Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.83962 | −1.30081 | −0.650404 | − | 0.759588i | \(-0.725400\pi\) | ||||
−0.650404 | + | 0.759588i | \(0.725400\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.38420 | 0.692102 | ||||||||
\(5\) | 0.446319 | 0.199600 | 0.0998000 | − | 0.995008i | \(-0.468180\pi\) | ||||
0.0998000 | + | 0.995008i | \(0.468180\pi\) | |||||||
\(6\) | −1.83962 | −0.751022 | ||||||||
\(7\) | 3.21050 | 1.21345 | 0.606727 | − | 0.794911i | \(-0.292482\pi\) | ||||
0.606727 | + | 0.794911i | \(0.292482\pi\) | |||||||
\(8\) | 1.13283 | 0.400517 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.821058 | −0.259641 | ||||||||
\(11\) | 0.755063 | 0.227660 | 0.113830 | − | 0.993500i | \(-0.463688\pi\) | ||||
0.113830 | + | 0.993500i | \(0.463688\pi\) | |||||||
\(12\) | 1.38420 | 0.399585 | ||||||||
\(13\) | −6.00546 | −1.66561 | −0.832807 | − | 0.553563i | \(-0.813268\pi\) | ||||
−0.832807 | + | 0.553563i | \(0.813268\pi\) | |||||||
\(14\) | −5.90609 | −1.57847 | ||||||||
\(15\) | 0.446319 | 0.115239 | ||||||||
\(16\) | −4.85239 | −1.21310 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.83962 | −0.433603 | ||||||||
\(19\) | −3.47410 | −0.797012 | −0.398506 | − | 0.917166i | \(-0.630471\pi\) | ||||
−0.398506 | + | 0.917166i | \(0.630471\pi\) | |||||||
\(20\) | 0.617796 | 0.138143 | ||||||||
\(21\) | 3.21050 | 0.700588 | ||||||||
\(22\) | −1.38903 | −0.296142 | ||||||||
\(23\) | −1.33575 | −0.278524 | −0.139262 | − | 0.990256i | \(-0.544473\pi\) | ||||
−0.139262 | + | 0.990256i | \(0.544473\pi\) | |||||||
\(24\) | 1.13283 | 0.231238 | ||||||||
\(25\) | −4.80080 | −0.960160 | ||||||||
\(26\) | 11.0478 | 2.16664 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.44398 | 0.839833 | ||||||||
\(29\) | −5.99876 | −1.11394 | −0.556971 | − | 0.830532i | \(-0.688037\pi\) | ||||
−0.556971 | + | 0.830532i | \(0.688037\pi\) | |||||||
\(30\) | −0.821058 | −0.149904 | ||||||||
\(31\) | 0.937935 | 0.168458 | 0.0842290 | − | 0.996446i | \(-0.473157\pi\) | ||||
0.0842290 | + | 0.996446i | \(0.473157\pi\) | |||||||
\(32\) | 6.66089 | 1.17749 | ||||||||
\(33\) | 0.755063 | 0.131440 | ||||||||
\(34\) | 1.83962 | 0.315492 | ||||||||
\(35\) | 1.43291 | 0.242205 | ||||||||
\(36\) | 1.38420 | 0.230701 | ||||||||
\(37\) | 7.61442 | 1.25180 | 0.625901 | − | 0.779902i | \(-0.284731\pi\) | ||||
0.625901 | + | 0.779902i | \(0.284731\pi\) | |||||||
\(38\) | 6.39102 | 1.03676 | ||||||||
\(39\) | −6.00546 | −0.961643 | ||||||||
\(40\) | 0.505605 | 0.0799432 | ||||||||
\(41\) | 4.83292 | 0.754776 | 0.377388 | − | 0.926055i | \(-0.376822\pi\) | ||||
0.377388 | + | 0.926055i | \(0.376822\pi\) | |||||||
\(42\) | −5.90609 | −0.911330 | ||||||||
\(43\) | 11.5470 | 1.76091 | 0.880454 | − | 0.474131i | \(-0.157238\pi\) | ||||
0.880454 | + | 0.474131i | \(0.157238\pi\) | |||||||
\(44\) | 1.04516 | 0.157564 | ||||||||
\(45\) | 0.446319 | 0.0665333 | ||||||||
\(46\) | 2.45728 | 0.362306 | ||||||||
\(47\) | 4.65967 | 0.679682 | 0.339841 | − | 0.940483i | \(-0.389627\pi\) | ||||
0.339841 | + | 0.940483i | \(0.389627\pi\) | |||||||
\(48\) | −4.85239 | −0.700382 | ||||||||
\(49\) | 3.30728 | 0.472469 | ||||||||
\(50\) | 8.83165 | 1.24898 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −8.31277 | −1.15277 | ||||||||
\(53\) | −0.522651 | −0.0717917 | −0.0358958 | − | 0.999356i | \(-0.511428\pi\) | ||||
−0.0358958 | + | 0.999356i | \(0.511428\pi\) | |||||||
\(54\) | −1.83962 | −0.250341 | ||||||||
\(55\) | 0.336999 | 0.0454410 | ||||||||
\(56\) | 3.63695 | 0.486008 | ||||||||
\(57\) | −3.47410 | −0.460155 | ||||||||
\(58\) | 11.0354 | 1.44902 | ||||||||
\(59\) | −3.59680 | −0.468264 | −0.234132 | − | 0.972205i | \(-0.575225\pi\) | ||||
−0.234132 | + | 0.972205i | \(0.575225\pi\) | |||||||
\(60\) | 0.617796 | 0.0797572 | ||||||||
\(61\) | −3.89238 | −0.498369 | −0.249184 | − | 0.968456i | \(-0.580163\pi\) | ||||
−0.249184 | + | 0.968456i | \(0.580163\pi\) | |||||||
\(62\) | −1.72544 | −0.219132 | ||||||||
\(63\) | 3.21050 | 0.404484 | ||||||||
\(64\) | −2.54873 | −0.318591 | ||||||||
\(65\) | −2.68035 | −0.332457 | ||||||||
\(66\) | −1.38903 | −0.170978 | ||||||||
\(67\) | −4.41034 | −0.538809 | −0.269404 | − | 0.963027i | \(-0.586827\pi\) | ||||
−0.269404 | + | 0.963027i | \(0.586827\pi\) | |||||||
\(68\) | −1.38420 | −0.167859 | ||||||||
\(69\) | −1.33575 | −0.160806 | ||||||||
\(70\) | −2.63600 | −0.315063 | ||||||||
\(71\) | −10.1666 | −1.20655 | −0.603275 | − | 0.797533i | \(-0.706138\pi\) | ||||
−0.603275 | + | 0.797533i | \(0.706138\pi\) | |||||||
\(72\) | 1.13283 | 0.133506 | ||||||||
\(73\) | 15.6550 | 1.83228 | 0.916142 | − | 0.400854i | \(-0.131287\pi\) | ||||
0.916142 | + | 0.400854i | \(0.131287\pi\) | |||||||
\(74\) | −14.0076 | −1.62836 | ||||||||
\(75\) | −4.80080 | −0.554349 | ||||||||
\(76\) | −4.80885 | −0.551613 | ||||||||
\(77\) | 2.42413 | 0.276255 | ||||||||
\(78\) | 11.0478 | 1.25091 | ||||||||
\(79\) | −15.3608 | −1.72822 | −0.864112 | − | 0.503300i | \(-0.832119\pi\) | ||||
−0.864112 | + | 0.503300i | \(0.832119\pi\) | |||||||
\(80\) | −2.16571 | −0.242134 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.89074 | −0.981818 | ||||||||
\(83\) | 3.70090 | 0.406226 | 0.203113 | − | 0.979155i | \(-0.434894\pi\) | ||||
0.203113 | + | 0.979155i | \(0.434894\pi\) | |||||||
\(84\) | 4.44398 | 0.484878 | ||||||||
\(85\) | −0.446319 | −0.0484101 | ||||||||
\(86\) | −21.2422 | −2.29060 | ||||||||
\(87\) | −5.99876 | −0.643135 | ||||||||
\(88\) | 0.855361 | 0.0911817 | ||||||||
\(89\) | 1.35034 | 0.143135 | 0.0715677 | − | 0.997436i | \(-0.477200\pi\) | ||||
0.0715677 | + | 0.997436i | \(0.477200\pi\) | |||||||
\(90\) | −0.821058 | −0.0865471 | ||||||||
\(91\) | −19.2805 | −2.02114 | ||||||||
\(92\) | −1.84895 | −0.192767 | ||||||||
\(93\) | 0.937935 | 0.0972593 | ||||||||
\(94\) | −8.57202 | −0.884136 | ||||||||
\(95\) | −1.55056 | −0.159084 | ||||||||
\(96\) | 6.66089 | 0.679824 | ||||||||
\(97\) | −12.1618 | −1.23484 | −0.617421 | − | 0.786633i | \(-0.711823\pi\) | ||||
−0.617421 | + | 0.786633i | \(0.711823\pi\) | |||||||
\(98\) | −6.08414 | −0.614591 | ||||||||
\(99\) | 0.755063 | 0.0758867 | ||||||||
\(100\) | −6.64528 | −0.664528 | ||||||||
\(101\) | −9.20932 | −0.916362 | −0.458181 | − | 0.888859i | \(-0.651499\pi\) | ||||
−0.458181 | + | 0.888859i | \(0.651499\pi\) | |||||||
\(102\) | 1.83962 | 0.182150 | ||||||||
\(103\) | 12.9331 | 1.27434 | 0.637170 | − | 0.770724i | \(-0.280105\pi\) | ||||
0.637170 | + | 0.770724i | \(0.280105\pi\) | |||||||
\(104\) | −6.80318 | −0.667106 | ||||||||
\(105\) | 1.43291 | 0.139837 | ||||||||
\(106\) | 0.961480 | 0.0933872 | ||||||||
\(107\) | 2.40569 | 0.232567 | 0.116284 | − | 0.993216i | \(-0.462902\pi\) | ||||
0.116284 | + | 0.993216i | \(0.462902\pi\) | |||||||
\(108\) | 1.38420 | 0.133195 | ||||||||
\(109\) | −4.36744 | −0.418325 | −0.209163 | − | 0.977881i | \(-0.567074\pi\) | ||||
−0.209163 | + | 0.977881i | \(0.567074\pi\) | |||||||
\(110\) | −0.619951 | −0.0591100 | ||||||||
\(111\) | 7.61442 | 0.722729 | ||||||||
\(112\) | −15.5786 | −1.47204 | ||||||||
\(113\) | −3.50544 | −0.329764 | −0.164882 | − | 0.986313i | \(-0.552724\pi\) | ||||
