Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,3,Mod(111,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.111");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.r (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.71936845953\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 111.16 | ||
Character | \(\chi\) | \(=\) | 320.111 |
Dual form | 320.3.r.a.271.16 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | 3.96156 | − | 3.96156i | 1.32052 | − | 1.32052i | 0.407168 | − | 0.913353i | \(-0.366517\pi\) |
0.913353 | − | 0.407168i | \(-0.133483\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.58114 | + | 1.58114i | −0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.171519 | −0.0245028 | −0.0122514 | − | 0.999925i | \(-0.503900\pi\) | ||||
−0.0122514 | + | 0.999925i | \(0.503900\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 22.3880i | − | 2.48755i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.37561 | − | 3.37561i | −0.306874 | − | 0.306874i | 0.536822 | − | 0.843696i | \(-0.319625\pi\) |
−0.843696 | + | 0.536822i | \(0.819625\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.2513 | − | 13.2513i | −1.01933 | − | 1.01933i | −0.999809 | − | 0.0195186i | \(-0.993787\pi\) |
−0.0195186 | − | 0.999809i | \(-0.506213\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 12.5276i | 0.835171i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.67091 | 0.0982886 | 0.0491443 | − | 0.998792i | \(-0.484351\pi\) | ||||
0.0491443 | + | 0.998792i | \(0.484351\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20.7019 | − | 20.7019i | 1.08957 | − | 1.08957i | 0.0940016 | − | 0.995572i | \(-0.470034\pi\) |
0.995572 | − | 0.0940016i | \(-0.0299659\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.679485 | + | 0.679485i | −0.0323564 | + | 0.0323564i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 29.6804 | 1.29045 | 0.645227 | − | 0.763991i | \(-0.276763\pi\) | ||||
0.645227 | + | 0.763991i | \(0.276763\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 5.00000i | − | 0.200000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −53.0373 | − | 53.0373i | −1.96434 | − | 1.96434i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.65510 | + | 7.65510i | 0.263969 | + | 0.263969i | 0.826664 | − | 0.562695i | \(-0.190236\pi\) |
−0.562695 | + | 0.826664i | \(0.690236\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 34.7971i | 1.12249i | 0.827651 | + | 0.561244i | \(0.189677\pi\) | ||||
−0.827651 | + | 0.561244i | \(0.810323\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −26.7454 | −0.810467 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.271196 | − | 0.271196i | 0.00774845 | − | 0.00774845i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.8454 | + | 10.8454i | −0.293119 | + | 0.293119i | −0.838311 | − | 0.545192i | \(-0.816457\pi\) |
0.545192 | + | 0.838311i | \(0.316457\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −104.991 | −2.69209 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 46.3942i | 1.13157i | 0.824554 | + | 0.565783i | \(0.191426\pi\) | ||||
−0.824554 | + | 0.565783i | \(0.808574\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 27.1102 | + | 27.1102i | 0.630470 | + | 0.630470i | 0.948186 | − | 0.317716i | \(-0.102916\pi\) |
−0.317716 | + | 0.948186i | \(0.602916\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 35.3985 | + | 35.3985i | 0.786633 | + | 0.786633i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 38.7366i | − | 0.824182i | −0.911143 | − | 0.412091i | \(-0.864798\pi\) | ||
0.911143 | − | 0.412091i | \(-0.135202\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.9706 | −0.999400 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.61940 | − | 6.61940i | 0.129792 | − | 0.129792i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 24.0547 | − | 24.0547i | 0.453863 | − | 0.453863i | −0.442772 | − | 0.896634i | \(-0.646005\pi\) |
0.896634 | + | 0.442772i | \(0.146005\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.6746 | 0.194084 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 164.024i | − | 2.87761i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 37.2621 | + | 37.2621i | 0.631562 | + | 0.631562i | 0.948460 | − | 0.316898i | \(-0.102641\pi\) |
−0.316898 | + | 0.948460i | \(0.602641\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 35.4044 | + | 35.4044i | 0.580401 | + | 0.580401i | 0.935013 | − | 0.354613i | \(-0.115387\pi\) |
−0.354613 | + | 0.935013i | \(0.615387\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.83997i | 0.0609519i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 41.9042 | 0.644680 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.1498 | − | 11.1498i | 0.166415 | − | 0.166415i | −0.618986 | − | 0.785402i | \(-0.712456\pi\) |
0.785402 | + | 0.618986i | \(0.212456\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 117.581 | − | 117.581i | 1.70407 | − | 1.70407i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.07991 | −0.0433790 | −0.0216895 | − | 0.999765i | \(-0.506905\pi\) | ||||
−0.0216895 | + | 0.999765i | \(0.506905\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 92.3346i | 1.26486i | 0.774619 | + | 0.632429i | \(0.217942\pi\) | ||||
−0.774619 | + | 0.632429i | \(0.782058\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −19.8078 | − | 19.8078i | −0.264104 | − | 0.264104i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.578983 | + | 0.578983i | 0.00751925 | + | 0.00751925i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 25.0660i | − | 0.317291i | −0.987336 | − | 0.158645i | \(-0.949287\pi\) | ||
0.987336 | − | 0.158645i | \(-0.0507127\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −218.729 | −2.70036 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 87.5940 | − | 87.5940i | 1.05535 | − | 1.05535i | 0.0569734 | − | 0.998376i | \(-0.481855\pi\) |
0.998376 | − | 0.0569734i | \(-0.0181450\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.64193 | + | 2.64193i | −0.0310816 | + | 0.0310816i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 60.6523 | 0.697153 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 135.913i | 1.52712i | 0.645738 | + | 0.763559i | \(0.276550\pi\) | ||||
−0.645738 | + | 0.763559i | \(0.723450\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.27285 | + | 2.27285i | 0.0249764 | + | 0.0249764i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 137.851 | + | 137.851i | 1.48227 | + | 1.48227i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 65.4652i | 0.689107i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 25.0559 | 0.258308 | 0.129154 | − | 0.991625i | \(-0.458774\pi\) | ||||
0.129154 | + | 0.991625i | \(0.458774\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −75.5731 | + | 75.5731i | −0.763364 | + | 0.763364i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 21.6565 | − | 21.6565i | 0.214421 | − | 0.214421i | −0.591721 | − | 0.806143i | \(-0.701551\pi\) |
0.806143 | + | 0.591721i | \(0.201551\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −59.5422 | −0.578079 | −0.289040 | − | 0.957317i | \(-0.593336\pi\) | ||||
−0.289040 | + | 0.957317i | \(0.593336\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 2.14872i | − | 0.0204640i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0199 | + | 12.0199i | 0.112336 | + | 0.112336i | 0.761040 | − | 0.648705i | \(-0.224689\pi\) |
−0.648705 | + | 0.761040i | \(0.724689\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −67.5716 | − | 67.5716i | −0.619923 | − | 0.619923i | 0.325589 | − | 0.945511i | \(-0.394437\pi\) |
