Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [575,2,Mod(26,575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(575, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 16]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("575.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 575 = 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 575.k (of order \(11\), degree \(10\), 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: | \(4.59139811622\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\Q(\zeta_{22})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 115) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{11}]$ |
Embedding invariants
Embedding label | 376.1 | ||
Root | \(-0.415415 + 0.909632i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 575.376 |
Dual form | 575.2.k.a.26.1 |
$q$-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 \(\left(\mathbb{Z}/575\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(e\left(\frac{3}{11}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0125459 | − | 0.0872586i | 0.00887129 | − | 0.0617012i | −0.984905 | − | 0.173096i | \(-0.944623\pi\) |
0.993776 | + | 0.111395i | \(0.0355319\pi\) | |||||||
\(3\) | 0.415415 | + | 0.909632i | 0.239840 | + | 0.525176i | 0.990826 | − | 0.135141i | \(-0.0431489\pi\) |
−0.750986 | + | 0.660318i | \(0.770422\pi\) | |||||||
\(4\) | 1.91153 | + | 0.561276i | 0.955765 | + | 0.280638i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.0845850 | − | 0.0248364i | 0.0345317 | − | 0.0101394i | ||||
\(7\) | 1.30075 | + | 0.835939i | 0.491636 | + | 0.315955i | 0.762863 | − | 0.646560i | \(-0.223793\pi\) |
−0.271227 | + | 0.962515i | \(0.587429\pi\) | |||||||
\(8\) | 0.146201 | − | 0.320135i | 0.0516897 | − | 0.113185i | ||||
\(9\) | 1.30972 | − | 1.51150i | 0.436574 | − | 0.503833i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.289532 | + | 2.01374i | 0.0872971 | + | 0.607165i | 0.985765 | + | 0.168126i | \(0.0537717\pi\) |
−0.898468 | + | 0.439038i | \(0.855319\pi\) | |||||||
\(12\) | 0.283524 | + | 1.97195i | 0.0818462 | + | 0.569253i | ||||
\(13\) | −1.80075 | + | 1.15727i | −0.499437 | + | 0.320969i | −0.765991 | − | 0.642851i | \(-0.777751\pi\) |
0.266554 | + | 0.963820i | \(0.414115\pi\) | |||||||
\(14\) | 0.0892619 | − | 0.103014i | 0.0238563 | − | 0.0275316i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.32584 | + | 2.13739i | 0.831460 | + | 0.534347i | ||||
\(17\) | 4.18251 | − | 1.22809i | 1.01441 | − | 0.297857i | 0.268052 | − | 0.963405i | \(-0.413620\pi\) |
0.746355 | + | 0.665548i | \(0.231802\pi\) | |||||||
\(18\) | −0.115460 | − | 0.133248i | −0.0272141 | − | 0.0314068i | ||||
\(19\) | −7.12381 | − | 2.09174i | −1.63431 | − | 0.479878i | −0.669499 | − | 0.742813i | \(-0.733491\pi\) |
−0.964814 | + | 0.262935i | \(0.915310\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.220047 | + | 1.53046i | −0.0480182 | + | 0.333974i | ||||
\(22\) | 0.179348 | 0.0382372 | ||||||||
\(23\) | 2.79310 | − | 3.89854i | 0.582402 | − | 0.812901i | ||||
\(24\) | 0.351939 | 0.0718392 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.0783898 | + | 0.171650i | 0.0153735 | + | 0.0336633i | ||||
\(27\) | 4.79746 | + | 1.40866i | 0.923273 | + | 0.271097i | ||||
\(28\) | 2.01722 | + | 2.32800i | 0.381219 | + | 0.439951i | ||||
\(29\) | −4.30111 | + | 1.26292i | −0.798695 | + | 0.234518i | −0.655519 | − | 0.755179i | \(-0.727550\pi\) |
−0.143177 | + | 0.989697i | \(0.545732\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.376329 | + | 0.824045i | −0.0675906 | + | 0.148003i | −0.940412 | − | 0.340037i | \(-0.889561\pi\) |
0.872822 | + | 0.488039i | \(0.162288\pi\) | |||||||
\(32\) | 0.689173 | − | 0.795348i | 0.121830 | − | 0.140599i | ||||
\(33\) | −1.71148 | + | 1.09990i | −0.297931 | + | 0.191469i | ||||
\(34\) | −0.0546886 | − | 0.380367i | −0.00937901 | − | 0.0652325i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.35194 | − | 2.15416i | 0.558656 | − | 0.359027i | ||||
\(37\) | −7.26571 | + | 8.38507i | −1.19447 | + | 1.37850i | −0.287248 | + | 0.957856i | \(0.592740\pi\) |
−0.907227 | + | 0.420641i | \(0.861805\pi\) | |||||||
\(38\) | −0.271897 | + | 0.595371i | −0.0441075 | + | 0.0965819i | ||||
\(39\) | −1.80075 | − | 1.15727i | −0.288350 | − | 0.185311i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.95750 | + | 4.56720i | 0.618058 | + | 0.713277i | 0.975337 | − | 0.220720i | \(-0.0708408\pi\) |
−0.357279 | + | 0.933998i | \(0.616295\pi\) | |||||||
\(42\) | 0.130785 | + | 0.0384020i | 0.0201806 | + | 0.00592556i | ||||
\(43\) | −2.24116 | − | 4.90745i | −0.341773 | − | 0.748379i | 0.658217 | − | 0.752828i | \(-0.271311\pi\) |
−0.999990 | + | 0.00444961i | \(0.998584\pi\) | |||||||
\(44\) | −0.576814 | + | 4.01183i | −0.0869579 | + | 0.604806i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.305139 | − | 0.292633i | −0.0449903 | − | 0.0431464i | ||||
\(47\) | 2.72825 | 0.397956 | 0.198978 | − | 0.980004i | \(-0.436238\pi\) | ||||
0.198978 | + | 0.980004i | \(0.436238\pi\) | |||||||
\(48\) | −0.562632 | + | 3.91319i | −0.0812089 | + | 0.564821i | ||||
\(49\) | −1.91476 | − | 4.19273i | −0.273537 | − | 0.598962i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.85459 | + | 3.29437i | 0.399723 | + | 0.461305i | ||||
\(52\) | −4.09173 | + | 1.20144i | −0.567420 | + | 0.166610i | ||||
\(53\) | 0.230732 | + | 0.148283i | 0.0316935 | + | 0.0203682i | 0.556392 | − | 0.830920i | \(-0.312185\pi\) |
−0.524698 | + | 0.851288i | \(0.675822\pi\) | |||||||
\(54\) | 0.183106 | − | 0.400947i | 0.0249176 | − | 0.0545620i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.457783 | − | 0.294199i | 0.0611738 | − | 0.0393140i | ||||
\(57\) | −1.05662 | − | 7.34898i | −0.139953 | − | 0.973396i | ||||
\(58\) | 0.0562393 | + | 0.391153i | 0.00738458 | + | 0.0513609i | ||||
\(59\) | 6.74757 | − | 4.33640i | 0.878458 | − | 0.564551i | −0.0218707 | − | 0.999761i | \(-0.506962\pi\) |
0.900329 | + | 0.435210i | \(0.143326\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.33718 | + | 2.92802i | −0.171208 | + | 0.374894i | −0.975713 | − | 0.219052i | \(-0.929704\pi\) |
0.804505 | + | 0.593946i | \(0.202431\pi\) | |||||||
\(62\) | 0.0671837 | + | 0.0431763i | 0.00853233 | + | 0.00548340i | ||||
\(63\) | 2.96714 | − | 0.871230i | 0.373824 | − | 0.109765i | ||||
\(64\) | 5.11714 | + | 5.90549i | 0.639642 | + | 0.738187i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.0745040 | + | 0.163141i | 0.00917081 | + | 0.0200813i | ||||
\(67\) | −0.279610 | + | 1.94473i | −0.0341598 | + | 0.237587i | −0.999747 | − | 0.0224928i | \(-0.992840\pi\) |
0.965587 | + | 0.260080i | \(0.0837488\pi\) | |||||||
\(68\) | 8.68428 | 1.05312 | ||||||||
\(69\) | 4.70653 | + | 0.921186i | 0.566600 | + | 0.110898i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.58700 | − | 11.0378i | 0.188342 | − | 1.30995i | −0.647959 | − | 0.761675i | \(-0.724377\pi\) |
0.836301 | − | 0.548271i | \(-0.184714\pi\) | |||||||
\(72\) | −0.292401 | − | 0.640269i | −0.0344598 | − | 0.0754564i | ||||
\(73\) | −9.95039 | − | 2.92170i | −1.16461 | − | 0.341959i | −0.358385 | − | 0.933574i | \(-0.616672\pi\) |
−0.806221 | + | 0.591615i | \(0.798491\pi\) | |||||||
\(74\) | 0.640515 | + | 0.739194i | 0.0744584 | + | 0.0859295i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.4433 | − | 7.99684i | −1.42735 | − | 0.917300i | ||||
\(77\) | −1.30675 | + | 2.86139i | −0.148919 | + | 0.326086i | ||||
\(78\) | −0.123574 | + | 0.142612i | −0.0139920 | + | 0.0161476i | ||||
\(79\) | 2.70849 | − | 1.74064i | 0.304729 | − | 0.195837i | −0.379335 | − | 0.925259i | \(-0.623847\pi\) |
0.684064 | + | 0.729422i | \(0.260211\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.142315 | − | 0.989821i | −0.0158128 | − | 0.109980i | ||||
\(82\) | 0.448178 | − | 0.288027i | 0.0494930 | − | 0.0318072i | ||||
\(83\) | −2.85563 | + | 3.29557i | −0.313446 | + | 0.361736i | −0.890510 | − | 0.454963i | \(-0.849653\pi\) |
0.577065 | + | 0.816698i | \(0.304198\pi\) | |||||||
\(84\) | −1.27964 | + | 2.80202i | −0.139620 | + | 0.305725i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.456334 | + | 0.133992i | −0.0492078 | + | 0.0144487i | ||||
\(87\) | −2.93553 | − | 3.38779i | −0.314722 | − | 0.363209i | ||||
\(88\) | 0.686997 | + | 0.201720i | 0.0732341 | + | 0.0215035i | ||||
\(89\) | 0.266861 | + | 0.584343i | 0.0282872 | + | 0.0619403i | 0.923248 | − | 0.384204i | \(-0.125524\pi\) |
−0.894961 | + | 0.446144i | \(0.852797\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.30972 | −0.346953 | ||||||||
\(92\) | 7.52725 | − | 5.88446i | 0.784770 | − | 0.613498i | ||||
\(93\) | −0.905910 | −0.0939385 | ||||||||
\(94\) | 0.0342284 | − | 0.238063i | 0.00353038 | − | 0.0245544i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00977 | + | 0.296494i | 0.103059 | + | 0.0302608i | ||||
\(97\) | −3.62848 | − | 4.18748i | −0.368416 | − | 0.425175i | 0.541026 | − | 0.841006i | \(-0.318036\pi\) |
−0.909442 | + | 0.415831i | \(0.863491\pi\) | |||||||
\(98\) | −0.389875 | + | 0.114478i | −0.0393833 | + | 0.0115640i | ||||
\(99\) | 3.42297 | + | 2.19981i | 0.344021 | + | 0.221089i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.94535 | + | 3.39912i | −0.293073 | + | 0.338225i | −0.883122 | − | 0.469143i | \(-0.844563\pi\) |
0.590049 | + | 0.807367i | \(0.299108\pi\) | |||||||
\(102\) | 0.323276 | − | 0.207757i | 0.0320091 | − | 0.0205710i | ||||
\(103\) | 1.38513 | + | 9.63380i | 0.136481 | + | 0.949247i | 0.936848 | + | 0.349737i | \(0.113729\pi\) |
−0.800367 | + | 0.599510i | \(0.795362\pi\) | |||||||
\(104\) | 0.107212 | + | 0.745675i | 0.0105130 | + | 0.0731194i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.0158337 | − | 0.0182730i | 0.00153790 | − | 0.00177483i | ||||
