Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.16689 | −0.825118 | −0.412559 | − | 0.910931i | \(-0.635365\pi\) | ||||
−0.412559 | + | 0.910931i | \(0.635365\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.638362 | −0.319181 | ||||||||
\(5\) | 1.66410 | 0.744210 | 0.372105 | − | 0.928191i | \(-0.378636\pi\) | ||||
0.372105 | + | 0.928191i | \(0.378636\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.970636 | −0.366866 | −0.183433 | − | 0.983032i | \(-0.558721\pi\) | ||||
−0.183433 | + | 0.983032i | \(0.558721\pi\) | |||||||
\(8\) | 3.07868 | 1.08848 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.94183 | −0.614061 | ||||||||
\(11\) | −3.13024 | −0.943802 | −0.471901 | − | 0.881652i | \(-0.656432\pi\) | ||||
−0.471901 | + | 0.881652i | \(0.656432\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.36483 | 0.933236 | 0.466618 | − | 0.884459i | \(-0.345472\pi\) | ||||
0.466618 | + | 0.884459i | \(0.345472\pi\) | |||||||
\(14\) | 1.13263 | 0.302707 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.31577 | −0.578943 | ||||||||
\(17\) | 3.46748 | 0.840988 | 0.420494 | − | 0.907295i | \(-0.361857\pi\) | ||||
0.420494 | + | 0.907295i | \(0.361857\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.42577 | 0.785926 | 0.392963 | − | 0.919554i | \(-0.371450\pi\) | ||||
0.392963 | + | 0.919554i | \(0.371450\pi\) | |||||||
\(20\) | −1.06230 | −0.237538 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.65265 | 0.778748 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.23076 | −0.446151 | ||||||||
\(26\) | −3.92639 | −0.770029 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.619617 | 0.117097 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.67837 | −1.19947 | −0.599735 | − | 0.800199i | \(-0.704727\pi\) | ||||
−0.599735 | + | 0.800199i | \(0.704727\pi\) | |||||||
\(32\) | −3.45511 | −0.610784 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.04618 | −0.693914 | ||||||||
\(35\) | −1.61524 | −0.273025 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.48322 | −0.572638 | −0.286319 | − | 0.958134i | \(-0.592432\pi\) | ||||
−0.286319 | + | 0.958134i | \(0.592432\pi\) | |||||||
\(38\) | −3.99751 | −0.648481 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.12325 | 0.810058 | ||||||||
\(41\) | −7.11748 | −1.11156 | −0.555782 | − | 0.831328i | \(-0.687581\pi\) | ||||
−0.555782 | + | 0.831328i | \(0.687581\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.93664 | 0.905330 | 0.452665 | − | 0.891681i | \(-0.350473\pi\) | ||||
0.452665 | + | 0.891681i | \(0.350473\pi\) | |||||||
\(44\) | 1.99822 | 0.301244 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.16689 | 0.172049 | ||||||||
\(47\) | −6.42522 | −0.937215 | −0.468607 | − | 0.883407i | \(-0.655244\pi\) | ||||
−0.468607 | + | 0.883407i | \(0.655244\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.05787 | −0.865409 | ||||||||
\(50\) | 2.60305 | 0.368127 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.14798 | −0.297871 | ||||||||
\(53\) | −8.21082 | −1.12784 | −0.563921 | − | 0.825828i | \(-0.690708\pi\) | ||||
−0.563921 | + | 0.825828i | \(0.690708\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.20904 | −0.702387 | ||||||||
\(56\) | −2.98828 | −0.399326 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.16689 | 0.153220 | ||||||||
\(59\) | 13.8303 | 1.80056 | 0.900278 | − | 0.435315i | \(-0.143363\pi\) | ||||
0.900278 | + | 0.435315i | \(0.143363\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.90373 | −0.243748 | −0.121874 | − | 0.992546i | \(-0.538890\pi\) | ||||
−0.121874 | + | 0.992546i | \(0.538890\pi\) | |||||||
\(62\) | 7.79294 | 0.989704 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.66329 | 1.08291 | ||||||||
\(65\) | 5.59943 | 0.694524 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.345727 | −0.0422372 | −0.0211186 | − | 0.999777i | \(-0.506723\pi\) | ||||
−0.0211186 | + | 0.999777i | \(0.506723\pi\) | |||||||
\(68\) | −2.21351 | −0.268427 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.88481 | 0.225278 | ||||||||
\(71\) | 9.30966 | 1.10485 | 0.552427 | − | 0.833561i | \(-0.313702\pi\) | ||||
0.552427 | + | 0.833561i | \(0.313702\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.86037 | 0.334781 | 0.167390 | − | 0.985891i | \(-0.446466\pi\) | ||||
0.167390 | + | 0.985891i | \(0.446466\pi\) | |||||||
\(74\) | 4.06455 | 0.472494 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.18688 | −0.250853 | ||||||||
\(77\) | 3.03832 | 0.346249 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.43789 | 0.386793 | 0.193396 | − | 0.981121i | \(-0.438050\pi\) | ||||
0.193396 | + | 0.981121i | \(0.438050\pi\) | |||||||
\(80\) | −3.85368 | −0.430855 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.30533 | 0.917171 | ||||||||
\(83\) | −1.04752 | −0.114980 | −0.0574901 | − | 0.998346i | \(-0.518310\pi\) | ||||
−0.0574901 | + | 0.998346i | \(0.518310\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.77025 | 0.625872 | ||||||||
\(86\) | −6.92743 | −0.747004 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.63701 | −1.02731 | ||||||||
\(89\) | 9.73586 | 1.03200 | 0.515999 | − | 0.856589i | \(-0.327421\pi\) | ||||
0.515999 | + | 0.856589i | \(0.327421\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.26602 | −0.342372 | ||||||||
\(92\) | 0.638362 | 0.0665538 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.49754 | 0.773312 | ||||||||
\(95\) | 5.70084 | 0.584894 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.02056 | −0.814364 | −0.407182 | − | 0.913347i | \(-0.633489\pi\) | ||||
−0.407182 | + | 0.913347i | \(0.633489\pi\) | |||||||
\(98\) | 7.06888 | 0.714065 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.42403 | 0.142403 | ||||||||
\(101\) | −14.3892 | −1.43178 | −0.715889 | − | 0.698215i | \(-0.753978\pi\) | ||||
−0.715889 | + | 0.698215i | \(0.753978\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.6662 | −1.54364 | −0.771818 | − | 0.635844i | \(-0.780652\pi\) | ||||
−0.771818 | + | 0.635844i | \(0.780652\pi\) | |||||||
\(104\) | 10.3592 | 1.01581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.58114 | 0.930603 | ||||||||
\(107\) | 6.90171 | 0.667214 | 0.333607 | − | 0.942712i | \(-0.391734\pi\) | ||||
0.333607 | + | 0.942712i | \(0.391734\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.1779 | −1.07065 | −0.535323 | − | 0.844647i | \(-0.679810\pi\) | ||||
−0.535323 | + | 0.844647i | \(0.679810\pi\) | |||||||
\(110\) | 6.07839 | 0.579552 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.24777 | 0.212394 | ||||||||
\(113\) | 11.3063 | 1.06360 | 0.531802 | − | 0.846868i | \(-0.321515\pi\) | ||||
