Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,6,Mod(274,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.274");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(52.1247414392\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 378 x^{16} + 59175 x^{14} + 4956036 x^{12} + 239061247 x^{10} + 6629044458 x^{8} + \cdots + 134659641600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.12 | ||
Root | \(4.20685i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.274 |
Dual form | 325.6.b.h.274.7 |
$q$-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 \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.20685i | 0.566897i | 0.958988 | + | 0.283448i | \(0.0914784\pi\) | ||||
−0.958988 | + | 0.283448i | \(0.908522\pi\) | |||||||
\(3\) | 29.5845i | 1.89785i | 0.315503 | + | 0.948925i | \(0.397827\pi\) | ||||
−0.315503 | + | 0.948925i | \(0.602173\pi\) | |||||||
\(4\) | 21.7161 | 0.678628 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −94.8732 | −1.07588 | ||||||||
\(7\) | − 11.5734i | − 0.0892722i | −0.999003 | − | 0.0446361i | \(-0.985787\pi\) | ||||
0.999003 | − | 0.0446361i | \(-0.0142128\pi\) | |||||||
\(8\) | 172.260i | 0.951609i | ||||||||
\(9\) | −632.245 | −2.60183 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −596.700 | −1.48687 | −0.743437 | − | 0.668806i | \(-0.766806\pi\) | ||||
−0.743437 | + | 0.668806i | \(0.766806\pi\) | |||||||
\(12\) | 642.461i | 1.28793i | ||||||||
\(13\) | − 169.000i | − 0.277350i | ||||||||
\(14\) | 37.1142 | 0.0506081 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 142.504 | 0.139164 | ||||||||
\(17\) | 2093.43i | 1.75686i | 0.477872 | + | 0.878429i | \(0.341408\pi\) | ||||
−0.477872 | + | 0.878429i | \(0.658592\pi\) | |||||||
\(18\) | − 2027.52i | − 1.47497i | ||||||||
\(19\) | −35.4251 | −0.0225127 | −0.0112563 | − | 0.999937i | \(-0.503583\pi\) | ||||
−0.0112563 | + | 0.999937i | \(0.503583\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 342.394 | 0.169425 | ||||||||
\(22\) | − 1913.53i | − 0.842904i | ||||||||
\(23\) | − 2783.24i | − 1.09706i | −0.836130 | − | 0.548531i | \(-0.815187\pi\) | ||||
0.836130 | − | 0.548531i | \(-0.184813\pi\) | |||||||
\(24\) | −5096.22 | −1.80601 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 541.958 | 0.157229 | ||||||||
\(27\) | − 11515.6i | − 3.04004i | ||||||||
\(28\) | − 251.329i | − 0.0605826i | ||||||||
\(29\) | 370.244 | 0.0817511 | 0.0408755 | − | 0.999164i | \(-0.486985\pi\) | ||||
0.0408755 | + | 0.999164i | \(0.486985\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5055.06 | 0.944761 | 0.472381 | − | 0.881395i | \(-0.343395\pi\) | ||||
0.472381 | + | 0.881395i | \(0.343395\pi\) | |||||||
\(32\) | 5969.30i | 1.03050i | ||||||||
\(33\) | − 17653.1i | − 2.82186i | ||||||||
\(34\) | −6713.33 | −0.995957 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −13729.9 | −1.76568 | ||||||||
\(37\) | 4124.15i | 0.495256i | 0.968855 | + | 0.247628i | \(0.0796511\pi\) | ||||
−0.968855 | + | 0.247628i | \(0.920349\pi\) | |||||||
\(38\) | − 113.603i | − 0.0127624i | ||||||||
\(39\) | 4999.79 | 0.526369 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18104.1 | −1.68197 | −0.840985 | − | 0.541058i | \(-0.818024\pi\) | ||||
−0.840985 | + | 0.541058i | \(0.818024\pi\) | |||||||
\(42\) | 1098.01i | 0.0960466i | ||||||||
\(43\) | 7906.34i | 0.652085i | 0.945355 | + | 0.326042i | \(0.105715\pi\) | ||||
−0.945355 | + | 0.326042i | \(0.894285\pi\) | |||||||
\(44\) | −12958.0 | −1.00903 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8925.44 | 0.621921 | ||||||||
\(47\) | − 13185.2i | − 0.870650i | −0.900273 | − | 0.435325i | \(-0.856634\pi\) | ||||
0.900273 | − | 0.435325i | \(-0.143366\pi\) | |||||||
\(48\) | 4215.93i | 0.264113i | ||||||||
\(49\) | 16673.1 | 0.992030 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −61933.3 | −3.33425 | ||||||||
\(52\) | − 3670.02i | − 0.188218i | ||||||||
\(53\) | − 38295.0i | − 1.87263i | −0.351160 | − | 0.936316i | \(-0.614213\pi\) | ||||
0.351160 | − | 0.936316i | \(-0.385787\pi\) | |||||||
\(54\) | 36929.0 | 1.72339 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1993.63 | 0.0849522 | ||||||||
\(57\) | − 1048.03i | − 0.0427256i | ||||||||
\(58\) | 1187.32i | 0.0463444i | ||||||||
\(59\) | −17886.6 | −0.668955 | −0.334477 | − | 0.942404i | \(-0.608560\pi\) | ||||
−0.334477 | + | 0.942404i | \(0.608560\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7392.00 | 0.254353 | 0.127177 | − | 0.991880i | \(-0.459408\pi\) | ||||
0.127177 | + | 0.991880i | \(0.459408\pi\) | |||||||
\(62\) | 16210.8i | 0.535582i | ||||||||
\(63\) | 7317.23i | 0.232271i | ||||||||
\(64\) | −14582.5 | −0.445023 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 56610.8 | 1.59970 | ||||||||
\(67\) | − 23357.0i | − 0.635667i | −0.948147 | − | 0.317834i | \(-0.897045\pi\) | ||||
0.948147 | − | 0.317834i | \(-0.102955\pi\) | |||||||
\(68\) | 45461.2i | 1.19225i | ||||||||
\(69\) | 82340.9 | 2.08206 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −33166.9 | −0.780835 | −0.390417 | − | 0.920638i | \(-0.627669\pi\) | ||||
−0.390417 | + | 0.920638i | \(0.627669\pi\) | |||||||
\(72\) | − 108910.i | − 2.47593i | ||||||||
\(73\) | 10831.7i | 0.237898i | 0.992900 | + | 0.118949i | \(0.0379525\pi\) | ||||
−0.992900 | + | 0.118949i | \(0.962047\pi\) | |||||||
\(74\) | −13225.5 | −0.280759 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −769.295 | −0.0152777 | ||||||||
\(77\) | 6905.85i | 0.132736i | ||||||||
\(78\) | 16033.6i | 0.298397i | ||||||||
\(79\) | 17755.2 | 0.320079 | 0.160039 | − | 0.987111i | \(-0.448838\pi\) | ||||
0.160039 | + | 0.987111i | \(0.448838\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 187049. | 3.16770 | ||||||||
\(82\) | − 58057.3i | − 0.953503i | ||||||||
\(83\) | 84243.8i | 1.34228i | 0.741331 | + | 0.671139i | \(0.234195\pi\) | ||||
−0.741331 | + | 0.671139i | \(0.765805\pi\) | |||||||
\(84\) | 7435.46 | 0.114977 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −25354.5 | −0.369665 | ||||||||
\(87\) | 10953.5i | 0.155151i | ||||||||
\(88\) | − 102787.i | − 1.41492i | ||||||||
\(89\) | 46498.8 | 0.622253 | 0.311126 | − | 0.950369i | \(-0.399294\pi\) | ||||
0.311126 | + | 0.950369i | \(0.399294\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1955.91 | −0.0247597 | ||||||||
\(92\) | − 60441.1i | − 0.744497i | ||||||||
\(93\) | 149552.i | 1.79301i | ||||||||
\(94\) | 42283.1 | 0.493568 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −176599. | −1.95573 | ||||||||
\(97\) | 154213.i | 1.66414i | 0.554667 | + | 0.832072i | \(0.312845\pi\) | ||||
−0.554667 | + | 0.832072i | \(0.687155\pi\) | |||||||
\(98\) | 53468.0i | 0.562379i | ||||||||
\(99\) | 377260. | 3.86860 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −110873. | −1.08149 | −0.540745 | − | 0.841187i | \(-0.681858\pi\) | ||||
−0.540745 | + | 0.841187i | \(0.681858\pi\) | |||||||
\(102\) | − 198611.i | − 1.89018i | ||||||||
\(103\) | − 104407.i | − 0.969699i | −0.874598 | − | 0.484849i | \(-0.838874\pi\) | ||||
0.874598 | − | 0.484849i | \(-0.161126\pi\) | |||||||
\(104\) | 29111.9 | 0.263929 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 122806. | 1.06159 | ||||||||
\(107\) | − 2229.04i | − 0.0188217i | −0.999956 | − | 0.00941084i | \(-0.997004\pi\) | ||||
