Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5733,2,Mod(1,5733)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5733, 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("5733.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5733.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: | \(45.7782354788\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.199374400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 8x^{4} + 10x^{2} - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 819) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.18733\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5733.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.345110 | −0.244030 | −0.122015 | − | 0.992528i | \(-0.538936\pi\) | ||||
−0.122015 | + | 0.992528i | \(0.538936\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.88090 | −0.940450 | ||||||||
\(5\) | −3.42059 | −1.52973 | −0.764867 | − | 0.644189i | \(-0.777195\pi\) | ||||
−0.764867 | + | 0.644189i | \(0.777195\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.33934 | 0.473527 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.18048 | 0.373300 | ||||||||
\(11\) | 1.68445 | 0.507880 | 0.253940 | − | 0.967220i | \(-0.418273\pi\) | ||||
0.253940 | + | 0.967220i | \(0.418273\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.29958 | 0.824895 | ||||||||
\(17\) | 4.05911 | 0.984480 | 0.492240 | − | 0.870460i | \(-0.336178\pi\) | ||||
0.492240 | + | 0.870460i | \(0.336178\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.06138 | −1.39058 | −0.695288 | − | 0.718731i | \(-0.744723\pi\) | ||||
−0.695288 | + | 0.718731i | \(0.744723\pi\) | |||||||
\(20\) | 6.43378 | 1.43864 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.581319 | −0.123938 | ||||||||
\(23\) | −5.79525 | −1.20839 | −0.604197 | − | 0.796835i | \(-0.706506\pi\) | ||||
−0.604197 | + | 0.796835i | \(0.706506\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.70042 | 1.34008 | ||||||||
\(26\) | 0.345110 | 0.0676816 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.48547 | 1.20432 | 0.602161 | − | 0.798375i | \(-0.294306\pi\) | ||||
0.602161 | + | 0.798375i | \(0.294306\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.299580 | −0.0538061 | −0.0269031 | − | 0.999638i | \(-0.508565\pi\) | ||||
−0.0269031 | + | 0.999638i | \(0.508565\pi\) | |||||||
\(32\) | −3.81739 | −0.674826 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.40084 | −0.240242 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.76180 | 1.27603 | 0.638016 | − | 0.770023i | \(-0.279755\pi\) | ||||
0.638016 | + | 0.770023i | \(0.279755\pi\) | |||||||
\(38\) | 2.09184 | 0.339342 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.58132 | −0.724370 | ||||||||
\(41\) | −9.90606 | −1.54707 | −0.773533 | − | 0.633755i | \(-0.781513\pi\) | ||||
−0.773533 | + | 0.633755i | \(0.781513\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.06138 | −0.924351 | −0.462176 | − | 0.886788i | \(-0.652931\pi\) | ||||
−0.462176 | + | 0.886788i | \(0.652931\pi\) | |||||||
\(44\) | −3.16827 | −0.477635 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00000 | 0.294884 | ||||||||
\(47\) | −7.47970 | −1.09103 | −0.545513 | − | 0.838102i | \(-0.683665\pi\) | ||||
−0.545513 | + | 0.838102i | \(0.683665\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.31238 | −0.327020 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.88090 | 0.260834 | ||||||||
\(53\) | −9.85437 | −1.35360 | −0.676801 | − | 0.736166i | \(-0.736634\pi\) | ||||
−0.676801 | + | 0.736166i | \(0.736634\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.76180 | −0.776921 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.23820 | −0.293890 | ||||||||
\(59\) | −3.75511 | −0.488873 | −0.244437 | − | 0.969665i | \(-0.578603\pi\) | ||||
−0.244437 | + | 0.969665i | \(0.578603\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.0000 | −1.28037 | −0.640184 | − | 0.768221i | \(-0.721142\pi\) | ||||
−0.640184 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(62\) | 0.103388 | 0.0131303 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.28174 | −0.660217 | ||||||||
\(65\) | 3.42059 | 0.424272 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.76180 | 1.19259 | 0.596297 | − | 0.802764i | \(-0.296638\pi\) | ||||
0.596297 | + | 0.802764i | \(0.296638\pi\) | |||||||
\(68\) | −7.63478 | −0.925853 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.52562 | −1.01181 | −0.505903 | − | 0.862591i | \(-0.668840\pi\) | ||||
−0.505903 | + | 0.862591i | \(0.668840\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.70042 | 0.199019 | 0.0995096 | − | 0.995037i | \(-0.468273\pi\) | ||||
0.0995096 | + | 0.995037i | \(0.468273\pi\) | |||||||
\(74\) | −2.67867 | −0.311390 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.4008 | 1.30777 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.4622 | 1.51462 | 0.757309 | − | 0.653057i | \(-0.226514\pi\) | ||||
0.757309 | + | 0.653057i | \(0.226514\pi\) | |||||||
\(80\) | −11.2865 | −1.26187 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.41868 | 0.377530 | ||||||||
\(83\) | 0.638526 | 0.0700873 | 0.0350437 | − | 0.999386i | \(-0.488843\pi\) | ||||
0.0350437 | + | 0.999386i | \(0.488843\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.8846 | −1.50599 | ||||||||
\(86\) | 2.09184 | 0.225569 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.25604 | 0.240495 | ||||||||
\(89\) | −12.9193 | −1.36944 | −0.684719 | − | 0.728807i | \(-0.740075\pi\) | ||||
−0.684719 | + | 0.728807i | \(0.740075\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.9003 | 1.13643 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.58132 | 0.266243 | ||||||||
\(95\) | 20.7335 | 2.12721 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.06138 | −0.412370 | −0.206185 | − | 0.978513i | \(-0.566105\pi\) | ||||
−0.206185 | + | 0.978513i | \(0.566105\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −12.6028 | −1.26028 | ||||||||
\(101\) | 9.51985 | 0.947260 | 0.473630 | − | 0.880724i | \(-0.342943\pi\) | ||||
0.473630 | + | 0.880724i | \(0.342943\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.36096 | 0.626764 | 0.313382 | − | 0.949627i | \(-0.398538\pi\) | ||||
