Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(218,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 15, 12]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.ct (of order \(20\), degree \(8\), 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(256\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{20})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 368.21 | ||
Character | \(\chi\) | \(=\) | 825.368 |
Dual form | 825.2.ct.c.482.21 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.520075 | − | 1.02071i | 0.367749 | − | 0.721748i | −0.630781 | − | 0.775961i | \(-0.717265\pi\) |
0.998529 | + | 0.0542137i | \(0.0172652\pi\) | |||||||
\(3\) | 0.989424 | − | 1.42163i | 0.571244 | − | 0.820780i | ||||
\(4\) | 0.404210 | + | 0.556347i | 0.202105 | + | 0.278174i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.936494 | − | 1.74927i | −0.382322 | − | 0.714135i | ||||
\(7\) | −0.785660 | + | 4.96046i | −0.296952 | + | 1.87488i | 0.162547 | + | 0.986701i | \(0.448029\pi\) |
−0.459499 | + | 0.888179i | \(0.651971\pi\) | |||||||
\(8\) | 3.04101 | − | 0.481648i | 1.07516 | − | 0.170288i | ||||
\(9\) | −1.04208 | − | 2.81319i | −0.347361 | − | 0.937732i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.47429 | + | 2.20860i | 0.746026 | + | 0.665917i | ||||
\(12\) | 1.19086 | − | 0.0241752i | 0.343771 | − | 0.00697879i | ||||
\(13\) | −0.692876 | + | 1.35985i | −0.192169 | + | 0.377153i | −0.966907 | − | 0.255129i | \(-0.917882\pi\) |
0.774738 | + | 0.632283i | \(0.217882\pi\) | |||||||
\(14\) | 4.65457 | + | 3.38174i | 1.24399 | + | 0.903809i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.664920 | − | 2.04641i | 0.166230 | − | 0.511603i | ||||
\(17\) | 0.979071 | − | 0.498862i | 0.237460 | − | 0.120992i | −0.331212 | − | 0.943556i | \(-0.607458\pi\) |
0.568672 | + | 0.822565i | \(0.307458\pi\) | |||||||
\(18\) | −3.41340 | − | 0.399414i | −0.804547 | − | 0.0941428i | ||||
\(19\) | 2.83907 | − | 3.90764i | 0.651327 | − | 0.896475i | −0.347829 | − | 0.937558i | \(-0.613081\pi\) |
0.999156 | + | 0.0410834i | \(0.0130809\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.27461 | + | 6.02492i | 1.36923 | + | 1.31475i | ||||
\(22\) | 3.54114 | − | 1.37688i | 0.754974 | − | 0.293552i | ||||
\(23\) | −2.45909 | + | 2.45909i | −0.512755 | + | 0.512755i | −0.915370 | − | 0.402614i | \(-0.868102\pi\) |
0.402614 | + | 0.915370i | \(0.368102\pi\) | |||||||
\(24\) | 2.32412 | − | 4.79975i | 0.474408 | − | 0.979745i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.02765 | + | 1.41444i | 0.201539 | + | 0.277395i | ||||
\(27\) | −5.03039 | − | 1.30198i | −0.968099 | − | 0.250567i | ||||
\(28\) | −3.07731 | + | 1.56797i | −0.581557 | + | 0.296318i | ||||
\(29\) | 6.36231 | − | 4.62249i | 1.18145 | − | 0.858374i | 0.189116 | − | 0.981955i | \(-0.439438\pi\) |
0.992335 | + | 0.123580i | \(0.0394377\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.04155 | + | 3.20556i | 0.187068 | + | 0.575736i | 0.999978 | − | 0.00665334i | \(-0.00211784\pi\) |
−0.812910 | + | 0.582390i | \(0.802118\pi\) | |||||||
\(32\) | 2.61126 | + | 2.61126i | 0.461611 | + | 0.461611i | ||||
\(33\) | 5.58793 | − | 1.33229i | 0.972734 | − | 0.231922i | ||||
\(34\) | − | 1.25879i | − | 0.215881i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.14389 | − | 1.71688i | 0.190649 | − | 0.286147i | ||||
\(37\) | 0.398241 | − | 2.51440i | 0.0654704 | − | 0.413364i | −0.933086 | − | 0.359653i | \(-0.882895\pi\) |
0.998557 | − | 0.0537110i | \(-0.0171050\pi\) | |||||||
\(38\) | −2.51202 | − | 4.93012i | −0.407504 | − | 0.799771i | ||||
\(39\) | 1.24765 | + | 2.33048i | 0.199785 | + | 0.373175i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.70838 | − | 2.35139i | 0.266805 | − | 0.367225i | −0.654503 | − | 0.756059i | \(-0.727122\pi\) |
0.921308 | + | 0.388834i | \(0.127122\pi\) | |||||||
\(42\) | 9.41294 | − | 3.27111i | 1.45245 | − | 0.504744i | ||||
\(43\) | −6.92718 | − | 6.92718i | −1.05638 | − | 1.05638i | −0.998312 | − | 0.0580719i | \(-0.981505\pi\) |
−0.0580719 | − | 0.998312i | \(-0.518495\pi\) | |||||||
\(44\) | −0.228615 | + | 2.26930i | −0.0344649 | + | 0.342110i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.23109 | + | 3.78891i | 0.181515 | + | 0.558645i | ||||
\(47\) | 0.860838 | + | 5.43512i | 0.125566 | + | 0.792794i | 0.967437 | + | 0.253114i | \(0.0814547\pi\) |
−0.841870 | + | 0.539680i | \(0.818545\pi\) | |||||||
\(48\) | −2.25136 | − | 2.97004i | −0.324956 | − | 0.428689i | ||||
\(49\) | −17.3315 | − | 5.63136i | −2.47594 | − | 0.804480i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.259518 | − | 1.88547i | 0.0363398 | − | 0.264018i | ||||
\(52\) | −1.03661 | + | 0.164183i | −0.143752 | + | 0.0227681i | ||||
\(53\) | 2.37596 | + | 1.21061i | 0.326364 | + | 0.166291i | 0.609494 | − | 0.792791i | \(-0.291373\pi\) |
−0.283130 | + | 0.959082i | \(0.591373\pi\) | |||||||
\(54\) | −3.94512 | + | 4.45742i | −0.536863 | + | 0.606578i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 15.4632i | 2.06636i | ||||||||
\(57\) | −2.74619 | − | 7.90243i | −0.363742 | − | 1.04670i | ||||
\(58\) | −1.40932 | − | 8.89808i | −0.185052 | − | 1.16838i | ||||
\(59\) | −3.38260 | + | 2.45760i | −0.440377 | + | 0.319953i | −0.785785 | − | 0.618500i | \(-0.787741\pi\) |
0.345408 | + | 0.938453i | \(0.387741\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.115104 | − | 0.354252i | 0.0147375 | − | 0.0453574i | −0.943417 | − | 0.331608i | \(-0.892409\pi\) |
0.958155 | + | 0.286250i | \(0.0924089\pi\) | |||||||
\(62\) | 3.81362 | + | 0.604018i | 0.484330 | + | 0.0767104i | ||||
\(63\) | 14.7735 | − | 2.95900i | 1.86128 | − | 0.372798i | ||||
\(64\) | 8.11621 | − | 2.63712i | 1.01453 | − | 0.329640i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.54627 | − | 6.39652i | 0.190332 | − | 0.787358i | ||||
\(67\) | −1.65535 | + | 1.65535i | −0.202233 | + | 0.202233i | −0.800956 | − | 0.598723i | \(-0.795675\pi\) |
0.598723 | + | 0.800956i | \(0.295675\pi\) | |||||||
\(68\) | 0.673291 | + | 0.343059i | 0.0816485 | + | 0.0416020i | ||||
\(69\) | 1.06284 | + | 5.92900i | 0.127951 | + | 0.713768i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.2370 | − | 3.97604i | −1.45226 | − | 0.471869i | −0.526567 | − | 0.850134i | \(-0.676521\pi\) |
−0.925697 | + | 0.378265i | \(0.876521\pi\) | |||||||
\(72\) | −4.52395 | − | 8.05303i | −0.533152 | − | 0.949058i | ||||
\(73\) | −3.04267 | − | 0.481911i | −0.356117 | − | 0.0564035i | −0.0241874 | − | 0.999707i | \(-0.507700\pi\) |
−0.331930 | + | 0.943304i | \(0.607700\pi\) | |||||||
