Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,4,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("75.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(4.42514325043\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.70156 | −1.66225 | −0.831127 | − | 0.556083i | \(-0.812304\pi\) | ||||
−0.831127 | + | 0.556083i | \(0.812304\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 14.1047 | 1.76309 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 14.1047 | 0.959702 | ||||||||
\(7\) | 16.2094 | 0.875224 | 0.437612 | − | 0.899164i | \(-0.355824\pi\) | ||||
0.437612 | + | 0.899164i | \(0.355824\pi\) | |||||||
\(8\) | −28.7016 | −1.26844 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −40.2094 | −1.10214 | −0.551072 | − | 0.834458i | \(-0.685781\pi\) | ||||
−0.551072 | + | 0.834458i | \(0.685781\pi\) | |||||||
\(12\) | −42.3141 | −1.01792 | ||||||||
\(13\) | −19.7906 | −0.422226 | −0.211113 | − | 0.977462i | \(-0.567709\pi\) | ||||
−0.211113 | + | 0.977462i | \(0.567709\pi\) | |||||||
\(14\) | −76.2094 | −1.45484 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 22.1047 | 0.345386 | ||||||||
\(17\) | −83.0156 | −1.18437 | −0.592184 | − | 0.805803i | \(-0.701734\pi\) | ||||
−0.592184 | + | 0.805803i | \(0.701734\pi\) | |||||||
\(18\) | −42.3141 | −0.554084 | ||||||||
\(19\) | −48.8375 | −0.589689 | −0.294844 | − | 0.955545i | \(-0.595268\pi\) | ||||
−0.294844 | + | 0.955545i | \(0.595268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −48.6281 | −0.505311 | ||||||||
\(22\) | 189.047 | 1.83204 | ||||||||
\(23\) | −1.61250 | −0.0146186 | −0.00730932 | − | 0.999973i | \(-0.502327\pi\) | ||||
−0.00730932 | + | 0.999973i | \(0.502327\pi\) | |||||||
\(24\) | 86.1047 | 0.732335 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 93.0469 | 0.701846 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 228.628 | 1.54309 | ||||||||
\(29\) | −24.5344 | −0.157101 | −0.0785504 | − | 0.996910i | \(-0.525029\pi\) | ||||
−0.0785504 | + | 0.996910i | \(0.525029\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −12.4187 | −0.0719507 | −0.0359754 | − | 0.999353i | \(-0.511454\pi\) | ||||
−0.0359754 | + | 0.999353i | \(0.511454\pi\) | |||||||
\(32\) | 125.686 | 0.694323 | ||||||||
\(33\) | 120.628 | 0.636323 | ||||||||
\(34\) | 390.303 | 1.96872 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 126.942 | 0.587695 | ||||||||
\(37\) | −325.884 | −1.44797 | −0.723987 | − | 0.689813i | \(-0.757693\pi\) | ||||
−0.723987 | + | 0.689813i | \(0.757693\pi\) | |||||||
\(38\) | 229.612 | 0.980212 | ||||||||
\(39\) | 59.3719 | 0.243772 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −242.419 | −0.923401 | −0.461701 | − | 0.887036i | \(-0.652761\pi\) | ||||
−0.461701 | + | 0.887036i | \(0.652761\pi\) | |||||||
\(42\) | 228.628 | 0.839954 | ||||||||
\(43\) | −367.350 | −1.30280 | −0.651399 | − | 0.758735i | \(-0.725818\pi\) | ||||
−0.651399 | + | 0.758735i | \(0.725818\pi\) | |||||||
\(44\) | −567.141 | −1.94317 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.58125 | 0.0242999 | ||||||||
\(47\) | 204.544 | 0.634804 | 0.317402 | − | 0.948291i | \(-0.397190\pi\) | ||||
0.317402 | + | 0.948291i | \(0.397190\pi\) | |||||||
\(48\) | −66.3141 | −0.199409 | ||||||||
\(49\) | −80.2562 | −0.233983 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 249.047 | 0.683795 | ||||||||
\(52\) | −279.141 | −0.744420 | ||||||||
\(53\) | 61.5281 | 0.159463 | 0.0797314 | − | 0.996816i | \(-0.474594\pi\) | ||||
0.0797314 | + | 0.996816i | \(0.474594\pi\) | |||||||
\(54\) | 126.942 | 0.319901 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −465.234 | −1.11017 | ||||||||
\(57\) | 146.512 | 0.340457 | ||||||||
\(58\) | 115.350 | 0.261141 | ||||||||
\(59\) | −112.209 | −0.247600 | −0.123800 | − | 0.992307i | \(-0.539508\pi\) | ||||
−0.123800 | + | 0.992307i | \(0.539508\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 477.350 | 1.00194 | 0.500970 | − | 0.865464i | \(-0.332977\pi\) | ||||
0.500970 | + | 0.865464i | \(0.332977\pi\) | |||||||
\(62\) | 58.3875 | 0.119600 | ||||||||
\(63\) | 145.884 | 0.291741 | ||||||||
\(64\) | −767.758 | −1.49953 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −567.141 | −1.05773 | ||||||||
\(67\) | −558.094 | −1.01764 | −0.508821 | − | 0.860872i | \(-0.669918\pi\) | ||||
−0.508821 | + | 0.860872i | \(0.669918\pi\) | |||||||
\(68\) | −1170.91 | −2.08814 | ||||||||
\(69\) | 4.83749 | 0.00844008 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 558.281 | 0.933180 | 0.466590 | − | 0.884474i | \(-0.345482\pi\) | ||||
0.466590 | + | 0.884474i | \(0.345482\pi\) | |||||||
\(72\) | −258.314 | −0.422814 | ||||||||
\(73\) | −1011.77 | −1.62217 | −0.811086 | − | 0.584927i | \(-0.801123\pi\) | ||||
−0.811086 | + | 0.584927i | \(0.801123\pi\) | |||||||
\(74\) | 1532.17 | 2.40690 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −688.837 | −1.03967 | ||||||||
\(77\) | −651.769 | −0.964623 | ||||||||
\(78\) | −279.141 | −0.405211 | ||||||||
\(79\) | 1150.47 | 1.63845 | 0.819227 | − | 0.573470i | \(-0.194403\pi\) | ||||
0.819227 | + | 0.573470i | \(0.194403\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1139.75 | 1.53493 | ||||||||
\(83\) | 1157.92 | 1.53131 | 0.765655 | − | 0.643251i | \(-0.222415\pi\) | ||||
0.765655 | + | 0.643251i | \(0.222415\pi\) | |||||||
\(84\) | −685.884 | −0.890906 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1727.12 | 2.16558 | ||||||||
\(87\) | 73.6032 | 0.0907022 | ||||||||
\(88\) | 1154.07 | 1.39801 | ||||||||
\(89\) | 96.9751 | 0.115498 | 0.0577491 | − | 0.998331i | \(-0.481608\pi\) | ||||
0.0577491 | + | 0.998331i | \(0.481608\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −320.794 | −0.369542 | ||||||||
\(92\) | −22.7438 | −0.0257739 | ||||||||
\(93\) | 37.2562 | 0.0415408 | ||||||||
\(94\) | −961.675 | −1.05520 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −377.058 | −0.400868 | ||||||||
\(97\) | 1152.37 | 1.20625 | 0.603123 | − | 0.797648i | \(-0.293923\pi\) | ||||
0.603123 | + | 0.797648i | \(0.293923\pi\) | |||||||
\(98\) | 377.330 | 0.388939 | ||||||||
\(99\) | −361.884 | −0.367381 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1156.49 | −1.13936 | −0.569679 | − | 0.821867i | \(-0.692932\pi\) | ||||
−0.569679 | + | 0.821867i | \(0.692932\pi\) | |||||||
\(102\) | −1170.91 | −1.13664 | ||||||||
\(103\) | 1333.70 | 1.27585 | 0.637927 | − | 0.770096i | \(-0.279792\pi\) | ||||
0.637927 | + | 0.770096i | \(0.279792\pi\) | |||||||
\(104\) | 568.022 | 0.535569 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −289.278 | −0.265068 | ||||||||
\(107\) | 798.263 | 0.721224 | 0.360612 | − | 0.932716i | \(-0.382568\pi\) | ||||
0.360612 | + | 0.932716i | \(0.382568\pi\) | |||||||
\(108\) | −380.827 | −0.339306 | ||||||||
\(109\) | −985.119 | −0.865663 | −0.432831 | − | 0.901475i | \(-0.642485\pi\) | ||||
−0.432831 | + | 0.901475i | \(0.642485\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 977.653 | 0.835988 | ||||||||
\(112\) | 358.303 | 0.302290 | ||||||||
\(113\) | −1888.25 | −1.57196 | −0.785979 | − | 0.618253i | \(-0.787841\pi\) | ||||