0.531802 | + | 0.846868i | \(0.321515\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.66410 | −0.155179 | ||||||||
\(116\) | 0.638362 | 0.0592704 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.1385 | −1.48567 | ||||||||
\(119\) | −3.36566 | −0.308530 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.20161 | −0.109238 | ||||||||
\(122\) | 2.22145 | 0.201120 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.26322 | 0.382848 | ||||||||
\(125\) | −12.0327 | −1.07624 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2943 | 1.17968 | 0.589840 | − | 0.807520i | \(-0.299191\pi\) | ||||
0.589840 | + | 0.807520i | \(0.299191\pi\) | |||||||
\(128\) | −3.19890 | −0.282745 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.53393 | −0.573064 | ||||||||
\(131\) | −7.78581 | −0.680250 | −0.340125 | − | 0.940380i | \(-0.610469\pi\) | ||||
−0.340125 | + | 0.940380i | \(0.610469\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.32518 | −0.288329 | ||||||||
\(134\) | 0.403426 | 0.0348507 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.6753 | 0.915398 | ||||||||
\(137\) | 7.77414 | 0.664189 | 0.332095 | − | 0.943246i | \(-0.392245\pi\) | ||||
0.332095 | + | 0.943246i | \(0.392245\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.7573 | −1.93025 | −0.965123 | − | 0.261798i | \(-0.915684\pi\) | ||||
−0.965123 | + | 0.261798i | \(0.915684\pi\) | |||||||
\(140\) | 1.03111 | 0.0871445 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.8634 | −0.911634 | ||||||||
\(143\) | −10.5327 | −0.880790 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.66410 | −0.138196 | ||||||||
\(146\) | −3.33774 | −0.276234 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.22356 | 0.182775 | ||||||||
\(149\) | 12.8192 | 1.05019 | 0.525093 | − | 0.851045i | \(-0.324030\pi\) | ||||
0.525093 | + | 0.851045i | \(0.324030\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.2566 | −1.40432 | −0.702159 | − | 0.712020i | \(-0.747781\pi\) | ||||
−0.702159 | + | 0.712020i | \(0.747781\pi\) | |||||||
\(152\) | 10.5469 | 0.855464 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.54539 | −0.285696 | ||||||||
\(155\) | −11.1135 | −0.892658 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.10782 | −0.487457 | −0.243728 | − | 0.969844i | \(-0.578371\pi\) | ||||
−0.243728 | + | 0.969844i | \(0.578371\pi\) | |||||||
\(158\) | −4.01165 | −0.319150 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.74967 | −0.454551 | ||||||||
\(161\) | 0.970636 | 0.0764968 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.4145 | 1.52066 | 0.760330 | − | 0.649537i | \(-0.225037\pi\) | ||||
0.760330 | + | 0.649537i | \(0.225037\pi\) | |||||||
\(164\) | 4.54353 | 0.354790 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.22234 | 0.0948722 | ||||||||
\(167\) | −6.86540 | −0.531260 | −0.265630 | − | 0.964075i | \(-0.585580\pi\) | ||||
−0.265630 | + | 0.964075i | \(0.585580\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.67792 | −0.129071 | ||||||||
\(170\) | −6.73327 | −0.516418 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.78973 | −0.288964 | ||||||||
\(173\) | 5.77618 | 0.439155 | 0.219577 | − | 0.975595i | \(-0.429532\pi\) | ||||
0.219577 | + | 0.975595i | \(0.429532\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.16525 | 0.163678 | ||||||||
\(176\) | 7.24891 | 0.546407 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.3607 | −0.851520 | ||||||||
\(179\) | 19.9440 | 1.49068 | 0.745342 | − | 0.666682i | \(-0.232286\pi\) | ||||
0.745342 | + | 0.666682i | \(0.232286\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.56445 | −0.562261 | −0.281130 | − | 0.959670i | \(-0.590709\pi\) | ||||
−0.281130 | + | 0.959670i | \(0.590709\pi\) | |||||||
\(182\) | 3.81110 | 0.282497 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.07868 | −0.226964 | ||||||||
\(185\) | −5.79645 | −0.426163 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.8540 | −0.793726 | ||||||||
\(188\) | 4.10162 | 0.299141 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.65227 | −0.482606 | ||||||||
\(191\) | 0.388024 | 0.0280764 | 0.0140382 | − | 0.999901i | \(-0.495531\pi\) | ||||
0.0140382 | + | 0.999901i | \(0.495531\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.75873 | −0.486504 | −0.243252 | − | 0.969963i | \(-0.578214\pi\) | ||||
−0.243252 | + | 0.969963i | \(0.578214\pi\) | |||||||
\(194\) | 9.35913 | 0.671946 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.86711 | 0.276222 | ||||||||
\(197\) | −9.18467 | −0.654381 | −0.327190 | − | 0.944958i | \(-0.606102\pi\) | ||||
−0.327190 | + | 0.944958i | \(0.606102\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.41182 | −0.241857 | −0.120929 | − | 0.992661i | \(-0.538587\pi\) | ||||
−0.120929 | + | 0.992661i | \(0.538587\pi\) | |||||||
\(200\) | −6.86779 | −0.485626 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.7906 | 1.18138 | ||||||||
\(203\) | 0.970636 | 0.0681253 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.8442 | −0.827237 | ||||||||
\(206\) | 18.2808 | 1.27368 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.79217 | −0.540290 | ||||||||
\(209\) | −10.7235 | −0.741759 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.15205 | −0.561210 | −0.280605 | − | 0.959823i | \(-0.590535\pi\) | ||||
−0.280605 | + | 0.959823i | \(0.590535\pi\) | |||||||
\(212\) | 5.24147 | 0.359986 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.05356 | −0.550530 | ||||||||
\(215\) | 9.87920 | 0.673756 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.48226 | 0.440045 | ||||||||
\(218\) | 13.0434 | 0.883409 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.32525 | 0.224189 | ||||||||
\(221\) | 11.6675 | 0.784840 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.2528 | −1.22230 | −0.611148 | − | 0.791516i | \(-0.709292\pi\) | ||||
−0.611148 | + | 0.791516i | \(0.709292\pi\) | |||||||
\(224\) | 3.35366 | 0.224076 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.1932 | −0.877599 | ||||||||
\(227\) | 21.0299 | 1.39581 | 0.697903 | − | 0.716193i | \(-0.254117\pi\) | ||||
0.697903 | + | 0.716193i | \(0.254117\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.19624 | −0.145132 | −0.0725659 | − | 0.997364i | \(-0.523119\pi\) | ||||
−0.0725659 | + | 0.997364i | \(0.523119\pi\) | |||||||
\(230\) | 1.94183 | 0.128041 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.07868 | −0.202126 | ||||||||
\(233\) | 17.1062 | 1.12067 | 0.560334 | − | 0.828267i | \(-0.310673\pi\) | ||||
0.560334 | + | 0.828267i | \(0.310673\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.6922 | −0.697485 | ||||||||
