Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(901,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.i (of order \(6\), 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: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.14 | ||
Character | \(\chi\) | \(=\) | 1078.901 |
Dual form | 1078.2.i.d.1011.14 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0.662827 | − | 0.382683i | 0.382683 | − | 0.220942i | −0.296302 | − | 0.955094i | \(-0.595753\pi\) |
0.678985 | + | 0.734152i | \(0.262420\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.77675 | − | 1.02581i | −0.794586 | − | 0.458755i | 0.0469885 | − | 0.998895i | \(-0.485038\pi\) |
−0.841575 | + | 0.540141i | \(0.818371\pi\) | |||||||
\(6\) | 0.765367 | 0.312460 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.20711 | + | 2.09077i | −0.402369 | + | 0.696923i | ||||
\(10\) | −1.02581 | − | 1.77675i | −0.324388 | − | 0.561857i | ||||
\(11\) | −3.14127 | − | 1.06416i | −0.947128 | − | 0.320857i | ||||
\(12\) | 0.662827 | + | 0.382683i | 0.191342 | + | 0.110471i | ||||
\(13\) | −6.59694 | −1.82966 | −0.914830 | − | 0.403838i | \(-0.867676\pi\) | ||||
−0.914830 | + | 0.403838i | \(0.867676\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.57024 | −0.405433 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.80554 | − | 3.12729i | −0.437908 | − | 0.758478i | 0.559620 | − | 0.828749i | \(-0.310947\pi\) |
−0.997528 | + | 0.0702708i | \(0.977614\pi\) | |||||||
\(18\) | −2.09077 | + | 1.20711i | −0.492799 | + | 0.284518i | ||||
\(19\) | −0.439269 | + | 0.760837i | −0.100775 | + | 0.174548i | −0.912004 | − | 0.410181i | \(-0.865466\pi\) |
0.811229 | + | 0.584729i | \(0.198799\pi\) | |||||||
\(20\) | − | 2.05161i | − | 0.458755i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.18834 | − | 2.49222i | −0.466555 | − | 0.531344i | ||||
\(23\) | −3.30966 | + | 5.73249i | −0.690111 | + | 1.19531i | 0.281690 | + | 0.959505i | \(0.409105\pi\) |
−0.971801 | + | 0.235802i | \(0.924228\pi\) | |||||||
\(24\) | 0.382683 | + | 0.662827i | 0.0781149 | + | 0.135299i | ||||
\(25\) | −0.395443 | − | 0.684927i | −0.0790886 | − | 0.136985i | ||||
\(26\) | −5.71311 | − | 3.29847i | −1.12043 | − | 0.646883i | ||||
\(27\) | 4.14386i | 0.797486i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.18955i | 1.14937i | 0.818375 | + | 0.574685i | \(0.194876\pi\) | ||||
−0.818375 | + | 0.574685i | \(0.805124\pi\) | |||||||
\(30\) | −1.35986 | − | 0.785118i | −0.248276 | − | 0.143342i | ||||
\(31\) | 5.61510 | − | 3.24188i | 1.00850 | − | 0.582259i | 0.0977497 | − | 0.995211i | \(-0.468836\pi\) |
0.910753 | + | 0.412952i | \(0.135502\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −2.48935 | + | 0.496755i | −0.433341 | + | 0.0864740i | ||||
\(34\) | − | 3.61108i | − | 0.619295i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.41421 | −0.402369 | ||||||||
\(37\) | 5.52454 | − | 9.56878i | 0.908229 | − | 1.57310i | 0.0917046 | − | 0.995786i | \(-0.470768\pi\) |
0.816524 | − | 0.577312i | \(-0.195898\pi\) | |||||||
\(38\) | −0.760837 | + | 0.439269i | −0.123424 | + | 0.0712589i | ||||
\(39\) | −4.37263 | + | 2.52454i | −0.700181 | + | 0.404250i | ||||
\(40\) | 1.02581 | − | 1.77675i | 0.162194 | − | 0.280929i | ||||
\(41\) | 2.36864 | 0.369919 | 0.184960 | − | 0.982746i | \(-0.440785\pi\) | ||||
0.184960 | + | 0.982746i | \(0.440785\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.81288i | 1.19145i | 0.803188 | + | 0.595726i | \(0.203136\pi\) | ||||
−0.803188 | + | 0.595726i | \(0.796864\pi\) | |||||||
\(44\) | −0.649042 | − | 3.25250i | −0.0978468 | − | 0.490333i | ||||
\(45\) | 4.28945 | − | 2.47652i | 0.639434 | − | 0.369177i | ||||
\(46\) | −5.73249 | + | 3.30966i | −0.845210 | + | 0.487982i | ||||
\(47\) | −4.97716 | − | 2.87357i | −0.725994 | − | 0.419153i | 0.0909611 | − | 0.995854i | \(-0.471006\pi\) |
−0.816955 | + | 0.576702i | \(0.804339\pi\) | |||||||
\(48\) | 0.765367i | 0.110471i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 0.790886i | − | 0.111848i | ||||||
\(51\) | −2.39352 | − | 1.38190i | −0.335160 | − | 0.193505i | ||||
\(52\) | −3.29847 | − | 5.71311i | −0.457415 | − | 0.792266i | ||||
\(53\) | −0.214882 | − | 0.372186i | −0.0295163 | − | 0.0511237i | 0.850890 | − | 0.525344i | \(-0.176063\pi\) |
−0.880406 | + | 0.474220i | \(0.842730\pi\) | |||||||
\(54\) | −2.07193 | + | 3.58869i | −0.281954 | + | 0.488359i | ||||
\(55\) | 4.48962 | + | 5.11308i | 0.605380 | + | 0.689448i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.672404i | 0.0890621i | ||||||||
\(58\) | −3.09477 | + | 5.36031i | −0.406364 | + | 0.703843i | ||||
\(59\) | 2.78725 | − | 1.60922i | 0.362870 | − | 0.209503i | −0.307469 | − | 0.951558i | \(-0.599482\pi\) |
0.670339 | + | 0.742055i | \(0.266149\pi\) | |||||||
\(60\) | −0.785118 | − | 1.35986i | −0.101358 | − | 0.175558i | ||||
\(61\) | −5.66711 | + | 9.81572i | −0.725599 | + | 1.25677i | 0.233129 | + | 0.972446i | \(0.425104\pi\) |
−0.958727 | + | 0.284328i | \(0.908230\pi\) | |||||||
\(62\) | 6.48376 | 0.823439 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 11.7211 | + | 6.76718i | 1.45382 | + | 0.839365i | ||||
\(66\) | −2.40422 | − | 0.814474i | −0.295939 | − | 0.100255i | ||||
\(67\) | −1.48123 | − | 2.56556i | −0.180961 | − | 0.313434i | 0.761247 | − | 0.648462i | \(-0.224587\pi\) |
−0.942208 | + | 0.335028i | \(0.891254\pi\) | |||||||
\(68\) | 1.80554 | − | 3.12729i | 0.218954 | − | 0.379239i | ||||
\(69\) | 5.06620i | 0.609899i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.13403 | −0.253263 | −0.126631 | − | 0.991950i | \(-0.540417\pi\) | ||||
−0.126631 | + | 0.991950i | \(0.540417\pi\) | |||||||
\(72\) | −2.09077 | − | 1.20711i | −0.246400 | − | 0.142259i | ||||
\(73\) | −5.41262 | − | 9.37493i | −0.633499 | − | 1.09725i | −0.986831 | − | 0.161754i | \(-0.948285\pi\) |
0.353332 | − | 0.935498i | \(-0.385049\pi\) | |||||||
\(74\) | 9.56878 | − | 5.52454i | 1.11235 | − | 0.642215i | ||||
\(75\) | −0.524221 | − | 0.302659i | −0.0605318 | − | 0.0349480i | ||||
\(76\) | −0.878539 | −0.100775 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.04908 | −0.571695 | ||||||||
\(79\) | −7.34847 | − | 4.24264i | −0.826767 | − | 0.477334i | 0.0259772 | − | 0.999663i | \(-0.491730\pi\) |
−0.852745 | + | 0.522328i | \(0.825064\pi\) | |||||||
\(80\) | 1.77675 | − | 1.02581i | 0.198647 | − | 0.114689i | ||||
\(81\) | −2.03553 | − | 3.52565i | −0.226170 | − | 0.391739i | ||||
\(82\) | 2.05130 | + | 1.18432i | 0.226528 | + | 0.130786i | ||||
\(83\) | −12.3153 | −1.35178 | −0.675892 | − | 0.737001i | \(-0.736241\pi\) | ||||
−0.675892 | + | 0.737001i | \(0.736241\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.40854i | 0.803569i | ||||||||
\(86\) | −3.90644 | + | 6.76615i | −0.421242 | + | 0.729613i | ||||
\(87\) | 2.36864 | + | 4.10260i | 0.253945 | + | 0.439845i | ||||
\(88\) | 1.06416 | − | 3.14127i | 0.113440 | − | 0.334860i | ||||
\(89\) | 5.82684 | + | 3.36413i | 0.617644 | + | 0.356597i | 0.775951 | − | 0.630793i | \(-0.217270\pi\) |
−0.158307 | + | 0.987390i | \(0.550604\pi\) | |||||||
\(90\) | 4.95303 | 0.522095 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.61931 | −0.690111 | ||||||||
\(93\) | 2.48123 | − | 4.29762i | 0.257291 | − | 0.445642i | ||||
\(94\) | −2.87357 | − | 4.97716i | −0.296386 | − | 0.513355i | ||||
\(95\) | 1.56094 | − | 0.901211i | 0.160149 | − | 0.0924622i | ||||
\(96\) | −0.382683 | + | 0.662827i | −0.0390575 | + | 0.0676495i | ||||
\(97\) | − | 9.23880i | − | 0.938058i | −0.883183 | − | 0.469029i | \(-0.844604\pi\) | ||
0.883183 | − | 0.469029i | \(-0.155396\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.01676 | − | 5.28311i | 0.604707 | − | 0.530973i | ||||
\(100\) | 0.395443 | − | 0.684927i | 0.0395443 | − | 0.0684927i | ||||
\(101\) | 0.929830 | + | 1.61051i | 0.0925216 | + | 0.160252i | 0.908572 | − | 0.417729i | \(-0.137174\pi\) |
−0.816050 | + | 0.577981i | \(0.803841\pi\) | |||||||
\(102\) | −1.38190 | − | 2.39352i | −0.136829 | − | 0.236994i | ||||
\(103\) | 5.81112 | + | 3.35505i | 0.572587 | + | 0.330583i | 0.758182 | − | 0.652043i | \(-0.226088\pi\) |
−0.185595 | + | 0.982626i | \(0.559421\pi\) | |||||||
\(104\) | − | 6.59694i | − | 0.646883i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 0.429764i | − | 0.0417423i | ||||||
\(107\) | 12.7768 | + | 7.37667i | 1.23518 | + | 0.713130i | 0.968105 | − | 0.250547i | \(-0.0806103\pi\) |
0.267073 | + | 0.963676i | \(0.413944\pi\) | |||||||
\(108\) | −3.58869 | + | 2.07193i | −0.345322 | + | 0.199372i | ||||
\(109\) | −5.19615 | + | 3.00000i | −0.497701 | + | 0.287348i | −0.727764 | − | 0.685828i | \(-0.759440\pi\) |
0.230063 | + | 0.973176i | \(0.426107\pi\) | |||||||
\(110\) | 1.33158 | + | 6.67287i | 0.126961 | + | 0.636233i | ||||
\(111\) | − | 8.45660i | − | 0.802665i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.597322 | −0.0561913 | −0.0280956 | − | 0.999605i | \(-0.508944\pi\) | ||||
−0.0280956 | + | 0.999605i | \(0.508944\pi\) | |||||||
\(114\) | −0.336202 | + | 0.582319i | −0.0314882 | + | 0.0545392i | ||||
\(115\) | 11.7609 | − | 6.79013i | 1.09671 | − | 0.633183i | ||||
\(116\) | −5.36031 | + | 3.09477i | −0.497692 | + | 0.287343i | ||||
