Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [513,2,Mod(235,513)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(513, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("513.235");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 513 = 3^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 513.h (of order \(3\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(4.09632562369\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 171) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 334.8 | ||
Character | \(\chi\) | \(=\) | 513.334 |
Dual form | 513.2.h.c.235.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/513\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.370889 | −0.262258 | −0.131129 | − | 0.991365i | \(-0.541860\pi\) | ||||
−0.131129 | + | 0.991365i | \(0.541860\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.86244 | −0.931221 | ||||||||
\(5\) | −1.77761 | − | 3.07890i | −0.794969 | − | 1.37693i | −0.922859 | − | 0.385139i | \(-0.874154\pi\) |
0.127889 | − | 0.991788i | \(-0.459180\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.124876 | − | 0.216291i | −0.0471985 | − | 0.0817503i | 0.841461 | − | 0.540318i | \(-0.181696\pi\) |
−0.888660 | + | 0.458568i | \(0.848363\pi\) | |||||||
\(8\) | 1.43254 | 0.506478 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.659294 | + | 1.14193i | 0.208487 | + | 0.361110i | ||||
\(11\) | 0.815815 | + | 1.41303i | 0.245977 | + | 0.426045i | 0.962406 | − | 0.271615i | \(-0.0875578\pi\) |
−0.716429 | + | 0.697660i | \(0.754224\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.32541 | −0.367604 | −0.183802 | − | 0.982963i | \(-0.558841\pi\) | ||||
−0.183802 | + | 0.982963i | \(0.558841\pi\) | |||||||
\(14\) | 0.0463150 | + | 0.0802199i | 0.0123782 | + | 0.0214397i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.19357 | 0.798393 | ||||||||
\(17\) | −3.73000 | + | 6.46055i | −0.904658 | + | 1.56691i | −0.0832816 | + | 0.996526i | \(0.526540\pi\) |
−0.821376 | + | 0.570387i | \(0.806793\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.07660 | − | 1.54315i | −0.935237 | − | 0.354022i | ||||
\(20\) | 3.31069 | + | 5.73428i | 0.740292 | + | 1.28222i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.302577 | − | 0.524078i | −0.0645096 | − | 0.111734i | ||||
\(23\) | 4.49143 | 0.936528 | 0.468264 | − | 0.883589i | \(-0.344880\pi\) | ||||
0.468264 | + | 0.883589i | \(0.344880\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.81976 | + | 6.61602i | −0.763952 | + | 1.32320i | ||||
\(26\) | 0.491582 | 0.0964071 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.232573 | + | 0.402829i | 0.0439522 | + | 0.0761275i | ||||
\(29\) | −2.06363 | + | 3.57430i | −0.383206 | + | 0.663732i | −0.991518 | − | 0.129966i | \(-0.958513\pi\) |
0.608313 | + | 0.793697i | \(0.291847\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.32871 | + | 7.49755i | −0.777460 | + | 1.34660i | 0.155941 | + | 0.987766i | \(0.450159\pi\) |
−0.933401 | + | 0.358834i | \(0.883174\pi\) | |||||||
\(32\) | −4.04953 | −0.715863 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.38342 | − | 2.39615i | 0.237254 | − | 0.410936i | ||||
\(35\) | −0.443959 | + | 0.768960i | −0.0750428 | + | 0.129978i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.10599 | 0.510622 | 0.255311 | − | 0.966859i | \(-0.417822\pi\) | ||||
0.255311 | + | 0.966859i | \(0.417822\pi\) | |||||||
\(38\) | 1.51197 | + | 0.572336i | 0.245274 | + | 0.0928452i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.54649 | − | 4.41064i | −0.402635 | − | 0.697384i | ||||
\(41\) | 2.77461 | + | 4.80577i | 0.433322 | + | 0.750535i | 0.997157 | − | 0.0753521i | \(-0.0240081\pi\) |
−0.563835 | + | 0.825887i | \(0.690675\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0406 | −1.53118 | −0.765591 | − | 0.643328i | \(-0.777553\pi\) | ||||
−0.765591 | + | 0.643328i | \(0.777553\pi\) | |||||||
\(44\) | −1.51941 | − | 2.63169i | −0.229059 | − | 0.396742i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.66582 | −0.245612 | ||||||||
\(47\) | 1.68288 | − | 2.91483i | 0.245473 | − | 0.425171i | −0.716792 | − | 0.697287i | \(-0.754390\pi\) |
0.962264 | + | 0.272116i | \(0.0877235\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.46881 | − | 6.00816i | 0.495545 | − | 0.858308i | ||||
\(50\) | 1.41671 | − | 2.45381i | 0.200353 | − | 0.347021i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.46851 | 0.342320 | ||||||||
\(53\) | −0.254182 | − | 0.440256i | −0.0349146 | − | 0.0604739i | 0.848040 | − | 0.529932i | \(-0.177783\pi\) |
−0.882955 | + | 0.469458i | \(0.844449\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.90039 | − | 5.02363i | 0.391089 | − | 0.677386i | ||||
\(56\) | −0.178889 | − | 0.309845i | −0.0239050 | − | 0.0414047i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.765376 | − | 1.32567i | 0.100499 | − | 0.174069i | ||||
\(59\) | −5.23121 | − | 9.06071i | −0.681045 | − | 1.17960i | −0.974662 | − | 0.223681i | \(-0.928192\pi\) |
0.293617 | − | 0.955923i | \(-0.405141\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.07050 | + | 3.58621i | −0.265100 | + | 0.459168i | −0.967590 | − | 0.252527i | \(-0.918738\pi\) |
0.702489 | + | 0.711694i | \(0.252072\pi\) | |||||||
\(62\) | 1.60547 | − | 2.78076i | 0.203895 | − | 0.353157i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.88521 | −0.610652 | ||||||||
\(65\) | 2.35606 | + | 4.08082i | 0.292234 | + | 0.506164i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.799350 | −0.0976561 | −0.0488281 | − | 0.998807i | \(-0.515549\pi\) | ||||
−0.0488281 | + | 0.998807i | \(0.515549\pi\) | |||||||
\(68\) | 6.94690 | − | 12.0324i | 0.842436 | − | 1.45914i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.164660 | − | 0.285199i | 0.0196806 | − | 0.0340878i | ||||
\(71\) | −5.60051 | + | 9.70037i | −0.664658 | + | 1.15122i | 0.314719 | + | 0.949185i | \(0.398090\pi\) |
−0.979378 | + | 0.202037i | \(0.935244\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.84754 | + | 3.20004i | −0.216239 | + | 0.374537i | −0.953655 | − | 0.300902i | \(-0.902712\pi\) |
0.737416 | + | 0.675439i | \(0.236046\pi\) | |||||||
\(74\) | −1.15198 | −0.133915 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.59244 | + | 2.87402i | 0.870912 | + | 0.329673i | ||||
\(77\) | 0.203751 | − | 0.352907i | 0.0232195 | − | 0.0402174i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.85529 | 1.10881 | 0.554403 | − | 0.832248i | \(-0.312947\pi\) | ||||
0.554403 | + | 0.832248i | \(0.312947\pi\) | |||||||
\(80\) | −5.67691 | − | 9.83269i | −0.634698 | − | 1.09933i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.02907 | − | 1.78241i | −0.113642 | − | 0.196834i | ||||
\(83\) | −0.185251 | − | 0.320865i | −0.0203340 | − | 0.0352195i | 0.855679 | − | 0.517506i | \(-0.173140\pi\) |
−0.876013 | + | 0.482287i | \(0.839806\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26.5219 | 2.87670 | ||||||||
\(86\) | 3.72396 | 0.401565 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.16868 | + | 2.02422i | 0.124582 | + | 0.215783i | ||||
\(89\) | −4.01034 | − | 6.94611i | −0.425095 | − | 0.736286i | 0.571334 | − | 0.820717i | \(-0.306426\pi\) |
−0.996429 | + | 0.0844315i | \(0.973093\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.165512 | + | 0.286675i | 0.0173504 | + | 0.0300517i | ||||
\(92\) | −8.36503 | −0.872115 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.624161 | + | 1.08108i | −0.0643772 | + | 0.111505i | ||||
\(95\) | 2.49539 | + | 15.2946i | 0.256022 | + | 1.56919i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.43155 | 0.653024 | 0.326512 | − | 0.945193i | \(-0.394127\pi\) | ||||
0.326512 | + | 0.945193i | \(0.394127\pi\) | |||||||
\(98\) | −1.28654 | + | 2.22836i | −0.129961 | + | 0.225098i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.11408 | − | 12.3220i | 0.711408 | − | 1.23220i | ||||
\(101\) | 3.78177 | − | 6.55021i | 0.376300 | − | 0.651771i | −0.614221 | − | 0.789134i | \(-0.710530\pi\) |
0.990521 | + | 0.137364i | \(0.0438629\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.90927 | + | 11.9672i | −0.680791 | + | 1.17916i | 0.293949 | + | 0.955821i | \(0.405030\pi\) |
−0.974740 | + | 0.223343i | \(0.928303\pi\) | |||||||
\(104\) | −1.89871 | −0.186183 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.0942734 | + | 0.163286i | 0.00915664 | + | 0.0158598i | ||||
\(107\) | −12.0119 | −1.16123 | −0.580616 | − | 0.814177i | \(-0.697188\pi\) | ||||