\(107\) | 3.07272 | − | 6.72833i | 0.297051 | − | 0.650452i | −0.700979 | − | 0.713182i | \(-0.747253\pi\) |
0.998031 | + | 0.0627299i | \(0.0199807\pi\) | |||||||
\(108\) | 8.37985 | + | 5.38540i | 0.806351 | + | 0.518210i | ||||
\(109\) | −9.99029 | + | 2.93341i | −0.956897 | + | 0.280970i | −0.722656 | − | 0.691208i | \(-0.757079\pi\) |
−0.234241 | + | 0.972179i | \(0.575260\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.6456 | − | 3.12583i | −1.01044 | − | 0.296691i | ||||
\(112\) | 2.53935 | + | 5.56040i | 0.239946 | + | 0.525408i | ||||
\(113\) | 2.78825 | − | 19.3927i | 0.262297 | − | 1.82431i | −0.253189 | − | 0.967417i | \(-0.581480\pi\) |
0.515486 | − | 0.856898i | \(-0.327611\pi\) | |||||||
\(114\) | −0.654518 | −0.0613012 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.93053 | −0.829179 | ||||||||
\(117\) | −0.609264 | + | 4.23753i | −0.0563265 | + | 0.391760i | ||||
\(118\) | −0.293734 | − | 0.643187i | −0.0270404 | − | 0.0592102i | ||||
\(119\) | 6.46699 | + | 1.89888i | 0.592828 | + | 0.174070i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.58311 | − | 1.93298i | 0.598465 | − | 0.175725i | ||||
\(122\) | 0.238719 | + | 0.153415i | 0.0216126 | + | 0.0138896i | ||||
\(123\) | −2.51047 | + | 5.49716i | −0.226361 | + | 0.495662i | ||||
\(124\) | −1.18188 | + | 1.36396i | −0.106136 | + | 0.122487i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.0387969 | − | 0.269839i | −0.00345631 | − | 0.0240391i | ||||
\(127\) | −2.49696 | − | 17.3667i | −0.221569 | − | 1.54105i | −0.732105 | − | 0.681192i | \(-0.761462\pi\) |
0.510536 | − | 0.859856i | \(-0.329447\pi\) | |||||||
\(128\) | 2.35017 | − | 1.51036i | 0.207727 | − | 0.133498i | ||||
\(129\) | 3.53296 | − | 4.07725i | 0.311060 | − | 0.358982i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.9767 | − | 7.05427i | −0.959035 | − | 0.616334i | −0.0353039 | − | 0.999377i | \(-0.511240\pi\) |
−0.923731 | + | 0.383043i | \(0.874876\pi\) | |||||||
\(132\) | −3.88890 | + | 1.14188i | −0.338486 | + | 0.0993883i | ||||
\(133\) | −7.51770 | − | 8.67589i | −0.651867 | − | 0.752295i | ||||
\(134\) | 0.166187 | + | 0.0487968i | 0.0143563 | + | 0.00421540i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.218329 | − | 1.51851i | 0.0187216 | − | 0.130211i | ||||
\(137\) | −21.5268 | −1.83916 | −0.919580 | − | 0.392903i | \(-0.871471\pi\) | ||||
−0.919580 | + | 0.392903i | \(0.871471\pi\) | |||||||
\(138\) | 0.139429 | − | 0.399128i | 0.0118690 | − | 0.0339760i | ||||
\(139\) | −16.3719 | −1.38864 | −0.694322 | − | 0.719665i | \(-0.744295\pi\) | ||||
−0.694322 | + | 0.719665i | \(0.744295\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.13336 | + | 2.48170i | 0.0954458 | + | 0.208997i | ||||
\(142\) | −0.943233 | − | 0.276958i | −0.0791544 | − | 0.0232418i | ||||
\(143\) | −2.85181 | − | 3.29117i | −0.238480 | − | 0.275221i | ||||
\(144\) | 7.58658 | − | 2.22762i | 0.632215 | − | 0.185635i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.379780 | + | 0.831602i | −0.0314308 | + | 0.0688239i | ||||
\(147\) | 3.01843 | − | 3.48345i | 0.248956 | − | 0.287310i | ||||
\(148\) | −18.5950 | + | 11.9502i | −1.52850 | + | 0.982304i | ||||
\(149\) | −2.74972 | − | 19.1247i | −0.225266 | − | 1.56676i | −0.717665 | − | 0.696389i | \(-0.754789\pi\) |
0.492399 | − | 0.870370i | \(-0.336120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.8366 | − | 10.8202i | 1.37015 | − | 0.880539i | 0.371297 | − | 0.928514i | \(-0.378913\pi\) |
0.998849 | + | 0.0479750i | \(0.0152768\pi\) | |||||||
\(152\) | −1.71114 | + | 1.97476i | −0.138792 | + | 0.160174i | ||||
\(153\) | 3.62165 | − | 7.93032i | 0.292793 | − | 0.641128i | ||||
\(154\) | 0.233287 | + | 0.149924i | 0.0187988 | + | 0.0120812i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.79263 | − | 3.22287i | −0.223590 | − | 0.258036i | ||||
\(157\) | 5.54048 | + | 1.62683i | 0.442179 | + | 0.129835i | 0.495241 | − | 0.868756i | \(-0.335080\pi\) |
−0.0530620 | + | 0.998591i | \(0.516898\pi\) | |||||||
\(158\) | −0.117905 | − | 0.258177i | −0.00938006 | − | 0.0205395i | ||||
\(159\) | −0.0390330 | + | 0.271480i | −0.00309552 | + | 0.0215298i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.89206 | − | 2.73614i | 0.543170 | − | 0.215638i | ||||
\(162\) | −0.0881559 | −0.00692618 | ||||||||
\(163\) | 1.25289 | − | 8.71401i | 0.0981335 | − | 0.682534i | −0.880064 | − | 0.474856i | \(-0.842500\pi\) |
0.978197 | − | 0.207678i | \(-0.0665906\pi\) | |||||||
\(164\) | 5.00143 | + | 10.9516i | 0.390546 | + | 0.855176i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.251740 | + | 0.290524i | 0.0195388 | + | 0.0225490i | ||||
\(167\) | −18.7367 | + | 5.50159i | −1.44989 | + | 0.425726i | −0.909505 | − | 0.415692i | \(-0.863539\pi\) |
−0.540384 | + | 0.841418i | \(0.681721\pi\) | |||||||
\(168\) | 0.457783 | + | 0.294199i | 0.0353187 | + | 0.0226980i | ||||
\(169\) | −3.49698 | + | 7.65732i | −0.268998 | + | 0.589024i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.4919 | + | 8.02803i | −0.955276 | + | 0.613919i | ||||
\(172\) | −1.52960 | − | 10.6386i | −0.116631 | − | 0.811188i | ||||
\(173\) | 3.07149 | + | 21.3627i | 0.233521 | + | 1.62417i | 0.682676 | + | 0.730721i | \(0.260816\pi\) |
−0.449155 | + | 0.893454i | \(0.648275\pi\) | |||||||
\(174\) | −0.332443 | + | 0.213648i | −0.0252024 | + | 0.0161966i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.34120 | + | 7.31621i | −0.251852 | + | 0.551480i | ||||
\(177\) | 6.74757 | + | 4.33640i | 0.507178 | + | 0.325944i | ||||
\(178\) | 0.0543370 | − | 0.0159548i | 0.00407273 | − | 0.00119586i | ||||
\(179\) | 10.0553 | + | 11.6044i | 0.751567 | + | 0.867354i | 0.994719 | − | 0.102634i | \(-0.0327270\pi\) |
−0.243152 | + | 0.969988i | \(0.578182\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.340209 | + | 0.744955i | 0.0252876 | + | 0.0553720i | 0.921854 | − | 0.387537i | \(-0.126674\pi\) |
−0.896567 | + | 0.442909i | \(0.853947\pi\) | |||||||
\(182\) | −0.0415234 | + | 0.288802i | −0.00307792 | + | 0.0214074i | ||||
\(183\) | −3.21890 | −0.237948 | ||||||||
\(184\) | −0.839703 | − | 1.46414i | −0.0619037 | − | 0.107938i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.0113655 | + | 0.0790485i | −0.000833356 | + | 0.00579612i | ||||
\(187\) | 3.68403 | + | 8.06690i | 0.269403 | + | 0.589910i | ||||
\(188\) | 5.21513 | + | 1.53130i | 0.380353 | + | 0.111682i | ||||
\(189\) | 5.06273 | + | 5.84270i | 0.368259 | + | 0.424994i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.58868 | − | 2.30630i | −0.259668 | − | 0.166878i | 0.404329 | − | 0.914613i | \(-0.367505\pi\) |
−0.663997 | + | 0.747735i | \(0.731141\pi\) | |||||||
\(192\) | −3.24609 | + | 7.10794i | −0.234266 | + | 0.512972i | ||||
\(193\) | 3.16580 | − | 3.65352i | 0.227879 | − | 0.262986i | −0.630283 | − | 0.776366i | \(-0.717061\pi\) |
0.858162 | + | 0.513379i | \(0.171607\pi\) | |||||||
\(194\) | −0.410917 | + | 0.264080i | −0.0295021 | + | 0.0189598i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.30684 | − | 9.08924i | −0.0933454 | − | 0.649232i | ||||
\(197\) | 0.220925 | − | 0.141980i | 0.0157403 | − | 0.0101157i | −0.532747 | − | 0.846275i | \(-0.678840\pi\) |
0.548487 | + | 0.836159i | \(0.315204\pi\) | |||||||
\(198\) | 0.234896 | − | 0.271085i | 0.0166934 | − | 0.0192652i | ||||
\(199\) | −1.79719 | + | 3.93530i | −0.127399 | + | 0.278966i | −0.962574 | − | 0.271019i | \(-0.912639\pi\) |
0.835175 | + | 0.549985i | \(0.185367\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.88514 | + | 0.553528i | −0.132968 | + | 0.0390429i | ||||
\(202\) | 0.259650 | + | 0.299652i | 0.0182689 | + | 0.0210835i | ||||
\(203\) | −6.65037 | − | 1.95273i | −0.466765 | − | 0.137054i | ||||
\(204\) | 3.60758 | + | 7.89950i | 0.252581 | + | 0.553076i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.858010 | 0.0597804 | ||||||||
\(207\) | −2.23445 | − | 9.32777i | −0.155305 | − | 0.648325i | ||||
\(208\) | −8.46252 | −0.586770 | ||||||||
\(209\) | 2.14964 | − | 14.9511i | 0.148694 | − | 1.03419i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.30147 | + | 1.85028i | 0.433811 | + | 0.127378i | 0.491345 | − | 0.870965i | \(-0.336506\pi\) |
−0.0575338 | + | 0.998344i | \(0.518324\pi\) | |||||||
\(212\) | 0.357824 | + | 0.412951i | 0.0245755 | + | 0.0283616i | ||||
\(213\) | 10.6996 | − | 3.14169i | 0.733125 | − | 0.215265i | ||||
\(214\) | −0.548554 | − | 0.352535i | −0.0374984 | − | 0.0240988i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.15235 | − | 1.32989i | 0.0784077 | − | 0.0904874i | ||||
\(217\) | −1.17836 | + | 0.757286i | −0.0799923 | + | 0.0514079i | ||||
\(218\) | 0.130629 | + | 0.908542i | 0.00884728 | + | 0.0615342i | ||||
\(219\) | −1.47587 | − | 10.2649i | −0.0997301 | − | 0.693638i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.11040 | + | 7.05178i | −0.411030 | + | 0.474354i | ||||
\(222\) | −0.406315 | + | 0.889705i | −0.0272701 | + | 0.0597131i | ||||
\(223\) | 7.74566 | + | 4.97783i | 0.518688 | + | 0.333340i | 0.773653 | − | 0.633610i | \(-0.218428\pi\) |
−0.254965 | + | 0.966950i | \(0.582064\pi\) | |||||||
\(224\) | 1.56130 | − | 0.458439i | 0.104319 | − | 0.0306308i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.65720 | − | 0.486598i | −0.110235 | − | 0.0323680i | ||||
\(227\) | 3.68538 | + | 8.06985i | 0.244607 | + | 0.535615i | 0.991619 | − | 0.129196i | \(-0.0412396\pi\) |
−0.747012 | + | 0.664810i | \(0.768512\pi\) | |||||||
\(228\) | 2.10504 | − | 14.6408i | 0.139409 | − | 0.969614i | ||||
\(229\) | −8.38484 | −0.554086 | −0.277043 | − | 0.960858i | \(-0.589354\pi\) | ||||
−0.277043 | + | 0.960858i | \(0.589354\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.14566 | −0.206969 | ||||||||
\(232\) | −0.224520 | + | 1.56157i | −0.0147405 | + | 0.102522i | ||||
