Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,4,Mod(566,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.566");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(33.4540829733\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 566.12 | ||
Character | \(\chi\) | \(=\) | 567.566 |
Dual form | 567.4.c.c.566.11 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.725795i | 0.256607i | 0.991735 | + | 0.128304i | \(0.0409532\pi\) | ||||
−0.991735 | + | 0.128304i | \(0.959047\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 7.47322 | 0.934153 | ||||||||
\(5\) | 11.0664 | 0.989805 | 0.494902 | − | 0.868949i | \(-0.335204\pi\) | ||||
0.494902 | + | 0.868949i | \(0.335204\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −17.8071 | + | 5.08977i | −0.961495 | + | 0.274822i | ||||
\(8\) | 11.2304i | 0.496318i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.03191i | 0.253991i | ||||||||
\(11\) | 0.253624i | 0.00695186i | 0.999994 | + | 0.00347593i | \(0.00110643\pi\) | ||||
−0.999994 | + | 0.00347593i | \(0.998894\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.3133i | 0.305368i | 0.988275 | + | 0.152684i | \(0.0487916\pi\) | ||||
−0.988275 | + | 0.152684i | \(0.951208\pi\) | |||||||
\(14\) | −3.69413 | − | 12.9243i | −0.0705214 | − | 0.246727i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 51.6348 | 0.806794 | ||||||||
\(17\) | −92.5854 | −1.32090 | −0.660449 | − | 0.750871i | \(-0.729634\pi\) | ||||
−0.660449 | + | 0.750871i | \(0.729634\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 130.104i | 1.57094i | 0.618899 | + | 0.785470i | \(0.287579\pi\) | ||||
−0.618899 | + | 0.785470i | \(0.712421\pi\) | |||||||
\(20\) | 82.7013 | 0.924629 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.184079 | −0.00178390 | ||||||||
\(23\) | 118.700i | 1.07612i | 0.842908 | + | 0.538058i | \(0.180842\pi\) | ||||
−0.842908 | + | 0.538058i | \(0.819158\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.53586 | −0.0202869 | ||||||||
\(26\) | −10.3885 | −0.0783597 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −133.077 | + | 38.0370i | −0.898183 | + | 0.256726i | ||||
\(29\) | 286.736i | 1.83605i | 0.396522 | + | 0.918025i | \(0.370217\pi\) | ||||
−0.396522 | + | 0.918025i | \(0.629783\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 247.365i | − | 1.43316i | −0.697503 | − | 0.716582i | \(-0.745705\pi\) | ||
0.697503 | − | 0.716582i | \(-0.254295\pi\) | |||||||
\(32\) | 127.319i | 0.703347i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 67.1981i | − | 0.338952i | ||||||
\(35\) | −197.060 | + | 56.3252i | −0.951692 | + | 0.272020i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 188.615 | 0.838058 | 0.419029 | − | 0.907973i | \(-0.362371\pi\) | ||||
0.419029 | + | 0.907973i | \(0.362371\pi\) | |||||||
\(38\) | −94.4288 | −0.403115 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 124.279i | 0.491258i | ||||||||
\(41\) | −106.487 | −0.405623 | −0.202811 | − | 0.979218i | \(-0.565008\pi\) | ||||
−0.202811 | + | 0.979218i | \(0.565008\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 43.1172 | 0.152914 | 0.0764572 | − | 0.997073i | \(-0.475639\pi\) | ||||
0.0764572 | + | 0.997073i | \(0.475639\pi\) | |||||||
\(44\) | 1.89539i | 0.00649410i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −86.1520 | −0.276139 | ||||||||
\(47\) | 137.764 | 0.427551 | 0.213776 | − | 0.976883i | \(-0.431424\pi\) | ||||
0.213776 | + | 0.976883i | \(0.431424\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 291.188 | − | 181.269i | 0.848946 | − | 0.528480i | ||||
\(50\) | − | 1.84052i | − | 0.00520576i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 106.966i | 0.285260i | ||||||||
\(53\) | 419.280i | 1.08665i | 0.839522 | + | 0.543325i | \(0.182835\pi\) | ||||
−0.839522 | + | 0.543325i | \(0.817165\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.80669i | 0.00688098i | ||||||||
\(56\) | −57.1602 | − | 199.981i | −0.136399 | − | 0.477207i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −208.111 | −0.471144 | ||||||||
\(59\) | 435.120 | 0.960132 | 0.480066 | − | 0.877232i | \(-0.340613\pi\) | ||||
0.480066 | + | 0.877232i | \(0.340613\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 188.798i | − | 0.396280i | −0.980174 | − | 0.198140i | \(-0.936510\pi\) | ||
0.980174 | − | 0.198140i | \(-0.0634901\pi\) | |||||||
\(62\) | 179.537 | 0.367761 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 320.670 | 0.626310 | ||||||||
\(65\) | 158.395i | 0.302254i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 370.699 | 0.675942 | 0.337971 | − | 0.941157i | \(-0.390259\pi\) | ||||
0.337971 | + | 0.941157i | \(0.390259\pi\) | |||||||
\(68\) | −691.911 | −1.23392 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −40.8806 | − | 143.025i | −0.0698024 | − | 0.244211i | ||||
\(71\) | 26.1630i | 0.0437321i | 0.999761 | + | 0.0218661i | \(0.00696074\pi\) | ||||
−0.999761 | + | 0.0218661i | \(0.993039\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 728.545i | − | 1.16808i | −0.811725 | − | 0.584039i | \(-0.801471\pi\) | ||
0.811725 | − | 0.584039i | \(-0.198529\pi\) | |||||||
\(74\) | 136.896i | 0.215052i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 972.295i | 1.46750i | ||||||||
\(77\) | −1.29089 | − | 4.51632i | −0.00191052 | − | 0.00668418i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 97.3557 | 0.138650 | 0.0693251 | − | 0.997594i | \(-0.477915\pi\) | ||||
0.0693251 | + | 0.997594i | \(0.477915\pi\) | |||||||
\(80\) | 571.409 | 0.798568 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 77.2880i | − | 0.104086i | ||||||
\(83\) | −802.718 | −1.06156 | −0.530781 | − | 0.847509i | \(-0.678101\pi\) | ||||
−0.530781 | + | 0.847509i | \(0.678101\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1024.58 | −1.30743 | ||||||||
\(86\) | 31.2943i | 0.0392390i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.84830 | −0.00345033 | ||||||||
\(89\) | 236.618 | 0.281814 | 0.140907 | − | 0.990023i | \(-0.454998\pi\) | ||||
0.140907 | + | 0.990023i | \(0.454998\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −72.8512 | − | 254.878i | −0.0839218 | − | 0.293610i | ||||
\(92\) | 887.072i | 1.00526i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 99.9883i | 0.109713i | ||||||||
\(95\) | 1439.77i | 1.55492i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1464.27i | 1.53272i | 0.642412 | + | 0.766360i | \(0.277934\pi\) | ||||
−0.642412 | + | 0.766360i | \(0.722066\pi\) | |||||||
\(98\) | 131.564 | + | 211.343i | 0.135612 | + | 0.217846i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −18.9510 | −0.0189510 | ||||||||
\(101\) | −1567.44 | −1.54422 | −0.772112 | − | 0.635487i | \(-0.780799\pi\) | ||||
−0.772112 | + | 0.635487i | \(0.780799\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 100.296i | 0.0959461i | 0.998849 | + | 0.0479730i | \(0.0152762\pi\) | ||||
−0.998849 | + | 0.0479730i | \(0.984724\pi\) | |||||||
\(104\) | −160.743 | −0.151560 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −304.311 | −0.278843 | ||||||||
\(107\) | 553.381i | 0.499976i | 0.968249 | + | 0.249988i | \(0.0804266\pi\) | ||||
−0.968249 | + | 0.249988i | \(0.919573\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −400.600 | −0.352023 | −0.176012 | − | 0.984388i | \(-0.556320\pi\) | ||||
−0.176012 | + | 0.984388i | \(0.556320\pi\) | |||||||
