Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(165,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 8x^{14} + 45x^{12} + 124x^{10} + 248x^{8} + 250x^{6} + 177x^{4} + 14x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 471.2 | ||
Root | \(-0.558788 + 0.967849i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.471 |
Dual form | 637.2.h.m.165.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.33152 | −1.64863 | −0.824315 | − | 0.566131i | \(-0.808440\pi\) | ||||
−0.824315 | + | 0.566131i | \(0.808440\pi\) | |||||||
\(3\) | 1.15450 | − | 1.99966i | 0.666553 | − | 1.15450i | −0.312309 | − | 0.949981i | \(-0.601102\pi\) |
0.978862 | − | 0.204523i | \(-0.0655643\pi\) | |||||||
\(4\) | 3.43596 | 1.71798 | ||||||||
\(5\) | 1.68556 | − | 2.91947i | 0.753804 | − | 1.30563i | −0.192162 | − | 0.981363i | \(-0.561550\pi\) |
0.945966 | − | 0.324264i | \(-0.105117\pi\) | |||||||
\(6\) | −2.69174 | + | 4.66224i | −1.09890 | + | 1.90335i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.34797 | −1.18369 | ||||||||
\(9\) | −1.16576 | − | 2.01915i | −0.388586 | − | 0.673050i | ||||
\(10\) | −3.92990 | + | 6.80679i | −1.24274 | + | 2.15250i | ||||
\(11\) | −1.16576 | + | 2.01915i | −0.351489 | + | 0.608797i | −0.986511 | − | 0.163697i | \(-0.947658\pi\) |
0.635021 | + | 0.772494i | \(0.280991\pi\) | |||||||
\(12\) | 3.96683 | − | 6.87075i | 1.14513 | − | 1.98342i | ||||
\(13\) | −0.408029 | − | 3.58239i | −0.113167 | − | 0.993576i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.89197 | − | 6.74108i | −1.00490 | − | 1.74054i | ||||
\(16\) | 0.933914 | 0.233479 | ||||||||
\(17\) | 5.45734 | 1.32360 | 0.661800 | − | 0.749681i | \(-0.269793\pi\) | ||||
0.661800 | + | 0.749681i | \(0.269793\pi\) | |||||||
\(18\) | 2.71798 | + | 4.70768i | 0.640634 | + | 1.10961i | ||||
\(19\) | −3.58410 | − | 6.20784i | −0.822248 | − | 1.42418i | −0.904004 | − | 0.427523i | \(-0.859386\pi\) |
0.0817564 | − | 0.996652i | \(-0.473947\pi\) | |||||||
\(20\) | 5.79151 | − | 10.0312i | 1.29502 | − | 2.24304i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.71798 | − | 4.70768i | 0.579476 | − | 1.00368i | ||||
\(23\) | −6.45242 | −1.34542 | −0.672711 | − | 0.739905i | \(-0.734870\pi\) | ||||
−0.672711 | + | 0.739905i | \(0.734870\pi\) | |||||||
\(24\) | −3.86524 | + | 6.69480i | −0.788989 | + | 1.36657i | ||||
\(25\) | −3.18221 | − | 5.51175i | −0.636442 | − | 1.10235i | ||||
\(26\) | 0.951325 | + | 8.35239i | 0.186570 | + | 1.63804i | ||||
\(27\) | 1.54354 | 0.297054 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.22143 | + | 7.31174i | 0.783900 | + | 1.35776i | 0.929654 | + | 0.368434i | \(0.120106\pi\) |
−0.145753 | + | 0.989321i | \(0.546561\pi\) | |||||||
\(30\) | 9.07418 | + | 15.7169i | 1.65671 | + | 2.86951i | ||||
\(31\) | −1.52560 | − | 2.64242i | −0.274007 | − | 0.474593i | 0.695877 | − | 0.718161i | \(-0.255016\pi\) |
−0.969884 | + | 0.243567i | \(0.921682\pi\) | |||||||
\(32\) | 4.51850 | 0.798766 | ||||||||
\(33\) | 2.69174 | + | 4.66224i | 0.468572 | + | 0.811591i | ||||
\(34\) | −12.7239 | −2.18213 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.00550 | − | 6.93773i | −0.667583 | − | 1.15629i | ||||
\(37\) | 3.05653 | 0.502491 | 0.251246 | − | 0.967923i | \(-0.419160\pi\) | ||||
0.251246 | + | 0.967923i | \(0.419160\pi\) | |||||||
\(38\) | 8.35637 | + | 14.4737i | 1.35558 | + | 2.34794i | ||||
\(39\) | −7.63463 | − | 3.31996i | −1.22252 | − | 0.531620i | ||||
\(40\) | −5.64320 | + | 9.77430i | −0.892268 | + | 1.54545i | ||||
\(41\) | −0.468833 | − | 0.812043i | −0.0732194 | − | 0.126820i | 0.827091 | − | 0.562068i | \(-0.189994\pi\) |
−0.900311 | + | 0.435248i | \(0.856661\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.04605 | − | 3.54385i | 0.312019 | − | 0.540433i | −0.666780 | − | 0.745254i | \(-0.732328\pi\) |
0.978799 | + | 0.204822i | \(0.0656614\pi\) | |||||||
\(44\) | −4.00550 | + | 6.93773i | −0.603852 | + | 1.04590i | ||||
\(45\) | −7.85981 | −1.17167 | ||||||||
\(46\) | 15.0439 | 2.21810 | ||||||||
\(47\) | −1.73168 | + | 2.99936i | −0.252591 | + | 0.437501i | −0.964239 | − | 0.265036i | \(-0.914616\pi\) |
0.711647 | + | 0.702537i | \(0.247950\pi\) | |||||||
\(48\) | 1.07821 | − | 1.86751i | 0.155626 | − | 0.269552i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 7.41937 | + | 12.8507i | 1.04926 | + | 1.81737i | ||||
\(51\) | 6.30052 | − | 10.9128i | 0.882249 | − | 1.52810i | ||||
\(52\) | −1.40197 | − | 12.3090i | −0.194418 | − | 1.70695i | ||||
\(53\) | 1.17194 | + | 2.02985i | 0.160978 | + | 0.278822i | 0.935220 | − | 0.354068i | \(-0.115202\pi\) |
−0.774242 | + | 0.632890i | \(0.781869\pi\) | |||||||
\(54\) | −3.59878 | −0.489732 | ||||||||
\(55\) | 3.92990 | + | 6.80679i | 0.529908 | + | 0.917828i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.5514 | −2.19229 | ||||||||
\(58\) | −9.84233 | − | 17.0474i | −1.29236 | − | 2.23844i | ||||
\(59\) | −7.24693 | −0.943470 | −0.471735 | − | 0.881740i | \(-0.656372\pi\) | ||||
−0.471735 | + | 0.881740i | \(0.656372\pi\) | |||||||
\(60\) | −13.3726 | − | 23.1621i | −1.72640 | − | 2.99022i | ||||
\(61\) | 3.19506 | + | 5.53401i | 0.409086 | + | 0.708558i | 0.994788 | − | 0.101969i | \(-0.0325143\pi\) |
−0.585702 | + | 0.810527i | \(0.699181\pi\) | |||||||
\(62\) | 3.55697 | + | 6.16085i | 0.451736 | + | 0.782429i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.4028 | −1.55035 | ||||||||
\(65\) | −11.1464 | − | 4.84710i | −1.38255 | − | 0.601208i | ||||
\(66\) | −6.27584 | − | 10.8701i | −0.772502 | − | 1.33801i | ||||
\(67\) | −2.30670 | + | 3.99532i | −0.281808 | + | 0.488106i | −0.971830 | − | 0.235682i | \(-0.924268\pi\) |
0.690022 | + | 0.723788i | \(0.257601\pi\) | |||||||
\(68\) | 18.7512 | 2.27392 | ||||||||
\(69\) | −7.44934 | + | 12.9026i | −0.896795 | + | 1.55329i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.79370 | − | 6.57088i | 0.450229 | − | 0.779819i | −0.548171 | − | 0.836366i | \(-0.684676\pi\) |
0.998400 | + | 0.0565468i | \(0.0180090\pi\) | |||||||
\(72\) | 3.90292 | + | 6.76006i | 0.459964 | + | 0.796680i | ||||
\(73\) | −1.03498 | − | 1.79264i | −0.121136 | − | 0.209813i | 0.799080 | − | 0.601224i | \(-0.205320\pi\) |
−0.920216 | + | 0.391412i | \(0.871987\pi\) | |||||||
\(74\) | −7.12636 | −0.828422 | ||||||||
\(75\) | −14.6955 | −1.69689 | ||||||||
\(76\) | −12.3148 | − | 21.3299i | −1.41261 | − | 2.44671i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 17.8002 | + | 7.74054i | 2.01548 | + | 0.876444i | ||||
\(79\) | 3.79434 | − | 6.57199i | 0.426897 | − | 0.739407i | −0.569699 | − | 0.821854i | \(-0.692940\pi\) |
0.996595 | + | 0.0824467i | \(0.0262734\pi\) | |||||||
\(80\) | 1.57417 | − | 2.72654i | 0.175997 | − | 0.304836i | ||||
\(81\) | 5.27929 | − | 9.14400i | 0.586588 | − | 1.01600i | ||||
\(82\) | 1.09309 | + | 1.89329i | 0.120712 | + | 0.209079i | ||||
\(83\) | 2.89335 | 0.317587 | 0.158793 | − | 0.987312i | \(-0.449240\pi\) | ||||
0.158793 | + | 0.987312i | \(0.449240\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.19866 | − | 15.9326i | 0.997735 | − | 1.72813i | ||||
\(86\) | −4.77039 | + | 8.26255i | −0.514404 | + | 0.890974i | ||||
\(87\) | 19.4946 | 2.09004 | ||||||||
\(88\) | 3.90292 | − | 6.76006i | 0.416053 | − | 0.720624i | ||||
\(89\) | −13.1597 | −1.39492 | −0.697461 | − | 0.716622i | \(-0.745687\pi\) | ||||
−0.697461 | + | 0.716622i | \(0.745687\pi\) | |||||||
\(90\) | 18.3253 | 1.93165 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −22.1703 | −2.31141 | ||||||||
\(93\) | −7.04526 | −0.730560 | ||||||||
\(94\) | 4.03744 | − | 6.99305i | 0.416430 | − | 0.721278i | ||||
\(95\) | −24.1648 | −2.47926 | ||||||||
\(96\) | 5.21663 | − | 9.03546i | 0.532420 | − | 0.922178i | ||||
\(97\) | −1.77856 | + | 3.08056i | −0.180585 | + | 0.312783i | −0.942080 | − | 0.335388i | \(-0.891133\pi\) |
0.761495 | + | 0.648171i | \(0.224466\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.43596 | 0.546335 | ||||||||
\(100\) | −10.9340 | − | 18.9382i | −1.09340 | − | 1.89382i | ||||
\(101\) | 2.36432 | − | 4.09513i | 0.235259 | − | 0.407481i | −0.724089 | − | 0.689707i | \(-0.757740\pi\) |
0.959348 | + | 0.282226i | \(0.0910728\pi\) | |||||||
\(102\) | −14.6898 | + | 25.4434i | −1.45450 | + | 2.51927i | ||||
\(103\) | −2.99143 | + | 5.18131i | −0.294754 | + | 0.510529i | −0.974928 | − | 0.222522i | \(-0.928571\pi\) |
0.680173 | + | 0.733051i | \(0.261904\pi\) | |||||||
\(104\) | 1.36607 | + | 11.9937i | 0.133954 | + | 1.17608i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.73239 | − | 4.73263i | −0.265393 | − | 0.459674i | ||||
\(107\) | 13.1826 | 1.27441 | 0.637206 | − | 0.770694i | \(-0.280090\pi\) | ||||
0.637206 | + | 0.770694i | \(0.280090\pi\) | |||||||
\(108\) | 5.30353 | 0.510333 | ||||||||
\(109\) | −2.05772 | − | 3.56408i | −0.197094 | − | 0.341377i | 0.750491 | − | 0.660881i | \(-0.229817\pi\) |
−0.947585 | + | 0.319504i | \(0.896484\pi\) | |||||||
\(110\) | −9.16263 | − | 15.8701i | −0.873623 | − | 1.51316i | ||||
\(111\) | 3.52878 | − | 6.11203i | 0.334937 | − | 0.580128i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.14026 | + | 12.3673i | −0.671699 | + | 1.16342i | 0.305723 | + | 0.952121i | \(0.401102\pi\) |
