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: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 33 x^{18} + 64 x^{17} + 453 x^{16} - 846 x^{15} - 3353 x^{14} + 5985 x^{13} + \cdots - 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.80084\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.80084 | −1.98049 | −0.990247 | − | 0.139326i | \(-0.955506\pi\) | ||||
−0.990247 | + | 0.139326i | \(0.955506\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 5.84471 | 2.92235 | ||||||||
\(5\) | −3.48103 | −1.55676 | −0.778381 | − | 0.627792i | \(-0.783959\pi\) | ||||
−0.778381 | + | 0.627792i | \(0.783959\pi\) | |||||||
\(6\) | −2.80084 | −1.14344 | ||||||||
\(7\) | −1.41384 | −0.534380 | −0.267190 | − | 0.963644i | \(-0.586095\pi\) | ||||
−0.267190 | + | 0.963644i | \(0.586095\pi\) | |||||||
\(8\) | −10.7684 | −3.80721 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 9.74980 | 3.08316 | ||||||||
\(11\) | −4.43439 | −1.33702 | −0.668509 | − | 0.743704i | \(-0.733067\pi\) | ||||
−0.668509 | + | 0.743704i | \(0.733067\pi\) | |||||||
\(12\) | 5.84471 | 1.68722 | ||||||||
\(13\) | −2.37735 | −0.659359 | −0.329680 | − | 0.944093i | \(-0.606941\pi\) | ||||
−0.329680 | + | 0.944093i | \(0.606941\pi\) | |||||||
\(14\) | 3.95993 | 1.05834 | ||||||||
\(15\) | −3.48103 | −0.898797 | ||||||||
\(16\) | 18.4712 | 4.61779 | ||||||||
\(17\) | −3.28679 | −0.797165 | −0.398582 | − | 0.917133i | \(-0.630498\pi\) | ||||
−0.398582 | + | 0.917133i | \(0.630498\pi\) | |||||||
\(18\) | −2.80084 | −0.660164 | ||||||||
\(19\) | −3.46248 | −0.794347 | −0.397173 | − | 0.917744i | \(-0.630009\pi\) | ||||
−0.397173 | + | 0.917744i | \(0.630009\pi\) | |||||||
\(20\) | −20.3456 | −4.54941 | ||||||||
\(21\) | −1.41384 | −0.308524 | ||||||||
\(22\) | 12.4200 | 2.64796 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −10.7684 | −2.19809 | ||||||||
\(25\) | 7.11755 | 1.42351 | ||||||||
\(26\) | 6.65859 | 1.30586 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −8.26345 | −1.56165 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 9.74980 | 1.78006 | ||||||||
\(31\) | −4.18385 | −0.751443 | −0.375721 | − | 0.926733i | \(-0.622605\pi\) | ||||
−0.375721 | + | 0.926733i | \(0.622605\pi\) | |||||||
\(32\) | −30.1980 | −5.33830 | ||||||||
\(33\) | −4.43439 | −0.771928 | ||||||||
\(34\) | 9.20579 | 1.57878 | ||||||||
\(35\) | 4.92160 | 0.831902 | ||||||||
\(36\) | 5.84471 | 0.974118 | ||||||||
\(37\) | −10.7653 | −1.76981 | −0.884905 | − | 0.465771i | \(-0.845777\pi\) | ||||
−0.884905 | + | 0.465771i | \(0.845777\pi\) | |||||||
\(38\) | 9.69784 | 1.57320 | ||||||||
\(39\) | −2.37735 | −0.380681 | ||||||||
\(40\) | 37.4851 | 5.92691 | ||||||||
\(41\) | 3.71341 | 0.579937 | 0.289968 | − | 0.957036i | \(-0.406355\pi\) | ||||
0.289968 | + | 0.957036i | \(0.406355\pi\) | |||||||
\(42\) | 3.95993 | 0.611030 | ||||||||
\(43\) | −7.08099 | −1.07984 | −0.539920 | − | 0.841716i | \(-0.681546\pi\) | ||||
−0.539920 | + | 0.841716i | \(0.681546\pi\) | |||||||
\(44\) | −25.9177 | −3.90724 | ||||||||
\(45\) | −3.48103 | −0.518921 | ||||||||
\(46\) | −2.80084 | −0.412961 | ||||||||
\(47\) | 1.63781 | 0.238899 | 0.119450 | − | 0.992840i | \(-0.461887\pi\) | ||||
0.119450 | + | 0.992840i | \(0.461887\pi\) | |||||||
\(48\) | 18.4712 | 2.66608 | ||||||||
\(49\) | −5.00107 | −0.714438 | ||||||||
\(50\) | −19.9351 | −2.81925 | ||||||||
\(51\) | −3.28679 | −0.460243 | ||||||||
\(52\) | −13.8949 | −1.92688 | ||||||||
\(53\) | 6.97182 | 0.957653 | 0.478827 | − | 0.877910i | \(-0.341062\pi\) | ||||
0.478827 | + | 0.877910i | \(0.341062\pi\) | |||||||
\(54\) | −2.80084 | −0.381146 | ||||||||
\(55\) | 15.4362 | 2.08142 | ||||||||
\(56\) | 15.2248 | 2.03449 | ||||||||
\(57\) | −3.46248 | −0.458616 | ||||||||
\(58\) | −2.80084 | −0.367768 | ||||||||
\(59\) | 12.2928 | 1.60039 | 0.800195 | − | 0.599740i | \(-0.204729\pi\) | ||||
0.800195 | + | 0.599740i | \(0.204729\pi\) | |||||||
\(60\) | −20.3456 | −2.62660 | ||||||||
\(61\) | 5.25185 | 0.672431 | 0.336215 | − | 0.941785i | \(-0.390853\pi\) | ||||
0.336215 | + | 0.941785i | \(0.390853\pi\) | |||||||
\(62\) | 11.7183 | 1.48823 | ||||||||
\(63\) | −1.41384 | −0.178127 | ||||||||
\(64\) | 47.6374 | 5.95467 | ||||||||
\(65\) | 8.27563 | 1.02647 | ||||||||
\(66\) | 12.4200 | 1.52880 | ||||||||
\(67\) | −11.9828 | −1.46393 | −0.731965 | − | 0.681342i | \(-0.761397\pi\) | ||||
−0.731965 | + | 0.681342i | \(0.761397\pi\) | |||||||
\(68\) | −19.2103 | −2.32960 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | −13.7846 | −1.64758 | ||||||||
\(71\) | 12.3124 | 1.46121 | 0.730604 | − | 0.682802i | \(-0.239239\pi\) | ||||
0.730604 | + | 0.682802i | \(0.239239\pi\) | |||||||
\(72\) | −10.7684 | −1.26907 | ||||||||
\(73\) | 8.68606 | 1.01663 | 0.508313 | − | 0.861172i | \(-0.330269\pi\) | ||||
0.508313 | + | 0.861172i | \(0.330269\pi\) | |||||||
\(74\) | 30.1520 | 3.50510 | ||||||||
\(75\) | 7.11755 | 0.821863 | ||||||||
\(76\) | −20.2372 | −2.32136 | ||||||||
\(77\) | 6.26950 | 0.714476 | ||||||||
\(78\) | 6.65859 | 0.753936 | ||||||||
\(79\) | 9.51988 | 1.07107 | 0.535535 | − | 0.844513i | \(-0.320110\pi\) | ||||
0.535535 | + | 0.844513i | \(0.320110\pi\) | |||||||
\(80\) | −64.2986 | −7.18881 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.4007 | −1.14856 | ||||||||
\(83\) | 2.12581 | 0.233338 | 0.116669 | − | 0.993171i | \(-0.462778\pi\) | ||||
0.116669 | + | 0.993171i | \(0.462778\pi\) | |||||||
\(84\) | −8.26345 | −0.901617 | ||||||||
\(85\) | 11.4414 | 1.24100 | ||||||||
\(86\) | 19.8327 | 2.13862 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 47.7513 | 5.09031 | ||||||||
\(89\) | −11.0119 | −1.16726 | −0.583632 | − | 0.812018i | \(-0.698369\pi\) | ||||
−0.583632 | + | 0.812018i | \(0.698369\pi\) | |||||||
\(90\) | 9.74980 | 1.02772 | ||||||||
\(91\) | 3.36119 | 0.352348 | ||||||||
\(92\) | 5.84471 | 0.609353 | ||||||||
\(93\) | −4.18385 | −0.433846 | ||||||||
\(94\) | −4.58725 | −0.473139 | ||||||||
\(95\) | 12.0530 | 1.23661 | ||||||||
\(96\) | −30.1980 | −3.08207 | ||||||||
\(97\) | 12.3407 | 1.25301 | 0.626505 | − | 0.779417i | \(-0.284485\pi\) | ||||
0.626505 | + | 0.779417i | \(0.284485\pi\) | |||||||
\(98\) | 14.0072 | 1.41494 | ||||||||
\(99\) | −4.43439 | −0.445673 | ||||||||
\(100\) | 41.6000 | 4.16000 | ||||||||
\(101\) | −17.4826 | −1.73959 | −0.869794 | − | 0.493416i | \(-0.835748\pi\) | ||||
−0.869794 | + | 0.493416i | \(0.835748\pi\) | |||||||
\(102\) | 9.20579 | 0.911509 | ||||||||
\(103\) | −10.0681 | −0.992040 | −0.496020 | − | 0.868311i | \(-0.665206\pi\) | ||||
−0.496020 | + | 0.868311i | \(0.665206\pi\) | |||||||
\(104\) | 25.6003 | 2.51032 | ||||||||
\(105\) | 4.92160 | 0.480299 | ||||||||
\(106\) | −19.5270 | −1.89663 | ||||||||
\(107\) | −8.64089 | −0.835346 | −0.417673 | − | 0.908597i | \(-0.637154\pi\) | ||||
−0.417673 | + | 0.908597i | \(0.637154\pi\) | |||||||
\(108\) | 5.84471 | 0.562407 | ||||||||
\(109\) | −7.68708 | −0.736289 | −0.368144 | − | 0.929769i | \(-0.620007\pi\) | ||||
−0.368144 | + | 0.929769i | \(0.620007\pi\) | |||||||
\(110\) | −43.2344 | −4.12224 | ||||||||
\(111\) | −10.7653 | −1.02180 | ||||||||