−0.164882 | + | 0.986313i | \(0.552724\pi\) | |||||||
\(114\) | 6.39102 | 0.598574 | ||||||||
\(115\) | −0.596173 | −0.0555934 | ||||||||
\(116\) | −8.30350 | −0.770961 | ||||||||
\(117\) | −6.00546 | −0.555205 | ||||||||
\(118\) | 6.61675 | 0.609122 | ||||||||
\(119\) | −3.21050 | −0.294306 | ||||||||
\(120\) | 0.505605 | 0.0461552 | ||||||||
\(121\) | −10.4299 | −0.948171 | ||||||||
\(122\) | 7.16051 | 0.648282 | ||||||||
\(123\) | 4.83292 | 0.435770 | ||||||||
\(124\) | 1.29829 | 0.116590 | ||||||||
\(125\) | −4.37428 | −0.391248 | ||||||||
\(126\) | −5.90609 | −0.526157 | ||||||||
\(127\) | 8.25531 | 0.732541 | 0.366270 | − | 0.930508i | \(-0.380635\pi\) | ||||
0.366270 | + | 0.930508i | \(0.380635\pi\) | |||||||
\(128\) | −8.63308 | −0.763064 | ||||||||
\(129\) | 11.5470 | 1.01666 | ||||||||
\(130\) | 4.93083 | 0.432462 | ||||||||
\(131\) | −22.4186 | −1.95872 | −0.979360 | − | 0.202122i | \(-0.935216\pi\) | ||||
−0.979360 | + | 0.202122i | \(0.935216\pi\) | |||||||
\(132\) | 1.04516 | 0.0909696 | ||||||||
\(133\) | −11.1536 | −0.967137 | ||||||||
\(134\) | 8.11335 | 0.700887 | ||||||||
\(135\) | 0.446319 | 0.0384130 | ||||||||
\(136\) | −1.13283 | −0.0971396 | ||||||||
\(137\) | −18.1655 | −1.55198 | −0.775992 | − | 0.630743i | \(-0.782750\pi\) | ||||
−0.775992 | + | 0.630743i | \(0.782750\pi\) | |||||||
\(138\) | 2.45728 | 0.209178 | ||||||||
\(139\) | 3.44808 | 0.292462 | 0.146231 | − | 0.989250i | \(-0.453286\pi\) | ||||
0.146231 | + | 0.989250i | \(0.453286\pi\) | |||||||
\(140\) | 1.98343 | 0.167631 | ||||||||
\(141\) | 4.65967 | 0.392415 | ||||||||
\(142\) | 18.7026 | 1.56949 | ||||||||
\(143\) | −4.53450 | −0.379194 | ||||||||
\(144\) | −4.85239 | −0.404366 | ||||||||
\(145\) | −2.67736 | −0.222343 | ||||||||
\(146\) | −28.7993 | −2.38345 | ||||||||
\(147\) | 3.30728 | 0.272780 | ||||||||
\(148\) | 10.5399 | 0.866375 | ||||||||
\(149\) | −8.39683 | −0.687895 | −0.343947 | − | 0.938989i | \(-0.611764\pi\) | ||||
−0.343947 | + | 0.938989i | \(0.611764\pi\) | |||||||
\(150\) | 8.83165 | 0.721101 | ||||||||
\(151\) | 4.71303 | 0.383541 | 0.191771 | − | 0.981440i | \(-0.438577\pi\) | ||||
0.191771 | + | 0.981440i | \(0.438577\pi\) | |||||||
\(152\) | −3.93557 | −0.319217 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −4.45947 | −0.359355 | ||||||||
\(155\) | 0.418618 | 0.0336242 | ||||||||
\(156\) | −8.31277 | −0.665554 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | 28.2580 | 2.24809 | ||||||||
\(159\) | −0.522651 | −0.0414489 | ||||||||
\(160\) | 2.97288 | 0.235027 | ||||||||
\(161\) | −4.28843 | −0.337976 | ||||||||
\(162\) | −1.83962 | −0.144534 | ||||||||
\(163\) | −2.89363 | −0.226646 | −0.113323 | − | 0.993558i | \(-0.536150\pi\) | ||||
−0.113323 | + | 0.993558i | \(0.536150\pi\) | |||||||
\(164\) | 6.68975 | 0.522381 | ||||||||
\(165\) | 0.336999 | 0.0262354 | ||||||||
\(166\) | −6.80824 | −0.528422 | ||||||||
\(167\) | −19.4708 | −1.50670 | −0.753349 | − | 0.657621i | \(-0.771563\pi\) | ||||
−0.753349 | + | 0.657621i | \(0.771563\pi\) | |||||||
\(168\) | 3.63695 | 0.280597 | ||||||||
\(169\) | 23.0655 | 1.77427 | ||||||||
\(170\) | 0.821058 | 0.0629723 | ||||||||
\(171\) | −3.47410 | −0.265671 | ||||||||
\(172\) | 15.9835 | 1.21873 | ||||||||
\(173\) | 7.43832 | 0.565525 | 0.282763 | − | 0.959190i | \(-0.408749\pi\) | ||||
0.282763 | + | 0.959190i | \(0.408749\pi\) | |||||||
\(174\) | 11.0354 | 0.836595 | ||||||||
\(175\) | −15.4129 | −1.16511 | ||||||||
\(176\) | −3.66386 | −0.276174 | ||||||||
\(177\) | −3.59680 | −0.270352 | ||||||||
\(178\) | −2.48411 | −0.186192 | ||||||||
\(179\) | 17.2445 | 1.28892 | 0.644458 | − | 0.764639i | \(-0.277083\pi\) | ||||
0.644458 | + | 0.764639i | \(0.277083\pi\) | |||||||
\(180\) | 0.617796 | 0.0460478 | ||||||||
\(181\) | 1.93638 | 0.143930 | 0.0719649 | − | 0.997407i | \(-0.477073\pi\) | ||||
0.0719649 | + | 0.997407i | \(0.477073\pi\) | |||||||
\(182\) | 35.4688 | 2.62912 | ||||||||
\(183\) | −3.89238 | −0.287733 | ||||||||
\(184\) | −1.51319 | −0.111554 | ||||||||
\(185\) | 3.39846 | 0.249860 | ||||||||
\(186\) | −1.72544 | −0.126516 | ||||||||
\(187\) | −0.755063 | −0.0552157 | ||||||||
\(188\) | 6.44992 | 0.470409 | ||||||||
\(189\) | 3.21050 | 0.233529 | ||||||||
\(190\) | 2.85243 | 0.206937 | ||||||||
\(191\) | −17.5547 | −1.27022 | −0.635108 | − | 0.772423i | \(-0.719045\pi\) | ||||
−0.635108 | + | 0.772423i | \(0.719045\pi\) | |||||||
\(192\) | −2.54873 | −0.183938 | ||||||||
\(193\) | −17.4943 | −1.25926 | −0.629632 | − | 0.776894i | \(-0.716794\pi\) | ||||
−0.629632 | + | 0.776894i | \(0.716794\pi\) | |||||||
\(194\) | 22.3731 | 1.60629 | ||||||||
\(195\) | −2.68035 | −0.191944 | ||||||||
\(196\) | 4.57795 | 0.326996 | ||||||||
\(197\) | 0.781602 | 0.0556868 | 0.0278434 | − | 0.999612i | \(-0.491136\pi\) | ||||
0.0278434 | + | 0.999612i | \(0.491136\pi\) | |||||||
\(198\) | −1.38903 | −0.0987141 | ||||||||
\(199\) | 3.72043 | 0.263734 | 0.131867 | − | 0.991267i | \(-0.457903\pi\) | ||||
0.131867 | + | 0.991267i | \(0.457903\pi\) | |||||||
\(200\) | −5.43850 | −0.384560 | ||||||||
\(201\) | −4.41034 | −0.311081 | ||||||||
\(202\) | 16.9417 | 1.19201 | ||||||||
\(203\) | −19.2590 | −1.35172 | ||||||||
\(204\) | −1.38420 | −0.0969136 | ||||||||
\(205\) | 2.15703 | 0.150653 | ||||||||
\(206\) | −23.7921 | −1.65767 | ||||||||
\(207\) | −1.33575 | −0.0928413 | ||||||||
\(208\) | 29.1408 | 2.02055 | ||||||||
\(209\) | −2.62316 | −0.181448 | ||||||||
\(210\) | −2.63600 | −0.181901 | ||||||||
\(211\) | −2.95112 | −0.203164 | −0.101582 | − | 0.994827i | \(-0.532390\pi\) | ||||
−0.101582 | + | 0.994827i | \(0.532390\pi\) | |||||||
\(212\) | −0.723455 | −0.0496871 | ||||||||
\(213\) | −10.1666 | −0.696602 | ||||||||
\(214\) | −4.42556 | −0.302525 | ||||||||
\(215\) | 5.15367 | 0.351477 | ||||||||
\(216\) | 1.13283 | 0.0770795 | ||||||||
\(217\) | 3.01123 | 0.204416 | ||||||||
\(218\) | 8.03444 | 0.544161 | ||||||||
\(219\) | 15.6550 | 1.05787 | ||||||||
\(220\) | 0.466475 | 0.0314498 | ||||||||
\(221\) | 6.00546 | 0.403971 | ||||||||
\(222\) | −14.0076 | −0.940131 | ||||||||
\(223\) | 5.81311 | 0.389275 | 0.194637 | − | 0.980875i | \(-0.437647\pi\) | ||||
0.194637 | + | 0.980875i | \(0.437647\pi\) | |||||||
\(224\) | 21.3847 | 1.42883 | ||||||||
\(225\) | −4.80080 | −0.320053 | ||||||||
\(226\) | 6.44867 | 0.428959 | ||||||||
\(227\) | −2.81084 | −0.186562 | −0.0932812 | − | 0.995640i | \(-0.529736\pi\) | ||||
−0.0932812 | + | 0.995640i | \(0.529736\pi\) | |||||||
\(228\) | −4.80885 | −0.318474 | ||||||||
\(229\) | 19.7529 | 1.30531 | 0.652655 | − | 0.757655i | \(-0.273655\pi\) | ||||
0.652655 | + | 0.757655i | \(0.273655\pi\) | |||||||
\(230\) | 1.09673 | 0.0723163 | ||||||||
\(231\) | 2.42413 | 0.159496 | ||||||||
\(232\) | −6.79559 | −0.446153 | ||||||||
\(233\) | −8.79173 | −0.575965 | −0.287983 | − | 0.957636i | \(-0.592985\pi\) | ||||
−0.287983 | + | 0.957636i | \(0.592985\pi\) | |||||||
\(234\) | 11.0478 | 0.722215 | ||||||||
\(235\) | 2.07970 | 0.135665 | ||||||||
\(236\) | −4.97871 | −0.324086 | ||||||||
\(237\) | −15.3608 | −0.997790 | ||||||||
\(238\) | 5.90609 | 0.382835 | ||||||||
