Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,3,Mod(224,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.224");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.d (of order \(2\), degree \(1\), 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: | \(6.13080594811\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 224.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.224 |
Dual form | 225.3.d.a.224.2 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 9.00000i | − 1.28571i | −0.765986 | − | 0.642857i | \(-0.777749\pi\) | ||||
0.765986 | − | 0.642857i | \(-0.222251\pi\) | |||||||
\(8\) | 8.48528 | 1.06066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.3848i | 1.67134i | 0.549229 | + | 0.835672i | \(0.314921\pi\) | ||||
−0.549229 | + | 0.835672i | \(0.685079\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.00000i | − 0.0769231i | −0.999260 | − | 0.0384615i | \(-0.987754\pi\) | ||||
0.999260 | − | 0.0384615i | \(-0.0122457\pi\) | |||||||
\(14\) | 12.7279i | 0.909137i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −26.8701 | −1.58059 | −0.790296 | − | 0.612725i | \(-0.790073\pi\) | ||||
−0.790296 | + | 0.612725i | \(0.790073\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −25.0000 | −1.31579 | −0.657895 | − | 0.753110i | \(-0.728553\pi\) | ||||
−0.657895 | + | 0.753110i | \(0.728553\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 26.0000i | − 1.18182i | ||||||||
\(23\) | −4.24264 | −0.184463 | −0.0922313 | − | 0.995738i | \(-0.529400\pi\) | ||||
−0.0922313 | + | 0.995738i | \(0.529400\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.41421i | 0.0543928i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 18.0000i | 0.642857i | ||||||||
\(29\) | 26.8701i | 0.926554i | 0.886214 | + | 0.463277i | \(0.153326\pi\) | ||||
−0.886214 | + | 0.463277i | \(0.846674\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −39.0000 | −1.25806 | −0.629032 | − | 0.777379i | \(-0.716549\pi\) | ||||
−0.629032 | + | 0.777379i | \(0.716549\pi\) | |||||||
\(32\) | −28.2843 | −0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 38.0000 | 1.11765 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 32.0000i | 0.864865i | 0.901666 | + | 0.432432i | \(0.142345\pi\) | ||||
−0.901666 | + | 0.432432i | \(0.857655\pi\) | |||||||
\(38\) | 35.3553 | 0.930404 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 5.65685i | − 0.137972i | −0.997618 | − | 0.0689860i | \(-0.978024\pi\) | ||||
0.997618 | − | 0.0689860i | \(-0.0219764\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 23.0000i | 0.534884i | 0.963574 | + | 0.267442i | \(0.0861783\pi\) | ||||
−0.963574 | + | 0.267442i | \(0.913822\pi\) | |||||||
\(44\) | − 36.7696i | − 0.835672i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | 0.130435 | ||||||||
\(47\) | 32.5269 | 0.692062 | 0.346031 | − | 0.938223i | \(-0.387529\pi\) | ||||
0.346031 | + | 0.938223i | \(0.387529\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −32.0000 | −0.653061 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000i | 0.0384615i | ||||||||
\(53\) | −96.1665 | −1.81446 | −0.907231 | − | 0.420632i | \(-0.861808\pi\) | ||||
−0.907231 | + | 0.420632i | \(0.861808\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 76.3675i | − 1.36371i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 38.0000i | − 0.655172i | ||||||||
\(59\) | − 9.89949i | − 0.167788i | −0.996475 | − | 0.0838940i | \(-0.973264\pi\) | ||||
0.996475 | − | 0.0838940i | \(-0.0267357\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 73.0000 | 1.19672 | 0.598361 | − | 0.801227i | \(-0.295819\pi\) | ||||
0.598361 | + | 0.801227i | \(0.295819\pi\) | |||||||
\(62\) | 55.1543 | 0.889586 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 56.0000 | 0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 63.0000i | 0.940299i | 0.882587 | + | 0.470149i | \(0.155800\pi\) | ||||
−0.882587 | + | 0.470149i | \(0.844200\pi\) | |||||||
\(68\) | 53.7401 | 0.790296 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 62.2254i | 0.876414i | 0.898874 | + | 0.438207i | \(0.144386\pi\) | ||||
−0.898874 | + | 0.438207i | \(0.855614\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 136.000i | − 1.86301i | −0.363724 | − | 0.931507i | \(-0.618495\pi\) | ||||
0.363724 | − | 0.931507i | \(-0.381505\pi\) | |||||||
\(74\) | − 45.2548i | − 0.611552i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 50.0000 | 0.657895 | ||||||||
\(77\) | 165.463 | 2.14887 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 24.0000 | 0.303797 | 0.151899 | − | 0.988396i | \(-0.451461\pi\) | ||||
0.151899 | + | 0.988396i | \(0.451461\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.00000i | 0.0975610i | ||||||||
\(83\) | −46.6690 | −0.562278 | −0.281139 | − | 0.959667i | \(-0.590712\pi\) | ||||
−0.281139 | + | 0.959667i | \(0.590712\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − 32.5269i | − 0.378220i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 156.000i | 1.77273i | ||||||||
\(89\) | − 101.823i | − 1.14408i | −0.820225 | − | 0.572041i | \(-0.806152\pi\) | ||||
0.820225 | − | 0.572041i | \(-0.193848\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.00000 | −0.0989011 | ||||||||
\(92\) | 8.48528 | 0.0922313 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −46.0000 | −0.489362 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 7.00000i | − 0.0721649i | −0.999349 | − | 0.0360825i | \(-0.988512\pi\) | ||||
0.999349 | − | 0.0360825i | \(-0.0114879\pi\) | |||||||
\(98\) | 45.2548 | 0.461784 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 50.9117i | − 0.504076i | −0.967717 | − | 0.252038i | \(-0.918899\pi\) | ||||
0.967717 | − | 0.252038i | \(-0.0811008\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 110.000i | − 1.06796i | −0.845497 | − | 0.533981i | \(-0.820696\pi\) | ||||
0.845497 | − | 0.533981i | \(-0.179304\pi\) | |||||||
\(104\) | − 8.48528i | − 0.0815892i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 136.000 | 1.28302 | ||||||||
\(107\) | −118.794 | −1.11022 | −0.555112 | − | 0.831776i | \(-0.687325\pi\) | ||||
−0.555112 | + | 0.831776i | \(0.687325\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 25.0000 | 0.229358 | 0.114679 | − | 0.993403i | \(-0.463416\pi\) | ||||
