Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [387,5,Mod(343,387)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(387, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("387.343");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 387 = 3^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 387.b (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: | \(40.0041757134\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 142x^{10} + 7173x^{8} + 157368x^{6} + 1510016x^{4} + 5098688x^{2} + 90352 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 43) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 343.4 | ||
Root | \(-3.65497i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 387.343 |
Dual form | 387.5.b.c.343.9 |
$q$-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 \(\left(\mathbb{Z}/387\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(173\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.65497i | − | 0.913743i | −0.889533 | − | 0.456872i | \(-0.848970\pi\) | ||
0.889533 | − | 0.456872i | \(-0.151030\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.64117 | 0.165073 | ||||||||
\(5\) | 45.6695i | 1.82678i | 0.407085 | + | 0.913390i | \(0.366545\pi\) | ||||
−0.407085 | + | 0.913390i | \(0.633455\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 34.3337i | − | 0.700688i | −0.936621 | − | 0.350344i | \(-0.886065\pi\) | ||
0.936621 | − | 0.350344i | \(-0.113935\pi\) | |||||||
\(8\) | − | 68.1330i | − | 1.06458i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 166.921 | 1.66921 | ||||||||
\(11\) | 103.099 | 0.852059 | 0.426030 | − | 0.904709i | \(-0.359912\pi\) | ||||
0.426030 | + | 0.904709i | \(0.359912\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 134.875 | 0.798079 | 0.399039 | − | 0.916934i | \(-0.369344\pi\) | ||||
0.399039 | + | 0.916934i | \(0.369344\pi\) | |||||||
\(14\) | −125.489 | −0.640249 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −206.765 | −0.807678 | ||||||||
\(17\) | −240.390 | −0.831800 | −0.415900 | − | 0.909410i | \(-0.636533\pi\) | ||||
−0.415900 | + | 0.909410i | \(0.636533\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 100.800i | 0.279225i | 0.990206 | + | 0.139613i | \(0.0445858\pi\) | ||||
−0.990206 | + | 0.139613i | \(0.955414\pi\) | |||||||
\(20\) | 120.621i | 0.301553i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 376.825i | − | 0.778564i | ||||||
\(23\) | 475.879 | 0.899582 | 0.449791 | − | 0.893134i | \(-0.351498\pi\) | ||||
0.449791 | + | 0.893134i | \(0.351498\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1460.70 | −2.33713 | ||||||||
\(26\) | − | 492.966i | − | 0.729239i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 90.6813i | − | 0.115665i | ||||||
\(29\) | − | 159.825i | − | 0.190041i | −0.995475 | − | 0.0950207i | \(-0.969708\pi\) | ||
0.995475 | − | 0.0950207i | \(-0.0302917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1118.26 | 1.16364 | 0.581822 | − | 0.813316i | \(-0.302340\pi\) | ||||
0.581822 | + | 0.813316i | \(0.302340\pi\) | |||||||
\(32\) | − | 334.405i | − | 0.326568i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 878.620i | 0.760051i | ||||||||
\(35\) | 1568.00 | 1.28000 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2451.77i | 1.79092i | 0.445145 | + | 0.895459i | \(0.353152\pi\) | ||||
−0.445145 | + | 0.895459i | \(0.646848\pi\) | |||||||
\(38\) | 368.423 | 0.255140 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3111.60 | 1.94475 | ||||||||
\(41\) | −1069.81 | −0.636416 | −0.318208 | − | 0.948021i | \(-0.603081\pi\) | ||||
−0.318208 | + | 0.948021i | \(0.603081\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1742.01 | + | 619.833i | 0.942138 | + | 0.335226i | ||||
\(44\) | 272.303 | 0.140652 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 1739.32i | − | 0.821987i | ||||||
\(47\) | 2933.56 | 1.32800 | 0.664002 | − | 0.747731i | \(-0.268857\pi\) | ||||
0.664002 | + | 0.747731i | \(0.268857\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1222.20 | 0.509036 | ||||||||
\(50\) | 5338.84i | 2.13553i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 356.229 | 0.131741 | ||||||||
\(53\) | 825.685 | 0.293943 | 0.146971 | − | 0.989141i | \(-0.453047\pi\) | ||||
0.146971 | + | 0.989141i | \(0.453047\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4708.49i | 1.55653i | ||||||||
\(56\) | −2339.26 | −0.745937 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −584.155 | −0.173649 | ||||||||
\(59\) | 1241.46 | 0.356639 | 0.178320 | − | 0.983973i | \(-0.442934\pi\) | ||||
0.178320 | + | 0.983973i | \(0.442934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6202.15i | 1.66680i | 0.552673 | + | 0.833398i | \(0.313608\pi\) | ||||
−0.552673 | + | 0.833398i | \(0.686392\pi\) | |||||||
\(62\) | − | 4087.22i | − | 1.06327i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4530.49 | −1.10608 | ||||||||
\(65\) | 6159.69i | 1.45791i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 265.952 | 0.0592452 | 0.0296226 | − | 0.999561i | \(-0.490569\pi\) | ||||
0.0296226 | + | 0.999561i | \(0.490569\pi\) | |||||||
\(68\) | −634.912 | −0.137308 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 5731.02i | − | 1.16959i | ||||||
\(71\) | − | 3861.16i | − | 0.765952i | −0.923758 | − | 0.382976i | \(-0.874899\pi\) | ||
0.923758 | − | 0.382976i | \(-0.125101\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8274.70i | − | 1.55277i | −0.630260 | − | 0.776384i | \(-0.717052\pi\) | ||
0.630260 | − | 0.776384i | \(-0.282948\pi\) | |||||||
\(74\) | 8961.14 | 1.63644 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 266.231i | 0.0460926i | ||||||||
\(77\) | − | 3539.78i | − | 0.597028i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4953.26 | 0.793665 | 0.396833 | − | 0.917891i | \(-0.370109\pi\) | ||||
0.396833 | + | 0.917891i | \(0.370109\pi\) | |||||||
\(80\) | − | 9442.88i | − | 1.47545i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3910.14i | 0.581520i | ||||||||
\(83\) | 13512.1 | 1.96140 | 0.980700 | − | 0.195519i | \(-0.0626392\pi\) | ||||
0.980700 | + | 0.195519i | \(0.0626392\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 10978.5i | − | 1.51952i | ||||||
\(86\) | 2265.47 | − | 6367.01i | 0.306311 | − | 0.860872i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 7024.45i | − | 0.907084i | ||||||
\(89\) | 5359.31i | 0.676595i | 0.941039 | + | 0.338298i | \(0.109851\pi\) | ||||
−0.941039 | + | 0.338298i | \(0.890149\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 4630.77i | − | 0.559204i | ||||||
\(92\) | 1256.88 | 0.148497 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 10722.1i | − | 1.21345i | ||||||
\(95\) | −4603.51 | −0.510084 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3191.32 | 0.339177 | 0.169588 | − | 0.985515i | \(-0.445756\pi\) | ||||
0.169588 | + | 0.985515i | \(0.445756\pi\) | |||||||
\(98\) | − | 4467.09i | − | 0.465128i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3857.97 | −0.385797 | ||||||||
\(101\) | −6784.27 | −0.665059 | −0.332529 | − | 0.943093i | \(-0.607902\pi\) | ||||
