Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(239,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.239");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.h (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: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.23 | ||
Character | \(\chi\) | \(=\) | 336.239 |
Dual form | 336.4.h.b.239.24 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 5.19367 | − | 0.160438i | 0.999523 | − | 0.0308762i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 7.59851i | − | 0.679631i | −0.940492 | − | 0.339816i | \(-0.889635\pi\) | ||
0.940492 | − | 0.339816i | \(-0.110365\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 26.9485 | − | 1.66652i | 0.998093 | − | 0.0617230i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0298576 | −0.000818399 | −0.000409200 | − | 1.00000i | \(-0.500130\pi\) | ||||
−0.000409200 | 1.00000i | \(0.500130\pi\) | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 40.1686 | 0.856981 | 0.428490 | − | 0.903546i | \(-0.359046\pi\) | ||||
0.428490 | + | 0.903546i | \(0.359046\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.21909 | − | 39.4642i | −0.0209844 | − | 0.679307i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.439999i | − | 0.00627738i | −0.999995 | − | 0.00313869i | \(-0.999001\pi\) | ||
0.999995 | − | 0.00313869i | \(-0.000999078\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.434338i | − | 0.00524441i | −0.999997 | − | 0.00262221i | \(-0.999165\pi\) | ||
0.999997 | − | 0.00262221i | \(-0.000834675\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.12306 | + | 36.3557i | 0.0116701 | + | 0.377784i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 139.817 | 1.26756 | 0.633781 | − | 0.773513i | \(-0.281502\pi\) | ||||
0.633781 | + | 0.773513i | \(0.281502\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 67.2627 | 0.538101 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 139.694 | − | 12.9789i | 0.995712 | − | 0.0925109i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 273.309i | − | 1.75008i | −0.484053 | − | 0.875039i | \(-0.660836\pi\) | ||
0.484053 | − | 0.875039i | \(-0.339164\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 149.527i | − | 0.866318i | −0.901318 | − | 0.433159i | \(-0.857399\pi\) | ||
0.901318 | − | 0.433159i | \(-0.142601\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.155070 | + | 0.00479027i | −0.000818009 | + | 2.52691e-5i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 53.1896 | 0.256876 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −290.284 | −1.28979 | −0.644897 | − | 0.764269i | \(-0.723100\pi\) | ||||
−0.644897 | + | 0.764269i | \(0.723100\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 208.622 | − | 6.44454i | 0.856572 | − | 0.0264603i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 57.4908i | − | 0.218989i | −0.993987 | − | 0.109495i | \(-0.965077\pi\) | ||
0.993987 | − | 0.109495i | \(-0.0349232\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 432.992i | 1.53560i | 0.640692 | + | 0.767798i | \(0.278648\pi\) | ||||
−0.640692 | + | 0.767798i | \(0.721352\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −12.6631 | − | 204.769i | −0.0419489 | − | 0.678335i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 317.042 | 0.983942 | 0.491971 | − | 0.870612i | \(-0.336277\pi\) | ||||
0.491971 | + | 0.870612i | \(0.336277\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0705924 | − | 2.28521i | −0.000193822 | − | 0.00627439i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 147.100i | − | 0.381239i | −0.981664 | − | 0.190620i | \(-0.938950\pi\) | ||
0.981664 | − | 0.190620i | \(-0.0610497\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.226873i | 0.000556210i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0696841 | − | 2.25581i | −0.000161928 | − | 0.00524191i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 488.249 | 1.07737 | 0.538683 | − | 0.842508i | \(-0.318922\pi\) | ||||
0.538683 | + | 0.842508i | \(0.318922\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −441.188 | −0.926038 | −0.463019 | − | 0.886348i | \(-0.653234\pi\) | ||||
−0.463019 | + | 0.886348i | \(0.653234\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.6656 | + | 188.640i | 0.0233291 | + | 0.377244i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 305.221i | − | 0.582431i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 440.204i | 0.802678i | 0.915930 | + | 0.401339i | \(0.131455\pi\) | ||||
−0.915930 | + | 0.401339i | \(0.868545\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 726.166 | − | 22.4319i | 1.26696 | − | 0.0391375i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 202.974 | 0.339275 | 0.169638 | − | 0.985507i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985507i | \(0.445740\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −542.719 | −0.870144 | −0.435072 | − | 0.900396i | \(-0.643277\pi\) | ||||
−0.435072 | + | 0.900396i | \(0.643277\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 349.341 | − | 10.7915i | 0.537845 | − | 0.0166145i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.209003i | − | 0.000309326i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 325.250i | − | 0.463209i | −0.972810 | − | 0.231605i | \(-0.925602\pi\) | ||
0.972810 | − | 0.231605i | \(-0.0743976\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 723.445 | − | 89.8205i | 0.992381 | − | 0.123211i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 376.536 | 0.497955 | 0.248977 | − | 0.968509i | \(-0.419906\pi\) | ||||
0.248977 | + | 0.968509i | \(0.419906\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.34334 | −0.00426631 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −43.8491 | − | 1419.48i | −0.0540358 | − | 1.74924i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 496.611i | 0.591468i | 0.955270 | + | 0.295734i | \(0.0955641\pi\) | ||||
−0.955270 | + | 0.295734i | \(0.904436\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 281.180i | 0.323908i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −23.9898 | − | 776.595i | −0.0267486 | − | 0.865905i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.30032 | −0.00356427 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 373.344 | 0.390797 | 0.195398 | − | 0.980724i | \(-0.437400\pi\) | ||||
0.195398 | + | 0.980724i | \(0.437400\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.804617 | + | 0.0497582i | −0.000816839 | + | 5.05141e-5i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 336.295i | 0.331313i | 0.986183 | + | 0.165657i | \(0.0529743\pi\) | ||||
−0.986183 | + | 0.165657i | \(0.947026\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 372.072i | − | 0.355936i | −0.984036 | − | 0.177968i | \(-0.943048\pi\) | ||
0.984036 | − | 0.177968i | \(-0.0569523\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 276.249 | − | 8.53360i | 0.256754 | − | 0.00793137i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1350.90 | −1.22053 | −0.610263 | − | 0.792199i | \(-0.708936\pi\) | ||||
−0.610263 | + | 0.792199i | \(0.708936\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 171.760 | 0.150932 | 0.0754662 | − | 0.997148i | \(-0.475955\pi\) | ||||
