Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,7,Mod(29,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.29");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.8032450172\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 1880 x^{10} + 1266870 x^{8} + 399545800 x^{6} + 62009694600 x^{4} + 4432082624000 x^{2} + 109931031040000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{8}\cdot 5^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 29.6 | ||
Root | \(29.1428i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.29 |
Dual form | 60.7.b.a.29.5 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −7.66273 | + | 25.8898i | −0.283805 | + | 0.958882i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 37.2664 | − | 119.316i | 0.298131 | − | 0.954525i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 46.7246i | 0.136223i | 0.997678 | + | 0.0681116i | \(0.0216974\pi\) | ||||
−0.997678 | + | 0.0681116i | \(0.978303\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −611.565 | − | 396.774i | −0.838909 | − | 0.544271i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 448.732i | − | 0.337139i | −0.985690 | − | 0.168569i | \(-0.946085\pi\) | ||
0.985690 | − | 0.168569i | \(-0.0539148\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2072.30i | − | 0.943241i | −0.881802 | − | 0.471620i | \(-0.843669\pi\) | ||
0.881802 | − | 0.471620i | \(-0.156331\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2803.50 | + | 1879.10i | 0.830665 | + | 0.556772i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5987.26 | 1.21866 | 0.609329 | − | 0.792918i | \(-0.291439\pi\) | ||||
0.609329 | + | 0.792918i | \(0.291439\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7407.66 | 1.07999 | 0.539996 | − | 0.841668i | \(-0.318426\pi\) | ||||
0.539996 | + | 0.841668i | \(0.318426\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1209.69 | − | 358.038i | −0.130622 | − | 0.0386608i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 17175.3 | 1.41163 | 0.705817 | − | 0.708395i | \(-0.250580\pi\) | ||||
0.705817 | + | 0.708395i | \(0.250580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12847.4 | − | 8892.93i | −0.822235 | − | 0.569148i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 14958.7 | − | 12792.9i | 0.759978 | − | 0.649948i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 37549.0i | − | 1.53959i | −0.638294 | − | 0.769793i | \(-0.720359\pi\) | ||
0.638294 | − | 0.769793i | \(-0.279641\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −17977.2 | −0.603444 | −0.301722 | − | 0.953396i | \(-0.597561\pi\) | ||||
−0.301722 | + | 0.953396i | \(0.597561\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11617.6 | + | 3438.51i | 0.323276 | + | 0.0956817i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5574.97 | + | 1741.26i | 0.130028 | + | 0.0406124i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 36228.1i | 0.715222i | 0.933871 | + | 0.357611i | \(0.116409\pi\) | ||||
−0.933871 | + | 0.357611i | \(0.883591\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 53651.5 | + | 15879.5i | 0.904457 | + | 0.267696i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 12817.7i | − | 0.185977i | −0.995667 | − | 0.0929886i | \(-0.970358\pi\) | ||
0.995667 | − | 0.0929886i | \(-0.0296420\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 25097.3i | − | 0.315661i | −0.987466 | − | 0.157831i | \(-0.949550\pi\) | ||
0.987466 | − | 0.157831i | \(-0.0504500\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −70132.1 | + | 58182.9i | −0.769625 | + | 0.638496i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −51821.1 | −0.499129 | −0.249564 | − | 0.968358i | \(-0.580287\pi\) | ||||
−0.249564 | + | 0.968358i | \(0.580287\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 115466. | 0.981443 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −45878.8 | + | 155009.i | −0.345861 | + | 1.16855i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −270680. | −1.81815 | −0.909073 | − | 0.416638i | \(-0.863208\pi\) | ||||
−0.909073 | + | 0.416638i | \(0.863208\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −53540.7 | − | 16722.6i | −0.321807 | − | 0.100512i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −56762.9 | + | 191783.i | −0.306507 | + | 1.03558i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 218274.i | − | 1.06279i | −0.847126 | − | 0.531393i | \(-0.821669\pi\) | ||
0.847126 | − | 0.531393i | \(-0.178331\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 38350.9 | 0.168961 | 0.0844804 | − | 0.996425i | \(-0.473077\pi\) | ||||
0.0844804 | + | 0.996425i | \(0.473077\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 18539.1 | − | 28575.1i | 0.0741424 | − | 0.114279i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −247258. | − | 77227.2i | −0.900347 | − | 0.281210i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 259141.i | 0.861613i | 0.902444 | + | 0.430807i | \(0.141771\pi\) | ||||
−0.902444 | + | 0.430807i | \(0.858229\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −131610. | + | 444666.i | −0.400629 | + | 1.35359i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 452834.i | − | 1.26521i | −0.774473 | − | 0.632607i | \(-0.781985\pi\) | ||
0.774473 | − | 0.632607i | \(-0.218015\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 78457.1i | − | 0.201680i | −0.994903 | − | 0.100840i | \(-0.967847\pi\) | ||
0.994903 | − | 0.100840i | \(-0.0321531\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 328683. | − | 264473.i | 0.779100 | − | 0.626900i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 20966.8 | 0.0459262 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −410751. | −0.833100 | −0.416550 | − | 0.909113i | \(-0.636761\pi\) | ||||
−0.416550 | + | 0.909113i | \(0.636761\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 216583. | + | 485306.i | 0.407538 | + | 0.913188i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 630723. | 1.10307 | 0.551536 | − | 0.834151i | \(-0.314042\pi\) | ||||
0.551536 | + | 0.834151i | \(0.314042\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 223124. | − | 714374.i | 0.363320 | − | 1.16324i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 972136. | + | 287728.i | 1.47628 | + | 0.436942i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 145021.i | − | 0.205713i | −0.994696 | − | 0.102857i | \(-0.967202\pi\) | ||
0.994696 | − | 0.102857i | \(-0.0327983\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 96827.4 | 0.128491 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 137754. | − | 465426.i | 0.171260 | − | 0.578631i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 276057. | − | 883849.i | 0.321979 | − | 1.03088i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.76304e6i | 1.93174i | 0.259035 | + | 0.965868i | \(0.416595\pi\) | ||||
−0.259035 | + | 0.965868i | \(0.583405\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −178045. | + | 274429.i | −0.183495 | + | 0.282829i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.01993e6i | − | 0.989929i | −0.868913 | − | 0.494965i | \(-0.835181\pi\) | ||
0.868913 | − | 0.494965i | \(-0.164819\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.45111e6i | − | 1.32797i | −0.747745 | − | 0.663986i | \(-0.768864\pi\) | ||
0.747745 | − | 0.663986i | \(-0.231136\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −87800.4 | + | 130992.i | −0.0758453 | + | 0.113156i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.63492e6 | 1.33459 | 0.667293 | − | 0.744796i | \(-0.267453\pi\) | ||||
0.667293 | + | 0.744796i | \(0.267453\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.13216e6 | −0.874239 | −0.437119 | − | 0.899403i | \(-0.644001\pi\) | ||||
