Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,3,Mod(949,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.949");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.g (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: | \(51.7712502285\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 949.5 | ||
Character | \(\chi\) | \(=\) | 1900.949 |
Dual form | 1900.3.g.c.949.6 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.42504 | −1.14168 | −0.570841 | − | 0.821061i | \(-0.693383\pi\) | ||||
−0.570841 | + | 0.821061i | \(0.693383\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.18599i | 1.31228i | 0.754637 | + | 0.656142i | \(0.227813\pi\) | ||||
−0.754637 | + | 0.656142i | \(0.772187\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.73093 | 0.303436 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.4382 | 1.03983 | 0.519916 | − | 0.854217i | \(-0.325963\pi\) | ||||
0.519916 | + | 0.854217i | \(0.325963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.1235 | 0.778734 | 0.389367 | − | 0.921083i | \(-0.372694\pi\) | ||||
0.389367 | + | 0.921083i | \(0.372694\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.19261i | − | 0.246624i | −0.992368 | − | 0.123312i | \(-0.960648\pi\) | ||
0.992368 | − | 0.123312i | \(-0.0393517\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.8104 | − | 15.6248i | −0.568967 | − | 0.822360i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 31.4624i | − | 1.49821i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.952351i | 0.0414066i | 0.999786 | + | 0.0207033i | \(0.00659053\pi\) | ||||
−0.999786 | + | 0.0207033i | \(0.993409\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 21.4719 | 0.795254 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 9.43887i | − | 0.325478i | −0.986669 | − | 0.162739i | \(-0.947967\pi\) | ||
0.986669 | − | 0.162739i | \(-0.0520329\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.52508i | − | 0.275002i | −0.990502 | − | 0.137501i | \(-0.956093\pi\) | ||
0.990502 | − | 0.137501i | \(-0.0439071\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −39.1762 | −1.18716 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 20.0029 | 0.540618 | 0.270309 | − | 0.962774i | \(-0.412874\pi\) | ||||
0.270309 | + | 0.962774i | \(0.412874\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −34.6736 | −0.889066 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 61.2499i | − | 1.49390i | −0.664881 | − | 0.746950i | \(-0.731518\pi\) | ||
0.664881 | − | 0.746950i | \(-0.268482\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 57.9875i | 1.34855i | 0.738482 | + | 0.674273i | \(0.235543\pi\) | ||||
−0.738482 | + | 0.674273i | \(0.764457\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 35.3773i | − | 0.752709i | −0.926476 | − | 0.376355i | \(-0.877177\pi\) | ||
0.926476 | − | 0.376355i | \(-0.122823\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −35.3824 | −0.722091 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.3599i | 0.281566i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −57.6953 | −1.08859 | −0.544296 | − | 0.838893i | \(-0.683203\pi\) | ||||
−0.544296 | + | 0.838893i | \(0.683203\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 37.0260 | + | 53.5158i | 0.649579 | + | 0.938873i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 16.7603i | − | 0.284073i | −0.989861 | − | 0.142037i | \(-0.954635\pi\) | ||
0.989861 | − | 0.142037i | \(-0.0453651\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −32.2192 | −0.528183 | −0.264092 | − | 0.964498i | \(-0.585072\pi\) | ||||
−0.264092 | + | 0.964498i | \(0.585072\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 25.0863i | 0.398195i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.07252 | −0.0906346 | −0.0453173 | − | 0.998973i | \(-0.514430\pi\) | ||||
−0.0453173 | + | 0.998973i | \(0.514430\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 3.26184i | − | 0.0472731i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 113.671i | 1.60101i | 0.599328 | + | 0.800503i | \(0.295434\pi\) | ||||
−0.599328 | + | 0.800503i | \(0.704566\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 27.9670i | 0.383109i | 0.981482 | + | 0.191554i | \(0.0613529\pi\) | ||||
−0.981482 | + | 0.191554i | \(0.938647\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 105.071i | 1.36456i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 65.7698i | − | 0.832529i | −0.909244 | − | 0.416264i | \(-0.863339\pi\) | ||
0.909244 | − | 0.416264i | \(-0.136661\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −98.1204 | −1.21136 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 60.2358i | − | 0.725733i | −0.931841 | − | 0.362866i | \(-0.881798\pi\) | ||
0.931841 | − | 0.362866i | \(-0.118202\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 32.3286i | 0.371593i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 97.9852i | − | 1.10096i | −0.834849 | − | 0.550478i | \(-0.814445\pi\) | ||
0.834849 | − | 0.550478i | \(-0.185555\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 92.9948i | 1.02192i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 29.1988i | 0.313965i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 92.0255 | 0.948717 | 0.474358 | − | 0.880332i | \(-0.342680\pi\) | ||||
0.474358 | + | 0.880332i | \(0.342680\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 31.2368 | 0.315523 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 64.7709 | 0.641296 | 0.320648 | − | 0.947198i | \(-0.396099\pi\) | ||||
0.320648 | + | 0.947198i | \(0.396099\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 204.226 | 1.98278 | 0.991390 | − | 0.130940i | \(-0.0417996\pi\) | ||||
0.991390 | + | 0.130940i | \(0.0417996\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 203.574 | 1.90256 | 0.951281 | − | 0.308324i | \(-0.0997680\pi\) | ||||