0.0754662 | + | 0.997148i | \(0.475955\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1507.64 | + | 46.5725i | −1.28918 | + | 0.0398240i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1132.11i | 0.942479i | 0.882005 | + | 0.471240i | \(0.156193\pi\) | ||||
−0.882005 | + | 0.471240i | \(0.843807\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1062.40i | − | 0.861475i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1082.48 | − | 66.9417i | 0.855347 | − | 0.0528954i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.08000 | 0.00237263 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1331.00 | −0.999999 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.22368 | − | 298.588i | −0.00676156 | − | 0.218885i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1460.91i | − | 1.04534i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2285.26i | 1.59673i | 0.602177 | + | 0.798363i | \(0.294300\pi\) | ||||
−0.602177 | + | 0.798363i | \(0.705700\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 69.4682 | + | 2248.82i | 0.0474134 | + | 1.53486i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1583.22 | −1.05593 | −0.527963 | − | 0.849267i | \(-0.677044\pi\) | ||||
−0.527963 | + | 0.849267i | \(0.677044\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.04036 | 0.00198220 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −98.6204 | − | 1061.47i | −0.0628733 | − | 0.676717i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2999.39i | 1.87047i | 0.354023 | + | 0.935237i | \(0.384814\pi\) | ||||
−0.354023 | + | 0.935237i | \(0.615186\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1324.48i | 0.808210i | 0.914712 | + | 0.404105i | \(0.132417\pi\) | ||||
−0.914712 | + | 0.404105i | \(0.867583\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1646.61 | − | 50.8654i | 0.983473 | − | 0.0303804i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.19933 | −0.000701353 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2076.74 | −1.18941 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −254.490 | + | 7.86144i | −0.142789 | + | 0.00441089i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2415.47i | − | 1.32808i | −0.747699 | − | 0.664038i | \(-0.768841\pi\) | ||
0.747699 | − | 0.664038i | \(-0.231159\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2734.78i | 1.47386i | 0.675967 | + | 0.736932i | \(0.263726\pi\) | ||||
−0.675967 | + | 0.736932i | \(0.736274\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.733268 | − | 11.8573i | −0.000387459 | − | 0.00626541i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1136.18 | −0.588777 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2957.87 | −1.50359 | −0.751794 | − | 0.659398i | \(-0.770811\pi\) | ||||
−0.751794 | + | 0.659398i | \(0.770811\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −23.6003 | − | 763.987i | −0.0117712 | − | 0.381057i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 978.721i | 0.479093i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 691.183i | − | 0.332133i | −0.986115 | − | 0.166066i | \(-0.946893\pi\) | ||
0.986115 | − | 0.166066i | \(-0.0531066\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0363989 | + | 1.17830i | 1.71737e−5 | + | 0.000555945i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1944.18 | −0.900868 | −0.450434 | − | 0.892810i | \(-0.648731\pi\) | ||||
−0.450434 | + | 0.892810i | \(0.648731\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −583.488 | −0.265584 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.723833 | − | 11.7048i | −0.000323701 | − | 0.00523441i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1459.20i | 0.641275i | 0.947202 | + | 0.320637i | \(0.103897\pi\) | ||||
−0.947202 | + | 0.320637i | \(0.896103\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 470.839i | 0.203383i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2535.81 | − | 78.3335i | 1.07685 | − | 0.0332650i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2398.75 | −1.00163 | −0.500813 | − | 0.865555i | \(-0.666966\pi\) | ||||
−0.500813 | + | 0.865555i | \(0.666966\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2169.01 | −0.890724 | −0.445362 | − | 0.895351i | \(-0.646925\pi\) | ||||
−0.445362 | + | 0.895351i | \(0.646925\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2291.39 | + | 70.7831i | −0.925596 | + | 0.0285925i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2205.73i | 0.876585i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0131373i | 5.13741e-6i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 90.8525 | + | 977.861i | 0.0349658 | + | 0.376344i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3345.58 | −1.26742 | −0.633712 | − | 0.773569i | \(-0.718470\pi\) | ||||
−0.633712 | + | 0.773569i | \(0.718470\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1400.64 | −0.522383 | −0.261192 | − | 0.965287i | \(-0.584115\pi\) | ||||
−0.261192 | + | 0.965287i | \(0.584115\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −48.9689 | − | 1585.22i | −0.0179833 | − | 0.582153i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3747.32i | − | 1.35526i | −0.735405 | − | 0.677628i | \(-0.763008\pi\) | ||
0.735405 | − | 0.677628i | \(-0.236992\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1160.47i | − | 0.413385i | −0.978406 | − | 0.206692i | \(-0.933730\pi\) | ||
0.978406 | − | 0.206692i | \(-0.0662699\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 70.6252 | + | 2286.27i | 0.0247837 | + | 0.802295i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1913.16 | 0.661467 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −436.844 | −0.148832 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3767.87 | − | 233.008i | 1.26515 | − | 0.0782377i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0129683i | 4.29203e-6i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3860.25i | − | 1.25948i | −0.776806 | − | 0.629740i | \(-0.783161\pi\) | ||
0.776806 | − | 0.629740i | \(-0.216839\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1054.18 | − | 32.5646i | 0.339114 | − | 0.0104755i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3290.09 | 1.04364 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1046.69 | 0.327437 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2818.71 | + | 87.0725i | −0.869729 | + | 0.0268667i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 17.6741i | − | 0.00537960i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4974.72i | 1.49386i | 0.664901 | + | 0.746932i | \(0.268474\pi\) | ||||
−0.664901 | + | 0.746932i | \(0.731526\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1812.63 | − | 112.095i | 0.537076 | − | 0.0332132i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3501.02 | 1.02366 | 0.511830 | − | 0.859087i | \(-0.328968\pi\) | ||||
0.511830 | + | 0.859087i | \(0.328968\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4196.81 | 1.21106 | 0.605530 | − | 0.795822i | \(-0.292961\pi\) | ||||
0.605530 | + | 0.795822i | \(0.292961\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.0335319 | − | 1.08549i | −9.55081e−6 | − | 0.000309178i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4918.36i | − | 1.38288i | −0.722432 | − | 0.691442i | \(-0.756976\pi\) | ||
