Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2475,2,Mod(199,2475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2475, 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("2475.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2475.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: | \(19.7629745003\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(-0.854638 + 0.854638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2475.199 |
Dual form | 2475.2.c.r.199.6 |
$q$-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 \(\left(\mathbb{Z}/2475\mathbb{Z}\right)^\times\).
\(n\) | \(551\) | \(2026\) | \(2377\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | \(-0.592721\pi\) | ||||
0.287190 | − | 0.957873i | \(-0.407279\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.34017 | −2.67009 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.07838i | − 0.407588i | −0.979014 | − | 0.203794i | \(-0.934673\pi\) | ||||
0.979014 | − | 0.203794i | \(-0.0653274\pi\) | |||||||
\(8\) | 9.04945i | 3.19946i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 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 | \(0.390003\pi\) | ||||
−0.338730 | + | 0.940883i | \(0.609997\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.26180 | −1.20714 | −0.603569 | − | 0.797311i | \(-0.706255\pi\) | ||||
−0.603569 | + | 0.797311i | \(0.706255\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.70928i | 0.577619i | ||||||||
\(23\) | 2.15676i | 0.449715i | 0.974392 | + | 0.224857i | \(0.0721916\pi\) | ||||
−0.974392 | + | 0.224857i | \(0.927808\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −11.7587 | −2.30608 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.75872i | 1.08830i | ||||||||
\(29\) | 1.41855 | 0.263418 | 0.131709 | − | 0.991288i | \(-0.457954\pi\) | ||||
0.131709 | + | 0.991288i | \(0.457954\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 21.0205 | 3.60499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 14.2557i | 2.31257i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.41855 | 1.47093 | 0.735465 | − | 0.677562i | \(-0.236964\pi\) | ||||
0.735465 | + | 0.677562i | \(0.236964\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 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 | \(0.110884\pi\) | ||||
−0.939937 | + | 0.341349i | \(0.889116\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.83710 | 0.833872 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 23.1773i | 3.21411i | ||||||||
\(53\) | − 0.156755i | − 0.0215320i | −0.999942 | − | 0.0107660i | \(-0.996573\pi\) | ||||
0.999942 | − | 0.0107660i | \(-0.00342699\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9.75872 | 1.30406 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 3.84324i | − 0.504643i | ||||||||
\(59\) | 6.15676 | 0.801541 | 0.400771 | − | 0.916178i | \(-0.368742\pi\) | ||||
0.400771 | + | 0.916178i | \(0.368742\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −24.8576 | −3.10720 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.68035i | 1.06047i | 0.847850 | + | 0.530237i | \(0.177897\pi\) | ||||
−0.847850 | + | 0.530237i | \(0.822103\pi\) | |||||||
\(68\) | − 41.4329i | − 5.02448i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.68035 | 0.555455 | 0.277727 | − | 0.960660i | \(-0.410419\pi\) | ||||
0.277727 | + | 0.960660i | \(0.410419\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 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 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.09890 | 0.911197 | 0.455599 | − | 0.890185i | \(-0.349425\pi\) | ||||
0.455599 | + | 0.890185i | \(0.349425\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 25.5174i | − 2.81793i | ||||||||
\(83\) | 11.0205i | 1.20966i | 0.796355 | + | 0.604830i | \(0.206759\pi\) | ||||
−0.796355 | + | 0.604830i | \(0.793241\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 20.5958 | 2.22090 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 9.04945i | − 0.964674i | ||||||||
\(89\) | −12.8371 | −1.36073 | −0.680365 | − | 0.732873i | \(-0.738179\pi\) | ||||
−0.680365 | + | 0.732873i | \(0.738179\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.68035 | −0.490634 | ||||||||
\(92\) | − 11.5174i | − 1.20078i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.6803 | 1.30788 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 14.6803i | − 1.49056i | −0.666750 | − | 0.745282i | \(-0.732315\pi\) | ||||
0.666750 | − | 0.745282i | \(-0.267685\pi\) | |||||||
\(98\) | − 15.8143i | − 1.59749i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.5753 | 1.54980 | 0.774900 | − | 0.632083i | \(-0.217800\pi\) | ||||
0.774900 | + | 0.632083i | \(0.217800\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 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 | \(0.0991458\pi\) | ||||