0.313382 | + | 0.949627i | \(0.398538\pi\) | |||||||
\(104\) | −1.33934 | −0.131333 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.40084 | 0.330319 | ||||||||
\(107\) | −15.6496 | −1.51291 | −0.756453 | − | 0.654048i | \(-0.773069\pi\) | ||||
−0.756453 | + | 0.654048i | \(0.773069\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 1.98845 | 0.189592 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.48547 | −0.610102 | −0.305051 | − | 0.952336i | \(-0.598674\pi\) | ||||
−0.305051 | + | 0.952336i | \(0.598674\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.8232 | 1.84852 | ||||||||
\(116\) | −12.1985 | −1.13260 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.29592 | 0.119300 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.16264 | −0.742058 | ||||||||
\(122\) | 3.45110 | 0.312448 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.563479 | 0.0506019 | ||||||||
\(125\) | −5.81644 | −0.520238 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | 9.45756 | 0.835938 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.18048 | −0.103535 | ||||||||
\(131\) | 18.4317 | 1.61038 | 0.805192 | − | 0.593014i | \(-0.202062\pi\) | ||||
0.805192 | + | 0.593014i | \(0.202062\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.36889 | −0.291028 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.43652 | 0.466178 | ||||||||
\(137\) | 9.21584 | 0.787363 | 0.393681 | − | 0.919247i | \(-0.371201\pi\) | ||||
0.393681 | + | 0.919247i | \(0.371201\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.2854 | 1.80540 | 0.902702 | − | 0.430267i | \(-0.141580\pi\) | ||||
0.902702 | + | 0.430267i | \(0.141580\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.94228 | 0.246910 | ||||||||
\(143\) | −1.68445 | −0.140861 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.1841 | −1.84229 | ||||||||
\(146\) | −0.586832 | −0.0485666 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −14.5992 | −1.20004 | ||||||||
\(149\) | −17.4375 | −1.42853 | −0.714266 | − | 0.699874i | \(-0.753239\pi\) | ||||
−0.714266 | + | 0.699874i | \(0.753239\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.36096 | 0.517647 | 0.258824 | − | 0.965925i | \(-0.416665\pi\) | ||||
0.258824 | + | 0.965925i | \(0.416665\pi\) | |||||||
\(152\) | −8.11823 | −0.658475 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.02474 | 0.0823090 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.1228 | −0.807884 | −0.403942 | − | 0.914785i | \(-0.632360\pi\) | ||||
−0.403942 | + | 0.914785i | \(0.632360\pi\) | |||||||
\(158\) | −4.64595 | −0.369612 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 13.0577 | 1.03230 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.52360 | −0.589294 | −0.294647 | − | 0.955606i | \(-0.595202\pi\) | ||||
−0.294647 | + | 0.955606i | \(0.595202\pi\) | |||||||
\(164\) | 18.6323 | 1.45494 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.220362 | −0.0171034 | ||||||||
\(167\) | 15.7013 | 1.21500 | 0.607502 | − | 0.794318i | \(-0.292172\pi\) | ||||
0.607502 | + | 0.794318i | \(0.292172\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 4.79170 | 0.367506 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.4008 | 0.869306 | ||||||||
\(173\) | 12.9921 | 0.987773 | 0.493887 | − | 0.869526i | \(-0.335576\pi\) | ||||
0.493887 | + | 0.869526i | \(0.335576\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.55797 | 0.418948 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.45856 | 0.334183 | ||||||||
\(179\) | −10.5446 | −0.788140 | −0.394070 | − | 0.919081i | \(-0.628933\pi\) | ||||
−0.394070 | + | 0.919081i | \(0.628933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.76180 | −0.572207 | ||||||||
\(185\) | −26.5499 | −1.95199 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.83736 | 0.499997 | ||||||||
\(188\) | 14.0686 | 1.02606 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.15533 | −0.519102 | ||||||||
\(191\) | −4.16250 | −0.301188 | −0.150594 | − | 0.988596i | \(-0.548119\pi\) | ||||
−0.150594 | + | 0.988596i | \(0.548119\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.3610 | −1.17769 | −0.588844 | − | 0.808247i | \(-0.700417\pi\) | ||||
−0.588844 | + | 0.808247i | \(0.700417\pi\) | |||||||
\(194\) | 1.40162 | 0.100631 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.75511 | 0.267540 | 0.133770 | − | 0.991012i | \(-0.457292\pi\) | ||||
0.133770 | + | 0.991012i | \(0.457292\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 27.5236 | 1.95110 | 0.975548 | − | 0.219786i | \(-0.0705361\pi\) | ||||
0.975548 | + | 0.219786i | \(0.0705361\pi\) | |||||||
\(200\) | 8.97412 | 0.634566 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.28539 | −0.231160 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 33.8846 | 2.36660 | ||||||||
\(206\) | −2.19523 | −0.152949 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.29958 | −0.228785 | ||||||||
\(209\) | −10.2101 | −0.706245 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.06138 | 0.141911 | 0.0709556 | − | 0.997479i | \(-0.477395\pi\) | ||||
0.0709556 | + | 0.997479i | \(0.477395\pi\) | |||||||
\(212\) | 18.5351 | 1.27299 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.40084 | 0.369194 | ||||||||
\(215\) | 20.7335 | 1.41401 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.45110 | −0.233738 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.8374 | 0.730655 | ||||||||
\(221\) | −4.05911 | −0.273046 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.06138 | 0.138040 | 0.0690200 | − | 0.997615i | \(-0.478013\pi\) | ||||
0.0690200 | + | 0.997615i | \(0.478013\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.23820 | 0.148883 | ||||||||
\(227\) | −17.4375 | −1.15736 | −0.578682 | − | 0.815553i | \(-0.696433\pi\) | ||||
−0.578682 | + | 0.815553i | \(0.696433\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.36096 | 0.552508 | 0.276254 | − | 0.961085i | \(-0.410907\pi\) | ||||
0.276254 | + | 0.961085i | \(0.410907\pi\) | |||||||
\(230\) | −6.84118 | −0.451094 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.68624 | 0.570279 | ||||||||
\(233\) | 25.5252 | 1.67221 | 0.836105 | − | 0.548570i | \(-0.184827\pi\) | ||||
