Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 | ||||||||
\(3\) | −3.32921 | −1.92212 | −0.961060 | − | 0.276341i | \(-0.910878\pi\) | ||||
−0.961060 | + | 0.276341i | \(0.910878\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.52319 | −1.33164 | −0.665820 | − | 0.746112i | \(-0.731918\pi\) | ||||
−0.665820 | + | 0.746112i | \(0.731918\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.08363 | 2.69454 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.52528 | −1.66593 | −0.832967 | − | 0.553323i | \(-0.813360\pi\) | ||||
−0.832967 | + | 0.553323i | \(0.813360\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.73778 | 0.481973 | 0.240986 | − | 0.970529i | \(-0.422529\pi\) | ||||
0.240986 | + | 0.970529i | \(0.422529\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.32921 | −0.859598 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.387977 | −0.0940983 | −0.0470491 | − | 0.998893i | \(-0.514982\pi\) | ||||
−0.0470491 | + | 0.998893i | \(0.514982\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.59581 | −1.28377 | −0.641884 | − | 0.766802i | \(-0.721847\pi\) | ||||
−0.641884 | + | 0.766802i | \(0.721847\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.7294 | 2.55957 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.11555 | 1.48370 | 0.741848 | − | 0.670569i | \(-0.233950\pi\) | ||||
0.741848 | + | 0.670569i | \(0.233950\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −16.9245 | −3.25712 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.31070 | −1.17187 | −0.585934 | − | 0.810359i | \(-0.699272\pi\) | ||||
−0.585934 | + | 0.810359i | \(0.699272\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.522093 | 0.0937706 | 0.0468853 | − | 0.998900i | \(-0.485070\pi\) | ||||
0.0468853 | + | 0.998900i | \(0.485070\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 18.3948 | 3.20212 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.52319 | −0.595528 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.36068 | −1.04569 | −0.522845 | − | 0.852428i | \(-0.675129\pi\) | ||||
−0.522845 | + | 0.852428i | \(0.675129\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.78542 | −0.926409 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.378927 | −0.0591784 | −0.0295892 | − | 0.999562i | \(-0.509420\pi\) | ||||
−0.0295892 | + | 0.999562i | \(0.509420\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.24950 | 1.10554 | 0.552770 | − | 0.833334i | \(-0.313571\pi\) | ||||
0.552770 | + | 0.833334i | \(0.313571\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.08363 | 1.20504 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.5319 | −1.53623 | −0.768117 | − | 0.640309i | \(-0.778806\pi\) | ||||
−0.768117 | + | 0.640309i | \(0.778806\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.41286 | 0.773266 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.29166 | 0.180868 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.65036 | 0.364055 | 0.182028 | − | 0.983293i | \(-0.441734\pi\) | ||||
0.182028 | + | 0.983293i | \(0.441734\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.52528 | −0.745028 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.6296 | 2.46755 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.27360 | 0.295997 | 0.147998 | − | 0.988988i | \(-0.452717\pi\) | ||||
0.147998 | + | 0.988988i | \(0.452717\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.4098 | −1.58891 | −0.794456 | − | 0.607322i | \(-0.792244\pi\) | ||||
−0.794456 | + | 0.607322i | \(0.792244\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −28.4802 | −3.58816 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.73778 | 0.215545 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.90341 | −0.354708 | −0.177354 | − | 0.984147i | \(-0.556754\pi\) | ||||
−0.177354 | + | 0.984147i | \(0.556754\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −23.6892 | −2.85184 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.08172 | −0.247055 | −0.123527 | − | 0.992341i | \(-0.539421\pi\) | ||||
−0.123527 | + | 0.992341i | \(0.539421\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.92974 | −0.694024 | −0.347012 | − | 0.937861i | \(-0.612804\pi\) | ||||
−0.347012 | + | 0.937861i | \(0.612804\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.32921 | −0.384424 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 19.4666 | 2.21842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.08975 | −0.910168 | −0.455084 | − | 0.890448i | \(-0.650391\pi\) | ||||
−0.455084 | + | 0.890448i | \(0.650391\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 32.0942 | 3.56602 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.29939 | 0.471919 | 0.235960 | − | 0.971763i | \(-0.424177\pi\) | ||||
0.235960 | + | 0.971763i | \(0.424177\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.387977 | −0.0420820 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21.0096 | 2.25247 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.2803 | −1.08971 | −0.544854 | − | 0.838531i | \(-0.683415\pi\) | ||||
−0.544854 | + | 0.838531i | \(0.683415\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.12252 | −0.641814 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.73816 | −0.180238 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.59581 | −0.574118 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.85465 | −0.391380 | −0.195690 | − | 0.980666i | \(-0.562695\pi\) | ||||
−0.195690 | + | 0.980666i | \(0.562695\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −44.6643 | −4.48893 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.96394 | −0.792442 | −0.396221 | − | 0.918155i | \(-0.629679\pi\) | ||||
−0.396221 | + | 0.918155i | \(0.629679\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.73166 | 0.958889 | 0.479444 | − | 0.877572i | \(-0.340838\pi\) | ||||
0.479444 | + | 0.877572i | \(0.340838\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.7294 | 1.14468 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.6679 | −1.12798 | −0.563990 | − | 0.825782i | \(-0.690734\pi\) | ||||
−0.563990 | + | 0.825782i | \(0.690734\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.42609 | 0.711290 | 0.355645 | − | 0.934621i | \(-0.384261\pi\) | ||||
0.355645 | + | 0.934621i | \(0.384261\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.1760 | 2.00994 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.2159 | 1.05510 | 0.527550 | − | 0.849524i | \(-0.323111\pi\) | ||||
