Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(126,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("625.126");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.d (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.99065012633\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 501.2 | ||
Root | \(1.20005i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 625.501 |
Dual form | 625.2.d.p.126.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.718805 | + | 2.21225i | −0.508272 | + | 1.56430i | 0.286928 | + | 0.957952i | \(0.407366\pi\) |
−0.795200 | + | 0.606348i | \(0.792634\pi\) | |||||||
\(3\) | −1.86261 | − | 1.35327i | −1.07538 | − | 0.781309i | −0.0985075 | − | 0.995136i | \(-0.531407\pi\) |
−0.976871 | + | 0.213828i | \(0.931407\pi\) | |||||||
\(4\) | −2.75935 | − | 2.00479i | −1.37968 | − | 1.00239i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.33262 | − | 3.14783i | 1.76879 | − | 1.28510i | ||||
\(7\) | −3.59425 | −1.35850 | −0.679249 | − | 0.733908i | \(-0.737694\pi\) | ||||
−0.679249 | + | 0.733908i | \(0.737694\pi\) | |||||||
\(8\) | 2.65482 | − | 1.92884i | 0.938622 | − | 0.681949i | ||||
\(9\) | 0.710939 | + | 2.18805i | 0.236980 | + | 0.729349i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.153825 | + | 0.473424i | −0.0463799 | + | 0.142743i | −0.971565 | − | 0.236774i | \(-0.923910\pi\) |
0.925185 | + | 0.379517i | \(0.123910\pi\) | |||||||
\(12\) | 2.42659 | + | 7.46828i | 0.700496 | + | 2.15591i | ||||
\(13\) | −0.818243 | − | 2.51829i | −0.226940 | − | 0.698449i | −0.998089 | − | 0.0617942i | \(-0.980318\pi\) |
0.771149 | − | 0.636655i | \(-0.219682\pi\) | |||||||
\(14\) | 2.58356 | − | 7.95139i | 0.690486 | − | 2.12510i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.250832 | + | 0.771980i | 0.0627079 | + | 0.192995i | ||||
\(17\) | 4.13180 | − | 3.00193i | 1.00211 | − | 0.728075i | 0.0395697 | − | 0.999217i | \(-0.487401\pi\) |
0.962539 | + | 0.271142i | \(0.0874013\pi\) | |||||||
\(18\) | −5.35154 | −1.26137 | ||||||||
\(19\) | 0.798724 | − | 0.580307i | 0.183240 | − | 0.133132i | −0.492384 | − | 0.870378i | \(-0.663874\pi\) |
0.675624 | + | 0.737247i | \(0.263874\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.69468 | + | 4.86397i | 1.46090 | + | 1.06141i | ||||
\(22\) | −0.936765 | − | 0.680599i | −0.199719 | − | 0.145104i | ||||
\(23\) | −1.98198 | + | 6.09991i | −0.413271 | + | 1.27192i | 0.500517 | + | 0.865727i | \(0.333143\pi\) |
−0.913788 | + | 0.406192i | \(0.866857\pi\) | |||||||
\(24\) | −7.55514 | −1.54219 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.15926 | 1.20793 | ||||||||
\(27\) | −0.497557 | + | 1.53132i | −0.0957548 | + | 0.294703i | ||||
\(28\) | 9.91780 | + | 7.20570i | 1.87429 | + | 1.36175i | ||||
\(29\) | 4.50623 | + | 3.27397i | 0.836786 | + | 0.607961i | 0.921471 | − | 0.388447i | \(-0.126988\pi\) |
−0.0846848 | + | 0.996408i | \(0.526988\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.89866 | + | 3.55908i | −0.879825 | + | 0.639230i | −0.933205 | − | 0.359344i | \(-0.883000\pi\) |
0.0533803 | + | 0.998574i | \(0.483000\pi\) | |||||||
\(32\) | 4.67497 | 0.826426 | ||||||||
\(33\) | 0.927185 | − | 0.673639i | 0.161402 | − | 0.117266i | ||||
\(34\) | 3.67107 | + | 11.2984i | 0.629584 | + | 1.93766i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.42484 | − | 7.46288i | 0.404139 | − | 1.24381i | ||||
\(37\) | 1.42028 | + | 4.37117i | 0.233493 | + | 0.718616i | 0.997318 | + | 0.0731932i | \(0.0233190\pi\) |
−0.763825 | + | 0.645423i | \(0.776681\pi\) | |||||||
\(38\) | 0.709660 | + | 2.18411i | 0.115122 | + | 0.354309i | ||||
\(39\) | −1.88385 | + | 5.79790i | −0.301658 | + | 0.928407i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.888346 | − | 2.73405i | −0.138736 | − | 0.426987i | 0.857416 | − | 0.514624i | \(-0.172068\pi\) |
−0.996152 | + | 0.0876372i | \(0.972068\pi\) | |||||||
\(42\) | −15.5725 | + | 11.3141i | −2.40289 | + | 1.74580i | ||||
\(43\) | 9.48858 | 1.44700 | 0.723498 | − | 0.690327i | \(-0.242533\pi\) | ||||
0.723498 | + | 0.690327i | \(0.242533\pi\) | |||||||
\(44\) | 1.37357 | − | 0.997959i | 0.207074 | − | 0.150448i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.0699 | − | 8.76929i | −1.77961 | − | 1.29296i | ||||
\(47\) | 4.34308 | + | 3.15543i | 0.633503 | + | 0.460267i | 0.857612 | − | 0.514297i | \(-0.171947\pi\) |
−0.224109 | + | 0.974564i | \(0.571947\pi\) | |||||||
\(48\) | 0.577493 | − | 1.77734i | 0.0833539 | − | 0.256537i | ||||
\(49\) | 5.91861 | 0.845515 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.7583 | −1.64650 | ||||||||
\(52\) | −2.79082 | + | 8.58926i | −0.387017 | + | 1.19112i | ||||
\(53\) | −0.248854 | − | 0.180803i | −0.0341827 | − | 0.0248352i | 0.570563 | − | 0.821254i | \(-0.306725\pi\) |
−0.604745 | + | 0.796419i | \(0.706725\pi\) | |||||||
\(54\) | −3.03003 | − | 2.20144i | −0.412334 | − | 0.299578i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.54209 | + | 6.93274i | −1.27512 | + | 0.926426i | ||||
\(57\) | −2.27302 | −0.301069 | ||||||||
\(58\) | −10.4820 | + | 7.61558i | −1.37635 | + | 0.999975i | ||||
\(59\) | −0.391355 | − | 1.20447i | −0.0509500 | − | 0.156808i | 0.922344 | − | 0.386369i | \(-0.126271\pi\) |
−0.973294 | + | 0.229561i | \(0.926271\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.92402 | + | 5.92152i | −0.246345 | + | 0.758173i | 0.749067 | + | 0.662494i | \(0.230502\pi\) |
−0.995412 | + | 0.0956787i | \(0.969498\pi\) | |||||||
\(62\) | −4.35242 | − | 13.3954i | −0.552757 | − | 1.70121i | ||||
\(63\) | −2.55529 | − | 7.86438i | −0.321936 | − | 0.990818i | ||||
\(64\) | −3.86206 | + | 11.8862i | −0.482757 | + | 1.48577i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.823796 | + | 2.53538i | 0.101402 | + | 0.312084i | ||||
\(67\) | −4.27667 | + | 3.10718i | −0.522479 | + | 0.379603i | −0.817537 | − | 0.575876i | \(-0.804661\pi\) |
0.295058 | + | 0.955479i | \(0.404661\pi\) | |||||||
\(68\) | −17.4193 | −2.11240 | ||||||||
\(69\) | 11.9465 | − | 8.67961i | 1.43818 | − | 1.04490i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.122941 | + | 0.0893215i | 0.0145904 | + | 0.0106005i | 0.595057 | − | 0.803684i | \(-0.297130\pi\) |
−0.580466 | + | 0.814284i | \(0.697130\pi\) | |||||||
\(72\) | 6.10782 | + | 4.43759i | 0.719813 | + | 0.522975i | ||||
\(73\) | 4.59634 | − | 14.1461i | 0.537961 | − | 1.65567i | −0.199202 | − | 0.979959i | \(-0.563835\pi\) |
0.737163 | − | 0.675715i | \(-0.236165\pi\) | |||||||
\(74\) | −10.6910 | −1.24281 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.36735 | −0.386262 | ||||||||
\(77\) | 0.552884 | − | 1.70160i | 0.0630070 | − | 0.193916i | ||||
\(78\) | −11.4723 | − | 8.33512i | −1.29898 | − | 0.943766i | ||||
\(79\) | 13.4205 | + | 9.75053i | 1.50992 | + | 1.09702i | 0.966213 | + | 0.257745i | \(0.0829795\pi\) |
0.543706 | + | 0.839275i | \(0.317021\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.58283 | − | 6.23579i | 0.953648 | − | 0.692866i | ||||
\(82\) | 6.68696 | 0.738451 | ||||||||
\(83\) | 11.8084 | − | 8.57929i | 1.29614 | − | 0.941700i | 0.296228 | − | 0.955117i | \(-0.404271\pi\) |
0.999910 | + | 0.0134174i | \(0.00427102\pi\) | |||||||
\(84\) | −8.72176 | − | 26.8428i | −0.951623 | − | 2.92879i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.82044 | + | 20.9912i | −0.735467 | + | 2.26354i | ||||
\(87\) | −3.96281 | − | 12.1963i | −0.424857 | − | 1.30758i | ||||
\(88\) | 0.504783 | + | 1.55356i | 0.0538101 | + | 0.165610i | ||||
\(89\) | 3.51731 | − | 10.8252i | 0.372834 | − | 1.14746i | −0.572095 | − | 0.820188i | \(-0.693869\pi\) |
0.944928 | − | 0.327277i | \(-0.106131\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.94097 | + | 9.05136i | 0.308297 | + | 0.948841i | ||||
\(92\) | 17.6980 | − | 12.8584i | 1.84514 | − | 1.34058i | ||||
\(93\) | 13.9407 | 1.44558 | ||||||||
\(94\) | −10.1024 | + | 7.33985i | −1.04199 | + | 0.757048i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.70766 | − | 6.32648i | −0.888721 | − | 0.645694i | ||||
\(97\) | 0.687010 | + | 0.499142i | 0.0697553 | + | 0.0506802i | 0.622116 | − | 0.782925i | \(-0.286273\pi\) |
−0.552361 | + | 0.833605i | \(0.686273\pi\) | |||||||
\(98\) | −4.25432 | + | 13.0935i | −0.429751 | + | 1.32264i | ||||
\(99\) | −1.14523 | −0.115100 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.2498 | −1.31841 | −0.659203 | − | 0.751965i | \(-0.729106\pi\) | ||||
−0.659203 | + | 0.751965i | \(0.729106\pi\) | |||||||
\(102\) | 8.45196 | − | 26.0125i | 0.836869 | − | 2.57562i | ||||
\(103\) | 0.672220 | + | 0.488396i | 0.0662358 | + | 0.0481231i | 0.620410 | − | 0.784277i | \(-0.286966\pi\) |
−0.554175 | + | 0.832400i | \(0.686966\pi\) | |||||||
\(104\) | −7.02968 | − | 5.10736i | −0.689317 | − | 0.500818i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.578859 | − | 0.420566i | 0.0562237 | − | 0.0408489i | ||||
\(107\) | 0.0722844 | 0.00698800 | 0.00349400 | − | 0.999994i | \(-0.498888\pi\) | ||||
0.00349400 | + | 0.999994i | \(0.498888\pi\) | |||||||
\(108\) | 4.44291 | − | 3.22796i | 0.427519 | − | 0.310611i | ||||
\(109\) | 1.72933 | + | 5.32232i | 0.165639 | + | 0.509785i | 0.999083 | − | 0.0428192i | \(-0.0136340\pi\) |
−0.833444 | + | 0.552605i | \(0.813634\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.26993 | − | 10.0638i | 0.310368 | − | 0.955215i | ||||
\(112\) | −0.901550 | − | 2.77469i | −0.0851885 | − | 0.262183i | ||||