\(236\) | −8.82876 | −0.574703 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.92737 | 0.254573 | ||||||||
\(239\) | −0.0237289 | −0.00153490 | −0.000767448 | − | 1.00000i | \(-0.500244\pi\) | ||||
−0.000767448 | 1.00000i | \(0.500244\pi\) | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.0526 | −1.16287 | −0.581437 | − | 0.813592i | \(-0.697509\pi\) | ||||
−0.581437 | + | 0.813592i | \(0.697509\pi\) | |||||||
\(242\) | 1.40215 | 0.0901338 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.21527 | 0.0777996 | ||||||||
\(245\) | −10.0809 | −0.644047 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.5271 | 0.733454 | ||||||||
\(248\) | −20.5606 | −1.30560 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.0409 | 0.888025 | ||||||||
\(251\) | 18.9850 | 1.19833 | 0.599163 | − | 0.800627i | \(-0.295500\pi\) | ||||
0.599163 | + | 0.800627i | \(0.295500\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.13024 | 0.196796 | ||||||||
\(254\) | −15.5130 | −0.973375 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.5938 | −0.849613 | ||||||||
\(257\) | 7.95157 | 0.496005 | 0.248003 | − | 0.968759i | \(-0.420226\pi\) | ||||
0.248003 | + | 0.968759i | \(0.420226\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.38094 | 0.210082 | ||||||||
\(260\) | −3.57446 | −0.221679 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.08521 | 0.561286 | ||||||||
\(263\) | 6.77467 | 0.417744 | 0.208872 | − | 0.977943i | \(-0.433021\pi\) | ||||
0.208872 | + | 0.977943i | \(0.433021\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.6637 | −0.839352 | ||||||||
\(266\) | 3.88012 | 0.237906 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.220699 | 0.0134813 | ||||||||
\(269\) | −28.4683 | −1.73574 | −0.867872 | − | 0.496787i | \(-0.834513\pi\) | ||||
−0.867872 | + | 0.496787i | \(0.834513\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.1005 | −1.28177 | −0.640883 | − | 0.767639i | \(-0.721432\pi\) | ||||
−0.640883 | + | 0.767639i | \(0.721432\pi\) | |||||||
\(272\) | −8.02989 | −0.486884 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.07158 | −0.548034 | ||||||||
\(275\) | 6.98280 | 0.421078 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.0874 | 1.32710 | 0.663551 | − | 0.748131i | \(-0.269049\pi\) | ||||
0.663551 | + | 0.748131i | \(0.269049\pi\) | |||||||
\(278\) | 26.5553 | 1.59268 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.97281 | −0.297182 | ||||||||
\(281\) | −21.4004 | −1.27664 | −0.638320 | − | 0.769771i | \(-0.720371\pi\) | ||||
−0.638320 | + | 0.769771i | \(0.720371\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.7098 | 0.874406 | 0.437203 | − | 0.899363i | \(-0.355969\pi\) | ||||
0.437203 | + | 0.899363i | \(0.355969\pi\) | |||||||
\(284\) | −5.94293 | −0.352648 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.2905 | 0.726755 | ||||||||
\(287\) | 6.90848 | 0.407795 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.97656 | −0.292739 | ||||||||
\(290\) | 1.94183 | 0.114028 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.82595 | −0.106856 | ||||||||
\(293\) | −24.7990 | −1.44877 | −0.724387 | − | 0.689394i | \(-0.757877\pi\) | ||||
−0.724387 | + | 0.689394i | \(0.757877\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.0151 | 1.33999 | ||||||||
\(296\) | −10.7237 | −0.623305 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.9586 | −0.866527 | ||||||||
\(299\) | −3.36483 | −0.194593 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.76232 | −0.332135 | ||||||||
\(302\) | 20.1365 | 1.15873 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.93330 | −0.455006 | ||||||||
\(305\) | −3.16801 | −0.181400 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.1800 | 1.83661 | 0.918304 | − | 0.395877i | \(-0.129559\pi\) | ||||
0.918304 | + | 0.395877i | \(0.129559\pi\) | |||||||
\(308\) | −1.93955 | −0.110516 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.9683 | 0.736548 | ||||||||
\(311\) | 24.4553 | 1.38673 | 0.693366 | − | 0.720585i | \(-0.256127\pi\) | ||||
0.693366 | + | 0.720585i | \(0.256127\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.1018 | 1.07970 | 0.539848 | − | 0.841763i | \(-0.318482\pi\) | ||||
0.539848 | + | 0.841763i | \(0.318482\pi\) | |||||||
\(314\) | 7.12717 | 0.402209 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.19462 | −0.123457 | ||||||||
\(317\) | 0.189764 | 0.0106582 | 0.00532909 | − | 0.999986i | \(-0.498304\pi\) | ||||
0.00532909 | + | 0.999986i | \(0.498304\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.13024 | 0.175260 | ||||||||
\(320\) | 14.4166 | 0.805913 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.13263 | −0.0631189 | ||||||||
\(323\) | 11.8788 | 0.660954 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.50611 | −0.416364 | ||||||||
\(326\) | −22.6546 | −1.25472 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −21.9125 | −1.20991 | ||||||||
\(329\) | 6.23655 | 0.343832 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.51985 | 0.0835385 | 0.0417692 | − | 0.999127i | \(-0.486701\pi\) | ||||
0.0417692 | + | 0.999127i | \(0.486701\pi\) | |||||||
\(332\) | 0.668697 | 0.0366995 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.01118 | 0.438352 | ||||||||
\(335\) | −0.575325 | −0.0314334 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.8217 | −0.807389 | −0.403694 | − | 0.914894i | \(-0.632274\pi\) | ||||
−0.403694 | + | 0.914894i | \(0.632274\pi\) | |||||||
\(338\) | 1.95796 | 0.106499 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.68351 | −0.199766 | ||||||||
\(341\) | 20.9049 | 1.13206 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.6744 | 0.684355 | ||||||||
\(344\) | 18.2771 | 0.985433 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.74018 | −0.362355 | ||||||||
\(347\) | −0.764551 | −0.0410433 | −0.0205216 | − | 0.999789i | \(-0.506533\pi\) | ||||
−0.0205216 | + | 0.999789i | \(0.506533\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.8271 | −1.00779 | −0.503896 | − | 0.863764i | \(-0.668101\pi\) | ||||
−0.503896 | + | 0.863764i | \(0.668101\pi\) | |||||||
\(350\) | −2.52662 | −0.135053 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.8153 | 0.576459 | ||||||||
\(353\) | −19.6288 | −1.04473 | −0.522367 | − | 0.852721i | \(-0.674951\pi\) | ||||
−0.522367 | + | 0.852721i | \(0.674951\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.4922 | 0.822243 | ||||||||
\(356\) | −6.21500 | −0.329394 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −23.2725 | −1.22999 | ||||||||
\(359\) | −8.40034 | −0.443353 | −0.221677 | − | 0.975120i | \(-0.571153\pi\) | ||||
−0.221677 | + | 0.975120i | \(0.571153\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.26409 | −0.382321 | ||||||||
