Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [775,2,Mod(51,775)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(775, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("775.51");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 775 = 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 775.bl (of order \(15\), degree \(8\), 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: | \(6.18840615665\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{15})\) |
Twist minimal: | no (minimal twist has level 155) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{15}]$ |
Embedding invariants
Embedding label | 276.1 | ||
Character | \(\chi\) | \(=\) | 775.276 |
Dual form | 775.2.bl.b.351.1 |
$q$-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 \(\left(\mathbb{Z}/775\mathbb{Z}\right)^\times\).
\(n\) | \(251\) | \(652\) |
\(\chi(n)\) | \(e\left(\frac{8}{15}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.03762 | + | 1.48042i | −1.44081 | + | 1.04681i | −0.452942 | + | 0.891540i | \(0.649625\pi\) |
−0.987872 | + | 0.155272i | \(0.950375\pi\) | |||||||
\(3\) | 0.203052 | − | 1.93191i | 0.117232 | − | 1.11539i | −0.764823 | − | 0.644240i | \(-0.777174\pi\) |
0.882055 | − | 0.471147i | \(-0.156160\pi\) | |||||||
\(4\) | 1.34222 | − | 4.13093i | 0.671111 | − | 2.06547i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44628 | + | 4.23709i | 0.998692 | + | 1.72978i | ||||
\(7\) | −0.816826 | + | 0.173622i | −0.308731 | + | 0.0656229i | −0.359672 | − | 0.933079i | \(-0.617111\pi\) |
0.0509406 | + | 0.998702i | \(0.483778\pi\) | |||||||
\(8\) | 1.82396 | + | 5.61358i | 0.644868 | + | 1.98470i | ||||
\(9\) | −0.756592 | − | 0.160819i | −0.252197 | − | 0.0536062i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.03538 | − | 3.37113i | −0.915201 | − | 1.01643i | −0.999800 | − | 0.0200184i | \(-0.993628\pi\) |
0.0845988 | − | 0.996415i | \(-0.473039\pi\) | |||||||
\(12\) | −7.70804 | − | 3.43184i | −2.22512 | − | 0.990687i | ||||
\(13\) | 5.75194 | − | 2.56093i | 1.59530 | − | 0.710274i | 0.599377 | − | 0.800467i | \(-0.295415\pi\) |
0.995924 | + | 0.0901931i | \(0.0287484\pi\) | |||||||
\(14\) | 1.40735 | − | 1.56302i | 0.376129 | − | 0.417734i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.99902 | − | 3.63200i | −1.24975 | − | 0.907999i | ||||
\(17\) | −0.865839 | + | 0.961611i | −0.209997 | + | 0.233225i | −0.838937 | − | 0.544229i | \(-0.816822\pi\) |
0.628940 | + | 0.777454i | \(0.283489\pi\) | |||||||
\(18\) | 1.77972 | − | 0.792384i | 0.419485 | − | 0.186767i | ||||
\(19\) | 0.526383 | + | 0.234361i | 0.120761 | + | 0.0537661i | 0.466228 | − | 0.884665i | \(-0.345613\pi\) |
−0.345467 | + | 0.938431i | \(0.612279\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.169563 | + | 1.61329i | 0.0370017 | + | 0.352048i | ||||
\(22\) | 11.1756 | + | 2.37545i | 2.38265 | + | 0.506448i | ||||
\(23\) | −0.729749 | − | 2.24594i | −0.152163 | − | 0.468310i | 0.845699 | − | 0.533660i | \(-0.179184\pi\) |
−0.997862 | + | 0.0653498i | \(0.979184\pi\) | |||||||
\(24\) | 11.2153 | − | 2.38388i | 2.28931 | − | 0.486608i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.92902 | + | 13.7335i | −1.55501 | + | 2.69335i | ||||
\(27\) | 1.33653 | − | 4.11341i | 0.257215 | − | 0.791626i | ||||
\(28\) | −0.379142 | + | 3.60729i | −0.0716511 | + | 0.681714i | ||||
\(29\) | −0.640127 | + | 0.465079i | −0.118869 | + | 0.0863630i | −0.645631 | − | 0.763649i | \(-0.723406\pi\) |
0.526763 | + | 0.850012i | \(0.323406\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.56993 | + | 3.18053i | 0.820783 | + | 0.571240i | ||||
\(32\) | 3.75801 | 0.664329 | ||||||||
\(33\) | −7.12905 | + | 5.17955i | −1.24101 | + | 0.901645i | ||||
\(34\) | 0.340664 | − | 3.24120i | 0.0584233 | − | 0.555861i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.67985 | + | 2.90958i | −0.279974 | + | 0.484930i | ||||
\(37\) | 5.64427 | + | 9.77616i | 0.927912 | + | 1.60719i | 0.786810 | + | 0.617196i | \(0.211731\pi\) |
0.141102 | + | 0.989995i | \(0.454935\pi\) | |||||||
\(38\) | −1.41952 | + | 0.301728i | −0.230276 | + | 0.0489468i | ||||
\(39\) | −3.77954 | − | 11.6322i | −0.605210 | − | 1.86265i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.17622 | − | 11.1910i | −0.183695 | − | 1.74774i | −0.566639 | − | 0.823966i | \(-0.691757\pi\) |
0.382944 | − | 0.923771i | \(-0.374910\pi\) | |||||||
\(42\) | −2.73384 | − | 3.03624i | −0.421841 | − | 0.468502i | ||||
\(43\) | −10.2075 | − | 4.54466i | −1.55663 | − | 0.693054i | −0.565349 | − | 0.824852i | \(-0.691259\pi\) |
−0.991277 | + | 0.131797i | \(0.957925\pi\) | |||||||
\(44\) | −18.0001 | + | 8.01414i | −2.71361 | + | 1.20818i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.81187 | + | 3.49603i | 0.709471 | + | 0.515461i | ||||
\(47\) | −6.73909 | − | 4.89623i | −0.982997 | − | 0.714189i | −0.0246207 | − | 0.999697i | \(-0.507838\pi\) |
−0.958376 | + | 0.285508i | \(0.907838\pi\) | |||||||
\(48\) | −8.03174 | + | 8.92015i | −1.15928 | + | 1.28751i | ||||
\(49\) | −5.75776 | + | 2.56352i | −0.822537 | + | 0.366217i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.68193 | + | 1.86798i | 0.235518 | + | 0.261569i | ||||
\(52\) | −2.85865 | − | 27.1982i | −0.396423 | − | 3.77171i | ||||
\(53\) | −5.22161 | − | 1.10989i | −0.717244 | − | 0.152455i | −0.165188 | − | 0.986262i | \(-0.552823\pi\) |
−0.552056 | + | 0.833807i | \(0.686156\pi\) | |||||||
\(54\) | 3.36622 | + | 10.3602i | 0.458085 | + | 1.40984i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.46450 | − | 4.26864i | −0.329333 | − | 0.570421i | ||||
\(57\) | 0.559646 | − | 0.969336i | 0.0741270 | − | 0.128392i | ||||
\(58\) | 0.615823 | − | 1.89531i | 0.0808615 | − | 0.248866i | ||||
\(59\) | 0.557834 | − | 5.30744i | 0.0726238 | − | 0.690969i | −0.896273 | − | 0.443503i | \(-0.853735\pi\) |
0.968897 | − | 0.247466i | \(-0.0795979\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.18717 | −0.536112 | −0.268056 | − | 0.963403i | \(-0.586381\pi\) | ||||
−0.268056 | + | 0.963403i | \(0.586381\pi\) | |||||||
\(62\) | −14.0203 | + | 0.284685i | −1.78058 | + | 0.0361551i | ||||
\(63\) | 0.645926 | 0.0813790 | ||||||||
\(64\) | 2.34063 | − | 1.70057i | 0.292579 | − | 0.212571i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.85838 | − | 21.1079i | 0.844208 | − | 2.59820i | ||||
\(67\) | 3.52238 | − | 6.10094i | 0.430327 | − | 0.745348i | −0.566574 | − | 0.824011i | \(-0.691732\pi\) |
0.996901 | + | 0.0786623i | \(0.0250649\pi\) | |||||||
\(68\) | 2.81020 | + | 4.86742i | 0.340787 | + | 0.590261i | ||||
\(69\) | −4.48712 | + | 0.953766i | −0.540185 | + | 0.114820i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.94921 | + | 0.626874i | 0.350007 | + | 0.0743962i | 0.379560 | − | 0.925167i | \(-0.376075\pi\) |
−0.0295537 | + | 0.999563i | \(0.509409\pi\) | |||||||
\(72\) | −0.477228 | − | 4.54052i | −0.0562418 | − | 0.535105i | ||||
\(73\) | −6.92763 | − | 7.69391i | −0.810818 | − | 0.900504i | 0.185808 | − | 0.982586i | \(-0.440510\pi\) |
−0.996626 | + | 0.0820820i | \(0.973843\pi\) | |||||||
\(74\) | −25.9736 | − | 11.5642i | −3.01938 | − | 1.34431i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.67465 | − | 1.85989i | 0.192096 | − | 0.213344i | ||||
\(77\) | 3.06468 | + | 2.22662i | 0.349252 | + | 0.253747i | ||||
\(78\) | 24.9218 | + | 18.1067i | 2.82183 | + | 2.05018i | ||||
\(79\) | 0.856267 | − | 0.950981i | 0.0963375 | − | 0.106994i | −0.693048 | − | 0.720891i | \(-0.743733\pi\) |
0.789386 | + | 0.613898i | \(0.210399\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.79521 | − | 4.36111i | −1.08836 | − | 0.484568i | ||||
\(82\) | 18.9640 | + | 21.0616i | 2.09422 | + | 2.32587i | ||||
\(83\) | 1.37104 | + | 13.0446i | 0.150492 | + | 1.43183i | 0.765563 | + | 0.643361i | \(0.222461\pi\) |
−0.615071 | + | 0.788472i | \(0.710873\pi\) | |||||||
\(84\) | 6.89197 | + | 1.46493i | 0.751976 | + | 0.159837i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 27.5269 | − | 5.85103i | 2.96831 | − | 0.630933i | ||||
\(87\) | 0.768511 | + | 1.33110i | 0.0823930 | + | 0.142709i | ||||
\(88\) | 13.3877 | − | 23.1882i | 1.42713 | − | 2.47187i | ||||
\(89\) | 1.14268 | − | 3.51681i | 0.121124 | − | 0.372782i | −0.872051 | − | 0.489415i | \(-0.837210\pi\) |
0.993175 | + | 0.116634i | \(0.0372103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.25370 | + | 3.09050i | −0.445909 | + | 0.323972i | ||||
\(92\) | −10.2573 | −1.06940 | ||||||||
\(93\) | 7.07242 | − | 8.18286i | 0.733376 | − | 0.848523i | ||||
\(94\) | 20.9802 | 2.16394 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.763071 | − | 7.26013i | 0.0778806 | − | 0.740984i | ||||
\(97\) | 1.67517 | − | 5.15563i | 0.170087 | − | 0.523475i | −0.829288 | − | 0.558822i | \(-0.811254\pi\) |
0.999375 | + | 0.0353469i | \(0.0112536\pi\) | |||||||
\(98\) | 7.93704 | − | 13.7473i | 0.801762 | − | 1.38869i | ||||
\(99\) | 1.75440 | + | 3.03871i | 0.176324 | + | 0.305402i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.705882 | + | 2.17248i | 0.0702379 | + | 0.216170i | 0.980014 | − | 0.198930i | \(-0.0637466\pi\) |
−0.909776 | + | 0.415100i | \(0.863747\pi\) | |||||||
\(102\) | −6.19252 | − | 1.31626i | −0.613151 | − | 0.130329i | ||||
\(103\) | −0.684777 | − | 6.51522i | −0.0674731 | − | 0.641963i | −0.975036 | − | 0.222047i | \(-0.928726\pi\) |
0.907563 | − | 0.419916i | \(-0.137941\pi\) | |||||||
\(104\) | 24.8673 | + | 27.6179i | 2.43844 | + | 2.70816i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.2828 | − | 5.46863i | 1.19301 | − | 0.531161i | ||||
\(107\) | 3.10153 | − | 3.44460i | 0.299836 | − | 0.333002i | −0.574334 | − | 0.818621i | \(-0.694739\pi\) |
0.874171 | + | 0.485619i | \(0.161406\pi\) | |||||||
