Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [176,4,Mod(1,176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("176.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 176 = 2^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 176.a (trivial) |
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: | yes |
Analytic conductor: | \(10.3843361610\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 88) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 176.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −7.00000 | −1.34715 | −0.673575 | − | 0.739119i | \(-0.735242\pi\) | ||||
−0.673575 | + | 0.739119i | \(0.735242\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.00000 | 0.804984 | 0.402492 | − | 0.915423i | \(-0.368144\pi\) | ||||
0.402492 | + | 0.915423i | \(0.368144\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | −0.107990 | −0.0539949 | − | 0.998541i | \(-0.517195\pi\) | ||||
−0.0539949 | + | 0.998541i | \(0.517195\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 22.0000 | 0.814815 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −63.0000 | −1.08444 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −38.0000 | −0.542138 | −0.271069 | − | 0.962560i | \(-0.587377\pi\) | ||||
−0.271069 | + | 0.962560i | \(0.587377\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −44.0000 | −0.531279 | −0.265639 | − | 0.964072i | \(-0.585583\pi\) | ||||
−0.265639 | + | 0.964072i | \(0.585583\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.0000 | 0.145479 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −175.000 | −1.58652 | −0.793261 | − | 0.608881i | \(-0.791619\pi\) | ||||
−0.793261 | + | 0.608881i | \(0.791619\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −44.0000 | −0.352000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 35.0000 | 0.249472 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −264.000 | −1.69047 | −0.845234 | − | 0.534396i | \(-0.820539\pi\) | ||||
−0.845234 | + | 0.534396i | \(0.820539\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −159.000 | −0.921201 | −0.460601 | − | 0.887607i | \(-0.652366\pi\) | ||||
−0.460601 | + | 0.887607i | \(0.652366\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −77.0000 | −0.406181 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −18.0000 | −0.0869302 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −173.000 | −0.768676 | −0.384338 | − | 0.923192i | \(-0.625570\pi\) | ||||
−0.384338 | + | 0.923192i | \(0.625570\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −220.000 | −0.838006 | −0.419003 | − | 0.907985i | \(-0.637620\pi\) | ||||
−0.419003 | + | 0.907985i | \(0.637620\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 542.000 | 1.92219 | 0.961096 | − | 0.276216i | \(-0.0890805\pi\) | ||||
0.961096 | + | 0.276216i | \(0.0890805\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 198.000 | 0.655913 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 264.000 | 0.819327 | 0.409663 | − | 0.912237i | \(-0.365646\pi\) | ||||
0.409663 | + | 0.912237i | \(0.365646\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −339.000 | −0.988338 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 266.000 | 0.730342 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 682.000 | 1.76755 | 0.883773 | − | 0.467916i | \(-0.154995\pi\) | ||||
0.883773 | + | 0.467916i | \(0.154995\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 99.0000 | 0.242712 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 308.000 | 0.715712 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −421.000 | −0.928975 | −0.464488 | − | 0.885580i | \(-0.653761\pi\) | ||||
−0.464488 | + | 0.885580i | \(0.653761\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 308.000 | 0.646481 | 0.323241 | − | 0.946317i | \(-0.395228\pi\) | ||||
0.323241 | + | 0.946317i | \(0.395228\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −44.0000 | −0.0879917 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −177.000 | −0.322746 | −0.161373 | − | 0.986893i | \(-0.551592\pi\) | ||||
−0.161373 | + | 0.986893i | \(0.551592\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1225.00 | 2.13729 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −365.000 | −0.610106 | −0.305053 | − | 0.952335i | \(-0.598674\pi\) | ||||
−0.305053 | + | 0.952335i | \(0.598674\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −528.000 | −0.846544 | −0.423272 | − | 0.906003i | \(-0.639119\pi\) | ||||
−0.423272 | + | 0.906003i | \(0.639119\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 308.000 | 0.474197 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −22.0000 | −0.0325602 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −686.000 | −0.976975 | −0.488488 | − | 0.872571i | \(-0.662451\pi\) | ||||
−0.488488 | + | 0.872571i | \(0.662451\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −839.000 | −1.15089 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −698.000 | −0.923078 | −0.461539 | − | 0.887120i | \(-0.652703\pi\) | ||||
−0.461539 | + | 0.887120i | \(0.652703\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −342.000 | −0.436413 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1848.00 | 2.27731 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 967.000 | 1.15171 | 0.575853 | − | 0.817553i | \(-0.304670\pi\) | ||||
0.575853 | + | 0.817553i | \(0.304670\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1113.00 | 1.24100 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −396.000 | −0.427671 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1127.00 | −1.17969 | −0.589843 | − | 0.807518i | \(-0.700810\pi\) | ||||
−0.589843 | + | 0.807518i | \(0.700810\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 242.000 | 0.245676 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 510.000 | 0.502445 | 0.251222 | − | 0.967929i | \(-0.419167\pi\) | ||||
0.251222 | + | 0.967929i | \(0.419167\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1056.00 | 1.01020 | 0.505101 | − | 0.863060i | \(-0.331455\pi\) | ||||
0.505101 | + | 0.863060i | \(0.331455\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 126.000 | 0.117108 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1046.00 | −0.945053 | −0.472526 | − | 0.881317i | \(-0.656658\pi\) | ||||
