Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1296,3,Mod(593,1296)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1296, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1296.593");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1296 = 2^{4} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1296.q (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(35.3134422611\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{8} \) |
Twist minimal: | no (minimal twist has level 162) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 593.3 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1296.593 |
Dual form | 1296.3.q.o.1025.3 |
$q$-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 \(\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.34486 | − | 0.776457i | 0.268973 | − | 0.155291i | −0.359448 | − | 0.933165i | \(-0.617035\pi\) |
0.628421 | + | 0.777874i | \(0.283702\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.19615 | − | 10.7321i | 0.885165 | − | 1.53315i | 0.0396398 | − | 0.999214i | \(-0.487379\pi\) |
0.845525 | − | 0.533936i | \(-0.179288\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.7279 | + | 7.34847i | 1.15708 | + | 0.668043i | 0.950603 | − | 0.310408i | \(-0.100466\pi\) |
0.206480 | + | 0.978451i | \(0.433799\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.40192 | + | 9.35641i | 0.415533 | + | 0.719724i | 0.995484 | − | 0.0949274i | \(-0.0302619\pi\) |
−0.579952 | + | 0.814651i | \(0.696929\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 28.9778i | 1.70457i | 0.523074 | + | 0.852287i | \(0.324785\pi\) | ||||
−0.523074 | + | 0.852287i | \(0.675215\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.60770 | −0.189879 | −0.0949393 | − | 0.995483i | \(-0.530266\pi\) | ||||
−0.0949393 | + | 0.995483i | \(0.530266\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 12.7279 | − | 7.34847i | 0.553388 | − | 0.319499i | −0.197099 | − | 0.980384i | \(-0.563152\pi\) |
0.750487 | + | 0.660885i | \(0.229819\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.2942 | + | 19.5622i | −0.451769 | + | 0.782487i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 24.3748 | + | 14.0728i | 0.840510 | + | 0.485268i | 0.857437 | − | 0.514588i | \(-0.172055\pi\) |
−0.0169278 | + | 0.999857i | \(0.505389\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | + | 6.92820i | 0.129032 | + | 0.223490i | 0.923302 | − | 0.384075i | \(-0.125480\pi\) |
−0.794270 | + | 0.607565i | \(0.792146\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 19.2442i | − | 0.549834i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 22.5692 | 0.609979 | 0.304989 | − | 0.952356i | \(-0.401347\pi\) | ||||
0.304989 | + | 0.952356i | \(0.401347\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −21.7816 | + | 12.5756i | −0.531259 | + | 0.306722i | −0.741529 | − | 0.670921i | \(-0.765899\pi\) |
0.210270 | + | 0.977643i | \(0.432566\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −26.5885 | + | 46.0526i | −0.618336 | + | 1.07099i | 0.371453 | + | 0.928452i | \(0.378860\pi\) |
−0.989789 | + | 0.142538i | \(0.954474\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 14.6969 | + | 8.48528i | 0.312701 | + | 0.180538i | 0.648134 | − | 0.761526i | \(-0.275549\pi\) |
−0.335434 | + | 0.942064i | \(0.608883\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −52.2846 | − | 90.5596i | −1.06703 | − | 1.84816i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 84.5482i | − | 1.59525i | −0.603154 | − | 0.797625i | \(-0.706090\pi\) | ||
0.603154 | − | 0.797625i | \(-0.293910\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 22.8231 | 0.414965 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 78.8641 | − | 45.5322i | 1.33668 | − | 0.771733i | 0.350367 | − | 0.936613i | \(-0.386057\pi\) |
0.986314 | + | 0.164880i | \(0.0527236\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | − | 11.2583i | 0.106557 | − | 0.184563i | −0.807816 | − | 0.589435i | \(-0.799351\pi\) |
0.914373 | + | 0.404872i | \(0.132684\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.5297 | + | 8.38872i | 0.223534 | + | 0.129057i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −20.5885 | − | 35.6603i | −0.307290 | − | 0.532243i | 0.670478 | − | 0.741929i | \(-0.266089\pi\) |
−0.977769 | + | 0.209687i | \(0.932756\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.3613i | 0.230442i | 0.993340 | + | 0.115221i | \(0.0367575\pi\) | ||||
−0.993340 | + | 0.115221i | \(0.963242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 71.5885 | 0.980664 | 0.490332 | − | 0.871536i | \(-0.336876\pi\) | ||||
0.490332 | + | 0.871536i | \(0.336876\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 157.728 | − | 91.0645i | 2.04842 | − | 1.18266i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −23.3731 | + | 40.4833i | −0.295862 | + | 0.512447i | −0.975185 | − | 0.221392i | \(-0.928940\pi\) |
0.679323 | + | 0.733839i | \(0.262273\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.2555 | − | 7.65308i | −0.159705 | − | 0.0922057i | 0.418017 | − | 0.908439i | \(-0.362725\pi\) |
−0.577723 | + | 0.816233i | \(0.696058\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.5000 | + | 38.9711i | 0.264706 | + | 0.458484i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 78.9756i | 0.887367i | 0.896184 | + | 0.443683i | \(0.146329\pi\) | ||||
−0.896184 | + | 0.443683i | \(0.853671\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 133.885 | 1.47126 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.85186 | + | 2.80122i | −0.0510722 | + | 0.0294865i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −45.5692 | + | 78.9282i | −0.469786 | + | 0.813693i | −0.999403 | − | 0.0345438i | \(-0.989002\pi\) |
0.529617 | + | 0.848237i | \(0.322336\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 76.6313 | + | 44.2431i | 0.758726 | + | 0.438051i | 0.828838 | − | 0.559488i | \(-0.189002\pi\) |
