Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,6,Mod(191,384)]
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, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.191");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.f (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: | \(61.5873868082\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 5192x^{16} + 8441320x^{12} + 4098006217x^{8} + 8949568544x^{4} + 8386816 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{87}\cdot 3^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.6 | ||
Root | \(0.860472 - 0.860472i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.191 |
Dual form | 384.6.f.e.191.5 |
$q$-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 | ||||||||
\(3\) | −10.7340 | + | 11.3040i | −0.688586 | + | 0.725154i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.25229 | 0.0760672 | 0.0380336 | − | 0.999276i | \(-0.487891\pi\) | ||||
0.0380336 | + | 0.999276i | \(0.487891\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 187.352i | 1.44515i | 0.691293 | + | 0.722575i | \(0.257041\pi\) | ||||
−0.691293 | + | 0.722575i | \(0.742959\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −12.5625 | − | 242.675i | −0.0516977 | − | 0.998663i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 712.864i | − | 1.77634i | −0.459518 | − | 0.888168i | \(-0.651978\pi\) | ||
0.459518 | − | 0.888168i | \(-0.348022\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 804.242i | 1.31986i | 0.751327 | + | 0.659930i | \(0.229414\pi\) | ||||
−0.751327 | + | 0.659930i | \(0.770586\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −45.6440 | + | 48.0680i | −0.0523788 | + | 0.0551605i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 309.664i | 0.259877i | 0.991522 | + | 0.129939i | \(0.0414780\pi\) | ||||
−0.991522 | + | 0.129939i | \(0.958522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2467.73 | 1.56824 | 0.784121 | − | 0.620608i | \(-0.213114\pi\) | ||||
0.784121 | + | 0.620608i | \(0.213114\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2117.83 | − | 2011.03i | −1.04796 | − | 0.995110i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3069.31 | 1.20982 | 0.604911 | − | 0.796293i | \(-0.293209\pi\) | ||||
0.604911 | + | 0.796293i | \(0.293209\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3106.92 | −0.994214 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2878.05 | + | 2462.87i | 0.759783 | + | 0.650177i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6325.12 | 1.39661 | 0.698303 | − | 0.715803i | \(-0.253939\pi\) | ||||
0.698303 | + | 0.715803i | \(0.253939\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9005.91i | − | 1.68315i | −0.540138 | − | 0.841576i | \(-0.681628\pi\) | ||
0.540138 | − | 0.841576i | \(-0.318372\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8058.25 | + | 7651.89i | 1.28812 | + | 1.22316i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 796.673i | 0.109928i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7350.14i | 0.882656i | 0.897346 | + | 0.441328i | \(0.145492\pi\) | ||||
−0.897346 | + | 0.441328i | \(0.854508\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9091.18 | − | 8632.73i | −0.957103 | − | 0.908838i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10389.8i | − | 0.965265i | −0.875823 | − | 0.482632i | \(-0.839681\pi\) | ||
0.875823 | − | 0.482632i | \(-0.160319\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3834.27 | 0.316236 | 0.158118 | − | 0.987420i | \(-0.449457\pi\) | ||||
0.158118 | + | 0.987420i | \(0.449457\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −53.4195 | − | 1031.92i | −0.00393250 | − | 0.0759655i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11195.2 | −0.739244 | −0.369622 | − | 0.929182i | \(-0.620513\pi\) | ||||
−0.369622 | + | 0.929182i | \(0.620513\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −18293.7 | −1.08846 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3500.45 | − | 3323.93i | −0.188451 | − | 0.178948i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7390.12 | 0.361378 | 0.180689 | − | 0.983540i | \(-0.442167\pi\) | ||||
0.180689 | + | 0.983540i | \(0.442167\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3031.30i | − | 0.135121i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −26488.6 | + | 27895.3i | −1.07987 | + | 1.13722i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9680.57i | 0.362052i | 0.983478 | + | 0.181026i | \(0.0579418\pi\) | ||||
−0.983478 | + | 0.181026i | \(0.942058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15417.8i | 0.530514i | 0.964178 | + | 0.265257i | \(0.0854568\pi\) | ||||
−0.964178 | + | 0.265257i | \(0.914543\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 45465.6 | − | 2353.62i | 1.44322 | − | 0.0747110i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3419.87i | 0.100398i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 34082.9 | 0.927577 | 0.463788 | − | 0.885946i | \(-0.346490\pi\) | ||||
0.463788 | + | 0.885946i | \(0.346490\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −32946.0 | + | 34695.6i | −0.833067 | + | 0.877308i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 17459.6 | 0.411044 | 0.205522 | − | 0.978652i | \(-0.434111\pi\) | ||||
0.205522 | + | 0.978652i | \(0.434111\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 23208.7 | 0.509735 | 0.254867 | − | 0.966976i | \(-0.417968\pi\) | ||||
0.254867 | + | 0.966976i | \(0.417968\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 33349.7 | − | 35120.7i | 0.684602 | − | 0.720958i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 133556. | 2.56707 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 41087.3i | 0.740696i | 0.928893 | + | 0.370348i | \(0.120762\pi\) | ||||
−0.928893 | + | 0.370348i | \(0.879238\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −58733.4 | + | 6097.23i | −0.994655 | + | 0.103257i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2074.09i | 0.0330470i | 0.999863 | + | 0.0165235i | \(0.00525983\pi\) | ||||
−0.999863 | + | 0.0165235i | \(0.994740\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1316.78i | 0.0197681i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −67893.8 | + | 71499.4i | −0.961683 | + | 1.01275i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 136300.i | 1.82398i | 0.410214 | + | 0.911989i | \(0.365454\pi\) | ||||
−0.410214 | + | 0.911989i | \(0.634546\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −150676. | −1.90740 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 101803. | + | 96669.4i | 1.22055 | + | 1.15900i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10493.5 | 0.119292 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −94090.8 | −1.01536 | −0.507678 | − | 0.861547i | \(-0.669496\pi\) | ||||
−0.507678 | + | 0.861547i | \(0.669496\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −172994. | + | 8955.39i | −1.77396 | + | 0.0918326i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −83946.4 | −0.818840 | −0.409420 | − | 0.912346i | \(-0.634269\pi\) | ||||
−0.409420 | + | 0.912346i | \(0.634269\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 101368.i | 0.941472i | 0.882274 | + | 0.470736i | \(0.156012\pi\) | ||||
−0.882274 | + | 0.470736i | \(0.843988\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9005.63 | − | 8551.49i | −0.0797151 | − | 0.0756952i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10903.6i | 0.0920680i | 0.998940 | + | 0.0460340i | \(0.0146583\pi\) | ||||