−0.437119 | + | 0.899403i | \(0.644001\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −937940. | − | 277607.i | −0.685813 | − | 0.202984i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.63589e6 | −1.13376 | −0.566878 | − | 0.823801i | \(-0.691849\pi\) | ||||
−0.566878 | + | 0.823801i | \(0.691849\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 640064. | − | 2.04929e6i | 0.420852 | − | 1.34744i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −822234. | + | 1.26735e6i | −0.513379 | + | 0.791294i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 279752.i | 0.166009i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.57020e6 | 0.886337 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 331849. | + | 98218.9i | 0.178330 | + | 0.0527813i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.53984e6 | + | 1.20149e6i | −0.788400 | + | 0.615163i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.64094e6i | 1.77747i | 0.458420 | + | 0.888735i | \(0.348415\pi\) | ||||
−0.458420 | + | 0.888735i | \(0.651585\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 649763. | + | 192314.i | 0.302682 | + | 0.0895862i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.48422e6i | 1.54986i | 0.632048 | + | 0.774930i | \(0.282215\pi\) | ||||
−0.632048 | + | 0.774930i | \(0.717785\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 346120.i | 0.147120i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −968941. | − | 2.26155e6i | −0.393818 | − | 0.919188i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.58430e6 | −0.616136 | −0.308068 | − | 0.951364i | \(-0.599682\pi\) | ||||
−0.308068 | + | 0.951364i | \(0.599682\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.22087e6 | 1.19930 | 0.599652 | − | 0.800261i | \(-0.295306\pi\) | ||||
0.599652 | + | 0.800261i | \(0.295306\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 397091. | − | 1.34164e6i | 0.141655 | − | 0.478606i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −929907. | −0.318003 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.48018e6 | − | 1.39932e6i | −1.46957 | − | 0.458999i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −884784. | + | 2.98939e6i | −0.278538 | + | 0.941088i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 774236.i | 0.234053i | 0.993129 | + | 0.117027i | \(0.0373363\pi\) | ||||
−0.993129 | + | 0.117027i | \(0.962664\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.15530e6 | −0.916452 | −0.458226 | − | 0.888836i | \(-0.651515\pi\) | ||||
−0.458226 | + | 0.888836i | \(0.651515\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.66160e6 | − | 2.37559e6i | −1.02234 | − | 0.663280i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −669946. | + | 2.14496e6i | −0.179906 | + | 0.576002i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.89669e6i | 0.748519i | 0.927324 | + | 0.374260i | \(0.122103\pi\) | ||||
−0.927324 | + | 0.374260i | \(0.877897\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.07415e6 | − | 7.00786e6i | 0.515999 | − | 1.74339i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 802511.i | 0.192297i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 913439.i | − | 0.210919i | −0.994424 | − | 0.105460i | \(-0.966369\pi\) | ||
0.994424 | − | 0.105460i | \(-0.0336314\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 843214. | − | 1.25802e6i | 0.187709 | − | 0.280050i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.94266e6 | 0.631817 | 0.315908 | − | 0.948790i | \(-0.397691\pi\) | ||||
0.315908 | + | 0.948790i | \(0.397691\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 532380. | 0.110296 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.53027e6 | − | 2.93916e6i | −0.906015 | − | 0.587808i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.80609e6 | 1.12136 | 0.560681 | − | 0.828032i | \(-0.310539\pi\) | ||||
0.560681 | + | 0.828032i | \(0.310539\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 415519. | − | 600290.i | 0.0775312 | − | 0.112008i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.65107e6 | + | 1.67257e6i | 1.01909 | + | 0.301624i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.83986e6i | 0.669508i | 0.942306 | + | 0.334754i | \(0.108653\pi\) | ||||
−0.942306 | + | 0.334754i | \(0.891347\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.37561e6 | 1.41247 | 0.706237 | − | 0.707975i | \(-0.250391\pi\) | ||||
0.706237 | + | 0.707975i | \(0.250391\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −293873. | + | 992898.i | −0.0479519 | + | 0.162014i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.32258e6 | + | 1.35009e6i | 0.682697 | + | 0.213230i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.68668e6i | − | 0.410857i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 597744. | + | 698937.i | 0.0885381 | + | 0.103527i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.85770e6i | 0.697156i | 0.937280 | + | 0.348578i | \(0.113335\pi\) | ||||
−0.937280 | + | 0.348578i | \(0.886665\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 7.86974e6i | − | 1.09468i | −0.836909 | − | 0.547342i | \(-0.815640\pi\) | ||
0.836909 | − | 0.547342i | \(-0.184360\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.89407e6 | − | 5.80969e6i | 0.525170 | − | 0.783518i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.01804e7 | 1.33158 | 0.665789 | − | 0.746140i | \(-0.268095\pi\) | ||||
0.665789 | + | 0.746140i | \(0.268095\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.73312e6 | −0.854392 | −0.427196 | − | 0.904159i | \(-0.640498\pi\) | ||||
−0.427196 | + | 0.904159i | \(0.640498\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.70912e6 | − | 1.98573e6i | −0.826186 | − | 0.244530i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.75446e6 | 0.209727 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.52936e6 | − | 477671.i | −0.177520 | − | 0.0554457i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.05038e7 | − | 6.81472e6i | −1.18423 | − | 0.768311i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3.32405e6i | − | 0.364107i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.09859e6 | 0.436301 | 0.218151 | − | 0.975915i | \(-0.429998\pi\) | ||||
0.218151 | + | 0.975915i | \(0.429998\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.17238e7 | + | 3.46995e6i | 1.21319 | + | 0.359074i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.99449e6 | − | 935285.i | −0.301306 | − | 0.0941085i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 839977.i | − | 0.0822031i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.03124e6 | + | 601196.i | 0.193388 | + | 0.0572379i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.24074e7i | − | 1.14949i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.83188e7i | 1.65189i | 0.563748 | + | 0.825947i | \(0.309359\pi\) | ||||
−0.563748 | + | 0.825947i | \(0.690641\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.32856e6 | + | 1.05361e7i | 0.380010 | + | 0.924982i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.59582e7 | −1.36429 | −0.682144 | − | 0.731218i | \(-0.738952\pi\) | ||||
−0.682144 | + | 0.731218i | \(0.738952\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.32756e7 | −1.10547 | −0.552735 | − | 0.833357i | \(-0.686416\pi\) | ||||
−0.552735 | + | 0.833357i | \(0.686416\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −160663. | + | 542827.i | −0.0130341 | + | 0.0440378i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.13333e7 | −0.895960 | −0.447980 | − | 0.894044i | \(-0.647856\pi\) | ||||
