \(-0.118009\pi\) | |||||||
\(614\) | −3.48558e8 | −1.50581 | ||||||||
\(615\) | − | 1.73265e7i | − | 0.0744877i | ||||||
\(616\) | 1.81793e8 | 0.777740 | ||||||||
\(617\) | − | 3.40980e6i | − | 0.0145169i | −0.999974 | − | 0.00725843i | \(-0.997690\pi\) | ||
0.999974 | − | 0.00725843i | \(-0.00231045\pi\) | |||||||
\(618\) | 3.56782e7i | 0.151160i | ||||||||
\(619\) | − | 7.78890e7i | − | 0.328401i | −0.986427 | − | 0.164200i | \(-0.947496\pi\) | ||
0.986427 | − | 0.164200i | \(-0.0525043\pi\) | |||||||
\(620\) | 3.86636e7i | 0.162228i | ||||||||
\(621\) | −1.50796e7 | − | 4.35518e7i | −0.0629674 | − | 0.181857i | ||||
\(622\) | 1.82105e8 | 0.756748 | ||||||||
\(623\) | −1.83501e8 | −0.758882 | ||||||||
\(624\) | 4.08395e7 | 0.168084 | ||||||||
\(625\) | 8.72821e7 | 0.357508 | ||||||||
\(626\) | − | 2.28474e8i | − | 0.931352i | ||||||
\(627\) | −2.21880e8 | −0.900153 | ||||||||
\(628\) | 6.00732e7i | 0.242550i | ||||||||
\(629\) | −1.12216e8 | −0.450923 | ||||||||
\(630\) | −2.17542e7 | −0.0870006 | ||||||||
\(631\) | − | 2.97365e8i | − | 1.18359i | −0.806089 | − | 0.591795i | \(-0.798420\pi\) | ||
0.806089 | − | 0.591795i | \(-0.201580\pi\) | |||||||
\(632\) | 3.18465e8i | 1.26157i | ||||||||
\(633\) | −1.59068e7 | −0.0627150 | ||||||||
\(634\) | 2.05075e8 | 0.804720 | ||||||||
\(635\) | 6.06291e7i | 0.236788i | ||||||||
\(636\) | 2.05844e7i | 0.0800142i | ||||||||
\(637\) | −8.10593e7 | −0.313606 | ||||||||
\(638\) | 4.91209e7i | 0.189149i | ||||||||
\(639\) | 1.06258e8 | 0.407247 | ||||||||
\(640\) | 1.79040e7i | 0.0682982i | ||||||||
\(641\) | 1.39938e8i | 0.531328i | 0.964066 | + | 0.265664i | \(0.0855912\pi\) | ||||
−0.964066 | + | 0.265664i | \(0.914409\pi\) | |||||||
\(642\) | 2.13670e8i | 0.807493i | ||||||||
\(643\) | 3.06153e8i | 1.15161i | 0.817587 | + | 0.575805i | \(0.195311\pi\) | ||||
−0.817587 | + | 0.575805i | \(0.804689\pi\) | |||||||
\(644\) | −6.31478e7 | + | 2.18647e7i | −0.236429 | + | 0.0818625i | ||||
\(645\) | 2.90284e7 | 0.108179 | ||||||||
\(646\) | −1.82887e8 | −0.678400 | ||||||||
\(647\) | 2.49111e8 | 0.919771 | 0.459885 | − | 0.887978i | \(-0.347890\pi\) | ||||
0.459885 | + | 0.887978i | \(0.347890\pi\) | |||||||
\(648\) | −3.28809e7 | −0.120842 | ||||||||
\(649\) | − | 2.23550e8i | − | 0.817788i | ||||||
\(650\) | −9.81145e7 | −0.357267 | ||||||||
\(651\) | − | 9.94412e7i | − | 0.360432i | ||||||
\(652\) | 1.11913e8 | 0.403772 | ||||||||
\(653\) | −4.16924e8 | −1.49733 | −0.748665 | − | 0.662948i | \(-0.769305\pi\) | ||||
−0.748665 | + | 0.662948i | \(0.769305\pi\) | |||||||
\(654\) | 1.88924e8i | 0.675390i | ||||||||
\(655\) | − | 8.95309e7i | − | 0.318602i | ||||||
\(656\) | 3.76237e7 | 0.133275 | ||||||||
\(657\) | 1.20269e8 | 0.424090 | ||||||||
\(658\) | 9.33431e7i | 0.327646i | ||||||||
\(659\) | 2.42010e8i | 0.845622i | 0.906218 | + | 0.422811i | \(0.138957\pi\) | ||||
−0.906218 | + | 0.422811i | \(0.861043\pi\) | |||||||
\(660\) | 3.08452e7 | 0.107289 | ||||||||
