Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3381,2,Mod(1,3381)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3381.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3381 = 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3381.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(26.9974209234\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 13x^{8} + 41x^{7} + 47x^{6} - 165x^{5} - 45x^{4} + 207x^{3} + 12x^{2} - 76x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 483) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(2.51520\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.51520 | 1.77852 | 0.889259 | − | 0.457404i | \(-0.151221\pi\) | ||||
0.889259 | + | 0.457404i | \(0.151221\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.32625 | 2.16313 | ||||||||
\(5\) | −4.31735 | −1.93078 | −0.965390 | − | 0.260811i | \(-0.916010\pi\) | ||||
−0.965390 | + | 0.260811i | \(0.916010\pi\) | |||||||
\(6\) | 2.51520 | 1.02683 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 5.85100 | 2.06864 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −10.8590 | −3.43393 | ||||||||
\(11\) | 1.72915 | 0.521359 | 0.260679 | − | 0.965425i | \(-0.416053\pi\) | ||||
0.260679 | + | 0.965425i | \(0.416053\pi\) | |||||||
\(12\) | 4.32625 | 1.24888 | ||||||||
\(13\) | 2.88941 | 0.801378 | 0.400689 | − | 0.916214i | \(-0.368771\pi\) | ||||
0.400689 | + | 0.916214i | \(0.368771\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.31735 | −1.11474 | ||||||||
\(16\) | 6.06395 | 1.51599 | ||||||||
\(17\) | 4.93124 | 1.19600 | 0.598001 | − | 0.801495i | \(-0.295962\pi\) | ||||
0.598001 | + | 0.801495i | \(0.295962\pi\) | |||||||
\(18\) | 2.51520 | 0.592839 | ||||||||
\(19\) | −2.44156 | −0.560132 | −0.280066 | − | 0.959981i | \(-0.590356\pi\) | ||||
−0.280066 | + | 0.959981i | \(0.590356\pi\) | |||||||
\(20\) | −18.6780 | −4.17652 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.34917 | 0.927245 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 5.85100 | 1.19433 | ||||||||
\(25\) | 13.6396 | 2.72791 | ||||||||
\(26\) | 7.26746 | 1.42527 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.05817 | 1.49636 | 0.748182 | − | 0.663493i | \(-0.230927\pi\) | ||||
0.748182 | + | 0.663493i | \(0.230927\pi\) | |||||||
\(30\) | −10.8590 | −1.98258 | ||||||||
\(31\) | −0.915859 | −0.164493 | −0.0822466 | − | 0.996612i | \(-0.526210\pi\) | ||||
−0.0822466 | + | 0.996612i | \(0.526210\pi\) | |||||||
\(32\) | 3.55007 | 0.627570 | ||||||||
\(33\) | 1.72915 | 0.301007 | ||||||||
\(34\) | 12.4031 | 2.12711 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.32625 | 0.721042 | ||||||||
\(37\) | −9.15581 | −1.50521 | −0.752603 | − | 0.658475i | \(-0.771202\pi\) | ||||
−0.752603 | + | 0.658475i | \(0.771202\pi\) | |||||||
\(38\) | −6.14102 | −0.996205 | ||||||||
\(39\) | 2.88941 | 0.462676 | ||||||||
\(40\) | −25.2608 | −3.99409 | ||||||||
\(41\) | 6.60783 | 1.03197 | 0.515985 | − | 0.856598i | \(-0.327426\pi\) | ||||
0.515985 | + | 0.856598i | \(0.327426\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.7440 | 1.63845 | 0.819223 | − | 0.573475i | \(-0.194405\pi\) | ||||
0.819223 | + | 0.573475i | \(0.194405\pi\) | |||||||
\(44\) | 7.48074 | 1.12776 | ||||||||
\(45\) | −4.31735 | −0.643593 | ||||||||
\(46\) | 2.51520 | 0.370847 | ||||||||
\(47\) | 0.399649 | 0.0582948 | 0.0291474 | − | 0.999575i | \(-0.490721\pi\) | ||||
0.0291474 | + | 0.999575i | \(0.490721\pi\) | |||||||
\(48\) | 6.06395 | 0.875255 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 34.3063 | 4.85164 | ||||||||
\(51\) | 4.93124 | 0.690512 | ||||||||
\(52\) | 12.5003 | 1.73348 | ||||||||
\(53\) | 6.54512 | 0.899042 | 0.449521 | − | 0.893270i | \(-0.351595\pi\) | ||||
0.449521 | + | 0.893270i | \(0.351595\pi\) | |||||||
\(54\) | 2.51520 | 0.342276 | ||||||||
\(55\) | −7.46536 | −1.00663 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.44156 | −0.323393 | ||||||||
\(58\) | 20.2679 | 2.66131 | ||||||||
\(59\) | 1.83508 | 0.238907 | 0.119454 | − | 0.992840i | \(-0.461886\pi\) | ||||
0.119454 | + | 0.992840i | \(0.461886\pi\) | |||||||
\(60\) | −18.6780 | −2.41131 | ||||||||
\(61\) | 1.30126 | 0.166609 | 0.0833045 | − | 0.996524i | \(-0.473453\pi\) | ||||
0.0833045 | + | 0.996524i | \(0.473453\pi\) | |||||||
\(62\) | −2.30357 | −0.292554 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.19874 | −0.399843 | ||||||||
\(65\) | −12.4746 | −1.54728 | ||||||||
\(66\) | 4.34917 | 0.535345 | ||||||||
\(67\) | −10.2140 | −1.24784 | −0.623918 | − | 0.781490i | \(-0.714460\pi\) | ||||
−0.623918 | + | 0.781490i | \(0.714460\pi\) | |||||||
\(68\) | 21.3338 | 2.58710 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.00190 | −1.06833 | −0.534164 | − | 0.845381i | \(-0.679374\pi\) | ||||
−0.534164 | + | 0.845381i | \(0.679374\pi\) | |||||||
\(72\) | 5.85100 | 0.689547 | ||||||||
\(73\) | 2.61716 | 0.306315 | 0.153158 | − | 0.988202i | \(-0.451056\pi\) | ||||
0.153158 | + | 0.988202i | \(0.451056\pi\) | |||||||
\(74\) | −23.0287 | −2.67703 | ||||||||
\(75\) | 13.6396 | 1.57496 | ||||||||
\(76\) | −10.5628 | −1.21164 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 7.26746 | 0.822877 | ||||||||
\(79\) | 10.1870 | 1.14613 | 0.573064 | − | 0.819510i | \(-0.305755\pi\) | ||||
0.573064 | + | 0.819510i | \(0.305755\pi\) | |||||||
\(80\) | −26.1802 | −2.92704 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 16.6200 | 1.83538 | ||||||||
\(83\) | 10.8838 | 1.19465 | 0.597327 | − | 0.801998i | \(-0.296229\pi\) | ||||
0.597327 | + | 0.801998i | \(0.296229\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21.2899 | −2.30922 | ||||||||
\(86\) | 27.0234 | 2.91400 | ||||||||
\(87\) | 8.05817 | 0.863926 | ||||||||
\(88\) | 10.1173 | 1.07850 | ||||||||
\(89\) | −14.9862 | −1.58854 | −0.794269 | − | 0.607566i | \(-0.792146\pi\) | ||||
−0.794269 | + | 0.607566i | \(0.792146\pi\) | |||||||
\(90\) | −10.8590 | −1.14464 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.32625 | 0.451043 | ||||||||
\(93\) | −0.915859 | −0.0949702 | ||||||||
\(94\) | 1.00520 | 0.103678 | ||||||||
\(95\) | 10.5411 | 1.08149 | ||||||||
\(96\) | 3.55007 | 0.362328 | ||||||||
\(97\) | 3.07116 | 0.311829 | 0.155914 | − | 0.987771i | \(-0.450168\pi\) | ||||
0.155914 | + | 0.987771i | \(0.450168\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.72915 | 0.173786 | ||||||||
\(100\) | 59.0081 | 5.90081 | ||||||||
\(101\) | −1.08810 | −0.108270 | −0.0541349 | − | 0.998534i | \(-0.517240\pi\) | ||||
−0.0541349 | + | 0.998534i | \(0.517240\pi\) | |||||||
\(102\) | 12.4031 | 1.22809 | ||||||||
\(103\) | 3.23110 | 0.318369 | 0.159185 | − | 0.987249i | \(-0.449113\pi\) | ||||
0.159185 | + | 0.987249i | \(0.449113\pi\) | |||||||
\(104\) | 16.9059 | 1.65776 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 16.4623 | 1.59896 | ||||||||
\(107\) | −0.936899 | −0.0905734 | −0.0452867 | − | 0.998974i | \(-0.514420\pi\) | ||||
−0.0452867 | + | 0.998974i | \(0.514420\pi\) | |||||||