−0.998940 | + | 0.0460340i | \(0.985342\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 128645.i | 1.03711i | 0.855044 | + | 0.518556i | \(0.173530\pi\) | ||||
−0.855044 | + | 0.518556i | \(0.826470\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −83086.3 | − | 78896.4i | −0.640062 | − | 0.607785i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 163476.i | 1.20436i | 0.798360 | + | 0.602181i | \(0.205701\pi\) | ||||
−0.798360 | + | 0.602181i | \(0.794299\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13051.6 | 0.0920278 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 195169. | − | 10103.3i | 1.31810 | − | 0.0682338i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −58016.0 | −0.375561 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −347125. | −2.15537 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 117446. | + | 111524.i | 0.699966 | + | 0.664668i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −26499.9 | −0.151694 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 199225.i | − | 1.09606i | −0.836458 | − | 0.548031i | \(-0.815378\pi\) | ||
0.836458 | − | 0.548031i | \(-0.184622\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −41157.0 | + | 43342.7i | −0.217756 | + | 0.229320i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 50397.5i | 0.256585i | 0.991736 | + | 0.128292i | \(0.0409496\pi\) | ||||
−0.991736 | + | 0.128292i | \(0.959050\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 462333.i | 2.26634i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 12238.3 | + | 10472.8i | 0.0577946 | + | 0.0494571i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 43239.6i | 0.196825i | 0.995146 | + | 0.0984125i | \(0.0313764\pi\) | ||||
−0.995146 | + | 0.0984125i | \(0.968624\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 82492.8 | 0.362142 | 0.181071 | − | 0.983470i | \(-0.442044\pi\) | ||||
0.181071 | + | 0.983470i | \(0.442044\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 120169. | − | 126551.i | 0.509033 | − | 0.536066i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 573315. | 2.34452 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 26896.2 | 0.106236 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 196365. | − | 206793.i | 0.749497 | − | 0.789299i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 444609. | 1.64064 | 0.820319 | − | 0.571906i | \(-0.193796\pi\) | ||||
0.820319 | + | 0.571906i | \(0.193796\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 198371.i | 0.708004i | 0.935245 | + | 0.354002i | \(0.115179\pi\) | ||||
−0.935245 | + | 0.354002i | \(0.884821\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 75147.6 | − | 3890.16i | 0.259530 | − | 0.0134351i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 38295.7i | − | 0.128033i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 82535.0i | 0.267232i | 0.991033 | + | 0.133616i | \(0.0426590\pi\) | ||||
−0.991033 | + | 0.133616i | \(0.957341\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −79325.6 | + | 83538.2i | −0.248840 | + | 0.262055i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 575042.i | 1.74837i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 328393. | 0.968111 | 0.484056 | − | 0.875037i | \(-0.339163\pi\) | ||||
0.484056 | + | 0.875037i | \(0.339163\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 34266.0 | + | 32538.0i | 0.0979835 | + | 0.0930424i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −650470. | −1.80483 | −0.902414 | − | 0.430870i | \(-0.858207\pi\) | ||||
−0.902414 | + | 0.430870i | \(0.858207\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −275512. | −0.742033 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −31000.9 | − | 598856.i | −0.0810745 | − | 1.56614i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −86336.1 | −0.219320 | −0.109660 | − | 0.993969i | \(-0.534976\pi\) | ||||
−0.109660 | + | 0.993969i | \(0.534976\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 582087.i | − | 1.43679i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −109430. | − | 103911.i | −0.262544 | − | 0.249304i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 417917.i | 0.974894i | 0.873153 | + | 0.487447i | \(0.162072\pi\) | ||||
−0.873153 | + | 0.487447i | \(0.837928\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 478809.i | − | 1.08634i | −0.839622 | − | 0.543170i | \(-0.817224\pi\) | ||
0.839622 | − | 0.543170i | \(-0.182776\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −174283. | − | 165494.i | −0.384705 | − | 0.365305i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 31254.9i | 0.0671412i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 220748. | 0.461629 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −461422. | + | 539209.i | −0.939603 | + | 1.09800i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 714309. | 1.41678 | 0.708391 | − | 0.705820i | \(-0.249421\pi\) | ||||
0.708391 | + | 0.705820i | \(0.249421\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −154226. | −0.298033 | −0.149017 | − | 0.988835i | \(-0.547611\pi\) | ||||
−0.149017 | + | 0.988835i | \(0.547611\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −38658.3 | − | 36708.8i | −0.0728041 | − | 0.0691328i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 321250. | 0.589764 | 0.294882 | − | 0.955534i | \(-0.404720\pi\) | ||||
0.294882 | + | 0.955534i | \(0.404720\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 100493.i | 0.179889i | 0.995947 | + | 0.0899443i | \(0.0286689\pi\) | ||||
−0.995947 | + | 0.0899443i | \(0.971331\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −365846. | + | 385275.i | −0.638717 | + | 0.672636i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.18502e6i | 2.01830i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 44180.3i | − | 0.0734250i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −38558.4 | − | 744846.i | −0.0625451 | − | 1.20821i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.75915e6i | − | 2.78572i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −648944. | −1.00346 | −0.501731 | − | 0.865024i | \(-0.667303\pi\) | ||||
−0.501731 | + | 0.865024i | \(0.667303\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −187411. | + | 197364.i | −0.283039 | + | 0.298070i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16304.4 | 0.0240552 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.68727e6 | 2.43241 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −249122. | + | 262352.i | −0.350996 | + | 0.369636i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −249044. | −0.343002 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 574520.i | − | 0.773648i | −0.922154 | − | 0.386824i | \(-0.873572\pi\) | ||
0.922154 | − | 0.386824i | \(-0.126428\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 39030.8 | + | 753972.i | 0.0513986 | + | 0.992884i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 412664.i | − | 0.531536i | −0.964037 | − | 0.265768i | \(-0.914375\pi\) | ||
0.964037 | − | 0.265768i | \(-0.0856255\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 32427.2i | 0.0408621i | 0.999791 | + | 0.0204311i | \(0.00650386\pi\) | ||||
−0.999791 | + | 0.0204311i | \(0.993496\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.43359e6 | + | 1.50973e6i | −1.76765 | + | 1.86152i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 455816.i | − | 0.550047i | −0.961438 | − | 0.275023i | \(-0.911314\pi\) | ||