−0.977422 | + | 0.211297i | \(0.932231\pi\) | |||||||
\(114\) | 38.5899 | 3.61427 | ||||||||
\(115\) | −10.8759 | + | 18.8376i | −1.01418 | + | 1.75662i | ||||
\(116\) | 14.5047 | + | 25.1229i | 1.34673 | + | 2.33260i | ||||
\(117\) | −6.75772 | + | 5.00007i | −0.624752 | + | 0.462257i | ||||
\(118\) | 16.8963 | 1.55543 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 13.0302 | + | 22.5689i | 1.18949 | + | 2.06025i | ||||
\(121\) | 2.78202 | + | 4.81860i | 0.252911 | + | 0.438054i | ||||
\(122\) | −7.44934 | − | 12.9026i | −0.674431 | − | 1.16815i | ||||
\(123\) | −2.16508 | −0.195219 | ||||||||
\(124\) | −5.24192 | − | 9.07927i | −0.470738 | − | 0.815343i | ||||
\(125\) | −4.59963 | −0.411403 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.53854 | + | 9.59304i | 0.491466 | + | 0.851244i | 0.999952 | − | 0.00982616i | \(-0.00312781\pi\) |
−0.508486 | + | 0.861071i | \(0.669794\pi\) | |||||||
\(128\) | 19.8803 | 1.75718 | ||||||||
\(129\) | −4.72433 | − | 8.18279i | −0.415954 | − | 0.720454i | ||||
\(130\) | 25.9881 | + | 11.3011i | 2.27931 | + | 0.991170i | ||||
\(131\) | −0.336006 | + | 0.581979i | −0.0293570 | + | 0.0508478i | −0.880331 | − | 0.474361i | \(-0.842679\pi\) |
0.850974 | + | 0.525208i | \(0.176013\pi\) | |||||||
\(132\) | 9.24873 | + | 16.0193i | 0.804998 | + | 1.39430i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.37810 | − | 9.31515i | 0.464597 | − | 0.804706i | ||||
\(135\) | 2.60172 | − | 4.50631i | 0.223920 | − | 0.387842i | ||||
\(136\) | −18.2710 | −1.56673 | ||||||||
\(137\) | 7.83875 | 0.669709 | 0.334855 | − | 0.942270i | \(-0.391313\pi\) | ||||
0.334855 | + | 0.942270i | \(0.391313\pi\) | |||||||
\(138\) | 17.3682 | − | 30.0827i | 1.47848 | − | 2.56081i | ||||
\(139\) | 1.63760 | − | 2.83641i | 0.138900 | − | 0.240581i | −0.788181 | − | 0.615444i | \(-0.788977\pi\) |
0.927080 | + | 0.374863i | \(0.122310\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.99846 | + | 6.92554i | 0.336731 | + | 0.583236i | ||||
\(142\) | −8.84506 | + | 15.3201i | −0.742261 | + | 1.28563i | ||||
\(143\) | 7.70905 | + | 3.35233i | 0.644663 | + | 0.280336i | ||||
\(144\) | −1.08872 | − | 1.88571i | −0.0907265 | − | 0.157143i | ||||
\(145\) | 28.4619 | 2.36363 | ||||||||
\(146\) | 2.41308 | + | 4.17957i | 0.199708 | + | 0.345904i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.5021 | 0.863270 | ||||||||
\(149\) | 7.08186 | + | 12.2661i | 0.580169 | + | 1.00488i | 0.995459 | + | 0.0951925i | \(0.0303467\pi\) |
−0.415290 | + | 0.909689i | \(0.636320\pi\) | |||||||
\(150\) | 34.2628 | 2.79754 | ||||||||
\(151\) | 0.673125 | + | 1.16589i | 0.0547781 | + | 0.0948785i | 0.892114 | − | 0.451810i | \(-0.149222\pi\) |
−0.837336 | + | 0.546689i | \(0.815888\pi\) | |||||||
\(152\) | 11.9994 | + | 20.7836i | 0.973283 | + | 1.68578i | ||||
\(153\) | −6.36194 | − | 11.0192i | −0.514332 | − | 0.890849i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.2860 | −0.826190 | ||||||||
\(156\) | −26.2323 | − | 11.4073i | −2.10026 | − | 0.913313i | ||||
\(157\) | −6.52006 | − | 11.2931i | −0.520357 | − | 0.901285i | −0.999720 | − | 0.0236682i | \(-0.992465\pi\) |
0.479363 | − | 0.877617i | \(-0.340868\pi\) | |||||||
\(158\) | −8.84657 | + | 15.3227i | −0.703795 | + | 1.21901i | ||||
\(159\) | 5.41202 | 0.429201 | ||||||||
\(160\) | 7.61620 | − | 13.1916i | 0.602113 | − | 1.04289i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −12.3087 | + | 21.3194i | −0.967067 | + | 1.67501i | ||||
\(163\) | −2.46628 | − | 4.27172i | −0.193174 | − | 0.334587i | 0.753127 | − | 0.657876i | \(-0.228545\pi\) |
−0.946300 | + | 0.323289i | \(0.895211\pi\) | |||||||
\(164\) | −1.61089 | − | 2.79015i | −0.125790 | − | 0.217874i | ||||
\(165\) | 18.1484 | 1.41285 | ||||||||
\(166\) | −6.74590 | −0.523583 | ||||||||
\(167\) | 1.82128 | + | 3.15455i | 0.140935 | + | 0.244107i | 0.927849 | − | 0.372956i | \(-0.121656\pi\) |
−0.786914 | + | 0.617063i | \(0.788322\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6670 | + | 2.92344i | −0.974387 | + | 0.224880i | ||||
\(170\) | −21.4468 | + | 37.1470i | −1.64490 | + | 2.84904i | ||||
\(171\) | −8.35637 | + | 14.4737i | −0.639028 | + | 1.10683i | ||||
\(172\) | 7.03014 | − | 12.1766i | 0.536043 | − | 0.928453i | ||||
\(173\) | 6.34584 | + | 10.9913i | 0.482465 | + | 0.835654i | 0.999797 | − | 0.0201306i | \(-0.00640819\pi\) |
−0.517332 | + | 0.855785i | \(0.673075\pi\) | |||||||
\(174\) | −45.4520 | −3.44571 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.08872 | + | 1.88571i | −0.0820652 | + | 0.142141i | ||||
\(177\) | −8.36661 | + | 14.4914i | −0.628873 | + | 1.08924i | ||||
\(178\) | 30.6820 | 2.29971 | ||||||||
\(179\) | 4.39469 | − | 7.61183i | 0.328475 | − | 0.568935i | −0.653735 | − | 0.756724i | \(-0.726799\pi\) |
0.982209 | + | 0.187789i | \(0.0601321\pi\) | |||||||
\(180\) | −27.0060 | −2.01291 | ||||||||
\(181\) | 17.1982 | 1.27833 | 0.639167 | − | 0.769068i | \(-0.279279\pi\) | ||||
0.639167 | + | 0.769068i | \(0.279279\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.7548 | 1.09071 | ||||||||
\(184\) | 21.6025 | 1.59256 | ||||||||
\(185\) | 5.15197 | − | 8.92347i | 0.378780 | − | 0.656066i | ||||
\(186\) | 16.4261 | 1.20442 | ||||||||
\(187\) | −6.36194 | + | 11.0192i | −0.465231 | + | 0.805804i | ||||
\(188\) | −5.94999 | + | 10.3057i | −0.433947 | + | 0.751619i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 56.3406 | 4.08738 | ||||||||
\(191\) | −0.533902 | − | 0.924745i | −0.0386318 | − | 0.0669122i | 0.846063 | − | 0.533083i | \(-0.178967\pi\) |
−0.884695 | + | 0.466171i | \(0.845633\pi\) | |||||||
\(192\) | −14.3191 | + | 24.8013i | −1.03339 | + | 1.78988i | ||||
\(193\) | −1.57790 | + | 2.73300i | −0.113580 | + | 0.196726i | −0.917211 | − | 0.398402i | \(-0.869565\pi\) |
0.803631 | + | 0.595127i | \(0.202898\pi\) | |||||||
\(194\) | 4.14674 | − | 7.18237i | 0.297719 | − | 0.515664i | ||||
\(195\) | −22.5611 | + | 16.6931i | −1.61564 | + | 1.19542i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.84783 | + | 15.3249i | 0.630382 | + | 1.09185i | 0.987474 | + | 0.157784i | \(0.0504351\pi\) |
−0.357092 | + | 0.934069i | \(0.616232\pi\) | |||||||
\(198\) | −12.6740 | −0.900704 | ||||||||
\(199\) | −12.9895 | −0.920803 | −0.460402 | − | 0.887711i | \(-0.652295\pi\) | ||||
−0.460402 | + | 0.887711i | \(0.652295\pi\) | |||||||
\(200\) | 10.6539 | + | 18.4532i | 0.753348 | + | 1.30484i | ||||
\(201\) | 5.32619 | + | 9.22522i | 0.375680 | + | 0.650697i | ||||
\(202\) | −5.51246 | + | 9.54785i | −0.387855 | + | 0.671785i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 21.6484 | − | 37.4960i | 1.51569 | − | 2.62525i | ||||
\(205\) | −3.16098 | −0.220773 | ||||||||
\(206\) | 6.97456 | − | 12.0803i | 0.485941 | − | 0.841674i | ||||
\(207\) | 7.52195 | + | 13.0284i | 0.522812 | + | 0.905537i | ||||
\(208\) | −0.381064 | − | 3.34565i | −0.0264220 | − | 0.231979i | ||||
\(209\) | 16.7127 | 1.15605 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.7701 | − | 23.8505i | −0.947974 | − | 1.64194i | −0.749685 | − | 0.661795i | \(-0.769795\pi\) |
−0.198289 | − | 0.980144i | \(-0.563538\pi\) | |||||||
\(212\) | 4.02673 | + | 6.97450i | 0.276557 | + | 0.479011i | ||||
\(213\) | −8.75967 | − | 15.1722i | −0.600203 | − | 1.03958i | ||||
\(214\) | −30.7355 | −2.10103 | ||||||||
\(215\) | −6.89746 | − | 11.9467i | −0.470403 | − | 0.814761i | ||||
\(216\) | −5.16771 | −0.351618 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.79761 | + | 8.30971i | 0.324935 | + | 0.562805i | ||||
\(219\) | −4.77956 | −0.322973 | ||||||||
\(220\) | 13.5030 | + | 23.3879i | 0.910372 | + | 1.57681i | ||||
\(221\) | −2.22675 | − | 19.5503i | −0.149788 | − | 1.31510i | ||||
\(222\) | −8.22740 | + | 14.2503i | −0.552187 | + | 0.956416i | ||||
\(223\) | −4.35098 | − | 7.53612i | −0.291363 | − | 0.504656i | 0.682769 | − | 0.730634i | \(-0.260776\pi\) |
−0.974132 | + | 0.225978i | \(0.927442\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.41937 | + | 12.8507i | −0.494625 | + | 0.856715i | ||||
\(226\) | 16.6476 | − | 28.8345i | 1.10738 | − | 1.91805i | ||||
\(227\) | 21.9669 | 1.45800 | 0.728998 | − | 0.684516i | \(-0.239987\pi\) | ||||
0.728998 | + | 0.684516i | \(0.239987\pi\) | |||||||
\(228\) | −56.8700 | −3.76631 | ||||||||
\(229\) | 10.2594 | − | 17.7698i | 0.677959 | − | 1.17426i | −0.297636 | − | 0.954679i | \(-0.596198\pi\) |
0.975595 | − | 0.219580i | \(-0.0704685\pi\) | |||||||
\(230\) | 25.3574 | − | 43.9203i | 1.67202 | − | 2.89602i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.1332 | − | 24.4795i | −0.927892 | − | 1.60716i | ||||
\(233\) | 8.64439 | − | 14.9725i | 0.566313 | − | 0.980883i | −0.430613 | − | 0.902537i | \(-0.641703\pi\) |
0.996926 | − | 0.0783463i | \(-0.0249640\pi\) | |||||||
\(234\) | 15.7557 | − | 11.6577i | 1.02998 | − | 0.762090i | ||||
\(235\) | 5.83769 | + | 10.1112i | 0.380809 | + | 0.659581i | ||||
\(236\) | −24.9002 | −1.62086 | ||||||||
\(237\) | −8.76116 | − | 15.1748i | −0.569099 | − | 0.985708i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.25961 | 0.210847 | 0.105423 | − | 0.994427i | \(-0.466380\pi\) | ||||
0.105423 | + | 0.994427i | \(0.466380\pi\) | |||||||