−0.951882 | + | 0.306464i | \(0.900854\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.31351 | −0.221594 | −0.110797 | − | 0.993843i | \(-0.535340\pi\) | ||||
−0.110797 | + | 0.993843i | \(0.535340\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 14.9216i | − 1.40996i | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.57531 | −0.703350 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 16.6803i | − 1.53555i | ||||||||
\(119\) | 8.36683 | 0.766987 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 11.2618i | 1.01960i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 24.9939 | 2.24451 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.24128i | 0.198881i | 0.995044 | + | 0.0994406i | \(0.0317053\pi\) | ||||
−0.995044 | + | 0.0994406i | \(0.968295\pi\) | |||||||
\(128\) | 28.5669i | 2.52498i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.68035 | −0.758405 | −0.379203 | − | 0.925314i | \(-0.623802\pi\) | ||||
−0.379203 | + | 0.925314i | \(0.623802\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 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 | \(-0.772173\pi\) | ||||
0.754608 | − | 0.656176i | \(-0.227827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.58145 | −0.727869 | −0.363935 | − | 0.931425i | \(-0.618567\pi\) | ||||
−0.363935 | + | 0.931425i | \(0.618567\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 12.6803i | − 1.06411i | ||||||||
\(143\) | 4.34017i | 0.362943i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −28.4391 | −2.35363 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 10.6803i | − 0.877919i | ||||||||
\(149\) | −18.0989 | −1.48272 | −0.741360 | − | 0.671108i | \(-0.765819\pi\) | ||||
−0.741360 | + | 0.671108i | \(0.765819\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.92162 | 0.235431 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 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 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.32580 | 0.183298 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 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 | \(0.0243269\pi\) | ||||
−0.997081 | + | 0.0763507i | \(0.975673\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.83710 | −0.449008 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 40.5958i | − 3.09540i | ||||||||
\(173\) | − 3.75872i | − 0.285770i | −0.989739 | − | 0.142885i | \(-0.954362\pi\) | ||||
0.989739 | − | 0.142885i | \(-0.0456380\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.8371 | −1.04301 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 34.7792i | 2.60681i | ||||||||
\(179\) | 15.1506 | 1.13241 | 0.566205 | − | 0.824264i | \(-0.308411\pi\) | ||||
0.566205 | + | 0.824264i | \(0.308411\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −19.5174 | −1.43885 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 7.75872i | − 0.567374i | ||||||||
\(188\) | − 24.9939i | − 1.82286i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.52359 | −0.182601 | −0.0913003 | − | 0.995823i | \(-0.529102\pi\) | ||||
−0.0913003 | + | 0.995823i | \(0.529102\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 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 | \(0.271079\pi\) | ||||
−0.658766 | + | 0.752348i | \(0.728921\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.5236 | −0.745998 | −0.372999 | − | 0.927832i | \(-0.621670\pi\) | ||||
−0.372999 | + | 0.927832i | \(0.621670\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 42.1978i | − 2.96903i | ||||||||
\(203\) | − 1.52973i | − 0.107366i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 18.5236 | 1.29060 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 17.1773 | 1.17421 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.04718i | 0.342625i | ||||||||
\(218\) | 6.26794i | 0.424518i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.6742 | 2.26517 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 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 | \(0.103875\pi\) | ||||
−0.947224 | + | 0.320573i | \(0.896125\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.36069 | 0.222081 | 0.111040 | − | 0.993816i | \(-0.464582\pi\) | ||||
0.111040 | + | 0.993816i | \(0.464582\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.8371i | 0.842797i | ||||||||
\(233\) | 2.39803i | 0.157100i | 0.996910 | + | 0.0785501i | \(0.0250291\pi\) | ||||
−0.996910 | + | 0.0785501i | \(0.974971\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −32.8781 | −2.14018 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 22.6681i | − 1.46935i | ||||||||
\(239\) | −7.20394 | −0.465984 | −0.232992 | − | 0.972479i | \(-0.574852\pi\) | ||||
−0.232992 | + | 0.972479i | \(0.574852\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 22.1978 | 1.42107 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.8371i | 1.45309i | ||||||||