0.961438 | − | 0.275023i | \(-0.0886856\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −47605.2 | −0.0562322 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −464453. | − | 441031.i | −0.537119 | − | 0.510033i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 784252. | 0.888098 | 0.444049 | − | 0.896002i | \(-0.353542\pi\) | ||||
0.444049 | + | 0.896002i | \(0.353542\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −74831.8 | −0.0829934 | −0.0414967 | − | 0.999139i | \(-0.513213\pi\) | ||||
−0.0414967 | + | 0.999139i | \(0.513213\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 561520. | − | 729372.i | 0.610028 | − | 0.792380i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −77790.0 | −0.0827959 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.98465e6i | 2.06986i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −23445.6 | − | 22263.3i | −0.0239642 | − | 0.0227557i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.22569e6i | − | 1.22799i | −0.789308 | − | 0.613997i | \(-0.789561\pi\) | ||
0.789308 | − | 0.613997i | \(-0.210439\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.18801e6i | − | 2.14905i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14884.9 | − | 14134.3i | −0.0143349 | − | 0.0136121i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 525291.i | 0.496098i | 0.968748 | + | 0.248049i | \(0.0797894\pi\) | ||||
−0.968748 | + | 0.248049i | \(0.920211\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.37706e6 | −1.27557 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −79459.6 | − | 1.53495e6i | −0.0722013 | − | 1.39474i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.47722e6 | 1.31691 | 0.658457 | − | 0.752619i | \(-0.271210\pi\) | ||||
0.658457 | + | 0.752619i | \(0.271210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 31424.9 | 0.0274890 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.54074e6 | − | 1.46304e6i | −1.32267 | − | 1.25597i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.20638e6 | −1.01649 | −0.508245 | − | 0.861212i | \(-0.669706\pi\) | ||||
−0.508245 | + | 0.861212i | \(0.669706\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.18886e6i | 0.983347i | 0.870780 | + | 0.491673i | \(0.163615\pi\) | ||||
−0.870780 | + | 0.491673i | \(0.836385\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.61736e6 | − | 1.70325e6i | 1.31341 | − | 1.38316i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.21481e6i | 1.76606i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 920507.i | 0.720821i | 0.932794 | + | 0.360411i | \(0.117363\pi\) | ||||
−0.932794 | + | 0.360411i | \(0.882637\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.18551e6 | + | 113137.i | −1.68090 | + | 0.0870152i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 703851.i | − | 0.531759i | −0.964006 | − | 0.265879i | \(-0.914338\pi\) | ||
0.964006 | − | 0.265879i | \(-0.0856623\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.10317e6 | 0.818799 | 0.409400 | − | 0.912355i | \(-0.365738\pi\) | ||||
0.409400 | + | 0.912355i | \(0.365738\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −112637. | + | 118619.i | −0.0821427 | + | 0.0865049i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.94654e6 | 1.39495 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.32397e6 | 0.932464 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.00997e6 | − | 1.06361e6i | 0.699160 | − | 0.736289i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.59372e6 | −1.08453 | −0.542266 | − | 0.840207i | \(-0.682433\pi\) | ||||
−0.542266 | + | 0.840207i | \(0.682433\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 41164.5i | 0.0275403i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.75569e6 | − | 2.05166e6i | 1.15493 | − | 1.34963i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.46847e6i | 1.59680i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 718357.i | 0.457008i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 901081. | − | 948934.i | 0.563842 | − | 0.593785i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 65560.8i | 0.0403547i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 900531. | 0.545322 | 0.272661 | − | 0.962110i | \(-0.412096\pi\) | ||||
0.272661 | + | 0.962110i | \(0.412096\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.14587e6 | − | 1.08808e6i | −0.682713 | − | 0.648285i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.15505e6 | −0.677173 | −0.338587 | − | 0.940935i | \(-0.609949\pi\) | ||||
−0.338587 | + | 0.940935i | \(0.609949\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.17256e6 | −1.25346 | −0.626732 | − | 0.779235i | \(-0.715608\pi\) | ||||
−0.626732 | + | 0.779235i | \(0.715608\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 193333. | − | 10008.2i | 0.109781 | − | 0.00568305i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.30916e6 | 0.731721 | 0.365860 | − | 0.930670i | \(-0.380775\pi\) | ||||
0.365860 | + | 0.930670i | \(0.380775\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.50895e6i | − | 2.48084i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −123254. | − | 117039.i | −0.0667635 | − | 0.0633967i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 764165.i | 0.407550i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.49871e6i | − | 1.31222i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.45420e6 | − | 1.38087e6i | −0.752067 | − | 0.714141i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.09744e6i | − | 1.06832i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −685986. | −0.344148 | −0.172074 | − | 0.985084i | \(-0.555047\pi\) | ||||
−0.172074 | + | 0.985084i | \(0.555047\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.78370e6 | − | 92336.5i | 0.881476 | − | 0.0456313i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 144930. | 0.0705582 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.99207e6 | 0.955500 | 0.477750 | − | 0.878496i | \(-0.341453\pi\) | ||||
0.477750 | + | 0.878496i | \(0.341453\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.84794e6 | − | 1.75475e6i | −0.873348 | − | 0.829307i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.41999e6 | −2.98985 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 278536.i | − | 0.127834i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −140096. | + | 147536.i | −0.0633691 | + | 0.0667344i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.29595e6i | 1.02362i | 0.859099 | + | 0.511810i | \(0.171025\pi\) | ||||
−0.859099 | + | 0.511810i | \(0.828975\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.29935e6i | − | 0.571036i | −0.958373 | − | 0.285518i | \(-0.907834\pi\) | ||
0.958373 | − | 0.285518i | \(-0.0921656\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.98074e6 | + | 2.31465e6i | −0.858143 | + | 1.00281i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 876536.i | 0.374398i | 0.982322 | + | 0.187199i | \(0.0599409\pi\) | ||||
−0.982322 | + | 0.187199i | \(0.940059\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 74243.2 | 0.0312670 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 622744. | − | 655816.i | 0.258606 | − | 0.272340i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 62753.1 | 0.0256980 | 0.0128490 | − | 0.999917i | \(-0.495910\pi\) | ||||
