Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2925,2,Mod(2224,2925)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2925, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2925.2224");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2925.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.3562425912\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 195) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2224.1 | ||
Root | \(0.264658 + 1.38923i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2925.2224 |
Dual form | 2925.2.c.w.2224.6 |
$q$-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 \(\left(\mathbb{Z}/2925\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(2251\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.77846i | − 1.96467i | −0.187142 | − | 0.982333i | \(-0.559922\pi\) | ||||
0.187142 | − | 0.982333i | \(-0.440078\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.71982 | −2.85991 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.71982i | − 1.02800i | −0.857791 | − | 0.513998i | \(-0.828164\pi\) | ||||
0.857791 | − | 0.513998i | \(-0.171836\pi\) | |||||||
\(8\) | 10.3354i | 3.65411i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.71982 | 0.820058 | 0.410029 | − | 0.912073i | \(-0.365519\pi\) | ||||
0.410029 | + | 0.912073i | \(0.365519\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.00000i | − 0.277350i | ||||||||
\(14\) | −7.55691 | −2.01967 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 17.2767 | 4.31918 | ||||||||
\(17\) | 2.83709i | 0.688095i | 0.938952 | + | 0.344048i | \(0.111798\pi\) | ||||
−0.938952 | + | 0.344048i | \(0.888202\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.55691 | 0.816012 | 0.408006 | − | 0.912979i | \(-0.366224\pi\) | ||||
0.408006 | + | 0.912979i | \(0.366224\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 7.55691i | − 1.61114i | ||||||||
\(23\) | − 4.83709i | − 1.00860i | −0.863528 | − | 0.504302i | \(-0.831750\pi\) | ||||
0.863528 | − | 0.504302i | \(-0.168250\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.77846 | −0.544900 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 15.5569i | 2.93998i | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.55691 | 1.35726 | 0.678631 | − | 0.734479i | \(-0.262574\pi\) | ||||
0.678631 | + | 0.734479i | \(0.262574\pi\) | |||||||
\(32\) | − 27.3319i | − 4.83165i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.88273 | 1.35188 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 4.27674i | − 0.703091i | −0.936171 | − | 0.351546i | \(-0.885656\pi\) | ||||
0.936171 | − | 0.351546i | \(-0.114344\pi\) | |||||||
\(38\) | − 9.88273i | − 1.60319i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.83709 | −0.443079 | −0.221540 | − | 0.975151i | \(-0.571108\pi\) | ||||
−0.221540 | + | 0.975151i | \(0.571108\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 11.1138i | − 1.69484i | −0.530921 | − | 0.847421i | \(-0.678154\pi\) | ||||
0.530921 | − | 0.847421i | \(-0.321846\pi\) | |||||||
\(44\) | −15.5569 | −2.34529 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.4396 | −1.98157 | ||||||||
\(47\) | 11.5569i | 1.68575i | 0.538110 | + | 0.842875i | \(0.319138\pi\) | ||||
−0.538110 | + | 0.842875i | \(0.680862\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.397442 | −0.0567775 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.71982i | 0.793197i | ||||||||
\(53\) | 1.16291i | 0.159738i | 0.996805 | + | 0.0798690i | \(0.0254502\pi\) | ||||
−0.996805 | + | 0.0798690i | \(0.974550\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 28.1104 | 3.75641 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 16.6707i | − 2.18898i | ||||||||
\(59\) | −2.11727 | −0.275645 | −0.137822 | − | 0.990457i | \(-0.544010\pi\) | ||||
−0.137822 | + | 0.990457i | \(0.544010\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.60256 | 0.845371 | 0.422685 | − | 0.906276i | \(-0.361088\pi\) | ||||
0.422685 | + | 0.906276i | \(0.361088\pi\) | |||||||
\(62\) | − 20.9966i | − 2.66657i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −41.3871 | −5.17339 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.88273i | 0.230013i | 0.993365 | + | 0.115006i | \(0.0366888\pi\) | ||||
−0.993365 | + | 0.115006i | \(0.963311\pi\) | |||||||
\(68\) | − 16.2277i | − 1.96789i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.71982 | 0.797496 | 0.398748 | − | 0.917060i | \(-0.369445\pi\) | ||||
0.398748 | + | 0.917060i | \(0.369445\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 9.11383i | − 1.06669i | −0.845897 | − | 0.533346i | \(-0.820934\pi\) | ||||
0.845897 | − | 0.533346i | \(-0.179066\pi\) | |||||||
\(74\) | −11.8827 | −1.38134 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −20.3449 | −2.33372 | ||||||||
\(77\) | − 7.39744i | − 0.843017i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.2767 | −1.15622 | −0.578112 | − | 0.815958i | \(-0.696210\pi\) | ||||
−0.578112 | + | 0.815958i | \(0.696210\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.88273i | 0.870502i | ||||||||
\(83\) | 2.11727i | 0.232400i | 0.993226 | + | 0.116200i | \(0.0370714\pi\) | ||||
−0.993226 | + | 0.116200i | \(0.962929\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −30.8793 | −3.32980 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 28.1104i | 2.99658i | ||||||||
\(89\) | 1.16291 | 0.123268 | 0.0616341 | − | 0.998099i | \(-0.480369\pi\) | ||||
0.0616341 | + | 0.998099i | \(0.480369\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.71982 | −0.285115 | ||||||||
\(92\) | 27.6673i | 2.88452i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 32.1104 | 3.31193 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 10.8371i | − 1.10034i | −0.835053 | − | 0.550170i | \(-0.814563\pi\) | ||||
0.835053 | − | 0.550170i | \(-0.185437\pi\) | |||||||
\(98\) | 1.10428i | 0.111549i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.67418 | −0.763610 | −0.381805 | − | 0.924243i | \(-0.624697\pi\) | ||||
−0.381805 | + | 0.924243i | \(0.624697\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 3.76547i | − 0.371023i | −0.982642 | − | 0.185511i | \(-0.940606\pi\) | ||||
0.982642 | − | 0.185511i | \(-0.0593941\pi\) | |||||||