\(108\) | 4.32625 | 0.416294 | ||||||||
\(109\) | −14.9782 | −1.43465 | −0.717324 | − | 0.696739i | \(-0.754633\pi\) | ||||
−0.717324 | + | 0.696739i | \(0.754633\pi\) | |||||||
\(110\) | −18.7769 | −1.79031 | ||||||||
\(111\) | −9.15581 | −0.869031 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.1424 | −1.33040 | −0.665201 | − | 0.746665i | \(-0.731654\pi\) | ||||
−0.665201 | + | 0.746665i | \(0.731654\pi\) | |||||||
\(114\) | −6.14102 | −0.575159 | ||||||||
\(115\) | −4.31735 | −0.402595 | ||||||||
\(116\) | 34.8617 | 3.23682 | ||||||||
\(117\) | 2.88941 | 0.267126 | ||||||||
\(118\) | 4.61560 | 0.424901 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −25.2608 | −2.30599 | ||||||||
\(121\) | −8.01004 | −0.728185 | ||||||||
\(122\) | 3.27293 | 0.296317 | ||||||||
\(123\) | 6.60783 | 0.595808 | ||||||||
\(124\) | −3.96224 | −0.355819 | ||||||||
\(125\) | −37.3000 | −3.33621 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.77968 | −0.157921 | −0.0789604 | − | 0.996878i | \(-0.525160\pi\) | ||||
−0.0789604 | + | 0.996878i | \(0.525160\pi\) | |||||||
\(128\) | −15.1456 | −1.33870 | ||||||||
\(129\) | 10.7440 | 0.945957 | ||||||||
\(130\) | −31.3762 | −2.75187 | ||||||||
\(131\) | −8.89264 | −0.776954 | −0.388477 | − | 0.921459i | \(-0.626999\pi\) | ||||
−0.388477 | + | 0.921459i | \(0.626999\pi\) | |||||||
\(132\) | 7.48074 | 0.651115 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −25.6902 | −2.21930 | ||||||||
\(135\) | −4.31735 | −0.371579 | ||||||||
\(136\) | 28.8527 | 2.47410 | ||||||||
\(137\) | 0.247404 | 0.0211371 | 0.0105686 | − | 0.999944i | \(-0.496636\pi\) | ||||
0.0105686 | + | 0.999944i | \(0.496636\pi\) | |||||||
\(138\) | 2.51520 | 0.214108 | ||||||||
\(139\) | 8.59949 | 0.729399 | 0.364699 | − | 0.931125i | \(-0.381172\pi\) | ||||
0.364699 | + | 0.931125i | \(0.381172\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.399649 | 0.0336565 | ||||||||
\(142\) | −22.6416 | −1.90004 | ||||||||
\(143\) | 4.99623 | 0.417805 | ||||||||
\(144\) | 6.06395 | 0.505329 | ||||||||
\(145\) | −34.7900 | −2.88915 | ||||||||
\(146\) | 6.58268 | 0.544787 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −39.6103 | −3.25595 | ||||||||
\(149\) | 4.50669 | 0.369202 | 0.184601 | − | 0.982814i | \(-0.440901\pi\) | ||||
0.184601 | + | 0.982814i | \(0.440901\pi\) | |||||||
\(150\) | 34.3063 | 2.80109 | ||||||||
\(151\) | −4.52766 | −0.368455 | −0.184228 | − | 0.982884i | \(-0.558978\pi\) | ||||
−0.184228 | + | 0.982884i | \(0.558978\pi\) | |||||||
\(152\) | −14.2856 | −1.15871 | ||||||||
\(153\) | 4.93124 | 0.398667 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.95409 | 0.317600 | ||||||||
\(156\) | 12.5003 | 1.00083 | ||||||||
\(157\) | 3.26727 | 0.260757 | 0.130378 | − | 0.991464i | \(-0.458381\pi\) | ||||
0.130378 | + | 0.991464i | \(0.458381\pi\) | |||||||
\(158\) | 25.6224 | 2.03841 | ||||||||
\(159\) | 6.54512 | 0.519062 | ||||||||
\(160\) | −15.3269 | −1.21170 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.51520 | 0.197613 | ||||||||
\(163\) | 10.6420 | 0.833549 | 0.416774 | − | 0.909010i | \(-0.363160\pi\) | ||||
0.416774 | + | 0.909010i | \(0.363160\pi\) | |||||||
\(164\) | 28.5871 | 2.23228 | ||||||||
\(165\) | −7.46536 | −0.581177 | ||||||||
\(166\) | 27.3750 | 2.12471 | ||||||||
\(167\) | −2.99812 | −0.232001 | −0.116001 | − | 0.993249i | \(-0.537007\pi\) | ||||
−0.116001 | + | 0.993249i | \(0.537007\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.65131 | −0.357793 | ||||||||
\(170\) | −53.5485 | −4.10698 | ||||||||
\(171\) | −2.44156 | −0.186711 | ||||||||
\(172\) | 46.4813 | 3.54416 | ||||||||
\(173\) | 13.2996 | 1.01115 | 0.505576 | − | 0.862782i | \(-0.331280\pi\) | ||||
0.505576 | + | 0.862782i | \(0.331280\pi\) | |||||||
\(174\) | 20.2679 | 1.53651 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.4855 | 0.790373 | ||||||||
\(177\) | 1.83508 | 0.137933 | ||||||||
\(178\) | −37.6934 | −2.82524 | ||||||||
\(179\) | 19.6297 | 1.46719 | 0.733596 | − | 0.679585i | \(-0.237840\pi\) | ||||
0.733596 | + | 0.679585i | \(0.237840\pi\) | |||||||
\(180\) | −18.6780 | −1.39217 | ||||||||
\(181\) | −19.2095 | −1.42783 | −0.713915 | − | 0.700232i | \(-0.753080\pi\) | ||||
−0.713915 | + | 0.700232i | \(0.753080\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.30126 | 0.0961917 | ||||||||
\(184\) | 5.85100 | 0.431341 | ||||||||
\(185\) | 39.5289 | 2.90622 | ||||||||
\(186\) | −2.30357 | −0.168906 | ||||||||
\(187\) | 8.52686 | 0.623546 | ||||||||
\(188\) | 1.72898 | 0.126099 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 26.5130 | 1.92345 | ||||||||
\(191\) | −7.15375 | −0.517627 | −0.258814 | − | 0.965927i | \(-0.583332\pi\) | ||||
−0.258814 | + | 0.965927i | \(0.583332\pi\) | |||||||
\(192\) | −3.19874 | −0.230849 | ||||||||
\(193\) | −21.9573 | −1.58052 | −0.790259 | − | 0.612772i | \(-0.790054\pi\) | ||||
−0.790259 | + | 0.612772i | \(0.790054\pi\) | |||||||
\(194\) | 7.72458 | 0.554593 | ||||||||
\(195\) | −12.4746 | −0.893325 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.21028 | 0.228723 | 0.114361 | − | 0.993439i | \(-0.463518\pi\) | ||||
0.114361 | + | 0.993439i | \(0.463518\pi\) | |||||||
\(198\) | 4.34917 | 0.309082 | ||||||||
\(199\) | −12.7170 | −0.901483 | −0.450741 | − | 0.892655i | \(-0.648840\pi\) | ||||
−0.450741 | + | 0.892655i | \(0.648840\pi\) | |||||||
\(200\) | 79.8050 | 5.64306 | ||||||||
\(201\) | −10.2140 | −0.720438 | ||||||||
\(202\) | −2.73679 | −0.192560 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 21.3338 | 1.49366 | ||||||||
\(205\) | −28.5283 | −1.99251 | ||||||||
\(206\) | 8.12686 | 0.566225 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 17.5212 | 1.21488 | ||||||||
\(209\) | −4.22183 | −0.292030 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.0500 | −1.17377 | −0.586884 | − | 0.809671i | \(-0.699646\pi\) | ||||
−0.586884 | + | 0.809671i | \(0.699646\pi\) | |||||||
\(212\) | 28.3159 | 1.94474 | ||||||||
\(213\) | −9.00190 | −0.616800 | ||||||||
\(214\) | −2.35649 | −0.161086 | ||||||||
\(215\) | −46.3857 | −3.16348 | ||||||||
\(216\) | 5.85100 | 0.398110 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −37.6732 | −2.55155 | ||||||||
\(219\) | 2.61716 | 0.176851 | ||||||||
\(220\) | −32.2970 | −2.17746 | ||||||||
\(221\) | 14.2484 | 0.958450 | ||||||||
\(222\) | −23.0287 | −1.54559 | ||||||||
\(223\) | −23.3278 | −1.56215 | −0.781073 | − | 0.624440i | \(-0.785327\pi\) | ||||
−0.781073 | + | 0.624440i | \(0.785327\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.6396 | 0.909303 | ||||||||
\(226\) | −35.5709 | −2.36614 | ||||||||
\(227\) | 7.67594 | 0.509470 | 0.254735 | − | 0.967011i | \(-0.418012\pi\) | ||||
0.254735 | + | 0.967011i | \(0.418012\pi\) | |||||||
\(228\) | −10.5628 | −0.699539 | ||||||||
\(229\) | 22.8736 | 1.51153 | 0.755766 | − | 0.654842i | \(-0.227265\pi\) | ||||
0.755766 | + | 0.654842i | \(0.227265\pi\) | |||||||
\(230\) | −10.8590 | −0.716023 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 47.1483 | 3.09544 | ||||||||