\(117\) | 7.96321 | − | 13.7927i | 0.736199 | − | 1.27513i | ||||
\(118\) | 3.21844 | 0.296282 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 1.57024i | − | 0.143342i | ||||||
\(121\) | 8.73512 | + | 6.68563i | 0.794102 | + | 0.607785i | ||||
\(122\) | −9.81572 | + | 5.66711i | −0.888673 | + | 0.513076i | ||||
\(123\) | 1.57000 | − | 0.906438i | 0.141562 | − | 0.0817308i | ||||
\(124\) | 5.61510 | + | 3.24188i | 0.504251 | + | 0.291130i | ||||
\(125\) | 11.8807i | 1.06264i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.33002i | − | 0.650434i | −0.945639 | − | 0.325217i | \(-0.894563\pi\) | ||
0.945639 | − | 0.325217i | \(-0.105437\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 2.98986 | + | 5.17859i | 0.263242 | + | 0.455949i | ||||
\(130\) | 6.76718 | + | 11.7211i | 0.593521 | + | 1.02801i | ||||
\(131\) | −4.41025 | + | 7.63878i | −0.385325 | + | 0.667403i | −0.991814 | − | 0.127689i | \(-0.959244\pi\) |
0.606489 | + | 0.795092i | \(0.292577\pi\) | |||||||
\(132\) | −1.67488 | − | 1.90747i | −0.145780 | − | 0.166024i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 2.96246i | − | 0.255917i | ||||||
\(135\) | 4.25080 | − | 7.36260i | 0.365850 | − | 0.633671i | ||||
\(136\) | 3.12729 | − | 1.80554i | 0.268163 | − | 0.154824i | ||||
\(137\) | −1.61810 | − | 2.80263i | −0.138244 | − | 0.239445i | 0.788588 | − | 0.614922i | \(-0.210812\pi\) |
−0.926832 | + | 0.375477i | \(0.877479\pi\) | |||||||
\(138\) | −2.53310 | + | 4.38746i | −0.215632 | + | 0.373485i | ||||
\(139\) | 2.47122 | 0.209606 | 0.104803 | − | 0.994493i | \(-0.466579\pi\) | ||||
0.104803 | + | 0.994493i | \(0.466579\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.39866 | −0.370434 | ||||||||
\(142\) | −1.84813 | − | 1.06702i | −0.155091 | − | 0.0895420i | ||||
\(143\) | 20.7227 | + | 7.02021i | 1.73292 | + | 0.587059i | ||||
\(144\) | −1.20711 | − | 2.09077i | −0.100592 | − | 0.174231i | ||||
\(145\) | 6.34928 | − | 10.9973i | 0.527279 | − | 0.913274i | ||||
\(146\) | − | 10.8252i | − | 0.895903i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.0491 | 0.908229 | ||||||||
\(149\) | −3.38495 | − | 1.95430i | −0.277306 | − | 0.160103i | 0.354897 | − | 0.934905i | \(-0.384516\pi\) |
−0.632203 | + | 0.774803i | \(0.717849\pi\) | |||||||
\(150\) | −0.302659 | − | 0.524221i | −0.0247120 | − | 0.0428024i | ||||
\(151\) | 20.9488 | − | 12.0948i | 1.70479 | − | 0.984259i | 0.764027 | − | 0.645185i | \(-0.223220\pi\) |
0.940760 | − | 0.339074i | \(-0.110114\pi\) | |||||||
\(152\) | −0.760837 | − | 0.439269i | −0.0617120 | − | 0.0356294i | ||||
\(153\) | 8.71792 | 0.704802 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.3022 | −1.06846 | ||||||||
\(156\) | −4.37263 | − | 2.52454i | −0.350090 | − | 0.202125i | ||||
\(157\) | −17.5828 | + | 10.1514i | −1.40326 | + | 0.810172i | −0.994726 | − | 0.102571i | \(-0.967293\pi\) |
−0.408534 | + | 0.912743i | \(0.633960\pi\) | |||||||
\(158\) | −4.24264 | − | 7.34847i | −0.337526 | − | 0.584613i | ||||
\(159\) | −0.284859 | − | 0.164463i | −0.0225908 | − | 0.0130428i | ||||
\(160\) | 2.05161 | 0.162194 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 4.07107i | − | 0.319853i | ||||||
\(163\) | 6.63031 | − | 11.4840i | 0.519326 | − | 0.899499i | −0.480422 | − | 0.877038i | \(-0.659516\pi\) |
0.999748 | − | 0.0224612i | \(-0.00715023\pi\) | |||||||
\(164\) | 1.18432 | + | 2.05130i | 0.0924798 | + | 0.160180i | ||||
\(165\) | 4.93253 | + | 1.67099i | 0.383997 | + | 0.130086i | ||||
\(166\) | −10.6654 | − | 6.15767i | −0.827795 | − | 0.477928i | ||||
\(167\) | −20.4160 | −1.57984 | −0.789920 | − | 0.613210i | \(-0.789878\pi\) | ||||
−0.789920 | + | 0.613210i | \(0.789878\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.5196 | 2.34766 | ||||||||
\(170\) | −3.70427 | + | 6.41598i | −0.284104 | + | 0.492083i | ||||
\(171\) | −1.06049 | − | 1.83682i | −0.0810977 | − | 0.140465i | ||||
\(172\) | −6.76615 | + | 3.90644i | −0.515914 | + | 0.297863i | ||||
\(173\) | −7.78809 | + | 13.4894i | −0.592117 | + | 1.02558i | 0.401830 | + | 0.915714i | \(0.368374\pi\) |
−0.993947 | + | 0.109863i | \(0.964959\pi\) | |||||||
\(174\) | 4.73728i | 0.359132i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.49222 | − | 2.18834i | 0.187859 | − | 0.164952i | ||||
\(177\) | 1.23165 | − | 2.13327i | 0.0925761 | − | 0.160347i | ||||
\(178\) | 3.36413 | + | 5.82684i | 0.252152 | + | 0.436740i | ||||
\(179\) | 2.25080 | + | 3.89850i | 0.168232 | + | 0.291387i | 0.937798 | − | 0.347180i | \(-0.112861\pi\) |
−0.769566 | + | 0.638567i | \(0.779527\pi\) | |||||||
\(180\) | 4.28945 | + | 2.47652i | 0.319717 | + | 0.184589i | ||||
\(181\) | 8.18338i | 0.608266i | 0.952630 | + | 0.304133i | \(0.0983667\pi\) | ||||
−0.952630 | + | 0.304133i | \(0.901633\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.67483i | 0.641262i | ||||||||
\(184\) | −5.73249 | − | 3.30966i | −0.422605 | − | 0.243991i | ||||
\(185\) | −19.6314 | + | 11.3342i | −1.44333 | + | 0.833308i | ||||
\(186\) | 4.29762 | − | 2.48123i | 0.315116 | − | 0.181933i | ||||
\(187\) | 2.34374 | + | 11.7450i | 0.171391 | + | 0.858882i | ||||
\(188\) | − | 5.74713i | − | 0.419153i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.80242 | 0.130761 | ||||||||
\(191\) | −5.18311 | + | 8.97741i | −0.375037 | + | 0.649582i | −0.990333 | − | 0.138714i | \(-0.955703\pi\) |
0.615296 | + | 0.788296i | \(0.289037\pi\) | |||||||
\(192\) | −0.662827 | + | 0.382683i | −0.0478354 | + | 0.0276178i | ||||
\(193\) | 1.40584 | − | 0.811664i | 0.101195 | − | 0.0584248i | −0.448549 | − | 0.893758i | \(-0.648059\pi\) |
0.549743 | + | 0.835334i | \(0.314726\pi\) | |||||||
\(194\) | 4.61940 | − | 8.00103i | 0.331653 | − | 0.574441i | ||||
\(195\) | 10.3587 | 0.741805 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.38713i | − | 0.312570i | −0.987712 | − | 0.156285i | \(-0.950048\pi\) | ||
0.987712 | − | 0.156285i | \(-0.0499518\pi\) | |||||||
\(198\) | 7.85223 | − | 1.56693i | 0.558033 | − | 0.111357i | ||||
\(199\) | −17.3760 | + | 10.0320i | −1.23175 | + | 0.711151i | −0.967394 | − | 0.253275i | \(-0.918492\pi\) |
−0.264355 | + | 0.964426i | \(0.585159\pi\) | |||||||
\(200\) | 0.684927 | − | 0.395443i | 0.0484317 | − | 0.0279620i | ||||
\(201\) | −1.96360 | − | 1.13368i | −0.138502 | − | 0.0799639i | ||||
\(202\) | 1.85966i | 0.130845i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 2.76380i | − | 0.193505i | ||||||
\(205\) | −4.20847 | − | 2.42976i | −0.293933 | − | 0.169702i | ||||
\(206\) | 3.35505 | + | 5.81112i | 0.233758 | + | 0.404880i | ||||
\(207\) | −7.99022 | − | 13.8395i | −0.555359 | − | 0.961909i | ||||
\(208\) | 3.29847 | − | 5.71311i | 0.228708 | − | 0.396133i | ||||
\(209\) | 2.18952 | − | 1.92254i | 0.151452 | − | 0.132985i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 8.56380i | − | 0.589556i | −0.955566 | − | 0.294778i | \(-0.904754\pi\) | ||
0.955566 | − | 0.294778i | \(-0.0952457\pi\) | |||||||
\(212\) | 0.214882 | − | 0.372186i | 0.0147581 | − | 0.0255619i | ||||
\(213\) | −1.41449 | + | 0.816659i | −0.0969195 | + | 0.0559565i | ||||
\(214\) | 7.37667 | + | 12.7768i | 0.504259 | + | 0.873402i | ||||
\(215\) | 8.01450 | − | 13.8815i | 0.546584 | − | 0.946712i | ||||
\(216\) | −4.14386 | −0.281954 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.00000 | −0.406371 | ||||||||
\(219\) | −7.17526 | − | 4.14264i | −0.484859 | − | 0.279934i | ||||
\(220\) | −2.18325 | + | 6.44466i | −0.147195 | + | 0.434499i | ||||
\(221\) | 11.9110 | + | 20.6305i | 0.801223 | + | 1.38776i | ||||
\(222\) | 4.22830 | − | 7.32363i | 0.283785 | − | 0.491530i | ||||
\(223\) | 8.24084i | 0.551848i | 0.961180 | + | 0.275924i | \(0.0889837\pi\) | ||||
−0.961180 | + | 0.275924i | \(0.911016\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.90937 | 0.127291 | ||||||||
\(226\) | −0.517296 | − | 0.298661i | −0.0344100 | − | 0.0198666i | ||||
\(227\) | 13.7397 | + | 23.7979i | 0.911938 | + | 1.57952i | 0.811324 | + | 0.584597i | \(0.198747\pi\) |
0.100614 | + | 0.994926i | \(0.467919\pi\) | |||||||
\(228\) | −0.582319 | + | 0.336202i | −0.0385650 | + | 0.0222655i | ||||
\(229\) | −0.0903638 | − | 0.0521716i | −0.00597141 | − | 0.00344759i | 0.497011 | − | 0.867744i | \(-0.334431\pi\) |
−0.502983 | + | 0.864296i | \(0.667764\pi\) | |||||||
\(230\) | 13.5803 | 0.895456 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.18955 | −0.406364 | ||||||||
\(233\) | −13.1269 | − | 7.57884i | −0.859974 | − | 0.496507i | 0.00402925 | − | 0.999992i | \(-0.498717\pi\) |
−0.864004 | + | 0.503485i | \(0.832051\pi\) | |||||||
\(234\) | 13.7927 | − | 7.96321i | 0.901656 | − | 0.520571i | ||||
\(235\) | 5.89544 | + | 10.2112i | 0.384576 | + | 0.666106i | ||||
\(236\) | 2.78725 | + | 1.60922i | 0.181435 | + | 0.104751i | ||||
\(237\) | −6.49435 | −0.421854 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 25.9135i | − | 1.67620i | −0.545515 | − | 0.838101i | \(-0.683666\pi\) | ||
0.545515 | − | 0.838101i | \(-0.316334\pi\) | |||||||
\(240\) | 0.785118 | − | 1.35986i | 0.0506792 | − | 0.0877789i | ||||
\(241\) | −3.65554 | − | 6.33158i | −0.235474 | − | 0.407853i | 0.723936 | − | 0.689867i | \(-0.242331\pi\) |
−0.959410 | + | 0.282014i | \(0.908998\pi\) | |||||||
