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 | 399.1 | ||
Root | \(0.755750 + 0.654861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 575.399 |
Dual form | 575.2.p.a.49.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0872586 | − | 0.0125459i | −0.0617012 | − | 0.00887129i | 0.111395 | − | 0.993776i | \(-0.464468\pi\) |
−0.173096 | + | 0.984905i | \(0.555377\pi\) | |||||||
\(3\) | −0.909632 | + | 0.415415i | −0.525176 | + | 0.239840i | −0.660318 | − | 0.750986i | \(-0.729578\pi\) |
0.135141 | + | 0.990826i | \(0.456851\pi\) | |||||||
\(4\) | −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 | \(-0.723793\pi\) |
0.962515 | + | 0.271227i | \(0.0874294\pi\) | |||||||
\(8\) | 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 | 0.985765 | + | 0.168126i | \(0.0537717\pi\) |
−0.898468 | + | 0.439038i | \(0.855319\pi\) | |||||||
\(12\) | 1.97195 | − | 0.283524i | 0.569253 | − | 0.0818462i | ||||
\(13\) | −1.15727 | − | 1.80075i | −0.320969 | − | 0.499437i | 0.642851 | − | 0.765991i | \(-0.277751\pi\) |
−0.963820 | + | 0.266554i | \(0.914115\pi\) | |||||||
\(14\) | −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 | −0.963405 | − | 0.268052i | \(-0.913620\pi\) |
0.665548 | − | 0.746355i | \(-0.268198\pi\) | |||||||
\(18\) | 0.133248 | − | 0.115460i | 0.0314068 | − | 0.0272141i | ||||
\(19\) | 7.12381 | + | 2.09174i | 1.63431 | + | 0.479878i | 0.964814 | − | 0.262935i | \(-0.0846905\pi\) |
0.669499 | + | 0.742813i | \(0.266509\pi\) | |||||||
\(20\) | 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 | 0.143177 | − | 0.989697i | \(-0.454268\pi\) |
0.655519 | + | 0.755179i | \(0.272450\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.376329 | + | 0.824045i | −0.0675906 | + | 0.148003i | −0.940412 | − | 0.340037i | \(-0.889561\pi\) |
0.872822 | + | 0.488039i | \(0.162288\pi\) | |||||||
\(32\) | −0.795348 | − | 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 | 0.957856 | + | 0.287248i | \(0.0927404\pi\) |
0.420641 | + | 0.907227i | \(0.361805\pi\) | |||||||
\(38\) | −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 | 0.975337 | − | 0.220720i | \(-0.0708408\pi\) |
−0.357279 | + | 0.933998i | \(0.616295\pi\) | |||||||
\(42\) | 0.0384020 | − | 0.130785i | 0.00592556 | − | 0.0201806i | ||||
\(43\) | 4.90745 | − | 2.24116i | 0.748379 | − | 0.341773i | −0.00444961 | − | 0.999990i | \(-0.501416\pi\) |
0.752828 | + | 0.658217i | \(0.228689\pi\) | |||||||
\(44\) | 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 | \(-0.824178\pi\) |
0.830920 | + | 0.556392i | \(0.187815\pi\) | |||||||
\(54\) | −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 | −0.900329 | − | 0.435210i | \(-0.856674\pi\) |
0.0218707 | + | 0.999761i | \(0.493038\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.33718 | + | 2.92802i | −0.171208 | + | 0.374894i | −0.975713 | − | 0.219052i | \(-0.929704\pi\) |
0.804505 | + | 0.593946i | \(0.202431\pi\) | |||||||
\(62\) | 0.0431763 | − | 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 | \(-0.416251\pi\) |
−0.0224928 | + | 0.999747i | \(0.507160\pi\) | |||||||
\(68\) | 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 | −0.647959 | − | 0.761675i | \(-0.724377\pi\) |
0.836301 | − | 0.548271i | \(-0.184714\pi\) | |||||||
\(72\) | −0.640269 | + | 0.292401i | −0.0754564 | + | 0.0344598i | ||||