0.114679 | + | 0.993403i | \(0.463416\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 36.0000i | 0.321429i | ||||||||
\(113\) | −45.2548 | −0.400485 | −0.200243 | − | 0.979746i | \(-0.564173\pi\) | ||||
−0.200243 | + | 0.979746i | \(0.564173\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − 53.7401i | − 0.463277i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.0000i | 0.118644i | ||||||||
\(119\) | 241.831i | 2.03219i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −217.000 | −1.79339 | ||||||||
\(122\) | −103.238 | −0.846210 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 78.0000 | 0.629032 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 80.0000i | − 0.629921i | −0.949105 | − | 0.314961i | \(-0.898009\pi\) | ||||
0.949105 | − | 0.314961i | \(-0.101991\pi\) | |||||||
\(128\) | 33.9411 | 0.265165 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 84.8528i | 0.647731i | 0.946103 | + | 0.323866i | \(0.104983\pi\) | ||||
−0.946103 | + | 0.323866i | \(0.895017\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 225.000i | 1.69173i | ||||||||
\(134\) | − 89.0955i | − 0.664891i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −228.000 | −1.67647 | ||||||||
\(137\) | 21.2132 | 0.154841 | 0.0774205 | − | 0.996999i | \(-0.475332\pi\) | ||||
0.0774205 | + | 0.996999i | \(0.475332\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −104.000 | −0.748201 | −0.374101 | − | 0.927388i | \(-0.622049\pi\) | ||||
−0.374101 | + | 0.927388i | \(0.622049\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 88.0000i | − 0.619718i | ||||||||
\(143\) | 18.3848 | 0.128565 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 192.333i | 1.31735i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 64.0000i | − 0.432432i | ||||||||
\(149\) | 171.120i | 1.14846i | 0.818696 | + | 0.574228i | \(0.194698\pi\) | ||||
−0.818696 | + | 0.574228i | \(0.805302\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.0000 | −0.112583 | −0.0562914 | − | 0.998414i | \(-0.517928\pi\) | ||||
−0.0562914 | + | 0.998414i | \(0.517928\pi\) | |||||||
\(152\) | −212.132 | −1.39561 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −234.000 | −1.51948 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 65.0000i | 0.414013i | 0.978340 | + | 0.207006i | \(0.0663721\pi\) | ||||
−0.978340 | + | 0.207006i | \(0.933628\pi\) | |||||||
\(158\) | −33.9411 | −0.214817 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 38.1838i | 0.237166i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 17.0000i | − 0.104294i | −0.998639 | − | 0.0521472i | \(-0.983393\pi\) | ||||
0.998639 | − | 0.0521472i | \(-0.0166065\pi\) | |||||||
\(164\) | 11.3137i | 0.0689860i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 66.0000 | 0.397590 | ||||||||
\(167\) | −254.558 | −1.52430 | −0.762151 | − | 0.647399i | \(-0.775857\pi\) | ||||
−0.762151 | + | 0.647399i | \(0.775857\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 168.000 | 0.994083 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 46.0000i | − 0.267442i | ||||||||
\(173\) | 173.948 | 1.00548 | 0.502741 | − | 0.864437i | \(-0.332325\pi\) | ||||
0.502741 | + | 0.864437i | \(0.332325\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 73.5391i | − 0.417836i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 144.000i | 0.808989i | ||||||||
\(179\) | 125.865i | 0.703156i | 0.936159 | + | 0.351578i | \(0.114355\pi\) | ||||
−0.936159 | + | 0.351578i | \(0.885645\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 119.000 | 0.657459 | 0.328729 | − | 0.944424i | \(-0.393380\pi\) | ||||
0.328729 | + | 0.944424i | \(0.393380\pi\) | |||||||
\(182\) | 12.7279 | 0.0699336 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −36.0000 | −0.195652 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 494.000i | − 2.64171i | ||||||||
\(188\) | −65.0538 | −0.346031 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.5563i | 0.0814469i | 0.999170 | + | 0.0407234i | \(0.0129663\pi\) | ||||
−0.999170 | + | 0.0407234i | \(0.987034\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 281.000i | − 1.45596i | −0.685599 | − | 0.727979i | \(-0.740460\pi\) | ||||
0.685599 | − | 0.727979i | \(-0.259540\pi\) | |||||||
\(194\) | 9.89949i | 0.0510283i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 64.0000 | 0.326531 | ||||||||
\(197\) | 224.860 | 1.14142 | 0.570711 | − | 0.821151i | \(-0.306668\pi\) | ||||
0.570711 | + | 0.821151i | \(0.306668\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −175.000 | −0.879397 | −0.439698 | − | 0.898145i | \(-0.644915\pi\) | ||||
−0.439698 | + | 0.898145i | \(0.644915\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 72.0000i | 0.356436i | ||||||||
\(203\) | 241.831 | 1.19128 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 155.563i | 0.755163i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.00000i | 0.0192308i | ||||||||
\(209\) | − 459.619i | − 2.19914i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −49.0000 | −0.232227 | −0.116114 | − | 0.993236i | \(-0.537044\pi\) | ||||
−0.116114 | + | 0.993236i | \(0.537044\pi\) | |||||||
\(212\) | 192.333 | 0.907231 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 168.000 | 0.785047 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 351.000i | 1.61751i | ||||||||
\(218\) | −35.3553 | −0.162180 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.8701i | 0.121584i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 265.000i | 1.18834i | 0.804339 | + | 0.594170i | \(0.202520\pi\) | ||||
−0.804339 | + | 0.594170i | \(0.797480\pi\) | |||||||
\(224\) | 254.558i | 1.13642i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 64.0000 | 0.283186 | ||||||||
\(227\) | −130.108 | −0.573161 | −0.286581 | − | 0.958056i | \(-0.592519\pi\) | ||||
−0.286581 | + | 0.958056i | \(0.592519\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 87.0000 | 0.379913 | 0.189956 | − | 0.981793i | \(-0.439165\pi\) | ||||
0.189956 | + | 0.981793i | \(0.439165\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 228.000i | 0.982759i | ||||||||
\(233\) | −152.735 | −0.655515 | −0.327758 | − | 0.944762i | \(-0.606293\pi\) | ||||
−0.327758 | + | 0.944762i | \(0.606293\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 19.7990i | 0.0838940i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 342.000i | − 1.43697i | ||||||||
