Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(214,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.214");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.h (of order \(3\), degree \(2\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 373.6 | ||
Root | \(-1.82904 - 1.05600i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.373 |
Dual form | 441.2.h.g.214.6 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.46050 | 1.73984 | 0.869920 | − | 0.493193i | \(-0.164170\pi\) | ||||
0.869920 | + | 0.493193i | \(0.164170\pi\) | |||||||
\(3\) | 1.25233 | + | 1.19652i | 0.723034 | + | 0.690812i | ||||
\(4\) | 4.05408 | 2.02704 | ||||||||
\(5\) | −1.82904 | − | 3.16799i | −0.817970 | − | 1.41677i | −0.907175 | − | 0.420753i | \(-0.861766\pi\) |
0.0892047 | − | 0.996013i | \(-0.471567\pi\) | |||||||
\(6\) | 3.08137 | + | 2.94405i | 1.25796 | + | 1.20190i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 5.05408 | 1.78689 | ||||||||
\(9\) | 0.136673 | + | 2.99689i | 0.0455577 | + | 0.998962i | ||||
\(10\) | −4.50036 | − | 7.79485i | −1.42314 | − | 2.46495i | ||||
\(11\) | −0.203210 | + | 0.351971i | −0.0612702 | + | 0.106123i | −0.895033 | − | 0.445999i | \(-0.852848\pi\) |
0.833763 | + | 0.552122i | \(0.186182\pi\) | |||||||
\(12\) | 5.07706 | + | 4.85080i | 1.46562 | + | 1.40030i | ||||
\(13\) | −0.243398 | + | 0.421578i | −0.0675065 | + | 0.116925i | −0.897803 | − | 0.440397i | \(-0.854838\pi\) |
0.830297 | + | 0.557322i | \(0.188171\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50000 | − | 6.15585i | 0.387298 | − | 1.58943i | ||||
\(16\) | 4.32743 | 1.08186 | ||||||||
\(17\) | 2.42792 | + | 4.20528i | 0.588857 | + | 1.01993i | 0.994382 | + | 0.105847i | \(0.0337553\pi\) |
−0.405525 | + | 0.914084i | \(0.632911\pi\) | |||||||
\(18\) | 0.336285 | + | 7.37385i | 0.0792631 | + | 1.73803i | ||||
\(19\) | −0.986757 | + | 1.70911i | −0.226378 | + | 0.392097i | −0.956732 | − | 0.290971i | \(-0.906022\pi\) |
0.730354 | + | 0.683069i | \(0.239355\pi\) | |||||||
\(20\) | −7.41507 | − | 12.8433i | −1.65806 | − | 2.87185i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.500000 | + | 0.866025i | −0.106600 | + | 0.184637i | ||||
\(23\) | −2.32383 | − | 4.02499i | −0.484552 | − | 0.839269i | 0.515290 | − | 0.857016i | \(-0.327684\pi\) |
−0.999843 | + | 0.0177464i | \(0.994351\pi\) | |||||||
\(24\) | 6.32939 | + | 6.04732i | 1.29198 | + | 1.23440i | ||||
\(25\) | −4.19076 | + | 7.25860i | −0.838151 | + | 1.45172i | ||||
\(26\) | −0.598883 | + | 1.03729i | −0.117451 | + | 0.203430i | ||||
\(27\) | −3.41468 | + | 3.91663i | −0.657155 | + | 0.753756i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.82383 | − | 6.62307i | −0.710068 | − | 1.22987i | −0.964831 | − | 0.262870i | \(-0.915331\pi\) |
0.254764 | − | 0.967003i | \(-0.418002\pi\) | |||||||
\(30\) | 3.69076 | − | 15.1465i | 0.673837 | − | 2.76536i | ||||
\(31\) | −7.02720 | −1.26212 | −0.631061 | − | 0.775733i | \(-0.717380\pi\) | ||||
−0.631061 | + | 0.775733i | \(0.717380\pi\) | |||||||
\(32\) | 0.539495 | 0.0953702 | ||||||||
\(33\) | −0.675627 | + | 0.197639i | −0.117612 | + | 0.0344045i | ||||
\(34\) | 5.97391 | + | 10.3471i | 1.02452 | + | 1.77452i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.554084 | + | 12.1496i | 0.0923474 | + | 2.02494i | ||||
\(37\) | −1.16372 | + | 2.01561i | −0.191314 | + | 0.331365i | −0.945686 | − | 0.325082i | \(-0.894608\pi\) |
0.754372 | + | 0.656447i | \(0.227941\pi\) | |||||||
\(38\) | −2.42792 | + | 4.20528i | −0.393861 | + | 0.682187i | ||||
\(39\) | −0.809243 | + | 0.236725i | −0.129583 | + | 0.0379063i | ||||
\(40\) | −9.24411 | − | 16.0113i | −1.46162 | − | 2.53160i | ||||
\(41\) | 3.75700 | − | 6.50731i | 0.586744 | − | 1.01627i | −0.407911 | − | 0.913022i | \(-0.633743\pi\) |
0.994655 | − | 0.103249i | \(-0.0329240\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.16372 | + | 2.01561i | 0.177465 | + | 0.307378i | 0.941012 | − | 0.338374i | \(-0.109877\pi\) |
−0.763547 | + | 0.645753i | \(0.776544\pi\) | |||||||
\(44\) | −0.823832 | + | 1.42692i | −0.124197 | + | 0.215116i | ||||
\(45\) | 9.24411 | − | 5.91439i | 1.37803 | − | 0.881666i | ||||
\(46\) | −5.71780 | − | 9.90352i | −0.843044 | − | 1.46019i | ||||
\(47\) | 6.31623 | 0.921317 | 0.460658 | − | 0.887578i | \(-0.347613\pi\) | ||||
0.460658 | + | 0.887578i | \(0.347613\pi\) | |||||||
\(48\) | 5.41938 | + | 5.17786i | 0.782220 | + | 0.747360i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −10.3114 | + | 17.8598i | −1.45825 | + | 2.52576i | ||||
\(51\) | −1.99115 | + | 8.17147i | −0.278816 | + | 1.14423i | ||||
\(52\) | −0.986757 | + | 1.70911i | −0.136839 | + | 0.237011i | ||||
\(53\) | 1.78434 | + | 3.09056i | 0.245097 | + | 0.424521i | 0.962159 | − | 0.272489i | \(-0.0878467\pi\) |
−0.717062 | + | 0.697010i | \(0.754513\pi\) | |||||||
\(54\) | −8.40183 | + | 9.63688i | −1.14334 | + | 1.31141i | ||||
\(55\) | 1.48672 | 0.200469 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.28074 | + | 0.959702i | −0.434544 | + | 0.127116i | ||||
\(58\) | −9.40856 | − | 16.2961i | −1.23540 | − | 2.13978i | ||||
\(59\) | −6.11839 | −0.796546 | −0.398273 | − | 0.917267i | \(-0.630390\pi\) | ||||
−0.398273 | + | 0.917267i | \(0.630390\pi\) | |||||||
\(60\) | 6.08113 | − | 24.9564i | 0.785070 | − | 3.22185i | ||||
\(61\) | 8.02712 | 1.02777 | 0.513884 | − | 0.857860i | \(-0.328206\pi\) | ||||
0.513884 | + | 0.857860i | \(0.328206\pi\) | |||||||
\(62\) | −17.2905 | −2.19589 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.32743 | −0.915929 | ||||||||
\(65\) | 1.78074 | 0.220873 | ||||||||
\(66\) | −1.66238 | + | 0.486291i | −0.204625 | + | 0.0598583i | ||||
\(67\) | 3.60078 | 0.439905 | 0.219952 | − | 0.975511i | \(-0.429410\pi\) | ||||
0.219952 | + | 0.975511i | \(0.429410\pi\) | |||||||
\(68\) | 9.84299 | + | 17.0486i | 1.19364 | + | 2.06744i | ||||
\(69\) | 1.90578 | − | 7.82115i | 0.229429 | − | 0.941555i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.46050 | 1.00408 | 0.502039 | − | 0.864845i | \(-0.332584\pi\) | ||||
0.502039 | + | 0.864845i | \(0.332584\pi\) | |||||||
\(72\) | 0.690757 | + | 15.1465i | 0.0814065 | + | 1.78503i | ||||
\(73\) | 0.986757 | + | 1.70911i | 0.115491 | + | 0.200037i | 0.917976 | − | 0.396636i | \(-0.129822\pi\) |
−0.802485 | + | 0.596673i | \(0.796489\pi\) | |||||||
\(74\) | −2.86333 | + | 4.95943i | −0.332855 | + | 0.576522i | ||||
\(75\) | −13.9333 | + | 4.07586i | −1.60888 | + | 0.470639i | ||||
\(76\) | −4.00040 | + | 6.92889i | −0.458877 | + | 0.794798i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.99115 | + | 0.582462i | −0.225453 | + | 0.0659509i | ||||
\(79\) | 8.16225 | 0.918325 | 0.459163 | − | 0.888352i | \(-0.348150\pi\) | ||||
0.459163 | + | 0.888352i | \(0.348150\pi\) | |||||||
\(80\) | −7.91503 | − | 13.7092i | −0.884928 | − | 1.53274i | ||||
\(81\) | −8.96264 | + | 0.819187i | −0.995849 | + | 0.0910208i | ||||
\(82\) | 9.24411 | − | 16.0113i | 1.02084 | − | 1.76815i | ||||
\(83\) | 6.08600 | + | 10.5413i | 0.668025 | + | 1.15705i | 0.978456 | + | 0.206457i | \(0.0661933\pi\) |
−0.310431 | + | 0.950596i | \(0.600473\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.88151 | − | 15.3832i | 0.963336 | − | 1.66855i | ||||
\(86\) | 2.86333 | + | 4.95943i | 0.308760 | + | 0.534789i | ||||
\(87\) | 3.13594 | − | 12.8696i | 0.336208 | − | 1.37976i | ||||
\(88\) | −1.02704 | + | 1.77889i | −0.109483 | + | 0.189630i | ||||
\(89\) | 7.41507 | − | 12.8433i | 0.785996 | − | 1.36139i | −0.142406 | − | 0.989808i | \(-0.545484\pi\) |
0.928402 | − | 0.371577i | \(-0.121183\pi\) | |||||||
\(90\) | 22.7452 | − | 14.5524i | 2.39755 | − | 1.53396i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.42101 | − | 16.3177i | −0.982208 | − | 1.70123i | ||||
\(93\) | −8.80039 | − | 8.40819i | −0.912558 | − | 0.871889i | ||||
\(94\) | 15.5411 | 1.60294 | ||||||||
\(95\) | 7.21926 | 0.740681 | ||||||||
\(96\) | 0.675627 | + | 0.645517i | 0.0689559 | + | 0.0658829i | ||||
\(97\) | −4.74375 | − | 8.21642i | −0.481655 | − | 0.834251i | 0.518123 | − | 0.855306i | \(-0.326631\pi\) |
−0.999778 | + | 0.0210547i | \(0.993298\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.08259 | − | 0.560893i | −0.108804 | − | 0.0563719i | ||||
\(100\) | −16.9897 | + | 29.4270i | −1.69897 | + | 2.94270i | ||||
\(101\) | 4.35588 | − | 7.54461i | 0.433426 | − | 0.750716i | −0.563739 | − | 0.825953i | \(-0.690638\pi\) |
0.997166 | + | 0.0752364i | \(0.0239711\pi\) | |||||||
\(102\) | −4.89922 | + | 20.1059i | −0.485095 | + | 1.99078i | ||||
\(103\) | 4.01356 | + | 6.95169i | 0.395468 | + | 0.684970i | 0.993161 | − | 0.116755i | \(-0.0372492\pi\) |
−0.597693 | + | 0.801725i | \(0.703916\pi\) | |||||||
\(104\) | −1.23016 | + | 2.13069i | −0.120627 | + | 0.208931i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.39037 | + | 7.60434i | 0.426430 | + | 0.738599i | ||||
\(107\) | −6.42101 | + | 11.1215i | −0.620742 | + | 1.07516i | 0.368605 | + | 0.929586i | \(0.379835\pi\) |
−0.989348 | + | 0.145571i | \(0.953498\pi\) | |||||||
\(108\) | −13.8434 | + | 15.8783i | −1.33208 | + | 1.52789i | ||||
\(109\) | −1.30039 | − | 2.25234i | −0.124555 | − | 0.215735i | 0.797004 | − | 0.603974i | \(-0.206417\pi\) |
−0.921559 | + | 0.388239i | \(0.873084\pi\) | |||||||
\(110\) | 3.65808 | 0.348784 | ||||||||
\(111\) | −3.86908 | + | 1.13181i | −0.367237 | + | 0.107427i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.97509 | − | 12.0812i | 0.656162 | − | 1.13651i | −0.325440 | − | 0.945563i | \(-0.605512\pi\) |
0.981601 | − | 0.190942i | \(-0.0611544\pi\) | |||||||