\(112\) | −26.1152 | −2.46765 | ||||||||
\(113\) | −5.51803 | −0.519092 | −0.259546 | − | 0.965731i | \(-0.583573\pi\) | ||||
−0.259546 | + | 0.965731i | \(0.583573\pi\) | |||||||
\(114\) | 9.69784 | 0.908286 | ||||||||
\(115\) | −3.48103 | −0.324607 | ||||||||
\(116\) | 5.84471 | 0.542667 | ||||||||
\(117\) | −2.37735 | −0.219786 | ||||||||
\(118\) | −34.4302 | −3.16956 | ||||||||
\(119\) | 4.64699 | 0.425989 | ||||||||
\(120\) | 37.4851 | 3.42191 | ||||||||
\(121\) | 8.66381 | 0.787619 | ||||||||
\(122\) | −14.7096 | −1.33174 | ||||||||
\(123\) | 3.71341 | 0.334827 | ||||||||
\(124\) | −24.4534 | −2.19598 | ||||||||
\(125\) | −7.37123 | −0.659303 | ||||||||
\(126\) | 3.95993 | 0.352778 | ||||||||
\(127\) | 12.7499 | 1.13137 | 0.565684 | − | 0.824622i | \(-0.308612\pi\) | ||||
0.565684 | + | 0.824622i | \(0.308612\pi\) | |||||||
\(128\) | −73.0287 | −6.45489 | ||||||||
\(129\) | −7.08099 | −0.623446 | ||||||||
\(130\) | −23.1787 | −2.03291 | ||||||||
\(131\) | −14.4611 | −1.26347 | −0.631735 | − | 0.775185i | \(-0.717657\pi\) | ||||
−0.631735 | + | 0.775185i | \(0.717657\pi\) | |||||||
\(132\) | −25.9177 | −2.25585 | ||||||||
\(133\) | 4.89537 | 0.424483 | ||||||||
\(134\) | 33.5619 | 2.89930 | ||||||||
\(135\) | −3.48103 | −0.299599 | ||||||||
\(136\) | 35.3935 | 3.03497 | ||||||||
\(137\) | 9.36729 | 0.800302 | 0.400151 | − | 0.916449i | \(-0.368958\pi\) | ||||
0.400151 | + | 0.916449i | \(0.368958\pi\) | |||||||
\(138\) | −2.80084 | −0.238423 | ||||||||
\(139\) | −7.17859 | −0.608880 | −0.304440 | − | 0.952532i | \(-0.598469\pi\) | ||||
−0.304440 | + | 0.952532i | \(0.598469\pi\) | |||||||
\(140\) | 28.7653 | 2.43111 | ||||||||
\(141\) | 1.63781 | 0.137929 | ||||||||
\(142\) | −34.4849 | −2.89391 | ||||||||
\(143\) | 10.5421 | 0.881575 | ||||||||
\(144\) | 18.4712 | 1.53926 | ||||||||
\(145\) | −3.48103 | −0.289084 | ||||||||
\(146\) | −24.3283 | −2.01342 | ||||||||
\(147\) | −5.00107 | −0.412481 | ||||||||
\(148\) | −62.9202 | −5.17201 | ||||||||
\(149\) | 12.0231 | 0.984974 | 0.492487 | − | 0.870320i | \(-0.336088\pi\) | ||||
0.492487 | + | 0.870320i | \(0.336088\pi\) | |||||||
\(150\) | −19.9351 | −1.62769 | ||||||||
\(151\) | 14.1232 | 1.14933 | 0.574665 | − | 0.818389i | \(-0.305132\pi\) | ||||
0.574665 | + | 0.818389i | \(0.305132\pi\) | |||||||
\(152\) | 37.2853 | 3.02424 | ||||||||
\(153\) | −3.28679 | −0.265722 | ||||||||
\(154\) | −17.5599 | −1.41501 | ||||||||
\(155\) | 14.5641 | 1.16982 | ||||||||
\(156\) | −13.8949 | −1.11248 | ||||||||
\(157\) | 12.7785 | 1.01983 | 0.509917 | − | 0.860224i | \(-0.329676\pi\) | ||||
0.509917 | + | 0.860224i | \(0.329676\pi\) | |||||||
\(158\) | −26.6637 | −2.12125 | ||||||||
\(159\) | 6.97182 | 0.552901 | ||||||||
\(160\) | 105.120 | 8.31046 | ||||||||
\(161\) | −1.41384 | −0.111426 | ||||||||
\(162\) | −2.80084 | −0.220055 | ||||||||
\(163\) | 18.0242 | 1.41177 | 0.705883 | − | 0.708328i | \(-0.250550\pi\) | ||||
0.705883 | + | 0.708328i | \(0.250550\pi\) | |||||||
\(164\) | 21.7038 | 1.69478 | ||||||||
\(165\) | 15.4362 | 1.20171 | ||||||||
\(166\) | −5.95405 | −0.462124 | ||||||||
\(167\) | 6.24398 | 0.483174 | 0.241587 | − | 0.970379i | \(-0.422332\pi\) | ||||
0.241587 | + | 0.970379i | \(0.422332\pi\) | |||||||
\(168\) | 15.2248 | 1.17462 | ||||||||
\(169\) | −7.34819 | −0.565246 | ||||||||
\(170\) | −32.0456 | −2.45778 | ||||||||
\(171\) | −3.46248 | −0.264782 | ||||||||
\(172\) | −41.3863 | −3.15567 | ||||||||
\(173\) | −21.4424 | −1.63024 | −0.815119 | − | 0.579293i | \(-0.803329\pi\) | ||||
−0.815119 | + | 0.579293i | \(0.803329\pi\) | |||||||
\(174\) | −2.80084 | −0.212331 | ||||||||
\(175\) | −10.0630 | −0.760694 | ||||||||
\(176\) | −81.9084 | −6.17407 | ||||||||
\(177\) | 12.2928 | 0.923985 | ||||||||
\(178\) | 30.8427 | 2.31176 | ||||||||
\(179\) | 19.8711 | 1.48524 | 0.742618 | − | 0.669715i | \(-0.233584\pi\) | ||||
0.742618 | + | 0.669715i | \(0.233584\pi\) | |||||||
\(180\) | −20.3456 | −1.51647 | ||||||||
\(181\) | −0.142040 | −0.0105578 | −0.00527889 | − | 0.999986i | \(-0.501680\pi\) | ||||
−0.00527889 | + | 0.999986i | \(0.501680\pi\) | |||||||
\(182\) | −9.41415 | −0.697823 | ||||||||
\(183\) | 5.25185 | 0.388228 | ||||||||
\(184\) | −10.7684 | −0.793857 | ||||||||
\(185\) | 37.4744 | 2.75517 | ||||||||
\(186\) | 11.7183 | 0.859228 | ||||||||
\(187\) | 14.5749 | 1.06582 | ||||||||
\(188\) | 9.57253 | 0.698148 | ||||||||
\(189\) | −1.41384 | −0.102841 | ||||||||
\(190\) | −33.7584 | −2.44910 | ||||||||
\(191\) | −14.5967 | −1.05618 | −0.528091 | − | 0.849188i | \(-0.677092\pi\) | ||||
−0.528091 | + | 0.849188i | \(0.677092\pi\) | |||||||
\(192\) | 47.6374 | 3.43793 | ||||||||
\(193\) | −17.3067 | −1.24576 | −0.622881 | − | 0.782317i | \(-0.714038\pi\) | ||||
−0.622881 | + | 0.782317i | \(0.714038\pi\) | |||||||
\(194\) | −34.5644 | −2.48158 | ||||||||
\(195\) | 8.27563 | 0.592630 | ||||||||
\(196\) | −29.2298 | −2.08784 | ||||||||
\(197\) | 2.11009 | 0.150338 | 0.0751689 | − | 0.997171i | \(-0.476050\pi\) | ||||
0.0751689 | + | 0.997171i | \(0.476050\pi\) | |||||||
\(198\) | 12.4200 | 0.882652 | ||||||||
\(199\) | 16.4313 | 1.16478 | 0.582391 | − | 0.812909i | \(-0.302117\pi\) | ||||
0.582391 | + | 0.812909i | \(0.302117\pi\) | |||||||
\(200\) | −76.6446 | −5.41959 | ||||||||
\(201\) | −11.9828 | −0.845201 | ||||||||
\(202\) | 48.9661 | 3.44524 | ||||||||
\(203\) | −1.41384 | −0.0992318 | ||||||||
\(204\) | −19.2103 | −1.34499 | ||||||||
\(205\) | −12.9265 | −0.902824 | ||||||||
\(206\) | 28.1992 | 1.96473 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −43.9125 | −3.04478 | ||||||||
\(209\) | 15.3540 | 1.06206 | ||||||||
\(210\) | −13.7846 | −0.951229 | ||||||||
\(211\) | 5.03335 | 0.346510 | 0.173255 | − | 0.984877i | \(-0.444572\pi\) | ||||
0.173255 | + | 0.984877i | \(0.444572\pi\) | |||||||
\(212\) | 40.7482 | 2.79860 | ||||||||
\(213\) | 12.3124 | 0.843629 | ||||||||
\(214\) | 24.2018 | 1.65440 | ||||||||
\(215\) | 24.6491 | 1.68105 | ||||||||
\(216\) | −10.7684 | −0.732697 | ||||||||
\(217\) | 5.91528 | 0.401556 | ||||||||
\(218\) | 21.5303 | 1.45821 | ||||||||
\(219\) | 8.68606 | 0.586949 | ||||||||
\(220\) | 90.2202 | 6.08264 | ||||||||
\(221\) | 7.81387 | 0.525618 | ||||||||
\(222\) | 30.1520 | 2.02367 | ||||||||
\(223\) | −4.74485 | −0.317739 | −0.158869 | − | 0.987300i | \(-0.550785\pi\) | ||||
−0.158869 | + | 0.987300i | \(0.550785\pi\) | |||||||
\(224\) | 42.6950 | 2.85268 | ||||||||
\(225\) | 7.11755 | 0.474503 | ||||||||
\(226\) | 15.4551 | 1.02806 | ||||||||
\(227\) | −15.9414 | −1.05806 | −0.529032 | − | 0.848602i | \(-0.677445\pi\) | ||||
−0.529032 | + | 0.848602i | \(0.677445\pi\) | |||||||
\(228\) | −20.2372 | −1.34024 | ||||||||
\(229\) | 24.6062 | 1.62602 | 0.813012 | − | 0.582247i | \(-0.197826\pi\) | ||||
0.813012 | + | 0.582247i | \(0.197826\pi\) | |||||||
\(230\) | 9.74980 | 0.642883 | ||||||||
\(231\) | 6.26950 | 0.412503 | ||||||||
\(232\) | −10.7684 | −0.706980 | ||||||||
\(233\) | −3.43090 | −0.224765 | −0.112383 | − | 0.993665i | \(-0.535848\pi\) | ||||
−0.112383 | + | 0.993665i | \(0.535848\pi\) | |||||||
\(234\) | 6.65859 | 0.435285 | ||||||||