\(73\) | 2.92170 | − | 9.95039i | 0.341959 | − | 1.16461i | −0.591615 | − | 0.806221i | \(-0.701509\pi\) |
0.933574 | − | 0.358385i | \(-0.116672\pi\) | |||||||
\(74\) | −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 | −0.684064 | − | 0.729422i | \(-0.739789\pi\) |
0.379335 | + | 0.925259i | \(0.376153\pi\) | |||||||
\(80\) | 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 | \(-0.349653\pi\) |
−0.816698 | + | 0.577065i | \(0.804198\pi\) | |||||||
\(84\) | 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 | 0.894961 | − | 0.446144i | \(-0.147203\pi\) |
−0.923248 | + | 0.384204i | \(0.874476\pi\) | |||||||
\(90\) | 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 | \(-0.818036\pi\) |
0.415831 | + | 0.909442i | \(0.363491\pi\) | |||||||
\(98\) | −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 | −0.883122 | − | 0.469143i | \(-0.844563\pi\) |
0.590049 | + | 0.807367i | \(0.299108\pi\) | |||||||
\(102\) | −0.207757 | − | 0.323276i | −0.0205710 | − | 0.0320091i | ||||
\(103\) | −9.63380 | + | 1.38513i | −0.949247 | + | 0.136481i | −0.599510 | − | 0.800367i | \(-0.704638\pi\) |
−0.349737 | + | 0.936848i | \(0.613729\pi\) | |||||||
\(104\) | −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 | \(-0.480019\pi\) |
−0.713182 | + | 0.700979i | \(0.752747\pi\) | |||||||
\(108\) | −5.38540 | + | 8.37985i | −0.518210 | + | 0.806351i | ||||
\(109\) | 9.99029 | − | 2.93341i | 0.956897 | − | 0.280970i | 0.234241 | − | 0.972179i | \(-0.424740\pi\) |
0.722656 | + | 0.691208i | \(0.242921\pi\) | |||||||
\(110\) | 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 | \(-0.0814795\pi\) |
0.856898 | + | 0.515486i | \(0.172389\pi\) | |||||||
\(114\) | 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 | \(-0.829447\pi\) |
−0.681192 | + | 0.732105i | \(0.738538\pi\) | |||||||
\(128\) | 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 | −0.0353039 | − | 0.999377i | \(-0.511240\pi\) |
−0.923731 | + | 0.383043i | \(0.874876\pi\) | |||||||
\(132\) | 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 | 0.717665 | + | 0.696389i | \(0.245211\pi\) |
−0.492399 | + | 0.870370i | \(0.663880\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.8366 | − | 10.8202i | 1.37015 | − | 0.880539i | 0.371297 | − | 0.928514i | \(-0.378913\pi\) |
0.998849 | + | 0.0479750i | \(0.0152768\pi\) | |||||||
\(152\) | 1.97476 | + | 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 | \(-0.835080\pi\) |
0.998591 | + | 0.0530620i | \(0.0168981\pi\) | |||||||
\(158\) | 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 | \(-0.342500\pi\) |
0.207678 | + | 0.978197i | \(0.433409\pi\) | |||||||
\(164\) | −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 | 0.841418 | + | 0.540384i | \(0.181721\pi\) |
−0.415692 | + | 0.909505i | \(0.636461\pi\) | |||||||
\(168\) | −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 | \(-0.851725\pi\) |
−0.730721 | + | 0.682676i | \(0.760816\pi\) | |||||||
\(174\) | 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 | 0.243152 | − | 0.969988i | \(-0.421818\pi\) |
−0.994719 | + | 0.102634i | \(0.967273\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.340209 | + | 0.744955i | 0.0252876 | + | 0.0553720i | 0.921854 | − | 0.387537i | \(-0.126674\pi\) |
−0.896567 | + | 0.442909i | \(0.853947\pi\) | |||||||