−0.332529 | + | 0.943093i | \(0.607902\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −650.667 | −0.0613316 | −0.0306658 | − | 0.999530i | \(-0.509763\pi\) | ||||
−0.0306658 | + | 0.999530i | \(0.509763\pi\) | |||||||
\(104\) | − | 9189.46i | − | 0.849617i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 3017.86i | − | 0.268588i | ||||||
\(107\) | −15902.5 | −1.38899 | −0.694495 | − | 0.719497i | \(-0.744372\pi\) | ||||
−0.694495 | + | 0.719497i | \(0.744372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17290.7 | 1.45533 | 0.727663 | − | 0.685935i | \(-0.240607\pi\) | ||||
0.727663 | + | 0.685935i | \(0.240607\pi\) | |||||||
\(110\) | 17209.4 | 1.42226 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7099.03i | 0.565930i | ||||||||
\(113\) | 15504.7i | 1.21425i | 0.794607 | + | 0.607124i | \(0.207677\pi\) | ||||
−0.794607 | + | 0.607124i | \(0.792323\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21733.2i | 1.64334i | ||||||||
\(116\) | − | 422.125i | − | 0.0313707i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 4537.51i | − | 0.325877i | ||||||
\(119\) | 8253.49i | 0.582832i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4011.56 | −0.273995 | ||||||||
\(122\) | 22668.7 | 1.52302 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2953.52 | 0.192086 | ||||||||
\(125\) | − | 38166.2i | − | 2.44264i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −24303.2 | −1.50680 | −0.753400 | − | 0.657562i | \(-0.771588\pi\) | ||||
−0.753400 | + | 0.657562i | \(0.771588\pi\) | |||||||
\(128\) | 11208.3i | 0.684102i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 22513.5 | 1.33216 | ||||||||
\(131\) | 6058.45i | 0.353036i | 0.984297 | + | 0.176518i | \(0.0564834\pi\) | ||||
−0.984297 | + | 0.176518i | \(0.943517\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3460.85 | 0.195650 | ||||||||
\(134\) | − | 972.046i | − | 0.0541349i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16378.5i | 0.885516i | ||||||||
\(137\) | 20546.4i | 1.09470i | 0.836905 | + | 0.547349i | \(0.184363\pi\) | ||||
−0.836905 | + | 0.547349i | \(0.815637\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7143.71 | −0.369738 | −0.184869 | − | 0.982763i | \(-0.559186\pi\) | ||||
−0.184869 | + | 0.982763i | \(0.559186\pi\) | |||||||
\(140\) | 4141.37 | 0.211294 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14112.4 | −0.699883 | ||||||||
\(143\) | 13905.5 | 0.680010 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7299.12 | 0.347164 | ||||||||
\(146\) | −30243.8 | −1.41883 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6475.54i | 0.295633i | ||||||||
\(149\) | − | 29115.5i | − | 1.31145i | −0.754999 | − | 0.655726i | \(-0.772363\pi\) | ||
0.754999 | − | 0.655726i | \(-0.227637\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 11488.6i | − | 0.503864i | −0.967745 | − | 0.251932i | \(-0.918934\pi\) | ||
0.967745 | − | 0.251932i | \(-0.0810659\pi\) | |||||||
\(152\) | 6867.83 | 0.297257 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12937.8 | −0.545530 | ||||||||
\(155\) | 51070.5i | 2.12572i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2810.63i | − | 0.114026i | −0.998373 | − | 0.0570131i | \(-0.981842\pi\) | ||
0.998373 | − | 0.0570131i | \(-0.0181577\pi\) | |||||||
\(158\) | − | 18104.0i | − | 0.725206i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 15272.1 | 0.596568 | ||||||||
\(161\) | − | 16338.7i | − | 0.630327i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 506.838i | − | 0.0190763i | −0.999955 | − | 0.00953815i | \(-0.996964\pi\) | ||
0.999955 | − | 0.00953815i | \(-0.00303613\pi\) | |||||||
\(164\) | −2825.56 | −0.105055 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 49386.3i | − | 1.79222i | ||||||
\(167\) | 45960.0 | 1.64796 | 0.823980 | − | 0.566619i | \(-0.191749\pi\) | ||||
0.823980 | + | 0.566619i | \(0.191749\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10369.6 | −0.363070 | ||||||||
\(170\) | −40126.1 | −1.38845 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4600.95 | + | 1637.09i | 0.155522 | + | 0.0553368i | ||||
\(173\) | 23016.4 | 0.769033 | 0.384516 | − | 0.923118i | \(-0.374368\pi\) | ||||
0.384516 | + | 0.923118i | \(0.374368\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 50151.4i | 1.63760i | ||||||||
\(176\) | −21317.4 | −0.688189 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 19588.1 | 0.618234 | ||||||||
\(179\) | − | 54490.4i | − | 1.70065i | −0.526260 | − | 0.850324i | \(-0.676406\pi\) | ||
0.526260 | − | 0.850324i | \(-0.323594\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24427.1 | 0.745616 | 0.372808 | − | 0.927909i | \(-0.378395\pi\) | ||||
0.372808 | + | 0.927909i | \(0.378395\pi\) | |||||||
\(182\) | −16925.3 | −0.510969 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 32423.1i | − | 0.957675i | ||||||
\(185\) | −111971. | −3.27161 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24784.0 | −0.708743 | ||||||||
\(188\) | 7748.04 | 0.219218 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16825.7i | 0.466086i | ||||||||
\(191\) | 25639.4i | 0.702815i | 0.936223 | + | 0.351408i | \(0.114297\pi\) | ||||
−0.936223 | + | 0.351408i | \(0.885703\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −45243.0 | −1.21461 | −0.607305 | − | 0.794469i | \(-0.707749\pi\) | ||||
−0.607305 | + | 0.794469i | \(0.707749\pi\) | |||||||
\(194\) | − | 11664.2i | − | 0.309921i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3228.03 | 0.0840282 | ||||||||
\(197\) | 19109.6 | 0.492401 | 0.246200 | − | 0.969219i | \(-0.420818\pi\) | ||||
0.246200 | + | 0.969219i | \(0.420818\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 41414.6i | − | 1.04580i | −0.852395 | − | 0.522899i | \(-0.824851\pi\) | ||
0.852395 | − | 0.522899i | \(-0.175149\pi\) | |||||||
\(200\) | 99522.2i | 2.48805i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 24796.3i | 0.607693i | ||||||||
\(203\) | −5487.38 | −0.133160 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 48857.9i | − | 1.16259i | ||||||
\(206\) | 2378.17i | 0.0560413i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −27887.6 | −0.644590 | ||||||||
\(209\) | 10392.4i | 0.237917i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 40579.3i | 0.911464i | 0.890117 | + | 0.455732i | \(0.150623\pi\) | ||||
−0.890117 | + | 0.455732i | \(0.849377\pi\) | |||||||
\(212\) | 2180.78 | 0.0485221 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 58123.4i | 1.26918i | ||||||||
\(215\) | −28307.5 | + | 79556.9i | −0.612384 | + | 1.72108i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 38394.1i | − | 0.815351i | ||||||
\(218\) | − | 63197.1i | − | 1.32979i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 12435.9i | 0.256941i | ||||||||
\(221\) | −32422.7 | −0.663842 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 76426.0i | 1.53685i | 0.639940 | + | 0.768425i | \(0.278959\pi\) | ||||
−0.639940 | + | 0.768425i | \(0.721041\pi\) | |||||||
\(224\) | −11481.4 | −0.228822 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 56669.4 | 1.10951 | ||||||||
\(227\) | − | 44850.6i | − | 0.870395i | −0.900335 | − | 0.435197i | \(-0.856679\pi\) | ||