\(113\) | 0.804183 | + | 2.47502i | 0.0756512 | + | 0.232830i | 0.981730 | − | 0.190278i | \(-0.0609389\pi\) |
−0.906079 | + | 0.423108i | \(0.860939\pi\) | |||||||
\(114\) | 1.63386 | − | 5.02850i | 0.153025 | − | 0.470962i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.87067 | − | 18.0681i | −0.545078 | − | 1.67758i | ||||
\(117\) | 4.92842 | − | 3.58071i | 0.455633 | − | 0.331036i | ||||
\(118\) | 2.94589 | 0.271191 | ||||||||
\(119\) | −14.8507 | + | 10.7897i | −1.36136 | + | 0.989088i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.69872 | + | 6.31999i | 0.790793 | + | 0.574544i | ||||
\(122\) | −11.7169 | − | 8.51284i | −1.06080 | − | 0.770716i | ||||
\(123\) | −2.04525 | + | 6.29464i | −0.184414 | + | 0.567568i | ||||
\(124\) | 20.6523 | 1.85463 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 19.2348 | 1.71357 | ||||||||
\(127\) | −1.52804 | + | 4.70281i | −0.135591 | + | 0.417307i | −0.995682 | − | 0.0928348i | \(-0.970407\pi\) |
0.860090 | + | 0.510142i | \(0.170407\pi\) | |||||||
\(128\) | −15.9549 | − | 11.5919i | −1.41023 | − | 1.02459i | ||||
\(129\) | −17.6735 | − | 12.8406i | −1.55607 | − | 1.13055i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.18711 | + | 1.58903i | −0.191089 | + | 0.138834i | −0.679216 | − | 0.733938i | \(-0.737680\pi\) |
0.488127 | + | 0.872772i | \(0.337680\pi\) | |||||||
\(132\) | −3.90893 | −0.340229 | ||||||||
\(133\) | −2.87081 | + | 2.08577i | −0.248931 | + | 0.180859i | ||||
\(134\) | −3.79979 | − | 11.6945i | −0.328252 | − | 1.01025i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.17896 | − | 15.9392i | 0.444092 | − | 1.36677i | ||||
\(137\) | 0.694787 | + | 2.13833i | 0.0593596 | + | 0.182690i | 0.976340 | − | 0.216243i | \(-0.0693804\pi\) |
−0.916980 | + | 0.398933i | \(0.869380\pi\) | |||||||
\(138\) | 10.6143 | + | 32.6675i | 0.903551 | + | 2.78085i | ||||
\(139\) | −3.33838 | + | 10.2745i | −0.283158 | + | 0.871469i | 0.703787 | + | 0.710411i | \(0.251491\pi\) |
−0.986945 | + | 0.161059i | \(0.948509\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.81933 | − | 11.7547i | −0.321645 | − | 0.989923i | ||||
\(142\) | −0.285972 | + | 0.207771i | −0.0239983 | + | 0.0174358i | ||||
\(143\) | 1.31809 | 0.110224 | ||||||||
\(144\) | −1.51080 | + | 1.09766i | −0.125900 | + | 0.0914719i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 27.9909 | + | 20.3365i | 2.31654 | + | 1.68306i | ||||
\(147\) | −11.0241 | − | 8.00945i | −0.909249 | − | 0.660608i | ||||
\(148\) | 4.84422 | − | 14.9090i | 0.398192 | − | 1.22551i | ||||
\(149\) | 12.1878 | 0.998460 | 0.499230 | − | 0.866469i | \(-0.333616\pi\) | ||||
0.499230 | + | 0.866469i | \(0.333616\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.0860 | 1.39044 | 0.695220 | − | 0.718797i | \(-0.255307\pi\) | ||||
0.695220 | + | 0.718797i | \(0.255307\pi\) | |||||||
\(152\) | 1.00115 | − | 3.08123i | 0.0812041 | − | 0.249920i | ||||
\(153\) | 9.50582 | + | 6.90638i | 0.768500 | + | 0.558348i | ||||
\(154\) | 3.36696 | + | 2.44624i | 0.271318 | + | 0.197124i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 16.8218 | − | 12.2217i | 1.34682 | − | 0.978522i | ||||
\(157\) | 7.49835 | 0.598433 | 0.299217 | − | 0.954185i | \(-0.403275\pi\) | ||||
0.299217 | + | 0.954185i | \(0.403275\pi\) | |||||||
\(158\) | −31.2173 | + | 22.6807i | −2.48352 | + | 1.80438i | ||||
\(159\) | 0.218843 | + | 0.673530i | 0.0173554 | + | 0.0534144i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.12372 | − | 21.9246i | 0.561428 | − | 1.72790i | ||||
\(162\) | 7.62577 | + | 23.4697i | 0.599137 | + | 1.84396i | ||||
\(163\) | −0.603383 | − | 1.85702i | −0.0472606 | − | 0.145453i | 0.924641 | − | 0.380839i | \(-0.124365\pi\) |
−0.971902 | + | 0.235386i | \(0.924365\pi\) | |||||||
\(164\) | −3.02993 | + | 9.32515i | −0.236597 | + | 0.728172i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.4917 | + | 32.2900i | 0.814310 | + | 2.50619i | ||||
\(167\) | −0.288478 | + | 0.209591i | −0.0223231 | + | 0.0162187i | −0.598891 | − | 0.800831i | \(-0.704392\pi\) |
0.576568 | + | 0.817049i | \(0.304392\pi\) | |||||||
\(168\) | 27.1550 | 2.09506 | ||||||||
\(169\) | 4.84494 | − | 3.52006i | 0.372688 | − | 0.270774i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.83758 | + | 1.33508i | 0.140523 | + | 0.102096i | ||||
\(172\) | −26.1824 | − | 19.0226i | −1.99639 | − | 1.45046i | ||||
\(173\) | 3.07482 | − | 9.46332i | 0.233774 | − | 0.719483i | −0.763508 | − | 0.645799i | \(-0.776524\pi\) |
0.997282 | − | 0.0736838i | \(-0.0234756\pi\) | |||||||
\(174\) | 29.8297 | 2.26138 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.404058 | −0.0304570 | ||||||||
\(177\) | −0.901021 | + | 2.77306i | −0.0677249 | + | 0.208436i | ||||
\(178\) | 21.4197 | + | 15.5624i | 1.60548 | + | 1.16645i | ||||
\(179\) | −12.4446 | − | 9.04154i | −0.930154 | − | 0.675797i | 0.0158762 | − | 0.999874i | \(-0.494946\pi\) |
−0.946031 | + | 0.324077i | \(0.894946\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.21576 | + | 5.24256i | −0.536343 | + | 0.389676i | −0.822725 | − | 0.568439i | \(-0.807547\pi\) |
0.286382 | + | 0.958116i | \(0.407547\pi\) | |||||||
\(182\) | −22.1379 | −1.64097 | ||||||||
\(183\) | 11.5971 | − | 8.42578i | 0.857282 | − | 0.622852i | ||||
\(184\) | 6.50395 | + | 20.0171i | 0.479478 | + | 1.47568i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −10.0206 | + | 30.8403i | −0.734748 | + | 2.26132i | ||||
\(187\) | 0.785612 | + | 2.41787i | 0.0574497 | + | 0.176812i | ||||
\(188\) | −5.65812 | − | 17.4139i | −0.412661 | − | 1.27004i | ||||
\(189\) | 1.78834 | − | 5.50395i | 0.130083 | − | 0.400353i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.51929 | − | 10.8313i | −0.254647 | − | 0.783724i | −0.993899 | − | 0.110294i | \(-0.964821\pi\) |
0.739252 | − | 0.673429i | \(-0.235179\pi\) | |||||||
\(192\) | 23.2787 | − | 16.9130i | 1.67999 | − | 1.22059i | ||||
\(193\) | −17.3321 | −1.24759 | −0.623795 | − | 0.781588i | \(-0.714410\pi\) | ||||
−0.623795 | + | 0.781588i | \(0.714410\pi\) | |||||||
\(194\) | −1.59806 | + | 1.16106i | −0.114734 | + | 0.0833589i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −16.3315 | − | 11.8655i | −1.16654 | − | 0.847539i | ||||
\(197\) | 21.0028 | + | 15.2595i | 1.49639 | + | 1.08719i | 0.971792 | + | 0.235842i | \(0.0757847\pi\) |
0.524599 | + | 0.851350i | \(0.324215\pi\) | |||||||
\(198\) | 0.823200 | − | 2.53355i | 0.0585023 | − | 0.180052i | ||||
\(199\) | −8.38571 | −0.594447 | −0.297223 | − | 0.954808i | \(-0.596061\pi\) | ||||
−0.297223 | + | 0.954808i | \(0.596061\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.1706 | 0.858450 | ||||||||
\(202\) | 9.52403 | − | 29.3120i | 0.670109 | − | 2.06238i | ||||
\(203\) | −16.1965 | − | 11.7675i | −1.13677 | − | 0.825913i | ||||
\(204\) | 32.4454 | + | 23.5730i | 2.27164 | + | 1.65044i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.56365 | + | 1.13606i | −0.108945 | + | 0.0791530i | ||||
\(207\) | −14.7559 | −1.02561 | ||||||||
\(208\) | 1.73883 | − | 1.26333i | 0.120566 | − | 0.0875965i | ||||
\(209\) | 0.151868 | + | 0.467401i | 0.0105049 | + | 0.0323308i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.91754 | − | 15.1346i | 0.338537 | − | 1.04191i | −0.626416 | − | 0.779489i | \(-0.715479\pi\) |
0.964953 | − | 0.262422i | \(-0.0845212\pi\) | |||||||
\(212\) | 0.324204 | + | 0.997797i | 0.0222664 | + | 0.0685290i | ||||
\(213\) | −0.108115 | − | 0.332743i | −0.00740789 | − | 0.0227991i | ||||
\(214\) | −0.0519584 | + | 0.159911i | −0.00355180 | + | 0.0109313i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.63275 | + | 5.02510i | 0.111095 | + | 0.341915i | ||||
\(217\) | 17.6070 | − | 12.7922i | 1.19524 | − | 0.868392i | ||||
\(218\) | −13.0174 | −0.881647 | ||||||||
\(219\) | −27.7046 | + | 20.1286i | −1.87210 | + | 1.36016i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.9406 | − | 7.94878i | −0.735941 | − | 0.534693i | ||||
\(222\) | 19.9133 | + | 14.4678i | 1.33649 | + | 0.971017i | ||||
\(223\) | 0.117335 | − | 0.361121i | 0.00785736 | − | 0.0241825i | −0.947051 | − | 0.321083i | \(-0.895953\pi\) |
0.954908 | + | 0.296901i | \(0.0959531\pi\) | |||||||
\(224\) | −16.8030 | −1.12270 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.05343 | −0.402668 | ||||||||
\(227\) | −6.27333 | + | 19.3073i | −0.416376 | + | 1.28147i | 0.494639 | + | 0.869099i | \(0.335300\pi\) |
−0.911015 | + | 0.412374i | \(0.864700\pi\) | |||||||
\(228\) | 6.27207 | + | 4.55693i | 0.415378 | + | 0.301790i | ||||
\(229\) | 9.63592 | + | 7.00091i | 0.636759 | + | 0.462633i | 0.858735 | − | 0.512419i | \(-0.171251\pi\) |
−0.221976 | + | 0.975052i | \(0.571251\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.33253 | + | 2.42123i | −0.219264 | + | 0.159305i | ||||
\(232\) | 18.2782 | 1.20002 | ||||||||
\(233\) | −15.4207 | + | 11.2038i | −1.01024 | + | 0.733984i | −0.964260 | − | 0.264958i | \(-0.914642\pi\) |
−0.0459827 | + | 0.998942i | \(0.514642\pi\) | |||||||
\(234\) | 4.37886 | + | 13.4767i | 0.286255 | + | 0.881003i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.33481 | + | 4.10813i | −0.0868889 | + | 0.267417i | ||||
\(237\) | −11.8020 | − | 36.3229i | −0.766624 | − | 2.35943i | ||||
\(238\) | −13.1947 | − | 40.6092i | −0.855288 | − | 2.63230i | ||||
\(239\) | 1.27467 | − | 3.92304i | 0.0824517 | − | 0.253760i | −0.901329 | − | 0.433135i | \(-0.857407\pi\) |
