Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.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: | \(32.0200112105\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 7 x^{14} - 7 x^{13} + 133 x^{12} - 99 x^{11} - 941 x^{10} + 1290 x^{9} + 3031 x^{8} + \cdots - 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.07374\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.34293 | −1.93004 | −0.965020 | − | 0.262175i | \(-0.915560\pi\) | ||||
−0.965020 | + | 0.262175i | \(0.915560\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 3.34293 | 1.36474 | ||||||||
\(7\) | 3.45446 | 1.30566 | 0.652831 | − | 0.757504i | \(-0.273581\pi\) | ||||
0.652831 | + | 0.757504i | \(0.273581\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 8.17517 | 2.72506 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 3.65066 | 1.10072 | 0.550358 | − | 0.834929i | \(-0.314491\pi\) | ||||
0.550358 | + | 0.834929i | \(0.314491\pi\) | |||||||
\(12\) | −3.34293 | −0.965020 | ||||||||
\(13\) | 3.49629 | 0.969697 | 0.484849 | − | 0.874598i | \(-0.338875\pi\) | ||||
0.484849 | + | 0.874598i | \(0.338875\pi\) | |||||||
\(14\) | −3.45446 | −0.923242 | ||||||||
\(15\) | 3.34293 | 0.863140 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.44571 | 1.07824 | 0.539122 | − | 0.842228i | \(-0.318756\pi\) | ||||
0.539122 | + | 0.842228i | \(0.318756\pi\) | |||||||
\(18\) | −8.17517 | −1.92691 | ||||||||
\(19\) | −6.26283 | −1.43679 | −0.718396 | − | 0.695635i | \(-0.755123\pi\) | ||||
−0.718396 | + | 0.695635i | \(0.755123\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −11.5480 | −2.51998 | ||||||||
\(22\) | −3.65066 | −0.778324 | ||||||||
\(23\) | −7.57267 | −1.57901 | −0.789506 | − | 0.613743i | \(-0.789663\pi\) | ||||
−0.789506 | + | 0.613743i | \(0.789663\pi\) | |||||||
\(24\) | 3.34293 | 0.682372 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.49629 | −0.685679 | ||||||||
\(27\) | −17.3002 | −3.32943 | ||||||||
\(28\) | 3.45446 | 0.652831 | ||||||||
\(29\) | −2.62514 | −0.487475 | −0.243738 | − | 0.969841i | \(-0.578374\pi\) | ||||
−0.243738 | + | 0.969841i | \(0.578374\pi\) | |||||||
\(30\) | −3.34293 | −0.610332 | ||||||||
\(31\) | 3.28327 | 0.589692 | 0.294846 | − | 0.955545i | \(-0.404732\pi\) | ||||
0.294846 | + | 0.955545i | \(0.404732\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −12.2039 | −2.12443 | ||||||||
\(34\) | −4.44571 | −0.762433 | ||||||||
\(35\) | −3.45446 | −0.583910 | ||||||||
\(36\) | 8.17517 | 1.36253 | ||||||||
\(37\) | −7.45793 | −1.22608 | −0.613038 | − | 0.790053i | \(-0.710053\pi\) | ||||
−0.613038 | + | 0.790053i | \(0.710053\pi\) | |||||||
\(38\) | 6.26283 | 1.01597 | ||||||||
\(39\) | −11.6879 | −1.87156 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 4.62987 | 0.723064 | 0.361532 | − | 0.932360i | \(-0.382254\pi\) | ||||
0.361532 | + | 0.932360i | \(0.382254\pi\) | |||||||
\(42\) | 11.5480 | 1.78190 | ||||||||
\(43\) | −9.40958 | −1.43495 | −0.717474 | − | 0.696585i | \(-0.754702\pi\) | ||||
−0.717474 | + | 0.696585i | \(0.754702\pi\) | |||||||
\(44\) | 3.65066 | 0.550358 | ||||||||
\(45\) | −8.17517 | −1.21868 | ||||||||
\(46\) | 7.57267 | 1.11653 | ||||||||
\(47\) | −4.02949 | −0.587762 | −0.293881 | − | 0.955842i | \(-0.594947\pi\) | ||||
−0.293881 | + | 0.955842i | \(0.594947\pi\) | |||||||
\(48\) | −3.34293 | −0.482510 | ||||||||
\(49\) | 4.93327 | 0.704753 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −14.8617 | −2.08105 | ||||||||
\(52\) | 3.49629 | 0.484849 | ||||||||
\(53\) | 4.07029 | 0.559098 | 0.279549 | − | 0.960131i | \(-0.409815\pi\) | ||||
0.279549 | + | 0.960131i | \(0.409815\pi\) | |||||||
\(54\) | 17.3002 | 2.35426 | ||||||||
\(55\) | −3.65066 | −0.492255 | ||||||||
\(56\) | −3.45446 | −0.461621 | ||||||||
\(57\) | 20.9362 | 2.77307 | ||||||||
\(58\) | 2.62514 | 0.344697 | ||||||||
\(59\) | 4.53317 | 0.590169 | 0.295085 | − | 0.955471i | \(-0.404652\pi\) | ||||
0.295085 | + | 0.955471i | \(0.404652\pi\) | |||||||
\(60\) | 3.34293 | 0.431570 | ||||||||
\(61\) | −11.7429 | −1.50352 | −0.751762 | − | 0.659435i | \(-0.770796\pi\) | ||||
−0.751762 | + | 0.659435i | \(0.770796\pi\) | |||||||
\(62\) | −3.28327 | −0.416975 | ||||||||
\(63\) | 28.2408 | 3.55800 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.49629 | −0.433662 | ||||||||
\(66\) | 12.2039 | 1.50220 | ||||||||
\(67\) | −2.55592 | −0.312255 | −0.156128 | − | 0.987737i | \(-0.549901\pi\) | ||||
−0.156128 | + | 0.987737i | \(0.549901\pi\) | |||||||
\(68\) | 4.44571 | 0.539122 | ||||||||
\(69\) | 25.3149 | 3.04756 | ||||||||
\(70\) | 3.45446 | 0.412887 | ||||||||
\(71\) | 13.5208 | 1.60462 | 0.802311 | − | 0.596906i | \(-0.203603\pi\) | ||||
0.802311 | + | 0.596906i | \(0.203603\pi\) | |||||||
\(72\) | −8.17517 | −0.963453 | ||||||||
\(73\) | −12.2418 | −1.43279 | −0.716395 | − | 0.697695i | \(-0.754209\pi\) | ||||
−0.716395 | + | 0.697695i | \(0.754209\pi\) | |||||||
\(74\) | 7.45793 | 0.866967 | ||||||||
\(75\) | −3.34293 | −0.386008 | ||||||||
\(76\) | −6.26283 | −0.718396 | ||||||||
\(77\) | 12.6111 | 1.43716 | ||||||||
\(78\) | 11.6879 | 1.32339 | ||||||||
\(79\) | −11.7450 | −1.32142 | −0.660708 | − | 0.750643i | \(-0.729744\pi\) | ||||
−0.660708 | + | 0.750643i | \(0.729744\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 33.3079 | 3.70088 | ||||||||
\(82\) | −4.62987 | −0.511284 | ||||||||
\(83\) | −9.38947 | −1.03063 | −0.515314 | − | 0.857001i | \(-0.672325\pi\) | ||||
−0.515314 | + | 0.857001i | \(0.672325\pi\) | |||||||
\(84\) | −11.5480 | −1.25999 | ||||||||
\(85\) | −4.44571 | −0.482205 | ||||||||
\(86\) | 9.40958 | 1.01466 | ||||||||
\(87\) | 8.77564 | 0.940848 | ||||||||
\(88\) | −3.65066 | −0.389162 | ||||||||
\(89\) | 1.01654 | 0.107753 | 0.0538763 | − | 0.998548i | \(-0.482842\pi\) | ||||
0.0538763 | + | 0.998548i | \(0.482842\pi\) | |||||||
\(90\) | 8.17517 | 0.861739 | ||||||||
\(91\) | 12.0778 | 1.26610 | ||||||||
\(92\) | −7.57267 | −0.789506 | ||||||||
\(93\) | −10.9757 | −1.13813 | ||||||||
\(94\) | 4.02949 | 0.415610 | ||||||||
\(95\) | 6.26283 | 0.642553 | ||||||||
\(96\) | 3.34293 | 0.341186 | ||||||||
\(97\) | 3.76457 | 0.382234 | 0.191117 | − | 0.981567i | \(-0.438789\pi\) | ||||
0.191117 | + | 0.981567i | \(0.438789\pi\) | |||||||
\(98\) | −4.93327 | −0.498336 | ||||||||
\(99\) | 29.8448 | 2.99951 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 9.63337 | 0.958556 | 0.479278 | − | 0.877663i | \(-0.340899\pi\) | ||||
0.479278 | + | 0.877663i | \(0.340899\pi\) | |||||||
\(102\) | 14.8617 | 1.47153 | ||||||||
\(103\) | −13.3052 | −1.31100 | −0.655498 | − | 0.755197i | \(-0.727541\pi\) | ||||
−0.655498 | + | 0.755197i | \(0.727541\pi\) | |||||||
\(104\) | −3.49629 | −0.342840 | ||||||||
\(105\) | 11.5480 | 1.12697 | ||||||||
\(106\) | −4.07029 | −0.395342 | ||||||||
\(107\) | −8.65878 | −0.837076 | −0.418538 | − | 0.908199i | \(-0.637457\pi\) | ||||
−0.418538 | + | 0.908199i | \(0.637457\pi\) | |||||||
\(108\) | −17.3002 | −1.66472 | ||||||||
\(109\) | −9.64624 | −0.923942 | −0.461971 | − | 0.886895i | \(-0.652858\pi\) | ||||
−0.461971 | + | 0.886895i | \(0.652858\pi\) | |||||||
