Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3381,2,Mod(1,3381)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3381.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3381 = 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3381.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: | \(26.9974209234\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 13x^{8} + 41x^{7} + 47x^{6} - 165x^{5} - 45x^{4} + 207x^{3} + 12x^{2} - 76x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 483) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.864859\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3381.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.864859 | 0.611548 | 0.305774 | − | 0.952104i | \(-0.401085\pi\) | ||||
0.305774 | + | 0.952104i | \(0.401085\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.25202 | −0.626009 | ||||||||
\(5\) | −2.49557 | −1.11605 | −0.558027 | − | 0.829823i | \(-0.688441\pi\) | ||||
−0.558027 | + | 0.829823i | \(0.688441\pi\) | |||||||
\(6\) | −0.864859 | −0.353077 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.81254 | −0.994383 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.15832 | −0.682521 | ||||||||
\(11\) | −3.98310 | −1.20095 | −0.600475 | − | 0.799644i | \(-0.705022\pi\) | ||||
−0.600475 | + | 0.799644i | \(0.705022\pi\) | |||||||
\(12\) | 1.25202 | 0.361426 | ||||||||
\(13\) | 2.80699 | 0.778518 | 0.389259 | − | 0.921128i | \(-0.372731\pi\) | ||||
0.389259 | + | 0.921128i | \(0.372731\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.49557 | 0.644354 | ||||||||
\(16\) | 0.0715855 | 0.0178964 | ||||||||
\(17\) | −6.98770 | −1.69477 | −0.847383 | − | 0.530983i | \(-0.821823\pi\) | ||||
−0.847383 | + | 0.530983i | \(0.821823\pi\) | |||||||
\(18\) | 0.864859 | 0.203849 | ||||||||
\(19\) | −5.98058 | −1.37204 | −0.686019 | − | 0.727583i | \(-0.740643\pi\) | ||||
−0.686019 | + | 0.727583i | \(0.740643\pi\) | |||||||
\(20\) | 3.12450 | 0.698660 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.44482 | −0.734438 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 2.81254 | 0.574107 | ||||||||
\(25\) | 1.22789 | 0.245577 | ||||||||
\(26\) | 2.42765 | 0.476101 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.06198 | −0.754291 | −0.377145 | − | 0.926154i | \(-0.623094\pi\) | ||||
−0.377145 | + | 0.926154i | \(0.623094\pi\) | |||||||
\(30\) | 2.15832 | 0.394054 | ||||||||
\(31\) | −3.44346 | −0.618464 | −0.309232 | − | 0.950987i | \(-0.600072\pi\) | ||||
−0.309232 | + | 0.950987i | \(0.600072\pi\) | |||||||
\(32\) | 5.68699 | 1.00533 | ||||||||
\(33\) | 3.98310 | 0.693368 | ||||||||
\(34\) | −6.04338 | −1.03643 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.25202 | −0.208670 | ||||||||
\(37\) | −1.47693 | −0.242805 | −0.121402 | − | 0.992603i | \(-0.538739\pi\) | ||||
−0.121402 | + | 0.992603i | \(0.538739\pi\) | |||||||
\(38\) | −5.17236 | −0.839067 | ||||||||
\(39\) | −2.80699 | −0.449477 | ||||||||
\(40\) | 7.01890 | 1.10978 | ||||||||
\(41\) | −7.65339 | −1.19526 | −0.597630 | − | 0.801772i | \(-0.703891\pi\) | ||||
−0.597630 | + | 0.801772i | \(0.703891\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.07993 | 1.07968 | 0.539840 | − | 0.841768i | \(-0.318485\pi\) | ||||
0.539840 | + | 0.841768i | \(0.318485\pi\) | |||||||
\(44\) | 4.98691 | 0.751805 | ||||||||
\(45\) | −2.49557 | −0.372018 | ||||||||
\(46\) | 0.864859 | 0.127517 | ||||||||
\(47\) | −3.04531 | −0.444204 | −0.222102 | − | 0.975023i | \(-0.571292\pi\) | ||||
−0.222102 | + | 0.975023i | \(0.571292\pi\) | |||||||
\(48\) | −0.0715855 | −0.0103325 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.06195 | 0.150182 | ||||||||
\(51\) | 6.98770 | 0.978473 | ||||||||
\(52\) | −3.51440 | −0.487359 | ||||||||
\(53\) | 9.57104 | 1.31468 | 0.657342 | − | 0.753593i | \(-0.271681\pi\) | ||||
0.657342 | + | 0.753593i | \(0.271681\pi\) | |||||||
\(54\) | −0.864859 | −0.117692 | ||||||||
\(55\) | 9.94011 | 1.34032 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.98058 | 0.792147 | ||||||||
\(58\) | −3.51304 | −0.461285 | ||||||||
\(59\) | −8.30618 | −1.08137 | −0.540686 | − | 0.841224i | \(-0.681835\pi\) | ||||
−0.540686 | + | 0.841224i | \(0.681835\pi\) | |||||||
\(60\) | −3.12450 | −0.403372 | ||||||||
\(61\) | −3.71282 | −0.475377 | −0.237689 | − | 0.971341i | \(-0.576390\pi\) | ||||
−0.237689 | + | 0.971341i | \(0.576390\pi\) | |||||||
\(62\) | −2.97811 | −0.378220 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.77528 | 0.596909 | ||||||||
\(65\) | −7.00504 | −0.868868 | ||||||||
\(66\) | 3.44482 | 0.424028 | ||||||||
\(67\) | 4.46957 | 0.546045 | 0.273023 | − | 0.962008i | \(-0.411977\pi\) | ||||
0.273023 | + | 0.962008i | \(0.411977\pi\) | |||||||
\(68\) | 8.74872 | 1.06094 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.49028 | −1.12629 | −0.563144 | − | 0.826359i | \(-0.690408\pi\) | ||||
−0.563144 | + | 0.826359i | \(0.690408\pi\) | |||||||
\(72\) | −2.81254 | −0.331461 | ||||||||
\(73\) | 12.9021 | 1.51008 | 0.755039 | − | 0.655680i | \(-0.227618\pi\) | ||||
0.755039 | + | 0.655680i | \(0.227618\pi\) | |||||||
\(74\) | −1.27733 | −0.148487 | ||||||||
\(75\) | −1.22789 | −0.141784 | ||||||||
\(76\) | 7.48779 | 0.858908 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.42765 | −0.274877 | ||||||||
\(79\) | 7.12304 | 0.801405 | 0.400702 | − | 0.916208i | \(-0.368766\pi\) | ||||
0.400702 | + | 0.916208i | \(0.368766\pi\) | |||||||
\(80\) | −0.178647 | −0.0199733 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.61911 | −0.730958 | ||||||||
\(83\) | 1.05716 | 0.116038 | 0.0580192 | − | 0.998315i | \(-0.481522\pi\) | ||||
0.0580192 | + | 0.998315i | \(0.481522\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.4383 | 1.89145 | ||||||||
\(86\) | 6.12315 | 0.660276 | ||||||||
\(87\) | 4.06198 | 0.435490 | ||||||||
\(88\) | 11.2026 | 1.19420 | ||||||||
\(89\) | −3.30053 | −0.349856 | −0.174928 | − | 0.984581i | \(-0.555969\pi\) | ||||
−0.174928 | + | 0.984581i | \(0.555969\pi\) | |||||||
\(90\) | −2.15832 | −0.227507 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.25202 | −0.130532 | ||||||||
\(93\) | 3.44346 | 0.357070 | ||||||||
\(94\) | −2.63377 | −0.271652 | ||||||||
\(95\) | 14.9250 | 1.53127 | ||||||||
\(96\) | −5.68699 | −0.580426 | ||||||||
\(97\) | −15.9312 | −1.61757 | −0.808786 | − | 0.588103i | \(-0.799875\pi\) | ||||
−0.808786 | + | 0.588103i | \(0.799875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.98310 | −0.400316 | ||||||||
\(100\) | −1.53733 | −0.153733 | ||||||||
\(101\) | 6.96429 | 0.692972 | 0.346486 | − | 0.938055i | \(-0.387375\pi\) | ||||
0.346486 | + | 0.938055i | \(0.387375\pi\) | |||||||
\(102\) | 6.04338 | 0.598383 | ||||||||
\(103\) | 6.00488 | 0.591678 | 0.295839 | − | 0.955238i | \(-0.404401\pi\) | ||||
0.295839 | + | 0.955238i | \(0.404401\pi\) | |||||||
\(104\) | −7.89475 | −0.774144 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.27760 | 0.803992 | ||||||||
\(107\) | 5.71797 | 0.552777 | 0.276388 | − | 0.961046i | \(-0.410862\pi\) | ||||
