Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.6 | ||
Root | \(-0.854638 - 0.854638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.2.c.g.199.1 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.70928i | 1.91575i | 0.287190 | + | 0.957873i | \(0.407279\pi\) | ||||
−0.287190 | + | 0.957873i | \(0.592721\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −5.34017 | −2.67009 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.70928 | −1.10606 | ||||||||
\(7\) | − 1.07838i | − 0.407588i | −0.979014 | − | 0.203794i | \(-0.934673\pi\) | ||||
0.979014 | − | 0.203794i | \(-0.0653274\pi\) | |||||||
\(8\) | − 9.04945i | − 3.19946i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | − 5.34017i | − 1.54158i | ||||||||
\(13\) | − 4.34017i | − 1.20375i | −0.798591 | − | 0.601874i | \(-0.794421\pi\) | ||||
0.798591 | − | 0.601874i | \(-0.205579\pi\) | |||||||
\(14\) | 2.92162 | 0.780836 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.8371 | 3.45928 | ||||||||
\(17\) | − 7.75872i | − 1.88177i | −0.338730 | − | 0.940883i | \(-0.609997\pi\) | ||||
0.338730 | − | 0.940883i | \(-0.390003\pi\) | |||||||
\(18\) | − 2.70928i | − 0.638582i | ||||||||
\(19\) | −5.26180 | −1.20714 | −0.603569 | − | 0.797311i | \(-0.706255\pi\) | ||||
−0.603569 | + | 0.797311i | \(0.706255\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.07838 | 0.235321 | ||||||||
\(22\) | 2.70928i | 0.577619i | ||||||||
\(23\) | − 2.15676i | − 0.449715i | −0.974392 | − | 0.224857i | \(-0.927808\pi\) | ||||
0.974392 | − | 0.224857i | \(-0.0721916\pi\) | |||||||
\(24\) | 9.04945 | 1.84721 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 11.7587 | 2.30608 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 5.75872i | 1.08830i | ||||||||
\(29\) | −1.41855 | −0.263418 | −0.131709 | − | 0.991288i | \(-0.542046\pi\) | ||||
−0.131709 | + | 0.991288i | \(0.542046\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.68035 | −0.840615 | −0.420307 | − | 0.907382i | \(-0.638078\pi\) | ||||
−0.420307 | + | 0.907382i | \(0.638078\pi\) | |||||||
\(32\) | 19.3896i | 3.42763i | ||||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | 21.0205 | 3.60499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.34017 | 0.890029 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | − 14.2557i | − 2.31257i | ||||||||
\(39\) | 4.34017 | 0.694984 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.41855 | −1.47093 | −0.735465 | − | 0.677562i | \(-0.763036\pi\) | ||||
−0.735465 | + | 0.677562i | \(0.763036\pi\) | |||||||
\(42\) | 2.92162i | 0.450816i | ||||||||
\(43\) | 7.60197i | 1.15929i | 0.814869 | + | 0.579645i | \(0.196809\pi\) | ||||
−0.814869 | + | 0.579645i | \(0.803191\pi\) | |||||||
\(44\) | −5.34017 | −0.805061 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.84324 | 0.861539 | ||||||||
\(47\) | − 4.68035i | − 0.682699i | −0.939937 | − | 0.341349i | \(-0.889116\pi\) | ||||
0.939937 | − | 0.341349i | \(-0.110884\pi\) | |||||||
\(48\) | 13.8371i | 1.99721i | ||||||||
\(49\) | 5.83710 | 0.833872 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.75872 | 1.08644 | ||||||||
\(52\) | 23.1773i | 3.21411i | ||||||||
\(53\) | 0.156755i | 0.0215320i | 0.999942 | + | 0.0107660i | \(0.00342699\pi\) | ||||
−0.999942 | + | 0.0107660i | \(0.996573\pi\) | |||||||
\(54\) | 2.70928 | 0.368686 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.75872 | −1.30406 | ||||||||
\(57\) | − 5.26180i | − 0.696942i | ||||||||
\(58\) | − 3.84324i | − 0.504643i | ||||||||
\(59\) | −6.15676 | −0.801541 | −0.400771 | − | 0.916178i | \(-0.631258\pi\) | ||||
−0.400771 | + | 0.916178i | \(0.631258\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.15676 | −0.532218 | −0.266109 | − | 0.963943i | \(-0.585738\pi\) | ||||
−0.266109 | + | 0.963943i | \(0.585738\pi\) | |||||||
\(62\) | − 12.6803i | − 1.61041i | ||||||||
\(63\) | 1.07838i | 0.135863i | ||||||||
\(64\) | −24.8576 | −3.10720 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.70928 | −0.333489 | ||||||||
\(67\) | 8.68035i | 1.06047i | 0.847850 | + | 0.530237i | \(0.177897\pi\) | ||||
−0.847850 | + | 0.530237i | \(0.822103\pi\) | |||||||
\(68\) | 41.4329i | 5.02448i | ||||||||
\(69\) | 2.15676 | 0.259643 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.68035 | −0.555455 | −0.277727 | − | 0.960660i | \(-0.589581\pi\) | ||||
−0.277727 | + | 0.960660i | \(0.589581\pi\) | |||||||
\(72\) | 9.04945i | 1.06649i | ||||||||
\(73\) | − 10.4969i | − 1.22857i | −0.789083 | − | 0.614286i | \(-0.789444\pi\) | ||||
0.789083 | − | 0.614286i | \(-0.210556\pi\) | |||||||
\(74\) | −5.41855 | −0.629894 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 28.0989 | 3.22316 | ||||||||
\(77\) | − 1.07838i | − 0.122893i | ||||||||
\(78\) | 11.7587i | 1.33141i | ||||||||
\(79\) | 8.09890 | 0.911197 | 0.455599 | − | 0.890185i | \(-0.349425\pi\) | ||||
0.455599 | + | 0.890185i | \(0.349425\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 25.5174i | − 2.81793i | ||||||||
\(83\) | − 11.0205i | − 1.20966i | −0.796355 | − | 0.604830i | \(-0.793241\pi\) | ||||
0.796355 | − | 0.604830i | \(-0.206759\pi\) | |||||||
\(84\) | −5.75872 | −0.628328 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −20.5958 | −2.22090 | ||||||||
\(87\) | − 1.41855i | − 0.152085i | ||||||||
\(88\) | − 9.04945i | − 0.964674i | ||||||||
\(89\) | 12.8371 | 1.36073 | 0.680365 | − | 0.732873i | \(-0.261821\pi\) | ||||
0.680365 | + | 0.732873i | \(0.261821\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.68035 | −0.490634 | ||||||||
\(92\) | 11.5174i | 1.20078i | ||||||||
\(93\) | − 4.68035i | − 0.485329i | ||||||||
\(94\) | 12.6803 | 1.30788 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −19.3896 | −1.97894 | ||||||||
\(97\) | − 14.6803i | − 1.49056i | −0.666750 | − | 0.745282i | \(-0.732315\pi\) | ||||
0.666750 | − | 0.745282i | \(-0.267685\pi\) | |||||||
\(98\) | 15.8143i | 1.59749i | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.5753 | −1.54980 | −0.774900 | − | 0.632083i | \(-0.782200\pi\) | ||||
−0.774900 | + | 0.632083i | \(0.782200\pi\) | |||||||
\(102\) | 21.0205i | 2.08134i | ||||||||
\(103\) | 6.83710i | 0.673680i | 0.941562 | + | 0.336840i | \(0.109358\pi\) | ||||
−0.941562 | + | 0.336840i | \(0.890642\pi\) | |||||||
\(104\) | −39.2762 | −3.85135 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.424694 | −0.0412499 | ||||||||
\(107\) | − 6.34017i | − 0.612928i | −0.951882 | − | 0.306464i | \(-0.900854\pi\) | ||||
0.951882 | − | 0.306464i | \(-0.0991458\pi\) | |||||||
\(108\) | 5.34017i | 0.513858i | ||||||||
\(109\) | −2.31351 | −0.221594 | −0.110797 | − | 0.993843i | \(-0.535340\pi\) | ||||
−0.110797 | + | 0.993843i | \(0.535340\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | − 14.9216i | − 1.40996i | ||||||||
\(113\) | − 6.00000i | − 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | 14.2557 | 1.33516 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.57531 | 0.703350 | ||||||||
\(117\) | 4.34017i | 0.401249i | ||||||||
\(118\) | − 16.6803i | − 1.53555i | ||||||||
