Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 4024) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 | ||||||||
\(3\) | −3.18633 | −1.83963 | −0.919814 | − | 0.392356i | \(-0.871660\pi\) | ||||
−0.919814 | + | 0.392356i | \(0.871660\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.57145 | −0.702775 | −0.351387 | − | 0.936230i | \(-0.614290\pi\) | ||||
−0.351387 | + | 0.936230i | \(0.614290\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.06067 | 1.15682 | 0.578412 | − | 0.815745i | \(-0.303673\pi\) | ||||
0.578412 | + | 0.815745i | \(0.303673\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.15268 | 2.38423 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.545150 | −0.164369 | −0.0821845 | − | 0.996617i | \(-0.526190\pi\) | ||||
−0.0821845 | + | 0.996617i | \(0.526190\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.64668 | −0.456707 | −0.228353 | − | 0.973578i | \(-0.573334\pi\) | ||||
−0.228353 | + | 0.973578i | \(0.573334\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.00716 | 1.29284 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.65160 | −0.885644 | −0.442822 | − | 0.896610i | \(-0.646023\pi\) | ||||
−0.442822 | + | 0.896610i | \(0.646023\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.61130 | 0.599074 | 0.299537 | − | 0.954085i | \(-0.403168\pi\) | ||||
0.299537 | + | 0.954085i | \(0.403168\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.75229 | −2.12812 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.92971 | 0.819402 | 0.409701 | − | 0.912220i | \(-0.365633\pi\) | ||||
0.409701 | + | 0.912220i | \(0.365633\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.53054 | −0.506108 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −13.2318 | −2.54646 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.11113 | 1.32050 | 0.660252 | − | 0.751044i | \(-0.270450\pi\) | ||||
0.660252 | + | 0.751044i | \(0.270450\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.75620 | 1.39305 | 0.696527 | − | 0.717531i | \(-0.254728\pi\) | ||||
0.696527 | + | 0.717531i | \(0.254728\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.73703 | 0.302378 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.80969 | −0.812986 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.57716 | −1.57448 | −0.787238 | − | 0.616650i | \(-0.788490\pi\) | ||||
−0.787238 | + | 0.616650i | \(0.788490\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.24686 | 0.840170 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.04104 | −0.162583 | −0.0812917 | − | 0.996690i | \(-0.525905\pi\) | ||||
−0.0812917 | + | 0.996690i | \(0.525905\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0422 | −1.53141 | −0.765707 | − | 0.643190i | \(-0.777611\pi\) | ||||
−0.765707 | + | 0.643190i | \(0.777611\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.2401 | −1.67557 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.76111 | 0.402749 | 0.201375 | − | 0.979514i | \(-0.435459\pi\) | ||||
0.201375 | + | 0.979514i | \(0.435459\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.36768 | 0.338240 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.6352 | 1.62925 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.38236 | −1.28877 | −0.644383 | − | 0.764703i | \(-0.722886\pi\) | ||||
−0.644383 | + | 0.764703i | \(0.722886\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.856678 | 0.115514 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.32047 | −1.10207 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.80183 | 0.364767 | 0.182383 | − | 0.983228i | \(-0.441619\pi\) | ||||
0.182383 | + | 0.983228i | \(0.441619\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.26624 | 0.674273 | 0.337136 | − | 0.941456i | \(-0.390542\pi\) | ||||
0.337136 | + | 0.941456i | \(0.390542\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 21.8920 | 2.75813 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.58768 | 0.320962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.28320 | −0.889784 | −0.444892 | − | 0.895584i | \(-0.646758\pi\) | ||||
−0.444892 | + | 0.895584i | \(0.646758\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.5214 | −1.50739 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.46671 | 0.411422 | 0.205711 | − | 0.978613i | \(-0.434049\pi\) | ||||
0.205711 | + | 0.978613i | \(0.434049\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.1421 | −1.77225 | −0.886123 | − | 0.463450i | \(-0.846612\pi\) | ||||
−0.886123 | + | 0.463450i | \(0.846612\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.06313 | 0.931050 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.66852 | −0.190146 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.12623 | 1.02678 | 0.513391 | − | 0.858155i | \(-0.328389\pi\) | ||||
0.513391 | + | 0.858155i | \(0.328389\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 20.7028 | 2.30031 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.33358 | −0.585436 | −0.292718 | − | 0.956199i | \(-0.594560\pi\) | ||||
−0.292718 | + | 0.956199i | \(0.594560\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.73832 | 0.622408 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −22.6584 | −2.42923 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.2732 | −1.30096 | −0.650481 | − | 0.759523i | \(-0.725432\pi\) | ||||
−0.650481 | + | 0.759523i | \(0.725432\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.03994 | −0.528329 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −24.7138 | −2.56270 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.10354 | −0.421014 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0744 | 1.22597 | 0.612983 | − | 0.790096i | \(-0.289970\pi\) | ||||
0.612983 | + | 0.790096i | \(0.289970\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.89929 | −0.391893 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.6218 | 1.85294 | 0.926468 | − | 0.376374i | \(-0.122829\pi\) | ||||
0.926468 | + | 0.376374i | \(0.122829\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.34086 | 0.132119 | 0.0660596 | − | 0.997816i | \(-0.478957\pi\) | ||||
0.0660596 | + | 0.997816i | \(0.478957\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 15.3252 | 1.49559 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.0262517 | −0.00253785 | −0.00126892 | − | 0.999999i | \(-0.500404\pi\) | ||||
