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: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
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 | 1.1 | ||
Root | \(1.61803\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61803 | −1.14412 | −0.572061 | − | 0.820211i | \(-0.693856\pi\) | ||||
−0.572061 | + | 0.820211i | \(0.693856\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | 0.618034 | 0.276393 | 0.138197 | − | 0.990405i | \(-0.455869\pi\) | ||||
0.138197 | + | 0.990405i | \(0.455869\pi\) | |||||||
\(6\) | −1.61803 | −0.660560 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 2.23607 | 0.674200 | 0.337100 | − | 0.941469i | \(-0.390554\pi\) | ||||
0.337100 | + | 0.941469i | \(0.390554\pi\) | |||||||
\(12\) | 0.618034 | 0.178411 | ||||||||
\(13\) | 2.38197 | 0.660639 | 0.330319 | − | 0.943869i | \(-0.392844\pi\) | ||||
0.330319 | + | 0.943869i | \(0.392844\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.618034 | 0.159576 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | −6.70820 | −1.62698 | −0.813489 | − | 0.581580i | \(-0.802435\pi\) | ||||
−0.813489 | + | 0.581580i | \(0.802435\pi\) | |||||||
\(18\) | −1.61803 | −0.381374 | ||||||||
\(19\) | 3.47214 | 0.796563 | 0.398281 | − | 0.917263i | \(-0.369607\pi\) | ||||
0.398281 | + | 0.917263i | \(0.369607\pi\) | |||||||
\(20\) | 0.381966 | 0.0854102 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.61803 | −0.771367 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 2.23607 | 0.456435 | ||||||||
\(25\) | −4.61803 | −0.923607 | ||||||||
\(26\) | −3.85410 | −0.755852 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.23607 | −1.52940 | −0.764700 | − | 0.644387i | \(-0.777113\pi\) | ||||
−0.764700 | + | 0.644387i | \(0.777113\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −6.70820 | −1.20483 | −0.602414 | − | 0.798183i | \(-0.705795\pi\) | ||||
−0.602414 | + | 0.798183i | \(0.705795\pi\) | |||||||
\(32\) | 3.38197 | 0.597853 | ||||||||
\(33\) | 2.23607 | 0.389249 | ||||||||
\(34\) | 10.8541 | 1.86146 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.618034 | 0.103006 | ||||||||
\(37\) | −11.0000 | −1.80839 | −0.904194 | − | 0.427121i | \(-0.859528\pi\) | ||||
−0.904194 | + | 0.427121i | \(0.859528\pi\) | |||||||
\(38\) | −5.61803 | −0.911365 | ||||||||
\(39\) | 2.38197 | 0.381420 | ||||||||
\(40\) | 1.38197 | 0.218508 | ||||||||
\(41\) | 1.47214 | 0.229909 | 0.114955 | − | 0.993371i | \(-0.463328\pi\) | ||||
0.114955 | + | 0.993371i | \(0.463328\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.61803 | −0.246748 | −0.123374 | − | 0.992360i | \(-0.539371\pi\) | ||||
−0.123374 | + | 0.992360i | \(0.539371\pi\) | |||||||
\(44\) | 1.38197 | 0.208339 | ||||||||
\(45\) | 0.618034 | 0.0921311 | ||||||||
\(46\) | 1.61803 | 0.238566 | ||||||||
\(47\) | 7.23607 | 1.05549 | 0.527744 | − | 0.849403i | \(-0.323038\pi\) | ||||
0.527744 | + | 0.849403i | \(0.323038\pi\) | |||||||
\(48\) | −4.85410 | −0.700629 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 7.47214 | 1.05672 | ||||||||
\(51\) | −6.70820 | −0.939336 | ||||||||
\(52\) | 1.47214 | 0.204149 | ||||||||
\(53\) | −13.0902 | −1.79807 | −0.899037 | − | 0.437874i | \(-0.855732\pi\) | ||||
−0.899037 | + | 0.437874i | \(0.855732\pi\) | |||||||
\(54\) | −1.61803 | −0.220187 | ||||||||
\(55\) | 1.38197 | 0.186344 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.47214 | 0.459896 | ||||||||
\(58\) | 13.3262 | 1.74982 | ||||||||
\(59\) | −9.38197 | −1.22143 | −0.610714 | − | 0.791851i | \(-0.709117\pi\) | ||||
−0.610714 | + | 0.791851i | \(0.709117\pi\) | |||||||
\(60\) | 0.381966 | 0.0493116 | ||||||||
\(61\) | 4.85410 | 0.621504 | 0.310752 | − | 0.950491i | \(-0.399419\pi\) | ||||
0.310752 | + | 0.950491i | \(0.399419\pi\) | |||||||
\(62\) | 10.8541 | 1.37847 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 1.47214 | 0.182596 | ||||||||
\(66\) | −3.61803 | −0.445349 | ||||||||
\(67\) | −5.09017 | −0.621863 | −0.310932 | − | 0.950432i | \(-0.600641\pi\) | ||||
−0.310932 | + | 0.950432i | \(0.600641\pi\) | |||||||
\(68\) | −4.14590 | −0.502764 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.38197 | 0.520044 | 0.260022 | − | 0.965603i | \(-0.416270\pi\) | ||||
0.260022 | + | 0.965603i | \(0.416270\pi\) | |||||||
\(72\) | 2.23607 | 0.263523 | ||||||||
\(73\) | 12.7082 | 1.48738 | 0.743691 | − | 0.668523i | \(-0.233073\pi\) | ||||
0.743691 | + | 0.668523i | \(0.233073\pi\) | |||||||
\(74\) | 17.7984 | 2.06902 | ||||||||
\(75\) | −4.61803 | −0.533245 | ||||||||
\(76\) | 2.14590 | 0.246151 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.85410 | −0.436391 | ||||||||
\(79\) | −9.47214 | −1.06570 | −0.532849 | − | 0.846210i | \(-0.678879\pi\) | ||||
−0.532849 | + | 0.846210i | \(0.678879\pi\) | |||||||
\(80\) | −3.00000 | −0.335410 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.38197 | −0.263044 | ||||||||
\(83\) | 9.18034 | 1.00767 | 0.503837 | − | 0.863799i | \(-0.331921\pi\) | ||||
0.503837 | + | 0.863799i | \(0.331921\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.14590 | −0.449686 | ||||||||
\(86\) | 2.61803 | 0.282310 | ||||||||
\(87\) | −8.23607 | −0.882999 | ||||||||
\(88\) | 5.00000 | 0.533002 | ||||||||
\(89\) | −11.6180 | −1.23151 | −0.615755 | − | 0.787938i | \(-0.711149\pi\) | ||||
−0.615755 | + | 0.787938i | \(0.711149\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.618034 | −0.0644345 | ||||||||
\(93\) | −6.70820 | −0.695608 | ||||||||
\(94\) | −11.7082 | −1.20761 | ||||||||
\(95\) | 2.14590 | 0.220164 | ||||||||
\(96\) | 3.38197 | 0.345170 | ||||||||
\(97\) | −10.4164 | −1.05763 | −0.528813 | − | 0.848738i | \(-0.677363\pi\) | ||||
−0.528813 | + | 0.848738i | \(0.677363\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.23607 | 0.224733 | ||||||||
\(100\) | −2.85410 | −0.285410 | ||||||||
\(101\) | −4.14590 | −0.412532 | −0.206266 | − | 0.978496i | \(-0.566131\pi\) | ||||
−0.206266 | + | 0.978496i | \(0.566131\pi\) | |||||||
\(102\) | 10.8541 | 1.07472 | ||||||||
\(103\) | 7.41641 | 0.730760 | 0.365380 | − | 0.930858i | \(-0.380939\pi\) | ||||
0.365380 | + | 0.930858i | \(0.380939\pi\) | |||||||
\(104\) | 5.32624 | 0.522281 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21.1803 | 2.05722 | ||||||||
\(107\) | 3.32624 | 0.321560 | 0.160780 | − | 0.986990i | \(-0.448599\pi\) | ||||
0.160780 | + | 0.986990i | \(0.448599\pi\) | |||||||
\(108\) | 0.618034 | 0.0594703 | ||||||||
\(109\) | 19.2705 | 1.84578 | 0.922890 | − | 0.385064i | \(-0.125820\pi\) | ||||
0.922890 | + | 0.385064i | \(0.125820\pi\) | |||||||
\(110\) | −2.23607 | −0.213201 | ||||||||
\(111\) | −11.0000 | −1.04407 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.909830 | −0.0855896 | −0.0427948 | − | 0.999084i | \(-0.513626\pi\) | ||||
−0.0427948 | + | 0.999084i | \(0.513626\pi\) | |||||||
\(114\) | −5.61803 | −0.526177 | ||||||||
\(115\) | −0.618034 | −0.0576320 | ||||||||
\(116\) | −5.09017 | −0.472610 | ||||||||