−0.945511 | + | 0.325589i | \(0.894437\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 85.9294i | 0.774139i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 58.3821 | 0.516656 | 0.258328 | − | 0.966057i | \(-0.416829\pi\) | ||||
0.258328 | + | 0.966057i | \(0.416829\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −46.9289 | + | 46.9289i | −0.408077 | + | 0.408077i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −296.669 | + | 296.669i | −2.53563 | + | 2.53563i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.286593 | −0.00240834 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 98.2105i | − | 0.811657i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 183.794 | + | 183.794i | 1.49426 | + | 1.49426i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.90569 | + | 7.90569i | 0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 209.273i | 1.64782i | 0.566721 | + | 0.823910i | \(0.308212\pi\) | ||||
−0.566721 | + | 0.823910i | \(0.691788\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 214.798 | 1.66510 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 89.9316 | − | 89.9316i | 0.686501 | − | 0.686501i | −0.274956 | − | 0.961457i | \(-0.588663\pi\) |
0.961457 | + | 0.274956i | \(0.0886633\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.55078 | + | 3.55078i | −0.0266976 | + | 0.0266976i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 167.719 | 1.24236 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0315i | 0.0732228i | 0.999330 | + | 0.0366114i | \(0.0116564\pi\) | ||||
−0.999330 | + | 0.0366114i | \(0.988344\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.11728 | − | 3.11728i | −0.0224265 | − | 0.0224265i | 0.695805 | − | 0.718231i | \(-0.255048\pi\) |
−0.718231 | + | 0.695805i | \(0.755048\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −153.457 | − | 153.457i | −1.08835 | − | 1.08835i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 89.4623i | 0.625610i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −24.2075 | −0.166949 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −194.000 | + | 194.000i | −1.31973 | + | 1.31973i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −65.2299 | + | 65.2299i | −0.437785 | + | 0.437785i | −0.891266 | − | 0.453481i | \(-0.850182\pi\) |
0.453481 | + | 0.891266i | \(0.350182\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −152.779 | −1.01178 | −0.505891 | − | 0.862597i | \(-0.668836\pi\) | ||||
−0.505891 | + | 0.862597i | \(0.668836\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 37.4082i | − | 0.244498i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −55.0190 | − | 55.0190i | −0.354962 | − | 0.354962i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −32.0163 | − | 32.0163i | −0.203926 | − | 0.203926i | 0.597754 | − | 0.801680i | \(-0.296060\pi\) |
−0.801680 | + | 0.597754i | \(0.796060\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 190.589i | − | 1.19867i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.09077 | −0.0316197 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.6884 | − | 13.6884i | 0.0839782 | − | 0.0839782i | −0.663870 | − | 0.747848i | \(-0.731087\pi\) |
0.747848 | + | 0.663870i | \(0.231087\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 42.2882 | − | 42.2882i | 0.256292 | − | 0.256292i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 165.352 | 0.990135 | 0.495067 | − | 0.868855i | \(-0.335143\pi\) | ||||
0.495067 | + | 0.868855i | \(0.335143\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 182.192i | 1.07806i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −463.473 | − | 463.473i | −2.71037 | − | 2.71037i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −69.7841 | − | 69.7841i | −0.403376 | − | 0.403376i | 0.476045 | − | 0.879421i | \(-0.342070\pi\) |
−0.879421 | + | 0.476045i | \(0.842070\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.857597i | 0.00490055i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 295.233 | 1.66798 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 28.0124 | − | 28.0124i | 0.156494 | − | 0.156494i | −0.624517 | − | 0.781011i | \(-0.714704\pi\) |
0.781011 | + | 0.624517i | \(0.214704\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 171.169 | − | 171.169i | 0.945686 | − | 0.945686i | −0.0529135 | − | 0.998599i | \(-0.516851\pi\) |
0.998599 | + | 0.0529135i | \(0.0168508\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 280.514 | 1.53286 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 34.2962i | − | 0.185385i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.64033 | − | 5.64033i | −0.0301622 | − | 0.0301622i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.09692 | + | 9.09692i | 0.0481318 | + | 0.0481318i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 255.795i | − | 1.33924i | −0.742704 | − | 0.669620i | \(-0.766457\pi\) | ||
0.742704 | − | 0.669620i | \(-0.233543\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 324.401 | 1.68083 | 0.840417 | − | 0.541941i | \(-0.182310\pi\) | ||||
0.840417 | + | 0.541941i | \(0.182310\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 166.006 | − | 166.006i | 0.851313 | − | 0.851313i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 138.367 | − | 138.367i | 0.702370 | − | 0.702370i | −0.262549 | − | 0.964919i | \(-0.584563\pi\) |
0.964919 | + | 0.262549i | \(0.0845631\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −244.276 | −1.22752 | −0.613759 | − | 0.789494i | \(-0.710343\pi\) | ||||
−0.613759 | + | 0.789494i | \(0.710343\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 88.3414i | − | 0.439509i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.31300 | − | 1.31300i | −0.00646797 | − | 0.00646797i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −73.3557 | − | 73.3557i | −0.357833 | − | 0.357833i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 664.485i | − | 3.21007i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −139.763 | −0.668723 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −128.059 | + | 128.059i | −0.606913 | + | 0.606913i | −0.942138 | − | 0.335225i | \(-0.891188\pi\) |
0.335225 | + | 0.942138i | \(0.391188\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.2013 | + | 12.2013i | −0.0572829 | + | 0.0572829i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −85.7300 | −0.398744 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 5.96838i | − | 0.0275040i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 365.789 | + | 365.789i | 1.67027 | + | 1.67027i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.1416 | − | 22.1416i | −0.100188 | − | 0.100188i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 158.100i | − | 0.708966i | −0.935062 | − | 0.354483i | \(-0.884657\pi\) | ||
0.935062 | − | 0.354483i | \(-0.115343\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −111.940 | −0.497510 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.0851 | − | 18.0851i | 0.0796702 | − | 0.0796702i | −0.666149 | − | 0.745819i | \(-0.732058\pi\) |
0.745819 | + | 0.666149i | \(0.232058\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −280.982 | + | 280.982i | −1.22700 | + | 1.22700i | −0.261900 | + | 0.965095i | \(0.584349\pi\) |
−0.965095 | + | 0.261900i | \(0.915651\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.58735 | 0.0198587 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 210.065i | 0.901565i | 0.892634 | + | 0.450782i | \(0.148855\pi\) | ||||
−0.892634 | + | 0.450782i | \(0.851145\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 61.2479 | + | 61.2479i | 0.260629 | + | 0.260629i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −99.3005 | − | 99.3005i | −0.418989 | − | 0.418989i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 43.3929i | 0.181560i | 0.995871 | + | 0.0907802i | \(0.0289361\pi\) | ||||