0.836105 | + | 0.548570i | \(0.184827\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.5850 | 1.66898 | ||||||||
\(236\) | 7.06298 | 0.459761 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.6438 | −1.07660 | −0.538301 | − | 0.842753i | \(-0.680933\pi\) | ||||
−0.538301 | + | 0.842753i | \(0.680933\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.10126 | −0.328601 | −0.164301 | − | 0.986410i | \(-0.552537\pi\) | ||||
−0.164301 | + | 0.986410i | \(0.552537\pi\) | |||||||
\(242\) | 2.81701 | 0.181084 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 18.8090 | 1.20412 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.06138 | 0.385676 | ||||||||
\(248\) | −0.401238 | −0.0254787 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.00731 | 0.126953 | ||||||||
\(251\) | 2.65749 | 0.167739 | 0.0838697 | − | 0.996477i | \(-0.473272\pi\) | ||||
0.0838697 | + | 0.996477i | \(0.473272\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.76180 | −0.613719 | ||||||||
\(254\) | −1.38044 | −0.0866165 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.29958 | 0.456224 | ||||||||
\(257\) | 10.9003 | 0.679941 | 0.339971 | − | 0.940436i | \(-0.389583\pi\) | ||||
0.339971 | + | 0.940436i | \(0.389583\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.43378 | −0.399006 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.36096 | −0.392981 | ||||||||
\(263\) | 7.88710 | 0.486339 | 0.243170 | − | 0.969984i | \(-0.421813\pi\) | ||||
0.243170 | + | 0.969984i | \(0.421813\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.7077 | 2.07065 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −18.3610 | −1.12157 | ||||||||
\(269\) | −8.80845 | −0.537061 | −0.268530 | − | 0.963271i | \(-0.586538\pi\) | ||||
−0.268530 | + | 0.963271i | \(0.586538\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.16264 | 0.0706253 | 0.0353126 | − | 0.999376i | \(-0.488757\pi\) | ||||
0.0353126 | + | 0.999376i | \(0.488757\pi\) | |||||||
\(272\) | 13.3934 | 0.812092 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.18048 | −0.192140 | ||||||||
\(275\) | 11.2865 | 0.680602 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.0614 | 0.965035 | 0.482517 | − | 0.875886i | \(-0.339723\pi\) | ||||
0.482517 | + | 0.875886i | \(0.339723\pi\) | |||||||
\(278\) | −7.34580 | −0.440572 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.92724 | 0.592210 | 0.296105 | − | 0.955155i | \(-0.404312\pi\) | ||||
0.296105 | + | 0.955155i | \(0.404312\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000 | 0.237775 | 0.118888 | − | 0.992908i | \(-0.462067\pi\) | ||||
0.118888 | + | 0.992908i | \(0.462067\pi\) | |||||||
\(284\) | 16.0358 | 0.951552 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.581319 | 0.0343741 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.523596 | −0.0307998 | ||||||||
\(290\) | 7.65597 | 0.449574 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.19832 | −0.187167 | ||||||||
\(293\) | 6.18147 | 0.361125 | 0.180563 | − | 0.983563i | \(-0.442208\pi\) | ||||
0.180563 | + | 0.983563i | \(0.442208\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.8447 | 0.747846 | ||||||||
\(296\) | 10.3957 | 0.604236 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.01784 | 0.348604 | ||||||||
\(299\) | 5.79525 | 0.335148 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.19523 | −0.126321 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −20.0000 | −1.14708 | ||||||||
\(305\) | 34.2059 | 1.95862 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.1841 | 1.49441 | 0.747204 | − | 0.664595i | \(-0.231396\pi\) | ||||
0.747204 | + | 0.664595i | \(0.231396\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.353648 | −0.0200858 | ||||||||
\(311\) | −4.08030 | −0.231372 | −0.115686 | − | 0.993286i | \(-0.536907\pi\) | ||||
−0.115686 | + | 0.993286i | \(0.536907\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.47640 | −0.139975 | −0.0699873 | − | 0.997548i | \(-0.522296\pi\) | ||||
−0.0699873 | + | 0.997548i | \(0.522296\pi\) | |||||||
\(314\) | 3.49346 | 0.197148 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −25.3211 | −1.42442 | ||||||||
\(317\) | −32.3969 | −1.81959 | −0.909794 | − | 0.415059i | \(-0.863761\pi\) | ||||
−0.909794 | + | 0.415059i | \(0.863761\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.9244 | 0.611651 | ||||||||
\(320\) | 18.0667 | 1.00996 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.6038 | −1.36899 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.70042 | −0.371672 | ||||||||
\(326\) | 2.59647 | 0.143805 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −13.2676 | −0.732578 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.40084 | 0.186927 | 0.0934636 | − | 0.995623i | \(-0.470206\pi\) | ||||
0.0934636 | + | 0.995623i | \(0.470206\pi\) | |||||||
\(332\) | −1.20100 | −0.0659136 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.41868 | −0.296497 | ||||||||
\(335\) | −33.3911 | −1.82435 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.9459 | 1.63126 | 0.815629 | − | 0.578575i | \(-0.196391\pi\) | ||||
0.815629 | + | 0.578575i | \(0.196391\pi\) | |||||||
\(338\) | −0.345110 | −0.0187715 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 26.1154 | 1.41631 | ||||||||
\(341\) | −0.504626 | −0.0273270 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.11823 | −0.437705 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.48371 | −0.241046 | ||||||||
\(347\) | −2.78206 | −0.149349 | −0.0746745 | − | 0.997208i | \(-0.523792\pi\) | ||||
−0.0746745 | + | 0.997208i | \(0.523792\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.1086 | 1.66520 | 0.832602 | − | 0.553872i | \(-0.186850\pi\) | ||||
0.832602 | + | 0.553872i | \(0.186850\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.43019 | −0.342730 | ||||||||
\(353\) | 32.3147 | 1.71994 | 0.859968 | − | 0.510348i | \(-0.170484\pi\) | ||||
0.859968 | + | 0.510348i | \(0.170484\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 29.1626 | 1.54779 | ||||||||
\(356\) | 24.2998 | 1.28789 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.63904 | 0.192329 | ||||||||
\(359\) | 25.5769 | 1.34990 | 0.674948 | − | 0.737866i | \(-0.264166\pi\) | ||||