\(235\) | −5.70127 | −0.371910 | ||||||||
\(236\) | 71.8479 | 4.67690 | ||||||||
\(237\) | 9.51988 | 0.618382 | ||||||||
\(238\) | −13.0155 | −0.843668 | ||||||||
\(239\) | 5.76650 | 0.373004 | 0.186502 | − | 0.982455i | \(-0.440285\pi\) | ||||
0.186502 | + | 0.982455i | \(0.440285\pi\) | |||||||
\(240\) | −64.2986 | −4.15046 | ||||||||
\(241\) | 19.8383 | 1.27790 | 0.638948 | − | 0.769250i | \(-0.279370\pi\) | ||||
0.638948 | + | 0.769250i | \(0.279370\pi\) | |||||||
\(242\) | −24.2659 | −1.55987 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 30.6955 | 1.96508 | ||||||||
\(245\) | 17.4089 | 1.11221 | ||||||||
\(246\) | −10.4007 | −0.663122 | ||||||||
\(247\) | 8.23153 | 0.523760 | ||||||||
\(248\) | 45.0534 | 2.86090 | ||||||||
\(249\) | 2.12581 | 0.134718 | ||||||||
\(250\) | 20.6456 | 1.30574 | ||||||||
\(251\) | −1.97792 | −0.124845 | −0.0624226 | − | 0.998050i | \(-0.519883\pi\) | ||||
−0.0624226 | + | 0.998050i | \(0.519883\pi\) | |||||||
\(252\) | −8.26345 | −0.520549 | ||||||||
\(253\) | −4.43439 | −0.278788 | ||||||||
\(254\) | −35.7103 | −2.24067 | ||||||||
\(255\) | 11.4414 | 0.716489 | ||||||||
\(256\) | 109.267 | 6.82919 | ||||||||
\(257\) | −0.846927 | −0.0528298 | −0.0264149 | − | 0.999651i | \(-0.508409\pi\) | ||||
−0.0264149 | + | 0.999651i | \(0.508409\pi\) | |||||||
\(258\) | 19.8327 | 1.23473 | ||||||||
\(259\) | 15.2204 | 0.945751 | ||||||||
\(260\) | 48.3686 | 2.99969 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 40.5031 | 2.50229 | ||||||||
\(263\) | 0.347153 | 0.0214064 | 0.0107032 | − | 0.999943i | \(-0.496593\pi\) | ||||
0.0107032 | + | 0.999943i | \(0.496593\pi\) | |||||||
\(264\) | 47.7513 | 2.93889 | ||||||||
\(265\) | −24.2691 | −1.49084 | ||||||||
\(266\) | −13.7112 | −0.840685 | ||||||||
\(267\) | −11.0119 | −0.673920 | ||||||||
\(268\) | −70.0359 | −4.27812 | ||||||||
\(269\) | 22.3131 | 1.36045 | 0.680227 | − | 0.733002i | \(-0.261881\pi\) | ||||
0.680227 | + | 0.733002i | \(0.261881\pi\) | |||||||
\(270\) | 9.74980 | 0.593354 | ||||||||
\(271\) | −21.0578 | −1.27917 | −0.639584 | − | 0.768721i | \(-0.720893\pi\) | ||||
−0.639584 | + | 0.768721i | \(0.720893\pi\) | |||||||
\(272\) | −60.7109 | −3.68114 | ||||||||
\(273\) | 3.36119 | 0.203428 | ||||||||
\(274\) | −26.2363 | −1.58499 | ||||||||
\(275\) | −31.5620 | −1.90326 | ||||||||
\(276\) | 5.84471 | 0.351810 | ||||||||
\(277\) | 2.42766 | 0.145864 | 0.0729320 | − | 0.997337i | \(-0.476764\pi\) | ||||
0.0729320 | + | 0.997337i | \(0.476764\pi\) | |||||||
\(278\) | 20.1061 | 1.20588 | ||||||||
\(279\) | −4.18385 | −0.250481 | ||||||||
\(280\) | −52.9978 | −3.16722 | ||||||||
\(281\) | 11.6621 | 0.695703 | 0.347852 | − | 0.937550i | \(-0.386911\pi\) | ||||
0.347852 | + | 0.937550i | \(0.386911\pi\) | |||||||
\(282\) | −4.58725 | −0.273167 | ||||||||
\(283\) | −7.95812 | −0.473061 | −0.236530 | − | 0.971624i | \(-0.576010\pi\) | ||||
−0.236530 | + | 0.971624i | \(0.576010\pi\) | |||||||
\(284\) | 71.9621 | 4.27016 | ||||||||
\(285\) | 12.0530 | 0.713956 | ||||||||
\(286\) | −29.5268 | −1.74595 | ||||||||
\(287\) | −5.25015 | −0.309906 | ||||||||
\(288\) | −30.1980 | −1.77943 | ||||||||
\(289\) | −6.19698 | −0.364528 | ||||||||
\(290\) | 9.74980 | 0.572528 | ||||||||
\(291\) | 12.3407 | 0.723426 | ||||||||
\(292\) | 50.7675 | 2.97094 | ||||||||
\(293\) | −25.6929 | −1.50099 | −0.750497 | − | 0.660874i | \(-0.770186\pi\) | ||||
−0.750497 | + | 0.660874i | \(0.770186\pi\) | |||||||
\(294\) | 14.0072 | 0.816916 | ||||||||
\(295\) | −42.7917 | −2.49143 | ||||||||
\(296\) | 115.926 | 6.73803 | ||||||||
\(297\) | −4.43439 | −0.257309 | ||||||||
\(298\) | −33.6749 | −1.95073 | ||||||||
\(299\) | −2.37735 | −0.137486 | ||||||||
\(300\) | 41.6000 | 2.40177 | ||||||||
\(301\) | 10.0114 | 0.577045 | ||||||||
\(302\) | −39.5568 | −2.27624 | ||||||||
\(303\) | −17.4826 | −1.00435 | ||||||||
\(304\) | −63.9560 | −3.66813 | ||||||||
\(305\) | −18.2818 | −1.04681 | ||||||||
\(306\) | 9.20579 | 0.526260 | ||||||||
\(307\) | 18.5614 | 1.05936 | 0.529679 | − | 0.848198i | \(-0.322312\pi\) | ||||
0.529679 | + | 0.848198i | \(0.322312\pi\) | |||||||
\(308\) | 36.6434 | 2.08795 | ||||||||
\(309\) | −10.0681 | −0.572755 | ||||||||
\(310\) | −40.7917 | −2.31682 | ||||||||
\(311\) | 9.91454 | 0.562202 | 0.281101 | − | 0.959678i | \(-0.409300\pi\) | ||||
0.281101 | + | 0.959678i | \(0.409300\pi\) | |||||||
\(312\) | 25.6003 | 1.44933 | ||||||||
\(313\) | 15.3040 | 0.865032 | 0.432516 | − | 0.901626i | \(-0.357626\pi\) | ||||
0.432516 | + | 0.901626i | \(0.357626\pi\) | |||||||
\(314\) | −35.7905 | −2.01977 | ||||||||
\(315\) | 4.92160 | 0.277301 | ||||||||
\(316\) | 55.6409 | 3.13004 | ||||||||
\(317\) | 17.3563 | 0.974829 | 0.487414 | − | 0.873171i | \(-0.337940\pi\) | ||||
0.487414 | + | 0.873171i | \(0.337940\pi\) | |||||||
\(318\) | −19.5270 | −1.09502 | ||||||||
\(319\) | −4.43439 | −0.248278 | ||||||||
\(320\) | −165.827 | −9.27001 | ||||||||
\(321\) | −8.64089 | −0.482288 | ||||||||
\(322\) | 3.95993 | 0.220678 | ||||||||
\(323\) | 11.3804 | 0.633225 | ||||||||
\(324\) | 5.84471 | 0.324706 | ||||||||
\(325\) | −16.9209 | −0.938604 | ||||||||
\(326\) | −50.4830 | −2.79599 | ||||||||
\(327\) | −7.68708 | −0.425096 | ||||||||
\(328\) | −39.9875 | −2.20794 | ||||||||
\(329\) | −2.31560 | −0.127663 | ||||||||
\(330\) | −43.2344 | −2.37998 | ||||||||
\(331\) | −25.6184 | −1.40811 | −0.704057 | − | 0.710144i | \(-0.748630\pi\) | ||||
−0.704057 | + | 0.710144i | \(0.748630\pi\) | |||||||
\(332\) | 12.4247 | 0.681895 | ||||||||
\(333\) | −10.7653 | −0.589937 | ||||||||
\(334\) | −17.4884 | −0.956922 | ||||||||
\(335\) | 41.7124 | 2.27899 | ||||||||
\(336\) | −26.1152 | −1.42470 | ||||||||
\(337\) | −16.3884 | −0.892734 | −0.446367 | − | 0.894850i | \(-0.647282\pi\) | ||||
−0.446367 | + | 0.894850i | \(0.647282\pi\) | |||||||
\(338\) | 20.5811 | 1.11947 | ||||||||
\(339\) | −5.51803 | −0.299698 | ||||||||
\(340\) | 66.8717 | 3.62663 | ||||||||
\(341\) | 18.5528 | 1.00469 | ||||||||
\(342\) | 9.69784 | 0.524399 | ||||||||
\(343\) | 16.9675 | 0.916161 | ||||||||
\(344\) | 76.2509 | 4.11117 | ||||||||
\(345\) | −3.48103 | −0.187412 | ||||||||
\(346\) | 60.0568 | 3.22868 | ||||||||
\(347\) | −25.0667 | −1.34565 | −0.672826 | − | 0.739800i | \(-0.734920\pi\) | ||||
−0.672826 | + | 0.739800i | \(0.734920\pi\) | |||||||
\(348\) | 5.84471 | 0.313309 | ||||||||
\(349\) | 22.4766 | 1.20315 | 0.601573 | − | 0.798818i | \(-0.294541\pi\) | ||||
0.601573 | + | 0.798818i | \(0.294541\pi\) | |||||||
\(350\) | 28.1850 | 1.50655 | ||||||||
\(351\) | −2.37735 | −0.126894 | ||||||||
\(352\) | 133.910 | 7.13741 | ||||||||
\(353\) | −2.42803 | −0.129231 | −0.0646156 | − | 0.997910i | \(-0.520582\pi\) | ||||
−0.0646156 | + | 0.997910i | \(0.520582\pi\) | |||||||
\(354\) | −34.4302 | −1.82995 | ||||||||
\(355\) | −42.8596 | −2.27475 | ||||||||
\(356\) | −64.3616 | −3.41116 | ||||||||
\(357\) | 4.64699 | 0.245945 | ||||||||
\(358\) | −55.6558 | −2.94150 | ||||||||
\(359\) | 36.3433 | 1.91812 | 0.959062 | − | 0.283195i | \(-0.0913943\pi\) | ||||
0.959062 | + | 0.283195i | \(0.0913943\pi\) | |||||||