\(242\) | 4.22202 | + | 10.1575i | 0.271402 | + | 0.652948i | ||||
\(243\) | −13.4645 | − | 7.77372i | −0.863747 | − | 0.498684i | ||||
\(244\) | −11.3342 | −0.725599 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.81288 | 0.115585 | ||||||||
\(247\) | 2.89783 | − | 5.01919i | 0.184385 | − | 0.319364i | ||||
\(248\) | 3.24188 | + | 5.61510i | 0.205860 | + | 0.356560i | ||||
\(249\) | −8.16294 | + | 4.71287i | −0.517305 | + | 0.298666i | ||||
\(250\) | −5.94033 | + | 10.2889i | −0.375699 | + | 0.650730i | ||||
\(251\) | − | 10.0161i | − | 0.632208i | −0.948724 | − | 0.316104i | \(-0.897625\pi\) | ||
0.948724 | − | 0.316104i | \(-0.102375\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.4968 | − | 14.4853i | 1.03715 | − | 0.910682i | ||||
\(254\) | 3.66501 | − | 6.34799i | 0.229963 | − | 0.398308i | ||||
\(255\) | 2.83512 | + | 4.91058i | 0.177542 | + | 0.307512i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 15.1654 | + | 8.75577i | 0.945994 | + | 0.546170i | 0.891834 | − | 0.452362i | \(-0.149419\pi\) |
0.0541598 | + | 0.998532i | \(0.482752\pi\) | |||||||
\(258\) | 5.97972i | 0.372281i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 13.5344i | 0.839365i | ||||||||
\(261\) | −12.9409 | − | 7.47145i | −0.801023 | − | 0.462471i | ||||
\(262\) | −7.63878 | + | 4.41025i | −0.471925 | + | 0.272466i | ||||
\(263\) | 7.34847 | − | 4.24264i | 0.453126 | − | 0.261612i | −0.256023 | − | 0.966671i | \(-0.582412\pi\) |
0.709150 | + | 0.705058i | \(0.249079\pi\) | |||||||
\(264\) | −0.496755 | − | 2.48935i | −0.0305732 | − | 0.153209i | ||||
\(265\) | 0.881709i | 0.0541629i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.14958 | 0.315149 | ||||||||
\(268\) | 1.48123 | − | 2.56556i | 0.0904805 | − | 0.156717i | ||||
\(269\) | −5.85020 | + | 3.37761i | −0.356693 | + | 0.205937i | −0.667629 | − | 0.744494i | \(-0.732691\pi\) |
0.310936 | + | 0.950431i | \(0.399357\pi\) | |||||||
\(270\) | 7.36260 | − | 4.25080i | 0.448073 | − | 0.258695i | ||||
\(271\) | 9.77158 | − | 16.9249i | 0.593581 | − | 1.02811i | −0.400164 | − | 0.916443i | \(-0.631047\pi\) |
0.993745 | − | 0.111669i | \(-0.0356197\pi\) | |||||||
\(272\) | 3.61108 | 0.218954 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 3.23620i | − | 0.195506i | ||||||
\(275\) | 0.513318 | + | 2.57235i | 0.0309543 | + | 0.155119i | ||||
\(276\) | −4.38746 | + | 2.53310i | −0.264094 | + | 0.152475i | ||||
\(277\) | −23.1011 | + | 13.3374i | −1.38801 | + | 0.801368i | −0.993091 | − | 0.117348i | \(-0.962561\pi\) |
−0.394919 | + | 0.918716i | \(0.629227\pi\) | |||||||
\(278\) | 2.14014 | + | 1.23561i | 0.128357 | + | 0.0741070i | ||||
\(279\) | 15.6532i | 0.937132i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.9533i | 1.24997i | 0.780636 | + | 0.624986i | \(0.214895\pi\) | ||||
−0.780636 | + | 0.624986i | \(0.785105\pi\) | |||||||
\(282\) | −3.80935 | − | 2.19933i | −0.226844 | − | 0.130968i | ||||
\(283\) | −5.03147 | − | 8.71476i | −0.299090 | − | 0.518039i | 0.676838 | − | 0.736132i | \(-0.263350\pi\) |
−0.975928 | + | 0.218093i | \(0.930016\pi\) | |||||||
\(284\) | −1.06702 | − | 1.84813i | −0.0633157 | − | 0.109666i | ||||
\(285\) | 0.689757 | − | 1.19469i | 0.0408577 | − | 0.0707675i | ||||
\(286\) | 14.4363 | + | 16.4410i | 0.853637 | + | 0.972180i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 2.41421i | − | 0.142259i | ||||||
\(289\) | 1.98005 | − | 3.42955i | 0.116474 | − | 0.201738i | ||||
\(290\) | 10.9973 | − | 6.34928i | 0.645782 | − | 0.372842i | ||||
\(291\) | −3.53553 | − | 6.12372i | −0.207257 | − | 0.358979i | ||||
\(292\) | 5.41262 | − | 9.37493i | 0.316749 | − | 0.548626i | ||||
\(293\) | −29.6429 | −1.73176 | −0.865879 | − | 0.500253i | \(-0.833240\pi\) | ||||
−0.865879 | + | 0.500253i | \(0.833240\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.60300 | −0.384442 | ||||||||
\(296\) | 9.56878 | + | 5.52454i | 0.556174 | + | 0.321107i | ||||
\(297\) | 4.40974 | − | 13.0170i | 0.255879 | − | 0.755321i | ||||
\(298\) | −1.95430 | − | 3.38495i | −0.113210 | − | 0.196085i | ||||
\(299\) | 21.8336 | − | 37.8169i | 1.26267 | − | 2.18701i | ||||
\(300\) | − | 0.605318i | − | 0.0349480i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 24.1895 | 1.39195 | ||||||||
\(303\) | 1.23263 | + | 0.711661i | 0.0708129 | + | 0.0408839i | ||||
\(304\) | −0.439269 | − | 0.760837i | −0.0251938 | − | 0.0436370i | ||||
\(305\) | 20.1380 | − | 11.6267i | 1.15310 | − | 0.665743i | ||||
\(306\) | 7.54994 | + | 4.35896i | 0.431601 | + | 0.249185i | ||||
\(307\) | 16.1877 | 0.923883 | 0.461941 | − | 0.886910i | \(-0.347153\pi\) | ||||
0.461941 | + | 0.886910i | \(0.347153\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.13569 | 0.292159 | ||||||||
\(310\) | −11.5200 | − | 6.65109i | −0.654293 | − | 0.377756i | ||||
\(311\) | −1.23529 | + | 0.713195i | −0.0700469 | + | 0.0404416i | −0.534614 | − | 0.845096i | \(-0.679543\pi\) |
0.464568 | + | 0.885538i | \(0.346210\pi\) | |||||||
\(312\) | −2.52454 | − | 4.37263i | −0.142924 | − | 0.247551i | ||||
\(313\) | 9.99982 | + | 5.77340i | 0.565223 | + | 0.326332i | 0.755239 | − | 0.655449i | \(-0.227521\pi\) |
−0.190016 | + | 0.981781i | \(0.560854\pi\) | |||||||
\(314\) | −20.3029 | −1.14576 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 8.48528i | − | 0.477334i | ||||||
\(317\) | −15.8620 | + | 27.4737i | −0.890896 | + | 1.54308i | −0.0520931 | + | 0.998642i | \(0.516589\pi\) |
−0.838803 | + | 0.544435i | \(0.816744\pi\) | |||||||
\(318\) | −0.164463 | − | 0.284859i | −0.00922265 | − | 0.0159741i | ||||
\(319\) | 6.58668 | − | 19.4430i | 0.368783 | − | 1.08860i | ||||
\(320\) | 1.77675 | + | 1.02581i | 0.0993233 | + | 0.0573443i | ||||
\(321\) | 11.2917 | 0.630242 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.17247 | 0.176521 | ||||||||
\(324\) | 2.03553 | − | 3.52565i | 0.113085 | − | 0.195869i | ||||
\(325\) | 2.60871 | + | 4.51842i | 0.144705 | + | 0.250637i | ||||
\(326\) | 11.4840 | − | 6.63031i | 0.636042 | − | 0.367219i | ||||
\(327\) | −2.29610 | + | 3.97696i | −0.126975 | + | 0.219927i | ||||
\(328\) | 2.36864i | 0.130786i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.43620 | + | 3.91338i | 0.189157 | + | 0.215425i | ||||
\(331\) | −15.9620 | + | 27.6469i | −0.877348 | + | 1.51961i | −0.0231086 | + | 0.999733i | \(0.507356\pi\) |
−0.854240 | + | 0.519879i | \(0.825977\pi\) | |||||||
\(332\) | −6.15767 | − | 10.6654i | −0.337946 | − | 0.585339i | ||||
\(333\) | 13.3374 | + | 23.1011i | 0.730886 | + | 1.26593i | ||||
\(334\) | −17.6808 | − | 10.2080i | −0.967450 | − | 0.558558i | ||||
\(335\) | 6.07782i | 0.332067i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.40854i | − | 0.0767278i | −0.999264 | − | 0.0383639i | \(-0.987785\pi\) | ||
0.999264 | − | 0.0383639i | \(-0.0122146\pi\) | |||||||
\(338\) | 26.4307 | + | 15.2598i | 1.43764 | + | 0.830023i | ||||
\(339\) | −0.395921 | + | 0.228585i | −0.0215035 | + | 0.0124150i | ||||
\(340\) | −6.41598 | + | 3.70427i | −0.347955 | + | 0.200892i | ||||
\(341\) | −21.0884 | + | 4.20824i | −1.14200 | + | 0.227889i | ||||
\(342\) | − | 2.12098i | − | 0.114689i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.81288 | −0.421242 | ||||||||
\(345\) | 5.19694 | − | 9.00137i | 0.279794 | − | 0.484617i | ||||
\(346\) | −13.4894 | + | 7.78809i | −0.725193 | + | 0.418690i | ||||
\(347\) | 9.55973 | − | 5.51931i | 0.513193 | − | 0.296292i | −0.220952 | − | 0.975285i | \(-0.570916\pi\) |
0.734145 | + | 0.678993i | \(0.237583\pi\) | |||||||
\(348\) | −2.36864 | + | 4.10260i | −0.126972 | + | 0.219923i | ||||
\(349\) | 15.5762 | 0.833773 | 0.416887 | − | 0.908958i | \(-0.363121\pi\) | ||||
0.416887 | + | 0.908958i | \(0.363121\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 27.3368i | − | 1.45913i | ||||||
\(352\) | 3.25250 | − | 0.649042i | 0.173359 | − | 0.0345941i | ||||
\(353\) | −5.44549 | + | 3.14396i | −0.289834 | + | 0.167336i | −0.637867 | − | 0.770146i | \(-0.720183\pi\) |
0.348033 | + | 0.937482i | \(0.386850\pi\) | |||||||
\(354\) | 2.13327 | − | 1.23165i | 0.113382 | − | 0.0654612i | ||||
\(355\) | 3.79164 | + | 2.18910i | 0.201239 | + | 0.116186i | ||||
\(356\) | 6.72825i | 0.356597i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.50159i | 0.237917i | ||||||||
\(359\) | −8.90941 | − | 5.14385i | −0.470221 | − | 0.271482i | 0.246111 | − | 0.969242i | \(-0.420847\pi\) |
−0.716332 | + | 0.697759i | \(0.754180\pi\) | |||||||
\(360\) | 2.47652 | + | 4.28945i | 0.130524 | + | 0.226074i | ||||
\(361\) | 9.11408 | + | 15.7861i | 0.479689 | + | 0.830845i | ||||
\(362\) | −4.09169 | + | 7.08701i | −0.215054 | + | 0.372485i | ||||
\(363\) | 8.34836 | + | 1.08864i | 0.438175 | + | 0.0571385i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.2092i | 1.16248i | ||||||||
\(366\) | −4.33742 | + | 7.51262i | −0.226720 | + | 0.392691i | ||||
\(367\) | 3.91575 | − | 2.26076i | 0.204401 | − | 0.118011i | −0.394306 | − | 0.918979i | \(-0.629015\pi\) |
0.598706 | + | 0.800969i | \(0.295682\pi\) | |||||||
\(368\) | −3.30966 | − | 5.73249i | −0.172528 | − | 0.298827i | ||||
\(369\) | −2.85920 | + | 4.95228i | −0.148844 | + | 0.257805i | ||||
\(370\) | −22.6684 | −1.17848 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.96246 | 0.257291 | ||||||||