\(233\) | 9.97561 | + | 21.8435i | 0.653524 | + | 1.43102i | 0.888435 | + | 0.459002i | \(0.151793\pi\) |
−0.234911 | + | 0.972017i | \(0.575480\pi\) | |||||||
\(234\) | 0.362117 | + | 0.106327i | 0.0236723 | + | 0.00695082i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 15.3321 | − | 4.50191i | 0.998034 | − | 0.293049i | ||||
\(237\) | 2.70849 | + | 1.74064i | 0.175935 | + | 0.113067i | ||||
\(238\) | 0.246828 | − | 0.540478i | 0.0159995 | − | 0.0350340i | ||||
\(239\) | 7.35914 | − | 8.49290i | 0.476023 | − | 0.549360i | −0.466054 | − | 0.884756i | \(-0.654325\pi\) |
0.942077 | + | 0.335396i | \(0.108870\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00004 | + | 27.8209i | 0.257665 | + | 1.79210i | 0.549355 | + | 0.835589i | \(0.314874\pi\) |
−0.291689 | + | 0.956513i | \(0.594217\pi\) | |||||||
\(242\) | −0.0860778 | − | 0.598684i | −0.00553329 | − | 0.0384849i | ||||
\(243\) | 13.4601 | − | 8.65025i | 0.863463 | − | 0.554914i | ||||
\(244\) | −4.19948 | + | 4.84646i | −0.268844 | + | 0.310263i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.448178 | + | 0.288027i | 0.0285748 | + | 0.0183639i | ||||
\(247\) | 15.2489 | − | 4.47747i | 0.970262 | − | 0.284895i | ||||
\(248\) | 0.208786 | + | 0.240952i | 0.0132579 | + | 0.0153004i | ||||
\(249\) | −4.18403 | − | 1.22854i | −0.265152 | − | 0.0778556i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.91272 | − | 27.2135i | 0.246969 | − | 1.71770i | −0.368572 | − | 0.929599i | \(-0.620153\pi\) |
0.615541 | − | 0.788105i | \(-0.288938\pi\) | |||||||
\(252\) | 6.16077 | 0.388092 | ||||||||
\(253\) | 8.65932 | + | 4.49583i | 0.544407 | + | 0.282650i | ||||
\(254\) | −1.54672 | −0.0970501 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.38987 | + | 13.9919i | 0.399367 | + | 0.874492i | ||||
\(257\) | 17.0432 | + | 5.00435i | 1.06313 | + | 0.312163i | 0.766110 | − | 0.642709i | \(-0.222190\pi\) |
0.297018 | + | 0.954872i | \(0.404008\pi\) | |||||||
\(258\) | −0.311451 | − | 0.359434i | −0.0193901 | − | 0.0223774i | ||||
\(259\) | −16.4603 | + | 4.83317i | −1.02279 | + | 0.300318i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.72435 | + | 8.15519i | −0.230531 | + | 0.504794i | ||||
\(262\) | −0.753257 | + | 0.869305i | −0.0465364 | + | 0.0537059i | ||||
\(263\) | 7.35320 | − | 4.72561i | 0.453417 | − | 0.291394i | −0.293930 | − | 0.955827i | \(-0.594963\pi\) |
0.747348 | + | 0.664433i | \(0.231327\pi\) | |||||||
\(264\) | 0.101897 | + | 0.708712i | 0.00627135 | + | 0.0436182i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.851362 | + | 0.547137i | −0.0522004 | + | 0.0335471i | ||||
\(267\) | −0.420680 | + | 0.485490i | −0.0257452 | + | 0.0297115i | ||||
\(268\) | −1.62601 | + | 3.56047i | −0.0993246 | + | 0.217491i | ||||
\(269\) | 2.46553 | + | 1.58450i | 0.150326 | + | 0.0966086i | 0.613642 | − | 0.789585i | \(-0.289704\pi\) |
−0.463316 | + | 0.886193i | \(0.653340\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.29616 | + | 4.95803i | 0.260973 | + | 0.301179i | 0.871081 | − | 0.491139i | \(-0.163419\pi\) |
−0.610108 | + | 0.792318i | \(0.708874\pi\) | |||||||
\(272\) | 16.5353 | + | 4.85519i | 1.00260 | + | 0.294389i | ||||
\(273\) | −1.37491 | − | 3.01063i | −0.0832132 | − | 0.182212i | ||||
\(274\) | −0.270073 | + | 1.87840i | −0.0163157 | + | 0.113478i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.47963 | + | 4.40253i | 0.510414 | + | 0.265001i | ||||
\(277\) | 22.7888 | 1.36924 | 0.684622 | − | 0.728898i | \(-0.259967\pi\) | ||||
0.684622 | + | 0.728898i | \(0.259967\pi\) | |||||||
\(278\) | −0.205400 | + | 1.42859i | −0.0123191 | + | 0.0856809i | ||||
\(279\) | 0.752658 | + | 1.64809i | 0.0450604 | + | 0.0986686i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.32744 | + | 10.7644i | 0.556429 | + | 0.642153i | 0.962369 | − | 0.271747i | \(-0.0876013\pi\) |
−0.405940 | + | 0.913900i | \(0.633056\pi\) | |||||||
\(282\) | 0.230769 | − | 0.0677599i | 0.0137421 | − | 0.00403504i | ||||
\(283\) | −19.9441 | − | 12.8173i | −1.18555 | − | 0.761910i | −0.209155 | − | 0.977882i | \(-0.567071\pi\) |
−0.976399 | + | 0.215973i | \(0.930708\pi\) | |||||||
\(284\) | 9.22884 | − | 20.2083i | 0.547631 | − | 1.19914i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.322961 | + | 0.207554i | −0.0190971 | + | 0.0122730i | ||||
\(287\) | 1.32981 | + | 9.24901i | 0.0784960 | + | 0.545952i | ||||
\(288\) | −0.299543 | − | 2.08337i | −0.0176507 | − | 0.122764i | ||||
\(289\) | 1.68384 | − | 1.08214i | 0.0990493 | − | 0.0636551i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.30175 | − | 5.04012i | 0.134931 | − | 0.295457i | ||||
\(292\) | −17.3806 | − | 11.1698i | −1.01712 | − | 0.653664i | ||||
\(293\) | −4.10110 | + | 1.20419i | −0.239589 | + | 0.0703497i | −0.399323 | − | 0.916810i | \(-0.630755\pi\) |
0.159734 | + | 0.987160i | \(0.448936\pi\) | |||||||
\(294\) | −0.266092 | − | 0.307087i | −0.0155188 | − | 0.0179097i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.62210 | + | 3.55191i | 0.0942827 | + | 0.206450i | ||||
\(297\) | −1.44766 | + | 10.0687i | −0.0840017 | + | 0.584245i | ||||
\(298\) | −1.70330 | −0.0986692 | ||||||||
\(299\) | −0.518014 | + | 10.2526i | −0.0299575 | + | 0.592926i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.18715 | − | 8.25681i | 0.0684262 | − | 0.475915i | ||||
\(302\) | −0.732929 | − | 1.60489i | −0.0421753 | − | 0.0923511i | ||||
\(303\) | −4.31549 | − | 1.26714i | −0.247918 | − | 0.0727954i | ||||
\(304\) | −19.2218 | − | 22.1831i | −1.10244 | − | 1.27229i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.646552 | − | 0.415514i | −0.0369609 | − | 0.0237533i | ||||
\(307\) | 3.71586 | − | 8.13661i | 0.212076 | − | 0.464381i | −0.773461 | − | 0.633844i | \(-0.781476\pi\) |
0.985536 | + | 0.169463i | \(0.0542034\pi\) | |||||||
\(308\) | −4.10393 | + | 4.73619i | −0.233843 | + | 0.269869i | ||||
\(309\) | −8.18781 | + | 5.26199i | −0.465788 | + | 0.299344i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.32224 | + | 23.1067i | 0.188387 | + | 1.31026i | 0.836185 | + | 0.548447i | \(0.184781\pi\) |
−0.647798 | + | 0.761812i | \(0.724310\pi\) | |||||||
\(312\) | −0.633752 | + | 0.407288i | −0.0358792 | + | 0.0230581i | ||||
\(313\) | −14.7416 | + | 17.0127i | −0.833244 | + | 0.961615i | −0.999701 | − | 0.0244337i | \(-0.992222\pi\) |
0.166457 | + | 0.986049i | \(0.446767\pi\) | |||||||
\(314\) | 0.211465 | − | 0.463045i | 0.0119337 | − | 0.0261311i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.15434 | − | 1.80708i | 0.346209 | − | 0.101656i | ||||
\(317\) | 8.34970 | + | 9.63606i | 0.468966 | + | 0.541215i | 0.940124 | − | 0.340834i | \(-0.110709\pi\) |
−0.471158 | + | 0.882049i | \(0.656164\pi\) | |||||||
\(318\) | 0.0231993 | + | 0.00681193i | 0.00130095 | + | 0.000381994i | ||||
\(319\) | −3.78849 | − | 8.29564i | −0.212115 | − | 0.464467i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.39676 | 0.412847 | ||||||||
\(322\) | −0.152285 | − | 0.635719i | −0.00848651 | − | 0.0354272i | ||||
\(323\) | −32.3642 | −1.80079 | ||||||||
\(324\) | 0.283524 | − | 1.97195i | 0.0157513 | − | 0.109553i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.744654 | − | 0.218650i | −0.0412426 | − | 0.0121099i | ||||
\(327\) | −6.81845 | − | 7.86891i | −0.377061 | − | 0.435151i | ||||
\(328\) | 2.04071 | − | 0.599206i | 0.112679 | − | 0.0330856i | ||||
\(329\) | 3.54876 | + | 2.28065i | 0.195650 | + | 0.125736i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.7382 | − | 12.3926i | 0.590227 | − | 0.681158i | −0.379545 | − | 0.925173i | \(-0.623919\pi\) |
0.969771 | + | 0.244015i | \(0.0784647\pi\) | |||||||
\(332\) | −7.30834 | + | 4.69678i | −0.401097 | + | 0.257769i | ||||
\(333\) | 3.15798 | + | 21.9642i | 0.173056 | + | 1.20363i | ||||
\(334\) | 0.244993 | + | 1.70396i | 0.0134054 | + | 0.0932366i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.00303 | + | 4.61974i | −0.218383 | + | 0.252028i | ||||
\(337\) | −11.3983 | + | 24.9589i | −0.620907 | + | 1.35960i | 0.293951 | + | 0.955821i | \(0.405030\pi\) |
−0.914858 | + | 0.403776i | \(0.867697\pi\) | |||||||
\(338\) | 0.624294 | + | 0.401210i | 0.0339571 | + | 0.0218229i | ||||
\(339\) | 18.7985 | − | 5.51975i | 1.02100 | − | 0.299792i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.76837 | − | 0.519240i | −0.0957626 | − | 0.0281184i | ||||
\(342\) | 0.543793 | + | 1.19074i | 0.0294050 | + | 0.0643879i | ||||
\(343\) | 2.55459 | − | 17.7675i | 0.137935 | − | 0.959357i | ||||
\(344\) | −1.89870 | −0.102371 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.90261 | 0.102285 | ||||||||
\(347\) | 0.858953 | − | 5.97415i | 0.0461110 | − | 0.320709i | −0.953691 | − | 0.300789i | \(-0.902750\pi\) |
0.999802 | − | 0.0199196i | \(-0.00634104\pi\) | |||||||
\(348\) | −3.70988 | − | 8.12350i | −0.198870 | − | 0.435465i | ||||
\(349\) | −8.00915 | − | 2.35170i | −0.428720 | − | 0.125883i | 0.0602518 | − | 0.998183i | \(-0.480810\pi\) |
−0.488972 | + | 0.872300i | \(0.662628\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.2692 | + | 3.01532i | −0.548130 | + | 0.160946i | ||||
\(352\) | 1.80116 | + | 1.15753i | 0.0960021 | + | 0.0616968i | ||||
\(353\) | 10.8642 | − | 23.7892i | 0.578242 | − | 1.26617i | −0.364049 | − | 0.931380i | \(-0.618606\pi\) |
0.942291 | − | 0.334794i | \(-0.108667\pi\) | |||||||
\(354\) | 0.463042 | − | 0.534379i | 0.0246104 | − | 0.0284019i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.182134 | + | 1.26677i | 0.00965310 | + | 0.0671388i | ||||
\(357\) | 0.959204 | + | 6.67141i | 0.0507664 | + | 0.353088i | ||||
\(358\) | 1.13874 | − | 0.731822i | 0.0601841 | − | 0.0386780i | ||||
\(359\) | −3.70672 | + | 4.27779i | −0.195633 | + | 0.225773i | −0.845088 | − | 0.534628i | \(-0.820452\pi\) |