−0.995871 | + | 0.0907802i | \(0.971064\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −395.278 | −1.64016 | −0.820079 | − | 0.572250i | \(-0.806071\pi\) | ||||
−0.820079 | + | 0.572250i | \(0.806071\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −389.174 | + | 389.174i | −1.60154 | + | 1.60154i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 77.4293 | − | 77.4293i | 0.316038 | − | 0.316038i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −548.653 | −2.22127 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 694.018i | − | 2.78722i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −38.4294 | − | 38.4294i | −0.153105 | − | 0.153105i | 0.626398 | − | 0.779503i | \(-0.284528\pi\) |
−0.779503 | + | 0.626398i | \(0.784528\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −100.190 | − | 100.190i | −0.396006 | − | 0.396006i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 20.9324i | 0.0820877i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 53.0395 | 0.206379 | 0.103190 | − | 0.994662i | \(-0.467095\pi\) | ||||
0.103190 | + | 0.994662i | \(0.467095\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.86019 | − | 1.86019i | 0.00718222 | − | 0.00718222i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 171.382 | − | 171.382i | 0.656636 | − | 0.656636i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −50.5789 | −0.192315 | −0.0961576 | − | 0.995366i | \(-0.530655\pi\) | ||||
−0.0961576 | + | 0.995366i | \(0.530655\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 76.0677i | 0.287048i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 538.430 | + | 538.430i | 2.01659 | + | 2.01659i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −50.4367 | − | 50.4367i | −0.187497 | − | 0.187497i | 0.607116 | − | 0.794613i | \(-0.292326\pi\) |
−0.794613 | + | 0.607116i | \(0.792326\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 201.624i | 0.744000i | 0.928233 | + | 0.372000i | \(0.121328\pi\) | ||||
−0.928233 | + | 0.372000i | \(0.878672\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 18.0081 | 0.0659636 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.8781 | + | 16.8781i | −0.0613748 | + | 0.0613748i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −65.2902 | + | 65.2902i | −0.235705 | + | 0.235705i | −0.815069 | − | 0.579364i | \(-0.803301\pi\) |
0.579364 | + | 0.815069i | \(0.303301\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 779.036 | 2.79224 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 543.533i | 1.93428i | 0.254241 | + | 0.967141i | \(0.418174\pi\) | ||||
−0.254241 | + | 0.967141i | \(0.581826\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −104.692 | − | 104.692i | −0.369935 | − | 0.369935i | 0.497518 | − | 0.867454i | \(-0.334245\pi\) |
−0.867454 | + | 0.497518i | \(0.834245\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 259.344 | + | 259.344i | 0.909980 | + | 0.909980i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 7.95751i | − | 0.0277265i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −286.208 | −0.990339 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 99.2604 | − | 99.2604i | 0.341101 | − | 0.341101i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 278.881 | − | 278.881i | 0.951813 | − | 0.951813i | −0.0470785 | − | 0.998891i | \(-0.514991\pi\) |
0.998891 | + | 0.0470785i | \(0.0149911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −117.833 | −0.399435 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 358.066i | 1.20561i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −393.303 | − | 393.303i | −1.31540 | − | 1.31540i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.64992 | − | 4.64992i | −0.0154483 | − | 0.0154483i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 171.588i | − | 0.566296i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −111.959 | −0.367078 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −165.375 | + | 165.375i | −0.538682 | + | 0.538682i | −0.923142 | − | 0.384460i | \(-0.874388\pi\) |
0.384460 | + | 0.923142i | \(0.374388\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −235.880 | + | 235.880i | −0.763366 | + | 0.763366i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 569.732 | 1.83194 | 0.915968 | − | 0.401252i | \(-0.131425\pi\) | ||||
0.915968 | + | 0.401252i | \(0.131425\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 167.015i | − | 0.533593i | −0.963753 | − | 0.266797i | \(-0.914035\pi\) | ||
0.963753 | − | 0.266797i | \(-0.0859652\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.07152 | − | 6.07152i | −0.0192747 | − | 0.0192747i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −326.774 | − | 326.774i | −1.03083 | − | 1.03083i | −0.999509 | − | 0.0313243i | \(-0.990028\pi\) |
−0.0313243 | − | 0.999509i | \(-0.509972\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 51.6813i | − | 0.162010i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 95.2353 | 0.296683 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 34.5909 | − | 34.5909i | 0.107093 | − | 0.107093i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −66.2563 | + | 66.2563i | −0.203866 | + | 0.203866i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −535.378 | −1.63724 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.64407i | 0.0201947i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 200.293 | + | 200.293i | 0.605115 | + | 0.605115i | 0.941665 | − | 0.336550i | \(-0.109260\pi\) |
−0.336550 | + | 0.941665i | \(0.609260\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 242.806 | + | 242.806i | 0.729148 | + | 0.729148i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 35.2588i | 0.105250i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.9488 | 0.0324891 | 0.0162445 | − | 0.999868i | \(-0.494829\pi\) | ||||
0.0162445 | + | 0.999868i | \(0.494829\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 231.284 | − | 231.284i | 0.682255 | − | 0.682255i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 117.461 | − | 117.461i | 0.344462 | − | 0.344462i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.8038 | 0.0489908 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 371.824i | 1.07775i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 34.7700 | + | 34.7700i | 0.100202 | + | 0.100202i | 0.755430 | − | 0.655229i | \(-0.227428\pi\) |
−0.655229 | + | 0.755430i | \(0.727428\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −169.969 | − | 169.969i | −0.487016 | − | 0.487016i | 0.420347 | − | 0.907363i | \(-0.361908\pi\) |
−0.907363 | + | 0.420347i | \(0.861908\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1405.62i | 4.00462i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 196.803 | 0.557516 | 0.278758 | − | 0.960361i | \(-0.410077\pi\) | ||||
0.278758 | + | 0.960361i | \(0.410077\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.86976 | − | 4.86976i | 0.0137176 | − | 0.0137176i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.13535 | + | 1.13535i | −0.00318026 | + | 0.00318026i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 80.5658 | 0.224417 | 0.112209 | − | 0.993685i | \(-0.464208\pi\) | ||||
0.112209 | + | 0.993685i | \(0.464208\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 496.137i | − | 1.37434i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −389.067 | − | 389.067i | −1.07181 | − | 1.07181i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −145.994 | − | 145.994i | −0.399983 | − | 0.399983i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 691.037i | − | 1.88294i | −0.337104 | − | 0.941468i | \(-0.609447\pi\) | ||