\(110\) | −2.03708 | −0.00176571 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −919.468 | + | 262.809i | −0.775728 | + | 0.221725i | ||||
\(113\) | 712.932i | 0.593513i | 0.954953 | + | 0.296756i | \(0.0959050\pi\) | ||||
−0.954953 | + | 0.296756i | \(0.904095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1313.58i | 1.06514i | ||||||||
\(116\) | 2142.84i | 1.71515i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 315.808i | 0.246377i | ||||||||
\(119\) | 1648.68 | − | 471.239i | 1.27004 | − | 0.363012i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1330.94 | 0.999952 | ||||||||
\(122\) | 137.029 | 0.101688 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 1848.61i | − | 1.33879i | ||||||
\(125\) | −1411.36 | −1.00988 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 102.170 | 0.0713865 | 0.0356932 | − | 0.999363i | \(-0.488636\pi\) | ||||
0.0356932 | + | 0.999363i | \(0.488636\pi\) | |||||||
\(128\) | 1251.30i | 0.864063i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −114.963 | −0.0775608 | ||||||||
\(131\) | −472.845 | −0.315364 | −0.157682 | − | 0.987490i | \(-0.550402\pi\) | ||||
−0.157682 | + | 0.987490i | \(0.550402\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −662.199 | − | 2316.78i | −0.431729 | − | 1.51045i | ||||
\(134\) | 269.052i | 0.173452i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 1039.77i | − | 0.655585i | ||||||
\(137\) | 2619.41i | 1.63351i | 0.576983 | + | 0.816756i | \(0.304230\pi\) | ||||
−0.576983 | + | 0.816756i | \(0.695770\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1242.37i | − | 0.758104i | −0.925375 | − | 0.379052i | \(-0.876250\pi\) | ||
0.925375 | − | 0.379052i | \(-0.123750\pi\) | |||||||
\(140\) | −1472.67 | + | 420.931i | −0.889026 | + | 0.254108i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −18.9890 | −0.0112220 | ||||||||
\(143\) | −3.63018 | −0.00212287 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3173.12i | 1.81733i | ||||||||
\(146\) | 528.775 | 0.299738 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1409.56 | 0.782874 | ||||||||
\(149\) | − | 1124.55i | − | 0.618302i | −0.951013 | − | 0.309151i | \(-0.899955\pi\) | ||
0.951013 | − | 0.309151i | \(-0.100045\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −475.597 | −0.256315 | −0.128157 | − | 0.991754i | \(-0.540906\pi\) | ||||
−0.128157 | + | 0.991754i | \(0.540906\pi\) | |||||||
\(152\) | −1461.12 | −0.779686 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.27792 | − | 0.936921i | 0.00171521 | − | 0.000490255i | ||||
\(155\) | − | 2737.43i | − | 1.41855i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1933.32i | − | 0.982775i | −0.870941 | − | 0.491388i | \(-0.836490\pi\) | ||
0.870941 | − | 0.491388i | \(-0.163510\pi\) | |||||||
\(158\) | 70.6603i | 0.0355787i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1408.96i | 0.696176i | ||||||||
\(161\) | −604.156 | − | 2113.71i | −0.295740 | − | 1.03468i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −743.323 | −0.357187 | −0.178594 | − | 0.983923i | \(-0.557155\pi\) | ||||
−0.178594 | + | 0.983923i | \(0.557155\pi\) | |||||||
\(164\) | −795.803 | −0.378913 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 582.609i | − | 0.272405i | ||||||
\(167\) | 3623.20 | 1.67887 | 0.839435 | − | 0.543460i | \(-0.182886\pi\) | ||||
0.839435 | + | 0.543460i | \(0.182886\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1992.13 | 0.906750 | ||||||||
\(170\) | − | 743.638i | − | 0.335496i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 322.225 | 0.142845 | ||||||||
\(173\) | 3297.00 | 1.44894 | 0.724470 | − | 0.689306i | \(-0.242085\pi\) | ||||
0.724470 | + | 0.689306i | \(0.242085\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 45.1564 | − | 12.9069i | 0.0195057 | − | 0.00557528i | ||||
\(176\) | 13.0958i | 0.00560872i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 171.736i | 0.0723155i | ||||||||
\(179\) | − | 2746.77i | − | 1.14695i | −0.819225 | − | 0.573473i | \(-0.805596\pi\) | ||
0.819225 | − | 0.573473i | \(-0.194404\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 738.434i | 0.303245i | 0.988438 | + | 0.151622i | \(0.0484498\pi\) | ||||
−0.988438 | + | 0.151622i | \(0.951550\pi\) | |||||||
\(182\) | 184.989 | − | 52.8751i | 0.0753424 | − | 0.0215350i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1333.05 | −0.534096 | ||||||||
\(185\) | 2087.28 | 0.829514 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 23.4819i | − | 0.00918270i | ||||||
\(188\) | 1029.54 | 0.399398 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1044.98 | −0.399005 | ||||||||
\(191\) | − | 3325.18i | − | 1.25970i | −0.776719 | − | 0.629848i | \(-0.783117\pi\) | ||
0.776719 | − | 0.629848i | \(-0.216883\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3321.49 | −1.23879 | −0.619394 | − | 0.785080i | \(-0.712622\pi\) | ||||
−0.619394 | + | 0.785080i | \(0.712622\pi\) | |||||||
\(194\) | −1062.76 | −0.393307 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2176.12 | − | 1354.66i | 0.793045 | − | 0.493681i | ||||
\(197\) | − | 501.482i | − | 0.181366i | −0.995880 | − | 0.0906830i | \(-0.971095\pi\) | ||
0.995880 | − | 0.0906830i | \(-0.0289050\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4067.59i | − | 1.44896i | −0.689294 | − | 0.724482i | \(-0.742079\pi\) | ||
0.689294 | − | 0.724482i | \(-0.257921\pi\) | |||||||
\(200\) | − | 28.4787i | − | 0.0100687i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 1137.64i | − | 0.396259i | ||||||
\(203\) | −1459.42 | − | 5105.94i | −0.504587 | − | 1.76535i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1178.43 | −0.401487 | ||||||||
\(206\) | −72.7943 | −0.0246205 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 739.062i | 0.246369i | ||||||||
\(209\) | −32.9974 | −0.0109210 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4913.90 | 1.60326 | 0.801628 | − | 0.597823i | \(-0.203968\pi\) | ||||
0.801628 | + | 0.597823i | \(0.203968\pi\) | |||||||
\(212\) | 3133.37i | 1.01510i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −401.642 | −0.128297 | ||||||||
\(215\) | 477.150 | 0.151355 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1259.03 | + | 4404.87i | 0.393865 | + | 1.37798i | ||||
\(218\) | − | 290.754i | − | 0.0903318i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 20.9750i | 0.00642789i | ||||||||
\(221\) | − | 1325.20i | − | 0.403360i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1193.16i | − | 0.358295i | −0.983822 | − | 0.179148i | \(-0.942666\pi\) | ||
0.983822 | − | 0.179148i | \(-0.0573340\pi\) | |||||||
\(224\) | −648.027 | − | 2267.20i | −0.193295 | − | 0.676265i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −517.443 | −0.152300 | ||||||||
\(227\) | −5608.63 | −1.63990 | −0.819951 | − | 0.572434i | \(-0.805999\pi\) | ||||
−0.819951 | + | 0.572434i | \(0.805999\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5333.05i | 1.53894i | 0.638681 | + | 0.769472i | \(0.279480\pi\) | ||||
−0.638681 | + | 0.769472i | \(0.720520\pi\) | |||||||
\(230\) | −953.388 | −0.273324 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3220.15 | −0.911265 | ||||||||
\(233\) | 111.828i | 0.0314424i | 0.999876 | + | 0.0157212i | \(0.00500442\pi\) | ||||
−0.999876 | + | 0.0157212i | \(0.994996\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1524.54 | 0.423192 | ||||||||
