Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1617,2,Mod(1,1617)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1617, 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("1617.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1617 = 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1617.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: | \(12.9118100068\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.3676752.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 8x^{3} + 14x^{2} + 11x - 10 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.49291\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1617.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.49291 | −1.76275 | −0.881377 | − | 0.472414i | \(-0.843383\pi\) | ||||
−0.881377 | + | 0.472414i | \(0.843383\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.21460 | 2.10730 | ||||||||
\(5\) | −0.880926 | −0.393962 | −0.196981 | − | 0.980407i | \(-0.563114\pi\) | ||||
−0.196981 | + | 0.980407i | \(0.563114\pi\) | |||||||
\(6\) | 2.49291 | 1.01773 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −5.52081 | −1.95190 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.19607 | 0.694458 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −4.21460 | −1.21665 | ||||||||
\(13\) | 7.12343 | 1.97568 | 0.987842 | − | 0.155462i | \(-0.0496867\pi\) | ||||
0.987842 | + | 0.155462i | \(0.0496867\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.880926 | 0.227454 | ||||||||
\(16\) | 5.33368 | 1.33342 | ||||||||
\(17\) | −2.49291 | −0.604620 | −0.302310 | − | 0.953210i | \(-0.597758\pi\) | ||||
−0.302310 | + | 0.953210i | \(0.597758\pi\) | |||||||
\(18\) | −2.49291 | −0.587585 | ||||||||
\(19\) | 2.63052 | 0.603482 | 0.301741 | − | 0.953390i | \(-0.402432\pi\) | ||||
0.301741 | + | 0.953390i | \(0.402432\pi\) | |||||||
\(20\) | −3.71275 | −0.830197 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.49291 | −0.531490 | ||||||||
\(23\) | 5.33368 | 1.11215 | 0.556074 | − | 0.831133i | \(-0.312307\pi\) | ||||
0.556074 | + | 0.831133i | \(0.312307\pi\) | |||||||
\(24\) | 5.52081 | 1.12693 | ||||||||
\(25\) | −4.22397 | −0.844794 | ||||||||
\(26\) | −17.7581 | −3.48264 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.773136 | 0.143568 | 0.0717839 | − | 0.997420i | \(-0.477131\pi\) | ||||
0.0717839 | + | 0.997420i | \(0.477131\pi\) | |||||||
\(30\) | −2.19607 | −0.400946 | ||||||||
\(31\) | −1.21460 | −0.218149 | −0.109075 | − | 0.994034i | \(-0.534789\pi\) | ||||
−0.109075 | + | 0.994034i | \(0.534789\pi\) | |||||||
\(32\) | −2.25476 | −0.398590 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 6.21460 | 1.06580 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.21460 | 0.702434 | ||||||||
\(37\) | 8.86675 | 1.45768 | 0.728842 | − | 0.684682i | \(-0.240059\pi\) | ||||
0.728842 | + | 0.684682i | \(0.240059\pi\) | |||||||
\(38\) | −6.55765 | −1.06379 | ||||||||
\(39\) | −7.12343 | −1.14066 | ||||||||
\(40\) | 4.86343 | 0.768975 | ||||||||
\(41\) | −6.19607 | −0.967664 | −0.483832 | − | 0.875161i | \(-0.660755\pi\) | ||||
−0.483832 | + | 0.875161i | \(0.660755\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.22921 | 0.492450 | 0.246225 | − | 0.969213i | \(-0.420810\pi\) | ||||
0.246225 | + | 0.969213i | \(0.420810\pi\) | |||||||
\(44\) | 4.21460 | 0.635375 | ||||||||
\(45\) | −0.880926 | −0.131321 | ||||||||
\(46\) | −13.2964 | −1.96044 | ||||||||
\(47\) | −9.75704 | −1.42321 | −0.711605 | − | 0.702580i | \(-0.752031\pi\) | ||||
−0.711605 | + | 0.702580i | \(0.752031\pi\) | |||||||
\(48\) | −5.33368 | −0.769850 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 10.5300 | 1.48916 | ||||||||
\(51\) | 2.49291 | 0.349077 | ||||||||
\(52\) | 30.0224 | 4.16336 | ||||||||
\(53\) | 8.93672 | 1.22755 | 0.613777 | − | 0.789480i | \(-0.289650\pi\) | ||||
0.613777 | + | 0.789480i | \(0.289650\pi\) | |||||||
\(54\) | 2.49291 | 0.339242 | ||||||||
\(55\) | −0.880926 | −0.118784 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.63052 | −0.348421 | ||||||||
\(58\) | −1.92736 | −0.253075 | ||||||||
\(59\) | 5.33368 | 0.694386 | 0.347193 | − | 0.937794i | \(-0.387135\pi\) | ||||
0.347193 | + | 0.937794i | \(0.387135\pi\) | |||||||
\(60\) | 3.71275 | 0.479315 | ||||||||
\(61\) | −9.08370 | −1.16305 | −0.581524 | − | 0.813529i | \(-0.697543\pi\) | ||||
−0.581524 | + | 0.813529i | \(0.697543\pi\) | |||||||
\(62\) | 3.02790 | 0.384544 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.04643 | −0.630804 | ||||||||
\(65\) | −6.27521 | −0.778345 | ||||||||
\(66\) | 2.49291 | 0.306856 | ||||||||
\(67\) | 11.2704 | 1.37690 | 0.688449 | − | 0.725284i | \(-0.258292\pi\) | ||||
0.688449 | + | 0.725284i | \(0.258292\pi\) | |||||||
\(68\) | −10.5066 | −1.27412 | ||||||||
\(69\) | −5.33368 | −0.642099 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.62963 | −0.905471 | −0.452735 | − | 0.891645i | \(-0.649552\pi\) | ||||
−0.452735 | + | 0.891645i | \(0.649552\pi\) | |||||||
\(72\) | −5.52081 | −0.650634 | ||||||||
\(73\) | −12.7766 | −1.49539 | −0.747694 | − | 0.664043i | \(-0.768839\pi\) | ||||
−0.747694 | + | 0.664043i | \(0.768839\pi\) | |||||||
\(74\) | −22.1040 | −2.56954 | ||||||||
\(75\) | 4.22397 | 0.487742 | ||||||||
\(76\) | 11.0866 | 1.27172 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 17.7581 | 2.01071 | ||||||||
\(79\) | −6.95896 | −0.782944 | −0.391472 | − | 0.920190i | \(-0.628034\pi\) | ||||
−0.391472 | + | 0.920190i | \(0.628034\pi\) | |||||||
\(80\) | −4.69858 | −0.525317 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 15.4462 | 1.70575 | ||||||||
\(83\) | −1.20524 | −0.132292 | −0.0661461 | − | 0.997810i | \(-0.521070\pi\) | ||||
−0.0661461 | + | 0.997810i | \(0.521070\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.19607 | 0.238197 | ||||||||
\(86\) | −8.05013 | −0.868068 | ||||||||
\(87\) | −0.773136 | −0.0828889 | ||||||||
\(88\) | −5.52081 | −0.588520 | ||||||||
\(89\) | 6.29395 | 0.667157 | 0.333578 | − | 0.942722i | \(-0.391744\pi\) | ||||
0.333578 | + | 0.942722i | \(0.391744\pi\) | |||||||
\(90\) | 2.19607 | 0.231486 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 22.4793 | 2.34363 | ||||||||
\(93\) | 1.21460 | 0.125949 | ||||||||
\(94\) | 24.3234 | 2.50877 | ||||||||
\(95\) | −2.31729 | −0.237749 | ||||||||
\(96\) | 2.25476 | 0.230126 | ||||||||
\(97\) | 1.29862 | 0.131855 | 0.0659275 | − | 0.997824i | \(-0.478999\pi\) | ||||
0.0659275 | + | 0.997824i | \(0.478999\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −17.8024 | −1.78024 | ||||||||
\(101\) | −9.89422 | −0.984512 | −0.492256 | − | 0.870451i | \(-0.663828\pi\) | ||||
−0.492256 | + | 0.870451i | \(0.663828\pi\) | |||||||
\(102\) | −6.21460 | −0.615337 | ||||||||
\(103\) | 11.1842 | 1.10202 | 0.551008 | − | 0.834500i | \(-0.314243\pi\) | ||||
0.551008 | + | 0.834500i | \(0.314243\pi\) | |||||||
\(104\) | −39.3271 | −3.85634 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −22.2785 | −2.16387 | ||||||||
\(107\) | 7.26605 | 0.702435 | 0.351218 | − | 0.936294i | \(-0.385768\pi\) | ||||