\(360\) | 37.4851 | 1.97564 | ||||||||
\(361\) | −7.01126 | −0.369014 | ||||||||
\(362\) | 0.397832 | 0.0209096 | ||||||||
\(363\) | 8.66381 | 0.454732 | ||||||||
\(364\) | 19.6451 | 1.02969 | ||||||||
\(365\) | −30.2364 | −1.58265 | ||||||||
\(366\) | −14.7096 | −0.768883 | ||||||||
\(367\) | 12.2035 | 0.637016 | 0.318508 | − | 0.947920i | \(-0.396818\pi\) | ||||
0.318508 | + | 0.947920i | \(0.396818\pi\) | |||||||
\(368\) | 18.4712 | 0.962876 | ||||||||
\(369\) | 3.71341 | 0.193312 | ||||||||
\(370\) | −104.960 | −5.45660 | ||||||||
\(371\) | −9.85701 | −0.511750 | ||||||||
\(372\) | −24.4534 | −1.26785 | ||||||||
\(373\) | 4.00742 | 0.207497 | 0.103748 | − | 0.994604i | \(-0.466916\pi\) | ||||
0.103748 | + | 0.994604i | \(0.466916\pi\) | |||||||
\(374\) | −40.8220 | −2.11086 | ||||||||
\(375\) | −7.37123 | −0.380649 | ||||||||
\(376\) | −17.6366 | −0.909539 | ||||||||
\(377\) | −2.37735 | −0.122440 | ||||||||
\(378\) | 3.95993 | 0.203677 | ||||||||
\(379\) | 3.66384 | 0.188199 | 0.0940993 | − | 0.995563i | \(-0.470003\pi\) | ||||
0.0940993 | + | 0.995563i | \(0.470003\pi\) | |||||||
\(380\) | 70.4461 | 3.61381 | ||||||||
\(381\) | 12.7499 | 0.653196 | ||||||||
\(382\) | 40.8831 | 2.09176 | ||||||||
\(383\) | −12.5542 | −0.641488 | −0.320744 | − | 0.947166i | \(-0.603933\pi\) | ||||
−0.320744 | + | 0.947166i | \(0.603933\pi\) | |||||||
\(384\) | −73.0287 | −3.72673 | ||||||||
\(385\) | −21.8243 | −1.11227 | ||||||||
\(386\) | 48.4732 | 2.46722 | ||||||||
\(387\) | −7.08099 | −0.359947 | ||||||||
\(388\) | 72.1279 | 3.66174 | ||||||||
\(389\) | 18.2759 | 0.926623 | 0.463312 | − | 0.886195i | \(-0.346661\pi\) | ||||
0.463312 | + | 0.886195i | \(0.346661\pi\) | |||||||
\(390\) | −23.1787 | −1.17370 | ||||||||
\(391\) | −3.28679 | −0.166220 | ||||||||
\(392\) | 53.8535 | 2.72001 | ||||||||
\(393\) | −14.4611 | −0.729464 | ||||||||
\(394\) | −5.91003 | −0.297743 | ||||||||
\(395\) | −33.1389 | −1.66740 | ||||||||
\(396\) | −25.9177 | −1.30241 | ||||||||
\(397\) | 9.01959 | 0.452680 | 0.226340 | − | 0.974048i | \(-0.427324\pi\) | ||||
0.226340 | + | 0.974048i | \(0.427324\pi\) | |||||||
\(398\) | −46.0213 | −2.30684 | ||||||||
\(399\) | 4.89537 | 0.245075 | ||||||||
\(400\) | 131.469 | 6.57347 | ||||||||
\(401\) | 6.66076 | 0.332622 | 0.166311 | − | 0.986073i | \(-0.446814\pi\) | ||||
0.166311 | + | 0.986073i | \(0.446814\pi\) | |||||||
\(402\) | 33.5619 | 1.67391 | ||||||||
\(403\) | 9.94650 | 0.495470 | ||||||||
\(404\) | −102.181 | −5.08369 | ||||||||
\(405\) | −3.48103 | −0.172974 | ||||||||
\(406\) | 3.95993 | 0.196528 | ||||||||
\(407\) | 47.7377 | 2.36627 | ||||||||
\(408\) | 35.3935 | 1.75224 | ||||||||
\(409\) | 3.95276 | 0.195451 | 0.0977257 | − | 0.995213i | \(-0.468843\pi\) | ||||
0.0977257 | + | 0.995213i | \(0.468843\pi\) | |||||||
\(410\) | 36.2050 | 1.78804 | ||||||||
\(411\) | 9.36729 | 0.462054 | ||||||||
\(412\) | −58.8451 | −2.89909 | ||||||||
\(413\) | −17.3800 | −0.855216 | ||||||||
\(414\) | −2.80084 | −0.137654 | ||||||||
\(415\) | −7.39999 | −0.363251 | ||||||||
\(416\) | 71.7913 | 3.51986 | ||||||||
\(417\) | −7.17859 | −0.351537 | ||||||||
\(418\) | −43.0040 | −2.10339 | ||||||||
\(419\) | 4.41044 | 0.215464 | 0.107732 | − | 0.994180i | \(-0.465641\pi\) | ||||
0.107732 | + | 0.994180i | \(0.465641\pi\) | |||||||
\(420\) | 28.7653 | 1.40360 | ||||||||
\(421\) | 14.8860 | 0.725497 | 0.362748 | − | 0.931887i | \(-0.381838\pi\) | ||||
0.362748 | + | 0.931887i | \(0.381838\pi\) | |||||||
\(422\) | −14.0976 | −0.686260 | ||||||||
\(423\) | 1.63781 | 0.0796331 | ||||||||
\(424\) | −75.0754 | −3.64598 | ||||||||
\(425\) | −23.3939 | −1.13477 | ||||||||
\(426\) | −34.4849 | −1.67080 | ||||||||
\(427\) | −7.42526 | −0.359333 | ||||||||
\(428\) | −50.5035 | −2.44118 | ||||||||
\(429\) | 10.5421 | 0.508978 | ||||||||
\(430\) | −69.0382 | −3.32932 | ||||||||
\(431\) | −2.60324 | −0.125393 | −0.0626967 | − | 0.998033i | \(-0.519970\pi\) | ||||
−0.0626967 | + | 0.998033i | \(0.519970\pi\) | |||||||
\(432\) | 18.4712 | 0.888695 | ||||||||
\(433\) | 5.93295 | 0.285119 | 0.142560 | − | 0.989786i | \(-0.454467\pi\) | ||||
0.142560 | + | 0.989786i | \(0.454467\pi\) | |||||||
\(434\) | −16.5678 | −0.795278 | ||||||||
\(435\) | −3.48103 | −0.166902 | ||||||||
\(436\) | −44.9287 | −2.15170 | ||||||||
\(437\) | −3.46248 | −0.165633 | ||||||||
\(438\) | −24.3283 | −1.16245 | ||||||||
\(439\) | −8.48828 | −0.405124 | −0.202562 | − | 0.979269i | \(-0.564927\pi\) | ||||
−0.202562 | + | 0.979269i | \(0.564927\pi\) | |||||||
\(440\) | −166.224 | −7.92440 | ||||||||
\(441\) | −5.00107 | −0.238146 | ||||||||
\(442\) | −21.8854 | −1.04098 | ||||||||
\(443\) | −21.2540 | −1.00981 | −0.504904 | − | 0.863176i | \(-0.668472\pi\) | ||||
−0.504904 | + | 0.863176i | \(0.668472\pi\) | |||||||
\(444\) | −62.9202 | −2.98606 | ||||||||
\(445\) | 38.3329 | 1.81715 | ||||||||
\(446\) | 13.2896 | 0.629279 | ||||||||
\(447\) | 12.0231 | 0.568675 | ||||||||
\(448\) | −67.3514 | −3.18206 | ||||||||
\(449\) | −10.8308 | −0.511139 | −0.255570 | − | 0.966791i | \(-0.582263\pi\) | ||||
−0.255570 | + | 0.966791i | \(0.582263\pi\) | |||||||
\(450\) | −19.9351 | −0.939750 | ||||||||
\(451\) | −16.4667 | −0.775386 | ||||||||
\(452\) | −32.2512 | −1.51697 | ||||||||
\(453\) | 14.1232 | 0.663566 | ||||||||
\(454\) | 44.6492 | 2.09549 | ||||||||
\(455\) | −11.7004 | −0.548522 | ||||||||
\(456\) | 37.2853 | 1.74605 | ||||||||
\(457\) | 2.24941 | 0.105223 | 0.0526114 | − | 0.998615i | \(-0.483246\pi\) | ||||
0.0526114 | + | 0.998615i | \(0.483246\pi\) | |||||||
\(458\) | −68.9180 | −3.22033 | ||||||||
\(459\) | −3.28679 | −0.153414 | ||||||||
\(460\) | −20.3456 | −0.948617 | ||||||||
\(461\) | 2.51632 | 0.117197 | 0.0585984 | − | 0.998282i | \(-0.481337\pi\) | ||||
0.0585984 | + | 0.998282i | \(0.481337\pi\) | |||||||
\(462\) | −17.5599 | −0.816959 | ||||||||
\(463\) | −15.2202 | −0.707341 | −0.353671 | − | 0.935370i | \(-0.615067\pi\) | ||||
−0.353671 | + | 0.935370i | \(0.615067\pi\) | |||||||
\(464\) | 18.4712 | 0.857502 | ||||||||
\(465\) | 14.5641 | 0.675394 | ||||||||
\(466\) | 9.60939 | 0.445146 | ||||||||
\(467\) | −6.08666 | −0.281657 | −0.140829 | − | 0.990034i | \(-0.544977\pi\) | ||||
−0.140829 | + | 0.990034i | \(0.544977\pi\) | |||||||
\(468\) | −13.8949 | −0.642293 | ||||||||
\(469\) | 16.9417 | 0.782295 | ||||||||
\(470\) | 15.9683 | 0.736564 | ||||||||
\(471\) | 12.7785 | 0.588801 | ||||||||
\(472\) | −132.374 | −6.09301 | ||||||||
\(473\) | 31.3998 | 1.44377 | ||||||||
\(474\) | −26.6637 | −1.22470 | ||||||||
\(475\) | −24.6443 | −1.13076 | ||||||||
\(476\) | 27.1603 | 1.24489 | ||||||||
\(477\) | 6.97182 | 0.319218 | ||||||||
\(478\) | −16.1510 | −0.738732 | ||||||||
\(479\) | −2.91970 | −0.133405 | −0.0667023 | − | 0.997773i | \(-0.521248\pi\) | ||||
−0.0667023 | + | 0.997773i | \(0.521248\pi\) | |||||||
\(480\) | 105.120 | 4.79805 | ||||||||
\(481\) | 25.5930 | 1.16694 | ||||||||
\(482\) | −55.5639 | −2.53087 | ||||||||
\(483\) | −1.41384 | −0.0643318 | ||||||||
\(484\) | 50.6374 | 2.30170 | ||||||||
\(485\) | −42.9584 | −1.95064 | ||||||||
\(486\) | −2.80084 | −0.127049 | ||||||||
