Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, 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("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 17x^{8} + 23x^{7} + 69x^{6} - 88x^{5} - 106x^{4} + 101x^{3} + 60x^{2} - 23x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.66000\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.24431 | −1.58697 | −0.793484 | − | 0.608591i | \(-0.791735\pi\) | ||||
−0.793484 | + | 0.608591i | \(0.791735\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.03693 | 1.51847 | ||||||||
\(5\) | −1.31370 | −0.587503 | −0.293752 | − | 0.955882i | \(-0.594904\pi\) | ||||
−0.293752 | + | 0.955882i | \(0.594904\pi\) | |||||||
\(6\) | 2.24431 | 0.916236 | ||||||||
\(7\) | −2.96709 | −1.12146 | −0.560728 | − | 0.828000i | \(-0.689479\pi\) | ||||
−0.560728 | + | 0.828000i | \(0.689479\pi\) | |||||||
\(8\) | −2.32720 | −0.822788 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.94835 | 0.932349 | ||||||||
\(11\) | 1.51682 | 0.457337 | 0.228668 | − | 0.973504i | \(-0.426563\pi\) | ||||
0.228668 | + | 0.973504i | \(0.426563\pi\) | |||||||
\(12\) | −3.03693 | −0.876687 | ||||||||
\(13\) | 0.902202 | 0.250226 | 0.125113 | − | 0.992143i | \(-0.460071\pi\) | ||||
0.125113 | + | 0.992143i | \(0.460071\pi\) | |||||||
\(14\) | 6.65908 | 1.77971 | ||||||||
\(15\) | 1.31370 | 0.339195 | ||||||||
\(16\) | −0.850911 | −0.212728 | ||||||||
\(17\) | 3.54263 | 0.859215 | 0.429607 | − | 0.903016i | \(-0.358652\pi\) | ||||
0.429607 | + | 0.903016i | \(0.358652\pi\) | |||||||
\(18\) | −2.24431 | −0.528989 | ||||||||
\(19\) | 0.438527 | 0.100605 | 0.0503025 | − | 0.998734i | \(-0.483981\pi\) | ||||
0.0503025 | + | 0.998734i | \(0.483981\pi\) | |||||||
\(20\) | −3.98961 | −0.892104 | ||||||||
\(21\) | 2.96709 | 0.647473 | ||||||||
\(22\) | −3.40420 | −0.725779 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 2.32720 | 0.475037 | ||||||||
\(25\) | −3.27420 | −0.654840 | ||||||||
\(26\) | −2.02482 | −0.397100 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −9.01086 | −1.70289 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −2.94835 | −0.538292 | ||||||||
\(31\) | −1.36633 | −0.245400 | −0.122700 | − | 0.992444i | \(-0.539155\pi\) | ||||
−0.122700 | + | 0.992444i | \(0.539155\pi\) | |||||||
\(32\) | 6.56410 | 1.16038 | ||||||||
\(33\) | −1.51682 | −0.264044 | ||||||||
\(34\) | −7.95077 | −1.36355 | ||||||||
\(35\) | 3.89786 | 0.658859 | ||||||||
\(36\) | 3.03693 | 0.506155 | ||||||||
\(37\) | −10.9378 | −1.79817 | −0.899084 | − | 0.437776i | \(-0.855766\pi\) | ||||
−0.899084 | + | 0.437776i | \(0.855766\pi\) | |||||||
\(38\) | −0.984190 | −0.159657 | ||||||||
\(39\) | −0.902202 | −0.144468 | ||||||||
\(40\) | 3.05723 | 0.483391 | ||||||||
\(41\) | 3.73744 | 0.583690 | 0.291845 | − | 0.956466i | \(-0.405731\pi\) | ||||
0.291845 | + | 0.956466i | \(0.405731\pi\) | |||||||
\(42\) | −6.65908 | −1.02752 | ||||||||
\(43\) | −6.23701 | −0.951135 | −0.475568 | − | 0.879679i | \(-0.657757\pi\) | ||||
−0.475568 | + | 0.879679i | \(0.657757\pi\) | |||||||
\(44\) | 4.60646 | 0.694450 | ||||||||
\(45\) | −1.31370 | −0.195834 | ||||||||
\(46\) | 2.24431 | 0.330906 | ||||||||
\(47\) | 4.40935 | 0.643170 | 0.321585 | − | 0.946881i | \(-0.395784\pi\) | ||||
0.321585 | + | 0.946881i | \(0.395784\pi\) | |||||||
\(48\) | 0.850911 | 0.122818 | ||||||||
\(49\) | 1.80364 | 0.257663 | ||||||||
\(50\) | 7.34832 | 1.03921 | ||||||||
\(51\) | −3.54263 | −0.496068 | ||||||||
\(52\) | 2.73993 | 0.379959 | ||||||||
\(53\) | −10.7318 | −1.47413 | −0.737065 | − | 0.675822i | \(-0.763789\pi\) | ||||
−0.737065 | + | 0.675822i | \(0.763789\pi\) | |||||||
\(54\) | 2.24431 | 0.305412 | ||||||||
\(55\) | −1.99264 | −0.268687 | ||||||||
\(56\) | 6.90501 | 0.922720 | ||||||||
\(57\) | −0.438527 | −0.0580843 | ||||||||
\(58\) | −2.24431 | −0.294692 | ||||||||
\(59\) | 7.80539 | 1.01618 | 0.508088 | − | 0.861305i | \(-0.330353\pi\) | ||||
0.508088 | + | 0.861305i | \(0.330353\pi\) | |||||||
\(60\) | 3.98961 | 0.515056 | ||||||||
\(61\) | 8.66624 | 1.10960 | 0.554799 | − | 0.831984i | \(-0.312795\pi\) | ||||
0.554799 | + | 0.831984i | \(0.312795\pi\) | |||||||
\(62\) | 3.06647 | 0.389442 | ||||||||
\(63\) | −2.96709 | −0.373819 | ||||||||
\(64\) | −13.0301 | −1.62876 | ||||||||
\(65\) | −1.18522 | −0.147009 | ||||||||
\(66\) | 3.40420 | 0.419029 | ||||||||
\(67\) | 1.02600 | 0.125346 | 0.0626729 | − | 0.998034i | \(-0.480038\pi\) | ||||
0.0626729 | + | 0.998034i | \(0.480038\pi\) | |||||||
\(68\) | 10.7587 | 1.30469 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | −8.74801 | −1.04559 | ||||||||
\(71\) | −11.2518 | −1.33535 | −0.667674 | − | 0.744454i | \(-0.732710\pi\) | ||||
−0.667674 | + | 0.744454i | \(0.732710\pi\) | |||||||
\(72\) | −2.32720 | −0.274263 | ||||||||
\(73\) | −2.88266 | −0.337390 | −0.168695 | − | 0.985668i | \(-0.553955\pi\) | ||||
−0.168695 | + | 0.985668i | \(0.553955\pi\) | |||||||
\(74\) | 24.5479 | 2.85363 | ||||||||
\(75\) | 3.27420 | 0.378072 | ||||||||
\(76\) | 1.33178 | 0.152765 | ||||||||
\(77\) | −4.50053 | −0.512883 | ||||||||
\(78\) | 2.02482 | 0.229266 | ||||||||
\(79\) | 16.1535 | 1.81741 | 0.908703 | − | 0.417443i | \(-0.137074\pi\) | ||||
0.908703 | + | 0.417443i | \(0.137074\pi\) | |||||||
\(80\) | 1.11784 | 0.124978 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.38797 | −0.926296 | ||||||||
\(83\) | 3.36143 | 0.368965 | 0.184483 | − | 0.982836i | \(-0.440939\pi\) | ||||
0.184483 | + | 0.982836i | \(0.440939\pi\) | |||||||
\(84\) | 9.01086 | 0.983165 | ||||||||
\(85\) | −4.65395 | −0.504792 | ||||||||
\(86\) | 13.9978 | 1.50942 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | −3.52993 | −0.376291 | ||||||||
\(89\) | −7.47996 | −0.792874 | −0.396437 | − | 0.918062i | \(-0.629753\pi\) | ||||
−0.396437 | + | 0.918062i | \(0.629753\pi\) | |||||||
\(90\) | 2.94835 | 0.310783 | ||||||||
\(91\) | −2.67692 | −0.280617 | ||||||||
\(92\) | −3.03693 | −0.316622 | ||||||||
\(93\) | 1.36633 | 0.141682 | ||||||||
\(94\) | −9.89596 | −1.02069 | ||||||||
\(95\) | −0.576092 | −0.0591057 | ||||||||
\(96\) | −6.56410 | −0.669946 | ||||||||
\(97\) | −15.6206 | −1.58603 | −0.793014 | − | 0.609203i | \(-0.791489\pi\) | ||||
−0.793014 | + | 0.609203i | \(0.791489\pi\) | |||||||
\(98\) | −4.04792 | −0.408902 | ||||||||
\(99\) | 1.51682 | 0.152446 | ||||||||
\(100\) | −9.94352 | −0.994352 | ||||||||
\(101\) | −3.63336 | −0.361533 | −0.180767 | − | 0.983526i | \(-0.557858\pi\) | ||||
−0.180767 | + | 0.983526i | \(0.557858\pi\) | |||||||
\(102\) | 7.95077 | 0.787243 | ||||||||
\(103\) | 10.2810 | 1.01302 | 0.506510 | − | 0.862234i | \(-0.330935\pi\) | ||||
0.506510 | + | 0.862234i | \(0.330935\pi\) | |||||||
\(104\) | −2.09960 | −0.205883 | ||||||||
\(105\) | −3.89786 | −0.380392 | ||||||||
\(106\) | 24.0856 | 2.33940 | ||||||||
\(107\) | 7.31175 | 0.706854 | 0.353427 | − | 0.935462i | \(-0.385016\pi\) | ||||
0.353427 | + | 0.935462i | \(0.385016\pi\) | |||||||
\(108\) | −3.03693 | −0.292229 | ||||||||
\(109\) | −3.37760 | −0.323515 | −0.161758 | − | 0.986831i | \(-0.551716\pi\) | ||||
−0.161758 | + | 0.986831i | \(0.551716\pi\) | |||||||
\(110\) | 4.47210 | 0.426398 | ||||||||