0.649454 | + | 0.760401i | \(0.274997\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.3894 | + | 19.5301i | 1.59944 | + | 1.02790i | ||||
\(362\) | 0.0692719 | − | 0.0203401i | 0.00364085 | − | 0.00106905i | ||||
\(363\) | 4.49302 | + | 5.18522i | 0.235822 | + | 0.272154i | ||||
\(364\) | −6.32663 | − | 1.85767i | −0.331605 | − | 0.0973682i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.0403840 | + | 0.280877i | −0.00211091 | + | 0.0146817i | ||||
\(367\) | 12.3147 | 0.642822 | 0.321411 | − | 0.946940i | \(-0.395843\pi\) | ||||
0.321411 | + | 0.946940i | \(0.395843\pi\) | |||||||
\(368\) | 17.6221 | − | 6.99596i | 0.918615 | − | 0.364690i | ||||
\(369\) | 12.0866 | 0.629201 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.176169 | + | 0.385756i | 0.00914624 | + | 0.0200275i | ||||
\(372\) | −1.73167 | − | 0.508465i | −0.0897831 | − | 0.0263627i | ||||
\(373\) | 19.0734 | + | 22.0119i | 0.987585 | + | 1.13973i | 0.990189 | + | 0.139737i | \(0.0446257\pi\) |
−0.00260397 | + | 0.999997i | \(0.500829\pi\) | |||||||
\(374\) | 0.750126 | − | 0.220257i | 0.0387881 | − | 0.0113892i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.398872 | − | 0.873407i | 0.0205702 | − | 0.0450426i | ||||
\(377\) | 6.28366 | − | 7.25173i | 0.323625 | − | 0.373483i | ||||
\(378\) | 0.573343 | − | 0.368465i | 0.0294896 | − | 0.0189518i | ||||
\(379\) | 4.74698 | + | 33.0160i | 0.243836 | + | 1.69592i | 0.632519 | + | 0.774545i | \(0.282021\pi\) |
−0.388683 | + | 0.921372i | \(0.627070\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.7601 | − | 9.48571i | 0.756181 | − | 0.485968i | ||||
\(382\) | −0.246268 | + | 0.284209i | −0.0126002 | + | 0.0145414i | ||||
\(383\) | −12.9139 | + | 28.2775i | −0.659870 | + | 1.44491i | 0.222773 | + | 0.974870i | \(0.428489\pi\) |
−0.882643 | + | 0.470044i | \(0.844238\pi\) | |||||||
\(384\) | 2.35017 | + | 1.51036i | 0.119931 | + | 0.0770753i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.279084 | − | 0.322080i | −0.0142050 | − | 0.0163934i | ||||
\(387\) | −10.3529 | − | 3.03988i | −0.526267 | − | 0.154526i | ||||
\(388\) | −4.58560 | − | 10.0411i | −0.232799 | − | 0.509758i | ||||
\(389\) | 1.80544 | − | 12.5571i | 0.0915394 | − | 0.636670i | −0.891465 | − | 0.453089i | \(-0.850322\pi\) |
0.983005 | − | 0.183581i | \(-0.0587690\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.89440 | − | 19.7358i | 0.348665 | − | 0.998085i | ||||
\(392\) | −1.62218 | −0.0819324 | ||||||||
\(393\) | 1.85692 | − | 12.9152i | 0.0936692 | − | 0.651484i | ||||
\(394\) | −0.00961727 | − | 0.0210589i | −0.000484511 | − | 0.00106093i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.30841 | + | 6.12623i | 0.266757 | + | 0.307855i | ||||
\(397\) | 11.8219 | − | 3.47123i | 0.593325 | − | 0.174216i | 0.0287344 | − | 0.999587i | \(-0.490852\pi\) |
0.564590 | + | 0.825371i | \(0.309034\pi\) | |||||||
\(398\) | 0.320841 | + | 0.206192i | 0.0160823 | + | 0.0103355i | ||||
\(399\) | 4.76890 | − | 10.4424i | 0.238744 | − | 0.522776i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.3895 | + | 18.2448i | −1.41770 | + | 0.911102i | −0.417705 | + | 0.908583i | \(0.637166\pi\) |
−0.999997 | + | 0.00251937i | \(0.999198\pi\) | |||||||
\(402\) | 0.0246493 | + | 0.171440i | 0.00122940 | + | 0.00855063i | ||||
\(403\) | −0.275970 | − | 1.91941i | −0.0137470 | − | 0.0956126i | ||||
\(404\) | −7.53797 | + | 4.84436i | −0.375028 | + | 0.241016i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.253827 | + | 0.555804i | −0.0125972 | + | 0.0275841i | ||||
\(407\) | −18.9890 | − | 12.2035i | −0.941249 | − | 0.604904i | ||||
\(408\) | 1.47199 | − | 0.432214i | 0.0728741 | − | 0.0213978i | ||||
\(409\) | −10.6316 | − | 12.2695i | −0.525698 | − | 0.606688i | 0.429350 | − | 0.903138i | \(-0.358743\pi\) |
−0.955048 | + | 0.296450i | \(0.904197\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.94256 | − | 19.5815i | −0.441104 | − | 0.965883i | ||||
\(412\) | −2.75950 | + | 19.1927i | −0.135951 | + | 0.945558i | ||||
\(413\) | 12.4018 | 0.610254 | ||||||||
\(414\) | −0.841961 | + | 0.0779495i | −0.0413801 | + | 0.00383101i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.320594 | + | 2.22978i | −0.0157184 | + | 0.109324i | ||||
\(417\) | −6.80112 | − | 14.8924i | −0.333052 | − | 0.729282i | ||||
\(418\) | −1.27764 | − | 0.375150i | −0.0624916 | − | 0.0183492i | ||||
\(419\) | 8.76692 | + | 10.1176i | 0.428292 | + | 0.494275i | 0.928345 | − | 0.371719i | \(-0.121232\pi\) |
−0.500053 | + | 0.865995i | \(0.666686\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.9478 | − | 7.03572i | −0.533563 | − | 0.342900i | 0.245954 | − | 0.969282i | \(-0.420899\pi\) |
−0.779517 | + | 0.626382i | \(0.784535\pi\) | |||||||
\(422\) | 0.240510 | − | 0.526644i | 0.0117079 | − | 0.0256366i | ||||
\(423\) | 3.57325 | − | 4.12375i | 0.173737 | − | 0.200504i | ||||
\(424\) | 0.0812036 | − | 0.0521864i | 0.00394360 | − | 0.00253439i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.139903 | − | 0.973048i | −0.00677833 | − | 0.0471443i | ||||
\(427\) | −4.18698 | + | 2.69081i | −0.202622 | + | 0.130217i | ||||
\(428\) | 9.65005 | − | 11.1367i | 0.466453 | − | 0.538315i | ||||
\(429\) | 1.80906 | − | 3.96130i | 0.0873424 | − | 0.191253i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.97982 | + | 2.63671i | −0.432543 | + | 0.127006i | −0.490754 | − | 0.871298i | \(-0.663279\pi\) |
0.0582112 | + | 0.998304i | \(0.481460\pi\) | |||||||
\(432\) | 12.9447 | + | 14.9390i | 0.622804 | + | 0.718754i | ||||
\(433\) | −32.5898 | − | 9.56922i | −1.56616 | − | 0.459867i | −0.620283 | − | 0.784378i | \(-0.712982\pi\) |
−0.945882 | + | 0.324511i | \(0.894800\pi\) | |||||||
\(434\) | 0.0512961 | + | 0.112323i | 0.00246229 | + | 0.00539167i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20.7432 | −0.993419 | ||||||||
\(437\) | −28.0522 | + | 21.9300i | −1.34192 | + | 1.04905i | ||||
\(438\) | −0.914218 | −0.0436830 | ||||||||
\(439\) | −4.53831 | + | 31.5646i | −0.216602 | + | 1.50650i | 0.533854 | + | 0.845577i | \(0.320743\pi\) |
−0.750456 | + | 0.660921i | \(0.770166\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.84511 | − | 2.59716i | −0.421196 | − | 0.123674i | ||||
\(442\) | 0.538668 | + | 0.621656i | 0.0256218 | + | 0.0295691i | ||||
\(443\) | 29.3691 | − | 8.62354i | 1.39537 | − | 0.409717i | 0.504277 | − | 0.863542i | \(-0.331759\pi\) |
0.891091 | + | 0.453825i | \(0.149941\pi\) | |||||||
\(444\) | −18.5950 | − | 11.9502i | −0.882477 | − | 0.567134i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.531535 | − | 0.613424i | 0.0251689 | − | 0.0290465i | ||||
\(447\) | 16.2542 | − | 10.4459i | 0.768797 | − | 0.494076i | ||||
\(448\) | 1.71947 | + | 11.9592i | 0.0812373 | + | 0.565018i | ||||
\(449\) | 2.39840 | + | 16.6812i | 0.113187 | + | 0.787236i | 0.964785 | + | 0.263040i | \(0.0847251\pi\) |
−0.851597 | + | 0.524196i | \(0.824366\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.05133 | + | 9.29173i | −0.379122 | + | 0.437530i | ||||
\(452\) | 16.2145 | − | 35.5048i | 0.762666 | − | 1.67001i | ||||
\(453\) | 16.8366 | + | 10.8202i | 0.791054 | + | 0.508380i | ||||
\(454\) | 0.750400 | − | 0.220337i | 0.0352180 | − | 0.0103409i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.50714 | − | 0.736163i | −0.117408 | − | 0.0344740i | ||||
\(457\) | 1.12972 | + | 2.47375i | 0.0528463 | + | 0.115717i | 0.934213 | − | 0.356715i | \(-0.116103\pi\) |
−0.881367 | + | 0.472432i | \(0.843376\pi\) | |||||||
\(458\) | −0.105195 | + | 0.731650i | −0.00491546 | + | 0.0341877i | ||||
\(459\) | 21.7954 | 1.01732 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.7457 | −1.66484 | −0.832421 | − | 0.554143i | \(-0.813046\pi\) | ||||
−0.832421 | + | 0.554143i | \(0.813046\pi\) | |||||||
\(462\) | −0.0394651 | + | 0.274486i | −0.00183608 | + | 0.0127702i | ||||
\(463\) | 17.3020 | + | 37.8860i | 0.804091 | + | 1.76071i | 0.630961 | + | 0.775814i | \(0.282661\pi\) |
0.173130 | + | 0.984899i | \(0.444612\pi\) | |||||||
\(464\) | −17.0041 | − | 4.99286i | −0.789397 | − | 0.231788i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.03119 | − | 0.596411i | 0.0940931 | − | 0.0276282i | ||||
\(467\) | −14.8682 | − | 9.55519i | −0.688017 | − | 0.442161i | 0.149364 | − | 0.988782i | \(-0.452278\pi\) |
−0.837380 | + | 0.546621i | \(0.815914\pi\) | |||||||
\(468\) | −3.54305 | + | 7.75819i | −0.163777 | + | 0.358623i | ||||
\(469\) | −1.98938 | + | 2.29587i | −0.0918610 | + | 0.106013i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.821781 | + | 5.71561i | 0.0378657 | + | 0.263361i | ||||
\(472\) | −0.401733 | − | 2.79411i | −0.0184913 | − | 0.128609i | ||||
\(473\) | 9.23343 | − | 5.93396i | 0.424553 | − | 0.272844i | ||||
\(474\) | 0.185866 | − | 0.214501i | 0.00853712 | − | 0.00985237i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11.2961 | + | 7.25953i | 0.517754 | + | 0.332740i | ||||
\(477\) | 0.526324 | − | 0.154543i | 0.0240987 | − | 0.00707602i | ||||
\(478\) | −0.648752 | − | 0.748699i | −0.0296732 | − | 0.0342447i | ||||
\(479\) | 11.4723 | + | 3.36858i | 0.524184 | + | 0.153914i | 0.533110 | − | 0.846046i | \(-0.321023\pi\) |
−0.00892633 | + | 0.999960i | \(0.502841\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.37991 | − | 23.5078i | 0.154111 | − | 1.07186i | ||||
\(482\) | 2.47780 | 0.112861 | ||||||||
\(483\) | 5.35195 | + | 5.13260i | 0.243522 | + | 0.233541i | ||||
\(484\) | 13.6687 | 0.621306 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.585941 | − | 1.28303i | −0.0265788 | − | 0.0581995i | ||||
\(487\) | −18.1024 | − | 5.31536i | −0.820300 | − | 0.240862i | −0.155455 | − | 0.987843i | \(-0.549684\pi\) |
−0.664845 | + | 0.746981i | \(0.731503\pi\) | |||||||
\(488\) | 0.741863 | + | 0.856156i | 0.0335826 | + | 0.0387563i | ||||