\(240\) | −3.63476 | − | 6.29559i | −0.234623 | − | 0.406379i | ||||
\(241\) | −1.46571 | −0.0944149 | −0.0472074 | − | 0.998885i | \(-0.515032\pi\) | ||||
−0.0472074 | + | 0.998885i | \(0.515032\pi\) | |||||||
\(242\) | −6.48632 | − | 11.2346i | −0.416956 | − | 0.722190i | ||||
\(243\) | −9.87462 | − | 17.1033i | −0.633457 | − | 1.09718i | ||||
\(244\) | 10.9781 | + | 19.0147i | 0.702802 | + | 1.21729i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.04791 | 0.321843 | ||||||||
\(247\) | −20.7765 | + | 15.3726i | −1.32198 | + | 0.978135i | ||||
\(248\) | 5.10768 | + | 8.84676i | 0.324338 | + | 0.561770i | ||||
\(249\) | 3.34039 | − | 5.78572i | 0.211688 | − | 0.366655i | ||||
\(250\) | 10.7241 | 0.678252 | ||||||||
\(251\) | −8.55142 | + | 14.8115i | −0.539761 | + | 0.934894i | 0.459156 | + | 0.888356i | \(0.348152\pi\) |
−0.998917 | + | 0.0465376i | \(0.985181\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.52195 | − | 13.0284i | 0.472901 | − | 0.819089i | ||||
\(254\) | −12.9132 | − | 22.3663i | −0.810246 | − | 1.40339i | ||||
\(255\) | −21.2398 | − | 36.7884i | −1.33009 | − | 2.30378i | ||||
\(256\) | −21.5456 | −1.34660 | ||||||||
\(257\) | 3.85011 | 0.240163 | 0.120082 | − | 0.992764i | \(-0.461684\pi\) | ||||
0.120082 | + | 0.992764i | \(0.461684\pi\) | |||||||
\(258\) | 11.0149 | + | 19.0783i | 0.685755 | + | 1.18776i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −38.2988 | − | 16.6544i | −2.37519 | − | 1.03286i | ||||
\(261\) | 9.84233 | − | 17.0474i | 0.609225 | − | 1.05521i | ||||
\(262\) | 0.783403 | − | 1.35689i | 0.0483988 | − | 0.0838292i | ||||
\(263\) | 15.2579 | − | 26.4275i | 0.940844 | − | 1.62959i | 0.176978 | − | 0.984215i | \(-0.443368\pi\) |
0.763866 | − | 0.645375i | \(-0.223299\pi\) | |||||||
\(264\) | −9.01187 | − | 15.6090i | −0.554642 | − | 0.960669i | ||||
\(265\) | 7.90147 | 0.485383 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.1929 | + | 26.3149i | −0.929790 | + | 1.61044i | ||||
\(268\) | −7.92573 | + | 13.7278i | −0.484141 | + | 0.838557i | ||||
\(269\) | 16.7771 | 1.02292 | 0.511460 | − | 0.859307i | \(-0.329105\pi\) | ||||
0.511460 | + | 0.859307i | \(0.329105\pi\) | |||||||
\(270\) | −6.06595 | + | 10.5065i | −0.369162 | + | 0.639407i | ||||
\(271\) | 31.1772 | 1.89388 | 0.946941 | − | 0.321407i | \(-0.104156\pi\) | ||||
0.946941 | + | 0.321407i | \(0.104156\pi\) | |||||||
\(272\) | 5.09669 | 0.309032 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.2762 | −1.10410 | ||||||||
\(275\) | 14.8387 | 0.894810 | ||||||||
\(276\) | −25.5956 | + | 44.3330i | −1.54068 | + | 2.66853i | ||||
\(277\) | 0.395882 | 0.0237863 | 0.0118931 | − | 0.999929i | \(-0.496214\pi\) | ||||
0.0118931 | + | 0.999929i | \(0.496214\pi\) | |||||||
\(278\) | −3.81810 | + | 6.61314i | −0.228994 | + | 0.396630i | ||||
\(279\) | −3.55697 | + | 6.16085i | −0.212950 | + | 0.368841i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.9459 | −1.36884 | −0.684420 | − | 0.729088i | \(-0.739944\pi\) | ||||
−0.684420 | + | 0.729088i | \(0.739944\pi\) | |||||||
\(282\) | −9.32247 | − | 16.1470i | −0.555145 | − | 0.961540i | ||||
\(283\) | −9.67575 | + | 16.7589i | −0.575164 | + | 0.996213i | 0.420860 | + | 0.907126i | \(0.361728\pi\) |
−0.996024 | + | 0.0890873i | \(0.971605\pi\) | |||||||
\(284\) | 13.0350 | − | 22.5773i | 0.773485 | − | 1.33972i | ||||
\(285\) | −27.8984 | + | 48.3214i | −1.65256 | + | 2.86231i | ||||
\(286\) | −17.9738 | − | 7.81600i | −1.06281 | − | 0.462170i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.26748 | − | 9.12354i | −0.310389 | − | 0.537610i | ||||
\(289\) | 12.7826 | 0.751916 | ||||||||
\(290\) | −66.3593 | −3.89675 | ||||||||
\(291\) | 4.10671 | + | 7.11303i | 0.240740 | + | 0.416973i | ||||
\(292\) | −3.55616 | − | 6.15945i | −0.208109 | − | 0.360455i | ||||
\(293\) | 7.88616 | − | 13.6592i | 0.460715 | − | 0.797981i | −0.538282 | − | 0.842765i | \(-0.680926\pi\) |
0.998997 | + | 0.0447835i | \(0.0142598\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.2151 | + | 21.1572i | −0.711192 | + | 1.23182i | ||||
\(296\) | −10.2332 | −0.594792 | ||||||||
\(297\) | −1.79939 | + | 3.11663i | −0.104411 | + | 0.180845i | ||||
\(298\) | −16.5115 | − | 28.5987i | −0.956483 | − | 1.65668i | ||||
\(299\) | 2.63277 | + | 23.1151i | 0.152257 | + | 1.33678i | ||||
\(300\) | −50.4932 | −2.91523 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.56940 | − | 2.71828i | −0.0903089 | − | 0.156420i | ||||
\(303\) | −5.45924 | − | 9.45568i | −0.313625 | − | 0.543215i | ||||
\(304\) | −3.34724 | − | 5.79759i | −0.191977 | − | 0.332515i | ||||
\(305\) | 21.5419 | 1.23348 | ||||||||
\(306\) | 14.8330 | + | 25.6914i | 0.847943 | + | 1.46868i | ||||
\(307\) | 19.2535 | 1.09885 | 0.549427 | − | 0.835542i | \(-0.314846\pi\) | ||||
0.549427 | + | 0.835542i | \(0.314846\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.90723 | + | 11.9637i | 0.392939 | + | 0.680590i | ||||
\(310\) | 23.9819 | 1.36208 | ||||||||
\(311\) | −1.53232 | − | 2.65405i | −0.0868898 | − | 0.150498i | 0.819305 | − | 0.573358i | \(-0.194359\pi\) |
−0.906195 | + | 0.422860i | \(0.861026\pi\) | |||||||
\(312\) | 25.5605 | + | 11.1151i | 1.44708 | + | 0.629271i | ||||
\(313\) | 17.6376 | − | 30.5492i | 0.996934 | − | 1.72674i | 0.430705 | − | 0.902493i | \(-0.358265\pi\) |
0.566229 | − | 0.824248i | \(-0.308402\pi\) | |||||||
\(314\) | 15.2016 | + | 26.3300i | 0.857877 | + | 1.48589i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.0372 | − | 22.5811i | 0.733401 | − | 1.27029i | ||||
\(317\) | −16.3533 | + | 28.3247i | −0.918490 | + | 1.59087i | −0.116781 | + | 0.993158i | \(0.537258\pi\) |
−0.801709 | + | 0.597714i | \(0.796076\pi\) | |||||||
\(318\) | −12.6182 | −0.707594 | ||||||||
\(319\) | −19.6847 | −1.10213 | ||||||||
\(320\) | −20.9056 | + | 36.2096i | −1.16866 | + | 2.02418i | ||||
\(321\) | 15.2194 | − | 26.3607i | 0.849463 | − | 1.47131i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.5596 | − | 33.8783i | −1.08833 | − | 1.88504i | ||||
\(324\) | 18.1394 | − | 31.4184i | 1.00775 | − | 1.74547i | ||||
\(325\) | −18.4468 | + | 13.6489i | −1.02324 | + | 0.757103i | ||||
\(326\) | 5.75016 | + | 9.95958i | 0.318472 | + | 0.551610i | ||||
\(327\) | −9.50260 | −0.525495 | ||||||||
\(328\) | 1.56964 | + | 2.71869i | 0.0866688 | + | 0.150115i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −42.3132 | −2.32926 | ||||||||
\(331\) | −2.38851 | − | 4.13703i | −0.131285 | − | 0.227392i | 0.792887 | − | 0.609368i | \(-0.208577\pi\) |
−0.924172 | + | 0.381977i | \(0.875244\pi\) | |||||||
\(332\) | 9.94145 | 0.545608 | ||||||||
\(333\) | −3.56318 | − | 6.17161i | −0.195261 | − | 0.338202i | ||||
\(334\) | −4.24635 | − | 7.35489i | −0.232350 | − | 0.402442i | ||||
\(335\) | 7.77615 | + | 13.4687i | 0.424856 | + | 0.735873i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.2392 | 1.42934 | 0.714669 | − | 0.699463i | \(-0.246577\pi\) | ||||
0.714669 | + | 0.699463i | \(0.246577\pi\) | |||||||
\(338\) | 29.5334 | − | 6.81603i | 1.60640 | − | 0.370743i | ||||
\(339\) | 16.4869 | + | 28.5562i | 0.895447 | + | 1.55096i | ||||
\(340\) | 31.6063 | − | 54.7437i | 1.71409 | − | 2.96889i | ||||
\(341\) | 7.11394 | 0.385241 | ||||||||
\(342\) | 19.4830 | − | 33.7456i | 1.05352 | − | 1.82475i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.85010 | + | 11.8647i | −0.369332 | + | 0.639702i | ||||
\(345\) | 25.1126 | + | 43.4963i | 1.35202 | + | 2.34176i | ||||
\(346\) | −14.7954 | − | 25.6264i | −0.795407 | − | 1.37768i | ||||
\(347\) | −10.4442 | −0.560675 | −0.280338 | − | 0.959901i | \(-0.590446\pi\) | ||||
−0.280338 | + | 0.959901i | \(0.590446\pi\) | |||||||
\(348\) | 66.9829 | 3.59066 | ||||||||
\(349\) | −11.7344 | − | 20.3246i | −0.628128 | − | 1.08795i | −0.987927 | − | 0.154920i | \(-0.950488\pi\) |
0.359799 | − | 0.933030i | \(-0.382845\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.629807 | − | 5.52955i | −0.0336166 | − | 0.295145i | ||||
\(352\) | −5.26748 | + | 9.12354i | −0.280758 | + | 0.486286i | ||||
\(353\) | −1.46567 | + | 2.53862i | −0.0780099 | + | 0.135117i | −0.902391 | − | 0.430918i | \(-0.858190\pi\) |
0.824381 | + | 0.566035i | \(0.191523\pi\) | |||||||
\(354\) | 19.5069 | − | 33.7869i | 1.03678 | − | 1.79575i | ||||
\(355\) | −12.7890 | − | 22.1512i | −0.678769 | − | 1.17566i | ||||
\(356\) | −45.2162 | −2.39645 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.2463 | + | 17.7471i | −0.541533 | + | 0.937963i | ||||
\(359\) | 8.55069 | − | 14.8102i | 0.451288 | − | 0.781654i | −0.547178 | − | 0.837016i | \(-0.684298\pi\) |
0.998466 | + | 0.0553624i | \(0.0176314\pi\) | |||||||
\(360\) | 26.3144 | 1.38689 | ||||||||
\(361\) | −16.1915 | + | 28.0445i | −0.852184 | + | 1.47603i | ||||
\(362\) | −40.0979 | −2.10750 | ||||||||
\(363\) | 12.8474 | 0.674314 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.97809 | −0.365250 | ||||||||
\(366\) | −34.4012 | −1.79818 | ||||||||
\(367\) | 0.524301 | − | 0.908115i | 0.0273683 | − | 0.0474032i | −0.852017 | − | 0.523514i | \(-0.824621\pi\) |
0.879385 | + | 0.476111i | \(0.157954\pi\) | |||||||
\(368\) | −6.02600 | −0.314127 | ||||||||