−0.580616 | + | 0.814177i | \(0.697188\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.62598 | + | 13.2086i | −0.730436 | + | 1.26515i | 0.226261 | + | 0.974067i | \(0.427350\pi\) |
−0.956697 | + | 0.291086i | \(0.905984\pi\) | |||||||
\(110\) | −1.07572 | + | 1.86321i | −0.102566 | + | 0.177650i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.398799 | − | 0.690740i | −0.0376830 | − | 0.0652688i | ||||
\(113\) | 1.46481 | − | 2.53713i | 0.137798 | − | 0.238673i | −0.788865 | − | 0.614567i | \(-0.789331\pi\) |
0.926663 | + | 0.375894i | \(0.122664\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.98399 | − | 13.8287i | −0.744511 | − | 1.28953i | ||||
\(116\) | 3.84338 | − | 6.65693i | 0.356849 | − | 0.618081i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.94020 | + | 3.36052i | 0.178610 | + | 0.309361i | ||||
\(119\) | 1.86314 | 0.170794 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.16889 | − | 7.22073i | 0.378990 | − | 0.656430i | ||||
\(122\) | 0.767926 | − | 1.33009i | 0.0695248 | − | 0.120420i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.06198 | − | 13.9638i | 0.723987 | − | 1.25398i | ||||
\(125\) | 9.38406 | 0.839336 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.949181 | − | 1.64403i | −0.0842262 | − | 0.145884i | 0.820835 | − | 0.571165i | \(-0.193509\pi\) |
−0.905061 | + | 0.425281i | \(0.860175\pi\) | |||||||
\(128\) | 9.91094 | 0.876012 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.873838 | − | 1.51353i | −0.0766407 | − | 0.132746i | ||||
\(131\) | −1.51445 | − | 2.62310i | −0.132318 | − | 0.229181i | 0.792252 | − | 0.610194i | \(-0.208909\pi\) |
−0.924570 | + | 0.381013i | \(0.875575\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.175300 | + | 1.07443i | 0.0152004 | + | 0.0931652i | ||||
\(134\) | 0.296470 | 0.0256111 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.34336 | + | 9.25497i | −0.458190 | + | 0.793608i | ||||
\(137\) | 2.12874 | − | 3.68708i | 0.181870 | − | 0.315009i | −0.760647 | − | 0.649166i | \(-0.775118\pi\) |
0.942517 | + | 0.334157i | \(0.108452\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.2721 | −1.46500 | −0.732502 | − | 0.680765i | \(-0.761648\pi\) | ||||
−0.732502 | + | 0.680765i | \(0.761648\pi\) | |||||||
\(140\) | 0.826848 | − | 1.43214i | 0.0698814 | − | 0.121038i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.07717 | − | 3.59776i | 0.174312 | − | 0.301917i | ||||
\(143\) | −1.08129 | − | 1.87285i | −0.0904222 | − | 0.156616i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.6732 | 1.21855 | ||||||||
\(146\) | 0.685234 | − | 1.18686i | 0.0567104 | − | 0.0982253i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.78473 | −0.475501 | ||||||||
\(149\) | 0.923073 | + | 1.59881i | 0.0756211 | + | 0.130980i | 0.901356 | − | 0.433079i | \(-0.142573\pi\) |
−0.825735 | + | 0.564058i | \(0.809239\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.59926 | − | 9.69820i | −0.455661 | − | 0.789228i | 0.543065 | − | 0.839691i | \(-0.317264\pi\) |
−0.998726 | + | 0.0504626i | \(0.983930\pi\) | |||||||
\(152\) | −5.83989 | − | 2.21061i | −0.473677 | − | 0.179305i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.0755689 | + | 0.130889i | −0.00608952 | + | 0.0105473i | ||||
\(155\) | 30.7790 | 2.47223 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.3856 | − | 17.9883i | −0.828858 | − | 1.43562i | −0.898935 | − | 0.438083i | \(-0.855658\pi\) |
0.0700766 | − | 0.997542i | \(-0.477676\pi\) | |||||||
\(158\) | −3.65522 | −0.290794 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.19847 | + | 12.4681i | 0.569089 | + | 0.985692i | ||||
\(161\) | −0.560870 | − | 0.971456i | −0.0442028 | − | 0.0765614i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.41671 | −0.424269 | −0.212135 | − | 0.977240i | \(-0.568042\pi\) | ||||
−0.212135 | + | 0.977240i | \(0.568042\pi\) | |||||||
\(164\) | −5.16755 | − | 8.95046i | −0.403518 | − | 0.698914i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.0687077 | + | 0.119005i | 0.00533275 | + | 0.00923660i | ||||
\(167\) | 1.50006 | 0.116078 | 0.0580392 | − | 0.998314i | \(-0.481515\pi\) | ||||
0.0580392 | + | 0.998314i | \(0.481515\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2433 | −0.864867 | ||||||||
\(170\) | −9.83667 | −0.754438 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 18.7001 | 1.42587 | ||||||||
\(173\) | −22.4134 | −1.70406 | −0.852031 | − | 0.523491i | \(-0.824629\pi\) | ||||
−0.852031 | + | 0.523491i | \(0.824629\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.90798 | 0.144230 | ||||||||
\(176\) | 2.60536 | + | 4.51262i | 0.196387 | + | 0.340151i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.48739 | + | 2.57623i | 0.111485 | + | 0.193097i | ||||
\(179\) | 12.7134 | 0.950242 | 0.475121 | − | 0.879920i | \(-0.342404\pi\) | ||||
0.475121 | + | 0.879920i | \(0.342404\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.31157 | + | 2.27170i | 0.0974880 | + | 0.168854i | 0.910644 | − | 0.413191i | \(-0.135586\pi\) |
−0.813156 | + | 0.582045i | \(0.802253\pi\) | |||||||
\(182\) | −0.0613866 | − | 0.106325i | −0.00455027 | − | 0.00788131i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.43414 | 0.474331 | ||||||||
\(185\) | −5.52123 | − | 9.56304i | −0.405929 | − | 0.703089i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.1720 | −0.890101 | ||||||||
\(188\) | −3.13426 | + | 5.42870i | −0.228589 | + | 0.395928i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.925514 | − | 5.67259i | −0.0671439 | − | 0.411533i | ||||
\(191\) | 1.70417 | + | 2.95170i | 0.123309 | + | 0.213578i | 0.921071 | − | 0.389395i | \(-0.127316\pi\) |
−0.797762 | + | 0.602973i | \(0.793983\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.248883 | − | 0.431077i | −0.0179150 | − | 0.0310296i | 0.856929 | − | 0.515435i | \(-0.172369\pi\) |
−0.874844 | + | 0.484405i | \(0.839036\pi\) | |||||||
\(194\) | −2.38539 | −0.171261 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.46046 | + | 11.1898i | −0.461461 | + | 0.799275i | ||||
\(197\) | 2.64398 | 0.188376 | 0.0941880 | − | 0.995554i | \(-0.469975\pi\) | ||||
0.0941880 | + | 0.995554i | \(0.469975\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.106311 | + | 0.184136i | 0.00753617 | + | 0.0130530i | 0.869769 | − | 0.493459i | \(-0.164268\pi\) |
−0.862233 | + | 0.506512i | \(0.830934\pi\) | |||||||
\(200\) | −5.47195 | + | 9.47770i | −0.386925 | + | 0.670174i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.40262 | + | 2.42940i | −0.0986877 | + | 0.170932i | ||||
\(203\) | 1.03079 | 0.0723470 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.86433 | − | 17.0855i | 0.688955 | − | 1.19330i | ||||
\(206\) | 2.56257 | − | 4.43851i | 0.178543 | − | 0.309245i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.23280 | −0.293492 | ||||||||
\(209\) | −1.14524 | − | 7.01930i | −0.0792177 | − | 0.485535i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.26187 | + | 7.38178i | 0.293400 | + | 0.508183i | 0.974611 | − | 0.223903i | \(-0.0718800\pi\) |
−0.681212 | + | 0.732086i | \(0.738547\pi\) | |||||||
\(212\) | 0.473399 | + | 0.819952i | 0.0325132 | + | 0.0563145i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.45508 | 0.304543 | ||||||||
\(215\) | 17.8483 | + | 30.9141i | 1.21724 | + | 2.10833i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.16220 | 0.146780 | ||||||||
\(218\) | 2.82839 | − | 4.89892i | 0.191563 | − | 0.331797i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.40181 | + | 9.35621i | −0.364190 | + | 0.630796i | ||||
\(221\) | 4.94380 | − | 8.56290i | 0.332556 | − | 0.576003i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.6032 | 1.04487 | 0.522433 | − | 0.852680i | \(-0.325025\pi\) | ||||
0.522433 | + | 0.852680i | \(0.325025\pi\) | |||||||
\(224\) | 0.505688 | + | 0.875877i | 0.0337877 | + | 0.0585220i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.543283 | + | 0.940994i | −0.0361386 | + | 0.0625940i | ||||
\(227\) | 0.595426 | + | 1.03131i | 0.0395198 | + | 0.0684503i | 0.885109 | − | 0.465384i | \(-0.154084\pi\) |
−0.845589 | + | 0.533835i | \(0.820751\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.98443 | + | 17.2935i | −0.659790 | + | 1.14279i | 0.320880 | + | 0.947120i | \(0.396021\pi\) |
−0.980670 | + | 0.195669i | \(0.937312\pi\) | |||||||
\(230\) | 2.96118 | + | 5.12891i | 0.195254 | + | 0.338190i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.95622 | + | 5.12032i | −0.194085 | + | 0.336166i | ||||