\(661\) | − | 4.85278e8i | − | 1.68030i | −0.542356 | − | 0.840149i | \(-0.682468\pi\) | ||
0.542356 | − | 0.840149i | \(-0.317532\pi\) | |||||||
\(662\) | 2.13413e8 | 0.735610 | ||||||||
\(663\) | − | 5.65329e7i | − | 0.193982i | ||||||
\(664\) | − | 4.01439e8i | − | 1.37125i | ||||||
\(665\) | − | 1.43296e8i | − | 0.487270i | ||||||
\(666\) | 6.14872e7i | 0.208143i | ||||||||
\(667\) | −2.19902e7 | − | 6.35102e7i | −0.0741056 | − | 0.214026i | ||||
\(668\) | −8.16752e7 | −0.274006 | ||||||||
\(669\) | −8.05706e7 | −0.269090 | ||||||||
\(670\) | 9.36183e7 | 0.311269 | ||||||||
\(671\) | 4.66111e8 | 1.54284 | ||||||||
\(672\) | 8.25426e7i | 0.272001i | ||||||||
\(673\) | −3.54234e8 | −1.16211 | −0.581053 | − | 0.813866i | \(-0.697359\pi\) | ||||
−0.581053 | + | 0.813866i | \(0.697359\pi\) | |||||||
\(674\) | − | 3.66996e8i | − | 1.19862i | ||||||
\(675\) | 4.54486e7 | 0.147778 | ||||||||
\(676\) | 7.46513e7 | 0.241656 | ||||||||
\(677\) | 1.26295e8i | 0.407023i | 0.979073 | + | 0.203512i | \(0.0652354\pi\) | ||||
−0.979073 | + | 0.203512i | \(0.934765\pi\) | |||||||
\(678\) | 2.58561e8i | 0.829611i | ||||||||
\(679\) | 6.41113e7 | 0.204798 | ||||||||
\(680\) | 9.46341e7 | 0.300968 | ||||||||
\(681\) | − | 1.09398e8i | − | 0.346391i | ||||||
\(682\) | − | 2.42820e8i | − | 0.765477i | ||||||
\(683\) | 2.78165e7 | 0.0873054 | 0.0436527 | − | 0.999047i | \(-0.486101\pi\) | ||||
0.0436527 | + | 0.999047i | \(0.486101\pi\) | |||||||
\(684\) | − | 5.81887e7i | − | 0.181832i | ||||||
\(685\) | 5.62196e7 | 0.174910 | ||||||||
\(686\) | 2.68646e8i | 0.832163i | ||||||||
\(687\) | − | 1.80225e8i | − | 0.555833i | ||||||
\(688\) | 6.30340e7i | 0.193557i | ||||||||
\(689\) | 7.21810e7i | 0.220681i | ||||||||
\(690\) | 6.86817e7 | − | 2.37807e7i | 0.209071 | − | 0.0723899i | ||||
\(691\) | 6.07780e8 | 1.84210 | 0.921048 | − | 0.389449i | \(-0.127335\pi\) | ||||
0.921048 | + | 0.389449i | \(0.127335\pi\) | |||||||
\(692\) | −8.41976e7 | −0.254086 | ||||||||
\(693\) | −7.93325e7 | −0.238370 | ||||||||
\(694\) | −1.71893e8 | −0.514256 | ||||||||
\(695\) | 1.55065e8i | 0.461912i | ||||||||
\(696\) | −4.79492e7 | −0.142218 | ||||||||
\(697\) | − | 5.20813e7i | − | 0.153810i | ||||||
\(698\) | 2.08710e7 | 0.0613730 | ||||||||
\(699\) | −2.09296e8 | −0.612814 | ||||||||
\(700\) | − | 6.58980e7i | − | 0.192122i | ||||||
\(701\) | − | 3.75291e8i | − | 1.08947i | −0.838609 | − | 0.544733i | \(-0.816631\pi\) | ||
0.838609 | − | 0.544733i | \(-0.183369\pi\) | |||||||
\(702\) | −3.09765e7 | −0.0895407 | ||||||||
\(703\) | −4.05019e8 | −1.16576 | ||||||||
\(704\) | 3.83885e8i | 1.10023i | ||||||||
\(705\) | 5.89507e7i | 0.168237i | ||||||||
\(706\) | −2.80797e8 | −0.797956 | ||||||||
\(707\) | − | 2.33481e8i | − | 0.660684i | ||||||
\(708\) | 5.86266e7 | 0.165194 | ||||||||
\(709\) | − | 4.32348e8i | − | 1.21309i | −0.795048 | − | 0.606547i | \(-0.792554\pi\) | ||
0.795048 | − | 0.606547i | \(-0.207446\pi\) | |||||||