\(248\) | − 42.3545i | − 2.68952i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.3197 | −0.966968 | −0.483484 | − | 0.875353i | \(-0.660629\pi\) | ||||
−0.483484 | + | 0.875353i | \(0.660629\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 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 | \(0.0413840\pi\) | ||||
−0.991560 | + | 0.129646i | \(0.958616\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.15676 | 0.134014 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 23.5174i | 1.45291i | ||||||||
\(263\) | 18.7070i | 1.15352i | 0.816912 | + | 0.576762i | \(0.195684\pi\) | ||||
−0.816912 | + | 0.576762i | \(0.804316\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 15.3730 | 0.942578 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 46.3545i | − 2.83155i | ||||||||
\(269\) | 23.3607 | 1.42433 | 0.712163 | − | 0.702014i | \(-0.247716\pi\) | ||||
0.712163 | + | 0.702014i | \(0.247716\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −41.6163 | −2.51414 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.0144i | 1.56305i | 0.623872 | + | 0.781526i | \(0.285558\pi\) | ||||
−0.623872 | + | 0.781526i | \(0.714442\pi\) | |||||||
\(278\) | 23.2495i | 1.39441i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.41855 | 0.561864 | 0.280932 | − | 0.959728i | \(-0.409357\pi\) | ||||
0.280932 | + | 0.959728i | \(0.409357\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 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 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −43.1978 | −2.54105 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 56.0554i | 3.28039i | ||||||||
\(293\) | 15.7587i | 0.920634i | 0.887754 | + | 0.460317i | \(0.152264\pi\) | ||||
−0.887754 | + | 0.460317i | \(0.847736\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −18.0989 | −1.05198 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 49.0349i | 2.84052i | ||||||||
\(299\) | 9.36069 | 0.541343 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.19779 | 0.472513 | ||||||||
\(302\) | − 62.1399i | − 3.57575i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −72.8080 | −4.17582 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.9216i | 1.07991i | 0.841693 | + | 0.539957i | \(0.181560\pi\) | ||||
−0.841693 | + | 0.539957i | \(0.818440\pi\) | |||||||
\(308\) | − 5.75872i | − 0.328134i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.8781 | 1.18389 | 0.591945 | − | 0.805978i | \(-0.298360\pi\) | ||||
0.591945 | + | 0.805978i | \(0.298360\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 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 | \(0.342925\pi\) | ||||
−0.473682 | + | 0.880696i | \(0.657075\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.41855 | −0.0794236 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 6.30122i | − 0.351154i | ||||||||
\(323\) | − 40.8248i | − 2.27155i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −17.6742 | −0.978884 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.34632 | 0.292537 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 13.5031i | − 0.735559i | −0.929913 | − | 0.367780i | \(-0.880118\pi\) | ||||
0.929913 | − | 0.367780i | \(-0.119882\pi\) | |||||||
\(338\) | 15.8143i | 0.860185i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.68035 | 0.253455 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 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 | \(0.0544346\pi\) | ||||
−0.985413 | + | 0.170179i | \(0.945565\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.1568 | −0.864851 | −0.432426 | − | 0.901670i | \(-0.642342\pi\) | ||||
−0.432426 | + | 0.901670i | \(0.642342\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 19.3896i | 1.03347i | ||||||||
\(353\) | 13.2039i | 0.702775i | 0.936230 | + | 0.351387i | \(0.114290\pi\) | ||||
−0.936230 | + | 0.351387i | \(0.885710\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 68.5523 | 3.63327 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 41.0472i | − 2.16941i | ||||||||
\(359\) | 3.31965 | 0.175205 | 0.0876023 | − | 0.996156i | \(-0.472080\pi\) | ||||
0.0876023 | + | 0.996156i | \(0.472080\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.68649 | 0.457184 | ||||||||
\(362\) | − 13.1050i | − 0.688786i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 24.9939 | 1.31003 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.1445i | 1.88673i | 0.331762 | + | 0.943363i | \(0.392357\pi\) | ||||
−0.331762 | + | 0.943363i | \(0.607643\pi\) | |||||||
\(368\) | 29.8432i | 1.55569i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.169042 | −0.00877620 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 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 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.83710i | 0.349817i | ||||||||
\(383\) | − 33.5585i | − 1.71476i | −0.514685 | − | 0.857379i | \(-0.672091\pi\) | ||||