\(487\) | 35.3220 | 1.60059 | 0.800297 | − | 0.599604i | \(-0.204675\pi\) | ||||
0.800297 | + | 0.599604i | \(0.204675\pi\) | |||||||
\(488\) | −56.5541 | −2.56008 | ||||||||
\(489\) | 18.0242 | 0.815084 | ||||||||
\(490\) | −48.7594 | −2.20273 | ||||||||
\(491\) | −5.12284 | −0.231190 | −0.115595 | − | 0.993296i | \(-0.536878\pi\) | ||||
−0.115595 | + | 0.993296i | \(0.536878\pi\) | |||||||
\(492\) | 21.7038 | 0.978482 | ||||||||
\(493\) | −3.28679 | −0.148030 | ||||||||
\(494\) | −23.0552 | −1.03730 | ||||||||
\(495\) | 15.4362 | 0.693807 | ||||||||
\(496\) | −77.2807 | −3.47001 | ||||||||
\(497\) | −17.4076 | −0.780840 | ||||||||
\(498\) | −5.95405 | −0.266807 | ||||||||
\(499\) | 8.30239 | 0.371666 | 0.185833 | − | 0.982581i | \(-0.440502\pi\) | ||||
0.185833 | + | 0.982581i | \(0.440502\pi\) | |||||||
\(500\) | −43.0827 | −1.92672 | ||||||||
\(501\) | 6.24398 | 0.278961 | ||||||||
\(502\) | 5.53984 | 0.247255 | ||||||||
\(503\) | −37.2320 | −1.66009 | −0.830045 | − | 0.557696i | \(-0.811686\pi\) | ||||
−0.830045 | + | 0.557696i | \(0.811686\pi\) | |||||||
\(504\) | 15.2248 | 0.678165 | ||||||||
\(505\) | 60.8575 | 2.70812 | ||||||||
\(506\) | 12.4200 | 0.552137 | ||||||||
\(507\) | −7.34819 | −0.326345 | ||||||||
\(508\) | 74.5192 | 3.30626 | ||||||||
\(509\) | −41.3069 | −1.83090 | −0.915449 | − | 0.402434i | \(-0.868164\pi\) | ||||
−0.915449 | + | 0.402434i | \(0.868164\pi\) | |||||||
\(510\) | −32.0456 | −1.41900 | ||||||||
\(511\) | −12.2807 | −0.543264 | ||||||||
\(512\) | −159.982 | −7.07027 | ||||||||
\(513\) | −3.46248 | −0.152872 | ||||||||
\(514\) | 2.37211 | 0.104629 | ||||||||
\(515\) | 35.0474 | 1.54437 | ||||||||
\(516\) | −41.3863 | −1.82193 | ||||||||
\(517\) | −7.26270 | −0.319413 | ||||||||
\(518\) | −42.6300 | −1.87305 | ||||||||
\(519\) | −21.4424 | −0.941219 | ||||||||
\(520\) | −89.1153 | −3.90796 | ||||||||
\(521\) | 24.8969 | 1.09075 | 0.545377 | − | 0.838191i | \(-0.316387\pi\) | ||||
0.545377 | + | 0.838191i | \(0.316387\pi\) | |||||||
\(522\) | −2.80084 | −0.122589 | ||||||||
\(523\) | 10.7859 | 0.471634 | 0.235817 | − | 0.971797i | \(-0.424223\pi\) | ||||
0.235817 | + | 0.971797i | \(0.424223\pi\) | |||||||
\(524\) | −84.5207 | −3.69230 | ||||||||
\(525\) | −10.0630 | −0.439187 | ||||||||
\(526\) | −0.972319 | −0.0423951 | ||||||||
\(527\) | 13.7515 | 0.599024 | ||||||||
\(528\) | −81.9084 | −3.56460 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 67.9738 | 2.95260 | ||||||||
\(531\) | 12.2928 | 0.533463 | ||||||||
\(532\) | 28.6120 | 1.24049 | ||||||||
\(533\) | −8.82808 | −0.382387 | ||||||||
\(534\) | 30.8427 | 1.33469 | ||||||||
\(535\) | 30.0792 | 1.30044 | ||||||||
\(536\) | 129.035 | 5.57348 | ||||||||
\(537\) | 19.8711 | 0.857501 | ||||||||
\(538\) | −62.4954 | −2.69437 | ||||||||
\(539\) | 22.1767 | 0.955217 | ||||||||
\(540\) | −20.3456 | −0.875534 | ||||||||
\(541\) | −42.3958 | −1.82274 | −0.911368 | − | 0.411592i | \(-0.864973\pi\) | ||||
−0.911368 | + | 0.411592i | \(0.864973\pi\) | |||||||
\(542\) | 58.9794 | 2.53338 | ||||||||
\(543\) | −0.142040 | −0.00609554 | ||||||||
\(544\) | 99.2546 | 4.25550 | ||||||||
\(545\) | 26.7589 | 1.14623 | ||||||||
\(546\) | −9.41415 | −0.402888 | ||||||||
\(547\) | −43.7711 | −1.87151 | −0.935757 | − | 0.352644i | \(-0.885283\pi\) | ||||
−0.935757 | + | 0.352644i | \(0.885283\pi\) | |||||||
\(548\) | 54.7491 | 2.33876 | ||||||||
\(549\) | 5.25185 | 0.224144 | ||||||||
\(550\) | 88.4000 | 3.76939 | ||||||||
\(551\) | −3.46248 | −0.147506 | ||||||||
\(552\) | −10.7684 | −0.458334 | ||||||||
\(553\) | −13.4595 | −0.572358 | ||||||||
\(554\) | −6.79949 | −0.288883 | ||||||||
\(555\) | 37.4744 | 1.59070 | ||||||||
\(556\) | −41.9567 | −1.77936 | ||||||||
\(557\) | −10.4656 | −0.443443 | −0.221722 | − | 0.975110i | \(-0.571168\pi\) | ||||
−0.221722 | + | 0.975110i | \(0.571168\pi\) | |||||||
\(558\) | 11.7183 | 0.496076 | ||||||||
\(559\) | 16.8340 | 0.712002 | ||||||||
\(560\) | 90.9077 | 3.84155 | ||||||||
\(561\) | 14.5749 | 0.615354 | ||||||||
\(562\) | −32.6637 | −1.37784 | ||||||||
\(563\) | 30.1027 | 1.26868 | 0.634338 | − | 0.773055i | \(-0.281273\pi\) | ||||
0.634338 | + | 0.773055i | \(0.281273\pi\) | |||||||
\(564\) | 9.57253 | 0.403076 | ||||||||
\(565\) | 19.2084 | 0.808103 | ||||||||
\(566\) | 22.2894 | 0.936894 | ||||||||
\(567\) | −1.41384 | −0.0593755 | ||||||||
\(568\) | −132.584 | −5.56312 | ||||||||
\(569\) | −7.93717 | −0.332744 | −0.166372 | − | 0.986063i | \(-0.553205\pi\) | ||||
−0.166372 | + | 0.986063i | \(0.553205\pi\) | |||||||
\(570\) | −33.7584 | −1.41399 | ||||||||
\(571\) | 42.1256 | 1.76290 | 0.881450 | − | 0.472277i | \(-0.156568\pi\) | ||||
0.881450 | + | 0.472277i | \(0.156568\pi\) | |||||||
\(572\) | 61.6155 | 2.57627 | ||||||||
\(573\) | −14.5967 | −0.609786 | ||||||||
\(574\) | 14.7048 | 0.613768 | ||||||||
\(575\) | 7.11755 | 0.296822 | ||||||||
\(576\) | 47.6374 | 1.98489 | ||||||||
\(577\) | −24.2008 | −1.00749 | −0.503745 | − | 0.863852i | \(-0.668045\pi\) | ||||
−0.503745 | + | 0.863852i | \(0.668045\pi\) | |||||||
\(578\) | 17.3568 | 0.721946 | ||||||||
\(579\) | −17.3067 | −0.719241 | ||||||||
\(580\) | −20.3456 | −0.844804 | ||||||||
\(581\) | −3.00554 | −0.124691 | ||||||||
\(582\) | −34.5644 | −1.43274 | ||||||||
\(583\) | −30.9158 | −1.28040 | ||||||||
\(584\) | −93.5350 | −3.87051 | ||||||||
\(585\) | 8.27563 | 0.342155 | ||||||||
\(586\) | 71.9616 | 2.97271 | ||||||||
\(587\) | 1.25188 | 0.0516706 | 0.0258353 | − | 0.999666i | \(-0.491775\pi\) | ||||
0.0258353 | + | 0.999666i | \(0.491775\pi\) | |||||||
\(588\) | −29.2298 | −1.20542 | ||||||||
\(589\) | 14.4865 | 0.596906 | ||||||||
\(590\) | 119.853 | 4.93425 | ||||||||
\(591\) | 2.11009 | 0.0867976 | ||||||||
\(592\) | −198.848 | −8.17262 | ||||||||
\(593\) | 16.3746 | 0.672426 | 0.336213 | − | 0.941786i | \(-0.390854\pi\) | ||||
0.336213 | + | 0.941786i | \(0.390854\pi\) | |||||||
\(594\) | 12.4200 | 0.509599 | ||||||||
\(595\) | −16.1763 | −0.663163 | ||||||||
\(596\) | 70.2717 | 2.87844 | ||||||||
\(597\) | 16.4313 | 0.672487 | ||||||||
\(598\) | 6.65859 | 0.272290 | ||||||||
\(599\) | −13.9988 | −0.571977 | −0.285989 | − | 0.958233i | \(-0.592322\pi\) | ||||
−0.285989 | + | 0.958233i | \(0.592322\pi\) | |||||||
\(600\) | −76.6446 | −3.12900 | ||||||||
\(601\) | −15.8577 | −0.646850 | −0.323425 | − | 0.946254i | \(-0.604834\pi\) | ||||
−0.323425 | + | 0.946254i | \(0.604834\pi\) | |||||||
\(602\) | −28.0402 | −1.14283 | ||||||||
\(603\) | −11.9828 | −0.487977 | ||||||||
\(604\) | 82.5460 | 3.35875 | ||||||||
\(605\) | −30.1589 | −1.22614 | ||||||||
\(606\) | 48.9661 | 1.98911 | ||||||||
\(607\) | −44.6641 | −1.81286 | −0.906430 | − | 0.422356i | \(-0.861203\pi\) | ||||
−0.906430 | + | 0.422356i | \(0.861203\pi\) | |||||||
\(608\) | 104.560 | 4.24046 | ||||||||
\(609\) | −1.41384 | −0.0572915 | ||||||||
\(610\) | 51.2045 | 2.07321 | ||||||||
\(611\) | −3.89366 | −0.157521 | ||||||||
\(612\) | −19.2103 | −0.776532 | ||||||||
\(613\) | 41.5875 | 1.67971 | 0.839853 | − | 0.542814i | \(-0.182641\pi\) | ||||
0.839853 | + | 0.542814i | \(0.182641\pi\) | |||||||