\(108\) | −15.1983 | − | 11.0422i | −1.46246 | − | 1.06254i | ||||
\(109\) | 0.480316 | + | 0.348970i | 0.0460059 | + | 0.0334252i | 0.610551 | − | 0.791977i | \(-0.290948\pi\) |
−0.564545 | + | 0.825403i | \(0.690948\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 20.0327 | − | 8.91914i | 1.90142 | − | 0.846567i | ||||
\(112\) | 4.71392 | + | 2.09877i | 0.445424 | + | 0.198315i | ||||
\(113\) | 6.46109 | + | 7.17577i | 0.607808 | + | 0.675039i | 0.965980 | − | 0.258616i | \(-0.0832665\pi\) |
−0.358172 | + | 0.933656i | \(0.616600\pi\) | |||||||
\(114\) | 0.294675 | + | 2.80365i | 0.0275988 | + | 0.262585i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.06202 | + | 3.26856i | 0.0986060 | + | 0.303478i | ||||
\(117\) | −4.76372 | + | 1.01256i | −0.440406 | + | 0.0936112i | ||||
\(118\) | 6.72056 | + | 11.6404i | 0.618678 | + | 1.07158i | ||||
\(119\) | 0.540283 | − | 0.935798i | 0.0495277 | − | 0.0857844i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00118 | + | 9.52556i | −0.0910160 | + | 0.865960i | ||||
\(122\) | 8.53186 | − | 6.19876i | 0.772438 | − | 0.561209i | ||||
\(123\) | −21.8588 | −1.97094 | ||||||||
\(124\) | 19.2724 | − | 14.6091i | 1.73071 | − | 1.31193i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.31615 | + | 0.956239i | −0.117252 | + | 0.0851886i | ||||
\(127\) | 1.28296 | − | 12.2066i | 0.113845 | − | 1.08316i | −0.777203 | − | 0.629250i | \(-0.783362\pi\) |
0.891048 | − | 0.453910i | \(-0.149971\pi\) | |||||||
\(128\) | −4.57435 | + | 14.0784i | −0.404319 | + | 1.24437i | ||||
\(129\) | −10.8525 | + | 18.7971i | −0.955510 | + | 1.65499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.2500 | + | 3.45404i | −1.41977 | + | 0.301781i | −0.852919 | − | 0.522042i | \(-0.825170\pi\) |
−0.566847 | + | 0.823823i | \(0.691837\pi\) | |||||||
\(132\) | 11.8276 | + | 36.4017i | 1.02946 | + | 3.16836i | ||||
\(133\) | −0.470654 | − | 0.100041i | −0.0408108 | − | 0.00867461i | ||||
\(134\) | 1.85467 | + | 17.6460i | 0.160219 | + | 1.52438i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.97734 | − | 3.10651i | −0.598302 | − | 0.266381i | ||||
\(137\) | −2.67643 | + | 1.19162i | −0.228663 | + | 0.101807i | −0.517870 | − | 0.855459i | \(-0.673275\pi\) |
0.289207 | + | 0.957266i | \(0.406608\pi\) | |||||||
\(138\) | 7.73106 | − | 8.58621i | 0.658111 | − | 0.730907i | ||||
\(139\) | −17.3423 | − | 12.6000i | −1.47096 | − | 1.06871i | −0.980335 | − | 0.197342i | \(-0.936769\pi\) |
−0.490624 | − | 0.871371i | \(-0.663231\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.8275 | + | 12.0251i | −0.911836 | + | 1.01270i | ||||
\(142\) | −6.93739 | + | 3.08873i | −0.582173 | + | 0.259200i | ||||
\(143\) | −26.0925 | − | 11.6171i | −2.18197 | − | 0.971474i | ||||
\(144\) | 3.19812 | + | 3.55188i | 0.266510 | + | 0.295990i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 25.5060 | + | 5.42148i | 2.11090 | + | 0.448685i | ||||
\(147\) | 3.78336 | + | 11.6440i | 0.312046 | + | 0.960379i | ||||
\(148\) | 47.9605 | − | 10.1943i | 3.94233 | − | 0.837968i | ||||
\(149\) | 3.94968 | + | 6.84105i | 0.323571 | + | 0.560441i | 0.981222 | − | 0.192882i | \(-0.0617834\pi\) |
−0.657651 | + | 0.753322i | \(0.728450\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.686047 | + | 2.11144i | −0.0558297 | + | 0.171826i | −0.975083 | − | 0.221840i | \(-0.928794\pi\) |
0.919253 | + | 0.393667i | \(0.128794\pi\) | |||||||
\(152\) | −0.355500 | + | 3.38236i | −0.0288349 | + | 0.274346i | ||||
\(153\) | 0.809732 | − | 0.588305i | 0.0654629 | − | 0.0475616i | ||||
\(154\) | −9.54097 | −0.768833 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −53.1249 | −4.25339 | ||||||||
\(157\) | 4.23067 | − | 3.07376i | 0.337644 | − | 0.245313i | −0.406023 | − | 0.913863i | \(-0.633085\pi\) |
0.743667 | + | 0.668550i | \(0.233085\pi\) | |||||||
\(158\) | −0.336898 | + | 3.20537i | −0.0268021 | + | 0.255005i | ||||
\(159\) | −3.20446 | + | 9.86231i | −0.254130 | + | 0.782132i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.986021 | + | 1.70784i | 0.0777094 | + | 0.134597i | ||||
\(162\) | 26.4151 | − | 5.61471i | 2.07537 | − | 0.441134i | ||||
\(163\) | −4.10314 | − | 12.6282i | −0.321382 | − | 0.989113i | −0.973047 | − | 0.230606i | \(-0.925929\pi\) |
0.651665 | − | 0.758507i | \(-0.274071\pi\) | |||||||
\(164\) | −47.8079 | − | 10.1619i | −3.73317 | − | 0.793510i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −22.1051 | − | 24.5502i | −1.71569 | − | 1.90547i | ||||
\(167\) | −5.80350 | − | 2.58388i | −0.449088 | − | 0.199947i | 0.169715 | − | 0.985493i | \(-0.445715\pi\) |
−0.618803 | + | 0.785546i | \(0.712382\pi\) | |||||||
\(168\) | −8.74704 | + | 3.89443i | −0.674849 | + | 0.300462i | ||||
\(169\) | 17.8278 | − | 19.7997i | 1.37137 | − | 1.52306i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.360568 | − | 0.261968i | −0.0275733 | − | 0.0200332i | ||||
\(172\) | −32.4744 | + | 36.0665i | −2.47615 | + | 2.75004i | ||||
\(173\) | −2.30333 | + | 1.02551i | −0.175119 | + | 0.0779679i | −0.492423 | − | 0.870356i | \(-0.663889\pi\) |
0.317305 | + | 0.948324i | \(0.397222\pi\) | |||||||
\(174\) | −3.53651 | − | 1.57456i | −0.268102 | − | 0.119367i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.92997 | + | 27.8768i | 0.220855 | + | 2.10129i | ||||
\(177\) | −10.1402 | − | 2.15537i | −0.762184 | − | 0.162007i | ||||
\(178\) | 2.87800 | + | 8.85757i | 0.215715 | + | 0.663903i | ||||
\(179\) | 11.6906 | − | 2.48491i | 0.873795 | − | 0.185731i | 0.250878 | − | 0.968019i | \(-0.419281\pi\) |
0.622917 | + | 0.782288i | \(0.285947\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.04742 | + | 12.2065i | −0.523830 | + | 0.907301i | 0.475785 | + | 0.879562i | \(0.342164\pi\) |
−0.999615 | + | 0.0277391i | \(0.991169\pi\) | |||||||
\(182\) | 4.09220 | − | 12.5945i | 0.303334 | − | 0.933567i | ||||
\(183\) | −0.850212 | + | 8.08923i | −0.0628495 | + | 0.597973i | ||||
\(184\) | 11.2767 | − | 8.19301i | 0.831330 | − | 0.603997i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.29685 | + | 27.1437i | −0.168413 | + | 1.99027i | ||||
\(187\) | 5.86986 | 0.429247 | ||||||||
\(188\) | −29.2714 | + | 21.2669i | −2.13483 | + | 1.55105i | ||||
\(189\) | −0.377533 | + | 3.59199i | −0.0274615 | + | 0.261279i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.140704 | + | 0.243707i | −0.0101810 | + | 0.0176340i | −0.871071 | − | 0.491157i | \(-0.836574\pi\) |
0.860890 | + | 0.508791i | \(0.169907\pi\) | |||||||
\(192\) | −2.81007 | − | 4.86719i | −0.202800 | − | 0.351259i | ||||
\(193\) | 23.6610 | − | 5.02930i | 1.70316 | − | 0.362017i | 0.749289 | − | 0.662243i | \(-0.230395\pi\) |
0.953868 | + | 0.300226i | \(0.0970621\pi\) | |||||||
\(194\) | 4.21913 | + | 12.9851i | 0.302916 | + | 0.932279i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.86154 | + | 27.2257i | 0.204396 | + | 1.94469i | ||||
\(197\) | 8.52507 | + | 9.46805i | 0.607386 | + | 0.674571i | 0.965889 | − | 0.258958i | \(-0.0833792\pi\) |
−0.358502 | + | 0.933529i | \(0.616713\pi\) | |||||||
\(198\) | −8.07337 | − | 3.59449i | −0.573749 | − | 0.255450i | ||||
\(199\) | 9.87056 | − | 4.39466i | 0.699705 | − | 0.311529i | −0.0258761 | − | 0.999665i | \(-0.508238\pi\) |
0.725582 | + | 0.688136i | \(0.241571\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.0712 | − | 8.04371i | −0.780904 | − | 0.567360i | ||||
\(202\) | −4.65449 | − | 3.38169i | −0.327489 | − | 0.237935i | ||||
\(203\) | 0.442124 | − | 0.491029i | 0.0310310 | − | 0.0344635i | ||||
\(204\) | 9.97401 | − | 4.44072i | 0.698320 | − | 0.310912i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 11.0405 | + | 12.2618i | 0.769231 | + | 0.854318i | ||||
\(207\) | 0.190934 | + | 1.81661i | 0.0132708 | + | 0.126263i | ||||
\(208\) | −38.0553 | − | 8.08891i | −2.63866 | − | 0.560865i | ||||
\(209\) | −0.807711 | − | 2.48588i | −0.0558705 | − | 0.171952i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.19907 | + | 3.80891i | 0.151391 | + | 0.262216i | 0.931739 | − | 0.363129i | \(-0.118292\pi\) |
−0.780348 | + | 0.625345i | \(0.784958\pi\) | |||||||
\(212\) | −11.5934 | + | 20.0804i | −0.796241 | + | 1.37913i | ||||
\(213\) | 1.80990 | − | 5.57031i | 0.124013 | − | 0.381671i | ||||
\(214\) | −1.22030 | + | 11.6103i | −0.0834177 | + | 0.793667i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 25.5287 | 1.73701 | ||||||||
\(217\) | −4.28505 | − | 1.80450i | −0.290888 | − | 0.122498i | ||||
\(218\) | −1.49532 | −0.101276 | ||||||||
\(219\) | −16.2706 | + | 11.8213i | −1.09946 | + | 0.798808i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.51763 | + | 7.74848i | −0.169354 | + | 0.521219i | ||||
\(222\) | −27.6150 | + | 47.8305i | −1.85340 | + | 3.21018i | ||||
\(223\) | 8.79878 | + | 15.2399i | 0.589210 | + | 1.02054i | 0.994336 | + | 0.106281i | \(0.0338943\pi\) |
−0.405126 | + | 0.914261i | \(0.632772\pi\) | |||||||
\(224\) | −3.06964 | + | 0.652473i | −0.205099 | + | 0.0435952i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −23.7884 | − | 5.05637i | −1.58238 | − | 0.336345i | ||||
\(227\) | 2.33539 | + | 22.2197i | 0.155005 | + | 1.47477i | 0.744836 | + | 0.667248i | \(0.232528\pi\) |
−0.589831 | + | 0.807527i | \(0.700806\pi\) | |||||||
\(228\) | −3.25309 | − | 3.61292i | −0.215441 | − | 0.239272i | ||||
\(229\) | 0.133599 | + | 0.0594822i | 0.00882849 | + | 0.00393070i | 0.411146 | − | 0.911569i | \(-0.365129\pi\) |
−0.402318 | + | 0.915500i | \(0.631795\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.92391 | − | 5.46855i | 0.323969 | − | 0.359804i | ||||
\(232\) | −3.77833 | − | 2.74512i | −0.248059 | − | 0.180226i | ||||
\(233\) | 7.02994 | + | 5.10755i | 0.460547 | + | 0.334607i | 0.793746 | − | 0.608250i | \(-0.208128\pi\) |