\(182\) | 0.288802 | + | 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 | 0.404329 | − | 0.914613i | \(-0.367505\pi\) |
−0.663997 | + | 0.747735i | \(0.731141\pi\) | |||||||
\(192\) | 7.10794 | + | 3.24609i | 0.512972 | + | 0.234266i | ||||
\(193\) | 3.65352 | + | 3.16580i | 0.262986 | + | 0.227879i | 0.776366 | − | 0.630283i | \(-0.217061\pi\) |
−0.513379 | + | 0.858162i | \(0.671607\pi\) | |||||||
\(194\) | 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 | \(-0.184796\pi\) |
−0.846275 | + | 0.532747i | \(0.821160\pi\) | |||||||
\(198\) | 0.271085 | + | 0.234896i | 0.0192652 | + | 0.0166934i | ||||
\(199\) | 1.79719 | − | 3.93530i | 0.127399 | − | 0.278966i | −0.835175 | − | 0.549985i | \(-0.814633\pi\) |
0.962574 | + | 0.271019i | \(0.0873607\pi\) | |||||||
\(200\) | 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 | 0.491345 | − | 0.870965i | \(-0.336506\pi\) |
−0.0575338 | + | 0.998344i | \(0.518324\pi\) | |||||||
\(212\) | 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 | \(-0.917936\pi\) |
0.633610 | + | 0.773653i | \(0.281572\pi\) | |||||||
\(224\) | −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 | \(-0.541240\pi\) |
0.664810 | + | 0.747012i | \(0.268512\pi\) | |||||||
\(228\) | 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 | \(-0.924520\pi\) |
−0.459002 | + | 0.888435i | \(0.651793\pi\) | |||||||
\(234\) | −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 | −0.942077 | − | 0.335396i | \(-0.891130\pi\) |
0.466054 | + | 0.884756i | \(0.345675\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00004 | + | 27.8209i | 0.257665 | + | 1.79210i | 0.549355 | + | 0.835589i | \(0.314874\pi\) |
−0.291689 | + | 0.956513i | \(0.594217\pi\) | |||||||
\(242\) | −0.598684 | + | 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 | −0.368572 | − | 0.929599i | \(-0.620153\pi\) |
0.615541 | − | 0.788105i | \(-0.288938\pi\) | |||||||
\(252\) | − | 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 | −0.642709 | − | 0.766110i | \(-0.722190\pi\) |
0.954872 | − | 0.297018i | \(-0.0959922\pi\) | |||||||
\(258\) | 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 | \(-0.0949633\pi\) |
−0.664433 | + | 0.747348i | \(0.731327\pi\) | |||||||
\(264\) | −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 | 0.463316 | − | 0.886193i | \(-0.346660\pi\) |
−0.613642 | + | 0.789585i | \(0.710296\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.29616 | + | 4.95803i | 0.260973 | + | 0.301179i | 0.871081 | − | 0.491139i | \(-0.163419\pi\) |
−0.610108 | + | 0.792318i | \(0.708874\pi\) | |||||||
\(272\) | 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 | 0.962369 | − | 0.271747i | \(-0.0876013\pi\) |
−0.405940 | + | 0.913900i | \(0.633056\pi\) | |||||||
\(282\) | −0.0677599 | − | 0.230769i | −0.00403504 | − | 0.0137421i | ||||
\(283\) | 12.8173 | − | 19.9441i | 0.761910 | − | 1.18555i | −0.215973 | − | 0.976399i | \(-0.569292\pi\) |
0.977882 | − | 0.209155i | \(-0.0670713\pi\) | |||||||
\(284\) | −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 | \(-0.130755\pi\) |
−0.987160 | + | 0.159734i | \(0.948936\pi\) | |||||||
\(294\) | 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 | \(-0.445797\pi\) |
−0.633844 | + | 0.773461i | \(0.718524\pi\) | |||||||
\(308\) | −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 | 0.836185 | + | 0.548447i | \(0.184781\pi\) |
