Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [575,2,Mod(49,575)]
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([11, 16]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("575.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 575 = 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 575.p (of order \(22\), degree \(10\), 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: | \(4.59139811622\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{22})\) |
Coefficient field: | \(\Q(\zeta_{44})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 115) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{22}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(-0.755750 + 0.654861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 575.49 |
Dual form | 575.2.p.a.399.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/575\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(e\left(\frac{8}{11}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0872586 | − | 0.0125459i | 0.0617012 | − | 0.00887129i | −0.111395 | − | 0.993776i | \(-0.535532\pi\) |
0.173096 | + | 0.984905i | \(0.444623\pi\) | |||||||
\(3\) | 0.909632 | + | 0.415415i | 0.525176 | + | 0.239840i | 0.660318 | − | 0.750986i | \(-0.270422\pi\) |
−0.135141 | + | 0.990826i | \(0.543149\pi\) | |||||||
\(4\) | −1.91153 | + | 0.561276i | −0.955765 | + | 0.280638i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.0845850 | + | 0.0248364i | 0.0345317 | + | 0.0101394i | ||||
\(7\) | −0.835939 | − | 1.30075i | −0.315955 | − | 0.491636i | 0.646560 | − | 0.762863i | \(-0.276207\pi\) |
−0.962515 | + | 0.271227i | \(0.912571\pi\) | |||||||
\(8\) | −0.320135 | + | 0.146201i | −0.113185 | + | 0.0516897i | ||||
\(9\) | −1.30972 | − | 1.51150i | −0.436574 | − | 0.503833i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.289532 | − | 2.01374i | 0.0872971 | − | 0.607165i | −0.898468 | − | 0.439038i | \(-0.855319\pi\) |
0.985765 | − | 0.168126i | \(-0.0537717\pi\) | |||||||
\(12\) | −1.97195 | − | 0.283524i | −0.569253 | − | 0.0818462i | ||||
\(13\) | 1.15727 | − | 1.80075i | 0.320969 | − | 0.499437i | −0.642851 | − | 0.765991i | \(-0.722249\pi\) |
0.963820 | + | 0.266554i | \(0.0858850\pi\) | |||||||
\(14\) | −0.0892619 | − | 0.103014i | −0.0238563 | − | 0.0275316i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.32584 | − | 2.13739i | 0.831460 | − | 0.534347i | ||||
\(17\) | 1.22809 | − | 4.18251i | 0.297857 | − | 1.01441i | −0.665548 | − | 0.746355i | \(-0.731802\pi\) |
0.963405 | − | 0.268052i | \(-0.0863798\pi\) | |||||||
\(18\) | −0.133248 | − | 0.115460i | −0.0314068 | − | 0.0272141i | ||||
\(19\) | 7.12381 | − | 2.09174i | 1.63431 | − | 0.479878i | 0.669499 | − | 0.742813i | \(-0.266509\pi\) |
0.964814 | + | 0.262935i | \(0.0846905\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.220047 | − | 1.53046i | −0.0480182 | − | 0.333974i | ||||
\(22\) | − | 0.179348i | − | 0.0382372i | ||||||
\(23\) | −3.89854 | + | 2.79310i | −0.812901 | + | 0.582402i | ||||
\(24\) | −0.351939 | −0.0718392 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.0783898 | − | 0.171650i | 0.0153735 | − | 0.0336633i | ||||
\(27\) | −1.40866 | − | 4.79746i | −0.271097 | − | 0.923273i | ||||
\(28\) | 2.32800 | + | 2.01722i | 0.439951 | + | 0.381219i | ||||
\(29\) | 4.30111 | + | 1.26292i | 0.798695 | + | 0.234518i | 0.655519 | − | 0.755179i | \(-0.272450\pi\) |
0.143177 | + | 0.989697i | \(0.454268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.376329 | − | 0.824045i | −0.0675906 | − | 0.148003i | 0.872822 | − | 0.488039i | \(-0.162288\pi\) |
−0.940412 | + | 0.340037i | \(0.889561\pi\) | |||||||
\(32\) | 0.795348 | − | 0.689173i | 0.140599 | − | 0.121830i | ||||
\(33\) | 1.09990 | − | 1.71148i | 0.191469 | − | 0.297931i | ||||
\(34\) | 0.0546886 | − | 0.380367i | 0.00937901 | − | 0.0652325i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.35194 | + | 2.15416i | 0.558656 | + | 0.359027i | ||||
\(37\) | −8.38507 | + | 7.26571i | −1.37850 | + | 1.19447i | −0.420641 | + | 0.907227i | \(0.638195\pi\) |
−0.957856 | + | 0.287248i | \(0.907260\pi\) | |||||||
\(38\) | 0.595371 | − | 0.271897i | 0.0965819 | − | 0.0441075i | ||||
\(39\) | 1.80075 | − | 1.15727i | 0.288350 | − | 0.185311i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.95750 | − | 4.56720i | 0.618058 | − | 0.713277i | −0.357279 | − | 0.933998i | \(-0.616295\pi\) |
0.975337 | + | 0.220720i | \(0.0708408\pi\) | |||||||
\(42\) | −0.0384020 | − | 0.130785i | −0.00592556 | − | 0.0201806i | ||||
\(43\) | −4.90745 | − | 2.24116i | −0.748379 | − | 0.341773i | 0.00444961 | − | 0.999990i | \(-0.498584\pi\) |
−0.752828 | + | 0.658217i | \(0.771311\pi\) | |||||||
\(44\) | 0.576814 | + | 4.01183i | 0.0869579 | + | 0.604806i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.305139 | + | 0.292633i | −0.0449903 | + | 0.0431464i | ||||
\(47\) | − | 2.72825i | − | 0.397956i | −0.980004 | − | 0.198978i | \(-0.936238\pi\) | ||
0.980004 | − | 0.198978i | \(-0.0637623\pi\) | |||||||
\(48\) | 3.91319 | − | 0.562632i | 0.564821 | − | 0.0812089i | ||||
\(49\) | 1.91476 | − | 4.19273i | 0.273537 | − | 0.598962i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.85459 | − | 3.29437i | 0.399723 | − | 0.461305i | ||||
\(52\) | −1.20144 | + | 4.09173i | −0.166610 | + | 0.567420i | ||||
\(53\) | 0.148283 | + | 0.230732i | 0.0203682 | + | 0.0316935i | 0.851288 | − | 0.524698i | \(-0.175822\pi\) |
−0.830920 | + | 0.556392i | \(0.812185\pi\) | |||||||
\(54\) | −0.183106 | − | 0.400947i | −0.0249176 | − | 0.0545620i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.457783 | + | 0.294199i | 0.0611738 | + | 0.0393140i | ||||
\(57\) | 7.34898 | + | 1.05662i | 0.973396 | + | 0.139953i | ||||
\(58\) | 0.391153 | + | 0.0562393i | 0.0513609 | + | 0.00738458i | ||||
\(59\) | −6.74757 | − | 4.33640i | −0.878458 | − | 0.564551i | 0.0218707 | − | 0.999761i | \(-0.493038\pi\) |
−0.900329 | + | 0.435210i | \(0.856674\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.33718 | − | 2.92802i | −0.171208 | − | 0.374894i | 0.804505 | − | 0.593946i | \(-0.202431\pi\) |
−0.975713 | + | 0.219052i | \(0.929704\pi\) | |||||||
\(62\) | −0.0431763 | − | 0.0671837i | −0.00548340 | − | 0.00853233i | ||||
\(63\) | −0.871230 | + | 2.96714i | −0.109765 | + | 0.373824i | ||||
\(64\) | −5.11714 | + | 5.90549i | −0.639642 | + | 0.738187i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.0745040 | − | 0.163141i | 0.00917081 | − | 0.0200813i | ||||
\(67\) | −1.94473 | + | 0.279610i | −0.237587 | + | 0.0341598i | −0.260080 | − | 0.965587i | \(-0.583749\pi\) |
0.0224928 | + | 0.999747i | \(0.492840\pi\) | |||||||
\(68\) | 8.68428i | 1.05312i | ||||||||
\(69\) | −4.70653 | + | 0.921186i | −0.566600 | + | 0.110898i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.58700 | + | 11.0378i | 0.188342 | + | 1.30995i | 0.836301 | + | 0.548271i | \(0.184714\pi\) |
−0.647959 | + | 0.761675i | \(0.724377\pi\) | |||||||
\(72\) | 0.640269 | + | 0.292401i | 0.0754564 | + | 0.0344598i | ||||
\(73\) | −2.92170 | − | 9.95039i | −0.341959 | − | 1.16461i | −0.933574 | − | 0.358385i | \(-0.883328\pi\) |
0.591615 | − | 0.806221i | \(-0.298491\pi\) | |||||||
\(74\) | −0.640515 | + | 0.739194i | −0.0744584 | + | 0.0859295i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.4433 | + | 7.99684i | −1.42735 | + | 0.917300i | ||||
\(77\) | −2.86139 | + | 1.30675i | −0.326086 | + | 0.148919i | ||||
\(78\) | 0.142612 | − | 0.123574i | 0.0161476 | − | 0.0139920i | ||||
\(79\) | −2.70849 | − | 1.74064i | −0.304729 | − | 0.195837i | 0.379335 | − | 0.925259i | \(-0.376153\pi\) |
−0.684064 | + | 0.729422i | \(0.739789\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.142315 | + | 0.989821i | −0.0158128 | + | 0.109980i | ||||
\(82\) | 0.288027 | − | 0.448178i | 0.0318072 | − | 0.0494930i | ||||
\(83\) | 3.29557 | − | 2.85563i | 0.361736 | − | 0.313446i | −0.454963 | − | 0.890510i | \(-0.650347\pi\) |
0.816698 | + | 0.577065i | \(0.195802\pi\) | |||||||
\(84\) | 1.27964 | + | 2.80202i | 0.139620 | + | 0.305725i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.456334 | − | 0.133992i | −0.0492078 | − | 0.0144487i | ||||
\(87\) | 3.38779 | + | 2.93553i | 0.363209 | + | 0.314722i | ||||
\(88\) | 0.201720 | + | 0.686997i | 0.0215035 | + | 0.0732341i | ||||
\(89\) | −0.266861 | + | 0.584343i | −0.0282872 | + | 0.0619403i | −0.923248 | − | 0.384204i | \(-0.874476\pi\) |
0.894961 | + | 0.446144i | \(0.147203\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.30972 | −0.346953 | ||||||||
\(92\) | 5.88446 | − | 7.52725i | 0.613498 | − | 0.784770i | ||||
\(93\) | − | 0.905910i | − | 0.0939385i | ||||||
\(94\) | −0.0342284 | − | 0.238063i | −0.00353038 | − | 0.0245544i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00977 | − | 0.296494i | 0.103059 | − | 0.0302608i | ||||
\(97\) | 4.18748 | + | 3.62848i | 0.425175 | + | 0.368416i | 0.841006 | − | 0.541026i | \(-0.181964\pi\) |
−0.415831 | + | 0.909442i | \(0.636509\pi\) | |||||||
\(98\) | 0.114478 | − | 0.389875i | 0.0115640 | − | 0.0393833i | ||||
\(99\) | −3.42297 | + | 2.19981i | −0.344021 | + | 0.221089i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.94535 | − | 3.39912i | −0.293073 | − | 0.338225i | 0.590049 | − | 0.807367i | \(-0.299108\pi\) |
−0.883122 | + | 0.469143i | \(0.844563\pi\) | |||||||
\(102\) | 0.207757 | − | 0.323276i | 0.0205710 | − | 0.0320091i | ||||
\(103\) | 9.63380 | + | 1.38513i | 0.949247 | + | 0.136481i | 0.599510 | − | 0.800367i | \(-0.295362\pi\) |
0.349737 | + | 0.936848i | \(0.386271\pi\) | |||||||
\(104\) | −0.107212 | + | 0.745675i | −0.0105130 | + | 0.0731194i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.0158337 | + | 0.0182730i | 0.00153790 | + | 0.00177483i | ||||
\(107\) | 6.72833 | − | 3.07272i | 0.650452 | − | 0.297051i | −0.0627299 | − | 0.998031i | \(-0.519981\pi\) |