\(114\) | −8.07227 | + | 2.36135i | −0.756038 | + | 0.221161i | ||||
\(115\) | −8.50075 | + | 14.7237i | −0.792699 | + | 1.37300i | ||||
\(116\) | −15.5021 | − | 26.8505i | −1.43934 | − | 2.49301i | ||||
\(117\) | −1.29669 | − | 0.671818i | −0.119879 | − | 0.0621096i | ||||
\(118\) | −15.0543 | −1.38586 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 7.58113 | − | 31.1122i | 0.692059 | − | 2.84014i | ||||
\(121\) | 5.41741 | + | 9.38323i | 0.492492 | + | 0.853021i | ||||
\(122\) | 19.7508 | 1.78815 | ||||||||
\(123\) | 12.4911 | − | 3.65399i | 1.12629 | − | 0.329469i | ||||
\(124\) | −28.4889 | −2.55837 | ||||||||
\(125\) | 12.3698 | 1.10639 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.5438 | −1.37929 | −0.689643 | − | 0.724149i | \(-0.742233\pi\) | ||||
−0.689643 | + | 0.724149i | \(0.742233\pi\) | |||||||
\(128\) | −19.1082 | −1.68894 | ||||||||
\(129\) | −0.954367 | + | 3.91663i | −0.0840273 | + | 0.344840i | ||||
\(130\) | 4.38151 | 0.384284 | ||||||||
\(131\) | −4.25696 | − | 7.37327i | −0.371932 | − | 0.644205i | 0.617931 | − | 0.786233i | \(-0.287971\pi\) |
−0.989863 | + | 0.142027i | \(0.954638\pi\) | |||||||
\(132\) | −2.73905 | + | 0.801244i | −0.238404 | + | 0.0697393i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.85973 | 0.765364 | ||||||||
\(135\) | 18.6534 | + | 3.65399i | 1.60543 | + | 0.314485i | ||||
\(136\) | 12.2709 | + | 21.2538i | 1.05222 | + | 1.82250i | ||||
\(137\) | −0.188621 | + | 0.326702i | −0.0161150 | + | 0.0279120i | −0.873970 | − | 0.485979i | \(-0.838463\pi\) |
0.857855 | + | 0.513891i | \(0.171796\pi\) | |||||||
\(138\) | 4.68919 | − | 19.2440i | 0.399170 | − | 1.63816i | ||||
\(139\) | −9.50067 | + | 16.4556i | −0.805837 | + | 1.39575i | 0.109888 | + | 0.993944i | \(0.464951\pi\) |
−0.915725 | + | 0.401806i | \(0.868383\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.91002 | + | 7.55750i | 0.666144 | + | 0.636457i | ||||
\(142\) | 20.8171 | 1.74693 | ||||||||
\(143\) | −0.0989221 | − | 0.171338i | −0.00827228 | − | 0.0143280i | ||||
\(144\) | 0.591443 | + | 12.9688i | 0.0492869 | + | 1.08073i | ||||
\(145\) | −13.9879 | + | 24.2277i | −1.16163 | + | 2.01200i | ||||
\(146\) | 2.42792 | + | 4.20528i | 0.200936 | + | 0.348032i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.71780 | + | 8.17147i | −0.387801 | + | 0.671691i | ||||
\(149\) | 4.85087 | + | 8.40196i | 0.397399 | + | 0.688315i | 0.993404 | − | 0.114665i | \(-0.0365795\pi\) |
−0.596005 | + | 0.802981i | \(0.703246\pi\) | |||||||
\(150\) | −34.2829 | + | 10.0287i | −2.79919 | + | 0.818837i | ||||
\(151\) | 6.41741 | − | 11.1153i | 0.522242 | − | 0.904549i | −0.477424 | − | 0.878673i | \(-0.658429\pi\) |
0.999665 | − | 0.0258756i | \(-0.00823738\pi\) | |||||||
\(152\) | −4.98715 | + | 8.63800i | −0.404511 | + | 0.700634i | ||||
\(153\) | −12.2709 | + | 7.85095i | −0.992045 | + | 0.634711i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.8530 | + | 22.2621i | 1.03238 | + | 1.78813i | ||||
\(156\) | −3.28074 | + | 0.959702i | −0.262669 | + | 0.0768377i | ||||
\(157\) | −20.9485 | −1.67187 | −0.835937 | − | 0.548825i | \(-0.815075\pi\) | ||||
−0.835937 | + | 0.548825i | \(0.815075\pi\) | |||||||
\(158\) | 20.0833 | 1.59774 | ||||||||
\(159\) | −1.46334 | + | 6.00541i | −0.116050 | + | 0.476260i | ||||
\(160\) | −0.986757 | − | 1.70911i | −0.0780100 | − | 0.135117i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −22.0526 | + | 2.01561i | −1.73262 | + | 0.158362i | ||||
\(163\) | 5.58113 | − | 9.66679i | 0.437148 | − | 0.757162i | −0.560321 | − | 0.828276i | \(-0.689322\pi\) |
0.997468 | + | 0.0711140i | \(0.0226554\pi\) | |||||||
\(164\) | 15.2312 | − | 26.3812i | 1.18936 | − | 2.06002i | ||||
\(165\) | 1.86186 | + | 1.77889i | 0.144946 | + | 0.138486i | ||||
\(166\) | 14.9746 | + | 25.9368i | 1.16226 | + | 2.01309i | ||||
\(167\) | 1.73012 | − | 2.99665i | 0.133880 | − | 0.231888i | −0.791289 | − | 0.611443i | \(-0.790590\pi\) |
0.925169 | + | 0.379555i | \(0.123923\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.38151 | + | 11.0531i | 0.490886 | + | 0.850239i | ||||
\(170\) | 21.8530 | − | 37.8505i | 1.67605 | − | 2.90300i | ||||
\(171\) | −5.25688 | − | 2.72361i | −0.402004 | − | 0.208279i | ||||
\(172\) | 4.71780 | + | 8.17147i | 0.359729 | + | 0.623069i | ||||
\(173\) | 6.05361 | 0.460247 | 0.230124 | − | 0.973161i | \(-0.426087\pi\) | ||||
0.230124 | + | 0.973161i | \(0.426087\pi\) | |||||||
\(174\) | 7.71599 | − | 31.6657i | 0.584948 | − | 2.40057i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.879379 | + | 1.52313i | −0.0662857 | + | 0.114810i | ||||
\(177\) | −7.66225 | − | 7.32078i | −0.575930 | − | 0.550263i | ||||
\(178\) | 18.2448 | − | 31.6010i | 1.36751 | − | 2.36859i | ||||
\(179\) | −4.56654 | − | 7.90947i | −0.341319 | − | 0.591182i | 0.643359 | − | 0.765565i | \(-0.277540\pi\) |
−0.984678 | + | 0.174383i | \(0.944207\pi\) | |||||||
\(180\) | 37.4764 | − | 23.9775i | 2.79333 | − | 1.78717i | ||||
\(181\) | −11.9478 | −0.888074 | −0.444037 | − | 0.896008i | \(-0.646454\pi\) | ||||
−0.444037 | + | 0.896008i | \(0.646454\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.0526 | + | 9.60462i | 0.743111 | + | 0.709994i | ||||
\(184\) | −11.7448 | − | 20.3427i | −0.865841 | − | 1.49968i | ||||
\(185\) | 8.51392 | 0.625956 | ||||||||
\(186\) | −21.6534 | − | 20.6884i | −1.58770 | − | 1.51695i | ||||
\(187\) | −1.97351 | −0.144318 | ||||||||
\(188\) | 25.6065 | 1.86755 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 17.7630 | 1.28867 | ||||||||
\(191\) | 9.14027 | 0.661367 | 0.330683 | − | 0.943742i | \(-0.392721\pi\) | ||||
0.330683 | + | 0.943742i | \(0.392721\pi\) | |||||||
\(192\) | −9.17638 | − | 8.76743i | −0.662248 | − | 0.632735i | ||||
\(193\) | 16.9430 | 1.21958 | 0.609792 | − | 0.792562i | \(-0.291253\pi\) | ||||
0.609792 | + | 0.792562i | \(0.291253\pi\) | |||||||
\(194\) | −11.6720 | − | 20.2165i | −0.838003 | − | 1.45146i | ||||
\(195\) | 2.23008 | + | 2.13069i | 0.159699 | + | 0.152582i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.3173 | −1.51880 | −0.759398 | − | 0.650627i | \(-0.774506\pi\) | ||||
−0.759398 | + | 0.650627i | \(0.774506\pi\) | |||||||
\(198\) | −2.66372 | − | 1.38008i | −0.189302 | − | 0.0980780i | ||||
\(199\) | 4.98715 | + | 8.63800i | 0.353530 | + | 0.612332i | 0.986865 | − | 0.161546i | \(-0.0516479\pi\) |
−0.633335 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(200\) | −21.1804 | + | 36.6856i | −1.49768 | + | 2.59406i | ||||
\(201\) | 4.50937 | + | 4.30841i | 0.318066 | + | 0.303892i | ||||
\(202\) | 10.7177 | − | 18.5635i | 0.754092 | − | 1.30613i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −8.07227 | + | 33.1278i | −0.565172 | + | 2.31941i | ||||
\(205\) | −27.4868 | −1.91976 | ||||||||
\(206\) | 9.87538 | + | 17.1047i | 0.688051 | + | 1.19174i | ||||
\(207\) | 11.7448 | − | 7.51437i | 0.816323 | − | 0.522284i | ||||
\(208\) | −1.05329 | + | 1.82435i | −0.0730324 | + | 0.126496i | ||||
\(209\) | −0.401038 | − | 0.694619i | −0.0277404 | − | 0.0480478i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.44592 | + | 4.23645i | −0.168384 | + | 0.291649i | −0.937852 | − | 0.347036i | \(-0.887188\pi\) |
0.769468 | + | 0.638685i | \(0.220521\pi\) | |||||||
\(212\) | 7.23385 | + | 12.5294i | 0.496823 | + | 0.860523i | ||||
\(213\) | 10.5954 | + | 10.1232i | 0.725982 | + | 0.693629i | ||||
\(214\) | −15.7989 | + | 27.3645i | −1.07999 | + | 1.87060i | ||||
\(215\) | 4.25696 | − | 7.37327i | 0.290322 | − | 0.502853i | ||||
\(216\) | −17.2581 | + | 19.7950i | −1.17426 | + | 1.34688i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.19961 | − | 5.54189i | −0.216705 | − | 0.375344i | ||||
\(219\) | −0.809243 | + | 3.32105i | −0.0546836 | + | 0.224416i | ||||
\(220\) | 6.02728 | 0.406359 | ||||||||
\(221\) | −2.36381 | −0.159007 | ||||||||
\(222\) | −9.51990 | + | 2.78482i | −0.638934 | + | 0.186905i | ||||
\(223\) | −11.7044 | − | 20.2727i | −0.783786 | − | 1.35756i | −0.929722 | − | 0.368263i | \(-0.879953\pi\) |
0.145936 | − | 0.989294i | \(-0.453381\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −22.3260 | − | 11.5672i | −1.48840 | − | 0.771144i | ||||
\(226\) | 17.1623 | − | 29.7259i | 1.14162 | − | 1.97734i | ||||
\(227\) | −3.05919 | + | 5.29868i | −0.203046 | + | 0.351686i | −0.949508 | − | 0.313742i | \(-0.898417\pi\) |
0.746463 | + | 0.665427i | \(0.231751\pi\) | |||||||
\(228\) | −13.3004 | + | 3.89071i | −0.880840 | + | 0.257669i | ||||
\(229\) | 0.730195 | + | 1.26473i | 0.0482526 | + | 0.0835760i | 0.889143 | − | 0.457630i | \(-0.151301\pi\) |
−0.840890 | + | 0.541206i | \(0.817968\pi\) | |||||||
\(230\) | −20.9161 | + | 36.2278i | −1.37917 | + | 2.38879i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.3260 | − | 33.4736i | −1.26881 | − | 2.19765i | ||||
\(233\) | 6.62422 | − | 11.4735i | 0.433967 | − | 0.751653i | −0.563244 | − | 0.826291i | \(-0.690447\pi\) |
0.997211 | + | 0.0746378i | \(0.0237801\pi\) | |||||||
\(234\) | −3.19050 | − | 1.65301i | −0.208570 | − | 0.108061i | ||||
\(235\) | −11.5526 | − | 20.0097i | −0.753610 | − | 1.30529i | ||||
\(236\) | −24.8045 | −1.61463 | ||||||||
\(237\) | 10.2219 | + | 9.76631i | 0.663981 | + | 0.634390i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.69436 | + | 16.7911i | −0.627076 | + | 1.08613i | 0.361060 | + | 0.932543i | \(0.382415\pi\) |
−0.988136 | + | 0.153584i | \(0.950918\pi\) | |||||||
\(240\) | 6.49115 | − | 26.6390i | 0.419002 | − | 1.71954i | ||||
\(241\) | −2.52684 | + | 4.37662i | −0.162768 | + | 0.281923i | −0.935860 | − | 0.352371i | \(-0.885376\pi\) |
0.773092 | + | 0.634294i | \(0.218709\pi\) | |||||||