\(710\) | 1.67570e8i | 0.468188i | ||||||||
\(711\) | − | 1.38975e8i | − | 0.386659i | ||||||
\(712\) | − | 4.37394e8i | − | 1.21181i | ||||||
\(713\) | 1.08704e8 | + | 3.13952e8i | 0.299902 | + | 0.866152i | ||||
\(714\) | −6.53907e7 | −0.179648 | ||||||||
\(715\) | 1.08161e8 | 0.295906 | ||||||||
\(716\) | 4.26751e7 | 0.116261 | ||||||||
\(717\) | 1.19287e8 | 0.323621 | ||||||||
\(718\) | 2.44677e8i | 0.661028i | ||||||||
\(719\) | −1.83199e8 | −0.492875 | −0.246437 | − | 0.969159i | \(-0.579260\pi\) | ||||
−0.246437 | + | 0.969159i | \(0.579260\pi\) | |||||||
\(720\) | − | 2.98333e7i | − | 0.0799290i | ||||||
\(721\) | −8.40284e7 | −0.224192 | ||||||||
\(722\) | −3.60734e8 | −0.958462 | ||||||||
\(723\) | − | 1.46028e8i | − | 0.386386i | ||||||
\(724\) | − | 1.26055e8i | − | 0.332157i | ||||||
\(725\) | 6.62763e7 | 0.173918 | ||||||||
\(726\) | −1.79947e7 | −0.0470258 | ||||||||
\(727\) | 3.32462e8i | 0.865244i | 0.901575 | + | 0.432622i | \(0.142412\pi\) | ||||
−0.901575 | + | 0.432622i | \(0.857588\pi\) | |||||||
\(728\) | 1.67178e8i | 0.433297i | ||||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 1.89666e8i | 0.487551i | ||||||||
\(731\) | 8.72560e7 | 0.223380 | ||||||||
\(732\) | 1.22239e8i | 0.311656i | ||||||||
\(733\) | 5.89347e8i | 1.49644i | 0.663450 | + | 0.748220i | \(0.269091\pi\) | ||||
−0.663450 | + | 0.748220i | \(0.730909\pi\) | |||||||
\(734\) | 1.20961e8i | 0.305884i | ||||||||
\(735\) | 5.92140e7i | 0.149129i | ||||||||
\(736\) | −9.02318e7 | − | 2.60600e8i | −0.226322 | − | 0.653644i | ||||
\(737\) | 3.41403e8 | 0.852836 | ||||||||
\(738\) | −2.85373e7 | −0.0709976 | ||||||||
\(739\) | 5.99727e8 | 1.48601 | 0.743003 | − | 0.669288i | \(-0.233401\pi\) | ||||
0.743003 | + | 0.669288i | \(0.233401\pi\) | |||||||
\(740\) | 5.63046e7 | 0.138947 | ||||||||
\(741\) | − | 2.04043e8i | − | 0.501497i | ||||||
\(742\) | 8.34906e7 | 0.204374 | ||||||||
\(743\) | − | 6.45667e7i | − | 0.157414i | −0.996898 | − | 0.0787068i | \(-0.974921\pi\) | ||
0.996898 | − | 0.0787068i | \(-0.0250791\pi\) | |||||||
\(744\) | 2.37029e8 | 0.575549 | ||||||||
\(745\) | 4.00631e7 | 0.0968894 | ||||||||
\(746\) | − | 4.34181e8i | − | 1.04581i | ||||||
\(747\) | 1.75184e8i | 0.420275i | ||||||||
\(748\) | 9.27169e7 | 0.221541 | ||||||||
\(749\) | −5.03231e8 | −1.19763 | ||||||||
\(750\) | 1.65012e8i | 0.391140i | ||||||||
\(751\) | 8.08683e7i | 0.190923i | 0.995433 | + | 0.0954616i | \(0.0304327\pi\) | ||||
−0.995433 | + | 0.0954616i | \(0.969567\pi\) | |||||||
\(752\) | −1.28009e8 | −0.301014 | ||||||||
\(753\) | − | 1.71431e6i | − | 0.00401517i | ||||||
\(754\) | −4.51721e7 | −0.105379 | ||||||||
\(755\) | − | 2.32004e7i | − | 0.0539082i | ||||||
\(756\) | − | 2.08052e7i | − | 0.0481510i | ||||||
\(757\) | 6.29360e7i | 0.145081i | 0.997365 | + | 0.0725406i | \(0.0231107\pi\) | ||||
−0.997365 | + | 0.0725406i | \(0.976889\pi\) | |||||||
\(758\) | 3.30113e8i | 0.757976i | ||||||||
\(759\) | 2.50466e8 | − | 8.67227e7i | 0.572826 | − | 0.198339i | ||||