0.276388 | + | 0.961046i | \(0.410862\pi\) | |||||||
\(108\) | 1.25202 | 0.120475 | ||||||||
\(109\) | 6.25586 | 0.599202 | 0.299601 | − | 0.954065i | \(-0.403146\pi\) | ||||
0.299601 | + | 0.954065i | \(0.403146\pi\) | |||||||
\(110\) | 8.59680 | 0.819673 | ||||||||
\(111\) | 1.47693 | 0.140184 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.79544 | −0.357045 | −0.178523 | − | 0.983936i | \(-0.557132\pi\) | ||||
−0.178523 | + | 0.983936i | \(0.557132\pi\) | |||||||
\(114\) | 5.17236 | 0.484436 | ||||||||
\(115\) | −2.49557 | −0.232713 | ||||||||
\(116\) | 5.08567 | 0.472193 | ||||||||
\(117\) | 2.80699 | 0.259506 | ||||||||
\(118\) | −7.18368 | −0.661311 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −7.01890 | −0.640735 | ||||||||
\(121\) | 4.86506 | 0.442279 | ||||||||
\(122\) | −3.21106 | −0.290716 | ||||||||
\(123\) | 7.65339 | 0.690083 | ||||||||
\(124\) | 4.31127 | 0.387164 | ||||||||
\(125\) | 9.41359 | 0.841977 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.8819 | 1.85297 | 0.926484 | − | 0.376333i | \(-0.122815\pi\) | ||||
0.926484 | + | 0.376333i | \(0.122815\pi\) | |||||||
\(128\) | −7.24404 | −0.640288 | ||||||||
\(129\) | −7.07993 | −0.623353 | ||||||||
\(130\) | −6.05837 | −0.531354 | ||||||||
\(131\) | 12.1488 | 1.06144 | 0.530722 | − | 0.847546i | \(-0.321921\pi\) | ||||
0.530722 | + | 0.847546i | \(0.321921\pi\) | |||||||
\(132\) | −4.98691 | −0.434055 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.86555 | 0.333933 | ||||||||
\(135\) | 2.49557 | 0.214785 | ||||||||
\(136\) | 19.6532 | 1.68525 | ||||||||
\(137\) | −0.828633 | −0.0707949 | −0.0353974 | − | 0.999373i | \(-0.511270\pi\) | ||||
−0.0353974 | + | 0.999373i | \(0.511270\pi\) | |||||||
\(138\) | −0.864859 | −0.0736217 | ||||||||
\(139\) | 0.546099 | 0.0463195 | 0.0231598 | − | 0.999732i | \(-0.492627\pi\) | ||||
0.0231598 | + | 0.999732i | \(0.492627\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.04531 | 0.256461 | ||||||||
\(142\) | −8.20775 | −0.688779 | ||||||||
\(143\) | −11.1805 | −0.934960 | ||||||||
\(144\) | 0.0715855 | 0.00596546 | ||||||||
\(145\) | 10.1370 | 0.841830 | ||||||||
\(146\) | 11.1585 | 0.923485 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.84914 | 0.151998 | ||||||||
\(149\) | −18.5487 | −1.51957 | −0.759783 | − | 0.650176i | \(-0.774695\pi\) | ||||
−0.759783 | + | 0.650176i | \(0.774695\pi\) | |||||||
\(150\) | −1.06195 | −0.0867077 | ||||||||
\(151\) | −5.77251 | −0.469760 | −0.234880 | − | 0.972024i | \(-0.575470\pi\) | ||||
−0.234880 | + | 0.972024i | \(0.575470\pi\) | |||||||
\(152\) | 16.8206 | 1.36433 | ||||||||
\(153\) | −6.98770 | −0.564922 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.59340 | 0.690239 | ||||||||
\(156\) | 3.51440 | 0.281377 | ||||||||
\(157\) | 14.1290 | 1.12761 | 0.563807 | − | 0.825906i | \(-0.309336\pi\) | ||||
0.563807 | + | 0.825906i | \(0.309336\pi\) | |||||||
\(158\) | 6.16043 | 0.490097 | ||||||||
\(159\) | −9.57104 | −0.759033 | ||||||||
\(160\) | −14.1923 | −1.12200 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.864859 | 0.0679498 | ||||||||
\(163\) | −16.7496 | −1.31193 | −0.655966 | − | 0.754790i | \(-0.727739\pi\) | ||||
−0.655966 | + | 0.754790i | \(0.727739\pi\) | |||||||
\(164\) | 9.58219 | 0.748243 | ||||||||
\(165\) | −9.94011 | −0.773837 | ||||||||
\(166\) | 0.914295 | 0.0709631 | ||||||||
\(167\) | 17.8518 | 1.38141 | 0.690707 | − | 0.723135i | \(-0.257299\pi\) | ||||
0.690707 | + | 0.723135i | \(0.257299\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.12084 | −0.393910 | ||||||||
\(170\) | 15.0817 | 1.15671 | ||||||||
\(171\) | −5.98058 | −0.457346 | ||||||||
\(172\) | −8.86420 | −0.675889 | ||||||||
\(173\) | 2.65359 | 0.201749 | 0.100874 | − | 0.994899i | \(-0.467836\pi\) | ||||
0.100874 | + | 0.994899i | \(0.467836\pi\) | |||||||
\(174\) | 3.51304 | 0.266323 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.285132 | −0.0214926 | ||||||||
\(177\) | 8.30618 | 0.624331 | ||||||||
\(178\) | −2.85450 | −0.213954 | ||||||||
\(179\) | 11.4696 | 0.857281 | 0.428640 | − | 0.903475i | \(-0.358993\pi\) | ||||
0.428640 | + | 0.903475i | \(0.358993\pi\) | |||||||
\(180\) | 3.12450 | 0.232887 | ||||||||
\(181\) | −15.8393 | −1.17732 | −0.588662 | − | 0.808380i | \(-0.700345\pi\) | ||||
−0.588662 | + | 0.808380i | \(0.700345\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.71282 | 0.274459 | ||||||||
\(184\) | −2.81254 | −0.207343 | ||||||||
\(185\) | 3.68577 | 0.270984 | ||||||||
\(186\) | 2.97811 | 0.218365 | ||||||||
\(187\) | 27.8327 | 2.03533 | ||||||||
\(188\) | 3.81278 | 0.278076 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.9080 | 0.936445 | ||||||||
\(191\) | 21.7951 | 1.57704 | 0.788518 | − | 0.615012i | \(-0.210849\pi\) | ||||
0.788518 | + | 0.615012i | \(0.210849\pi\) | |||||||
\(192\) | −4.77528 | −0.344626 | ||||||||
\(193\) | 16.0333 | 1.15411 | 0.577053 | − | 0.816707i | \(-0.304203\pi\) | ||||
0.577053 | + | 0.816707i | \(0.304203\pi\) | |||||||
\(194\) | −13.7783 | −0.989223 | ||||||||
\(195\) | 7.00504 | 0.501641 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.6653 | 0.759870 | 0.379935 | − | 0.925013i | \(-0.375946\pi\) | ||||
0.379935 | + | 0.925013i | \(0.375946\pi\) | |||||||
\(198\) | −3.44482 | −0.244813 | ||||||||
\(199\) | −3.65905 | −0.259383 | −0.129691 | − | 0.991554i | \(-0.541399\pi\) | ||||
−0.129691 | + | 0.991554i | \(0.541399\pi\) | |||||||
\(200\) | −3.45347 | −0.244198 | ||||||||
\(201\) | −4.46957 | −0.315259 | ||||||||
\(202\) | 6.02313 | 0.423786 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −8.74872 | −0.612533 | ||||||||
\(205\) | 19.0996 | 1.33397 | ||||||||
\(206\) | 5.19338 | 0.361840 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0.200939 | 0.0139326 | ||||||||
\(209\) | 23.8212 | 1.64775 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.1857 | −1.94039 | −0.970193 | − | 0.242332i | \(-0.922088\pi\) | ||||
−0.970193 | + | 0.242332i | \(0.922088\pi\) | |||||||
\(212\) | −11.9831 | −0.823004 | ||||||||
\(213\) | 9.49028 | 0.650263 | ||||||||
\(214\) | 4.94524 | 0.338050 | ||||||||
\(215\) | −17.6685 | −1.20498 | ||||||||
\(216\) | 2.81254 | 0.191369 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.41044 | 0.366441 | ||||||||
\(219\) | −12.9021 | −0.871844 | ||||||||
\(220\) | −12.4452 | −0.839055 | ||||||||
\(221\) | −19.6144 | −1.31940 | ||||||||
\(222\) | 1.27733 | 0.0857290 | ||||||||
\(223\) | 24.2280 | 1.62243 | 0.811215 | − | 0.584748i | \(-0.198807\pi\) | ||||
0.811215 | + | 0.584748i | \(0.198807\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.22789 | 0.0818590 | ||||||||
\(226\) | −3.28252 | −0.218350 | ||||||||
\(227\) | −8.03654 | −0.533404 | −0.266702 | − | 0.963779i | \(-0.585934\pi\) | ||||
−0.266702 | + | 0.963779i | \(0.585934\pi\) | |||||||
\(228\) | −7.48779 | −0.495891 | ||||||||
\(229\) | 13.7790 | 0.910542 | 0.455271 | − | 0.890353i | \(-0.349542\pi\) | ||||
0.455271 | + | 0.890353i | \(0.349542\pi\) | |||||||
\(230\) | −2.15832 | −0.142315 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.4245 | 0.750054 | ||||||||