−0.647798 | + | 0.761812i | \(0.724310\pi\) | |||||||
\(312\) | 0.407288 | + | 0.633752i | 0.0230581 | + | 0.0358792i | ||||
\(313\) | −17.0127 | − | 14.7416i | −0.961615 | − | 0.833244i | 0.0244337 | − | 0.999701i | \(-0.492222\pi\) |
−0.986049 | + | 0.166457i | \(0.946767\pi\) | |||||||
\(314\) | −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 | \(-0.610709\pi\) |
0.882049 | + | 0.471158i | \(0.156164\pi\) | |||||||
\(318\) | −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 | −0.379545 | − | 0.925173i | \(-0.623919\pi\) |
0.969771 | + | 0.244015i | \(0.0784647\pi\) | |||||||
\(332\) | 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 | \(-0.0949701\pi\) |
0.403776 | + | 0.914858i | \(0.367697\pi\) | |||||||
\(338\) | −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 | \(-0.506341\pi\) |
−0.300789 | + | 0.953691i | \(0.597250\pi\) | |||||||
\(348\) | 8.12350 | − | 3.70988i | 0.435465 | − | 0.198870i | ||||
\(349\) | 8.00915 | + | 2.35170i | 0.428720 | + | 0.125883i | 0.488972 | − | 0.872300i | \(-0.337372\pi\) |
−0.0602518 | + | 0.998183i | \(0.519190\pi\) | |||||||
\(350\) | 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 | \(-0.118606\pi\) |
0.334794 | + | 0.942291i | \(0.391333\pi\) | |||||||
\(354\) | −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 | −0.649454 | − | 0.760401i | \(-0.725003\pi\) |
0.845088 | + | 0.534628i | \(0.179548\pi\) | |||||||
\(360\) | 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 | \(-0.999171\pi\) |
−0.139737 | + | 0.990189i | \(0.544626\pi\) | |||||||
\(374\) | −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 | −0.632519 | − | 0.774545i | \(-0.717979\pi\) |
0.388683 | − | 0.921372i | \(-0.372930\pi\) | |||||||
\(380\) | 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 | \(-0.655762\pi\) |
−0.974870 | + | 0.222773i | \(0.928489\pi\) | |||||||
\(384\) | −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 | 0.891465 | + | 0.453089i | \(0.149678\pi\) |
−0.983005 | + | 0.183581i | \(0.941231\pi\) | |||||||
\(390\) | 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 | −0.999587 | − | 0.0287344i | \(-0.990852\pi\) |
0.825371 | − | 0.564590i | \(-0.190966\pi\) | |||||||
\(398\) | −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 | −0.417705 | + | 0.908583i | \(0.637166\pi\) |
−0.999997 | + | 0.00251937i | \(0.999198\pi\) | |||||||
\(402\) | 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 | 0.955048 | − | 0.296450i | \(-0.0958028\pi\) |
−0.429350 | + | 0.903138i | \(0.641257\pi\) | |||||||
\(410\) | 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 | 0.500053 | − | 0.865995i | \(-0.333314\pi\) |
−0.928345 | + | 0.371719i | \(0.878768\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.9478 | − | 7.03572i | −0.533563 | − | 0.342900i | 0.245954 | − | 0.969282i | \(-0.420899\pi\) |
−0.779517 | + | 0.626382i | \(0.784535\pi\) | |||||||
\(422\) | −0.526644 | − | 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 | −0.490754 | − | 0.871298i | \(-0.663279\pi\) |
0.0582112 | + | 0.998304i | \(0.481460\pi\) | |||||||
\(432\) | 14.9390 | − | 12.9447i | 0.718754 | − | 0.622804i | ||||
\(433\) | 9.56922 | − | 32.5898i | 0.459867 | − | 1.56616i | −0.324511 | − | 0.945882i | \(-0.605200\pi\) |
0.784378 | − | 0.620283i | \(-0.212982\pi\) | |||||||