−0.00126892 | + | 0.999999i | \(0.500404\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.350614 | 0.0335828 | 0.0167914 | − | 0.999859i | \(-0.494655\pi\) | ||||
0.0167914 | + | 0.999859i | \(0.494655\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 30.5160 | 2.89645 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.16637 | 0.203795 | 0.101897 | − | 0.994795i | \(-0.467509\pi\) | ||||
0.101897 | + | 0.994795i | \(0.467509\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.17535 | −0.575855 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.7782 | −1.08889 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.1763 | −1.02453 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7028 | −0.972983 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.31710 | 0.299093 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8339 | 1.05845 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.24877 | 0.288282 | 0.144141 | − | 0.989557i | \(-0.453958\pi\) | ||||
0.144141 | + | 0.989557i | \(0.453958\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 31.9976 | 2.81723 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.29059 | 0.462241 | 0.231120 | − | 0.972925i | \(-0.425761\pi\) | ||||
0.231120 | + | 0.972925i | \(0.425761\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.99233 | 0.693023 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 20.7932 | 1.78959 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.5680 | 1.41550 | 0.707751 | − | 0.706462i | \(-0.249710\pi\) | ||||
0.707751 | + | 0.706462i | \(0.249710\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.2940 | 1.21240 | 0.606202 | − | 0.795311i | \(-0.292692\pi\) | ||||
0.606202 | + | 0.795311i | \(0.292692\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.79780 | −0.740909 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.897688 | 0.0750685 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.1748 | −0.928016 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.54421 | −0.622236 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.98494 | 0.244536 | 0.122268 | − | 0.992497i | \(-0.460983\pi\) | ||||
0.122268 | + | 0.992497i | \(0.460983\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.2406 | 0.914744 | 0.457372 | − | 0.889276i | \(-0.348791\pi\) | ||||
0.457372 | + | 0.889276i | \(0.348791\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −26.1188 | −2.11158 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.1885 | −0.979003 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.9185 | 0.951201 | 0.475601 | − | 0.879661i | \(-0.342231\pi\) | ||||
0.475601 | + | 0.879661i | \(0.342231\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 29.8953 | 2.37085 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0275 | 0.947903 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.8331 | −0.926840 | −0.463420 | − | 0.886139i | \(-0.653378\pi\) | ||||
−0.463420 | + | 0.886139i | \(0.653378\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.72966 | −0.212503 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.94973 | 0.460404 | 0.230202 | − | 0.973143i | \(-0.426061\pi\) | ||||
0.230202 | + | 0.973143i | \(0.426061\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.2884 | −0.791419 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.6778 | 1.42833 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.47330 | −0.644213 | −0.322107 | − | 0.946703i | \(-0.604391\pi\) | ||||
−0.322107 | + | 0.946703i | \(0.604391\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.74514 | −0.585477 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.92754 | −0.671035 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.8938 | 1.41219 | 0.706094 | − | 0.708118i | \(-0.250455\pi\) | ||||
0.706094 | + | 0.708118i | \(0.250455\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.01854 | 0.596013 | 0.298007 | − | 0.954564i | \(-0.403678\pi\) | ||||
0.298007 | + | 0.954564i | \(0.403678\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.7800 | −1.24041 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.0500 | 1.10650 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.99067 | 0.145572 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −40.4982 | −2.94581 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.1165 | −1.74501 | −0.872503 | − | 0.488609i | \(-0.837504\pi\) | ||||
−0.872503 | + | 0.488609i | \(0.837504\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.50608 | −0.612281 | −0.306140 | − | 0.951986i | \(-0.599038\pi\) | ||||
−0.306140 | + | 0.951986i | \(0.599038\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.24519 | −0.590450 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.3232 | −1.80420 | −0.902101 | − | 0.431524i | \(-0.857976\pi\) | ||||
−0.902101 | + | 0.431524i | \(0.857976\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.62162 | −0.256730 | −0.128365 | − | 0.991727i | \(-0.540973\pi\) | ||||
−0.128365 | + | 0.991727i | \(0.540973\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.2066 | 1.63687 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.7648 | 1.52759 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.63595 | 0.114259 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 28.1080 | 1.95364 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.42355 | −0.0984692 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.15954 | −0.217512 | −0.108756 | − | 0.994068i | \(-0.534687\pi\) | ||||
−0.108756 | + | 0.994068i | \(0.534687\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.0461 | −0.756864 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.7808 | 1.07624 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.7391 | 1.61152 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 48.2476 | 3.26027 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.01302 | 0.404480 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.82132 | −0.121965 | −0.0609824 | − | 0.998139i | \(-0.519423\pi\) | ||||
−0.0609824 | + | 0.998139i | \(0.519423\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.1001 | −1.20668 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.8468 | 1.31728 | 0.658638 | − | 0.752460i | \(-0.271133\pi\) | ||||
0.658638 | + | 0.752460i | \(0.271133\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.0063 | −0.991645 | −0.495822 | − | 0.868424i | \(-0.665133\pi\) | ||||