\(233\) | −1.83601 | −0.120281 | −0.0601405 | − | 0.998190i | \(-0.519155\pi\) | ||||
−0.0601405 | + | 0.998190i | \(0.519155\pi\) | |||||||
\(234\) | 2.42765 | 0.158700 | ||||||||
\(235\) | 7.59979 | 0.495756 | ||||||||
\(236\) | 10.3995 | 0.676949 | ||||||||
\(237\) | −7.12304 | −0.462691 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.42206 | −0.286039 | −0.143020 | − | 0.989720i | \(-0.545681\pi\) | ||||
−0.143020 | + | 0.989720i | \(0.545681\pi\) | |||||||
\(240\) | 0.178647 | 0.0115316 | ||||||||
\(241\) | −28.4589 | −1.83320 | −0.916598 | − | 0.399810i | \(-0.869076\pi\) | ||||
−0.916598 | + | 0.399810i | \(0.869076\pi\) | |||||||
\(242\) | 4.20760 | 0.270475 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.64851 | 0.297591 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.61911 | 0.422019 | ||||||||
\(247\) | −16.7874 | −1.06816 | ||||||||
\(248\) | 9.68486 | 0.614989 | ||||||||
\(249\) | −1.05716 | −0.0669948 | ||||||||
\(250\) | 8.14143 | 0.514909 | ||||||||
\(251\) | −26.7064 | −1.68569 | −0.842846 | − | 0.538156i | \(-0.819121\pi\) | ||||
−0.842846 | + | 0.538156i | \(0.819121\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.98310 | −0.250415 | ||||||||
\(254\) | 18.0599 | 1.13318 | ||||||||
\(255\) | −17.4383 | −1.09203 | ||||||||
\(256\) | −15.8156 | −0.988476 | ||||||||
\(257\) | 4.36432 | 0.272239 | 0.136119 | − | 0.990692i | \(-0.456537\pi\) | ||||
0.136119 | + | 0.990692i | \(0.456537\pi\) | |||||||
\(258\) | −6.12315 | −0.381210 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 8.77043 | 0.543919 | ||||||||
\(261\) | −4.06198 | −0.251430 | ||||||||
\(262\) | 10.5070 | 0.649124 | ||||||||
\(263\) | 1.54914 | 0.0955242 | 0.0477621 | − | 0.998859i | \(-0.484791\pi\) | ||||
0.0477621 | + | 0.998859i | \(0.484791\pi\) | |||||||
\(264\) | −11.2026 | −0.689473 | ||||||||
\(265\) | −23.8852 | −1.46726 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.30053 | 0.201989 | ||||||||
\(268\) | −5.59599 | −0.341829 | ||||||||
\(269\) | −3.71532 | −0.226527 | −0.113264 | − | 0.993565i | \(-0.536130\pi\) | ||||
−0.113264 | + | 0.993565i | \(0.536130\pi\) | |||||||
\(270\) | 2.15832 | 0.131351 | ||||||||
\(271\) | 4.02009 | 0.244203 | 0.122101 | − | 0.992518i | \(-0.461037\pi\) | ||||
0.122101 | + | 0.992518i | \(0.461037\pi\) | |||||||
\(272\) | −0.500218 | −0.0303302 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.716651 | −0.0432945 | ||||||||
\(275\) | −4.89079 | −0.294925 | ||||||||
\(276\) | 1.25202 | 0.0753626 | ||||||||
\(277\) | −11.3927 | −0.684523 | −0.342261 | − | 0.939605i | \(-0.611193\pi\) | ||||
−0.342261 | + | 0.939605i | \(0.611193\pi\) | |||||||
\(278\) | 0.472299 | 0.0283266 | ||||||||
\(279\) | −3.44346 | −0.206155 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.9503 | −1.66738 | −0.833689 | − | 0.552235i | \(-0.813775\pi\) | ||||
−0.833689 | + | 0.552235i | \(0.813775\pi\) | |||||||
\(282\) | 2.63377 | 0.156838 | ||||||||
\(283\) | −29.9754 | −1.78185 | −0.890925 | − | 0.454150i | \(-0.849943\pi\) | ||||
−0.890925 | + | 0.454150i | \(0.849943\pi\) | |||||||
\(284\) | 11.8820 | 0.705067 | ||||||||
\(285\) | −14.9250 | −0.884079 | ||||||||
\(286\) | −9.66956 | −0.571773 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.68699 | 0.335109 | ||||||||
\(289\) | 31.8279 | 1.87223 | ||||||||
\(290\) | 8.76706 | 0.514819 | ||||||||
\(291\) | 15.9312 | 0.933906 | ||||||||
\(292\) | −16.1537 | −0.945322 | ||||||||
\(293\) | −4.87346 | −0.284711 | −0.142355 | − | 0.989816i | \(-0.545468\pi\) | ||||
−0.142355 | + | 0.989816i | \(0.545468\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.7287 | 1.20687 | ||||||||
\(296\) | 4.15391 | 0.241441 | ||||||||
\(297\) | 3.98310 | 0.231123 | ||||||||
\(298\) | −16.0420 | −0.929288 | ||||||||
\(299\) | 2.80699 | 0.162332 | ||||||||
\(300\) | 1.53733 | 0.0887580 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4.99241 | −0.287281 | ||||||||
\(303\) | −6.96429 | −0.400088 | ||||||||
\(304\) | −0.428122 | −0.0245545 | ||||||||
\(305\) | 9.26560 | 0.530547 | ||||||||
\(306\) | −6.04338 | −0.345477 | ||||||||
\(307\) | −27.9064 | −1.59270 | −0.796351 | − | 0.604835i | \(-0.793239\pi\) | ||||
−0.796351 | + | 0.604835i | \(0.793239\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.00488 | −0.341606 | ||||||||
\(310\) | 7.43209 | 0.422114 | ||||||||
\(311\) | 27.0086 | 1.53152 | 0.765758 | − | 0.643129i | \(-0.222364\pi\) | ||||
0.765758 | + | 0.643129i | \(0.222364\pi\) | |||||||
\(312\) | 7.89475 | 0.446952 | ||||||||
\(313\) | 4.21402 | 0.238190 | 0.119095 | − | 0.992883i | \(-0.462001\pi\) | ||||
0.119095 | + | 0.992883i | \(0.462001\pi\) | |||||||
\(314\) | 12.2196 | 0.689590 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.91818 | −0.501687 | ||||||||
\(317\) | −7.99795 | −0.449210 | −0.224605 | − | 0.974450i | \(-0.572109\pi\) | ||||
−0.224605 | + | 0.974450i | \(0.572109\pi\) | |||||||
\(318\) | −8.27760 | −0.464185 | ||||||||
\(319\) | 16.1793 | 0.905865 | ||||||||
\(320\) | −11.9170 | −0.666183 | ||||||||
\(321\) | −5.71797 | −0.319146 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 41.7905 | 2.32528 | ||||||||
\(324\) | −1.25202 | −0.0695566 | ||||||||
\(325\) | 3.44666 | 0.191186 | ||||||||
\(326\) | −14.4861 | −0.802309 | ||||||||
\(327\) | −6.25586 | −0.345950 | ||||||||
\(328\) | 21.5255 | 1.18854 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −8.59680 | −0.473238 | ||||||||
\(331\) | 24.0871 | 1.32395 | 0.661974 | − | 0.749527i | \(-0.269719\pi\) | ||||
0.661974 | + | 0.749527i | \(0.269719\pi\) | |||||||
\(332\) | −1.32358 | −0.0726411 | ||||||||
\(333\) | −1.47693 | −0.0809350 | ||||||||
\(334\) | 15.4393 | 0.844801 | ||||||||
\(335\) | −11.1541 | −0.609416 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.91298 | −0.376574 | −0.188287 | − | 0.982114i | \(-0.560294\pi\) | ||||
−0.188287 | + | 0.982114i | \(0.560294\pi\) | |||||||
\(338\) | −4.42880 | −0.240895 | ||||||||
\(339\) | 3.79544 | 0.206140 | ||||||||
\(340\) | −21.8331 | −1.18406 | ||||||||
\(341\) | 13.7156 | 0.742743 | ||||||||
\(342\) | −5.17236 | −0.279689 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −19.9126 | −1.07361 | ||||||||
\(345\) | 2.49557 | 0.134357 | ||||||||
\(346\) | 2.29499 | 0.123379 | ||||||||
\(347\) | 12.1876 | 0.654266 | 0.327133 | − | 0.944978i | \(-0.393917\pi\) | ||||
0.327133 | + | 0.944978i | \(0.393917\pi\) | |||||||
\(348\) | −5.08567 | −0.272621 | ||||||||
\(349\) | 27.0701 | 1.44903 | 0.724515 | − | 0.689259i | \(-0.242064\pi\) | ||||
0.724515 | + | 0.689259i | \(0.242064\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.80699 | −0.149826 | ||||||||
\(352\) | −22.6518 | −1.20735 | ||||||||
\(353\) | −28.5772 | −1.52101 | −0.760505 | − | 0.649332i | \(-0.775049\pi\) | ||||
−0.760505 | + | 0.649332i | \(0.775049\pi\) | |||||||
\(354\) | 7.18368 | 0.381808 | ||||||||
\(355\) | 23.6837 | 1.25700 | ||||||||
\(356\) | 4.13233 | 0.219013 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.91962 | 0.524268 | ||||||||