0.514685 | − | 0.857379i | \(-0.327909\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.0722347 | 0.00367665 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 78.3956i | 3.97993i | ||||||||
\(389\) | 12.8371 | 0.650867 | 0.325433 | − | 0.945565i | \(-0.394490\pi\) | ||||
0.325433 | + | 0.945565i | \(0.394490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.7337 | −0.846258 | ||||||||
\(392\) | 52.8225i | 2.66794i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 57.2183 | 2.88262 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.31965i | 0.266986i | 0.991050 | + | 0.133493i | \(0.0426193\pi\) | ||||
−0.991050 | + | 0.133493i | \(0.957381\pi\) | |||||||
\(398\) | 28.5113i | 1.42914i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.00000 | −0.0998752 | −0.0499376 | − | 0.998752i | \(-0.515902\pi\) | ||||
−0.0499376 | + | 0.998752i | \(0.515902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.3135i | 1.01189i | ||||||||
\(404\) | −83.1748 | −4.13810 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.14447 | −0.205687 | ||||||||
\(407\) | − 2.00000i | − 0.0991363i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.1978 | −1.29540 | −0.647699 | − | 0.761897i | \(-0.724268\pi\) | ||||
−0.647699 | + | 0.761897i | \(0.724268\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 36.5113i | − 1.79878i | ||||||||
\(413\) | − 6.63931i | − 0.326699i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −84.1543 | −4.12600 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 14.2557i | − 0.697267i | ||||||||
\(419\) | −2.83710 | −0.138601 | −0.0693007 | − | 0.997596i | \(-0.522077\pi\) | ||||
−0.0693007 | + | 0.997596i | \(0.522077\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.41855 | 0.0688909 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.48255i | 0.216926i | ||||||||
\(428\) | − 33.8576i | − 1.63657i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.5708 | −1.13536 | −0.567682 | − | 0.823248i | \(-0.692160\pi\) | ||||
−0.567682 | + | 0.823248i | \(0.692160\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 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 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.77924 | −0.228101 | −0.114050 | − | 0.993475i | \(-0.536383\pi\) | ||||
−0.114050 | + | 0.993475i | \(0.536383\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 91.2327i | − 4.33950i | ||||||||
\(443\) | − 20.1978i | − 0.959626i | −0.877371 | − | 0.479813i | \(-0.840704\pi\) | ||||
0.877371 | − | 0.479813i | \(-0.159296\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.84324 | −0.276686 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 26.8059i | 1.26646i | ||||||||
\(449\) | −21.5708 | −1.01799 | −0.508994 | − | 0.860770i | \(-0.669982\pi\) | ||||
−0.508994 | + | 0.860770i | \(0.669982\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.41855 | −0.443502 | ||||||||
\(452\) | − 32.0410i | − 1.50708i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 26.1711 | 1.22827 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 28.1711i | − 1.31779i | −0.752235 | − | 0.658895i | \(-0.771024\pi\) | ||||
0.752235 | − | 0.658895i | \(-0.228976\pi\) | |||||||
\(458\) | − 9.10504i | − 0.425451i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.47187 | 0.0685520 | 0.0342760 | − | 0.999412i | \(-0.489087\pi\) | ||||
0.0342760 | + | 0.999412i | \(0.489087\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 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 | \(0.106222\pi\) | ||||
−0.944834 | + | 0.327548i | \(0.893778\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.36069 | 0.432237 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 55.7152i | 2.56450i | ||||||||
\(473\) | − 7.60197i | − 0.349539i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −44.6803 | −2.04792 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.5174i | 0.892707i | ||||||||
\(479\) | −13.8432 | −0.632514 | −0.316257 | − | 0.948674i | \(-0.602426\pi\) | ||||
−0.316257 | + | 0.948674i | \(0.602426\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.68035 | 0.395790 | ||||||||
\(482\) | 14.0989i | 0.642187i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.34017 | −0.242735 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.9939i | 1.85761i | 0.370570 | + | 0.928804i | \(0.379162\pi\) | ||||
−0.370570 | + | 0.928804i | \(0.620838\pi\) | |||||||
\(488\) | − 37.6163i | − 1.70281i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.8371 | −1.57218 | −0.786088 | − | 0.618114i | \(-0.787897\pi\) | ||||
−0.786088 | + | 0.618114i | \(0.787897\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.0061i | 0.495692i | ||||||||
\(494\) | 61.8720 | 2.78375 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −64.7624 | −2.90792 | ||||||||
\(497\) | − 5.04718i | − 0.226397i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.1506 | −0.678235 | −0.339117 | − | 0.940744i | \(-0.610128\pi\) | ||||
