Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [931,2,Mod(1,931)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(931, 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("931.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 931 = 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 931.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: | \(7.43407242818\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 133) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 931.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.30278 | 0.921201 | 0.460601 | − | 0.887607i | \(-0.347634\pi\) | ||||
0.460601 | + | 0.887607i | \(0.347634\pi\) | |||||||
\(3\) | 3.30278 | 1.90686 | 0.953429 | − | 0.301617i | \(-0.0975264\pi\) | ||||
0.953429 | + | 0.301617i | \(0.0975264\pi\) | |||||||
\(4\) | −0.302776 | −0.151388 | ||||||||
\(5\) | 3.00000 | 1.34164 | 0.670820 | − | 0.741620i | \(-0.265942\pi\) | ||||
0.670820 | + | 0.741620i | \(0.265942\pi\) | |||||||
\(6\) | 4.30278 | 1.75660 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 7.90833 | 2.63611 | ||||||||
\(10\) | 3.90833 | 1.23592 | ||||||||
\(11\) | −4.30278 | −1.29734 | −0.648668 | − | 0.761072i | \(-0.724674\pi\) | ||||
−0.648668 | + | 0.761072i | \(0.724674\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.60555 | −0.445300 | −0.222650 | − | 0.974898i | \(-0.571471\pi\) | ||||
−0.222650 | + | 0.974898i | \(0.571471\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.90833 | 2.55832 | ||||||||
\(16\) | −3.30278 | −0.825694 | ||||||||
\(17\) | 1.69722 | 0.411637 | 0.205819 | − | 0.978590i | \(-0.434014\pi\) | ||||
0.205819 | + | 0.978590i | \(0.434014\pi\) | |||||||
\(18\) | 10.3028 | 2.42839 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −0.908327 | −0.203108 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.60555 | −1.19511 | ||||||||
\(23\) | −3.00000 | −0.625543 | −0.312772 | − | 0.949828i | \(-0.601257\pi\) | ||||
−0.312772 | + | 0.949828i | \(0.601257\pi\) | |||||||
\(24\) | −9.90833 | −2.02253 | ||||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | −2.09167 | −0.410211 | ||||||||
\(27\) | 16.2111 | 3.11983 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.908327 | −0.168672 | −0.0843360 | − | 0.996437i | \(-0.526877\pi\) | ||||
−0.0843360 | + | 0.996437i | \(0.526877\pi\) | |||||||
\(30\) | 12.9083 | 2.35673 | ||||||||
\(31\) | 2.30278 | 0.413591 | 0.206795 | − | 0.978384i | \(-0.433697\pi\) | ||||
0.206795 | + | 0.978384i | \(0.433697\pi\) | |||||||
\(32\) | 1.69722 | 0.300030 | ||||||||
\(33\) | −14.2111 | −2.47384 | ||||||||
\(34\) | 2.21110 | 0.379201 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.39445 | −0.399075 | ||||||||
\(37\) | −3.60555 | −0.592749 | −0.296374 | − | 0.955072i | \(-0.595778\pi\) | ||||
−0.296374 | + | 0.955072i | \(0.595778\pi\) | |||||||
\(38\) | −1.30278 | −0.211338 | ||||||||
\(39\) | −5.30278 | −0.849124 | ||||||||
\(40\) | −9.00000 | −1.42302 | ||||||||
\(41\) | −4.30278 | −0.671981 | −0.335990 | − | 0.941865i | \(-0.609071\pi\) | ||||
−0.335990 | + | 0.941865i | \(0.609071\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0000 | −1.52499 | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 1.30278 | 0.196401 | ||||||||
\(45\) | 23.7250 | 3.53671 | ||||||||
\(46\) | −3.90833 | −0.576251 | ||||||||
\(47\) | 8.21110 | 1.19771 | 0.598856 | − | 0.800857i | \(-0.295622\pi\) | ||||
0.598856 | + | 0.800857i | \(0.295622\pi\) | |||||||
\(48\) | −10.9083 | −1.57448 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.21110 | 0.736961 | ||||||||
\(51\) | 5.60555 | 0.784934 | ||||||||
\(52\) | 0.486122 | 0.0674130 | ||||||||
\(53\) | 3.90833 | 0.536850 | 0.268425 | − | 0.963301i | \(-0.413497\pi\) | ||||
0.268425 | + | 0.963301i | \(0.413497\pi\) | |||||||
\(54\) | 21.1194 | 2.87399 | ||||||||
\(55\) | −12.9083 | −1.74056 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.30278 | −0.437463 | ||||||||
\(58\) | −1.18335 | −0.155381 | ||||||||
\(59\) | −8.21110 | −1.06899 | −0.534497 | − | 0.845170i | \(-0.679499\pi\) | ||||
−0.534497 | + | 0.845170i | \(0.679499\pi\) | |||||||
\(60\) | −3.00000 | −0.387298 | ||||||||
\(61\) | −10.2111 | −1.30740 | −0.653699 | − | 0.756755i | \(-0.726784\pi\) | ||||
−0.653699 | + | 0.756755i | \(0.726784\pi\) | |||||||
\(62\) | 3.00000 | 0.381000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.81665 | 1.10208 | ||||||||
\(65\) | −4.81665 | −0.597432 | ||||||||
\(66\) | −18.5139 | −2.27890 | ||||||||
\(67\) | 8.90833 | 1.08833 | 0.544163 | − | 0.838980i | \(-0.316847\pi\) | ||||
0.544163 | + | 0.838980i | \(0.316847\pi\) | |||||||
\(68\) | −0.513878 | −0.0623169 | ||||||||
\(69\) | −9.90833 | −1.19282 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.21110 | −0.262410 | −0.131205 | − | 0.991355i | \(-0.541885\pi\) | ||||
−0.131205 | + | 0.991355i | \(0.541885\pi\) | |||||||
\(72\) | −23.7250 | −2.79602 | ||||||||
\(73\) | 16.5139 | 1.93280 | 0.966402 | − | 0.257037i | \(-0.0827461\pi\) | ||||
0.966402 | + | 0.257037i | \(0.0827461\pi\) | |||||||
\(74\) | −4.69722 | −0.546041 | ||||||||
\(75\) | 13.2111 | 1.52549 | ||||||||
\(76\) | 0.302776 | 0.0347307 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.90833 | −0.782214 | ||||||||
\(79\) | −3.21110 | −0.361277 | −0.180639 | − | 0.983550i | \(-0.557816\pi\) | ||||
−0.180639 | + | 0.983550i | \(0.557816\pi\) | |||||||
\(80\) | −9.90833 | −1.10778 | ||||||||
\(81\) | 29.8167 | 3.31296 | ||||||||
\(82\) | −5.60555 | −0.619030 | ||||||||
\(83\) | 2.09167 | 0.229591 | 0.114795 | − | 0.993389i | \(-0.463379\pi\) | ||||
0.114795 | + | 0.993389i | \(0.463379\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.09167 | 0.552269 | ||||||||
\(86\) | −13.0278 | −1.40482 | ||||||||
\(87\) | −3.00000 | −0.321634 | ||||||||
\(88\) | 12.9083 | 1.37603 | ||||||||
\(89\) | 3.39445 | 0.359811 | 0.179905 | − | 0.983684i | \(-0.442421\pi\) | ||||
0.179905 | + | 0.983684i | \(0.442421\pi\) | |||||||
\(90\) | 30.9083 | 3.25802 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.908327 | 0.0946996 | ||||||||
\(93\) | 7.60555 | 0.788659 | ||||||||
\(94\) | 10.6972 | 1.10333 | ||||||||
\(95\) | −3.00000 | −0.307794 | ||||||||
\(96\) | 5.60555 | 0.572114 | ||||||||
\(97\) | −2.39445 | −0.243119 | −0.121560 | − | 0.992584i | \(-0.538790\pi\) | ||||
−0.121560 | + | 0.992584i | \(0.538790\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −34.0278 | −3.41992 | ||||||||
\(100\) | −1.21110 | −0.121110 | ||||||||
\(101\) | 11.6056 | 1.15480 | 0.577398 | − | 0.816463i | \(-0.304068\pi\) | ||||
0.577398 | + | 0.816463i | \(0.304068\pi\) | |||||||
\(102\) | 7.30278 | 0.723083 | ||||||||
\(103\) | 1.78890 | 0.176265 | 0.0881327 | − | 0.996109i | \(-0.471910\pi\) | ||||
0.0881327 | + | 0.996109i | \(0.471910\pi\) | |||||||
\(104\) | 4.81665 | 0.472312 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.09167 | 0.494547 | ||||||||
\(107\) | −20.2111 | −1.95388 | −0.976941 | − | 0.213512i | \(-0.931510\pi\) | ||||
−0.976941 | + | 0.213512i | \(0.931510\pi\) | |||||||
\(108\) | −4.90833 | −0.472304 | ||||||||
