Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,3,Mod(151,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("475.151");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.c (of order \(2\), degree \(1\), 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: | \(12.9428125571\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 42x^{12} + 677x^{10} + 5313x^{8} + 21125x^{6} + 40138x^{4} + 30565x^{2} + 3675 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.2 | ||
Root | \(-3.01757i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.151 |
Dual form | 475.3.c.i.151.13 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.01757i | − | 1.50879i | −0.656423 | − | 0.754393i | \(-0.727931\pi\) | ||
0.656423 | − | 0.754393i | \(-0.272069\pi\) | |||||||
\(3\) | 4.83172i | 1.61057i | 0.592885 | + | 0.805287i | \(0.297989\pi\) | ||||
−0.592885 | + | 0.805287i | \(0.702011\pi\) | |||||||
\(4\) | −5.10575 | −1.27644 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 14.5801 | 2.43001 | ||||||||
\(7\) | −6.15539 | −0.879341 | −0.439671 | − | 0.898159i | \(-0.644905\pi\) | ||||
−0.439671 | + | 0.898159i | \(0.644905\pi\) | |||||||
\(8\) | 3.33669i | 0.417086i | ||||||||
\(9\) | −14.3455 | −1.59395 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.09534 | 0.463213 | 0.231606 | − | 0.972810i | \(-0.425602\pi\) | ||||
0.231606 | + | 0.972810i | \(0.425602\pi\) | |||||||
\(12\) | − | 24.6696i | − | 2.05580i | ||||||
\(13\) | − | 4.20326i | − | 0.323328i | −0.986846 | − | 0.161664i | \(-0.948314\pi\) | ||
0.986846 | − | 0.161664i | \(-0.0516861\pi\) | |||||||
\(14\) | 18.5743i | 1.32674i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −10.3543 | −0.647144 | ||||||||
\(17\) | 1.29941 | 0.0764361 | 0.0382180 | − | 0.999269i | \(-0.487832\pi\) | ||||
0.0382180 | + | 0.999269i | \(0.487832\pi\) | |||||||
\(18\) | 43.2887i | 2.40493i | ||||||||
\(19\) | 18.3714 | − | 4.84663i | 0.966918 | − | 0.255086i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 29.7411i | − | 1.41624i | ||||||
\(22\) | − | 15.3756i | − | 0.698889i | ||||||
\(23\) | −37.1355 | −1.61459 | −0.807293 | − | 0.590151i | \(-0.799068\pi\) | ||||
−0.807293 | + | 0.590151i | \(0.799068\pi\) | |||||||
\(24\) | −16.1219 | −0.671748 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −12.6837 | −0.487833 | ||||||||
\(27\) | − | 25.8282i | − | 0.956599i | ||||||
\(28\) | 31.4279 | 1.12242 | ||||||||
\(29\) | − | 42.9209i | − | 1.48003i | −0.672590 | − | 0.740015i | \(-0.734818\pi\) | ||
0.672590 | − | 0.740015i | \(-0.265182\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 52.1594i | − | 1.68256i | −0.540599 | − | 0.841280i | \(-0.681802\pi\) | ||
0.540599 | − | 0.841280i | \(-0.318198\pi\) | |||||||
\(32\) | 44.5916i | 1.39349i | ||||||||
\(33\) | 24.6193i | 0.746038i | ||||||||
\(34\) | − | 3.92107i | − | 0.115326i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 73.2448 | 2.03458 | ||||||||
\(37\) | − | 41.8600i | − | 1.13135i | −0.824628 | − | 0.565676i | \(-0.808615\pi\) | ||
0.824628 | − | 0.565676i | \(-0.191385\pi\) | |||||||
\(38\) | −14.6251 | − | 55.4372i | −0.384870 | − | 1.45887i | ||||
\(39\) | 20.3090 | 0.520744 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.13498i | − | 0.174024i | −0.996207 | − | 0.0870119i | \(-0.972268\pi\) | ||
0.996207 | − | 0.0870119i | \(-0.0277318\pi\) | |||||||
\(42\) | −89.7461 | −2.13681 | ||||||||
\(43\) | −59.2867 | −1.37876 | −0.689380 | − | 0.724400i | \(-0.742117\pi\) | ||||
−0.689380 | + | 0.724400i | \(0.742117\pi\) | |||||||
\(44\) | −26.0155 | −0.591262 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 112.059i | 2.43607i | ||||||||
\(47\) | −57.1573 | −1.21611 | −0.608057 | − | 0.793894i | \(-0.708051\pi\) | ||||
−0.608057 | + | 0.793894i | \(0.708051\pi\) | |||||||
\(48\) | − | 50.0291i | − | 1.04227i | ||||||
\(49\) | −11.1112 | −0.226759 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.27840i | 0.123106i | ||||||||
\(52\) | 21.4608i | 0.412708i | ||||||||
\(53\) | − | 61.6167i | − | 1.16258i | −0.813697 | − | 0.581290i | \(-0.802548\pi\) | ||
0.813697 | − | 0.581290i | \(-0.197452\pi\) | |||||||
\(54\) | −77.9384 | −1.44330 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 20.5386i | − | 0.366761i | ||||||
\(57\) | 23.4176 | + | 88.7657i | 0.410835 | + | 1.55729i | ||||
\(58\) | −129.517 | −2.23305 | ||||||||
\(59\) | − | 54.5223i | − | 0.924106i | −0.886852 | − | 0.462053i | \(-0.847113\pi\) | ||
0.886852 | − | 0.462053i | \(-0.152887\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 38.4303 | 0.630006 | 0.315003 | − | 0.949091i | \(-0.397995\pi\) | ||||
0.315003 | + | 0.949091i | \(0.397995\pi\) | |||||||
\(62\) | −157.395 | −2.53863 | ||||||||
\(63\) | 88.3024 | 1.40163 | ||||||||
\(64\) | 93.1413 | 1.45533 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 74.2904 | 1.12561 | ||||||||
\(67\) | 44.7851i | 0.668435i | 0.942496 | + | 0.334217i | \(0.108472\pi\) | ||||
−0.942496 | + | 0.334217i | \(0.891528\pi\) | |||||||
\(68\) | −6.63448 | −0.0975659 | ||||||||
\(69\) | − | 179.428i | − | 2.60041i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.0537i | 0.183855i | 0.995766 | + | 0.0919277i | \(0.0293029\pi\) | ||||
−0.995766 | + | 0.0919277i | \(0.970697\pi\) | |||||||
\(72\) | − | 47.8666i | − | 0.664814i | ||||||
\(73\) | 134.087 | 1.83681 | 0.918406 | − | 0.395638i | \(-0.129477\pi\) | ||||
0.918406 | + | 0.395638i | \(0.129477\pi\) | |||||||
\(74\) | −126.316 | −1.70697 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −93.8001 | + | 24.7457i | −1.23421 | + | 0.325601i | ||||
\(77\) | −31.3638 | −0.407322 | ||||||||
\(78\) | − | 61.2839i | − | 0.785691i | ||||||
\(79\) | 128.146i | 1.62210i | 0.584977 | + | 0.811050i | \(0.301103\pi\) | ||||
−0.584977 | + | 0.811050i | \(0.698897\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.31527 | −0.0532750 | ||||||||
\(82\) | −21.5303 | −0.262565 | ||||||||
\(83\) | −23.2187 | −0.279743 | −0.139872 | − | 0.990170i | \(-0.544669\pi\) | ||||
−0.139872 | + | 0.990170i | \(0.544669\pi\) | |||||||
\(84\) | 151.851i | 1.80775i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 178.902i | 2.08026i | ||||||||
\(87\) | 207.382 | 2.38370 | ||||||||
\(88\) | 17.0015i | 0.193199i | ||||||||
\(89\) | 21.0659i | 0.236695i | 0.992972 | + | 0.118348i | \(0.0377597\pi\) | ||||
−0.992972 | + | 0.118348i | \(0.962240\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.8727i | 0.284316i | ||||||||
\(92\) | 189.605 | 2.06092 | ||||||||
\(93\) | 252.020 | 2.70989 | ||||||||
\(94\) | 172.476i | 1.83486i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −215.454 | −2.24432 | ||||||||
\(97\) | 75.9288i | 0.782771i | 0.920227 | + | 0.391385i | \(0.128004\pi\) | ||||
−0.920227 | + | 0.391385i | \(0.871996\pi\) | |||||||
\(98\) | 33.5288i | 0.342130i | ||||||||
\(99\) | −73.0954 | −0.738337 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 137.524 | 1.36162 | 0.680810 | − | 0.732460i | \(-0.261628\pi\) | ||||
0.680810 | + | 0.732460i | \(0.261628\pi\) | |||||||
\(102\) | 18.9455 | 0.185741 | ||||||||
\(103\) | 13.7280i | 0.133281i | 0.997777 | + | 0.0666407i | \(0.0212281\pi\) | ||||
−0.997777 | + | 0.0666407i | \(0.978772\pi\) | |||||||
\(104\) | 14.0250 | 0.134856 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −185.933 | −1.75408 | ||||||||
\(107\) | 64.4608i | 0.602437i | 0.953555 | + | 0.301219i | \(0.0973934\pi\) | ||||