0.0128490 | + | 0.999917i | \(0.495910\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.61357e6 | 1.45938 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.72604e6 | − | 3.92391e6i | 1.48416 | − | 1.56298i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 98690.2 | 0.0387741 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 928044.i | 0.359669i | 0.983697 | + | 0.179835i | \(0.0575563\pi\) | ||||
−0.983697 | + | 0.179835i | \(0.942444\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.52134e6 | + | 130522.i | −0.963974 | + | 0.0499020i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.38455e6i | 0.522246i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.81032e6i | 0.673726i | 0.941554 | + | 0.336863i | \(0.109366\pi\) | ||||
−0.941554 | + | 0.336863i | \(0.890634\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 284450. | − | 299556.i | 0.104455 | − | 0.110002i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.08692e6i | 1.84332i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 776668. | 0.277739 | 0.138870 | − | 0.990311i | \(-0.455653\pi\) | ||||
0.138870 | + | 0.990311i | \(0.455653\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.25205e6 | + | 2.13848e6i | 0.794814 | + | 0.754733i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.03072e6 | 1.75240 | 0.876199 | − | 0.481949i | \(-0.160071\pi\) | ||||
0.876199 | + | 0.481949i | \(0.160071\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 567920. | 0.195270 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −48168.2 | − | 930481.i | −0.0163487 | − | 0.315813i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.51637e6 | 1.51327 | 0.756633 | − | 0.653839i | \(-0.226843\pi\) | ||||
0.756633 | + | 0.653839i | \(0.226843\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 950455.i | 0.314405i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −569695. | − | 540967.i | −0.186063 | − | 0.176681i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 174715.i | 0.0563427i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.80508e6i | − | 1.53012i | −0.643961 | − | 0.765058i | \(-0.722710\pi\) | ||
0.643961 | − | 0.765058i | \(-0.277290\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.22623e6 | − | 4.96268e6i | −1.64345 | − | 1.56057i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 5.82811e6i | − | 1.80995i | −0.425463 | − | 0.904976i | \(-0.639889\pi\) | ||
0.425463 | − | 0.904976i | \(-0.360111\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.24293e6 | 2.22153 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −249751. | + | 25927.2i | −0.0756606 | + | 0.00785449i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.23965e6 | 1.56789 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21312.8 | 0.00629987 | 0.00314994 | − | 0.999995i | \(-0.498997\pi\) | ||||
0.00314994 | + | 0.999995i | \(0.498997\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −488782. | − | 464134.i | −0.142728 | − | 0.135531i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.81367e6 | −0.523219 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8819.61i | 0.00251379i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −885478. | + | 932502.i | −0.249366 | + | 0.262609i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 653173.i | − | 0.181758i | −0.995862 | − | 0.0908789i | \(-0.971032\pi\) | ||
0.995862 | − | 0.0908789i | \(-0.0289676\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.56795e6i | 1.25608i | 0.778183 | + | 0.628038i | \(0.216142\pi\) | ||||
−0.778183 | + | 0.628038i | \(0.783858\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 140640. | + | 2.71680e6i | 0.0382172 | + | 0.738255i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 962100.i | − | 0.258373i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.88855e6 | −0.766672 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.15397e6 | + | 6.48078e6i | −1.61440 | + | 1.70014i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.33039e6 | 1.12288 | 0.561441 | − | 0.827517i | \(-0.310247\pi\) | ||||
0.561441 | + | 0.827517i | \(0.310247\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.95867e6 | −1.27100 | −0.635500 | − | 0.772101i | \(-0.719206\pi\) | ||||
−0.635500 | + | 0.772101i | \(0.719206\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −288704. | + | 304036.i | −0.0731526 | + | 0.0770374i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.57423e6 | 1.89729 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.57813e6i | − | 0.390825i | −0.980721 | − | 0.195412i | \(-0.937395\pi\) | ||
0.980721 | − | 0.195412i | \(-0.0626045\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 229815. | + | 4.43942e6i | 0.0562708 | + | 1.08700i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.24569e6i | 0.543676i | 0.962343 | + | 0.271838i | \(0.0876315\pi\) | ||||
−0.962343 | + | 0.271838i | \(0.912368\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 579585.i | 0.138745i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.77243e6 | + | 5.02588e6i | −1.12972 | + | 1.18972i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.24299e6i | 1.46143i | 0.682685 | + | 0.730713i | \(0.260812\pi\) | ||||
−0.682685 | + | 0.730713i | \(0.739188\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.40650e6 | −1.71464 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.24239e6 | − | 2.12931e6i | −0.513413 | − | 0.487522i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −640718. | −0.145090 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.12647e6 | −1.14823 | −0.574113 | − | 0.818776i | \(-0.694653\pi\) | ||||
−0.574113 | + | 0.818776i | \(0.694653\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −762660. | + | 891229.i | −0.168966 | + | 0.197450i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.78319e6 | 1.48656 | 0.743278 | − | 0.668982i | \(-0.233270\pi\) | ||||
0.743278 | + | 0.668982i | \(0.233270\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.59144e6i | 1.64578i | 0.568201 | + | 0.822890i | \(0.307639\pi\) | ||||
−0.568201 | + | 0.822890i | \(0.692361\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 432896. | + | 411066.i | 0.0928435 | + | 0.0881616i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.08139e6i | 1.29036i | 0.764031 | + | 0.645179i | \(0.223217\pi\) | ||||
−0.764031 | + | 0.645179i | \(0.776783\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.38550e6i | 1.34049i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −932979. | − | 885931.i | −0.193785 | − | 0.184013i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.73331e6i | − | 0.561741i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.66702e6 | −1.55917 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −92838.8 | − | 1.79340e6i | −0.0186824 | − | 0.360895i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.75608e6 | −1.94284 | −0.971419 | − | 0.237373i | \(-0.923714\pi\) | ||||
−0.971419 | + | 0.237373i | \(0.923714\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.91129e6 | −1.16498 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.50029e6 | − | 6.17250e6i | −1.26784 | − | 1.20391i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −400101. | −0.0772352 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 5.95397e6i | − | 1.13759i | −0.822481 | − | 0.568793i | \(-0.807411\pi\) | ||