\(111\) | 10.9378 | 1.03817 | ||||||||
\(112\) | 2.52473 | 0.238565 | ||||||||
\(113\) | −2.02102 | −0.190122 | −0.0950610 | − | 0.995471i | \(-0.530305\pi\) | ||||
−0.0950610 | + | 0.995471i | \(0.530305\pi\) | |||||||
\(114\) | 0.984190 | 0.0921779 | ||||||||
\(115\) | 1.31370 | 0.122503 | ||||||||
\(116\) | 3.03693 | 0.281972 | ||||||||
\(117\) | 0.902202 | 0.0834086 | ||||||||
\(118\) | −17.5177 | −1.61264 | ||||||||
\(119\) | −10.5113 | −0.963571 | ||||||||
\(120\) | −3.05723 | −0.279086 | ||||||||
\(121\) | −8.69927 | −0.790843 | ||||||||
\(122\) | −19.4497 | −1.76090 | ||||||||
\(123\) | −3.73744 | −0.336993 | ||||||||
\(124\) | −4.14945 | −0.372632 | ||||||||
\(125\) | 10.8698 | 0.972224 | ||||||||
\(126\) | 6.65908 | 0.593238 | ||||||||
\(127\) | 2.41766 | 0.214533 | 0.107266 | − | 0.994230i | \(-0.465790\pi\) | ||||
0.107266 | + | 0.994230i | \(0.465790\pi\) | |||||||
\(128\) | 16.1153 | 1.42441 | ||||||||
\(129\) | 6.23701 | 0.549138 | ||||||||
\(130\) | 2.66000 | 0.233298 | ||||||||
\(131\) | 3.99026 | 0.348630 | 0.174315 | − | 0.984690i | \(-0.444229\pi\) | ||||
0.174315 | + | 0.984690i | \(0.444229\pi\) | |||||||
\(132\) | −4.60646 | −0.400941 | ||||||||
\(133\) | −1.30115 | −0.112824 | ||||||||
\(134\) | −2.30266 | −0.198920 | ||||||||
\(135\) | 1.31370 | 0.113065 | ||||||||
\(136\) | −8.24440 | −0.706951 | ||||||||
\(137\) | 6.48948 | 0.554434 | 0.277217 | − | 0.960807i | \(-0.410588\pi\) | ||||
0.277217 | + | 0.960807i | \(0.410588\pi\) | |||||||
\(138\) | −2.24431 | −0.191048 | ||||||||
\(139\) | −18.9540 | −1.60766 | −0.803830 | − | 0.594859i | \(-0.797208\pi\) | ||||
−0.803830 | + | 0.594859i | \(0.797208\pi\) | |||||||
\(140\) | 11.8375 | 1.00045 | ||||||||
\(141\) | −4.40935 | −0.371335 | ||||||||
\(142\) | 25.2526 | 2.11915 | ||||||||
\(143\) | 1.36847 | 0.114438 | ||||||||
\(144\) | −0.850911 | −0.0709093 | ||||||||
\(145\) | −1.31370 | −0.109097 | ||||||||
\(146\) | 6.46958 | 0.535427 | ||||||||
\(147\) | −1.80364 | −0.148762 | ||||||||
\(148\) | −33.2174 | −2.73046 | ||||||||
\(149\) | 22.8616 | 1.87290 | 0.936448 | − | 0.350807i | \(-0.114093\pi\) | ||||
0.936448 | + | 0.350807i | \(0.114093\pi\) | |||||||
\(150\) | −7.34832 | −0.599988 | ||||||||
\(151\) | 16.8032 | 1.36743 | 0.683714 | − | 0.729750i | \(-0.260364\pi\) | ||||
0.683714 | + | 0.729750i | \(0.260364\pi\) | |||||||
\(152\) | −1.02054 | −0.0827765 | ||||||||
\(153\) | 3.54263 | 0.286405 | ||||||||
\(154\) | 10.1006 | 0.813929 | ||||||||
\(155\) | 1.79495 | 0.144174 | ||||||||
\(156\) | −2.73993 | −0.219370 | ||||||||
\(157\) | 4.66486 | 0.372296 | 0.186148 | − | 0.982522i | \(-0.440400\pi\) | ||||
0.186148 | + | 0.982522i | \(0.440400\pi\) | |||||||
\(158\) | −36.2534 | −2.88416 | ||||||||
\(159\) | 10.7318 | 0.851089 | ||||||||
\(160\) | −8.62324 | −0.681727 | ||||||||
\(161\) | 2.96709 | 0.233840 | ||||||||
\(162\) | −2.24431 | −0.176330 | ||||||||
\(163\) | −6.11817 | −0.479212 | −0.239606 | − | 0.970870i | \(-0.577018\pi\) | ||||
−0.239606 | + | 0.970870i | \(0.577018\pi\) | |||||||
\(164\) | 11.3503 | 0.886312 | ||||||||
\(165\) | 1.99264 | 0.155127 | ||||||||
\(166\) | −7.54410 | −0.585536 | ||||||||
\(167\) | 5.11459 | 0.395779 | 0.197889 | − | 0.980224i | \(-0.436591\pi\) | ||||
0.197889 | + | 0.980224i | \(0.436591\pi\) | |||||||
\(168\) | −6.90501 | −0.532733 | ||||||||
\(169\) | −12.1860 | −0.937387 | ||||||||
\(170\) | 10.4449 | 0.801088 | ||||||||
\(171\) | 0.438527 | 0.0335350 | ||||||||
\(172\) | −18.9414 | −1.44427 | ||||||||
\(173\) | 10.5173 | 0.799614 | 0.399807 | − | 0.916599i | \(-0.369077\pi\) | ||||
0.399807 | + | 0.916599i | \(0.369077\pi\) | |||||||
\(174\) | 2.24431 | 0.170141 | ||||||||
\(175\) | 9.71485 | 0.734374 | ||||||||
\(176\) | −1.29068 | −0.0972883 | ||||||||
\(177\) | −7.80539 | −0.586689 | ||||||||
\(178\) | 16.7873 | 1.25826 | ||||||||
\(179\) | 10.1812 | 0.760981 | 0.380491 | − | 0.924785i | \(-0.375755\pi\) | ||||
0.380491 | + | 0.924785i | \(0.375755\pi\) | |||||||
\(180\) | −3.98961 | −0.297368 | ||||||||
\(181\) | 21.6445 | 1.60882 | 0.804412 | − | 0.594072i | \(-0.202481\pi\) | ||||
0.804412 | + | 0.594072i | \(0.202481\pi\) | |||||||
\(182\) | 6.00784 | 0.445330 | ||||||||
\(183\) | −8.66624 | −0.640627 | ||||||||
\(184\) | 2.32720 | 0.171563 | ||||||||
\(185\) | 14.3690 | 1.05643 | ||||||||
\(186\) | −3.06647 | −0.224845 | ||||||||
\(187\) | 5.37352 | 0.392951 | ||||||||
\(188\) | 13.3909 | 0.976632 | ||||||||
\(189\) | 2.96709 | 0.215824 | ||||||||
\(190\) | 1.29293 | 0.0937989 | ||||||||
\(191\) | 17.2119 | 1.24541 | 0.622705 | − | 0.782457i | \(-0.286034\pi\) | ||||
0.622705 | + | 0.782457i | \(0.286034\pi\) | |||||||
\(192\) | 13.0301 | 0.940364 | ||||||||
\(193\) | −7.97678 | −0.574181 | −0.287090 | − | 0.957903i | \(-0.592688\pi\) | ||||
−0.287090 | + | 0.957903i | \(0.592688\pi\) | |||||||
\(194\) | 35.0574 | 2.51698 | ||||||||
\(195\) | 1.18522 | 0.0848754 | ||||||||
\(196\) | 5.47752 | 0.391252 | ||||||||
\(197\) | 5.13962 | 0.366183 | 0.183092 | − | 0.983096i | \(-0.441390\pi\) | ||||
0.183092 | + | 0.983096i | \(0.441390\pi\) | |||||||
\(198\) | −3.40420 | −0.241926 | ||||||||
\(199\) | 21.9501 | 1.55600 | 0.777999 | − | 0.628265i | \(-0.216235\pi\) | ||||
0.777999 | + | 0.628265i | \(0.216235\pi\) | |||||||
\(200\) | 7.61970 | 0.538794 | ||||||||
\(201\) | −1.02600 | −0.0723684 | ||||||||
\(202\) | 8.15440 | 0.573741 | ||||||||
\(203\) | −2.96709 | −0.208249 | ||||||||
\(204\) | −10.7587 | −0.753262 | ||||||||
\(205\) | −4.90986 | −0.342920 | ||||||||
\(206\) | −23.0738 | −1.60763 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −0.767694 | −0.0532300 | ||||||||
\(209\) | 0.665164 | 0.0460104 | ||||||||
\(210\) | 8.74801 | 0.603670 | ||||||||
\(211\) | 7.00040 | 0.481927 | 0.240964 | − | 0.970534i | \(-0.422537\pi\) | ||||
0.240964 | + | 0.970534i | \(0.422537\pi\) | |||||||
\(212\) | −32.5918 | −2.23841 | ||||||||
\(213\) | 11.2518 | 0.770963 | ||||||||
\(214\) | −16.4098 | −1.12175 | ||||||||
\(215\) | 8.19355 | 0.558795 | ||||||||
\(216\) | 2.32720 | 0.158346 | ||||||||
\(217\) | 4.05403 | 0.275206 | ||||||||
\(218\) | 7.58038 | 0.513408 | ||||||||
\(219\) | 2.88266 | 0.194792 | ||||||||
\(220\) | −6.05150 | −0.407992 | ||||||||
\(221\) | 3.19617 | 0.214998 | ||||||||
\(222\) | −24.5479 | −1.64755 | ||||||||
\(223\) | 19.3205 | 1.29380 | 0.646899 | − | 0.762575i | \(-0.276065\pi\) | ||||
0.646899 | + | 0.762575i | \(0.276065\pi\) | |||||||
\(224\) | −19.4763 | −1.30131 | ||||||||
\(225\) | −3.27420 | −0.218280 | ||||||||
\(226\) | 4.53581 | 0.301717 | ||||||||
\(227\) | −4.35027 | −0.288738 | −0.144369 | − | 0.989524i | \(-0.546115\pi\) | ||||
−0.144369 | + | 0.989524i | \(0.546115\pi\) | |||||||
\(228\) | −1.33178 | −0.0881990 | ||||||||
\(229\) | 14.2691 | 0.942927 | 0.471464 | − | 0.881886i | \(-0.343726\pi\) | ||||
0.471464 | + | 0.881886i | \(0.343726\pi\) | |||||||
\(230\) | −2.94835 | −0.194408 | ||||||||
\(231\) | 4.50053 | 0.296113 | ||||||||
\(232\) | −2.32720 | −0.152788 | ||||||||
\(233\) | 1.10104 | 0.0721315 | 0.0360657 | − | 0.999349i | \(-0.488517\pi\) | ||||
0.0360657 | + | 0.999349i | \(0.488517\pi\) | |||||||