\(359\) | −19.4627 | −1.02720 | −0.513601 | − | 0.858029i | \(-0.671689\pi\) | ||||
−0.513601 | + | 0.858029i | \(0.671689\pi\) | |||||||
\(360\) | 7.01890 | 0.369928 | ||||||||
\(361\) | 16.7673 | 0.882489 | ||||||||
\(362\) | −13.6987 | −0.719990 | ||||||||
\(363\) | −4.86506 | −0.255350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −32.1982 | −1.68533 | ||||||||
\(366\) | 3.21106 | 0.167845 | ||||||||
\(367\) | 4.81840 | 0.251518 | 0.125759 | − | 0.992061i | \(-0.459863\pi\) | ||||
0.125759 | + | 0.992061i | \(0.459863\pi\) | |||||||
\(368\) | 0.0715855 | 0.00373165 | ||||||||
\(369\) | −7.65339 | −0.398420 | ||||||||
\(370\) | 3.18768 | 0.165719 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.31127 | −0.223529 | ||||||||
\(373\) | −24.6352 | −1.27556 | −0.637782 | − | 0.770217i | \(-0.720148\pi\) | ||||
−0.637782 | + | 0.770217i | \(0.720148\pi\) | |||||||
\(374\) | 24.0714 | 1.24470 | ||||||||
\(375\) | −9.41359 | −0.486116 | ||||||||
\(376\) | 8.56505 | 0.441709 | ||||||||
\(377\) | −11.4019 | −0.587229 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.7983 | 1.63337 | 0.816684 | − | 0.577085i | \(-0.195810\pi\) | ||||
0.816684 | + | 0.577085i | \(0.195810\pi\) | |||||||
\(380\) | −18.6863 | −0.958588 | ||||||||
\(381\) | −20.8819 | −1.06981 | ||||||||
\(382\) | 18.8497 | 0.964433 | ||||||||
\(383\) | −22.3654 | −1.14282 | −0.571409 | − | 0.820666i | \(-0.693603\pi\) | ||||
−0.571409 | + | 0.820666i | \(0.693603\pi\) | |||||||
\(384\) | 7.24404 | 0.369671 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.8666 | 0.705791 | ||||||||
\(387\) | 7.07993 | 0.359893 | ||||||||
\(388\) | 19.9462 | 1.01262 | ||||||||
\(389\) | 19.9097 | 1.00946 | 0.504730 | − | 0.863277i | \(-0.331592\pi\) | ||||
0.504730 | + | 0.863277i | \(0.331592\pi\) | |||||||
\(390\) | 6.05837 | 0.306778 | ||||||||
\(391\) | −6.98770 | −0.353383 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.1488 | −0.612825 | ||||||||
\(394\) | 9.22397 | 0.464697 | ||||||||
\(395\) | −17.7761 | −0.894411 | ||||||||
\(396\) | 4.98691 | 0.250602 | ||||||||
\(397\) | 27.1066 | 1.36044 | 0.680222 | − | 0.733006i | \(-0.261883\pi\) | ||||
0.680222 | + | 0.733006i | \(0.261883\pi\) | |||||||
\(398\) | −3.16456 | −0.158625 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.0878987 | 0.00439494 | ||||||||
\(401\) | −34.1782 | −1.70678 | −0.853390 | − | 0.521274i | \(-0.825457\pi\) | ||||
−0.853390 | + | 0.521274i | \(0.825457\pi\) | |||||||
\(402\) | −3.86555 | −0.192796 | ||||||||
\(403\) | −9.66574 | −0.481485 | ||||||||
\(404\) | −8.71941 | −0.433807 | ||||||||
\(405\) | −2.49557 | −0.124006 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.88274 | 0.291596 | ||||||||
\(408\) | −19.6532 | −0.972977 | ||||||||
\(409\) | 15.1477 | 0.749006 | 0.374503 | − | 0.927226i | \(-0.377813\pi\) | ||||
0.374503 | + | 0.927226i | \(0.377813\pi\) | |||||||
\(410\) | 16.5185 | 0.815789 | ||||||||
\(411\) | 0.828633 | 0.0408734 | ||||||||
\(412\) | −7.51822 | −0.370396 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.864859 | 0.0425055 | ||||||||
\(415\) | −2.63822 | −0.129505 | ||||||||
\(416\) | 15.9633 | 0.782665 | ||||||||
\(417\) | −0.546099 | −0.0267426 | ||||||||
\(418\) | 20.6020 | 1.00768 | ||||||||
\(419\) | 14.0504 | 0.686405 | 0.343202 | − | 0.939262i | \(-0.388488\pi\) | ||||
0.343202 | + | 0.939262i | \(0.388488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.0914 | −1.27161 | −0.635807 | − | 0.771848i | \(-0.719333\pi\) | ||||
−0.635807 | + | 0.771848i | \(0.719333\pi\) | |||||||
\(422\) | −24.3767 | −1.18664 | ||||||||
\(423\) | −3.04531 | −0.148068 | ||||||||
\(424\) | −26.9189 | −1.30730 | ||||||||
\(425\) | −8.58009 | −0.416195 | ||||||||
\(426\) | 8.20775 | 0.397667 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.15900 | −0.346043 | ||||||||
\(429\) | 11.1805 | 0.539799 | ||||||||
\(430\) | −15.2808 | −0.736904 | ||||||||
\(431\) | 3.09446 | 0.149055 | 0.0745274 | − | 0.997219i | \(-0.476255\pi\) | ||||
0.0745274 | + | 0.997219i | \(0.476255\pi\) | |||||||
\(432\) | −0.0715855 | −0.00344416 | ||||||||
\(433\) | 18.9836 | 0.912293 | 0.456146 | − | 0.889905i | \(-0.349229\pi\) | ||||
0.456146 | + | 0.889905i | \(0.349229\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.1370 | −0.486031 | ||||||||
\(436\) | −7.83244 | −0.375106 | ||||||||
\(437\) | −5.98058 | −0.286090 | ||||||||
\(438\) | −11.1585 | −0.533174 | ||||||||
\(439\) | −11.9712 | −0.571355 | −0.285677 | − | 0.958326i | \(-0.592219\pi\) | ||||
−0.285677 | + | 0.958326i | \(0.592219\pi\) | |||||||
\(440\) | −27.9569 | −1.33280 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16.9637 | −0.806879 | ||||||||
\(443\) | 19.4820 | 0.925616 | 0.462808 | − | 0.886458i | \(-0.346842\pi\) | ||||
0.462808 | + | 0.886458i | \(0.346842\pi\) | |||||||
\(444\) | −1.84914 | −0.0877562 | ||||||||
\(445\) | 8.23672 | 0.390458 | ||||||||
\(446\) | 20.9539 | 0.992194 | ||||||||
\(447\) | 18.5487 | 0.877322 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.9358 | −1.22399 | −0.611993 | − | 0.790864i | \(-0.709632\pi\) | ||||
−0.611993 | + | 0.790864i | \(0.709632\pi\) | |||||||
\(450\) | 1.06195 | 0.0500607 | ||||||||
\(451\) | 30.4842 | 1.43545 | ||||||||
\(452\) | 4.75196 | 0.223513 | ||||||||
\(453\) | 5.77251 | 0.271216 | ||||||||
\(454\) | −6.95048 | −0.326202 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −16.8206 | −0.787697 | ||||||||
\(457\) | 4.61332 | 0.215802 | 0.107901 | − | 0.994162i | \(-0.465587\pi\) | ||||
0.107901 | + | 0.994162i | \(0.465587\pi\) | |||||||
\(458\) | 11.9169 | 0.556840 | ||||||||
\(459\) | 6.98770 | 0.326158 | ||||||||
\(460\) | 3.12450 | 0.145681 | ||||||||
\(461\) | 13.8181 | 0.643571 | 0.321786 | − | 0.946813i | \(-0.395717\pi\) | ||||
0.321786 | + | 0.946813i | \(0.395717\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.1291 | −1.58611 | −0.793057 | − | 0.609147i | \(-0.791512\pi\) | ||||
−0.793057 | + | 0.609147i | \(0.791512\pi\) | |||||||
\(464\) | −0.290779 | −0.0134991 | ||||||||
\(465\) | −8.59340 | −0.398510 | ||||||||
\(466\) | −1.58789 | −0.0735576 | ||||||||
\(467\) | −27.9716 | −1.29437 | −0.647185 | − | 0.762333i | \(-0.724054\pi\) | ||||
−0.647185 | + | 0.762333i | \(0.724054\pi\) | |||||||
\(468\) | −3.51440 | −0.162453 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 6.57275 | 0.303179 | ||||||||
\(471\) | −14.1290 | −0.651029 | ||||||||
\(472\) | 23.3614 | 1.07530 | ||||||||
\(473\) | −28.2001 | −1.29664 | ||||||||
\(474\) | −6.16043 | −0.282958 | ||||||||
\(475\) | −7.34346 | −0.336941 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.57104 | 0.438228 | ||||||||
\(478\) | −3.82446 | −0.174927 | ||||||||
\(479\) | −32.6269 | −1.49076 | −0.745380 | − | 0.666639i | \(-0.767732\pi\) | ||||
−0.745380 | + | 0.666639i | \(0.767732\pi\) | |||||||
\(480\) | 14.1923 | 0.647787 | ||||||||
\(481\) | −4.14571 | −0.189028 | ||||||||
\(482\) | −24.6129 | −1.12109 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.09115 | −0.276870 | ||||||||