−0.785979 | + | 0.618253i | \(0.787841\pi\) | |||||||
\(114\) | −688.837 | −0.565926 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −346.050 | −0.276982 | ||||||||
\(117\) | −178.116 | −0.140742 | ||||||||
\(118\) | 527.559 | 0.411574 | ||||||||
\(119\) | −1345.63 | −1.03659 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 285.794 | 0.214721 | ||||||||
\(122\) | −2244.29 | −1.66548 | ||||||||
\(123\) | 727.256 | 0.533126 | ||||||||
\(124\) | −175.163 | −0.126855 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −685.884 | −0.484948 | ||||||||
\(127\) | 620.859 | 0.433798 | 0.216899 | − | 0.976194i | \(-0.430406\pi\) | ||||
0.216899 | + | 0.976194i | \(0.430406\pi\) | |||||||
\(128\) | 2604.17 | 1.79827 | ||||||||
\(129\) | 1102.05 | 0.752171 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2588.35 | −1.72630 | −0.863151 | − | 0.504947i | \(-0.831512\pi\) | ||||
−0.863151 | + | 0.504947i | \(0.831512\pi\) | |||||||
\(132\) | 1701.42 | 1.12189 | ||||||||
\(133\) | −791.625 | −0.516110 | ||||||||
\(134\) | 2623.91 | 1.69158 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2382.68 | 1.50230 | ||||||||
\(137\) | 1656.29 | 1.03289 | 0.516447 | − | 0.856319i | \(-0.327254\pi\) | ||||
0.516447 | + | 0.856319i | \(0.327254\pi\) | |||||||
\(138\) | −22.7438 | −0.0140295 | ||||||||
\(139\) | −153.256 | −0.0935182 | −0.0467591 | − | 0.998906i | \(-0.514889\pi\) | ||||
−0.0467591 | + | 0.998906i | \(0.514889\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −613.631 | −0.366504 | ||||||||
\(142\) | −2624.79 | −1.55118 | ||||||||
\(143\) | 795.769 | 0.465353 | ||||||||
\(144\) | 198.942 | 0.115129 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4756.89 | 2.69646 | ||||||||
\(147\) | 240.769 | 0.135090 | ||||||||
\(148\) | −4596.50 | −2.55290 | ||||||||
\(149\) | 1483.38 | 0.815591 | 0.407795 | − | 0.913073i | \(-0.366298\pi\) | ||||
0.407795 | + | 0.913073i | \(0.366298\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −394.281 | −0.212491 | −0.106246 | − | 0.994340i | \(-0.533883\pi\) | ||||
−0.106246 | + | 0.994340i | \(0.533883\pi\) | |||||||
\(152\) | 1401.71 | 0.747986 | ||||||||
\(153\) | −747.141 | −0.394789 | ||||||||
\(154\) | 3064.33 | 1.60345 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 837.422 | 0.429791 | ||||||||
\(157\) | −1727.05 | −0.877922 | −0.438961 | − | 0.898506i | \(-0.644653\pi\) | ||||
−0.438961 | + | 0.898506i | \(0.644653\pi\) | |||||||
\(158\) | −5409.00 | −2.72352 | ||||||||
\(159\) | −184.584 | −0.0920659 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −26.1376 | −0.0127946 | ||||||||
\(162\) | −380.827 | −0.184695 | ||||||||
\(163\) | 2034.28 | 0.977529 | 0.488764 | − | 0.872416i | \(-0.337448\pi\) | ||||
0.488764 | + | 0.872416i | \(0.337448\pi\) | |||||||
\(164\) | −3419.24 | −1.62804 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5444.06 | −2.54543 | ||||||||
\(167\) | −192.900 | −0.0893835 | −0.0446918 | − | 0.999001i | \(-0.514231\pi\) | ||||
−0.0446918 | + | 0.999001i | \(0.514231\pi\) | |||||||
\(168\) | 1395.70 | 0.640957 | ||||||||
\(169\) | −1805.33 | −0.821726 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −439.537 | −0.196563 | ||||||||
\(172\) | −5181.36 | −2.29695 | ||||||||
\(173\) | 1239.91 | 0.544905 | 0.272452 | − | 0.962169i | \(-0.412165\pi\) | ||||
0.272452 | + | 0.962169i | \(0.412165\pi\) | |||||||
\(174\) | −346.050 | −0.150770 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −888.816 | −0.380665 | ||||||||
\(177\) | 336.628 | 0.142952 | ||||||||
\(178\) | −455.934 | −0.191987 | ||||||||
\(179\) | −2636.86 | −1.10105 | −0.550525 | − | 0.834818i | \(-0.685573\pi\) | ||||
−0.550525 | + | 0.834818i | \(0.685573\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3317.58 | 1.36240 | 0.681199 | − | 0.732099i | \(-0.261459\pi\) | ||||
0.681199 | + | 0.732099i | \(0.261459\pi\) | |||||||
\(182\) | 1508.23 | 0.614272 | ||||||||
\(183\) | −1432.05 | −0.578471 | ||||||||
\(184\) | 46.2812 | 0.0185429 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −175.163 | −0.0690513 | ||||||||
\(187\) | 3338.01 | 1.30534 | ||||||||
\(188\) | 2885.02 | 1.11921 | ||||||||
\(189\) | −437.653 | −0.168437 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −624.506 | −0.236585 | −0.118292 | − | 0.992979i | \(-0.537742\pi\) | ||||
−0.118292 | + | 0.992979i | \(0.537742\pi\) | |||||||
\(192\) | 2303.27 | 0.865752 | ||||||||
\(193\) | 436.144 | 0.162665 | 0.0813324 | − | 0.996687i | \(-0.474082\pi\) | ||||
0.0813324 | + | 0.996687i | \(0.474082\pi\) | |||||||
\(194\) | −5417.96 | −2.00509 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1131.99 | −0.412532 | ||||||||
\(197\) | −3355.81 | −1.21366 | −0.606831 | − | 0.794831i | \(-0.707560\pi\) | ||||
−0.606831 | + | 0.794831i | \(0.707560\pi\) | |||||||
\(198\) | 1701.42 | 0.610681 | ||||||||
\(199\) | 3799.77 | 1.35356 | 0.676780 | − | 0.736185i | \(-0.263375\pi\) | ||||
0.676780 | + | 0.736185i | \(0.263375\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1674.28 | 0.587536 | ||||||||
\(202\) | 5437.31 | 1.89390 | ||||||||
\(203\) | −397.687 | −0.137498 | ||||||||
\(204\) | 3512.73 | 1.20559 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6270.46 | −2.12079 | ||||||||
\(207\) | −14.5125 | −0.00487288 | ||||||||
\(208\) | −437.466 | −0.145831 | ||||||||
\(209\) | 1963.72 | 0.649922 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2365.27 | 0.771715 | 0.385857 | − | 0.922558i | \(-0.373906\pi\) | ||||
0.385857 | + | 0.922558i | \(0.373906\pi\) | |||||||
\(212\) | 867.834 | 0.281147 | ||||||||
\(213\) | −1674.84 | −0.538772 | ||||||||
\(214\) | −3753.08 | −1.19886 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 774.942 | 0.244112 | ||||||||
\(217\) | −201.300 | −0.0629730 | ||||||||
\(218\) | 4631.60 | 1.43895 | ||||||||
\(219\) | 3035.31 | 0.936562 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1642.93 | 0.500070 | ||||||||
\(222\) | −4596.50 | −1.38962 | ||||||||
\(223\) | 3328.58 | 0.999545 | 0.499772 | − | 0.866157i | \(-0.333417\pi\) | ||||
0.499772 | + | 0.866157i | \(0.333417\pi\) | |||||||
\(224\) | 2037.29 | 0.607688 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8877.71 | 2.61299 | ||||||||
\(227\) | 527.100 | 0.154118 | 0.0770592 | − | 0.997027i | \(-0.475447\pi\) | ||||
0.0770592 | + | 0.997027i | \(0.475447\pi\) | |||||||
\(228\) | 2066.51 | 0.600255 | ||||||||
\(229\) | 2566.06 | 0.740479 | 0.370240 | − | 0.928936i | \(-0.379276\pi\) | ||||
0.370240 | + | 0.928936i | \(0.379276\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1955.31 | 0.556925 | ||||||||
\(232\) | 704.175 | 0.199273 | ||||||||
\(233\) | −5534.99 | −1.55626 | −0.778132 | − | 0.628101i | \(-0.783832\pi\) | ||||
−0.778132 | + | 0.628101i | \(0.783832\pi\) | |||||||
\(234\) | 837.422 | 0.233949 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1582.68 | −0.436541 | ||||||||
\(237\) | −3451.41 | −0.945962 | ||||||||
\(238\) | 6326.57 | 1.72307 | ||||||||
\(239\) | 1010.01 | 0.273355 | 0.136678 | − | 0.990616i | \(-0.456358\pi\) | ||||