\(119\) | −8.36683 | −0.766987 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − 11.2618i | − 1.01960i | ||||||||
\(123\) | − 9.41855i | − 0.849242i | ||||||||
\(124\) | 24.9939 | 2.24451 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.92162 | −0.260279 | ||||||||
\(127\) | 2.24128i | 0.198881i | 0.995044 | + | 0.0994406i | \(0.0317053\pi\) | ||||
−0.995044 | + | 0.0994406i | \(0.968295\pi\) | |||||||
\(128\) | − 28.5669i | − 2.52498i | ||||||||
\(129\) | −7.60197 | −0.669316 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.68035 | 0.758405 | 0.379203 | − | 0.925314i | \(-0.376198\pi\) | ||||
0.379203 | + | 0.925314i | \(0.376198\pi\) | |||||||
\(132\) | − 5.34017i | − 0.464802i | ||||||||
\(133\) | 5.67420i | 0.492016i | ||||||||
\(134\) | −23.5174 | −2.03160 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −70.2122 | −6.02064 | ||||||||
\(137\) | 15.3607i | 1.31235i | 0.754608 | + | 0.656176i | \(0.227827\pi\) | ||||
−0.754608 | + | 0.656176i | \(0.772173\pi\) | |||||||
\(138\) | 5.84324i | 0.497410i | ||||||||
\(139\) | −8.58145 | −0.727869 | −0.363935 | − | 0.931425i | \(-0.618567\pi\) | ||||
−0.363935 | + | 0.931425i | \(0.618567\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.68035 | 0.394156 | ||||||||
\(142\) | − 12.6803i | − 1.06411i | ||||||||
\(143\) | − 4.34017i | − 0.362943i | ||||||||
\(144\) | −13.8371 | −1.15309 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 28.4391 | 2.35363 | ||||||||
\(147\) | 5.83710i | 0.481436i | ||||||||
\(148\) | − 10.6803i | − 0.877919i | ||||||||
\(149\) | 18.0989 | 1.48272 | 0.741360 | − | 0.671108i | \(-0.234181\pi\) | ||||
0.741360 | + | 0.671108i | \(0.234181\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.9360 | 1.86651 | 0.933253 | − | 0.359221i | \(-0.116958\pi\) | ||||
0.933253 | + | 0.359221i | \(0.116958\pi\) | |||||||
\(152\) | 47.6163i | 3.86220i | ||||||||
\(153\) | 7.75872i | 0.627256i | ||||||||
\(154\) | 2.92162 | 0.235431 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −23.1773 | −1.85567 | ||||||||
\(157\) | 10.9939i | 0.877405i | 0.898632 | + | 0.438703i | \(0.144562\pi\) | ||||
−0.898632 | + | 0.438703i | \(0.855438\pi\) | |||||||
\(158\) | 21.9421i | 1.74562i | ||||||||
\(159\) | −0.156755 | −0.0124315 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.32580 | −0.183298 | ||||||||
\(162\) | 2.70928i | 0.212861i | ||||||||
\(163\) | − 6.52359i | − 0.510967i | −0.966813 | − | 0.255484i | \(-0.917765\pi\) | ||||
0.966813 | − | 0.255484i | \(-0.0822347\pi\) | |||||||
\(164\) | 50.2967 | 3.92751 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 29.8576 | 2.31740 | ||||||||
\(167\) | − 1.97334i | − 0.152701i | −0.997081 | − | 0.0763507i | \(-0.975673\pi\) | ||||
0.997081 | − | 0.0763507i | \(-0.0243269\pi\) | |||||||
\(168\) | − 9.75872i | − 0.752902i | ||||||||
\(169\) | −5.83710 | −0.449008 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.26180 | 0.402380 | ||||||||
\(172\) | − 40.5958i | − 3.09540i | ||||||||
\(173\) | 3.75872i | 0.285770i | 0.989739 | + | 0.142885i | \(0.0456380\pi\) | ||||
−0.989739 | + | 0.142885i | \(0.954362\pi\) | |||||||
\(174\) | 3.84324 | 0.291356 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 13.8371 | 1.04301 | ||||||||
\(177\) | − 6.15676i | − 0.462770i | ||||||||
\(178\) | 34.7792i | 2.60681i | ||||||||
\(179\) | −15.1506 | −1.13241 | −0.566205 | − | 0.824264i | \(-0.691589\pi\) | ||||
−0.566205 | + | 0.824264i | \(0.691589\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.83710 | 0.359539 | 0.179769 | − | 0.983709i | \(-0.442465\pi\) | ||||
0.179769 | + | 0.983709i | \(0.442465\pi\) | |||||||
\(182\) | − 12.6803i | − 0.939930i | ||||||||
\(183\) | − 4.15676i | − 0.307276i | ||||||||
\(184\) | −19.5174 | −1.43885 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 12.6803 | 0.929768 | ||||||||
\(187\) | − 7.75872i | − 0.567374i | ||||||||
\(188\) | 24.9939i | 1.82286i | ||||||||
\(189\) | −1.07838 | −0.0784404 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.52359 | 0.182601 | 0.0913003 | − | 0.995823i | \(-0.470898\pi\) | ||||
0.0913003 | + | 0.995823i | \(0.470898\pi\) | |||||||
\(192\) | − 24.8576i | − 1.79394i | ||||||||
\(193\) | 0.0266620i | 0.00191917i | 1.00000 | 0.000959586i | \(0.000305446\pi\) | |||||
−1.00000 | 0.000959586i | \(0.999695\pi\) | ||||||||
\(194\) | 39.7731 | 2.85554 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −31.1711 | −2.22651 | ||||||||
\(197\) | − 21.1194i | − 1.50470i | −0.658766 | − | 0.752348i | \(-0.728921\pi\) | ||||
0.658766 | − | 0.752348i | \(-0.271079\pi\) | |||||||
\(198\) | − 2.70928i | − 0.192540i | ||||||||
\(199\) | −10.5236 | −0.745998 | −0.372999 | − | 0.927832i | \(-0.621670\pi\) | ||||
−0.372999 | + | 0.927832i | \(0.621670\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.68035 | −0.612264 | ||||||||
\(202\) | − 42.1978i | − 2.96903i | ||||||||
\(203\) | 1.52973i | 0.107366i | ||||||||
\(204\) | −41.4329 | −2.90089 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −18.5236 | −1.29060 | ||||||||
\(207\) | 2.15676i | 0.149905i | ||||||||
\(208\) | − 60.0554i | − 4.16409i | ||||||||
\(209\) | −5.26180 | −0.363966 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.57531 | 0.659191 | 0.329596 | − | 0.944122i | \(-0.393088\pi\) | ||||
0.329596 | + | 0.944122i | \(0.393088\pi\) | |||||||
\(212\) | − 0.837101i | − 0.0574924i | ||||||||
\(213\) | − 4.68035i | − 0.320692i | ||||||||
\(214\) | 17.1773 | 1.17421 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −9.04945 | −0.615737 | ||||||||
\(217\) | 5.04718i | 0.342625i | ||||||||
\(218\) | − 6.26794i | − 0.424518i | ||||||||
\(219\) | 10.4969 | 0.709317 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −33.6742 | −2.26517 | ||||||||
\(222\) | − 5.41855i | − 0.363669i | ||||||||
\(223\) | − 2.15676i | − 0.144427i | −0.997389 | − | 0.0722135i | \(-0.976994\pi\) | ||||
0.997389 | − | 0.0722135i | \(-0.0230063\pi\) | |||||||
\(224\) | 20.9093 | 1.39706 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.2557 | 1.08131 | ||||||||
\(227\) | − 9.65983i | − 0.641145i | −0.947224 | − | 0.320573i | \(-0.896125\pi\) | ||||
0.947224 | − | 0.320573i | \(-0.103875\pi\) | |||||||
\(228\) | 28.0989i | 1.86089i | ||||||||
\(229\) | 3.36069 | 0.222081 | 0.111040 | − | 0.993816i | \(-0.464582\pi\) | ||||
0.111040 | + | 0.993816i | \(0.464582\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.07838 | 0.0709520 | ||||||||
\(232\) | 12.8371i | 0.842797i | ||||||||
\(233\) | − 2.39803i | − 0.157100i | −0.996910 | − | 0.0785501i | \(-0.974971\pi\) | ||||
0.996910 | − | 0.0785501i | \(-0.0250291\pi\) | |||||||
\(234\) | −11.7587 | −0.768692 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 32.8781 | 2.14018 | ||||||||
\(237\) | 8.09890i | 0.526080i | ||||||||
\(238\) | − 22.6681i | − 1.46935i | ||||||||
\(239\) | 7.20394 | 0.465984 | 0.232992 | − | 0.972479i | \(-0.425148\pi\) | ||||
0.232992 | + | 0.972479i | \(0.425148\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.20394 | −0.335215 | −0.167608 | − | 0.985854i | \(-0.553604\pi\) | ||||
−0.167608 | + | 0.985854i | \(0.553604\pi\) | |||||||