0.713182 | + | 0.700979i | \(0.247253\pi\) | |||||||
\(108\) | 5.38540 | + | 8.37985i | 0.518210 | + | 0.806351i | ||||
\(109\) | 9.99029 | + | 2.93341i | 0.956897 | + | 0.280970i | 0.722656 | − | 0.691208i | \(-0.242921\pi\) |
0.234241 | + | 0.972179i | \(0.424740\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.6456 | + | 3.12583i | −1.01044 | + | 0.296691i | ||||
\(112\) | −5.56040 | − | 2.53935i | −0.525408 | − | 0.239946i | ||||
\(113\) | −19.3927 | + | 2.78825i | −1.82431 | + | 0.262297i | −0.967417 | − | 0.253189i | \(-0.918520\pi\) |
−0.856898 | + | 0.515486i | \(0.827611\pi\) | |||||||
\(114\) | 0.654518 | 0.0613012 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.93053 | −0.829179 | ||||||||
\(117\) | −4.23753 | + | 0.609264i | −0.391760 | + | 0.0563265i | ||||
\(118\) | −0.643187 | − | 0.293734i | −0.0592102 | − | 0.0270404i | ||||
\(119\) | −6.46699 | + | 1.89888i | −0.592828 | + | 0.174070i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.58311 | + | 1.93298i | 0.598465 | + | 0.175725i | ||||
\(122\) | −0.153415 | − | 0.238719i | −0.0138896 | − | 0.0216126i | ||||
\(123\) | 5.49716 | − | 2.51047i | 0.495662 | − | 0.226361i | ||||
\(124\) | 1.18188 | + | 1.36396i | 0.106136 | + | 0.122487i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.0387969 | + | 0.269839i | −0.00345631 | + | 0.0240391i | ||||
\(127\) | 17.3667 | + | 2.49696i | 1.54105 | + | 0.221569i | 0.859856 | − | 0.510536i | \(-0.170553\pi\) |
0.681192 | + | 0.732105i | \(0.261462\pi\) | |||||||
\(128\) | −1.51036 | + | 2.35017i | −0.133498 | + | 0.207727i | ||||
\(129\) | −3.53296 | − | 4.07725i | −0.311060 | − | 0.358982i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.9767 | + | 7.05427i | −0.959035 | + | 0.616334i | −0.923731 | − | 0.383043i | \(-0.874876\pi\) |
−0.0353039 | + | 0.999377i | \(0.511240\pi\) | |||||||
\(132\) | −1.14188 | + | 3.88890i | −0.0993883 | + | 0.338486i | ||||
\(133\) | −8.67589 | − | 7.51770i | −0.752295 | − | 0.651867i | ||||
\(134\) | −0.166187 | + | 0.0487968i | −0.0143563 | + | 0.00421540i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.218329 | + | 1.51851i | 0.0187216 | + | 0.130211i | ||||
\(137\) | 21.5268i | 1.83916i | 0.392903 | + | 0.919580i | \(0.371471\pi\) | ||||
−0.392903 | + | 0.919580i | \(0.628529\pi\) | |||||||
\(138\) | −0.399128 | + | 0.139429i | −0.0339760 | + | 0.0118690i | ||||
\(139\) | 16.3719 | 1.38864 | 0.694322 | − | 0.719665i | \(-0.255705\pi\) | ||||
0.694322 | + | 0.719665i | \(0.255705\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.13336 | − | 2.48170i | 0.0954458 | − | 0.208997i | ||||
\(142\) | 0.276958 | + | 0.943233i | 0.0232418 | + | 0.0791544i | ||||
\(143\) | −3.29117 | − | 2.85181i | −0.275221 | − | 0.238480i | ||||
\(144\) | −7.58658 | − | 2.22762i | −0.632215 | − | 0.185635i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.379780 | − | 0.831602i | −0.0314308 | − | 0.0688239i | ||||
\(147\) | 3.48345 | − | 3.01843i | 0.287310 | − | 0.248956i | ||||
\(148\) | 11.9502 | − | 18.5950i | 0.982304 | − | 1.52850i | ||||
\(149\) | 2.74972 | − | 19.1247i | 0.225266 | − | 1.56676i | −0.492399 | − | 0.870370i | \(-0.663880\pi\) |
0.717665 | − | 0.696389i | \(-0.245211\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.8366 | + | 10.8202i | 1.37015 | + | 0.880539i | 0.998849 | − | 0.0479750i | \(-0.0152768\pi\) |
0.371297 | + | 0.928514i | \(0.378913\pi\) | |||||||
\(152\) | −1.97476 | + | 1.71114i | −0.160174 | + | 0.138792i | ||||
\(153\) | −7.93032 | + | 3.62165i | −0.641128 | + | 0.292793i | ||||
\(154\) | −0.233287 | + | 0.149924i | −0.0187988 | + | 0.0120812i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.79263 | + | 3.22287i | −0.223590 | + | 0.258036i | ||||
\(157\) | −1.62683 | − | 5.54048i | −0.129835 | − | 0.442179i | 0.868756 | − | 0.495241i | \(-0.164920\pi\) |
−0.998591 | + | 0.0530620i | \(0.983102\pi\) | |||||||
\(158\) | −0.258177 | − | 0.117905i | −0.0205395 | − | 0.00938006i | ||||
\(159\) | 0.0390330 | + | 0.271480i | 0.00309552 | + | 0.0215298i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.89206 | + | 2.73614i | 0.543170 | + | 0.215638i | ||||
\(162\) | 0.0881559i | 0.00692618i | ||||||||
\(163\) | −8.71401 | + | 1.25289i | −0.682534 | + | 0.0981335i | −0.474856 | − | 0.880064i | \(-0.657500\pi\) |
−0.207678 | + | 0.978197i | \(0.566591\pi\) | |||||||
\(164\) | −5.00143 | + | 10.9516i | −0.390546 | + | 0.855176i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.251740 | − | 0.290524i | 0.0195388 | − | 0.0225490i | ||||
\(167\) | −5.50159 | + | 18.7367i | −0.425726 | + | 1.44989i | 0.415692 | + | 0.909505i | \(0.363539\pi\) |
−0.841418 | + | 0.540384i | \(0.818279\pi\) | |||||||
\(168\) | 0.294199 | + | 0.457783i | 0.0226980 | + | 0.0353187i | ||||
\(169\) | 3.49698 | + | 7.65732i | 0.268998 | + | 0.589024i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.4919 | − | 8.02803i | −0.955276 | − | 0.613919i | ||||
\(172\) | 10.6386 | + | 1.52960i | 0.811188 | + | 0.116631i | ||||
\(173\) | 21.3627 | + | 3.07149i | 1.62417 | + | 0.233521i | 0.893454 | − | 0.449155i | \(-0.148275\pi\) |
0.730721 | + | 0.682676i | \(0.239184\pi\) | |||||||
\(174\) | 0.332443 | + | 0.213648i | 0.0252024 | + | 0.0161966i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.34120 | − | 7.31621i | −0.251852 | − | 0.551480i | ||||
\(177\) | −4.33640 | − | 6.74757i | −0.325944 | − | 0.507178i | ||||
\(178\) | −0.0159548 | + | 0.0543370i | −0.00119586 | + | 0.00407273i | ||||
\(179\) | −10.0553 | + | 11.6044i | −0.751567 | + | 0.867354i | −0.994719 | − | 0.102634i | \(-0.967273\pi\) |
0.243152 | + | 0.969988i | \(0.421818\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.340209 | − | 0.744955i | 0.0252876 | − | 0.0553720i | −0.896567 | − | 0.442909i | \(-0.853947\pi\) |
0.921854 | + | 0.387537i | \(0.126674\pi\) | |||||||
\(182\) | −0.288802 | + | 0.0415234i | −0.0214074 | + | 0.00307792i | ||||
\(183\) | − | 3.21890i | − | 0.237948i | ||||||
\(184\) | 0.839703 | − | 1.46414i | 0.0619037 | − | 0.107938i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.0113655 | − | 0.0790485i | −0.000833356 | − | 0.00579612i | ||||
\(187\) | −8.06690 | − | 3.68403i | −0.589910 | − | 0.269403i | ||||
\(188\) | 1.53130 | + | 5.21513i | 0.111682 | + | 0.380353i | ||||
\(189\) | −5.06273 | + | 5.84270i | −0.368259 | + | 0.424994i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.58868 | + | 2.30630i | −0.259668 | + | 0.166878i | −0.663997 | − | 0.747735i | \(-0.731141\pi\) |
0.404329 | + | 0.914613i | \(0.367505\pi\) | |||||||
\(192\) | −7.10794 | + | 3.24609i | −0.512972 | + | 0.234266i | ||||
\(193\) | −3.65352 | + | 3.16580i | −0.262986 | + | 0.227879i | −0.776366 | − | 0.630283i | \(-0.782939\pi\) |
0.513379 | + | 0.858162i | \(0.328393\pi\) | |||||||
\(194\) | 0.410917 | + | 0.264080i | 0.0295021 | + | 0.0189598i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.30684 | + | 9.08924i | −0.0933454 | + | 0.649232i | ||||
\(197\) | 0.141980 | − | 0.220925i | 0.0101157 | − | 0.0157403i | −0.836159 | − | 0.548487i | \(-0.815204\pi\) |
0.846275 | + | 0.532747i | \(0.178840\pi\) | |||||||
\(198\) | −0.271085 | + | 0.234896i | −0.0192652 | + | 0.0166934i | ||||
\(199\) | 1.79719 | + | 3.93530i | 0.127399 | + | 0.278966i | 0.962574 | − | 0.271019i | \(-0.0873607\pi\) |
−0.835175 | + | 0.549985i | \(0.814633\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.88514 | − | 0.553528i | −0.132968 | − | 0.0390429i | ||||
\(202\) | −0.299652 | − | 0.259650i | −0.0210835 | − | 0.0182689i | ||||
\(203\) | −1.95273 | − | 6.65037i | −0.137054 | − | 0.466765i | ||||
\(204\) | −3.60758 | + | 7.89950i | −0.252581 | + | 0.553076i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.858010 | 0.0597804 | ||||||||
\(207\) | 9.32777 | + | 2.23445i | 0.648325 | + | 0.155305i | ||||
\(208\) | − | 8.46252i | − | 0.586770i | ||||||
\(209\) | −2.14964 | − | 14.9511i | −0.148694 | − | 1.03419i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.30147 | − | 1.85028i | 0.433811 | − | 0.127378i | −0.0575338 | − | 0.998344i | \(-0.518324\pi\) |
0.491345 | + | 0.870965i | \(0.336506\pi\) | |||||||
\(212\) | −0.412951 | − | 0.357824i | −0.0283616 | − | 0.0245755i | ||||
\(213\) | −3.14169 | + | 10.6996i | −0.215265 | + | 0.733125i | ||||
\(214\) | 0.548554 | − | 0.352535i | 0.0374984 | − | 0.0240988i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.15235 | + | 1.32989i | 0.0784077 | + | 0.0904874i | ||||
\(217\) | −0.757286 | + | 1.17836i | −0.0514079 | + | 0.0799923i | ||||
\(218\) | 0.908542 | + | 0.130629i | 0.0615342 | + | 0.00884728i | ||||
\(219\) | 1.47587 | − | 10.2649i | 0.0997301 | − | 0.693638i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.11040 | − | 7.05178i | −0.411030 | − | 0.474354i | ||||
\(222\) | −0.889705 | + | 0.406315i | −0.0597131 | + | 0.0272701i | ||||
\(223\) | 4.97783 | + | 7.74566i | 0.333340 | + | 0.518688i | 0.966950 | − | 0.254965i | \(-0.0820639\pi\) |
−0.633610 | + | 0.773653i | \(0.718428\pi\) | |||||||
\(224\) | −1.56130 | − | 0.458439i | −0.104319 | − | 0.0306308i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.65720 | + | 0.486598i | −0.110235 | + | 0.0323680i | ||||
\(227\) | −8.06985 | − | 3.68538i | −0.535615 | − | 0.244607i | 0.129196 | − | 0.991619i | \(-0.458760\pi\) |
−0.664810 | + | 0.747012i | \(0.731488\pi\) | |||||||
\(228\) | −14.6408 | + | 2.10504i | −0.969614 | + | 0.139409i | ||||
\(229\) | 8.38484 | 0.554086 | 0.277043 | − | 0.960858i | \(-0.410646\pi\) | ||||
0.277043 | + | 0.960858i | \(0.410646\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.14566 | −0.206969 | ||||||||
\(232\) | −1.56157 | + | 0.224520i | −0.102522 | + | 0.0147405i | ||||