\(369\) | −1.09309 | + | 1.89329i | −0.0569041 | + | 0.0985608i | ||||
\(370\) | −12.0119 | + | 20.8052i | −0.624468 | + | 1.08161i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −24.2073 | −1.25509 | ||||||||
\(373\) | 7.50536 | + | 12.9997i | 0.388613 | + | 0.673098i | 0.992263 | − | 0.124152i | \(-0.0396210\pi\) |
−0.603650 | + | 0.797249i | \(0.706288\pi\) | |||||||
\(374\) | 14.8330 | − | 25.6914i | 0.766994 | − | 1.32847i | ||||
\(375\) | −5.31029 | + | 9.19768i | −0.274222 | + | 0.474966i | ||||
\(376\) | 5.79761 | − | 10.0418i | 0.298989 | − | 0.517864i | ||||
\(377\) | 24.4710 | − | 18.1062i | 1.26032 | − | 0.932517i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.5749 | + | 23.5123i | 0.697294 | + | 1.20775i | 0.969401 | + | 0.245481i | \(0.0789459\pi\) |
−0.272108 | + | 0.962267i | \(0.587721\pi\) | |||||||
\(380\) | −83.0294 | −4.25932 | ||||||||
\(381\) | 25.5771 | 1.31035 | ||||||||
\(382\) | 1.24480 | + | 2.15606i | 0.0636895 | + | 0.110314i | ||||
\(383\) | 8.01320 | + | 13.8793i | 0.409455 | + | 0.709197i | 0.994829 | − | 0.101566i | \(-0.0323854\pi\) |
−0.585373 | + | 0.810764i | \(0.699052\pi\) | |||||||
\(384\) | 22.9519 | − | 39.7538i | 1.17126 | − | 2.02868i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.67890 | − | 6.37203i | 0.187251 | − | 0.324328i | ||||
\(387\) | −9.54077 | −0.484985 | ||||||||
\(388\) | −6.11107 | + | 10.5847i | −0.310242 | + | 0.537356i | ||||
\(389\) | −3.99714 | − | 6.92324i | −0.202663 | − | 0.351022i | 0.746723 | − | 0.665136i | \(-0.231626\pi\) |
−0.949386 | + | 0.314113i | \(0.898293\pi\) | |||||||
\(390\) | 52.6017 | − | 38.9202i | 2.66359 | − | 1.97080i | ||||
\(391\) | −35.2130 | −1.78080 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.775840 | + | 1.34379i | 0.0391360 | + | 0.0677855i | ||||
\(394\) | −20.6289 | − | 35.7302i | −1.03927 | − | 1.80006i | ||||
\(395\) | −12.7912 | − | 22.1550i | −0.643593 | − | 1.11474i | ||||
\(396\) | 18.6778 | 0.938593 | ||||||||
\(397\) | 6.10435 | + | 10.5731i | 0.306369 | + | 0.530646i | 0.977565 | − | 0.210633i | \(-0.0675526\pi\) |
−0.671196 | + | 0.741280i | \(0.734219\pi\) | |||||||
\(398\) | 30.2853 | 1.51806 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.97191 | − | 5.14750i | −0.148596 | − | 0.257375i | ||||
\(401\) | 37.8412 | 1.88970 | 0.944850 | − | 0.327503i | \(-0.106207\pi\) | ||||
0.944850 | + | 0.327503i | \(0.106207\pi\) | |||||||
\(402\) | −12.4181 | − | 21.5087i | −0.619358 | − | 1.07276i | ||||
\(403\) | −8.84370 | + | 6.54349i | −0.440536 | + | 0.325955i | ||||
\(404\) | 8.12373 | − | 14.0707i | 0.404171 | − | 0.700044i | ||||
\(405\) | −17.7971 | − | 30.8255i | −0.884345 | − | 1.53173i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.56318 | + | 6.17161i | −0.176620 | + | 0.305915i | ||||
\(408\) | −21.0939 | + | 36.5358i | −1.04431 | + | 1.80879i | ||||
\(409\) | 0.235074 | 0.0116237 | 0.00581184 | − | 0.999983i | \(-0.498150\pi\) | ||||
0.00581184 | + | 0.999983i | \(0.498150\pi\) | |||||||
\(410\) | 7.36988 | 0.363972 | ||||||||
\(411\) | 9.04986 | − | 15.6748i | 0.446397 | − | 0.773182i | ||||
\(412\) | −10.2784 | + | 17.8028i | −0.506382 | + | 0.877080i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −17.5375 | − | 30.3759i | −0.861923 | − | 1.49290i | ||||
\(415\) | 4.87692 | − | 8.44706i | 0.239398 | − | 0.414650i | ||||
\(416\) | −1.84368 | − | 16.1870i | −0.0903938 | − | 0.793635i | ||||
\(417\) | −3.78124 | − | 6.54930i | −0.185168 | − | 0.320720i | ||||
\(418\) | −38.9660 | −1.90589 | ||||||||
\(419\) | −0.222023 | − | 0.384555i | −0.0108465 | − | 0.0187868i | 0.860551 | − | 0.509364i | \(-0.170119\pi\) |
−0.871398 | + | 0.490577i | \(0.836786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.45998 | 0.461051 | 0.230526 | − | 0.973066i | \(-0.425955\pi\) | ||||
0.230526 | + | 0.973066i | \(0.425955\pi\) | |||||||
\(422\) | 32.1052 | + | 55.6079i | 1.56286 | + | 2.70695i | ||||
\(423\) | 8.07488 | 0.392614 | ||||||||
\(424\) | −3.92361 | − | 6.79588i | −0.190547 | − | 0.330037i | ||||
\(425\) | −17.3664 | − | 30.0795i | −0.842395 | − | 1.45907i | ||||
\(426\) | 20.4233 | + | 35.3742i | 0.989513 | + | 1.71389i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 45.2950 | 2.18942 | ||||||||
\(429\) | 15.6036 | − | 11.5452i | 0.753351 | − | 0.557407i | ||||
\(430\) | 16.0815 | + | 27.8540i | 0.775520 | + | 1.34324i | ||||
\(431\) | −10.7723 | + | 18.6582i | −0.518883 | + | 0.898732i | 0.480876 | + | 0.876789i | \(0.340319\pi\) |
−0.999759 | + | 0.0219436i | \(0.993015\pi\) | |||||||
\(432\) | 1.44153 | 0.0693557 | ||||||||
\(433\) | 6.57949 | − | 11.3960i | 0.316190 | − | 0.547657i | −0.663500 | − | 0.748176i | \(-0.730930\pi\) |
0.979690 | + | 0.200519i | \(0.0642630\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 32.8593 | − | 56.9141i | 1.57548 | − | 2.72882i | ||||
\(436\) | −7.07026 | − | 12.2461i | −0.338604 | − | 0.586479i | ||||
\(437\) | 23.1261 | + | 40.0555i | 1.10627 | + | 1.91612i | ||||
\(438\) | 11.1436 | 0.532463 | ||||||||
\(439\) | −29.7847 | −1.42155 | −0.710773 | − | 0.703422i | \(-0.751655\pi\) | ||||
−0.710773 | + | 0.703422i | \(0.751655\pi\) | |||||||
\(440\) | −13.1572 | − | 22.7889i | −0.627245 | − | 1.08642i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.19171 | + | 45.5819i | 0.246944 | + | 2.16811i | ||||
\(443\) | −7.42333 | + | 12.8576i | −0.352693 | + | 0.610883i | −0.986720 | − | 0.162428i | \(-0.948067\pi\) |
0.634027 | + | 0.773311i | \(0.281401\pi\) | |||||||
\(444\) | 12.1248 | − | 21.0007i | 0.575416 | − | 0.996649i | ||||
\(445\) | −22.1814 | + | 38.4193i | −1.05150 | + | 1.82125i | ||||
\(446\) | 10.1444 | + | 17.5706i | 0.480351 | + | 0.831992i | ||||
\(447\) | 32.7041 | 1.54685 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.1114 | − | 22.7095i | 0.618763 | − | 1.07173i | −0.370949 | − | 0.928653i | \(-0.620968\pi\) |
0.989712 | − | 0.143075i | \(-0.0456992\pi\) | |||||||
\(450\) | 17.2984 | − | 29.9617i | 0.815454 | − | 1.41241i | ||||
\(451\) | 2.18618 | 0.102943 | ||||||||
\(452\) | −24.5337 | + | 42.4936i | −1.15397 | + | 1.99873i | ||||
\(453\) | 3.10850 | 0.146050 | ||||||||
\(454\) | −51.2162 | −2.40369 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 55.4136 | 2.59498 | ||||||||
\(457\) | −15.8708 | −0.742406 | −0.371203 | − | 0.928552i | \(-0.621055\pi\) | ||||
−0.371203 | + | 0.928552i | \(0.621055\pi\) | |||||||
\(458\) | −23.9199 | + | 41.4305i | −1.11770 | + | 1.93592i | ||||
\(459\) | 8.42361 | 0.393180 | ||||||||
\(460\) | −37.3693 | + | 64.7255i | −1.74235 | + | 3.01784i | ||||
\(461\) | −11.0443 | + | 19.1293i | −0.514384 | + | 0.890940i | 0.485476 | + | 0.874250i | \(0.338646\pi\) |
−0.999861 | + | 0.0166900i | \(0.994687\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.2887 | 0.849949 | 0.424974 | − | 0.905205i | \(-0.360283\pi\) | ||||
0.424974 | + | 0.905205i | \(0.360283\pi\) | |||||||
\(464\) | 3.94246 | + | 6.82854i | 0.183024 | + | 0.317007i | ||||
\(465\) | −11.8752 | + | 20.5685i | −0.550699 | + | 0.953839i | ||||
\(466\) | −20.1545 | + | 34.9087i | −0.933641 | + | 1.61711i | ||||
\(467\) | −2.26659 | + | 3.92585i | −0.104885 | + | 0.181667i | −0.913691 | − | 0.406409i | \(-0.866781\pi\) |
0.808806 | + | 0.588076i | \(0.200114\pi\) | |||||||
\(468\) | −23.2193 | + | 17.1801i | −1.07331 | + | 0.794148i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −13.6107 | − | 23.5744i | −0.627813 | − | 1.08740i | ||||
\(471\) | −30.1097 | −1.38738 | ||||||||
\(472\) | 24.2625 | 1.11677 | ||||||||
\(473\) | 4.77039 | + | 8.26255i | 0.219343 | + | 0.379912i | ||||
\(474\) | 20.4268 | + | 35.3802i | 0.938233 | + | 1.62507i | ||||
\(475\) | −22.8107 | + | 39.5093i | −1.04663 | + | 1.81281i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.73239 | − | 4.73263i | 0.125107 | − | 0.216692i | ||||
\(478\) | −7.59984 | −0.347609 | ||||||||
\(479\) | 5.22303 | − | 9.04655i | 0.238646 | − | 0.413347i | −0.721680 | − | 0.692227i | \(-0.756630\pi\) |
0.960326 | + | 0.278880i | \(0.0899630\pi\) | |||||||
\(480\) | −17.5859 | − | 30.4596i | −0.802681 | − | 1.39028i | ||||
\(481\) | −1.24715 | − | 10.9497i | −0.0568653 | − | 0.499263i | ||||
\(482\) | 3.41733 | 0.155655 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.55891 | + | 16.5565i | 0.434496 | + | 0.752569i | ||||
\(485\) | 5.99573 | + | 10.3849i | 0.272252 | + | 0.471555i | ||||
\(486\) | 23.0228 | + | 39.8767i | 1.04434 | + | 1.80884i | ||||
\(487\) | 35.9143 | 1.62743 | 0.813715 | − | 0.581263i | \(-0.197441\pi\) | ||||
0.813715 | + | 0.581263i | \(0.197441\pi\) | |||||||
\(488\) | −10.6970 | − | 18.5277i | −0.484229 | − | 0.838710i | ||||
\(489\) | −11.3893 | −0.515042 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.85124 | − | 6.67054i | −0.173804 | − | 0.301037i | 0.765943 | − | 0.642909i | \(-0.222273\pi\) |
−0.939747 | + | 0.341871i | \(0.888939\pi\) | |||||||
\(492\) | −7.43913 | −0.335382 | ||||||||
\(493\) | 23.0378 | + | 39.9026i | 1.03757 | + | 1.79712i | ||||
\(494\) | 48.4407 | − | 35.8415i | 2.17945 | − | 1.61258i | ||||
\(495\) | 9.16263 | − | 15.8701i | 0.411830 | − | 0.713310i | ||||