\(233\) | −6.18432 | + | 10.7115i | −0.405148 | + | 0.701737i | −0.994339 | − | 0.106257i | \(-0.966113\pi\) |
0.589191 | + | 0.807994i | \(0.299447\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.9660 | −0.780573 | ||||||||
\(236\) | 9.74281 | + | 16.8750i | 0.634203 | + | 1.09847i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.691019 | −0.0447921 | ||||||||
\(239\) | −8.11631 | + | 14.0579i | −0.525000 | + | 0.909327i | 0.474576 | + | 0.880215i | \(0.342602\pi\) |
−0.999576 | + | 0.0291128i | \(0.990732\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.24347 | + | 9.08196i | −0.337762 | + | 0.585020i | −0.984011 | − | 0.178106i | \(-0.943003\pi\) |
0.646250 | + | 0.763126i | \(0.276336\pi\) | |||||||
\(242\) | −1.54620 | + | 2.67809i | −0.0993933 | + | 0.172154i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.85619 | − | 6.67911i | 0.246867 | − | 0.427586i | ||||
\(245\) | −24.6647 | −1.57577 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.40319 | + | 2.04531i | 0.343797 | + | 0.130140i | ||||
\(248\) | −6.20104 | + | 10.7405i | −0.393767 | + | 0.682024i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.48044 | −0.220123 | ||||||||
\(251\) | 7.02198 | + | 12.1624i | 0.443223 | + | 0.767685i | 0.997927 | − | 0.0643630i | \(-0.0205016\pi\) |
−0.554703 | + | 0.832048i | \(0.687168\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.66418 | + | 6.34654i | 0.230365 | + | 0.399004i | ||||
\(254\) | 0.352041 | + | 0.609753i | 0.0220890 | + | 0.0382593i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.09457 | 0.380910 | ||||||||
\(257\) | −17.1607 | −1.07045 | −0.535227 | − | 0.844709i | \(-0.679774\pi\) | ||||
−0.535227 | + | 0.844709i | \(0.679774\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.387862 | − | 0.671797i | −0.0241006 | − | 0.0417435i | ||||
\(260\) | −4.38803 | − | 7.60029i | −0.272134 | − | 0.471350i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.561691 | + | 0.972878i | 0.0347014 | + | 0.0601046i | ||||
\(263\) | −19.4995 | −1.20239 | −0.601194 | − | 0.799103i | \(-0.705308\pi\) | ||||
−0.601194 | + | 0.799103i | \(0.705308\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.903671 | + | 1.56520i | −0.0555121 | + | 0.0961498i | ||||
\(266\) | −0.0650167 | − | 0.398496i | −0.00398643 | − | 0.0244333i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.48874 | 0.0909394 | ||||||||
\(269\) | 11.5796 | − | 20.0564i | 0.706020 | − | 1.22286i | −0.260303 | − | 0.965527i | \(-0.583822\pi\) |
0.966322 | − | 0.257335i | \(-0.0828443\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.0388 | + | 19.1197i | −0.670557 | + | 1.16144i | 0.307190 | + | 0.951648i | \(0.400611\pi\) |
−0.977746 | + | 0.209790i | \(0.932722\pi\) | |||||||
\(272\) | −11.9120 | + | 20.6322i | −0.722272 | + | 1.25101i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.789525 | + | 1.36750i | −0.0476970 | + | 0.0826136i | ||||
\(275\) | −12.4649 | −0.751660 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.7992 | + | 25.6330i | 0.889199 | + | 1.54014i | 0.840824 | + | 0.541309i | \(0.182071\pi\) |
0.0483752 | + | 0.998829i | \(0.484596\pi\) | |||||||
\(278\) | 6.40605 | 0.384209 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.635988 | + | 1.10156i | −0.0380075 | + | 0.0658310i | ||||
\(281\) | 14.4042 | − | 24.9487i | 0.859280 | − | 1.48832i | −0.0133368 | − | 0.999911i | \(-0.504245\pi\) |
0.872617 | − | 0.488406i | \(-0.162421\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.01020 | − | 13.8741i | −0.476157 | − | 0.824728i | 0.523470 | − | 0.852044i | \(-0.324637\pi\) |
−0.999627 | + | 0.0273162i | \(0.991304\pi\) | |||||||
\(284\) | 10.4306 | − | 18.0664i | 0.618944 | − | 1.07204i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.401040 | + | 0.694621i | 0.0237140 | + | 0.0410738i | ||||
\(287\) | 0.692963 | − | 1.20025i | 0.0409043 | − | 0.0708483i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19.3258 | − | 33.4732i | −1.13681 | − | 1.96901i | ||||
\(290\) | −5.44215 | −0.319574 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.44094 | − | 5.95989i | 0.201366 | − | 0.348776i | ||||
\(293\) | 0.400378 | − | 0.693475i | 0.0233903 | − | 0.0405132i | −0.854093 | − | 0.520120i | \(-0.825887\pi\) |
0.877484 | + | 0.479607i | \(0.159221\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.5980 | + | 32.2127i | −1.08282 | + | 1.87550i | ||||
\(296\) | 4.44945 | 0.258619 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.342358 | − | 0.592981i | −0.0198322 | − | 0.0343504i | ||||
\(299\) | −5.95301 | −0.344271 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.25383 | + | 2.17170i | 0.0722696 | + | 0.125175i | ||||
\(302\) | 2.07670 | + | 3.59696i | 0.119501 | + | 0.206982i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −13.0189 | − | 4.92815i | −0.746686 | − | 0.282649i | ||||
\(305\) | 14.7221 | 0.842987 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.29987 | − | 3.98349i | 0.131260 | − | 0.227350i | −0.792902 | − | 0.609349i | \(-0.791431\pi\) |
0.924163 | + | 0.381999i | \(0.124764\pi\) | |||||||
\(308\) | −0.379474 | + | 0.657268i | −0.0216225 | + | 0.0374513i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −11.4156 | −0.648362 | ||||||||
\(311\) | −16.4116 | + | 28.4257i | −0.930615 | + | 1.61187i | −0.148342 | + | 0.988936i | \(0.547394\pi\) |
−0.782273 | + | 0.622936i | \(0.785940\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.19380 | − | 15.9241i | 0.519664 | − | 0.900085i | −0.480074 | − | 0.877228i | \(-0.659390\pi\) |
0.999739 | − | 0.0228573i | \(-0.00727633\pi\) | |||||||
\(314\) | 3.85189 | + | 6.67167i | 0.217375 | + | 0.376504i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −18.3549 | −1.03254 | ||||||||
\(317\) | 0.679102 | − | 1.17624i | 0.0381422 | − | 0.0660642i | −0.846324 | − | 0.532668i | \(-0.821189\pi\) |
0.884466 | + | 0.466604i | \(0.154523\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.73415 | −0.377040 | ||||||||
\(320\) | 8.68398 | + | 15.0411i | 0.485449 | + | 0.840823i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.208021 | + | 0.360302i | 0.0115925 | + | 0.0200789i | ||||
\(323\) | 25.1753 | − | 20.5812i | 1.40079 | − | 1.14517i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.06277 | − | 8.76897i | 0.280832 | − | 0.486415i | ||||
\(326\) | 2.00900 | 0.111268 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.97473 | + | 6.88444i | 0.219468 | + | 0.380130i | ||||
\(329\) | −0.840601 | −0.0463438 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.39869 | + | 14.5470i | 0.461634 | + | 0.799573i | 0.999043 | − | 0.0437490i | \(-0.0139302\pi\) |
−0.537409 | + | 0.843322i | \(0.680597\pi\) | |||||||
\(332\) | 0.345020 | + | 0.597592i | 0.0189354 | + | 0.0327971i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.556357 | −0.0304425 | ||||||||
\(335\) | 1.42093 | + | 2.46112i | 0.0776336 | + | 0.134465i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.2612 | − | 31.6293i | −0.994750 | − | 1.72296i | −0.585999 | − | 0.810312i | \(-0.699298\pi\) |
−0.408751 | − | 0.912646i | \(-0.634035\pi\) | |||||||
\(338\) | 4.17001 | 0.226819 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −49.3954 | −2.67884 | ||||||||
\(341\) | −14.1257 | −0.764951 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.48094 | −0.187953 | ||||||||
\(344\) | −14.3836 | −0.775511 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.31290 | 0.446904 | ||||||||
\(347\) | −5.07542 | − | 8.79089i | −0.272463 | − | 0.471920i | 0.697029 | − | 0.717043i | \(-0.254505\pi\) |
−0.969492 | + | 0.245123i | \(0.921172\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.63614 | + | 14.9582i | 0.462282 | + | 0.800696i | 0.999074 | − | 0.0430183i | \(-0.0136974\pi\) |
−0.536792 | + | 0.843715i | \(0.680364\pi\) | |||||||
\(350\) | −0.707649 | −0.0378254 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.30367 | − | 5.72212i | −0.176086 | − | 0.304990i | ||||
\(353\) | 8.45158 | + | 14.6386i | 0.449832 | + | 0.779132i | 0.998375 | − | 0.0569905i | \(-0.0181505\pi\) |
−0.548543 | + | 0.836123i | \(0.684817\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 39.8220 | 2.11353 | ||||||||
\(356\) | 7.46902 | + | 12.9367i | 0.395857 | + | 0.685645i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.71525 | −0.249209 | ||||||||
\(359\) | −3.82747 | + | 6.62938i | −0.202006 | + | 0.349885i | −0.949175 | − | 0.314750i | \(-0.898079\pi\) |
0.747168 | + | 0.664635i | \(0.231413\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.2374 | + | 12.5816i | 0.749337 | + | 0.662189i | ||||