\(362\) | 8.82690 | 0.463931 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.08491 | 0.109279 | ||||||||
\(365\) | 4.75995 | 0.249147 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.7870 | −1.60707 | −0.803534 | − | 0.595260i | \(-0.797049\pi\) | ||||
−0.803534 | + | 0.595260i | \(0.797049\pi\) | |||||||
\(368\) | 2.31577 | 0.120718 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.76383 | 0.351635 | ||||||||
\(371\) | 7.96972 | 0.413767 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.79852 | −0.196680 | −0.0983399 | − | 0.995153i | \(-0.531353\pi\) | ||||
−0.0983399 | + | 0.995153i | \(0.531353\pi\) | |||||||
\(374\) | 12.6655 | 0.654918 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.7812 | −1.02014 | ||||||||
\(377\) | −3.36483 | −0.173298 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.4712 | 0.537867 | 0.268934 | − | 0.963159i | \(-0.413329\pi\) | ||||
0.268934 | + | 0.963159i | \(0.413329\pi\) | |||||||
\(380\) | −3.63920 | −0.186687 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.452783 | −0.0231664 | ||||||||
\(383\) | 13.4398 | 0.686740 | 0.343370 | − | 0.939200i | \(-0.388432\pi\) | ||||
0.343370 | + | 0.939200i | \(0.388432\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.05608 | 0.257682 | ||||||||
\(386\) | 7.88671 | 0.401423 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.12002 | 0.259930 | ||||||||
\(389\) | −29.5183 | −1.49664 | −0.748319 | − | 0.663339i | \(-0.769139\pi\) | ||||
−0.748319 | + | 0.663339i | \(0.769139\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.46748 | −0.175358 | ||||||||
\(392\) | −18.6503 | −0.941980 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.7175 | 0.539941 | ||||||||
\(395\) | 5.72101 | 0.287855 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.4511 | −1.12679 | −0.563394 | − | 0.826189i | \(-0.690505\pi\) | ||||
−0.563394 | + | 0.826189i | \(0.690505\pi\) | |||||||
\(398\) | 3.98123 | 0.199561 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.16592 | 0.258296 | ||||||||
\(401\) | −31.5457 | −1.57532 | −0.787659 | − | 0.616111i | \(-0.788707\pi\) | ||||
−0.787659 | + | 0.616111i | \(0.788707\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.4716 | −1.11939 | ||||||||
\(404\) | 9.18551 | 0.456996 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.13263 | −0.0562114 | ||||||||
\(407\) | 10.9033 | 0.540457 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.5651 | −1.80803 | −0.904015 | − | 0.427501i | \(-0.859394\pi\) | ||||
−0.904015 | + | 0.427501i | \(0.859394\pi\) | |||||||
\(410\) | 13.8209 | 0.682568 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.0007 | 0.492699 | ||||||||
\(413\) | −13.4242 | −0.660563 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.74318 | −0.0855695 | ||||||||
\(416\) | −11.6259 | −0.570005 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12.5131 | 0.612038 | ||||||||
\(419\) | −32.5009 | −1.58777 | −0.793887 | − | 0.608065i | \(-0.791946\pi\) | ||||
−0.793887 | + | 0.608065i | \(0.791946\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.1960 | 1.08177 | 0.540885 | − | 0.841097i | \(-0.318090\pi\) | ||||
0.540885 | + | 0.841097i | \(0.318090\pi\) | |||||||
\(422\) | 9.51256 | 0.463064 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −25.2785 | −1.22763 | ||||||||
\(425\) | −7.73511 | −0.375208 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.84783 | 0.0894227 | ||||||||
\(428\) | −4.40579 | −0.212962 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.5280 | −0.555928 | ||||||||
\(431\) | 10.1047 | 0.486726 | 0.243363 | − | 0.969935i | \(-0.421749\pi\) | ||||
0.243363 | + | 0.969935i | \(0.421749\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.99683 | 0.0959617 | 0.0479808 | − | 0.998848i | \(-0.484721\pi\) | ||||
0.0479808 | + | 0.998848i | \(0.484721\pi\) | |||||||
\(434\) | −7.56410 | −0.363089 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.13553 | 0.341730 | ||||||||
\(437\) | −3.42577 | −0.163877 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.5731 | −1.31599 | −0.657997 | − | 0.753021i | \(-0.728596\pi\) | ||||
−0.657997 | + | 0.753021i | \(0.728596\pi\) | |||||||
\(440\) | −16.0370 | −0.764534 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.6147 | −0.647585 | ||||||||
\(443\) | −11.2234 | −0.533240 | −0.266620 | − | 0.963802i | \(-0.585907\pi\) | ||||
−0.266620 | + | 0.963802i | \(0.585907\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.2015 | 0.768024 | ||||||||
\(446\) | 21.2990 | 1.00854 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.40890 | −0.397283 | ||||||||
\(449\) | −25.2119 | −1.18982 | −0.594911 | − | 0.803791i | \(-0.702813\pi\) | ||||
−0.594911 | + | 0.803791i | \(0.702813\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.2794 | 1.04910 | ||||||||
\(452\) | −7.21749 | −0.339482 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −24.5397 | −1.15170 | ||||||||
\(455\) | −5.43501 | −0.254797 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.1195 | 0.894375 | 0.447187 | − | 0.894440i | \(-0.352426\pi\) | ||||
0.447187 | + | 0.894440i | \(0.352426\pi\) | |||||||
\(458\) | 2.56278 | 0.119751 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.06230 | 0.0495300 | ||||||||
\(461\) | −28.0742 | −1.30754 | −0.653772 | − | 0.756692i | \(-0.726814\pi\) | ||||
−0.653772 | + | 0.756692i | \(0.726814\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.4780 | −0.533430 | −0.266715 | − | 0.963775i | \(-0.585938\pi\) | ||||
−0.266715 | + | 0.963775i | \(0.585938\pi\) | |||||||
\(464\) | 2.31577 | 0.107507 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.9611 | −0.924682 | ||||||||
\(467\) | −34.8739 | −1.61377 | −0.806886 | − | 0.590707i | \(-0.798849\pi\) | ||||
−0.806886 | + | 0.590707i | \(0.798849\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.335575 | 0.0154954 | ||||||||
\(470\) | 12.4767 | 0.575507 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 42.5792 | 1.95987 | ||||||||
\(473\) | −18.5831 | −0.854452 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.64206 | −0.350642 | ||||||||
\(476\) | 2.14851 | 0.0984769 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.0276891 | 0.00126647 | ||||||||
\(479\) | −3.69004 | −0.168602 | −0.0843011 | − | 0.996440i | \(-0.526866\pi\) | ||||
−0.0843011 | + | 0.996440i | \(0.526866\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.7205 | −0.534407 | ||||||||
\(482\) | 21.0655 | 0.959507 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.767064 | 0.0348665 | ||||||||
\(485\) | −13.3470 | −0.606058 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.7082 | −1.43684 | −0.718418 | − | 0.695612i | \(-0.755133\pi\) | ||||