\(233\) | 21.8435 | + | 9.97561i | 1.43102 | + | 0.653524i | 0.972017 | − | 0.234911i | \(-0.0754799\pi\) |
0.459002 | + | 0.888435i | \(0.348207\pi\) | |||||||
\(234\) | −0.362117 | + | 0.106327i | −0.0236723 | + | 0.00695082i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 15.3321 | + | 4.50191i | 0.998034 | + | 0.293049i | ||||
\(237\) | −1.74064 | − | 2.70849i | −0.113067 | − | 0.175935i | ||||
\(238\) | −0.540478 | + | 0.246828i | −0.0350340 | + | 0.0159995i | ||||
\(239\) | −7.35914 | − | 8.49290i | −0.476023 | − | 0.549360i | 0.466054 | − | 0.884756i | \(-0.345675\pi\) |
−0.942077 | + | 0.335396i | \(0.891130\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00004 | − | 27.8209i | 0.257665 | − | 1.79210i | −0.291689 | − | 0.956513i | \(-0.594217\pi\) |
0.549355 | − | 0.835589i | \(-0.314874\pi\) | |||||||
\(242\) | 0.598684 | + | 0.0860778i | 0.0384849 | + | 0.00553329i | ||||
\(243\) | −8.65025 | + | 13.4601i | −0.554914 | + | 0.863463i | ||||
\(244\) | 4.19948 | + | 4.84646i | 0.268844 | + | 0.310263i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.448178 | − | 0.288027i | 0.0285748 | − | 0.0183639i | ||||
\(247\) | 4.47747 | − | 15.2489i | 0.284895 | − | 0.970262i | ||||
\(248\) | 0.240952 | + | 0.208786i | 0.0153004 | + | 0.0132579i | ||||
\(249\) | 4.18403 | − | 1.22854i | 0.265152 | − | 0.0778556i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.91272 | + | 27.2135i | 0.246969 | + | 1.71770i | 0.615541 | + | 0.788105i | \(0.288938\pi\) |
−0.368572 | + | 0.929599i | \(0.620153\pi\) | |||||||
\(252\) | − | 6.16077i | − | 0.388092i | ||||||
\(253\) | 4.49583 | + | 8.65932i | 0.282650 | + | 0.544407i | ||||
\(254\) | 1.54672 | 0.0970501 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.38987 | − | 13.9919i | 0.399367 | − | 0.874492i | ||||
\(257\) | −5.00435 | − | 17.0432i | −0.312163 | − | 1.06313i | −0.954872 | − | 0.297018i | \(-0.904008\pi\) |
0.642709 | − | 0.766110i | \(-0.277810\pi\) | |||||||
\(258\) | −0.359434 | − | 0.311451i | −0.0223774 | − | 0.0193901i | ||||
\(259\) | 16.4603 | + | 4.83317i | 1.02279 | + | 0.300318i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.72435 | − | 8.15519i | −0.230531 | − | 0.504794i | ||||
\(262\) | −0.869305 | + | 0.753257i | −0.0537059 | + | 0.0465364i | ||||
\(263\) | −4.72561 | + | 7.35320i | −0.291394 | + | 0.453417i | −0.955827 | − | 0.293930i | \(-0.905037\pi\) |
0.664433 | + | 0.747348i | \(0.268673\pi\) | |||||||
\(264\) | −0.101897 | + | 0.708712i | −0.00627135 | + | 0.0436182i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.851362 | − | 0.547137i | −0.0522004 | − | 0.0335471i | ||||
\(267\) | −0.485490 | + | 0.420680i | −0.0297115 | + | 0.0257452i | ||||
\(268\) | 3.56047 | − | 1.62601i | 0.217491 | − | 0.0993246i | ||||
\(269\) | −2.46553 | + | 1.58450i | −0.150326 | + | 0.0966086i | −0.613642 | − | 0.789585i | \(-0.710296\pi\) |
0.463316 | + | 0.886193i | \(0.346660\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.29616 | − | 4.95803i | 0.260973 | − | 0.301179i | −0.610108 | − | 0.792318i | \(-0.708874\pi\) |
0.871081 | + | 0.491139i | \(0.163419\pi\) | |||||||
\(272\) | −4.85519 | − | 16.5353i | −0.294389 | − | 1.00260i | ||||
\(273\) | −3.01063 | − | 1.37491i | −0.182212 | − | 0.0832132i | ||||
\(274\) | 0.270073 | + | 1.87840i | 0.0163157 | + | 0.113478i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.47963 | − | 4.40253i | 0.510414 | − | 0.265001i | ||||
\(277\) | − | 22.7888i | − | 1.36924i | −0.728898 | − | 0.684622i | \(-0.759967\pi\) | ||
0.728898 | − | 0.684622i | \(-0.240033\pi\) | |||||||
\(278\) | 1.42859 | − | 0.205400i | 0.0856809 | − | 0.0123191i | ||||
\(279\) | −0.752658 | + | 1.64809i | −0.0450604 | + | 0.0986686i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.32744 | − | 10.7644i | 0.556429 | − | 0.642153i | −0.405940 | − | 0.913900i | \(-0.633056\pi\) |
0.962369 | + | 0.271747i | \(0.0876013\pi\) | |||||||
\(282\) | 0.0677599 | − | 0.230769i | 0.00403504 | − | 0.0137421i | ||||
\(283\) | −12.8173 | − | 19.9441i | −0.761910 | − | 1.18555i | −0.977882 | − | 0.209155i | \(-0.932929\pi\) |
0.215973 | − | 0.976399i | \(-0.430708\pi\) | |||||||
\(284\) | −9.22884 | − | 20.2083i | −0.547631 | − | 1.19914i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.322961 | − | 0.207554i | −0.0190971 | − | 0.0122730i | ||||
\(287\) | −9.24901 | − | 1.32981i | −0.545952 | − | 0.0784960i | ||||
\(288\) | −2.08337 | − | 0.299543i | −0.122764 | − | 0.0176507i | ||||
\(289\) | −1.68384 | − | 1.08214i | −0.0990493 | − | 0.0636551i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.30175 | + | 5.04012i | 0.134931 | + | 0.295457i | ||||
\(292\) | 11.1698 | + | 17.3806i | 0.653664 | + | 1.01712i | ||||
\(293\) | 1.20419 | − | 4.10110i | 0.0703497 | − | 0.239589i | −0.916810 | − | 0.399323i | \(-0.869245\pi\) |
0.987160 | + | 0.159734i | \(0.0510635\pi\) | |||||||
\(294\) | 0.266092 | − | 0.307087i | 0.0155188 | − | 0.0179097i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.62210 | − | 3.55191i | 0.0942827 | − | 0.206450i | ||||
\(297\) | −10.0687 | + | 1.44766i | −0.584245 | + | 0.0840017i | ||||
\(298\) | − | 1.70330i | − | 0.0986692i | ||||||
\(299\) | 0.518014 | + | 10.2526i | 0.0299575 | + | 0.592926i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.18715 | + | 8.25681i | 0.0684262 | + | 0.475915i | ||||
\(302\) | 1.60489 | + | 0.732929i | 0.0923511 | + | 0.0421753i | ||||
\(303\) | −1.26714 | − | 4.31549i | −0.0727954 | − | 0.247918i | ||||
\(304\) | 19.2218 | − | 22.1831i | 1.10244 | − | 1.27229i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.646552 | + | 0.415514i | −0.0369609 | + | 0.0237533i | ||||
\(307\) | 8.13661 | − | 3.71586i | 0.464381 | − | 0.212076i | −0.169463 | − | 0.985536i | \(-0.554203\pi\) |
0.633844 | + | 0.773461i | \(0.281476\pi\) | |||||||
\(308\) | 4.73619 | − | 4.10393i | 0.269869 | − | 0.233843i | ||||
\(309\) | 8.18781 | + | 5.26199i | 0.465788 | + | 0.299344i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.32224 | − | 23.1067i | 0.188387 | − | 1.31026i | −0.647798 | − | 0.761812i | \(-0.724310\pi\) |
0.836185 | − | 0.548447i | \(-0.184781\pi\) | |||||||
\(312\) | −0.407288 | + | 0.633752i | −0.0230581 | + | 0.0358792i | ||||
\(313\) | 17.0127 | − | 14.7416i | 0.961615 | − | 0.833244i | −0.0244337 | − | 0.999701i | \(-0.507778\pi\) |
0.986049 | + | 0.166457i | \(0.0532328\pi\) | |||||||
\(314\) | −0.211465 | − | 0.463045i | −0.0119337 | − | 0.0261311i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.15434 | + | 1.80708i | 0.346209 | + | 0.101656i | ||||
\(317\) | −9.63606 | − | 8.34970i | −0.541215 | − | 0.468966i | 0.340834 | − | 0.940124i | \(-0.389291\pi\) |
−0.882049 | + | 0.471158i | \(0.843836\pi\) | |||||||
\(318\) | 0.00681193 | + | 0.0231993i | 0.000381994 | + | 0.00130095i | ||||
\(319\) | 3.78849 | − | 8.29564i | 0.212115 | − | 0.464467i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.39676 | 0.412847 | ||||||||
\(322\) | 0.635719 | + | 0.152285i | 0.0354272 | + | 0.00848651i | ||||
\(323\) | − | 32.3642i | − | 1.80079i | ||||||
\(324\) | −0.283524 | − | 1.97195i | −0.0157513 | − | 0.109553i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.744654 | + | 0.218650i | −0.0412426 | + | 0.0121099i | ||||
\(327\) | 7.86891 | + | 6.81845i | 0.435151 | + | 0.377061i | ||||
\(328\) | −0.599206 | + | 2.04071i | −0.0330856 | + | 0.112679i | ||||
\(329\) | −3.54876 | + | 2.28065i | −0.195650 | + | 0.125736i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.7382 | + | 12.3926i | 0.590227 | + | 0.681158i | 0.969771 | − | 0.244015i | \(-0.0784647\pi\) |
−0.379545 | + | 0.925173i | \(0.623919\pi\) | |||||||
\(332\) | −4.69678 | + | 7.30834i | −0.257769 | + | 0.401097i | ||||
\(333\) | 21.9642 | + | 3.15798i | 1.20363 | + | 0.173056i | ||||
\(334\) | −0.244993 | + | 1.70396i | −0.0134054 | + | 0.0932366i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.00303 | − | 4.61974i | −0.218383 | − | 0.252028i | ||||
\(337\) | −24.9589 | + | 11.3983i | −1.35960 | + | 0.620907i | −0.955821 | − | 0.293951i | \(-0.905030\pi\) |
−0.403776 | + | 0.914858i | \(0.632303\pi\) | |||||||
\(338\) | 0.401210 | + | 0.624294i | 0.0218229 | + | 0.0339571i | ||||
\(339\) | −18.7985 | − | 5.51975i | −1.02100 | − | 0.299792i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.76837 | + | 0.519240i | −0.0957626 | + | 0.0281184i | ||||
\(342\) | −1.19074 | − | 0.543793i | −0.0643879 | − | 0.0294050i | ||||
\(343\) | −17.7675 | + | 2.55459i | −0.959357 | + | 0.137935i | ||||
\(344\) | 1.89870 | 0.102371 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.90261 | 0.102285 | ||||||||
\(347\) | 5.97415 | − | 0.858953i | 0.320709 | − | 0.0461110i | 0.0199196 | − | 0.999802i | \(-0.493659\pi\) |
0.300789 | + | 0.953691i | \(0.402750\pi\) | |||||||
\(348\) | −8.12350 | − | 3.70988i | −0.435465 | − | 0.198870i | ||||
\(349\) | 8.00915 | − | 2.35170i | 0.428720 | − | 0.125883i | −0.0602518 | − | 0.998183i | \(-0.519190\pi\) |
0.488972 | + | 0.872300i | \(0.337372\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.2692 | − | 3.01532i | −0.548130 | − | 0.160946i | ||||
\(352\) | −1.15753 | − | 1.80116i | −0.0616968 | − | 0.0960021i | ||||
\(353\) | −23.7892 | + | 10.8642i | −1.26617 | + | 0.578242i | −0.931380 | − | 0.364049i | \(-0.881394\pi\) |
−0.334794 | + | 0.942291i | \(0.608667\pi\) | |||||||
\(354\) | −0.463042 | − | 0.534379i | −0.0246104 | − | 0.0284019i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.182134 | − | 1.26677i | 0.00965310 | − | 0.0671388i | ||||
\(357\) | −6.67141 | − | 0.959204i | −0.353088 | − | 0.0507664i | ||||
\(358\) | −0.731822 | + | 1.13874i | −0.0386780 | + | 0.0601841i | ||||
\(359\) | 3.70672 | + | 4.27779i | 0.195633 | + | 0.225773i | 0.845088 | − | 0.534628i | \(-0.179548\pi\) |