−0.447980 | + | 0.894044i | \(0.647856\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.93119e6 | + | 6.18306e6i | −0.148806 | + | 0.476431i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.14747e6 | − | 1.06343e7i | 0.236438 | − | 0.798844i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.61780e7i | 1.18503i | 0.805559 | + | 0.592516i | \(0.201865\pi\) | ||||
−0.805559 | + | 0.592516i | \(0.798135\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.34658e7 | 0.962014 | 0.481007 | − | 0.876717i | \(-0.340271\pi\) | ||||
0.481007 | + | 0.876717i | \(0.340271\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.42241e7 | + | 1.88851e6i | −0.991301 | + | 0.131614i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.30300e6 | − | 1.37769e7i | 0.292599 | − | 0.936812i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.53509e7i | − | 1.01869i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.83306e6 | + | 1.63293e7i | −0.313058 | + | 1.05772i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00586e7i | 0.636088i | 0.948076 | + | 0.318044i | \(0.103026\pi\) | ||||
−0.948076 | + | 0.318044i | \(0.896974\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.70712e6i | − | 0.475917i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.67853e7 | + | 1.12507e7i | 1.01230 | + | 0.678514i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.26371e7 | −1.33359 | −0.666794 | − | 0.745242i | \(-0.732334\pi\) | ||||
−0.666794 | + | 0.745242i | \(0.732334\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.69274e6 | −0.0974298 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.48984e7 | + | 2.29636e7i | −0.837952 | + | 1.29157i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.98035e6 | −0.328745 | −0.164373 | − | 0.986398i | \(-0.552560\pi\) | ||||
−0.164373 | + | 0.986398i | \(0.552560\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.00873e7 | + | 3.22964e7i | −0.542046 | + | 1.73546i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.75458e6 | + | 1.11126e6i | 0.197255 | + | 0.0583824i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 2.69315e7i | − | 1.38358i | −0.722099 | − | 0.691790i | \(-0.756823\pi\) | ||
0.722099 | − | 0.691790i | \(-0.243177\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.49610e7 | 1.25416 | 0.627082 | − | 0.778953i | \(-0.284249\pi\) | ||||
0.627082 | + | 0.778953i | \(0.284249\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −741962. | + | 2.50684e6i | −0.0364665 | + | 0.123208i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.99054e6 | + | 5.76505e6i | −0.191882 | + | 0.277208i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 3.43348e7i | − | 1.61546i | −0.589554 | − | 0.807729i | \(-0.700697\pi\) | ||
0.589554 | − | 0.807729i | \(-0.299303\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.09942e7 | + | 7.13287e6i | 0.506235 | + | 0.328437i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.83941e7i | − | 1.27970i | −0.768498 | − | 0.639852i | \(-0.778996\pi\) | ||
0.768498 | − | 0.639852i | \(-0.221004\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.60334e7i | 1.14861i | 0.818642 | + | 0.574304i | \(0.194727\pi\) | ||||
−0.818642 | + | 0.574304i | \(0.805273\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.07673e7 | + | 1.39198e7i | 0.897111 | + | 0.601309i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 598903. | 0.0253344 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.17098e7 | 0.485126 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.56449e7 | − | 1.35097e7i | −1.85231 | − | 0.548236i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.71810e7 | 0.683040 | 0.341520 | − | 0.939875i | \(-0.389058\pi\) | ||||
0.341520 | + | 0.939875i | \(0.389058\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.60435e7 | − | 8.13429e6i | −1.01446 | − | 0.316850i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.74060e6 | − | 6.71243e6i | −0.219123 | − | 0.256218i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 3.55925e7i | − | 1.33151i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.17266e6 | 0.0430004 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.64057e7 | + | 7.81541e6i | 0.949225 | + | 0.280947i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.42920e6 | − | 4.57586e6i | 0.0503726 | − | 0.161277i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.77788e7i | − | 1.65128i | −0.564198 | − | 0.825640i | \(-0.690814\pi\) | ||
0.564198 | − | 0.825640i | \(-0.309186\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.75690e7 | + | 1.11195e7i | 1.27337 | + | 0.376885i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.05727e6i | − | 0.0351482i | −0.999846 | − | 0.0175741i | \(-0.994406\pi\) | ||
0.999846 | − | 0.0175741i | \(-0.00559430\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 634349.i | 0.0206869i | 0.999947 | + | 0.0103435i | \(0.00329248\pi\) | ||||
−0.999947 | + | 0.0103435i | \(0.996708\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.71857e6 | − | 3.27689e6i | −0.0869779 | − | 0.104841i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.82810e7 | 0.573881 | 0.286941 | − | 0.957948i | \(-0.407362\pi\) | ||||
0.286941 | + | 0.957948i | \(0.407362\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.68494e7 | −0.519054 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.25280e7 | + | 4.23279e7i | −0.378762 | + | 1.27971i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.43516e7 | 1.31614 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.84288e7 | + | 2.66237e7i | −0.536844 | + | 0.775566i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.67548e6 | − | 2.93115e7i | 0.248113 | − | 0.838292i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.42132e6i | − | 0.0679930i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.94881e7 | 1.36464 | 0.682318 | − | 0.731056i | \(-0.260972\pi\) | ||||
0.682318 | + | 0.731056i | \(0.260972\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.43744e7 | − | 2.21559e7i | 0.389274 | − | 0.600006i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.09196e7 | + | 9.65728e6i | 0.822431 | + | 0.256874i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.06094e7i | 0.538488i | 0.963072 | + | 0.269244i | \(0.0867738\pi\) | ||||
−0.963072 | + | 0.269244i | \(0.913226\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.25354e7 | − | 4.23530e7i | 0.321766 | − | 1.08714i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.06694e6i | 0.203444i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.08922e7i | 0.269919i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.81510e7 | + | 3.22743e7i | 1.17260 | + | 0.785958i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.00318e7 | 0.479438 | 0.239719 | − | 0.970842i | \(-0.422945\pi\) | ||||
0.239719 | + | 0.970842i | \(0.422945\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.79347e6 | −0.0421909 | −0.0210955 | − | 0.999777i | \(-0.506715\pi\) | ||||
−0.0210955 | + | 0.999777i | \(0.506715\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.65108e7 | − | 3.09988e7i | −0.613058 | − | 0.716843i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.48583e7 | −1.92917 | −0.964585 | − | 0.263774i | \(-0.915033\pi\) | ||||
−0.964585 | + | 0.263774i | \(0.915033\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.40302e7 | − | 1.68755e7i | −1.20768 | − | 0.377200i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.24274e6 | − | 2.14367e6i | −0.159184 | − | 0.0471143i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.28803e7i | 1.14291i | 0.820635 | + | 0.571453i | \(0.193620\pi\) | ||||
−0.820635 | + | 0.571453i | \(0.806380\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.82753e6 | 0.166381 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.20320e7 | + | 4.06522e7i | −0.251547 | + | 0.849893i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.36116e6 | − | 2.92382e6i | −0.192509 | − | 0.0601273i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.30840e7i | 0.466995i | 0.972357 | + | 0.233498i | \(0.0750171\pi\) | ||||