0.136678 | + | 0.990616i | \(0.456358\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4074.29 | −1.08900 | −0.544498 | − | 0.838762i | \(-0.683280\pi\) | ||||
−0.544498 | + | 0.838762i | \(0.683280\pi\) | |||||||
\(242\) | −1343.68 | −0.356921 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 6732.87 | 1.76651 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3419.24 | −0.886190 | ||||||||
\(247\) | 966.525 | 0.248982 | ||||||||
\(248\) | 356.437 | 0.0912653 | ||||||||
\(249\) | −3473.77 | −0.884103 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1773.98 | 0.446107 | 0.223054 | − | 0.974806i | \(-0.428398\pi\) | ||||
0.223054 | + | 0.974806i | \(0.428398\pi\) | |||||||
\(252\) | 2057.65 | 0.514365 | ||||||||
\(253\) | 64.8375 | 0.0161119 | ||||||||
\(254\) | −2919.01 | −0.721082 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6101.62 | −1.48965 | ||||||||
\(257\) | −662.784 | −0.160869 | −0.0804345 | − | 0.996760i | \(-0.525631\pi\) | ||||
−0.0804345 | + | 0.996760i | \(0.525631\pi\) | |||||||
\(258\) | −5181.36 | −1.25030 | ||||||||
\(259\) | −5282.38 | −1.26730 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −220.810 | −0.0523669 | ||||||||
\(262\) | 12169.3 | 2.86955 | ||||||||
\(263\) | −712.312 | −0.167008 | −0.0835039 | − | 0.996507i | \(-0.526611\pi\) | ||||
−0.0835039 | + | 0.996507i | \(0.526611\pi\) | |||||||
\(264\) | −3462.22 | −0.807139 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3721.87 | 0.857905 | ||||||||
\(267\) | −290.925 | −0.0666829 | ||||||||
\(268\) | −7871.74 | −1.79419 | ||||||||
\(269\) | −3136.41 | −0.710894 | −0.355447 | − | 0.934696i | \(-0.615671\pi\) | ||||
−0.355447 | + | 0.934696i | \(0.615671\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2275.69 | −0.510105 | −0.255053 | − | 0.966927i | \(-0.582093\pi\) | ||||
−0.255053 | + | 0.966927i | \(0.582093\pi\) | |||||||
\(272\) | −1835.03 | −0.409064 | ||||||||
\(273\) | 962.381 | 0.213355 | ||||||||
\(274\) | −7787.15 | −1.71693 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 68.2313 | 0.0148806 | ||||||||
\(277\) | −5171.00 | −1.12164 | −0.560821 | − | 0.827937i | \(-0.689515\pi\) | ||||
−0.560821 | + | 0.827937i | \(0.689515\pi\) | |||||||
\(278\) | 720.544 | 0.155451 | ||||||||
\(279\) | −111.769 | −0.0239836 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2240.14 | 0.475571 | 0.237785 | − | 0.971318i | \(-0.423578\pi\) | ||||
0.237785 | + | 0.971318i | \(0.423578\pi\) | |||||||
\(282\) | 2885.02 | 0.609222 | ||||||||
\(283\) | −225.244 | −0.0473123 | −0.0236561 | − | 0.999720i | \(-0.507531\pi\) | ||||
−0.0236561 | + | 0.999720i | \(0.507531\pi\) | |||||||
\(284\) | 7874.38 | 1.64528 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3741.36 | −0.773535 | ||||||||
\(287\) | −3929.46 | −0.808183 | ||||||||
\(288\) | 1131.17 | 0.231441 | ||||||||
\(289\) | 1978.59 | 0.402726 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3457.12 | −0.696427 | ||||||||
\(292\) | −14270.7 | −2.86003 | ||||||||
\(293\) | −1139.86 | −0.227274 | −0.113637 | − | 0.993522i | \(-0.536250\pi\) | ||||
−0.113637 | + | 0.993522i | \(0.536250\pi\) | |||||||
\(294\) | −1131.99 | −0.224554 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9353.39 | 1.83667 | ||||||||
\(297\) | 1085.65 | 0.212108 | ||||||||
\(298\) | −6974.19 | −1.35572 | ||||||||
\(299\) | 31.9123 | 0.00617237 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5954.51 | −1.14024 | ||||||||
\(302\) | 1853.74 | 0.353214 | ||||||||
\(303\) | 3469.47 | 0.657808 | ||||||||
\(304\) | −1079.54 | −0.203670 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3512.73 | 0.656240 | ||||||||
\(307\) | −5244.86 | −0.975049 | −0.487525 | − | 0.873109i | \(-0.662100\pi\) | ||||
−0.487525 | + | 0.873109i | \(0.662100\pi\) | |||||||
\(308\) | −9192.99 | −1.70071 | ||||||||
\(309\) | −4001.09 | −0.736615 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5188.26 | −0.945977 | −0.472989 | − | 0.881068i | \(-0.656825\pi\) | ||||
−0.472989 | + | 0.881068i | \(0.656825\pi\) | |||||||
\(312\) | −1704.07 | −0.309211 | ||||||||
\(313\) | −486.656 | −0.0878832 | −0.0439416 | − | 0.999034i | \(-0.513992\pi\) | ||||
−0.0439416 | + | 0.999034i | \(0.513992\pi\) | |||||||
\(314\) | 8119.85 | 1.45933 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16227.0 | 2.88873 | ||||||||
\(317\) | 4218.87 | 0.747493 | 0.373747 | − | 0.927531i | \(-0.378073\pi\) | ||||
0.373747 | + | 0.927531i | \(0.378073\pi\) | |||||||
\(318\) | 867.834 | 0.153037 | ||||||||
\(319\) | 986.512 | 0.173148 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2394.79 | −0.416399 | ||||||||
\(322\) | 122.887 | 0.0212678 | ||||||||
\(323\) | 4054.27 | 0.698408 | ||||||||
\(324\) | 1142.48 | 0.195898 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9564.30 | −1.62490 | ||||||||
\(327\) | 2955.36 | 0.499791 | ||||||||
\(328\) | 6957.80 | 1.17128 | ||||||||
\(329\) | 3315.53 | 0.555595 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7439.94 | 1.23546 | 0.617728 | − | 0.786392i | \(-0.288053\pi\) | ||||
0.617728 | + | 0.786392i | \(0.288053\pi\) | |||||||
\(332\) | 16332.2 | 2.69983 | ||||||||
\(333\) | −2932.96 | −0.482658 | ||||||||
\(334\) | 906.931 | 0.148578 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1074.91 | −0.174527 | ||||||||
\(337\) | 6555.39 | 1.05963 | 0.529815 | − | 0.848113i | \(-0.322261\pi\) | ||||
0.529815 | + | 0.848113i | \(0.322261\pi\) | |||||||
\(338\) | 8487.88 | 1.36592 | ||||||||
\(339\) | 5664.74 | 0.907571 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 499.350 | 0.0793000 | ||||||||
\(342\) | 2066.51 | 0.326737 | ||||||||
\(343\) | −6860.72 | −1.08001 | ||||||||
\(344\) | 10543.5 | 1.65252 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5829.51 | −0.905770 | ||||||||
\(347\) | −1950.56 | −0.301763 | −0.150881 | − | 0.988552i | \(-0.548211\pi\) | ||||
−0.150881 | + | 0.988552i | \(0.548211\pi\) | |||||||
\(348\) | 1038.15 | 0.159916 | ||||||||
\(349\) | −1426.74 | −0.218830 | −0.109415 | − | 0.993996i | \(-0.534898\pi\) | ||||
−0.109415 | + | 0.993996i | \(0.534898\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 534.347 | 0.0812573 | ||||||||
\(352\) | −5053.75 | −0.765244 | ||||||||
\(353\) | 7078.96 | 1.06735 | 0.533676 | − | 0.845689i | \(-0.320810\pi\) | ||||
0.533676 | + | 0.845689i | \(0.320810\pi\) | |||||||
\(354\) | −1582.68 | −0.237623 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1367.80 | 0.203633 | ||||||||
\(357\) | 4036.89 | 0.598474 | ||||||||
\(358\) | 12397.4 | 1.83023 | ||||||||
\(359\) | −5409.79 | −0.795314 | −0.397657 | − | 0.917534i | \(-0.630177\pi\) | ||||
−0.397657 | + | 0.917534i | \(0.630177\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4473.90 | −0.652267 | ||||||||
\(362\) | −15597.8 | −2.26465 | ||||||||
\(363\) | −857.381 | −0.123969 | ||||||||
\(364\) | −4524.69 | −0.651534 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6732.87 | 0.961565 | ||||||||
\(367\) | −4940.09 | −0.702645 | −0.351322 | − | 0.936255i | \(-0.614268\pi\) | ||||
−0.351322 | + | 0.936255i | \(0.614268\pi\) | |||||||