\(760\) | 3.41562e8 | 0.778088 | ||||||||
\(761\) | −5.45904e8 | −1.23869 | −0.619344 | − | 0.785119i | \(-0.712602\pi\) | ||||
−0.619344 | + | 0.785119i | \(0.712602\pi\) | |||||||
\(762\) | 9.98583e7 | 0.225694 | ||||||||
\(763\) | −4.44950e8 | −1.00170 | ||||||||
\(764\) | − | 1.47240e8i | − | 0.330176i | ||||||
\(765\) | −4.12974e7 | −0.0922441 | ||||||||
\(766\) | 6.49548e8i | 1.44519i | ||||||||
\(767\) | 2.05579e8 | 0.455609 | ||||||||
\(768\) | −2.44565e8 | −0.539897 | ||||||||
\(769\) | 1.19089e8i | 0.261874i | 0.991391 | + | 0.130937i | \(0.0417985\pi\) | ||||
−0.991391 | + | 0.130937i | \(0.958201\pi\) | |||||||
\(770\) | − | 1.25108e8i | − | 0.274040i | ||||||
\(771\) | 8.17100e7 | 0.178284 | ||||||||
\(772\) | −3.02345e8 | −0.657129 | ||||||||
\(773\) | 3.69267e8i | 0.799470i | 0.916631 | + | 0.399735i | \(0.130898\pi\) | ||||
−0.916631 | + | 0.399735i | \(0.869102\pi\) | |||||||
\(774\) | − | 4.78108e7i | − | 0.103111i | ||||||
\(775\) | −3.27625e8 | −0.703837 | ||||||||
\(776\) | 1.52816e8i | 0.327027i | ||||||||
\(777\) | −1.44813e8 | −0.308706 | ||||||||
\(778\) | 1.89295e8i | 0.401977i | ||||||||
\(779\) | − | 1.87976e8i | − | 0.397641i | ||||||
\(780\) | 2.83655e7i | 0.0597733i | ||||||||
\(781\) | 6.11086e8i | 1.28277i | ||||||||
\(782\) | 2.06449e8 | − | 7.14821e7i | 0.431710 | − | 0.149478i | ||||
\(783\) | 2.09246e7 | 0.0435884 | ||||||||
\(784\) | −1.28581e8 | −0.266826 | ||||||||
\(785\) | 1.53882e8 | 0.318110 | ||||||||
\(786\) | −1.47460e8 | −0.303674 | ||||||||
\(787\) | 9.26119e8i | 1.89995i | 0.312324 | + | 0.949976i | \(0.398893\pi\) | ||||
−0.312324 | + | 0.949976i | \(0.601107\pi\) | |||||||
\(788\) | −2.24136e8 | −0.458070 | ||||||||
\(789\) | 3.14153e8i | 0.639602i | ||||||||
\(790\) | 2.19165e8 | 0.444519 | ||||||||
\(791\) | −6.08957e8 | −1.23043 | ||||||||
\(792\) | − | 1.89098e8i | − | 0.380637i | ||||||
\(793\) | 4.28640e8i | 0.859555i | ||||||||
\(794\) | −3.23523e7 | −0.0646315 | ||||||||
\(795\) | 5.27284e7 | 0.104940 | ||||||||
\(796\) | 4.13783e7i | 0.0820415i | ||||||||
\(797\) | − | 7.70727e8i | − | 1.52239i | −0.648523 | − | 0.761195i | \(-0.724613\pi\) | ||
0.648523 | − | 0.761195i | \(-0.275387\pi\) | |||||||
\(798\) | −2.36014e8 | −0.464439 | ||||||||
\(799\) | 1.77199e8i | 0.347393i | ||||||||
\(800\) | 2.71950e8 | 0.531152 | ||||||||
\(801\) | 1.90875e8i | 0.371407i | ||||||||
\(802\) | − | 5.38919e8i | − | 1.04472i | ||||||
\(803\) | 6.91666e8i | 1.33582i | ||||||||
\(804\) | 8.95339e7i | 0.172274i | ||||||||
\(805\) | 5.60078e7 | + | 1.61757e8i | 0.107365 | + | 0.310082i | ||||
\(806\) | 2.23300e8 | 0.426465 | ||||||||
\(807\) | −5.04714e8 | −0.960339 | ||||||||
\(808\) | 5.56527e8 | 1.05500 | ||||||||
\(809\) | 5.09249e8 | 0.961800 | 0.480900 | − | 0.876775i | \(-0.340310\pi\) | ||||
0.480900 | + | 0.876775i | \(0.340310\pi\) | |||||||
\(810\) | 2.26284e7i | 0.0425793i | ||||||||