\(104\) | 10.3354 | 1.01347 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.23109 | 0.313832 | ||||||||
\(107\) | 12.6026i | 1.21834i | 0.793041 | + | 0.609168i | \(0.208496\pi\) | ||||
−0.793041 | + | 0.609168i | \(0.791504\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.4396 | −1.09572 | −0.547860 | − | 0.836570i | \(-0.684557\pi\) | ||||
−0.547860 | + | 0.836570i | \(0.684557\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 46.9897i | − 4.44011i | ||||||||
\(113\) | − 13.1138i | − 1.23365i | −0.787102 | − | 0.616823i | \(-0.788420\pi\) | ||||
0.787102 | − | 0.616823i | \(-0.211580\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −34.3189 | −3.18643 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.88273i | 0.541550i | ||||||||
\(119\) | 7.71639 | 0.707360 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.60256 | −0.327505 | ||||||||
\(122\) | − 18.3449i | − 1.66087i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −43.2242 | −3.88165 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 13.4396i | − 1.19258i | −0.802771 | − | 0.596288i | \(-0.796642\pi\) | ||||
0.802771 | − | 0.596288i | \(-0.203358\pi\) | |||||||
\(128\) | 60.3285i | 5.33234i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.43965 | 0.824746 | 0.412373 | − | 0.911015i | \(-0.364700\pi\) | ||||
0.412373 | + | 0.911015i | \(0.364700\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 9.67418i | − 0.838858i | ||||||||
\(134\) | 5.23109 | 0.451898 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −29.3224 | −2.51437 | ||||||||
\(137\) | − 1.76547i | − 0.150834i | −0.997152 | − | 0.0754170i | \(-0.975971\pi\) | ||||
0.997152 | − | 0.0754170i | \(-0.0240288\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.27674 | 0.532386 | 0.266193 | − | 0.963920i | \(-0.414234\pi\) | ||||
0.266193 | + | 0.963920i | \(0.414234\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 18.6707i | − 1.56681i | ||||||||
\(143\) | − 2.71982i | − 0.227443i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −25.3224 | −2.09570 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 24.4622i | 2.01078i | ||||||||
\(149\) | −20.8302 | −1.70648 | −0.853239 | − | 0.521520i | \(-0.825365\pi\) | ||||
−0.853239 | + | 0.521520i | \(0.825365\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.99656 | 0.406614 | 0.203307 | − | 0.979115i | \(-0.434831\pi\) | ||||
0.203307 | + | 0.979115i | \(0.434831\pi\) | |||||||
\(152\) | 36.7620i | 2.98179i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −20.5535 | −1.65625 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.87930i | 0.708645i | 0.935123 | + | 0.354322i | \(0.115288\pi\) | ||||
−0.935123 | + | 0.354322i | \(0.884712\pi\) | |||||||
\(158\) | 28.5535i | 2.27159i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.1560 | −1.03684 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.8337i | 1.08354i | 0.840528 | + | 0.541768i | \(0.182245\pi\) | ||||
−0.840528 | + | 0.541768i | \(0.817755\pi\) | |||||||
\(164\) | 16.2277 | 1.26717 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.88273 | 0.456589 | ||||||||
\(167\) | 9.88273i | 0.764749i | 0.924007 | + | 0.382374i | \(0.124894\pi\) | ||||
−0.924007 | + | 0.382374i | \(0.875106\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 63.5691i | 4.84710i | ||||||||
\(173\) | 13.1138i | 0.997026i | 0.866882 | + | 0.498513i | \(0.166120\pi\) | ||||
−0.866882 | + | 0.498513i | \(0.833880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 46.9897 | 3.54198 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 3.23109i | − 0.242181i | ||||||||
\(179\) | 8.55348 | 0.639317 | 0.319658 | − | 0.947533i | \(-0.396432\pi\) | ||||
0.319658 | + | 0.947533i | \(0.396432\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.72326 | 0.276748 | 0.138374 | − | 0.990380i | \(-0.455812\pi\) | ||||
0.138374 | + | 0.990380i | \(0.455812\pi\) | |||||||
\(182\) | 7.55691i | 0.560156i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 49.9931 | 3.68554 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.71639i | 0.564278i | ||||||||
\(188\) | − 66.1035i | − 4.82109i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.23453 | 0.306400 | 0.153200 | − | 0.988195i | \(-0.451042\pi\) | ||||
0.153200 | + | 0.988195i | \(0.451042\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.3906i | 1.68369i | 0.539719 | + | 0.841845i | \(0.318530\pi\) | ||||
−0.539719 | + | 0.841845i | \(0.681470\pi\) | |||||||
\(194\) | −30.1104 | −2.16180 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.27330 | 0.162379 | ||||||||
\(197\) | − 14.5535i | − 1.03689i | −0.855110 | − | 0.518446i | \(-0.826511\pi\) | ||||
0.855110 | − | 0.518446i | \(-0.173489\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.1138 | 1.07139 | 0.535695 | − | 0.844411i | \(-0.320050\pi\) | ||||
0.535695 | + | 0.844411i | \(0.320050\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 21.3224i | 1.50024i | ||||||||
\(203\) | − 16.3189i | − 1.14537i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.4622 | −0.728935 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 17.2767i | − 1.19793i | ||||||||
\(209\) | 9.67418 | 0.669177 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.2277 | −1.25484 | −0.627422 | − | 0.778680i | \(-0.715890\pi\) | ||||
−0.627422 | + | 0.778680i | \(0.715890\pi\) | |||||||
\(212\) | − 6.65164i | − 0.456836i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 35.0157 | 2.39362 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 20.5535i | − 1.39526i | ||||||||
\(218\) | 31.7846i | 2.15272i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.83709 | 0.190843 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 10.1173i | − 0.677502i | −0.940876 | − | 0.338751i | \(-0.889996\pi\) | ||||
0.940876 | − | 0.338751i | \(-0.110004\pi\) | |||||||
\(224\) | −74.3380 | −4.96692 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −36.4362 | −2.42370 | ||||||||
\(227\) | − 11.3224i | − 0.751493i | −0.926723 | − | 0.375746i | \(-0.877386\pi\) | ||||
0.926723 | − | 0.375746i | \(-0.122614\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.23453 | 0.411990 | 0.205995 | − | 0.978553i | \(-0.433957\pi\) | ||||
0.205995 | + | 0.978553i | \(0.433957\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 62.0122i | 4.07130i | ||||||||
