Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [619,2,Mod(1,619)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(619, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("619.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 619.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: | \(4.94273988512\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.22 | ||
Character | \(\chi\) | \(=\) | 619.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.77256 | 1.25339 | 0.626696 | − | 0.779264i | \(-0.284407\pi\) | ||||
0.626696 | + | 0.779264i | \(0.284407\pi\) | |||||||
\(3\) | −2.61871 | −1.51191 | −0.755956 | − | 0.654623i | \(-0.772828\pi\) | ||||
−0.755956 | + | 0.654623i | \(0.772828\pi\) | |||||||
\(4\) | 1.14198 | 0.570991 | ||||||||
\(5\) | 2.86335 | 1.28053 | 0.640265 | − | 0.768154i | \(-0.278824\pi\) | ||||
0.640265 | + | 0.768154i | \(0.278824\pi\) | |||||||
\(6\) | −4.64183 | −1.89502 | ||||||||
\(7\) | 2.04983 | 0.774763 | 0.387381 | − | 0.921920i | \(-0.373380\pi\) | ||||
0.387381 | + | 0.921920i | \(0.373380\pi\) | |||||||
\(8\) | −1.52089 | −0.537716 | ||||||||
\(9\) | 3.85763 | 1.28588 | ||||||||
\(10\) | 5.07548 | 1.60501 | ||||||||
\(11\) | −3.53364 | −1.06543 | −0.532716 | − | 0.846294i | \(-0.678829\pi\) | ||||
−0.532716 | + | 0.846294i | \(0.678829\pi\) | |||||||
\(12\) | −2.99052 | −0.863288 | ||||||||
\(13\) | 5.12412 | 1.42117 | 0.710587 | − | 0.703609i | \(-0.248429\pi\) | ||||
0.710587 | + | 0.703609i | \(0.248429\pi\) | |||||||
\(14\) | 3.63345 | 0.971081 | ||||||||
\(15\) | −7.49829 | −1.93605 | ||||||||
\(16\) | −4.97984 | −1.24496 | ||||||||
\(17\) | 5.62332 | 1.36386 | 0.681928 | − | 0.731419i | \(-0.261142\pi\) | ||||
0.681928 | + | 0.731419i | \(0.261142\pi\) | |||||||
\(18\) | 6.83790 | 1.61171 | ||||||||
\(19\) | 4.67171 | 1.07176 | 0.535881 | − | 0.844293i | \(-0.319979\pi\) | ||||
0.535881 | + | 0.844293i | \(0.319979\pi\) | |||||||
\(20\) | 3.26990 | 0.731171 | ||||||||
\(21\) | −5.36791 | −1.17137 | ||||||||
\(22\) | −6.26360 | −1.33540 | ||||||||
\(23\) | −1.06415 | −0.221892 | −0.110946 | − | 0.993826i | \(-0.535388\pi\) | ||||
−0.110946 | + | 0.993826i | \(0.535388\pi\) | |||||||
\(24\) | 3.98277 | 0.812980 | ||||||||
\(25\) | 3.19879 | 0.639759 | ||||||||
\(26\) | 9.08283 | 1.78129 | ||||||||
\(27\) | −2.24589 | −0.432221 | ||||||||
\(28\) | 2.34087 | 0.442383 | ||||||||
\(29\) | 8.34802 | 1.55019 | 0.775094 | − | 0.631846i | \(-0.217703\pi\) | ||||
0.775094 | + | 0.631846i | \(0.217703\pi\) | |||||||
\(30\) | −13.2912 | −2.42663 | ||||||||
\(31\) | −4.96773 | −0.892230 | −0.446115 | − | 0.894976i | \(-0.647193\pi\) | ||||
−0.446115 | + | 0.894976i | \(0.647193\pi\) | |||||||
\(32\) | −5.78530 | −1.02271 | ||||||||
\(33\) | 9.25357 | 1.61084 | ||||||||
\(34\) | 9.96770 | 1.70945 | ||||||||
\(35\) | 5.86939 | 0.992108 | ||||||||
\(36\) | 4.40535 | 0.734224 | ||||||||
\(37\) | −1.19702 | −0.196788 | −0.0983940 | − | 0.995148i | \(-0.531371\pi\) | ||||
−0.0983940 | + | 0.995148i | \(0.531371\pi\) | |||||||
\(38\) | 8.28090 | 1.34334 | ||||||||
\(39\) | −13.4186 | −2.14869 | ||||||||
\(40\) | −4.35485 | −0.688562 | ||||||||
\(41\) | −1.05581 | −0.164889 | −0.0824447 | − | 0.996596i | \(-0.526273\pi\) | ||||
−0.0824447 | + | 0.996596i | \(0.526273\pi\) | |||||||
\(42\) | −9.51495 | −1.46819 | ||||||||
\(43\) | 6.18169 | 0.942699 | 0.471350 | − | 0.881946i | \(-0.343767\pi\) | ||||
0.471350 | + | 0.881946i | \(0.343767\pi\) | |||||||
\(44\) | −4.03535 | −0.608352 | ||||||||
\(45\) | 11.0458 | 1.64661 | ||||||||
\(46\) | −1.88628 | −0.278117 | ||||||||
\(47\) | 11.1882 | 1.63196 | 0.815981 | − | 0.578079i | \(-0.196198\pi\) | ||||
0.815981 | + | 0.578079i | \(0.196198\pi\) | |||||||
\(48\) | 13.0408 | 1.88227 | ||||||||
\(49\) | −2.79820 | −0.399743 | ||||||||
\(50\) | 5.67006 | 0.801868 | ||||||||
\(51\) | −14.7258 | −2.06203 | ||||||||
\(52\) | 5.85165 | 0.811478 | ||||||||
\(53\) | −2.73223 | −0.375301 | −0.187650 | − | 0.982236i | \(-0.560087\pi\) | ||||
−0.187650 | + | 0.982236i | \(0.560087\pi\) | |||||||
\(54\) | −3.98098 | −0.541743 | ||||||||
\(55\) | −10.1181 | −1.36432 | ||||||||
\(56\) | −3.11757 | −0.416603 | ||||||||
\(57\) | −12.2338 | −1.62041 | ||||||||
\(58\) | 14.7974 | 1.94299 | ||||||||
\(59\) | −10.0977 | −1.31461 | −0.657304 | − | 0.753626i | \(-0.728303\pi\) | ||||
−0.657304 | + | 0.753626i | \(0.728303\pi\) | |||||||
\(60\) | −8.56291 | −1.10547 | ||||||||
\(61\) | −6.59654 | −0.844601 | −0.422300 | − | 0.906456i | \(-0.638777\pi\) | ||||
−0.422300 | + | 0.906456i | \(0.638777\pi\) | |||||||
\(62\) | −8.80562 | −1.11831 | ||||||||
\(63\) | 7.90749 | 0.996250 | ||||||||
\(64\) | −0.295133 | −0.0368917 | ||||||||
\(65\) | 14.6722 | 1.81986 | ||||||||
\(66\) | 16.4025 | 2.01901 | ||||||||
\(67\) | −14.7096 | −1.79706 | −0.898530 | − | 0.438913i | \(-0.855364\pi\) | ||||
−0.898530 | + | 0.438913i | \(0.855364\pi\) | |||||||
\(68\) | 6.42173 | 0.778749 | ||||||||
\(69\) | 2.78671 | 0.335481 | ||||||||
\(70\) | 10.4039 | 1.24350 | ||||||||
\(71\) | 8.64906 | 1.02646 | 0.513228 | − | 0.858253i | \(-0.328450\pi\) | ||||
0.513228 | + | 0.858253i | \(0.328450\pi\) | |||||||
\(72\) | −5.86704 | −0.691437 | ||||||||
\(73\) | −9.61528 | −1.12538 | −0.562692 | − | 0.826667i | \(-0.690234\pi\) | ||||
−0.562692 | + | 0.826667i | \(0.690234\pi\) | |||||||
\(74\) | −2.12179 | −0.246653 | ||||||||
\(75\) | −8.37671 | −0.967259 | ||||||||
\(76\) | 5.33500 | 0.611967 | ||||||||
\(77\) | −7.24336 | −0.825457 | ||||||||
\(78\) | −23.7853 | −2.69315 | ||||||||
\(79\) | 2.15346 | 0.242283 | 0.121142 | − | 0.992635i | \(-0.461344\pi\) | ||||
0.121142 | + | 0.992635i | \(0.461344\pi\) | |||||||
\(80\) | −14.2590 | −1.59421 | ||||||||
\(81\) | −5.69157 | −0.632397 | ||||||||
\(82\) | −1.87149 | −0.206671 | ||||||||
\(83\) | −15.2974 | −1.67911 | −0.839554 | − | 0.543277i | \(-0.817183\pi\) | ||||
−0.839554 | + | 0.543277i | \(0.817183\pi\) | |||||||
\(84\) | −6.13005 | −0.668843 | ||||||||
\(85\) | 16.1016 | 1.74646 | ||||||||
\(86\) | 10.9574 | 1.18157 | ||||||||
\(87\) | −21.8610 | −2.34375 | ||||||||
\(88\) | 5.37428 | 0.572900 | ||||||||
\(89\) | −3.00189 | −0.318200 | −0.159100 | − | 0.987262i | \(-0.550859\pi\) | ||||
−0.159100 | + | 0.987262i | \(0.550859\pi\) | |||||||
\(90\) | 19.5793 | 2.06384 | ||||||||
\(91\) | 10.5036 | 1.10107 | ||||||||
\(92\) | −1.21525 | −0.126698 | ||||||||
\(93\) | 13.0090 | 1.34897 | ||||||||
\(94\) | 19.8317 | 2.04549 | ||||||||
\(95\) | 13.3767 | 1.37243 | ||||||||
\(96\) | 15.1500 | 1.54624 | ||||||||
\(97\) | 2.92181 | 0.296665 | 0.148333 | − | 0.988938i | \(-0.452609\pi\) | ||||
0.148333 | + | 0.988938i | \(0.452609\pi\) | |||||||
\(98\) | −4.95998 | −0.501034 | ||||||||
\(99\) | −13.6315 | −1.37001 | ||||||||
\(100\) | 3.65296 | 0.365296 | ||||||||
\(101\) | 1.50237 | 0.149492 | 0.0747459 | − | 0.997203i | \(-0.476185\pi\) | ||||
0.0747459 | + | 0.997203i | \(0.476185\pi\) | |||||||
\(102\) | −26.1025 | −2.58453 | ||||||||
\(103\) | −6.10995 | −0.602031 | −0.301016 | − | 0.953619i | \(-0.597326\pi\) | ||||
−0.301016 | + | 0.953619i | \(0.597326\pi\) | |||||||
\(104\) | −7.79323 | −0.764189 | ||||||||
\(105\) | −15.3702 | −1.49998 | ||||||||