0.527550 | + | 0.849524i | \(0.323111\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.11555 | 0.663529 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.0475 | 1.29870 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.36692 | 0.125305 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.5287 | 1.77534 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.26153 | 0.113748 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.0569 | 1.77976 | 0.889879 | − | 0.456197i | \(-0.150789\pi\) | ||||
0.889879 | + | 0.456197i | \(0.150789\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −24.1351 | −2.12498 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.7178 | −1.19853 | −0.599264 | − | 0.800552i | \(-0.704540\pi\) | ||||
−0.599264 | + | 0.800552i | \(0.704540\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.7151 | 1.70952 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.9245 | −1.45663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.6918 | −0.913466 | −0.456733 | − | 0.889604i | \(-0.650981\pi\) | ||||
−0.456733 | + | 0.889604i | \(0.650981\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.0365 | −0.851283 | −0.425641 | − | 0.904892i | \(-0.639951\pi\) | ||||
−0.425641 | + | 0.904892i | \(0.639951\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 35.0629 | 2.95283 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.60170 | −0.802935 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.31070 | −0.524075 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −18.0205 | −1.48631 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.350067 | 0.0286786 | 0.0143393 | − | 0.999897i | \(-0.495435\pi\) | ||||
0.0143393 | + | 0.999897i | \(0.495435\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.2194 | −0.994397 | −0.497198 | − | 0.867637i | \(-0.665638\pi\) | ||||
−0.497198 | + | 0.867637i | \(0.665638\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.13626 | −0.253552 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.522093 | 0.0419355 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.78816 | −0.302328 | −0.151164 | − | 0.988509i | \(-0.548302\pi\) | ||||
−0.151164 | + | 0.988509i | \(0.548302\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.82361 | −0.699758 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −25.0694 | −1.97575 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.3411 | −0.966632 | −0.483316 | − | 0.875446i | \(-0.660568\pi\) | ||||
−0.483316 | + | 0.875446i | \(0.660568\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 18.3948 | 1.43203 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.32443 | 0.257252 | 0.128626 | − | 0.991693i | \(-0.458943\pi\) | ||||
0.128626 | + | 0.991693i | \(0.458943\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.98013 | −0.767702 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −45.2345 | −3.45917 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.2332 | −1.15816 | −0.579081 | − | 0.815270i | \(-0.696588\pi\) | ||||
−0.579081 | + | 0.815270i | \(0.696588\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.52319 | −0.266328 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.56927 | −0.568942 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.6343 | −0.944329 | −0.472164 | − | 0.881511i | \(-0.656527\pi\) | ||||
−0.472164 | + | 0.881511i | \(0.656527\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.70222 | −0.423842 | −0.211921 | − | 0.977287i | \(-0.567972\pi\) | ||||
−0.211921 | + | 0.977287i | \(0.567972\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 41.3148 | 3.05408 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.36068 | −0.467647 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.14368 | 0.156761 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 59.6281 | 4.33731 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.7428 | 1.21147 | 0.605733 | − | 0.795668i | \(-0.292880\pi\) | ||||
0.605733 | + | 0.795668i | \(0.292880\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.8560 | 1.21332 | 0.606661 | − | 0.794961i | \(-0.292509\pi\) | ||||
0.606661 | + | 0.794961i | \(0.292509\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.78542 | −0.414303 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.1703 | −1.79331 | −0.896655 | − | 0.442730i | \(-0.854010\pi\) | ||||
−0.896655 | + | 0.442730i | \(0.854010\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.56757 | 0.607339 | 0.303669 | − | 0.952777i | \(-0.401788\pi\) | ||||
0.303669 | + | 0.952777i | \(0.401788\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.66605 | 0.681791 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 22.2338 | 1.56051 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.378927 | −0.0264654 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 57.5195 | 3.99788 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 30.9184 | 2.13867 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.0578 | −1.72505 | −0.862526 | − | 0.506012i | \(-0.831119\pi\) | ||||
−0.862526 | + | 0.506012i | \(0.831119\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.93048 | 0.474868 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.24950 | 0.494412 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.83943 | −0.124869 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.7414 | 1.33400 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.674218 | −0.0453528 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.6344 | −1.64964 | −0.824821 | − | 0.565394i | \(-0.808724\pi\) | ||||
−0.824821 | + | 0.565394i | \(0.808724\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.08363 | 0.538909 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.99145 | −0.530411 | −0.265206 | − | 0.964192i | \(-0.585440\pi\) | ||||
−0.265206 | + | 0.964192i | \(0.585440\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.67952 | −0.507477 | −0.253738 | − | 0.967273i | \(-0.581660\pi\) | ||||
−0.253738 | + | 0.967273i | \(0.581660\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −64.8084 | −4.26408 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.9288 | −1.04353 | −0.521764 | − | 0.853090i | \(-0.674726\pi\) | ||||