\(110\) | 3.65066 | 0.348077 | ||||||||
\(111\) | 24.9313 | 2.36638 | ||||||||
\(112\) | 3.45446 | 0.326415 | ||||||||
\(113\) | −9.31138 | −0.875941 | −0.437971 | − | 0.898989i | \(-0.644303\pi\) | ||||
−0.437971 | + | 0.898989i | \(0.644303\pi\) | |||||||
\(114\) | −20.9362 | −1.96085 | ||||||||
\(115\) | 7.57267 | 0.706155 | ||||||||
\(116\) | −2.62514 | −0.243738 | ||||||||
\(117\) | 28.5828 | 2.64248 | ||||||||
\(118\) | −4.53317 | −0.417313 | ||||||||
\(119\) | 15.3575 | 1.40782 | ||||||||
\(120\) | −3.34293 | −0.305166 | ||||||||
\(121\) | 2.32733 | 0.211575 | ||||||||
\(122\) | 11.7429 | 1.06315 | ||||||||
\(123\) | −15.4773 | −1.39554 | ||||||||
\(124\) | 3.28327 | 0.294846 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −28.2408 | −2.51589 | ||||||||
\(127\) | −7.95062 | −0.705503 | −0.352752 | − | 0.935717i | \(-0.614754\pi\) | ||||
−0.352752 | + | 0.935717i | \(0.614754\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 31.4556 | 2.76951 | ||||||||
\(130\) | 3.49629 | 0.306645 | ||||||||
\(131\) | 12.6694 | 1.10693 | 0.553467 | − | 0.832871i | \(-0.313304\pi\) | ||||
0.553467 | + | 0.832871i | \(0.313304\pi\) | |||||||
\(132\) | −12.2039 | −1.06221 | ||||||||
\(133\) | −21.6347 | −1.87596 | ||||||||
\(134\) | 2.55592 | 0.220798 | ||||||||
\(135\) | 17.3002 | 1.48897 | ||||||||
\(136\) | −4.44571 | −0.381217 | ||||||||
\(137\) | 0.305403 | 0.0260923 | 0.0130462 | − | 0.999915i | \(-0.495847\pi\) | ||||
0.0130462 | + | 0.999915i | \(0.495847\pi\) | |||||||
\(138\) | −25.3149 | −2.15495 | ||||||||
\(139\) | 4.21702 | 0.357683 | 0.178841 | − | 0.983878i | \(-0.442765\pi\) | ||||
0.178841 | + | 0.983878i | \(0.442765\pi\) | |||||||
\(140\) | −3.45446 | −0.291955 | ||||||||
\(141\) | 13.4703 | 1.13440 | ||||||||
\(142\) | −13.5208 | −1.13464 | ||||||||
\(143\) | 12.7638 | 1.06736 | ||||||||
\(144\) | 8.17517 | 0.681264 | ||||||||
\(145\) | 2.62514 | 0.218006 | ||||||||
\(146\) | 12.2418 | 1.01314 | ||||||||
\(147\) | −16.4916 | −1.36020 | ||||||||
\(148\) | −7.45793 | −0.613038 | ||||||||
\(149\) | −10.9607 | −0.897937 | −0.448968 | − | 0.893548i | \(-0.648208\pi\) | ||||
−0.448968 | + | 0.893548i | \(0.648208\pi\) | |||||||
\(150\) | 3.34293 | 0.272949 | ||||||||
\(151\) | −5.55463 | −0.452030 | −0.226015 | − | 0.974124i | \(-0.572570\pi\) | ||||
−0.226015 | + | 0.974124i | \(0.572570\pi\) | |||||||
\(152\) | 6.26283 | 0.507983 | ||||||||
\(153\) | 36.3445 | 2.93828 | ||||||||
\(154\) | −12.6111 | −1.01623 | ||||||||
\(155\) | −3.28327 | −0.263718 | ||||||||
\(156\) | −11.6879 | −0.935778 | ||||||||
\(157\) | −10.1392 | −0.809193 | −0.404597 | − | 0.914495i | \(-0.632588\pi\) | ||||
−0.404597 | + | 0.914495i | \(0.632588\pi\) | |||||||
\(158\) | 11.7450 | 0.934382 | ||||||||
\(159\) | −13.6067 | −1.07908 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −26.1595 | −2.06166 | ||||||||
\(162\) | −33.3079 | −2.61692 | ||||||||
\(163\) | 11.3585 | 0.889668 | 0.444834 | − | 0.895613i | \(-0.353263\pi\) | ||||
0.444834 | + | 0.895613i | \(0.353263\pi\) | |||||||
\(164\) | 4.62987 | 0.361532 | ||||||||
\(165\) | 12.2039 | 0.950072 | ||||||||
\(166\) | 9.38947 | 0.728764 | ||||||||
\(167\) | 10.1324 | 0.784071 | 0.392036 | − | 0.919950i | \(-0.371771\pi\) | ||||
0.392036 | + | 0.919950i | \(0.371771\pi\) | |||||||
\(168\) | 11.5480 | 0.890948 | ||||||||
\(169\) | −0.775935 | −0.0596873 | ||||||||
\(170\) | 4.44571 | 0.340971 | ||||||||
\(171\) | −51.1997 | −3.91534 | ||||||||
\(172\) | −9.40958 | −0.717474 | ||||||||
\(173\) | −17.6077 | −1.33869 | −0.669344 | − | 0.742953i | \(-0.733425\pi\) | ||||
−0.669344 | + | 0.742953i | \(0.733425\pi\) | |||||||
\(174\) | −8.77564 | −0.665280 | ||||||||
\(175\) | 3.45446 | 0.261132 | ||||||||
\(176\) | 3.65066 | 0.275179 | ||||||||
\(177\) | −15.1541 | −1.13905 | ||||||||
\(178\) | −1.01654 | −0.0761926 | ||||||||
\(179\) | −24.2483 | −1.81241 | −0.906203 | − | 0.422843i | \(-0.861032\pi\) | ||||
−0.906203 | + | 0.422843i | \(0.861032\pi\) | |||||||
\(180\) | −8.17517 | −0.609341 | ||||||||
\(181\) | −5.16159 | −0.383658 | −0.191829 | − | 0.981428i | \(-0.561442\pi\) | ||||
−0.191829 | + | 0.981428i | \(0.561442\pi\) | |||||||
\(182\) | −12.0778 | −0.895266 | ||||||||
\(183\) | 39.2557 | 2.90186 | ||||||||
\(184\) | 7.57267 | 0.558265 | ||||||||
\(185\) | 7.45793 | 0.548318 | ||||||||
\(186\) | 10.9757 | 0.804779 | ||||||||
\(187\) | 16.2298 | 1.18684 | ||||||||
\(188\) | −4.02949 | −0.293881 | ||||||||
\(189\) | −59.7629 | −4.34711 | ||||||||
\(190\) | −6.26283 | −0.454353 | ||||||||
\(191\) | −14.8898 | −1.07739 | −0.538695 | − | 0.842501i | \(-0.681083\pi\) | ||||
−0.538695 | + | 0.842501i | \(0.681083\pi\) | |||||||
\(192\) | −3.34293 | −0.241255 | ||||||||
\(193\) | 10.3403 | 0.744312 | 0.372156 | − | 0.928170i | \(-0.378619\pi\) | ||||
0.372156 | + | 0.928170i | \(0.378619\pi\) | |||||||
\(194\) | −3.76457 | −0.270280 | ||||||||
\(195\) | 11.6879 | 0.836985 | ||||||||
\(196\) | 4.93327 | 0.352376 | ||||||||
\(197\) | 26.7271 | 1.90423 | 0.952114 | − | 0.305744i | \(-0.0989052\pi\) | ||||
0.952114 | + | 0.305744i | \(0.0989052\pi\) | |||||||
\(198\) | −29.8448 | −2.12098 | ||||||||
\(199\) | −0.620373 | −0.0439771 | −0.0219885 | − | 0.999758i | \(-0.507000\pi\) | ||||
−0.0219885 | + | 0.999758i | \(0.507000\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 8.54426 | 0.602665 | ||||||||
\(202\) | −9.63337 | −0.677802 | ||||||||
\(203\) | −9.06842 | −0.636478 | ||||||||
\(204\) | −14.8617 | −1.04053 | ||||||||
\(205\) | −4.62987 | −0.323364 | ||||||||
\(206\) | 13.3052 | 0.927014 | ||||||||
\(207\) | −61.9079 | −4.30290 | ||||||||
\(208\) | 3.49629 | 0.242424 | ||||||||
\(209\) | −22.8635 | −1.58150 | ||||||||
\(210\) | −11.5480 | −0.796888 | ||||||||
\(211\) | −4.78650 | −0.329516 | −0.164758 | − | 0.986334i | \(-0.552684\pi\) | ||||
−0.164758 | + | 0.986334i | \(0.552684\pi\) | |||||||
\(212\) | 4.07029 | 0.279549 | ||||||||
\(213\) | −45.1990 | −3.09699 | ||||||||
\(214\) | 8.65878 | 0.591902 | ||||||||
\(215\) | 9.40958 | 0.641728 | ||||||||
\(216\) | 17.3002 | 1.17713 | ||||||||
\(217\) | 11.3419 | 0.769938 | ||||||||
\(218\) | 9.64624 | 0.653326 | ||||||||
\(219\) | 40.9233 | 2.76534 | ||||||||
\(220\) | −3.65066 | −0.246128 | ||||||||
\(221\) | 15.5435 | 1.04557 | ||||||||
\(222\) | −24.9313 | −1.67328 | ||||||||
\(223\) | −27.9906 | −1.87439 | −0.937195 | − | 0.348806i | \(-0.886587\pi\) | ||||
−0.937195 | + | 0.348806i | \(0.886587\pi\) | |||||||
\(224\) | −3.45446 | −0.230811 | ||||||||
\(225\) | 8.17517 | 0.545012 | ||||||||
\(226\) | 9.31138 | 0.619384 | ||||||||
\(227\) | −4.43698 | −0.294493 | −0.147246 | − | 0.989100i | \(-0.547041\pi\) | ||||
−0.147246 | + | 0.989100i | \(0.547041\pi\) | |||||||
\(228\) | 20.9362 | 1.38653 | ||||||||
\(229\) | 27.5641 | 1.82149 | 0.910744 | − | 0.412972i | \(-0.135509\pi\) | ||||
0.910744 | + | 0.412972i | \(0.135509\pi\) | |||||||
\(230\) | −7.57267 | −0.499327 | ||||||||
\(231\) | −42.1578 | −2.77378 | ||||||||
\(232\) | 2.62514 | 0.172349 | ||||||||
\(233\) | −11.9986 | −0.786057 | −0.393029 | − | 0.919526i | \(-0.628573\pi\) | ||||