−0.953555 | + | 0.301219i | \(0.902607\pi\) | |||||||
\(108\) | 131.872i | 1.22104i | ||||||||
\(109\) | 46.6388i | 0.427879i | 0.976847 | + | 0.213939i | \(0.0686295\pi\) | ||||
−0.976847 | + | 0.213939i | \(0.931371\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 202.256 | 1.82213 | ||||||||
\(112\) | 63.7348 | 0.569061 | ||||||||
\(113\) | 56.7151i | 0.501904i | 0.968000 | + | 0.250952i | \(0.0807436\pi\) | ||||
−0.968000 | + | 0.250952i | \(0.919256\pi\) | |||||||
\(114\) | 267.857 | − | 70.6643i | 2.34962 | − | 0.619862i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 219.143i | 1.88917i | ||||||||
\(117\) | 60.2981i | 0.515368i | ||||||||
\(118\) | −164.525 | −1.39428 | ||||||||
\(119\) | −7.99839 | −0.0672134 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −95.0375 | −0.785434 | ||||||||
\(122\) | − | 115.966i | − | 0.950544i | ||||||
\(123\) | 34.4742 | 0.280278 | ||||||||
\(124\) | 266.313i | 2.14768i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 266.459i | − | 2.11475i | ||||||
\(127\) | − | 238.179i | − | 1.87542i | −0.347417 | − | 0.937711i | \(-0.612941\pi\) | ||
0.347417 | − | 0.937711i | \(-0.387059\pi\) | |||||||
\(128\) | − | 102.694i | − | 0.802299i | ||||||
\(129\) | − | 286.457i | − | 2.22060i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −41.0781 | −0.313573 | −0.156787 | − | 0.987633i | \(-0.550113\pi\) | ||||
−0.156787 | + | 0.987633i | \(0.550113\pi\) | |||||||
\(132\) | − | 125.700i | − | 0.952271i | ||||||
\(133\) | −113.083 | + | 29.8329i | −0.850251 | + | 0.224308i | ||||
\(134\) | 135.142 | 1.00853 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.33573i | 0.0318804i | ||||||||
\(137\) | −141.611 | −1.03366 | −0.516829 | − | 0.856088i | \(-0.672888\pi\) | ||||
−0.516829 | + | 0.856088i | \(0.672888\pi\) | |||||||
\(138\) | −541.438 | −3.92347 | ||||||||
\(139\) | −133.167 | −0.958038 | −0.479019 | − | 0.877805i | \(-0.659007\pi\) | ||||
−0.479019 | + | 0.877805i | \(0.659007\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 276.168i | − | 1.95864i | ||||||
\(142\) | 39.3906 | 0.277398 | ||||||||
\(143\) | − | 21.4171i | − | 0.149770i | ||||||
\(144\) | 148.538 | 1.03152 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 404.618i | − | 2.77136i | ||||||
\(147\) | − | 53.6861i | − | 0.365211i | ||||||
\(148\) | 213.727i | 1.44410i | ||||||||
\(149\) | −275.472 | −1.84881 | −0.924403 | − | 0.381417i | \(-0.875436\pi\) | ||||
−0.924403 | + | 0.381417i | \(0.875436\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 141.099i | 0.934430i | 0.884144 | + | 0.467215i | \(0.154743\pi\) | ||||
−0.884144 | + | 0.467215i | \(0.845257\pi\) | |||||||
\(152\) | 16.1717 | + | 61.2998i | 0.106393 | + | 0.403288i | ||||
\(153\) | −18.6408 | −0.121835 | ||||||||
\(154\) | 94.6426i | 0.614562i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −103.693 | −0.664697 | ||||||||
\(157\) | −134.179 | −0.854644 | −0.427322 | − | 0.904099i | \(-0.640543\pi\) | ||||
−0.427322 | + | 0.904099i | \(0.640543\pi\) | |||||||
\(158\) | 386.690 | 2.44740 | ||||||||
\(159\) | 297.715 | 1.87242 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 228.583 | 1.41977 | ||||||||
\(162\) | 13.0217i | 0.0803806i | ||||||||
\(163\) | 176.426 | 1.08237 | 0.541183 | − | 0.840905i | \(-0.317976\pi\) | ||||
0.541183 | + | 0.840905i | \(0.317976\pi\) | |||||||
\(164\) | 36.4294i | 0.222131i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 70.0641i | 0.422073i | ||||||||
\(167\) | 174.834i | 1.04691i | 0.852053 | + | 0.523455i | \(0.175357\pi\) | ||||
−0.852053 | + | 0.523455i | \(0.824643\pi\) | |||||||
\(168\) | 99.2369 | 0.590696 | ||||||||
\(169\) | 151.333 | 0.895459 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −263.548 | + | 69.5276i | −1.54122 | + | 0.406594i | ||||
\(172\) | 302.703 | 1.75990 | ||||||||
\(173\) | − | 254.288i | − | 1.46987i | −0.678135 | − | 0.734937i | \(-0.737212\pi\) | ||
0.678135 | − | 0.734937i | \(-0.262788\pi\) | |||||||
\(174\) | − | 625.790i | − | 3.59649i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −52.7587 | −0.299765 | ||||||||
\(177\) | 263.437 | 1.48834 | ||||||||
\(178\) | 63.5678 | 0.357122 | ||||||||
\(179\) | − | 207.084i | − | 1.15689i | −0.815720 | − | 0.578447i | \(-0.803659\pi\) | ||
0.815720 | − | 0.578447i | \(-0.196341\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 137.706i | 0.760805i | 0.924821 | + | 0.380402i | \(0.124214\pi\) | ||||
−0.924821 | + | 0.380402i | \(0.875786\pi\) | |||||||
\(182\) | 78.0729 | 0.428972 | ||||||||
\(183\) | 185.685i | 1.01467i | ||||||||
\(184\) | − | 123.909i | − | 0.673421i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 760.488i | − | 4.08864i | ||||||
\(187\) | 6.62095 | 0.0354061 | ||||||||
\(188\) | 291.831 | 1.55229 | ||||||||
\(189\) | 158.983i | 0.841178i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 28.0282 | 0.146745 | 0.0733723 | − | 0.997305i | \(-0.476624\pi\) | ||||
0.0733723 | + | 0.997305i | \(0.476624\pi\) | |||||||
\(192\) | 450.033i | 2.34392i | ||||||||
\(193\) | − | 250.152i | − | 1.29612i | −0.761588 | − | 0.648062i | \(-0.775580\pi\) | ||
0.761588 | − | 0.648062i | \(-0.224420\pi\) | |||||||
\(194\) | 229.121 | 1.18103 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 56.7309 | 0.289443 | ||||||||
\(197\) | 48.2838 | 0.245096 | 0.122548 | − | 0.992463i | \(-0.460894\pi\) | ||||
0.122548 | + | 0.992463i | \(0.460894\pi\) | |||||||
\(198\) | 220.571i | 1.11399i | ||||||||
\(199\) | −265.858 | −1.33597 | −0.667984 | − | 0.744175i | \(-0.732843\pi\) | ||||
−0.667984 | + | 0.744175i | \(0.732843\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −216.389 | −1.07656 | ||||||||
\(202\) | − | 414.988i | − | 2.05440i | ||||||
\(203\) | 264.195i | 1.30145i | ||||||||
\(204\) | − | 32.0560i | − | 0.157137i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 41.4252 | 0.201093 | ||||||||
\(207\) | 532.729 | 2.57357 | ||||||||
\(208\) | 43.5219i | 0.209240i | ||||||||
\(209\) | 93.6087 | − | 24.6952i | 0.447889 | − | 0.118159i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 182.771i | 0.866213i | 0.901343 | + | 0.433107i | \(0.142583\pi\) | ||||
−0.901343 | + | 0.433107i | \(0.857417\pi\) | |||||||
\(212\) | 314.600i | 1.48396i | ||||||||
\(213\) | −63.0720 | −0.296113 | ||||||||
\(214\) | 194.515 | 0.908949 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 86.1806 | 0.398984 | ||||||||
\(217\) | 321.061i | 1.47955i | ||||||||
\(218\) | 140.736 | 0.645577 | ||||||||
\(219\) | 647.873i | 2.95832i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 5.46178i | − | 0.0247139i | ||||||
\(222\) | − | 610.323i | − | 2.74920i | ||||||
\(223\) | 106.620i | 0.478118i | 0.971005 | + | 0.239059i | \(0.0768390\pi\) | ||||
−0.971005 | + | 0.239059i | \(0.923161\pi\) | |||||||
\(224\) | − | 274.479i | − | 1.22535i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 171.142 | 0.757266 | ||||||||
\(227\) | − | 35.0010i | − | 0.154189i | −0.997024 | − | 0.0770947i | \(-0.975436\pi\) | ||
0.997024 | − | 0.0770947i | \(-0.0245644\pi\) | |||||||
\(228\) | −119.564 | − | 453.216i | −0.524405 | − | 1.98779i | ||||
\(229\) | −77.3701 | −0.337861 | −0.168930 | − | 0.985628i | \(-0.554031\pi\) | ||||
−0.168930 | + | 0.985628i | \(0.554031\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 151.541i | − | 0.656022i | ||||||