\(242\) | 2.70928i | 0.174159i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 22.1978 | 1.42107 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 25.5174 | 1.62693 | ||||||||
\(247\) | 22.8371i | 1.45309i | ||||||||
\(248\) | 42.3545i | 2.68952i | ||||||||
\(249\) | 11.0205 | 0.698397 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.3197 | 0.966968 | 0.483484 | − | 0.875353i | \(-0.339371\pi\) | ||||
0.483484 | + | 0.875353i | \(0.339371\pi\) | |||||||
\(252\) | − 5.75872i | − 0.362765i | ||||||||
\(253\) | − 2.15676i | − 0.135594i | ||||||||
\(254\) | −6.07223 | −0.381006 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 27.6803 | 1.73002 | ||||||||
\(257\) | − 4.15676i | − 0.259291i | −0.991560 | − | 0.129646i | \(-0.958616\pi\) | ||||
0.991560 | − | 0.129646i | \(-0.0413840\pi\) | |||||||
\(258\) | − 20.5958i | − 1.28224i | ||||||||
\(259\) | 2.15676 | 0.134014 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.41855 | 0.0878061 | ||||||||
\(262\) | 23.5174i | 1.45291i | ||||||||
\(263\) | − 18.7070i | − 1.15352i | −0.816912 | − | 0.576762i | \(-0.804316\pi\) | ||||
0.816912 | − | 0.576762i | \(-0.195684\pi\) | |||||||
\(264\) | 9.04945 | 0.556955 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −15.3730 | −0.942578 | ||||||||
\(267\) | 12.8371i | 0.785618i | ||||||||
\(268\) | − 46.3545i | − 2.83155i | ||||||||
\(269\) | −23.3607 | −1.42433 | −0.712163 | − | 0.702014i | \(-0.752284\pi\) | ||||
−0.712163 | + | 0.702014i | \(0.752284\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.57531 | −0.338676 | −0.169338 | − | 0.985558i | \(-0.554163\pi\) | ||||
−0.169338 | + | 0.985558i | \(0.554163\pi\) | |||||||
\(272\) | − 107.358i | − 6.50955i | ||||||||
\(273\) | − 4.68035i | − 0.283267i | ||||||||
\(274\) | −41.6163 | −2.51414 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −11.5174 | −0.693269 | ||||||||
\(277\) | 26.0144i | 1.56305i | 0.623872 | + | 0.781526i | \(0.285558\pi\) | ||||
−0.623872 | + | 0.781526i | \(0.714442\pi\) | |||||||
\(278\) | − 23.2495i | − 1.39441i | ||||||||
\(279\) | 4.68035 | 0.280205 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.41855 | −0.561864 | −0.280932 | − | 0.959728i | \(-0.590643\pi\) | ||||
−0.280932 | + | 0.959728i | \(0.590643\pi\) | |||||||
\(282\) | 12.6803i | 0.755104i | ||||||||
\(283\) | 14.2413i | 0.846556i | 0.906000 | + | 0.423278i | \(0.139121\pi\) | ||||
−0.906000 | + | 0.423278i | \(0.860879\pi\) | |||||||
\(284\) | 24.9939 | 1.48311 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.7587 | 0.695308 | ||||||||
\(287\) | 10.1568i | 0.599534i | ||||||||
\(288\) | − 19.3896i | − 1.14254i | ||||||||
\(289\) | −43.1978 | −2.54105 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.6803 | 0.860577 | ||||||||
\(292\) | 56.0554i | 3.28039i | ||||||||
\(293\) | − 15.7587i | − 0.920634i | −0.887754 | − | 0.460317i | \(-0.847736\pi\) | ||||
0.887754 | − | 0.460317i | \(-0.152264\pi\) | |||||||
\(294\) | −15.8143 | −0.922310 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 18.0989 | 1.05198 | ||||||||
\(297\) | − 1.00000i | − 0.0580259i | ||||||||
\(298\) | 49.0349i | 2.84052i | ||||||||
\(299\) | −9.36069 | −0.541343 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.19779 | 0.472513 | ||||||||
\(302\) | 62.1399i | 3.57575i | ||||||||
\(303\) | − 15.5753i | − 0.894778i | ||||||||
\(304\) | −72.8080 | −4.17582 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −21.0205 | −1.20166 | ||||||||
\(307\) | 18.9216i | 1.07991i | 0.841693 | + | 0.539957i | \(0.181560\pi\) | ||||
−0.841693 | + | 0.539957i | \(0.818440\pi\) | |||||||
\(308\) | 5.75872i | 0.328134i | ||||||||
\(309\) | −6.83710 | −0.388949 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.8781 | −1.18389 | −0.591945 | − | 0.805978i | \(-0.701640\pi\) | ||||
−0.591945 | + | 0.805978i | \(0.701640\pi\) | |||||||
\(312\) | − 39.2762i | − 2.22358i | ||||||||
\(313\) | 6.31351i | 0.356861i | 0.983953 | + | 0.178430i | \(0.0571019\pi\) | ||||
−0.983953 | + | 0.178430i | \(0.942898\pi\) | |||||||
\(314\) | −29.7854 | −1.68089 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −43.2495 | −2.43297 | ||||||||
\(317\) | − 31.3607i | − 1.76139i | −0.473682 | − | 0.880696i | \(-0.657075\pi\) | ||||
0.473682 | − | 0.880696i | \(-0.342925\pi\) | |||||||
\(318\) | − 0.424694i | − 0.0238156i | ||||||||
\(319\) | −1.41855 | −0.0794236 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.34017 | 0.353874 | ||||||||
\(322\) | − 6.30122i | − 0.351154i | ||||||||
\(323\) | 40.8248i | 2.27155i | ||||||||
\(324\) | −5.34017 | −0.296676 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17.6742 | 0.978884 | ||||||||
\(327\) | − 2.31351i | − 0.127937i | ||||||||
\(328\) | 85.2327i | 4.70619i | ||||||||
\(329\) | −5.04718 | −0.278260 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.2039 | 1.05554 | 0.527772 | − | 0.849386i | \(-0.323028\pi\) | ||||
0.527772 | + | 0.849386i | \(0.323028\pi\) | |||||||
\(332\) | 58.8515i | 3.22989i | ||||||||
\(333\) | − 2.00000i | − 0.109599i | ||||||||
\(334\) | 5.34632 | 0.292537 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 14.9216 | 0.814041 | ||||||||
\(337\) | − 13.5031i | − 0.735559i | −0.929913 | − | 0.367780i | \(-0.880118\pi\) | ||||
0.929913 | − | 0.367780i | \(-0.119882\pi\) | |||||||
\(338\) | − 15.8143i | − 0.860185i | ||||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.68035 | −0.253455 | ||||||||
\(342\) | 14.2557i | 0.770857i | ||||||||
\(343\) | − 13.8432i | − 0.747465i | ||||||||
\(344\) | 68.7936 | 3.70910 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.1834 | −0.547464 | ||||||||
\(347\) | − 6.34017i | − 0.340358i | −0.985413 | − | 0.170179i | \(-0.945565\pi\) | ||||
0.985413 | − | 0.170179i | \(-0.0544346\pi\) | |||||||
\(348\) | 7.57531i | 0.406079i | ||||||||
\(349\) | −16.1568 | −0.864851 | −0.432426 | − | 0.901670i | \(-0.642342\pi\) | ||||
−0.432426 | + | 0.901670i | \(0.642342\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.34017 | −0.231661 | ||||||||
\(352\) | 19.3896i | 1.03347i | ||||||||
\(353\) | − 13.2039i | − 0.702775i | −0.936230 | − | 0.351387i | \(-0.885710\pi\) | ||||
0.936230 | − | 0.351387i | \(-0.114290\pi\) | |||||||
\(354\) | 16.6803 | 0.886550 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −68.5523 | −3.63327 | ||||||||
\(357\) | − 8.36683i | − 0.442820i | ||||||||
\(358\) | − 41.0472i | − 2.16941i | ||||||||
\(359\) | −3.31965 | −0.175205 | −0.0876023 | − | 0.996156i | \(-0.527920\pi\) | ||||
−0.0876023 | + | 0.996156i | \(0.527920\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.68649 | 0.457184 | ||||||||
\(362\) | 13.1050i | 0.688786i | ||||||||
\(363\) | 1.00000i | 0.0524864i | ||||||||
\(364\) | 24.9939 | 1.31003 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.2618 | 0.588663 | ||||||||
\(367\) | 36.1445i | 1.88673i | 0.331762 | + | 0.943363i | \(0.392357\pi\) | ||||
−0.331762 | + | 0.943363i | \(0.607643\pi\) | |||||||
\(368\) | − 29.8432i | − 1.55569i | ||||||||
\(369\) | 9.41855 | 0.490310 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.169042 | 0.00877620 | ||||||||