\(233\) | 6.83709i | 0.447913i | 0.974599 | + | 0.223956i | \(0.0718973\pi\) | ||||
−0.974599 | + | 0.223956i | \(0.928103\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.1104 | 0.788319 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 21.4396i | − 1.38973i | ||||||||
\(239\) | 1.28018 | 0.0828077 | 0.0414039 | − | 0.999142i | \(-0.486817\pi\) | ||||
0.0414039 | + | 0.999142i | \(0.486817\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.00000 | −0.386494 | −0.193247 | − | 0.981150i | \(-0.561902\pi\) | ||||
−0.193247 | + | 0.981150i | \(0.561902\pi\) | |||||||
\(242\) | 10.0096i | 0.643438i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −37.7655 | −2.41769 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 3.55691i | − 0.226321i | ||||||||
\(248\) | 78.1035i | 4.95958i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.2277 | −1.15052 | −0.575260 | − | 0.817971i | \(-0.695099\pi\) | ||||
−0.575260 | + | 0.817971i | \(0.695099\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 13.1560i | − 0.827113i | ||||||||
\(254\) | −37.3415 | −2.34301 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 84.8459 | 5.30287 | ||||||||
\(257\) | − 1.11383i | − 0.0694787i | −0.999396 | − | 0.0347394i | \(-0.988940\pi\) | ||||
0.999396 | − | 0.0347394i | \(-0.0110601\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.6320 | −0.722776 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 26.2277i | − 1.62035i | ||||||||
\(263\) | 8.00000i | 0.493301i | 0.969104 | + | 0.246651i | \(0.0793300\pi\) | ||||
−0.969104 | + | 0.246651i | \(0.920670\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −26.8793 | −1.64808 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 10.7689i | − 0.657816i | ||||||||
\(269\) | 15.6742 | 0.955672 | 0.477836 | − | 0.878449i | \(-0.341421\pi\) | ||||
0.477836 | + | 0.878449i | \(0.341421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.443086 | 0.0269155 | 0.0134578 | − | 0.999909i | \(-0.495716\pi\) | ||||
0.0134578 | + | 0.999909i | \(0.495716\pi\) | |||||||
\(272\) | 49.0157i | 2.97201i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.90528 | −0.296339 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 4.87930i | − 0.293168i | −0.989198 | − | 0.146584i | \(-0.953172\pi\) | ||||
0.989198 | − | 0.146584i | \(-0.0468279\pi\) | |||||||
\(278\) | − 17.4396i | − 1.04596i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.11383 | 0.543685 | 0.271843 | − | 0.962342i | \(-0.412367\pi\) | ||||
0.271843 | + | 0.962342i | \(0.412367\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 33.3415i | − 1.98195i | −0.134063 | − | 0.990973i | \(-0.542802\pi\) | ||||
0.134063 | − | 0.990973i | \(-0.457198\pi\) | |||||||
\(284\) | −38.4362 | −2.28077 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.55691 | −0.446850 | ||||||||
\(287\) | 7.71639i | 0.455484i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.95092 | 0.526525 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 52.1295i | 3.05065i | ||||||||
\(293\) | − 29.4328i | − 1.71948i | −0.510731 | − | 0.859740i | \(-0.670625\pi\) | ||||
0.510731 | − | 0.859740i | \(-0.329375\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 44.2017 | 2.56917 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 57.8759i | 3.35266i | ||||||||
\(299\) | −4.83709 | −0.279736 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.2277 | −1.74229 | ||||||||
\(302\) | − 13.8827i | − 0.798862i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 61.4519 | 3.52451 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 21.8337i | − 1.24611i | −0.782177 | − | 0.623056i | \(-0.785891\pi\) | ||||
0.782177 | − | 0.623056i | \(-0.214109\pi\) | |||||||
\(308\) | 42.3121i | 2.41095i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.1070 | −1.42368 | −0.711842 | − | 0.702339i | \(-0.752139\pi\) | ||||
−0.711842 | + | 0.702339i | \(0.752139\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 8.22766i | − 0.465055i | −0.972590 | − | 0.232527i | \(-0.925300\pi\) | ||||
0.972590 | − | 0.232527i | \(-0.0746995\pi\) | |||||||
\(314\) | 24.6707 | 1.39225 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 58.7811 | 3.30670 | ||||||||
\(317\) | − 27.6742i | − 1.55434i | −0.629293 | − | 0.777168i | \(-0.716655\pi\) | ||||
0.629293 | − | 0.777168i | \(-0.283345\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.3189 | 0.913685 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 36.5535i | 2.03705i | ||||||||
\(323\) | 10.0913i | 0.561494i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 38.4362 | 2.12878 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 29.3224i | − 1.61906i | ||||||||
\(329\) | 31.4328 | 1.73294 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.2311 | −0.727247 | −0.363623 | − | 0.931546i | \(-0.618460\pi\) | ||||
−0.363623 | + | 0.931546i | \(0.618460\pi\) | |||||||
\(332\) | − 12.1104i | − 0.664644i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 27.4588 | 1.50248 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 4.32582i | − 0.235642i | −0.993035 | − | 0.117821i | \(-0.962409\pi\) | ||||
0.993035 | − | 0.117821i | \(-0.0375910\pi\) | |||||||
\(338\) | 2.77846i | 0.151128i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.5535 | 1.11303 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 17.9578i | − 0.969630i | ||||||||
\(344\) | 114.866 | 6.19314 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 36.4362 | 1.95882 | ||||||||
\(347\) | − 6.27674i | − 0.336953i | −0.985706 | − | 0.168476i | \(-0.946115\pi\) | ||||
0.985706 | − | 0.168476i | \(-0.0538847\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.6673 | −0.945709 | −0.472855 | − | 0.881140i | \(-0.656776\pi\) | ||||
−0.472855 | + | 0.881140i | \(0.656776\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 74.3380i | − 3.96223i | ||||||||
\(353\) | − 13.7655i | − 0.732662i | −0.930485 | − | 0.366331i | \(-0.880614\pi\) | ||||
0.930485 | − | 0.366331i | \(-0.119386\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.65164 | −0.352536 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 23.7655i | − 1.25604i | ||||||||
\(359\) | 0.996562 | 0.0525965 | 0.0262983 | − | 0.999654i | \(-0.491628\pi\) | ||||
