Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 6 x^{10} - 12 x^{9} + 43 x^{8} + 72 x^{7} + 155 x^{6} + 162 x^{5} + 541 x^{4} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 366.1 | ||
Root | \(0.0651271 + 0.200441i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.366 |
Dual form | 605.2.g.p.81.1 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.22061 | + | 1.61337i | −1.57021 | + | 1.14082i | −0.643253 | + | 0.765654i | \(0.722416\pi\) |
−0.926956 | + | 0.375170i | \(0.877584\pi\) | |||||||
\(3\) | −0.0651271 | − | 0.200441i | −0.0376012 | − | 0.115725i | 0.930494 | − | 0.366307i | \(-0.119378\pi\) |
−0.968095 | + | 0.250582i | \(0.919378\pi\) | |||||||
\(4\) | 1.71012 | − | 5.26321i | 0.855061 | − | 2.63161i | ||||
\(5\) | 0.809017 | + | 0.587785i | 0.361803 | + | 0.262866i | ||||
\(6\) | 0.468007 | + | 0.340027i | 0.191063 | + | 0.138815i | ||||
\(7\) | 0.717944 | − | 2.20960i | 0.271357 | − | 0.835152i | −0.718803 | − | 0.695214i | \(-0.755310\pi\) |
0.990160 | − | 0.139938i | \(-0.0446903\pi\) | |||||||
\(8\) | 2.99759 | + | 9.22564i | 1.05981 | + | 3.26175i | ||||
\(9\) | 2.39112 | − | 1.73725i | 0.797039 | − | 0.579082i | ||||
\(10\) | −2.74483 | −0.867990 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.16634 | −0.336693 | ||||||||
\(13\) | −0.432072 | + | 0.313919i | −0.119835 | + | 0.0870654i | −0.646089 | − | 0.763262i | \(-0.723596\pi\) |
0.526253 | + | 0.850328i | \(0.323596\pi\) | |||||||
\(14\) | 1.97063 | + | 6.06498i | 0.526673 | + | 1.62093i | ||||
\(15\) | 0.0651271 | − | 0.200441i | 0.0168158 | − | 0.0517536i | ||||
\(16\) | −12.5865 | − | 9.14464i | −3.14663 | − | 2.28616i | ||||
\(17\) | 1.95904 | + | 1.42333i | 0.475138 | + | 0.345208i | 0.799440 | − | 0.600746i | \(-0.205130\pi\) |
−0.324302 | + | 0.945953i | \(0.605130\pi\) | |||||||
\(18\) | −2.50692 | + | 7.71550i | −0.590886 | + | 1.81856i | ||||
\(19\) | −1.53136 | − | 4.71304i | −0.351318 | − | 1.08125i | −0.958114 | − | 0.286388i | \(-0.907546\pi\) |
0.606796 | − | 0.794858i | \(-0.292454\pi\) | |||||||
\(20\) | 4.47716 | − | 3.25284i | 1.00112 | − | 0.727358i | ||||
\(21\) | −0.489652 | −0.106851 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.53407 | −0.945419 | −0.472709 | − | 0.881218i | \(-0.656724\pi\) | ||||
−0.472709 | + | 0.881218i | \(0.656724\pi\) | |||||||
\(24\) | 1.65397 | − | 1.20168i | 0.337615 | − | 0.245292i | ||||
\(25\) | 0.309017 | + | 0.951057i | 0.0618034 | + | 0.190211i | ||||
\(26\) | 0.452997 | − | 1.39418i | 0.0888401 | − | 0.273422i | ||||
\(27\) | −1.01546 | − | 0.737773i | −0.195425 | − | 0.141984i | ||||
\(28\) | −10.4018 | − | 7.55738i | −1.96576 | − | 1.42821i | ||||
\(29\) | 1.69640 | − | 5.22097i | 0.315013 | − | 0.969510i | −0.660736 | − | 0.750618i | \(-0.729756\pi\) |
0.975749 | − | 0.218892i | \(-0.0702441\pi\) | |||||||
\(30\) | 0.178763 | + | 0.550175i | 0.0326375 | + | 0.100448i | ||||
\(31\) | −0.844952 | + | 0.613894i | −0.151758 | + | 0.110259i | −0.661073 | − | 0.750321i | \(-0.729899\pi\) |
0.509315 | + | 0.860580i | \(0.329899\pi\) | |||||||
\(32\) | 23.3026 | 4.11936 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.64663 | −1.13989 | ||||||||
\(35\) | 1.87960 | − | 1.36561i | 0.317711 | − | 0.230830i | ||||
\(36\) | −5.05440 | − | 15.5559i | −0.842401 | − | 2.59264i | ||||
\(37\) | 2.31443 | − | 7.12308i | 0.380490 | − | 1.17103i | −0.559210 | − | 0.829026i | \(-0.688895\pi\) |
0.939700 | − | 0.342001i | \(-0.111105\pi\) | |||||||
\(38\) | 11.0044 | + | 7.99518i | 1.78515 | + | 1.29699i | ||||
\(39\) | 0.0910617 | + | 0.0661602i | 0.0145815 | + | 0.0105941i | ||||
\(40\) | −2.99759 | + | 9.22564i | −0.473961 | + | 1.45870i | ||||
\(41\) | −3.27626 | − | 10.0833i | −0.511666 | − | 1.57475i | −0.789267 | − | 0.614050i | \(-0.789539\pi\) |
0.277600 | − | 0.960697i | \(-0.410461\pi\) | |||||||
\(42\) | 1.08733 | − | 0.789989i | 0.167778 | − | 0.121898i | ||||
\(43\) | −4.32331 | −0.659299 | −0.329650 | − | 0.944103i | \(-0.606931\pi\) | ||||
−0.329650 | + | 0.944103i | \(0.606931\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.95558 | 0.440592 | ||||||||
\(46\) | 10.0684 | − | 7.31513i | 1.48451 | − | 1.07856i | ||||
\(47\) | 2.09160 | + | 6.43727i | 0.305091 | + | 0.938973i | 0.979643 | + | 0.200746i | \(0.0643366\pi\) |
−0.674553 | + | 0.738227i | \(0.735663\pi\) | |||||||
\(48\) | −1.01323 | + | 3.11842i | −0.146248 | + | 0.450105i | ||||
\(49\) | 1.29622 | + | 0.941756i | 0.185174 | + | 0.134537i | ||||
\(50\) | −2.22061 | − | 1.61337i | −0.314042 | − | 0.228165i | ||||
\(51\) | 0.157706 | − | 0.485370i | 0.0220833 | − | 0.0679653i | ||||
\(52\) | 0.913325 | + | 2.81093i | 0.126655 | + | 0.389805i | ||||
\(53\) | 3.66814 | − | 2.66506i | 0.503858 | − | 0.366074i | −0.306631 | − | 0.951829i | \(-0.599202\pi\) |
0.810489 | + | 0.585754i | \(0.199202\pi\) | |||||||
\(54\) | 3.44523 | 0.468837 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 22.5371 | 3.01165 | ||||||||
\(57\) | −0.844952 | + | 0.613894i | −0.111917 | + | 0.0813122i | ||||
\(58\) | 4.65631 | + | 14.3307i | 0.611404 | + | 1.88171i | ||||
\(59\) | −1.99169 | + | 6.12978i | −0.259296 | + | 0.798030i | 0.733657 | + | 0.679520i | \(0.237812\pi\) |
−0.992953 | + | 0.118510i | \(0.962188\pi\) | |||||||
\(60\) | −0.943587 | − | 0.685556i | −0.121817 | − | 0.0885049i | ||||
\(61\) | 5.50019 | + | 3.99612i | 0.704227 | + | 0.511651i | 0.881306 | − | 0.472546i | \(-0.156665\pi\) |
−0.177079 | + | 0.984197i | \(0.556665\pi\) | |||||||
\(62\) | 0.885873 | − | 2.72644i | 0.112506 | − | 0.346258i | ||||
\(63\) | −2.12194 | − | 6.53066i | −0.267339 | − | 0.822786i | ||||
\(64\) | −26.5730 | + | 19.3064i | −3.32163 | + | 2.41330i | ||||
\(65\) | −0.534070 | −0.0662433 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.721104 | 0.0880968 | 0.0440484 | − | 0.999029i | \(-0.485974\pi\) | ||||
0.0440484 | + | 0.999029i | \(0.485974\pi\) | |||||||
\(68\) | 10.8415 | − | 7.87680i | 1.31472 | − | 0.955203i | ||||
\(69\) | 0.295291 | + | 0.908812i | 0.0355489 | + | 0.109408i | ||||
\(70\) | −1.97063 | + | 6.06498i | −0.235535 | + | 0.724903i | ||||
\(71\) | −3.66814 | − | 2.66506i | −0.435328 | − | 0.316284i | 0.348448 | − | 0.937328i | \(-0.386709\pi\) |
−0.783776 | + | 0.621044i | \(0.786709\pi\) | |||||||
\(72\) | 23.1948 | + | 16.8520i | 2.73353 | + | 1.98603i | ||||
\(73\) | −0.330074 | + | 1.01586i | −0.0386322 | + | 0.118898i | −0.968513 | − | 0.248964i | \(-0.919910\pi\) |
0.929881 | + | 0.367862i | \(0.119910\pi\) | |||||||
\(74\) | 6.35271 | + | 19.5516i | 0.738487 | + | 2.27283i | ||||
\(75\) | 0.170505 | − | 0.123879i | 0.0196882 | − | 0.0143043i | ||||
\(76\) | −27.4245 | −3.14581 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.308953 | −0.0349821 | ||||||||
\(79\) | 3.75920 | − | 2.73122i | 0.422943 | − | 0.307286i | −0.355878 | − | 0.934533i | \(-0.615818\pi\) |
0.778821 | + | 0.627246i | \(0.215818\pi\) | |||||||
\(80\) | −4.80762 | − | 14.7963i | −0.537509 | − | 1.65428i | ||||
\(81\) | 2.65823 | − | 8.18119i | 0.295359 | − | 0.909021i | ||||
\(82\) | 23.5434 | + | 17.1053i | 2.59993 | + | 1.88896i | ||||
\(83\) | 11.0044 | + | 7.99518i | 1.20789 | + | 0.877585i | 0.995038 | − | 0.0994991i | \(-0.0317240\pi\) |
0.212854 | + | 0.977084i | \(0.431724\pi\) | |||||||
\(84\) | −0.837365 | + | 2.57714i | −0.0913640 | + | 0.281189i | ||||
\(85\) | 0.748288 | + | 2.30299i | 0.0811633 | + | 0.249795i | ||||
\(86\) | 9.60040 | − | 6.97510i | 1.03524 | − | 0.752144i | ||||
\(87\) | −1.15698 | −0.124041 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.7148 | 1.34776 | 0.673881 | − | 0.738840i | \(-0.264626\pi\) | ||||
0.673881 | + | 0.738840i | \(0.264626\pi\) | |||||||
\(90\) | −6.56320 | + | 4.76844i | −0.691822 | + | 0.502638i | ||||
\(91\) | 0.383432 | + | 1.18008i | 0.0401946 | + | 0.123706i | ||||
\(92\) | −7.75381 | + | 23.8638i | −0.808391 | + | 2.48797i | ||||
\(93\) | 0.178079 | + | 0.129382i | 0.0184659 | + | 0.0134163i | ||||
\(94\) | −15.0303 | − | 10.9202i | −1.55026 | − | 1.12633i | ||||
\(95\) | 1.53136 | − | 4.71304i | 0.157114 | − | 0.483548i | ||||
\(96\) | −1.51763 | − | 4.67079i | −0.154893 | − | 0.476711i | ||||
\(97\) | −3.85026 | + | 2.79738i | −0.390935 | + | 0.284031i | −0.765839 | − | 0.643033i | \(-0.777676\pi\) |
0.374904 | + | 0.927064i | \(0.377676\pi\) | |||||||
\(98\) | −4.39779 | −0.444244 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.53407 | 0.553407 | ||||||||
\(101\) | −5.32211 | + | 3.86674i | −0.529570 | + | 0.384755i | −0.820197 | − | 0.572082i | \(-0.806136\pi\) |
0.290627 | + | 0.956836i | \(0.406136\pi\) | |||||||
\(102\) | 0.432876 | + | 1.33226i | 0.0428611 | + | 0.131913i | ||||
\(103\) | 5.05440 | − | 15.5559i | 0.498025 | − | 1.53276i | −0.314163 | − | 0.949369i | \(-0.601724\pi\) |
0.812188 | − | 0.583395i | \(-0.198276\pi\) | |||||||
\(104\) | −4.19127 | − | 3.04514i | −0.410988 | − | 0.298600i | ||||
\(105\) | −0.396137 | − | 0.287810i | −0.0386590 | − | 0.0280874i | ||||
\(106\) | −3.84579 | + | 11.8361i | −0.373536 | + | 1.14963i | ||||
\(107\) | −3.15530 | − | 9.71101i | −0.305034 | − | 0.938798i | −0.979664 | − | 0.200643i | \(-0.935697\pi\) |
0.674630 | − | 0.738156i | \(-0.264303\pi\) | |||||||
\(108\) | −5.61961 | + | 4.08289i | −0.540747 | + | 0.392876i | ||||
\(109\) | 12.0919 | 1.15819 | 0.579095 | − | 0.815260i | \(-0.303406\pi\) | ||||
0.579095 | + | 0.815260i | \(0.303406\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.57849 | −0.149823 | ||||||||
\(112\) | −29.2424 | + | 21.2459i | −2.76315 | + | 2.00755i | ||||
\(113\) | −3.35068 | − | 10.3123i | −0.315205 | − | 0.970102i | −0.975670 | − | 0.219245i | \(-0.929641\pi\) |
0.660465 | − | 0.750857i | \(-0.270359\pi\) | |||||||