−0.495822 | + | 0.868424i | \(0.665133\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.31646 | 0.349798 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.99972 | −0.524079 | −0.262039 | − | 0.965057i | \(-0.584395\pi\) | ||||
−0.262039 | + | 0.965057i | \(0.584395\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.33895 | −0.283042 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −29.0792 | −1.88889 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.0846 | 0.652318 | 0.326159 | − | 0.945315i | \(-0.394246\pi\) | ||||
0.326159 | + | 0.945315i | \(0.394246\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.19257 | 0.527730 | 0.263865 | − | 0.964560i | \(-0.415003\pi\) | ||||
0.263865 | + | 0.964560i | \(0.415003\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −26.2706 | −1.68526 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.72070 | −0.237707 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.29998 | −0.273601 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.9945 | 1.07698 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.1224 | −0.891396 | −0.445698 | − | 0.895183i | \(-0.647044\pi\) | ||||
−0.445698 | + | 0.895183i | \(0.647044\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.14228 | −0.134684 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −18.2842 | −1.14500 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.57153 | 0.0980294 | 0.0490147 | − | 0.998798i | \(-0.484392\pi\) | ||||
0.0490147 | + | 0.998798i | \(0.484392\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.3125 | −1.82139 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 50.8637 | 3.14838 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.79538 | −0.357358 | −0.178679 | − | 0.983907i | \(-0.557182\pi\) | ||||
−0.178679 | + | 0.983907i | \(0.557182\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.7439 | 0.905713 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 39.1066 | 2.39328 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.77372 | 0.108145 | 0.0540727 | − | 0.998537i | \(-0.482780\pi\) | ||||
0.0540727 | + | 0.998537i | \(0.482780\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.7882 | −1.01981 | −0.509905 | − | 0.860231i | \(-0.670319\pi\) | ||||
−0.509905 | + | 0.860231i | \(0.670319\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.0589 | 0.971928 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.37952 | 0.0831885 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.1740 | 0.911716 | 0.455858 | − | 0.890053i | \(-0.349333\pi\) | ||||
0.455858 | + | 0.890053i | \(0.349333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 55.4776 | 3.32136 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.1977 | −1.86110 | −0.930548 | − | 0.366170i | \(-0.880669\pi\) | ||||
−0.930548 | + | 0.366170i | \(0.880669\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.6509 | 0.870908 | 0.435454 | − | 0.900211i | \(-0.356588\pi\) | ||||
0.435454 | + | 0.900211i | \(0.356588\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.0752 | 0.774509 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.18628 | −0.188080 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.66579 | −0.215635 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −38.4729 | −2.25532 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.59868 | 0.385499 | 0.192749 | − | 0.981248i | \(-0.438260\pi\) | ||||
0.192749 | + | 0.981248i | \(0.438260\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.40293 | −0.256349 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.21333 | 0.418560 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.47098 | −0.374226 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.7357 | −1.77158 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −59.3351 | −3.40871 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.27564 | −0.473862 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.4053 | −1.56410 | −0.782052 | − | 0.623213i | \(-0.785827\pi\) | ||||
−0.782052 | + | 0.623213i | \(0.785827\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.27243 | −0.243050 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.28546 | −0.129596 | −0.0647982 | − | 0.997898i | \(-0.520640\pi\) | ||||
−0.0647982 | + | 0.997898i | \(0.520640\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.2333 | 1.20018 | 0.600090 | − | 0.799933i | \(-0.295132\pi\) | ||||
0.600090 | + | 0.799933i | \(0.295132\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −34.4022 | −1.93834 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.7858 | 1.56060 | 0.780302 | − | 0.625403i | \(-0.215065\pi\) | ||||
0.780302 | + | 0.625403i | \(0.215065\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.87664 | −0.217050 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.0836465 | 0.00466869 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.53545 | −0.530566 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.16699 | 0.231143 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.11717 | −0.0617798 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.45084 | 0.465910 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.7972 | −1.58284 | −0.791418 | − | 0.611275i | \(-0.790657\pi\) | ||||
−0.791418 | + | 0.611275i | \(0.790657\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −68.5024 | −3.75391 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.4452 | 0.625318 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.5387 | 0.791974 | 0.395987 | − | 0.918256i | \(-0.370402\pi\) | ||||
0.395987 | + | 0.918256i | \(0.370402\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.90275 | −0.374906 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.22829 | −0.228975 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.1780 | −0.765539 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19.6767 | 1.05936 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.66898 | −0.250644 | −0.125322 | − | 0.992116i | \(-0.539996\pi\) | ||||
−0.125322 | + | 0.992116i | \(0.539996\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.22552 | −0.386773 | −0.193387 | − | 0.981123i | \(-0.561947\pi\) | ||||
−0.193387 | + | 0.981123i | \(0.561947\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.7886 | 1.16299 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.51906 | 0.240525 | 0.120263 | − | 0.992742i | \(-0.461626\pi\) | ||||