−0.472526 | + | 0.881317i | \(0.656658\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 250.000 | 0.219685 | 0.109842 | − | 0.993949i | \(-0.464965\pi\) | ||||
0.109842 | + | 0.993949i | \(0.464965\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1211.00 | 1.03552 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1401.00 | 1.16633 | 0.583164 | − | 0.812355i | \(-0.301815\pi\) | ||||
0.583164 | + | 0.812355i | \(0.301815\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1575.00 | −1.27713 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 76.0000 | 0.0585455 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1540.00 | 1.12892 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1521.00 | −1.08834 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 132.000 | 0.0922292 | 0.0461146 | − | 0.998936i | \(-0.485316\pi\) | ||||
0.0461146 | + | 0.998936i | \(0.485316\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3794.00 | −2.58948 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2054.00 | 1.36991 | 0.684957 | − | 0.728583i | \(-0.259821\pi\) | ||||
0.684957 | + | 0.728583i | \(0.259821\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 88.0000 | 0.0573727 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 315.000 | 0.200821 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 889.000 | 0.554397 | 0.277199 | − | 0.960813i | \(-0.410594\pi\) | ||||
0.277199 | + | 0.960813i | \(0.410594\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2638.00 | −1.60973 | −0.804864 | − | 0.593459i | \(-0.797762\pi\) | ||||
−0.804864 | + | 0.593459i | \(0.797762\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1848.00 | −1.10376 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2376.00 | −1.36080 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2373.00 | 1.33144 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3338.00 | 1.83530 | 0.917650 | − | 0.397390i | \(-0.130084\pi\) | ||||
0.917650 | + | 0.397390i | \(0.130084\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 430.000 | 0.231741 | 0.115871 | − | 0.993264i | \(-0.463034\pi\) | ||||
0.115871 | + | 0.993264i | \(0.463034\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −836.000 | −0.441742 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1431.00 | −0.741553 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1159.00 | −0.589161 | −0.294580 | − | 0.955627i | \(-0.595180\pi\) | ||||
−0.294580 | + | 0.955627i | \(0.595180\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4774.00 | −2.38115 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 350.000 | 0.171328 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1012.00 | −0.486294 | −0.243147 | − | 0.969989i | \(-0.578180\pi\) | ||||
−0.243147 | + | 0.969989i | \(0.578180\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −693.000 | −0.326970 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1584.00 | −0.733974 | −0.366987 | − | 0.930226i | \(-0.619611\pi\) | ||||
−0.366987 | + | 0.930226i | \(0.619611\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2197.00 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −968.000 | −0.432894 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 474.000 | 0.208310 | 0.104155 | − | 0.994561i | \(-0.466786\pi\) | ||||
0.104155 | + | 0.994561i | \(0.466786\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 88.0000 | 0.0380124 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2947.00 | 1.25147 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1665.00 | −0.695240 | −0.347620 | − | 0.937636i | \(-0.613010\pi\) | ||||
−0.347620 | + | 0.937636i | \(0.613010\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2543.00 | 1.04431 | 0.522154 | − | 0.852851i | \(-0.325129\pi\) | ||||
0.522154 | + | 0.852851i | \(0.325129\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2156.00 | −0.870908 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1557.00 | −0.618773 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −418.000 | −0.163461 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −70.0000 | −0.0269405 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1631.00 | 0.617880 | 0.308940 | − | 0.951082i | \(-0.400026\pi\) | ||||
0.308940 | + | 0.951082i | \(0.400026\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 484.000 | 0.180513 | 0.0902567 | − | 0.995919i | \(-0.471231\pi\) | ||||
0.0902567 | + | 0.995919i | \(0.471231\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1966.00 | 0.711024 | 0.355512 | − | 0.934672i | \(-0.384307\pi\) | ||||
0.355512 | + | 0.934672i | \(0.384307\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −968.000 | −0.344823 | −0.172411 | − | 0.985025i | \(-0.555156\pi\) | ||||
−0.172411 | + | 0.985025i | \(0.555156\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1239.00 | 0.434788 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 528.000 | 0.182553 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1980.00 | −0.674581 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3850.00 | −1.29272 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −484.000 | −0.160187 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2948.00 | 0.961842 | 0.480921 | − | 0.876764i | \(-0.340302\pi\) | ||||
0.480921 | + | 0.876764i | \(0.340302\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2555.00 | 0.821905 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4878.00 | 1.54733 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 318.000 | 0.0994804 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3696.00 | 1.14042 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1995.00 | −0.599081 | −0.299541 | − | 0.954084i | \(-0.596833\pi\) | ||||
−0.299541 | + | 0.954084i | \(0.596833\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −968.000 | −0.286815 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6026.00 | 1.76194 | 0.880968 | − | 0.473175i | \(-0.156892\pi\) | ||||
0.880968 | + | 0.473175i | \(0.156892\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4417.00 | −1.27460 | −0.637300 | − | 0.770615i | \(-0.719949\pi\) | ||||
−0.637300 | + | 0.770615i | \(0.719949\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 154.000 | 0.0438634 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5808.00 | 1.63302 | 0.816512 | − | 0.577328i | \(-0.195905\pi\) | ||||