0.951281 | + | 0.308324i | \(0.0997680\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 63.6932i | − | 0.584341i | −0.956366 | − | 0.292171i | \(-0.905622\pi\) | ||
0.956366 | − | 0.292171i | \(-0.0943775\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −68.5107 | −0.617213 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.01143 | −0.0178003 | −0.00890013 | − | 0.999960i | \(-0.502833\pi\) | ||||
−0.00890013 | + | 0.999960i | \(0.502833\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 27.6467 | 0.236296 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 38.5133 | 0.323641 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.83149 | 0.0812520 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 209.783i | 1.70556i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −41.7788 | −0.328967 | −0.164484 | − | 0.986380i | \(-0.552596\pi\) | ||||
−0.164484 | + | 0.986380i | \(0.552596\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 198.610i | − | 1.53961i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −50.6875 | −0.386928 | −0.193464 | − | 0.981107i | \(-0.561972\pi\) | ||||
−0.193464 | + | 0.981107i | \(0.561972\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 143.530 | − | 99.3041i | 1.07917 | − | 0.746647i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 30.0467i | 0.219319i | 0.993969 | + | 0.109659i | \(0.0349760\pi\) | ||||
−0.993969 | + | 0.109659i | \(0.965024\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 210.679 | 1.51567 | 0.757837 | − | 0.652444i | \(-0.226256\pi\) | ||||
0.757837 | + | 0.652444i | \(0.226256\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 121.169i | 0.859354i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 115.795 | 0.809753 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 121.186 | 0.824397 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 263.989 | 1.77174 | 0.885868 | − | 0.463938i | \(-0.153564\pi\) | ||||
0.885868 | + | 0.463938i | \(0.153564\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 90.3173i | − | 0.598128i | −0.954233 | − | 0.299064i | \(-0.903326\pi\) | ||
0.954233 | − | 0.299064i | \(-0.0966743\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 11.4497i | − | 0.0748348i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 108.051i | 0.688222i | 0.938929 | + | 0.344111i | \(0.111820\pi\) | ||||
−0.938929 | + | 0.344111i | \(0.888180\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 197.609 | 1.24282 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.74829 | −0.0543372 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 127.846i | 0.784333i | 0.919894 | + | 0.392167i | \(0.128274\pi\) | ||||
−0.919894 | + | 0.392167i | \(0.871726\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −143.920 | −0.861798 | −0.430899 | − | 0.902400i | \(-0.641803\pi\) | ||||
−0.430899 | + | 0.902400i | \(0.641803\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −66.5138 | −0.393573 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −29.5224 | − | 42.6703i | −0.172645 | − | 0.249534i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −291.098 | −1.68265 | −0.841323 | − | 0.540532i | \(-0.818223\pi\) | ||||
−0.841323 | + | 0.540532i | \(0.818223\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 57.4048i | 0.324321i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 91.3328i | − | 0.510239i | −0.966910 | − | 0.255120i | \(-0.917885\pi\) | ||
0.966910 | − | 0.255120i | \(-0.0821148\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 182.671i | − | 1.00923i | −0.863344 | − | 0.504617i | \(-0.831634\pi\) | ||
0.863344 | − | 0.504617i | \(-0.168366\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 110.352 | 0.603017 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 47.9558i | − | 0.256448i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 197.240i | 1.04360i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 358.406 | 1.87647 | 0.938235 | − | 0.345998i | \(-0.112460\pi\) | ||||
0.938235 | + | 0.345998i | \(0.112460\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 131.778 | 0.682786 | 0.341393 | − | 0.939921i | \(-0.389101\pi\) | ||||
0.341393 | + | 0.939921i | \(0.389101\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 35.9154i | 0.182312i | 0.995837 | + | 0.0911558i | \(0.0290561\pi\) | ||||
−0.995837 | + | 0.0911558i | \(0.970944\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −121.742 | −0.611769 | −0.305885 | − | 0.952069i | \(-0.598952\pi\) | ||||
−0.305885 | + | 0.952069i | \(0.598952\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.7986 | 0.103476 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 86.7054 | 0.427120 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.60080i | 0.0125643i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −123.651 | − | 178.719i | −0.591631 | − | 0.855117i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 272.967i | 1.29368i | 0.762626 | + | 0.646840i | \(0.223910\pi\) | ||||
−0.762626 | + | 0.646840i | \(0.776090\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 389.330i | − | 1.82784i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 78.3113 | 0.360881 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 95.7881i | − | 0.437388i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 42.4441i | − | 0.192055i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 81.1828 | 0.364048 | 0.182024 | − | 0.983294i | \(-0.441735\pi\) | ||||
0.182024 | + | 0.983294i | \(0.441735\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 337.268 | 1.48576 | 0.742882 | − | 0.669423i | \(-0.233459\pi\) | ||||
0.742882 | + | 0.669423i | \(0.233459\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 240.819 | 1.05161 | 0.525806 | − | 0.850605i | \(-0.323764\pi\) | ||||
0.525806 | + | 0.850605i | \(0.323764\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 359.872i | − | 1.55789i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 136.526i | − | 0.585948i | −0.956120 | − | 0.292974i | \(-0.905355\pi\) | ||