0.0262983 | + | 0.999654i | \(0.491628\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.34836 | −0.334124 | ||||||||
\(362\) | − 10.3449i | − 0.543717i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 15.5569 | 0.815404 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.2277i | 0.742678i | 0.928497 | + | 0.371339i | \(0.121101\pi\) | ||||
−0.928497 | + | 0.371339i | \(0.878899\pi\) | |||||||
\(368\) | − 83.5691i | − 4.35634i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.16291 | 0.164210 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 15.6742i | − 0.811578i | −0.913967 | − | 0.405789i | \(-0.866997\pi\) | ||||
0.913967 | − | 0.405789i | \(-0.133003\pi\) | |||||||
\(374\) | 21.4396 | 1.10862 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −119.445 | −6.15991 | ||||||||
\(377\) | − 6.00000i | − 0.309016i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.2017 | −1.34589 | −0.672945 | − | 0.739693i | \(-0.734971\pi\) | ||||
−0.672945 | + | 0.739693i | \(0.734971\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 11.7655i | − 0.601974i | ||||||||
\(383\) | 22.4362i | 1.14644i | 0.819403 | + | 0.573218i | \(0.194305\pi\) | ||||
−0.819403 | + | 0.573218i | \(0.805695\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 64.9897 | 3.30789 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 61.9862i | 3.14687i | ||||||||
\(389\) | 31.6742 | 1.60594 | 0.802972 | − | 0.596016i | \(-0.203251\pi\) | ||||
0.802972 | + | 0.596016i | \(0.203251\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.7233 | 0.694015 | ||||||||
\(392\) | − 4.10771i | − 0.207471i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −40.4362 | −2.03715 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.9509i | 0.900931i | 0.892794 | + | 0.450465i | \(0.148742\pi\) | ||||
−0.892794 | + | 0.450465i | \(0.851258\pi\) | |||||||
\(398\) | − 41.9931i | − 2.10493i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.5829 | −0.678297 | −0.339149 | − | 0.940733i | \(-0.610139\pi\) | ||||
−0.339149 | + | 0.940733i | \(0.610139\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 7.55691i | − 0.376437i | ||||||||
\(404\) | 43.8950 | 2.18386 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −45.3415 | −2.25026 | ||||||||
\(407\) | − 11.6320i | − 0.576576i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0000 | 0.692255 | 0.346128 | − | 0.938187i | \(-0.387496\pi\) | ||||
0.346128 | + | 0.938187i | \(0.387496\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 21.5378i | 1.06109i | ||||||||
\(413\) | 5.75859i | 0.283362i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −27.3319 | −1.34006 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 26.8793i | − 1.31471i | ||||||||
\(419\) | 12.3189 | 0.601820 | 0.300910 | − | 0.953653i | \(-0.402710\pi\) | ||||
0.300910 | + | 0.953653i | \(0.402710\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.7880 | 1.11062 | 0.555310 | − | 0.831644i | \(-0.312600\pi\) | ||||
0.555310 | + | 0.831644i | \(0.312600\pi\) | |||||||
\(422\) | 50.6448i | 2.46535i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.0191 | −0.583699 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 17.9578i | − 0.869039i | ||||||||
\(428\) | − 72.0844i | − 3.48433i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.99656 | 0.433349 | 0.216675 | − | 0.976244i | \(-0.430479\pi\) | ||||
0.216675 | + | 0.976244i | \(0.430479\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.3258i | 0.976797i | 0.872621 | + | 0.488398i | \(0.162419\pi\) | ||||
−0.872621 | + | 0.488398i | \(0.837581\pi\) | |||||||
\(434\) | −57.1070 | −2.74122 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 65.4328 | 3.13366 | ||||||||
\(437\) | − 17.2051i | − 0.823032i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.3906 | 1.21183 | 0.605913 | − | 0.795531i | \(-0.292808\pi\) | ||||
0.605913 | + | 0.795531i | \(0.292808\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 7.88273i | − 0.374943i | ||||||||
\(443\) | 10.9284i | 0.519223i | 0.965713 | + | 0.259611i | \(0.0835945\pi\) | ||||
−0.965713 | + | 0.259611i | \(0.916406\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −28.1104 | −1.33107 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 112.566i | 5.31823i | ||||||||
\(449\) | 2.83709 | 0.133891 | 0.0669453 | − | 0.997757i | \(-0.478675\pi\) | ||||
0.0669453 | + | 0.997757i | \(0.478675\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.71639 | −0.363350 | ||||||||
\(452\) | 75.0088i | 3.52812i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −31.4588 | −1.47643 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 13.7164i | − 0.641625i | −0.947143 | − | 0.320813i | \(-0.896044\pi\) | ||||
0.947143 | − | 0.320813i | \(-0.103956\pi\) | |||||||
\(458\) | − 17.3224i | − 0.809422i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.6251 | 0.914032 | 0.457016 | − | 0.889458i | \(-0.348918\pi\) | ||||
0.457016 | + | 0.889458i | \(0.348918\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 27.0388i | − 1.25660i | −0.777972 | − | 0.628299i | \(-0.783751\pi\) | ||||
0.777972 | − | 0.628299i | \(-0.216249\pi\) | |||||||
\(464\) | 103.660 | 4.81231 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.9966 | 0.879999 | ||||||||
\(467\) | − 28.9215i | − 1.33833i | −0.743115 | − | 0.669164i | \(-0.766652\pi\) | ||||
0.743115 | − | 0.669164i | \(-0.233348\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.12070 | 0.236452 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 21.8827i | − 1.00723i | ||||||||
\(473\) | − 30.2277i | − 1.38987i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −44.1364 | −2.02299 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 3.55691i | − 0.162689i | ||||||||
\(479\) | −12.1595 | −0.555580 | −0.277790 | − | 0.960642i | \(-0.589602\pi\) | ||||
−0.277790 | + | 0.960642i | \(0.589602\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.27674 | −0.195002 | ||||||||
\(482\) | 16.6707i | 0.759332i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 20.6060 | 0.936636 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 0.159472i | − 0.00722636i | −0.999993 | − | 0.00361318i | \(-0.998850\pi\) | ||||
0.999993 | − | 0.00361318i | \(-0.00115011\pi\) | |||||||