\(434\) | −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 | −0.533854 | − | 0.845577i | \(-0.679257\pi\) |
0.750456 | − | 0.660921i | \(-0.229834\pi\) | |||||||
\(440\) | 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 | 0.863542 | + | 0.504277i | \(0.168241\pi\) |
−0.453825 | + | 0.891091i | \(0.649941\pi\) | |||||||
\(444\) | 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 | −0.964785 | − | 0.263040i | \(-0.915275\pi\) |
0.851597 | − | 0.524196i | \(-0.175634\pi\) | |||||||
\(450\) | 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 | \(-0.616103\pi\) |
0.472432 | + | 0.881367i | \(0.343376\pi\) | |||||||
\(458\) | −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 | −0.775814 | + | 0.630961i | \(0.782661\pi\) |
−0.984899 | + | 0.173130i | \(0.944612\pi\) | |||||||
\(464\) | 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 | \(-0.952278\pi\) |
0.546621 | + | 0.837380i | \(0.315914\pi\) | |||||||
\(468\) | −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 | 0.00892633 | − | 0.999960i | \(-0.497159\pi\) |
−0.533110 | + | 0.846046i | \(0.678977\pi\) | |||||||
\(480\) | 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 | 0.746981 | + | 0.664845i | \(0.231503\pi\) |
−0.987843 | + | 0.155455i | \(0.950316\pi\) | |||||||
\(488\) | −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 | −0.585214 | − | 0.810879i | \(-0.698990\pi\) |
0.996055 | − | 0.0887373i | \(-0.0282832\pi\) | |||||||
\(492\) | 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 | 0.336694 | − | 0.941614i | \(-0.390691\pi\) |
−0.716655 | + | 0.697428i | \(0.754328\pi\) | |||||||
\(500\) | 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 | \(-0.539757\pi\) |
0.668283 | + | 0.743907i | \(0.267030\pi\) | |||||||
\(504\) | −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 | −0.999894 | − | 0.0145879i | \(-0.995356\pi\) |
0.643766 | − | 0.765222i | \(-0.277371\pi\) | |||||||
\(510\) | 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 | −0.983930 | − | 0.178557i | \(-0.942857\pi\) |
0.779281 | + | 0.626674i | \(0.215584\pi\) | |||||||
\(522\) | 0.427296 | − | 0.664885i | 0.0187022 | − | 0.0291012i | ||||
\(523\) | −5.09404 | − | 17.3487i | −0.222747 | − | 0.758605i | −0.992711 | − | 0.120519i | \(-0.961544\pi\) |
0.769964 | − | 0.638087i | \(-0.220274\pi\) | |||||||
\(524\) | 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 | 0.987217 | + | 0.159384i | \(0.0509507\pi\) |
−0.902324 | + | 0.431059i | \(0.858140\pi\) | |||||||
\(542\) | −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 | \(-0.950155\pi\) |
0.0137919 | + | 0.999905i | \(0.495610\pi\) | |||||||
\(548\) | 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 | \(-0.575779\pi\) |
0.928343 | + | 0.371724i | \(0.121233\pi\) | |||||||
\(558\) | 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 | \(-0.547375\pi\) |
0.136341 | + | 0.990662i | \(0.456466\pi\) | |||||||
\(564\) | −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 | −0.316373 | − | 0.948635i | \(-0.602465\pi\) |
0.246721 | + | 0.969087i | \(0.420647\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.8922 | − | 5.84086i | −0.832461 | − | 0.244433i | −0.162387 | − | 0.986727i | \(-0.551919\pi\) |
−0.670074 | + | 0.742295i | \(0.733738\pi\) | |||||||
\(572\) | −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 | \(-0.621986\pi\) |