\(232\) | 143.214 | 0.617300 | ||||||||
\(233\) | 89.0034 | 0.381989 | 0.190994 | − | 0.981591i | \(-0.438829\pi\) | ||||
0.190994 | + | 0.981591i | \(0.438829\pi\) | |||||||
\(234\) | 181.954 | 0.777581 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 278.377i | 1.17956i | ||||||||
\(237\) | −619.165 | −2.61251 | ||||||||
\(238\) | 24.1357i | 0.101411i | ||||||||
\(239\) | 47.2189 | 0.197569 | 0.0987843 | − | 0.995109i | \(-0.468505\pi\) | ||||
0.0987843 | + | 0.995109i | \(0.468505\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 73.1493i | 0.303524i | 0.988417 | + | 0.151762i | \(0.0484947\pi\) | ||||
−0.988417 | + | 0.151762i | \(0.951505\pi\) | |||||||
\(242\) | 286.783i | 1.18505i | ||||||||
\(243\) | − | 253.304i | − | 1.04240i | ||||||
\(244\) | −196.216 | −0.804163 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 104.029i | − | 0.422880i | ||||||
\(247\) | −20.3717 | − | 77.2200i | −0.0824765 | − | 0.312632i | ||||
\(248\) | 174.039 | 0.701772 | ||||||||
\(249\) | − | 112.186i | − | 0.450547i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 266.248 | 1.06075 | 0.530374 | − | 0.847764i | \(-0.322051\pi\) | ||||
0.530374 | + | 0.847764i | \(0.322051\pi\) | |||||||
\(252\) | −450.850 | −1.78909 | ||||||||
\(253\) | −189.218 | −0.747896 | ||||||||
\(254\) | −718.721 | −2.82961 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 62.6778 | 0.244835 | ||||||||
\(257\) | − | 76.0071i | − | 0.295747i | −0.989006 | − | 0.147874i | \(-0.952757\pi\) | ||
0.989006 | − | 0.147874i | \(-0.0472429\pi\) | |||||||
\(258\) | −864.405 | −3.35041 | ||||||||
\(259\) | 257.665i | 0.994845i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 615.723i | 2.35909i | ||||||||
\(262\) | 123.956i | 0.473115i | ||||||||
\(263\) | 291.378 | 1.10790 | 0.553951 | − | 0.832549i | \(-0.313119\pi\) | ||||
0.553951 | + | 0.832549i | \(0.313119\pi\) | |||||||
\(264\) | −82.1468 | −0.311162 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 90.0231 | + | 341.238i | 0.338433 | + | 1.28285i | ||||
\(267\) | −101.784 | −0.381215 | ||||||||
\(268\) | − | 228.662i | − | 0.853215i | ||||||
\(269\) | − | 406.215i | − | 1.51009i | −0.655672 | − | 0.755046i | \(-0.727615\pi\) | ||
0.655672 | − | 0.755046i | \(-0.272385\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −289.751 | −1.06919 | −0.534596 | − | 0.845108i | \(-0.679536\pi\) | ||||
−0.534596 | + | 0.845108i | \(0.679536\pi\) | |||||||
\(272\) | −13.4545 | −0.0494652 | ||||||||
\(273\) | −125.010 | −0.457912 | ||||||||
\(274\) | 427.322i | 1.55957i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 916.116i | 3.31926i | ||||||||
\(277\) | 102.717 | 0.370820 | 0.185410 | − | 0.982661i | \(-0.440639\pi\) | ||||
0.185410 | + | 0.982661i | \(0.440639\pi\) | |||||||
\(278\) | 401.842i | 1.44547i | ||||||||
\(279\) | 748.255i | 2.68192i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 0.126667i | − | 0.000450774i | −1.00000 | 0.000225387i | \(-0.999928\pi\) | |||
1.00000 | 0.000225387i | \(-7.17429e-5\pi\) | ||||||||
\(282\) | −833.358 | −2.95517 | ||||||||
\(283\) | 84.2579 | 0.297731 | 0.148866 | − | 0.988857i | \(-0.452438\pi\) | ||||
0.148866 | + | 0.988857i | \(0.452438\pi\) | |||||||
\(284\) | − | 66.6491i | − | 0.234680i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −64.6275 | −0.225970 | ||||||||
\(287\) | 43.9186i | 0.153026i | ||||||||
\(288\) | − | 639.691i | − | 2.22115i | ||||||
\(289\) | −287.312 | −0.994158 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −366.867 | −1.26071 | ||||||||
\(292\) | −684.617 | −2.34458 | ||||||||
\(293\) | − | 404.118i | − | 1.37924i | −0.724171 | − | 0.689621i | \(-0.757777\pi\) | ||
0.724171 | − | 0.689621i | \(-0.242223\pi\) | |||||||
\(294\) | −162.002 | −0.551026 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 139.674 | 0.471871 | ||||||||
\(297\) | − | 131.603i | − | 0.443109i | ||||||
\(298\) | 831.258i | 2.78946i | ||||||||
\(299\) | 156.090i | 0.522041i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 364.933 | 1.21240 | ||||||||
\(302\) | 425.777 | 1.40986 | ||||||||
\(303\) | 664.476i | 2.19299i | ||||||||
\(304\) | −190.224 | + | 50.1835i | −0.625736 | + | 0.165077i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 56.2499i | 0.183823i | ||||||||
\(307\) | − | 158.822i | − | 0.517335i | −0.965966 | − | 0.258667i | \(-0.916717\pi\) | ||
0.965966 | − | 0.258667i | \(-0.0832833\pi\) | |||||||
\(308\) | 160.136 | 0.519921 | ||||||||
\(309\) | −66.3298 | −0.214659 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 256.822 | 0.825793 | 0.412897 | − | 0.910778i | \(-0.364517\pi\) | ||||
0.412897 | + | 0.910778i | \(0.364517\pi\) | |||||||
\(312\) | 67.7648i | 0.217195i | ||||||||
\(313\) | −429.290 | −1.37153 | −0.685766 | − | 0.727822i | \(-0.740533\pi\) | ||||
−0.685766 | + | 0.727822i | \(0.740533\pi\) | |||||||
\(314\) | 404.895i | 1.28948i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 654.281i | − | 2.07051i | ||||||
\(317\) | − | 230.765i | − | 0.727966i | −0.931406 | − | 0.363983i | \(-0.881417\pi\) | ||
0.931406 | − | 0.363983i | \(-0.118583\pi\) | |||||||
\(318\) | − | 898.376i | − | 2.82508i | ||||||
\(319\) | − | 218.696i | − | 0.685569i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −311.457 | −0.970270 | ||||||||
\(322\) | − | 689.767i | − | 2.14213i | ||||||
\(323\) | 23.8721 | − | 6.29778i | 0.0739074 | − | 0.0194978i | ||||
\(324\) | 22.0327 | 0.0680022 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 532.378i | − | 1.63306i | ||||||
\(327\) | −225.346 | −0.689130 | ||||||||
\(328\) | 23.8072 | 0.0725829 | ||||||||
\(329\) | 351.826 | 1.06938 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 528.588i | 1.59694i | 0.602032 | + | 0.798472i | \(0.294358\pi\) | ||||
−0.602032 | + | 0.798472i | \(0.705642\pi\) | |||||||
\(332\) | 118.549 | 0.357075 | ||||||||
\(333\) | 600.505i | 1.80332i | ||||||||
\(334\) | 527.575 | 1.57957 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 307.949i | 0.916515i | ||||||||
\(337\) | 61.4407i | 0.182317i | 0.995836 | + | 0.0911583i | \(0.0290569\pi\) | ||||
−0.995836 | + | 0.0911583i | \(0.970943\pi\) | |||||||
\(338\) | − | 456.657i | − | 1.35106i | ||||||
\(339\) | −274.032 | −0.808353 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 265.770i | − | 0.779383i | ||||||
\(342\) | 209.805 | + | 795.277i | 0.613464 | + | 2.32537i | ||||
\(343\) | 370.008 | 1.07874 | ||||||||
\(344\) | − | 197.821i | − | 0.575061i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −767.333 | −2.21773 | ||||||||
\(347\) | 555.017 | 1.59947 | 0.799737 | − | 0.600351i | \(-0.204972\pi\) | ||||
0.799737 | + | 0.600351i | \(0.204972\pi\) | |||||||
\(348\) | −1058.84 | −3.04264 | ||||||||
\(349\) | 34.6618 | 0.0993176 | 0.0496588 | − | 0.998766i | \(-0.484187\pi\) | ||||
0.0496588 | + | 0.998766i | \(0.484187\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −108.563 | −0.309295 | ||||||||
\(352\) | 227.209i | 0.645481i | ||||||||
\(353\) | 493.002 | 1.39661 | 0.698303 | − | 0.715802i | \(-0.253939\pi\) | ||||
0.698303 | + | 0.715802i | \(0.253939\pi\) | |||||||
\(354\) | − | 794.939i | − | 2.24559i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 107.557i | − | 0.302127i | ||||||
\(357\) | − | 38.6460i | − | 0.108252i | ||||||
\(358\) | −624.892 | −1.74551 | ||||||||
\(359\) | 145.520 | 0.405349 | 0.202675 | − | 0.979246i | \(-0.435037\pi\) | ||||