0.351218 | + | 0.936294i | \(0.385768\pi\) | |||||||
\(108\) | −4.21460 | −0.405550 | ||||||||
\(109\) | 0.456074 | 0.0436839 | 0.0218420 | − | 0.999761i | \(-0.493047\pi\) | ||||
0.0218420 | + | 0.999761i | \(0.493047\pi\) | |||||||
\(110\) | 2.19607 | 0.209387 | ||||||||
\(111\) | −8.86675 | −0.841594 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.3518 | −1.35010 | −0.675050 | − | 0.737772i | \(-0.735878\pi\) | ||||
−0.675050 | + | 0.737772i | \(0.735878\pi\) | |||||||
\(114\) | 6.55765 | 0.614180 | ||||||||
\(115\) | −4.69858 | −0.438144 | ||||||||
\(116\) | 3.25846 | 0.302541 | ||||||||
\(117\) | 7.12343 | 0.658561 | ||||||||
\(118\) | −13.2964 | −1.22403 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4.86343 | −0.443968 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 22.6448 | 2.05017 | ||||||||
\(123\) | 6.19607 | 0.558681 | ||||||||
\(124\) | −5.11907 | −0.459706 | ||||||||
\(125\) | 8.12564 | 0.726779 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.91977 | 0.791502 | 0.395751 | − | 0.918358i | \(-0.370484\pi\) | ||||
0.395751 | + | 0.918358i | \(0.370484\pi\) | |||||||
\(128\) | 17.0898 | 1.51054 | ||||||||
\(129\) | −3.22921 | −0.284316 | ||||||||
\(130\) | 15.6436 | 1.37203 | ||||||||
\(131\) | 12.3871 | 1.08227 | 0.541134 | − | 0.840936i | \(-0.317995\pi\) | ||||
0.541134 | + | 0.840936i | \(0.317995\pi\) | |||||||
\(132\) | −4.21460 | −0.366834 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −28.0961 | −2.42713 | ||||||||
\(135\) | 0.880926 | 0.0758181 | ||||||||
\(136\) | 13.7629 | 1.18016 | ||||||||
\(137\) | 22.1256 | 1.89032 | 0.945160 | − | 0.326607i | \(-0.105905\pi\) | ||||
0.945160 | + | 0.326607i | \(0.105905\pi\) | |||||||
\(138\) | 13.2964 | 1.13186 | ||||||||
\(139\) | 2.63553 | 0.223543 | 0.111771 | − | 0.993734i | \(-0.464348\pi\) | ||||
0.111771 | + | 0.993734i | \(0.464348\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.75704 | 0.821691 | ||||||||
\(142\) | 19.0200 | 1.59612 | ||||||||
\(143\) | 7.12343 | 0.595691 | ||||||||
\(144\) | 5.33368 | 0.444473 | ||||||||
\(145\) | −0.681076 | −0.0565602 | ||||||||
\(146\) | 31.8509 | 2.63600 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 37.3698 | 3.07178 | ||||||||
\(149\) | 0.768125 | 0.0629273 | 0.0314636 | − | 0.999505i | \(-0.489983\pi\) | ||||
0.0314636 | + | 0.999505i | \(0.489983\pi\) | |||||||
\(150\) | −10.5300 | −0.859769 | ||||||||
\(151\) | −14.0353 | −1.14218 | −0.571090 | − | 0.820887i | \(-0.693479\pi\) | ||||
−0.571090 | + | 0.820887i | \(0.693479\pi\) | |||||||
\(152\) | −14.5226 | −1.17794 | ||||||||
\(153\) | −2.49291 | −0.201540 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.06998 | 0.0859426 | ||||||||
\(156\) | −30.0224 | −2.40372 | ||||||||
\(157\) | 5.63810 | 0.449970 | 0.224985 | − | 0.974362i | \(-0.427767\pi\) | ||||
0.224985 | + | 0.974362i | \(0.427767\pi\) | |||||||
\(158\) | 17.3481 | 1.38014 | ||||||||
\(159\) | −8.93672 | −0.708728 | ||||||||
\(160\) | 1.98628 | 0.157029 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.49291 | −0.195862 | ||||||||
\(163\) | 10.8997 | 0.853727 | 0.426864 | − | 0.904316i | \(-0.359618\pi\) | ||||
0.426864 | + | 0.904316i | \(0.359618\pi\) | |||||||
\(164\) | −26.1140 | −2.03916 | ||||||||
\(165\) | 0.880926 | 0.0685800 | ||||||||
\(166\) | 3.00455 | 0.233198 | ||||||||
\(167\) | 9.17688 | 0.710128 | 0.355064 | − | 0.934842i | \(-0.384459\pi\) | ||||
0.355064 | + | 0.934842i | \(0.384459\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37.7432 | 2.90333 | ||||||||
\(170\) | −5.47461 | −0.419883 | ||||||||
\(171\) | 2.63052 | 0.201161 | ||||||||
\(172\) | 13.6098 | 1.03774 | ||||||||
\(173\) | −2.51837 | −0.191468 | −0.0957342 | − | 0.995407i | \(-0.530520\pi\) | ||||
−0.0957342 | + | 0.995407i | \(0.530520\pi\) | |||||||
\(174\) | 1.92736 | 0.146113 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.33368 | 0.402041 | ||||||||
\(177\) | −5.33368 | −0.400904 | ||||||||
\(178\) | −15.6902 | −1.17603 | ||||||||
\(179\) | 24.5313 | 1.83356 | 0.916778 | − | 0.399398i | \(-0.130781\pi\) | ||||
0.916778 | + | 0.399398i | \(0.130781\pi\) | |||||||
\(180\) | −3.71275 | −0.276732 | ||||||||
\(181\) | 12.8187 | 0.952805 | 0.476403 | − | 0.879227i | \(-0.341940\pi\) | ||||
0.476403 | + | 0.879227i | \(0.341940\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.08370 | 0.671486 | ||||||||
\(184\) | −29.4462 | −2.17080 | ||||||||
\(185\) | −7.81095 | −0.574272 | ||||||||
\(186\) | −3.02790 | −0.222016 | ||||||||
\(187\) | −2.49291 | −0.182300 | ||||||||
\(188\) | −41.1221 | −2.99913 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.77680 | 0.419093 | ||||||||
\(191\) | 22.0785 | 1.59755 | 0.798774 | − | 0.601631i | \(-0.205482\pi\) | ||||
0.798774 | + | 0.601631i | \(0.205482\pi\) | |||||||
\(192\) | 5.04643 | 0.364195 | ||||||||
\(193\) | 18.4453 | 1.32772 | 0.663860 | − | 0.747857i | \(-0.268917\pi\) | ||||
0.663860 | + | 0.747857i | \(0.268917\pi\) | |||||||
\(194\) | −3.23734 | −0.232428 | ||||||||
\(195\) | 6.27521 | 0.449377 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.57707 | −0.326102 | −0.163051 | − | 0.986618i | \(-0.552134\pi\) | ||||
−0.163051 | + | 0.986618i | \(0.552134\pi\) | |||||||
\(198\) | −2.49291 | −0.177163 | ||||||||
\(199\) | −2.19106 | −0.155320 | −0.0776601 | − | 0.996980i | \(-0.524745\pi\) | ||||
−0.0776601 | + | 0.996980i | \(0.524745\pi\) | |||||||
\(200\) | 23.3197 | 1.64895 | ||||||||
\(201\) | −11.2704 | −0.794953 | ||||||||
\(202\) | 24.6654 | 1.73545 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 10.5066 | 0.735611 | ||||||||
\(205\) | 5.45828 | 0.381223 | ||||||||
\(206\) | −27.8813 | −1.94258 | ||||||||
\(207\) | 5.33368 | 0.370716 | ||||||||
\(208\) | 37.9941 | 2.63441 | ||||||||
\(209\) | 2.63052 | 0.181957 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.97047 | −0.686395 | −0.343198 | − | 0.939263i | \(-0.611510\pi\) | ||||
−0.343198 | + | 0.939263i | \(0.611510\pi\) | |||||||
\(212\) | 37.6648 | 2.58683 | ||||||||
\(213\) | 7.62963 | 0.522774 | ||||||||
\(214\) | −18.1136 | −1.23822 | ||||||||
\(215\) | −2.84469 | −0.194007 | ||||||||
\(216\) | 5.52081 | 0.375644 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.13695 | −0.0770040 | ||||||||
\(219\) | 12.7766 | 0.863363 | ||||||||
\(220\) | −3.71275 | −0.250314 | ||||||||
\(221\) | −17.7581 | −1.19454 | ||||||||
\(222\) | 22.1040 | 1.48352 | ||||||||
\(223\) | −15.2015 | −1.01796 | −0.508982 | − | 0.860777i | \(-0.669978\pi\) | ||||
−0.508982 | + | 0.860777i | \(0.669978\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.22397 | −0.281598 | ||||||||
\(226\) | 35.7776 | 2.37989 | ||||||||
\(227\) | −11.0661 | −0.734485 | −0.367243 | − | 0.930125i | \(-0.619698\pi\) | ||||
−0.367243 | + | 0.930125i | \(0.619698\pi\) | |||||||
\(228\) | −11.0866 | −0.734227 | ||||||||
\(229\) | −2.86577 | −0.189375 | −0.0946877 | − | 0.995507i | \(-0.530185\pi\) | ||||
−0.0946877 | + | 0.995507i | \(0.530185\pi\) | |||||||
\(230\) | 11.7131 | 0.772341 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.26834 | −0.280230 | ||||||||