−0.393029 | + | 0.919526i | \(0.628573\pi\) | |||||||
\(234\) | −28.5828 | −1.86852 | ||||||||
\(235\) | 4.02949 | 0.262855 | ||||||||
\(236\) | 4.53317 | 0.295085 | ||||||||
\(237\) | 39.2627 | 2.55039 | ||||||||
\(238\) | −15.3575 | −0.995480 | ||||||||
\(239\) | 20.7284 | 1.34081 | 0.670406 | − | 0.741995i | \(-0.266120\pi\) | ||||
0.670406 | + | 0.741995i | \(0.266120\pi\) | |||||||
\(240\) | 3.34293 | 0.215785 | ||||||||
\(241\) | 21.3272 | 1.37381 | 0.686904 | − | 0.726748i | \(-0.258969\pi\) | ||||
0.686904 | + | 0.726748i | \(0.258969\pi\) | |||||||
\(242\) | −2.32733 | −0.149606 | ||||||||
\(243\) | −59.4453 | −3.81342 | ||||||||
\(244\) | −11.7429 | −0.751762 | ||||||||
\(245\) | −4.93327 | −0.315175 | ||||||||
\(246\) | 15.4773 | 0.986798 | ||||||||
\(247\) | −21.8967 | −1.39325 | ||||||||
\(248\) | −3.28327 | −0.208488 | ||||||||
\(249\) | 31.3883 | 1.98915 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 13.0329 | 0.822630 | 0.411315 | − | 0.911493i | \(-0.365070\pi\) | ||||
0.411315 | + | 0.911493i | \(0.365070\pi\) | |||||||
\(252\) | 28.2408 | 1.77900 | ||||||||
\(253\) | −27.6453 | −1.73804 | ||||||||
\(254\) | 7.95062 | 0.498866 | ||||||||
\(255\) | 14.8617 | 0.930676 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.04869 | 0.564442 | 0.282221 | − | 0.959349i | \(-0.408929\pi\) | ||||
0.282221 | + | 0.959349i | \(0.408929\pi\) | |||||||
\(258\) | −31.4556 | −1.95834 | ||||||||
\(259\) | −25.7631 | −1.60084 | ||||||||
\(260\) | −3.49629 | −0.216831 | ||||||||
\(261\) | −21.4609 | −1.32840 | ||||||||
\(262\) | −12.6694 | −0.782721 | ||||||||
\(263\) | 18.8162 | 1.16025 | 0.580127 | − | 0.814526i | \(-0.303003\pi\) | ||||
0.580127 | + | 0.814526i | \(0.303003\pi\) | |||||||
\(264\) | 12.2039 | 0.751098 | ||||||||
\(265\) | −4.07029 | −0.250036 | ||||||||
\(266\) | 21.6347 | 1.32651 | ||||||||
\(267\) | −3.39821 | −0.207967 | ||||||||
\(268\) | −2.55592 | −0.156128 | ||||||||
\(269\) | −22.5925 | −1.37749 | −0.688744 | − | 0.725005i | \(-0.741838\pi\) | ||||
−0.688744 | + | 0.725005i | \(0.741838\pi\) | |||||||
\(270\) | −17.3002 | −1.05286 | ||||||||
\(271\) | 22.2738 | 1.35304 | 0.676518 | − | 0.736426i | \(-0.263488\pi\) | ||||
0.676518 | + | 0.736426i | \(0.263488\pi\) | |||||||
\(272\) | 4.44571 | 0.269561 | ||||||||
\(273\) | −40.3752 | −2.44362 | ||||||||
\(274\) | −0.305403 | −0.0184501 | ||||||||
\(275\) | 3.65066 | 0.220143 | ||||||||
\(276\) | 25.3149 | 1.52378 | ||||||||
\(277\) | 28.2150 | 1.69527 | 0.847637 | − | 0.530576i | \(-0.178024\pi\) | ||||
0.847637 | + | 0.530576i | \(0.178024\pi\) | |||||||
\(278\) | −4.21702 | −0.252920 | ||||||||
\(279\) | 26.8413 | 1.60694 | ||||||||
\(280\) | 3.45446 | 0.206443 | ||||||||
\(281\) | −11.5833 | −0.691000 | −0.345500 | − | 0.938419i | \(-0.612291\pi\) | ||||
−0.345500 | + | 0.938419i | \(0.612291\pi\) | |||||||
\(282\) | −13.4703 | −0.802145 | ||||||||
\(283\) | −11.3650 | −0.675579 | −0.337789 | − | 0.941222i | \(-0.609679\pi\) | ||||
−0.337789 | + | 0.941222i | \(0.609679\pi\) | |||||||
\(284\) | 13.5208 | 0.802311 | ||||||||
\(285\) | −20.9362 | −1.24015 | ||||||||
\(286\) | −12.7638 | −0.754738 | ||||||||
\(287\) | 15.9937 | 0.944078 | ||||||||
\(288\) | −8.17517 | −0.481727 | ||||||||
\(289\) | 2.76436 | 0.162610 | ||||||||
\(290\) | −2.62514 | −0.154153 | ||||||||
\(291\) | −12.5847 | −0.737727 | ||||||||
\(292\) | −12.2418 | −0.716395 | ||||||||
\(293\) | 2.36108 | 0.137936 | 0.0689678 | − | 0.997619i | \(-0.478029\pi\) | ||||
0.0689678 | + | 0.997619i | \(0.478029\pi\) | |||||||
\(294\) | 16.4916 | 0.961808 | ||||||||
\(295\) | −4.53317 | −0.263932 | ||||||||
\(296\) | 7.45793 | 0.433484 | ||||||||
\(297\) | −63.1573 | −3.66476 | ||||||||
\(298\) | 10.9607 | 0.634937 | ||||||||
\(299\) | −26.4763 | −1.53116 | ||||||||
\(300\) | −3.34293 | −0.193004 | ||||||||
\(301\) | −32.5050 | −1.87356 | ||||||||
\(302\) | 5.55463 | 0.319633 | ||||||||
\(303\) | −32.2037 | −1.85005 | ||||||||
\(304\) | −6.26283 | −0.359198 | ||||||||
\(305\) | 11.7429 | 0.672396 | ||||||||
\(306\) | −36.3445 | −2.07768 | ||||||||
\(307\) | −6.48616 | −0.370185 | −0.185092 | − | 0.982721i | \(-0.559258\pi\) | ||||
−0.185092 | + | 0.982721i | \(0.559258\pi\) | |||||||
\(308\) | 12.6111 | 0.718581 | ||||||||
\(309\) | 44.4782 | 2.53028 | ||||||||
\(310\) | 3.28327 | 0.186477 | ||||||||
\(311\) | −25.2762 | −1.43328 | −0.716640 | − | 0.697443i | \(-0.754321\pi\) | ||||
−0.716640 | + | 0.697443i | \(0.754321\pi\) | |||||||
\(312\) | 11.6879 | 0.661695 | ||||||||
\(313\) | 7.61926 | 0.430666 | 0.215333 | − | 0.976541i | \(-0.430916\pi\) | ||||
0.215333 | + | 0.976541i | \(0.430916\pi\) | |||||||
\(314\) | 10.1392 | 0.572186 | ||||||||
\(315\) | −28.2408 | −1.59119 | ||||||||
\(316\) | −11.7450 | −0.660708 | ||||||||
\(317\) | 16.5917 | 0.931884 | 0.465942 | − | 0.884815i | \(-0.345716\pi\) | ||||
0.465942 | + | 0.884815i | \(0.345716\pi\) | |||||||
\(318\) | 13.6067 | 0.763026 | ||||||||
\(319\) | −9.58348 | −0.536572 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 28.9457 | 1.61559 | ||||||||
\(322\) | 26.1595 | 1.45781 | ||||||||
\(323\) | −27.8427 | −1.54921 | ||||||||
\(324\) | 33.3079 | 1.85044 | ||||||||
\(325\) | 3.49629 | 0.193939 | ||||||||
\(326\) | −11.3585 | −0.629090 | ||||||||
\(327\) | 32.2467 | 1.78325 | ||||||||
\(328\) | −4.62987 | −0.255642 | ||||||||
\(329\) | −13.9197 | −0.767418 | ||||||||
\(330\) | −12.2039 | −0.671803 | ||||||||
\(331\) | −16.0676 | −0.883157 | −0.441578 | − | 0.897223i | \(-0.645581\pi\) | ||||
−0.441578 | + | 0.897223i | \(0.645581\pi\) | |||||||
\(332\) | −9.38947 | −0.515314 | ||||||||
\(333\) | −60.9699 | −3.34113 | ||||||||
\(334\) | −10.1324 | −0.554422 | ||||||||
\(335\) | 2.55592 | 0.139645 | ||||||||
\(336\) | −11.5480 | −0.629995 | ||||||||
\(337\) | −32.4640 | −1.76843 | −0.884213 | − | 0.467084i | \(-0.845305\pi\) | ||||
−0.884213 | + | 0.467084i | \(0.845305\pi\) | |||||||
\(338\) | 0.775935 | 0.0422053 | ||||||||
\(339\) | 31.1273 | 1.69060 | ||||||||
\(340\) | −4.44571 | −0.241103 | ||||||||
\(341\) | 11.9861 | 0.649083 | ||||||||
\(342\) | 51.1997 | 2.76856 | ||||||||
\(343\) | −7.13943 | −0.385493 | ||||||||
\(344\) | 9.40958 | 0.507331 | ||||||||
\(345\) | −25.3149 | −1.36291 | ||||||||
\(346\) | 17.6077 | 0.946595 | ||||||||
\(347\) | −25.8709 | −1.38882 | −0.694410 | − | 0.719579i | \(-0.744335\pi\) | ||||
−0.694410 | + | 0.719579i | \(0.744335\pi\) | |||||||
\(348\) | 8.77564 | 0.470424 | ||||||||
\(349\) | 16.1470 | 0.864330 | 0.432165 | − | 0.901794i | \(-0.357750\pi\) | ||||
0.432165 | + | 0.901794i | \(0.357750\pi\) | |||||||
\(350\) | −3.45446 | −0.184648 | ||||||||
\(351\) | −60.4867 | −3.22854 | ||||||||
\(352\) | −3.65066 | −0.194581 | ||||||||
\(353\) | 26.9240 | 1.43302 | 0.716511 | − | 0.697576i | \(-0.245738\pi\) | ||||
0.716511 | + | 0.697576i | \(0.245738\pi\) | |||||||
\(354\) | 15.1541 | 0.805430 | ||||||||
\(355\) | −13.5208 | −0.717609 | ||||||||
\(356\) | 1.01654 | 0.0538763 | ||||||||
\(357\) | −51.3391 | −2.71715 | ||||||||
\(358\) | 24.2483 | 1.28156 | ||||||||