\(233\) | 23.5559 | 1.54320 | 0.771599 | − | 0.636110i | \(-0.219457\pi\) | ||||
0.771599 | + | 0.636110i | \(0.219457\pi\) | |||||||
\(234\) | 7.26746 | 0.475089 | ||||||||
\(235\) | −1.72543 | −0.112554 | ||||||||
\(236\) | 7.93902 | 0.516786 | ||||||||
\(237\) | 10.1870 | 0.661718 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.1829 | 0.852732 | 0.426366 | − | 0.904551i | \(-0.359794\pi\) | ||||
0.426366 | + | 0.904551i | \(0.359794\pi\) | |||||||
\(240\) | −26.1802 | −1.68993 | ||||||||
\(241\) | 17.2670 | 1.11227 | 0.556134 | − | 0.831093i | \(-0.312284\pi\) | ||||
0.556134 | + | 0.831093i | \(0.312284\pi\) | |||||||
\(242\) | −20.1469 | −1.29509 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 5.62957 | 0.360396 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 16.6200 | 1.05966 | ||||||||
\(247\) | −7.05467 | −0.448878 | ||||||||
\(248\) | −5.35869 | −0.340277 | ||||||||
\(249\) | 10.8838 | 0.689734 | ||||||||
\(250\) | −93.8171 | −5.93352 | ||||||||
\(251\) | −4.74956 | −0.299790 | −0.149895 | − | 0.988702i | \(-0.547894\pi\) | ||||
−0.149895 | + | 0.988702i | \(0.547894\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.72915 | 0.108711 | ||||||||
\(254\) | −4.47625 | −0.280865 | ||||||||
\(255\) | −21.2899 | −1.33323 | ||||||||
\(256\) | −31.6969 | −1.98105 | ||||||||
\(257\) | −1.42884 | −0.0891283 | −0.0445641 | − | 0.999007i | \(-0.514190\pi\) | ||||
−0.0445641 | + | 0.999007i | \(0.514190\pi\) | |||||||
\(258\) | 27.0234 | 1.68240 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −53.9683 | −3.34697 | ||||||||
\(261\) | 8.05817 | 0.498788 | ||||||||
\(262\) | −22.3668 | −1.38183 | ||||||||
\(263\) | 8.81746 | 0.543708 | 0.271854 | − | 0.962339i | \(-0.412363\pi\) | ||||
0.271854 | + | 0.962339i | \(0.412363\pi\) | |||||||
\(264\) | 10.1173 | 0.622674 | ||||||||
\(265\) | −28.2576 | −1.73585 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.9862 | −0.917143 | ||||||||
\(268\) | −44.1882 | −2.69922 | ||||||||
\(269\) | 12.9185 | 0.787658 | 0.393829 | − | 0.919184i | \(-0.371150\pi\) | ||||
0.393829 | + | 0.919184i | \(0.371150\pi\) | |||||||
\(270\) | −10.8590 | −0.660859 | ||||||||
\(271\) | −13.3485 | −0.810865 | −0.405433 | − | 0.914125i | \(-0.632879\pi\) | ||||
−0.405433 | + | 0.914125i | \(0.632879\pi\) | |||||||
\(272\) | 29.9028 | 1.81312 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.622271 | 0.0375927 | ||||||||
\(275\) | 23.5848 | 1.42222 | ||||||||
\(276\) | 4.32625 | 0.260410 | ||||||||
\(277\) | −15.4986 | −0.931221 | −0.465610 | − | 0.884990i | \(-0.654165\pi\) | ||||
−0.465610 | + | 0.884990i | \(0.654165\pi\) | |||||||
\(278\) | 21.6295 | 1.29725 | ||||||||
\(279\) | −0.915859 | −0.0548311 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.6088 | 1.40838 | 0.704192 | − | 0.710009i | \(-0.251309\pi\) | ||||
0.704192 | + | 0.710009i | \(0.251309\pi\) | |||||||
\(282\) | 1.00520 | 0.0598587 | ||||||||
\(283\) | −23.6814 | −1.40772 | −0.703858 | − | 0.710341i | \(-0.748541\pi\) | ||||
−0.703858 | + | 0.710341i | \(0.748541\pi\) | |||||||
\(284\) | −38.9445 | −2.31093 | ||||||||
\(285\) | 10.5411 | 0.624400 | ||||||||
\(286\) | 12.5665 | 0.743074 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.55007 | 0.209190 | ||||||||
\(289\) | 7.31715 | 0.430421 | ||||||||
\(290\) | −87.5039 | −5.13840 | ||||||||
\(291\) | 3.07116 | 0.180034 | ||||||||
\(292\) | 11.3225 | 0.662598 | ||||||||
\(293\) | −21.1268 | −1.23424 | −0.617121 | − | 0.786868i | \(-0.711701\pi\) | ||||
−0.617121 | + | 0.786868i | \(0.711701\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.92270 | −0.461277 | ||||||||
\(296\) | −53.5706 | −3.11373 | ||||||||
\(297\) | 1.72915 | 0.100336 | ||||||||
\(298\) | 11.3352 | 0.656633 | ||||||||
\(299\) | 2.88941 | 0.167099 | ||||||||
\(300\) | 59.0081 | 3.40684 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −11.3880 | −0.655305 | ||||||||
\(303\) | −1.08810 | −0.0625096 | ||||||||
\(304\) | −14.8055 | −0.849153 | ||||||||
\(305\) | −5.61799 | −0.321685 | ||||||||
\(306\) | 12.4031 | 0.709037 | ||||||||
\(307\) | 1.97923 | 0.112961 | 0.0564804 | − | 0.998404i | \(-0.482012\pi\) | ||||
0.0564804 | + | 0.998404i | \(0.482012\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.23110 | 0.183811 | ||||||||
\(310\) | 9.94534 | 0.564857 | ||||||||
\(311\) | 3.89679 | 0.220967 | 0.110483 | − | 0.993878i | \(-0.464760\pi\) | ||||
0.110483 | + | 0.993878i | \(0.464760\pi\) | |||||||
\(312\) | 16.9059 | 0.957110 | ||||||||
\(313\) | −17.6584 | −0.998111 | −0.499056 | − | 0.866570i | \(-0.666320\pi\) | ||||
−0.499056 | + | 0.866570i | \(0.666320\pi\) | |||||||
\(314\) | 8.21786 | 0.463761 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 44.0716 | 2.47922 | ||||||||
\(317\) | −12.3323 | −0.692652 | −0.346326 | − | 0.938114i | \(-0.612571\pi\) | ||||
−0.346326 | + | 0.938114i | \(0.612571\pi\) | |||||||
\(318\) | 16.4623 | 0.923161 | ||||||||
\(319\) | 13.9338 | 0.780142 | ||||||||
\(320\) | 13.8101 | 0.772008 | ||||||||
\(321\) | −0.936899 | −0.0522926 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.0399 | −0.669919 | ||||||||
\(324\) | 4.32625 | 0.240347 | ||||||||
\(325\) | 39.4103 | 2.18609 | ||||||||
\(326\) | 26.7669 | 1.48248 | ||||||||
\(327\) | −14.9782 | −0.828295 | ||||||||
\(328\) | 38.6624 | 2.13477 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −18.7769 | −1.03363 | ||||||||
\(331\) | 5.80565 | 0.319107 | 0.159554 | − | 0.987189i | \(-0.448995\pi\) | ||||
0.159554 | + | 0.987189i | \(0.448995\pi\) | |||||||
\(332\) | 47.0861 | 2.58419 | ||||||||
\(333\) | −9.15581 | −0.501735 | ||||||||
\(334\) | −7.54087 | −0.412618 | ||||||||
\(335\) | 44.0973 | 2.40930 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.5441 | −1.22805 | −0.614027 | − | 0.789285i | \(-0.710452\pi\) | ||||
−0.614027 | + | 0.789285i | \(0.710452\pi\) | |||||||
\(338\) | −11.6990 | −0.636341 | ||||||||
\(339\) | −14.1424 | −0.768108 | ||||||||
\(340\) | −92.1056 | −4.99512 | ||||||||
\(341\) | −1.58366 | −0.0857599 | ||||||||
\(342\) | −6.14102 | −0.332068 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 62.8631 | 3.38935 | ||||||||
\(345\) | −4.31735 | −0.232439 | ||||||||
\(346\) | 33.4513 | 1.79835 | ||||||||
\(347\) | −7.49730 | −0.402476 | −0.201238 | − | 0.979542i | \(-0.564497\pi\) | ||||
−0.201238 | + | 0.979542i | \(0.564497\pi\) | |||||||
\(348\) | 34.8617 | 1.86878 | ||||||||
\(349\) | 7.97347 | 0.426810 | 0.213405 | − | 0.976964i | \(-0.431545\pi\) | ||||
0.213405 | + | 0.976964i | \(0.431545\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.88941 | 0.154225 | ||||||||
\(352\) | 6.13861 | 0.327189 | ||||||||
\(353\) | 29.5289 | 1.57167 | 0.785833 | − | 0.618439i | \(-0.212235\pi\) | ||||
0.785833 | + | 0.618439i | \(0.212235\pi\) | |||||||
\(354\) | 4.61560 | 0.245317 | ||||||||
\(355\) | 38.8644 | 2.06271 | ||||||||
\(356\) | −64.8342 | −3.43621 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 49.3727 | 2.60943 | ||||||||