−0.972357 | + | 0.233498i | \(0.924983\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.08574e6 | + | 7.83888e6i | −0.101222 | + | 0.156018i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.26474e7i | − | 0.247674i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 5.13180e7i | − | 0.988879i | −0.869212 | − | 0.494440i | \(-0.835373\pi\) | ||
0.869212 | − | 0.494440i | \(-0.164627\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.93070e7 | − | 4.90730e7i | −0.366117 | − | 0.930569i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.78127e7 | −1.45220 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.54962e7 | −0.284648 | −0.142324 | − | 0.989820i | \(-0.545458\pi\) | ||||
−0.142324 | + | 0.989820i | \(0.545458\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.42633e7 | − | 2.78996e7i | −1.70438 | − | 0.504455i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.93567e7 | 0.344536 | 0.172268 | − | 0.985050i | \(-0.444890\pi\) | ||||
0.172268 | + | 0.985050i | \(0.444890\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 781358. | − | 2.50167e6i | 0.0136920 | − | 0.0438377i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.95793e6 | + | 1.53486e7i | −0.171805 | + | 0.264811i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 6.41643e6i | − | 0.109005i | −0.998514 | − | 0.0545023i | \(-0.982643\pi\) | ||
0.998514 | − | 0.0545023i | \(-0.0173572\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.02833e8 | 1.72030 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.02059e7 | − | 2.66987e7i | −1.48613 | − | 0.439858i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.53072e7 | + | 4.90090e7i | −0.248373 | + | 0.795214i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.10971e7i | 1.29609i | 0.761604 | + | 0.648043i | \(0.224412\pi\) | ||||
−0.761604 | + | 0.648043i | \(0.775588\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.96098e6 | − | 2.65222e6i | −0.141071 | − | 0.0417534i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.16305e8i | 1.80370i | 0.432047 | + | 0.901851i | \(0.357792\pi\) | ||||
−0.432047 | + | 0.901851i | \(0.642208\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.72541e7i | 0.569193i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.59758e7 | − | 7.75607e6i | 0.993161 | − | 0.116755i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.62567e7 | 0.241129 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.34494e7 | −0.635059 | −0.317529 | − | 0.948248i | \(-0.602853\pi\) | ||||
−0.317529 | + | 0.948248i | \(0.602853\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.21401e7 | − | 4.10173e7i | 0.174862 | − | 0.590801i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.01988e7 | 0.144776 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.35048e7 | − | 7.52551e7i | 0.328861 | − | 1.05291i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.46807e7 | + | 8.33878e7i | −0.340368 | + | 1.14999i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.29244e8i | 1.75698i | 0.477757 | + | 0.878492i | \(0.341450\pi\) | ||||
−0.477757 | + | 0.878492i | \(0.658550\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.10725e7 | 1.08649 | 0.543247 | − | 0.839573i | \(-0.317195\pi\) | ||||
0.543247 | + | 0.839573i | \(0.317195\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.16920e7 | + | 2.05612e7i | 0.418724 | + | 0.271661i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.69209e7 | − | 5.32443e7i | −1.00202 | − | 0.693596i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.79193e6i | 0.0230164i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.12563e6 | − | 2.40751e7i | 0.0902509 | − | 0.304928i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.64885e7i | 0.205944i | 0.994684 | + | 0.102972i | \(0.0328352\pi\) | ||||
−0.994684 | + | 0.102972i | \(0.967165\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6.35196e7i | − | 0.782428i | −0.920300 | − | 0.391214i | \(-0.872055\pi\) | ||
0.920300 | − | 0.391214i | \(-0.127945\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.05584e7 | − | 1.05268e8i | 0.857198 | − | 1.27888i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.27229e8 | 1.52455 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.43748e8 | −1.69905 | −0.849526 | − | 0.527546i | \(-0.823112\pi\) | ||||
−0.849526 | + | 0.527546i | \(0.823112\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.06149e7 | − | 4.58138e7i | −0.823342 | − | 0.534171i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.14621e7 | 0.706962 | 0.353481 | − | 0.935442i | \(-0.384998\pi\) | ||||
0.353481 | + | 0.935442i | \(0.384998\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.73033e7 | − | 5.40443e6i | −0.196358 | − | 0.0613295i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.00448e7 | − | 5.93277e6i | −0.224429 | − | 0.0664255i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.12007e7i | 0.565635i | 0.959174 | + | 0.282818i | \(0.0912692\pi\) | ||||
−0.959174 | + | 0.282818i | \(0.908731\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.75173e6 | −0.0627002 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.41782e7 | − | 8.16901e7i | 0.260094 | − | 0.878770i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.60841e6 | − | 1.15530e7i | 0.0383073 | − | 0.122648i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.05860e8i | 1.10913i | 0.832140 | + | 0.554566i | \(0.187116\pi\) | ||||
−0.832140 | + | 0.554566i | \(0.812884\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.95614e7 | − | 7.65947e7i | 0.926153 | − | 0.792065i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.30381e8i | − | 1.33079i | −0.746491 | − | 0.665396i | \(-0.768263\pi\) | ||
0.746491 | − | 0.665396i | \(-0.231737\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.84090e7i | 0.286229i | 0.989706 | + | 0.143115i | \(0.0457117\pi\) | ||||
−0.989706 | + | 0.143115i | \(0.954288\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.03990e7 | − | 3.37810e7i | −0.501260 | − | 0.335980i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.48443e7 | 0.734866 | 0.367433 | − | 0.930050i | \(-0.380237\pi\) | ||||
0.367433 | + | 0.930050i | \(0.380237\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.21083e7 | −0.117372 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.49947e7 | − | 2.21966e7i | −0.717741 | − | 0.212433i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.12619e7 | −0.106422 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.51694e7 | − | 6.58758e7i | −0.888007 | − | 0.614675i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.65538e8 | + | 1.07399e8i | 1.52526 | + | 0.989564i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 1.80284e8i | − | 1.64041i | −0.572072 | − | 0.820203i | \(-0.693860\pi\) | ||
0.572072 | − | 0.820203i | \(-0.306140\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.50756e7 | 0.674627 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.07768e7 | − | 6.14942e6i | −0.184390 | − | 0.0545749i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.10359e8 | + | 6.57023e7i | 1.84389 | + | 0.575911i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.11747e8i | 0.967497i | 0.875207 | + | 0.483748i | \(0.160725\pi\) | ||||
−0.875207 | + | 0.483748i | \(0.839275\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.36488e7 | + | 6.99944e6i | 0.202247 | + | 0.0598600i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.05636e8i | 0.892418i | 0.894929 | + | 0.446209i | \(0.147226\pi\) | ||||