−0.0701121 | + | 0.997539i | \(0.522336\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −76.3538 | − | 132.249i | −0.741299 | − | 1.28397i | −0.951904 | − | 0.306397i | \(-0.900877\pi\) |
0.210605 | − | 0.977571i | \(-0.432457\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 60.0062i | 0.560805i | 0.959882 | + | 0.280403i | \(0.0904680\pi\) | ||||
−0.959882 | + | 0.280403i | \(0.909532\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −93.9423 | −0.861856 | −0.430928 | − | 0.902386i | \(-0.641814\pi\) | ||||
−0.430928 | + | 0.902386i | \(0.641814\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 76.7279 | − | 44.2989i | 0.679008 | − | 0.392025i | −0.120473 | − | 0.992717i | \(-0.538441\pi\) |
0.799481 | + | 0.600691i | \(0.205108\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.4115 | − | 19.7654i | 0.0992308 | − | 0.171873i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 310.991 | + | 179.551i | 2.61337 | + | 1.50883i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 47.5000 | + | 82.2724i | 0.392562 | + | 0.679937i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 73.9008i | 0.591206i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −78.8231 | −0.620654 | −0.310327 | − | 0.950630i | \(-0.600439\pi\) | ||||
−0.310327 | + | 0.950630i | \(0.600439\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −71.5157 | + | 41.2896i | −0.545921 | + | 0.315188i | −0.747475 | − | 0.664290i | \(-0.768734\pi\) |
0.201554 | + | 0.979477i | \(0.435401\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −22.3538 | + | 38.7180i | −0.168074 | + | 0.291113i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 185.970 | + | 107.370i | 1.35745 | + | 0.783723i | 0.989279 | − | 0.146036i | \(-0.0466515\pi\) |
0.368169 | + | 0.929759i | \(0.379985\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −30.3923 | − | 52.6410i | −0.218650 | − | 0.378712i | 0.735746 | − | 0.677258i | \(-0.236832\pi\) |
−0.954395 | + | 0.298546i | \(0.903499\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 158.783i | 1.11037i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 43.7077 | 0.301432 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 26.5369 | − | 15.3211i | 0.178100 | − | 0.102826i | −0.408300 | − | 0.912848i | \(-0.633878\pi\) |
0.586400 | + | 0.810022i | \(0.300545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0000 | − | 27.7128i | 0.105960 | − | 0.183529i | −0.808170 | − | 0.588949i | \(-0.799542\pi\) |
0.914130 | + | 0.405421i | \(0.132875\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.7589 | + | 6.21166i | 0.0694123 | + | 0.0400752i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −124.854 | − | 216.253i | −0.795247 | − | 1.37741i | −0.922682 | − | 0.385562i | \(-0.874008\pi\) |
0.127435 | − | 0.991847i | \(-0.459326\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 182.129i | − | 1.13124i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.7846 | 0.0784332 | 0.0392166 | − | 0.999231i | \(-0.487514\pi\) | ||||
0.0392166 | + | 0.999231i | \(0.487514\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 201.292 | − | 116.216i | 1.20534 | − | 0.695902i | 0.243601 | − | 0.969876i | \(-0.421671\pi\) |
0.961737 | + | 0.273973i | \(0.0883379\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.1384 | − | 45.2731i | 0.154665 | − | 0.267888i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.6608 | + | 10.7738i | 0.107866 | + | 0.0622765i | 0.552963 | − | 0.833206i | \(-0.313497\pi\) |
−0.445096 | + | 0.895483i | \(0.646831\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 139.962 | + | 242.420i | 0.799780 | + | 1.38526i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 277.741i | − | 1.55162i | −0.630964 | − | 0.775812i | \(-0.717341\pi\) | ||
0.630964 | − | 0.775812i | \(-0.282659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 174.277 | 0.962856 | 0.481428 | − | 0.876486i | \(-0.340118\pi\) | ||||
0.481428 | + | 0.876486i | \(0.340118\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 30.3525 | − | 17.5240i | 0.164068 | − | 0.0947245i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −212.942 | + | 368.827i | −1.13873 | + | 1.97234i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −131.745 | − | 76.0629i | −0.689764 | − | 0.398235i | 0.113760 | − | 0.993508i | \(-0.463711\pi\) |
−0.803523 | + | 0.595273i | \(0.797044\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27.5000 | + | 47.6314i | 0.142487 | + | 0.246795i | 0.928433 | − | 0.371501i | \(-0.121157\pi\) |
−0.785946 | + | 0.618296i | \(0.787823\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 133.298i | 0.676638i | 0.941031 | + | 0.338319i | \(0.109858\pi\) | ||||
−0.941031 | + | 0.338319i | \(0.890142\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 208.862 | 1.04956 | 0.524778 | − | 0.851239i | \(-0.324148\pi\) | ||||
0.524778 | + | 0.851239i | \(0.324148\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 302.060 | − | 174.394i | 1.48798 | − | 0.859085i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.5289 | + | 33.8250i | −0.0952627 | + | 0.165000i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −45.9185 | − | 26.5110i | −0.219706 | − | 0.126847i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −43.7269 | − | 75.7372i | −0.207236 | − | 0.358944i | 0.743607 | − | 0.668617i | \(-0.233114\pi\) |
−0.950843 | + | 0.309673i | \(0.899780\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 82.5792i | 0.384089i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 99.1384 | 0.456859 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −271.128 | + | 156.536i | −1.22682 | + | 0.708306i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 111.296 | − | 192.771i | 0.499086 | − | 0.864442i | −0.500914 | − | 0.865497i | \(-0.667003\pi\) |
0.999999 | + | 0.00105540i | \(0.000335944\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −260.079 | − | 150.157i | −1.14572 | − | 0.661484i | −0.197882 | − | 0.980226i | \(-0.563406\pi\) |