\(239\) | −11.7069 | −0.757258 | −0.378629 | − | 0.925549i | \(-0.623604\pi\) | ||||
−0.378629 | + | 0.925549i | \(0.623604\pi\) | |||||||
\(240\) | −2.16571 | −0.139796 | ||||||||
\(241\) | 21.6664 | 1.39565 | 0.697826 | − | 0.716267i | \(-0.254151\pi\) | ||||
0.697826 | + | 0.716267i | \(0.254151\pi\) | |||||||
\(242\) | 19.1870 | 1.23339 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −5.38785 | −0.344922 | ||||||||
\(245\) | 1.47610 | 0.0943048 | ||||||||
\(246\) | −8.89074 | −0.566853 | ||||||||
\(247\) | 20.8635 | 1.32752 | ||||||||
\(248\) | 1.06252 | 0.0674703 | ||||||||
\(249\) | 3.70090 | 0.234535 | ||||||||
\(250\) | 8.04702 | 0.508938 | ||||||||
\(251\) | −16.4457 | −1.03804 | −0.519022 | − | 0.854761i | \(-0.673704\pi\) | ||||
−0.519022 | + | 0.854761i | \(0.673704\pi\) | |||||||
\(252\) | 4.44398 | 0.279944 | ||||||||
\(253\) | −1.00858 | −0.0634088 | ||||||||
\(254\) | −15.1866 | −0.952895 | ||||||||
\(255\) | −0.446319 | −0.0279496 | ||||||||
\(256\) | 20.9791 | 1.31119 | ||||||||
\(257\) | −2.86778 | −0.178887 | −0.0894437 | − | 0.995992i | \(-0.528509\pi\) | ||||
−0.0894437 | + | 0.995992i | \(0.528509\pi\) | |||||||
\(258\) | −21.2422 | −1.32248 | ||||||||
\(259\) | 24.4461 | 1.51900 | ||||||||
\(260\) | −3.71015 | −0.230094 | ||||||||
\(261\) | −5.99876 | −0.371314 | ||||||||
\(262\) | 41.2417 | 2.54792 | ||||||||
\(263\) | 12.7348 | 0.785263 | 0.392631 | − | 0.919696i | \(-0.371565\pi\) | ||||
0.392631 | + | 0.919696i | \(0.371565\pi\) | |||||||
\(264\) | 0.855361 | 0.0526438 | ||||||||
\(265\) | −0.233269 | −0.0143296 | ||||||||
\(266\) | 20.5183 | 1.25806 | ||||||||
\(267\) | 1.35034 | 0.0826392 | ||||||||
\(268\) | −6.10481 | −0.372910 | ||||||||
\(269\) | −22.2195 | −1.35475 | −0.677373 | − | 0.735640i | \(-0.736882\pi\) | ||||
−0.677373 | + | 0.735640i | \(0.736882\pi\) | |||||||
\(270\) | −0.821058 | −0.0499680 | ||||||||
\(271\) | 6.43735 | 0.391041 | 0.195520 | − | 0.980700i | \(-0.437360\pi\) | ||||
0.195520 | + | 0.980700i | \(0.437360\pi\) | |||||||
\(272\) | 4.85239 | 0.294219 | ||||||||
\(273\) | −19.2805 | −1.16691 | ||||||||
\(274\) | 33.4176 | 2.01883 | ||||||||
\(275\) | −3.62491 | −0.218590 | ||||||||
\(276\) | −1.84895 | −0.111294 | ||||||||
\(277\) | 12.7060 | 0.763430 | 0.381715 | − | 0.924280i | \(-0.375334\pi\) | ||||
0.381715 | + | 0.924280i | \(0.375334\pi\) | |||||||
\(278\) | −6.34315 | −0.380437 | ||||||||
\(279\) | 0.937935 | 0.0561527 | ||||||||
\(280\) | 1.62324 | 0.0970073 | ||||||||
\(281\) | −20.0757 | −1.19761 | −0.598807 | − | 0.800893i | \(-0.704358\pi\) | ||||
−0.598807 | + | 0.800893i | \(0.704358\pi\) | |||||||
\(282\) | −8.57202 | −0.510456 | ||||||||
\(283\) | −17.1401 | −1.01887 | −0.509437 | − | 0.860508i | \(-0.670146\pi\) | ||||
−0.509437 | + | 0.860508i | \(0.670146\pi\) | |||||||
\(284\) | −14.0726 | −0.835056 | ||||||||
\(285\) | −1.55056 | −0.0918470 | ||||||||
\(286\) | 8.34176 | 0.493259 | ||||||||
\(287\) | 15.5161 | 0.915885 | ||||||||
\(288\) | 6.66089 | 0.392496 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 4.92533 | 0.289225 | ||||||||
\(291\) | −12.1618 | −0.712937 | ||||||||
\(292\) | 21.6698 | 1.26813 | ||||||||
\(293\) | 14.7028 | 0.858945 | 0.429473 | − | 0.903080i | \(-0.358699\pi\) | ||||
0.429473 | + | 0.903080i | \(0.358699\pi\) | |||||||
\(294\) | −6.08414 | −0.354834 | ||||||||
\(295\) | −1.60532 | −0.0934655 | ||||||||
\(296\) | 8.62586 | 0.501368 | ||||||||
\(297\) | 0.755063 | 0.0438132 | ||||||||
\(298\) | 15.4470 | 0.894819 | ||||||||
\(299\) | 8.02181 | 0.463913 | ||||||||
\(300\) | −6.64528 | −0.383665 | ||||||||
\(301\) | 37.0717 | 2.13678 | ||||||||
\(302\) | −8.67019 | −0.498913 | ||||||||
\(303\) | −9.20932 | −0.529062 | ||||||||
\(304\) | 16.8577 | 0.966853 | ||||||||
\(305\) | −1.73725 | −0.0994744 | ||||||||
\(306\) | 1.83962 | 0.105164 | ||||||||
\(307\) | −12.8210 | −0.731736 | −0.365868 | − | 0.930667i | \(-0.619228\pi\) | ||||
−0.365868 | + | 0.930667i | \(0.619228\pi\) | |||||||
\(308\) | 3.35549 | 0.191197 | ||||||||
\(309\) | 12.9331 | 0.735740 | ||||||||
\(310\) | −0.770098 | −0.0437387 | ||||||||
\(311\) | −10.9232 | −0.619399 | −0.309699 | − | 0.950834i | \(-0.600228\pi\) | ||||
−0.309699 | + | 0.950834i | \(0.600228\pi\) | |||||||
\(312\) | −6.80318 | −0.385154 | ||||||||
\(313\) | −19.8697 | −1.12310 | −0.561552 | − | 0.827442i | \(-0.689795\pi\) | ||||
−0.561552 | + | 0.827442i | \(0.689795\pi\) | |||||||
\(314\) | −1.83962 | −0.103816 | ||||||||
\(315\) | 1.43291 | 0.0807351 | ||||||||
\(316\) | −21.2624 | −1.19611 | ||||||||
\(317\) | 8.79359 | 0.493897 | 0.246948 | − | 0.969029i | \(-0.420572\pi\) | ||||
0.246948 | + | 0.969029i | \(0.420572\pi\) | |||||||
\(318\) | 0.961480 | 0.0539171 | ||||||||
\(319\) | −4.52945 | −0.253600 | ||||||||
\(320\) | −1.13755 | −0.0635907 | ||||||||
\(321\) | 2.40569 | 0.134273 | ||||||||
\(322\) | 7.88909 | 0.439642 | ||||||||
\(323\) | 3.47410 | 0.193304 | ||||||||
\(324\) | 1.38420 | 0.0769002 | ||||||||
\(325\) | 28.8310 | 1.59926 | ||||||||
\(326\) | 5.32318 | 0.294824 | ||||||||
\(327\) | −4.36744 | −0.241520 | ||||||||
\(328\) | 5.47489 | 0.302300 | ||||||||
\(329\) | 14.9598 | 0.824762 | ||||||||
\(330\) | −0.619951 | −0.0341272 | ||||||||
\(331\) | −18.6818 | −1.02684 | −0.513422 | − | 0.858136i | \(-0.671622\pi\) | ||||
−0.513422 | + | 0.858136i | \(0.671622\pi\) | |||||||
\(332\) | 5.12279 | 0.281150 | ||||||||
\(333\) | 7.61442 | 0.417268 | ||||||||
\(334\) | 35.8189 | 1.95992 | ||||||||
\(335\) | −1.96842 | −0.107546 | ||||||||
\(336\) | −15.5786 | −0.849881 | ||||||||
\(337\) | −10.3404 | −0.563276 | −0.281638 | − | 0.959521i | \(-0.590878\pi\) | ||||
−0.281638 | + | 0.959521i | \(0.590878\pi\) | |||||||
\(338\) | −42.4318 | −2.30799 | ||||||||
\(339\) | −3.50544 | −0.190389 | ||||||||
\(340\) | −0.617796 | −0.0335047 | ||||||||
\(341\) | 0.708200 | 0.0383512 | ||||||||
\(342\) | 6.39102 | 0.345587 | ||||||||
\(343\) | −11.8555 | −0.640135 | ||||||||
\(344\) | 13.0809 | 0.705273 | ||||||||
\(345\) | −0.596173 | −0.0320969 | ||||||||
\(346\) | −13.6837 | −0.735640 | ||||||||
\(347\) | −11.9471 | −0.641356 | −0.320678 | − | 0.947188i | \(-0.603911\pi\) | ||||
−0.320678 | + | 0.947188i | \(0.603911\pi\) | |||||||
\(348\) | −8.30350 | −0.445114 | ||||||||
\(349\) | −24.1205 | −1.29114 | −0.645571 | − | 0.763700i | \(-0.723380\pi\) | ||||
−0.645571 | + | 0.763700i | \(0.723380\pi\) | |||||||
\(350\) | 28.3540 | 1.51558 | ||||||||
\(351\) | −6.00546 | −0.320548 | ||||||||
\(352\) | 5.02939 | 0.268067 | ||||||||
\(353\) | −30.4099 | −1.61855 | −0.809277 | − | 0.587427i | \(-0.800141\pi\) | ||||
−0.809277 | + | 0.587427i | \(0.800141\pi\) | |||||||
\(354\) | 6.61675 | 0.351677 | ||||||||
\(355\) | −4.53754 | −0.240828 | ||||||||
\(356\) | 1.86914 | 0.0990642 | ||||||||
\(357\) | −3.21050 | −0.169917 | ||||||||
\(358\) | −31.7234 | −1.67663 | ||||||||
\(359\) | −1.91066 | −0.100841 | −0.0504204 | − | 0.998728i | \(-0.516056\pi\) | ||||
−0.0504204 | + | 0.998728i | \(0.516056\pi\) | |||||||
\(360\) | 0.505605 | 0.0266477 | ||||||||
\(361\) | −6.93065 | −0.364771 | ||||||||
\(362\) | −3.56220 | −0.187225 | ||||||||