\(359\) | 9.66274 | 0.509980 | 0.254990 | − | 0.966944i | \(-0.417928\pi\) | ||||
0.254990 | + | 0.966944i | \(0.417928\pi\) | |||||||
\(360\) | 8.17517 | 0.430869 | ||||||||
\(361\) | 20.2230 | 1.06437 | ||||||||
\(362\) | 5.16159 | 0.271287 | ||||||||
\(363\) | −7.78009 | −0.408349 | ||||||||
\(364\) | 12.0778 | 0.633048 | ||||||||
\(365\) | 12.2418 | 0.640763 | ||||||||
\(366\) | −39.2557 | −2.05193 | ||||||||
\(367\) | 23.3113 | 1.21684 | 0.608419 | − | 0.793616i | \(-0.291804\pi\) | ||||
0.608419 | + | 0.793616i | \(0.291804\pi\) | |||||||
\(368\) | −7.57267 | −0.394753 | ||||||||
\(369\) | 37.8500 | 1.97039 | ||||||||
\(370\) | −7.45793 | −0.387719 | ||||||||
\(371\) | 14.0606 | 0.729992 | ||||||||
\(372\) | −10.9757 | −0.569065 | ||||||||
\(373\) | 18.7188 | 0.969223 | 0.484612 | − | 0.874729i | \(-0.338961\pi\) | ||||
0.484612 | + | 0.874729i | \(0.338961\pi\) | |||||||
\(374\) | −16.2298 | −0.839223 | ||||||||
\(375\) | 3.34293 | 0.172628 | ||||||||
\(376\) | 4.02949 | 0.207805 | ||||||||
\(377\) | −9.17824 | −0.472704 | ||||||||
\(378\) | 59.7629 | 3.07387 | ||||||||
\(379\) | −28.5930 | −1.46872 | −0.734362 | − | 0.678758i | \(-0.762519\pi\) | ||||
−0.734362 | + | 0.678758i | \(0.762519\pi\) | |||||||
\(380\) | 6.26283 | 0.321276 | ||||||||
\(381\) | 26.5784 | 1.36165 | ||||||||
\(382\) | 14.8898 | 0.761830 | ||||||||
\(383\) | −4.40398 | −0.225033 | −0.112516 | − | 0.993650i | \(-0.535891\pi\) | ||||
−0.112516 | + | 0.993650i | \(0.535891\pi\) | |||||||
\(384\) | 3.34293 | 0.170593 | ||||||||
\(385\) | −12.6111 | −0.642719 | ||||||||
\(386\) | −10.3403 | −0.526308 | ||||||||
\(387\) | −76.9250 | −3.91032 | ||||||||
\(388\) | 3.76457 | 0.191117 | ||||||||
\(389\) | −24.5618 | −1.24533 | −0.622667 | − | 0.782487i | \(-0.713951\pi\) | ||||
−0.622667 | + | 0.782487i | \(0.713951\pi\) | |||||||
\(390\) | −11.6879 | −0.591838 | ||||||||
\(391\) | −33.6659 | −1.70256 | ||||||||
\(392\) | −4.93327 | −0.249168 | ||||||||
\(393\) | −42.3530 | −2.13643 | ||||||||
\(394\) | −26.7271 | −1.34649 | ||||||||
\(395\) | 11.7450 | 0.590955 | ||||||||
\(396\) | 29.8448 | 1.49976 | ||||||||
\(397\) | 15.5751 | 0.781691 | 0.390845 | − | 0.920456i | \(-0.372183\pi\) | ||||
0.390845 | + | 0.920456i | \(0.372183\pi\) | |||||||
\(398\) | 0.620373 | 0.0310965 | ||||||||
\(399\) | 72.3232 | 3.62069 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | −8.54426 | −0.426149 | ||||||||
\(403\) | 11.4793 | 0.571823 | ||||||||
\(404\) | 9.63337 | 0.479278 | ||||||||
\(405\) | −33.3079 | −1.65508 | ||||||||
\(406\) | 9.06842 | 0.450058 | ||||||||
\(407\) | −27.2264 | −1.34956 | ||||||||
\(408\) | 14.8617 | 0.735764 | ||||||||
\(409\) | −22.2350 | −1.09945 | −0.549724 | − | 0.835346i | \(-0.685267\pi\) | ||||
−0.549724 | + | 0.835346i | \(0.685267\pi\) | |||||||
\(410\) | 4.62987 | 0.228653 | ||||||||
\(411\) | −1.02094 | −0.0503593 | ||||||||
\(412\) | −13.3052 | −0.655498 | ||||||||
\(413\) | 15.6597 | 0.770561 | ||||||||
\(414\) | 61.9079 | 3.04261 | ||||||||
\(415\) | 9.38947 | 0.460911 | ||||||||
\(416\) | −3.49629 | −0.171420 | ||||||||
\(417\) | −14.0972 | −0.690343 | ||||||||
\(418\) | 22.8635 | 1.11829 | ||||||||
\(419\) | 21.5003 | 1.05036 | 0.525179 | − | 0.850992i | \(-0.323998\pi\) | ||||
0.525179 | + | 0.850992i | \(0.323998\pi\) | |||||||
\(420\) | 11.5480 | 0.563485 | ||||||||
\(421\) | −35.3921 | −1.72490 | −0.862452 | − | 0.506139i | \(-0.831072\pi\) | ||||
−0.862452 | + | 0.506139i | \(0.831072\pi\) | |||||||
\(422\) | 4.78650 | 0.233003 | ||||||||
\(423\) | −32.9418 | −1.60168 | ||||||||
\(424\) | −4.07029 | −0.197671 | ||||||||
\(425\) | 4.44571 | 0.215649 | ||||||||
\(426\) | 45.1990 | 2.18990 | ||||||||
\(427\) | −40.5653 | −1.96309 | ||||||||
\(428\) | −8.65878 | −0.418538 | ||||||||
\(429\) | −42.6684 | −2.06005 | ||||||||
\(430\) | −9.40958 | −0.453770 | ||||||||
\(431\) | 17.4615 | 0.841089 | 0.420544 | − | 0.907272i | \(-0.361839\pi\) | ||||
0.420544 | + | 0.907272i | \(0.361839\pi\) | |||||||
\(432\) | −17.3002 | −0.832358 | ||||||||
\(433\) | 25.5592 | 1.22830 | 0.614149 | − | 0.789190i | \(-0.289499\pi\) | ||||
0.614149 | + | 0.789190i | \(0.289499\pi\) | |||||||
\(434\) | −11.3419 | −0.544429 | ||||||||
\(435\) | −8.77564 | −0.420760 | ||||||||
\(436\) | −9.64624 | −0.461971 | ||||||||
\(437\) | 47.4264 | 2.26871 | ||||||||
\(438\) | −40.9233 | −1.95539 | ||||||||
\(439\) | 0.954774 | 0.0455689 | 0.0227844 | − | 0.999740i | \(-0.492747\pi\) | ||||
0.0227844 | + | 0.999740i | \(0.492747\pi\) | |||||||
\(440\) | 3.65066 | 0.174038 | ||||||||
\(441\) | 40.3303 | 1.92049 | ||||||||
\(442\) | −15.5435 | −0.739330 | ||||||||
\(443\) | −22.2117 | −1.05531 | −0.527654 | − | 0.849459i | \(-0.676928\pi\) | ||||
−0.527654 | + | 0.849459i | \(0.676928\pi\) | |||||||
\(444\) | 24.9313 | 1.18319 | ||||||||
\(445\) | −1.01654 | −0.0481884 | ||||||||
\(446\) | 27.9906 | 1.32539 | ||||||||
\(447\) | 36.6409 | 1.73305 | ||||||||
\(448\) | 3.45446 | 0.163208 | ||||||||
\(449\) | −10.9315 | −0.515891 | −0.257945 | − | 0.966159i | \(-0.583045\pi\) | ||||
−0.257945 | + | 0.966159i | \(0.583045\pi\) | |||||||
\(450\) | −8.17517 | −0.385381 | ||||||||
\(451\) | 16.9021 | 0.795888 | ||||||||
\(452\) | −9.31138 | −0.437971 | ||||||||
\(453\) | 18.5687 | 0.872436 | ||||||||
\(454\) | 4.43698 | 0.208238 | ||||||||
\(455\) | −12.0778 | −0.566216 | ||||||||
\(456\) | −20.9362 | −0.980427 | ||||||||
\(457\) | 18.8479 | 0.881667 | 0.440833 | − | 0.897589i | \(-0.354683\pi\) | ||||
0.440833 | + | 0.897589i | \(0.354683\pi\) | |||||||
\(458\) | −27.5641 | −1.28799 | ||||||||
\(459\) | −76.9119 | −3.58994 | ||||||||
\(460\) | 7.57267 | 0.353078 | ||||||||
\(461\) | −13.9256 | −0.648580 | −0.324290 | − | 0.945958i | \(-0.605125\pi\) | ||||
−0.324290 | + | 0.945958i | \(0.605125\pi\) | |||||||
\(462\) | 42.1578 | 1.96136 | ||||||||
\(463\) | −7.79458 | −0.362245 | −0.181123 | − | 0.983461i | \(-0.557973\pi\) | ||||
−0.181123 | + | 0.983461i | \(0.557973\pi\) | |||||||
\(464\) | −2.62514 | −0.121869 | ||||||||
\(465\) | 10.9757 | 0.508987 | ||||||||
\(466\) | 11.9986 | 0.555826 | ||||||||
\(467\) | −30.0377 | −1.38998 | −0.694990 | − | 0.719019i | \(-0.744591\pi\) | ||||
−0.694990 | + | 0.719019i | \(0.744591\pi\) | |||||||
\(468\) | 28.5828 | 1.32124 | ||||||||
\(469\) | −8.82931 | −0.407700 | ||||||||
\(470\) | −4.02949 | −0.185867 | ||||||||
\(471\) | 33.8945 | 1.56178 | ||||||||
\(472\) | −4.53317 | −0.208656 | ||||||||
\(473\) | −34.3512 | −1.57947 | ||||||||
\(474\) | −39.2627 | −1.80340 | ||||||||
\(475\) | −6.26283 | −0.287358 | ||||||||
\(476\) | 15.3575 | 0.703911 | ||||||||
\(477\) | 33.2753 | 1.52357 | ||||||||
\(478\) | −20.7284 | −0.948097 | ||||||||
\(479\) | −12.4327 | −0.568063 | −0.284032 | − | 0.958815i | \(-0.591672\pi\) | ||||
−0.284032 | + | 0.958815i | \(0.591672\pi\) | |||||||
\(480\) | −3.34293 | −0.152583 | ||||||||
\(481\) | −26.0751 | −1.18892 | ||||||||
\(482\) | −21.3272 | −0.971429 | ||||||||
\(483\) | 87.4493 | 3.97908 | ||||||||
\(484\) | 2.32733 | 0.105788 | ||||||||
\(485\) | −3.76457 | −0.170940 | ||||||||
\(486\) | 59.4453 | 2.69650 | ||||||||