0.337104 | − | 0.941468i | \(-0.390553\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1038.67 | 2.81483 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.12585 | + | 4.12585i | −0.0111209 | + | 0.0111209i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −484.976 | + | 484.976i | −1.30020 | + | 1.30020i | −0.371952 | + | 0.928252i | \(0.621311\pi\) |
−0.928252 | + | 0.371952i | \(0.878689\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 62.6378 | 0.167034 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 202.879i | − | 0.538142i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −205.910 | − | 205.910i | −0.543298 | − | 0.543298i | 0.381196 | − | 0.924494i | \(-0.375512\pi\) |
−0.924494 | + | 0.381196i | \(0.875512\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 829.048 | + | 829.048i | 2.17598 | + | 2.17598i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 616.816i | 1.61049i | 0.592945 | + | 0.805243i | \(0.297965\pi\) | ||||
−0.592945 | + | 0.805243i | \(0.702035\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.83090 | −0.00475559 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 606.942 | − | 606.942i | 1.56833 | − | 1.56833i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −122.768 | + | 122.768i | −0.315599 | + | 0.315599i | −0.847074 | − | 0.531475i | \(-0.821638\pi\) |
0.531475 | + | 0.847074i | \(0.321638\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 49.5932 | 0.126837 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 712.540i | − | 1.81308i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 39.6328 | + | 39.6328i | 0.100336 | + | 0.100336i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 314.618 | + | 314.618i | 0.792489 | + | 0.792489i | 0.981898 | − | 0.189410i | \(-0.0606574\pi\) |
−0.189410 | + | 0.981898i | \(0.560657\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 28.1332i | 0.0705094i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −268.277 | −0.669020 | −0.334510 | − | 0.942392i | \(-0.608571\pi\) | ||||
−0.334510 | + | 0.942392i | \(0.608571\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 461.106 | − | 461.106i | 1.14418 | − | 1.14418i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 345.841 | − | 345.841i | 0.853929 | − | 0.853929i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 73.2197 | 0.179901 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 39.2885i | 0.0960598i | 0.998846 | + | 0.0480299i | \(0.0152943\pi\) | ||||
−0.998846 | + | 0.0480299i | \(0.984706\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 39.7405 | + | 39.7405i | 0.0966922 | + | 0.0966922i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.39118 | − | 6.39118i | −0.0154750 | − | 0.0154750i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 276.996i | 0.667461i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −24.6986 | −0.0592292 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −496.748 | + | 496.748i | −1.18556 | + | 1.18556i | −0.207272 | + | 0.978283i | \(0.566459\pi\) |
−0.978283 | + | 0.207272i | \(0.933541\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −364.178 | + | 364.178i | −0.865031 | + | 0.865031i | −0.991917 | − | 0.126886i | \(-0.959502\pi\) |
0.126886 | + | 0.991917i | \(0.459502\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −867.233 | −2.05020 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 8.35453i | − | 0.0196577i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.07255 | − | 6.07255i | −0.0142214 | − | 0.0142214i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 354.410 | + | 354.410i | 0.826131 | + | 0.826131i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 20.0721i | − | 0.0465710i | −0.999729 | − | 0.0232855i | \(-0.992587\pi\) | ||
0.999729 | − | 0.0232855i | \(-0.00741267\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −232.812 | −0.537672 | −0.268836 | − | 0.963186i | \(-0.586639\pi\) | ||||
−0.268836 | + | 0.963186i | \(0.586639\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −95.8997 | + | 95.8997i | −0.220459 | + | 0.220459i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 614.441 | − | 614.441i | 1.40604 | − | 1.40604i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.2811 | −0.0507541 | −0.0253771 | − | 0.999678i | \(-0.508079\pi\) | ||||
−0.0253771 | + | 0.999678i | \(0.508079\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1096.35i | 2.48606i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.0164 | + | 35.0164i | 0.0790437 | + | 0.0790437i | 0.745523 | − | 0.666480i | \(-0.232200\pi\) |
−0.666480 | + | 0.745523i | \(0.732200\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −214.898 | − | 214.898i | −0.482917 | − | 0.482917i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 516.825i | 1.15621i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −412.188 | −0.918014 | −0.459007 | − | 0.888433i | \(-0.651795\pi\) | ||||
−0.459007 | + | 0.888433i | \(0.651795\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 156.609 | − | 156.609i | 0.347248 | − | 0.347248i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −605.244 | + | 605.244i | −1.33608 | + | 1.33608i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.18738 | −0.0157964 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 174.028i | 0.380805i | 0.981706 | + | 0.190402i | \(0.0609793\pi\) | ||||
−0.981706 | + | 0.190402i | \(0.939021\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −88.6203 | − | 88.6203i | −0.193072 | − | 0.193072i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 464.386 | + | 464.386i | 1.00734 | + | 1.00734i | 0.999973 | + | 0.00737146i | \(0.00234643\pi\) |
0.00737146 | + | 0.999973i | \(0.497654\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 158.361i | 0.342033i | 0.985268 | + | 0.171016i | \(0.0547051\pi\) | ||||
−0.985268 | + | 0.171016i | \(0.945295\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −435.923 | −0.937469 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.3660 | − | 13.3660i | 0.0286210 | − | 0.0286210i | −0.692651 | − | 0.721272i | \(-0.743558\pi\) |
0.721272 | + | 0.692651i | \(0.243558\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.91241 | + | 1.91241i | −0.00407763 | + | 0.00407763i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −253.669 | −0.538576 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 183.027i | − | 0.386949i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −103.509 | − | 103.509i | −0.217915 | − | 0.217915i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −538.536 | − | 538.536i | −1.12901 | − | 1.12901i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 457.254i | 0.954602i | 0.878740 | + | 0.477301i | \(0.158385\pi\) | ||||
−0.878740 | + | 0.477301i | \(0.841615\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 287.430 | 0.597569 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.1674 | + | 20.1674i | −0.0417545 | + | 0.0417545i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −39.6168 | + | 39.6168i | −0.0816842 | + | 0.0816842i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 235.510 | 0.483592 | 0.241796 | − | 0.970327i | \(-0.422263\pi\) | ||||
0.241796 | + | 0.970327i | \(0.422263\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 108.455i | − | 0.221790i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −408.205 | − | 408.205i | −0.831375 | − | 0.831375i | 0.156330 | − | 0.987705i | \(-0.450034\pi\) |