−0.620067 | + | 0.784549i | \(0.712895\pi\) | |||||||
\(578\) | 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 | \(-0.789202\pi\) |
−0.583439 | + | 0.812157i | \(0.698293\pi\) | |||||||
\(588\) | 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 | \(-0.937261\pi\) |
0.0542739 | + | 0.998526i | \(0.482716\pi\) | |||||||
\(594\) | −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 | 0.999720 | + | 0.0236658i | \(0.00753375\pi\) |
−0.636792 | + | 0.771036i | \(0.719739\pi\) | |||||||
\(602\) | −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 | 0.999069 | + | 0.0431477i | \(0.0137386\pi\) |
0.184891 | + | 0.982759i | \(0.440807\pi\) | |||||||
\(608\) | −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 | \(-0.487706\pi\) |
−0.729900 | + | 0.683554i | \(0.760433\pi\) | |||||||
\(614\) | 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 | −0.819438 | − | 0.573168i | \(-0.805714\pi\) |
0.999233 | − | 0.0391580i | \(-0.0124676\pi\) | |||||||
\(618\) | −0.780473 | + | 0.356430i | −0.0313952 | + | 0.0143377i | ||||
\(619\) | −4.22984 | + | 29.4192i | −0.170012 | + | 1.18246i | 0.708842 | + | 0.705367i | \(0.249218\pi\) |
−0.878854 | + | 0.477091i | \(0.841691\pi\) | |||||||
\(620\) | 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 | −0.789273 | − | 0.614042i | \(-0.789542\pi\) |
0.230677 | + | 0.973030i | \(0.425906\pi\) | |||||||
\(632\) | −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 | −0.977793 | − | 0.209573i | \(-0.932793\pi\) |
0.481934 | − | 0.876208i | \(-0.339935\pi\) | |||||||
\(642\) | −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 | \(-0.684307\pi\) |
0.274222 | + | 0.961666i | \(0.411580\pi\) | |||||||
\(648\) | 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 | 0.999972 | + | 0.00745135i | \(0.00237186\pi\) |
0.149686 | + | 0.988734i | \(0.452174\pi\) | |||||||
\(654\) | 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 | −0.775335 | − | 0.631551i | \(-0.782419\pi\) |
0.985030 | + | 0.172381i | \(0.0551460\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.9778 | − | 8.50866i | 1.12711 | − | 0.330949i | 0.335537 | − | 0.942027i | \(-0.391082\pi\) |
0.791570 | + | 0.611078i | \(0.209264\pi\) | |||||||
\(662\) | −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 | \(-0.105442\pi\) |
−0.971352 | + | 0.237646i | \(0.923624\pi\) | |||||||
\(674\) | −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 | −0.987431 | − | 0.158052i | \(-0.949479\pi\) |
0.266425 | − | 0.963856i | \(-0.414158\pi\) | |||||||
\(678\) | 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 | \(-0.965010\pi\) |
0.512696 | + | 0.858570i | \(0.328647\pi\) | |||||||
\(684\) | 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 | −0.950029 | − | 0.312161i | \(-0.898947\pi\) |
0.823600 | − | 0.567171i | \(-0.191962\pi\) | |||||||
\(702\) | 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 | −0.401745 | − | 0.915752i | \(-0.631596\pi\) |
−0.833062 | + | 0.553180i | \(0.813414\pi\) | |||||||
\(710\) | 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 | 0.163685 | − | 0.986513i | \(-0.447662\pi\) |
0.671050 | + | 0.741412i | \(0.265844\pi\) | |||||||
\(720\) | 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 | \(-0.541287\pi\) |
−0.999914 | + | 0.0130932i | \(0.995832\pi\) | |||||||