0.900335 | − | 0.435197i | \(-0.143321\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −68025.3 | −1.29718 | −0.648589 | − | 0.761139i | \(-0.724640\pi\) | ||||
−0.648589 | + | 0.761139i | \(0.724640\pi\) | |||||||
\(230\) | 79434.1 | 1.50159 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10889.3 | −0.202314 | ||||||||
\(233\) | 61038.6i | 1.12433i | 0.827026 | + | 0.562164i | \(0.190031\pi\) | ||||
−0.827026 | + | 0.562164i | \(0.809969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 133974.i | 2.42597i | ||||||||
\(236\) | 3278.91 | 0.0588716 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 30166.3 | 0.532559 | ||||||||
\(239\) | 18090.2 | 0.316699 | 0.158349 | − | 0.987383i | \(-0.449383\pi\) | ||||
0.158349 | + | 0.987383i | \(0.449383\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 63866.5i | − | 1.09961i | −0.835293 | − | 0.549805i | \(-0.814702\pi\) | ||
0.835293 | − | 0.549805i | \(-0.185298\pi\) | |||||||
\(242\) | 14662.1i | 0.250361i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 16380.9i | 0.275144i | ||||||||
\(245\) | 55817.1i | 0.929897i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13595.5i | 0.222844i | ||||||||
\(248\) | − | 76190.5i | − | 1.23879i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −139497. | −2.23195 | ||||||||
\(251\) | −29813.8 | −0.473227 | −0.236613 | − | 0.971604i | \(-0.576037\pi\) | ||||
−0.236613 | + | 0.971604i | \(0.576037\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 49062.7 | 0.766497 | ||||||||
\(254\) | 88827.5i | 1.37683i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31521.7 | −0.480983 | ||||||||
\(257\) | − | 56144.1i | − | 0.850037i | −0.905185 | − | 0.425018i | \(-0.860268\pi\) | ||
0.905185 | − | 0.425018i | \(-0.139732\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 84178.3 | 1.25487 | ||||||||
\(260\) | 16268.8i | 0.240663i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 22143.5 | 0.322584 | ||||||||
\(263\) | 7995.51i | 0.115594i | 0.998328 | + | 0.0577969i | \(0.0184076\pi\) | ||||
−0.998328 | + | 0.0577969i | \(0.981592\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37708.6i | 0.536969i | ||||||||
\(266\) | − | 12649.3i | − | 0.178774i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 702.424 | 0.00977980 | ||||||||
\(269\) | −6211.47 | −0.0858401 | −0.0429200 | − | 0.999079i | \(-0.513666\pi\) | ||||
−0.0429200 | + | 0.999079i | \(0.513666\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15284.9 | −0.208125 | −0.104063 | − | 0.994571i | \(-0.533184\pi\) | ||||
−0.104063 | + | 0.994571i | \(0.533184\pi\) | |||||||
\(272\) | 49704.4 | 0.671826 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 75096.4 | 1.00027 | ||||||||
\(275\) | −150597. | −1.99137 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 44696.5i | − | 0.582525i | −0.956643 | − | 0.291262i | \(-0.905925\pi\) | ||
0.956643 | − | 0.291262i | \(-0.0940753\pi\) | |||||||
\(278\) | 26110.1i | 0.337846i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 106833.i | − | 1.36266i | ||||||
\(281\) | −91345.4 | −1.15684 | −0.578421 | − | 0.815739i | \(-0.696331\pi\) | ||||
−0.578421 | + | 0.815739i | \(0.696331\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25305.7 | 0.315970 | 0.157985 | − | 0.987442i | \(-0.449500\pi\) | ||||
0.157985 | + | 0.987442i | \(0.449500\pi\) | |||||||
\(284\) | − | 10198.0i | − | 0.126438i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 50824.4i | − | 0.621355i | ||||||
\(287\) | 36730.7i | 0.445929i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −25733.6 | −0.308109 | ||||||||
\(290\) | − | 26678.1i | − | 0.317219i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 21854.9i | − | 0.256320i | ||||||
\(293\) | −5876.11 | −0.0684470 | −0.0342235 | − | 0.999414i | \(-0.510896\pi\) | ||||
−0.0342235 | + | 0.999414i | \(0.510896\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 56696.9i | 0.651501i | ||||||||
\(296\) | 167046. | 1.90657 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −106417. | −1.19833 | ||||||||
\(299\) | 64184.3 | 0.717938 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21281.2 | − | 59809.8i | 0.234889 | − | 0.660145i | ||||
\(302\) | −41990.5 | −0.460402 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 20842.0i | − | 0.225524i | ||||||
\(305\) | −283249. | −3.04487 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −82720.6 | −0.877681 | −0.438841 | − | 0.898565i | \(-0.644611\pi\) | ||||
−0.438841 | + | 0.898565i | \(0.644611\pi\) | |||||||
\(308\) | − | 9349.16i | − | 0.0985533i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 186661. | 1.94236 | ||||||||
\(311\) | −160383. | −1.65820 | −0.829102 | − | 0.559097i | \(-0.811148\pi\) | ||||
−0.829102 | + | 0.559097i | \(0.811148\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 182768.i | 1.86557i | 0.360429 | + | 0.932787i | \(0.382630\pi\) | ||||
−0.360429 | + | 0.932787i | \(0.617370\pi\) | |||||||
\(314\) | −10272.8 | −0.104191 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13082.4 | 0.131013 | ||||||||
\(317\) | 99340.5 | 0.988571 | 0.494286 | − | 0.869300i | \(-0.335430\pi\) | ||||
0.494286 | + | 0.869300i | \(0.335430\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 16477.8i | − | 0.161926i | ||||||
\(320\) | − | 206905.i | − | 2.02056i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −59717.5 | −0.575957 | ||||||||
\(323\) | − | 24231.4i | − | 0.232260i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −197013. | −1.86521 | ||||||||
\(326\) | −1852.48 | −0.0174308 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 72889.7i | 0.677514i | ||||||||
\(329\) | − | 100720.i | − | 0.930517i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 128433.i | − | 1.17225i | −0.810221 | − | 0.586124i | \(-0.800653\pi\) | ||
0.810221 | − | 0.586124i | \(-0.199347\pi\) | |||||||
\(332\) | 35687.7 | 0.323775 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 167982.i | − | 1.50581i | ||||||
\(335\) | 12145.9i | 0.108228i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −78727.5 | −0.693213 | −0.346606 | − | 0.938011i | \(-0.612666\pi\) | ||||
−0.346606 | + | 0.938011i | \(0.612666\pi\) | |||||||
\(338\) | 37900.8i | 0.331753i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 28996.1i | − | 0.250831i | ||||||
\(341\) | 115292. | 0.991493 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 124398.i | − | 1.05736i | ||||||
\(344\) | 42231.1 | − | 118689.i | 0.356874 | − | 1.00298i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 84124.3i | − | 0.702699i | ||||||
\(347\) | 136310.i | 1.13205i | 0.824387 | + | 0.566027i | \(0.191520\pi\) | ||||
−0.824387 | + | 0.566027i | \(0.808480\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 48465.9i | − | 0.397910i | −0.980009 | − | 0.198955i | \(-0.936245\pi\) | ||
0.980009 | − | 0.198955i | \(-0.0637548\pi\) | |||||||
\(350\) | 183302. | 1.49634 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 34476.9i | − | 0.278255i | ||||||
\(353\) | −25854.2 | −0.207483 | −0.103741 | − | 0.994604i | \(-0.533081\pi\) | ||||