\(239\) | − 277.186i | − 1.15977i | −0.814697 | − | 0.579887i | \(-0.803097\pi\) | ||||
0.814697 | − | 0.579887i | \(-0.196903\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 415.000 | 1.72199 | 0.860996 | − | 0.508612i | \(-0.169841\pi\) | ||||
0.860996 | + | 0.508612i | \(0.169841\pi\) | |||||||
\(242\) | 306.884 | 1.26812 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −146.000 | −0.598361 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 25.0000i | 0.101215i | ||||||||
\(248\) | −330.926 | −1.33438 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 373.352i | − 1.48746i | −0.668480 | − | 0.743730i | \(-0.733055\pi\) | ||||
0.668480 | − | 0.743730i | \(-0.266945\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 78.0000i | − 0.308300i | ||||||||
\(254\) | 113.137i | 0.445422i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −272.000 | −1.06250 | ||||||||
\(257\) | 271.529 | 1.05653 | 0.528267 | − | 0.849079i | \(-0.322842\pi\) | ||||
0.528267 | + | 0.849079i | \(0.322842\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 288.000 | 1.11197 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 120.000i | − 0.458015i | ||||||||
\(263\) | −209.304 | −0.795831 | −0.397916 | − | 0.917422i | \(-0.630266\pi\) | ||||
−0.397916 | + | 0.917422i | \(0.630266\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − 318.198i | − 1.19623i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 126.000i | − 0.470149i | ||||||||
\(269\) | − 94.7523i | − 0.352239i | −0.984369 | − | 0.176120i | \(-0.943645\pi\) | ||||
0.984369 | − | 0.176120i | \(-0.0563545\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −176.000 | −0.649446 | −0.324723 | − | 0.945809i | \(-0.605271\pi\) | ||||
−0.324723 | + | 0.945809i | \(0.605271\pi\) | |||||||
\(272\) | 107.480 | 0.395148 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −30.0000 | −0.109489 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 303.000i | 1.09386i | 0.837177 | + | 0.546931i | \(0.184204\pi\) | ||||
−0.837177 | + | 0.546931i | \(0.815796\pi\) | |||||||
\(278\) | 147.078 | 0.529058 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 513.360i | − 1.82690i | −0.406948 | − | 0.913451i | \(-0.633407\pi\) | ||||
0.406948 | − | 0.913451i | \(-0.366593\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 393.000i | 1.38869i | 0.719641 | + | 0.694346i | \(0.244306\pi\) | ||||
−0.719641 | + | 0.694346i | \(0.755694\pi\) | |||||||
\(284\) | − 124.451i | − 0.438207i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −26.0000 | −0.0909091 | ||||||||
\(287\) | −50.9117 | −0.177393 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 433.000 | 1.49827 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 272.000i | 0.931507i | ||||||||
\(293\) | 46.6690 | 0.159280 | 0.0796400 | − | 0.996824i | \(-0.474623\pi\) | ||||
0.0796400 | + | 0.996824i | \(0.474623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 271.529i | 0.917328i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 242.000i | − 0.812081i | ||||||||
\(299\) | 4.24264i | 0.0141894i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 207.000 | 0.687708 | ||||||||
\(302\) | 24.0416 | 0.0796080 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 100.000 | 0.328947 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 289.000i | 0.941368i | 0.882302 | + | 0.470684i | \(0.155993\pi\) | ||||
−0.882302 | + | 0.470684i | \(0.844007\pi\) | |||||||
\(308\) | −330.926 | −1.07443 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 462.448i | 1.48697i | 0.668752 | + | 0.743485i | \(0.266829\pi\) | ||||
−0.668752 | + | 0.743485i | \(0.733171\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 481.000i | 1.53674i | 0.640005 | + | 0.768371i | \(0.278932\pi\) | ||||
−0.640005 | + | 0.768371i | \(0.721068\pi\) | |||||||
\(314\) | − 91.9239i | − 0.292751i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −48.0000 | −0.151899 | ||||||||
\(317\) | −11.3137 | −0.0356899 | −0.0178450 | − | 0.999841i | \(-0.505681\pi\) | ||||
−0.0178450 | + | 0.999841i | \(0.505681\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −494.000 | −1.54859 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 54.0000i | − 0.167702i | ||||||||
\(323\) | 671.751 | 2.07973 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 24.0416i | 0.0737473i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 48.0000i | − 0.146341i | ||||||||
\(329\) | − 292.742i | − 0.889794i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −72.0000 | −0.217523 | −0.108761 | − | 0.994068i | \(-0.534688\pi\) | ||||
−0.108761 | + | 0.994068i | \(0.534688\pi\) | |||||||
\(332\) | 93.3381 | 0.281139 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 360.000 | 1.07784 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 335.000i | − 0.994065i | −0.867732 | − | 0.497033i | \(-0.834423\pi\) | ||||
0.867732 | − | 0.497033i | \(-0.165577\pi\) | |||||||
\(338\) | −237.588 | −0.702923 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 717.006i | − 2.10266i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 153.000i | − 0.446064i | ||||||||
\(344\) | 195.161i | 0.567330i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −246.000 | −0.710983 | ||||||||
\(347\) | −383.252 | −1.10447 | −0.552236 | − | 0.833688i | \(-0.686225\pi\) | ||||
−0.552236 | + | 0.833688i | \(0.686225\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −568.000 | −1.62751 | −0.813754 | − | 0.581210i | \(-0.802579\pi\) | ||||
−0.813754 | + | 0.581210i | \(0.802579\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 520.000i | − 1.47727i | ||||||||
\(353\) | −131.522 | −0.372583 | −0.186292 | − | 0.982495i | \(-0.559647\pi\) | ||||
−0.186292 | + | 0.982495i | \(0.559647\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 203.647i | 0.572041i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 178.000i | − 0.497207i | ||||||||
\(359\) | 424.264i | 1.18179i | 0.806747 | + | 0.590897i | \(0.201226\pi\) | ||||
−0.806747 | + | 0.590897i | \(0.798774\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 264.000 | 0.731302 | ||||||||
\(362\) | −168.291 | −0.464893 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 18.0000 | 0.0494505 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 369.000i | − 1.00545i | −0.864447 | − | 0.502725i | \(-0.832331\pi\) | ||||