\(496\) | −1.42478 | − | 2.46780i | −0.0639747 | − | 0.110807i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.78816 | + | 13.4895i | −0.348996 | + | 0.604479i | ||||
\(499\) | −4.24539 | + | 7.35323i | −0.190050 | + | 0.329176i | −0.945266 | − | 0.326299i | \(-0.894198\pi\) |
0.755217 | + | 0.655475i | \(0.227532\pi\) | |||||||
\(500\) | −15.8041 | −0.706783 | ||||||||
\(501\) | 8.41071 | 0.375763 | ||||||||
\(502\) | 19.9378 | − | 34.5332i | 0.889866 | − | 1.54129i | ||||
\(503\) | −15.2000 | + | 26.3272i | −0.677736 | + | 1.17387i | 0.297924 | + | 0.954589i | \(0.403706\pi\) |
−0.975661 | + | 0.219285i | \(0.929628\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.97041 | − | 13.8052i | −0.354679 | − | 0.614321i | ||||
\(506\) | −17.5375 | + | 30.3759i | −0.779639 | + | 1.35037i | ||||
\(507\) | −8.77825 | + | 28.7048i | −0.389856 | + | 1.27483i | ||||
\(508\) | 19.0302 | + | 32.9613i | 0.844330 | + | 1.46242i | ||||
\(509\) | −15.5801 | −0.690578 | −0.345289 | − | 0.938496i | \(-0.612219\pi\) | ||||
−0.345289 | + | 0.938496i | \(0.612219\pi\) | |||||||
\(510\) | 49.5209 | + | 85.7727i | 2.19282 | + | 3.79808i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 10.4733 | 0.462860 | ||||||||
\(513\) | −5.53218 | − | 9.58202i | −0.244252 | − | 0.423057i | ||||
\(514\) | −8.97660 | −0.395941 | ||||||||
\(515\) | 10.0845 | + | 17.4668i | 0.444374 | + | 0.769678i | ||||
\(516\) | −16.2326 | − | 28.1157i | −0.714602 | − | 1.23773i | ||||
\(517\) | −4.03744 | − | 6.99305i | −0.177566 | − | 0.307554i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.3052 | 1.28635 | ||||||||
\(520\) | 37.3179 | + | 16.2279i | 1.63650 | + | 0.711642i | ||||
\(521\) | −13.5787 | − | 23.5190i | −0.594893 | − | 1.03039i | −0.993562 | − | 0.113290i | \(-0.963861\pi\) |
0.398669 | − | 0.917095i | \(-0.369472\pi\) | |||||||
\(522\) | −22.9476 | + | 39.7463i | −1.00439 | + | 1.73965i | ||||
\(523\) | −18.0575 | −0.789598 | −0.394799 | − | 0.918767i | \(-0.629186\pi\) | ||||
−0.394799 | + | 0.918767i | \(0.629186\pi\) | |||||||
\(524\) | −1.15450 | + | 1.99966i | −0.0504347 | + | 0.0873555i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −35.5741 | + | 61.6161i | −1.55110 | + | 2.68659i | ||||
\(527\) | −8.32574 | − | 14.4206i | −0.362675 | − | 0.628172i | ||||
\(528\) | 2.51386 | + | 4.35413i | 0.109402 | + | 0.189489i | ||||
\(529\) | 18.6337 | 0.810160 | ||||||||
\(530\) | −18.4224 | −0.800217 | ||||||||
\(531\) | 8.44816 | + | 14.6326i | 0.366619 | + | 0.635003i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.71776 | + | 2.01088i | −0.117719 | + | 0.0871009i | ||||
\(534\) | 35.4225 | − | 61.3535i | 1.53288 | − | 2.65503i | ||||
\(535\) | 22.2201 | − | 38.4863i | 0.960657 | − | 1.66391i | ||||
\(536\) | 7.72276 | − | 13.3762i | 0.333572 | − | 0.577764i | ||||
\(537\) | −10.1474 | − | 17.5758i | −0.437892 | − | 0.758451i | ||||
\(538\) | −39.1162 | −1.68642 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.93941 | − | 15.4835i | 0.384691 | − | 0.666305i | ||||
\(541\) | −19.9941 | + | 34.6308i | −0.859613 | + | 1.48889i | 0.0126849 | + | 0.999920i | \(0.495962\pi\) |
−0.872298 | + | 0.488974i | \(0.837371\pi\) | |||||||
\(542\) | −72.6902 | −3.12231 | ||||||||
\(543\) | 19.8554 | − | 34.3906i | 0.852077 | − | 1.47584i | ||||
\(544\) | 24.6590 | 1.05725 | ||||||||
\(545\) | −13.8736 | −0.594282 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.6124 | −0.966836 | −0.483418 | − | 0.875390i | \(-0.660605\pi\) | ||||
−0.483418 | + | 0.875390i | \(0.660605\pi\) | |||||||
\(548\) | 26.9336 | 1.15055 | ||||||||
\(549\) | 7.44934 | − | 12.9026i | 0.317930 | − | 0.550671i | ||||
\(550\) | −34.5968 | −1.47521 | ||||||||
\(551\) | 30.2600 | − | 52.4119i | 1.28912 | − | 2.23282i | ||||
\(552\) | 24.9402 | − | 43.1976i | 1.06152 | − | 1.83861i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.923005 | −0.0392147 | ||||||||
\(555\) | −11.8959 | − | 20.6043i | −0.504954 | − | 0.874606i | ||||
\(556\) | 5.62674 | − | 9.74581i | 0.238627 | − | 0.413314i | ||||
\(557\) | 4.98686 | − | 8.63750i | 0.211300 | − | 0.365983i | −0.740822 | − | 0.671702i | \(-0.765564\pi\) |
0.952122 | + | 0.305719i | \(0.0988969\pi\) | |||||||
\(558\) | 8.29313 | − | 14.3641i | 0.351076 | − | 0.608082i | ||||
\(559\) | −13.5303 | − | 5.88374i | −0.572271 | − | 0.248856i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.6898 | + | 25.4434i | 0.620202 | + | 1.07422i | ||||
\(562\) | 53.4988 | 2.25671 | ||||||||
\(563\) | −21.5279 | −0.907294 | −0.453647 | − | 0.891181i | \(-0.649877\pi\) | ||||
−0.453647 | + | 0.891181i | \(0.649877\pi\) | |||||||
\(564\) | 13.7386 | + | 23.7959i | 0.578498 | + | 1.00199i | ||||
\(565\) | 24.0707 | + | 41.6916i | 1.01266 | + | 1.75398i | ||||
\(566\) | 22.5592 | − | 39.0736i | 0.948232 | − | 1.64239i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.7012 | + | 21.9991i | −0.532930 | + | 0.923061i | ||||
\(569\) | −33.1004 | −1.38764 | −0.693819 | − | 0.720149i | \(-0.744073\pi\) | ||||
−0.693819 | + | 0.720149i | \(0.744073\pi\) | |||||||
\(570\) | 65.0454 | − | 112.662i | 2.72445 | − | 4.71889i | ||||
\(571\) | −9.96786 | − | 17.2648i | −0.417142 | − | 0.722511i | 0.578509 | − | 0.815676i | \(-0.303635\pi\) |
−0.995651 | + | 0.0931651i | \(0.970302\pi\) | |||||||
\(572\) | 26.4880 | + | 11.5185i | 1.10752 | + | 0.481611i | ||||
\(573\) | −2.46557 | −0.103001 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.5330 | + | 35.5641i | 0.856283 | + | 1.48313i | ||||
\(576\) | 14.4586 | + | 25.0431i | 0.602443 | + | 1.04346i | ||||
\(577\) | −14.7348 | − | 25.5214i | −0.613416 | − | 1.06247i | −0.990660 | − | 0.136354i | \(-0.956462\pi\) |
0.377244 | − | 0.926114i | \(-0.376872\pi\) | |||||||
\(578\) | −29.8028 | −1.23963 | ||||||||
\(579\) | 3.64338 | + | 6.31052i | 0.151414 | + | 0.262256i | ||||
\(580\) | 97.7939 | 4.06067 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −9.57486 | − | 16.5841i | −0.396891 | − | 0.687435i | ||||
\(583\) | −5.46477 | −0.226328 | ||||||||
\(584\) | 3.46509 | + | 6.00171i | 0.143386 | + | 0.248353i | ||||
\(585\) | 3.20703 | + | 28.1569i | 0.132594 | + | 1.16414i | ||||
\(586\) | −18.3867 | + | 31.8467i | −0.759548 | + | 1.31558i | ||||
\(587\) | −3.49429 | − | 6.05229i | −0.144225 | − | 0.249805i | 0.784859 | − | 0.619675i | \(-0.212736\pi\) |
−0.929084 | + | 0.369870i | \(0.879402\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.9358 | + | 18.9414i | −0.450603 | + | 0.780467i | ||||
\(590\) | 28.4797 | − | 49.3283i | 1.17249 | − | 2.03082i | ||||
\(591\) | 40.8594 | 1.68073 | ||||||||
\(592\) | 2.85454 | 0.117321 | ||||||||
\(593\) | −0.485124 | + | 0.840259i | −0.0199216 | + | 0.0345053i | −0.875814 | − | 0.482648i | \(-0.839675\pi\) |
0.855893 | + | 0.517153i | \(0.173008\pi\) | |||||||
\(594\) | 4.19530 | − | 7.26648i | 0.172135 | − | 0.298147i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 24.3330 | + | 42.1460i | 0.996719 | + | 1.72637i | ||||
\(597\) | −14.9965 | + | 25.9746i | −0.613764 | + | 1.06307i | ||||
\(598\) | −6.13835 | − | 53.8931i | −0.251016 | − | 2.20385i | ||||
\(599\) | 11.2999 | + | 19.5720i | 0.461702 | + | 0.799692i | 0.999046 | − | 0.0436716i | \(-0.0139055\pi\) |
−0.537344 | + | 0.843363i | \(0.680572\pi\) | |||||||
\(600\) | 49.2001 | 2.00858 | ||||||||
\(601\) | 15.2146 | + | 26.3525i | 0.620617 | + | 1.07494i | 0.989371 | + | 0.145414i | \(0.0464513\pi\) |
−0.368754 | + | 0.929527i | \(0.620215\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.7562 | 0.438027 | ||||||||
\(604\) | 2.31283 | + | 4.00594i | 0.0941078 | + | 0.163000i | ||||
\(605\) | 18.7570 | 0.762581 | ||||||||
\(606\) | 12.7283 | + | 22.0461i | 0.517052 | + | 0.895560i | ||||
\(607\) | 16.0788 | + | 27.8493i | 0.652618 | + | 1.13037i | 0.982485 | + | 0.186340i | \(0.0596626\pi\) |
−0.329868 | + | 0.944027i | \(0.607004\pi\) | |||||||
\(608\) | −16.1947 | − | 28.0501i | −0.656784 | − | 1.13758i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −50.2252 | −2.03356 | ||||||||
\(611\) | 11.4514 | + | 4.97973i | 0.463276 | + | 0.201458i | ||||
\(612\) | −21.8594 | − | 37.8616i | −0.883613 | − | 1.53046i | ||||
\(613\) | −6.96043 | + | 12.0558i | −0.281129 | + | 0.486930i | −0.971663 | − | 0.236370i | \(-0.924042\pi\) |
0.690534 | + | 0.723300i | \(0.257376\pi\) | |||||||
\(614\) | −44.8898 | −1.81160 | ||||||||
\(615\) | −3.64937 | + | 6.32089i | −0.147157 | + | 0.254883i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.08394 | − | 8.80565i | 0.204672 | − | 0.354502i | −0.745356 | − | 0.666666i | \(-0.767721\pi\) |
0.950028 | + | 0.312164i | \(0.101054\pi\) | |||||||
\(618\) | −16.1043 | − | 27.8935i | −0.647810 | − | 1.12204i | ||||
\(619\) | 21.8952 | + | 37.9237i | 0.880044 | + | 1.52428i | 0.851291 | + | 0.524694i | \(0.175820\pi\) |
0.0287526 | + | 0.999587i | \(0.490846\pi\) | |||||||
\(620\) | −35.3422 | −1.41938 | ||||||||
\(621\) | −9.95954 | −0.399663 | ||||||||
\(622\) | 3.57262 | + | 6.18796i | 0.143249 | + | 0.248115i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.13009 | − | 3.10056i | −0.285432 | − | 0.124122i | ||||
\(625\) | 8.15812 | − | 14.1303i | 0.326325 | − | 0.565211i | ||||
\(626\) | −41.1223 | + | 71.2258i | −1.64358 | + | 2.84676i | ||||