0.816512 | + | 0.577328i | \(0.195905\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2376.00 | 0.659545 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4802.00 | 1.31613 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −626.000 | −0.169425 | −0.0847125 | − | 0.996405i | \(-0.526997\pi\) | ||||
−0.0847125 | + | 0.996405i | \(0.526997\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3520.00 | −0.940843 | −0.470421 | − | 0.882442i | \(-0.655898\pi\) | ||||
−0.470421 | + | 0.882442i | \(0.655898\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4928.00 | 1.30095 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3051.00 | −0.795597 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4886.00 | 1.24352 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3921.00 | −0.986021 | −0.493011 | − | 0.870023i | \(-0.664104\pi\) | ||||
−0.493011 | + | 0.870023i | \(0.664104\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1925.00 | −0.478355 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2394.00 | 0.587914 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4598.00 | 1.11601 | 0.558007 | − | 0.829837i | \(-0.311566\pi\) | ||||
0.558007 | + | 0.829837i | \(0.311566\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 346.000 | 0.0830092 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5808.00 | −1.37742 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5838.00 | 1.36877 | 0.684385 | − | 0.729121i | \(-0.260071\pi\) | ||||
0.684385 | + | 0.729121i | \(0.260071\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6138.00 | 1.42285 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6769.00 | −1.55152 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5038.00 | −1.14190 | −0.570952 | − | 0.820983i | \(-0.693426\pi\) | ||||
−0.570952 | + | 0.820983i | \(0.693426\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8096.00 | 1.81475 | 0.907374 | − | 0.420323i | \(-0.138083\pi\) | ||||
0.907374 | + | 0.420323i | \(0.138083\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −484.000 | −0.106132 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7014.00 | 1.52141 | 0.760705 | − | 0.649098i | \(-0.224854\pi\) | ||||
0.760705 | + | 0.649098i | \(0.224854\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3498.00 | −0.750609 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4362.00 | −0.926032 | −0.463016 | − | 0.886350i | \(-0.653233\pi\) | ||||
−0.463016 | + | 0.886350i | \(0.653233\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4620.00 | −0.970426 | −0.485213 | − | 0.874396i | \(-0.661258\pi\) | ||||
−0.485213 | + | 0.874396i | \(0.661258\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2772.00 | 0.576137 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 440.000 | 0.0904961 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3469.00 | −0.706086 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7889.00 | 1.58921 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7172.00 | −1.43001 | −0.715005 | − | 0.699120i | \(-0.753575\pi\) | ||||
−0.715005 | + | 0.699120i | \(0.753575\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3789.00 | −0.747811 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 385.000 | 0.0752187 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1084.00 | −0.207577 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3570.00 | −0.676868 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2772.00 | 0.520407 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7348.00 | −1.36603 | −0.683017 | − | 0.730402i | \(-0.739333\pi\) | ||||
−0.683017 | + | 0.730402i | \(0.739333\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7392.00 | −1.36089 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5508.00 | 1.00428 | 0.502138 | − | 0.864787i | \(-0.332547\pi\) | ||||
0.502138 | + | 0.864787i | \(0.332547\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7009.00 | −1.26573 | −0.632863 | − | 0.774264i | \(-0.718120\pi\) | ||||
−0.632863 | + | 0.774264i | \(0.718120\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −396.000 | −0.0708320 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 853.000 | 0.151133 | 0.0755666 | − | 0.997141i | \(-0.475923\pi\) | ||||
0.0755666 | + | 0.997141i | \(0.475923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2904.00 | −0.509695 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7322.00 | 1.27313 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1672.00 | 0.288027 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1750.00 | −0.295949 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −528.000 | −0.0884790 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3631.00 | −0.602954 | −0.301477 | − | 0.953473i | \(-0.597480\pi\) | ||||
−0.301477 | + | 0.953473i | \(0.597480\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3806.00 | −0.626329 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1593.00 | −0.259806 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11574.0 | 1.87085 | 0.935424 | − | 0.353527i | \(-0.115018\pi\) | ||||
0.935424 | + | 0.353527i | \(0.115018\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9807.00 | −1.57122 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1749.00 | −0.277753 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1364.00 | 0.214720 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11025.0 | 1.72048 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1056.00 | 0.163369 | 0.0816845 | − | 0.996658i | \(-0.473970\pi\) | ||||
0.0816845 | + | 0.996658i | \(0.473970\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6810.00 | 1.04450 | 0.522251 | − | 0.852792i | \(-0.325093\pi\) | ||||
0.522251 | + | 0.852792i | \(0.325093\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9923.00 | 1.49617 | 0.748085 | − | 0.663603i | \(-0.230974\pi\) | ||||
0.748085 | + | 0.663603i | \(0.230974\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3285.00 | −0.491126 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −532.000 | −0.0788695 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2200.00 | 0.323431 | 0.161715 | − | 0.986837i | \(-0.448297\pi\) | ||||