−0.987705 | + | 0.156330i | \(0.950034\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.7909 | + | 12.7909i | 0.0259451 | + | 0.0259451i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 238.983i | − | 0.482794i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.528264 | 0.00106290 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −600.932 | + | 600.932i | −1.20427 | + | 1.20427i | −0.231418 | + | 0.972854i | \(0.574337\pi\) |
−0.972854 | + | 0.231418i | \(0.925663\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 655.054 | − | 655.054i | 1.30749 | − | 1.30749i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 559.682 | 1.11269 | 0.556344 | − | 0.830952i | \(-0.312204\pi\) | ||||
0.556344 | + | 0.830952i | \(0.312204\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 68.4840i | 0.135612i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 721.765 | + | 721.765i | 1.42360 | + | 1.42360i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −56.7719 | − | 56.7719i | −0.111536 | − | 0.111536i | 0.649136 | − | 0.760672i | \(-0.275131\pi\) |
−0.760672 | + | 0.649136i | \(0.775131\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 15.8372i | − | 0.0309925i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2195.94 | −4.28059 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 94.1444 | − | 94.1444i | 0.182805 | − | 0.182805i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −130.760 | + | 130.760i | −0.252920 | + | 0.252920i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −552.908 | −1.06533 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 482.298i | − | 0.925716i | −0.886433 | − | 0.462858i | \(-0.846824\pi\) | ||
0.886433 | − | 0.462858i | \(-0.153176\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 221.568 | + | 221.568i | 0.423649 | + | 0.423649i | 0.886458 | − | 0.462809i | \(-0.153158\pi\) |
−0.462809 | + | 0.886458i | \(0.653158\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.39742 | + | 3.39742i | 0.00647128 | + | 0.00647128i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 58.1427i | 0.110328i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 351.928 | 0.665271 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 834.224 | − | 834.224i | 1.57104 | − | 1.57104i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 614.782 | − | 614.782i | 1.15344 | − | 1.15344i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −38.0103 | −0.0710473 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 221.946i | − | 0.413306i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 165.306 | + | 165.306i | 0.306690 | + | 0.306690i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −111.572 | − | 111.572i | −0.206232 | − | 0.206232i | 0.596432 | − | 0.802664i | \(-0.296585\pi\) |
−0.802664 | + | 0.596432i | \(0.796585\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1356.19i | − | 2.49760i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 213.680 | 0.392073 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −258.971 | + | 258.971i | −0.473438 | + | 0.473438i | −0.903025 | − | 0.429587i | \(-0.858659\pi\) |
0.429587 | + | 0.903025i | \(0.358659\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 792.633 | − | 792.633i | 1.44378 | − | 1.44378i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 316.950 | 0.575227 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.29930i | 0.00777450i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −135.866 | − | 135.866i | −0.244804 | − | 0.244804i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 637.308 | + | 637.308i | 1.14418 | + | 1.14418i | 0.987678 | + | 0.156502i | \(0.0500218\pi\) |
0.156502 | + | 0.987678i | \(0.449978\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 718.489i | − | 1.28531i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −44.6890 | −0.0796596 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −456.197 | + | 456.197i | −0.810297 | + | 0.810297i | −0.984678 | − | 0.174381i | \(-0.944208\pi\) |
0.174381 | + | 0.984678i | \(0.444208\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −92.3102 | + | 92.3102i | −0.163381 | + | 0.163381i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 37.5163 | 0.0661663 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 43.4831i | 0.0764202i | 0.999270 | + | 0.0382101i | \(0.0121656\pi\) | ||||
−0.999270 | + | 0.0382101i | \(0.987834\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 448.304 | + | 448.304i | 0.785120 | + | 0.785120i | 0.980690 | − | 0.195570i | \(-0.0626556\pi\) |
−0.195570 | + | 0.980690i | \(0.562656\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1013.35 | − | 1013.35i | −1.76849 | − | 1.76849i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 148.402i | − | 0.258091i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −766.758 | −1.32887 | −0.664435 | − | 0.747346i | \(-0.731328\pi\) | ||||
−0.664435 | + | 0.747346i | \(0.731328\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1285.13 | − | 1285.13i | 2.21958 | − | 2.21958i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.0241 | + | 15.0241i | −0.0258590 | + | 0.0258590i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −162.399 | −0.278557 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 938.149i | − | 1.60367i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −422.279 | − | 422.279i | −0.719384 | − | 0.719384i | 0.249095 | − | 0.968479i | \(-0.419867\pi\) |
−0.968479 | + | 0.249095i | \(0.919867\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 720.366 | + | 720.366i | 1.22303 | + | 1.22303i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 1096.30i | − | 1.85499i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 868.212 | 1.46410 | 0.732051 | − | 0.681250i | \(-0.238563\pi\) | ||||
0.732051 | + | 0.681250i | \(0.238563\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.453143 | − | 0.453143i | 0.000761584 | − | 0.000761584i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −967.715 | + | 967.715i | −1.62096 | + | 1.62096i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −669.140 | −1.11710 | −0.558548 | − | 0.829473i | \(-0.688641\pi\) | ||||
−0.558548 | + | 0.829473i | \(0.688641\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 528.062i | − | 0.878639i | −0.898331 | − | 0.439319i | \(-0.855220\pi\) | ||
0.898331 | − | 0.439319i | \(-0.144780\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −249.622 | − | 249.622i | −0.413966 | − | 0.413966i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 155.284 | + | 155.284i | 0.256668 | + | 0.256668i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 323.639i | − | 0.533178i | −0.963810 | − | 0.266589i | \(-0.914103\pi\) | ||
0.963810 | − | 0.266589i | \(-0.0858966\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.4030 | −0.0170822 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −513.309 | + | 513.309i | −0.840112 | + | 0.840112i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 275.335 | − | 275.335i | 0.449161 | − | 0.449161i | −0.445915 | − | 0.895075i | \(-0.647122\pi\) |
0.895075 | + | 0.445915i | \(0.147122\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −581.207 | −0.945052 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 0.213607i | − | 0.000346203i | −1.00000 | 0.000173102i | \(-0.999945\pi\) | |||
1.00000 | 0.000173102i | \(-5.51000e-5\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.0310 | + | 25.0310i | 0.0404378 | + | 0.0404378i | 0.727037 | − | 0.686599i | \(-0.240897\pi\) |