\(811\) | −9.15685e8 | −1.71666 | −0.858328 | − | 0.513101i | \(-0.828497\pi\) | ||||
−0.858328 | + | 0.513101i | \(0.828497\pi\) | |||||||
\(812\) | − | 3.03395e7i | − | 0.0566684i | ||||||
\(813\) | 3.01851e8 | 0.561721 | ||||||||
\(814\) | −3.53612e8 | −0.655622 | ||||||||
\(815\) | − | 2.86672e8i | − | 0.529556i | ||||||
\(816\) | − | 8.96755e7i | − | 0.165045i | ||||||
\(817\) | 3.14932e8 | 0.577498 | ||||||||
\(818\) | 6.46049e7 | 0.118034 | ||||||||
\(819\) | − | 7.29550e7i | − | 0.132802i | ||||||
\(820\) | 2.61319e7i | 0.0473947i | ||||||||
\(821\) | 4.22090e8 | 0.762738 | 0.381369 | − | 0.924423i | \(-0.375453\pi\) | ||||
0.381369 | + | 0.924423i | \(0.375453\pi\) | |||||||
\(822\) | − | 9.25956e7i | − | 0.166715i | ||||||
\(823\) | −8.84464e8 | −1.58665 | −0.793324 | − | 0.608800i | \(-0.791651\pi\) | ||||
−0.793324 | + | 0.608800i | \(0.791651\pi\) | |||||||
\(824\) | − | 2.00291e8i | − | 0.357997i | ||||||
\(825\) | 2.61374e8i | 0.465479i | ||||||||
\(826\) | − | 2.37790e8i | − | 0.421943i | ||||||
\(827\) | − | 1.06398e9i | − | 1.88111i | −0.339636 | − | 0.940557i | \(-0.610304\pi\) | ||
0.339636 | − | 0.940557i | \(-0.389696\pi\) | |||||||
\(828\) | 2.27432e7 | + | 6.56852e7i | 0.0400646 | + | 0.115712i | ||||
\(829\) | 8.34964e8 | 1.46556 | 0.732781 | − | 0.680465i | \(-0.238222\pi\) | ||||
0.732781 | + | 0.680465i | \(0.238222\pi\) | |||||||
\(830\) | −2.76267e8 | −0.483165 | ||||||||
\(831\) | 4.76428e8 | 0.830223 | ||||||||
\(832\) | −3.53024e8 | −0.612963 | ||||||||
\(833\) | 1.77990e8i | 0.307937i | ||||||||
\(834\) | 2.55397e8 | 0.440269 | ||||||||
\(835\) | 2.09217e8i | 0.359366i | ||||||||
\(836\) | 3.34642e8 | 0.572745 | ||||||||
\(837\) | −1.03437e8 | −0.176400 | ||||||||
\(838\) | 1.89786e8i | 0.322502i | ||||||||
\(839\) | − | 3.90151e8i | − | 0.660613i | −0.943874 | − | 0.330307i | \(-0.892848\pi\) | ||
0.943874 | − | 0.330307i | \(-0.107152\pi\) | |||||||
\(840\) | 1.22124e8 | 0.206046 | ||||||||
\(841\) | −5.64310e8 | −0.948701 | ||||||||
\(842\) | − | 5.49693e8i | − | 0.920839i | ||||||
\(843\) | − | 1.88589e8i | − | 0.314800i | ||||||
\(844\) | 2.39908e7 | 0.0399040 | ||||||||
\(845\) | − | 1.91224e8i | − | 0.316937i | ||||||
\(846\) | 9.70939e7 | 0.160354 | ||||||||
\(847\) | − | 4.23808e7i | − | 0.0697459i | ||||||
\(848\) | 1.14497e8i | 0.187762i | ||||||||
\(849\) | − | 5.38012e8i | − | 0.879162i | ||||||
\(850\) | 2.15440e8i | 0.350808i | ||||||||
\(851\) | 4.57198e8 | − | 1.58303e8i | 0.741850 | − | 0.256862i | ||||
\(852\) | −1.60259e8 | −0.259121 | ||||||||
\(853\) | −1.58229e8 | −0.254940 | −0.127470 | − | 0.991842i | \(-0.540686\pi\) | ||||
−0.127470 | + | 0.991842i | \(0.540686\pi\) | |||||||
\(854\) | 4.95802e8 | 0.796039 | ||||||||
\(855\) | −1.49054e8 | −0.238477 | ||||||||
\(856\) | − | 1.19950e9i | − | 1.91241i | ||||||
\(857\) | −3.52002e8 | −0.559245 | −0.279623 | − | 0.960110i | \(-0.590209\pi\) | ||||
−0.279623 | + | 0.960110i | \(0.590209\pi\) | |||||||
\(858\) | − | 1.78145e8i | − | 0.282041i | ||||||