\(614\) | −51.9876 | −2.09805 | ||||||||
\(615\) | −12.9265 | −0.521246 | ||||||||
\(616\) | −67.5125 | −2.72016 | ||||||||
\(617\) | −38.3035 | −1.54204 | −0.771020 | − | 0.636811i | \(-0.780253\pi\) | ||||
−0.771020 | + | 0.636811i | \(0.780253\pi\) | |||||||
\(618\) | 28.1992 | 1.13434 | ||||||||
\(619\) | −35.0276 | −1.40788 | −0.703939 | − | 0.710260i | \(-0.748577\pi\) | ||||
−0.703939 | + | 0.710260i | \(0.748577\pi\) | |||||||
\(620\) | 85.1229 | 3.41862 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −27.7690 | −1.11344 | ||||||||
\(623\) | 15.5691 | 0.623762 | ||||||||
\(624\) | −43.9125 | −1.75791 | ||||||||
\(625\) | −9.92828 | −0.397131 | ||||||||
\(626\) | −42.8640 | −1.71319 | ||||||||
\(627\) | 15.3540 | 0.613178 | ||||||||
\(628\) | 74.6865 | 2.98031 | ||||||||
\(629\) | 35.3835 | 1.41083 | ||||||||
\(630\) | −13.7846 | −0.549192 | ||||||||
\(631\) | 0.0346178 | 0.00137811 | 0.000689056 | − | 1.00000i | \(-0.499781\pi\) | ||||
0.000689056 | 1.00000i | \(0.499781\pi\) | ||||||||
\(632\) | −102.514 | −4.07778 | ||||||||
\(633\) | 5.03335 | 0.200058 | ||||||||
\(634\) | −48.6123 | −1.93064 | ||||||||
\(635\) | −44.3826 | −1.76127 | ||||||||
\(636\) | 40.7482 | 1.61577 | ||||||||
\(637\) | 11.8893 | 0.471071 | ||||||||
\(638\) | 12.4200 | 0.491713 | ||||||||
\(639\) | 12.3124 | 0.487069 | ||||||||
\(640\) | 254.215 | 10.0487 | ||||||||
\(641\) | −1.97337 | −0.0779435 | −0.0389718 | − | 0.999240i | \(-0.512408\pi\) | ||||
−0.0389718 | + | 0.999240i | \(0.512408\pi\) | |||||||
\(642\) | 24.2018 | 0.955167 | ||||||||
\(643\) | −29.6819 | −1.17054 | −0.585270 | − | 0.810838i | \(-0.699012\pi\) | ||||
−0.585270 | + | 0.810838i | \(0.699012\pi\) | |||||||
\(644\) | −8.26345 | −0.325626 | ||||||||
\(645\) | 24.6491 | 0.970557 | ||||||||
\(646\) | −31.8748 | −1.25410 | ||||||||
\(647\) | −8.97043 | −0.352664 | −0.176332 | − | 0.984331i | \(-0.556423\pi\) | ||||
−0.176332 | + | 0.984331i | \(0.556423\pi\) | |||||||
\(648\) | −10.7684 | −0.423023 | ||||||||
\(649\) | −54.5112 | −2.13975 | ||||||||
\(650\) | 47.3928 | 1.85890 | ||||||||
\(651\) | 5.91528 | 0.231838 | ||||||||
\(652\) | 105.346 | 4.12568 | ||||||||
\(653\) | −24.5006 | −0.958784 | −0.479392 | − | 0.877601i | \(-0.659143\pi\) | ||||
−0.479392 | + | 0.877601i | \(0.659143\pi\) | |||||||
\(654\) | 21.5303 | 0.841901 | ||||||||
\(655\) | 50.3394 | 1.96692 | ||||||||
\(656\) | 68.5910 | 2.67803 | ||||||||
\(657\) | 8.68606 | 0.338875 | ||||||||
\(658\) | 6.48562 | 0.252836 | ||||||||
\(659\) | −21.1494 | −0.823863 | −0.411931 | − | 0.911215i | \(-0.635146\pi\) | ||||
−0.411931 | + | 0.911215i | \(0.635146\pi\) | |||||||
\(660\) | 90.2202 | 3.51182 | ||||||||
\(661\) | −29.9812 | −1.16613 | −0.583067 | − | 0.812424i | \(-0.698147\pi\) | ||||
−0.583067 | + | 0.812424i | \(0.698147\pi\) | |||||||
\(662\) | 71.7530 | 2.78876 | ||||||||
\(663\) | 7.81387 | 0.303466 | ||||||||
\(664\) | −22.8915 | −0.888364 | ||||||||
\(665\) | −17.0409 | −0.660819 | ||||||||
\(666\) | 30.1520 | 1.16837 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 36.4942 | 1.41200 | ||||||||
\(669\) | −4.74485 | −0.183447 | ||||||||
\(670\) | −116.830 | −4.51353 | ||||||||
\(671\) | −23.2888 | −0.899052 | ||||||||
\(672\) | 42.6950 | 1.64699 | ||||||||
\(673\) | −11.6843 | −0.450398 | −0.225199 | − | 0.974313i | \(-0.572303\pi\) | ||||
−0.225199 | + | 0.974313i | \(0.572303\pi\) | |||||||
\(674\) | 45.9013 | 1.76805 | ||||||||
\(675\) | 7.11755 | 0.273954 | ||||||||
\(676\) | −42.9480 | −1.65185 | ||||||||
\(677\) | 47.4614 | 1.82409 | 0.912046 | − | 0.410088i | \(-0.134502\pi\) | ||||
0.912046 | + | 0.410088i | \(0.134502\pi\) | |||||||
\(678\) | 15.4551 | 0.593550 | ||||||||
\(679\) | −17.4478 | −0.669583 | ||||||||
\(680\) | −123.206 | −4.72473 | ||||||||
\(681\) | −15.9414 | −0.610874 | ||||||||
\(682\) | −51.9635 | −1.98979 | ||||||||
\(683\) | 48.2425 | 1.84595 | 0.922975 | − | 0.384860i | \(-0.125750\pi\) | ||||
0.922975 | + | 0.384860i | \(0.125750\pi\) | |||||||
\(684\) | −20.2372 | −0.773787 | ||||||||
\(685\) | −32.6078 | −1.24588 | ||||||||
\(686\) | −47.5234 | −1.81445 | ||||||||
\(687\) | 24.6062 | 0.938785 | ||||||||
\(688\) | −130.794 | −4.98648 | ||||||||
\(689\) | −16.5745 | −0.631437 | ||||||||
\(690\) | 9.74980 | 0.371168 | ||||||||
\(691\) | −17.1961 | −0.654172 | −0.327086 | − | 0.944995i | \(-0.606067\pi\) | ||||
−0.327086 | + | 0.944995i | \(0.606067\pi\) | |||||||
\(692\) | −125.325 | −4.76413 | ||||||||
\(693\) | 6.26950 | 0.238159 | ||||||||
\(694\) | 70.2079 | 2.66506 | ||||||||
\(695\) | 24.9889 | 0.947881 | ||||||||
\(696\) | −10.7684 | −0.408175 | ||||||||
\(697\) | −12.2052 | −0.462305 | ||||||||
\(698\) | −62.9534 | −2.38282 | ||||||||
\(699\) | −3.43090 | −0.129768 | ||||||||
\(700\) | −58.8155 | −2.22302 | ||||||||
\(701\) | −27.6256 | −1.04340 | −0.521702 | − | 0.853128i | \(-0.674703\pi\) | ||||
−0.521702 | + | 0.853128i | \(0.674703\pi\) | |||||||
\(702\) | 6.65859 | 0.251312 | ||||||||
\(703\) | 37.2747 | 1.40584 | ||||||||
\(704\) | −211.243 | −7.96151 | ||||||||
\(705\) | −5.70127 | −0.214722 | ||||||||
\(706\) | 6.80053 | 0.255941 | ||||||||
\(707\) | 24.7176 | 0.929600 | ||||||||
\(708\) | 71.8479 | 2.70021 | ||||||||
\(709\) | 8.10255 | 0.304298 | 0.152149 | − | 0.988358i | \(-0.451381\pi\) | ||||
0.152149 | + | 0.988358i | \(0.451381\pi\) | |||||||
\(710\) | 120.043 | 4.50513 | ||||||||
\(711\) | 9.51988 | 0.357023 | ||||||||
\(712\) | 118.581 | 4.44402 | ||||||||
\(713\) | −4.18385 | −0.156687 | ||||||||
\(714\) | −13.0155 | −0.487092 | ||||||||
\(715\) | −36.6974 | −1.37240 | ||||||||
\(716\) | 116.141 | 4.34038 | ||||||||
\(717\) | 5.76650 | 0.215354 | ||||||||
\(718\) | −101.792 | −3.79883 | ||||||||
\(719\) | 21.9351 | 0.818041 | 0.409020 | − | 0.912525i | \(-0.365870\pi\) | ||||
0.409020 | + | 0.912525i | \(0.365870\pi\) | |||||||
\(720\) | −64.2986 | −2.39627 | ||||||||
\(721\) | 14.2347 | 0.530126 | ||||||||
\(722\) | 19.6374 | 0.730829 | ||||||||
\(723\) | 19.8383 | 0.737794 | ||||||||
\(724\) | −0.830184 | −0.0308536 | ||||||||
\(725\) | 7.11755 | 0.264339 | ||||||||
\(726\) | −24.2659 | −0.900594 | ||||||||
\(727\) | 49.7966 | 1.84685 | 0.923427 | − | 0.383773i | \(-0.125376\pi\) | ||||
0.923427 | + | 0.383773i | \(0.125376\pi\) | |||||||
\(728\) | −36.1946 | −1.34146 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 84.6873 | 3.13442 | ||||||||
\(731\) | 23.2737 | 0.860811 | ||||||||
\(732\) | 30.6955 | 1.13454 | ||||||||
\(733\) | −5.55178 | −0.205060 | −0.102530 | − | 0.994730i | \(-0.532694\pi\) | ||||
−0.102530 | + | 0.994730i | \(0.532694\pi\) | |||||||
\(734\) | −34.1799 | −1.26160 | ||||||||
\(735\) | 17.4089 | 0.642135 | ||||||||
\(736\) | −30.1980 | −1.11311 | ||||||||
\(737\) | 53.1363 | 1.95730 | ||||||||
\(738\) | −10.4007 | −0.382854 | ||||||||
\(739\) | −35.1640 | −1.29353 | −0.646765 | − | 0.762689i | \(-0.723879\pi\) | ||||
−0.646765 | + | 0.762689i | \(0.723879\pi\) | |||||||
\(740\) | 219.027 | 8.05159 | ||||||||
\(741\) | 8.23153 | 0.302393 | ||||||||
\(742\) | 27.6079 | 1.01352 | ||||||||
\(743\) | 49.3711 | 1.81125 | 0.905625 | − | 0.424079i | \(-0.139402\pi\) | ||||