−0.339117 | + | 0.940744i | \(0.610128\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 41.5052i | 1.85247i | ||||||||
\(503\) | 6.65368i | 0.296673i | 0.988937 | + | 0.148337i | \(0.0473919\pi\) | ||||
−0.988937 | + | 0.148337i | \(0.952608\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.84324 | −0.259764 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 11.9688i | − 0.531030i | ||||||||
\(509\) | 41.3484 | 1.83274 | 0.916368 | − | 0.400337i | \(-0.131107\pi\) | ||||
0.916368 | + | 0.400337i | \(0.131107\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.3197 | −0.500752 | ||||||||
\(512\) | − 17.8599i | − 0.789303i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.2618 | 0.496736 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 4.68035i | − 0.205841i | ||||||||
\(518\) | − 5.84324i | − 0.256737i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.67420 | −0.336213 | −0.168106 | − | 0.985769i | \(-0.553765\pi\) | ||||
−0.168106 | + | 0.985769i | \(0.553765\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 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 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.3484 | 0.797757 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 30.3012i | − 1.31372i | ||||||||
\(533\) | − 40.8781i | − 1.77063i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −78.5523 | −3.39294 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 150.439 | 6.45001 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.0661i | 0.986235i | 0.869963 | + | 0.493117i | \(0.164143\pi\) | ||||
−0.869963 | + | 0.493117i | \(0.835857\pi\) | |||||||
\(548\) | 82.0288i | 3.50409i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.46412 | −0.317982 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 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 | \(0.0720683\pi\) | ||||
−0.974479 | + | 0.224480i | \(0.927932\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.9939 | 1.39549 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 25.5174i | − 1.07639i | ||||||||
\(563\) | 36.2122i | 1.52616i | 0.646303 | + | 0.763080i | \(0.276314\pi\) | ||||
−0.646303 | + | 0.763080i | \(0.723686\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 38.5835 | 1.62179 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 42.3545i | 1.77716i | ||||||||
\(569\) | −27.5753 | −1.15602 | −0.578008 | − | 0.816031i | \(-0.696170\pi\) | ||||
−0.578008 | + | 0.816031i | \(0.696170\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −27.5174 | −1.14856 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 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 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.8843 | 0.493043 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 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 | \(0.0560107\pi\) | ||||
−0.984558 | + | 0.175056i | \(0.943989\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.6270 | 1.01474 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 27.6742i | 1.13740i | ||||||||
\(593\) | − 7.56093i | − 0.310490i | −0.987876 | − | 0.155245i | \(-0.950383\pi\) | ||||
0.987876 | − | 0.155245i | \(-0.0496167\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 96.6512 | 3.95899 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 25.3607i | − 1.03708i | ||||||||
\(599\) | 5.67420 | 0.231842 | 0.115921 | − | 0.993258i | \(-0.463018\pi\) | ||||
0.115921 | + | 0.993258i | \(0.463018\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −122.482 | −4.98373 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.24128i | 0.0909706i | 0.998965 | + | 0.0454853i | \(0.0144834\pi\) | ||||
−0.998965 | + | 0.0454853i | \(0.985517\pi\) | |||||||
\(608\) | 102.024i | 4.13763i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.3135 | 0.821797 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 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 | \(0.0734416\pi\) | ||||
−0.973501 | + | 0.228682i | \(0.926558\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 45.1917 | 1.81641 | 0.908203 | − | 0.418530i | \(-0.137455\pi\) | ||||
0.908203 | + | 0.418530i | \(0.137455\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 56.5646i | − 2.26803i | ||||||||
\(623\) | 13.8432i | 0.554618i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.1050 | 0.683655 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 84.9647 | 3.37438 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 25.3340i | − 1.00377i | ||||||||
\(638\) | 3.84324i | 0.152156i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.210079 | −0.00829764 | −0.00414882 | − | 0.999991i | \(-0.501321\pi\) | ||||
−0.00414882 | + | 0.999991i | \(0.501321\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 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 | \(0.0983152\pi\) | ||||