\(236\) | 3251.75 | 0.896910 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 342.023 | + | 1196.61i | 0.0931515 | + | 0.325901i | ||||
\(239\) | − | 4771.99i | − | 1.29152i | −0.763539 | − | 0.645762i | \(-0.776540\pi\) | ||
0.763539 | − | 0.645762i | \(-0.223460\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5336.30i | 1.42631i | 0.701005 | + | 0.713156i | \(0.252735\pi\) | ||||
−0.701005 | + | 0.713156i | \(0.747265\pi\) | |||||||
\(242\) | 965.987i | 0.256595i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 1410.93i | − | 0.370186i | ||||||
\(245\) | 3222.39 | − | 2005.98i | 0.840290 | − | 0.523092i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1862.21 | −0.479715 | ||||||||
\(248\) | 2778.01 | 0.711305 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 1024.36i | − | 0.259144i | ||||||
\(251\) | 3081.73 | 0.774970 | 0.387485 | − | 0.921876i | \(-0.373344\pi\) | ||||
0.387485 | + | 0.921876i | \(0.373344\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30.1052 | −0.00748101 | ||||||||
\(254\) | 74.1542i | 0.0183183i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1657.18 | 0.404585 | ||||||||
\(257\) | −2135.10 | −0.518226 | −0.259113 | − | 0.965847i | \(-0.583430\pi\) | ||||
−0.259113 | + | 0.965847i | \(0.583430\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3358.70 | + | 960.009i | −0.805789 | + | 0.230317i | ||||
\(260\) | 1183.72i | 0.282352i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 343.189i | − | 0.0809248i | ||||||
\(263\) | − | 1650.23i | − | 0.386911i | −0.981109 | − | 0.193455i | \(-0.938031\pi\) | ||
0.981109 | − | 0.193455i | \(-0.0619695\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4639.90i | 1.07557i | ||||||||
\(266\) | 1681.51 | − | 480.621i | 0.387593 | − | 0.110785i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2770.32 | 0.631433 | ||||||||
\(269\) | 5477.73 | 1.24157 | 0.620787 | − | 0.783979i | \(-0.286813\pi\) | ||||
0.620787 | + | 0.783979i | \(0.286813\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3607.16i | − | 0.808558i | −0.914636 | − | 0.404279i | \(-0.867523\pi\) | ||
0.914636 | − | 0.404279i | \(-0.132477\pi\) | |||||||
\(272\) | −4780.63 | −1.06569 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1901.15 | −0.419171 | ||||||||
\(275\) | − | 0.643154i | − | 0.000141032i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2977.98 | 0.645954 | 0.322977 | − | 0.946407i | \(-0.395316\pi\) | ||||
0.322977 | + | 0.946407i | \(0.395316\pi\) | |||||||
\(278\) | 901.707 | 0.194535 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −632.554 | − | 2213.06i | −0.135008 | − | 0.472342i | ||||
\(281\) | − | 5700.01i | − | 1.21009i | −0.796193 | − | 0.605043i | \(-0.793156\pi\) | ||
0.796193 | − | 0.605043i | \(-0.206844\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 550.467i | − | 0.115625i | −0.998327 | − | 0.0578125i | \(-0.981587\pi\) | ||
0.998327 | − | 0.0578125i | \(-0.0184126\pi\) | |||||||
\(284\) | 195.522i | 0.0408525i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 2.63477i | − | 0.000544746i | ||||||
\(287\) | 1896.23 | − | 541.996i | 0.390004 | − | 0.111474i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3659.06 | 0.744771 | ||||||||
\(290\) | −2303.03 | −0.466341 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 5444.58i | − | 1.09116i | ||||||
\(293\) | −7830.00 | −1.56121 | −0.780603 | − | 0.625027i | \(-0.785088\pi\) | ||||
−0.780603 | + | 0.625027i | \(0.785088\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4815.19 | 0.950343 | ||||||||
\(296\) | 2118.22i | 0.415943i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 816.195 | 0.158661 | ||||||||
\(299\) | −1698.98 | −0.328611 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −767.795 | + | 219.457i | −0.147026 | + | 0.0420242i | ||||
\(302\) | − | 345.186i | − | 0.0657722i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6717.89i | 1.26742i | ||||||||
\(305\) | − | 2089.30i | − | 0.392240i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5845.06i | − | 1.08663i | −0.839529 | − | 0.543315i | \(-0.817169\pi\) | ||
0.839529 | − | 0.543315i | \(-0.182831\pi\) | |||||||
\(308\) | −9.64709 | − | 33.7514i | −0.00178472 | − | 0.00624405i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1986.81 | 0.364011 | ||||||||
\(311\) | 5819.70 | 1.06111 | 0.530554 | − | 0.847651i | \(-0.321984\pi\) | ||||
0.530554 | + | 0.847651i | \(0.321984\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6644.41i | − | 1.19989i | −0.800043 | − | 0.599943i | \(-0.795190\pi\) | ||
0.800043 | − | 0.599943i | \(-0.204810\pi\) | |||||||
\(314\) | 1403.19 | 0.252187 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 727.561 | 0.129521 | ||||||||
\(317\) | 6012.31i | 1.06525i | 0.846350 | + | 0.532626i | \(0.178795\pi\) | ||||
−0.846350 | + | 0.532626i | \(0.821205\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −72.7230 | −0.0127640 | ||||||||
\(320\) | 3548.65 | 0.619924 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1534.12 | − | 438.494i | 0.265507 | − | 0.0758892i | ||||
\(323\) | − | 12045.7i | − | 2.07505i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 36.2964i | − | 0.00619496i | ||||||
\(326\) | − | 539.500i | − | 0.0916569i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 1195.89i | − | 0.201318i | ||||||
\(329\) | −2453.18 | + | 701.186i | −0.411088 | + | 0.117500i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2742.49 | −0.455410 | −0.227705 | − | 0.973730i | \(-0.573122\pi\) | ||||
−0.227705 | + | 0.973730i | \(0.573122\pi\) | |||||||
\(332\) | −5998.89 | −0.991662 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2629.70i | 0.430811i | ||||||||
\(335\) | 4102.29 | 0.669050 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3906.54 | −0.631462 | −0.315731 | − | 0.948849i | \(-0.602250\pi\) | ||||
−0.315731 | + | 0.948849i | \(0.602250\pi\) | |||||||
\(338\) | 1445.88i | 0.232679i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7656.93 | −1.22134 | ||||||||
\(341\) | 62.7377 | 0.00996316 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4262.62 | + | 4709.96i | −0.671019 | + | 0.741440i | ||||
\(344\) | 484.223i | 0.0758941i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2392.95i | 0.371809i | ||||||||
\(347\) | 588.749i | 0.0910827i | 0.998962 | + | 0.0455413i | \(0.0145013\pi\) | ||||
−0.998962 | + | 0.0455413i | \(0.985499\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 7344.28i | − | 1.12645i | −0.826304 | − | 0.563224i | \(-0.809561\pi\) | ||
0.826304 | − | 0.563224i | \(-0.190439\pi\) | |||||||
\(350\) | 9.36780 | + | 32.7743i | 0.00143066 | + | 0.00500532i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −32.2913 | −0.00488957 | ||||||||
\(353\) | 8741.54 | 1.31803 | 0.659016 | − | 0.752129i | \(-0.270973\pi\) | ||||
0.659016 | + | 0.752129i | \(0.270973\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 289.529i | 0.0432863i | ||||||||
\(356\) | 1768.30 | 0.263257 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1993.59 | 0.294315 | ||||||||
\(359\) | 7817.81i | 1.14933i | 0.818390 | + | 0.574663i | \(0.194867\pi\) | ||||
−0.818390 | + | 0.574663i | \(0.805133\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10068.0 | −1.46785 | ||||||||
\(362\) | −535.952 | −0.0778149 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −544.433 | − | 1904.76i | −0.0783957 | − | 0.274276i | ||||