0.864447 | − | 0.502725i | \(-0.167669\pi\) | |||||||
\(368\) | 16.9706 | 0.0461157 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 865.499i | 2.33288i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 313.000i | − 0.839142i | −0.907723 | − | 0.419571i | \(-0.862181\pi\) | ||||
0.907723 | − | 0.419571i | \(-0.137819\pi\) | |||||||
\(374\) | 698.621i | 1.86797i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 276.000 | 0.734043 | ||||||||
\(377\) | 26.8701 | 0.0712734 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 47.0000 | 0.124011 | 0.0620053 | − | 0.998076i | \(-0.480250\pi\) | ||||
0.0620053 | + | 0.998076i | \(0.480250\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 22.0000i | − 0.0575916i | ||||||||
\(383\) | 373.352 | 0.974810 | 0.487405 | − | 0.873176i | \(-0.337943\pi\) | ||||
0.487405 | + | 0.873176i | \(0.337943\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 397.394i | 1.02952i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.0000i | 0.0360825i | ||||||||
\(389\) | − 390.323i | − 1.00340i | −0.865041 | − | 0.501700i | \(-0.832708\pi\) | ||||
0.865041 | − | 0.501700i | \(-0.167292\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 114.000 | 0.291560 | ||||||||
\(392\) | −271.529 | −0.692676 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −318.000 | −0.807107 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 47.0000i | − 0.118388i | −0.998247 | − | 0.0591940i | \(-0.981147\pi\) | ||||
0.998247 | − | 0.0591940i | \(-0.0188530\pi\) | |||||||
\(398\) | 247.487 | 0.621828 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 152.735i | 0.380885i | 0.981698 | + | 0.190443i | \(0.0609923\pi\) | ||||
−0.981698 | + | 0.190443i | \(0.939008\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 39.0000i | 0.0967742i | ||||||||
\(404\) | 101.823i | 0.252038i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −342.000 | −0.842365 | ||||||||
\(407\) | −588.313 | −1.44549 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 103.000 | 0.251834 | 0.125917 | − | 0.992041i | \(-0.459813\pi\) | ||||
0.125917 | + | 0.992041i | \(0.459813\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 220.000i | 0.533981i | ||||||||
\(413\) | −89.0955 | −0.215727 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 28.2843i | 0.0679910i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 650.000i | 1.55502i | ||||||||
\(419\) | 39.5980i | 0.0945059i | 0.998883 | + | 0.0472530i | \(0.0150467\pi\) | ||||
−0.998883 | + | 0.0472530i | \(0.984953\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −560.000 | −1.33017 | −0.665083 | − | 0.746769i | \(-0.731604\pi\) | ||||
−0.665083 | + | 0.746769i | \(0.731604\pi\) | |||||||
\(422\) | 69.2965 | 0.164210 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −816.000 | −1.92453 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 657.000i | − 1.53864i | ||||||||
\(428\) | 237.588 | 0.555112 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 479.418i | 1.11234i | 0.831069 | + | 0.556170i | \(0.187730\pi\) | ||||
−0.831069 | + | 0.556170i | \(0.812270\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 257.000i | 0.593533i | 0.954950 | + | 0.296767i | \(0.0959084\pi\) | ||||
−0.954950 | + | 0.296767i | \(0.904092\pi\) | |||||||
\(434\) | − 496.389i | − 1.14375i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −50.0000 | −0.114679 | ||||||||
\(437\) | 106.066 | 0.242714 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 167.000 | 0.380410 | 0.190205 | − | 0.981744i | \(-0.439085\pi\) | ||||
0.190205 | + | 0.981744i | \(0.439085\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 38.0000i | − 0.0859729i | ||||||||
\(443\) | 169.706 | 0.383083 | 0.191541 | − | 0.981485i | \(-0.438651\pi\) | ||||
0.191541 | + | 0.981485i | \(0.438651\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − 374.767i | − 0.840284i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 504.000i | − 1.12500i | ||||||||
\(449\) | 690.136i | 1.53705i | 0.639819 | + | 0.768526i | \(0.279009\pi\) | ||||
−0.639819 | + | 0.768526i | \(0.720991\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 104.000 | 0.230599 | ||||||||
\(452\) | 90.5097 | 0.200243 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 184.000 | 0.405286 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 50.0000i | − 0.109409i | −0.998503 | − | 0.0547046i | \(-0.982578\pi\) | ||||
0.998503 | − | 0.0547046i | \(-0.0174217\pi\) | |||||||
\(458\) | −123.037 | −0.268639 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 152.735i | − 0.331313i | −0.986184 | − | 0.165656i | \(-0.947026\pi\) | ||||
0.986184 | − | 0.165656i | \(-0.0529742\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 240.000i | 0.518359i | 0.965829 | + | 0.259179i | \(0.0834520\pi\) | ||||
−0.965829 | + | 0.259179i | \(0.916548\pi\) | |||||||
\(464\) | − 107.480i | − 0.231638i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 216.000 | 0.463519 | ||||||||
\(467\) | −592.555 | −1.26886 | −0.634428 | − | 0.772982i | \(-0.718764\pi\) | ||||
−0.634428 | + | 0.772982i | \(0.718764\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 567.000 | 1.20896 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 84.0000i | − 0.177966i | ||||||||
\(473\) | −422.850 | −0.893974 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − 483.661i | − 1.01609i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 392.000i | 0.820084i | ||||||||
\(479\) | 496.389i | 1.03630i | 0.855289 | + | 0.518151i | \(0.173380\pi\) | ||||
−0.855289 | + | 0.518151i | \(0.826620\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.0000 | 0.0665281 | ||||||||
\(482\) | −586.899 | −1.21763 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 434.000 | 0.896694 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 545.000i | 1.11910i | 0.828798 | + | 0.559548i | \(0.189025\pi\) | ||||
−0.828798 | + | 0.559548i | \(0.810975\pi\) | |||||||
\(488\) | 619.426 | 1.26931 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 905.097i | − 1.84337i | −0.387934 | − | 0.921687i | \(-0.626811\pi\) | ||||
0.387934 | − | 0.921687i | \(-0.373189\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 722.000i | − 1.46450i | ||||||||
\(494\) | − 35.3553i | − 0.0715695i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 156.000 | 0.314516 | ||||||||