0.674948 | + | 0.737866i | \(0.264166\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.7403 | 0.933700 | ||||||||
\(362\) | 3.45110 | 0.181386 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.81644 | −0.304446 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.23820 | 0.325631 | 0.162816 | − | 0.986656i | \(-0.447942\pi\) | ||||
0.162816 | + | 0.986656i | \(0.447942\pi\) | |||||||
\(368\) | −19.1219 | −0.996798 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.16264 | 0.476343 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.63904 | 0.188422 | 0.0942112 | − | 0.995552i | \(-0.469967\pi\) | ||||
0.0942112 | + | 0.995552i | \(0.469967\pi\) | |||||||
\(374\) | −2.35964 | −0.122014 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.0178 | −0.516631 | ||||||||
\(377\) | −6.48547 | −0.334019 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.5635 | 1.26174 | 0.630871 | − | 0.775888i | \(-0.282698\pi\) | ||||
0.630871 | + | 0.775888i | \(0.282698\pi\) | |||||||
\(380\) | −38.9976 | −2.00053 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.43652 | 0.0734988 | ||||||||
\(383\) | −25.5557 | −1.30583 | −0.652917 | − | 0.757429i | \(-0.726455\pi\) | ||||
−0.652917 | + | 0.757429i | \(0.726455\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.64633 | 0.287391 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.63904 | 0.387814 | ||||||||
\(389\) | 2.76088 | 0.139982 | 0.0699911 | − | 0.997548i | \(-0.477703\pi\) | ||||
0.0699911 | + | 0.997548i | \(0.477703\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.5236 | −1.18964 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.29592 | −0.0652877 | ||||||||
\(395\) | −46.0487 | −2.31696 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.2240 | −1.26596 | −0.632979 | − | 0.774169i | \(-0.718168\pi\) | ||||
−0.632979 | + | 0.774169i | \(0.718168\pi\) | |||||||
\(398\) | −9.49867 | −0.476125 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 22.1086 | 1.10543 | ||||||||
\(401\) | −32.3969 | −1.61782 | −0.808911 | − | 0.587931i | \(-0.799943\pi\) | ||||
−0.808911 | + | 0.587931i | \(0.799943\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.299580 | 0.0149231 | ||||||||
\(404\) | −17.9059 | −0.890851 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.0743 | 0.648071 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.46222 | 0.368983 | 0.184491 | − | 0.982834i | \(-0.440936\pi\) | ||||
0.184491 | + | 0.982834i | \(0.440936\pi\) | |||||||
\(410\) | −11.6939 | −0.577520 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11.9643 | −0.589440 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.18413 | −0.107215 | ||||||||
\(416\) | 3.81739 | 0.187163 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.52360 | 0.172345 | ||||||||
\(419\) | 36.7600 | 1.79584 | 0.897921 | − | 0.440156i | \(-0.145077\pi\) | ||||
0.897921 | + | 0.440156i | \(0.145077\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.28539 | 0.355068 | 0.177534 | − | 0.984115i | \(-0.443188\pi\) | ||||
0.177534 | + | 0.984115i | \(0.443188\pi\) | |||||||
\(422\) | −0.711402 | −0.0346305 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13.1983 | −0.640967 | ||||||||
\(425\) | 27.1978 | 1.31929 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 29.4354 | 1.42281 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.15533 | −0.345061 | ||||||||
\(431\) | −0.510783 | −0.0246035 | −0.0123018 | − | 0.999924i | \(-0.503916\pi\) | ||||
−0.0123018 | + | 0.999924i | \(0.503916\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.1228 | −0.486469 | −0.243234 | − | 0.969968i | \(-0.578208\pi\) | ||||
−0.243234 | + | 0.969968i | \(0.578208\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.8090 | −0.900787 | ||||||||
\(437\) | 35.1272 | 1.68036 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.2854 | −1.39772 | −0.698858 | − | 0.715261i | \(-0.746308\pi\) | ||||
−0.698858 | + | 0.715261i | \(0.746308\pi\) | |||||||
\(440\) | −7.71699 | −0.367893 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.40084 | 0.0666312 | ||||||||
\(443\) | 38.5173 | 1.83001 | 0.915006 | − | 0.403440i | \(-0.132186\pi\) | ||||
0.915006 | + | 0.403440i | \(0.132186\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 44.1914 | 2.09488 | ||||||||
\(446\) | −0.711402 | −0.0336859 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.0834 | 1.04218 | 0.521090 | − | 0.853502i | \(-0.325526\pi\) | ||||
0.521090 | + | 0.853502i | \(0.325526\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.6862 | −0.785724 | ||||||||
\(452\) | 12.1985 | 0.573770 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.01784 | 0.282431 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.4480 | 1.70497 | 0.852484 | − | 0.522754i | \(-0.175095\pi\) | ||||
0.852484 | + | 0.522754i | \(0.175095\pi\) | |||||||
\(458\) | −2.88545 | −0.134828 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −37.2854 | −1.73844 | ||||||||
\(461\) | −22.7736 | −1.06067 | −0.530337 | − | 0.847787i | \(-0.677934\pi\) | ||||
−0.530337 | + | 0.847787i | \(0.677934\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.7618 | −0.639565 | −0.319783 | − | 0.947491i | \(-0.603610\pi\) | ||||
−0.319783 | + | 0.947491i | \(0.603610\pi\) | |||||||
\(464\) | 21.3993 | 0.993439 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.80899 | −0.408069 | ||||||||
\(467\) | −13.5790 | −0.628359 | −0.314180 | − | 0.949364i | \(-0.601729\pi\) | ||||
−0.314180 | + | 0.949364i | \(0.601729\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −8.82963 | −0.407280 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.02935 | −0.231495 | ||||||||
\(473\) | −10.2101 | −0.469459 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −40.6138 | −1.86349 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.74396 | 0.262723 | ||||||||
\(479\) | 14.4243 | 0.659061 | 0.329531 | − | 0.944145i | \(-0.393109\pi\) | ||||
0.329531 | + | 0.944145i | \(0.393109\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.76180 | −0.353908 | ||||||||
\(482\) | 1.76050 | 0.0801884 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.3531 | 0.697868 | ||||||||
\(485\) | 13.8923 | 0.630817 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.2854 | −1.14579 | −0.572895 | − | 0.819629i | \(-0.694180\pi\) | ||||