\(74\) | −2.35934 | − | 1.71416i | −0.274268 | − | 0.199267i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.32159 | 0.381012 | ||||||||
\(77\) | −12.8996 | + | 10.5384i | −1.47005 | + | 1.20096i | ||||
\(78\) | 3.02761 | − | 0.0614626i | 0.342809 | − | 0.00695926i | ||||
\(79\) | −10.0969 | + | 3.28067i | −1.13598 | + | 0.369104i | −0.815847 | − | 0.578267i | \(-0.803729\pi\) |
−0.320138 | + | 0.947371i | \(0.603729\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.82813 | + | 5.86316i | −0.758681 | + | 0.651462i | ||||
\(82\) | −1.51159 | − | 2.96666i | −0.166927 | − | 0.327612i | ||||
\(83\) | −7.12939 | − | 13.9922i | −0.782552 | − | 1.53585i | −0.843147 | − | 0.537683i | \(-0.819300\pi\) |
0.0605952 | − | 0.998162i | \(-0.480700\pi\) | |||||||
\(84\) | −0.815688 | + | 5.92619i | −0.0889989 | + | 0.646601i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.6733 | + | 3.46795i | −1.15093 | + | 0.373959i | ||||
\(87\) | −0.276465 | − | 13.6185i | −0.0296401 | − | 1.46005i | ||||
\(88\) | 8.58809 | + | 5.52462i | 0.915494 | + | 0.588926i | ||||
\(89\) | 16.3927 | 1.73762 | 0.868812 | − | 0.495141i | \(-0.164884\pi\) | ||||
0.868812 | + | 0.495141i | \(0.164884\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.20110 | − | 4.50536i | −0.650052 | − | 0.472290i | ||||
\(92\) | −2.36209 | − | 0.374119i | −0.246265 | − | 0.0390046i | ||||
\(93\) | 5.58767 | + | 1.69096i | 0.579414 | + | 0.175344i | ||||
\(94\) | 5.99535 | + | 1.94801i | 0.618374 | + | 0.200922i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.29591 | − | 1.12861i | 0.642573 | − | 0.115189i | ||||
\(97\) | −8.19608 | − | 4.17611i | −0.832186 | − | 0.424020i | −0.0146467 | − | 0.999893i | \(-0.504662\pi\) |
−0.817539 | + | 0.575873i | \(0.804662\pi\) | |||||||
\(98\) | −14.7617 | + | 14.7617i | −1.49115 | + | 1.49115i | ||||
\(99\) | 3.63480 | − | 9.26219i | 0.365311 | − | 0.930885i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.7859 | − | 4.15438i | 1.27224 | − | 0.413377i | 0.406401 | − | 0.913695i | \(-0.366784\pi\) |
0.865842 | + | 0.500318i | \(0.166784\pi\) | |||||||
\(102\) | −1.78954 | − | 1.24548i | −0.177190 | − | 0.123320i | ||||
\(103\) | 0.253756 | + | 0.0401910i | 0.0250034 | + | 0.00396014i | 0.168924 | − | 0.985629i | \(-0.445971\pi\) |
−0.143920 | + | 0.989589i | \(0.545971\pi\) | |||||||
\(104\) | −1.45207 | + | 4.46902i | −0.142387 | + | 0.438224i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.47136 | − | 1.79555i | 0.240040 | − | 0.174399i | ||||
\(107\) | 1.52518 | + | 9.62961i | 0.147445 | + | 0.930930i | 0.944854 | + | 0.327491i | \(0.106203\pi\) |
−0.797409 | + | 0.603439i | \(0.793797\pi\) | |||||||
\(108\) | −1.30898 | − | 3.32492i | −0.125957 | − | 0.319940i | ||||
\(109\) | − | 15.6106i | − | 1.49522i | −0.664138 | − | 0.747610i | \(-0.731201\pi\) | ||
0.664138 | − | 0.747610i | \(-0.268799\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.18052 | − | 3.05395i | −0.301882 | − | 0.289869i | ||||
\(112\) | 9.62876 | + | 4.90610i | 0.909832 | + | 0.463583i | ||||
\(113\) | −13.6384 | + | 2.16011i | −1.28299 | + | 0.203206i | −0.760443 | − | 0.649404i | \(-0.775018\pi\) |
−0.522548 | + | 0.852610i | \(0.675018\pi\) | |||||||
\(114\) | −9.49428 | − | 1.30680i | −0.889220 | − | 0.122393i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.14341 | + | 1.67120i | 0.477554 | + | 0.155167i | ||||
\(117\) | 4.54754 | + | 0.532124i | 0.420421 | + | 0.0491949i | ||||
\(118\) | 0.749281 | + | 4.73078i | 0.0689769 | + | 0.435503i | ||||
\(119\) | 1.70537 | + | 5.24859i | 0.156331 | + | 0.481137i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.24420 | + | 10.9294i | 0.113110 | + | 0.993583i | ||||
\(122\) | −0.301725 | − | 0.301725i | −0.0273169 | − | 0.0273169i | ||||
\(123\) | −1.65250 | − | 4.75521i | −0.149001 | − | 0.428763i | ||||
\(124\) | −1.36240 | + | 1.87518i | −0.122347 | + | 0.168396i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.66306 | − | 16.6183i | 0.415418 | − | 1.48047i | ||||
\(127\) | 5.87766 | + | 11.5356i | 0.521558 | + | 1.02362i | 0.990125 | + | 0.140188i | \(0.0447706\pi\) |
−0.468567 | + | 0.883428i | \(0.655229\pi\) | |||||||
\(128\) | 0.373933 | − | 2.36092i | 0.0330513 | − | 0.208678i | ||||
\(129\) | −16.7018 | + | 2.99399i | −1.47051 | + | 0.263606i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 12.5208i | − | 1.09394i | −0.837151 | − | 0.546972i | \(-0.815780\pi\) | ||
0.837151 | − | 0.546972i | \(-0.184220\pi\) | |||||||
\(132\) | 2.99991 | + | 2.57030i | 0.261109 | + | 0.223716i | ||||
\(133\) | 17.1532 | + | 17.1532i | 1.48737 | + | 1.48737i | ||||
\(134\) | 0.828715 | + | 2.55052i | 0.0715901 | + | 0.220332i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.73709 | − | 1.98861i | 0.234703 | − | 0.170522i | ||||
\(137\) | 15.3097 | − | 7.80069i | 1.30800 | − | 0.666458i | 0.345671 | − | 0.938356i | \(-0.387651\pi\) |
0.962326 | + | 0.271898i | \(0.0876512\pi\) | |||||||
\(138\) | 6.60452 | + | 1.99868i | 0.562214 | + | 0.170139i | ||||
\(139\) | 5.91581 | + | 8.14241i | 0.501772 | + | 0.690630i | 0.982505 | − | 0.186237i | \(-0.0596293\pi\) |
−0.480733 | + | 0.876867i | \(0.659629\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.57848 | + | 4.15384i | 0.722438 | + | 0.349816i | ||||
\(142\) | −10.4225 | + | 10.4225i | −0.874639 | + | 0.874639i | ||||
\(143\) | −4.71772 | + | 1.83437i | −0.394516 | + | 0.153397i | ||||
\(144\) | −6.44986 | + | 0.261982i | −0.537488 | + | 0.0218318i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.07431 | + | 2.85504i | −0.171671 | + | 0.236285i | ||||
\(147\) | −25.1540 | + | 19.0673i | −2.07466 | + | 1.57264i | ||||
\(148\) | 1.55985 | − | 0.794783i | 0.128219 | − | 0.0653308i | ||||
\(149\) | −1.39935 | + | 4.30677i | −0.114640 | + | 0.352824i | −0.991872 | − | 0.127242i | \(-0.959387\pi\) |
0.877232 | + | 0.480067i | \(0.159387\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.9954 | − | 8.71514i | −0.976169 | − | 0.709228i | −0.0193196 | − | 0.999813i | \(-0.506150\pi\) |
−0.956849 | + | 0.290585i | \(0.906150\pi\) | |||||||
\(152\) | 6.75152 | − | 13.2506i | 0.547620 | − | 1.07477i | ||||
\(153\) | −2.42367 | − | 2.23446i | −0.195942 | − | 0.180646i | ||||
\(154\) | 4.04784 | + | 18.6475i | 0.326184 | + | 1.50266i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.792241 | + | 1.63613i | −0.0634300 | + | 0.130995i | ||||
\(157\) | 0.992931 | − | 0.157265i | 0.0792445 | − | 0.0125511i | −0.116686 | − | 0.993169i | \(-0.537227\pi\) |
0.195931 | + | 0.980618i | \(0.437227\pi\) | |||||||
\(158\) | −1.90253 | + | 12.0121i | −0.151357 | + | 0.955632i | ||||