\(373\) | 17.0814 | + | 9.86195i | 0.884442 | + | 0.510633i | 0.872120 | − | 0.489291i | \(-0.162745\pi\) |
0.0123213 | + | 0.999924i | \(0.496078\pi\) | |||||||
\(374\) | −3.84277 | + | 11.3434i | −0.198705 | + | 0.586551i | ||||
\(375\) | 4.54653 | + | 7.87482i | 0.234782 | + | 0.406654i | ||||
\(376\) | 2.87357 | − | 4.97716i | 0.148193 | − | 0.256677i | ||||
\(377\) | − | 40.8321i | − | 2.10296i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.6268 | −1.83003 | −0.915014 | − | 0.403423i | \(-0.867820\pi\) | ||||
−0.915014 | + | 0.403423i | \(0.867820\pi\) | |||||||
\(380\) | 1.56094 | + | 0.901211i | 0.0800747 | + | 0.0462311i | ||||
\(381\) | −2.80508 | − | 4.85854i | −0.143708 | − | 0.248910i | ||||
\(382\) | −8.97741 | + | 5.18311i | −0.459324 | + | 0.265191i | ||||
\(383\) | −18.7384 | − | 10.8186i | −0.957488 | − | 0.552806i | −0.0620891 | − | 0.998071i | \(-0.519776\pi\) |
−0.895399 | + | 0.445265i | \(0.853110\pi\) | |||||||
\(384\) | −0.765367 | −0.0390575 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.62333 | 0.0826252 | ||||||||
\(387\) | −16.3349 | − | 9.43098i | −0.830351 | − | 0.479403i | ||||
\(388\) | 8.00103 | − | 4.61940i | 0.406191 | − | 0.234514i | ||||
\(389\) | 4.32349 | + | 7.48851i | 0.219210 | + | 0.379682i | 0.954567 | − | 0.297998i | \(-0.0963188\pi\) |
−0.735357 | + | 0.677680i | \(0.762985\pi\) | |||||||
\(390\) | 8.97094 | + | 5.17937i | 0.454261 | + | 0.262268i | ||||
\(391\) | 23.9029 | 1.20882 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.75092i | 0.340539i | ||||||||
\(394\) | 2.19356 | − | 3.79936i | 0.110510 | − | 0.191409i | ||||
\(395\) | 8.70426 | + | 15.0762i | 0.437959 | + | 0.758567i | ||||
\(396\) | 7.58369 | + | 2.56911i | 0.381095 | + | 0.129103i | ||||
\(397\) | 31.3257 | + | 18.0859i | 1.57219 | + | 0.907705i | 0.995900 | + | 0.0904617i | \(0.0288343\pi\) |
0.576292 | + | 0.817244i | \(0.304499\pi\) | |||||||
\(398\) | −20.0640 | −1.00572 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.790886 | 0.0395443 | ||||||||
\(401\) | 4.49678 | − | 7.78865i | 0.224558 | − | 0.388947i | −0.731628 | − | 0.681704i | \(-0.761239\pi\) |
0.956187 | + | 0.292757i | \(0.0945727\pi\) | |||||||
\(402\) | −1.13368 | − | 1.96360i | −0.0565430 | − | 0.0979354i | ||||
\(403\) | −37.0425 | + | 21.3865i | −1.84522 | + | 1.06534i | ||||
\(404\) | −0.929830 | + | 1.61051i | −0.0462608 | + | 0.0801260i | ||||
\(405\) | 8.35225i | 0.415027i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −27.5368 | + | 24.1791i | −1.36495 | + | 1.19851i | ||||
\(408\) | 1.38190 | − | 2.39352i | 0.0684143 | − | 0.118497i | ||||
\(409\) | −4.79140 | − | 8.29894i | −0.236919 | − | 0.410356i | 0.722909 | − | 0.690943i | \(-0.242804\pi\) |
−0.959829 | + | 0.280587i | \(0.909471\pi\) | |||||||
\(410\) | −2.42976 | − | 4.20847i | −0.119997 | − | 0.207842i | ||||
\(411\) | −2.14504 | − | 1.23844i | −0.105807 | − | 0.0610877i | ||||
\(412\) | 6.71011i | 0.330583i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 15.9804i | − | 0.785396i | ||||||
\(415\) | 21.8813 | + | 12.6331i | 1.07411 | + | 0.620137i | ||||
\(416\) | 5.71311 | − | 3.29847i | 0.280108 | − | 0.161721i | ||||
\(417\) | 1.63799 | − | 0.945695i | 0.0802128 | − | 0.0463109i | ||||
\(418\) | 2.85745 | − | 0.570209i | 0.139762 | − | 0.0278898i | ||||
\(419\) | − | 37.9064i | − | 1.85185i | −0.377709 | − | 0.925924i | \(-0.623288\pi\) | ||
0.377709 | − | 0.925924i | \(-0.376712\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.88394 | 0.140555 | 0.0702774 | − | 0.997527i | \(-0.477612\pi\) | ||||
0.0702774 | + | 0.997527i | \(0.477612\pi\) | |||||||
\(422\) | 4.28190 | − | 7.41646i | 0.208440 | − | 0.361028i | ||||
\(423\) | 12.0159 | − | 6.93740i | 0.584235 | − | 0.337308i | ||||
\(424\) | 0.372186 | − | 0.214882i | 0.0180750 | − | 0.0104356i | ||||
\(425\) | −1.42798 | + | 2.47333i | −0.0692670 | + | 0.119974i | ||||
\(426\) | −1.63332 | −0.0791345 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 14.7533i | 0.713130i | ||||||||
\(429\) | 16.4221 | − | 3.27706i | 0.792867 | − | 0.158218i | ||||
\(430\) | 13.8815 | − | 8.01450i | 0.669426 | − | 0.386493i | ||||
\(431\) | −28.0651 | + | 16.2034i | −1.35185 | + | 0.780490i | −0.988508 | − | 0.151167i | \(-0.951697\pi\) |
−0.363339 | + | 0.931657i | \(0.618363\pi\) | |||||||
\(432\) | −3.58869 | − | 2.07193i | −0.172661 | − | 0.0996858i | ||||
\(433\) | − | 10.2319i | − | 0.491714i | −0.969306 | − | 0.245857i | \(-0.920931\pi\) | ||
0.969306 | − | 0.245857i | \(-0.0790694\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 9.71905i | − | 0.465993i | ||||||
\(436\) | −5.19615 | − | 3.00000i | −0.248851 | − | 0.143674i | ||||
\(437\) | −2.90766 | − | 5.03622i | −0.139092 | − | 0.240915i | ||||
\(438\) | −4.14264 | − | 7.17526i | −0.197943 | − | 0.342847i | ||||
\(439\) | −14.4363 | + | 25.0044i | −0.689008 | + | 1.19340i | 0.283152 | + | 0.959075i | \(0.408620\pi\) |
−0.972159 | + | 0.234321i | \(0.924713\pi\) | |||||||
\(440\) | −5.11308 | + | 4.48962i | −0.243757 | + | 0.214034i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 23.8221i | 1.13310i | ||||||||
\(443\) | 4.28018 | − | 7.41349i | 0.203358 | − | 0.352226i | −0.746251 | − | 0.665665i | \(-0.768148\pi\) |
0.949608 | + | 0.313439i | \(0.101481\pi\) | |||||||
\(444\) | 7.32363 | − | 4.22830i | 0.347564 | − | 0.200666i | ||||
\(445\) | −6.90188 | − | 11.9544i | −0.327181 | − | 0.566694i | ||||
\(446\) | −4.12042 | + | 7.13678i | −0.195108 | + | 0.337936i | ||||
\(447\) | −2.99152 | −0.141494 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.8089 | −0.510102 | −0.255051 | − | 0.966928i | \(-0.582092\pi\) | ||||
−0.255051 | + | 0.966928i | \(0.582092\pi\) | |||||||
\(450\) | 1.65356 | + | 0.954684i | 0.0779496 | + | 0.0450042i | ||||
\(451\) | −7.44052 | − | 2.52061i | −0.350361 | − | 0.118691i | ||||
\(452\) | −0.298661 | − | 0.517296i | −0.0140478 | − | 0.0243315i | ||||
\(453\) | 9.25694 | − | 16.0335i | 0.434929 | − | 0.753319i | ||||
\(454\) | 27.4795i | 1.28967i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.672404 | −0.0314882 | ||||||||
\(457\) | −21.1220 | − | 12.1948i | −0.988044 | − | 0.570448i | −0.0833551 | − | 0.996520i | \(-0.526564\pi\) |
−0.904689 | + | 0.426072i | \(0.859897\pi\) | |||||||
\(458\) | −0.0521716 | − | 0.0903638i | −0.00243782 | − | 0.00422242i | ||||
\(459\) | 12.9590 | − | 7.48190i | 0.604876 | − | 0.349225i | ||||
\(460\) | 11.7609 | + | 6.79013i | 0.548353 | + | 0.316592i | ||||
\(461\) | 1.13186 | 0.0527158 | 0.0263579 | − | 0.999653i | \(-0.491609\pi\) | ||||
0.0263579 | + | 0.999653i | \(0.491609\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.38388 | 0.296684 | 0.148342 | − | 0.988936i | \(-0.452606\pi\) | ||||
0.148342 | + | 0.988936i | \(0.452606\pi\) | |||||||
\(464\) | −5.36031 | − | 3.09477i | −0.248846 | − | 0.143671i | ||||
\(465\) | −8.81704 | + | 5.09052i | −0.408881 | + | 0.236067i | ||||
\(466\) | −7.57884 | − | 13.1269i | −0.351083 | − | 0.608094i | ||||
\(467\) | −30.9033 | − | 17.8420i | −1.43003 | − | 0.825629i | −0.432910 | − | 0.901437i | \(-0.642513\pi\) |
−0.997122 | + | 0.0758078i | \(0.975846\pi\) | |||||||
\(468\) | 15.9264 | 0.736199 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 11.7909i | 0.543873i | ||||||||
\(471\) | −7.76957 | + | 13.4573i | −0.358003 | + | 0.620079i | ||||
\(472\) | 1.60922 | + | 2.78725i | 0.0740704 | + | 0.128294i | ||||
\(473\) | 8.31417 | − | 24.5423i | 0.382286 | − | 1.12846i | ||||
\(474\) | −5.62427 | − | 3.24718i | −0.258331 | − | 0.149148i | ||||
\(475\) | 0.694824 | 0.0318807 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.03754 | 0.0475058 | ||||||||
\(478\) | 12.9567 | − | 22.4417i | 0.592627 | − | 1.02646i | ||||
\(479\) | −5.79094 | − | 10.0302i | −0.264595 | − | 0.458291i | 0.702863 | − | 0.711325i | \(-0.251905\pi\) |
−0.967457 | + | 0.253034i | \(0.918571\pi\) | |||||||
\(480\) | 1.35986 | − | 0.785118i | 0.0620690 | − | 0.0358356i | ||||
\(481\) | −36.4450 | + | 63.1246i | −1.66175 | + | 2.87824i | ||||
\(482\) | − | 7.31108i | − | 0.333011i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.42237 | + | 10.9077i | −0.0646532 | + | 0.495802i | ||||
\(485\) | −9.47721 | + | 16.4150i | −0.430338 | + | 0.745368i | ||||
\(486\) | −7.77372 | − | 13.4645i | −0.352623 | − | 0.610761i | ||||
\(487\) | −20.0319 | − | 34.6963i | −0.907732 | − | 1.57224i | −0.817207 | − | 0.576344i | \(-0.804479\pi\) |
−0.0905248 | − | 0.995894i | \(-0.528854\pi\) | |||||||
\(488\) | −9.81572 | − | 5.66711i | −0.444337 | − | 0.256538i | ||||
\(489\) | − | 10.1492i | − | 0.458964i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19.7876i | − | 0.893003i | −0.894783 | − | 0.446502i | \(-0.852670\pi\) | ||
0.894783 | − | 0.446502i | \(-0.147330\pi\) | |||||||
\(492\) | 1.57000 | + | 0.906438i | 0.0707810 | + | 0.0408654i | ||||
\(493\) | 19.3565 | − | 11.1755i | 0.871773 | − | 0.503318i | ||||
\(494\) | 5.01919 | − | 2.89783i | 0.225824 | − | 0.130380i | ||||
\(495\) | −16.1097 | + | 3.21473i | −0.724078 | + | 0.144491i | ||||
\(496\) | 6.48376i | 0.291130i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −9.42575 | −0.422378 | ||||||||