0.161715 | + | 0.986837i | \(0.448297\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4923.00 | −0.717743 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −847.000 | −0.122468 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4752.00 | −0.681455 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8935.00 | −1.27085 | −0.635427 | − | 0.772161i | \(-0.719176\pi\) | ||||
−0.635427 | + | 0.772161i | \(0.719176\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4840.00 | −0.682819 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1364.00 | −0.190877 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9122.00 | 1.26627 | 0.633136 | − | 0.774041i | \(-0.281767\pi\) | ||||
0.633136 | + | 0.774041i | \(0.281767\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10647.0 | 1.46616 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8963.00 | −1.21477 | −0.607386 | − | 0.794407i | \(-0.707782\pi\) | ||||
−0.607386 | + | 0.794407i | \(0.707782\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −924.000 | −0.124247 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1721.00 | 0.229606 | 0.114803 | − | 0.993388i | \(-0.463376\pi\) | ||||
0.114803 | + | 0.993388i | \(0.463376\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −198.000 | −0.0262104 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11924.0 | 1.56623 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7351.00 | −0.958125 | −0.479062 | − | 0.877781i | \(-0.659023\pi\) | ||||
−0.479062 | + | 0.877781i | \(0.659023\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6650.00 | 0.860115 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14378.0 | −1.84548 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6174.00 | −0.786450 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8338.00 | −1.05409 | −0.527043 | − | 0.849839i | \(-0.676699\pi\) | ||||
−0.527043 | + | 0.849839i | \(0.676699\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −616.000 | −0.0772897 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11814.0 | −1.47123 | −0.735615 | − | 0.677400i | \(-0.763107\pi\) | ||||
−0.735615 | + | 0.677400i | \(0.763107\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7551.00 | −0.926450 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1903.00 | −0.231765 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7278.00 | −0.879887 | −0.439944 | − | 0.898025i | \(-0.645002\pi\) | ||||
−0.439944 | + | 0.898025i | \(0.645002\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6223.00 | −0.746856 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 842.000 | 0.100320 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6282.00 | −0.743063 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18466.0 | 2.16855 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3828.00 | 0.446325 | 0.223162 | − | 0.974781i | \(-0.428362\pi\) | ||||
0.223162 | + | 0.974781i | \(0.428362\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15466.0 | −1.79042 | −0.895210 | − | 0.445645i | \(-0.852974\pi\) | ||||
−0.895210 | + | 0.445645i | \(0.852974\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5808.00 | 0.667600 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1672.00 | 0.190833 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −616.000 | −0.0698134 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2710.00 | 0.302868 | 0.151434 | − | 0.988467i | \(-0.451611\pi\) | ||||
0.151434 | + | 0.988467i | \(0.451611\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3347.00 | −0.371470 | −0.185735 | − | 0.982600i | \(-0.559467\pi\) | ||||
−0.185735 | + | 0.982600i | \(0.559467\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16632.0 | 1.83320 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7700.00 | 0.842885 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2464.00 | −0.267882 | −0.133941 | − | 0.990989i | \(-0.542763\pi\) | ||||
−0.133941 | + | 0.990989i | \(0.542763\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7458.00 | −0.805313 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5955.00 | 0.638669 | 0.319335 | − | 0.947642i | \(-0.396541\pi\) | ||||
0.319335 | + | 0.947642i | \(0.396541\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8703.00 | 0.927105 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23366.0 | −2.47242 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13173.0 | −1.38457 | −0.692285 | − | 0.721624i | \(-0.743396\pi\) | ||||
−0.692285 | + | 0.721624i | \(0.743396\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2420.00 | −0.252668 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3010.00 | −0.312190 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6292.00 | −0.644042 | −0.322021 | − | 0.946732i | \(-0.604362\pi\) | ||||
−0.322021 | + | 0.946732i | \(0.604362\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1330.00 | −0.135249 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10164.0 | 1.02686 | 0.513432 | − | 0.858130i | \(-0.328374\pi\) | ||||
0.513432 | + | 0.858130i | \(0.328374\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5677.00 | −0.569833 | −0.284916 | − | 0.958552i | \(-0.591966\pi\) | ||||
−0.284916 | + | 0.958552i | \(0.591966\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10017.0 | 0.998983 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6675.00 | 0.661418 | 0.330709 | − | 0.943733i | \(-0.392712\pi\) | ||||
0.330709 | + | 0.943733i | \(0.392712\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 354.000 | 0.0348533 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8113.00 | 0.793689 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5962.00 | 0.579562 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1936.00 | 0.187010 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15004.0 | 1.44022 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6424.00 | −0.612777 | −0.306388 | − | 0.951907i | \(-0.599121\pi\) | ||||
−0.306388 | + | 0.951907i | \(0.599121\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2450.00 | −0.230805 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10143.0 | −0.949629 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21369.0 | 1.98834 | 0.994170 | − | 0.107822i | \(-0.0343876\pi\) | ||||