−0.947842 | + | 0.318742i | \(0.896740\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −114.971 | − | 199.136i | −0.502057 | − | 0.869589i | −0.999997 | − | 0.00237731i | \(-0.999243\pi\) |
0.497940 | − | 0.867212i | \(-0.334090\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 116.246i | − | 0.498908i | −0.968387 | − | 0.249454i | \(-0.919749\pi\) | ||
0.968387 | − | 0.249454i | \(-0.0802512\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 26.3538 | 0.112144 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −142.362 | + | 82.1930i | −0.595659 | + | 0.343904i | −0.767332 | − | 0.641250i | \(-0.778416\pi\) |
0.171673 | + | 0.985154i | \(0.445083\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 40.6558 | − | 70.4179i | 0.168696 | − | 0.292190i | −0.769265 | − | 0.638929i | \(-0.779378\pi\) |
0.937962 | + | 0.346739i | \(0.112711\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −140.631 | − | 81.1935i | −0.574005 | − | 0.331402i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.4885 | − | 33.7551i | −0.0789008 | − | 0.136660i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 396.371i | − | 1.57917i | −0.613642 | − | 0.789584i | \(-0.710296\pi\) | ||
0.613642 | − | 0.789584i | \(-0.289704\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 216.000 | 0.853755 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 186.164 | − | 107.482i | 0.724372 | − | 0.418216i | −0.0919879 | − | 0.995760i | \(-0.529322\pi\) |
0.816360 | + | 0.577544i | \(0.195989\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 139.842 | − | 242.214i | 0.539932 | − | 0.935189i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 275.304 | + | 158.947i | 1.04678 | + | 0.604360i | 0.921747 | − | 0.387792i | \(-0.126762\pi\) |
0.125036 | + | 0.992152i | \(0.460095\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −65.6481 | − | 113.706i | −0.247729 | − | 0.429078i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 208.528i | 0.775199i | 0.921828 | + | 0.387599i | \(0.126696\pi\) | ||||
−0.921828 | + | 0.387599i | \(0.873304\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −409.885 | −1.51249 | −0.756245 | − | 0.654289i | \(-0.772968\pi\) | ||||
−0.756245 | + | 0.654289i | \(0.772968\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −287.504 | + | 165.991i | −1.04547 | + | 0.603602i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −248.708 | + | 430.774i | −0.897862 | + | 1.55514i | −0.0676390 | + | 0.997710i | \(0.521547\pi\) |
−0.830223 | + | 0.557432i | \(0.811787\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −186.427 | − | 107.634i | −0.663442 | − | 0.383039i | 0.130145 | − | 0.991495i | \(-0.458456\pi\) |
−0.793587 | + | 0.608456i | \(0.791789\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −148.354 | − | 256.956i | −0.524218 | − | 0.907973i | −0.999602 | − | 0.0281946i | \(-0.991024\pi\) |
0.475384 | − | 0.879778i | \(-0.342309\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 311.682i | 1.08600i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −550.711 | −1.90558 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −295.284 | + | 170.482i | −1.00779 | + | 0.581850i | −0.910545 | − | 0.413410i | \(-0.864338\pi\) |
−0.0972490 | + | 0.995260i | \(0.531004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 70.7077 | − | 122.469i | 0.239687 | − | 0.415150i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 137.511 | + | 79.3917i | 0.459901 | + | 0.265524i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 329.492 | + | 570.697i | 1.09466 | + | 1.89600i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 20.1879i | − | 0.0661898i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 114.354 | 0.372488 | 0.186244 | − | 0.982504i | \(-0.440368\pi\) | ||||
0.186244 | + | 0.982504i | \(0.440368\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −169.929 | + | 98.1083i | −0.546394 | + | 0.315461i | −0.747666 | − | 0.664074i | \(-0.768826\pi\) |
0.201272 | + | 0.979535i | \(0.435492\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 73.3616 | − | 127.066i | 0.234382 | − | 0.405962i | −0.724711 | − | 0.689053i | \(-0.758027\pi\) |
0.959093 | + | 0.283092i | \(0.0913600\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 41.6908 | + | 24.0702i | 0.131517 | + | 0.0759311i | 0.564315 | − | 0.825560i | \(-0.309140\pi\) |
−0.432798 | + | 0.901491i | \(0.642474\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 206.827 | + | 358.235i | 0.648360 | + | 1.12299i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 104.543i | − | 0.323662i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −244.042 | −0.750899 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 182.129 | − | 105.152i | 0.553583 | − | 0.319612i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −49.7269 | + | 86.1295i | −0.150232 | + | 0.260210i | −0.931313 | − | 0.364220i | \(-0.881335\pi\) |
0.781080 | + | 0.624430i | \(0.214669\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −55.3773 | − | 31.9721i | −0.165305 | − | 0.0954391i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 212.631 | + | 368.287i | 0.630952 | + | 1.09284i | 0.987358 | + | 0.158509i | \(0.0506687\pi\) |
−0.356406 | + | 0.934331i | \(0.615998\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 117.576i | 0.344796i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −688.631 | −2.00767 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 33.5768 | − | 19.3856i | 0.0967630 | − | 0.0558662i | −0.450838 | − | 0.892606i | \(-0.648875\pi\) |
0.547601 | + | 0.836740i | \(0.315541\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 325.985 | − | 564.622i | 0.934053 | − | 1.61783i | 0.157739 | − | 0.987481i | \(-0.449579\pi\) |
0.776314 | − | 0.630347i | \(-0.217087\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.03625 | + | 0.598281i | 0.00293556 | + | 0.00169485i | 0.501467 | − | 0.865177i | \(-0.332794\pi\) |
−0.498532 | + | 0.866872i | \(0.666127\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.7039 | + | 22.0038i | 0.0357856 | + | 0.0619825i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 534.573i | 1.48906i | 0.667589 | + | 0.744530i | \(0.267326\pi\) | ||||