\(363\) | −10.4299 | −0.547427 | ||||||||
\(364\) | −26.6881 | −1.39884 | ||||||||
\(365\) | 6.98714 | 0.365724 | ||||||||
\(366\) | 7.16051 | 0.374286 | ||||||||
\(367\) | −18.2460 | −0.952436 | −0.476218 | − | 0.879327i | \(-0.657993\pi\) | ||||
−0.476218 | + | 0.879327i | \(0.657993\pi\) | |||||||
\(368\) | 6.48160 | 0.337877 | ||||||||
\(369\) | 4.83292 | 0.251592 | ||||||||
\(370\) | −6.25188 | −0.325020 | ||||||||
\(371\) | −1.67797 | −0.0871158 | ||||||||
\(372\) | 1.29829 | 0.0673133 | ||||||||
\(373\) | 23.9197 | 1.23851 | 0.619257 | − | 0.785189i | \(-0.287434\pi\) | ||||
0.619257 | + | 0.785189i | \(0.287434\pi\) | |||||||
\(374\) | 1.38903 | 0.0718250 | ||||||||
\(375\) | −4.37428 | −0.225887 | ||||||||
\(376\) | 5.27862 | 0.272224 | ||||||||
\(377\) | 36.0253 | 1.85540 | ||||||||
\(378\) | −5.90609 | −0.303777 | ||||||||
\(379\) | −27.7164 | −1.42370 | −0.711848 | − | 0.702333i | \(-0.752142\pi\) | ||||
−0.711848 | + | 0.702333i | \(0.752142\pi\) | |||||||
\(380\) | −2.14628 | −0.110102 | ||||||||
\(381\) | 8.25531 | 0.422933 | ||||||||
\(382\) | 32.2941 | 1.65231 | ||||||||
\(383\) | −22.7856 | −1.16429 | −0.582146 | − | 0.813084i | \(-0.697787\pi\) | ||||
−0.582146 | + | 0.813084i | \(0.697787\pi\) | |||||||
\(384\) | −8.63308 | −0.440555 | ||||||||
\(385\) | 1.08193 | 0.0551405 | ||||||||
\(386\) | 32.1828 | 1.63806 | ||||||||
\(387\) | 11.5470 | 0.586970 | ||||||||
\(388\) | −16.8344 | −0.854636 | ||||||||
\(389\) | −8.42203 | −0.427014 | −0.213507 | − | 0.976942i | \(-0.568489\pi\) | ||||
−0.213507 | + | 0.976942i | \(0.568489\pi\) | |||||||
\(390\) | 4.93083 | 0.249682 | ||||||||
\(391\) | 1.33575 | 0.0675520 | ||||||||
\(392\) | 3.74660 | 0.189232 | ||||||||
\(393\) | −22.4186 | −1.13087 | ||||||||
\(394\) | −1.43785 | −0.0724379 | ||||||||
\(395\) | −6.85581 | −0.344953 | ||||||||
\(396\) | 1.04516 | 0.0525213 | ||||||||
\(397\) | 23.1340 | 1.16106 | 0.580532 | − | 0.814237i | \(-0.302845\pi\) | ||||
0.580532 | + | 0.814237i | \(0.302845\pi\) | |||||||
\(398\) | −6.84418 | −0.343068 | ||||||||
\(399\) | −11.1536 | −0.558377 | ||||||||
\(400\) | 23.2953 | 1.16477 | ||||||||
\(401\) | 7.12378 | 0.355745 | 0.177872 | − | 0.984054i | \(-0.443079\pi\) | ||||
0.177872 | + | 0.984054i | \(0.443079\pi\) | |||||||
\(402\) | 8.11335 | 0.404657 | ||||||||
\(403\) | −5.63273 | −0.280586 | ||||||||
\(404\) | −12.7476 | −0.634215 | ||||||||
\(405\) | 0.446319 | 0.0221778 | ||||||||
\(406\) | 35.4292 | 1.75832 | ||||||||
\(407\) | 5.74937 | 0.284986 | ||||||||
\(408\) | −1.13283 | −0.0560836 | ||||||||
\(409\) | −4.09474 | −0.202472 | −0.101236 | − | 0.994862i | \(-0.532280\pi\) | ||||
−0.101236 | + | 0.994862i | \(0.532280\pi\) | |||||||
\(410\) | −3.96811 | −0.195971 | ||||||||
\(411\) | −18.1655 | −0.896038 | ||||||||
\(412\) | 17.9021 | 0.881972 | ||||||||
\(413\) | −11.5475 | −0.568217 | ||||||||
\(414\) | 2.45728 | 0.120769 | ||||||||
\(415\) | 1.65178 | 0.0810827 | ||||||||
\(416\) | −40.0017 | −1.96124 | ||||||||
\(417\) | 3.44808 | 0.168853 | ||||||||
\(418\) | 4.82562 | 0.236029 | ||||||||
\(419\) | −4.09700 | −0.200152 | −0.100076 | − | 0.994980i | \(-0.531909\pi\) | ||||
−0.100076 | + | 0.994980i | \(0.531909\pi\) | |||||||
\(420\) | 1.98343 | 0.0967816 | ||||||||
\(421\) | 16.7932 | 0.818453 | 0.409226 | − | 0.912433i | \(-0.365799\pi\) | ||||
0.409226 | + | 0.912433i | \(0.365799\pi\) | |||||||
\(422\) | 5.42895 | 0.264277 | ||||||||
\(423\) | 4.65967 | 0.226561 | ||||||||
\(424\) | −0.592076 | −0.0287538 | ||||||||
\(425\) | 4.80080 | 0.232873 | ||||||||
\(426\) | 18.7026 | 0.906146 | ||||||||
\(427\) | −12.4965 | −0.604747 | ||||||||
\(428\) | 3.32997 | 0.160960 | ||||||||
\(429\) | −4.53450 | −0.218928 | ||||||||
\(430\) | −9.48080 | −0.457205 | ||||||||
\(431\) | −38.3833 | −1.84886 | −0.924430 | − | 0.381351i | \(-0.875459\pi\) | ||||
−0.924430 | + | 0.381351i | \(0.875459\pi\) | |||||||
\(432\) | −4.85239 | −0.233461 | ||||||||
\(433\) | 21.1848 | 1.01808 | 0.509038 | − | 0.860744i | \(-0.330001\pi\) | ||||
0.509038 | + | 0.860744i | \(0.330001\pi\) | |||||||
\(434\) | −5.53953 | −0.265906 | ||||||||
\(435\) | −2.67736 | −0.128370 | ||||||||
\(436\) | −6.04543 | −0.289524 | ||||||||
\(437\) | 4.64054 | 0.221987 | ||||||||
\(438\) | −28.7993 | −1.37609 | ||||||||
\(439\) | −5.09873 | −0.243349 | −0.121675 | − | 0.992570i | \(-0.538826\pi\) | ||||
−0.121675 | + | 0.992570i | \(0.538826\pi\) | |||||||
\(440\) | 0.381764 | 0.0181999 | ||||||||
\(441\) | 3.30728 | 0.157490 | ||||||||
\(442\) | −11.0478 | −0.525488 | ||||||||
\(443\) | 9.28038 | 0.440924 | 0.220462 | − | 0.975396i | \(-0.429243\pi\) | ||||
0.220462 | + | 0.975396i | \(0.429243\pi\) | |||||||
\(444\) | 10.5399 | 0.500202 | ||||||||
\(445\) | 0.602681 | 0.0285698 | ||||||||
\(446\) | −10.6939 | −0.506372 | ||||||||
\(447\) | −8.39683 | −0.397156 | ||||||||
\(448\) | −8.18267 | −0.386595 | ||||||||
\(449\) | 26.1201 | 1.23269 | 0.616343 | − | 0.787478i | \(-0.288614\pi\) | ||||
0.616343 | + | 0.787478i | \(0.288614\pi\) | |||||||
\(450\) | 8.83165 | 0.416328 | ||||||||
\(451\) | 3.64916 | 0.171832 | ||||||||
\(452\) | −4.85224 | −0.228230 | ||||||||
\(453\) | 4.71303 | 0.221438 | ||||||||
\(454\) | 5.17089 | 0.242682 | ||||||||
\(455\) | −8.60525 | −0.403421 | ||||||||
\(456\) | −3.93557 | −0.184300 | ||||||||
\(457\) | −31.8956 | −1.49201 | −0.746006 | − | 0.665940i | \(-0.768031\pi\) | ||||
−0.746006 | + | 0.665940i | \(0.768031\pi\) | |||||||
\(458\) | −36.3379 | −1.69796 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −0.825224 | −0.0384763 | ||||||||
\(461\) | −17.8924 | −0.833334 | −0.416667 | − | 0.909059i | \(-0.636802\pi\) | ||||
−0.416667 | + | 0.909059i | \(0.636802\pi\) | |||||||
\(462\) | −4.45947 | −0.207474 | ||||||||
\(463\) | −15.5257 | −0.721538 | −0.360769 | − | 0.932655i | \(-0.617486\pi\) | ||||
−0.360769 | + | 0.932655i | \(0.617486\pi\) | |||||||
\(464\) | 29.1083 | 1.35132 | ||||||||
\(465\) | 0.418618 | 0.0194130 | ||||||||
\(466\) | 16.1734 | 0.749220 | ||||||||
\(467\) | −28.7219 | −1.32909 | −0.664545 | − | 0.747248i | \(-0.731375\pi\) | ||||
−0.664545 | + | 0.747248i | \(0.731375\pi\) | |||||||
\(468\) | −8.31277 | −0.384258 | ||||||||
\(469\) | −14.1594 | −0.653819 | ||||||||
\(470\) | −3.82586 | −0.176474 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −4.07458 | −0.187548 | ||||||||
\(473\) | 8.71876 | 0.400889 | ||||||||
\(474\) | 28.2580 | 1.29793 | ||||||||
\(475\) | 16.6784 | 0.765259 | ||||||||
\(476\) | −4.44398 | −0.203689 | ||||||||
\(477\) | −0.522651 | −0.0239306 | ||||||||
\(478\) | 21.5363 | 0.985047 | ||||||||
\(479\) | 4.37172 | 0.199749 | 0.0998744 | − | 0.995000i | \(-0.468156\pi\) | ||||
0.0998744 | + | 0.995000i | \(0.468156\pi\) | |||||||
\(480\) | 2.97288 | 0.135693 | ||||||||
\(481\) | −45.7281 | −2.08502 | ||||||||
\(482\) | −39.8579 | −1.81548 | ||||||||
\(483\) | −4.28843 | −0.195130 | ||||||||
\(484\) | −14.4371 | −0.656230 | ||||||||
\(485\) | −5.42804 | −0.246475 | ||||||||
\(486\) | −1.83962 | −0.0834469 | ||||||||
\(487\) | −13.5242 | −0.612839 | −0.306419 | − | 0.951897i | \(-0.599131\pi\) | ||||