0.994170 | + | 0.107822i | \(0.0343876\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7084.00 | 0.655112 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1848.00 | −0.169856 | −0.0849278 | − | 0.996387i | \(-0.527066\pi\) | ||||
−0.0849278 | + | 0.996387i | \(0.527066\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10032.0 | 0.916468 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2178.00 | 0.197765 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 730.000 | 0.0658853 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19228.0 | 1.72498 | 0.862488 | − | 0.506077i | \(-0.168905\pi\) | ||||
0.862488 | + | 0.506077i | \(0.168905\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11088.0 | 0.988773 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10878.0 | −0.964266 | −0.482133 | − | 0.876098i | \(-0.660138\pi\) | ||||
−0.482133 | + | 0.876098i | \(0.660138\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4590.00 | 0.404460 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15379.0 | 1.34715 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10047.0 | 0.874903 | 0.437451 | − | 0.899242i | \(-0.355881\pi\) | ||||
0.437451 | + | 0.899242i | \(0.355881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1056.00 | 0.0914182 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1540.00 | −0.132539 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9504.00 | 0.813197 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2904.00 | 0.247036 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3318.00 | −0.280624 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5827.00 | −0.489991 | −0.244996 | − | 0.969524i | \(-0.578787\pi\) | ||||
−0.244996 | + | 0.969524i | \(0.578787\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −836.000 | −0.0698962 | −0.0349481 | − | 0.999389i | \(-0.511127\pi\) | ||||
−0.0349481 | + | 0.999389i | \(0.511127\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −616.000 | −0.0512085 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6042.00 | 0.499419 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18458.0 | 1.51705 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9262.00 | −0.756943 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9414.00 | −0.760753 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11655.0 | 0.936593 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3729.00 | −0.297995 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7172.00 | −0.569960 | −0.284980 | − | 0.958533i | \(-0.591987\pi\) | ||||
−0.284980 | + | 0.958533i | \(0.591987\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17801.0 | −1.40684 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2250.00 | 0.176843 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11264.0 | 0.880464 | 0.440232 | − | 0.897884i | \(-0.354896\pi\) | ||||
0.440232 | + | 0.897884i | \(0.354896\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6776.00 | 0.526763 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11616.0 | 0.898109 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1372.00 | 0.105503 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10899.0 | 0.833580 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 306.000 | 0.0232776 | 0.0116388 | − | 0.999932i | \(-0.496295\pi\) | ||||
0.0116388 | + | 0.999932i | \(0.496295\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2926.00 | 0.220206 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23804.0 | −1.78192 | −0.890958 | − | 0.454085i | \(-0.849966\pi\) | ||||
−0.890958 | + | 0.454085i | \(0.849966\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12609.0 | 0.938875 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1678.00 | 0.124285 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4664.00 | −0.343629 | −0.171815 | − | 0.985129i | \(-0.554963\pi\) | ||||
−0.171815 | + | 0.985129i | \(0.554963\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11572.0 | −0.848114 | −0.424057 | − | 0.905635i | \(-0.639394\pi\) | ||||
−0.424057 | + | 0.905635i | \(0.639394\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11417.0 | −0.832377 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7700.00 | 0.558456 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24407.0 | −1.76096 | −0.880482 | − | 0.474079i | \(-0.842781\pi\) | ||||
−0.880482 | + | 0.474079i | \(0.842781\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3388.00 | −0.243179 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1396.00 | 0.0996830 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7502.00 | 0.532935 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18436.0 | −1.29631 | −0.648156 | − | 0.761508i | \(-0.724460\pi\) | ||||
−0.648156 | + | 0.761508i | \(0.724460\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6996.00 | 0.489415 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13762.0 | −0.957856 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11044.0 | −0.764794 | −0.382397 | − | 0.923998i | \(-0.624901\pi\) | ||||
−0.382397 | + | 0.923998i | \(0.624901\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 684.000 | 0.0471282 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6776.00 | 0.464528 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8800.00 | −0.600264 | −0.300132 | − | 0.953898i | \(-0.597031\pi\) | ||||
−0.300132 | + | 0.953898i | \(0.597031\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10826.0 | −0.734778 | −0.367389 | − | 0.930067i | \(-0.619748\pi\) | ||||
−0.367389 | + | 0.930067i | \(0.619748\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3894.00 | −0.262978 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1089.00 | 0.0731804 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4066.00 | −0.271884 | −0.135942 | − | 0.990717i | \(-0.543406\pi\) | ||||
−0.135942 | + | 0.990717i | \(0.543406\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3696.00 | −0.245927 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4752.00 | 0.313102 | 0.156551 | − | 0.987670i | \(-0.449962\pi\) | ||||
0.156551 | + | 0.987670i | \(0.449962\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13860.0 | 0.908763 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3806.00 | −0.248337 | −0.124168 | − | 0.992261i | \(-0.539626\pi\) | ||||
−0.124168 | + | 0.992261i | \(0.539626\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5185.00 | 0.336676 | 0.168338 | − | 0.985729i | \(-0.446160\pi\) | ||||