0.999956 | − | 0.00941084i | \(-0.00299561\pi\) | |||||||
\(108\) | − 250075.i | − 2.06305i | ||||||||
\(109\) | 47011.7 | 0.379000 | 0.189500 | − | 0.981881i | \(-0.439313\pi\) | ||||
0.189500 | + | 0.981881i | \(0.439313\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −122011. | −0.939921 | ||||||||
\(112\) | − 1649.26i | − 0.0124235i | ||||||||
\(113\) | − 198706.i | − 1.46391i | −0.681352 | − | 0.731956i | \(-0.738608\pi\) | ||||
0.681352 | − | 0.731956i | \(-0.261392\pi\) | |||||||
\(114\) | 3360.89 | 0.0242210 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8040.27 | 0.0554786 | ||||||||
\(117\) | 106849.i | 0.721618i | ||||||||
\(118\) | − 57359.5i | − 0.379228i | ||||||||
\(119\) | 24228.2 | 0.156839 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 194999. | 1.21079 | ||||||||
\(122\) | 23705.0i | 0.144192i | ||||||||
\(123\) | − 535603.i | − 3.19213i | ||||||||
\(124\) | 109776. | 0.641142 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −23465.3 | −0.131674 | ||||||||
\(127\) | 87410.5i | 0.480899i | 0.970662 | + | 0.240450i | \(0.0772949\pi\) | ||||
−0.970662 | + | 0.240450i | \(0.922705\pi\) | |||||||
\(128\) | 144254.i | 0.778219i | ||||||||
\(129\) | −233905. | −1.23756 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19351.5 | −0.0985226 | −0.0492613 | − | 0.998786i | \(-0.515687\pi\) | ||||
−0.0492613 | + | 0.998786i | \(0.515687\pi\) | |||||||
\(132\) | − 383356.i | − 1.91500i | ||||||||
\(133\) | 409.989i | 0.00200975i | ||||||||
\(134\) | 74902.4 | 0.360358 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −360614. | −1.67184 | ||||||||
\(137\) | − 79960.9i | − 0.363979i | −0.983300 | − | 0.181989i | \(-0.941746\pi\) | ||||
0.983300 | − | 0.181989i | \(-0.0582537\pi\) | |||||||
\(138\) | 264055.i | 1.18031i | ||||||||
\(139\) | −285962. | −1.25537 | −0.627684 | − | 0.778468i | \(-0.715997\pi\) | ||||
−0.627684 | + | 0.778468i | \(0.715997\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 390079. | 1.65236 | ||||||||
\(142\) | − 106361.i | − 0.442652i | ||||||||
\(143\) | 100842.i | 0.412385i | ||||||||
\(144\) | −90097.7 | −0.362083 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −34735.8 | −0.134864 | ||||||||
\(147\) | 493265.i | 1.88272i | ||||||||
\(148\) | 89560.4i | 0.336095i | ||||||||
\(149\) | −506571. | −1.86928 | −0.934641 | − | 0.355593i | \(-0.884279\pi\) | ||||
−0.934641 | + | 0.355593i | \(0.884279\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −353322. | −1.26104 | −0.630519 | − | 0.776174i | \(-0.717158\pi\) | ||||
−0.630519 | + | 0.776174i | \(0.717158\pi\) | |||||||
\(152\) | − 6102.31i | − 0.0214232i | ||||||||
\(153\) | − 1.32356e6i | − 4.57105i | ||||||||
\(154\) | −22146.0 | −0.0752479 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 108576. | 0.357209 | ||||||||
\(157\) | 222777.i | 0.721308i | 0.932700 | + | 0.360654i | \(0.117446\pi\) | ||||
−0.932700 | + | 0.360654i | \(0.882554\pi\) | |||||||
\(158\) | 56938.2i | 0.181452i | ||||||||
\(159\) | 1.13294e6 | 3.55397 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −32211.6 | −0.0979371 | ||||||||
\(162\) | 599840.i | 1.79576i | ||||||||
\(163\) | 485830.i | 1.43224i | 0.697978 | + | 0.716120i | \(0.254083\pi\) | ||||
−0.697978 | + | 0.716120i | \(0.745917\pi\) | |||||||
\(164\) | −393151. | −1.14143 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −270157. | −0.760933 | ||||||||
\(167\) | 492737.i | 1.36717i | 0.729869 | + | 0.683587i | \(0.239581\pi\) | ||||
−0.729869 | + | 0.683587i | \(0.760419\pi\) | |||||||
\(168\) | 58980.7i | 0.161226i | ||||||||
\(169\) | −28561.0 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22397.3 | 0.0585742 | ||||||||
\(172\) | 171695.i | 0.442523i | ||||||||
\(173\) | 608498.i | 1.54577i | 0.634549 | + | 0.772883i | \(0.281186\pi\) | ||||
−0.634549 | + | 0.772883i | \(0.718814\pi\) | |||||||
\(174\) | −35126.3 | −0.0879547 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −85032.3 | −0.206920 | ||||||||
\(177\) | − 529166.i | − 1.26958i | ||||||||
\(178\) | 149115.i | 0.352753i | ||||||||
\(179\) | 270050. | 0.629958 | 0.314979 | − | 0.949099i | \(-0.398003\pi\) | ||||
0.314979 | + | 0.949099i | \(0.398003\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −602323. | −1.36657 | −0.683286 | − | 0.730151i | \(-0.739450\pi\) | ||||
−0.683286 | + | 0.730151i | \(0.739450\pi\) | |||||||
\(182\) | − 6272.30i | − 0.0140362i | ||||||||
\(183\) | 218689.i | 0.482724i | ||||||||
\(184\) | 479440. | 1.04397 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −479590. | −1.01645 | ||||||||
\(187\) | − 1.24915e6i | − 2.61223i | ||||||||
\(188\) | − 286332.i | − 0.590847i | ||||||||
\(189\) | −133275. | −0.271391 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −138491. | −0.274688 | −0.137344 | − | 0.990523i | \(-0.543857\pi\) | ||||
−0.137344 | + | 0.990523i | \(0.543857\pi\) | |||||||
\(192\) | − 431417.i | − 0.844586i | ||||||||
\(193\) | 58857.2i | 0.113738i | 0.998382 | + | 0.0568691i | \(0.0181118\pi\) | ||||
−0.998382 | + | 0.0568691i | \(0.981888\pi\) | |||||||
\(194\) | −494537. | −0.943398 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 362074. | 0.673220 | ||||||||
\(197\) | − 271860.i | − 0.499091i | −0.968363 | − | 0.249545i | \(-0.919719\pi\) | ||||
0.968363 | − | 0.249545i | \(-0.0802812\pi\) | |||||||
\(198\) | 1.20982e6i | 2.19309i | ||||||||
\(199\) | 71334.8 | 0.127694 | 0.0638468 | − | 0.997960i | \(-0.479663\pi\) | ||||
0.0638468 | + | 0.997960i | \(0.479663\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 691006. | 1.20640 | ||||||||
\(202\) | − 355553.i | − 0.613093i | ||||||||
\(203\) | − 4284.99i | − 0.00729810i | ||||||||
\(204\) | −1.34495e6 | −2.26272 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 334818. | 0.549719 | ||||||||
\(207\) | 1.75969e6i | 2.85437i | ||||||||
\(208\) | − 24083.2i | − 0.0385973i | ||||||||
\(209\) | 21138.1 | 0.0334735 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 480921. | 0.743648 | 0.371824 | − | 0.928303i | \(-0.378732\pi\) | ||||
0.371824 | + | 0.928303i | \(0.378732\pi\) | |||||||
\(212\) | − 831618.i | − 1.27082i | ||||||||
\(213\) | − 981228.i | − 1.48191i | ||||||||
\(214\) | 7148.20 | 0.0106699 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.98368e6 | 2.89292 | ||||||||
\(217\) | − 58504.3i | − 0.0843409i | ||||||||
\(218\) | 150759.i | 0.214854i | ||||||||
\(219\) | −320452. | −0.451495 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 353790. | 0.487265 | ||||||||
\(222\) | − 391271.i | − 0.532838i | ||||||||
\(223\) | 1.34684e6i | 1.81365i | 0.421511 | + | 0.906823i | \(0.361500\pi\) | ||||
−0.421511 | + | 0.906823i | \(0.638500\pi\) | |||||||
\(224\) | 69085.1 | 0.0919950 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 637221. | 0.829887 | ||||||||
\(227\) | − 719772.i | − 0.927108i | −0.886069 | − | 0.463554i | \(-0.846574\pi\) | ||||
0.886069 | − | 0.463554i | \(-0.153426\pi\) | |||||||
\(228\) | − 22759.2i | − 0.0289948i | ||||||||
\(229\) | 568410. | 0.716264 | 0.358132 | − | 0.933671i | \(-0.383414\pi\) | ||||
0.358132 | + | 0.933671i | \(0.383414\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −204306. | −0.251914 | ||||||||
\(232\) | 63778.2i | 0.0777951i | ||||||||