\(242\) | 13.3296 | + | 23.0875i | 0.856857 | + | 1.48412i | ||||
\(243\) | −12.2044 | − | 9.69810i | −0.782911 | − | 0.622133i | ||||
\(244\) | 32.5426 | 2.08333 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 30.7345 | − | 8.99066i | 1.95956 | − | 0.573223i | ||||
\(247\) | −0.480350 | − | 0.831990i | −0.0305639 | − | 0.0529383i | ||||
\(248\) | −35.5161 | −2.25527 | ||||||||
\(249\) | −4.99115 | + | 20.4832i | −0.316301 | + | 1.29807i | ||||
\(250\) | 30.4360 | 1.92494 | ||||||||
\(251\) | 15.0928 | 0.952647 | 0.476324 | − | 0.879270i | \(-0.341969\pi\) | ||||
0.476324 | + | 0.879270i | \(0.341969\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.88891 | 0.118755 | ||||||||
\(254\) | −38.2455 | −2.39974 | ||||||||
\(255\) | 29.5290 | − | 8.63800i | 1.84918 | − | 0.540933i | ||||
\(256\) | −32.3609 | −2.02256 | ||||||||
\(257\) | −3.85592 | − | 6.67865i | −0.240526 | − | 0.416603i | 0.720338 | − | 0.693623i | \(-0.243986\pi\) |
−0.960864 | + | 0.277020i | \(0.910653\pi\) | |||||||
\(258\) | −2.34822 | + | 9.63688i | −0.146194 | + | 0.599966i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7.21926 | 0.447720 | ||||||||
\(261\) | 19.3260 | − | 12.3648i | 1.19625 | − | 0.765361i | ||||
\(262\) | −10.4743 | − | 18.1420i | −0.647102 | − | 1.12081i | ||||
\(263\) | −2.10603 | + | 3.64776i | −0.129864 | + | 0.224930i | −0.923624 | − | 0.383301i | \(-0.874787\pi\) |
0.793760 | + | 0.608231i | \(0.208121\pi\) | |||||||
\(264\) | −3.41468 | + | 0.998883i | −0.210159 | + | 0.0614770i | ||||
\(265\) | 6.52724 | − | 11.3055i | 0.400965 | − | 0.694492i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.6534 | − | 7.21177i | 1.50876 | − | 0.441353i | ||||
\(268\) | 14.5979 | 0.891706 | ||||||||
\(269\) | −10.3753 | − | 17.9706i | −0.632596 | − | 1.09569i | −0.987019 | − | 0.160603i | \(-0.948656\pi\) |
0.354423 | − | 0.935085i | \(-0.384677\pi\) | |||||||
\(270\) | 45.8968 | + | 8.99066i | 2.79319 | + | 0.547154i | ||||
\(271\) | 14.2444 | − | 24.6721i | 0.865287 | − | 1.49872i | −0.00147433 | − | 0.999999i | \(-0.500469\pi\) |
0.866762 | − | 0.498723i | \(-0.166197\pi\) | |||||||
\(272\) | 10.5067 | + | 18.1981i | 0.637060 | + | 1.10342i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.464103 | + | 0.803851i | −0.0280375 | + | 0.0485624i | ||||
\(275\) | −1.70321 | − | 2.95005i | −0.102707 | − | 0.177895i | ||||
\(276\) | 7.72620 | − | 31.7076i | 0.465063 | − | 1.90857i | ||||
\(277\) | −8.58113 | + | 14.8629i | −0.515590 | + | 0.893028i | 0.484246 | + | 0.874932i | \(0.339094\pi\) |
−0.999836 | + | 0.0180962i | \(0.994239\pi\) | |||||||
\(278\) | −23.3765 | + | 40.4892i | −1.40203 | + | 2.42838i | ||||
\(279\) | −0.960429 | − | 21.0597i | −0.0574994 | − | 1.26081i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.72140 | − | 8.17770i | −0.281655 | − | 0.487841i | 0.690138 | − | 0.723678i | \(-0.257550\pi\) |
−0.971793 | + | 0.235837i | \(0.924217\pi\) | |||||||
\(282\) | 19.4626 | + | 18.5953i | 1.15898 | + | 1.10733i | ||||
\(283\) | 16.8684 | 1.00272 | 0.501362 | − | 0.865237i | \(-0.332832\pi\) | ||||
0.501362 | + | 0.865237i | \(0.332832\pi\) | |||||||
\(284\) | 34.2996 | 2.03531 | ||||||||
\(285\) | 9.04092 | + | 8.63800i | 0.535538 | + | 0.511671i | ||||
\(286\) | −0.243398 | − | 0.421578i | −0.0143924 | − | 0.0249284i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.0737345 | + | 1.61680i | 0.00434485 | + | 0.0952711i | ||||
\(289\) | −3.28959 | + | 5.69774i | −0.193505 | + | 0.335161i | ||||
\(290\) | −34.4172 | + | 59.6124i | −2.02105 | + | 3.50056i | ||||
\(291\) | 3.89037 | − | 15.9657i | 0.228057 | − | 0.935926i | ||||
\(292\) | 4.00040 | + | 6.92889i | 0.234105 | + | 0.405483i | ||||
\(293\) | 1.86143 | − | 3.22409i | 0.108746 | − | 0.188353i | −0.806517 | − | 0.591211i | \(-0.798650\pi\) |
0.915262 | + | 0.402858i | \(0.131983\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.1908 | + | 19.3830i | 0.651551 | + | 1.12852i | ||||
\(296\) | −5.88151 | + | 10.1871i | −0.341856 | + | 0.592112i | ||||
\(297\) | −0.684641 | − | 1.99777i | −0.0397269 | − | 0.115922i | ||||
\(298\) | 11.9356 | + | 20.6731i | 0.691411 | + | 1.19756i | ||||
\(299\) | 2.26247 | 0.130842 | ||||||||
\(300\) | −56.4868 | + | 16.5239i | −3.26126 | + | 0.954006i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 15.7901 | − | 27.3492i | 0.908617 | − | 1.57377i | ||||
\(303\) | 14.4823 | − | 4.23645i | 0.831986 | − | 0.243378i | ||||
\(304\) | −4.27012 | + | 7.39607i | −0.244908 | + | 0.424194i | ||||
\(305\) | −14.6819 | − | 25.4298i | −0.840683 | − | 1.45611i | ||||
\(306\) | −30.1926 | + | 19.3173i | −1.72600 | + | 1.10430i | ||||
\(307\) | 30.5691 | 1.74467 | 0.872335 | − | 0.488908i | \(-0.162605\pi\) | ||||
0.872335 | + | 0.488908i | \(0.162605\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.29153 | + | 13.5081i | −0.187249 | + | 0.768451i | ||||
\(310\) | 31.6249 | + | 54.7759i | 1.79617 | + | 3.11106i | ||||
\(311\) | −10.4348 | −0.591702 | −0.295851 | − | 0.955234i | \(-0.595603\pi\) | ||||
−0.295851 | + | 0.955234i | \(0.595603\pi\) | |||||||
\(312\) | −4.08998 | + | 1.19643i | −0.231550 | + | 0.0677343i | ||||
\(313\) | −0.619860 | −0.0350366 | −0.0175183 | − | 0.999847i | \(-0.505577\pi\) | ||||
−0.0175183 | + | 0.999847i | \(0.505577\pi\) | |||||||
\(314\) | −51.5440 | −2.90879 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 33.0905 | 1.86148 | ||||||||
\(317\) | 10.2484 | 0.575610 | 0.287805 | − | 0.957689i | \(-0.407075\pi\) | ||||
0.287805 | + | 0.957689i | \(0.407075\pi\) | |||||||
\(318\) | −3.60056 | + | 14.7763i | −0.201909 | + | 0.828616i | ||||
\(319\) | 3.10817 | 0.174024 | ||||||||
\(320\) | 13.4021 | + | 23.2132i | 0.749203 | + | 1.29766i | ||||
\(321\) | −21.3484 | + | 6.24496i | −1.19155 | + | 0.348560i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.58307 | −0.533216 | ||||||||
\(324\) | −36.3353 | + | 3.32105i | −2.01863 | + | 0.184503i | ||||
\(325\) | −2.04005 | − | 3.53346i | −0.113161 | − | 0.196001i | ||||
\(326\) | 13.7324 | − | 23.7852i | 0.760567 | − | 1.31734i | ||||
\(327\) | 1.06645 | − | 4.37662i | 0.0589750 | − | 0.242028i | ||||
\(328\) | 18.9882 | − | 32.8885i | 1.04845 | − | 1.81596i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.58113 | + | 4.37697i | 0.252183 | + | 0.240944i | ||||
\(331\) | −20.3638 | −1.11930 | −0.559648 | − | 0.828730i | \(-0.689064\pi\) | ||||
−0.559648 | + | 0.828730i | \(0.689064\pi\) | |||||||
\(332\) | 24.6731 | + | 42.7351i | 1.35411 | + | 2.34539i | ||||
\(333\) | −6.19961 | − | 3.21204i | −0.339737 | − | 0.176019i | ||||
\(334\) | 4.25696 | − | 7.37327i | 0.232930 | − | 0.403447i | ||||
\(335\) | −6.58596 | − | 11.4072i | −0.359829 | − | 0.623242i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.85594 | − | 4.94662i | 0.155573 | − | 0.269460i | −0.777695 | − | 0.628642i | \(-0.783611\pi\) |
0.933267 | + | 0.359182i | \(0.116944\pi\) | |||||||
\(338\) | 15.7017 | + | 27.1962i | 0.854062 | + | 1.47928i | ||||
\(339\) | 23.1906 | − | 6.78385i | 1.25954 | − | 0.368448i | ||||
\(340\) | 36.0064 | − | 62.3649i | 1.95272 | − | 3.38221i | ||||
\(341\) | 1.42800 | − | 2.47337i | 0.0773305 | − | 0.133940i | ||||
\(342\) | −12.9346 | − | 6.70145i | −0.699422 | − | 0.362373i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.88151 | + | 10.1871i | 0.317110 | + | 0.549251i | ||||
\(345\) | −28.2630 | + | 8.26768i | −1.52163 | + | 0.445117i | ||||
\(346\) | 14.8949 | 0.800756 | ||||||||
\(347\) | 8.88132 | 0.476774 | 0.238387 | − | 0.971170i | \(-0.423381\pi\) | ||||
0.238387 | + | 0.971170i | \(0.423381\pi\) | |||||||
\(348\) | 12.7134 | − | 52.1744i | 0.681507 | − | 2.79684i | ||||
\(349\) | 10.4874 | + | 18.1648i | 0.561379 | + | 0.972337i | 0.997376 | + | 0.0723893i | \(0.0230624\pi\) |
−0.435997 | + | 0.899948i | \(0.643604\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.820039 | − | 2.39285i | −0.0437704 | − | 0.127721i | ||||
\(352\) | −0.109631 | + | 0.189886i | −0.00584335 | + | 0.0101210i | ||||
\(353\) | −7.38268 | + | 12.7872i | −0.392941 | + | 0.680593i | −0.992836 | − | 0.119485i | \(-0.961876\pi\) |
0.599895 | + | 0.800078i | \(0.295209\pi\) | |||||||
\(354\) | −18.8530 | − | 18.0128i | −1.00203 | − | 0.957370i | ||||
\(355\) | −15.4746 | − | 26.8028i | −0.821306 | − | 1.42254i | ||||
\(356\) | 30.0613 | − | 52.0677i | 1.59325 | − | 2.75959i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.2360 | − | 19.4613i | −0.593840 | − | 1.02856i | ||||
\(359\) | −3.60603 | + | 6.24583i | −0.190319 | + | 0.329642i | −0.945356 | − | 0.326040i | \(-0.894286\pi\) |
0.755037 | + | 0.655682i | \(0.227619\pi\) | |||||||
\(360\) | 46.7205 | − | 29.8918i | 2.46239 | − | 1.57544i | ||||
\(361\) | 7.55262 | + | 13.0815i | 0.397506 | + | 0.688501i | ||||
\(362\) | −29.3977 | −1.54511 | ||||||||
\(363\) | −4.44284 | + | 18.2330i | −0.233188 | + | 0.956983i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.60963 | − | 6.25206i | 0.188937 | − | 0.327248i | ||||
\(366\) | 24.7345 | + | 23.6322i | 1.29289 | + | 1.23528i | ||||
\(367\) | −5.48711 | + | 9.50396i | −0.286425 | + | 0.496103i | −0.972954 | − | 0.231000i | \(-0.925800\pi\) |
0.686529 | + | 0.727103i | \(0.259134\pi\) | |||||||
\(368\) | −10.0562 | − | 17.4179i | −0.524217 | − | 0.907970i | ||||
\(369\) | 20.0151 | + | 10.3699i | 1.04195 | + | 0.539836i | ||||
\(370\) | 20.9485 | 1.08906 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −35.6775 | − | 34.0875i | −1.84979 | − | 1.76736i | ||||
\(373\) | 0.271884 | + | 0.470916i | 0.0140776 | + | 0.0243831i | 0.872978 | − | 0.487759i | \(-0.162185\pi\) |