0.722432 | − | 0.691442i | \(-0.243024\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 2409.04i | − | 0.668717i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −52.1824 | − | 1689.24i | −0.0143022 | − | 0.462988i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1041.63 | 0.281913 | 0.140957 | − | 0.990016i | \(-0.454982\pi\) | ||||
0.140957 | + | 0.990016i | \(0.454982\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2047.75 | 0.547332 | 0.273666 | − | 0.961825i | \(-0.411764\pi\) | ||||
0.273666 | + | 0.961825i | \(0.411764\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3742.93 | − | 582.567i | 0.988103 | − | 0.153793i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 372.327i | 0.0970902i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 17.4467i | − | 0.00449436i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1955.61 | − | 60.4106i | 0.497717 | − | 0.0153750i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 741.223 | 0.186397 | 0.0931983 | − | 0.995648i | \(-0.470291\pi\) | ||||
0.0931983 | + | 0.995648i | \(0.470291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.17460 | −0.00103737 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.3642 | + | 0.536397i | −0.00426427 | + | 0.000131727i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7849.47i | 1.90520i | 0.304225 | + | 0.952600i | \(0.401602\pi\) | ||||
−0.304225 | + | 0.952600i | \(0.598398\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2031.99i | − | 0.487497i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −455.475 | − | 7365.28i | −0.108020 | − | 1.74674i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1518.51 | 0.356029 | 0.178014 | − | 0.984028i | \(-0.443033\pi\) | ||||
0.178014 | + | 0.984028i | \(0.443033\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1117.74 | −0.259102 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 79.6750 | + | 2579.23i | 0.0182623 | + | 0.591186i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2768.04i | 0.627398i | 0.949522 | + | 0.313699i | \(0.101568\pi\) | ||||
−0.949522 | + | 0.313699i | \(0.898432\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2789.15i | 0.625199i | 0.949885 | + | 0.312599i | \(0.101200\pi\) | ||||
−0.949885 | + | 0.312599i | \(0.898800\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 45.1118 | + | 1460.36i | 0.0100011 | + | 0.323754i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.00830 | −0.000440382 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2896.05 | −0.628184 | −0.314092 | − | 0.949393i | \(-0.601700\pi\) | ||||
−0.314092 | + | 0.949393i | \(0.601700\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −249.190 | − | 4029.53i | −0.0534717 | − | 0.864666i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4683.57i | − | 0.994300i | −0.867665 | − | 0.497150i | \(-0.834380\pi\) | ||
0.867665 | − | 0.497150i | \(-0.165620\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8527.52i | 1.79120i | 0.444864 | + | 0.895598i | \(0.353252\pi\) | ||||
−0.444864 | + | 0.895598i | \(0.646748\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.1408 | + | 0.529495i | −0.00356257 | + | 0.000110051i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 402.436 | 0.0827701 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4912.81 | 0.999961 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1939.03 | − | 59.8983i | 0.390611 | − | 0.0120663i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8621.57i | − | 1.71904i | −0.511106 | − | 0.859518i | \(-0.670764\pi\) | ||
0.511106 | − | 0.859518i | \(-0.329236\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3709.96i | − | 0.732212i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.17094 | + | 0.387519i | −0.000814890 | + | 7.57109e-5i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5616.26 | 1.08628 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3030.94 | −0.580401 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 53.9544 | + | 1746.61i | 0.0102297 | + | 0.331155i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3352.37i | 0.629364i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4270.07i | − | 0.793830i | −0.917855 | − | 0.396915i | \(-0.870081\pi\) | ||
0.917855 | − | 0.396915i | \(-0.129919\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −59.6944 | − | 1932.42i | −0.0109900 | − | 0.355766i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8868.46 | 1.61699 | 0.808496 | − | 0.588502i | \(-0.200282\pi\) | ||||
0.808496 | + | 0.588502i | \(0.200282\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6273.41 | −1.13289 | −0.566444 | − | 0.824100i | \(-0.691681\pi\) | ||||
−0.566444 | + | 0.824100i | \(0.691681\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1433.38 | − | 88.6415i | 0.256387 | − | 0.0158552i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 11021.1i | − | 1.95271i | −0.216178 | − | 0.976354i | \(-0.569359\pi\) | ||
0.216178 | − | 0.976354i | \(-0.430641\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.16034i | 0.00143226i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7016.13 | + | 216.735i | −1.21994 | + | 0.0376852i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.191108 | −3.29212e−5 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2701.84 | 0.461143 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 892.066 | − | 27.5568i | 0.150860 | − | 0.00466022i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2219.29i | 0.371895i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1923.51i | 0.319414i | 0.987164 | + | 0.159707i | \(0.0510549\pi\) | ||||
−0.987164 | + | 0.159707i | \(0.948945\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7822.73 | + | 483.765i | −1.28734 | + | 0.0796100i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3344.89 | 0.545525 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7227.06 | −1.16820 | −0.584100 | − | 0.811682i | \(-0.698552\pi\) | ||||
−0.584100 | + | 0.811682i | \(0.698552\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 181.633 | + | 5879.82i | 0.0291002 | + | 0.942030i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.46451i | 0.000708994i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 343.000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −170.449 | − | 5517.78i | −0.0265991 | − | 0.861064i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7023.96 | 1.08665 | 0.543323 | − | 0.839524i | \(-0.317166\pi\) | ||||
0.543323 | + | 0.839524i | \(0.317166\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10241.7 | 1.57085 | 0.785425 | − | 0.618957i | \(-0.212444\pi\) | ||||
0.785425 | + | 0.618957i | \(0.212444\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5611.32 | − | 521.345i | 0.853306 | − | 0.0792801i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10999.2i | 1.65843i | 0.558930 | + | 0.829215i | \(0.311212\pi\) | ||||
−0.558930 | + | 0.829215i | \(0.688788\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1542.30i | − | 0.230582i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.9965 | − | 0.494147i | 0.00237150 | − | 7.32578e-5i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10462.6 | −1.53815 | −0.769076 | − | 0.639157i | \(-0.779283\pi\) | ||||