\(233\) | − 282144.i | − 0.340472i | −0.985403 | − | 0.170236i | \(-0.945547\pi\) | ||||
0.985403 | − | 0.170236i | \(-0.0544531\pi\) | |||||||
\(234\) | −342650. | −0.409083 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −388426. | −0.453972 | ||||||||
\(237\) | 525278.i | 0.607461i | ||||||||
\(238\) | 77696.1i | 0.0889113i | ||||||||
\(239\) | 143244. | 0.162211 | 0.0811056 | − | 0.996706i | \(-0.474155\pi\) | ||||
0.0811056 | + | 0.996706i | \(0.474155\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −369914. | −0.410259 | −0.205130 | − | 0.978735i | \(-0.565762\pi\) | ||||
−0.205130 | + | 0.978735i | \(0.565762\pi\) | |||||||
\(242\) | 625334.i | 0.686395i | ||||||||
\(243\) | 2.73547e6i | 2.97178i | ||||||||
\(244\) | 160525. | 0.172611 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.71760e6 | 1.80961 | ||||||||
\(247\) | 5986.84i | 0.00624389i | ||||||||
\(248\) | 870783.i | 0.899043i | ||||||||
\(249\) | −2.49231e6 | −2.54744 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −731868. | −0.733244 | −0.366622 | − | 0.930370i | \(-0.619486\pi\) | ||||
−0.366622 | + | 0.930370i | \(0.619486\pi\) | |||||||
\(252\) | 158902.i | 0.157626i | ||||||||
\(253\) | 1.66076e6i | 1.63119i | ||||||||
\(254\) | −280312. | −0.272620 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −929240. | −0.886192 | ||||||||
\(257\) | 1.05879e6i | 0.999951i | 0.866040 | + | 0.499975i | \(0.166658\pi\) | ||||
−0.866040 | + | 0.499975i | \(0.833342\pi\) | |||||||
\(258\) | − 750100.i | − 0.701568i | ||||||||
\(259\) | 47730.4 | 0.0442126 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −234085. | −0.212703 | ||||||||
\(262\) | − 62057.3i | − 0.0558521i | ||||||||
\(263\) | − 318172.i | − 0.283644i | −0.989892 | − | 0.141822i | \(-0.954704\pi\) | ||||
0.989892 | − | 0.141822i | \(-0.0452960\pi\) | |||||||
\(264\) | 3.04091e6 | 2.68531 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1314.77 | −0.00113932 | ||||||||
\(267\) | 1.37565e6i | 1.18094i | ||||||||
\(268\) | − 507223.i | − 0.431382i | ||||||||
\(269\) | −1.13453e6 | −0.955954 | −0.477977 | − | 0.878372i | \(-0.658630\pi\) | ||||
−0.477977 | + | 0.878372i | \(0.658630\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.05400e6 | −0.871805 | −0.435902 | − | 0.899994i | \(-0.643571\pi\) | ||||
−0.435902 | + | 0.899994i | \(0.643571\pi\) | |||||||
\(272\) | 298324.i | 0.244492i | ||||||||
\(273\) | − 57864.6i | − 0.0469901i | ||||||||
\(274\) | 256423. | 0.206338 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.78812e6 | 1.41294 | ||||||||
\(277\) | − 2.18170e6i | − 1.70843i | −0.519922 | − | 0.854214i | \(-0.674039\pi\) | ||||
0.519922 | − | 0.854214i | \(-0.325961\pi\) | |||||||
\(278\) | − 917037.i | − 0.711664i | ||||||||
\(279\) | −3.19604e6 | −2.45811 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.11562e6 | −1.59835 | −0.799176 | − | 0.601097i | \(-0.794730\pi\) | ||||
−0.799176 | + | 0.601097i | \(0.794730\pi\) | |||||||
\(282\) | 1.25093e6i | 0.936718i | ||||||||
\(283\) | 390968.i | 0.290185i | 0.989418 | + | 0.145092i | \(0.0463480\pi\) | ||||
−0.989418 | + | 0.145092i | \(0.953652\pi\) | |||||||
\(284\) | −720256. | −0.529896 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −323386. | −0.233779 | ||||||||
\(287\) | 209527.i | 0.150153i | ||||||||
\(288\) | − 3.77406e6i | − 2.68119i | ||||||||
\(289\) | −2.96261e6 | −2.08655 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.56231e6 | −3.15830 | ||||||||
\(292\) | 235223.i | 0.161444i | ||||||||
\(293\) | 2.44684e6i | 1.66508i | 0.553961 | + | 0.832542i | \(0.313116\pi\) | ||||
−0.553961 | + | 0.832542i | \(0.686884\pi\) | |||||||
\(294\) | −1.58183e6 | −1.06731 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −710424. | −0.471290 | ||||||||
\(297\) | 6.87138e6i | 4.52015i | ||||||||
\(298\) | − 1.62450e6i | − 1.05969i | ||||||||
\(299\) | −470368. | −0.304270 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 91503.3 | 0.0582131 | ||||||||
\(302\) | − 1.13305e6i | − 0.714878i | ||||||||
\(303\) | − 3.28013e6i | − 2.05251i | ||||||||
\(304\) | −5048.23 | −0.00313296 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.24447e6 | 2.59131 | ||||||||
\(307\) | − 1.58927e6i | − 0.962390i | −0.876614 | − | 0.481195i | \(-0.840203\pi\) | ||||
0.876614 | − | 0.481195i | \(-0.159797\pi\) | |||||||
\(308\) | 149968.i | 0.0900787i | ||||||||
\(309\) | 3.08884e6 | 1.84034 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.15211e6 | 1.84799 | 0.923996 | − | 0.382403i | \(-0.124903\pi\) | ||||
0.923996 | + | 0.382403i | \(0.124903\pi\) | |||||||
\(312\) | 861261.i | 0.500897i | ||||||||
\(313\) | − 1.58939e6i | − 0.917001i | −0.888694 | − | 0.458500i | \(-0.848387\pi\) | ||||
0.888694 | − | 0.458500i | \(-0.151613\pi\) | |||||||
\(314\) | −714412. | −0.408907 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 385573. | 0.217215 | ||||||||
\(317\) | − 1.45529e6i | − 0.813396i | −0.913563 | − | 0.406698i | \(-0.866680\pi\) | ||||
0.913563 | − | 0.406698i | \(-0.133320\pi\) | |||||||
\(318\) | 3.63317e6i | 2.01473i | ||||||||
\(319\) | −220925. | −0.121554 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 65945.1 | 0.0357207 | ||||||||
\(322\) | − 103298.i | − 0.0555202i | ||||||||
\(323\) | − 74160.0i | − 0.0395516i | ||||||||
\(324\) | 4.06198e6 | 2.14969 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.55799e6 | −0.811932 | ||||||||
\(327\) | 1.39082e6i | 0.719285i | ||||||||
\(328\) | − 3.11861e6i | − 1.60058i | ||||||||
\(329\) | −152598. | −0.0777248 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.21928e6 | 1.61506 | 0.807530 | − | 0.589826i | \(-0.200804\pi\) | ||||
0.807530 | + | 0.589826i | \(0.200804\pi\) | |||||||
\(332\) | 1.82945e6i | 0.910908i | ||||||||
\(333\) | − 2.60747e6i | − 1.28857i | ||||||||
\(334\) | −1.58013e6 | −0.775046 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 48792.7 | 0.0235780 | ||||||||
\(337\) | − 3.07320e6i | − 1.47406i | −0.675859 | − | 0.737031i | \(-0.736227\pi\) | ||||
0.675859 | − | 0.737031i | \(-0.263773\pi\) | |||||||
\(338\) | − 91590.9i | − 0.0436074i | ||||||||
\(339\) | 5.87863e6 | 2.77829 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.01635e6 | −1.40474 | ||||||||
\(342\) | 71824.9i | 0.0332055i | ||||||||
\(343\) | − 387478.i | − 0.177833i | ||||||||
\(344\) | −1.36194e6 | −0.620530 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.95136e6 | −0.876289 | ||||||||
\(347\) | − 679230.i | − 0.302826i | −0.988471 | − | 0.151413i | \(-0.951618\pi\) | ||||
0.988471 | − | 0.151413i | \(-0.0483823\pi\) | |||||||
\(348\) | 237868.i | 0.105290i | ||||||||
\(349\) | −3.00182e6 | −1.31923 | −0.659616 | − | 0.751603i | \(-0.729281\pi\) | ||||
−0.659616 | + | 0.751603i | \(0.729281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.94614e6 | −0.843154 | ||||||||
\(352\) | − 3.56188e6i | − 1.53222i | ||||||||
\(353\) | − 2.13910e6i | − 0.913682i | −0.889548 | − | 0.456841i | \(-0.848981\pi\) | ||||
0.889548 | − | 0.456841i | \(-0.151019\pi\) | |||||||
\(354\) | 1.69696e6 | 0.719718 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.00977e6 | 0.422278 | ||||||||
\(357\) | 716779.i | 0.297656i | ||||||||
\(358\) | 866010.i | 0.357121i | ||||||||
\(359\) | −4.04695e6 | −1.65726 | −0.828631 | − | 0.559795i | \(-0.810880\pi\) | ||||