\(359\) | −13.1206 | −0.692481 | −0.346241 | − | 0.938146i | \(-0.612542\pi\) | ||||
−0.346241 | + | 0.938146i | \(0.612542\pi\) | |||||||
\(360\) | −25.2608 | −1.33136 | ||||||||
\(361\) | −13.0388 | −0.686252 | ||||||||
\(362\) | −48.3158 | −2.53942 | ||||||||
\(363\) | −8.01004 | −0.420418 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.2992 | −0.591427 | ||||||||
\(366\) | 3.27293 | 0.171079 | ||||||||
\(367\) | −5.26368 | −0.274762 | −0.137381 | − | 0.990518i | \(-0.543868\pi\) | ||||
−0.137381 | + | 0.990518i | \(0.543868\pi\) | |||||||
\(368\) | 6.06395 | 0.316105 | ||||||||
\(369\) | 6.60783 | 0.343990 | ||||||||
\(370\) | 99.4232 | 5.16876 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.96224 | −0.205432 | ||||||||
\(373\) | −12.6495 | −0.654968 | −0.327484 | − | 0.944857i | \(-0.606201\pi\) | ||||
−0.327484 | + | 0.944857i | \(0.606201\pi\) | |||||||
\(374\) | 21.4468 | 1.10899 | ||||||||
\(375\) | −37.3000 | −1.92616 | ||||||||
\(376\) | 2.33834 | 0.120591 | ||||||||
\(377\) | 23.2834 | 1.19915 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.7987 | 0.657426 | 0.328713 | − | 0.944430i | \(-0.393385\pi\) | ||||
0.328713 | + | 0.944430i | \(0.393385\pi\) | |||||||
\(380\) | 45.6034 | 2.33940 | ||||||||
\(381\) | −1.77968 | −0.0911756 | ||||||||
\(382\) | −17.9931 | −0.920609 | ||||||||
\(383\) | 16.6269 | 0.849595 | 0.424797 | − | 0.905288i | \(-0.360345\pi\) | ||||
0.424797 | + | 0.905288i | \(0.360345\pi\) | |||||||
\(384\) | −15.1456 | −0.772897 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −55.2270 | −2.81098 | ||||||||
\(387\) | 10.7440 | 0.546149 | ||||||||
\(388\) | 13.2866 | 0.674525 | ||||||||
\(389\) | −29.8703 | −1.51448 | −0.757242 | − | 0.653134i | \(-0.773454\pi\) | ||||
−0.757242 | + | 0.653134i | \(0.773454\pi\) | |||||||
\(390\) | −31.3762 | −1.58880 | ||||||||
\(391\) | 4.93124 | 0.249384 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.89264 | −0.448574 | ||||||||
\(394\) | 8.07450 | 0.406787 | ||||||||
\(395\) | −43.9810 | −2.21292 | ||||||||
\(396\) | 7.48074 | 0.375921 | ||||||||
\(397\) | 5.98437 | 0.300347 | 0.150173 | − | 0.988660i | \(-0.452017\pi\) | ||||
0.150173 | + | 0.988660i | \(0.452017\pi\) | |||||||
\(398\) | −31.9858 | −1.60330 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 82.7095 | 4.13548 | ||||||||
\(401\) | −15.8635 | −0.792185 | −0.396092 | − | 0.918211i | \(-0.629634\pi\) | ||||
−0.396092 | + | 0.918211i | \(0.629634\pi\) | |||||||
\(402\) | −25.6902 | −1.28131 | ||||||||
\(403\) | −2.64629 | −0.131821 | ||||||||
\(404\) | −4.70738 | −0.234201 | ||||||||
\(405\) | −4.31735 | −0.214531 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.8318 | −0.784752 | ||||||||
\(408\) | 28.8527 | 1.42842 | ||||||||
\(409\) | −24.9384 | −1.23313 | −0.616563 | − | 0.787306i | \(-0.711475\pi\) | ||||
−0.616563 | + | 0.787306i | \(0.711475\pi\) | |||||||
\(410\) | −71.7546 | −3.54371 | ||||||||
\(411\) | 0.247404 | 0.0122035 | ||||||||
\(412\) | 13.9785 | 0.688673 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.51520 | 0.123616 | ||||||||
\(415\) | −46.9893 | −2.30661 | ||||||||
\(416\) | 10.2576 | 0.502921 | ||||||||
\(417\) | 8.59949 | 0.421119 | ||||||||
\(418\) | −10.6188 | −0.519380 | ||||||||
\(419\) | 13.2262 | 0.646140 | 0.323070 | − | 0.946375i | \(-0.395285\pi\) | ||||
0.323070 | + | 0.946375i | \(0.395285\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.82168 | −0.283731 | −0.141866 | − | 0.989886i | \(-0.545310\pi\) | ||||
−0.141866 | + | 0.989886i | \(0.545310\pi\) | |||||||
\(422\) | −42.8841 | −2.08757 | ||||||||
\(423\) | 0.399649 | 0.0194316 | ||||||||
\(424\) | 38.2955 | 1.85979 | ||||||||
\(425\) | 67.2599 | 3.26259 | ||||||||
\(426\) | −22.6416 | −1.09699 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.05326 | −0.195922 | ||||||||
\(429\) | 4.99623 | 0.241220 | ||||||||
\(430\) | −116.669 | −5.62630 | ||||||||
\(431\) | 6.21912 | 0.299565 | 0.149782 | − | 0.988719i | \(-0.452143\pi\) | ||||
0.149782 | + | 0.988719i | \(0.452143\pi\) | |||||||
\(432\) | 6.06395 | 0.291752 | ||||||||
\(433\) | 2.16316 | 0.103955 | 0.0519774 | − | 0.998648i | \(-0.483448\pi\) | ||||
0.0519774 | + | 0.998648i | \(0.483448\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −34.7900 | −1.66805 | ||||||||
\(436\) | −64.7993 | −3.10333 | ||||||||
\(437\) | −2.44156 | −0.116796 | ||||||||
\(438\) | 6.58268 | 0.314533 | ||||||||
\(439\) | −11.5256 | −0.550085 | −0.275042 | − | 0.961432i | \(-0.588692\pi\) | ||||
−0.275042 | + | 0.961432i | \(0.588692\pi\) | |||||||
\(440\) | −43.6798 | −2.08235 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 35.8376 | 1.70462 | ||||||||
\(443\) | 9.13040 | 0.433799 | 0.216899 | − | 0.976194i | \(-0.430406\pi\) | ||||
0.216899 | + | 0.976194i | \(0.430406\pi\) | |||||||
\(444\) | −39.6103 | −1.87982 | ||||||||
\(445\) | 64.7009 | 3.06712 | ||||||||
\(446\) | −58.6742 | −2.77830 | ||||||||
\(447\) | 4.50669 | 0.213159 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.6827 | −0.976079 | −0.488039 | − | 0.872822i | \(-0.662288\pi\) | ||||
−0.488039 | + | 0.872822i | \(0.662288\pi\) | |||||||
\(450\) | 34.3063 | 1.61721 | ||||||||
\(451\) | 11.4259 | 0.538026 | ||||||||
\(452\) | −61.1834 | −2.87783 | ||||||||
\(453\) | −4.52766 | −0.212728 | ||||||||
\(454\) | 19.3066 | 0.906102 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −14.2856 | −0.668983 | ||||||||
\(457\) | 24.5958 | 1.15054 | 0.575271 | − | 0.817963i | \(-0.304897\pi\) | ||||
0.575271 | + | 0.817963i | \(0.304897\pi\) | |||||||
\(458\) | 57.5318 | 2.68829 | ||||||||
\(459\) | 4.93124 | 0.230171 | ||||||||
\(460\) | −18.6780 | −0.870864 | ||||||||
\(461\) | 3.35047 | 0.156047 | 0.0780235 | − | 0.996952i | \(-0.475139\pi\) | ||||
0.0780235 | + | 0.996952i | \(0.475139\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.2309 | −1.40495 | −0.702476 | − | 0.711708i | \(-0.747922\pi\) | ||||
−0.702476 | + | 0.711708i | \(0.747922\pi\) | |||||||
\(464\) | 48.8643 | 2.26847 | ||||||||
\(465\) | 3.95409 | 0.183366 | ||||||||
\(466\) | 59.2479 | 2.74460 | ||||||||
\(467\) | 30.1416 | 1.39479 | 0.697394 | − | 0.716688i | \(-0.254343\pi\) | ||||
0.697394 | + | 0.716688i | \(0.254343\pi\) | |||||||
\(468\) | 12.5003 | 0.577827 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.33980 | −0.200180 | ||||||||
\(471\) | 3.26727 | 0.150548 | ||||||||
\(472\) | 10.7371 | 0.494213 | ||||||||
\(473\) | 18.5780 | 0.854218 | ||||||||
\(474\) | 25.6224 | 1.17688 | ||||||||
\(475\) | −33.3018 | −1.52799 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.54512 | 0.299681 | ||||||||
\(478\) | 33.1577 | 1.51660 | ||||||||
\(479\) | −29.0344 | −1.32662 | −0.663308 | − | 0.748347i | \(-0.730848\pi\) | ||||
−0.663308 | + | 0.748347i | \(0.730848\pi\) | |||||||
\(480\) | −15.3269 | −0.699575 | ||||||||
\(481\) | −26.4549 | −1.20624 | ||||||||
\(482\) | 43.4301 | 1.97819 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −34.6534 | −1.57516 | ||||||||