−0.769076 | + | 0.639157i | \(0.779283\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6858.81 | 0.999972 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6912.78 | + | 213.542i | −0.999523 | + | 0.0308762i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4123.86i | 0.591377i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2957.89i | 0.420711i | 0.977625 | + | 0.210355i | \(0.0674621\pi\) | ||||
−0.977625 | + | 0.210355i | \(0.932538\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −95.8096 | − | 1549.29i | −0.0135167 | − | 0.218572i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1029.70 | 0.144095 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4947.61 | −0.686803 | −0.343402 | − | 0.939189i | \(-0.611579\pi\) | ||||
−0.343402 | + | 0.939189i | \(0.611579\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −234.385 | − | 7587.49i | −0.0322762 | − | 1.04484i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 10978.4i | − | 1.49978i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7756.85i | − | 1.05130i | −0.850701 | − | 0.525650i | \(-0.823822\pi\) | ||
0.850701 | − | 0.525650i | \(-0.176178\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 366.642 | + | 11868.9i | 0.0493009 | + | 1.59596i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7742.65 | −1.03298 | −0.516489 | − | 0.856294i | \(-0.672761\pi\) | ||||
−0.516489 | + | 0.856294i | \(0.672761\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.58811 | −0.000210228 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 721.590 | + | 11668.5i | 0.0947816 | + | 1.53267i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7875.98i | 1.02655i | 0.858224 | + | 0.513275i | \(0.171568\pi\) | ||||
−0.858224 | + | 0.513275i | \(0.828432\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 61.5195i | − | 0.00795697i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8222.72 | + | 254.008i | −1.05542 | + | 0.0326030i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2471.42 | −0.314811 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10206.3 | 1.29028 | 0.645140 | − | 0.764065i | \(-0.276799\pi\) | ||||
0.645140 | + | 0.764065i | \(0.276799\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.7907 | − | 0.487788i | 0.00198126 | − | 6.12029e-5i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 11841.0i | − | 1.47459i | −0.675570 | − | 0.737296i | \(-0.736103\pi\) | ||
0.675570 | − | 0.737296i | \(-0.263897\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6006.28i | − | 0.742418i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −682.502 | − | 5497.11i | −0.0837378 | − | 0.674453i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.66717 | 0.00105557 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13143.7 | 1.58903 | 0.794517 | − | 0.607241i | \(-0.207724\pi\) | ||||
0.794517 | + | 0.607241i | \(0.207724\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 481.214 | + | 15577.8i | 0.0577532 | + | 1.86958i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3417.74i | 0.407206i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2861.11i | − | 0.338426i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 212.497 | + | 6878.94i | 0.0249545 | + | 0.807825i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9151.59 | −1.06703 | −0.533514 | − | 0.845791i | \(-0.679129\pi\) | ||||
−0.533514 | + | 0.845791i | \(0.679129\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4546.98 | 0.526380 | 0.263190 | − | 0.964744i | \(-0.415225\pi\) | ||||
0.263190 | + | 0.964744i | \(0.415225\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8543.80 | − | 528.356i | 0.982066 | − | 0.0607318i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 29.5955i | − | 0.00337787i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3088.31i | − | 0.350009i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.22896 | + | 0.192418i | −0.000701018 | + | 2.16551e-5i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1673.79 | −0.187061 | −0.0935307 | − | 0.995616i | \(-0.529815\pi\) | ||||
−0.0935307 | + | 0.995616i | \(0.529815\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7444.60 | 0.826246 | 0.413123 | − | 0.910675i | \(-0.364438\pi\) | ||||
0.413123 | + | 0.910675i | \(0.364438\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10785.9 | + | 333.187i | −1.18884 | + | 0.0367244i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 60.7279i | − | 0.00664762i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 7622.30i | − | 0.828685i | −0.910121 | − | 0.414343i | \(-0.864012\pi\) | ||
0.910121 | − | 0.414343i | \(-0.135988\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1320.48 | + | 81.6595i | −0.142585 | + | 0.00881757i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11283.3 | −1.21012 | −0.605062 | − | 0.796178i | \(-0.706852\pi\) | ||||
−0.605062 | + | 0.796178i | \(0.706852\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3773.50 | 0.401980 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −387.533 | − | 12545.2i | −0.0410060 | − | 1.32744i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1115.19i | − | 0.117214i | −0.998281 | − | 0.0586072i | \(-0.981334\pi\) | ||
0.998281 | − | 0.0586072i | \(-0.0186660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.71653i | 0.000179221i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 438.762 | + | 14203.6i | 0.0455074 | + | 1.47316i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2136.55 | 0.220138 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5761.30 | 0.589720 | 0.294860 | − | 0.955540i | \(-0.404727\pi\) | ||||
0.294860 | + | 0.955540i | \(0.404727\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.71072 | − | 61.4655i | −0.000580727 | − | 0.00625046i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13482.7i | 1.36215i | 0.732212 | + | 0.681077i | \(0.238488\pi\) | ||||
−0.732212 | + | 0.681077i | \(0.761512\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2543.21i | 0.255276i | 0.991821 | + | 0.127638i | \(0.0407396\pi\) | ||||
−0.991821 | + | 0.127638i | \(0.959260\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5900.96 | + | 182.286i | −0.588496 | + | 0.0181792i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10843.8 | 1.07450 | 0.537248 | − | 0.843424i | \(-0.319464\pi\) | ||||
0.537248 | + | 0.843424i | \(0.319464\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3081.43 | −0.303384 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15362.2 | + | 474.553i | −1.50287 | + | 0.0464251i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 12.9281i | − | 0.00125673i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 29.2147i | − | 0.00282203i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −245.144 | − | 3964.11i | −0.0235312 | − | 0.380512i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3170.33 | −0.302414 | −0.151207 | − | 0.988502i | \(-0.548316\pi\) | ||||
−0.151207 | + | 0.988502i | \(0.548316\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11660.3 | −1.10533 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 157.024 | + | 5083.16i | 0.0147926 | + | 0.478865i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 2836.85i | − | 0.265598i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5722.95i | 0.532509i | 0.963903 | + | 0.266254i | \(0.0857861\pi\) | ||||