−0.572895 | + | 0.819629i | \(0.694180\pi\) | |||||||
\(488\) | −13.3934 | −0.606289 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.8887 | 0.581661 | 0.290830 | − | 0.956775i | \(-0.406068\pi\) | ||||
0.290830 | + | 0.956775i | \(0.406068\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.3253 | 1.18563 | ||||||||
\(494\) | −2.09184 | −0.0941164 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.988487 | −0.0443844 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.2455 | 0.906314 | 0.453157 | − | 0.891431i | \(-0.350298\pi\) | ||||
0.453157 | + | 0.891431i | \(0.350298\pi\) | |||||||
\(500\) | 10.9401 | 0.489258 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.917127 | −0.0409334 | ||||||||
\(503\) | 1.48383 | 0.0661606 | 0.0330803 | − | 0.999453i | \(-0.489468\pi\) | ||||
0.0330803 | + | 0.999453i | \(0.489468\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.5635 | −1.44906 | ||||||||
\(506\) | 3.36889 | 0.149766 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.52360 | −0.333806 | ||||||||
\(509\) | −25.8902 | −1.14756 | −0.573782 | − | 0.819008i | \(-0.694524\pi\) | ||||
−0.573782 | + | 0.819008i | \(0.694524\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −21.4343 | −0.947271 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.76180 | −0.165926 | ||||||||
\(515\) | −21.7582 | −0.958781 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.5992 | −0.554110 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.58132 | 0.200904 | ||||||||
\(521\) | 38.9340 | 1.70573 | 0.852865 | − | 0.522131i | \(-0.174863\pi\) | ||||
0.852865 | + | 0.522131i | \(0.174863\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.7618 | 1.12648 | 0.563242 | − | 0.826292i | \(-0.309554\pi\) | ||||
0.563242 | + | 0.826292i | \(0.309554\pi\) | |||||||
\(524\) | −34.6681 | −1.51448 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.72192 | −0.118681 | ||||||||
\(527\) | −1.21603 | −0.0529710 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.5850 | 0.460216 | ||||||||
\(530\) | −11.6329 | −0.505300 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.90606 | 0.429079 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 53.5309 | 2.31434 | ||||||||
\(536\) | 13.0743 | 0.564725 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.03988 | 0.131059 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.2382 | 1.04208 | 0.521041 | − | 0.853532i | \(-0.325544\pi\) | ||||
0.521041 | + | 0.853532i | \(0.325544\pi\) | |||||||
\(542\) | −0.401238 | −0.0172347 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −15.4952 | −0.664352 | ||||||||
\(545\) | −34.2059 | −1.46522 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.1086 | −0.902537 | −0.451269 | − | 0.892388i | \(-0.649028\pi\) | ||||
−0.451269 | + | 0.892388i | \(0.649028\pi\) | |||||||
\(548\) | −17.3341 | −0.740475 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.89508 | −0.166087 | ||||||||
\(551\) | −39.3109 | −1.67470 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5.54294 | −0.235497 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −40.0357 | −1.69789 | ||||||||
\(557\) | −30.2016 | −1.27968 | −0.639842 | − | 0.768506i | \(-0.721000\pi\) | ||||
−0.639842 | + | 0.768506i | \(0.721000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.06138 | 0.256369 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.42599 | −0.144517 | ||||||||
\(563\) | −17.8237 | −0.751178 | −0.375589 | − | 0.926786i | \(-0.622560\pi\) | ||||
−0.375589 | + | 0.926786i | \(0.622560\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.1841 | 0.933294 | ||||||||
\(566\) | −1.38044 | −0.0580242 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.4187 | −0.479117 | ||||||||
\(569\) | 0.921351 | 0.0386250 | 0.0193125 | − | 0.999813i | \(-0.493852\pi\) | ||||
0.0193125 | + | 0.999813i | \(0.493852\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.4622 | 0.730771 | 0.365386 | − | 0.930856i | \(-0.380937\pi\) | ||||
0.365386 | + | 0.930856i | \(0.380937\pi\) | |||||||
\(572\) | 3.16827 | 0.132472 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38.8306 | −1.61935 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.6390 | 0.484540 | 0.242270 | − | 0.970209i | \(-0.422108\pi\) | ||||
0.242270 | + | 0.970209i | \(0.422108\pi\) | |||||||
\(578\) | 0.180698 | 0.00751606 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 41.7261 | 1.73258 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.5992 | −0.687467 | ||||||||
\(584\) | 2.27744 | 0.0942410 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.13329 | −0.0881252 | ||||||||
\(587\) | 25.9114 | 1.06948 | 0.534739 | − | 0.845017i | \(-0.320410\pi\) | ||||
0.534739 | + | 0.845017i | \(0.320410\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.81587 | 0.0748215 | ||||||||
\(590\) | −4.43282 | −0.182496 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 25.6107 | 1.05259 | ||||||||
\(593\) | 38.0887 | 1.56412 | 0.782058 | − | 0.623205i | \(-0.214170\pi\) | ||||
0.782058 | + | 0.623205i | \(0.214170\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 32.7981 | 1.34346 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.00000 | −0.0817861 | ||||||||
\(599\) | −35.0450 | −1.43190 | −0.715950 | − | 0.698151i | \(-0.754006\pi\) | ||||
−0.715950 | + | 0.698151i | \(0.754006\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.5708 | −1.65492 | −0.827459 | − | 0.561527i | \(-0.810214\pi\) | ||||
−0.827459 | + | 0.561527i | \(0.810214\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.9643 | −0.486821 | ||||||||
\(605\) | 27.9210 | 1.13515 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.4837 | 1.23730 | 0.618648 | − | 0.785668i | \(-0.287681\pi\) | ||||
0.618648 | + | 0.785668i | \(0.287681\pi\) | |||||||
\(608\) | 23.1387 | 0.938396 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.8048 | −0.477962 | ||||||||
\(611\) | 7.47970 | 0.302596 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.9244 | −0.522013 | −0.261007 | − | 0.965337i | \(-0.584054\pi\) | ||||
−0.261007 | + | 0.965337i | \(0.584054\pi\) | |||||||