\(365\) | − | 8062.34i | − | 1.15617i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2406.54i | − | 0.342290i | −0.985246 | − | 0.171145i | \(-0.945253\pi\) | ||
0.985246 | − | 0.171145i | \(-0.0547466\pi\) | |||||||
\(368\) | 6129.05i | 0.868204i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1514.94i | 0.212859i | ||||||||
\(371\) | −2134.04 | − | 7466.17i | −0.298635 | − | 1.04481i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4370.16 | 0.606644 | 0.303322 | − | 0.952888i | \(-0.401904\pi\) | ||||
0.303322 | + | 0.952888i | \(0.401904\pi\) | |||||||
\(374\) | 17.0430 | 0.00235635 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1547.14i | 0.212201i | ||||||||
\(377\) | −4104.12 | −0.560671 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11260.9 | 1.52620 | 0.763102 | − | 0.646278i | \(-0.223675\pi\) | ||||
0.763102 | + | 0.646278i | \(0.223675\pi\) | |||||||
\(380\) | 10759.8i | 1.45254i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2413.40 | 0.323247 | ||||||||
\(383\) | −2973.14 | −0.396659 | −0.198330 | − | 0.980135i | \(-0.563552\pi\) | ||||
−0.198330 | + | 0.980135i | \(0.563552\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.2854 | − | 49.9791i | −0.00189105 | − | 0.00661603i | ||||
\(386\) | − | 2410.72i | − | 0.317882i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10942.8i | 1.43179i | ||||||||
\(389\) | − | 6598.27i | − | 0.860014i | −0.902826 | − | 0.430007i | \(-0.858511\pi\) | ||
0.902826 | − | 0.430007i | \(-0.141489\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10989.9i | − | 1.42144i | ||||||
\(392\) | 2035.72 | + | 3270.16i | 0.262294 | + | 0.421347i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 363.973 | 0.0465398 | ||||||||
\(395\) | 1077.37 | 0.137237 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 5908.48i | − | 0.746947i | −0.927641 | − | 0.373474i | \(-0.878167\pi\) | ||
0.927641 | − | 0.373474i | \(-0.121833\pi\) | |||||||
\(398\) | 2952.24 | 0.371815 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −130.939 | −0.0163673 | ||||||||
\(401\) | 5597.44i | 0.697064i | 0.937297 | + | 0.348532i | \(0.113320\pi\) | ||||
−0.937297 | + | 0.348532i | \(0.886680\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3540.60 | 0.437642 | ||||||||
\(404\) | −11713.9 | −1.44254 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3705.87 | − | 1059.24i | 0.453003 | − | 0.129481i | ||||
\(407\) | 47.8373i | 0.00582606i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1095.31i | 0.132420i | 0.997806 | + | 0.0662099i | \(0.0210907\pi\) | ||||
−0.997806 | + | 0.0662099i | \(0.978909\pi\) | |||||||
\(410\) | − | 855.296i | − | 0.103025i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 749.533i | 0.0896283i | ||||||||
\(413\) | −7748.24 | + | 2214.66i | −0.923162 | + | 0.263865i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8883.16 | −1.05074 | ||||||||
\(416\) | −1822.36 | −0.214780 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 23.9494i | − | 0.00280240i | ||||||
\(419\) | 13593.6 | 1.58494 | 0.792468 | − | 0.609913i | \(-0.208796\pi\) | ||||
0.792468 | + | 0.609913i | \(0.208796\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5684.27 | −0.658039 | −0.329019 | − | 0.944323i | \(-0.606718\pi\) | ||||
−0.329019 | + | 0.944323i | \(0.606718\pi\) | |||||||
\(422\) | 3566.49i | 0.411407i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4708.68 | −0.539324 | ||||||||
\(425\) | 234.784 | 0.0267969 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 960.938 | + | 3361.95i | 0.108906 | + | 0.381021i | ||||
\(428\) | 4135.54i | 0.467054i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 346.314i | 0.0388389i | ||||||||
\(431\) | − | 4806.22i | − | 0.537140i | −0.963260 | − | 0.268570i | \(-0.913449\pi\) | ||
0.963260 | − | 0.268570i | \(-0.0865511\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9621.49i | 1.06785i | 0.845532 | + | 0.533925i | \(0.179284\pi\) | ||||
−0.845532 | + | 0.533925i | \(0.820716\pi\) | |||||||
\(434\) | −3197.03 | + | 913.800i | −0.353600 | + | 0.101069i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2993.77 | −0.328844 | ||||||||
\(437\) | −15443.3 | −1.69051 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12932.6i | 1.40601i | 0.711183 | + | 0.703007i | \(0.248160\pi\) | ||||
−0.711183 | + | 0.703007i | \(0.751840\pi\) | |||||||
\(440\) | −31.5202 | −0.00341516 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 961.823 | 0.103505 | ||||||||
\(443\) | 13164.7i | 1.41191i | 0.708259 | + | 0.705953i | \(0.249481\pi\) | ||||
−0.708259 | + | 0.705953i | \(0.750519\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2618.49 | 0.278940 | ||||||||
\(446\) | 865.990 | 0.0919413 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5710.22 | + | 1632.14i | −0.602194 | + | 0.172124i | ||||
\(449\) | − | 7787.86i | − | 0.818557i | −0.912410 | − | 0.409278i | \(-0.865781\pi\) | ||
0.912410 | − | 0.409278i | \(-0.134219\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 27.0077i | − | 0.00281983i | ||||||
\(452\) | 5327.90i | 0.554432i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 4070.72i | − | 0.420811i | ||||||
\(455\) | −806.197 | − | 2820.57i | −0.0830662 | − | 0.290616i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4817.13 | 0.493076 | 0.246538 | − | 0.969133i | \(-0.420707\pi\) | ||||
0.246538 | + | 0.969133i | \(0.420707\pi\) | |||||||
\(458\) | −3870.71 | −0.394904 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9816.65i | 0.995008i | ||||||||
\(461\) | 51.2892 | 0.00518172 | 0.00259086 | − | 0.999997i | \(-0.499175\pi\) | ||||
0.00259086 | + | 0.999997i | \(0.499175\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9574.86 | −0.961083 | −0.480542 | − | 0.876972i | \(-0.659560\pi\) | ||||
−0.480542 | + | 0.876972i | \(0.659560\pi\) | |||||||
\(464\) | 14805.5i | 1.48131i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −81.1641 | −0.00806835 | ||||||||
\(467\) | 12806.5 | 1.26898 | 0.634492 | − | 0.772929i | \(-0.281209\pi\) | ||||
0.634492 | + | 0.772929i | \(0.281209\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6601.09 | + | 1886.77i | −0.649915 | + | 0.185764i | ||||
\(470\) | 1106.51i | 0.108594i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4886.57i | 0.476531i | ||||||||
\(473\) | 10.9356i | 0.00106304i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 329.925i | − | 0.0318695i | ||||||
\(476\) | 12321.0 | − | 3521.67i | 1.18641 | − | 0.339108i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3463.49 | 0.331415 | ||||||||
\(479\) | 5085.57 | 0.485106 | 0.242553 | − | 0.970138i | \(-0.422015\pi\) | ||||
0.242553 | + | 0.970138i | \(0.422015\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2699.70i | 0.255916i | ||||||||
\(482\) | −3873.06 | −0.366002 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9946.38 | 0.934107 | ||||||||
\(485\) | 16204.1i | 1.51709i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16991.3 | 1.58100 | 0.790501 | − | 0.612461i | \(-0.209820\pi\) | ||||
0.790501 | + | 0.612461i | \(0.209820\pi\) | |||||||
\(488\) | 2120.27 | 0.196681 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1455.93 | + | 2338.80i | 0.134229 | + | 0.215625i | ||||
\(491\) | − | 9301.80i | − | 0.854958i | −0.904025 | − | 0.427479i | \(-0.859402\pi\) | ||