−0.103741 | + | 0.994604i | \(0.533081\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 176337. | 1.39923 | ||||||||
\(356\) | 14154.9i | 0.111688i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −199161. | −1.55395 | ||||||||
\(359\) | 125163. | 0.971155 | 0.485577 | − | 0.874194i | \(-0.338609\pi\) | ||||
0.485577 | + | 0.874194i | \(0.338609\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 120160. | 0.922033 | ||||||||
\(362\) | − | 89280.5i | − | 0.681301i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 12230.7i | − | 0.0923097i | ||||||
\(365\) | 377901. | 2.83657 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 112207. | 0.833082 | 0.416541 | − | 0.909117i | \(-0.363242\pi\) | ||||
0.416541 | + | 0.909117i | \(0.363242\pi\) | |||||||
\(368\) | −98395.3 | −0.726572 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 409251.i | 2.98941i | ||||||||
\(371\) | − | 28348.9i | − | 0.205962i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 35635.8i | − | 0.256135i | −0.991765 | − | 0.128068i | \(-0.959123\pi\) | ||
0.991765 | − | 0.128068i | \(-0.0408775\pi\) | |||||||
\(374\) | 90585.0i | 0.647609i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 199872.i | − | 1.41376i | ||||||
\(377\) | − | 21556.4i | − | 0.151668i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −205315. | −1.42936 | −0.714679 | − | 0.699452i | \(-0.753427\pi\) | ||||
−0.714679 | + | 0.699452i | \(0.753427\pi\) | |||||||
\(380\) | −12158.6 | −0.0842012 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 93711.3 | 0.642193 | ||||||||
\(383\) | − | 164110.i | − | 1.11876i | −0.828912 | − | 0.559380i | \(-0.811039\pi\) | ||
0.828912 | − | 0.559380i | \(-0.188961\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 161660. | 1.09064 | ||||||||
\(386\) | 165362.i | 1.10984i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8428.81 | 0.0559890 | ||||||||
\(389\) | − | 190984.i | − | 1.26211i | −0.775738 | − | 0.631055i | \(-0.782622\pi\) | ||
0.775738 | − | 0.631055i | \(-0.217378\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −114397. | −0.748272 | ||||||||
\(392\) | − | 83271.8i | − | 0.541908i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 69845.0i | − | 0.449928i | ||||||
\(395\) | 226213.i | 1.44985i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −170575. | −1.08226 | −0.541132 | − | 0.840938i | \(-0.682004\pi\) | ||||
−0.541132 | + | 0.840938i | \(0.682004\pi\) | |||||||
\(398\) | −151369. | −0.955590 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 302023. | 1.88765 | ||||||||
\(401\) | −52348.9 | −0.325551 | −0.162775 | − | 0.986663i | \(-0.552045\pi\) | ||||
−0.162775 | + | 0.986663i | \(0.552045\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 150826. | 0.928679 | ||||||||
\(404\) | −17918.4 | −0.109783 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20056.2i | 0.121674i | ||||||||
\(407\) | 252775.i | 1.52597i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 164844.i | − | 0.985430i | −0.870191 | − | 0.492715i | \(-0.836004\pi\) | ||
0.870191 | − | 0.492715i | \(-0.163996\pi\) | |||||||
\(410\) | −178574. | −1.06231 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1718.52 | −0.0101242 | ||||||||
\(413\) | − | 42624.0i | − | 0.249893i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 617090.i | 3.58305i | ||||||||
\(416\) | − | 45103.0i | − | 0.260627i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 37984.1 | 0.217395 | ||||||||
\(419\) | − | 37268.6i | − | 0.212283i | −0.994351 | − | 0.106141i | \(-0.966150\pi\) | ||
0.994351 | − | 0.106141i | \(-0.0338496\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 99646.0i | − | 0.562206i | −0.959678 | − | 0.281103i | \(-0.909300\pi\) | ||
0.959678 | − | 0.281103i | \(-0.0907003\pi\) | |||||||
\(422\) | 148316. | 0.832844 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 56256.4i | − | 0.312925i | ||||||
\(425\) | 351139. | 1.94402 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 212943. | 1.16790 | ||||||||
\(428\) | −42001.4 | −0.229285 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 290778. | + | 103463.i | 1.57262 | + | 0.559562i | ||||
\(431\) | −144175. | −0.776133 | −0.388067 | − | 0.921631i | \(-0.626857\pi\) | ||||
−0.388067 | + | 0.921631i | \(0.626857\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 220583.i | − | 1.17651i | −0.808675 | − | 0.588256i | \(-0.799815\pi\) | ||
0.808675 | − | 0.588256i | \(-0.200185\pi\) | |||||||
\(434\) | −140329. | −0.745022 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 45667.8 | 0.240235 | ||||||||
\(437\) | 47968.8i | 0.251186i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 68794.6 | 0.356965 | 0.178482 | − | 0.983943i | \(-0.442881\pi\) | ||||
0.178482 | + | 0.983943i | \(0.442881\pi\) | |||||||
\(440\) | 320803. | 1.65704 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 118504.i | 0.606581i | ||||||||
\(443\) | −321595. | −1.63871 | −0.819355 | − | 0.573286i | \(-0.805668\pi\) | ||||
−0.819355 | + | 0.573286i | \(0.805668\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −244757. | −1.23599 | ||||||||
\(446\) | 279335. | 1.40429 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 155549.i | 0.775015i | ||||||||
\(449\) | − | 2687.03i | − | 0.0133285i | −0.999978 | − | 0.00666423i | \(-0.997879\pi\) | ||
0.999978 | − | 0.00666423i | \(-0.00212131\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −110297. | −0.542264 | ||||||||
\(452\) | 40950.7i | 0.200440i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −163928. | −0.795318 | ||||||||
\(455\) | 211485. | 1.02154 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 222198.i | 1.06392i | 0.846770 | + | 0.531959i | \(0.178544\pi\) | ||||
−0.846770 | + | 0.531959i | \(0.821456\pi\) | |||||||
\(458\) | 248631.i | 1.18529i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 57401.0i | 0.271271i | ||||||||
\(461\) | 63915.9 | 0.300751 | 0.150375 | − | 0.988629i | \(-0.451952\pi\) | ||||
0.150375 | + | 0.988629i | \(0.451952\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 94323.6i | − | 0.440006i | −0.975499 | − | 0.220003i | \(-0.929393\pi\) | ||
0.975499 | − | 0.220003i | \(-0.0706067\pi\) | |||||||
\(464\) | 33046.2i | 0.153492i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 223094. | 1.02735 | ||||||||
\(467\) | − | 288915.i | − | 1.32476i | −0.749170 | − | 0.662378i | \(-0.769547\pi\) | ||
0.749170 | − | 0.662378i | \(-0.230453\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 9131.11i | − | 0.0415124i | ||||||
\(470\) | 489673. | 2.21672 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 84584.4i | − | 0.379670i | ||||||
\(473\) | 179600. | + | 63904.3i | 0.802757 | + | 0.285632i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 147240.i | − | 0.652586i | ||||||
\(476\) | 21798.9i | 0.0962100i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 66119.0i | − | 0.289381i | ||||||
\(479\) | −328139. | −1.43017 | −0.715084 | − | 0.699039i | \(-0.753612\pi\) | ||||
−0.715084 | + | 0.699039i | \(0.753612\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 330683.i | 1.42929i | ||||||||