−0.521764 | + | 0.853090i | \(0.674726\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.5319 | −0.687025 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 26.9325 | 1.74945 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.51600 | 0.486170 | 0.243085 | − | 0.970005i | \(-0.421841\pi\) | ||||
0.243085 | + | 0.970005i | \(0.421841\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.7076 | −0.882981 | −0.441491 | − | 0.897266i | \(-0.645550\pi\) | ||||
−0.441491 | + | 0.897266i | \(0.645550\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −56.0749 | −3.59721 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.41286 | 0.345815 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.72427 | −0.618741 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.3136 | −0.907085 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.9123 | 1.13061 | 0.565307 | − | 0.824881i | \(-0.308758\pi\) | ||||
0.565307 | + | 0.824881i | \(0.308758\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −39.3154 | −2.47174 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.29166 | 0.0808867 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 30.3400 | 1.89255 | 0.946277 | − | 0.323357i | \(-0.104811\pi\) | ||||
0.946277 | + | 0.323357i | \(0.104811\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.4099 | 1.39248 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −51.0134 | −3.15765 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.83186 | −0.606258 | −0.303129 | − | 0.952950i | \(-0.598031\pi\) | ||||
−0.303129 | + | 0.952950i | \(0.598031\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.65036 | 0.162811 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 34.2252 | 2.09455 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.8472 | 1.51496 | 0.757479 | − | 0.652860i | \(-0.226431\pi\) | ||||
0.757479 | + | 0.652860i | \(0.226431\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.65273 | 0.100396 | 0.0501981 | − | 0.998739i | \(-0.484015\pi\) | ||||
0.0501981 | + | 0.998739i | \(0.484015\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 20.3831 | 1.23364 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.52528 | −0.333187 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 32.5275 | 1.95439 | 0.977194 | − | 0.212348i | \(-0.0681109\pi\) | ||||
0.977194 | + | 0.212348i | \(0.0681109\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.22040 | 0.252669 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.1653 | 1.44158 | 0.720790 | − | 0.693153i | \(-0.243779\pi\) | ||||
0.720790 | + | 0.693153i | \(0.243779\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.51886 | 0.506394 | 0.253197 | − | 0.967415i | \(-0.418518\pi\) | ||||
0.253197 | + | 0.967415i | \(0.418518\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.6296 | 1.10352 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.33503 | 0.0788044 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8495 | −0.991146 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.8329 | 0.752279 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.3056 | 0.952583 | 0.476291 | − | 0.879288i | \(-0.341981\pi\) | ||||
0.476291 | + | 0.879288i | \(0.341981\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.27360 | 0.132374 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 93.5124 | 5.42614 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.3652 | 0.715100 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.5414 | −1.47218 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 26.5136 | 1.52317 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.4098 | −0.710583 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.8430 | 1.76030 | 0.880152 | − | 0.474691i | \(-0.157440\pi\) | ||||
0.880152 | + | 0.474691i | \(0.157440\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −32.3987 | −1.84310 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.3602 | −0.870996 | −0.435498 | − | 0.900190i | \(-0.643428\pi\) | ||||
−0.435498 | + | 0.900190i | \(0.643428\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.36416 | −0.529293 | −0.264647 | − | 0.964345i | \(-0.585255\pi\) | ||||
−0.264647 | + | 0.964345i | \(0.585255\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −28.4802 | −1.60468 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.9725 | 0.616276 | 0.308138 | − | 0.951342i | \(-0.400294\pi\) | ||||
0.308138 | + | 0.951342i | \(0.400294\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.8684 | 1.95225 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 38.8449 | 2.16811 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.17105 | 0.120800 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.73778 | 0.0963945 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −24.7230 | −1.36719 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 37.1059 | 2.04571 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.5549 | −0.690079 | −0.345039 | − | 0.938588i | \(-0.612134\pi\) | ||||
−0.345039 | + | 0.938588i | \(0.612134\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −51.4174 | −2.81766 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.90341 | −0.158630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.75915 | −0.0958273 | −0.0479136 | − | 0.998851i | \(-0.515257\pi\) | ||||
−0.0479136 | + | 0.998851i | \(0.515257\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −37.3399 | −2.02803 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.88471 | −0.156216 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.59180 | 0.301929 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −23.6892 | −1.27538 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.9952 | 1.23445 | 0.617224 | − | 0.786788i | \(-0.288257\pi\) | ||||
0.617224 | + | 0.786788i | \(0.288257\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.9881 | 0.588182 | 0.294091 | − | 0.955777i | \(-0.404983\pi\) | ||||
0.294091 | + | 0.955777i | \(0.404983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −29.4110 | −1.56984 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.29570 | −0.494760 | −0.247380 | − | 0.968919i | \(-0.579570\pi\) | ||||
−0.247380 | + | 0.968919i | \(0.579570\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.08172 | −0.110486 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.55075 | −0.240851 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.92789 | 0.365640 | 0.182820 | − | 0.983146i | \(-0.441477\pi\) | ||||