\(159\) | 4.07188 | − | 2.17994i | 0.322921 | − | 0.172880i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.2662 | − | 14.1302i | −0.809091 | − | 1.11362i | ||||
\(162\) | 2.43342 | + | 10.0188i | 0.191187 | + | 0.787151i | ||||
\(163\) | 2.76654 | − | 5.42964i | 0.216692 | − | 0.425282i | −0.756915 | − | 0.653514i | \(-0.773294\pi\) |
0.973607 | + | 0.228231i | \(0.0732942\pi\) | |||||||
\(164\) | 1.99873 | 0.156075 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.9897 | −1.39627 | ||||||||
\(167\) | −0.721896 | + | 1.41680i | −0.0558620 | + | 0.109635i | −0.917250 | − | 0.398313i | \(-0.869596\pi\) |
0.861388 | + | 0.507948i | \(0.169596\pi\) | |||||||
\(168\) | 21.9830 | + | 15.2997i | 1.69603 | + | 1.18040i | ||||
\(169\) | 6.27211 | + | 8.63281i | 0.482470 | + | 0.664062i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.9515 | − | 3.91477i | −1.06690 | − | 0.299370i | ||||
\(172\) | 1.05388 | − | 6.65395i | 0.0803577 | − | 0.507359i | ||||
\(173\) | 8.04216 | − | 1.27375i | 0.611434 | − | 0.0968417i | 0.156965 | − | 0.987604i | \(-0.449829\pi\) |
0.454469 | + | 0.890762i | \(0.349829\pi\) | |||||||
\(174\) | −14.0442 | − | 6.80044i | −1.06469 | − | 0.515540i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.16491 | − | 3.59488i | 0.464697 | − | 0.270974i | ||||
\(177\) | 0.146986 | + | 7.24043i | 0.0110481 | + | 0.544224i | ||||
\(178\) | 8.52545 | − | 16.7321i | 0.639009 | − | 1.25413i | ||||
\(179\) | −7.66272 | − | 5.56729i | −0.572738 | − | 0.416119i | 0.263361 | − | 0.964697i | \(-0.415169\pi\) |
−0.836099 | + | 0.548579i | \(0.815169\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.60665 | − | 4.94477i | 0.119422 | − | 0.367542i | −0.873422 | − | 0.486964i | \(-0.838104\pi\) |
0.992844 | + | 0.119422i | \(0.0381043\pi\) | |||||||
\(182\) | −7.82369 | + | 3.98637i | −0.579930 | + | 0.295489i | ||||
\(183\) | −0.389731 | − | 0.514141i | −0.0288097 | − | 0.0380064i | ||||
\(184\) | −6.29369 | + | 8.66252i | −0.463977 | + | 0.638609i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.63198 | − | 4.82394i | 0.339633 | − | 0.353708i | ||||
\(187\) | 3.52429 | + | 0.928046i | 0.257722 | + | 0.0678654i | ||||
\(188\) | −2.67585 | + | 2.67585i | −0.195157 | + | 0.195157i | ||||
\(189\) | 10.4106 | − | 23.9302i | 0.757261 | − | 1.74066i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.79938 | + | 2.47664i | 0.130199 | + | 0.179203i | 0.869139 | − | 0.494568i | \(-0.164674\pi\) |
−0.738940 | + | 0.673771i | \(0.764674\pi\) | |||||||
\(192\) | 4.28136 | − | 14.1475i | 0.308980 | − | 1.02101i | ||||
\(193\) | −15.4958 | + | 7.89550i | −1.11541 | + | 0.568330i | −0.911764 | − | 0.410714i | \(-0.865279\pi\) |
−0.203647 | + | 0.979044i | \(0.565279\pi\) | |||||||
\(194\) | −8.52516 | + | 6.19389i | −0.612071 | + | 0.444695i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.87259 | − | 11.9186i | −0.276614 | − | 0.851329i | ||||
\(197\) | −14.2002 | − | 14.2002i | −1.01172 | − | 1.01172i | −0.999930 | − | 0.0117932i | \(-0.996246\pi\) |
−0.0117932 | − | 0.999930i | \(-0.503754\pi\) | |||||||
\(198\) | −7.56360 | − | 8.52710i | −0.537522 | − | 0.605994i | ||||
\(199\) | − | 2.36532i | − | 0.167673i | −0.996480 | − | 0.0838365i | \(-0.973283\pi\) | ||
0.996480 | − | 0.0838365i | \(-0.0267173\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.715456 | + | 3.99113i | 0.0504644 | + | 0.281513i | ||||
\(202\) | 2.40922 | − | 15.2112i | 0.169512 | − | 1.07026i | ||||
\(203\) | 17.9311 | + | 35.1917i | 1.25851 | + | 2.46997i | ||||
\(204\) | 1.15387 | − | 0.617742i | 0.0807873 | − | 0.0432506i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.172996 | − | 0.238108i | 0.0120532 | − | 0.0165898i | ||||
\(207\) | 9.48046 | + | 4.35532i | 0.658938 | + | 0.302716i | ||||
\(208\) | 2.32210 | + | 2.32210i | 0.161009 | + | 0.161009i | ||||
\(209\) | 15.6551 | − | 3.39828i | 1.08288 | − | 0.235064i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.43819 | + | 13.6593i | 0.305538 | + | 0.940348i | 0.979476 | + | 0.201561i | \(0.0646013\pi\) |
−0.673938 | + | 0.738788i | \(0.735399\pi\) | |||||||
\(212\) | 0.286866 | + | 1.81120i | 0.0197021 | + | 0.124394i | ||||
\(213\) | −17.7600 | + | 13.4625i | −1.21690 | + | 0.922437i | ||||
\(214\) | 10.6222 | + | 3.45136i | 0.726119 | + | 0.235930i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −15.9246 | − | 1.53646i | −1.08353 | − | 0.104543i | ||||
\(217\) | −16.7194 | + | 2.64809i | −1.13499 | + | 0.179764i | ||||
\(218\) | −15.9338 | − | 8.11866i | −1.07917 | − | 0.549865i | ||||
\(219\) | −3.69559 | + | 3.84875i | −0.249725 | + | 0.260074i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.67704i | 0.112810i | ||||||||
\(222\) | −4.77130 | + | 1.65809i | −0.320228 | + | 0.111283i | ||||
\(223\) | 3.46659 | + | 21.8872i | 0.232140 | + | 1.46567i | 0.778247 | + | 0.627958i | \(0.216109\pi\) |
−0.546108 | + | 0.837715i | \(0.683891\pi\) | |||||||
\(224\) | −15.0046 | + | 10.9015i | −1.00254 | + | 0.728388i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.88815 | + | 15.0442i | −0.325155 | + | 1.00072i | ||||
\(227\) | 11.4208 | + | 1.80888i | 0.758028 | + | 0.120060i | 0.523472 | − | 0.852043i | \(-0.324636\pi\) |
0.234556 | + | 0.972103i | \(0.424636\pi\) | |||||||
\(228\) | 3.28645 | − | 4.72208i | 0.217651 | − | 0.312727i | ||||
\(229\) | −0.497218 | + | 0.161556i | −0.0328571 | + | 0.0106759i | −0.325399 | − | 0.945577i | \(-0.605499\pi\) |
0.292542 | + | 0.956253i | \(0.405499\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.21858 | + | 28.7655i | 0.145972 | + | 1.89263i | ||||
\(232\) | 17.1214 | − | 17.1214i | 1.12408 | − | 1.12408i | ||||
\(233\) | −16.1559 | − | 8.23186i | −1.05841 | − | 0.539287i | −0.163966 | − | 0.986466i | \(-0.552429\pi\) |
−0.894444 | + | 0.447179i | \(0.852429\pi\) | |||||||
\(234\) | 2.90821 | − | 4.36496i | 0.190115 | − | 0.285346i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.73456 | − | 0.888513i | −0.178005 | − | 0.0578373i | ||||
\(237\) | −5.32616 | + | 17.6000i | −0.345971 | + | 1.14324i | ||||
\(238\) | 6.24418 | + | 0.988981i | 0.404750 | + | 0.0641061i | ||||
\(239\) | 7.09547 | + | 5.15516i | 0.458968 | + | 0.333460i | 0.793126 | − | 0.609057i | \(-0.208452\pi\) |
−0.334158 | + | 0.942517i | \(0.608452\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.80930 | −0.631873 | −0.315936 | − | 0.948780i | \(-0.602319\pi\) | ||||
−0.315936 | + | 0.948780i | \(0.602319\pi\) | |||||||
\(242\) | 11.8028 | + | 4.41415i | 0.758712 | + | 0.283752i | ||||
\(243\) | 1.57935 | + | 15.5082i | 0.101315 | + | 0.994854i | ||||