\(488\) | 68.2399i | 3.08907i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.2277 | 1.90571 | 0.952854 | − | 0.303430i | \(-0.0981318\pi\) | ||||
0.952854 | + | 0.303430i | \(0.0981318\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.0225i | 0.766657i | ||||||||
\(494\) | −9.88273 | −0.444645 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 130.559 | 5.86226 | ||||||||
\(497\) | − 18.2767i | − 0.819824i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.79145 | −0.348793 | −0.174397 | − | 0.984676i | \(-0.555797\pi\) | ||||
−0.174397 | + | 0.984676i | \(0.555797\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 50.6448i | 2.26039i | ||||||||
\(503\) | 27.3484i | 1.21940i | 0.792631 | + | 0.609702i | \(0.208711\pi\) | ||||
−0.792631 | + | 0.609702i | \(0.791289\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −36.5535 | −1.62500 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 76.8724i | 3.41066i | ||||||||
\(509\) | −33.4819 | −1.48406 | −0.742029 | − | 0.670368i | \(-0.766136\pi\) | ||||
−0.742029 | + | 0.670368i | \(0.766136\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.7880 | −1.09656 | ||||||||
\(512\) | − 115.084i | − 5.08603i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.09472 | −0.136502 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.4328i | 1.38241i | ||||||||
\(518\) | 32.3189i | 1.42001i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.3484 | 0.760045 | 0.380023 | − | 0.924977i | \(-0.375916\pi\) | ||||
0.380023 | + | 0.924977i | \(0.375916\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.00000i | 0.174908i | 0.996169 | + | 0.0874539i | \(0.0278730\pi\) | ||||
−0.996169 | + | 0.0874539i | \(0.972127\pi\) | |||||||
\(524\) | −53.9931 | −2.35870 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.2277 | 0.969172 | ||||||||
\(527\) | 21.4396i | 0.933926i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.397442 | −0.0172801 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 55.3346i | 2.39906i | ||||||||
\(533\) | 2.83709i | 0.122888i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −19.4588 | −0.840490 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 43.5500i | − 1.87758i | ||||||||
\(539\) | −1.08097 | −0.0465608 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.6448 | −1.40351 | −0.701754 | − | 0.712419i | \(-0.747599\pi\) | ||||
−0.701754 | + | 0.712419i | \(0.747599\pi\) | |||||||
\(542\) | − 1.23109i | − 0.0528800i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 77.5432 | 3.32464 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.2277i | 1.46347i | 0.681590 | + | 0.731734i | \(0.261289\pi\) | ||||
−0.681590 | + | 0.731734i | \(0.738711\pi\) | |||||||
\(548\) | 10.0982i | 0.431372i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.3415 | 0.909178 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.9509i | 1.18859i | ||||||||
\(554\) | −13.5569 | −0.575978 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −35.9018 | −1.52258 | ||||||||
\(557\) | − 6.65164i | − 0.281839i | −0.990021 | − | 0.140919i | \(-0.954994\pi\) | ||||
0.990021 | − | 0.140919i | \(-0.0450059\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.1138 | −0.470065 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 25.3224i | − 1.06816i | ||||||||
\(563\) | 40.2699i | 1.69717i | 0.529057 | + | 0.848586i | \(0.322546\pi\) | ||||
−0.529057 | + | 0.848586i | \(0.677454\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −92.6379 | −3.89386 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 69.4519i | 2.91414i | ||||||||
\(569\) | −13.4328 | −0.563131 | −0.281566 | − | 0.959542i | \(-0.590854\pi\) | ||||
−0.281566 | + | 0.959542i | \(0.590854\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.7164 | −1.49468 | −0.747342 | − | 0.664439i | \(-0.768670\pi\) | ||||
−0.747342 | + | 0.664439i | \(0.768670\pi\) | |||||||
\(572\) | 15.5569i | 0.650467i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 21.4396 | 0.894874 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 13.7164i | − 0.571021i | −0.958376 | − | 0.285510i | \(-0.907837\pi\) | ||||
0.958376 | − | 0.285510i | \(-0.0921631\pi\) | |||||||
\(578\) | − 24.8697i | − 1.03444i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.75859 | 0.238907 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.16291i | 0.130994i | ||||||||
\(584\) | 94.1948 | 3.89781 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −81.7777 | −3.37821 | ||||||||
\(587\) | − 30.6707i | − 1.26592i | −0.774186 | − | 0.632959i | \(-0.781840\pi\) | ||||
0.774186 | − | 0.632959i | \(-0.218160\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.8793 | 1.10754 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 73.8881i | − 3.03678i | ||||||||
\(593\) | − 45.6673i | − 1.87533i | −0.347538 | − | 0.937666i | \(-0.612982\pi\) | ||||
0.347538 | − | 0.937666i | \(-0.387018\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 119.145 | 4.88038 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13.4396i | 0.549588i | ||||||||
\(599\) | −40.2208 | −1.64338 | −0.821688 | − | 0.569937i | \(-0.806968\pi\) | ||||
−0.821688 | + | 0.569937i | \(0.806968\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.3974 | 0.709656 | 0.354828 | − | 0.934932i | \(-0.384539\pi\) | ||||
0.354828 | + | 0.934932i | \(0.384539\pi\) | |||||||
\(602\) | 83.9862i | 3.42302i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −28.5795 | −1.16288 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 14.2277i | − 0.577483i | −0.957407 | − | 0.288741i | \(-0.906763\pi\) | ||||
0.957407 | − | 0.288741i | \(-0.0932368\pi\) | |||||||
\(608\) | − 97.2173i | − 3.94268i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.5569 | 0.467543 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.8302i | 1.64912i | 0.565777 | + | 0.824558i | \(0.308576\pi\) | ||||
−0.565777 | + | 0.824558i | \(0.691424\pi\) | |||||||
\(614\) | −60.6639 | −2.44819 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 76.4553 | 3.08047 | ||||||||
\(617\) | − 5.11383i | − 0.205875i | −0.994688 | − | 0.102937i | \(-0.967176\pi\) | ||||
0.994688 | − | 0.102937i | \(-0.0328242\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.5569 | −0.464512 | −0.232256 | − | 0.972655i | \(-0.574611\pi\) | ||||