0.956120 | − | 0.292974i | \(-0.0946449\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 225.264i | 0.950483i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 320.734 | 1.34198 | 0.670991 | − | 0.741466i | \(-0.265869\pi\) | ||||
0.670991 | + | 0.741466i | \(0.265869\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 359.039i | 1.48979i | 0.667183 | + | 0.744894i | \(0.267500\pi\) | ||||
−0.667183 | + | 0.744894i | \(0.732500\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 142.820 | 0.587736 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −109.439 | − | 158.179i | −0.443074 | − | 0.640400i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 206.310i | 0.828556i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 103.786 | 0.413490 | 0.206745 | − | 0.978395i | \(-0.433713\pi\) | ||||
0.206745 | + | 0.978395i | \(0.433713\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.8931i | 0.0430559i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 56.5607 | 0.220080 | 0.110040 | − | 0.993927i | \(-0.464902\pi\) | ||||
0.110040 | + | 0.993927i | \(0.464902\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 183.746i | 0.709444i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 25.7769i | − | 0.0987620i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 280.514i | − | 1.06659i | −0.845929 | − | 0.533296i | \(-0.820953\pi\) | ||
0.845929 | − | 0.533296i | \(-0.179047\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 335.603i | 1.25694i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 102.156i | 0.379763i | 0.981807 | + | 0.189881i | \(0.0608103\pi\) | ||||
−0.981807 | + | 0.189881i | \(0.939190\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 476.115 | 1.75688 | 0.878441 | − | 0.477851i | \(-0.158584\pi\) | ||||
0.878441 | + | 0.477851i | \(0.158584\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 318.511i | − | 1.16671i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 264.070i | 0.953323i | 0.879087 | + | 0.476661i | \(0.158153\pi\) | ||||
−0.879087 | + | 0.476661i | \(0.841847\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 23.2814i | − | 0.0834457i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 242.447i | − | 0.862800i | −0.902161 | − | 0.431400i | \(-0.858020\pi\) | ||
0.902161 | − | 0.431400i | \(-0.141980\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 271.524i | 0.959450i | 0.877419 | + | 0.479725i | \(0.159264\pi\) | ||||
−0.877419 | + | 0.479725i | \(0.840736\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 562.641 | 1.96042 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 271.422 | 0.939176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −315.191 | −1.08313 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −188.495 | −0.643328 | −0.321664 | − | 0.946854i | \(-0.604242\pi\) | ||||
−0.321664 | + | 0.946854i | \(0.604242\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 245.598 | 0.826931 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.64117i | 0.0322447i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −532.672 | −1.76968 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −221.843 | −0.732156 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 262.646 | 0.855524 | 0.427762 | − | 0.903891i | \(-0.359302\pi\) | ||||
0.427762 | + | 0.903891i | \(0.359302\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −699.484 | −2.26370 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 352.334 | 1.13291 | 0.566454 | − | 0.824093i | \(-0.308315\pi\) | ||||
0.566454 | + | 0.824093i | \(0.308315\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 483.965i | 1.54621i | 0.634277 | + | 0.773106i | \(0.281298\pi\) | ||||
−0.634277 | + | 0.773106i | \(0.718702\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 80.3004 | 0.253313 | 0.126657 | − | 0.991947i | \(-0.459575\pi\) | ||||
0.126657 | + | 0.991947i | \(0.459575\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 107.963i | − | 0.338443i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −697.251 | −2.17212 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −65.5089 | + | 45.3238i | −0.202814 | + | 0.140321i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 218.152i | 0.667132i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 324.976 | 0.987769 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 583.642i | 1.76327i | 0.471933 | + | 0.881634i | \(0.343556\pi\) | ||||
−0.471933 | + | 0.881634i | \(0.656444\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 54.6263 | 0.164043 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −413.317 | −1.22646 | −0.613230 | − | 0.789904i | \(-0.710130\pi\) | ||||
−0.613230 | + | 0.789904i | \(0.710130\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.88924 | 0.0203222 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 97.5112i | − | 0.285957i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 125.091i | 0.364696i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 207.384i | 0.597648i | 0.954308 | + | 0.298824i | \(0.0965944\pi\) | ||||
−0.954308 | + | 0.298824i | \(0.903406\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 176.833 | 0.506684 | 0.253342 | − | 0.967377i | \(-0.418470\pi\) | ||||
0.253342 | + | 0.967377i | \(0.418470\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 217.371 | 0.619291 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 398.294i | 1.12831i | 0.825668 | + | 0.564156i | \(0.190798\pi\) | ||||
−0.825668 | + | 0.564156i | \(0.809202\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −131.910 | −0.369495 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −89.1125 | −0.248224 | −0.124112 | − | 0.992268i | \(-0.539608\pi\) | ||||