0.822481 | − | 0.568793i | \(-0.192589\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.52497e6 | + | 3.71217e6i | −0.666628 | + | 0.702030i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.28879e6i | − | 0.615649i | −0.951443 | − | 0.307824i | \(-0.900399\pi\) | ||
0.951443 | − | 0.307824i | \(-0.0996009\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.95866e6i | 0.362946i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −735622. | + | 38080.9i | −0.134940 | + | 0.00698545i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.27109e6i | 0.594020i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −845037. | −0.151923 | −0.0759616 | − | 0.997111i | \(-0.524203\pi\) | ||||
−0.0759616 | + | 0.997111i | \(0.524203\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.98214e6 | − | 7.35293e6i | 1.24278 | − | 1.30878i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.09603e6 | 0.193153 | 0.0965765 | − | 0.995326i | \(-0.469211\pi\) | ||||
0.0965765 | + | 0.995326i | \(0.469211\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −356964. | −0.0622868 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.95734e6 | − | 3.11439e6i | 0.510954 | − | 0.538088i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.06884e6 | 0.182861 | 0.0914303 | − | 0.995811i | \(-0.470856\pi\) | ||||
0.0914303 | + | 0.995811i | \(0.470856\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.34820e6i | 0.736643i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.10225e6 | + | 6.07768e6i | 1.19152 | + | 1.01963i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 431045.i | 0.0716152i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.98067e6i | 1.31315i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 926732. | − | 975947.i | 0.151020 | − | 0.159041i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.98135e6i | 0.803995i | 0.915641 | + | 0.401997i | \(0.131684\pi\) | ||||
−0.915641 | + | 0.401997i | \(0.868316\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.41829e6 | 0.546455 | 0.273228 | − | 0.961949i | \(-0.411909\pi\) | ||||
0.273228 | + | 0.961949i | \(0.411909\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.57993e6 | + | 6.24812e6i | 1.04189 | + | 0.989352i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.78880e6 | 0.437413 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.98435e6 | 0.463671 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.34923e6 | − | 121613.i | 0.361568 | − | 0.0187173i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.35589e6 | 1.27402 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 46365.0i | 0.00700335i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.72415e6 | − | 4.48592e6i | −0.706949 | − | 0.671299i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.30409e7i | 1.93347i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.98082e6i | 1.17234i | 0.810187 | + | 0.586171i | \(0.199365\pi\) | ||||
−0.810187 | + | 0.586171i | \(0.800635\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.41248e6 | + | 5.13954e6i | 0.787765 | + | 0.748039i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 547034.i | 0.0788902i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.94344e6 | 1.13512 | 0.567558 | − | 0.823333i | \(-0.307888\pi\) | ||||
0.567558 | + | 0.823333i | \(0.307888\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.74151e6 | − | 193686.i | 0.529805 | − | 0.0274264i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.56087e7 | 2.19021 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.69779e6 | −1.07042 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −353307. | − | 335490.i | −0.0486877 | − | 0.0462325i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.79798e6 | −1.33813 | −0.669065 | − | 0.743203i | \(-0.733305\pi\) | ||||
−0.669065 | + | 0.743203i | \(0.733305\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.08368e6i | 0.417387i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.36951e6 | + | 2.49535e6i | −0.317871 | + | 0.334752i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 671056.i | − | 0.0892252i | −0.999004 | − | 0.0446126i | \(-0.985795\pi\) | ||
0.999004 | − | 0.0446126i | \(-0.0142054\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 695145.i | 0.0916124i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.14233e6 | − | 1.10038e7i | −0.149222 | − | 1.43742i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 3.33810e6i | − | 0.432233i | −0.976368 | − | 0.216117i | \(-0.930661\pi\) | ||
0.976368 | − | 0.216117i | \(-0.0693392\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.06507e7 | 1.36706 | 0.683528 | − | 0.729924i | \(-0.260445\pi\) | ||||
0.683528 | + | 0.729924i | \(0.260445\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.66740e6 | + | 8.07458e6i | −0.975576 | + | 1.02739i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.53611e6 | −1.20282 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.00078e6 | −1.00044 | −0.500222 | − | 0.865897i | \(-0.666748\pi\) | ||||
−0.500222 | + | 0.865897i | \(0.666748\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.65546e6 | − | 1.74338e6i | 0.205221 | − | 0.216120i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −388584. | −0.0477578 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 5.26816e6i | − | 0.641929i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 829916. | − | 42962.2i | 0.100264 | − | 0.00519036i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.20246e7i | − | 1.44037i | −0.693780 | − | 0.720187i | \(-0.744056\pi\) | ||
0.693780 | − | 0.720187i | \(-0.255944\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.22241e7i | − | 2.63959i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.44830e6 | + | 3.63143e6i | −0.406103 | + | 0.427670i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.80287e6i | 1.14477i | 0.819987 | + | 0.572383i | \(0.193981\pi\) | ||||
−0.819987 | + | 0.572383i | \(0.806019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −246701. | −0.0285679 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.13598e6 | − | 1.07869e6i | −0.130447 | − | 0.123869i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.41689e6 | 1.07236 | 0.536180 | − | 0.844104i | \(-0.319867\pi\) | ||||
0.536180 | + | 0.844104i | \(0.319867\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.79726e6 | 0.541760 | 0.270880 | − | 0.962613i | \(-0.412685\pi\) | ||||
0.270880 | + | 0.962613i | \(0.412685\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −428168. | − | 8.27108e6i | −0.0479536 | − | 0.926337i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.47607e6 | −0.163953 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.86218e6i | − | 0.866106i | −0.901368 | − | 0.433053i | \(-0.857436\pi\) | ||
0.901368 | − | 0.433053i | \(-0.142564\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.33955e7 | − | 1.27200e7i | −1.46358 | − | 1.38978i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 9.00365e6i | − | 0.975699i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.35943e7i | 1.46119i | 0.682811 | + | 0.730595i | \(0.260757\pi\) | ||||
−0.682811 | + | 0.730595i | \(0.739243\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 499416. | + | 474231.i | 0.0532445 | + | 0.0505594i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.62327e7i | 1.71664i | 0.513115 | + | 0.858320i | \(0.328491\pi\) | ||||
−0.513115 | + | 0.858320i | \(0.671509\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.88310e6 | −0.512235 | −0.256117 | − | 0.966646i | \(-0.582443\pi\) | ||||