0.182820 | + | 0.983146i | \(0.441477\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.3131 | 0.648058 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −65.0151 | −3.41241 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.92974 | −0.310377 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.8469 | −1.19260 | −0.596299 | − | 0.802762i | \(-0.703363\pi\) | ||||
−0.596299 | + | 0.802762i | \(0.703363\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.06310 | −0.159459 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.33773 | −0.484791 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.2536 | 1.77358 | 0.886791 | − | 0.462170i | \(-0.152929\pi\) | ||||
0.886791 | + | 0.462170i | \(0.152929\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.32921 | −0.171920 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.9666 | −0.564808 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.97208 | 0.306765 | 0.153383 | − | 0.988167i | \(-0.450983\pi\) | ||||
0.153383 | + | 0.988167i | \(0.450983\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −66.7735 | −3.42091 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.609099 | 0.0311235 | 0.0155617 | − | 0.999879i | \(-0.495046\pi\) | ||||
0.0155617 | + | 0.999879i | \(0.495046\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.4666 | 0.992110 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 58.6023 | 2.97892 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.5434 | −1.29510 | −0.647550 | − | 0.762023i | \(-0.724206\pi\) | ||||
−0.647550 | + | 0.762023i | \(0.724206\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.76067 | −0.139613 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 45.6693 | 2.30371 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.08975 | −0.407040 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.07445 | 0.355057 | 0.177528 | − | 0.984116i | \(-0.443190\pi\) | ||||
0.177528 | + | 0.984116i | \(0.443190\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −65.6357 | −3.28589 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.907280 | 0.0451949 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 32.0942 | 1.59477 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.1445 | 1.74205 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.3593 | −1.15504 | −0.577520 | − | 0.816376i | \(-0.695980\pi\) | ||||
−0.577520 | + | 0.816376i | \(0.695980\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 35.5954 | 1.75579 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.01031 | −0.394161 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.29939 | 0.211049 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 33.4135 | 1.63627 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.1281 | 1.22759 | 0.613794 | − | 0.789466i | \(-0.289642\pi\) | ||||
0.613794 | + | 0.789466i | \(0.289642\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.6301 | −0.566816 | −0.283408 | − | 0.958999i | \(-0.591465\pi\) | ||||
−0.283408 | + | 0.958999i | \(0.591465\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −85.1359 | −4.13945 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.387977 | −0.0188197 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 43.7221 | 2.11586 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 31.9661 | 1.54334 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.2487 | −1.02352 | −0.511758 | − | 0.859130i | \(-0.671005\pi\) | ||||
−0.511758 | + | 0.859130i | \(0.671005\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.0804 | 0.868886 | 0.434443 | − | 0.900699i | \(-0.356945\pi\) | ||||
0.434443 | + | 0.900699i | \(0.356945\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 21.0096 | 1.00733 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −39.8173 | −1.90472 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.9207 | 1.04622 | 0.523109 | − | 0.852266i | \(-0.324772\pi\) | ||||
0.523109 | + | 0.852266i | \(0.324772\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 43.7556 | 2.08360 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.3202 | 1.20300 | 0.601499 | − | 0.798873i | \(-0.294570\pi\) | ||||
0.601499 | + | 0.798873i | \(0.294570\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.2803 | −0.487332 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.16545 | −0.0551238 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.82913 | −0.369479 | −0.184740 | − | 0.982787i | \(-0.559144\pi\) | ||||
−0.184740 | + | 0.982787i | \(0.559144\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.09368 | 0.0985874 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 40.6808 | 1.91135 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.12252 | −0.287028 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.68277 | 0.406163 | 0.203081 | − | 0.979162i | \(-0.434904\pi\) | ||||
0.203081 | + | 0.979162i | \(0.434904\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.56631 | 0.306489 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.3552 | 0.668589 | 0.334294 | − | 0.942469i | \(-0.391502\pi\) | ||||
0.334294 | + | 0.942469i | \(0.391502\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.4161 | 1.64593 | 0.822963 | − | 0.568094i | \(-0.192319\pi\) | ||||
0.822963 | + | 0.568094i | \(0.192319\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.73816 | −0.0806050 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.3096 | −0.708446 | −0.354223 | − | 0.935161i | \(-0.615255\pi\) | ||||
−0.354223 | + | 0.935161i | \(0.615255\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.2293 | 0.472343 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.6116 | 0.581111 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −40.0555 | −1.84176 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.59581 | −0.256753 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.4246 | 0.980963 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.4266 | 0.659169 | 0.329585 | − | 0.944126i | \(-0.393091\pi\) | ||||
0.329585 | + | 0.944126i | \(0.393091\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.0534 | −0.503994 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 83.4614 | 3.79762 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.85465 | −0.175030 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.3549 | −1.42082 | −0.710412 | − | 0.703786i | \(-0.751491\pi\) | ||||