\(106\) | −4.84306 | −0.470399 | ||||||||
\(107\) | 14.3894 | 1.39108 | 0.695538 | − | 0.718490i | \(-0.255166\pi\) | ||||
0.695538 | + | 0.718490i | \(0.255166\pi\) | |||||||
\(108\) | −2.56476 | −0.246795 | ||||||||
\(109\) | −6.64977 | −0.636933 | −0.318466 | − | 0.947934i | \(-0.603168\pi\) | ||||
−0.318466 | + | 0.947934i | \(0.603168\pi\) | |||||||
\(110\) | −17.9349 | −1.71003 | ||||||||
\(111\) | 3.13463 | 0.297526 | ||||||||
\(112\) | −10.2078 | −0.964549 | ||||||||
\(113\) | 0.748342 | 0.0703980 | 0.0351990 | − | 0.999380i | \(-0.488793\pi\) | ||||
0.0351990 | + | 0.999380i | \(0.488793\pi\) | |||||||
\(114\) | −21.6853 | −2.03101 | ||||||||
\(115\) | −3.04705 | −0.284139 | ||||||||
\(116\) | 9.53328 | 0.885143 | ||||||||
\(117\) | 19.7670 | 1.82746 | ||||||||
\(118\) | −17.8988 | −1.64772 | ||||||||
\(119\) | 11.5269 | 1.05666 | ||||||||
\(120\) | 11.4041 | 1.04105 | ||||||||
\(121\) | 1.48660 | 0.135145 | ||||||||
\(122\) | −11.6928 | −1.05862 | ||||||||
\(123\) | 2.76485 | 0.249298 | ||||||||
\(124\) | −5.67306 | −0.509455 | ||||||||
\(125\) | −5.15749 | −0.461300 | ||||||||
\(126\) | 14.0165 | 1.24869 | ||||||||
\(127\) | −15.3680 | −1.36369 | −0.681846 | − | 0.731496i | \(-0.738823\pi\) | ||||
−0.681846 | + | 0.731496i | \(0.738823\pi\) | |||||||
\(128\) | 11.0475 | 0.976467 | ||||||||
\(129\) | −16.1880 | −1.42528 | ||||||||
\(130\) | 26.0073 | 2.28099 | ||||||||
\(131\) | −14.3661 | −1.25517 | −0.627584 | − | 0.778549i | \(-0.715956\pi\) | ||||
−0.627584 | + | 0.778549i | \(0.715956\pi\) | |||||||
\(132\) | 10.5674 | 0.919775 | ||||||||
\(133\) | 9.57620 | 0.830362 | ||||||||
\(134\) | −26.0736 | −2.25242 | ||||||||
\(135\) | −6.43077 | −0.553473 | ||||||||
\(136\) | −8.55246 | −0.733368 | ||||||||
\(137\) | −18.9233 | −1.61672 | −0.808362 | − | 0.588686i | \(-0.799646\pi\) | ||||
−0.808362 | + | 0.588686i | \(0.799646\pi\) | |||||||
\(138\) | 4.93962 | 0.420489 | ||||||||
\(139\) | 14.9651 | 1.26932 | 0.634661 | − | 0.772791i | \(-0.281140\pi\) | ||||
0.634661 | + | 0.772791i | \(0.281140\pi\) | |||||||
\(140\) | 6.70273 | 0.566484 | ||||||||
\(141\) | −29.2985 | −2.46738 | ||||||||
\(142\) | 15.3310 | 1.28655 | ||||||||
\(143\) | −18.1068 | −1.51416 | ||||||||
\(144\) | −19.2104 | −1.60087 | ||||||||
\(145\) | 23.9033 | 1.98506 | ||||||||
\(146\) | −17.0437 | −1.41055 | ||||||||
\(147\) | 7.32766 | 0.604375 | ||||||||
\(148\) | −1.36697 | −0.112364 | ||||||||
\(149\) | −8.62743 | −0.706786 | −0.353393 | − | 0.935475i | \(-0.614972\pi\) | ||||
−0.353393 | + | 0.935475i | \(0.614972\pi\) | |||||||
\(150\) | −14.8482 | −1.21235 | ||||||||
\(151\) | 6.43359 | 0.523558 | 0.261779 | − | 0.965128i | \(-0.415691\pi\) | ||||
0.261779 | + | 0.965128i | \(0.415691\pi\) | |||||||
\(152\) | −7.10516 | −0.576305 | ||||||||
\(153\) | 21.6927 | 1.75375 | ||||||||
\(154\) | −12.8393 | −1.03462 | ||||||||
\(155\) | −14.2244 | −1.14253 | ||||||||
\(156\) | −15.3238 | −1.22688 | ||||||||
\(157\) | 16.5731 | 1.32268 | 0.661338 | − | 0.750088i | \(-0.269989\pi\) | ||||
0.661338 | + | 0.750088i | \(0.269989\pi\) | |||||||
\(158\) | 3.81715 | 0.303676 | ||||||||
\(159\) | 7.15492 | 0.567422 | ||||||||
\(160\) | −16.5654 | −1.30961 | ||||||||
\(161\) | −2.18134 | −0.171913 | ||||||||
\(162\) | −10.0887 | −0.792641 | ||||||||
\(163\) | 9.34785 | 0.732180 | 0.366090 | − | 0.930579i | \(-0.380696\pi\) | ||||
0.366090 | + | 0.930579i | \(0.380696\pi\) | |||||||
\(164\) | −1.20571 | −0.0941504 | ||||||||
\(165\) | 26.4962 | 2.06273 | ||||||||
\(166\) | −27.1156 | −2.10458 | ||||||||
\(167\) | 5.82612 | 0.450839 | 0.225419 | − | 0.974262i | \(-0.427625\pi\) | ||||
0.225419 | + | 0.974262i | \(0.427625\pi\) | |||||||
\(168\) | 8.16400 | 0.629867 | ||||||||
\(169\) | 13.2566 | 1.01974 | ||||||||
\(170\) | 28.5410 | 2.18900 | ||||||||
\(171\) | 18.0217 | 1.37816 | ||||||||
\(172\) | 7.05938 | 0.538273 | ||||||||
\(173\) | 18.4409 | 1.40204 | 0.701019 | − | 0.713143i | \(-0.252729\pi\) | ||||
0.701019 | + | 0.713143i | \(0.252729\pi\) | |||||||
\(174\) | −38.7500 | −2.93763 | ||||||||
\(175\) | 6.55698 | 0.495661 | ||||||||
\(176\) | 17.5970 | 1.32642 | ||||||||
\(177\) | 26.4429 | 1.98757 | ||||||||
\(178\) | −5.32105 | −0.398829 | ||||||||
\(179\) | 12.2662 | 0.916817 | 0.458409 | − | 0.888741i | \(-0.348420\pi\) | ||||
0.458409 | + | 0.888741i | \(0.348420\pi\) | |||||||
\(180\) | 12.6141 | 0.940197 | ||||||||
\(181\) | −2.30343 | −0.171212 | −0.0856061 | − | 0.996329i | \(-0.527283\pi\) | ||||
−0.0856061 | + | 0.996329i | \(0.527283\pi\) | |||||||
\(182\) | 18.6182 | 1.38008 | ||||||||
\(183\) | 17.2744 | 1.27696 | ||||||||
\(184\) | 1.61846 | 0.119315 | ||||||||
\(185\) | −3.42748 | −0.251993 | ||||||||
\(186\) | 23.0593 | 1.69079 | ||||||||
\(187\) | −19.8708 | −1.45310 | ||||||||
\(188\) | 12.7767 | 0.931835 | ||||||||
\(189\) | −4.60369 | −0.334869 | ||||||||
\(190\) | 23.7111 | 1.72019 | ||||||||
\(191\) | 19.8066 | 1.43315 | 0.716577 | − | 0.697508i | \(-0.245708\pi\) | ||||
0.716577 | + | 0.697508i | \(0.245708\pi\) | |||||||
\(192\) | 0.772868 | 0.0557770 | ||||||||
\(193\) | 5.55014 | 0.399508 | 0.199754 | − | 0.979846i | \(-0.435986\pi\) | ||||
0.199754 | + | 0.979846i | \(0.435986\pi\) | |||||||
\(194\) | 5.17910 | 0.371838 | ||||||||
\(195\) | −38.4221 | −2.75146 | ||||||||
\(196\) | −3.19549 | −0.228249 | ||||||||
\(197\) | 4.81650 | 0.343162 | 0.171581 | − | 0.985170i | \(-0.445113\pi\) | ||||
0.171581 | + | 0.985170i | \(0.445113\pi\) | |||||||
\(198\) | −24.1627 | −1.71717 | ||||||||
\(199\) | −23.4188 | −1.66011 | −0.830056 | − | 0.557681i | \(-0.811691\pi\) | ||||
−0.830056 | + | 0.557681i | \(0.811691\pi\) | |||||||
\(200\) | −4.86502 | −0.344009 | ||||||||
\(201\) | 38.5201 | 2.71700 | ||||||||
\(202\) | 2.66305 | 0.187372 | ||||||||
\(203\) | 17.1120 | 1.20103 | ||||||||
\(204\) | −16.8166 | −1.17740 | ||||||||
\(205\) | −3.02315 | −0.211146 | ||||||||
\(206\) | −10.8303 | −0.754581 | ||||||||
\(207\) | −4.10512 | −0.285325 | ||||||||
\(208\) | −25.5173 | −1.76931 | ||||||||
\(209\) | −16.5081 | −1.14189 | ||||||||
\(210\) | −27.2447 | −1.88006 | ||||||||
\(211\) | 21.7797 | 1.49937 | 0.749687 | − | 0.661793i | \(-0.230204\pi\) | ||||
0.749687 | + | 0.661793i | \(0.230204\pi\) | |||||||
\(212\) | −3.12016 | −0.214293 | ||||||||
\(213\) | −22.6494 | −1.55191 | ||||||||
\(214\) | 25.5061 | 1.74356 | ||||||||
\(215\) | 17.7004 | 1.20716 | ||||||||
\(216\) | 3.41575 | 0.232413 | ||||||||
\(217\) | −10.1830 | −0.691267 | ||||||||
\(218\) | −11.7871 | −0.798326 | ||||||||
\(219\) | 25.1796 | 1.70148 | ||||||||
\(220\) | −11.5546 | −0.779013 | ||||||||
\(221\) | 28.8146 | 1.93828 | ||||||||
\(222\) | 5.55634 | 0.372917 | ||||||||
\(223\) | −15.6515 | −1.04810 | −0.524049 | − | 0.851688i | \(-0.675579\pi\) | ||||
−0.524049 | + | 0.851688i | \(0.675579\pi\) | |||||||
\(224\) | −11.8589 | −0.792355 | ||||||||
\(225\) | 12.3398 | 0.822651 | ||||||||
\(226\) | 1.32648 | 0.0882363 | ||||||||
\(227\) | 12.2763 | 0.814807 | 0.407404 | − | 0.913248i | \(-0.366434\pi\) | ||||
0.407404 | + | 0.913248i | \(0.366434\pi\) | |||||||
\(228\) | −13.9708 | −0.925240 | ||||||||
\(229\) | −0.387189 | −0.0255862 | −0.0127931 | − | 0.999918i | \(-0.504072\pi\) | ||||