−0.963903 | + | 0.266254i | \(0.914214\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −110.892 | − | 3589.78i | −0.0102550 | − | 0.331974i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13139.2 | −1.20767 | −0.603834 | − | 0.797110i | \(-0.706361\pi\) | ||||
−0.603834 | + | 0.797110i | \(0.706361\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −120.256 | −0.0109859 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.378088 | + | 6.11389i | 3.43309e−5 | + | 0.000555149i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1420.82i | 0.128234i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 13089.1i | − | 1.17425i | −0.809498 | − | 0.587123i | \(-0.800261\pi\) | ||
0.809498 | − | 0.587123i | \(-0.199739\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10097.4 | + | 311.919i | −0.900439 | + | 0.0278154i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17972.9 | −1.59318 | −0.796592 | − | 0.604518i | \(-0.793366\pi\) | ||||
−0.796592 | + | 0.604518i | \(0.793366\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2555.34 | 0.225171 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3030.44 | + | 93.6133i | −0.265457 | + | 0.00820022i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18517.0i | 1.61248i | 0.591588 | + | 0.806240i | \(0.298501\pi\) | ||||
−0.591588 | + | 0.806240i | \(0.701499\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 3799.03i | − | 0.328883i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.63723 | − | 60.6746i | −0.000485166 | − | 0.00522192i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2827.20 | −0.241905 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.46609 | −0.000805257 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 234.110 | + | 7578.59i | 0.0198001 | + | 0.640969i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5545.36i | 0.466308i | 0.972440 | + | 0.233154i | \(0.0749047\pi\) | ||||
−0.972440 | + | 0.233154i | \(0.925095\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 10763.5i | − | 0.899912i | −0.893051 | − | 0.449956i | \(-0.851440\pi\) | ||
0.893051 | − | 0.449956i | \(-0.148560\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 75.5402 | + | 2445.38i | 0.00627971 | + | 0.203286i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −65.7918 | −0.00543821 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7381.88 | 0.606714 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13157.6 | − | 813.677i | 1.07531 | − | 0.0664983i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2309.32i | − | 0.187669i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10264.8i | 0.829508i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12458.3 | + | 384.850i | −1.00115 | + | 0.0309264i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.46302 | 0.000116914 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9149.30 | −0.727097 | −0.363548 | − | 0.931575i | \(-0.618435\pi\) | ||||
−0.363548 | + | 0.931575i | \(0.618435\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11265.1 | + | 347.990i | −0.890300 | + | 0.0275022i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1305.12i | − | 0.102578i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4297.91i | − | 0.335951i | −0.985791 | − | 0.167976i | \(-0.946277\pi\) | ||
0.985791 | − | 0.167976i | \(-0.0537230\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11889.4 | + | 735.249i | −0.924272 | + | 0.0571578i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −118.708 | −0.00917813 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2276.75 | 0.175077 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 353.881 | + | 11455.8i | 0.0270656 | + | 0.876167i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1753.57i | 0.133395i | 0.997773 | + | 0.0666975i | \(0.0212462\pi\) | ||||
−0.997773 | + | 0.0666975i | \(0.978754\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17392.7i | 1.31598i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.00210772 | + | 0.0682309i | 1.58624e−7 | + | 5.13496e-6i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10323.1 | −0.772764 | −0.386382 | − | 0.922339i | \(-0.626275\pi\) | ||||
−0.386382 | + | 0.922339i | \(0.626275\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8602.36 | 0.640538 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 628.744 | + | 5064.12i | 0.0465692 | + | 0.375085i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 15103.5i | − | 1.11278i | −0.830920 | − | 0.556391i | \(-0.812186\pi\) | ||
0.830920 | − | 0.556391i | \(-0.187814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9072.75i | 0.664944i | 0.943113 | + | 0.332472i | \(0.107883\pi\) | ||||
−0.943113 | + | 0.332472i | \(0.892117\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17375.9 | + | 536.757i | −1.26682 | + | 0.0391333i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9404.49 | 0.682077 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3540.84 | 0.255472 | 0.127736 | − | 0.991808i | \(-0.459229\pi\) | ||||
0.127736 | + | 0.991808i | \(0.459229\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7274.45 | + | 224.715i | −0.522134 | + | 0.0161292i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2635.75i | 0.188209i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.39203i | 0.000312006i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −508.657 | − | 8225.25i | −0.0359494 | − | 0.581320i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11465.3 | 0.806171 | 0.403085 | − | 0.915162i | \(-0.367938\pi\) | ||||
0.403085 | + | 0.915162i | \(0.367938\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −64.9452 | −0.00454333 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −601.210 | − | 19462.3i | −0.0418452 | − | 1.35461i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4829.33i | 0.334430i | 0.985920 | + | 0.167215i | \(0.0534774\pi\) | ||||
−0.985920 | + | 0.167215i | \(0.946523\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 23.4034i | − | 0.00161251i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −186.183 | − | 6027.10i | −0.0127638 | − | 0.413188i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9235.49 | 0.629970 | 0.314985 | − | 0.949097i | \(-0.398001\pi\) | ||||
0.314985 | + | 0.949097i | \(0.398001\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7969.74 | 0.540919 | 0.270460 | − | 0.962731i | \(-0.412824\pi\) | ||||
0.270460 | + | 0.962731i | \(0.412824\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 733.609 | + | 11862.8i | 0.0495437 | + | 0.801148i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10113.6i | 0.679631i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12277.3i | 0.820953i | 0.911871 | + | 0.410477i | \(0.134638\pi\) | ||||
−0.911871 | + | 0.410477i | \(0.865362\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9936.35 | − | 306.943i | 0.661152 | − | 0.0204236i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12735.1 | 0.843219 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2671.59 | 0.176027 | 0.0880135 | − | 0.996119i | \(-0.471948\pi\) | ||||
0.0880135 | + | 0.996119i | \(0.471948\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2268.83 | + | 70.0862i | −0.148761 | + | 0.00459536i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 16638.0i | − | 1.08561i | −0.839860 | − | 0.542803i | \(-0.817363\pi\) | ||