−0.256117 | + | 0.966646i | \(0.582443\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.83365e6 | + | 7.55931e6i | 0.919203 | + | 0.786599i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.55360e7 | −2.63592 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.59643e6 | 0.982675 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.98855e7 | + | 1.88828e7i | 2.02008 | + | 1.91821i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.27607e6 | −0.229382 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.15393e6i | − | 0.215356i | −0.994186 | − | 0.107678i | \(-0.965658\pi\) | ||
0.994186 | − | 0.107678i | \(-0.0343416\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.96577e6 | − | 7.33569e6i | 0.690971 | − | 0.727665i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 847163.i | − | 0.0833744i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.47126e7i | − | 1.43661i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −219337. | − | 4.23701e6i | −0.0212500 | − | 0.410494i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1.32161e7i | − | 1.27045i | −0.772327 | − | 0.635226i | \(-0.780907\pi\) | ||
0.772327 | − | 0.635226i | \(-0.219093\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.78560e7 | −1.70316 | −0.851581 | − | 0.524223i | \(-0.824356\pi\) | ||||
−0.851581 | + | 0.524223i | \(0.824356\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −175011. | + | 184305.i | −0.0165641 | + | 0.0174437i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −640030. | −0.0601090 | −0.0300545 | − | 0.999548i | \(-0.509568\pi\) | ||||
−0.0300545 | + | 0.999548i | \(0.509568\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.90093e6 | 0.643126 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.81112e7 | + | 1.90730e7i | −1.67492 | + | 1.76387i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.04740e6 | 0.554991 | 0.277496 | − | 0.960727i | \(-0.410496\pi\) | ||||
0.277496 | + | 0.960727i | \(0.410496\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 214304.i | 0.0195177i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −291561. | − | 5.63218e6i | −0.0263521 | − | 0.509053i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.15627e6i | 0.821306i | 0.911792 | + | 0.410653i | \(0.134699\pi\) | ||||
−0.911792 | + | 0.410653i | \(0.865301\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 267971.i | − | 0.0238553i | −0.999929 | − | 0.0119276i | \(-0.996203\pi\) | ||
0.999929 | − | 0.0119276i | \(-0.00379677\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.67324e6 | − | 2.81521e6i | 0.236186 | − | 0.248729i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.96597e6i | 0.172394i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.94138e7 | 1.68964 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.49440e6 | + | 6.16690e6i | 0.561014 | + | 0.532723i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.09908e7 | 0.942372 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.72475e7 | 1.46787 | 0.733935 | − | 0.679220i | \(-0.237682\pi\) | ||||
0.733935 | + | 0.679220i | \(0.237682\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.94188e6 | − | 7.65192e6i | −0.755387 | − | 0.646415i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.03336e7 | −1.70507 | −0.852535 | − | 0.522670i | \(-0.824936\pi\) | ||||
−0.852535 | + | 0.522670i | \(0.824936\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.76281e7i | − | 1.46734i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.66477e6 | + | 4.42954e6i | 0.385445 | + | 0.366008i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 2.64704e6i | − | 0.217125i | −0.994090 | − | 0.108562i | \(-0.965375\pi\) | ||
0.994090 | − | 0.108562i | \(-0.0346247\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 183867.i | 0.0149719i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −366558. | − | 348074.i | −0.0296313 | − | 0.0281371i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.94344e6i | 0.476969i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.33199e6 | 0.504481 | 0.252240 | − | 0.967665i | \(-0.418833\pi\) | ||||
0.252240 | + | 0.967665i | \(0.418833\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.67781e6 | − | 3.24108e7i | −0.132712 | − | 2.56364i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 350783. | 0.0275471 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.21734e6 | 0.250850 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.15256e6 | + | 4.89273e6i | 0.398869 | + | 0.378755i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.12150e6 | 0.470503 | 0.235252 | − | 0.971934i | \(-0.424409\pi\) | ||||
0.235252 | + | 0.971934i | \(0.424409\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.81381e7i | 1.38422i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 510994. | − | 538131.i | 0.0387207 | − | 0.0407770i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1.57275e7i | − | 1.18335i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.03996e7i | − | 0.776965i | −0.921456 | − | 0.388483i | \(-0.872999\pi\) | ||
0.921456 | − | 0.388483i | \(-0.127001\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.97087e6 | − | 516162.i | 0.739706 | − | 0.0382923i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.76420e7i | − | 2.03632i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.43790e6 | 0.178341 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.41816e6 | + | 8.86522e6i | −0.611532 | + | 0.644008i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.48619e6 | 0.107214 | 0.0536071 | − | 0.998562i | \(-0.482928\pi\) | ||||
0.0536071 | + | 0.998562i | \(0.482928\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.89915e7 | −1.36057 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 803244. | − | 845901.i | 0.0571481 | − | 0.0601830i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.96516e7 | −1.38852 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47337.8i | 0.00332179i | 0.999999 | + | 0.00166089i | \(0.000528679\pi\) | ||||
−0.999999 | + | 0.00166089i | \(0.999471\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.21749e6 | + | 1.41765e7i | 0.154541 | + | 0.987986i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.18733e6i | 0.0821824i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 9.51842e6i | − | 0.654342i | −0.944965 | − | 0.327171i | \(-0.893905\pi\) | ||
0.944965 | − | 0.327171i | \(-0.106095\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 834998. | − | 879341.i | 0.0570121 | − | 0.0600398i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.42965e7i | − | 1.64769i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.02926e7 | −0.693292 | −0.346646 | − | 0.937996i | \(-0.612679\pi\) | ||||
−0.346646 | + | 0.937996i | \(0.612679\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.24345e7 | − | 2.13032e7i | −1.50097 | − | 1.42528i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.27872e7 | −1.51433 | −0.757163 | − | 0.653226i | \(-0.773415\pi\) | ||||
−0.757163 | + | 0.653226i | \(0.773415\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.89061e6 | 0.124799 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 503329. | − | 26055.8i | 0.0330028 | − | 0.00170845i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.04280e6 | −0.133052 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.50137e7i | 1.61837i | 0.587554 | + | 0.809185i | \(0.300091\pi\) | ||||