−0.710412 | + | 0.703786i | \(0.751491\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 41.0862 | 1.85798 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.3116 | 1.32282 | 0.661408 | − | 0.750026i | \(-0.269959\pi\) | ||||
0.661408 | + | 0.750026i | \(0.269959\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.44841 | 0.110271 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −44.6643 | −2.00751 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.33429 | 0.328988 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.7006 | 1.37435 | 0.687173 | − | 0.726494i | \(-0.258852\pi\) | ||||
0.687173 | + | 0.726494i | \(0.258852\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.0677 | −0.494470 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.3924 | 0.641726 | 0.320863 | − | 0.947126i | \(-0.396027\pi\) | ||||
0.320863 | + | 0.947126i | \(0.396027\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.96394 | −0.354391 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 33.2259 | 1.47562 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.7988 | −1.14351 | −0.571757 | − | 0.820423i | \(-0.693738\pi\) | ||||
−0.571757 | + | 0.820423i | \(0.693738\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.8916 | 0.924190 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 94.7061 | 4.18138 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.73166 | 0.428828 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 58.1916 | 2.55927 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 50.7146 | 2.22612 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.1557 | −1.27733 | −0.638667 | − | 0.769483i | \(-0.720514\pi\) | ||||
−0.638667 | + | 0.769483i | \(0.720514\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.3934 | 0.716834 | 0.358417 | − | 0.933562i | \(-0.383317\pi\) | ||||
0.358417 | + | 0.933562i | \(0.383317\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.7294 | 0.511914 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.202560 | −0.00882365 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.6311 | 1.20135 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.3789 | 0.797577 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.658490 | −0.0285224 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.6679 | −0.504448 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 42.0621 | 1.81511 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −29.9075 | −1.28821 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.3310 | −0.573144 | −0.286572 | − | 0.958059i | \(-0.592516\pi\) | ||||
−0.286572 | + | 0.958059i | \(0.592516\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.9839 | 0.814676 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.42609 | 0.318099 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.68959 | 0.286026 | 0.143013 | − | 0.989721i | \(-0.454321\pi\) | ||||
0.143013 | + | 0.989721i | \(0.454321\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −100.316 | −4.28139 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.3135 | 1.50440 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.5017 | 1.21202 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 21.1760 | 0.898873 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.2134 | 1.66152 | 0.830762 | − | 0.556628i | \(-0.187905\pi\) | ||||
0.830762 | + | 0.556628i | \(0.187905\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.5980 | 0.532840 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.13676 | −0.301314 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.57461 | −0.277087 | −0.138543 | − | 0.990356i | \(-0.544242\pi\) | ||||
−0.138543 | + | 0.990356i | \(0.544242\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.2159 | 0.471855 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −113.074 | −4.74866 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.6404 | 0.655678 | 0.327839 | − | 0.944734i | \(-0.393680\pi\) | ||||
0.327839 | + | 0.944734i | \(0.393680\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.0018 | 1.46478 | 0.732391 | − | 0.680885i | \(-0.238405\pi\) | ||||
0.732391 | + | 0.680885i | \(0.238405\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −55.7402 | −2.32858 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.11555 | 0.296739 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.7384 | 0.613569 | 0.306784 | − | 0.951779i | \(-0.400747\pi\) | ||||
0.306784 | + | 0.951779i | \(0.400747\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −56.1172 | −2.33215 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.1476 | −0.628426 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.6440 | −0.606492 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.0475 | 0.580795 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −47.1194 | −1.94483 | −0.972413 | − | 0.233267i | \(-0.925059\pi\) | ||||
−0.972413 | + | 0.233267i | \(0.925059\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.92153 | −0.120380 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 83.7972 | 3.44696 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.2906 | 0.792171 | 0.396086 | − | 0.918214i | \(-0.370368\pi\) | ||||
0.396086 | + | 0.918214i | \(0.370368\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.36692 | 0.0560381 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −28.5232 | −1.16738 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.0078 | 0.735779 | 0.367889 | − | 0.929870i | \(-0.380081\pi\) | ||||
0.367889 | + | 0.929870i | \(0.380081\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.2601 | 1.35671 | 0.678354 | − | 0.734735i | \(-0.262694\pi\) | ||||
0.678354 | + | 0.734735i | \(0.262694\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −23.4701 | −0.955775 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.5287 | 0.793955 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.6848 | 1.69193 | 0.845966 | − | 0.533236i | \(-0.179024\pi\) | ||||
0.845966 | + | 0.533236i | \(0.179024\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −74.0209 | −2.99948 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.3021 | −0.740423 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.9945 | −0.524844 | −0.262422 | − | 0.964953i | \(-0.584521\pi\) | ||||