−0.232256 | + | 0.972655i | \(0.574611\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 69.7586i | 2.79706i | ||||||||
\(623\) | − 3.16291i | − 0.126719i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −22.8602 | −0.913677 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 50.7880i | − 2.02666i | ||||||||
\(629\) | 12.1335 | 0.483794 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.2242 | 1.40225 | 0.701127 | − | 0.713036i | \(-0.252681\pi\) | ||||
0.701127 | + | 0.713036i | \(0.252681\pi\) | |||||||
\(632\) | − 106.214i | − 4.22496i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −76.8915 | −3.05375 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.397442i | 0.0157472i | ||||||||
\(638\) | − 45.3415i | − 1.79509i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.9018 | 0.865071 | 0.432535 | − | 0.901617i | \(-0.357619\pi\) | ||||
0.432535 | + | 0.901617i | \(0.357619\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 7.50783i | − 0.296080i | −0.988981 | − | 0.148040i | \(-0.952704\pi\) | ||||
0.988981 | − | 0.148040i | \(-0.0472964\pi\) | |||||||
\(644\) | 75.2502 | 2.96527 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 28.0382 | 1.10315 | ||||||||
\(647\) | 14.0422i | 0.552056i | 0.961150 | + | 0.276028i | \(0.0890183\pi\) | ||||
−0.961150 | + | 0.276028i | \(0.910982\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.75859 | −0.226044 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 79.1261i | − 3.09882i | ||||||||
\(653\) | 7.99312i | 0.312795i | 0.987694 | + | 0.156398i | \(0.0499881\pi\) | ||||
−0.987694 | + | 0.156398i | \(0.950012\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −49.0157 | −1.91374 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 87.3346i | − 3.40466i | ||||||||
\(659\) | −25.3415 | −0.987164 | −0.493582 | − | 0.869699i | \(-0.664313\pi\) | ||||
−0.493582 | + | 0.869699i | \(0.664313\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.4396 | 1.06728 | 0.533639 | − | 0.845712i | \(-0.320824\pi\) | ||||
0.533639 | + | 0.845712i | \(0.320824\pi\) | |||||||
\(662\) | 36.7620i | 1.42880i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21.8827 | −0.849215 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 29.0225i | − 1.12376i | ||||||||
\(668\) | − 56.5275i | − 2.18711i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.9578 | 0.693253 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 27.1070i | − 1.04490i | −0.852671 | − | 0.522448i | \(-0.825019\pi\) | ||||
0.852671 | − | 0.522448i | \(-0.174981\pi\) | |||||||
\(674\) | −12.0191 | −0.462959 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.71982 | 0.219993 | ||||||||
\(677\) | 36.5957i | 1.40649i | 0.710949 | + | 0.703243i | \(0.248265\pi\) | ||||
−0.710949 | + | 0.703243i | \(0.751735\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.4750 | −1.13115 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 57.1070i | − 2.18674i | ||||||||
\(683\) | − 13.4656i | − 0.515248i | −0.966245 | − | 0.257624i | \(-0.917060\pi\) | ||||
0.966245 | − | 0.257624i | \(-0.0829396\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −49.8950 | −1.90500 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 192.011i | − 7.32034i | ||||||||
\(689\) | 1.16291 | 0.0443033 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.5500 | 1.12414 | 0.562068 | − | 0.827091i | \(-0.310006\pi\) | ||||
0.562068 | + | 0.827091i | \(0.310006\pi\) | |||||||
\(692\) | − 75.0088i | − 2.85141i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.4396 | −0.662000 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 8.04908i | − 0.304881i | ||||||||
\(698\) | 49.0878i | 1.85800i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.6604 | −1.64903 | −0.824516 | − | 0.565839i | \(-0.808552\pi\) | ||||
−0.824516 | + | 0.565839i | \(0.808552\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 15.2120i | − 0.573731i | ||||||||
\(704\) | −112.566 | −4.24248 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −38.2468 | −1.43944 | ||||||||
\(707\) | 20.8724i | 0.784988i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.7880 | 1.00604 | 0.503022 | − | 0.864273i | \(-0.332221\pi\) | ||||
0.503022 | + | 0.864273i | \(0.332221\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.0191i | 0.450435i | ||||||||
\(713\) | − 36.5535i | − 1.36894i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −48.9244 | −1.82839 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 2.76891i | − 0.103335i | ||||||||
\(719\) | −34.8793 | −1.30078 | −0.650389 | − | 0.759601i | \(-0.725394\pi\) | ||||
−0.650389 | + | 0.759601i | \(0.725394\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.2414 | −0.381410 | ||||||||
\(722\) | 17.6386i | 0.656443i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −21.2964 | −0.791475 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.4396i | 1.38856i | 0.719705 | + | 0.694280i | \(0.244277\pi\) | ||||
−0.719705 | + | 0.694280i | \(0.755723\pi\) | |||||||
\(728\) | − 28.1104i | − 1.04184i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.5309 | 1.16621 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.1560i | 1.74175i | 0.491506 | + | 0.870874i | \(0.336446\pi\) | ||||
−0.491506 | + | 0.870874i | \(0.663554\pi\) | |||||||
\(734\) | 39.5309 | 1.45911 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −132.207 | −4.87322 | ||||||||
\(737\) | 5.12070i | 0.188624i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.7914 | 1.16947 | 0.584734 | − | 0.811225i | \(-0.301199\pi\) | ||||
0.584734 | + | 0.811225i | \(0.301199\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 8.78801i | − 0.322618i | ||||||||
\(743\) | 16.6776i | 0.611842i | 0.952057 | + | 0.305921i | \(0.0989644\pi\) | ||||
−0.952057 | + | 0.305921i | \(0.901036\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −43.5500 | −1.59448 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 44.1364i | − 1.61379i | ||||||||
\(749\) | 34.2767 | 1.25244 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.1855 | 0.590616 | 0.295308 | − | 0.955402i | \(-0.404578\pi\) | ||||
0.295308 | + | 0.955402i | \(0.404578\pi\) | |||||||