\(114\) | 0.885873 | − | 2.72644i | 0.0829696 | − | 0.255354i | ||||
\(115\) | −3.66814 | − | 2.66506i | −0.342056 | − | 0.248518i | ||||
\(116\) | −24.5780 | − | 17.8570i | −2.28201 | − | 1.65798i | ||||
\(117\) | −0.487780 | + | 1.50123i | −0.0450952 | + | 0.138789i | ||||
\(118\) | −5.46683 | − | 16.8252i | −0.503263 | − | 1.54888i | ||||
\(119\) | 4.55148 | − | 3.30684i | 0.417233 | − | 0.303138i | ||||
\(120\) | 2.04442 | 0.186629 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −18.6610 | −1.68949 | ||||||||
\(123\) | −1.80773 | + | 1.31339i | −0.162998 | + | 0.118425i | ||||
\(124\) | 1.78608 | + | 5.49700i | 0.160395 | + | 0.493645i | ||||
\(125\) | −0.309017 | + | 0.951057i | −0.0276393 | + | 0.0850651i | ||||
\(126\) | 15.2484 | + | 11.0786i | 1.35843 | + | 0.986959i | ||||
\(127\) | −6.57077 | − | 4.77394i | −0.583062 | − | 0.423619i | 0.256765 | − | 0.966474i | \(-0.417343\pi\) |
−0.839827 | + | 0.542855i | \(0.817343\pi\) | |||||||
\(128\) | 13.4581 | − | 41.4199i | 1.18954 | − | 3.66104i | ||||
\(129\) | 0.281565 | + | 0.866568i | 0.0247904 | + | 0.0762971i | ||||
\(130\) | 1.18596 | − | 0.861652i | 0.104016 | − | 0.0755719i | ||||
\(131\) | −5.79861 | −0.506627 | −0.253313 | − | 0.967384i | \(-0.581520\pi\) | ||||
−0.253313 | + | 0.967384i | \(0.581520\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.5134 | −0.998336 | ||||||||
\(134\) | −1.60129 | + | 1.16341i | −0.138330 | + | 0.100503i | ||||
\(135\) | −0.387870 | − | 1.19374i | −0.0333825 | − | 0.102741i | ||||
\(136\) | −7.25870 | + | 22.3400i | −0.622429 | + | 1.91564i | ||||
\(137\) | −7.17335 | − | 5.21174i | −0.612860 | − | 0.445269i | 0.237560 | − | 0.971373i | \(-0.423652\pi\) |
−0.850420 | + | 0.526104i | \(0.823652\pi\) | |||||||
\(138\) | −2.12198 | − | 1.54171i | −0.180635 | − | 0.131239i | ||||
\(139\) | 5.21211 | − | 16.0412i | 0.442085 | − | 1.36060i | −0.443563 | − | 0.896243i | \(-0.646286\pi\) |
0.885649 | − | 0.464356i | \(-0.153714\pi\) | |||||||
\(140\) | −3.97315 | − | 12.2281i | −0.335792 | − | 1.03346i | ||||
\(141\) | 1.15407 | − | 0.838482i | 0.0971904 | − | 0.0706130i | ||||
\(142\) | 12.4452 | 1.04438 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −45.9823 | −3.83186 | ||||||||
\(145\) | 4.44122 | − | 3.22674i | 0.368823 | − | 0.267966i | ||||
\(146\) | −0.905994 | − | 2.78836i | −0.0749806 | − | 0.230767i | ||||
\(147\) | 0.104347 | − | 0.321148i | 0.00860643 | − | 0.0264879i | ||||
\(148\) | −33.5323 | − | 24.3627i | −2.75634 | − | 2.00260i | ||||
\(149\) | 3.61301 | + | 2.62501i | 0.295990 | + | 0.215049i | 0.725862 | − | 0.687841i | \(-0.241441\pi\) |
−0.429872 | + | 0.902890i | \(0.641441\pi\) | |||||||
\(150\) | −0.178763 | + | 0.550175i | −0.0145959 | + | 0.0449216i | ||||
\(151\) | 3.55783 | + | 10.9499i | 0.289532 | + | 0.891088i | 0.985004 | + | 0.172534i | \(0.0551955\pi\) |
−0.695472 | + | 0.718554i | \(0.744804\pi\) | |||||||
\(152\) | 38.8904 | − | 28.2555i | 3.15443 | − | 2.29183i | ||||
\(153\) | 7.15698 | 0.578607 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.04442 | −0.0838897 | ||||||||
\(156\) | 0.503942 | − | 0.366135i | 0.0403476 | − | 0.0293143i | ||||
\(157\) | −1.82665 | − | 5.62185i | −0.145783 | − | 0.448673i | 0.851328 | − | 0.524633i | \(-0.175798\pi\) |
−0.997111 | + | 0.0759609i | \(0.975798\pi\) | |||||||
\(158\) | −3.94126 | + | 12.1300i | −0.313550 | + | 0.965007i | ||||
\(159\) | −0.773082 | − | 0.561677i | −0.0613094 | − | 0.0445439i | ||||
\(160\) | 18.8522 | + | 13.6969i | 1.49040 | + | 1.08284i | ||||
\(161\) | −3.25521 | + | 10.0185i | −0.256546 | + | 0.789568i | ||||
\(162\) | 7.29638 | + | 22.4559i | 0.573258 | + | 1.76431i | ||||
\(163\) | −19.0111 | + | 13.8124i | −1.48906 | + | 1.08187i | −0.514572 | + | 0.857447i | \(0.672049\pi\) |
−0.974492 | + | 0.224422i | \(0.927951\pi\) | |||||||
\(164\) | −58.6734 | −4.58162 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −37.3357 | −2.89781 | ||||||||
\(167\) | 11.5159 | − | 8.36682i | 0.891130 | − | 0.647444i | −0.0450426 | − | 0.998985i | \(-0.514342\pi\) |
0.936172 | + | 0.351541i | \(0.114342\pi\) | |||||||
\(168\) | −1.46778 | − | 4.51735i | −0.113241 | − | 0.348521i | ||||
\(169\) | −3.92908 | + | 12.0925i | −0.302237 | + | 0.930190i | ||||
\(170\) | −5.37724 | − | 3.90679i | −0.412415 | − | 0.299637i | ||||
\(171\) | −11.8494 | − | 8.60907i | −0.906144 | − | 0.658352i | ||||
\(172\) | −7.39339 | + | 22.7545i | −0.563741 | + | 1.73502i | ||||
\(173\) | 1.99169 | + | 6.12978i | 0.151425 | + | 0.466039i | 0.997781 | − | 0.0665789i | \(-0.0212084\pi\) |
−0.846356 | + | 0.532618i | \(0.821208\pi\) | |||||||
\(174\) | 2.56919 | − | 1.86663i | 0.194770 | − | 0.141509i | ||||
\(175\) | 2.32331 | 0.175626 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.35837 | 0.102101 | ||||||||
\(178\) | −28.2346 | + | 20.5136i | −2.11627 | + | 1.53756i | ||||
\(179\) | 5.24689 | + | 16.1483i | 0.392171 | + | 1.20698i | 0.931143 | + | 0.364655i | \(0.118813\pi\) |
−0.538971 | + | 0.842324i | \(0.681187\pi\) | |||||||
\(180\) | 5.05440 | − | 15.5559i | 0.376733 | − | 1.15947i | ||||
\(181\) | −3.63220 | − | 2.63895i | −0.269980 | − | 0.196152i | 0.444555 | − | 0.895751i | \(-0.353362\pi\) |
−0.714535 | + | 0.699600i | \(0.753362\pi\) | |||||||
\(182\) | −2.75536 | − | 2.00189i | −0.204241 | − | 0.148390i | ||||
\(183\) | 0.442774 | − | 1.36272i | 0.0327308 | − | 0.100735i | ||||
\(184\) | −13.5913 | − | 41.8297i | −1.00196 | − | 3.08373i | ||||
\(185\) | 6.05926 | − | 4.40231i | 0.445485 | − | 0.323664i | ||||
\(186\) | −0.604184 | −0.0443009 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 37.4576 | 2.73188 | ||||||||
\(189\) | −2.35923 | + | 1.71408i | −0.171608 | + | 0.124681i | ||||
\(190\) | 4.20331 | + | 12.9365i | 0.304940 | + | 0.938510i | ||||
\(191\) | −0.852636 | + | 2.62414i | −0.0616946 | + | 0.189876i | −0.977153 | − | 0.212535i | \(-0.931828\pi\) |
0.915459 | + | 0.402412i | \(0.131828\pi\) | |||||||
\(192\) | 5.60042 | + | 4.06894i | 0.404175 | + | 0.293651i | ||||
\(193\) | 9.54932 | + | 6.93799i | 0.687375 | + | 0.499407i | 0.875796 | − | 0.482681i | \(-0.160337\pi\) |
−0.188421 | + | 0.982088i | \(0.560337\pi\) | |||||||
\(194\) | 4.03673 | − | 12.4238i | 0.289821 | − | 0.891976i | ||||
\(195\) | 0.0347825 | + | 0.107049i | 0.00249082 | + | 0.00766597i | ||||
\(196\) | 7.17335 | − | 5.21174i | 0.512382 | − | 0.372267i | ||||
\(197\) | 6.51035 | 0.463843 | 0.231922 | − | 0.972734i | \(-0.425499\pi\) | ||||
0.231922 | + | 0.972734i | \(0.425499\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.9586 | 1.69838 | 0.849190 | − | 0.528087i | \(-0.177090\pi\) | ||||
0.849190 | + | 0.528087i | \(0.177090\pi\) | |||||||
\(200\) | −7.84779 | + | 5.70176i | −0.554923 | + | 0.403175i | ||||
\(201\) | −0.0469634 | − | 0.144539i | −0.00331254 | − | 0.0101950i | ||||
\(202\) | 5.57986 | − | 17.1730i | 0.392598 | − | 1.20829i | ||||
\(203\) | −10.3184 | − | 7.49672i | −0.724207 | − | 0.526167i | ||||
\(204\) | −2.28491 | − | 1.66008i | −0.159976 | − | 0.116229i | ||||
\(205\) | 3.27626 | − | 10.0833i | 0.228824 | − | 0.704248i | ||||
\(206\) | 13.8735 | + | 42.6981i | 0.966610 | + | 2.97492i | ||||
\(207\) | −10.8415 | + | 7.87680i | −0.753536 | + | 0.547476i | ||||
\(208\) | 8.30895 | 0.576122 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.34401 | 0.0927455 | ||||||||
\(211\) | −13.6455 | + | 9.91402i | −0.939394 | + | 0.682510i | −0.948275 | − | 0.317451i | \(-0.897173\pi\) |
0.00888082 | + | 0.999961i | \(0.497173\pi\) | |||||||
\(212\) | −7.75381 | − | 23.8638i | −0.532534 | − | 1.63897i | ||||
\(213\) | −0.295291 | + | 0.908812i | −0.0202330 | + | 0.0622708i | ||||
\(214\) | 22.6741 | + | 16.4737i | 1.54997 | + | 1.12612i | ||||
\(215\) | −3.49763 | − | 2.54118i | −0.238537 | − | 0.173307i | ||||
\(216\) | 3.76250 | − | 11.5798i | 0.256006 | − | 0.787904i | ||||
\(217\) | 0.749833 | + | 2.30775i | 0.0509020 | + | 0.156660i | ||||
\(218\) | −26.8513 | + | 19.5086i | −1.81860 | + | 1.32129i | ||||
\(219\) | 0.225117 | 0.0152120 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.29326 | −0.0869939 | ||||||||
\(222\) | 3.50521 | − | 2.54668i | 0.235254 | − | 0.170922i | ||||
\(223\) | −7.73080 | − | 23.7929i | −0.517693 | − | 1.59329i | −0.778329 | − | 0.627857i | \(-0.783932\pi\) |
0.260636 | − | 0.965437i | \(-0.416068\pi\) | |||||||
\(224\) | 16.7300 | − | 51.4895i | 1.11782 | − | 3.44029i | ||||
\(225\) | 2.39112 | + | 1.73725i | 0.159408 | + | 0.115816i | ||||
\(226\) | 24.0781 | + | 17.4938i | 1.60165 | + | 1.16367i | ||||
\(227\) | −1.23896 | + | 3.81313i | −0.0822327 | + | 0.253086i | −0.983717 | − | 0.179726i | \(-0.942479\pi\) |
0.901484 | + | 0.432813i | \(0.142479\pi\) | |||||||
\(228\) | 1.78608 | + | 5.49700i | 0.118286 | + | 0.364047i | ||||
\(229\) | 14.0224 | − | 10.1879i | 0.926628 | − | 0.673235i | −0.0185367 | − | 0.999828i | \(-0.505901\pi\) |
0.945165 | + | 0.326593i | \(0.105901\pi\) | |||||||
\(230\) | 12.4452 | 0.820614 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 53.2519 | 3.49616 | ||||||||
\(233\) | 1.70910 | − | 1.24173i | 0.111967 | − | 0.0813485i | −0.530393 | − | 0.847752i | \(-0.677956\pi\) |
0.642360 | + | 0.766403i | \(0.277956\pi\) | |||||||
\(234\) | −1.33887 | − | 4.12062i | −0.0875247 | − | 0.269373i | ||||
\(235\) | −2.09160 | + | 6.43727i | −0.136441 | + | 0.419921i | ||||
\(236\) | 28.8563 | + | 20.9653i | 1.87839 | + | 1.36473i | ||||
\(237\) | −0.792274 | − | 0.575621i | −0.0514637 | − | 0.0373906i | ||||
\(238\) | −4.77190 | + | 14.6864i | −0.309317 | + | 0.951979i | ||||
\(239\) | 7.39629 | + | 22.7634i | 0.478426 | + | 1.47244i | 0.841281 | + | 0.540598i | \(0.181802\pi\) |
−0.362855 | + | 0.931846i | \(0.618198\pi\) | |||||||