\(109\) | 4.21110 | 0.403350 | 0.201675 | − | 0.979452i | \(-0.435361\pi\) | ||||
0.201675 | + | 0.979452i | \(0.435361\pi\) | |||||||
\(110\) | −16.8167 | −1.60341 | ||||||||
\(111\) | −11.9083 | −1.13029 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3028 | 1.25142 | 0.625710 | − | 0.780056i | \(-0.284809\pi\) | ||||
0.625710 | + | 0.780056i | \(0.284809\pi\) | |||||||
\(114\) | −4.30278 | −0.402992 | ||||||||
\(115\) | −9.00000 | −0.839254 | ||||||||
\(116\) | 0.275019 | 0.0255349 | ||||||||
\(117\) | −12.6972 | −1.17386 | ||||||||
\(118\) | −10.6972 | −0.984759 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −29.7250 | −2.71351 | ||||||||
\(121\) | 7.51388 | 0.683080 | ||||||||
\(122\) | −13.3028 | −1.20438 | ||||||||
\(123\) | −14.2111 | −1.28137 | ||||||||
\(124\) | −0.697224 | −0.0626126 | ||||||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.81665 | 0.871087 | 0.435544 | − | 0.900168i | \(-0.356556\pi\) | ||||
0.435544 | + | 0.900168i | \(0.356556\pi\) | |||||||
\(128\) | 8.09167 | 0.715210 | ||||||||
\(129\) | −33.0278 | −2.90793 | ||||||||
\(130\) | −6.27502 | −0.550356 | ||||||||
\(131\) | 2.48612 | 0.217213 | 0.108607 | − | 0.994085i | \(-0.465361\pi\) | ||||
0.108607 | + | 0.994085i | \(0.465361\pi\) | |||||||
\(132\) | 4.30278 | 0.374509 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.6056 | 1.00257 | ||||||||
\(135\) | 48.6333 | 4.18569 | ||||||||
\(136\) | −5.09167 | −0.436607 | ||||||||
\(137\) | −21.6333 | −1.84826 | −0.924129 | − | 0.382080i | \(-0.875208\pi\) | ||||
−0.924129 | + | 0.382080i | \(0.875208\pi\) | |||||||
\(138\) | −12.9083 | −1.09883 | ||||||||
\(139\) | −5.00000 | −0.424094 | −0.212047 | − | 0.977259i | \(-0.568013\pi\) | ||||
−0.212047 | + | 0.977259i | \(0.568013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 27.1194 | 2.28387 | ||||||||
\(142\) | −2.88057 | −0.241732 | ||||||||
\(143\) | 6.90833 | 0.577703 | ||||||||
\(144\) | −26.1194 | −2.17662 | ||||||||
\(145\) | −2.72498 | −0.226297 | ||||||||
\(146\) | 21.5139 | 1.78050 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.09167 | 0.0897350 | ||||||||
\(149\) | 8.21110 | 0.672680 | 0.336340 | − | 0.941741i | \(-0.390811\pi\) | ||||
0.336340 | + | 0.941741i | \(0.390811\pi\) | |||||||
\(150\) | 17.2111 | 1.40528 | ||||||||
\(151\) | −4.90833 | −0.399434 | −0.199717 | − | 0.979854i | \(-0.564002\pi\) | ||||
−0.199717 | + | 0.979854i | \(0.564002\pi\) | |||||||
\(152\) | 3.00000 | 0.243332 | ||||||||
\(153\) | 13.4222 | 1.08512 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.90833 | 0.554890 | ||||||||
\(156\) | 1.60555 | 0.128547 | ||||||||
\(157\) | 13.5139 | 1.07852 | 0.539262 | − | 0.842138i | \(-0.318703\pi\) | ||||
0.539262 | + | 0.842138i | \(0.318703\pi\) | |||||||
\(158\) | −4.18335 | −0.332809 | ||||||||
\(159\) | 12.9083 | 1.02370 | ||||||||
\(160\) | 5.09167 | 0.402532 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 38.8444 | 3.05191 | ||||||||
\(163\) | 9.30278 | 0.728650 | 0.364325 | − | 0.931272i | \(-0.381300\pi\) | ||||
0.364325 | + | 0.931272i | \(0.381300\pi\) | |||||||
\(164\) | 1.30278 | 0.101730 | ||||||||
\(165\) | −42.6333 | −3.31900 | ||||||||
\(166\) | 2.72498 | 0.211500 | ||||||||
\(167\) | −11.6056 | −0.898065 | −0.449032 | − | 0.893516i | \(-0.648231\pi\) | ||||
−0.449032 | + | 0.893516i | \(0.648231\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4222 | −0.801708 | ||||||||
\(170\) | 6.63331 | 0.508751 | ||||||||
\(171\) | −7.90833 | −0.604765 | ||||||||
\(172\) | 3.02776 | 0.230864 | ||||||||
\(173\) | 13.8167 | 1.05046 | 0.525230 | − | 0.850960i | \(-0.323979\pi\) | ||||
0.525230 | + | 0.850960i | \(0.323979\pi\) | |||||||
\(174\) | −3.90833 | −0.296289 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 14.2111 | 1.07120 | ||||||||
\(177\) | −27.1194 | −2.03842 | ||||||||
\(178\) | 4.42221 | 0.331458 | ||||||||
\(179\) | 20.7250 | 1.54906 | 0.774529 | − | 0.632539i | \(-0.217987\pi\) | ||||
0.774529 | + | 0.632539i | \(0.217987\pi\) | |||||||
\(180\) | −7.18335 | −0.535415 | ||||||||
\(181\) | 14.3028 | 1.06312 | 0.531558 | − | 0.847022i | \(-0.321607\pi\) | ||||
0.531558 | + | 0.847022i | \(0.321607\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −33.7250 | −2.49302 | ||||||||
\(184\) | 9.00000 | 0.663489 | ||||||||
\(185\) | −10.8167 | −0.795256 | ||||||||
\(186\) | 9.90833 | 0.726514 | ||||||||
\(187\) | −7.30278 | −0.534032 | ||||||||
\(188\) | −2.48612 | −0.181319 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.90833 | −0.283540 | ||||||||
\(191\) | −14.3305 | −1.03692 | −0.518460 | − | 0.855102i | \(-0.673495\pi\) | ||||
−0.518460 | + | 0.855102i | \(0.673495\pi\) | |||||||
\(192\) | 29.1194 | 2.10151 | ||||||||
\(193\) | 2.11943 | 0.152560 | 0.0762799 | − | 0.997086i | \(-0.475696\pi\) | ||||
0.0762799 | + | 0.997086i | \(0.475696\pi\) | |||||||
\(194\) | −3.11943 | −0.223962 | ||||||||
\(195\) | −15.9083 | −1.13922 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.90833 | 0.278457 | 0.139228 | − | 0.990260i | \(-0.455538\pi\) | ||||
0.139228 | + | 0.990260i | \(0.455538\pi\) | |||||||
\(198\) | −44.3305 | −3.15043 | ||||||||
\(199\) | −15.4222 | −1.09325 | −0.546626 | − | 0.837377i | \(-0.684088\pi\) | ||||
−0.546626 | + | 0.837377i | \(0.684088\pi\) | |||||||
\(200\) | −12.0000 | −0.848528 | ||||||||
\(201\) | 29.4222 | 2.07528 | ||||||||
\(202\) | 15.1194 | 1.06380 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.69722 | −0.118829 | ||||||||
\(205\) | −12.9083 | −0.901557 | ||||||||
\(206\) | 2.33053 | 0.162376 | ||||||||
\(207\) | −23.7250 | −1.64900 | ||||||||
\(208\) | 5.30278 | 0.367681 | ||||||||
\(209\) | 4.30278 | 0.297629 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.3028 | −0.778115 | −0.389058 | − | 0.921213i | \(-0.627199\pi\) | ||||
−0.389058 | + | 0.921213i | \(0.627199\pi\) | |||||||
\(212\) | −1.18335 | −0.0812725 | ||||||||
\(213\) | −7.30278 | −0.500378 | ||||||||
\(214\) | −26.3305 | −1.79992 | ||||||||
\(215\) | −30.0000 | −2.04598 | ||||||||
\(216\) | −48.6333 | −3.30908 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.48612 | 0.371567 | ||||||||
\(219\) | 54.5416 | 3.68558 | ||||||||
\(220\) | 3.90833 | 0.263499 | ||||||||
\(221\) | −2.72498 | −0.183302 | ||||||||
\(222\) | −15.5139 | −1.04122 | ||||||||
\(223\) | 8.81665 | 0.590407 | 0.295203 | − | 0.955434i | \(-0.404613\pi\) | ||||
0.295203 | + | 0.955434i | \(0.404613\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 31.6333 | 2.10889 | ||||||||
\(226\) | 17.3305 | 1.15281 | ||||||||
\(227\) | −0.119429 | −0.00792681 | −0.00396341 | − | 0.999992i | \(-0.501262\pi\) | ||||
−0.00396341 | + | 0.999992i | \(0.501262\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 15.2111 | 1.00518 | 0.502589 | − | 0.864525i | \(-0.332381\pi\) | ||||
0.502589 | + | 0.864525i | \(0.332381\pi\) | |||||||
\(230\) | −11.7250 | −0.773122 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.72498 | 0.178904 | ||||||||
\(233\) | −12.9083 | −0.845653 | −0.422826 | − | 0.906211i | \(-0.638962\pi\) | ||||