\(372\) | 24.9939i | 1.29587i | ||||||||
\(373\) | − 2.81044i | − 0.145519i | −0.997350 | − | 0.0727595i | \(-0.976819\pi\) | ||||
0.997350 | − | 0.0727595i | \(-0.0231806\pi\) | |||||||
\(374\) | 21.0205 | 1.08695 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −42.3545 | −2.18427 | ||||||||
\(377\) | 6.15676i | 0.317089i | ||||||||
\(378\) | − 2.92162i | − 0.150272i | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.24128 | −0.114824 | ||||||||
\(382\) | 6.83710i | 0.349817i | ||||||||
\(383\) | 33.5585i | 1.71476i | 0.514685 | + | 0.857379i | \(0.327909\pi\) | ||||
−0.514685 | + | 0.857379i | \(0.672091\pi\) | |||||||
\(384\) | 28.5669 | 1.45780 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.0722347 | −0.00367665 | ||||||||
\(387\) | − 7.60197i | − 0.386430i | ||||||||
\(388\) | 78.3956i | 3.97993i | ||||||||
\(389\) | −12.8371 | −0.650867 | −0.325433 | − | 0.945565i | \(-0.605510\pi\) | ||||
−0.325433 | + | 0.945565i | \(0.605510\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.7337 | −0.846258 | ||||||||
\(392\) | − 52.8225i | − 2.66794i | ||||||||
\(393\) | 8.68035i | 0.437866i | ||||||||
\(394\) | 57.2183 | 2.88262 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.34017 | 0.268354 | ||||||||
\(397\) | 5.31965i | 0.266986i | 0.991050 | + | 0.133493i | \(0.0426193\pi\) | ||||
−0.991050 | + | 0.133493i | \(0.957381\pi\) | |||||||
\(398\) | − 28.5113i | − 1.42914i | ||||||||
\(399\) | −5.67420 | −0.284065 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | − 23.5174i | − 1.17294i | ||||||||
\(403\) | 20.3135i | 1.01189i | ||||||||
\(404\) | 83.1748 | 4.13810 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.14447 | −0.205687 | ||||||||
\(407\) | 2.00000i | 0.0991363i | ||||||||
\(408\) | − 70.2122i | − 3.47602i | ||||||||
\(409\) | −26.1978 | −1.29540 | −0.647699 | − | 0.761897i | \(-0.724268\pi\) | ||||
−0.647699 | + | 0.761897i | \(0.724268\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.3607 | −0.757687 | ||||||||
\(412\) | − 36.5113i | − 1.79878i | ||||||||
\(413\) | 6.63931i | 0.326699i | ||||||||
\(414\) | −5.84324 | −0.287180 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 84.1543 | 4.12600 | ||||||||
\(417\) | − 8.58145i | − 0.420235i | ||||||||
\(418\) | − 14.2557i | − 0.697267i | ||||||||
\(419\) | 2.83710 | 0.138601 | 0.0693007 | − | 0.997596i | \(-0.477923\pi\) | ||||
0.0693007 | + | 0.997596i | \(0.477923\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.4764 | 0.559326 | 0.279663 | − | 0.960098i | \(-0.409777\pi\) | ||||
0.279663 | + | 0.960098i | \(0.409777\pi\) | |||||||
\(422\) | 25.9421i | 1.26284i | ||||||||
\(423\) | 4.68035i | 0.227566i | ||||||||
\(424\) | 1.41855 | 0.0688909 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.6803 | 0.614365 | ||||||||
\(427\) | 4.48255i | 0.216926i | ||||||||
\(428\) | 33.8576i | 1.63657i | ||||||||
\(429\) | 4.34017 | 0.209546 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.5708 | 1.13536 | 0.567682 | − | 0.823248i | \(-0.307840\pi\) | ||||
0.567682 | + | 0.823248i | \(0.307840\pi\) | |||||||
\(432\) | − 13.8371i | − 0.665738i | ||||||||
\(433\) | − 14.9939i | − 0.720559i | −0.932844 | − | 0.360279i | \(-0.882681\pi\) | ||||
0.932844 | − | 0.360279i | \(-0.117319\pi\) | |||||||
\(434\) | −13.6742 | −0.656383 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.3545 | 0.591676 | ||||||||
\(437\) | 11.3484i | 0.542868i | ||||||||
\(438\) | 28.4391i | 1.35887i | ||||||||
\(439\) | −4.77924 | −0.228101 | −0.114050 | − | 0.993475i | \(-0.536383\pi\) | ||||
−0.114050 | + | 0.993475i | \(0.536383\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.83710 | −0.277957 | ||||||||
\(442\) | − 91.2327i | − 4.33950i | ||||||||
\(443\) | 20.1978i | 0.959626i | 0.877371 | + | 0.479813i | \(0.159296\pi\) | ||||
−0.877371 | + | 0.479813i | \(0.840704\pi\) | |||||||
\(444\) | 10.6803 | 0.506867 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.84324 | 0.276686 | ||||||||
\(447\) | 18.0989i | 0.856048i | ||||||||
\(448\) | 26.8059i | 1.26646i | ||||||||
\(449\) | 21.5708 | 1.01799 | 0.508994 | − | 0.860770i | \(-0.330018\pi\) | ||||
0.508994 | + | 0.860770i | \(0.330018\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.41855 | −0.443502 | ||||||||
\(452\) | 32.0410i | 1.50708i | ||||||||
\(453\) | 22.9360i | 1.07763i | ||||||||
\(454\) | 26.1711 | 1.22827 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −47.6163 | −2.22984 | ||||||||
\(457\) | − 28.1711i | − 1.31779i | −0.752235 | − | 0.658895i | \(-0.771024\pi\) | ||||
0.752235 | − | 0.658895i | \(-0.228976\pi\) | |||||||
\(458\) | 9.10504i | 0.425451i | ||||||||
\(459\) | −7.75872 | −0.362146 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.47187 | −0.0685520 | −0.0342760 | − | 0.999412i | \(-0.510913\pi\) | ||||
−0.0342760 | + | 0.999412i | \(0.510913\pi\) | |||||||
\(462\) | 2.92162i | 0.135926i | ||||||||
\(463\) | − 23.2039i | − 1.07838i | −0.842185 | − | 0.539189i | \(-0.818731\pi\) | ||||
0.842185 | − | 0.539189i | \(-0.181269\pi\) | |||||||
\(464\) | −19.6286 | −0.911236 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.49693 | 0.300964 | ||||||||
\(467\) | − 14.1568i | − 0.655097i | −0.944834 | − | 0.327548i | \(-0.893778\pi\) | ||||
0.944834 | − | 0.327548i | \(-0.106222\pi\) | |||||||
\(468\) | − 23.1773i | − 1.07137i | ||||||||
\(469\) | 9.36069 | 0.432237 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.9939 | −0.506570 | ||||||||
\(472\) | 55.7152i | 2.56450i | ||||||||
\(473\) | 7.60197i | 0.349539i | ||||||||
\(474\) | −21.9421 | −1.00784 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 44.6803 | 2.04792 | ||||||||
\(477\) | − 0.156755i | − 0.00717734i | ||||||||
\(478\) | 19.5174i | 0.892707i | ||||||||
\(479\) | 13.8432 | 0.632514 | 0.316257 | − | 0.948674i | \(-0.397574\pi\) | ||||
0.316257 | + | 0.948674i | \(0.397574\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.68035 | 0.395790 | ||||||||
\(482\) | − 14.0989i | − 0.642187i | ||||||||
\(483\) | − 2.32580i | − 0.105827i | ||||||||
\(484\) | −5.34017 | −0.242735 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.70928 | −0.122895 | ||||||||
\(487\) | 40.9939i | 1.85761i | 0.370570 | + | 0.928804i | \(0.379162\pi\) | ||||
−0.370570 | + | 0.928804i | \(0.620838\pi\) | |||||||
\(488\) | 37.6163i | 1.70281i | ||||||||
\(489\) | 6.52359 | 0.295007 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.8371 | 1.57218 | 0.786088 | − | 0.618114i | \(-0.212103\pi\) | ||||
0.786088 | + | 0.618114i | \(0.212103\pi\) | |||||||
\(492\) | 50.2967i | 2.26755i | ||||||||
\(493\) | 11.0061i | 0.495692i | ||||||||
\(494\) | −61.8720 | −2.78375 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −64.7624 | −2.90792 | ||||||||
\(497\) | 5.04718i | 0.226397i | ||||||||
\(498\) | 29.8576i | 1.33795i | ||||||||
\(499\) | −15.1506 | −0.678235 | −0.339117 | − | 0.940744i | \(-0.610128\pi\) | ||||
−0.339117 | + | 0.940744i | \(0.610128\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.97334 | 0.0881622 | ||||||||