−0.587554 | + | 0.809185i | \(0.699909\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.38553e7 | + | 1.31566e7i | 0.890486 | + | 0.845580i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 843530.i | 0.0538559i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.21276e7i | 1.40344i | 0.712452 | + | 0.701721i | \(0.247585\pi\) | ||||
−0.712452 | + | 0.701721i | \(0.752415\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.47333e7 | + | 2.34860e7i | 1.55839 | + | 1.47981i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.81968e7i | − | 1.13902i | −0.821983 | − | 0.569512i | \(-0.807132\pi\) | ||
0.821983 | − | 0.569512i | \(-0.192868\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.41018e7 | −1.49878 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 319549. | − | 16542.1i | 0.0197417 | − | 0.00102197i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.78552e6 | −0.477858 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.64592e7 | 1.00367 | 0.501837 | − | 0.864962i | \(-0.332658\pi\) | ||||
0.501837 | + | 0.864962i | \(0.332658\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.93791e6 | − | 5.63847e6i | −0.359747 | − | 0.341606i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.17589e6 | 0.492137 | 0.246069 | − | 0.969252i | \(-0.420861\pi\) | ||||
0.246069 | + | 0.969252i | \(0.420861\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.79806e7i | 1.67341i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.47814e7 | − | 1.55664e7i | 0.878340 | − | 0.924985i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 2.56391e7i | − | 1.51377i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1.24463e7i | − | 0.730152i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.82040e7 | + | 1.55779e7i | 1.06112 | + | 0.908040i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 350963.i | 0.0203276i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.85675e6 | 0.337070 | 0.168535 | − | 0.985696i | \(-0.446096\pi\) | ||||
0.168535 | + | 0.985696i | \(0.446096\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.58565e7 | + | 1.66986e7i | −0.906809 | + | 0.954965i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.06275e7 | −1.74048 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.23996e7 | −0.700205 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −337315. | + | 355228.i | −0.0189286 | + | 0.0199338i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.92534e6 | 0.107365 | 0.0536825 | − | 0.998558i | \(-0.482904\pi\) | ||||
0.0536825 | + | 0.998558i | \(0.482904\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.46675e6i | − | 0.192112i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.30765e7 | − | 1.71227e6i | 1.82154 | − | 0.0942955i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1.65447e7i | − | 0.905460i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.44524e6i | 0.132994i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.29493e7 | − | 1.36370e7i | 0.699941 | − | 0.737112i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5.47170e6i | − | 0.293935i | −0.989141 | − | 0.146967i | \(-0.953049\pi\) | ||
0.989141 | − | 0.146967i | \(-0.0469512\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.39885e7 | −1.28071 | −0.640354 | − | 0.768080i | \(-0.721212\pi\) | ||||
−0.640354 | + | 0.768080i | \(0.721212\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.34389e7 | − | 1.27612e7i | −0.713078 | − | 0.677119i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.39642e6 | 0.0736415 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.46192e6 | 0.495934 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.89288e6 | + | 3.65653e7i | 0.0986081 | + | 1.90485i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.38393e6 | −0.123434 | −0.0617170 | − | 0.998094i | \(-0.519658\pi\) | ||||
−0.0617170 | + | 0.998094i | \(0.519658\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.45230e7i | − | 0.747407i | −0.927548 | − | 0.373703i | \(-0.878088\pi\) | ||
0.927548 | − | 0.373703i | \(-0.121912\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.50363e7 | − | 2.37738e7i | −1.28066 | − | 1.21608i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 124756.i | − | 0.00634303i | −0.999995 | − | 0.00317152i | \(-0.998990\pi\) | ||
0.999995 | − | 0.00317152i | \(-0.00100953\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 3.63133e7i | − | 1.83518i | −0.397527 | − | 0.917590i | \(-0.630132\pi\) | ||
0.397527 | − | 0.917590i | \(-0.369868\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.04054e7 | − | 9.88072e6i | −0.522707 | − | 0.496348i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 5.66489e6i | − | 0.282865i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.76598e6 | −0.137288 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.21804e7 | − | 2.59195e7i | 1.09435 | − | 1.27883i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.33073e6 | −0.408581 | −0.204291 | − | 0.978910i | \(-0.565489\pi\) | ||||
−0.204291 | + | 0.978910i | \(0.565489\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.94960e7 | 0.950506 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.95635e6 | + | 7.55513e6i | 0.385607 | + | 0.366162i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.17155e6 | −0.0564444 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.50344e7i | − | 3.11483i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.18415e7 | + | 1.24703e7i | −0.563814 | + | 0.593756i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.25599e7i | 1.06786i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 750959.i | 0.0353381i | 0.999844 | + | 0.0176691i | \(0.00562453\pi\) | ||||
−0.999844 | + | 0.0176691i | \(0.994375\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −131825. | − | 2.54651e6i | −0.00616711 | − | 0.119132i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.08548e7i | 0.969960i | 0.874525 | + | 0.484980i | \(0.161173\pi\) | ||||
−0.874525 | + | 0.484980i | \(0.838827\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.96062e7 | 1.36899 | 0.684494 | − | 0.729019i | \(-0.260023\pi\) | ||||
0.684494 | + | 0.729019i | \(0.260023\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.08942e7 | + | 2.20038e7i | −0.960545 | + | 1.01156i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −205022. | −0.00937074 | −0.00468537 | − | 0.999989i | \(-0.501491\pi\) | ||||
−0.00468537 | + | 0.999989i | \(0.501491\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −367126. | −0.0166830 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.42114e7 | + | 1.49662e7i | −0.642082 | + | 0.676180i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.92897e7 | 1.31573 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.74109e7i | 1.22427i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.18202e6 | + | 2.28335e7i | 0.0524916 | + | 1.01400i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 4.96480e6i | − | 0.219221i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.06342e6i | 0.0905918i | 0.998974 | + | 0.0452959i | \(0.0144231\pi\) | ||||
−0.998974 | + | 0.0452959i | \(0.985577\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.71070e7 | − | 1.80154e7i | 0.746794 | − | 0.786453i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.20461e7i | 0.522887i | 0.965219 | + | 0.261444i | \(0.0841985\pi\) | ||||