0.168338 | + | 0.985729i | \(0.446160\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6125.00 | −0.395794 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1934.00 | −0.124373 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8189.00 | −0.524096 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3388.00 | 0.215795 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6574.00 | 0.416729 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13049.0 | 0.823253 | 0.411626 | − | 0.911353i | \(-0.364961\pi\) | ||||
0.411626 | + | 0.911353i | \(0.364961\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20636.0 | −1.29575 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1188.00 | 0.0742431 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8030.00 | −0.497123 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9959.00 | 0.613661 | 0.306831 | − | 0.951764i | \(-0.400731\pi\) | ||||
0.306831 | + | 0.951764i | \(0.400731\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12197.0 | −0.748060 | −0.374030 | − | 0.927417i | \(-0.622024\pi\) | ||||
−0.374030 | + | 0.927417i | \(0.622024\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −34146.0 | −2.08449 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5759.00 | 0.349938 | 0.174969 | − | 0.984574i | \(-0.444018\pi\) | ||||
0.174969 | + | 0.984574i | \(0.444018\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4631.00 | −0.280097 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2226.00 | −0.134015 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25209.0 | −1.51073 | −0.755363 | − | 0.655306i | \(-0.772540\pi\) | ||||
−0.755363 | + | 0.655306i | \(0.772540\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18486.0 | 1.10276 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11616.0 | −0.689777 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4062.00 | 0.240111 | 0.120055 | − | 0.992767i | \(-0.461693\pi\) | ||||
0.120055 | + | 0.992767i | \(0.461693\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31173.0 | 1.83433 | 0.917163 | − | 0.398513i | \(-0.130474\pi\) | ||||
0.917163 | + | 0.398513i | \(0.130474\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 792.000 | 0.0461841 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 46200.0 | 2.68197 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13965.0 | 0.807052 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3388.00 | 0.194921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26690.0 | −1.52871 | −0.764357 | − | 0.644794i | \(-0.776943\pi\) | ||||
−0.764357 | + | 0.644794i | \(0.776943\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1540.00 | −0.0878143 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7398.00 | −0.419983 | −0.209991 | − | 0.977703i | \(-0.567344\pi\) | ||||
−0.209991 | + | 0.977703i | \(0.567344\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2254.00 | 0.127394 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42182.0 | −2.37359 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27960.0 | −1.56641 | −0.783206 | − | 0.621762i | \(-0.786417\pi\) | ||||
−0.783206 | + | 0.621762i | \(0.786417\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8001.00 | 0.446281 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 30919.0 | 1.71708 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19465.0 | −1.07161 | −0.535806 | − | 0.844341i | \(-0.679992\pi\) | ||||
−0.535806 | + | 0.844341i | \(0.679992\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −484.000 | −0.0265305 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23742.0 | −1.29581 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8360.00 | 0.454315 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −40656.0 | −2.19993 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13518.0 | 0.728342 | 0.364171 | − | 0.931332i | \(-0.381352\pi\) | ||||
0.364171 | + | 0.931332i | \(0.381352\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7612.00 | 0.408381 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16632.0 | −0.888507 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1020.00 | −0.0542589 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14727.0 | 0.780090 | 0.390045 | − | 0.920796i | \(-0.372459\pi\) | ||||
0.390045 | + | 0.920796i | \(0.372459\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15092.0 | −0.796054 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27825.0 | 1.46151 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4382.00 | 0.228241 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15711.0 | −0.814912 | −0.407456 | − | 0.913225i | \(-0.633584\pi\) | ||||
−0.407456 | + | 0.913225i | \(0.633584\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2112.00 | −0.109092 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24640.0 | 1.26746 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11616.0 | 0.595045 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12099.0 | −0.617231 | −0.308616 | − | 0.951187i | \(-0.599866\pi\) | ||||
−0.308616 | + | 0.951187i | \(0.599866\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11843.0 | −0.601687 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20596.0 | −1.04209 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9812.00 | 0.494426 | 0.247213 | − | 0.968961i | \(-0.420485\pi\) | ||||
0.247213 | + | 0.968961i | \(0.420485\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21357.0 | 1.07179 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1947.00 | −0.0973116 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11854.0 | 0.590063 | 0.295031 | − | 0.955488i | \(-0.404670\pi\) | ||||
0.295031 | + | 0.955488i | \(0.404670\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18788.0 | −0.927678 | −0.463839 | − | 0.885919i | \(-0.653528\pi\) | ||||
−0.463839 | + | 0.885919i | \(0.653528\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30042.0 | 1.47739 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15356.0 | −0.752137 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2092.00 | 0.102056 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16559.0 | 0.804589 | 0.402295 | − | 0.915510i | \(-0.368213\pi\) | ||||