\(859\) | −5.14413e7 | −0.0811582 | −0.0405791 | − | 0.999176i | \(-0.512920\pi\) | ||||
−0.0405791 | + | 0.999176i | \(0.512920\pi\) | |||||||
\(860\) | −4.37810e7 | −0.0688319 | ||||||||
\(861\) | − | 6.72103e7i | − | 0.105300i | ||||||
\(862\) | − | 2.59161e8i | − | 0.404620i | ||||||
\(863\) | 4.96102e8 | 0.771861 | 0.385930 | − | 0.922528i | \(-0.373881\pi\) | ||||
0.385930 | + | 0.922528i | \(0.373881\pi\) | |||||||
\(864\) | 8.58594e7 | 0.133121 | ||||||||
\(865\) | 2.15678e8i | 0.333240i | ||||||||
\(866\) | 6.69290e8i | 1.03053i | ||||||||
\(867\) | 2.52132e8 | 0.386876 | ||||||||
\(868\) | 1.49978e8i | 0.229334i | ||||||||
\(869\) | 7.99243e8 | 1.21792 | ||||||||
\(870\) | 3.29983e7i | 0.0501111i | ||||||||
\(871\) | 3.13958e8i | 0.475135i | ||||||||
\(872\) | − | 1.06059e9i | − | 1.59954i | ||||||
\(873\) | − | 6.66874e7i | − | 0.100231i | ||||||
\(874\) | 7.45134e8 | − | 2.57999e8i | 1.11609 | − | 0.386442i | ||||
\(875\) | −3.88632e8 | −0.580116 | ||||||||
\(876\) | −1.81391e8 | −0.269838 | ||||||||
\(877\) | 4.89169e8 | 0.725203 | 0.362602 | − | 0.931944i | \(-0.381889\pi\) | ||||
0.362602 | + | 0.931944i | \(0.381889\pi\) | |||||||
\(878\) | −3.34635e8 | −0.494410 | ||||||||
\(879\) | − | 5.20455e8i | − | 0.766332i | ||||||
\(880\) | 1.71571e8 | 0.251765 | ||||||||
\(881\) | − | 3.68496e8i | − | 0.538896i | −0.963015 | − | 0.269448i | \(-0.913159\pi\) | ||
0.963015 | − | 0.269448i | \(-0.0868412\pi\) | |||||||
\(882\) | 9.75275e7 | 0.142142 | ||||||||
\(883\) | 7.59012e8 | 1.10247 | 0.551235 | − | 0.834350i | \(-0.314157\pi\) | ||||
0.551235 | + | 0.834350i | \(0.314157\pi\) | |||||||
\(884\) | 8.52634e7i | 0.123426i | ||||||||
\(885\) | − | 1.50176e8i | − | 0.216656i | ||||||
\(886\) | −9.29603e8 | −1.33658 | ||||||||
\(887\) | −2.70519e8 | −0.387638 | −0.193819 | − | 0.981037i | \(-0.562087\pi\) | ||||
−0.193819 | + | 0.981037i | \(0.562087\pi\) | |||||||
\(888\) | − | 3.45178e8i | − | 0.492951i | ||||||
\(889\) | 2.35184e8i | 0.334736i | ||||||||
\(890\) | −3.01011e8 | −0.426985 | ||||||||
\(891\) | 8.25203e7i | 0.116662i | ||||||||
\(892\) | 1.21517e8 | 0.171216 | ||||||||
\(893\) | 6.39562e8i | 0.898107i | ||||||||
\(894\) | − | 6.59854e7i | − | 0.0923496i | ||||||
\(895\) | − | 1.09315e8i | − | 0.152479i | ||||||
\(896\) | 6.94504e7i | 0.0965497i | ||||||||
\(897\) | 7.97511e7 | + | 2.30331e8i | 0.110499 | + | 0.319135i | ||||
\(898\) | 1.97046e8 | 0.272107 | ||||||||
\(899\) | −1.50839e8 | −0.207603 | ||||||||
\(900\) | −6.85460e7 | −0.0940274 | ||||||||
\(901\) | 1.58495e8 | 0.216691 | ||||||||
\(902\) | − | 1.64117e8i | − | 0.223633i | ||||||
\(903\) | 1.12603e8 | 0.152928 | ||||||||
\(904\) | − | 1.45151e9i | − | 1.96479i | ||||||
\(905\) | −3.22898e8 | −0.435631 | ||||||||
\(906\) | −3.82119e7 | −0.0513823 | ||||||||
\(907\) | 1.23189e9i | 1.65101i | 0.564394 | + | 0.825505i | \(0.309110\pi\) | ||||
−0.564394 | + | 0.825505i | \(0.690890\pi\) | |||||||