\(244\) | 0.243613 | − | 0.0791547i | 0.0155957 | − | 0.00506736i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.71309 | − | 0.786357i | −0.364254 | − | 0.0501363i | ||||
\(247\) | 3.34667 | + | 6.56821i | 0.212943 | + | 0.417925i | ||||
\(248\) | 4.71132 | + | 9.24648i | 0.299169 | + | 0.587152i | ||||
\(249\) | −26.9458 | − | 3.70885i | −1.70762 | − | 0.235039i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.24182 | + | 2.02809i | −0.393980 | + | 0.128012i | −0.499306 | − | 0.866426i | \(-0.666411\pi\) |
0.105326 | + | 0.994438i | \(0.466411\pi\) | |||||||
\(252\) | 7.61781 | + | 7.02312i | 0.479877 | + | 0.442415i | ||||
\(253\) | −11.5156 | + | 0.653360i | −0.723981 | + | 0.0410764i | ||||
\(254\) | 14.8312 | 0.930594 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.5928 | + | 8.42266i | 0.724550 | + | 0.526416i | ||||
\(257\) | −5.82033 | − | 0.921849i | −0.363062 | − | 0.0575034i | −0.0277614 | − | 0.999615i | \(-0.508838\pi\) |
−0.335301 | + | 0.942111i | \(0.608838\pi\) | |||||||
\(258\) | −5.63022 | + | 18.6047i | −0.350522 | + | 1.15828i | ||||
\(259\) | 12.1597 | + | 3.95092i | 0.755566 | + | 0.245498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.6340 | − | 13.0814i | −1.21531 | − | 0.809718i | ||||
\(262\) | −12.7800 | − | 6.51174i | −0.789551 | − | 0.402296i | ||||
\(263\) | −2.77979 | + | 2.77979i | −0.171409 | + | 0.171409i | −0.787598 | − | 0.616189i | \(-0.788676\pi\) |
0.616189 | + | 0.787598i | \(0.288676\pi\) | |||||||
\(264\) | 16.3512 | − | 6.74293i | 1.00635 | − | 0.414999i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 26.4293 | − | 8.58739i | 1.62048 | − | 0.526527i | ||||
\(267\) | 16.2193 | − | 23.3044i | 0.992608 | − | 1.42621i | ||||
\(268\) | −1.59005 | − | 0.251840i | −0.0971279 | − | 0.0153836i | ||||
\(269\) | 4.83416 | − | 14.8780i | 0.294744 | − | 0.907129i | −0.688563 | − | 0.725176i | \(-0.741758\pi\) |
0.983307 | − | 0.181952i | \(-0.0582417\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.90672 | − | 2.11186i | 0.176571 | − | 0.128286i | −0.495990 | − | 0.868328i | \(-0.665195\pi\) |
0.672560 | + | 0.740042i | \(0.265195\pi\) | |||||||
\(272\) | −0.369873 | − | 2.33529i | −0.0224269 | − | 0.141598i | ||||
\(273\) | −12.5405 | + | 4.35798i | −0.758985 | + | 0.263757i | ||||
\(274\) | − | 19.6837i | − | 1.18913i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.86897 | + | 2.98787i | −0.172692 | + | 0.179849i | ||||
\(277\) | 4.07663 | + | 2.07715i | 0.244941 | + | 0.124804i | 0.572152 | − | 0.820148i | \(-0.306109\pi\) |
−0.327211 | + | 0.944951i | \(0.606109\pi\) | |||||||
\(278\) | 11.3877 | − | 1.80363i | 0.682987 | − | 0.108174i | ||||
\(279\) | 7.93249 | − | 6.27055i | 0.474906 | − | 0.375408i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.26028 | − | 2.03409i | −0.373457 | − | 0.121344i | 0.116274 | − | 0.993217i | \(-0.462905\pi\) |
−0.489731 | + | 0.871874i | \(0.662905\pi\) | |||||||
\(282\) | 8.70130 | − | 6.59579i | 0.518155 | − | 0.392774i | ||||
\(283\) | −1.49478 | − | 9.43766i | −0.0888554 | − | 0.561011i | −0.991447 | − | 0.130512i | \(-0.958338\pi\) |
0.902591 | − | 0.430499i | \(-0.141662\pi\) | |||||||
\(284\) | −2.73425 | − | 8.41517i | −0.162248 | − | 0.499349i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.581224 | + | 5.76941i | −0.0343685 | + | 0.341153i | ||||
\(287\) | 10.3218 | + | 10.3218i | 0.609275 | + | 0.609275i | ||||
\(288\) | 4.62484 | − | 10.0671i | 0.272521 | − | 0.593212i | ||||
\(289\) | −9.28263 | + | 12.7764i | −0.546037 | + | 0.751556i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.0463 | + | 7.51988i | −0.823408 | + | 0.440823i | ||||
\(292\) | −0.961767 | − | 1.88757i | −0.0562831 | − | 0.110462i | ||||
\(293\) | 3.84569 | − | 24.2807i | 0.224667 | − | 1.41849i | −0.575050 | − | 0.818118i | \(-0.695018\pi\) |
0.799718 | − | 0.600376i | \(-0.204982\pi\) | |||||||
\(294\) | 6.38014 | + | 35.5912i | 0.372097 | + | 2.07572i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 7.83810i | − | 0.455581i | ||||||
\(297\) | −9.57109 | − | 14.3316i | −0.555371 | − | 0.831603i | ||||
\(298\) | 3.66817 | + | 3.66817i | 0.212492 | + | 0.212492i | ||||
\(299\) | −1.64014 | − | 5.04782i | −0.0948516 | − | 0.291923i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 39.8044 | − | 28.9196i | 2.29429 | − | 1.66690i | ||||
\(302\) | −15.1341 | + | 7.71120i | −0.870868 | + | 0.443730i | ||||
\(303\) | 6.74464 | − | 22.2873i | 0.387469 | − | 1.28037i | ||||
\(304\) | −6.10890 | − | 8.40818i | −0.350369 | − | 0.482242i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.54122 | + | 1.31176i | −0.202438 | + | 0.0749884i | ||||
\(307\) | 14.8223 | − | 14.8223i | 0.845954 | − | 0.845954i | −0.143672 | − | 0.989625i | \(-0.545891\pi\) |
0.989625 | + | 0.143672i | \(0.0458910\pi\) | |||||||
\(308\) | −11.0772 | − | 2.91693i | −0.631180 | − | 0.166208i | ||||
\(309\) | 0.308209 | − | 0.320982i | 0.0175334 | − | 0.0182601i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.39052 | + | 10.1722i | −0.419078 | + | 0.576812i | −0.965403 | − | 0.260762i | \(-0.916026\pi\) |
0.546325 | + | 0.837573i | \(0.316026\pi\) | |||||||
\(312\) | 4.91659 | + | 6.48607i | 0.278347 | + | 0.367201i | ||||
\(313\) | −30.4832 | + | 15.5320i | −1.72301 | + | 0.877919i | −0.745652 | + | 0.666335i | \(0.767862\pi\) |
−0.977360 | + | 0.211583i | \(0.932138\pi\) | |||||||
\(314\) | 0.355878 | − | 1.09528i | 0.0200834 | − | 0.0618102i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.90644 | − | 4.29128i | −0.332263 | − | 0.241403i | ||||
\(317\) | −8.63473 | + | 16.9466i | −0.484975 | + | 0.951817i | 0.510775 | + | 0.859715i | \(0.329359\pi\) |
−0.995750 | + | 0.0921020i | \(0.970641\pi\) | |||||||
\(318\) | −0.107389 | − | 5.28992i | −0.00602209 | − | 0.296644i | ||||
\(319\) | 25.9514 | + | 2.61440i | 1.45300 | + | 0.146379i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.1988 | + | 7.35952i | 0.848316 | + | 0.410768i | ||||
\(322\) | −19.7620 | + | 3.12999i | −1.10129 | + | 0.174428i | ||||
\(323\) | 0.830277 | − | 5.24216i | 0.0461979 | − | 0.291682i | ||||
\(324\) | −6.02195 | − | 1.42886i | −0.334553 | − | 0.0793813i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.10325 | − | 5.64765i | −0.227258 | − | 0.312794i | ||||
\(327\) | −22.1925 | − | 15.4455i | −1.22725 | − | 0.854135i | ||||
\(328\) | 4.06266 | − | 7.97343i | 0.224323 | − | 0.440259i | ||||
\(329\) | −27.6370 | −1.52368 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.67705 | −0.476934 | −0.238467 | − | 0.971151i | \(-0.576645\pi\) | ||||
−0.238467 | + | 0.971151i | \(0.576645\pi\) | |||||||
\(332\) | 4.90276 | − | 9.62221i | 0.269074 | − | 0.528087i | ||||