0.904025 | − | 0.427479i | \(-0.140598\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 26547.5i | − | 2.42524i | ||||||
\(494\) | − | 1351.58i | − | 0.123098i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 12772.6i | − | 1.15627i | ||||||
\(497\) | −133.164 | − | 465.889i | −0.0120185 | − | 0.0420482i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −500.665 | −0.0449155 | −0.0224577 | − | 0.999748i | \(-0.507149\pi\) | ||||
−0.0224577 | + | 0.999748i | \(0.507149\pi\) | |||||||
\(500\) | −10547.4 | −0.943386 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2236.71i | 0.198863i | ||||||||
\(503\) | −3581.09 | −0.317441 | −0.158721 | − | 0.987324i | \(-0.550737\pi\) | ||||
−0.158721 | + | 0.987324i | \(0.550737\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17345.9 | −1.52848 | ||||||||
\(506\) | − | 21.8502i | − | 0.00191968i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 763.536 | 0.0666859 | ||||||||
\(509\) | 10170.7 | 0.885679 | 0.442839 | − | 0.896601i | \(-0.353971\pi\) | ||||
0.442839 | + | 0.896601i | \(0.353971\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3708.13 | + | 12973.3i | 0.321014 | + | 1.12310i | ||||
\(512\) | 11213.1i | 0.967882i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 1549.65i | − | 0.132981i | ||||||
\(515\) | 1109.91i | 0.0949679i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.9402i | 0.00297228i | ||||||||
\(518\) | −696.770 | − | 2437.73i | −0.0591010 | − | 0.206771i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1778.84 | −0.150014 | ||||||||
\(521\) | −389.899 | −0.0327865 | −0.0163933 | − | 0.999866i | \(-0.505218\pi\) | ||||
−0.0163933 | + | 0.999866i | \(0.505218\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 14306.4i | − | 1.19613i | −0.801448 | − | 0.598065i | \(-0.795937\pi\) | ||
0.801448 | − | 0.598065i | \(-0.204063\pi\) | |||||||
\(524\) | −3533.68 | −0.294598 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1197.73 | 0.0992842 | ||||||||
\(527\) | 22902.4i | 1.89306i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1922.70 | −0.158026 | ||||||||
\(530\) | −3367.62 | −0.276000 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4948.76 | − | 17313.8i | −0.403301 | − | 1.41099i | ||||
\(533\) | − | 1524.18i | − | 0.123864i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6123.91i | 0.494878i | ||||||||
\(536\) | 4163.10i | 0.335482i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3975.71i | 0.318597i | ||||||||
\(539\) | 45.9740 | + | 73.8523i | 0.00367392 | + | 0.00590175i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21775.6 | 1.73051 | 0.865257 | − | 0.501328i | \(-0.167155\pi\) | ||||
0.865257 | + | 0.501328i | \(0.167155\pi\) | |||||||
\(542\) | 2618.06 | 0.207482 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 11787.9i | − | 0.929050i | ||||||
\(545\) | −4433.18 | −0.348434 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17921.7 | −1.40087 | −0.700436 | − | 0.713715i | \(-0.747011\pi\) | ||||
−0.700436 | + | 0.713715i | \(0.747011\pi\) | |||||||
\(548\) | 19575.4i | 1.52595i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.466799 | 3.61897e−5 | ||||||||
\(551\) | −37305.4 | −2.88433 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1733.63 | + | 495.518i | −0.133312 | + | 0.0381041i | ||||
\(554\) | 2161.40i | 0.165757i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 9284.51i | − | 0.708185i | ||||||
\(557\) | 19309.8i | 1.46891i | 0.678657 | + | 0.734455i | \(0.262562\pi\) | ||||
−0.678657 | + | 0.734455i | \(0.737438\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 617.148i | 0.0466951i | ||||||||
\(560\) | −10175.2 | + | 2908.34i | −0.767819 | + | 0.219464i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4137.04 | 0.310517 | ||||||||
\(563\) | −6464.49 | −0.483918 | −0.241959 | − | 0.970287i | \(-0.577790\pi\) | ||||
−0.241959 | + | 0.970287i | \(0.577790\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7889.55i | 0.587462i | ||||||||
\(566\) | 399.527 | 0.0296702 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −293.821 | −0.0217050 | ||||||||
\(569\) | 19961.2i | 1.47068i | 0.677698 | + | 0.735341i | \(0.262978\pi\) | ||||
−0.677698 | + | 0.735341i | \(0.737022\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12515.1 | −0.917235 | −0.458617 | − | 0.888634i | \(-0.651655\pi\) | ||||
−0.458617 | + | 0.888634i | \(0.651655\pi\) | |||||||
\(572\) | −27.1292 | −0.00198309 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 393.378 | + | 1376.28i | 0.0286051 | + | 0.100078i | ||||
\(575\) | − | 301.007i | − | 0.0218310i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 547.118i | 0.0394746i | 0.999805 | + | 0.0197373i | \(0.00628298\pi\) | ||||
−0.999805 | + | 0.0197373i | \(0.993717\pi\) | |||||||
\(578\) | 2655.73i | 0.191114i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 23713.4i | 1.69766i | ||||||||
\(581\) | 14294.1 | − | 4085.65i | 1.02069 | − | 0.291741i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −106.339 | −0.00755425 | ||||||||
\(584\) | 8181.85 | 0.579739 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 5682.98i | − | 0.400617i | ||||||
\(587\) | −1804.83 | −0.126905 | −0.0634525 | − | 0.997985i | \(-0.520211\pi\) | ||||
−0.0634525 | + | 0.997985i | \(0.520211\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32183.2 | 2.25142 | ||||||||
\(590\) | 3494.84i | 0.243865i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9739.11 | 0.676140 | ||||||||
\(593\) | 20359.7 | 1.40990 | 0.704951 | − | 0.709256i | \(-0.250969\pi\) | ||||
0.704951 | + | 0.709256i | \(0.250969\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18244.9 | − | 5214.89i | 1.25709 | − | 0.359311i | ||||
\(596\) | − | 8404.03i | − | 0.577588i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 1233.11i | − | 0.0843241i | ||||||
\(599\) | 4317.81i | 0.294526i | 0.989097 | + | 0.147263i | \(0.0470463\pi\) | ||||
−0.989097 | + | 0.147263i | \(0.952954\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7999.97i | 0.542971i | 0.962443 | + | 0.271485i | \(0.0875149\pi\) | ||||
−0.962443 | + | 0.271485i | \(0.912485\pi\) | |||||||
\(602\) | −159.281 | − | 557.262i | −0.0107837 | − | 0.0377281i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3554.24 | −0.239437 | ||||||||
\(605\) | 14728.6 | 0.989757 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3556.10i | 0.237789i | 0.992907 | + | 0.118894i | \(0.0379350\pi\) | ||||
−0.992907 | + | 0.118894i | \(0.962065\pi\) | |||||||
\(608\) | −16564.7 | −1.10492 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1516.41 | 0.100652 | ||||||||
\(611\) | 1971.85i | 0.130560i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7113.75 | −0.468714 | −0.234357 | − | 0.972151i | \(-0.575298\pi\) | ||||
−0.234357 | + | 0.972151i | \(0.575298\pi\) | |||||||
\(614\) | 4242.32 | 0.278837 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 50.7200 | − | 14.4972i | 0.00331748 | − | 0.000948227i | ||||
\(617\) | − | 913.301i | − | 0.0595917i | −0.999556 | − | 0.0297959i | \(-0.990514\pi\) | ||
0.999556 | − | 0.0297959i | \(-0.00948572\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 946.665i | − | 0.0614696i | −0.999528 | − | 0.0307348i | \(-0.990215\pi\) | ||
0.999528 | − | 0.0307348i | \(-0.00978473\pi\) | |||||||
\(620\) | − | 20457.4i | − | 1.32514i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4223.91i | 0.272288i | ||||||||