−0.858901 | + | 0.512142i | \(0.828852\pi\) | |||||||
\(374\) | −4.85584 | −0.251090 | ||||||||
\(375\) | 15.4911 | + | 14.8008i | 0.799959 | + | 0.764309i | ||||
\(376\) | 31.9228 | 1.64629 | ||||||||
\(377\) | 3.72286 | 0.191737 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.6912 | −1.16557 | −0.582785 | − | 0.812626i | \(-0.698037\pi\) | ||||
−0.582785 | + | 0.812626i | \(0.698037\pi\) | |||||||
\(380\) | 29.2675 | 1.50139 | ||||||||
\(381\) | −19.4660 | − | 18.5985i | −0.997272 | − | 0.952827i | ||||
\(382\) | 22.4897 | 1.15067 | ||||||||
\(383\) | 17.8569 | + | 30.9291i | 0.912447 | + | 1.58041i | 0.810596 | + | 0.585606i | \(0.199143\pi\) |
0.101851 | + | 0.994800i | \(0.467523\pi\) | |||||||
\(384\) | −23.9298 | − | 22.8633i | −1.22116 | − | 1.16674i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 41.6883 | 2.12188 | ||||||||
\(387\) | −5.88151 | + | 3.76300i | −0.298974 | + | 0.191284i | ||||
\(388\) | −19.2316 | − | 33.3101i | −0.976336 | − | 1.69106i | ||||
\(389\) | −19.3296 | + | 33.4798i | −0.980048 | + | 1.69749i | −0.317892 | + | 0.948127i | \(0.602975\pi\) |
−0.662156 | + | 0.749366i | \(0.730359\pi\) | |||||||
\(390\) | 5.48711 | + | 5.24258i | 0.277851 | + | 0.265468i | ||||
\(391\) | 11.2842 | − | 19.5447i | 0.570664 | − | 0.988420i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.49115 | − | 14.3273i | 0.176105 | − | 0.722718i | ||||
\(394\) | −52.4513 | −2.64246 | ||||||||
\(395\) | −14.9291 | − | 25.8579i | −0.751163 | − | 1.30105i | ||||
\(396\) | −4.38891 | − | 2.27391i | −0.220551 | − | 0.114268i | ||||
\(397\) | −5.97391 | + | 10.3471i | −0.299822 | + | 0.519307i | −0.976095 | − | 0.217344i | \(-0.930261\pi\) |
0.676273 | + | 0.736651i | \(0.263594\pi\) | |||||||
\(398\) | 12.2709 | + | 21.2538i | 0.615085 | + | 1.06536i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.1352 | + | 31.4111i | −0.906761 | + | 1.57056i | ||||
\(401\) | −16.1783 | − | 28.0216i | −0.807906 | − | 1.39933i | −0.914312 | − | 0.405011i | \(-0.867268\pi\) |
0.106406 | − | 0.994323i | \(-0.466066\pi\) | |||||||
\(402\) | 11.0953 | + | 10.6009i | 0.553385 | + | 0.528723i | ||||
\(403\) | 1.71041 | − | 2.96251i | 0.0852015 | − | 0.147573i | ||||
\(404\) | 17.6591 | − | 30.5865i | 0.878573 | − | 1.52173i | ||||
\(405\) | 18.9882 | + | 26.8952i | 0.943530 | + | 1.33643i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.472958 | − | 0.819187i | −0.0234437 | − | 0.0406056i | ||||
\(408\) | −10.0634 | + | 41.2993i | −0.498213 | + | 2.04462i | ||||
\(409\) | −18.9750 | −0.938254 | −0.469127 | − | 0.883131i | \(-0.655431\pi\) | ||||
−0.469127 | + | 0.883131i | \(0.655431\pi\) | |||||||
\(410\) | −67.6313 | −3.34007 | ||||||||
\(411\) | −0.627122 | + | 0.183450i | −0.0309336 | + | 0.00904890i | ||||
\(412\) | 16.2713 | + | 28.1827i | 0.801630 | + | 1.38846i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 28.8982 | − | 18.4891i | 1.42027 | − | 0.908691i | ||||
\(415\) | 22.2630 | − | 38.5607i | 1.09285 | − | 1.89287i | ||||
\(416\) | −0.131312 | + | 0.227439i | −0.00643811 | + | 0.0111511i | ||||
\(417\) | −31.5875 | + | 9.24018i | −1.54685 | + | 0.452494i | ||||
\(418\) | −0.986757 | − | 1.70911i | −0.0482639 | − | 0.0835955i | ||||
\(419\) | −8.64523 | + | 14.9740i | −0.422347 | + | 0.731526i | −0.996169 | − | 0.0874539i | \(-0.972127\pi\) |
0.573822 | + | 0.818980i | \(0.305460\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.30039 | − | 16.1087i | −0.453273 | − | 0.785092i | 0.545314 | − | 0.838232i | \(-0.316410\pi\) |
−0.998587 | + | 0.0531397i | \(0.983077\pi\) | |||||||
\(422\) | −6.01819 | + | 10.4238i | −0.292961 | + | 0.507423i | ||||
\(423\) | 0.863259 | + | 18.9290i | 0.0419731 | + | 0.920360i | ||||
\(424\) | 9.01819 | + | 15.6200i | 0.437962 | + | 0.758572i | ||||
\(425\) | −40.6993 | −1.97421 | ||||||||
\(426\) | 26.0699 | + | 24.9081i | 1.26309 | + | 1.20680i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −26.0313 | + | 45.0876i | −1.25827 | + | 2.17939i | ||||
\(429\) | 0.0811263 | − | 0.332935i | 0.00391682 | − | 0.0160742i | ||||
\(430\) | 10.4743 | − | 18.1420i | 0.505114 | − | 0.874883i | ||||
\(431\) | 7.93920 | + | 13.7511i | 0.382418 | + | 0.662367i | 0.991407 | − | 0.130811i | \(-0.0417582\pi\) |
−0.608990 | + | 0.793178i | \(0.708425\pi\) | |||||||
\(432\) | −14.7768 | + | 16.9489i | −0.710948 | + | 0.815456i | ||||
\(433\) | −40.4367 | −1.94326 | −0.971631 | − | 0.236501i | \(-0.923999\pi\) | ||||
−0.971631 | + | 0.236501i | \(0.923999\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −46.5064 | + | 13.6043i | −2.22981 | + | 0.652278i | ||||
\(436\) | −5.27188 | − | 9.13117i | −0.252477 | − | 0.437304i | ||||
\(437\) | 9.17223 | 0.438767 | ||||||||
\(438\) | −1.99115 | + | 8.17147i | −0.0951406 | + | 0.390448i | ||||
\(439\) | −12.4609 | −0.594728 | −0.297364 | − | 0.954764i | \(-0.596108\pi\) | ||||
−0.297364 | + | 0.954764i | \(0.596108\pi\) | |||||||
\(440\) | 7.51399 | 0.358216 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.81616 | −0.276646 | ||||||||
\(443\) | −8.23073 | −0.391054 | −0.195527 | − | 0.980698i | \(-0.562642\pi\) | ||||
−0.195527 | + | 0.980698i | \(0.562642\pi\) | |||||||
\(444\) | −15.6856 | + | 4.58845i | −0.744405 | + | 0.217758i | ||||
\(445\) | −54.2498 | −2.57169 | ||||||||
\(446\) | −28.7988 | − | 49.8810i | −1.36366 | − | 2.36193i | ||||
\(447\) | −3.97822 | + | 16.3262i | −0.188163 | + | 0.772204i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.64474 | 0.266392 | 0.133196 | − | 0.991090i | \(-0.457476\pi\) | ||||
0.133196 | + | 0.991090i | \(0.457476\pi\) | |||||||
\(450\) | −54.9332 | − | 28.4611i | −2.58957 | − | 1.34167i | ||||
\(451\) | 1.52692 | + | 2.64471i | 0.0718999 | + | 0.124534i | ||||
\(452\) | 28.2776 | − | 48.9783i | 1.33007 | − | 2.30374i | ||||
\(453\) | 21.3364 | − | 6.24146i | 1.00247 | − | 0.293249i | ||||
\(454\) | −7.52716 | + | 13.0374i | −0.353267 | + | 0.611876i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −16.5811 | + | 4.85041i | −0.776482 | + | 0.227141i | ||||
\(457\) | 5.06887 | 0.237112 | 0.118556 | − | 0.992947i | \(-0.462174\pi\) | ||||
0.118556 | + | 0.992947i | \(0.462174\pi\) | |||||||
\(458\) | 1.79665 | + | 3.11188i | 0.0839518 | + | 0.145409i | ||||
\(459\) | −24.7611 | − | 4.85041i | −1.15575 | − | 0.226398i | ||||
\(460\) | −34.4628 | + | 59.6913i | −1.60683 | + | 2.78312i | ||||
\(461\) | −3.88831 | − | 6.73475i | −0.181097 | − | 0.313669i | 0.761158 | − | 0.648567i | \(-0.224631\pi\) |
−0.942254 | + | 0.334898i | \(0.891298\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.58998 | − | 7.95008i | 0.213314 | − | 0.369472i | −0.739435 | − | 0.673228i | \(-0.764907\pi\) |
0.952750 | + | 0.303756i | \(0.0982408\pi\) | |||||||
\(464\) | −16.5474 | − | 28.6609i | −0.768192 | − | 1.33055i | ||||
\(465\) | −10.5408 | + | 43.2584i | −0.488818 | + | 2.00606i | ||||
\(466\) | 16.2989 | − | 28.2306i | 0.755033 | − | 1.30776i | ||||
\(467\) | −6.88272 | + | 11.9212i | −0.318494 | + | 0.551648i | −0.980174 | − | 0.198138i | \(-0.936511\pi\) |
0.661680 | + | 0.749787i | \(0.269844\pi\) | |||||||
\(468\) | −5.25688 | − | 2.72361i | −0.242999 | − | 0.125899i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −28.4253 | − | 49.2340i | −1.31116 | − | 2.27100i | ||||
\(471\) | −26.2345 | − | 25.0654i | −1.20882 | − | 1.15495i | ||||
\(472\) | −30.9228 | −1.42334 | ||||||||
\(473\) | −0.945916 | −0.0434933 | ||||||||
\(474\) | 25.1509 | + | 24.0301i | 1.15522 | + | 1.10374i | ||||
\(475\) | −8.27052 | − | 14.3250i | −0.379477 | − | 0.657274i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.01819 | + | 5.76985i | −0.412914 | + | 0.264183i | ||||
\(478\) | −23.8530 | + | 41.3146i | −1.09101 | + | 1.88969i | ||||
\(479\) | 4.35588 | − | 7.54461i | 0.199025 | − | 0.344722i | −0.749187 | − | 0.662358i | \(-0.769556\pi\) |
0.948213 | + | 0.317636i | \(0.102889\pi\) | |||||||
\(480\) | 0.809243 | − | 3.32105i | 0.0369367 | − | 0.151585i | ||||
\(481\) | −0.566492 | − | 0.981194i | −0.0258298 | − | 0.0447386i | ||||
\(482\) | −6.21731 | + | 10.7687i | −0.283191 | + | 0.490501i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.9626 | + | 38.0404i | 0.998302 | + | 1.72911i | ||||
\(485\) | −17.3530 | + | 30.0563i | −0.787960 | + | 1.36479i | ||||
\(486\) | −30.0289 | − | 23.8622i | −1.36214 | − | 1.08241i | ||||
\(487\) | 9.01819 | + | 15.6200i | 0.408653 | + | 0.707808i | 0.994739 | − | 0.102441i | \(-0.0326653\pi\) |
−0.586086 | + | 0.810249i | \(0.699332\pi\) | |||||||
\(488\) | 40.5697 | 1.83651 | ||||||||
\(489\) | 18.5560 | − | 5.42810i | 0.839129 | − | 0.245467i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.02344 | + | 1.77266i | −0.0461874 | + | 0.0799989i | −0.888195 | − | 0.459467i | \(-0.848040\pi\) |
0.842007 | + | 0.539466i | \(0.181374\pi\) | |||||||
\(492\) | 50.6402 | − | 14.8136i | 2.28303 | − | 0.667848i | ||||
\(493\) | 18.5679 | − | 32.1606i | 0.836257 | − | 1.44844i | ||||
\(494\) | −1.18190 | − | 2.04712i | −0.0531763 | − | 0.0921041i | ||||
\(495\) | 0.203194 | + | 4.45552i | 0.00913290 | + | 0.200261i | ||||
\(496\) | −30.4097 | −1.36544 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −12.2807 | + | 50.3990i | −0.550313 | + | 2.25843i | ||||
\(499\) | 19.5438 | + | 33.8508i | 0.874899 | + | 1.51537i | 0.856870 | + | 0.515532i | \(0.172406\pi\) |
0.0180291 | + | 0.999837i | \(0.494261\pi\) | |||||||
\(500\) | 50.1484 | 2.24270 | ||||||||
\(501\) | 5.75223 | − | 1.68268i | 0.256991 | − | 0.0751766i | ||||
\(502\) | 37.1358 | 1.65745 | ||||||||
\(503\) | −5.11846 | −0.228221 | −0.114111 | − | 0.993468i | \(-0.536402\pi\) | ||||