\(240\) | −2.65268 | + | 1.92729i | −0.171230 | + | 0.124406i | ||||
\(241\) | 14.5134 | 0.934889 | 0.467444 | − | 0.884023i | \(-0.345175\pi\) | ||||
0.467444 | + | 0.884023i | \(0.345175\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.57849 | −0.357860 | ||||||||
\(244\) | 30.4384 | − | 22.1148i | 1.94862 | − | 1.41576i | ||||
\(245\) | 0.495110 | + | 1.52379i | 0.0316314 | + | 0.0973516i | ||||
\(246\) | 1.89528 | − | 5.83307i | 0.120839 | − | 0.371903i | ||||
\(247\) | 2.14117 | + | 1.55565i | 0.136239 | + | 0.0989836i | ||||
\(248\) | −8.19638 | − | 5.95502i | −0.520471 | − | 0.378144i | ||||
\(249\) | 0.885873 | − | 2.72644i | 0.0561399 | − | 0.172781i | ||||
\(250\) | −0.848198 | − | 2.61048i | −0.0536447 | − | 0.165102i | ||||
\(251\) | −23.3051 | + | 16.9321i | −1.47100 | + | 1.06875i | −0.490680 | + | 0.871340i | \(0.663252\pi\) |
−0.980322 | + | 0.197406i | \(0.936748\pi\) | |||||||
\(252\) | −38.0011 | −2.39384 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 22.2933 | 1.39880 | ||||||||
\(255\) | 0.412880 | − | 0.299975i | 0.0258556 | − | 0.0187852i | ||||
\(256\) | 16.6403 | + | 51.2135i | 1.04002 | + | 3.20084i | ||||
\(257\) | −8.54421 | + | 26.2964i | −0.532973 | + | 1.64032i | 0.215014 | + | 0.976611i | \(0.431020\pi\) |
−0.747988 | + | 0.663713i | \(0.768980\pi\) | |||||||
\(258\) | −2.02334 | − | 1.47004i | −0.125968 | − | 0.0915209i | ||||
\(259\) | −14.0776 | − | 10.2279i | −0.874737 | − | 0.635533i | ||||
\(260\) | −0.913325 | + | 2.81093i | −0.0566420 | + | 0.174326i | ||||
\(261\) | −5.01384 | − | 15.4310i | −0.310349 | − | 0.955155i | ||||
\(262\) | 12.8764 | − | 9.35529i | 0.795510 | − | 0.577972i | ||||
\(263\) | −3.13325 | −0.193205 | −0.0966024 | − | 0.995323i | \(-0.530798\pi\) | ||||
−0.0966024 | + | 0.995323i | \(0.530798\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.53407 | 0.278526 | ||||||||
\(266\) | 25.5667 | − | 18.5753i | 1.56760 | − | 1.13893i | ||||
\(267\) | −0.828077 | − | 2.54856i | −0.0506775 | − | 0.155969i | ||||
\(268\) | 1.23318 | − | 3.79532i | 0.0753282 | − | 0.231836i | ||||
\(269\) | −14.5648 | − | 10.5819i | −0.888029 | − | 0.645191i | 0.0473345 | − | 0.998879i | \(-0.484927\pi\) |
−0.935363 | + | 0.353688i | \(0.884927\pi\) | |||||||
\(270\) | 2.78725 | + | 2.02506i | 0.169627 | + | 0.123241i | ||||
\(271\) | −6.28314 | + | 19.3375i | −0.381674 | + | 1.17467i | 0.557191 | + | 0.830384i | \(0.311879\pi\) |
−0.938865 | + | 0.344286i | \(0.888121\pi\) | |||||||
\(272\) | −11.6417 | − | 35.8295i | −0.705883 | − | 2.17248i | ||||
\(273\) | 0.211565 | − | 0.153711i | 0.0128045 | − | 0.00930301i | ||||
\(274\) | 24.3377 | 1.47029 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.28826 | 0.318316 | ||||||||
\(277\) | −20.6216 | + | 14.9824i | −1.23903 | + | 0.900208i | −0.997533 | − | 0.0701941i | \(-0.977638\pi\) |
−0.241496 | + | 0.970402i | \(0.577638\pi\) | |||||||
\(278\) | 14.3063 | + | 44.0304i | 0.858037 | + | 2.64077i | ||||
\(279\) | −0.953893 | + | 2.93578i | −0.0571081 | + | 0.175761i | ||||
\(280\) | 18.2329 | + | 13.2470i | 1.08962 | + | 0.791658i | ||||
\(281\) | 14.7828 | + | 10.7403i | 0.881869 | + | 0.640715i | 0.933745 | − | 0.357938i | \(-0.116520\pi\) |
−0.0518765 | + | 0.998654i | \(0.516520\pi\) | |||||||
\(282\) | −1.20996 | + | 3.72389i | −0.0720523 | + | 0.221754i | ||||
\(283\) | 3.41581 | + | 10.5128i | 0.203049 | + | 0.624919i | 0.999788 | + | 0.0205961i | \(0.00655640\pi\) |
−0.796739 | + | 0.604323i | \(0.793444\pi\) | |||||||
\(284\) | −20.2997 | + | 14.7486i | −1.20457 | + | 0.875170i | ||||
\(285\) | −1.04442 | −0.0618660 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −24.6323 | −1.45400 | ||||||||
\(288\) | 55.7193 | − | 40.4824i | 3.28329 | − | 2.38545i | ||||
\(289\) | −3.44130 | − | 10.5912i | −0.202429 | − | 0.623014i | ||||
\(290\) | −4.65631 | + | 14.3307i | −0.273428 | + | 0.841525i | ||||
\(291\) | 0.811466 | + | 0.589564i | 0.0475690 | + | 0.0345609i | ||||
\(292\) | 4.78223 | + | 3.47449i | 0.279859 | + | 0.203329i | ||||
\(293\) | −8.38651 | + | 25.8110i | −0.489945 | + | 1.50790i | 0.334744 | + | 0.942309i | \(0.391350\pi\) |
−0.824689 | + | 0.565586i | \(0.808650\pi\) | |||||||
\(294\) | 0.286415 | + | 0.881496i | 0.0167041 | + | 0.0514099i | ||||
\(295\) | −5.21430 | + | 3.78841i | −0.303589 | + | 0.220570i | ||||
\(296\) | 72.6527 | 4.22285 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.2582 | −0.710098 | ||||||||
\(299\) | 1.95904 | − | 1.42333i | 0.113294 | − | 0.0823132i | ||||
\(300\) | −0.360418 | − | 1.10925i | −0.0208088 | − | 0.0640428i | ||||
\(301\) | −3.10390 | + | 9.55281i | −0.178906 | + | 0.550615i | ||||
\(302\) | −25.5667 | − | 18.5753i | −1.47120 | − | 1.06889i | ||||
\(303\) | 1.12167 | + | 0.814938i | 0.0644380 | + | 0.0468170i | ||||
\(304\) | −23.8246 | + | 73.3245i | −1.36643 | + | 4.20545i | ||||
\(305\) | 2.10088 | + | 6.46586i | 0.120296 | + | 0.370234i | ||||
\(306\) | −15.8929 | + | 11.5468i | −0.908534 | + | 0.660089i | ||||
\(307\) | −11.7385 | −0.669951 | −0.334976 | − | 0.942227i | \(-0.608728\pi\) | ||||
−0.334976 | + | 0.942227i | \(0.608728\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.44721 | −0.196105 | ||||||||
\(310\) | 2.31925 | − | 1.68503i | 0.131724 | − | 0.0957033i | ||||
\(311\) | 3.28844 | + | 10.1208i | 0.186471 | + | 0.573897i | 0.999971 | − | 0.00766747i | \(-0.00244066\pi\) |
−0.813500 | + | 0.581565i | \(0.802441\pi\) | |||||||
\(312\) | −0.337404 | + | 1.03842i | −0.0191017 | + | 0.0587891i | ||||
\(313\) | 21.9896 | + | 15.9764i | 1.24293 | + | 0.903040i | 0.997790 | − | 0.0664478i | \(-0.0211666\pi\) |
0.245138 | + | 0.969488i | \(0.421167\pi\) | |||||||
\(314\) | 13.1264 | + | 9.53688i | 0.740765 | + | 0.538198i | ||||
\(315\) | 2.12194 | − | 6.53066i | 0.119558 | − | 0.367961i | ||||
\(316\) | −7.94630 | − | 24.4562i | −0.447014 | − | 1.37577i | ||||
\(317\) | −4.02834 | + | 2.92676i | −0.226254 | + | 0.164383i | −0.695137 | − | 0.718877i | \(-0.744657\pi\) |
0.468883 | + | 0.883260i | \(0.344657\pi\) | |||||||
\(318\) | 2.62291 | 0.147085 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −32.8461 | −1.83615 | ||||||||
\(321\) | −1.74099 | + | 1.26490i | −0.0971724 | + | 0.0705998i | ||||
\(322\) | −8.93498 | − | 27.4990i | −0.497927 | − | 1.53246i | ||||
\(323\) | 3.70820 | − | 11.4127i | 0.206330 | − | 0.635018i | ||||
\(324\) | −38.5134 | − | 27.9817i | −2.13964 | − | 1.55454i | ||||
\(325\) | −0.432072 | − | 0.313919i | −0.0239670 | − | 0.0174131i | ||||
\(326\) | 19.9318 | − | 61.3438i | 1.10392 | − | 3.39752i | ||||
\(327\) | −0.787509 | − | 2.42370i | −0.0435493 | − | 0.134031i | ||||
\(328\) | 83.2040 | − | 60.4512i | 4.59417 | − | 3.33786i | ||||
\(329\) | 15.7255 | 0.866973 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.55477 | 0.415247 | 0.207624 | − | 0.978209i | \(-0.433427\pi\) | ||||
0.207624 | + | 0.978209i | \(0.433427\pi\) | |||||||
\(332\) | 60.8992 | − | 44.2459i | 3.34228 | − | 2.42831i | ||||
\(333\) | −6.84049 | − | 21.0529i | −0.374856 | − | 1.15369i | ||||
\(334\) | −12.0737 | + | 37.1589i | −0.660641 | + | 2.03324i | ||||
\(335\) | 0.583385 | + | 0.423854i | 0.0318737 | + | 0.0231576i | ||||
\(336\) | 6.16302 | + | 4.47769i | 0.336220 | + | 0.244278i | ||||
\(337\) | −1.14060 | + | 3.51039i | −0.0621322 | + | 0.191223i | −0.977304 | − | 0.211840i | \(-0.932054\pi\) |
0.915172 | + | 0.403063i | \(0.132054\pi\) | |||||||
\(338\) | −10.7846 | − | 33.1917i | −0.586607 | − | 1.80539i | ||||
\(339\) | −1.84879 | + | 1.34323i | −0.100413 | + | 0.0729540i | ||||
\(340\) | 13.4008 | 0.726761 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 40.2024 | 2.17390 | ||||||||
\(343\) | 16.1687 | − | 11.7473i | 0.873029 | − | 0.634293i | ||||
\(344\) | −12.9595 | − | 39.8853i | −0.698731 | − | 2.15047i | ||||
\(345\) | −0.295291 | + | 0.908812i | −0.0158979 | + | 0.0489288i | ||||
\(346\) | −14.3124 | − | 10.3985i | −0.769437 | − | 0.559029i | ||||
\(347\) | −12.7546 | − | 9.26674i | −0.684701 | − | 0.497465i | 0.190213 | − | 0.981743i | \(-0.439082\pi\) |
−0.874914 | + | 0.484278i | \(0.839082\pi\) | |||||||
\(348\) | −1.97857 | + | 6.08941i | −0.106063 | + | 0.326427i | ||||
\(349\) | 3.26254 | + | 10.0411i | 0.174640 | + | 0.537485i | 0.999617 | − | 0.0276805i | \(-0.00881211\pi\) |
−0.824977 | + | 0.565166i | \(0.808812\pi\) | |||||||
\(350\) | −5.15918 | + | 3.74836i | −0.275770 | + | 0.200358i | ||||
\(351\) | 0.670351 | 0.0357807 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.5528 | −1.30681 | −0.653407 | − | 0.757007i | \(-0.726661\pi\) | ||||
−0.653407 | + | 0.757007i | \(0.726661\pi\) | |||||||
\(354\) | −3.01641 | + | 2.19155i | −0.160321 | + | 0.116480i | ||||
\(355\) | −1.40110 | − | 4.31216i | −0.0743629 | − | 0.228866i | ||||
\(356\) | 21.7438 | − | 66.9205i | 1.15242 | − | 3.54678i | ||||
\(357\) | −0.959250 | − | 0.696936i | −0.0507689 | − | 0.0368858i | ||||
\(358\) | −37.7044 | − | 27.3939i | −1.99274 | − | 1.44781i | ||||
\(359\) | 5.15142 | − | 15.8544i | 0.271882 | − | 0.836766i | −0.718146 | − | 0.695892i | \(-0.755009\pi\) |
0.990028 | − | 0.140873i | \(-0.0449910\pi\) | |||||||
\(360\) | 8.85963 | + | 27.2671i | 0.466943 | + | 1.43710i | ||||
\(361\) | −4.49635 | + | 3.26679i | −0.236650 | + | 0.171936i | ||||
\(362\) | 12.3233 | 0.647699 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.86675 | 0.359915 | ||||||||
\(365\) | −0.864144 | + | 0.627837i | −0.0452314 | + | 0.0328625i | ||||
\(366\) | 1.21534 | + | 3.74042i | 0.0635267 | + | 0.195515i | ||||
\(367\) | 4.72144 | − | 14.5311i | 0.246457 | − | 0.758517i | −0.748936 | − | 0.662642i | \(-0.769435\pi\) |
0.995393 | − | 0.0958749i | \(-0.0305649\pi\) | |||||||
\(368\) | 57.0682 | + | 41.4624i | 2.97488 | + | 2.16138i | ||||