−0.965219 | + | 0.261444i | \(0.915801\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.90309e7 | 1.68464 | 0.842319 | − | 0.538979i | \(-0.181190\pi\) | ||||
0.842319 | + | 0.538979i | \(0.181190\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −465326. | − | 441860.i | −0.0199709 | − | 0.0189639i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.19857e7 | −0.511509 | −0.255754 | − | 0.966742i | \(-0.582324\pi\) | ||||
−0.255754 | + | 0.966742i | \(0.582324\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.73252e7 | 1.58397 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.34650e6 | + | 4.18689e7i | 0.183420 | + | 1.76684i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.76267e7 | −1.15931 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.77710e6i | 0.0741575i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.79037e7 | − | 2.64966e7i | −1.15792 | − | 1.09953i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 5.69635e7i | − | 2.35070i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.28845e6i | 0.0939139i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.12033e6 | − | 7.71084e6i | −0.331401 | − | 0.314690i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 2.03603e6i | − | 0.0826349i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.52158e6 | −0.222867 | −0.111433 | − | 0.993772i | \(-0.535544\pi\) | ||||
−0.111433 | + | 0.993772i | \(0.535544\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.05458e6 | + | 2.03717e7i | 0.0423321 | + | 0.817745i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 521804. | 0.0208310 | 0.0104155 | − | 0.999946i | \(-0.496685\pi\) | ||||
0.0104155 | + | 0.999946i | \(0.496685\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.47854e6 | 0.0587026 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −741101. | − | 703729.i | −0.0292634 | − | 0.0277877i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.44206e6 | −0.370803 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.42906e6i | 0.251107i | 0.992087 | + | 0.125554i | \(0.0400707\pi\) | ||||
−0.992087 | + | 0.125554i | \(0.959929\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.66630e6 | + | 1.01796e7i | −0.375501 | + | 0.395442i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.40417e7i | 0.542521i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.28363e7i | − | 0.877549i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.45995e7 | − | 1.27344e6i | 0.940213 | − | 0.0486720i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1.52604e7i | − | 0.580132i | −0.957007 | − | 0.290066i | \(-0.906323\pi\) | ||
0.957007 | − | 0.290066i | \(-0.0936772\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.51438e7 | −1.70696 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.23983e7 | − | 1.30567e7i | 0.466292 | − | 0.491055i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 938684. | 0.0351148 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.99702e7 | −0.743078 | −0.371539 | − | 0.928417i | \(-0.621170\pi\) | ||||
−0.371539 | + | 0.928417i | \(0.621170\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.33203e7 | − | 2.45587e7i | 0.863118 | − | 0.908954i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.96538e7 | −0.723557 | −0.361778 | − | 0.932264i | \(-0.617830\pi\) | ||||
−0.361778 | + | 0.932264i | \(0.617830\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 3.18895e7i | − | 1.16780i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.96210e6 | + | 2.29287e6i | −0.0714729 | + | 0.0835218i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1.78564e7i | − | 0.647024i | −0.946224 | − | 0.323512i | \(-0.895136\pi\) | ||
0.946224 | − | 0.323512i | \(-0.104864\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.86654e7i | 0.672779i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.40525e7 | + | 1.47988e7i | −0.503853 | + | 0.530610i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 2.73344e7i | − | 0.974939i | −0.873140 | − | 0.487469i | \(-0.837920\pi\) | ||
0.873140 | − | 0.487469i | \(-0.162080\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.03745e6 | 0.107771 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.09694e7 | + | 4.83991e7i | 1.79899 | + | 1.70827i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.10101e6 | −0.284441 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.24773e7 | −1.83300 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.64602e6 | − | 136976.i | 0.0919448 | − | 0.00475970i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −655813. | −0.0226705 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.89954e6i | 0.168496i | 0.996445 | + | 0.0842479i | \(0.0268488\pi\) | ||||
−0.996445 | + | 0.0842479i | \(0.973151\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.63815e6 | − | 8.20255e6i | −0.295537 | − | 0.280633i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 4.88073e7i | − | 1.66126i | −0.556828 | − | 0.830628i | \(-0.687982\pi\) | ||
0.556828 | − | 0.830628i | \(-0.312018\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.54552e7i | 0.523350i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.82455e7 | + | 2.68212e7i | 0.951565 | + | 0.903579i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.11727e7i | 0.374474i | 0.982315 | + | 0.187237i | \(0.0599533\pi\) | ||||
−0.982315 | + | 0.187237i | \(0.940047\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.71632e7 | 3.24000 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.12189e7 | − | 1.61611e6i | 1.03573 | − | 0.0536164i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.07531e7 | −0.685014 | −0.342507 | − | 0.939515i | \(-0.611276\pi\) | ||||
−0.342507 | + | 0.939515i | \(0.611276\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.36605e6 | 0.0448617 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.37096e7 | + | 2.25139e7i | 0.774695 | + | 0.735629i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.17686e7 | 0.382589 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.17133e7i | 0.378873i | 0.981893 | + | 0.189436i | \(0.0606661\pi\) | ||||
−0.981893 | + | 0.189436i | \(0.939334\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.36337e6 | − | 7.75441e6i | 0.236976 | − | 0.249560i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 427325.i | 0.0136836i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.69725e7i | 1.17799i | 0.808137 | + | 0.588995i | \(0.200476\pi\) | ||||
−0.808137 | + | 0.588995i | \(0.799524\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.81024e7 | + | 2.11541e7i | −0.573882 | + | 0.670627i |
(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 | 384.6.f.e.191.6 | yes | 20 | |
3.2 | odd | 2 | 384.6.f.f.191.5 | yes | 20 | ||
4.3 | odd | 2 | 384.6.f.f.191.15 | yes | 20 | ||
8.3 | odd | 2 | 384.6.f.f.191.6 | yes | 20 | ||
8.5 | even | 2 | inner | 384.6.f.e.191.15 | yes | 20 | |
12.11 | even | 2 | inner | 384.6.f.e.191.16 | yes | 20 | |
24.5 | odd | 2 | 384.6.f.f.191.16 | yes | 20 | ||
24.11 | even | 2 | inner | 384.6.f.e.191.5 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.6.f.e.191.5 | ✓ | 20 | 24.11 | even | 2 | inner | |
384.6.f.e.191.6 | yes | 20 | 1.1 | even | 1 | trivial | |
384.6.f.e.191.15 | yes | 20 | 8.5 | even | 2 | inner | |
384.6.f.e.191.16 | yes | 20 | 12.11 | even | 2 | inner | |
384.6.f.f.191.5 | yes | 20 | 3.2 | odd | 2 | ||
384.6.f.f.191.6 | yes | 20 | 8.3 | odd | 2 | ||
384.6.f.f.191.15 | yes | 20 | 4.3 | odd | 2 | ||
384.6.f.f.191.16 | yes | 20 | 24.5 | odd | 2 |