\(752\) | 199.666i | 7.28106i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16.6707 | −0.607113 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.3258i | 0.447990i | 0.974590 | + | 0.223995i | \(0.0719099\pi\) | ||||
−0.974590 | + | 0.223995i | \(0.928090\pi\) | |||||||
\(758\) | 72.8002i | 2.64422i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.00687569 | 0.000249244 0 | 0.000124622 | − | 1.00000i | \(-0.499960\pi\) | ||||
0.000124622 | 1.00000i | \(0.499960\pi\) | ||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.1138i | 1.12640i | ||||||||
\(764\) | −24.2208 | −0.876277 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 62.3380 | 2.25237 | ||||||||
\(767\) | 2.11727i | 0.0764501i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.3258 | 0.732968 | 0.366484 | − | 0.930424i | \(-0.380561\pi\) | ||||
0.366484 | + | 0.930424i | \(0.380561\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 133.790i | − 4.81520i | ||||||||
\(773\) | 9.90184i | 0.356144i | 0.984017 | + | 0.178072i | \(0.0569861\pi\) | ||||
−0.984017 | + | 0.178072i | \(0.943014\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 112.005 | 4.02076 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 88.0054i | − 3.15514i | ||||||||
\(779\) | −10.0913 | −0.361558 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.2767 | 0.653993 | ||||||||
\(782\) | − 38.1295i | − 1.36351i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.86651 | −0.245232 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.3449i | 1.29556i | 0.761829 | + | 0.647778i | \(0.224302\pi\) | ||||
−0.761829 | + | 0.647778i | \(0.775698\pi\) | |||||||
\(788\) | 83.2433i | 2.96542i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.6673 | −1.26818 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 6.60256i | − 0.234464i | ||||||||
\(794\) | 49.8759 | 1.77003 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −86.4484 | −3.06408 | ||||||||
\(797\) | − 18.8371i | − 0.667244i | −0.942707 | − | 0.333622i | \(-0.891729\pi\) | ||||
0.942707 | − | 0.333622i | \(-0.108271\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.7880 | −1.15996 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 37.7395i | 1.33263i | ||||||||
\(803\) | − 24.7880i | − 0.874750i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.9966 | −0.739572 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 79.3155i | − 2.79031i | ||||||||
\(809\) | 32.2277 | 1.13306 | 0.566532 | − | 0.824040i | \(-0.308285\pi\) | ||||
0.566532 | + | 0.824040i | \(0.308285\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.0034 | −0.807760 | −0.403880 | − | 0.914812i | \(-0.632339\pi\) | ||||
−0.403880 | + | 0.914812i | \(0.632339\pi\) | |||||||
\(812\) | 93.3415i | 3.27564i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −32.3189 | −1.13278 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 39.5309i | − 1.38301i | ||||||||
\(818\) | − 38.8984i | − 1.36005i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.9372 | −1.74282 | −0.871410 | − | 0.490556i | \(-0.836794\pi\) | ||||
−0.871410 | + | 0.490556i | \(0.836794\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 28.2345i | − 0.984194i | −0.870540 | − | 0.492097i | \(-0.836231\pi\) | ||||
0.870540 | − | 0.492097i | \(-0.163769\pi\) | |||||||
\(824\) | 38.9175 | 1.35576 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.0000 | 0.556711 | ||||||||
\(827\) | 9.55004i | 0.332087i | 0.986118 | + | 0.166044i | \(0.0530993\pi\) | ||||
−0.986118 | + | 0.166044i | \(0.946901\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.9862 | 1.31932 | 0.659658 | − | 0.751565i | \(-0.270701\pi\) | ||||
0.659658 | + | 0.751565i | \(0.270701\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 41.3871i | 1.43484i | ||||||||
\(833\) | − 1.12758i | − 0.0390683i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −55.3346 | −1.91379 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 34.2277i | − 1.18237i | ||||||||
\(839\) | −4.72670 | −0.163184 | −0.0815919 | − | 0.996666i | \(-0.526000\pi\) | ||||
−0.0815919 | + | 0.996666i | \(0.526000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | − 63.3155i | − 2.18200i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 104.259 | 3.58874 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.79832i | 0.336674i | ||||||||
\(848\) | 20.0913i | 0.689938i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.6870 | −0.709140 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.3611i | 1.65585i | 0.560836 | + | 0.827927i | \(0.310480\pi\) | ||||
−0.560836 | + | 0.827927i | \(0.689520\pi\) | |||||||
\(854\) | −49.8950 | −1.70737 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −130.252 | −4.45193 | ||||||||
\(857\) | − 6.83709i | − 0.233551i | −0.993158 | − | 0.116775i | \(-0.962744\pi\) | ||||
0.993158 | − | 0.116775i | \(-0.0372557\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.6026 | −0.429994 | −0.214997 | − | 0.976615i | \(-0.568974\pi\) | ||||
−0.214997 | + | 0.976615i | \(0.568974\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 24.9966i | − 0.851386i | ||||||||
\(863\) | 8.20855i | 0.279422i | 0.990192 | + | 0.139711i | \(0.0446174\pi\) | ||||
−0.990192 | + | 0.139711i | \(0.955383\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 56.4744 | 1.91908 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 117.562i | 3.99032i | ||||||||
\(869\) | −27.9509 | −0.948170 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.88273 | 0.0637940 | ||||||||
\(872\) | − 118.233i | − 4.00387i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −47.8037 | −1.61698 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.5309i | 0.456907i | 0.973555 | + | 0.228454i | \(0.0733669\pi\) | ||||
−0.973555 | + | 0.228454i | \(0.926633\pi\) | |||||||
\(878\) | − 70.5466i | − 2.38083i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.34836 | 0.314954 | 0.157477 | − | 0.987523i | \(-0.449664\pi\) | ||||
0.157477 | + | 0.987523i | \(0.449664\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.1001i | 1.85427i | 0.374733 | + | 0.927133i | \(0.377734\pi\) | ||||
−0.374733 | + | 0.927133i | \(0.622266\pi\) | |||||||
\(884\) | −16.2277 | −0.545795 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.3640 | 1.02010 | ||||||||
\(887\) | − 0.133492i | − 0.00448223i | −0.999997 | − | 0.00224112i | \(-0.999287\pi\) | ||||