−0.262422 | + | 0.964953i | \(0.584521\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.26153 | 0.0508697 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.4959 | −0.825132 | −0.412566 | − | 0.910928i | \(-0.635367\pi\) | ||||
−0.412566 | + | 0.910928i | \(0.635367\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.209415 | −0.00841712 | −0.00420856 | − | 0.999991i | \(-0.501340\pi\) | ||||
−0.00420856 | + | 0.999991i | \(0.501340\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −120.427 | −4.83257 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 36.2194 | 1.45110 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −102.934 | −4.11078 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.46780 | 0.0983976 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.8125 | −0.669296 | −0.334648 | − | 0.942343i | \(-0.608617\pi\) | ||||
−0.334648 | + | 0.942343i | \(0.608617\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 83.4228 | 3.31576 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.0569 | 0.795932 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.40634 | 0.372693 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.8278 | −0.665699 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 44.1851 | 1.74521 | 0.872603 | − | 0.488430i | \(-0.162430\pi\) | ||||
0.872603 | + | 0.488430i | \(0.162430\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.10631 | 0.0436287 | 0.0218143 | − | 0.999762i | \(-0.493056\pi\) | ||||
0.0218143 | + | 0.999762i | \(0.493056\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.1351 | −0.950319 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.6633 | −0.930300 | −0.465150 | − | 0.885232i | \(-0.654000\pi\) | ||||
−0.465150 | + | 0.885232i | \(0.654000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.5622 | −0.493111 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.12385 | 0.240013 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.0014 | 1.40884 | 0.704421 | − | 0.709782i | \(-0.251207\pi\) | ||||
0.704421 | + | 0.709782i | \(0.251207\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.7178 | −0.535998 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −47.9339 | −1.87008 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.6542 | −1.27203 | −0.636013 | − | 0.771678i | \(-0.719418\pi\) | ||||
−0.636013 | + | 0.771678i | \(0.719418\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.8672 | −0.656060 | −0.328030 | − | 0.944667i | \(-0.606385\pi\) | ||||
−0.328030 | + | 0.944667i | \(0.606385\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.24461 | 0.0871735 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.7151 | 0.764519 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −44.9041 | −1.73869 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 82.0131 | 3.17081 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 68.5676 | 2.64702 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.0636 | −0.387924 | −0.193962 | − | 0.981009i | \(-0.562134\pi\) | ||||
−0.193962 | + | 0.981009i | \(0.562134\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.9245 | −0.651423 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.33195 | 0.166490 | 0.0832451 | − | 0.996529i | \(-0.473472\pi\) | ||||
0.0832451 | + | 0.996529i | \(0.473472\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.5806 | 0.521177 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.6052 | 1.01951 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.37360 | −0.129087 | −0.0645437 | − | 0.997915i | \(-0.520559\pi\) | ||||
−0.0645437 | + | 0.997915i | \(0.520559\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.6918 | −0.408515 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.5667 | 0.975431 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.60574 | 0.175465 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.5945 | 1.23995 | 0.619976 | − | 0.784621i | \(-0.287142\pi\) | ||||
0.619976 | + | 0.784621i | \(0.287142\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 157.361 | 5.97764 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.0365 | −0.380705 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.147015 | 0.00556859 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 53.0302 | 2.00579 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.5703 | −0.701391 | −0.350696 | − | 0.936489i | \(-0.614055\pi\) | ||||
−0.350696 | + | 0.936489i | \(0.614055\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.5932 | 1.34242 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 35.0629 | 1.32054 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.0585 | 1.05525 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.6997 | −1.56607 | −0.783033 | − | 0.621980i | \(-0.786329\pi\) | ||||
−0.783033 | + | 0.621980i | \(0.786329\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −65.3946 | −2.45249 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.71498 | 0.139127 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.60170 | −0.359083 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −25.0223 | −0.934477 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.4863 | 1.36071 | 0.680356 | − | 0.732882i | \(-0.261825\pi\) | ||||
0.680356 | + | 0.732882i | \(0.261825\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34.2865 | −1.27689 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 45.6353 | 1.69720 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.31070 | −0.234373 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.6843 | 0.618787 | 0.309393 | − | 0.950934i | \(-0.399874\pi\) | ||||
0.309393 | + | 0.950934i | \(0.399874\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 90.4024 | 3.34824 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.81264 | −0.104029 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.7386 | 0.433574 | 0.216787 | − | 0.976219i | \(-0.430442\pi\) | ||||
0.216787 | + | 0.976219i | \(0.430442\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.0205 | −0.664697 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.0421 | 0.590920 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.97439 | −0.366914 | −0.183457 | − | 0.983028i | \(-0.558729\pi\) | ||||
−0.183457 | + | 0.983028i | \(0.558729\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 32.3741 | 1.18929 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.5671 | −1.01134 | −0.505670 | − | 0.862727i | \(-0.668755\pi\) | ||||