−0.828631 | + | 0.559795i | \(0.810880\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.47484e6 | −0.999493 | ||||||||
\(362\) | − 1.93156e6i | − 0.774705i | ||||||||
\(363\) | 5.76897e6i | 2.29790i | ||||||||
\(364\) | −42474.7 | −0.0168026 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −701303. | −0.273655 | ||||||||
\(367\) | 1.59021e6i | 0.616295i | 0.951339 | + | 0.308148i | \(0.0997090\pi\) | ||||
−0.951339 | + | 0.308148i | \(0.900291\pi\) | |||||||
\(368\) | − 396624.i | − 0.152672i | ||||||||
\(369\) | 1.14463e7 | 4.37620 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −443204. | −0.167174 | ||||||||
\(372\) | 3.24768e6i | 1.21679i | ||||||||
\(373\) | 3.36023e6i | 1.25054i | 0.780409 | + | 0.625270i | \(0.215011\pi\) | ||||
−0.780409 | + | 0.625270i | \(0.784989\pi\) | |||||||
\(374\) | 4.00584e6 | 1.48086 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.27128e6 | 0.828518 | ||||||||
\(377\) | − 62571.3i | − 0.0226737i | ||||||||
\(378\) | − 427394.i | − 0.153850i | ||||||||
\(379\) | −849174. | −0.303668 | −0.151834 | − | 0.988406i | \(-0.548518\pi\) | ||||
−0.151834 | + | 0.988406i | \(0.548518\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.58600e6 | −0.912674 | ||||||||
\(382\) | − 444121.i | − 0.155720i | ||||||||
\(383\) | 4.04395e6i | 1.40867i | 0.709868 | + | 0.704335i | \(0.248755\pi\) | ||||
−0.709868 | + | 0.704335i | \(0.751245\pi\) | |||||||
\(384\) | −4.26768e6 | −1.47694 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −188746. | −0.0644777 | ||||||||
\(387\) | − 4.99874e6i | − 1.69662i | ||||||||
\(388\) | 3.34890e6i | 1.12934i | ||||||||
\(389\) | 2.94042e6 | 0.985226 | 0.492613 | − | 0.870249i | \(-0.336042\pi\) | ||||
0.492613 | + | 0.870249i | \(0.336042\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.82653e6 | 1.92738 | ||||||||
\(392\) | 2.87209e6i | 0.944025i | ||||||||
\(393\) | − 572504.i | − 0.186981i | ||||||||
\(394\) | 871814. | 0.282933 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.19263e6 | 2.62534 | ||||||||
\(397\) | − 1.24060e6i | − 0.395053i | −0.980298 | − | 0.197526i | \(-0.936709\pi\) | ||||
0.980298 | − | 0.197526i | \(-0.0632908\pi\) | |||||||
\(398\) | 228760.i | 0.0723890i | ||||||||
\(399\) | −12129.3 | −0.00381421 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −972004. | −0.301861 | −0.150931 | − | 0.988544i | \(-0.548227\pi\) | ||||
−0.150931 | + | 0.988544i | \(0.548227\pi\) | |||||||
\(402\) | 2.21595e6i | 0.683904i | ||||||||
\(403\) | − 854305.i | − 0.262030i | ||||||||
\(404\) | −2.40773e6 | −0.733930 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13741.3 | 0.00413727 | ||||||||
\(407\) | − 2.46088e6i | − 0.736383i | ||||||||
\(408\) | − 1.06686e7i | − 3.17290i | ||||||||
\(409\) | −571971. | −0.169070 | −0.0845348 | − | 0.996421i | \(-0.526940\pi\) | ||||
−0.0845348 | + | 0.996421i | \(0.526940\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.36561e6 | 0.690777 | ||||||||
\(412\) | − 2.26731e6i | − 0.658065i | ||||||||
\(413\) | 207009.i | 0.0597191i | ||||||||
\(414\) | −5.64306e6 | −1.61813 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.00881e6 | 0.285809 | ||||||||
\(417\) | − 8.46005e6i | − 2.38250i | ||||||||
\(418\) | 67786.9i | 0.0189760i | ||||||||
\(419\) | 4.06416e6 | 1.13093 | 0.565465 | − | 0.824772i | \(-0.308697\pi\) | ||||
0.565465 | + | 0.824772i | \(0.308697\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.73588e6 | −1.02728 | −0.513639 | − | 0.858007i | \(-0.671703\pi\) | ||||
−0.513639 | + | 0.858007i | \(0.671703\pi\) | |||||||
\(422\) | 1.54224e6i | 0.421572i | ||||||||
\(423\) | 8.33631e6i | 2.26528i | ||||||||
\(424\) | 6.59668e6 | 1.78201 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.14665e6 | 0.840088 | ||||||||
\(427\) | − 85550.6i | − 0.0227067i | ||||||||
\(428\) | − 48406.0i | − 0.0127729i | ||||||||
\(429\) | −2.98337e6 | −0.782644 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.53689e6 | −0.398520 | −0.199260 | − | 0.979947i | \(-0.563854\pi\) | ||||
−0.199260 | + | 0.979947i | \(0.563854\pi\) | |||||||
\(432\) | − 1.64103e6i | − 0.423065i | ||||||||
\(433\) | − 112160.i | − 0.0287487i | −0.999897 | − | 0.0143744i | \(-0.995424\pi\) | ||||
0.999897 | − | 0.0143744i | \(-0.00457566\pi\) | |||||||
\(434\) | 187615. | 0.0478126 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.02091e6 | 0.257200 | ||||||||
\(437\) | 98596.5i | 0.0246978i | ||||||||
\(438\) | − 1.02764e6i | − 0.255951i | ||||||||
\(439\) | 164279. | 0.0406837 | 0.0203418 | − | 0.999793i | \(-0.493525\pi\) | ||||
0.0203418 | + | 0.999793i | \(0.493525\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.05415e7 | −2.58110 | ||||||||
\(442\) | 1.13455e6i | 0.276229i | ||||||||
\(443\) | − 4.62345e6i | − 1.11933i | −0.828720 | − | 0.559664i | \(-0.810930\pi\) | ||||
0.828720 | − | 0.559664i | \(-0.189070\pi\) | |||||||
\(444\) | −2.64960e6 | −0.637857 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.31910e6 | −1.02815 | ||||||||
\(447\) | − 1.49867e7i | − 3.54761i | ||||||||
\(448\) | 168769.i | 0.0397282i | ||||||||
\(449\) | −421554. | −0.0986820 | −0.0493410 | − | 0.998782i | \(-0.515712\pi\) | ||||
−0.0493410 | + | 0.998782i | \(0.515712\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.08027e7 | 2.50088 | ||||||||
\(452\) | − 4.31512e6i | − 0.993452i | ||||||||
\(453\) | − 1.04529e7i | − 2.39326i | ||||||||
\(454\) | 2.30820e6 | 0.525574 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 180534. | 0.0406581 | ||||||||
\(457\) | 5.34433e6i | 1.19702i | 0.801114 | + | 0.598512i | \(0.204241\pi\) | ||||
−0.801114 | + | 0.598512i | \(0.795759\pi\) | |||||||
\(458\) | 1.82281e6i | 0.406047i | ||||||||
\(459\) | 2.41072e7 | 5.34091 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.95164e6 | −1.08517 | −0.542584 | − | 0.840002i | \(-0.682554\pi\) | ||||
−0.542584 | + | 0.840002i | \(0.682554\pi\) | |||||||
\(462\) | − 655180.i | − 0.142809i | ||||||||
\(463\) | 3.87726e6i | 0.840567i | 0.907393 | + | 0.420283i | \(0.138069\pi\) | ||||
−0.907393 | + | 0.420283i | \(0.861931\pi\) | |||||||
\(464\) | 52761.5 | 0.0113768 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 904795. | 0.193013 | ||||||||
\(467\) | − 1.64031e6i | − 0.348043i | −0.984742 | − | 0.174022i | \(-0.944324\pi\) | ||||
0.984742 | − | 0.174022i | \(-0.0556763\pi\) | |||||||
\(468\) | 2.32035e6i | 0.489711i | ||||||||
\(469\) | −270320. | −0.0567474 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.59075e6 | −1.36893 | ||||||||
\(472\) | − 3.08113e6i | − 0.636583i | ||||||||
\(473\) | − 4.71771e6i | − 0.969568i | ||||||||
\(474\) | −1.68449e6 | −0.344368 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 526141. | 0.106435 | ||||||||
\(477\) | 2.42118e7i | 4.87227i | ||||||||
\(478\) | 459361.i | 0.0919570i | ||||||||
\(479\) | −2.63694e6 | −0.525123 | −0.262561 | − | 0.964915i | \(-0.584567\pi\) | ||||
−0.262561 | + | 0.964915i | \(0.584567\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 696981. | 0.137359 | ||||||||
\(482\) | − 1.18626e6i | − 0.232575i | ||||||||
\(483\) | − 952965.i | − 0.185870i | ||||||||
\(484\) | 4.23463e6 | 0.821678 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.77225e6 | −1.68469 | ||||||||