\(485\) | −13.2593 | −0.602072 | ||||||||
\(486\) | 2.51520 | 0.114092 | ||||||||
\(487\) | −17.3057 | −0.784195 | −0.392097 | − | 0.919924i | \(-0.628250\pi\) | ||||
−0.392097 | + | 0.919924i | \(0.628250\pi\) | |||||||
\(488\) | 7.61365 | 0.344654 | ||||||||
\(489\) | 10.6420 | 0.481250 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.2287 | 0.642133 | 0.321067 | − | 0.947057i | \(-0.395959\pi\) | ||||
0.321067 | + | 0.947057i | \(0.395959\pi\) | |||||||
\(492\) | 28.5871 | 1.28881 | ||||||||
\(493\) | 39.7368 | 1.78965 | ||||||||
\(494\) | −17.7439 | −0.798337 | ||||||||
\(495\) | −7.46536 | −0.335543 | ||||||||
\(496\) | −5.55372 | −0.249369 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 27.3750 | 1.22670 | ||||||||
\(499\) | 11.1172 | 0.497672 | 0.248836 | − | 0.968546i | \(-0.419952\pi\) | ||||
0.248836 | + | 0.968546i | \(0.419952\pi\) | |||||||
\(500\) | −161.369 | −7.21665 | ||||||||
\(501\) | −2.99812 | −0.133946 | ||||||||
\(502\) | −11.9461 | −0.533181 | ||||||||
\(503\) | −25.5401 | −1.13878 | −0.569389 | − | 0.822068i | \(-0.692820\pi\) | ||||
−0.569389 | + | 0.822068i | \(0.692820\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.69770 | 0.209045 | ||||||||
\(506\) | 4.34917 | 0.193344 | ||||||||
\(507\) | −4.65131 | −0.206572 | ||||||||
\(508\) | −7.69933 | −0.341602 | ||||||||
\(509\) | −30.3594 | −1.34566 | −0.672829 | − | 0.739798i | \(-0.734921\pi\) | ||||
−0.672829 | + | 0.739798i | \(0.734921\pi\) | |||||||
\(510\) | −53.5485 | −2.37117 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −49.4328 | −2.18464 | ||||||||
\(513\) | −2.44156 | −0.107798 | ||||||||
\(514\) | −3.59381 | −0.158516 | ||||||||
\(515\) | −13.9498 | −0.614701 | ||||||||
\(516\) | 46.4813 | 2.04622 | ||||||||
\(517\) | 0.691053 | 0.0303925 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.2996 | 0.583789 | ||||||||
\(520\) | −72.9889 | −3.20077 | ||||||||
\(521\) | 24.7007 | 1.08216 | 0.541079 | − | 0.840972i | \(-0.318016\pi\) | ||||
0.541079 | + | 0.840972i | \(0.318016\pi\) | |||||||
\(522\) | 20.2679 | 0.887104 | ||||||||
\(523\) | 28.5353 | 1.24776 | 0.623881 | − | 0.781519i | \(-0.285555\pi\) | ||||
0.623881 | + | 0.781519i | \(0.285555\pi\) | |||||||
\(524\) | −38.4718 | −1.68065 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.1777 | 0.966994 | ||||||||
\(527\) | −4.51632 | −0.196734 | ||||||||
\(528\) | 10.4855 | 0.456322 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −71.0737 | −3.08724 | ||||||||
\(531\) | 1.83508 | 0.0796357 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.0927 | 0.826998 | ||||||||
\(534\) | −37.6934 | −1.63115 | ||||||||
\(535\) | 4.04493 | 0.174877 | ||||||||
\(536\) | −59.7619 | −2.58132 | ||||||||
\(537\) | 19.6297 | 0.847084 | ||||||||
\(538\) | 32.4928 | 1.40086 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −18.6780 | −0.803771 | ||||||||
\(541\) | −7.74392 | −0.332937 | −0.166469 | − | 0.986047i | \(-0.553236\pi\) | ||||
−0.166469 | + | 0.986047i | \(0.553236\pi\) | |||||||
\(542\) | −33.5743 | −1.44214 | ||||||||
\(543\) | −19.2095 | −0.824358 | ||||||||
\(544\) | 17.5063 | 0.750575 | ||||||||
\(545\) | 64.6661 | 2.76999 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.8996 | 1.57771 | 0.788856 | − | 0.614578i | \(-0.210674\pi\) | ||||
0.788856 | + | 0.614578i | \(0.210674\pi\) | |||||||
\(548\) | 1.07033 | 0.0457222 | ||||||||
\(549\) | 1.30126 | 0.0555363 | ||||||||
\(550\) | 59.3207 | 2.52944 | ||||||||
\(551\) | −19.6745 | −0.838162 | ||||||||
\(552\) | 5.85100 | 0.249035 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −38.9821 | −1.65619 | ||||||||
\(555\) | 39.5289 | 1.67791 | ||||||||
\(556\) | 37.2035 | 1.57778 | ||||||||
\(557\) | 28.2645 | 1.19760 | 0.598802 | − | 0.800897i | \(-0.295644\pi\) | ||||
0.598802 | + | 0.800897i | \(0.295644\pi\) | |||||||
\(558\) | −2.30357 | −0.0975180 | ||||||||
\(559\) | 31.0438 | 1.31301 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.52686 | 0.360004 | ||||||||
\(562\) | 59.3810 | 2.50484 | ||||||||
\(563\) | 9.62212 | 0.405524 | 0.202762 | − | 0.979228i | \(-0.435008\pi\) | ||||
0.202762 | + | 0.979228i | \(0.435008\pi\) | |||||||
\(564\) | 1.72898 | 0.0728032 | ||||||||
\(565\) | 61.0576 | 2.56871 | ||||||||
\(566\) | −59.5637 | −2.50365 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −52.6701 | −2.20999 | ||||||||
\(569\) | −15.7146 | −0.658791 | −0.329396 | − | 0.944192i | \(-0.606845\pi\) | ||||
−0.329396 | + | 0.944192i | \(0.606845\pi\) | |||||||
\(570\) | 26.5130 | 1.11051 | ||||||||
\(571\) | 11.3442 | 0.474739 | 0.237369 | − | 0.971419i | \(-0.423715\pi\) | ||||
0.237369 | + | 0.971419i | \(0.423715\pi\) | |||||||
\(572\) | 21.6149 | 0.903766 | ||||||||
\(573\) | −7.15375 | −0.298852 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.6396 | 0.568809 | ||||||||
\(576\) | −3.19874 | −0.133281 | ||||||||
\(577\) | 7.95051 | 0.330984 | 0.165492 | − | 0.986211i | \(-0.447079\pi\) | ||||
0.165492 | + | 0.986211i | \(0.447079\pi\) | |||||||
\(578\) | 18.4041 | 0.765511 | ||||||||
\(579\) | −21.9573 | −0.912513 | ||||||||
\(580\) | −150.510 | −6.24959 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.72458 | 0.320194 | ||||||||
\(583\) | 11.3175 | 0.468723 | ||||||||
\(584\) | 15.3130 | 0.633655 | ||||||||
\(585\) | −12.4746 | −0.515762 | ||||||||
\(586\) | −53.1383 | −2.19512 | ||||||||
\(587\) | −21.2897 | −0.878718 | −0.439359 | − | 0.898311i | \(-0.644794\pi\) | ||||
−0.439359 | + | 0.898311i | \(0.644794\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.23613 | 0.0921379 | ||||||||
\(590\) | −19.9272 | −0.820390 | ||||||||
\(591\) | 3.21028 | 0.132053 | ||||||||
\(592\) | −55.5203 | −2.28187 | ||||||||
\(593\) | 9.67715 | 0.397393 | 0.198696 | − | 0.980061i | \(-0.436329\pi\) | ||||
0.198696 | + | 0.980061i | \(0.436329\pi\) | |||||||
\(594\) | 4.34917 | 0.178448 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.4971 | 0.798631 | ||||||||
\(597\) | −12.7170 | −0.520471 | ||||||||
\(598\) | 7.26746 | 0.297188 | ||||||||
\(599\) | 25.9792 | 1.06148 | 0.530740 | − | 0.847535i | \(-0.321914\pi\) | ||||
0.530740 | + | 0.847535i | \(0.321914\pi\) | |||||||
\(600\) | 79.8050 | 3.25802 | ||||||||
\(601\) | −31.2857 | −1.27617 | −0.638084 | − | 0.769967i | \(-0.720273\pi\) | ||||
−0.638084 | + | 0.769967i | \(0.720273\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.2140 | −0.415945 | ||||||||
\(604\) | −19.5878 | −0.797015 | ||||||||
\(605\) | 34.5822 | 1.40597 | ||||||||
\(606\) | −2.73679 | −0.111174 | ||||||||
\(607\) | −28.9163 | −1.17368 | −0.586838 | − | 0.809704i | \(-0.699628\pi\) | ||||
−0.586838 | + | 0.809704i | \(0.699628\pi\) | |||||||
\(608\) | −8.66771 | −0.351522 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.1304 | −0.572123 | ||||||||
\(611\) | 1.15475 | 0.0467162 | ||||||||
\(612\) | 21.3338 | 0.862367 | ||||||||
\(613\) | −47.9848 | −1.93809 | −0.969043 | − | 0.246892i | \(-0.920591\pi\) | ||||
−0.969043 | + | 0.246892i | \(0.920591\pi\) | |||||||