\(233\) | −14.6048 | −0.956794 | −0.478397 | − | 0.878144i | \(-0.658782\pi\) | ||||
−0.478397 | + | 0.878144i | \(0.658782\pi\) | |||||||
\(234\) | −17.7581 | −1.16088 | ||||||||
\(235\) | 8.59523 | 0.560691 | ||||||||
\(236\) | 22.4793 | 1.46328 | ||||||||
\(237\) | 6.95896 | 0.452033 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.4800 | 1.19537 | 0.597686 | − | 0.801730i | \(-0.296087\pi\) | ||||
0.597686 | + | 0.801730i | \(0.296087\pi\) | |||||||
\(240\) | 4.69858 | 0.303292 | ||||||||
\(241\) | 25.9433 | 1.67115 | 0.835577 | − | 0.549373i | \(-0.185134\pi\) | ||||
0.835577 | + | 0.549373i | \(0.185134\pi\) | |||||||
\(242\) | −2.49291 | −0.160250 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −38.2842 | −2.45089 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.4462 | −0.984817 | ||||||||
\(247\) | 18.7383 | 1.19229 | ||||||||
\(248\) | 6.70560 | 0.425806 | ||||||||
\(249\) | 1.20524 | 0.0763789 | ||||||||
\(250\) | −20.2565 | −1.28113 | ||||||||
\(251\) | 26.4331 | 1.66844 | 0.834221 | − | 0.551430i | \(-0.185918\pi\) | ||||
0.834221 | + | 0.551430i | \(0.185918\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.33368 | 0.335325 | ||||||||
\(254\) | −22.2362 | −1.39522 | ||||||||
\(255\) | −2.19607 | −0.137523 | ||||||||
\(256\) | −32.5106 | −2.03191 | ||||||||
\(257\) | −4.63900 | −0.289373 | −0.144686 | − | 0.989478i | \(-0.546217\pi\) | ||||
−0.144686 | + | 0.989478i | \(0.546217\pi\) | |||||||
\(258\) | 8.05013 | 0.501179 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −26.4475 | −1.64021 | ||||||||
\(261\) | 0.773136 | 0.0478559 | ||||||||
\(262\) | −30.8800 | −1.90777 | ||||||||
\(263\) | 19.6266 | 1.21023 | 0.605114 | − | 0.796139i | \(-0.293128\pi\) | ||||
0.605114 | + | 0.796139i | \(0.293128\pi\) | |||||||
\(264\) | 5.52081 | 0.339782 | ||||||||
\(265\) | −7.87259 | −0.483610 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.29395 | −0.385183 | ||||||||
\(268\) | 47.5003 | 2.90154 | ||||||||
\(269\) | −22.5633 | −1.37571 | −0.687855 | − | 0.725848i | \(-0.741447\pi\) | ||||
−0.687855 | + | 0.725848i | \(0.741447\pi\) | |||||||
\(270\) | −2.19607 | −0.133649 | ||||||||
\(271\) | −17.1535 | −1.04200 | −0.521002 | − | 0.853556i | \(-0.674441\pi\) | ||||
−0.521002 | + | 0.853556i | \(0.674441\pi\) | |||||||
\(272\) | −13.2964 | −0.806212 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −55.1572 | −3.33217 | ||||||||
\(275\) | −4.22397 | −0.254715 | ||||||||
\(276\) | −22.4793 | −1.35310 | ||||||||
\(277\) | −26.1496 | −1.57117 | −0.785587 | − | 0.618751i | \(-0.787639\pi\) | ||||
−0.785587 | + | 0.618751i | \(0.787639\pi\) | |||||||
\(278\) | −6.57014 | −0.394051 | ||||||||
\(279\) | −1.21460 | −0.0727164 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.79972 | 0.524947 | 0.262474 | − | 0.964939i | \(-0.415462\pi\) | ||||
0.262474 | + | 0.964939i | \(0.415462\pi\) | |||||||
\(282\) | −24.3234 | −1.44844 | ||||||||
\(283\) | 13.7499 | 0.817346 | 0.408673 | − | 0.912681i | \(-0.365992\pi\) | ||||
0.408673 | + | 0.912681i | \(0.365992\pi\) | |||||||
\(284\) | −32.1559 | −1.90810 | ||||||||
\(285\) | 2.31729 | 0.137265 | ||||||||
\(286\) | −17.7581 | −1.05006 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.25476 | −0.132863 | ||||||||
\(289\) | −10.7854 | −0.634435 | ||||||||
\(290\) | 1.69786 | 0.0997018 | ||||||||
\(291\) | −1.29862 | −0.0761265 | ||||||||
\(292\) | −53.8483 | −3.15124 | ||||||||
\(293\) | 17.4266 | 1.01807 | 0.509037 | − | 0.860744i | \(-0.330001\pi\) | ||||
0.509037 | + | 0.860744i | \(0.330001\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.69858 | −0.273562 | ||||||||
\(296\) | −48.9516 | −2.84526 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −1.91487 | −0.110925 | ||||||||
\(299\) | 37.9941 | 2.19725 | ||||||||
\(300\) | 17.8024 | 1.02782 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 34.9889 | 2.01338 | ||||||||
\(303\) | 9.89422 | 0.568408 | ||||||||
\(304\) | 14.0303 | 0.804695 | ||||||||
\(305\) | 8.00207 | 0.458197 | ||||||||
\(306\) | 6.21460 | 0.355265 | ||||||||
\(307\) | −0.804963 | −0.0459416 | −0.0229708 | − | 0.999736i | \(-0.507312\pi\) | ||||
−0.0229708 | + | 0.999736i | \(0.507312\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.1842 | −0.636249 | ||||||||
\(310\) | −2.66736 | −0.151496 | ||||||||
\(311\) | −10.8250 | −0.613830 | −0.306915 | − | 0.951737i | \(-0.599297\pi\) | ||||
−0.306915 | + | 0.951737i | \(0.599297\pi\) | |||||||
\(312\) | 39.3271 | 2.22646 | ||||||||
\(313\) | 24.7315 | 1.39791 | 0.698953 | − | 0.715168i | \(-0.253650\pi\) | ||||
0.698953 | + | 0.715168i | \(0.253650\pi\) | |||||||
\(314\) | −14.0553 | −0.793186 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −29.3292 | −1.64990 | ||||||||
\(317\) | −12.2819 | −0.689821 | −0.344911 | − | 0.938636i | \(-0.612091\pi\) | ||||
−0.344911 | + | 0.938636i | \(0.612091\pi\) | |||||||
\(318\) | 22.2785 | 1.24931 | ||||||||
\(319\) | 0.773136 | 0.0432873 | ||||||||
\(320\) | 4.44553 | 0.248513 | ||||||||
\(321\) | −7.26605 | −0.405551 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.55765 | −0.364877 | ||||||||
\(324\) | 4.21460 | 0.234145 | ||||||||
\(325\) | −30.0891 | −1.66905 | ||||||||
\(326\) | −27.1719 | −1.50491 | ||||||||
\(327\) | −0.456074 | −0.0252209 | ||||||||
\(328\) | 34.2073 | 1.88878 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.19607 | −0.120890 | ||||||||
\(331\) | −13.1987 | −0.725468 | −0.362734 | − | 0.931893i | \(-0.618157\pi\) | ||||
−0.362734 | + | 0.931893i | \(0.618157\pi\) | |||||||
\(332\) | −5.07960 | −0.278779 | ||||||||
\(333\) | 8.86675 | 0.485895 | ||||||||
\(334\) | −22.8771 | −1.25178 | ||||||||
\(335\) | −9.92839 | −0.542446 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.468940 | 0.0255448 | 0.0127724 | − | 0.999918i | \(-0.495934\pi\) | ||||
0.0127724 | + | 0.999918i | \(0.495934\pi\) | |||||||
\(338\) | −94.0905 | −5.11785 | ||||||||
\(339\) | 14.3518 | 0.779480 | ||||||||
\(340\) | 9.25557 | 0.501954 | ||||||||
\(341\) | −1.21460 | −0.0657745 | ||||||||
\(342\) | −6.55765 | −0.354597 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −17.8278 | −0.961213 | ||||||||
\(345\) | 4.69858 | 0.252963 | ||||||||
\(346\) | 6.27808 | 0.337512 | ||||||||
\(347\) | 3.49417 | 0.187577 | 0.0937885 | − | 0.995592i | \(-0.470102\pi\) | ||||
0.0937885 | + | 0.995592i | \(0.470102\pi\) | |||||||
\(348\) | −3.25846 | −0.174672 | ||||||||
\(349\) | −15.7180 | −0.841365 | −0.420683 | − | 0.907208i | \(-0.638209\pi\) | ||||
−0.420683 | + | 0.907208i | \(0.638209\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.12343 | −0.380221 | ||||||||
\(352\) | −2.25476 | −0.120179 | ||||||||
\(353\) | 35.2242 | 1.87480 | 0.937398 | − | 0.348261i | \(-0.113228\pi\) | ||||
0.937398 | + | 0.348261i | \(0.113228\pi\) | |||||||
\(354\) | 13.2964 | 0.706695 | ||||||||
\(355\) | 6.72114 | 0.356721 | ||||||||
\(356\) | 26.5265 | 1.40590 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −61.1543 | −3.23211 | ||||||||
\(359\) | 23.2190 | 1.22545 | 0.612725 | − | 0.790296i | \(-0.290073\pi\) | ||||