\(368\) | −35.6437 | −0.00504907 | ||||||||
\(369\) | −2181.77 | −0.307800 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 997.332 | 0.139566 | ||||||||
\(372\) | 525.488 | 0.0732399 | ||||||||
\(373\) | −12891.9 | −1.78959 | −0.894797 | − | 0.446473i | \(-0.852680\pi\) | ||||
−0.894797 | + | 0.446473i | \(0.852680\pi\) | |||||||
\(374\) | −15693.8 | −2.16981 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5870.72 | −0.805211 | ||||||||
\(377\) | 485.551 | 0.0663320 | ||||||||
\(378\) | 2057.65 | 0.279985 | ||||||||
\(379\) | −9475.15 | −1.28418 | −0.642092 | − | 0.766627i | \(-0.721933\pi\) | ||||
−0.642092 | + | 0.766627i | \(0.721933\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1862.58 | −0.250453 | ||||||||
\(382\) | 2936.16 | 0.393264 | ||||||||
\(383\) | 5800.97 | 0.773931 | 0.386966 | − | 0.922094i | \(-0.373523\pi\) | ||||
0.386966 | + | 0.922094i | \(0.373523\pi\) | |||||||
\(384\) | −7812.52 | −1.03823 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2050.56 | −0.270390 | ||||||||
\(387\) | −3306.15 | −0.434266 | ||||||||
\(388\) | 16253.9 | 2.12672 | ||||||||
\(389\) | 13779.7 | 1.79603 | 0.898016 | − | 0.439962i | \(-0.145008\pi\) | ||||
0.898016 | + | 0.439962i | \(0.145008\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 133.862 | 0.0173138 | ||||||||
\(392\) | 2303.48 | 0.296794 | ||||||||
\(393\) | 7765.06 | 0.996680 | ||||||||
\(394\) | 15777.5 | 2.01741 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5104.27 | −0.647725 | ||||||||
\(397\) | 2816.46 | 0.356056 | 0.178028 | − | 0.984025i | \(-0.443028\pi\) | ||||
0.178028 | + | 0.984025i | \(0.443028\pi\) | |||||||
\(398\) | −17864.8 | −2.24996 | ||||||||
\(399\) | 2374.88 | 0.297976 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11986.4 | 1.49270 | 0.746352 | − | 0.665551i | \(-0.231804\pi\) | ||||
0.746352 | + | 0.665551i | \(0.231804\pi\) | |||||||
\(402\) | −7871.74 | −0.976633 | ||||||||
\(403\) | 245.775 | 0.0303794 | ||||||||
\(404\) | −16311.9 | −2.00879 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1869.75 | 0.228557 | ||||||||
\(407\) | 13103.6 | 1.59588 | ||||||||
\(408\) | −7148.03 | −0.867354 | ||||||||
\(409\) | −3339.07 | −0.403683 | −0.201841 | − | 0.979418i | \(-0.564693\pi\) | ||||
−0.201841 | + | 0.979418i | \(0.564693\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4968.87 | −0.596342 | ||||||||
\(412\) | 18811.4 | 2.24944 | ||||||||
\(413\) | −1818.84 | −0.216706 | ||||||||
\(414\) | 68.2313 | 0.00809996 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2487.40 | −0.293161 | ||||||||
\(417\) | 459.769 | 0.0539927 | ||||||||
\(418\) | −9232.57 | −1.08033 | ||||||||
\(419\) | 1688.52 | 0.196873 | 0.0984363 | − | 0.995143i | \(-0.468616\pi\) | ||||
0.0984363 | + | 0.995143i | \(0.468616\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2664.27 | −0.308429 | −0.154214 | − | 0.988037i | \(-0.549285\pi\) | ||||
−0.154214 | + | 0.988037i | \(0.549285\pi\) | |||||||
\(422\) | −11120.5 | −1.28279 | ||||||||
\(423\) | 1840.89 | 0.211601 | ||||||||
\(424\) | −1765.95 | −0.202269 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7874.38 | 0.895575 | ||||||||
\(427\) | 7737.54 | 0.876923 | ||||||||
\(428\) | 11259.2 | 1.27158 | ||||||||
\(429\) | −2387.31 | −0.268672 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12266.0 | 1.37084 | 0.685420 | − | 0.728148i | \(-0.259619\pi\) | ||||
0.685420 | + | 0.728148i | \(0.259619\pi\) | |||||||
\(432\) | −596.827 | −0.0664695 | ||||||||
\(433\) | 15647.3 | 1.73664 | 0.868318 | − | 0.496008i | \(-0.165201\pi\) | ||||
0.868318 | + | 0.496008i | \(0.165201\pi\) | |||||||
\(434\) | 946.425 | 0.104677 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13894.8 | −1.52624 | ||||||||
\(437\) | 78.7503 | 0.00862045 | ||||||||
\(438\) | −14270.7 | −1.55680 | ||||||||
\(439\) | 16131.0 | 1.75373 | 0.876867 | − | 0.480733i | \(-0.159629\pi\) | ||||
0.876867 | + | 0.480733i | \(0.159629\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −722.306 | −0.0779944 | ||||||||
\(442\) | −7724.34 | −0.831243 | ||||||||
\(443\) | −10053.7 | −1.07825 | −0.539127 | − | 0.842225i | \(-0.681246\pi\) | ||||
−0.539127 | + | 0.842225i | \(0.681246\pi\) | |||||||
\(444\) | 13789.5 | 1.47392 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −15649.5 | −1.66150 | ||||||||
\(447\) | −4450.13 | −0.470882 | ||||||||
\(448\) | −12444.9 | −1.31242 | ||||||||
\(449\) | 7477.71 | 0.785957 | 0.392979 | − | 0.919548i | \(-0.371445\pi\) | ||||
0.392979 | + | 0.919548i | \(0.371445\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9747.51 | 1.01772 | ||||||||
\(452\) | −26633.1 | −2.77150 | ||||||||
\(453\) | 1182.84 | 0.122682 | ||||||||
\(454\) | −2478.19 | −0.256184 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4205.14 | −0.431850 | ||||||||
\(457\) | −1363.46 | −0.139562 | −0.0697812 | − | 0.997562i | \(-0.522230\pi\) | ||||
−0.0697812 | + | 0.997562i | \(0.522230\pi\) | |||||||
\(458\) | −12064.5 | −1.23086 | ||||||||
\(459\) | 2241.42 | 0.227932 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5276.77 | 0.533109 | 0.266555 | − | 0.963820i | \(-0.414115\pi\) | ||||
0.266555 | + | 0.963820i | \(0.414115\pi\) | |||||||
\(462\) | −9192.99 | −0.925751 | ||||||||
\(463\) | −5740.02 | −0.576159 | −0.288079 | − | 0.957607i | \(-0.593017\pi\) | ||||
−0.288079 | + | 0.957607i | \(0.593017\pi\) | |||||||
\(464\) | −542.325 | −0.0542604 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 26023.1 | 2.58690 | ||||||||
\(467\) | −6233.36 | −0.617657 | −0.308828 | − | 0.951118i | \(-0.599937\pi\) | ||||
−0.308828 | + | 0.951118i | \(0.599937\pi\) | |||||||
\(468\) | −2512.27 | −0.248140 | ||||||||
\(469\) | −9046.35 | −0.890664 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5181.16 | 0.506869 | ||||||||
\(472\) | 3220.58 | 0.314067 | ||||||||
\(473\) | 14770.9 | 1.43587 | ||||||||
\(474\) | 16227.0 | 1.57243 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −18979.7 | −1.82759 | ||||||||
\(477\) | 553.753 | 0.0531543 | ||||||||
\(478\) | −4748.61 | −0.454385 | ||||||||
\(479\) | −19688.2 | −1.87803 | −0.939013 | − | 0.343881i | \(-0.888258\pi\) | ||||
−0.939013 | + | 0.343881i | \(0.888258\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6449.46 | 0.611372 | ||||||||
\(482\) | 19155.5 | 1.81019 | ||||||||
\(483\) | 78.4127 | 0.00738696 | ||||||||
\(484\) | 4031.03 | 0.378572 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1142.48 | 0.106634 | ||||||||
\(487\) | 3955.08 | 0.368012 | 0.184006 | − | 0.982925i | \(-0.441093\pi\) | ||||
0.184006 | + | 0.982925i | \(0.441093\pi\) | |||||||
\(488\) | −13700.7 | −1.27090 | ||||||||
\(489\) | −6102.84 | −0.564377 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13893.5 | −1.27699 | −0.638497 | − | 0.769624i | \(-0.720443\pi\) | ||||
−0.638497 | + | 0.769624i | \(0.720443\pi\) | |||||||
\(492\) | 10257.7 | 0.939947 | ||||||||
\(493\) | 2036.74 | 0.186065 | ||||||||
\(494\) | −4544.18 | −0.413871 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −274.512 | −0.0248508 | ||||||||
\(497\) | 9049.39 | 0.816741 | ||||||||