\(369\) | −25.3511 | − | 18.4187i | −1.31973 | − | 0.958837i | ||||
\(370\) | −6.35271 | + | 19.5516i | −0.330262 | + | 1.01644i | ||||
\(371\) | −3.25521 | − | 10.0185i | −0.169002 | − | 0.520134i | ||||
\(372\) | 0.985499 | − | 0.716007i | 0.0510958 | − | 0.0371232i | ||||
\(373\) | −17.8461 | −0.924033 | −0.462017 | − | 0.886871i | \(-0.652874\pi\) | ||||
−0.462017 | + | 0.886871i | \(0.652874\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.210756 | 0.0108834 | ||||||||
\(376\) | −53.1182 | + | 38.5926i | −2.73936 | + | 1.99026i | ||||
\(377\) | 0.905994 | + | 2.78836i | 0.0466611 | + | 0.143608i | ||||
\(378\) | 2.47348 | − | 7.61260i | 0.127222 | − | 0.391550i | ||||
\(379\) | −1.53102 | − | 1.11235i | −0.0786431 | − | 0.0571375i | 0.547769 | − | 0.836630i | \(-0.315477\pi\) |
−0.626412 | + | 0.779492i | \(0.715477\pi\) | |||||||
\(380\) | −22.1869 | − | 16.1197i | −1.13816 | − | 0.826925i | ||||
\(381\) | −0.528957 | + | 1.62796i | −0.0270993 | + | 0.0834031i | ||||
\(382\) | −2.34034 | − | 7.20282i | −0.119742 | − | 0.368528i | ||||
\(383\) | −4.30153 | + | 3.12524i | −0.219798 | + | 0.159692i | −0.692236 | − | 0.721672i | \(-0.743374\pi\) |
0.472438 | + | 0.881364i | \(0.343374\pi\) | |||||||
\(384\) | −9.17873 | −0.468400 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −32.3988 | −1.64906 | ||||||||
\(387\) | −10.3375 | + | 7.51067i | −0.525487 | + | 0.381789i | ||||
\(388\) | 8.13879 | + | 25.0486i | 0.413184 | + | 1.27165i | ||||
\(389\) | −8.29010 | + | 25.5143i | −0.420325 | + | 1.29363i | 0.487076 | + | 0.873360i | \(0.338064\pi\) |
−0.907401 | + | 0.420267i | \(0.861936\pi\) | |||||||
\(390\) | −0.249948 | − | 0.181598i | −0.0126566 | − | 0.00919558i | ||||
\(391\) | −8.88244 | − | 6.45347i | −0.449204 | − | 0.326366i | ||||
\(392\) | −4.80277 | + | 14.7814i | −0.242577 | + | 0.746574i | ||||
\(393\) | 0.377647 | + | 1.16228i | 0.0190498 | + | 0.0586291i | ||||
\(394\) | −14.4569 | + | 10.5036i | −0.728331 | + | 0.529163i | ||||
\(395\) | 4.64663 | 0.233797 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.5972 | 1.58582 | 0.792909 | − | 0.609340i | \(-0.208565\pi\) | ||||
0.792909 | + | 0.609340i | \(0.208565\pi\) | |||||||
\(398\) | −53.2027 | + | 38.6541i | −2.66681 | + | 1.93755i | ||||
\(399\) | 0.749833 | + | 2.30775i | 0.0375386 | + | 0.115532i | ||||
\(400\) | 4.80762 | − | 14.7963i | 0.240381 | − | 0.739817i | ||||
\(401\) | 2.53730 | + | 1.84346i | 0.126707 | + | 0.0920580i | 0.649334 | − | 0.760504i | \(-0.275048\pi\) |
−0.522627 | + | 0.852562i | \(0.675048\pi\) | |||||||
\(402\) | 0.337481 | + | 0.245195i | 0.0168320 | + | 0.0122292i | ||||
\(403\) | 0.172367 | − | 0.530492i | 0.00858623 | − | 0.0264257i | ||||
\(404\) | 11.2500 | + | 34.6240i | 0.559709 | + | 1.72261i | ||||
\(405\) | 6.95933 | − | 5.05625i | 0.345812 | − | 0.251247i | ||||
\(406\) | 35.0080 | 1.73742 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 4.95058 | 0.245090 | ||||||||
\(409\) | 0.343459 | − | 0.249537i | 0.0169829 | − | 0.0123388i | −0.579261 | − | 0.815142i | \(-0.696659\pi\) |
0.596244 | + | 0.802803i | \(0.296659\pi\) | |||||||
\(410\) | 8.99277 | + | 27.6769i | 0.444121 | + | 1.36687i | ||||
\(411\) | −0.577466 | + | 1.77726i | −0.0284843 | + | 0.0876656i | ||||
\(412\) | −73.2302 | − | 53.2048i | −3.60779 | − | 2.62121i | ||||
\(413\) | 12.1145 | + | 8.80168i | 0.596114 | + | 0.433102i | ||||
\(414\) | 11.3665 | − | 34.9826i | 0.558635 | − | 1.71930i | ||||
\(415\) | 4.20331 | + | 12.9365i | 0.206333 | + | 0.635026i | ||||
\(416\) | −10.0684 | + | 7.31513i | −0.493644 | + | 0.358654i | ||||
\(417\) | −3.55477 | −0.174078 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.71174 | 0.327890 | 0.163945 | − | 0.986469i | \(-0.447578\pi\) | ||||
0.163945 | + | 0.986469i | \(0.447578\pi\) | |||||||
\(420\) | −2.19225 | + | 1.59276i | −0.106971 | + | 0.0777189i | ||||
\(421\) | 0.859031 | + | 2.64383i | 0.0418666 | + | 0.128852i | 0.969805 | − | 0.243881i | \(-0.0784207\pi\) |
−0.927939 | + | 0.372733i | \(0.878421\pi\) | |||||||
\(422\) | 14.3063 | − | 44.0304i | 0.696422 | − | 2.14337i | ||||
\(423\) | 16.1844 | + | 11.7586i | 0.786912 | + | 0.571725i | ||||
\(424\) | 35.5825 | + | 25.8522i | 1.72804 | + | 1.25549i | ||||
\(425\) | −0.748288 | + | 2.30299i | −0.0362973 | + | 0.111712i | ||||
\(426\) | −0.810523 | − | 2.49453i | −0.0392699 | − | 0.120860i | ||||
\(427\) | 12.7787 | − | 9.28424i | 0.618403 | − | 0.449296i | ||||
\(428\) | −56.5070 | −2.73137 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.8667 | 0.572265 | ||||||||
\(431\) | 13.1032 | − | 9.52000i | 0.631157 | − | 0.458562i | −0.225644 | − | 0.974210i | \(-0.572449\pi\) |
0.856801 | + | 0.515647i | \(0.172449\pi\) | |||||||
\(432\) | 6.03440 | + | 18.5720i | 0.290330 | + | 0.893545i | ||||
\(433\) | 2.41878 | − | 7.44423i | 0.116239 | − | 0.357747i | −0.875964 | − | 0.482376i | \(-0.839774\pi\) |
0.992203 | + | 0.124629i | \(0.0397740\pi\) | |||||||
\(434\) | −5.38834 | − | 3.91486i | −0.258648 | − | 0.187919i | ||||
\(435\) | −0.936014 | − | 0.680054i | −0.0448784 | − | 0.0326061i | ||||
\(436\) | 20.6786 | − | 63.6421i | 0.990323 | − | 3.04790i | ||||
\(437\) | 6.94329 | + | 21.3692i | 0.332143 | + | 1.02223i | ||||
\(438\) | −0.499897 | + | 0.363196i | −0.0238860 | + | 0.0173542i | ||||
\(439\) | −20.7355 | −0.989650 | −0.494825 | − | 0.868993i | \(-0.664768\pi\) | ||||
−0.494825 | + | 0.868993i | \(0.664768\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.73546 | 0.225498 | ||||||||
\(442\) | 2.87182 | − | 2.08650i | 0.136599 | − | 0.0992447i | ||||
\(443\) | 1.63860 | + | 5.04309i | 0.0778522 | + | 0.239604i | 0.982407 | − | 0.186753i | \(-0.0597965\pi\) |
−0.904555 | + | 0.426358i | \(0.859796\pi\) | |||||||
\(444\) | −2.69941 | + | 8.30792i | −0.128108 | + | 0.394276i | ||||
\(445\) | 10.2865 | + | 7.47355i | 0.487625 | + | 0.354280i | ||||
\(446\) | 55.5539 | + | 40.3623i | 2.63055 | + | 1.91121i | ||||
\(447\) | 0.290853 | − | 0.895154i | 0.0137569 | − | 0.0423393i | ||||
\(448\) | 23.5816 | + | 72.5767i | 1.11413 | + | 3.42893i | ||||
\(449\) | 24.2730 | − | 17.6353i | 1.14551 | − | 0.832263i | 0.157634 | − | 0.987498i | \(-0.449613\pi\) |
0.987878 | + | 0.155235i | \(0.0496133\pi\) | |||||||
\(450\) | −8.11256 | −0.382430 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −60.0061 | −2.82245 | ||||||||
\(453\) | 1.96309 | − | 1.42627i | 0.0922340 | − | 0.0670119i | ||||
\(454\) | −3.40073 | − | 10.4664i | −0.159604 | − | 0.491211i | ||||
\(455\) | −0.383432 | + | 1.18008i | −0.0179756 | + | 0.0553232i | ||||
\(456\) | −8.19638 | − | 5.95502i | −0.383831 | − | 0.278869i | ||||
\(457\) | 30.3490 | + | 22.0498i | 1.41966 | + | 1.03145i | 0.991827 | + | 0.127591i | \(0.0407244\pi\) |
0.427837 | + | 0.903856i | \(0.359276\pi\) | |||||||
\(458\) | −14.7015 | + | 45.2467i | −0.686958 | + | 2.11424i | ||||
\(459\) | −0.939232 | − | 2.89066i | −0.0438396 | − | 0.134924i | ||||
\(460\) | −20.2997 | + | 14.7486i | −0.946480 | + | 0.687658i | ||||
\(461\) | −15.7829 | −0.735083 | −0.367542 | − | 0.930007i | \(-0.619800\pi\) | ||||
−0.367542 | + | 0.930007i | \(0.619800\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.5672 | −0.769941 | −0.384970 | − | 0.922929i | \(-0.625788\pi\) | ||||
−0.384970 | + | 0.922929i | \(0.625788\pi\) | |||||||
\(464\) | −69.0956 | + | 50.2009i | −3.20768 | + | 2.33052i | ||||
\(465\) | 0.0680200 | + | 0.209344i | 0.00315435 | + | 0.00970809i | ||||
\(466\) | −1.79187 | + | 5.51480i | −0.0830067 | + | 0.255468i | ||||
\(467\) | −2.99369 | − | 2.17505i | −0.138532 | − | 0.100649i | 0.516361 | − | 0.856371i | \(-0.327286\pi\) |
−0.654893 | + | 0.755722i | \(0.727286\pi\) | |||||||
\(468\) | 7.06714 | + | 5.13458i | 0.326679 | + | 0.237346i | ||||
\(469\) | 0.517712 | − | 1.59335i | 0.0239057 | − | 0.0735742i | ||||
\(470\) | −5.74107 | − | 17.6692i | −0.264816 | − | 0.815019i | ||||
\(471\) | −1.00788 | + | 0.732270i | −0.0464408 | + | 0.0337412i | ||||
\(472\) | −62.5214 | −2.87778 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 2.68802 | 0.123465 | ||||||||
\(475\) | 4.00915 | − | 2.91282i | 0.183952 | − | 0.133649i | ||||
\(476\) | −9.62103 | − | 29.6105i | −0.440979 | − | 1.35719i | ||||
\(477\) | 4.14108 | − | 12.7449i | 0.189607 | − | 0.583550i | ||||
\(478\) | −53.1501 | − | 38.6158i | −2.43103 | − | 1.76624i | ||||
\(479\) | 1.02303 | + | 0.743275i | 0.0467435 | + | 0.0339611i | 0.610912 | − | 0.791699i | \(-0.290803\pi\) |
−0.564168 | + | 0.825660i | \(0.690803\pi\) | |||||||
\(480\) | 1.51763 | − | 4.67079i | 0.0692702 | − | 0.213192i | ||||
\(481\) | 1.23607 | + | 3.80423i | 0.0563598 | + | 0.173458i | ||||
\(482\) | −32.2286 | + | 23.4154i | −1.46797 | + | 1.06654i | ||||
\(483\) | 2.22012 | 0.101019 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.75919 | −0.216104 | ||||||||
\(486\) | 12.3877 | − | 9.00016i | 0.561915 | − | 0.408255i | ||||
\(487\) | 6.67545 | + | 20.5449i | 0.302494 | + | 0.930979i | 0.980601 | + | 0.196016i | \(0.0628005\pi\) |
−0.678107 | + | 0.734963i | \(0.737199\pi\) | |||||||
\(488\) | −20.3794 | + | 62.7215i | −0.922534 | + | 2.83927i | ||||
\(489\) | 4.00670 | + | 2.91104i | 0.181189 | + | 0.131642i | ||||
\(490\) | −3.55789 | − | 2.58496i | −0.160729 | − | 0.116776i | ||||
\(491\) | −7.89140 | + | 24.2872i | −0.356134 | + | 1.09607i | 0.599215 | + | 0.800588i | \(0.295479\pi\) |
−0.955349 | + | 0.295479i | \(0.904521\pi\) | |||||||
\(492\) | 3.82123 | + | 11.7605i | 0.172274 | + | 0.530206i | ||||
\(493\) | 10.7545 | − | 7.81358i | 0.484357 | − | 0.351906i | ||||
\(494\) | −7.26454 | −0.326847 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.2488 | 0.729594 | ||||||||
\(497\) | −8.52224 | + | 6.19177i | −0.382275 | + | 0.277739i | ||||