\(489\) | 8.44701 | − | 2.48026i | 0.381987 | − | 0.112161i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.10363 | − | 19.9342i | 0.410841 | − | 0.899616i | −0.585214 | − | 0.810879i | \(-0.698990\pi\) |
0.996055 | − | 0.0887373i | \(-0.0282832\pi\) | |||||||
\(492\) | −7.88425 | + | 9.09891i | −0.355450 | + | 0.410211i | ||||
\(493\) | −16.4384 | + | 10.5643i | −0.740349 | + | 0.475794i | ||||
\(494\) | −0.199387 | − | 1.38677i | −0.00897086 | − | 0.0623937i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.01291 | + | 1.93628i | −0.135284 | + | 0.0869416i | ||||
\(497\) | 11.2912 | − | 13.0308i | 0.506480 | − | 0.584509i | ||||
\(498\) | −0.159693 | + | 0.349679i | −0.00715602 | + | 0.0156695i | ||||
\(499\) | 8.48768 | + | 5.45470i | 0.379961 | + | 0.244186i | 0.716655 | − | 0.697428i | \(-0.245672\pi\) |
−0.336694 | + | 0.941614i | \(0.609309\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.7879 | − | 14.7581i | −0.571323 | − | 0.659341i | ||||
\(502\) | −2.32553 | − | 0.682837i | −0.103793 | − | 0.0304765i | ||||
\(503\) | −5.56885 | − | 12.1941i | −0.248303 | − | 0.543707i | 0.743907 | − | 0.668283i | \(-0.232970\pi\) |
−0.992210 | + | 0.124576i | \(0.960243\pi\) | |||||||
\(504\) | 0.154886 | − | 1.07726i | 0.00689918 | − | 0.0479849i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.500939 | − | 0.699196i | 0.0222694 | − | 0.0310831i | ||||
\(507\) | −8.41804 | −0.373858 | ||||||||
\(508\) | 4.97451 | − | 34.5985i | 0.220708 | − | 1.53506i | ||||
\(509\) | 8.03460 | + | 17.5933i | 0.356127 | + | 0.779810i | 0.999894 | + | 0.0145879i | \(0.00464363\pi\) |
−0.643766 | + | 0.765222i | \(0.722629\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.5006 | − | 12.1183i | −0.464518 | − | 0.536082i | ||||
\(512\) | 6.66205 | − | 1.95615i | 0.294424 | − | 0.0864506i | ||||
\(513\) | −31.2297 | − | 20.0701i | −1.37882 | − | 0.886116i | ||||
\(514\) | 0.650495 | − | 1.42439i | 0.0286921 | − | 0.0628270i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.04182 | − | 5.81083i | 0.398044 | − | 0.255807i | ||||
\(517\) | 0.789915 | + | 5.49398i | 0.0347404 | + | 0.241625i | ||||
\(518\) | 0.215227 | + | 1.49694i | 0.00945652 | + | 0.0657716i | ||||
\(519\) | −18.1562 | + | 11.6683i | −0.796970 | + | 0.512182i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.67119 | + | 10.2285i | −0.204648 | + | 0.448117i | −0.983930 | − | 0.178557i | \(-0.942857\pi\) |
0.779281 | + | 0.626674i | \(0.215584\pi\) | |||||||
\(522\) | 0.664885 | + | 0.427296i | 0.0291012 | + | 0.0187022i | ||||
\(523\) | −17.3487 | + | 5.09404i | −0.758605 | + | 0.222747i | −0.638087 | − | 0.769964i | \(-0.720274\pi\) |
−0.120519 | + | 0.992711i | \(0.538456\pi\) | |||||||
\(524\) | −17.0228 | − | 19.6454i | −0.743645 | − | 0.858212i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.320098 | − | 0.700917i | −0.0139569 | − | 0.0305614i | ||||
\(527\) | −0.561992 | + | 3.90874i | −0.0244808 | + | 0.170267i | ||||
\(528\) | −8.04304 | −0.350028 | ||||||||
\(529\) | −7.39715 | − | 21.7780i | −0.321615 | − | 0.946870i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.28297 | − | 15.8784i | 0.0990725 | − | 0.689064i | ||||
\(532\) | −9.50074 | − | 20.8037i | −0.411909 | − | 0.901955i | ||||
\(533\) | −12.4119 | − | 3.64448i | −0.537621 | − | 0.157860i | ||||
\(534\) | 0.0370854 | + | 0.0427988i | 0.00160484 | + | 0.00185209i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.581697 | + | 0.373834i | 0.0251255 | + | 0.0161472i | ||||
\(537\) | −6.37863 | + | 13.9672i | −0.275258 | + | 0.602731i | ||||
\(538\) | 0.169194 | − | 0.195260i | 0.00729445 | − | 0.00841825i | ||||
\(539\) | 7.88869 | − | 5.06975i | 0.339790 | − | 0.218370i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.97456 | + | 13.7333i | 0.0848928 | + | 0.590442i | 0.987217 | + | 0.159384i | \(0.0509507\pi\) |
−0.902324 | + | 0.431059i | \(0.858140\pi\) | |||||||
\(542\) | 0.486530 | − | 0.312674i | 0.0208983 | − | 0.0134305i | ||||
\(543\) | −0.536306 | + | 0.618931i | −0.0230151 | + | 0.0265609i | ||||
\(544\) | 1.90571 | − | 4.17292i | 0.0817065 | − | 0.178912i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.279953 | + | 0.0822015i | −0.0119809 | + | 0.00351790i | ||||
\(547\) | −19.7384 | − | 22.7793i | −0.843952 | − | 0.973973i | 0.155953 | − | 0.987764i | \(-0.450155\pi\) |
−0.999905 | + | 0.0137919i | \(0.995610\pi\) | |||||||
\(548\) | −41.1491 | − | 12.0825i | −1.75780 | − | 0.516138i | ||||
\(549\) | 2.67436 | + | 5.85603i | 0.114139 | + | 0.249929i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.2819 | 1.41786 | ||||||||
\(552\) | 0.983001 | − | 1.37204i | 0.0418393 | − | 0.0583981i | ||||
\(553\) | 4.97813 | 0.211692 | ||||||||
\(554\) | 0.285906 | − | 1.98852i | 0.0121470 | − | 0.0844840i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −31.2953 | − | 9.18913i | −1.32722 | − | 0.389706i | ||||
\(557\) | 14.1622 | + | 16.3440i | 0.600071 | + | 0.692519i | 0.971796 | − | 0.235824i | \(-0.0757788\pi\) |
−0.371724 | + | 0.928343i | \(0.621233\pi\) | |||||||
\(558\) | 0.153253 | − | 0.0449991i | 0.00648771 | − | 0.00190496i | ||||
\(559\) | 9.71499 | + | 6.24345i | 0.410900 | + | 0.264070i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.80751 | + | 6.70222i | −0.245193 | + | 0.282968i | ||||
\(562\) | 1.05631 | − | 0.678850i | 0.0445578 | − | 0.0286356i | ||||
\(563\) | 0.0407395 | + | 0.283349i | 0.00171696 | + | 0.0119418i | 0.990662 | − | 0.136341i | \(-0.0435344\pi\) |
−0.988945 | + | 0.148283i | \(0.952625\pi\) | |||||||
\(564\) | 0.773524 | + | 5.37998i | 0.0325712 | + | 0.226538i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.36864 | + | 1.57949i | −0.0575281 | + | 0.0663910i | ||||
\(567\) | 0.642315 | − | 1.40647i | 0.0269747 | − | 0.0590663i | ||||
\(568\) | −3.30156 | − | 2.12179i | −0.138531 | − | 0.0890282i | ||||
\(569\) | 1.66147 | − | 0.487852i | 0.0696525 | − | 0.0204518i | −0.246721 | − | 0.969087i | \(-0.579353\pi\) |
0.316373 | + | 0.948635i | \(0.397535\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.8922 | − | 5.84086i | −0.832461 | − | 0.244433i | −0.162387 | − | 0.986727i | \(-0.551919\pi\) |
−0.670074 | + | 0.742295i | \(0.733738\pi\) | |||||||
\(572\) | −3.60407 | − | 7.89181i | −0.150694 | − | 0.329973i | ||||
\(573\) | 0.607097 | − | 4.22245i | 0.0253618 | − | 0.176395i | ||||
\(574\) | 0.823739 | 0.0343822 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 15.6282 | 0.651174 | ||||||||
\(577\) | 3.43290 | − | 23.8763i | 0.142913 | − | 0.993985i | −0.784549 | − | 0.620067i | \(-0.787105\pi\) |
0.927462 | − | 0.373917i | \(-0.121986\pi\) | |||||||
\(578\) | −0.0733005 | − | 0.160506i | −0.00304890 | − | 0.00667616i | ||||
\(579\) | 4.63848 | + | 1.36198i | 0.192769 | + | 0.0566020i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.46934 | + | 1.89957i | −0.268394 | + | 0.0788074i | ||||
\(582\) | −0.410917 | − | 0.264080i | −0.0170330 | − | 0.0109465i | ||||
\(583\) | −0.231798 | + | 0.507567i | −0.00960009 | + | 0.0210213i | ||||
\(584\) | −2.39009 | + | 2.75831i | −0.0989026 | + | 0.114140i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.0536241 | + | 0.372964i | 0.00221519 | + | 0.0154070i | ||||
\(587\) | −4.77952 | − | 33.2423i | −0.197272 | − | 1.37206i | −0.812157 | − | 0.583439i | \(-0.801707\pi\) |
0.614885 | − | 0.788617i | \(-0.289202\pi\) | |||||||
\(588\) | 7.72499 | − | 4.96455i | 0.318573 | − | 0.204734i | ||||
\(589\) | 4.40458 | − | 5.08316i | 0.181488 | − | 0.209448i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.220925 | + | 0.141980i | 0.00908764 | + | 0.00584027i | ||||
\(592\) | −42.0867 | + | 12.3578i | −1.72975 | + | 0.507901i | ||||
\(593\) | 19.5470 | + | 22.5585i | 0.802700 | + | 0.926365i | 0.998526 | − | 0.0542739i | \(-0.0172844\pi\) |
−0.195827 | + | 0.980639i | \(0.562739\pi\) | |||||||
\(594\) | 0.860418 | + | 0.252641i | 0.0353034 | + | 0.0103660i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.47807 | − | 38.1008i | 0.224391 | − | 1.56067i | ||||
\(597\) | −4.32625 | −0.177062 | ||||||||
\(598\) | 0.888133 | + | 0.173830i | 0.0363185 | + | 0.00710843i | ||||
\(599\) | 4.70186 | 0.192113 | 0.0960564 | − | 0.995376i | \(-0.469377\pi\) | ||||
0.0960564 | + | 0.995376i | \(0.469377\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.89729 | + | 19.4823i | 0.362928 | + | 0.794701i | 0.999720 | + | 0.0236658i | \(0.00753375\pi\) |
−0.636792 | + | 0.771036i | \(0.719739\pi\) | |||||||
\(602\) | −0.705584 | − | 0.207178i | −0.0287575 | − | 0.00844395i | ||||
\(603\) | 2.57325 | + | 2.96969i | 0.104791 | + | 0.120935i | ||||
\(604\) | 38.2569 | − | 11.2332i | 1.55665 | − | 0.457073i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.164711 | + | 0.360666i | −0.00669091 | + | 0.0146511i | ||||
\(607\) | −25.2756 | + | 29.1696i | −1.02591 | + | 1.18396i | −0.0431477 | + | 0.999069i | \(0.513739\pi\) |
−0.982759 | + | 0.184891i | \(0.940807\pi\) | |||||||
\(608\) | −6.57319 | + | 4.22433i | −0.266578 | + | 0.171319i | ||||
\(609\) | −0.986403 | − | 6.86058i | −0.0399711 | − | 0.278005i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.91289 | + | 3.15732i | −0.198754 | + | 0.127732i | ||||
\(612\) | 11.3740 | − | 13.1263i | 0.459766 | − | 0.530599i | ||||
\(613\) | −7.81638 | + | 17.1155i | −0.315700 | + | 0.691288i | −0.999254 | − | 0.0386125i | \(-0.987706\pi\) |
0.683554 | + | 0.729900i | \(0.260433\pi\) | |||||||
\(614\) | −0.663370 | − | 0.426322i | −0.0267714 | − | 0.0172050i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.724983 | + | 0.836675i | 0.0292104 | + | 0.0337106i | ||||
\(617\) | 15.2099 | + | 4.46602i | 0.612326 | + | 0.179795i | 0.573168 | − | 0.819438i | \(-0.305714\pi\) |
0.0391580 | + | 0.999233i | \(0.487532\pi\) | |||||||