0.839860 | − | 0.542803i | \(-0.182637\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 30122.8i | − | 1.95596i | −0.208698 | − | 0.977980i | \(-0.566923\pi\) | ||
0.208698 | − | 0.977980i | \(-0.433077\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 19531.7 | − | 1814.68i | 1.26213 | − | 0.117263i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3476.27 | −0.223554 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2692.90 | −0.172345 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.00208060 | + | 0.0673529i | 1.32522e−7 | + | 4.28998e-6i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 127.725i | 0.00809654i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 4373.21i | − | 0.275903i | −0.990439 | − | 0.137952i | \(-0.955948\pi\) | ||
0.990439 | − | 0.137952i | \(-0.0440518\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −619.329 | − | 20048.9i | −0.0388880 | − | 1.25888i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17364.6 | 1.08518 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1968.26 | −0.122426 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5469.84 | − | 338.260i | 0.338628 | − | 0.0209411i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 9337.02i | − | 0.575335i | −0.957730 | − | 0.287668i | \(-0.907120\pi\) | ||
0.957730 | − | 0.287668i | \(-0.0928799\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22548.8i | 1.38295i | 0.722400 | + | 0.691476i | \(0.243039\pi\) | ||||
−0.722400 | + | 0.691476i | \(0.756961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17087.7 | − | 527.854i | 1.04314 | − | 0.0322236i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21092.7 | 1.28167 | 0.640834 | − | 0.767680i | \(-0.278589\pi\) | ||||
0.640834 | + | 0.767680i | \(0.278589\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.5779 | −0.000881716 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5436.16 | − | 167.928i | 0.327281 | − | 0.0101100i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23059.3i | 1.38190i | 0.722902 | + | 0.690951i | \(0.242808\pi\) | ||||
−0.722902 | + | 0.690951i | \(0.757192\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12030.1i | 0.717641i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14625.5 | + | 904.453i | −0.868485 | + | 0.0537079i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22080.3 | −1.30520 | −0.652601 | − | 0.757702i | \(-0.726322\pi\) | ||||
−0.652601 | + | 0.757702i | \(0.726322\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22653.9 | −1.33303 | −0.666516 | − | 0.745491i | \(-0.732215\pi\) | ||||
−0.666516 | + | 0.745491i | \(0.732215\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.83560 | − | 91.7937i | −0.000166102 | − | 0.00537703i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 23.1022i | − | 0.00134717i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 38213.4i | − | 2.21833i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 798.131 | + | 25837.1i | 0.0461249 | + | 1.49315i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.1728 | 0.000757869 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3686.80 | 0.211168 | 0.105584 | − | 0.994410i | \(-0.466329\pi\) | ||||
0.105584 | + | 0.994410i | \(0.466329\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9396.23 | − | 872.997i | 0.535794 | − | 0.0497803i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 23120.2i | − | 1.31253i | −0.754531 | − | 0.656264i | \(-0.772136\pi\) | ||
0.754531 | − | 0.656264i | \(-0.227864\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2613.41i | 0.147707i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18183.2 | − | 561.695i | 1.02317 | − | 0.0316068i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14836.8 | 0.831207 | 0.415603 | − | 0.909546i | \(-0.363570\pi\) | ||||
0.415603 | + | 0.909546i | \(0.363570\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22790.9 | 1.27123 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21796.9 | − | 673.326i | 1.21048 | − | 0.0373930i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 5908.77i | − | 0.326715i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 25813.4i | − | 1.42111i | −0.703642 | − | 0.710555i | \(-0.748444\pi\) | ||
0.703642 | − | 0.710555i | \(-0.251556\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.348308 | − | 5.63232i | −1.90925e−5 | − | 0.000308736i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10064.1 | 0.549285 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.2959 | −0.00137468 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −789.089 | − | 25544.3i | −0.0426983 | − | 1.38223i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16480.0i | 0.887931i | 0.896044 | + | 0.443965i | \(0.146429\pi\) | ||||
−0.896044 | + | 0.443965i | \(0.853571\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 126.081i | 0.00676422i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −386.501 | − | 12511.8i | −0.0206475 | − | 0.668399i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2354.07 | −0.125225 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2993.67 | 0.158575 | 0.0792875 | − | 0.996852i | \(-0.474735\pi\) | ||||
0.0792875 | + | 0.996852i | \(0.474735\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −542.037 | − | 8765.02i | −0.0285907 | − | 0.462326i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 20906.5i | − | 1.09811i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.11316i | 0.000476661i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5409.87 | − | 167.116i | 0.281779 | − | 0.00870442i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17596.5 | −0.912711 | −0.456355 | − | 0.889798i | \(-0.650845\pi\) | ||||
−0.456355 | + | 0.889798i | \(0.650845\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2604.51 | 0.134531 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10635.3 | − | 328.535i | 0.547071 | − | 0.0168995i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 18383.5i | − | 0.941719i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33368.5i | 1.70229i | 0.524927 | + | 0.851147i | \(0.324093\pi\) | ||||
−0.524927 | + | 0.851147i | \(0.675907\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19346.1 | − | 3626.17i | 0.982883 | − | 0.184228i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 190.516 | 0.00963953 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23542.7 | −1.18632 | −0.593158 | − | 0.805086i | \(-0.702119\pi\) | ||||
−0.593158 | + | 0.805086i | \(0.702119\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 59.7352 | + | 1933.74i | 0.00299778 | + | 0.0970439i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 13.1434i | − | 0.000656911i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23280.9i | 1.15886i | 0.815021 | + | 0.579432i | \(0.196726\pi\) | ||||
−0.815021 | + | 0.579432i | \(0.803274\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.79911 | − | 90.6125i | −0.000138769 | − | 0.00449222i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35371.0 | 1.74648 | 0.873242 | − | 0.487287i | \(-0.162013\pi\) | ||||