\(234\) | −2.02482 | −0.132367 | ||||||||
\(235\) | −5.79256 | −0.377865 | ||||||||
\(236\) | 23.7044 | 1.54303 | ||||||||
\(237\) | −16.1535 | −1.04928 | ||||||||
\(238\) | 23.5907 | 1.52916 | ||||||||
\(239\) | 3.57602 | 0.231314 | 0.115657 | − | 0.993289i | \(-0.463103\pi\) | ||||
0.115657 | + | 0.993289i | \(0.463103\pi\) | |||||||
\(240\) | −1.11784 | −0.0721563 | ||||||||
\(241\) | 23.8181 | 1.53426 | 0.767130 | − | 0.641492i | \(-0.221684\pi\) | ||||
0.767130 | + | 0.641492i | \(0.221684\pi\) | |||||||
\(242\) | 19.5239 | 1.25504 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 26.3188 | 1.68489 | ||||||||
\(245\) | −2.36943 | −0.151378 | ||||||||
\(246\) | 8.38797 | 0.534797 | ||||||||
\(247\) | 0.395640 | 0.0251740 | ||||||||
\(248\) | 3.17972 | 0.201912 | ||||||||
\(249\) | −3.36143 | −0.213022 | ||||||||
\(250\) | −24.3952 | −1.54289 | ||||||||
\(251\) | −11.0028 | −0.694489 | −0.347245 | − | 0.937775i | \(-0.612883\pi\) | ||||
−0.347245 | + | 0.937775i | \(0.612883\pi\) | |||||||
\(252\) | −9.01086 | −0.567631 | ||||||||
\(253\) | −1.51682 | −0.0953614 | ||||||||
\(254\) | −5.42599 | −0.340457 | ||||||||
\(255\) | 4.65395 | 0.291442 | ||||||||
\(256\) | −10.1076 | −0.631727 | ||||||||
\(257\) | 22.5544 | 1.40691 | 0.703453 | − | 0.710742i | \(-0.251640\pi\) | ||||
0.703453 | + | 0.710742i | \(0.251640\pi\) | |||||||
\(258\) | −13.9978 | −0.871465 | ||||||||
\(259\) | 32.4536 | 2.01657 | ||||||||
\(260\) | −3.59943 | −0.223227 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | −8.95538 | −0.553265 | ||||||||
\(263\) | 10.0124 | 0.617390 | 0.308695 | − | 0.951161i | \(-0.400108\pi\) | ||||
0.308695 | + | 0.951161i | \(0.400108\pi\) | |||||||
\(264\) | 3.52993 | 0.217252 | ||||||||
\(265\) | 14.0984 | 0.866056 | ||||||||
\(266\) | 2.92018 | 0.179048 | ||||||||
\(267\) | 7.47996 | 0.457766 | ||||||||
\(268\) | 3.11589 | 0.190333 | ||||||||
\(269\) | −12.9882 | −0.791902 | −0.395951 | − | 0.918272i | \(-0.629585\pi\) | ||||
−0.395951 | + | 0.918272i | \(0.629585\pi\) | |||||||
\(270\) | −2.94835 | −0.179431 | ||||||||
\(271\) | 15.5385 | 0.943894 | 0.471947 | − | 0.881627i | \(-0.343551\pi\) | ||||
0.471947 | + | 0.881627i | \(0.343551\pi\) | |||||||
\(272\) | −3.01447 | −0.182779 | ||||||||
\(273\) | 2.67692 | 0.162014 | ||||||||
\(274\) | −14.5644 | −0.879868 | ||||||||
\(275\) | −4.96635 | −0.299482 | ||||||||
\(276\) | 3.03693 | 0.182802 | ||||||||
\(277\) | 17.5683 | 1.05557 | 0.527787 | − | 0.849377i | \(-0.323022\pi\) | ||||
0.527787 | + | 0.849377i | \(0.323022\pi\) | |||||||
\(278\) | 42.5387 | 2.55130 | ||||||||
\(279\) | −1.36633 | −0.0818001 | ||||||||
\(280\) | −9.07109 | −0.542101 | ||||||||
\(281\) | −13.1371 | −0.783693 | −0.391846 | − | 0.920031i | \(-0.628164\pi\) | ||||
−0.391846 | + | 0.920031i | \(0.628164\pi\) | |||||||
\(282\) | 9.89596 | 0.589296 | ||||||||
\(283\) | −7.30957 | −0.434509 | −0.217254 | − | 0.976115i | \(-0.569710\pi\) | ||||
−0.217254 | + | 0.976115i | \(0.569710\pi\) | |||||||
\(284\) | −34.1710 | −2.02768 | ||||||||
\(285\) | 0.576092 | 0.0341247 | ||||||||
\(286\) | −3.07128 | −0.181609 | ||||||||
\(287\) | −11.0893 | −0.654582 | ||||||||
\(288\) | 6.56410 | 0.386793 | ||||||||
\(289\) | −4.44975 | −0.261750 | ||||||||
\(290\) | 2.94835 | 0.173133 | ||||||||
\(291\) | 15.6206 | 0.915694 | ||||||||
\(292\) | −8.75444 | −0.512315 | ||||||||
\(293\) | −8.00780 | −0.467821 | −0.233910 | − | 0.972258i | \(-0.575152\pi\) | ||||
−0.233910 | + | 0.972258i | \(0.575152\pi\) | |||||||
\(294\) | 4.04792 | 0.236080 | ||||||||
\(295\) | −10.2539 | −0.597007 | ||||||||
\(296\) | 25.4545 | 1.47951 | ||||||||
\(297\) | −1.51682 | −0.0880145 | ||||||||
\(298\) | −51.3085 | −2.97222 | ||||||||
\(299\) | −0.902202 | −0.0521757 | ||||||||
\(300\) | 9.94352 | 0.574089 | ||||||||
\(301\) | 18.5058 | 1.06666 | ||||||||
\(302\) | −37.7117 | −2.17006 | ||||||||
\(303\) | 3.63336 | 0.208731 | ||||||||
\(304\) | −0.373147 | −0.0214015 | ||||||||
\(305\) | −11.3848 | −0.651893 | ||||||||
\(306\) | −7.95077 | −0.454515 | ||||||||
\(307\) | −30.5296 | −1.74242 | −0.871208 | − | 0.490915i | \(-0.836663\pi\) | ||||
−0.871208 | + | 0.490915i | \(0.836663\pi\) | |||||||
\(308\) | −13.6678 | −0.778795 | ||||||||
\(309\) | −10.2810 | −0.584867 | ||||||||
\(310\) | −4.02842 | −0.228799 | ||||||||
\(311\) | 26.8315 | 1.52148 | 0.760738 | − | 0.649060i | \(-0.224837\pi\) | ||||
0.760738 | + | 0.649060i | \(0.224837\pi\) | |||||||
\(312\) | 2.09960 | 0.118867 | ||||||||
\(313\) | 7.67441 | 0.433783 | 0.216892 | − | 0.976196i | \(-0.430408\pi\) | ||||
0.216892 | + | 0.976196i | \(0.430408\pi\) | |||||||
\(314\) | −10.4694 | −0.590822 | ||||||||
\(315\) | 3.89786 | 0.219620 | ||||||||
\(316\) | 49.0569 | 2.75967 | ||||||||
\(317\) | −11.3137 | −0.635441 | −0.317721 | − | 0.948184i | \(-0.602917\pi\) | ||||
−0.317721 | + | 0.948184i | \(0.602917\pi\) | |||||||
\(318\) | −24.0856 | −1.35065 | ||||||||
\(319\) | 1.51682 | 0.0849253 | ||||||||
\(320\) | 17.1176 | 0.956901 | ||||||||
\(321\) | −7.31175 | −0.408102 | ||||||||
\(322\) | −6.65908 | −0.371096 | ||||||||
\(323\) | 1.55354 | 0.0864412 | ||||||||
\(324\) | 3.03693 | 0.168718 | ||||||||
\(325\) | −2.95399 | −0.163858 | ||||||||
\(326\) | 13.7311 | 0.760493 | ||||||||
\(327\) | 3.37760 | 0.186782 | ||||||||
\(328\) | −8.69775 | −0.480253 | ||||||||
\(329\) | −13.0830 | −0.721287 | ||||||||
\(330\) | −4.47210 | −0.246181 | ||||||||
\(331\) | 34.5401 | 1.89849 | 0.949247 | − | 0.314531i | \(-0.101847\pi\) | ||||
0.949247 | + | 0.314531i | \(0.101847\pi\) | |||||||
\(332\) | 10.2084 | 0.560261 | ||||||||
\(333\) | −10.9378 | −0.599389 | ||||||||
\(334\) | −11.4787 | −0.628088 | ||||||||
\(335\) | −1.34785 | −0.0736411 | ||||||||
\(336\) | −2.52473 | −0.137735 | ||||||||
\(337\) | 22.5432 | 1.22801 | 0.614004 | − | 0.789303i | \(-0.289558\pi\) | ||||
0.614004 | + | 0.789303i | \(0.289558\pi\) | |||||||
\(338\) | 27.3492 | 1.48760 | ||||||||
\(339\) | 2.02102 | 0.109767 | ||||||||
\(340\) | −14.1337 | −0.766509 | ||||||||
\(341\) | −2.07247 | −0.112231 | ||||||||
\(342\) | −0.984190 | −0.0532189 | ||||||||
\(343\) | 15.4181 | 0.832498 | ||||||||
\(344\) | 14.5147 | 0.782583 | ||||||||
\(345\) | −1.31370 | −0.0707271 | ||||||||
\(346\) | −23.6041 | −1.26896 | ||||||||
\(347\) | 15.7661 | 0.846367 | 0.423184 | − | 0.906044i | \(-0.360913\pi\) | ||||
0.423184 | + | 0.906044i | \(0.360913\pi\) | |||||||
\(348\) | −3.03693 | −0.162797 | ||||||||
\(349\) | −18.6754 | −0.999673 | −0.499836 | − | 0.866120i | \(-0.666607\pi\) | ||||
−0.499836 | + | 0.866120i | \(0.666607\pi\) | |||||||
\(350\) | −21.8031 | −1.16543 | ||||||||
\(351\) | −0.902202 | −0.0481560 | ||||||||
\(352\) | 9.95653 | 0.530685 | ||||||||
\(353\) | −22.1152 | −1.17708 | −0.588538 | − | 0.808470i | \(-0.700296\pi\) | ||||
−0.588538 | + | 0.808470i | \(0.700296\pi\) | |||||||
\(354\) | 17.5177 | 0.931057 | ||||||||
\(355\) | 14.7815 | 0.784521 | ||||||||
\(356\) | −22.7161 | −1.20395 | ||||||||
\(357\) | 10.5113 | 0.556318 | ||||||||
\(358\) | −22.8499 | −1.20765 | ||||||||
\(359\) | −31.7410 | −1.67523 | −0.837613 | − | 0.546264i | \(-0.816049\pi\) | ||||