\(487\) | −15.1280 | −0.685515 | −0.342758 | − | 0.939424i | \(-0.611361\pi\) | ||||
−0.342758 | + | 0.939424i | \(0.611361\pi\) | |||||||
\(488\) | 11.7429 | 0.531576 | ||||||||
\(489\) | −37.9707 | −1.71710 | ||||||||
\(490\) | 4.93327 | 0.222862 | ||||||||
\(491\) | −28.3599 | −1.27986 | −0.639932 | − | 0.768431i | \(-0.721038\pi\) | ||||
−0.639932 | + | 0.768431i | \(0.721038\pi\) | |||||||
\(492\) | −15.4773 | −0.697772 | ||||||||
\(493\) | −11.6706 | −0.525617 | ||||||||
\(494\) | 21.8967 | 0.985178 | ||||||||
\(495\) | −29.8448 | −1.34142 | ||||||||
\(496\) | 3.28327 | 0.147423 | ||||||||
\(497\) | 46.7070 | 2.09509 | ||||||||
\(498\) | −31.3883 | −1.40654 | ||||||||
\(499\) | 12.2680 | 0.549190 | 0.274595 | − | 0.961560i | \(-0.411456\pi\) | ||||
0.274595 | + | 0.961560i | \(0.411456\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −33.8720 | −1.51329 | ||||||||
\(502\) | −13.0329 | −0.581687 | ||||||||
\(503\) | −0.349538 | −0.0155851 | −0.00779257 | − | 0.999970i | \(-0.502480\pi\) | ||||
−0.00779257 | + | 0.999970i | \(0.502480\pi\) | |||||||
\(504\) | −28.2408 | −1.25794 | ||||||||
\(505\) | −9.63337 | −0.428679 | ||||||||
\(506\) | 27.6453 | 1.22898 | ||||||||
\(507\) | 2.59390 | 0.115199 | ||||||||
\(508\) | −7.95062 | −0.352752 | ||||||||
\(509\) | 14.2824 | 0.633058 | 0.316529 | − | 0.948583i | \(-0.397483\pi\) | ||||
0.316529 | + | 0.948583i | \(0.397483\pi\) | |||||||
\(510\) | −14.8617 | −0.658087 | ||||||||
\(511\) | −42.2886 | −1.87074 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 108.348 | 4.78370 | ||||||||
\(514\) | −9.04869 | −0.399121 | ||||||||
\(515\) | 13.3052 | 0.586295 | ||||||||
\(516\) | 31.4556 | 1.38475 | ||||||||
\(517\) | −14.7103 | −0.646958 | ||||||||
\(518\) | 25.7631 | 1.13197 | ||||||||
\(519\) | 58.8612 | 2.58372 | ||||||||
\(520\) | 3.49629 | 0.153323 | ||||||||
\(521\) | −2.68168 | −0.117486 | −0.0587432 | − | 0.998273i | \(-0.518709\pi\) | ||||
−0.0587432 | + | 0.998273i | \(0.518709\pi\) | |||||||
\(522\) | 21.4609 | 0.939320 | ||||||||
\(523\) | 0.564206 | 0.0246710 | 0.0123355 | − | 0.999924i | \(-0.496073\pi\) | ||||
0.0123355 | + | 0.999924i | \(0.496073\pi\) | |||||||
\(524\) | 12.6694 | 0.553467 | ||||||||
\(525\) | −11.5480 | −0.503996 | ||||||||
\(526\) | −18.8162 | −0.820424 | ||||||||
\(527\) | 14.5965 | 0.635832 | ||||||||
\(528\) | −12.2039 | −0.531107 | ||||||||
\(529\) | 34.3454 | 1.49328 | ||||||||
\(530\) | 4.07029 | 0.176802 | ||||||||
\(531\) | 37.0595 | 1.60824 | ||||||||
\(532\) | −21.6347 | −0.937982 | ||||||||
\(533\) | 16.1874 | 0.701154 | ||||||||
\(534\) | 3.39821 | 0.147055 | ||||||||
\(535\) | 8.65878 | 0.374352 | ||||||||
\(536\) | 2.55592 | 0.110399 | ||||||||
\(537\) | 81.0605 | 3.49802 | ||||||||
\(538\) | 22.5925 | 0.974031 | ||||||||
\(539\) | 18.0097 | 0.775733 | ||||||||
\(540\) | 17.3002 | 0.744484 | ||||||||
\(541\) | −0.472310 | −0.0203062 | −0.0101531 | − | 0.999948i | \(-0.503232\pi\) | ||||
−0.0101531 | + | 0.999948i | \(0.503232\pi\) | |||||||
\(542\) | −22.2738 | −0.956740 | ||||||||
\(543\) | 17.2548 | 0.740475 | ||||||||
\(544\) | −4.44571 | −0.190608 | ||||||||
\(545\) | 9.64624 | 0.413200 | ||||||||
\(546\) | 40.3752 | 1.72790 | ||||||||
\(547\) | −10.3468 | −0.442399 | −0.221199 | − | 0.975229i | \(-0.570997\pi\) | ||||
−0.221199 | + | 0.975229i | \(0.570997\pi\) | |||||||
\(548\) | 0.305403 | 0.0130462 | ||||||||
\(549\) | −96.0002 | −4.09719 | ||||||||
\(550\) | −3.65066 | −0.155665 | ||||||||
\(551\) | 16.4408 | 0.700401 | ||||||||
\(552\) | −25.3149 | −1.07747 | ||||||||
\(553\) | −40.5726 | −1.72532 | ||||||||
\(554\) | −28.2150 | −1.19874 | ||||||||
\(555\) | −24.9313 | −1.05828 | ||||||||
\(556\) | 4.21702 | 0.178841 | ||||||||
\(557\) | 19.3194 | 0.818591 | 0.409296 | − | 0.912402i | \(-0.365774\pi\) | ||||
0.409296 | + | 0.912402i | \(0.365774\pi\) | |||||||
\(558\) | −26.8413 | −1.13628 | ||||||||
\(559\) | −32.8987 | −1.39146 | ||||||||
\(560\) | −3.45446 | −0.145977 | ||||||||
\(561\) | −54.2550 | −2.29065 | ||||||||
\(562\) | 11.5833 | 0.488610 | ||||||||
\(563\) | 31.5587 | 1.33004 | 0.665020 | − | 0.746825i | \(-0.268423\pi\) | ||||
0.665020 | + | 0.746825i | \(0.268423\pi\) | |||||||
\(564\) | 13.4703 | 0.567202 | ||||||||
\(565\) | 9.31138 | 0.391733 | ||||||||
\(566\) | 11.3650 | 0.477706 | ||||||||
\(567\) | 115.061 | 4.83210 | ||||||||
\(568\) | −13.5208 | −0.567320 | ||||||||
\(569\) | 5.72419 | 0.239970 | 0.119985 | − | 0.992776i | \(-0.461715\pi\) | ||||
0.119985 | + | 0.992776i | \(0.461715\pi\) | |||||||
\(570\) | 20.9362 | 0.876921 | ||||||||
\(571\) | 33.3106 | 1.39400 | 0.697002 | − | 0.717069i | \(-0.254517\pi\) | ||||
0.697002 | + | 0.717069i | \(0.254517\pi\) | |||||||
\(572\) | 12.7638 | 0.533681 | ||||||||
\(573\) | 49.7756 | 2.07941 | ||||||||
\(574\) | −15.9937 | −0.667564 | ||||||||
\(575\) | −7.57267 | −0.315802 | ||||||||
\(576\) | 8.17517 | 0.340632 | ||||||||
\(577\) | −28.0651 | −1.16836 | −0.584182 | − | 0.811623i | \(-0.698584\pi\) | ||||
−0.584182 | + | 0.811623i | \(0.698584\pi\) | |||||||
\(578\) | −2.76436 | −0.114982 | ||||||||
\(579\) | −34.5669 | −1.43655 | ||||||||
\(580\) | 2.62514 | 0.109003 | ||||||||
\(581\) | −32.4355 | −1.34565 | ||||||||
\(582\) | 12.5847 | 0.521652 | ||||||||
\(583\) | 14.8593 | 0.615408 | ||||||||
\(584\) | 12.2418 | 0.506568 | ||||||||
\(585\) | −28.5828 | −1.18175 | ||||||||
\(586\) | −2.36108 | −0.0975352 | ||||||||
\(587\) | 7.95389 | 0.328292 | 0.164146 | − | 0.986436i | \(-0.447513\pi\) | ||||
0.164146 | + | 0.986436i | \(0.447513\pi\) | |||||||
\(588\) | −16.4916 | −0.680101 | ||||||||
\(589\) | −20.5625 | −0.847265 | ||||||||
\(590\) | 4.53317 | 0.186628 | ||||||||
\(591\) | −89.3468 | −3.67524 | ||||||||
\(592\) | −7.45793 | −0.306519 | ||||||||
\(593\) | 19.8773 | 0.816264 | 0.408132 | − | 0.912923i | \(-0.366180\pi\) | ||||
0.408132 | + | 0.912923i | \(0.366180\pi\) | |||||||
\(594\) | 63.1573 | 2.59138 | ||||||||
\(595\) | −15.3575 | −0.629597 | ||||||||
\(596\) | −10.9607 | −0.448968 | ||||||||
\(597\) | 2.07386 | 0.0848775 | ||||||||
\(598\) | 26.4763 | 1.08270 | ||||||||
\(599\) | −0.352831 | −0.0144163 | −0.00720814 | − | 0.999974i | \(-0.502294\pi\) | ||||
−0.00720814 | + | 0.999974i | \(0.502294\pi\) | |||||||
\(600\) | 3.34293 | 0.136474 | ||||||||
\(601\) | −6.66728 | −0.271964 | −0.135982 | − | 0.990711i | \(-0.543419\pi\) | ||||
−0.135982 | + | 0.990711i | \(0.543419\pi\) | |||||||
\(602\) | 32.5050 | 1.32480 | ||||||||
\(603\) | −20.8951 | −0.850914 | ||||||||
\(604\) | −5.55463 | −0.226015 | ||||||||
\(605\) | −2.32733 | −0.0946194 | ||||||||
\(606\) | 32.2037 | 1.30818 | ||||||||
\(607\) | −32.8036 | −1.33146 | −0.665729 | − | 0.746194i | \(-0.731879\pi\) | ||||
−0.665729 | + | 0.746194i | \(0.731879\pi\) | |||||||
\(608\) | 6.26283 | 0.253991 | ||||||||
\(609\) | 30.3151 | 1.22843 | ||||||||
\(610\) | −11.7429 | −0.475456 | ||||||||
\(611\) | −14.0883 | −0.569951 | ||||||||
\(612\) | 36.3445 | 1.46914 | ||||||||
\(613\) | 16.3431 | 0.660090 | 0.330045 | − | 0.943965i | \(-0.392936\pi\) | ||||
0.330045 | + | 0.943965i | \(0.392936\pi\) | |||||||