−0.124112 | + | 0.992268i | \(0.539608\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −127.271 | + | 337.821i | −0.352552 | + | 0.935792i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −33.6733 | −0.0927639 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 450.345i | − | 1.22710i | −0.789656 | − | 0.613550i | \(-0.789741\pi\) | ||
0.789656 | − | 0.613550i | \(-0.210259\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 167.269i | − | 0.453303i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 529.989i | − | 1.42854i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −442.338 | −1.18589 | −0.592946 | − | 0.805242i | \(-0.702035\pi\) | ||||
−0.592946 | + | 0.805242i | \(0.702035\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 95.5549i | − | 0.253461i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 573.993i | − | 1.51449i | −0.653128 | − | 0.757247i | \(-0.726544\pi\) | ||
0.653128 | − | 0.757247i | \(-0.273456\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 143.094 | 0.375576 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 159.706 | 0.416987 | 0.208494 | − | 0.978024i | \(-0.433144\pi\) | ||||
0.208494 | + | 0.978024i | \(0.433144\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 158.360i | 0.409198i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −620.531 | −1.59519 | −0.797597 | − | 0.603190i | \(-0.793896\pi\) | ||||
−0.797597 | + | 0.603190i | \(0.793896\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.99284 | 0.0102119 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 173.607 | 0.441748 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 765.284i | − | 1.92767i | −0.266506 | − | 0.963833i | \(-0.585869\pi\) | ||
0.266506 | − | 0.963833i | \(-0.414131\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −491.595 | + | 340.121i | −1.23207 | + | 0.852433i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 255.996i | 0.638393i | 0.947688 | + | 0.319197i | \(0.103413\pi\) | ||||
−0.947688 | + | 0.319197i | \(0.896587\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 86.3040i | − | 0.214154i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 228.796 | 0.562152 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 225.432i | − | 0.551179i | −0.961275 | − | 0.275589i | \(-0.911127\pi\) | ||
0.961275 | − | 0.275589i | \(-0.0888730\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 102.911i | − | 0.250392i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 153.960 | 0.372785 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −721.584 | −1.73042 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −314.462 | −0.750506 | −0.375253 | − | 0.926922i | \(-0.622444\pi\) | ||||
−0.375253 | + | 0.926922i | \(0.622444\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 354.990i | 0.843206i | 0.906781 | + | 0.421603i | \(0.138532\pi\) | ||||
−0.906781 | + | 0.421603i | \(0.861468\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 96.6129i | − | 0.228399i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 295.965i | − | 0.693127i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −396.602 | −0.924480 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 178.559i | − | 0.414290i | −0.978310 | − | 0.207145i | \(-0.933583\pi\) | ||
0.978310 | − | 0.207145i | \(-0.0664172\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.2858 | 0.0861104 | 0.0430552 | − | 0.999073i | \(-0.486291\pi\) | ||||
0.0430552 | + | 0.999073i | \(0.486291\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.8803 | − | 10.2953i | 0.0340511 | − | 0.0235590i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 365.662i | 0.832944i | 0.909149 | + | 0.416472i | \(0.136734\pi\) | ||||
−0.909149 | + | 0.416472i | \(0.863266\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −96.6269 | −0.219109 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 177.806i | 0.401367i | 0.979656 | + | 0.200684i | \(0.0643163\pi\) | ||||
−0.979656 | + | 0.200684i | \(0.935684\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −904.172 | −2.02276 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 204.290i | − | 0.454988i | −0.973780 | − | 0.227494i | \(-0.926947\pi\) | ||
0.973780 | − | 0.227494i | \(-0.0730532\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 700.586i | − | 1.55341i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 309.341i | 0.682871i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 229.796i | − | 0.502837i | −0.967879 | − | 0.251418i | \(-0.919103\pi\) | ||
0.967879 | − | 0.251418i | \(-0.0808970\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 90.0232i | − | 0.196129i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −249.439 | −0.541082 | −0.270541 | − | 0.962708i | \(-0.587203\pi\) | ||||
−0.270541 | + | 0.962708i | \(0.587203\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 907.359i | − | 1.95974i | −0.199639 | − | 0.979869i | \(-0.563977\pi\) | ||
0.199639 | − | 0.979869i | \(-0.436023\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 270.399i | − | 0.579013i | −0.957176 | − | 0.289507i | \(-0.906509\pi\) | ||
0.957176 | − | 0.289507i | \(-0.0934912\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 55.7821i | − | 0.118938i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 370.079i | − | 0.785730i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 663.270i | 1.40226i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −157.562 | −0.330318 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 221.920 | 0.463299 | 0.231649 | − | 0.972799i | \(-0.425588\pi\) | ||||
0.231649 | + | 0.972799i | \(0.425588\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 202.500 | 0.420997 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 29.9633 | 0.0620358 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −881.561 | −1.81019 | −0.905094 | − | 0.425212i | \(-0.860199\pi\) | ||||
−0.905094 | + | 0.425212i | \(0.860199\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 437.879i | − | 0.895458i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 91.7890 | 0.186943 | 0.0934715 | − | 0.995622i | \(-0.470204\pi\) | ||||