\(502\) | 41.5052i | 1.85247i | ||||||||
\(503\) | − 6.65368i | − 0.296673i | −0.988937 | − | 0.148337i | \(-0.952608\pi\) | ||||
0.988937 | − | 0.148337i | \(-0.0473919\pi\) | |||||||
\(504\) | 9.75872 | 0.434688 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.84324 | 0.259764 | ||||||||
\(507\) | − 5.83710i | − 0.259235i | ||||||||
\(508\) | − 11.9688i | − 0.531030i | ||||||||
\(509\) | −41.3484 | −1.83274 | −0.916368 | − | 0.400337i | \(-0.868893\pi\) | ||||
−0.916368 | + | 0.400337i | \(0.868893\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.3197 | −0.500752 | ||||||||
\(512\) | 17.8599i | 0.789303i | ||||||||
\(513\) | 5.26180i | 0.232314i | ||||||||
\(514\) | 11.2618 | 0.496736 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 40.5958 | 1.78713 | ||||||||
\(517\) | − 4.68035i | − 0.205841i | ||||||||
\(518\) | 5.84324i | 0.256737i | ||||||||
\(519\) | −3.75872 | −0.164990 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.67420 | 0.336213 | 0.168106 | − | 0.985769i | \(-0.446235\pi\) | ||||
0.168106 | + | 0.985769i | \(0.446235\pi\) | |||||||
\(522\) | 3.84324i | 0.168214i | ||||||||
\(523\) | 23.2351i | 1.01600i | 0.861357 | + | 0.508001i | \(0.169615\pi\) | ||||
−0.861357 | + | 0.508001i | \(0.830385\pi\) | |||||||
\(524\) | −46.3545 | −2.02501 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 50.6824 | 2.20986 | ||||||||
\(527\) | 36.3135i | 1.58184i | ||||||||
\(528\) | 13.8371i | 0.602183i | ||||||||
\(529\) | 18.3484 | 0.797757 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.15676 | 0.267180 | ||||||||
\(532\) | − 30.3012i | − 1.31372i | ||||||||
\(533\) | 40.8781i | 1.77063i | ||||||||
\(534\) | −34.7792 | −1.50505 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 78.5523 | 3.39294 | ||||||||
\(537\) | − 15.1506i | − 0.653797i | ||||||||
\(538\) | − 63.2905i | − 2.72865i | ||||||||
\(539\) | 5.83710 | 0.251422 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0000 | −0.773880 | −0.386940 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386940 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(542\) | − 15.1050i | − 0.648817i | ||||||||
\(543\) | 4.83710i | 0.207580i | ||||||||
\(544\) | 150.439 | 6.45001 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 12.6803 | 0.542669 | ||||||||
\(547\) | 23.0661i | 0.986235i | 0.869963 | + | 0.493117i | \(0.164143\pi\) | ||||
−0.869963 | + | 0.493117i | \(0.835857\pi\) | |||||||
\(548\) | − 82.0288i | − 3.50409i | ||||||||
\(549\) | 4.15676 | 0.177406 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.46412 | 0.317982 | ||||||||
\(552\) | − 19.5174i | − 0.830718i | ||||||||
\(553\) | − 8.73367i | − 0.371393i | ||||||||
\(554\) | −70.4801 | −2.99441 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 45.8264 | 1.94347 | ||||||||
\(557\) | − 10.5958i | − 0.448960i | −0.974479 | − | 0.224480i | \(-0.927932\pi\) | ||||
0.974479 | − | 0.224480i | \(-0.0720683\pi\) | |||||||
\(558\) | 12.6803i | 0.536802i | ||||||||
\(559\) | 32.9939 | 1.39549 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.75872 | 0.327574 | ||||||||
\(562\) | − 25.5174i | − 1.07639i | ||||||||
\(563\) | − 36.2122i | − 1.52616i | −0.646303 | − | 0.763080i | \(-0.723686\pi\) | ||||
0.646303 | − | 0.763080i | \(-0.276314\pi\) | |||||||
\(564\) | −24.9939 | −1.05243 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −38.5835 | −1.62179 | ||||||||
\(567\) | − 1.07838i | − 0.0452876i | ||||||||
\(568\) | 42.3545i | 1.77716i | ||||||||
\(569\) | 27.5753 | 1.15602 | 0.578008 | − | 0.816031i | \(-0.303830\pi\) | ||||
0.578008 | + | 0.816031i | \(0.303830\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.9299 | −1.16883 | −0.584414 | − | 0.811456i | \(-0.698676\pi\) | ||||
−0.584414 | + | 0.811456i | \(0.698676\pi\) | |||||||
\(572\) | 23.1773i | 0.969091i | ||||||||
\(573\) | 2.52359i | 0.105425i | ||||||||
\(574\) | −27.5174 | −1.14856 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 24.8576 | 1.03573 | ||||||||
\(577\) | − 41.4017i | − 1.72358i | −0.507268 | − | 0.861788i | \(-0.669345\pi\) | ||||
0.507268 | − | 0.861788i | \(-0.330655\pi\) | |||||||
\(578\) | − 117.035i | − 4.86800i | ||||||||
\(579\) | −0.0266620 | −0.00110803 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.8843 | −0.493043 | ||||||||
\(582\) | 39.7731i | 1.64865i | ||||||||
\(583\) | 0.156755i | 0.00649215i | ||||||||
\(584\) | −94.9914 | −3.93077 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 42.6947 | 1.76370 | ||||||||
\(587\) | − 8.48255i | − 0.350112i | −0.984558 | − | 0.175056i | \(-0.943989\pi\) | ||||
0.984558 | − | 0.175056i | \(-0.0560107\pi\) | |||||||
\(588\) | − 31.1711i | − 1.28548i | ||||||||
\(589\) | 24.6270 | 1.01474 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.1194 | 0.868737 | ||||||||
\(592\) | 27.6742i | 1.13740i | ||||||||
\(593\) | 7.56093i | 0.310490i | 0.987876 | + | 0.155245i | \(0.0496167\pi\) | ||||
−0.987876 | + | 0.155245i | \(0.950383\pi\) | |||||||
\(594\) | 2.70928 | 0.111163 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −96.6512 | −3.95899 | ||||||||
\(597\) | − 10.5236i | − 0.430702i | ||||||||
\(598\) | − 25.3607i | − 1.03708i | ||||||||
\(599\) | −5.67420 | −0.231842 | −0.115921 | − | 0.993258i | \(-0.536982\pi\) | ||||
−0.115921 | + | 0.993258i | \(0.536982\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.31965 | −0.0538298 | −0.0269149 | − | 0.999638i | \(-0.508568\pi\) | ||||
−0.0269149 | + | 0.999638i | \(0.508568\pi\) | |||||||
\(602\) | 22.2101i | 0.905215i | ||||||||
\(603\) | − 8.68035i | − 0.353491i | ||||||||
\(604\) | −122.482 | −4.98373 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 42.1978 | 1.71417 | ||||||||
\(607\) | 2.24128i | 0.0909706i | 0.998965 | + | 0.0454853i | \(0.0144834\pi\) | ||||
−0.998965 | + | 0.0454853i | \(0.985517\pi\) | |||||||
\(608\) | − 102.024i | − 4.13763i | ||||||||
\(609\) | −1.52973 | −0.0619879 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.3135 | −0.821797 | ||||||||
\(612\) | − 41.4329i | − 1.67483i | ||||||||
\(613\) | 42.8638i | 1.73125i | 0.500692 | + | 0.865626i | \(0.333079\pi\) | ||||
−0.500692 | + | 0.865626i | \(0.666921\pi\) | |||||||
\(614\) | −51.2639 | −2.06884 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.75872 | −0.393190 | ||||||||
\(617\) | − 11.3607i | − 0.457364i | −0.973501 | − | 0.228682i | \(-0.926558\pi\) | ||||
0.973501 | − | 0.228682i | \(-0.0734416\pi\) | |||||||
\(618\) | − 18.5236i | − 0.745128i | ||||||||
\(619\) | 45.1917 | 1.81641 | 0.908203 | − | 0.418530i | \(-0.137455\pi\) | ||||
0.908203 | + | 0.418530i | \(0.137455\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.15676 | −0.0865476 | ||||||||
\(622\) | − 56.5646i | − 2.26803i | ||||||||
\(623\) | − 13.8432i | − 0.554618i | ||||||||
\(624\) | 60.0554 | 2.40414 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −17.1050 | −0.683655 | ||||||||
\(627\) | − 5.26180i | − 0.210136i | ||||||||
\(628\) | − 58.7091i | − 2.34275i | ||||||||
\(629\) | 15.5174 | 0.618721 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.78992 | −0.389731 | −0.194865 | − | 0.980830i | \(-0.562427\pi\) | ||||