\(618\) | 0.356430 | + | 0.780473i | 0.0143377 | + | 0.0313952i | ||||
\(619\) | 4.22984 | − | 29.4192i | 0.170012 | − | 1.18246i | −0.708842 | − | 0.705367i | \(-0.750782\pi\) |
0.878854 | − | 0.477091i | \(-0.158309\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.8915 | − | 14.7685i | 0.758091 | − | 0.592641i | ||||
\(622\) | 2.05794 | 0.0825158 | ||||||||
\(623\) | −0.141357 | + | 0.983162i | −0.00566336 | + | 0.0393896i | ||||
\(624\) | −3.51546 | − | 7.69778i | −0.140731 | − | 0.308158i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.29956 | + | 1.49977i | 0.0519408 | + | 0.0599429i | ||||
\(627\) | 14.4930 | − | 4.25553i | 0.578794 | − | 0.169949i | ||||
\(628\) | 9.67769 | + | 6.21947i | 0.386182 | + | 0.248184i | ||||
\(629\) | −20.0912 | + | 43.9936i | −0.801089 | + | 1.75414i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.0318 | + | 9.01768i | −0.558597 | + | 0.358988i | −0.789273 | − | 0.614042i | \(-0.789542\pi\) |
0.230677 | + | 0.973030i | \(0.425906\pi\) | |||||||
\(632\) | −0.161257 | − | 1.12156i | −0.00641444 | − | 0.0446134i | ||||
\(633\) | 0.934652 | + | 6.50065i | 0.0371491 | + | 0.258378i | ||||
\(634\) | 0.945584 | − | 0.607690i | 0.0375539 | − | 0.0241345i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.226988 | + | 0.497034i | −0.00900066 | + | 0.0197087i | ||||
\(637\) | 8.30012 | + | 5.33416i | 0.328863 | + | 0.211347i | ||||
\(638\) | −0.771397 | + | 0.226502i | −0.0305399 | + | 0.00896732i | ||||
\(639\) | −14.6051 | − | 16.8552i | −0.577769 | − | 0.666781i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.5542 | − | 27.4898i | −0.495859 | − | 1.08578i | −0.977793 | − | 0.209573i | \(-0.932793\pi\) |
0.481934 | − | 0.876208i | \(-0.339935\pi\) | |||||||
\(642\) | 0.0927990 | − | 0.645431i | 0.00366248 | − | 0.0254731i | ||||
\(643\) | 7.45857 | 0.294137 | 0.147069 | − | 0.989126i | \(-0.453016\pi\) | ||||
0.147069 | + | 0.989126i | \(0.453016\pi\) | |||||||
\(644\) | 14.7101 | − | 1.36187i | 0.579659 | − | 0.0536653i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.406038 | + | 2.82406i | −0.0159754 | + | 0.111111i | ||||
\(647\) | −3.17102 | − | 6.94356i | −0.124666 | − | 0.272980i | 0.837001 | − | 0.547202i | \(-0.184307\pi\) |
−0.961666 | + | 0.274222i | \(0.911580\pi\) | |||||||
\(648\) | −0.337683 | − | 0.0991526i | −0.0132654 | − | 0.00389508i | ||||
\(649\) | 10.6860 | + | 12.3323i | 0.419462 | + | 0.484085i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.17836 | − | 0.757286i | −0.0461836 | − | 0.0296804i | ||||
\(652\) | 7.28589 | − | 15.9539i | 0.285337 | − | 0.624802i | ||||
\(653\) | 25.4564 | − | 29.3782i | 0.996185 | − | 1.14966i | 0.00745135 | − | 0.999972i | \(-0.497628\pi\) |
0.988734 | − | 0.149686i | \(-0.0478264\pi\) | |||||||
\(654\) | −0.772173 | + | 0.496246i | −0.0301944 | + | 0.0194047i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.40014 | + | 23.6485i | 0.132753 | + | 0.923319i | ||||
\(657\) | −17.4484 | + | 11.2134i | −0.680726 | + | 0.437476i | ||||
\(658\) | 0.243529 | − | 0.281047i | 0.00949374 | − | 0.0109564i | ||||
\(659\) | −5.38310 | + | 11.7873i | −0.209696 | + | 0.459170i | −0.985030 | − | 0.172381i | \(-0.944854\pi\) |
0.775335 | + | 0.631551i | \(0.217581\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.9778 | − | 8.50866i | 1.12711 | − | 0.330949i | 0.335537 | − | 0.942027i | \(-0.391082\pi\) |
0.791570 | + | 0.611078i | \(0.209264\pi\) | |||||||
\(662\) | −0.946639 | − | 1.09248i | −0.0367922 | − | 0.0424604i | ||||
\(663\) | −8.95287 | − | 2.62880i | −0.347701 | − | 0.102094i | ||||
\(664\) | 0.637531 | + | 1.39600i | 0.0247410 | + | 0.0541753i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.95619 | 0.0758007 | ||||||||
\(667\) | −7.08990 | + | 20.2955i | −0.274522 | + | 0.785844i | ||||
\(668\) | −38.9037 | −1.50523 | ||||||||
\(669\) | −1.31033 | + | 9.11356i | −0.0506604 | + | 0.352351i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.28342 | − | 1.84498i | −0.242569 | − | 0.0712246i | ||||
\(672\) | 1.06560 | + | 1.22977i | 0.0411064 | + | 0.0474393i | ||||
\(673\) | −2.27218 | + | 0.667173i | −0.0875862 | + | 0.0257176i | −0.325232 | − | 0.945634i | \(-0.605442\pi\) |
0.237646 | + | 0.971352i | \(0.423624\pi\) | |||||||
\(674\) | 2.03488 | + | 1.30773i | 0.0783805 | + | 0.0503721i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.9824 | + | 12.6744i | −0.422402 | + | 0.487478i | ||||
\(677\) | 29.1912 | − | 18.7600i | 1.12191 | − | 0.721006i | 0.158052 | − | 0.987431i | \(-0.449479\pi\) |
0.963856 | + | 0.266425i | \(0.0858423\pi\) | |||||||
\(678\) | −0.245801 | − | 1.70958i | −0.00943993 | − | 0.0656562i | ||||
\(679\) | −1.21925 | − | 8.48004i | −0.0467904 | − | 0.325434i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.80963 | + | 6.70467i | −0.222626 | + | 0.256924i | ||||
\(682\) | −0.0674940 | + | 0.147791i | −0.00258448 | + | 0.00565922i | ||||
\(683\) | 19.5711 | + | 12.5776i | 0.748869 | + | 0.481269i | 0.858570 | − | 0.512696i | \(-0.171353\pi\) |
−0.109702 | + | 0.993965i | \(0.534990\pi\) | |||||||
\(684\) | −28.3845 | + | 8.33444i | −1.08531 | + | 0.318675i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.51832 | − | 0.445819i | −0.0579698 | − | 0.0170215i | ||||
\(687\) | −3.48319 | − | 7.62712i | −0.132892 | − | 0.290993i | ||||
\(688\) | 3.03539 | − | 21.1116i | 0.115723 | − | 0.804872i | ||||
\(689\) | −0.587093 | −0.0223665 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.0096 | −1.71225 | −0.856123 | − | 0.516772i | \(-0.827133\pi\) | ||||
−0.856123 | + | 0.516772i | \(0.827133\pi\) | |||||||
\(692\) | −6.11911 | + | 42.5593i | −0.232614 | + | 1.61786i | ||||
\(693\) | 2.61351 | + | 5.72279i | 0.0992790 | + | 0.217391i | ||||
\(694\) | −0.510520 | − | 0.149902i | −0.0193791 | − | 0.00569020i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.51372 | + | 0.444470i | −0.0573776 | + | 0.0168476i | ||||
\(697\) | 22.1612 | + | 14.2422i | 0.839417 | + | 0.539461i | ||||
\(698\) | −0.305688 | + | 0.669363i | −0.0115705 | + | 0.0253358i | ||||
\(699\) | −15.7256 | + | 18.1483i | −0.594796 | + | 0.686431i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.34738 | − | 23.2815i | −0.126429 | − | 0.879332i | −0.950029 | − | 0.312161i | \(-0.898947\pi\) |
0.823600 | − | 0.567171i | \(-0.191962\pi\) | |||||||
\(702\) | 0.134276 | + | 0.933908i | 0.00506791 | + | 0.0352481i | ||||
\(703\) | 69.2989 | − | 44.5357i | 2.61366 | − | 1.67969i | ||||
\(704\) | −10.4105 | + | 12.0144i | −0.392362 | + | 0.452810i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.93952 | − | 1.24645i | −0.0729946 | − | 0.0469108i | ||||
\(707\) | −6.67261 | + | 1.95925i | −0.250949 | + | 0.0736854i | ||||
\(708\) | 10.4643 | + | 12.0764i | 0.393271 | + | 0.453859i | ||||
\(709\) | 32.8793 | + | 9.65422i | 1.23481 | + | 0.362572i | 0.833062 | − | 0.553180i | \(-0.186586\pi\) |
0.401745 | + | 0.915752i | \(0.368404\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.916390 | − | 6.37363i | 0.0343673 | − | 0.239030i | ||||
\(712\) | 0.226084 | 0.00847285 | ||||||||
\(713\) | 2.16144 | + | 3.76877i | 0.0809467 | + | 0.141142i | ||||
\(714\) | 0.594172 | 0.0222363 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.7077 | + | 27.8260i | 0.474909 | + | 1.03990i | ||||
\(717\) | 10.7825 | + | 3.16603i | 0.402680 | + | 0.118238i | ||||
\(718\) | 0.326770 | + | 0.377112i | 0.0121949 | + | 0.0140737i | ||||
\(719\) | −22.3827 | + | 6.57217i | −0.834735 | + | 0.245100i | −0.671050 | − | 0.741412i | \(-0.734156\pi\) |
−0.163685 | + | 0.986513i | \(0.552338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.25157 | + | 13.6890i | −0.232821 | + | 0.509806i | ||||
\(722\) | 2.08543 | − | 2.40672i | 0.0776117 | − | 0.0895687i | ||||
\(723\) | −23.6451 | + | 15.1958i | −0.879371 | + | 0.565138i | ||||
\(724\) | 0.232195 | + | 1.61495i | 0.00862947 | + | 0.0600193i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.508824 | − | 0.327001i | 0.0188842 | − | 0.0121362i | ||||
\(727\) | 26.3834 | − | 30.4481i | 0.978507 | − | 1.12926i | −0.0130932 | − | 0.999914i | \(-0.504168\pi\) |
0.991600 | − | 0.129343i | \(-0.0412867\pi\) | |||||||
\(728\) | −0.483883 | + | 1.05956i | −0.0179339 | + | 0.0392698i | ||||
\(729\) | 10.9363 | + | 7.02833i | 0.405048 | + | 0.260309i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.4005 | − | 17.7731i | −0.569607 | − | 0.657361i | ||||
\(732\) | −6.15303 | − | 1.80669i | −0.227422 | − | 0.0667773i | ||||
\(733\) | 9.43781 | + | 20.6659i | 0.348594 | + | 0.763313i | 0.999990 | + | 0.00457542i | \(0.00145641\pi\) |
−0.651396 | + | 0.758738i | \(0.725816\pi\) | |||||||
\(734\) | 0.154499 | − | 1.07456i | 0.00570266 | − | 0.0396629i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.17576 | − | 4.90825i | −0.0433391 | − | 0.180921i | ||||
\(737\) | −3.99714 | −0.147236 | ||||||||
\(738\) | 0.151637 | − | 1.05466i | 0.00558182 | − | 0.0388224i | ||||
\(739\) | −7.47356 | − | 16.3648i | −0.274919 | − | 0.601989i | 0.720930 | − | 0.693008i | \(-0.243715\pi\) |
−0.995849 | + | 0.0910188i | \(0.970988\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.4075 | + | 12.0109i | 0.382328 | + | 0.441230i | ||||
\(742\) | 0.0358708 | − | 0.0105326i | 0.00131686 | − | 0.000386664i | ||||
\(743\) | 4.89833 | + | 3.14797i | 0.179702 | + | 0.115488i | 0.627399 | − | 0.778698i | \(-0.284119\pi\) |
−0.447697 | + | 0.894185i | \(0.647756\pi\) | |||||||
\(744\) | −0.132445 | + | 0.290013i | −0.00485566 | + | 0.0106324i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.16002 | − | 1.38816i | 0.0790840 | − | 0.0508242i | ||||
\(747\) | 1.24117 | + | 8.63256i | 0.0454122 | + | 0.315849i | ||||
\(748\) | 2.51438 | + | 17.4879i | 0.0919347 | + | 0.639420i | ||||