\(614\) | −9.03641 | −0.364680 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.6300 | 1.55519 | 0.777593 | − | 0.628768i | \(-0.216440\pi\) | ||||
0.777593 | + | 0.628768i | \(0.216440\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.8846 | 0.718841 | 0.359420 | − | 0.933176i | \(-0.382974\pi\) | ||||
0.359420 | + | 0.933176i | \(0.382974\pi\) | |||||||
\(620\) | −1.92743 | −0.0774075 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.40815 | 0.0564617 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.6065 | −0.544259 | ||||||||
\(626\) | 0.854632 | 0.0341579 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19.0399 | 0.759774 | ||||||||
\(629\) | 31.5060 | 1.25623 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.1699 | −1.71857 | −0.859284 | − | 0.511498i | \(-0.829091\pi\) | ||||
−0.859284 | + | 0.511498i | \(0.829091\pi\) | |||||||
\(632\) | 18.0304 | 0.717213 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.1805 | 0.444034 | ||||||||
\(635\) | −13.6824 | −0.542968 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.77013 | −0.149261 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −32.3504 | −1.27876 | ||||||||
\(641\) | −43.2455 | −1.70809 | −0.854046 | − | 0.520197i | \(-0.825859\pi\) | ||||
−0.854046 | + | 0.520197i | \(0.825859\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 47.5236 | 1.87415 | 0.937074 | − | 0.349131i | \(-0.113523\pi\) | ||||
0.937074 | + | 0.349131i | \(0.113523\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.49102 | 0.334075 | ||||||||
\(647\) | −11.5905 | −0.455670 | −0.227835 | − | 0.973700i | \(-0.573165\pi\) | ||||
−0.227835 | + | 0.973700i | \(0.573165\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.32528 | −0.248289 | ||||||||
\(650\) | 2.31238 | 0.0906991 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.1511 | 0.554201 | ||||||||
\(653\) | −39.0586 | −1.52848 | −0.764241 | − | 0.644931i | \(-0.776886\pi\) | ||||
−0.764241 | + | 0.644931i | \(0.776886\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −63.0472 | −2.46346 | ||||||||
\(656\) | −32.6858 | −1.27617 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.5446 | 0.410759 | 0.205379 | − | 0.978682i | \(-0.434157\pi\) | ||||
0.205379 | + | 0.978682i | \(0.434157\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.25970 | 0.0489965 | 0.0244983 | − | 0.999700i | \(-0.492201\pi\) | ||||
0.0244983 | + | 0.999700i | \(0.492201\pi\) | |||||||
\(662\) | −1.17366 | −0.0456157 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.855201 | 0.0331882 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −37.5850 | −1.45530 | ||||||||
\(668\) | −29.5326 | −1.14265 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 11.5236 | 0.445195 | ||||||||
\(671\) | −16.8445 | −0.650274 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.46222 | 0.287647 | 0.143824 | − | 0.989603i | \(-0.454060\pi\) | ||||
0.143824 | + | 0.989603i | \(0.454060\pi\) | |||||||
\(674\) | −10.3346 | −0.398075 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.88090 | −0.0723423 | ||||||||
\(677\) | 11.7151 | 0.450247 | 0.225124 | − | 0.974330i | \(-0.427721\pi\) | ||||
0.225124 | + | 0.974330i | \(0.427721\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −18.5961 | −0.713128 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.174152 | 0.00666861 | ||||||||
\(683\) | −4.38430 | −0.167761 | −0.0838803 | − | 0.996476i | \(-0.526731\pi\) | ||||
−0.0838803 | + | 0.996476i | \(0.526731\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.5236 | −1.20445 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −20.0000 | −0.762493 | ||||||||
\(689\) | 9.85437 | 0.375422 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.176824 | 0.00672669 | 0.00336335 | − | 0.999994i | \(-0.498929\pi\) | ||||
0.00336335 | + | 0.999994i | \(0.498929\pi\) | |||||||
\(692\) | −24.4369 | −0.928951 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.960117 | 0.0364456 | ||||||||
\(695\) | −72.8086 | −2.76179 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −40.2098 | −1.52306 | ||||||||
\(698\) | −10.7359 | −0.406359 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.1536 | −1.55435 | −0.777175 | − | 0.629284i | \(-0.783348\pi\) | ||||
−0.777175 | + | 0.629284i | \(0.783348\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −47.0472 | −1.77442 | ||||||||
\(704\) | −8.89681 | −0.335311 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.1521 | −0.419715 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.2455 | 1.28612 | 0.643059 | − | 0.765817i | \(-0.277665\pi\) | ||||
0.643059 | + | 0.765817i | \(0.277665\pi\) | |||||||
\(710\) | −10.0643 | −0.377707 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −17.3032 | −0.648466 | ||||||||
\(713\) | 1.73614 | 0.0650190 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.76180 | 0.215479 | ||||||||
\(716\) | 19.8333 | 0.741205 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.82683 | −0.329414 | ||||||||
\(719\) | 17.7203 | 0.660855 | 0.330428 | − | 0.943831i | \(-0.392807\pi\) | ||||
0.330428 | + | 0.943831i | \(0.392807\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.12236 | −0.227850 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.8090 | 0.699031 | ||||||||
\(725\) | 43.4554 | 1.61389 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.122756 | −0.00455277 | −0.00227638 | − | 0.999997i | \(-0.500725\pi\) | ||||
−0.00227638 | + | 0.999997i | \(0.500725\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.00731 | 0.0742939 | ||||||||
\(731\) | −24.6038 | −0.910005 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.2240 | 0.636184 | 0.318092 | − | 0.948060i | \(-0.396958\pi\) | ||||
0.318092 | + | 0.948060i | \(0.396958\pi\) | |||||||
\(734\) | −2.15287 | −0.0794637 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.1228 | 0.815456 | ||||||||
\(737\) | 16.4432 | 0.605694 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.0399 | −0.479680 | −0.239840 | − | 0.970812i | \(-0.577095\pi\) | ||||
−0.239840 | + | 0.970812i | \(0.577095\pi\) | |||||||
\(740\) | 49.9377 | 1.83575 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.3377 | 1.03961 | 0.519806 | − | 0.854285i | \(-0.326004\pi\) | ||||
0.519806 | + | 0.854285i | \(0.326004\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 59.6464 | 2.18527 | ||||||||