0.0934715 | + | 0.995622i | \(0.470204\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −39.5736 | −0.0802709 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1044.19 | −2.10098 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −471.959 | −0.945809 | −0.472905 | − | 0.881114i | \(-0.656795\pi\) | ||||
−0.472905 | + | 0.881114i | \(0.656795\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 492.933 | 0.983899 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 888.718i | 1.76684i | 0.468586 | + | 0.883418i | \(0.344763\pi\) | ||||
−0.468586 | + | 0.883418i | \(0.655237\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 227.813 | 0.449335 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 418.738i | 0.822669i | 0.911485 | + | 0.411334i | \(0.134937\pi\) | ||||
−0.911485 | + | 0.411334i | \(0.865063\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −256.904 | −0.502748 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −232.119 | − | 335.494i | −0.452473 | − | 0.653985i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 404.652i | − | 0.782692i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 997.023 | 1.92105 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 186.146i | 0.357285i | 0.983914 | + | 0.178643i | \(0.0571706\pi\) | ||||
−0.983914 | + | 0.178643i | \(0.942829\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −674.426 | −1.28953 | −0.644766 | − | 0.764380i | \(-0.723045\pi\) | ||||
−0.644766 | + | 0.764380i | \(0.723045\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −35.7424 | −0.0678223 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 528.093 | 0.998285 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 45.7712i | − | 0.0861981i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 620.066i | − | 1.16335i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 312.819i | 0.582531i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −404.710 | −0.750853 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −641.545 | −1.18585 | −0.592925 | − | 0.805258i | \(-0.702027\pi\) | ||||
−0.592925 | + | 0.805258i | \(0.702027\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 625.657i | 1.15222i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −183.171 | −0.334865 | −0.167432 | − | 0.985884i | \(-0.553548\pi\) | ||||
−0.167432 | + | 0.985884i | \(0.553548\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −87.9882 | −0.160270 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −147.481 | + | 102.038i | −0.267660 | + | 0.185187i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 604.161 | 1.09251 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 713.778i | − | 1.28147i | −0.767763 | − | 0.640734i | \(-0.778630\pi\) | ||
0.767763 | − | 0.640734i | \(-0.221370\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 587.039i | 1.05016i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 164.251i | 0.292782i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 316.069 | 0.561401 | 0.280700 | − | 0.959795i | \(-0.409433\pi\) | ||||
0.280700 | + | 0.959795i | \(0.409433\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 901.333i | − | 1.58965i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 883.884i | 1.55340i | 0.629871 | + | 0.776699i | \(0.283108\pi\) | ||||
−0.629871 | + | 0.776699i | \(0.716892\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 168.849 | 0.295708 | 0.147854 | − | 0.989009i | \(-0.452763\pi\) | ||||
0.147854 | + | 0.989009i | \(0.452763\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1227.56 | −2.14233 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 380.352i | 0.659188i | 0.944123 | + | 0.329594i | \(0.106912\pi\) | ||||
−0.944123 | + | 0.329594i | \(0.893088\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −451.344 | −0.779524 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 553.326 | 0.952368 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −659.929 | −1.13195 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 123.630i | 0.210613i | 0.994440 | + | 0.105306i | \(0.0335823\pi\) | ||||
−0.994440 | + | 0.105306i | \(0.966418\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −133.203 | + | 92.1593i | −0.226151 | + | 0.156467i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 123.012i | − | 0.208142i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 191.622i | − | 0.323141i | −0.986861 | − | 0.161570i | \(-0.948344\pi\) | ||
0.986861 | − | 0.161570i | \(-0.0516559\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 416.972 | 0.698446 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 277.360i | − | 0.463038i | −0.972830 | − | 0.231519i | \(-0.925630\pi\) | ||
0.972830 | − | 0.231519i | \(-0.0743695\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 603.631i | 1.00438i | 0.864758 | + | 0.502188i | \(0.167472\pi\) | ||||
−0.864758 | + | 0.502188i | \(0.832528\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.5836 | −0.0275018 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1035.05 | 1.70519 | 0.852597 | − | 0.522568i | \(-0.175026\pi\) | ||||
0.852597 | + | 0.522568i | \(0.175026\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −296.970 | −0.487635 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 358.144i | − | 0.586160i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 965.052i | − | 1.57431i | −0.616756 | − | 0.787155i | \(-0.711553\pi\) | ||
0.616756 | − | 0.787155i | \(-0.288447\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 967.261i | − | 1.56768i | −0.620960 | − | 0.783842i | \(-0.713257\pi\) | ||
0.620960 | − | 0.783842i | \(-0.286743\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −995.539 | −1.60830 | −0.804151 | − | 0.594425i | \(-0.797380\pi\) | ||||