\(627\) | 19.2949 | − | 33.4198i | 0.770565 | − | 1.33466i | ||||
\(628\) | −22.4027 | − | 38.8026i | −0.893964 | − | 1.54839i | ||||
\(629\) | 16.6806 | 0.665097 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.04464 | + | 13.9337i | −0.320252 | + | 0.554693i | −0.980540 | − | 0.196320i | \(-0.937101\pi\) |
0.660288 | + | 0.751013i | \(0.270434\pi\) | |||||||
\(632\) | −12.7033 | + | 22.0028i | −0.505312 | + | 0.875226i | ||||
\(633\) | −63.5906 | −2.52750 | ||||||||
\(634\) | 38.1279 | − | 66.0394i | 1.51425 | − | 2.62276i | ||||
\(635\) | 37.3421 | 1.48188 | ||||||||
\(636\) | 18.5955 | 0.737359 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 45.8951 | 1.81700 | ||||||||
\(639\) | −17.6901 | −0.699810 | ||||||||
\(640\) | 33.5094 | − | 58.0399i | 1.32457 | − | 2.29423i | ||||
\(641\) | −49.2508 | −1.94529 | −0.972645 | − | 0.232296i | \(-0.925376\pi\) | ||||
−0.972645 | + | 0.232296i | \(0.925376\pi\) | |||||||
\(642\) | −35.4842 | + | 61.4605i | −1.40045 | + | 2.42565i | ||||
\(643\) | 1.33579 | − | 2.31366i | 0.0526784 | − | 0.0912417i | −0.838484 | − | 0.544927i | \(-0.816558\pi\) |
0.891162 | + | 0.453685i | \(0.149891\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −31.8526 | −1.25419 | ||||||||
\(646\) | 45.6036 | + | 78.9877i | 1.79425 | + | 3.10773i | ||||
\(647\) | 16.6814 | − | 28.8930i | 0.655814 | − | 1.13590i | −0.325876 | − | 0.945413i | \(-0.605659\pi\) |
0.981689 | − | 0.190490i | \(-0.0610076\pi\) | |||||||
\(648\) | −17.6749 | + | 30.6138i | −0.694336 | + | 1.20262i | ||||
\(649\) | 8.44816 | − | 14.6326i | 0.331619 | − | 0.574382i | ||||
\(650\) | 43.0090 | − | 31.8226i | 1.68695 | − | 1.24818i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.47404 | − | 14.6775i | −0.331869 | − | 0.574814i | ||||
\(653\) | 23.8487 | 0.933274 | 0.466637 | − | 0.884449i | \(-0.345466\pi\) | ||||
0.466637 | + | 0.884449i | \(0.345466\pi\) | |||||||
\(654\) | 22.1554 | 0.866347 | ||||||||
\(655\) | 1.13271 | + | 1.96192i | 0.0442588 | + | 0.0766585i | ||||
\(656\) | −0.437850 | − | 0.758379i | −0.0170952 | − | 0.0296097i | ||||
\(657\) | −2.41308 | + | 4.17957i | −0.0941431 | + | 0.163061i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.58114 | − | 14.8630i | 0.334274 | − | 0.578979i | −0.649071 | − | 0.760727i | \(-0.724842\pi\) |
0.983345 | + | 0.181749i | \(0.0581757\pi\) | |||||||
\(660\) | 62.3571 | 2.42725 | ||||||||
\(661\) | −0.233201 | + | 0.403917i | −0.00907048 | + | 0.0157105i | −0.870525 | − | 0.492124i | \(-0.836221\pi\) |
0.861455 | + | 0.507835i | \(0.169554\pi\) | |||||||
\(662\) | 5.56886 | + | 9.64554i | 0.216440 | + | 0.374885i | ||||
\(663\) | −41.6648 | − | 18.1182i | −1.61813 | − | 0.703652i | ||||
\(664\) | −9.68686 | −0.375923 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.30760 | + | 14.3892i | 0.321913 | + | 0.557570i | ||||
\(667\) | −27.2384 | − | 47.1784i | −1.05468 | − | 1.82675i | ||||
\(668\) | 6.25786 | + | 10.8389i | 0.242124 | + | 0.419371i | ||||
\(669\) | −20.0929 | −0.776837 | ||||||||
\(670\) | −18.1302 | − | 31.4024i | −0.700431 | − | 1.21318i | ||||
\(671\) | −14.8987 | −0.575157 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.77061 | − | 15.1911i | −0.338082 | − | 0.585576i | 0.645990 | − | 0.763346i | \(-0.276445\pi\) |
−0.984072 | + | 0.177770i | \(0.943112\pi\) | |||||||
\(674\) | −61.1770 | −2.35645 | ||||||||
\(675\) | −4.91186 | − | 8.50759i | −0.189058 | − | 0.327457i | ||||
\(676\) | −43.5234 | + | 10.0448i | −1.67398 | + | 0.386339i | ||||
\(677\) | −4.85980 | + | 8.41743i | −0.186777 | + | 0.323508i | −0.944174 | − | 0.329447i | \(-0.893138\pi\) |
0.757397 | + | 0.652955i | \(0.226471\pi\) | |||||||
\(678\) | −38.4395 | − | 66.5792i | −1.47626 | − | 2.55696i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −30.7968 | + | 53.3417i | −1.18101 | + | 2.04556i | ||||
\(681\) | 25.3609 | − | 43.9263i | 0.971831 | − | 1.68326i | ||||
\(682\) | −16.5863 | −0.635121 | ||||||||
\(683\) | −36.1154 | −1.38192 | −0.690960 | − | 0.722893i | \(-0.742812\pi\) | ||||
−0.690960 | + | 0.722893i | \(0.742812\pi\) | |||||||
\(684\) | −28.7122 | + | 49.7310i | −1.09784 | + | 1.90151i | ||||
\(685\) | 13.2127 | − | 22.8850i | 0.504830 | − | 0.874391i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.6890 | − | 41.0305i | −0.903791 | − | 1.56541i | ||||
\(688\) | 1.91083 | − | 3.30966i | 0.0728498 | − | 0.126179i | ||||
\(689\) | 6.79354 | − | 5.02657i | 0.258813 | − | 0.191497i | ||||
\(690\) | −58.5504 | − | 101.412i | −2.22897 | − | 3.86070i | ||||
\(691\) | 8.77269 | 0.333729 | 0.166864 | − | 0.985980i | \(-0.446636\pi\) | ||||
0.166864 | + | 0.985980i | \(0.446636\pi\) | |||||||
\(692\) | 21.8041 | + | 37.7657i | 0.828866 | + | 1.43564i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.3509 | 0.924346 | ||||||||
\(695\) | −5.52055 | − | 9.56187i | −0.209406 | − | 0.362703i | ||||
\(696\) | −65.2674 | −2.47396 | ||||||||
\(697\) | −2.55858 | − | 4.43160i | −0.0969132 | − | 0.167859i | ||||
\(698\) | 27.3589 | + | 47.3870i | 1.03555 | + | 1.79363i | ||||
\(699\) | −19.9600 | − | 34.5717i | −0.754955 | − | 1.30762i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.51585 | 0.0572530 | 0.0286265 | − | 0.999590i | \(-0.490887\pi\) | ||||
0.0286265 | + | 0.999590i | \(0.490887\pi\) | |||||||
\(702\) | 1.46841 | + | 12.8922i | 0.0554214 | + | 0.486586i | ||||
\(703\) | −10.9549 | − | 18.9745i | −0.413172 | − | 0.715636i | ||||
\(704\) | 14.4586 | − | 25.0431i | 0.544930 | − | 0.943847i | ||||
\(705\) | 26.9586 | 1.01532 | ||||||||
\(706\) | 3.41724 | − | 5.91883i | 0.128609 | − | 0.222758i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −28.7473 | + | 49.7919i | −1.08039 | + | 1.87129i | ||||
\(709\) | 7.55100 | + | 13.0787i | 0.283584 | + | 0.491182i | 0.972265 | − | 0.233883i | \(-0.0751433\pi\) |
−0.688681 | + | 0.725065i | \(0.741810\pi\) | |||||||
\(710\) | 29.8177 | + | 51.6458i | 1.11904 | + | 1.93823i | ||||
\(711\) | −17.6931 | −0.663544 | ||||||||
\(712\) | 44.0582 | 1.65115 | ||||||||
\(713\) | 9.84384 | + | 17.0500i | 0.368655 | + | 0.638528i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.7811 | − | 16.8558i | 0.851964 | − | 0.630372i | ||||
\(716\) | 15.1000 | − | 26.1540i | 0.564314 | − | 0.977420i | ||||
\(717\) | 3.76324 | − | 6.51812i | 0.140541 | − | 0.243424i | ||||
\(718\) | −19.9361 | + | 34.5303i | −0.744007 | + | 1.28866i | ||||
\(719\) | −9.59946 | − | 16.6267i | −0.357999 | − | 0.620073i | 0.629627 | − | 0.776897i | \(-0.283208\pi\) |
−0.987626 | + | 0.156824i | \(0.949874\pi\) | |||||||
\(720\) | −7.34039 | −0.273560 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 37.7507 | − | 65.3861i | 1.40494 | − | 2.43342i | ||||
\(723\) | −1.69217 | + | 2.93093i | −0.0629325 | + | 0.109002i | ||||
\(724\) | 59.0925 | 2.19615 | ||||||||
\(725\) | 26.8670 | − | 46.5350i | 0.997815 | − | 1.72827i | ||||
\(726\) | −29.9539 | −1.11169 | ||||||||
\(727\) | −2.41101 | −0.0894195 | −0.0447098 | − | 0.999000i | \(-0.514236\pi\) | ||||
−0.0447098 | + | 0.999000i | \(0.514236\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.9254 | −0.515755 | ||||||||
\(730\) | 16.2695 | 0.602162 | ||||||||
\(731\) | 11.1660 | − | 19.3400i | 0.412988 | − | 0.715317i | ||||
\(732\) | 50.6971 | 1.87382 | ||||||||
\(733\) | 6.74959 | − | 11.6906i | 0.249302 | − | 0.431804i | −0.714030 | − | 0.700115i | \(-0.753132\pi\) |
0.963332 | + | 0.268311i | \(0.0864655\pi\) | |||||||
\(734\) | −1.22241 | + | 2.11728i | −0.0451201 | + | 0.0781504i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29.1553 | −1.07468 | ||||||||
\(737\) | −5.37810 | − | 9.31515i | −0.198105 | − | 0.343128i | ||||
\(738\) | 2.54856 | − | 4.41423i | 0.0938138 | − | 0.162490i | ||||
\(739\) | 0.0214096 | − | 0.0370824i | 0.000787563 | − | 0.00136410i | −0.865631 | − | 0.500682i | \(-0.833083\pi\) |
0.866419 | + | 0.499318i | \(0.166416\pi\) | |||||||
\(740\) | 17.7020 | − | 30.6607i | 0.650737 | − | 1.12711i | ||||
\(741\) | 6.75345 | + | 59.2936i | 0.248094 | + | 2.17820i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.8254 | + | 18.7501i | 0.397145 | + | 0.687875i | 0.993372 | − | 0.114941i | \(-0.0366678\pi\) |
−0.596228 | + | 0.802815i | \(0.703334\pi\) | |||||||
\(744\) | 23.5873 | 0.864753 | ||||||||
\(745\) | 47.7475 | 1.74933 | ||||||||
\(746\) | −17.4989 | − | 30.3089i | −0.640679 | − | 1.10969i | ||||
\(747\) | −3.37295 | − | 5.84212i | −0.123410 | − | 0.213752i | ||||
\(748\) | −21.8594 | + | 37.8616i | −0.799258 | + | 1.38436i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 12.3810 | − | 21.4445i | 0.452091 | − | 0.783044i | ||||
\(751\) | −44.8858 | −1.63791 | −0.818953 | − | 0.573860i | \(-0.805445\pi\) | ||||
−0.818953 | + | 0.573860i | \(0.805445\pi\) | |||||||
\(752\) | −1.61724 | + | 2.80114i | −0.0589747 | + | 0.102147i | ||||
\(753\) | 19.7453 | + | 34.1999i | 0.719559 | + | 1.24631i | ||||
\(754\) | −57.0545 | + | 42.2149i | −2.07780 | + | 1.53738i | ||||
\(755\) | 4.53837 | 0.165168 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.77726 | + | 6.54240i | 0.137287 | + | 0.237788i | 0.926469 | − | 0.376372i | \(-0.122828\pi\) |
−0.789182 | + | 0.614159i | \(0.789495\pi\) | |||||||