\(117\) | 2.38197 | 0.220213 | ||||||||
\(118\) | 15.1803 | 1.39746 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.38197 | 0.126156 | ||||||||
\(121\) | −6.00000 | −0.545455 | ||||||||
\(122\) | −7.85410 | −0.711077 | ||||||||
\(123\) | 1.47214 | 0.132738 | ||||||||
\(124\) | −4.14590 | −0.372313 | ||||||||
\(125\) | −5.94427 | −0.531672 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 22.2705 | 1.97619 | 0.988094 | − | 0.153851i | \(-0.0491675\pi\) | ||||
0.988094 | + | 0.153851i | \(0.0491675\pi\) | |||||||
\(128\) | −13.6180 | −1.20368 | ||||||||
\(129\) | −1.61803 | −0.142460 | ||||||||
\(130\) | −2.38197 | −0.208912 | ||||||||
\(131\) | −15.1803 | −1.32631 | −0.663156 | − | 0.748481i | \(-0.730784\pi\) | ||||
−0.663156 | + | 0.748481i | \(0.730784\pi\) | |||||||
\(132\) | 1.38197 | 0.120285 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.23607 | 0.711488 | ||||||||
\(135\) | 0.618034 | 0.0531919 | ||||||||
\(136\) | −15.0000 | −1.28624 | ||||||||
\(137\) | −16.4164 | −1.40255 | −0.701274 | − | 0.712892i | \(-0.747385\pi\) | ||||
−0.701274 | + | 0.712892i | \(0.747385\pi\) | |||||||
\(138\) | 1.61803 | 0.137736 | ||||||||
\(139\) | 11.3820 | 0.965406 | 0.482703 | − | 0.875784i | \(-0.339655\pi\) | ||||
0.482703 | + | 0.875784i | \(0.339655\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.23607 | 0.609387 | ||||||||
\(142\) | −7.09017 | −0.594994 | ||||||||
\(143\) | 5.32624 | 0.445402 | ||||||||
\(144\) | −4.85410 | −0.404508 | ||||||||
\(145\) | −5.09017 | −0.422716 | ||||||||
\(146\) | −20.5623 | −1.70175 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.79837 | −0.558823 | ||||||||
\(149\) | −19.2361 | −1.57588 | −0.787940 | − | 0.615752i | \(-0.788852\pi\) | ||||
−0.787940 | + | 0.615752i | \(0.788852\pi\) | |||||||
\(150\) | 7.47214 | 0.610097 | ||||||||
\(151\) | −15.2361 | −1.23989 | −0.619947 | − | 0.784644i | \(-0.712846\pi\) | ||||
−0.619947 | + | 0.784644i | \(0.712846\pi\) | |||||||
\(152\) | 7.76393 | 0.629738 | ||||||||
\(153\) | −6.70820 | −0.542326 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.14590 | −0.333007 | ||||||||
\(156\) | 1.47214 | 0.117865 | ||||||||
\(157\) | 0.291796 | 0.0232879 | 0.0116439 | − | 0.999932i | \(-0.496294\pi\) | ||||
0.0116439 | + | 0.999932i | \(0.496294\pi\) | |||||||
\(158\) | 15.3262 | 1.21929 | ||||||||
\(159\) | −13.0902 | −1.03812 | ||||||||
\(160\) | 2.09017 | 0.165242 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.61803 | −0.127125 | ||||||||
\(163\) | −0.618034 | −0.0484082 | −0.0242041 | − | 0.999707i | \(-0.507705\pi\) | ||||
−0.0242041 | + | 0.999707i | \(0.507705\pi\) | |||||||
\(164\) | 0.909830 | 0.0710458 | ||||||||
\(165\) | 1.38197 | 0.107586 | ||||||||
\(166\) | −14.8541 | −1.15290 | ||||||||
\(167\) | 7.18034 | 0.555631 | 0.277816 | − | 0.960634i | \(-0.410390\pi\) | ||||
0.277816 | + | 0.960634i | \(0.410390\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.32624 | −0.563557 | ||||||||
\(170\) | 6.70820 | 0.514496 | ||||||||
\(171\) | 3.47214 | 0.265521 | ||||||||
\(172\) | −1.00000 | −0.0762493 | ||||||||
\(173\) | 3.47214 | 0.263982 | 0.131991 | − | 0.991251i | \(-0.457863\pi\) | ||||
0.131991 | + | 0.991251i | \(0.457863\pi\) | |||||||
\(174\) | 13.3262 | 1.01026 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.8541 | −0.818159 | ||||||||
\(177\) | −9.38197 | −0.705192 | ||||||||
\(178\) | 18.7984 | 1.40900 | ||||||||
\(179\) | 1.85410 | 0.138582 | 0.0692910 | − | 0.997596i | \(-0.477926\pi\) | ||||
0.0692910 | + | 0.997596i | \(0.477926\pi\) | |||||||
\(180\) | 0.381966 | 0.0284701 | ||||||||
\(181\) | 1.94427 | 0.144517 | 0.0722583 | − | 0.997386i | \(-0.476979\pi\) | ||||
0.0722583 | + | 0.997386i | \(0.476979\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.85410 | 0.358826 | ||||||||
\(184\) | −2.23607 | −0.164845 | ||||||||
\(185\) | −6.79837 | −0.499826 | ||||||||
\(186\) | 10.8541 | 0.795861 | ||||||||
\(187\) | −15.0000 | −1.09691 | ||||||||
\(188\) | 4.47214 | 0.326164 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.47214 | −0.251895 | ||||||||
\(191\) | 16.1803 | 1.17077 | 0.585384 | − | 0.810756i | \(-0.300944\pi\) | ||||
0.585384 | + | 0.810756i | \(0.300944\pi\) | |||||||
\(192\) | 4.23607 | 0.305712 | ||||||||
\(193\) | 8.29180 | 0.596857 | 0.298428 | − | 0.954432i | \(-0.403538\pi\) | ||||
0.298428 | + | 0.954432i | \(0.403538\pi\) | |||||||
\(194\) | 16.8541 | 1.21005 | ||||||||
\(195\) | 1.47214 | 0.105422 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.5066 | −1.81727 | −0.908634 | − | 0.417593i | \(-0.862874\pi\) | ||||
−0.908634 | + | 0.417593i | \(0.862874\pi\) | |||||||
\(198\) | −3.61803 | −0.257122 | ||||||||
\(199\) | 6.90983 | 0.489825 | 0.244912 | − | 0.969545i | \(-0.421241\pi\) | ||||
0.244912 | + | 0.969545i | \(0.421241\pi\) | |||||||
\(200\) | −10.3262 | −0.730175 | ||||||||
\(201\) | −5.09017 | −0.359033 | ||||||||
\(202\) | 6.70820 | 0.471988 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.14590 | −0.290271 | ||||||||
\(205\) | 0.909830 | 0.0635453 | ||||||||
\(206\) | −12.0000 | −0.836080 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −11.5623 | −0.801702 | ||||||||
\(209\) | 7.76393 | 0.537042 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.4164 | 0.717095 | 0.358548 | − | 0.933511i | \(-0.383272\pi\) | ||||
0.358548 | + | 0.933511i | \(0.383272\pi\) | |||||||
\(212\) | −8.09017 | −0.555635 | ||||||||
\(213\) | 4.38197 | 0.300247 | ||||||||
\(214\) | −5.38197 | −0.367904 | ||||||||
\(215\) | −1.00000 | −0.0681994 | ||||||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −31.1803 | −2.11180 | ||||||||
\(219\) | 12.7082 | 0.858741 | ||||||||
\(220\) | 0.854102 | 0.0575835 | ||||||||
\(221\) | −15.9787 | −1.07484 | ||||||||
\(222\) | 17.7984 | 1.19455 | ||||||||
\(223\) | 17.8541 | 1.19560 | 0.597800 | − | 0.801646i | \(-0.296042\pi\) | ||||
0.597800 | + | 0.801646i | \(0.296042\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.61803 | −0.307869 | ||||||||
\(226\) | 1.47214 | 0.0979250 | ||||||||
\(227\) | −24.3262 | −1.61459 | −0.807295 | − | 0.590149i | \(-0.799069\pi\) | ||||
−0.807295 | + | 0.590149i | \(0.799069\pi\) | |||||||
\(228\) | 2.14590 | 0.142116 | ||||||||
\(229\) | 16.3262 | 1.07887 | 0.539434 | − | 0.842028i | \(-0.318638\pi\) | ||||
0.539434 | + | 0.842028i | \(0.318638\pi\) | |||||||
\(230\) | 1.00000 | 0.0659380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18.4164 | −1.20910 | ||||||||
\(233\) | −11.0902 | −0.726541 | −0.363271 | − | 0.931684i | \(-0.618340\pi\) | ||||
−0.363271 | + | 0.931684i | \(0.618340\pi\) | |||||||
\(234\) | −3.85410 | −0.251951 | ||||||||
\(235\) | 4.47214 | 0.291730 | ||||||||
\(236\) | −5.79837 | −0.377442 | ||||||||
\(237\) | −9.47214 | −0.615281 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.79837 | −0.310381 | −0.155191 | − | 0.987885i | \(-0.549599\pi\) | ||||
−0.155191 | + | 0.987885i | \(0.549599\pi\) | |||||||