−0.718418 | + | 0.695612i | \(0.755133\pi\) | |||||||
\(488\) | −5.86098 | −0.265314 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11.7634 | 0.531414 | ||||||||
\(491\) | −21.1652 | −0.955173 | −0.477587 | − | 0.878585i | \(-0.658488\pi\) | ||||
−0.477587 | + | 0.878585i | \(0.658488\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.46748 | −0.156168 | ||||||||
\(494\) | −13.4509 | −0.605186 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.4656 | 0.694424 | ||||||||
\(497\) | −9.03629 | −0.405333 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 40.2349 | 1.80116 | 0.900582 | − | 0.434687i | \(-0.143141\pi\) | ||||
0.900582 | + | 0.434687i | \(0.143141\pi\) | |||||||
\(500\) | 7.68124 | 0.343515 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −22.1535 | −0.988759 | ||||||||
\(503\) | 5.43044 | 0.242131 | 0.121066 | − | 0.992644i | \(-0.461369\pi\) | ||||
0.121066 | + | 0.992644i | \(0.461369\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.9451 | −1.06554 | ||||||||
\(506\) | −3.65265 | −0.162380 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.48659 | −0.376531 | ||||||||
\(509\) | 0.165579 | 0.00733915 | 0.00366958 | − | 0.999993i | \(-0.498832\pi\) | ||||
0.00366958 | + | 0.999993i | \(0.498832\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.77638 | −0.122820 | ||||||||
\(512\) | 22.2603 | 0.983776 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.27862 | −0.409263 | ||||||||
\(515\) | −26.0702 | −1.14879 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.1125 | 0.884545 | ||||||||
\(518\) | −3.94520 | −0.173342 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 17.2389 | 0.755975 | ||||||||
\(521\) | 2.11999 | 0.0928786 | 0.0464393 | − | 0.998921i | \(-0.485213\pi\) | ||||
0.0464393 | + | 0.998921i | \(0.485213\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.1662 | −0.444538 | −0.222269 | − | 0.974985i | \(-0.571346\pi\) | ||||
−0.222269 | + | 0.974985i | \(0.571346\pi\) | |||||||
\(524\) | 4.97017 | 0.217123 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.90531 | −0.344688 | ||||||||
\(527\) | −23.1571 | −1.00874 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 15.9440 | 0.692564 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.12267 | 0.0920293 | ||||||||
\(533\) | −23.9491 | −1.03735 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.4852 | 0.496547 | ||||||||
\(536\) | −1.06438 | −0.0459743 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 33.2195 | 1.43219 | ||||||||
\(539\) | 18.9626 | 0.816775 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.0049 | −0.731100 | −0.365550 | − | 0.930792i | \(-0.619119\pi\) | ||||
−0.365550 | + | 0.930792i | \(0.619119\pi\) | |||||||
\(542\) | 24.6220 | 1.05761 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −11.9806 | −0.513662 | ||||||||
\(545\) | −18.6011 | −0.796786 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.79318 | −0.247698 | −0.123849 | − | 0.992301i | \(-0.539524\pi\) | ||||
−0.123849 | + | 0.992301i | \(0.539524\pi\) | |||||||
\(548\) | −4.96271 | −0.211997 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.14817 | −0.347439 | ||||||||
\(551\) | −3.42577 | −0.145943 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.33694 | −0.141901 | ||||||||
\(554\) | −25.7736 | −1.09502 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.5274 | 0.616097 | ||||||||
\(557\) | 11.4176 | 0.483779 | 0.241890 | − | 0.970304i | \(-0.422233\pi\) | ||||
0.241890 | + | 0.970304i | \(0.422233\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.9758 | 0.844886 | ||||||||
\(560\) | 3.74052 | 0.158066 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 24.9720 | 1.05338 | ||||||||
\(563\) | −39.9407 | −1.68330 | −0.841650 | − | 0.540023i | \(-0.818416\pi\) | ||||
−0.841650 | + | 0.540023i | \(0.818416\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.8148 | 0.791546 | ||||||||
\(566\) | −17.1647 | −0.721488 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 28.6615 | 1.20261 | ||||||||
\(569\) | 9.79116 | 0.410467 | 0.205233 | − | 0.978713i | \(-0.434205\pi\) | ||||
0.205233 | + | 0.978713i | \(0.434205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.3432 | 1.22798 | 0.613988 | − | 0.789315i | \(-0.289564\pi\) | ||||
0.613988 | + | 0.789315i | \(0.289564\pi\) | |||||||
\(572\) | 6.72368 | 0.281131 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.06145 | −0.336479 | ||||||||
\(575\) | 2.23076 | 0.0930289 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.0324 | −1.12537 | −0.562687 | − | 0.826670i | \(-0.690233\pi\) | ||||
−0.562687 | + | 0.826670i | \(0.690233\pi\) | |||||||
\(578\) | 5.80711 | 0.241544 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.06230 | 0.0441096 | ||||||||
\(581\) | 1.01676 | 0.0421823 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.7018 | 1.06446 | ||||||||
\(584\) | 8.80618 | 0.364402 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.9378 | 1.19541 | ||||||||
\(587\) | 4.30700 | 0.177769 | 0.0888845 | − | 0.996042i | \(-0.471670\pi\) | ||||
0.0888845 | + | 0.996042i | \(0.471670\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.8786 | −0.942695 | ||||||||
\(590\) | −26.8562 | −1.10565 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.06635 | 0.331525 | ||||||||
\(593\) | 16.2048 | 0.665453 | 0.332727 | − | 0.943023i | \(-0.392031\pi\) | ||||
0.332727 | + | 0.943023i | \(0.392031\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.60082 | −0.229611 | ||||||||
\(596\) | −8.18326 | −0.335200 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.92639 | 0.160562 | ||||||||
\(599\) | −14.9770 | −0.611945 | −0.305973 | − | 0.952040i | \(-0.598982\pi\) | ||||
−0.305973 | + | 0.952040i | \(0.598982\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.1354 | 1.10688 | 0.553438 | − | 0.832890i | \(-0.313315\pi\) | ||||
0.553438 | + | 0.832890i | \(0.313315\pi\) | |||||||
\(602\) | 6.72401 | 0.274050 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.0159 | 0.448232 | ||||||||
\(605\) | −1.99961 | −0.0812957 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.67826 | −0.189885 | −0.0949423 | − | 0.995483i | \(-0.530267\pi\) | ||||
−0.0949423 | + | 0.995483i | \(0.530267\pi\) | |||||||
\(608\) | −11.8364 | −0.480031 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.69672 | 0.149676 | ||||||||
\(611\) | −21.6198 | −0.874642 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.1493 | −1.58122 | −0.790612 | − | 0.612317i | \(-0.790238\pi\) | ||||
−0.790612 | + | 0.612317i | \(0.790238\pi\) | |||||||