0.983781 | + | 0.179375i | \(0.0574074\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00169 | + | 15.3936i | 0.322187 | + | 0.991590i | 0.972694 | + | 0.232090i | \(0.0745564\pi\) |
−0.650507 | + | 0.759500i | \(0.725444\pi\) | |||||||
\(242\) | −20.2341 | + | 14.7009i | −1.30070 | + | 0.945012i | ||||
\(243\) | −19.5948 | −1.25701 | ||||||||
\(244\) | 17.1804 | − | 12.4823i | 1.09986 | − | 0.799099i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −12.4552 | − | 9.04923i | −0.794115 | − | 0.576958i | ||||
\(247\) | −2.11493 | − | 1.53659i | −0.134570 | − | 0.0977708i | ||||
\(248\) | −6.14016 | + | 18.8975i | −0.389901 | + | 1.19999i | ||||
\(249\) | −33.6045 | −2.12960 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.8718 | 0.749344 | 0.374672 | − | 0.927157i | \(-0.377755\pi\) | ||||
0.374672 | + | 0.927157i | \(0.377755\pi\) | |||||||
\(252\) | −8.71546 | + | 26.8234i | −0.549022 | + | 1.68972i | ||||
\(253\) | −2.58297 | − | 1.87663i | −0.162390 | − | 0.117983i | ||||
\(254\) | −9.30546 | − | 6.76081i | −0.583876 | − | 0.424211i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.8908 | − | 12.2719i | 1.05568 | − | 0.766993i | ||||
\(257\) | 18.9164 | 1.17997 | 0.589986 | − | 0.807414i | \(-0.299133\pi\) | ||||
0.589986 | + | 0.807414i | \(0.299133\pi\) | |||||||
\(258\) | 41.1105 | − | 29.8685i | 2.55943 | − | 1.85953i | ||||
\(259\) | −5.10484 | − | 15.7111i | −0.317199 | − | 0.976239i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.95994 | + | 12.1874i | −0.245114 | + | 0.754383i | ||||
\(262\) | −1.94323 | − | 5.98065i | −0.120053 | − | 0.369486i | ||||
\(263\) | 2.08495 | + | 6.41680i | 0.128563 | + | 0.395677i | 0.994533 | − | 0.104419i | \(-0.0332982\pi\) |
−0.865970 | + | 0.500096i | \(0.833298\pi\) | |||||||
\(264\) | 1.16217 | − | 3.57679i | 0.0715266 | − | 0.220136i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.55069 | − | 7.85022i | −0.156393 | − | 0.481328i | ||||
\(267\) | −21.2007 | + | 15.4032i | −1.29746 | + | 0.942661i | ||||
\(268\) | 18.0301 | 1.10136 | ||||||||
\(269\) | 20.4947 | − | 14.8903i | 1.24959 | − | 0.907877i | 0.251387 | − | 0.967887i | \(-0.419113\pi\) |
0.998198 | + | 0.0600099i | \(0.0191132\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.61070 | − | 5.52950i | −0.462317 | − | 0.335893i | 0.332122 | − | 0.943236i | \(-0.392235\pi\) |
−0.794440 | + | 0.607343i | \(0.792235\pi\) | |||||||
\(272\) | 3.35382 | + | 2.43669i | 0.203355 | + | 0.147746i | ||||
\(273\) | 6.77103 | − | 20.8391i | 0.409801 | − | 1.26124i | ||||
\(274\) | −5.22995 | −0.315953 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −50.3653 | −3.03163 | ||||||||
\(277\) | 1.84402 | − | 5.67530i | 0.110796 | − | 0.340996i | −0.880251 | − | 0.474509i | \(-0.842626\pi\) |
0.991047 | + | 0.133513i | \(0.0426258\pi\) | |||||||
\(278\) | −20.3301 | − | 14.7707i | −1.21932 | − | 0.885887i | ||||
\(279\) | −11.2701 | − | 8.18820i | −0.674722 | − | 0.490215i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.95766 | + | 6.50812i | −0.534369 | + | 0.388242i | −0.821990 | − | 0.569503i | \(-0.807136\pi\) |
0.287620 | + | 0.957744i | \(0.407136\pi\) | |||||||
\(282\) | 28.7497 | 1.71202 | ||||||||
\(283\) | −2.44652 | + | 1.77750i | −0.145431 | + | 0.105661i | −0.658121 | − | 0.752912i | \(-0.728649\pi\) |
0.512691 | + | 0.858573i | \(0.328649\pi\) | |||||||
\(284\) | −0.160166 | − | 0.492939i | −0.00950409 | − | 0.0292506i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.947447 | + | 2.91594i | −0.0560237 | + | 0.172423i | ||||
\(287\) | 3.19293 | + | 9.82684i | 0.188473 | + | 0.580060i | ||||
\(288\) | 3.32362 | + | 10.2291i | 0.195846 | + | 0.602753i | ||||
\(289\) | 2.80691 | − | 8.63880i | 0.165113 | − | 0.508164i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.604161 | − | 1.85942i | −0.0354165 | − | 0.109001i | ||||
\(292\) | −41.0428 | + | 29.8194i | −2.40185 | + | 1.74505i | ||||
\(293\) | −6.26426 | −0.365962 | −0.182981 | − | 0.983116i | \(-0.558575\pi\) | ||||
−0.182981 | + | 0.983116i | \(0.558575\pi\) | |||||||
\(294\) | 25.6431 | − | 18.6308i | 1.49553 | − | 1.08657i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 12.2019 | + | 8.86520i | 0.709221 | + | 0.515279i | ||||
\(297\) | −0.648428 | − | 0.471111i | −0.0376256 | − | 0.0273366i | ||||
\(298\) | −8.76062 | + | 26.9624i | −0.507489 | + | 1.56189i | ||||
\(299\) | 16.9831 | 0.982158 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −34.1043 | −1.96574 | ||||||||
\(302\) | −12.2815 | + | 37.7986i | −0.706721 | + | 2.17506i | ||||
\(303\) | 24.6793 | + | 17.9305i | 1.41779 | + | 1.03008i | ||||
\(304\) | 0.648331 | + | 0.471040i | 0.0371843 | + | 0.0270160i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −22.1115 | + | 16.0650i | −1.26403 | + | 0.918372i | ||||
\(307\) | −25.8734 | −1.47667 | −0.738337 | − | 0.674432i | \(-0.764388\pi\) | ||||
−0.738337 | + | 0.674432i | \(0.764388\pi\) | |||||||
\(308\) | −4.93696 | + | 3.58691i | −0.281309 | + | 0.204383i | ||||
\(309\) | −0.591154 | − | 1.81938i | −0.0336296 | − | 0.103501i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.78201 | + | 8.56214i | −0.157753 | + | 0.485514i | −0.998429 | − | 0.0560237i | \(-0.982158\pi\) |
0.840676 | + | 0.541538i | \(0.182158\pi\) | |||||||
\(312\) | 6.18194 | + | 19.0261i | 0.349984 | + | 1.07714i | ||||
\(313\) | 10.2678 | + | 31.6011i | 0.580372 | + | 1.78620i | 0.617110 | + | 0.786877i | \(0.288304\pi\) |
−0.0367373 | + | 0.999325i | \(0.511696\pi\) | |||||||
\(314\) | −5.38985 | + | 16.5882i | −0.304167 | + | 0.936129i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.4840 | − | 53.8103i | −0.983554 | − | 3.02707i | ||||
\(317\) | −21.0096 | + | 15.2644i | −1.18002 | + | 0.857332i | −0.992174 | − | 0.124867i | \(-0.960150\pi\) |
−0.187843 | + | 0.982199i | \(0.560150\pi\) | |||||||
\(318\) | −1.64733 | −0.0923774 | ||||||||
\(319\) | −2.24315 | + | 1.62974i | −0.125592 | + | 0.0912480i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.134638 | − | 0.0978200i | −0.00751475 | − | 0.00545978i | ||||
\(322\) | 43.3821 | + | 31.5190i | 2.41759 | + | 1.75648i | ||||
\(323\) | 1.55813 | − | 4.79543i | 0.0866966 | − | 0.266825i | ||||
\(324\) | −36.1845 | −2.01025 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.54192 | 0.251554 | ||||||||
\(327\) | 3.98145 | − | 12.2536i | 0.220175 | − | 0.677628i | ||||
\(328\) | −7.63195 | − | 5.54494i | −0.421404 | − | 0.306168i | ||||
\(329\) | −15.6101 | − | 11.3414i | −0.860612 | − | 0.625272i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.81206 | + | 7.12888i | −0.539320 | + | 0.391839i | −0.823832 | − | 0.566834i | \(-0.808168\pi\) |
0.284513 | + | 0.958672i | \(0.408168\pi\) | |||||||
\(332\) | −49.7832 | −2.73221 | ||||||||
\(333\) | −8.55460 | + | 6.21528i | −0.468789 | + | 0.340595i | ||||
\(334\) | −0.256310 | − | 0.788841i | −0.0140247 | − | 0.0431635i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.07565 | + | 6.38820i | −0.113236 | + | 0.348505i | ||||
\(337\) | 9.34835 | + | 28.7713i | 0.509237 | + | 1.56727i | 0.793529 | + | 0.608533i | \(0.208241\pi\) |
−0.284292 | + | 0.958738i | \(0.591759\pi\) | |||||||
\(338\) | 4.30469 | + | 13.2485i | 0.234144 | + | 0.720622i | ||||
\(339\) | 1.85148 | − | 5.69828i | 0.100559 | − | 0.309488i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.931421 | − | 2.86662i | −0.0504393 | − | 0.155236i | ||||
\(342\) | −4.27440 | + | 3.10554i | −0.231133 | + | 0.167928i | ||||
\(343\) | 3.88680 | 0.209867 | ||||||||
\(344\) | 25.1905 | − | 18.3020i | 1.35818 | − | 0.986777i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.7251 | + | 13.6046i | 1.00667 | + | 0.731386i | ||||
\(347\) | −10.7828 | − | 7.83419i | −0.578853 | − | 0.420561i | 0.259457 | − | 0.965755i | \(-0.416456\pi\) |
−0.838310 | + | 0.545193i | \(0.816456\pi\) | |||||||
\(348\) | −13.5161 | + | 41.5984i | −0.724541 | + | 2.22991i | ||||
\(349\) | −27.4444 | −1.46906 | −0.734532 | − | 0.678574i | \(-0.762598\pi\) | ||||
−0.734532 | + | 0.678574i | \(0.762598\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.26344 | 0.227566 | ||||||||
\(352\) | −0.719127 | + | 2.21325i | −0.0383296 | + | 0.117966i | ||||
\(353\) | 12.5854 | + | 9.14382i | 0.669853 | + | 0.486676i | 0.869976 | − | 0.493094i | \(-0.164134\pi\) |
−0.200123 | + | 0.979771i | \(0.564134\pi\) | |||||||
\(354\) | −5.48705 | − | 3.98658i | −0.291634 | − | 0.211884i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −31.4076 | + | 22.8190i | −1.66460 | + | 1.20940i | ||||
\(357\) | 42.2624 | 2.23676 | ||||||||
\(358\) | 28.9474 | − | 21.0315i | 1.52992 | − | 1.11155i | ||||
\(359\) | −6.79310 | − | 20.9070i | −0.358526 | − | 1.10343i | −0.953937 | − | 0.300008i | \(-0.903011\pi\) |
0.595410 | − | 0.803422i | \(-0.296989\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.57012 | + | 17.1431i | −0.293164 | + | 0.902267i | ||||
\(362\) | −6.41114 | − | 19.7315i | −0.336962 | − | 1.03706i | ||||
\(363\) | −7.64970 | − | 23.5434i | −0.401505 | − | 1.23571i | ||||
\(364\) | 10.0309 | − | 30.8719i | 0.525762 | − | 1.61813i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.3039 | + | 31.7122i | 0.538594 | + | 1.65762i | ||||
\(367\) | 9.79748 | − | 7.11829i | 0.511424 | − | 0.371571i | −0.301939 | − | 0.953327i | \(-0.597634\pi\) |
0.813364 | + | 0.581756i | \(0.197634\pi\) | |||||||
\(368\) | −5.20615 | −0.271389 | ||||||||
\(369\) | 5.35066 | − | 3.88749i | 0.278544 | − | 0.202374i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.894441 | + | 0.649850i | 0.0464371 | + | 0.0337385i | ||||