−0.333199 | + | 0.942856i | \(0.608128\pi\) | |||||||
\(234\) | 8.20763 | − | 9.11550i | 0.536549 | − | 0.595899i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −21.1759 | − | 9.42813i | −1.37844 | − | 0.613719i | ||||
\(237\) | −1.66334 | − | 1.84733i | −0.108046 | − | 0.119997i | ||||
\(238\) | 0.284480 | + | 2.70664i | 0.0184401 | + | 0.175446i | ||||
\(239\) | 10.2336 | + | 2.17521i | 0.661954 | + | 0.140703i | 0.526624 | − | 0.850098i | \(-0.323457\pi\) |
0.135329 | + | 0.990801i | \(0.456791\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.32178 | + | 1.13118i | −0.342806 | + | 0.0728657i | −0.376098 | − | 0.926580i | \(-0.622734\pi\) |
0.0332916 | + | 0.999446i | \(0.489401\pi\) | |||||||
\(242\) | −12.0618 | − | 20.8916i | −0.775360 | − | 1.34296i | ||||
\(243\) | −3.92655 | + | 6.80098i | −0.251888 | + | 0.436283i | ||||
\(244\) | −5.62011 | + | 17.2969i | −0.359791 | + | 1.10732i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 44.5398 | − | 32.3601i | 2.83976 | − | 2.06320i | ||||
\(247\) | 3.62790 | 0.230838 | ||||||||
\(248\) | −9.51879 | + | 31.4548i | −0.604444 | + | 1.99738i | ||||
\(249\) | 25.4794 | 1.61469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.20823 | − | 11.4955i | 0.0762626 | − | 0.725590i | −0.887857 | − | 0.460120i | \(-0.847806\pi\) |
0.964119 | − | 0.265470i | \(-0.0855270\pi\) | |||||||
\(252\) | 0.866976 | − | 2.66828i | 0.0546143 | − | 0.168086i | ||||
\(253\) | −5.35627 | + | 9.27734i | −0.336746 | + | 0.583261i | ||||
\(254\) | 15.4566 | + | 26.7717i | 0.969836 | + | 1.67981i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.73302 | − | 29.9552i | −0.608314 | − | 1.87220i | ||||
\(257\) | 18.5574 | + | 3.94450i | 1.15758 | + | 0.246051i | 0.746397 | − | 0.665501i | \(-0.231782\pi\) |
0.411184 | + | 0.911552i | \(0.365115\pi\) | |||||||
\(258\) | −5.71426 | − | 54.3675i | −0.355754 | − | 3.38477i | ||||
\(259\) | −6.30774 | − | 7.00546i | −0.391944 | − | 0.435298i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.559108 | − | 0.248931i | 0.0346079 | − | 0.0154084i | ||||
\(262\) | 27.9978 | − | 31.0947i | 1.72971 | − | 1.92104i | ||||
\(263\) | 4.21884 | + | 3.06516i | 0.260145 | + | 0.189006i | 0.710211 | − | 0.703989i | \(-0.248600\pi\) |
−0.450066 | + | 0.892995i | \(0.648600\pi\) | |||||||
\(264\) | −42.0790 | − | 30.5722i | −2.58978 | − | 1.88159i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.10711 | − | 0.492919i | 0.0678815 | − | 0.0302228i | ||||
\(267\) | −6.56213 | − | 2.92165i | −0.401596 | − | 0.178802i | ||||
\(268\) | −20.4748 | − | 22.7395i | −1.25069 | − | 1.38904i | ||||
\(269\) | −0.120184 | − | 1.14347i | −0.00732773 | − | 0.0697187i | 0.990247 | − | 0.139324i | \(-0.0444928\pi\) |
−0.997575 | + | 0.0696049i | \(0.977826\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.88599 | + | 11.9599i | 0.236057 | + | 0.726509i | 0.996979 | + | 0.0776663i | \(0.0247469\pi\) |
−0.760922 | + | 0.648843i | \(0.775253\pi\) | |||||||
\(272\) | 7.82091 | − | 1.66239i | 0.474212 | − | 0.100797i | ||||
\(273\) | 5.10683 | + | 8.84529i | 0.309079 | + | 0.535341i | ||||
\(274\) | 3.68944 | − | 6.39030i | 0.222887 | − | 0.386052i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.08276 | + | 19.8161i | −0.125367 | + | 1.19279i | ||||
\(277\) | −17.6504 | + | 12.8237i | −1.06051 | + | 0.770503i | −0.974182 | − | 0.225764i | \(-0.927512\pi\) |
−0.0863249 | + | 0.996267i | \(0.527512\pi\) | |||||||
\(278\) | 53.9902 | 3.23812 | ||||||||
\(279\) | −2.94608 | − | 3.14129i | −0.176377 | − | 0.188064i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.1753 | − | 18.2909i | 1.50183 | − | 1.09114i | 0.532185 | − | 0.846628i | \(-0.321371\pi\) |
0.969645 | − | 0.244515i | \(-0.0786289\pi\) | |||||||
\(282\) | 4.26005 | − | 40.5317i | 0.253683 | − | 2.41363i | ||||
\(283\) | −5.60243 | + | 17.2425i | −0.333030 | + | 1.02496i | 0.634654 | + | 0.772796i | \(0.281142\pi\) |
−0.967684 | + | 0.252165i | \(0.918858\pi\) | |||||||
\(284\) | 6.54806 | − | 11.3416i | 0.388556 | − | 0.672999i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 70.3648 | − | 14.9565i | 4.16076 | − | 0.884397i | ||||
\(287\) | 2.90377 | + | 8.93687i | 0.171404 | + | 0.527527i | ||||
\(288\) | −2.84328 | − | 0.604359i | −0.167542 | − | 0.0356122i | ||||
\(289\) | 1.60196 | + | 15.2417i | 0.0942332 | + | 0.896569i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.62005 | − | 4.28312i | −0.563937 | − | 0.251081i | ||||
\(292\) | −41.0814 | + | 18.2906i | −2.40411 | + | 1.07038i | ||||
\(293\) | 7.83301 | − | 8.69944i | 0.457609 | − | 0.508226i | −0.469544 | − | 0.882909i | \(-0.655582\pi\) |
0.927153 | + | 0.374683i | \(0.122248\pi\) | |||||||
\(294\) | −24.9470 | − | 18.1250i | −1.45494 | − | 1.05707i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −44.5843 | + | 49.5159i | −2.59141 | + | 2.87805i | ||||
\(297\) | −17.9237 | + | 7.98014i | −1.04004 | + | 0.463055i | ||||
\(298\) | −18.1755 | − | 8.09227i | −1.05288 | − | 0.468773i | ||||
\(299\) | −9.94915 | − | 11.0497i | −0.575374 | − | 0.639018i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.12679 | + | 1.93996i | 0.526059 | + | 0.111817i | ||||
\(302\) | −1.72790 | − | 5.31794i | −0.0994296 | − | 0.306013i | ||||
\(303\) | 4.34036 | − | 0.922572i | 0.249347 | − | 0.0530004i | ||||
\(304\) | −1.78020 | − | 3.08339i | −0.102101 | − | 0.176845i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.778988 | + | 2.39748i | −0.0445318 | + | 0.137055i | ||||
\(307\) | −1.22753 | + | 11.6792i | −0.0700591 | + | 0.666568i | 0.901985 | + | 0.431768i | \(0.142110\pi\) |
−0.972044 | + | 0.234800i | \(0.924557\pi\) | |||||||
\(308\) | 13.3115 | − | 9.67136i | 0.758492 | − | 0.551077i | ||||
\(309\) | −12.7258 | −0.723947 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.833220 | −0.0472476 | −0.0236238 | − | 0.999721i | \(-0.507520\pi\) | ||||
−0.0236238 | + | 0.999721i | \(0.507520\pi\) | |||||||
\(312\) | 58.4047 | − | 42.4335i | 3.30651 | − | 2.40232i | ||||
\(313\) | 1.10756 | − | 10.5377i | 0.0626029 | − | 0.595627i | −0.917583 | − | 0.397545i | \(-0.869862\pi\) |
0.980186 | − | 0.198082i | \(-0.0634711\pi\) | |||||||
\(314\) | −4.07004 | + | 12.5263i | −0.229686 | + | 0.706900i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.77914 | − | 4.81361i | −0.156339 | − | 0.270787i | ||||
\(317\) | 30.4268 | − | 6.46741i | 1.70894 | − | 0.363246i | 0.753274 | − | 0.657707i | \(-0.228474\pi\) |
0.955663 | + | 0.294461i | \(0.0951403\pi\) | |||||||
\(318\) | −8.07086 | − | 24.8396i | −0.452591 | − | 1.39293i | ||||
\(319\) | 3.51087 | + | 0.746258i | 0.196571 | + | 0.0417824i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.02488 | − | 6.69130i | −0.336276 | − | 0.373472i | ||||
\(322\) | −4.53745 | − | 2.02020i | −0.252862 | − | 0.112581i | ||||
\(323\) | −0.681127 | + | 0.303257i | −0.0378989 | + | 0.0168737i | ||||
\(324\) | −31.1628 | + | 34.6098i | −1.73127 | + | 1.92277i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 27.0555 | + | 19.6570i | 1.49847 | + | 1.08870i | ||||
\(327\) | 0.771706 | − | 0.857067i | 0.0426755 | − | 0.0473959i | ||||
\(328\) | 60.6761 | − | 27.0147i | 3.35028 | − | 1.49164i | ||||
\(329\) | 6.35476 | + | 2.82932i | 0.350349 | + | 0.155986i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.934022 | + | 8.88662i | 0.0513385 | + | 0.488453i | 0.989737 | + | 0.142899i | \(0.0456424\pi\) |
−0.938399 | + | 0.345554i | \(0.887691\pi\) | |||||||
\(332\) | 55.7267 | + | 11.8451i | 3.05840 | + | 0.650083i | ||||
\(333\) | −2.69822 | − | 8.30427i | −0.147862 | − | 0.455071i | ||||
\(334\) | 15.6505 | − | 3.32662i | 0.856359 | − | 0.182025i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.01180 | − | 8.68070i | 0.273416 | − | 0.473571i | ||||
\(337\) | −7.20064 | + | 22.1613i | −0.392244 | + | 1.20720i | 0.538843 | + | 0.842406i | \(0.318861\pi\) |
−0.931087 | + | 0.364796i | \(0.881139\pi\) | |||||||
\(338\) | −7.01432 | + | 66.7368i | −0.381529 | + | 3.63000i | ||||
\(339\) | 15.1749 | − | 11.0252i | 0.824185 | − | 0.598805i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.14947 | − | 25.0599i | −0.170554 | − | 1.35707i | ||||
\(342\) | 1.12252 | 0.0606990 | ||||||||
\(343\) | 8.98713 | − | 6.52953i | 0.485260 | − | 0.352562i | ||||
\(344\) | 6.89377 | − | 65.5898i | 0.371687 | − | 3.53637i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.17512 | − | 5.49947i | 0.170696 | − | 0.295654i | ||||
\(347\) | −9.63256 | − | 16.6841i | −0.517103 | − | 0.895648i | −0.999803 | − | 0.0198624i | \(-0.993677\pi\) |
0.482700 | − | 0.875786i | \(-0.339656\pi\) | |||||||
\(348\) | 6.53020 | − | 1.38804i | 0.350055 | − | 0.0744065i | ||||
\(349\) | 10.0809 | + | 31.0259i | 0.539619 | + | 1.66078i | 0.733451 | + | 0.679743i | \(0.237908\pi\) |
−0.193832 | + | 0.981035i | \(0.562092\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.84652 | − | 27.0828i | −0.151936 | − | 1.44557i | ||||
\(352\) | −11.4070 | − | 12.6687i | −0.607995 | − | 0.675247i | ||||
\(353\) | 11.6241 | + | 5.17536i | 0.618686 | + | 0.275457i | 0.692051 | − | 0.721848i | \(-0.256707\pi\) |
−0.0733652 | + | 0.997305i | \(0.523374\pi\) | |||||||
\(354\) | 23.8527 | − | 10.6199i | 1.26776 | − | 0.564442i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −12.9940 | − | 9.44069i | −0.688680 | − | 0.500355i | ||||
\(357\) | −1.69817 | − | 1.23379i | −0.0898766 | − | 0.0652992i | ||||
\(358\) | −20.1422 | + | 22.3702i | −1.06455 | + | 1.18230i | ||||
\(359\) | −5.85762 | + | 2.60798i | −0.309153 | + | 0.137644i | −0.555449 | − | 0.831551i | \(-0.687453\pi\) |
0.246295 | + | 0.969195i | \(0.420787\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.4913 | − | 13.8730i | −0.657438 | − | 0.730159i | ||||