\(487\) | − 3.47150e6i | − 0.663277i | −0.943407 | − | 0.331639i | \(-0.892399\pi\) | ||||
0.943407 | − | 0.331639i | \(-0.107601\pi\) | |||||||
\(488\) | 1.27334e6i | 0.242045i | ||||||||
\(489\) | −1.43731e7 | −2.71817 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.74272e6 | −0.513425 | −0.256713 | − | 0.966488i | \(-0.582639\pi\) | ||||
−0.256713 | + | 0.966488i | \(0.582639\pi\) | |||||||
\(492\) | − 1.16312e7i | − 2.16627i | ||||||||
\(493\) | 775082.i | 0.143625i | ||||||||
\(494\) | −19198.9 | −0.00353964 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 720368. | 0.131477 | ||||||||
\(497\) | 383854.i | 0.0697068i | ||||||||
\(498\) | − 7.99248e6i | − 1.44414i | ||||||||
\(499\) | 1.00565e7 | 1.80799 | 0.903996 | − | 0.427540i | \(-0.140620\pi\) | ||||
0.903996 | + | 0.427540i | \(0.140620\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.45774e7 | −2.59469 | ||||||||
\(502\) | − 2.34699e6i | − 0.415674i | ||||||||
\(503\) | 5.52516e6i | 0.973699i | 0.873486 | + | 0.486850i | \(0.161854\pi\) | ||||
−0.873486 | + | 0.486850i | \(0.838146\pi\) | |||||||
\(504\) | −1.26046e6 | −0.221031 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.32580e6 | −0.924717 | ||||||||
\(507\) | − 844964.i | − 0.145988i | ||||||||
\(508\) | 1.89821e6i | 0.326352i | ||||||||
\(509\) | 6.59944e6 | 1.12905 | 0.564524 | − | 0.825416i | \(-0.309060\pi\) | ||||
0.564524 | + | 0.825416i | \(0.309060\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 125360. | 0.0212377 | ||||||||
\(512\) | 1.63618e6i | 0.275839i | ||||||||
\(513\) | 407943.i | 0.0684393i | ||||||||
\(514\) | −3.39540e6 | −0.566869 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.07951e6 | −0.839842 | ||||||||
\(517\) | 7.86763e6i | 1.29455i | ||||||||
\(518\) | 153064.i | 0.0250640i | ||||||||
\(519\) | −1.80021e7 | −2.93363 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −653159. | −0.105420 | −0.0527102 | − | 0.998610i | \(-0.516786\pi\) | ||||
−0.0527102 | + | 0.998610i | \(0.516786\pi\) | |||||||
\(522\) | − 750677.i | − 0.120580i | ||||||||
\(523\) | 3.60676e6i | 0.576584i | 0.957543 | + | 0.288292i | \(0.0930874\pi\) | ||||
−0.957543 | + | 0.288292i | \(0.906913\pi\) | |||||||
\(524\) | −420239. | −0.0668602 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.02033e6 | 0.160797 | ||||||||
\(527\) | 1.05824e7i | 1.65981i | ||||||||
\(528\) | − 2.51564e6i | − 0.392703i | ||||||||
\(529\) | −1.31008e6 | −0.203544 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.13087e7 | 1.74051 | ||||||||
\(532\) | 8903.36i | 0.00136388i | ||||||||
\(533\) | 3.05960e6i | 0.466495i | ||||||||
\(534\) | −4.41149e6 | −0.669472 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.02346e6 | 0.604906 | ||||||||
\(537\) | 7.98931e6i | 1.19557i | ||||||||
\(538\) | − 3.63828e6i | − 0.541927i | ||||||||
\(539\) | −9.94881e6 | −1.47502 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.92001e6 | −0.282040 | −0.141020 | − | 0.990007i | \(-0.545038\pi\) | ||||
−0.141020 | + | 0.990007i | \(0.545038\pi\) | |||||||
\(542\) | − 3.38004e6i | − 0.494223i | ||||||||
\(543\) | − 1.78194e7i | − 2.59355i | ||||||||
\(544\) | −1.24963e7 | −1.81044 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 185563. | 0.0266385 | ||||||||
\(547\) | 7.41583e6i | 1.05972i | 0.848085 | + | 0.529860i | \(0.177756\pi\) | ||||
−0.848085 | + | 0.529860i | \(0.822244\pi\) | |||||||
\(548\) | − 1.73644e6i | − 0.247006i | ||||||||
\(549\) | −4.67356e6 | −0.661784 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13115.9 | −0.00184043 | ||||||||
\(552\) | 1.41840e7i | 1.98130i | ||||||||
\(553\) | − 205488.i | − 0.0285741i | ||||||||
\(554\) | 6.99640e6 | 0.968502 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.20998e6 | −0.851928 | ||||||||
\(557\) | − 3.52870e6i | − 0.481922i | −0.970535 | − | 0.240961i | \(-0.922537\pi\) | ||||
0.970535 | − | 0.240961i | \(-0.0774626\pi\) | |||||||
\(558\) | − 1.02492e7i | − 1.39349i | ||||||||
\(559\) | 1.33617e6 | 0.180856 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.69556e7 | 4.95761 | ||||||||
\(562\) | − 6.78449e6i | − 0.906100i | ||||||||
\(563\) | − 4.31809e6i | − 0.574144i | −0.957909 | − | 0.287072i | \(-0.907318\pi\) | ||||
0.957909 | − | 0.287072i | \(-0.0926818\pi\) | |||||||
\(564\) | 8.47100e6 | 1.12134 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.25378e6 | −0.164505 | ||||||||
\(567\) | − 2.16480e6i | − 0.282787i | ||||||||
\(568\) | − 5.71332e6i | − 0.743049i | ||||||||
\(569\) | 3.99812e6 | 0.517696 | 0.258848 | − | 0.965918i | \(-0.416657\pi\) | ||||
0.258848 | + | 0.965918i | \(0.416657\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 298969. | 0.0383739 | 0.0191869 | − | 0.999816i | \(-0.493892\pi\) | ||||
0.0191869 | + | 0.999816i | \(0.493892\pi\) | |||||||
\(572\) | 2.18990e6i | 0.279856i | ||||||||
\(573\) | − 4.09720e6i | − 0.521316i | ||||||||
\(574\) | −671921. | −0.0851213 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 9.21972e6 | 1.15787 | ||||||||
\(577\) | − 2.22363e6i | − 0.278050i | −0.990289 | − | 0.139025i | \(-0.955603\pi\) | ||||
0.990289 | − | 0.139025i | \(-0.0443969\pi\) | |||||||
\(578\) | − 9.50064e6i | − 1.18286i | ||||||||
\(579\) | −1.74126e6 | −0.215858 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 974988. | 0.119828 | ||||||||
\(582\) | − 1.46307e7i | − 1.79043i | ||||||||
\(583\) | 2.28506e7i | 2.78437i | ||||||||
\(584\) | −1.86587e6 | −0.226386 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.84665e6 | −0.943931 | ||||||||
\(587\) | − 3.25215e6i | − 0.389560i | −0.980847 | − | 0.194780i | \(-0.937601\pi\) | ||||
0.980847 | − | 0.194780i | \(-0.0623993\pi\) | |||||||
\(588\) | 1.07118e7i | 1.27767i | ||||||||
\(589\) | −179076. | −0.0212691 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.04285e6 | 0.947199 | ||||||||
\(592\) | 587709.i | 0.0689220i | ||||||||
\(593\) | 1.23502e7i | 1.44224i | 0.692810 | + | 0.721121i | \(0.256373\pi\) | ||||
−0.692810 | + | 0.721121i | \(0.743627\pi\) | |||||||
\(594\) | −2.20355e7 | −2.56246 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.10007e7 | −1.26855 | ||||||||
\(597\) | 2.11041e6i | 0.242343i | ||||||||
\(598\) | − 1.50840e6i | − 0.172490i | ||||||||
\(599\) | 1.26026e7 | 1.43513 | 0.717567 | − | 0.696490i | \(-0.245256\pi\) | ||||
0.717567 | + | 0.696490i | \(0.245256\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.10475e7 | 1.24760 | 0.623802 | − | 0.781582i | \(-0.285587\pi\) | ||||
0.623802 | + | 0.781582i | \(0.285587\pi\) | |||||||
\(602\) | 293437.i | 0.0330008i | ||||||||
\(603\) | 1.47673e7i | 1.65390i | ||||||||
\(604\) | −7.67277e6 | −0.855776 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.05189e7 | 1.16356 | ||||||||
\(607\) | 1.47315e7i | 1.62284i | 0.584462 | + | 0.811421i | \(0.301306\pi\) | ||||
−0.584462 | + | 0.811421i | \(0.698694\pi\) | |||||||
\(608\) | − 211463.i | − 0.0231993i | ||||||||
\(609\) | 126769. | 0.0138507 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.22831e6 | −0.241475 | ||||||||
\(612\) | − 2.87426e7i | − 3.10204i | ||||||||
\(613\) | − 6.38520e6i | − 0.686315i | −0.939278 | − | 0.343157i | \(-0.888504\pi\) | ||||
0.939278 | − | 0.343157i | \(-0.111496\pi\) | |||||||
\(614\) | 5.09655e6 | 0.545576 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.18960e6 | −0.126313 | ||||||||