−0.952679 | + | 0.303979i | \(0.901685\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.15676 | −0.241674 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 34.8371i | 1.36433i | ||||||||
\(653\) | 17.8310i | 0.697779i | 0.937164 | + | 0.348890i | \(0.113441\pi\) | ||||
−0.937164 | + | 0.348890i | \(0.886559\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 130.325 | 5.08835 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 13.6742i | − 0.533076i | ||||||||
\(659\) | −32.3135 | −1.25876 | −0.629378 | − | 0.777099i | \(-0.716690\pi\) | ||||
−0.629378 | + | 0.777099i | \(0.716690\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −99.7296 | −3.87026 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.05947i | 0.118463i | ||||||||
\(668\) | − 10.5380i | − 0.407726i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.15676 | 0.160470 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 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 | \(0.249618\pi\) | ||||
−0.707954 | + | 0.706258i | \(0.750382\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.8310 | −0.607536 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 12.6803i | − 0.485556i | ||||||||
\(683\) | 17.3074i | 0.662248i | 0.943587 | + | 0.331124i | \(0.107428\pi\) | ||||
−0.943587 | + | 0.331124i | \(0.892572\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −37.5052 | −1.43195 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.1773 | 0.652040 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 73.0759i | 2.76795i | ||||||||
\(698\) | 43.7731i | 1.65684i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.1050 | 0.646048 | 0.323024 | − | 0.946391i | \(-0.395300\pi\) | ||||
0.323024 | + | 0.946391i | \(0.395300\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 10.5236i | − 0.396905i | ||||||||
\(704\) | 24.8576 | 0.936857 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 35.7731 | 1.34634 | ||||||||
\(707\) | − 16.7961i | − 0.631681i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.1506 | −0.944551 | −0.472276 | − | 0.881451i | \(-0.656567\pi\) | ||||
−0.472276 | + | 0.881451i | \(0.656567\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 116.169i | − 4.35361i | ||||||||
\(713\) | − 10.0944i | − 0.378037i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −80.9069 | −3.02363 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 8.99386i | − 0.335648i | ||||||||
\(719\) | −1.78992 | −0.0667528 | −0.0333764 | − | 0.999443i | \(-0.510626\pi\) | ||||
−0.0333764 | + | 0.999443i | \(0.510626\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.37298 | 0.274584 | ||||||||
\(722\) | − 23.5341i | − 0.875848i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −25.8310 | −0.960000 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 25.9877i | − 0.963831i | −0.876218 | − | 0.481915i | \(-0.839941\pi\) | ||||
0.876218 | − | 0.481915i | \(-0.160059\pi\) | |||||||
\(728\) | − 42.3545i | − 1.56976i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −58.9816 | −2.18151 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 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 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.6163 | 1.75160 | 0.875798 | − | 0.482678i | \(-0.160336\pi\) | ||||
0.875798 | + | 0.482678i | \(0.160336\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.457980i | 0.0168130i | ||||||||
\(743\) | − 0.550252i | − 0.0201868i | −0.999949 | − | 0.0100934i | \(-0.996787\pi\) | ||||
0.999949 | − | 0.0100934i | \(-0.00321288\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.61425 | −0.278778 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16.6803 | −0.607462 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1.31965i | − 0.0479636i | −0.999712 | − | 0.0239818i | \(-0.992366\pi\) | ||||
0.999712 | − | 0.0239818i | \(-0.00763438\pi\) | |||||||
\(758\) | − 54.1855i | − 1.96811i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.21461 | 0.0802797 | 0.0401399 | − | 0.999194i | \(-0.487220\pi\) | ||||
0.0401399 | + | 0.999194i | \(0.487220\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.49484i | 0.0903192i | ||||||||
\(764\) | 13.4764 | 0.487559 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −90.9192 | −3.28504 | ||||||||
\(767\) | − 26.7214i | − 0.964853i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.3668 | 0.518081 | 0.259041 | − | 0.965866i | \(-0.416594\pi\) | ||||
0.259041 | + | 0.965866i | \(0.416594\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 0.142380i | − 0.00512436i | ||||||||
\(773\) | − 40.1568i | − 1.44434i | −0.691717 | − | 0.722169i | \(-0.743145\pi\) | ||||
0.691717 | − | 0.722169i | \(-0.256855\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 132.849 | 4.76900 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 34.7792i | − 1.24690i | ||||||||