\(362\) | −0.486446 | − | 0.842549i | −0.0255670 | − | 0.0442834i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.308256 | − | 0.533915i | −0.0161570 | − | 0.0279848i | ||||
\(365\) | 13.1368 | 0.687613 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.3888 | − | 21.4579i | 0.646688 | − | 1.12010i | −0.337221 | − | 0.941425i | \(-0.609487\pi\) |
0.983909 | − | 0.178670i | \(-0.0571796\pi\) | |||||||
\(368\) | 14.3437 | 0.747717 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.04776 | + | 3.54683i | 0.106458 | + | 0.184391i | ||||
\(371\) | −0.0634823 | + | 0.109955i | −0.00329584 | + | 0.00570856i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.5863 | − | 20.0681i | 0.599917 | − | 1.03909i | −0.392916 | − | 0.919574i | \(-0.628534\pi\) |
0.992833 | − | 0.119512i | \(-0.0381330\pi\) | |||||||
\(374\) | 4.51444 | 0.233436 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.41078 | − | 4.17560i | 0.124327 | − | 0.215340i | ||||
\(377\) | 2.73516 | − | 4.73744i | 0.140868 | − | 0.243990i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.0801 | 1.49374 | 0.746871 | − | 0.664969i | \(-0.231555\pi\) | ||||
0.746871 | + | 0.664969i | \(0.231555\pi\) | |||||||
\(380\) | −4.64752 | − | 28.4852i | −0.238413 | − | 1.46126i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.632057 | − | 1.09475i | −0.0323388 | − | 0.0560125i | ||||
\(383\) | −1.41428 | − | 2.44960i | −0.0722662 | − | 0.125169i | 0.827628 | − | 0.561277i | \(-0.189690\pi\) |
−0.899894 | + | 0.436108i | \(0.856356\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.44875 | −0.0738353 | ||||||||
\(386\) | 0.0923078 | + | 0.159882i | 0.00469834 | + | 0.00813777i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.9784 | −0.608110 | ||||||||
\(389\) | 9.58295 | − | 16.5982i | 0.485875 | − | 0.841560i | −0.513993 | − | 0.857794i | \(-0.671834\pi\) |
0.999868 | + | 0.0162341i | \(0.00516771\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.7530 | + | 29.0171i | −0.847238 | + | 1.46746i | ||||
\(392\) | 4.96920 | − | 8.60691i | 0.250983 | − | 0.434715i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.980624 | −0.0494031 | ||||||||
\(395\) | −17.5188 | − | 30.3435i | −0.881467 | − | 1.52675i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.9590 | − | 27.6417i | 0.800958 | − | 1.38730i | −0.118029 | − | 0.993010i | \(-0.537658\pi\) |
0.918986 | − | 0.394289i | \(-0.129009\pi\) | |||||||
\(398\) | −0.0394295 | − | 0.0682939i | −0.00197642 | − | 0.00342326i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.1987 | + | 21.1287i | −0.609934 | + | 1.05644i | ||||
\(401\) | 19.1703 | + | 33.2040i | 0.957320 | + | 1.65813i | 0.728967 | + | 0.684548i | \(0.240001\pi\) |
0.228353 | + | 0.973578i | \(0.426666\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.73734 | − | 9.93737i | 0.285797 | − | 0.495015i | ||||
\(404\) | −7.04332 | + | 12.1994i | −0.350418 | + | 0.606942i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.382307 | −0.0189736 | ||||||||
\(407\) | 2.53391 | + | 4.38887i | 0.125601 | + | 0.217548i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.29288 | 0.113375 | 0.0566877 | − | 0.998392i | \(-0.481946\pi\) | ||||
0.0566877 | + | 0.998392i | \(0.481946\pi\) | |||||||
\(410\) | −3.65857 | + | 6.33683i | −0.180684 | + | 0.312954i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.8681 | − | 22.2882i | 0.633966 | − | 1.09806i | ||||
\(413\) | −1.30650 | + | 2.26292i | −0.0642886 | + | 0.111351i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.658608 | + | 1.14074i | −0.0323298 | + | 0.0559968i | ||||
\(416\) | 5.36731 | 0.263154 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.424756 | + | 2.60338i | 0.0207755 | + | 0.127335i | ||||
\(419\) | −5.32211 | + | 9.21817i | −0.260002 | + | 0.450337i | −0.966242 | − | 0.257636i | \(-0.917057\pi\) |
0.706240 | + | 0.707972i | \(0.250390\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.8645 | 1.26056 | 0.630280 | − | 0.776367i | \(-0.282940\pi\) | ||||
0.630280 | + | 0.776367i | \(0.282940\pi\) | |||||||
\(422\) | −1.58068 | − | 2.73782i | −0.0769464 | − | 0.133275i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.364125 | − | 0.630684i | −0.0176835 | − | 0.0306287i | ||||
\(425\) | −28.4954 | − | 49.3555i | −1.38223 | − | 2.39409i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.03422 | 0.0500494 | ||||||||
\(428\) | 22.3714 | 1.08136 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.61973 | − | 11.4657i | −0.319232 | − | 0.552926i | ||||
\(431\) | 9.52984 | + | 16.5062i | 0.459036 | + | 0.795074i | 0.998910 | − | 0.0466716i | \(-0.0148614\pi\) |
−0.539874 | + | 0.841746i | \(0.681528\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.3288 | + | 23.0861i | 0.640540 | + | 1.10945i | 0.985312 | + | 0.170761i | \(0.0546226\pi\) |
−0.344773 | + | 0.938686i | \(0.612044\pi\) | |||||||
\(434\) | −0.801937 | −0.0384942 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.2029 | − | 24.6002i | 0.680197 | − | 1.17814i | ||||
\(437\) | −18.3098 | − | 6.93094i | −0.875876 | − | 0.331552i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.94705 | −0.0929274 | −0.0464637 | − | 0.998920i | \(-0.514795\pi\) | ||||
−0.0464637 | + | 0.998920i | \(0.514795\pi\) | |||||||
\(440\) | 4.15492 | − | 7.19653i | 0.198078 | − | 0.343081i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.83360 | + | 3.17589i | −0.0872154 | + | 0.151062i | ||||
\(443\) | 3.28115 | − | 5.68312i | 0.155892 | − | 0.270013i | −0.777491 | − | 0.628894i | \(-0.783508\pi\) |
0.933384 | + | 0.358880i | \(0.116841\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.2576 | + | 24.6949i | −0.675875 | + | 1.17065i | ||||
\(446\) | −5.78704 | −0.274024 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.610044 | + | 1.05663i | 0.0288219 | + | 0.0499209i | ||||
\(449\) | 35.5348 | 1.67699 | 0.838495 | − | 0.544910i | \(-0.183436\pi\) | ||||
0.838495 | + | 0.544910i | \(0.183436\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.52714 | + | 7.84124i | −0.213175 | + | 0.369229i | ||||
\(452\) | −2.72813 | + | 4.72526i | −0.128320 | + | 0.222257i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.220837 | − | 0.382501i | −0.0103644 | − | 0.0179516i | ||||
\(455\) | 0.588430 | − | 1.01919i | 0.0275860 | − | 0.0477804i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.32444 | − | 5.75809i | −0.155511 | − | 0.269352i | 0.777734 | − | 0.628593i | \(-0.216369\pi\) |
−0.933245 | + | 0.359241i | \(0.883036\pi\) | |||||||
\(458\) | 3.70311 | − | 6.41398i | 0.173035 | − | 0.299706i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.8697 | + | 25.7551i | 0.693304 | + | 1.20084i | ||||
\(461\) | 6.97181 | 0.324709 | 0.162355 | − | 0.986732i | \(-0.448091\pi\) | ||||
0.162355 | + | 0.986732i | \(0.448091\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.59691 | − | 14.8903i | 0.399532 | − | 0.692010i | −0.594136 | − | 0.804365i | \(-0.702506\pi\) |
0.993668 | + | 0.112354i | \(0.0358392\pi\) | |||||||
\(464\) | −6.59033 | + | 11.4148i | −0.305949 | + | 0.529919i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.29369 | − | 3.97280i | 0.106253 | − | 0.184036i | ||||
\(467\) | −36.5485 | −1.69126 | −0.845632 | − | 0.533766i | \(-0.820776\pi\) | ||||
−0.845632 | + | 0.533766i | \(0.820776\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.0998193 | + | 0.172892i | 0.00460923 | + | 0.00798341i | ||||
\(470\) | 4.43804 | 0.204712 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.49390 | − | 12.9798i | −0.344935 | − | 0.597444i | ||||
\(473\) | −8.19130 | − | 14.1877i | −0.376636 | − | 0.652353i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.7811 | − | 21.0764i | 1.18292 | − | 0.967054i | ||||
\(476\) | −3.47000 | −0.159047 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.01025 | − | 5.21391i | 0.137686 | − | 0.238479i | ||||
\(479\) | −9.98270 | + | 17.2905i | −0.456121 | + | 0.790025i | −0.998752 | − | 0.0499464i | \(-0.984095\pi\) |
0.542631 | + | 0.839971i | \(0.317428\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.11673 | −0.187707 | ||||||||
\(482\) | 1.94475 | − | 3.36840i | 0.0885807 | − | 0.153426i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.76432 | + | 13.4482i | −0.352924 | + | 0.611281i | ||||
\(485\) | −11.4327 | − | 19.8021i | −0.519134 | − | 0.899167i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.541412 | 0.0245337 | 0.0122669 | − | 0.999925i | \(-0.496095\pi\) | ||||