−0.0127931 | + | 0.999918i | \(0.504072\pi\) | |||||||
\(230\) | −5.40109 | −0.356137 | ||||||||
\(231\) | 18.9682 | 1.24802 | ||||||||
\(232\) | −12.6964 | −0.833561 | ||||||||
\(233\) | −9.67415 | −0.633775 | −0.316887 | − | 0.948463i | \(-0.602638\pi\) | ||||
−0.316887 | + | 0.948463i | \(0.602638\pi\) | |||||||
\(234\) | 35.0382 | 2.29052 | ||||||||
\(235\) | 32.0357 | 2.08978 | ||||||||
\(236\) | −11.5314 | −0.750629 | ||||||||
\(237\) | −5.63929 | −0.366311 | ||||||||
\(238\) | 20.4321 | 1.32442 | ||||||||
\(239\) | −5.72187 | −0.370117 | −0.185058 | − | 0.982728i | \(-0.559247\pi\) | ||||
−0.185058 | + | 0.982728i | \(0.559247\pi\) | |||||||
\(240\) | 37.3403 | 2.41030 | ||||||||
\(241\) | −4.51000 | −0.290515 | −0.145257 | − | 0.989394i | \(-0.546401\pi\) | ||||
−0.145257 | + | 0.989394i | \(0.546401\pi\) | |||||||
\(242\) | 2.63509 | 0.169390 | ||||||||
\(243\) | 21.6422 | 1.38835 | ||||||||
\(244\) | −7.53313 | −0.482259 | ||||||||
\(245\) | −8.01223 | −0.511883 | ||||||||
\(246\) | 4.90088 | 0.312468 | ||||||||
\(247\) | 23.9384 | 1.52316 | ||||||||
\(248\) | 7.55538 | 0.479767 | ||||||||
\(249\) | 40.0594 | 2.53866 | ||||||||
\(250\) | −9.14198 | −0.578190 | ||||||||
\(251\) | 23.1844 | 1.46338 | 0.731692 | − | 0.681636i | \(-0.238731\pi\) | ||||
0.731692 | + | 0.681636i | \(0.238731\pi\) | |||||||
\(252\) | 9.03021 | 0.568850 | ||||||||
\(253\) | 3.76034 | 0.236410 | ||||||||
\(254\) | −27.2408 | −1.70924 | ||||||||
\(255\) | −42.1653 | −2.64049 | ||||||||
\(256\) | 20.1726 | 1.26079 | ||||||||
\(257\) | 6.28231 | 0.391880 | 0.195940 | − | 0.980616i | \(-0.437224\pi\) | ||||
0.195940 | + | 0.980616i | \(0.437224\pi\) | |||||||
\(258\) | −28.6943 | −1.78643 | ||||||||
\(259\) | −2.45368 | −0.152464 | ||||||||
\(260\) | 16.7553 | 1.03912 | ||||||||
\(261\) | 32.2036 | 1.99335 | ||||||||
\(262\) | −25.4648 | −1.57322 | ||||||||
\(263\) | −29.6312 | −1.82714 | −0.913568 | − | 0.406685i | \(-0.866685\pi\) | ||||
−0.913568 | + | 0.406685i | \(0.866685\pi\) | |||||||
\(264\) | −14.0737 | −0.866175 | ||||||||
\(265\) | −7.82335 | −0.480584 | ||||||||
\(266\) | 16.9744 | 1.04077 | ||||||||
\(267\) | 7.86108 | 0.481091 | ||||||||
\(268\) | −16.7981 | −1.02610 | ||||||||
\(269\) | 4.54785 | 0.277287 | 0.138644 | − | 0.990342i | \(-0.455726\pi\) | ||||
0.138644 | + | 0.990342i | \(0.455726\pi\) | |||||||
\(270\) | −11.3990 | −0.693718 | ||||||||
\(271\) | −30.0453 | −1.82512 | −0.912560 | − | 0.408943i | \(-0.865898\pi\) | ||||
−0.912560 | + | 0.408943i | \(0.865898\pi\) | |||||||
\(272\) | −28.0033 | −1.69795 | ||||||||
\(273\) | −27.5058 | −1.66473 | ||||||||
\(274\) | −33.5427 | −2.02639 | ||||||||
\(275\) | −11.3034 | −0.681619 | ||||||||
\(276\) | 3.18237 | 0.191556 | ||||||||
\(277\) | −26.4968 | −1.59204 | −0.796018 | − | 0.605273i | \(-0.793064\pi\) | ||||
−0.796018 | + | 0.605273i | \(0.793064\pi\) | |||||||
\(278\) | 26.5266 | 1.59096 | ||||||||
\(279\) | −19.1637 | −1.14730 | ||||||||
\(280\) | −8.92670 | −0.533473 | ||||||||
\(281\) | 10.2039 | 0.608716 | 0.304358 | − | 0.952558i | \(-0.401558\pi\) | ||||
0.304358 | + | 0.952558i | \(0.401558\pi\) | |||||||
\(282\) | −51.9335 | −3.09260 | ||||||||
\(283\) | −3.47496 | −0.206565 | −0.103282 | − | 0.994652i | \(-0.532935\pi\) | ||||
−0.103282 | + | 0.994652i | \(0.532935\pi\) | |||||||
\(284\) | 9.87707 | 0.586096 | ||||||||
\(285\) | −35.0298 | −2.07499 | ||||||||
\(286\) | −32.0954 | −1.89784 | ||||||||
\(287\) | −2.16423 | −0.127750 | ||||||||
\(288\) | −22.3176 | −1.31508 | ||||||||
\(289\) | 14.6218 | 0.860103 | ||||||||
\(290\) | 42.3702 | 2.48806 | ||||||||
\(291\) | −7.65138 | −0.448532 | ||||||||
\(292\) | −10.9805 | −0.642584 | ||||||||
\(293\) | −13.5197 | −0.789830 | −0.394915 | − | 0.918718i | \(-0.629226\pi\) | ||||
−0.394915 | + | 0.918718i | \(0.629226\pi\) | |||||||
\(294\) | 12.9887 | 0.757519 | ||||||||
\(295\) | −28.9133 | −1.68340 | ||||||||
\(296\) | 1.82053 | 0.105816 | ||||||||
\(297\) | 7.93616 | 0.460503 | ||||||||
\(298\) | −15.2927 | −0.885880 | ||||||||
\(299\) | −5.45285 | −0.315347 | ||||||||
\(300\) | −9.56605 | −0.552296 | ||||||||
\(301\) | 12.6714 | 0.730368 | ||||||||
\(302\) | 11.4039 | 0.656223 | ||||||||
\(303\) | −3.93428 | −0.226018 | ||||||||
\(304\) | −23.2644 | −1.33430 | ||||||||
\(305\) | −18.8882 | −1.08154 | ||||||||
\(306\) | 38.4517 | 2.19814 | ||||||||
\(307\) | 7.10925 | 0.405747 | 0.202873 | − | 0.979205i | \(-0.434972\pi\) | ||||
0.202873 | + | 0.979205i | \(0.434972\pi\) | |||||||
\(308\) | −8.27178 | −0.471328 | ||||||||
\(309\) | 16.0002 | 0.910218 | ||||||||
\(310\) | −25.2136 | −1.43204 | ||||||||
\(311\) | 10.0199 | 0.568177 | 0.284088 | − | 0.958798i | \(-0.408309\pi\) | ||||
0.284088 | + | 0.958798i | \(0.408309\pi\) | |||||||
\(312\) | 20.4082 | 1.15539 | ||||||||
\(313\) | −15.6347 | −0.883726 | −0.441863 | − | 0.897083i | \(-0.645682\pi\) | ||||
−0.441863 | + | 0.897083i | \(0.645682\pi\) | |||||||
\(314\) | 29.3769 | 1.65783 | ||||||||
\(315\) | 22.6419 | 1.27573 | ||||||||
\(316\) | 2.45921 | 0.138342 | ||||||||
\(317\) | −25.7276 | −1.44501 | −0.722503 | − | 0.691368i | \(-0.757008\pi\) | ||||
−0.722503 | + | 0.691368i | \(0.757008\pi\) | |||||||
\(318\) | 12.6825 | 0.711202 | ||||||||
\(319\) | −29.4989 | −1.65162 | ||||||||
\(320\) | −0.845071 | −0.0472409 | ||||||||
\(321\) | −37.6816 | −2.10318 | ||||||||
\(322\) | −3.86656 | −0.215475 | ||||||||
\(323\) | 26.2705 | 1.46173 | ||||||||
\(324\) | −6.49967 | −0.361093 | ||||||||
\(325\) | 16.3910 | 0.909209 | ||||||||
\(326\) | 16.5697 | 0.917709 | ||||||||
\(327\) | 17.4138 | 0.962986 | ||||||||
\(328\) | 1.60577 | 0.0886638 | ||||||||
\(329\) | 22.9338 | 1.26438 | ||||||||
\(330\) | 46.9663 | 2.58541 | ||||||||
\(331\) | −8.78459 | −0.482845 | −0.241422 | − | 0.970420i | \(-0.577614\pi\) | ||||
−0.241422 | + | 0.970420i | \(0.577614\pi\) | |||||||
\(332\) | −17.4693 | −0.958755 | ||||||||
\(333\) | −4.61764 | −0.253045 | ||||||||
\(334\) | 10.3272 | 0.565078 | ||||||||
\(335\) | −42.1187 | −2.30119 | ||||||||
\(336\) | 26.7313 | 1.45831 | ||||||||
\(337\) | −33.9248 | −1.84800 | −0.924001 | − | 0.382391i | \(-0.875101\pi\) | ||||
−0.924001 | + | 0.382391i | \(0.875101\pi\) | |||||||
\(338\) | 23.4981 | 1.27813 | ||||||||
\(339\) | −1.95969 | −0.106436 | ||||||||
\(340\) | 18.3877 | 0.997212 | ||||||||
\(341\) | 17.5542 | 0.950611 | ||||||||
\(342\) | 31.9447 | 1.72737 | ||||||||
\(343\) | −20.0846 | −1.08447 | ||||||||
\(344\) | −9.40168 | −0.506905 | ||||||||
\(345\) | 7.97934 | 0.429593 | ||||||||
\(346\) | 32.6877 | 1.75730 | ||||||||
\(347\) | −7.68216 | −0.412400 | −0.206200 | − | 0.978510i | \(-0.566110\pi\) | ||||
−0.206200 | + | 0.978510i | \(0.566110\pi\) | |||||||
\(348\) | −24.9649 | −1.33826 | ||||||||
\(349\) | 31.7792 | 1.70110 | 0.850550 | − | 0.525895i | \(-0.176269\pi\) | ||||
0.850550 | + | 0.525895i | \(0.176269\pi\) | |||||||
\(350\) | 11.6227 | 0.621258 | ||||||||
\(351\) | −11.5082 | −0.614262 | ||||||||
\(352\) | 20.4432 | 1.08962 | ||||||||
\(353\) | 26.2450 | 1.39688 | 0.698439 | − | 0.715669i | \(-0.253878\pi\) | ||||
0.698439 | + | 0.715669i | \(0.253878\pi\) | |||||||
\(354\) | 46.8718 | 2.49121 | ||||||||