−0.194865 | + | 0.980830i | \(0.562427\pi\) | |||||||
\(632\) | − 73.2905i | − 2.91534i | ||||||||
\(633\) | 9.57531i | 0.380584i | ||||||||
\(634\) | 84.9647 | 3.37438 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.837101 | 0.0331932 | ||||||||
\(637\) | − 25.3340i | − 1.00377i | ||||||||
\(638\) | − 3.84324i | − 0.152156i | ||||||||
\(639\) | 4.68035 | 0.185152 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.210079 | 0.00829764 | 0.00414882 | − | 0.999991i | \(-0.498679\pi\) | ||||
0.00414882 | + | 0.999991i | \(0.498679\pi\) | |||||||
\(642\) | 17.1773i | 0.677933i | ||||||||
\(643\) | 14.5236i | 0.572754i | 0.958117 | + | 0.286377i | \(0.0924511\pi\) | ||||
−0.958117 | + | 0.286377i | \(0.907549\pi\) | |||||||
\(644\) | 12.4202 | 0.489423 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −110.606 | −4.35172 | ||||||||
\(647\) | − 15.4641i | − 0.607957i | −0.952679 | − | 0.303979i | \(-0.901685\pi\) | ||||
0.952679 | − | 0.303979i | \(-0.0983152\pi\) | |||||||
\(648\) | − 9.04945i | − 0.355496i | ||||||||
\(649\) | −6.15676 | −0.241674 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.04718 | −0.197815 | ||||||||
\(652\) | 34.8371i | 1.36433i | ||||||||
\(653\) | − 17.8310i | − 0.697779i | −0.937164 | − | 0.348890i | \(-0.886559\pi\) | ||||
0.937164 | − | 0.348890i | \(-0.113441\pi\) | |||||||
\(654\) | 6.26794 | 0.245096 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −130.325 | −5.08835 | ||||||||
\(657\) | 10.4969i | 0.409524i | ||||||||
\(658\) | − 13.6742i | − 0.533076i | ||||||||
\(659\) | 32.3135 | 1.25876 | 0.629378 | − | 0.777099i | \(-0.283310\pi\) | ||||
0.629378 | + | 0.777099i | \(0.283310\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.68649 | −0.221179 | −0.110589 | − | 0.993866i | \(-0.535274\pi\) | ||||
−0.110589 | + | 0.993866i | \(0.535274\pi\) | |||||||
\(662\) | 52.0288i | 2.02215i | ||||||||
\(663\) | − 33.6742i | − 1.30780i | ||||||||
\(664\) | −99.7296 | −3.87026 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.41855 | 0.209965 | ||||||||
\(667\) | 3.05947i | 0.118463i | ||||||||
\(668\) | 10.5380i | 0.407726i | ||||||||
\(669\) | 2.15676 | 0.0833850 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.15676 | −0.160470 | ||||||||
\(672\) | 20.9093i | 0.806595i | ||||||||
\(673\) | − 21.0205i | − 0.810281i | −0.914254 | − | 0.405141i | \(-0.867223\pi\) | ||||
0.914254 | − | 0.405141i | \(-0.132777\pi\) | |||||||
\(674\) | 36.5835 | 1.40915 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 31.1711 | 1.19889 | ||||||||
\(677\) | − 36.7526i | − 1.41252i | −0.707954 | − | 0.706258i | \(-0.750382\pi\) | ||||
0.707954 | − | 0.706258i | \(-0.249618\pi\) | |||||||
\(678\) | 16.2557i | 0.624295i | ||||||||
\(679\) | −15.8310 | −0.607536 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.65983 | 0.370165 | ||||||||
\(682\) | − 12.6803i | − 0.485556i | ||||||||
\(683\) | − 17.3074i | − 0.662248i | −0.943587 | − | 0.331124i | \(-0.892572\pi\) | ||||
0.943587 | − | 0.331124i | \(-0.107428\pi\) | |||||||
\(684\) | −28.0989 | −1.07439 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 37.5052 | 1.43195 | ||||||||
\(687\) | 3.36069i | 0.128218i | ||||||||
\(688\) | 105.189i | 4.01030i | ||||||||
\(689\) | 0.680346 | 0.0259191 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.6742 | 0.672358 | 0.336179 | − | 0.941798i | \(-0.390865\pi\) | ||||
0.336179 | + | 0.941798i | \(0.390865\pi\) | |||||||
\(692\) | − 20.0722i | − 0.763032i | ||||||||
\(693\) | 1.07838i | 0.0409642i | ||||||||
\(694\) | 17.1773 | 0.652040 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.8371 | −0.486589 | ||||||||
\(697\) | 73.0759i | 2.76795i | ||||||||
\(698\) | − 43.7731i | − 1.65684i | ||||||||
\(699\) | 2.39803 | 0.0907019 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.1050 | −0.646048 | −0.323024 | − | 0.946391i | \(-0.604700\pi\) | ||||
−0.323024 | + | 0.946391i | \(0.604700\pi\) | |||||||
\(702\) | − 11.7587i | − 0.443804i | ||||||||
\(703\) | − 10.5236i | − 0.396905i | ||||||||
\(704\) | −24.8576 | −0.936857 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 35.7731 | 1.34634 | ||||||||
\(707\) | 16.7961i | 0.631681i | ||||||||
\(708\) | 32.8781i | 1.23564i | ||||||||
\(709\) | −25.1506 | −0.944551 | −0.472276 | − | 0.881451i | \(-0.656567\pi\) | ||||
−0.472276 | + | 0.881451i | \(0.656567\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.09890 | −0.303732 | ||||||||
\(712\) | − 116.169i | − 4.35361i | ||||||||
\(713\) | 10.0944i | 0.378037i | ||||||||
\(714\) | 22.6681 | 0.848331 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 80.9069 | 3.02363 | ||||||||
\(717\) | 7.20394i | 0.269036i | ||||||||
\(718\) | − 8.99386i | − 0.335648i | ||||||||
\(719\) | 1.78992 | 0.0667528 | 0.0333764 | − | 0.999443i | \(-0.489374\pi\) | ||||
0.0333764 | + | 0.999443i | \(0.489374\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.37298 | 0.274584 | ||||||||
\(722\) | 23.5341i | 0.875848i | ||||||||
\(723\) | − 5.20394i | − 0.193536i | ||||||||
\(724\) | −25.8310 | −0.960000 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.70928 | −0.100551 | ||||||||
\(727\) | − 25.9877i | − 0.963831i | −0.876218 | − | 0.481915i | \(-0.839941\pi\) | ||||
0.876218 | − | 0.481915i | \(-0.160059\pi\) | |||||||
\(728\) | 42.3545i | 1.56976i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 58.9816 | 2.18151 | ||||||||
\(732\) | 22.1978i | 0.820454i | ||||||||
\(733\) | − 41.0205i | − 1.51513i | −0.652761 | − | 0.757564i | \(-0.726390\pi\) | ||||
0.652761 | − | 0.757564i | \(-0.273610\pi\) | |||||||
\(734\) | −97.9253 | −3.61449 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 41.8187 | 1.54146 | ||||||||
\(737\) | 8.68035i | 0.319745i | ||||||||
\(738\) | 25.5174i | 0.939310i | ||||||||
\(739\) | 47.6163 | 1.75160 | 0.875798 | − | 0.482678i | \(-0.160336\pi\) | ||||
0.875798 | + | 0.482678i | \(0.160336\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.8371 | −0.838942 | ||||||||
\(742\) | 0.457980i | 0.0168130i | ||||||||
\(743\) | 0.550252i | 0.0201868i | 0.999949 | + | 0.0100934i | \(0.00321288\pi\) | ||||
−0.999949 | + | 0.0100934i | \(0.996787\pi\) | |||||||
\(744\) | −42.3545 | −1.55279 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.61425 | 0.278778 | ||||||||
\(747\) | 11.0205i | 0.403220i | ||||||||
\(748\) | 41.4329i | 1.51494i | ||||||||
\(749\) | −6.83710 | −0.249822 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.5585 | 1.51649 | 0.758245 | − | 0.651969i | \(-0.226057\pi\) | ||||
0.758245 | + | 0.651969i | \(0.226057\pi\) | |||||||
\(752\) | − 64.7624i | − 2.36164i | ||||||||
\(753\) | 15.3197i | 0.558279i | ||||||||
\(754\) | −16.6803 | −0.607462 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.75872 | 0.209443 | ||||||||
\(757\) | − 1.31965i | − 0.0479636i | −0.999712 | − | 0.0239818i | \(-0.992366\pi\) | ||||
0.999712 | − | 0.0239818i | \(-0.00763438\pi\) | |||||||
\(758\) | 54.1855i | 1.96811i | ||||||||