\(333\) | −7.48848 | + | 1.49988i | −0.410366 | + | 0.0821928i | ||||
\(334\) | 1.07069 | + | 1.47368i | 0.0585858 | + | 0.0806364i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 16.5016 | − | 8.83436i | 0.900236 | − | 0.481954i | ||||
\(337\) | 0.193407 | − | 1.22112i | 0.0105355 | − | 0.0665188i | −0.981860 | − | 0.189605i | \(-0.939279\pi\) |
0.992396 | + | 0.123086i | \(0.0392792\pi\) | |||||||
\(338\) | 12.0735 | − | 1.91226i | 0.656713 | − | 0.104013i | ||||
\(339\) | −10.4233 | + | 21.5260i | −0.566113 | + | 1.16913i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.50270 | + | 10.2319i | −0.243835 | + | 0.554086i | ||||
\(342\) | −11.2517 | + | 12.2044i | −0.608420 | + | 0.659938i | ||||
\(343\) | 25.5904 | − | 50.2239i | 1.38175 | − | 2.71184i | ||||
\(344\) | −24.4020 | − | 17.7291i | −1.31567 | − | 0.955890i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.88240 | − | 8.87112i | 0.154959 | − | 0.476915i | ||||
\(347\) | 9.45182 | − | 4.81594i | 0.507400 | − | 0.258533i | −0.181498 | − | 0.983391i | \(-0.558095\pi\) |
0.688898 | + | 0.724858i | \(0.258095\pi\) | |||||||
\(348\) | 7.46484 | − | 5.65853i | 0.400158 | − | 0.303329i | ||||
\(349\) | 2.30547 | − | 3.17321i | 0.123409 | − | 0.169858i | −0.742842 | − | 0.669466i | \(-0.766523\pi\) |
0.866251 | + | 0.499609i | \(0.166523\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.25593 | − | 5.93844i | 0.280541 | − | 0.316971i | ||||
\(352\) | 0.693792 | + | 12.2282i | 0.0369792 | + | 0.651768i | ||||
\(353\) | 26.0709 | − | 26.0709i | 1.38761 | − | 1.38761i | 0.557302 | − | 0.830310i | \(-0.311836\pi\) |
0.830310 | − | 0.557302i | \(-0.188164\pi\) | |||||||
\(354\) | 7.46679 | + | 3.61554i | 0.396855 | + | 0.192164i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.62610 | + | 9.12004i | 0.351182 | + | 0.483361i | ||||
\(357\) | 9.14890 | + | 2.76866i | 0.484211 | + | 0.146533i | ||||
\(358\) | −9.66775 | + | 4.92596i | −0.510956 | + | 0.260345i | ||||
\(359\) | 9.77829 | − | 7.10434i | 0.516078 | − | 0.374953i | −0.299046 | − | 0.954239i | \(-0.596669\pi\) |
0.815124 | + | 0.579286i | \(0.196669\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.33804 | − | 4.11806i | −0.0704231 | − | 0.216740i | ||||
\(362\) | −4.21157 | − | 4.21157i | −0.221355 | − | 0.221355i | ||||
\(363\) | 16.7687 | + | 9.04501i | 0.880126 | + | 0.474740i | ||||
\(364\) | − | 5.27108i | − | 0.276279i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.727475 | + | 0.130408i | −0.0380257 | + | 0.00681655i | ||||
\(367\) | 2.44544 | − | 15.4399i | 0.127651 | − | 0.805955i | −0.837916 | − | 0.545799i | \(-0.816226\pi\) |
0.965567 | − | 0.260156i | \(-0.0837739\pi\) | |||||||
\(368\) | 3.39721 | + | 6.66741i | 0.177092 | + | 0.347563i | ||||
\(369\) | −8.39519 | − | 2.35568i | −0.437036 | − | 0.122632i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.87191 | + | 10.8348i | −0.408689 | + | 0.562512i | ||||
\(372\) | 1.31783 | + | 3.79219i | 0.0683264 | + | 0.196616i | ||||
\(373\) | −1.12896 | − | 1.12896i | −0.0584553 | − | 0.0584553i | 0.677275 | − | 0.735730i | \(-0.263161\pi\) |
−0.735730 | + | 0.677275i | \(0.763161\pi\) | |||||||
\(374\) | 2.78016 | − | 3.11461i | 0.143758 | − | 0.161052i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.23563 | + | 16.1136i | 0.270007 | + | 0.830996i | ||||
\(377\) | 1.87758 | + | 11.8546i | 0.0967002 | + | 0.610541i | ||||
\(378\) | −19.0113 | − | 23.0717i | −0.977838 | − | 1.18668i | ||||
\(379\) | −23.2364 | − | 7.54997i | −1.19358 | − | 0.387816i | −0.356182 | − | 0.934417i | \(-0.615922\pi\) |
−0.837393 | + | 0.546601i | \(0.815922\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.2148 | + | 3.05768i | 1.13810 | + | 0.156650i | ||||
\(382\) | 3.46373 | − | 0.548601i | 0.177220 | − | 0.0280689i | ||||
\(383\) | 18.5155 | + | 9.43410i | 0.946096 | + | 0.482060i | 0.857771 | − | 0.514032i | \(-0.171849\pi\) |
0.0883249 | + | 0.996092i | \(0.471849\pi\) | |||||||
\(384\) | −2.98638 | − | 2.86754i | −0.152398 | − | 0.146334i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 19.9229i | 1.01405i | ||||||||
\(387\) | −12.2688 | + | 26.7062i | −0.623658 | + | 1.35755i | ||||
\(388\) | −0.989569 | − | 6.24789i | −0.0502377 | − | 0.317189i | ||||
\(389\) | −10.6648 | + | 7.74846i | −0.540729 | + | 0.392863i | −0.824356 | − | 0.566072i | \(-0.808462\pi\) |
0.283627 | + | 0.958935i | \(0.408462\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.18088 | + | 3.63437i | −0.0597195 | + | 0.183798i | ||||
\(392\) | −55.4177 | − | 8.77730i | −2.79902 | − | 0.443321i | ||||
\(393\) | −17.7999 | − | 12.3883i | −0.897888 | − | 0.624909i | ||||
\(394\) | −21.8794 | + | 7.10905i | −1.10227 | + | 0.358149i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.62222 | − | 1.72166i | 0.332779 | − | 0.0865166i | ||||
\(397\) | 3.62715 | − | 3.62715i | 0.182041 | − | 0.182041i | −0.610203 | − | 0.792245i | \(-0.708912\pi\) |
0.792245 | + | 0.610203i | \(0.208912\pi\) | |||||||
\(398\) | −2.41429 | − | 1.23014i | −0.121018 | − | 0.0616615i | ||||
\(399\) | 41.3573 | − | 7.41377i | 2.07045 | − | 0.371153i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.06221 | + | 1.31989i | 0.202857 | + | 0.0659122i | 0.408683 | − | 0.912676i | \(-0.365988\pi\) |
−0.205826 | + | 0.978589i | \(0.565988\pi\) | |||||||
\(402\) | 4.44586 | + | 1.34542i | 0.221739 | + | 0.0671034i | ||||
\(403\) | −5.08074 | − | 0.804710i | −0.253090 | − | 0.0400854i | ||||
\(404\) | 7.47946 | + | 5.43414i | 0.372117 | + | 0.270359i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 45.2459 | 2.24551 | ||||||||
\(407\) | 6.53865 | − | 5.34179i | 0.324109 | − | 0.264782i | ||||
\(408\) | −0.118936 | − | 5.85871i | −0.00588821 | − | 0.290049i | ||||
\(409\) | 4.94918 | − | 1.60809i | 0.244721 | − | 0.0795147i | −0.184088 | − | 0.982910i | \(-0.558933\pi\) |
0.428809 | + | 0.903395i | \(0.358933\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.05807 | − | 29.4830i | 0.200170 | − | 1.45429i | ||||
\(412\) | 0.0802106 | + | 0.157422i | 0.00395169 | + | 0.00775563i | ||||
\(413\) | −9.53328 | − | 18.7101i | −0.469102 | − | 0.920665i | ||||
\(414\) | 9.37605 | − | 7.41166i | 0.460808 | − | 0.364263i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.36020 | + | 1.74163i | −0.262805 | + | 0.0853906i | ||||
\(417\) | 17.4288 | − | 0.353816i | 0.853490 | − | 0.0173265i | ||||
\(418\) | 4.67318 | − | 17.7466i | 0.228573 | − | 0.868014i | ||||
\(419\) | 24.7300 | 1.20814 | 0.604069 | − | 0.796932i | \(-0.293545\pi\) | ||||
0.604069 | + | 0.796932i | \(0.293545\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.6821 | − | 20.1122i | −1.34914 | − | 0.980210i | −0.999054 | − | 0.0434931i | \(-0.986151\pi\) |