0.612725 | + | 0.790296i | \(0.290073\pi\) | |||||||
\(360\) | 4.86343 | 0.256325 | ||||||||
\(361\) | −12.0804 | −0.635809 | ||||||||
\(362\) | −31.9558 | −1.67956 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.2552 | 0.589127 | ||||||||
\(366\) | −22.6448 | −1.18366 | ||||||||
\(367\) | 19.7507 | 1.03098 | 0.515490 | − | 0.856896i | \(-0.327610\pi\) | ||||
0.515490 | + | 0.856896i | \(0.327610\pi\) | |||||||
\(368\) | 28.4481 | 1.48296 | ||||||||
\(369\) | −6.19607 | −0.322555 | ||||||||
\(370\) | 19.4720 | 1.01230 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.11907 | 0.265412 | ||||||||
\(373\) | −24.9656 | −1.29267 | −0.646335 | − | 0.763054i | \(-0.723699\pi\) | ||||
−0.646335 | + | 0.763054i | \(0.723699\pi\) | |||||||
\(374\) | 6.21460 | 0.321350 | ||||||||
\(375\) | −8.12564 | −0.419606 | ||||||||
\(376\) | 53.8668 | 2.77797 | ||||||||
\(377\) | 5.50738 | 0.283644 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.3261 | −0.838613 | −0.419307 | − | 0.907845i | \(-0.637727\pi\) | ||||
−0.419307 | + | 0.907845i | \(0.637727\pi\) | |||||||
\(380\) | −9.76647 | −0.501009 | ||||||||
\(381\) | −8.91977 | −0.456974 | ||||||||
\(382\) | −55.0398 | −2.81608 | ||||||||
\(383\) | 12.1079 | 0.618687 | 0.309343 | − | 0.950950i | \(-0.399891\pi\) | ||||
0.309343 | + | 0.950950i | \(0.399891\pi\) | |||||||
\(384\) | −17.0898 | −0.872112 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −45.9824 | −2.34044 | ||||||||
\(387\) | 3.22921 | 0.164150 | ||||||||
\(388\) | 5.47317 | 0.277858 | ||||||||
\(389\) | −18.1998 | −0.922765 | −0.461382 | − | 0.887201i | \(-0.652646\pi\) | ||||
−0.461382 | + | 0.887201i | \(0.652646\pi\) | |||||||
\(390\) | −15.6436 | −0.792142 | ||||||||
\(391\) | −13.2964 | −0.672427 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.3871 | −0.624848 | ||||||||
\(394\) | 11.4102 | 0.574838 | ||||||||
\(395\) | 6.13033 | 0.308450 | ||||||||
\(396\) | 4.21460 | 0.211792 | ||||||||
\(397\) | −0.0579458 | −0.00290822 | −0.00145411 | − | 0.999999i | \(-0.500463\pi\) | ||||
−0.00145411 | + | 0.999999i | \(0.500463\pi\) | |||||||
\(398\) | 5.46212 | 0.273791 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −22.5293 | −1.12646 | ||||||||
\(401\) | −16.8849 | −0.843194 | −0.421597 | − | 0.906783i | \(-0.638530\pi\) | ||||
−0.421597 | + | 0.906783i | \(0.638530\pi\) | |||||||
\(402\) | 28.0961 | 1.40131 | ||||||||
\(403\) | −8.65214 | −0.430994 | ||||||||
\(404\) | −41.7002 | −2.07466 | ||||||||
\(405\) | −0.880926 | −0.0437736 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.86675 | 0.439508 | ||||||||
\(408\) | −13.7629 | −0.681364 | ||||||||
\(409\) | −1.08636 | −0.0537171 | −0.0268586 | − | 0.999639i | \(-0.508550\pi\) | ||||
−0.0268586 | + | 0.999639i | \(0.508550\pi\) | |||||||
\(410\) | −13.6070 | −0.672002 | ||||||||
\(411\) | −22.1256 | −1.09138 | ||||||||
\(412\) | 47.1371 | 2.32228 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −13.2964 | −0.653482 | ||||||||
\(415\) | 1.06173 | 0.0521181 | ||||||||
\(416\) | −16.0616 | −0.787487 | ||||||||
\(417\) | −2.63553 | −0.129062 | ||||||||
\(418\) | −6.55765 | −0.320745 | ||||||||
\(419\) | 18.7222 | 0.914638 | 0.457319 | − | 0.889303i | \(-0.348810\pi\) | ||||
0.457319 | + | 0.889303i | \(0.348810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.6579 | 0.519433 | 0.259716 | − | 0.965685i | \(-0.416371\pi\) | ||||
0.259716 | + | 0.965685i | \(0.416371\pi\) | |||||||
\(422\) | 24.8555 | 1.20995 | ||||||||
\(423\) | −9.75704 | −0.474403 | ||||||||
\(424\) | −49.3380 | −2.39606 | ||||||||
\(425\) | 10.5300 | 0.510779 | ||||||||
\(426\) | −19.0200 | −0.921522 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 30.6235 | 1.48024 | ||||||||
\(429\) | −7.12343 | −0.343922 | ||||||||
\(430\) | 7.09157 | 0.341986 | ||||||||
\(431\) | 19.7490 | 0.951275 | 0.475638 | − | 0.879641i | \(-0.342217\pi\) | ||||
0.475638 | + | 0.879641i | \(0.342217\pi\) | |||||||
\(432\) | −5.33368 | −0.256617 | ||||||||
\(433\) | −34.6826 | −1.66674 | −0.833370 | − | 0.552715i | \(-0.813592\pi\) | ||||
−0.833370 | + | 0.552715i | \(0.813592\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.681076 | 0.0326551 | ||||||||
\(436\) | 1.92217 | 0.0920552 | ||||||||
\(437\) | 14.0303 | 0.671162 | ||||||||
\(438\) | −31.8509 | −1.52190 | ||||||||
\(439\) | −5.59033 | −0.266812 | −0.133406 | − | 0.991061i | \(-0.542591\pi\) | ||||
−0.133406 | + | 0.991061i | \(0.542591\pi\) | |||||||
\(440\) | 4.86343 | 0.231855 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 44.2693 | 2.10568 | ||||||||
\(443\) | 10.9065 | 0.518185 | 0.259093 | − | 0.965852i | \(-0.416577\pi\) | ||||
0.259093 | + | 0.965852i | \(0.416577\pi\) | |||||||
\(444\) | −37.3698 | −1.77349 | ||||||||
\(445\) | −5.54450 | −0.262835 | ||||||||
\(446\) | 37.8959 | 1.79442 | ||||||||
\(447\) | −0.768125 | −0.0363311 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.97164 | 0.470591 | 0.235295 | − | 0.971924i | \(-0.424394\pi\) | ||||
0.235295 | + | 0.971924i | \(0.424394\pi\) | |||||||
\(450\) | 10.5300 | 0.496388 | ||||||||
\(451\) | −6.19607 | −0.291762 | ||||||||
\(452\) | −60.4870 | −2.84507 | ||||||||
\(453\) | 14.0353 | 0.659438 | ||||||||
\(454\) | 27.5869 | 1.29472 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.5226 | 0.680083 | ||||||||
\(457\) | −5.76803 | −0.269817 | −0.134909 | − | 0.990858i | \(-0.543074\pi\) | ||||
−0.134909 | + | 0.990858i | \(0.543074\pi\) | |||||||
\(458\) | 7.14411 | 0.333822 | ||||||||
\(459\) | 2.49291 | 0.116359 | ||||||||
\(460\) | −19.8026 | −0.923303 | ||||||||
\(461\) | −25.9921 | −1.21057 | −0.605286 | − | 0.796008i | \(-0.706941\pi\) | ||||
−0.605286 | + | 0.796008i | \(0.706941\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.09937 | 0.283462 | 0.141731 | − | 0.989905i | \(-0.454733\pi\) | ||||
0.141731 | + | 0.989905i | \(0.454733\pi\) | |||||||
\(464\) | 4.12366 | 0.191436 | ||||||||
\(465\) | −1.06998 | −0.0496190 | ||||||||
\(466\) | 36.4085 | 1.68659 | ||||||||
\(467\) | −23.8540 | −1.10383 | −0.551915 | − | 0.833900i | \(-0.686103\pi\) | ||||
−0.551915 | + | 0.833900i | \(0.686103\pi\) | |||||||
\(468\) | 30.0224 | 1.38779 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −21.4271 | −0.988360 | ||||||||
\(471\) | −5.63810 | −0.259790 | ||||||||
\(472\) | −29.4462 | −1.35537 | ||||||||
\(473\) | 3.22921 | 0.148479 | ||||||||
\(474\) | −17.3481 | −0.796823 | ||||||||
\(475\) | −11.1112 | −0.509818 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.93672 | 0.409184 | ||||||||
\(478\) | −46.0690 | −2.10715 | ||||||||
\(479\) | −9.26889 | −0.423506 | −0.211753 | − | 0.977323i | \(-0.567917\pi\) | ||||
−0.211753 | + | 0.977323i | \(0.567917\pi\) | |||||||
\(480\) | −1.98628 | −0.0906609 | ||||||||
\(481\) | 63.1616 | 2.87992 | ||||||||
\(482\) | −64.6743 | −2.94583 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.21460 | 0.191573 | ||||||||
\(485\) | −1.14399 | −0.0519458 | ||||||||
\(486\) | 2.49291 | 0.113081 | ||||||||
\(487\) | 38.4123 | 1.74063 | 0.870313 | − | 0.492498i | \(-0.163916\pi\) | ||||