\(759\) | 2.15676 | 0.0782853 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.21461 | −0.0802797 | −0.0401399 | − | 0.999194i | \(-0.512780\pi\) | ||||
−0.0401399 | + | 0.999194i | \(0.512780\pi\) | |||||||
\(762\) | − 6.07223i | − 0.219974i | ||||||||
\(763\) | 2.49484i | 0.0903192i | ||||||||
\(764\) | −13.4764 | −0.487559 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −90.9192 | −3.28504 | ||||||||
\(767\) | 26.7214i | 0.964853i | ||||||||
\(768\) | 27.6803i | 0.998828i | ||||||||
\(769\) | 14.3668 | 0.518081 | 0.259041 | − | 0.965866i | \(-0.416594\pi\) | ||||
0.259041 | + | 0.965866i | \(0.416594\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.15676 | 0.149702 | ||||||||
\(772\) | − 0.142380i | − 0.00512436i | ||||||||
\(773\) | 40.1568i | 1.44434i | 0.691717 | + | 0.722169i | \(0.256855\pi\) | ||||
−0.691717 | + | 0.722169i | \(0.743145\pi\) | |||||||
\(774\) | 20.5958 | 0.740302 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −132.849 | −4.76900 | ||||||||
\(777\) | 2.15676i | 0.0773732i | ||||||||
\(778\) | − 34.7792i | − 1.24690i | ||||||||
\(779\) | 49.5585 | 1.77562 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.68035 | −0.167476 | ||||||||
\(782\) | − 45.3361i | − 1.62122i | ||||||||
\(783\) | 1.41855i | 0.0506949i | ||||||||
\(784\) | 80.7686 | 2.88459 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −23.5174 | −0.838840 | ||||||||
\(787\) | − 49.5897i | − 1.76768i | −0.467788 | − | 0.883841i | \(-0.654949\pi\) | ||||
0.467788 | − | 0.883841i | \(-0.345051\pi\) | |||||||
\(788\) | 112.781i | 4.01767i | ||||||||
\(789\) | 18.7070 | 0.665987 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.47027 | −0.230056 | ||||||||
\(792\) | 9.04945i | 0.321558i | ||||||||
\(793\) | 18.0410i | 0.640656i | ||||||||
\(794\) | −14.4124 | −0.511477 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 56.1978 | 1.99188 | ||||||||
\(797\) | 46.7091i | 1.65452i | 0.561818 | + | 0.827261i | \(0.310102\pi\) | ||||
−0.561818 | + | 0.827261i | \(0.689898\pi\) | |||||||
\(798\) | − 15.3730i | − 0.544198i | ||||||||
\(799\) | −36.3135 | −1.28468 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.8371 | −0.453577 | ||||||||
\(802\) | 5.41855i | 0.191336i | ||||||||
\(803\) | − 10.4969i | − 0.370429i | ||||||||
\(804\) | 46.3545 | 1.63480 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −55.0349 | −1.93852 | ||||||||
\(807\) | − 23.3607i | − 0.822335i | ||||||||
\(808\) | 140.948i | 4.95853i | ||||||||
\(809\) | 18.5814 | 0.653289 | 0.326644 | − | 0.945147i | \(-0.394082\pi\) | ||||
0.326644 | + | 0.945147i | \(0.394082\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.3028 | 0.958732 | 0.479366 | − | 0.877615i | \(-0.340867\pi\) | ||||
0.479366 | + | 0.877615i | \(0.340867\pi\) | |||||||
\(812\) | − 8.16904i | − 0.286677i | ||||||||
\(813\) | − 5.57531i | − 0.195535i | ||||||||
\(814\) | −5.41855 | −0.189920 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 107.358 | 3.75829 | ||||||||
\(817\) | − 40.0000i | − 1.39942i | ||||||||
\(818\) | − 70.9770i | − 2.48165i | ||||||||
\(819\) | 4.68035 | 0.163545 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.2085 | −1.08918 | −0.544592 | − | 0.838701i | \(-0.683315\pi\) | ||||
−0.544592 | + | 0.838701i | \(0.683315\pi\) | |||||||
\(822\) | − 41.6163i | − 1.45154i | ||||||||
\(823\) | − 50.1855i | − 1.74936i | −0.484704 | − | 0.874678i | \(-0.661073\pi\) | ||||
0.484704 | − | 0.874678i | \(-0.338927\pi\) | |||||||
\(824\) | 61.8720 | 2.15541 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17.9877 | −0.625873 | ||||||||
\(827\) | − 27.3874i | − 0.952352i | −0.879350 | − | 0.476176i | \(-0.842023\pi\) | ||||
0.879350 | − | 0.476176i | \(-0.157977\pi\) | |||||||
\(828\) | − 11.5174i | − 0.400259i | ||||||||
\(829\) | 26.1978 | 0.909887 | 0.454943 | − | 0.890520i | \(-0.349659\pi\) | ||||
0.454943 | + | 0.890520i | \(0.349659\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.0144 | −0.902429 | ||||||||
\(832\) | 107.886i | 3.74029i | ||||||||
\(833\) | − 45.2885i | − 1.56915i | ||||||||
\(834\) | 23.2495 | 0.805065 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 28.0989 | 0.971821 | ||||||||
\(837\) | 4.68035i | 0.161776i | ||||||||
\(838\) | 7.68649i | 0.265525i | ||||||||
\(839\) | −7.20394 | −0.248708 | −0.124354 | − | 0.992238i | \(-0.539686\pi\) | ||||
−0.124354 | + | 0.992238i | \(0.539686\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.9877 | −0.930611 | ||||||||
\(842\) | 31.0928i | 1.07153i | ||||||||
\(843\) | − 9.41855i | − 0.324392i | ||||||||
\(844\) | −51.1338 | −1.76010 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.6803 | −0.435959 | ||||||||
\(847\) | − 1.07838i | − 0.0370535i | ||||||||
\(848\) | 2.16904i | 0.0744852i | ||||||||
\(849\) | −14.2413 | −0.488759 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.31351 | 0.147865 | ||||||||
\(852\) | 24.9939i | 0.856275i | ||||||||
\(853\) | 39.8043i | 1.36287i | 0.731877 | + | 0.681437i | \(0.238644\pi\) | ||||
−0.731877 | + | 0.681437i | \(0.761356\pi\) | |||||||
\(854\) | −12.1445 | −0.415575 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −57.3751 | −1.96104 | ||||||||
\(857\) | 36.9504i | 1.26220i | 0.775701 | + | 0.631100i | \(0.217396\pi\) | ||||
−0.775701 | + | 0.631100i | \(0.782604\pi\) | |||||||
\(858\) | 11.7587i | 0.401436i | ||||||||
\(859\) | −57.5052 | −1.96205 | −0.981025 | − | 0.193879i | \(-0.937893\pi\) | ||||
−0.981025 | + | 0.193879i | \(0.937893\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.1568 | −0.346141 | ||||||||
\(862\) | 63.8597i | 2.17507i | ||||||||
\(863\) | − 1.89657i | − 0.0645599i | −0.999479 | − | 0.0322800i | \(-0.989723\pi\) | ||||
0.999479 | − | 0.0322800i | \(-0.0102768\pi\) | |||||||
\(864\) | 19.3896 | 0.659648 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 40.6225 | 1.38041 | ||||||||
\(867\) | − 43.1978i | − 1.46707i | ||||||||
\(868\) | − 26.9528i | − 0.914838i | ||||||||
\(869\) | 8.09890 | 0.274736 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.6742 | 1.27654 | ||||||||
\(872\) | 20.9360i | 0.708982i | ||||||||
\(873\) | 14.6803i | 0.496854i | ||||||||
\(874\) | −30.7460 | −1.04000 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −56.0554 | −1.89394 | ||||||||
\(877\) | − 32.5380i | − 1.09873i | −0.835583 | − | 0.549365i | \(-0.814870\pi\) | ||||
0.835583 | − | 0.549365i | \(-0.185130\pi\) | |||||||
\(878\) | − 12.9483i | − 0.436983i | ||||||||
\(879\) | 15.7587 | 0.531529 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.1978 | 0.613099 | 0.306550 | − | 0.951855i | \(-0.400825\pi\) | ||||
0.306550 | + | 0.951855i | \(0.400825\pi\) | |||||||
\(882\) | − 15.8143i | − 0.532496i | ||||||||
\(883\) | 36.3956i | 1.22481i | 0.790545 | + | 0.612405i | \(0.209798\pi\) | ||||
−0.790545 | + | 0.612405i | \(0.790202\pi\) | |||||||
\(884\) | 179.826 | 6.04821 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −54.7214 | −1.83840 | ||||||||
\(887\) | − 27.8699i | − 0.935780i | −0.883787 | − | 0.467890i | \(-0.845014\pi\) | ||||
0.883787 | − | 0.467890i | \(-0.154986\pi\) | |||||||
\(888\) | 18.0989i | 0.607359i | ||||||||