\(485\) | 39.7576 | 1.80530 | ||||||||
\(486\) | −0.864859 | −0.0392308 | ||||||||
\(487\) | −25.9421 | −1.17555 | −0.587775 | − | 0.809025i | \(-0.699996\pi\) | ||||
−0.587775 | + | 0.809025i | \(0.699996\pi\) | |||||||
\(488\) | 10.4424 | 0.472707 | ||||||||
\(489\) | 16.7496 | 0.757444 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.0005 | 1.17339 | 0.586693 | − | 0.809810i | \(-0.300430\pi\) | ||||
0.586693 | + | 0.809810i | \(0.300430\pi\) | |||||||
\(492\) | −9.58219 | −0.431998 | ||||||||
\(493\) | 28.3839 | 1.27835 | ||||||||
\(494\) | −14.5187 | −0.653229 | ||||||||
\(495\) | 9.94011 | 0.446775 | ||||||||
\(496\) | −0.246502 | −0.0110683 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.914295 | −0.0409705 | ||||||||
\(499\) | −23.2072 | −1.03890 | −0.519448 | − | 0.854502i | \(-0.673862\pi\) | ||||
−0.519448 | + | 0.854502i | \(0.673862\pi\) | |||||||
\(500\) | −11.7860 | −0.527085 | ||||||||
\(501\) | −17.8518 | −0.797560 | ||||||||
\(502\) | −23.0973 | −1.03088 | ||||||||
\(503\) | 12.5204 | 0.558256 | 0.279128 | − | 0.960254i | \(-0.409955\pi\) | ||||
0.279128 | + | 0.960254i | \(0.409955\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.3799 | −0.773395 | ||||||||
\(506\) | −3.44482 | −0.153141 | ||||||||
\(507\) | 5.12084 | 0.227424 | ||||||||
\(508\) | −26.1445 | −1.15998 | ||||||||
\(509\) | −24.2118 | −1.07317 | −0.536585 | − | 0.843847i | \(-0.680286\pi\) | ||||
−0.536585 | + | 0.843847i | \(0.680286\pi\) | |||||||
\(510\) | −15.0817 | −0.667828 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.809780 | 0.0357875 | ||||||||
\(513\) | 5.98058 | 0.264049 | ||||||||
\(514\) | 3.77452 | 0.166487 | ||||||||
\(515\) | −14.9856 | −0.660345 | ||||||||
\(516\) | 8.86420 | 0.390225 | ||||||||
\(517\) | 12.1298 | 0.533466 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.65359 | −0.116480 | ||||||||
\(520\) | 19.7019 | 0.863987 | ||||||||
\(521\) | −6.82821 | −0.299149 | −0.149575 | − | 0.988750i | \(-0.547790\pi\) | ||||
−0.149575 | + | 0.988750i | \(0.547790\pi\) | |||||||
\(522\) | −3.51304 | −0.153762 | ||||||||
\(523\) | −9.54004 | −0.417157 | −0.208579 | − | 0.978006i | \(-0.566884\pi\) | ||||
−0.208579 | + | 0.978006i | \(0.566884\pi\) | |||||||
\(524\) | −15.2105 | −0.664474 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.33979 | 0.0584177 | ||||||||
\(527\) | 24.0619 | 1.04815 | ||||||||
\(528\) | 0.285132 | 0.0124088 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −20.6574 | −0.897298 | ||||||||
\(531\) | −8.30618 | −0.360457 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.4830 | −0.930530 | ||||||||
\(534\) | 2.85450 | 0.123526 | ||||||||
\(535\) | −14.2696 | −0.616929 | ||||||||
\(536\) | −12.5708 | −0.542978 | ||||||||
\(537\) | −11.4696 | −0.494951 | ||||||||
\(538\) | −3.21323 | −0.138532 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.12450 | −0.134457 | ||||||||
\(541\) | 33.1748 | 1.42629 | 0.713147 | − | 0.701014i | \(-0.247269\pi\) | ||||
0.713147 | + | 0.701014i | \(0.247269\pi\) | |||||||
\(542\) | 3.47681 | 0.149342 | ||||||||
\(543\) | 15.8393 | 0.679728 | ||||||||
\(544\) | −39.7390 | −1.70379 | ||||||||
\(545\) | −15.6119 | −0.668742 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.2100 | 0.735848 | 0.367924 | − | 0.929856i | \(-0.380069\pi\) | ||||
0.367924 | + | 0.929856i | \(0.380069\pi\) | |||||||
\(548\) | 1.03746 | 0.0443182 | ||||||||
\(549\) | −3.71282 | −0.158459 | ||||||||
\(550\) | −4.22984 | −0.180361 | ||||||||
\(551\) | 24.2930 | 1.03492 | ||||||||
\(552\) | 2.81254 | 0.119710 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −9.85311 | −0.418619 | ||||||||
\(555\) | −3.68577 | −0.156452 | ||||||||
\(556\) | −0.683726 | −0.0289964 | ||||||||
\(557\) | 17.8924 | 0.758125 | 0.379062 | − | 0.925371i | \(-0.376247\pi\) | ||||
0.379062 | + | 0.925371i | \(0.376247\pi\) | |||||||
\(558\) | −2.97811 | −0.126073 | ||||||||
\(559\) | 19.8733 | 0.840550 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −27.8327 | −1.17510 | ||||||||
\(562\) | −24.1731 | −1.01968 | ||||||||
\(563\) | 16.4160 | 0.691852 | 0.345926 | − | 0.938262i | \(-0.387565\pi\) | ||||
0.345926 | + | 0.938262i | \(0.387565\pi\) | |||||||
\(564\) | −3.81278 | −0.160547 | ||||||||
\(565\) | 9.47180 | 0.398482 | ||||||||
\(566\) | −25.9245 | −1.08969 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 26.6918 | 1.11996 | ||||||||
\(569\) | 4.94134 | 0.207152 | 0.103576 | − | 0.994622i | \(-0.466972\pi\) | ||||
0.103576 | + | 0.994622i | \(0.466972\pi\) | |||||||
\(570\) | −12.9080 | −0.540657 | ||||||||
\(571\) | −42.8618 | −1.79371 | −0.896855 | − | 0.442325i | \(-0.854154\pi\) | ||||
−0.896855 | + | 0.442325i | \(0.854154\pi\) | |||||||
\(572\) | 13.9982 | 0.585293 | ||||||||
\(573\) | −21.7951 | −0.910502 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.22789 | 0.0512063 | ||||||||
\(576\) | 4.77528 | 0.198970 | ||||||||
\(577\) | 13.8130 | 0.575043 | 0.287522 | − | 0.957774i | \(-0.407169\pi\) | ||||
0.287522 | + | 0.957774i | \(0.407169\pi\) | |||||||
\(578\) | 27.5267 | 1.14496 | ||||||||
\(579\) | −16.0333 | −0.666323 | ||||||||
\(580\) | −12.6917 | −0.526993 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 13.7783 | 0.571128 | ||||||||
\(583\) | −38.1224 | −1.57887 | ||||||||
\(584\) | −36.2877 | −1.50160 | ||||||||
\(585\) | −7.00504 | −0.289623 | ||||||||
\(586\) | −4.21486 | −0.174114 | ||||||||
\(587\) | 19.9885 | 0.825012 | 0.412506 | − | 0.910955i | \(-0.364654\pi\) | ||||
0.412506 | + | 0.910955i | \(0.364654\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.5939 | 0.848556 | ||||||||
\(590\) | 17.9274 | 0.738059 | ||||||||
\(591\) | −10.6653 | −0.438711 | ||||||||
\(592\) | −0.105726 | −0.00434533 | ||||||||
\(593\) | −2.72068 | −0.111725 | −0.0558625 | − | 0.998438i | \(-0.517791\pi\) | ||||
−0.0558625 | + | 0.998438i | \(0.517791\pi\) | |||||||
\(594\) | 3.44482 | 0.141343 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 23.2233 | 0.951262 | ||||||||
\(597\) | 3.65905 | 0.149755 | ||||||||
\(598\) | 2.42765 | 0.0992739 | ||||||||
\(599\) | 17.4698 | 0.713799 | 0.356899 | − | 0.934143i | \(-0.383834\pi\) | ||||
0.356899 | + | 0.934143i | \(0.383834\pi\) | |||||||
\(600\) | 3.45347 | 0.140987 | ||||||||
\(601\) | 27.6015 | 1.12589 | 0.562944 | − | 0.826495i | \(-0.309669\pi\) | ||||
0.562944 | + | 0.826495i | \(0.309669\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.46957 | 0.182015 | ||||||||
\(604\) | 7.22728 | 0.294074 | ||||||||
\(605\) | −12.1411 | −0.493607 | ||||||||
\(606\) | −6.02313 | −0.244673 | ||||||||
\(607\) | −12.9173 | −0.524295 | −0.262148 | − | 0.965028i | \(-0.584431\pi\) | ||||
−0.262148 | + | 0.965028i | \(0.584431\pi\) | |||||||
\(608\) | −34.0115 | −1.37935 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.01345 | 0.324455 | ||||||||
\(611\) | −8.54814 | −0.345821 | ||||||||
\(612\) | 8.74872 | 0.353646 | ||||||||
\(613\) | −38.8541 | −1.56930 | −0.784651 | − | 0.619937i | \(-0.787158\pi\) | ||||
−0.784651 | + | 0.619937i | \(0.787158\pi\) | |||||||