−0.114111 | + | 0.993468i | \(0.536402\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.8683 | −1.41812 | ||||||||
\(506\) | 4.64766 | 0.206614 | ||||||||
\(507\) | −5.23350 | + | 21.4778i | −0.232428 | + | 0.953862i | ||||
\(508\) | −63.0157 | −2.79587 | ||||||||
\(509\) | −14.7636 | − | 25.5713i | −0.654386 | − | 1.13343i | −0.982047 | − | 0.188634i | \(-0.939594\pi\) |
0.327662 | − | 0.944795i | \(-0.393739\pi\) | |||||||
\(510\) | 72.6562 | − | 21.2538i | 3.21727 | − | 0.941136i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −41.4078 | −1.82998 | ||||||||
\(513\) | −3.32451 | − | 9.70083i | −0.146780 | − | 0.428302i | ||||
\(514\) | −9.48751 | − | 16.4328i | −0.418476 | − | 0.724822i | ||||
\(515\) | 14.6819 | − | 25.4298i | 0.646962 | − | 1.12057i | ||||
\(516\) | −3.86908 | + | 15.8783i | −0.170327 | + | 0.699005i | ||||
\(517\) | −1.28352 | + | 2.22313i | −0.0564493 | + | 0.0977730i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.58113 | + | 7.24327i | 0.332775 | + | 0.317944i | ||||
\(520\) | 9.00000 | 0.394676 | ||||||||
\(521\) | 0.532351 | + | 0.922058i | 0.0233227 | + | 0.0403961i | 0.877451 | − | 0.479666i | \(-0.159242\pi\) |
−0.854128 | + | 0.520062i | \(0.825909\pi\) | |||||||
\(522\) | 47.5516 | − | 30.4236i | 2.08128 | − | 1.33160i | ||||
\(523\) | 6.69094 | − | 11.5890i | 0.292574 | − | 0.506754i | −0.681843 | − | 0.731498i | \(-0.738821\pi\) |
0.974418 | + | 0.224745i | \(0.0721548\pi\) | |||||||
\(524\) | −17.2581 | − | 29.8918i | −0.753922 | − | 1.30583i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.18190 | + | 8.97532i | −0.225942 | + | 0.391343i | ||||
\(527\) | −17.0615 | − | 29.5513i | −0.743210 | − | 1.28728i | ||||
\(528\) | −2.92373 | + | 0.855268i | −0.127239 | + | 0.0372208i | ||||
\(529\) | 0.699612 | − | 1.21176i | 0.0304179 | − | 0.0526853i | ||||
\(530\) | 16.0603 | − | 27.8173i | 0.697615 | − | 1.20830i | ||||
\(531\) | −0.836219 | − | 18.3361i | −0.0362888 | − | 0.795719i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.82889 | + | 3.16774i | 0.0792181 | + | 0.137210i | ||||
\(534\) | 60.6598 | − | 17.7446i | 2.62501 | − | 0.767883i | ||||
\(535\) | 46.9771 | 2.03100 | ||||||||
\(536\) | 18.1986 | 0.786061 | ||||||||
\(537\) | 3.74503 | − | 15.3693i | 0.161610 | − | 0.663232i | ||||
\(538\) | −25.5286 | − | 44.2168i | −1.10062 | − | 1.90632i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 75.6224 | + | 14.8136i | 3.25427 | + | 0.637475i | ||||
\(541\) | 17.0438 | − | 29.5207i | 0.732769 | − | 1.26919i | −0.222927 | − | 0.974835i | \(-0.571561\pi\) |
0.955695 | − | 0.294358i | \(-0.0951056\pi\) | |||||||
\(542\) | 35.0485 | − | 60.7058i | 1.50546 | − | 2.60754i | ||||
\(543\) | −14.9626 | − | 14.2958i | −0.642108 | − | 0.613492i | ||||
\(544\) | 1.30985 | + | 2.26873i | 0.0561594 | + | 0.0972709i | ||||
\(545\) | −4.75692 | + | 8.23922i | −0.203764 | + | 0.352930i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.97150 | + | 5.14678i | 0.127052 | + | 0.220060i | 0.922533 | − | 0.385918i | \(-0.126115\pi\) |
−0.795481 | + | 0.605978i | \(0.792782\pi\) | |||||||
\(548\) | −0.764686 | + | 1.32448i | −0.0326658 | + | 0.0565788i | ||||
\(549\) | 1.09709 | + | 24.0564i | 0.0468227 | + | 1.02670i | ||||
\(550\) | −4.19076 | − | 7.25860i | −0.178694 | − | 0.309508i | ||||
\(551\) | 15.0928 | 0.642974 | ||||||||
\(552\) | 9.63198 | − | 39.5287i | 0.409964 | − | 1.68245i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −21.1139 | + | 36.5704i | −0.897044 | + | 1.55373i | ||||
\(555\) | 10.6623 | + | 10.1871i | 0.452587 | + | 0.432418i | ||||
\(556\) | −38.5165 | + | 66.7126i | −1.63346 | + | 2.82924i | ||||
\(557\) | 15.0402 | + | 26.0503i | 0.637272 | + | 1.10379i | 0.986029 | + | 0.166575i | \(0.0532707\pi\) |
−0.348756 | + | 0.937213i | \(0.613396\pi\) | |||||||
\(558\) | −2.36314 | − | 51.8175i | −0.100040 | − | 2.19361i | ||||
\(559\) | −1.13298 | −0.0479202 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.47150 | − | 2.36135i | −0.104347 | − | 0.0996963i | ||||
\(562\) | −11.6170 | − | 20.1213i | −0.490035 | − | 0.848765i | ||||
\(563\) | −19.6212 | −0.826935 | −0.413468 | − | 0.910519i | \(-0.635683\pi\) | ||||
−0.413468 | + | 0.910519i | \(0.635683\pi\) | |||||||
\(564\) | 32.0679 | + | 30.6388i | 1.35030 | + | 1.29012i | ||||
\(565\) | −51.0308 | −2.14688 | ||||||||
\(566\) | 41.5049 | 1.74458 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 42.7601 | 1.79417 | ||||||||
\(569\) | −1.37432 | −0.0576144 | −0.0288072 | − | 0.999585i | \(-0.509171\pi\) | ||||
−0.0288072 | + | 0.999585i | \(0.509171\pi\) | |||||||
\(570\) | 22.2452 | + | 21.2538i | 0.931750 | + | 0.890226i | ||||
\(571\) | 17.3815 | 0.727394 | 0.363697 | − | 0.931517i | \(-0.381514\pi\) | ||||
0.363697 | + | 0.931517i | \(0.381514\pi\) | |||||||
\(572\) | −0.401038 | − | 0.694619i | −0.0167683 | − | 0.0290435i | ||||
\(573\) | 11.4467 | + | 10.9365i | 0.478191 | + | 0.456880i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 38.9545 | 1.62451 | ||||||||
\(576\) | −1.00146 | − | 21.9595i | −0.0417276 | − | 0.914978i | ||||
\(577\) | 13.5274 | + | 23.4301i | 0.563153 | + | 0.975409i | 0.997219 | + | 0.0745283i | \(0.0237451\pi\) |
−0.434066 | + | 0.900881i | \(0.642922\pi\) | |||||||
\(578\) | −8.09406 | + | 14.0193i | −0.336668 | + | 0.583127i | ||||
\(579\) | 21.2183 | + | 20.2727i | 0.881801 | + | 0.842503i | ||||
\(580\) | −56.7080 | + | 98.2211i | −2.35467 | + | 4.07841i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 9.57227 | − | 39.2837i | 0.396783 | − | 1.62836i | ||||
\(583\) | −1.45038 | −0.0600687 | ||||||||
\(584\) | 4.98715 | + | 8.63800i | 0.206370 | + | 0.357443i | ||||
\(585\) | 0.243379 | + | 5.33667i | 0.0100625 | + | 0.220644i | ||||
\(586\) | 4.58005 | − | 7.93288i | 0.189200 | − | 0.327704i | ||||
\(587\) | −3.75700 | − | 6.50731i | −0.155068 | − | 0.268585i | 0.778016 | − | 0.628245i | \(-0.216226\pi\) |
−0.933084 | + | 0.359659i | \(0.882893\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.93414 | − | 12.0103i | 0.285716 | − | 0.494875i | ||||
\(590\) | 27.5349 | + | 47.6919i | 1.13359 | + | 1.96344i | ||||
\(591\) | −26.6964 | − | 25.5066i | −1.09814 | − | 1.04920i | ||||
\(592\) | −5.03590 | + | 8.72243i | −0.206974 | + | 0.358490i | ||||
\(593\) | −17.7904 | + | 30.8139i | −0.730565 | + | 1.26538i | 0.226077 | + | 0.974109i | \(0.427410\pi\) |
−0.956642 | + | 0.291266i | \(0.905924\pi\) | |||||||
\(594\) | −1.68456 | − | 4.91551i | −0.0691184 | − | 0.201686i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.6659 | + | 34.0623i | 0.805545 | + | 1.39524i | ||||
\(597\) | −4.08998 | + | 16.7849i | −0.167392 | + | 0.686960i | ||||
\(598\) | 5.56681 | 0.227644 | ||||||||
\(599\) | −11.4821 | −0.469146 | −0.234573 | − | 0.972099i | \(-0.575369\pi\) | ||||
−0.234573 | + | 0.972099i | \(0.575369\pi\) | |||||||
\(600\) | −70.4201 | + | 20.5997i | −2.87489 | + | 0.840980i | ||||
\(601\) | 0.190030 | + | 0.329142i | 0.00775150 | + | 0.0134260i | 0.869875 | − | 0.493272i | \(-0.164199\pi\) |
−0.862124 | + | 0.506698i | \(0.830866\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.492129 | + | 10.7911i | 0.0200411 | + | 0.439448i | ||||
\(604\) | 26.0167 | − | 45.0623i | 1.05861 | − | 1.83356i | ||||
\(605\) | 19.8173 | − | 34.3246i | 0.805688 | − | 1.39549i | ||||
\(606\) | 35.6337 | − | 10.4238i | 1.44752 | − | 0.423438i | ||||
\(607\) | 9.27044 | + | 16.0569i | 0.376275 | + | 0.651728i | 0.990517 | − | 0.137390i | \(-0.0438713\pi\) |
−0.614242 | + | 0.789118i | \(0.710538\pi\) | |||||||
\(608\) | −0.532351 | + | 0.922058i | −0.0215897 | + | 0.0373944i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −36.1249 | − | 62.5702i | −1.46265 | − | 2.53339i | ||||
\(611\) | −1.53736 | + | 2.66278i | −0.0621949 | + | 0.107725i | ||||
\(612\) | −49.7473 | + | 31.8284i | −2.01092 | + | 1.28659i | ||||
\(613\) | −3.66225 | − | 6.34321i | −0.147917 | − | 0.256200i | 0.782540 | − | 0.622600i | \(-0.213924\pi\) |
−0.930457 | + | 0.366400i | \(0.880590\pi\) | |||||||
\(614\) | 75.2154 | 3.03545 | ||||||||
\(615\) | −34.4226 | − | 32.8885i | −1.38805 | − | 1.32619i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.7427 | − | 22.0710i | 0.513002 | − | 0.888546i | −0.486884 | − | 0.873466i | \(-0.661867\pi\) |
0.999886 | − | 0.0150791i | \(-0.00480000\pi\) | |||||||
\(618\) | −8.09884 | + | 33.2368i | −0.325783 | + | 1.33698i | ||||
\(619\) | −16.4482 | + | 28.4891i | −0.661108 | + | 1.14507i | 0.319217 | + | 0.947682i | \(0.396580\pi\) |
−0.980325 | + | 0.197391i | \(0.936753\pi\) | |||||||
\(620\) | 52.1072 | + | 90.2523i | 2.09267 | + | 3.62462i | ||||
\(621\) | 23.6995 | + | 4.64247i | 0.951030 | + | 0.186296i | ||||
\(622\) | −25.6748 | −1.02947 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.50194 | + | 1.02441i | −0.140190 | + | 0.0410092i | ||||
\(625\) | −1.67111 | − | 2.89444i | −0.0668443 | − | 0.115778i | ||||
\(626\) | −1.52517 | −0.0609580 | ||||||||
\(627\) | 0.328893 | − | 1.34974i | 0.0131347 | − | 0.0539036i | ||||
\(628\) | −84.9271 | −3.38896 | ||||||||
\(629\) | −11.3016 | −0.450626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.8683 | 1.18904 | 0.594519 | − | 0.804082i | \(-0.297343\pi\) | ||||
0.594519 | + | 0.804082i | \(0.297343\pi\) | |||||||
\(632\) | 41.2527 | 1.64094 | ||||||||
\(633\) | −8.13210 | + | 2.37885i | −0.323222 | + | 0.0945509i | ||||
\(634\) | 25.2163 | 1.00147 | ||||||||
\(635\) | 28.4301 | + | 49.2424i | 1.12822 | + | 1.95413i | ||||
\(636\) | −5.93251 | + | 24.3464i | −0.235239 | + | 0.965399i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.64766 | 0.302774 | ||||||||