\(498\) | 16332.2 | 1.46960 | ||||||||
\(499\) | 13523.7 | 1.21324 | 0.606618 | − | 0.794993i | \(-0.292526\pi\) | ||||
0.606618 | + | 0.794993i | \(0.292526\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 578.700 | 0.0516056 | ||||||||
\(502\) | −8340.50 | −0.741543 | ||||||||
\(503\) | −13135.4 | −1.16437 | −0.582184 | − | 0.813057i | \(-0.697802\pi\) | ||||
−0.582184 | + | 0.813057i | \(0.697802\pi\) | |||||||
\(504\) | −4187.11 | −0.370057 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −304.837 | −0.0267820 | ||||||||
\(507\) | 5415.99 | 0.474423 | ||||||||
\(508\) | 8757.03 | 0.764823 | ||||||||
\(509\) | −2222.71 | −0.193556 | −0.0967778 | − | 0.995306i | \(-0.530854\pi\) | ||||
−0.0967778 | + | 0.995306i | \(0.530854\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16400.1 | −1.41976 | ||||||||
\(512\) | 7853.76 | 0.677911 | ||||||||
\(513\) | 1318.61 | 0.113486 | ||||||||
\(514\) | 3116.12 | 0.267405 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 15544.1 | 1.32614 | ||||||||
\(517\) | −8224.57 | −0.699645 | ||||||||
\(518\) | 24835.4 | 2.10658 | ||||||||
\(519\) | −3719.73 | −0.314601 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4916.42 | −0.413421 | −0.206710 | − | 0.978402i | \(-0.566276\pi\) | ||||
−0.206710 | + | 0.978402i | \(0.566276\pi\) | |||||||
\(522\) | 1038.15 | 0.0870471 | ||||||||
\(523\) | −17743.4 | −1.48349 | −0.741746 | − | 0.670681i | \(-0.766002\pi\) | ||||
−0.741746 | + | 0.670681i | \(0.766002\pi\) | |||||||
\(524\) | −36507.9 | −3.04362 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3348.98 | 0.277609 | ||||||||
\(527\) | 1030.95 | 0.0852161 | ||||||||
\(528\) | 2666.45 | 0.219777 | ||||||||
\(529\) | −12164.4 | −0.999786 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1009.88 | −0.0825334 | ||||||||
\(532\) | −11165.6 | −0.909946 | ||||||||
\(533\) | 4797.62 | 0.389884 | ||||||||
\(534\) | 1367.80 | 0.110844 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 16018.2 | 1.29082 | ||||||||
\(537\) | 7910.58 | 0.635692 | ||||||||
\(538\) | 14746.0 | 1.18169 | ||||||||
\(539\) | 3227.05 | 0.257883 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12671.3 | −1.00699 | −0.503495 | − | 0.863998i | \(-0.667953\pi\) | ||||
−0.503495 | + | 0.863998i | \(0.667953\pi\) | |||||||
\(542\) | 10699.3 | 0.847924 | ||||||||
\(543\) | −9952.74 | −0.786580 | ||||||||
\(544\) | −10433.9 | −0.822334 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4524.69 | −0.354650 | ||||||||
\(547\) | −5250.90 | −0.410443 | −0.205221 | − | 0.978716i | \(-0.565791\pi\) | ||||
−0.205221 | + | 0.978716i | \(0.565791\pi\) | |||||||
\(548\) | 23361.5 | 1.82108 | ||||||||
\(549\) | 4296.15 | 0.333980 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1198.20 | 0.0926406 | ||||||||
\(552\) | −138.844 | −0.0107057 | ||||||||
\(553\) | 18648.4 | 1.43401 | ||||||||
\(554\) | 24311.8 | 1.86445 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2161.63 | −0.164881 | ||||||||
\(557\) | −25830.2 | −1.96492 | −0.982462 | − | 0.186465i | \(-0.940297\pi\) | ||||
−0.982462 | + | 0.186465i | \(0.940297\pi\) | |||||||
\(558\) | 525.488 | 0.0398668 | ||||||||
\(559\) | 7270.09 | 0.550075 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10014.0 | −0.753640 | ||||||||
\(562\) | −10532.1 | −0.790519 | ||||||||
\(563\) | −2021.14 | −0.151298 | −0.0756490 | − | 0.997135i | \(-0.524103\pi\) | ||||
−0.0756490 | + | 0.997135i | \(0.524103\pi\) | |||||||
\(564\) | −8655.07 | −0.646178 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1059.00 | 0.0786450 | ||||||||
\(567\) | 1312.96 | 0.0972471 | ||||||||
\(568\) | −16023.5 | −1.18368 | ||||||||
\(569\) | 8706.51 | 0.641469 | 0.320734 | − | 0.947169i | \(-0.396070\pi\) | ||||
0.320734 | + | 0.947169i | \(0.396070\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12194.5 | −0.893740 | −0.446870 | − | 0.894599i | \(-0.647461\pi\) | ||||
−0.446870 | + | 0.894599i | \(0.647461\pi\) | |||||||
\(572\) | 11224.1 | 0.820458 | ||||||||
\(573\) | 1873.52 | 0.136592 | ||||||||
\(574\) | 18474.6 | 1.34340 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6909.82 | −0.499842 | ||||||||
\(577\) | 15264.0 | 1.10130 | 0.550649 | − | 0.834737i | \(-0.314380\pi\) | ||||
0.550649 | + | 0.834737i | \(0.314380\pi\) | |||||||
\(578\) | −9302.48 | −0.669433 | ||||||||
\(579\) | −1308.43 | −0.0939146 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18769.2 | 1.34024 | ||||||||
\(582\) | 16253.9 | 1.15764 | ||||||||
\(583\) | −2474.01 | −0.175751 | ||||||||
\(584\) | 29039.3 | 2.05763 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5359.12 | 0.377787 | ||||||||
\(587\) | 8456.89 | 0.594639 | 0.297319 | − | 0.954778i | \(-0.403907\pi\) | ||||
0.297319 | + | 0.954778i | \(0.403907\pi\) | |||||||
\(588\) | 3395.97 | 0.238176 | ||||||||
\(589\) | 606.500 | 0.0424285 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10067.4 | 0.700708 | ||||||||
\(592\) | −7203.57 | −0.500110 | ||||||||
\(593\) | 1225.23 | 0.0848467 | 0.0424234 | − | 0.999100i | \(-0.486492\pi\) | ||||
0.0424234 | + | 0.999100i | \(0.486492\pi\) | |||||||
\(594\) | −5104.27 | −0.352577 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20922.6 | 1.43796 | ||||||||
\(597\) | −11399.3 | −0.781478 | ||||||||
\(598\) | −150.038 | −0.0102600 | ||||||||
\(599\) | −16060.0 | −1.09548 | −0.547741 | − | 0.836648i | \(-0.684512\pi\) | ||||
−0.547741 | + | 0.836648i | \(0.684512\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9699.93 | 0.658350 | 0.329175 | − | 0.944269i | \(-0.393229\pi\) | ||||
0.329175 | + | 0.944269i | \(0.393229\pi\) | |||||||
\(602\) | 27995.5 | 1.89537 | ||||||||
\(603\) | −5022.84 | −0.339214 | ||||||||
\(604\) | −5561.21 | −0.374640 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −16311.9 | −1.09344 | ||||||||
\(607\) | −23661.2 | −1.58217 | −0.791087 | − | 0.611703i | \(-0.790485\pi\) | ||||
−0.791087 | + | 0.611703i | \(0.790485\pi\) | |||||||
\(608\) | −6138.19 | −0.409435 | ||||||||
\(609\) | 1193.06 | 0.0793847 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4048.05 | −0.268030 | ||||||||
\(612\) | −10538.2 | −0.696047 | ||||||||
\(613\) | 8085.63 | 0.532749 | 0.266375 | − | 0.963870i | \(-0.414174\pi\) | ||||
0.266375 | + | 0.963870i | \(0.414174\pi\) | |||||||
\(614\) | 24659.0 | 1.62078 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18706.8 | 1.22357 | ||||||||
\(617\) | 11035.1 | 0.720029 | 0.360014 | − | 0.932947i | \(-0.382772\pi\) | ||||
0.360014 | + | 0.932947i | \(0.382772\pi\) | |||||||
\(618\) | 18811.4 | 1.22444 | ||||||||
\(619\) | −16826.3 | −1.09258 | −0.546290 | − | 0.837596i | \(-0.683960\pi\) | ||||
−0.546290 | + | 0.837596i | \(0.683960\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 43.5374 | 0.00281336 | ||||||||
\(622\) | 24392.9 | 1.57245 | ||||||||
\(623\) | 1571.90 | 0.101087 | ||||||||
\(624\) | 1312.40 | 0.0841954 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2288.04 | 0.146084 | ||||||||
\(627\) | −5891.17 | −0.375233 | ||||||||
\(628\) | −24359.5 | −1.54785 | ||||||||