−0.350089 | − | 0.936716i | \(-0.613849\pi\) | |||||||
\(422\) | 16.2504 | + | 2.57380i | 0.791055 | + | 0.125291i | ||||
\(423\) | 14.3930 | − | 8.08555i | 0.699811 | − | 0.393133i | ||||
\(424\) | 7.80841 | + | 2.53711i | 0.379210 | + | 0.123213i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.50472 | + | 25.1293i | 0.218254 | + | 1.21752i | ||||
\(427\) | 1.66682 | + | 0.849289i | 0.0806632 | + | 0.0411000i | ||||
\(428\) | −4.74091 | + | 4.74091i | −0.229161 | + | 0.229161i | ||||
\(429\) | −2.06003 | + | 8.52184i | −0.0994592 | + | 0.411438i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.44652 | + | 2.74444i | −0.406855 | + | 0.132195i | −0.505293 | − | 0.862948i | \(-0.668615\pi\) |
0.0984380 | + | 0.995143i | \(0.468615\pi\) | |||||||
\(432\) | −6.00920 | + | 9.42855i | −0.289118 | + | 0.453631i | ||||
\(433\) | −4.62630 | − | 0.732734i | −0.222326 | − | 0.0352130i | 0.0442775 | − | 0.999019i | \(-0.485901\pi\) |
−0.266603 | + | 0.963806i | \(0.585901\pi\) | |||||||
\(434\) | −5.99242 | + | 18.4428i | −0.287645 | + | 0.885281i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.68489 | − | 6.30994i | 0.415931 | − | 0.302191i | ||||
\(437\) | 2.62772 | + | 16.5908i | 0.125701 | + | 0.793643i | ||||
\(438\) | 2.00645 | + | 5.77374i | 0.0958718 | + | 0.275880i | ||||
\(439\) | 7.92565i | 0.378271i | 0.981951 | + | 0.189135i | \(0.0605685\pi\) | ||||
−0.981951 | + | 0.189135i | \(0.939432\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.21878 | + | 54.6254i | 0.105656 | + | 2.60121i | ||||
\(442\) | 1.71176 | + | 0.872185i | 0.0814201 | + | 0.0414856i | ||||
\(443\) | 23.6460 | − | 3.74516i | 1.12346 | − | 0.177938i | 0.433057 | − | 0.901367i | \(-0.357435\pi\) |
0.690399 | + | 0.723429i | \(0.257435\pi\) | |||||||
\(444\) | 0.413462 | − | 3.00391i | 0.0196220 | − | 0.142559i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 24.1432 | + | 7.84461i | 1.14321 | + | 0.371453i | ||||
\(447\) | 4.73809 | + | 6.25059i | 0.224104 | + | 0.295643i | ||||
\(448\) | 6.70474 | + | 42.3321i | 0.316769 | + | 2.00000i | ||||
\(449\) | 1.55638 | + | 4.79005i | 0.0734502 | + | 0.226057i | 0.981041 | − | 0.193799i | \(-0.0620809\pi\) |
−0.907591 | + | 0.419855i | \(0.862081\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.42030 | − | 2.04488i | 0.443585 | − | 0.0962898i | ||||
\(452\) | −6.71454 | − | 6.71454i | −0.315825 | − | 0.315825i | ||||
\(453\) | −24.2582 | + | 8.43004i | −1.13975 | + | 0.396078i | ||||
\(454\) | 7.78603 | − | 10.7166i | 0.365417 | − | 0.502953i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.1574 | − | 22.7086i | −0.569322 | − | 1.06343i | ||||
\(457\) | 4.47419 | + | 8.78108i | 0.209294 | + | 0.410762i | 0.971660 | − | 0.236384i | \(-0.0759624\pi\) |
−0.762366 | + | 0.647146i | \(0.775962\pi\) | |||||||
\(458\) | −0.0936897 | + | 0.591534i | −0.00437783 | + | 0.0276406i | ||||
\(459\) | −5.57462 | + | 1.23474i | −0.260201 | + | 0.0576326i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 25.5778i | − | 1.19127i | −0.803253 | − | 0.595637i | \(-0.796900\pi\) | ||
0.803253 | − | 0.595637i | \(-0.203100\pi\) | |||||||
\(462\) | 30.5149 | + | 12.6957i | 1.41968 | + | 0.590657i | ||||
\(463\) | 14.0174 | + | 14.0174i | 0.651445 | + | 0.651445i | 0.953341 | − | 0.301896i | \(-0.0976195\pi\) |
−0.301896 | + | 0.953341i | \(0.597619\pi\) | |||||||
\(464\) | −5.22910 | − | 16.0935i | −0.242755 | − | 0.747122i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.8046 | + | 12.2093i | −0.778458 | + | 0.565583i | ||||
\(467\) | 6.84812 | − | 3.48929i | 0.316893 | − | 0.161465i | −0.288308 | − | 0.957538i | \(-0.593093\pi\) |
0.605201 | + | 0.796073i | \(0.293093\pi\) | |||||||
\(468\) | 1.54212 | + | 2.74510i | 0.0712844 | + | 0.126892i | ||||
\(469\) | −6.91074 | − | 9.51182i | −0.319108 | − | 0.439215i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.758857 | − | 1.56719i | 0.0349663 | − | 0.0722121i | ||||
\(472\) | −9.10281 | + | 9.10281i | −0.418991 | + | 0.418991i | ||||
\(473\) | −1.84049 | − | 32.4392i | −0.0846260 | − | 1.49155i | ||||
\(474\) | 15.1944 | + | 14.5898i | 0.697902 | + | 0.670130i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.23071 | + | 3.07031i | −0.102244 | + | 0.140727i | ||||
\(477\) | 0.929743 | − | 7.94561i | 0.0425700 | − | 0.363804i | ||||
\(478\) | 8.95208 | − | 4.56131i | 0.409459 | − | 0.208630i | ||||
\(479\) | −10.0266 | + | 30.8588i | −0.458129 | + | 1.40998i | 0.409293 | + | 0.912403i | \(0.365775\pi\) |
−0.867422 | + | 0.497573i | \(0.834225\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.14326 | + | 2.28371i | 0.143320 | + | 0.104128i | ||||
\(482\) | −5.10157 | + | 10.0124i | −0.232370 | + | 0.456052i | ||||
\(483\) | −30.2456 | + | 0.614008i | −1.37622 | + | 0.0279383i | ||||
\(484\) | −5.57762 | + | 5.10998i | −0.253528 | + | 0.232272i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 16.6507 | + | 6.45340i | 0.755292 | + | 0.292732i | ||||
\(487\) | 1.37486 | − | 0.217757i | 0.0623009 | − | 0.00986750i | −0.125206 | − | 0.992131i | \(-0.539959\pi\) |
0.187507 | + | 0.982263i | \(0.439959\pi\) | |||||||
\(488\) | 0.179406 | − | 1.13272i | 0.00812131 | − | 0.0512760i | ||||
\(489\) | −4.98168 | − | 9.30522i | −0.225279 | − | 0.420797i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.7755 | + | 18.9604i | 0.621681 | + | 0.855671i | 0.997474 | − | 0.0710327i | \(-0.0226295\pi\) |
−0.375793 | + | 0.926704i | \(0.622629\pi\) | |||||||
\(492\) | 1.97759 | − | 2.84147i | 0.0891568 | − | 0.128103i | ||||
\(493\) | 3.92317 | − | 7.69966i | 0.176691 | − | 0.346775i | ||||
\(494\) | 8.44472 | 0.379946 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.25246 | 0.325645 | ||||||||
\(497\) | 29.3371 | − | 57.5774i | 1.31595 | − | 2.58270i | ||||
\(498\) | −17.7995 | + | 25.5748i | −0.797614 | + | 1.14603i | ||||
\(499\) | −24.4808 | − | 33.6949i | −1.09591 | − | 1.50839i | −0.840695 | − | 0.541509i | \(-0.817853\pi\) |
−0.255217 | − | 0.966884i | \(-0.582147\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.29991 | + | 2.42809i | 0.0580757 | + | 0.108479i | ||||
\(502\) | −1.17613 | + | 7.42581i | −0.0524934 | + | 0.331430i | ||||
\(503\) | 21.8011 | − | 3.45295i | 0.972062 | − | 0.153960i | 0.349848 | − | 0.936806i | \(-0.386233\pi\) |
0.622214 | + | 0.782847i | \(0.286233\pi\) | |||||||
\(504\) | 43.5010 | − | 16.1139i | 1.93769 | − | 0.717772i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.32210 | + | 12.0939i | −0.236596 | + | 0.537637i | ||||
\(507\) | 18.4785 | − | 0.375126i | 0.820657 | − | 0.0166599i | ||||