\(614\) | −37.5506 | −1.51542 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.35403 | 0.376885 | ||||||||
\(617\) | 5.78299 | 0.232815 | 0.116407 | − | 0.993202i | \(-0.462862\pi\) | ||||
0.116407 | + | 0.993202i | \(0.462862\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 49.3680 | 1.98427 | 0.992134 | − | 0.125181i | \(-0.0399511\pi\) | ||||
0.992134 | + | 0.125181i | \(0.0399511\pi\) | |||||||
\(620\) | 7.09444 | 0.284919 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −28.5367 | −1.14422 | ||||||||
\(623\) | −9.44997 | −0.378605 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.86995 | −0.354798 | ||||||||
\(626\) | −22.2897 | −0.890876 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.89900 | 0.155587 | ||||||||
\(629\) | −12.0780 | −0.481582 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.3185 | −0.649628 | −0.324814 | − | 0.945778i | \(-0.605302\pi\) | ||||
−0.324814 | + | 0.945778i | \(0.605302\pi\) | |||||||
\(632\) | 10.5842 | 0.421016 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.221434 | −0.00879426 | ||||||||
\(635\) | 22.1231 | 0.877930 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.3837 | −0.807631 | ||||||||
\(638\) | −3.65265 | −0.144610 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.32330 | −0.210422 | ||||||||
\(641\) | −11.2290 | −0.443521 | −0.221760 | − | 0.975101i | \(-0.571180\pi\) | ||||
−0.221760 | + | 0.975101i | \(0.571180\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.6694 | 0.854556 | 0.427278 | − | 0.904120i | \(-0.359472\pi\) | ||||
0.427278 | + | 0.904120i | \(0.359472\pi\) | |||||||
\(644\) | −0.619617 | −0.0244163 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.8613 | −0.545365 | ||||||||
\(647\) | 6.83356 | 0.268655 | 0.134327 | − | 0.990937i | \(-0.457113\pi\) | ||||
0.134327 | + | 0.990937i | \(0.457113\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −43.2922 | −1.69937 | ||||||||
\(650\) | 8.75883 | 0.343549 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.3935 | −0.485366 | ||||||||
\(653\) | 41.1434 | 1.61006 | 0.805032 | − | 0.593231i | \(-0.202148\pi\) | ||||
0.805032 | + | 0.593231i | \(0.202148\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.9564 | −0.506249 | ||||||||
\(656\) | 16.4824 | 0.643531 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.27738 | −0.283702 | ||||||||
\(659\) | 37.5297 | 1.46195 | 0.730974 | − | 0.682405i | \(-0.239066\pi\) | ||||
0.730974 | + | 0.682405i | \(0.239066\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.9108 | 0.541068 | 0.270534 | − | 0.962710i | \(-0.412800\pi\) | ||||
0.270534 | + | 0.962710i | \(0.412800\pi\) | |||||||
\(662\) | −1.77350 | −0.0689291 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.22498 | −0.125154 | ||||||||
\(665\) | −5.53344 | −0.214578 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 4.38261 | 0.169568 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.671343 | 0.0259362 | ||||||||
\(671\) | 5.95913 | 0.230050 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.5659 | −1.56370 | −0.781850 | − | 0.623467i | \(-0.785724\pi\) | ||||
−0.781850 | + | 0.623467i | \(0.785724\pi\) | |||||||
\(674\) | 17.2953 | 0.666191 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.07112 | 0.0411970 | ||||||||
\(677\) | 1.71291 | 0.0658325 | 0.0329163 | − | 0.999458i | \(-0.489521\pi\) | ||||
0.0329163 | + | 0.999458i | \(0.489521\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.78504 | 0.298762 | ||||||||
\(680\) | 17.7648 | 0.681249 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −24.3937 | −0.934085 | ||||||||
\(683\) | 8.39156 | 0.321094 | 0.160547 | − | 0.987028i | \(-0.448674\pi\) | ||||
0.160547 | + | 0.987028i | \(0.448674\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.9370 | 0.494296 | ||||||||
\(686\) | −14.7897 | −0.564673 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13.7479 | −0.524134 | ||||||||
\(689\) | −27.6280 | −1.05254 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.31311 | 0.354288 | 0.177144 | − | 0.984185i | \(-0.443314\pi\) | ||||
0.177144 | + | 0.984185i | \(0.443314\pi\) | |||||||
\(692\) | −3.68729 | −0.140170 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.892149 | 0.0338655 | ||||||||
\(695\) | −37.8705 | −1.43651 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.6797 | −0.934812 | ||||||||
\(698\) | 21.9692 | 0.831548 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.38221 | −0.0522428 | ||||||||
\(701\) | −12.1056 | −0.457222 | −0.228611 | − | 0.973518i | \(-0.573418\pi\) | ||||
−0.228611 | + | 0.973518i | \(0.573418\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.9327 | −0.450051 | ||||||||
\(704\) | −27.1181 | −1.02205 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.9046 | 0.862028 | ||||||||
\(707\) | 13.9667 | 0.525270 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.0136 | 1.23985 | 0.619925 | − | 0.784661i | \(-0.287163\pi\) | ||||
0.619925 | + | 0.784661i | \(0.287163\pi\) | |||||||
\(710\) | −18.0778 | −0.678447 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 29.9736 | 1.12331 | ||||||||
\(713\) | 6.67837 | 0.250107 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.5275 | −0.655493 | ||||||||
\(716\) | −12.7315 | −0.475798 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.80230 | 0.365818 | ||||||||
\(719\) | −17.2610 | −0.643727 | −0.321864 | − | 0.946786i | \(-0.604309\pi\) | ||||
−0.321864 | + | 0.946786i | \(0.604309\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.2062 | 0.566307 | ||||||||
\(722\) | 8.47641 | 0.315459 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.82885 | 0.179463 | ||||||||
\(725\) | 2.23076 | 0.0828482 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.5001 | −0.611955 | −0.305977 | − | 0.952039i | \(-0.598983\pi\) | ||||
−0.305977 | + | 0.952039i | \(0.598983\pi\) | |||||||
\(728\) | −10.0551 | −0.372665 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.55435 | −0.205576 | ||||||||
\(731\) | 20.5852 | 0.761372 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.7144 | −0.802039 | −0.401020 | − | 0.916069i | \(-0.631344\pi\) | ||||
−0.401020 | + | 0.916069i | \(0.631344\pi\) | |||||||
\(734\) | 35.9251 | 1.32602 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.45511 | 0.127357 | ||||||||
\(737\) | 1.08221 | 0.0398636 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.4134 | −0.566993 | −0.283496 | − | 0.958973i | \(-0.591494\pi\) | ||||
−0.283496 | + | 0.958973i | \(0.591494\pi\) | |||||||
\(740\) | 3.70023 | 0.136023 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.29980 | −0.341406 | ||||||||
\(743\) | −47.2089 | −1.73193 | −0.865964 | − | 0.500106i | \(-0.833294\pi\) | ||||