\(482\) | −233430. | −1.00476 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10595.2 | −0.0452292 | ||||||||
\(485\) | 145746.i | 0.619602i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −225179. | −0.949447 | −0.474723 | − | 0.880135i | \(-0.657452\pi\) | ||||
−0.474723 | + | 0.880135i | \(0.657452\pi\) | |||||||
\(488\) | 422571. | 1.77443 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 204010. | 0.849687 | ||||||||
\(491\) | − | 119348.i | − | 0.495053i | −0.968881 | − | 0.247526i | \(-0.920382\pi\) | ||
0.968881 | − | 0.247526i | \(-0.0796177\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 38420.3i | 0.158076i | ||||||||
\(494\) | 49691.1 | 0.203622 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −231218. | −0.939849 | ||||||||
\(497\) | −132568. | −0.536693 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 184960.i | 0.742807i | 0.928471 | + | 0.371404i | \(0.121123\pi\) | ||||
−0.928471 | + | 0.371404i | \(0.878877\pi\) | |||||||
\(500\) | − | 100804.i | − | 0.403214i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 108968.i | 0.432408i | ||||||||
\(503\) | − | 340779.i | − | 1.34691i | −0.739230 | − | 0.673453i | \(-0.764810\pi\) | ||
0.739230 | − | 0.673453i | \(-0.235190\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 309834.i | − | 1.21492i | ||||||
\(506\) | − | 179323.i | − | 0.700382i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −64188.9 | −0.248732 | ||||||||
\(509\) | −35186.6 | −0.135813 | −0.0679066 | − | 0.997692i | \(-0.521632\pi\) | ||||
−0.0679066 | + | 0.997692i | \(0.521632\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −284101. | −1.08801 | ||||||||
\(512\) | 294544.i | 1.12360i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −205205. | −0.776715 | ||||||||
\(515\) | − | 29715.7i | − | 0.112039i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 302448. | 1.13154 | ||||||||
\(518\) | − | 307669.i | − | 1.14663i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 419678. | 1.55206 | ||||||||
\(521\) | − | 167672.i | − | 0.617712i | −0.951109 | − | 0.308856i | \(-0.900054\pi\) | ||
0.951109 | − | 0.308856i | \(-0.0999460\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 388697.i | − | 1.42105i | −0.703674 | − | 0.710523i | \(-0.748459\pi\) | ||
0.703674 | − | 0.710523i | \(-0.251541\pi\) | |||||||
\(524\) | 16001.4i | 0.0582768i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 29223.4 | 0.105623 | ||||||||
\(527\) | −268819. | −0.967918 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −53380.2 | −0.190752 | ||||||||
\(530\) | 137824. | 0.490652 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9140.71 | 0.0322966 | ||||||||
\(533\) | −144292. | −0.507910 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 726262.i | − | 2.53738i | ||||||
\(536\) | − | 18120.1i | − | 0.0630711i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 22702.8i | 0.0784358i | ||||||||
\(539\) | 126007. | 0.433729 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 258688. | 0.883856 | 0.441928 | − | 0.897050i | \(-0.354295\pi\) | ||||
0.441928 | + | 0.897050i | \(0.354295\pi\) | |||||||
\(542\) | 55865.9i | 0.190173i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 80387.8i | 0.271639i | ||||||||
\(545\) | 789659.i | 2.65856i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11333.8 | −0.0378791 | −0.0189395 | − | 0.999821i | \(-0.506029\pi\) | ||||
−0.0189395 | + | 0.999821i | \(0.506029\pi\) | |||||||
\(548\) | 54266.5i | 0.180705i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 550430.i | 1.81960i | ||||||||
\(551\) | 16110.4 | 0.0530644 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 170064.i | − | 0.556112i | ||||||
\(554\) | −163365. | −0.532278 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18867.8 | −0.0610338 | ||||||||
\(557\) | 90762.0 | 0.292546 | 0.146273 | − | 0.989244i | \(-0.453272\pi\) | ||||
0.146273 | + | 0.989244i | \(0.453272\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 234955. | + | 83600.2i | 0.751900 | + | 0.267537i | ||||
\(560\) | −324209. | −1.03383 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 333865.i | 1.05706i | ||||||||
\(563\) | −198527. | −0.626329 | −0.313165 | − | 0.949699i | \(-0.601389\pi\) | ||||
−0.313165 | + | 0.949699i | \(0.601389\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −708094. | −2.21817 | ||||||||
\(566\) | − | 92491.8i | − | 0.288716i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −263073. | −0.815415 | ||||||||
\(569\) | −204563. | −0.631832 | −0.315916 | − | 0.948787i | \(-0.602312\pi\) | ||||
−0.315916 | + | 0.948787i | \(0.602312\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 103248.i | − | 0.316670i | −0.987385 | − | 0.158335i | \(-0.949387\pi\) | ||
0.987385 | − | 0.158335i | \(-0.0506127\pi\) | |||||||
\(572\) | 36726.9 | 0.112252 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 134250. | 0.407465 | ||||||||
\(575\) | −695119. | −2.10244 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 214909.i | − | 0.645510i | −0.946482 | − | 0.322755i | \(-0.895391\pi\) | ||
0.946482 | − | 0.322755i | \(-0.104609\pi\) | |||||||
\(578\) | 94055.5i | 0.281533i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 19278.2 | 0.0573075 | ||||||||
\(581\) | − | 463920.i | − | 1.37433i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 85127.5 | 0.250457 | ||||||||
\(584\) | −563780. | −1.65304 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21477.0i | 0.0625430i | ||||||||
\(587\) | 508043.i | 1.47443i | 0.675657 | + | 0.737216i | \(0.263860\pi\) | ||||
−0.675657 | + | 0.737216i | \(0.736140\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 112721.i | 0.324919i | ||||||||
\(590\) | 207226. | 0.595305 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 506941.i | − | 1.44648i | ||||||
\(593\) | 182995.i | 0.520390i | 0.965556 | + | 0.260195i | \(0.0837869\pi\) | ||||
−0.965556 | + | 0.260195i | \(0.916213\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −376933. | −1.06471 | ||||||||
\(596\) | − | 76899.1i | − | 0.216486i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 234592.i | − | 0.656011i | ||||||
\(599\) | 173564. | 0.483733 | 0.241867 | − | 0.970310i | \(-0.422240\pi\) | ||||
0.241867 | + | 0.970310i | \(0.422240\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 370900.i | 1.02685i | 0.858134 | + | 0.513426i | \(0.171624\pi\) | ||||
−0.858134 | + | 0.513426i | \(0.828376\pi\) | |||||||
\(602\) | −218603. | − | 77782.1i | −0.603203 | − | 0.214628i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 30343.4i | − | 0.0831744i | ||||||
\(605\) | − | 183206.i | − | 0.500529i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 274917.i | − | 0.746147i | −0.927802 | − | 0.373074i | \(-0.878304\pi\) | ||
0.927802 | − | 0.373074i | \(-0.121696\pi\) | |||||||
\(608\) | 33708.2 | 0.0911861 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.03527e6i | 2.78223i | ||||||||
\(611\) | 395665. | 1.05985 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 358829. | 0.954919 | 0.477459 | − | 0.878654i | \(-0.341558\pi\) | ||||