−0.649454 | + | 0.760401i | \(0.725003\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.3894 | − | 19.5301i | 1.59944 | − | 1.02790i | ||||
\(362\) | 0.0203401 | − | 0.0692719i | 0.00106905 | − | 0.00364085i | ||||
\(363\) | 5.18522 | + | 4.49302i | 0.272154 | + | 0.235822i | ||||
\(364\) | 6.32663 | − | 1.85767i | 0.331605 | − | 0.0973682i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.0403840 | − | 0.280877i | −0.00211091 | − | 0.0146817i | ||||
\(367\) | − | 12.3147i | − | 0.642822i | −0.946940 | − | 0.321411i | \(-0.895843\pi\) | ||
0.946940 | − | 0.321411i | \(-0.104157\pi\) | |||||||
\(368\) | −6.99596 | + | 17.6221i | −0.364690 | + | 0.918615i | ||||
\(369\) | −12.0866 | −0.629201 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.176169 | − | 0.385756i | 0.00914624 | − | 0.0200275i | ||||
\(372\) | 0.508465 | + | 1.73167i | 0.0263627 | + | 0.0897831i | ||||
\(373\) | 22.0119 | + | 19.0734i | 1.13973 | + | 0.987585i | 0.999997 | − | 0.00260397i | \(-0.000828872\pi\) |
0.139737 | + | 0.990189i | \(0.455374\pi\) | |||||||
\(374\) | −0.750126 | − | 0.220257i | −0.0387881 | − | 0.0113892i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.398872 | + | 0.873407i | 0.0205702 | + | 0.0450426i | ||||
\(377\) | 7.25173 | − | 6.28366i | 0.373483 | − | 0.323625i | ||||
\(378\) | −0.368465 | + | 0.573343i | −0.0189518 | + | 0.0294896i | ||||
\(379\) | −4.74698 | + | 33.0160i | −0.243836 | + | 1.69592i | 0.388683 | + | 0.921372i | \(0.372930\pi\) |
−0.632519 | + | 0.774545i | \(0.717979\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.7601 | + | 9.48571i | 0.756181 | + | 0.485968i | ||||
\(382\) | −0.284209 | + | 0.246268i | −0.0145414 | + | 0.0126002i | ||||
\(383\) | 28.2775 | − | 12.9139i | 1.44491 | − | 0.659870i | 0.470044 | − | 0.882643i | \(-0.344238\pi\) |
0.974870 | + | 0.222773i | \(0.0715108\pi\) | |||||||
\(384\) | −2.35017 | + | 1.51036i | −0.119931 | + | 0.0770753i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.279084 | + | 0.322080i | −0.0142050 | + | 0.0163934i | ||||
\(387\) | 3.03988 | + | 10.3529i | 0.154526 | + | 0.526267i | ||||
\(388\) | −10.0411 | − | 4.58560i | −0.509758 | − | 0.232799i | ||||
\(389\) | −1.80544 | − | 12.5571i | −0.0915394 | − | 0.636670i | −0.983005 | − | 0.183581i | \(-0.941231\pi\) |
0.891465 | − | 0.453089i | \(-0.149678\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.89440 | + | 19.7358i | 0.348665 | + | 0.998085i | ||||
\(392\) | 1.62218i | 0.0819324i | ||||||||
\(393\) | −12.9152 | + | 1.85692i | −0.651484 | + | 0.0936692i | ||||
\(394\) | 0.00961727 | − | 0.0210589i | 0.000484511 | − | 0.00106093i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.30841 | − | 6.12623i | 0.266757 | − | 0.307855i | ||||
\(397\) | 3.47123 | − | 11.8219i | 0.174216 | − | 0.593325i | −0.825371 | − | 0.564590i | \(-0.809034\pi\) |
0.999587 | − | 0.0287344i | \(-0.00914770\pi\) | |||||||
\(398\) | 0.206192 | + | 0.320841i | 0.0103355 | + | 0.0160823i | ||||
\(399\) | −4.76890 | − | 10.4424i | −0.238744 | − | 0.522776i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.3895 | − | 18.2448i | −1.41770 | − | 0.911102i | −0.999997 | − | 0.00251937i | \(-0.999198\pi\) |
−0.417705 | − | 0.908583i | \(-0.637166\pi\) | |||||||
\(402\) | −0.171440 | − | 0.0246493i | −0.00855063 | − | 0.00122940i | ||||
\(403\) | −1.91941 | − | 0.275970i | −0.0956126 | − | 0.0137470i | ||||
\(404\) | 7.53797 | + | 4.84436i | 0.375028 | + | 0.241016i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.253827 | − | 0.555804i | −0.0125972 | − | 0.0275841i | ||||
\(407\) | 12.2035 | + | 18.9890i | 0.604904 | + | 0.941249i | ||||
\(408\) | −0.432214 | + | 1.47199i | −0.0213978 | + | 0.0728741i | ||||
\(409\) | 10.6316 | − | 12.2695i | 0.525698 | − | 0.606688i | −0.429350 | − | 0.903138i | \(-0.641257\pi\) |
0.955048 | + | 0.296450i | \(0.0958028\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.94256 | + | 19.5815i | −0.441104 | + | 0.965883i | ||||
\(412\) | −19.1927 | + | 2.75950i | −0.945558 | + | 0.135951i | ||||
\(413\) | 12.4018i | 0.610254i | ||||||||
\(414\) | 0.841961 | + | 0.0779495i | 0.0413801 | + | 0.00383101i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.320594 | − | 2.22978i | −0.0157184 | − | 0.109324i | ||||
\(417\) | 14.8924 | + | 6.80112i | 0.729282 | + | 0.333052i | ||||
\(418\) | −0.375150 | − | 1.27764i | −0.0183492 | − | 0.0624916i | ||||
\(419\) | −8.76692 | + | 10.1176i | −0.428292 | + | 0.494275i | −0.928345 | − | 0.371719i | \(-0.878768\pi\) |
0.500053 | + | 0.865995i | \(0.333314\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.9478 | + | 7.03572i | −0.533563 | + | 0.342900i | −0.779517 | − | 0.626382i | \(-0.784535\pi\) |
0.245954 | + | 0.969282i | \(0.420899\pi\) | |||||||
\(422\) | 0.526644 | − | 0.240510i | 0.0256366 | − | 0.0117079i | ||||
\(423\) | −4.12375 | + | 3.57325i | −0.200504 | + | 0.173737i | ||||
\(424\) | −0.0812036 | − | 0.0521864i | −0.00394360 | − | 0.00253439i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.139903 | + | 0.973048i | −0.00677833 | + | 0.0471443i | ||||
\(427\) | −2.69081 | + | 4.18698i | −0.130217 | + | 0.202622i | ||||
\(428\) | −11.1367 | + | 9.65005i | −0.538315 | + | 0.466453i | ||||
\(429\) | −1.80906 | − | 3.96130i | −0.0873424 | − | 0.191253i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.97982 | − | 2.63671i | −0.432543 | − | 0.127006i | 0.0582112 | − | 0.998304i | \(-0.481460\pi\) |
−0.490754 | + | 0.871298i | \(0.663279\pi\) | |||||||
\(432\) | −14.9390 | − | 12.9447i | −0.718754 | − | 0.622804i | ||||
\(433\) | −9.56922 | − | 32.5898i | −0.459867 | − | 1.56616i | −0.784378 | − | 0.620283i | \(-0.787018\pi\) |
0.324511 | − | 0.945882i | \(-0.394800\pi\) | |||||||
\(434\) | −0.0512961 | + | 0.112323i | −0.00246229 | + | 0.00539167i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20.7432 | −0.993419 | ||||||||
\(437\) | −21.9300 | + | 28.0522i | −1.04905 | + | 1.34192i | ||||
\(438\) | − | 0.914218i | − | 0.0436830i | ||||||
\(439\) | 4.53831 | + | 31.5646i | 0.216602 | + | 1.50650i | 0.750456 | + | 0.660921i | \(0.229834\pi\) |
−0.533854 | + | 0.845577i | \(0.679257\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.84511 | + | 2.59716i | −0.421196 | + | 0.123674i | ||||
\(442\) | −0.621656 | − | 0.538668i | −0.0295691 | − | 0.0256218i | ||||
\(443\) | −8.62354 | + | 29.3691i | −0.409717 | + | 1.39537i | 0.453825 | + | 0.891091i | \(0.350059\pi\) |
−0.863542 | + | 0.504277i | \(0.831759\pi\) | |||||||
\(444\) | 18.5950 | − | 11.9502i | 0.882477 | − | 0.567134i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.531535 | + | 0.613424i | 0.0251689 | + | 0.0290465i | ||||
\(447\) | 10.4459 | − | 16.2542i | 0.494076 | − | 0.768797i | ||||
\(448\) | 11.9592 | + | 1.71947i | 0.565018 | + | 0.0812373i | ||||
\(449\) | −2.39840 | + | 16.6812i | −0.113187 | + | 0.787236i | 0.851597 | + | 0.524196i | \(0.175634\pi\) |
−0.964785 | + | 0.263040i | \(0.915275\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.05133 | − | 9.29173i | −0.379122 | − | 0.437530i | ||||
\(452\) | 35.5048 | − | 16.2145i | 1.67001 | − | 0.762666i | ||||
\(453\) | 10.8202 | + | 16.8366i | 0.508380 | + | 0.791054i | ||||
\(454\) | −0.750400 | − | 0.220337i | −0.0352180 | − | 0.0103409i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.50714 | + | 0.736163i | −0.117408 | + | 0.0344740i | ||||
\(457\) | −2.47375 | − | 1.12972i | −0.115717 | − | 0.0528463i | 0.356715 | − | 0.934213i | \(-0.383897\pi\) |
−0.472432 | + | 0.881367i | \(0.656624\pi\) | |||||||
\(458\) | 0.731650 | − | 0.105195i | 0.0341877 | − | 0.00491546i | ||||
\(459\) | −21.7954 | −1.01732 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.7457 | −1.66484 | −0.832421 | − | 0.554143i | \(-0.813046\pi\) | ||||
−0.832421 | + | 0.554143i | \(0.813046\pi\) | |||||||
\(462\) | −0.274486 | + | 0.0394651i | −0.0127702 | + | 0.00183608i | ||||
\(463\) | 37.8860 | + | 17.3020i | 1.76071 | + | 0.804091i | 0.984899 | + | 0.173130i | \(0.0553880\pi\) |
0.775814 | + | 0.630961i | \(0.217339\pi\) | |||||||
\(464\) | 17.0041 | − | 4.99286i | 0.789397 | − | 0.231788i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.03119 | + | 0.596411i | 0.0940931 | + | 0.0276282i | ||||
\(467\) | 9.55519 | + | 14.8682i | 0.442161 | + | 0.688017i | 0.988782 | − | 0.149364i | \(-0.0477225\pi\) |
−0.546621 | + | 0.837380i | \(0.684086\pi\) | |||||||
\(468\) | 7.75819 | − | 3.54305i | 0.358623 | − | 0.163777i | ||||
\(469\) | 1.98938 | + | 2.29587i | 0.0918610 | + | 0.106013i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.821781 | − | 5.71561i | 0.0378657 | − | 0.263361i | ||||
\(472\) | 2.79411 | + | 0.401733i | 0.128609 | + | 0.0184913i | ||||
\(473\) | −5.93396 | + | 9.23343i | −0.272844 | + | 0.424553i | ||||
\(474\) | −0.185866 | − | 0.214501i | −0.00853712 | − | 0.00985237i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11.2961 | − | 7.25953i | 0.517754 | − | 0.332740i | ||||
\(477\) | 0.154543 | − | 0.526324i | 0.00707602 | − | 0.0240987i | ||||
\(478\) | −0.748699 | − | 0.648752i | −0.0342447 | − | 0.0296732i | ||||
\(479\) | −11.4723 | + | 3.36858i | −0.524184 | + | 0.153914i | −0.533110 | − | 0.846046i | \(-0.678977\pi\) |
0.00892633 | + | 0.999960i | \(0.497159\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.37991 | + | 23.5078i | 0.154111 | + | 1.07186i | ||||
\(482\) | − | 2.47780i | − | 0.112861i | ||||||
\(483\) | 5.13260 | + | 5.35195i | 0.233541 | + | 0.243522i | ||||
\(484\) | −13.6687 | −0.621306 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.585941 | + | 1.28303i | −0.0265788 | + | 0.0581995i | ||||
\(487\) | 5.31536 | + | 18.1024i | 0.240862 | + | 0.820300i | 0.987843 | + | 0.155455i | \(0.0496843\pi\) |
−0.746981 | + | 0.664845i | \(0.768497\pi\) | |||||||
\(488\) | 0.856156 | + | 0.741863i | 0.0387563 | + | 0.0335826i | ||||