0.999997 | − | 0.00224112i | \(-0.000713370\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.5535 | −1.22596 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 57.8690i | 1.93760i | ||||||||
\(893\) | 41.1070i | 1.37559i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 164.083 | 5.48162 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 7.88273i | − 0.263050i | ||||||||
\(899\) | 45.3415 | 1.51222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.29928 | −0.109915 | ||||||||
\(902\) | 21.4396i | 0.713862i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 135.536 | 4.50787 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 58.5466i | − 1.94401i | −0.234964 | − | 0.972004i | \(-0.575497\pi\) | ||||
0.234964 | − | 0.972004i | \(-0.424503\pi\) | |||||||
\(908\) | 64.7620i | 2.14920i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.4622 | −1.67189 | −0.835943 | − | 0.548816i | \(-0.815079\pi\) | ||||
−0.835943 | + | 0.548816i | \(0.815079\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.75859i | 0.190582i | ||||||||
\(914\) | −38.1104 | −1.26058 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −35.6604 | −1.17825 | ||||||||
\(917\) | − 25.6742i | − 0.847836i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −56.9735 | −1.87938 | −0.939691 | − | 0.342026i | \(-0.888887\pi\) | ||||
−0.939691 | + | 0.342026i | \(0.888887\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 54.5275i | − 1.79577i | ||||||||
\(923\) | − 6.71982i | − 0.221186i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −75.1261 | −2.46880 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 163.992i | − 5.38329i | ||||||||
\(929\) | −36.5957 | −1.20067 | −0.600333 | − | 0.799750i | \(-0.704965\pi\) | ||||
−0.600333 | + | 0.799750i | \(0.704965\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.41367 | −0.0463311 | ||||||||
\(932\) | − 39.1070i | − 1.28099i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −80.3572 | −2.62937 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 47.1070i | − 1.53892i | −0.638697 | − | 0.769459i | \(-0.720526\pi\) | ||||
0.638697 | − | 0.769459i | \(-0.279474\pi\) | |||||||
\(938\) | − 14.2277i | − 0.464549i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.3611 | 1.18534 | 0.592670 | − | 0.805446i | \(-0.298074\pi\) | ||||
0.592670 | + | 0.805446i | \(0.298074\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.7233i | 0.446891i | ||||||||
\(944\) | −36.5795 | −1.19056 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −83.9862 | −2.73063 | ||||||||
\(947\) | − 44.5795i | − 1.44864i | −0.689465 | − | 0.724319i | \(-0.742154\pi\) | ||||
0.689465 | − | 0.724319i | \(-0.257846\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.11383 | −0.295847 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 79.7517i | 2.58477i | ||||||||
\(953\) | 19.8596i | 0.643317i | 0.946856 | + | 0.321658i | \(0.104240\pi\) | ||||
−0.946856 | + | 0.321658i | \(0.895760\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.32238 | −0.236823 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33.7846i | 1.09153i | ||||||||
\(959\) | −4.80176 | −0.155057 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.1070 | 0.842160 | ||||||||
\(962\) | 11.8827i | 0.383115i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 34.3189 | 1.10534 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.4068i | 1.52450i | 0.647283 | + | 0.762250i | \(0.275905\pi\) | ||||
−0.647283 | + | 0.762250i | \(0.724095\pi\) | |||||||
\(968\) | − 37.2338i | − 1.19674i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.6448 | 0.341607 | 0.170803 | − | 0.985305i | \(-0.445364\pi\) | ||||
0.170803 | + | 0.985305i | \(0.445364\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 17.0716i | − 0.547291i | ||||||||
\(974\) | −0.443086 | −0.0141974 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 114.071 | 3.65131 | ||||||||
\(977\) | 1.21199i | 0.0387750i | 0.999812 | + | 0.0193875i | \(0.00617162\pi\) | ||||
−0.999812 | + | 0.0193875i | \(0.993828\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.16291 | 0.101087 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 117.328i | − 3.74408i | ||||||||
\(983\) | 51.8759i | 1.65458i | 0.561773 | + | 0.827291i | \(0.310119\pi\) | ||||
−0.561773 | + | 0.827291i | \(0.689881\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 47.2964 | 1.50622 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20.3449i | 0.647258i | ||||||||
\(989\) | −53.7586 | −1.70942 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.6251 | −0.686944 | −0.343472 | − | 0.939163i | \(-0.611603\pi\) | ||||
−0.343472 | + | 0.939163i | \(0.611603\pi\) | |||||||
\(992\) | − 206.545i | − 6.55781i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −50.7811 | −1.61068 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.2051i | 0.734913i | 0.930041 | + | 0.367457i | \(0.119771\pi\) | ||||
−0.930041 | + | 0.367457i | \(0.880229\pi\) | |||||||
\(998\) | 21.6482i | 0.685262i | ||||||||
\(999\) | 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 | 2925.2.c.w.2224.1 | 6 | ||
3.2 | odd | 2 | 975.2.c.i.274.6 | 6 | |||
5.2 | odd | 4 | 2925.2.a.bh.1.3 | 3 | |||
5.3 | odd | 4 | 585.2.a.n.1.1 | 3 | |||
5.4 | even | 2 | inner | 2925.2.c.w.2224.6 | 6 | ||
15.2 | even | 4 | 975.2.a.o.1.1 | 3 | |||
15.8 | even | 4 | 195.2.a.e.1.3 | ✓ | 3 | ||
15.14 | odd | 2 | 975.2.c.i.274.1 | 6 | |||
20.3 | even | 4 | 9360.2.a.dd.1.3 | 3 | |||
60.23 | odd | 4 | 3120.2.a.bj.1.3 | 3 | |||
65.38 | odd | 4 | 7605.2.a.bx.1.3 | 3 | |||
105.83 | odd | 4 | 9555.2.a.bq.1.3 | 3 | |||
195.38 | even | 4 | 2535.2.a.bc.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.a.e.1.3 | ✓ | 3 | 15.8 | even | 4 | ||
585.2.a.n.1.1 | 3 | 5.3 | odd | 4 | |||
975.2.a.o.1.1 | 3 | 15.2 | even | 4 | |||
975.2.c.i.274.1 | 6 | 15.14 | odd | 2 | |||
975.2.c.i.274.6 | 6 | 3.2 | odd | 2 | |||
2535.2.a.bc.1.1 | 3 | 195.38 | even | 4 | |||
2925.2.a.bh.1.3 | 3 | 5.2 | odd | 4 | |||
2925.2.c.w.2224.1 | 6 | 1.1 | even | 1 | trivial | ||
2925.2.c.w.2224.6 | 6 | 5.4 | even | 2 | inner | ||
3120.2.a.bj.1.3 | 3 | 60.23 | odd | 4 | |||
7605.2.a.bx.1.3 | 3 | 65.38 | odd | 4 | |||
9360.2.a.dd.1.3 | 3 | 20.3 | even | 4 | |||
9555.2.a.bq.1.3 | 3 | 105.83 | odd | 4 |