\(746\) | −1.25587 | −0.0459807 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.8604 | −0.470222 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.81587 | −0.0662619 | −0.0331309 | − | 0.999451i | \(-0.510548\pi\) | ||||
−0.0331309 | + | 0.999451i | \(0.510548\pi\) | |||||||
\(752\) | −24.6799 | −0.899982 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.23820 | 0.0815105 | ||||||||
\(755\) | −21.7582 | −0.791862 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.0687 | −1.23825 | −0.619124 | − | 0.785293i | \(-0.712512\pi\) | ||||
−0.619124 | + | 0.785293i | \(0.712512\pi\) | |||||||
\(758\) | −8.47710 | −0.307902 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 27.7691 | 1.00729 | ||||||||
\(761\) | −28.7968 | −1.04388 | −0.521942 | − | 0.852981i | \(-0.674792\pi\) | ||||
−0.521942 | + | 0.852981i | \(0.674792\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 7.82925 | 0.283252 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.81952 | 0.318662 | ||||||||
\(767\) | 3.75511 | 0.135589 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.3395 | −0.697399 | −0.348699 | − | 0.937235i | \(-0.613377\pi\) | ||||
−0.348699 | + | 0.937235i | \(0.613377\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 30.7733 | 1.10756 | ||||||||
\(773\) | −22.2080 | −0.798765 | −0.399383 | − | 0.916784i | \(-0.630775\pi\) | ||||
−0.399383 | + | 0.916784i | \(0.630775\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00731 | −0.0721047 | ||||||||
\(776\) | −5.43955 | −0.195269 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.952807 | −0.0341598 | ||||||||
\(779\) | 60.0444 | 2.15131 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.3610 | −0.513875 | ||||||||
\(782\) | 8.11823 | 0.290307 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 34.6258 | 1.23585 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.9459 | −1.28133 | −0.640667 | − | 0.767819i | \(-0.721342\pi\) | ||||
−0.640667 | + | 0.767819i | \(0.721342\pi\) | |||||||
\(788\) | −7.06298 | −0.251608 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15.8919 | 0.565407 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.0000 | 0.355110 | ||||||||
\(794\) | 8.70506 | 0.308931 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −51.7691 | −1.83491 | ||||||||
\(797\) | −11.4659 | −0.406144 | −0.203072 | − | 0.979164i | \(-0.565093\pi\) | ||||
−0.203072 | + | 0.979164i | \(0.565093\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.3610 | −1.07409 | ||||||||
\(800\) | −25.5781 | −0.904323 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.1805 | 0.394796 | ||||||||
\(803\) | 2.86427 | 0.101078 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.103388 | −0.00364169 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.7503 | 0.448553 | ||||||||
\(809\) | 45.9029 | 1.61386 | 0.806931 | − | 0.590646i | \(-0.201127\pi\) | ||||
0.806931 | + | 0.590646i | \(0.201127\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.8846 | 0.628012 | 0.314006 | − | 0.949421i | \(-0.398329\pi\) | ||||
0.314006 | + | 0.949421i | \(0.398329\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.51208 | −0.158148 | ||||||||
\(815\) | 25.7351 | 0.901462 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.7403 | 1.28538 | ||||||||
\(818\) | −2.57529 | −0.0900428 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −63.7334 | −2.22567 | ||||||||
\(821\) | −6.51599 | −0.227409 | −0.113705 | − | 0.993515i | \(-0.536272\pi\) | ||||
−0.113705 | + | 0.993515i | \(0.536272\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.7219 | −1.00118 | −0.500592 | − | 0.865684i | \(-0.666884\pi\) | ||||
−0.500592 | + | 0.865684i | \(0.666884\pi\) | |||||||
\(824\) | 8.51947 | 0.296790 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.3905 | 1.40452 | 0.702258 | − | 0.711923i | \(-0.252175\pi\) | ||||
0.702258 | + | 0.711923i | \(0.252175\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.0000 | 0.625166 | 0.312583 | − | 0.949890i | \(-0.398806\pi\) | ||||
0.312583 | + | 0.949890i | \(0.398806\pi\) | |||||||
\(830\) | 0.753766 | 0.0261636 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.28174 | 0.183111 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −53.7077 | −1.85863 | ||||||||
\(836\) | 19.2041 | 0.664188 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.6862 | −0.438239 | ||||||||
\(839\) | −20.1983 | −0.697324 | −0.348662 | − | 0.937249i | \(-0.613364\pi\) | ||||
−0.348662 | + | 0.937249i | \(0.613364\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0614 | 0.450392 | ||||||||
\(842\) | −2.51426 | −0.0866472 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.87724 | −0.133460 | ||||||||
\(845\) | −3.42059 | −0.117672 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −32.5153 | −1.11658 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.38622 | −0.321945 | ||||||||
\(851\) | −44.9816 | −1.54195 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.2996 | −0.763523 | −0.381762 | − | 0.924261i | \(-0.624682\pi\) | ||||
−0.381762 | + | 0.924261i | \(0.624682\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20.9601 | −0.716402 | ||||||||
\(857\) | 28.7663 | 0.982639 | 0.491319 | − | 0.870979i | \(-0.336515\pi\) | ||||
0.491319 | + | 0.870979i | \(0.336515\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.2025 | 0.348106 | 0.174053 | − | 0.984736i | \(-0.444314\pi\) | ||||
0.174053 | + | 0.984736i | \(0.444314\pi\) | |||||||
\(860\) | −38.9976 | −1.32981 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.176276 | 0.00600399 | ||||||||
\(863\) | −21.3932 | −0.728232 | −0.364116 | − | 0.931354i | \(-0.618629\pi\) | ||||
−0.364116 | + | 0.931354i | \(0.618629\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.4407 | −1.51103 | ||||||||
\(866\) | 3.49346 | 0.118713 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.6764 | 0.769244 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.76180 | −0.330766 | ||||||||
\(872\) | 13.3934 | 0.453557 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12.1228 | −0.410058 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.87724 | 0.333531 | 0.166765 | − | 0.985997i | \(-0.446668\pi\) | ||||