\(629\) | 27053.5 | 1.71493 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3705.91 | −0.233803 | −0.116902 | − | 0.993144i | \(-0.537296\pi\) | ||||
−0.116902 | + | 0.993144i | \(0.537296\pi\) | |||||||
\(632\) | −33020.2 | −2.07828 | ||||||||
\(633\) | −7095.81 | −0.445550 | ||||||||
\(634\) | −19835.3 | −1.24252 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2603.50 | −0.162320 | ||||||||
\(637\) | 1588.32 | 0.0987937 | ||||||||
\(638\) | −4638.15 | −0.287815 | ||||||||
\(639\) | 5024.53 | 0.311060 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24597.4 | −1.51566 | −0.757829 | − | 0.652453i | \(-0.773740\pi\) | ||||
−0.757829 | + | 0.652453i | \(0.773740\pi\) | |||||||
\(642\) | 11259.2 | 0.692160 | ||||||||
\(643\) | 21479.5 | 1.31737 | 0.658685 | − | 0.752419i | \(-0.271113\pi\) | ||||
0.658685 | + | 0.752419i | \(0.271113\pi\) | |||||||
\(644\) | −368.662 | −0.0225580 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −19061.4 | −1.16093 | ||||||||
\(647\) | −27119.7 | −1.64789 | −0.823946 | − | 0.566668i | \(-0.808232\pi\) | ||||
−0.823946 | + | 0.566668i | \(0.808232\pi\) | |||||||
\(648\) | −2324.83 | −0.140938 | ||||||||
\(649\) | 4511.87 | 0.272891 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 603.900 | 0.0363575 | ||||||||
\(652\) | 28692.9 | 1.72347 | ||||||||
\(653\) | −18476.4 | −1.10725 | −0.553627 | − | 0.832765i | \(-0.686757\pi\) | ||||
−0.553627 | + | 0.832765i | \(0.686757\pi\) | |||||||
\(654\) | −13894.8 | −0.830779 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5358.59 | −0.318930 | ||||||||
\(657\) | −9105.92 | −0.540724 | ||||||||
\(658\) | −15588.1 | −0.923540 | ||||||||
\(659\) | −19273.5 | −1.13928 | −0.569641 | − | 0.821894i | \(-0.692918\pi\) | ||||
−0.569641 | + | 0.821894i | \(0.692918\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25605.3 | 1.50670 | 0.753352 | − | 0.657618i | \(-0.228436\pi\) | ||||
0.753352 | + | 0.657618i | \(0.228436\pi\) | |||||||
\(662\) | −34979.3 | −2.05364 | ||||||||
\(663\) | −4928.79 | −0.288716 | ||||||||
\(664\) | −33234.3 | −1.94238 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13789.5 | 0.802300 | ||||||||
\(667\) | 39.5616 | 0.00229660 | ||||||||
\(668\) | −2720.79 | −0.157591 | ||||||||
\(669\) | −9985.75 | −0.577087 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19193.9 | −1.10428 | ||||||||
\(672\) | −6111.87 | −0.350849 | ||||||||
\(673\) | −7855.52 | −0.449938 | −0.224969 | − | 0.974366i | \(-0.572228\pi\) | ||||
−0.224969 | + | 0.974366i | \(0.572228\pi\) | |||||||
\(674\) | −30820.6 | −1.76137 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −25463.6 | −1.44877 | ||||||||
\(677\) | 6763.09 | 0.383939 | 0.191970 | − | 0.981401i | \(-0.438512\pi\) | ||||
0.191970 | + | 0.981401i | \(0.438512\pi\) | |||||||
\(678\) | −26633.1 | −1.50861 | ||||||||
\(679\) | 18679.3 | 1.05574 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1581.30 | −0.0889803 | ||||||||
\(682\) | −2347.72 | −0.131817 | ||||||||
\(683\) | −15608.6 | −0.874447 | −0.437224 | − | 0.899353i | \(-0.644038\pi\) | ||||
−0.437224 | + | 0.899353i | \(0.644038\pi\) | |||||||
\(684\) | −6199.54 | −0.346557 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 32256.1 | 1.79525 | ||||||||
\(687\) | −7698.17 | −0.427516 | ||||||||
\(688\) | −8120.16 | −0.449968 | ||||||||
\(689\) | −1217.68 | −0.0673293 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6203.15 | 0.341504 | 0.170752 | − | 0.985314i | \(-0.445380\pi\) | ||||
0.170752 | + | 0.985314i | \(0.445380\pi\) | |||||||
\(692\) | 17488.5 | 0.960714 | ||||||||
\(693\) | −5865.92 | −0.321541 | ||||||||
\(694\) | 9170.69 | 0.501606 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2112.53 | −0.115050 | ||||||||
\(697\) | 20124.5 | 1.09365 | ||||||||
\(698\) | 6707.90 | 0.363750 | ||||||||
\(699\) | 16605.0 | 0.898509 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16507.9 | −0.889435 | −0.444718 | − | 0.895671i | \(-0.646696\pi\) | ||||
−0.444718 | + | 0.895671i | \(0.646696\pi\) | |||||||
\(702\) | −2512.27 | −0.135070 | ||||||||
\(703\) | 15915.4 | 0.853854 | ||||||||
\(704\) | 30871.1 | 1.65269 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33282.2 | −1.77421 | ||||||||
\(707\) | −18746.0 | −0.997193 | ||||||||
\(708\) | 4748.03 | 0.252037 | ||||||||
\(709\) | −25539.6 | −1.35283 | −0.676416 | − | 0.736520i | \(-0.736468\pi\) | ||||
−0.676416 | + | 0.736520i | \(0.736468\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10354.2 | 0.546151 | ||||||||
\(712\) | −2783.34 | −0.146503 | ||||||||
\(713\) | 20.0252 | 0.00105182 | ||||||||
\(714\) | −18979.7 | −0.994815 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −37192.1 | −1.94125 | ||||||||
\(717\) | −3030.02 | −0.157822 | ||||||||
\(718\) | 25434.4 | 1.32201 | ||||||||
\(719\) | −7353.45 | −0.381415 | −0.190708 | − | 0.981647i | \(-0.561078\pi\) | ||||
−0.190708 | + | 0.981647i | \(0.561078\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21618.4 | 1.11666 | ||||||||
\(722\) | 21034.3 | 1.08423 | ||||||||
\(723\) | 12222.9 | 0.628732 | ||||||||
\(724\) | 46793.4 | 2.40202 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4031.03 | 0.206068 | ||||||||
\(727\) | 21696.5 | 1.10685 | 0.553424 | − | 0.832900i | \(-0.313321\pi\) | ||||
0.553424 | + | 0.832900i | \(0.313321\pi\) | |||||||
\(728\) | 9207.28 | 0.468742 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30495.8 | 1.54299 | ||||||||
\(732\) | −20198.6 | −1.01989 | ||||||||
\(733\) | −90.2714 | −0.00454877 | −0.00227439 | − | 0.999997i | \(-0.500724\pi\) | ||||
−0.00227439 | + | 0.999997i | \(0.500724\pi\) | |||||||
\(734\) | 23226.1 | 1.16797 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −202.668 | −0.0101501 | ||||||||
\(737\) | 22440.6 | 1.12159 | ||||||||
\(738\) | 10257.7 | 0.511642 | ||||||||
\(739\) | 14273.1 | 0.710479 | 0.355239 | − | 0.934775i | \(-0.384399\pi\) | ||||
0.355239 | + | 0.934775i | \(0.384399\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2899.57 | −0.143750 | ||||||||
\(742\) | −4689.02 | −0.231994 | ||||||||
\(743\) | −15866.6 | −0.783429 | −0.391715 | − | 0.920087i | \(-0.628118\pi\) | ||||
−0.391715 | + | 0.920087i | \(0.628118\pi\) | |||||||
\(744\) | −1069.31 | −0.0526921 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 60612.2 | 2.97476 | ||||||||
\(747\) | 10421.3 | 0.510437 | ||||||||
\(748\) | 47081.5 | 2.30143 | ||||||||
\(749\) | 12939.3 | 0.631232 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26776.9 | 1.30107 | 0.650534 | − | 0.759477i | \(-0.274545\pi\) | ||||
0.650534 | + | 0.759477i | \(0.274545\pi\) | |||||||
\(752\) | 4521.37 | 0.219252 | ||||||||
\(753\) | −5321.95 | −0.257560 | ||||||||
\(754\) | −2282.85 | −0.110261 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −6172.96 | −0.296969 | ||||||||
\(757\) | −30478.0 | −1.46333 | −0.731666 | − | 0.681663i | \(-0.761257\pi\) | ||||
−0.731666 | + | 0.681663i | \(0.761257\pi\) | |||||||
\(758\) | 44548.0 | 2.13464 | ||||||||
\(759\) | −194.512 | −0.00930218 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29104.7 | 1.38639 | 0.693195 | − | 0.720750i | \(-0.256202\pi\) | ||||