0.120263 | + | 0.992742i | \(0.461626\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.44776 | −0.289137 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 35.6115 | 1.88476 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.1764 | 0.642644 | 0.321322 | − | 0.946970i | \(-0.395873\pi\) | ||||
0.321322 | + | 0.946970i | \(0.395873\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.1811 | −0.641110 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 34.1027 | 1.78993 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.7951 | 1.24549 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.4937 | −1.59176 | −0.795878 | − | 0.605457i | \(-0.792990\pi\) | ||||
−0.795878 | + | 0.605457i | \(0.792990\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.44624 | −0.387636 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −28.7163 | −1.49088 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.7772 | −1.38647 | −0.693235 | − | 0.720711i | \(-0.743815\pi\) | ||||
−0.693235 | + | 0.720711i | \(0.743815\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −37.7066 | −1.94716 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.7098 | −0.603083 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.4204 | −0.946193 | −0.473096 | − | 0.881011i | \(-0.656864\pi\) | ||||
−0.473096 | + | 0.881011i | \(0.656864\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.3516 | −0.530331 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.8232 | 0.655236 | 0.327618 | − | 0.944810i | \(-0.393754\pi\) | ||||
0.327618 | + | 0.944810i | \(0.393754\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.62200 | 0.133630 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −71.8283 | −3.65124 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.97406 | 0.302897 | 0.151448 | − | 0.988465i | \(-0.451606\pi\) | ||||
0.151448 | + | 0.988465i | \(0.451606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.3498 | −0.725698 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.8575 | −0.850351 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.3414 | −0.721596 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.22139 | 0.211866 | 0.105933 | − | 0.994373i | \(-0.466217\pi\) | ||||
0.105933 | + | 0.994373i | \(0.466217\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −25.4662 | −1.27490 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.8341 | −1.24015 | −0.620077 | − | 0.784541i | \(-0.712899\pi\) | ||||
−0.620077 | + | 0.784541i | \(0.712899\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.7720 | −0.636217 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −32.5335 | −1.61660 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.22099 | 0.258795 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.51909 | −0.371795 | −0.185897 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185897 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −52.7912 | −2.60400 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.57546 | 0.421971 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.38146 | 0.411430 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −45.5454 | −2.23037 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.7864 | −1.50402 | −0.752008 | − | 0.659154i | \(-0.770915\pi\) | ||||
−0.752008 | + | 0.659154i | \(0.770915\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.6540 | −1.78641 | −0.893203 | − | 0.449654i | \(-0.851547\pi\) | ||||
−0.893203 | + | 0.449654i | \(0.851547\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.7493 | 0.960246 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.24053 | 0.448231 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.1182 | 0.780014 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.86033 | −0.138098 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.47534 | 0.311906 | 0.155953 | − | 0.987764i | \(-0.450155\pi\) | ||||
0.155953 | + | 0.987764i | \(0.450155\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.97327 | −0.287057 | −0.143529 | − | 0.989646i | \(-0.545845\pi\) | ||||
−0.143529 | + | 0.989646i | \(0.545845\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 35.6066 | 1.70720 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.2617 | 0.490882 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.5237 | 0.597724 | 0.298862 | − | 0.954296i | \(-0.403393\pi\) | ||||
0.298862 | + | 0.954296i | \(0.403393\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.9353 | 0.806442 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.1272 | 1.33636 | 0.668182 | − | 0.743997i | \(-0.267073\pi\) | ||||
0.668182 | + | 0.743997i | \(0.267073\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.2868 | 0.914282 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.51099 | −0.449855 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.84589 | 0.181499 | 0.0907493 | − | 0.995874i | \(-0.471074\pi\) | ||||
0.0907493 | + | 0.995874i | \(0.471074\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.567524 | 0.0267237 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −35.8161 | −1.68279 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.92002 | 0.371296 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.3780 | 1.37424 | 0.687122 | − | 0.726542i | \(-0.258874\pi\) | ||||
0.687122 | + | 0.726542i | \(0.258874\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 48.3173 | 2.25526 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.2331 | 0.523179 | 0.261590 | − | 0.965179i | \(-0.415753\pi\) | ||||
0.261590 | + | 0.965179i | \(0.415753\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.77063 | −0.314658 | −0.157329 | − | 0.987546i | \(-0.550288\pi\) | ||||
−0.157329 | + | 0.987546i | \(0.550288\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 38.8365 | 1.80100 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −37.2784 | −1.72504 | −0.862518 | − | 0.506026i | \(-0.831114\pi\) | ||||
−0.862518 | + | 0.506026i | \(0.831114\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.2914 | −1.02932 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −37.9763 | −1.74986 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.47448 | 0.251717 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.60801 | −0.303196 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −67.1091 | −3.07271 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.4426 | 1.48234 | 0.741171 | − | 0.671317i | \(-0.234271\pi\) | ||||