−0.837613 | + | 0.546264i | \(0.816049\pi\) | |||||||
\(360\) | 3.05723 | 0.161130 | ||||||||
\(361\) | −18.8077 | −0.989879 | ||||||||
\(362\) | −48.5770 | −2.55315 | ||||||||
\(363\) | 8.69927 | 0.456593 | ||||||||
\(364\) | −8.12961 | −0.426108 | ||||||||
\(365\) | 3.78694 | 0.198218 | ||||||||
\(366\) | 19.4497 | 1.01665 | ||||||||
\(367\) | 7.88341 | 0.411511 | 0.205755 | − | 0.978603i | \(-0.434035\pi\) | ||||
0.205755 | + | 0.978603i | \(0.434035\pi\) | |||||||
\(368\) | 0.850911 | 0.0443568 | ||||||||
\(369\) | 3.73744 | 0.194563 | ||||||||
\(370\) | −32.2485 | −1.67652 | ||||||||
\(371\) | 31.8423 | 1.65317 | ||||||||
\(372\) | 4.14945 | 0.215139 | ||||||||
\(373\) | −19.3349 | −1.00112 | −0.500561 | − | 0.865701i | \(-0.666873\pi\) | ||||
−0.500561 | + | 0.865701i | \(0.666873\pi\) | |||||||
\(374\) | −12.0598 | −0.623600 | ||||||||
\(375\) | −10.8698 | −0.561314 | ||||||||
\(376\) | −10.2614 | −0.529193 | ||||||||
\(377\) | 0.902202 | 0.0464658 | ||||||||
\(378\) | −6.65908 | −0.342506 | ||||||||
\(379\) | −13.7522 | −0.706405 | −0.353202 | − | 0.935547i | \(-0.614907\pi\) | ||||
−0.353202 | + | 0.935547i | \(0.614907\pi\) | |||||||
\(380\) | −1.74955 | −0.0897500 | ||||||||
\(381\) | −2.41766 | −0.123861 | ||||||||
\(382\) | −38.6289 | −1.97642 | ||||||||
\(383\) | 9.78378 | 0.499928 | 0.249964 | − | 0.968255i | \(-0.419581\pi\) | ||||
0.249964 | + | 0.968255i | \(0.419581\pi\) | |||||||
\(384\) | −16.1153 | −0.822381 | ||||||||
\(385\) | 5.91234 | 0.301321 | ||||||||
\(386\) | 17.9024 | 0.911206 | ||||||||
\(387\) | −6.23701 | −0.317045 | ||||||||
\(388\) | −47.4386 | −2.40833 | ||||||||
\(389\) | 20.3246 | 1.03050 | 0.515250 | − | 0.857040i | \(-0.327699\pi\) | ||||
0.515250 | + | 0.857040i | \(0.327699\pi\) | |||||||
\(390\) | −2.66000 | −0.134695 | ||||||||
\(391\) | −3.54263 | −0.179159 | ||||||||
\(392\) | −4.19742 | −0.212002 | ||||||||
\(393\) | −3.99026 | −0.201282 | ||||||||
\(394\) | −11.5349 | −0.581120 | ||||||||
\(395\) | −21.2208 | −1.06773 | ||||||||
\(396\) | 4.60646 | 0.231483 | ||||||||
\(397\) | −15.0836 | −0.757024 | −0.378512 | − | 0.925596i | \(-0.623564\pi\) | ||||
−0.378512 | + | 0.925596i | \(0.623564\pi\) | |||||||
\(398\) | −49.2628 | −2.46932 | ||||||||
\(399\) | 1.30115 | 0.0651390 | ||||||||
\(400\) | 2.78605 | 0.139303 | ||||||||
\(401\) | 31.7667 | 1.58635 | 0.793176 | − | 0.608993i | \(-0.208426\pi\) | ||||
0.793176 | + | 0.608993i | \(0.208426\pi\) | |||||||
\(402\) | 2.30266 | 0.114846 | ||||||||
\(403\) | −1.23271 | −0.0614055 | ||||||||
\(404\) | −11.0343 | −0.548976 | ||||||||
\(405\) | −1.31370 | −0.0652782 | ||||||||
\(406\) | 6.65908 | 0.330484 | ||||||||
\(407\) | −16.5907 | −0.822369 | ||||||||
\(408\) | 8.24440 | 0.408159 | ||||||||
\(409\) | −2.67330 | −0.132186 | −0.0660931 | − | 0.997813i | \(-0.521053\pi\) | ||||
−0.0660931 | + | 0.997813i | \(0.521053\pi\) | |||||||
\(410\) | 11.0193 | 0.544202 | ||||||||
\(411\) | −6.48948 | −0.320102 | ||||||||
\(412\) | 31.2228 | 1.53824 | ||||||||
\(413\) | −23.1593 | −1.13960 | ||||||||
\(414\) | 2.24431 | 0.110302 | ||||||||
\(415\) | −4.41591 | −0.216768 | ||||||||
\(416\) | 5.92215 | 0.290357 | ||||||||
\(417\) | 18.9540 | 0.928183 | ||||||||
\(418\) | −1.49283 | −0.0730169 | ||||||||
\(419\) | 28.1776 | 1.37657 | 0.688284 | − | 0.725442i | \(-0.258364\pi\) | ||||
0.688284 | + | 0.725442i | \(0.258364\pi\) | |||||||
\(420\) | −11.8375 | −0.577613 | ||||||||
\(421\) | 27.5851 | 1.34441 | 0.672207 | − | 0.740363i | \(-0.265346\pi\) | ||||
0.672207 | + | 0.740363i | \(0.265346\pi\) | |||||||
\(422\) | −15.7111 | −0.764803 | ||||||||
\(423\) | 4.40935 | 0.214390 | ||||||||
\(424\) | 24.9751 | 1.21290 | ||||||||
\(425\) | −11.5993 | −0.562648 | ||||||||
\(426\) | −25.2526 | −1.22349 | ||||||||
\(427\) | −25.7135 | −1.24437 | ||||||||
\(428\) | 22.2053 | 1.07333 | ||||||||
\(429\) | −1.36847 | −0.0660706 | ||||||||
\(430\) | −18.3889 | −0.886790 | ||||||||
\(431\) | 5.24056 | 0.252429 | 0.126215 | − | 0.992003i | \(-0.459717\pi\) | ||||
0.126215 | + | 0.992003i | \(0.459717\pi\) | |||||||
\(432\) | 0.850911 | 0.0409395 | ||||||||
\(433\) | −21.8854 | −1.05174 | −0.525872 | − | 0.850564i | \(-0.676261\pi\) | ||||
−0.525872 | + | 0.850564i | \(0.676261\pi\) | |||||||
\(434\) | −9.09851 | −0.436742 | ||||||||
\(435\) | 1.31370 | 0.0629870 | ||||||||
\(436\) | −10.2575 | −0.491247 | ||||||||
\(437\) | −0.438527 | −0.0209776 | ||||||||
\(438\) | −6.46958 | −0.309129 | ||||||||
\(439\) | −13.9271 | −0.664702 | −0.332351 | − | 0.943156i | \(-0.607842\pi\) | ||||
−0.332351 | + | 0.943156i | \(0.607842\pi\) | |||||||
\(440\) | 4.63726 | 0.221072 | ||||||||
\(441\) | 1.80364 | 0.0858875 | ||||||||
\(442\) | −7.17320 | −0.341194 | ||||||||
\(443\) | −27.5227 | −1.30764 | −0.653821 | − | 0.756649i | \(-0.726835\pi\) | ||||
−0.653821 | + | 0.756649i | \(0.726835\pi\) | |||||||
\(444\) | 33.2174 | 1.57643 | ||||||||
\(445\) | 9.82640 | 0.465816 | ||||||||
\(446\) | −43.3613 | −2.05322 | ||||||||
\(447\) | −22.8616 | −1.08132 | ||||||||
\(448\) | 38.6614 | 1.82658 | ||||||||
\(449\) | 35.1874 | 1.66060 | 0.830298 | − | 0.557320i | \(-0.188170\pi\) | ||||
0.830298 | + | 0.557320i | \(0.188170\pi\) | |||||||
\(450\) | 7.34832 | 0.346403 | ||||||||
\(451\) | 5.66900 | 0.266943 | ||||||||
\(452\) | −6.13771 | −0.288694 | ||||||||
\(453\) | −16.8032 | −0.789484 | ||||||||
\(454\) | 9.76336 | 0.458217 | ||||||||
\(455\) | 3.51666 | 0.164864 | ||||||||
\(456\) | 1.02054 | 0.0477911 | ||||||||
\(457\) | −18.3507 | −0.858409 | −0.429205 | − | 0.903207i | \(-0.641206\pi\) | ||||
−0.429205 | + | 0.903207i | \(0.641206\pi\) | |||||||
\(458\) | −32.0242 | −1.49639 | ||||||||
\(459\) | −3.54263 | −0.165356 | ||||||||
\(460\) | 3.98961 | 0.186016 | ||||||||
\(461\) | −24.7369 | −1.15211 | −0.576056 | − | 0.817410i | \(-0.695409\pi\) | ||||
−0.576056 | + | 0.817410i | \(0.695409\pi\) | |||||||
\(462\) | −10.1006 | −0.469922 | ||||||||
\(463\) | 12.6364 | 0.587264 | 0.293632 | − | 0.955919i | \(-0.405136\pi\) | ||||
0.293632 | + | 0.955919i | \(0.405136\pi\) | |||||||
\(464\) | −0.850911 | −0.0395026 | ||||||||
\(465\) | −1.79495 | −0.0832386 | ||||||||
\(466\) | −2.47107 | −0.114470 | ||||||||
\(467\) | −20.5427 | −0.950603 | −0.475301 | − | 0.879823i | \(-0.657661\pi\) | ||||
−0.475301 | + | 0.879823i | \(0.657661\pi\) | |||||||
\(468\) | 2.73993 | 0.126653 | ||||||||
\(469\) | −3.04424 | −0.140570 | ||||||||
\(470\) | 13.0003 | 0.599659 | ||||||||
\(471\) | −4.66486 | −0.214945 | ||||||||
\(472\) | −18.1647 | −0.836097 | ||||||||
\(473\) | −9.46039 | −0.434989 | ||||||||
\(474\) | 36.2534 | 1.66517 | ||||||||
\(475\) | −1.43582 | −0.0658801 | ||||||||
\(476\) | −31.9222 | −1.46315 | ||||||||
\(477\) | −10.7318 | −0.491376 | ||||||||
\(478\) | −8.02570 | −0.367087 | ||||||||
\(479\) | −14.3319 | −0.654842 | −0.327421 | − | 0.944879i | \(-0.606179\pi\) | ||||
−0.327421 | + | 0.944879i | \(0.606179\pi\) | |||||||
\(480\) | 8.62324 | 0.393595 | ||||||||
\(481\) | −9.86814 | −0.449948 | ||||||||
\(482\) | −53.4553 | −2.43482 | ||||||||
\(483\) | −2.96709 | −0.135007 | ||||||||
\(484\) | −26.4191 | −1.20087 | ||||||||
\(485\) | 20.5207 | 0.931797 | ||||||||