0.0122669 | + | 0.999925i | \(0.496095\pi\) | |||||||
\(488\) | −2.96607 | + | 5.13738i | −0.134268 | + | 0.232558i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.14787 | 0.413259 | ||||||||
\(491\) | −3.67184 | − | 6.35982i | −0.165708 | − | 0.287015i | 0.771199 | − | 0.636595i | \(-0.219658\pi\) |
−0.936906 | + | 0.349580i | \(0.886324\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.3946 | − | 26.6643i | −0.693340 | − | 1.20090i | ||||
\(494\) | −2.00398 | − | 0.758583i | −0.0901635 | − | 0.0341302i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.8241 | + | 23.9440i | −0.620718 | + | 1.07512i | ||||
\(497\) | 2.79747 | 0.125484 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.97373 | + | 10.3468i | 0.267421 | + | 0.463187i | 0.968195 | − | 0.250197i | \(-0.0804952\pi\) |
−0.700774 | + | 0.713383i | \(0.747162\pi\) | |||||||
\(500\) | −17.4773 | −0.781607 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.60437 | − | 4.51091i | −0.116239 | − | 0.201332i | ||||
\(503\) | −14.7358 | − | 25.5232i | −0.657038 | − | 1.13802i | −0.981379 | − | 0.192083i | \(-0.938476\pi\) |
0.324341 | − | 0.945940i | \(-0.394858\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.8900 | −1.19659 | ||||||||
\(506\) | −1.35900 | − | 2.35386i | −0.0604151 | − | 0.104642i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.76779 | + | 3.06191i | 0.0784332 | + | 0.135850i | ||||
\(509\) | −17.9044 | −0.793600 | −0.396800 | − | 0.917905i | \(-0.629879\pi\) | ||||
−0.396800 | + | 0.917905i | \(0.629879\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.922853 | 0.0408246 | ||||||||
\(512\) | −22.0823 | −0.975909 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.36470 | 0.280735 | ||||||||
\(515\) | 49.1278 | 2.16483 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.49166 | 0.241523 | ||||||||
\(518\) | 0.143854 | + | 0.249162i | 0.00632058 | + | 0.0109476i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.37515 | + | 5.84593i | 0.148010 | + | 0.256361i | ||||
\(521\) | 27.8411 | 1.21974 | 0.609871 | − | 0.792501i | \(-0.291221\pi\) | ||||
0.609871 | + | 0.792501i | \(0.291221\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.9624 | − | 22.4515i | −0.566805 | − | 0.981735i | −0.996879 | − | 0.0789417i | \(-0.974846\pi\) |
0.430074 | − | 0.902794i | \(-0.358487\pi\) | |||||||
\(524\) | 2.82057 | + | 4.88537i | 0.123217 | + | 0.213418i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.23214 | 0.315336 | ||||||||
\(527\) | −32.2922 | − | 55.9317i | −1.40667 | − | 2.43642i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.82704 | −0.122915 | ||||||||
\(530\) | 0.335162 | − | 0.580517i | 0.0145585 | − | 0.0252161i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.326485 | − | 2.00107i | −0.0141549 | − | 0.0867574i | ||||
\(533\) | −3.67751 | − | 6.36964i | −0.159291 | − | 0.275900i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.3524 | + | 36.9834i | 0.923144 | + | 1.59893i | ||||
\(536\) | −1.14510 | −0.0494607 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.29474 | + | 7.43871i | −0.185159 | + | 0.320705i | ||||
\(539\) | 11.3196 | 0.487571 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.3043 | − | 21.3116i | −0.529001 | − | 0.916257i | −0.999428 | − | 0.0338181i | \(-0.989233\pi\) |
0.470427 | − | 0.882439i | \(-0.344100\pi\) | |||||||
\(542\) | 4.09415 | − | 7.09128i | 0.175859 | − | 0.304597i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15.1048 | − | 26.1622i | 0.647611 | − | 1.12170i | ||||
\(545\) | 54.2239 | 2.32270 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.44357 | + | 11.1606i | −0.275507 | + | 0.477192i | −0.970263 | − | 0.242054i | \(-0.922179\pi\) |
0.694756 | + | 0.719246i | \(0.255512\pi\) | |||||||
\(548\) | −3.96465 | + | 6.86697i | −0.169361 | + | 0.293343i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.62308 | 0.197129 | ||||||||
\(551\) | 13.9283 | − | 11.3865i | 0.593364 | − | 0.485083i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.23068 | − | 2.13161i | −0.0523340 | − | 0.0906452i | ||||
\(554\) | −5.48887 | − | 9.50700i | −0.233200 | − | 0.403914i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 32.1684 | 1.36424 | ||||||||
\(557\) | 11.8767 | + | 20.5710i | 0.503231 | + | 0.871622i | 0.999993 | + | 0.00373498i | \(0.00118888\pi\) |
−0.496762 | + | 0.867887i | \(0.665478\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.3080 | 0.562868 | ||||||||
\(560\) | −1.41781 | + | 2.45573i | −0.0599136 | + | 0.103773i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.34234 | + | 9.25321i | −0.225353 | + | 0.390323i | ||||
\(563\) | −13.3440 | + | 23.1125i | −0.562383 | + | 0.974077i | 0.434904 | + | 0.900477i | \(0.356782\pi\) |
−0.997288 | + | 0.0735999i | \(0.976551\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.4154 | −0.438181 | ||||||||
\(566\) | 2.97090 | + | 5.14574i | 0.124876 | + | 0.216292i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.02294 | + | 13.8961i | −0.336635 | + | 0.583069i | ||||
\(569\) | −6.57047 | − | 11.3804i | −0.275448 | − | 0.477090i | 0.694800 | − | 0.719203i | \(-0.255493\pi\) |
−0.970248 | + | 0.242113i | \(0.922160\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.08070 | + | 1.87182i | −0.0452258 | + | 0.0783333i | −0.887752 | − | 0.460322i | \(-0.847734\pi\) |
0.842526 | + | 0.538655i | \(0.181067\pi\) | |||||||
\(572\) | 2.01384 | + | 3.48808i | 0.0842031 | + | 0.145844i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.257012 | + | 0.445158i | −0.0107275 | + | 0.0185805i | ||||
\(575\) | −17.1562 | + | 29.7154i | −0.715463 | + | 1.23922i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.53956 | 0.188985 | 0.0944923 | − | 0.995526i | \(-0.469877\pi\) | ||||
0.0944923 | + | 0.995526i | \(0.469877\pi\) | |||||||
\(578\) | 7.16772 | + | 12.4149i | 0.298138 | + | 0.516390i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −27.3281 | −1.13474 | ||||||||
\(581\) | −0.0462667 | + | 0.0801364i | −0.00191947 | + | 0.00332462i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.414731 | − | 0.718336i | 0.0171764 | − | 0.0297504i | ||||
\(584\) | −2.64668 | + | 4.58418i | −0.109520 | + | 0.189695i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.148496 | + | 0.257202i | −0.00613430 | + | 0.0106249i | ||||
\(587\) | −24.2678 | −1.00164 | −0.500819 | − | 0.865552i | \(-0.666968\pi\) | ||||
−0.500819 | + | 0.865552i | \(0.666968\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.2163 | − | 23.8847i | 1.20384 | − | 0.984152i | ||||
\(590\) | 6.89781 | − | 11.9474i | 0.283978 | − | 0.491865i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.91920 | 0.407677 | ||||||||
\(593\) | −16.5350 | − | 28.6395i | −0.679013 | − | 1.17608i | −0.975279 | − | 0.220979i | \(-0.929075\pi\) |
0.296266 | − | 0.955106i | \(-0.404259\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.31193 | − | 5.73644i | −0.135776 | − | 0.235171i | ||||
\(596\) | −1.71917 | − | 2.97769i | −0.0704199 | − | 0.121971i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.20791 | 0.0902880 | ||||||||
\(599\) | 13.2848 | 0.542803 | 0.271401 | − | 0.962466i | \(-0.412513\pi\) | ||||
0.271401 | + | 0.962466i | \(0.412513\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.35146 | − | 12.7331i | −0.299872 | − | 0.519394i | 0.676234 | − | 0.736687i | \(-0.263611\pi\) |
−0.976106 | + | 0.217293i | \(0.930277\pi\) | |||||||
\(602\) | −0.465032 | − | 0.805459i | −0.0189533 | − | 0.0328280i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.4283 | + | 18.0623i | 0.424321 | + | 0.734946i | ||||
\(605\) | −29.6426 | −1.20514 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.19304 | + | 2.06641i | −0.0484241 | + | 0.0838729i | −0.889221 | − | 0.457477i | \(-0.848753\pi\) |
0.840797 | + | 0.541350i | \(0.182087\pi\) | |||||||
\(608\) | 16.5083 | + | 6.24903i | 0.669502 | + | 0.253431i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.46028 | −0.221080 | ||||||||
\(611\) | −2.23051 | + | 3.86336i | −0.0902368 | + | 0.156295i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.16079 | − | 3.74260i | 0.0872736 | − | 0.151162i | −0.819084 | − | 0.573673i | \(-0.805518\pi\) |
0.906358 | + | 0.422511i | \(0.138851\pi\) | |||||||
\(614\) | −0.852996 | + | 1.47743i | −0.0344241 | + | 0.0596243i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.291880 | − | 0.505552i | 0.0117602 | − | 0.0203693i | ||||
\(617\) | 9.61045 | 0.386902 | 0.193451 | − | 0.981110i | \(-0.438032\pi\) | ||||