\(498\) | 2.43157 | + | 7.48360i | 0.108961 | + | 0.335348i | ||||
\(499\) | 7.52809 | − | 23.1691i | 0.337003 | − | 1.03719i | −0.628723 | − | 0.777629i | \(-0.716422\pi\) |
0.965727 | − | 0.259561i | \(-0.0835778\pi\) | |||||||
\(500\) | 4.47716 | + | 3.25284i | 0.200225 | + | 0.145472i | ||||
\(501\) | −2.42705 | − | 1.76336i | −0.108433 | − | 0.0787809i | ||||
\(502\) | 24.4337 | − | 75.1993i | 1.09053 | − | 3.35631i | ||||
\(503\) | 3.86147 | + | 11.8844i | 0.172175 | + | 0.529899i | 0.999493 | − | 0.0318342i | \(-0.0101349\pi\) |
−0.827319 | + | 0.561733i | \(0.810135\pi\) | |||||||
\(504\) | 53.8888 | − | 39.1525i | 2.40040 | − | 1.74399i | ||||
\(505\) | −6.57849 | −0.292739 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.67971 | 0.119010 | ||||||||
\(508\) | −36.3631 | + | 26.4193i | −1.61335 | + | 1.17217i | ||||
\(509\) | 7.55493 | + | 23.2517i | 0.334866 | + | 1.03061i | 0.966788 | + | 0.255580i | \(0.0822665\pi\) |
−0.631922 | + | 0.775032i | \(0.717734\pi\) | |||||||
\(510\) | −0.432876 | + | 1.33226i | −0.0191681 | + | 0.0589933i | ||||
\(511\) | 2.00768 | + | 1.45866i | 0.0888144 | + | 0.0645275i | ||||
\(512\) | −49.1101 | − | 35.6806i | −2.17038 | − | 1.57687i | ||||
\(513\) | −1.92212 | + | 5.91568i | −0.0848638 | + | 0.261184i | ||||
\(514\) | −23.4524 | − | 72.1790i | −1.03444 | − | 3.18368i | ||||
\(515\) | 13.2326 | − | 9.61405i | 0.583098 | − | 0.423646i | ||||
\(516\) | 5.04245 | 0.221981 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 47.7622 | 2.09855 | ||||||||
\(519\) | 1.09895 | − | 0.798430i | 0.0482383 | − | 0.0350472i | ||||
\(520\) | −1.60092 | − | 4.92714i | −0.0702052 | − | 0.216069i | ||||
\(521\) | −0.0121810 | + | 0.0374891i | −0.000533658 | + | 0.00164243i | −0.951323 | − | 0.308196i | \(-0.900275\pi\) |
0.950789 | + | 0.309838i | \(0.100275\pi\) | |||||||
\(522\) | 36.0297 | + | 26.1771i | 1.57698 | + | 1.14574i | ||||
\(523\) | −17.0637 | − | 12.3975i | −0.746142 | − | 0.542104i | 0.148486 | − | 0.988914i | \(-0.452560\pi\) |
−0.894629 | + | 0.446810i | \(0.852560\pi\) | |||||||
\(524\) | −9.91632 | + | 30.5193i | −0.433197 | + | 1.33324i | ||||
\(525\) | −0.151311 | − | 0.465687i | −0.00660375 | − | 0.0203242i | ||||
\(526\) | 6.95774 | − | 5.05509i | 0.303372 | − | 0.220413i | ||||
\(527\) | −2.52907 | −0.110168 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.44221 | −0.106183 | ||||||||
\(530\) | −10.0684 | + | 7.31513i | −0.437344 | + | 0.317749i | ||||
\(531\) | 5.88659 | + | 18.1171i | 0.255456 | + | 0.786214i | ||||
\(532\) | −19.6893 | + | 60.5973i | −0.853638 | + | 2.62723i | ||||
\(533\) | 4.58092 | + | 3.32823i | 0.198422 | + | 0.144162i | ||||
\(534\) | 5.95060 | + | 4.32336i | 0.257508 | + | 0.187090i | ||||
\(535\) | 3.15530 | − | 9.71101i | 0.136415 | − | 0.419843i | ||||
\(536\) | 2.16157 | + | 6.65264i | 0.0933658 | + | 0.287350i | ||||
\(537\) | 2.89506 | − | 2.10338i | 0.124931 | − | 0.0907677i | ||||
\(538\) | 49.4152 | 2.13044 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.94622 | −0.298918 | ||||||||
\(541\) | −27.0537 | + | 19.6557i | −1.16313 | + | 0.845064i | −0.990171 | − | 0.139865i | \(-0.955333\pi\) |
−0.172960 | + | 0.984929i | \(0.555333\pi\) | |||||||
\(542\) | −17.2461 | − | 53.0781i | −0.740785 | − | 2.27990i | ||||
\(543\) | −0.292398 | + | 0.899909i | −0.0125480 | + | 0.0386188i | ||||
\(544\) | 45.6509 | + | 33.1673i | 1.95726 | + | 1.42204i | ||||
\(545\) | 9.78252 | + | 7.10742i | 0.419037 | + | 0.304448i | ||||
\(546\) | −0.221811 | + | 0.682664i | −0.00949264 | + | 0.0292153i | ||||
\(547\) | −10.1378 | − | 31.2010i | −0.433461 | − | 1.33406i | −0.894655 | − | 0.446757i | \(-0.852579\pi\) |
0.461194 | − | 0.887299i | \(-0.347421\pi\) | |||||||
\(548\) | −39.6978 | + | 28.8421i | −1.69581 | + | 1.23208i | ||||
\(549\) | 20.0938 | 0.857584 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.2044 | −1.15895 | ||||||||
\(552\) | −7.49921 | + | 5.44850i | −0.319188 | + | 0.231903i | ||||
\(553\) | −3.33602 | − | 10.2672i | −0.141862 | − | 0.436606i | ||||
\(554\) | 21.6203 | − | 66.5403i | 0.918557 | − | 2.82703i | ||||
\(555\) | −1.27702 | − | 0.927812i | −0.0542066 | − | 0.0393834i | ||||
\(556\) | −75.5151 | − | 54.8649i | −3.20255 | − | 2.32679i | ||||
\(557\) | −8.75528 | + | 26.9460i | −0.370973 | + | 1.14174i | 0.575182 | + | 0.818025i | \(0.304931\pi\) |
−0.946155 | + | 0.323712i | \(0.895069\pi\) | |||||||
\(558\) | −2.61827 | − | 8.05821i | −0.110840 | − | 0.341131i | ||||
\(559\) | 1.86798 | − | 1.35717i | 0.0790072 | − | 0.0574021i | ||||
\(560\) | −36.1456 | −1.52743 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −50.1550 | −2.11566 | ||||||||
\(563\) | 23.4907 | − | 17.0670i | 0.990015 | − | 0.719288i | 0.0300908 | − | 0.999547i | \(-0.490420\pi\) |
0.959924 | + | 0.280259i | \(0.0904203\pi\) | |||||||
\(564\) | −2.43951 | − | 7.50803i | −0.102722 | − | 0.316145i | ||||
\(565\) | 3.35068 | − | 10.3123i | 0.140964 | − | 0.433843i | ||||
\(566\) | −24.5461 | − | 17.8338i | −1.03175 | − | 0.749611i | ||||
\(567\) | −16.1687 | − | 11.7473i | −0.679022 | − | 0.493339i | ||||
\(568\) | 13.5913 | − | 41.8297i | 0.570278 | − | 1.75513i | ||||
\(569\) | −8.87181 | − | 27.3046i | −0.371925 | − | 1.14467i | −0.945530 | − | 0.325536i | \(-0.894455\pi\) |
0.573604 | − | 0.819133i | \(-0.305545\pi\) | |||||||
\(570\) | 2.31925 | − | 1.68503i | 0.0971425 | − | 0.0705782i | ||||
\(571\) | −0.824301 | −0.0344959 | −0.0172480 | − | 0.999851i | \(-0.505490\pi\) | ||||
−0.0172480 | + | 0.999851i | \(0.505490\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.581515 | 0.0242931 | ||||||||
\(574\) | 54.6987 | − | 39.7409i | 2.28308 | − | 1.65875i | ||||
\(575\) | −1.40110 | − | 4.31216i | −0.0584301 | − | 0.179829i | ||||
\(576\) | −29.9991 | + | 92.3278i | −1.24996 | + | 3.84699i | ||||
\(577\) | 25.5181 | + | 18.5400i | 1.06233 | + | 0.771829i | 0.974518 | − | 0.224307i | \(-0.0720120\pi\) |
0.0878137 | + | 0.996137i | \(0.472012\pi\) | |||||||
\(578\) | 24.7293 | + | 17.9669i | 1.02861 | + | 0.747325i | ||||
\(579\) | 0.768735 | − | 2.36592i | 0.0319475 | − | 0.0983244i | ||||
\(580\) | −9.38797 | − | 28.8932i | −0.389814 | − | 1.19973i | ||||
\(581\) | 25.5667 | − | 18.5753i | 1.06069 | − | 0.770634i | ||||
\(582\) | −2.75313 | −0.114121 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −10.3614 | −0.428758 | ||||||||
\(585\) | −1.27702 | + | 0.927812i | −0.0527984 | + | 0.0383603i | ||||
\(586\) | −23.0195 | − | 70.8467i | −0.950927 | − | 2.92665i | ||||
\(587\) | −8.27348 | + | 25.4632i | −0.341483 | + | 1.05098i | 0.621957 | + | 0.783052i | \(0.286338\pi\) |
−0.963440 | + | 0.267925i | \(0.913662\pi\) | |||||||
\(588\) | −1.51183 | − | 1.09841i | −0.0623466 | − | 0.0452975i | ||||
\(589\) | 4.18723 | + | 3.04220i | 0.172532 | + | 0.125352i | ||||
\(590\) | 5.46683 | − | 16.8252i | 0.225066 | − | 0.692682i | ||||
\(591\) | −0.424000 | − | 1.30494i | −0.0174410 | − | 0.0536780i | ||||
\(592\) | −94.2686 | + | 68.4902i | −3.87442 | + | 2.81493i | ||||
\(593\) | 11.0731 | 0.454719 | 0.227360 | − | 0.973811i | \(-0.426991\pi\) | ||||
0.227360 | + | 0.973811i | \(0.426991\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.62593 | 0.230641 | ||||||||
\(596\) | 19.9947 | − | 14.5270i | 0.819014 | − | 0.595048i | ||||
\(597\) | −1.56036 | − | 4.80228i | −0.0638611 | − | 0.196544i | ||||
\(598\) | −2.05392 | + | 6.32132i | −0.0839911 | + | 0.258498i | ||||
\(599\) | 9.65553 | + | 7.01515i | 0.394514 | + | 0.286631i | 0.767303 | − | 0.641285i | \(-0.221598\pi\) |
−0.372789 | + | 0.927916i | \(0.621598\pi\) | |||||||
\(600\) | 1.65397 | + | 1.20168i | 0.0675230 | + | 0.0490583i | ||||
\(601\) | −1.62683 | + | 5.00687i | −0.0663598 | + | 0.204235i | −0.978738 | − | 0.205113i | \(-0.934244\pi\) |
0.912378 | + | 0.409348i | \(0.134244\pi\) | |||||||
\(602\) | −8.51965 | − | 26.2208i | −0.347235 | − | 1.06868i | ||||
\(603\) | 1.72424 | − | 1.25274i | 0.0702166 | − | 0.0510153i | ||||
\(604\) | 63.7158 | 2.59256 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.80558 | −0.154591 | ||||||||
\(607\) | 29.0001 | − | 21.0698i | 1.17708 | − | 0.855196i | 0.185237 | − | 0.982694i | \(-0.440695\pi\) |
0.991839 | + | 0.127498i | \(0.0406946\pi\) | |||||||
\(608\) | −35.6847 | − | 109.826i | −1.44720 | − | 4.45404i | ||||
\(609\) | −0.830644 | + | 2.55646i | −0.0336594 | + | 0.103593i | ||||
\(610\) | −15.0971 | − | 10.9687i | −0.611262 | − | 0.444108i | ||||
\(611\) | −2.92450 | − | 2.12477i | −0.118313 | − | 0.0859591i | ||||
\(612\) | 12.2393 | − | 37.6687i | 0.494744 | − | 1.52267i | ||||
\(613\) | −2.02647 | − | 6.23683i | −0.0818483 | − | 0.251903i | 0.901755 | − | 0.432247i | \(-0.142279\pi\) |
−0.983604 | + | 0.180344i | \(0.942279\pi\) | |||||||
\(614\) | 26.0666 | − | 18.9385i | 1.05196 | − | 0.764296i | ||||
\(615\) | −2.23448 | −0.0901029 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.7986 | 0.716545 | 0.358272 | − | 0.933617i | \(-0.383366\pi\) | ||||
0.358272 | + | 0.933617i | \(0.383366\pi\) | |||||||
\(618\) | 7.65491 | − | 5.56161i | 0.307925 | − | 0.223721i | ||||
\(619\) | 13.8719 | + | 42.6934i | 0.557559 | + | 1.71599i | 0.689087 | + | 0.724679i | \(0.258012\pi\) |
−0.131527 | + | 0.991313i | \(0.541988\pi\) | |||||||
\(620\) | −1.78608 | + | 5.49700i | −0.0717308 | + | 0.220765i | ||||
\(621\) | 4.60415 | + | 3.34511i | 0.184758 | + | 0.134235i | ||||
\(622\) | −23.6309 | − | 17.1689i | −0.947513 | − | 0.688409i | ||||
\(623\) | 9.12849 | − | 28.0946i | 0.365725 | − | 1.12559i | ||||
\(624\) | −0.541138 | − | 1.66545i | −0.0216629 | − | 0.0666715i | ||||
\(625\) | −0.809017 | + | 0.587785i | −0.0323607 | + | 0.0235114i | ||||