0.870313 | + | 0.492498i | \(0.163916\pi\) | |||||||
\(488\) | 50.1494 | 2.27015 | ||||||||
\(489\) | −10.8997 | −0.492900 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.1820 | −0.549767 | −0.274884 | − | 0.961477i | \(-0.588639\pi\) | ||||
−0.274884 | + | 0.961477i | \(0.588639\pi\) | |||||||
\(492\) | 26.1140 | 1.17731 | ||||||||
\(493\) | −1.92736 | −0.0868039 | ||||||||
\(494\) | −46.7129 | −2.10171 | ||||||||
\(495\) | −0.880926 | −0.0395947 | ||||||||
\(496\) | −6.47831 | −0.290884 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.00455 | −0.134637 | ||||||||
\(499\) | 7.21460 | 0.322970 | 0.161485 | − | 0.986875i | \(-0.448372\pi\) | ||||
0.161485 | + | 0.986875i | \(0.448372\pi\) | |||||||
\(500\) | 34.2463 | 1.53154 | ||||||||
\(501\) | −9.17688 | −0.409993 | ||||||||
\(502\) | −65.8954 | −2.94105 | ||||||||
\(503\) | 3.49548 | 0.155856 | 0.0779280 | − | 0.996959i | \(-0.475170\pi\) | ||||
0.0779280 | + | 0.996959i | \(0.475170\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.71608 | 0.387860 | ||||||||
\(506\) | −13.2964 | −0.591096 | ||||||||
\(507\) | −37.7432 | −1.67624 | ||||||||
\(508\) | 37.5933 | 1.66793 | ||||||||
\(509\) | 34.2725 | 1.51910 | 0.759552 | − | 0.650447i | \(-0.225418\pi\) | ||||
0.759552 | + | 0.650447i | \(0.225418\pi\) | |||||||
\(510\) | 5.47461 | 0.242420 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 46.8663 | 2.07122 | ||||||||
\(513\) | −2.63052 | −0.116140 | ||||||||
\(514\) | 11.5646 | 0.510093 | ||||||||
\(515\) | −9.85249 | −0.434152 | ||||||||
\(516\) | −13.6098 | −0.599140 | ||||||||
\(517\) | −9.75704 | −0.429114 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.51837 | 0.110544 | ||||||||
\(520\) | 34.6443 | 1.51925 | ||||||||
\(521\) | −6.00786 | −0.263209 | −0.131604 | − | 0.991302i | \(-0.542013\pi\) | ||||
−0.131604 | + | 0.991302i | \(0.542013\pi\) | |||||||
\(522\) | −1.92736 | −0.0843582 | ||||||||
\(523\) | 2.98731 | 0.130626 | 0.0653130 | − | 0.997865i | \(-0.479195\pi\) | ||||
0.0653130 | + | 0.997865i | \(0.479195\pi\) | |||||||
\(524\) | 52.2068 | 2.28067 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −48.9273 | −2.13333 | ||||||||
\(527\) | 3.02790 | 0.131897 | ||||||||
\(528\) | −5.33368 | −0.232119 | ||||||||
\(529\) | 5.44812 | 0.236875 | ||||||||
\(530\) | 19.6257 | 0.852485 | ||||||||
\(531\) | 5.33368 | 0.231462 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −44.1373 | −1.91180 | ||||||||
\(534\) | 15.6902 | 0.678983 | ||||||||
\(535\) | −6.40085 | −0.276733 | ||||||||
\(536\) | −62.2217 | −2.68757 | ||||||||
\(537\) | −24.5313 | −1.05860 | ||||||||
\(538\) | 56.2483 | 2.42504 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.71275 | 0.159772 | ||||||||
\(541\) | −0.0373463 | −0.00160564 | −0.000802822 | − | 1.00000i | \(-0.500256\pi\) | ||||
−0.000802822 | 1.00000i | \(0.500256\pi\) | ||||||||
\(542\) | 42.7622 | 1.83680 | ||||||||
\(543\) | −12.8187 | −0.550102 | ||||||||
\(544\) | 5.62092 | 0.240995 | ||||||||
\(545\) | −0.401767 | −0.0172098 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.1882 | −0.692156 | −0.346078 | − | 0.938206i | \(-0.612487\pi\) | ||||
−0.346078 | + | 0.938206i | \(0.612487\pi\) | |||||||
\(548\) | 93.2508 | 3.98348 | ||||||||
\(549\) | −9.08370 | −0.387683 | ||||||||
\(550\) | 10.5300 | 0.449000 | ||||||||
\(551\) | 2.03375 | 0.0866406 | ||||||||
\(552\) | 29.4462 | 1.25331 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 65.1885 | 2.76959 | ||||||||
\(555\) | 7.81095 | 0.331556 | ||||||||
\(556\) | 11.1077 | 0.471072 | ||||||||
\(557\) | 33.4158 | 1.41587 | 0.707937 | − | 0.706275i | \(-0.249626\pi\) | ||||
0.707937 | + | 0.706275i | \(0.249626\pi\) | |||||||
\(558\) | 3.02790 | 0.128181 | ||||||||
\(559\) | 23.0030 | 0.972925 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.49291 | 0.105251 | ||||||||
\(562\) | −21.9369 | −0.925353 | ||||||||
\(563\) | 0.284245 | 0.0119795 | 0.00598974 | − | 0.999982i | \(-0.498093\pi\) | ||||
0.00598974 | + | 0.999982i | \(0.498093\pi\) | |||||||
\(564\) | 41.1221 | 1.73155 | ||||||||
\(565\) | 12.6428 | 0.531888 | ||||||||
\(566\) | −34.2772 | −1.44078 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 42.1217 | 1.76739 | ||||||||
\(569\) | −15.4749 | −0.648741 | −0.324371 | − | 0.945930i | \(-0.605153\pi\) | ||||
−0.324371 | + | 0.945930i | \(0.605153\pi\) | |||||||
\(570\) | −5.77680 | −0.241964 | ||||||||
\(571\) | −10.7334 | −0.449179 | −0.224589 | − | 0.974453i | \(-0.572104\pi\) | ||||
−0.224589 | + | 0.974453i | \(0.572104\pi\) | |||||||
\(572\) | 30.0224 | 1.25530 | ||||||||
\(573\) | −22.0785 | −0.922345 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.5293 | −0.939536 | ||||||||
\(576\) | −5.04643 | −0.210268 | ||||||||
\(577\) | 11.9907 | 0.499179 | 0.249589 | − | 0.968352i | \(-0.419704\pi\) | ||||
0.249589 | + | 0.968352i | \(0.419704\pi\) | |||||||
\(578\) | 26.8870 | 1.11835 | ||||||||
\(579\) | −18.4453 | −0.766559 | ||||||||
\(580\) | −2.87046 | −0.119190 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.23734 | 0.134192 | ||||||||
\(583\) | 8.93672 | 0.370121 | ||||||||
\(584\) | 70.5372 | 2.91885 | ||||||||
\(585\) | −6.27521 | −0.259448 | ||||||||
\(586\) | −43.4430 | −1.79462 | ||||||||
\(587\) | 34.2223 | 1.41251 | 0.706254 | − | 0.707959i | \(-0.250384\pi\) | ||||
0.706254 | + | 0.707959i | \(0.250384\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.19504 | −0.131649 | ||||||||
\(590\) | 11.7131 | 0.482222 | ||||||||
\(591\) | 4.57707 | 0.188275 | ||||||||
\(592\) | 47.2924 | 1.94370 | ||||||||
\(593\) | −29.5003 | −1.21143 | −0.605716 | − | 0.795681i | \(-0.707113\pi\) | ||||
−0.605716 | + | 0.795681i | \(0.707113\pi\) | |||||||
\(594\) | 2.49291 | 0.102285 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.23734 | 0.132607 | ||||||||
\(597\) | 2.19106 | 0.0896741 | ||||||||
\(598\) | −94.7158 | −3.87322 | ||||||||
\(599\) | −21.1061 | −0.862373 | −0.431186 | − | 0.902263i | \(-0.641905\pi\) | ||||
−0.431186 | + | 0.902263i | \(0.641905\pi\) | |||||||
\(600\) | −23.3197 | −0.952024 | ||||||||
\(601\) | 20.4406 | 0.833789 | 0.416894 | − | 0.908955i | \(-0.363118\pi\) | ||||
0.416894 | + | 0.908955i | \(0.363118\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.2704 | 0.458966 | ||||||||
\(604\) | −59.1534 | −2.40692 | ||||||||
\(605\) | −0.880926 | −0.0358147 | ||||||||
\(606\) | −24.6654 | −1.00196 | ||||||||
\(607\) | −42.5633 | −1.72759 | −0.863795 | − | 0.503843i | \(-0.831919\pi\) | ||||
−0.863795 | + | 0.503843i | \(0.831919\pi\) | |||||||
\(608\) | −5.93119 | −0.240542 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.9484 | −0.807689 | ||||||||
\(611\) | −69.5036 | −2.81181 | ||||||||
\(612\) | −10.5066 | −0.424705 | ||||||||
\(613\) | −0.696566 | −0.0281340 | −0.0140670 | − | 0.999901i | \(-0.504478\pi\) | ||||
−0.0140670 | + | 0.999901i | \(0.504478\pi\) | |||||||
\(614\) | 2.00670 | 0.0809838 | ||||||||
\(615\) | −5.45828 | −0.220099 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.6494 | −0.549504 | −0.274752 | − | 0.961515i | \(-0.588596\pi\) | ||||