0.477459 | + | 0.878654i | \(0.341558\pi\) | |||||||
\(614\) | 302342.i | 0.801975i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −241176. | −0.635583 | ||||||||
\(617\) | −275204. | −0.722909 | −0.361455 | − | 0.932390i | \(-0.617720\pi\) | ||||
−0.361455 | + | 0.932390i | \(0.617720\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −303567. | −0.792270 | −0.396135 | − | 0.918192i | \(-0.629649\pi\) | ||||
−0.396135 | + | 0.918192i | \(0.629649\pi\) | |||||||
\(620\) | 134886.i | 0.350900i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 586196.i | 1.51517i | ||||||||
\(623\) | 184005. | 0.474082 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 830093. | 2.12504 | ||||||||
\(626\) | 668013. | 1.70466 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 7423.36i | − | 0.0188227i | ||||||
\(629\) | − | 589380.i | − | 1.48968i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 350000.i | 0.879041i | 0.898233 | + | 0.439520i | \(0.144852\pi\) | ||||
−0.898233 | + | 0.439520i | \(0.855148\pi\) | |||||||
\(632\) | − | 337481.i | − | 0.844918i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 363087.i | − | 0.903300i | ||||||
\(635\) | − | 1.10991e6i | − | 2.75259i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 164844. | 0.406251 | ||||||||
\(638\) | −60225.9 | −0.147959 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −511879. | −1.24970 | ||||||||
\(641\) | 404169.i | 0.983665i | 0.870690 | + | 0.491832i | \(0.163673\pi\) | ||||
−0.870690 | + | 0.491832i | \(0.836327\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 488598. | 1.18176 | 0.590881 | − | 0.806759i | \(-0.298780\pi\) | ||||
0.590881 | + | 0.806759i | \(0.298780\pi\) | |||||||
\(644\) | − | 43153.3i | − | 0.104050i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −88565.2 | −0.212226 | ||||||||
\(647\) | 111849.i | 0.267191i | 0.991036 | + | 0.133595i | \(0.0426523\pi\) | ||||
−0.991036 | + | 0.133595i | \(0.957348\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 127994. | 0.303878 | ||||||||
\(650\) | 720077.i | 1.70433i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 1338.65i | − | 0.00314899i | ||||||
\(653\) | 92008.4i | 0.215775i | 0.994163 | + | 0.107887i | \(0.0344086\pi\) | ||||
−0.994163 | + | 0.107887i | \(0.965591\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −276686. | −0.644919 | ||||||||
\(656\) | 221201. | 0.514019 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −368129. | −0.850254 | ||||||||
\(659\) | 532415. | 1.22597 | 0.612985 | − | 0.790095i | \(-0.289969\pi\) | ||||
0.612985 | + | 0.790095i | \(0.289969\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −770144. | −1.76266 | −0.881331 | − | 0.472499i | \(-0.843352\pi\) | ||||
−0.881331 | + | 0.472499i | \(0.843352\pi\) | |||||||
\(662\) | −469418. | −1.07113 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 920618.i | − | 2.08806i | ||||||
\(665\) | 158055.i | 0.357410i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 76057.3i | − | 0.170958i | ||||||
\(668\) | 121388. | 0.272034 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 44392.9 | 0.0988926 | ||||||||
\(671\) | 639437.i | 1.42021i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 296438.i | 0.654492i | 0.944939 | + | 0.327246i | \(0.106121\pi\) | ||||
−0.944939 | + | 0.327246i | \(0.893879\pi\) | |||||||
\(674\) | 287747.i | 0.633418i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −27388.0 | −0.0599332 | ||||||||
\(677\) | 255234.i | 0.556880i | 0.960454 | + | 0.278440i | \(0.0898174\pi\) | ||||
−0.960454 | + | 0.278440i | \(0.910183\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 109570.i | − | 0.237657i | ||||||
\(680\) | −747998. | −1.61764 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 421389.i | − | 0.905970i | ||||||
\(683\) | −659236. | −1.41319 | −0.706594 | − | 0.707620i | \(-0.749769\pi\) | ||||
−0.706594 | + | 0.707620i | \(0.749769\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −938343. | −1.99977 | ||||||||
\(686\) | −454671. | −0.966159 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −360188. | − | 128160.i | −0.760944 | − | 0.270755i | ||||
\(689\) | 111365. | 0.234589 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 428774.i | − | 0.897993i | −0.893534 | − | 0.448996i | \(-0.851782\pi\) | ||
0.893534 | − | 0.448996i | \(-0.148218\pi\) | |||||||
\(692\) | 60790.2 | 0.126947 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 498208. | 1.03441 | ||||||||
\(695\) | − | 326250.i | − | 0.675430i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 257173. | 0.529370 | ||||||||
\(698\) | −177141. | −0.363588 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 132459.i | 0.270324i | ||||||||
\(701\) | −446529. | −0.908686 | −0.454343 | − | 0.890827i | \(-0.650126\pi\) | ||||
−0.454343 | + | 0.890827i | \(0.650126\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −247139. | −0.500070 | ||||||||
\(704\) | −467090. | −0.942443 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 94496.5i | 0.189586i | ||||||||
\(707\) | 232929.i | 0.465999i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43598.6 | −0.0867321 | −0.0433660 | − | 0.999059i | \(-0.513808\pi\) | ||||
−0.0433660 | + | 0.999059i | \(0.513808\pi\) | |||||||
\(710\) | − | 644509.i | − | 1.27853i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 365146. | 0.720288 | ||||||||
\(713\) | 532157. | 1.04679 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 635059.i | 1.24223i | ||||||||
\(716\) | − | 143919.i | − | 0.280731i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 457469.i | − | 0.887386i | ||||||
\(719\) | −46047.8 | −0.0890741 | −0.0445370 | − | 0.999008i | \(-0.514181\pi\) | ||||
−0.0445370 | + | 0.999008i | \(0.514181\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22339.8i | 0.0429743i | ||||||||
\(722\) | − | 439183.i | − | 0.842502i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 64516.2 | 0.123081 | ||||||||
\(725\) | 233457.i | 0.444151i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 275601.i | 0.521450i | 0.965413 | + | 0.260725i | \(0.0839615\pi\) | ||||
−0.965413 | + | 0.260725i | \(0.916038\pi\) | |||||||
\(728\) | −315508. | −0.595317 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 1.38122e6i | − | 2.59189i | ||||||
\(731\) | −418763. | − | 149002.i | −0.783670 | − | 0.278841i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 324631.i | − | 0.604201i | −0.953276 | − | 0.302101i | \(-0.902312\pi\) | ||
0.953276 | − | 0.302101i | \(-0.0976879\pi\) | |||||||
\(734\) | − | 410114.i | − | 0.761223i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 159137.i | − | 0.293775i | ||||||
\(737\) | 27419.4 | 0.0504804 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 359031.i | − | 0.657421i | −0.944431 | − | 0.328710i | \(-0.893386\pi\) | ||
0.944431 | − | 0.328710i | \(-0.106614\pi\) | |||||||
\(740\) | −295735. | −0.540056 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −103614. | −0.188197 | ||||||||
\(743\) | 164101.i | 0.297259i | 0.988893 | + | 0.148629i | \(0.0474862\pi\) | ||||