−0.686599 | + | 0.727037i | \(0.740897\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1574.17 | − | 1574.17i | −2.53489 | − | 2.53489i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 23.3118i | − | 0.0374186i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −553.680 | + | 553.680i | −0.883063 | + | 0.883063i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.1216 | + | 18.1216i | −0.0288102 | + | 0.0288102i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 856.751 | 1.35777 | 0.678884 | − | 0.734246i | \(-0.262464\pi\) | ||||
0.678884 | + | 0.734246i | \(0.262464\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1014.62i | 1.60288i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −330.890 | − | 330.890i | −0.521086 | − | 0.521086i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 648.922 | + | 648.922i | 1.01872 | + | 1.01872i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 68.9529i | 0.107907i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −286.443 | −0.446869 | −0.223434 | − | 0.974719i | \(-0.571727\pi\) | ||||
−0.223434 | + | 0.974719i | \(0.571727\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 870.643 | − | 870.643i | 1.35403 | − | 1.35403i | 0.472934 | − | 0.881098i | \(-0.343195\pi\) |
0.881098 | − | 0.472934i | \(-0.156805\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −339.625 | + | 339.625i | −0.526550 | + | 0.526550i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 982.880 | 1.51913 | 0.759567 | − | 0.650428i | \(-0.225411\pi\) | ||||
0.759567 | + | 0.650428i | \(0.225411\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 251.565i | − | 0.387619i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.6441 | − | 23.6441i | −0.0363197 | − | 0.0363197i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −576.699 | − | 576.699i | −0.883153 | − | 0.883153i | 0.110701 | − | 0.993854i | \(-0.464690\pi\) |
−0.993854 | + | 0.110701i | \(0.964690\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 284.389i | 0.434181i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2067.18 | 3.14640 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −339.061 | + | 339.061i | −0.514508 | + | 0.514508i | −0.915904 | − | 0.401397i | \(-0.868525\pi\) |
0.401397 | + | 0.915904i | \(0.368525\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 715.682 | − | 715.682i | 1.08273 | − | 1.08273i | 0.0864713 | − | 0.996254i | \(-0.472441\pi\) |
0.996254 | − | 0.0864713i | \(-0.0275591\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −175.431 | −0.264601 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 11.2285i | − | 0.0168850i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 227.207 | + | 227.207i | 0.340640 | + | 0.340640i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −626.321 | − | 626.321i | −0.936205 | − | 0.936205i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 239.023i | − | 0.356220i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 965.990 | 1.43535 | 0.717675 | − | 0.696378i | \(-0.245206\pi\) | ||||
0.717675 | + | 0.696378i | \(0.245206\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −265.186 | + | 265.186i | −0.392869 | + | 0.392869i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −109.057 | + | 109.057i | −0.161089 | + | 0.161089i | −0.783049 | − | 0.621960i | \(-0.786337\pi\) |
0.621960 | + | 0.783049i | \(0.286337\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.29757 | −0.00632926 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 143.291i | − | 0.210412i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −666.862 | − | 666.862i | −0.976372 | − | 0.976372i | 0.0233557 | − | 0.999727i | \(-0.492565\pi\) |
−0.999727 | + | 0.0233557i | \(0.992565\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.8612 | − | 15.8612i | −0.0231551 | − | 0.0231551i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2226.26i | 3.24055i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −637.511 | −0.925270 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −452.813 | + | 452.813i | −0.655301 | + | 0.655301i | −0.954264 | − | 0.298964i | \(-0.903359\pi\) |
0.298964 | + | 0.954264i | \(0.403359\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.9622 | − | 12.9622i | 0.0187045 | − | 0.0187045i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.85770 | 0.0141837 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 77.5204i | 0.111220i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 832.184 | + | 832.184i | 1.19054 | + | 1.19054i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 357.476 | + | 357.476i | 0.509951 | + | 0.509951i | 0.914511 | − | 0.404560i | \(-0.132575\pi\) |
−0.404560 | + | 0.914511i | \(0.632575\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 449.041i | 0.638749i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 485.275 | 0.688333 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.71452 | + | 3.71452i | −0.00525391 | + | 0.00525391i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 237.180 | − | 237.180i | 0.334527 | − | 0.334527i | −0.519776 | − | 0.854303i | \(-0.673984\pi\) |
0.854303 | + | 0.519776i | \(0.173984\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −561.176 | −0.789277 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1032.79i | 1.44852i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −141.452 | − | 141.452i | −0.197835 | − | 0.197835i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 171.904 | + | 171.904i | 0.239754 | + | 0.239754i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1109.99i | 1.54379i | 0.635748 | + | 0.771896i | \(0.280692\pi\) | ||||
−0.635748 | + | 0.771896i | \(0.719308\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.2126 | 0.0141645 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1565.92 | + | 1565.92i | −2.16586 | + | 2.16586i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 38.2755 | − | 38.2755i | 0.0527938 | − | 0.0527938i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1085.51 | 1.49313 | 0.746565 | − | 0.665312i | \(-0.231702\pi\) | ||||
0.746565 | + | 0.665312i | \(0.231702\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1114.91i | 1.52938i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.2986 | + | 45.2986i | 0.0619680 | + | 0.0619680i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 631.788 | + | 631.788i | 0.861921 | + | 0.861921i | 0.991561 | − | 0.129640i | \(-0.0413821\pi\) |
−0.129640 | + | 0.991561i | \(0.541382\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 613.482i | − | 0.834669i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −75.2749 | −0.102137 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −107.907 | + | 107.907i | −0.146017 | + | 0.146017i | −0.776336 | − | 0.630319i | \(-0.782924\pi\) |
0.630319 | + | 0.776336i | \(0.282924\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2173.52 | + | 2173.52i | −2.93323 | + | 2.93323i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 148.683 | 0.200112 | 0.100056 | − | 0.994982i | \(-0.468098\pi\) | ||||
0.100056 | + | 0.994982i | \(0.468098\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 206.275i | − | 0.276879i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1961.05 | − | 1961.05i | −2.62524 | − | 2.62524i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.06165 | − | 2.06165i | −0.00275253 | − | 0.00275253i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 374.911i | − | 0.499216i | −0.968347 | − | 0.249608i | \(-0.919698\pi\) | ||
0.968347 | − | 0.249608i | \(-0.0803018\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −304.481 | −0.404358 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 241.565 | − | 241.565i | 0.319953 | − | 0.319953i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1001.97 | + | 1001.97i | −1.32360 | + | 1.32360i | −0.412768 | + | 0.910836i | \(0.635438\pi\) |