−0.894929 | + | 0.446209i | \(0.852774\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2.24816e8i | − | 1.87623i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.61085e7 | + | 3.14705e7i | 0.215262 | + | 0.259471i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.11585e7 | 0.172352 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.60397e8 | 1.29091 | 0.645455 | − | 0.763798i | \(-0.276668\pi\) | ||||
0.645455 | + | 0.763798i | \(0.276668\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.25489e7 | + | 7.61850e7i | −0.179313 | + | 0.605838i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.96577e7 | −0.468773 | −0.234386 | − | 0.972144i | \(-0.575308\pi\) | ||||
−0.234386 | + | 0.972144i | \(0.575308\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.21693e8 | − | 3.80090e7i | −0.944912 | − | 0.295129i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.07949e6 | + | 1.37832e7i | −0.0313027 | + | 0.105761i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 2.85507e7i | − | 0.216503i | −0.994124 | − | 0.108251i | \(-0.965475\pi\) | ||
0.994124 | − | 0.108251i | \(-0.0345251\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.66588e6 | 0.0274736 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.10809e8 | − | 9.47657e7i | 0.820770 | − | 0.701939i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.73140e8 | − | 5.40777e7i | −1.26758 | − | 0.395910i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.32538e7i | 0.168276i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.44906e7 | + | 1.50319e8i | −0.318248 | + | 1.07525i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.71342e7i | 0.121158i | 0.998163 | + | 0.0605788i | \(0.0192946\pi\) | ||||
−0.998163 | + | 0.0605788i | \(0.980705\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.49188e8i | 1.04286i | 0.853293 | + | 0.521432i | \(0.174602\pi\) | ||||
−0.853293 | + | 0.521432i | \(0.825398\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.23574e7 | + | 1.53576e7i | 0.0853983 | + | 0.106132i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.07634e8 | −0.735391 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.46956e8 | 0.992708 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.66053e7 | + | 1.33489e8i | −0.578443 | + | 0.891581i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.65622e7 | −0.175421 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.09278e7 | − | 1.95072e8i | 0.397882 | − | 1.27389i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.94132e7 | − | 2.94238e7i | −0.641979 | − | 0.190010i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 5.18132e7i | − | 0.330883i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.39377e6 | −0.0530109 | −0.0265055 | − | 0.999649i | \(-0.508438\pi\) | ||||
−0.0265055 | + | 0.999649i | \(0.508438\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.41801e7 | + | 2.16843e8i | −0.400867 | + | 1.35440i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.21917e7 | + | 1.35085e8i | −0.260638 | + | 0.834483i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.88362e7i | 0.542785i | 0.962469 | + | 0.271393i | \(0.0874842\pi\) | ||||
−0.962469 | + | 0.271393i | \(0.912516\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.34541e7 | − | 1.52166e7i | −0.141743 | − | 0.0919605i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.78150e8i | − | 1.66274i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1.91921e7i | − | 0.113488i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.80765e7 | + | 1.01565e8i | −0.398215 | + | 0.594110i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.17471e7 | −0.183713 | −0.0918563 | − | 0.995772i | \(-0.529280\pi\) | ||||
−0.0918563 | + | 0.995772i | \(0.529280\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.20091e7 | −0.297744 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.95576e7 | + | 2.05873e7i | 0.393963 | + | 0.116603i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.40188e8 | −0.785571 | −0.392786 | − | 0.919630i | \(-0.628489\pi\) | ||||
−0.392786 | + | 0.919630i | \(0.628489\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.09640e7 | + | 1.95188e8i | −0.338009 | + | 1.08220i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.26757e7 | + | 1.01197e7i | −0.124397 | + | 0.0555162i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.89176e8i | − | 1.02690i | −0.858118 | − | 0.513452i | \(-0.828366\pi\) | ||
0.858118 | − | 0.513452i | \(-0.171634\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.79939e7 | −0.150368 | −0.0751839 | − | 0.997170i | \(-0.523954\pi\) | ||||
−0.0751839 | + | 0.997170i | \(0.523954\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.25765e8 | − | 3.72232e7i | −0.668491 | − | 0.197856i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.20659e8 | − | 1.52739e8i | −1.16069 | − | 0.803428i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.22774e7i | 0.272136i | 0.990699 | + | 0.136068i | \(0.0434466\pi\) | ||||
−0.990699 | + | 0.136068i | \(0.956553\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.03746e8 | + | 6.03037e7i | 1.04967 | + | 0.310677i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.94702e7i | 0.150264i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.21463e8i | 0.612968i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.20572e8 | + | 1.45335e8i | 0.602255 | + | 0.725942i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.79365e8 | −1.38120 | −0.690601 | − | 0.723236i | \(-0.742654\pi\) | ||||
−0.690601 | + | 0.723236i | \(0.742654\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.33169e8 | −0.651714 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.80097e7 | + | 2.63569e8i | −0.377908 | + | 1.27683i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.41885e7 | 0.211907 | 0.105953 | − | 0.994371i | \(-0.466211\pi\) | ||||
0.105953 | + | 0.994371i | \(0.466211\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.33788e7 | + | 1.04254e7i | 0.158460 | + | 0.0494927i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.15941e7 | − | 1.74319e8i | 0.242481 | − | 0.819261i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.93133e7i | 0.462090i | 0.972943 | + | 0.231045i | \(0.0742145\pi\) | ||||
−0.972943 | + | 0.231045i | \(0.925786\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.93309e7 | −0.273311 | −0.136656 | − | 0.990619i | \(-0.543635\pi\) | ||||
−0.136656 | + | 0.990619i | \(0.543635\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.02820e8 | − | 1.58482e8i | 0.468951 | − | 0.722816i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.85158e7 | − | 1.87349e8i | 0.264245 | − | 0.846031i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.86583e8i | − | 1.28140i | −0.767792 | − | 0.640699i | \(-0.778645\pi\) | ||
0.767792 | − | 0.640699i | \(-0.221355\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.34440e7 | + | 4.54226e7i | −0.0595217 | + | 0.201104i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.07389e8i | 0.470799i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.08241e8i | − | 0.469905i | −0.972007 | − | 0.234952i | \(-0.924507\pi\) | ||
0.972007 | − | 0.234952i | \(-0.0754934\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.40859e7 | − | 3.59345e7i | 0.103547 | − | 0.154485i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.93425e8 | 0.823486 | 0.411743 | − | 0.911300i | \(-0.364920\pi\) | ||||
0.411743 | + | 0.911300i | \(0.364920\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.00769e7 | −0.379788 | −0.189894 | − | 0.981805i | \(-0.560814\pi\) | ||||