0.905625 | + | 0.424079i | \(0.139402\pi\) | |||||||
\(744\) | 45.0534 | 1.65174 | ||||||||
\(745\) | −41.8529 | −1.53337 | ||||||||
\(746\) | −11.2242 | −0.410946 | ||||||||
\(747\) | 2.12581 | 0.0777792 | ||||||||
\(748\) | 85.1862 | 3.11471 | ||||||||
\(749\) | 12.2168 | 0.446392 | ||||||||
\(750\) | 20.6456 | 0.753872 | ||||||||
\(751\) | 26.4065 | 0.963587 | 0.481793 | − | 0.876285i | \(-0.339986\pi\) | ||||
0.481793 | + | 0.876285i | \(0.339986\pi\) | |||||||
\(752\) | 30.2523 | 1.10319 | ||||||||
\(753\) | −1.97792 | −0.0720794 | ||||||||
\(754\) | 6.65859 | 0.242491 | ||||||||
\(755\) | −49.1633 | −1.78923 | ||||||||
\(756\) | −8.26345 | −0.300539 | ||||||||
\(757\) | 41.0628 | 1.49245 | 0.746227 | − | 0.665692i | \(-0.231863\pi\) | ||||
0.746227 | + | 0.665692i | \(0.231863\pi\) | |||||||
\(758\) | −10.2618 | −0.372726 | ||||||||
\(759\) | −4.43439 | −0.160958 | ||||||||
\(760\) | −129.791 | −4.70802 | ||||||||
\(761\) | 39.5526 | 1.43378 | 0.716890 | − | 0.697187i | \(-0.245565\pi\) | ||||
0.716890 | + | 0.697187i | \(0.245565\pi\) | |||||||
\(762\) | −35.7103 | −1.29365 | ||||||||
\(763\) | 10.8683 | 0.393458 | ||||||||
\(764\) | −85.3135 | −3.08653 | ||||||||
\(765\) | 11.4414 | 0.413665 | ||||||||
\(766\) | 35.1622 | 1.27046 | ||||||||
\(767\) | −29.2244 | −1.05523 | ||||||||
\(768\) | 109.267 | 3.94283 | ||||||||
\(769\) | −9.25396 | −0.333706 | −0.166853 | − | 0.985982i | \(-0.553361\pi\) | ||||
−0.166853 | + | 0.985982i | \(0.553361\pi\) | |||||||
\(770\) | 61.1263 | 2.20284 | ||||||||
\(771\) | −0.846927 | −0.0305013 | ||||||||
\(772\) | −101.152 | −3.64055 | ||||||||
\(773\) | −32.8456 | −1.18137 | −0.590687 | − | 0.806901i | \(-0.701143\pi\) | ||||
−0.590687 | + | 0.806901i | \(0.701143\pi\) | |||||||
\(774\) | 19.8327 | 0.712872 | ||||||||
\(775\) | −29.7788 | −1.06969 | ||||||||
\(776\) | −132.890 | −4.77047 | ||||||||
\(777\) | 15.2204 | 0.546030 | ||||||||
\(778\) | −51.1878 | −1.83517 | ||||||||
\(779\) | −12.8576 | −0.460671 | ||||||||
\(780\) | 48.3686 | 1.73187 | ||||||||
\(781\) | −54.5978 | −1.95366 | ||||||||
\(782\) | 9.20579 | 0.329198 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | −92.3756 | −3.29913 | ||||||||
\(785\) | −44.4822 | −1.58764 | ||||||||
\(786\) | 40.5031 | 1.44470 | ||||||||
\(787\) | −25.5920 | −0.912257 | −0.456129 | − | 0.889914i | \(-0.650764\pi\) | ||||
−0.456129 | + | 0.889914i | \(0.650764\pi\) | |||||||
\(788\) | 12.3329 | 0.439340 | ||||||||
\(789\) | 0.347153 | 0.0123590 | ||||||||
\(790\) | 92.8169 | 3.30228 | ||||||||
\(791\) | 7.80158 | 0.277392 | ||||||||
\(792\) | 47.7513 | 1.69677 | ||||||||
\(793\) | −12.4855 | −0.443373 | ||||||||
\(794\) | −25.2624 | −0.896530 | ||||||||
\(795\) | −24.2691 | −0.860736 | ||||||||
\(796\) | 96.0359 | 3.40390 | ||||||||
\(797\) | −11.2097 | −0.397069 | −0.198534 | − | 0.980094i | \(-0.563618\pi\) | ||||
−0.198534 | + | 0.980094i | \(0.563618\pi\) | |||||||
\(798\) | −13.7112 | −0.485370 | ||||||||
\(799\) | −5.38315 | −0.190442 | ||||||||
\(800\) | −214.935 | −7.59912 | ||||||||
\(801\) | −11.0119 | −0.389088 | ||||||||
\(802\) | −18.6557 | −0.658756 | ||||||||
\(803\) | −38.5174 | −1.35925 | ||||||||
\(804\) | −70.0359 | −2.46997 | ||||||||
\(805\) | 4.92160 | 0.173464 | ||||||||
\(806\) | −27.8586 | −0.981276 | ||||||||
\(807\) | 22.3131 | 0.785458 | ||||||||
\(808\) | 188.260 | 6.62297 | ||||||||
\(809\) | 8.56734 | 0.301212 | 0.150606 | − | 0.988594i | \(-0.451878\pi\) | ||||
0.150606 | + | 0.988594i | \(0.451878\pi\) | |||||||
\(810\) | 9.74980 | 0.342573 | ||||||||
\(811\) | 21.1612 | 0.743069 | 0.371535 | − | 0.928419i | \(-0.378832\pi\) | ||||
0.371535 | + | 0.928419i | \(0.378832\pi\) | |||||||
\(812\) | −8.26345 | −0.289990 | ||||||||
\(813\) | −21.0578 | −0.738528 | ||||||||
\(814\) | −133.706 | −4.68638 | ||||||||
\(815\) | −62.7428 | −2.19778 | ||||||||
\(816\) | −60.7109 | −2.12531 | ||||||||
\(817\) | 24.5177 | 0.857767 | ||||||||
\(818\) | −11.0710 | −0.387090 | ||||||||
\(819\) | 3.36119 | 0.117449 | ||||||||
\(820\) | −75.5514 | −2.63837 | ||||||||
\(821\) | −11.7177 | −0.408950 | −0.204475 | − | 0.978872i | \(-0.565549\pi\) | ||||
−0.204475 | + | 0.978872i | \(0.565549\pi\) | |||||||
\(822\) | −26.2363 | −0.915096 | ||||||||
\(823\) | −3.38360 | −0.117945 | −0.0589724 | − | 0.998260i | \(-0.518782\pi\) | ||||
−0.0589724 | + | 0.998260i | \(0.518782\pi\) | |||||||
\(824\) | 108.417 | 3.77690 | ||||||||
\(825\) | −31.5620 | −1.09885 | ||||||||
\(826\) | 48.6787 | 1.69375 | ||||||||
\(827\) | 10.4103 | 0.362003 | 0.181001 | − | 0.983483i | \(-0.442066\pi\) | ||||
0.181001 | + | 0.983483i | \(0.442066\pi\) | |||||||
\(828\) | 5.84471 | 0.203118 | ||||||||
\(829\) | −14.8931 | −0.517259 | −0.258630 | − | 0.965977i | \(-0.583271\pi\) | ||||
−0.258630 | + | 0.965977i | \(0.583271\pi\) | |||||||
\(830\) | 20.7262 | 0.719417 | ||||||||
\(831\) | 2.42766 | 0.0842146 | ||||||||
\(832\) | −113.251 | −3.92627 | ||||||||
\(833\) | 16.4375 | 0.569525 | ||||||||
\(834\) | 20.1061 | 0.696217 | ||||||||
\(835\) | −21.7355 | −0.752187 | ||||||||
\(836\) | 89.7394 | 3.10370 | ||||||||
\(837\) | −4.18385 | −0.144615 | ||||||||
\(838\) | −12.3529 | −0.426725 | ||||||||
\(839\) | −35.8545 | −1.23784 | −0.618918 | − | 0.785456i | \(-0.712429\pi\) | ||||
−0.618918 | + | 0.785456i | \(0.712429\pi\) | |||||||
\(840\) | −52.9978 | −1.82860 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −41.6932 | −1.43684 | ||||||||
\(843\) | 11.6621 | 0.401664 | ||||||||
\(844\) | 29.4184 | 1.01262 | ||||||||
\(845\) | 25.5793 | 0.879953 | ||||||||
\(846\) | −4.58725 | −0.157713 | ||||||||
\(847\) | −12.2492 | −0.420888 | ||||||||
\(848\) | 128.778 | 4.42224 | ||||||||
\(849\) | −7.95812 | −0.273122 | ||||||||
\(850\) | 65.5226 | 2.24741 | ||||||||
\(851\) | −10.7653 | −0.369031 | ||||||||
\(852\) | 71.9621 | 2.46538 | ||||||||
\(853\) | 11.4424 | 0.391779 | 0.195890 | − | 0.980626i | \(-0.437241\pi\) | ||||
0.195890 | + | 0.980626i | \(0.437241\pi\) | |||||||
\(854\) | 20.7970 | 0.711657 | ||||||||
\(855\) | 12.0530 | 0.412203 | ||||||||
\(856\) | 93.0486 | 3.18034 | ||||||||
\(857\) | −34.4455 | −1.17664 | −0.588319 | − | 0.808629i | \(-0.700210\pi\) | ||||
−0.588319 | + | 0.808629i | \(0.700210\pi\) | |||||||
\(858\) | −29.5268 | −1.00803 | ||||||||
\(859\) | −2.68062 | −0.0914617 | −0.0457308 | − | 0.998954i | \(-0.514562\pi\) | ||||
−0.0457308 | + | 0.998954i | \(0.514562\pi\) | |||||||
\(860\) | 144.067 | 4.91263 | ||||||||
\(861\) | −5.25015 | −0.178925 | ||||||||
\(862\) | 7.29125 | 0.248341 | ||||||||
\(863\) | 40.5322 | 1.37973 | 0.689866 | − | 0.723937i | \(-0.257670\pi\) | ||||
0.689866 | + | 0.723937i | \(0.257670\pi\) | |||||||
\(864\) | −30.1980 | −1.02736 | ||||||||
\(865\) | 74.6417 | 2.53789 | ||||||||
\(866\) | −16.6172 | −0.564677 | ||||||||
\(867\) | −6.19698 | −0.210460 | ||||||||
\(868\) | 34.5731 | 1.17349 | ||||||||
\(869\) | −42.2148 | −1.43204 | ||||||||
\(870\) | 9.74980 | 0.330549 | ||||||||
\(871\) | 28.4873 | 0.965256 | ||||||||
\(872\) | 82.7776 | 2.80320 | ||||||||
\(873\) | 12.3407 | 0.417670 | ||||||||