\(489\) | −8.44701 | − | 2.48026i | −0.381987 | − | 0.112161i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.10363 | + | 19.9342i | 0.410841 | + | 0.899616i | 0.996055 | + | 0.0887373i | \(0.0282832\pi\) |
−0.585214 | + | 0.810879i | \(0.698990\pi\) | |||||||
\(492\) | −9.09891 | + | 7.88425i | −0.410211 | + | 0.355450i | ||||
\(493\) | 10.5643 | − | 16.4384i | 0.475794 | − | 0.740349i | ||||
\(494\) | 0.199387 | − | 1.38677i | 0.00897086 | − | 0.0623937i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.01291 | − | 1.93628i | −0.135284 | − | 0.0869416i | ||||
\(497\) | 13.0308 | − | 11.2912i | 0.584509 | − | 0.506480i | ||||
\(498\) | 0.349679 | − | 0.159693i | 0.0156695 | − | 0.00715602i | ||||
\(499\) | −8.48768 | + | 5.45470i | −0.379961 | + | 0.244186i | −0.716655 | − | 0.697428i | \(-0.754328\pi\) |
0.336694 | + | 0.941614i | \(0.390691\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.7879 | + | 14.7581i | −0.571323 | + | 0.659341i | ||||
\(502\) | 0.682837 | + | 2.32553i | 0.0304765 | + | 0.103793i | ||||
\(503\) | −12.1941 | − | 5.56885i | −0.543707 | − | 0.248303i | 0.124576 | − | 0.992210i | \(-0.460243\pi\) |
−0.668283 | + | 0.743907i | \(0.732970\pi\) | |||||||
\(504\) | −0.154886 | − | 1.07726i | −0.00689918 | − | 0.0479849i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.500939 | + | 0.699196i | 0.0222694 | + | 0.0310831i | ||||
\(507\) | 8.41804i | 0.373858i | ||||||||
\(508\) | −34.5985 | + | 4.97451i | −1.53506 | + | 0.220708i | ||||
\(509\) | −8.03460 | + | 17.5933i | −0.356127 | + | 0.779810i | 0.643766 | + | 0.765222i | \(0.277371\pi\) |
−0.999894 | + | 0.0145879i | \(0.995356\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.5006 | + | 12.1183i | −0.464518 | + | 0.536082i | ||||
\(512\) | 1.95615 | − | 6.66205i | 0.0864506 | − | 0.294424i | ||||
\(513\) | −20.0701 | − | 31.2297i | −0.886116 | − | 1.37882i | ||||
\(514\) | −0.650495 | − | 1.42439i | −0.0286921 | − | 0.0628270i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.04182 | + | 5.81083i | 0.398044 | + | 0.255807i | ||||
\(517\) | −5.49398 | − | 0.789915i | −0.241625 | − | 0.0347404i | ||||
\(518\) | 1.49694 | + | 0.215227i | 0.0657716 | + | 0.00945652i | ||||
\(519\) | 18.1562 | + | 11.6683i | 0.796970 | + | 0.512182i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.67119 | − | 10.2285i | −0.204648 | − | 0.448117i | 0.779281 | − | 0.626674i | \(-0.215584\pi\) |
−0.983930 | + | 0.178557i | \(0.942857\pi\) | |||||||
\(522\) | −0.427296 | − | 0.664885i | −0.0187022 | − | 0.0291012i | ||||
\(523\) | 5.09404 | − | 17.3487i | 0.222747 | − | 0.758605i | −0.769964 | − | 0.638087i | \(-0.779726\pi\) |
0.992711 | − | 0.120519i | \(-0.0384558\pi\) | |||||||
\(524\) | 17.0228 | − | 19.6454i | 0.743645 | − | 0.858212i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.320098 | + | 0.700917i | −0.0139569 | + | 0.0305614i | ||||
\(527\) | −3.90874 | + | 0.561992i | −0.170267 | + | 0.0244808i | ||||
\(528\) | − | 8.04304i | − | 0.350028i | ||||||
\(529\) | 7.39715 | − | 21.7780i | 0.321615 | − | 0.946870i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.28297 | + | 15.8784i | 0.0990725 | + | 0.689064i | ||||
\(532\) | 20.8037 | + | 9.50074i | 0.901955 | + | 0.411909i | ||||
\(533\) | −3.64448 | − | 12.4119i | −0.157860 | − | 0.537621i | ||||
\(534\) | −0.0370854 | + | 0.0427988i | −0.00160484 | + | 0.00185209i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.581697 | − | 0.373834i | 0.0251255 | − | 0.0161472i | ||||
\(537\) | −13.9672 | + | 6.37863i | −0.602731 | + | 0.275258i | ||||
\(538\) | −0.195260 | + | 0.169194i | −0.00841825 | + | 0.00729445i | ||||
\(539\) | −7.88869 | − | 5.06975i | −0.339790 | − | 0.218370i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.97456 | − | 13.7333i | 0.0848928 | − | 0.590442i | −0.902324 | − | 0.431059i | \(-0.858140\pi\) |
0.987217 | − | 0.159384i | \(-0.0509507\pi\) | |||||||
\(542\) | 0.312674 | − | 0.486530i | 0.0134305 | − | 0.0208983i | ||||
\(543\) | 0.618931 | − | 0.536306i | 0.0265609 | − | 0.0230151i | ||||
\(544\) | −1.90571 | − | 4.17292i | −0.0817065 | − | 0.178912i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.279953 | − | 0.0822015i | −0.0119809 | − | 0.00351790i | ||||
\(547\) | 22.7793 | + | 19.7384i | 0.973973 | + | 0.843952i | 0.987764 | − | 0.155953i | \(-0.0498448\pi\) |
−0.0137919 | + | 0.999905i | \(0.504390\pi\) | |||||||
\(548\) | −12.0825 | − | 41.1491i | −0.516138 | − | 1.75780i | ||||
\(549\) | −2.67436 | + | 5.85603i | −0.114139 | + | 0.249929i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.2819 | 1.41786 | ||||||||
\(552\) | 1.37204 | − | 0.983001i | 0.0583981 | − | 0.0418393i | ||||
\(553\) | 4.97813i | 0.211692i | ||||||||
\(554\) | −0.285906 | − | 1.98852i | −0.0121470 | − | 0.0844840i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −31.2953 | + | 9.18913i | −1.32722 | + | 0.389706i | ||||
\(557\) | −16.3440 | − | 14.1622i | −0.692519 | − | 0.600071i | 0.235824 | − | 0.971796i | \(-0.424221\pi\) |
−0.928343 | + | 0.371724i | \(0.878767\pi\) | |||||||
\(558\) | −0.0449991 | + | 0.153253i | −0.00190496 | + | 0.00648771i | ||||
\(559\) | −9.71499 | + | 6.24345i | −0.410900 | + | 0.264070i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.80751 | − | 6.70222i | −0.245193 | − | 0.282968i | ||||
\(562\) | 0.678850 | − | 1.05631i | 0.0286356 | − | 0.0445578i | ||||
\(563\) | 0.283349 | + | 0.0407395i | 0.0119418 | + | 0.00171696i | 0.148283 | − | 0.988945i | \(-0.452625\pi\) |
−0.136341 | + | 0.990662i | \(0.543534\pi\) | |||||||
\(564\) | −0.773524 | + | 5.37998i | −0.0325712 | + | 0.226538i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.36864 | − | 1.57949i | −0.0575281 | − | 0.0663910i | ||||
\(567\) | 1.40647 | − | 0.642315i | 0.0590663 | − | 0.0269747i | ||||
\(568\) | −2.12179 | − | 3.30156i | −0.0890282 | − | 0.138531i | ||||
\(569\) | −1.66147 | − | 0.487852i | −0.0696525 | − | 0.0204518i | 0.246721 | − | 0.969087i | \(-0.420647\pi\) |
−0.316373 | + | 0.948635i | \(0.602465\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.8922 | + | 5.84086i | −0.832461 | + | 0.244433i | −0.670074 | − | 0.742295i | \(-0.733738\pi\) |
−0.162387 | + | 0.986727i | \(0.551919\pi\) | |||||||
\(572\) | 7.89181 | + | 3.60407i | 0.329973 | + | 0.150694i | ||||
\(573\) | −4.22245 | + | 0.607097i | −0.176395 | + | 0.0253618i | ||||
\(574\) | −0.823739 | −0.0343822 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 15.6282 | 0.651174 | ||||||||
\(577\) | 23.8763 | − | 3.43290i | 0.993985 | − | 0.142913i | 0.373917 | − | 0.927462i | \(-0.378014\pi\) |
0.620067 | + | 0.784549i | \(0.287105\pi\) | |||||||
\(578\) | −0.160506 | − | 0.0733005i | −0.00667616 | − | 0.00304890i | ||||
\(579\) | −4.63848 | + | 1.36198i | −0.192769 | + | 0.0566020i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.46934 | − | 1.89957i | −0.268394 | − | 0.0788074i | ||||
\(582\) | 0.264080 | + | 0.410917i | 0.0109465 | + | 0.0170330i | ||||
\(583\) | 0.507567 | − | 0.231798i | 0.0210213 | − | 0.00960009i | ||||
\(584\) | 2.39009 | + | 2.75831i | 0.0989026 | + | 0.114140i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.0536241 | − | 0.372964i | 0.00221519 | − | 0.0154070i | ||||
\(587\) | 33.2423 | + | 4.77952i | 1.37206 | + | 0.197272i | 0.788617 | − | 0.614885i | \(-0.210798\pi\) |
0.583439 | + | 0.812157i | \(0.301707\pi\) | |||||||
\(588\) | −4.96455 | + | 7.72499i | −0.204734 | + | 0.318573i | ||||
\(589\) | −4.40458 | − | 5.08316i | −0.181488 | − | 0.209448i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.220925 | − | 0.141980i | 0.00908764 | − | 0.00584027i | ||||
\(592\) | −12.3578 | + | 42.0867i | −0.507901 | + | 1.72975i | ||||
\(593\) | 22.5585 | + | 19.5470i | 0.926365 | + | 0.802700i | 0.980639 | − | 0.195827i | \(-0.0627389\pi\) |
−0.0542739 | + | 0.998526i | \(0.517284\pi\) | |||||||
\(594\) | −0.860418 | + | 0.252641i | −0.0353034 | + | 0.0103660i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.47807 | + | 38.1008i | 0.224391 | + | 1.56067i | ||||
\(597\) | 4.32625i | 0.177062i | ||||||||
\(598\) | 0.173830 | + | 0.888133i | 0.00710843 | + | 0.0363185i | ||||
\(599\) | −4.70186 | −0.192113 | −0.0960564 | − | 0.995376i | \(-0.530623\pi\) | ||||
−0.0960564 | + | 0.995376i | \(0.530623\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.89729 | − | 19.4823i | 0.362928 | − | 0.794701i | −0.636792 | − | 0.771036i | \(-0.719739\pi\) |
0.999720 | − | 0.0236658i | \(-0.00753375\pi\) | |||||||
\(602\) | 0.207178 | + | 0.705584i | 0.00844395 | + | 0.0287575i | ||||
\(603\) | 2.96969 | + | 2.57325i | 0.120935 | + | 0.104791i | ||||
\(604\) | −38.2569 | − | 11.2332i | −1.55665 | − | 0.457073i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.164711 | − | 0.360666i | −0.00669091 | − | 0.0146511i | ||||
\(607\) | −29.1696 | + | 25.2756i | −1.18396 | + | 1.02591i | −0.184891 | + | 0.982759i | \(0.559193\pi\) |
−0.999069 | + | 0.0431477i | \(0.986261\pi\) | |||||||
\(608\) | 4.22433 | − | 6.57319i | 0.171319 | − | 0.266578i | ||||
\(609\) | 0.986403 | − | 6.86058i | 0.0399711 | − | 0.278005i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.91289 | − | 3.15732i | −0.198754 | − | 0.127732i | ||||
\(612\) | 13.1263 | − | 11.3740i | 0.530599 | − | 0.459766i | ||||
\(613\) | 17.1155 | − | 7.81638i | 0.691288 | − | 0.315700i | −0.0386125 | − | 0.999254i | \(-0.512294\pi\) |
0.729900 | + | 0.683554i | \(0.239567\pi\) | |||||||
\(614\) | 0.663370 | − | 0.426322i | 0.0267714 | − | 0.0172050i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.724983 | − | 0.836675i | 0.0292104 | − | 0.0337106i | ||||
\(617\) | −4.46602 | − | 15.2099i | −0.179795 | − | 0.612326i | −0.999233 | − | 0.0391580i | \(-0.987532\pi\) |
0.819438 | − | 0.573168i | \(-0.194286\pi\) | |||||||