0.193451 | + | 0.981110i | \(0.438032\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.79677 | − | 3.11209i | −0.0722182 | − | 0.125086i | 0.827655 | − | 0.561237i | \(-0.189674\pi\) |
−0.899873 | + | 0.436152i | \(0.856341\pi\) | |||||||
\(620\) | −57.3241 | −2.30219 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.08687 | − | 10.5428i | 0.244061 | − | 0.422727i | ||||
\(623\) | −1.00159 | + | 1.73480i | −0.0401277 | + | 0.0695032i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.41765 | + | 4.18750i | 0.0967061 | + | 0.167500i | ||||
\(626\) | −3.40988 | + | 5.90608i | −0.136286 | + | 0.236055i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19.3425 | + | 33.5022i | 0.771850 | + | 1.33688i | ||||
\(629\) | −11.5853 | + | 20.0664i | −0.461938 | + | 0.800100i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.6319 | + | 21.8792i | 0.502870 | + | 0.870996i | 0.999994 | + | 0.00331669i | \(0.00105574\pi\) |
−0.497125 | + | 0.867679i | \(0.665611\pi\) | |||||||
\(632\) | 14.1181 | 0.561586 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.251872 | + | 0.436254i | −0.0100031 | + | 0.0173259i | ||||
\(635\) | −3.37454 | + | 5.84487i | −0.133915 | + | 0.231947i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.59761 | + | 7.96330i | −0.182164 | + | 0.315517i | ||||
\(638\) | 2.49762 | 0.0988818 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −17.6177 | − | 30.5148i | −0.696402 | − | 1.20620i | ||||
\(641\) | 23.3043 | 0.920463 | 0.460231 | − | 0.887799i | \(-0.347766\pi\) | ||||
0.460231 | + | 0.887799i | \(0.347766\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.62978 | − | 14.9472i | −0.340325 | − | 0.589461i | 0.644168 | − | 0.764884i | \(-0.277204\pi\) |
−0.984493 | + | 0.175423i | \(0.943871\pi\) | |||||||
\(644\) | 1.04459 | + | 1.80928i | 0.0411625 | + | 0.0712956i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.33724 | + | 7.63333i | −0.367369 | + | 0.300329i | ||||
\(647\) | 35.6673 | 1.40223 | 0.701114 | − | 0.713049i | \(-0.252686\pi\) | ||||
0.701114 | + | 0.713049i | \(0.252686\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.53539 | − | 14.7837i | 0.335043 | − | 0.580312i | ||||
\(650\) | −1.87772 | + | 3.25231i | −0.0736504 | + | 0.127566i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.0883 | 0.395088 | ||||||||
\(653\) | 8.46548 | − | 14.6626i | 0.331280 | − | 0.573794i | −0.651483 | − | 0.758663i | \(-0.725853\pi\) |
0.982763 | + | 0.184869i | \(0.0591862\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.38418 | + | 9.32566i | −0.210377 | + | 0.364384i | ||||
\(656\) | 8.86092 | + | 15.3476i | 0.345961 | + | 0.599222i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.311770 | 0.0121540 | ||||||||
\(659\) | −2.26182 | + | 3.91760i | −0.0881082 | + | 0.152608i | −0.906711 | − | 0.421752i | \(-0.861415\pi\) |
0.818603 | + | 0.574359i | \(0.194749\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.0800 | 0.781021 | 0.390510 | − | 0.920599i | \(-0.372299\pi\) | ||||
0.390510 | + | 0.920599i | \(0.372299\pi\) | |||||||
\(662\) | −3.11498 | − | 5.39530i | −0.121067 | − | 0.209694i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.265379 | − | 0.459651i | −0.0102987 | − | 0.0178379i | ||||
\(665\) | 2.99646 | − | 2.44965i | 0.116198 | − | 0.0949933i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.26864 | + | 16.0537i | −0.358883 | + | 0.621604i | ||||
\(668\) | −2.79378 | −0.108095 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.527007 | − | 0.912803i | −0.0203600 | − | 0.0352646i | ||||
\(671\) | −6.75658 | −0.260835 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.72911 | + | 15.1193i | 0.336482 | + | 0.582805i | 0.983768 | − | 0.179443i | \(-0.0574294\pi\) |
−0.647286 | + | 0.762247i | \(0.724096\pi\) | |||||||
\(674\) | 6.77287 | + | 11.7310i | 0.260881 | + | 0.451860i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.9399 | 0.805382 | ||||||||
\(677\) | 20.4904 | + | 35.4905i | 0.787511 | + | 1.36401i | 0.927487 | + | 0.373854i | \(0.121964\pi\) |
−0.139976 | + | 0.990155i | \(0.544703\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.803143 | − | 1.39108i | −0.0308218 | − | 0.0533849i | ||||
\(680\) | 37.9936 | 1.45699 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.23907 | 0.200614 | ||||||||
\(683\) | −20.9461 | −0.801480 | −0.400740 | − | 0.916192i | \(-0.631247\pi\) | ||||
−0.400740 | + | 0.916192i | \(0.631247\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.1362 | −0.578325 | ||||||||
\(686\) | 1.29104 | 0.0492922 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −32.0655 | −1.22248 | ||||||||
\(689\) | 0.336897 | + | 0.583522i | 0.0128347 | + | 0.0222304i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.5768 | − | 18.3195i | −0.402359 | − | 0.696907i | 0.591651 | − | 0.806194i | \(-0.298476\pi\) |
−0.994010 | + | 0.109288i | \(0.965143\pi\) | |||||||
\(692\) | 41.7437 | 1.58686 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.88242 | + | 3.26044i | 0.0714556 | + | 0.123765i | ||||
\(695\) | 30.7031 | + | 53.1793i | 1.16463 | + | 2.01720i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41.3972 | −1.56803 | ||||||||
\(698\) | −3.20305 | − | 5.54785i | −0.121237 | − | 0.209989i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.55350 | −0.134310 | ||||||||
\(701\) | 1.32346 | − | 2.29231i | 0.0499865 | − | 0.0865792i | −0.839950 | − | 0.542665i | \(-0.817415\pi\) |
0.889936 | + | 0.456085i | \(0.150749\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.6619 | − | 4.79300i | −0.477552 | − | 0.180771i | ||||
\(704\) | −3.98543 | − | 6.90297i | −0.150207 | − | 0.260165i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.13460 | − | 5.42928i | −0.117972 | − | 0.204334i | ||||
\(707\) | −1.88900 | −0.0710432 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.4226 | + | 23.2486i | −0.504097 | + | 0.873121i | 0.495892 | + | 0.868384i | \(0.334841\pi\) |
−0.999989 | + | 0.00473700i | \(0.998492\pi\) | |||||||
\(710\) | −14.7695 | −0.554291 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.74496 | − | 9.95056i | −0.215301 | − | 0.372913i | ||||
\(713\) | −19.4421 | + | 33.6748i | −0.728113 | + | 1.26113i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.84422 | + | 6.65839i | −0.143766 | + | 0.249010i | ||||
\(716\) | −23.6779 | −0.884885 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.41957 | − | 2.45876i | 0.0529778 | − | 0.0917602i | ||||
\(719\) | −1.94193 | + | 3.36352i | −0.0724217 | + | 0.125438i | −0.899962 | − | 0.435968i | \(-0.856406\pi\) |
0.827540 | + | 0.561406i | \(0.189739\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.45120 | 0.128529 | ||||||||
\(722\) | −5.28049 | − | 4.66638i | −0.196520 | − | 0.173665i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.44272 | − | 4.23091i | −0.0907828 | − | 0.157240i | ||||
\(725\) | −15.7651 | − | 27.3060i | −0.585502 | − | 1.01412i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −52.3039 | −1.93984 | −0.969922 | − | 0.243417i | \(-0.921732\pi\) | ||||
−0.969922 | + | 0.243417i | \(0.921732\pi\) | |||||||
\(728\) | 0.237102 | + | 0.410673i | 0.00878758 | + | 0.0152205i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.87230 | −0.180332 | ||||||||
\(731\) | 37.4516 | − | 64.8680i | 1.38520 | − | 2.39923i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.06517 | − | 5.30902i | 0.113215 | − | 0.196093i | −0.803850 | − | 0.594832i | \(-0.797219\pi\) |
0.917065 | + | 0.398739i | \(0.130552\pi\) | |||||||
\(734\) | −4.59485 | + | 7.95852i | −0.169599 | + | 0.293754i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.1882 | −0.670426 | ||||||||
\(737\) | −0.652121 | − | 1.12951i | −0.0240212 | − | 0.0416059i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.68714 | + | 11.5825i | −0.245990 | + | 0.426068i | −0.962410 | − | 0.271602i | \(-0.912447\pi\) |
0.716419 | + | 0.697670i | \(0.245780\pi\) | |||||||
\(740\) | 10.2830 | + | 17.8106i | 0.378009 | + | 0.654731i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.0235449 | − | 0.0407809i | 0.000864360 | − | 0.00149712i | ||||
\(743\) | −1.37195 | − | 2.37629i | −0.0503321 | − | 0.0871778i | 0.839762 | − | 0.542955i | \(-0.182695\pi\) |
−0.890094 | + | 0.455777i | \(0.849361\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.28172 | − | 5.68410i | 0.120233 | − | 0.208249i | ||||
\(746\) | −4.29724 | + | 7.44304i | −0.157333 | + | 0.272509i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 22.6696 | 0.828881 | ||||||||