−0.505670 | + | 0.862727i | \(0.668755\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.350067 | 0.0128255 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 34.7547 | 1.27161 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 41.1083 | 1.50206 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.82038 | −0.285370 | −0.142685 | − | 0.989768i | \(-0.545574\pi\) | ||||
−0.142685 | + | 0.989768i | \(0.545574\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −59.6338 | −2.17318 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.2194 | −0.444708 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.4393 | −0.488459 | −0.244229 | − | 0.969717i | \(-0.578535\pi\) | ||||
−0.244229 | + | 0.969717i | \(0.578535\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 130.889 | 4.75098 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.6221 | −0.747552 | −0.373776 | − | 0.927519i | \(-0.621937\pi\) | ||||
−0.373776 | + | 0.927519i | \(0.621937\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.1635 | −0.947183 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.13626 | −0.113392 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.95100 | 0.142662 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.16314 | 0.186188 | 0.0930938 | − | 0.995657i | \(-0.470324\pi\) | ||||
0.0930938 | + | 0.995657i | \(0.470324\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −101.008 | −3.63772 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.7570 | −0.674642 | −0.337321 | − | 0.941390i | \(-0.609521\pi\) | ||||
−0.337321 | + | 0.941390i | \(0.609521\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.522093 | 0.0187541 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −74.6072 | −2.67652 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.12040 | 0.0759713 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.5021 | 0.411577 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 106.805 | 3.81691 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.78816 | −0.135205 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 54.5548 | 1.94467 | 0.972334 | − | 0.233595i | \(-0.0750491\pi\) | ||||
0.972334 | + | 0.233595i | \(0.0750491\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 32.7323 | 1.16530 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −39.5156 | −1.40501 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.5655 | −0.765812 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.82361 | −0.312941 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.46737 | −0.299930 | −0.149965 | − | 0.988691i | \(-0.547916\pi\) | ||||
−0.149965 | + | 0.988691i | \(0.547916\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.08613 | 0.144557 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −83.1020 | −2.93626 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.7635 | 1.15620 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.0694 | −0.883581 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −82.7214 | −2.91193 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.8394 | 0.802990 | 0.401495 | − | 0.915861i | \(-0.368491\pi\) | ||||
0.401495 | + | 0.915861i | \(0.368491\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.6554 | 1.70852 | 0.854261 | − | 0.519845i | \(-0.174010\pi\) | ||||
0.854261 | + | 0.519845i | \(0.174010\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.50228 | −0.192973 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.3411 | −0.432291 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40.5669 | −1.41925 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −49.4922 | −1.72940 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.3604 | 1.65289 | 0.826444 | − | 0.563018i | \(-0.190360\pi\) | ||||
0.826444 | + | 0.563018i | \(0.190360\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.9653 | 0.835378 | 0.417689 | − | 0.908590i | \(-0.362840\pi\) | ||||
0.417689 | + | 0.908590i | \(0.362840\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.3948 | 0.640425 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.80582 | −0.340982 | −0.170491 | − | 0.985359i | \(-0.554535\pi\) | ||||
−0.170491 | + | 0.985359i | \(0.554535\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.5094 | −1.61534 | −0.807669 | − | 0.589636i | \(-0.799271\pi\) | ||||
−0.807669 | + | 0.589636i | \(0.799271\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −108.291 | −3.75657 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.10006 | −0.0727629 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.32443 | 0.115047 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.83614 | −0.305422 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −44.6851 | −1.54270 | −0.771350 | − | 0.636411i | \(-0.780418\pi\) | ||||
−0.771350 | + | 0.636411i | \(0.780418\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.8249 | 0.373273 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −80.4513 | −2.77089 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.98013 | −0.343327 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −68.8033 | −2.36411 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.3611 | −0.973349 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −45.2598 | −1.55148 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.9669 | −1.12877 | −0.564383 | − | 0.825513i | \(-0.690886\pi\) | ||||
−0.564383 | + | 0.825513i | \(0.690886\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −45.2345 | −1.54699 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.4828 | −0.665521 | −0.332761 | − | 0.943011i | \(-0.607980\pi\) | ||||
−0.332761 | + | 0.943011i | \(0.607980\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.73928 | 0.229941 | 0.114971 | − | 0.993369i | \(-0.463323\pi\) | ||||
0.114971 | + | 0.993369i | \(0.463323\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.44460 | −0.151471 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.8087 | 1.15086 | 0.575431 | − | 0.817851i | \(-0.304834\pi\) | ||||
0.575431 | + | 0.817851i | \(0.304834\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.2332 | −0.517945 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 56.0954 | 1.90510 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 44.6981 | 1.51628 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.04547 | −0.170959 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −31.1595 | −1.05459 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.52319 | −0.119106 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.6520 | −0.798671 | −0.399336 | − | 0.916805i | \(-0.630759\pi\) | ||||