−0.804151 | + | 0.594425i | \(0.797380\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.4487i | 0.0329287i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 900.091 | 1.44477 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 423.510 | + | 612.122i | 0.675454 | + | 0.976271i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 83.8643i | − | 0.133330i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 689.387 | 1.09253 | 0.546266 | − | 0.837612i | \(-0.316049\pi\) | ||||
0.546266 | + | 0.837612i | \(0.316049\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 934.922i | − | 1.47697i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −358.196 | −0.562317 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 310.429i | 0.485804i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 732.715i | − | 1.14308i | −0.820574 | − | 0.571540i | \(-0.806346\pi\) | ||
0.820574 | − | 0.571540i | \(-0.193654\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 509.087i | 0.791738i | 0.918307 | + | 0.395869i | \(0.129557\pi\) | ||||
−0.918307 | + | 0.395869i | \(0.870443\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1046.09i | 1.61683i | 0.588611 | + | 0.808416i | \(0.299675\pi\) | ||||
−0.588611 | + | 0.808416i | \(0.700325\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 191.707i | − | 0.295389i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −268.220 | −0.412012 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 351.804i | − | 0.538750i | −0.963035 | − | 0.269375i | \(-0.913183\pi\) | ||
0.963035 | − | 0.269375i | \(-0.0868171\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 76.3757i | 0.116249i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1238.23i | 1.87895i | 0.342621 | + | 0.939474i | \(0.388685\pi\) | ||||
−0.342621 | + | 0.939474i | \(0.611315\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 414.630i | − | 0.627277i | −0.949542 | − | 0.313638i | \(-0.898452\pi\) | ||
0.949542 | − | 0.313638i | \(-0.101548\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 145.373i | 0.219265i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.98912 | 0.0134769 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −278.055 | −0.415627 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −368.528 | −0.549222 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1163.57 | −1.72892 | −0.864462 | − | 0.502698i | \(-0.832341\pi\) | ||||
−0.864462 | + | 0.502698i | \(0.832341\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −71.7621 | −0.106000 | −0.0530001 | − | 0.998595i | \(-0.516878\pi\) | ||||
−0.0530001 | + | 0.998595i | \(0.516878\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 845.345i | 1.24499i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1155.16 | −1.69627 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 558.227 | 0.817316 | 0.408658 | − | 0.912688i | \(-0.365997\pi\) | ||||
0.408658 | + | 0.912688i | \(0.365997\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −824.816 | −1.20061 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −584.081 | −0.847723 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 310.776 | 0.449748 | 0.224874 | − | 0.974388i | \(-0.427803\pi\) | ||||
0.224874 | + | 0.974388i | \(0.427803\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 286.941i | 0.414056i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −256.797 | −0.368432 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 467.607i | 0.668965i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 940.642 | 1.34186 | 0.670929 | − | 0.741522i | \(-0.265896\pi\) | ||||
0.670929 | + | 0.741522i | \(0.265896\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −216.238 | − | 312.541i | −0.307594 | − | 0.444582i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 594.985i | 0.841563i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 780.564 | 1.10094 | 0.550468 | − | 0.834856i | \(-0.314449\pi\) | ||||
0.550468 | + | 0.834856i | \(0.314449\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 179.612i | − | 0.252620i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.11886 | 0.0113869 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1098.53 | −1.53212 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 606.339 | 0.843308 | 0.421654 | − | 0.906757i | \(-0.361450\pi\) | ||||
0.421654 | + | 0.906757i | \(0.361450\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1876.02i | 2.60197i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 1229.72i | − | 1.70086i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 266.418i | 0.366463i | 0.983070 | + | 0.183231i | \(0.0586557\pi\) | ||||
−0.983070 | + | 0.183231i | \(0.941344\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 393.919 | 0.540355 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 243.119 | 0.332584 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 951.526i | − | 1.29813i | −0.760735 | − | 0.649063i | \(-0.775161\pi\) | ||
0.760735 | − | 0.649063i | \(-0.224839\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −69.4584 | −0.0942448 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −504.613 | −0.682832 | −0.341416 | − | 0.939912i | \(-0.610906\pi\) | ||||
−0.341416 | + | 0.939912i | \(0.610906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 374.835 | + | 541.769i | 0.505850 | + | 0.731133i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1081.91 | 1.45613 | 0.728067 | − | 0.685506i | \(-0.240419\pi\) | ||||
0.728067 | + | 0.685506i | \(0.240419\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 164.500i | − | 0.220214i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1870.03i | 2.49670i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 873.565i | − | 1.16320i | −0.813474 | − | 0.581601i | \(-0.802426\pi\) | ||
0.813474 | − | 0.581601i | \(-0.197574\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −355.472 | −0.472074 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 264.661i | − | 0.349619i | −0.984602 | − | 0.174809i | \(-0.944069\pi\) | ||