−0.910836 | + | 0.412768i | \(0.864562\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −793.815 | −1.04587 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 592.474i | 0.778547i | 0.921122 | + | 0.389274i | \(0.127274\pi\) | ||||
−0.921122 | + | 0.389274i | \(0.872726\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.5898 | + | 11.5898i | 0.0151898 | + | 0.0151898i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 59.1475 | + | 59.1475i | 0.0773170 | + | 0.0773170i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 987.541i | − | 1.28754i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 327.948 | 0.426461 | 0.213230 | − | 0.977002i | \(-0.431601\pi\) | ||||
0.213230 | + | 0.977002i | \(0.431601\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 210.119 | − | 210.119i | 0.272528 | − | 0.272528i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −969.561 | + | 969.561i | −1.25428 | + | 1.25428i | −0.300503 | + | 0.953781i | \(0.597154\pi\) |
−0.953781 | + | 0.300503i | \(0.902846\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 173.986 | 0.224497 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 14.7386i | − | 0.0189685i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 960.449 | + | 960.449i | 1.23293 | + | 1.23293i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.3966 | + | 10.3966i | 0.0133119 | + | 0.0133119i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 812.011i | − | 1.03705i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 101.245 | 0.128974 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 688.958 | − | 688.958i | 0.875423 | − | 0.875423i | −0.117634 | − | 0.993057i | \(-0.537531\pi\) |
0.993057 | + | 0.117634i | \(0.0375310\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −200.372 | + | 200.372i | −0.253956 | + | 0.253956i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.0137 | −0.0126595 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 938.307i | − | 1.18324i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 301.347 | + | 301.347i | 0.379053 | + | 0.379053i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −773.816 | − | 773.816i | −0.970911 | − | 0.970911i | 0.0286777 | − | 0.999589i | \(-0.490870\pi\) |
−0.999589 | + | 0.0286777i | \(0.990870\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 64.7252i | − | 0.0810077i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3042.83 | 3.79878 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 311.686 | − | 311.686i | 0.388152 | − | 0.388152i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.04921 | − | 8.04921i | 0.00999902 | − | 0.00999902i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −399.616 | −0.495187 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1530.90i | 1.89233i | 0.323683 | + | 0.946166i | \(0.395079\pi\) | ||||
−0.323683 | + | 0.946166i | \(0.604921\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 780.206 | + | 780.206i | 0.962029 | + | 0.962029i | 0.999305 | − | 0.0372757i | \(-0.0118680\pi\) |
−0.0372757 | + | 0.999305i | \(0.511868\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 798.746 | + | 798.746i | 0.982468 | + | 0.982468i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 43.2867i | 0.0531125i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1122.47 | 1.37389 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 50.8844 | − | 50.8844i | 0.0621300 | − | 0.0621300i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 800.338 | − | 800.338i | 0.974833 | − | 0.974833i | −0.0248582 | − | 0.999691i | \(-0.507913\pi\) |
0.999691 | + | 0.0248582i | \(0.00791342\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −469.516 | −0.570493 | −0.285247 | − | 0.958454i | \(-0.592076\pi\) | ||||
−0.285247 | + | 0.958454i | \(0.592076\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 133.727i | 0.162093i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −135.500 | − | 135.500i | −0.163845 | − | 0.163845i | 0.620423 | − | 0.784268i | \(-0.286961\pi\) |
−0.784268 | + | 0.620423i | \(0.786961\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −846.287 | − | 846.287i | −1.02085 | − | 1.02085i | −0.999778 | − | 0.0210744i | \(-0.993291\pi\) |
−0.0210744 | − | 0.999778i | \(-0.506709\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 517.303i | 0.622506i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −81.8252 | −0.0982295 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −261.445 | + | 261.445i | −0.313108 | + | 0.313108i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1845.54 | − | 1845.54i | 2.20495 | − | 2.20495i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 915.064 | 1.09066 | 0.545330 | − | 0.838222i | \(-0.316404\pi\) | ||||
0.545330 | + | 0.838222i | \(0.316404\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 723.799i | − | 0.860641i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2153.24 | + | 2153.24i | 2.55426 | + | 2.55426i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −288.071 | − | 288.071i | −0.340912 | − | 0.340912i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.8450i | 0.0198878i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −829.486 | −0.977015 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −321.896 | + | 321.896i | −0.378256 | + | 0.378256i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 431.036 | − | 431.036i | 0.505318 | − | 0.505318i | −0.407768 | − | 0.913086i | \(-0.633693\pi\) |
0.913086 | + | 0.407768i | \(0.133693\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1465.63 | 1.71419 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1485.67i | − | 1.73357i | −0.498686 | − | 0.866783i | \(-0.666184\pi\) | ||
0.498686 | − | 0.866783i | \(-0.333816\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −562.643 | − | 562.643i | −0.654998 | − | 0.654998i | 0.299194 | − | 0.954192i | \(-0.403282\pi\) |
−0.954192 | + | 0.299194i | \(0.903282\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −31.5242 | − | 31.5242i | −0.0366134 | − | 0.0366134i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 812.826i | 0.941861i | 0.882170 | + | 0.470930i | \(0.156082\pi\) | ||||
−0.882170 | + | 0.470930i | \(0.843918\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 220.677 | 0.255118 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1133.83 | + | 1133.83i | −1.30776 | + | 1.30776i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −84.6130 | + | 84.6130i | −0.0973683 | + | 0.0973683i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −295.498 | −0.339263 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 560.950i | − | 0.642555i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.35598 | − | 1.35598i | −0.00154969 | − | 0.00154969i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 502.264 | + | 502.264i | 0.572707 | + | 0.572707i | 0.932884 | − | 0.360177i | \(-0.117284\pi\) |
−0.360177 | + | 0.932884i | \(0.617284\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 2209.61i | − | 2.51378i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −979.412 | −1.11171 | −0.555853 | − | 0.831281i | \(-0.687608\pi\) | ||||
−0.555853 | + | 0.831281i | \(0.687608\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 891.876 | − | 891.876i | 1.01005 | − | 1.01005i | 0.0101028 | − | 0.999949i | \(-0.496784\pi\) |
0.999949 | − | 0.0101028i | \(-0.00321589\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −466.804 | + | 466.804i | −0.527462 | + | 0.527462i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1509.83 | 1.70218 | 0.851090 | − | 0.525019i | \(-0.175942\pi\) | ||||