−0.306419 | + | 0.951897i | \(0.599131\pi\) | |||||||
\(488\) | −4.40942 | −0.199605 | ||||||||
\(489\) | −2.89363 | −0.130854 | ||||||||
\(490\) | −2.71547 | −0.122672 | ||||||||
\(491\) | 33.9148 | 1.53055 | 0.765276 | − | 0.643702i | \(-0.222602\pi\) | ||||
0.765276 | + | 0.643702i | \(0.222602\pi\) | |||||||
\(492\) | 6.68975 | 0.301597 | ||||||||
\(493\) | 5.99876 | 0.270171 | ||||||||
\(494\) | −38.3810 | −1.72684 | ||||||||
\(495\) | 0.336999 | 0.0151470 | ||||||||
\(496\) | −4.55122 | −0.204356 | ||||||||
\(497\) | −32.6398 | −1.46409 | ||||||||
\(498\) | −6.80824 | −0.305085 | ||||||||
\(499\) | 13.9621 | 0.625030 | 0.312515 | − | 0.949913i | \(-0.398829\pi\) | ||||
0.312515 | + | 0.949913i | \(0.398829\pi\) | |||||||
\(500\) | −6.05490 | −0.270783 | ||||||||
\(501\) | −19.4708 | −0.869892 | ||||||||
\(502\) | 30.2539 | 1.35030 | ||||||||
\(503\) | −1.05698 | −0.0471283 | −0.0235642 | − | 0.999722i | \(-0.507501\pi\) | ||||
−0.0235642 | + | 0.999722i | \(0.507501\pi\) | |||||||
\(504\) | 3.63695 | 0.162003 | ||||||||
\(505\) | −4.11030 | −0.182906 | ||||||||
\(506\) | 1.85540 | 0.0824827 | ||||||||
\(507\) | 23.0655 | 1.02438 | ||||||||
\(508\) | 11.4270 | 0.506993 | ||||||||
\(509\) | 11.0058 | 0.487823 | 0.243911 | − | 0.969798i | \(-0.421569\pi\) | ||||
0.243911 | + | 0.969798i | \(0.421569\pi\) | |||||||
\(510\) | 0.821058 | 0.0363571 | ||||||||
\(511\) | 50.2604 | 2.22339 | ||||||||
\(512\) | −21.3273 | −0.942543 | ||||||||
\(513\) | −3.47410 | −0.153385 | ||||||||
\(514\) | 5.27563 | 0.232698 | ||||||||
\(515\) | 5.77230 | 0.254358 | ||||||||
\(516\) | 15.9835 | 0.703633 | ||||||||
\(517\) | 3.51834 | 0.154737 | ||||||||
\(518\) | −44.9715 | −1.97593 | ||||||||
\(519\) | 7.43832 | 0.326506 | ||||||||
\(520\) | −3.03639 | −0.133154 | ||||||||
\(521\) | −17.9608 | −0.786876 | −0.393438 | − | 0.919351i | \(-0.628714\pi\) | ||||
−0.393438 | + | 0.919351i | \(0.628714\pi\) | |||||||
\(522\) | 11.0354 | 0.483008 | ||||||||
\(523\) | −0.352744 | −0.0154244 | −0.00771220 | − | 0.999970i | \(-0.502455\pi\) | ||||
−0.00771220 | + | 0.999970i | \(0.502455\pi\) | |||||||
\(524\) | −31.0319 | −1.35563 | ||||||||
\(525\) | −15.4129 | −0.672676 | ||||||||
\(526\) | −23.4272 | −1.02148 | ||||||||
\(527\) | −0.937935 | −0.0408571 | ||||||||
\(528\) | −3.66386 | −0.159449 | ||||||||
\(529\) | −21.2158 | −0.922424 | ||||||||
\(530\) | 0.429127 | 0.0186401 | ||||||||
\(531\) | −3.59680 | −0.156088 | ||||||||
\(532\) | −15.4388 | −0.669357 | ||||||||
\(533\) | −29.0239 | −1.25717 | ||||||||
\(534\) | −2.48411 | −0.107498 | ||||||||
\(535\) | 1.07371 | 0.0464204 | ||||||||
\(536\) | −4.99618 | −0.215802 | ||||||||
\(537\) | 17.2445 | 0.744156 | ||||||||
\(538\) | 40.8754 | 1.76226 | ||||||||
\(539\) | 2.49721 | 0.107562 | ||||||||
\(540\) | 0.617796 | 0.0265857 | ||||||||
\(541\) | −0.711043 | −0.0305701 | −0.0152851 | − | 0.999883i | \(-0.504866\pi\) | ||||
−0.0152851 | + | 0.999883i | \(0.504866\pi\) | |||||||
\(542\) | −11.8423 | −0.508669 | ||||||||
\(543\) | 1.93638 | 0.0830979 | ||||||||
\(544\) | −6.66089 | −0.285583 | ||||||||
\(545\) | −1.94927 | −0.0834977 | ||||||||
\(546\) | 35.4688 | 1.51792 | ||||||||
\(547\) | −19.5158 | −0.834436 | −0.417218 | − | 0.908807i | \(-0.636995\pi\) | ||||
−0.417218 | + | 0.908807i | \(0.636995\pi\) | |||||||
\(548\) | −25.1447 | −1.07413 | ||||||||
\(549\) | −3.89238 | −0.166123 | ||||||||
\(550\) | 6.66845 | 0.284344 | ||||||||
\(551\) | 20.8403 | 0.887826 | ||||||||
\(552\) | −1.51319 | −0.0644055 | ||||||||
\(553\) | −49.3157 | −2.09712 | ||||||||
\(554\) | −23.3742 | −0.993076 | ||||||||
\(555\) | 3.39846 | 0.144257 | ||||||||
\(556\) | 4.77284 | 0.202413 | ||||||||
\(557\) | −7.48203 | −0.317024 | −0.158512 | − | 0.987357i | \(-0.550670\pi\) | ||||
−0.158512 | + | 0.987357i | \(0.550670\pi\) | |||||||
\(558\) | −1.72544 | −0.0730438 | ||||||||
\(559\) | −69.3453 | −2.93299 | ||||||||
\(560\) | −6.95301 | −0.293818 | ||||||||
\(561\) | −0.755063 | −0.0318788 | ||||||||
\(562\) | 36.9316 | 1.55787 | ||||||||
\(563\) | 13.2808 | 0.559721 | 0.279860 | − | 0.960041i | \(-0.409712\pi\) | ||||
0.279860 | + | 0.960041i | \(0.409712\pi\) | |||||||
\(564\) | 6.44992 | 0.271591 | ||||||||
\(565\) | −1.56454 | −0.0658208 | ||||||||
\(566\) | 31.5313 | 1.32536 | ||||||||
\(567\) | 3.21050 | 0.134828 | ||||||||
\(568\) | −11.5170 | −0.483244 | ||||||||
\(569\) | 34.2610 | 1.43630 | 0.718148 | − | 0.695891i | \(-0.244990\pi\) | ||||
0.718148 | + | 0.695891i | \(0.244990\pi\) | |||||||
\(570\) | 2.85243 | 0.119475 | ||||||||
\(571\) | 26.5105 | 1.10943 | 0.554714 | − | 0.832041i | \(-0.312828\pi\) | ||||
0.554714 | + | 0.832041i | \(0.312828\pi\) | |||||||
\(572\) | −6.27667 | −0.262441 | ||||||||
\(573\) | −17.5547 | −0.733360 | ||||||||
\(574\) | −28.5437 | −1.19139 | ||||||||
\(575\) | 6.41269 | 0.267428 | ||||||||
\(576\) | −2.54873 | −0.106197 | ||||||||
\(577\) | 27.5838 | 1.14833 | 0.574165 | − | 0.818740i | \(-0.305327\pi\) | ||||
0.574165 | + | 0.818740i | \(0.305327\pi\) | |||||||
\(578\) | −1.83962 | −0.0765181 | ||||||||
\(579\) | −17.4943 | −0.727036 | ||||||||
\(580\) | −3.70601 | −0.153884 | ||||||||
\(581\) | 11.8817 | 0.492936 | ||||||||
\(582\) | 22.3731 | 0.927394 | ||||||||
\(583\) | −0.394635 | −0.0163441 | ||||||||
\(584\) | 17.7345 | 0.733860 | ||||||||
\(585\) | −2.68035 | −0.110819 | ||||||||
\(586\) | −27.0475 | −1.11732 | ||||||||
\(587\) | −40.4654 | −1.67019 | −0.835093 | − | 0.550109i | \(-0.814586\pi\) | ||||
−0.835093 | + | 0.550109i | \(0.814586\pi\) | |||||||
\(588\) | 4.57795 | 0.188791 | ||||||||
\(589\) | −3.25847 | −0.134263 | ||||||||
\(590\) | 2.95318 | 0.121581 | ||||||||
\(591\) | 0.781602 | 0.0321508 | ||||||||
\(592\) | −36.9481 | −1.51856 | ||||||||
\(593\) | 24.0408 | 0.987239 | 0.493620 | − | 0.869678i | \(-0.335674\pi\) | ||||
0.493620 | + | 0.869678i | \(0.335674\pi\) | |||||||
\(594\) | −1.38903 | −0.0569926 | ||||||||
\(595\) | −1.43291 | −0.0587434 | ||||||||
\(596\) | −11.6229 | −0.476093 | ||||||||
\(597\) | 3.72043 | 0.152267 | ||||||||
\(598\) | −14.7571 | −0.603462 | ||||||||
\(599\) | 22.8014 | 0.931639 | 0.465819 | − | 0.884880i | \(-0.345760\pi\) | ||||
0.465819 | + | 0.884880i | \(0.345760\pi\) | |||||||
\(600\) | −5.43850 | −0.222026 | ||||||||
\(601\) | −11.5020 | −0.469175 | −0.234587 | − | 0.972095i | \(-0.575374\pi\) | ||||
−0.234587 | + | 0.972095i | \(0.575374\pi\) | |||||||
\(602\) | −68.1979 | −2.77954 | ||||||||
\(603\) | −4.41034 | −0.179603 | ||||||||
\(604\) | 6.52379 | 0.265449 | ||||||||
\(605\) | −4.65505 | −0.189255 | ||||||||
\(606\) | 16.9417 | 0.688208 | ||||||||
\(607\) | 26.0331 | 1.05665 | 0.528326 | − | 0.849042i | \(-0.322820\pi\) | ||||
0.528326 | + | 0.849042i | \(0.322820\pi\) | |||||||
\(608\) | −23.1406 | −0.938474 | ||||||||
\(609\) | −19.2590 | −0.780414 | ||||||||
\(610\) | 3.19587 | 0.129397 | ||||||||
\(611\) | −27.9834 | −1.13209 | ||||||||
\(612\) | −1.38420 | −0.0559531 | ||||||||
\(613\) | 42.7072 | 1.72493 | 0.862464 | − | 0.506119i | \(-0.168920\pi\) | ||||
0.862464 | + | 0.506119i | \(0.168920\pi\) | |||||||
\(614\) | 23.5859 | 0.951848 | ||||||||