\(908\) | 1.64995e8i | 0.220400i | ||||||||
\(909\) | −2.42863e8 | −0.323348 | ||||||||
\(910\) | 1.15051e8 | 0.152674 | ||||||||
\(911\) | − | 1.21327e9i | − | 1.60473i | −0.596832 | − | 0.802366i | \(-0.703574\pi\) | ||
0.596832 | − | 0.802366i | \(-0.296426\pi\) | |||||||
\(912\) | − | 3.23665e8i | − | 0.426688i | ||||||
\(913\) | −1.00748e9 | −1.32381 | ||||||||
\(914\) | − | 2.31941e8i | − | 0.303766i | ||||||
\(915\) | 3.13123e8 | 0.408744 | ||||||||
\(916\) | 2.71817e8i | 0.353663i | ||||||||
\(917\) | − | 3.47295e8i | − | 0.450392i | ||||||
\(918\) | 6.80182e7i | 0.0879220i | ||||||||
\(919\) | − | 6.64269e8i | − | 0.855850i | −0.903814 | − | 0.427925i | \(-0.859245\pi\) | ||
0.903814 | − | 0.427925i | \(-0.140755\pi\) | |||||||
\(920\) | −3.85566e8 | + | 1.33501e8i | −0.495148 | + | 0.171443i | ||||
\(921\) | −8.53902e8 | −1.09302 | ||||||||
\(922\) | 2.07767e8 | 0.265084 | ||||||||
\(923\) | −5.61961e8 | −0.714663 | ||||||||
\(924\) | 1.19650e8 | 0.151669 | ||||||||
\(925\) | 4.77110e8i | 0.602828i | ||||||||
\(926\) | 1.06645e9 | 1.34310 | ||||||||
\(927\) | 8.74049e7i | 0.109723i | ||||||||
\(928\) | 1.25206e8 | 0.156669 | ||||||||
\(929\) | −9.67171e8 | −1.20630 | −0.603151 | − | 0.797627i | \(-0.706088\pi\) | ||||
−0.603151 | + | 0.797627i | \(0.706088\pi\) | |||||||
\(930\) | − | 1.63121e8i | − | 0.202797i | ||||||
\(931\) | 6.42418e8i | 0.796102i | ||||||||
\(932\) | 3.15662e8 | 0.389919 | ||||||||
\(933\) | 4.46124e8 | 0.549301 | ||||||||
\(934\) | − | 2.27847e8i | − | 0.279642i | ||||||
\(935\) | − | 2.37501e8i | − | 0.290556i | ||||||
\(936\) | 1.73896e8 | 0.212062 | ||||||||
\(937\) | − | 2.93220e8i | − | 0.356430i | −0.983992 | − | 0.178215i | \(-0.942968\pi\) | ||
0.983992 | − | 0.178215i | \(-0.0570323\pi\) | |||||||
\(938\) | 3.63150e8 | 0.440026 | ||||||||
\(939\) | − | 5.59718e8i | − | 0.676040i | ||||||
\(940\) | − | 8.89100e7i | − | 0.107045i | ||||||
\(941\) | 1.21758e9i | 1.46127i | 0.682769 | + | 0.730635i | \(0.260776\pi\) | ||||
−0.682769 | + | 0.730635i | \(0.739224\pi\) | |||||||
\(942\) | − | 2.53448e8i | − | 0.303205i | ||||||
\(943\) | 7.34712e7 | + | 2.12194e8i | 0.0876157 | + | 0.253045i | ||||
\(944\) | 3.26100e8 | 0.387646 | ||||||||
\(945\) | −5.32938e7 | −0.0631512 | ||||||||
\(946\) | 2.74959e8 | 0.324784 | ||||||||
\(947\) | 8.42419e8 | 0.991924 | 0.495962 | − | 0.868344i | \(-0.334816\pi\) | ||||
0.495962 | + | 0.868344i | \(0.334816\pi\) | |||||||
\(948\) | 2.09603e8i | 0.246022i | ||||||||
\(949\) | −6.36063e8 | −0.744220 | ||||||||
\(950\) | 7.77586e8i | 0.906938i | ||||||||
\(951\) | 5.02395e8 | 0.584122 | ||||||||
\(952\) | 3.67091e8 | 0.425464 | ||||||||
\(953\) | 1.79752e8i | 0.207680i | 0.994594 | + | 0.103840i | \(0.0331129\pi\) | ||||
−0.994594 | + | 0.103840i | \(0.966887\pi\) | |||||||
\(954\) | − | 8.68455e7i | − | 0.100023i | ||||||
\(955\) | −3.77165e8 | −0.433033 | ||||||||
\(956\) | −1.79910e8 | −0.205912 | ||||||||
\(957\) | 1.20337e8i | 0.137298i | ||||||||