\(639\) | 1.15632 | + | 25.3552i | 0.0457434 | + | 1.00303i | ||||
\(640\) | 34.9496 | + | 60.5344i | 1.38150 | + | 2.39283i | ||||
\(641\) | −5.73025 | + | 9.92509i | −0.226331 | + | 0.392017i | −0.956718 | − | 0.291016i | \(-0.906007\pi\) |
0.730387 | + | 0.683034i | \(0.239340\pi\) | |||||||
\(642\) | −52.5278 | + | 15.3658i | −2.07311 | + | 0.606438i | ||||
\(643\) | 8.69078 | − | 15.0529i | 0.342731 | − | 0.593627i | −0.642208 | − | 0.766531i | \(-0.721981\pi\) |
0.984939 | + | 0.172903i | \(0.0553147\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.1534 | − | 4.14024i | 0.557290 | − | 0.163022i | ||||
\(646\) | −23.5792 | −0.927711 | ||||||||
\(647\) | −12.6720 | − | 21.9485i | −0.498186 | − | 0.862883i | 0.501812 | − | 0.864977i | \(-0.332667\pi\) |
−0.999998 | + | 0.00209358i | \(0.999334\pi\) | |||||||
\(648\) | −45.2979 | + | 4.14024i | −1.77947 | + | 0.162644i | ||||
\(649\) | 1.24332 | − | 2.15349i | 0.0488045 | − | 0.0845320i | ||||
\(650\) | −5.01954 | − | 8.69410i | −0.196883 | − | 0.341011i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 22.6264 | − | 39.1900i | 0.886116 | − | 1.53480i | ||||
\(653\) | −7.04163 | − | 12.1965i | −0.275560 | − | 0.477284i | 0.694716 | − | 0.719284i | \(-0.255530\pi\) |
−0.970276 | + | 0.242000i | \(0.922197\pi\) | |||||||
\(654\) | 2.62401 | − | 10.7687i | 0.102607 | − | 0.421089i | ||||
\(655\) | −15.5723 | + | 26.9720i | −0.608459 | + | 1.05388i | ||||
\(656\) | 16.2581 | − | 28.1599i | 0.634774 | − | 1.09946i | ||||
\(657\) | −4.98715 | + | 3.19079i | −0.194567 | + | 0.124484i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.0854 | − | 33.0569i | −0.743462 | − | 1.28771i | −0.950910 | − | 0.309467i | \(-0.899849\pi\) |
0.207449 | − | 0.978246i | \(-0.433484\pi\) | |||||||
\(660\) | 7.54815 | + | 7.21177i | 0.293812 | + | 0.280718i | ||||
\(661\) | −0.353732 | −0.0137586 | −0.00687930 | − | 0.999976i | \(-0.502190\pi\) | ||||
−0.00687930 | + | 0.999976i | \(0.502190\pi\) | |||||||
\(662\) | −50.1052 | −1.94740 | ||||||||
\(663\) | −2.96027 | − | 2.82834i | −0.114967 | − | 0.109844i | ||||
\(664\) | 30.7591 | + | 53.2764i | 1.19369 | + | 2.06752i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −15.2542 | − | 7.90324i | −0.591087 | − | 0.306244i | ||||
\(667\) | −17.7719 | + | 30.7818i | −0.688130 | + | 1.19188i | ||||
\(668\) | 7.01403 | − | 12.1487i | 0.271381 | − | 0.470046i | ||||
\(669\) | 9.59884 | − | 39.3927i | 0.371112 | − | 1.52301i | ||||
\(670\) | −16.2048 | − | 28.0675i | −0.626045 | − | 1.08434i | ||||
\(671\) | −1.63119 | + | 2.82531i | −0.0629715 | + | 0.109070i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.5555 | + | 18.2827i | 0.406886 | + | 0.704748i | 0.994539 | − | 0.104365i | \(-0.0332811\pi\) |
−0.587653 | + | 0.809113i | \(0.699948\pi\) | |||||||
\(674\) | 7.02704 | − | 12.1712i | 0.270672 | − | 0.468817i | ||||
\(675\) | −14.1192 | − | 41.1994i | −0.543447 | − | 1.58577i | ||||
\(676\) | 25.8712 | + | 44.8102i | 0.995046 | + | 1.72347i | ||||
\(677\) | 21.1464 | 0.812721 | 0.406361 | − | 0.913713i | \(-0.366798\pi\) | ||||
0.406361 | + | 0.913713i | \(0.366798\pi\) | |||||||
\(678\) | 57.0605 | − | 16.6917i | 2.19140 | − | 0.641041i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 44.8879 | − | 77.7482i | 1.72137 | − | 2.98151i | ||||
\(681\) | −10.1711 | + | 2.97532i | −0.389758 | + | 0.114014i | ||||
\(682\) | 3.51360 | − | 6.08573i | 0.134543 | − | 0.233035i | ||||
\(683\) | −17.3858 | − | 30.1131i | −0.665249 | − | 1.15224i | −0.979218 | − | 0.202811i | \(-0.934992\pi\) |
0.313969 | − | 0.949433i | \(-0.398341\pi\) | |||||||
\(684\) | −21.3118 | − | 11.0417i | −0.814878 | − | 0.422191i | ||||
\(685\) | 1.37998 | 0.0527264 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.598835 | + | 2.45756i | −0.0228470 | + | 0.0937618i | ||||
\(688\) | 5.03590 | + | 8.72243i | 0.191992 | + | 0.332539i | ||||
\(689\) | −1.73722 | −0.0661827 | ||||||||
\(690\) | −69.5413 | + | 20.3427i | −2.64739 | + | 0.774432i | ||||
\(691\) | 34.6492 | 1.31812 | 0.659059 | − | 0.752091i | \(-0.270955\pi\) | ||||
0.659059 | + | 0.752091i | \(0.270955\pi\) | |||||||
\(692\) | 24.5418 | 0.932940 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.8525 | 0.829511 | ||||||||
\(695\) | 69.5083 | 2.63660 | ||||||||
\(696\) | 15.8493 | − | 65.0440i | 0.600766 | − | 2.46548i | ||||
\(697\) | 36.4868 | 1.38203 | ||||||||
\(698\) | 25.8044 | + | 44.6945i | 0.976710 | + | 1.69171i | ||||
\(699\) | 22.0240 | − | 6.44260i | 0.833024 | − | 0.243681i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.6050 | −1.83579 | −0.917894 | − | 0.396826i | \(-0.870111\pi\) | ||||
−0.917894 | + | 0.396826i | \(0.870111\pi\) | |||||||
\(702\) | −2.01771 | − | 5.88763i | −0.0761535 | − | 0.222214i | ||||
\(703\) | −2.29661 | − | 3.97784i | −0.0866182 | − | 0.150027i | ||||
\(704\) | 1.48901 | − | 2.57904i | 0.0561192 | − | 0.0972012i | ||||
\(705\) | 9.47434 | − | 38.8818i | 0.356824 | − | 1.46437i | ||||
\(706\) | −18.1651 | + | 31.4629i | −0.683654 | + | 1.18412i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −31.0634 | − | 29.6791i | −1.16743 | − | 1.11541i | ||||
\(709\) | 4.10817 | 0.154286 | 0.0771428 | − | 0.997020i | \(-0.475420\pi\) | ||||
0.0771428 | + | 0.997020i | \(0.475420\pi\) | |||||||
\(710\) | −38.0753 | − | 65.9483i | −1.42894 | − | 2.47500i | ||||
\(711\) | 1.11556 | + | 24.4613i | 0.0418368 | + | 0.917372i | ||||
\(712\) | 37.4764 | − | 64.9110i | 1.40449 | − | 2.43264i | ||||
\(713\) | 16.3300 | + | 28.2844i | 0.611564 | + | 1.05926i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.361864 | + | 0.626767i | −0.0135330 | + | 0.0234398i | ||||
\(716\) | −18.5131 | − | 32.0657i | −0.691868 | − | 1.19835i | ||||
\(717\) | −32.2315 | + | 9.42856i | −1.20371 | + | 0.352116i | ||||
\(718\) | −8.87266 | + | 15.3679i | −0.331125 | + | 0.573525i | ||||
\(719\) | −24.1408 | + | 41.8131i | −0.900299 | + | 1.55936i | −0.0731939 | + | 0.997318i | \(0.523319\pi\) |
−0.827106 | + | 0.562047i | \(0.810014\pi\) | |||||||
\(720\) | 40.0032 | − | 25.5941i | 1.49083 | − | 0.953837i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.5833 | + | 32.1872i | 0.691597 | + | 1.19788i | ||||
\(723\) | −8.40116 | + | 2.45756i | −0.312443 | + | 0.0913977i | ||||
\(724\) | −48.4375 | −1.80016 | ||||||||
\(725\) | 64.0990 | 2.38058 | ||||||||
\(726\) | −10.9316 | + | 44.8623i | −0.405711 | + | 1.66500i | ||||
\(727\) | 20.5151 | + | 35.5332i | 0.760863 | + | 1.31785i | 0.942406 | + | 0.334470i | \(0.108557\pi\) |
−0.181543 | + | 0.983383i | \(0.558109\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.67996 | − | 26.7480i | −0.136295 | − | 0.990668i | ||||
\(730\) | 8.88151 | − | 15.3832i | 0.328720 | − | 0.569359i | ||||
\(731\) | −5.65082 | + | 9.78750i | −0.209003 | + | 0.362004i | ||||
\(732\) | 40.7542 | + | 38.9379i | 1.50632 | + | 1.43919i | ||||
\(733\) | −15.2714 | − | 26.4508i | −0.564062 | − | 0.976983i | −0.997136 | − | 0.0756253i | \(-0.975905\pi\) |
0.433075 | − | 0.901358i | \(-0.357429\pi\) | |||||||
\(734\) | −13.5011 | + | 23.3845i | −0.498334 | + | 0.863139i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.25370 | − | 2.17147i | −0.0462118 | − | 0.0800413i | ||||
\(737\) | −0.731715 | + | 1.26737i | −0.0269531 | + | 0.0466841i | ||||
\(738\) | 49.2474 | + | 25.5152i | 1.81282 | + | 0.939228i | ||||
\(739\) | −11.9100 | − | 20.6288i | −0.438117 | − | 0.758841i | 0.559427 | − | 0.828880i | \(-0.311021\pi\) |
−0.997544 | + | 0.0700384i | \(0.977688\pi\) | |||||||
\(740\) | 34.5161 | 1.26884 | ||||||||
\(741\) | 0.393936 | − | 1.61668i | 0.0144716 | − | 0.0593901i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.26089 | + | 9.11213i | −0.193003 | + | 0.334292i | −0.946244 | − | 0.323453i | \(-0.895156\pi\) |
0.753241 | + | 0.657745i | \(0.228490\pi\) | |||||||
\(744\) | −44.4779 | − | 42.4957i | −1.63064 | − | 1.55797i | ||||
\(745\) | 17.7449 | − | 30.7350i | 0.650121 | − | 1.12604i | ||||
\(746\) | 0.668971 | + | 1.15869i | 0.0244928 | + | 0.0424227i | ||||
\(747\) | −30.7591 | + | 19.6797i | −1.12542 | + | 0.720044i | ||||
\(748\) | −8.00079 | −0.292538 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 38.1160 | + | 36.4174i | 1.39180 | + | 1.32977i | ||||
\(751\) | 5.13521 | + | 8.89445i | 0.187386 | + | 0.324563i | 0.944378 | − | 0.328862i | \(-0.106665\pi\) |
−0.756992 | + | 0.653425i | \(0.773332\pi\) | |||||||
\(752\) | 27.3330 | 0.996734 | ||||||||
\(753\) | 18.9012 | + | 18.0588i | 0.688797 | + | 0.658100i | ||||
\(754\) | 9.16010 | 0.333591 | ||||||||
\(755\) | −46.9507 | −1.70871 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.03930 | 0.292193 | 0.146097 | − | 0.989270i | \(-0.453329\pi\) | ||||
0.146097 | + | 0.989270i | \(0.453329\pi\) | |||||||
\(758\) | −55.8319 | −2.02791 | ||||||||
\(759\) | 2.36554 | + | 2.26012i | 0.0858636 | + | 0.0820371i | ||||
\(760\) | 36.4868 | 1.32351 | ||||||||
\(761\) | −13.8302 | − | 23.9547i | −0.501345 | − | 0.868355i | −0.999999 | − | 0.00155404i | \(-0.999505\pi\) |
0.498654 | − | 0.866801i | \(-0.333828\pi\) | |||||||
\(762\) | −47.8961 | − | 45.7616i | −1.73509 | − | 1.65777i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 37.0554 | 1.34062 | ||||||||
\(765\) | 47.3157 | + | 24.5144i | 1.71070 | + | 0.886320i | ||||
\(766\) | 43.9371 | + | 76.1013i | 1.58751 | + | 2.74965i | ||||
\(767\) | 1.48920 | − | 2.57938i | 0.0537720 | − | 0.0931359i | ||||
\(768\) | −40.5266 | − | 38.7205i | −1.46238 | − | 1.39721i | ||||
\(769\) | 16.9613 | − | 29.3778i | 0.611640 | − | 1.05939i | −0.379324 | − | 0.925264i | \(-0.623843\pi\) |