0.202675 | + | 0.979246i | \(0.435037\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 314.020 | − | 178.079i | 0.869862 | − | 0.493295i | ||||
\(362\) | 415.537 | 1.14789 | ||||||||
\(363\) | − | 459.195i | − | 1.26500i | ||||||
\(364\) | − | 132.100i | − | 0.362911i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 560.317 | 1.53092 | ||||||||
\(367\) | −342.929 | −0.934413 | −0.467206 | − | 0.884148i | \(-0.654739\pi\) | ||||
−0.467206 | + | 0.884148i | \(0.654739\pi\) | |||||||
\(368\) | 384.512 | 1.04487 | ||||||||
\(369\) | 102.355i | 0.277385i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 379.275i | 1.02230i | ||||||||
\(372\) | −1286.75 | −3.45900 | ||||||||
\(373\) | 16.6464i | 0.0446283i | 0.999751 | + | 0.0223141i | \(0.00710340\pi\) | ||||
−0.999751 | + | 0.0223141i | \(0.992897\pi\) | |||||||
\(374\) | − | 19.9792i | − | 0.0534203i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 190.716i | − | 0.507224i | ||||||
\(377\) | −180.408 | −0.478535 | ||||||||
\(378\) | 479.742 | 1.26916 | ||||||||
\(379\) | 312.804i | 0.825341i | 0.910880 | + | 0.412671i | \(0.135404\pi\) | ||||
−0.910880 | + | 0.412671i | \(0.864596\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1150.81 | 3.02051 | ||||||||
\(382\) | − | 84.5772i | − | 0.221406i | ||||||
\(383\) | 493.251i | 1.28786i | 0.765083 | + | 0.643931i | \(0.222698\pi\) | ||||
−0.765083 | + | 0.643931i | \(0.777302\pi\) | |||||||
\(384\) | 496.190 | 1.29216 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −754.852 | −1.95557 | ||||||||
\(387\) | 850.500 | 2.19767 | ||||||||
\(388\) | − | 387.673i | − | 0.999158i | ||||||
\(389\) | −407.055 | −1.04641 | −0.523207 | − | 0.852205i | \(-0.675265\pi\) | ||||
−0.523207 | + | 0.852205i | \(0.675265\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −48.2543 | −0.123413 | ||||||||
\(392\) | − | 37.0745i | − | 0.0945778i | ||||||
\(393\) | − | 198.478i | − | 0.505033i | ||||||
\(394\) | − | 145.700i | − | 0.369797i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 373.207 | 0.942442 | ||||||||
\(397\) | −208.967 | −0.526366 | −0.263183 | − | 0.964746i | \(-0.584772\pi\) | ||||
−0.263183 | + | 0.964746i | \(0.584772\pi\) | |||||||
\(398\) | 802.245i | 2.01569i | ||||||||
\(399\) | −144.144 | − | 546.388i | −0.361264 | − | 1.36939i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 240.966i | − | 0.600913i | −0.953796 | − | 0.300456i | \(-0.902861\pi\) | ||
0.953796 | − | 0.300456i | \(-0.0971390\pi\) | |||||||
\(402\) | 652.971i | 1.62430i | ||||||||
\(403\) | −219.240 | −0.544019 | ||||||||
\(404\) | −702.162 | −1.73802 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 797.227 | 1.96361 | ||||||||
\(407\) | − | 213.291i | − | 0.524056i | ||||||
\(408\) | −20.9491 | −0.0513457 | ||||||||
\(409\) | 259.859i | 0.635352i | 0.948199 | + | 0.317676i | \(0.102902\pi\) | ||||
−0.948199 | + | 0.317676i | \(0.897098\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 684.226i | − | 1.66478i | ||||||
\(412\) | − | 70.0916i | − | 0.170125i | ||||||
\(413\) | 335.606i | 0.812605i | ||||||||
\(414\) | − | 1607.55i | − | 3.88297i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 187.430 | 0.450554 | ||||||||
\(417\) | − | 643.427i | − | 1.54299i | ||||||
\(418\) | −74.5197 | − | 282.471i | −0.178277 | − | 0.675769i | ||||
\(419\) | −729.115 | −1.74013 | −0.870066 | − | 0.492935i | \(-0.835924\pi\) | ||||
−0.870066 | + | 0.492935i | \(0.835924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 608.641i | − | 1.44570i | −0.691003 | − | 0.722851i | \(-0.742831\pi\) | ||
0.691003 | − | 0.722851i | \(-0.257169\pi\) | |||||||
\(422\) | 551.525 | 1.30693 | ||||||||
\(423\) | 819.953 | 1.93842 | ||||||||
\(424\) | 205.596 | 0.484895 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 190.324i | 0.446771i | ||||||||
\(427\) | −236.554 | −0.553990 | ||||||||
\(428\) | − | 329.121i | − | 0.768973i | ||||||
\(429\) | 103.481 | 0.241215 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 537.936i | − | 1.24811i | −0.781380 | − | 0.624056i | \(-0.785484\pi\) | ||
0.781380 | − | 0.624056i | \(-0.214516\pi\) | |||||||
\(432\) | 267.433i | 0.619058i | ||||||||
\(433\) | 255.532i | 0.590144i | 0.955475 | + | 0.295072i | \(0.0953437\pi\) | ||||
−0.955475 | + | 0.295072i | \(0.904656\pi\) | |||||||
\(434\) | 968.826 | 2.23232 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 238.126i | − | 0.546160i | ||||||
\(437\) | −682.233 | + | 179.982i | −1.56117 | + | 0.411858i | ||||
\(438\) | 1955.00 | 4.46348 | ||||||||
\(439\) | − | 699.710i | − | 1.59387i | −0.604063 | − | 0.796937i | \(-0.706452\pi\) | ||
0.604063 | − | 0.796937i | \(-0.293548\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 159.396 | 0.361442 | ||||||||
\(442\) | −16.4813 | −0.0372880 | ||||||||
\(443\) | −682.143 | −1.53983 | −0.769913 | − | 0.638149i | \(-0.779701\pi\) | ||||
−0.769913 | + | 0.638149i | \(0.779701\pi\) | |||||||
\(444\) | −1032.67 | −2.32583 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 321.735 | 0.721378 | ||||||||
\(447\) | − | 1331.01i | − | 2.97764i | ||||||
\(448\) | −573.321 | −1.27973 | ||||||||
\(449\) | − | 675.642i | − | 1.50477i | −0.658723 | − | 0.752386i | \(-0.728903\pi\) | ||
0.658723 | − | 0.752386i | \(-0.271097\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 36.3551i | − | 0.0806100i | ||||||
\(452\) | − | 289.573i | − | 0.640649i | ||||||
\(453\) | −681.751 | −1.50497 | ||||||||
\(454\) | −105.618 | −0.232639 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −296.183 | + | 78.1372i | −0.649525 | + | 0.171353i | ||||
\(457\) | −124.772 | −0.273024 | −0.136512 | − | 0.990638i | \(-0.543589\pi\) | ||||
−0.136512 | + | 0.990638i | \(0.543589\pi\) | |||||||
\(458\) | 233.470i | 0.509759i | ||||||||
\(459\) | − | 33.5615i | − | 0.0731187i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 328.840 | 0.713320 | 0.356660 | − | 0.934234i | \(-0.383916\pi\) | ||||
0.356660 | + | 0.934234i | \(0.383916\pi\) | |||||||
\(462\) | −457.287 | −0.989798 | ||||||||
\(463\) | −122.860 | −0.265356 | −0.132678 | − | 0.991159i | \(-0.542358\pi\) | ||||
−0.132678 | + | 0.991159i | \(0.542358\pi\) | |||||||
\(464\) | 444.416i | 0.957793i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 268.574i | − | 0.576340i | ||||||
\(467\) | 653.452 | 1.39925 | 0.699627 | − | 0.714508i | \(-0.253349\pi\) | ||||
0.699627 | + | 0.714508i | \(0.253349\pi\) | |||||||
\(468\) | − | 307.867i | − | 0.657836i | ||||||
\(469\) | − | 275.670i | − | 0.587782i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 648.316i | − | 1.37647i | ||||||
\(472\) | 181.924 | 0.385432 | ||||||||
\(473\) | −302.086 | −0.638659 | ||||||||
\(474\) | 1868.38i | 3.94172i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 40.8378 | 0.0857937 | ||||||||
\(477\) | 883.925i | 1.85309i | ||||||||
\(478\) | − | 142.487i | − | 0.298089i | ||||||
\(479\) | 360.148 | 0.751874 | 0.375937 | − | 0.926645i | \(-0.377321\pi\) | ||||
0.375937 | + | 0.926645i | \(0.377321\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −175.949 | −0.365798 | ||||||||
\(482\) | 220.733 | 0.457953 | ||||||||
\(483\) | 1104.45i | 2.28665i | ||||||||
\(484\) | 485.238 | 1.00256 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −764.363 | −1.57276 | ||||||||
\(487\) | 47.1304i | 0.0967770i | 0.998829 | + | 0.0483885i | \(0.0154085\pi\) | ||||