\(614\) | 6.48616 | 0.261760 | ||||||||
\(615\) | 15.4773 | 0.624106 | ||||||||
\(616\) | −12.6111 | −0.508114 | ||||||||
\(617\) | 28.0275 | 1.12834 | 0.564172 | − | 0.825657i | \(-0.309195\pi\) | ||||
0.564172 | + | 0.825657i | \(0.309195\pi\) | |||||||
\(618\) | −44.4782 | −1.78917 | ||||||||
\(619\) | 20.9690 | 0.842815 | 0.421407 | − | 0.906871i | \(-0.361536\pi\) | ||||
0.421407 | + | 0.906871i | \(0.361536\pi\) | |||||||
\(620\) | −3.28327 | −0.131859 | ||||||||
\(621\) | 131.009 | 5.25721 | ||||||||
\(622\) | 25.2762 | 1.01348 | ||||||||
\(623\) | 3.51158 | 0.140688 | ||||||||
\(624\) | −11.6879 | −0.467889 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −7.61926 | −0.304527 | ||||||||
\(627\) | 76.4309 | 3.05236 | ||||||||
\(628\) | −10.1392 | −0.404597 | ||||||||
\(629\) | −33.1558 | −1.32201 | ||||||||
\(630\) | 28.2408 | 1.12514 | ||||||||
\(631\) | −34.5444 | −1.37519 | −0.687594 | − | 0.726095i | \(-0.741333\pi\) | ||||
−0.687594 | + | 0.726095i | \(0.741333\pi\) | |||||||
\(632\) | 11.7450 | 0.467191 | ||||||||
\(633\) | 16.0009 | 0.635979 | ||||||||
\(634\) | −16.5917 | −0.658941 | ||||||||
\(635\) | 7.95062 | 0.315511 | ||||||||
\(636\) | −13.6067 | −0.539541 | ||||||||
\(637\) | 17.2482 | 0.683397 | ||||||||
\(638\) | 9.58348 | 0.379414 | ||||||||
\(639\) | 110.535 | 4.37269 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 37.2692 | 1.47205 | 0.736023 | − | 0.676956i | \(-0.236701\pi\) | ||||
0.736023 | + | 0.676956i | \(0.236701\pi\) | |||||||
\(642\) | −28.9457 | −1.14240 | ||||||||
\(643\) | 16.9416 | 0.668112 | 0.334056 | − | 0.942553i | \(-0.391583\pi\) | ||||
0.334056 | + | 0.942553i | \(0.391583\pi\) | |||||||
\(644\) | −26.1595 | −1.03083 | ||||||||
\(645\) | −31.4556 | −1.23856 | ||||||||
\(646\) | 27.8427 | 1.09546 | ||||||||
\(647\) | −26.5263 | −1.04286 | −0.521428 | − | 0.853296i | \(-0.674600\pi\) | ||||
−0.521428 | + | 0.853296i | \(0.674600\pi\) | |||||||
\(648\) | −33.3079 | −1.30846 | ||||||||
\(649\) | 16.5491 | 0.649608 | ||||||||
\(650\) | −3.49629 | −0.137136 | ||||||||
\(651\) | −37.9152 | −1.48601 | ||||||||
\(652\) | 11.3585 | 0.444834 | ||||||||
\(653\) | −29.6548 | −1.16048 | −0.580242 | − | 0.814444i | \(-0.697042\pi\) | ||||
−0.580242 | + | 0.814444i | \(0.697042\pi\) | |||||||
\(654\) | −32.2467 | −1.26095 | ||||||||
\(655\) | −12.6694 | −0.495036 | ||||||||
\(656\) | 4.62987 | 0.180766 | ||||||||
\(657\) | −100.079 | −3.90444 | ||||||||
\(658\) | 13.9197 | 0.542646 | ||||||||
\(659\) | −43.3932 | −1.69036 | −0.845180 | − | 0.534481i | \(-0.820507\pi\) | ||||
−0.845180 | + | 0.534481i | \(0.820507\pi\) | |||||||
\(660\) | 12.2039 | 0.475036 | ||||||||
\(661\) | −8.56314 | −0.333068 | −0.166534 | − | 0.986036i | \(-0.553257\pi\) | ||||
−0.166534 | + | 0.986036i | \(0.553257\pi\) | |||||||
\(662\) | 16.0676 | 0.624486 | ||||||||
\(663\) | −51.9609 | −2.01799 | ||||||||
\(664\) | 9.38947 | 0.364382 | ||||||||
\(665\) | 21.6347 | 0.838957 | ||||||||
\(666\) | 60.9699 | 2.36254 | ||||||||
\(667\) | 19.8793 | 0.769729 | ||||||||
\(668\) | 10.1324 | 0.392036 | ||||||||
\(669\) | 93.5706 | 3.61765 | ||||||||
\(670\) | −2.55592 | −0.0987438 | ||||||||
\(671\) | −42.8693 | −1.65495 | ||||||||
\(672\) | 11.5480 | 0.445474 | ||||||||
\(673\) | 27.5521 | 1.06205 | 0.531027 | − | 0.847355i | \(-0.321806\pi\) | ||||
0.531027 | + | 0.847355i | \(0.321806\pi\) | |||||||
\(674\) | 32.4640 | 1.25047 | ||||||||
\(675\) | −17.3002 | −0.665886 | ||||||||
\(676\) | −0.775935 | −0.0298437 | ||||||||
\(677\) | 11.9822 | 0.460515 | 0.230258 | − | 0.973130i | \(-0.426043\pi\) | ||||
0.230258 | + | 0.973130i | \(0.426043\pi\) | |||||||
\(678\) | −31.1273 | −1.19544 | ||||||||
\(679\) | 13.0045 | 0.499068 | ||||||||
\(680\) | 4.44571 | 0.170485 | ||||||||
\(681\) | 14.8325 | 0.568383 | ||||||||
\(682\) | −11.9861 | −0.458971 | ||||||||
\(683\) | −36.5333 | −1.39791 | −0.698954 | − | 0.715166i | \(-0.746351\pi\) | ||||
−0.698954 | + | 0.715166i | \(0.746351\pi\) | |||||||
\(684\) | −51.1997 | −1.95767 | ||||||||
\(685\) | −0.305403 | −0.0116688 | ||||||||
\(686\) | 7.13943 | 0.272585 | ||||||||
\(687\) | −92.1449 | −3.51555 | ||||||||
\(688\) | −9.40958 | −0.358737 | ||||||||
\(689\) | 14.2309 | 0.542155 | ||||||||
\(690\) | 25.3149 | 0.963722 | ||||||||
\(691\) | 29.2002 | 1.11083 | 0.555413 | − | 0.831575i | \(-0.312560\pi\) | ||||
0.555413 | + | 0.831575i | \(0.312560\pi\) | |||||||
\(692\) | −17.6077 | −0.669344 | ||||||||
\(693\) | 103.098 | 3.91635 | ||||||||
\(694\) | 25.8709 | 0.982044 | ||||||||
\(695\) | −4.21702 | −0.159961 | ||||||||
\(696\) | −8.77564 | −0.332640 | ||||||||
\(697\) | 20.5831 | 0.779640 | ||||||||
\(698\) | −16.1470 | −0.611174 | ||||||||
\(699\) | 40.1106 | 1.51712 | ||||||||
\(700\) | 3.45446 | 0.130566 | ||||||||
\(701\) | 12.8440 | 0.485112 | 0.242556 | − | 0.970137i | \(-0.422014\pi\) | ||||
0.242556 | + | 0.970137i | \(0.422014\pi\) | |||||||
\(702\) | 60.4867 | 2.28292 | ||||||||
\(703\) | 46.7078 | 1.76162 | ||||||||
\(704\) | 3.65066 | 0.137589 | ||||||||
\(705\) | −13.4703 | −0.507321 | ||||||||
\(706\) | −26.9240 | −1.01330 | ||||||||
\(707\) | 33.2781 | 1.25155 | ||||||||
\(708\) | −15.1541 | −0.569525 | ||||||||
\(709\) | −36.5289 | −1.37187 | −0.685936 | − | 0.727662i | \(-0.740607\pi\) | ||||
−0.685936 | + | 0.727662i | \(0.740607\pi\) | |||||||
\(710\) | 13.5208 | 0.507426 | ||||||||
\(711\) | −96.0174 | −3.60093 | ||||||||
\(712\) | −1.01654 | −0.0380963 | ||||||||
\(713\) | −24.8631 | −0.931131 | ||||||||
\(714\) | 51.3391 | 1.92132 | ||||||||
\(715\) | −12.7638 | −0.477338 | ||||||||
\(716\) | −24.2483 | −0.906203 | ||||||||
\(717\) | −69.2937 | −2.58782 | ||||||||
\(718\) | −9.66274 | −0.360610 | ||||||||
\(719\) | 29.5026 | 1.10026 | 0.550130 | − | 0.835079i | \(-0.314578\pi\) | ||||
0.550130 | + | 0.835079i | \(0.314578\pi\) | |||||||
\(720\) | −8.17517 | −0.304671 | ||||||||
\(721\) | −45.9621 | −1.71172 | ||||||||
\(722\) | −20.2230 | −0.752623 | ||||||||
\(723\) | −71.2955 | −2.65151 | ||||||||
\(724\) | −5.16159 | −0.191829 | ||||||||
\(725\) | −2.62514 | −0.0974951 | ||||||||
\(726\) | 7.78009 | 0.288746 | ||||||||
\(727\) | 35.2323 | 1.30670 | 0.653348 | − | 0.757058i | \(-0.273364\pi\) | ||||
0.653348 | + | 0.757058i | \(0.273364\pi\) | |||||||
\(728\) | −12.0778 | −0.447633 | ||||||||
\(729\) | 98.7977 | 3.65918 | ||||||||
\(730\) | −12.2418 | −0.453088 | ||||||||
\(731\) | −41.8323 | −1.54722 | ||||||||
\(732\) | 39.2557 | 1.45093 | ||||||||
\(733\) | −43.3304 | −1.60045 | −0.800223 | − | 0.599703i | \(-0.795285\pi\) | ||||
−0.800223 | + | 0.599703i | \(0.795285\pi\) | |||||||
\(734\) | −23.3113 | −0.860434 | ||||||||
\(735\) | 16.4916 | 0.608301 | ||||||||
\(736\) | 7.57267 | 0.279132 | ||||||||
\(737\) | −9.33080 | −0.343704 | ||||||||
\(738\) | −37.8500 | −1.39328 | ||||||||
\(739\) | 21.8997 | 0.805592 | 0.402796 | − | 0.915290i | \(-0.368038\pi\) | ||||
0.402796 | + | 0.915290i | \(0.368038\pi\) | |||||||
\(740\) | 7.45793 | 0.274159 | ||||||||
\(741\) | 73.1991 | 2.68903 | ||||||||
\(742\) | −14.0606 | −0.516183 | ||||||||