\(614\) | −24.1351 | −0.974013 | ||||||||
\(615\) | −19.0996 | −0.770170 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.3417 | −1.02022 | −0.510108 | − | 0.860110i | \(-0.670395\pi\) | ||||
−0.510108 | + | 0.860110i | \(0.670395\pi\) | |||||||
\(618\) | −5.19338 | −0.208908 | ||||||||
\(619\) | 35.5852 | 1.43029 | 0.715145 | − | 0.698976i | \(-0.246361\pi\) | ||||
0.715145 | + | 0.698976i | \(0.246361\pi\) | |||||||
\(620\) | −10.7591 | −0.432096 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 23.3586 | 0.936596 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.200939 | −0.00804401 | ||||||||
\(625\) | −29.6317 | −1.18527 | ||||||||
\(626\) | 3.64453 | 0.145665 | ||||||||
\(627\) | −23.8212 | −0.951328 | ||||||||
\(628\) | −17.6897 | −0.705897 | ||||||||
\(629\) | 10.3203 | 0.411498 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.5559 | −0.499842 | −0.249921 | − | 0.968266i | \(-0.580405\pi\) | ||||
−0.249921 | + | 0.968266i | \(0.580405\pi\) | |||||||
\(632\) | −20.0338 | −0.796903 | ||||||||
\(633\) | 28.1857 | 1.12028 | ||||||||
\(634\) | −6.91710 | −0.274713 | ||||||||
\(635\) | −52.1123 | −2.06801 | ||||||||
\(636\) | 11.9831 | 0.475161 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13.9928 | 0.553980 | ||||||||
\(639\) | −9.49028 | −0.375429 | ||||||||
\(640\) | 18.0780 | 0.714596 | ||||||||
\(641\) | −44.0488 | −1.73982 | −0.869912 | − | 0.493207i | \(-0.835825\pi\) | ||||
−0.869912 | + | 0.493207i | \(0.835825\pi\) | |||||||
\(642\) | −4.94524 | −0.195173 | ||||||||
\(643\) | 27.1797 | 1.07186 | 0.535931 | − | 0.844262i | \(-0.319961\pi\) | ||||
0.535931 | + | 0.844262i | \(0.319961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.6685 | 0.695696 | ||||||||
\(646\) | 36.1429 | 1.42202 | ||||||||
\(647\) | 33.7648 | 1.32743 | 0.663716 | − | 0.747985i | \(-0.268978\pi\) | ||||
0.663716 | + | 0.747985i | \(0.268978\pi\) | |||||||
\(648\) | −2.81254 | −0.110487 | ||||||||
\(649\) | 33.0843 | 1.29867 | ||||||||
\(650\) | 2.98087 | 0.116919 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.9708 | 0.821281 | ||||||||
\(653\) | 31.9330 | 1.24963 | 0.624817 | − | 0.780771i | \(-0.285174\pi\) | ||||
0.624817 | + | 0.780771i | \(0.285174\pi\) | |||||||
\(654\) | −5.41044 | −0.211565 | ||||||||
\(655\) | −30.3182 | −1.18463 | ||||||||
\(656\) | −0.547872 | −0.0213908 | ||||||||
\(657\) | 12.9021 | 0.503359 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 47.4986 | 1.85028 | 0.925142 | − | 0.379622i | \(-0.123946\pi\) | ||||
0.925142 | + | 0.379622i | \(0.123946\pi\) | |||||||
\(660\) | 12.4452 | 0.484429 | ||||||||
\(661\) | −29.4292 | −1.14466 | −0.572332 | − | 0.820022i | \(-0.693961\pi\) | ||||
−0.572332 | + | 0.820022i | \(0.693961\pi\) | |||||||
\(662\) | 20.8320 | 0.809658 | ||||||||
\(663\) | 19.6144 | 0.761759 | ||||||||
\(664\) | −2.97330 | −0.115387 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.27733 | −0.0494956 | ||||||||
\(667\) | −4.06198 | −0.157281 | ||||||||
\(668\) | −22.3508 | −0.864778 | ||||||||
\(669\) | −24.2280 | −0.936710 | ||||||||
\(670\) | −9.64677 | −0.372687 | ||||||||
\(671\) | 14.7885 | 0.570904 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.8311 | −0.841528 | −0.420764 | − | 0.907170i | \(-0.638238\pi\) | ||||
−0.420764 | + | 0.907170i | \(0.638238\pi\) | |||||||
\(674\) | −5.97876 | −0.230293 | ||||||||
\(675\) | −1.22789 | −0.0472613 | ||||||||
\(676\) | 6.41138 | 0.246591 | ||||||||
\(677\) | 31.9593 | 1.22830 | 0.614148 | − | 0.789191i | \(-0.289500\pi\) | ||||
0.614148 | + | 0.789191i | \(0.289500\pi\) | |||||||
\(678\) | 3.28252 | 0.126065 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −49.0459 | −1.88083 | ||||||||
\(681\) | 8.03654 | 0.307961 | ||||||||
\(682\) | 11.8621 | 0.454223 | ||||||||
\(683\) | 5.80239 | 0.222022 | 0.111011 | − | 0.993819i | \(-0.464591\pi\) | ||||
0.111011 | + | 0.993819i | \(0.464591\pi\) | |||||||
\(684\) | 7.48779 | 0.286303 | ||||||||
\(685\) | 2.06791 | 0.0790109 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.7790 | −0.525702 | ||||||||
\(688\) | 0.506820 | 0.0193223 | ||||||||
\(689\) | 26.8658 | 1.02350 | ||||||||
\(690\) | 2.15832 | 0.0821658 | ||||||||
\(691\) | 50.4258 | 1.91829 | 0.959145 | − | 0.282916i | \(-0.0913019\pi\) | ||||
0.959145 | + | 0.282916i | \(0.0913019\pi\) | |||||||
\(692\) | −3.32235 | −0.126297 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.5406 | 0.400115 | ||||||||
\(695\) | −1.36283 | −0.0516951 | ||||||||
\(696\) | −11.4245 | −0.433044 | ||||||||
\(697\) | 53.4796 | 2.02568 | ||||||||
\(698\) | 23.4118 | 0.886151 | ||||||||
\(699\) | 1.83601 | 0.0694443 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.8283 | 1.08883 | 0.544414 | − | 0.838817i | \(-0.316752\pi\) | ||||
0.544414 | + | 0.838817i | \(0.316752\pi\) | |||||||
\(702\) | −2.42765 | −0.0916257 | ||||||||
\(703\) | 8.83286 | 0.333138 | ||||||||
\(704\) | −19.0204 | −0.716858 | ||||||||
\(705\) | −7.59979 | −0.286225 | ||||||||
\(706\) | −24.7153 | −0.930171 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −10.3995 | −0.390837 | ||||||||
\(709\) | 32.4556 | 1.21889 | 0.609447 | − | 0.792826i | \(-0.291391\pi\) | ||||
0.609447 | + | 0.792826i | \(0.291391\pi\) | |||||||
\(710\) | 20.4831 | 0.768715 | ||||||||
\(711\) | 7.12304 | 0.267135 | ||||||||
\(712\) | 9.28288 | 0.347891 | ||||||||
\(713\) | −3.44346 | −0.128959 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.9017 | 1.04347 | ||||||||
\(716\) | −14.3602 | −0.536665 | ||||||||
\(717\) | 4.42206 | 0.165145 | ||||||||
\(718\) | −16.8325 | −0.628184 | ||||||||
\(719\) | −16.0351 | −0.598009 | −0.299004 | − | 0.954252i | \(-0.596655\pi\) | ||||
−0.299004 | + | 0.954252i | \(0.596655\pi\) | |||||||
\(720\) | −0.178647 | −0.00665777 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 14.5014 | 0.539685 | ||||||||
\(723\) | 28.4589 | 1.05840 | ||||||||
\(724\) | 19.8310 | 0.737015 | ||||||||
\(725\) | −4.98765 | −0.185237 | ||||||||
\(726\) | −4.20760 | −0.156159 | ||||||||
\(727\) | 40.6150 | 1.50633 | 0.753164 | − | 0.657833i | \(-0.228527\pi\) | ||||
0.753164 | + | 0.657833i | \(0.228527\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −27.8469 | −1.03066 | ||||||||
\(731\) | −49.4724 | −1.82980 | ||||||||
\(732\) | −4.64851 | −0.171814 | ||||||||
\(733\) | −2.41457 | −0.0891843 | −0.0445922 | − | 0.999005i | \(-0.514199\pi\) | ||||
−0.0445922 | + | 0.999005i | \(0.514199\pi\) | |||||||
\(734\) | 4.16724 | 0.153816 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.68699 | 0.209625 | ||||||||
\(737\) | −17.8027 | −0.655772 | ||||||||
\(738\) | −6.61911 | −0.243653 | ||||||||
\(739\) | 2.79635 | 0.102865 | 0.0514327 | − | 0.998676i | \(-0.483621\pi\) | ||||
0.0514327 | + | 0.998676i | \(0.483621\pi\) | |||||||
\(740\) | −4.61466 | −0.169638 | ||||||||
\(741\) | 16.7874 | 0.616700 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.56515 | 0.130793 | 0.0653964 | − | 0.997859i | \(-0.479169\pi\) | ||||
0.0653964 | + | 0.997859i | \(0.479169\pi\) | |||||||