0.873242 | + | 0.487287i | \(0.162013\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18354.0 | −0.902602 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10147.1 | − | 627.506i | 0.497005 | − | 0.0307353i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 9456.29i | − | 0.461316i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 8592.26i | − | 0.417492i | −0.977970 | − | 0.208746i | \(-0.933062\pi\) | ||
0.977970 | − | 0.208746i | \(-0.0669381\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3849.67 | − | 118.920i | 0.186308 | − | 0.00575522i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20780.3 | 1.00168 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5401.34 | 0.259333 | 0.129666 | − | 0.991558i | \(-0.458609\pi\) | ||||
0.129666 | + | 0.991558i | \(0.458609\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −21.6815 | + | 0.669763i | −0.00103688 | + | 3.20301e-5i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 34301.0i | − | 1.63391i | −0.576698 | − | 0.816957i | \(-0.695659\pi\) | ||
0.576698 | − | 0.816957i | \(-0.304341\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1202.32i | 0.0570471i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −90.0980 | + | 5.57174i | −0.00425817 | + | 0.000263329i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19612.3 | 0.923282 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23217.6 | −1.08875 | −0.544375 | − | 0.838842i | \(-0.683233\pi\) | ||||
−0.544375 | + | 0.838842i | \(0.683233\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1259.35 | + | 40767.6i | 0.0588254 | + | 1.90429i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 9655.19i | − | 0.449254i | −0.974445 | − | 0.224627i | \(-0.927884\pi\) | ||
0.974445 | − | 0.224627i | \(-0.0721163\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 10057.6i | − | 0.466167i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −326.007 | − | 10553.5i | −0.0150521 | − | 0.487264i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.9704 | −0.00114847 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.06030 | −0.000277663 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3547.26 | − | 38179.8i | −0.161901 | − | 1.74257i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22475.4i | 1.02189i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 7935.72i | − | 0.359438i | −0.983718 | − | 0.179719i | \(-0.942481\pi\) | ||
0.983718 | − | 0.179719i | \(-0.0575189\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7886.66 | − | 243.626i | 0.355859 | − | 0.0109928i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7924.79 | −0.356224 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17721.9 | −0.793597 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5805.16 | + | 179.327i | −0.258978 | + | 0.00800009i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13066.5i | 0.580726i | 0.956917 | + | 0.290363i | \(0.0937760\pi\) | ||||
−0.956917 | + | 0.290363i | \(0.906224\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 139.498i | − | 0.00617658i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 827.612 | + | 13382.9i | 0.0365072 | + | 0.590340i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.2043 | 0.000712125 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7436.82 | 0.325607 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 444.097 | + | 14376.3i | 0.0193717 | + | 0.627099i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5705.93i | − | 0.247973i | −0.992284 | − | 0.123986i | \(-0.960432\pi\) | ||
0.992284 | − | 0.123986i | \(-0.0395679\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35006.8i | 1.51573i | 0.652413 | + | 0.757864i | \(0.273757\pi\) | ||||
−0.652413 | + | 0.757864i | \(0.726243\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 447.484 | + | 14485.9i | 0.0193038 | + | 0.624900i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5251.96 | −0.225728 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 188.065 | 0.00805330 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 468.592 | + | 7577.38i | 0.0199926 | + | 0.323291i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15875.8i | 0.674869i | 0.941349 | + | 0.337435i | \(0.109559\pi\) | ||||
−0.941349 | + | 0.337435i | \(0.890441\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32848.1i | 1.39127i | 0.718397 | + | 0.695634i | \(0.244876\pi\) | ||||
−0.718397 | + | 0.695634i | \(0.755124\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.4305 | + | 0.322207i | −0.000440172 | + | 1.35973e-5i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10175.0 | −0.427836 | −0.213918 | − | 0.976852i | \(-0.568622\pi\) | ||||
−0.213918 | + | 0.976852i | \(0.568622\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8733.63 | 0.365901 | 0.182950 | − | 0.983122i | \(-0.441435\pi\) | ||||
0.182950 | + | 0.983122i | \(0.441435\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15041.1 | + | 464.635i | −0.627884 | + | 0.0193959i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.5600i | 0.000896769i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14772.9i | 0.612258i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1940.70 | − | 20888.1i | −0.0801439 | − | 0.862603i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23404.1 | −0.963050 | −0.481525 | − | 0.876432i | \(-0.659917\pi\) | ||||
−0.481525 | + | 0.876432i | \(0.659917\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −50308.9 | −2.06277 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −751.421 | − | 24324.9i | −0.0307002 | − | 0.993826i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4433.63i | 0.180499i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 9316.99i | − | 0.377964i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1368.13 | + | 44289.2i | 0.0553054 | + | 1.79034i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −40586.7 | −1.63489 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4019.79 | 0.161354 | 0.0806771 | − | 0.996740i | \(-0.474292\pi\) | ||||
0.0806771 | + | 0.996740i | \(0.474292\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −88.9387 | + | 5.50005i | −0.00355747 | + | 0.000219997i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 34890.1i | − | 1.39069i | −0.718676 | − | 0.695345i | \(-0.755251\pi\) | ||
0.718676 | − | 0.695345i | \(-0.244749\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22977.7i | 0.912675i | 0.889807 | + | 0.456338i | \(0.150839\pi\) | ||||
−0.889807 | + | 0.456338i | \(0.849161\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2090.12 | − | 64.5658i | 0.0827306 | − | 0.00255563i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2184.37 | 0.0861607 | 0.0430804 | − | 0.999072i | \(-0.486283\pi\) | ||||
0.0430804 | + | 0.999072i | \(0.486283\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11087.7 | 0.435830 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25515.5 | − | 788.199i | 0.999484 | − | 0.0308750i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.71118i | 0.000379090i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17682.3i | 0.687880i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10061.1 | − | 622.185i | 0.390052 | − | 0.0241212i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10226.4 | 0.395102 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −48020.9 | −1.84898 | −0.924488 | − | 0.381211i | \(-0.875507\pi\) | ||||