−0.422826 | + | 0.906211i | \(0.638962\pi\) | |||||||
\(234\) | −16.5416 | −1.08136 | ||||||||
\(235\) | 24.6333 | 1.60690 | ||||||||
\(236\) | 2.48612 | 0.161833 | ||||||||
\(237\) | −10.6056 | −0.688905 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.42221 | 0.0919948 | 0.0459974 | − | 0.998942i | \(-0.485353\pi\) | ||||
0.0459974 | + | 0.998942i | \(0.485353\pi\) | |||||||
\(240\) | −32.7250 | −2.11239 | ||||||||
\(241\) | 13.3944 | 0.862812 | 0.431406 | − | 0.902158i | \(-0.358018\pi\) | ||||
0.431406 | + | 0.902158i | \(0.358018\pi\) | |||||||
\(242\) | 9.78890 | 0.629254 | ||||||||
\(243\) | 49.8444 | 3.19752 | ||||||||
\(244\) | 3.09167 | 0.197924 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −18.5139 | −1.18040 | ||||||||
\(247\) | 1.60555 | 0.102159 | ||||||||
\(248\) | −6.90833 | −0.438679 | ||||||||
\(249\) | 6.90833 | 0.437797 | ||||||||
\(250\) | −3.90833 | −0.247184 | ||||||||
\(251\) | 5.09167 | 0.321384 | 0.160692 | − | 0.987005i | \(-0.448627\pi\) | ||||
0.160692 | + | 0.987005i | \(0.448627\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.9083 | 0.811540 | ||||||||
\(254\) | 12.7889 | 0.802447 | ||||||||
\(255\) | 16.8167 | 1.05310 | ||||||||
\(256\) | −7.09167 | −0.443230 | ||||||||
\(257\) | −9.90833 | −0.618064 | −0.309032 | − | 0.951052i | \(-0.600005\pi\) | ||||
−0.309032 | + | 0.951052i | \(0.600005\pi\) | |||||||
\(258\) | −43.0278 | −2.67879 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.45837 | 0.0904440 | ||||||||
\(261\) | −7.18335 | −0.444638 | ||||||||
\(262\) | 3.23886 | 0.200097 | ||||||||
\(263\) | −13.3028 | −0.820284 | −0.410142 | − | 0.912022i | \(-0.634521\pi\) | ||||
−0.410142 | + | 0.912022i | \(0.634521\pi\) | |||||||
\(264\) | 42.6333 | 2.62390 | ||||||||
\(265\) | 11.7250 | 0.720260 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.2111 | 0.686108 | ||||||||
\(268\) | −2.69722 | −0.164759 | ||||||||
\(269\) | 11.7250 | 0.714885 | 0.357442 | − | 0.933935i | \(-0.383649\pi\) | ||||
0.357442 | + | 0.933935i | \(0.383649\pi\) | |||||||
\(270\) | 63.3583 | 3.85586 | ||||||||
\(271\) | −7.09167 | −0.430788 | −0.215394 | − | 0.976527i | \(-0.569104\pi\) | ||||
−0.215394 | + | 0.976527i | \(0.569104\pi\) | |||||||
\(272\) | −5.60555 | −0.339886 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −28.1833 | −1.70262 | ||||||||
\(275\) | −17.2111 | −1.03787 | ||||||||
\(276\) | 3.00000 | 0.180579 | ||||||||
\(277\) | −6.60555 | −0.396889 | −0.198445 | − | 0.980112i | \(-0.563589\pi\) | ||||
−0.198445 | + | 0.980112i | \(0.563589\pi\) | |||||||
\(278\) | −6.51388 | −0.390676 | ||||||||
\(279\) | 18.2111 | 1.09027 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.00000 | 0.178965 | 0.0894825 | − | 0.995988i | \(-0.471479\pi\) | ||||
0.0894825 | + | 0.995988i | \(0.471479\pi\) | |||||||
\(282\) | 35.3305 | 2.10390 | ||||||||
\(283\) | 12.3305 | 0.732974 | 0.366487 | − | 0.930423i | \(-0.380560\pi\) | ||||
0.366487 | + | 0.930423i | \(0.380560\pi\) | |||||||
\(284\) | 0.669468 | 0.0397256 | ||||||||
\(285\) | −9.90833 | −0.586919 | ||||||||
\(286\) | 9.00000 | 0.532181 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 13.4222 | 0.790911 | ||||||||
\(289\) | −14.1194 | −0.830555 | ||||||||
\(290\) | −3.55004 | −0.208465 | ||||||||
\(291\) | −7.90833 | −0.463594 | ||||||||
\(292\) | −5.00000 | −0.292603 | ||||||||
\(293\) | −30.6333 | −1.78962 | −0.894808 | − | 0.446450i | \(-0.852688\pi\) | ||||
−0.894808 | + | 0.446450i | \(0.852688\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.6333 | −1.43421 | ||||||||
\(296\) | 10.8167 | 0.628705 | ||||||||
\(297\) | −69.7527 | −4.04746 | ||||||||
\(298\) | 10.6972 | 0.619674 | ||||||||
\(299\) | 4.81665 | 0.278554 | ||||||||
\(300\) | −4.00000 | −0.230940 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.39445 | −0.367959 | ||||||||
\(303\) | 38.3305 | 2.20203 | ||||||||
\(304\) | 3.30278 | 0.189427 | ||||||||
\(305\) | −30.6333 | −1.75406 | ||||||||
\(306\) | 17.4861 | 0.999615 | ||||||||
\(307\) | −18.3028 | −1.04459 | −0.522297 | − | 0.852763i | \(-0.674925\pi\) | ||||
−0.522297 | + | 0.852763i | \(0.674925\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.90833 | 0.336113 | ||||||||
\(310\) | 9.00000 | 0.511166 | ||||||||
\(311\) | −15.5139 | −0.879711 | −0.439856 | − | 0.898068i | \(-0.644970\pi\) | ||||
−0.439856 | + | 0.898068i | \(0.644970\pi\) | |||||||
\(312\) | 15.9083 | 0.900632 | ||||||||
\(313\) | −9.02776 | −0.510279 | −0.255139 | − | 0.966904i | \(-0.582121\pi\) | ||||
−0.255139 | + | 0.966904i | \(0.582121\pi\) | |||||||
\(314\) | 17.6056 | 0.993539 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.972244 | 0.0546930 | ||||||||
\(317\) | 23.2111 | 1.30367 | 0.651833 | − | 0.758363i | \(-0.274000\pi\) | ||||
0.651833 | + | 0.758363i | \(0.274000\pi\) | |||||||
\(318\) | 16.8167 | 0.943031 | ||||||||
\(319\) | 3.90833 | 0.218824 | ||||||||
\(320\) | 26.4500 | 1.47860 | ||||||||
\(321\) | −66.7527 | −3.72577 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.69722 | −0.0944361 | ||||||||
\(324\) | −9.02776 | −0.501542 | ||||||||
\(325\) | −6.42221 | −0.356240 | ||||||||
\(326\) | 12.1194 | 0.671233 | ||||||||
\(327\) | 13.9083 | 0.769132 | ||||||||
\(328\) | 12.9083 | 0.712743 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −55.5416 | −3.05747 | ||||||||
\(331\) | 15.3028 | 0.841117 | 0.420558 | − | 0.907266i | \(-0.361834\pi\) | ||||
0.420558 | + | 0.907266i | \(0.361834\pi\) | |||||||
\(332\) | −0.633308 | −0.0347573 | ||||||||
\(333\) | −28.5139 | −1.56255 | ||||||||
\(334\) | −15.1194 | −0.827298 | ||||||||
\(335\) | 26.7250 | 1.46014 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.7250 | −1.34686 | −0.673428 | − | 0.739253i | \(-0.735179\pi\) | ||||
−0.673428 | + | 0.739253i | \(0.735179\pi\) | |||||||
\(338\) | −13.5778 | −0.738535 | ||||||||
\(339\) | 43.9361 | 2.38628 | ||||||||
\(340\) | −1.54163 | −0.0836069 | ||||||||
\(341\) | −9.90833 | −0.536566 | ||||||||
\(342\) | −10.3028 | −0.557110 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 30.0000 | 1.61749 | ||||||||
\(345\) | −29.7250 | −1.60034 | ||||||||
\(346\) | 18.0000 | 0.967686 | ||||||||
\(347\) | 25.5416 | 1.37115 | 0.685573 | − | 0.728004i | \(-0.259552\pi\) | ||||
0.685573 | + | 0.728004i | \(0.259552\pi\) | |||||||
\(348\) | 0.908327 | 0.0486914 | ||||||||
\(349\) | 10.5139 | 0.562795 | 0.281397 | − | 0.959591i | \(-0.409202\pi\) | ||||
0.281397 | + | 0.959591i | \(0.409202\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.0278 | −1.38926 | ||||||||
\(352\) | −7.30278 | −0.389239 | ||||||||
\(353\) | 0.908327 | 0.0483454 | 0.0241727 | − | 0.999708i | \(-0.492305\pi\) | ||||
0.0241727 | + | 0.999708i | \(0.492305\pi\) | |||||||
\(354\) | −35.3305 | −1.87780 | ||||||||
\(355\) | −6.63331 | −0.352059 | ||||||||
\(356\) | −1.02776 | −0.0544710 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 27.0000 | 1.42699 | ||||||||
\(359\) | 28.5416 | 1.50637 | 0.753185 | − | 0.657809i | \(-0.228517\pi\) | ||||
0.753185 | + | 0.657809i | \(0.228517\pi\) | |||||||