\(614\) | 4.97818 | 0.200903 | ||||||||
\(615\) | −28.5283 | −1.15037 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.9964 | 1.69071 | 0.845355 | − | 0.534205i | \(-0.179389\pi\) | ||||
0.845355 | + | 0.534205i | \(0.179389\pi\) | |||||||
\(618\) | 8.12686 | 0.326910 | ||||||||
\(619\) | 9.42381 | 0.378775 | 0.189388 | − | 0.981902i | \(-0.439350\pi\) | ||||
0.189388 | + | 0.981902i | \(0.439350\pi\) | |||||||
\(620\) | 17.1064 | 0.687009 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 9.80123 | 0.392994 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 17.5212 | 0.701411 | ||||||||
\(625\) | 92.8396 | 3.71358 | ||||||||
\(626\) | −44.4144 | −1.77516 | ||||||||
\(627\) | −4.22183 | −0.168603 | ||||||||
\(628\) | 14.1350 | 0.564050 | ||||||||
\(629\) | −45.1495 | −1.80023 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.84273 | 0.272405 | 0.136202 | − | 0.990681i | \(-0.456510\pi\) | ||||
0.136202 | + | 0.990681i | \(0.456510\pi\) | |||||||
\(632\) | 59.6042 | 2.37093 | ||||||||
\(633\) | −17.0500 | −0.677675 | ||||||||
\(634\) | −31.0183 | −1.23189 | ||||||||
\(635\) | 7.68350 | 0.304910 | ||||||||
\(636\) | 28.3159 | 1.12280 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 35.0463 | 1.38750 | ||||||||
\(639\) | −9.00190 | −0.356110 | ||||||||
\(640\) | 65.3891 | 2.58473 | ||||||||
\(641\) | 7.02021 | 0.277282 | 0.138641 | − | 0.990343i | \(-0.455727\pi\) | ||||
0.138641 | + | 0.990343i | \(0.455727\pi\) | |||||||
\(642\) | −2.35649 | −0.0930033 | ||||||||
\(643\) | 47.1743 | 1.86037 | 0.930185 | − | 0.367090i | \(-0.119646\pi\) | ||||
0.930185 | + | 0.367090i | \(0.119646\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −46.3857 | −1.82643 | ||||||||
\(646\) | −30.2829 | −1.19146 | ||||||||
\(647\) | −23.9670 | −0.942239 | −0.471119 | − | 0.882070i | \(-0.656150\pi\) | ||||
−0.471119 | + | 0.882070i | \(0.656150\pi\) | |||||||
\(648\) | 5.85100 | 0.229849 | ||||||||
\(649\) | 3.17313 | 0.124556 | ||||||||
\(650\) | 99.1249 | 3.88800 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 46.0401 | 1.80307 | ||||||||
\(653\) | −18.3313 | −0.717359 | −0.358679 | − | 0.933461i | \(-0.616773\pi\) | ||||
−0.358679 | + | 0.933461i | \(0.616773\pi\) | |||||||
\(654\) | −37.6732 | −1.47314 | ||||||||
\(655\) | 38.3927 | 1.50013 | ||||||||
\(656\) | 40.0695 | 1.56445 | ||||||||
\(657\) | 2.61716 | 0.102105 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.4341 | 0.640183 | 0.320092 | − | 0.947387i | \(-0.396286\pi\) | ||||
0.320092 | + | 0.947387i | \(0.396286\pi\) | |||||||
\(660\) | −32.2970 | −1.25716 | ||||||||
\(661\) | 30.0350 | 1.16823 | 0.584113 | − | 0.811672i | \(-0.301442\pi\) | ||||
0.584113 | + | 0.811672i | \(0.301442\pi\) | |||||||
\(662\) | 14.6024 | 0.567538 | ||||||||
\(663\) | 14.2484 | 0.553361 | ||||||||
\(664\) | 63.6812 | 2.47131 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −23.0287 | −0.892345 | ||||||||
\(667\) | 8.05817 | 0.312014 | ||||||||
\(668\) | −12.9706 | −0.501848 | ||||||||
\(669\) | −23.3278 | −0.901906 | ||||||||
\(670\) | 110.914 | 4.28497 | ||||||||
\(671\) | 2.25007 | 0.0868630 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.0642 | 0.657776 | 0.328888 | − | 0.944369i | \(-0.393326\pi\) | ||||
0.328888 | + | 0.944369i | \(0.393326\pi\) | |||||||
\(674\) | −56.7030 | −2.18412 | ||||||||
\(675\) | 13.6396 | 0.524987 | ||||||||
\(676\) | −20.1227 | −0.773951 | ||||||||
\(677\) | 37.6555 | 1.44722 | 0.723610 | − | 0.690209i | \(-0.242482\pi\) | ||||
0.723610 | + | 0.690209i | \(0.242482\pi\) | |||||||
\(678\) | −35.5709 | −1.36609 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −124.567 | −4.77694 | ||||||||
\(681\) | 7.67594 | 0.294143 | ||||||||
\(682\) | −3.98322 | −0.152526 | ||||||||
\(683\) | −40.7749 | −1.56021 | −0.780104 | − | 0.625649i | \(-0.784834\pi\) | ||||
−0.780104 | + | 0.625649i | \(0.784834\pi\) | |||||||
\(684\) | −10.5628 | −0.403879 | ||||||||
\(685\) | −1.06813 | −0.0408111 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.8736 | 0.872683 | ||||||||
\(688\) | 65.1511 | 2.48386 | ||||||||
\(689\) | 18.9116 | 0.720473 | ||||||||
\(690\) | −10.8590 | −0.413396 | ||||||||
\(691\) | −3.98906 | −0.151751 | −0.0758756 | − | 0.997117i | \(-0.524175\pi\) | ||||
−0.0758756 | + | 0.997117i | \(0.524175\pi\) | |||||||
\(692\) | 57.5376 | 2.18725 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.8572 | −0.715811 | ||||||||
\(695\) | −37.1270 | −1.40831 | ||||||||
\(696\) | 47.1483 | 1.78715 | ||||||||
\(697\) | 32.5848 | 1.23424 | ||||||||
\(698\) | 20.0549 | 0.759089 | ||||||||
\(699\) | 23.5559 | 0.890965 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.27653 | 0.123753 | 0.0618763 | − | 0.998084i | \(-0.480292\pi\) | ||||
0.0618763 | + | 0.998084i | \(0.480292\pi\) | |||||||
\(702\) | 7.26746 | 0.274292 | ||||||||
\(703\) | 22.3545 | 0.843114 | ||||||||
\(704\) | −5.53111 | −0.208461 | ||||||||
\(705\) | −1.72543 | −0.0649833 | ||||||||
\(706\) | 74.2712 | 2.79523 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7.93902 | 0.298367 | ||||||||
\(709\) | −7.16279 | −0.269004 | −0.134502 | − | 0.990913i | \(-0.542944\pi\) | ||||
−0.134502 | + | 0.990913i | \(0.542944\pi\) | |||||||
\(710\) | 97.7519 | 3.66856 | ||||||||
\(711\) | 10.1870 | 0.382043 | ||||||||
\(712\) | −87.6844 | −3.28611 | ||||||||
\(713\) | −0.915859 | −0.0342992 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.5705 | −0.806690 | ||||||||
\(716\) | 84.9230 | 3.17372 | ||||||||
\(717\) | 13.1829 | 0.492325 | ||||||||
\(718\) | −33.0011 | −1.23159 | ||||||||
\(719\) | −49.3742 | −1.84135 | −0.920673 | − | 0.390335i | \(-0.872359\pi\) | ||||
−0.920673 | + | 0.390335i | \(0.872359\pi\) | |||||||
\(720\) | −26.1802 | −0.975679 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −32.7952 | −1.22051 | ||||||||
\(723\) | 17.2670 | 0.642168 | ||||||||
\(724\) | −83.1051 | −3.08858 | ||||||||
\(725\) | 109.910 | 4.08195 | ||||||||
\(726\) | −20.1469 | −0.747721 | ||||||||
\(727\) | 15.4034 | 0.571281 | 0.285640 | − | 0.958337i | \(-0.407794\pi\) | ||||
0.285640 | + | 0.958337i | \(0.407794\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −28.4198 | −1.05186 | ||||||||
\(731\) | 52.9813 | 1.95958 | ||||||||
\(732\) | 5.62957 | 0.208075 | ||||||||
\(733\) | −12.2110 | −0.451025 | −0.225512 | − | 0.974240i | \(-0.572406\pi\) | ||||
−0.225512 | + | 0.974240i | \(0.572406\pi\) | |||||||
\(734\) | −13.2392 | −0.488669 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.55007 | 0.130857 | ||||||||
\(737\) | −17.6615 | −0.650570 | ||||||||
\(738\) | 16.6200 | 0.611792 | ||||||||
\(739\) | 32.4803 | 1.19481 | 0.597404 | − | 0.801940i | \(-0.296199\pi\) | ||||
0.597404 | + | 0.801940i | \(0.296199\pi\) | |||||||
\(740\) | 171.012 | 6.28652 | ||||||||
\(741\) | −7.05467 | −0.259160 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.1671 | −1.47359 | −0.736795 | − | 0.676117i | \(-0.763662\pi\) | ||||
−0.736795 | + | 0.676117i | \(0.763662\pi\) | |||||||