−0.924488 | + | 0.381211i | \(0.875507\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1383.22 | − | 44777.6i | −0.0530773 | − | 1.71822i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48557.5i | 1.85692i | 0.371438 | + | 0.928458i | \(0.378865\pi\) | ||||
−0.371438 | + | 0.928458i | \(0.621135\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 34418.8i | − | 1.31176i | −0.754865 | − | 0.655880i | \(-0.772298\pi\) | ||
0.754865 | − | 0.655880i | \(-0.227702\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −595.217 | − | 19268.3i | −0.0226079 | − | 0.731863i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1694.17 | −0.0641314 | −0.0320657 | − | 0.999486i | \(-0.510209\pi\) | ||||
−0.0320657 | + | 0.999486i | \(0.510209\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15996.8 | −0.603506 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.6003 | + | 2.68182i | −0.000812164 | + | 0.000100835i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 137.703i | − | 0.00516020i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18226.9i | 0.680736i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29169.0 | − | 901.059i | 1.08576 | − | 0.0335401i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −40867.1 | −1.51612 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −64.7237 | −0.00239318 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15741.7 | + | 486.277i | −0.580124 | + | 0.0179206i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16481.2i | 0.605364i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 18211.1i | − | 0.666691i | −0.942805 | − | 0.333346i | \(-0.891822\pi\) | ||
0.942805 | − | 0.333346i | \(-0.108178\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 560.443 | + | 9062.66i | 0.0204496 | + | 0.330681i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7379.36 | 0.268374 | 0.134187 | − | 0.990956i | \(-0.457158\pi\) | ||||
0.134187 | + | 0.990956i | \(0.457158\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.2425 | −0.000407526 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 537.846 | + | 17411.1i | 0.0194324 | + | 0.629064i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 11082.5i | − | 0.399103i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 4388.74i | − | 0.157531i | −0.996893 | − | 0.0787656i | \(-0.974902\pi\) | ||
0.996893 | − | 0.0787656i | \(-0.0250979\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −685.080 | − | 22177.4i | −0.0245105 | − | 0.793451i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8153.16 | 0.290752 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19525.3 | −0.694041 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −620.067 | − | 10026.8i | −0.0219694 | − | 0.355257i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27520.1i | 0.971910i | 0.873984 | + | 0.485955i | \(0.161528\pi\) | ||||
−0.873984 | + | 0.485955i | \(0.838472\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.2825i | 0.000749202i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 46059.9 | − | 1422.83i | 1.61622 | − | 0.0499266i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.0998239 | 3.49154e−6 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46438.8 | 1.61909 | 0.809546 | − | 0.587057i | \(-0.199714\pi\) | ||||
0.809546 | + | 0.587057i | \(0.199714\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32582.0 | + | 1006.49i | −1.13235 | + | 0.0349793i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 17701.1i | − | 0.613219i | −0.951835 | − | 0.306610i | \(-0.900805\pi\) | ||
0.951835 | − | 0.306610i | \(-0.0991946\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 8038.21i | − | 0.277582i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7430.29 | − | 690.343i | 0.255775 | − | 0.0237639i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 55200.9 | 1.89418 | 0.947090 | − | 0.320967i | \(-0.104008\pi\) | ||||
0.947090 | + | 0.320967i | \(0.104008\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21800.2 | −0.745696 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1768.20 | − | 57240.2i | −0.0602922 | − | 1.95178i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3055.84i | 0.103870i | 0.998650 | + | 0.0519351i | \(0.0165389\pi\) | ||||
−0.998650 | + | 0.0519351i | \(0.983461\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25421.4i | 0.861381i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.30923 | + | 42.3822i | 4.42228e−5 | + | 0.00143158i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20995.7 | −0.706973 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7432.66 | 0.249494 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −36404.7 | + | 2251.30i | −1.21820 | + | 0.0753346i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10642.7i | 0.355028i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 9976.97i | − | 0.331787i | −0.986144 | − | 0.165893i | \(-0.946949\pi\) | ||
0.986144 | − | 0.165893i | \(-0.0530508\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.992554 | + | 0.0306609i | −3.29055e−5 | + | 1.01648e-6i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25909.3 | −0.856301 | −0.428150 | − | 0.903707i | \(-0.640835\pi\) | ||||
−0.428150 | + | 0.903707i | \(0.640835\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9271.39 | −0.305475 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14032.5 | − | 433.477i | 0.460923 | − | 0.0142383i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27062.6i | 0.886193i | 0.896474 | + | 0.443096i | \(0.146120\pi\) | ||||
−0.896474 | + | 0.443096i | \(0.853880\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 14.8276i | − | 0.000484057i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4628.68 | − | 286.242i | 0.150645 | − | 0.00931600i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −44352.2 | −1.43908 | −0.719540 | − | 0.694451i | \(-0.755647\pi\) | ||||
−0.719540 | + | 0.694451i | \(0.755647\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28474.0 | −0.921074 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 356.058 | + | 11526.3i | 0.0114827 | + | 0.371718i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 60539.8i | 1.94646i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 21159.0i | − | 0.678243i | −0.940742 | − | 0.339122i | \(-0.889870\pi\) | ||
0.940742 | − | 0.339122i | \(-0.110130\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 308.604 | + | 9990.11i | 0.00986229 | + | 0.319261i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8817.84 | −0.280949 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27664.4 | 0.878775 | 0.439388 | − | 0.898298i | \(-0.355195\pi\) | ||||
0.439388 | + | 0.898298i | \(0.355195\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −40551.1 | + | 3767.57i | −1.28426 | + | 0.119320i |
(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 | 336.4.h.b.239.23 | yes | 24 | |
3.2 | odd | 2 | inner | 336.4.h.b.239.1 | ✓ | 24 | |
4.3 | odd | 2 | inner | 336.4.h.b.239.2 | yes | 24 | |
12.11 | even | 2 | inner | 336.4.h.b.239.24 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.4.h.b.239.1 | ✓ | 24 | 3.2 | odd | 2 | inner | |
336.4.h.b.239.2 | yes | 24 | 4.3 | odd | 2 | inner | |
336.4.h.b.239.23 | yes | 24 | 1.1 | even | 1 | trivial | |
336.4.h.b.239.24 | yes | 24 | 12.11 | even | 2 | inner |