\(499\) | 13.3276 | − | 23.0841i | 0.596627 | − | 1.03339i | −0.396688 | − | 0.917953i | \(-0.629841\pi\) |
0.993315 | − | 0.115435i | \(-0.0368260\pi\) | |||||||
\(500\) | −10.2889 | + | 5.94033i | −0.460136 | + | 0.265660i | ||||
\(501\) | −13.5323 | + | 7.81288i | −0.604579 | + | 0.349054i | ||||
\(502\) | 5.00803 | − | 8.67417i | 0.223519 | − | 0.387147i | ||||
\(503\) | −10.9142 | −0.486638 | −0.243319 | − | 0.969946i | \(-0.578236\pi\) | ||||
−0.243319 | + | 0.969946i | \(0.578236\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3.81530i | − | 0.169779i | ||||||
\(506\) | 21.5293 | − | 4.29621i | 0.957094 | − | 0.190990i | ||||
\(507\) | 20.2292 | − | 11.6793i | 0.898410 | − | 0.518697i | ||||
\(508\) | 6.34799 | − | 3.66501i | 0.281646 | − | 0.162609i | ||||
\(509\) | 19.4284 | + | 11.2170i | 0.861149 | + | 0.497184i | 0.864397 | − | 0.502810i | \(-0.167701\pi\) |
−0.00324816 | + | 0.999995i | \(0.501034\pi\) | |||||||
\(510\) | 5.67025i | 0.251083i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −3.15280 | − | 1.82027i | −0.139200 | − | 0.0803669i | ||||
\(514\) | 8.75577 | + | 15.1654i | 0.386200 | + | 0.668919i | ||||
\(515\) | −6.88327 | − | 11.9222i | −0.303313 | − | 0.525354i | ||||
\(516\) | −2.98986 | + | 5.17859i | −0.131621 | + | 0.227975i | ||||
\(517\) | 12.5767 | + | 14.3231i | 0.553121 | + | 0.629931i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.9215i | 0.523295i | ||||||||
\(520\) | −6.76718 | + | 11.7211i | −0.296760 | + | 0.514004i | ||||
\(521\) | −33.9574 | + | 19.6053i | −1.48770 | + | 0.858925i | −0.999902 | − | 0.0140307i | \(-0.995534\pi\) |
−0.487800 | + | 0.872955i | \(0.662200\pi\) | |||||||
\(522\) | −7.47145 | − | 12.9409i | −0.327016 | − | 0.566409i | ||||
\(523\) | 9.04494 | − | 15.6663i | 0.395508 | − | 0.685039i | −0.597658 | − | 0.801751i | \(-0.703902\pi\) |
0.993166 | + | 0.116712i | \(0.0372353\pi\) | |||||||
\(524\) | −8.82050 | −0.385325 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.48528 | 0.369976 | ||||||||
\(527\) | −20.2766 | − | 11.7067i | −0.883262 | − | 0.509952i | ||||
\(528\) | 0.814474 | − | 2.40422i | 0.0354454 | − | 0.104630i | ||||
\(529\) | −10.4077 | − | 18.0266i | −0.452507 | − | 0.783764i | ||||
\(530\) | −0.440854 | + | 0.763582i | −0.0191495 | + | 0.0331679i | ||||
\(531\) | 7.77001i | 0.337190i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.6258 | −0.676827 | ||||||||
\(534\) | 4.45967 | + | 2.57479i | 0.192989 | + | 0.111422i | ||||
\(535\) | −15.1341 | − | 26.2130i | −0.654303 | − | 1.13329i | ||||
\(536\) | 2.56556 | − | 1.48123i | 0.110816 | − | 0.0639794i | ||||
\(537\) | 2.98378 | + | 1.72269i | 0.128760 | + | 0.0743394i | ||||
\(538\) | −6.75523 | −0.291238 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.50159 | 0.365850 | ||||||||
\(541\) | −8.33615 | − | 4.81288i | −0.358399 | − | 0.206922i | 0.309979 | − | 0.950743i | \(-0.399678\pi\) |
−0.668378 | + | 0.743822i | \(0.733011\pi\) | |||||||
\(542\) | 16.9249 | − | 9.77158i | 0.726985 | − | 0.419725i | ||||
\(543\) | 3.13164 | + | 5.42416i | 0.134392 | + | 0.232773i | ||||
\(544\) | 3.12729 | + | 1.80554i | 0.134081 | + | 0.0774119i | ||||
\(545\) | 12.3097 | 0.527289 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 10.2834i | − | 0.439685i | −0.975535 | − | 0.219843i | \(-0.929446\pi\) | ||
0.975535 | − | 0.219843i | \(-0.0705544\pi\) | |||||||
\(548\) | 1.61810 | − | 2.80263i | 0.0691218 | − | 0.119722i | ||||
\(549\) | −13.6816 | − | 23.6972i | −0.583917 | − | 1.01137i | ||||
\(550\) | −0.841631 | + | 2.48438i | −0.0358873 | + | 0.105934i | ||||
\(551\) | −4.70924 | − | 2.71888i | −0.200620 | − | 0.115828i | ||||
\(552\) | −5.06620 | −0.215632 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −26.6748 | −1.13330 | ||||||||
\(555\) | −8.67483 | + | 15.0252i | −0.368226 | + | 0.637786i | ||||
\(556\) | 1.23561 | + | 2.14014i | 0.0524016 | + | 0.0907622i | ||||
\(557\) | −32.2426 | + | 18.6153i | −1.36616 | + | 0.788755i | −0.990436 | − | 0.137974i | \(-0.955941\pi\) |
−0.375729 | + | 0.926730i | \(0.622608\pi\) | |||||||
\(558\) | −7.82660 | + | 13.5561i | −0.331326 | + | 0.573874i | ||||
\(559\) | − | 51.5411i | − | 2.17995i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.04812 | + | 6.88801i | 0.255352 | + | 0.290812i | ||||
\(562\) | −10.4767 | + | 18.1461i | −0.441932 | + | 0.765448i | ||||
\(563\) | −8.09387 | − | 14.0190i | −0.341116 | − | 0.590830i | 0.643524 | − | 0.765426i | \(-0.277471\pi\) |
−0.984640 | + | 0.174596i | \(0.944138\pi\) | |||||||
\(564\) | −2.19933 | − | 3.80935i | −0.0926086 | − | 0.160403i | ||||
\(565\) | 1.06129 | + | 0.612736i | 0.0446488 | + | 0.0257780i | ||||
\(566\) | − | 10.0629i | − | 0.422977i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 2.13403i | − | 0.0895420i | ||||||
\(569\) | 26.4052 | + | 15.2451i | 1.10696 | + | 0.639106i | 0.938042 | − | 0.346523i | \(-0.112638\pi\) |
0.168923 | + | 0.985629i | \(0.445971\pi\) | |||||||
\(570\) | 1.19469 | − | 0.689757i | 0.0500402 | − | 0.0288907i | ||||
\(571\) | 35.0634 | − | 20.2439i | 1.46736 | − | 0.847179i | 0.468025 | − | 0.883715i | \(-0.344966\pi\) |
0.999332 | + | 0.0365365i | \(0.0116325\pi\) | |||||||
\(572\) | 4.28169 | + | 21.4565i | 0.179026 | + | 0.897142i | ||||
\(573\) | 7.93396i | 0.331446i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.23512 | 0.218320 | ||||||||
\(576\) | 1.20711 | − | 2.09077i | 0.0502961 | − | 0.0871154i | ||||
\(577\) | 22.1360 | − | 12.7802i | 0.921533 | − | 0.532047i | 0.0374092 | − | 0.999300i | \(-0.488090\pi\) |
0.884124 | + | 0.467253i | \(0.154756\pi\) | |||||||
\(578\) | 3.42955 | − | 1.98005i | 0.142651 | − | 0.0823594i | ||||
\(579\) | 0.621221 | − | 1.07599i | 0.0258170 | − | 0.0447164i | ||||
\(580\) | 12.6986 | 0.527279 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 7.07107i | − | 0.293105i | ||||||
\(583\) | 0.278935 | + | 1.39781i | 0.0115523 | + | 0.0578912i | ||||
\(584\) | 9.37493 | − | 5.41262i | 0.387937 | − | 0.223976i | ||||
\(585\) | −28.2972 | + | 16.3374i | −1.16995 | + | 0.675469i | ||||
\(586\) | −25.6715 | − | 14.8215i | −1.06048 | − | 0.612269i | ||||
\(587\) | 7.18094i | 0.296389i | 0.988958 | + | 0.148195i | \(0.0473462\pi\) | ||||
−0.988958 | + | 0.148195i | \(0.952654\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.69624i | 0.234709i | ||||||||
\(590\) | −5.71837 | − | 3.30150i | −0.235421 | − | 0.135921i | ||||
\(591\) | −1.67888 | − | 2.90791i | −0.0690599 | − | 0.119615i | ||||
\(592\) | 5.52454 | + | 9.56878i | 0.227057 | + | 0.393274i | ||||
\(593\) | −9.88857 | + | 17.1275i | −0.406075 | + | 0.703343i | −0.994446 | − | 0.105249i | \(-0.966436\pi\) |
0.588371 | + | 0.808591i | \(0.299770\pi\) | |||||||
\(594\) | 10.3274 | − | 9.06816i | 0.423740 | − | 0.372071i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 3.90860i | − | 0.160103i | ||||||
\(597\) | −7.67817 | + | 13.2990i | −0.314247 | + | 0.544291i | ||||
\(598\) | 37.8169 | − | 21.8336i | 1.54645 | − | 0.892842i | ||||
\(599\) | 6.87989 | + | 11.9163i | 0.281105 | + | 0.486888i | 0.971657 | − | 0.236395i | \(-0.0759658\pi\) |
−0.690552 | + | 0.723282i | \(0.742632\pi\) | |||||||
\(600\) | 0.302659 | − | 0.524221i | 0.0123560 | − | 0.0214012i | ||||
\(601\) | 11.0384 | 0.450266 | 0.225133 | − | 0.974328i | \(-0.427718\pi\) | ||||
0.225133 | + | 0.974328i | \(0.427718\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.15201 | 0.291252 | ||||||||
\(604\) | 20.9488 | + | 12.0948i | 0.852393 | + | 0.492129i | ||||
\(605\) | −8.66194 | − | 20.8392i | −0.352158 | − | 0.847235i | ||||
\(606\) | 0.711661 | + | 1.23263i | 0.0289093 | + | 0.0500723i | ||||
\(607\) | 5.90718 | − | 10.2315i | 0.239765 | − | 0.415285i | −0.720882 | − | 0.693058i | \(-0.756263\pi\) |
0.960647 | + | 0.277773i | \(0.0895963\pi\) | |||||||
\(608\) | − | 0.878539i | − | 0.0356294i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 23.2534 | 0.941503 | ||||||||
\(611\) | 32.8340 | + | 18.9567i | 1.32832 | + | 0.766907i | ||||
\(612\) | 4.35896 | + | 7.54994i | 0.176200 | + | 0.305188i | ||||
\(613\) | −18.3140 | + | 10.5736i | −0.739697 | + | 0.427064i | −0.821959 | − | 0.569546i | \(-0.807119\pi\) |
0.0822621 | + | 0.996611i | \(0.473786\pi\) | |||||||
\(614\) | 14.0190 | + | 8.09387i | 0.565760 | + | 0.326642i | ||||
\(615\) | −3.71932 | −0.149978 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.8743 | −1.76631 | −0.883157 | − | 0.469078i | \(-0.844586\pi\) | ||||
−0.883157 | + | 0.469078i | \(0.844586\pi\) | |||||||
\(618\) | 4.44764 | + | 2.56785i | 0.178910 | + | 0.103294i | ||||
\(619\) | −4.12964 | + | 2.38425i | −0.165984 | + | 0.0958310i | −0.580691 | − | 0.814124i | \(-0.697218\pi\) |
0.414707 | + | 0.909955i | \(0.363884\pi\) | |||||||
\(620\) | −6.65109 | − | 11.5200i | −0.267114 | − | 0.462655i | ||||
\(621\) | −23.7546 | − | 13.7148i | −0.953241 | − | 0.550354i | ||||
\(622\) | −1.42639 | −0.0571931 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 5.04908i | − | 0.202125i | ||||||
\(625\) | 10.2100 | − | 17.6843i | 0.408401 | − | 0.707372i | ||||
\(626\) | 5.77340 | + | 9.99982i | 0.230751 | + | 0.399673i | ||||
\(627\) | 0.715547 | − | 2.11220i | 0.0285762 | − | 0.0843532i | ||||