\(360\) | −71.1749 | −3.75125 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 18.6333 | 0.979345 | ||||||||
\(363\) | 24.8167 | 1.30254 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 49.5416 | 2.59313 | ||||||||
\(366\) | −43.9361 | −2.29658 | ||||||||
\(367\) | −36.0278 | −1.88063 | −0.940317 | − | 0.340300i | \(-0.889471\pi\) | ||||
−0.940317 | + | 0.340300i | \(0.889471\pi\) | |||||||
\(368\) | 9.90833 | 0.516507 | ||||||||
\(369\) | −34.0278 | −1.77141 | ||||||||
\(370\) | −14.0917 | −0.732591 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.30278 | −0.119393 | ||||||||
\(373\) | −1.11943 | −0.0579619 | −0.0289809 | − | 0.999580i | \(-0.509226\pi\) | ||||
−0.0289809 | + | 0.999580i | \(0.509226\pi\) | |||||||
\(374\) | −9.51388 | −0.491951 | ||||||||
\(375\) | −9.90833 | −0.511664 | ||||||||
\(376\) | −24.6333 | −1.27037 | ||||||||
\(377\) | 1.45837 | 0.0751096 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.8167 | −0.761080 | −0.380540 | − | 0.924764i | \(-0.624262\pi\) | ||||
−0.380540 | + | 0.924764i | \(0.624262\pi\) | |||||||
\(380\) | 0.908327 | 0.0465962 | ||||||||
\(381\) | 32.4222 | 1.66104 | ||||||||
\(382\) | −18.6695 | −0.955213 | ||||||||
\(383\) | 36.6333 | 1.87187 | 0.935937 | − | 0.352167i | \(-0.114555\pi\) | ||||
0.935937 | + | 0.352167i | \(0.114555\pi\) | |||||||
\(384\) | 26.7250 | 1.36380 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.76114 | 0.140538 | ||||||||
\(387\) | −79.0833 | −4.02003 | ||||||||
\(388\) | 0.724981 | 0.0368053 | ||||||||
\(389\) | 37.1472 | 1.88344 | 0.941719 | − | 0.336402i | \(-0.109210\pi\) | ||||
0.941719 | + | 0.336402i | \(0.109210\pi\) | |||||||
\(390\) | −20.7250 | −1.04945 | ||||||||
\(391\) | −5.09167 | −0.257497 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.21110 | 0.414195 | ||||||||
\(394\) | 5.09167 | 0.256515 | ||||||||
\(395\) | −9.63331 | −0.484704 | ||||||||
\(396\) | 10.3028 | 0.517734 | ||||||||
\(397\) | −0.972244 | −0.0487955 | −0.0243978 | − | 0.999702i | \(-0.507767\pi\) | ||||
−0.0243978 | + | 0.999702i | \(0.507767\pi\) | |||||||
\(398\) | −20.0917 | −1.00710 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.2111 | −0.660555 | ||||||||
\(401\) | −21.5139 | −1.07435 | −0.537176 | − | 0.843470i | \(-0.680509\pi\) | ||||
−0.537176 | + | 0.843470i | \(0.680509\pi\) | |||||||
\(402\) | 38.3305 | 1.91175 | ||||||||
\(403\) | −3.69722 | −0.184172 | ||||||||
\(404\) | −3.51388 | −0.174822 | ||||||||
\(405\) | 89.4500 | 4.44480 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.5139 | 0.768994 | ||||||||
\(408\) | −16.8167 | −0.832548 | ||||||||
\(409\) | −10.0917 | −0.499001 | −0.249501 | − | 0.968375i | \(-0.580266\pi\) | ||||
−0.249501 | + | 0.968375i | \(0.580266\pi\) | |||||||
\(410\) | −16.8167 | −0.830515 | ||||||||
\(411\) | −71.4500 | −3.52437 | ||||||||
\(412\) | −0.541635 | −0.0266844 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −30.9083 | −1.51906 | ||||||||
\(415\) | 6.27502 | 0.308029 | ||||||||
\(416\) | −2.72498 | −0.133603 | ||||||||
\(417\) | −16.5139 | −0.808688 | ||||||||
\(418\) | 5.60555 | 0.274176 | ||||||||
\(419\) | −15.0000 | −0.732798 | −0.366399 | − | 0.930458i | \(-0.619409\pi\) | ||||
−0.366399 | + | 0.930458i | \(0.619409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.3944 | −1.09144 | −0.545719 | − | 0.837968i | \(-0.683744\pi\) | ||||
−0.545719 | + | 0.837968i | \(0.683744\pi\) | |||||||
\(422\) | −14.7250 | −0.716801 | ||||||||
\(423\) | 64.9361 | 3.15730 | ||||||||
\(424\) | −11.7250 | −0.569415 | ||||||||
\(425\) | 6.78890 | 0.329310 | ||||||||
\(426\) | −9.51388 | −0.460949 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.11943 | 0.295794 | ||||||||
\(429\) | 22.8167 | 1.10160 | ||||||||
\(430\) | −39.0833 | −1.88476 | ||||||||
\(431\) | 11.2111 | 0.540020 | 0.270010 | − | 0.962858i | \(-0.412973\pi\) | ||||
0.270010 | + | 0.962858i | \(0.412973\pi\) | |||||||
\(432\) | −53.5416 | −2.57602 | ||||||||
\(433\) | 29.4222 | 1.41394 | 0.706970 | − | 0.707243i | \(-0.250061\pi\) | ||||
0.706970 | + | 0.707243i | \(0.250061\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.00000 | −0.431517 | ||||||||
\(436\) | −1.27502 | −0.0610623 | ||||||||
\(437\) | 3.00000 | 0.143509 | ||||||||
\(438\) | 71.0555 | 3.39516 | ||||||||
\(439\) | −37.2111 | −1.77599 | −0.887995 | − | 0.459854i | \(-0.847902\pi\) | ||||
−0.887995 | + | 0.459854i | \(0.847902\pi\) | |||||||
\(440\) | 38.7250 | 1.84614 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.55004 | −0.168858 | ||||||||
\(443\) | 9.11943 | 0.433277 | 0.216639 | − | 0.976252i | \(-0.430491\pi\) | ||||
0.216639 | + | 0.976252i | \(0.430491\pi\) | |||||||
\(444\) | 3.60555 | 0.171112 | ||||||||
\(445\) | 10.1833 | 0.482737 | ||||||||
\(446\) | 11.4861 | 0.543884 | ||||||||
\(447\) | 27.1194 | 1.28270 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.5139 | −0.873724 | −0.436862 | − | 0.899529i | \(-0.643910\pi\) | ||||
−0.436862 | + | 0.899529i | \(0.643910\pi\) | |||||||
\(450\) | 41.2111 | 1.94271 | ||||||||
\(451\) | 18.5139 | 0.871784 | ||||||||
\(452\) | −4.02776 | −0.189450 | ||||||||
\(453\) | −16.2111 | −0.761664 | ||||||||
\(454\) | −0.155590 | −0.00730219 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.90833 | 0.464000 | ||||||||
\(457\) | 18.6972 | 0.874619 | 0.437310 | − | 0.899311i | \(-0.355931\pi\) | ||||
0.437310 | + | 0.899311i | \(0.355931\pi\) | |||||||
\(458\) | 19.8167 | 0.925971 | ||||||||
\(459\) | 27.5139 | 1.28424 | ||||||||
\(460\) | 2.72498 | 0.127053 | ||||||||
\(461\) | 9.90833 | 0.461477 | 0.230738 | − | 0.973016i | \(-0.425886\pi\) | ||||
0.230738 | + | 0.973016i | \(0.425886\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.4500 | 1.32218 | 0.661091 | − | 0.750306i | \(-0.270094\pi\) | ||||
0.661091 | + | 0.750306i | \(0.270094\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 22.8167 | 1.05810 | ||||||||
\(466\) | −16.8167 | −0.779016 | ||||||||
\(467\) | 37.5416 | 1.73722 | 0.868610 | − | 0.495497i | \(-0.165014\pi\) | ||||
0.868610 | + | 0.495497i | \(0.165014\pi\) | |||||||
\(468\) | 3.84441 | 0.177708 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 32.0917 | 1.48028 | ||||||||
\(471\) | 44.6333 | 2.05659 | ||||||||
\(472\) | 24.6333 | 1.13384 | ||||||||
\(473\) | 43.0278 | 1.97842 | ||||||||
\(474\) | −13.8167 | −0.634620 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.9083 | 1.41520 | ||||||||
\(478\) | 1.85281 | 0.0847457 | ||||||||
\(479\) | 4.30278 | 0.196599 | 0.0982994 | − | 0.995157i | \(-0.468660\pi\) | ||||
0.0982994 | + | 0.995157i | \(0.468660\pi\) | |||||||
\(480\) | 16.8167 | 0.767572 | ||||||||
\(481\) | 5.78890 | 0.263951 | ||||||||
\(482\) | 17.4500 | 0.794824 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.27502 | −0.103410 | ||||||||
\(485\) | −7.18335 | −0.326179 | ||||||||
\(486\) | 64.9361 | 2.94556 | ||||||||
\(487\) | 33.4222 | 1.51450 | 0.757252 | − | 0.653122i | \(-0.226541\pi\) | ||||
0.757252 | + | 0.653122i | \(0.226541\pi\) | |||||||
\(488\) | 30.6333 | 1.38670 | ||||||||