\(240\) | −3.00000 | −0.193649 | ||||||||
\(241\) | 11.0000 | 0.708572 | 0.354286 | − | 0.935137i | \(-0.384724\pi\) | ||||
0.354286 | + | 0.935137i | \(0.384724\pi\) | |||||||
\(242\) | 9.70820 | 0.624067 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.00000 | 0.192055 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.38197 | −0.151869 | ||||||||
\(247\) | 8.27051 | 0.526240 | ||||||||
\(248\) | −15.0000 | −0.952501 | ||||||||
\(249\) | 9.18034 | 0.581780 | ||||||||
\(250\) | 9.61803 | 0.608298 | ||||||||
\(251\) | −23.1246 | −1.45961 | −0.729806 | − | 0.683654i | \(-0.760390\pi\) | ||||
−0.729806 | + | 0.683654i | \(0.760390\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.23607 | −0.140580 | ||||||||
\(254\) | −36.0344 | −2.26100 | ||||||||
\(255\) | −4.14590 | −0.259626 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 3.23607 | 0.201860 | 0.100930 | − | 0.994894i | \(-0.467818\pi\) | ||||
0.100930 | + | 0.994894i | \(0.467818\pi\) | |||||||
\(258\) | 2.61803 | 0.162992 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.909830 | 0.0564253 | ||||||||
\(261\) | −8.23607 | −0.509800 | ||||||||
\(262\) | 24.5623 | 1.51746 | ||||||||
\(263\) | −0.0557281 | −0.00343634 | −0.00171817 | − | 0.999999i | \(-0.500547\pi\) | ||||
−0.00171817 | + | 0.999999i | \(0.500547\pi\) | |||||||
\(264\) | 5.00000 | 0.307729 | ||||||||
\(265\) | −8.09017 | −0.496975 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.6180 | −0.711012 | ||||||||
\(268\) | −3.14590 | −0.192166 | ||||||||
\(269\) | 32.0902 | 1.95657 | 0.978286 | − | 0.207259i | \(-0.0664543\pi\) | ||||
0.978286 | + | 0.207259i | \(0.0664543\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −21.9443 | −1.33302 | −0.666510 | − | 0.745496i | \(-0.732213\pi\) | ||||
−0.666510 | + | 0.745496i | \(0.732213\pi\) | |||||||
\(272\) | 32.5623 | 1.97438 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 26.5623 | 1.60469 | ||||||||
\(275\) | −10.3262 | −0.622696 | ||||||||
\(276\) | −0.618034 | −0.0372013 | ||||||||
\(277\) | 4.27051 | 0.256590 | 0.128295 | − | 0.991736i | \(-0.459050\pi\) | ||||
0.128295 | + | 0.991736i | \(0.459050\pi\) | |||||||
\(278\) | −18.4164 | −1.10454 | ||||||||
\(279\) | −6.70820 | −0.401610 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.70820 | −0.221213 | −0.110606 | − | 0.993864i | \(-0.535279\pi\) | ||||
−0.110606 | + | 0.993864i | \(0.535279\pi\) | |||||||
\(282\) | −11.7082 | −0.697213 | ||||||||
\(283\) | 26.2148 | 1.55831 | 0.779154 | − | 0.626833i | \(-0.215649\pi\) | ||||
0.779154 | + | 0.626833i | \(0.215649\pi\) | |||||||
\(284\) | 2.70820 | 0.160702 | ||||||||
\(285\) | 2.14590 | 0.127112 | ||||||||
\(286\) | −8.61803 | −0.509595 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.38197 | 0.199284 | ||||||||
\(289\) | 28.0000 | 1.64706 | ||||||||
\(290\) | 8.23607 | 0.483639 | ||||||||
\(291\) | −10.4164 | −0.610621 | ||||||||
\(292\) | 7.85410 | 0.459627 | ||||||||
\(293\) | −12.0000 | −0.701047 | −0.350524 | − | 0.936554i | \(-0.613996\pi\) | ||||
−0.350524 | + | 0.936554i | \(0.613996\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.79837 | −0.337594 | ||||||||
\(296\) | −24.5967 | −1.42966 | ||||||||
\(297\) | 2.23607 | 0.129750 | ||||||||
\(298\) | 31.1246 | 1.80300 | ||||||||
\(299\) | −2.38197 | −0.137753 | ||||||||
\(300\) | −2.85410 | −0.164782 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 24.6525 | 1.41859 | ||||||||
\(303\) | −4.14590 | −0.238176 | ||||||||
\(304\) | −16.8541 | −0.966649 | ||||||||
\(305\) | 3.00000 | 0.171780 | ||||||||
\(306\) | 10.8541 | 0.620488 | ||||||||
\(307\) | −16.1246 | −0.920280 | −0.460140 | − | 0.887846i | \(-0.652201\pi\) | ||||
−0.460140 | + | 0.887846i | \(0.652201\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.41641 | 0.421905 | ||||||||
\(310\) | 6.70820 | 0.381000 | ||||||||
\(311\) | −15.3262 | −0.869071 | −0.434536 | − | 0.900655i | \(-0.643087\pi\) | ||||
−0.434536 | + | 0.900655i | \(0.643087\pi\) | |||||||
\(312\) | 5.32624 | 0.301539 | ||||||||
\(313\) | 2.47214 | 0.139733 | 0.0698667 | − | 0.997556i | \(-0.477743\pi\) | ||||
0.0698667 | + | 0.997556i | \(0.477743\pi\) | |||||||
\(314\) | −0.472136 | −0.0266442 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.85410 | −0.329319 | ||||||||
\(317\) | 14.5066 | 0.814771 | 0.407385 | − | 0.913256i | \(-0.366441\pi\) | ||||
0.407385 | + | 0.913256i | \(0.366441\pi\) | |||||||
\(318\) | 21.1803 | 1.18773 | ||||||||
\(319\) | −18.4164 | −1.03112 | ||||||||
\(320\) | 2.61803 | 0.146353 | ||||||||
\(321\) | 3.32624 | 0.185652 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.2918 | −1.29599 | ||||||||
\(324\) | 0.618034 | 0.0343352 | ||||||||
\(325\) | −11.0000 | −0.610170 | ||||||||
\(326\) | 1.00000 | 0.0553849 | ||||||||
\(327\) | 19.2705 | 1.06566 | ||||||||
\(328\) | 3.29180 | 0.181759 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.23607 | −0.123091 | ||||||||
\(331\) | −13.4164 | −0.737432 | −0.368716 | − | 0.929542i | \(-0.620203\pi\) | ||||
−0.368716 | + | 0.929542i | \(0.620203\pi\) | |||||||
\(332\) | 5.67376 | 0.311388 | ||||||||
\(333\) | −11.0000 | −0.602796 | ||||||||
\(334\) | −11.6180 | −0.635711 | ||||||||
\(335\) | −3.14590 | −0.171879 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.50658 | −0.408909 | −0.204455 | − | 0.978876i | \(-0.565542\pi\) | ||||
−0.204455 | + | 0.978876i | \(0.565542\pi\) | |||||||
\(338\) | 11.8541 | 0.644778 | ||||||||
\(339\) | −0.909830 | −0.0494152 | ||||||||
\(340\) | −2.56231 | −0.138961 | ||||||||
\(341\) | −15.0000 | −0.812296 | ||||||||
\(342\) | −5.61803 | −0.303788 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.61803 | −0.195071 | ||||||||
\(345\) | −0.618034 | −0.0332738 | ||||||||
\(346\) | −5.61803 | −0.302027 | ||||||||
\(347\) | 5.18034 | 0.278095 | 0.139048 | − | 0.990286i | \(-0.455596\pi\) | ||||
0.139048 | + | 0.990286i | \(0.455596\pi\) | |||||||
\(348\) | −5.09017 | −0.272862 | ||||||||
\(349\) | 11.8541 | 0.634536 | 0.317268 | − | 0.948336i | \(-0.397235\pi\) | ||||
0.317268 | + | 0.948336i | \(0.397235\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.38197 | 0.127140 | ||||||||
\(352\) | 7.56231 | 0.403072 | ||||||||
\(353\) | −30.3050 | −1.61297 | −0.806485 | − | 0.591255i | \(-0.798633\pi\) | ||||
−0.806485 | + | 0.591255i | \(0.798633\pi\) | |||||||
\(354\) | 15.1803 | 0.806826 | ||||||||
\(355\) | 2.70820 | 0.143737 | ||||||||
\(356\) | −7.18034 | −0.380557 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.00000 | −0.158555 | ||||||||
\(359\) | 23.0902 | 1.21865 | 0.609326 | − | 0.792920i | \(-0.291440\pi\) | ||||
0.609326 | + | 0.792920i | \(0.291440\pi\) | |||||||
\(360\) | 1.38197 | 0.0728360 | ||||||||
\(361\) | −6.94427 | −0.365488 | ||||||||
\(362\) | −3.14590 | −0.165345 | ||||||||
\(363\) | −6.00000 | −0.314918 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.85410 | 0.411102 | ||||||||
\(366\) | −7.85410 | −0.410540 | ||||||||