\(889\) | 2.41694 | 0.0810616 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 11.5174i | 0.385633i | ||||||||
\(893\) | 24.6270i | 0.824112i | ||||||||
\(894\) | −49.0349 | −1.63997 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −30.8059 | −1.02915 | ||||||||
\(897\) | − 9.36069i | − 0.312544i | ||||||||
\(898\) | 58.4412i | 1.95021i | ||||||||
\(899\) | 6.63931 | 0.221433 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.21622 | 0.0405182 | ||||||||
\(902\) | − 25.5174i | − 0.849638i | ||||||||
\(903\) | 8.19779i | 0.272805i | ||||||||
\(904\) | −54.2967 | −1.80588 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −62.1399 | −2.06446 | ||||||||
\(907\) | 27.9376i | 0.927653i | 0.885926 | + | 0.463826i | \(0.153524\pi\) | ||||
−0.885926 | + | 0.463826i | \(0.846476\pi\) | |||||||
\(908\) | 51.5851i | 1.71191i | ||||||||
\(909\) | 15.5753 | 0.516600 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.8843 | −0.393744 | −0.196872 | − | 0.980429i | \(-0.563078\pi\) | ||||
−0.196872 | + | 0.980429i | \(0.563078\pi\) | |||||||
\(912\) | − 72.8080i | − 2.41091i | ||||||||
\(913\) | − 11.0205i | − 0.364726i | ||||||||
\(914\) | 76.3234 | 2.52455 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.9467 | −0.592975 | ||||||||
\(917\) | − 9.36069i | − 0.309117i | ||||||||
\(918\) | − 21.0205i | − 0.693781i | ||||||||
\(919\) | 45.6041 | 1.50434 | 0.752170 | − | 0.658970i | \(-0.229007\pi\) | ||||
0.752170 | + | 0.658970i | \(0.229007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.9216 | −0.623489 | ||||||||
\(922\) | − 3.98771i | − 0.131328i | ||||||||
\(923\) | 20.3135i | 0.668627i | ||||||||
\(924\) | −5.75872 | −0.189448 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 62.8659 | 2.06590 | ||||||||
\(927\) | − 6.83710i | − 0.224560i | ||||||||
\(928\) | − 27.5052i | − 0.902901i | ||||||||
\(929\) | 25.1506 | 0.825165 | 0.412582 | − | 0.910920i | \(-0.364627\pi\) | ||||
0.412582 | + | 0.910920i | \(0.364627\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.7136 | −1.00660 | ||||||||
\(932\) | 12.8059i | 0.419471i | ||||||||
\(933\) | − 20.8781i | − 0.683520i | ||||||||
\(934\) | 38.3545 | 1.25500 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 39.2762 | 1.28378 | ||||||||
\(937\) | − 5.33403i | − 0.174255i | −0.996197 | − | 0.0871276i | \(-0.972231\pi\) | ||||
0.996197 | − | 0.0871276i | \(-0.0277688\pi\) | |||||||
\(938\) | 25.3607i | 0.828056i | ||||||||
\(939\) | −6.31351 | −0.206034 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56.8203 | 1.85229 | 0.926144 | − | 0.377170i | \(-0.123103\pi\) | ||||
0.926144 | + | 0.377170i | \(0.123103\pi\) | |||||||
\(942\) | − 29.7854i | − 0.970460i | ||||||||
\(943\) | 20.3135i | 0.661499i | ||||||||
\(944\) | −85.1917 | −2.77275 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20.5958 | −0.669628 | ||||||||
\(947\) | 20.9939i | 0.682209i | 0.940025 | + | 0.341104i | \(0.110801\pi\) | ||||
−0.940025 | + | 0.341104i | \(0.889199\pi\) | |||||||
\(948\) | − 43.2495i | − 1.40468i | ||||||||
\(949\) | −45.5585 | −1.47889 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.3607 | 1.01694 | ||||||||
\(952\) | 75.7152i | 2.45395i | ||||||||
\(953\) | − 25.2351i | − 0.817446i | −0.912658 | − | 0.408723i | \(-0.865974\pi\) | ||||
0.912658 | − | 0.408723i | \(-0.134026\pi\) | |||||||
\(954\) | 0.424694 | 0.0137500 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −38.4703 | −1.24422 | ||||||||
\(957\) | − 1.41855i | − 0.0458552i | ||||||||
\(958\) | 37.5052i | 1.21174i | ||||||||
\(959\) | 16.5646 | 0.534900 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.09436 | −0.293367 | ||||||||
\(962\) | 23.5174i | 0.758233i | ||||||||
\(963\) | 6.34017i | 0.204309i | ||||||||
\(964\) | 27.7899 | 0.895053 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.30122 | 0.202739 | ||||||||
\(967\) | − 13.1317i | − 0.422287i | −0.977455 | − | 0.211144i | \(-0.932281\pi\) | ||||
0.977455 | − | 0.211144i | \(-0.0677187\pi\) | |||||||
\(968\) | − 9.04945i | − 0.290860i | ||||||||
\(969\) | −40.8248 | −1.31148 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.94053 | 0.286915 | 0.143458 | − | 0.989656i | \(-0.454178\pi\) | ||||
0.143458 | + | 0.989656i | \(0.454178\pi\) | |||||||
\(972\) | − 5.34017i | − 0.171286i | ||||||||
\(973\) | 9.25404i | 0.296671i | ||||||||
\(974\) | −111.064 | −3.55871 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −57.5174 | −1.84109 | ||||||||
\(977\) | − 50.3956i | − 1.61230i | −0.591713 | − | 0.806149i | \(-0.701548\pi\) | ||||
0.591713 | − | 0.806149i | \(-0.298452\pi\) | |||||||
\(978\) | 17.6742i | 0.565159i | ||||||||
\(979\) | 12.8371 | 0.410276 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.31351 | 0.0738647 | ||||||||
\(982\) | 94.3833i | 3.01189i | ||||||||
\(983\) | − 32.1978i | − 1.02695i | −0.858105 | − | 0.513475i | \(-0.828358\pi\) | ||||
0.858105 | − | 0.513475i | \(-0.171642\pi\) | |||||||
\(984\) | −85.2327 | −2.71712 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −29.8187 | −0.949620 | ||||||||
\(987\) | − 5.04718i | − 0.160654i | ||||||||
\(988\) | − 121.954i | − 3.87988i | ||||||||
\(989\) | 16.3956 | 0.521349 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.7747 | −1.48585 | −0.742924 | − | 0.669376i | \(-0.766562\pi\) | ||||
−0.742924 | + | 0.669376i | \(0.766562\pi\) | |||||||
\(992\) | − 90.7501i | − 2.88132i | ||||||||
\(993\) | 19.2039i | 0.609419i | ||||||||
\(994\) | −13.6742 | −0.433719 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −58.8515 | −1.86478 | ||||||||
\(997\) | − 38.2122i | − 1.21019i | −0.796153 | − | 0.605096i | \(-0.793135\pi\) | ||||
0.796153 | − | 0.605096i | \(-0.206865\pi\) | |||||||
\(998\) | − 41.0472i | − 1.29933i | ||||||||
\(999\) | 2.00000 | 0.0632772 |
(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 | 825.2.c.g.199.6 | 6 | ||
3.2 | odd | 2 | 2475.2.c.r.199.1 | 6 | |||
5.2 | odd | 4 | 165.2.a.c.1.1 | ✓ | 3 | ||
5.3 | odd | 4 | 825.2.a.k.1.3 | 3 | |||
5.4 | even | 2 | inner | 825.2.c.g.199.1 | 6 | ||
15.2 | even | 4 | 495.2.a.e.1.3 | 3 | |||
15.8 | even | 4 | 2475.2.a.bb.1.1 | 3 | |||
15.14 | odd | 2 | 2475.2.c.r.199.6 | 6 | |||
20.7 | even | 4 | 2640.2.a.be.1.2 | 3 | |||
35.27 | even | 4 | 8085.2.a.bk.1.1 | 3 | |||
55.32 | even | 4 | 1815.2.a.m.1.3 | 3 | |||
55.43 | even | 4 | 9075.2.a.cf.1.1 | 3 | |||
60.47 | odd | 4 | 7920.2.a.cj.1.2 | 3 | |||
165.32 | odd | 4 | 5445.2.a.z.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.a.c.1.1 | ✓ | 3 | 5.2 | odd | 4 | ||
495.2.a.e.1.3 | 3 | 15.2 | even | 4 | |||
825.2.a.k.1.3 | 3 | 5.3 | odd | 4 | |||
825.2.c.g.199.1 | 6 | 5.4 | even | 2 | inner | ||
825.2.c.g.199.6 | 6 | 1.1 | even | 1 | trivial | ||
1815.2.a.m.1.3 | 3 | 55.32 | even | 4 | |||
2475.2.a.bb.1.1 | 3 | 15.8 | even | 4 | |||
2475.2.c.r.199.1 | 6 | 3.2 | odd | 2 | |||
2475.2.c.r.199.6 | 6 | 15.14 | odd | 2 | |||
2640.2.a.be.1.2 | 3 | 20.7 | even | 4 | |||
5445.2.a.z.1.1 | 3 | 165.32 | odd | 4 | |||
7920.2.a.cj.1.2 | 3 | 60.47 | odd | 4 | |||
8085.2.a.bk.1.1 | 3 | 35.27 | even | 4 | |||
9075.2.a.cf.1.1 | 3 | 55.43 | even | 4 |