\(743\) | 29.8275 | 1.09426 | 0.547132 | − | 0.837047i | \(-0.315720\pi\) | ||||
0.547132 | + | 0.837047i | \(0.315720\pi\) | |||||||
\(744\) | 10.9757 | 0.402390 | ||||||||
\(745\) | 10.9607 | 0.401569 | ||||||||
\(746\) | −18.7188 | −0.685344 | ||||||||
\(747\) | −76.7605 | −2.80852 | ||||||||
\(748\) | 16.2298 | 0.593420 | ||||||||
\(749\) | −29.9114 | −1.09294 | ||||||||
\(750\) | −3.34293 | −0.122066 | ||||||||
\(751\) | −41.1292 | −1.50083 | −0.750413 | − | 0.660970i | \(-0.770145\pi\) | ||||
−0.750413 | + | 0.660970i | \(0.770145\pi\) | |||||||
\(752\) | −4.02949 | −0.146940 | ||||||||
\(753\) | −43.5681 | −1.58771 | ||||||||
\(754\) | 9.17824 | 0.334252 | ||||||||
\(755\) | 5.55463 | 0.202154 | ||||||||
\(756\) | −59.7629 | −2.17356 | ||||||||
\(757\) | 6.82806 | 0.248170 | 0.124085 | − | 0.992272i | \(-0.460400\pi\) | ||||
0.124085 | + | 0.992272i | \(0.460400\pi\) | |||||||
\(758\) | 28.5930 | 1.03854 | ||||||||
\(759\) | 92.4162 | 3.35449 | ||||||||
\(760\) | −6.26283 | −0.227177 | ||||||||
\(761\) | −54.4981 | −1.97555 | −0.987777 | − | 0.155872i | \(-0.950181\pi\) | ||||
−0.987777 | + | 0.155872i | \(0.950181\pi\) | |||||||
\(762\) | −26.5784 | −0.962832 | ||||||||
\(763\) | −33.3225 | −1.20636 | ||||||||
\(764\) | −14.8898 | −0.538695 | ||||||||
\(765\) | −36.3445 | −1.31404 | ||||||||
\(766\) | 4.40398 | 0.159122 | ||||||||
\(767\) | 15.8493 | 0.572285 | ||||||||
\(768\) | −3.34293 | −0.120628 | ||||||||
\(769\) | 11.2232 | 0.404719 | 0.202359 | − | 0.979311i | \(-0.435139\pi\) | ||||
0.202359 | + | 0.979311i | \(0.435139\pi\) | |||||||
\(770\) | 12.6111 | 0.454471 | ||||||||
\(771\) | −30.2491 | −1.08940 | ||||||||
\(772\) | 10.3403 | 0.372156 | ||||||||
\(773\) | 50.1349 | 1.80323 | 0.901613 | − | 0.432544i | \(-0.142384\pi\) | ||||
0.901613 | + | 0.432544i | \(0.142384\pi\) | |||||||
\(774\) | 76.9250 | 2.76501 | ||||||||
\(775\) | 3.28327 | 0.117938 | ||||||||
\(776\) | −3.76457 | −0.135140 | ||||||||
\(777\) | 86.1242 | 3.08969 | ||||||||
\(778\) | 24.5618 | 0.880584 | ||||||||
\(779\) | −28.9961 | −1.03889 | ||||||||
\(780\) | 11.6879 | 0.418492 | ||||||||
\(781\) | 49.3598 | 1.76623 | ||||||||
\(782\) | 33.6659 | 1.20389 | ||||||||
\(783\) | 45.4155 | 1.62302 | ||||||||
\(784\) | 4.93327 | 0.176188 | ||||||||
\(785\) | 10.1392 | 0.361882 | ||||||||
\(786\) | 42.3530 | 1.51068 | ||||||||
\(787\) | −26.6032 | −0.948303 | −0.474152 | − | 0.880443i | \(-0.657245\pi\) | ||||
−0.474152 | + | 0.880443i | \(0.657245\pi\) | |||||||
\(788\) | 26.7271 | 0.952114 | ||||||||
\(789\) | −62.9011 | −2.23934 | ||||||||
\(790\) | −11.7450 | −0.417868 | ||||||||
\(791\) | −32.1658 | −1.14368 | ||||||||
\(792\) | −29.8448 | −1.06049 | ||||||||
\(793\) | −41.0566 | −1.45796 | ||||||||
\(794\) | −15.5751 | −0.552739 | ||||||||
\(795\) | 13.6067 | 0.482580 | ||||||||
\(796\) | −0.620373 | −0.0219885 | ||||||||
\(797\) | 36.3267 | 1.28676 | 0.643379 | − | 0.765548i | \(-0.277532\pi\) | ||||
0.643379 | + | 0.765548i | \(0.277532\pi\) | |||||||
\(798\) | −72.3232 | −2.56021 | ||||||||
\(799\) | −17.9140 | −0.633750 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 8.31036 | 0.293632 | ||||||||
\(802\) | 1.00000 | 0.0353112 | ||||||||
\(803\) | −44.6905 | −1.57709 | ||||||||
\(804\) | 8.54426 | 0.301333 | ||||||||
\(805\) | 26.1595 | 0.922000 | ||||||||
\(806\) | −11.4793 | −0.404340 | ||||||||
\(807\) | 75.5251 | 2.65861 | ||||||||
\(808\) | −9.63337 | −0.338901 | ||||||||
\(809\) | −44.2243 | −1.55484 | −0.777421 | − | 0.628980i | \(-0.783473\pi\) | ||||
−0.777421 | + | 0.628980i | \(0.783473\pi\) | |||||||
\(810\) | 33.3079 | 1.17032 | ||||||||
\(811\) | 3.63339 | 0.127585 | 0.0637927 | − | 0.997963i | \(-0.479680\pi\) | ||||
0.0637927 | + | 0.997963i | \(0.479680\pi\) | |||||||
\(812\) | −9.06842 | −0.318239 | ||||||||
\(813\) | −74.4596 | −2.61141 | ||||||||
\(814\) | 27.2264 | 0.954284 | ||||||||
\(815\) | −11.3585 | −0.397872 | ||||||||
\(816\) | −14.8617 | −0.520264 | ||||||||
\(817\) | 58.9306 | 2.06172 | ||||||||
\(818\) | 22.2350 | 0.777427 | ||||||||
\(819\) | 98.7380 | 3.45019 | ||||||||
\(820\) | −4.62987 | −0.161682 | ||||||||
\(821\) | 20.5307 | 0.716528 | 0.358264 | − | 0.933620i | \(-0.383369\pi\) | ||||
0.358264 | + | 0.933620i | \(0.383369\pi\) | |||||||
\(822\) | 1.02094 | 0.0356094 | ||||||||
\(823\) | 18.6824 | 0.651227 | 0.325614 | − | 0.945503i | \(-0.394429\pi\) | ||||
0.325614 | + | 0.945503i | \(0.394429\pi\) | |||||||
\(824\) | 13.3052 | 0.463507 | ||||||||
\(825\) | −12.2039 | −0.424885 | ||||||||
\(826\) | −15.6597 | −0.544869 | ||||||||
\(827\) | 43.2438 | 1.50373 | 0.751867 | − | 0.659315i | \(-0.229153\pi\) | ||||
0.751867 | + | 0.659315i | \(0.229153\pi\) | |||||||
\(828\) | −61.9079 | −2.15145 | ||||||||
\(829\) | 7.38348 | 0.256439 | 0.128219 | − | 0.991746i | \(-0.459074\pi\) | ||||
0.128219 | + | 0.991746i | \(0.459074\pi\) | |||||||
\(830\) | −9.38947 | −0.325913 | ||||||||
\(831\) | −94.3207 | −3.27195 | ||||||||
\(832\) | 3.49629 | 0.121212 | ||||||||
\(833\) | 21.9319 | 0.759895 | ||||||||
\(834\) | 14.0972 | 0.488146 | ||||||||
\(835\) | −10.1324 | −0.350647 | ||||||||
\(836\) | −22.8635 | −0.790750 | ||||||||
\(837\) | −56.8013 | −1.96334 | ||||||||
\(838\) | −21.5003 | −0.742716 | ||||||||
\(839\) | 33.9771 | 1.17302 | 0.586509 | − | 0.809942i | \(-0.300502\pi\) | ||||
0.586509 | + | 0.809942i | \(0.300502\pi\) | |||||||
\(840\) | −11.5480 | −0.398444 | ||||||||
\(841\) | −22.1087 | −0.762368 | ||||||||
\(842\) | 35.3921 | 1.21969 | ||||||||
\(843\) | 38.7220 | 1.33366 | ||||||||
\(844\) | −4.78650 | −0.164758 | ||||||||
\(845\) | 0.775935 | 0.0266930 | ||||||||
\(846\) | 32.9418 | 1.13256 | ||||||||
\(847\) | 8.03966 | 0.276246 | ||||||||
\(848\) | 4.07029 | 0.139774 | ||||||||
\(849\) | 37.9924 | 1.30389 | ||||||||
\(850\) | −4.44571 | −0.152487 | ||||||||
\(851\) | 56.4765 | 1.93599 | ||||||||
\(852\) | −45.1990 | −1.54849 | ||||||||
\(853\) | 39.3182 | 1.34623 | 0.673114 | − | 0.739539i | \(-0.264956\pi\) | ||||
0.673114 | + | 0.739539i | \(0.264956\pi\) | |||||||
\(854\) | 40.5653 | 1.38812 | ||||||||
\(855\) | 51.1997 | 1.75099 | ||||||||
\(856\) | 8.65878 | 0.295951 | ||||||||
\(857\) | −55.1736 | −1.88469 | −0.942347 | − | 0.334636i | \(-0.891387\pi\) | ||||
−0.942347 | + | 0.334636i | \(0.891387\pi\) | |||||||
\(858\) | 42.6684 | 1.45668 | ||||||||
\(859\) | 23.4800 | 0.801129 | 0.400564 | − | 0.916269i | \(-0.368814\pi\) | ||||
0.400564 | + | 0.916269i | \(0.368814\pi\) | |||||||
\(860\) | 9.40958 | 0.320864 | ||||||||
\(861\) | −53.4658 | −1.82211 | ||||||||
\(862\) | −17.4615 | −0.594740 | ||||||||
\(863\) | 35.4240 | 1.20585 | 0.602923 | − | 0.797799i | \(-0.294003\pi\) | ||||
0.602923 | + | 0.797799i | \(0.294003\pi\) | |||||||
\(864\) | 17.3002 | 0.588566 | ||||||||
\(865\) | 17.6077 | 0.598679 | ||||||||
\(866\) | −25.5592 | −0.868538 | ||||||||
\(867\) | −9.24107 | −0.313843 | ||||||||
\(868\) | 11.3419 | 0.384969 | ||||||||
\(869\) | −42.8770 | −1.45450 | ||||||||
\(870\) | 8.77564 | 0.297522 | ||||||||
\(871\) | −8.93624 | −0.302793 | ||||||||
\(872\) | 9.64624 | 0.326663 | ||||||||