0.741171 | + | 0.671317i | \(0.234271\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.7705 | 0.719074 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −38.3237 | −1.74379 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.9743 | −0.861577 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.8614 | −0.900004 | −0.450002 | − | 0.893028i | \(-0.648577\pi\) | ||||
−0.450002 | + | 0.893028i | \(0.648577\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 37.7041 | 1.70504 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.44852 | −0.0653710 | −0.0326855 | − | 0.999466i | \(-0.510406\pi\) | ||||
−0.0326855 | + | 0.999466i | \(0.510406\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.9670 | −1.16950 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.12754 | 0.275413 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.6104 | 0.475943 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.13499 | −0.319406 | −0.159703 | − | 0.987165i | \(-0.551054\pi\) | ||||
−0.159703 | + | 0.987165i | \(0.551054\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.9578 | −0.846972 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.2632 | −1.30220 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 32.7824 | 1.45592 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.4239 | −0.595005 | −0.297502 | − | 0.954721i | \(-0.596154\pi\) | ||||
−0.297502 | + | 0.954721i | \(0.596154\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −46.3449 | −2.05018 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −34.5523 | −1.52552 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.10710 | −0.0928501 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.50522 | −0.0661995 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 26.9987 | 1.18511 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.8555 | −0.694640 | −0.347320 | − | 0.937747i | \(-0.612908\pi\) | ||||
−0.347320 | + | 0.937747i | \(0.612908\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.0927 | −1.62195 | −0.810974 | − | 0.585082i | \(-0.801062\pi\) | ||||
−0.810974 | + | 0.585082i | \(0.801062\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 24.6785 | 1.07706 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −28.3226 | −1.23375 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.55736 | −0.328581 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.0406 | 0.869687 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.71426 | 0.0742529 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0412533 | 0.00178353 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −60.2018 | −2.59790 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.29074 | −0.0555962 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.4083 | −1.43633 | −0.718167 | − | 0.695871i | \(-0.755019\pi\) | ||||
−0.718167 | + | 0.695871i | \(0.755019\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25.5497 | −1.09644 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.550973 | −0.0236011 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.3912 | −0.658081 | −0.329041 | − | 0.944316i | \(-0.606725\pi\) | ||||
−0.329041 | + | 0.944316i | \(0.606725\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 37.6677 | 1.60762 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.5693 | 0.791079 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.9323 | 1.18780 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −47.9544 | −2.03555 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.8442 | 1.56114 | 0.780570 | − | 0.625068i | \(-0.214929\pi\) | ||||
0.780570 | + | 0.625068i | \(0.214929\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.5362 | 0.699407 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.34294 | −0.267799 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.6230 | 0.953445 | 0.476723 | − | 0.879054i | \(-0.341825\pi\) | ||||
0.476723 | + | 0.879054i | \(0.341825\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.40434 | −0.143222 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 63.3645 | 2.66106 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.5554 | −1.23903 | −0.619514 | − | 0.784986i | \(-0.712670\pi\) | ||||
−0.619514 | + | 0.784986i | \(0.712670\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.1394 | −1.21945 | −0.609723 | − | 0.792614i | \(-0.708719\pi\) | ||||
−0.609723 | + | 0.792614i | \(0.708719\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 76.8429 | 3.21016 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.94429 | −0.414706 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.88102 | 0.119939 | 0.0599693 | − | 0.998200i | \(-0.480900\pi\) | ||||
0.0599693 | + | 0.998200i | \(0.480900\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 27.1031 | 1.12637 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.3243 | −0.677246 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.11480 | 0.211833 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.5088 | 0.765246 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.1371 | −0.872422 | −0.436211 | − | 0.899844i | \(-0.643680\pi\) | ||||
−0.436211 | + | 0.899844i | \(0.643680\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.2538 | 0.834542 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 80.6880 | 3.31906 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.4767 | −0.840879 | −0.420439 | − | 0.907321i | \(-0.638124\pi\) | ||||
−0.420439 | + | 0.907321i | \(0.638124\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.5631 | 0.720016 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.5397 | 0.472287 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.4801 | −1.00023 | −0.500115 | − | 0.865959i | \(-0.666709\pi\) | ||||
−0.500115 | + | 0.865959i | \(0.666709\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.3885 | −1.40274 | −0.701368 | − | 0.712799i | \(-0.747427\pi\) | ||||
−0.701368 | + | 0.712799i | \(0.747427\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −52.0944 | −2.12145 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.8190 | 0.683788 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.6276 | −0.837247 | −0.418624 | − | 0.908160i | \(-0.637487\pi\) | ||||
−0.418624 | + | 0.908160i | \(0.637487\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −69.3498 | −2.81019 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.54666 | −0.183938 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.90684 | 0.0770164 | 0.0385082 | − | 0.999258i | \(-0.487739\pi\) | ||||