0.984602 | − | 0.174809i | \(-0.0559309\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 37.3095i | − | 0.0491561i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 681.093 | 0.894998 | 0.447499 | − | 0.894284i | \(-0.352315\pi\) | ||||
0.447499 | + | 0.894284i | \(0.352315\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 585.085 | 0.766822 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 169.674i | − | 0.221218i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 962.529 | 1.25166 | 0.625832 | − | 0.779958i | \(-0.284760\pi\) | ||||
0.625832 | + | 0.779958i | \(0.284760\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −193.723 | −0.251262 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.0726 | −0.0350227 | −0.0175114 | − | 0.999847i | \(-0.505574\pi\) | ||||
−0.0175114 | + | 0.999847i | \(0.505574\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 629.338i | − | 0.809959i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −957.019 | + | 662.134i | −1.22852 | + | 0.849980i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1300.19i | 1.66478i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 202.670i | − | 0.258838i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −49.7504 | −0.0632152 | −0.0316076 | − | 0.999500i | \(-0.510063\pi\) | ||||
−0.0316076 | + | 0.999500i | \(0.510063\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 960.771i | 1.21771i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 18.4770i | − | 0.0233590i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −326.172 | −0.411314 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 221.385 | 0.277773 | 0.138886 | − | 0.990308i | \(-0.455648\pi\) | ||||
0.138886 | + | 0.990308i | \(0.455648\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −148.324 | −0.185636 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 267.590i | − | 0.334070i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 319.890i | 0.398369i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 349.889i | − | 0.433568i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 933.918 | 1.15441 | 0.577205 | − | 0.816599i | \(-0.304143\pi\) | ||||
0.577205 | + | 0.816599i | \(0.304143\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1390.98i | − | 1.71514i | −0.514364 | − | 0.857572i | \(-0.671972\pi\) | ||
0.514364 | − | 0.857572i | \(-0.328028\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1630.71 | −2.00580 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 906.045 | − | 626.867i | 1.10899 | − | 0.767279i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 253.962i | 0.310088i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1066.11 | 1.29855 | 0.649275 | − | 0.760553i | \(-0.275072\pi\) | ||||
0.649275 | + | 0.760553i | \(0.275072\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 495.548i | − | 0.602124i | −0.953605 | − | 0.301062i | \(-0.902659\pi\) | ||
0.953605 | − | 0.301062i | \(-0.0973411\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1036.35 | −1.25314 | −0.626571 | − | 0.779365i | \(-0.715542\pi\) | ||||
−0.626571 | + | 0.779365i | \(0.715542\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 355.400i | − | 0.428710i | −0.976756 | − | 0.214355i | \(-0.931235\pi\) | ||
0.976756 | − | 0.214355i | \(-0.0687649\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 904.453i | − | 1.08839i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 148.345i | 0.178085i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 183.049i | − | 0.218697i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 429.992i | − | 0.512505i | −0.966610 | − | 0.256253i | \(-0.917512\pi\) | ||
0.966610 | − | 0.256253i | \(-0.0824879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 751.908 | 0.894064 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 830.391i | 0.985043i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 90.3120i | 0.106626i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 929.983i | − | 1.09539i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.0497i | 0.0223851i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 557.873i | − | 0.654013i | −0.945022 | − | 0.327007i | \(-0.893960\pi\) | ||
0.945022 | − | 0.327007i | \(-0.106040\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 813.712 | 0.949489 | 0.474745 | − | 0.880124i | \(-0.342540\pi\) | ||||
0.474745 | + | 0.880124i | \(0.342540\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 368.216 | 0.428657 | 0.214328 | − | 0.976762i | \(-0.431244\pi\) | ||||
0.214328 | + | 0.976762i | \(0.431244\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1927.07 | −2.23818 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 963.303 | 1.11623 | 0.558113 | − | 0.829765i | \(-0.311526\pi\) | ||||
0.558113 | + | 0.829765i | \(0.311526\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −929.632 | −1.07224 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 752.285i | − | 0.865691i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −61.4754 | −0.0705802 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 251.315 | 0.287875 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −938.800 | −1.07047 | −0.535234 | − | 0.844704i | \(-0.679777\pi\) | ||||
−0.535234 | + | 0.844704i | \(0.679777\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 645.604 | 0.734476 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 417.023 | 0.473352 | 0.236676 | − | 0.971589i | \(-0.423942\pi\) | ||||
0.236676 | + | 0.971589i | \(0.423942\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 326.997i | 0.370325i | 0.982708 | + | 0.185163i | \(0.0592812\pi\) | ||||
−0.982708 | + | 0.185163i | \(0.940719\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 366.885 | 0.413624 | 0.206812 | − | 0.978381i | \(-0.433691\pi\) | ||||