\(355\) | 24.7653 | 1.31441 | ||||||||
\(356\) | −3.42811 | −0.181689 | ||||||||
\(357\) | −30.1855 | −1.59758 | ||||||||
\(358\) | 21.7426 | 1.14913 | ||||||||
\(359\) | −30.5776 | −1.61382 | −0.806911 | − | 0.590673i | \(-0.798862\pi\) | ||||
−0.806911 | + | 0.590673i | \(0.798862\pi\) | |||||||
\(360\) | −16.7994 | −0.885407 | ||||||||
\(361\) | 2.82484 | 0.148676 | ||||||||
\(362\) | −4.08297 | −0.214596 | ||||||||
\(363\) | −3.89296 | −0.204328 | ||||||||
\(364\) | 11.9949 | 0.628703 | ||||||||
\(365\) | −27.5320 | −1.44109 | ||||||||
\(366\) | 30.6200 | 1.60053 | ||||||||
\(367\) | −22.2568 | −1.16179 | −0.580897 | − | 0.813977i | \(-0.697298\pi\) | ||||
−0.580897 | + | 0.813977i | \(0.697298\pi\) | |||||||
\(368\) | 5.29932 | 0.276246 | ||||||||
\(369\) | −4.07292 | −0.212028 | ||||||||
\(370\) | −6.07542 | −0.315846 | ||||||||
\(371\) | −5.60061 | −0.290769 | ||||||||
\(372\) | 14.8561 | 0.770252 | ||||||||
\(373\) | −7.73776 | −0.400646 | −0.200323 | − | 0.979730i | \(-0.564199\pi\) | ||||
−0.200323 | + | 0.979730i | \(0.564199\pi\) | |||||||
\(374\) | −35.2222 | −1.82130 | ||||||||
\(375\) | 13.5060 | 0.697445 | ||||||||
\(376\) | −17.0160 | −0.877532 | ||||||||
\(377\) | 42.7762 | 2.20309 | ||||||||
\(378\) | −8.16033 | −0.419722 | ||||||||
\(379\) | −7.45714 | −0.383047 | −0.191524 | − | 0.981488i | \(-0.561343\pi\) | ||||
−0.191524 | + | 0.981488i | \(0.561343\pi\) | |||||||
\(380\) | 15.2760 | 0.783642 | ||||||||
\(381\) | 40.2444 | 2.06178 | ||||||||
\(382\) | 35.1084 | 1.79630 | ||||||||
\(383\) | −15.2271 | −0.778068 | −0.389034 | − | 0.921223i | \(-0.627191\pi\) | ||||
−0.389034 | + | 0.921223i | \(0.627191\pi\) | |||||||
\(384\) | −28.9301 | −1.47633 | ||||||||
\(385\) | −20.7403 | −1.05702 | ||||||||
\(386\) | 9.83797 | 0.500740 | ||||||||
\(387\) | 23.8467 | 1.21220 | ||||||||
\(388\) | 3.33666 | 0.169393 | ||||||||
\(389\) | 26.8823 | 1.36299 | 0.681494 | − | 0.731823i | \(-0.261330\pi\) | ||||
0.681494 | + | 0.731823i | \(0.261330\pi\) | |||||||
\(390\) | −68.1056 | −3.44866 | ||||||||
\(391\) | −5.98409 | −0.302628 | ||||||||
\(392\) | 4.25576 | 0.214948 | ||||||||
\(393\) | 37.6205 | 1.89770 | ||||||||
\(394\) | 8.53756 | 0.430116 | ||||||||
\(395\) | 6.16612 | 0.310251 | ||||||||
\(396\) | −15.5669 | −0.782266 | ||||||||
\(397\) | −8.28463 | −0.415794 | −0.207897 | − | 0.978151i | \(-0.566662\pi\) | ||||
−0.207897 | + | 0.978151i | \(0.566662\pi\) | |||||||
\(398\) | −41.5112 | −2.08077 | ||||||||
\(399\) | −25.0773 | −1.25543 | ||||||||
\(400\) | −15.9295 | −0.796474 | ||||||||
\(401\) | −8.88838 | −0.443865 | −0.221932 | − | 0.975062i | \(-0.571236\pi\) | ||||
−0.221932 | + | 0.975062i | \(0.571236\pi\) | |||||||
\(402\) | 68.2793 | 3.40546 | ||||||||
\(403\) | −25.4552 | −1.26802 | ||||||||
\(404\) | 1.71568 | 0.0853584 | ||||||||
\(405\) | −16.2970 | −0.809803 | ||||||||
\(406\) | 30.3321 | 1.50536 | ||||||||
\(407\) | 4.22982 | 0.209664 | ||||||||
\(408\) | 22.3964 | 1.10879 | ||||||||
\(409\) | 14.7487 | 0.729278 | 0.364639 | − | 0.931149i | \(-0.381192\pi\) | ||||
0.364639 | + | 0.931149i | \(0.381192\pi\) | |||||||
\(410\) | −5.35873 | −0.264649 | ||||||||
\(411\) | 49.5545 | 2.44434 | ||||||||
\(412\) | −6.97745 | −0.343754 | ||||||||
\(413\) | −20.6986 | −1.01851 | ||||||||
\(414\) | −7.27658 | −0.357625 | ||||||||
\(415\) | −43.8019 | −2.15015 | ||||||||
\(416\) | −29.6446 | −1.45344 | ||||||||
\(417\) | −39.1892 | −1.91910 | ||||||||
\(418\) | −29.2617 | −1.43124 | ||||||||
\(419\) | −8.87226 | −0.433438 | −0.216719 | − | 0.976234i | \(-0.569536\pi\) | ||||
−0.216719 | + | 0.976234i | \(0.569536\pi\) | |||||||
\(420\) | −17.5525 | −0.856474 | ||||||||
\(421\) | 30.8807 | 1.50503 | 0.752516 | − | 0.658574i | \(-0.228840\pi\) | ||||
0.752516 | + | 0.658574i | \(0.228840\pi\) | |||||||
\(422\) | 38.6058 | 1.87930 | ||||||||
\(423\) | 43.1598 | 2.09850 | ||||||||
\(424\) | 4.15543 | 0.201805 | ||||||||
\(425\) | 17.9878 | 0.872539 | ||||||||
\(426\) | −40.1475 | −1.94515 | ||||||||
\(427\) | −13.5218 | −0.654365 | ||||||||
\(428\) | 16.4324 | 0.794291 | ||||||||
\(429\) | 47.4164 | 2.28928 | ||||||||
\(430\) | 31.3750 | 1.51304 | ||||||||
\(431\) | 32.0482 | 1.54371 | 0.771853 | − | 0.635801i | \(-0.219330\pi\) | ||||
0.771853 | + | 0.635801i | \(0.219330\pi\) | |||||||
\(432\) | 11.1842 | 0.538099 | ||||||||
\(433\) | 2.86180 | 0.137529 | 0.0687647 | − | 0.997633i | \(-0.478094\pi\) | ||||
0.0687647 | + | 0.997633i | \(0.478094\pi\) | |||||||
\(434\) | −18.0500 | −0.866428 | ||||||||
\(435\) | −62.5958 | −3.00124 | ||||||||
\(436\) | −7.59392 | −0.363683 | ||||||||
\(437\) | −4.97142 | −0.237815 | ||||||||
\(438\) | 44.6325 | 2.13262 | ||||||||
\(439\) | −25.1526 | −1.20047 | −0.600234 | − | 0.799824i | \(-0.704926\pi\) | ||||
−0.600234 | + | 0.799824i | \(0.704926\pi\) | |||||||
\(440\) | 15.3885 | 0.733616 | ||||||||
\(441\) | −10.7944 | −0.514020 | ||||||||
\(442\) | 51.0757 | 2.42942 | ||||||||
\(443\) | 23.2449 | 1.10440 | 0.552199 | − | 0.833712i | \(-0.313789\pi\) | ||||
0.552199 | + | 0.833712i | \(0.313789\pi\) | |||||||
\(444\) | 3.57969 | 0.169885 | ||||||||
\(445\) | −8.59548 | −0.407465 | ||||||||
\(446\) | −27.7432 | −1.31368 | ||||||||
\(447\) | 22.5927 | 1.06860 | ||||||||
\(448\) | −0.604973 | −0.0285823 | ||||||||
\(449\) | 2.42638 | 0.114508 | 0.0572539 | − | 0.998360i | \(-0.481766\pi\) | ||||
0.0572539 | + | 0.998360i | \(0.481766\pi\) | |||||||
\(450\) | 21.8730 | 1.03110 | ||||||||
\(451\) | 3.73084 | 0.175678 | ||||||||
\(452\) | 0.854592 | 0.0401966 | ||||||||
\(453\) | −16.8477 | −0.791573 | ||||||||
\(454\) | 21.7605 | 1.02127 | ||||||||
\(455\) | 30.0754 | 1.40996 | ||||||||
\(456\) | 18.6063 | 0.871322 | ||||||||
\(457\) | 27.2030 | 1.27250 | 0.636252 | − | 0.771481i | \(-0.280484\pi\) | ||||
0.636252 | + | 0.771481i | \(0.280484\pi\) | |||||||
\(458\) | −0.686318 | −0.0320695 | ||||||||
\(459\) | −12.6294 | −0.589488 | ||||||||
\(460\) | −3.47968 | −0.162241 | ||||||||
\(461\) | −23.3601 | −1.08799 | −0.543995 | − | 0.839089i | \(-0.683089\pi\) | ||||
−0.543995 | + | 0.839089i | \(0.683089\pi\) | |||||||
\(462\) | 33.6224 | 1.56426 | ||||||||
\(463\) | 30.9316 | 1.43751 | 0.718756 | − | 0.695262i | \(-0.244712\pi\) | ||||
0.718756 | + | 0.695262i | \(0.244712\pi\) | |||||||
\(464\) | −41.5718 | −1.92992 | ||||||||
\(465\) | 37.2495 | 1.72740 | ||||||||
\(466\) | −17.1480 | −0.794368 | ||||||||
\(467\) | −22.6883 | −1.04989 | −0.524944 | − | 0.851137i | \(-0.675914\pi\) | ||||
−0.524944 | + | 0.851137i | \(0.675914\pi\) | |||||||
\(468\) | 22.5735 | 1.04346 | ||||||||
\(469\) | −30.1521 | −1.39229 | ||||||||
\(470\) | 56.7853 | 2.61931 | ||||||||
\(471\) | −43.4001 | −1.99977 | ||||||||
\(472\) | 15.3575 | 0.706886 | ||||||||
\(473\) | −21.8439 | −1.00438 | ||||||||
\(474\) | −9.99599 | −0.459131 | ||||||||
\(475\) | 14.9438 | 0.685670 | ||||||||
\(476\) | 13.1635 | 0.603346 | ||||||||
\(477\) | −10.5399 | −0.482591 | ||||||||
\(478\) | −10.1424 | −0.463902 | ||||||||
\(479\) | 20.3393 | 0.929324 | 0.464662 | − | 0.885488i | \(-0.346176\pi\) | ||||
0.464662 | + | 0.885488i | \(0.346176\pi\) | |||||||
\(480\) | 43.3799 | 1.98001 | ||||||||