\(749\) | 1.49999 | + | 2.59806i | 0.0548085 | + | 0.0949311i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.9472 | −0.764374 | −0.382187 | − | 0.924085i | \(-0.624829\pi\) | ||||
−0.382187 | + | 0.924085i | \(0.624829\pi\) | |||||||
\(752\) | 5.37439 | − | 9.30871i | 0.195984 | − | 0.339454i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.01444 | + | 1.75706i | −0.0369438 | + | 0.0639885i | ||||
\(755\) | −19.9065 | + | 34.4791i | −0.724473 | + | 1.25482i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.65990 | − | 6.33913i | 0.133021 | − | 0.230400i | −0.791819 | − | 0.610756i | \(-0.790865\pi\) |
0.924840 | + | 0.380357i | \(0.124199\pi\) | |||||||
\(758\) | −10.7855 | −0.391746 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.57474 | + | 21.9100i | 0.129670 | + | 0.794761i | ||||
\(761\) | −6.05266 | + | 10.4835i | −0.219409 | + | 0.380027i | −0.954627 | − | 0.297803i | \(-0.903746\pi\) |
0.735219 | + | 0.677830i | \(0.237079\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.80919 | 0.137902 | ||||||||
\(764\) | −3.17391 | − | 5.49737i | −0.114828 | − | 0.198888i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.524540 | + | 0.908530i | 0.0189524 | + | 0.0328265i | ||||
\(767\) | 6.93352 | + | 12.0092i | 0.250355 | + | 0.433627i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.9659 | −1.04454 | −0.522269 | − | 0.852781i | \(-0.674914\pi\) | ||||
−0.522269 | + | 0.852781i | \(0.674914\pi\) | |||||||
\(770\) | 0.537327 | 0.0193639 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.463529 | + | 0.802856i | 0.0166828 | + | 0.0288954i | ||||
\(773\) | −21.7876 | − | 37.7372i | −0.783645 | − | 1.35731i | −0.929805 | − | 0.368052i | \(-0.880025\pi\) |
0.146160 | − | 0.989261i | \(-0.453309\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.0693 | − | 57.2777i | −1.18788 | − | 2.05748i | ||||
\(776\) | 9.21343 | 0.330743 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.55421 | + | 6.15608i | −0.127425 | + | 0.220706i | ||||
\(779\) | −3.89499 | − | 23.8729i | −0.139552 | − | 0.855334i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.2759 | −0.653964 | ||||||||
\(782\) | 6.21352 | − | 10.7621i | 0.222195 | − | 0.384853i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11.0779 | − | 19.1875i | 0.395639 | − | 0.685267i | ||||
\(785\) | −36.9229 | + | 63.9523i | −1.31783 | + | 2.28255i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.10060 | − | 5.37040i | 0.110525 | − | 0.191434i | −0.805457 | − | 0.592654i | \(-0.798080\pi\) |
0.915982 | + | 0.401220i | \(0.131414\pi\) | |||||||
\(788\) | −4.92426 | −0.175420 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.49754 | + | 11.2541i | 0.231172 | + | 0.400402i | ||||
\(791\) | −0.731677 | −0.0260155 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.74427 | − | 4.75322i | 0.0974520 | − | 0.168792i | ||||
\(794\) | −5.91901 | + | 10.2520i | −0.210058 | + | 0.363831i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.197997 | − | 0.342942i | −0.00701784 | − | 0.0121552i | ||||
\(797\) | 19.1606 | − | 33.1871i | 0.678702 | − | 1.17555i | −0.296671 | − | 0.954980i | \(-0.595876\pi\) |
0.975372 | − | 0.220566i | \(-0.0707904\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.5543 | + | 21.7446i | 0.444138 | + | 0.769269i | ||||
\(800\) | 15.4683 | − | 26.7918i | 0.546885 | − | 0.947233i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.11006 | − | 12.3150i | −0.251065 | − | 0.434857i | ||||
\(803\) | −6.02902 | −0.212759 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.99401 | + | 3.45373i | −0.0702797 | + | 0.121728i | ||||
\(806\) | −2.12792 | + | 3.68566i | −0.0749527 | + | 0.129822i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.41752 | − | 9.38342i | 0.190588 | − | 0.330108i | ||||
\(809\) | 36.9557 | 1.29929 | 0.649647 | − | 0.760236i | \(-0.274917\pi\) | ||||
0.649647 | + | 0.760236i | \(0.274917\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.0016 | + | 36.3759i | 0.737467 | + | 1.27733i | 0.953632 | + | 0.300974i | \(0.0973118\pi\) |
−0.216165 | + | 0.976357i | \(0.569355\pi\) | |||||||
\(812\) | −1.91978 | −0.0673710 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.939801 | − | 1.62778i | −0.0329400 | − | 0.0570537i | ||||
\(815\) | 9.62877 | + | 16.6775i | 0.337281 | + | 0.584188i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40.9317 | + | 15.4942i | 1.43202 | + | 0.542072i | ||||
\(818\) | −0.850402 | −0.0297336 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −18.3717 | + | 31.8208i | −0.641569 | + | 1.11123i | ||||
\(821\) | −8.86017 | + | 15.3463i | −0.309222 | + | 0.535588i | −0.978192 | − | 0.207701i | \(-0.933402\pi\) |
0.668970 | + | 0.743289i | \(0.266735\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.2027 | −1.01794 | −0.508971 | − | 0.860784i | \(-0.669974\pi\) | ||||
−0.508971 | + | 0.860784i | \(0.669974\pi\) | |||||||
\(824\) | −9.89779 | + | 17.1435i | −0.344806 | + | 0.597221i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.484566 | − | 0.839294i | 0.0168602 | − | 0.0292028i | ||||
\(827\) | −7.34515 | − | 12.7222i | −0.255416 | − | 0.442393i | 0.709593 | − | 0.704612i | \(-0.248879\pi\) |
−0.965008 | + | 0.262219i | \(0.915546\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.88680 | −0.100263 | −0.0501314 | − | 0.998743i | \(-0.515964\pi\) | ||||
−0.0501314 | + | 0.998743i | \(0.515964\pi\) | |||||||
\(830\) | 0.244270 | − | 0.423089i | 0.00847875 | − | 0.0146856i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.47493 | 0.224478 | ||||||||
\(833\) | 25.8773 | + | 44.8209i | 0.896596 | + | 1.55295i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.66652 | − | 4.61855i | −0.0922788 | − | 0.159831i | ||||
\(836\) | 2.13294 | + | 13.0730i | 0.0737692 | + | 0.452140i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.97391 | − | 3.41892i | 0.0681877 | − | 0.118105i | ||||
\(839\) | 15.1184 | 0.521946 | 0.260973 | − | 0.965346i | \(-0.415957\pi\) | ||||
0.260973 | + | 0.965346i | \(0.415957\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.98290 | + | 10.3627i | 0.206307 | + | 0.357334i | ||||
\(842\) | −9.59288 | −0.330592 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.93749 | − | 13.7481i | −0.273220 | − | 0.473230i | ||||
\(845\) | 19.9861 | + | 34.6170i | 0.687543 | + | 1.19086i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.08237 | −0.0715511 | ||||||||
\(848\) | −0.811749 | − | 1.40599i | −0.0278756 | − | 0.0482819i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.5686 | + | 18.3054i | 0.362501 | + | 0.627871i | ||||
\(851\) | 13.9503 | 0.478212 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.1014 | 0.893696 | 0.446848 | − | 0.894610i | \(-0.352546\pi\) | ||||
0.446848 | + | 0.894610i | \(0.352546\pi\) | |||||||
\(854\) | −0.383581 | −0.0131259 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.2075 | −0.588139 | ||||||||
\(857\) | −41.6454 | −1.42258 | −0.711291 | − | 0.702898i | \(-0.751889\pi\) | ||||
−0.711291 | + | 0.702898i | \(0.751889\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.44030 | 0.322099 | 0.161049 | − | 0.986946i | \(-0.448512\pi\) | ||||
0.161049 | + | 0.986946i | \(0.448512\pi\) | |||||||
\(860\) | −33.2414 | − | 57.5758i | −1.13352 | − | 1.96332i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.53451 | − | 6.12196i | −0.120386 | − | 0.208515i | ||||
\(863\) | −31.0403 | −1.05662 | −0.528311 | − | 0.849051i | \(-0.677175\pi\) | ||||
−0.528311 | + | 0.849051i | \(0.677175\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.8422 | + | 69.0088i | 1.35468 | + | 2.34637i | ||||
\(866\) | −4.94349 | − | 8.56238i | −0.167987 | − | 0.290962i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.02698 | −0.136684 | ||||||||
\(869\) | 8.04009 | + | 13.9258i | 0.272741 | + | 0.472402i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.05947 | 0.0358988 | ||||||||
\(872\) | −10.9245 | + | 18.9218i | −0.369950 | + | 0.640772i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.79090 | + | 2.57061i | 0.229706 | + | 0.0869522i | ||||
\(875\) | −1.17184 | − | 2.02969i | −0.0396154 | − | 0.0686159i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.7277 | + | 35.9014i | 0.699924 | + | 1.21230i | 0.968492 | + | 0.249044i | \(0.0801163\pi\) |
−0.268568 | + | 0.963261i | \(0.586550\pi\) | |||||||
\(878\) | 0.722138 | 0.0243710 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.26261 | − | 16.0433i | 0.312243 | − | 0.540820i | ||||
\(881\) | −15.2233 | −0.512886 | −0.256443 | − | 0.966559i | \(-0.582551\pi\) | ||||