\(749\) | 9.62131 | − | 6.18324i | 0.351555 | − | 0.225931i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.84740 | − | 8.42462i | 0.140393 | − | 0.307419i | −0.826354 | − | 0.563151i | \(-0.809589\pi\) |
0.966748 | + | 0.255732i | \(0.0823164\pi\) | |||||||
\(752\) | 9.07372 | + | 5.83133i | 0.330885 | + | 0.212647i | ||||
\(753\) | 26.3797 | − | 7.74578i | 0.961330 | − | 0.282272i | ||||
\(754\) | −0.553942 | − | 0.639283i | −0.0201734 | − | 0.0232813i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 6.39819 | + | 14.0101i | 0.232700 | + | 0.509542i | ||||
\(757\) | −1.15607 | + | 8.04064i | −0.0420180 | + | 0.292242i | 0.957968 | + | 0.286877i | \(0.0926169\pi\) |
−0.999986 | + | 0.00536536i | \(0.998292\pi\) | |||||||
\(758\) | 2.94048 | 0.106803 | ||||||||
\(759\) | −0.492336 | + | 9.74443i | −0.0178707 | + | 0.353700i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.15984 | + | 28.9323i | −0.150794 | + | 1.04880i | 0.764099 | + | 0.645099i | \(0.223184\pi\) |
−0.914893 | + | 0.403697i | \(0.867725\pi\) | |||||||
\(762\) | −0.642532 | − | 1.40695i | −0.0232765 | − | 0.0509684i | ||||
\(763\) | −15.4470 | − | 4.53565i | −0.559219 | − | 0.164201i | ||||
\(764\) | −5.56539 | − | 6.42281i | −0.201349 | − | 0.232369i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.30544 | + | 1.48162i | 0.0832990 | + | 0.0535330i | ||||
\(767\) | −7.13228 | + | 15.6175i | −0.257532 | + | 0.563915i | ||||
\(768\) | −10.0730 | + | 11.6249i | −0.363478 | + | 0.419476i | ||||
\(769\) | 12.2803 | − | 7.89208i | 0.442840 | − | 0.284596i | −0.300158 | − | 0.953889i | \(-0.597040\pi\) |
0.742998 | + | 0.669294i | \(0.233403\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.52790 | + | 17.5820i | 0.0910403 | + | 0.633199i | ||||
\(772\) | 8.10215 | − | 5.20693i | 0.291603 | − | 0.187402i | ||||
\(773\) | −11.3054 | + | 13.0471i | −0.406625 | + | 0.469271i | −0.921716 | − | 0.387865i | \(-0.873213\pi\) |
0.515091 | + | 0.857136i | \(0.327758\pi\) | |||||||
\(774\) | −0.395142 | + | 0.865241i | −0.0142031 | + | 0.0311004i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.87104 | + | 0.549388i | −0.0671666 | + | 0.0197219i | ||||
\(777\) | −11.2342 | − | 12.9650i | −0.403026 | − | 0.465117i | ||||
\(778\) | −1.07306 | − | 0.315080i | −0.0384712 | − | 0.0112962i | ||||
\(779\) | −18.6391 | − | 40.8139i | −0.667815 | − | 1.46231i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.6867 | 0.811795 | ||||||||
\(782\) | −1.63563 | − | 0.849200i | −0.0584899 | − | 0.0303673i | ||||
\(783\) | −22.4134 | −0.800991 | ||||||||
\(784\) | 2.59332 | − | 18.0369i | 0.0926186 | − | 0.644176i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.10366 | − | 0.324065i | −0.0393663 | − | 0.0115590i | ||||
\(787\) | 10.0471 | + | 11.5950i | 0.358142 | + | 0.413318i | 0.906016 | − | 0.423243i | \(-0.139108\pi\) |
−0.547875 | + | 0.836561i | \(0.684563\pi\) | |||||||
\(788\) | 0.501995 | − | 0.147399i | 0.0178828 | − | 0.00525087i | ||||
\(789\) | 7.35320 | + | 4.72561i | 0.261781 | + | 0.168236i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.8380 | − | 22.8942i | 0.705356 | − | 0.814025i | ||||
\(792\) | 1.20467 | − | 0.774198i | 0.0428063 | − | 0.0275099i | ||||
\(793\) | −0.980582 | − | 6.82010i | −0.0348215 | − | 0.242189i | ||||
\(794\) | −0.154578 | − | 1.07511i | −0.00548577 | − | 0.0381544i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.64417 | + | 6.51371i | −0.200052 | + | 0.230872i | ||||
\(797\) | −10.4360 | + | 22.8517i | −0.369663 | + | 0.809448i | 0.629803 | + | 0.776755i | \(0.283136\pi\) |
−0.999465 | + | 0.0326932i | \(0.989592\pi\) | |||||||
\(798\) | −0.851362 | − | 0.547137i | −0.0301379 | − | 0.0193685i | ||||
\(799\) | 11.4109 | − | 3.35055i | 0.403690 | − | 0.118534i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.23275 | + | 0.361967i | 0.0435570 | + | 0.0127895i | ||||
\(802\) | 1.23584 | + | 2.70612i | 0.0436392 | + | 0.0955565i | ||||
\(803\) | 3.00258 | − | 20.8834i | 0.105959 | − | 0.736959i | ||||
\(804\) | −3.91419 | −0.138043 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.170947 | −0.00602136 | ||||||||
\(807\) | −0.417094 | + | 2.90095i | −0.0146824 | + | 0.102118i | ||||
\(808\) | 0.657563 | + | 1.43986i | 0.0231330 | + | 0.0506542i | ||||
\(809\) | −21.8919 | − | 6.42804i | −0.769678 | − | 0.225998i | −0.126761 | − | 0.991933i | \(-0.540458\pi\) |
−0.642917 | + | 0.765935i | \(0.722276\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.7803 | − | 12.2678i | 1.46711 | − | 0.430781i | 0.551949 | − | 0.833878i | \(-0.313884\pi\) |
0.915157 | + | 0.403097i | \(0.132066\pi\) | |||||||
\(812\) | −11.6164 | − | 7.46538i | −0.407654 | − | 0.261984i | ||||
\(813\) | −2.72530 | + | 5.96757i | −0.0955803 | + | 0.209292i | ||||
\(814\) | −1.30309 | + | 1.50385i | −0.0456734 | + | 0.0527099i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.45256 | + | 17.0579i | 0.0858567 | + | 0.597147i | ||||
\(817\) | 5.70046 | + | 39.6476i | 0.199434 | + | 1.38709i | ||||
\(818\) | −1.20400 | + | 0.773766i | −0.0420970 | + | 0.0270541i | ||||
\(819\) | −4.33481 | + | 5.00264i | −0.151471 | + | 0.174806i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.9122 | + | 26.2927i | 1.42785 | + | 0.917621i | 0.999905 | + | 0.0138148i | \(0.00439753\pi\) |
0.427942 | + | 0.903806i | \(0.359239\pi\) | |||||||
\(822\) | −1.82085 | + | 0.534648i | −0.0635093 | + | 0.0186480i | ||||
\(823\) | 0.752583 | + | 0.868528i | 0.0262334 | + | 0.0302750i | 0.768715 | − | 0.639592i | \(-0.220897\pi\) |
−0.742481 | + | 0.669867i | \(0.766351\pi\) | |||||||
\(824\) | 3.28662 | + | 0.965039i | 0.114495 | + | 0.0336187i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.155592 | − | 1.08217i | 0.00541374 | − | 0.0376534i | ||||
\(827\) | 15.3873 | 0.535069 | 0.267534 | − | 0.963548i | \(-0.413791\pi\) | ||||
0.267534 | + | 0.963548i | \(0.413791\pi\) | |||||||
\(828\) | 0.964240 | − | 19.0844i | 0.0335096 | − | 0.663230i | ||||
\(829\) | −43.7168 | −1.51835 | −0.759174 | − | 0.650888i | \(-0.774397\pi\) | ||||
−0.759174 | + | 0.650888i | \(0.774397\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.46680 | + | 20.7294i | 0.328400 | + | 0.719095i | ||||
\(832\) | −16.0489 | − | 4.71239i | −0.556396 | − | 0.163373i | ||||
\(833\) | −13.1576 | − | 15.1846i | −0.455883 | − | 0.526117i | ||||
\(834\) | −1.38481 | + | 0.406618i | −0.0479522 | + | 0.0140800i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.5008 | − | 27.3729i | 0.432349 | − | 0.946712i | ||||
\(837\) | −2.96623 | + | 3.42321i | −0.102528 | + | 0.118323i | ||||
\(838\) | 0.992833 | − | 0.638055i | 0.0342969 | − | 0.0220413i | ||||
\(839\) | 1.60650 | + | 11.1735i | 0.0554627 | + | 0.385751i | 0.998579 | + | 0.0532888i | \(0.0169704\pi\) |
−0.943116 | + | 0.332462i | \(0.892121\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.49181 | + | 4.81469i | −0.258338 | + | 0.166024i | ||||
\(842\) | −0.751277 | + | 0.867020i | −0.0258907 | + | 0.0298795i | ||||
\(843\) | −5.91692 | + | 12.9563i | −0.203790 | + | 0.446237i | ||||
\(844\) | 11.0069 | + | 7.07372i | 0.378874 | + | 0.243488i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.315003 | − | 0.363533i | −0.0108300 | − | 0.0124985i | ||||
\(847\) | 10.1788 | + | 2.98877i | 0.349748 | + | 0.102695i | ||||
\(848\) | 0.450441 | + | 0.986328i | 0.0154682 | + | 0.0338707i | ||||
\(849\) | 3.37394 | − | 23.4663i | 0.115793 | − | 0.805361i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.3956 | + | 51.7460i | 0.424917 | + | 1.77383i | ||||
\(852\) | 22.2160 | 0.761106 | ||||||||
\(853\) | 2.37985 | − | 16.5522i | 0.0814845 | − | 0.566737i | −0.907651 | − | 0.419727i | \(-0.862126\pi\) |
0.989135 | − | 0.147010i | \(-0.0469650\pi\) | |||||||
\(854\) | 0.182267 | + | 0.399108i | 0.00623704 | + | 0.0136572i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.70474 | − | 1.96737i | −0.0582667 | − | 0.0672433i | ||||
\(857\) | 5.93618 | − | 1.74302i | 0.202776 | − | 0.0595405i | −0.178767 | − | 0.983891i | \(-0.557211\pi\) |
0.381543 | + | 0.924351i | \(0.375393\pi\) | |||||||
\(858\) | −0.322961 | − | 0.207554i | −0.0110257 | − | 0.00708579i | ||||
\(859\) | −3.60612 | + | 7.89631i | −0.123039 | + | 0.269419i | −0.961122 | − | 0.276125i | \(-0.910950\pi\) |
0.838082 | + | 0.545544i | \(0.183677\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.86077 | + | 5.05181i | −0.267894 | + | 0.172165i | ||||
\(862\) | 0.117416 | + | 0.816646i | 0.00399921 | + | 0.0278151i | ||||
\(863\) | 1.61006 | + | 11.1982i | 0.0548072 | + | 0.381192i | 0.998701 | + | 0.0509446i | \(0.0162232\pi\) |
−0.943894 | + | 0.330248i | \(0.892868\pi\) | |||||||
\(864\) | 4.42666 | − | 2.84484i | 0.150598 | − | 0.0967834i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.24386 | + | 2.72368i | −0.0422682 | + | 0.0925546i | ||||
\(867\) | 1.68384 | + | 1.08214i | 0.0571861 | + | 0.0367513i | ||||
\(868\) | −2.67752 | + | 0.786189i | −0.0908808 | + | 0.0266850i | ||||
\(869\) | 4.28939 | + | 4.95022i | 0.145508 | + | 0.167925i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.74707 | − | 3.82555i | −0.0591973 | − | 0.129624i | ||||
\(872\) | −0.521499 | + | 3.62711i | −0.0176602 | + | 0.122829i | ||||
\(873\) | −11.0817 | −0.375058 | ||||||||
\(874\) | 1.56164 | + | 2.72293i | 0.0528232 | + | 0.0921045i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.94027 | − | 20.4500i | 0.0993426 | − | 0.690943i | ||||
\(877\) | −10.2913 | − | 22.5349i | −0.347514 | − | 0.760950i | −0.999995 | − | 0.00314460i | \(-0.998999\pi\) |
0.652481 | − | 0.757805i | \(-0.273728\pi\) | |||||||
\(878\) | 2.69735 | + | 0.792013i | 0.0910311 | + | 0.0267291i | ||||
\(879\) | −2.79903 | − | 3.23025i | −0.0944090 | − | 0.108954i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.0492 | + | 18.0261i | 0.945000 | + | 0.607315i | 0.919808 | − | 0.392368i | \(-0.128344\pi\) |