\(367\) | −10.8541 | −0.566580 | −0.283290 | − | 0.959034i | \(-0.591426\pi\) | ||||
−0.283290 | + | 0.959034i | \(0.591426\pi\) | |||||||
\(368\) | 4.85410 | 0.253038 | ||||||||
\(369\) | 1.47214 | 0.0766363 | ||||||||
\(370\) | 11.0000 | 0.571863 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.14590 | −0.214955 | ||||||||
\(373\) | 24.4164 | 1.26423 | 0.632117 | − | 0.774873i | \(-0.282186\pi\) | ||||
0.632117 | + | 0.774873i | \(0.282186\pi\) | |||||||
\(374\) | 24.2705 | 1.25500 | ||||||||
\(375\) | −5.94427 | −0.306961 | ||||||||
\(376\) | 16.1803 | 0.834437 | ||||||||
\(377\) | −19.6180 | −1.01038 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.41641 | 0.380955 | 0.190478 | − | 0.981692i | \(-0.438996\pi\) | ||||
0.190478 | + | 0.981692i | \(0.438996\pi\) | |||||||
\(380\) | 1.32624 | 0.0680346 | ||||||||
\(381\) | 22.2705 | 1.14095 | ||||||||
\(382\) | −26.1803 | −1.33950 | ||||||||
\(383\) | 0.708204 | 0.0361875 | 0.0180938 | − | 0.999836i | \(-0.494240\pi\) | ||||
0.0180938 | + | 0.999836i | \(0.494240\pi\) | |||||||
\(384\) | −13.6180 | −0.694942 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.4164 | −0.682877 | ||||||||
\(387\) | −1.61803 | −0.0822493 | ||||||||
\(388\) | −6.43769 | −0.326824 | ||||||||
\(389\) | 5.29180 | 0.268305 | 0.134152 | − | 0.990961i | \(-0.457169\pi\) | ||||
0.134152 | + | 0.990961i | \(0.457169\pi\) | |||||||
\(390\) | −2.38197 | −0.120616 | ||||||||
\(391\) | 6.70820 | 0.339248 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.1803 | −0.765747 | ||||||||
\(394\) | 41.2705 | 2.07918 | ||||||||
\(395\) | −5.85410 | −0.294552 | ||||||||
\(396\) | 1.38197 | 0.0694464 | ||||||||
\(397\) | −22.0689 | −1.10761 | −0.553803 | − | 0.832648i | \(-0.686824\pi\) | ||||
−0.553803 | + | 0.832648i | \(0.686824\pi\) | |||||||
\(398\) | −11.1803 | −0.560420 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 22.4164 | 1.12082 | ||||||||
\(401\) | 33.1803 | 1.65695 | 0.828474 | − | 0.560028i | \(-0.189210\pi\) | ||||
0.828474 | + | 0.560028i | \(0.189210\pi\) | |||||||
\(402\) | 8.23607 | 0.410778 | ||||||||
\(403\) | −15.9787 | −0.795956 | ||||||||
\(404\) | −2.56231 | −0.127479 | ||||||||
\(405\) | 0.618034 | 0.0307104 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.5967 | −1.21922 | ||||||||
\(408\) | −15.0000 | −0.742611 | ||||||||
\(409\) | −6.41641 | −0.317271 | −0.158635 | − | 0.987337i | \(-0.550709\pi\) | ||||
−0.158635 | + | 0.987337i | \(0.550709\pi\) | |||||||
\(410\) | −1.47214 | −0.0727036 | ||||||||
\(411\) | −16.4164 | −0.809762 | ||||||||
\(412\) | 4.58359 | 0.225817 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.61803 | 0.0795220 | ||||||||
\(415\) | 5.67376 | 0.278514 | ||||||||
\(416\) | 8.05573 | 0.394965 | ||||||||
\(417\) | 11.3820 | 0.557377 | ||||||||
\(418\) | −12.5623 | −0.614442 | ||||||||
\(419\) | −15.6738 | −0.765713 | −0.382857 | − | 0.923808i | \(-0.625060\pi\) | ||||
−0.382857 | + | 0.923808i | \(0.625060\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.2705 | −0.500554 | −0.250277 | − | 0.968174i | \(-0.580522\pi\) | ||||
−0.250277 | + | 0.968174i | \(0.580522\pi\) | |||||||
\(422\) | −16.8541 | −0.820445 | ||||||||
\(423\) | 7.23607 | 0.351830 | ||||||||
\(424\) | −29.2705 | −1.42150 | ||||||||
\(425\) | 30.9787 | 1.50269 | ||||||||
\(426\) | −7.09017 | −0.343520 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.05573 | 0.0993674 | ||||||||
\(429\) | 5.32624 | 0.257153 | ||||||||
\(430\) | 1.61803 | 0.0780285 | ||||||||
\(431\) | 0.673762 | 0.0324540 | 0.0162270 | − | 0.999868i | \(-0.494835\pi\) | ||||
0.0162270 | + | 0.999868i | \(0.494835\pi\) | |||||||
\(432\) | −4.85410 | −0.233543 | ||||||||
\(433\) | −19.1246 | −0.919070 | −0.459535 | − | 0.888160i | \(-0.651984\pi\) | ||||
−0.459535 | + | 0.888160i | \(0.651984\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.09017 | −0.244055 | ||||||||
\(436\) | 11.9098 | 0.570377 | ||||||||
\(437\) | −3.47214 | −0.166095 | ||||||||
\(438\) | −20.5623 | −0.982505 | ||||||||
\(439\) | −23.6525 | −1.12887 | −0.564436 | − | 0.825477i | \(-0.690906\pi\) | ||||
−0.564436 | + | 0.825477i | \(0.690906\pi\) | |||||||
\(440\) | 3.09017 | 0.147318 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 25.8541 | 1.22975 | ||||||||
\(443\) | −9.52786 | −0.452682 | −0.226341 | − | 0.974048i | \(-0.572676\pi\) | ||||
−0.226341 | + | 0.974048i | \(0.572676\pi\) | |||||||
\(444\) | −6.79837 | −0.322637 | ||||||||
\(445\) | −7.18034 | −0.340381 | ||||||||
\(446\) | −28.8885 | −1.36791 | ||||||||
\(447\) | −19.2361 | −0.909835 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.4377 | −0.870129 | −0.435064 | − | 0.900399i | \(-0.643274\pi\) | ||||
−0.435064 | + | 0.900399i | \(0.643274\pi\) | |||||||
\(450\) | 7.47214 | 0.352240 | ||||||||
\(451\) | 3.29180 | 0.155005 | ||||||||
\(452\) | −0.562306 | −0.0264486 | ||||||||
\(453\) | −15.2361 | −0.715853 | ||||||||
\(454\) | 39.3607 | 1.84729 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.76393 | 0.363579 | ||||||||
\(457\) | −14.3262 | −0.670153 | −0.335077 | − | 0.942191i | \(-0.608762\pi\) | ||||
−0.335077 | + | 0.942191i | \(0.608762\pi\) | |||||||
\(458\) | −26.4164 | −1.23436 | ||||||||
\(459\) | −6.70820 | −0.313112 | ||||||||
\(460\) | −0.381966 | −0.0178093 | ||||||||
\(461\) | −25.4508 | −1.18536 | −0.592682 | − | 0.805436i | \(-0.701931\pi\) | ||||
−0.592682 | + | 0.805436i | \(0.701931\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.2918 | 0.803618 | 0.401809 | − | 0.915724i | \(-0.368382\pi\) | ||||
0.401809 | + | 0.915724i | \(0.368382\pi\) | |||||||
\(464\) | 39.9787 | 1.85597 | ||||||||
\(465\) | −4.14590 | −0.192261 | ||||||||
\(466\) | 17.9443 | 0.831252 | ||||||||
\(467\) | 15.1803 | 0.702462 | 0.351231 | − | 0.936289i | \(-0.385763\pi\) | ||||
0.351231 | + | 0.936289i | \(0.385763\pi\) | |||||||
\(468\) | 1.47214 | 0.0680495 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7.23607 | −0.333775 | ||||||||
\(471\) | 0.291796 | 0.0134453 | ||||||||
\(472\) | −20.9787 | −0.965624 | ||||||||
\(473\) | −3.61803 | −0.166357 | ||||||||
\(474\) | 15.3262 | 0.703957 | ||||||||
\(475\) | −16.0344 | −0.735711 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.0902 | −0.599358 | ||||||||
\(478\) | 7.76393 | 0.355114 | ||||||||
\(479\) | −21.0000 | −0.959514 | −0.479757 | − | 0.877401i | \(-0.659275\pi\) | ||||
−0.479757 | + | 0.877401i | \(0.659275\pi\) | |||||||
\(480\) | 2.09017 | 0.0954028 | ||||||||
\(481\) | −26.2016 | −1.19469 | ||||||||
\(482\) | −17.7984 | −0.810694 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.70820 | −0.168555 | ||||||||
\(485\) | −6.43769 | −0.292321 | ||||||||
\(486\) | −1.61803 | −0.0733955 | ||||||||
\(487\) | −29.2918 | −1.32734 | −0.663669 | − | 0.748026i | \(-0.731002\pi\) | ||||
−0.663669 | + | 0.748026i | \(0.731002\pi\) | |||||||
\(488\) | 10.8541 | 0.491342 | ||||||||