\(497\) | 560.029 | 1.12682 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.00000 | −0.0140281 | −0.00701403 | − | 0.999975i | \(-0.502233\pi\) | ||||
−0.00701403 | + | 0.999975i | \(0.502233\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 528.000i | 1.05179i | ||||||||
\(503\) | −786.303 | −1.56323 | −0.781613 | − | 0.623764i | \(-0.785603\pi\) | ||||
−0.781613 | + | 0.623764i | \(0.785603\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 110.309i | 0.218001i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 160.000i | 0.314961i | ||||||||
\(509\) | − 578.413i | − 1.13637i | −0.822900 | − | 0.568186i | \(-0.807645\pi\) | ||||
0.822900 | − | 0.568186i | \(-0.192355\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1224.00 | −2.39530 | ||||||||
\(512\) | 248.902 | 0.486136 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −384.000 | −0.747082 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 598.000i | 1.15667i | ||||||||
\(518\) | −407.294 | −0.786281 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 414.365i | 0.795325i | 0.917532 | + | 0.397663i | \(0.130179\pi\) | ||||
−0.917532 | + | 0.397663i | \(0.869821\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 263.000i | 0.502868i | 0.967874 | + | 0.251434i | \(0.0809022\pi\) | ||||
−0.967874 | + | 0.251434i | \(0.919098\pi\) | |||||||
\(524\) | − 169.706i | − 0.323866i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 296.000 | 0.562738 | ||||||||
\(527\) | 1047.93 | 1.98849 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −511.000 | −0.965974 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 450.000i | − 0.845865i | ||||||||
\(533\) | −5.65685 | −0.0106132 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 534.573i | 0.997337i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 134.000i | 0.249071i | ||||||||
\(539\) | − 588.313i | − 1.09149i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 489.000 | 0.903882 | 0.451941 | − | 0.892048i | \(-0.350732\pi\) | ||||
0.451941 | + | 0.892048i | \(0.350732\pi\) | |||||||
\(542\) | 248.902 | 0.459228 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 760.000 | 1.39706 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.0000i | 0.0182815i | 0.999958 | + | 0.00914077i | \(0.00290964\pi\) | ||||
−0.999958 | + | 0.00914077i | \(0.997090\pi\) | |||||||
\(548\) | −42.4264 | −0.0774205 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 671.751i | − 1.21915i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 216.000i | − 0.390597i | ||||||||
\(554\) | − 428.507i | − 0.773478i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 208.000 | 0.374101 | ||||||||
\(557\) | 623.668 | 1.11969 | 0.559846 | − | 0.828597i | \(-0.310860\pi\) | ||||
0.559846 | + | 0.828597i | \(0.310860\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.0000 | 0.0411449 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 726.000i | 1.29181i | ||||||||
\(563\) | 63.6396 | 0.113037 | 0.0565183 | − | 0.998402i | \(-0.482000\pi\) | ||||
0.0565183 | + | 0.998402i | \(0.482000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − 555.786i | − 0.981954i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 528.000i | 0.929577i | ||||||||
\(569\) | 810.344i | 1.42416i | 0.702101 | + | 0.712078i | \(0.252246\pi\) | ||||
−0.702101 | + | 0.712078i | \(0.747754\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 377.000 | 0.660245 | 0.330123 | − | 0.943938i | \(-0.392910\pi\) | ||||
0.330123 | + | 0.943938i | \(0.392910\pi\) | |||||||
\(572\) | −36.7696 | −0.0642824 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 72.0000 | 0.125436 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 791.000i | 1.37088i | 0.728127 | + | 0.685442i | \(0.240391\pi\) | ||||
−0.728127 | + | 0.685442i | \(0.759609\pi\) | |||||||
\(578\) | −612.354 | −1.05944 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 420.021i | 0.722928i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1768.00i | − 3.03259i | ||||||||
\(584\) | − 1154.00i | − 1.97602i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −66.0000 | −0.112628 | ||||||||
\(587\) | 356.382 | 0.607124 | 0.303562 | − | 0.952812i | \(-0.401824\pi\) | ||||
0.303562 | + | 0.952812i | \(0.401824\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 975.000 | 1.65535 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 128.000i | − 0.216216i | ||||||||
\(593\) | 435.578 | 0.734533 | 0.367266 | − | 0.930116i | \(-0.380294\pi\) | ||||
0.367266 | + | 0.930116i | \(0.380294\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 342.240i | − 0.574228i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 6.00000i | − 0.0100334i | ||||||||
\(599\) | 1108.74i | 1.85099i | 0.378759 | + | 0.925495i | \(0.376351\pi\) | ||||
−0.378759 | + | 0.925495i | \(0.623649\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 233.000 | 0.387687 | 0.193844 | − | 0.981032i | \(-0.437905\pi\) | ||||
0.193844 | + | 0.981032i | \(0.437905\pi\) | |||||||
\(602\) | −292.742 | −0.486283 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 34.0000 | 0.0562914 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 776.000i | − 1.27842i | −0.769033 | − | 0.639209i | \(-0.779262\pi\) | ||||
0.769033 | − | 0.639209i | \(-0.220738\pi\) | |||||||
\(608\) | 707.107 | 1.16300 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 32.5269i | − 0.0532355i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 376.000i | − 0.613377i | −0.951810 | − | 0.306688i | \(-0.900779\pi\) | ||||
0.951810 | − | 0.306688i | \(-0.0992210\pi\) | |||||||
\(614\) | − 408.708i | − 0.665648i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1404.00 | 2.27922 | ||||||||
\(617\) | 593.970 | 0.962674 | 0.481337 | − | 0.876536i | \(-0.340151\pi\) | ||||
0.481337 | + | 0.876536i | \(0.340151\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1031.00 | −1.66559 | −0.832795 | − | 0.553582i | \(-0.813261\pi\) | ||||
−0.832795 | + | 0.553582i | \(0.813261\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 654.000i | − 1.05145i | ||||||||
\(623\) | −916.410 | −1.47096 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − 680.237i | − 1.08664i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 130.000i | − 0.207006i | ||||||||