\(508\) | −4.04197 | + | 7.93281i | −0.179333 | + | 0.351961i | ||||
\(509\) | 17.0516 | + | 12.3887i | 0.755799 | + | 0.549120i | 0.897619 | − | 0.440773i | \(-0.145295\pi\) |
−0.141820 | + | 0.989892i | \(0.545295\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.78101 | − | 14.7144i | 0.211499 | − | 0.650928i | ||||
\(512\) | 18.8858 | − | 9.62280i | 0.834643 | − | 0.425272i | ||||
\(513\) | −19.3693 | + | 15.9606i | −0.855176 | + | 0.704676i | ||||
\(514\) | −3.96794 | + | 5.46141i | −0.175018 | + | 0.240892i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8.41674 | − | 8.08180i | −0.370526 | − | 0.355782i | ||||
\(517\) | −9.87402 | + | 15.3493i | −0.434259 | + | 0.675061i | ||||
\(518\) | 10.3567 | − | 10.3567i | 0.455046 | − | 0.455046i | ||||
\(519\) | 6.14629 | − | 12.6933i | 0.269792 | − | 0.557173i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.00371 | − | 9.63978i | −0.306838 | − | 0.422326i | 0.627554 | − | 0.778573i | \(-0.284056\pi\) |
−0.934392 | + | 0.356247i | \(0.884056\pi\) | |||||||
\(522\) | −23.5634 | + | 13.2372i | −1.03134 | + | 0.579377i | ||||
\(523\) | 1.99875 | − | 1.01842i | 0.0873994 | − | 0.0445322i | −0.409744 | − | 0.912200i | \(-0.634382\pi\) |
0.497144 | + | 0.867668i | \(0.334382\pi\) | |||||||
\(524\) | 6.96589 | − | 5.06101i | 0.304306 | − | 0.221091i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.39165 | + | 4.28304i | 0.0606786 | + | 0.186750i | ||||
\(527\) | 2.61889 | + | 2.61889i | 0.114080 | + | 0.114080i | ||||
\(528\) | 0.989106 | − | 12.3211i | 0.0430453 | − | 0.536207i | ||||
\(529\) | 10.9058i | 0.474164i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.4387 | + | 6.95489i | 0.453000 | + | 0.301817i | ||||
\(532\) | −2.60964 | + | 16.4766i | −0.113142 | + | 0.714351i | ||||
\(533\) | 2.01383 | + | 3.95236i | 0.0872285 | + | 0.171196i | ||||
\(534\) | −15.3517 | − | 28.6752i | −0.664332 | − | 1.24090i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.23662 | + | 5.83121i | −0.182994 | + | 0.251870i | ||||
\(537\) | −15.4963 | + | 5.38517i | −0.668715 | + | 0.232387i | ||||
\(538\) | −12.6719 | − | 12.6719i | −0.546326 | − | 0.546326i | ||||
\(539\) | −30.4458 | − | 52.2120i | −1.31140 | − | 2.24893i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.38230 | + | 19.6427i | 0.274396 | + | 0.844505i | 0.989378 | + | 0.145362i | \(0.0464348\pi\) |
−0.714982 | + | 0.699143i | \(0.753565\pi\) | |||||||
\(542\) | −0.643869 | − | 4.06523i | −0.0276565 | − | 0.174617i | ||||
\(543\) | −5.43999 | − | 7.17654i | −0.233452 | − | 0.307975i | ||||
\(544\) | 3.85927 | + | 1.25395i | 0.165465 | + | 0.0537628i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.07379 | + | 15.0666i | −0.0887499 | + | 0.644792i | ||||
\(547\) | 28.1759 | − | 4.46262i | 1.20471 | − | 0.190808i | 0.478381 | − | 0.878152i | \(-0.341224\pi\) |
0.726331 | + | 0.687345i | \(0.241224\pi\) | |||||||
\(548\) | 10.5282 | + | 5.36440i | 0.449744 | + | 0.229156i | ||||
\(549\) | −1.11653 | + | 0.0453513i | −0.0476523 | + | 0.00193555i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 37.9852i | − | 1.61822i | ||||||
\(552\) | 6.08780 | + | 17.5182i | 0.259114 | + | 0.745625i | ||||
\(553\) | −8.34093 | − | 52.6626i | −0.354693 | − | 2.23944i | ||||
\(554\) | 4.24031 | − | 3.08076i | 0.180153 | − | 0.130889i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.13878 | + | 6.58248i | −0.0907044 | + | 0.279159i | ||||
\(557\) | −2.14716 | − | 0.340076i | −0.0909779 | − | 0.0144095i | 0.110780 | − | 0.993845i | \(-0.464665\pi\) |
−0.201757 | + | 0.979436i | \(0.564665\pi\) | |||||||
\(558\) | −2.27489 | − | 11.3579i | −0.0963036 | − | 0.480818i | ||||
\(559\) | 14.2196 | − | 4.62022i | 0.601423 | − | 0.195414i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.80636 | − | 4.09202i | 0.202924 | − | 0.172765i | ||||
\(562\) | −5.33202 | + | 5.33202i | −0.224918 | + | 0.224918i | ||||
\(563\) | −6.80089 | − | 3.46523i | −0.286623 | − | 0.146042i | 0.304768 | − | 0.952427i | \(-0.401421\pi\) |
−0.591391 | + | 0.806385i | \(0.701421\pi\) | |||||||
\(564\) | 1.15653 | + | 6.45163i | 0.0486987 | + | 0.271663i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.4105 | − | 3.38257i | −0.437585 | − | 0.142180i | ||||
\(567\) | −23.7194 | − | 38.4771i | −0.996122 | − | 1.61589i | ||||
\(568\) | −39.1278 | − | 6.19724i | −1.64177 | − | 0.260030i | ||||
\(569\) | −23.3553 | − | 16.9686i | −0.979104 | − | 0.711361i | −0.0215960 | − | 0.999767i | \(-0.506875\pi\) |
−0.957508 | + | 0.288406i | \(0.906875\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.1746 | 0.676888 | 0.338444 | − | 0.940987i | \(-0.390099\pi\) | ||||
0.338444 | + | 0.940987i | \(0.390099\pi\) | |||||||
\(572\) | −2.92750 | − | 1.88322i | −0.122405 | − | 0.0787415i | ||||
\(573\) | 5.30122 | − | 0.107619i | 0.221462 | − | 0.00449583i | ||||
\(574\) | 15.9036 | − | 5.16739i | 0.663803 | − | 0.215683i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −15.8765 | − | 20.0844i | −0.661520 | − | 0.836850i | ||||
\(577\) | −12.9071 | − | 25.3316i | −0.537329 | − | 1.05457i | −0.986902 | − | 0.161323i | \(-0.948424\pi\) |
0.449573 | − | 0.893244i | \(-0.351576\pi\) | |||||||
\(578\) | 8.21332 | + | 16.1195i | 0.341629 | + | 0.670485i | ||||
\(579\) | −4.10739 | + | 29.8413i | −0.170697 | + | 1.24016i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 75.0092 | − | 24.3720i | 3.11190 | − | 1.01112i | ||||
\(582\) | 0.370448 | + | 18.2480i | 0.0153556 | + | 0.756405i | ||||
\(583\) | 3.20506 | + | 8.24295i | 0.132740 | + | 0.341388i | ||||
\(584\) | −9.48489 | −0.392487 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.7834 | − | 16.5531i | −0.941174 | − | 0.683803i | ||||
\(587\) | 6.14738 | + | 0.973649i | 0.253729 | + | 0.0401868i | 0.282003 | − | 0.959413i | \(-0.409001\pi\) |
−0.0282739 | + | 0.999600i | \(0.509001\pi\) | |||||||
\(588\) | −20.7755 | − | 6.28715i | −0.856768 | − | 0.259278i | ||||
\(589\) | 15.4832 | + | 5.03081i | 0.637975 | + | 0.207291i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −34.2375 | + | 6.13747i | −1.40834 | + | 0.252462i | ||||
\(592\) | −4.88069 | − | 2.48684i | −0.200595 | − | 0.102208i | ||||
\(593\) | 22.4284 | − | 22.4284i | 0.921024 | − | 0.921024i | −0.0760779 | − | 0.997102i | \(-0.524240\pi\) |
0.997102 | + | 0.0760779i | \(0.0242398\pi\) | |||||||
\(594\) | −19.6060 | + | 2.31575i | −0.804444 | + | 0.0950166i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.96169 | + | 0.962312i | −0.121316 | + | 0.0394178i | ||||
\(597\) | −3.36262 | − | 2.34030i | −0.137623 | − | 0.0957822i | ||||