−0.274752 | + | 0.961515i | \(0.588596\pi\) | |||||||
\(618\) | 27.8813 | 1.12155 | ||||||||
\(619\) | −35.2791 | −1.41799 | −0.708994 | − | 0.705215i | \(-0.750851\pi\) | ||||
−0.708994 | + | 0.705215i | \(0.750851\pi\) | |||||||
\(620\) | 4.50953 | 0.181107 | ||||||||
\(621\) | −5.33368 | −0.214033 | ||||||||
\(622\) | 26.9858 | 1.08203 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −37.9941 | −1.52098 | ||||||||
\(625\) | 13.9618 | 0.558470 | ||||||||
\(626\) | −61.6534 | −2.46416 | ||||||||
\(627\) | −2.63052 | −0.105053 | ||||||||
\(628\) | 23.7624 | 0.948222 | ||||||||
\(629\) | −22.1040 | −0.881345 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.4853 | 0.656271 | 0.328136 | − | 0.944631i | \(-0.393580\pi\) | ||||
0.328136 | + | 0.944631i | \(0.393580\pi\) | |||||||
\(632\) | 38.4191 | 1.52823 | ||||||||
\(633\) | 9.97047 | 0.396291 | ||||||||
\(634\) | 30.6177 | 1.21598 | ||||||||
\(635\) | −7.85766 | −0.311822 | ||||||||
\(636\) | −37.6648 | −1.49350 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.92736 | −0.0763049 | ||||||||
\(639\) | −7.62963 | −0.301824 | ||||||||
\(640\) | −15.0549 | −0.595096 | ||||||||
\(641\) | 6.46868 | 0.255497 | 0.127749 | − | 0.991807i | \(-0.459225\pi\) | ||||
0.127749 | + | 0.991807i | \(0.459225\pi\) | |||||||
\(642\) | 18.1136 | 0.714887 | ||||||||
\(643\) | −18.2913 | −0.721338 | −0.360669 | − | 0.932694i | \(-0.617452\pi\) | ||||
−0.360669 | + | 0.932694i | \(0.617452\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.84469 | 0.112010 | ||||||||
\(646\) | 16.3476 | 0.643189 | ||||||||
\(647\) | −18.0021 | −0.707734 | −0.353867 | − | 0.935296i | \(-0.615133\pi\) | ||||
−0.353867 | + | 0.935296i | \(0.615133\pi\) | |||||||
\(648\) | −5.52081 | −0.216878 | ||||||||
\(649\) | 5.33368 | 0.209365 | ||||||||
\(650\) | 75.0095 | 2.94212 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 45.9377 | 1.79906 | ||||||||
\(653\) | −5.00885 | −0.196011 | −0.0980057 | − | 0.995186i | \(-0.531246\pi\) | ||||
−0.0980057 | + | 0.995186i | \(0.531246\pi\) | |||||||
\(654\) | 1.13695 | 0.0444583 | ||||||||
\(655\) | −10.9121 | −0.426373 | ||||||||
\(656\) | −33.0478 | −1.29030 | ||||||||
\(657\) | −12.7766 | −0.498463 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.2762 | 1.68580 | 0.842901 | − | 0.538068i | \(-0.180846\pi\) | ||||
0.842901 | + | 0.538068i | \(0.180846\pi\) | |||||||
\(660\) | 3.71275 | 0.144519 | ||||||||
\(661\) | 19.0415 | 0.740628 | 0.370314 | − | 0.928907i | \(-0.379250\pi\) | ||||
0.370314 | + | 0.928907i | \(0.379250\pi\) | |||||||
\(662\) | 32.9033 | 1.27882 | ||||||||
\(663\) | 17.7581 | 0.689666 | ||||||||
\(664\) | 6.65389 | 0.258221 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −22.1040 | −0.856513 | ||||||||
\(667\) | 4.12366 | 0.159669 | ||||||||
\(668\) | 38.6769 | 1.49645 | ||||||||
\(669\) | 15.2015 | 0.587722 | ||||||||
\(670\) | 24.7506 | 0.956199 | ||||||||
\(671\) | −9.08370 | −0.350672 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.68181 | 0.373206 | 0.186603 | − | 0.982435i | \(-0.440252\pi\) | ||||
0.186603 | + | 0.982435i | \(0.440252\pi\) | |||||||
\(674\) | −1.16903 | −0.0450292 | ||||||||
\(675\) | 4.22397 | 0.162581 | ||||||||
\(676\) | 159.073 | 6.11818 | ||||||||
\(677\) | 23.4995 | 0.903160 | 0.451580 | − | 0.892231i | \(-0.350861\pi\) | ||||
0.451580 | + | 0.892231i | \(0.350861\pi\) | |||||||
\(678\) | −35.7776 | −1.37403 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −12.1241 | −0.464937 | ||||||||
\(681\) | 11.0661 | 0.424055 | ||||||||
\(682\) | 3.02790 | 0.115944 | ||||||||
\(683\) | −26.4226 | −1.01103 | −0.505517 | − | 0.862817i | \(-0.668698\pi\) | ||||
−0.505517 | + | 0.862817i | \(0.668698\pi\) | |||||||
\(684\) | 11.0866 | 0.423906 | ||||||||
\(685\) | −19.4911 | −0.744715 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.86577 | 0.109336 | ||||||||
\(688\) | 17.2236 | 0.656642 | ||||||||
\(689\) | 63.6601 | 2.42526 | ||||||||
\(690\) | −11.7131 | −0.445911 | ||||||||
\(691\) | 29.0351 | 1.10455 | 0.552274 | − | 0.833663i | \(-0.313760\pi\) | ||||
0.552274 | + | 0.833663i | \(0.313760\pi\) | |||||||
\(692\) | −10.6139 | −0.403482 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.71066 | −0.330652 | ||||||||
\(695\) | −2.32171 | −0.0880673 | ||||||||
\(696\) | 4.26834 | 0.161791 | ||||||||
\(697\) | 15.4462 | 0.585068 | ||||||||
\(698\) | 39.1836 | 1.48312 | ||||||||
\(699\) | 14.6048 | 0.552405 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.9866 | 0.566037 | 0.283019 | − | 0.959114i | \(-0.408664\pi\) | ||||
0.283019 | + | 0.959114i | \(0.408664\pi\) | |||||||
\(702\) | 17.7581 | 0.670235 | ||||||||
\(703\) | 23.3241 | 0.879687 | ||||||||
\(704\) | −5.04643 | −0.190195 | ||||||||
\(705\) | −8.59523 | −0.323715 | ||||||||
\(706\) | −87.8108 | −3.30480 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −22.4793 | −0.844825 | ||||||||
\(709\) | −4.29492 | −0.161299 | −0.0806496 | − | 0.996743i | \(-0.525699\pi\) | ||||
−0.0806496 | + | 0.996743i | \(0.525699\pi\) | |||||||
\(710\) | −16.7552 | −0.628812 | ||||||||
\(711\) | −6.95896 | −0.260981 | ||||||||
\(712\) | −34.7477 | −1.30222 | ||||||||
\(713\) | −6.47831 | −0.242614 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.27521 | −0.234680 | ||||||||
\(716\) | 103.390 | 3.86385 | ||||||||
\(717\) | −18.4800 | −0.690148 | ||||||||
\(718\) | −57.8828 | −2.16017 | ||||||||
\(719\) | 26.0471 | 0.971395 | 0.485697 | − | 0.874127i | \(-0.338566\pi\) | ||||
0.485697 | + | 0.874127i | \(0.338566\pi\) | |||||||
\(720\) | −4.69858 | −0.175106 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 30.1153 | 1.12078 | ||||||||
\(723\) | −25.9433 | −0.964841 | ||||||||
\(724\) | 54.0257 | 2.00785 | ||||||||
\(725\) | −3.26570 | −0.121285 | ||||||||
\(726\) | 2.49291 | 0.0925206 | ||||||||
\(727\) | 39.2855 | 1.45702 | 0.728510 | − | 0.685035i | \(-0.240213\pi\) | ||||
0.728510 | + | 0.685035i | \(0.240213\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −28.0583 | −1.03849 | ||||||||
\(731\) | −8.05013 | −0.297745 | ||||||||
\(732\) | 38.2842 | 1.41502 | ||||||||
\(733\) | 8.55811 | 0.316101 | 0.158050 | − | 0.987431i | \(-0.449479\pi\) | ||||
0.158050 | + | 0.987431i | \(0.449479\pi\) | |||||||
\(734\) | −49.2368 | −1.81736 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.0262 | −0.443291 | ||||||||
\(737\) | 11.2704 | 0.415151 | ||||||||
\(738\) | 15.4462 | 0.568584 | ||||||||
\(739\) | −12.2262 | −0.449747 | −0.224874 | − | 0.974388i | \(-0.572197\pi\) | ||||
−0.224874 | + | 0.974388i | \(0.572197\pi\) | |||||||
\(740\) | −32.9201 | −1.21017 | ||||||||
\(741\) | −18.7383 | −0.688369 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.0257 | −0.881416 | −0.440708 | − | 0.897650i | \(-0.645273\pi\) | ||||
−0.440708 | + | 0.897650i | \(0.645273\pi\) | |||||||
\(744\) | −6.70560 | −0.245839 | ||||||||
\(745\) | −0.676662 | −0.0247910 | ||||||||
\(746\) | 62.2370 | 2.27866 | ||||||||
\(747\) | −1.20524 | −0.0440974 | ||||||||
\(748\) | −10.5066 | −0.384160 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 20.2565 | 0.739662 | ||||||||