−0.256443 | + | 0.966559i | \(0.582551\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.314882 | − | 0.545392i | −0.0105966 | − | 0.0183539i | 0.860678 | − | 0.509149i | \(-0.170040\pi\) |
−0.871275 | + | 0.490795i | \(0.836706\pi\) | |||||||
\(884\) | −9.20753 | + | 15.9479i | −0.309683 | + | 0.536386i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.21694 | + | 2.10781i | −0.0408840 | + | 0.0708132i | ||||
\(887\) | 1.12719 | 0.0378474 | 0.0189237 | − | 0.999821i | \(-0.493976\pi\) | ||||
0.0189237 | + | 0.999821i | \(0.493976\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.237059 | + | 0.410599i | −0.00795071 | + | 0.0137710i | ||||
\(890\) | 5.28798 | − | 9.15906i | 0.177254 | − | 0.307012i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −29.0600 | −0.973000 | ||||||||
\(893\) | −11.3584 | + | 9.28567i | −0.380095 | + | 0.310733i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.5994 | − | 39.1432i | −0.755413 | − | 1.30841i | ||||
\(896\) | −1.23763 | − | 2.14365i | −0.0413465 | − | 0.0716142i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.1795 | −0.439804 | ||||||||
\(899\) | −17.8657 | − | 30.9443i | −0.595854 | − | 1.03205i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.79240 | 0.126343 | ||||||||
\(902\) | 1.67907 | − | 2.90823i | 0.0559068 | − | 0.0968334i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.09840 | − | 3.63453i | 0.0697917 | − | 0.120883i | ||||
\(905\) | 4.66290 | − | 8.07637i | 0.155000 | − | 0.268468i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.7319 | 0.954028 | 0.477014 | − | 0.878896i | \(-0.341719\pi\) | ||||
0.477014 | + | 0.878896i | \(0.341719\pi\) | |||||||
\(908\) | −1.10895 | − | 1.92075i | −0.0368016 | − | 0.0637423i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.218242 | + | 0.378006i | −0.00723466 | + | 0.0125308i | ||||
\(911\) | 19.6724 | + | 34.0735i | 0.651774 | + | 1.12891i | 0.982692 | + | 0.185246i | \(0.0593083\pi\) |
−0.330918 | + | 0.943660i | \(0.607358\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.302262 | − | 0.523532i | 0.0100034 | − | 0.0173264i | ||||
\(914\) | 1.23300 | + | 2.13561i | 0.0407839 | + | 0.0706398i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.5954 | − | 32.2082i | 0.614410 | − | 1.06419i | ||||
\(917\) | −0.378235 | + | 0.655122i | −0.0124904 | + | 0.0216340i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.3218 | 0.472433 | 0.236217 | − | 0.971700i | \(-0.424093\pi\) | ||||
0.236217 | + | 0.971700i | \(0.424093\pi\) | |||||||
\(920\) | −11.4374 | − | 19.8101i | −0.377079 | − | 0.653120i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.58577 | −0.0851577 | ||||||||
\(923\) | 7.42300 | − | 12.8570i | 0.244331 | − | 0.423194i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.8641 | + | 20.5493i | −0.390091 | + | 0.675657i | ||||
\(926\) | −3.18850 | + | 5.52264i | −0.104781 | + | 0.181485i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.35672 | − | 14.4743i | 0.274323 | − | 0.475141i | ||||
\(929\) | −1.78788 | −0.0586586 | −0.0293293 | − | 0.999570i | \(-0.509337\pi\) | ||||
−0.0293293 | + | 0.999570i | \(0.509337\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.4124 | + | 19.1400i | −0.767312 | + | 0.627288i | ||||
\(932\) | 11.5179 | − | 19.9496i | 0.377282 | − | 0.653472i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.5555 | 0.443548 | ||||||||
\(935\) | 21.6369 | + | 37.4763i | 0.707603 | + | 1.22560i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.96721 | + | 12.0676i | 0.227609 | + | 0.394230i | 0.957099 | − | 0.289761i | \(-0.0935759\pi\) |
−0.729490 | + | 0.683991i | \(0.760243\pi\) | |||||||
\(938\) | −0.0370219 | − | 0.0641238i | −0.00120881 | − | 0.00209372i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 22.2859 | 0.726886 | ||||||||
\(941\) | 45.4329 | 1.48107 | 0.740535 | − | 0.672017i | \(-0.234572\pi\) | ||||
0.740535 | + | 0.672017i | \(0.234572\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.4620 | + | 21.5848i | 0.405818 | + | 0.702897i | ||||
\(944\) | −16.7062 | − | 28.9360i | −0.543741 | − | 0.941787i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.03806 | + | 5.26208i | 0.0987759 | + | 0.171085i | ||||
\(947\) | 5.17499 | 0.168165 | 0.0840823 | − | 0.996459i | \(-0.473204\pi\) | ||||
0.0840823 | + | 0.996459i | \(0.473204\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.44876 | − | 4.24138i | 0.0794902 | − | 0.137681i | ||||
\(950\) | −9.56194 | + | 7.81702i | −0.310230 | + | 0.253618i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.66902 | 0.0865035 | ||||||||
\(953\) | −12.9234 | + | 22.3840i | −0.418630 | + | 0.725088i | −0.995802 | − | 0.0915347i | \(-0.970823\pi\) |
0.577172 | + | 0.816622i | \(0.304156\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.05867 | − | 10.4939i | 0.196054 | − | 0.339575i | ||||
\(956\) | 15.1162 | − | 26.1819i | 0.488891 | − | 0.846785i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.70247 | − | 6.41287i | 0.119621 | − | 0.207190i | ||||
\(959\) | −1.06331 | −0.0343360 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.9755 | − | 38.0628i | −0.708888 | − | 1.22783i | ||||
\(962\) | 1.52685 | 0.0492276 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.76565 | − | 16.9146i | 0.314531 | − | 0.544783i | ||||
\(965\) | −0.884830 | + | 1.53257i | −0.0284837 | + | 0.0493352i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.0699 | − | 22.6377i | −0.420299 | − | 0.727979i | 0.575670 | − | 0.817682i | \(-0.304741\pi\) |
−0.995969 | + | 0.0897035i | \(0.971408\pi\) | |||||||
\(968\) | 5.97209 | − | 10.3440i | 0.191950 | − | 0.332468i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.24028 | + | 7.34438i | 0.136147 | + | 0.235814i | ||||
\(971\) | −6.28902 | + | 10.8929i | −0.201824 | + | 0.349570i | −0.949116 | − | 0.314926i | \(-0.898020\pi\) |
0.747292 | + | 0.664496i | \(0.231354\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.15687 | + | 3.73581i | 0.0691461 | + | 0.119764i | ||||
\(974\) | −0.200804 | −0.00643417 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.61229 | + | 11.4528i | −0.211654 | + | 0.366596i | ||||
\(977\) | −18.8495 | + | 32.6483i | −0.603050 | + | 1.04451i | 0.389307 | + | 0.921108i | \(0.372715\pi\) |
−0.992356 | + | 0.123405i | \(0.960619\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.54338 | − | 11.3335i | 0.209127 | − | 0.362219i | ||||
\(980\) | 45.9366 | 1.46739 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.36185 | + | 2.35879i | 0.0434583 | + | 0.0752719i | ||||
\(983\) | 23.2447 | 0.741390 | 0.370695 | − | 0.928755i | \(-0.379119\pi\) | ||||
0.370695 | + | 0.928755i | \(0.379119\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.69996 | − | 8.14056i | −0.149753 | − | 0.259380i | ||||
\(986\) | 5.70970 | + | 9.88950i | 0.181834 | + | 0.314946i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.0631 | − | 3.80927i | −0.320151 | − | 0.121189i | ||||
\(989\) | −45.0968 | −1.43400 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.8484 | + | 20.5220i | −0.376376 | + | 0.651903i | −0.990532 | − | 0.137282i | \(-0.956163\pi\) |
0.614156 | + | 0.789185i | \(0.289497\pi\) | |||||||
\(992\) | 17.5293 | − | 30.3616i | 0.556555 | − | 0.963982i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.03755 | −0.0329091 | ||||||||
\(995\) | 0.377957 | − | 0.654641i | 0.0119820 | − | 0.0207535i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.46564 | − | 16.3950i | 0.299780 | − | 0.519234i | −0.676306 | − | 0.736621i | \(-0.736420\pi\) |
0.976085 | + | 0.217387i | \(0.0697535\pi\) | |||||||
\(998\) | −2.21559 | − | 3.83752i | −0.0701333 | − | 0.121475i | ||||
\(999\) | 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 | 513.2.h.c.334.8 | 32 | ||
3.2 | odd | 2 | 171.2.h.c.49.9 | yes | 32 | ||
9.2 | odd | 6 | 171.2.g.c.106.8 | ✓ | 32 | ||
9.7 | even | 3 | 513.2.g.c.505.9 | 32 | |||
19.7 | even | 3 | 513.2.g.c.64.9 | 32 | |||
57.26 | odd | 6 | 171.2.g.c.121.8 | yes | 32 | ||
171.7 | even | 3 | inner | 513.2.h.c.235.8 | 32 | ||
171.83 | odd | 6 | 171.2.h.c.7.9 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.2.g.c.106.8 | ✓ | 32 | 9.2 | odd | 6 | ||
171.2.g.c.121.8 | yes | 32 | 57.26 | odd | 6 | ||
171.2.h.c.7.9 | yes | 32 | 171.83 | odd | 6 | ||
171.2.h.c.49.9 | yes | 32 | 3.2 | odd | 2 | ||
513.2.g.c.64.9 | 32 | 19.7 | even | 3 | |||
513.2.g.c.505.9 | 32 | 9.7 | even | 3 | |||
513.2.h.c.235.8 | 32 | 171.7 | even | 3 | inner | ||
513.2.h.c.334.8 | 32 | 1.1 | even | 1 | trivial |