\(623\) | −4213.48 | + | 1204.33i | −0.270962 | + | 0.0774485i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15301.6 | −0.979302 | ||||||||
\(626\) | 4822.48 | 0.307900 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 14448.1i | − | 0.918062i | ||||||
\(629\) | −17463.0 | −1.10699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3209.46 | 0.202482 | 0.101241 | − | 0.994862i | \(-0.467719\pi\) | ||||
0.101241 | + | 0.994862i | \(0.467719\pi\) | |||||||
\(632\) | 1093.34i | 0.0688146i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4363.71 | −0.273352 | ||||||||
\(635\) | 1130.64 | 0.0706587 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2594.54 | + | 4167.85i | 0.161381 | + | 0.259241i | ||||
\(638\) | − | 52.7820i | − | 0.00327533i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 13847.3i | 0.855253i | ||||||||
\(641\) | 14303.4i | 0.881359i | 0.897665 | + | 0.440679i | \(0.145262\pi\) | ||||
−0.897665 | + | 0.440679i | \(0.854738\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 974.886i | 0.0597912i | 0.999553 | + | 0.0298956i | \(0.00951748\pi\) | ||||
−0.999553 | + | 0.0298956i | \(0.990483\pi\) | |||||||
\(644\) | −4514.99 | − | 15796.2i | −0.276267 | − | 0.966549i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8742.73 | 0.532474 | ||||||||
\(647\) | −12668.5 | −0.769783 | −0.384891 | − | 0.922962i | \(-0.625761\pi\) | ||||
−0.384891 | + | 0.922962i | \(0.625761\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 110.357i | 0.00667470i | ||||||||
\(650\) | 26.3438 | 0.00158967 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5555.01 | −0.333667 | ||||||||
\(653\) | 15873.3i | 0.951256i | 0.879646 | + | 0.475628i | \(0.157779\pi\) | ||||
−0.879646 | + | 0.475628i | \(0.842221\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5232.67 | −0.312149 | ||||||||
\(656\) | −5498.45 | −0.327254 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −508.918 | − | 1780.50i | −0.0301515 | − | 0.105488i | ||||
\(659\) | − | 30496.7i | − | 1.80271i | −0.433084 | − | 0.901353i | \(-0.642575\pi\) | ||
0.433084 | − | 0.901353i | \(-0.357425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 16702.5i | − | 0.982829i | −0.870926 | − | 0.491415i | \(-0.836480\pi\) | ||
0.870926 | − | 0.491415i | \(-0.163520\pi\) | |||||||
\(662\) | − | 1990.49i | − | 0.116862i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 9014.83i | − | 0.526873i | ||||||
\(665\) | −7328.13 | − | 25638.3i | −0.427327 | − | 1.49505i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34035.5 | −1.97580 | ||||||||
\(668\) | 27076.9 | 1.56832 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2977.42i | 0.171683i | ||||||||
\(671\) | 47.8836 | 0.00275488 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24890.4 | 1.42564 | 0.712820 | − | 0.701347i | \(-0.247418\pi\) | ||||
0.712820 | + | 0.701347i | \(0.247418\pi\) | |||||||
\(674\) | − | 2835.35i | − | 0.162038i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14887.6 | 0.847043 | ||||||||
\(677\) | 1512.55 | 0.0858672 | 0.0429336 | − | 0.999078i | \(-0.486330\pi\) | ||||
0.0429336 | + | 0.999078i | \(0.486330\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7452.79 | − | 26074.4i | −0.421225 | − | 1.47370i | ||||
\(680\) | − | 11506.5i | − | 0.648901i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 45.5347i | 0.00255662i | ||||||||
\(683\) | − | 2180.44i | − | 0.122156i | −0.998133 | − | 0.0610778i | \(-0.980546\pi\) | ||
0.998133 | − | 0.0610778i | \(-0.0194538\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28987.3i | 1.61686i | ||||||||
\(686\) | −3418.47 | − | 3093.79i | −0.190259 | − | 0.172189i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2226.35 | 0.123370 | ||||||||
\(689\) | −6001.26 | −0.331828 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27904.8i | 1.53625i | 0.640301 | + | 0.768124i | \(0.278810\pi\) | ||||
−0.640301 | + | 0.768124i | \(0.721190\pi\) | |||||||
\(692\) | 24639.2 | 1.35353 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −427.311 | −0.0233725 | ||||||||
\(695\) | − | 13748.5i | − | 0.750375i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9859.17 | 0.535786 | ||||||||
\(698\) | 5330.44 | 0.289055 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 337.464 | − | 96.4565i | 0.0182213 | − | 0.00520816i | ||||
\(701\) | − | 15696.6i | − | 0.845722i | −0.906195 | − | 0.422861i | \(-0.861026\pi\) | ||
0.906195 | − | 0.422861i | \(-0.138974\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24539.6i | 1.31654i | ||||||||
\(704\) | 81.3297i | 0.00435402i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6344.57i | 0.338217i | ||||||||
\(707\) | 27911.7 | − | 7977.94i | 1.48476 | − | 0.424386i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18506.9 | −0.980313 | −0.490157 | − | 0.871634i | \(-0.663060\pi\) | ||||
−0.490157 | + | 0.871634i | \(0.663060\pi\) | |||||||
\(710\) | −210.139 | −0.0111076 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2657.31i | 0.139869i | ||||||||
\(713\) | 29362.3 | 1.54225 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −40.1729 | −0.00210123 | ||||||||
\(716\) | − | 20527.2i | − | 1.07142i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5674.13 | −0.294926 | ||||||||
\(719\) | −12998.8 | −0.674232 | −0.337116 | − | 0.941463i | \(-0.609451\pi\) | ||||
−0.337116 | + | 0.941463i | \(0.609451\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −510.483 | − | 1785.98i | −0.0263681 | − | 0.0922517i | ||||
\(722\) | − | 7307.32i | − | 0.376662i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5518.48i | 0.283277i | ||||||||
\(725\) | − | 727.121i | − | 0.0372477i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1900.80i | − | 0.0969693i | −0.998824 | − | 0.0484846i | \(-0.984561\pi\) | ||
0.998824 | − | 0.0484846i | \(-0.0154392\pi\) | |||||||
\(728\) | 2862.38 | − | 818.148i | 0.145724 | − | 0.0416519i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5851.61 | 0.296682 | ||||||||
\(731\) | −3992.03 | −0.201984 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5547.48i | 0.279538i | 0.990184 | + | 0.139769i | \(0.0446359\pi\) | ||||
−0.990184 | + | 0.139769i | \(0.955364\pi\) | |||||||
\(734\) | 1746.65 | 0.0878341 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15112.8 | −0.756883 | ||||||||
\(737\) | 94.0181i | 0.00469905i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15681.5 | −0.780586 | −0.390293 | − | 0.920691i | \(-0.627626\pi\) | ||||
−0.390293 | + | 0.920691i | \(0.627626\pi\) | |||||||
\(740\) | 15598.7 | 0.774892 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5418.91 | − | 1548.88i | 0.268106 | − | 0.0766321i | ||||
\(743\) | − | 18081.9i | − | 0.892815i | −0.894830 | − | 0.446408i | \(-0.852703\pi\) | ||
0.894830 | − | 0.446408i | \(-0.147297\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 12444.7i | − | 0.611998i | ||||||
\(746\) | 3171.84i | 0.155669i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 175.485i | − | 0.00857804i | ||||||
\(749\) | −2816.59 | − | 9854.14i | −0.137404 | − | 0.480724i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22182.7 | 1.07784 | 0.538921 | − | 0.842357i | \(-0.318832\pi\) | ||||
0.538921 | + | 0.842357i | \(0.318832\pi\) | |||||||
\(752\) | 7113.40 | 0.344945 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 2978.75i | − | 0.143872i | ||||||