\(372\) | −38.4673 | − | 27.9481i | −1.99443 | − | 1.44904i | ||||
\(373\) | −2.18971 | + | 6.73922i | −0.113379 | + | 0.348944i | −0.991605 | − | 0.129301i | \(-0.958727\pi\) |
0.878227 | + | 0.478245i | \(0.158727\pi\) | |||||||
\(374\) | −5.91364 | −0.305787 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17.6164 | 0.908499 | ||||||||
\(377\) | 4.55762 | − | 14.0269i | 0.234729 | − | 0.722423i | ||||
\(378\) | 10.8907 | + | 7.91253i | 0.560155 | + | 0.406977i | ||||
\(379\) | 17.3963 | + | 12.6391i | 0.893586 | + | 0.649228i | 0.936810 | − | 0.349837i | \(-0.113763\pi\) |
−0.0432246 | + | 0.999065i | \(0.513763\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.21029 | − | 6.69167i | 0.471858 | − | 0.342825i | ||||
\(382\) | 26.4912 | 1.35541 | ||||||||
\(383\) | 20.1297 | − | 14.6251i | 1.02858 | − | 0.747305i | 0.0605541 | − | 0.998165i | \(-0.480713\pi\) |
0.968023 | + | 0.250860i | \(0.0807132\pi\) | |||||||
\(384\) | 14.0309 | + | 43.1825i | 0.716009 | + | 2.20365i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.4584 | − | 38.3429i | 0.634115 | − | 1.95160i | ||||
\(387\) | 6.74581 | + | 20.7615i | 0.342909 | + | 1.05536i | ||||
\(388\) | −0.895030 | − | 2.75462i | −0.0454383 | − | 0.139845i | ||||
\(389\) | −10.9436 | + | 33.6809i | −0.554862 | + | 1.70769i | 0.141446 | + | 0.989946i | \(0.454825\pi\) |
−0.696308 | + | 0.717743i | \(0.745175\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.1223 | + | 31.1534i | 0.511909 | + | 1.57549i | ||||
\(392\) | 15.7129 | − | 11.4161i | 0.793619 | − | 0.576598i | ||||
\(393\) | 6.22412 | 0.313965 | ||||||||
\(394\) | −48.8547 | + | 35.4950i | −2.46127 | + | 1.78821i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.16011 | + | 2.29595i | 0.158801 | + | 0.115376i | ||||
\(397\) | 4.44720 | + | 3.23108i | 0.223199 | + | 0.162163i | 0.693765 | − | 0.720201i | \(-0.255950\pi\) |
−0.470567 | + | 0.882364i | \(0.655950\pi\) | |||||||
\(398\) | 6.02769 | − | 18.5513i | 0.302141 | − | 0.929893i | ||||
\(399\) | 8.16980 | 0.409001 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.8463 | 1.24077 | 0.620383 | − | 0.784299i | \(-0.286977\pi\) | ||||
0.620383 | + | 0.784299i | \(0.286977\pi\) | |||||||
\(402\) | −8.74830 | + | 26.9245i | −0.436326 | + | 1.34287i | ||||
\(403\) | 12.9711 | + | 9.42406i | 0.646137 | + | 0.469446i | ||||
\(404\) | 36.5609 | + | 26.5631i | 1.81897 | + | 1.32156i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 37.6747 | − | 27.3723i | 1.86976 | − | 1.35846i | ||||
\(407\) | −2.28789 | −0.113407 | ||||||||
\(408\) | −31.2164 | + | 22.6800i | −1.54544 | + | 1.12283i | ||||
\(409\) | 1.21492 | + | 3.73915i | 0.0600741 | + | 0.184889i | 0.976590 | − | 0.215109i | \(-0.0690107\pi\) |
−0.916516 | + | 0.399998i | \(0.869011\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.59962 | − | 4.92312i | 0.0789033 | − | 0.242839i | ||||
\(412\) | −0.875761 | − | 2.69531i | −0.0431456 | − | 0.132789i | ||||
\(413\) | 1.40663 | + | 4.32915i | 0.0692155 | + | 0.213023i | ||||
\(414\) | 10.6066 | − | 32.6439i | 0.521288 | − | 1.60436i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.82526 | − | 11.7730i | −0.187549 | − | 0.577216i | ||||
\(417\) | 20.1222 | − | 14.6196i | 0.985388 | − | 0.715926i | ||||
\(418\) | −1.14317 | −0.0559144 | ||||||||
\(419\) | 3.85581 | − | 2.80141i | 0.188369 | − | 0.136858i | −0.489604 | − | 0.871945i | \(-0.662859\pi\) |
0.677973 | + | 0.735087i | \(0.262859\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.9913 | − | 9.43872i | −0.633157 | − | 0.460015i | 0.224336 | − | 0.974512i | \(-0.427979\pi\) |
−0.857492 | + | 0.514497i | \(0.827979\pi\) | |||||||
\(422\) | 29.9469 | + | 21.7577i | 1.45779 | + | 1.05915i | ||||
\(423\) | −3.81657 | + | 11.7462i | −0.185568 | + | 0.571119i | ||||
\(424\) | −1.00940 | −0.0490209 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.813824 | 0.0394299 | ||||||||
\(427\) | 6.91540 | − | 21.2834i | 0.334659 | − | 1.02998i | ||||
\(428\) | −0.199458 | − | 0.144915i | −0.00964118 | − | 0.00700473i | ||||
\(429\) | −2.45508 | − | 1.78372i | −0.118533 | − | 0.0861189i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.4684 | − | 24.3162i | 1.61212 | − | 1.17127i | 0.755841 | − | 0.654755i | \(-0.227228\pi\) |
0.856277 | − | 0.516517i | \(-0.172772\pi\) | |||||||
\(432\) | −1.30695 | −0.0628808 | ||||||||
\(433\) | 12.2852 | − | 8.92574i | 0.590391 | − | 0.428944i | −0.252065 | − | 0.967710i | \(-0.581110\pi\) |
0.842455 | + | 0.538767i | \(0.181110\pi\) | |||||||
\(434\) | 15.6437 | + | 48.1462i | 0.750920 | + | 2.31109i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.89829 | − | 18.1531i | 0.282477 | − | 0.869375i | ||||
\(437\) | 1.95676 | + | 6.02230i | 0.0936047 | + | 0.288086i | ||||
\(438\) | −24.6153 | − | 75.7582i | −1.17617 | − | 3.61986i | ||||
\(439\) | 5.29018 | − | 16.2815i | 0.252486 | − | 0.777074i | −0.741828 | − | 0.670590i | \(-0.766041\pi\) |
0.994314 | − | 0.106483i | \(-0.0339591\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.20777 | + | 12.9502i | 0.200370 | + | 0.616675i | ||||
\(442\) | 25.4488 | − | 18.4897i | 1.21048 | − | 0.879464i | ||||
\(443\) | −35.3909 | −1.68147 | −0.840736 | − | 0.541445i | \(-0.817877\pi\) | ||||
−0.840736 | + | 0.541445i | \(0.817877\pi\) | |||||||
\(444\) | −29.1987 | + | 21.2141i | −1.38571 | + | 1.00678i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.714551 | + | 0.519152i | 0.0338350 | + | 0.0245825i | ||||
\(447\) | −22.7011 | − | 16.4933i | −1.07372 | − | 0.780106i | ||||
\(448\) | 13.8812 | − | 42.7219i | 0.655824 | − | 2.01842i | ||||
\(449\) | 20.6830 | 0.976090 | 0.488045 | − | 0.872818i | \(-0.337710\pi\) | ||||
0.488045 | + | 0.872818i | \(0.337710\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.43101 | 0.0673838 | ||||||||
\(452\) | 2.74287 | − | 8.44168i | 0.129014 | − | 0.397063i | ||||
\(453\) | −31.8246 | − | 23.1219i | −1.49525 | − | 1.08636i | ||||
\(454\) | −38.2034 | − | 27.7564i | −1.79298 | − | 1.30267i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.03447 | + | 4.38430i | −0.282590 | + | 0.205314i | ||||
\(457\) | −41.7664 | −1.95375 | −0.976876 | − | 0.213807i | \(-0.931414\pi\) | ||||
−0.976876 | + | 0.213807i | \(0.931414\pi\) | |||||||
\(458\) | −22.4141 | + | 16.2848i | −1.04734 | + | 0.760940i | ||||
\(459\) | 2.54112 | + | 7.82075i | 0.118609 | + | 0.365041i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.29979 | + | 10.1557i | −0.153686 | + | 0.472998i | −0.998025 | − | 0.0628112i | \(-0.979993\pi\) |
0.844339 | + | 0.535809i | \(0.179993\pi\) | |||||||
\(462\) | −2.96093 | − | 9.11279i | −0.137755 | − | 0.423965i | ||||
\(463\) | 2.41971 | + | 7.44709i | 0.112453 | + | 0.346096i | 0.991407 | − | 0.130811i | \(-0.0417581\pi\) |
−0.878954 | + | 0.476906i | \(0.841758\pi\) | |||||||
\(464\) | −1.39713 | + | 4.29994i | −0.0648603 | + | 0.199620i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.7012 | − | 42.1678i | −0.634694 | − | 1.95339i | ||||
\(467\) | 4.02971 | − | 2.92776i | 0.186473 | − | 0.135480i | −0.490632 | − | 0.871367i | \(-0.663234\pi\) |
0.677105 | + | 0.735886i | \(0.263234\pi\) | |||||||
\(468\) | −20.7778 | −0.960455 | ||||||||
\(469\) | 15.3714 | − | 11.1680i | 0.709786 | − | 0.515690i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.9665 | − | 10.1473i | −0.643542 | − | 0.467561i | ||||
\(472\) | −3.36220 | − | 2.44278i | −0.154758 | − | 0.112438i | ||||
\(473\) | −1.45958 | + | 4.49213i | −0.0671116 | + | 0.206548i | ||||
\(474\) | 88.8388 | 4.08050 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 62.6094 | 2.86970 | ||||||||
\(477\) | 0.218685 | − | 0.673043i | 0.0100129 | − | 0.0308165i | ||||
\(478\) | 7.76252 | + | 5.63980i | 0.355049 | + | 0.257958i | ||||
\(479\) | 13.2663 | + | 9.63854i | 0.606153 | + | 0.440396i | 0.848058 | − | 0.529904i | \(-0.177772\pi\) |
−0.241904 | + | 0.970300i | \(0.577772\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.84576 | − | 7.15336i | 0.448928 | − | 0.326165i | ||||
\(482\) | −37.6498 | −1.71490 | ||||||||
\(483\) | −42.9385 | + | 31.1966i | −1.95377 | + | 1.41950i | ||||
\(484\) | −11.3326 | − | 34.8782i | −0.515118 | − | 1.58537i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 14.0848 | − | 43.3486i | 0.638901 | − | 1.96633i | ||||
\(487\) | −0.270856 | − | 0.833609i | −0.0122737 | − | 0.0377744i | 0.944732 | − | 0.327843i | \(-0.106322\pi\) |
−0.957006 | + | 0.290069i | \(0.906322\pi\) | |||||||
\(488\) | 6.31375 | + | 19.4317i | 0.285810 | + | 0.879633i | ||||
\(489\) | −1.38918 | + | 4.27545i | −0.0628208 | + | 0.193343i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.77366 | + | 11.6141i | 0.170303 | + | 0.524138i | 0.999388 | − | 0.0349842i | \(-0.0111381\pi\) |
−0.829085 | + | 0.559123i | \(0.811138\pi\) | |||||||
\(492\) | 18.2630 | − | 13.2688i | 0.823359 | − | 0.598205i | ||||
\(493\) | 28.4471 | 1.28119 | ||||||||
\(494\) | 4.91955 | − | 3.57426i | 0.221341 | − | 0.160814i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.97628 | − | 2.88894i | −0.178540 | − | 0.129717i | ||||
\(497\) | −0.441879 | − | 0.321044i | −0.0198210 | − | 0.0144008i | ||||
\(498\) | 24.1551 | − | 74.3417i | 1.08241 | − | 3.33133i | ||||
\(499\) | −3.34603 | −0.149789 | −0.0748945 | − | 0.997191i | \(-0.523862\pi\) | ||||