\(618\) | 0.780473 | + | 0.356430i | 0.0313952 | + | 0.0143377i | ||||
\(619\) | −4.22984 | − | 29.4192i | −0.170012 | − | 1.18246i | −0.878854 | − | 0.477091i | \(-0.841691\pi\) |
0.708842 | − | 0.705367i | \(-0.249218\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.8915 | + | 14.7685i | 0.758091 | + | 0.592641i | ||||
\(622\) | − | 2.05794i | − | 0.0825158i | ||||||
\(623\) | 0.983162 | − | 0.141357i | 0.0393896 | − | 0.00566336i | ||||
\(624\) | 3.51546 | − | 7.69778i | 0.140731 | − | 0.308158i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.29956 | − | 1.49977i | 0.0519408 | − | 0.0599429i | ||||
\(627\) | 4.25553 | − | 14.4930i | 0.169949 | − | 0.578794i | ||||
\(628\) | 6.21947 | + | 9.67769i | 0.248184 | + | 0.386182i | ||||
\(629\) | 20.0912 | + | 43.9936i | 0.801089 | + | 1.75414i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.0318 | − | 9.01768i | −0.558597 | − | 0.358988i | 0.230677 | − | 0.973030i | \(-0.425906\pi\) |
−0.789273 | + | 0.614042i | \(0.789542\pi\) | |||||||
\(632\) | 1.12156 | + | 0.161257i | 0.0446134 | + | 0.00641444i | ||||
\(633\) | 6.50065 | + | 0.934652i | 0.258378 | + | 0.0371491i | ||||
\(634\) | −0.945584 | − | 0.607690i | −0.0375539 | − | 0.0241345i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.226988 | − | 0.497034i | −0.00900066 | − | 0.0197087i | ||||
\(637\) | −5.33416 | − | 8.30012i | −0.211347 | − | 0.328863i | ||||
\(638\) | 0.226502 | − | 0.771397i | 0.00896732 | − | 0.0305399i | ||||
\(639\) | 14.6051 | − | 16.8552i | 0.577769 | − | 0.666781i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.5542 | + | 27.4898i | −0.495859 | + | 1.08578i | 0.481934 | + | 0.876208i | \(0.339935\pi\) |
−0.977793 | + | 0.209573i | \(0.932793\pi\) | |||||||
\(642\) | 0.645431 | − | 0.0927990i | 0.0254731 | − | 0.00366248i | ||||
\(643\) | 7.45857i | 0.294137i | 0.989126 | + | 0.147069i | \(0.0469838\pi\) | ||||
−0.989126 | + | 0.147069i | \(0.953016\pi\) | |||||||
\(644\) | −14.7101 | − | 1.36187i | −0.579659 | − | 0.0536653i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.406038 | − | 2.82406i | −0.0159754 | − | 0.111111i | ||||
\(647\) | 6.94356 | + | 3.17102i | 0.272980 | + | 0.124666i | 0.547202 | − | 0.837001i | \(-0.315693\pi\) |
−0.274222 | + | 0.961666i | \(0.588420\pi\) | |||||||
\(648\) | −0.0991526 | − | 0.337683i | −0.00389508 | − | 0.0132654i | ||||
\(649\) | −10.6860 | + | 12.3323i | −0.419462 | + | 0.484085i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.17836 | + | 0.757286i | −0.0461836 | + | 0.0296804i | ||||
\(652\) | 15.9539 | − | 7.28589i | 0.624802 | − | 0.285337i | ||||
\(653\) | −29.3782 | + | 25.4564i | −1.14966 | + | 0.996185i | −0.149686 | + | 0.988734i | \(0.547826\pi\) |
−0.999972 | + | 0.00745135i | \(0.997628\pi\) | |||||||
\(654\) | 0.772173 | + | 0.496246i | 0.0301944 | + | 0.0194047i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.40014 | − | 23.6485i | 0.132753 | − | 0.923319i | ||||
\(657\) | −11.2134 | + | 17.4484i | −0.437476 | + | 0.680726i | ||||
\(658\) | −0.281047 | + | 0.243529i | −0.0109564 | + | 0.00949374i | ||||
\(659\) | 5.38310 | + | 11.7873i | 0.209696 | + | 0.459170i | 0.985030 | − | 0.172381i | \(-0.0551460\pi\) |
−0.775335 | + | 0.631551i | \(0.782419\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.9778 | + | 8.50866i | 1.12711 | + | 0.330949i | 0.791570 | − | 0.611078i | \(-0.209264\pi\) |
0.335537 | + | 0.942027i | \(0.391082\pi\) | |||||||
\(662\) | 1.09248 | + | 0.946639i | 0.0424604 | + | 0.0367922i | ||||
\(663\) | −2.62880 | − | 8.95287i | −0.102094 | − | 0.347701i | ||||
\(664\) | −0.637531 | + | 1.39600i | −0.0247410 | + | 0.0541753i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.95619 | 0.0758007 | ||||||||
\(667\) | −20.2955 | + | 7.08990i | −0.785844 | + | 0.274522i | ||||
\(668\) | − | 38.9037i | − | 1.50523i | ||||||
\(669\) | 1.31033 | + | 9.11356i | 0.0506604 | + | 0.352351i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.28342 | + | 1.84498i | −0.242569 | + | 0.0712246i | ||||
\(672\) | −1.22977 | − | 1.06560i | −0.0474393 | − | 0.0411064i | ||||
\(673\) | 0.667173 | − | 2.27218i | 0.0257176 | − | 0.0875862i | −0.945634 | − | 0.325232i | \(-0.894558\pi\) |
0.971352 | + | 0.237646i | \(0.0763758\pi\) | |||||||
\(674\) | −2.03488 | + | 1.30773i | −0.0783805 | + | 0.0503721i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.9824 | − | 12.6744i | −0.422402 | − | 0.487478i | ||||
\(677\) | 18.7600 | − | 29.1912i | 0.721006 | − | 1.12191i | −0.266425 | − | 0.963856i | \(-0.585842\pi\) |
0.987431 | − | 0.158052i | \(-0.0505213\pi\) | |||||||
\(678\) | −1.70958 | − | 0.245801i | −0.0656562 | − | 0.00943993i | ||||
\(679\) | 1.21925 | − | 8.48004i | 0.0467904 | − | 0.325434i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.80963 | − | 6.70467i | −0.222626 | − | 0.256924i | ||||
\(682\) | −0.147791 | + | 0.0674940i | −0.00565922 | + | 0.00258448i | ||||
\(683\) | 12.5776 | + | 19.5711i | 0.481269 | + | 0.748869i | 0.993965 | − | 0.109702i | \(-0.0349895\pi\) |
−0.512696 | + | 0.858570i | \(0.671353\pi\) | |||||||
\(684\) | 28.3845 | + | 8.33444i | 1.08531 | + | 0.318675i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.51832 | + | 0.445819i | −0.0579698 | + | 0.0170215i | ||||
\(687\) | 7.62712 | + | 3.48319i | 0.290993 | + | 0.132892i | ||||
\(688\) | −21.1116 | + | 3.03539i | −0.804872 | + | 0.115723i | ||||
\(689\) | 0.587093 | 0.0223665 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.0096 | −1.71225 | −0.856123 | − | 0.516772i | \(-0.827133\pi\) | ||||
−0.856123 | + | 0.516772i | \(0.827133\pi\) | |||||||
\(692\) | −42.5593 | + | 6.11911i | −1.61786 | + | 0.232614i | ||||
\(693\) | 5.72279 | + | 2.61351i | 0.217391 | + | 0.0992790i | ||||
\(694\) | 0.510520 | − | 0.149902i | 0.0193791 | − | 0.00569020i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.51372 | − | 0.444470i | −0.0573776 | − | 0.0168476i | ||||
\(697\) | −14.2422 | − | 22.1612i | −0.539461 | − | 0.839417i | ||||
\(698\) | 0.669363 | − | 0.305688i | 0.0253358 | − | 0.0115705i | ||||
\(699\) | 15.7256 | + | 18.1483i | 0.594796 | + | 0.686431i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.34738 | + | 23.2815i | −0.126429 | + | 0.879332i | 0.823600 | + | 0.567171i | \(0.191962\pi\) |
−0.950029 | + | 0.312161i | \(0.898947\pi\) | |||||||
\(702\) | −0.933908 | − | 0.134276i | −0.0352481 | − | 0.00506791i | ||||
\(703\) | −44.5357 | + | 69.2989i | −1.67969 | + | 2.61366i | ||||
\(704\) | 10.4105 | + | 12.0144i | 0.392362 | + | 0.452810i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.93952 | + | 1.24645i | −0.0729946 | + | 0.0469108i | ||||
\(707\) | −1.95925 | + | 6.67261i | −0.0736854 | + | 0.250949i | ||||
\(708\) | 12.0764 | + | 10.4643i | 0.453859 | + | 0.393271i | ||||
\(709\) | −32.8793 | + | 9.65422i | −1.23481 | + | 0.362572i | −0.833062 | − | 0.553180i | \(-0.813414\pi\) |
−0.401745 | + | 0.915752i | \(0.631596\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.916390 | + | 6.37363i | 0.0343673 | + | 0.239030i | ||||
\(712\) | − | 0.226084i | − | 0.00847285i | ||||||
\(713\) | 3.76877 | + | 2.16144i | 0.141142 | + | 0.0809467i | ||||
\(714\) | −0.594172 | −0.0222363 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.7077 | − | 27.8260i | 0.474909 | − | 1.03990i | ||||
\(717\) | −3.16603 | − | 10.7825i | −0.118238 | − | 0.402680i | ||||
\(718\) | 0.377112 | + | 0.326770i | 0.0140737 | + | 0.0121949i | ||||
\(719\) | 22.3827 | + | 6.57217i | 0.834735 | + | 0.245100i | 0.671050 | − | 0.741412i | \(-0.265844\pi\) |
0.163685 | + | 0.986513i | \(0.447662\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.25157 | − | 13.6890i | −0.232821 | − | 0.509806i | ||||
\(722\) | 2.40672 | − | 2.08543i | 0.0895687 | − | 0.0776117i | ||||
\(723\) | 15.1958 | − | 23.6451i | 0.565138 | − | 0.879371i | ||||
\(724\) | −0.232195 | + | 1.61495i | −0.00862947 | + | 0.0600193i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.508824 | + | 0.327001i | 0.0188842 | + | 0.0121362i | ||||
\(727\) | 30.4481 | − | 26.3834i | 1.12926 | − | 0.978507i | 0.129343 | − | 0.991600i | \(-0.458713\pi\) |
0.999914 | + | 0.0130932i | \(0.00416783\pi\) | |||||||
\(728\) | 1.05956 | − | 0.483883i | 0.0392698 | − | 0.0179339i | ||||
\(729\) | −10.9363 | + | 7.02833i | −0.405048 | + | 0.260309i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.4005 | + | 17.7731i | −0.569607 | + | 0.657361i | ||||
\(732\) | 1.80669 | + | 6.15303i | 0.0667773 | + | 0.227422i | ||||
\(733\) | 20.6659 | + | 9.43781i | 0.763313 | + | 0.348594i | 0.758738 | − | 0.651396i | \(-0.225816\pi\) |
0.00457542 | + | 0.999990i | \(0.498544\pi\) | |||||||
\(734\) | −0.154499 | − | 1.07456i | −0.00570266 | − | 0.0396629i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.17576 | + | 4.90825i | −0.0433391 | + | 0.180921i | ||||
\(737\) | 3.99714i | 0.147236i | ||||||||
\(738\) | −1.05466 | + | 0.151637i | −0.0388224 | + | 0.00558182i | ||||
\(739\) | 7.47356 | − | 16.3648i | 0.274919 | − | 0.601989i | −0.720930 | − | 0.693008i | \(-0.756285\pi\) |
0.995849 | + | 0.0910188i | \(0.0290123\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.4075 | − | 12.0109i | 0.382328 | − | 0.441230i | ||||
\(742\) | 0.0105326 | − | 0.0358708i | 0.000386664 | − | 0.00131686i | ||||
\(743\) | 3.14797 | + | 4.89833i | 0.115488 | + | 0.179702i | 0.894185 | − | 0.447697i | \(-0.147756\pi\) |
−0.778698 | + | 0.627399i | \(0.784119\pi\) | |||||||
\(744\) | 0.132445 | + | 0.290013i | 0.00485566 | + | 0.0106324i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.16002 | + | 1.38816i | 0.0790840 | + | 0.0508242i | ||||
\(747\) | −8.63256 | − | 1.24117i | −0.315849 | − | 0.0454122i | ||||
\(748\) | 17.4879 | + | 2.51438i | 0.639420 | + | 0.0919347i | ||||