\(628\) | −17.5828 | − | 10.1514i | −0.701630 | − | 0.405086i | ||||
\(629\) | −39.8991 | −1.59088 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.66195 | −0.265208 | −0.132604 | − | 0.991169i | \(-0.542334\pi\) | ||||
−0.132604 | + | 0.991169i | \(0.542334\pi\) | |||||||
\(632\) | 4.24264 | − | 7.34847i | 0.168763 | − | 0.292306i | ||||
\(633\) | −3.27722 | − | 5.67632i | −0.130258 | − | 0.225613i | ||||
\(634\) | −27.4737 | + | 15.8620i | −1.09112 | + | 0.629959i | ||||
\(635\) | −7.51918 | + | 13.0236i | −0.298390 | + | 0.516826i | ||||
\(636\) | − | 0.328927i | − | 0.0130428i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 15.4257 | − | 13.5448i | 0.610711 | − | 0.536244i | ||||
\(639\) | 2.57600 | − | 4.46177i | 0.101905 | − | 0.176505i | ||||
\(640\) | 1.02581 | + | 1.77675i | 0.0405486 | + | 0.0702322i | ||||
\(641\) | 5.76074 | + | 9.97789i | 0.227535 | + | 0.394103i | 0.957077 | − | 0.289833i | \(-0.0935999\pi\) |
−0.729542 | + | 0.683936i | \(0.760267\pi\) | |||||||
\(642\) | 9.77892 | + | 5.64586i | 0.385943 | + | 0.222824i | ||||
\(643\) | 21.7793i | 0.858892i | 0.903093 | + | 0.429446i | \(0.141291\pi\) | ||||
−0.903093 | + | 0.429446i | \(0.858709\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 12.2681i | − | 0.483055i | ||||||
\(646\) | 2.74744 | + | 1.58624i | 0.108097 | + | 0.0624096i | ||||
\(647\) | 15.2087 | − | 8.78075i | 0.597916 | − | 0.345207i | −0.170306 | − | 0.985391i | \(-0.554475\pi\) |
0.768221 | + | 0.640185i | \(0.221142\pi\) | |||||||
\(648\) | 3.52565 | − | 2.03553i | 0.138501 | − | 0.0799633i | ||||
\(649\) | −10.4680 | + | 2.08891i | −0.410904 | + | 0.0819967i | ||||
\(650\) | 5.21742i | 0.204644i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.2606 | 0.519326 | ||||||||
\(653\) | −13.2213 | + | 22.9000i | −0.517390 | + | 0.896146i | 0.482406 | + | 0.875948i | \(0.339763\pi\) |
−0.999796 | + | 0.0201984i | \(0.993570\pi\) | |||||||
\(654\) | −3.97696 | + | 2.29610i | −0.155512 | + | 0.0897846i | ||||
\(655\) | 15.6718 | − | 9.04812i | 0.612348 | − | 0.353539i | ||||
\(656\) | −1.18432 | + | 2.05130i | −0.0462399 | + | 0.0800898i | ||||
\(657\) | 26.1344 | 1.01960 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.9324i | 1.51659i | 0.651910 | + | 0.758296i | \(0.273968\pi\) | ||||
−0.651910 | + | 0.758296i | \(0.726032\pi\) | |||||||
\(660\) | 1.01915 | + | 5.10719i | 0.0396703 | + | 0.198797i | ||||
\(661\) | −10.2982 | + | 5.94569i | −0.400555 | + | 0.231261i | −0.686723 | − | 0.726919i | \(-0.740952\pi\) |
0.286168 | + | 0.958179i | \(0.407618\pi\) | |||||||
\(662\) | −27.6469 | + | 15.9620i | −1.07453 | + | 0.620379i | ||||
\(663\) | 15.7899 | + | 9.11631i | 0.613229 | + | 0.354048i | ||||
\(664\) | − | 12.3153i | − | 0.477928i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 26.6748i | 1.03363i | ||||||||
\(667\) | −35.4815 | − | 20.4853i | −1.37385 | − | 0.793193i | ||||
\(668\) | −10.2080 | − | 17.6808i | −0.394960 | − | 0.684091i | ||||
\(669\) | 3.15363 | + | 5.46225i | 0.121927 | + | 0.211183i | ||||
\(670\) | −3.03891 | + | 5.26354i | −0.117403 | + | 0.203348i | ||||
\(671\) | 28.2474 | − | 24.8031i | 1.09048 | − | 0.957512i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.4386i | 0.672210i | 0.941825 | + | 0.336105i | \(0.109110\pi\) | ||||
−0.941825 | + | 0.336105i | \(0.890890\pi\) | |||||||
\(674\) | 0.704268 | − | 1.21983i | 0.0271274 | − | 0.0469860i | ||||
\(675\) | 2.83824 | − | 1.63866i | 0.109244 | − | 0.0630720i | ||||
\(676\) | 15.2598 | + | 26.4307i | 0.586915 | + | 1.01657i | ||||
\(677\) | 20.7150 | − | 35.8794i | 0.796141 | − | 1.37896i | −0.125970 | − | 0.992034i | \(-0.540204\pi\) |
0.922112 | − | 0.386923i | \(-0.126462\pi\) | |||||||
\(678\) | −0.457170 | −0.0175575 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −7.40854 | −0.284104 | ||||||||
\(681\) | 18.2141 | + | 10.5159i | 0.697967 | + | 0.402971i | ||||
\(682\) | −20.3672 | − | 6.89978i | −0.779902 | − | 0.264206i | ||||
\(683\) | −10.7076 | − | 18.5462i | −0.409717 | − | 0.709650i | 0.585141 | − | 0.810931i | \(-0.301039\pi\) |
−0.994858 | + | 0.101281i | \(0.967706\pi\) | |||||||
\(684\) | 1.06049 | − | 1.83682i | 0.0405488 | − | 0.0702327i | ||||
\(685\) | 6.63943i | 0.253679i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.0798608 | −0.00304688 | ||||||||
\(688\) | −6.76615 | − | 3.90644i | −0.257957 | − | 0.148932i | ||||
\(689\) | 1.41756 | + | 2.45529i | 0.0540048 | + | 0.0935391i | ||||
\(690\) | 9.00137 | − | 5.19694i | 0.342676 | − | 0.197844i | ||||
\(691\) | −11.6732 | − | 6.73955i | −0.444071 | − | 0.256384i | 0.261252 | − | 0.965271i | \(-0.415865\pi\) |
−0.705323 | + | 0.708886i | \(0.749198\pi\) | |||||||
\(692\) | −15.5762 | −0.592117 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.0386 | 0.419020 | ||||||||
\(695\) | −4.39074 | − | 2.53499i | −0.166550 | − | 0.0961578i | ||||
\(696\) | −4.10260 | + | 2.36864i | −0.155509 | + | 0.0897830i | ||||
\(697\) | −4.27667 | − | 7.40741i | −0.161990 | − | 0.280576i | ||||
\(698\) | 13.4894 | + | 7.78809i | 0.510580 | + | 0.294783i | ||||
\(699\) | −11.6012 | −0.438797 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 26.4644i | − | 0.999545i | −0.866157 | − | 0.499773i | \(-0.833417\pi\) | ||
0.866157 | − | 0.499773i | \(-0.166583\pi\) | |||||||
\(702\) | 13.6684 | − | 23.6743i | 0.515880 | − | 0.893531i | ||||
\(703\) | 4.85352 | + | 8.40654i | 0.183054 | + | 0.317059i | ||||
\(704\) | 3.14127 | + | 1.06416i | 0.118391 | + | 0.0401071i | ||||
\(705\) | 7.81532 | + | 4.51218i | 0.294342 | + | 0.169938i | ||||
\(706\) | −6.28791 | −0.236649 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.46329 | 0.0925761 | ||||||||
\(709\) | −9.38888 | + | 16.2620i | −0.352607 | + | 0.610733i | −0.986705 | − | 0.162519i | \(-0.948038\pi\) |
0.634099 | + | 0.773252i | \(0.281371\pi\) | |||||||
\(710\) | 2.18910 | + | 3.79164i | 0.0821556 | + | 0.142298i | ||||
\(711\) | 17.7408 | − | 10.2426i | 0.665331 | − | 0.384129i | ||||
\(712\) | −3.36413 | + | 5.82684i | −0.126076 | + | 0.218370i | ||||
\(713\) | 42.9181i | 1.60729i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −29.6177 | − | 33.7307i | −1.10764 | − | 1.26146i | ||||
\(716\) | −2.25080 | + | 3.89850i | −0.0841162 | + | 0.145694i | ||||
\(717\) | −9.91665 | − | 17.1761i | −0.370344 | − | 0.641455i | ||||
\(718\) | −5.14385 | − | 8.90941i | −0.191967 | − | 0.332496i | ||||
\(719\) | 3.00287 | + | 1.73371i | 0.111988 | + | 0.0646564i | 0.554948 | − | 0.831885i | \(-0.312738\pi\) |
−0.442960 | + | 0.896542i | \(0.646072\pi\) | |||||||
\(720\) | 4.95303i | 0.184589i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.2282i | 0.678382i | ||||||||
\(723\) | −4.84598 | − | 2.79783i | −0.180224 | − | 0.104052i | ||||
\(724\) | −7.08701 | + | 4.09169i | −0.263387 | + | 0.152066i | ||||
\(725\) | 4.23939 | − | 2.44761i | 0.157447 | − | 0.0909021i | ||||
\(726\) | 6.68557 | + | 5.11696i | 0.248125 | + | 0.189908i | ||||
\(727\) | 21.6647i | 0.803500i | 0.915749 | + | 0.401750i | \(0.131598\pi\) | ||||
−0.915749 | + | 0.401750i | \(0.868402\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.313708 | 0.0116188 | ||||||||
\(730\) | −11.1046 | + | 19.2337i | −0.410999 | + | 0.711872i | ||||
\(731\) | 24.4331 | − | 14.1065i | 0.903691 | − | 0.521746i | ||||
\(732\) | −7.51262 | + | 4.33742i | −0.277675 | + | 0.160315i | ||||
\(733\) | 7.45423 | − | 12.9111i | 0.275328 | − | 0.476883i | −0.694890 | − | 0.719116i | \(-0.744547\pi\) |
0.970218 | + | 0.242234i | \(0.0778801\pi\) | |||||||
\(734\) | 4.52152 | 0.166892 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 6.61931i | − | 0.243991i | ||||||
\(737\) | 1.92276 | + | 9.63539i | 0.0708258 | + | 0.354924i | ||||
\(738\) | −4.95228 | + | 2.85920i | −0.182296 | + | 0.105249i | ||||
\(739\) | 4.11862 | − | 2.37789i | 0.151506 | − | 0.0874719i | −0.422331 | − | 0.906442i | \(-0.638788\pi\) |
0.573836 | + | 0.818970i | \(0.305455\pi\) | |||||||
\(740\) | −19.6314 | − | 11.3342i | −0.721666 | − | 0.416654i | ||||
\(741\) | − | 4.43581i | − | 0.162954i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.8792i | 0.545864i | 0.962033 | + | 0.272932i | \(0.0879934\pi\) | ||||
−0.962033 | + | 0.272932i | \(0.912007\pi\) | |||||||
\(744\) | 4.29762 | + | 2.48123i | 0.157558 | + | 0.0909663i | ||||
\(745\) | 4.00947 | + | 6.94461i | 0.146896 | + | 0.254431i | ||||
\(746\) | 9.86195 | + | 17.0814i | 0.361072 | + | 0.625395i | ||||
\(747\) | 14.8659 | − | 25.7485i | 0.543916 | − | 0.942090i | ||||
\(748\) | −8.99962 | + | 7.90226i | −0.329059 | + | 0.288935i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 9.09306i | 0.332032i | ||||||||
\(751\) | −8.24101 | + | 14.2739i | −0.300719 | + | 0.520860i | −0.976299 | − | 0.216426i | \(-0.930560\pi\) |
0.675580 | + | 0.737287i | \(0.263893\pi\) | |||||||
\(752\) | 4.97716 | − | 2.87357i | 0.181498 | − | 0.104788i | ||||
\(753\) | −3.83298 | − | 6.63892i | −0.139682 | − | 0.241936i | ||||
\(754\) | 20.4160 | − | 35.3616i | 0.743508 | − | 1.28779i | ||||
\(755\) | −49.6276 | −1.80613 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.82008 | −0.138843 | −0.0694216 | − | 0.997587i | \(-0.522115\pi\) | ||||