\(629\) | − 859.842i | − 1.36700i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 745.000 | 1.18067 | 0.590333 | − | 0.807160i | \(-0.298997\pi\) | ||||
0.590333 | + | 0.807160i | \(0.298997\pi\) | |||||||
\(632\) | 203.647 | 0.322226 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16.0000 | 0.0252366 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.0000i | 0.0502355i | ||||||||
\(638\) | 698.621 | 1.09502 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 203.647i | 0.317702i | 0.987303 | + | 0.158851i | \(0.0507789\pi\) | ||||
−0.987303 | + | 0.158851i | \(0.949221\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1032.00i | 1.60498i | 0.596668 | + | 0.802488i | \(0.296491\pi\) | ||||
−0.596668 | + | 0.802488i | \(0.703509\pi\) | |||||||
\(644\) | − 76.3675i | − 0.118583i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −950.000 | −1.47059 | ||||||||
\(647\) | −56.5685 | −0.0874321 | −0.0437160 | − | 0.999044i | \(-0.513920\pi\) | ||||
−0.0437160 | + | 0.999044i | \(0.513920\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 182.000 | 0.280431 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 34.0000i | 0.0521472i | ||||||||
\(653\) | −272.943 | −0.417983 | −0.208992 | − | 0.977917i | \(-0.567018\pi\) | ||||
−0.208992 | + | 0.977917i | \(0.567018\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 22.6274i | 0.0344930i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 414.000i | 0.629179i | ||||||||
\(659\) | − 379.009i | − 0.575128i | −0.957761 | − | 0.287564i | \(-0.907155\pi\) | ||||
0.957761 | − | 0.287564i | \(-0.0928454\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −440.000 | −0.665658 | −0.332829 | − | 0.942987i | \(-0.608003\pi\) | ||||
−0.332829 | + | 0.942987i | \(0.608003\pi\) | |||||||
\(662\) | 101.823 | 0.153812 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −396.000 | −0.596386 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 114.000i | − 0.170915i | ||||||||
\(668\) | 509.117 | 0.762151 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1342.09i | 2.00013i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 264.000i | 0.392273i | 0.980577 | + | 0.196137i | \(0.0628396\pi\) | ||||
−0.980577 | + | 0.196137i | \(0.937160\pi\) | |||||||
\(674\) | 473.762i | 0.702910i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −336.000 | −0.497041 | ||||||||
\(677\) | −538.815 | −0.795887 | −0.397943 | − | 0.917410i | \(-0.630276\pi\) | ||||
−0.397943 | + | 0.917410i | \(0.630276\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −63.0000 | −0.0927835 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1014.00i | 1.48680i | ||||||||
\(683\) | −576.999 | −0.844801 | −0.422401 | − | 0.906409i | \(-0.638812\pi\) | ||||
−0.422401 | + | 0.906409i | \(0.638812\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 216.375i | 0.315415i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 92.0000i | − 0.133721i | ||||||||
\(689\) | 96.1665i | 0.139574i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −182.000 | −0.263386 | −0.131693 | − | 0.991291i | \(-0.542041\pi\) | ||||
−0.131693 | + | 0.991291i | \(0.542041\pi\) | |||||||
\(692\) | −347.897 | −0.502741 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 542.000 | 0.780980 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 152.000i | 0.218077i | ||||||||
\(698\) | 803.273 | 1.15082 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 558.614i | 0.796882i | 0.917194 | + | 0.398441i | \(0.130449\pi\) | ||||
−0.917194 | + | 0.398441i | \(0.869551\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 800.000i | − 1.13798i | ||||||||
\(704\) | 1029.55i | 1.46243i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 186.000 | 0.263456 | ||||||||
\(707\) | −458.205 | −0.648098 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −607.000 | −0.856135 | −0.428068 | − | 0.903747i | \(-0.640806\pi\) | ||||
−0.428068 | + | 0.903747i | \(0.640806\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 864.000i | − 1.21348i | ||||||||
\(713\) | 165.463 | 0.232066 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − 251.730i | − 0.351578i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 600.000i | − 0.835655i | ||||||||
\(719\) | 106.066i | 0.147519i | 0.997276 | + | 0.0737594i | \(0.0234997\pi\) | ||||
−0.997276 | + | 0.0737594i | \(0.976500\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −990.000 | −1.37309 | ||||||||
\(722\) | −373.352 | −0.517109 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −238.000 | −0.328729 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 71.0000i | 0.0976616i | 0.998807 | + | 0.0488308i | \(0.0155495\pi\) | ||||
−0.998807 | + | 0.0488308i | \(0.984450\pi\) | |||||||
\(728\) | −76.3675 | −0.104900 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 618.011i | − 0.845433i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 904.000i | 1.23329i | 0.787242 | + | 0.616644i | \(0.211508\pi\) | ||||
−0.787242 | + | 0.616644i | \(0.788492\pi\) | |||||||
\(734\) | 521.845i | 0.710960i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 120.000 | 0.163043 | ||||||||
\(737\) | −1158.24 | −1.57156 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 800.000 | 1.08254 | 0.541272 | − | 0.840848i | \(-0.317943\pi\) | ||||
0.541272 | + | 0.840848i | \(0.317943\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 1224.00i | − 1.64960i | ||||||||
\(743\) | −418.607 | −0.563401 | −0.281701 | − | 0.959502i | \(-0.590899\pi\) | ||||
−0.281701 | + | 0.959502i | \(0.590899\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 442.649i | 0.593363i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 988.000i | 1.32086i | ||||||||
\(749\) | 1069.15i | 1.42743i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −704.000 | −0.937417 | −0.468708 | − | 0.883353i | \(-0.655280\pi\) | ||||
−0.468708 | + | 0.883353i | \(0.655280\pi\) | |||||||
\(752\) | −130.108 | −0.173015 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −38.0000 | −0.0503979 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 977.000i | − 1.29062i | −0.763920 | − | 0.645310i | \(-0.776728\pi\) | ||||
0.763920 | − | 0.645310i | \(-0.223272\pi\) | |||||||
\(758\) | −66.4680 | −0.0876887 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 746.705i | − 0.981215i | −0.871381 | − | 0.490608i | \(-0.836775\pi\) | ||||