\(755\) | −5263.12 | −0.253701 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2531.12 | −0.121526 | −0.0607630 | − | 0.998152i | \(-0.519353\pi\) | ||||
−0.0607630 | + | 0.998152i | \(0.519353\pi\) | |||||||
\(758\) | 8173.08i | 0.391636i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16169.2 | −0.771737 | ||||||||
\(761\) | 3794.03 | 0.180727 | 0.0903637 | − | 0.995909i | \(-0.471197\pi\) | ||||
0.0903637 | + | 0.995909i | \(0.471197\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7133.54 | − | 2038.96i | 0.338469 | − | 0.0967437i | ||||
\(764\) | − | 24849.8i | − | 1.17675i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 2157.89i | − | 0.101786i | ||||||
\(767\) | 6227.98i | 0.293193i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6378.70i | 0.299118i | 0.988753 | + | 0.149559i | \(0.0477854\pi\) | ||||
−0.988753 | + | 0.149559i | \(0.952215\pi\) | |||||||
\(770\) | 36.2746 | − | 10.3683i | 0.00169772 | − | 0.000485256i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −24822.2 | −1.15722 | ||||||||
\(773\) | −29728.9 | −1.38328 | −0.691638 | − | 0.722244i | \(-0.743111\pi\) | ||||
−0.691638 | + | 0.722244i | \(0.743111\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 627.283i | 0.0290744i | ||||||||
\(776\) | −16444.3 | −0.760716 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4788.99 | 0.220686 | ||||||||
\(779\) | − | 13854.4i | − | 0.637209i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.63557 | −0.000304020 | ||||||||
\(782\) | 7976.42 | 0.364752 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 15035.5 | − | 9359.77i | 0.684924 | − | 0.426374i | ||||
\(785\) | − | 21394.8i | − | 0.972755i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 3738.07i | − | 0.169311i | −0.996410 | − | 0.0846556i | \(-0.973021\pi\) | ||
0.996410 | − | 0.0846556i | \(-0.0269790\pi\) | |||||||
\(788\) | − | 3747.68i | − | 0.169423i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 781.952i | 0.0352160i | ||||||||
\(791\) | −3628.66 | − | 12695.3i | −0.163110 | − | 0.570660i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2702.31 | 0.121011 | ||||||||
\(794\) | 4288.35 | 0.191672 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 30398.0i | − | 1.35355i | ||||||
\(797\) | 10754.8 | 0.477985 | 0.238992 | − | 0.971021i | \(-0.423183\pi\) | ||||
0.238992 | + | 0.971021i | \(0.423183\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12754.9 | −0.564751 | ||||||||
\(800\) | − | 322.864i | − | 0.0142687i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4062.60 | −0.178872 | ||||||||
\(803\) | 184.776 | 0.00812032 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6685.81 | − | 23391.0i | −0.292725 | − | 1.02413i | ||||
\(806\) | 2569.75i | 0.112302i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 17603.0i | − | 0.766426i | ||||||
\(809\) | 31037.7i | 1.34886i | 0.738340 | + | 0.674429i | \(0.235610\pi\) | ||||
−0.738340 | + | 0.674429i | \(0.764390\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 3943.22i | − | 0.170734i | −0.996350 | − | 0.0853669i | \(-0.972794\pi\) | ||
0.996350 | − | 0.0853669i | \(-0.0272062\pi\) | |||||||
\(812\) | −10906.6 | − | 38157.8i | −0.471361 | − | 1.64911i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −34.7201 | −0.00149501 | ||||||||
\(815\) | −8225.87 | −0.353546 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5609.72i | 0.240219i | ||||||||
\(818\) | −794.973 | −0.0339799 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8806.64 | −0.375050 | ||||||||
\(821\) | 28968.6i | 1.23144i | 0.787965 | + | 0.615720i | \(0.211135\pi\) | ||||
−0.787965 | + | 0.615720i | \(0.788865\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37286.3 | 1.57924 | 0.789622 | − | 0.613594i | \(-0.210277\pi\) | ||||
0.789622 | + | 0.613594i | \(0.210277\pi\) | |||||||
\(824\) | −1126.36 | −0.0476198 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1607.39 | − | 5623.64i | −0.0677098 | − | 0.236890i | ||||
\(827\) | − | 13151.6i | − | 0.552992i | −0.961015 | − | 0.276496i | \(-0.910827\pi\) | ||
0.961015 | − | 0.276496i | \(-0.0891732\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 27671.1i | − | 1.15929i | −0.814867 | − | 0.579647i | \(-0.803190\pi\) | ||
0.814867 | − | 0.579647i | \(-0.196810\pi\) | |||||||
\(830\) | − | 6447.35i | − | 0.269628i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4589.84i | 0.191255i | ||||||||
\(833\) | −26959.8 | + | 16782.8i | −1.12137 | + | 0.698068i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 40095.6 | 1.66175 | ||||||||
\(836\) | −246.597 | −0.0102018 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9866.14i | 0.406707i | ||||||||
\(839\) | 16997.4 | 0.699424 | 0.349712 | − | 0.936857i | \(-0.386279\pi\) | ||||
0.349712 | + | 0.936857i | \(0.386279\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −57828.3 | −2.37108 | ||||||||
\(842\) | − | 4125.62i | − | 0.168858i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 36722.7 | 1.49769 | ||||||||
\(845\) | 22045.6 | 0.897506 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23700.2 | + | 6774.16i | −0.961449 | + | 0.274809i | ||||
\(848\) | 21649.4i | 0.876703i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 170.405i | 0.00687628i | ||||||||
\(851\) | 22388.6i | 0.901848i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 15161.5i | − | 0.608582i | −0.952579 | − | 0.304291i | \(-0.901581\pi\) | ||
0.952579 | − | 0.304291i | \(-0.0984195\pi\) | |||||||
\(854\) | −2440.09 | + | 697.445i | −0.0977729 | + | 0.0279462i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6214.69 | −0.248147 | ||||||||
\(857\) | −28373.7 | −1.13095 | −0.565477 | − | 0.824764i | \(-0.691308\pi\) | ||||
−0.565477 | + | 0.824764i | \(0.691308\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38580.5i | 1.53242i | 0.642590 | + | 0.766210i | \(0.277860\pi\) | ||||
−0.642590 | + | 0.766210i | \(0.722140\pi\) | |||||||
\(860\) | 3565.85 | 0.141389 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3488.33 | 0.137834 | ||||||||
\(863\) | 112.649i | 0.00444337i | 0.999998 | + | 0.00222168i | \(0.000707185\pi\) | ||||
−0.999998 | + | 0.00222168i | \(0.999293\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36485.8 | 1.43417 | ||||||||
\(866\) | −6983.23 | −0.274018 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9409.03 | + | 32918.5i | 0.367930 | + | 1.28724i | ||||
\(869\) | 24.6917i | 0.000963878i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5305.91i | 0.206411i | ||||||||
\(872\) | − | 4498.90i | − | 0.174716i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 11208.7i | − | 0.433799i | ||||||
\(875\) | 25132.2 | − | 7183.49i | 0.970999 | − | 0.277538i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20758.6 | −0.799279 | −0.399639 | − | 0.916672i | \(-0.630865\pi\) | ||||
−0.399639 | + | 0.916672i | \(0.630865\pi\) | |||||||
\(878\) | −9386.43 | −0.360794 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 144.923i | 0.00555154i | ||||||||
\(881\) | 18603.4 | 0.711425 | 0.355712 | − | 0.934595i | \(-0.384238\pi\) | ||||
0.355712 | + | 0.934595i | \(0.384238\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17188.8 | 0.655096 | 0.327548 | − | 0.944835i | \(-0.393778\pi\) | ||||
0.327548 | + | 0.944835i | \(0.393778\pi\) | |||||||
\(884\) | − | 9903.50i | − | 0.376800i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9554.89 | −0.362305 | ||||||||