0.693195 | + | 0.720750i | \(0.256202\pi\) | |||||||
\(762\) | 8757.03 | 0.416317 | ||||||||
\(763\) | −15968.2 | −0.757649 | ||||||||
\(764\) | −8808.47 | −0.417119 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27273.6 | −1.28647 | ||||||||
\(767\) | 2220.69 | 0.104543 | ||||||||
\(768\) | 18304.9 | 0.860052 | ||||||||
\(769\) | 4170.65 | 0.195575 | 0.0977876 | − | 0.995207i | \(-0.468823\pi\) | ||||
0.0977876 | + | 0.995207i | \(0.468823\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1988.35 | 0.0928778 | ||||||||
\(772\) | 6151.67 | 0.286792 | ||||||||
\(773\) | 17738.5 | 0.825367 | 0.412684 | − | 0.910874i | \(-0.364591\pi\) | ||||
0.412684 | + | 0.910874i | \(0.364591\pi\) | |||||||
\(774\) | 15544.1 | 0.721860 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −33075.0 | −1.53005 | ||||||||
\(777\) | 15847.1 | 0.731677 | ||||||||
\(778\) | −64786.0 | −2.98546 | ||||||||
\(779\) | 11839.1 | 0.544519 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22448.1 | −1.02850 | ||||||||
\(782\) | −629.363 | −0.0287800 | ||||||||
\(783\) | 662.429 | 0.0302341 | ||||||||
\(784\) | −1774.04 | −0.0808145 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −36507.9 | −1.65674 | ||||||||
\(787\) | 3807.92 | 0.172475 | 0.0862374 | − | 0.996275i | \(-0.472516\pi\) | ||||
0.0862374 | + | 0.996275i | \(0.472516\pi\) | |||||||
\(788\) | −47332.6 | −2.13979 | ||||||||
\(789\) | 2136.94 | 0.0964220 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30607.3 | −1.37582 | ||||||||
\(792\) | 10386.6 | 0.466002 | ||||||||
\(793\) | −9447.06 | −0.423045 | ||||||||
\(794\) | −13241.8 | −0.591856 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 53594.5 | 2.38644 | ||||||||
\(797\) | −23840.3 | −1.05956 | −0.529779 | − | 0.848136i | \(-0.677725\pi\) | ||||
−0.529779 | + | 0.848136i | \(0.677725\pi\) | |||||||
\(798\) | −11165.6 | −0.495312 | ||||||||
\(799\) | −16980.3 | −0.751841 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 872.775 | 0.0384994 | ||||||||
\(802\) | −56355.0 | −2.48125 | ||||||||
\(803\) | 40682.6 | 1.78787 | ||||||||
\(804\) | 23615.2 | 1.03588 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1155.53 | −0.0504983 | ||||||||
\(807\) | 9409.24 | 0.410435 | ||||||||
\(808\) | 33193.1 | 1.44521 | ||||||||
\(809\) | −1984.22 | −0.0862316 | −0.0431158 | − | 0.999070i | \(-0.513728\pi\) | ||||
−0.0431158 | + | 0.999070i | \(0.513728\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9713.78 | −0.420588 | −0.210294 | − | 0.977638i | \(-0.567442\pi\) | ||||
−0.210294 | + | 0.977638i | \(0.567442\pi\) | |||||||
\(812\) | −5609.25 | −0.242421 | ||||||||
\(813\) | 6827.08 | 0.294509 | ||||||||
\(814\) | −61607.4 | −2.65275 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5505.10 | 0.236173 | ||||||||
\(817\) | 17940.5 | 0.768246 | ||||||||
\(818\) | 15698.8 | 0.671023 | ||||||||
\(819\) | −2887.14 | −0.123181 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19235.4 | −0.817686 | −0.408843 | − | 0.912605i | \(-0.634068\pi\) | ||||
−0.408843 | + | 0.912605i | \(0.634068\pi\) | |||||||
\(822\) | 23361.5 | 0.991271 | ||||||||
\(823\) | 12717.6 | 0.538650 | 0.269325 | − | 0.963049i | \(-0.413199\pi\) | ||||
0.269325 | + | 0.963049i | \(0.413199\pi\) | |||||||
\(824\) | −38279.2 | −1.61835 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8551.41 | 0.360220 | ||||||||
\(827\) | 6744.75 | 0.283601 | 0.141800 | − | 0.989895i | \(-0.454711\pi\) | ||||
0.141800 | + | 0.989895i | \(0.454711\pi\) | |||||||
\(828\) | −204.694 | −0.00859131 | ||||||||
\(829\) | 3404.22 | 0.142622 | 0.0713108 | − | 0.997454i | \(-0.477282\pi\) | ||||
0.0713108 | + | 0.997454i | \(0.477282\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15513.0 | 0.647581 | ||||||||
\(832\) | 15194.4 | 0.633139 | ||||||||
\(833\) | 6662.52 | 0.277122 | ||||||||
\(834\) | −2161.63 | −0.0897496 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 27697.7 | 1.14587 | ||||||||
\(837\) | 335.306 | 0.0138469 | ||||||||
\(838\) | −7938.69 | −0.327252 | ||||||||
\(839\) | −21361.9 | −0.879015 | −0.439508 | − | 0.898239i | \(-0.644847\pi\) | ||||
−0.439508 | + | 0.898239i | \(0.644847\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23787.1 | −0.975319 | ||||||||
\(842\) | 12526.2 | 0.512687 | ||||||||
\(843\) | −6720.41 | −0.274571 | ||||||||
\(844\) | 33361.4 | 1.36060 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8655.07 | −0.351735 | ||||||||
\(847\) | 4632.54 | 0.187929 | ||||||||
\(848\) | 1360.06 | 0.0550762 | ||||||||
\(849\) | 675.732 | 0.0273158 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 525.488 | 0.0211674 | ||||||||
\(852\) | −23623.1 | −0.949901 | ||||||||
\(853\) | 10728.9 | 0.430657 | 0.215328 | − | 0.976542i | \(-0.430918\pi\) | ||||
0.215328 | + | 0.976542i | \(0.430918\pi\) | |||||||
\(854\) | −36378.5 | −1.45767 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22911.4 | −0.914830 | ||||||||
\(857\) | 42895.2 | 1.70977 | 0.854885 | − | 0.518817i | \(-0.173627\pi\) | ||||
0.854885 | + | 0.518817i | \(0.173627\pi\) | |||||||
\(858\) | 11224.1 | 0.446601 | ||||||||
\(859\) | 35530.5 | 1.41127 | 0.705637 | − | 0.708574i | \(-0.250661\pi\) | ||||
0.705637 | + | 0.708574i | \(0.250661\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11788.4 | 0.466605 | ||||||||
\(862\) | −57669.3 | −2.27868 | ||||||||
\(863\) | −5704.35 | −0.225004 | −0.112502 | − | 0.993652i | \(-0.535886\pi\) | ||||
−0.112502 | + | 0.993652i | \(0.535886\pi\) | |||||||
\(864\) | −3393.52 | −0.133623 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −73567.0 | −2.88673 | ||||||||
\(867\) | −5935.78 | −0.232514 | ||||||||
\(868\) | −2839.27 | −0.111027 | ||||||||
\(869\) | −46259.6 | −1.80581 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11045.0 | 0.429674 | ||||||||
\(872\) | 28274.4 | 1.09804 | ||||||||
\(873\) | 10371.4 | 0.402082 | ||||||||
\(874\) | −370.249 | −0.0143294 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 42812.0 | 1.65124 | ||||||||
\(877\) | −50249.0 | −1.93476 | −0.967382 | − | 0.253324i | \(-0.918476\pi\) | ||||
−0.967382 | + | 0.253324i | \(0.918476\pi\) | |||||||
\(878\) | −75840.7 | −2.91515 | ||||||||
\(879\) | 3419.58 | 0.131217 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26864.5 | −1.02734 | −0.513672 | − | 0.857987i | \(-0.671715\pi\) | ||||
−0.513672 | + | 0.857987i | \(0.671715\pi\) | |||||||
\(882\) | 3395.97 | 0.129646 | ||||||||
\(883\) | −18942.1 | −0.721918 | −0.360959 | − | 0.932582i | \(-0.617551\pi\) | ||||
−0.360959 | + | 0.932582i | \(0.617551\pi\) | |||||||
\(884\) | 23173.0 | 0.881667 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 47268.2 | 1.79233 | ||||||||
\(887\) | 25344.8 | 0.959409 | 0.479705 | − | 0.877430i | \(-0.340744\pi\) | ||||
0.479705 | + | 0.877430i | \(0.340744\pi\) | |||||||
\(888\) | −28060.2 | −1.06040 | ||||||||
\(889\) | 10063.7 | 0.379670 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3256.96 | −0.122460 | ||||||||
\(892\) | 46948.6 | 1.76228 | ||||||||
\(893\) | −9989.40 | −0.374337 | ||||||||