−0.189894 | + | 0.981805i | \(0.560814\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.56920e8 | − | 2.19723e8i | 1.07281 | − | 0.917489i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.77606e6 | 0.0280229 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.59721e7 | + | 2.28503e8i | 0.352142 | + | 0.935947i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.60591e7 | + | 2.54713e7i | 0.349136 | + | 0.103335i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.16907e8i | 0.871611i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.54497e8 | 0.614939 | 0.307469 | − | 0.951558i | \(-0.400518\pi\) | ||||
0.307469 | + | 0.951558i | \(0.400518\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.14064e7 | + | 1.06112e8i | −0.123825 | + | 0.418362i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.34421e8 | + | 1.35685e8i | 1.69664 | + | 0.529920i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.39280e8i | − | 0.925737i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.79673e8 | + | 2.76938e8i | −0.688620 | + | 1.06140i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 2.72023e8i | − | 1.03284i | −0.856337 | − | 0.516418i | \(-0.827265\pi\) | ||
0.856337 | − | 0.516418i | \(-0.172735\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.76649e8i | 1.04063i | 0.853975 | + | 0.520314i | \(0.174185\pi\) | ||||
−0.853975 | + | 0.520314i | \(0.825815\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.71604e7 | − | 7.03601e7i | 0.175751 | − | 0.262209i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.70822e7 | 0.321526 | 0.160763 | − | 0.986993i | \(-0.448604\pi\) | ||||
0.160763 | + | 0.986993i | \(0.448604\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.79465e7 | −0.358306 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.17468e7 | + | 6.43652e6i | 0.0788230 | + | 0.0233296i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.42171e8 | 0.869726 | 0.434863 | − | 0.900497i | \(-0.356797\pi\) | ||||
0.434863 | + | 0.900497i | \(0.356797\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.15722e8 | + | 1.29845e8i | 1.47938 | + | 0.462062i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.11297e7 | + | 4.79816e7i | −0.109769 | + | 0.169192i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 4.98679e8i | − | 1.74247i | −0.490869 | − | 0.871234i | \(-0.663320\pi\) | ||
0.490869 | − | 0.871234i | \(-0.336680\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.09071e8 | −0.377665 | −0.188832 | − | 0.982009i | \(-0.560470\pi\) | ||||
−0.188832 | + | 0.982009i | \(0.560470\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.21226e8 | + | 9.50747e7i | 1.10222 | + | 0.326230i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.12975e7 | + | 1.28986e7i | 0.140430 | + | 0.0438611i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 6.44916e8i | − | 2.17333i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.74270e8 | − | 1.40372e8i | −1.58397 | − | 0.468816i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.72093e7i | − | 0.0569633i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 2.24827e8i | − | 0.737571i | −0.929515 | − | 0.368785i | \(-0.879774\pi\) | ||
0.929515 | − | 0.368785i | \(-0.120226\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.05947e8 | + | 3.13300e7i | −0.994798 | + | 0.101871i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.36225e8 | −0.439027 | −0.219513 | − | 0.975609i | \(-0.570447\pi\) | ||||
−0.219513 | + | 0.975609i | \(0.570447\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.23774e7 | −0.263147 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.22283e8 | − | 4.13154e8i | 0.387192 | − | 1.30819i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.37618e8 | 0.745791 | 0.372895 | − | 0.927873i | \(-0.378365\pi\) | ||||
0.372895 | + | 0.927873i | \(0.378365\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.90413e7 | + | 1.89032e8i | −0.183689 | + | 0.588117i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.01727e8 | − | 3.43702e8i | 0.313738 | − | 1.06002i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.60930e8i | 1.71495i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.59119e8 | −1.39153 | −0.695763 | − | 0.718271i | \(-0.744934\pi\) | ||||
−0.695763 | + | 0.718271i | \(0.744934\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.28226e7 | − | 8.31907e6i | −0.0385279 | − | 0.0249963i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.20030e8 | − | 3.84300e8i | 0.357550 | − | 1.14476i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 7.67432e7i | − | 0.226643i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.68440e7 | − | 2.93417e8i | 0.254278 | − | 0.859119i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.74480e8i | 1.37741i | 0.725040 | + | 0.688706i | \(0.241821\pi\) | ||||
−0.725040 | + | 0.688706i | \(0.758179\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.68366e8i | 0.772433i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.45280e8 | − | 9.73772e7i | −0.414609 | − | 0.277901i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.76556e7 | 0.134851 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.42288e8 | 1.24098 | 0.620492 | − | 0.784213i | \(-0.286933\pi\) | ||||
0.620492 | + | 0.784213i | \(0.286933\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.51201e8 | + | 1.62975e8i | 0.698895 | + | 0.453432i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.08764e8 | −0.851841 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.46543e7 | + | 1.10952e8i | −0.0948068 | + | 0.303542i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.18844e8 | − | 1.23967e8i | −1.13631 | − | 0.336318i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.01334e8i | 0.810703i | 0.914161 | + | 0.405352i | \(0.132851\pi\) | ||||
−0.914161 | + | 0.405352i | \(0.867149\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.78025e7 | 0.180901 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.03185e8 | + | 3.48627e8i | −0.273024 | + | 0.922458i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.33920e8 | + | 4.82407e8i | −0.876252 | + | 1.26590i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 9.93407e7i | − | 0.258538i | −0.991610 | − | 0.129269i | \(-0.958737\pi\) | ||
0.991610 | − | 0.129269i | \(-0.0412630\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.01021e7 | − | 3.82730e8i | 0.155134 | − | 0.987893i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.50264e8i | − | 0.384683i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.97037e8i | 0.754221i | 0.926168 | + | 0.377110i | \(0.123082\pi\) | ||||
−0.926168 | + | 0.377110i | \(0.876918\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.23708e8 | + | 2.16972e8i | 0.815251 | + | 0.546440i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.16285e8 | 0.290483 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.04157e8 | 0.753642 | 0.376821 | − | 0.926286i | \(-0.377017\pi\) | ||||
0.376821 | + | 0.926286i | \(0.377017\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.97432e8 | + | 1.17630e8i | 0.976805 | + | 0.289110i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.58582e8 | 0.630422 | 0.315211 | − | 0.949022i | \(-0.397925\pi\) | ||||
0.315211 | + | 0.949022i | \(0.397925\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.23785e7 | + | 2.88530e7i | 0.223410 | + | 0.0697786i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.85728e8 | − | 2.50254e8i | −0.925378 | − | 0.600370i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.63911e7i | 0.181802i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.18305e8 | −1.45977 | −0.729883 | − | 0.683572i | \(-0.760426\pi\) | ||||
−0.729883 | + | 0.683572i | \(0.760426\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.60416e8 | − | 7.70765e7i | −0.609933 | − | 0.180525i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.17587e8 | + | 3.76477e8i | −0.273223 | + | 0.874776i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.16925e7i | 0.0730581i | 0.999333 | + | 0.0365291i | \(0.0116301\pi\) | ||||