0.851090 | + | 0.525019i | \(0.175942\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 35.8944i | − | 0.0403761i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 738.345 | + | 738.345i | 0.828670 | + | 0.828670i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −801.921 | − | 801.921i | −0.898007 | − | 0.898007i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 88.5829i | 0.0989753i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3116.19 | −3.47402 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −266.375 | + | 266.375i | −0.296302 | + | 0.296302i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.1932 | − | 40.1932i | 0.0446095 | − | 0.0446095i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −36.8419 | −0.0407995 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 541.284i | 0.598104i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −490.723 | − | 490.723i | −0.541040 | − | 0.541040i | 0.382794 | − | 0.923834i | \(-0.374962\pi\) |
−0.923834 | + | 0.382794i | \(0.874962\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −484.846 | − | 484.846i | −0.533384 | − | 0.533384i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1408.50i | − | 1.54610i | −0.634345 | − | 0.773050i | \(-0.718730\pi\) | ||
0.634345 | − | 0.773050i | \(-0.281270\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −591.366 | −0.647718 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −443.531 | + | 443.531i | −0.484734 | + | 0.484734i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.4250 | + | 15.4250i | −0.0168212 | + | 0.0168212i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1138.06 | 1.23837 | 0.619185 | − | 0.785245i | \(-0.287463\pi\) | ||||
0.619185 | + | 0.785245i | \(0.287463\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1310.29i | 1.42268i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 40.8127 | + | 40.8127i | 0.0442174 | + | 0.0442174i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 54.2270 | + | 54.2270i | 0.0586238 | + | 0.0586238i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1333.03i | 1.43800i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −713.947 | −0.768511 | −0.384256 | − | 0.923227i | \(-0.625542\pi\) | ||||
−0.384256 | + | 0.923227i | \(0.625542\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1013.78 | + | 1013.78i | −1.08892 | + | 1.08892i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2257.03 | − | 2257.03i | 2.41911 | − | 2.41911i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.8363 | 0.0190762 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1123.98i | 1.19955i | 0.800170 | + | 0.599774i | \(0.204743\pi\) | ||||
−0.800170 | + | 0.599774i | \(0.795257\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −661.639 | − | 661.639i | −0.704621 | − | 0.704621i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 576.544 | + | 576.544i | 0.612693 | + | 0.612693i | 0.943647 | − | 0.330954i | \(-0.107370\pi\) |
−0.330954 | + | 0.943647i | \(0.607370\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1377.00i | 1.46023i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −28.7670 | −0.0304412 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 609.274 | − | 609.274i | 0.643372 | − | 0.643372i | −0.308010 | − | 0.951383i | \(-0.599663\pi\) |
0.951383 | + | 0.308010i | \(0.0996632\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1223.55 | − | 1223.55i | 1.28930 | − | 1.28930i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2589.07 | −2.72247 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 324.830i | 0.340850i | 0.985371 | + | 0.170425i | \(0.0545141\pi\) | ||||
−0.985371 | + | 0.170425i | \(0.945486\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 404.447 | + | 404.447i | 0.423505 | + | 0.423505i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −204.739 | − | 204.739i | −0.213938 | − | 0.213938i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1.72060i | − | 0.00179416i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −249.838 | −0.259977 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 269.102 | − | 269.102i | 0.279441 | − | 0.279441i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −512.923 | + | 512.923i | −0.531526 | + | 0.531526i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1268.54 | −1.31183 | −0.655913 | − | 0.754837i | \(-0.727716\pi\) | ||||
−0.655913 | + | 0.754837i | \(0.727716\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 274.068i | − | 0.282836i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 78.3203 | + | 78.3203i | 0.0806594 | + | 0.0806594i | 0.746285 | − | 0.665626i | \(-0.231835\pi\) |
−0.665626 | + | 0.746285i | \(0.731835\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.534674 | + | 0.534674i | 0.000549510 | + | 0.000549510i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 524.957i | 0.538418i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1521.08 | −1.55689 | −0.778445 | − | 0.627713i | \(-0.783991\pi\) | ||||
−0.778445 | + | 0.627713i | \(0.783991\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 458.791 | − | 458.791i | 0.468632 | − | 0.468632i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1512.79 | + | 1512.79i | −1.54209 | + | 1.54209i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −407.983 | −0.415039 | −0.207519 | − | 0.978231i | \(-0.566539\pi\) | ||||
−0.207519 | + | 0.978231i | \(0.566539\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 437.554i | 0.444218i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26.3209 | + | 26.3209i | 0.0266676 | + | 0.0266676i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 804.643 | + | 804.643i | 0.813592 | + | 0.813592i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 482.285i | − | 0.486665i | −0.969943 | − | 0.243332i | \(-0.921759\pi\) | ||
0.969943 | − | 0.243332i | \(-0.0782406\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1586.95 | 1.59813 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 386.234 | − | 386.234i | 0.388175 | − | 0.388175i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.88526 | + | 1.88526i | −0.00189093 | + | 0.00189093i | −0.708052 | − | 0.706161i | \(-0.750426\pi\) |
0.706161 | + | 0.708052i | \(0.250426\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1150.42 | 1.15157 |
(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 | 320.3.r.a.111.16 | 32 | ||
4.3 | odd | 2 | 80.3.r.a.51.5 | yes | 32 | ||
8.3 | odd | 2 | 640.3.r.a.351.16 | 32 | |||
8.5 | even | 2 | 640.3.r.b.351.1 | 32 | |||
16.3 | odd | 4 | 640.3.r.b.31.1 | 32 | |||
16.5 | even | 4 | 80.3.r.a.11.5 | ✓ | 32 | ||
16.11 | odd | 4 | inner | 320.3.r.a.271.16 | 32 | ||
16.13 | even | 4 | 640.3.r.a.31.16 | 32 | |||
20.3 | even | 4 | 400.3.k.h.99.13 | 32 | |||
20.7 | even | 4 | 400.3.k.g.99.4 | 32 | |||
20.19 | odd | 2 | 400.3.r.f.51.12 | 32 | |||
80.37 | odd | 4 | 400.3.k.h.299.13 | 32 | |||
80.53 | odd | 4 | 400.3.k.g.299.4 | 32 | |||
80.69 | even | 4 | 400.3.r.f.251.12 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.3.r.a.11.5 | ✓ | 32 | 16.5 | even | 4 | ||
80.3.r.a.51.5 | yes | 32 | 4.3 | odd | 2 | ||
320.3.r.a.111.16 | 32 | 1.1 | even | 1 | trivial | ||
320.3.r.a.271.16 | 32 | 16.11 | odd | 4 | inner | ||
400.3.k.g.99.4 | 32 | 20.7 | even | 4 | |||
400.3.k.g.299.4 | 32 | 80.53 | odd | 4 | |||
400.3.k.h.99.13 | 32 | 20.3 | even | 4 | |||
400.3.k.h.299.13 | 32 | 80.37 | odd | 4 | |||
400.3.r.f.51.12 | 32 | 20.19 | odd | 2 | |||
400.3.r.f.251.12 | 32 | 80.69 | even | 4 | |||
640.3.r.a.31.16 | 32 | 16.13 | even | 4 | |||
640.3.r.a.351.16 | 32 | 8.3 | odd | 2 | |||
640.3.r.b.31.1 | 32 | 16.3 | odd | 4 | |||
640.3.r.b.351.1 | 32 | 8.5 | even | 2 |