\(873\) | 30.7760 | 1.04161 | ||||||||
\(874\) | −47.4264 | −1.60422 | ||||||||
\(875\) | −3.45446 | −0.116782 | ||||||||
\(876\) | 40.9233 | 1.38267 | ||||||||
\(877\) | −20.9567 | −0.707656 | −0.353828 | − | 0.935310i | \(-0.615120\pi\) | ||||
−0.353828 | + | 0.935310i | \(0.615120\pi\) | |||||||
\(878\) | −0.954774 | −0.0322221 | ||||||||
\(879\) | −7.89291 | −0.266221 | ||||||||
\(880\) | −3.65066 | −0.123064 | ||||||||
\(881\) | −16.7761 | −0.565200 | −0.282600 | − | 0.959238i | \(-0.591197\pi\) | ||||
−0.282600 | + | 0.959238i | \(0.591197\pi\) | |||||||
\(882\) | −40.3303 | −1.35799 | ||||||||
\(883\) | 20.5408 | 0.691253 | 0.345626 | − | 0.938372i | \(-0.387666\pi\) | ||||
0.345626 | + | 0.938372i | \(0.387666\pi\) | |||||||
\(884\) | 15.5435 | 0.522785 | ||||||||
\(885\) | 15.1541 | 0.509399 | ||||||||
\(886\) | 22.2117 | 0.746216 | ||||||||
\(887\) | −24.4967 | −0.822517 | −0.411259 | − | 0.911519i | \(-0.634911\pi\) | ||||
−0.411259 | + | 0.911519i | \(0.634911\pi\) | |||||||
\(888\) | −24.9313 | −0.836641 | ||||||||
\(889\) | −27.4651 | −0.921149 | ||||||||
\(890\) | 1.01654 | 0.0340744 | ||||||||
\(891\) | 121.596 | 4.07362 | ||||||||
\(892\) | −27.9906 | −0.937195 | ||||||||
\(893\) | 25.2360 | 0.844491 | ||||||||
\(894\) | −36.6409 | −1.22545 | ||||||||
\(895\) | 24.2483 | 0.810533 | ||||||||
\(896\) | −3.45446 | −0.115405 | ||||||||
\(897\) | 88.5083 | 2.95521 | ||||||||
\(898\) | 10.9315 | 0.364790 | ||||||||
\(899\) | −8.61902 | −0.287460 | ||||||||
\(900\) | 8.17517 | 0.272506 | ||||||||
\(901\) | 18.0953 | 0.602843 | ||||||||
\(902\) | −16.9021 | −0.562778 | ||||||||
\(903\) | 108.662 | 3.61604 | ||||||||
\(904\) | 9.31138 | 0.309692 | ||||||||
\(905\) | 5.16159 | 0.171577 | ||||||||
\(906\) | −18.5687 | −0.616905 | ||||||||
\(907\) | −44.9621 | −1.49294 | −0.746471 | − | 0.665418i | \(-0.768254\pi\) | ||||
−0.746471 | + | 0.665418i | \(0.768254\pi\) | |||||||
\(908\) | −4.43698 | −0.147246 | ||||||||
\(909\) | 78.7545 | 2.61212 | ||||||||
\(910\) | 12.0778 | 0.400375 | ||||||||
\(911\) | −37.0311 | −1.22689 | −0.613447 | − | 0.789736i | \(-0.710218\pi\) | ||||
−0.613447 | + | 0.789736i | \(0.710218\pi\) | |||||||
\(912\) | 20.9362 | 0.693267 | ||||||||
\(913\) | −34.2778 | −1.13443 | ||||||||
\(914\) | −18.8479 | −0.623433 | ||||||||
\(915\) | −39.2557 | −1.29775 | ||||||||
\(916\) | 27.5641 | 0.910744 | ||||||||
\(917\) | 43.7660 | 1.44528 | ||||||||
\(918\) | 76.9119 | 2.53847 | ||||||||
\(919\) | −0.942269 | −0.0310826 | −0.0155413 | − | 0.999879i | \(-0.504947\pi\) | ||||
−0.0155413 | + | 0.999879i | \(0.504947\pi\) | |||||||
\(920\) | −7.57267 | −0.249664 | ||||||||
\(921\) | 21.6828 | 0.714472 | ||||||||
\(922\) | 13.9256 | 0.458615 | ||||||||
\(923\) | 47.2726 | 1.55600 | ||||||||
\(924\) | −42.1578 | −1.38689 | ||||||||
\(925\) | −7.45793 | −0.245215 | ||||||||
\(926\) | 7.79458 | 0.256146 | ||||||||
\(927\) | −108.772 | −3.57254 | ||||||||
\(928\) | 2.62514 | 0.0861743 | ||||||||
\(929\) | 28.8335 | 0.945996 | 0.472998 | − | 0.881063i | \(-0.343172\pi\) | ||||
0.472998 | + | 0.881063i | \(0.343172\pi\) | |||||||
\(930\) | −10.9757 | −0.359908 | ||||||||
\(931\) | −30.8962 | −1.01258 | ||||||||
\(932\) | −11.9986 | −0.393029 | ||||||||
\(933\) | 84.4965 | 2.76629 | ||||||||
\(934\) | 30.0377 | 0.982864 | ||||||||
\(935\) | −16.2298 | −0.530771 | ||||||||
\(936\) | −28.5828 | −0.934258 | ||||||||
\(937\) | −37.0807 | −1.21137 | −0.605686 | − | 0.795704i | \(-0.707101\pi\) | ||||
−0.605686 | + | 0.795704i | \(0.707101\pi\) | |||||||
\(938\) | 8.82931 | 0.288287 | ||||||||
\(939\) | −25.4707 | −0.831204 | ||||||||
\(940\) | 4.02949 | 0.131427 | ||||||||
\(941\) | 19.3937 | 0.632217 | 0.316108 | − | 0.948723i | \(-0.397624\pi\) | ||||
0.316108 | + | 0.948723i | \(0.397624\pi\) | |||||||
\(942\) | −33.8945 | −1.10434 | ||||||||
\(943\) | −35.0605 | −1.14173 | ||||||||
\(944\) | 4.53317 | 0.147542 | ||||||||
\(945\) | 59.7629 | 1.94409 | ||||||||
\(946\) | 34.3512 | 1.11685 | ||||||||
\(947\) | −59.4392 | −1.93151 | −0.965757 | − | 0.259449i | \(-0.916459\pi\) | ||||
−0.965757 | + | 0.259449i | \(0.916459\pi\) | |||||||
\(948\) | 39.2627 | 1.27519 | ||||||||
\(949\) | −42.8008 | −1.38937 | ||||||||
\(950\) | 6.26283 | 0.203193 | ||||||||
\(951\) | −55.4649 | −1.79857 | ||||||||
\(952\) | −15.3575 | −0.497740 | ||||||||
\(953\) | −32.8523 | −1.06419 | −0.532095 | − | 0.846685i | \(-0.678595\pi\) | ||||
−0.532095 | + | 0.846685i | \(0.678595\pi\) | |||||||
\(954\) | −33.2753 | −1.07733 | ||||||||
\(955\) | 14.8898 | 0.481824 | ||||||||
\(956\) | 20.7284 | 0.670406 | ||||||||
\(957\) | 32.0369 | 1.03561 | ||||||||
\(958\) | 12.4327 | 0.401681 | ||||||||
\(959\) | 1.05500 | 0.0340678 | ||||||||
\(960\) | 3.34293 | 0.107893 | ||||||||
\(961\) | −20.2202 | −0.652263 | ||||||||
\(962\) | 26.0751 | 0.840696 | ||||||||
\(963\) | −70.7870 | −2.28108 | ||||||||
\(964\) | 21.3272 | 0.686904 | ||||||||
\(965\) | −10.3403 | −0.332866 | ||||||||
\(966\) | −87.4493 | −2.81363 | ||||||||
\(967\) | −3.24879 | −0.104474 | −0.0522370 | − | 0.998635i | \(-0.516635\pi\) | ||||
−0.0522370 | + | 0.998635i | \(0.516635\pi\) | |||||||
\(968\) | −2.32733 | −0.0748032 | ||||||||
\(969\) | 93.0763 | 2.99004 | ||||||||
\(970\) | 3.76457 | 0.120873 | ||||||||
\(971\) | −13.5736 | −0.435598 | −0.217799 | − | 0.975994i | \(-0.569888\pi\) | ||||
−0.217799 | + | 0.975994i | \(0.569888\pi\) | |||||||
\(972\) | −59.4453 | −1.90671 | ||||||||
\(973\) | 14.5675 | 0.467013 | ||||||||
\(974\) | 15.1280 | 0.484733 | ||||||||
\(975\) | −11.6879 | −0.374311 | ||||||||
\(976\) | −11.7429 | −0.375881 | ||||||||
\(977\) | −21.3061 | −0.681644 | −0.340822 | − | 0.940128i | \(-0.610705\pi\) | ||||
−0.340822 | + | 0.940128i | \(0.610705\pi\) | |||||||
\(978\) | 37.9707 | 1.21417 | ||||||||
\(979\) | 3.71103 | 0.118605 | ||||||||
\(980\) | −4.93327 | −0.157588 | ||||||||
\(981\) | −78.8597 | −2.51780 | ||||||||
\(982\) | 28.3599 | 0.905001 | ||||||||
\(983\) | 60.6251 | 1.93364 | 0.966821 | − | 0.255456i | \(-0.0822257\pi\) | ||||
0.966821 | + | 0.255456i | \(0.0822257\pi\) | |||||||
\(984\) | 15.4773 | 0.493399 | ||||||||
\(985\) | −26.7271 | −0.851596 | ||||||||
\(986\) | 11.6706 | 0.371668 | ||||||||
\(987\) | 46.5326 | 1.48115 | ||||||||
\(988\) | −21.8967 | −0.696626 | ||||||||
\(989\) | 71.2557 | 2.26580 | ||||||||
\(990\) | 29.8448 | 0.948530 | ||||||||
\(991\) | 17.5578 | 0.557741 | 0.278870 | − | 0.960329i | \(-0.410040\pi\) | ||||
0.278870 | + | 0.960329i | \(0.410040\pi\) | |||||||
\(992\) | −3.28327 | −0.104244 | ||||||||
\(993\) | 53.7130 | 1.70453 | ||||||||
\(994\) | −46.7070 | −1.48146 | ||||||||
\(995\) | 0.620373 | 0.0196671 | ||||||||
\(996\) | 31.3883 | 0.994577 | ||||||||
\(997\) | 26.6488 | 0.843976 | 0.421988 | − | 0.906602i | \(-0.361333\pi\) | ||||
0.421988 | + | 0.906602i | \(0.361333\pi\) | |||||||
\(998\) | −12.2680 | −0.388336 | ||||||||
\(999\) | 129.024 | 4.08214 |
(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 | 4010.2.a.k.1.1 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.k.1.1 | ✓ | 15 | 1.1 | even | 1 | trivial |