\(779\) | −49.5585 | −1.77562 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.68035 | −0.167476 | ||||||||
\(782\) | 45.3361i | 1.62122i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 80.7686 | 2.88459 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 49.5897i | − 1.76768i | −0.467788 | − | 0.883841i | \(-0.654949\pi\) | ||||
0.467788 | − | 0.883841i | \(-0.345051\pi\) | |||||||
\(788\) | − 112.781i | − 4.01767i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.47027 | 0.230056 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 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 | \(-0.689898\pi\) | ||||
0.561818 | − | 0.827261i | \(-0.310102\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.3135 | −1.28468 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.41855i | 0.191336i | ||||||||
\(803\) | 10.4969i | 0.370429i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 55.0349 | 1.93852 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 140.948i | 4.95853i | ||||||||
\(809\) | −18.5814 | −0.653289 | −0.326644 | − | 0.945147i | \(-0.605918\pi\) | ||||
−0.326644 | + | 0.945147i | \(0.605918\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.41855 | −0.189920 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 40.0000i | − 1.39942i | ||||||||
\(818\) | 70.9770i | 2.48165i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.2085 | 1.08918 | 0.544592 | − | 0.838701i | \(-0.316685\pi\) | ||||
0.544592 | + | 0.838701i | \(0.316685\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 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 | \(0.157977\pi\) | ||||
−0.879350 | + | 0.476176i | \(0.842023\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.1978 | 0.909887 | 0.454943 | − | 0.890520i | \(-0.349659\pi\) | ||||
0.454943 | + | 0.890520i | \(0.349659\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 107.886i | 3.74029i | ||||||||
\(833\) | 45.2885i | 1.56915i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −28.0989 | −0.971821 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.68649i | 0.265525i | ||||||||
\(839\) | 7.20394 | 0.248708 | 0.124354 | − | 0.992238i | \(-0.460314\pi\) | ||||
0.124354 | + | 0.992238i | \(0.460314\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.9877 | −0.930611 | ||||||||
\(842\) | − 31.0928i | − 1.07153i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −51.1338 | −1.76010 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1.07838i | − 0.0370535i | ||||||||
\(848\) | − 2.16904i | − 0.0744852i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.31351 | −0.147865 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 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 | \(-0.782604\pi\) | ||||
0.775701 | − | 0.631100i | \(-0.217396\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −57.5052 | −1.96205 | −0.981025 | − | 0.193879i | \(-0.937893\pi\) | ||||
−0.981025 | + | 0.193879i | \(0.937893\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 63.8597i | 2.17507i | ||||||||
\(863\) | 1.89657i | 0.0645599i | 0.999479 | + | 0.0322800i | \(0.0102768\pi\) | ||||
−0.999479 | + | 0.0322800i | \(0.989723\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −40.6225 | −1.38041 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 26.9528i | − 0.914838i | ||||||||
\(869\) | −8.09890 | −0.274736 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.6742 | 1.27654 | ||||||||
\(872\) | − 20.9360i | − 0.708982i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −30.7460 | −1.04000 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 32.5380i | − 1.09873i | −0.835583 | − | 0.549365i | \(-0.814870\pi\) | ||||
0.835583 | − | 0.549365i | \(-0.185130\pi\) | |||||||
\(878\) | 12.9483i | 0.436983i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.1978 | −0.613099 | −0.306550 | − | 0.951855i | \(-0.599175\pi\) | ||||
−0.306550 | + | 0.951855i | \(0.599175\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 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 | \(0.154986\pi\) | ||||
−0.883787 | + | 0.467890i | \(0.845014\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.41694 | 0.0810616 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.5174i | 0.385633i | ||||||||
\(893\) | − 24.6270i | − 0.824112i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 30.8059 | 1.02915 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 58.4412i | 1.95021i | ||||||||
\(899\) | −6.63931 | −0.221433 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.21622 | 0.0405182 | ||||||||
\(902\) | 25.5174i | 0.849638i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −54.2967 | −1.80588 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.9376i | 0.927653i | 0.885926 | + | 0.463826i | \(0.153524\pi\) | ||||
−0.885926 | + | 0.463826i | \(0.846476\pi\) | |||||||