−0.667589 | + | 0.744530i | \(0.732674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −347.985 | −0.963946 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 96.2767 | − | 55.5854i | 0.263772 | − | 0.152289i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 132.354 | − | 229.244i | 0.360637 | − | 0.624642i | −0.627429 | − | 0.778674i | \(-0.715893\pi\) |
0.988066 | + | 0.154032i | \(0.0492259\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −907.376 | − | 523.874i | −2.44576 | − | 1.41206i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.5077 | − | 61.5012i | −0.0951950 | − | 0.164883i | 0.814495 | − | 0.580171i | \(-0.197014\pi\) |
−0.909690 | + | 0.415288i | \(0.863681\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 304.080i | 0.806579i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 696.785 | 1.83848 | 0.919241 | − | 0.393696i | \(-0.128804\pi\) | ||||
0.919241 | + | 0.393696i | \(0.128804\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −376.986 | + | 217.653i | −0.984297 | + | 0.568284i | −0.903565 | − | 0.428452i | \(-0.859059\pi\) |
−0.0807324 | + | 0.996736i | \(0.525726\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 141.415 | − | 244.939i | 0.367313 | − | 0.636204i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 45.9374 | + | 26.5220i | 0.118091 | + | 0.0681799i | 0.557882 | − | 0.829920i | \(-0.311614\pi\) |
−0.439791 | + | 0.898100i | \(0.644947\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 212.942 | + | 368.827i | 0.544609 | + | 0.943291i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 72.5927i | 0.183779i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 63.7077 | 0.160473 | 0.0802363 | − | 0.996776i | \(-0.474432\pi\) | ||||
0.0802363 | + | 0.996776i | \(0.474432\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −544.463 | + | 314.346i | −1.35776 | + | 0.783904i | −0.989322 | − | 0.145747i | \(-0.953441\pi\) |
−0.368440 | + | 0.929651i | \(0.620108\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −43.2154 | + | 74.8513i | −0.107234 | + | 0.185735i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 287.259 | + | 165.849i | 0.705797 | + | 0.407492i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −267.640 | − | 463.567i | −0.654377 | − | 1.13341i | −0.982050 | − | 0.188623i | \(-0.939597\pi\) |
0.327672 | − | 0.944791i | \(-0.393736\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1128.50i | − | 2.73244i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −23.7691 | −0.0572750 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −333.705 | + | 192.665i | −0.796433 | + | 0.459821i | −0.842222 | − | 0.539130i | \(-0.818753\pi\) |
0.0457895 | + | 0.998951i | \(0.485420\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 377.660 | − | 654.126i | 0.897054 | − | 1.55374i | 0.0658113 | − | 0.997832i | \(-0.479036\pi\) |
0.831242 | − | 0.555910i | \(-0.187630\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −566.868 | − | 327.282i | −1.33381 | − | 0.770074i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −80.5500 | − | 139.517i | −0.188642 | − | 0.326737i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 107.709i | 0.249904i | 0.992163 | + | 0.124952i | \(0.0398777\pi\) | ||||
−0.992163 | + | 0.124952i | \(0.960122\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 655.123 | 1.51299 | 0.756493 | − | 0.654002i | \(-0.226911\pi\) | ||||
0.756493 | + | 0.654002i | \(0.226911\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −45.9185 | + | 26.5110i | −0.105077 | + | 0.0606660i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −236.000 | + | 408.764i | −0.537585 | + | 0.931125i | 0.461448 | + | 0.887167i | \(0.347330\pi\) |
−0.999033 | + | 0.0439580i | \(0.986003\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −728.516 | − | 420.609i | −1.64451 | − | 0.949455i | −0.979203 | − | 0.202881i | \(-0.934970\pi\) |
−0.665302 | − | 0.746575i | \(-0.731697\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 61.3212 | + | 106.211i | 0.137800 | + | 0.238677i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 382.751i | − | 0.852453i | −0.904616 | − | 0.426227i | \(-0.859843\pi\) | ||
0.904616 | − | 0.426227i | \(-0.140157\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −369.646 | −0.819615 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 180.056 | − | 103.956i | 0.395728 | − | 0.228474i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −161.852 | + | 280.336i | −0.354162 | + | 0.613426i | −0.986974 | − | 0.160879i | \(-0.948567\pi\) |
0.632812 | + | 0.774305i | \(0.281900\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −555.582 | − | 320.765i | −1.20517 | − | 0.695803i | −0.243467 | − | 0.969909i | \(-0.578285\pi\) |
−0.961700 | + | 0.274106i | \(0.911618\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 64.7461 | + | 112.144i | 0.139840 | + | 0.242211i | 0.927436 | − | 0.373982i | \(-0.122008\pi\) |
−0.787596 | + | 0.616192i | \(0.788674\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 672.730i | − | 1.44054i | −0.693696 | − | 0.720268i | \(-0.744019\pi\) | ||
0.693696 | − | 0.720268i | \(-0.255981\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −510.277 | −1.08801 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −676.832 | + | 390.769i | −1.43093 | + | 0.826150i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 40.7461 | − | 70.5744i | 0.0857813 | − | 0.148578i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 108.786 | + | 62.8074i | 0.227110 | + | 0.131122i | 0.609238 | − | 0.792987i | \(-0.291475\pi\) |
−0.382128 | + | 0.924109i | \(0.624809\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 121.917 | + | 211.167i | 0.253466 | + | 0.439016i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 141.530i | 0.291815i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 448.631 | 0.921213 | 0.460606 | − | 0.887604i | \(-0.347632\pi\) | ||||