\(489\) | 30.7250 | 1.38943 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 4.30278 | 0.193984 | ||||||||
\(493\) | −1.54163 | −0.0694317 | ||||||||
\(494\) | 2.09167 | 0.0941088 | ||||||||
\(495\) | −102.083 | −4.58830 | ||||||||
\(496\) | −7.60555 | −0.341499 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 9.00000 | 0.403300 | ||||||||
\(499\) | −26.9361 | −1.20582 | −0.602912 | − | 0.797807i | \(-0.705993\pi\) | ||||
−0.602912 | + | 0.797807i | \(0.705993\pi\) | |||||||
\(500\) | 0.908327 | 0.0406216 | ||||||||
\(501\) | −38.3305 | −1.71248 | ||||||||
\(502\) | 6.63331 | 0.296059 | ||||||||
\(503\) | 22.4222 | 0.999757 | 0.499878 | − | 0.866096i | \(-0.333378\pi\) | ||||
0.499878 | + | 0.866096i | \(0.333378\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 34.8167 | 1.54932 | ||||||||
\(506\) | 16.8167 | 0.747591 | ||||||||
\(507\) | −34.4222 | −1.52874 | ||||||||
\(508\) | −2.97224 | −0.131872 | ||||||||
\(509\) | 9.63331 | 0.426989 | 0.213494 | − | 0.976944i | \(-0.431515\pi\) | ||||
0.213494 | + | 0.976944i | \(0.431515\pi\) | |||||||
\(510\) | 21.9083 | 0.970117 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −25.4222 | −1.12351 | ||||||||
\(513\) | −16.2111 | −0.715738 | ||||||||
\(514\) | −12.9083 | −0.569362 | ||||||||
\(515\) | 5.36669 | 0.236485 | ||||||||
\(516\) | 10.0000 | 0.440225 | ||||||||
\(517\) | −35.3305 | −1.55384 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 45.6333 | 2.00308 | ||||||||
\(520\) | 14.4500 | 0.633673 | ||||||||
\(521\) | 6.63331 | 0.290610 | 0.145305 | − | 0.989387i | \(-0.453584\pi\) | ||||
0.145305 | + | 0.989387i | \(0.453584\pi\) | |||||||
\(522\) | −9.35829 | −0.409601 | ||||||||
\(523\) | 41.6611 | 1.82171 | 0.910856 | − | 0.412725i | \(-0.135423\pi\) | ||||
0.910856 | + | 0.412725i | \(0.135423\pi\) | |||||||
\(524\) | −0.752737 | −0.0328835 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.3305 | −0.755647 | ||||||||
\(527\) | 3.90833 | 0.170249 | ||||||||
\(528\) | 46.9361 | 2.04263 | ||||||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | 15.2750 | 0.663504 | ||||||||
\(531\) | −64.9361 | −2.81799 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.90833 | 0.299233 | ||||||||
\(534\) | 14.6056 | 0.632044 | ||||||||
\(535\) | −60.6333 | −2.62141 | ||||||||
\(536\) | −26.7250 | −1.15434 | ||||||||
\(537\) | 68.4500 | 2.95383 | ||||||||
\(538\) | 15.2750 | 0.658553 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −14.7250 | −0.633662 | ||||||||
\(541\) | 31.2111 | 1.34187 | 0.670935 | − | 0.741516i | \(-0.265893\pi\) | ||||
0.670935 | + | 0.741516i | \(0.265893\pi\) | |||||||
\(542\) | −9.23886 | −0.396843 | ||||||||
\(543\) | 47.2389 | 2.02721 | ||||||||
\(544\) | 2.88057 | 0.123503 | ||||||||
\(545\) | 12.6333 | 0.541151 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.5139 | −1.21917 | −0.609583 | − | 0.792722i | \(-0.708663\pi\) | ||||
−0.609583 | + | 0.792722i | \(0.708663\pi\) | |||||||
\(548\) | 6.55004 | 0.279804 | ||||||||
\(549\) | −80.7527 | −3.44644 | ||||||||
\(550\) | −22.4222 | −0.956086 | ||||||||
\(551\) | 0.908327 | 0.0386960 | ||||||||
\(552\) | 29.7250 | 1.26518 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8.60555 | −0.365615 | ||||||||
\(555\) | −35.7250 | −1.51644 | ||||||||
\(556\) | 1.51388 | 0.0642027 | ||||||||
\(557\) | 24.1194 | 1.02197 | 0.510987 | − | 0.859589i | \(-0.329280\pi\) | ||||
0.510987 | + | 0.859589i | \(0.329280\pi\) | |||||||
\(558\) | 23.7250 | 1.00436 | ||||||||
\(559\) | 16.0555 | 0.679076 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.1194 | −1.01832 | ||||||||
\(562\) | 3.90833 | 0.164863 | ||||||||
\(563\) | 9.78890 | 0.412553 | 0.206276 | − | 0.978494i | \(-0.433865\pi\) | ||||
0.206276 | + | 0.978494i | \(0.433865\pi\) | |||||||
\(564\) | −8.21110 | −0.345750 | ||||||||
\(565\) | 39.9083 | 1.67896 | ||||||||
\(566\) | 16.0639 | 0.675217 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.63331 | 0.278327 | ||||||||
\(569\) | 28.8167 | 1.20806 | 0.604028 | − | 0.796963i | \(-0.293561\pi\) | ||||
0.604028 | + | 0.796963i | \(0.293561\pi\) | |||||||
\(570\) | −12.9083 | −0.540670 | ||||||||
\(571\) | −9.60555 | −0.401980 | −0.200990 | − | 0.979593i | \(-0.564416\pi\) | ||||
−0.200990 | + | 0.979593i | \(0.564416\pi\) | |||||||
\(572\) | −2.09167 | −0.0874572 | ||||||||
\(573\) | −47.3305 | −1.97726 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.0000 | −0.500435 | ||||||||
\(576\) | 69.7250 | 2.90521 | ||||||||
\(577\) | −1.48612 | −0.0618681 | −0.0309340 | − | 0.999521i | \(-0.509848\pi\) | ||||
−0.0309340 | + | 0.999521i | \(0.509848\pi\) | |||||||
\(578\) | −18.3944 | −0.765108 | ||||||||
\(579\) | 7.00000 | 0.290910 | ||||||||
\(580\) | 0.825058 | 0.0342587 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −10.3028 | −0.427064 | ||||||||
\(583\) | −16.8167 | −0.696475 | ||||||||
\(584\) | −49.5416 | −2.05005 | ||||||||
\(585\) | −38.0917 | −1.57490 | ||||||||
\(586\) | −39.9083 | −1.64860 | ||||||||
\(587\) | 28.4222 | 1.17311 | 0.586555 | − | 0.809909i | \(-0.300484\pi\) | ||||
0.586555 | + | 0.809909i | \(0.300484\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.30278 | −0.0948842 | ||||||||
\(590\) | −32.0917 | −1.32119 | ||||||||
\(591\) | 12.9083 | 0.530978 | ||||||||
\(592\) | 11.9083 | 0.489429 | ||||||||
\(593\) | −16.8167 | −0.690577 | −0.345289 | − | 0.938497i | \(-0.612219\pi\) | ||||
−0.345289 | + | 0.938497i | \(0.612219\pi\) | |||||||
\(594\) | −90.8722 | −3.72853 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.48612 | −0.101836 | ||||||||
\(597\) | −50.9361 | −2.08468 | ||||||||
\(598\) | 6.27502 | 0.256605 | ||||||||
\(599\) | 9.90833 | 0.404843 | 0.202422 | − | 0.979298i | \(-0.435119\pi\) | ||||
0.202422 | + | 0.979298i | \(0.435119\pi\) | |||||||
\(600\) | −39.6333 | −1.61802 | ||||||||
\(601\) | 9.48612 | 0.386947 | 0.193473 | − | 0.981106i | \(-0.438025\pi\) | ||||
0.193473 | + | 0.981106i | \(0.438025\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 70.4500 | 2.86894 | ||||||||
\(604\) | 1.48612 | 0.0604694 | ||||||||
\(605\) | 22.5416 | 0.916448 | ||||||||
\(606\) | 49.9361 | 2.02851 | ||||||||
\(607\) | 13.0000 | 0.527654 | 0.263827 | − | 0.964570i | \(-0.415015\pi\) | ||||
0.263827 | + | 0.964570i | \(0.415015\pi\) | |||||||
\(608\) | −1.69722 | −0.0688315 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −39.9083 | −1.61584 | ||||||||
\(611\) | −13.1833 | −0.533341 | ||||||||
\(612\) | −4.06392 | −0.164274 | ||||||||
\(613\) | 31.7250 | 1.28136 | 0.640680 | − | 0.767808i | \(-0.278653\pi\) | ||||
0.640680 | + | 0.767808i | \(0.278653\pi\) | |||||||
\(614\) | −23.8444 | −0.962282 | ||||||||
\(615\) | −42.6333 | −1.71914 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.1194 | −1.45411 | −0.727057 | − | 0.686577i | \(-0.759112\pi\) | ||||
−0.727057 | + | 0.686577i | \(0.759112\pi\) | |||||||
\(618\) | 7.69722 | 0.309628 | ||||||||
\(619\) | 1.66947 | 0.0671016 | 0.0335508 | − | 0.999437i | \(-0.489318\pi\) | ||||
0.0335508 | + | 0.999437i | \(0.489318\pi\) | |||||||