−0.998829 | + | 0.0483885i | \(0.984591\pi\) | |||||||
\(488\) | 128.230i | 0.262766i | ||||||||
\(489\) | 852.440i | 1.74323i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −744.260 | −1.51580 | −0.757902 | − | 0.652369i | \(-0.773775\pi\) | ||||
−0.757902 | + | 0.652369i | \(0.773775\pi\) | |||||||
\(492\) | −176.017 | −0.357758 | ||||||||
\(493\) | − | 55.7720i | − | 0.113128i | ||||||
\(494\) | −233.017 | + | 61.4731i | −0.471695 | + | 0.124439i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 540.074i | 1.08886i | ||||||||
\(497\) | − | 80.3508i | − | 0.161672i | ||||||
\(498\) | −338.530 | −0.679779 | ||||||||
\(499\) | 814.737 | 1.63274 | 0.816370 | − | 0.577529i | \(-0.195983\pi\) | ||||
0.816370 | + | 0.577529i | \(0.195983\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −844.750 | −1.68613 | ||||||||
\(502\) | − | 803.423i | − | 1.60044i | ||||||
\(503\) | −618.711 | −1.23004 | −0.615020 | − | 0.788511i | \(-0.710852\pi\) | ||||
−0.615020 | + | 0.788511i | \(0.710852\pi\) | |||||||
\(504\) | 294.637i | 0.584598i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 570.979i | 1.12842i | ||||||||
\(507\) | 731.197i | 1.44220i | ||||||||
\(508\) | 1216.08i | 2.39386i | ||||||||
\(509\) | 309.300i | 0.607661i | 0.952726 | + | 0.303831i | \(0.0982657\pi\) | ||||
−0.952726 | + | 0.303831i | \(0.901734\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −825.360 | −1.61519 | ||||||||
\(512\) | − | 599.912i | − | 1.17170i | ||||||
\(513\) | −125.180 | − | 474.501i | −0.244015 | − | 0.924954i | ||||
\(514\) | −229.357 | −0.446220 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1462.58i | 2.83445i | ||||||||
\(517\) | −291.236 | −0.563319 | ||||||||
\(518\) | 777.523 | 1.50101 | ||||||||
\(519\) | 1228.65 | 2.36734 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 163.664i | 0.314134i | 0.987588 | + | 0.157067i | \(0.0502039\pi\) | ||||
−0.987588 | + | 0.157067i | \(0.949796\pi\) | |||||||
\(522\) | 1857.99 | 3.55937 | ||||||||
\(523\) | − | 579.994i | − | 1.10897i | −0.832192 | − | 0.554487i | \(-0.812914\pi\) | ||
0.832192 | − | 0.554487i | \(-0.187086\pi\) | |||||||
\(524\) | 209.734 | 0.400257 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 879.256i | − | 1.67159i | ||||||
\(527\) | − | 67.7766i | − | 0.128608i | ||||||
\(528\) | − | 254.915i | − | 0.482794i | ||||||
\(529\) | 850.044 | 1.60689 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 782.152i | 1.47298i | ||||||||
\(532\) | 577.376 | − | 152.320i | 1.08529 | − | 0.286315i | ||||
\(533\) | −29.9902 | −0.0562668 | ||||||||
\(534\) | 307.142i | 0.575172i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −149.434 | −0.278795 | ||||||||
\(537\) | 1000.57 | 1.86327 | ||||||||
\(538\) | −1225.78 | −2.27841 | ||||||||
\(539\) | −56.6152 | −0.105037 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −706.641 | −1.30618 | −0.653088 | − | 0.757282i | \(-0.726527\pi\) | ||||
−0.653088 | + | 0.757282i | \(0.726527\pi\) | |||||||
\(542\) | 874.345i | 1.61318i | ||||||||
\(543\) | −665.356 | −1.22533 | ||||||||
\(544\) | 57.9429i | 0.106513i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 377.226i | 0.690891i | ||||||||
\(547\) | 726.986i | 1.32904i | 0.747269 | + | 0.664521i | \(0.231364\pi\) | ||||
−0.747269 | + | 0.664521i | \(0.768636\pi\) | |||||||
\(548\) | 723.032 | 1.31940 | ||||||||
\(549\) | −551.304 | −1.00420 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −208.022 | − | 788.519i | −0.377535 | − | 1.43107i | ||||
\(552\) | 598.696 | 1.08459 | ||||||||
\(553\) | − | 788.788i | − | 1.42638i | ||||||
\(554\) | − | 309.957i | − | 0.559489i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 679.919 | 1.22288 | ||||||||
\(557\) | −12.5711 | −0.0225692 | −0.0112846 | − | 0.999936i | \(-0.503592\pi\) | ||||
−0.0112846 | + | 0.999936i | \(0.503592\pi\) | |||||||
\(558\) | 2257.91 | 4.04644 | ||||||||
\(559\) | 249.198i | 0.445792i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.9906i | 0.0570242i | ||||||||
\(562\) | −0.382228 | −0.000680122 | ||||||||
\(563\) | − | 635.525i | − | 1.12882i | −0.825495 | − | 0.564410i | \(-0.809104\pi\) | ||
0.825495 | − | 0.564410i | \(-0.190896\pi\) | |||||||
\(564\) | 1410.05i | 2.50008i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 254.255i | − | 0.449213i | ||||||
\(567\) | 26.5622 | 0.0468469 | ||||||||
\(568\) | −43.5562 | −0.0766834 | ||||||||
\(569\) | 306.296i | 0.538306i | 0.963097 | + | 0.269153i | \(0.0867438\pi\) | ||||
−0.963097 | + | 0.269153i | \(0.913256\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 127.895 | 0.223984 | 0.111992 | − | 0.993709i | \(-0.464277\pi\) | ||||
0.111992 | + | 0.993709i | \(0.464277\pi\) | |||||||
\(572\) | 109.350i | 0.191172i | ||||||||
\(573\) | 135.425i | 0.236343i | ||||||||
\(574\) | 132.528 | 0.230884 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1336.16 | −2.31973 | ||||||||
\(577\) | 558.970 | 0.968752 | 0.484376 | − | 0.874860i | \(-0.339047\pi\) | ||||
0.484376 | + | 0.874860i | \(0.339047\pi\) | |||||||
\(578\) | 866.984i | 1.49997i | ||||||||
\(579\) | 1208.66 | 2.08750 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 142.920 | 0.245990 | ||||||||
\(582\) | 1107.05i | 1.90214i | ||||||||
\(583\) | − | 313.958i | − | 0.538521i | ||||||
\(584\) | 447.407i | 0.766109i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1219.46 | −2.08098 | ||||||||
\(587\) | −140.817 | −0.239893 | −0.119946 | − | 0.992780i | \(-0.538272\pi\) | ||||
−0.119946 | + | 0.992780i | \(0.538272\pi\) | |||||||
\(588\) | 274.108i | 0.466170i | ||||||||
\(589\) | −252.797 | − | 958.243i | −0.429198 | − | 1.62690i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 233.294i | 0.394745i | ||||||||
\(592\) | 433.432i | 0.732148i | ||||||||
\(593\) | −340.511 | −0.574218 | −0.287109 | − | 0.957898i | \(-0.592694\pi\) | ||||
−0.287109 | + | 0.957898i | \(0.592694\pi\) | |||||||
\(594\) | −397.123 | −0.668557 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1406.49 | 2.35989 | ||||||||
\(597\) | − | 1284.55i | − | 2.15168i | ||||||
\(598\) | 471.014 | 0.787648 | ||||||||
\(599\) | 694.681i | 1.15973i | 0.814711 | + | 0.579867i | \(0.196896\pi\) | ||||
−0.814711 | + | 0.579867i | \(0.803104\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 243.254i | 0.404749i | 0.979308 | + | 0.202375i | \(0.0648658\pi\) | ||||
−0.979308 | + | 0.202375i | \(0.935134\pi\) | |||||||
\(602\) | − | 1101.21i | − | 1.82925i | ||||||
\(603\) | − | 642.467i | − | 1.06545i | ||||||
\(604\) | − | 720.416i | − | 1.19274i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2005.11 | 3.30876 | ||||||||
\(607\) | 942.849i | 1.55329i | 0.629936 | + | 0.776647i | \(0.283081\pi\) | ||||
−0.629936 | + | 0.776647i | \(0.716919\pi\) | |||||||
\(608\) | 216.119 | + | 819.213i | 0.355459 | + | 1.34739i | ||||
\(609\) | −1276.52 | −2.09609 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 240.247i | 0.393203i | ||||||||
\(612\) | 95.1752 | 0.155515 | ||||||||
\(613\) | 402.930 | 0.657308 | 0.328654 | − | 0.944450i | \(-0.393405\pi\) | ||||
0.328654 | + | 0.944450i | \(0.393405\pi\) | |||||||
\(614\) | −479.256 | −0.780548 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 104.651i | − | 0.169888i | ||||||
\(617\) | −964.671 | −1.56349 | −0.781743 | − | 0.623600i | \(-0.785669\pi\) | ||||
−0.781743 | + | 0.623600i | \(0.785669\pi\) | |||||||