\(615\) | 2.15703 | 0.0869797 | ||||||||
\(616\) | 2.74613 | 0.110645 | ||||||||
\(617\) | 12.5604 | 0.505663 | 0.252831 | − | 0.967510i | \(-0.418638\pi\) | ||||
0.252831 | + | 0.967510i | \(0.418638\pi\) | |||||||
\(618\) | −23.7921 | −0.957057 | ||||||||
\(619\) | 2.29891 | 0.0924010 | 0.0462005 | − | 0.998932i | \(-0.485289\pi\) | ||||
0.0462005 | + | 0.998932i | \(0.485289\pi\) | |||||||
\(620\) | 0.579453 | 0.0232714 | ||||||||
\(621\) | −1.33575 | −0.0536020 | ||||||||
\(622\) | 20.0946 | 0.805719 | ||||||||
\(623\) | 4.33525 | 0.173688 | ||||||||
\(624\) | 29.1408 | 1.16657 | ||||||||
\(625\) | 22.0517 | 0.882067 | ||||||||
\(626\) | 36.5527 | 1.46094 | ||||||||
\(627\) | −2.62316 | −0.104759 | ||||||||
\(628\) | 1.38420 | 0.0552357 | ||||||||
\(629\) | −7.61442 | −0.303607 | ||||||||
\(630\) | −2.63600 | −0.105021 | ||||||||
\(631\) | 7.25565 | 0.288843 | 0.144421 | − | 0.989516i | \(-0.453868\pi\) | ||||
0.144421 | + | 0.989516i | \(0.453868\pi\) | |||||||
\(632\) | −17.4012 | −0.692183 | ||||||||
\(633\) | −2.95112 | −0.117297 | ||||||||
\(634\) | −16.1769 | −0.642465 | ||||||||
\(635\) | 3.68451 | 0.146215 | ||||||||
\(636\) | −0.723455 | −0.0286869 | ||||||||
\(637\) | −19.8617 | −0.786951 | ||||||||
\(638\) | 8.33246 | 0.329885 | ||||||||
\(639\) | −10.1666 | −0.402184 | ||||||||
\(640\) | −3.85311 | −0.152308 | ||||||||
\(641\) | 22.8705 | 0.903332 | 0.451666 | − | 0.892187i | \(-0.350830\pi\) | ||||
0.451666 | + | 0.892187i | \(0.350830\pi\) | |||||||
\(642\) | −4.42556 | −0.174663 | ||||||||
\(643\) | 27.5324 | 1.08577 | 0.542887 | − | 0.839806i | \(-0.317331\pi\) | ||||
0.542887 | + | 0.839806i | \(0.317331\pi\) | |||||||
\(644\) | −5.93606 | −0.233914 | ||||||||
\(645\) | 5.15367 | 0.202926 | ||||||||
\(646\) | −6.39102 | −0.251451 | ||||||||
\(647\) | −13.7759 | −0.541586 | −0.270793 | − | 0.962638i | \(-0.587286\pi\) | ||||
−0.270793 | + | 0.962638i | \(0.587286\pi\) | |||||||
\(648\) | 1.13283 | 0.0445019 | ||||||||
\(649\) | −2.71582 | −0.106605 | ||||||||
\(650\) | −53.0381 | −2.08032 | ||||||||
\(651\) | 3.01123 | 0.118020 | ||||||||
\(652\) | −4.00537 | −0.156862 | ||||||||
\(653\) | 31.2456 | 1.22273 | 0.611367 | − | 0.791347i | \(-0.290620\pi\) | ||||
0.611367 | + | 0.791347i | \(0.290620\pi\) | |||||||
\(654\) | 8.03444 | 0.314171 | ||||||||
\(655\) | −10.0058 | −0.390961 | ||||||||
\(656\) | −23.4512 | −0.915616 | ||||||||
\(657\) | 15.6550 | 0.610761 | ||||||||
\(658\) | −27.5204 | −1.07286 | ||||||||
\(659\) | −23.7045 | −0.923396 | −0.461698 | − | 0.887037i | \(-0.652760\pi\) | ||||
−0.461698 | + | 0.887037i | \(0.652760\pi\) | |||||||
\(660\) | 0.466475 | 0.0181575 | ||||||||
\(661\) | −19.8230 | −0.771026 | −0.385513 | − | 0.922702i | \(-0.625976\pi\) | ||||
−0.385513 | + | 0.922702i | \(0.625976\pi\) | |||||||
\(662\) | 34.3674 | 1.33573 | ||||||||
\(663\) | 6.00546 | 0.233233 | ||||||||
\(664\) | 4.19250 | 0.162700 | ||||||||
\(665\) | −4.97805 | −0.193041 | ||||||||
\(666\) | −14.0076 | −0.542785 | ||||||||
\(667\) | 8.01287 | 0.310260 | ||||||||
\(668\) | −26.9516 | −1.04279 | ||||||||
\(669\) | 5.81311 | 0.224748 | ||||||||
\(670\) | 3.62114 | 0.139897 | ||||||||
\(671\) | −2.93900 | −0.113459 | ||||||||
\(672\) | 21.3847 | 0.824934 | ||||||||
\(673\) | 41.4024 | 1.59594 | 0.797972 | − | 0.602694i | \(-0.205906\pi\) | ||||
0.797972 | + | 0.602694i | \(0.205906\pi\) | |||||||
\(674\) | 19.0224 | 0.732714 | ||||||||
\(675\) | −4.80080 | −0.184783 | ||||||||
\(676\) | 31.9274 | 1.22798 | ||||||||
\(677\) | 40.4080 | 1.55301 | 0.776503 | − | 0.630114i | \(-0.216992\pi\) | ||||
0.776503 | + | 0.630114i | \(0.216992\pi\) | |||||||
\(678\) | 6.44867 | 0.247660 | ||||||||
\(679\) | −39.0454 | −1.49842 | ||||||||
\(680\) | −0.505605 | −0.0193891 | ||||||||
\(681\) | −2.81084 | −0.107712 | ||||||||
\(682\) | −1.30282 | −0.0498875 | ||||||||
\(683\) | −45.2385 | −1.73100 | −0.865501 | − | 0.500907i | \(-0.833000\pi\) | ||||
−0.865501 | + | 0.500907i | \(0.833000\pi\) | |||||||
\(684\) | −4.80885 | −0.183871 | ||||||||
\(685\) | −8.10761 | −0.309776 | ||||||||
\(686\) | 21.8095 | 0.832692 | ||||||||
\(687\) | 19.7529 | 0.753621 | ||||||||
\(688\) | −56.0308 | −2.13615 | ||||||||
\(689\) | 3.13876 | 0.119577 | ||||||||
\(690\) | 1.09673 | 0.0417518 | ||||||||
\(691\) | −46.2740 | −1.76034 | −0.880172 | − | 0.474655i | \(-0.842573\pi\) | ||||
−0.880172 | + | 0.474655i | \(0.842573\pi\) | |||||||
\(692\) | 10.2962 | 0.391401 | ||||||||
\(693\) | 2.42413 | 0.0920850 | ||||||||
\(694\) | 21.9782 | 0.834280 | ||||||||
\(695\) | 1.53894 | 0.0583754 | ||||||||
\(696\) | −6.79559 | −0.257586 | ||||||||
\(697\) | −4.83292 | −0.183060 | ||||||||
\(698\) | 44.3726 | 1.67953 | ||||||||
\(699\) | −8.79173 | −0.332534 | ||||||||
\(700\) | −21.3346 | −0.806374 | ||||||||
\(701\) | 8.49922 | 0.321011 | 0.160505 | − | 0.987035i | \(-0.448688\pi\) | ||||
0.160505 | + | 0.987035i | \(0.448688\pi\) | |||||||
\(702\) | 11.0478 | 0.416971 | ||||||||
\(703\) | −26.4532 | −0.997702 | ||||||||
\(704\) | −1.92445 | −0.0725304 | ||||||||
\(705\) | 2.07970 | 0.0783260 | ||||||||
\(706\) | 55.9426 | 2.10543 | ||||||||
\(707\) | −29.5665 | −1.11196 | ||||||||
\(708\) | −4.97871 | −0.187111 | ||||||||
\(709\) | −12.5160 | −0.470048 | −0.235024 | − | 0.971990i | \(-0.575517\pi\) | ||||
−0.235024 | + | 0.971990i | \(0.575517\pi\) | |||||||
\(710\) | 8.34735 | 0.313270 | ||||||||
\(711\) | −15.3608 | −0.576075 | ||||||||
\(712\) | 1.52970 | 0.0573281 | ||||||||
\(713\) | −1.25285 | −0.0469196 | ||||||||
\(714\) | 5.90609 | 0.221030 | ||||||||
\(715\) | −2.02383 | −0.0756871 | ||||||||
\(716\) | 23.8699 | 0.892061 | ||||||||
\(717\) | −11.7069 | −0.437203 | ||||||||
\(718\) | 3.51489 | 0.131175 | ||||||||
\(719\) | 13.9248 | 0.519306 | 0.259653 | − | 0.965702i | \(-0.416392\pi\) | ||||
0.259653 | + | 0.965702i | \(0.416392\pi\) | |||||||
\(720\) | −2.16571 | −0.0807114 | ||||||||
\(721\) | 41.5218 | 1.54635 | ||||||||
\(722\) | 12.7498 | 0.474497 | ||||||||
\(723\) | 21.6664 | 0.805780 | ||||||||
\(724\) | 2.68034 | 0.0996140 | ||||||||
\(725\) | 28.7988 | 1.06956 | ||||||||
\(726\) | 19.1870 | 0.712097 | ||||||||
\(727\) | 20.0022 | 0.741839 | 0.370919 | − | 0.928665i | \(-0.379043\pi\) | ||||
0.370919 | + | 0.928665i | \(0.379043\pi\) | |||||||
\(728\) | −21.8416 | −0.809503 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −12.8537 | −0.475736 | ||||||||
\(731\) | −11.5470 | −0.427083 | ||||||||
\(732\) | −5.38785 | −0.199141 | ||||||||
\(733\) | −34.0639 | −1.25818 | −0.629090 | − | 0.777332i | \(-0.716572\pi\) | ||||
−0.629090 | + | 0.777332i | \(0.716572\pi\) | |||||||
\(734\) | 33.5658 | 1.23894 | ||||||||
\(735\) | 1.47610 | 0.0544469 | ||||||||
\(736\) | −8.89731 | −0.327959 | ||||||||
\(737\) | −3.33009 | −0.122665 | ||||||||
\(738\) | −8.89074 | −0.327273 | ||||||||
\(739\) | −23.0416 | −0.847600 | −0.423800 | − | 0.905756i | \(-0.639304\pi\) | ||||
−0.423800 | + | 0.905756i | \(0.639304\pi\) | |||||||
\(740\) | 4.70416 | 0.172928 | ||||||||
\(741\) | 20.8635 | 0.766441 | ||||||||
\(742\) | 3.08683 | 0.113321 | ||||||||
\(743\) | 33.6432 | 1.23425 | 0.617126 | − | 0.786865i | \(-0.288297\pi\) | ||||