0.0385082 | + | 0.999258i | \(0.487739\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.21266 | −0.210195 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.1072 | 0.769227 | 0.384613 | − | 0.923078i | \(-0.374335\pi\) | ||||
0.384613 | + | 0.923078i | \(0.374335\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.2943 | 0.775504 | 0.387752 | − | 0.921764i | \(-0.373252\pi\) | ||||
0.387752 | + | 0.921764i | \(0.373252\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −51.9972 | −2.08658 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −37.5643 | −1.50498 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.94368 | −0.237747 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.53591 | 0.181147 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.9720 | 1.39442 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.1125 | 1.75609 | 0.878045 | − | 0.478577i | \(-0.158847\pi\) | ||||
0.878045 | + | 0.478577i | \(0.158847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.0673 | 0.400140 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.10529 | −0.202597 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.89881 | −0.154477 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.7962 | 0.980924 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.0671 | 0.516120 | 0.258060 | − | 0.966129i | \(-0.416917\pi\) | ||||
0.258060 | + | 0.966129i | \(0.416917\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.6402 | −0.932279 | −0.466139 | − | 0.884711i | \(-0.654356\pi\) | ||||
−0.466139 | + | 0.884711i | \(0.654356\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −50.2827 | −1.97988 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.2476 | 0.678073 | 0.339036 | − | 0.940773i | \(-0.389899\pi\) | ||||
0.339036 | + | 0.940773i | \(0.389899\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.52742 | −0.0599563 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −75.6407 | −2.96459 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.73847 | −0.185431 | −0.0927154 | − | 0.995693i | \(-0.529555\pi\) | ||||
−0.0927154 | + | 0.995693i | \(0.529555\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.31390 | −0.324851 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −108.307 | −4.22544 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.0030 | 1.05189 | 0.525943 | − | 0.850520i | \(-0.323712\pi\) | ||||
0.525943 | + | 0.850520i | \(0.323712\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.0848 | 1.55912 | 0.779560 | − | 0.626328i | \(-0.215443\pi\) | ||||
0.779560 | + | 0.626328i | \(0.215443\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.1595 | −0.744092 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.5596 | −0.487039 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.9447 | 1.08202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.80333 | 0.224370 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.87089 | −0.110830 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.5878 | −0.677959 | −0.338980 | − | 0.940794i | \(-0.610082\pi\) | ||||
−0.338980 | + | 0.940794i | \(0.610082\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 33.4836 | 1.28878 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.6314 | −1.06196 | −0.530981 | − | 0.847384i | \(-0.678177\pi\) | ||||
−0.530981 | + | 0.847384i | \(0.678177\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.9556 | 1.41823 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −63.2383 | −2.42330 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.4621 | 0.591639 | 0.295820 | − | 0.955244i | \(-0.404407\pi\) | ||||
0.295820 | + | 0.955244i | \(0.404407\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.0359 | −0.994780 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 47.8150 | 1.82426 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.4498 | 0.588589 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.92880 | −0.377709 | −0.188855 | − | 0.982005i | \(-0.560478\pi\) | ||||
−0.188855 | + | 0.982005i | \(0.560478\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −11.9344 | −0.453351 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.4624 | −0.852046 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.80147 | 0.143991 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.4897 | 0.964110 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −50.4195 | −1.90432 | −0.952158 | − | 0.305605i | \(-0.901141\pi\) | ||||
−0.952158 | + | 0.305605i | \(0.901141\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.0089 | −0.943227 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.8253 | 0.520692 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 56.9950 | 2.14352 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −49.2180 | −1.84842 | −0.924210 | − | 0.381885i | \(-0.875275\pi\) | ||||
−0.924210 | + | 0.381885i | \(0.875275\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 65.2770 | 2.44808 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.4796 | 1.14147 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.41067 | −0.0527562 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −32.1328 | −1.20002 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.8606 | 0.405033 | 0.202516 | − | 0.979279i | \(-0.435088\pi\) | ||||
0.202516 | + | 0.979279i | \(0.435088\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.10394 | 0.152839 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.1042 | −0.970826 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.9950 | −0.668317 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.7206 | −0.545958 | −0.272979 | − | 0.962020i | \(-0.588009\pi\) | ||||
−0.272979 | + | 0.962020i | \(0.588009\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.5981 | 0.799931 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.6700 | 1.35629 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.9113 | 1.32642 | 0.663208 | − | 0.748435i | \(-0.269195\pi\) | ||||
0.663208 | + | 0.748435i | \(0.269195\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.8554 | 0.437291 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.97044 | 0.146253 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.0887 | −1.14362 | −0.571808 | − | 0.820387i | \(-0.693758\pi\) | ||||
−0.571808 | + | 0.820387i | \(0.693758\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.7011 | 0.503324 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.9725 | −0.842779 | −0.421389 | − | 0.906880i | \(-0.638457\pi\) | ||||