\(894\) | 20922.6 | 0.782725 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 42212.0 | 1.57389 | ||||||||
\(897\) | −95.7370 | −0.00356362 | ||||||||
\(898\) | −35156.9 | −1.30646 | ||||||||
\(899\) | 304.686 | 0.0113035 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5107.79 | −0.188863 | ||||||||
\(902\) | −45828.5 | −1.69171 | ||||||||
\(903\) | 17863.5 | 0.658318 | ||||||||
\(904\) | 54195.6 | 1.99394 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5561.21 | −0.203928 | ||||||||
\(907\) | −4800.11 | −0.175728 | −0.0878639 | − | 0.996132i | \(-0.528004\pi\) | ||||
−0.0878639 | + | 0.996132i | \(0.528004\pi\) | |||||||
\(908\) | 7434.58 | 0.271724 | ||||||||
\(909\) | −10408.4 | −0.379786 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25731.7 | −0.935819 | −0.467909 | − | 0.883776i | \(-0.654993\pi\) | ||||
−0.467909 | + | 0.883776i | \(0.654993\pi\) | |||||||
\(912\) | 3238.61 | 0.117589 | ||||||||
\(913\) | −46559.4 | −1.68772 | ||||||||
\(914\) | 6410.40 | 0.231988 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 36193.4 | 1.30553 | ||||||||
\(917\) | −41955.6 | −1.51090 | ||||||||
\(918\) | −10538.2 | −0.378880 | ||||||||
\(919\) | −12751.9 | −0.457722 | −0.228861 | − | 0.973459i | \(-0.573500\pi\) | ||||
−0.228861 | + | 0.973459i | \(0.573500\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15734.6 | 0.562945 | ||||||||
\(922\) | −24809.0 | −0.886163 | ||||||||
\(923\) | −11048.7 | −0.394012 | ||||||||
\(924\) | 27579.0 | 0.981907 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 26987.1 | 0.957722 | ||||||||
\(927\) | 12003.3 | 0.425285 | ||||||||
\(928\) | −3083.63 | −0.109079 | ||||||||
\(929\) | 15557.8 | 0.549444 | 0.274722 | − | 0.961524i | \(-0.411414\pi\) | ||||
0.274722 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3919.51 | 0.137977 | ||||||||
\(932\) | −78069.3 | −2.74383 | ||||||||
\(933\) | 15564.8 | 0.546160 | ||||||||
\(934\) | 29306.5 | 1.02670 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5112.20 | 0.178523 | ||||||||
\(937\) | 23858.0 | 0.831811 | 0.415905 | − | 0.909408i | \(-0.363465\pi\) | ||||
0.415905 | + | 0.909408i | \(0.363465\pi\) | |||||||
\(938\) | 42532.0 | 1.48051 | ||||||||
\(939\) | 1459.97 | 0.0507394 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9748.00 | 0.337700 | 0.168850 | − | 0.985642i | \(-0.445995\pi\) | ||||
0.168850 | + | 0.985642i | \(0.445995\pi\) | |||||||
\(942\) | −24359.5 | −0.842544 | ||||||||
\(943\) | 390.899 | 0.0134989 | ||||||||
\(944\) | −2480.35 | −0.0855176 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −69446.4 | −2.38678 | ||||||||
\(947\) | 51537.0 | 1.76845 | 0.884227 | − | 0.467057i | \(-0.154686\pi\) | ||||
0.884227 | + | 0.467057i | \(0.154686\pi\) | |||||||
\(948\) | −48681.0 | −1.66781 | ||||||||
\(949\) | 20023.5 | 0.684923 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12656.6 | −0.431566 | ||||||||
\(952\) | 38621.7 | 1.31485 | ||||||||
\(953\) | 5631.36 | 0.191414 | 0.0957071 | − | 0.995410i | \(-0.469489\pi\) | ||||
0.0957071 | + | 0.995410i | \(0.469489\pi\) | |||||||
\(954\) | −2603.50 | −0.0883559 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14245.8 | 0.481948 | ||||||||
\(957\) | −2959.54 | −0.0999668 | ||||||||
\(958\) | 92565.1 | 3.12176 | ||||||||
\(959\) | 26847.4 | 0.904013 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29636.8 | −0.994823 | ||||||||
\(962\) | −30322.5 | −1.01625 | ||||||||
\(963\) | 7184.36 | 0.240408 | ||||||||
\(964\) | −57466.5 | −1.91999 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −368.662 | −0.0122790 | ||||||||
\(967\) | 43360.9 | 1.44198 | 0.720989 | − | 0.692946i | \(-0.243688\pi\) | ||||
0.720989 | + | 0.692946i | \(0.243688\pi\) | |||||||
\(968\) | −8202.72 | −0.272361 | ||||||||
\(969\) | −12162.8 | −0.403226 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12920.0 | 0.427007 | 0.213503 | − | 0.976942i | \(-0.431513\pi\) | ||||
0.213503 | + | 0.976942i | \(0.431513\pi\) | |||||||
\(972\) | −3427.44 | −0.113102 | ||||||||
\(973\) | −2484.19 | −0.0818493 | ||||||||
\(974\) | −18595.0 | −0.611728 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10551.7 | 0.346056 | ||||||||
\(977\) | 10650.4 | 0.348759 | 0.174379 | − | 0.984679i | \(-0.444208\pi\) | ||||
0.174379 | + | 0.984679i | \(0.444208\pi\) | |||||||
\(978\) | 28692.9 | 0.938137 | ||||||||
\(979\) | −3899.31 | −0.127296 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8866.07 | −0.288554 | ||||||||
\(982\) | 65321.0 | 2.12269 | ||||||||
\(983\) | 49450.3 | 1.60450 | 0.802248 | − | 0.596991i | \(-0.203637\pi\) | ||||
0.802248 | + | 0.596991i | \(0.203637\pi\) | |||||||
\(984\) | −20873.4 | −0.676239 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9575.85 | −0.309287 | ||||||||
\(987\) | −9946.58 | −0.320773 | ||||||||
\(988\) | 13632.5 | 0.438976 | ||||||||
\(989\) | 592.351 | 0.0190452 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9410.47 | 0.301648 | 0.150824 | − | 0.988561i | \(-0.451807\pi\) | ||||
0.150824 | + | 0.988561i | \(0.451807\pi\) | |||||||
\(992\) | −1560.86 | −0.0499571 | ||||||||
\(993\) | −22319.8 | −0.713291 | ||||||||
\(994\) | −42546.3 | −1.35763 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −48996.5 | −1.55875 | ||||||||
\(997\) | −532.117 | −0.0169030 | −0.00845151 | − | 0.999964i | \(-0.502690\pi\) | ||||
−0.00845151 | + | 0.999964i | \(0.502690\pi\) | |||||||
\(998\) | −63582.6 | −2.01671 | ||||||||
\(999\) | 8798.88 | 0.278663 |
(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 | 75.4.a.c.1.1 | 2 | ||
3.2 | odd | 2 | 225.4.a.o.1.2 | 2 | |||
4.3 | odd | 2 | 1200.4.a.bt.1.1 | 2 | |||
5.2 | odd | 4 | 15.4.b.a.4.1 | ✓ | 4 | ||
5.3 | odd | 4 | 15.4.b.a.4.4 | yes | 4 | ||
5.4 | even | 2 | 75.4.a.f.1.2 | 2 | |||
15.2 | even | 4 | 45.4.b.b.19.4 | 4 | |||
15.8 | even | 4 | 45.4.b.b.19.1 | 4 | |||
15.14 | odd | 2 | 225.4.a.i.1.1 | 2 | |||
20.3 | even | 4 | 240.4.f.f.49.4 | 4 | |||
20.7 | even | 4 | 240.4.f.f.49.2 | 4 | |||
20.19 | odd | 2 | 1200.4.a.bn.1.2 | 2 | |||
40.3 | even | 4 | 960.4.f.p.769.1 | 4 | |||
40.13 | odd | 4 | 960.4.f.q.769.3 | 4 | |||
40.27 | even | 4 | 960.4.f.p.769.3 | 4 | |||
40.37 | odd | 4 | 960.4.f.q.769.1 | 4 | |||
60.23 | odd | 4 | 720.4.f.j.289.1 | 4 | |||
60.47 | odd | 4 | 720.4.f.j.289.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.4.b.a.4.1 | ✓ | 4 | 5.2 | odd | 4 | ||
15.4.b.a.4.4 | yes | 4 | 5.3 | odd | 4 | ||
45.4.b.b.19.1 | 4 | 15.8 | even | 4 | |||
45.4.b.b.19.4 | 4 | 15.2 | even | 4 | |||
75.4.a.c.1.1 | 2 | 1.1 | even | 1 | trivial | ||
75.4.a.f.1.2 | 2 | 5.4 | even | 2 | |||
225.4.a.i.1.1 | 2 | 15.14 | odd | 2 | |||
225.4.a.o.1.2 | 2 | 3.2 | odd | 2 | |||
240.4.f.f.49.2 | 4 | 20.7 | even | 4 | |||
240.4.f.f.49.4 | 4 | 20.3 | even | 4 | |||
720.4.f.j.289.1 | 4 | 60.23 | odd | 4 | |||
720.4.f.j.289.2 | 4 | 60.47 | odd | 4 | |||
960.4.f.p.769.1 | 4 | 40.3 | even | 4 | |||
960.4.f.p.769.3 | 4 | 40.27 | even | 4 | |||
960.4.f.q.769.1 | 4 | 40.37 | odd | 4 | |||
960.4.f.q.769.3 | 4 | 40.13 | odd | 4 | |||
1200.4.a.bn.1.2 | 2 | 20.19 | odd | 2 | |||
1200.4.a.bt.1.1 | 2 | 4.3 | odd | 2 |