0.990964 | − | 0.134128i | \(-0.0428233\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.16225 | − | 12.9776i | 0.113886 | − | 0.467376i | ||||
\(772\) | 68.6883 | 2.47215 | ||||||||
\(773\) | 14.2978 | + | 24.7645i | 0.514256 | + | 0.890717i | 0.999863 | + | 0.0165403i | \(0.00526518\pi\) |
−0.485607 | + | 0.874177i | \(0.661401\pi\) | |||||||
\(774\) | −14.4715 | + | 9.25888i | −0.520167 | + | 0.332804i | ||||
\(775\) | 29.4493 | − | 51.0077i | 1.05785 | − | 1.83225i | ||||
\(776\) | −23.9753 | − | 41.5265i | −0.860664 | − | 1.49071i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −47.5605 | + | 82.3772i | −1.70513 | + | 2.95337i | ||||
\(779\) | 7.41449 | + | 12.8423i | 0.265652 | + | 0.460122i | ||||
\(780\) | 9.04092 | + | 8.63800i | 0.323717 | + | 0.309290i | ||||
\(781\) | −1.71926 | + | 2.97785i | −0.0615200 | + | 0.106556i | ||||
\(782\) | 27.7647 | − | 48.0899i | 0.992864 | − | 1.71969i | ||||
\(783\) | 38.9973 | + | 7.63912i | 1.39365 | + | 0.273000i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 38.3157 | + | 66.3647i | 1.36754 | + | 2.36866i | ||||
\(786\) | 8.58998 | − | 35.2524i | 0.306394 | − | 1.25741i | ||||
\(787\) | 46.0035 | 1.63985 | 0.819923 | − | 0.572473i | \(-0.194016\pi\) | ||||
0.819923 | + | 0.572473i | \(0.194016\pi\) | |||||||
\(788\) | −86.4222 | −3.07866 | ||||||||
\(789\) | −7.00207 | + | 2.04829i | −0.249280 | + | 0.0729210i | ||||
\(790\) | −36.7330 | − | 63.6235i | −1.30690 | − | 2.26362i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.47150 | − | 2.83480i | −0.194421 | − | 0.100730i | ||||
\(793\) | −1.95379 | + | 3.38406i | −0.0693810 | + | 0.120171i | ||||
\(794\) | −14.6988 | + | 25.4591i | −0.521642 | + | 0.903511i | ||||
\(795\) | 21.7016 | − | 6.34827i | 0.769675 | − | 0.225150i | ||||
\(796\) | 20.2183 | + | 35.0192i | 0.716620 | + | 1.24122i | ||||
\(797\) | 18.4558 | − | 31.9664i | 0.653739 | − | 1.13231i | −0.328469 | − | 0.944515i | \(-0.606533\pi\) |
0.982208 | − | 0.187795i | \(-0.0601339\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.3353 | + | 26.5615i | 0.542524 | + | 0.939679i | ||||
\(800\) | −2.26089 | + | 3.91598i | −0.0799346 | + | 0.138451i | ||||
\(801\) | 39.5033 | + | 20.4668i | 1.39578 | + | 0.723158i | ||||
\(802\) | −39.8068 | − | 68.9474i | −1.40563 | − | 2.43462i | ||||
\(803\) | −0.802077 | −0.0283047 | ||||||||
\(804\) | 18.2814 | + | 17.4666i | 0.644734 | + | 0.616001i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.20847 | − | 7.28928i | 0.148237 | − | 0.256754i | ||||
\(807\) | 8.50885 | − | 34.9195i | 0.299526 | − | 1.22923i | ||||
\(808\) | 22.0150 | − | 38.1311i | 0.774484 | − | 1.34145i | ||||
\(809\) | −23.8444 | − | 41.2996i | −0.838323 | − | 1.45202i | −0.891296 | − | 0.453422i | \(-0.850203\pi\) |
0.0529735 | − | 0.998596i | \(-0.483130\pi\) | |||||||
\(810\) | 46.7205 | + | 66.1758i | 1.64159 | + | 2.32518i | ||||
\(811\) | −6.02728 | −0.211646 | −0.105823 | − | 0.994385i | \(-0.533748\pi\) | ||||
−0.105823 | + | 0.994385i | \(0.533748\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 47.3594 | − | 13.8539i | 1.66097 | − | 0.485877i | ||||
\(814\) | −1.16372 | − | 2.01561i | −0.0407882 | − | 0.0706472i | ||||
\(815\) | −40.8324 | −1.43030 | ||||||||
\(816\) | −8.61654 | + | 35.3615i | −0.301639 | + | 1.23790i | ||||
\(817\) | −4.59322 | −0.160696 | ||||||||
\(818\) | −46.6881 | −1.63241 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −111.434 | −3.89143 | ||||||||
\(821\) | −39.2642 | −1.37033 | −0.685165 | − | 0.728388i | \(-0.740270\pi\) | ||||
−0.685165 | + | 0.728388i | \(0.740270\pi\) | |||||||
\(822\) | −1.54304 | + | 0.451379i | −0.0538196 | + | 0.0157436i | ||||
\(823\) | 22.7630 | 0.793469 | 0.396735 | − | 0.917933i | \(-0.370143\pi\) | ||||
0.396735 | + | 0.917933i | \(0.370143\pi\) | |||||||
\(824\) | 20.2849 | + | 35.1344i | 0.706657 | + | 1.22397i | ||||
\(825\) | 1.39681 | − | 5.73237i | 0.0486306 | − | 0.199575i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.9286 | −1.00595 | −0.502973 | − | 0.864302i | \(-0.667760\pi\) | ||||
−0.502973 | + | 0.864302i | \(0.667760\pi\) | |||||||
\(828\) | 47.6146 | − | 30.4639i | 1.65472 | − | 1.05869i | ||||
\(829\) | −16.9883 | − | 29.4247i | −0.590029 | − | 1.02196i | −0.994228 | − | 0.107290i | \(-0.965783\pi\) |
0.404198 | − | 0.914671i | \(-0.367551\pi\) | |||||||
\(830\) | 54.7783 | − | 94.8788i | 1.90138 | − | 3.29329i | ||||
\(831\) | −28.5303 | + | 8.34585i | −0.989704 | + | 0.289514i | ||||
\(832\) | 1.78348 | − | 3.08908i | 0.0618312 | − | 0.107095i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −77.7213 | + | 22.7355i | −2.69127 | + | 0.787267i | ||||
\(835\) | −12.6578 | −0.438041 | ||||||||
\(836\) | −1.62584 | − | 2.81604i | −0.0562310 | − | 0.0973949i | ||||
\(837\) | 23.9956 | − | 27.5229i | 0.829410 | − | 0.951332i | ||||
\(838\) | −21.2716 | + | 36.8435i | −0.734816 | + | 1.27274i | ||||
\(839\) | 19.0206 | + | 32.9446i | 0.656663 | + | 1.13737i | 0.981474 | + | 0.191595i | \(0.0613659\pi\) |
−0.324811 | + | 0.945779i | \(0.605301\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.7434 | + | 25.5363i | −0.508392 | + | 0.880561i | ||||
\(842\) | −22.8837 | − | 39.6356i | −0.788623 | − | 1.36593i | ||||
\(843\) | 3.87203 | − | 15.8905i | 0.133360 | − | 0.547296i | ||||
\(844\) | −9.91595 | + | 17.1749i | −0.341321 | + | 0.591185i | ||||
\(845\) | 23.3441 | − | 40.4331i | 0.803060 | − | 1.39094i | ||||
\(846\) | 2.12405 | + | 46.5749i | 0.0730264 | + | 1.60128i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.72159 | + | 13.3742i | 0.265161 | + | 0.459272i | ||||
\(849\) | 21.1249 | + | 20.1834i | 0.725004 | + | 0.692694i | ||||
\(850\) | −100.141 | −3.43480 | ||||||||
\(851\) | 10.8171 | 0.370806 | ||||||||
\(852\) | 42.9545 | + | 41.0402i | 1.47160 | + | 1.40601i | ||||
\(853\) | 4.90746 | + | 8.49996i | 0.168028 | + | 0.291033i | 0.937726 | − | 0.347374i | \(-0.112927\pi\) |
−0.769698 | + | 0.638408i | \(0.779593\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.986679 | + | 21.6353i | 0.0337437 | + | 0.739912i | ||||
\(856\) | −32.4523 | + | 56.2091i | −1.10920 | + | 1.92119i | ||||
\(857\) | 13.3680 | − | 23.1541i | 0.456642 | − | 0.790928i | −0.542139 | − | 0.840289i | \(-0.682385\pi\) |
0.998781 | + | 0.0493613i | \(0.0157186\pi\) | |||||||
\(858\) | 0.199612 | − | 0.819187i | 0.00681463 | − | 0.0279666i | ||||
\(859\) | −9.24411 | − | 16.0113i | −0.315405 | − | 0.546297i | 0.664119 | − | 0.747627i | \(-0.268807\pi\) |
−0.979523 | + | 0.201330i | \(0.935474\pi\) | |||||||
\(860\) | 17.2581 | − | 29.8918i | 0.588495 | − | 1.01930i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.5344 | + | 33.8346i | 0.665345 | + | 1.15241i | ||||
\(863\) | 4.57393 | − | 7.92228i | 0.155698 | − | 0.269677i | −0.777615 | − | 0.628741i | \(-0.783571\pi\) |
0.933313 | + | 0.359064i | \(0.116904\pi\) | |||||||
\(864\) | −1.84220 | + | 2.11300i | −0.0626730 | + | 0.0718858i | ||||
\(865\) | −11.0723 | − | 19.1777i | −0.376469 | − | 0.652063i | ||||
\(866\) | −99.4946 | −3.38097 | ||||||||
\(867\) | −10.9371 | + | 3.19940i | −0.371444 | + | 0.108657i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.65865 | + | 2.87287i | −0.0562660 | + | 0.0974555i | ||||
\(870\) | −114.429 | + | 33.4736i | −3.87951 | + | 1.13486i | ||||
\(871\) | −0.876423 | + | 1.51801i | −0.0296964 | + | 0.0514358i | ||||
\(872\) | −6.57227 | − | 11.3835i | −0.222565 | − | 0.385494i | ||||
\(873\) | 23.9753 | − | 15.3395i | 0.811442 | − | 0.519162i | ||||
\(874\) | 22.5683 | 0.763385 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.28074 | + | 13.4638i | −0.110846 | + | 0.454901i | ||||
\(877\) | −11.3442 | − | 19.6487i | −0.383065 | − | 0.663488i | 0.608434 | − | 0.793605i | \(-0.291798\pi\) |
−0.991499 | + | 0.130117i | \(0.958465\pi\) | |||||||
\(878\) | −30.6602 | −1.03473 | ||||||||
\(879\) | 6.18882 | − | 1.81039i | 0.208744 | − | 0.0610630i | ||||
\(880\) | 6.43367 | 0.216879 | ||||||||
\(881\) | −15.3696 | −0.517815 | −0.258907 | − | 0.965902i | \(-0.583362\pi\) | ||||
−0.258907 | + | 0.965902i | \(0.583362\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.6372 | 0.997370 | 0.498685 | − | 0.866783i | \(-0.333817\pi\) | ||||
0.498685 | + | 0.866783i | \(0.333817\pi\) | |||||||
\(884\) | −9.58307 | −0.322313 | ||||||||
\(885\) | −9.17758 | + | 37.6639i | −0.308501 | + | 1.26606i | ||||
\(886\) | −20.2518 | −0.680371 | ||||||||
\(887\) | −9.38252 | − | 16.2510i | −0.315034 | − | 0.545655i | 0.664410 | − | 0.747368i | \(-0.268683\pi\) |
−0.979445 | + | 0.201712i | \(0.935349\pi\) | |||||||
\(888\) | −19.5547 | + | 5.72026i | −0.656212 | + | 0.191959i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −133.482 | −4.47432 | ||||||||
\(891\) | 1.53297 | − | 3.32105i | 0.0513565 | − | 0.111259i | ||||
\(892\) | −47.4507 | − | 82.1870i | −1.58877 | − | 2.75183i | ||||
\(893\) | −6.23258 | + | 10.7952i | −0.208565 | + | 0.361246i | ||||
\(894\) | −9.78843 | + | 40.1707i | −0.327374 | + | 1.34351i | ||||
\(895\) | −16.7047 | + | 28.9335i | −0.558378 | + | 0.967139i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.83336 | + | 2.70709i | 0.0946031 | + | 0.0903871i | ||||
\(898\) | 13.8889 | 0.463479 | ||||||||
\(899\) | 26.8708 | + | 46.5416i | 0.896192 | + | 1.55225i | ||||
\(900\) | −90.5114 | − | 46.8943i | −3.01705 | − | 1.56314i | ||||
\(901\) | −8.66445 | + | 15.0073i | −0.288655 | + | 0.499965i | ||||
\(902\) | 3.75700 | + | 6.50731i | 0.125094 | + | 0.216670i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 35.2527 | − | 61.0595i | 1.17249 | − | 2.03081i | ||||