−0.865964 | + | 0.500106i | \(0.833294\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.3324 | 0.781559 | ||||||||
\(746\) | 4.43246 | 0.162284 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.92881 | 0.253342 | ||||||||
\(749\) | −6.69905 | −0.244778 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.92362 | −0.0701939 | −0.0350969 | − | 0.999384i | \(-0.511174\pi\) | ||||
−0.0350969 | + | 0.999384i | \(0.511174\pi\) | |||||||
\(752\) | 14.8793 | 0.542594 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.92639 | 0.142991 | ||||||||
\(755\) | −28.7167 | −1.04511 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.3233 | −1.21116 | −0.605578 | − | 0.795786i | \(-0.707058\pi\) | ||||
−0.605578 | + | 0.795786i | \(0.707058\pi\) | |||||||
\(758\) | −12.2187 | −0.443804 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 17.5511 | 0.636645 | ||||||||
\(761\) | −12.2967 | −0.445754 | −0.222877 | − | 0.974847i | \(-0.571545\pi\) | ||||
−0.222877 | + | 0.974847i | \(0.571545\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.8496 | 0.392783 | ||||||||
\(764\) | −0.247700 | −0.00896147 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.6828 | −0.566641 | ||||||||
\(767\) | 46.5367 | 1.68034 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.7078 | 0.782803 | 0.391401 | − | 0.920220i | \(-0.371990\pi\) | ||||
0.391401 | + | 0.920220i | \(0.371990\pi\) | |||||||
\(770\) | −5.89991 | −0.212618 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.31452 | 0.155283 | ||||||||
\(773\) | 39.5976 | 1.42423 | 0.712114 | − | 0.702064i | \(-0.247738\pi\) | ||||
0.712114 | + | 0.702064i | \(0.247738\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.8978 | 0.535145 | ||||||||
\(776\) | −24.6928 | −0.886419 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.4447 | 1.23490 | ||||||||
\(779\) | −24.3829 | −0.873606 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.1414 | −1.04276 | ||||||||
\(782\) | 4.04618 | 0.144691 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 14.0286 | 0.501022 | ||||||||
\(785\) | −10.1640 | −0.362770 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.7413 | −1.27404 | −0.637020 | − | 0.770847i | \(-0.719833\pi\) | ||||
−0.637020 | + | 0.770847i | \(0.719833\pi\) | |||||||
\(788\) | 5.86314 | 0.208866 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.67580 | −0.237514 | ||||||||
\(791\) | −10.9743 | −0.390200 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.40573 | −0.227474 | ||||||||
\(794\) | 26.1980 | 0.929732 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.17798 | 0.0771963 | ||||||||
\(797\) | 42.4281 | 1.50288 | 0.751440 | − | 0.659801i | \(-0.229360\pi\) | ||||
0.751440 | + | 0.659801i | \(0.229360\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.2793 | −0.788187 | ||||||||
\(800\) | 7.70752 | 0.272502 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 36.8105 | 1.29982 | ||||||||
\(803\) | −8.95364 | −0.315967 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.61524 | 0.0569297 | ||||||||
\(806\) | 26.2219 | 0.923627 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −44.2998 | −1.55846 | ||||||||
\(809\) | 44.7480 | 1.57325 | 0.786627 | − | 0.617428i | \(-0.211825\pi\) | ||||
0.786627 | + | 0.617428i | \(0.211825\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.1461 | −1.72575 | −0.862877 | − | 0.505414i | \(-0.831340\pi\) | ||||
−0.862877 | + | 0.505414i | \(0.831340\pi\) | |||||||
\(812\) | −0.619617 | −0.0217443 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12.7230 | −0.445941 | ||||||||
\(815\) | 32.3078 | 1.13169 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.3376 | 0.711522 | ||||||||
\(818\) | 42.6676 | 1.49184 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.56090 | 0.264038 | ||||||||
\(821\) | 25.4417 | 0.887921 | 0.443960 | − | 0.896046i | \(-0.353573\pi\) | ||||
0.443960 | + | 0.896046i | \(0.353573\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.39388 | −0.153161 | −0.0765804 | − | 0.997063i | \(-0.524400\pi\) | ||||
−0.0765804 | + | 0.997063i | \(0.524400\pi\) | |||||||
\(824\) | −48.2313 | −1.68022 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.6646 | 0.545042 | ||||||||
\(827\) | 35.1132 | 1.22101 | 0.610503 | − | 0.792014i | \(-0.290967\pi\) | ||||
0.610503 | + | 0.792014i | \(0.290967\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.5291 | 0.435152 | 0.217576 | − | 0.976043i | \(-0.430185\pi\) | ||||
0.217576 | + | 0.976043i | \(0.430185\pi\) | |||||||
\(830\) | 2.03411 | 0.0706049 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 29.1505 | 1.01061 | ||||||||
\(833\) | −21.0055 | −0.727799 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.4247 | −0.395369 | ||||||||
\(836\) | 6.84546 | 0.236755 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 37.9251 | 1.31010 | ||||||||
\(839\) | 1.22438 | 0.0422703 | 0.0211352 | − | 0.999777i | \(-0.493272\pi\) | ||||
0.0211352 | + | 0.999777i | \(0.493272\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −25.9004 | −0.892587 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.20396 | 0.179128 | ||||||||
\(845\) | −2.79224 | −0.0960559 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.16633 | 0.0400755 | ||||||||
\(848\) | 19.0144 | 0.652956 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.02604 | 0.309591 | ||||||||
\(851\) | 3.48322 | 0.119403 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.0204 | 1.09636 | 0.548178 | − | 0.836361i | \(-0.315322\pi\) | ||||
0.548178 | + | 0.836361i | \(0.315322\pi\) | |||||||
\(854\) | −2.15622 | −0.0737842 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 21.2482 | 0.726248 | ||||||||
\(857\) | −31.7302 | −1.08388 | −0.541941 | − | 0.840416i | \(-0.682310\pi\) | ||||
−0.541941 | + | 0.840416i | \(0.682310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.2799 | 0.930778 | 0.465389 | − | 0.885106i | \(-0.345915\pi\) | ||||
0.465389 | + | 0.885106i | \(0.345915\pi\) | |||||||
\(860\) | −6.30650 | −0.215050 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.7911 | −0.401606 | ||||||||
\(863\) | 19.1687 | 0.652512 | 0.326256 | − | 0.945282i | \(-0.394213\pi\) | ||||
0.326256 | + | 0.945282i | \(0.394213\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.61217 | 0.326824 | ||||||||
\(866\) | −2.33009 | −0.0791797 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.13803 | −0.140454 | ||||||||
\(869\) | −10.7614 | −0.365056 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.16331 | −0.0394173 | ||||||||
\(872\) | −34.4131 | −1.16538 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.99751 | 0.135218 | ||||||||