\(362\) | −3.71073 | − | 35.3053i | −0.195032 | − | 1.85560i | ||||
\(363\) | 18.1992 | + | 3.86836i | 0.955210 | + | 0.203036i | ||||
\(364\) | 7.05722 | + | 21.7199i | 0.369899 | + | 1.13843i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −10.2430 | − | 17.7414i | −0.535411 | − | 0.927359i | ||||
\(367\) | 10.9471 | − | 18.9610i | 0.571435 | − | 0.989754i | −0.424984 | − | 0.905201i | \(-0.639720\pi\) |
0.996419 | − | 0.0845536i | \(-0.0269464\pi\) | |||||||
\(368\) | −4.50921 | + | 13.8779i | −0.235059 | + | 0.723436i | ||||
\(369\) | −0.909800 | + | 8.65617i | −0.0473623 | + | 0.450622i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.45785 | 0.231440 | ||||||||
\(372\) | −24.3101 | − | 40.1989i | −1.26042 | − | 2.08422i | ||||
\(373\) | −4.62775 | −0.239616 | −0.119808 | − | 0.992797i | \(-0.538228\pi\) | ||||
−0.119808 | + | 0.992797i | \(0.538228\pi\) | |||||||
\(374\) | −11.9605 | + | 8.68984i | −0.618465 | + | 0.449341i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.1936 | − | 46.7610i | 0.783548 | − | 2.41151i | ||||
\(377\) | −2.49093 | + | 4.31443i | −0.128290 | + | 0.222204i | ||||
\(378\) | −4.54837 | − | 7.87801i | −0.233943 | − | 0.405201i | ||||
\(379\) | 14.1342 | − | 3.00432i | 0.726025 | − | 0.154321i | 0.169949 | − | 0.985453i | \(-0.445640\pi\) |
0.556076 | + | 0.831131i | \(0.312306\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −23.3215 | − | 4.95714i | −1.19480 | − | 0.253962i | ||||
\(382\) | −0.0740861 | − | 0.704882i | −0.00379057 | − | 0.0360649i | ||||
\(383\) | −13.6515 | − | 15.1615i | −0.697560 | − | 0.774718i | 0.285426 | − | 0.958401i | \(-0.407865\pi\) |
−0.982986 | + | 0.183682i | \(0.941198\pi\) | |||||||
\(384\) | 26.2693 | + | 11.6959i | 1.34055 | + | 0.596852i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −40.7666 | + | 45.2759i | −2.07497 | + | 2.30449i | ||||
\(387\) | 6.99203 | + | 5.08001i | 0.355425 | + | 0.258231i | ||||
\(388\) | −19.0491 | − | 13.8400i | −0.967072 | − | 0.702619i | ||||
\(389\) | 4.17983 | − | 4.64217i | 0.211926 | − | 0.235367i | −0.627805 | − | 0.778371i | \(-0.716046\pi\) |
0.839730 | + | 0.543004i | \(0.182713\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.79156 | + | 1.24288i | 0.141175 | + | 0.0628553i | ||||
\(392\) | −24.8925 | − | 27.6459i | −1.25726 | − | 1.39633i | ||||
\(393\) | 3.37330 | + | 32.0948i | 0.170160 | + | 1.61897i | ||||
\(394\) | −31.3875 | − | 6.67162i | −1.58128 | − | 0.336111i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 14.9075 | − | 3.16869i | 0.749131 | − | 0.159233i | ||||
\(397\) | −15.7955 | − | 27.3586i | −0.792753 | − | 1.37309i | −0.924256 | − | 0.381773i | \(-0.875314\pi\) |
0.131503 | − | 0.991316i | \(-0.458020\pi\) | |||||||
\(398\) | −13.6065 | + | 23.5672i | −0.682033 | + | 1.18132i | ||||
\(399\) | −0.288836 | + | 0.888946i | −0.0144599 | + | 0.0445030i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.67599 | + | 1.21768i | −0.0836950 | + | 0.0608080i | −0.628846 | − | 0.777530i | \(-0.716472\pi\) |
0.545151 | + | 0.838338i | \(0.316472\pi\) | |||||||
\(402\) | 34.4670 | 1.71906 | ||||||||
\(403\) | 34.4311 | + | 6.59097i | 1.71513 | + | 0.328320i | ||||
\(404\) | 9.92182 | 0.493629 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.173954 | + | 1.65506i | −0.00863317 | + | 0.0821391i | ||||
\(407\) | 15.8242 | − | 48.7019i | 0.784377 | − | 2.41406i | ||||
\(408\) | −7.41825 | + | 12.8488i | −0.367258 | + | 0.636110i | ||||
\(409\) | −11.9560 | − | 20.7083i | −0.591184 | − | 1.02396i | −0.994073 | − | 0.108712i | \(-0.965327\pi\) |
0.402890 | − | 0.915249i | \(-0.368006\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.75865 | + | 5.41258i | 0.0867479 | + | 0.266983i | ||||
\(412\) | −27.8330 | − | 5.91609i | −1.37124 | − | 0.291465i | ||||
\(413\) | 0.465833 | + | 4.43211i | 0.0229221 | + | 0.218090i | ||||
\(414\) | −3.07840 | − | 3.41891i | −0.151295 | − | 0.168030i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 21.6159 | − | 9.62401i | 1.05981 | − | 0.471856i | ||||
\(417\) | −27.8633 | + | 30.9454i | −1.36447 | + | 1.51540i | ||||
\(418\) | 5.32594 | + | 3.86952i | 0.260500 | + | 0.189265i | ||||
\(419\) | 24.7274 | + | 17.9655i | 1.20801 | + | 0.877673i | 0.995049 | − | 0.0993864i | \(-0.0316880\pi\) |
0.212965 | + | 0.977060i | \(0.431688\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.5099 | − | 9.13160i | 0.999592 | − | 0.445047i | 0.159329 | − | 0.987226i | \(-0.449067\pi\) |
0.840263 | + | 0.542178i | \(0.182400\pi\) | |||||||
\(422\) | −10.1196 | − | 4.50555i | −0.492616 | − | 0.219327i | ||||
\(423\) | 4.31134 | + | 4.78822i | 0.209624 | + | 0.232811i | ||||
\(424\) | −3.29358 | − | 31.3364i | −0.159951 | − | 1.52183i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.55848 | + | 14.0296i | 0.220859 | + | 0.679735i | ||||
\(427\) | 3.42019 | − | 0.726984i | 0.165515 | − | 0.0351812i | ||||
\(428\) | −10.0665 | − | 17.4356i | −0.486581 | − | 0.842783i | ||||
\(429\) | −27.7414 | + | 48.0495i | −1.33937 | + | 2.31985i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.72251 | − | 16.3886i | 0.0829704 | − | 0.789411i | −0.871357 | − | 0.490649i | \(-0.836760\pi\) |
0.954328 | − | 0.298762i | \(-0.0965736\pi\) | |||||||
\(432\) | −21.6212 | + | 15.7087i | −1.04025 | + | 0.755787i | ||||
\(433\) | −30.3372 | −1.45791 | −0.728957 | − | 0.684560i | \(-0.759994\pi\) | ||||
−0.728957 | + | 0.684560i | \(0.759994\pi\) | |||||||
\(434\) | 11.4027 | − | 2.66676i | 0.547347 | − | 0.128009i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.08626 | − | 1.51576i | 0.0999138 | − | 0.0725916i | ||||
\(437\) | 0.142232 | − | 1.35325i | 0.00680388 | − | 0.0647346i | ||||
\(438\) | 15.6528 | − | 48.1745i | 0.747921 | − | 2.30187i | ||||
\(439\) | 8.25197 | − | 14.2928i | 0.393845 | − | 0.682160i | −0.599108 | − | 0.800668i | \(-0.704478\pi\) |
0.992953 | + | 0.118508i | \(0.0378113\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.76854 | − | 1.01358i | 0.227073 | − | 0.0482659i | ||||
\(442\) | −6.34100 | − | 19.5156i | −0.301611 | − | 0.928262i | ||||
\(443\) | −24.6936 | − | 5.24879i | −1.17323 | − | 0.249377i | −0.420241 | − | 0.907413i | \(-0.638054\pi\) |
−0.752987 | + | 0.658035i | \(0.771388\pi\) | |||||||
\(444\) | −9.95602 | − | 94.7252i | −0.472492 | − | 4.49546i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −40.4900 | − | 18.0273i | −1.91726 | − | 0.853618i | ||||
\(447\) | 14.0183 | − | 6.24133i | 0.663041 | − | 0.295205i | ||||
\(448\) | −1.61664 | + | 1.79546i | −0.0763788 | + | 0.0848273i | ||||
\(449\) | −2.11185 | − | 1.53435i | −0.0996644 | − | 0.0724104i | 0.536837 | − | 0.843686i | \(-0.319619\pi\) |
−0.636501 | + | 0.771276i | \(0.719619\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −34.1560 | + | 37.9340i | −1.60834 | + | 1.78624i | ||||
\(452\) | 38.3148 | − | 17.0589i | 1.80218 | − | 0.802381i | ||||
\(453\) | 3.93980 | + | 1.75411i | 0.185108 | + | 0.0824153i | ||||
\(454\) | −37.6531 | − | 41.8180i | −1.76715 | − | 1.96261i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.46222 | + | 1.37359i | 0.302621 | + | 0.0643241i | ||||
\(457\) | 2.89306 | + | 8.90392i | 0.135332 | + | 0.416508i | 0.995641 | − | 0.0932637i | \(-0.0297300\pi\) |
−0.860310 | + | 0.509771i | \(0.829730\pi\) | |||||||
\(458\) | −0.360283 | + | 0.0765805i | −0.0168349 | + | 0.00357837i | ||||
\(459\) | 2.79828 | + | 4.84677i | 0.130613 | + | 0.226228i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.44913 | + | 16.7707i | −0.253791 | + | 0.781089i | 0.740274 | + | 0.672305i | \(0.234696\pi\) |
−0.994065 | + | 0.108784i | \(0.965304\pi\) | |||||||
\(462\) | −1.93731 | + | 18.4323i | −0.0901318 | + | 0.857546i | ||||
\(463\) | 4.70265 | − | 3.41667i | 0.218551 | − | 0.158786i | −0.473123 | − | 0.880996i | \(-0.656874\pi\) |
0.691674 | + | 0.722210i | \(0.256874\pi\) | |||||||
\(464\) | 4.88917 | 0.226974 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.8856 | −1.01383 | ||||||||
\(467\) | 6.54431 | − | 4.75472i | 0.302834 | − | 0.220022i | −0.425981 | − | 0.904732i | \(-0.640071\pi\) |
0.728816 | + | 0.684710i | \(0.240071\pi\) | |||||||
\(468\) | −2.21115 | + | 21.0377i | −0.102210 | + | 0.972467i | ||||
\(469\) | −1.81792 | + | 5.59497i | −0.0839436 | + | 0.258352i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.07918 | − | 8.79739i | −0.234036 | − | 0.405362i | ||||
\(472\) | 30.8112 | − | 6.54912i | 1.41820 | − | 0.301448i | ||||
\(473\) | 15.6629 | + | 48.2055i | 0.720181 | + | 2.21649i | ||||
\(474\) | 6.12406 | + | 1.30171i | 0.281287 | + | 0.0597895i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.14054 | − | 3.48792i | −0.143946 | − | 0.159869i | ||||
\(477\) | 3.77214 | + | 1.67947i | 0.172715 | + | 0.0768975i | ||||
\(478\) | −24.0723 | + | 10.7177i | −1.10104 | + | 0.490215i | ||||
\(479\) | 6.09262 | − | 6.76654i | 0.278379 | − | 0.309171i | −0.587700 | − | 0.809079i | \(-0.699966\pi\) |
0.866078 | + | 0.499908i | \(0.166633\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 57.5015 | + | 41.7773i | 2.62184 | + | 1.90488i | ||||
\(482\) | 9.16915 | − | 10.1834i | 0.417643 | − | 0.463840i | ||||
\(483\) | 3.49960 | − | 1.55812i | 0.159237 | − | 0.0708970i | ||||
\(484\) | 38.0056 | + | 16.9212i | 1.72753 | + | 0.769145i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.06748 | − | 19.6707i | −0.0937826 | − | 0.892282i | ||||
\(487\) | 40.2479 | + | 8.55495i | 1.82381 | + | 0.387662i | 0.987115 | − | 0.160013i | \(-0.0511537\pi\) |
0.836691 | + | 0.547675i | \(0.184487\pi\) | |||||||
\(488\) | −7.63725 | − | 23.5050i | −0.345722 | − | 1.06402i | ||||