\(751\) | 7.51318 | 0.274160 | 0.137080 | − | 0.990560i | \(-0.456228\pi\) | ||||
0.137080 | + | 0.990560i | \(0.456228\pi\) | |||||||
\(752\) | −52.0409 | −1.89774 | ||||||||
\(753\) | −26.4331 | −0.963276 | ||||||||
\(754\) | −13.7294 | −0.499995 | ||||||||
\(755\) | 12.3641 | 0.449976 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.97814 | 0.326316 | 0.163158 | − | 0.986600i | \(-0.447832\pi\) | ||||
0.163158 | + | 0.986600i | \(0.447832\pi\) | |||||||
\(758\) | 40.6994 | 1.47827 | ||||||||
\(759\) | −5.33368 | −0.193600 | ||||||||
\(760\) | 12.7933 | 0.464063 | ||||||||
\(761\) | 2.79331 | 0.101257 | 0.0506287 | − | 0.998718i | \(-0.483877\pi\) | ||||
0.0506287 | + | 0.998718i | \(0.483877\pi\) | |||||||
\(762\) | 22.2362 | 0.805532 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 93.0523 | 3.36652 | ||||||||
\(765\) | 2.19607 | 0.0793991 | ||||||||
\(766\) | −30.1840 | −1.09059 | ||||||||
\(767\) | 37.9941 | 1.37189 | ||||||||
\(768\) | 32.5106 | 1.17312 | ||||||||
\(769\) | −5.83905 | −0.210561 | −0.105281 | − | 0.994443i | \(-0.533574\pi\) | ||||
−0.105281 | + | 0.994443i | \(0.533574\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.63900 | 0.167069 | ||||||||
\(772\) | 77.7395 | 2.79791 | ||||||||
\(773\) | 5.13156 | 0.184570 | 0.0922848 | − | 0.995733i | \(-0.470583\pi\) | ||||
0.0922848 | + | 0.995733i | \(0.470583\pi\) | |||||||
\(774\) | −8.05013 | −0.289356 | ||||||||
\(775\) | 5.13045 | 0.184291 | ||||||||
\(776\) | −7.16944 | −0.257368 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 45.3704 | 1.62661 | ||||||||
\(779\) | −16.2989 | −0.583968 | ||||||||
\(780\) | 26.4475 | 0.946974 | ||||||||
\(781\) | −7.62963 | −0.273010 | ||||||||
\(782\) | 33.1467 | 1.18532 | ||||||||
\(783\) | −0.773136 | −0.0276296 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.96675 | −0.177271 | ||||||||
\(786\) | 30.8800 | 1.10145 | ||||||||
\(787\) | 10.8644 | 0.387273 | 0.193636 | − | 0.981073i | \(-0.437972\pi\) | ||||
0.193636 | + | 0.981073i | \(0.437972\pi\) | |||||||
\(788\) | −19.2905 | −0.687196 | ||||||||
\(789\) | −19.6266 | −0.698725 | ||||||||
\(790\) | −15.2824 | −0.543722 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.52081 | −0.196173 | ||||||||
\(793\) | −64.7071 | −2.29782 | ||||||||
\(794\) | 0.144454 | 0.00512647 | ||||||||
\(795\) | 7.87259 | 0.279212 | ||||||||
\(796\) | −9.23445 | −0.327306 | ||||||||
\(797\) | 15.9000 | 0.563208 | 0.281604 | − | 0.959531i | \(-0.409134\pi\) | ||||
0.281604 | + | 0.959531i | \(0.409134\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.3234 | 0.860501 | ||||||||
\(800\) | 9.52405 | 0.336726 | ||||||||
\(801\) | 6.29395 | 0.222386 | ||||||||
\(802\) | 42.0927 | 1.48634 | ||||||||
\(803\) | −12.7766 | −0.450877 | ||||||||
\(804\) | −47.5003 | −1.67521 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21.5690 | 0.759736 | ||||||||
\(807\) | 22.5633 | 0.794266 | ||||||||
\(808\) | 54.6241 | 1.92167 | ||||||||
\(809\) | −39.4022 | −1.38531 | −0.692653 | − | 0.721271i | \(-0.743558\pi\) | ||||
−0.692653 | + | 0.721271i | \(0.743558\pi\) | |||||||
\(810\) | 2.19607 | 0.0771620 | ||||||||
\(811\) | 14.2370 | 0.499928 | 0.249964 | − | 0.968255i | \(-0.419581\pi\) | ||||
0.249964 | + | 0.968255i | \(0.419581\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.1535 | 0.601601 | ||||||||
\(814\) | −22.1040 | −0.774745 | ||||||||
\(815\) | −9.60179 | −0.336336 | ||||||||
\(816\) | 13.2964 | 0.465466 | ||||||||
\(817\) | 8.49449 | 0.297185 | ||||||||
\(818\) | 2.70820 | 0.0946901 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.0045 | 0.803352 | ||||||||
\(821\) | −31.2643 | −1.09113 | −0.545565 | − | 0.838068i | \(-0.683685\pi\) | ||||
−0.545565 | + | 0.838068i | \(0.683685\pi\) | |||||||
\(822\) | 55.1572 | 1.92383 | ||||||||
\(823\) | 34.7684 | 1.21195 | 0.605975 | − | 0.795483i | \(-0.292783\pi\) | ||||
0.605975 | + | 0.795483i | \(0.292783\pi\) | |||||||
\(824\) | −61.7460 | −2.15103 | ||||||||
\(825\) | 4.22397 | 0.147060 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.62027 | 0.299756 | 0.149878 | − | 0.988704i | \(-0.452112\pi\) | ||||
0.149878 | + | 0.988704i | \(0.452112\pi\) | |||||||
\(828\) | 22.4793 | 0.781211 | ||||||||
\(829\) | 4.55830 | 0.158316 | 0.0791582 | − | 0.996862i | \(-0.474777\pi\) | ||||
0.0791582 | + | 0.996862i | \(0.474777\pi\) | |||||||
\(830\) | −2.64679 | −0.0918714 | ||||||||
\(831\) | 26.1496 | 0.907118 | ||||||||
\(832\) | −35.9479 | −1.24627 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 6.57014 | 0.227505 | ||||||||
\(835\) | −8.08415 | −0.279764 | ||||||||
\(836\) | 11.0866 | 0.383438 | ||||||||
\(837\) | 1.21460 | 0.0419828 | ||||||||
\(838\) | −46.6727 | −1.61228 | ||||||||
\(839\) | 5.51585 | 0.190428 | 0.0952141 | − | 0.995457i | \(-0.469646\pi\) | ||||
0.0952141 | + | 0.995457i | \(0.469646\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4023 | −0.979388 | ||||||||
\(842\) | −26.5691 | −0.915632 | ||||||||
\(843\) | −8.79972 | −0.303079 | ||||||||
\(844\) | −42.0216 | −1.44644 | ||||||||
\(845\) | −33.2490 | −1.14380 | ||||||||
\(846\) | 24.3234 | 0.836257 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 47.6656 | 1.63684 | ||||||||
\(849\) | −13.7499 | −0.471895 | ||||||||
\(850\) | −26.2503 | −0.900378 | ||||||||
\(851\) | 47.2924 | 1.62116 | ||||||||
\(852\) | 32.1559 | 1.10164 | ||||||||
\(853\) | 41.9614 | 1.43673 | 0.718366 | − | 0.695666i | \(-0.244890\pi\) | ||||
0.718366 | + | 0.695666i | \(0.244890\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.31729 | −0.0792497 | ||||||||
\(856\) | −40.1145 | −1.37108 | ||||||||
\(857\) | 9.11350 | 0.311311 | 0.155656 | − | 0.987811i | \(-0.450251\pi\) | ||||
0.155656 | + | 0.987811i | \(0.450251\pi\) | |||||||
\(858\) | 17.7581 | 0.606251 | ||||||||
\(859\) | 42.2991 | 1.44323 | 0.721614 | − | 0.692296i | \(-0.243401\pi\) | ||||
0.721614 | + | 0.692296i | \(0.243401\pi\) | |||||||
\(860\) | −11.9893 | −0.408830 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −49.2325 | −1.67686 | ||||||||
\(863\) | −13.7735 | −0.468855 | −0.234427 | − | 0.972134i | \(-0.575322\pi\) | ||||
−0.234427 | + | 0.972134i | \(0.575322\pi\) | |||||||
\(864\) | 2.25476 | 0.0767086 | ||||||||
\(865\) | 2.21850 | 0.0754313 | ||||||||
\(866\) | 86.4607 | 2.93805 | ||||||||
\(867\) | 10.7854 | 0.366291 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.95896 | −0.236066 | ||||||||
\(870\) | −1.69786 | −0.0575629 | ||||||||
\(871\) | 80.2839 | 2.72032 | ||||||||
\(872\) | −2.51790 | −0.0852667 | ||||||||
\(873\) | 1.29862 | 0.0439516 | ||||||||
\(874\) | −34.9764 | −1.18309 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 53.8483 | 1.81937 | ||||||||
\(877\) | 44.1197 | 1.48982 | 0.744908 | − | 0.667167i | \(-0.232493\pi\) | ||||
0.744908 | + | 0.667167i | \(0.232493\pi\) | |||||||
\(878\) | 13.9362 | 0.470324 | ||||||||
\(879\) | −17.4266 | −0.587786 | ||||||||
\(880\) | −4.69858 | −0.158389 | ||||||||
\(881\) | −57.8355 | −1.94853 | −0.974263 | − | 0.225414i | \(-0.927627\pi\) | ||||