\(744\) | −9.68486 | −0.355064 | ||||||||
\(745\) | 46.2896 | 1.69592 | ||||||||
\(746\) | −21.3060 | −0.780069 | ||||||||
\(747\) | 1.05716 | 0.0386795 | ||||||||
\(748\) | −34.8470 | −1.27413 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −8.14143 | −0.297283 | ||||||||
\(751\) | −3.79314 | −0.138413 | −0.0692067 | − | 0.997602i | \(-0.522047\pi\) | ||||
−0.0692067 | + | 0.997602i | \(0.522047\pi\) | |||||||
\(752\) | −0.218000 | −0.00794964 | ||||||||
\(753\) | 26.7064 | 0.973234 | ||||||||
\(754\) | −9.86106 | −0.359119 | ||||||||
\(755\) | 14.4057 | 0.524278 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.45659 | −0.234669 | −0.117334 | − | 0.993092i | \(-0.537435\pi\) | ||||
−0.117334 | + | 0.993092i | \(0.537435\pi\) | |||||||
\(758\) | 27.5010 | 0.998883 | ||||||||
\(759\) | 3.98310 | 0.144577 | ||||||||
\(760\) | −41.9770 | −1.52267 | ||||||||
\(761\) | −22.4004 | −0.812014 | −0.406007 | − | 0.913870i | \(-0.633079\pi\) | ||||
−0.406007 | + | 0.913870i | \(0.633079\pi\) | |||||||
\(762\) | −18.0599 | −0.654241 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −27.2878 | −0.987239 | ||||||||
\(765\) | 17.4383 | 0.630483 | ||||||||
\(766\) | −19.3429 | −0.698888 | ||||||||
\(767\) | −23.3153 | −0.841867 | ||||||||
\(768\) | 15.8156 | 0.570697 | ||||||||
\(769\) | 53.5732 | 1.93190 | 0.965950 | − | 0.258731i | \(-0.0833042\pi\) | ||||
0.965950 | + | 0.258731i | \(0.0833042\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.36432 | −0.157177 | ||||||||
\(772\) | −20.0740 | −0.722481 | ||||||||
\(773\) | −44.5244 | −1.60143 | −0.800715 | − | 0.599045i | \(-0.795547\pi\) | ||||
−0.800715 | + | 0.599045i | \(0.795547\pi\) | |||||||
\(774\) | 6.12315 | 0.220092 | ||||||||
\(775\) | −4.22817 | −0.151880 | ||||||||
\(776\) | 44.8072 | 1.60849 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.2191 | 0.617333 | ||||||||
\(779\) | 45.7717 | 1.63994 | ||||||||
\(780\) | −8.77043 | −0.314032 | ||||||||
\(781\) | 37.8007 | 1.35262 | ||||||||
\(782\) | −6.04338 | −0.216111 | ||||||||
\(783\) | 4.06198 | 0.145163 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −35.2599 | −1.25848 | ||||||||
\(786\) | −10.5070 | −0.374772 | ||||||||
\(787\) | −15.2713 | −0.544364 | −0.272182 | − | 0.962246i | \(-0.587745\pi\) | ||||
−0.272182 | + | 0.962246i | \(0.587745\pi\) | |||||||
\(788\) | −13.3531 | −0.475685 | ||||||||
\(789\) | −1.54914 | −0.0551509 | ||||||||
\(790\) | −15.3738 | −0.546975 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 11.2026 | 0.398068 | ||||||||
\(793\) | −10.4218 | −0.370090 | ||||||||
\(794\) | 23.4434 | 0.831977 | ||||||||
\(795\) | 23.8852 | 0.847122 | ||||||||
\(796\) | 4.58119 | 0.162376 | ||||||||
\(797\) | 38.5369 | 1.36505 | 0.682524 | − | 0.730863i | \(-0.260882\pi\) | ||||
0.682524 | + | 0.730863i | \(0.260882\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.2797 | 0.752822 | ||||||||
\(800\) | 6.98297 | 0.246885 | ||||||||
\(801\) | −3.30053 | −0.116619 | ||||||||
\(802\) | −29.5594 | −1.04378 | ||||||||
\(803\) | −51.3904 | −1.81353 | ||||||||
\(804\) | 5.59599 | 0.197355 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.35951 | −0.294451 | ||||||||
\(807\) | 3.71532 | 0.130786 | ||||||||
\(808\) | −19.5873 | −0.689080 | ||||||||
\(809\) | −36.3518 | −1.27806 | −0.639031 | − | 0.769181i | \(-0.720664\pi\) | ||||
−0.639031 | + | 0.769181i | \(0.720664\pi\) | |||||||
\(810\) | −2.15832 | −0.0758356 | ||||||||
\(811\) | −21.9469 | −0.770661 | −0.385330 | − | 0.922779i | \(-0.625912\pi\) | ||||
−0.385330 | + | 0.922779i | \(0.625912\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.02009 | −0.140991 | ||||||||
\(814\) | 5.08774 | 0.178325 | ||||||||
\(815\) | 41.7999 | 1.46419 | ||||||||
\(816\) | 0.500218 | 0.0175111 | ||||||||
\(817\) | −42.3421 | −1.48136 | ||||||||
\(818\) | 13.1006 | 0.458053 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −23.9130 | −0.835080 | ||||||||
\(821\) | −13.0796 | −0.456481 | −0.228241 | − | 0.973605i | \(-0.573297\pi\) | ||||
−0.228241 | + | 0.973605i | \(0.573297\pi\) | |||||||
\(822\) | 0.716651 | 0.0249961 | ||||||||
\(823\) | 31.6053 | 1.10169 | 0.550845 | − | 0.834608i | \(-0.314306\pi\) | ||||
0.550845 | + | 0.834608i | \(0.314306\pi\) | |||||||
\(824\) | −16.8890 | −0.588355 | ||||||||
\(825\) | 4.89079 | 0.170275 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.5412 | 0.749060 | 0.374530 | − | 0.927215i | \(-0.377804\pi\) | ||||
0.374530 | + | 0.927215i | \(0.377804\pi\) | |||||||
\(828\) | −1.25202 | −0.0435106 | ||||||||
\(829\) | 33.3139 | 1.15704 | 0.578519 | − | 0.815669i | \(-0.303631\pi\) | ||||
0.578519 | + | 0.815669i | \(0.303631\pi\) | |||||||
\(830\) | −2.28169 | −0.0791986 | ||||||||
\(831\) | 11.3927 | 0.395209 | ||||||||
\(832\) | 13.4041 | 0.464704 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.472299 | −0.0163544 | ||||||||
\(835\) | −44.5505 | −1.54173 | ||||||||
\(836\) | −29.8246 | −1.03151 | ||||||||
\(837\) | 3.44346 | 0.119023 | ||||||||
\(838\) | 12.1516 | 0.419769 | ||||||||
\(839\) | 4.75994 | 0.164331 | 0.0821656 | − | 0.996619i | \(-0.473816\pi\) | ||||
0.0821656 | + | 0.996619i | \(0.473816\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.5003 | −0.431045 | ||||||||
\(842\) | −22.5654 | −0.777653 | ||||||||
\(843\) | 27.9503 | 0.962661 | ||||||||
\(844\) | 35.2891 | 1.21470 | ||||||||
\(845\) | 12.7794 | 0.439625 | ||||||||
\(846\) | −2.63377 | −0.0905507 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.685147 | 0.0235281 | ||||||||
\(849\) | 29.9754 | 1.02875 | ||||||||
\(850\) | −7.42057 | −0.254524 | ||||||||
\(851\) | −1.47693 | −0.0506283 | ||||||||
\(852\) | −11.8820 | −0.407070 | ||||||||
\(853\) | 34.8330 | 1.19266 | 0.596330 | − | 0.802740i | \(-0.296625\pi\) | ||||
0.596330 | + | 0.802740i | \(0.296625\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.9250 | 0.510423 | ||||||||
\(856\) | −16.0820 | −0.549672 | ||||||||
\(857\) | 19.8576 | 0.678323 | 0.339161 | − | 0.940728i | \(-0.389857\pi\) | ||||
0.339161 | + | 0.940728i | \(0.389857\pi\) | |||||||
\(858\) | 9.66956 | 0.330113 | ||||||||
\(859\) | 33.7997 | 1.15323 | 0.576615 | − | 0.817016i | \(-0.304373\pi\) | ||||
0.576615 | + | 0.817016i | \(0.304373\pi\) | |||||||
\(860\) | 22.1213 | 0.754329 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.67627 | 0.0911541 | ||||||||
\(863\) | 35.6001 | 1.21184 | 0.605921 | − | 0.795525i | \(-0.292805\pi\) | ||||
0.605921 | + | 0.795525i | \(0.292805\pi\) | |||||||
\(864\) | −5.68699 | −0.193475 | ||||||||
\(865\) | −6.62224 | −0.225163 | ||||||||
\(866\) | 16.4181 | 0.557911 | ||||||||
\(867\) | −31.8279 | −1.08093 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.3718 | −0.962446 | ||||||||
\(870\) | −8.76706 | −0.297231 | ||||||||
\(871\) | 12.5460 | 0.425106 | ||||||||
\(872\) | −17.5948 | −0.595836 | ||||||||
\(873\) | −15.9312 | −0.539191 | ||||||||
\(874\) | −5.17236 | −0.174958 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16.1537 | 0.545782 | ||||||||