\(617\) | 1.69836e7i | 1.79604i | 0.439954 | + | 0.898020i | \(0.354995\pi\) | ||||
−0.439954 | + | 0.898020i | \(0.645005\pi\) | |||||||
\(618\) | 9.90544e6i | 1.04328i | ||||||||
\(619\) | 1.06421e7 | 1.11635 | 0.558175 | − | 0.829723i | \(-0.311502\pi\) | ||||
0.558175 | + | 0.829723i | \(0.311502\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.20508e7 | −3.33511 | ||||||||
\(622\) | 1.01083e7i | 1.04762i | ||||||||
\(623\) | − 538150.i | − 0.0555499i | ||||||||
\(624\) | 712492. | 0.0732518 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.09694e6 | 0.519845 | ||||||||
\(627\) | 625362.i | 0.0635276i | ||||||||
\(628\) | 4.83784e6i | 0.489500i | ||||||||
\(629\) | −8.63362e6 | −0.870095 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.93725e6 | 0.893574 | 0.446787 | − | 0.894640i | \(-0.352568\pi\) | ||||
0.446787 | + | 0.894640i | \(0.352568\pi\) | |||||||
\(632\) | 3.05850e6i | 0.304590i | ||||||||
\(633\) | 1.42278e7i | 1.41133i | ||||||||
\(634\) | 4.66691e6 | 0.461111 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.46030e7 | 2.41183 | ||||||||
\(637\) | − 2.81775e6i | − 0.275140i | ||||||||
\(638\) | − 708473.i | − 0.0689083i | ||||||||
\(639\) | 2.09696e7 | 2.03160 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.12700e7 | −1.08337 | −0.541686 | − | 0.840581i | \(-0.682214\pi\) | ||||
−0.541686 | + | 0.840581i | \(0.682214\pi\) | |||||||
\(642\) | 211476.i | 0.0202499i | ||||||||
\(643\) | − 1.16584e7i | − 1.11202i | −0.831177 | − | 0.556008i | \(-0.812332\pi\) | ||||
0.831177 | − | 0.556008i | \(-0.187668\pi\) | |||||||
\(644\) | −699510. | −0.0664629 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 237820. | 0.0224217 | ||||||||
\(647\) | 8.09860e6i | 0.760587i | 0.924866 | + | 0.380294i | \(0.124177\pi\) | ||||
−0.924866 | + | 0.380294i | \(0.875823\pi\) | |||||||
\(648\) | 3.22211e7i | 3.01441i | ||||||||
\(649\) | 1.06729e7 | 0.994651 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.73082e6 | 0.160066 | ||||||||
\(652\) | 1.05503e7i | 0.971958i | ||||||||
\(653\) | 2.50550e6i | 0.229938i | 0.993369 | + | 0.114969i | \(0.0366769\pi\) | ||||
−0.993369 | + | 0.114969i | \(0.963323\pi\) | |||||||
\(654\) | −4.46015e6 | −0.407760 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.57992e6 | −0.234070 | ||||||||
\(657\) | − 6.84831e6i | − 0.618971i | ||||||||
\(658\) | − 489360.i | − 0.0440619i | ||||||||
\(659\) | 2.14090e7 | 1.92036 | 0.960182 | − | 0.279376i | \(-0.0901274\pi\) | ||||
0.960182 | + | 0.279376i | \(0.0901274\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.59525e7 | 1.42012 | 0.710060 | − | 0.704141i | \(-0.248668\pi\) | ||||
0.710060 | + | 0.704141i | \(0.248668\pi\) | |||||||
\(662\) | 1.03238e7i | 0.915572i | ||||||||
\(663\) | 1.04667e7i | 0.924755i | ||||||||
\(664\) | −1.45118e7 | −1.27732 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.36177e6 | 0.730488 | ||||||||
\(667\) | − 1.03048e6i | − 0.0896860i | ||||||||
\(668\) | 1.07003e7i | 0.927803i | ||||||||
\(669\) | −3.98455e7 | −3.44203 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.41080e6 | −0.378191 | ||||||||
\(672\) | 2.04385e6i | 0.174593i | ||||||||
\(673\) | − 9.71969e6i | − 0.827208i | −0.910457 | − | 0.413604i | \(-0.864270\pi\) | ||||
0.910457 | − | 0.413604i | \(-0.135730\pi\) | |||||||
\(674\) | 9.85529e6 | 0.835641 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −620234. | −0.0522022 | ||||||||
\(677\) | 1.01440e7i | 0.850628i | 0.905046 | + | 0.425314i | \(0.139836\pi\) | ||||
−0.905046 | + | 0.425314i | \(0.860164\pi\) | |||||||
\(678\) | 1.88519e7i | 1.57500i | ||||||||
\(679\) | 1.78477e6 | 0.148562 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.12941e7 | 1.75951 | ||||||||
\(682\) | − 9.67300e6i | − 0.796343i | ||||||||
\(683\) | 6.41414e6i | 0.526122i | 0.964779 | + | 0.263061i | \(0.0847321\pi\) | ||||
−0.964779 | + | 0.263061i | \(0.915268\pi\) | |||||||
\(684\) | 486383. | 0.0397501 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.24259e6 | 0.100813 | ||||||||
\(687\) | 1.68161e7i | 1.35936i | ||||||||
\(688\) | 1.12669e6i | 0.0907471i | ||||||||
\(689\) | −6.47185e6 | −0.519374 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.38877e6 | −0.668349 | −0.334175 | − | 0.942511i | \(-0.608458\pi\) | ||||
−0.334175 | + | 0.942511i | \(0.608458\pi\) | |||||||
\(692\) | 1.32142e7i | 1.04900i | ||||||||
\(693\) | − 4.36619e6i | − 0.345358i | ||||||||
\(694\) | 2.17819e6 | 0.171671 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.88685e6 | −0.147643 | ||||||||
\(697\) | − 3.78998e7i | − 2.95498i | ||||||||
\(698\) | − 9.62639e6i | − 0.747868i | ||||||||
\(699\) | 8.34712e6 | 0.646165 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.05150e6 | −0.388263 | −0.194131 | − | 0.980976i | \(-0.562189\pi\) | ||||
−0.194131 | + | 0.980976i | \(0.562189\pi\) | |||||||
\(702\) | − 6.24099e6i | − 0.477981i | ||||||||
\(703\) | − 146098.i | − 0.0111495i | ||||||||
\(704\) | 8.70138e6 | 0.661693 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.85979e6 | 0.517963 | ||||||||
\(707\) | 1.28318e6i | 0.0965470i | ||||||||
\(708\) | − 1.14914e7i | − 0.861570i | ||||||||
\(709\) | −1.37386e7 | −1.02642 | −0.513212 | − | 0.858262i | \(-0.671545\pi\) | ||||
−0.513212 | + | 0.858262i | \(0.671545\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.12256e7 | −0.832791 | ||||||||
\(712\) | 8.00986e6i | 0.592141i | ||||||||
\(713\) | − 1.40694e7i | − 1.03646i | ||||||||
\(714\) | −2.29860e6 | −0.168740 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.86443e6 | 0.427507 | ||||||||
\(717\) | 4.23780e6i | 0.307852i | ||||||||
\(718\) | − 1.29780e7i | − 0.939496i | ||||||||
\(719\) | 8.31655e6 | 0.599958 | 0.299979 | − | 0.953946i | \(-0.403020\pi\) | ||||
0.299979 | + | 0.953946i | \(0.403020\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.20835e6 | −0.0865671 | ||||||||
\(722\) | − 7.93646e6i | − 0.566609i | ||||||||
\(723\) | − 1.09437e7i | − 0.778610i | ||||||||
\(724\) | −1.30801e7 | −0.927395 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.85002e7 | −1.30267 | ||||||||
\(727\) | 4.72548e6i | 0.331596i | 0.986160 | + | 0.165798i | \(0.0530200\pi\) | ||||
−0.986160 | + | 0.165798i | \(0.946980\pi\) | |||||||
\(728\) | − 336924.i | − 0.0235615i | ||||||||
\(729\) | −3.54746e7 | −2.47229 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.65514e7 | −1.14562 | ||||||||
\(732\) | 4.74907e6i | 0.327590i | ||||||||
\(733\) | − 1.07477e6i | − 0.0738847i | −0.999317 | − | 0.0369423i | \(-0.988238\pi\) | ||||
0.999317 | − | 0.0369423i | \(-0.0117618\pi\) | |||||||
\(734\) | −5.09956e6 | −0.349376 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.66140e7 | 1.13052 | ||||||||
\(737\) | 1.39371e7i | 0.945157i | ||||||||
\(738\) | 3.67064e7i | 2.48086i | ||||||||
\(739\) | 2.04180e7 | 1.37531 | 0.687657 | − | 0.726036i | \(-0.258639\pi\) | ||||
0.687657 | + | 0.726036i | \(0.258639\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −177118. | −0.0118500 | ||||||||
\(742\) | − 1.42129e6i | − 0.0947703i | ||||||||
\(743\) | 2.55138e7i | 1.69552i | 0.530377 | + | 0.847762i | \(0.322050\pi\) | ||||
−0.530377 | + | 0.847762i | \(0.677950\pi\) | |||||||