−0.988893 | + | 0.148629i | \(0.952514\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.32969e6 | 2.39573 | ||||||||
\(746\) | −130248. | −0.234042 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −65458.9 | −0.116994 | ||||||||
\(749\) | 545994.i | 0.973249i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 862173.i | 1.52867i | 0.644818 | + | 0.764336i | \(0.276933\pi\) | ||||
−0.644818 | + | 0.764336i | \(0.723067\pi\) | |||||||
\(752\) | −606559. | −1.07260 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −78788.1 | −0.138586 | ||||||||
\(755\) | 524679. | 0.920449 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 878771.i | 1.53350i | 0.641946 | + | 0.766750i | \(0.278127\pi\) | ||||
−0.641946 | + | 0.766750i | \(0.721873\pi\) | |||||||
\(758\) | 750419.i | 1.30607i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 313651.i | 0.543024i | ||||||||
\(761\) | 452736.i | 0.781763i | 0.920441 | + | 0.390882i | \(0.127830\pi\) | ||||
−0.920441 | + | 0.390882i | \(0.872170\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 593655.i | − | 1.01973i | ||||||
\(764\) | 67718.1i | 0.116016i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −599816. | −1.02226 | ||||||||
\(767\) | 167442. | 0.284626 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 379858. | 0.642346 | 0.321173 | − | 0.947021i | \(-0.395923\pi\) | ||||
0.321173 | + | 0.947021i | \(0.395923\pi\) | |||||||
\(770\) | − | 590863.i | − | 0.996564i | ||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −119495. | −0.200500 | ||||||||
\(773\) | − | 466697.i | − | 0.781044i | −0.920594 | − | 0.390522i | \(-0.872295\pi\) | ||
0.920594 | − | 0.390522i | \(-0.127705\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.63345e6 | −2.71958 | ||||||||
\(776\) | − | 217434.i | − | 0.361080i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −698041. | −1.15325 | ||||||||
\(779\) | − | 107838.i | − | 0.177703i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 398083.i | − | 0.652636i | ||||||
\(782\) | 418117.i | 0.683729i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −252708. | −0.411137 | ||||||||
\(785\) | 128360. | 0.208301 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 946342. | 1.52791 | 0.763956 | − | 0.645268i | \(-0.223254\pi\) | ||||
0.763956 | + | 0.645268i | \(0.223254\pi\) | |||||||
\(788\) | 50471.7 | 0.0812822 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 826803. | 1.32479 | ||||||||
\(791\) | 532335. | 0.850810 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 836517.i | 1.33024i | ||||||||
\(794\) | 623446.i | 0.988912i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 109383.i | − | 0.172633i | ||||||
\(797\) | 561047. | 0.883248 | 0.441624 | − | 0.897200i | \(-0.354403\pi\) | ||||
0.441624 | + | 0.897200i | \(0.354403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −705199. | −1.10463 | ||||||||
\(800\) | 488468.i | 0.763231i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 191334.i | 0.297470i | ||||||||
\(803\) | − | 853115.i | − | 1.32305i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 746181. | 1.15147 | ||||||||
\(806\) | − | 551264.i | − | 0.848574i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 462232.i | 0.708007i | ||||||||
\(809\) | 938377. | 1.43377 | 0.716886 | − | 0.697190i | \(-0.245567\pi\) | ||||
0.716886 | + | 0.697190i | \(0.245567\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 526766.i | − | 0.800896i | −0.916319 | − | 0.400448i | \(-0.868854\pi\) | ||
0.916319 | − | 0.400448i | \(-0.131146\pi\) | |||||||
\(812\) | −14493.1 | −0.0219811 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 923886. | 1.39434 | ||||||||
\(815\) | 23147.1 | 0.0348482 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −62479.4 | + | 175596.i | −0.0936036 | + | 0.263069i | ||||
\(818\) | −602499. | −0.900430 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 129042.i | − | 0.191913i | ||||||
\(821\) | 1.19525e6 | 1.77325 | 0.886626 | − | 0.462486i | \(-0.153043\pi\) | ||||
0.886626 | + | 0.462486i | \(0.153043\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 230617. | 0.340480 | 0.170240 | − | 0.985403i | \(-0.445546\pi\) | ||||
0.170240 | + | 0.985403i | \(0.445546\pi\) | |||||||
\(824\) | 44331.9i | 0.0652923i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −155789. | −0.228338 | ||||||||
\(827\) | 353042. | 0.516197 | 0.258099 | − | 0.966119i | \(-0.416904\pi\) | ||||
0.258099 | + | 0.966119i | \(0.416904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.18220e6i | 1.72021i | 0.510116 | + | 0.860106i | \(0.329603\pi\) | ||||
−0.510116 | + | 0.860106i | \(0.670397\pi\) | |||||||
\(830\) | 2.25545e6 | 3.27399 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −611051. | −0.882736 | ||||||||
\(833\) | −293804. | −0.423416 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.09897e6i | 3.01046i | ||||||||
\(836\) | 27448.2i | 0.0392737i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −136216. | −0.193972 | ||||||||
\(839\) | 229327.i | 0.325785i | 0.986644 | + | 0.162892i | \(0.0520823\pi\) | ||||
−0.986644 | + | 0.162892i | \(0.947918\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 681737. | 0.963884 | ||||||||
\(842\) | −364204. | −0.513712 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 107177.i | 0.150458i | ||||||||
\(845\) | − | 473577.i | − | 0.663250i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 137732.i | 0.191985i | ||||||||
\(848\) | −170723. | −0.237411 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 1.28340e6i | − | 1.77634i | ||||||
\(851\) | 1.16674e6i | 1.61108i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 736313. | 1.01196 | 0.505981 | − | 0.862545i | \(-0.331131\pi\) | ||||
0.505981 | + | 0.862545i | \(0.331131\pi\) | |||||||
\(854\) | − | 778301.i | − | 1.06717i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.08349e6i | 1.47869i | ||||||||
\(857\) | −1.18206e6 | −1.60945 | −0.804726 | − | 0.593646i | \(-0.797688\pi\) | ||||
−0.804726 | + | 0.593646i | \(0.797688\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.14109e6i | − | 1.54645i | −0.634133 | − | 0.773224i | \(-0.718643\pi\) | ||
0.634133 | − | 0.773224i | \(-0.281357\pi\) | |||||||
\(860\) | −74764.9 | + | 210123.i | −0.101088 | + | 0.284104i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 526957.i | 0.709186i | ||||||||
\(863\) | − | 81940.4i | − | 0.110021i | −0.998486 | − | 0.0550106i | \(-0.982481\pi\) | ||
0.998486 | − | 0.0550106i | \(-0.0175193\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.05115e6i | 1.40485i | ||||||||
\(866\) | −806224. | −1.07503 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 101405.i | − | 0.134593i | ||||||
\(869\) | 510677. | 0.676250 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35870.3 | 0.0472823 | ||||||||
\(872\) | − | 1.17807e6i | − | 1.54931i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 175325. | 0.229520 | ||||||||
\(875\) | −1.31039e6 | −1.71153 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −347511. | −0.451824 | −0.225912 | − | 0.974148i | \(-0.572536\pi\) | ||||
−0.225912 | + | 0.974148i | \(0.572536\pi\) | |||||||