\(489\) | −0.618034 | −0.0279485 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.79837 | 0.442194 | 0.221097 | − | 0.975252i | \(-0.429036\pi\) | ||||
0.221097 | + | 0.975252i | \(0.429036\pi\) | |||||||
\(492\) | 0.909830 | 0.0410183 | ||||||||
\(493\) | 55.2492 | 2.48830 | ||||||||
\(494\) | −13.3820 | −0.602083 | ||||||||
\(495\) | 1.38197 | 0.0621148 | ||||||||
\(496\) | 32.5623 | 1.46209 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −14.8541 | −0.665628 | ||||||||
\(499\) | −38.3951 | −1.71880 | −0.859401 | − | 0.511302i | \(-0.829163\pi\) | ||||
−0.859401 | + | 0.511302i | \(0.829163\pi\) | |||||||
\(500\) | −3.67376 | −0.164296 | ||||||||
\(501\) | 7.18034 | 0.320794 | ||||||||
\(502\) | 37.4164 | 1.66998 | ||||||||
\(503\) | −36.3262 | −1.61971 | −0.809853 | − | 0.586632i | \(-0.800453\pi\) | ||||
−0.809853 | + | 0.586632i | \(0.800453\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.56231 | −0.114021 | ||||||||
\(506\) | 3.61803 | 0.160841 | ||||||||
\(507\) | −7.32624 | −0.325370 | ||||||||
\(508\) | 13.7639 | 0.610676 | ||||||||
\(509\) | 15.5967 | 0.691314 | 0.345657 | − | 0.938361i | \(-0.387656\pi\) | ||||
0.345657 | + | 0.938361i | \(0.387656\pi\) | |||||||
\(510\) | 6.70820 | 0.297044 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5.29180 | 0.233867 | ||||||||
\(513\) | 3.47214 | 0.153299 | ||||||||
\(514\) | −5.23607 | −0.230953 | ||||||||
\(515\) | 4.58359 | 0.201977 | ||||||||
\(516\) | −1.00000 | −0.0440225 | ||||||||
\(517\) | 16.1803 | 0.711611 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.47214 | 0.152410 | ||||||||
\(520\) | 3.29180 | 0.144355 | ||||||||
\(521\) | −3.52786 | −0.154559 | −0.0772793 | − | 0.997009i | \(-0.524623\pi\) | ||||
−0.0772793 | + | 0.997009i | \(0.524623\pi\) | |||||||
\(522\) | 13.3262 | 0.583274 | ||||||||
\(523\) | −21.4164 | −0.936474 | −0.468237 | − | 0.883603i | \(-0.655111\pi\) | ||||
−0.468237 | + | 0.883603i | \(0.655111\pi\) | |||||||
\(524\) | −9.38197 | −0.409853 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.0901699 | 0.00393160 | ||||||||
\(527\) | 45.0000 | 1.96023 | ||||||||
\(528\) | −10.8541 | −0.472364 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 13.0902 | 0.568601 | ||||||||
\(531\) | −9.38197 | −0.407143 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.50658 | 0.151887 | ||||||||
\(534\) | 18.7984 | 0.813485 | ||||||||
\(535\) | 2.05573 | 0.0888769 | ||||||||
\(536\) | −11.3820 | −0.491626 | ||||||||
\(537\) | 1.85410 | 0.0800104 | ||||||||
\(538\) | −51.9230 | −2.23856 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.381966 | 0.0164372 | ||||||||
\(541\) | −5.12461 | −0.220324 | −0.110162 | − | 0.993914i | \(-0.535137\pi\) | ||||
−0.110162 | + | 0.993914i | \(0.535137\pi\) | |||||||
\(542\) | 35.5066 | 1.52514 | ||||||||
\(543\) | 1.94427 | 0.0834367 | ||||||||
\(544\) | −22.6869 | −0.972694 | ||||||||
\(545\) | 11.9098 | 0.510161 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.7984 | 0.547219 | 0.273609 | − | 0.961841i | \(-0.411782\pi\) | ||||
0.273609 | + | 0.961841i | \(0.411782\pi\) | |||||||
\(548\) | −10.1459 | −0.433411 | ||||||||
\(549\) | 4.85410 | 0.207168 | ||||||||
\(550\) | 16.7082 | 0.712440 | ||||||||
\(551\) | −28.5967 | −1.21826 | ||||||||
\(552\) | −2.23607 | −0.0951734 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.90983 | −0.293571 | ||||||||
\(555\) | −6.79837 | −0.288575 | ||||||||
\(556\) | 7.03444 | 0.298327 | ||||||||
\(557\) | −5.81966 | −0.246587 | −0.123293 | − | 0.992370i | \(-0.539346\pi\) | ||||
−0.123293 | + | 0.992370i | \(0.539346\pi\) | |||||||
\(558\) | 10.8541 | 0.459491 | ||||||||
\(559\) | −3.85410 | −0.163011 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.0000 | −0.633300 | ||||||||
\(562\) | 6.00000 | 0.253095 | ||||||||
\(563\) | 23.5066 | 0.990684 | 0.495342 | − | 0.868698i | \(-0.335043\pi\) | ||||
0.495342 | + | 0.868698i | \(0.335043\pi\) | |||||||
\(564\) | 4.47214 | 0.188311 | ||||||||
\(565\) | −0.562306 | −0.0236564 | ||||||||
\(566\) | −42.4164 | −1.78289 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.79837 | 0.411131 | ||||||||
\(569\) | −16.3607 | −0.685875 | −0.342938 | − | 0.939358i | \(-0.611422\pi\) | ||||
−0.342938 | + | 0.939358i | \(0.611422\pi\) | |||||||
\(570\) | −3.47214 | −0.145432 | ||||||||
\(571\) | −44.4164 | −1.85877 | −0.929384 | − | 0.369113i | \(-0.879661\pi\) | ||||
−0.929384 | + | 0.369113i | \(0.879661\pi\) | |||||||
\(572\) | 3.29180 | 0.137637 | ||||||||
\(573\) | 16.1803 | 0.675943 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.61803 | 0.192585 | ||||||||
\(576\) | 4.23607 | 0.176503 | ||||||||
\(577\) | 36.8328 | 1.53337 | 0.766685 | − | 0.642023i | \(-0.221905\pi\) | ||||
0.766685 | + | 0.642023i | \(0.221905\pi\) | |||||||
\(578\) | −45.3050 | −1.88444 | ||||||||
\(579\) | 8.29180 | 0.344595 | ||||||||
\(580\) | −3.14590 | −0.130626 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 16.8541 | 0.698625 | ||||||||
\(583\) | −29.2705 | −1.21226 | ||||||||
\(584\) | 28.4164 | 1.17588 | ||||||||
\(585\) | 1.47214 | 0.0608653 | ||||||||
\(586\) | 19.4164 | 0.802084 | ||||||||
\(587\) | 31.0344 | 1.28093 | 0.640464 | − | 0.767988i | \(-0.278742\pi\) | ||||
0.640464 | + | 0.767988i | \(0.278742\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.2918 | −0.959722 | ||||||||
\(590\) | 9.38197 | 0.386249 | ||||||||
\(591\) | −25.5066 | −1.04920 | ||||||||
\(592\) | 53.3951 | 2.19453 | ||||||||
\(593\) | 32.0689 | 1.31691 | 0.658456 | − | 0.752620i | \(-0.271210\pi\) | ||||
0.658456 | + | 0.752620i | \(0.271210\pi\) | |||||||
\(594\) | −3.61803 | −0.148450 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.8885 | −0.486974 | ||||||||
\(597\) | 6.90983 | 0.282801 | ||||||||
\(598\) | 3.85410 | 0.157606 | ||||||||
\(599\) | −15.5066 | −0.633582 | −0.316791 | − | 0.948495i | \(-0.602605\pi\) | ||||
−0.316791 | + | 0.948495i | \(0.602605\pi\) | |||||||
\(600\) | −10.3262 | −0.421567 | ||||||||
\(601\) | −0.909830 | −0.0371127 | −0.0185564 | − | 0.999828i | \(-0.505907\pi\) | ||||
−0.0185564 | + | 0.999828i | \(0.505907\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.09017 | −0.207288 | ||||||||
\(604\) | −9.41641 | −0.383148 | ||||||||
\(605\) | −3.70820 | −0.150760 | ||||||||
\(606\) | 6.70820 | 0.272502 | ||||||||
\(607\) | 33.7984 | 1.37183 | 0.685917 | − | 0.727680i | \(-0.259401\pi\) | ||||
0.685917 | + | 0.727680i | \(0.259401\pi\) | |||||||
\(608\) | 11.7426 | 0.476227 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.85410 | −0.196537 | ||||||||
\(611\) | 17.2361 | 0.697297 | ||||||||
\(612\) | −4.14590 | −0.167588 | ||||||||
\(613\) | −11.6525 | −0.470639 | −0.235320 | − | 0.971918i | \(-0.575614\pi\) | ||||
−0.235320 | + | 0.971918i | \(0.575614\pi\) | |||||||
\(614\) | 26.0902 | 1.05291 | ||||||||
\(615\) | 0.909830 | 0.0366879 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.67376 | −0.107642 | −0.0538208 | − | 0.998551i | \(-0.517140\pi\) | ||||
−0.0538208 | + | 0.998551i | \(0.517140\pi\) | |||||||