\(744\) | −2.57617e7 | −1.70625 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.07758e7 | −0.708926 | ||||||||
\(747\) | − 5.32627e7i | − 3.49238i | ||||||||
\(748\) | − 2.71267e7i | − 1.77273i | ||||||||
\(749\) | −25797.6 | −0.00168025 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.09344e7 | 1.35444 | 0.677220 | − | 0.735780i | \(-0.263184\pi\) | ||||
0.677220 | + | 0.735780i | \(0.263184\pi\) | |||||||
\(752\) | − 1.87896e6i | − 0.121163i | ||||||||
\(753\) | − 2.16520e7i | − 1.39159i | ||||||||
\(754\) | 200657. | 0.0128536 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.89422e6 | −0.184173 | ||||||||
\(757\) | − 6.00641e6i | − 0.380956i | −0.981691 | − | 0.190478i | \(-0.938996\pi\) | ||||
0.981691 | − | 0.190478i | \(-0.0610039\pi\) | |||||||
\(758\) | − 2.72317e6i | − 0.172148i | ||||||||
\(759\) | −4.91328e7 | −3.09576 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.48972e6 | −0.281033 | −0.140517 | − | 0.990078i | \(-0.544876\pi\) | ||||
−0.140517 | + | 0.990078i | \(0.544876\pi\) | |||||||
\(762\) | − 8.29291e6i | − 0.517392i | ||||||||
\(763\) | − 544085.i | − 0.0338342i | ||||||||
\(764\) | −3.00749e6 | −0.186411 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.29684e7 | −0.798570 | ||||||||
\(767\) | 3.02283e6i | 0.185535i | ||||||||
\(768\) | − 2.74911e7i | − 1.68186i | ||||||||
\(769\) | −2.20361e7 | −1.34375 | −0.671877 | − | 0.740663i | \(-0.734512\pi\) | ||||
−0.671877 | + | 0.740663i | \(0.734512\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.13239e7 | −1.89776 | ||||||||
\(772\) | 1.27815e6i | 0.0771859i | ||||||||
\(773\) | 9.09786e6i | 0.547634i | 0.961782 | + | 0.273817i | \(0.0882863\pi\) | ||||
−0.961782 | + | 0.273817i | \(0.911714\pi\) | |||||||
\(774\) | 1.60302e7 | 0.961806 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.65646e7 | −1.58361 | ||||||||
\(777\) | 1.41208e6i | 0.0839088i | ||||||||
\(778\) | 9.42950e6i | 0.558521i | ||||||||
\(779\) | 641341. | 0.0378656 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.97907e7 | 1.16100 | ||||||||
\(782\) | 1.86848e7i | 1.09263i | ||||||||
\(783\) | − 4.26360e6i | − 0.248526i | ||||||||
\(784\) | 2.37598e6 | 0.138055 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.83594e6 | 0.105999 | ||||||||
\(787\) | 1.65992e7i | 0.955325i | 0.878544 | + | 0.477662i | \(0.158516\pi\) | ||||
−0.878544 | + | 0.477662i | \(0.841484\pi\) | |||||||
\(788\) | − 5.90374e6i | − 0.338697i | ||||||||
\(789\) | 9.41298e6 | 0.538313 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.29971e6 | −0.130687 | ||||||||
\(792\) | 6.49867e7i | 3.68139i | ||||||||
\(793\) | − 1.24925e6i | − 0.0705449i | ||||||||
\(794\) | 3.97841e6 | 0.223954 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.54911e6 | 0.0866564 | ||||||||
\(797\) | 2.41936e7i | 1.34913i | 0.738213 | + | 0.674567i | \(0.235670\pi\) | ||||
−0.738213 | + | 0.674567i | \(0.764330\pi\) | |||||||
\(798\) | − 38897.0i | − 0.00216226i | ||||||||
\(799\) | 2.76024e7 | 1.52961 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.93986e7 | −1.61900 | ||||||||
\(802\) | − 3.11707e6i | − 0.171124i | ||||||||
\(803\) | − 6.46329e6i | − 0.353724i | ||||||||
\(804\) | 1.50059e7 | 0.818697 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.73963e6 | 0.148544 | ||||||||
\(807\) | − 3.35647e7i | − 1.81426i | ||||||||
\(808\) | − 1.90989e7i | − 1.02916i | ||||||||
\(809\) | 1.25176e7 | 0.672433 | 0.336216 | − | 0.941785i | \(-0.390853\pi\) | ||||
0.336216 | + | 0.941785i | \(0.390853\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.21034e7 | −0.646183 | −0.323091 | − | 0.946368i | \(-0.604722\pi\) | ||||
−0.323091 | + | 0.946368i | \(0.604722\pi\) | |||||||
\(812\) | − 93053.3i | − 0.00495270i | ||||||||
\(813\) | − 3.11822e7i | − 1.65455i | ||||||||
\(814\) | 7.89166e6 | 0.417453 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.82576e6 | −0.464010 | ||||||||
\(817\) | − 280083.i | − 0.0146802i | ||||||||
\(818\) | − 1.83423e6i | − 0.0958450i | ||||||||
\(819\) | 1.23661e6 | 0.0644205 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.24362e6 | 0.478613 | 0.239306 | − | 0.970944i | \(-0.423080\pi\) | ||||
0.239306 | + | 0.970944i | \(0.423080\pi\) | |||||||
\(822\) | 7.58615e6i | 0.391599i | ||||||||
\(823\) | 2.93437e7i | 1.51013i | 0.655648 | + | 0.755067i | \(0.272396\pi\) | ||||
−0.655648 | + | 0.755067i | \(0.727604\pi\) | |||||||
\(824\) | 1.79851e7 | 0.922774 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −663846. | −0.0338545 | ||||||||
\(827\) | − 1.74083e6i | − 0.0885099i | −0.999020 | − | 0.0442550i | \(-0.985909\pi\) | ||||
0.999020 | − | 0.0442550i | \(-0.0140914\pi\) | |||||||
\(828\) | 3.82136e7i | 1.93706i | ||||||||
\(829\) | −2.00227e7 | −1.01190 | −0.505948 | − | 0.862564i | \(-0.668857\pi\) | ||||
−0.505948 | + | 0.862564i | \(0.668857\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.45447e7 | 3.24234 | ||||||||
\(832\) | 2.46444e6i | 0.123427i | ||||||||
\(833\) | 3.49039e7i | 1.74286i | ||||||||
\(834\) | 2.71301e7 | 1.35063 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 459038. | 0.0227160 | ||||||||
\(837\) | − 5.82123e7i | − 2.87211i | ||||||||
\(838\) | 1.30332e7i | 0.641121i | ||||||||
\(839\) | −1.34556e7 | −0.659931 | −0.329966 | − | 0.943993i | \(-0.607037\pi\) | ||||
−0.329966 | + | 0.943993i | \(0.607037\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.03741e7 | −0.993317 | ||||||||
\(842\) | − 1.19804e7i | − 0.582360i | ||||||||
\(843\) | − 6.25897e7i | − 3.03343i | ||||||||
\(844\) | 1.04437e7 | 0.504661 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.67333e7 | −1.28418 | ||||||||
\(847\) | − 2.25681e6i | − 0.108090i | ||||||||
\(848\) | − 5.45720e6i | − 0.260604i | ||||||||
\(849\) | −1.15666e7 | −0.550727 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.14785e7 | 0.543326 | ||||||||
\(852\) | − 2.13084e7i | − 1.00566i | ||||||||
\(853\) | − 2.46799e7i | − 1.16137i | −0.814129 | − | 0.580685i | \(-0.802785\pi\) | ||||
0.814129 | − | 0.580685i | \(-0.197215\pi\) | |||||||
\(854\) | 274348. | 0.0128723 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 383973. | 0.0179109 | ||||||||
\(857\) | 1.53970e6i | 0.0716118i | 0.999359 | + | 0.0358059i | \(0.0113998\pi\) | ||||
−0.999359 | + | 0.0358059i | \(0.988600\pi\) | |||||||
\(858\) | − 9.56723e6i | − 0.443678i | ||||||||
\(859\) | −2.43418e7 | −1.12556 | −0.562781 | − | 0.826606i | \(-0.690268\pi\) | ||||
−0.562781 | + | 0.826606i | \(0.690268\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.19875e6 | −0.284968 | ||||||||
\(862\) | − 4.92858e6i | − 0.225920i | ||||||||
\(863\) | 2.27132e7i | 1.03813i | 0.854735 | + | 0.519064i | \(0.173720\pi\) | ||||
−0.854735 | + | 0.519064i | \(0.826280\pi\) | |||||||
\(864\) | 6.87403e7 | 3.13276 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 359681. | 0.0162976 | ||||||||
\(867\) | − 8.76474e7i | − 3.95996i | ||||||||
\(868\) | − 1.27049e6i | − 0.0572361i | ||||||||
\(869\) | −1.05945e7 | −0.475917 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.94733e6 | −0.176302 | ||||||||
\(872\) | 8.09821e6i | 0.360660i | ||||||||
\(873\) | − 9.75003e7i | − 4.32982i | ||||||||
\(874\) | −316184. | −0.0140011 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.95897e6 | −0.306397 | ||||||||