0.460606 | + | 0.887604i | \(0.347632\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −391.579 | + | 226.078i | −0.797514 | + | 0.460445i | −0.842601 | − | 0.538538i | \(-0.818977\pi\) |
0.0450873 | + | 0.998983i | \(0.485643\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −407.798 | + | 706.327i | −0.827176 | + | 1.43271i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 175.591 | + | 101.377i | 0.353301 | + | 0.203979i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 63.2961 | + | 109.632i | 0.126846 | + | 0.219704i | 0.922453 | − | 0.386109i | \(-0.126181\pi\) |
−0.795607 | + | 0.605813i | \(0.792848\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 296.822i | 0.590103i | 0.955481 | + | 0.295051i | \(0.0953367\pi\) | ||||
−0.955481 | + | 0.295051i | \(0.904663\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 137.412 | 0.272102 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 567.113 | − | 327.423i | 1.11417 | − | 0.643267i | 0.174265 | − | 0.984699i | \(-0.444245\pi\) |
0.939907 | + | 0.341432i | \(0.110912\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 443.573 | − | 768.291i | 0.868049 | − | 1.50350i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −205.371 | − | 118.571i | −0.398778 | − | 0.230235i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 124.708 | + | 216.000i | 0.241214 | + | 0.417795i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 690.006i | 1.32439i | 0.749333 | + | 0.662193i | \(0.230374\pi\) | ||||
−0.749333 | + | 0.662193i | \(0.769626\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −616.238 | −1.17828 | −0.589138 | − | 0.808032i | \(-0.700533\pi\) | ||||
−0.589138 | + | 0.808032i | \(0.700533\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −200.764 | + | 115.911i | −0.380956 | + | 0.219945i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −156.500 | + | 271.066i | −0.295841 | + | 0.512412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −235.325 | − | 135.865i | −0.441511 | − | 0.254906i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 46.5922 | + | 80.7001i | 0.0870883 | + | 0.150841i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1536.85i | − | 2.85129i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −548.734 | −1.01430 | −0.507148 | − | 0.861859i | \(-0.669300\pi\) | ||||
−0.507148 | + | 0.861859i | \(0.669300\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −126.340 | + | 72.9422i | −0.231816 | + | 0.133839i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −409.885 | + | 709.941i | −0.749332 | + | 1.29788i | 0.198811 | + | 0.980038i | \(0.436292\pi\) |
−0.948143 | + | 0.317843i | \(0.897041\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −87.9368 | − | 50.7703i | −0.159595 | − | 0.0921421i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 289.646 | + | 501.682i | 0.523772 | + | 0.907201i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 125.808i | 0.225867i | 0.993603 | + | 0.112934i | \(0.0360247\pi\) | ||||
−0.993603 | + | 0.112934i | \(0.963975\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −574.515 | −1.02776 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 440.625 | − | 254.395i | 0.782638 | − | 0.451856i | −0.0547261 | − | 0.998501i | \(-0.517429\pi\) |
0.837365 | + | 0.546645i | \(0.184095\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 68.7923 | − | 119.152i | 0.121756 | − | 0.210888i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −83.8832 | − | 48.4300i | −0.147422 | − | 0.0851143i | 0.424474 | − | 0.905440i | \(-0.360459\pi\) |
−0.571897 | + | 0.820326i | \(0.693792\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −227.100 | − | 393.349i | −0.397723 | − | 0.688877i | 0.595721 | − | 0.803191i | \(-0.296866\pi\) |
−0.993445 | + | 0.114314i | \(0.963533\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 331.981i | 0.577359i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.1230 | −0.0678041 | −0.0339021 | − | 0.999425i | \(-0.510793\pi\) | ||||
−0.0339021 | + | 0.999425i | \(0.510793\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −164.266 | + | 94.8393i | −0.282731 | + | 0.163235i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 621.300 | − | 1076.12i | 1.06569 | − | 1.84584i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 363.061 | + | 209.614i | 0.618503 | + | 0.357093i | 0.776286 | − | 0.630381i | \(-0.217101\pi\) |
−0.157783 | + | 0.987474i | \(0.550435\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.4308 | − | 24.9948i | −0.0245005 | − | 0.0424361i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 329.210i | 0.555160i | 0.960703 | + | 0.277580i | \(0.0895323\pi\) | ||||
−0.960703 | + | 0.277580i | \(0.910468\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 557.654 | 0.937233 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 159.556 | − | 92.1197i | 0.266371 | − | 0.153789i | −0.360867 | − | 0.932617i | \(-0.617519\pi\) |
0.627237 | + | 0.778828i | \(0.284186\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −109.208 | + | 189.153i | −0.181710 | + | 0.314731i | −0.942463 | − | 0.334311i | \(-0.891497\pi\) |
0.760753 | + | 0.649041i | \(0.224830\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 127.762 | + | 73.7634i | 0.211177 | + | 0.121923i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.13467 | + | 8.89350i | 0.00845909 | + | 0.0146516i | 0.870224 | − | 0.492656i | \(-0.163974\pi\) |
−0.861765 | + | 0.507308i | \(0.830641\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 183.347i | 0.300078i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −180.585 | −0.294592 | −0.147296 | − | 0.989092i | \(-0.547057\pi\) | ||||
−0.147296 | + | 0.989092i | \(0.547057\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −784.800 | + | 453.104i | −1.27196 | + | 0.734367i | −0.975357 | − | 0.220633i | \(-0.929188\pi\) |
−0.296604 | + | 0.955000i | \(0.595854\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 380.823 | − | 659.605i | 0.615223 | − | 1.06560i | −0.375122 | − | 0.926975i | \(-0.622399\pi\) |