0.402295 | + | 0.915510i | \(0.368213\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 27447.0 | 1.32832 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3870.00 | 0.186548 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26610.0 | 1.27762 | 0.638809 | − | 0.769365i | \(-0.279427\pi\) | ||||
0.638809 | + | 0.769365i | \(0.279427\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13475.0 | 0.644416 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7040.00 | 0.335348 | 0.167674 | − | 0.985843i | \(-0.446374\pi\) | ||||
0.167674 | + | 0.985843i | \(0.446374\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −500.000 | −0.0237237 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7524.00 | −0.355596 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18128.0 | −0.850081 | −0.425041 | − | 0.905174i | \(-0.639740\pi\) | ||||
−0.425041 | + | 0.905174i | \(0.639740\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −32186.0 | −1.50344 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9570.00 | 0.445290 | 0.222645 | − | 0.974900i | \(-0.428531\pi\) | ||||
0.222645 | + | 0.974900i | \(0.428531\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6996.00 | 0.324263 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2422.00 | −0.111826 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9680.00 | 0.445214 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4015.00 | −0.183954 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9240.00 | −0.421725 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10431.0 | −0.474265 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16280.0 | 0.737382 | 0.368691 | − | 0.929552i | \(-0.379806\pi\) | ||||
0.368691 | + | 0.929552i | \(0.379806\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −40866.0 | −1.84394 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2802.00 | −0.125952 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −42966.0 | −1.91679 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −603.000 | −0.0267997 | −0.0133998 | − | 0.999910i | \(-0.504265\pi\) | ||||
−0.0133998 | + | 0.999910i | \(0.504265\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10032.0 | −0.444189 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21274.0 | 0.938427 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5808.00 | −0.255243 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3150.00 | 0.137917 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35266.0 | 1.53832 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23276.0 | 1.01155 | 0.505773 | − | 0.862667i | \(-0.331207\pi\) | ||||
0.505773 | + | 0.862667i | \(0.331207\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45662.0 | 1.97708 | 0.988539 | − | 0.150968i | \(-0.0482390\pi\) | ||||
0.988539 | + | 0.150968i | \(0.0482390\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −56672.0 | −2.44474 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9108.00 | −0.391459 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23848.0 | −1.02122 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33222.0 | 1.41225 | 0.706124 | − | 0.708088i | \(-0.250442\pi\) | ||||
0.706124 | + | 0.708088i | \(0.250442\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3569.00 | 0.151163 | 0.0755817 | − | 0.997140i | \(-0.475919\pi\) | ||||
0.0755817 | + | 0.997140i | \(0.475919\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3388.00 | 0.142976 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41008.0 | 1.72429 | 0.862145 | − | 0.506662i | \(-0.169121\pi\) | ||||
0.862145 | + | 0.506662i | \(0.169121\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17839.0 | −0.747375 | −0.373688 | − | 0.927555i | \(-0.621907\pi\) | ||||
−0.373688 | + | 0.927555i | \(0.621907\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −49098.0 | −2.04957 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12882.0 | 0.535816 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14256.0 | −0.590837 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5565.00 | −0.229814 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20731.0 | −0.853056 | −0.426528 | − | 0.904474i | \(-0.640263\pi\) | ||||
−0.426528 | + | 0.904474i | \(0.640263\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 45307.0 | 1.85768 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30534.0 | 1.24751 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19773.0 | −0.804984 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −242.000 | −0.00981726 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 32340.0 | 1.30731 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 30275.0 | 1.21952 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9102.00 | 0.365354 | 0.182677 | − | 0.983173i | \(-0.441524\pi\) | ||||
0.182677 | + | 0.983173i | \(0.441524\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8712.00 | −0.348473 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12936.0 | 0.515619 | 0.257809 | − | 0.966196i | \(-0.416999\pi\) | ||||
0.257809 | + | 0.966196i | \(0.416999\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15113.0 | −0.600290 | −0.300145 | − | 0.953894i | \(-0.597035\pi\) | ||||
−0.300145 | + | 0.953894i | \(0.597035\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3080.00 | −0.121912 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29216.0 | −1.15240 | −0.576202 | − | 0.817308i | \(-0.695466\pi\) | ||||
−0.576202 | + | 0.817308i | \(0.695466\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4266.00 | 0.167686 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24283.0 | 0.951204 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7546.00 | −0.294569 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −24794.0 | −0.961225 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3042.00 | 0.117530 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29304.0 | 1.12831 | 0.564154 | − | 0.825670i | \(-0.309202\pi\) | ||||
0.564154 | + | 0.825670i | \(0.309202\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 50204.0 | 1.92644 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23715.0 | −0.906900 | −0.453450 | − | 0.891282i | \(-0.649807\pi\) | ||||
−0.453450 | + | 0.891282i | \(0.649807\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6028.00 | −0.229738 | −0.114869 | − | 0.993381i | \(-0.536645\pi\) | ||||