\(877\) | − 1.86650e7i | − 0.819464i | −0.912206 | − | 0.409732i | \(-0.865622\pi\) | ||||
0.912206 | − | 0.409732i | \(-0.134378\pi\) | |||||||
\(878\) | 526817.i | 0.0230634i | ||||||||
\(879\) | −7.23886e7 | −3.16008 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.91491e7 | 1.26528 | 0.632639 | − | 0.774447i | \(-0.281972\pi\) | ||||
0.632639 | + | 0.774447i | \(0.281972\pi\) | |||||||
\(882\) | − 3.38049e7i | − 1.46322i | ||||||||
\(883\) | 837238.i | 0.0361366i | 0.999837 | + | 0.0180683i | \(0.00575163\pi\) | ||||
−0.999837 | + | 0.0180683i | \(0.994248\pi\) | |||||||
\(884\) | 7.68295e6 | 0.330672 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.48267e7 | 0.634543 | ||||||||
\(887\) | 2.00532e7i | 0.855806i | 0.903825 | + | 0.427903i | \(0.140748\pi\) | ||||
−0.903825 | + | 0.427903i | \(0.859252\pi\) | |||||||
\(888\) | − 2.10176e7i | − 0.894437i | ||||||||
\(889\) | 1.01164e6 | 0.0429309 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.11612e8 | −4.70997 | ||||||||
\(892\) | 2.92480e7i | 1.23079i | ||||||||
\(893\) | 467088.i | 0.0196006i | ||||||||
\(894\) | 4.80600e7 | 2.01113 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.66951e6 | 0.0694733 | ||||||||
\(897\) | − 1.39156e7i | − 0.577459i | ||||||||
\(898\) | − 1.35186e6i | − 0.0559425i | ||||||||
\(899\) | 1.87161e6 | 0.0772353 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.01680e7 | 3.28995 | ||||||||
\(902\) | 3.46428e7i | 1.41774i | ||||||||
\(903\) | 2.70708e6i | 0.110480i | ||||||||
\(904\) | 3.42290e7 | 1.39307 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.35208e7 | 1.35673 | ||||||||
\(907\) | − 2.26638e7i | − 0.914775i | −0.889267 | − | 0.457388i | \(-0.848785\pi\) | ||||
0.889267 | − | 0.457388i | \(-0.151215\pi\) | |||||||
\(908\) | − 1.56306e7i | − 0.629162i | ||||||||
\(909\) | 7.00989e7 | 2.81386 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.78322e7 | −0.711885 | −0.355942 | − | 0.934508i | \(-0.615840\pi\) | ||||
−0.355942 | + | 0.934508i | \(0.615840\pi\) | |||||||
\(912\) | − 149350.i | − 0.00594589i | ||||||||
\(913\) | − 5.02682e7i | − 1.99580i | ||||||||
\(914\) | −1.71385e7 | −0.678589 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.23436e7 | 0.486077 | ||||||||
\(917\) | 223962.i | 0.00879533i | ||||||||
\(918\) | 7.73083e7i | 3.02775i | ||||||||
\(919\) | 1.61471e7 | 0.630677 | 0.315338 | − | 0.948979i | \(-0.397882\pi\) | ||||
0.315338 | + | 0.948979i | \(0.397882\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.70178e7 | 1.82647 | ||||||||
\(922\) | − 1.58792e7i | − 0.615178i | ||||||||
\(923\) | 5.60521e6i | 0.216565i | ||||||||
\(924\) | −4.43674e6 | −0.170956 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.24338e7 | −0.476514 | ||||||||
\(927\) | 6.60109e7i | 2.52299i | ||||||||
\(928\) | 2.21010e6i | 0.0842445i | ||||||||
\(929\) | 4.41295e7 | 1.67761 | 0.838803 | − | 0.544435i | \(-0.183256\pi\) | ||||
0.838803 | + | 0.544435i | \(0.183256\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −590644. | −0.0223332 | ||||||||
\(932\) | − 6.12708e6i | − 0.231054i | ||||||||
\(933\) | 9.32536e7i | 3.50721i | ||||||||
\(934\) | 5.26022e6 | 0.197305 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.84058e7 | −0.686698 | ||||||||
\(937\) | 2.76747e7i | 1.02976i | 0.857263 | + | 0.514878i | \(0.172163\pi\) | ||||
−0.857263 | + | 0.514878i | \(0.827837\pi\) | |||||||
\(938\) | − 866876.i | − 0.0321699i | ||||||||
\(939\) | 4.70214e7 | 1.74033 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.84362e6 | −0.362394 | −0.181197 | − | 0.983447i | \(-0.557997\pi\) | ||||
−0.181197 | + | 0.983447i | \(0.557997\pi\) | |||||||
\(942\) | − 2.11356e7i | − 0.776044i | ||||||||
\(943\) | 5.03882e7i | 1.84522i | ||||||||
\(944\) | −2.54891e6 | −0.0930947 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.51290e7 | 0.549645 | ||||||||
\(947\) | 1.20978e7i | 0.438360i | 0.975684 | + | 0.219180i | \(0.0703382\pi\) | ||||
−0.975684 | + | 0.219180i | \(0.929662\pi\) | |||||||
\(948\) | 1.14070e7i | 0.412240i | ||||||||
\(949\) | 1.83056e6 | 0.0659810 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.30541e7 | 1.54370 | ||||||||
\(952\) | 4.17353e6i | 0.149249i | ||||||||
\(953\) | 2.22761e7i | 0.794524i | 0.917705 | + | 0.397262i | \(0.130040\pi\) | ||||
−0.917705 | + | 0.397262i | \(0.869960\pi\) | |||||||
\(954\) | −7.76437e7 | −2.76207 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.11070e6 | 0.110081 | ||||||||
\(957\) | − 6.53596e6i | − 0.230690i | ||||||||
\(958\) | − 8.45627e6i | − 0.297690i | ||||||||
\(959\) | −925420. | −0.0324932 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.07551e6 | −0.107426 | ||||||||
\(962\) | 2.23511e6i | 0.0778685i | ||||||||
\(963\) | 1.40930e6i | 0.0489708i | ||||||||
\(964\) | −8.03309e6 | −0.278413 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.05602e6 | 0.105369 | ||||||||
\(967\) | − 1.59432e7i | − 0.548288i | −0.961689 | − | 0.274144i | \(-0.911605\pi\) | ||||
0.961689 | − | 0.274144i | \(-0.0883945\pi\) | |||||||
\(968\) | 3.35905e7i | 1.15220i | ||||||||
\(969\) | 2.19399e6 | 0.0750629 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.41319e6 | 0.0481008 | 0.0240504 | − | 0.999711i | \(-0.492344\pi\) | ||||
0.0240504 | + | 0.999711i | \(0.492344\pi\) | |||||||
\(972\) | 5.94038e7i | 2.01673i | ||||||||
\(973\) | 3.30955e6i | 0.112069i | ||||||||
\(974\) | 1.11326e7 | 0.376010 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.05339e6 | 0.0353969 | ||||||||
\(977\) | − 3.55699e7i | − 1.19219i | −0.802913 | − | 0.596096i | \(-0.796718\pi\) | ||||
0.802913 | − | 0.596096i | \(-0.203282\pi\) | |||||||
\(978\) | − 4.60923e7i | − 1.54092i | ||||||||
\(979\) | −2.77458e7 | −0.925211 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.97229e7 | −0.986095 | ||||||||
\(982\) | − 8.79548e6i | − 0.291059i | ||||||||
\(983\) | − 4.80377e7i | − 1.58562i | −0.609471 | − | 0.792808i | \(-0.708618\pi\) | ||||
0.609471 | − | 0.792808i | \(-0.291382\pi\) | |||||||
\(984\) | 9.22627e7 | 3.03765 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.48557e6 | −0.0814206 | ||||||||
\(987\) | − 4.51455e6i | − 0.147510i | ||||||||
\(988\) | 130011.i | 0.00423728i | ||||||||
\(989\) | 2.20052e7 | 0.715377 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.57999e7 | −1.48143 | −0.740714 | − | 0.671821i | \(-0.765512\pi\) | ||||
−0.740714 | + | 0.671821i | \(0.765512\pi\) | |||||||
\(992\) | 3.01752e7i | 0.973577i | ||||||||
\(993\) | 9.52409e7i | 3.06514i | ||||||||
\(994\) | −1.23096e6 | −0.0395166 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.41233e7 | −1.72877 | ||||||||
\(997\) | − 1.03492e7i | − 0.329738i | −0.986315 | − | 0.164869i | \(-0.947280\pi\) | ||||
0.986315 | − | 0.164869i | \(-0.0527202\pi\) | |||||||
\(998\) | 3.22498e7i | 1.02494i | ||||||||
\(999\) | 4.74922e7 | 1.50560 |
(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 | 325.6.b.h.274.12 | 18 | ||
5.2 | odd | 4 | 325.6.a.i.1.4 | yes | 9 | ||
5.3 | odd | 4 | 325.6.a.h.1.6 | ✓ | 9 | ||
5.4 | even | 2 | inner | 325.6.b.h.274.7 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
325.6.a.h.1.6 | ✓ | 9 | 5.3 | odd | 4 | ||
325.6.a.i.1.4 | yes | 9 | 5.2 | odd | 4 | ||
325.6.b.h.274.7 | 18 | 5.4 | even | 2 | inner | ||
325.6.b.h.274.12 | 18 | 1.1 | even | 1 | trivial |