0.617126 | + | 0.786865i | \(0.288297\pi\) | |||||||
\(744\) | 1.06252 | 0.0389540 | ||||||||
\(745\) | −3.74766 | −0.137304 | ||||||||
\(746\) | −44.0031 | −1.61107 | ||||||||
\(747\) | 3.70090 | 0.135409 | ||||||||
\(748\) | −1.04516 | −0.0382149 | ||||||||
\(749\) | 7.72347 | 0.282209 | ||||||||
\(750\) | 8.04702 | 0.293836 | ||||||||
\(751\) | −8.22992 | −0.300314 | −0.150157 | − | 0.988662i | \(-0.547978\pi\) | ||||
−0.150157 | + | 0.988662i | \(0.547978\pi\) | |||||||
\(752\) | −22.6105 | −0.824520 | ||||||||
\(753\) | −16.4457 | −0.599315 | ||||||||
\(754\) | −66.2729 | −2.41352 | ||||||||
\(755\) | 2.10352 | 0.0765548 | ||||||||
\(756\) | 4.44398 | 0.161626 | ||||||||
\(757\) | 36.0285 | 1.30948 | 0.654738 | − | 0.755856i | \(-0.272779\pi\) | ||||
0.654738 | + | 0.755856i | \(0.272779\pi\) | |||||||
\(758\) | 50.9877 | 1.85196 | ||||||||
\(759\) | −1.00858 | −0.0366091 | ||||||||
\(760\) | −1.75652 | −0.0637157 | ||||||||
\(761\) | −9.75040 | −0.353452 | −0.176726 | − | 0.984260i | \(-0.556551\pi\) | ||||
−0.176726 | + | 0.984260i | \(0.556551\pi\) | |||||||
\(762\) | −15.1866 | −0.550154 | ||||||||
\(763\) | −14.0217 | −0.507618 | ||||||||
\(764\) | −24.2993 | −0.879119 | ||||||||
\(765\) | −0.446319 | −0.0161367 | ||||||||
\(766\) | 41.9169 | 1.51452 | ||||||||
\(767\) | 21.6005 | 0.779947 | ||||||||
\(768\) | 20.9791 | 0.757016 | ||||||||
\(769\) | 9.07378 | 0.327209 | 0.163604 | − | 0.986526i | \(-0.447688\pi\) | ||||
0.163604 | + | 0.986526i | \(0.447688\pi\) | |||||||
\(770\) | −1.99035 | −0.0717272 | ||||||||
\(771\) | −2.86778 | −0.103281 | ||||||||
\(772\) | −24.2156 | −0.871538 | ||||||||
\(773\) | −10.3566 | −0.372499 | −0.186250 | − | 0.982502i | \(-0.559633\pi\) | ||||
−0.186250 | + | 0.982502i | \(0.559633\pi\) | |||||||
\(774\) | −21.2422 | −0.763535 | ||||||||
\(775\) | −4.50284 | −0.161747 | ||||||||
\(776\) | −13.7773 | −0.494575 | ||||||||
\(777\) | 24.4461 | 0.876997 | ||||||||
\(778\) | 15.4933 | 0.555463 | ||||||||
\(779\) | −16.7900 | −0.601566 | ||||||||
\(780\) | −3.71015 | −0.132845 | ||||||||
\(781\) | −7.67641 | −0.274684 | ||||||||
\(782\) | −2.45728 | −0.0878722 | ||||||||
\(783\) | −5.99876 | −0.214378 | ||||||||
\(784\) | −16.0482 | −0.573150 | ||||||||
\(785\) | 0.446319 | 0.0159298 | ||||||||
\(786\) | 41.2417 | 1.47104 | ||||||||
\(787\) | 47.6846 | 1.69977 | 0.849886 | − | 0.526967i | \(-0.176671\pi\) | ||||
0.849886 | + | 0.526967i | \(0.176671\pi\) | |||||||
\(788\) | 1.08190 | 0.0385409 | ||||||||
\(789\) | 12.7348 | 0.453372 | ||||||||
\(790\) | 12.6121 | 0.448718 | ||||||||
\(791\) | −11.2542 | −0.400153 | ||||||||
\(792\) | 0.855361 | 0.0303939 | ||||||||
\(793\) | 23.3755 | 0.830090 | ||||||||
\(794\) | −42.5579 | −1.51032 | ||||||||
\(795\) | −0.233269 | −0.00827321 | ||||||||
\(796\) | 5.14983 | 0.182531 | ||||||||
\(797\) | −43.3536 | −1.53566 | −0.767831 | − | 0.640652i | \(-0.778664\pi\) | ||||
−0.767831 | + | 0.640652i | \(0.778664\pi\) | |||||||
\(798\) | 20.5183 | 0.726341 | ||||||||
\(799\) | −4.65967 | −0.164847 | ||||||||
\(800\) | −31.9776 | −1.13058 | ||||||||
\(801\) | 1.35034 | 0.0477118 | ||||||||
\(802\) | −13.1051 | −0.462755 | ||||||||
\(803\) | 11.8205 | 0.417138 | ||||||||
\(804\) | −6.10481 | −0.215300 | ||||||||
\(805\) | −1.91401 | −0.0674600 | ||||||||
\(806\) | 10.3621 | 0.364989 | ||||||||
\(807\) | −22.2195 | −0.782163 | ||||||||
\(808\) | −10.4326 | −0.367018 | ||||||||
\(809\) | 27.1159 | 0.953345 | 0.476672 | − | 0.879081i | \(-0.341843\pi\) | ||||
0.476672 | + | 0.879081i | \(0.341843\pi\) | |||||||
\(810\) | −0.821058 | −0.0288490 | ||||||||
\(811\) | 46.4477 | 1.63100 | 0.815500 | − | 0.578758i | \(-0.196462\pi\) | ||||
0.815500 | + | 0.578758i | \(0.196462\pi\) | |||||||
\(812\) | −26.6584 | −0.935525 | ||||||||
\(813\) | 6.43735 | 0.225768 | ||||||||
\(814\) | −10.5767 | −0.370712 | ||||||||
\(815\) | −1.29148 | −0.0452386 | ||||||||
\(816\) | 4.85239 | 0.169868 | ||||||||
\(817\) | −40.1156 | −1.40347 | ||||||||
\(818\) | 7.53277 | 0.263377 | ||||||||
\(819\) | −19.2805 | −0.673715 | ||||||||
\(820\) | 2.98576 | 0.104267 | ||||||||
\(821\) | −34.2620 | −1.19575 | −0.597876 | − | 0.801589i | \(-0.703988\pi\) | ||||
−0.597876 | + | 0.801589i | \(0.703988\pi\) | |||||||
\(822\) | 33.4176 | 1.16557 | ||||||||
\(823\) | −21.4199 | −0.746651 | −0.373326 | − | 0.927700i | \(-0.621783\pi\) | ||||
−0.373326 | + | 0.927700i | \(0.621783\pi\) | |||||||
\(824\) | 14.6511 | 0.510394 | ||||||||
\(825\) | −3.62491 | −0.126203 | ||||||||
\(826\) | 21.2431 | 0.739141 | ||||||||
\(827\) | 24.3985 | 0.848419 | 0.424210 | − | 0.905564i | \(-0.360552\pi\) | ||||
0.424210 | + | 0.905564i | \(0.360552\pi\) | |||||||
\(828\) | −1.84895 | −0.0642556 | ||||||||
\(829\) | 55.4033 | 1.92424 | 0.962119 | − | 0.272631i | \(-0.0878937\pi\) | ||||
0.962119 | + | 0.272631i | \(0.0878937\pi\) | |||||||
\(830\) | −3.03865 | −0.105473 | ||||||||
\(831\) | 12.7060 | 0.440767 | ||||||||
\(832\) | 15.3063 | 0.530649 | ||||||||
\(833\) | −3.30728 | −0.114590 | ||||||||
\(834\) | −6.34315 | −0.219645 | ||||||||
\(835\) | −8.69020 | −0.300737 | ||||||||
\(836\) | −3.63099 | −0.125580 | ||||||||
\(837\) | 0.937935 | 0.0324198 | ||||||||
\(838\) | 7.53692 | 0.260359 | ||||||||
\(839\) | −35.7078 | −1.23277 | −0.616384 | − | 0.787445i | \(-0.711403\pi\) | ||||
−0.616384 | + | 0.787445i | \(0.711403\pi\) | |||||||
\(840\) | 1.62324 | 0.0560072 | ||||||||
\(841\) | 6.98513 | 0.240867 | ||||||||
\(842\) | −30.8932 | −1.06465 | ||||||||
\(843\) | −20.0757 | −0.691443 | ||||||||
\(844\) | −4.08495 | −0.140610 | ||||||||
\(845\) | 10.2946 | 0.354144 | ||||||||
\(846\) | −8.57202 | −0.294712 | ||||||||
\(847\) | −33.4851 | −1.15056 | ||||||||
\(848\) | 2.53611 | 0.0870903 | ||||||||
\(849\) | −17.1401 | −0.588247 | ||||||||
\(850\) | −8.83165 | −0.302923 | ||||||||
\(851\) | −10.1710 | −0.348657 | ||||||||
\(852\) | −14.0726 | −0.482120 | ||||||||
\(853\) | −38.9845 | −1.33480 | −0.667402 | − | 0.744697i | \(-0.732594\pi\) | ||||
−0.667402 | + | 0.744697i | \(0.732594\pi\) | |||||||
\(854\) | 22.9888 | 0.786660 | ||||||||
\(855\) | −1.55056 | −0.0530279 | ||||||||
\(856\) | 2.72525 | 0.0931471 | ||||||||
\(857\) | −7.36037 | −0.251425 | −0.125713 | − | 0.992067i | \(-0.540122\pi\) | ||||
−0.125713 | + | 0.992067i | \(0.540122\pi\) | |||||||
\(858\) | 8.34176 | 0.284783 | ||||||||
\(859\) | 7.23709 | 0.246926 | 0.123463 | − | 0.992349i | \(-0.460600\pi\) | ||||
0.123463 | + | 0.992349i | \(0.460600\pi\) | |||||||
\(860\) | 7.13372 | 0.243258 | ||||||||
\(861\) | 15.5161 | 0.528786 | ||||||||
\(862\) | 70.6108 | 2.40501 | ||||||||
\(863\) | 44.5640 | 1.51697 | 0.758487 | − | 0.651688i | \(-0.225939\pi\) | ||||
0.758487 | + | 0.651688i | \(0.225939\pi\) | |||||||
\(864\) | 6.66089 | 0.226608 | ||||||||
\(865\) | 3.31987 | 0.112879 | ||||||||
\(866\) | −38.9720 | −1.32432 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 4.16816 | 0.141477 | ||||||||
\(869\) | −11.5984 | −0.393448 | ||||||||
\(870\) | 4.92533 | 0.166984 | ||||||||
\(871\) | 26.4861 | 0.897448 | ||||||||
\(872\) | −4.94758 | −0.167546 | ||||||||