−0.999333 | + | 0.0365291i | \(0.988370\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.99536e8 | + | 5.90576e7i | 0.456348 | + | 0.135067i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.25119e8i | 1.64534i | 0.568520 | + | 0.822669i | \(0.307516\pi\) | ||||
−0.568520 | + | 0.822669i | \(0.692484\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 5.28999e7i | − | 0.119092i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.19900e8 | + | 3.48356e8i | −0.937910 | + | 0.778107i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.52329e8 | −1.00246 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.41653e7 | 0.0751288 | 0.0375644 | − | 0.999294i | \(-0.488040\pi\) | ||||
0.0375644 | + | 0.999294i | \(0.488040\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.73462e8 | − | 5.86071e8i | 0.378479 | − | 1.27875i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.77153e8 | −1.03304 | −0.516522 | − | 0.856274i | \(-0.672774\pi\) | ||||
−0.516522 | + | 0.856274i | \(0.672774\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.30961e8 | + | 1.59870e8i | 0.496173 | + | 0.343449i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.29710e7 | − | 4.38248e7i | 0.0276511 | − | 0.0934237i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 9.49494e7i | − | 0.200854i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.03201e8 | −0.426553 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.80361e8 | − | 5.61682e8i | −1.00065 | − | 1.17005i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.45620e8 | + | 1.07949e8i | 0.714480 | + | 0.223157i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.04787e8i | 0.830429i | 0.909724 | + | 0.415214i | \(0.136293\pi\) | ||||
−0.909724 | + | 0.415214i | \(0.863707\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.58259e7 | − | 1.54830e8i | 0.0932996 | − | 0.315228i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 7.64365e7i | − | 0.154444i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 7.94746e7i | − | 0.159371i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.58850e8 | − | 5.08636e8i | −1.51027 | − | 1.01229i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.00656e8 | −1.38398 | −0.691990 | − | 0.721907i | \(-0.743266\pi\) | ||||
−0.691990 | + | 0.721907i | \(0.743266\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.10266e8 | −0.608267 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.75406e7 | + | 8.86900e7i | −0.111964 | + | 0.172575i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.52062e7 | −0.0679943 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.57520e7 | + | 2.99067e7i | 0.183553 | + | 0.0573299i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.97252e8 | + | 2.06369e8i | 1.32669 | + | 0.392667i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 7.73522e7i | − | 0.146092i | −0.997329 | − | 0.0730461i | \(-0.976728\pi\) | ||
0.997329 | − | 0.0730461i | \(-0.0232720\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.60258e8 | −0.487913 | −0.243956 | − | 0.969786i | \(-0.578445\pi\) | ||||
−0.243956 | + | 0.969786i | \(0.578445\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.91270e8 | + | 6.46236e8i | −0.355938 | + | 1.20260i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.08988e8 | − | 3.40406e7i | −0.201328 | − | 0.0628817i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.85912e8i | − | 0.340911i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.92162e7 | − | 3.84185e7i | −0.107793 | − | 0.0699341i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 3.85083e8i | − | 0.695865i | −0.937520 | − | 0.347933i | \(-0.886884\pi\) | ||
0.937520 | − | 0.347933i | \(-0.113116\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 5.06014e8i | − | 0.907742i | −0.891067 | − | 0.453871i | \(-0.850043\pi\) | ||
0.891067 | − | 0.453871i | \(-0.149957\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.18678e8 | − | 1.47490e8i | −0.211352 | − | 0.262665i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.19429e8 | 1.44875 | 0.724377 | − | 0.689404i | \(-0.242127\pi\) | ||||
0.724377 | + | 0.689404i | \(0.242127\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.12105e9 | 1.96772 | 0.983858 | − | 0.178953i | \(-0.0572710\pi\) | ||||
0.983858 | + | 0.178953i | \(0.0572710\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.88922e8 | + | 2.63099e8i | 1.54903 | + | 0.458475i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.91324e8 | 1.19604 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.09663e8 | − | 3.51106e8i | 0.188365 | − | 0.603085i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.68915e8 | + | 2.29981e8i | −0.458604 | + | 0.392207i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 5.59565e8i | − | 0.947468i | −0.880668 | − | 0.473734i | \(-0.842906\pi\) | ||
0.880668 | − | 0.473734i | \(-0.157094\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.15101e8 | −1.37032 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.35119e8 | + | 2.17577e8i | 1.22708 | + | 0.363186i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.98399e7 | − | 6.35212e7i | 0.0328828 | − | 0.105281i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.33670e7i | 0.120740i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.74000e8 | − | 1.99487e8i | −1.10138 | − | 0.325980i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.22231e8i | 1.00963i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.75527e8i | 1.24954i | 0.780809 | + | 0.624769i | \(0.214807\pi\) | ||||
−0.780809 | + | 0.624769i | \(0.785193\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.19515e8 | + | 4.30999e8i | −0.831189 | + | 0.689570i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.08412e8 | 0.807742 | 0.403871 | − | 0.914816i | \(-0.367664\pi\) | ||||
0.403871 | + | 0.914816i | \(0.367664\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.02867e8 | 0.635597 | 0.317798 | − | 0.948158i | \(-0.397056\pi\) | ||||
0.317798 | + | 0.948158i | \(0.397056\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.58924e6 | + | 1.55055e7i | −0.00719004 | + | 0.0242927i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.50809e8 | 0.390222 | 0.195111 | − | 0.980781i | \(-0.437493\pi\) | ||||
0.195111 | + | 0.980781i | \(0.437493\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.16372e8 | − | 6.92758e8i | 0.334313 | − | 1.07037i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.97288e7 | + | 3.03164e8i | −0.137681 | + | 0.465179i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.84317e8i | 0.280870i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.37019e8 | 0.812709 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.99529e8 | − | 1.07822e9i | 1.05139 | − | 1.62055i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.61391e7 | − | 7.19485e7i | −0.0837995 | − | 0.107398i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 9.44801e7i | − | 0.140069i | −0.997545 | − | 0.0700344i | \(-0.977689\pi\) | ||
0.997545 | − | 0.0700344i | \(-0.0223109\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.31654e8 | + | 4.44813e8i | −0.193850 | + | 0.654955i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 5.66238e8i | − | 0.828079i | −0.910259 | − | 0.414039i | \(-0.864118\pi\) | ||
0.910259 | − | 0.414039i | \(-0.135882\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 7.41125e8i | − | 1.07649i | −0.842789 | − | 0.538244i | \(-0.819088\pi\) | ||
0.842789 | − | 0.538244i | \(-0.180912\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.10159e8 | − | 6.11930e8i | 0.591729 | − | 0.882819i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.32272e8 | 1.04930 | 0.524652 | − | 0.851317i | \(-0.324195\pi\) | ||||