\(728\) | −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 | \(-0.774184\pi\) |
−0.00457542 | + | 0.999990i | \(0.501456\pi\) | |||||||
\(734\) | −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 | 0.995849 | − | 0.0910188i | \(-0.0290123\pi\) |
−0.720930 | + | 0.693008i | \(0.756285\pi\) | |||||||
\(740\) | 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 | \(-0.852244\pi\) |
0.778698 | + | 0.627399i | \(0.215881\pi\) | |||||||
\(744\) | 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 | −0.826354 | − | 0.563151i | \(-0.809589\pi\) |
0.966748 | + | 0.255732i | \(0.0823164\pi\) | |||||||
\(752\) | 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 | \(-0.407383\pi\) |
0.00536536 | + | 0.999986i | \(0.498292\pi\) | |||||||
\(758\) | 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 | 0.764099 | + | 0.645099i | \(0.223184\pi\) |
−0.914893 | + | 0.403697i | \(0.867725\pi\) | |||||||
\(762\) | −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 | −0.742998 | − | 0.669294i | \(-0.766597\pi\) |
0.300158 | + | 0.953889i | \(0.402960\pi\) | |||||||
\(770\) | 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 | \(-0.373213\pi\) |
−0.857136 | + | 0.515091i | \(0.827758\pi\) | |||||||
\(774\) | 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 | \(-0.639108\pi\) |
0.836561 | + | 0.547875i | \(0.184563\pi\) | |||||||
\(788\) | 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 | \(-0.216864\pi\) |
0.0326932 | + | 0.999465i | \(0.489592\pi\) | |||||||
\(798\) | 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 | 0.642917 | − | 0.765935i | \(-0.277724\pi\) |
0.126761 | + | 0.991933i | \(0.459542\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.7803 | − | 12.2678i | 1.46711 | − | 0.430781i | 0.551949 | − | 0.833878i | \(-0.313884\pi\) |
0.915157 | + | 0.403097i | \(0.132066\pi\) | |||||||
\(812\) | −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 | 0.999905 | + | 0.0138148i | \(0.00439753\pi\) |
0.427942 | + | 0.903806i | \(0.359239\pi\) | |||||||
\(822\) | 0.534648 | + | 1.82085i | 0.0186480 | + | 0.0635093i | ||||
\(823\) | −0.868528 | + | 0.752583i | −0.0302750 | + | 0.0262334i | −0.669867 | − | 0.742481i | \(-0.733649\pi\) |
0.639592 | + | 0.768715i | \(0.279103\pi\) | |||||||
\(824\) | −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 | −0.998579 | − | 0.0532888i | \(-0.983030\pi\) |
0.943116 | − | 0.332462i | \(-0.107879\pi\) | |||||||
\(840\) | 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 | \(-0.362126\pi\) |
0.147010 | + | 0.989135i | \(0.453035\pi\) | |||||||
\(854\) | −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 | \(-0.124607\pi\) |
−0.983891 | + | 0.178767i | \(0.942789\pi\) | |||||||
\(858\) | 0.207554 | − | 0.322961i | 0.00708579 | − | 0.0110257i | ||||
\(859\) | 3.60612 | − | 7.89631i | 0.123039 | − | 0.269419i | −0.838082 | − | 0.545544i | \(-0.816323\pi\) |
0.961122 | + | 0.276125i | \(0.0890504\pi\) | |||||||
\(860\) | 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 | \(-0.607132\pi\) |
−0.0509446 | + | 0.998701i | \(0.516223\pi\) | |||||||
\(864\) | −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 | \(-0.773728\pi\) |
−0.00314460 | + | 0.999995i | \(0.501001\pi\) | |||||||
\(878\) | −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 | 0.919808 | − | 0.392368i | \(-0.128344\pi\) |