\(875\) | 11.6794 | 0.394836 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.5102 | −0.625044 | −0.312522 | − | 0.949911i | \(-0.601174\pi\) | ||||
−0.312522 | + | 0.949911i | \(0.601174\pi\) | |||||||
\(878\) | 32.1749 | 1.08585 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 12.0629 | 0.406642 | ||||||||
\(881\) | −3.89803 | −0.131328 | −0.0656640 | − | 0.997842i | \(-0.520917\pi\) | ||||
−0.0656640 | + | 0.997842i | \(0.520917\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.4260 | 0.721043 | 0.360522 | − | 0.932751i | \(-0.382599\pi\) | ||||
0.360522 | + | 0.932751i | \(0.382599\pi\) | |||||||
\(884\) | −7.44808 | −0.250506 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.0965 | 0.439986 | ||||||||
\(887\) | 40.8605 | 1.37196 | 0.685981 | − | 0.727619i | \(-0.259373\pi\) | ||||
0.685981 | + | 0.727619i | \(0.259373\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.9039 | −0.432784 | ||||||||
\(890\) | −18.9054 | −0.633710 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.6519 | 0.390133 | ||||||||
\(893\) | −22.0113 | −0.736581 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 33.1889 | 1.10938 | ||||||||
\(896\) | 3.10496 | 0.103730 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29.4196 | 0.981743 | ||||||||
\(899\) | 6.67837 | 0.222736 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.4709 | −0.948502 | ||||||||
\(902\) | −25.9977 | −0.865627 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 34.8085 | 1.15771 | ||||||||
\(905\) | −12.5880 | −0.418440 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.6638 | 0.752539 | 0.376269 | − | 0.926510i | \(-0.377207\pi\) | ||||
0.376269 | + | 0.926510i | \(0.377207\pi\) | |||||||
\(908\) | −13.4247 | −0.445515 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.34207 | 0.210238 | ||||||||
\(911\) | 25.2415 | 0.836290 | 0.418145 | − | 0.908380i | \(-0.362680\pi\) | ||||
0.418145 | + | 0.908380i | \(0.362680\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.27899 | 0.108519 | ||||||||
\(914\) | −22.3105 | −0.737964 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.40200 | 0.0463233 | ||||||||
\(917\) | 7.55719 | 0.249560 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.3262 | −0.538552 | −0.269276 | − | 0.963063i | \(-0.586784\pi\) | ||||
−0.269276 | + | 0.963063i | \(0.586784\pi\) | |||||||
\(920\) | −5.12325 | −0.168909 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 32.7595 | 1.07888 | ||||||||
\(923\) | 31.3254 | 1.03109 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.77022 | 0.255483 | ||||||||
\(926\) | 13.3936 | 0.440142 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.45511 | 0.113420 | ||||||||
\(929\) | 17.1115 | 0.561410 | 0.280705 | − | 0.959794i | \(-0.409432\pi\) | ||||
0.280705 | + | 0.959794i | \(0.409432\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.7529 | −0.680148 | ||||||||
\(932\) | −10.9200 | −0.357696 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 40.6941 | 1.33155 | ||||||||
\(935\) | −18.0623 | −0.590699 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −56.6451 | −1.85051 | −0.925257 | − | 0.379342i | \(-0.876150\pi\) | ||||
−0.925257 | + | 0.379342i | \(0.876150\pi\) | |||||||
\(938\) | −0.391579 | −0.0127855 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.82552 | 0.222624 | ||||||||
\(941\) | −17.5292 | −0.571435 | −0.285717 | − | 0.958314i | \(-0.592232\pi\) | ||||
−0.285717 | + | 0.958314i | \(0.592232\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.11748 | 0.231777 | ||||||||
\(944\) | −32.0279 | −1.04242 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.6845 | 0.705023 | ||||||||
\(947\) | −3.76309 | −0.122284 | −0.0611420 | − | 0.998129i | \(-0.519474\pi\) | ||||
−0.0611420 | + | 0.998129i | \(0.519474\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.62466 | 0.312430 | ||||||||
\(950\) | 8.91746 | 0.289321 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.3618 | −0.335828 | ||||||||
\(953\) | −49.0028 | −1.58736 | −0.793679 | − | 0.608337i | \(-0.791837\pi\) | ||||
−0.793679 | + | 0.608337i | \(0.791837\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.645713 | 0.0208948 | ||||||||
\(956\) | 0.0151476 | 0.000489910 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.30588 | 0.139117 | ||||||||
\(959\) | −7.54585 | −0.243668 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.6006 | 0.438729 | ||||||||
\(962\) | 13.6765 | 0.440948 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.5241 | 0.371167 | ||||||||
\(965\) | −11.2472 | −0.362061 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.49183 | −0.240921 | −0.120461 | − | 0.992718i | \(-0.538437\pi\) | ||||
−0.120461 | + | 0.992718i | \(0.538437\pi\) | |||||||
\(968\) | −3.69939 | −0.118903 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 15.5746 | 0.500069 | ||||||||
\(971\) | −27.8867 | −0.894926 | −0.447463 | − | 0.894303i | \(-0.647672\pi\) | ||||
−0.447463 | + | 0.894303i | \(0.647672\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.0890 | 0.708141 | ||||||||
\(974\) | 37.0001 | 1.18556 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.40860 | 0.141116 | ||||||||
\(977\) | 50.8283 | 1.62614 | 0.813071 | − | 0.582165i | \(-0.197794\pi\) | ||||
0.813071 | + | 0.582165i | \(0.197794\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.4755 | −0.974003 | ||||||||
\(980\) | 6.43528 | 0.205567 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 24.6975 | 0.788130 | ||||||||
\(983\) | −41.3134 | −1.31769 | −0.658847 | − | 0.752277i | \(-0.728956\pi\) | ||||
−0.658847 | + | 0.752277i | \(0.728956\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.2843 | −0.486997 | ||||||||
\(986\) | 4.04618 | 0.128857 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.35849 | −0.234105 | ||||||||
\(989\) | −5.93664 | −0.188774 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.8775 | −1.20322 | −0.601610 | − | 0.798790i | \(-0.705474\pi\) | ||||
−0.601610 | + | 0.798790i | \(0.705474\pi\) | |||||||
\(992\) | 23.0745 | 0.732617 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.5444 | 0.334447 | ||||||||
\(995\) | −5.67762 | −0.179993 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52.4367 | −1.66069 | −0.830344 | − | 0.557252i | \(-0.811856\pi\) | ||||
−0.830344 | + | 0.557252i | \(0.811856\pi\) | |||||||
\(998\) | −46.9498 | −1.48617 | ||||||||
\(999\) | 0 | 0 |
(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 | 6003.2.a.u.1.6 | yes | 22 | |
3.2 | odd | 2 | 6003.2.a.t.1.17 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.t.1.17 | ✓ | 22 | 3.2 | odd | 2 | ||
6003.2.a.u.1.6 | yes | 22 | 1.1 | even | 1 | trivial |