\(620\) | −2.09167 | −0.0840036 | ||||||||
\(621\) | −48.6333 | −1.95159 | ||||||||
\(622\) | −20.2111 | −0.810391 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 17.5139 | 0.701116 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | −11.7611 | −0.470070 | ||||||||
\(627\) | 14.2111 | 0.567537 | ||||||||
\(628\) | −4.09167 | −0.163276 | ||||||||
\(629\) | −6.11943 | −0.243998 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.2389 | −1.48246 | −0.741228 | − | 0.671254i | \(-0.765756\pi\) | ||||
−0.741228 | + | 0.671254i | \(0.765756\pi\) | |||||||
\(632\) | 9.63331 | 0.383192 | ||||||||
\(633\) | −37.3305 | −1.48376 | ||||||||
\(634\) | 30.2389 | 1.20094 | ||||||||
\(635\) | 29.4500 | 1.16869 | ||||||||
\(636\) | −3.90833 | −0.154975 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.09167 | 0.201581 | ||||||||
\(639\) | −17.4861 | −0.691740 | ||||||||
\(640\) | 24.2750 | 0.959554 | ||||||||
\(641\) | −0.908327 | −0.0358768 | −0.0179384 | − | 0.999839i | \(-0.505710\pi\) | ||||
−0.0179384 | + | 0.999839i | \(0.505710\pi\) | |||||||
\(642\) | −86.9638 | −3.43219 | ||||||||
\(643\) | −37.6056 | −1.48302 | −0.741509 | − | 0.670943i | \(-0.765890\pi\) | ||||
−0.741509 | + | 0.670943i | \(0.765890\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −99.0833 | −3.90140 | ||||||||
\(646\) | −2.21110 | −0.0869947 | ||||||||
\(647\) | 13.4222 | 0.527681 | 0.263841 | − | 0.964566i | \(-0.415011\pi\) | ||||
0.263841 | + | 0.964566i | \(0.415011\pi\) | |||||||
\(648\) | −89.4500 | −3.51393 | ||||||||
\(649\) | 35.3305 | 1.38684 | ||||||||
\(650\) | −8.36669 | −0.328169 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.81665 | −0.110309 | ||||||||
\(653\) | 4.81665 | 0.188490 | 0.0942451 | − | 0.995549i | \(-0.469956\pi\) | ||||
0.0942451 | + | 0.995549i | \(0.469956\pi\) | |||||||
\(654\) | 18.1194 | 0.708526 | ||||||||
\(655\) | 7.45837 | 0.291422 | ||||||||
\(656\) | 14.2111 | 0.554850 | ||||||||
\(657\) | 130.597 | 5.09508 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.3305 | −0.908828 | −0.454414 | − | 0.890790i | \(-0.650151\pi\) | ||||
−0.454414 | + | 0.890790i | \(0.650151\pi\) | |||||||
\(660\) | 12.9083 | 0.502456 | ||||||||
\(661\) | 15.2111 | 0.591643 | 0.295822 | − | 0.955243i | \(-0.404407\pi\) | ||||
0.295822 | + | 0.955243i | \(0.404407\pi\) | |||||||
\(662\) | 19.9361 | 0.774838 | ||||||||
\(663\) | −9.00000 | −0.349531 | ||||||||
\(664\) | −6.27502 | −0.243518 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −37.1472 | −1.43942 | ||||||||
\(667\) | 2.72498 | 0.105512 | ||||||||
\(668\) | 3.51388 | 0.135956 | ||||||||
\(669\) | 29.1194 | 1.12582 | ||||||||
\(670\) | 34.8167 | 1.34508 | ||||||||
\(671\) | 43.9361 | 1.69613 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.09167 | 0.157722 | 0.0788612 | − | 0.996886i | \(-0.474872\pi\) | ||||
0.0788612 | + | 0.996886i | \(0.474872\pi\) | |||||||
\(674\) | −32.2111 | −1.24073 | ||||||||
\(675\) | 64.8444 | 2.49586 | ||||||||
\(676\) | 3.15559 | 0.121369 | ||||||||
\(677\) | 28.9361 | 1.11210 | 0.556052 | − | 0.831147i | \(-0.312316\pi\) | ||||
0.556052 | + | 0.831147i | \(0.312316\pi\) | |||||||
\(678\) | 57.2389 | 2.19825 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −15.2750 | −0.585770 | ||||||||
\(681\) | −0.394449 | −0.0151153 | ||||||||
\(682\) | −12.9083 | −0.494285 | ||||||||
\(683\) | −2.21110 | −0.0846055 | −0.0423027 | − | 0.999105i | \(-0.513469\pi\) | ||||
−0.0423027 | + | 0.999105i | \(0.513469\pi\) | |||||||
\(684\) | 2.39445 | 0.0915540 | ||||||||
\(685\) | −64.8999 | −2.47970 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 50.2389 | 1.91673 | ||||||||
\(688\) | 33.0278 | 1.25917 | ||||||||
\(689\) | −6.27502 | −0.239059 | ||||||||
\(690\) | −38.7250 | −1.47423 | ||||||||
\(691\) | 20.1833 | 0.767811 | 0.383905 | − | 0.923372i | \(-0.374579\pi\) | ||||
0.383905 | + | 0.923372i | \(0.374579\pi\) | |||||||
\(692\) | −4.18335 | −0.159027 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 33.2750 | 1.26310 | ||||||||
\(695\) | −15.0000 | −0.568982 | ||||||||
\(696\) | 9.00000 | 0.341144 | ||||||||
\(697\) | −7.30278 | −0.276612 | ||||||||
\(698\) | 13.6972 | 0.518448 | ||||||||
\(699\) | −42.6333 | −1.61254 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.78890 | 0.256413 | 0.128207 | − | 0.991747i | \(-0.459078\pi\) | ||||
0.128207 | + | 0.991747i | \(0.459078\pi\) | |||||||
\(702\) | −33.9083 | −1.27979 | ||||||||
\(703\) | 3.60555 | 0.135986 | ||||||||
\(704\) | −37.9361 | −1.42977 | ||||||||
\(705\) | 81.3583 | 3.06413 | ||||||||
\(706\) | 1.18335 | 0.0445358 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 8.21110 | 0.308592 | ||||||||
\(709\) | −4.39445 | −0.165037 | −0.0825185 | − | 0.996590i | \(-0.526296\pi\) | ||||
−0.0825185 | + | 0.996590i | \(0.526296\pi\) | |||||||
\(710\) | −8.64171 | −0.324318 | ||||||||
\(711\) | −25.3944 | −0.952366 | ||||||||
\(712\) | −10.1833 | −0.381637 | ||||||||
\(713\) | −6.90833 | −0.258719 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.7250 | 0.775070 | ||||||||
\(716\) | −6.27502 | −0.234508 | ||||||||
\(717\) | 4.69722 | 0.175421 | ||||||||
\(718\) | 37.1833 | 1.38767 | ||||||||
\(719\) | −15.6333 | −0.583024 | −0.291512 | − | 0.956567i | \(-0.594158\pi\) | ||||
−0.291512 | + | 0.956567i | \(0.594158\pi\) | |||||||
\(720\) | −78.3583 | −2.92024 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.30278 | 0.0484843 | ||||||||
\(723\) | 44.2389 | 1.64526 | ||||||||
\(724\) | −4.33053 | −0.160943 | ||||||||
\(725\) | −3.63331 | −0.134938 | ||||||||
\(726\) | 32.3305 | 1.19990 | ||||||||
\(727\) | −51.6611 | −1.91600 | −0.958001 | − | 0.286764i | \(-0.907421\pi\) | ||||
−0.958001 | + | 0.286764i | \(0.907421\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 75.1749 | 2.78426 | ||||||||
\(730\) | 64.5416 | 2.38879 | ||||||||
\(731\) | −16.9722 | −0.627741 | ||||||||
\(732\) | 10.2111 | 0.377413 | ||||||||
\(733\) | −32.0000 | −1.18195 | −0.590973 | − | 0.806691i | \(-0.701256\pi\) | ||||
−0.590973 | + | 0.806691i | \(0.701256\pi\) | |||||||
\(734\) | −46.9361 | −1.73244 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.09167 | −0.187682 | ||||||||
\(737\) | −38.3305 | −1.41192 | ||||||||
\(738\) | −44.3305 | −1.63183 | ||||||||
\(739\) | −47.4222 | −1.74445 | −0.872227 | − | 0.489101i | \(-0.837325\pi\) | ||||
−0.872227 | + | 0.489101i | \(0.837325\pi\) | |||||||
\(740\) | 3.27502 | 0.120392 | ||||||||
\(741\) | 5.30278 | 0.194802 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.6333 | 1.12383 | 0.561914 | − | 0.827196i | \(-0.310065\pi\) | ||||
0.561914 | + | 0.827196i | \(0.310065\pi\) | |||||||
\(744\) | −22.8167 | −0.836499 | ||||||||
\(745\) | 24.6333 | 0.902495 | ||||||||
\(746\) | −1.45837 | −0.0533946 | ||||||||
\(747\) | 16.5416 | 0.605227 | ||||||||
\(748\) | 2.21110 | 0.0808459 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −12.9083 | −0.471345 | ||||||||
\(751\) | −49.3583 | −1.80111 | −0.900555 | − | 0.434743i | \(-0.856839\pi\) | ||||
−0.900555 | + | 0.434743i | \(0.856839\pi\) | |||||||