\(878\) | − | 251443.i | − | 0.326174i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 973553.i | − | 1.25717i | ||||||
\(881\) | −150733. | −0.194204 | −0.0971018 | − | 0.995274i | \(-0.530957\pi\) | ||||
−0.0971018 | + | 0.995274i | \(0.530957\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.40226e6 | −1.79849 | −0.899246 | − | 0.437443i | \(-0.855884\pi\) | ||||
−0.899246 | + | 0.437443i | \(0.855884\pi\) | |||||||
\(884\) | −85633.9 | −0.109583 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.17542e6i | 1.49736i | ||||||||
\(887\) | 900825.i | 1.14497i | 0.819916 | + | 0.572484i | \(0.194020\pi\) | ||||
−0.819916 | + | 0.572484i | \(0.805980\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 834419.i | 1.05580i | ||||||||
\(890\) | 894581.i | 1.12938i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 201854.i | 0.253693i | ||||||||
\(893\) | 295704.i | 0.370813i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.48855e6 | 3.10671 | ||||||||
\(896\) | 384824. | 0.479343 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9821.02 | −0.0121788 | ||||||||
\(899\) | − | 178726.i | − | 0.221140i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −198487. | −0.244502 | ||||||||
\(902\) | 403133.i | 0.495490i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.05638e6 | 1.29266 | ||||||||
\(905\) | 1.11557e6i | 1.36208i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 754265. | 0.916874 | 0.458437 | − | 0.888727i | \(-0.348409\pi\) | ||||
0.458437 | + | 0.888727i | \(0.348409\pi\) | |||||||
\(908\) | − | 118458.i | − | 0.143679i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | − | 772972.i | − | 0.933429i | ||||||
\(911\) | 834583.i | 1.00562i | 0.864398 | + | 0.502809i | \(0.167700\pi\) | ||||
−0.864398 | + | 0.502809i | \(0.832300\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.39308e6 | 1.67123 | ||||||||
\(914\) | 812128. | 0.972148 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −179666. | −0.214129 | ||||||||
\(917\) | 208009. | 0.247368 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −558842. | −0.661696 | −0.330848 | − | 0.943684i | \(-0.607335\pi\) | ||||
−0.330848 | + | 0.943684i | \(0.607335\pi\) | |||||||
\(920\) | 1.48075e6 | 1.74946 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 233611.i | − | 0.274809i | ||||||
\(923\) | − | 520776.i | − | 0.611290i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 3.58131e6i | − | 4.18560i | ||||||
\(926\) | −344750. | −0.402052 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −53446.3 | −0.0620614 | ||||||||
\(929\) | − | 911473.i | − | 1.05612i | −0.849208 | − | 0.528059i | \(-0.822920\pi\) | ||
0.849208 | − | 0.528059i | \(-0.177080\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 123198.i | 0.142136i | ||||||||
\(932\) | 161213.i | 0.185596i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.05598e6 | −1.21049 | ||||||||
\(935\) | − | 1.13187e6i | − | 1.29472i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 297178.i | 0.338484i | 0.985575 | + | 0.169242i | \(0.0541319\pi\) | ||||
−0.985575 | + | 0.169242i | \(0.945868\pi\) | |||||||
\(938\) | −33374.0 | −0.0379317 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 353849.i | 0.400463i | ||||||||
\(941\) | 44565.6 | 0.0503292 | 0.0251646 | − | 0.999683i | \(-0.491989\pi\) | ||||
0.0251646 | + | 0.999683i | \(0.491989\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −509102. | −0.572508 | ||||||||
\(944\) | −256691. | −0.288049 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 233568. | − | 656433.i | 0.260995 | − | 0.733514i | ||||
\(947\) | 1.06777e6 | 1.19064 | 0.595319 | − | 0.803490i | \(-0.297026\pi\) | ||||
0.595319 | + | 0.803490i | \(0.297026\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.11605e6i | − | 1.23923i | ||||||
\(950\) | −538157. | −0.596296 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 562335. | 0.620470 | ||||||||
\(953\) | − | 1.12239e6i | − | 1.23583i | −0.786246 | − | 0.617913i | \(-0.787978\pi\) | ||
0.786246 | − | 0.617913i | \(-0.212022\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.17094e6 | −1.28389 | ||||||||
\(956\) | 47779.2 | 0.0522785 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.19934e6i | 1.30681i | ||||||||
\(959\) | 705433. | 0.767041 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 326988. | 0.354066 | ||||||||
\(962\) | 1.20864e6 | 1.30601 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 168682.i | − | 0.181516i | ||||||
\(965\) | − | 2.06623e6i | − | 2.21883i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 769222. | 0.822619 | 0.411310 | − | 0.911496i | \(-0.365072\pi\) | ||||
0.411310 | + | 0.911496i | \(0.365072\pi\) | |||||||
\(968\) | 273319.i | 0.291689i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 532697. | 0.566157 | ||||||||
\(971\) | −1.12938e6 | −1.19785 | −0.598926 | − | 0.800804i | \(-0.704406\pi\) | ||||
−0.598926 | + | 0.800804i | \(0.704406\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 245270.i | 0.259071i | ||||||||
\(974\) | 823025.i | 0.867551i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 1.28239e6i | − | 1.34623i | ||||||
\(977\) | 986156. | 1.03313 | 0.516567 | − | 0.856247i | \(-0.327210\pi\) | ||||
0.516567 | + | 0.856247i | \(0.327210\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 552540.i | 0.576499i | ||||||||
\(980\) | 147422.i | 0.153501i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −436213. | −0.452351 | ||||||||
\(983\) | − | 777551.i | − | 0.804677i | −0.915491 | − | 0.402339i | \(-0.868197\pi\) | ||
0.915491 | − | 0.402339i | \(-0.131803\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 872725.i | 0.899508i | ||||||||
\(986\) | 140425. | 0.144441 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 35908.0i | 0.0367856i | ||||||||
\(989\) | 828987. | + | 294965.i | 0.847530 | + | 0.301563i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.84394e6i | − | 1.87759i | −0.344478 | − | 0.938794i | \(-0.611944\pi\) | ||
0.344478 | − | 0.938794i | \(-0.388056\pi\) | |||||||
\(992\) | − | 373953.i | − | 0.380009i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 484533.i | 0.490400i | ||||||||
\(995\) | 1.89139e6 | 1.91044 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 105165.i | 0.105799i | 0.998600 | + | 0.0528996i | \(0.0168463\pi\) | ||||
−0.998600 | + | 0.0528996i | \(0.983154\pi\) | |||||||
\(998\) | 676023. | 0.678735 | ||||||||
\(999\) | 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 | 387.5.b.c.343.4 | 12 | ||
3.2 | odd | 2 | 43.5.b.b.42.9 | yes | 12 | ||
12.11 | even | 2 | 688.5.b.d.257.7 | 12 | |||
43.42 | odd | 2 | inner | 387.5.b.c.343.9 | 12 | ||
129.128 | even | 2 | 43.5.b.b.42.4 | ✓ | 12 | ||
516.515 | odd | 2 | 688.5.b.d.257.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.5.b.b.42.4 | ✓ | 12 | 129.128 | even | 2 | ||
43.5.b.b.42.9 | yes | 12 | 3.2 | odd | 2 | ||
387.5.b.c.343.4 | 12 | 1.1 | even | 1 | trivial | ||
387.5.b.c.343.9 | 12 | 43.42 | odd | 2 | inner | ||
688.5.b.d.257.6 | 12 | 516.515 | odd | 2 | |||
688.5.b.d.257.7 | 12 | 12.11 | even | 2 |