0.166765 | + | 0.985997i | \(0.446668\pi\) | |||||||
\(878\) | 10.1067 | 0.341084 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −19.0115 | −0.640878 | ||||||||
\(881\) | 48.9373 | 1.64874 | 0.824370 | − | 0.566051i | \(-0.191530\pi\) | ||||
0.824370 | + | 0.566051i | \(0.191530\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.2455 | 1.35437 | 0.677185 | − | 0.735813i | \(-0.263200\pi\) | ||||
0.677185 | + | 0.735813i | \(0.263200\pi\) | |||||||
\(884\) | 7.63478 | 0.256786 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.2927 | −0.446577 | ||||||||
\(887\) | −42.4275 | −1.42458 | −0.712288 | − | 0.701887i | \(-0.752341\pi\) | ||||
−0.712288 | + | 0.701887i | \(0.752341\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −15.2509 | −0.511212 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.87724 | −0.129820 | ||||||||
\(893\) | 45.3373 | 1.51715 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.0687 | 1.20564 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.62120 | −0.254323 | ||||||||
\(899\) | −1.94292 | −0.0647999 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40.0000 | −1.33259 | ||||||||
\(902\) | 5.75859 | 0.191740 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.68624 | −0.288900 | ||||||||
\(905\) | 34.2059 | 1.13704 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.9060 | −1.42467 | −0.712336 | − | 0.701839i | \(-0.752363\pi\) | ||||
−0.712336 | + | 0.701839i | \(0.752363\pi\) | |||||||
\(908\) | 32.7981 | 1.08844 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.1979 | 1.23242 | 0.616210 | − | 0.787582i | \(-0.288667\pi\) | ||||
0.616210 | + | 0.787582i | \(0.288667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.07556 | 0.0355959 | ||||||||
\(914\) | −12.5786 | −0.416062 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.7261 | −0.519606 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.2455 | 1.72342 | 0.861710 | − | 0.507401i | \(-0.169394\pi\) | ||||
0.861710 | + | 0.507401i | \(0.169394\pi\) | |||||||
\(920\) | 26.5499 | 0.875325 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.85940 | 0.258836 | ||||||||
\(923\) | 8.52562 | 0.280624 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 52.0073 | 1.70999 | ||||||||
\(926\) | 4.74933 | 0.156073 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −24.7576 | −0.812708 | ||||||||
\(929\) | 9.48934 | 0.311335 | 0.155668 | − | 0.987810i | \(-0.450247\pi\) | ||||
0.155668 | + | 0.987810i | \(0.450247\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −48.0103 | −1.57263 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.68624 | 0.153338 | ||||||||
\(935\) | −23.3878 | −0.764863 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −57.1699 | −1.86766 | −0.933830 | − | 0.357716i | \(-0.883556\pi\) | ||||
−0.933830 | + | 0.357716i | \(0.883556\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −48.1228 | −1.56959 | ||||||||
\(941\) | 16.4339 | 0.535730 | 0.267865 | − | 0.963456i | \(-0.413682\pi\) | ||||
0.267865 | + | 0.963456i | \(0.413682\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 57.4082 | 1.86947 | ||||||||
\(944\) | −12.3903 | −0.403269 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.52360 | 0.114562 | ||||||||
\(947\) | 6.43378 | 0.209070 | 0.104535 | − | 0.994521i | \(-0.466665\pi\) | ||||
0.104535 | + | 0.994521i | \(0.466665\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.70042 | −0.0551980 | ||||||||
\(950\) | 14.0162 | 0.454746 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.1678 | 0.653300 | 0.326650 | − | 0.945145i | \(-0.394080\pi\) | ||||
0.326650 | + | 0.945145i | \(0.394080\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.2382 | 0.460737 | ||||||||
\(956\) | 31.3054 | 1.01249 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.97796 | −0.160831 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9103 | −0.997105 | ||||||||
\(962\) | 2.67867 | 0.0863639 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.59496 | 0.309033 | ||||||||
\(965\) | 55.9641 | 1.80155 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.59916 | 0.276530 | 0.138265 | − | 0.990395i | \(-0.455847\pi\) | ||||
0.138265 | + | 0.990395i | \(0.455847\pi\) | |||||||
\(968\) | −10.9325 | −0.351385 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.79437 | −0.153938 | ||||||||
\(971\) | 54.0180 | 1.73352 | 0.866760 | − | 0.498725i | \(-0.166198\pi\) | ||||
0.866760 | + | 0.498725i | \(0.166198\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.72624 | 0.279607 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −32.9958 | −1.05617 | ||||||||
\(977\) | 37.8576 | 1.21117 | 0.605586 | − | 0.795780i | \(-0.292939\pi\) | ||||
0.605586 | + | 0.795780i | \(0.292939\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.7618 | −0.695510 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.44803 | −0.141942 | ||||||||
\(983\) | −11.0554 | −0.352612 | −0.176306 | − | 0.984335i | \(-0.556415\pi\) | ||||
−0.176306 | + | 0.984335i | \(0.556415\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.8447 | −0.409265 | ||||||||
\(986\) | −9.08512 | −0.289329 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.4008 | −0.362709 | ||||||||
\(989\) | 35.1272 | 1.11698 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.47640 | −0.142198 | −0.0710988 | − | 0.997469i | \(-0.522651\pi\) | ||||
−0.0710988 | + | 0.997469i | \(0.522651\pi\) | |||||||
\(992\) | 1.14361 | 0.0363098 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −94.1469 | −2.98466 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.4480 | 0.520914 | 0.260457 | − | 0.965485i | \(-0.416127\pi\) | ||||
0.260457 | + | 0.965485i | \(0.416127\pi\) | |||||||
\(998\) | −6.98693 | −0.221167 | ||||||||
\(999\) | 0 | 0 |
(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 | 5733.2.a.bv.1.3 | 6 | ||
3.2 | odd | 2 | inner | 5733.2.a.bv.1.4 | 6 | ||
7.6 | odd | 2 | 819.2.a.m.1.3 | ✓ | 6 | ||
21.20 | even | 2 | 819.2.a.m.1.4 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
819.2.a.m.1.3 | ✓ | 6 | 7.6 | odd | 2 | ||
819.2.a.m.1.4 | yes | 6 | 21.20 | even | 2 | ||
5733.2.a.bv.1.3 | 6 | 1.1 | even | 1 | trivial | ||
5733.2.a.bv.1.4 | 6 | 3.2 | odd | 2 | inner |