\(758\) | −31.6500 | − | 54.8194i | −1.14958 | − | 1.99113i | ||||
\(759\) | −17.3682 | − | 30.0827i | −0.630427 | − | 1.09193i | ||||
\(760\) | 80.9030 | 2.93466 | ||||||||
\(761\) | −11.6946 | − | 20.2556i | −0.423928 | − | 0.734265i | 0.572392 | − | 0.819980i | \(-0.306016\pi\) |
−0.996320 | + | 0.0857157i | \(0.972682\pi\) | |||||||
\(762\) | −59.6333 | −2.16029 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.83447 | − | 3.17739i | −0.0663687 | − | 0.114954i | ||||
\(765\) | −42.8937 | −1.55082 | ||||||||
\(766\) | −18.6829 | − | 32.3597i | −0.675040 | − | 1.16920i | ||||
\(767\) | 2.95696 | + | 25.9613i | 0.106769 | + | 0.937409i | ||||
\(768\) | −24.8745 | + | 43.0838i | −0.897580 | + | 1.55465i | ||||
\(769\) | 21.9255 | + | 37.9760i | 0.790652 | + | 1.36945i | 0.925564 | + | 0.378592i | \(0.123592\pi\) |
−0.134911 | + | 0.990858i | \(0.543075\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.44497 | − | 7.69891i | 0.160082 | − | 0.277270i | ||||
\(772\) | −5.42160 | + | 9.39049i | −0.195128 | + | 0.337971i | ||||
\(773\) | −43.1225 | −1.55101 | −0.775505 | − | 0.631341i | \(-0.782505\pi\) | ||||
−0.775505 | + | 0.631341i | \(0.782505\pi\) | |||||||
\(774\) | 22.2445 | 0.799560 | ||||||||
\(775\) | −9.70959 | + | 16.8175i | −0.348779 | + | 0.604103i | ||||
\(776\) | 5.95457 | − | 10.3136i | 0.213756 | − | 0.370237i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.31939 | + | 16.1417i | 0.334116 | + | 0.578706i | ||||
\(779\) | −3.36069 | + | 5.82088i | −0.120409 | + | 0.208555i | ||||
\(780\) | −77.5193 | + | 57.3568i | −2.77563 | + | 2.05370i | ||||
\(781\) | 8.84506 | + | 15.3201i | 0.316501 | + | 0.548196i | ||||
\(782\) | 82.0997 | 2.93588 | ||||||||
\(783\) | 6.51594 | + | 11.2859i | 0.232861 | + | 0.403326i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −43.9597 | −1.56899 | ||||||||
\(786\) | −1.80888 | − | 3.13308i | −0.0645207 | − | 0.111753i | ||||
\(787\) | −24.8960 | −0.887446 | −0.443723 | − | 0.896164i | \(-0.646343\pi\) | ||||
−0.443723 | + | 0.896164i | \(0.646343\pi\) | |||||||
\(788\) | 30.4008 | + | 52.6558i | 1.08298 | + | 1.87578i | ||||
\(789\) | −35.2307 | − | 61.0213i | −1.25424 | − | 2.17242i | ||||
\(790\) | 29.8228 | + | 51.6546i | 1.06105 | + | 1.83779i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −18.1994 | −0.646689 | ||||||||
\(793\) | 18.5213 | − | 13.7040i | 0.657711 | − | 0.486643i | ||||
\(794\) | −14.2324 | − | 24.6512i | −0.505089 | − | 0.874839i | ||||
\(795\) | 9.12227 | − | 15.8002i | 0.323534 | − | 0.560377i | ||||
\(796\) | −44.6315 | −1.58192 | ||||||||
\(797\) | −15.6211 | + | 27.0565i | −0.553327 | + | 0.958391i | 0.444704 | + | 0.895677i | \(0.353309\pi\) |
−0.998032 | + | 0.0627134i | \(0.980025\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.45037 | + | 16.3685i | −0.334330 | + | 0.579077i | ||||
\(800\) | −14.3788 | − | 24.9049i | −0.508368 | − | 0.880520i | ||||
\(801\) | 15.3410 | + | 26.5714i | 0.542047 | + | 0.938853i | ||||
\(802\) | −88.2274 | −3.11542 | ||||||||
\(803\) | 4.82615 | 0.170311 | ||||||||
\(804\) | 18.3006 | + | 31.6975i | 0.645412 | + | 1.11789i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.6192 | − | 15.2563i | 0.726281 | − | 0.537379i | ||||
\(807\) | 19.3693 | − | 33.5486i | 0.681831 | − | 1.18097i | ||||
\(808\) | −7.91568 | + | 13.7104i | −0.278473 | + | 0.482329i | ||||
\(809\) | −19.7729 | + | 34.2477i | −0.695179 | + | 1.20409i | 0.274941 | + | 0.961461i | \(0.411342\pi\) |
−0.970120 | + | 0.242624i | \(0.921992\pi\) | |||||||
\(810\) | 41.4942 | + | 71.8701i | 1.45796 | + | 2.52526i | ||||
\(811\) | −43.8260 | −1.53894 | −0.769470 | − | 0.638683i | \(-0.779480\pi\) | ||||
−0.769470 | + | 0.638683i | \(0.779480\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 35.9942 | − | 62.3439i | 1.26237 | − | 2.18649i | ||||
\(814\) | 8.30760 | − | 14.3892i | 0.291181 | − | 0.504341i | ||||
\(815\) | −16.6282 | −0.582461 | ||||||||
\(816\) | 5.88415 | − | 10.1916i | 0.205986 | − | 0.356779i | ||||
\(817\) | −29.3329 | −1.02623 | ||||||||
\(818\) | −0.548079 | −0.0191631 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.8610 | −0.379283 | ||||||||
\(821\) | 45.0324 | 1.57164 | 0.785820 | − | 0.618455i | \(-0.212241\pi\) | ||||
0.785820 | + | 0.618455i | \(0.212241\pi\) | |||||||
\(822\) | −21.0999 | + | 36.5461i | −0.735943 | + | 1.27469i | ||||
\(823\) | 25.1987 | 0.878373 | 0.439186 | − | 0.898396i | \(-0.355267\pi\) | ||||
0.439186 | + | 0.898396i | \(0.355267\pi\) | |||||||
\(824\) | 10.0152 | − | 17.3469i | 0.348896 | − | 0.604306i | ||||
\(825\) | 17.1314 | − | 29.6724i | 0.596438 | − | 1.03306i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.3091 | −0.775762 | −0.387881 | − | 0.921709i | \(-0.626793\pi\) | ||||
−0.387881 | + | 0.921709i | \(0.626793\pi\) | |||||||
\(828\) | 25.8452 | + | 44.7651i | 0.898181 | + | 1.55570i | ||||
\(829\) | −13.0981 | + | 22.6866i | −0.454917 | + | 0.787939i | −0.998683 | − | 0.0512972i | \(-0.983664\pi\) |
0.543766 | + | 0.839237i | \(0.316998\pi\) | |||||||
\(830\) | −11.3706 | + | 19.6945i | −0.394679 | + | 0.683605i | ||||
\(831\) | 0.457047 | − | 0.791629i | 0.0158548 | − | 0.0274613i | ||||
\(832\) | 5.06069 | + | 44.4316i | 0.175448 | + | 1.54039i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.81601 | + | 15.2698i | 0.305274 | + | 0.528749i | ||||
\(835\) | 12.2795 | 0.424950 | ||||||||
\(836\) | 57.4244 | 1.98606 | ||||||||
\(837\) | −2.35483 | − | 4.07868i | −0.0813947 | − | 0.140980i | ||||
\(838\) | 0.517650 | + | 0.896597i | 0.0178819 | + | 0.0309724i | ||||
\(839\) | −21.7207 | + | 37.6214i | −0.749882 | + | 1.29883i | 0.197997 | + | 0.980203i | \(0.436557\pi\) |
−0.947879 | + | 0.318631i | \(0.896777\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.1410 | + | 36.6173i | −0.729000 | + | 1.26266i | ||||
\(842\) | −22.0561 | −0.760103 | ||||||||
\(843\) | −26.4912 | + | 45.8840i | −0.912404 | + | 1.58033i | ||||
\(844\) | −47.3136 | − | 81.9496i | −1.62860 | − | 2.82082i | ||||
\(845\) | −12.8161 | + | 41.9086i | −0.440888 | + | 1.44170i | ||||
\(846\) | −18.8267 | −0.647275 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.09449 | + | 1.89571i | 0.0375849 | + | 0.0650989i | ||||
\(849\) | 22.3414 | + | 38.6964i | 0.766754 | + | 1.32806i | ||||
\(850\) | 40.4901 | + | 70.1308i | 1.38880 | + | 2.40547i | ||||
\(851\) | −19.7220 | −0.676063 | ||||||||
\(852\) | −30.0979 | − | 52.1311i | −1.03114 | − | 1.78598i | ||||
\(853\) | 1.15312 | 0.0394820 | 0.0197410 | − | 0.999805i | \(-0.493716\pi\) | ||||
0.0197410 | + | 0.999805i | \(0.493716\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 28.1703 | + | 48.7924i | 0.963404 | + | 1.66866i | ||||
\(856\) | −44.1350 | −1.50850 | ||||||||
\(857\) | 12.5043 | + | 21.6582i | 0.427140 | + | 0.739828i | 0.996618 | − | 0.0821785i | \(-0.0261878\pi\) |
−0.569477 | + | 0.822007i | \(0.692854\pi\) | |||||||
\(858\) | −36.3801 | + | 26.9178i | −1.24200 | + | 0.918959i | ||||
\(859\) | 2.04457 | − | 3.54130i | 0.0697598 | − | 0.120827i | −0.829036 | − | 0.559196i | \(-0.811110\pi\) |
0.898795 | + | 0.438368i | \(0.144443\pi\) | |||||||
\(860\) | −23.6994 | − | 41.0486i | −0.808143 | − | 1.39974i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25.1158 | − | 43.5018i | 0.855447 | − | 1.48168i | ||||
\(863\) | −8.69644 | + | 15.0627i | −0.296030 | + | 0.512739i | −0.975224 | − | 0.221220i | \(-0.928996\pi\) |
0.679194 | + | 0.733959i | \(0.262330\pi\) | |||||||
\(864\) | 6.97447 | 0.237276 | ||||||||
\(865\) | 42.7851 | 1.45474 | ||||||||
\(866\) | −15.3402 | + | 26.5700i | −0.521280 | + | 0.902884i | ||||
\(867\) | 14.7575 | − | 25.5608i | 0.501192 | − | 0.868090i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.84657 | + | 15.3227i | 0.300099 | + | 0.519787i | ||||
\(870\) | −76.6121 | + | 132.696i | −2.59739 | + | 4.49881i | ||||
\(871\) | 15.2540 | + | 6.63329i | 0.516862 | + | 0.224760i | ||||
\(872\) | 6.88919 | + | 11.9324i | 0.233298 | + | 0.404083i | ||||
\(873\) | 8.29348 | 0.280692 | ||||||||
\(874\) | −53.9188 | − | 93.3901i | −1.82383 | − | 3.15897i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.4224 | −0.554862 | ||||||||
\(877\) | 7.49082 | + | 12.9745i | 0.252947 | + | 0.438117i | 0.964336 | − | 0.264681i | \(-0.0852668\pi\) |
−0.711389 | + | 0.702799i | \(0.751933\pi\) | |||||||
\(878\) | 69.4434 | 2.34360 | ||||||||
\(879\) | −18.2092 | − | 31.5393i | −0.614182 | − | 1.06379i | ||||
\(880\) | 3.67019 | + | 6.35696i | 0.123722 | + | 0.214293i | ||||
\(881\) | −21.3382 | − | 36.9588i | −0.718901 | − | 1.24517i | −0.961436 | − | 0.275030i | \(-0.911312\pi\) |
0.242534 | − | 0.970143i | \(-0.422021\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.8874 | 1.20771 | 0.603854 | − | 0.797095i | \(-0.293631\pi\) | ||||
0.603854 | + | 0.797095i | \(0.293631\pi\) | |||||||
\(884\) | −7.65104 | − | 67.1742i | −0.257332 | − | 2.25931i | ||||
\(885\) | 28.2048 | + | 48.8521i | 0.948094 | + | 1.64215i | ||||
\(886\) | 17.3076 | − | 29.9777i | 0.581461 | − | 1.00712i | ||||
\(887\) | 27.6672 | 0.928975 | 0.464488 | − | 0.885580i | \(-0.346239\pi\) | ||||
0.464488 | + | 0.885580i | \(0.346239\pi\) | |||||||