0.990345 | − | 0.138622i | \(-0.0442674\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 847.571 | + | 489.345i | 1.36047 | + | 0.785466i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −224.975 | − | 389.668i | −0.359960 | − | 0.623469i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 654.006i | 1.03975i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −601.108 | −0.952627 | −0.476313 | − | 0.879276i | \(-0.658027\pi\) | ||||
−0.476313 | + | 0.879276i | \(0.658027\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −106.006 | + | 61.2027i | −0.166939 | + | 0.0963823i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 564.875 | − | 978.392i | 0.886774 | − | 1.53594i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 500.089 | + | 288.727i | 0.780170 | + | 0.450431i | 0.836491 | − | 0.547981i | \(-0.184604\pi\) |
−0.0563204 | + | 0.998413i | \(0.517937\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 65.0615 | + | 112.690i | 0.101184 | + | 0.175256i | 0.912173 | − | 0.409806i | \(-0.134403\pi\) |
−0.810989 | + | 0.585062i | \(0.801070\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 985.467i | 1.52313i | 0.648087 | + | 0.761567i | \(0.275570\pi\) | ||||
−0.648087 | + | 0.761567i | \(0.724430\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1338.37 | 2.06220 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 519.895 | − | 300.161i | 0.796163 | − | 0.459665i | −0.0459644 | − | 0.998943i | \(-0.514636\pi\) |
0.842128 | + | 0.539278i | \(0.181303\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −64.1192 | + | 111.058i | −0.0978919 | + | 0.169554i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.5004 | + | 7.79445i | 0.0204862 | + | 0.0118277i | 0.510208 | − | 0.860051i | \(-0.329568\pi\) |
−0.489722 | + | 0.871879i | \(0.662902\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −203.915 | − | 353.192i | −0.308495 | − | 0.534329i | 0.669538 | − | 0.742778i | \(-0.266492\pi\) |
−0.978033 | + | 0.208448i | \(0.933159\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 69.4272i | 0.104402i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 413.654 | 0.620170 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 165.463 | − | 95.5301i | 0.246592 | − | 0.142370i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 237.285 | − | 410.989i | 0.352577 | − | 0.610682i | −0.634123 | − | 0.773232i | \(-0.718639\pi\) |
0.986700 | + | 0.162550i | \(0.0519720\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 244.346 | + | 141.073i | 0.360925 | + | 0.208380i | 0.669486 | − | 0.742824i | \(-0.266514\pi\) |
−0.308562 | + | 0.951204i | \(0.599848\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 564.708 | + | 978.102i | 0.831675 | + | 1.44050i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1085.46i | 1.58926i | 0.607095 | + | 0.794629i | \(0.292335\pi\) | ||||
−0.607095 | + | 0.794629i | \(0.707665\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 333.473 | 0.486822 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 791.067 | − | 456.723i | 1.14814 | − | 0.662878i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −503.888 | + | 872.760i | −0.729216 | + | 1.26304i | 0.227999 | + | 0.973661i | \(0.426782\pi\) |
−0.957215 | + | 0.289378i | \(0.906552\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −81.7470 | − | 47.1966i | −0.117622 | − | 0.0679088i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −364.413 | − | 631.183i | −0.522831 | − | 0.905570i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 216.731i | − | 0.309174i | −0.987979 | − | 0.154587i | \(-0.950595\pi\) | ||
0.987979 | − | 0.154587i | \(-0.0494047\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −81.4229 | −0.115822 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 949.639 | − | 548.274i | 1.34319 | − | 0.775494i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −497.248 | + | 861.259i | −0.701337 | + | 1.21475i | 0.266660 | + | 0.963791i | \(0.414080\pi\) |
−0.967997 | + | 0.250961i | \(0.919253\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 101.823 | + | 58.7878i | 0.142810 | + | 0.0824513i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 123.289 | + | 213.542i | 0.172432 | + | 0.298660i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 340.912i | − | 0.474148i | −0.971492 | − | 0.237074i | \(-0.923812\pi\) | ||
0.971492 | − | 0.237074i | \(-0.0761884\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1892.40 | −2.62469 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −550.589 | + | 317.883i | −0.759433 | + | 0.438459i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −485.888 | + | 841.583i | −0.668347 | + | 1.15761i | 0.310019 | + | 0.950730i | \(0.399665\pi\) |
−0.978366 | + | 0.206881i | \(0.933669\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1334.50 | − | 770.474i | −1.82558 | − | 1.05400i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −114.585 | − | 198.466i | −0.156323 | − | 0.270759i | 0.777217 | − | 0.629233i | \(-0.216631\pi\) |
−0.933540 | + | 0.358473i | \(0.883297\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 605.175i | − | 0.821132i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 629.892 | 0.852357 | 0.426179 | − | 0.904639i | \(-0.359859\pi\) | ||||
0.426179 | + | 0.904639i | \(0.359859\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −162.825 | + | 94.0071i | −0.219145 | + | 0.126524i | −0.605554 | − | 0.795804i | \(-0.707049\pi\) |
0.386409 | + | 0.922327i | \(0.373715\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.7923 | − | 41.2095i | 0.0319360 | − | 0.0553148i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 643.989 | + | 371.807i | 0.859799 | + | 0.496405i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −693.335 | − | 1200.89i | −0.923215 | − | 1.59906i | −0.794407 | − | 0.607386i | \(-0.792218\pi\) |