\(481\) | −6.13365 | −0.279670 | ||||||||
\(482\) | −7.99426 | −0.364129 | ||||||||
\(483\) | 5.71228 | 0.259918 | ||||||||
\(484\) | 1.69767 | 0.0771667 | ||||||||
\(485\) | 8.36618 | 0.379889 | ||||||||
\(486\) | 38.3622 | 1.74015 | ||||||||
\(487\) | −6.65399 | −0.301521 | −0.150761 | − | 0.988570i | \(-0.548172\pi\) | ||||
−0.150761 | + | 0.988570i | \(0.548172\pi\) | |||||||
\(488\) | 10.0326 | 0.454156 | ||||||||
\(489\) | −24.4793 | −1.10699 | ||||||||
\(490\) | −14.2022 | −0.641589 | ||||||||
\(491\) | −5.39859 | −0.243635 | −0.121817 | − | 0.992553i | \(-0.538872\pi\) | ||||
−0.121817 | + | 0.992553i | \(0.538872\pi\) | |||||||
\(492\) | 3.15741 | 0.142347 | ||||||||
\(493\) | 46.9436 | 2.11423 | ||||||||
\(494\) | 42.4323 | 1.90912 | ||||||||
\(495\) | −39.0317 | −1.75435 | ||||||||
\(496\) | 24.7385 | 1.11079 | ||||||||
\(497\) | 17.7291 | 0.795259 | ||||||||
\(498\) | 71.0079 | 3.18194 | ||||||||
\(499\) | 17.6044 | 0.788082 | 0.394041 | − | 0.919093i | \(-0.371077\pi\) | ||||
0.394041 | + | 0.919093i | \(0.371077\pi\) | |||||||
\(500\) | −5.88976 | −0.263398 | ||||||||
\(501\) | −15.2569 | −0.681628 | ||||||||
\(502\) | 41.0957 | 1.83419 | ||||||||
\(503\) | −15.7102 | −0.700485 | −0.350242 | − | 0.936659i | \(-0.613901\pi\) | ||||
−0.350242 | + | 0.936659i | \(0.613901\pi\) | |||||||
\(504\) | −12.0264 | −0.535700 | ||||||||
\(505\) | 4.30183 | 0.191429 | ||||||||
\(506\) | 6.66544 | 0.296315 | ||||||||
\(507\) | −34.7151 | −1.54175 | ||||||||
\(508\) | −17.5500 | −0.778656 | ||||||||
\(509\) | 31.5509 | 1.39847 | 0.699234 | − | 0.714893i | \(-0.253525\pi\) | ||||
0.699234 | + | 0.714893i | \(0.253525\pi\) | |||||||
\(510\) | −74.7407 | −3.30957 | ||||||||
\(511\) | −19.7097 | −0.871906 | ||||||||
\(512\) | 13.6623 | 0.603793 | ||||||||
\(513\) | −10.4921 | −0.463239 | ||||||||
\(514\) | 11.1358 | 0.491179 | ||||||||
\(515\) | −17.4949 | −0.770919 | ||||||||
\(516\) | −18.4865 | −0.813821 | ||||||||
\(517\) | −39.5349 | −1.73874 | ||||||||
\(518\) | −4.34930 | −0.191097 | ||||||||
\(519\) | −48.2914 | −2.11976 | ||||||||
\(520\) | −22.3148 | −0.978567 | ||||||||
\(521\) | 13.8794 | 0.608067 | 0.304034 | − | 0.952661i | \(-0.401666\pi\) | ||||
0.304034 | + | 0.952661i | \(0.401666\pi\) | |||||||
\(522\) | 57.0829 | 2.49845 | ||||||||
\(523\) | −36.7351 | −1.60631 | −0.803156 | − | 0.595769i | \(-0.796847\pi\) | ||||
−0.803156 | + | 0.595769i | \(0.796847\pi\) | |||||||
\(524\) | −16.4058 | −0.716690 | ||||||||
\(525\) | −17.1708 | −0.749396 | ||||||||
\(526\) | −52.5232 | −2.29012 | ||||||||
\(527\) | −27.9351 | −1.21687 | ||||||||
\(528\) | −46.0813 | −2.00543 | ||||||||
\(529\) | −21.8676 | −0.950764 | ||||||||
\(530\) | −13.8674 | −0.602360 | ||||||||
\(531\) | −38.9532 | −1.69042 | ||||||||
\(532\) | 10.9358 | 0.474129 | ||||||||
\(533\) | −5.41008 | −0.234337 | ||||||||
\(534\) | 13.9343 | 0.602995 | ||||||||
\(535\) | 41.2019 | 1.78131 | ||||||||
\(536\) | 22.3717 | 0.966308 | ||||||||
\(537\) | −32.1216 | −1.38615 | ||||||||
\(538\) | 8.06135 | 0.347550 | ||||||||
\(539\) | 9.88782 | 0.425898 | ||||||||
\(540\) | −7.34383 | −0.316028 | ||||||||
\(541\) | 41.6749 | 1.79174 | 0.895872 | − | 0.444312i | \(-0.146552\pi\) | ||||
0.895872 | + | 0.444312i | \(0.146552\pi\) | |||||||
\(542\) | −53.2572 | −2.28759 | ||||||||
\(543\) | 6.03200 | 0.258858 | ||||||||
\(544\) | −32.5326 | −1.39482 | ||||||||
\(545\) | −19.0406 | −0.815612 | ||||||||
\(546\) | −48.7558 | −2.08655 | ||||||||
\(547\) | −14.3379 | −0.613044 | −0.306522 | − | 0.951864i | \(-0.599165\pi\) | ||||
−0.306522 | + | 0.951864i | \(0.599165\pi\) | |||||||
\(548\) | −21.6100 | −0.923135 | ||||||||
\(549\) | −25.4470 | −1.08605 | ||||||||
\(550\) | −20.0360 | −0.854336 | ||||||||
\(551\) | 38.9995 | 1.66143 | ||||||||
\(552\) | −4.23829 | −0.180393 | ||||||||
\(553\) | 4.41423 | 0.187712 | ||||||||
\(554\) | −46.9672 | −1.99544 | ||||||||
\(555\) | 8.97556 | 0.380991 | ||||||||
\(556\) | 17.0898 | 0.724771 | ||||||||
\(557\) | −23.1687 | −0.981688 | −0.490844 | − | 0.871248i | \(-0.663311\pi\) | ||||
−0.490844 | + | 0.871248i | \(0.663311\pi\) | |||||||
\(558\) | −33.9688 | −1.43802 | ||||||||
\(559\) | 31.6757 | 1.33974 | ||||||||
\(560\) | −29.2286 | −1.23513 | ||||||||
\(561\) | 52.0358 | 2.19695 | ||||||||
\(562\) | 18.0871 | 0.762959 | ||||||||
\(563\) | 24.3544 | 1.02642 | 0.513208 | − | 0.858264i | \(-0.328457\pi\) | ||||
0.513208 | + | 0.858264i | \(0.328457\pi\) | |||||||
\(564\) | −33.4584 | −1.40885 | ||||||||
\(565\) | 2.14277 | 0.0901469 | ||||||||
\(566\) | −6.15959 | −0.258907 | ||||||||
\(567\) | −11.6667 | −0.489957 | ||||||||
\(568\) | −13.1543 | −0.551942 | ||||||||
\(569\) | 5.41237 | 0.226899 | 0.113449 | − | 0.993544i | \(-0.463810\pi\) | ||||
0.113449 | + | 0.993544i | \(0.463810\pi\) | |||||||
\(570\) | −62.0925 | −2.60077 | ||||||||
\(571\) | −1.81071 | −0.0757760 | −0.0378880 | − | 0.999282i | \(-0.512063\pi\) | ||||
−0.0378880 | + | 0.999282i | \(0.512063\pi\) | |||||||
\(572\) | −20.6776 | −0.864574 | ||||||||
\(573\) | −51.8677 | −2.16680 | ||||||||
\(574\) | −3.83623 | −0.160121 | ||||||||
\(575\) | −3.40401 | −0.141957 | ||||||||
\(576\) | −1.13852 | −0.0474382 | ||||||||
\(577\) | 10.7228 | 0.446395 | 0.223198 | − | 0.974773i | \(-0.428350\pi\) | ||||
0.223198 | + | 0.974773i | \(0.428350\pi\) | |||||||
\(578\) | 25.9180 | 1.07805 | ||||||||
\(579\) | −14.5342 | −0.604020 | ||||||||
\(580\) | 27.2972 | 1.13345 | ||||||||
\(581\) | −31.3571 | −1.30091 | ||||||||
\(582\) | −13.5625 | −0.562186 | ||||||||
\(583\) | 9.65472 | 0.399858 | ||||||||
\(584\) | 14.6238 | 0.605137 | ||||||||
\(585\) | 56.5998 | 2.34011 | ||||||||
\(586\) | −23.9646 | −0.989967 | ||||||||
\(587\) | 12.1605 | 0.501919 | 0.250960 | − | 0.967998i | \(-0.419254\pi\) | ||||
0.250960 | + | 0.967998i | \(0.419254\pi\) | |||||||
\(588\) | 8.36806 | 0.345093 | ||||||||
\(589\) | −23.2078 | −0.956259 | ||||||||
\(590\) | −51.2506 | −2.10995 | ||||||||
\(591\) | −12.6130 | −0.518830 | ||||||||
\(592\) | 5.96095 | 0.244993 | ||||||||
\(593\) | −42.9648 | −1.76435 | −0.882177 | − | 0.470918i | \(-0.843923\pi\) | ||||
−0.882177 | + | 0.470918i | \(0.843923\pi\) | |||||||
\(594\) | 14.0673 | 0.577190 | ||||||||
\(595\) | 33.0055 | 1.35309 | ||||||||
\(596\) | −9.85236 | −0.403569 | ||||||||
\(597\) | 61.3269 | 2.50994 | ||||||||
\(598\) | −9.66553 | −0.395253 | ||||||||
\(599\) | 22.5413 | 0.921012 | 0.460506 | − | 0.887656i | \(-0.347668\pi\) | ||||
0.460506 | + | 0.887656i | \(0.347668\pi\) | |||||||
\(600\) | 12.7401 | 0.520111 | ||||||||
\(601\) | 1.68713 | 0.0688197 | 0.0344098 | − | 0.999408i | \(-0.489045\pi\) | ||||
0.0344098 | + | 0.999408i | \(0.489045\pi\) | |||||||
\(602\) | 22.4609 | 0.915438 | ||||||||
\(603\) | −56.7441 | −2.31080 | ||||||||
\(604\) | 7.34704 | 0.298947 | ||||||||
\(605\) | 4.25665 | 0.173057 | ||||||||
\(606\) | −6.97376 | −0.283289 | ||||||||
\(607\) | 30.1716 | 1.22463 | 0.612313 | − | 0.790615i | \(-0.290239\pi\) | ||||
0.612313 | + | 0.790615i | \(0.290239\pi\) | |||||||
\(608\) | −27.0272 | −1.09610 | ||||||||
\(609\) | −44.8114 | −1.81585 | ||||||||
\(610\) | −33.4806 | −1.35559 | ||||||||
\(611\) | 57.3295 | 2.31930 | ||||||||