\(618\) | 200.155i | 0.323875i | ||||||||
\(619\) | 830.004 | 1.34088 | 0.670439 | − | 0.741964i | \(-0.266106\pi\) | ||||
0.670439 | + | 0.741964i | \(0.266106\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 959.142i | 1.54451i | ||||||||
\(622\) | − | 774.978i | − | 1.24595i | ||||||
\(623\) | − | 129.669i | − | 0.208136i | ||||||
\(624\) | −210.286 | −0.336996 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1295.41i | 2.06935i | ||||||||
\(627\) | 119.321 | + | 452.291i | 0.190304 | + | 0.721358i | ||||
\(628\) | 685.085 | 1.09090 | ||||||||
\(629\) | − | 54.3935i | − | 0.0864761i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 775.784 | 1.22945 | 0.614726 | − | 0.788741i | \(-0.289267\pi\) | ||||
0.614726 | + | 0.788741i | \(0.289267\pi\) | |||||||
\(632\) | −427.583 | −0.676555 | ||||||||
\(633\) | −883.099 | −1.39510 | ||||||||
\(634\) | −696.351 | −1.09834 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1520.06 | −2.39003 | ||||||||
\(637\) | 46.7032i | 0.0733174i | ||||||||
\(638\) | −659.933 | −1.03438 | ||||||||
\(639\) | − | 187.263i | − | 0.293056i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 277.516i | − | 0.432943i | −0.976289 | − | 0.216471i | \(-0.930545\pi\) | ||
0.976289 | − | 0.216471i | \(-0.0694548\pi\) | |||||||
\(642\) | 939.843i | 1.46393i | ||||||||
\(643\) | 617.315 | 0.960055 | 0.480027 | − | 0.877254i | \(-0.340627\pi\) | ||||
0.480027 | + | 0.877254i | \(0.340627\pi\) | |||||||
\(644\) | −1167.09 | −1.81225 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −19.0040 | − | 72.0358i | −0.0294180 | − | 0.111511i | ||||
\(647\) | −642.107 | −0.992437 | −0.496218 | − | 0.868198i | \(-0.665278\pi\) | ||||
−0.496218 | + | 0.868198i | \(0.665278\pi\) | |||||||
\(648\) | − | 14.3987i | − | 0.0222202i | ||||||
\(649\) | − | 277.809i | − | 0.428058i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1551.28 | −2.38292 | ||||||||
\(652\) | −900.786 | −1.38157 | ||||||||
\(653\) | 803.876 | 1.23105 | 0.615525 | − | 0.788117i | \(-0.288944\pi\) | ||||
0.615525 | + | 0.788117i | \(0.288944\pi\) | |||||||
\(654\) | 679.997i | 1.03975i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 73.8777i | 0.112619i | ||||||||
\(657\) | −1923.56 | −2.92779 | ||||||||
\(658\) | − | 1061.66i | − | 1.61346i | ||||||
\(659\) | − | 1024.56i | − | 1.55472i | −0.629054 | − | 0.777362i | \(-0.716558\pi\) | ||
0.629054 | − | 0.777362i | \(-0.283442\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1059.45i | 1.60281i | 0.598125 | + | 0.801403i | \(0.295913\pi\) | ||||
−0.598125 | + | 0.801403i | \(0.704087\pi\) | |||||||
\(662\) | 1595.05 | 2.40945 | ||||||||
\(663\) | 26.3898 | 0.0398036 | ||||||||
\(664\) | − | 77.4734i | − | 0.116677i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1812.07 | 2.72082 | ||||||||
\(667\) | 1593.89i | 2.38964i | ||||||||
\(668\) | − | 892.659i | − | 1.33632i | ||||||
\(669\) | −515.160 | −0.770045 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 195.816 | 0.291826 | ||||||||
\(672\) | 1326.21 | 1.97352 | ||||||||
\(673\) | − | 766.057i | − | 1.13827i | −0.822243 | − | 0.569136i | \(-0.807278\pi\) | ||
0.822243 | − | 0.569136i | \(-0.192722\pi\) | |||||||
\(674\) | 185.402 | 0.275077 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −772.666 | −1.14300 | ||||||||
\(677\) | − | 386.540i | − | 0.570960i | −0.958385 | − | 0.285480i | \(-0.907847\pi\) | ||
0.958385 | − | 0.285480i | \(-0.0921531\pi\) | |||||||
\(678\) | 826.911i | 1.21963i | ||||||||
\(679\) | − | 467.371i | − | 0.688323i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 169.115 | 0.248334 | ||||||||
\(682\) | −801.979 | −1.17592 | ||||||||
\(683\) | − | 1160.28i | − | 1.69880i | −0.527746 | − | 0.849402i | \(-0.676963\pi\) | ||
0.527746 | − | 0.849402i | \(-0.323037\pi\) | |||||||
\(684\) | 1345.61 | − | 354.991i | 1.96727 | − | 0.518992i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 1116.53i | − | 1.62759i | ||||||
\(687\) | − | 373.831i | − | 0.544149i | ||||||
\(688\) | 613.873 | 0.892257 | ||||||||
\(689\) | −258.991 | −0.375894 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −180.805 | −0.261657 | −0.130828 | − | 0.991405i | \(-0.541764\pi\) | ||||
−0.130828 | + | 0.991405i | \(0.541764\pi\) | |||||||
\(692\) | 1298.33i | 1.87620i | ||||||||
\(693\) | 449.931 | 0.649251 | ||||||||
\(694\) | − | 1674.81i | − | 2.41327i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 691.968i | 0.994207i | ||||||||
\(697\) | − | 9.27128i | − | 0.0133017i | ||||||
\(698\) | − | 104.595i | − | 0.149849i | ||||||
\(699\) | 430.040i | 0.615221i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1195.12 | 1.70488 | 0.852442 | − | 0.522821i | \(-0.175121\pi\) | ||||
0.852442 | + | 0.522821i | \(0.175121\pi\) | |||||||
\(702\) | 327.596i | 0.466661i | ||||||||
\(703\) | −202.880 | − | 769.029i | −0.288592 | − | 1.09393i | ||||
\(704\) | 474.586 | 0.674128 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 1487.67i | − | 2.10718i | ||||||
\(707\) | −846.512 | −1.19733 | ||||||||
\(708\) | −1345.04 | −1.89978 | ||||||||
\(709\) | 352.953 | 0.497818 | 0.248909 | − | 0.968527i | \(-0.419928\pi\) | ||||
0.248909 | + | 0.968527i | \(0.419928\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1838.32i | − | 2.58554i | ||||||
\(712\) | −70.2902 | −0.0987221 | ||||||||
\(713\) | 1936.96i | 2.71664i | ||||||||
\(714\) | −116.617 | −0.163329 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1057.32i | 1.47670i | ||||||||
\(717\) | 228.149i | 0.318199i | ||||||||
\(718\) | − | 439.118i | − | 0.611585i | ||||||
\(719\) | 388.649 | 0.540541 | 0.270271 | − | 0.962784i | \(-0.412887\pi\) | ||||
0.270271 | + | 0.962784i | \(0.412887\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 84.5010i | − | 0.117200i | ||||||
\(722\) | −537.368 | − | 947.579i | −0.744277 | − | 1.31244i | ||||
\(723\) | −353.437 | −0.488848 | ||||||||
\(724\) | − | 703.091i | − | 0.971120i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1385.65 | −1.90862 | ||||||||
\(727\) | 1159.46 | 1.59486 | 0.797431 | − | 0.603410i | \(-0.206192\pi\) | ||||
0.797431 | + | 0.603410i | \(0.206192\pi\) | |||||||
\(728\) | −86.3292 | −0.118584 | ||||||||
\(729\) | 1185.06 | 1.62559 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −77.0379 | −0.105387 | ||||||||
\(732\) | − | 948.060i | − | 1.29516i | ||||||
\(733\) | −420.415 | −0.573554 | −0.286777 | − | 0.957997i | \(-0.592584\pi\) | ||||
−0.286777 | + | 0.957997i | \(0.592584\pi\) | |||||||
\(734\) | 1034.81i | 1.40983i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 1655.93i | − | 2.24991i | ||||||
\(737\) | 228.195i | 0.309627i | ||||||||
\(738\) | 308.864 | 0.418515 | ||||||||
\(739\) | 117.628 | 0.159173 | 0.0795863 | − | 0.996828i | \(-0.474640\pi\) | ||||
0.0795863 | + | 0.996828i | \(0.474640\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 373.106 | − | 98.4303i | 0.503517 | − | 0.132834i | ||||
\(742\) | 1144.49 | 1.54244 | ||||||||
\(743\) | − | 131.785i | − | 0.177368i | −0.996060 | − | 0.0886842i | \(-0.971734\pi\) | ||
0.996060 | − | 0.0886842i | \(-0.0282662\pi\) | |||||||
\(744\) | 840.911i | 1.13026i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 50.2316 | 0.0673346 | ||||||||
\(747\) | 333.084 | 0.445896 | ||||||||
\(748\) | −33.8049 | −0.0451937 | ||||||||