\(489\) | −25.2296 | + | 5.36271i | −1.14092 | + | 0.242510i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.46138 | + | 16.3876i | −0.426986 | + | 0.739562i | −0.996604 | − | 0.0823481i | \(-0.973758\pi\) |
0.569617 | + | 0.821910i | \(0.307091\pi\) | |||||||
\(492\) | −29.3393 | + | 90.2971i | −1.32272 | + | 4.07091i | ||||
\(493\) | 0.107021 | − | 1.01824i | 0.00481998 | − | 0.0458591i | ||||
\(494\) | −7.39228 | + | 5.37081i | −0.332595 | + | 0.241644i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.2935 | − | 32.4975i | −0.507091 | − | 1.45918i | ||||
\(497\) | −2.51783 | −0.112940 | ||||||||
\(498\) | −51.9172 | + | 37.7201i | −2.32647 | + | 1.69028i | ||||
\(499\) | −0.831837 | + | 7.91440i | −0.0372382 | + | 0.354297i | 0.959998 | + | 0.280006i | \(0.0903363\pi\) |
−0.997237 | + | 0.0742919i | \(0.976330\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.17023 | + | 10.6872i | −0.275666 | + | 0.477467i | ||||
\(502\) | 14.5562 | + | 25.2121i | 0.649676 | + | 1.12527i | ||||
\(503\) | −7.35909 | + | 1.56422i | −0.328125 | + | 0.0697452i | −0.369029 | − | 0.929418i | \(-0.620310\pi\) |
0.0409035 | + | 0.999163i | \(0.486976\pi\) | |||||||
\(504\) | 1.17815 | + | 3.62596i | 0.0524788 | + | 0.161513i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.82028 | − | 26.8332i | −0.125377 | − | 1.19288i | ||||
\(507\) | −34.6313 | − | 38.4619i | −1.53803 | − | 1.70816i | ||||
\(508\) | −48.7026 | − | 21.6838i | −2.16083 | − | 0.962062i | ||||
\(509\) | 12.2699 | − | 5.46290i | 0.543852 | − | 0.242139i | −0.116374 | − | 0.993205i | \(-0.537127\pi\) |
0.660226 | + | 0.751067i | \(0.270460\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.99450 | + | 5.08180i | 0.309418 | + | 0.224806i | ||||
\(512\) | 40.2267 | + | 29.2264i | 1.77779 | + | 1.29164i | ||||
\(513\) | 1.66755 | − | 1.85200i | 0.0736240 | − | 0.0817677i | ||||
\(514\) | −43.6525 | + | 19.4353i | −1.92543 | + | 0.857255i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 63.0831 | + | 70.0608i | 2.77708 | + | 3.08426i | ||||
\(517\) | 3.94984 | + | 37.5803i | 0.173714 | + | 1.65278i | ||||
\(518\) | 23.2238 | + | 4.93636i | 1.02039 | + | 0.216891i | ||||
\(519\) | 1.51349 | + | 4.65804i | 0.0664349 | + | 0.204465i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.74556 | + | 16.8798i | 0.426961 | + | 0.739518i | 0.996601 | − | 0.0823761i | \(-0.0262509\pi\) |
−0.569640 | + | 0.821894i | \(0.692918\pi\) | |||||||
\(522\) | −0.770727 | + | 1.33494i | −0.0337338 | + | 0.0584287i | ||||
\(523\) | 1.93469 | − | 5.95438i | 0.0845983 | − | 0.260367i | −0.899805 | − | 0.436292i | \(-0.856292\pi\) |
0.984404 | + | 0.175925i | \(0.0562916\pi\) | |||||||
\(524\) | −7.54266 | + | 71.7636i | −0.329503 | + | 3.13501i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.1341 | −0.572674 | ||||||||
\(527\) | −7.01525 | + | 1.64067i | −0.305589 | + | 0.0714685i | ||||
\(528\) | 54.4503 | 2.36965 | ||||||||
\(529\) | 14.0957 | − | 10.2411i | 0.612856 | − | 0.445266i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.27559 | + | 3.92585i | −0.0553558 | + | 0.170368i | ||||
\(532\) | −1.04498 | + | 1.80996i | −0.0453057 | + | 0.0784718i | ||||
\(533\) | −35.4248 | − | 61.3576i | −1.53442 | − | 2.65769i | ||||
\(534\) | 17.6964 | − | 3.76148i | 0.765797 | − | 0.162775i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 40.6728 | + | 8.64527i | 1.75680 | + | 0.373419i | ||||
\(537\) | −2.42682 | − | 23.0897i | −0.104725 | − | 0.996394i | ||||
\(538\) | 1.93770 | + | 2.15204i | 0.0835403 | + | 0.0927809i | ||||
\(539\) | 26.1189 | + | 11.6289i | 1.12502 | + | 0.500892i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.4535 | − | 27.1584i | 1.05134 | − | 1.16763i | 0.0658608 | − | 0.997829i | \(-0.479021\pi\) |
0.985478 | − | 0.169802i | \(-0.0543127\pi\) | |||||||
\(542\) | −25.6237 | − | 18.6167i | −1.10063 | − | 0.799657i | ||||
\(543\) | 22.1508 | + | 16.0935i | 0.950582 | + | 0.690638i | ||||
\(544\) | −3.25383 | + | 3.61375i | −0.139507 | + | 0.154938i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −23.5005 | − | 10.4631i | −1.00573 | − | 0.447779i | ||||
\(547\) | −7.61131 | − | 8.45322i | −0.325436 | − | 0.361433i | 0.558119 | − | 0.829761i | \(-0.311523\pi\) |
−0.883555 | + | 0.468328i | \(0.844857\pi\) | |||||||
\(548\) | 1.33015 | + | 12.6556i | 0.0568214 | + | 0.540619i | ||||
\(549\) | 3.16798 | + | 0.673375i | 0.135206 | + | 0.0287390i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.445948 | + | 0.0947892i | −0.0189980 | + | 0.00403815i | ||||
\(552\) | −13.5384 | − | 23.4492i | −0.576232 | − | 0.998062i | ||||
\(553\) | −0.534310 | + | 0.925453i | −0.0227212 | + | 0.0393542i | ||||
\(554\) | 16.9802 | − | 52.2597i | 0.721420 | − | 2.22030i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −75.3268 | + | 54.7281i | −3.19457 | + | 2.32099i | ||||
\(557\) | −17.9263 | −0.759560 | −0.379780 | − | 0.925077i | \(-0.624000\pi\) | ||||
−0.379780 | + | 0.925077i | \(0.624000\pi\) | |||||||
\(558\) | 10.6534 | + | 2.03933i | 0.450995 | + | 0.0863317i | ||||
\(559\) | −70.3514 | −2.97555 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.19188 | − | 11.3400i | 0.0503214 | − | 0.478776i | ||||
\(562\) | −24.2194 | + | 74.5397i | −1.02163 | + | 3.14427i | ||||
\(563\) | 16.5969 | − | 28.7466i | 0.699474 | − | 1.21152i | −0.269175 | − | 0.963091i | \(-0.586751\pi\) |
0.968649 | − | 0.248433i | \(-0.0799157\pi\) | |||||||
\(564\) | 35.1421 | + | 60.8678i | 1.47975 | + | 2.56300i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14.1105 | − | 43.4276i | −0.593108 | − | 1.82540i | ||||
\(567\) | 8.75817 | + | 1.86161i | 0.367808 | + | 0.0781801i | ||||
\(568\) | 1.86024 | + | 17.6990i | 0.0780540 | + | 0.742634i | ||||
\(569\) | 18.2648 | + | 20.2851i | 0.765699 | + | 0.850395i | 0.992334 | − | 0.123585i | \(-0.0394391\pi\) |
−0.226635 | + | 0.973980i | \(0.572772\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.0994 | − | 12.0654i | 1.13408 | − | 0.504923i | 0.248137 | − | 0.968725i | \(-0.420182\pi\) |
0.885939 | + | 0.463802i | \(0.153515\pi\) | |||||||
\(572\) | −83.0116 | + | 92.1937i | −3.47089 | + | 3.85481i | ||||
\(573\) | 0.442248 | + | 0.321312i | 0.0184752 | + | 0.0134230i | ||||
\(574\) | −19.1471 | − | 13.9111i | −0.799182 | − | 0.580640i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.04439 | + | 0.910221i | −0.0851829 | + | 0.0379259i | ||||
\(577\) | 1.84475 | + | 0.821336i | 0.0767979 | + | 0.0341926i | 0.444776 | − | 0.895642i | \(-0.353283\pi\) |
−0.367978 | + | 0.929834i | \(0.619950\pi\) | |||||||
\(578\) | −25.8282 | − | 28.6851i | −1.07431 | − | 1.19314i | ||||
\(579\) | −4.91174 | − | 46.7321i | −0.204125 | − | 1.94212i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.38474 | − | 10.4171i | −0.140422 | − | 0.432176i | ||||
\(582\) | 25.9428 | − | 5.51431i | 1.07536 | − | 0.228576i | ||||
\(583\) | 12.1080 | + | 20.9717i | 0.501462 | + | 0.868558i | ||||
\(584\) | 30.5547 | − | 52.9222i | 1.26436 | − | 2.18994i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.08189 | + | 29.3222i | −0.127312 | + | 1.21129i | ||||
\(587\) | 2.75988 | − | 2.00517i | 0.113913 | − | 0.0827623i | −0.529371 | − | 0.848391i | \(-0.677572\pi\) |
0.643283 | + | 0.765628i | \(0.277572\pi\) | |||||||
\(588\) | 53.1786 | 2.19305 | ||||||||
\(589\) | 1.66014 | + | 2.74519i | 0.0684049 | + | 0.113114i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.0224 | − | 14.5471i | 0.823612 | − | 0.598389i | ||||
\(592\) | 7.29120 | − | 69.3711i | 0.299667 | − | 2.85114i | ||||
\(593\) | 4.48436 | − | 13.8014i | 0.184151 | − | 0.566757i | −0.815782 | − | 0.578359i | \(-0.803693\pi\) |
0.999933 | + | 0.0116020i | \(0.00369312\pi\) | |||||||
\(594\) | 24.7077 | − | 42.7950i | 1.01377 | − | 1.75590i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 33.5613 | − | 7.13367i | 1.37472 | − | 0.292206i | ||||
\(597\) | −6.48584 | − | 19.9613i | −0.265448 | − | 0.816964i | ||||
\(598\) | 36.6307 | + | 7.78609i | 1.49794 | + | 0.318397i | ||||
\(599\) | −0.0589838 | − | 0.561194i | −0.00241001 | − | 0.0229298i | 0.993251 | − | 0.115986i | \(-0.0370029\pi\) |
−0.995661 | + | 0.0930566i | \(0.970336\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.9005 | − | 8.86028i | −0.811759 | − | 0.361419i | −0.0414913 | − | 0.999139i | \(-0.513211\pi\) |
−0.770268 | + | 0.637720i | \(0.779878\pi\) | |||||||
\(602\) | −21.4689 | + | 9.55855i | −0.875005 | + | 0.389577i | ||||
\(603\) | −3.64615 | + | 4.04946i | −0.148483 | + | 0.164907i | ||||
\(604\) | 7.80137 | + | 5.66803i | 0.317433 | + | 0.230629i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.47821 | + | 8.30539i | −0.303781 | + | 0.337384i | ||||
\(607\) | 9.52379 | − | 4.24026i | 0.386559 | − | 0.172107i | −0.204250 | − | 0.978919i | \(-0.565476\pi\) |
0.590809 | + | 0.806812i | \(0.298809\pi\) | |||||||
\(608\) | 1.97815 | + | 0.880731i | 0.0802248 | + | 0.0357184i | ||||
\(609\) | −0.858848 | − | 0.953847i | −0.0348023 | − | 0.0386518i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −51.3017 | − | 10.9045i | −2.07545 | − | 0.441150i | ||||
\(612\) | −1.34341 | − | 4.13458i | −0.0543040 | − | 0.167131i | ||||
\(613\) | −16.2216 | + | 3.44801i | −0.655184 | + | 0.139264i | −0.523497 | − | 0.852028i | \(-0.675373\pi\) |
−0.131687 | + | 0.991291i | \(0.542039\pi\) | |||||||
\(614\) | −14.7888 | − | 25.6150i | −0.596829 | − | 1.03374i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.90945 | + | 21.2651i | −0.278390 | + | 0.856795i | ||||
\(617\) | 1.61141 | − | 15.3315i | 0.0648729 | − | 0.617224i | −0.912991 | − | 0.407980i | \(-0.866233\pi\) |
0.977864 | − | 0.209244i | \(-0.0671002\pi\) | |||||||
\(618\) | 25.9304 | − | 18.8395i | 1.04307 | − | 0.757837i | ||||