\(486\) | 2.24431 | 0.101804 | ||||||||
\(487\) | −6.62111 | −0.300031 | −0.150016 | − | 0.988684i | \(-0.547932\pi\) | ||||
−0.150016 | + | 0.988684i | \(0.547932\pi\) | |||||||
\(488\) | −20.1680 | −0.912964 | ||||||||
\(489\) | 6.11817 | 0.276673 | ||||||||
\(490\) | 5.31775 | 0.240231 | ||||||||
\(491\) | −16.2298 | −0.732440 | −0.366220 | − | 0.930528i | \(-0.619348\pi\) | ||||
−0.366220 | + | 0.930528i | \(0.619348\pi\) | |||||||
\(492\) | −11.3503 | −0.511713 | ||||||||
\(493\) | 3.54263 | 0.159552 | ||||||||
\(494\) | −0.887939 | −0.0399503 | ||||||||
\(495\) | −1.99264 | −0.0895624 | ||||||||
\(496\) | 1.16263 | 0.0522035 | ||||||||
\(497\) | 33.3852 | 1.49753 | ||||||||
\(498\) | 7.54410 | 0.338059 | ||||||||
\(499\) | −11.1031 | −0.497043 | −0.248521 | − | 0.968626i | \(-0.579945\pi\) | ||||
−0.248521 | + | 0.968626i | \(0.579945\pi\) | |||||||
\(500\) | 33.0108 | 1.47629 | ||||||||
\(501\) | −5.11459 | −0.228503 | ||||||||
\(502\) | 24.6937 | 1.10213 | ||||||||
\(503\) | 7.73894 | 0.345062 | 0.172531 | − | 0.985004i | \(-0.444805\pi\) | ||||
0.172531 | + | 0.985004i | \(0.444805\pi\) | |||||||
\(504\) | 6.90501 | 0.307573 | ||||||||
\(505\) | 4.77314 | 0.212402 | ||||||||
\(506\) | 3.40420 | 0.151335 | ||||||||
\(507\) | 12.1860 | 0.541201 | ||||||||
\(508\) | 7.34227 | 0.325761 | ||||||||
\(509\) | 12.1628 | 0.539105 | 0.269553 | − | 0.962986i | \(-0.413124\pi\) | ||||
0.269553 | + | 0.962986i | \(0.413124\pi\) | |||||||
\(510\) | −10.4449 | −0.462508 | ||||||||
\(511\) | 8.55312 | 0.378368 | ||||||||
\(512\) | −9.54594 | −0.421875 | ||||||||
\(513\) | −0.438527 | −0.0193614 | ||||||||
\(514\) | −50.6191 | −2.23271 | ||||||||
\(515\) | −13.5062 | −0.595152 | ||||||||
\(516\) | 18.9414 | 0.833848 | ||||||||
\(517\) | 6.68817 | 0.294146 | ||||||||
\(518\) | −72.8359 | −3.20022 | ||||||||
\(519\) | −10.5173 | −0.461658 | ||||||||
\(520\) | 2.75824 | 0.120957 | ||||||||
\(521\) | −19.3594 | −0.848152 | −0.424076 | − | 0.905627i | \(-0.639401\pi\) | ||||
−0.424076 | + | 0.905627i | \(0.639401\pi\) | |||||||
\(522\) | −2.24431 | −0.0982308 | ||||||||
\(523\) | 4.25739 | 0.186163 | 0.0930814 | − | 0.995659i | \(-0.470328\pi\) | ||||
0.0930814 | + | 0.995659i | \(0.470328\pi\) | |||||||
\(524\) | 12.1181 | 0.529383 | ||||||||
\(525\) | −9.71485 | −0.423991 | ||||||||
\(526\) | −22.4709 | −0.979777 | ||||||||
\(527\) | −4.84041 | −0.210852 | ||||||||
\(528\) | 1.29068 | 0.0561694 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −31.6411 | −1.37440 | ||||||||
\(531\) | 7.80539 | 0.338725 | ||||||||
\(532\) | −3.95150 | −0.171319 | ||||||||
\(533\) | 3.37192 | 0.146054 | ||||||||
\(534\) | −16.7873 | −0.726459 | ||||||||
\(535\) | −9.60543 | −0.415279 | ||||||||
\(536\) | −2.38770 | −0.103133 | ||||||||
\(537\) | −10.1812 | −0.439353 | ||||||||
\(538\) | 29.1495 | 1.25672 | ||||||||
\(539\) | 2.73579 | 0.117839 | ||||||||
\(540\) | 3.98961 | 0.171685 | ||||||||
\(541\) | 16.3992 | 0.705057 | 0.352528 | − | 0.935801i | \(-0.385322\pi\) | ||||
0.352528 | + | 0.935801i | \(0.385322\pi\) | |||||||
\(542\) | −34.8731 | −1.49793 | ||||||||
\(543\) | −21.6445 | −0.928855 | ||||||||
\(544\) | 23.2542 | 0.997016 | ||||||||
\(545\) | 4.43714 | 0.190066 | ||||||||
\(546\) | −6.00784 | −0.257112 | ||||||||
\(547\) | −16.7707 | −0.717065 | −0.358533 | − | 0.933517i | \(-0.616723\pi\) | ||||
−0.358533 | + | 0.933517i | \(0.616723\pi\) | |||||||
\(548\) | 19.7081 | 0.841889 | ||||||||
\(549\) | 8.66624 | 0.369866 | ||||||||
\(550\) | 11.1460 | 0.475269 | ||||||||
\(551\) | 0.438527 | 0.0186819 | ||||||||
\(552\) | −2.32720 | −0.0990520 | ||||||||
\(553\) | −47.9288 | −2.03814 | ||||||||
\(554\) | −39.4286 | −1.67516 | ||||||||
\(555\) | −14.3690 | −0.609930 | ||||||||
\(556\) | −57.5621 | −2.44118 | ||||||||
\(557\) | 36.1688 | 1.53252 | 0.766261 | − | 0.642530i | \(-0.222115\pi\) | ||||
0.766261 | + | 0.642530i | \(0.222115\pi\) | |||||||
\(558\) | 3.06647 | 0.129814 | ||||||||
\(559\) | −5.62705 | −0.237999 | ||||||||
\(560\) | −3.31674 | −0.140158 | ||||||||
\(561\) | −5.37352 | −0.226870 | ||||||||
\(562\) | 29.4837 | 1.24370 | ||||||||
\(563\) | 15.4439 | 0.650883 | 0.325441 | − | 0.945562i | \(-0.394487\pi\) | ||||
0.325441 | + | 0.945562i | \(0.394487\pi\) | |||||||
\(564\) | −13.3909 | −0.563859 | ||||||||
\(565\) | 2.65501 | 0.111697 | ||||||||
\(566\) | 16.4049 | 0.689551 | ||||||||
\(567\) | −2.96709 | −0.124606 | ||||||||
\(568\) | 26.1852 | 1.09871 | ||||||||
\(569\) | −18.1051 | −0.759007 | −0.379503 | − | 0.925190i | \(-0.623905\pi\) | ||||
−0.379503 | + | 0.925190i | \(0.623905\pi\) | |||||||
\(570\) | −1.29293 | −0.0541548 | ||||||||
\(571\) | 40.4246 | 1.69171 | 0.845857 | − | 0.533409i | \(-0.179089\pi\) | ||||
0.845857 | + | 0.533409i | \(0.179089\pi\) | |||||||
\(572\) | 4.15596 | 0.173769 | ||||||||
\(573\) | −17.2119 | −0.719038 | ||||||||
\(574\) | 24.8879 | 1.03880 | ||||||||
\(575\) | 3.27420 | 0.136544 | ||||||||
\(576\) | −13.0301 | −0.542919 | ||||||||
\(577\) | −5.89094 | −0.245243 | −0.122621 | − | 0.992454i | \(-0.539130\pi\) | ||||
−0.122621 | + | 0.992454i | \(0.539130\pi\) | |||||||
\(578\) | 9.98663 | 0.415389 | ||||||||
\(579\) | 7.97678 | 0.331504 | ||||||||
\(580\) | −3.98961 | −0.165660 | ||||||||
\(581\) | −9.97368 | −0.413778 | ||||||||
\(582\) | −35.0574 | −1.45318 | ||||||||
\(583\) | −16.2782 | −0.674174 | ||||||||
\(584\) | 6.70851 | 0.277600 | ||||||||
\(585\) | −1.18522 | −0.0490029 | ||||||||
\(586\) | 17.9720 | 0.742416 | ||||||||
\(587\) | −13.3990 | −0.553036 | −0.276518 | − | 0.961009i | \(-0.589181\pi\) | ||||
−0.276518 | + | 0.961009i | \(0.589181\pi\) | |||||||
\(588\) | −5.47752 | −0.225889 | ||||||||
\(589\) | −0.599173 | −0.0246885 | ||||||||
\(590\) | 23.0130 | 0.947430 | ||||||||
\(591\) | −5.13962 | −0.211416 | ||||||||
\(592\) | 9.30713 | 0.382521 | ||||||||
\(593\) | 7.11166 | 0.292041 | 0.146020 | − | 0.989282i | \(-0.453353\pi\) | ||||
0.146020 | + | 0.989282i | \(0.453353\pi\) | |||||||
\(594\) | 3.40420 | 0.139676 | ||||||||
\(595\) | 13.8087 | 0.566101 | ||||||||
\(596\) | 69.4291 | 2.84393 | ||||||||
\(597\) | −21.9501 | −0.898356 | ||||||||
\(598\) | 2.02482 | 0.0828011 | ||||||||
\(599\) | 0.867674 | 0.0354522 | 0.0177261 | − | 0.999843i | \(-0.494357\pi\) | ||||
0.0177261 | + | 0.999843i | \(0.494357\pi\) | |||||||
\(600\) | −7.61970 | −0.311073 | ||||||||
\(601\) | 2.04317 | 0.0833424 | 0.0416712 | − | 0.999131i | \(-0.486732\pi\) | ||||
0.0416712 | + | 0.999131i | \(0.486732\pi\) | |||||||
\(602\) | −41.5327 | −1.69275 | ||||||||
\(603\) | 1.02600 | 0.0417819 | ||||||||
\(604\) | 51.0302 | 2.07639 | ||||||||
\(605\) | 11.4282 | 0.464623 | ||||||||
\(606\) | −8.15440 | −0.331250 | ||||||||
\(607\) | 45.7094 | 1.85529 | 0.927644 | − | 0.373465i | \(-0.121830\pi\) | ||||
0.927644 | + | 0.373465i | \(0.121830\pi\) | |||||||
\(608\) | 2.87853 | 0.116740 | ||||||||
\(609\) | 2.96709 | 0.120233 | ||||||||
\(610\) | 25.5511 | 1.03453 | ||||||||
\(611\) | 3.97813 | 0.160938 | ||||||||
\(612\) | 10.7587 | 0.434896 | ||||||||
\(613\) | 21.0161 | 0.848831 | 0.424416 | − | 0.905467i | \(-0.360480\pi\) | ||||