\(873\) | −12.1618 | −0.411614 | ||||||||
\(874\) | −8.53683 | −0.288763 | ||||||||
\(875\) | −14.0436 | −0.474761 | ||||||||
\(876\) | 21.6698 | 0.732153 | ||||||||
\(877\) | 58.5585 | 1.97738 | 0.988690 | − | 0.149974i | \(-0.0479190\pi\) | ||||
0.988690 | + | 0.149974i | \(0.0479190\pi\) | |||||||
\(878\) | 9.37973 | 0.316551 | ||||||||
\(879\) | 14.7028 | 0.495912 | ||||||||
\(880\) | −1.63525 | −0.0551243 | ||||||||
\(881\) | −14.2452 | −0.479932 | −0.239966 | − | 0.970781i | \(-0.577136\pi\) | ||||
−0.239966 | + | 0.970781i | \(0.577136\pi\) | |||||||
\(882\) | −6.08414 | −0.204864 | ||||||||
\(883\) | 36.4077 | 1.22522 | 0.612609 | − | 0.790386i | \(-0.290120\pi\) | ||||
0.612609 | + | 0.790386i | \(0.290120\pi\) | |||||||
\(884\) | 8.31277 | 0.279589 | ||||||||
\(885\) | −1.60532 | −0.0539623 | ||||||||
\(886\) | −17.0724 | −0.573558 | ||||||||
\(887\) | 1.35943 | 0.0456453 | 0.0228226 | − | 0.999740i | \(-0.492735\pi\) | ||||
0.0228226 | + | 0.999740i | \(0.492735\pi\) | |||||||
\(888\) | 8.62586 | 0.289465 | ||||||||
\(889\) | 26.5036 | 0.888904 | ||||||||
\(890\) | −1.10870 | −0.0371638 | ||||||||
\(891\) | 0.755063 | 0.0252956 | ||||||||
\(892\) | 8.04653 | 0.269418 | ||||||||
\(893\) | −16.1881 | −0.541715 | ||||||||
\(894\) | 15.4470 | 0.516624 | ||||||||
\(895\) | 7.69656 | 0.257268 | ||||||||
\(896\) | −27.7165 | −0.925943 | ||||||||
\(897\) | 8.02181 | 0.267841 | ||||||||
\(898\) | −48.0511 | −1.60349 | ||||||||
\(899\) | −5.62645 | −0.187652 | ||||||||
\(900\) | −6.64528 | −0.221509 | ||||||||
\(901\) | 0.522651 | 0.0174120 | ||||||||
\(902\) | −6.71308 | −0.223521 | ||||||||
\(903\) | 37.0717 | 1.23367 | ||||||||
\(904\) | −3.97107 | −0.132076 | ||||||||
\(905\) | 0.864242 | 0.0287284 | ||||||||
\(906\) | −8.67019 | −0.288048 | ||||||||
\(907\) | 17.4641 | 0.579887 | 0.289943 | − | 0.957044i | \(-0.406364\pi\) | ||||
0.289943 | + | 0.957044i | \(0.406364\pi\) | |||||||
\(908\) | −3.89078 | −0.129120 | ||||||||
\(909\) | −9.20932 | −0.305454 | ||||||||
\(910\) | 15.8304 | 0.524773 | ||||||||
\(911\) | 32.8539 | 1.08850 | 0.544249 | − | 0.838923i | \(-0.316815\pi\) | ||||
0.544249 | + | 0.838923i | \(0.316815\pi\) | |||||||
\(912\) | 16.8577 | 0.558213 | ||||||||
\(913\) | 2.79441 | 0.0924815 | ||||||||
\(914\) | 58.6757 | 1.94082 | ||||||||
\(915\) | −1.73725 | −0.0574316 | ||||||||
\(916\) | 27.3421 | 0.903407 | ||||||||
\(917\) | −71.9748 | −2.37682 | ||||||||
\(918\) | 1.83962 | 0.0607165 | ||||||||
\(919\) | −22.6488 | −0.747114 | −0.373557 | − | 0.927607i | \(-0.621862\pi\) | ||||
−0.373557 | + | 0.927607i | \(0.621862\pi\) | |||||||
\(920\) | −0.675364 | −0.0222661 | ||||||||
\(921\) | −12.8210 | −0.422468 | ||||||||
\(922\) | 32.9153 | 1.08401 | ||||||||
\(923\) | 61.0549 | 2.00965 | ||||||||
\(924\) | 3.35549 | 0.110387 | ||||||||
\(925\) | −36.5553 | −1.20193 | ||||||||
\(926\) | 28.5613 | 0.938583 | ||||||||
\(927\) | 12.9331 | 0.424780 | ||||||||
\(928\) | −39.9571 | −1.31165 | ||||||||
\(929\) | −4.60508 | −0.151088 | −0.0755438 | − | 0.997142i | \(-0.524069\pi\) | ||||
−0.0755438 | + | 0.997142i | \(0.524069\pi\) | |||||||
\(930\) | −0.770098 | −0.0252525 | ||||||||
\(931\) | −11.4898 | −0.376563 | ||||||||
\(932\) | −12.1695 | −0.398626 | ||||||||
\(933\) | −10.9232 | −0.357610 | ||||||||
\(934\) | 52.8374 | 1.72889 | ||||||||
\(935\) | −0.336999 | −0.0110211 | ||||||||
\(936\) | −6.80318 | −0.222369 | ||||||||
\(937\) | −37.9397 | −1.23943 | −0.619717 | − | 0.784825i | \(-0.712753\pi\) | ||||
−0.619717 | + | 0.784825i | \(0.712753\pi\) | |||||||
\(938\) | 26.0479 | 0.850493 | ||||||||
\(939\) | −19.8697 | −0.648424 | ||||||||
\(940\) | 2.87872 | 0.0938936 | ||||||||
\(941\) | −39.5174 | −1.28823 | −0.644116 | − | 0.764928i | \(-0.722774\pi\) | ||||
−0.644116 | + | 0.764928i | \(0.722774\pi\) | |||||||
\(942\) | −1.83962 | −0.0599381 | ||||||||
\(943\) | −6.45560 | −0.210223 | ||||||||
\(944\) | 17.4531 | 0.568050 | ||||||||
\(945\) | 1.43291 | 0.0466124 | ||||||||
\(946\) | −16.0392 | −0.521479 | ||||||||
\(947\) | 46.1968 | 1.50119 | 0.750597 | − | 0.660760i | \(-0.229766\pi\) | ||||
0.750597 | + | 0.660760i | \(0.229766\pi\) | |||||||
\(948\) | −21.2624 | −0.690572 | ||||||||
\(949\) | −94.0157 | −3.05188 | ||||||||
\(950\) | −30.6820 | −0.995455 | ||||||||
\(951\) | 8.79359 | 0.285152 | ||||||||
\(952\) | −3.63695 | −0.117874 | ||||||||
\(953\) | −29.7051 | −0.962242 | −0.481121 | − | 0.876654i | \(-0.659770\pi\) | ||||
−0.481121 | + | 0.876654i | \(0.659770\pi\) | |||||||
\(954\) | 0.961480 | 0.0311291 | ||||||||
\(955\) | −7.83502 | −0.253535 | ||||||||
\(956\) | −16.2048 | −0.524099 | ||||||||
\(957\) | −4.52945 | −0.146416 | ||||||||
\(958\) | −8.04230 | −0.259835 | ||||||||
\(959\) | −58.3203 | −1.88326 | ||||||||
\(960\) | −1.13755 | −0.0367141 | ||||||||
\(961\) | −30.1203 | −0.971622 | ||||||||
\(962\) | 84.1223 | 2.71221 | ||||||||
\(963\) | 2.40569 | 0.0775224 | ||||||||
\(964\) | 29.9906 | 0.965933 | ||||||||
\(965\) | −7.80802 | −0.251349 | ||||||||
\(966\) | 7.88909 | 0.253827 | ||||||||
\(967\) | −9.07931 | −0.291971 | −0.145986 | − | 0.989287i | \(-0.546635\pi\) | ||||
−0.145986 | + | 0.989287i | \(0.546635\pi\) | |||||||
\(968\) | −11.8153 | −0.379758 | ||||||||
\(969\) | 3.47410 | 0.111604 | ||||||||
\(970\) | 9.98553 | 0.320616 | ||||||||
\(971\) | 13.8983 | 0.446018 | 0.223009 | − | 0.974816i | \(-0.428412\pi\) | ||||
0.223009 | + | 0.974816i | \(0.428412\pi\) | |||||||
\(972\) | 1.38420 | 0.0443983 | ||||||||
\(973\) | 11.0700 | 0.354889 | ||||||||
\(974\) | 24.8793 | 0.797185 | ||||||||
\(975\) | 28.8310 | 0.923331 | ||||||||
\(976\) | 18.8874 | 0.604570 | ||||||||
\(977\) | −23.1988 | −0.742196 | −0.371098 | − | 0.928594i | \(-0.621019\pi\) | ||||
−0.371098 | + | 0.928594i | \(0.621019\pi\) | |||||||
\(978\) | 5.32318 | 0.170216 | ||||||||
\(979\) | 1.01959 | 0.0325862 | ||||||||
\(980\) | 2.04323 | 0.0652685 | ||||||||
\(981\) | −4.36744 | −0.139442 | ||||||||
\(982\) | −62.3903 | −1.99095 | ||||||||
\(983\) | −4.95426 | −0.158016 | −0.0790082 | − | 0.996874i | \(-0.525175\pi\) | ||||
−0.0790082 | + | 0.996874i | \(0.525175\pi\) | |||||||
\(984\) | 5.47489 | 0.174533 | ||||||||
\(985\) | 0.348844 | 0.0111151 | ||||||||
\(986\) | −11.0354 | −0.351440 | ||||||||
\(987\) | 14.9598 | 0.476177 | ||||||||
\(988\) | 28.8794 | 0.918775 | ||||||||
\(989\) | −15.4240 | −0.490455 | ||||||||
\(990\) | −0.619951 | −0.0197033 | ||||||||
\(991\) | −30.3631 | −0.964516 | −0.482258 | − | 0.876029i | \(-0.660183\pi\) | ||||
−0.482258 | + | 0.876029i | \(0.660183\pi\) | |||||||
\(992\) | 6.24748 | 0.198358 | ||||||||
\(993\) | −18.6818 | −0.592848 | ||||||||
\(994\) | 60.0448 | 1.90450 | ||||||||
\(995\) | 1.66050 | 0.0526414 | ||||||||
\(996\) | 5.12279 | 0.162322 | ||||||||
\(997\) | −33.7430 | −1.06865 | −0.534326 | − | 0.845278i | \(-0.679435\pi\) | ||||
−0.534326 | + | 0.845278i | \(0.679435\pi\) | |||||||
\(998\) | −25.6850 | −0.813044 | ||||||||
\(999\) | 7.61442 | 0.240910 |
(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 | 8007.2.a.e.1.10 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.e.1.10 | ✓ | 46 | 1.1 | even | 1 | trivial |