\(958\) | 2.55633e8i | 0.290750i | ||||||||
\(959\) | 2.18079e8 | 0.247262 | ||||||||
\(960\) | 2.57885e8i | 0.291482i | ||||||||
\(961\) | −1.41858e8 | −0.159839 | ||||||||
\(962\) | − | 3.25185e8i | − | 0.365263i | ||||||
\(963\) | 5.23452e8i | 0.586135i | ||||||||
\(964\) | 2.20241e8i | 0.245848i | ||||||||
\(965\) | 7.74477e8i | 0.861839i | ||||||||
\(966\) | 2.66420e8 | − | 9.22468e7i | 0.295553 | − | 0.102334i | ||||
\(967\) | 1.27323e9 | 1.40808 | 0.704039 | − | 0.710161i | \(-0.251378\pi\) | ||||
0.704039 | + | 0.710161i | \(0.251378\pi\) | |||||||
\(968\) | 1.01019e8 | 0.111372 | ||||||||
\(969\) | −4.48039e8 | −0.492430 | ||||||||
\(970\) | 1.05167e8 | 0.115229 | ||||||||
\(971\) | − | 3.28170e7i | − | 0.0358461i | −0.999839 | − | 0.0179230i | \(-0.994295\pi\) | ||
0.999839 | − | 0.0179230i | \(-0.00570538\pi\) | |||||||
\(972\) | −2.16412e7 | −0.0235658 | ||||||||
\(973\) | 6.01505e8i | 0.652981i | ||||||||
\(974\) | −1.02075e9 | −1.10470 | ||||||||
\(975\) | −2.40362e8 | −0.259330 | ||||||||
\(976\) | 6.79932e8i | 0.731335i | ||||||||
\(977\) | 7.22268e8i | 0.774488i | 0.921977 | + | 0.387244i | \(0.126573\pi\) | ||||
−0.921977 | + | 0.387244i | \(0.873427\pi\) | |||||||
\(978\) | −4.72158e8 | −0.504744 | ||||||||
\(979\) | −1.09772e9 | −1.16988 | ||||||||
\(980\) | − | 8.93071e7i | − | 0.0948873i | ||||||
\(981\) | 4.62829e8i | 0.490246i | ||||||||
\(982\) | −4.71358e8 | −0.497756 | ||||||||
\(983\) | 1.40301e9i | 1.47706i | 0.674219 | + | 0.738532i | \(0.264481\pi\) | ||||
−0.674219 | + | 0.738532i | \(0.735519\pi\) | |||||||
\(984\) | 1.60203e8 | 0.168146 | ||||||||
\(985\) | 5.74138e8i | 0.600770i | ||||||||
\(986\) | 9.91889e7i | 0.103474i | ||||||||
\(987\) | 2.28673e8i | 0.237828i | ||||||||
\(988\) | 3.07740e8i | 0.319090i | ||||||||
\(989\) | −3.55506e8 | + | 1.23092e8i | −0.367500 | + | 0.127245i | ||||
\(990\) | −1.30135e8 | −0.134119 | ||||||||
\(991\) | 1.77438e8 | 0.182316 | 0.0911581 | − | 0.995836i | \(-0.470943\pi\) | ||||
0.0911581 | + | 0.995836i | \(0.470943\pi\) | |||||||
\(992\) | −6.18934e8 | −0.634030 | ||||||||
\(993\) | 5.22823e8 | 0.533958 | ||||||||
\(994\) | 6.50012e8i | 0.661854i | ||||||||
\(995\) | 1.05993e8 | 0.107599 | ||||||||
\(996\) | − | 2.64215e8i | − | 0.267411i | ||||||
\(997\) | −1.51194e9 | −1.52563 | −0.762813 | − | 0.646619i | \(-0.776182\pi\) | ||||
−0.762813 | + | 0.646619i | \(0.776182\pi\) | |||||||
\(998\) | −1.25469e9 | −1.26224 | ||||||||
\(999\) | 1.50632e8i | 0.151085i |
(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 | 69.7.d.a.22.18 | yes | 24 | |
3.2 | odd | 2 | 207.7.d.e.91.7 | 24 | |||
23.22 | odd | 2 | inner | 69.7.d.a.22.17 | ✓ | 24 | |
69.68 | even | 2 | 207.7.d.e.91.8 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.7.d.a.22.17 | ✓ | 24 | 23.22 | odd | 2 | inner | |
69.7.d.a.22.18 | yes | 24 | 1.1 | even | 1 | trivial | |
207.7.d.e.91.7 | 24 | 3.2 | odd | 2 | |||
207.7.d.e.91.8 | 24 | 69.68 | even | 2 |