0.424416 | + | 0.905467i | \(0.360480\pi\) | |||||||
\(614\) | 68.5179 | 2.76516 | ||||||||
\(615\) | 4.90986 | 0.197985 | ||||||||
\(616\) | 10.4736 | 0.421994 | ||||||||
\(617\) | −16.5056 | −0.664489 | −0.332244 | − | 0.943193i | \(-0.607806\pi\) | ||||
−0.332244 | + | 0.943193i | \(0.607806\pi\) | |||||||
\(618\) | 23.0738 | 0.928165 | ||||||||
\(619\) | 30.3608 | 1.22030 | 0.610152 | − | 0.792284i | \(-0.291108\pi\) | ||||
0.610152 | + | 0.792284i | \(0.291108\pi\) | |||||||
\(620\) | 5.45113 | 0.218923 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −60.2182 | −2.41453 | ||||||||
\(623\) | 22.1937 | 0.889173 | ||||||||
\(624\) | 0.767694 | 0.0307324 | ||||||||
\(625\) | 2.09137 | 0.0836548 | ||||||||
\(626\) | −17.2238 | −0.688400 | ||||||||
\(627\) | −0.665164 | −0.0265641 | ||||||||
\(628\) | 14.1669 | 0.565319 | ||||||||
\(629\) | −38.7487 | −1.54501 | ||||||||
\(630\) | −8.74801 | −0.348529 | ||||||||
\(631\) | 0.182379 | 0.00726040 | 0.00363020 | − | 0.999993i | \(-0.498844\pi\) | ||||
0.00363020 | + | 0.999993i | \(0.498844\pi\) | |||||||
\(632\) | −37.5923 | −1.49534 | ||||||||
\(633\) | −7.00040 | −0.278241 | ||||||||
\(634\) | 25.3915 | 1.00842 | ||||||||
\(635\) | −3.17608 | −0.126039 | ||||||||
\(636\) | 32.5918 | 1.29235 | ||||||||
\(637\) | 1.62725 | 0.0644738 | ||||||||
\(638\) | −3.40420 | −0.134774 | ||||||||
\(639\) | −11.2518 | −0.445116 | ||||||||
\(640\) | −21.1706 | −0.836843 | ||||||||
\(641\) | −7.86588 | −0.310684 | −0.155342 | − | 0.987861i | \(-0.549648\pi\) | ||||
−0.155342 | + | 0.987861i | \(0.549648\pi\) | |||||||
\(642\) | 16.4098 | 0.647645 | ||||||||
\(643\) | 11.3455 | 0.447423 | 0.223711 | − | 0.974655i | \(-0.428183\pi\) | ||||
0.223711 | + | 0.974655i | \(0.428183\pi\) | |||||||
\(644\) | 9.01086 | 0.355077 | ||||||||
\(645\) | −8.19355 | −0.322621 | ||||||||
\(646\) | −3.48663 | −0.137179 | ||||||||
\(647\) | 22.3414 | 0.878330 | 0.439165 | − | 0.898406i | \(-0.355274\pi\) | ||||
0.439165 | + | 0.898406i | \(0.355274\pi\) | |||||||
\(648\) | −2.32720 | −0.0914209 | ||||||||
\(649\) | 11.8393 | 0.464735 | ||||||||
\(650\) | 6.62967 | 0.260037 | ||||||||
\(651\) | −4.05403 | −0.158890 | ||||||||
\(652\) | −18.5804 | −0.727667 | ||||||||
\(653\) | 39.1961 | 1.53386 | 0.766931 | − | 0.641729i | \(-0.221783\pi\) | ||||
0.766931 | + | 0.641729i | \(0.221783\pi\) | |||||||
\(654\) | −7.58038 | −0.296416 | ||||||||
\(655\) | −5.24199 | −0.204821 | ||||||||
\(656\) | −3.18023 | −0.124167 | ||||||||
\(657\) | −2.88266 | −0.112463 | ||||||||
\(658\) | 29.3622 | 1.14466 | ||||||||
\(659\) | −15.0318 | −0.585557 | −0.292778 | − | 0.956180i | \(-0.594580\pi\) | ||||
−0.292778 | + | 0.956180i | \(0.594580\pi\) | |||||||
\(660\) | 6.05150 | 0.235554 | ||||||||
\(661\) | −39.2171 | −1.52537 | −0.762685 | − | 0.646770i | \(-0.776119\pi\) | ||||
−0.762685 | + | 0.646770i | \(0.776119\pi\) | |||||||
\(662\) | −77.5187 | −3.01285 | ||||||||
\(663\) | −3.19617 | −0.124129 | ||||||||
\(664\) | −7.82271 | −0.303580 | ||||||||
\(665\) | 1.70932 | 0.0662845 | ||||||||
\(666\) | 24.5479 | 0.951212 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 15.5327 | 0.600976 | ||||||||
\(669\) | −19.3205 | −0.746975 | ||||||||
\(670\) | 3.02500 | 0.116866 | ||||||||
\(671\) | 13.1451 | 0.507460 | ||||||||
\(672\) | 19.4763 | 0.751314 | ||||||||
\(673\) | 11.9758 | 0.461635 | 0.230818 | − | 0.972997i | \(-0.425860\pi\) | ||||
0.230818 | + | 0.972997i | \(0.425860\pi\) | |||||||
\(674\) | −50.5941 | −1.94881 | ||||||||
\(675\) | 3.27420 | 0.126024 | ||||||||
\(676\) | −37.0081 | −1.42339 | ||||||||
\(677\) | 22.1732 | 0.852185 | 0.426093 | − | 0.904680i | \(-0.359890\pi\) | ||||
0.426093 | + | 0.904680i | \(0.359890\pi\) | |||||||
\(678\) | −4.53581 | −0.174197 | ||||||||
\(679\) | 46.3477 | 1.77866 | ||||||||
\(680\) | 10.8306 | 0.415336 | ||||||||
\(681\) | 4.35027 | 0.166703 | ||||||||
\(682\) | 4.65127 | 0.178106 | ||||||||
\(683\) | −3.66223 | −0.140131 | −0.0700657 | − | 0.997542i | \(-0.522321\pi\) | ||||
−0.0700657 | + | 0.997542i | \(0.522321\pi\) | |||||||
\(684\) | 1.33178 | 0.0509217 | ||||||||
\(685\) | −8.52522 | −0.325732 | ||||||||
\(686\) | −34.6030 | −1.32115 | ||||||||
\(687\) | −14.2691 | −0.544399 | ||||||||
\(688\) | 5.30715 | 0.202333 | ||||||||
\(689\) | −9.68228 | −0.368865 | ||||||||
\(690\) | 2.94835 | 0.112242 | ||||||||
\(691\) | 14.7825 | 0.562354 | 0.281177 | − | 0.959656i | \(-0.409275\pi\) | ||||
0.281177 | + | 0.959656i | \(0.409275\pi\) | |||||||
\(692\) | 31.9403 | 1.21419 | ||||||||
\(693\) | −4.50053 | −0.170961 | ||||||||
\(694\) | −35.3840 | −1.34316 | ||||||||
\(695\) | 24.8999 | 0.944505 | ||||||||
\(696\) | 2.32720 | 0.0882121 | ||||||||
\(697\) | 13.2404 | 0.501515 | ||||||||
\(698\) | 41.9135 | 1.58645 | ||||||||
\(699\) | −1.10104 | −0.0416451 | ||||||||
\(700\) | 29.5033 | 1.11512 | ||||||||
\(701\) | 19.8395 | 0.749328 | 0.374664 | − | 0.927161i | \(-0.377758\pi\) | ||||
0.374664 | + | 0.927161i | \(0.377758\pi\) | |||||||
\(702\) | 2.02482 | 0.0764220 | ||||||||
\(703\) | −4.79653 | −0.180905 | ||||||||
\(704\) | −19.7642 | −0.744891 | ||||||||
\(705\) | 5.79256 | 0.218160 | ||||||||
\(706\) | 49.6335 | 1.86798 | ||||||||
\(707\) | 10.7805 | 0.405443 | ||||||||
\(708\) | −23.7044 | −0.890867 | ||||||||
\(709\) | 17.7266 | 0.665735 | 0.332868 | − | 0.942974i | \(-0.391984\pi\) | ||||
0.332868 | + | 0.942974i | \(0.391984\pi\) | |||||||
\(710\) | −33.1743 | −1.24501 | ||||||||
\(711\) | 16.1535 | 0.605802 | ||||||||
\(712\) | 17.4073 | 0.652367 | ||||||||
\(713\) | 1.36633 | 0.0511695 | ||||||||
\(714\) | −23.5907 | −0.882859 | ||||||||
\(715\) | −1.79776 | −0.0672325 | ||||||||
\(716\) | 30.9197 | 1.15552 | ||||||||
\(717\) | −3.57602 | −0.133549 | ||||||||
\(718\) | 71.2367 | 2.65853 | ||||||||
\(719\) | 18.0624 | 0.673612 | 0.336806 | − | 0.941574i | \(-0.390653\pi\) | ||||
0.336806 | + | 0.941574i | \(0.390653\pi\) | |||||||
\(720\) | 1.11784 | 0.0416595 | ||||||||
\(721\) | −30.5048 | −1.13606 | ||||||||
\(722\) | 42.2103 | 1.57091 | ||||||||
\(723\) | −23.8181 | −0.885805 | ||||||||
\(724\) | 65.7329 | 2.44294 | ||||||||
\(725\) | −3.27420 | −0.121601 | ||||||||
\(726\) | −19.5239 | −0.724599 | ||||||||
\(727\) | −20.3044 | −0.753048 | −0.376524 | − | 0.926407i | \(-0.622881\pi\) | ||||
−0.376524 | + | 0.926407i | \(0.622881\pi\) | |||||||
\(728\) | 6.22971 | 0.230888 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.49908 | −0.314565 | ||||||||
\(731\) | −22.0954 | −0.817229 | ||||||||
\(732\) | −26.3188 | −0.972770 | ||||||||
\(733\) | −6.63182 | −0.244952 | −0.122476 | − | 0.992471i | \(-0.539083\pi\) | ||||
−0.122476 | + | 0.992471i | \(0.539083\pi\) | |||||||
\(734\) | −17.6928 | −0.653054 | ||||||||
\(735\) | 2.36943 | 0.0873979 | ||||||||
\(736\) | −6.56410 | −0.241956 | ||||||||
\(737\) | 1.55625 | 0.0573253 | ||||||||
\(738\) | −8.38797 | −0.308765 | ||||||||
\(739\) | 26.4937 | 0.974588 | 0.487294 | − | 0.873238i | \(-0.337984\pi\) | ||||
0.487294 | + | 0.873238i | \(0.337984\pi\) | |||||||
\(740\) | 43.6377 | 1.60415 | ||||||||
\(741\) | −0.395640 | −0.0145342 | ||||||||
\(742\) | −71.4641 | −2.62353 | ||||||||