\(618\) | −12.0000 | −0.482711 | ||||||||
\(619\) | 19.6180 | 0.788515 | 0.394258 | − | 0.919000i | \(-0.371002\pi\) | ||||
0.394258 | + | 0.919000i | \(0.371002\pi\) | |||||||
\(620\) | −2.56231 | −0.102905 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 24.7984 | 0.994324 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −11.5623 | −0.462863 | ||||||||
\(625\) | 19.4164 | 0.776656 | ||||||||
\(626\) | −4.00000 | −0.159872 | ||||||||
\(627\) | 7.76393 | 0.310062 | ||||||||
\(628\) | 0.180340 | 0.00719634 | ||||||||
\(629\) | 73.7902 | 2.94221 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.1246 | 0.641911 | 0.320955 | − | 0.947094i | \(-0.395996\pi\) | ||||
0.320955 | + | 0.947094i | \(0.395996\pi\) | |||||||
\(632\) | −21.1803 | −0.842509 | ||||||||
\(633\) | 10.4164 | 0.414015 | ||||||||
\(634\) | −23.4721 | −0.932198 | ||||||||
\(635\) | 13.7639 | 0.546205 | ||||||||
\(636\) | −8.09017 | −0.320796 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 29.7984 | 1.17973 | ||||||||
\(639\) | 4.38197 | 0.173348 | ||||||||
\(640\) | −8.41641 | −0.332688 | ||||||||
\(641\) | 17.7984 | 0.702994 | 0.351497 | − | 0.936189i | \(-0.385673\pi\) | ||||
0.351497 | + | 0.936189i | \(0.385673\pi\) | |||||||
\(642\) | −5.38197 | −0.212409 | ||||||||
\(643\) | 11.9787 | 0.472394 | 0.236197 | − | 0.971705i | \(-0.424099\pi\) | ||||
0.236197 | + | 0.971705i | \(0.424099\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.00000 | −0.0393750 | ||||||||
\(646\) | 37.6869 | 1.48277 | ||||||||
\(647\) | 24.0344 | 0.944891 | 0.472446 | − | 0.881360i | \(-0.343371\pi\) | ||||
0.472446 | + | 0.881360i | \(0.343371\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | −20.9787 | −0.823487 | ||||||||
\(650\) | 17.7984 | 0.698110 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.381966 | −0.0149589 | ||||||||
\(653\) | 27.7426 | 1.08565 | 0.542827 | − | 0.839845i | \(-0.317354\pi\) | ||||
0.542827 | + | 0.839845i | \(0.317354\pi\) | |||||||
\(654\) | −31.1803 | −1.21925 | ||||||||
\(655\) | −9.38197 | −0.366584 | ||||||||
\(656\) | −7.14590 | −0.279000 | ||||||||
\(657\) | 12.7082 | 0.495794 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.65248 | 0.376007 | 0.188004 | − | 0.982168i | \(-0.439798\pi\) | ||||
0.188004 | + | 0.982168i | \(0.439798\pi\) | |||||||
\(660\) | 0.854102 | 0.0332459 | ||||||||
\(661\) | −14.4164 | −0.560733 | −0.280367 | − | 0.959893i | \(-0.590456\pi\) | ||||
−0.280367 | + | 0.959893i | \(0.590456\pi\) | |||||||
\(662\) | 21.7082 | 0.843713 | ||||||||
\(663\) | −15.9787 | −0.620562 | ||||||||
\(664\) | 20.5279 | 0.796636 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 17.7984 | 0.689673 | ||||||||
\(667\) | 8.23607 | 0.318902 | ||||||||
\(668\) | 4.43769 | 0.171700 | ||||||||
\(669\) | 17.8541 | 0.690279 | ||||||||
\(670\) | 5.09017 | 0.196650 | ||||||||
\(671\) | 10.8541 | 0.419018 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.4164 | 0.478617 | 0.239309 | − | 0.970944i | \(-0.423079\pi\) | ||||
0.239309 | + | 0.970944i | \(0.423079\pi\) | |||||||
\(674\) | 12.1459 | 0.467843 | ||||||||
\(675\) | −4.61803 | −0.177748 | ||||||||
\(676\) | −4.52786 | −0.174149 | ||||||||
\(677\) | 1.25735 | 0.0483240 | 0.0241620 | − | 0.999708i | \(-0.492308\pi\) | ||||
0.0241620 | + | 0.999708i | \(0.492308\pi\) | |||||||
\(678\) | 1.47214 | 0.0565370 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9.27051 | −0.355508 | ||||||||
\(681\) | −24.3262 | −0.932183 | ||||||||
\(682\) | 24.2705 | 0.929366 | ||||||||
\(683\) | 26.0132 | 0.995366 | 0.497683 | − | 0.867359i | \(-0.334184\pi\) | ||||
0.497683 | + | 0.867359i | \(0.334184\pi\) | |||||||
\(684\) | 2.14590 | 0.0820505 | ||||||||
\(685\) | −10.1459 | −0.387655 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.3262 | 0.622885 | ||||||||
\(688\) | 7.85410 | 0.299435 | ||||||||
\(689\) | −31.1803 | −1.18788 | ||||||||
\(690\) | 1.00000 | 0.0380693 | ||||||||
\(691\) | 7.72949 | 0.294044 | 0.147022 | − | 0.989133i | \(-0.453031\pi\) | ||||
0.147022 | + | 0.989133i | \(0.453031\pi\) | |||||||
\(692\) | 2.14590 | 0.0815748 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.38197 | −0.318175 | ||||||||
\(695\) | 7.03444 | 0.266832 | ||||||||
\(696\) | −18.4164 | −0.698072 | ||||||||
\(697\) | −9.87539 | −0.374057 | ||||||||
\(698\) | −19.1803 | −0.725987 | ||||||||
\(699\) | −11.0902 | −0.419469 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.4508 | 1.41450 | 0.707250 | − | 0.706964i | \(-0.249936\pi\) | ||||
0.707250 | + | 0.706964i | \(0.249936\pi\) | |||||||
\(702\) | −3.85410 | −0.145464 | ||||||||
\(703\) | −38.1935 | −1.44049 | ||||||||
\(704\) | 9.47214 | 0.356995 | ||||||||
\(705\) | 4.47214 | 0.168430 | ||||||||
\(706\) | 49.0344 | 1.84544 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −5.79837 | −0.217916 | ||||||||
\(709\) | −2.56231 | −0.0962294 | −0.0481147 | − | 0.998842i | \(-0.515321\pi\) | ||||
−0.0481147 | + | 0.998842i | \(0.515321\pi\) | |||||||
\(710\) | −4.38197 | −0.164452 | ||||||||
\(711\) | −9.47214 | −0.355233 | ||||||||
\(712\) | −25.9787 | −0.973593 | ||||||||
\(713\) | 6.70820 | 0.251224 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.29180 | 0.123106 | ||||||||
\(716\) | 1.14590 | 0.0428242 | ||||||||
\(717\) | −4.79837 | −0.179199 | ||||||||
\(718\) | −37.3607 | −1.39429 | ||||||||
\(719\) | 3.00000 | 0.111881 | 0.0559406 | − | 0.998434i | \(-0.482184\pi\) | ||||
0.0559406 | + | 0.998434i | \(0.482184\pi\) | |||||||
\(720\) | −3.00000 | −0.111803 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 11.2361 | 0.418163 | ||||||||
\(723\) | 11.0000 | 0.409094 | ||||||||
\(724\) | 1.20163 | 0.0446581 | ||||||||
\(725\) | 38.0344 | 1.41256 | ||||||||
\(726\) | 9.70820 | 0.360305 | ||||||||
\(727\) | −18.8885 | −0.700537 | −0.350269 | − | 0.936649i | \(-0.613910\pi\) | ||||
−0.350269 | + | 0.936649i | \(0.613910\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −12.7082 | −0.470352 | ||||||||
\(731\) | 10.8541 | 0.401453 | ||||||||
\(732\) | 3.00000 | 0.110883 | ||||||||
\(733\) | −25.5967 | −0.945437 | −0.472719 | − | 0.881213i | \(-0.656727\pi\) | ||||
−0.472719 | + | 0.881213i | \(0.656727\pi\) | |||||||
\(734\) | 17.5623 | 0.648237 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.38197 | −0.124661 | ||||||||
\(737\) | −11.3820 | −0.419260 | ||||||||
\(738\) | −2.38197 | −0.0876814 | ||||||||
\(739\) | 45.2492 | 1.66452 | 0.832260 | − | 0.554386i | \(-0.187047\pi\) | ||||
0.832260 | + | 0.554386i | \(0.187047\pi\) | |||||||
\(740\) | −4.20163 | −0.154455 | ||||||||
\(741\) | 8.27051 | 0.303825 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.6738 | 0.428269 | 0.214134 | − | 0.976804i | \(-0.431307\pi\) | ||||
0.214134 | + | 0.976804i | \(0.431307\pi\) | |||||||
\(744\) | −15.0000 | −0.549927 | ||||||||
\(745\) | −11.8885 | −0.435563 | ||||||||
\(746\) | −39.5066 | −1.44644 | ||||||||
\(747\) | 9.18034 | 0.335891 | ||||||||