\(744\) | −5.35869 | −0.196459 | ||||||||
\(745\) | −19.4570 | −0.712848 | ||||||||
\(746\) | −31.8162 | −1.16487 | ||||||||
\(747\) | 10.8838 | 0.398218 | ||||||||
\(748\) | 36.8893 | 1.34881 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −93.8171 | −3.42572 | ||||||||
\(751\) | 44.3036 | 1.61666 | 0.808330 | − | 0.588729i | \(-0.200372\pi\) | ||||
0.808330 | + | 0.588729i | \(0.200372\pi\) | |||||||
\(752\) | 2.42345 | 0.0883741 | ||||||||
\(753\) | −4.74956 | −0.173084 | ||||||||
\(754\) | 58.5624 | 2.13272 | ||||||||
\(755\) | 19.5475 | 0.711406 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.4696 | 1.50724 | 0.753620 | − | 0.657311i | \(-0.228306\pi\) | ||||
0.753620 | + | 0.657311i | \(0.228306\pi\) | |||||||
\(758\) | 32.1914 | 1.16924 | ||||||||
\(759\) | 1.72915 | 0.0627642 | ||||||||
\(760\) | 61.6758 | 2.23722 | ||||||||
\(761\) | 3.17300 | 0.115021 | 0.0575107 | − | 0.998345i | \(-0.481684\pi\) | ||||
0.0575107 | + | 0.998345i | \(0.481684\pi\) | |||||||
\(762\) | −4.47625 | −0.162157 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −30.9489 | −1.11969 | ||||||||
\(765\) | −21.2899 | −0.769739 | ||||||||
\(766\) | 41.8200 | 1.51102 | ||||||||
\(767\) | 5.30230 | 0.191455 | ||||||||
\(768\) | −31.6969 | −1.14376 | ||||||||
\(769\) | 13.6487 | 0.492184 | 0.246092 | − | 0.969246i | \(-0.420853\pi\) | ||||
0.246092 | + | 0.969246i | \(0.420853\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.42884 | −0.0514582 | ||||||||
\(772\) | −94.9927 | −3.41886 | ||||||||
\(773\) | 28.4748 | 1.02417 | 0.512083 | − | 0.858936i | \(-0.328874\pi\) | ||||
0.512083 | + | 0.858936i | \(0.328874\pi\) | |||||||
\(774\) | 27.0234 | 0.971335 | ||||||||
\(775\) | −12.4919 | −0.448723 | ||||||||
\(776\) | 17.9693 | 0.645061 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −75.1299 | −2.69354 | ||||||||
\(779\) | −16.1334 | −0.578040 | ||||||||
\(780\) | −53.9683 | −1.93237 | ||||||||
\(781\) | −15.5656 | −0.556982 | ||||||||
\(782\) | 12.4031 | 0.443533 | ||||||||
\(783\) | 8.05817 | 0.287975 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.1060 | −0.503464 | ||||||||
\(786\) | −22.3668 | −0.797797 | ||||||||
\(787\) | −48.0679 | −1.71343 | −0.856717 | − | 0.515786i | \(-0.827500\pi\) | ||||
−0.856717 | + | 0.515786i | \(0.827500\pi\) | |||||||
\(788\) | 13.8885 | 0.494756 | ||||||||
\(789\) | 8.81746 | 0.313910 | ||||||||
\(790\) | −110.621 | −3.93572 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 10.1173 | 0.359501 | ||||||||
\(793\) | 3.75987 | 0.133517 | ||||||||
\(794\) | 15.0519 | 0.534172 | ||||||||
\(795\) | −28.2576 | −1.00219 | ||||||||
\(796\) | −55.0168 | −1.95002 | ||||||||
\(797\) | 28.0705 | 0.994308 | 0.497154 | − | 0.867662i | \(-0.334378\pi\) | ||||
0.497154 | + | 0.867662i | \(0.334378\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.97077 | 0.0697207 | ||||||||
\(800\) | 48.4214 | 1.71195 | ||||||||
\(801\) | −14.9862 | −0.529513 | ||||||||
\(802\) | −39.8999 | −1.40892 | ||||||||
\(803\) | 4.52546 | 0.159700 | ||||||||
\(804\) | −44.1882 | −1.55840 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.65597 | −0.234446 | ||||||||
\(807\) | 12.9185 | 0.454754 | ||||||||
\(808\) | −6.36645 | −0.223971 | ||||||||
\(809\) | 42.7600 | 1.50336 | 0.751681 | − | 0.659527i | \(-0.229243\pi\) | ||||
0.751681 | + | 0.659527i | \(0.229243\pi\) | |||||||
\(810\) | −10.8590 | −0.381547 | ||||||||
\(811\) | −50.7214 | −1.78107 | −0.890534 | − | 0.454916i | \(-0.849669\pi\) | ||||
−0.890534 | + | 0.454916i | \(0.849669\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.3485 | −0.468153 | ||||||||
\(814\) | −39.8201 | −1.39569 | ||||||||
\(815\) | −45.9455 | −1.60940 | ||||||||
\(816\) | 29.9028 | 1.04681 | ||||||||
\(817\) | −26.2321 | −0.917746 | ||||||||
\(818\) | −62.7252 | −2.19314 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −123.421 | −4.31004 | ||||||||
\(821\) | 42.2837 | 1.47571 | 0.737856 | − | 0.674959i | \(-0.235839\pi\) | ||||
0.737856 | + | 0.674959i | \(0.235839\pi\) | |||||||
\(822\) | 0.622271 | 0.0217042 | ||||||||
\(823\) | −16.4856 | −0.574650 | −0.287325 | − | 0.957833i | \(-0.592766\pi\) | ||||
−0.287325 | + | 0.957833i | \(0.592766\pi\) | |||||||
\(824\) | 18.9051 | 0.658591 | ||||||||
\(825\) | 23.5848 | 0.821119 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.3447 | 0.742229 | 0.371115 | − | 0.928587i | \(-0.378976\pi\) | ||||
0.371115 | + | 0.928587i | \(0.378976\pi\) | |||||||
\(828\) | 4.32625 | 0.150348 | ||||||||
\(829\) | −8.82638 | −0.306553 | −0.153276 | − | 0.988183i | \(-0.548982\pi\) | ||||
−0.153276 | + | 0.988183i | \(0.548982\pi\) | |||||||
\(830\) | −118.188 | −4.10235 | ||||||||
\(831\) | −15.4986 | −0.537640 | ||||||||
\(832\) | −9.24248 | −0.320425 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 21.6295 | 0.748967 | ||||||||
\(835\) | 12.9439 | 0.447943 | ||||||||
\(836\) | −18.2647 | −0.631697 | ||||||||
\(837\) | −0.915859 | −0.0316567 | ||||||||
\(838\) | 33.2665 | 1.14917 | ||||||||
\(839\) | 32.7270 | 1.12986 | 0.564932 | − | 0.825138i | \(-0.308903\pi\) | ||||
0.564932 | + | 0.825138i | \(0.308903\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.9341 | 1.23911 | ||||||||
\(842\) | −14.6427 | −0.504621 | ||||||||
\(843\) | 23.6088 | 0.813131 | ||||||||
\(844\) | −73.7624 | −2.53901 | ||||||||
\(845\) | 20.0813 | 0.690819 | ||||||||
\(846\) | 1.00520 | 0.0345594 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 39.6893 | 1.36294 | ||||||||
\(849\) | −23.6814 | −0.812745 | ||||||||
\(850\) | 169.172 | 5.80257 | ||||||||
\(851\) | −9.15581 | −0.313857 | ||||||||
\(852\) | −38.9445 | −1.33422 | ||||||||
\(853\) | −8.42097 | −0.288329 | −0.144164 | − | 0.989554i | \(-0.546049\pi\) | ||||
−0.144164 | + | 0.989554i | \(0.546049\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.5411 | 0.360497 | ||||||||
\(856\) | −5.48179 | −0.187364 | ||||||||
\(857\) | 5.60723 | 0.191539 | 0.0957697 | − | 0.995404i | \(-0.469469\pi\) | ||||
0.0957697 | + | 0.995404i | \(0.469469\pi\) | |||||||
\(858\) | 12.5665 | 0.429014 | ||||||||
\(859\) | −6.20674 | −0.211771 | −0.105886 | − | 0.994378i | \(-0.533768\pi\) | ||||
−0.105886 | + | 0.994378i | \(0.533768\pi\) | |||||||
\(860\) | −200.676 | −6.84300 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.6424 | 0.532781 | ||||||||
\(863\) | −7.30992 | −0.248833 | −0.124416 | − | 0.992230i | \(-0.539706\pi\) | ||||
−0.124416 | + | 0.992230i | \(0.539706\pi\) | |||||||
\(864\) | 3.55007 | 0.120776 | ||||||||
\(865\) | −57.4192 | −1.95231 | ||||||||
\(866\) | 5.44079 | 0.184886 | ||||||||
\(867\) | 7.31715 | 0.248504 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.6149 | 0.597544 | ||||||||
\(870\) | −87.5039 | −2.96666 | ||||||||
\(871\) | −29.5124 | −0.999988 | ||||||||
\(872\) | −87.6372 | −2.96777 | ||||||||
\(873\) | 3.07116 | 0.103943 | ||||||||
\(874\) | −6.14102 | −0.207723 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.3225 | 0.382551 | ||||||||