\(626\) | −74.6063 | −2.98187 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −32.7128 | −1.30538 | ||||||||
\(629\) | 14.6726 | − | 10.6602i | 0.585033 | − | 0.425052i | ||||
\(630\) | 5.82436 | + | 17.9255i | 0.232048 | + | 0.714170i | ||||
\(631\) | 6.77092 | − | 20.8388i | 0.269546 | − | 0.829578i | −0.721065 | − | 0.692867i | \(-0.756347\pi\) |
0.990611 | − | 0.136710i | \(-0.0436529\pi\) | |||||||
\(632\) | 36.4658 | + | 26.4939i | 1.45053 | + | 1.05387i | ||||
\(633\) | 2.87587 | + | 2.08944i | 0.114305 | + | 0.0830477i | ||||
\(634\) | 4.22344 | − | 12.9984i | 0.167734 | − | 0.516232i | ||||
\(635\) | −2.50981 | − | 7.72440i | −0.0995988 | − | 0.306534i | ||||
\(636\) | −4.27829 | + | 3.10836i | −0.169645 | + | 0.123254i | ||||
\(637\) | −0.855693 | −0.0339038 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.4008 | −0.530128 | ||||||||
\(640\) | 35.2339 | − | 25.5989i | 1.39274 | − | 1.01189i | ||||
\(641\) | 11.0423 | + | 33.9846i | 0.436143 | + | 1.34231i | 0.891911 | + | 0.452211i | \(0.149365\pi\) |
−0.455768 | + | 0.890099i | \(0.650635\pi\) | |||||||
\(642\) | 1.82530 | − | 5.61770i | 0.0720389 | − | 0.221713i | ||||
\(643\) | −0.333437 | − | 0.242256i | −0.0131495 | − | 0.00955364i | 0.581191 | − | 0.813767i | \(-0.302587\pi\) |
−0.594341 | + | 0.804213i | \(0.702587\pi\) | |||||||
\(644\) | 47.1627 | + | 34.2657i | 1.85847 | + | 1.35026i | ||||
\(645\) | −0.281565 | + | 0.866568i | −0.0110866 | + | 0.0341211i | ||||
\(646\) | 10.1784 | + | 31.3258i | 0.400463 | + | 1.23250i | ||||
\(647\) | 13.3880 | − | 9.72692i | 0.526335 | − | 0.382405i | −0.292650 | − | 0.956220i | \(-0.594537\pi\) |
0.818985 | + | 0.573815i | \(0.194537\pi\) | |||||||
\(648\) | 83.4450 | 3.27803 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.46593 | 0.0574985 | ||||||||
\(651\) | 0.413733 | − | 0.300594i | 0.0162155 | − | 0.0117812i | ||||
\(652\) | 40.1862 | + | 123.680i | 1.57381 | + | 4.84370i | ||||
\(653\) | 3.40167 | − | 10.4693i | 0.133118 | − | 0.409694i | −0.862175 | − | 0.506611i | \(-0.830898\pi\) |
0.995292 | + | 0.0969171i | \(0.0308982\pi\) | |||||||
\(654\) | 5.65907 | + | 4.11156i | 0.221287 | + | 0.160775i | ||||
\(655\) | −4.69117 | − | 3.40833i | −0.183299 | − | 0.133175i | ||||
\(656\) | −50.9714 | + | 156.874i | −1.99010 | + | 6.12490i | ||||
\(657\) | 0.975559 | + | 3.00246i | 0.0380602 | + | 0.117137i | ||||
\(658\) | −34.9201 | + | 25.3710i | −1.36133 | + | 0.989063i | ||||
\(659\) | −42.9980 | −1.67497 | −0.837483 | − | 0.546464i | \(-0.815974\pi\) | ||||
−0.837483 | + | 0.546464i | \(0.815974\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.4927 | 0.758177 | 0.379089 | − | 0.925360i | \(-0.376238\pi\) | ||||
0.379089 | + | 0.925360i | \(0.376238\pi\) | |||||||
\(662\) | −16.7762 | + | 12.1886i | −0.652025 | + | 0.473724i | ||||
\(663\) | 0.0842262 | + | 0.259221i | 0.00327107 | + | 0.0100673i | ||||
\(664\) | −40.7739 | + | 125.489i | −1.58233 | + | 4.86992i | ||||
\(665\) | −9.31452 | − | 6.76739i | −0.361201 | − | 0.262428i | ||||
\(666\) | 49.1561 | + | 35.7140i | 1.90476 | + | 1.38389i | ||||
\(667\) | −7.69158 | + | 23.6722i | −0.297819 | + | 0.916593i | ||||
\(668\) | −24.3427 | − | 74.9191i | −0.941847 | − | 2.89871i | ||||
\(669\) | −4.26559 | + | 3.09913i | −0.164917 | + | 0.119819i | ||||
\(670\) | −1.97930 | −0.0764672 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −11.4102 | −0.440157 | ||||||||
\(673\) | −5.50668 | + | 4.00084i | −0.212267 | + | 0.154221i | −0.688839 | − | 0.724915i | \(-0.741879\pi\) |
0.476572 | + | 0.879136i | \(0.341879\pi\) | |||||||
\(674\) | −3.13074 | − | 9.63542i | −0.120592 | − | 0.371143i | ||||
\(675\) | 0.387870 | − | 1.19374i | 0.0149291 | − | 0.0459471i | ||||
\(676\) | 56.9260 | + | 41.3592i | 2.18946 | + | 1.59074i | ||||
\(677\) | −0.825760 | − | 0.599950i | −0.0317365 | − | 0.0230579i | 0.571804 | − | 0.820390i | \(-0.306244\pi\) |
−0.603540 | + | 0.797332i | \(0.706244\pi\) | |||||||
\(678\) | 1.93833 | − | 5.96556i | 0.0744410 | − | 0.229106i | ||||
\(679\) | 3.41683 | + | 10.5159i | 0.131126 | + | 0.403564i | ||||
\(680\) | −19.0035 | + | 13.8069i | −0.728752 | + | 0.529469i | ||||
\(681\) | 0.844996 | 0.0323803 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.09820 | 0.0802853 | 0.0401426 | − | 0.999194i | \(-0.487219\pi\) | ||||
0.0401426 | + | 0.999194i | \(0.487219\pi\) | |||||||
\(684\) | −65.5753 | + | 47.6432i | −2.50733 | + | 1.82168i | ||||
\(685\) | −2.73998 | − | 8.43278i | −0.104689 | − | 0.322200i | ||||
\(686\) | −16.9518 | + | 52.1722i | −0.647222 | + | 1.99194i | ||||
\(687\) | −2.95531 | − | 2.14716i | −0.112752 | − | 0.0819192i | ||||
\(688\) | 54.4155 | + | 39.5352i | 2.07457 | + | 1.50726i | ||||
\(689\) | −0.748288 | + | 2.30299i | −0.0285075 | + | 0.0877371i | ||||
\(690\) | −0.810523 | − | 2.49453i | −0.0308561 | − | 0.0949652i | ||||
\(691\) | −9.70416 | + | 7.05048i | −0.369164 | + | 0.268213i | −0.756864 | − | 0.653572i | \(-0.773270\pi\) |
0.387700 | + | 0.921785i | \(0.373270\pi\) | |||||||
\(692\) | 35.6684 | 1.35591 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 43.2736 | 1.64264 | ||||||||
\(695\) | 13.6455 | − | 9.91402i | 0.517603 | − | 0.376060i | ||||
\(696\) | −3.46814 | − | 10.6738i | −0.131460 | − | 0.404591i | ||||
\(697\) | 7.93351 | − | 24.4168i | 0.300503 | − | 0.924854i | ||||
\(698\) | −23.4447 | − | 17.0336i | −0.887397 | − | 0.644732i | ||||
\(699\) | −0.360202 | − | 0.261702i | −0.0136241 | − | 0.00989848i | ||||
\(700\) | 3.97315 | − | 12.2281i | 0.150171 | − | 0.462179i | ||||
\(701\) | −9.07256 | − | 27.9225i | −0.342666 | − | 1.05462i | −0.962822 | − | 0.270138i | \(-0.912931\pi\) |
0.620156 | − | 0.784479i | \(-0.287069\pi\) | |||||||
\(702\) | −1.48859 | + | 1.08152i | −0.0561832 | + | 0.0408195i | ||||
\(703\) | −37.1156 | −1.39984 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.42651 | 0.0537255 | ||||||||
\(706\) | 54.5222 | − | 39.6127i | 2.05197 | − | 1.49084i | ||||
\(707\) | 4.72298 | + | 14.5358i | 0.177626 | + | 0.546677i | ||||
\(708\) | 2.32298 | − | 7.14940i | 0.0873029 | − | 0.268691i | ||||
\(709\) | 30.3746 | + | 22.0685i | 1.14074 | + | 0.828799i | 0.987223 | − | 0.159347i | \(-0.0509387\pi\) |
0.153521 | + | 0.988145i | \(0.450939\pi\) | |||||||
\(710\) | 10.0684 | + | 7.31513i | 0.377861 | + | 0.274532i | ||||
\(711\) | 4.24388 | − | 13.0613i | 0.159158 | − | 0.489838i | ||||
\(712\) | 38.1137 | + | 117.302i | 1.42837 | + | 4.39607i | ||||
\(713\) | 3.83107 | − | 2.78344i | 0.143475 | − | 0.104241i | ||||
\(714\) | 3.25454 | 0.121798 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 93.9647 | 3.51162 | ||||||||
\(717\) | 4.08102 | − | 2.96503i | 0.152408 | − | 0.110731i | ||||
\(718\) | 14.1398 | + | 43.5177i | 0.527691 | + | 1.62407i | ||||
\(719\) | −1.23452 | + | 3.79947i | −0.0460399 | + | 0.141696i | −0.971434 | − | 0.237310i | \(-0.923734\pi\) |
0.925394 | + | 0.379007i | \(0.123734\pi\) | |||||||
\(720\) | −37.2005 | − | 27.0277i | −1.38638 | − | 1.00726i | ||||
\(721\) | −30.7435 | − | 22.3365i | −1.14495 | − | 0.831853i | ||||
\(722\) | 4.71411 | − | 14.5085i | 0.175441 | − | 0.539952i | ||||
\(723\) | −0.945215 | − | 2.90907i | −0.0351529 | − | 0.108190i | ||||
\(724\) | −20.1009 | + | 14.6041i | −0.747043 | + | 0.542759i | ||||
\(725\) | 5.48965 | 0.203881 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.4990 | −0.945706 | −0.472853 | − | 0.881141i | \(-0.656776\pi\) | ||||
−0.472853 | + | 0.881141i | \(0.656776\pi\) | |||||||
\(728\) | −9.73765 | + | 7.07481i | −0.360901 | + | 0.262210i | ||||
\(729\) | −7.61138 | − | 23.4254i | −0.281903 | − | 0.867608i | ||||
\(730\) | 0.905994 | − | 2.78836i | 0.0335324 | − | 0.103202i | ||||
\(731\) | −8.46956 | − | 6.15350i | −0.313258 | − | 0.227595i | ||||
\(732\) | −6.41508 | − | 4.66083i | −0.237108 | − | 0.172269i | ||||
\(733\) | 11.1872 | − | 34.4306i | 0.413208 | − | 1.27172i | −0.500637 | − | 0.865658i | \(-0.666901\pi\) |
0.913844 | − | 0.406065i | \(-0.133099\pi\) | |||||||
\(734\) | 12.9595 | + | 39.8853i | 0.478345 | + | 1.47219i | ||||
\(735\) | 0.273185 | − | 0.198481i | 0.0100766 | − | 0.00732107i | ||||
\(736\) | −105.656 | −3.89452 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 86.0111 | 3.16611 | ||||||||
\(739\) | −4.90274 | + | 3.56205i | −0.180350 | + | 0.131032i | −0.674298 | − | 0.738460i | \(-0.735553\pi\) |
0.493948 | + | 0.869492i | \(0.335553\pi\) | |||||||
\(740\) | −12.8082 | − | 39.4196i | −0.470839 | − | 1.44909i | ||||
\(741\) | 0.172367 | − | 0.530492i | 0.00633207 | − | 0.0194881i | ||||
\(742\) | 23.3921 | + | 16.9953i | 0.858750 | + | 0.623918i | ||||
\(743\) | 29.3567 | + | 21.3289i | 1.07699 | + | 0.782482i | 0.977156 | − | 0.212522i | \(-0.0681676\pi\) |
0.0998379 | + | 0.995004i | \(0.468168\pi\) | |||||||
\(744\) | −0.659821 | + | 2.03072i | −0.0241902 | + | 0.0744499i | ||||
\(745\) | 1.38005 | + | 4.24735i | 0.0505611 | + | 0.155611i | ||||
\(746\) | 39.6291 | − | 28.7923i | 1.45093 | − | 1.05416i | ||||
\(747\) | 40.2024 | 1.47093 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.7228 | −0.866812 | ||||||||
\(750\) | −0.468007 | + | 0.340027i | −0.0170892 | + | 0.0124160i | ||||
\(751\) | −4.86192 | − | 14.9634i | −0.177414 | − | 0.546024i | 0.822322 | − | 0.569023i | \(-0.192678\pi\) |
−0.999735 | + | 0.0229993i | \(0.992678\pi\) | |||||||
\(752\) | 32.5406 | − | 100.150i | 1.18663 | − | 3.65209i | ||||
\(753\) | 4.91168 | + | 3.56854i | 0.178991 | + | 0.130045i | ||||
\(754\) | −6.51052 | − | 4.73017i | −0.237099 | − | 0.172263i | ||||
\(755\) | −3.55783 | + | 10.9499i | −0.129483 | + | 0.398507i | ||||
\(756\) | 4.98699 | + | 15.3484i | 0.181375 | + | 0.558216i | ||||
\(757\) | 20.3381 | − | 14.7765i | 0.739202 | − | 0.537062i | −0.153259 | − | 0.988186i | \(-0.548977\pi\) |