\(748\) | −9.27051 | −0.338963 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 9.61803 | 0.351201 | ||||||||
\(751\) | 32.9787 | 1.20341 | 0.601705 | − | 0.798718i | \(-0.294488\pi\) | ||||
0.601705 | + | 0.798718i | \(0.294488\pi\) | |||||||
\(752\) | −35.1246 | −1.28086 | ||||||||
\(753\) | −23.1246 | −0.842708 | ||||||||
\(754\) | 31.7426 | 1.15600 | ||||||||
\(755\) | −9.41641 | −0.342698 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.0000 | −0.617876 | −0.308938 | − | 0.951082i | \(-0.599973\pi\) | ||||
−0.308938 | + | 0.951082i | \(0.599973\pi\) | |||||||
\(758\) | −12.0000 | −0.435860 | ||||||||
\(759\) | −2.23607 | −0.0811641 | ||||||||
\(760\) | 4.79837 | 0.174055 | ||||||||
\(761\) | 14.4721 | 0.524615 | 0.262307 | − | 0.964984i | \(-0.415517\pi\) | ||||
0.262307 | + | 0.964984i | \(0.415517\pi\) | |||||||
\(762\) | −36.0344 | −1.30539 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.0000 | 0.361787 | ||||||||
\(765\) | −4.14590 | −0.149895 | ||||||||
\(766\) | −1.14590 | −0.0414030 | ||||||||
\(767\) | −22.3475 | −0.806922 | ||||||||
\(768\) | 13.5623 | 0.489388 | ||||||||
\(769\) | −33.2361 | −1.19852 | −0.599262 | − | 0.800553i | \(-0.704539\pi\) | ||||
−0.599262 | + | 0.800553i | \(0.704539\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.23607 | 0.116544 | ||||||||
\(772\) | 5.12461 | 0.184439 | ||||||||
\(773\) | 19.9443 | 0.717346 | 0.358673 | − | 0.933463i | \(-0.383229\pi\) | ||||
0.358673 | + | 0.933463i | \(0.383229\pi\) | |||||||
\(774\) | 2.61803 | 0.0941033 | ||||||||
\(775\) | 30.9787 | 1.11279 | ||||||||
\(776\) | −23.2918 | −0.836127 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.56231 | −0.306974 | ||||||||
\(779\) | 5.11146 | 0.183137 | ||||||||
\(780\) | 0.909830 | 0.0325771 | ||||||||
\(781\) | 9.79837 | 0.350613 | ||||||||
\(782\) | −10.8541 | −0.388142 | ||||||||
\(783\) | −8.23607 | −0.294333 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.180340 | 0.00643661 | ||||||||
\(786\) | 24.5623 | 0.876108 | ||||||||
\(787\) | 48.5755 | 1.73153 | 0.865764 | − | 0.500452i | \(-0.166833\pi\) | ||||
0.865764 | + | 0.500452i | \(0.166833\pi\) | |||||||
\(788\) | −15.7639 | −0.561567 | ||||||||
\(789\) | −0.0557281 | −0.00198397 | ||||||||
\(790\) | 9.47214 | 0.337003 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.00000 | 0.177667 | ||||||||
\(793\) | 11.5623 | 0.410590 | ||||||||
\(794\) | 35.7082 | 1.26724 | ||||||||
\(795\) | −8.09017 | −0.286929 | ||||||||
\(796\) | 4.27051 | 0.151364 | ||||||||
\(797\) | −44.1803 | −1.56495 | −0.782474 | − | 0.622683i | \(-0.786043\pi\) | ||||
−0.782474 | + | 0.622683i | \(0.786043\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48.5410 | −1.71726 | ||||||||
\(800\) | −15.6180 | −0.552181 | ||||||||
\(801\) | −11.6180 | −0.410503 | ||||||||
\(802\) | −53.6869 | −1.89575 | ||||||||
\(803\) | 28.4164 | 1.00279 | ||||||||
\(804\) | −3.14590 | −0.110947 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 25.8541 | 0.910672 | ||||||||
\(807\) | 32.0902 | 1.12963 | ||||||||
\(808\) | −9.27051 | −0.326135 | ||||||||
\(809\) | −9.43769 | −0.331812 | −0.165906 | − | 0.986142i | \(-0.553055\pi\) | ||||
−0.165906 | + | 0.986142i | \(0.553055\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −8.52786 | −0.299454 | −0.149727 | − | 0.988727i | \(-0.547839\pi\) | ||||
−0.149727 | + | 0.988727i | \(0.547839\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.9443 | −0.769619 | ||||||||
\(814\) | 39.7984 | 1.39493 | ||||||||
\(815\) | −0.381966 | −0.0133797 | ||||||||
\(816\) | 32.5623 | 1.13991 | ||||||||
\(817\) | −5.61803 | −0.196550 | ||||||||
\(818\) | 10.3820 | 0.362997 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.562306 | 0.0196366 | ||||||||
\(821\) | −29.1246 | −1.01646 | −0.508228 | − | 0.861223i | \(-0.669699\pi\) | ||||
−0.508228 | + | 0.861223i | \(0.669699\pi\) | |||||||
\(822\) | 26.5623 | 0.926467 | ||||||||
\(823\) | −39.8541 | −1.38923 | −0.694613 | − | 0.719383i | \(-0.744425\pi\) | ||||
−0.694613 | + | 0.719383i | \(0.744425\pi\) | |||||||
\(824\) | 16.5836 | 0.577717 | ||||||||
\(825\) | −10.3262 | −0.359513 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.2148 | −0.981124 | −0.490562 | − | 0.871406i | \(-0.663208\pi\) | ||||
−0.490562 | + | 0.871406i | \(0.663208\pi\) | |||||||
\(828\) | −0.618034 | −0.0214782 | ||||||||
\(829\) | 30.4164 | 1.05641 | 0.528203 | − | 0.849118i | \(-0.322866\pi\) | ||||
0.528203 | + | 0.849118i | \(0.322866\pi\) | |||||||
\(830\) | −9.18034 | −0.318654 | ||||||||
\(831\) | 4.27051 | 0.148142 | ||||||||
\(832\) | 10.0902 | 0.349814 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −18.4164 | −0.637708 | ||||||||
\(835\) | 4.43769 | 0.153573 | ||||||||
\(836\) | 4.79837 | 0.165955 | ||||||||
\(837\) | −6.70820 | −0.231869 | ||||||||
\(838\) | 25.3607 | 0.876070 | ||||||||
\(839\) | −16.7426 | −0.578020 | −0.289010 | − | 0.957326i | \(-0.593326\pi\) | ||||
−0.289010 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.8328 | 1.33906 | ||||||||
\(842\) | 16.6180 | 0.572695 | ||||||||
\(843\) | −3.70820 | −0.127717 | ||||||||
\(844\) | 6.43769 | 0.221595 | ||||||||
\(845\) | −4.52786 | −0.155763 | ||||||||
\(846\) | −11.7082 | −0.402536 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 63.5410 | 2.18201 | ||||||||
\(849\) | 26.2148 | 0.899689 | ||||||||
\(850\) | −50.1246 | −1.71926 | ||||||||
\(851\) | 11.0000 | 0.377075 | ||||||||
\(852\) | 2.70820 | 0.0927815 | ||||||||
\(853\) | 47.1246 | 1.61352 | 0.806758 | − | 0.590882i | \(-0.201220\pi\) | ||||
0.806758 | + | 0.590882i | \(0.201220\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.14590 | 0.0733882 | ||||||||
\(856\) | 7.43769 | 0.254215 | ||||||||
\(857\) | −39.7082 | −1.35641 | −0.678203 | − | 0.734874i | \(-0.737241\pi\) | ||||
−0.678203 | + | 0.734874i | \(0.737241\pi\) | |||||||
\(858\) | −8.61803 | −0.294215 | ||||||||
\(859\) | 14.0000 | 0.477674 | 0.238837 | − | 0.971060i | \(-0.423234\pi\) | ||||
0.238837 | + | 0.971060i | \(0.423234\pi\) | |||||||
\(860\) | −0.618034 | −0.0210748 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.09017 | −0.0371313 | ||||||||
\(863\) | −8.06888 | −0.274668 | −0.137334 | − | 0.990525i | \(-0.543853\pi\) | ||||
−0.137334 | + | 0.990525i | \(0.543853\pi\) | |||||||
\(864\) | 3.38197 | 0.115057 | ||||||||
\(865\) | 2.14590 | 0.0729627 | ||||||||
\(866\) | 30.9443 | 1.05153 | ||||||||
\(867\) | 28.0000 | 0.950930 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.1803 | −0.718494 | ||||||||
\(870\) | 8.23607 | 0.279229 | ||||||||
\(871\) | −12.1246 | −0.410827 | ||||||||
\(872\) | 43.0902 | 1.45922 | ||||||||
\(873\) | −10.4164 | −0.352542 | ||||||||
\(874\) | 5.61803 | 0.190033 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.85410 | 0.265366 | ||||||||
\(877\) | 16.5836 | 0.559988 | 0.279994 | − | 0.960002i | \(-0.409667\pi\) | ||||
0.279994 | + | 0.960002i | \(0.409667\pi\) | |||||||