\(749\) | − | 396.781i | − | 0.529748i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 162.721i | − | 0.216672i | −0.994114 | − | 0.108336i | \(-0.965448\pi\) | ||
0.994114 | − | 0.108336i | \(-0.0345522\pi\) | |||||||
\(752\) | 591.824 | 0.787001 | ||||||||
\(753\) | 1286.44i | 1.70841i | ||||||||
\(754\) | 544.394i | 0.722008i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 811.725i | − | 1.07371i | ||||||
\(757\) | 1220.77 | 1.61264 | 0.806322 | − | 0.591477i | \(-0.201455\pi\) | ||||
0.806322 | + | 0.591477i | \(0.201455\pi\) | |||||||
\(758\) | 943.910 | 1.24526 | ||||||||
\(759\) | − | 914.248i | − | 1.20454i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −164.940 | −0.216741 | −0.108370 | − | 0.994111i | \(-0.534563\pi\) | ||||
−0.108370 | + | 0.994111i | \(0.534563\pi\) | |||||||
\(762\) | − | 3472.66i | − | 4.55730i | ||||||
\(763\) | − | 287.080i | − | 0.376251i | ||||||
\(764\) | −143.105 | −0.187310 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1488.42 | 1.94311 | ||||||||
\(767\) | −229.172 | −0.298789 | ||||||||
\(768\) | 302.842i | 0.394325i | ||||||||
\(769\) | −1070.57 | −1.39216 | −0.696079 | − | 0.717965i | \(-0.745074\pi\) | ||||
−0.696079 | + | 0.717965i | \(0.745074\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 367.245 | 0.476323 | ||||||||
\(772\) | 1277.21i | 1.65442i | ||||||||
\(773\) | 181.214i | 0.234430i | 0.993107 | + | 0.117215i | \(0.0373967\pi\) | ||||
−0.993107 | + | 0.117215i | \(0.962603\pi\) | |||||||
\(774\) | − | 2566.45i | − | 3.31582i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −253.350 | −0.326483 | ||||||||
\(777\) | −1244.96 | −1.60227 | ||||||||
\(778\) | 1228.32i | 1.57882i | ||||||||
\(779\) | −34.5806 | − | 131.080i | −0.0443910 | − | 0.168267i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 66.5132i | 0.0851641i | ||||||||
\(782\) | 145.611i | 0.186203i | ||||||||
\(783\) | −1108.57 | −1.41580 | ||||||||
\(784\) | 115.048 | 0.146745 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −598.922 | −0.761987 | ||||||||
\(787\) | 1339.67i | 1.70225i | 0.524966 | + | 0.851123i | \(0.324078\pi\) | ||||
−0.524966 | + | 0.851123i | \(0.675922\pi\) | |||||||
\(788\) | −246.525 | −0.312849 | ||||||||
\(789\) | 1407.86i | 1.78436i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 349.104i | − | 0.441345i | ||||||
\(792\) | − | 243.896i | − | 0.307950i | ||||||
\(793\) | − | 161.533i | − | 0.203698i | ||||||
\(794\) | 630.574i | 0.794174i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1357.40 | 1.70528 | ||||||||
\(797\) | − | 456.100i | − | 0.572272i | −0.958189 | − | 0.286136i | \(-0.907629\pi\) | ||
0.958189 | − | 0.286136i | \(-0.0923708\pi\) | |||||||
\(798\) | −1648.77 | + | 434.966i | −2.06612 | + | 0.545071i | ||||
\(799\) | −74.2710 | −0.0929549 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 302.201i | − | 0.377280i | ||||||
\(802\) | −727.133 | −0.906649 | ||||||||
\(803\) | 683.220 | 0.850835 | ||||||||
\(804\) | 1104.83 | 1.37417 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 661.572i | 0.820809i | ||||||||
\(807\) | 1962.72 | 2.43212 | ||||||||
\(808\) | 458.873i | 0.567913i | ||||||||
\(809\) | −415.566 | −0.513678 | −0.256839 | − | 0.966454i | \(-0.582681\pi\) | ||||
−0.256839 | + | 0.966454i | \(0.582681\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 891.629i | 1.09942i | 0.835356 | + | 0.549710i | \(0.185262\pi\) | ||||
−0.835356 | + | 0.549710i | \(0.814738\pi\) | |||||||
\(812\) | − | 1348.91i | − | 1.66122i | ||||||
\(813\) | − | 1400.00i | − | 1.72201i | ||||||
\(814\) | −643.621 | −0.790690 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 65.0085i | − | 0.0796673i | ||||||
\(817\) | −1089.18 | + | 287.341i | −1.33315 | + | 0.351702i | ||||
\(818\) | 784.143 | 0.958611 | ||||||||
\(819\) | − | 371.158i | − | 0.453185i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −241.578 | −0.294249 | −0.147124 | − | 0.989118i | \(-0.547002\pi\) | ||||
−0.147124 | + | 0.989118i | \(0.547002\pi\) | |||||||
\(822\) | −2064.70 | −2.51180 | ||||||||
\(823\) | 585.888 | 0.711894 | 0.355947 | − | 0.934506i | \(-0.384158\pi\) | ||||
0.355947 | + | 0.934506i | \(0.384158\pi\) | |||||||
\(824\) | −45.8060 | −0.0555897 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1012.72 | 1.22605 | ||||||||
\(827\) | − | 61.7508i | − | 0.0746684i | −0.999303 | − | 0.0373342i | \(-0.988113\pi\) | ||
0.999303 | − | 0.0373342i | \(-0.0118866\pi\) | |||||||
\(828\) | −2719.98 | −3.28500 | ||||||||
\(829\) | 776.948i | 0.937211i | 0.883408 | + | 0.468606i | \(0.155243\pi\) | ||||
−0.883408 | + | 0.468606i | \(0.844757\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 496.301i | 0.597233i | ||||||||
\(832\) | − | 391.498i | − | 0.470550i | ||||||
\(833\) | −14.4380 | −0.0173325 | ||||||||
\(834\) | −1941.59 | −2.32804 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −477.943 | + | 126.088i | −0.571702 | + | 0.150823i | ||||
\(837\) | −1347.18 | −1.60954 | ||||||||
\(838\) | 2200.16i | 2.62549i | ||||||||
\(839\) | − | 997.057i | − | 1.18839i | −0.804322 | − | 0.594194i | \(-0.797471\pi\) | ||
0.804322 | − | 0.594194i | \(-0.202529\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1001.20 | −1.19049 | ||||||||
\(842\) | −1836.62 | −2.18126 | ||||||||
\(843\) | 0.612022 | 0.000726005 | ||||||||
\(844\) | − | 933.183i | − | 1.10567i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 2474.27i | − | 2.92467i | ||||||
\(847\) | 584.993 | 0.690665 | ||||||||
\(848\) | 637.998i | 0.752357i | ||||||||
\(849\) | 407.111i | 0.479518i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1554.49i | 1.82667i | ||||||||
\(852\) | 322.030 | 0.377969 | ||||||||
\(853\) | 56.0425 | 0.0657004 | 0.0328502 | − | 0.999460i | \(-0.489542\pi\) | ||||
0.0328502 | + | 0.999460i | \(0.489542\pi\) | |||||||
\(854\) | 713.818i | 0.835853i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −215.085 | −0.251268 | ||||||||
\(857\) | − | 926.670i | − | 1.08129i | −0.841249 | − | 0.540647i | \(-0.818179\pi\) | ||
0.841249 | − | 0.540647i | \(-0.181821\pi\) | |||||||
\(858\) | − | 312.262i | − | 0.363942i | ||||||
\(859\) | 83.5317 | 0.0972429 | 0.0486215 | − | 0.998817i | \(-0.484517\pi\) | ||||
0.0486215 | + | 0.998817i | \(0.484517\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −212.202 | −0.246460 | ||||||||
\(862\) | −1623.26 | −1.88313 | ||||||||
\(863\) | − | 187.981i | − | 0.217823i | −0.994051 | − | 0.108911i | \(-0.965264\pi\) | ||
0.994051 | − | 0.108911i | \(-0.0347364\pi\) | |||||||
\(864\) | 1151.72 | 1.33301 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 771.088 | 0.890402 | ||||||||
\(867\) | − | 1388.21i | − | 1.60116i | ||||||
\(868\) | − | 1639.26i | − | 1.88855i | ||||||
\(869\) | 652.946i | 0.751377i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 188.244 | 0.216124 | ||||||||
\(872\) | −155.619 | −0.178462 | ||||||||
\(873\) | − | 1089.24i | − | 1.24770i | ||||||
\(874\) | 543.109 | + | 2058.69i | 0.621406 | + | 2.35548i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 3307.88i | − | 3.77612i | ||||||
\(877\) | − | 732.648i | − | 0.835402i | −0.908585 | − | 0.417701i | \(-0.862836\pi\) | ||
0.908585 | − | 0.417701i | \(-0.137164\pi\) | |||||||
\(878\) | −2111.43 | −2.40482 | ||||||||
\(879\) | 1952.59 | 2.22137 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1157.50 | 1.31385 | 0.656925 | − | 0.753956i | \(-0.271857\pi\) | ||||