−0.0694216 | + | 0.997587i | \(0.522115\pi\) | |||||||
\(758\) | −30.8537 | − | 17.8134i | −1.12066 | − | 0.647012i | ||||
\(759\) | 5.39126 | − | 15.9143i | 0.195690 | − | 0.577652i | ||||
\(760\) | 0.901211 | + | 1.56094i | 0.0326903 | + | 0.0566213i | ||||
\(761\) | −0.927001 | + | 1.60561i | −0.0336038 | + | 0.0582034i | −0.882338 | − | 0.470616i | \(-0.844032\pi\) |
0.848734 | + | 0.528819i | \(0.177365\pi\) | |||||||
\(762\) | − | 5.61016i | − | 0.203235i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.3662 | −0.375037 | ||||||||
\(765\) | −15.4895 | − | 8.94289i | −0.560026 | − | 0.323331i | ||||
\(766\) | −10.8186 | − | 18.7384i | −0.390893 | − | 0.677046i | ||||
\(767\) | −18.3873 | + | 10.6159i | −0.663928 | + | 0.383319i | ||||
\(768\) | −0.662827 | − | 0.382683i | −0.0239177 | − | 0.0138089i | ||||
\(769\) | −8.92308 | −0.321775 | −0.160887 | − | 0.986973i | \(-0.551436\pi\) | ||||
−0.160887 | + | 0.986973i | \(0.551436\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.4028 | 0.482688 | ||||||||
\(772\) | 1.40584 | + | 0.811664i | 0.0505974 | + | 0.0292124i | ||||
\(773\) | −17.6034 | + | 10.1633i | −0.633151 | + | 0.365550i | −0.781971 | − | 0.623315i | \(-0.785786\pi\) |
0.148821 | + | 0.988864i | \(0.452452\pi\) | |||||||
\(774\) | −9.43098 | − | 16.3349i | −0.338989 | − | 0.587147i | ||||
\(775\) | −4.44091 | − | 2.56396i | −0.159522 | − | 0.0921001i | ||||
\(776\) | 9.23880 | 0.331653 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.64698i | 0.310009i | ||||||||
\(779\) | −1.04047 | + | 1.80215i | −0.0372787 | + | 0.0645686i | ||||
\(780\) | 5.17937 | + | 8.97094i | 0.185451 | + | 0.321211i | ||||
\(781\) | 6.70356 | + | 2.27096i | 0.239872 | + | 0.0812612i | ||||
\(782\) | 20.7005 | + | 11.9514i | 0.740248 | + | 0.427382i | ||||
\(783\) | −25.6486 | −0.916607 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 41.6536 | 1.48668 | ||||||||
\(786\) | −3.37546 | + | 5.84647i | −0.120399 | + | 0.208537i | ||||
\(787\) | 19.2008 | + | 33.2568i | 0.684435 | + | 1.18548i | 0.973614 | + | 0.228201i | \(0.0732843\pi\) |
−0.289179 | + | 0.957275i | \(0.593382\pi\) | |||||||
\(788\) | 3.79936 | − | 2.19356i | 0.135347 | − | 0.0781425i | ||||
\(789\) | 3.24718 | − | 5.62427i | 0.115603 | − | 0.200229i | ||||
\(790\) | 17.4085i | 0.619367i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.28311 | + | 6.01676i | 0.187727 | + | 0.213796i | ||||
\(793\) | 37.3855 | − | 64.7537i | 1.32760 | − | 2.29947i | ||||
\(794\) | 18.0859 | + | 31.3257i | 0.641845 | + | 1.11171i | ||||
\(795\) | 0.337415 | + | 0.584420i | 0.0119669 | + | 0.0207273i | ||||
\(796\) | −17.3760 | − | 10.0320i | −0.615875 | − | 0.355575i | ||||
\(797\) | − | 42.5849i | − | 1.50843i | −0.656625 | − | 0.754217i | \(-0.728017\pi\) | ||
0.656625 | − | 0.754217i | \(-0.271983\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.7533i | 0.734201i | ||||||||
\(800\) | 0.684927 | + | 0.395443i | 0.0242158 | + | 0.0139810i | ||||
\(801\) | −14.0672 | + | 8.12172i | −0.497041 | + | 0.286967i | ||||
\(802\) | 7.78865 | − | 4.49678i | 0.275027 | − | 0.158787i | ||||
\(803\) | 7.02603 | + | 35.2091i | 0.247943 | + | 1.24250i | ||||
\(804\) | − | 2.26737i | − | 0.0799639i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −42.7730 | −1.50661 | ||||||||
\(807\) | −2.58511 | + | 4.47755i | −0.0910003 | + | 0.157617i | ||||
\(808\) | −1.61051 | + | 0.929830i | −0.0566577 | + | 0.0327113i | ||||
\(809\) | −6.42504 | + | 3.70950i | −0.225892 | + | 0.130419i | −0.608676 | − | 0.793419i | \(-0.708299\pi\) |
0.382783 | + | 0.923838i | \(0.374966\pi\) | |||||||
\(810\) | −4.17613 | + | 7.23326i | −0.146734 | + | 0.254151i | ||||
\(811\) | 43.2953 | 1.52030 | 0.760151 | − | 0.649746i | \(-0.225125\pi\) | ||||
0.760151 | + | 0.649746i | \(0.225125\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 14.9577i | − | 0.524589i | ||||||
\(814\) | −35.9371 | + | 7.17132i | −1.25959 | + | 0.251355i | ||||
\(815\) | −23.5608 | + | 13.6028i | −0.825298 | + | 0.476486i | ||||
\(816\) | 2.39352 | − | 1.38190i | 0.0837900 | − | 0.0483762i | ||||
\(817\) | −5.94432 | − | 3.43196i | −0.207966 | − | 0.120069i | ||||
\(818\) | − | 9.58279i | − | 0.335055i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 4.85953i | − | 0.169702i | ||||||
\(821\) | −20.8680 | − | 12.0481i | −0.728297 | − | 0.420482i | 0.0895019 | − | 0.995987i | \(-0.471472\pi\) |
−0.817799 | + | 0.575504i | \(0.804806\pi\) | |||||||
\(822\) | −1.23844 | − | 2.14504i | −0.0431956 | − | 0.0748169i | ||||
\(823\) | −1.25003 | − | 2.16512i | −0.0435735 | − | 0.0754714i | 0.843416 | − | 0.537261i | \(-0.180541\pi\) |
−0.886990 | + | 0.461789i | \(0.847208\pi\) | |||||||
\(824\) | −3.35505 | + | 5.81112i | −0.116879 | + | 0.202440i | ||||
\(825\) | 1.32464 | + | 1.50859i | 0.0461180 | + | 0.0525223i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.9902i | 1.14718i | 0.819142 | + | 0.573591i | \(0.194450\pi\) | ||||
−0.819142 | + | 0.573591i | \(0.805550\pi\) | |||||||
\(828\) | 7.99022 | − | 13.8395i | 0.277679 | − | 0.480955i | ||||
\(829\) | −24.6422 | + | 14.2272i | −0.855858 | + | 0.494130i | −0.862623 | − | 0.505847i | \(-0.831180\pi\) |
0.00676498 | + | 0.999977i | \(0.497847\pi\) | |||||||
\(830\) | 12.6331 | + | 21.8813i | 0.438503 | + | 0.759509i | ||||
\(831\) | −10.2080 | + | 17.6808i | −0.354112 | + | 0.613340i | ||||
\(832\) | 6.59694 | 0.228708 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.89139 | 0.0654935 | ||||||||
\(835\) | 36.2742 | + | 20.9429i | 1.25532 | + | 0.724759i | ||||
\(836\) | 2.75972 | + | 0.934908i | 0.0954471 | + | 0.0323345i | ||||
\(837\) | 13.4339 | + | 23.2682i | 0.464344 | + | 0.804267i | ||||
\(838\) | 18.9532 | − | 32.8279i | 0.654727 | − | 1.13402i | ||||
\(839\) | 26.5407i | 0.916288i | 0.888878 | + | 0.458144i | \(0.151486\pi\) | ||||
−0.888878 | + | 0.458144i | \(0.848514\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.31052 | −0.321052 | ||||||||
\(842\) | 2.49757 | + | 1.44197i | 0.0860719 | + | 0.0496937i | ||||
\(843\) | 8.01850 | + | 13.8884i | 0.276172 | + | 0.478344i | ||||
\(844\) | 7.41646 | − | 4.28190i | 0.255285 | − | 0.147389i | ||||
\(845\) | −54.2256 | − | 31.3072i | −1.86542 | − | 1.07700i | ||||
\(846\) | 13.8748 | 0.477025 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.429764 | 0.0147581 | ||||||||
\(849\) | −6.66999 | − | 3.85092i | −0.228913 | − | 0.132163i | ||||
\(850\) | −2.47333 | + | 1.42798i | −0.0848344 | + | 0.0489792i | ||||
\(851\) | 36.5686 | + | 63.3388i | 1.25356 | + | 2.17122i | ||||
\(852\) | −1.41449 | − | 0.816659i | −0.0484598 | − | 0.0279783i | ||||
\(853\) | 0.431373 | 0.0147699 | 0.00738496 | − | 0.999973i | \(-0.497649\pi\) | ||||
0.00738496 | + | 0.999973i | \(0.497649\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.35143i | 0.148816i | ||||||||
\(856\) | −7.37667 | + | 12.7768i | −0.252129 | + | 0.436701i | ||||
\(857\) | 8.75672 | + | 15.1671i | 0.299124 | + | 0.518098i | 0.975936 | − | 0.218058i | \(-0.0699723\pi\) |
−0.676812 | + | 0.736156i | \(0.736639\pi\) | |||||||
\(858\) | 15.8605 | + | 5.37304i | 0.541468 | + | 0.183432i | ||||
\(859\) | −39.3879 | − | 22.7406i | −1.34390 | − | 0.775901i | −0.356522 | − | 0.934287i | \(-0.616038\pi\) |
−0.987377 | + | 0.158386i | \(0.949371\pi\) | |||||||
\(860\) | 16.0290 | 0.546584 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −32.4068 | −1.10378 | ||||||||
\(863\) | −11.8660 | + | 20.5525i | −0.403922 | + | 0.699614i | −0.994195 | − | 0.107590i | \(-0.965687\pi\) |
0.590273 | + | 0.807204i | \(0.299020\pi\) | |||||||
\(864\) | −2.07193 | − | 3.58869i | −0.0704885 | − | 0.122090i | ||||
\(865\) | 27.6749 | − | 15.9781i | 0.940976 | − | 0.543273i | ||||
\(866\) | 5.11596 | − | 8.86110i | 0.173847 | − | 0.301112i | ||||
\(867\) | − | 3.03093i | − | 0.102936i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.5686 | + | 21.1472i | 0.629898 | + | 0.717371i | ||||
\(870\) | 4.85953 | − | 8.41695i | 0.164753 | − | 0.285361i | ||||
\(871\) | 9.77158 | + | 16.9249i | 0.331097 | + | 0.573477i | ||||
\(872\) | −3.00000 | − | 5.19615i | −0.101593 | − | 0.175964i | ||||
\(873\) | 19.3162 | + | 11.1522i | 0.653754 | + | 0.377445i | ||||
\(874\) | − | 5.81532i | − | 0.196706i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 8.28528i | − | 0.279934i | ||||||
\(877\) | 28.8886 | + | 16.6788i | 0.975499 | + | 0.563205i | 0.900908 | − | 0.434010i | \(-0.142902\pi\) |
0.0745907 | + | 0.997214i | \(0.476235\pi\) | |||||||
\(878\) | −25.0044 | + | 14.4363i | −0.843859 | + | 0.487202i | ||||
\(879\) | −19.6481 | + | 11.3439i | −0.662715 | + | 0.382619i | ||||
\(880\) | −6.67287 | + | 1.33158i | −0.224942 | + | 0.0448877i | ||||
\(881\) | 18.7347i | 0.631187i | 0.948895 | + | 0.315593i | \(0.102204\pi\) | ||||
−0.948895 | + | 0.315593i | \(0.897796\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.0705 | 0.877342 | 0.438671 | − | 0.898648i | \(-0.355449\pi\) | ||||
0.438671 | + | 0.898648i | \(0.355449\pi\) | |||||||
\(884\) | −11.9110 | + | 20.6305i | −0.400611 | + | 0.693879i | ||||
\(885\) | −4.37665 | + | 2.52686i | −0.147119 | + | 0.0849394i | ||||
\(886\) | 7.41349 | − | 4.28018i | 0.249061 | − | 0.143796i | ||||