\(888\) | −11.8142 | + | 20.4629i | −0.396460 | + | 0.686689i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 51.7163 | − | 89.5752i | 1.73353 | − | 3.00257i | ||||
\(891\) | 12.3087 | + | 21.3194i | 0.412359 | + | 0.714226i | ||||
\(892\) | −14.9498 | − | 25.8938i | −0.500557 | − | 0.866990i | ||||
\(893\) | 24.8260 | 0.830771 | ||||||||
\(894\) | −76.2502 | −2.55019 | ||||||||
\(895\) | −14.8150 | − | 25.6604i | −0.495211 | − | 0.857731i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 49.2618 | + | 21.4218i | 1.64480 | + | 0.715253i | ||||
\(898\) | −30.5693 | + | 52.9476i | −1.02011 | + | 1.76688i | ||||
\(899\) | 12.8805 | − | 22.3096i | 0.429588 | − | 0.744068i | ||||
\(900\) | −25.4927 | + | 44.1546i | −0.849756 | + | 1.47182i | ||||
\(901\) | 6.39566 | + | 11.0776i | 0.213070 | + | 0.369048i | ||||
\(902\) | −5.09712 | −0.169716 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 23.9054 | − | 41.4053i | 0.795081 | − | 1.37712i | ||||
\(905\) | 28.9886 | − | 50.2097i | 0.963614 | − | 1.66903i | ||||
\(906\) | −7.24752 | −0.240783 | ||||||||
\(907\) | −9.09663 | + | 15.7558i | −0.302049 | + | 0.523164i | −0.976600 | − | 0.215064i | \(-0.931004\pi\) |
0.674551 | + | 0.738228i | \(0.264337\pi\) | |||||||
\(908\) | 75.4775 | 2.50481 | ||||||||
\(909\) | −11.0249 | −0.365673 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.1527 | −1.09840 | −0.549199 | − | 0.835691i | \(-0.685067\pi\) | ||||
−0.549199 | + | 0.835691i | \(0.685067\pi\) | |||||||
\(912\) | −15.4576 | −0.511852 | ||||||||
\(913\) | −3.37295 | + | 5.84212i | −0.111628 | + | 0.193346i | ||||
\(914\) | 37.0031 | 1.22395 | ||||||||
\(915\) | 24.8702 | − | 43.0764i | 0.822182 | − | 1.42406i | ||||
\(916\) | 35.2508 | − | 61.0562i | 1.16472 | − | 2.01736i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −19.6398 | −0.648209 | ||||||||
\(919\) | −1.49164 | − | 2.58359i | −0.0492046 | − | 0.0852249i | 0.840374 | − | 0.542007i | \(-0.182335\pi\) |
−0.889579 | + | 0.456782i | \(0.849002\pi\) | |||||||
\(920\) | 36.4122 | − | 63.0679i | 1.20048 | − | 2.07929i | ||||
\(921\) | 22.2282 | − | 38.5004i | 0.732444 | − | 1.26863i | ||||
\(922\) | 25.7500 | − | 44.6002i | 0.848030 | − | 1.46883i | ||||
\(923\) | −25.0874 | − | 10.9094i | −0.825761 | − | 0.359087i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.72654 | − | 16.8469i | −0.319807 | − | 0.553921i | ||||
\(926\) | −42.6404 | −1.40125 | ||||||||
\(927\) | 13.9491 | 0.458149 | ||||||||
\(928\) | 19.0746 | + | 33.0381i | 0.626153 | + | 1.08453i | ||||
\(929\) | 16.6990 | + | 28.9235i | 0.547876 | + | 0.948948i | 0.998420 | + | 0.0561943i | \(0.0178966\pi\) |
−0.450544 | + | 0.892754i | \(0.648770\pi\) | |||||||
\(930\) | 27.6872 | − | 47.9557i | 0.907899 | − | 1.57253i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 29.7018 | − | 51.4450i | 0.972915 | − | 1.68514i | ||||
\(933\) | −7.07627 | −0.231667 | ||||||||
\(934\) | 5.28459 | − | 9.15318i | 0.172917 | − | 0.299501i | ||||
\(935\) | 21.4468 | + | 37.1470i | 0.701386 | + | 1.21484i | ||||
\(936\) | 22.6246 | − | 16.7401i | 0.739510 | − | 0.547166i | ||||
\(937\) | 51.3187 | 1.67651 | 0.838254 | − | 0.545279i | \(-0.183576\pi\) | ||||
0.838254 | + | 0.545279i | \(0.183576\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −40.7253 | − | 70.5382i | −1.32902 | − | 2.30193i | ||||
\(940\) | 20.0581 | + | 34.7416i | 0.654223 | + | 1.13315i | ||||
\(941\) | 9.50195 | + | 16.4579i | 0.309755 | + | 0.536511i | 0.978309 | − | 0.207153i | \(-0.0664197\pi\) |
−0.668554 | + | 0.743664i | \(0.733086\pi\) | |||||||
\(942\) | 70.2013 | 2.28728 | ||||||||
\(943\) | 3.02511 | + | 5.23964i | 0.0985110 | + | 0.170626i | ||||
\(944\) | −6.76801 | −0.220280 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.1222 | − | 19.2643i | −0.361615 | − | 0.626335i | ||||
\(947\) | −46.7080 | −1.51780 | −0.758902 | − | 0.651204i | \(-0.774264\pi\) | ||||
−0.758902 | + | 0.651204i | \(0.774264\pi\) | |||||||
\(948\) | −30.1030 | − | 52.1400i | −0.977701 | − | 1.69343i | ||||
\(949\) | −5.99964 | + | 4.43916i | −0.194757 | + | 0.144101i | ||||
\(950\) | 53.1835 | − | 92.1165i | 1.72550 | − | 2.98865i | ||||
\(951\) | 37.7598 | + | 65.4019i | 1.22444 | + | 2.12080i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.865567 | − | 1.49921i | 0.0280385 | − | 0.0485640i | −0.851666 | − | 0.524085i | \(-0.824407\pi\) |
0.879704 | + | 0.475521i | \(0.157741\pi\) | |||||||
\(954\) | −6.37060 | + | 11.0342i | −0.206256 | + | 0.357246i | ||||
\(955\) | −3.59969 | −0.116483 | ||||||||
\(956\) | 11.1999 | 0.362231 | ||||||||
\(957\) | −22.7260 | + | 39.3626i | −0.734628 | + | 1.27241i | ||||
\(958\) | −12.1776 | + | 21.0922i | −0.393439 | + | 0.681457i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 48.2712 | + | 83.6082i | 1.55795 | + | 2.69844i | ||||
\(961\) | 10.8451 | − | 18.7842i | 0.349841 | − | 0.605942i | ||||
\(962\) | 2.90776 | + | 25.5294i | 0.0937499 | + | 0.823100i | ||||
\(963\) | −15.3677 | − | 26.6177i | −0.495218 | − | 0.857744i | ||||
\(964\) | −5.03613 | −0.162203 | ||||||||
\(965\) | 5.31928 | + | 9.21326i | 0.171234 | + | 0.296585i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.88811 | −0.157191 | −0.0785955 | − | 0.996907i | \(-0.525044\pi\) | ||||
−0.0785955 | + | 0.996907i | \(0.525044\pi\) | |||||||
\(968\) | −9.31411 | − | 16.1325i | −0.299367 | − | 0.518519i | ||||
\(969\) | −90.3267 | −2.90171 | ||||||||
\(970\) | −13.9791 | − | 24.2126i | −0.448843 | − | 0.777419i | ||||
\(971\) | 4.28576 | + | 7.42316i | 0.137537 | + | 0.238220i | 0.926564 | − | 0.376138i | \(-0.122748\pi\) |
−0.789027 | + | 0.614359i | \(0.789415\pi\) | |||||||
\(972\) | −33.9288 | − | 58.7664i | −1.08827 | − | 1.88493i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −83.7347 | −2.68303 | ||||||||
\(975\) | 5.99619 | + | 52.6450i | 0.192032 | + | 1.68599i | ||||
\(976\) | 2.98392 | + | 5.16829i | 0.0955128 | + | 0.165433i | ||||
\(977\) | 20.0191 | − | 34.6741i | 0.640467 | − | 1.10932i | −0.344861 | − | 0.938654i | \(-0.612074\pi\) |
0.985329 | − | 0.170668i | \(-0.0545927\pi\) | |||||||
\(978\) | 26.5543 | 0.849114 | ||||||||
\(979\) | 15.3410 | − | 26.5714i | 0.490300 | − | 0.849225i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.79761 | + | 8.30971i | −0.153176 | + | 0.265309i | ||||
\(982\) | 8.97922 | + | 15.5525i | 0.286539 | + | 0.496299i | ||||
\(983\) | 11.9560 | + | 20.7084i | 0.381337 | + | 0.660496i | 0.991254 | − | 0.131970i | \(-0.0421303\pi\) |
−0.609916 | + | 0.792466i | \(0.708797\pi\) | |||||||
\(984\) | 7.24862 | 0.231077 | ||||||||
\(985\) | 59.6541 | 1.90074 | ||||||||
\(986\) | −53.7130 | − | 93.0336i | −1.71057 | − | 2.96279i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −71.3872 | + | 52.8197i | −2.27113 | + | 1.68042i | ||||
\(989\) | −13.2019 | + | 22.8664i | −0.419797 | + | 0.727110i | ||||
\(990\) | −21.3628 | + | 37.0015i | −0.678955 | + | 1.17598i | ||||
\(991\) | −20.5069 | + | 35.5190i | −0.651424 | + | 1.12830i | 0.331354 | + | 0.943506i | \(0.392495\pi\) |
−0.982778 | + | 0.184792i | \(0.940839\pi\) | |||||||
\(992\) | −6.89345 | − | 11.9398i | −0.218867 | − | 0.379089i | ||||
\(993\) | −11.0302 | −0.350033 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.8946 | + | 37.9226i | −0.694106 | + | 1.20223i | ||||
\(996\) | 11.4774 | − | 19.8795i | 0.363677 | − | 0.629907i | ||||
\(997\) | −25.4245 | −0.805201 | −0.402600 | − | 0.915376i | \(-0.631894\pi\) | ||||
−0.402600 | + | 0.915376i | \(0.631894\pi\) | |||||||
\(998\) | 9.89819 | − | 17.1442i | 0.313322 | − | 0.542689i | ||||
\(999\) | 4.71787 | 0.149267 |
(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 | 637.2.h.m.471.2 | 16 | ||
7.2 | even | 3 | 637.2.f.l.393.8 | yes | 16 | ||
7.3 | odd | 6 | 637.2.g.m.263.8 | 16 | |||
7.4 | even | 3 | 637.2.g.m.263.7 | 16 | |||
7.5 | odd | 6 | 637.2.f.l.393.7 | yes | 16 | ||
7.6 | odd | 2 | inner | 637.2.h.m.471.1 | 16 | ||
13.9 | even | 3 | 637.2.g.m.373.7 | 16 | |||
91.9 | even | 3 | 637.2.f.l.295.8 | yes | 16 | ||
91.16 | even | 3 | 8281.2.a.ci.1.1 | 8 | |||
91.23 | even | 6 | 8281.2.a.cl.1.7 | 8 | |||
91.48 | odd | 6 | 637.2.g.m.373.8 | 16 | |||
91.61 | odd | 6 | 637.2.f.l.295.7 | ✓ | 16 | ||
91.68 | odd | 6 | 8281.2.a.ci.1.2 | 8 | |||
91.74 | even | 3 | inner | 637.2.h.m.165.2 | 16 | ||
91.75 | odd | 6 | 8281.2.a.cl.1.8 | 8 | |||
91.87 | odd | 6 | inner | 637.2.h.m.165.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.f.l.295.7 | ✓ | 16 | 91.61 | odd | 6 | ||
637.2.f.l.295.8 | yes | 16 | 91.9 | even | 3 | ||
637.2.f.l.393.7 | yes | 16 | 7.5 | odd | 6 | ||
637.2.f.l.393.8 | yes | 16 | 7.2 | even | 3 | ||
637.2.g.m.263.7 | 16 | 7.4 | even | 3 | |||
637.2.g.m.263.8 | 16 | 7.3 | odd | 6 | |||
637.2.g.m.373.7 | 16 | 13.9 | even | 3 | |||
637.2.g.m.373.8 | 16 | 91.48 | odd | 6 | |||
637.2.h.m.165.1 | 16 | 91.87 | odd | 6 | inner | ||
637.2.h.m.165.2 | 16 | 91.74 | even | 3 | inner | ||
637.2.h.m.471.1 | 16 | 7.6 | odd | 2 | inner | ||
637.2.h.m.471.2 | 16 | 1.1 | even | 1 | trivial | ||
8281.2.a.ci.1.1 | 8 | 91.16 | even | 3 | |||
8281.2.a.ci.1.2 | 8 | 91.68 | odd | 6 | |||
8281.2.a.cl.1.7 | 8 | 91.23 | even | 6 | |||
8281.2.a.cl.1.8 | 8 | 91.75 | odd | 6 |