0.206812 | + | 0.978381i | \(0.433691\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 383.780i | − | 0.431699i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1122.32 | −1.25961 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −552.765 | + | 382.442i | −0.618998 | + | 0.428267i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 33.0214i | − | 0.0368132i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −80.4671 | −0.0895073 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 241.894i | 0.268473i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1824.43 | 2.02041 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −948.571 | −1.04583 | −0.522917 | − | 0.852384i | \(-0.675156\pi\) | ||||
−0.522917 | + | 0.852384i | \(0.675156\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 176.885 | 0.194592 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1288.33i | 1.41419i | 0.707118 | + | 0.707096i | \(0.249995\pi\) | ||||
−0.707118 | + | 0.707096i | \(0.750005\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 688.987i | − | 0.754641i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 465.615i | − | 0.507759i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.3298 | 0.0221216 | 0.0110608 | − | 0.999939i | \(-0.496479\pi\) | ||||
0.0110608 | + | 0.999939i | \(0.496479\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −899.573 | −0.976735 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1150.76i | 1.24676i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 557.727 | 0.601648 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 356.003 | 0.383210 | 0.191605 | − | 0.981472i | \(-0.438631\pi\) | ||||
0.191605 | + | 0.981472i | \(0.438631\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 382.498 | + | 552.845i | 0.410846 | + | 0.593819i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1206.76 | −1.29342 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 822.306i | − | 0.877595i | −0.898586 | − | 0.438797i | \(-0.855405\pi\) | ||
0.898586 | − | 0.438797i | \(-0.144595\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 1657.60i | − | 1.76528i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1734.01i | − | 1.84273i | −0.388699 | − | 0.921365i | \(-0.627075\pi\) | ||
0.388699 | − | 0.921365i | \(-0.372925\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 58.3314 | 0.0618572 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1226.54i | − | 1.29518i | −0.761988 | − | 0.647591i | \(-0.775777\pi\) | ||
0.761988 | − | 0.647591i | \(-0.224223\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 283.125i | 0.298340i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −275.032 | −0.289203 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1329.78 | 1.39537 | 0.697683 | − | 0.716406i | \(-0.254214\pi\) | ||||
0.697683 | + | 0.716406i | \(0.254214\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 369.779i | 0.386394i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −276.009 | −0.287809 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 888.323 | 0.924374 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 555.946 | 0.577307 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1006.28i | 1.04062i | 0.853978 | + | 0.520309i | \(0.174183\pi\) | ||||
−0.853978 | + | 0.520309i | \(0.825817\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 224.371 | − | 155.236i | 0.231549 | − | 0.160202i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1521.07i | 1.56650i | 0.621710 | + | 0.783248i | \(0.286438\pi\) | ||||
−0.621710 | + | 0.783248i | \(0.713562\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1935.29i | 1.98900i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 750.278 | 0.767940 | 0.383970 | − | 0.923346i | \(-0.374557\pi\) | ||||
0.383970 | + | 0.923346i | \(0.374557\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1120.77i | − | 1.14481i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 173.941i | − | 0.177310i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 603.980 | 0.614425 | 0.307213 | − | 0.951641i | \(-0.400604\pi\) | ||||
0.307213 | + | 0.951641i | \(0.400604\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1113.06 | −1.12772 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −55.2244 | −0.0558386 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1522.67i | − | 1.53650i | −0.640152 | − | 0.768248i | \(-0.721129\pi\) | ||
0.640152 | − | 0.768248i | \(-0.278871\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 1999.00i | − | 2.01309i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1616.79i | 1.62165i | 0.585285 | + | 0.810827i | \(0.300982\pi\) | ||||
−0.585285 | + | 0.810827i | \(0.699018\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 429.498 | 0.429928 |
(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 | 1900.3.g.c.949.5 | 24 | ||
5.2 | odd | 4 | 1900.3.e.f.1101.10 | 12 | |||
5.3 | odd | 4 | 380.3.e.a.341.3 | ✓ | 12 | ||
5.4 | even | 2 | inner | 1900.3.g.c.949.20 | 24 | ||
15.8 | even | 4 | 3420.3.o.a.721.6 | 12 | |||
19.18 | odd | 2 | inner | 1900.3.g.c.949.19 | 24 | ||
20.3 | even | 4 | 1520.3.h.b.721.10 | 12 | |||
95.18 | even | 4 | 380.3.e.a.341.10 | yes | 12 | ||
95.37 | even | 4 | 1900.3.e.f.1101.3 | 12 | |||
95.94 | odd | 2 | inner | 1900.3.g.c.949.6 | 24 | ||
285.113 | odd | 4 | 3420.3.o.a.721.5 | 12 | |||
380.303 | odd | 4 | 1520.3.h.b.721.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.3.e.a.341.3 | ✓ | 12 | 5.3 | odd | 4 | ||
380.3.e.a.341.10 | yes | 12 | 95.18 | even | 4 | ||
1520.3.h.b.721.3 | 12 | 380.303 | odd | 4 | |||
1520.3.h.b.721.10 | 12 | 20.3 | even | 4 | |||
1900.3.e.f.1101.3 | 12 | 95.37 | even | 4 | |||
1900.3.e.f.1101.10 | 12 | 5.2 | odd | 4 | |||
1900.3.g.c.949.5 | 24 | 1.1 | even | 1 | trivial | ||
1900.3.g.c.949.6 | 24 | 95.94 | odd | 2 | inner | ||
1900.3.g.c.949.19 | 24 | 19.18 | odd | 2 | inner | ||
1900.3.g.c.949.20 | 24 | 5.4 | even | 2 | inner | ||
3420.3.o.a.721.5 | 12 | 285.113 | odd | 4 | |||
3420.3.o.a.721.6 | 12 | 15.8 | even | 4 |