\(908\) | − 51.5851i | − 1.71191i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.8843 | 0.393744 | 0.196872 | − | 0.980429i | \(-0.436922\pi\) | ||||
0.196872 | + | 0.980429i | \(0.436922\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 11.0205i | − 0.364726i | ||||||||
\(914\) | −76.3234 | −2.52455 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.9467 | −0.592975 | ||||||||
\(917\) | 9.36069i | 0.309117i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.6041 | 1.50434 | 0.752170 | − | 0.658970i | \(-0.229007\pi\) | ||||
0.752170 | + | 0.658970i | \(0.229007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 3.98771i | − 0.131328i | ||||||||
\(923\) | − 20.3135i | − 0.668627i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −62.8659 | −2.06590 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 27.5052i | − 0.902901i | ||||||||
\(929\) | −25.1506 | −0.825165 | −0.412582 | − | 0.910920i | \(-0.635373\pi\) | ||||
−0.412582 | + | 0.910920i | \(0.635373\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.7136 | −1.00660 | ||||||||
\(932\) | − 12.8059i | − 0.419471i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 38.3545 | 1.25500 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 5.33403i | − 0.174255i | −0.996197 | − | 0.0871276i | \(-0.972231\pi\) | ||||
0.996197 | − | 0.0871276i | \(-0.0277688\pi\) | |||||||
\(938\) | − 25.3607i | − 0.828056i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −56.8203 | −1.85229 | −0.926144 | − | 0.377170i | \(-0.876897\pi\) | ||||
−0.926144 | + | 0.377170i | \(0.876897\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 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 | \(-0.889199\pi\) | ||||
0.940025 | − | 0.341104i | \(-0.110801\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45.5585 | −1.47889 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 75.7152i | 2.45395i | ||||||||
\(953\) | 25.2351i | 0.817446i | 0.912658 | + | 0.408723i | \(0.134026\pi\) | ||||
−0.912658 | + | 0.408723i | \(0.865974\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 38.4703 | 1.24422 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 37.5052i | 1.21174i | ||||||||
\(959\) | −16.5646 | −0.534900 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.09436 | −0.293367 | ||||||||
\(962\) | − 23.5174i | − 0.758233i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 27.7899 | 0.895053 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 13.1317i | − 0.422287i | −0.977455 | − | 0.211144i | \(-0.932281\pi\) | ||||
0.977455 | − | 0.211144i | \(-0.0677187\pi\) | |||||||
\(968\) | 9.04945i | 0.290860i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.94053 | −0.286915 | −0.143458 | − | 0.989656i | \(-0.545822\pi\) | ||||
−0.143458 | + | 0.989656i | \(0.545822\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 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 | \(0.298452\pi\) | ||||
−0.591713 | + | 0.806149i | \(0.701548\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.8371 | 0.410276 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 94.3833i | 3.01189i | ||||||||
\(983\) | 32.1978i | 1.02695i | 0.858105 | + | 0.513475i | \(0.171642\pi\) | ||||
−0.858105 | + | 0.513475i | \(0.828358\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 29.8187 | 0.949620 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −13.6742 | −0.433719 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 38.2122i | − 1.21019i | −0.796153 | − | 0.605096i | \(-0.793135\pi\) | ||||
0.796153 | − | 0.605096i | \(-0.206865\pi\) | |||||||
\(998\) | 41.0472i | 1.29933i | ||||||||
\(999\) | 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 | 2475.2.c.r.199.1 | 6 | ||
3.2 | odd | 2 | 825.2.c.g.199.6 | 6 | |||
5.2 | odd | 4 | 495.2.a.e.1.3 | 3 | |||
5.3 | odd | 4 | 2475.2.a.bb.1.1 | 3 | |||
5.4 | even | 2 | inner | 2475.2.c.r.199.6 | 6 | ||
15.2 | even | 4 | 165.2.a.c.1.1 | ✓ | 3 | ||
15.8 | even | 4 | 825.2.a.k.1.3 | 3 | |||
15.14 | odd | 2 | 825.2.c.g.199.1 | 6 | |||
20.7 | even | 4 | 7920.2.a.cj.1.2 | 3 | |||
55.32 | even | 4 | 5445.2.a.z.1.1 | 3 | |||
60.47 | odd | 4 | 2640.2.a.be.1.2 | 3 | |||
105.62 | odd | 4 | 8085.2.a.bk.1.1 | 3 | |||
165.32 | odd | 4 | 1815.2.a.m.1.3 | 3 | |||
165.98 | odd | 4 | 9075.2.a.cf.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.a.c.1.1 | ✓ | 3 | 15.2 | even | 4 | ||
495.2.a.e.1.3 | 3 | 5.2 | odd | 4 | |||
825.2.a.k.1.3 | 3 | 15.8 | even | 4 | |||
825.2.c.g.199.1 | 6 | 15.14 | odd | 2 | |||
825.2.c.g.199.6 | 6 | 3.2 | odd | 2 | |||
1815.2.a.m.1.3 | 3 | 165.32 | odd | 4 | |||
2475.2.a.bb.1.1 | 3 | 5.3 | odd | 4 | |||
2475.2.c.r.199.1 | 6 | 1.1 | even | 1 | trivial | ||
2475.2.c.r.199.6 | 6 | 5.4 | even | 2 | inner | ||
2640.2.a.be.1.2 | 3 | 60.47 | odd | 4 | |||
5445.2.a.z.1.1 | 3 | 55.32 | even | 4 | |||
7920.2.a.cj.1.2 | 3 | 20.7 | even | 4 | |||
8085.2.a.bk.1.1 | 3 | 105.62 | odd | 4 | |||
9075.2.a.cf.1.1 | 3 | 165.98 | odd | 4 |