\(877\) | −32.7872 | −1.10715 | −0.553573 | − | 0.832801i | \(-0.686736\pi\) | ||||
−0.553573 | + | 0.832801i | \(0.686736\pi\) | |||||||
\(878\) | −28.9891 | −0.978335 | ||||||||
\(879\) | −21.1268 | −0.712590 | ||||||||
\(880\) | −45.2695 | −1.52604 | ||||||||
\(881\) | −17.0828 | −0.575533 | −0.287767 | − | 0.957701i | \(-0.592913\pi\) | ||||
−0.287767 | + | 0.957701i | \(0.592913\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.9824 | 0.908030 | 0.454015 | − | 0.890994i | \(-0.349991\pi\) | ||||
0.454015 | + | 0.890994i | \(0.349991\pi\) | |||||||
\(884\) | 61.6421 | 2.07325 | ||||||||
\(885\) | −7.92270 | −0.266319 | ||||||||
\(886\) | 22.9648 | 0.771518 | ||||||||
\(887\) | −6.80466 | −0.228478 | −0.114239 | − | 0.993453i | \(-0.536443\pi\) | ||||
−0.114239 | + | 0.993453i | \(0.536443\pi\) | |||||||
\(888\) | −53.5706 | −1.79771 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 162.736 | 5.45492 | ||||||||
\(891\) | 1.72915 | 0.0579287 | ||||||||
\(892\) | −100.922 | −3.37912 | ||||||||
\(893\) | −0.975766 | −0.0326528 | ||||||||
\(894\) | 11.3352 | 0.379107 | ||||||||
\(895\) | −84.7484 | −2.83283 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.88941 | 0.0964746 | ||||||||
\(898\) | −52.0213 | −1.73597 | ||||||||
\(899\) | −7.38015 | −0.246142 | ||||||||
\(900\) | 59.0081 | 1.96694 | ||||||||
\(901\) | 32.2756 | 1.07526 | ||||||||
\(902\) | 28.7386 | 0.956889 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −82.7469 | −2.75212 | ||||||||
\(905\) | 82.9342 | 2.75683 | ||||||||
\(906\) | −11.3880 | −0.378340 | ||||||||
\(907\) | −5.42913 | −0.180271 | −0.0901357 | − | 0.995929i | \(-0.528730\pi\) | ||||
−0.0901357 | + | 0.995929i | \(0.528730\pi\) | |||||||
\(908\) | 33.2081 | 1.10205 | ||||||||
\(909\) | −1.08810 | −0.0360899 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.8106 | −0.523829 | −0.261914 | − | 0.965091i | \(-0.584354\pi\) | ||||
−0.261914 | + | 0.965091i | \(0.584354\pi\) | |||||||
\(912\) | −14.8055 | −0.490259 | ||||||||
\(913\) | 18.8198 | 0.622843 | ||||||||
\(914\) | 61.8634 | 2.04626 | ||||||||
\(915\) | −5.61799 | −0.185725 | ||||||||
\(916\) | 98.9571 | 3.26963 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 12.4031 | 0.409363 | ||||||||
\(919\) | 37.3581 | 1.23233 | 0.616165 | − | 0.787617i | \(-0.288686\pi\) | ||||
0.616165 | + | 0.787617i | \(0.288686\pi\) | |||||||
\(920\) | −25.2608 | −0.832825 | ||||||||
\(921\) | 1.97923 | 0.0652180 | ||||||||
\(922\) | 8.42712 | 0.277532 | ||||||||
\(923\) | −26.0102 | −0.856135 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −124.881 | −4.10607 | ||||||||
\(926\) | −76.0370 | −2.49873 | ||||||||
\(927\) | 3.23110 | 0.106123 | ||||||||
\(928\) | 28.6071 | 0.939073 | ||||||||
\(929\) | −32.7069 | −1.07308 | −0.536539 | − | 0.843875i | \(-0.680269\pi\) | ||||
−0.536539 | + | 0.843875i | \(0.680269\pi\) | |||||||
\(930\) | 9.94534 | 0.326121 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 101.909 | 3.33813 | ||||||||
\(933\) | 3.89679 | 0.127575 | ||||||||
\(934\) | 75.8123 | 2.48065 | ||||||||
\(935\) | −36.8135 | −1.20393 | ||||||||
\(936\) | 16.9059 | 0.552588 | ||||||||
\(937\) | −49.2657 | −1.60944 | −0.804721 | − | 0.593654i | \(-0.797685\pi\) | ||||
−0.804721 | + | 0.593654i | \(0.797685\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.6584 | −0.576260 | ||||||||
\(940\) | −7.46462 | −0.243469 | ||||||||
\(941\) | 10.8684 | 0.354299 | 0.177149 | − | 0.984184i | \(-0.443312\pi\) | ||||
0.177149 | + | 0.984184i | \(0.443312\pi\) | |||||||
\(942\) | 8.21786 | 0.267752 | ||||||||
\(943\) | 6.60783 | 0.215181 | ||||||||
\(944\) | 11.1278 | 0.362180 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 46.7275 | 1.51924 | ||||||||
\(947\) | 31.5907 | 1.02656 | 0.513279 | − | 0.858222i | \(-0.328431\pi\) | ||||
0.513279 | + | 0.858222i | \(0.328431\pi\) | |||||||
\(948\) | 44.0716 | 1.43138 | ||||||||
\(949\) | 7.56204 | 0.245474 | ||||||||
\(950\) | −83.7608 | −2.71756 | ||||||||
\(951\) | −12.3323 | −0.399903 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.60480 | −0.246344 | −0.123172 | − | 0.992385i | \(-0.539307\pi\) | ||||
−0.123172 | + | 0.992385i | \(0.539307\pi\) | |||||||
\(954\) | 16.4623 | 0.532987 | ||||||||
\(955\) | 30.8853 | 0.999424 | ||||||||
\(956\) | 57.0326 | 1.84457 | ||||||||
\(957\) | 13.9338 | 0.450415 | ||||||||
\(958\) | −73.0274 | −2.35941 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 13.8101 | 0.445719 | ||||||||
\(961\) | −30.1612 | −0.972942 | ||||||||
\(962\) | −66.5394 | −2.14532 | ||||||||
\(963\) | −0.936899 | −0.0301911 | ||||||||
\(964\) | 74.7015 | 2.40597 | ||||||||
\(965\) | 94.7973 | 3.05163 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3379 | 0.332446 | 0.166223 | − | 0.986088i | \(-0.446843\pi\) | ||||
0.166223 | + | 0.986088i | \(0.446843\pi\) | |||||||
\(968\) | −46.8667 | −1.50635 | ||||||||
\(969\) | −12.0399 | −0.386778 | ||||||||
\(970\) | −33.3498 | −1.07080 | ||||||||
\(971\) | −19.7589 | −0.634095 | −0.317047 | − | 0.948410i | \(-0.602691\pi\) | ||||
−0.317047 | + | 0.948410i | \(0.602691\pi\) | |||||||
\(972\) | 4.32625 | 0.138765 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −43.5273 | −1.39470 | ||||||||
\(975\) | 39.4103 | 1.26214 | ||||||||
\(976\) | 7.89075 | 0.252577 | ||||||||
\(977\) | −19.6177 | −0.627626 | −0.313813 | − | 0.949485i | \(-0.601607\pi\) | ||||
−0.313813 | + | 0.949485i | \(0.601607\pi\) | |||||||
\(978\) | 26.7669 | 0.855911 | ||||||||
\(979\) | −25.9135 | −0.828198 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.9782 | −0.478216 | ||||||||
\(982\) | 35.7881 | 1.14205 | ||||||||
\(983\) | 15.1056 | 0.481794 | 0.240897 | − | 0.970551i | \(-0.422558\pi\) | ||||
0.240897 | + | 0.970551i | \(0.422558\pi\) | |||||||
\(984\) | 38.6624 | 1.23251 | ||||||||
\(985\) | −13.8599 | −0.441613 | ||||||||
\(986\) | 99.9461 | 3.18293 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −30.5203 | −0.970979 | ||||||||
\(989\) | 10.7440 | 0.341640 | ||||||||
\(990\) | −18.7769 | −0.596769 | ||||||||
\(991\) | 41.2825 | 1.31138 | 0.655690 | − | 0.755030i | \(-0.272378\pi\) | ||||
0.655690 | + | 0.755030i | \(0.272378\pi\) | |||||||
\(992\) | −3.25136 | −0.103231 | ||||||||
\(993\) | 5.80565 | 0.184237 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 54.9037 | 1.74056 | ||||||||
\(996\) | 47.0861 | 1.49198 | ||||||||
\(997\) | −18.5381 | −0.587107 | −0.293554 | − | 0.955943i | \(-0.594838\pi\) | ||||
−0.293554 | + | 0.955943i | \(0.594838\pi\) | |||||||
\(998\) | 27.9619 | 0.885119 | ||||||||
\(999\) | −9.15581 | −0.289677 |
(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.bj.1.9 | 10 | ||
7.3 | odd | 6 | 483.2.i.h.415.2 | yes | 20 | ||
7.5 | odd | 6 | 483.2.i.h.277.2 | ✓ | 20 | ||
7.6 | odd | 2 | 3381.2.a.bi.1.9 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.h.277.2 | ✓ | 20 | 7.5 | odd | 6 | ||
483.2.i.h.415.2 | yes | 20 | 7.3 | odd | 6 | ||
3381.2.a.bi.1.9 | 10 | 7.6 | odd | 2 | |||
3381.2.a.bj.1.9 | 10 | 1.1 | even | 1 | trivial |