−0.114869 | + | 0.993381i | \(0.536645\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 26523.0 | 1.00741 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18786.0 | −0.711130 | −0.355565 | − | 0.934652i | \(-0.615712\pi\) | ||||
−0.355565 | + | 0.934652i | \(0.615712\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −264.000 | −0.00995982 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9229.00 | −0.347007 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11616.0 | −0.435291 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14985.0 | −0.559657 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 41976.0 | 1.55726 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25916.0 | −0.958254 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7588.00 | 0.279638 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22887.0 | 0.840652 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2156.00 | 0.0789292 | 0.0394646 | − | 0.999221i | \(-0.487435\pi\) | ||||
0.0394646 | + | 0.999221i | \(0.487435\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11220.0 | 0.409399 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51732.0 | 1.88140 | 0.940701 | − | 0.339236i | \(-0.110169\pi\) | ||||
0.940701 | + | 0.339236i | \(0.110169\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7678.00 | −0.278318 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −19404.0 | −0.701067 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4108.00 | −0.147937 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18254.0 | 0.655216 | 0.327608 | − | 0.944814i | \(-0.393757\pi\) | ||||
0.327608 | + | 0.944814i | \(0.393757\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 51436.0 | 1.84025 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7612.00 | 0.270574 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23232.0 | 0.823127 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5610.00 | 0.198125 | 0.0990625 | − | 0.995081i | \(-0.468416\pi\) | ||||
0.0990625 | + | 0.995081i | \(0.468416\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14916.0 | 0.525083 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −38556.0 | −1.35291 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3762.00 | −0.131583 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37180.0 | −1.29628 | −0.648142 | − | 0.761520i | \(-0.724454\pi\) | ||||
−0.648142 | + | 0.761520i | \(0.724454\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 49063.0 | 1.70512 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31278.0 | −1.08356 | −0.541782 | − | 0.840519i | \(-0.682250\pi\) | ||||
−0.541782 | + | 0.840519i | \(0.682250\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38500.0 | 1.32951 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −630.000 | −0.0216867 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47475.0 | 1.62907 | 0.814535 | − | 0.580114i | \(-0.196992\pi\) | ||||
0.814535 | + | 0.580114i | \(0.196992\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5971.00 | −0.203599 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20462.0 | 0.695519 | 0.347759 | − | 0.937584i | \(-0.386943\pi\) | ||||
0.347759 | + | 0.937584i | \(0.386943\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14679.0 | 0.497384 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20328.0 | 0.686636 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1778.00 | −0.0598693 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4510.00 | −0.151388 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23012.0 | −0.770043 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4356.00 | 0.145310 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52360.0 | −1.74125 | −0.870623 | − | 0.491952i | \(-0.836284\pi\) | ||||
−0.870623 | + | 0.491952i | \(0.836284\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11704.0 | −0.388015 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −56247.0 | −1.85896 | −0.929481 | − | 0.368870i | \(-0.879745\pi\) | ||||
−0.929481 | + | 0.368870i | \(0.879745\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5276.00 | 0.173834 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18155.0 | −0.594503 | −0.297252 | − | 0.954799i | \(-0.596070\pi\) | ||||
−0.297252 | + | 0.954799i | \(0.596070\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10637.0 | 0.347252 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5500.00 | 0.179003 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1191.00 | −0.0386439 | −0.0193220 | − | 0.999813i | \(-0.506151\pi\) | ||||
−0.0193220 | + | 0.999813i | \(0.506151\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17694.0 | 0.572363 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3696.00 | 0.119195 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −94850.0 | −3.04960 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28864.0 | −0.925222 | −0.462611 | − | 0.886561i | \(-0.653087\pi\) | ||||
−0.462611 | + | 0.886561i | \(0.653087\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25417.0 | 0.812270 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8712.00 | −0.277577 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51610.0 | 1.63942 | 0.819712 | − | 0.572776i | \(-0.194134\pi\) | ||||
0.819712 | + | 0.572776i | \(0.194134\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6055.00 | −0.191763 |
(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 | 176.4.a.a.1.1 | 1 | ||
3.2 | odd | 2 | 1584.4.a.g.1.1 | 1 | |||
4.3 | odd | 2 | 88.4.a.b.1.1 | ✓ | 1 | ||
8.3 | odd | 2 | 704.4.a.a.1.1 | 1 | |||
8.5 | even | 2 | 704.4.a.k.1.1 | 1 | |||
11.10 | odd | 2 | 1936.4.a.b.1.1 | 1 | |||
12.11 | even | 2 | 792.4.a.b.1.1 | 1 | |||
20.19 | odd | 2 | 2200.4.a.a.1.1 | 1 | |||
44.43 | even | 2 | 968.4.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
88.4.a.b.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
176.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
704.4.a.a.1.1 | 1 | 8.3 | odd | 2 | |||
704.4.a.k.1.1 | 1 | 8.5 | even | 2 | |||
792.4.a.b.1.1 | 1 | 12.11 | even | 2 | |||
968.4.a.e.1.1 | 1 | 44.43 | even | 2 | |||
1584.4.a.g.1.1 | 1 | 3.2 | odd | 2 | |||
1936.4.a.b.1.1 | 1 | 11.10 | odd | 2 | |||
2200.4.a.a.1.1 | 1 | 20.19 | odd | 2 |