\(743\) | −41.8653 | −1.53589 | −0.767945 | − | 0.640516i | \(-0.778721\pi\) | ||||
−0.767945 | + | 0.640516i | \(0.778721\pi\) | |||||||
\(744\) | −3.17972 | −0.116574 | ||||||||
\(745\) | −30.0332 | −1.10033 | ||||||||
\(746\) | 43.3935 | 1.58875 | ||||||||
\(747\) | 3.36143 | 0.122988 | ||||||||
\(748\) | 16.3190 | 0.596682 | ||||||||
\(749\) | −21.6946 | −0.792705 | ||||||||
\(750\) | 24.3952 | 0.890787 | ||||||||
\(751\) | −13.9711 | −0.509811 | −0.254905 | − | 0.966966i | \(-0.582044\pi\) | ||||
−0.254905 | + | 0.966966i | \(0.582044\pi\) | |||||||
\(752\) | −3.75197 | −0.136820 | ||||||||
\(753\) | 11.0028 | 0.400964 | ||||||||
\(754\) | −2.02482 | −0.0737397 | ||||||||
\(755\) | −22.0744 | −0.803368 | ||||||||
\(756\) | 9.01086 | 0.327722 | ||||||||
\(757\) | 1.79857 | 0.0653703 | 0.0326852 | − | 0.999466i | \(-0.489594\pi\) | ||||
0.0326852 | + | 0.999466i | \(0.489594\pi\) | |||||||
\(758\) | 30.8643 | 1.12104 | ||||||||
\(759\) | 1.51682 | 0.0550569 | ||||||||
\(760\) | 1.34068 | 0.0486315 | ||||||||
\(761\) | −22.2173 | −0.805378 | −0.402689 | − | 0.915337i | \(-0.631924\pi\) | ||||
−0.402689 | + | 0.915337i | \(0.631924\pi\) | |||||||
\(762\) | 5.42599 | 0.196563 | ||||||||
\(763\) | 10.0216 | 0.362808 | ||||||||
\(764\) | 52.2714 | 1.89111 | ||||||||
\(765\) | −4.65395 | −0.168264 | ||||||||
\(766\) | −21.9578 | −0.793369 | ||||||||
\(767\) | 7.04204 | 0.254273 | ||||||||
\(768\) | 10.1076 | 0.364728 | ||||||||
\(769\) | −41.3008 | −1.48934 | −0.744672 | − | 0.667431i | \(-0.767394\pi\) | ||||
−0.744672 | + | 0.667431i | \(0.767394\pi\) | |||||||
\(770\) | −13.2691 | −0.478186 | ||||||||
\(771\) | −22.5544 | −0.812278 | ||||||||
\(772\) | −24.2249 | −0.871874 | ||||||||
\(773\) | −19.5525 | −0.703254 | −0.351627 | − | 0.936140i | \(-0.614371\pi\) | ||||
−0.351627 | + | 0.936140i | \(0.614371\pi\) | |||||||
\(774\) | 13.9978 | 0.503140 | ||||||||
\(775\) | 4.47364 | 0.160698 | ||||||||
\(776\) | 36.3521 | 1.30497 | ||||||||
\(777\) | −32.4536 | −1.16426 | ||||||||
\(778\) | −45.6148 | −1.63537 | ||||||||
\(779\) | 1.63897 | 0.0587221 | ||||||||
\(780\) | 3.59943 | 0.128880 | ||||||||
\(781\) | −17.0670 | −0.610704 | ||||||||
\(782\) | 7.95077 | 0.284319 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | −1.53474 | −0.0548120 | ||||||||
\(785\) | −6.12821 | −0.218725 | ||||||||
\(786\) | 8.95538 | 0.319428 | ||||||||
\(787\) | 13.6255 | 0.485695 | 0.242848 | − | 0.970064i | \(-0.421919\pi\) | ||||
0.242848 | + | 0.970064i | \(0.421919\pi\) | |||||||
\(788\) | 15.6087 | 0.556036 | ||||||||
\(789\) | −10.0124 | −0.356450 | ||||||||
\(790\) | 47.6260 | 1.69446 | ||||||||
\(791\) | 5.99656 | 0.213213 | ||||||||
\(792\) | −3.52993 | −0.125430 | ||||||||
\(793\) | 7.81870 | 0.277650 | ||||||||
\(794\) | 33.8523 | 1.20137 | ||||||||
\(795\) | −14.0984 | −0.500018 | ||||||||
\(796\) | 66.6608 | 2.36273 | ||||||||
\(797\) | 14.3368 | 0.507836 | 0.253918 | − | 0.967226i | \(-0.418281\pi\) | ||||
0.253918 | + | 0.967226i | \(0.418281\pi\) | |||||||
\(798\) | −2.92018 | −0.103373 | ||||||||
\(799\) | 15.6207 | 0.552621 | ||||||||
\(800\) | −21.4922 | −0.759863 | ||||||||
\(801\) | −7.47996 | −0.264291 | ||||||||
\(802\) | −71.2943 | −2.51749 | ||||||||
\(803\) | −4.37246 | −0.154301 | ||||||||
\(804\) | −3.11589 | −0.109889 | ||||||||
\(805\) | −3.89786 | −0.137382 | ||||||||
\(806\) | 2.76658 | 0.0974486 | ||||||||
\(807\) | 12.9882 | 0.457205 | ||||||||
\(808\) | 8.45555 | 0.297465 | ||||||||
\(809\) | −45.8588 | −1.61231 | −0.806155 | − | 0.591705i | \(-0.798455\pi\) | ||||
−0.806155 | + | 0.591705i | \(0.798455\pi\) | |||||||
\(810\) | 2.94835 | 0.103594 | ||||||||
\(811\) | 13.4624 | 0.472728 | 0.236364 | − | 0.971665i | \(-0.424044\pi\) | ||||
0.236364 | + | 0.971665i | \(0.424044\pi\) | |||||||
\(812\) | −9.01086 | −0.316219 | ||||||||
\(813\) | −15.5385 | −0.544958 | ||||||||
\(814\) | 37.2346 | 1.30507 | ||||||||
\(815\) | 8.03742 | 0.281539 | ||||||||
\(816\) | 3.01447 | 0.105527 | ||||||||
\(817\) | −2.73510 | −0.0956889 | ||||||||
\(818\) | 5.99972 | 0.209775 | ||||||||
\(819\) | −2.67692 | −0.0935391 | ||||||||
\(820\) | −14.9109 | −0.520712 | ||||||||
\(821\) | 48.9229 | 1.70742 | 0.853711 | − | 0.520748i | \(-0.174347\pi\) | ||||
0.853711 | + | 0.520748i | \(0.174347\pi\) | |||||||
\(822\) | 14.5644 | 0.507992 | ||||||||
\(823\) | 6.18455 | 0.215580 | 0.107790 | − | 0.994174i | \(-0.465623\pi\) | ||||
0.107790 | + | 0.994174i | \(0.465623\pi\) | |||||||
\(824\) | −23.9260 | −0.833500 | ||||||||
\(825\) | 4.96635 | 0.172906 | ||||||||
\(826\) | 51.9767 | 1.80850 | ||||||||
\(827\) | −21.6665 | −0.753417 | −0.376709 | − | 0.926332i | \(-0.622944\pi\) | ||||
−0.376709 | + | 0.926332i | \(0.622944\pi\) | |||||||
\(828\) | −3.03693 | −0.105541 | ||||||||
\(829\) | −51.9818 | −1.80540 | −0.902702 | − | 0.430267i | \(-0.858420\pi\) | ||||
−0.902702 | + | 0.430267i | \(0.858420\pi\) | |||||||
\(830\) | 9.91066 | 0.344004 | ||||||||
\(831\) | −17.5683 | −0.609436 | ||||||||
\(832\) | −11.7558 | −0.407557 | ||||||||
\(833\) | 6.38963 | 0.221387 | ||||||||
\(834\) | −42.5387 | −1.47300 | ||||||||
\(835\) | −6.71902 | −0.232521 | ||||||||
\(836\) | 2.02006 | 0.0698652 | ||||||||
\(837\) | 1.36633 | 0.0472273 | ||||||||
\(838\) | −63.2394 | −2.18457 | ||||||||
\(839\) | −29.1361 | −1.00589 | −0.502946 | − | 0.864318i | \(-0.667750\pi\) | ||||
−0.502946 | + | 0.864318i | \(0.667750\pi\) | |||||||
\(840\) | 9.07109 | 0.312982 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −61.9095 | −2.13354 | ||||||||
\(843\) | 13.1371 | 0.452465 | ||||||||
\(844\) | 21.2597 | 0.731790 | ||||||||
\(845\) | 16.0088 | 0.550718 | ||||||||
\(846\) | −9.89596 | −0.340230 | ||||||||
\(847\) | 25.8115 | 0.886895 | ||||||||
\(848\) | 9.13183 | 0.313588 | ||||||||
\(849\) | 7.30957 | 0.250864 | ||||||||
\(850\) | 26.0324 | 0.892904 | ||||||||
\(851\) | 10.9378 | 0.374944 | ||||||||
\(852\) | 34.1710 | 1.17068 | ||||||||
\(853\) | −6.26515 | −0.214515 | −0.107257 | − | 0.994231i | \(-0.534207\pi\) | ||||
−0.107257 | + | 0.994231i | \(0.534207\pi\) | |||||||
\(854\) | 57.7092 | 1.97477 | ||||||||
\(855\) | −0.576092 | −0.0197019 | ||||||||
\(856\) | −17.0159 | −0.581591 | ||||||||
\(857\) | 32.0046 | 1.09326 | 0.546628 | − | 0.837376i | \(-0.315911\pi\) | ||||
0.546628 | + | 0.837376i | \(0.315911\pi\) | |||||||
\(858\) | 3.07128 | 0.104852 | ||||||||
\(859\) | −2.27931 | −0.0777690 | −0.0388845 | − | 0.999244i | \(-0.512380\pi\) | ||||
−0.0388845 | + | 0.999244i | \(0.512380\pi\) | |||||||
\(860\) | 24.8832 | 0.848511 | ||||||||
\(861\) | 11.0893 | 0.377923 | ||||||||
\(862\) | −11.7615 | −0.400597 | ||||||||
\(863\) | 23.3854 | 0.796048 | 0.398024 | − | 0.917375i | \(-0.369696\pi\) | ||||
0.398024 | + | 0.917375i | \(0.369696\pi\) | |||||||
\(864\) | −6.56410 | −0.223315 | ||||||||
\(865\) | −13.8165 | −0.469776 | ||||||||
\(866\) | 49.1176 | 1.66908 | ||||||||
\(867\) | 4.44975 | 0.151122 | ||||||||
\(868\) | 12.3118 | 0.417890 | ||||||||
\(869\) | 24.5018 | 0.831167 | ||||||||
\(870\) | −2.94835 | −0.0999583 | ||||||||
\(871\) | 0.925659 | 0.0313648 | ||||||||
\(872\) | 7.86033 | 0.266185 | ||||||||
\(873\) | −15.6206 | −0.528676 | ||||||||