0.524652 | + | 0.851317i | \(0.324195\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.70121e8 | −0.242133 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.17772e8 | − | 9.71875e7i | 0.307871 | − | 0.137397i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.83873e8 | −0.539055 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.58155e8 | + | 1.43098e8i | 0.639062 | + | 0.199601i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.21482e8 | + | 2.72736e8i | 1.27676 | + | 0.377889i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.75025e8i | 0.929053i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.62063e9 | −2.21570 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.98577e6 | + | 3.03599e7i | −0.0122037 | + | 0.0412323i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.12129e8 | − | 9.99341e8i | 0.421103 | − | 1.34824i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.14826e8i | 0.958029i | 0.877807 | + | 0.479014i | \(0.159006\pi\) | ||||
−0.877807 | + | 0.479014i | \(0.840994\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.04679e8 | + | 6.23750e8i | −0.538790 | + | 0.830461i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.40325e9i | − | 1.85601i | −0.372570 | − | 0.928004i | \(-0.621523\pi\) | ||
0.372570 | − | 0.928004i | \(-0.378477\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 2.83025e8i | − | 0.371889i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.07517e8 | + | 7.20654e7i | 0.140350 | + | 0.0940726i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.62799e8 | −0.211127 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.41305e9 | −1.82059 | −0.910295 | − | 0.413960i | \(-0.864145\pi\) | ||||
−0.910295 | + | 0.413960i | \(0.864145\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.23699e9 | + | 3.66117e8i | 1.58338 | + | 0.468641i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.38409e8 | −1.19340 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.22174e8 | − | 4.65438e8i | 0.407067 | − | 0.588081i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.75762e8 | + | 8.87448e8i | −0.722776 | + | 1.11405i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1.19239e9i | − | 1.48721i | −0.668621 | − | 0.743604i | \(-0.733115\pi\) | ||
0.668621 | − | 0.743604i | \(-0.266885\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.55331e8 | 1.05995 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.73724e7 | + | 8.10155e6i | 0.0337030 | + | 0.00997523i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.20562e8 | − | 1.00123e8i | −0.392173 | − | 0.122489i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.46631e9i | 1.78241i | 0.453598 | + | 0.891206i | \(0.350140\pi\) | ||||
−0.453598 | + | 0.891206i | \(0.649860\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.64232e7 | − | 4.86085e6i | −0.0198363 | − | 0.00587105i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.75926e8i | 0.331149i | 0.986197 | + | 0.165575i | \(0.0529479\pi\) | ||||
−0.986197 | + | 0.165575i | \(0.947052\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.20149e8i | − | 0.262532i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.05670e8 | − | 4.52734e7i | 0.125215 | − | 0.0536472i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.93474e8 | −0.345557 | −0.172778 | − | 0.984961i | \(-0.555274\pi\) | ||||
−0.172778 | + | 0.984961i | \(0.555274\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.62587e8 | −0.190233 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.40082e8 | + | 4.73292e8i | −0.162870 | + | 0.550284i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.98288e8 | 0.575707 | 0.287854 | − | 0.957674i | \(-0.407058\pi\) | ||||
0.287854 | + | 0.957674i | \(0.407058\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.79599e8 | + | 1.81029e8i | 0.665453 | + | 0.207844i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.29113e8 | − | 4.36228e8i | 0.147310 | − | 0.497712i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 7.40258e7i | − | 0.0839320i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.64324e8 | −0.635856 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.99862e8 | − | 6.48695e8i | −1.11960 | − | 0.726376i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.38983e8 | − | 2.93277e8i | −1.04490 | − | 0.326359i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.12248e9i | 1.24137i | 0.784060 | + | 0.620685i | \(0.213145\pi\) | ||||
−0.784060 | + | 0.620685i | \(0.786855\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.39855e8 | + | 1.14826e9i | −0.373527 | + | 1.26202i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.83802e8i | 0.309997i | 0.987915 | + | 0.154998i | \(0.0495373\pi\) | ||||
−0.987915 | + | 0.154998i | \(0.950463\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.50494e8i | 0.163373i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.48068e8 | − | 6.81130e8i | −0.591317 | − | 0.734879i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.06216e8 | 0.221125 | 0.110562 | − | 0.993869i | \(-0.464735\pi\) | ||||
0.110562 | + | 0.993869i | \(0.464735\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.50757e7 | −0.0693539 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.92392e8 | + | 4.49213e8i | 0.733407 | + | 0.475823i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.13092e9 | −1.19061 | −0.595306 | − | 0.803499i | \(-0.702969\pi\) | ||||
−0.595306 | + | 0.803499i | \(0.702969\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.79387e8 | − | 1.21468e9i | 0.396985 | − | 1.27102i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.26875e7 | + | 1.85539e7i | 0.0651972 | + | 0.0192967i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 4.31054e8i | − | 0.445598i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.33850e8 | −0.343029 | −0.171514 | − | 0.985182i | \(-0.554866\pi\) | ||||
−0.171514 | + | 0.985182i | \(0.554866\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.79214e8 | + | 1.28124e9i | −0.387290 | + | 1.30852i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.50919e8 | + | 8.03366e8i | −0.254721 | + | 0.815538i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 5.06430e7i | − | 0.0511015i | −0.999674 | − | 0.0255508i | \(-0.991866\pi\) | ||
0.999674 | − | 0.0255508i | \(-0.00813395\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.63464e8 | + | 5.41924e8i | 0.464857 | + | 0.543553i |
(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 | 60.7.b.a.29.6 | yes | 12 | |
3.2 | odd | 2 | inner | 60.7.b.a.29.8 | yes | 12 | |
4.3 | odd | 2 | 240.7.c.e.209.7 | 12 | |||
5.2 | odd | 4 | 300.7.g.i.101.12 | 12 | |||
5.3 | odd | 4 | 300.7.g.i.101.1 | 12 | |||
5.4 | even | 2 | inner | 60.7.b.a.29.7 | yes | 12 | |
12.11 | even | 2 | 240.7.c.e.209.5 | 12 | |||
15.2 | even | 4 | 300.7.g.i.101.11 | 12 | |||
15.8 | even | 4 | 300.7.g.i.101.2 | 12 | |||
15.14 | odd | 2 | inner | 60.7.b.a.29.5 | ✓ | 12 | |
20.19 | odd | 2 | 240.7.c.e.209.6 | 12 | |||
60.59 | even | 2 | 240.7.c.e.209.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.b.a.29.5 | ✓ | 12 | 15.14 | odd | 2 | inner | |
60.7.b.a.29.6 | yes | 12 | 1.1 | even | 1 | trivial | |
60.7.b.a.29.7 | yes | 12 | 5.4 | even | 2 | inner | |
60.7.b.a.29.8 | yes | 12 | 3.2 | odd | 2 | inner | |
240.7.c.e.209.5 | 12 | 12.11 | even | 2 | |||
240.7.c.e.209.6 | 12 | 20.19 | odd | 2 | |||
240.7.c.e.209.7 | 12 | 4.3 | odd | 2 | |||
240.7.c.e.209.8 | 12 | 60.59 | even | 2 | |||
300.7.g.i.101.1 | 12 | 5.3 | odd | 4 | |||
300.7.g.i.101.2 | 12 | 15.8 | even | 4 | |||
300.7.g.i.101.11 | 12 | 15.2 | even | 4 | |||
300.7.g.i.101.12 | 12 | 5.2 | odd | 4 |