\(612\) | 24.7727 | 1.00138 | ||||||||
\(613\) | −27.4753 | −1.10972 | −0.554858 | − | 0.831945i | \(-0.687227\pi\) | ||||
−0.554858 | + | 0.831945i | \(0.687227\pi\) | |||||||
\(614\) | 12.6016 | 0.508559 | ||||||||
\(615\) | 7.91675 | 0.319234 | ||||||||
\(616\) | 11.0164 | 0.443862 | ||||||||
\(617\) | 31.5957 | 1.27199 | 0.635997 | − | 0.771691i | \(-0.280589\pi\) | ||||
0.635997 | + | 0.771691i | \(0.280589\pi\) | |||||||
\(618\) | 28.3613 | 1.14086 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | −16.2440 | −0.652373 | ||||||||
\(621\) | 2.38997 | 0.0959063 | ||||||||
\(622\) | 17.7609 | 0.712148 | ||||||||
\(623\) | −6.15337 | −0.246530 | ||||||||
\(624\) | 66.8223 | 2.67503 | ||||||||
\(625\) | −30.7617 | −1.23047 | ||||||||
\(626\) | −27.7135 | −1.10765 | ||||||||
\(627\) | 43.2299 | 1.72644 | ||||||||
\(628\) | 18.9262 | 0.755236 | ||||||||
\(629\) | −6.73120 | −0.268391 | ||||||||
\(630\) | 40.1343 | 1.59899 | ||||||||
\(631\) | −19.8225 | −0.789122 | −0.394561 | − | 0.918870i | \(-0.629103\pi\) | ||||
−0.394561 | + | 0.918870i | \(0.629103\pi\) | |||||||
\(632\) | −3.27518 | −0.130280 | ||||||||
\(633\) | −57.0346 | −2.26692 | ||||||||
\(634\) | −45.6038 | −1.81116 | ||||||||
\(635\) | −44.0041 | −1.74625 | ||||||||
\(636\) | 8.17079 | 0.323993 | ||||||||
\(637\) | −14.3383 | −0.568104 | ||||||||
\(638\) | −52.2886 | −2.07013 | ||||||||
\(639\) | 33.3649 | 1.31990 | ||||||||
\(640\) | 31.6328 | 1.25040 | ||||||||
\(641\) | 0.200424 | 0.00791629 | 0.00395814 | − | 0.999992i | \(-0.498740\pi\) | ||||
0.00395814 | + | 0.999992i | \(0.498740\pi\) | |||||||
\(642\) | −66.7931 | −2.63611 | ||||||||
\(643\) | 20.3895 | 0.804084 | 0.402042 | − | 0.915621i | \(-0.368301\pi\) | ||||
0.402042 | + | 0.915621i | \(0.368301\pi\) | |||||||
\(644\) | −2.49105 | −0.0981610 | ||||||||
\(645\) | −46.3521 | −1.82511 | ||||||||
\(646\) | 46.5661 | 1.83212 | ||||||||
\(647\) | −9.68654 | −0.380817 | −0.190409 | − | 0.981705i | \(-0.560981\pi\) | ||||
−0.190409 | + | 0.981705i | \(0.560981\pi\) | |||||||
\(648\) | 8.65626 | 0.340050 | ||||||||
\(649\) | 35.6816 | 1.40063 | ||||||||
\(650\) | 29.0541 | 1.13959 | ||||||||
\(651\) | 26.6663 | 1.04513 | ||||||||
\(652\) | 10.6751 | 0.418068 | ||||||||
\(653\) | 47.7775 | 1.86968 | 0.934839 | − | 0.355073i | \(-0.115544\pi\) | ||||
0.934839 | + | 0.355073i | \(0.115544\pi\) | |||||||
\(654\) | 30.8671 | 1.20700 | ||||||||
\(655\) | −41.1351 | −1.60728 | ||||||||
\(656\) | 5.25775 | 0.205281 | ||||||||
\(657\) | −37.0922 | −1.44711 | ||||||||
\(658\) | 40.6517 | 1.58477 | ||||||||
\(659\) | 41.6564 | 1.62270 | 0.811352 | − | 0.584558i | \(-0.198732\pi\) | ||||
0.811352 | + | 0.584558i | \(0.198732\pi\) | |||||||
\(660\) | 30.2582 | 1.17780 | ||||||||
\(661\) | −6.19890 | −0.241109 | −0.120555 | − | 0.992707i | \(-0.538467\pi\) | ||||
−0.120555 | + | 0.992707i | \(0.538467\pi\) | |||||||
\(662\) | −15.5712 | −0.605194 | ||||||||
\(663\) | −75.4569 | −2.93050 | ||||||||
\(664\) | 23.2657 | 0.902884 | ||||||||
\(665\) | 27.4201 | 1.06330 | ||||||||
\(666\) | −8.18507 | −0.317165 | ||||||||
\(667\) | −8.88358 | −0.343974 | ||||||||
\(668\) | 6.65332 | 0.257425 | ||||||||
\(669\) | 40.9866 | 1.58463 | ||||||||
\(670\) | −74.6580 | −2.88429 | ||||||||
\(671\) | 23.3098 | 0.899865 | ||||||||
\(672\) | 31.0550 | 1.19797 | ||||||||
\(673\) | −2.62521 | −0.101195 | −0.0505973 | − | 0.998719i | \(-0.516112\pi\) | ||||
−0.0505973 | + | 0.998719i | \(0.516112\pi\) | |||||||
\(674\) | −60.1338 | −2.31627 | ||||||||
\(675\) | −7.18413 | −0.276517 | ||||||||
\(676\) | 15.1388 | 0.582261 | ||||||||
\(677\) | 9.70520 | 0.373001 | 0.186501 | − | 0.982455i | \(-0.440285\pi\) | ||||
0.186501 | + | 0.982455i | \(0.440285\pi\) | |||||||
\(678\) | −3.47367 | −0.133406 | ||||||||
\(679\) | 5.98922 | 0.229845 | ||||||||
\(680\) | −24.4887 | −0.939100 | ||||||||
\(681\) | −32.1481 | −1.23192 | ||||||||
\(682\) | 31.1159 | 1.19149 | ||||||||
\(683\) | 25.9542 | 0.993109 | 0.496554 | − | 0.868006i | \(-0.334598\pi\) | ||||
0.496554 | + | 0.868006i | \(0.334598\pi\) | |||||||
\(684\) | 20.5805 | 0.786914 | ||||||||
\(685\) | −54.1840 | −2.07026 | ||||||||
\(686\) | −35.6013 | −1.35926 | ||||||||
\(687\) | 1.01394 | 0.0386841 | ||||||||
\(688\) | −30.7838 | −1.17362 | ||||||||
\(689\) | −14.0003 | −0.533368 | ||||||||
\(690\) | 14.1439 | 0.538448 | ||||||||
\(691\) | 2.19332 | 0.0834379 | 0.0417189 | − | 0.999129i | \(-0.486717\pi\) | ||||
0.0417189 | + | 0.999129i | \(0.486717\pi\) | |||||||
\(692\) | 21.0592 | 0.800551 | ||||||||
\(693\) | −27.9422 | −1.06144 | ||||||||
\(694\) | −13.6171 | −0.516899 | ||||||||
\(695\) | 42.8503 | 1.62540 | ||||||||
\(696\) | 33.2482 | 1.26027 | ||||||||
\(697\) | −5.93715 | −0.224885 | ||||||||
\(698\) | 56.3306 | 2.13214 | ||||||||
\(699\) | 25.3338 | 0.958211 | ||||||||
\(700\) | 7.48795 | 0.283018 | ||||||||
\(701\) | −47.1625 | −1.78130 | −0.890652 | − | 0.454685i | \(-0.849752\pi\) | ||||
−0.890652 | + | 0.454685i | \(0.849752\pi\) | |||||||
\(702\) | −20.3990 | −0.769911 | ||||||||
\(703\) | −5.59210 | −0.210910 | ||||||||
\(704\) | 1.04289 | 0.0393056 | ||||||||
\(705\) | −83.8921 | −3.15956 | ||||||||
\(706\) | 46.5209 | 1.75084 | ||||||||
\(707\) | 3.07961 | 0.115821 | ||||||||
\(708\) | 30.1973 | 1.13489 | ||||||||
\(709\) | 4.76966 | 0.179128 | 0.0895642 | − | 0.995981i | \(-0.471453\pi\) | ||||
0.0895642 | + | 0.995981i | \(0.471453\pi\) | |||||||
\(710\) | 43.8981 | 1.64747 | ||||||||
\(711\) | 8.30726 | 0.311547 | ||||||||
\(712\) | 4.56556 | 0.171101 | ||||||||
\(713\) | 5.28643 | 0.197978 | ||||||||
\(714\) | −53.5057 | −2.00240 | ||||||||
\(715\) | −51.8461 | −1.93893 | ||||||||
\(716\) | 14.0078 | 0.523494 | ||||||||
\(717\) | 14.9839 | 0.559584 | ||||||||
\(718\) | −54.2007 | −2.02275 | ||||||||
\(719\) | 40.2443 | 1.50086 | 0.750430 | − | 0.660950i | \(-0.229847\pi\) | ||||
0.750430 | + | 0.660950i | \(0.229847\pi\) | |||||||
\(720\) | −55.0062 | −2.04996 | ||||||||
\(721\) | −12.5244 | −0.466431 | ||||||||
\(722\) | 5.00720 | 0.186349 | ||||||||
\(723\) | 11.8104 | 0.439233 | ||||||||
\(724\) | −2.63047 | −0.0977606 | ||||||||
\(725\) | 26.7036 | 0.991746 | ||||||||
\(726\) | −6.90052 | −0.256102 | ||||||||
\(727\) | −10.1045 | −0.374756 | −0.187378 | − | 0.982288i | \(-0.559999\pi\) | ||||
−0.187378 | + | 0.982288i | \(0.559999\pi\) | |||||||
\(728\) | −15.9748 | −0.592065 | ||||||||
\(729\) | −39.6000 | −1.46667 | ||||||||
\(730\) | −48.8021 | −1.80625 | ||||||||
\(731\) | 34.7616 | 1.28571 | ||||||||
\(732\) | 19.7271 | 0.729134 | ||||||||
\(733\) | 19.0825 | 0.704827 | 0.352413 | − | 0.935844i | \(-0.385361\pi\) | ||||
0.352413 | + | 0.935844i | \(0.385361\pi\) | |||||||
\(734\) | −39.4515 | −1.45618 | ||||||||
\(735\) | 20.9817 | 0.773921 | ||||||||
\(736\) | 6.15646 | 0.226930 | ||||||||
\(737\) | 51.9783 | 1.91464 | ||||||||
\(738\) | −7.21951 | −0.265754 | ||||||||
\(739\) | 21.7844 | 0.801351 | 0.400675 | − | 0.916220i | \(-0.368776\pi\) | ||||
0.400675 | + | 0.916220i | \(0.368776\pi\) | |||||||
\(740\) | −3.91412 | −0.143886 | ||||||||
\(741\) | −62.6876 | −2.30289 | ||||||||
\(742\) | −9.92744 | −0.364448 | ||||||||
\(743\) | 41.4086 | 1.51913 | 0.759567 | − | 0.650429i | \(-0.225411\pi\) | ||||