\(874\) | 9.69784 | 0.328034 | ||||||||
\(875\) | 10.4217 | 0.352318 | ||||||||
\(876\) | 50.7675 | 1.71527 | ||||||||
\(877\) | 26.5521 | 0.896600 | 0.448300 | − | 0.893883i | \(-0.352030\pi\) | ||||
0.448300 | + | 0.893883i | \(0.352030\pi\) | |||||||
\(878\) | 23.7743 | 0.802344 | ||||||||
\(879\) | −25.6929 | −0.866599 | ||||||||
\(880\) | 285.125 | 9.61157 | ||||||||
\(881\) | 2.87095 | 0.0967248 | 0.0483624 | − | 0.998830i | \(-0.484600\pi\) | ||||
0.0483624 | + | 0.998830i | \(0.484600\pi\) | |||||||
\(882\) | 14.0072 | 0.471647 | ||||||||
\(883\) | 28.0387 | 0.943578 | 0.471789 | − | 0.881711i | \(-0.343608\pi\) | ||||
0.471789 | + | 0.881711i | \(0.343608\pi\) | |||||||
\(884\) | 45.6698 | 1.53604 | ||||||||
\(885\) | −42.7917 | −1.43843 | ||||||||
\(886\) | 59.5290 | 1.99992 | ||||||||
\(887\) | 17.7793 | 0.596972 | 0.298486 | − | 0.954414i | \(-0.403518\pi\) | ||||
0.298486 | + | 0.954414i | \(0.403518\pi\) | |||||||
\(888\) | 115.926 | 3.89021 | ||||||||
\(889\) | −18.0262 | −0.604580 | ||||||||
\(890\) | −107.364 | −3.59886 | ||||||||
\(891\) | −4.43439 | −0.148558 | ||||||||
\(892\) | −27.7323 | −0.928544 | ||||||||
\(893\) | −5.67089 | −0.189769 | ||||||||
\(894\) | −33.6749 | −1.12626 | ||||||||
\(895\) | −69.1718 | −2.31216 | ||||||||
\(896\) | 103.251 | 3.44936 | ||||||||
\(897\) | −2.37735 | −0.0793775 | ||||||||
\(898\) | 30.3355 | 1.01231 | ||||||||
\(899\) | −4.18385 | −0.139539 | ||||||||
\(900\) | 41.6000 | 1.38667 | ||||||||
\(901\) | −22.9149 | −0.763407 | ||||||||
\(902\) | 46.1206 | 1.53565 | ||||||||
\(903\) | 10.0114 | 0.333157 | ||||||||
\(904\) | 59.4203 | 1.97629 | ||||||||
\(905\) | 0.494446 | 0.0164360 | ||||||||
\(906\) | −39.5568 | −1.31419 | ||||||||
\(907\) | 48.0328 | 1.59490 | 0.797451 | − | 0.603383i | \(-0.206181\pi\) | ||||
0.797451 | + | 0.603383i | \(0.206181\pi\) | |||||||
\(908\) | −93.1725 | −3.09204 | ||||||||
\(909\) | −17.4826 | −0.579862 | ||||||||
\(910\) | 32.7709 | 1.08634 | ||||||||
\(911\) | 36.9017 | 1.22261 | 0.611304 | − | 0.791396i | \(-0.290645\pi\) | ||||
0.611304 | + | 0.791396i | \(0.290645\pi\) | |||||||
\(912\) | −63.9560 | −2.11779 | ||||||||
\(913\) | −9.42666 | −0.311977 | ||||||||
\(914\) | −6.30023 | −0.208393 | ||||||||
\(915\) | −18.2818 | −0.604379 | ||||||||
\(916\) | 143.816 | 4.75181 | ||||||||
\(917\) | 20.4456 | 0.675172 | ||||||||
\(918\) | 9.20579 | 0.303836 | ||||||||
\(919\) | −9.31252 | −0.307192 | −0.153596 | − | 0.988134i | \(-0.549085\pi\) | ||||
−0.153596 | + | 0.988134i | \(0.549085\pi\) | |||||||
\(920\) | 37.4851 | 1.23585 | ||||||||
\(921\) | 18.5614 | 0.611620 | ||||||||
\(922\) | −7.04781 | −0.232107 | ||||||||
\(923\) | −29.2708 | −0.963460 | ||||||||
\(924\) | 36.6434 | 1.20548 | ||||||||
\(925\) | −76.6228 | −2.51934 | ||||||||
\(926\) | 42.6293 | 1.40088 | ||||||||
\(927\) | −10.0681 | −0.330680 | ||||||||
\(928\) | −30.1980 | −0.991297 | ||||||||
\(929\) | −30.7813 | −1.00990 | −0.504951 | − | 0.863148i | \(-0.668489\pi\) | ||||
−0.504951 | + | 0.863148i | \(0.668489\pi\) | |||||||
\(930\) | −40.7917 | −1.33761 | ||||||||
\(931\) | 17.3161 | 0.567512 | ||||||||
\(932\) | −20.0526 | −0.656844 | ||||||||
\(933\) | 9.91454 | 0.324587 | ||||||||
\(934\) | 17.0478 | 0.557820 | ||||||||
\(935\) | −50.7357 | −1.65924 | ||||||||
\(936\) | 25.6003 | 0.836772 | ||||||||
\(937\) | 40.1120 | 1.31040 | 0.655202 | − | 0.755454i | \(-0.272584\pi\) | ||||
0.655202 | + | 0.755454i | \(0.272584\pi\) | |||||||
\(938\) | −47.4510 | −1.54933 | ||||||||
\(939\) | 15.3040 | 0.499426 | ||||||||
\(940\) | −33.3222 | −1.08685 | ||||||||
\(941\) | −47.6356 | −1.55287 | −0.776437 | − | 0.630194i | \(-0.782975\pi\) | ||||
−0.776437 | + | 0.630194i | \(0.782975\pi\) | |||||||
\(942\) | −35.7905 | −1.16612 | ||||||||
\(943\) | 3.71341 | 0.120925 | ||||||||
\(944\) | 227.063 | 7.39027 | ||||||||
\(945\) | 4.92160 | 0.160100 | ||||||||
\(946\) | −87.9460 | −2.85937 | ||||||||
\(947\) | 36.9283 | 1.20001 | 0.600004 | − | 0.799997i | \(-0.295166\pi\) | ||||
0.600004 | + | 0.799997i | \(0.295166\pi\) | |||||||
\(948\) | 55.6409 | 1.80713 | ||||||||
\(949\) | −20.6498 | −0.670322 | ||||||||
\(950\) | 69.0248 | 2.23946 | ||||||||
\(951\) | 17.3563 | 0.562818 | ||||||||
\(952\) | −50.0406 | −1.62183 | ||||||||
\(953\) | 9.59892 | 0.310939 | 0.155470 | − | 0.987841i | \(-0.450311\pi\) | ||||
0.155470 | + | 0.987841i | \(0.450311\pi\) | |||||||
\(954\) | −19.5270 | −0.632208 | ||||||||
\(955\) | 50.8115 | 1.64422 | ||||||||
\(956\) | 33.7035 | 1.09005 | ||||||||
\(957\) | −4.43439 | −0.143343 | ||||||||
\(958\) | 8.17762 | 0.264207 | ||||||||
\(959\) | −13.2438 | −0.427665 | ||||||||
\(960\) | −165.827 | −5.35204 | ||||||||
\(961\) | −13.4954 | −0.435334 | ||||||||
\(962\) | −71.6819 | −2.31112 | ||||||||
\(963\) | −8.64089 | −0.278449 | ||||||||
\(964\) | 115.949 | 3.73446 | ||||||||
\(965\) | 60.2450 | 1.93935 | ||||||||
\(966\) | 3.95993 | 0.127409 | ||||||||
\(967\) | −31.4665 | −1.01190 | −0.505948 | − | 0.862564i | \(-0.668857\pi\) | ||||
−0.505948 | + | 0.862564i | \(0.668857\pi\) | |||||||
\(968\) | −93.2954 | −2.99863 | ||||||||
\(969\) | 11.3804 | 0.365593 | ||||||||
\(970\) | 120.320 | 3.86323 | ||||||||
\(971\) | 31.9428 | 1.02509 | 0.512547 | − | 0.858659i | \(-0.328702\pi\) | ||||
0.512547 | + | 0.858659i | \(0.328702\pi\) | |||||||
\(972\) | 5.84471 | 0.187469 | ||||||||
\(973\) | 10.1493 | 0.325373 | ||||||||
\(974\) | −98.9314 | −3.16997 | ||||||||
\(975\) | −16.9209 | −0.541903 | ||||||||
\(976\) | 97.0078 | 3.10515 | ||||||||
\(977\) | −18.8977 | −0.604592 | −0.302296 | − | 0.953214i | \(-0.597753\pi\) | ||||
−0.302296 | + | 0.953214i | \(0.597753\pi\) | |||||||
\(978\) | −50.4830 | −1.61427 | ||||||||
\(979\) | 48.8313 | 1.56065 | ||||||||
\(980\) | 101.750 | 3.25027 | ||||||||
\(981\) | −7.68708 | −0.245430 | ||||||||
\(982\) | 14.3482 | 0.457871 | ||||||||
\(983\) | 9.51432 | 0.303460 | 0.151730 | − | 0.988422i | \(-0.451516\pi\) | ||||
0.151730 | + | 0.988422i | \(0.451516\pi\) | |||||||
\(984\) | −39.9875 | −1.27475 | ||||||||
\(985\) | −7.34528 | −0.234040 | ||||||||
\(986\) | 9.20579 | 0.293172 | ||||||||
\(987\) | −2.31560 | −0.0737063 | ||||||||
\(988\) | 48.1109 | 1.53061 | ||||||||
\(989\) | −7.08099 | −0.225162 | ||||||||
\(990\) | −43.2344 | −1.37408 | ||||||||
\(991\) | 37.2984 | 1.18482 | 0.592412 | − | 0.805635i | \(-0.298176\pi\) | ||||
0.592412 | + | 0.805635i | \(0.298176\pi\) | |||||||
\(992\) | 126.344 | 4.01143 | ||||||||
\(993\) | −25.6184 | −0.812974 | ||||||||
\(994\) | 48.7560 | 1.54645 | ||||||||
\(995\) | −57.1977 | −1.81329 | ||||||||
\(996\) | 12.4247 | 0.393692 | ||||||||
\(997\) | −5.35625 | −0.169634 | −0.0848171 | − | 0.996397i | \(-0.527031\pi\) | ||||
−0.0848171 | + | 0.996397i | \(0.527031\pi\) | |||||||
\(998\) | −23.2537 | −0.736082 | ||||||||
\(999\) | −10.7653 | −0.340600 |
(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.o.1.1 | ✓ | 20 | |
3.2 | odd | 2 | 6003.2.a.s.1.20 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.o.1.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
6003.2.a.s.1.20 | 20 | 3.2 | odd | 2 |