−0.0748945 | + | 0.997191i | \(0.523862\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.820954 | 0.0366775 | ||||||||
\(502\) | −8.53353 | + | 26.2635i | −0.380870 | + | 1.17220i | ||||
\(503\) | 9.61274 | + | 6.98407i | 0.428611 | + | 0.311404i | 0.781093 | − | 0.624414i | \(-0.214662\pi\) |
−0.352482 | + | 0.935819i | \(0.614662\pi\) | |||||||
\(504\) | −21.9530 | − | 15.9498i | −0.977864 | − | 0.710460i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.00824 | − | 4.36524i | 0.267099 | − | 0.194059i | ||||
\(507\) | −13.7878 | −0.612339 | ||||||||
\(508\) | 13.6445 | − | 9.91333i | 0.605378 | − | 0.439833i | ||||
\(509\) | 11.2230 | + | 34.5407i | 0.497449 | + | 1.53099i | 0.813105 | + | 0.582118i | \(0.197776\pi\) |
−0.315655 | + | 0.948874i | \(0.602224\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.5204 | + | 50.8445i | −0.730819 | + | 2.24923i | ||||
\(512\) | 2.81886 | + | 8.67556i | 0.124577 | + | 0.383409i | ||||
\(513\) | 0.491226 | + | 1.51184i | 0.0216882 | + | 0.0667493i | ||||
\(514\) | −13.5972 | + | 41.8478i | −0.599746 | + | 1.84583i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 23.0249 | + | 70.8634i | 1.01362 | + | 3.11959i | ||||
\(517\) | −2.16193 | + | 1.57074i | −0.0950816 | + | 0.0690809i | ||||
\(518\) | 38.4263 | 1.68835 | ||||||||
\(519\) | −18.5336 | + | 13.4654i | −0.813534 | + | 0.591067i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.165221 | − | 0.120040i | −0.00723845 | − | 0.00525904i | 0.584160 | − | 0.811638i | \(-0.301424\pi\) |
−0.591399 | + | 0.806379i | \(0.701424\pi\) | |||||||
\(522\) | −24.1153 | − | 17.5208i | −1.05550 | − | 0.766864i | ||||
\(523\) | −8.66211 | + | 26.6592i | −0.378768 | + | 1.16573i | 0.562134 | + | 0.827046i | \(0.309981\pi\) |
−0.940901 | + | 0.338681i | \(0.890019\pi\) | |||||||
\(524\) | 9.22069 | 0.402808 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.6943 | −0.684303 | ||||||||
\(527\) | −9.55616 | + | 29.4108i | −0.416273 | + | 1.28116i | ||||
\(528\) | 0.752603 | + | 0.546798i | 0.0327529 | + | 0.0237963i | ||||
\(529\) | −14.6732 | − | 10.6607i | −0.637967 | − | 0.463510i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.35720 | − | 1.71260i | 0.102294 | − | 0.0743207i | ||||
\(532\) | 12.1031 | 0.524736 | ||||||||
\(533\) | −6.15825 | + | 4.47423i | −0.266743 | + | 0.193800i | ||||
\(534\) | −18.8366 | − | 57.9732i | −0.815141 | − | 2.50875i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.36054 | + | 16.4981i | −0.231540 | + | 0.712608i | ||||
\(537\) | 10.9439 | + | 33.6818i | 0.472263 | + | 1.45348i | ||||
\(538\) | 18.2094 | + | 56.0427i | 0.785062 | + | 2.41617i | ||||
\(539\) | −0.910429 | + | 2.80201i | −0.0392149 | + | 0.120691i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.88071 | − | 8.86590i | −0.123851 | − | 0.381175i | 0.869839 | − | 0.493336i | \(-0.164223\pi\) |
−0.993690 | + | 0.112161i | \(0.964223\pi\) | |||||||
\(542\) | 17.7033 | − | 12.8622i | 0.760421 | − | 0.552478i | ||||
\(543\) | 20.5347 | 0.881230 | ||||||||
\(544\) | 19.3161 | − | 14.0339i | 0.828169 | − | 0.601700i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 41.2343 | + | 29.9585i | 1.76466 | + | 1.28210i | ||||
\(547\) | −16.2109 | − | 11.7779i | −0.693129 | − | 0.503588i | 0.184558 | − | 0.982822i | \(-0.440915\pi\) |
−0.877687 | + | 0.479234i | \(0.840915\pi\) | |||||||
\(548\) | 2.36974 | − | 7.29332i | 0.101230 | − | 0.311555i | ||||
\(549\) | −14.3244 | −0.611351 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.49914 | 0.234271 | ||||||||
\(552\) | 14.9741 | − | 46.0857i | 0.637342 | − | 1.96154i | ||||
\(553\) | −48.2364 | − | 35.0458i | −2.05122 | − | 1.49030i | ||||
\(554\) | 11.2297 | + | 8.15886i | 0.477105 | + | 0.346637i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 29.8099 | − | 21.6582i | 1.26422 | − | 0.918511i | ||||
\(557\) | 28.9839 | 1.22809 | 0.614043 | − | 0.789272i | \(-0.289542\pi\) | ||||
0.614043 | + | 0.789272i | \(0.289542\pi\) | |||||||
\(558\) | 26.2154 | − | 19.0466i | 1.10979 | − | 0.806306i | ||||
\(559\) | −7.76397 | − | 23.8950i | −0.328381 | − | 1.01065i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.80873 | − | 5.56669i | 0.0763645 | − | 0.235026i | ||||
\(562\) | −7.95880 | − | 24.4947i | −0.335722 | − | 1.03325i | ||||
\(563\) | −4.23431 | − | 13.0319i | −0.178455 | − | 0.549228i | 0.821320 | − | 0.570468i | \(-0.193238\pi\) |
−0.999774 | + | 0.0212408i | \(0.993238\pi\) | |||||||
\(564\) | −13.0268 | + | 40.0923i | −0.548526 | + | 1.68819i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.17371 | − | 6.69000i | −0.0913680 | − | 0.281202i | ||||
\(567\) | −30.8488 | + | 22.4130i | −1.29553 | + | 0.941256i | ||||
\(568\) | 0.498673 | 0.0209239 | ||||||||
\(569\) | −28.0043 | + | 20.3463i | −1.17400 | + | 0.852962i | −0.991482 | − | 0.130241i | \(-0.958425\pi\) |
−0.182519 | + | 0.983202i | \(0.558425\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.3182 | + | 24.9337i | 1.43617 | + | 1.04344i | 0.988825 | + | 0.149082i | \(0.0476317\pi\) |
0.447349 | + | 0.894360i | \(0.352368\pi\) | |||||||
\(572\) | −3.63707 | − | 2.64248i | −0.152073 | − | 0.110488i | ||||
\(573\) | −8.10252 | + | 24.9370i | −0.338488 | + | 1.04176i | ||||
\(574\) | −24.0346 | −1.00318 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −28.7532 | −1.19805 | ||||||||
\(577\) | 10.6008 | − | 32.6259i | 0.441317 | − | 1.35824i | −0.445155 | − | 0.895454i | \(-0.646851\pi\) |
0.886472 | − | 0.462782i | \(-0.153149\pi\) | |||||||
\(578\) | 17.0936 | + | 12.4192i | 0.710999 | + | 0.516571i | ||||
\(579\) | 32.2829 | + | 23.4549i | 1.34163 | + | 0.974752i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −42.4422 | + | 30.8361i | −1.76080 | + | 1.27930i | ||||
\(582\) | 4.54777 | 0.188511 | ||||||||
\(583\) | 0.123876 | − | 0.0900014i | 0.00513043 | − | 0.00372748i | ||||
\(584\) | −15.0831 | − | 46.4210i | −0.624143 | − | 1.92091i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.50278 | − | 13.8581i | 0.186008 | − | 0.572474i | ||||
\(587\) | −9.19392 | − | 28.2960i | −0.379474 | − | 1.16790i | −0.940411 | − | 0.340041i | \(-0.889559\pi\) |
0.560937 | − | 0.827859i | \(-0.310441\pi\) | |||||||
\(588\) | 14.3620 | + | 44.2018i | 0.592280 | + | 1.82285i | ||||
\(589\) | −1.84731 | + | 5.68545i | −0.0761173 | + | 0.234265i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.4700 | − | 56.8449i | −0.759755 | − | 2.33828i | ||||
\(592\) | −3.01821 | + | 2.19286i | −0.124048 | + | 0.0901259i | ||||
\(593\) | 14.8105 | 0.608195 | 0.304098 | − | 0.952641i | \(-0.401645\pi\) | ||||
0.304098 | + | 0.952641i | \(0.401645\pi\) | |||||||
\(594\) | 1.50831 | − | 1.09585i | 0.0618867 | − | 0.0449633i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −33.6303 | − | 24.4339i | −1.37755 | − | 1.00085i | ||||
\(597\) | 15.6193 | + | 11.3481i | 0.639256 | + | 0.464446i | ||||
\(598\) | −12.2075 | + | 37.5709i | −0.499203 | + | 1.53639i | ||||
\(599\) | 27.2394 | 1.11297 | 0.556486 | − | 0.830857i | \(-0.312149\pi\) | ||||
0.556486 | + | 0.830857i | \(0.312149\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.1682 | 1.35296 | 0.676480 | − | 0.736461i | \(-0.263505\pi\) | ||||
0.676480 | + | 0.736461i | \(0.263505\pi\) | |||||||
\(602\) | 24.5143 | − | 75.4474i | 0.999130 | − | 3.07501i | ||||
\(603\) | −9.83912 | − | 7.14854i | −0.400680 | − | 0.291111i | ||||
\(604\) | −47.1463 | − | 34.2538i | −1.91836 | − | 1.39377i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −57.4065 | + | 41.7082i | −2.33198 | + | 1.69428i | ||||
\(607\) | −5.79849 | −0.235353 | −0.117677 | − | 0.993052i | \(-0.537545\pi\) | ||||
−0.117677 | + | 0.993052i | \(0.537545\pi\) | |||||||
\(608\) | 3.73401 | − | 2.71292i | 0.151434 | − | 0.110023i | ||||
\(609\) | 14.2433 | + | 43.8364i | 0.577168 | + | 1.77634i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.39261 | − | 13.5191i | 0.177706 | − | 0.546922i | ||||
\(612\) | −12.3841 | − | 38.1143i | −0.500597 | − | 1.54068i | ||||
\(613\) | −1.25045 | − | 3.84848i | −0.0505051 | − | 0.155439i | 0.922623 | − | 0.385703i | \(-0.126041\pi\) |
−0.973128 | + | 0.230264i | \(0.926041\pi\) | |||||||
\(614\) | 18.5979 | − | 57.2385i | 0.750551 | − | 2.30996i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.81431 | − | 5.58389i | −0.0731008 | − | 0.224981i | ||||
\(617\) | 30.0752 | − | 21.8509i | 1.21078 | − | 0.879683i | 0.215479 | − | 0.976509i | \(-0.430869\pi\) |
0.995301 | + | 0.0968252i | \(0.0308688\pi\) | |||||||
\(618\) | 4.44986 | 0.179000 | ||||||||
\(619\) | 30.5095 | − | 22.1664i | 1.22628 | − | 0.890944i | 0.229674 | − | 0.973268i | \(-0.426234\pi\) |
0.996606 | + | 0.0823236i | \(0.0262341\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.35477 | − | 6.07010i | −0.335266 | − | 0.243585i | ||||
\(622\) | −16.9419 | − | 12.3090i | −0.679309 | − | 0.493547i | ||||
\(623\) | −12.6421 | + | 38.9083i | −0.506494 | + | 1.55883i | ||||
\(624\) | −4.94839 | −0.198094 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −77.2903 | −3.08914 | ||||||||
\(627\) | 0.349647 | − | 1.07610i | 0.0139636 | − | 0.0429754i | ||||
\(628\) | −20.6906 | − | 15.0326i | −0.825644 | − | 0.599866i | ||||
\(629\) | 18.9903 | + | 13.7972i | 0.757192 | + | 0.550132i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.9850 | + | 10.8872i | −0.596543 | + | 0.433414i | −0.844650 | − | 0.535319i | \(-0.820192\pi\) |
0.248107 | + | 0.968733i | \(0.420192\pi\) | |||||||
\(632\) | 54.4362 | 2.16536 | ||||||||