\(752\) | −27.1194 | −0.988944 | ||||||||
\(753\) | 16.8167 | 0.612833 | ||||||||
\(754\) | 1.89992 | 0.0691911 | ||||||||
\(755\) | −14.7250 | −0.535897 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | −19.3028 | −0.701108 | ||||||||
\(759\) | 42.6333 | 1.54749 | ||||||||
\(760\) | 9.00000 | 0.326464 | ||||||||
\(761\) | 9.78890 | 0.354847 | 0.177424 | − | 0.984135i | \(-0.443224\pi\) | ||||
0.177424 | + | 0.984135i | \(0.443224\pi\) | |||||||
\(762\) | 42.2389 | 1.53015 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.33894 | 0.156977 | ||||||||
\(765\) | 40.2666 | 1.45584 | ||||||||
\(766\) | 47.7250 | 1.72437 | ||||||||
\(767\) | 13.1833 | 0.476023 | ||||||||
\(768\) | −23.4222 | −0.845176 | ||||||||
\(769\) | 10.7889 | 0.389058 | 0.194529 | − | 0.980897i | \(-0.437682\pi\) | ||||
0.194529 | + | 0.980897i | \(0.437682\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −32.7250 | −1.17856 | ||||||||
\(772\) | −0.641712 | −0.0230957 | ||||||||
\(773\) | 43.8167 | 1.57598 | 0.787988 | − | 0.615691i | \(-0.211123\pi\) | ||||
0.787988 | + | 0.615691i | \(0.211123\pi\) | |||||||
\(774\) | −103.028 | −3.70326 | ||||||||
\(775\) | 9.21110 | 0.330873 | ||||||||
\(776\) | 7.18335 | 0.257867 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 48.3944 | 1.73503 | ||||||||
\(779\) | 4.30278 | 0.154163 | ||||||||
\(780\) | 4.81665 | 0.172464 | ||||||||
\(781\) | 9.51388 | 0.340433 | ||||||||
\(782\) | −6.63331 | −0.237207 | ||||||||
\(783\) | −14.7250 | −0.526228 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 40.5416 | 1.44699 | ||||||||
\(786\) | 10.6972 | 0.381557 | ||||||||
\(787\) | −11.6333 | −0.414683 | −0.207341 | − | 0.978269i | \(-0.566481\pi\) | ||||
−0.207341 | + | 0.978269i | \(0.566481\pi\) | |||||||
\(788\) | −1.18335 | −0.0421550 | ||||||||
\(789\) | −43.9361 | −1.56417 | ||||||||
\(790\) | −12.5500 | −0.446510 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 102.083 | 3.62737 | ||||||||
\(793\) | 16.3944 | 0.582184 | ||||||||
\(794\) | −1.26662 | −0.0449505 | ||||||||
\(795\) | 38.7250 | 1.37343 | ||||||||
\(796\) | 4.66947 | 0.165505 | ||||||||
\(797\) | −36.9083 | −1.30736 | −0.653680 | − | 0.756771i | \(-0.726776\pi\) | ||||
−0.653680 | + | 0.756771i | \(0.726776\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.9361 | 0.493023 | ||||||||
\(800\) | 6.78890 | 0.240024 | ||||||||
\(801\) | 26.8444 | 0.948501 | ||||||||
\(802\) | −28.0278 | −0.989694 | ||||||||
\(803\) | −71.0555 | −2.50749 | ||||||||
\(804\) | −8.90833 | −0.314172 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.81665 | −0.169659 | ||||||||
\(807\) | 38.7250 | 1.36318 | ||||||||
\(808\) | −34.8167 | −1.22485 | ||||||||
\(809\) | 10.0278 | 0.352557 | 0.176279 | − | 0.984340i | \(-0.443594\pi\) | ||||
0.176279 | + | 0.984340i | \(0.443594\pi\) | |||||||
\(810\) | 116.533 | 4.09456 | ||||||||
\(811\) | −40.0555 | −1.40654 | −0.703270 | − | 0.710923i | \(-0.748277\pi\) | ||||
−0.703270 | + | 0.710923i | \(0.748277\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.4222 | −0.821453 | ||||||||
\(814\) | 20.2111 | 0.708399 | ||||||||
\(815\) | 27.9083 | 0.977586 | ||||||||
\(816\) | −18.5139 | −0.648115 | ||||||||
\(817\) | 10.0000 | 0.349856 | ||||||||
\(818\) | −13.1472 | −0.459681 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.90833 | 0.136485 | ||||||||
\(821\) | −8.36669 | −0.292000 | −0.146000 | − | 0.989285i | \(-0.546640\pi\) | ||||
−0.146000 | + | 0.989285i | \(0.546640\pi\) | |||||||
\(822\) | −93.0833 | −3.24665 | ||||||||
\(823\) | −34.2389 | −1.19349 | −0.596746 | − | 0.802430i | \(-0.703540\pi\) | ||||
−0.596746 | + | 0.802430i | \(0.703540\pi\) | |||||||
\(824\) | −5.36669 | −0.186958 | ||||||||
\(825\) | −56.8444 | −1.97907 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.0000 | −1.56480 | −0.782402 | − | 0.622774i | \(-0.786006\pi\) | ||||
−0.782402 | + | 0.622774i | \(0.786006\pi\) | |||||||
\(828\) | 7.18335 | 0.249639 | ||||||||
\(829\) | 18.0555 | 0.627094 | 0.313547 | − | 0.949573i | \(-0.398483\pi\) | ||||
0.313547 | + | 0.949573i | \(0.398483\pi\) | |||||||
\(830\) | 8.17494 | 0.283756 | ||||||||
\(831\) | −21.8167 | −0.756811 | ||||||||
\(832\) | −14.1556 | −0.490757 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −21.5139 | −0.744965 | ||||||||
\(835\) | −34.8167 | −1.20488 | ||||||||
\(836\) | −1.30278 | −0.0450574 | ||||||||
\(837\) | 37.3305 | 1.29033 | ||||||||
\(838\) | −19.5416 | −0.675055 | ||||||||
\(839\) | 17.2111 | 0.594193 | 0.297097 | − | 0.954847i | \(-0.403982\pi\) | ||||
0.297097 | + | 0.954847i | \(0.403982\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1749 | −0.971550 | ||||||||
\(842\) | −29.1749 | −1.00543 | ||||||||
\(843\) | 9.90833 | 0.341261 | ||||||||
\(844\) | 3.42221 | 0.117797 | ||||||||
\(845\) | −31.2666 | −1.07560 | ||||||||
\(846\) | 84.5971 | 2.90851 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −12.9083 | −0.443274 | ||||||||
\(849\) | 40.7250 | 1.39768 | ||||||||
\(850\) | 8.84441 | 0.303361 | ||||||||
\(851\) | 10.8167 | 0.370790 | ||||||||
\(852\) | 2.21110 | 0.0757511 | ||||||||
\(853\) | 36.3305 | 1.24393 | 0.621967 | − | 0.783044i | \(-0.286334\pi\) | ||||
0.621967 | + | 0.783044i | \(0.286334\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −23.7250 | −0.811377 | ||||||||
\(856\) | 60.6333 | 2.07240 | ||||||||
\(857\) | −42.9083 | −1.46572 | −0.732860 | − | 0.680379i | \(-0.761815\pi\) | ||||
−0.732860 | + | 0.680379i | \(0.761815\pi\) | |||||||
\(858\) | 29.7250 | 1.01479 | ||||||||
\(859\) | 23.6972 | 0.808539 | 0.404269 | − | 0.914640i | \(-0.367526\pi\) | ||||
0.404269 | + | 0.914640i | \(0.367526\pi\) | |||||||
\(860\) | 9.08327 | 0.309737 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.6056 | 0.497467 | ||||||||
\(863\) | 37.5416 | 1.27793 | 0.638966 | − | 0.769235i | \(-0.279362\pi\) | ||||
0.638966 | + | 0.769235i | \(0.279362\pi\) | |||||||
\(864\) | 27.5139 | 0.936041 | ||||||||
\(865\) | 41.4500 | 1.40934 | ||||||||
\(866\) | 38.3305 | 1.30252 | ||||||||
\(867\) | −46.6333 | −1.58375 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.8167 | 0.468698 | ||||||||
\(870\) | −11.7250 | −0.397514 | ||||||||
\(871\) | −14.3028 | −0.484631 | ||||||||
\(872\) | −12.6333 | −0.427818 | ||||||||
\(873\) | −18.9361 | −0.640889 | ||||||||
\(874\) | 3.90833 | 0.132201 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.5139 | −0.557952 | ||||||||
\(877\) | −29.8167 | −1.00684 | −0.503418 | − | 0.864043i | \(-0.667925\pi\) | ||||
−0.503418 | + | 0.864043i | \(0.667925\pi\) | |||||||
\(878\) | −48.4777 | −1.63604 | ||||||||
\(879\) | −101.175 | −3.41255 | ||||||||
\(880\) | 42.6333 | 1.43717 | ||||||||
\(881\) | −48.7527 | −1.64252 | −0.821261 | − | 0.570553i | \(-0.806729\pi\) | ||||
−0.821261 | + | 0.570553i | \(0.806729\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.7889 | −1.06978 | −0.534891 | − | 0.844921i | \(-0.679647\pi\) | ||||
−0.534891 | + | 0.844921i | \(0.679647\pi\) | |||||||
\(884\) | 0.825058 | 0.0277497 | ||||||||
\(885\) | −81.3583 | −2.73483 | ||||||||