0.0251917 | + | 0.999683i | \(0.491980\pi\) | |||||||
\(882\) | 0.739229 | + | 0.337594i | 0.0248911 | + | 0.0113674i | ||||
\(883\) | −9.88198 | − | 8.56278i | −0.332555 | − | 0.288161i | 0.472537 | − | 0.881311i | \(-0.343338\pi\) |
−0.805092 | + | 0.593150i | \(0.797884\pi\) | |||||||
\(884\) | 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 | \(-0.0603115\pi\) |
−0.579303 | + | 0.815112i | \(0.696675\pi\) | |||||||
\(888\) | −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 | \(-0.297578\pi\) |
−0.978543 | + | 0.206042i | \(0.933942\pi\) | |||||||
\(908\) | −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 | −0.154844 | − | 0.987939i | \(-0.549488\pi\) |
0.999920 | + | 0.0126696i | \(0.00403297\pi\) | |||||||
\(912\) | −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 | −0.873448 | − | 0.486917i | \(-0.838121\pi\) |
0.606266 | + | 0.795262i | \(0.292667\pi\) | |||||||
\(930\) | 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 | \(-0.140720\pi\) |
−0.991677 | + | 0.128754i | \(0.958902\pi\) | |||||||
\(938\) | −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 | −0.980405 | − | 0.196995i | \(-0.936882\pi\) |
0.996191 | + | 0.0871966i | \(0.0277908\pi\) | |||||||
\(942\) | − | 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 | \(-0.844317\pi\) |
0.996631 | + | 0.0820124i | \(0.0261347\pi\) | |||||||
\(948\) | −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 | \(-0.251370\pi\) |
−0.938445 | + | 0.345429i | \(0.887734\pi\) | |||||||
\(954\) | 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 | 0.537092 | − | 0.843523i | \(-0.319523\pi\) |
−0.911374 | + | 0.411580i | \(0.864977\pi\) | |||||||
\(972\) | −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 | \(-0.508332\pi\) |
0.256525 | + | 0.966538i | \(0.417423\pi\) | |||||||
\(978\) | 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 | −0.967926 | − | 0.251236i | \(-0.919163\pi\) |
0.678442 | − | 0.734654i | \(-0.262655\pi\) | |||||||
\(984\) | −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 | 0.950431 | + | 0.310935i | \(0.100642\pi\) |
−0.999533 | + | 0.0305723i | \(0.990267\pi\) | |||||||
\(992\) | 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 | \(-0.472028\pi\) |
−0.695360 | + | 0.718661i | \(0.744755\pi\) | |||||||
\(998\) | 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.399.1 | 20 | ||
5.2 | odd | 4 | 575.2.k.a.376.1 | 10 | |||
5.3 | odd | 4 | 115.2.g.a.31.1 | yes | 10 | ||
5.4 | even | 2 | inner | 575.2.p.a.399.2 | 20 | ||
23.3 | even | 11 | inner | 575.2.p.a.49.2 | 20 | ||
115.3 | odd | 44 | 115.2.g.a.26.1 | ✓ | 10 | ||
115.49 | even | 22 | inner | 575.2.p.a.49.1 | 20 | ||
115.53 | even | 44 | 2645.2.a.o.1.4 | 5 | |||
115.72 | odd | 44 | 575.2.k.a.26.1 | 10 | |||
115.108 | odd | 44 | 2645.2.a.n.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.2.g.a.26.1 | ✓ | 10 | 115.3 | odd | 44 | ||
115.2.g.a.31.1 | yes | 10 | 5.3 | odd | 4 | ||
575.2.k.a.26.1 | 10 | 115.72 | odd | 44 | |||
575.2.k.a.376.1 | 10 | 5.2 | odd | 4 | |||
575.2.p.a.49.1 | 20 | 115.49 | even | 22 | inner | ||
575.2.p.a.49.2 | 20 | 23.3 | even | 11 | inner | ||
575.2.p.a.399.1 | 20 | 1.1 | even | 1 | trivial | ||
575.2.p.a.399.2 | 20 | 5.4 | even | 2 | inner | ||
2645.2.a.n.1.4 | 5 | 115.108 | odd | 44 | |||
2645.2.a.o.1.4 | 5 | 115.53 | even | 44 |