\(633\) | −29.6406 | + | 21.5352i | −1.17811 | + | 0.855947i | ||||
\(634\) | −18.6669 | − | 57.4507i | −0.741356 | − | 2.28166i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.746419 | − | 2.29724i | 0.0295975 | − | 0.0910916i | ||||
\(637\) | −4.84286 | − | 14.9048i | −0.191881 | − | 0.590549i | ||||
\(638\) | −1.99302 | − | 6.13388i | −0.0789043 | − | 0.242843i | ||||
\(639\) | −0.108036 | + | 0.332502i | −0.00427385 | + | 0.0131536i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.09121 | − | 18.7468i | −0.240588 | − | 0.740454i | −0.996331 | − | 0.0855856i | \(-0.972724\pi\) |
0.755743 | − | 0.654869i | \(-0.227276\pi\) | |||||||
\(642\) | 0.313181 | − | 0.227539i | 0.0123603 | − | 0.00898026i | ||||
\(643\) | −42.5897 | −1.67957 | −0.839787 | − | 0.542916i | \(-0.817320\pi\) | ||||
−0.839787 | + | 0.542916i | \(0.817320\pi\) | |||||||
\(644\) | −63.6110 | + | 46.2161i | −2.50662 | + | 1.82117i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.48871 | + | 6.89395i | 0.373328 | + | 0.271239i | ||||
\(647\) | 22.1685 | + | 16.1064i | 0.871535 | + | 0.633207i | 0.930998 | − | 0.365023i | \(-0.118939\pi\) |
−0.0594633 | + | 0.998230i | \(0.518939\pi\) | |||||||
\(648\) | 10.7580 | − | 33.1099i | 0.422616 | − | 1.30068i | ||||
\(649\) | 0.630424 | 0.0247463 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −50.1062 | −1.96382 | ||||||||
\(652\) | −2.05799 | + | 6.33384i | −0.0805971 | + | 0.248052i | ||||
\(653\) | 17.3465 | + | 12.6030i | 0.678820 | + | 0.493192i | 0.872966 | − | 0.487781i | \(-0.162193\pi\) |
−0.194146 | + | 0.980973i | \(0.562193\pi\) | |||||||
\(654\) | 24.2463 | + | 17.6160i | 0.948105 | + | 0.688838i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.88781 | − | 1.37157i | 0.0737064 | − | 0.0535509i | ||||
\(657\) | 34.2200 | 1.33505 | ||||||||
\(658\) | 36.3107 | − | 26.3812i | 1.41554 | − | 1.02845i | ||||
\(659\) | −11.3515 | − | 34.9363i | −0.442191 | − | 1.36092i | −0.885535 | − | 0.464572i | \(-0.846208\pi\) |
0.443344 | − | 0.896351i | \(-0.353792\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.86750 | + | 14.9806i | −0.189324 | + | 0.582678i | −0.999996 | − | 0.00282182i | \(-0.999102\pi\) |
0.810672 | + | 0.585500i | \(0.199102\pi\) | |||||||
\(662\) | −8.71794 | − | 26.8310i | −0.338832 | − | 1.04282i | ||||
\(663\) | 9.62119 | + | 29.6110i | 0.373656 | + | 1.14999i | ||||
\(664\) | 14.8011 | − | 45.5530i | 0.574393 | − | 1.76780i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.60069 | − | 23.3925i | −0.294521 | − | 0.906442i | ||||
\(667\) | −28.9022 | + | 20.9987i | −1.11910 | + | 0.813071i | ||||
\(668\) | 1.21620 | 0.0470561 | ||||||||
\(669\) | −0.707244 | + | 0.513843i | −0.0273436 | + | 0.0198663i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.50743 | − | 1.82175i | −0.0967982 | − | 0.0703280i | ||||
\(672\) | 31.2975 | + | 22.7389i | 1.20733 | + | 0.877173i | ||||
\(673\) | −9.58283 | + | 29.4929i | −0.369391 | + | 1.13687i | 0.577795 | + | 0.816182i | \(0.303913\pi\) |
−0.947186 | + | 0.320686i | \(0.896087\pi\) | |||||||
\(674\) | −70.3690 | −2.71051 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.4259 | −0.785611 | ||||||||
\(677\) | 2.96620 | − | 9.12902i | 0.114000 | − | 0.350857i | −0.877737 | − | 0.479143i | \(-0.840948\pi\) |
0.991737 | + | 0.128286i | \(0.0409476\pi\) | |||||||
\(678\) | 11.2752 | + | 8.19190i | 0.433021 | + | 0.314608i | ||||
\(679\) | −2.46928 | − | 1.79404i | −0.0947624 | − | 0.0688489i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37.8127 | − | 27.4726i | 1.44899 | − | 1.05275i | ||||
\(682\) | 7.01120 | 0.268473 | ||||||||
\(683\) | −0.702510 | + | 0.510403i | −0.0268808 | + | 0.0195300i | −0.601145 | − | 0.799140i | \(-0.705288\pi\) |
0.574264 | + | 0.818670i | \(0.305288\pi\) | |||||||
\(684\) | −2.39398 | − | 7.36793i | −0.0915363 | − | 0.281720i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.79385 | + | 8.59859i | −0.106670 | + | 0.328296i | ||||
\(687\) | −8.47388 | − | 26.0799i | −0.323299 | − | 0.995011i | ||||
\(688\) | 2.38004 | + | 7.32500i | 0.0907381 | + | 0.279263i | ||||
\(689\) | −0.251692 | + | 0.774627i | −0.00958868 | + | 0.0295109i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.05970 | − | 12.4945i | −0.154438 | − | 0.475312i | 0.843665 | − | 0.536869i | \(-0.180393\pi\) |
−0.998104 | + | 0.0615577i | \(0.980393\pi\) | |||||||
\(692\) | −27.4565 | + | 19.9483i | −1.04374 | + | 0.758320i | ||||
\(693\) | 4.11625 | 0.156364 | ||||||||
\(694\) | 25.0820 | − | 18.2231i | 0.952099 | − | 0.691740i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −34.0452 | − | 24.7353i | −1.29048 | − | 0.937589i | ||||
\(697\) | −11.8779 | − | 8.62979i | −0.449907 | − | 0.326877i | ||||
\(698\) | 19.7272 | − | 60.7139i | 0.746684 | − | 2.29806i | ||||
\(699\) | 43.8844 | 1.65986 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.13602 | 0.269524 | 0.134762 | − | 0.990878i | \(-0.456973\pi\) | ||||
0.134762 | + | 0.990878i | \(0.456973\pi\) | |||||||
\(702\) | −3.06458 | + | 9.43181i | −0.115665 | + | 0.355981i | ||||
\(703\) | 3.67103 | + | 2.66716i | 0.138456 | + | 0.100594i | ||||
\(704\) | −5.03313 | − | 3.65678i | −0.189693 | − | 0.137820i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −29.2749 | + | 21.2695i | −1.10178 | + | 0.800486i | ||||
\(707\) | 47.6231 | 1.79105 | ||||||||
\(708\) | 8.04563 | − | 5.84549i | 0.302373 | − | 0.219687i | ||||
\(709\) | −2.47372 | − | 7.61333i | −0.0929025 | − | 0.285925i | 0.893799 | − | 0.448468i | \(-0.148030\pi\) |
−0.986701 | + | 0.162543i | \(0.948030\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.7935 | + | 36.2966i | −0.442290 | + | 1.36123i | ||||
\(712\) | −11.5422 | − | 35.5232i | −0.432562 | − | 1.33129i | ||||
\(713\) | −12.0010 | − | 36.9354i | −0.449442 | − | 1.38324i | ||||
\(714\) | −30.3784 | + | 93.4952i | −1.13688 | + | 3.49897i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.2127 | + | 49.8976i | 0.605898 | + | 1.86476i | ||||
\(717\) | −7.68313 | + | 5.58212i | −0.286932 | + | 0.208468i | ||||
\(718\) | 51.1345 | 1.90832 | ||||||||
\(719\) | 33.3774 | − | 24.2501i | 1.24477 | − | 0.904375i | 0.246859 | − | 0.969051i | \(-0.420602\pi\) |
0.997906 | + | 0.0646763i | \(0.0206015\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.41612 | − | 1.75542i | −0.0899811 | − | 0.0653751i | ||||
\(722\) | −33.9210 | − | 24.6450i | −1.26241 | − | 0.917193i | ||||
\(723\) | 11.5155 | − | 35.4409i | 0.428265 | − | 1.31806i | ||||
\(724\) | 30.4210 | 1.13059 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 57.5825 | 2.13709 | ||||||||
\(727\) | −12.1321 | + | 37.3387i | −0.449954 | + | 1.38482i | 0.427005 | + | 0.904249i | \(0.359569\pi\) |
−0.876959 | + | 0.480566i | \(0.840431\pi\) | |||||||
\(728\) | 25.2664 | + | 18.3571i | 0.936436 | + | 0.680360i | ||||
\(729\) | 10.7490 | + | 7.80957i | 0.398109 | + | 0.289243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.2050 | − | 28.4841i | 1.45005 | − | 1.05352i | ||||
\(732\) | −48.8924 | −1.80711 | ||||||||
\(733\) | 0.737868 | − | 0.536092i | 0.0272538 | − | 0.0198010i | −0.574075 | − | 0.818803i | \(-0.694638\pi\) |
0.601329 | + | 0.799002i | \(0.294638\pi\) | |||||||
\(734\) | 8.70498 | + | 26.7912i | 0.321307 | + | 0.988880i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.26570 | + | 28.5169i | −0.341538 | + | 1.05115i | ||||
\(737\) | −0.813158 | − | 2.50264i | −0.0299531 | − | 0.0921860i | ||||
\(738\) | 4.75402 | + | 14.6314i | 0.174998 | + | 0.538588i | ||||
\(739\) | −3.61367 | + | 11.1217i | −0.132931 | + | 0.409119i | −0.995262 | − | 0.0972247i | \(-0.969003\pi\) |
0.862331 | + | 0.506344i | \(0.169003\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.85988 | + | 5.72413i | 0.0683245 | + | 0.210281i | ||||
\(742\) | −2.08056 | + | 1.51162i | −0.0763798 | + | 0.0554932i | ||||
\(743\) | −11.5631 | −0.424211 | −0.212105 | − | 0.977247i | \(-0.568032\pi\) | ||||
−0.212105 | + | 0.977247i | \(0.568032\pi\) | |||||||
\(744\) | 37.0101 | − | 26.8894i | 1.35685 | − | 0.985813i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13.3349 | − | 9.68837i | −0.488225 | − | 0.354717i | ||||
\(747\) | 27.1669 | + | 19.7379i | 0.993986 | + | 0.722173i | ||||
\(748\) | 2.67953 | − | 8.24673i | 0.0979732 | − | 0.301530i | ||||
\(749\) | −0.259808 | −0.00949318 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.2430 | −0.994112 | −0.497056 | − | 0.867718i | \(-0.665586\pi\) | ||||
−0.497056 | + | 0.867718i | \(0.665586\pi\) | |||||||
\(752\) | −1.34655 | + | 4.14425i | −0.0491036 | + | 0.151125i | ||||
\(753\) | −22.1126 | − | 16.0658i | −0.805828 | − | 0.585469i | ||||
\(754\) | 27.7551 | + | 20.1652i | 1.01078 | + | 0.734374i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −15.9689 | + | 11.6021i | −0.580784 | + | 0.421964i | ||||
\(757\) | −17.1080 | −0.621800 | −0.310900 | − | 0.950443i | \(-0.600630\pi\) | ||||
−0.310900 | + | 0.950443i | \(0.600630\pi\) | |||||||
\(758\) | −40.4655 | + | 29.3999i | −1.46977 | + | 1.06785i | ||||
\(759\) | 2.27147 | + | 6.99088i | 0.0824493 | + | 0.253753i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.6553 | − | 35.8713i | 0.422504 | − | 1.30033i | −0.482861 | − | 0.875697i | \(-0.660402\pi\) |
0.905364 | − | 0.424635i | \(-0.139598\pi\) | |||||||
\(762\) | 8.18327 | + | 25.1855i | 0.296449 | + | 0.912375i | ||||
\(763\) | −6.21562 | − | 19.1297i | −0.225021 | − | 0.692542i | ||||