−0.421389 | + | 0.906880i | \(0.638457\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.69069 | −0.171853 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −38.1494 | −1.39581 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.0803477 | −0.00293584 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.7768 | 1.45148 | 0.725739 | − | 0.687971i | \(-0.241498\pi\) | ||||
0.725739 | + | 0.687971i | \(0.241498\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 44.9985 | 1.63984 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.6640 | −0.642859 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.07248 | −0.329745 | −0.164872 | − | 0.986315i | \(-0.552721\pi\) | ||||
−0.164872 | + | 0.986315i | \(0.552721\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.82602 | 0.247769 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.44813 | −0.124995 | −0.0624973 | − | 0.998045i | \(-0.519906\pi\) | ||||
−0.0624973 | + | 0.998045i | \(0.519906\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.07311 | 0.0388493 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 41.0444 | 1.48396 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.61371 | −0.166591 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.8510 | −0.607664 | −0.303832 | − | 0.952726i | \(-0.598266\pi\) | ||||
−0.303832 | + | 0.952726i | \(0.598266\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.00741 | −0.180337 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.58677 | −0.0930396 | −0.0465198 | − | 0.998917i | \(-0.514813\pi\) | ||||
−0.0465198 | + | 0.998917i | \(0.514813\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.6274 | −0.705036 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 93.3992 | 3.35068 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.71848 | −0.0973995 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.88988 | −0.0676251 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −94.0931 | −3.36261 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.7294 | −0.668480 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.6266 | 1.19866 | 0.599329 | − | 0.800503i | \(-0.295434\pi\) | ||||
0.599329 | + | 0.800503i | \(0.295434\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.4660 | 0.657406 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.63053 | 0.235754 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.67181 | −0.307945 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −46.9790 | −1.66617 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.9826 | 1.52252 | 0.761261 | − | 0.648445i | \(-0.224580\pi\) | ||||
0.761261 | + | 0.648445i | \(0.224580\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.0825 | −0.356693 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −87.7866 | −3.10179 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.25471 | 0.291302 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.9007 | −0.666162 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.65164 | −0.198947 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.7197 | −0.447202 | −0.223601 | − | 0.974681i | \(-0.571781\pi\) | ||||
−0.223601 | + | 0.974681i | \(0.571781\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.3898 | −0.821326 | −0.410663 | − | 0.911787i | \(-0.634703\pi\) | ||||
−0.410663 | + | 0.911787i | \(0.634703\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 53.4927 | 1.87607 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.5952 | 0.651360 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.2231 | −0.917430 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −36.0491 | −1.25966 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.6853 | −0.721923 | −0.360961 | − | 0.932581i | \(-0.617551\pi\) | ||||
−0.360961 | + | 0.932581i | \(0.617551\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.0268 | −0.558658 | −0.279329 | − | 0.960195i | \(-0.590112\pi\) | ||||
−0.279329 | + | 0.960195i | \(0.590112\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.39562 | −0.153036 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.5677 | −1.34113 | −0.670565 | − | 0.741851i | \(-0.733948\pi\) | ||||
−0.670565 | + | 0.741851i | \(0.733948\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.3558 | 1.33215 | 0.666075 | − | 0.745885i | \(-0.267973\pi\) | ||||
0.666075 | + | 0.745885i | \(0.267973\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −48.3493 | −1.67722 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.64583 | −0.299560 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.34972 | −0.323560 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −102.629 | −3.54736 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.6698 | −0.575505 | −0.287752 | − | 0.957705i | \(-0.592908\pi\) | ||||
−0.287752 | + | 0.957705i | \(0.592908\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.5682 | 0.743730 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 99.4059 | 3.42372 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.1678 | 0.556189 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32.7577 | −1.12557 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −46.6827 | −1.60215 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.6355 | −1.29013 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.3583 | 0.525859 | 0.262929 | − | 0.964815i | \(-0.415311\pi\) | ||||
0.262929 | + | 0.964815i | \(0.415311\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −29.3513 | −1.00379 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.90657 | 0.235924 | 0.117962 | − | 0.993018i | \(-0.462364\pi\) | ||||
0.117962 | + | 0.993018i | \(0.462364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.8992 | 1.46370 | 0.731851 | − | 0.681465i | \(-0.238657\pi\) | ||||
0.731851 | + | 0.681465i | \(0.238657\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.1525 | 0.345997 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42.2767 | 1.43912 | 0.719558 | − | 0.694432i | \(-0.244344\pi\) | ||||
0.719558 | + | 0.694432i | \(0.244344\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.3154 | 0.452737 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.6804 | 0.396687 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.97517 | −0.168771 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.9931 | 0.406370 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 86.3641 | 2.92298 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.2196 | 1.22444 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.5272 | 0.355478 | 0.177739 | − | 0.984078i | \(-0.443122\pi\) | ||||