0.759567 | + | 0.650429i | \(0.225411\pi\) | |||||||
\(744\) | −19.7853 | −0.725365 | ||||||||
\(745\) | −24.7034 | −0.905061 | ||||||||
\(746\) | −13.7157 | −0.502167 | ||||||||
\(747\) | −59.0117 | −2.15913 | ||||||||
\(748\) | −22.6921 | −0.829704 | ||||||||
\(749\) | 29.4958 | 1.07775 | ||||||||
\(750\) | 23.9402 | 0.874172 | ||||||||
\(751\) | −5.81495 | −0.212191 | −0.106095 | − | 0.994356i | \(-0.533835\pi\) | ||||
−0.106095 | + | 0.994356i | \(0.533835\pi\) | |||||||
\(752\) | −55.7153 | −2.03173 | ||||||||
\(753\) | −60.7131 | −2.21251 | ||||||||
\(754\) | 75.8236 | 2.76133 | ||||||||
\(755\) | 18.4216 | 0.670432 | ||||||||
\(756\) | −5.25733 | −0.191207 | ||||||||
\(757\) | −41.1295 | −1.49488 | −0.747438 | − | 0.664332i | \(-0.768716\pi\) | ||||
−0.747438 | + | 0.664332i | \(0.768716\pi\) | |||||||
\(758\) | −13.2183 | −0.480109 | ||||||||
\(759\) | −9.84723 | −0.357432 | ||||||||
\(760\) | −20.3446 | −0.737976 | ||||||||
\(761\) | −4.58159 | −0.166083 | −0.0830413 | − | 0.996546i | \(-0.526463\pi\) | ||||
−0.0830413 | + | 0.996546i | \(0.526463\pi\) | |||||||
\(762\) | 71.3357 | 2.58422 | ||||||||
\(763\) | −13.6309 | −0.493472 | ||||||||
\(764\) | 22.6188 | 0.818318 | ||||||||
\(765\) | 62.1139 | 2.24573 | ||||||||
\(766\) | −26.9910 | −0.975224 | ||||||||
\(767\) | −51.7418 | −1.86829 | ||||||||
\(768\) | −52.8261 | −1.90620 | ||||||||
\(769\) | −36.3140 | −1.30951 | −0.654757 | − | 0.755839i | \(-0.727229\pi\) | ||||
−0.654757 | + | 0.755839i | \(0.727229\pi\) | |||||||
\(770\) | −36.7635 | −1.32486 | ||||||||
\(771\) | −16.4515 | −0.592488 | ||||||||
\(772\) | 6.33816 | 0.228115 | ||||||||
\(773\) | −32.7511 | −1.17798 | −0.588988 | − | 0.808141i | \(-0.700474\pi\) | ||||
−0.588988 | + | 0.808141i | \(0.700474\pi\) | |||||||
\(774\) | 42.2698 | 1.51936 | ||||||||
\(775\) | −15.8907 | −0.570812 | ||||||||
\(776\) | −4.44376 | −0.159522 | ||||||||
\(777\) | 6.42547 | 0.230512 | ||||||||
\(778\) | 47.6507 | 1.70836 | ||||||||
\(779\) | −4.93242 | −0.176722 | ||||||||
\(780\) | −43.8773 | −1.57106 | ||||||||
\(781\) | −30.5627 | −1.09362 | ||||||||
\(782\) | −10.6072 | −0.379312 | ||||||||
\(783\) | −18.7487 | −0.670024 | ||||||||
\(784\) | 13.9346 | 0.497664 | ||||||||
\(785\) | 47.4546 | 1.69373 | ||||||||
\(786\) | 66.6848 | 2.37857 | ||||||||
\(787\) | 5.41033 | 0.192857 | 0.0964286 | − | 0.995340i | \(-0.469258\pi\) | ||||
0.0964286 | + | 0.995340i | \(0.469258\pi\) | |||||||
\(788\) | 5.50036 | 0.195942 | ||||||||
\(789\) | 77.5954 | 2.76247 | ||||||||
\(790\) | 10.9298 | 0.388866 | ||||||||
\(791\) | 1.53397 | 0.0545418 | ||||||||
\(792\) | 20.7320 | 0.736680 | ||||||||
\(793\) | −33.8015 | −1.20033 | ||||||||
\(794\) | −14.6850 | −0.521153 | ||||||||
\(795\) | 20.4871 | 0.726601 | ||||||||
\(796\) | −26.7438 | −0.947908 | ||||||||
\(797\) | −27.9992 | −0.991781 | −0.495890 | − | 0.868385i | \(-0.665158\pi\) | ||||
−0.495890 | + | 0.868385i | \(0.665158\pi\) | |||||||
\(798\) | −44.4511 | −1.57355 | ||||||||
\(799\) | 62.9146 | 2.22576 | ||||||||
\(800\) | −18.5060 | −0.654285 | ||||||||
\(801\) | −11.5802 | −0.409166 | ||||||||
\(802\) | −15.7552 | −0.556336 | ||||||||
\(803\) | 33.9769 | 1.19902 | ||||||||
\(804\) | 43.9892 | 1.55138 | ||||||||
\(805\) | −6.24594 | −0.220140 | ||||||||
\(806\) | −45.1210 | −1.58932 | ||||||||
\(807\) | −11.9095 | −0.419234 | ||||||||
\(808\) | −2.28495 | −0.0803842 | ||||||||
\(809\) | −39.7925 | −1.39903 | −0.699515 | − | 0.714618i | \(-0.746600\pi\) | ||||
−0.699515 | + | 0.714618i | \(0.746600\pi\) | |||||||
\(810\) | −28.8874 | −1.01500 | ||||||||
\(811\) | −13.6384 | −0.478910 | −0.239455 | − | 0.970907i | \(-0.576969\pi\) | ||||
−0.239455 | + | 0.970907i | \(0.576969\pi\) | |||||||
\(812\) | 19.5416 | 0.685776 | ||||||||
\(813\) | 78.6798 | 2.75942 | ||||||||
\(814\) | 7.49762 | 0.262792 | ||||||||
\(815\) | 26.7662 | 0.937579 | ||||||||
\(816\) | 73.3323 | 2.56715 | ||||||||
\(817\) | 28.8790 | 1.01035 | ||||||||
\(818\) | 26.1431 | 0.914072 | ||||||||
\(819\) | 40.5189 | 1.41585 | ||||||||
\(820\) | −3.45238 | −0.120562 | ||||||||
\(821\) | 31.0452 | 1.08348 | 0.541742 | − | 0.840545i | \(-0.317765\pi\) | ||||
0.541742 | + | 0.840545i | \(0.317765\pi\) | |||||||
\(822\) | 87.8386 | 3.06372 | ||||||||
\(823\) | 5.73117 | 0.199776 | 0.0998880 | − | 0.994999i | \(-0.468152\pi\) | ||||
0.0998880 | + | 0.994999i | \(0.468152\pi\) | |||||||
\(824\) | 9.29257 | 0.323722 | ||||||||
\(825\) | 29.6002 | 1.03055 | ||||||||
\(826\) | −36.6895 | −1.27659 | ||||||||
\(827\) | 3.33423 | 0.115942 | 0.0579712 | − | 0.998318i | \(-0.481537\pi\) | ||||
0.0579712 | + | 0.998318i | \(0.481537\pi\) | |||||||
\(828\) | −4.68797 | −0.162918 | ||||||||
\(829\) | −18.3208 | −0.636306 | −0.318153 | − | 0.948039i | \(-0.603063\pi\) | ||||
−0.318153 | + | 0.948039i | \(0.603063\pi\) | |||||||
\(830\) | −77.6416 | −2.69498 | ||||||||
\(831\) | 69.3873 | 2.40702 | ||||||||
\(832\) | −1.51230 | −0.0524295 | ||||||||
\(833\) | −15.7352 | −0.545191 | ||||||||
\(834\) | −69.4653 | −2.40539 | ||||||||
\(835\) | 16.6822 | 0.577313 | ||||||||
\(836\) | −18.8520 | −0.652009 | ||||||||
\(837\) | 11.1570 | 0.385641 | ||||||||
\(838\) | −15.7266 | −0.543268 | ||||||||
\(839\) | 18.4923 | 0.638426 | 0.319213 | − | 0.947683i | \(-0.396581\pi\) | ||||
0.319213 | + | 0.947683i | \(0.396581\pi\) | |||||||
\(840\) | 23.3764 | 0.806563 | ||||||||
\(841\) | 40.6894 | 1.40308 | ||||||||
\(842\) | 54.7380 | 1.88639 | ||||||||
\(843\) | −26.7211 | −0.920325 | ||||||||
\(844\) | 24.8720 | 0.856129 | ||||||||
\(845\) | 37.9583 | 1.30580 | ||||||||
\(846\) | 76.5035 | 2.63025 | ||||||||
\(847\) | 3.04727 | 0.104705 | ||||||||
\(848\) | 13.6061 | 0.467235 | ||||||||
\(849\) | 9.09990 | 0.312308 | ||||||||
\(850\) | 31.8846 | 1.09363 | ||||||||
\(851\) | 1.27381 | 0.0436656 | ||||||||
\(852\) | −25.8652 | −0.886126 | ||||||||
\(853\) | 33.9838 | 1.16358 | 0.581791 | − | 0.813338i | \(-0.302352\pi\) | ||||
0.581791 | + | 0.813338i | \(0.302352\pi\) | |||||||
\(854\) | −23.9682 | −0.820176 | ||||||||
\(855\) | 51.6026 | 1.76477 | ||||||||
\(856\) | −21.8847 | −0.748004 | ||||||||
\(857\) | 27.2950 | 0.932381 | 0.466190 | − | 0.884684i | \(-0.345626\pi\) | ||||
0.466190 | + | 0.884684i | \(0.345626\pi\) | |||||||
\(858\) | 84.0485 | 2.86937 | ||||||||
\(859\) | −43.5056 | −1.48439 | −0.742196 | − | 0.670183i | \(-0.766216\pi\) | ||||
−0.742196 | + | 0.670183i | \(0.766216\pi\) | |||||||
\(860\) | 20.2135 | 0.689275 | ||||||||
\(861\) | 5.66748 | 0.193147 | ||||||||
\(862\) | 56.8074 | 1.93487 | ||||||||
\(863\) | −4.61472 | −0.157087 | −0.0785434 | − | 0.996911i | \(-0.525027\pi\) | ||||
−0.0785434 | + | 0.996911i | \(0.525027\pi\) | |||||||
\(864\) | 12.9931 | 0.442036 | ||||||||
\(865\) | 52.8029 | 1.79535 | ||||||||
\(866\) | 5.07272 | 0.172378 | ||||||||
\(867\) | −38.2901 | −1.30040 | ||||||||
\(868\) | −11.6288 | −0.394707 | ||||||||
\(869\) | −7.60955 | −0.258136 | ||||||||
\(870\) | −110.955 | −3.76173 | ||||||||
\(871\) | −75.3735 | −2.55394 | ||||||||
\(872\) | 10.1136 | 0.342489 | ||||||||
\(873\) | 11.2713 | 0.381475 | ||||||||
\(874\) | −8.81215 | −0.298076 | ||||||||