0.871381 | − | 0.490608i | \(-0.163225\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 225.000i | − 0.294889i | ||||||||
\(764\) | − 31.1127i | − 0.0407234i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −528.000 | −0.689295 | ||||||||
\(767\) | −9.89949 | −0.0129068 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1337.00 | −1.73862 | −0.869311 | − | 0.494266i | \(-0.835437\pi\) | ||||
−0.869311 | + | 0.494266i | \(0.835437\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 562.000i | 0.727979i | ||||||||
\(773\) | −1170.97 | −1.51484 | −0.757418 | − | 0.652930i | \(-0.773540\pi\) | ||||
−0.757418 | + | 0.652930i | \(0.773540\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − 59.3970i | − 0.0765425i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 552.000i | 0.709512i | ||||||||
\(779\) | 141.421i | 0.181542i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1144.00 | −1.46479 | ||||||||
\(782\) | −161.220 | −0.206164 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 128.000 | 0.163265 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 703.000i | 0.893266i | 0.894717 | + | 0.446633i | \(0.147377\pi\) | ||||
−0.894717 | + | 0.446633i | \(0.852623\pi\) | |||||||
\(788\) | −449.720 | −0.570711 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 407.294i | 0.514910i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 73.0000i | − 0.0920555i | ||||||||
\(794\) | 66.4680i | 0.0837129i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 350.000 | 0.439698 | ||||||||
\(797\) | −1538.66 | −1.93057 | −0.965285 | − | 0.261199i | \(-0.915882\pi\) | ||||
−0.965285 | + | 0.261199i | \(0.915882\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −874.000 | −1.09387 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 216.000i | − 0.269327i | ||||||||
\(803\) | 2500.33 | 3.11374 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 55.1543i | − 0.0684297i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 432.000i | − 0.534653i | ||||||||
\(809\) | 73.5391i | 0.0909012i | 0.998967 | + | 0.0454506i | \(0.0144724\pi\) | ||||
−0.998967 | + | 0.0454506i | \(0.985528\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1095.00 | 1.35018 | 0.675092 | − | 0.737733i | \(-0.264104\pi\) | ||||
0.675092 | + | 0.737733i | \(0.264104\pi\) | |||||||
\(812\) | −483.661 | −0.595642 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 832.000 | 1.02211 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 575.000i | − 0.703794i | ||||||||
\(818\) | −145.664 | −0.178073 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1166.73i | 1.42110i | 0.703645 | + | 0.710552i | \(0.251555\pi\) | ||||
−0.703645 | + | 0.710552i | \(0.748445\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1015.00i | 1.23329i | 0.787240 | + | 0.616646i | \(0.211509\pi\) | ||||
−0.787240 | + | 0.616646i | \(0.788491\pi\) | |||||||
\(824\) | − 933.381i | − 1.13274i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 126.000 | 0.152542 | ||||||||
\(827\) | −379.009 | −0.458294 | −0.229147 | − | 0.973392i | \(-0.573594\pi\) | ||||
−0.229147 | + | 0.973392i | \(0.573594\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −150.000 | −0.180941 | −0.0904704 | − | 0.995899i | \(-0.528837\pi\) | ||||
−0.0904704 | + | 0.995899i | \(0.528837\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 56.0000i | − 0.0673077i | ||||||||
\(833\) | 859.842 | 1.03222 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 919.239i | 1.09957i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 56.0000i | − 0.0668258i | ||||||||
\(839\) | − 660.438i | − 0.787173i | −0.919288 | − | 0.393586i | \(-0.871234\pi\) | ||||
0.919288 | − | 0.393586i | \(-0.128766\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 119.000 | 0.141498 | ||||||||
\(842\) | 791.960 | 0.940570 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 98.0000 | 0.116114 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1953.00i | 2.30579i | ||||||||
\(848\) | 384.666 | 0.453616 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 135.765i | − 0.159535i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 297.000i | 0.348183i | 0.984729 | + | 0.174091i | \(0.0556988\pi\) | ||||
−0.984729 | + | 0.174091i | \(0.944301\pi\) | |||||||
\(854\) | 929.138i | 1.08798i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1008.00 | −1.17757 | ||||||||
\(857\) | 1165.31 | 1.35976 | 0.679879 | − | 0.733325i | \(-0.262032\pi\) | ||||
0.679879 | + | 0.733325i | \(0.262032\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1286.00 | 1.49709 | 0.748545 | − | 0.663084i | \(-0.230753\pi\) | ||||
0.748545 | + | 0.663084i | \(0.230753\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 678.000i | − 0.786543i | ||||||||
\(863\) | −633.568 | −0.734146 | −0.367073 | − | 0.930192i | \(-0.619640\pi\) | ||||
−0.367073 | + | 0.930192i | \(0.619640\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − 363.453i | − 0.419692i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 702.000i | − 0.808756i | ||||||||
\(869\) | 441.235i | 0.507750i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 63.0000 | 0.0723307 | ||||||||
\(872\) | 212.132 | 0.243271 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −150.000 | −0.171625 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1599.00i | − 1.82326i | −0.411011 | − | 0.911631i | \(-0.634824\pi\) | ||||
0.411011 | − | 0.911631i | \(-0.365176\pi\) | |||||||
\(878\) | −236.174 | −0.268991 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 961.665i | − 1.09156i | −0.837928 | − | 0.545780i | \(-0.816233\pi\) | ||||
0.837928 | − | 0.545780i | \(-0.183767\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 193.000i | 0.218573i | 0.994010 | + | 0.109287i | \(0.0348566\pi\) | ||||
−0.994010 | + | 0.109287i | \(0.965143\pi\) | |||||||
\(884\) | − 53.7401i | − 0.0607920i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −240.000 | −0.270880 | ||||||||
\(887\) | 700.036 | 0.789217 | 0.394609 | − | 0.918849i | \(-0.370880\pi\) | ||||
0.394609 | + | 0.918849i | \(0.370880\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −720.000 | −0.809899 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 530.000i | − 0.594170i | ||||||||
\(893\) | −813.173 | −0.910608 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − 305.470i | − 0.340926i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 976.000i | − 1.08686i | ||||||||