0.177739 | + | 0.984078i | \(0.443122\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.0255 | −0.709174 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.8995 | 0.906266 | 0.453133 | − | 0.891443i | \(-0.350306\pi\) | ||||
0.453133 | + | 0.891443i | \(0.350306\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.1797 | −0.914669 | −0.457334 | − | 0.889295i | \(-0.651196\pi\) | ||||
−0.457334 | + | 0.889295i | \(0.651196\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.0292 | 0.471586 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.2469 | 0.444787 | 0.222393 | − | 0.974957i | \(-0.428613\pi\) | ||||
0.222393 | + | 0.974957i | \(0.428613\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.94340 | 0.333491 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.2862 | −0.378100 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.21010 | 0.241277 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −29.6907 | −0.992450 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.6187 | 0.688437 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 55.1553 | 1.83953 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.2607 | 1.14139 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 97.9339 | 3.25904 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.6007 | −0.418863 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.9672 | 0.961840 | 0.480920 | − | 0.876764i | \(-0.340303\pi\) | ||||
0.480920 | + | 0.876764i | \(0.340303\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 133.196 | 4.41782 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.28341 | 0.307573 | 0.153787 | − | 0.988104i | \(-0.450853\pi\) | ||||
0.153787 | + | 0.988104i | \(0.450853\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.90760 | 0.0962275 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26.3689 | 0.871729 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.1927 | 0.534731 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.2457 | −0.634859 | −0.317429 | − | 0.948282i | \(-0.602820\pi\) | ||||
−0.317429 | + | 0.948282i | \(0.602820\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 87.3223 | 2.87737 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.70855 | −0.187899 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.2354 | 0.796854 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.59078 | 0.315002 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.1294 | 1.25098 | 0.625492 | − | 0.780230i | \(-0.284898\pi\) | ||||
0.625492 | + | 0.780230i | \(0.284898\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.18273 | 0.202631 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.28222 | 0.238409 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.12825 | −0.102305 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.539014 | −0.0176088 | −0.00880440 | − | 0.999961i | \(-0.502803\pi\) | ||||
−0.00880440 | + | 0.999961i | \(0.502803\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −67.6564 | −2.20788 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.9849 | 0.390695 | 0.195348 | − | 0.980734i | \(-0.437416\pi\) | ||||
0.195348 | + | 0.980734i | \(0.437416\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.09099 | −0.133221 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 63.6409 | 2.07024 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 59.1562 | 1.92232 | 0.961158 | − | 0.275997i | \(-0.0890081\pi\) | ||||
0.961158 | + | 0.275997i | \(0.0890081\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.9342 | 0.809397 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −88.5345 | −2.87093 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.7815 | −1.48301 | −0.741505 | − | 0.670948i | \(-0.765887\pi\) | ||||
−0.741505 | + | 0.670948i | \(0.765887\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37.8979 | 1.22635 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.3522 | 0.399291 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 50.7092 | 1.63749 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.1586 | 0.940599 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.187770 | −0.00605080 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.3669 | 0.430295 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.8467 | −1.44217 | −0.721086 | − | 0.692846i | \(-0.756357\pi\) | ||||
−0.721086 | + | 0.692846i | \(0.756357\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 30.3831 | 0.976044 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.2798 | 0.329895 | 0.164948 | − | 0.986302i | \(-0.447254\pi\) | ||||
0.164948 | + | 0.986302i | \(0.447254\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 43.7492 | 1.40254 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.2774 | −0.425217 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.74691 | 0.311831 | 0.155916 | − | 0.987770i | \(-0.450167\pi\) | ||||
0.155916 | + | 0.987770i | \(0.450167\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.69076 | 0.213838 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.50783 | 0.0800689 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.1336 | −1.24817 | −0.624084 | − | 0.781357i | \(-0.714528\pi\) | ||||
−0.624084 | + | 0.781357i | \(0.714528\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 39.7942 | 1.26795 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −26.9271 | −0.857100 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −39.4628 | −1.25484 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.3199 | −1.18551 | −0.592754 | − | 0.805384i | \(-0.701959\pi\) | ||||
−0.592754 | + | 0.805384i | \(0.701959\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 91.7573 | 2.91183 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.69120 | 0.180423 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −55.6608 | −1.76279 | −0.881397 | − | 0.472376i | \(-0.843396\pi\) | ||||
−0.881397 | + | 0.472376i | \(0.843396\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 126.723 | 4.00934 |
(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 | 8048.2.a.v.1.1 | 28 | ||
4.3 | odd | 2 | 4024.2.a.d.1.28 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.28 | ✓ | 28 | 4.3 | odd | 2 | ||
8048.2.a.v.1.1 | 28 | 1.1 | even | 1 | trivial |