\(619\) | 40.5205 | 1.62866 | 0.814328 | − | 0.580406i | \(-0.197106\pi\) | ||||
0.814328 | + | 0.580406i | \(0.197106\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.2138 | −0.409865 | ||||||||
\(622\) | 1.69779 | − | 1.23351i | 0.0680750 | − | 0.0494594i | ||||
\(623\) | −0.322777 | + | 3.07102i | −0.0129318 | + | 0.123038i | ||||
\(624\) | −23.3542 | + | 71.8769i | −0.934917 | + | 2.87738i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.3434 | + | 23.1115i | 0.533310 | + | 0.923721i | ||||
\(627\) | −4.96649 | + | 1.05566i | −0.198343 | + | 0.0421590i | ||||
\(628\) | −7.01901 | − | 21.6023i | −0.280089 | − | 0.862025i | ||||
\(629\) | −14.2879 | − | 3.03698i | −0.569695 | − | 0.121093i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.30926 | − | 5.89653i | −0.211358 | − | 0.234737i | 0.628139 | − | 0.778101i | \(-0.283817\pi\) |
−0.839497 | + | 0.543364i | \(0.817150\pi\) | |||||||
\(632\) | 6.90021 | + | 3.07217i | 0.274475 | + | 0.122204i | ||||
\(633\) | 7.80498 | − | 3.47500i | 0.310220 | − | 0.138119i | ||||
\(634\) | −52.4237 | + | 58.2224i | −2.08201 | + | 2.31231i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 36.4394 | + | 26.4748i | 1.44492 | + | 1.04979i | ||||
\(637\) | −26.5533 | + | 29.4904i | −1.05208 | + | 1.16845i | ||||
\(638\) | −8.25858 | + | 3.67696i | −0.326960 | + | 0.145572i | ||||
\(639\) | −2.13053 | − | 0.948575i | −0.0842827 | − | 0.0375251i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.39369 | + | 32.2888i | 0.134043 | + | 1.27533i | 0.830210 | + | 0.557450i | \(0.188220\pi\) |
−0.696168 | + | 0.717879i | \(0.745113\pi\) | |||||||
\(642\) | 22.1823 | + | 4.71500i | 0.875466 | + | 0.186086i | ||||
\(643\) | 11.0420 | + | 33.9837i | 0.435453 | + | 1.34019i | 0.892622 | + | 0.450806i | \(0.148863\pi\) |
−0.457169 | + | 0.889380i | \(0.651137\pi\) | |||||||
\(644\) | 8.37843 | − | 1.78089i | 0.330156 | − | 0.0701769i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.938929 | − | 1.62627i | 0.0369417 | − | 0.0639849i | ||||
\(647\) | 1.45217 | − | 4.46933i | 0.0570909 | − | 0.175708i | −0.918445 | − | 0.395550i | \(-0.870554\pi\) |
0.975536 | + | 0.219842i | \(0.0705542\pi\) | |||||||
\(648\) | 6.61533 | − | 62.9407i | 0.259875 | − | 2.47254i | ||||
\(649\) | −19.5853 | + | 14.2295i | −0.768790 | + | 0.558558i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.35622 | + | 7.91190i | −0.170734 | + | 0.310092i | ||||
\(652\) | −57.6734 | −2.25866 | ||||||||
\(653\) | 35.7838 | − | 25.9985i | 1.40033 | − | 1.01740i | 0.405689 | − | 0.914011i | \(-0.367032\pi\) |
0.994641 | − | 0.103388i | \(-0.0329683\pi\) | |||||||
\(654\) | −0.303627 | + | 2.88882i | −0.0118728 | + | 0.112962i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −34.7657 | + | 60.2159i | −1.35737 | + | 2.35104i | ||||
\(657\) | 4.00407 | + | 6.93524i | 0.156213 | + | 0.270570i | ||||
\(658\) | −17.1371 | + | 3.64261i | −0.668075 | + | 0.142004i | ||||
\(659\) | −4.42186 | − | 13.6091i | −0.172251 | − | 0.530135i | 0.827246 | − | 0.561840i | \(-0.189906\pi\) |
−0.999497 | + | 0.0317052i | \(0.989906\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.03732 | + | 19.3838i | 0.0792424 | + | 0.753941i | 0.959929 | + | 0.280242i | \(0.0904148\pi\) |
−0.880687 | + | 0.473699i | \(0.842919\pi\) | |||||||
\(662\) | −15.0591 | − | 16.7248i | −0.585288 | − | 0.650028i | ||||
\(663\) | 14.4581 | + | 6.43718i | 0.561507 | + | 0.249999i | ||||
\(664\) | −70.7263 | + | 31.4894i | −2.74471 | + | 1.22202i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 17.7917 | + | 12.9264i | 0.689415 | + | 0.500889i | ||||
\(667\) | 1.51167 | + | 1.09829i | 0.0585321 | + | 0.0425260i | ||||
\(668\) | −18.4634 | + | 20.5057i | −0.714371 | + | 0.793390i | ||||
\(669\) | 31.2288 | − | 13.9039i | 1.20737 | − | 0.537557i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.7096 | + | 14.1155i | 0.490650 | + | 0.544923i | ||||
\(672\) | 0.637221 | + | 6.06275i | 0.0245813 | + | 0.233876i | ||||
\(673\) | −10.2436 | − | 2.17735i | −0.394863 | − | 0.0839307i | 0.00620110 | − | 0.999981i | \(-0.498026\pi\) |
−0.401064 | + | 0.916050i | \(0.631359\pi\) | |||||||
\(674\) | −18.1358 | − | 55.8162i | −0.698564 | − | 2.14996i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −57.8626 | − | 100.221i | −2.22548 | − | 3.85465i | ||||
\(677\) | −14.1405 | + | 24.4920i | −0.543462 | + | 0.941304i | 0.455240 | + | 0.890369i | \(0.349554\pi\) |
−0.998702 | + | 0.0509354i | \(0.983780\pi\) | |||||||
\(678\) | −14.5987 | + | 44.9302i | −0.560660 | + | 1.72553i | ||||
\(679\) | −0.473190 | + | 4.50210i | −0.0181594 | + | 0.172775i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 43.4006 | 1.66312 | ||||||||
\(682\) | 43.5165 | + | 46.4000i | 1.66633 | + | 1.77675i | ||||
\(683\) | −2.92111 | −0.111773 | −0.0558866 | − | 0.998437i | \(-0.517799\pi\) | ||||
−0.0558866 | + | 0.998437i | \(0.517799\pi\) | |||||||
\(684\) | −1.56613 | + | 1.13786i | −0.0598826 | + | 0.0435072i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.64592 | + | 26.6094i | −0.330103 | + | 1.01595i | ||||
\(687\) | 0.142042 | − | 0.246023i | 0.00541923 | − | 0.00938638i | ||||
\(688\) | 34.5211 | + | 59.7924i | 1.31611 | + | 2.27956i | ||||
\(689\) | −32.8768 | + | 6.98817i | −1.25250 | + | 0.266228i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.1035 | + | 4.69823i | 0.840855 | + | 0.178729i | 0.608154 | − | 0.793819i | \(-0.291910\pi\) |
0.232701 | + | 0.972548i | \(0.425244\pi\) | |||||||
\(692\) | 1.14473 | + | 10.8913i | 0.0435160 | + | 0.414027i | ||||
\(693\) | −1.96063 | − | 2.17750i | −0.0744782 | − | 0.0827164i | ||||
\(694\) | 44.3268 | + | 19.7356i | 1.68262 | + | 0.749152i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.07050 | + | 6.74198i | −0.230102 | + | 0.255554i | ||||
\(697\) | 11.7798 | + | 8.55852i | 0.446191 | + | 0.324177i | ||||
\(698\) | −66.4723 | − | 48.2949i | −2.51601 | − | 1.82799i | ||||
\(699\) | 11.2948 | − | 12.5441i | 0.427207 | − | 0.474461i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.8525 | − | 11.5103i | −0.976436 | − | 0.434737i | −0.144437 | − | 0.989514i | \(-0.546137\pi\) |
−0.831999 | + | 0.554777i | \(0.812804\pi\) | |||||||
\(702\) | 45.8940 | + | 50.9704i | 1.73216 | + | 1.92376i | ||||
\(703\) | 0.679898 | + | 6.46880i | 0.0256428 | + | 0.243975i | ||||
\(704\) | −12.8375 | − | 2.72871i | −0.483833 | − | 0.102842i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31.3471 | + | 6.66303i | −1.17976 | + | 0.250766i | ||||
\(707\) | −0.953773 | − | 1.65198i | −0.0358703 | − | 0.0621292i | ||||
\(708\) | −22.5141 | + | 38.9955i | −0.846131 | + | 1.46554i | ||||
\(709\) | −4.96572 | + | 15.2829i | −0.186492 | + | 0.573962i | −0.999971 | − | 0.00763191i | \(-0.997571\pi\) |
0.813479 | + | 0.581594i | \(0.197571\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.800780 | + | 0.581801i | −0.0300316 | + | 0.0218192i | ||||
\(712\) | 21.8261 | 0.817969 | ||||||||
\(713\) | 3.80837 | − | 12.5847i | 0.142625 | − | 0.471303i | ||||
\(714\) | 5.28675 | 0.197851 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.42636 | − | 51.6283i | 0.202792 | − | 1.92944i | ||||
\(717\) | 6.28024 | − | 19.3286i | 0.234540 | − | 0.721840i | ||||
\(718\) | 8.07470 | − | 13.9858i | 0.301345 | − | 0.521945i | ||||
\(719\) | −14.2609 | − | 24.7007i | −0.531843 | − | 0.921179i | −0.999309 | − | 0.0371679i | \(-0.988166\pi\) |
0.467466 | − | 0.884011i | \(-0.345167\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.69053 | + | 5.20291i | 0.0629585 | + | 0.193766i | ||||
\(722\) | 45.9904 | + | 9.77556i | 1.71159 | + | 0.363809i | ||||
\(723\) | 1.10474 | + | 10.5109i | 0.0410857 | + | 0.390904i | ||||
\(724\) | 40.9650 | + | 45.4962i | 1.52245 | + | 1.69085i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −42.8098 | + | 19.0602i | −1.58882 | + | 0.707389i | ||||
\(727\) | −3.67677 | + | 4.08346i | −0.136364 | + | 0.151447i | −0.807459 | − | 0.589924i | \(-0.799158\pi\) |
0.671095 | + | 0.741371i | \(0.265824\pi\) | |||||||
\(728\) | −25.1074 | − | 18.2416i | −0.930540 | − | 0.676077i | ||||
\(729\) | −13.6817 | − | 9.94036i | −0.506731 | − | 0.368162i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.2082 | − | 5.88068i | 0.488524 | − | 0.217505i | ||||
\(732\) | 32.2749 | + | 14.3697i | 1.19291 | + | 0.531119i | ||||
\(733\) | −27.4651 | − | 30.5031i | −1.01445 | − | 1.12666i | −0.991914 | − | 0.126911i | \(-0.959494\pi\) |
−0.0225327 | − | 0.999746i | \(-0.507173\pi\) | |||||||
\(734\) | 5.76407 | + | 54.8415i | 0.212756 | + | 2.02424i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.74241 | − | 8.44026i | −0.101086 | − | 0.311112i | ||||
\(737\) | −31.2588 | + | 6.64426i | −1.15143 | + | 0.244745i | ||||
\(738\) | −10.9609 | − | 18.9848i | −0.403476 | − | 0.698842i | ||||
\(739\) | 6.42893 | − | 11.1352i | 0.236492 | − | 0.409616i | −0.723213 | − | 0.690625i | \(-0.757336\pi\) |
0.959705 | + | 0.281009i | \(0.0906689\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.736652 | − | 7.00878i | 0.0270616 | − | 0.257474i | ||||
\(742\) | −9.08340 | + | 6.59948i | −0.333462 | + | 0.242274i | ||||
\(743\) | −5.08104 | −0.186405 | −0.0932026 | − | 0.995647i | \(-0.529710\pi\) | ||||
−0.0932026 | + | 0.995647i | \(0.529710\pi\) | |||||||
\(744\) | 58.8350 | + | 24.7764i | 2.15700 | + | 0.908346i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.42959 | − | 6.85100i | 0.345242 | − | 0.250833i | ||||
\(747\) | 1.06050 | − | 10.0899i | 0.0388015 | − | 0.369172i | ||||
\(748\) | 7.87865 | − | 24.2480i | 0.288072 | − | 0.886595i | ||||
\(749\) | −1.93536 | + | 3.35213i | −0.0707164 | + | 0.122484i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.81891 | − | 1.44940i | 0.248825 | − | 0.0528895i | −0.0818103 | − | 0.996648i | \(-0.526070\pi\) |