\(749\) | −9.62131 | − | 6.18324i | −0.351555 | − | 0.225931i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.84740 | + | 8.42462i | 0.140393 | + | 0.307419i | 0.966748 | − | 0.255732i | \(-0.0823164\pi\) |
−0.826354 | + | 0.563151i | \(0.809589\pi\) | |||||||
\(752\) | −5.83133 | − | 9.07372i | −0.212647 | − | 0.330885i | ||||
\(753\) | −7.74578 | + | 26.3797i | −0.282272 | + | 0.961330i | ||||
\(754\) | 0.553942 | − | 0.639283i | 0.0201734 | − | 0.0232813i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 6.39819 | − | 14.0101i | 0.232700 | − | 0.509542i | ||||
\(757\) | −8.04064 | + | 1.15607i | −0.292242 | + | 0.0420180i | −0.286877 | − | 0.957968i | \(-0.592617\pi\) |
−0.00536536 | + | 0.999986i | \(0.501708\pi\) | |||||||
\(758\) | 2.94048i | 0.106803i | ||||||||
\(759\) | 0.492336 | + | 9.74443i | 0.0178707 | + | 0.353700i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.15984 | − | 28.9323i | −0.150794 | − | 1.04880i | −0.914893 | − | 0.403697i | \(-0.867725\pi\) |
0.764099 | − | 0.645099i | \(-0.223184\pi\) | |||||||
\(762\) | 1.40695 | + | 0.642532i | 0.0509684 | + | 0.0232765i | ||||
\(763\) | −4.53565 | − | 15.4470i | −0.164201 | − | 0.559219i | ||||
\(764\) | 5.56539 | − | 6.42281i | 0.201349 | − | 0.232369i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.30544 | − | 1.48162i | 0.0832990 | − | 0.0535330i | ||||
\(767\) | −15.6175 | + | 7.13228i | −0.563915 | + | 0.257532i | ||||
\(768\) | 11.6249 | − | 10.0730i | 0.419476 | − | 0.363478i | ||||
\(769\) | −12.2803 | − | 7.89208i | −0.442840 | − | 0.284596i | 0.300158 | − | 0.953889i | \(-0.402960\pi\) |
−0.742998 | + | 0.669294i | \(0.766597\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.52790 | − | 17.5820i | 0.0910403 | − | 0.633199i | ||||
\(772\) | 5.20693 | − | 8.10215i | 0.187402 | − | 0.291603i | ||||
\(773\) | 13.0471 | − | 11.3054i | 0.469271 | − | 0.406625i | −0.387865 | − | 0.921716i | \(-0.626787\pi\) |
0.857136 | + | 0.515091i | \(0.172242\pi\) | |||||||
\(774\) | 0.395142 | + | 0.865241i | 0.0142031 | + | 0.0311004i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.87104 | − | 0.549388i | −0.0671666 | − | 0.0197219i | ||||
\(777\) | 12.9650 | + | 11.2342i | 0.465117 | + | 0.403026i | ||||
\(778\) | −0.315080 | − | 1.07306i | −0.0112962 | − | 0.0384712i | ||||
\(779\) | 18.6391 | − | 40.8139i | 0.667815 | − | 1.46231i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.6867 | 0.811795 | ||||||||
\(782\) | 0.849200 | + | 1.63563i | 0.0303673 | + | 0.0584899i | ||||
\(783\) | − | 22.4134i | − | 0.800991i | ||||||
\(784\) | −2.59332 | − | 18.0369i | −0.0926186 | − | 0.644176i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.10366 | + | 0.324065i | −0.0393663 | + | 0.0115590i | ||||
\(787\) | −11.5950 | − | 10.0471i | −0.413318 | − | 0.358142i | 0.423243 | − | 0.906016i | \(-0.360892\pi\) |
−0.836561 | + | 0.547875i | \(0.815437\pi\) | |||||||
\(788\) | −0.147399 | + | 0.501995i | −0.00525087 | + | 0.0178828i | ||||
\(789\) | −7.35320 | + | 4.72561i | −0.261781 | + | 0.168236i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.8380 | + | 22.8942i | 0.705356 | + | 0.814025i | ||||
\(792\) | 0.774198 | − | 1.20467i | 0.0275099 | − | 0.0428063i | ||||
\(793\) | −6.82010 | − | 0.980582i | −0.242189 | − | 0.0348215i | ||||
\(794\) | 0.154578 | − | 1.07511i | 0.00548577 | − | 0.0381544i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.64417 | − | 6.51371i | −0.200052 | − | 0.230872i | ||||
\(797\) | −22.8517 | + | 10.4360i | −0.809448 | + | 0.369663i | −0.776755 | − | 0.629803i | \(-0.783136\pi\) |
−0.0326932 | + | 0.999465i | \(0.510408\pi\) | |||||||
\(798\) | −0.547137 | − | 0.851362i | −0.0193685 | − | 0.0301379i | ||||
\(799\) | −11.4109 | − | 3.35055i | −0.403690 | − | 0.118534i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.23275 | − | 0.361967i | 0.0435570 | − | 0.0127895i | ||||
\(802\) | −2.70612 | − | 1.23584i | −0.0955565 | − | 0.0436392i | ||||
\(803\) | −20.8834 | + | 3.00258i | −0.736959 | + | 0.105959i | ||||
\(804\) | 3.91419 | 0.138043 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.170947 | −0.00602136 | ||||||||
\(807\) | −2.90095 | + | 0.417094i | −0.102118 | + | 0.0146824i | ||||
\(808\) | 1.43986 | + | 0.657563i | 0.0506542 | + | 0.0231330i | ||||
\(809\) | 21.8919 | − | 6.42804i | 0.769678 | − | 0.225998i | 0.126761 | − | 0.991933i | \(-0.459542\pi\) |
0.642917 | + | 0.765935i | \(0.277724\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.7803 | + | 12.2678i | 1.46711 | + | 0.430781i | 0.915157 | − | 0.403097i | \(-0.132066\pi\) |
0.551949 | + | 0.833878i | \(0.313884\pi\) | |||||||
\(812\) | 7.46538 | + | 11.6164i | 0.261984 | + | 0.407654i | ||||
\(813\) | 5.96757 | − | 2.72530i | 0.209292 | − | 0.0955803i | ||||
\(814\) | 1.30309 | + | 1.50385i | 0.0456734 | + | 0.0527099i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.45256 | − | 17.0579i | 0.0858567 | − | 0.597147i | ||||
\(817\) | −39.6476 | − | 5.70046i | −1.38709 | − | 0.199434i | ||||
\(818\) | 0.773766 | − | 1.20400i | 0.0270541 | − | 0.0420970i | ||||
\(819\) | 4.33481 | + | 5.00264i | 0.151471 | + | 0.174806i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.9122 | − | 26.2927i | 1.42785 | − | 0.917621i | 0.427942 | − | 0.903806i | \(-0.359239\pi\) |
0.999905 | − | 0.0138148i | \(-0.00439753\pi\) | |||||||
\(822\) | −0.534648 | + | 1.82085i | −0.0186480 | + | 0.0635093i | ||||
\(823\) | 0.868528 | + | 0.752583i | 0.0302750 | + | 0.0262334i | 0.669867 | − | 0.742481i | \(-0.266351\pi\) |
−0.639592 | + | 0.768715i | \(0.720897\pi\) | |||||||
\(824\) | −3.28662 | + | 0.965039i | −0.114495 | + | 0.0336187i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.155592 | + | 1.08217i | 0.00541374 | + | 0.0376534i | ||||
\(827\) | − | 15.3873i | − | 0.535069i | −0.963548 | − | 0.267534i | \(-0.913791\pi\) | ||
0.963548 | − | 0.267534i | \(-0.0862089\pi\) | |||||||
\(828\) | −19.0844 | + | 0.964240i | −0.663230 | + | 0.0335096i | ||||
\(829\) | 43.7168 | 1.51835 | 0.759174 | − | 0.650888i | \(-0.225603\pi\) | ||||
0.759174 | + | 0.650888i | \(0.225603\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.46680 | − | 20.7294i | 0.328400 | − | 0.719095i | ||||
\(832\) | 4.71239 | + | 16.0489i | 0.163373 | + | 0.556396i | ||||
\(833\) | −15.1846 | − | 13.1576i | −0.526117 | − | 0.455883i | ||||
\(834\) | 1.38481 | + | 0.406618i | 0.0479522 | + | 0.0140800i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.5008 | + | 27.3729i | 0.432349 | + | 0.946712i | ||||
\(837\) | −3.42321 | + | 2.96623i | −0.118323 | + | 0.102528i | ||||
\(838\) | −0.638055 | + | 0.992833i | −0.0220413 | + | 0.0342969i | ||||
\(839\) | −1.60650 | + | 11.1735i | −0.0554627 | + | 0.385751i | 0.943116 | + | 0.332462i | \(0.107879\pi\) |
−0.998579 | + | 0.0532888i | \(0.983030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.49181 | − | 4.81469i | −0.258338 | − | 0.166024i | ||||
\(842\) | −0.867020 | + | 0.751277i | −0.0298795 | + | 0.0258907i | ||||
\(843\) | 12.9563 | − | 5.91692i | 0.446237 | − | 0.203790i | ||||
\(844\) | −11.0069 | + | 7.07372i | −0.378874 | + | 0.243488i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.315003 | + | 0.363533i | −0.0108300 | + | 0.0124985i | ||||
\(847\) | −2.98877 | − | 10.1788i | −0.102695 | − | 0.349748i | ||||
\(848\) | 0.986328 | + | 0.450441i | 0.0338707 | + | 0.0154682i | ||||
\(849\) | −3.37394 | − | 23.4663i | −0.115793 | − | 0.805361i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.3956 | − | 51.7460i | 0.424917 | − | 1.77383i | ||||
\(852\) | − | 22.2160i | − | 0.761106i | ||||||
\(853\) | −16.5522 | + | 2.37985i | −0.566737 | + | 0.0814845i | −0.419727 | − | 0.907651i | \(-0.637874\pi\) |
−0.147010 | + | 0.989135i | \(0.546965\pi\) | |||||||
\(854\) | −0.182267 | + | 0.399108i | −0.00623704 | + | 0.0136572i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.70474 | + | 1.96737i | −0.0582667 | + | 0.0672433i | ||||
\(857\) | 1.74302 | − | 5.93618i | 0.0595405 | − | 0.202776i | −0.924351 | − | 0.381543i | \(-0.875393\pi\) |
0.983891 | + | 0.178767i | \(0.0572109\pi\) | |||||||
\(858\) | −0.207554 | − | 0.322961i | −0.00708579 | − | 0.0110257i | ||||
\(859\) | 3.60612 | + | 7.89631i | 0.123039 | + | 0.269419i | 0.961122 | − | 0.276125i | \(-0.0890504\pi\) |
−0.838082 | + | 0.545544i | \(0.816323\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.86077 | − | 5.05181i | −0.267894 | − | 0.172165i | ||||
\(862\) | −0.816646 | − | 0.117416i | −0.0278151 | − | 0.00399921i | ||||
\(863\) | 11.1982 | + | 1.61006i | 0.381192 | + | 0.0548072i | 0.330248 | − | 0.943894i | \(-0.392868\pi\) |
0.0509446 | + | 0.998701i | \(0.483777\pi\) | |||||||
\(864\) | −4.42666 | − | 2.84484i | −0.150598 | − | 0.0967834i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.24386 | − | 2.72368i | −0.0422682 | − | 0.0925546i | ||||
\(867\) | −1.08214 | − | 1.68384i | −0.0367513 | − | 0.0571861i | ||||
\(868\) | 0.786189 | − | 2.67752i | 0.0266850 | − | 0.0908808i | ||||
\(869\) | −4.28939 | + | 4.95022i | −0.145508 | + | 0.167925i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.74707 | + | 3.82555i | −0.0591973 | + | 0.129624i | ||||
\(872\) | −3.62711 | + | 0.521499i | −0.122829 | + | 0.0176602i | ||||
\(873\) | − | 11.0817i | − | 0.375058i | ||||||
\(874\) | −1.56164 | + | 2.72293i | −0.0528232 | + | 0.0921045i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.94027 | + | 20.4500i | 0.0993426 | + | 0.690943i | ||||
\(877\) | 22.5349 | + | 10.2913i | 0.760950 | + | 0.347514i | 0.757805 | − | 0.652481i | \(-0.226272\pi\) |
0.00314460 | + | 0.999995i | \(0.498999\pi\) | |||||||
\(878\) | 0.792013 | + | 2.69735i | 0.0267291 | + | 0.0910311i | ||||
\(879\) | 2.79903 | − | 3.23025i | 0.0944090 | − | 0.108954i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.0492 | − | 18.0261i | 0.945000 | − | 0.607315i | 0.0251917 | − | 0.999683i | \(-0.491980\pi\) |