\(905\) | 21.8530 | + | 37.8505i | 0.726419 | + | 1.25819i | ||||
\(906\) | 52.4983 | − | 15.3571i | 1.74414 | − | 0.510207i | ||||
\(907\) | 15.5541 | − | 26.9405i | 0.516465 | − | 0.894543i | −0.483352 | − | 0.875426i | \(-0.660581\pi\) |
0.999817 | − | 0.0191175i | \(-0.00608567\pi\) | |||||||
\(908\) | −12.4022 | + | 21.4813i | −0.411582 | + | 0.712881i | ||||
\(909\) | 23.2056 | + | 12.0229i | 0.769683 | + | 0.398775i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.73764 | − | 15.1340i | −0.289491 | − | 0.501413i | 0.684197 | − | 0.729297i | \(-0.260153\pi\) |
−0.973688 | + | 0.227884i | \(0.926819\pi\) | |||||||
\(912\) | −14.1972 | + | 4.15304i | −0.470115 | + | 0.137521i | ||||
\(913\) | −4.94695 | −0.163720 | ||||||||
\(914\) | 12.4720 | 0.412536 | ||||||||
\(915\) | 12.0407 | − | 49.4138i | 0.398053 | − | 1.63357i | ||||
\(916\) | 2.96027 | + | 5.12734i | 0.0978101 | + | 0.169412i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −60.9248 | − | 11.9345i | −2.01082 | − | 0.393896i | ||||
\(919\) | −21.0993 | + | 36.5451i | −0.696002 | + | 1.20551i | 0.273840 | + | 0.961775i | \(0.411706\pi\) |
−0.969842 | + | 0.243736i | \(0.921627\pi\) | |||||||
\(920\) | −42.9635 | + | 74.4150i | −1.41647 | + | 2.45339i | ||||
\(921\) | 38.2827 | + | 36.5766i | 1.26146 | + | 1.20524i | ||||
\(922\) | −9.56720 | − | 16.5709i | −0.315079 | − | 0.545733i | ||||
\(923\) | −2.05927 | + | 3.56676i | −0.0677818 | + | 0.117401i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.75370 | − | 16.8939i | −0.320700 | − | 0.555468i | ||||
\(926\) | 11.2937 | − | 19.5612i | 0.371133 | − | 0.642821i | ||||
\(927\) | −20.2849 | + | 12.9783i | −0.666242 | + | 0.426263i | ||||
\(928\) | −2.06294 | − | 3.57311i | −0.0677193 | − | 0.117293i | ||||
\(929\) | −48.4111 | −1.58832 | −0.794159 | − | 0.607710i | \(-0.792088\pi\) | ||||
−0.794159 | + | 0.607710i | \(0.792088\pi\) | |||||||
\(930\) | −25.9357 | + | 106.438i | −0.850465 | + | 3.49022i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 26.8551 | − | 46.5145i | 0.879670 | − | 1.52363i | ||||
\(933\) | −13.0678 | − | 12.4854i | −0.427821 | − | 0.408755i | ||||
\(934\) | −16.9350 | + | 29.3322i | −0.554129 | + | 0.959780i | ||||
\(935\) | 3.60963 | + | 6.25206i | 0.118048 | + | 0.204464i | ||||
\(936\) | −6.55357 | − | 3.39543i | −0.214210 | − | 0.110983i | ||||
\(937\) | 22.6750 | 0.740762 | 0.370381 | − | 0.928880i | \(-0.379227\pi\) | ||||
0.370381 | + | 0.928880i | \(0.379227\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.776271 | − | 0.741676i | −0.0253327 | − | 0.0242037i | ||||
\(940\) | −46.8353 | − | 81.1211i | −1.52760 | − | 2.64588i | ||||
\(941\) | 49.9505 | 1.62834 | 0.814170 | − | 0.580627i | \(-0.197192\pi\) | ||||
0.814170 | + | 0.580627i | \(0.197192\pi\) | |||||||
\(942\) | −64.5502 | − | 61.6735i | −2.10316 | − | 2.00943i | ||||
\(943\) | −34.9225 | −1.13723 | ||||||||
\(944\) | −26.4769 | −0.861749 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.32743 | −0.0756713 | ||||||||
\(947\) | 17.7123 | 0.575571 | 0.287786 | − | 0.957695i | \(-0.407081\pi\) | ||||
0.287786 | + | 0.957695i | \(0.407081\pi\) | |||||||
\(948\) | 41.4403 | + | 39.5934i | 1.34592 | + | 1.28594i | ||||
\(949\) | −0.960699 | −0.0311856 | ||||||||
\(950\) | −20.3496 | − | 35.2466i | −0.660230 | − | 1.14355i | ||||
\(951\) | 12.8345 | + | 12.2625i | 0.416186 | + | 0.397638i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.0229 | 1.23168 | 0.615842 | − | 0.787870i | \(-0.288816\pi\) | ||||
0.615842 | + | 0.787870i | \(0.288816\pi\) | |||||||
\(954\) | −22.1893 | + | 14.1967i | −0.718405 | + | 0.459636i | ||||
\(955\) | −16.7179 | − | 28.9563i | −0.540979 | − | 0.937002i | ||||
\(956\) | −39.3017 | + | 68.0726i | −1.27111 | + | 2.20163i | ||||
\(957\) | 3.89246 | + | 3.71899i | 0.125825 | + | 0.120218i | ||||
\(958\) | 10.7177 | − | 18.5635i | 0.346272 | − | 0.599761i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −10.9911 | + | 45.1066i | −0.354738 | + | 1.45581i | ||||
\(961\) | 18.3815 | 0.592952 | ||||||||
\(962\) | −1.39386 | − | 2.41423i | −0.0449398 | − | 0.0778380i | ||||
\(963\) | −34.2075 | − | 17.7230i | −1.10232 | − | 0.571116i | ||||
\(964\) | −10.2440 | + | 17.7432i | −0.329938 | + | 0.571469i | ||||
\(965\) | −30.9894 | − | 53.6752i | −0.997583 | − | 1.72786i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.5064 | − | 26.8579i | 0.498652 | − | 0.863691i | −0.501346 | − | 0.865247i | \(-0.667162\pi\) |
0.999999 | + | 0.00155529i | \(0.000495066\pi\) | |||||||
\(968\) | 27.3801 | + | 47.4236i | 0.880028 | + | 1.52425i | ||||
\(969\) | −12.0012 | − | 11.4663i | −0.385534 | − | 0.368352i | ||||
\(970\) | −42.6972 | + | 73.9537i | −1.37092 | + | 2.37451i | ||||
\(971\) | −7.28376 | + | 12.6158i | −0.233747 | + | 0.404862i | −0.958908 | − | 0.283718i | \(-0.908432\pi\) |
0.725161 | + | 0.688580i | \(0.241765\pi\) | |||||||
\(972\) | −49.4776 | − | 39.3169i | −1.58699 | − | 1.26109i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 22.1893 | + | 38.4330i | 0.710991 | + | 1.23147i | ||||
\(975\) | 1.67305 | − | 6.86603i | 0.0535804 | − | 0.219889i | ||||
\(976\) | 34.7368 | 1.11190 | ||||||||
\(977\) | −47.8797 | −1.53181 | −0.765904 | − | 0.642955i | \(-0.777708\pi\) | ||||
−0.765904 | + | 0.642955i | \(0.777708\pi\) | |||||||
\(978\) | 45.6570 | − | 13.3559i | 1.45995 | − | 0.427074i | ||||
\(979\) | 3.01364 | + | 5.21978i | 0.0963163 | + | 0.166825i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.57227 | − | 4.20495i | 0.209836 | − | 0.134254i | ||||
\(982\) | −2.51819 | + | 4.36163i | −0.0803586 | + | 0.139185i | ||||
\(983\) | −22.2128 | + | 38.4737i | −0.708479 | + | 1.22712i | 0.256942 | + | 0.966427i | \(0.417285\pi\) |
−0.965421 | + | 0.260695i | \(0.916048\pi\) | |||||||
\(984\) | 63.1313 | − | 18.4676i | 2.01255 | − | 0.588724i | ||||
\(985\) | 38.9902 | + | 67.5329i | 1.24233 | + | 2.15178i | ||||
\(986\) | 45.6864 | − | 79.1313i | 1.45495 | − | 2.52005i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.94738 | − | 3.37296i | −0.0619544 | − | 0.107308i | ||||
\(989\) | 5.40856 | − | 9.36790i | 0.171982 | − | 0.297882i | ||||
\(990\) | 0.499960 | + | 10.9628i | 0.0158898 | + | 0.348422i | ||||
\(991\) | 20.8078 | + | 36.0401i | 0.660981 | + | 1.14485i | 0.980358 | + | 0.197225i | \(0.0631929\pi\) |
−0.319377 | + | 0.947628i | \(0.603474\pi\) | |||||||
\(992\) | −3.79114 | −0.120369 | ||||||||
\(993\) | −25.5023 | − | 24.3657i | −0.809290 | − | 0.773223i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.2434 | − | 31.5985i | 0.578354 | − | 1.00174i | ||||
\(996\) | −20.2345 | + | 83.0405i | −0.641155 | + | 2.63124i | ||||
\(997\) | 6.51407 | − | 11.2827i | 0.206303 | − | 0.357327i | −0.744244 | − | 0.667908i | \(-0.767190\pi\) |
0.950547 | + | 0.310581i | \(0.100523\pi\) | |||||||
\(998\) | 48.0875 | + | 83.2901i | 1.52218 | + | 2.63650i | ||||
\(999\) | −3.92070 | − | 11.4405i | −0.124045 | − | 0.361962i |
(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 | 441.2.h.g.373.6 | 12 | ||
3.2 | odd | 2 | 1323.2.h.g.226.2 | 12 | |||
7.2 | even | 3 | 441.2.f.g.148.1 | ✓ | 12 | ||
7.3 | odd | 6 | 441.2.g.g.67.1 | 12 | |||
7.4 | even | 3 | 441.2.g.g.67.2 | 12 | |||
7.5 | odd | 6 | 441.2.f.g.148.2 | yes | 12 | ||
7.6 | odd | 2 | inner | 441.2.h.g.373.5 | 12 | ||
9.2 | odd | 6 | 1323.2.g.g.667.5 | 12 | |||
9.7 | even | 3 | 441.2.g.g.79.2 | 12 | |||
21.2 | odd | 6 | 1323.2.f.g.442.6 | 12 | |||
21.5 | even | 6 | 1323.2.f.g.442.5 | 12 | |||
21.11 | odd | 6 | 1323.2.g.g.361.5 | 12 | |||
21.17 | even | 6 | 1323.2.g.g.361.6 | 12 | |||
21.20 | even | 2 | 1323.2.h.g.226.1 | 12 | |||
63.2 | odd | 6 | 1323.2.f.g.883.6 | 12 | |||
63.5 | even | 6 | 3969.2.a.bd.1.2 | 6 | |||
63.11 | odd | 6 | 1323.2.h.g.802.2 | 12 | |||
63.16 | even | 3 | 441.2.f.g.295.1 | yes | 12 | ||
63.20 | even | 6 | 1323.2.g.g.667.6 | 12 | |||
63.23 | odd | 6 | 3969.2.a.bd.1.1 | 6 | |||
63.25 | even | 3 | inner | 441.2.h.g.214.6 | 12 | ||
63.34 | odd | 6 | 441.2.g.g.79.1 | 12 | |||
63.38 | even | 6 | 1323.2.h.g.802.1 | 12 | |||
63.40 | odd | 6 | 3969.2.a.be.1.5 | 6 | |||
63.47 | even | 6 | 1323.2.f.g.883.5 | 12 | |||
63.52 | odd | 6 | inner | 441.2.h.g.214.5 | 12 | ||
63.58 | even | 3 | 3969.2.a.be.1.6 | 6 | |||
63.61 | odd | 6 | 441.2.f.g.295.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.g.148.1 | ✓ | 12 | 7.2 | even | 3 | ||
441.2.f.g.148.2 | yes | 12 | 7.5 | odd | 6 | ||
441.2.f.g.295.1 | yes | 12 | 63.16 | even | 3 | ||
441.2.f.g.295.2 | yes | 12 | 63.61 | odd | 6 | ||
441.2.g.g.67.1 | 12 | 7.3 | odd | 6 | |||
441.2.g.g.67.2 | 12 | 7.4 | even | 3 | |||
441.2.g.g.79.1 | 12 | 63.34 | odd | 6 | |||
441.2.g.g.79.2 | 12 | 9.7 | even | 3 | |||
441.2.h.g.214.5 | 12 | 63.52 | odd | 6 | inner | ||
441.2.h.g.214.6 | 12 | 63.25 | even | 3 | inner | ||
441.2.h.g.373.5 | 12 | 7.6 | odd | 2 | inner | ||
441.2.h.g.373.6 | 12 | 1.1 | even | 1 | trivial | ||
1323.2.f.g.442.5 | 12 | 21.5 | even | 6 | |||
1323.2.f.g.442.6 | 12 | 21.2 | odd | 6 | |||
1323.2.f.g.883.5 | 12 | 63.47 | even | 6 | |||
1323.2.f.g.883.6 | 12 | 63.2 | odd | 6 | |||
1323.2.g.g.361.5 | 12 | 21.11 | odd | 6 | |||
1323.2.g.g.361.6 | 12 | 21.17 | even | 6 | |||
1323.2.g.g.667.5 | 12 | 9.2 | odd | 6 | |||
1323.2.g.g.667.6 | 12 | 63.20 | even | 6 | |||
1323.2.h.g.226.1 | 12 | 21.20 | even | 2 | |||
1323.2.h.g.226.2 | 12 | 3.2 | odd | 2 | |||
1323.2.h.g.802.1 | 12 | 63.38 | even | 6 | |||
1323.2.h.g.802.2 | 12 | 63.11 | odd | 6 | |||
3969.2.a.bd.1.1 | 6 | 63.23 | odd | 6 | |||
3969.2.a.bd.1.2 | 6 | 63.5 | even | 6 | |||
3969.2.a.be.1.5 | 6 | 63.40 | odd | 6 | |||
3969.2.a.be.1.6 | 6 | 63.58 | even | 3 |