0.892461 | + | 0.451124i | \(0.148977\pi\) | |||||||
\(758\) | 5.19442 | 0.188670 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 48.0712 | 1.74372 | ||||||||
\(761\) | −12.5162 | + | 9.09358i | −0.453714 | + | 0.329642i | −0.791060 | − | 0.611738i | \(-0.790471\pi\) |
0.337347 | + | 0.941380i | \(0.390471\pi\) | |||||||
\(762\) | −1.45190 | − | 4.46848i | −0.0525967 | − | 0.161876i | ||||
\(763\) | 8.68128 | − | 26.7182i | 0.314283 | − | 0.967264i | ||||
\(764\) | 12.3533 | + | 8.97521i | 0.446927 | + | 0.324712i | ||||
\(765\) | 5.79012 | + | 4.20677i | 0.209342 | + | 0.152096i | ||||
\(766\) | 4.50985 | − | 13.8799i | 0.162948 | − | 0.501501i | ||||
\(767\) | −1.06370 | − | 3.27373i | −0.0384080 | − | 0.118208i | ||||
\(768\) | 9.18154 | − | 6.67078i | 0.331310 | − | 0.240711i | ||||
\(769\) | −17.3220 | −0.624647 | −0.312323 | − | 0.949976i | \(-0.601107\pi\) | ||||
−0.312323 | + | 0.949976i | \(0.601107\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.82733 | 0.209866 | ||||||||
\(772\) | 52.8466 | − | 38.3953i | 1.90199 | − | 1.38188i | ||||
\(773\) | −7.01440 | − | 21.5881i | −0.252290 | − | 0.776470i | −0.994351 | − | 0.106138i | \(-0.966152\pi\) |
0.742061 | − | 0.670332i | \(-0.233848\pi\) | |||||||
\(774\) | 10.8382 | − | 33.3565i | 0.389571 | − | 1.19898i | ||||
\(775\) | −0.844952 | − | 0.613894i | −0.0303516 | − | 0.0220517i | ||||
\(776\) | −37.3491 | − | 27.1357i | −1.34076 | − | 0.974116i | ||||
\(777\) | −1.13327 | + | 3.48783i | −0.0406557 | + | 0.125125i | ||||
\(778\) | −22.7549 | − | 70.0323i | −0.815802 | − | 2.51078i | ||||
\(779\) | −42.5059 | + | 30.8823i | −1.52293 | + | 1.10647i | ||||
\(780\) | 0.622906 | 0.0223036 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 30.1363 | 1.07767 | ||||||||
\(783\) | −5.57451 | + | 4.05012i | −0.199217 | + | 0.144739i | ||||
\(784\) | −7.70282 | − | 23.7069i | −0.275101 | − | 0.846673i | ||||
\(785\) | 1.82665 | − | 5.62185i | 0.0651959 | − | 0.200652i | ||||
\(786\) | −2.71379 | − | 1.97168i | −0.0967976 | − | 0.0703276i | ||||
\(787\) | 2.50894 | + | 1.82285i | 0.0894342 | + | 0.0649777i | 0.631604 | − | 0.775291i | \(-0.282397\pi\) |
−0.542170 | + | 0.840269i | \(0.682397\pi\) | |||||||
\(788\) | 11.1335 | − | 34.2654i | 0.396614 | − | 1.22065i | ||||
\(789\) | 0.204060 | + | 0.628032i | 0.00726473 | + | 0.0223585i | ||||
\(790\) | −10.3184 | + | 7.49672i | −0.367111 | + | 0.266721i | ||||
\(791\) | −25.1918 | −0.895716 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.63093 | −0.128938 | ||||||||
\(794\) | −70.1651 | + | 50.9779i | −2.49007 | + | 1.80914i | ||||
\(795\) | −0.295291 | − | 0.908812i | −0.0104729 | − | 0.0322323i | ||||
\(796\) | 40.9721 | − | 126.099i | 1.45222 | − | 4.46947i | ||||
\(797\) | 15.4456 | + | 11.2219i | 0.547113 | + | 0.397501i | 0.826720 | − | 0.562614i | \(-0.190204\pi\) |
−0.279607 | + | 0.960115i | \(0.590204\pi\) | |||||||
\(798\) | −5.38834 | − | 3.91486i | −0.190745 | − | 0.138584i | ||||
\(799\) | −5.06483 | + | 15.5879i | −0.179181 | + | 0.551461i | ||||
\(800\) | 7.20091 | + | 22.1621i | 0.254590 | + | 0.783549i | ||||
\(801\) | 30.4025 | − | 22.0887i | 1.07422 | − | 0.780466i | ||||
\(802\) | −8.60855 | −0.303978 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.841051 | −0.0296616 | ||||||||
\(805\) | −8.52224 | + | 6.19177i | −0.300370 | + | 0.218231i | ||||
\(806\) | 0.473118 | + | 1.45611i | 0.0166649 | + | 0.0512892i | ||||
\(807\) | −1.17249 | + | 3.60854i | −0.0412735 | + | 0.127027i | ||||
\(808\) | −51.6266 | − | 37.5089i | −1.81622 | − | 1.31956i | ||||
\(809\) | 3.61546 | + | 2.62679i | 0.127113 | + | 0.0923529i | 0.649525 | − | 0.760340i | \(-0.274968\pi\) |
−0.522412 | + | 0.852693i | \(0.674968\pi\) | |||||||
\(810\) | −7.29638 | + | 22.4559i | −0.256369 | + | 0.789021i | ||||
\(811\) | 1.50391 | + | 4.62855i | 0.0528093 | + | 0.162530i | 0.973983 | − | 0.226622i | \(-0.0727681\pi\) |
−0.921174 | + | 0.389152i | \(0.872768\pi\) | |||||||
\(812\) | −57.1025 | + | 41.4874i | −2.00390 | + | 1.45592i | ||||
\(813\) | 4.28523 | 0.150290 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.4990 | −0.823135 | ||||||||
\(816\) | −6.42350 | + | 4.66695i | −0.224868 | + | 0.163376i | ||||
\(817\) | 6.62055 | + | 20.3759i | 0.231624 | + | 0.712864i | ||||
\(818\) | −0.360093 | + | 1.10825i | −0.0125903 | + | 0.0387491i | ||||
\(819\) | 2.96693 | + | 2.15560i | 0.103673 | + | 0.0753227i | ||||
\(820\) | −47.4678 | − | 34.4873i | −1.65765 | − | 1.20435i | ||||
\(821\) | −5.25483 | + | 16.1727i | −0.183395 | + | 0.564432i | −0.999917 | − | 0.0128826i | \(-0.995899\pi\) |
0.816522 | + | 0.577314i | \(0.195899\pi\) | |||||||
\(822\) | −1.58504 | − | 4.87826i | −0.0552847 | − | 0.170149i | ||||
\(823\) | 17.5944 | − | 12.7831i | 0.613302 | − | 0.445590i | −0.237274 | − | 0.971443i | \(-0.576254\pi\) |
0.850575 | + | 0.525853i | \(0.176254\pi\) | |||||||
\(824\) | 158.664 | 5.52731 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −41.1019 | −1.43012 | ||||||||
\(827\) | −16.7535 | + | 12.1721i | −0.582575 | + | 0.423266i | −0.839652 | − | 0.543125i | \(-0.817241\pi\) |
0.257076 | + | 0.966391i | \(0.417241\pi\) | |||||||
\(828\) | 22.9170 | + | 70.5314i | 0.796422 | + | 2.45113i | ||||
\(829\) | 3.49466 | − | 10.7555i | 0.121375 | − | 0.373552i | −0.871849 | − | 0.489775i | \(-0.837079\pi\) |
0.993223 | + | 0.116223i | \(0.0370788\pi\) | |||||||
\(830\) | −30.2052 | − | 21.9454i | −1.04844 | − | 0.761735i | ||||
\(831\) | 4.34612 | + | 3.15764i | 0.150765 | + | 0.109537i | ||||
\(832\) | 5.42081 | − | 16.6835i | 0.187933 | − | 0.578397i | ||||
\(833\) | 1.19892 | + | 3.68988i | 0.0415400 | + | 0.127847i | ||||
\(834\) | 7.89375 | − | 5.73515i | 0.273338 | − | 0.198592i | ||||
\(835\) | 14.2345 | 0.492604 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.31093 | 0.0453122 | ||||||||
\(838\) | −14.9042 | + | 10.8285i | −0.514856 | + | 0.374065i | ||||
\(839\) | −13.4448 | − | 41.3789i | −0.464167 | − | 1.42856i | −0.860027 | − | 0.510248i | \(-0.829554\pi\) |
0.395860 | − | 0.918311i | \(-0.370446\pi\) | |||||||
\(840\) | 1.46778 | − | 4.51735i | 0.0506431 | − | 0.155863i | ||||
\(841\) | −0.919270 | − | 0.667889i | −0.0316990 | − | 0.0230307i | ||||
\(842\) | −6.17304 | − | 4.48497i | −0.212737 | − | 0.154562i | ||||
\(843\) | 1.19004 | − | 3.66257i | 0.0409871 | − | 0.126145i | ||||
\(844\) | 28.8442 | + | 88.7733i | 0.992858 | + | 3.05570i | ||||
\(845\) | −10.2865 | + | 7.47355i | −0.353865 | + | 0.257098i | ||||
\(846\) | −54.9102 | −1.88785 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −70.5401 | −2.42236 | ||||||||
\(849\) | 1.88473 | − | 1.36933i | 0.0646836 | − | 0.0469954i | ||||
\(850\) | −2.05392 | − | 6.32132i | −0.0704489 | − | 0.216819i | ||||
\(851\) | −10.4938 | + | 32.2966i | −0.359722 | + | 1.10711i | ||||
\(852\) | 4.27829 | + | 3.10836i | 0.146572 | + | 0.106491i | ||||
\(853\) | −0.902527 | − | 0.655724i | −0.0309019 | − | 0.0224516i | 0.572227 | − | 0.820095i | \(-0.306080\pi\) |
−0.603129 | + | 0.797644i | \(0.706080\pi\) | |||||||
\(854\) | −13.3975 | + | 41.2334i | −0.458454 | + | 1.41098i | ||||
\(855\) | −4.52606 | − | 13.9298i | −0.154788 | − | 0.476388i | ||||
\(856\) | 80.1319 | − | 58.2192i | 2.73885 | − | 1.98989i | ||||
\(857\) | −7.80361 | −0.266566 | −0.133283 | − | 0.991078i | \(-0.542552\pi\) | ||||
−0.133283 | + | 0.991078i | \(0.542552\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.5341 | 1.04181 | 0.520905 | − | 0.853615i | \(-0.325595\pi\) | ||||
0.520905 | + | 0.853615i | \(0.325595\pi\) | |||||||
\(860\) | −19.3562 | + | 14.0631i | −0.660039 | + | 0.479547i | ||||
\(861\) | 1.60423 | + | 4.93731i | 0.0546720 | + | 0.168263i | ||||
\(862\) | −13.7377 | + | 42.2804i | −0.467910 | + | 1.44008i | ||||
\(863\) | 3.47035 | + | 2.52136i | 0.118132 | + | 0.0858281i | 0.645283 | − | 0.763944i | \(-0.276740\pi\) |
−0.527150 | + | 0.849772i | \(0.676740\pi\) | |||||||
\(864\) | −23.6628 | − | 17.1920i | −0.805025 | − | 0.584885i | ||||
\(865\) | −1.99169 | + | 6.12978i | −0.0677194 | + | 0.208419i | ||||
\(866\) | 6.63912 | + | 20.4331i | 0.225607 | + | 0.694346i | ||||
\(867\) | −1.89879 | + | 1.37955i | −0.0644864 | + | 0.0468521i | ||||
\(868\) | 13.4285 | 0.455792 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 3.17570 | 0.107666 | ||||||||
\(871\) | −0.311569 | + | 0.226368i | −0.0105571 | + | 0.00767018i | ||||
\(872\) | 36.2465 | + | 111.555i | 1.22746 | + | 3.77773i | ||||
\(873\) | −4.34668 | + | 13.3777i | −0.147113 | + | 0.452767i | ||||
\(874\) | −49.8948 | − | 36.2507i | −1.68772 | − | 1.22620i | ||||
\(875\) | 1.87960 | + | 1.36561i | 0.0635421 | + | 0.0461660i | ||||
\(876\) | 0.384977 | − | 1.18484i | 0.0130072 | − | 0.0400320i | ||||
\(877\) | −3.51180 | − | 10.8082i | −0.118585 | − | 0.364967i | 0.874093 | − | 0.485759i | \(-0.161457\pi\) |
−0.992678 | + | 0.120792i | \(0.961457\pi\) | |||||||
\(878\) | 46.0454 | − | 33.4539i | 1.55396 | − | 1.12902i | ||||
\(879\) | 5.71977 | 0.192923 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.3277 | −0.381639 | −0.190820 | − | 0.981625i | \(-0.561115\pi\) | ||||
−0.190820 | + | 0.981625i | \(0.561115\pi\) | |||||||
\(882\) | −10.5156 | + | 7.64005i | −0.354080 | + | 0.257254i | ||||
\(883\) | 9.66860 | + | 29.7569i | 0.325374 | + | 1.00140i | 0.971271 | + | 0.237975i | \(0.0764836\pi\) |
−0.645897 | + | 0.763425i | \(0.723516\pi\) | |||||||
\(884\) | −2.21163 | + | 6.80669i | −0.0743851 | + | 0.228934i | ||||
\(885\) | 1.09895 | + | 0.798430i | 0.0369406 | + | 0.0268389i | ||||
\(886\) | −11.7751 | − | 8.55508i | −0.395591 | − | 0.287413i | ||||
\(887\) | 8.73959 | − | 26.8977i | 0.293447 | − | 0.903137i | −0.690292 | − | 0.723531i | \(-0.742518\pi\) |