−0.128808 | − | 0.991670i | \(-0.541115\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 49.6933i | − | 0.0658189i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1222.12 | 1.61443 | 0.807215 | − | 0.590258i | \(-0.200974\pi\) | ||||
0.807215 | + | 0.590258i | \(0.200974\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 489.896 | − | 282.841i | 0.643752 | − | 0.371671i | −0.142306 | − | 0.989823i | \(-0.545452\pi\) |
0.786059 | + | 0.618152i | \(0.212118\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −582.081 | + | 1008.19i | −0.762884 | + | 1.32135i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 852.036 | + | 491.923i | 1.11087 | + | 0.641360i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 299.408 | + | 518.589i | 0.389347 | + | 0.674368i | 0.992362 | − | 0.123362i | \(-0.0393675\pi\) |
−0.603015 | + | 0.797730i | \(0.706034\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 446.970i | − | 0.578228i | −0.957295 | − | 0.289114i | \(-0.906639\pi\) | ||
0.957295 | − | 0.289114i | \(-0.0933607\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −180.708 | −0.233171 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 78.5814 | − | 45.3690i | 0.100875 | − | 0.0582400i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −120.231 | + | 208.246i | −0.153945 | + | 0.266640i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −335.823 | − | 193.887i | −0.427800 | − | 0.246990i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −477.650 | − | 827.314i | −0.606925 | − | 1.05122i | −0.991744 | − | 0.128233i | \(-0.959070\pi\) |
0.384819 | − | 0.922992i | \(-0.374264\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1097.93i | − | 1.38803i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 140.450 | 0.177112 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −192.141 | + | 110.933i | −0.241081 | + | 0.139188i | −0.615673 | − | 0.788002i | \(-0.711116\pi\) |
0.374593 | + | 0.927189i | \(0.377783\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −245.885 | + | 425.885i | −0.307740 | + | 0.533022i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 911.172 | + | 526.066i | 1.13471 | + | 0.655125i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −141.415 | − | 244.939i | −0.175671 | − | 0.304271i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1180.17i | − | 1.45881i | −0.684084 | − | 0.729403i | \(-0.739798\pi\) | ||
0.684084 | − | 0.729403i | \(-0.260202\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 627.307 | 0.773499 | 0.386749 | − | 0.922185i | \(-0.373598\pi\) | ||||
0.386749 | + | 0.922185i | \(0.373598\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.1936 | − | 9.92670i | 0.0210964 | − | 0.0121800i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 95.9230 | − | 166.144i | 0.117409 | − | 0.203358i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 338.512 | + | 195.440i | 0.412317 | + | 0.238051i | 0.691785 | − | 0.722104i | \(-0.256825\pi\) |
−0.279468 | + | 0.960155i | \(0.590158\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 163.100 | + | 282.497i | 0.198177 | + | 0.343253i | 0.947937 | − | 0.318456i | \(-0.103164\pi\) |
−0.749760 | + | 0.661710i | \(0.769831\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1103.70i | − | 1.33458i | −0.744799 | − | 0.667289i | \(-0.767455\pi\) | ||
0.744799 | − | 0.667289i | \(-0.232545\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −441.569 | −0.532653 | −0.266326 | − | 0.963883i | \(-0.585810\pi\) | ||||
−0.266326 | + | 0.963883i | \(0.585810\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2624.22 | − | 1515.09i | 3.15032 | − | 1.81884i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 180.473 | − | 312.588i | 0.216135 | − | 0.374357i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −436.443 | − | 251.980i | −0.520194 | − | 0.300334i | 0.216820 | − | 0.976212i | \(-0.430431\pi\) |
−0.737014 | + | 0.675878i | \(0.763765\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.4134 | − | 42.2853i | −0.0290290 | − | 0.0502798i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 81.1815i | − | 0.0960728i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1177.27 | 1.38993 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 287.259 | − | 165.849i | 0.337555 | − | 0.194887i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −472.415 | + | 818.247i | −0.553828 | + | 0.959258i | 0.444166 | + | 0.895945i | \(0.353500\pi\) |
−0.997994 | + | 0.0633136i | \(0.979833\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 642.051 | + | 370.689i | 0.749185 | + | 0.432542i | 0.825399 | − | 0.564549i | \(-0.190950\pi\) |
−0.0762145 | + | 0.997091i | \(0.524283\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −680.631 | − | 1178.89i | −0.792352 | − | 1.37239i | −0.924507 | − | 0.381165i | \(-0.875523\pi\) |
0.132154 | − | 0.991229i | \(-0.457811\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 805.003i | 0.932796i | 0.884575 | + | 0.466398i | \(0.154449\pi\) | ||||
−0.884575 | + | 0.466398i | \(0.845551\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.4617 | 0.0386841 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −594.981 | + | 343.513i | −0.684673 | + | 0.395296i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 222.435 | − | 385.268i | 0.255378 | − | 0.442328i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 793.107 | + | 457.901i | 0.906408 | + | 0.523315i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.3461 | − | 36.9725i | −0.0243399 | − | 0.0421580i | 0.853599 | − | 0.520931i | \(-0.174415\pi\) |
−0.877939 | + | 0.478773i | \(0.841082\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 264.567i | − | 0.300303i | −0.988663 | − | 0.150151i | \(-0.952024\pi\) | ||
0.988663 | − | 0.150151i | \(-0.0479761\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 393.338 | 0.445457 | 0.222728 | − | 0.974881i | \(-0.428504\pi\) | ||||
0.222728 | + | 0.974881i | \(0.428504\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1340.65 | + | 774.026i | −1.51145 | + | 0.872634i | −0.511535 | + | 0.859262i | \(0.670923\pi\) |