0.656925 | + | 0.753956i | \(0.271857\pi\) | |||||||
\(882\) | − | 480.988i | − | 0.545338i | ||||||
\(883\) | 1565.09 | 1.77247 | 0.886234 | − | 0.463237i | \(-0.153312\pi\) | ||||
0.886234 | + | 0.463237i | \(0.153312\pi\) | |||||||
\(884\) | 27.8865i | 0.0315458i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2058.42i | 2.32327i | ||||||||
\(887\) | 618.630i | 0.697440i | 0.937227 | + | 0.348720i | \(0.113384\pi\) | ||||
−0.937227 | + | 0.348720i | \(0.886616\pi\) | |||||||
\(888\) | 674.865i | 0.759983i | ||||||||
\(889\) | 1466.08i | 1.64914i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.9878 | −0.0246776 | ||||||||
\(892\) | − | 544.377i | − | 0.610288i | ||||||
\(893\) | −1050.06 | + | 277.021i | −1.17588 | + | 0.310213i | ||||
\(894\) | −4016.41 | −4.49262 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 632.123i | 0.705495i | ||||||||
\(897\) | −754.185 | −0.840786 | ||||||||
\(898\) | −2038.80 | −2.27038 | ||||||||
\(899\) | −2238.73 | −2.49024 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 80.0655i | − | 0.0888630i | ||||||
\(902\) | −109.704 | −0.121623 | ||||||||
\(903\) | 1763.25i | 1.95266i | ||||||||
\(904\) | −189.241 | −0.209337 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2057.23i | 2.27068i | ||||||||
\(907\) | − | 289.512i | − | 0.319197i | −0.987182 | − | 0.159598i | \(-0.948980\pi\) | ||
0.987182 | − | 0.159598i | \(-0.0510199\pi\) | |||||||
\(908\) | 178.706i | 0.196813i | ||||||||
\(909\) | −1972.85 | −2.17035 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1095.19i | − | 1.20219i | −0.799179 | − | 0.601093i | \(-0.794732\pi\) | ||
0.799179 | − | 0.601093i | \(-0.205268\pi\) | |||||||
\(912\) | −242.473 | − | 919.108i | −0.265870 | − | 1.00779i | ||||
\(913\) | −118.307 | −0.129580 | ||||||||
\(914\) | 376.509i | 0.411935i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 395.032 | 0.431258 | ||||||||
\(917\) | 252.852 | 0.275738 | ||||||||
\(918\) | −101.274 | −0.110321 | ||||||||
\(919\) | −393.630 | −0.428324 | −0.214162 | − | 0.976798i | \(-0.568702\pi\) | ||||
−0.214162 | + | 0.976798i | \(0.568702\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 767.382 | 0.833206 | ||||||||
\(922\) | − | 992.300i | − | 1.07625i | ||||||
\(923\) | 54.8683 | 0.0594456 | ||||||||
\(924\) | 773.731i | 0.837372i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 370.739i | 0.400366i | ||||||||
\(927\) | − | 196.935i | − | 0.212444i | ||||||
\(928\) | 1913.91 | 2.06241 | ||||||||
\(929\) | −826.818 | −0.890008 | −0.445004 | − | 0.895529i | \(-0.646798\pi\) | ||||
−0.445004 | + | 0.895529i | \(0.646798\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −204.128 | + | 53.8518i | −0.219257 | + | 0.0578429i | ||||
\(932\) | −454.429 | −0.487585 | ||||||||
\(933\) | 1240.89i | 1.33000i | ||||||||
\(934\) | − | 1971.84i | − | 2.11118i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −201.196 | −0.214953 | ||||||||
\(937\) | 360.005 | 0.384210 | 0.192105 | − | 0.981374i | \(-0.438469\pi\) | ||||
0.192105 | + | 0.981374i | \(0.438469\pi\) | |||||||
\(938\) | −831.854 | −0.886838 | ||||||||
\(939\) | − | 2074.21i | − | 2.20896i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 499.144i | 0.530440i | 0.964188 | + | 0.265220i | \(0.0854445\pi\) | ||||
−0.964188 | + | 0.265220i | \(0.914555\pi\) | |||||||
\(942\) | −1956.34 | −2.07680 | ||||||||
\(943\) | 264.961i | 0.280976i | ||||||||
\(944\) | 564.540i | 0.598030i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 911.566i | 0.963600i | ||||||||
\(947\) | 404.548 | 0.427189 | 0.213594 | − | 0.976922i | \(-0.431483\pi\) | ||||
0.213594 | + | 0.976922i | \(0.431483\pi\) | |||||||
\(948\) | 3161.30 | 3.33471 | ||||||||
\(949\) | − | 563.604i | − | 0.593893i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1114.99 | 1.17244 | ||||||||
\(952\) | − | 26.6881i | − | 0.0280338i | ||||||
\(953\) | 441.098i | 0.462852i | 0.972852 | + | 0.231426i | \(0.0743392\pi\) | ||||
−0.972852 | + | 0.231426i | \(0.925661\pi\) | |||||||
\(954\) | 2667.31 | 2.79592 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −241.088 | −0.252184 | ||||||||
\(957\) | 1056.68 | 1.10416 | ||||||||
\(958\) | − | 1086.77i | − | 1.13442i | ||||||
\(959\) | 871.673 | 0.908939 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1759.60 | −1.83101 | ||||||||
\(962\) | 530.938i | 0.551911i | ||||||||
\(963\) | − | 924.725i | − | 0.960254i | ||||||
\(964\) | − | 373.482i | − | 0.387429i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3332.76 | 3.45007 | ||||||||
\(967\) | 1146.66 | 1.18579 | 0.592897 | − | 0.805279i | \(-0.297984\pi\) | ||||
0.592897 | + | 0.805279i | \(0.297984\pi\) | |||||||
\(968\) | − | 317.110i | − | 0.327593i | ||||||
\(969\) | 30.4291 | + | 115.343i | 0.0314026 | + | 0.119033i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.3147i | 0.0384292i | 0.999815 | + | 0.0192146i | \(0.00611657\pi\) | ||||
−0.999815 | + | 0.0192146i | \(0.993883\pi\) | |||||||
\(972\) | 1293.31i | 1.33056i | ||||||||
\(973\) | 819.696 | 0.842442 | ||||||||
\(974\) | 142.219 | 0.146016 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −397.920 | −0.407705 | ||||||||
\(977\) | 892.499i | 0.913509i | 0.889593 | + | 0.456755i | \(0.150988\pi\) | ||||
−0.889593 | + | 0.456755i | \(0.849012\pi\) | |||||||
\(978\) | 2572.30 | 2.63017 | ||||||||
\(979\) | 107.338i | 0.109640i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 669.058i | − | 0.682017i | ||||||
\(982\) | 2245.86i | 2.28702i | ||||||||
\(983\) | 336.089i | 0.341902i | 0.985280 | + | 0.170951i | \(0.0546839\pi\) | ||||
−0.985280 | + | 0.170951i | \(0.945316\pi\) | |||||||
\(984\) | 115.030i | 0.116900i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −168.296 | −0.170686 | ||||||||
\(987\) | 1699.92i | 1.72231i | ||||||||
\(988\) | 104.013 | + | 394.266i | 0.105276 | + | 0.399055i | ||||
\(989\) | 2201.64 | 2.22613 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 552.478i | − | 0.557495i | −0.960364 | − | 0.278747i | \(-0.910081\pi\) | ||
0.960364 | − | 0.278747i | \(-0.0899192\pi\) | |||||||
\(992\) | 2325.87 | 2.34463 | ||||||||
\(993\) | −2553.99 | −2.57200 | ||||||||
\(994\) | −242.464 | −0.243928 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 572.795i | 0.575095i | ||||||||
\(997\) | −459.052 | −0.460433 | −0.230217 | − | 0.973139i | \(-0.573943\pi\) | ||||
−0.230217 | + | 0.973139i | \(0.573943\pi\) | |||||||
\(998\) | − | 2458.53i | − | 2.46346i | ||||||
\(999\) | −1081.17 | −1.08225 |
(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 | 475.3.c.i.151.2 | yes | 14 | |
5.2 | odd | 4 | 475.3.d.d.474.25 | 28 | |||
5.3 | odd | 4 | 475.3.d.d.474.4 | 28 | |||
5.4 | even | 2 | 475.3.c.h.151.13 | yes | 14 | ||
19.18 | odd | 2 | inner | 475.3.c.i.151.13 | yes | 14 | |
95.18 | even | 4 | 475.3.d.d.474.26 | 28 | |||
95.37 | even | 4 | 475.3.d.d.474.3 | 28 | |||
95.94 | odd | 2 | 475.3.c.h.151.2 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.3.c.h.151.2 | ✓ | 14 | 95.94 | odd | 2 | ||
475.3.c.h.151.13 | yes | 14 | 5.4 | even | 2 | ||
475.3.c.i.151.2 | yes | 14 | 1.1 | even | 1 | trivial | |
475.3.c.i.151.13 | yes | 14 | 19.18 | odd | 2 | inner | |
475.3.d.d.474.3 | 28 | 95.37 | even | 4 | |||
475.3.d.d.474.4 | 28 | 5.3 | odd | 4 | |||
475.3.d.d.474.25 | 28 | 5.2 | odd | 4 | |||
475.3.d.d.474.26 | 28 | 95.18 | even | 4 |