0.330636 | + | 0.943758i | \(0.392737\pi\) | |||||||
\(752\) | 15.9057 | + | 48.9527i | 0.580021 | + | 1.78512i | ||||
\(753\) | −21.9629 | − | 4.66836i | −0.800373 | − | 0.170125i | ||||
\(754\) | −1.31157 | − | 12.4788i | −0.0477646 | − | 0.454450i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 14.3315 | + | 6.38081i | 0.521233 | + | 0.232068i | ||||
\(757\) | 13.3881 | − | 5.96076i | 0.486598 | − | 0.216648i | −0.148748 | − | 0.988875i | \(-0.547524\pi\) |
0.635346 | + | 0.772228i | \(0.280858\pi\) | |||||||
\(758\) | −24.3525 | + | 27.0461i | −0.884521 | + | 0.982360i | ||||
\(759\) | 16.8354 | + | 12.2316i | 0.611085 | + | 0.443979i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0905 | − | 23.4234i | 0.764530 | − | 0.849097i | −0.227672 | − | 0.973738i | \(-0.573111\pi\) |
0.992202 | + | 0.124641i | \(0.0397779\pi\) | |||||||
\(762\) | 54.8589 | − | 24.4248i | 1.98733 | − | 0.884816i | ||||
\(763\) | −0.452923 | − | 0.201654i | −0.0163969 | − | 0.00730038i | ||||
\(764\) | 0.817880 | + | 0.908348i | 0.0295899 | + | 0.0328629i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 50.2619 | + | 10.6835i | 1.81604 | + | 0.386011i | ||||
\(767\) | −10.3833 | − | 31.9566i | −0.374921 | − | 1.15389i | ||||
\(768\) | −59.8469 | + | 12.7209i | −2.15954 | + | 0.459024i | ||||
\(769\) | −21.8896 | − | 37.9139i | −0.789358 | − | 1.36721i | −0.926361 | − | 0.376638i | \(-0.877080\pi\) |
0.137002 | − | 0.990571i | \(-0.456253\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.3885 | − | 35.0503i | 0.410148 | − | 1.26231i | ||||
\(772\) | 10.9826 | − | 104.492i | 0.395273 | − | 3.76077i | ||||
\(773\) | 19.6555 | − | 14.2806i | 0.706960 | − | 0.513637i | −0.175231 | − | 0.984527i | \(-0.556067\pi\) |
0.882192 | + | 0.470891i | \(0.156067\pi\) | |||||||
\(774\) | −21.7676 | −0.782421 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 31.9970 | 1.14862 | ||||||||
\(777\) | −14.8147 | + | 10.7635i | −0.531474 | + | 0.386138i | ||||
\(778\) | −1.64455 | + | 15.6469i | −0.0589600 | + | 0.560967i | ||||
\(779\) | 2.00359 | − | 6.16640i | 0.0717859 | − | 0.220934i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.83869 | − | 11.8450i | −0.244708 | − | 0.423846i | ||||
\(782\) | −7.52812 | + | 1.60015i | −0.269205 | + | 0.0572213i | ||||
\(783\) | 1.05751 | + | 3.25469i | 0.0377925 | + | 0.116313i | ||||
\(784\) | 38.0938 | + | 8.09709i | 1.36049 | + | 0.289182i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −54.3871 | − | 60.4030i | −1.93992 | − | 2.15450i | ||||
\(787\) | −13.2640 | − | 5.90552i | −0.472811 | − | 0.210509i | 0.156476 | − | 0.987682i | \(-0.449986\pi\) |
−0.629287 | + | 0.777173i | \(0.716653\pi\) | |||||||
\(788\) | 50.5544 | − | 22.5083i | 1.80093 | − | 0.801824i | ||||
\(789\) | 6.77825 | − | 7.52801i | 0.241312 | − | 0.268004i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.52346 | − | 4.73957i | −0.231947 | − | 0.168520i | ||||
\(792\) | −13.8581 | + | 15.3910i | −0.492426 | + | 0.546895i | ||||
\(793\) | −24.0844 | + | 10.7230i | −0.855261 | + | 0.380787i | ||||
\(794\) | 72.6873 | + | 32.3625i | 2.57957 | + | 1.14850i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.90555 | − | 46.6732i | −0.173873 | − | 1.65429i | ||||
\(797\) | −21.3661 | − | 4.54149i | −0.756824 | − | 0.160868i | −0.186689 | − | 0.982419i | \(-0.559776\pi\) |
−0.570135 | + | 0.821551i | \(0.693109\pi\) | |||||||
\(798\) | −0.727472 | − | 2.23893i | −0.0257522 | − | 0.0792572i | ||||
\(799\) | 10.5432 | − | 2.24103i | 0.372993 | − | 0.0792821i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.43011 | + | 2.47703i | −0.0505306 | + | 0.0875215i | ||||
\(802\) | 1.61236 | − | 4.96233i | 0.0569344 | − | 0.175226i | ||||
\(803\) | −4.90919 | + | 46.7078i | −0.173242 | + | 1.64828i | ||||
\(804\) | −48.0881 | + | 34.9380i | −1.69594 | + | 1.23217i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −79.9147 | + | 37.5424i | −2.81488 | + | 1.32238i | ||||
\(807\) | −2.23349 | −0.0786224 | ||||||||
\(808\) | −10.9079 | + | 7.92505i | −0.383739 | + | 0.278802i | ||||
\(809\) | −2.04937 | + | 19.4984i | −0.0720520 | + | 0.685529i | 0.897562 | + | 0.440888i | \(0.145337\pi\) |
−0.969614 | + | 0.244640i | \(0.921330\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.447413 | + | 0.774942i | −0.0157108 | + | 0.0272119i | −0.873774 | − | 0.486332i | \(-0.838334\pi\) |
0.858063 | + | 0.513544i | \(0.171668\pi\) | |||||||
\(812\) | −1.43498 | − | 2.48546i | −0.0503579 | − | 0.0872224i | ||||
\(813\) | 23.8944 | − | 5.07891i | 0.838013 | − | 0.178125i | ||||
\(814\) | 39.8554 | + | 122.662i | 1.39693 | + | 4.29931i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.62353 | − | 15.4468i | −0.0568348 | − | 0.540747i | ||||
\(817\) | −4.30795 | − | 4.78447i | −0.150716 | − | 0.167387i | ||||
\(818\) | 55.0186 | + | 24.4959i | 1.92368 | + | 0.856477i | ||||
\(819\) | 3.71533 | − | 1.65417i | 0.129824 | − | 0.0578014i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.2838 | + | 22.0025i | 1.05691 | + | 0.767892i | 0.973515 | − | 0.228624i | \(-0.0734228\pi\) |
0.0833978 | + | 0.996516i | \(0.473423\pi\) | |||||||
\(822\) | −11.5963 | − | 8.42522i | −0.404468 | − | 0.293863i | ||||
\(823\) | 20.4074 | − | 22.6647i | 0.711356 | − | 0.790041i | −0.273784 | − | 0.961791i | \(-0.588275\pi\) |
0.985141 | + | 0.171750i | \(0.0549421\pi\) | |||||||
\(824\) | 35.3247 | − | 15.7276i | 1.23059 | − | 0.547896i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.51055 | − | 8.34131i | −0.261325 | − | 0.290231i | ||||
\(827\) | 2.77030 | + | 26.3577i | 0.0963329 | + | 0.916546i | 0.930810 | + | 0.365504i | \(0.119103\pi\) |
−0.834477 | + | 0.551043i | \(0.814230\pi\) | |||||||
\(828\) | 7.76059 | + | 1.64956i | 0.269699 | + | 0.0573263i | ||||
\(829\) | −11.3256 | − | 34.8565i | −0.393354 | − | 1.21062i | −0.930236 | − | 0.366961i | \(-0.880398\pi\) |
0.536883 | − | 0.843657i | \(-0.319602\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.1903 | + | 36.7027i | 0.735084 | + | 1.27320i | ||||
\(832\) | 9.10815 | − | 15.7758i | 0.315768 | − | 0.546927i | ||||
\(833\) | 2.52018 | − | 7.75632i | 0.0873191 | − | 0.268740i | ||||
\(834\) | 10.9628 | − | 104.304i | 0.379611 | − | 3.61176i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −11.3531 | −0.392656 | ||||||||
\(837\) | 19.1907 | − | 14.5471i | 0.663326 | − | 0.502822i | ||||
\(838\) | −76.9815 | −2.65928 | ||||||||
\(839\) | −1.83042 | + | 1.32988i | −0.0631933 | + | 0.0459126i | −0.618933 | − | 0.785443i | \(-0.712435\pi\) |
0.555740 | + | 0.831356i | \(0.312435\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.76803 | + | 26.9852i | −0.302346 | + | 0.930525i | ||||
\(842\) | −28.2728 | + | 48.9699i | −0.974345 | + | 1.68762i | ||||
\(843\) | −30.2244 | − | 52.3503i | −1.04098 | − | 1.80304i | ||||
\(844\) | 18.6860 | − | 3.97183i | 0.643198 | − | 0.136716i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −15.8734 | − | 3.37400i | −0.545739 | − | 0.116001i | ||||
\(847\) | −0.836057 | − | 7.95455i | −0.0287273 | − | 0.273322i | ||||
\(848\) | 22.0718 | + | 24.5132i | 0.757949 | + | 0.841788i | ||||
\(849\) | 32.1733 | + | 14.3245i | 1.10419 | + | 0.491615i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.8377 | − | 19.8108i | 0.611469 | − | 0.679106i | ||||
\(852\) | −20.5813 | − | 14.9532i | −0.705103 | − | 0.512287i | ||||
\(853\) | −5.35391 | − | 3.88984i | −0.183314 | − | 0.133186i | 0.492344 | − | 0.870401i | \(-0.336140\pi\) |
−0.675658 | + | 0.737215i | \(0.736140\pi\) | |||||||
\(854\) | −5.89281 | + | 6.54462i | −0.201648 | + | 0.223952i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 24.9936 | + | 11.1279i | 0.854265 | + | 0.380343i | ||||
\(857\) | 25.2061 | + | 27.9942i | 0.861023 | + | 0.956263i | 0.999418 | − | 0.0341142i | \(-0.0108610\pi\) |
−0.138395 | + | 0.990377i | \(0.544194\pi\) | |||||||
\(858\) | −14.6069 | − | 138.975i | −0.498671 | − | 4.74454i | ||||
\(859\) | −16.0689 | − | 3.41555i | −0.548264 | − | 0.116537i | −0.0745524 | − | 0.997217i | \(-0.523753\pi\) |
−0.473712 | + | 0.880680i | \(0.657086\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.8548 | − | 3.79516i | 0.608491 | − | 0.129339i | ||||
\(862\) | 20.7521 | + | 35.9437i | 0.706820 | + | 1.22425i | ||||
\(863\) | 12.8552 | − | 22.2659i | 0.437598 | − | 0.757941i | −0.559906 | − | 0.828556i | \(-0.689163\pi\) |
0.997504 | + | 0.0706147i | \(0.0224961\pi\) | |||||||
\(864\) | 5.02269 | − | 15.4582i | 0.170875 | − | 0.525900i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 61.8156 | − | 44.9117i | 2.10058 | − | 1.52616i | ||||
\(867\) | 29.7708 | 1.01107 | ||||||||
\(868\) | −13.2058 | + | 15.2792i | −0.448233 | + | 0.518610i | ||||
\(869\) | −5.80497 | −0.196920 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.63644 | − | 44.1128i | 0.157100 | − | 1.49471i | ||||
\(872\) | −1.08289 | + | 3.33280i | −0.0366714 | + | 0.112863i | ||||
\(873\) | −2.09654 | + | 3.63131i | −0.0709571 | + | 0.122901i | ||||
\(874\) | 1.71355 | + | 2.96796i | 0.0579618 | + | 0.100393i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 26.9942 | + | 83.0795i | 0.912048 | + | 2.80699i | ||||
\(877\) | −17.1239 | − | 3.63980i | −0.578234 | − | 0.122907i | −0.0904951 | − | 0.995897i | \(-0.528845\pi\) |
−0.487739 | + | 0.872989i | \(0.662178\pi\) | |||||||
\(878\) | 4.34498 | + | 41.3397i | 0.146636 | + | 1.39515i | ||||
\(879\) | −15.2160 | − | 16.8991i | −0.513223 | − | 0.569992i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.66292 | + | 3.85698i | −0.291861 | + | 0.129945i | −0.547444 | − | 0.836842i | \(-0.684399\pi\) |
0.255583 | + | 0.966787i | \(0.417733\pi\) | |||||||