0.983739 | − | 0.179606i | \(-0.0574821\pi\) | |||||||
\(888\) | −4.73166 | − | 14.5626i | −0.158784 | − | 0.488687i | ||||
\(889\) | −15.2660 | + | 11.0914i | −0.512004 | + | 0.371993i | ||||
\(890\) | −34.8998 | −1.16984 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −138.448 | −4.63558 | ||||||||
\(893\) | 27.1361 | − | 19.7155i | 0.908076 | − | 0.659756i | ||||
\(894\) | 0.798342 | + | 2.45704i | 0.0267005 | + | 0.0821758i | ||||
\(895\) | −5.24689 | + | 16.1483i | −0.175384 | + | 0.539777i | ||||
\(896\) | −81.8594 | − | 59.4743i | −2.73473 | − | 1.98690i | ||||
\(897\) | −0.412880 | − | 0.299975i | −0.0137857 | − | 0.0100159i | ||||
\(898\) | −25.4485 | + | 78.3224i | −0.849228 | + | 2.61365i | ||||
\(899\) | 1.77175 | + | 5.45287i | 0.0590911 | + | 0.181864i | ||||
\(900\) | 13.2326 | − | 9.61405i | 0.441087 | − | 0.320468i | ||||
\(901\) | 10.9793 | 0.365774 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.11692 | 0.0704467 | ||||||||
\(904\) | 85.0938 | − | 61.8243i | 2.83018 | − | 2.05625i | ||||
\(905\) | −1.38738 | − | 4.26991i | −0.0461180 | − | 0.141937i | ||||
\(906\) | −2.05816 | + | 6.33437i | −0.0683778 | + | 0.210445i | ||||
\(907\) | −27.1964 | − | 19.7593i | −0.903041 | − | 0.656098i | 0.0362044 | − | 0.999344i | \(-0.488473\pi\) |
−0.939245 | + | 0.343247i | \(0.888473\pi\) | |||||||
\(908\) | 17.9505 | + | 13.0418i | 0.595710 | + | 0.432808i | ||||
\(909\) | −6.00830 | + | 18.4916i | −0.199283 | + | 0.613329i | ||||
\(910\) | −1.05245 | − | 3.23912i | −0.0348885 | − | 0.107376i | ||||
\(911\) | −6.09274 | + | 4.42664i | −0.201862 | + | 0.146661i | −0.684124 | − | 0.729366i | \(-0.739815\pi\) |
0.482262 | + | 0.876027i | \(0.339815\pi\) | |||||||
\(912\) | 16.2488 | 0.538053 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −102.968 | −3.40587 | ||||||||
\(915\) | 1.15920 | − | 0.842206i | 0.0383219 | − | 0.0278425i | ||||
\(916\) | −29.6410 | − | 91.2256i | −0.979366 | − | 3.01418i | ||||
\(917\) | −4.16307 | + | 12.8126i | −0.137477 | + | 0.423110i | ||||
\(918\) | 6.74937 | + | 4.90370i | 0.222762 | + | 0.161846i | ||||
\(919\) | 32.3950 | + | 23.5364i | 1.06861 | + | 0.776393i | 0.975662 | − | 0.219278i | \(-0.0703701\pi\) |
0.0929506 | + | 0.995671i | \(0.470370\pi\) | |||||||
\(920\) | 13.5913 | − | 41.8297i | 0.448091 | − | 1.37908i | ||||
\(921\) | 0.764494 | + | 2.35287i | 0.0251909 | + | 0.0775298i | ||||
\(922\) | 35.0477 | − | 25.4636i | 1.15423 | − | 0.838601i | ||||
\(923\) | 2.42151 | 0.0797050 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.48965 | 0.246258 | ||||||||
\(926\) | 36.7892 | − | 26.7289i | 1.20897 | − | 0.878367i | ||||
\(927\) | −14.9387 | − | 45.9766i | −0.490652 | − | 1.51007i | ||||
\(928\) | 39.5305 | − | 121.662i | 1.29765 | − | 3.99376i | ||||
\(929\) | −41.5355 | − | 30.1773i | −1.36274 | − | 0.990085i | −0.998266 | − | 0.0588702i | \(-0.981250\pi\) |
−0.364470 | − | 0.931215i | \(-0.618750\pi\) | |||||||
\(930\) | −0.488795 | − | 0.355130i | −0.0160282 | − | 0.0116452i | ||||
\(931\) | 2.45356 | − | 7.55128i | 0.0804122 | − | 0.247483i | ||||
\(932\) | −3.61273 | − | 11.1188i | −0.118339 | − | 0.364210i | ||||
\(933\) | 1.81445 | − | 1.31828i | 0.0594025 | − | 0.0431584i | ||||
\(934\) | 10.1570 | 0.332346 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −15.3120 | −0.500488 | ||||||||
\(937\) | −29.0041 | + | 21.0727i | −0.947523 | + | 0.688416i | −0.950220 | − | 0.311581i | \(-0.899142\pi\) |
0.00269678 | + | 0.999996i | \(0.499142\pi\) | |||||||
\(938\) | 1.42103 | + | 4.37348i | 0.0463982 | + | 0.142799i | ||||
\(939\) | 1.77020 | − | 5.44812i | 0.0577683 | − | 0.177793i | ||||
\(940\) | 30.3039 | + | 22.0170i | 0.988403 | + | 0.718117i | ||||
\(941\) | −0.491243 | − | 0.356909i | −0.0160141 | − | 0.0116349i | 0.579749 | − | 0.814795i | \(-0.303150\pi\) |
−0.595764 | + | 0.803160i | \(0.703150\pi\) | |||||||
\(942\) | 1.05670 | − | 3.25217i | 0.0344290 | − | 0.105962i | ||||
\(943\) | 14.8548 | + | 45.7184i | 0.483739 | + | 1.48880i | ||||
\(944\) | 81.1231 | − | 58.9394i | 2.64033 | − | 1.91831i | ||||
\(945\) | −2.91616 | −0.0948628 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.3851 | −0.857401 | −0.428701 | − | 0.903447i | \(-0.641028\pi\) | ||||
−0.428701 | + | 0.903447i | \(0.641028\pi\) | |||||||
\(948\) | −4.38450 | + | 3.18552i | −0.142402 | + | 0.103461i | ||||
\(949\) | −0.176282 | − | 0.542542i | −0.00572237 | − | 0.0176116i | ||||
\(950\) | −4.20331 | + | 12.9365i | −0.136374 | + | 0.419715i | ||||
\(951\) | 0.848997 | + | 0.616832i | 0.0275306 | + | 0.0200022i | ||||
\(952\) | 44.1512 | + | 32.0777i | 1.43095 | + | 1.03964i | ||||
\(953\) | 10.9267 | − | 33.6288i | 0.353949 | − | 1.08934i | −0.602667 | − | 0.797993i | \(-0.705895\pi\) |
0.956616 | − | 0.291351i | \(-0.0941048\pi\) | |||||||
\(954\) | 11.3665 | + | 34.9826i | 0.368005 | + | 1.13260i | ||||
\(955\) | −2.23223 | + | 1.62181i | −0.0722332 | + | 0.0524805i | ||||
\(956\) | 132.457 | 4.28398 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.47093 | −0.112141 | ||||||||
\(959\) | −16.6659 | + | 12.1085i | −0.538171 | + | 0.391004i | ||||
\(960\) | 2.13917 | + | 6.58369i | 0.0690414 | + | 0.212488i | ||||
\(961\) | −9.24245 | + | 28.4453i | −0.298143 | + | 0.917591i | ||||
\(962\) | −8.88244 | − | 6.45347i | −0.286381 | − | 0.208068i | ||||
\(963\) | −24.4151 | − | 17.7386i | −0.786766 | − | 0.571619i | ||||
\(964\) | 24.8196 | − | 76.3870i | 0.799387 | − | 2.46026i | ||||
\(965\) | 3.64751 | + | 11.2259i | 0.117418 | + | 0.361374i | ||||
\(966\) | −4.93002 | + | 3.58187i | −0.158621 | + | 0.115245i | ||||
\(967\) | 3.86872 | 0.124410 | 0.0622048 | − | 0.998063i | \(-0.480187\pi\) | ||||
0.0622048 | + | 0.998063i | \(0.480187\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.52907 | −0.0812455 | ||||||||
\(970\) | 10.5683 | − | 7.67832i | 0.339328 | − | 0.246536i | ||||
\(971\) | 7.44965 | + | 22.9277i | 0.239070 | + | 0.735783i | 0.996555 | + | 0.0829306i | \(0.0264280\pi\) |
−0.757485 | + | 0.652853i | \(0.773572\pi\) | |||||||
\(972\) | −9.53989 | + | 29.3608i | −0.305992 | + | 0.941747i | ||||
\(973\) | −31.7027 | − | 23.0334i | −1.01634 | − | 0.738417i | ||||
\(974\) | −47.9701 | − | 34.8523i | −1.53706 | − | 1.11674i | ||||
\(975\) | −0.0347825 | + | 0.107049i | −0.00111393 | + | 0.00342833i | ||||
\(976\) | −32.6851 | − | 100.594i | −1.04623 | − | 3.21995i | ||||
\(977\) | −8.74895 | + | 6.35649i | −0.279904 | + | 0.203362i | −0.718875 | − | 0.695139i | \(-0.755343\pi\) |
0.438972 | + | 0.898501i | \(0.355343\pi\) | |||||||
\(978\) | −13.5939 | −0.434685 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 8.86675 | 0.283238 | ||||||||
\(981\) | 28.9130 | − | 21.0066i | 0.923123 | − | 0.670688i | ||||
\(982\) | −21.6605 | − | 66.6642i | −0.691215 | − | 2.12734i | ||||
\(983\) | −11.9616 | + | 36.8139i | −0.381515 | + | 1.17418i | 0.557463 | + | 0.830202i | \(0.311775\pi\) |
−0.938977 | + | 0.343979i | \(0.888225\pi\) | |||||||
\(984\) | −17.5357 | − | 12.7405i | −0.559019 | − | 0.406151i | ||||
\(985\) | 5.26698 | + | 3.82669i | 0.167820 | + | 0.121928i | ||||
\(986\) | −11.2753 | + | 34.7018i | −0.359079 | + | 1.10513i | ||||
\(987\) | −1.02415 | − | 3.15202i | −0.0325992 | − | 0.100330i | ||||
\(988\) | 11.8494 | − | 8.60907i | 0.376979 | − | 0.273891i | ||||
\(989\) | 19.6022 | 0.623314 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.4533 | 1.95213 | 0.976064 | − | 0.217485i | \(-0.0697854\pi\) | ||||
0.976064 | + | 0.217485i | \(0.0697854\pi\) | |||||||
\(992\) | −19.6896 | + | 14.3053i | −0.625145 | + | 0.454195i | ||||
\(993\) | −0.492020 | − | 1.51428i | −0.0156138 | − | 0.0480543i | ||||
\(994\) | 8.93498 | − | 27.4990i | 0.283400 | − | 0.872216i | ||||
\(995\) | 19.3829 | + | 14.0825i | 0.614480 | + | 0.446446i | ||||
\(996\) | −12.8349 | − | 9.32508i | −0.406688 | − | 0.295476i | ||||
\(997\) | 11.8470 | − | 36.4613i | 0.375198 | − | 1.15474i | −0.568147 | − | 0.822927i | \(-0.692339\pi\) |
0.943345 | − | 0.331814i | \(-0.107661\pi\) | |||||||
\(998\) | 20.6633 | + | 63.5951i | 0.654085 | + | 2.01307i | ||||
\(999\) | −7.60542 | + | 5.52566i | −0.240625 | + | 0.174824i |
(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 | 605.2.g.p.366.1 | 12 | ||
11.2 | odd | 10 | 605.2.a.h.1.1 | yes | 3 | ||
11.3 | even | 5 | inner | 605.2.g.p.511.3 | 12 | ||
11.4 | even | 5 | inner | 605.2.g.p.81.1 | 12 | ||
11.5 | even | 5 | inner | 605.2.g.p.251.3 | 12 | ||
11.6 | odd | 10 | 605.2.g.o.251.1 | 12 | |||
11.7 | odd | 10 | 605.2.g.o.81.3 | 12 | |||
11.8 | odd | 10 | 605.2.g.o.511.1 | 12 | |||
11.9 | even | 5 | 605.2.a.g.1.3 | ✓ | 3 | ||
11.10 | odd | 2 | 605.2.g.o.366.3 | 12 | |||
33.2 | even | 10 | 5445.2.a.bb.1.3 | 3 | |||
33.20 | odd | 10 | 5445.2.a.bd.1.1 | 3 | |||
44.31 | odd | 10 | 9680.2.a.bz.1.2 | 3 | |||
44.35 | even | 10 | 9680.2.a.cb.1.2 | 3 | |||
55.9 | even | 10 | 3025.2.a.u.1.1 | 3 | |||
55.24 | odd | 10 | 3025.2.a.p.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.a.g.1.3 | ✓ | 3 | 11.9 | even | 5 | ||
605.2.a.h.1.1 | yes | 3 | 11.2 | odd | 10 | ||
605.2.g.o.81.3 | 12 | 11.7 | odd | 10 | |||
605.2.g.o.251.1 | 12 | 11.6 | odd | 10 | |||
605.2.g.o.366.3 | 12 | 11.10 | odd | 2 | |||
605.2.g.o.511.1 | 12 | 11.8 | odd | 10 | |||
605.2.g.p.81.1 | 12 | 11.4 | even | 5 | inner | ||
605.2.g.p.251.3 | 12 | 11.5 | even | 5 | inner | ||
605.2.g.p.366.1 | 12 | 1.1 | even | 1 | trivial | ||
605.2.g.p.511.3 | 12 | 11.3 | even | 5 | inner | ||
3025.2.a.p.1.3 | 3 | 55.24 | odd | 10 | |||
3025.2.a.u.1.1 | 3 | 55.9 | even | 10 | |||
5445.2.a.bb.1.3 | 3 | 33.2 | even | 10 | |||
5445.2.a.bd.1.1 | 3 | 33.20 | odd | 10 | |||
9680.2.a.bz.1.2 | 3 | 44.31 | odd | 10 | |||
9680.2.a.cb.1.2 | 3 | 44.35 | even | 10 |