\(886\) | 11.8806 | 0.399136 | ||||||||
\(887\) | −40.8167 | −1.37049 | −0.685245 | − | 0.728313i | \(-0.740305\pi\) | ||||
−0.685245 | + | 0.728313i | \(0.740305\pi\) | |||||||
\(888\) | 35.7250 | 1.19885 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 13.2666 | 0.444698 | ||||||||
\(891\) | −128.294 | −4.29802 | ||||||||
\(892\) | −2.66947 | −0.0893804 | ||||||||
\(893\) | −8.21110 | −0.274774 | ||||||||
\(894\) | 35.3305 | 1.18163 | ||||||||
\(895\) | 62.1749 | 2.07828 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.9083 | 0.531164 | ||||||||
\(898\) | −24.1194 | −0.804876 | ||||||||
\(899\) | −2.09167 | −0.0697612 | ||||||||
\(900\) | −9.57779 | −0.319260 | ||||||||
\(901\) | 6.63331 | 0.220988 | ||||||||
\(902\) | 24.1194 | 0.803089 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −39.9083 | −1.32733 | ||||||||
\(905\) | 42.9083 | 1.42632 | ||||||||
\(906\) | −21.1194 | −0.701646 | ||||||||
\(907\) | −26.8167 | −0.890432 | −0.445216 | − | 0.895423i | \(-0.646873\pi\) | ||||
−0.445216 | + | 0.895423i | \(0.646873\pi\) | |||||||
\(908\) | 0.0361603 | 0.00120002 | ||||||||
\(909\) | 91.7805 | 3.04417 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | 10.9083 | 0.361211 | ||||||||
\(913\) | −9.00000 | −0.297857 | ||||||||
\(914\) | 24.3583 | 0.805701 | ||||||||
\(915\) | −101.175 | −3.34474 | ||||||||
\(916\) | −4.60555 | −0.152172 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 35.8444 | 1.18304 | ||||||||
\(919\) | −44.0278 | −1.45234 | −0.726171 | − | 0.687514i | \(-0.758702\pi\) | ||||
−0.726171 | + | 0.687514i | \(0.758702\pi\) | |||||||
\(920\) | 27.0000 | 0.890164 | ||||||||
\(921\) | −60.4500 | −1.99189 | ||||||||
\(922\) | 12.9083 | 0.425113 | ||||||||
\(923\) | 3.55004 | 0.116851 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.4222 | −0.474199 | ||||||||
\(926\) | 37.0639 | 1.21800 | ||||||||
\(927\) | 14.1472 | 0.464655 | ||||||||
\(928\) | −1.54163 | −0.0506066 | ||||||||
\(929\) | 6.51388 | 0.213713 | 0.106857 | − | 0.994274i | \(-0.465921\pi\) | ||||
0.106857 | + | 0.994274i | \(0.465921\pi\) | |||||||
\(930\) | 29.7250 | 0.974721 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.90833 | 0.128022 | ||||||||
\(933\) | −51.2389 | −1.67748 | ||||||||
\(934\) | 48.9083 | 1.60033 | ||||||||
\(935\) | −21.9083 | −0.716479 | ||||||||
\(936\) | 38.0917 | 1.24507 | ||||||||
\(937\) | 4.11943 | 0.134576 | 0.0672879 | − | 0.997734i | \(-0.478565\pi\) | ||||
0.0672879 | + | 0.997734i | \(0.478565\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.8167 | −0.973030 | ||||||||
\(940\) | −7.45837 | −0.243265 | ||||||||
\(941\) | −6.00000 | −0.195594 | −0.0977972 | − | 0.995206i | \(-0.531180\pi\) | ||||
−0.0977972 | + | 0.995206i | \(0.531180\pi\) | |||||||
\(942\) | 58.1472 | 1.89454 | ||||||||
\(943\) | 12.9083 | 0.420353 | ||||||||
\(944\) | 27.1194 | 0.882662 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 56.0555 | 1.82252 | ||||||||
\(947\) | 26.0917 | 0.847865 | 0.423933 | − | 0.905694i | \(-0.360649\pi\) | ||||
0.423933 | + | 0.905694i | \(0.360649\pi\) | |||||||
\(948\) | 3.21110 | 0.104292 | ||||||||
\(949\) | −26.5139 | −0.860677 | ||||||||
\(950\) | −5.21110 | −0.169070 | ||||||||
\(951\) | 76.6611 | 2.48591 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.3305 | −1.14447 | −0.572234 | − | 0.820090i | \(-0.693923\pi\) | ||||
−0.572234 | + | 0.820090i | \(0.693923\pi\) | |||||||
\(954\) | 40.2666 | 1.30368 | ||||||||
\(955\) | −42.9916 | −1.39118 | ||||||||
\(956\) | −0.430609 | −0.0139269 | ||||||||
\(957\) | 12.9083 | 0.417267 | ||||||||
\(958\) | 5.60555 | 0.181107 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 87.3583 | 2.81948 | ||||||||
\(961\) | −25.6972 | −0.828943 | ||||||||
\(962\) | 7.54163 | 0.243152 | ||||||||
\(963\) | −159.836 | −5.15064 | ||||||||
\(964\) | −4.05551 | −0.130619 | ||||||||
\(965\) | 6.35829 | 0.204681 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.3028 | 0.974472 | 0.487236 | − | 0.873270i | \(-0.338005\pi\) | ||||
0.487236 | + | 0.873270i | \(0.338005\pi\) | |||||||
\(968\) | −22.5416 | −0.724516 | ||||||||
\(969\) | −5.60555 | −0.180076 | ||||||||
\(970\) | −9.35829 | −0.300477 | ||||||||
\(971\) | −24.6333 | −0.790520 | −0.395260 | − | 0.918569i | \(-0.629346\pi\) | ||||
−0.395260 | + | 0.918569i | \(0.629346\pi\) | |||||||
\(972\) | −15.0917 | −0.484066 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 43.5416 | 1.39516 | ||||||||
\(975\) | −21.2111 | −0.679299 | ||||||||
\(976\) | 33.7250 | 1.07951 | ||||||||
\(977\) | 47.4500 | 1.51806 | 0.759029 | − | 0.651056i | \(-0.225674\pi\) | ||||
0.759029 | + | 0.651056i | \(0.225674\pi\) | |||||||
\(978\) | 40.0278 | 1.27995 | ||||||||
\(979\) | −14.6056 | −0.466795 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.3028 | 1.06328 | ||||||||
\(982\) | −15.6333 | −0.498879 | ||||||||
\(983\) | −23.0555 | −0.735357 | −0.367678 | − | 0.929953i | \(-0.619847\pi\) | ||||
−0.367678 | + | 0.929953i | \(0.619847\pi\) | |||||||
\(984\) | 42.6333 | 1.35910 | ||||||||
\(985\) | 11.7250 | 0.373589 | ||||||||
\(986\) | −2.00840 | −0.0639606 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.486122 | −0.0154656 | ||||||||
\(989\) | 30.0000 | 0.953945 | ||||||||
\(990\) | −132.992 | −4.22675 | ||||||||
\(991\) | −53.0278 | −1.68448 | −0.842241 | − | 0.539101i | \(-0.818764\pi\) | ||||
−0.842241 | + | 0.539101i | \(0.818764\pi\) | |||||||
\(992\) | 3.90833 | 0.124090 | ||||||||
\(993\) | 50.5416 | 1.60389 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −46.2666 | −1.46675 | ||||||||
\(996\) | −2.09167 | −0.0662772 | ||||||||
\(997\) | −37.7250 | −1.19476 | −0.597381 | − | 0.801958i | \(-0.703792\pi\) | ||||
−0.597381 | + | 0.801958i | \(0.703792\pi\) | |||||||
\(998\) | −35.0917 | −1.11081 | ||||||||
\(999\) | −58.4500 | −1.84927 |
(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 | 931.2.a.g.1.2 | 2 | ||
3.2 | odd | 2 | 8379.2.a.bf.1.1 | 2 | |||
7.2 | even | 3 | 931.2.f.g.704.1 | 4 | |||
7.3 | odd | 6 | 931.2.f.h.324.1 | 4 | |||
7.4 | even | 3 | 931.2.f.g.324.1 | 4 | |||
7.5 | odd | 6 | 931.2.f.h.704.1 | 4 | |||
7.6 | odd | 2 | 133.2.a.b.1.2 | ✓ | 2 | ||
21.20 | even | 2 | 1197.2.a.h.1.1 | 2 | |||
28.27 | even | 2 | 2128.2.a.l.1.2 | 2 | |||
35.34 | odd | 2 | 3325.2.a.n.1.1 | 2 | |||
56.13 | odd | 2 | 8512.2.a.bh.1.2 | 2 | |||
56.27 | even | 2 | 8512.2.a.l.1.1 | 2 | |||
133.132 | even | 2 | 2527.2.a.d.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
133.2.a.b.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
931.2.a.g.1.2 | 2 | 1.1 | even | 1 | trivial | ||
931.2.f.g.324.1 | 4 | 7.4 | even | 3 | |||
931.2.f.g.704.1 | 4 | 7.2 | even | 3 | |||
931.2.f.h.324.1 | 4 | 7.3 | odd | 6 | |||
931.2.f.h.704.1 | 4 | 7.5 | odd | 6 | |||
1197.2.a.h.1.1 | 2 | 21.20 | even | 2 | |||
2128.2.a.l.1.2 | 2 | 28.27 | even | 2 | |||
2527.2.a.d.1.1 | 2 | 133.132 | even | 2 | |||
3325.2.a.n.1.1 | 2 | 35.34 | odd | 2 | |||
8379.2.a.bf.1.1 | 2 | 3.2 | odd | 2 | |||
8512.2.a.l.1.1 | 2 | 56.27 | even | 2 | |||
8512.2.a.bh.1.2 | 2 | 56.13 | odd | 2 |