\(887\) | 13230.6 | 0.500835 | 0.250417 | − | 0.968138i | \(-0.419432\pi\) | ||||
0.250417 | + | 0.968138i | \(0.419432\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1819.35 | + | 520.020i | −0.0686377 | + | 0.0196186i | ||||
\(890\) | 1900.49i | 0.0715782i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 8916.74i | − | 0.334703i | ||||||
\(893\) | 17923.6i | 0.671657i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 30396.7i | − | 1.13525i | ||||||
\(896\) | −6368.82 | − | 22282.0i | −0.237463 | − | 0.830792i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5652.39 | 0.210048 | ||||||||
\(899\) | 70928.4 | 2.63136 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 38819.2i | − | 1.43535i | ||||||
\(902\) | 19.6021 | 0.000723590 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8006.50 | −0.294571 | ||||||||
\(905\) | 8171.77i | 0.300153i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43505.9 | −1.59271 | −0.796356 | − | 0.604828i | \(-0.793242\pi\) | ||||
−0.796356 | + | 0.604828i | \(0.793242\pi\) | |||||||
\(908\) | −41914.5 | −1.53192 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2047.16 | − | 585.134i | 0.0745743 | − | 0.0213154i | ||||
\(911\) | 17204.7i | 0.625703i | 0.949802 | + | 0.312852i | \(0.101284\pi\) | ||||
−0.949802 | + | 0.312852i | \(0.898716\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 203.588i | − | 0.00737984i | ||||||
\(914\) | 3496.25i | 0.126527i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 39855.1i | 1.43761i | ||||||||
\(917\) | 8420.02 | − | 2406.68i | 0.303221 | − | 0.0866690i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18441.8 | 0.661956 | 0.330978 | − | 0.943639i | \(-0.392621\pi\) | ||||
0.330978 | + | 0.943639i | \(0.392621\pi\) | |||||||
\(920\) | −14752.0 | −0.528650 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 37.2254i | 0.00132967i | ||||||||
\(923\) | −374.478 | −0.0133544 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −478.302 | −0.0170016 | ||||||||
\(926\) | − | 6949.39i | − | 0.246621i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −36507.0 | −1.29138 | ||||||||
\(929\) | −34469.4 | −1.21734 | −0.608668 | − | 0.793425i | \(-0.708296\pi\) | ||||
−0.608668 | + | 0.793425i | \(0.708296\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23583.7 | + | 37884.7i | 0.830210 | + | 1.33364i | ||||
\(932\) | 835.713i | 0.0293720i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9294.92i | 0.325631i | ||||||||
\(935\) | − | 259.859i | − | 0.00908908i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8204.91i | − | 0.286065i | −0.989718 | − | 0.143032i | \(-0.954315\pi\) | ||
0.989718 | − | 0.143032i | \(-0.0456853\pi\) | |||||||
\(938\) | −1369.41 | − | 4791.04i | −0.0476683 | − | 0.166773i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11393.2 | 0.395326 | ||||||||
\(941\) | 23911.3 | 0.828359 | 0.414179 | − | 0.910195i | \(-0.364069\pi\) | ||||
0.414179 | + | 0.910195i | \(0.364069\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 12640.1i | − | 0.436497i | ||||||
\(944\) | 22467.3 | 0.774628 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.93698 | −0.000272784 | ||||||||
\(947\) | − | 39859.6i | − | 1.36775i | −0.729597 | − | 0.683877i | \(-0.760292\pi\) | ||
0.729597 | − | 0.683877i | \(-0.239708\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10427.9 | 0.356694 | ||||||||
\(950\) | 239.458 | 0.00817794 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5292.20 | + | 18515.3i | 0.180169 | + | 0.630342i | ||||
\(953\) | 10983.4i | 0.373334i | 0.982423 | + | 0.186667i | \(0.0597685\pi\) | ||||
−0.982423 | + | 0.186667i | \(0.940232\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 36797.6i | − | 1.24685i | ||||||
\(956\) | − | 35662.1i | − | 1.20648i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3691.09i | 0.124482i | ||||||||
\(959\) | −13332.2 | − | 46644.2i | −0.448925 | − | 1.57061i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31398.5 | −1.05396 | ||||||||
\(962\) | −1959.43 | −0.0656699 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 39879.3i | 1.33239i | ||||||||
\(965\) | −36756.8 | −1.22616 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14827.6 | 0.493096 | 0.246548 | − | 0.969131i | \(-0.420704\pi\) | ||||
0.246548 | + | 0.969131i | \(0.420704\pi\) | |||||||
\(968\) | 14946.9i | 0.496294i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11760.9 | −0.389297 | ||||||||
\(971\) | 8249.56 | 0.272648 | 0.136324 | − | 0.990664i | \(-0.456471\pi\) | ||||
0.136324 | + | 0.990664i | \(0.456471\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6323.38 | + | 22123.1i | 0.208344 | + | 0.728913i | ||||
\(974\) | 12332.2i | 0.405697i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 9748.54i | − | 0.319716i | ||||||
\(977\) | − | 4774.55i | − | 0.156347i | −0.996940 | − | 0.0781737i | \(-0.975091\pi\) | ||
0.996940 | − | 0.0781737i | \(-0.0249089\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 60.0119i | 0.00195913i | ||||||||
\(980\) | 24081.7 | − | 14991.1i | 0.784960 | − | 0.488648i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6751.20 | 0.219389 | ||||||||
\(983\) | 17940.0 | 0.582094 | 0.291047 | − | 0.956709i | \(-0.405996\pi\) | ||||
0.291047 | + | 0.956709i | \(0.405996\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 5549.57i | − | 0.179517i | ||||||
\(986\) | 19268.1 | 0.622333 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13916.7 | −0.448127 | ||||||||
\(989\) | 5118.02i | 0.164554i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1714.50 | 0.0549574 | 0.0274787 | − | 0.999622i | \(-0.491252\pi\) | ||||
0.0274787 | + | 0.999622i | \(0.491252\pi\) | |||||||
\(992\) | 31494.4 | 1.00801 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 338.140 | − | 96.6498i | 0.0107899 | − | 0.00308405i | ||||
\(995\) | − | 45013.4i | − | 1.43419i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34637.3i | 1.10028i | 0.835074 | + | 0.550138i | \(0.185425\pi\) | ||||
−0.835074 | + | 0.550138i | \(0.814575\pi\) | |||||||
\(998\) | − | 363.380i | − | 0.0115256i | ||||||
\(999\) | 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 | 567.4.c.c.566.12 | 44 | ||
3.2 | odd | 2 | inner | 567.4.c.c.566.33 | 44 | ||
7.6 | odd | 2 | inner | 567.4.c.c.566.34 | 44 | ||
9.2 | odd | 6 | 189.4.o.a.125.10 | 44 | |||
9.4 | even | 3 | 189.4.o.a.62.9 | 44 | |||
9.5 | odd | 6 | 63.4.o.a.20.14 | yes | 44 | ||
9.7 | even | 3 | 63.4.o.a.41.13 | yes | 44 | ||
21.20 | even | 2 | inner | 567.4.c.c.566.11 | 44 | ||
63.13 | odd | 6 | 189.4.o.a.62.10 | 44 | |||
63.20 | even | 6 | 189.4.o.a.125.9 | 44 | |||
63.34 | odd | 6 | 63.4.o.a.41.14 | yes | 44 | ||
63.41 | even | 6 | 63.4.o.a.20.13 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.o.a.20.13 | ✓ | 44 | 63.41 | even | 6 | ||
63.4.o.a.20.14 | yes | 44 | 9.5 | odd | 6 | ||
63.4.o.a.41.13 | yes | 44 | 9.7 | even | 3 | ||
63.4.o.a.41.14 | yes | 44 | 63.34 | odd | 6 | ||
189.4.o.a.62.9 | 44 | 9.4 | even | 3 | |||
189.4.o.a.62.10 | 44 | 63.13 | odd | 6 | |||
189.4.o.a.125.9 | 44 | 63.20 | even | 6 | |||
189.4.o.a.125.10 | 44 | 9.2 | odd | 6 | |||
567.4.c.c.566.11 | 44 | 21.20 | even | 2 | inner | ||
567.4.c.c.566.12 | 44 | 1.1 | even | 1 | trivial | ||
567.4.c.c.566.33 | 44 | 3.2 | odd | 2 | inner | ||
567.4.c.c.566.34 | 44 | 7.6 | odd | 2 | inner |