0.919808 | + | 0.392368i | \(0.128344\pi\) | |||||||
\(882\) | −0.739229 | + | 0.337594i | −0.0248911 | + | 0.0113674i | ||||
\(883\) | 9.88198 | − | 8.56278i | 0.332555 | − | 0.288161i | −0.472537 | − | 0.881311i | \(-0.656662\pi\) |
0.805092 | + | 0.593150i | \(0.202116\pi\) | |||||||
\(884\) | 15.6382 | + | 10.0501i | 0.525969 | + | 0.338020i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.384017 | + | 2.67090i | −0.0129013 | + | 0.0897305i | ||||
\(887\) | −11.9964 | + | 18.6668i | −0.402800 | + | 0.626770i | −0.982103 | − | 0.188343i | \(-0.939688\pi\) |
0.579303 | + | 0.815112i | \(0.303325\pi\) | |||||||
\(888\) | 2.95103 | − | 2.55708i | 0.0990301 | − | 0.0858101i | ||||
\(889\) | −11.2696 | − | 24.6770i | −0.377971 | − | 0.827641i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.95204 | + | 0.573170i | 0.0653957 | + | 0.0192019i | ||||
\(892\) | −13.8627 | − | 12.0121i | −0.464158 | − | 0.402195i | ||||
\(893\) | −5.70679 | − | 19.4355i | −0.190970 | − | 0.650385i | ||||
\(894\) | 0.707574 | − | 1.54937i | 0.0236648 | − | 0.0518187i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.31954 | 0.144306 | ||||||||
\(897\) | −3.78790 | + | 9.54133i | −0.126474 | + | 0.318576i | ||||
\(898\) | 1.48567i | 0.0495775i | ||||||||
\(899\) | −0.577928 | − | 4.01958i | −0.0192750 | − | 0.134060i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.14714 | − | 0.336832i | 0.0382169 | − | 0.0112215i | ||||
\(902\) | −0.819121 | − | 0.709772i | −0.0272737 | − | 0.0236328i | ||||
\(903\) | −2.35013 | + | 8.00382i | −0.0782076 | + | 0.266351i | ||||
\(904\) | 5.80064 | − | 3.72784i | 0.192926 | − | 0.123986i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.15539 | + | 1.33339i | 0.0383853 | + | 0.0442990i | ||||
\(907\) | 11.5834 | − | 18.0240i | 0.384619 | − | 0.598479i | −0.593924 | − | 0.804521i | \(-0.702422\pi\) |
0.978543 | + | 0.206042i | \(0.0660585\pi\) | |||||||
\(908\) | 17.4943 | + | 2.51530i | 0.580568 | + | 0.0834730i | ||||
\(909\) | −1.28017 | + | 8.90379i | −0.0424606 | + | 0.295320i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.5067 | + | 29.4363i | 0.845076 | + | 0.975269i | 0.999920 | − | 0.0126696i | \(-0.00403297\pi\) |
−0.154844 | + | 0.987939i | \(0.549488\pi\) | |||||||
\(912\) | 26.6999 | − | 12.1935i | 0.884123 | − | 0.403766i | ||||
\(913\) | −4.79631 | − | 7.46321i | −0.158735 | − | 0.246996i | ||||
\(914\) | −0.230030 | − | 0.0675428i | −0.00760870 | − | 0.00223412i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.0279 | + | 4.70621i | −0.529576 | + | 0.155497i | ||||
\(917\) | 18.3516 | + | 8.38091i | 0.606024 | + | 0.276762i | ||||
\(918\) | −1.90184 | + | 0.273443i | −0.0627700 | + | 0.00902496i | ||||
\(919\) | −29.9408 | −0.987657 | −0.493829 | − | 0.869559i | \(-0.664403\pi\) | ||||
−0.493829 | + | 0.869559i | \(0.664403\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.94494 | 0.294746 | ||||||||
\(922\) | −3.11912 | + | 0.448462i | −0.102723 | + | 0.0147693i | ||||
\(923\) | 21.7129 | + | 9.91594i | 0.714688 | + | 0.326387i | ||||
\(924\) | 6.01302 | − | 1.76558i | 0.197814 | − | 0.0580834i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.52295 | + | 1.03443i | 0.115771 | + | 0.0339935i | ||||
\(927\) | −10.5240 | − | 16.3756i | −0.345653 | − | 0.537846i | ||||
\(928\) | 4.29124 | − | 1.95974i | 0.140867 | − | 0.0643318i | ||||
\(929\) | −8.14358 | − | 9.39819i | −0.267182 | − | 0.308345i | 0.606266 | − | 0.795262i | \(-0.292667\pi\) |
−0.873448 | + | 0.486917i | \(0.838121\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.87026 | − | 33.8734i | 0.159616 | − | 1.11016i | ||||
\(932\) | −47.3537 | − | 6.80843i | −1.55112 | − | 0.223017i | ||||
\(933\) | 12.6209 | − | 19.6385i | 0.413189 | − | 0.642934i | ||||
\(934\) | 1.02031 | + | 1.17750i | 0.0333855 | + | 0.0385289i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.26750 | − | 0.814576i | 0.0414297 | − | 0.0266252i | ||||
\(937\) | 2.68807 | − | 9.15473i | 0.0878155 | − | 0.299072i | −0.903861 | − | 0.427826i | \(-0.859280\pi\) |
0.991677 | + | 0.128754i | \(0.0410978\pi\) | |||||||
\(938\) | 0.202394 | + | 0.175376i | 0.00660840 | + | 0.00572621i | ||||
\(939\) | 21.5992 | − | 6.34209i | 0.704863 | − | 0.206966i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.484266 | + | 3.36814i | 0.0157866 | + | 0.109798i | 0.996191 | − | 0.0871966i | \(-0.0277908\pi\) |
−0.980405 | + | 0.196995i | \(0.936882\pi\) | |||||||
\(942\) | − | 0.509046i | − | 0.0165856i | ||||||
\(943\) | −2.67180 | + | 28.8591i | −0.0870058 | + | 0.939782i | ||||
\(944\) | −31.7099 | −1.03207 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.401948 | + | 0.880143i | −0.0130684 | + | 0.0286159i | ||||
\(947\) | −3.50424 | − | 11.9343i | −0.113872 | − | 0.387814i | 0.882759 | − | 0.469826i | \(-0.155683\pi\) |
−0.996631 | + | 0.0820124i | \(0.973865\pi\) | |||||||
\(948\) | 4.84750 | + | 4.20038i | 0.157439 | + | 0.136422i | ||||
\(949\) | −21.2993 | − | 6.25405i | −0.691405 | − | 0.203015i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.29668 | − | 11.5981i | −0.171757 | − | 0.376095i | ||||
\(952\) | 1.79269 | − | 1.55338i | 0.0581015 | − | 0.0503452i | ||||
\(953\) | 7.23572 | − | 11.2590i | 0.234388 | − | 0.364715i | −0.704057 | − | 0.710143i | \(-0.748630\pi\) |
0.938445 | + | 0.345429i | \(0.112266\pi\) | |||||||
\(954\) | 0.00688198 | − | 0.0478652i | 0.000222812 | − | 0.00154969i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 18.8341 | + | 12.1039i | 0.609137 | + | 0.391469i | ||||
\(957\) | 6.89227 | − | 5.97219i | 0.222795 | − | 0.193053i | ||||
\(958\) | −0.958797 | + | 0.437868i | −0.0309773 | + | 0.0141469i | ||||
\(959\) | 28.0009 | − | 17.9951i | 0.904197 | − | 0.581092i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.7633 | − | 22.8080i | 0.637524 | − | 0.735742i | ||||
\(962\) | 0.589852 | + | 2.00885i | 0.0190176 | + | 0.0647680i | ||||
\(963\) | −13.4567 | − | 6.14545i | −0.433635 | − | 0.198034i | ||||
\(964\) | 7.96900 | + | 55.4256i | 0.256664 | + | 1.78514i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.515009 | + | 0.402610i | 0.0165701 | + | 0.0129538i | ||||
\(967\) | − | 24.7635i | − | 0.796341i | −0.917311 | − | 0.398170i | \(-0.869645\pi\) | ||
0.917311 | − | 0.398170i | \(-0.130355\pi\) | |||||||
\(968\) | −2.39008 | + | 0.343642i | −0.0768202 | + | 0.0110451i | ||||
\(969\) | 13.4446 | − | 29.4395i | 0.431902 | − | 0.945734i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.6629 | + | 13.4597i | −0.374281 | + | 0.431944i | −0.911374 | − | 0.411580i | \(-0.864977\pi\) |
0.537092 | + | 0.843523i | \(0.319523\pi\) | |||||||
\(972\) | 8.98041 | − | 30.5845i | 0.288047 | − | 0.980997i | ||||
\(973\) | −13.6859 | − | 21.2956i | −0.438749 | − | 0.682707i | ||||
\(974\) | 0.690922 | + | 1.51291i | 0.0221386 | + | 0.0484767i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.7056 | − | 6.88004i | −0.342676 | − | 0.220225i | ||||
\(977\) | −7.20015 | − | 1.03522i | −0.230353 | − | 0.0331198i | 0.0261716 | − | 0.999657i | \(-0.491668\pi\) |
−0.256525 | + | 0.966538i | \(0.582577\pi\) | |||||||
\(978\) | −0.768191 | − | 0.110449i | −0.0245640 | − | 0.00353178i | ||||
\(979\) | 1.09945 | + | 0.706574i | 0.0351386 | + | 0.0225822i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.65065 | − | 18.9423i | −0.276194 | − | 0.604780i | ||||
\(982\) | 1.04446 | + | 1.62521i | 0.0333301 | + | 0.0518627i | ||||
\(983\) | 9.07613 | − | 30.9104i | 0.289483 | − | 0.985890i | −0.678442 | − | 0.734654i | \(-0.737345\pi\) |
0.967926 | − | 0.251236i | \(-0.0808372\pi\) | |||||||
\(984\) | −1.39280 | + | 1.60738i | −0.0444008 | + | 0.0512412i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.715594 | − | 1.56693i | 0.0227892 | − | 0.0499013i | ||||
\(987\) | −4.17548 | + | 0.600344i | −0.132907 | + | 0.0191092i | ||||
\(988\) | 31.6618i | 1.00729i | ||||||||
\(989\) | 25.3916 | − | 4.96978i | 0.807407 | − | 0.158030i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.54572 | − | 10.7507i | −0.0491013 | − | 0.341507i | −0.999533 | − | 0.0305723i | \(-0.990267\pi\) |
0.950431 | − | 0.310935i | \(-0.100642\pi\) | |||||||
\(992\) | −0.867221 | − | 0.396047i | −0.0275343 | − | 0.0125745i | ||||
\(993\) | 4.61978 | + | 15.7335i | 0.146604 | + | 0.499288i | ||||
\(994\) | 0.995387 | − | 1.14874i | 0.0315718 | − | 0.0364358i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.30834 | + | 4.69678i | −0.231574 | + | 0.148823i | ||||
\(997\) | 19.1851 | − | 8.76152i | 0.607597 | − | 0.277480i | −0.0877636 | − | 0.996141i | \(-0.527972\pi\) |
0.695360 | + | 0.718661i | \(0.255245\pi\) | |||||||
\(998\) | −0.672189 | + | 0.582455i | −0.0212778 | + | 0.0184373i | ||||
\(999\) | 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.p.a.49.2 | 20 | ||
5.2 | odd | 4 | 575.2.k.a.26.1 | 10 | |||
5.3 | odd | 4 | 115.2.g.a.26.1 | ✓ | 10 | ||
5.4 | even | 2 | inner | 575.2.p.a.49.1 | 20 | ||
23.8 | even | 11 | inner | 575.2.p.a.399.1 | 20 | ||
115.8 | odd | 44 | 115.2.g.a.31.1 | yes | 10 | ||
115.13 | odd | 44 | 2645.2.a.n.1.4 | 5 | |||
115.33 | even | 44 | 2645.2.a.o.1.4 | 5 | |||
115.54 | even | 22 | inner | 575.2.p.a.399.2 | 20 | ||
115.77 | odd | 44 | 575.2.k.a.376.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.2.g.a.26.1 | ✓ | 10 | 5.3 | odd | 4 | ||
115.2.g.a.31.1 | yes | 10 | 115.8 | odd | 44 | ||
575.2.k.a.26.1 | 10 | 5.2 | odd | 4 | |||
575.2.k.a.376.1 | 10 | 115.77 | odd | 44 | |||
575.2.p.a.49.1 | 20 | 5.4 | even | 2 | inner | ||
575.2.p.a.49.2 | 20 | 1.1 | even | 1 | trivial | ||
575.2.p.a.399.1 | 20 | 23.8 | even | 11 | inner | ||
575.2.p.a.399.2 | 20 | 115.54 | even | 22 | inner | ||
2645.2.a.n.1.4 | 5 | 115.13 | odd | 44 | |||
2645.2.a.o.1.4 | 5 | 115.33 | even | 44 |