−0.999911 | + | 0.0133715i | \(0.995744\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −488.400 | + | 845.933i | −0.549381 | + | 0.951556i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −53.0221 | − | 30.6123i | −0.0593752 | − | 0.0342803i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −215.654 | − | 373.523i | −0.240954 | − | 0.417344i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 225.165i | 0.250461i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2450.02 | 2.71922 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 234.379 | − | 135.319i | 0.258982 | − | 0.149523i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 688.746 | − | 1192.94i | 0.759367 | − | 1.31526i | −0.183806 | − | 0.982962i | \(-0.558842\pi\) |
0.943174 | − | 0.332300i | \(-0.107825\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1217.70 | + | 703.038i | 1.33666 | + | 0.771721i | 0.986311 | − | 0.164898i | \(-0.0527294\pi\) |
0.350350 | + | 0.936619i | \(0.386063\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −112.477 | − | 194.816i | −0.123195 | − | 0.213380i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1023.35i | 1.11597i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −479.992 | −0.522299 | −0.261149 | − | 0.965298i | \(-0.584101\pi\) | ||||
−0.261149 | + | 0.965298i | \(0.584101\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −153.083 | + | 88.3827i | −0.165854 | + | 0.0957560i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −254.902 | + | 441.503i | −0.275570 | + | 0.477301i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −587.800 | − | 339.366i | −0.632723 | − | 0.365303i | 0.149083 | − | 0.988825i | \(-0.452368\pi\) |
−0.781806 | + | 0.623522i | \(0.785701\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 188.627 | + | 326.711i | 0.202607 | + | 0.350925i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 661.362i | 0.707339i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −666.600 | −0.711420 | −0.355710 | − | 0.934596i | \(-0.615761\pi\) | ||||
−0.355710 | + | 0.934596i | \(0.615761\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1037.46 | − | 598.978i | 1.10251 | − | 0.636533i | 0.165629 | − | 0.986188i | \(-0.447034\pi\) |
0.936879 | + | 0.349655i | \(0.113701\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −184.823 | + | 320.123i | −0.195995 | + | 0.339473i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 393.793 | + | 227.357i | 0.415832 | + | 0.240081i | 0.693293 | − | 0.720656i | \(-0.256159\pi\) |
−0.277460 | + | 0.960737i | \(0.589493\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 386.715 | + | 669.811i | 0.407498 | + | 0.705807i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1060.16i | 1.11245i | 0.831033 | + | 0.556224i | \(0.187750\pi\) | ||||
−0.831033 | + | 0.556224i | \(0.812250\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −236.238 | −0.247370 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2304.60 | − | 1330.56i | 2.40313 | − | 1.38745i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 448.500 | − | 776.825i | 0.466701 | − | 0.808350i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 73.9675 | + | 42.7051i | 0.0766502 | + | 0.0442540i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −827.657 | − | 1433.54i | −0.855902 | − | 1.48247i | −0.875805 | − | 0.482664i | \(-0.839669\pi\) |
0.0199032 | − | 0.999802i | \(-0.493664\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 797.780i | 0.821606i | 0.911724 | + | 0.410803i | \(0.134752\pi\) | ||||
−0.911724 | + | 0.410803i | \(0.865248\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −753.261 | −0.774164 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −270.574 | + | 156.216i | −0.276944 | + | 0.159894i | −0.632039 | − | 0.774936i | \(-0.717782\pi\) |
0.355095 | + | 0.934830i | \(0.384448\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −580.350 | + | 1005.20i | −0.592799 | + | 1.02676i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 320.553 | + | 185.072i | 0.326097 | + | 0.188272i | 0.654107 | − | 0.756402i | \(-0.273045\pi\) |
−0.328010 | + | 0.944674i | \(0.606378\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 103.500 | + | 179.267i | 0.105076 | + | 0.181997i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 781.538i | 0.790230i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1324.48 | 1.33651 | 0.668256 | − | 0.743931i | \(-0.267041\pi\) | ||||
0.668256 | + | 0.743931i | \(0.267041\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 280.890 | − | 162.172i | 0.282302 | − | 0.162987i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −439.623 | + | 761.449i | −0.440946 | + | 0.763741i | −0.997760 | − | 0.0668966i | \(-0.978690\pi\) |
0.556814 | + | 0.830637i | \(0.312024\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1296.3.q.o.593.3 | 8 | ||
3.2 | odd | 2 | inner | 1296.3.q.o.593.2 | 8 | ||
4.3 | odd | 2 | 162.3.d.c.107.2 | 8 | |||
9.2 | odd | 6 | 1296.3.e.d.161.2 | 4 | |||
9.4 | even | 3 | inner | 1296.3.q.o.1025.2 | 8 | ||
9.5 | odd | 6 | inner | 1296.3.q.o.1025.3 | 8 | ||
9.7 | even | 3 | 1296.3.e.d.161.3 | 4 | |||
12.11 | even | 2 | 162.3.d.c.107.3 | 8 | |||
36.7 | odd | 6 | 162.3.b.b.161.4 | yes | 4 | ||
36.11 | even | 6 | 162.3.b.b.161.1 | ✓ | 4 | ||
36.23 | even | 6 | 162.3.d.c.53.2 | 8 | |||
36.31 | odd | 6 | 162.3.d.c.53.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
162.3.b.b.161.1 | ✓ | 4 | 36.11 | even | 6 | ||
162.3.b.b.161.4 | yes | 4 | 36.7 | odd | 6 | ||
162.3.d.c.53.2 | 8 | 36.23 | even | 6 | |||
162.3.d.c.53.3 | 8 | 36.31 | odd | 6 | |||
162.3.d.c.107.2 | 8 | 4.3 | odd | 2 | |||
162.3.d.c.107.3 | 8 | 12.11 | even | 2 | |||
1296.3.e.d.161.2 | 4 | 9.2 | odd | 6 | |||
1296.3.e.d.161.3 | 4 | 9.7 | even | 3 | |||
1296.3.q.o.593.2 | 8 | 3.2 | odd | 2 | inner | ||
1296.3.q.o.593.3 | 8 | 1.1 | even | 1 | trivial | ||
1296.3.q.o.1025.2 | 8 | 9.4 | even | 3 | inner | ||
1296.3.q.o.1025.3 | 8 | 9.5 | odd | 6 | inner |