\(874\) | 0.984190 | 0.0332907 | ||||||||
\(875\) | −32.2517 | −1.09031 | ||||||||
\(876\) | 8.75444 | 0.295785 | ||||||||
\(877\) | −37.0607 | −1.25145 | −0.625725 | − | 0.780044i | \(-0.715197\pi\) | ||||
−0.625725 | + | 0.780044i | \(0.715197\pi\) | |||||||
\(878\) | 31.2566 | 1.05486 | ||||||||
\(879\) | 8.00780 | 0.270096 | ||||||||
\(880\) | 1.69556 | 0.0571572 | ||||||||
\(881\) | 20.0136 | 0.674274 | 0.337137 | − | 0.941456i | \(-0.390541\pi\) | ||||
0.337137 | + | 0.941456i | \(0.390541\pi\) | |||||||
\(882\) | −4.04792 | −0.136301 | ||||||||
\(883\) | 32.4866 | 1.09326 | 0.546631 | − | 0.837374i | \(-0.315910\pi\) | ||||
0.546631 | + | 0.837374i | \(0.315910\pi\) | |||||||
\(884\) | 9.70655 | 0.326467 | ||||||||
\(885\) | 10.2539 | 0.344682 | ||||||||
\(886\) | 61.7695 | 2.07519 | ||||||||
\(887\) | 19.3042 | 0.648170 | 0.324085 | − | 0.946028i | \(-0.394944\pi\) | ||||
0.324085 | + | 0.946028i | \(0.394944\pi\) | |||||||
\(888\) | −25.4545 | −0.854196 | ||||||||
\(889\) | −7.17343 | −0.240589 | ||||||||
\(890\) | −22.0535 | −0.739235 | ||||||||
\(891\) | 1.51682 | 0.0508152 | ||||||||
\(892\) | 58.6751 | 1.96459 | ||||||||
\(893\) | 1.93362 | 0.0647061 | ||||||||
\(894\) | 51.3085 | 1.71601 | ||||||||
\(895\) | −13.3751 | −0.447079 | ||||||||
\(896\) | −47.8156 | −1.59741 | ||||||||
\(897\) | 0.902202 | 0.0301237 | ||||||||
\(898\) | −78.9715 | −2.63531 | ||||||||
\(899\) | −1.36633 | −0.0455697 | ||||||||
\(900\) | −9.94352 | −0.331451 | ||||||||
\(901\) | −38.0189 | −1.26659 | ||||||||
\(902\) | −12.7230 | −0.423630 | ||||||||
\(903\) | −18.5058 | −0.615834 | ||||||||
\(904\) | 4.70332 | 0.156430 | ||||||||
\(905\) | −28.4343 | −0.945189 | ||||||||
\(906\) | 37.7117 | 1.25289 | ||||||||
\(907\) | −10.6991 | −0.355259 | −0.177629 | − | 0.984097i | \(-0.556843\pi\) | ||||
−0.177629 | + | 0.984097i | \(0.556843\pi\) | |||||||
\(908\) | −13.2115 | −0.438438 | ||||||||
\(909\) | −3.63336 | −0.120511 | ||||||||
\(910\) | −7.89248 | −0.261633 | ||||||||
\(911\) | 30.1038 | 0.997384 | 0.498692 | − | 0.866779i | \(-0.333814\pi\) | ||||
0.498692 | + | 0.866779i | \(0.333814\pi\) | |||||||
\(912\) | 0.373147 | 0.0123561 | ||||||||
\(913\) | 5.09867 | 0.168741 | ||||||||
\(914\) | 41.1847 | 1.36227 | ||||||||
\(915\) | 11.3848 | 0.376370 | ||||||||
\(916\) | 43.3342 | 1.43180 | ||||||||
\(917\) | −11.8395 | −0.390973 | ||||||||
\(918\) | 7.95077 | 0.262414 | ||||||||
\(919\) | 7.97055 | 0.262924 | 0.131462 | − | 0.991321i | \(-0.458033\pi\) | ||||
0.131462 | + | 0.991321i | \(0.458033\pi\) | |||||||
\(920\) | −3.05723 | −0.100794 | ||||||||
\(921\) | 30.5296 | 1.00598 | ||||||||
\(922\) | 55.5173 | 1.82837 | ||||||||
\(923\) | −10.1514 | −0.334138 | ||||||||
\(924\) | 13.6678 | 0.449638 | ||||||||
\(925\) | 35.8126 | 1.17751 | ||||||||
\(926\) | −28.3600 | −0.931969 | ||||||||
\(927\) | 10.2810 | 0.337673 | ||||||||
\(928\) | 6.56410 | 0.215477 | ||||||||
\(929\) | 45.5813 | 1.49548 | 0.747738 | − | 0.663994i | \(-0.231140\pi\) | ||||
0.747738 | + | 0.663994i | \(0.231140\pi\) | |||||||
\(930\) | 4.02842 | 0.132097 | ||||||||
\(931\) | 0.790944 | 0.0259221 | ||||||||
\(932\) | 3.34378 | 0.109529 | ||||||||
\(933\) | −26.8315 | −0.878424 | ||||||||
\(934\) | 46.1042 | 1.50858 | ||||||||
\(935\) | −7.05918 | −0.230860 | ||||||||
\(936\) | −2.09960 | −0.0686276 | ||||||||
\(937\) | 42.9955 | 1.40460 | 0.702301 | − | 0.711880i | \(-0.252156\pi\) | ||||
0.702301 | + | 0.711880i | \(0.252156\pi\) | |||||||
\(938\) | 6.83221 | 0.223080 | ||||||||
\(939\) | −7.67441 | −0.250445 | ||||||||
\(940\) | −17.5916 | −0.573775 | ||||||||
\(941\) | −22.3893 | −0.729870 | −0.364935 | − | 0.931033i | \(-0.618909\pi\) | ||||
−0.364935 | + | 0.931033i | \(0.618909\pi\) | |||||||
\(942\) | 10.4694 | 0.341111 | ||||||||
\(943\) | −3.73744 | −0.121708 | ||||||||
\(944\) | −6.64170 | −0.216169 | ||||||||
\(945\) | −3.89786 | −0.126797 | ||||||||
\(946\) | 21.2321 | 0.690314 | ||||||||
\(947\) | −14.3161 | −0.465211 | −0.232605 | − | 0.972571i | \(-0.574725\pi\) | ||||
−0.232605 | + | 0.972571i | \(0.574725\pi\) | |||||||
\(948\) | −49.0569 | −1.59330 | ||||||||
\(949\) | −2.60074 | −0.0844237 | ||||||||
\(950\) | 3.22243 | 0.104550 | ||||||||
\(951\) | 11.3137 | 0.366872 | ||||||||
\(952\) | 24.4619 | 0.792815 | ||||||||
\(953\) | 46.4935 | 1.50607 | 0.753036 | − | 0.657979i | \(-0.228589\pi\) | ||||
0.753036 | + | 0.657979i | \(0.228589\pi\) | |||||||
\(954\) | 24.0856 | 0.779798 | ||||||||
\(955\) | −22.6112 | −0.731682 | ||||||||
\(956\) | 10.8601 | 0.351242 | ||||||||
\(957\) | −1.51682 | −0.0490317 | ||||||||
\(958\) | 32.1653 | 1.03921 | ||||||||
\(959\) | −19.2549 | −0.621773 | ||||||||
\(960\) | −17.1176 | −0.552467 | ||||||||
\(961\) | −29.1331 | −0.939779 | ||||||||
\(962\) | 22.1472 | 0.714053 | ||||||||
\(963\) | 7.31175 | 0.235618 | ||||||||
\(964\) | 72.3340 | 2.32972 | ||||||||
\(965\) | 10.4791 | 0.337333 | ||||||||
\(966\) | 6.65908 | 0.214252 | ||||||||
\(967\) | −6.58785 | −0.211851 | −0.105926 | − | 0.994374i | \(-0.533781\pi\) | ||||
−0.105926 | + | 0.994374i | \(0.533781\pi\) | |||||||
\(968\) | 20.2449 | 0.650696 | ||||||||
\(969\) | −1.55354 | −0.0499069 | ||||||||
\(970\) | −46.0548 | −1.47873 | ||||||||
\(971\) | 7.43166 | 0.238493 | 0.119247 | − | 0.992865i | \(-0.461952\pi\) | ||||
0.119247 | + | 0.992865i | \(0.461952\pi\) | |||||||
\(972\) | −3.03693 | −0.0974096 | ||||||||
\(973\) | 56.2383 | 1.80292 | ||||||||
\(974\) | 14.8598 | 0.476140 | ||||||||
\(975\) | 2.95399 | 0.0946034 | ||||||||
\(976\) | −7.37420 | −0.236042 | ||||||||
\(977\) | 36.1933 | 1.15793 | 0.578963 | − | 0.815354i | \(-0.303458\pi\) | ||||
0.578963 | + | 0.815354i | \(0.303458\pi\) | |||||||
\(978\) | −13.7311 | −0.439071 | ||||||||
\(979\) | −11.3457 | −0.362610 | ||||||||
\(980\) | −7.19581 | −0.229862 | ||||||||
\(981\) | −3.37760 | −0.107838 | ||||||||
\(982\) | 36.4247 | 1.16236 | ||||||||
\(983\) | 25.3261 | 0.807779 | 0.403889 | − | 0.914808i | \(-0.367658\pi\) | ||||
0.403889 | + | 0.914808i | \(0.367658\pi\) | |||||||
\(984\) | 8.69775 | 0.277274 | ||||||||
\(985\) | −6.75191 | −0.215134 | ||||||||
\(986\) | −7.95077 | −0.253204 | ||||||||
\(987\) | 13.0830 | 0.416435 | ||||||||
\(988\) | 1.20153 | 0.0382258 | ||||||||
\(989\) | 6.23701 | 0.198325 | ||||||||
\(990\) | 4.47210 | 0.142133 | ||||||||
\(991\) | −23.1884 | −0.736603 | −0.368302 | − | 0.929706i | \(-0.620061\pi\) | ||||
−0.368302 | + | 0.929706i | \(0.620061\pi\) | |||||||
\(992\) | −8.96874 | −0.284758 | ||||||||
\(993\) | −34.5401 | −1.09610 | ||||||||
\(994\) | −74.9268 | −2.37654 | ||||||||
\(995\) | −28.8357 | −0.914154 | ||||||||
\(996\) | −10.2084 | −0.323467 | ||||||||
\(997\) | 7.28351 | 0.230671 | 0.115336 | − | 0.993327i | \(-0.463206\pi\) | ||||
0.115336 | + | 0.993327i | \(0.463206\pi\) | |||||||
\(998\) | 24.9188 | 0.788791 | ||||||||
\(999\) | 10.9378 | 0.346058 |
(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 | 2001.2.a.k.1.2 | ✓ | 10 | |
3.2 | odd | 2 | 6003.2.a.k.1.9 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.k.1.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
6003.2.a.k.1.9 | 10 | 3.2 | odd | 2 |