−0.974263 | + | 0.225414i | \(0.927627\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.2117 | −0.377303 | −0.188651 | − | 0.982044i | \(-0.560412\pi\) | ||||
−0.188651 | + | 0.982044i | \(0.560412\pi\) | |||||||
\(884\) | −74.8432 | −2.51725 | ||||||||
\(885\) | 4.69858 | 0.157941 | ||||||||
\(886\) | −27.1890 | −0.913433 | ||||||||
\(887\) | −22.1324 | −0.743134 | −0.371567 | − | 0.928406i | \(-0.621179\pi\) | ||||
−0.371567 | + | 0.928406i | \(0.621179\pi\) | |||||||
\(888\) | 48.9516 | 1.64271 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 13.8219 | 0.463313 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −64.0681 | −2.14516 | ||||||||
\(893\) | −25.6661 | −0.858882 | ||||||||
\(894\) | 1.91487 | 0.0640428 | ||||||||
\(895\) | −21.6103 | −0.722351 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −37.9941 | −1.26859 | ||||||||
\(898\) | −24.8584 | −0.829536 | ||||||||
\(899\) | −0.939054 | −0.0313192 | ||||||||
\(900\) | −17.8024 | −0.593412 | ||||||||
\(901\) | −22.2785 | −0.742203 | ||||||||
\(902\) | 15.4462 | 0.514304 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 79.2333 | 2.63526 | ||||||||
\(905\) | −11.2923 | −0.375369 | ||||||||
\(906\) | −34.9889 | −1.16243 | ||||||||
\(907\) | −26.0093 | −0.863624 | −0.431812 | − | 0.901964i | \(-0.642126\pi\) | ||||
−0.431812 | + | 0.901964i | \(0.642126\pi\) | |||||||
\(908\) | −46.6394 | −1.54778 | ||||||||
\(909\) | −9.89422 | −0.328171 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.6978 | 1.08333 | 0.541664 | − | 0.840595i | \(-0.317795\pi\) | ||||
0.541664 | + | 0.840595i | \(0.317795\pi\) | |||||||
\(912\) | −14.0303 | −0.464591 | ||||||||
\(913\) | −1.20524 | −0.0398876 | ||||||||
\(914\) | 14.3792 | 0.475621 | ||||||||
\(915\) | −8.00207 | −0.264540 | ||||||||
\(916\) | −12.0781 | −0.399071 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.21460 | −0.205112 | ||||||||
\(919\) | −0.123800 | −0.00408377 | −0.00204189 | − | 0.999998i | \(-0.500650\pi\) | ||||
−0.00204189 | + | 0.999998i | \(0.500650\pi\) | |||||||
\(920\) | 25.9399 | 0.855215 | ||||||||
\(921\) | 0.804963 | 0.0265244 | ||||||||
\(922\) | 64.7960 | 2.13394 | ||||||||
\(923\) | −54.3491 | −1.78892 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −37.4529 | −1.23144 | ||||||||
\(926\) | −15.2052 | −0.499673 | ||||||||
\(927\) | 11.1842 | 0.367339 | ||||||||
\(928\) | −1.74324 | −0.0572246 | ||||||||
\(929\) | −6.93559 | −0.227549 | −0.113775 | − | 0.993507i | \(-0.536294\pi\) | ||||
−0.113775 | + | 0.993507i | \(0.536294\pi\) | |||||||
\(930\) | 2.66736 | 0.0874660 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −61.5536 | −2.01625 | ||||||||
\(933\) | 10.8250 | 0.354395 | ||||||||
\(934\) | 59.4658 | 1.94578 | ||||||||
\(935\) | 2.19607 | 0.0718192 | ||||||||
\(936\) | −39.3271 | −1.28545 | ||||||||
\(937\) | −29.6703 | −0.969288 | −0.484644 | − | 0.874712i | \(-0.661051\pi\) | ||||
−0.484644 | + | 0.874712i | \(0.661051\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.7315 | −0.807082 | ||||||||
\(940\) | 36.2255 | 1.18155 | ||||||||
\(941\) | −36.2313 | −1.18111 | −0.590554 | − | 0.806998i | \(-0.701091\pi\) | ||||
−0.590554 | + | 0.806998i | \(0.701091\pi\) | |||||||
\(942\) | 14.0553 | 0.457946 | ||||||||
\(943\) | −33.0478 | −1.07619 | ||||||||
\(944\) | 28.4481 | 0.925907 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.05013 | −0.261732 | ||||||||
\(947\) | 18.1200 | 0.588820 | 0.294410 | − | 0.955679i | \(-0.404877\pi\) | ||||
0.294410 | + | 0.955679i | \(0.404877\pi\) | |||||||
\(948\) | 29.3292 | 0.952569 | ||||||||
\(949\) | −91.0132 | −2.95441 | ||||||||
\(950\) | 27.6993 | 0.898684 | ||||||||
\(951\) | 12.2819 | 0.398268 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −58.5262 | −1.89585 | −0.947924 | − | 0.318496i | \(-0.896822\pi\) | ||||
−0.947924 | + | 0.318496i | \(0.896822\pi\) | |||||||
\(954\) | −22.2785 | −0.721292 | ||||||||
\(955\) | −19.4496 | −0.629373 | ||||||||
\(956\) | 77.8859 | 2.51901 | ||||||||
\(957\) | −0.773136 | −0.0249919 | ||||||||
\(958\) | 23.1065 | 0.746538 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −4.44553 | −0.143479 | ||||||||
\(961\) | −29.5247 | −0.952411 | ||||||||
\(962\) | −157.456 | −5.07660 | ||||||||
\(963\) | 7.26605 | 0.234145 | ||||||||
\(964\) | 109.341 | 3.52163 | ||||||||
\(965\) | −16.2489 | −0.523071 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.1143 | 1.61157 | 0.805783 | − | 0.592210i | \(-0.201745\pi\) | ||||
0.805783 | + | 0.592210i | \(0.201745\pi\) | |||||||
\(968\) | −5.52081 | −0.177446 | ||||||||
\(969\) | 6.55765 | 0.210662 | ||||||||
\(970\) | 2.85186 | 0.0915678 | ||||||||
\(971\) | 6.63946 | 0.213070 | 0.106535 | − | 0.994309i | \(-0.466024\pi\) | ||||
0.106535 | + | 0.994309i | \(0.466024\pi\) | |||||||
\(972\) | −4.21460 | −0.135183 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −95.7584 | −3.06830 | ||||||||
\(975\) | 30.0891 | 0.963624 | ||||||||
\(976\) | −48.4495 | −1.55083 | ||||||||
\(977\) | −28.6357 | −0.916136 | −0.458068 | − | 0.888917i | \(-0.651458\pi\) | ||||
−0.458068 | + | 0.888917i | \(0.651458\pi\) | |||||||
\(978\) | 27.1719 | 0.868861 | ||||||||
\(979\) | 6.29395 | 0.201155 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.456074 | 0.0145613 | ||||||||
\(982\) | 30.3687 | 0.969105 | ||||||||
\(983\) | 3.66881 | 0.117017 | 0.0585084 | − | 0.998287i | \(-0.481366\pi\) | ||||
0.0585084 | + | 0.998287i | \(0.481366\pi\) | |||||||
\(984\) | −34.2073 | −1.09049 | ||||||||
\(985\) | 4.03206 | 0.128472 | ||||||||
\(986\) | 4.80473 | 0.153014 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 78.9745 | 2.51252 | ||||||||
\(989\) | 17.2236 | 0.547677 | ||||||||
\(990\) | 2.19607 | 0.0697957 | ||||||||
\(991\) | −33.0334 | −1.04934 | −0.524670 | − | 0.851305i | \(-0.675811\pi\) | ||||
−0.524670 | + | 0.851305i | \(0.675811\pi\) | |||||||
\(992\) | 2.73864 | 0.0869520 | ||||||||
\(993\) | 13.1987 | 0.418849 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.93016 | 0.0611902 | ||||||||
\(996\) | 5.07960 | 0.160953 | ||||||||
\(997\) | 12.3774 | 0.391996 | 0.195998 | − | 0.980604i | \(-0.437205\pi\) | ||||
0.195998 | + | 0.980604i | \(0.437205\pi\) | |||||||
\(998\) | −17.9854 | −0.569317 | ||||||||
\(999\) | −8.86675 | −0.280531 |
(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 | 1617.2.a.ba.1.1 | 5 | ||
3.2 | odd | 2 | 4851.2.a.ca.1.5 | 5 | |||
7.2 | even | 3 | 231.2.i.f.67.5 | ✓ | 10 | ||
7.4 | even | 3 | 231.2.i.f.100.5 | yes | 10 | ||
7.6 | odd | 2 | 1617.2.a.bb.1.1 | 5 | |||
21.2 | odd | 6 | 693.2.i.j.298.1 | 10 | |||
21.11 | odd | 6 | 693.2.i.j.100.1 | 10 | |||
21.20 | even | 2 | 4851.2.a.bz.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.i.f.67.5 | ✓ | 10 | 7.2 | even | 3 | ||
231.2.i.f.100.5 | yes | 10 | 7.4 | even | 3 | ||
693.2.i.j.100.1 | 10 | 21.11 | odd | 6 | |||
693.2.i.j.298.1 | 10 | 21.2 | odd | 6 | |||
1617.2.a.ba.1.1 | 5 | 1.1 | even | 1 | trivial | ||
1617.2.a.bb.1.1 | 5 | 7.6 | odd | 2 | |||
4851.2.a.bz.1.5 | 5 | 21.20 | even | 2 | |||
4851.2.a.ca.1.5 | 5 | 3.2 | odd | 2 |