\(877\) | 14.8802 | 0.502470 | 0.251235 | − | 0.967926i | \(-0.419163\pi\) | ||||
0.251235 | + | 0.967926i | \(0.419163\pi\) | |||||||
\(878\) | −10.3534 | −0.349411 | ||||||||
\(879\) | 4.87346 | 0.164378 | ||||||||
\(880\) | 0.711568 | 0.0239869 | ||||||||
\(881\) | −25.2288 | −0.849980 | −0.424990 | − | 0.905198i | \(-0.639722\pi\) | ||||
−0.424990 | + | 0.905198i | \(0.639722\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.13080 | −0.172665 | −0.0863325 | − | 0.996266i | \(-0.527515\pi\) | ||||
−0.0863325 | + | 0.996266i | \(0.527515\pi\) | |||||||
\(884\) | 24.5575 | 0.825959 | ||||||||
\(885\) | −20.7287 | −0.696787 | ||||||||
\(886\) | 16.8492 | 0.566059 | ||||||||
\(887\) | −4.27219 | −0.143446 | −0.0717231 | − | 0.997425i | \(-0.522850\pi\) | ||||
−0.0717231 | + | 0.997425i | \(0.522850\pi\) | |||||||
\(888\) | −4.15391 | −0.139396 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.12361 | 0.238784 | ||||||||
\(891\) | −3.98310 | −0.133439 | ||||||||
\(892\) | −30.3340 | −1.01566 | ||||||||
\(893\) | 18.2127 | 0.609465 | ||||||||
\(894\) | 16.0420 | 0.536525 | ||||||||
\(895\) | −28.6233 | −0.956772 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.80699 | −0.0937225 | ||||||||
\(898\) | −22.4308 | −0.748526 | ||||||||
\(899\) | 13.9873 | 0.466501 | ||||||||
\(900\) | −1.53733 | −0.0512445 | ||||||||
\(901\) | −66.8795 | −2.22808 | ||||||||
\(902\) | 26.3646 | 0.877844 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.6748 | 0.355039 | ||||||||
\(905\) | 39.5280 | 1.31396 | ||||||||
\(906\) | 4.99241 | 0.165862 | ||||||||
\(907\) | −29.2234 | −0.970346 | −0.485173 | − | 0.874418i | \(-0.661243\pi\) | ||||
−0.485173 | + | 0.874418i | \(0.661243\pi\) | |||||||
\(908\) | 10.0619 | 0.333916 | ||||||||
\(909\) | 6.96429 | 0.230991 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.3422 | −1.60165 | −0.800824 | − | 0.598900i | \(-0.795605\pi\) | ||||
−0.800824 | + | 0.598900i | \(0.795605\pi\) | |||||||
\(912\) | 0.428122 | 0.0141766 | ||||||||
\(913\) | −4.21077 | −0.139356 | ||||||||
\(914\) | 3.98987 | 0.131973 | ||||||||
\(915\) | −9.26560 | −0.306311 | ||||||||
\(916\) | −17.2516 | −0.570008 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.04338 | 0.199461 | ||||||||
\(919\) | 30.7928 | 1.01576 | 0.507881 | − | 0.861427i | \(-0.330429\pi\) | ||||
0.507881 | + | 0.861427i | \(0.330429\pi\) | |||||||
\(920\) | 7.01890 | 0.231406 | ||||||||
\(921\) | 27.9064 | 0.919547 | ||||||||
\(922\) | 11.9507 | 0.393575 | ||||||||
\(923\) | −26.6391 | −0.876835 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.81349 | −0.0596273 | ||||||||
\(926\) | −29.5169 | −0.969985 | ||||||||
\(927\) | 6.00488 | 0.197226 | ||||||||
\(928\) | −23.1004 | −0.758309 | ||||||||
\(929\) | −24.6571 | −0.808975 | −0.404487 | − | 0.914544i | \(-0.632550\pi\) | ||||
−0.404487 | + | 0.914544i | \(0.632550\pi\) | |||||||
\(930\) | −7.43209 | −0.243708 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.29872 | 0.0752970 | ||||||||
\(933\) | −27.0086 | −0.884221 | ||||||||
\(934\) | −24.1915 | −0.791569 | ||||||||
\(935\) | −69.4585 | −2.27154 | ||||||||
\(936\) | −7.89475 | −0.258048 | ||||||||
\(937\) | 35.2046 | 1.15008 | 0.575042 | − | 0.818124i | \(-0.304986\pi\) | ||||
0.575042 | + | 0.818124i | \(0.304986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.21402 | −0.137519 | ||||||||
\(940\) | −9.51508 | −0.310348 | ||||||||
\(941\) | −22.0830 | −0.719885 | −0.359942 | − | 0.932975i | \(-0.617204\pi\) | ||||
−0.359942 | + | 0.932975i | \(0.617204\pi\) | |||||||
\(942\) | −12.2196 | −0.398135 | ||||||||
\(943\) | −7.65339 | −0.249229 | ||||||||
\(944\) | −0.594602 | −0.0193526 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.3891 | −0.792958 | ||||||||
\(947\) | 5.85753 | 0.190344 | 0.0951720 | − | 0.995461i | \(-0.469660\pi\) | ||||
0.0951720 | + | 0.995461i | \(0.469660\pi\) | |||||||
\(948\) | 8.91818 | 0.289649 | ||||||||
\(949\) | 36.2160 | 1.17562 | ||||||||
\(950\) | −6.35106 | −0.206056 | ||||||||
\(951\) | 7.99795 | 0.259351 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.8701 | −1.58306 | −0.791530 | − | 0.611131i | \(-0.790715\pi\) | ||||
−0.791530 | + | 0.611131i | \(0.790715\pi\) | |||||||
\(954\) | 8.27760 | 0.267997 | ||||||||
\(955\) | −54.3912 | −1.76006 | ||||||||
\(956\) | 5.53650 | 0.179063 | ||||||||
\(957\) | −16.1793 | −0.523001 | ||||||||
\(958\) | −28.2177 | −0.911672 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 11.9170 | 0.384621 | ||||||||
\(961\) | −19.1426 | −0.617503 | ||||||||
\(962\) | −3.58545 | −0.115600 | ||||||||
\(963\) | 5.71797 | 0.184259 | ||||||||
\(964\) | 35.6310 | 1.14760 | ||||||||
\(965\) | −40.0124 | −1.28804 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.7300 | 0.377213 | 0.188606 | − | 0.982053i | \(-0.439603\pi\) | ||||
0.188606 | + | 0.982053i | \(0.439603\pi\) | |||||||
\(968\) | −13.6832 | −0.439794 | ||||||||
\(969\) | −41.7905 | −1.34250 | ||||||||
\(970\) | 34.3847 | 1.10403 | ||||||||
\(971\) | −24.3527 | −0.781516 | −0.390758 | − | 0.920493i | \(-0.627787\pi\) | ||||
−0.390758 | + | 0.920493i | \(0.627787\pi\) | |||||||
\(972\) | 1.25202 | 0.0401585 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −22.4363 | −0.718905 | ||||||||
\(975\) | −3.44666 | −0.110381 | ||||||||
\(976\) | −0.265784 | −0.00850753 | ||||||||
\(977\) | 50.9094 | 1.62874 | 0.814368 | − | 0.580348i | \(-0.197084\pi\) | ||||
0.814368 | + | 0.580348i | \(0.197084\pi\) | |||||||
\(978\) | 14.4861 | 0.463214 | ||||||||
\(979\) | 13.1463 | 0.420159 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.25586 | 0.199734 | ||||||||
\(982\) | 22.4868 | 0.717581 | ||||||||
\(983\) | −33.5958 | −1.07154 | −0.535770 | − | 0.844364i | \(-0.679979\pi\) | ||||
−0.535770 | + | 0.844364i | \(0.679979\pi\) | |||||||
\(984\) | −21.5255 | −0.686207 | ||||||||
\(985\) | −26.6160 | −0.848056 | ||||||||
\(986\) | 24.5481 | 0.781770 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 21.0181 | 0.668675 | ||||||||
\(989\) | 7.07993 | 0.225129 | ||||||||
\(990\) | 8.59680 | 0.273224 | ||||||||
\(991\) | 10.4350 | 0.331480 | 0.165740 | − | 0.986169i | \(-0.446999\pi\) | ||||
0.165740 | + | 0.986169i | \(0.446999\pi\) | |||||||
\(992\) | −19.5829 | −0.621758 | ||||||||
\(993\) | −24.0871 | −0.764382 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.13142 | 0.289485 | ||||||||
\(996\) | 1.32358 | 0.0419394 | ||||||||
\(997\) | 15.1736 | 0.480553 | 0.240277 | − | 0.970704i | \(-0.422762\pi\) | ||||
0.240277 | + | 0.970704i | \(0.422762\pi\) | |||||||
\(998\) | −20.0710 | −0.635335 | ||||||||
\(999\) | 1.47693 | 0.0467278 |
(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 | 3381.2.a.bi.1.6 | 10 | ||
7.2 | even | 3 | 483.2.i.h.277.5 | ✓ | 20 | ||
7.4 | even | 3 | 483.2.i.h.415.5 | yes | 20 | ||
7.6 | odd | 2 | 3381.2.a.bj.1.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.h.277.5 | ✓ | 20 | 7.2 | even | 3 | ||
483.2.i.h.415.5 | yes | 20 | 7.4 | even | 3 | ||
3381.2.a.bi.1.6 | 10 | 1.1 | even | 1 | trivial | ||
3381.2.a.bj.1.6 | 10 | 7.6 | odd | 2 |