\(878\) | 38.2705 | 1.29157 | ||||||||
\(879\) | −12.0000 | −0.404750 | ||||||||
\(880\) | −6.70820 | −0.226134 | ||||||||
\(881\) | −1.81966 | −0.0613059 | −0.0306530 | − | 0.999530i | \(-0.509759\pi\) | ||||
−0.0306530 | + | 0.999530i | \(0.509759\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.90983 | −0.131576 | −0.0657881 | − | 0.997834i | \(-0.520956\pi\) | ||||
−0.0657881 | + | 0.997834i | \(0.520956\pi\) | |||||||
\(884\) | −9.87539 | −0.332145 | ||||||||
\(885\) | −5.79837 | −0.194910 | ||||||||
\(886\) | 15.4164 | 0.517924 | ||||||||
\(887\) | −9.79837 | −0.328997 | −0.164499 | − | 0.986377i | \(-0.552601\pi\) | ||||
−0.164499 | + | 0.986377i | \(0.552601\pi\) | |||||||
\(888\) | −24.5967 | −0.825413 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 11.6180 | 0.389437 | ||||||||
\(891\) | 2.23607 | 0.0749111 | ||||||||
\(892\) | 11.0344 | 0.369460 | ||||||||
\(893\) | 25.1246 | 0.840763 | ||||||||
\(894\) | 31.1246 | 1.04096 | ||||||||
\(895\) | 1.14590 | 0.0383031 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.38197 | −0.0795315 | ||||||||
\(898\) | 29.8328 | 0.995534 | ||||||||
\(899\) | 55.2492 | 1.84266 | ||||||||
\(900\) | −2.85410 | −0.0951367 | ||||||||
\(901\) | 87.8115 | 2.92543 | ||||||||
\(902\) | −5.32624 | −0.177344 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.03444 | −0.0676645 | ||||||||
\(905\) | 1.20163 | 0.0399434 | ||||||||
\(906\) | 24.6525 | 0.819024 | ||||||||
\(907\) | 48.9787 | 1.62631 | 0.813156 | − | 0.582046i | \(-0.197748\pi\) | ||||
0.813156 | + | 0.582046i | \(0.197748\pi\) | |||||||
\(908\) | −15.0344 | −0.498935 | ||||||||
\(909\) | −4.14590 | −0.137511 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.59675 | −0.251691 | −0.125846 | − | 0.992050i | \(-0.540164\pi\) | ||||
−0.125846 | + | 0.992050i | \(0.540164\pi\) | |||||||
\(912\) | −16.8541 | −0.558095 | ||||||||
\(913\) | 20.5279 | 0.679373 | ||||||||
\(914\) | 23.1803 | 0.766737 | ||||||||
\(915\) | 3.00000 | 0.0991769 | ||||||||
\(916\) | 10.0902 | 0.333389 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 10.8541 | 0.358239 | ||||||||
\(919\) | −50.1246 | −1.65346 | −0.826729 | − | 0.562600i | \(-0.809801\pi\) | ||||
−0.826729 | + | 0.562600i | \(0.809801\pi\) | |||||||
\(920\) | −1.38197 | −0.0455621 | ||||||||
\(921\) | −16.1246 | −0.531324 | ||||||||
\(922\) | 41.1803 | 1.35620 | ||||||||
\(923\) | 10.4377 | 0.343561 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 50.7984 | 1.67024 | ||||||||
\(926\) | −27.9787 | −0.919438 | ||||||||
\(927\) | 7.41641 | 0.243587 | ||||||||
\(928\) | −27.8541 | −0.914356 | ||||||||
\(929\) | −28.9098 | −0.948501 | −0.474250 | − | 0.880390i | \(-0.657281\pi\) | ||||
−0.474250 | + | 0.880390i | \(0.657281\pi\) | |||||||
\(930\) | 6.70820 | 0.219971 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.85410 | −0.224514 | ||||||||
\(933\) | −15.3262 | −0.501759 | ||||||||
\(934\) | −24.5623 | −0.803703 | ||||||||
\(935\) | −9.27051 | −0.303178 | ||||||||
\(936\) | 5.32624 | 0.174094 | ||||||||
\(937\) | −2.70820 | −0.0884732 | −0.0442366 | − | 0.999021i | \(-0.514086\pi\) | ||||
−0.0442366 | + | 0.999021i | \(0.514086\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.47214 | 0.0806751 | ||||||||
\(940\) | 2.76393 | 0.0901495 | ||||||||
\(941\) | 15.0557 | 0.490803 | 0.245401 | − | 0.969422i | \(-0.421080\pi\) | ||||
0.245401 | + | 0.969422i | \(0.421080\pi\) | |||||||
\(942\) | −0.472136 | −0.0153830 | ||||||||
\(943\) | −1.47214 | −0.0479393 | ||||||||
\(944\) | 45.5410 | 1.48223 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.85410 | 0.190333 | ||||||||
\(947\) | −18.9443 | −0.615606 | −0.307803 | − | 0.951450i | \(-0.599594\pi\) | ||||
−0.307803 | + | 0.951450i | \(0.599594\pi\) | |||||||
\(948\) | −5.85410 | −0.190132 | ||||||||
\(949\) | 30.2705 | 0.982622 | ||||||||
\(950\) | 25.9443 | 0.841743 | ||||||||
\(951\) | 14.5066 | 0.470408 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.1591 | 0.393870 | 0.196935 | − | 0.980417i | \(-0.436901\pi\) | ||||
0.196935 | + | 0.980417i | \(0.436901\pi\) | |||||||
\(954\) | 21.1803 | 0.685739 | ||||||||
\(955\) | 10.0000 | 0.323592 | ||||||||
\(956\) | −2.96556 | −0.0959130 | ||||||||
\(957\) | −18.4164 | −0.595318 | ||||||||
\(958\) | 33.9787 | 1.09780 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.61803 | 0.0844967 | ||||||||
\(961\) | 14.0000 | 0.451613 | ||||||||
\(962\) | 42.3951 | 1.36687 | ||||||||
\(963\) | 3.32624 | 0.107187 | ||||||||
\(964\) | 6.79837 | 0.218961 | ||||||||
\(965\) | 5.12461 | 0.164967 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.3607 | 1.61949 | 0.809745 | − | 0.586782i | \(-0.199605\pi\) | ||||
0.809745 | + | 0.586782i | \(0.199605\pi\) | |||||||
\(968\) | −13.4164 | −0.431220 | ||||||||
\(969\) | −23.2918 | −0.748240 | ||||||||
\(970\) | 10.4164 | 0.334451 | ||||||||
\(971\) | 19.6869 | 0.631783 | 0.315892 | − | 0.948795i | \(-0.397696\pi\) | ||||
0.315892 | + | 0.948795i | \(0.397696\pi\) | |||||||
\(972\) | 0.618034 | 0.0198234 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 47.3951 | 1.51864 | ||||||||
\(975\) | −11.0000 | −0.352282 | ||||||||
\(976\) | −23.5623 | −0.754211 | ||||||||
\(977\) | 49.7984 | 1.59319 | 0.796596 | − | 0.604513i | \(-0.206632\pi\) | ||||
0.796596 | + | 0.604513i | \(0.206632\pi\) | |||||||
\(978\) | 1.00000 | 0.0319765 | ||||||||
\(979\) | −25.9787 | −0.830283 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.2705 | 0.615260 | ||||||||
\(982\) | −15.8541 | −0.505925 | ||||||||
\(983\) | 7.40325 | 0.236127 | 0.118064 | − | 0.993006i | \(-0.462331\pi\) | ||||
0.118064 | + | 0.993006i | \(0.462331\pi\) | |||||||
\(984\) | 3.29180 | 0.104939 | ||||||||
\(985\) | −15.7639 | −0.502281 | ||||||||
\(986\) | −89.3951 | −2.84692 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.11146 | 0.162617 | ||||||||
\(989\) | 1.61803 | 0.0514505 | ||||||||
\(990\) | −2.23607 | −0.0710669 | ||||||||
\(991\) | −35.5755 | −1.13009 | −0.565046 | − | 0.825059i | \(-0.691142\pi\) | ||||
−0.565046 | + | 0.825059i | \(0.691142\pi\) | |||||||
\(992\) | −22.6869 | −0.720310 | ||||||||
\(993\) | −13.4164 | −0.425757 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.27051 | 0.135384 | ||||||||
\(996\) | 5.67376 | 0.179780 | ||||||||
\(997\) | −57.7214 | −1.82805 | −0.914027 | − | 0.405654i | \(-0.867044\pi\) | ||||
−0.914027 | + | 0.405654i | \(0.867044\pi\) | |||||||
\(998\) | 62.1246 | 1.96652 | ||||||||
\(999\) | −11.0000 | −0.348025 |
(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.r.1.1 | 2 | ||
7.6 | odd | 2 | 483.2.a.d.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 1449.2.a.h.1.2 | 2 | |||
28.27 | even | 2 | 7728.2.a.bn.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.a.d.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
1449.2.a.h.1.2 | 2 | 21.20 | even | 2 | |||
3381.2.a.r.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7728.2.a.bn.1.1 | 2 | 28.27 | even | 2 |