\(764\) | −12.0034 | + | 36.9428i | −0.434269 | + | 1.33654i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.8850 | + | 55.0445i | 0.646213 | + | 1.98884i | ||||
\(767\) | −2.71297 | + | 1.97109i | −0.0979598 | + | 0.0711720i | ||||
\(768\) | −48.0682 | −1.73451 | ||||||||
\(769\) | 4.80028 | − | 3.48761i | 0.173102 | − | 0.125766i | −0.497861 | − | 0.867257i | \(-0.665881\pi\) |
0.670963 | + | 0.741491i | \(0.265881\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −35.2338 | − | 25.5989i | −1.26892 | − | 0.921921i | ||||
\(772\) | 47.8253 | + | 34.7471i | 1.72127 | + | 1.25058i | ||||
\(773\) | −7.28997 | + | 22.4362i | −0.262202 | + | 0.806975i | 0.730123 | + | 0.683316i | \(0.239463\pi\) |
−0.992325 | + | 0.123659i | \(0.960537\pi\) | |||||||
\(774\) | −50.7786 | −1.82520 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.78666 | 0.100035 | ||||||||
\(777\) | −11.7529 | + | 36.1718i | −0.421634 | + | 1.29766i | ||||
\(778\) | −66.6444 | − | 48.4200i | −2.38932 | − | 1.73594i | ||||
\(779\) | −2.29613 | − | 1.66824i | −0.0822674 | − | 0.0597708i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0611983 | + | 0.0444632i | −0.00218985 | + | 0.00159102i | ||||
\(782\) | −76.1952 | −2.72473 | ||||||||
\(783\) | −7.25561 | + | 5.27151i | −0.259294 | + | 0.188388i | ||||
\(784\) | 1.48457 | + | 4.56905i | 0.0530205 | + | 0.163180i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.47393 | + | 13.7693i | −0.159580 | + | 0.491136i | ||||
\(787\) | 5.63359 | + | 17.3384i | 0.200816 | + | 0.618048i | 0.999859 | + | 0.0167744i | \(0.00533970\pi\) |
−0.799043 | + | 0.601273i | \(0.794660\pi\) | |||||||
\(788\) | −27.3623 | − | 84.2125i | −0.974741 | − | 2.99994i | ||||
\(789\) | 4.80020 | − | 14.7735i | 0.170892 | − | 0.525950i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.89043 | − | 8.89584i | −0.102772 | − | 0.316300i | ||||
\(792\) | −3.04040 | + | 2.20898i | −0.108036 | + | 0.0784926i | ||||
\(793\) | 16.4864 | 0.585451 | ||||||||
\(794\) | −10.3446 | + | 7.51583i | −0.367118 | + | 0.266727i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.1391 | + | 16.8116i | 0.820145 | + | 0.595870i | ||||
\(797\) | −8.76130 | − | 6.36546i | −0.310341 | − | 0.225476i | 0.421702 | − | 0.906735i | \(-0.361433\pi\) |
−0.732043 | + | 0.681259i | \(0.761433\pi\) | |||||||
\(798\) | −5.87249 | + | 18.0737i | −0.207884 | + | 0.639801i | ||||
\(799\) | 27.4171 | 0.969948 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 26.1865 | 0.925256 | ||||||||
\(802\) | −17.8596 | + | 54.9663i | −0.630646 | + | 1.94093i | ||||
\(803\) | 5.99007 | + | 4.35204i | 0.211385 | + | 0.153580i | ||||
\(804\) | −33.5830 | − | 24.3995i | −1.18438 | − | 0.860505i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −30.1721 | + | 21.9213i | −1.06277 | + | 0.772145i | ||||
\(807\) | −58.3242 | −2.05311 | ||||||||
\(808\) | −35.1759 | + | 25.5568i | −1.23749 | + | 0.899086i | ||||
\(809\) | 13.8494 | + | 42.6242i | 0.486920 | + | 1.49859i | 0.829180 | + | 0.558981i | \(0.188808\pi\) |
−0.342260 | + | 0.939605i | \(0.611192\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.946507 | + | 2.91305i | −0.0332363 | + | 0.102291i | −0.966298 | − | 0.257424i | \(-0.917126\pi\) |
0.933062 | + | 0.359715i | \(0.117126\pi\) | |||||||
\(812\) | 21.1006 | + | 64.9411i | 0.740487 | + | 2.27899i | ||||
\(813\) | 6.69289 | + | 20.5986i | 0.234730 | + | 0.722425i | ||||
\(814\) | 1.64455 | − | 5.06140i | 0.0576414 | − | 0.177402i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.94937 | − | 9.07721i | −0.103248 | − | 0.317766i | ||||
\(817\) | 7.57876 | − | 5.50629i | 0.265147 | − | 0.192641i | ||||
\(818\) | −9.14524 | −0.319756 | ||||||||
\(819\) | −17.7140 | + | 12.8699i | −0.618976 | + | 0.449712i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.4400 | − | 11.9444i | −0.573761 | − | 0.416862i | 0.262708 | − | 0.964875i | \(-0.415384\pi\) |
−0.836470 | + | 0.548013i | \(0.815384\pi\) | |||||||
\(822\) | 9.74137 | + | 7.07752i | 0.339769 | + | 0.246857i | ||||
\(823\) | 15.4623 | − | 47.5879i | 0.538980 | − | 1.65881i | −0.195907 | − | 0.980622i | \(-0.562765\pi\) |
0.734888 | − | 0.678189i | \(-0.237235\pi\) | |||||||
\(824\) | 2.72666 | 0.0949879 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.5883 | −0.368413 | ||||||||
\(827\) | 9.77399 | − | 30.0812i | 0.339875 | − | 1.04603i | −0.624396 | − | 0.781108i | \(-0.714655\pi\) |
0.964271 | − | 0.264919i | \(-0.0853453\pi\) | |||||||
\(828\) | 40.7169 | + | 29.5825i | 1.41501 | + | 1.02806i | ||||
\(829\) | −26.8083 | − | 19.4774i | −0.931090 | − | 0.676477i | 0.0151691 | − | 0.999885i | \(-0.495171\pi\) |
−0.946260 | + | 0.323408i | \(0.895171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.1149 | + | 8.07543i | −0.385571 | + | 0.280133i | ||||
\(832\) | 33.0930 | 1.14729 | ||||||||
\(833\) | 24.4545 | − | 17.7672i | 0.847298 | − | 0.615598i | ||||
\(834\) | 17.8784 | + | 55.0241i | 0.619078 | + | 1.90533i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.517983 | − | 1.59419i | 0.0179148 | − | 0.0551361i | ||||
\(837\) | −3.01274 | − | 9.27227i | −0.104136 | − | 0.320496i | ||||
\(838\) | 3.42586 | + | 10.5437i | 0.118344 | + | 0.364226i | ||||
\(839\) | 3.20925 | − | 9.87707i | 0.110796 | − | 0.340994i | −0.880251 | − | 0.474508i | \(-0.842626\pi\) |
0.991047 | + | 0.133514i | \(0.0426260\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.625759 | + | 1.92589i | 0.0215779 | + | 0.0664099i | ||||
\(842\) | 30.2191 | − | 21.9554i | 1.04142 | − | 0.756634i | ||||
\(843\) | 25.4918 | 0.877986 | ||||||||
\(844\) | −43.9110 | + | 31.9032i | −1.51148 | + | 1.09815i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −23.2422 | − | 16.8864i | −0.799082 | − | 0.580567i | ||||
\(847\) | −31.2653 | − | 22.7156i | −1.07429 | − | 0.780517i | ||||
\(848\) | 0.0771558 | − | 0.237461i | 0.00264954 | − | 0.00815445i | ||||
\(849\) | 6.96235 | 0.238947 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29.4787 | −1.01052 | ||||||||
\(852\) | −0.368752 | + | 1.13490i | −0.0126332 | + | 0.0388811i | ||||
\(853\) | −7.53563 | − | 5.47496i | −0.258015 | − | 0.187459i | 0.451256 | − | 0.892394i | \(-0.350976\pi\) |
−0.709272 | + | 0.704935i | \(0.750976\pi\) | |||||||
\(854\) | 42.1135 | + | 30.5972i | 1.44109 | + | 1.04702i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.191902 | − | 0.139425i | 0.00655909 | − | 0.00476546i | ||||
\(857\) | 34.0314 | 1.16249 | 0.581245 | − | 0.813729i | \(-0.302566\pi\) | ||||
0.581245 | + | 0.813729i | \(0.302566\pi\) | |||||||
\(858\) | 5.71077 | − | 4.14912i | 0.194963 | − | 0.141649i | ||||
\(859\) | 10.3287 | + | 31.7884i | 0.352410 | + | 1.08461i | 0.957496 | + | 0.288446i | \(0.0931386\pi\) |
−0.605086 | + | 0.796160i | \(0.706861\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.35114 | − | 22.6245i | 0.250526 | − | 0.771040i | ||||
\(862\) | 29.7364 | + | 91.5193i | 1.01283 | + | 3.11716i | ||||
\(863\) | −5.12659 | − | 15.7780i | −0.174511 | − | 0.537091i | 0.825099 | − | 0.564987i | \(-0.191119\pi\) |
−0.999611 | + | 0.0278969i | \(0.991119\pi\) | |||||||
\(864\) | −2.32606 | + | 7.15889i | −0.0791343 | + | 0.243550i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.9153 | + | 33.5939i | 0.370918 | + | 1.14157i | ||||
\(867\) | −16.9188 | + | 12.2922i | −0.574592 | + | 0.417465i | ||||
\(868\) | −74.2296 | −2.51952 | ||||||||
\(869\) | −6.68054 | + | 4.85370i | −0.226622 | + | 0.164650i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.3242 | + | 8.22748i | 0.383704 | + | 0.278778i | ||||
\(872\) | 14.8570 | + | 10.7942i | 0.503120 | + | 0.365538i | ||||
\(873\) | −0.603724 | + | 1.85807i | −0.0204330 | + | 0.0628862i | ||||
\(874\) | −14.7294 | −0.498229 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 116.800 | 3.94632 | ||||||||
\(877\) | 10.1833 | − | 31.3409i | 0.343865 | − | 1.05831i | −0.618324 | − | 0.785923i | \(-0.712188\pi\) |
0.962189 | − | 0.272383i | \(-0.0878118\pi\) | |||||||
\(878\) | 32.2162 | + | 23.4064i | 1.08724 | + | 0.789929i | ||||
\(879\) | 11.6679 | + | 8.47721i | 0.393548 | + | 0.285929i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.5119 | − | 29.4337i | 1.36488 | − | 0.991645i | 0.366765 | − | 0.930314i | \(-0.380465\pi\) |
0.998117 | − | 0.0613312i | \(-0.0195346\pi\) | |||||||
\(882\) | −31.6737 | −1.06651 | ||||||||
\(883\) | 10.1398 | − | 7.36700i | 0.341232 | − | 0.247919i | −0.403950 | − | 0.914781i | \(-0.632363\pi\) |
0.745181 | + | 0.666862i | \(0.232363\pi\) | |||||||
\(884\) | 14.2532 | + | 43.8670i | 0.479389 | + | 1.47541i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.4391 | − | 78.2936i | 0.854645 | − | 2.63033i | ||||
\(887\) | −8.32361 | − | 25.6174i | −0.279480 | − | 0.860150i | −0.987999 | − | 0.154459i | \(-0.950637\pi\) |
0.708520 | − | 0.705691i | \(-0.249363\pi\) | |||||||
\(888\) | −10.7304 | − | 33.0248i | −0.360089 | − | 1.10824i | ||||
\(889\) | 5.49214 | − | 16.9031i | 0.184200 | − | 0.566911i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.63192 | + | 5.02254i | 0.0546715 | + | 0.168261i | ||||
\(892\) | −1.04774 | + | 0.761229i | −0.0350810 | + | 0.0254878i | ||||
\(893\) | 5.30004 | 0.177359 | ||||||||
\(894\) | 52.8050 | − | 38.3651i | 1.76606 | − | 1.28312i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 57.3460 | + | 41.6643i | 1.91579 | + | 1.39191i | ||||
\(897\) | −31.6329 | − | 22.9826i | −1.05619 | − | 0.767368i | ||||