\(899\) | − 1047.93i | − 1.16566i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2584.00 | 2.86792 | ||||||||
\(902\) | −147.078 | −0.163058 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −384.000 | −0.424779 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 240.000i | − 0.264609i | −0.991209 | − | 0.132304i | \(-0.957762\pi\) | ||||
0.991209 | − | 0.132304i | \(-0.0422376\pi\) | |||||||
\(908\) | 260.215 | 0.286581 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 171.120i | 0.187837i | 0.995580 | + | 0.0939187i | \(0.0299394\pi\) | ||||
−0.995580 | + | 0.0939187i | \(0.970061\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 858.000i | − 0.939759i | ||||||||
\(914\) | 70.7107i | 0.0773640i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −174.000 | −0.189956 | ||||||||
\(917\) | 763.675 | 0.832798 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −343.000 | −0.373232 | −0.186616 | − | 0.982433i | \(-0.559752\pi\) | ||||
−0.186616 | + | 0.982433i | \(0.559752\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 216.000i | 0.234273i | ||||||||
\(923\) | 62.2254 | 0.0674165 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − 339.411i | − 0.366535i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 760.000i | − 0.818966i | ||||||||
\(929\) | − 719.835i | − 0.774849i | −0.921901 | − | 0.387424i | \(-0.873365\pi\) | ||||
0.921901 | − | 0.387424i | \(-0.126635\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 800.000 | 0.859291 | ||||||||
\(932\) | 305.470 | 0.327758 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 838.000 | 0.897216 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 609.000i | 0.649947i | 0.945723 | + | 0.324973i | \(0.105355\pi\) | ||||
−0.945723 | + | 0.324973i | \(0.894645\pi\) | |||||||
\(938\) | −801.859 | −0.854860 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 111.723i | − 0.118728i | −0.998236 | − | 0.0593639i | \(-0.981093\pi\) | ||||
0.998236 | − | 0.0593639i | \(-0.0189072\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0000i | 0.0254507i | ||||||||
\(944\) | 39.5980i | 0.0419470i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 598.000 | 0.632135 | ||||||||
\(947\) | 1022.48 | 1.07970 | 0.539850 | − | 0.841761i | \(-0.318481\pi\) | ||||
0.539850 | + | 0.841761i | \(0.318481\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −136.000 | −0.143309 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2052.00i | 2.15546i | ||||||||
\(953\) | 1380.27 | 1.44834 | 0.724172 | − | 0.689619i | \(-0.242222\pi\) | ||||
0.724172 | + | 0.689619i | \(0.242222\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 554.372i | 0.579887i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 702.000i | − 0.732777i | ||||||||
\(959\) | − 190.919i | − 0.199081i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 560.000 | 0.582726 | ||||||||
\(962\) | −45.2548 | −0.0470424 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −830.000 | −0.860996 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 584.000i | 0.603930i | 0.953319 | + | 0.301965i | \(0.0976425\pi\) | ||||
−0.953319 | + | 0.301965i | \(0.902357\pi\) | |||||||
\(968\) | −1841.31 | −1.90218 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1030.96i | − 1.06175i | −0.847449 | − | 0.530876i | \(-0.821863\pi\) | ||||
0.847449 | − | 0.530876i | \(-0.178137\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 936.000i | 0.961973i | ||||||||
\(974\) | − 770.746i | − 0.791321i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −292.000 | −0.299180 | ||||||||
\(977\) | −1028.13 | −1.05234 | −0.526169 | − | 0.850380i | \(-0.676372\pi\) | ||||
−0.526169 | + | 0.850380i | \(0.676372\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1872.00 | 1.91216 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1280.00i | 1.30346i | ||||||||
\(983\) | −1323.70 | −1.34660 | −0.673298 | − | 0.739371i | \(-0.735123\pi\) | ||||
−0.673298 | + | 0.739371i | \(0.735123\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1021.06i | 1.03556i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 50.0000i | − 0.0506073i | ||||||||
\(989\) | − 97.5807i | − 0.0986661i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −961.000 | −0.969728 | −0.484864 | − | 0.874590i | \(-0.661131\pi\) | ||||
−0.484864 | + | 0.874590i | \(0.661131\pi\) | |||||||
\(992\) | 1103.09 | 1.11198 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −792.000 | −0.796781 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 600.000i | − 0.601805i | −0.953655 | − | 0.300903i | \(-0.902712\pi\) | ||||
0.953655 | − | 0.300903i | \(-0.0972879\pi\) | |||||||
\(998\) | 9.89949 | 0.00991933 | ||||||||
\(999\) | 0 | 0 |
(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 | 225.3.d.a.224.1 | 4 | ||
3.2 | odd | 2 | inner | 225.3.d.a.224.3 | 4 | ||
4.3 | odd | 2 | 3600.3.c.e.449.3 | 4 | |||
5.2 | odd | 4 | 225.3.c.b.26.1 | yes | 2 | ||
5.3 | odd | 4 | 225.3.c.a.26.2 | yes | 2 | ||
5.4 | even | 2 | inner | 225.3.d.a.224.4 | 4 | ||
12.11 | even | 2 | 3600.3.c.e.449.4 | 4 | |||
15.2 | even | 4 | 225.3.c.b.26.2 | yes | 2 | ||
15.8 | even | 4 | 225.3.c.a.26.1 | ✓ | 2 | ||
15.14 | odd | 2 | inner | 225.3.d.a.224.2 | 4 | ||
20.3 | even | 4 | 3600.3.l.j.1601.1 | 2 | |||
20.7 | even | 4 | 3600.3.l.b.1601.1 | 2 | |||
20.19 | odd | 2 | 3600.3.c.e.449.1 | 4 | |||
60.23 | odd | 4 | 3600.3.l.j.1601.2 | 2 | |||
60.47 | odd | 4 | 3600.3.l.b.1601.2 | 2 | |||
60.59 | even | 2 | 3600.3.c.e.449.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.3.c.a.26.1 | ✓ | 2 | 15.8 | even | 4 | ||
225.3.c.a.26.2 | yes | 2 | 5.3 | odd | 4 | ||
225.3.c.b.26.1 | yes | 2 | 5.2 | odd | 4 | ||
225.3.c.b.26.2 | yes | 2 | 15.2 | even | 4 | ||
225.3.d.a.224.1 | 4 | 1.1 | even | 1 | trivial | ||
225.3.d.a.224.2 | 4 | 15.14 | odd | 2 | inner | ||
225.3.d.a.224.3 | 4 | 3.2 | odd | 2 | inner | ||
225.3.d.a.224.4 | 4 | 5.4 | even | 2 | inner | ||
3600.3.c.e.449.1 | 4 | 20.19 | odd | 2 | |||
3600.3.c.e.449.2 | 4 | 60.59 | even | 2 | |||
3600.3.c.e.449.3 | 4 | 4.3 | odd | 2 | |||
3600.3.c.e.449.4 | 4 | 12.11 | even | 2 | |||
3600.3.l.b.1601.1 | 2 | 20.7 | even | 4 | |||
3600.3.l.b.1601.2 | 2 | 60.47 | odd | 4 | |||
3600.3.l.j.1601.1 | 2 | 20.3 | even | 4 | |||
3600.3.l.j.1601.2 | 2 | 60.23 | odd | 4 |