\(875\) | −10.5720 | −0.357398 | ||||||||
\(876\) | 28.7547 | 0.971530 | ||||||||
\(877\) | −13.5433 | −0.457326 | −0.228663 | − | 0.973506i | \(-0.573435\pi\) | ||||
−0.228663 | + | 0.973506i | \(0.573435\pi\) | |||||||
\(878\) | −44.5846 | −1.50466 | ||||||||
\(879\) | 35.4042 | 1.19415 | ||||||||
\(880\) | 50.3863 | 1.69852 | ||||||||
\(881\) | −47.1407 | −1.58821 | −0.794105 | − | 0.607781i | \(-0.792060\pi\) | ||||
−0.794105 | + | 0.607781i | \(0.792060\pi\) | |||||||
\(882\) | −19.1338 | −0.644268 | ||||||||
\(883\) | −6.77213 | −0.227900 | −0.113950 | − | 0.993486i | \(-0.536350\pi\) | ||||
−0.113950 | + | 0.993486i | \(0.536350\pi\) | |||||||
\(884\) | 32.9057 | 1.10674 | ||||||||
\(885\) | 75.7154 | 2.54515 | ||||||||
\(886\) | 41.2030 | 1.38424 | ||||||||
\(887\) | −50.0073 | −1.67908 | −0.839540 | − | 0.543298i | \(-0.817175\pi\) | ||||
−0.839540 | + | 0.543298i | \(0.817175\pi\) | |||||||
\(888\) | −4.76744 | −0.159985 | ||||||||
\(889\) | −31.5018 | −1.05654 | ||||||||
\(890\) | −15.2360 | −0.510713 | ||||||||
\(891\) | 20.1119 | 0.673776 | ||||||||
\(892\) | −17.8737 | −0.598455 | ||||||||
\(893\) | 52.2678 | 1.74908 | ||||||||
\(894\) | 40.0470 | 1.33937 | ||||||||
\(895\) | 35.1224 | 1.17401 | ||||||||
\(896\) | 22.6454 | 0.756530 | ||||||||
\(897\) | 14.2794 | 0.476776 | ||||||||
\(898\) | 4.30091 | 0.143523 | ||||||||
\(899\) | −41.4707 | −1.38312 | ||||||||
\(900\) | 14.0918 | 0.469726 | ||||||||
\(901\) | −15.3642 | −0.511856 | ||||||||
\(902\) | 6.61315 | 0.220194 | ||||||||
\(903\) | −33.1827 | −1.10425 | ||||||||
\(904\) | −1.13815 | −0.0378542 | ||||||||
\(905\) | −6.59552 | −0.219243 | ||||||||
\(906\) | −29.8636 | −0.992151 | ||||||||
\(907\) | 24.6019 | 0.816893 | 0.408446 | − | 0.912782i | \(-0.366071\pi\) | ||||
0.408446 | + | 0.912782i | \(0.366071\pi\) | |||||||
\(908\) | 14.0193 | 0.465247 | ||||||||
\(909\) | 5.79560 | 0.192228 | ||||||||
\(910\) | 53.3106 | 1.76723 | ||||||||
\(911\) | −1.01613 | −0.0336659 | −0.0168329 | − | 0.999858i | \(-0.505358\pi\) | ||||
−0.0168329 | + | 0.999858i | \(0.505358\pi\) | |||||||
\(912\) | 60.9226 | 2.01735 | ||||||||
\(913\) | 54.0555 | 1.78897 | ||||||||
\(914\) | 48.2191 | 1.59495 | ||||||||
\(915\) | 49.4628 | 1.63519 | ||||||||
\(916\) | −0.442163 | −0.0146095 | ||||||||
\(917\) | −29.4480 | −0.972458 | ||||||||
\(918\) | −22.3863 | −0.738859 | ||||||||
\(919\) | −48.5457 | −1.60137 | −0.800687 | − | 0.599083i | \(-0.795532\pi\) | ||||
−0.800687 | + | 0.599083i | \(0.795532\pi\) | |||||||
\(920\) | 4.63424 | 0.152786 | ||||||||
\(921\) | −18.6171 | −0.613453 | ||||||||
\(922\) | −41.4073 | −1.36368 | ||||||||
\(923\) | 44.3188 | 1.45877 | ||||||||
\(924\) | 21.6614 | 0.712607 | ||||||||
\(925\) | −3.82900 | −0.125897 | ||||||||
\(926\) | 54.8282 | 1.80177 | ||||||||
\(927\) | −23.5699 | −0.774138 | ||||||||
\(928\) | −48.2958 | −1.58539 | ||||||||
\(929\) | 2.94386 | 0.0965849 | 0.0482925 | − | 0.998833i | \(-0.484622\pi\) | ||||
0.0482925 | + | 0.998833i | \(0.484622\pi\) | |||||||
\(930\) | 66.0270 | 2.16511 | ||||||||
\(931\) | −13.0724 | −0.428429 | ||||||||
\(932\) | −11.0477 | −0.361880 | ||||||||
\(933\) | −26.2392 | −0.859033 | ||||||||
\(934\) | −40.2164 | −1.31592 | ||||||||
\(935\) | −56.8971 | −1.86073 | ||||||||
\(936\) | −30.0634 | −0.982653 | ||||||||
\(937\) | −5.08901 | −0.166251 | −0.0831254 | − | 0.996539i | \(-0.526490\pi\) | ||||
−0.0831254 | + | 0.996539i | \(0.526490\pi\) | |||||||
\(938\) | −53.4465 | −1.74509 | ||||||||
\(939\) | 40.9427 | 1.33612 | ||||||||
\(940\) | 36.5841 | 1.19324 | ||||||||
\(941\) | 41.0134 | 1.33700 | 0.668500 | − | 0.743713i | \(-0.266937\pi\) | ||||
0.668500 | + | 0.743713i | \(0.266937\pi\) | |||||||
\(942\) | −76.9294 | −2.50650 | ||||||||
\(943\) | 1.12354 | 0.0365876 | ||||||||
\(944\) | 50.2849 | 1.63663 | ||||||||
\(945\) | −13.1820 | −0.428810 | ||||||||
\(946\) | −38.7196 | −1.25888 | ||||||||
\(947\) | 2.68330 | 0.0871955 | 0.0435977 | − | 0.999049i | \(-0.486118\pi\) | ||||
0.0435977 | + | 0.999049i | \(0.486118\pi\) | |||||||
\(948\) | −6.43996 | −0.209160 | ||||||||
\(949\) | −49.2699 | −1.59937 | ||||||||
\(950\) | 26.4889 | 0.859413 | ||||||||
\(951\) | 67.3731 | 2.18472 | ||||||||
\(952\) | −17.5311 | −0.568186 | ||||||||
\(953\) | −9.99036 | −0.323620 | −0.161810 | − | 0.986822i | \(-0.551733\pi\) | ||||
−0.161810 | + | 0.986822i | \(0.551733\pi\) | |||||||
\(954\) | −18.6827 | −0.604876 | ||||||||
\(955\) | 56.7133 | 1.83520 | ||||||||
\(956\) | −6.53427 | −0.211333 | ||||||||
\(957\) | 77.2489 | 2.49710 | ||||||||
\(958\) | 36.0526 | 1.16481 | ||||||||
\(959\) | −38.7895 | −1.25258 | ||||||||
\(960\) | 2.21299 | 0.0714241 | ||||||||
\(961\) | −6.32167 | −0.203925 | ||||||||
\(962\) | −10.8723 | −0.350536 | ||||||||
\(963\) | 55.5090 | 1.78875 | ||||||||
\(964\) | −5.15034 | −0.165881 | ||||||||
\(965\) | 15.8920 | 0.511582 | ||||||||
\(966\) | 10.1254 | 0.325779 | ||||||||
\(967\) | 48.6395 | 1.56414 | 0.782071 | − | 0.623190i | \(-0.214164\pi\) | ||||
0.782071 | + | 0.623190i | \(0.214164\pi\) | |||||||
\(968\) | −2.26095 | −0.0726698 | ||||||||
\(969\) | −68.7948 | −2.21001 | ||||||||
\(970\) | 14.8296 | 0.476150 | ||||||||
\(971\) | 39.2714 | 1.26028 | 0.630140 | − | 0.776481i | \(-0.282997\pi\) | ||||
0.630140 | + | 0.776481i | \(0.282997\pi\) | |||||||
\(972\) | 24.7150 | 0.792735 | ||||||||
\(973\) | 30.6759 | 0.983423 | ||||||||
\(974\) | −11.7946 | −0.377924 | ||||||||
\(975\) | −42.9232 | −1.37464 | ||||||||
\(976\) | 32.8497 | 1.05149 | ||||||||
\(977\) | −16.3579 | −0.523334 | −0.261667 | − | 0.965158i | \(-0.584272\pi\) | ||||
−0.261667 | + | 0.965158i | \(0.584272\pi\) | |||||||
\(978\) | −43.3911 | −1.38749 | ||||||||
\(979\) | 10.6076 | 0.339021 | ||||||||
\(980\) | −9.14982 | −0.292280 | ||||||||
\(981\) | −25.6524 | −0.819017 | ||||||||
\(982\) | −9.56934 | −0.305370 | ||||||||
\(983\) | 3.32253 | 0.105972 | 0.0529861 | − | 0.998595i | \(-0.483126\pi\) | ||||
0.0529861 | + | 0.998595i | \(0.483126\pi\) | |||||||
\(984\) | −4.20504 | −0.134052 | ||||||||
\(985\) | 13.7914 | 0.439429 | ||||||||
\(986\) | 83.2105 | 2.64996 | ||||||||
\(987\) | −60.0570 | −1.91164 | ||||||||
\(988\) | 27.3372 | 0.869712 | ||||||||
\(989\) | −6.57828 | −0.209177 | ||||||||
\(990\) | −69.1862 | −2.19888 | ||||||||
\(991\) | −7.41851 | −0.235657 | −0.117828 | − | 0.993034i | \(-0.537593\pi\) | ||||
−0.117828 | + | 0.993034i | \(0.537593\pi\) | |||||||
\(992\) | 28.7398 | 0.912490 | ||||||||
\(993\) | 23.0043 | 0.730019 | ||||||||
\(994\) | 31.4260 | 0.996771 | ||||||||
\(995\) | −67.0562 | −2.12582 | ||||||||
\(996\) | 45.7471 | 1.44955 | ||||||||
\(997\) | −19.6099 | −0.621050 | −0.310525 | − | 0.950565i | \(-0.600505\pi\) | ||||
−0.310525 | + | 0.950565i | \(0.600505\pi\) | |||||||
\(998\) | 31.2050 | 0.987776 | ||||||||
\(999\) | 2.68836 | 0.0850560 |
(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 | 619.2.a.b.1.22 | ✓ | 30 | |
3.2 | odd | 2 | 5571.2.a.g.1.9 | 30 | |||
4.3 | odd | 2 | 9904.2.a.n.1.25 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
619.2.a.b.1.22 | ✓ | 30 | 1.1 | even | 1 | trivial | |
5571.2.a.g.1.9 | 30 | 3.2 | odd | 2 | |||
9904.2.a.n.1.25 | 30 | 4.3 | odd | 2 |