\(898\) | −14.8670 | + | 45.7560i | −0.496119 | + | 1.52690i | ||||
\(899\) | −33.7268 | −1.12485 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.57097 | −0.0523366 | ||||||||
\(902\) | −1.02862 | + | 3.16577i | −0.0342493 | + | 0.105409i | ||||
\(903\) | 63.5231 | + | 46.1522i | 2.11392 | + | 1.53585i | ||||
\(904\) | 6.90889 | + | 5.01961i | 0.229786 | + | 0.166950i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 74.0272 | − | 53.7839i | 2.45939 | − | 1.78685i | ||||
\(907\) | 28.6510 | 0.951342 | 0.475671 | − | 0.879623i | \(-0.342205\pi\) | ||||
0.475671 | + | 0.879623i | \(0.342205\pi\) | |||||||
\(908\) | 56.0174 | − | 40.6991i | 1.85900 | − | 1.35065i | ||||
\(909\) | −9.41982 | − | 28.9912i | −0.312436 | − | 0.961578i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.75047 | + | 8.46508i | −0.0911271 | + | 0.280461i | −0.986225 | − | 0.165409i | \(-0.947106\pi\) |
0.895098 | + | 0.445870i | \(0.147106\pi\) | |||||||
\(912\) | −0.570146 | − | 1.75473i | −0.0188794 | − | 0.0581048i | ||||
\(913\) | 2.24522 | + | 6.91008i | 0.0743060 | + | 0.228690i | ||||
\(914\) | 30.0219 | − | 92.3980i | 0.993037 | − | 3.05625i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.5536 | − | 38.6359i | −0.414782 | − | 1.27657i | ||||
\(917\) | 7.86102 | − | 5.71137i | 0.259594 | − | 0.188606i | ||||
\(918\) | −19.1280 | −0.631320 | ||||||||
\(919\) | −13.9071 | + | 10.1041i | −0.458753 | + | 0.333303i | −0.793042 | − | 0.609167i | \(-0.791504\pi\) |
0.334289 | + | 0.942471i | \(0.391504\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 48.1921 | + | 35.0136i | 1.58798 | + | 1.15374i | ||||
\(922\) | −20.0951 | − | 14.5999i | −0.661796 | − | 0.480823i | ||||
\(923\) | 0.124343 | − | 0.382687i | 0.00409279 | − | 0.0125963i | ||||
\(924\) | 14.0497 | 0.462200 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18.2141 | −0.598554 | ||||||||
\(927\) | −0.590726 | + | 1.81807i | −0.0194020 | + | 0.0597132i | ||||
\(928\) | 21.0665 | + | 15.3057i | 0.691542 | + | 0.502435i | ||||
\(929\) | −28.1367 | − | 20.4425i | −0.923137 | − | 0.670698i | 0.0211662 | − | 0.999776i | \(-0.493262\pi\) |
−0.944303 | + | 0.329078i | \(0.893262\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.72733 | − | 3.43461i | 0.154932 | − | 0.112565i | ||||
\(932\) | 65.0123 | 2.12955 | ||||||||
\(933\) | 16.7686 | − | 12.1831i | 0.548981 | − | 0.398858i | ||||
\(934\) | 3.58036 | + | 11.0192i | 0.117153 | + | 0.360560i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.17747 | − | 19.0123i | 0.201917 | − | 0.621437i | ||||
\(937\) | 5.11071 | + | 15.7291i | 0.166960 | + | 0.513849i | 0.999175 | − | 0.0406033i | \(-0.0129280\pi\) |
−0.832216 | + | 0.554452i | \(0.812928\pi\) | |||||||
\(938\) | 13.6574 | + | 42.0331i | 0.445929 | + | 1.37243i | ||||
\(939\) | 23.6398 | − | 72.7557i | 0.771455 | − | 2.37429i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.7310 | + | 39.1818i | 0.415017 | + | 1.27729i | 0.912235 | + | 0.409666i | \(0.134355\pi\) |
−0.497218 | + | 0.867626i | \(0.665645\pi\) | |||||||
\(942\) | 32.4875 | − | 23.6036i | 1.05850 | − | 0.769045i | ||||
\(943\) | 18.4381 | 0.600428 | ||||||||
\(944\) | 0.831660 | − | 0.604236i | 0.0270682 | − | 0.0196662i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.88857 | − | 6.45792i | −0.288992 | − | 0.209965i | ||||
\(947\) | −30.0234 | − | 21.8133i | −0.975629 | − | 0.708836i | −0.0189019 | − | 0.999821i | \(-0.506017\pi\) |
−0.956728 | + | 0.290985i | \(0.906017\pi\) | |||||||
\(948\) | −40.2537 | + | 123.888i | −1.30738 | + | 4.02370i | ||||
\(949\) | −39.3849 | −1.27849 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 59.7895 | 1.93881 | ||||||||
\(952\) | −18.6145 | + | 57.2894i | −0.603298 | + | 1.85676i | ||||
\(953\) | 16.9054 | + | 12.2825i | 0.547619 | + | 0.397869i | 0.826907 | − | 0.562339i | \(-0.190098\pi\) |
−0.279288 | + | 0.960207i | \(0.590098\pi\) | |||||||
\(954\) | 1.33175 | + | 0.967573i | 0.0431170 | + | 0.0313263i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −11.3821 | + | 8.26960i | −0.368124 | + | 0.267458i | ||||
\(957\) | 6.38358 | 0.206352 | ||||||||
\(958\) | −30.8588 | + | 22.4202i | −0.997002 | + | 0.724364i | ||||
\(959\) | −2.49723 | − | 7.68570i | −0.0806399 | − | 0.248184i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.75025 | − | 5.38670i | 0.0564595 | − | 0.173765i | ||||
\(962\) | 8.74788 | + | 26.9232i | 0.282043 | + | 0.868039i | ||||
\(963\) | 0.0513898 | + | 0.158162i | 0.00165601 | + | 0.00509669i | ||||
\(964\) | 17.0595 | − | 52.5038i | 0.549450 | − | 1.69103i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −38.1505 | − | 117.415i | −1.22747 | − | 3.77777i | ||||
\(967\) | 6.69912 | − | 4.86720i | 0.215429 | − | 0.156518i | −0.474838 | − | 0.880073i | \(-0.657493\pi\) |
0.690267 | + | 0.723555i | \(0.257493\pi\) | |||||||
\(968\) | 35.2838 | 1.13407 | ||||||||
\(969\) | −9.39167 | + | 6.82345i | −0.301704 | + | 0.219201i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.3643 | + | 15.5220i | 0.685612 | + | 0.498126i | 0.875215 | − | 0.483735i | \(-0.160720\pi\) |
−0.189603 | + | 0.981861i | \(0.560720\pi\) | |||||||
\(972\) | 54.0689 | + | 39.2834i | 1.73426 | + | 1.26001i | ||||
\(973\) | 11.9990 | − | 36.9290i | 0.384669 | − | 1.18389i | ||||
\(974\) | 2.03885 | 0.0653289 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.05390 | −0.161771 | ||||||||
\(977\) | −7.82677 | + | 24.0883i | −0.250401 | + | 0.770654i | 0.744300 | + | 0.667845i | \(0.232783\pi\) |
−0.994701 | + | 0.102809i | \(0.967217\pi\) | |||||||
\(978\) | −8.45983 | − | 6.14643i | −0.270516 | − | 0.196541i | ||||
\(979\) | 4.58384 | + | 3.33036i | 0.146500 | + | 0.106439i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.4160 | + | 7.56769i | −0.332558 | + | 0.241618i | ||||
\(982\) | −28.4059 | −0.906470 | ||||||||
\(983\) | −4.14873 | + | 3.01423i | −0.132324 | + | 0.0961390i | −0.651978 | − | 0.758238i | \(-0.726061\pi\) |
0.519654 | + | 0.854377i | \(0.326061\pi\) | |||||||
\(984\) | 6.71158 | + | 20.6561i | 0.213957 | + | 0.658493i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −20.4479 | + | 62.9322i | −0.651194 | + | 2.00417i | ||||
\(987\) | 13.7276 | + | 42.2492i | 0.436954 | + | 1.34481i | ||||
\(988\) | 2.75531 | + | 8.47998i | 0.0876582 | + | 0.269784i | ||||
\(989\) | −18.8062 | + | 57.8795i | −0.598002 | + | 1.84046i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.20120 | − | 25.2407i | −0.260520 | − | 0.801797i | −0.992692 | − | 0.120677i | \(-0.961493\pi\) |
0.732172 | − | 0.681120i | \(-0.238507\pi\) | |||||||
\(992\) | −22.9011 | + | 16.6386i | −0.727110 | + | 0.528277i | ||||
\(993\) | 27.9233 | 0.886120 | ||||||||
\(994\) | 1.02785 | − | 0.746780i | 0.0326016 | − | 0.0236864i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 92.7267 | + | 67.3699i | 2.93816 | + | 2.13470i | ||||
\(997\) | 35.9991 | + | 26.1549i | 1.14010 | + | 0.828332i | 0.987133 | − | 0.159899i | \(-0.0511168\pi\) |
0.152968 | + | 0.988231i | \(0.451117\pi\) | |||||||
\(998\) | 2.40514 | − | 7.40227i | 0.0761335 | − | 0.234315i | ||||
\(999\) | −7.40034 | −0.234136 |
(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 | 625.2.d.p.501.2 | 16 | ||
5.2 | odd | 4 | 625.2.e.k.124.2 | 32 | |||
5.3 | odd | 4 | 625.2.e.k.124.7 | 32 | |||
5.4 | even | 2 | 625.2.d.n.501.3 | 16 | |||
25.2 | odd | 20 | 625.2.e.j.249.2 | 32 | |||
25.3 | odd | 20 | 625.2.e.j.374.2 | 32 | |||
25.4 | even | 10 | 625.2.d.m.251.2 | 16 | |||
25.6 | even | 5 | inner | 625.2.d.p.126.2 | 16 | ||
25.8 | odd | 20 | 625.2.e.k.499.2 | 32 | |||
25.9 | even | 10 | 625.2.a.g.1.6 | yes | 8 | ||
25.11 | even | 5 | 625.2.d.q.376.3 | 16 | |||
25.12 | odd | 20 | 625.2.b.d.624.3 | 16 | |||
25.13 | odd | 20 | 625.2.b.d.624.14 | 16 | |||
25.14 | even | 10 | 625.2.d.m.376.2 | 16 | |||
25.16 | even | 5 | 625.2.a.e.1.3 | ✓ | 8 | ||
25.17 | odd | 20 | 625.2.e.k.499.7 | 32 | |||
25.19 | even | 10 | 625.2.d.n.126.3 | 16 | |||
25.21 | even | 5 | 625.2.d.q.251.3 | 16 | |||
25.22 | odd | 20 | 625.2.e.j.374.7 | 32 | |||
25.23 | odd | 20 | 625.2.e.j.249.7 | 32 | |||
75.41 | odd | 10 | 5625.2.a.be.1.6 | 8 | |||
75.59 | odd | 10 | 5625.2.a.s.1.3 | 8 | |||
100.59 | odd | 10 | 10000.2.a.be.1.8 | 8 | |||
100.91 | odd | 10 | 10000.2.a.bn.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
625.2.a.e.1.3 | ✓ | 8 | 25.16 | even | 5 | ||
625.2.a.g.1.6 | yes | 8 | 25.9 | even | 10 | ||
625.2.b.d.624.3 | 16 | 25.12 | odd | 20 | |||
625.2.b.d.624.14 | 16 | 25.13 | odd | 20 | |||
625.2.d.m.251.2 | 16 | 25.4 | even | 10 | |||
625.2.d.m.376.2 | 16 | 25.14 | even | 10 | |||
625.2.d.n.126.3 | 16 | 25.19 | even | 10 | |||
625.2.d.n.501.3 | 16 | 5.4 | even | 2 | |||
625.2.d.p.126.2 | 16 | 25.6 | even | 5 | inner | ||
625.2.d.p.501.2 | 16 | 1.1 | even | 1 | trivial | ||
625.2.d.q.251.3 | 16 | 25.21 | even | 5 | |||
625.2.d.q.376.3 | 16 | 25.11 | even | 5 | |||
625.2.e.j.249.2 | 32 | 25.2 | odd | 20 | |||
625.2.e.j.249.7 | 32 | 25.23 | odd | 20 | |||
625.2.e.j.374.2 | 32 | 25.3 | odd | 20 | |||
625.2.e.j.374.7 | 32 | 25.22 | odd | 20 | |||
625.2.e.k.124.2 | 32 | 5.2 | odd | 4 | |||
625.2.e.k.124.7 | 32 | 5.3 | odd | 4 | |||
625.2.e.k.499.2 | 32 | 25.8 | odd | 20 | |||
625.2.e.k.499.7 | 32 | 25.17 | odd | 20 | |||
5625.2.a.s.1.3 | 8 | 75.59 | odd | 10 | |||
5625.2.a.be.1.6 | 8 | 75.41 | odd | 10 | |||
10000.2.a.be.1.8 | 8 | 100.59 | odd | 10 | |||
10000.2.a.bn.1.1 | 8 | 100.91 | odd | 10 |