\(882\) | −8.21593 | + | 9.12471i | −0.276645 | + | 0.307245i | ||||
\(883\) | 17.9126 | + | 13.0142i | 0.602806 | + | 0.437964i | 0.846874 | − | 0.531794i | \(-0.178482\pi\) |
−0.244068 | + | 0.969758i | \(0.578482\pi\) | |||||||
\(884\) | 28.6292 | + | 20.8004i | 0.962905 | + | 0.699592i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 58.0865 | − | 25.8618i | 1.95145 | − | 0.868843i | ||||
\(887\) | 29.2198 | + | 13.0095i | 0.981104 | + | 0.436816i | 0.833674 | − | 0.552257i | \(-0.186233\pi\) |
0.147430 | + | 0.989072i | \(0.452900\pi\) | |||||||
\(888\) | 86.6072 | + | 96.1871i | 2.90635 | + | 3.22783i | ||||
\(889\) | 1.07137 | + | 10.1934i | 0.0359326 | + | 0.341876i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.0303 | + | 46.2585i | 0.503534 | + | 1.54972i | ||||
\(892\) | 74.7651 | − | 15.8918i | 2.50332 | − | 0.532097i | ||||
\(893\) | −2.39986 | − | 4.15667i | −0.0803081 | − | 0.139098i | ||||
\(894\) | −19.3241 | + | 33.4703i | −0.646294 | + | 1.11941i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.29213 | − | 12.2938i | 0.0431671 | − | 0.410707i | ||||
\(897\) | −23.3671 | + | 16.9772i | −0.780205 | + | 0.566852i | ||||
\(898\) | 6.57462 | 0.219398 | ||||||||
\(899\) | −4.40453 | + | 0.0894351i | −0.146899 | + | 0.00298283i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.58836 | − | 4.06018i | 0.186175 | − | 0.135264i | ||||
\(902\) | 13.4386 | − | 127.860i | 0.447458 | − | 4.25728i | ||||
\(903\) | 5.60103 | − | 17.2382i | 0.186391 | − | 0.573651i | ||||
\(904\) | −28.4970 | + | 49.3582i | −0.947795 | + | 1.64163i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.6246 | + | 2.25833i | −0.352979 | + | 0.0750280i | ||||
\(907\) | 10.3373 | + | 31.8148i | 0.343243 | + | 1.05639i | 0.962518 | + | 0.271219i | \(0.0874266\pi\) |
−0.619275 | + | 0.785174i | \(0.712573\pi\) | |||||||
\(908\) | 94.9228 | + | 20.1765i | 3.15012 | + | 0.669579i | ||||
\(909\) | −0.184689 | − | 1.75720i | −0.00612576 | − | 0.0582827i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.9176 | − | 18.2177i | −1.35566 | − | 0.603579i | −0.405144 | − | 0.914253i | \(-0.632779\pi\) |
−0.950517 | + | 0.310673i | \(0.899445\pi\) | |||||||
\(912\) | −6.31830 | + | 2.81309i | −0.209220 | + | 0.0931507i | ||||
\(913\) | 39.8134 | − | 44.2173i | 1.31763 | − | 1.46338i | ||||
\(914\) | −19.0765 | − | 13.8599i | −0.630993 | − | 0.458443i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.425037 | − | 0.472051i | 0.0140436 | − | 0.0155970i | ||||
\(917\) | 12.6737 | − | 5.64270i | 0.418523 | − | 0.186338i | ||||
\(918\) | −12.8771 | − | 5.73324i | −0.425007 | − | 0.189225i | ||||
\(919\) | −19.0879 | − | 21.1993i | −0.629652 | − | 0.699300i | 0.340925 | − | 0.940091i | \(-0.389260\pi\) |
−0.970577 | + | 0.240791i | \(0.922593\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.3139 | + | 4.74297i | 0.735268 | + | 0.156286i | ||||
\(922\) | −13.7244 | − | 42.2393i | −0.451988 | − | 1.39108i | ||||
\(923\) | 18.5690 | − | 3.94697i | 0.611208 | − | 0.129916i | ||||
\(924\) | −15.9813 | − | 27.6803i | −0.525745 | − | 0.910616i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.52410 | + | 13.9237i | −0.148671 | + | 0.457563i | ||||
\(927\) | −0.529671 | + | 5.03949i | −0.0173967 | + | 0.165518i | ||||
\(928\) | −2.40560 | + | 1.74777i | −0.0789678 | + | 0.0573735i | ||||
\(929\) | −47.0642 | −1.54413 | −0.772064 | − | 0.635545i | \(-0.780775\pi\) | ||||
−0.772064 | + | 0.635545i | \(0.780775\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.63157 | −0.119020 | ||||||||
\(932\) | 30.5347 | − | 22.1847i | 1.00020 | − | 0.726685i | ||||
\(933\) | −0.169187 | + | 1.60970i | −0.00553893 | + | 0.0526994i | ||||
\(934\) | −6.29584 | + | 19.3766i | −0.206006 | + | 0.634022i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −14.3729 | − | 24.8946i | −0.469794 | − | 0.813707i | ||||
\(937\) | −30.1300 | + | 6.40434i | −0.984306 | + | 0.209221i | −0.671830 | − | 0.740705i | \(-0.734492\pi\) |
−0.312476 | + | 0.949926i | \(0.601158\pi\) | |||||||
\(938\) | −4.57867 | − | 14.0917i | −0.149499 | − | 0.460110i | ||||
\(939\) | −20.1330 | − | 4.27940i | −0.657015 | − | 0.139653i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.90260 | + | 2.11305i | 0.0620230 | + | 0.0688835i | 0.773358 | − | 0.633970i | \(-0.218576\pi\) |
−0.711335 | + | 0.702853i | \(0.751909\pi\) | |||||||
\(942\) | 23.3732 | + | 10.4064i | 0.761541 | + | 0.339060i | ||||
\(943\) | −24.2759 | + | 10.8083i | −0.790531 | + | 0.351967i | ||||
\(944\) | −22.0652 | + | 24.5059i | −0.718161 | + | 0.797599i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −103.279 | − | 75.0367i | −3.35790 | − | 2.43965i | ||||
\(947\) | −6.97644 | + | 7.74812i | −0.226704 | + | 0.251780i | −0.845756 | − | 0.533570i | \(-0.820850\pi\) |
0.619052 | + | 0.785350i | \(0.287517\pi\) | |||||||
\(948\) | −9.86375 | + | 4.39162i | −0.320360 | + | 0.142633i | ||||
\(949\) | −59.5509 | − | 26.5138i | −1.93310 | − | 0.860673i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.31623 | − | 60.0949i | −0.204818 | − | 1.94871i | ||||
\(952\) | 6.23863 | + | 1.32606i | 0.202195 | + | 0.0429779i | ||||
\(953\) | 14.6425 | + | 45.0649i | 0.474316 | + | 1.45979i | 0.846878 | + | 0.531788i | \(0.178479\pi\) |
−0.372562 | + | 0.928007i | \(0.621521\pi\) | |||||||
\(954\) | −10.1725 | + | 2.16223i | −0.329347 | + | 0.0700048i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 22.7213 | − | 39.3545i | 0.734861 | − | 1.27282i | ||||
\(957\) | 2.15459 | − | 6.63114i | 0.0696479 | − | 0.214354i | ||||
\(958\) | −2.39714 | + | 22.8072i | −0.0774480 | + | 0.736868i | ||||
\(959\) | 1.97929 | − | 1.43804i | 0.0639145 | − | 0.0464366i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.7684 | + | 29.0696i | 0.347369 | + | 0.937728i | ||||
\(962\) | −179.014 | −5.77164 | ||||||||
\(963\) | −2.90055 | + | 2.10737i | −0.0934690 | + | 0.0679092i | ||||
\(964\) | −2.47018 | + | 23.5022i | −0.0795593 | + | 0.756956i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.82418 | + | 8.35572i | −0.155215 | + | 0.268841i | ||||
\(967\) | −11.3526 | − | 19.6633i | −0.365075 | − | 0.632329i | 0.623713 | − | 0.781653i | \(-0.285623\pi\) |
−0.988788 | + | 0.149325i | \(0.952290\pi\) | |||||||
\(968\) | −55.2986 | + | 11.7541i | −1.77736 | + | 0.377790i | ||||
\(969\) | 0.447561 | + | 1.37745i | 0.0143777 | + | 0.0442501i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.75452 | + | 54.7506i | 0.184671 | + | 1.75703i | 0.558475 | + | 0.829522i | \(0.311387\pi\) |
−0.373803 | + | 0.927508i | \(0.621947\pi\) | |||||||
\(972\) | 22.8241 | + | 25.3487i | 0.732083 | + | 0.813060i | ||||
\(973\) | 16.3533 | + | 7.28096i | 0.524263 | + | 0.233417i | ||||
\(974\) | −94.6747 | + | 42.1519i | −3.03357 | + | 1.35063i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.9317 | + | 15.2078i | 0.670008 | + | 0.486790i | ||||
\(977\) | 11.0724 | + | 8.04457i | 0.354238 | + | 0.257369i | 0.750645 | − | 0.660706i | \(-0.229743\pi\) |
−0.396407 | + | 0.918075i | \(0.629743\pi\) | |||||||
\(978\) | 43.4692 | − | 48.2774i | 1.38999 | − | 1.54374i | ||||
\(979\) | −15.3241 | + | 6.82273i | −0.489761 | + | 0.218055i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.307282 | − | 0.341272i | −0.00981077 | − | 0.0108960i | ||||
\(982\) | −4.98178 | − | 47.3985i | −0.158975 | − | 1.51255i | ||||
\(983\) | 40.3260 | + | 8.57156i | 1.28620 | + | 0.273390i | 0.799758 | − | 0.600322i | \(-0.204961\pi\) |
0.486443 | + | 0.873713i | \(0.338294\pi\) | |||||||
\(984\) | −39.8696 | − | 122.706i | −1.27100 | − | 3.91172i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.28935 | + | 2.23321i | 0.0410611 | + | 0.0711200i | ||||
\(987\) | 6.75633 | − | 11.7023i | 0.215056 | − | 0.372488i | ||||
\(988\) | 4.86945 | − | 14.9866i | 0.154918 | − | 0.476788i | ||||
\(989\) | −2.75812 | + | 26.2418i | −0.0877032 | + | 0.834441i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.9979 | −1.11174 | −0.555872 | − | 0.831268i | \(-0.687616\pi\) | ||||
−0.555872 | + | 0.831268i | \(0.687616\pi\) | |||||||
\(992\) | 17.1738 | + | 11.9525i | 0.545270 | + | 0.379492i | ||||
\(993\) | 17.3578 | 0.550833 | ||||||||
\(994\) | 5.13038 | − | 3.72744i | 0.162726 | − | 0.118227i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 34.1990 | − | 105.254i | 1.08364 | − | 3.33509i | ||||
\(997\) | −1.03226 | + | 1.78793i | −0.0326920 | + | 0.0566242i | −0.881908 | − | 0.471421i | \(-0.843741\pi\) |
0.849216 | + | 0.528045i | \(0.177075\pi\) | |||||||
\(998\) | −10.0216 | − | 17.3580i | −0.317230 | − | 0.549458i | ||||
\(999\) | 47.7571 | − | 10.1511i | 1.51097 | − | 0.321166i |
(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 | 775.2.bl.b.276.1 | 40 | ||
5.2 | odd | 4 | 775.2.ck.b.524.1 | 80 | |||
5.3 | odd | 4 | 775.2.ck.b.524.10 | 80 | |||
5.4 | even | 2 | 155.2.q.b.121.5 | yes | 40 | ||
31.10 | even | 15 | inner | 775.2.bl.b.351.1 | 40 | ||
155.14 | even | 30 | 4805.2.a.ba.1.2 | 20 | |||
155.72 | odd | 60 | 775.2.ck.b.599.10 | 80 | |||
155.79 | odd | 30 | 4805.2.a.z.1.2 | 20 | |||
155.103 | odd | 60 | 775.2.ck.b.599.1 | 80 | |||
155.134 | even | 30 | 155.2.q.b.41.5 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
155.2.q.b.41.5 | ✓ | 40 | 155.134 | even | 30 | ||
155.2.q.b.121.5 | yes | 40 | 5.4 | even | 2 | ||
775.2.bl.b.276.1 | 40 | 1.1 | even | 1 | trivial | ||
775.2.bl.b.351.1 | 40 | 31.10 | even | 15 | inner | ||
775.2.ck.b.524.1 | 80 | 5.2 | odd | 4 | |||
775.2.ck.b.524.10 | 80 | 5.3 | odd | 4 | |||
775.2.ck.b.599.1 | 80 | 155.103 | odd | 60 | |||
775.2.ck.b.599.10 | 80 | 155.72 | odd | 60 | |||
4805.2.a.z.1.2 | 20 | 155.79 | odd | 30 | |||
4805.2.a.ba.1.2 | 20 | 155.14 | even | 30 |