\(887\) | 26.0619 | − | 45.1405i | 0.875073 | − | 1.51567i | 0.0183874 | − | 0.999831i | \(-0.494147\pi\) |
0.856685 | − | 0.515839i | \(-0.172520\pi\) | |||||||
\(888\) | 8.45660 | 0.283785 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 13.8038i | − | 0.462703i | ||||||
\(891\) | 2.64229 | + | 13.2411i | 0.0885202 | + | 0.443595i | ||||
\(892\) | −7.13678 | + | 4.12042i | −0.238957 | + | 0.137962i | ||||
\(893\) | 4.37263 | − | 2.52454i | 0.146324 | − | 0.0844805i | ||||
\(894\) | −2.59073 | − | 1.49576i | −0.0866469 | − | 0.0500256i | ||||
\(895\) | − | 9.23553i | − | 0.308710i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 33.4214i | − | 1.11591i | ||||||
\(898\) | −9.36075 | − | 5.40443i | −0.312372 | − | 0.180348i | ||||
\(899\) | 20.0658 | + | 34.7550i | 0.669232 | + | 1.15914i | ||||
\(900\) | 0.954684 | + | 1.65356i | 0.0318228 | + | 0.0551187i | ||||
\(901\) | −0.775955 | + | 1.34399i | −0.0258508 | + | 0.0447749i | ||||
\(902\) | −5.18338 | − | 5.90318i | −0.172588 | − | 0.196554i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 0.597322i | − | 0.0198666i | ||||||
\(905\) | 8.39456 | − | 14.5398i | 0.279045 | − | 0.483319i | ||||
\(906\) | 16.0335 | − | 9.25694i | 0.532677 | − | 0.307541i | ||||
\(907\) | −15.2867 | − | 26.4774i | −0.507587 | − | 0.879166i | −0.999961 | − | 0.00878294i | \(-0.997204\pi\) |
0.492374 | − | 0.870383i | \(-0.336129\pi\) | |||||||
\(908\) | −13.7397 | + | 23.7979i | −0.455969 | + | 0.789761i | ||||
\(909\) | −4.48962 | −0.148911 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.343220 | 0.0113714 | 0.00568569 | − | 0.999984i | \(-0.498190\pi\) | ||||
0.00568569 | + | 0.999984i | \(0.498190\pi\) | |||||||
\(912\) | −0.582319 | − | 0.336202i | −0.0192825 | − | 0.0111328i | ||||
\(913\) | 38.6858 | + | 13.1055i | 1.28031 | + | 0.433729i | ||||
\(914\) | −12.1948 | − | 21.1220i | −0.403367 | − | 0.698653i | ||||
\(915\) | 8.89870 | − | 15.4130i | 0.294182 | − | 0.509538i | ||||
\(916\) | − | 0.104343i | − | 0.00344759i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 14.9638 | 0.493879 | ||||||||
\(919\) | −44.2268 | − | 25.5344i | −1.45891 | − | 0.842301i | −0.459950 | − | 0.887945i | \(-0.652133\pi\) |
−0.998958 | + | 0.0456441i | \(0.985466\pi\) | |||||||
\(920\) | 6.79013 | + | 11.7609i | 0.223864 | + | 0.387744i | ||||
\(921\) | 10.7297 | − | 6.19478i | 0.353555 | − | 0.204125i | ||||
\(922\) | 0.980215 | + | 0.565928i | 0.0322817 | + | 0.0186378i | ||||
\(923\) | 14.0781 | 0.463385 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.73856 | −0.287322 | ||||||||
\(926\) | 5.52860 | + | 3.19194i | 0.181681 | + | 0.104894i | ||||
\(927\) | −14.0293 | + | 8.09982i | −0.460783 | + | 0.266033i | ||||
\(928\) | −3.09477 | − | 5.36031i | −0.101591 | − | 0.175961i | ||||
\(929\) | 50.7827 | + | 29.3194i | 1.66613 | + | 0.961939i | 0.969695 | + | 0.244317i | \(0.0785638\pi\) |
0.696433 | + | 0.717622i | \(0.254770\pi\) | |||||||
\(930\) | −10.1810 | −0.333850 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 15.1577i | − | 0.496507i | ||||||
\(933\) | −0.545856 | + | 0.945450i | −0.0178705 | + | 0.0309527i | ||||
\(934\) | −17.8420 | − | 30.9033i | −0.583808 | − | 1.01119i | ||||
\(935\) | 7.88388 | − | 23.2722i | 0.257831 | − | 0.761082i | ||||
\(936\) | 13.7927 | + | 7.96321i | 0.450828 | + | 0.260286i | ||||
\(937\) | −40.2806 | −1.31591 | −0.657955 | − | 0.753057i | \(-0.728578\pi\) | ||||
−0.657955 | + | 0.753057i | \(0.728578\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.83754 | 0.288402 | ||||||||
\(940\) | −5.89544 | + | 10.2112i | −0.192288 | + | 0.333053i | ||||
\(941\) | 1.37193 | + | 2.37625i | 0.0447236 | + | 0.0774636i | 0.887521 | − | 0.460768i | \(-0.152426\pi\) |
−0.842797 | + | 0.538231i | \(0.819093\pi\) | |||||||
\(942\) | −13.4573 | + | 7.76957i | −0.438462 | + | 0.253146i | ||||
\(943\) | −7.83938 | + | 13.5782i | −0.255285 | + | 0.442167i | ||||
\(944\) | 3.21844i | 0.104751i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.4714 | − | 17.0972i | 0.633071 | − | 0.555878i | ||||
\(947\) | 20.4229 | − | 35.3736i | 0.663657 | − | 1.14949i | −0.315991 | − | 0.948762i | \(-0.602337\pi\) |
0.979648 | − | 0.200725i | \(-0.0643297\pi\) | |||||||
\(948\) | −3.24718 | − | 5.62427i | −0.105463 | − | 0.182668i | ||||
\(949\) | 35.7067 | + | 61.8458i | 1.15909 | + | 2.00760i | ||||
\(950\) | 0.601735 | + | 0.347412i | 0.0195229 | + | 0.0112715i | ||||
\(951\) | 24.2804i | 0.787347i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.21096i | 0.104013i | 0.998647 | + | 0.0520065i | \(0.0165617\pi\) | ||||
−0.998647 | + | 0.0520065i | \(0.983438\pi\) | |||||||
\(954\) | 0.898537 | + | 0.518771i | 0.0290912 | + | 0.0167958i | ||||
\(955\) | 18.4182 | − | 10.6337i | 0.595998 | − | 0.344099i | ||||
\(956\) | 22.4417 | − | 12.9567i | 0.725817 | − | 0.419051i | ||||
\(957\) | −3.07469 | − | 15.4080i | −0.0993907 | − | 0.498069i | ||||
\(958\) | − | 11.5819i | − | 0.374193i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.57024 | 0.0506792 | ||||||||
\(961\) | 5.51960 | − | 9.56023i | 0.178052 | − | 0.308395i | ||||
\(962\) | −63.1246 | + | 36.4450i | −2.03522 | + | 1.17503i | ||||
\(963\) | −30.8459 | + | 17.8089i | −0.993994 | + | 0.573883i | ||||
\(964\) | 3.65554 | − | 6.33158i | 0.117737 | − | 0.203927i | ||||
\(965\) | −3.33044 | −0.107211 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31.1521i | − | 1.00178i | −0.865510 | − | 0.500892i | \(-0.833005\pi\) | ||
0.865510 | − | 0.500892i | \(-0.166995\pi\) | |||||||
\(968\) | −6.68563 | + | 8.73512i | −0.214884 | + | 0.280757i | ||||
\(969\) | 2.10280 | − | 1.21405i | 0.0675517 | − | 0.0390010i | ||||
\(970\) | −16.4150 | + | 9.47721i | −0.527054 | + | 0.304295i | ||||
\(971\) | 19.3805 | + | 11.1894i | 0.621951 | + | 0.359084i | 0.777628 | − | 0.628724i | \(-0.216423\pi\) |
−0.155677 | + | 0.987808i | \(0.549756\pi\) | |||||||
\(972\) | − | 15.5474i | − | 0.498684i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 40.0638i | − | 1.28373i | ||||||
\(975\) | 3.45825 | + | 1.99662i | 0.110753 | + | 0.0639431i | ||||
\(976\) | −5.66711 | − | 9.81572i | −0.181400 | − | 0.314193i | ||||
\(977\) | −8.83203 | − | 15.2975i | −0.282562 | − | 0.489411i | 0.689453 | − | 0.724330i | \(-0.257851\pi\) |
−0.972015 | + | 0.234919i | \(0.924518\pi\) | |||||||
\(978\) | 5.07462 | − | 8.78950i | 0.162268 | − | 0.281057i | ||||
\(979\) | −14.7237 | − | 16.7683i | −0.470571 | − | 0.535918i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 14.4853i | − | 0.462479i | ||||||
\(982\) | 9.89382 | − | 17.1366i | 0.315724 | − | 0.546851i | ||||
\(983\) | −36.5871 | + | 21.1236i | −1.16695 | + | 0.673737i | −0.952959 | − | 0.303099i | \(-0.901979\pi\) |
−0.213988 | + | 0.976836i | \(0.568645\pi\) | |||||||
\(984\) | 0.906438 | + | 1.57000i | 0.0288962 | + | 0.0500497i | ||||
\(985\) | −4.50034 | + | 7.79482i | −0.143393 | + | 0.248364i | ||||
\(986\) | 22.3510 | 0.711799 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.79566 | 0.184385 | ||||||||
\(989\) | −44.7873 | − | 25.8579i | −1.42415 | − | 0.822235i | ||||
\(990\) | −15.5588 | − | 5.27083i | −0.494491 | − | 0.167518i | ||||
\(991\) | 1.72788 | + | 2.99278i | 0.0548881 | + | 0.0950689i | 0.892164 | − | 0.451712i | \(-0.149186\pi\) |
−0.837276 | + | 0.546781i | \(0.815853\pi\) | |||||||
\(992\) | −3.24188 | + | 5.61510i | −0.102930 | + | 0.178280i | ||||
\(993\) | 24.4335i | 0.775374i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 41.1636 | 1.30497 | ||||||||
\(996\) | −8.16294 | − | 4.71287i | −0.258653 | − | 0.149333i | ||||
\(997\) | −9.28384 | − | 16.0801i | −0.294022 | − | 0.509262i | 0.680735 | − | 0.732530i | \(-0.261661\pi\) |
−0.974757 | + | 0.223269i | \(0.928327\pi\) | |||||||
\(998\) | 23.0841 | − | 13.3276i | 0.730716 | − | 0.421879i | ||||
\(999\) | 39.6517 | + | 22.8929i | 1.25452 | + | 0.724300i |
(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 | 1078.2.i.d.901.14 | 32 | ||
7.2 | even | 3 | 1078.2.c.c.1077.6 | yes | 16 | ||
7.3 | odd | 6 | inner | 1078.2.i.d.1011.8 | 32 | ||
7.4 | even | 3 | inner | 1078.2.i.d.1011.7 | 32 | ||
7.5 | odd | 6 | 1078.2.c.c.1077.3 | ✓ | 16 | ||
7.6 | odd | 2 | inner | 1078.2.i.d.901.13 | 32 | ||
11.10 | odd | 2 | inner | 1078.2.i.d.901.8 | 32 | ||
77.10 | even | 6 | inner | 1078.2.i.d.1011.14 | 32 | ||
77.32 | odd | 6 | inner | 1078.2.i.d.1011.13 | 32 | ||
77.54 | even | 6 | 1078.2.c.c.1077.11 | yes | 16 | ||
77.65 | odd | 6 | 1078.2.c.c.1077.14 | yes | 16 | ||
77.76 | even | 2 | inner | 1078.2.i.d.901.7 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1078.2.c.c.1077.3 | ✓ | 16 | 7.5 | odd | 6 | ||
1078.2.c.c.1077.6 | yes | 16 | 7.2 | even | 3 | ||
1078.2.c.c.1077.11 | yes | 16 | 77.54 | even | 6 | ||
1078.2.c.c.1077.14 | yes | 16 | 77.65 | odd | 6 | ||
1078.2.i.d.901.7 | 32 | 77.76 | even | 2 | inner | ||
1078.2.i.d.901.8 | 32 | 11.10 | odd | 2 | inner | ||
1078.2.i.d.901.13 | 32 | 7.6 | odd | 2 | inner | ||
1078.2.i.d.901.14 | 32 | 1.1 | even | 1 | trivial | ||
1078.2.i.d.1011.7 | 32 | 7.4 | even | 3 | inner | ||
1078.2.i.d.1011.8 | 32 | 7.3 | odd | 6 | inner | ||
1078.2.i.d.1011.13 | 32 | 77.32 | odd | 6 | inner | ||
1078.2.i.d.1011.14 | 32 | 77.10 | even | 6 | inner |