−0.399336 | + | 0.916805i | \(0.630759\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −54.2847 | −1.83098 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.5868 | −1.56955 | −0.784775 | − | 0.619781i | \(-0.787222\pi\) | ||||
−0.784775 | + | 0.619781i | \(0.787222\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.2188 | 1.15155 | 0.575777 | − | 0.817607i | \(-0.304700\pi\) | ||||
0.575777 | + | 0.817607i | \(0.304700\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.56927 | −0.254438 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.1754 | 0.677423 | 0.338712 | − | 0.940890i | \(-0.390009\pi\) | ||||
0.338712 | + | 0.940890i | \(0.390009\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −70.6641 | −2.37000 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −177.329 | −5.94076 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 58.9345 | 1.97217 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.6343 | −0.422317 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −41.1665 | −1.37451 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.29477 | −0.109887 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.02828 | −0.0342570 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 85.0326 | 2.82971 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.70222 | −0.189548 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.96954 | 0.0986018 | 0.0493009 | − | 0.998784i | \(-0.484301\pi\) | ||||
0.0493009 | + | 0.998784i | \(0.484301\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −64.3776 | −2.13527 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.0975 | 0.964044 | 0.482022 | − | 0.876159i | \(-0.339902\pi\) | ||||
0.482022 | + | 0.876159i | \(0.339902\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.7553 | −0.786186 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 41.3148 | 1.36583 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 48.3303 | 1.59601 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.9984 | 1.28644 | 0.643220 | − | 0.765682i | \(-0.277598\pi\) | ||||
0.643220 | + | 0.765682i | \(0.277598\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −102.683 | −3.38352 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.61756 | −0.119074 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.36068 | −0.209138 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 78.6671 | 2.58377 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.2944 | 1.12516 | 0.562581 | − | 0.826742i | \(-0.309808\pi\) | ||||
0.562581 | + | 0.826742i | \(0.309808\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.2893 | −0.992693 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 51.1372 | 1.67416 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.14368 | 0.0701059 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.9481 | 1.43572 | 0.717861 | − | 0.696187i | \(-0.245122\pi\) | ||||
0.717861 | + | 0.696187i | \(0.245122\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.1752 | 1.01737 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.11656 | −0.264592 | −0.132296 | − | 0.991210i | \(-0.542235\pi\) | ||||
−0.132296 | + | 0.991210i | \(0.542235\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.69627 | −0.0878027 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 59.6281 | 1.93970 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.65365 | −0.281206 | −0.140603 | − | 0.990066i | \(-0.544904\pi\) | ||||
−0.140603 | + | 0.990066i | \(0.544904\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.3046 | −0.334501 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −36.5297 | −1.18456 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.73648 | 0.315395 | 0.157698 | − | 0.987487i | \(-0.449593\pi\) | ||||
0.157698 | + | 0.987487i | \(0.449593\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.7428 | 0.541784 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −116.084 | −3.75247 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 37.6694 | 1.21641 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7274 | −0.991207 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −94.3191 | −3.03939 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.8560 | 0.542614 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.3305 | −0.878888 | −0.439444 | − | 0.898270i | \(-0.644825\pi\) | ||||
−0.439444 | + | 0.898270i | \(0.644825\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.22787 | −0.232193 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.6894 | 0.663953 | 0.331977 | − | 0.943288i | \(-0.392284\pi\) | ||||
0.331977 | + | 0.943288i | \(0.392284\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.3604 | 1.13360 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.78542 | −0.185282 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.8460 | 0.442972 | 0.221486 | − | 0.975164i | \(-0.428909\pi\) | ||||
0.221486 | + | 0.975164i | \(0.428909\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 56.8014 | 1.81538 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 60.0298 | 1.91660 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.8718 | −0.442440 | −0.221220 | − | 0.975224i | \(-0.571004\pi\) | ||||
−0.221220 | + | 0.975224i | \(0.571004\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.1703 | −0.801993 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −123.533 | −3.93210 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 51.5842 | 1.64028 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.0743 | 1.14594 | 0.572968 | − | 0.819578i | \(-0.305792\pi\) | ||||
0.572968 | + | 0.819578i | \(0.305792\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 41.7978 | 1.32641 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.56757 | 0.271610 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.5095 | 0.491191 | 0.245596 | − | 0.969372i | \(-0.421017\pi\) | ||||
0.245596 | + | 0.969372i | \(0.421017\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 107.651 | 3.40593 |
(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 | 8020.2.a.f.1.2 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.f.1.2 | ✓ | 37 | 1.1 | even | 1 | trivial |