0.0251917 | + | 0.999683i | \(0.491980\pi\) | |||||||
\(882\) | −0.337594 | + | 0.739229i | −0.0113674 | + | 0.0248911i | ||||
\(883\) | −8.56278 | + | 9.88198i | −0.288161 | + | 0.332555i | −0.881311 | − | 0.472537i | \(-0.843338\pi\) |
0.593150 | + | 0.805092i | \(0.297884\pi\) | |||||||
\(884\) | −15.6382 | + | 10.0501i | −0.525969 | + | 0.338020i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.384017 | − | 2.67090i | −0.0129013 | − | 0.0897305i | ||||
\(887\) | −18.6668 | + | 11.9964i | −0.626770 | + | 0.402800i | −0.815112 | − | 0.579303i | \(-0.803325\pi\) |
0.188343 | + | 0.982103i | \(0.439688\pi\) | |||||||
\(888\) | −2.55708 | + | 2.95103i | −0.0858101 | + | 0.0990301i | ||||
\(889\) | 11.2696 | − | 24.6770i | 0.377971 | − | 0.827641i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.95204 | − | 0.573170i | 0.0653957 | − | 0.0192019i | ||||
\(892\) | 12.0121 | + | 13.8627i | 0.402195 | + | 0.464158i | ||||
\(893\) | −19.4355 | − | 5.70679i | −0.650385 | − | 0.190970i | ||||
\(894\) | −0.707574 | − | 1.54937i | −0.0236648 | − | 0.0518187i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.31954 | 0.144306 | ||||||||
\(897\) | −9.54133 | + | 3.78790i | −0.318576 | + | 0.126474i | ||||
\(898\) | 1.48567 | 0.0495775 | ||||||||
\(899\) | 0.577928 | − | 4.01958i | 0.0192750 | − | 0.134060i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.14714 | + | 0.336832i | 0.0382169 | + | 0.0112215i | ||||
\(902\) | 0.709772 | + | 0.819121i | 0.0236328 | + | 0.0272737i | ||||
\(903\) | 8.00382 | − | 2.35013i | 0.266351 | − | 0.0782076i | ||||
\(904\) | −5.80064 | − | 3.72784i | −0.192926 | − | 0.123986i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.15539 | − | 1.33339i | 0.0383853 | − | 0.0442990i | ||||
\(907\) | 18.0240 | − | 11.5834i | 0.598479 | − | 0.384619i | −0.206042 | − | 0.978543i | \(-0.566058\pi\) |
0.804521 | + | 0.593924i | \(0.202422\pi\) | |||||||
\(908\) | 2.51530 | + | 17.4943i | 0.0834730 | + | 0.580568i | ||||
\(909\) | 1.28017 | + | 8.90379i | 0.0424606 | + | 0.295320i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.5067 | − | 29.4363i | 0.845076 | − | 0.975269i | −0.154844 | − | 0.987939i | \(-0.549488\pi\) |
0.999920 | + | 0.0126696i | \(0.00403297\pi\) | |||||||
\(912\) | 12.1935 | − | 26.6999i | 0.403766 | − | 0.884123i | ||||
\(913\) | −7.46321 | − | 4.79631i | −0.246996 | − | 0.158735i | ||||
\(914\) | 0.230030 | − | 0.0675428i | 0.00760870 | − | 0.00223412i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.0279 | − | 4.70621i | −0.529576 | − | 0.155497i | ||||
\(917\) | −8.38091 | − | 18.3516i | −0.276762 | − | 0.606024i | ||||
\(918\) | 0.273443 | − | 1.90184i | 0.00902496 | − | 0.0627700i | ||||
\(919\) | 29.9408 | 0.987657 | 0.493829 | − | 0.869559i | \(-0.335597\pi\) | ||||
0.493829 | + | 0.869559i | \(0.335597\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.94494 | 0.294746 | ||||||||
\(922\) | −0.448462 | + | 3.11912i | −0.0147693 | + | 0.102723i | ||||
\(923\) | 9.91594 | + | 21.7129i | 0.326387 | + | 0.714688i | ||||
\(924\) | −6.01302 | − | 1.76558i | −0.197814 | − | 0.0580834i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.52295 | − | 1.03443i | 0.115771 | − | 0.0339935i | ||||
\(927\) | 16.3756 | + | 10.5240i | 0.537846 | + | 0.345653i | ||||
\(928\) | −1.95974 | + | 4.29124i | −0.0643318 | + | 0.140867i | ||||
\(929\) | 8.14358 | − | 9.39819i | 0.267182 | − | 0.308345i | −0.606266 | − | 0.795262i | \(-0.707333\pi\) |
0.873448 | + | 0.486917i | \(0.161879\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.87026 | + | 33.8734i | 0.159616 | + | 1.11016i | ||||
\(932\) | 6.80843 | + | 47.3537i | 0.223017 | + | 1.55112i | ||||
\(933\) | −19.6385 | + | 12.6209i | −0.642934 | + | 0.413189i | ||||
\(934\) | −1.02031 | + | 1.17750i | −0.0333855 | + | 0.0385289i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.26750 | + | 0.814576i | 0.0414297 | + | 0.0266252i | ||||
\(937\) | 9.15473 | − | 2.68807i | 0.299072 | − | 0.0878155i | −0.128754 | − | 0.991677i | \(-0.541098\pi\) |
0.427826 | + | 0.903861i | \(0.359280\pi\) | |||||||
\(938\) | 0.175376 | + | 0.202394i | 0.00572621 | + | 0.00660840i | ||||
\(939\) | −21.5992 | − | 6.34209i | −0.704863 | − | 0.206966i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.484266 | − | 3.36814i | 0.0157866 | − | 0.109798i | −0.980405 | − | 0.196995i | \(-0.936882\pi\) |
0.996191 | + | 0.0871966i | \(0.0277908\pi\) | |||||||
\(942\) | 0.509046 | 0.0165856 | ||||||||
\(943\) | 28.8591 | − | 2.67180i | 0.939782 | − | 0.0870058i | ||||
\(944\) | 31.7099 | 1.03207 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.401948 | − | 0.880143i | −0.0130684 | − | 0.0286159i | ||||
\(947\) | 11.9343 | + | 3.50424i | 0.387814 | + | 0.113872i | 0.469826 | − | 0.882759i | \(-0.344317\pi\) |
−0.0820124 | + | 0.996631i | \(0.526135\pi\) | |||||||
\(948\) | 4.20038 | + | 4.84750i | 0.136422 | + | 0.157439i | ||||
\(949\) | 21.2993 | − | 6.25405i | 0.691405 | − | 0.203015i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.29668 | + | 11.5981i | −0.171757 | + | 0.376095i | ||||
\(952\) | 1.55338 | − | 1.79269i | 0.0503452 | − | 0.0581015i | ||||
\(953\) | −11.2590 | + | 7.23572i | −0.364715 | + | 0.234388i | −0.710143 | − | 0.704057i | \(-0.751370\pi\) |
0.345429 | + | 0.938445i | \(0.387734\pi\) | |||||||
\(954\) | −0.00688198 | − | 0.0478652i | −0.000222812 | − | 0.00154969i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 18.8341 | − | 12.1039i | 0.609137 | − | 0.391469i | ||||
\(957\) | 5.97219 | − | 6.89227i | 0.193053 | − | 0.222795i | ||||
\(958\) | 0.437868 | − | 0.958797i | 0.0141469 | − | 0.0309773i | ||||
\(959\) | −28.0009 | − | 17.9951i | −0.904197 | − | 0.581092i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.7633 | + | 22.8080i | 0.637524 | + | 0.735742i | ||||
\(962\) | −2.00885 | − | 0.589852i | −0.0647680 | − | 0.0190176i | ||||
\(963\) | −6.14545 | − | 13.4567i | −0.198034 | − | 0.433635i | ||||
\(964\) | −7.96900 | + | 55.4256i | −0.256664 | + | 1.78514i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.515009 | − | 0.402610i | 0.0165701 | − | 0.0129538i | ||||
\(967\) | 24.7635 | 0.796341 | 0.398170 | − | 0.917311i | \(-0.369645\pi\) | ||||
0.398170 | + | 0.917311i | \(0.369645\pi\) | |||||||
\(968\) | 0.343642 | − | 2.39008i | 0.0110451 | − | 0.0768202i | ||||
\(969\) | −13.4446 | − | 29.4395i | −0.431902 | − | 0.945734i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.6629 | − | 13.4597i | −0.374281 | − | 0.431944i | 0.537092 | − | 0.843523i | \(-0.319523\pi\) |
−0.911374 | + | 0.411580i | \(0.864977\pi\) | |||||||
\(972\) | 30.5845 | − | 8.98041i | 0.980997 | − | 0.288047i | ||||
\(973\) | −21.2956 | − | 13.6859i | −0.682707 | − | 0.438749i | ||||
\(974\) | −0.690922 | + | 1.51291i | −0.0221386 | + | 0.0484767i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.7056 | + | 6.88004i | −0.342676 | + | 0.220225i | ||||
\(977\) | 1.03522 | + | 7.20015i | 0.0331198 | + | 0.230353i | 0.999657 | − | 0.0261716i | \(-0.00833162\pi\) |
−0.966538 | + | 0.256525i | \(0.917423\pi\) | |||||||
\(978\) | −0.110449 | − | 0.768191i | −0.00353178 | − | 0.0245640i | ||||
\(979\) | −1.09945 | + | 0.706574i | −0.0351386 | + | 0.0225822i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.65065 | + | 18.9423i | −0.276194 | + | 0.604780i | ||||
\(982\) | −1.62521 | − | 1.04446i | −0.0518627 | − | 0.0333301i | ||||
\(983\) | −30.9104 | + | 9.07613i | −0.985890 | + | 0.289483i | −0.734654 | − | 0.678442i | \(-0.762655\pi\) |
−0.251236 | + | 0.967926i | \(0.580837\pi\) | |||||||
\(984\) | 1.39280 | + | 1.60738i | 0.0444008 | + | 0.0512412i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.715594 | + | 1.56693i | 0.0227892 | + | 0.0499013i | ||||
\(987\) | −0.600344 | + | 4.17548i | −0.0191092 | + | 0.132907i | ||||
\(988\) | 31.6618 | 1.00729 | ||||||||
\(989\) | −25.3916 | − | 4.96978i | −0.807407 | − | 0.158030i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.54572 | + | 10.7507i | −0.0491013 | + | 0.341507i | 0.950431 | + | 0.310935i | \(0.100642\pi\) |
−0.999533 | + | 0.0305723i | \(0.990267\pi\) | |||||||
\(992\) | 0.396047 | + | 0.867221i | 0.0125745 | + | 0.0275343i | ||||
\(993\) | 15.7335 | + | 4.61978i | 0.499288 | + | 0.146604i | ||||
\(994\) | −0.995387 | − | 1.14874i | −0.0315718 | − | 0.0364358i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.30834 | − | 4.69678i | −0.231574 | − | 0.148823i | ||||
\(997\) | 8.76152 | − | 19.1851i | 0.277480 | − | 0.607597i | −0.718661 | − | 0.695360i | \(-0.755245\pi\) |
0.996141 | + | 0.0877636i | \(0.0279720\pi\) | |||||||
\(998\) | 0.582455 | − | 0.672189i | 0.0184373 | − | 0.0212778i | ||||
\(999\) | −46.6687 | + | 29.9922i | −1.47653 | + | 0.948910i |
(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 | 575.2.k.a.376.1 | 10 | ||
5.2 | odd | 4 | 575.2.p.a.399.2 | 20 | |||
5.3 | odd | 4 | 575.2.p.a.399.1 | 20 | |||
5.4 | even | 2 | 115.2.g.a.31.1 | yes | 10 | ||
23.3 | even | 11 | inner | 575.2.k.a.26.1 | 10 | ||
115.3 | odd | 44 | 575.2.p.a.49.2 | 20 | |||
115.39 | even | 22 | 2645.2.a.n.1.4 | 5 | |||
115.49 | even | 22 | 115.2.g.a.26.1 | ✓ | 10 | ||
115.72 | odd | 44 | 575.2.p.a.49.1 | 20 | |||
115.99 | odd | 22 | 2645.2.a.o.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.2.g.a.26.1 | ✓ | 10 | 115.49 | even | 22 | ||
115.2.g.a.31.1 | yes | 10 | 5.4 | even | 2 | ||
575.2.k.a.26.1 | 10 | 23.3 | even | 11 | inner | ||
575.2.k.a.376.1 | 10 | 1.1 | even | 1 | trivial | ||
575.2.p.a.49.1 | 20 | 115.72 | odd | 44 | |||
575.2.p.a.49.2 | 20 | 115.3 | odd | 44 | |||
575.2.p.a.399.1 | 20 | 5.3 | odd | 4 | |||
575.2.p.a.399.2 | 20 | 5.2 | odd | 4 | |||
2645.2.a.n.1.4 | 5 | 115.39 | even | 22 | |||
2645.2.a.o.1.4 | 5 | 115.99 | odd | 22 |