\(598\) | −6.00533 | − | 0.951151i | −0.245576 | − | 0.0388955i | ||||
\(599\) | −8.57757 | + | 26.3990i | −0.350470 | + | 1.07864i | 0.608120 | + | 0.793845i | \(0.291924\pi\) |
−0.958590 | + | 0.284790i | \(0.908076\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.66252 | + | 1.20790i | −0.0678158 | + | 0.0492711i | −0.621177 | − | 0.783671i | \(-0.713345\pi\) |
0.553361 | + | 0.832942i | \(0.313345\pi\) | |||||||
\(602\) | −8.81709 | − | 55.6689i | −0.359358 | − | 2.26890i | ||||
\(603\) | 6.38181 | + | 2.93180i | 0.259888 | + | 0.119392i | ||||
\(604\) | − | 10.1963i | − | 0.414883i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −19.2410 | − | 18.4753i | −0.781613 | − | 0.750510i | ||||
\(607\) | −31.0024 | − | 15.7965i | −1.25835 | − | 0.641161i | −0.307716 | − | 0.951478i | \(-0.599565\pi\) |
−0.950633 | + | 0.310318i | \(0.899565\pi\) | |||||||
\(608\) | 17.6174 | − | 2.79033i | 0.714482 | − | 0.113163i | ||||
\(609\) | 67.7711 | + | 9.32810i | 2.74622 | + | 0.377994i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.98738 | − | 2.59526i | −0.323135 | − | 0.104993i | ||||
\(612\) | 0.263467 | − | 2.25159i | 0.0106500 | − | 0.0910153i | ||||
\(613\) | 6.30583 | + | 39.8135i | 0.254690 | + | 1.60805i | 0.700993 | + | 0.713168i | \(0.252740\pi\) |
−0.446303 | + | 0.894882i | \(0.647260\pi\) | |||||||
\(614\) | −7.42049 | − | 22.8379i | −0.299467 | − | 0.921663i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −34.1520 | + | 38.2605i | −1.37602 | + | 1.54156i | ||||
\(617\) | −16.1295 | − | 16.1295i | −0.649350 | − | 0.649350i | 0.303486 | − | 0.952836i | \(-0.401850\pi\) |
−0.952836 | + | 0.303486i | \(0.901850\pi\) | |||||||
\(618\) | −0.167336 | − | 0.481526i | −0.00673125 | − | 0.0193698i | ||||
\(619\) | −24.6397 | + | 33.9136i | −0.990352 | + | 1.36310i | −0.0592909 | + | 0.998241i | \(0.518884\pi\) |
−0.931061 | + | 0.364862i | \(0.881116\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.5719 | − | 9.16849i | 0.624877 | − | 0.367919i | ||||
\(622\) | 6.53917 | + | 12.8338i | 0.262197 | + | 0.514590i | ||||
\(623\) | −12.8791 | + | 81.3155i | −0.515991 | + | 3.25784i | ||||
\(624\) | 5.59871 | − | 1.00363i | 0.224128 | − | 0.0401775i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 39.1921i | 1.56643i | ||||||||
\(627\) | 10.6584 | − | 25.6181i | 0.425655 | − | 1.02309i | ||||
\(628\) | 0.488846 | + | 0.488846i | 0.0195071 | + | 0.0195071i | ||||
\(629\) | −0.864429 | − | 2.66044i | −0.0344671 | − | 0.106079i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.8060 | + | 20.9288i | −1.14675 | + | 0.833161i | −0.988045 | − | 0.154166i | \(-0.950731\pi\) |
−0.158703 | + | 0.987326i | \(0.550731\pi\) | |||||||
\(632\) | −29.1245 | + | 14.8397i | −1.15851 | + | 0.590290i | ||||
\(633\) | 23.8098 | + | 7.20540i | 0.946356 | + | 0.286389i | ||||
\(634\) | 12.8068 | + | 17.6270i | 0.508622 | + | 0.700059i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.85870 | + | 1.38423i | 0.113355 | + | 0.0548882i | ||||
\(637\) | 19.6664 | − | 19.6664i | 0.779211 | − | 0.779211i | ||||
\(638\) | 16.1652 | − | 25.1290i | 0.639987 | − | 0.994868i | ||||
\(639\) | 1.56658 | + | 38.5684i | 0.0619729 | + | 1.52574i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.1215 | + | 15.3074i | −0.439273 | + | 0.604607i | −0.970050 | − | 0.242904i | \(-0.921900\pi\) |
0.530778 | + | 0.847511i | \(0.321900\pi\) | |||||||
\(642\) | 15.4164 | − | 11.6860i | 0.608438 | − | 0.461210i | ||||
\(643\) | −22.6393 | + | 11.5353i | −0.892808 | + | 0.454908i | −0.839306 | − | 0.543659i | \(-0.817038\pi\) |
−0.0535022 | + | 0.998568i | \(0.517038\pi\) | |||||||
\(644\) | 3.71161 | − | 11.4232i | 0.146258 | − | 0.450135i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.91890 | − | 3.57379i | −0.193531 | − | 0.140609i | ||||
\(647\) | 13.5047 | − | 26.5045i | 0.530925 | − | 1.04200i | −0.457346 | − | 0.889289i | \(-0.651200\pi\) |
0.988271 | − | 0.152710i | \(-0.0488000\pi\) | |||||||
\(648\) | −17.9404 | + | 21.1187i | −0.704766 | + | 0.829620i | ||||
\(649\) | −13.7974 | − | 1.38998i | −0.541595 | − | 0.0545615i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.7779 | + | 26.3889i | −0.500807 | + | 1.03426i | ||||
\(652\) | 4.13903 | − | 0.655558i | 0.162097 | − | 0.0256736i | ||||
\(653\) | −1.55945 | + | 9.84599i | −0.0610261 | + | 0.385303i | 0.938204 | + | 0.346082i | \(0.112488\pi\) |
−0.999231 | + | 0.0392220i | \(0.987512\pi\) | |||||||
\(654\) | −27.3070 | + | 14.6192i | −1.06779 | + | 0.571655i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.67598 | − | 5.05955i | −0.143523 | − | 0.197542i | ||||
\(657\) | 1.81500 | + | 9.06181i | 0.0708099 | + | 0.353535i | ||||
\(658\) | −14.3733 | + | 28.2093i | −0.560331 | + | 1.09971i | ||||
\(659\) | 6.35103 | 0.247401 | 0.123701 | − | 0.992320i | \(-0.460524\pi\) | ||||
0.123701 | + | 0.992320i | \(0.460524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.7960 | −0.497706 | −0.248853 | − | 0.968541i | \(-0.580054\pi\) | ||||
−0.248853 | + | 0.968541i | \(0.580054\pi\) | |||||||
\(662\) | −4.51272 | + | 8.85671i | −0.175392 | + | 0.344226i | ||||
\(663\) | 2.38413 | + | 1.65930i | 0.0925919 | + | 0.0644418i | ||||
\(664\) | −28.4198 | − | 39.1166i | −1.10290 | − | 1.51802i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.36364 | + | 8.42358i | −0.0915893 | + | 0.326407i | ||||
\(667\) | −4.27837 | + | 27.0126i | −0.165659 | + | 1.04593i | ||||
\(668\) | −1.08003 | + | 0.171060i | −0.0417876 | + | 0.00661851i | ||||
\(669\) | 34.5454 | + | 16.7275i | 1.33560 | + | 0.646721i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.06720 | − | 0.622305i | 0.0411988 | − | 0.0240238i | ||||
\(672\) | 0.652005 | + | 32.1173i | 0.0251516 | + | 1.23895i | ||||
\(673\) | −3.92516 | + | 7.70355i | −0.151304 | + | 0.296950i | −0.954201 | − | 0.299168i | \(-0.903291\pi\) |
0.802897 | + | 0.596118i | \(0.203291\pi\) | |||||||
\(674\) | −1.14582 | − | 0.832487i | −0.0441353 | − | 0.0320662i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.26759 | + | 6.97893i | −0.0872151 | + | 0.268421i | ||||
\(677\) | 8.95043 | − | 4.56047i | 0.343993 | − | 0.175273i | −0.273455 | − | 0.961885i | \(-0.588167\pi\) |
0.617448 | + | 0.786612i | \(0.288167\pi\) | |||||||
\(678\) | 16.5509 | + | 21.8342i | 0.635632 | + | 0.838538i | ||||
\(679\) | 27.1548 | − | 37.3754i | 1.04211 | − | 1.43433i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.8716 | − | 14.4465i | 0.531561 | − | 0.553591i | ||||
\(682\) | 8.10196 | + | 9.91726i | 0.310240 | + | 0.379752i | ||||
\(683\) | 0.790707 | − | 0.790707i | 0.0302555 | − | 0.0302555i | −0.691817 | − | 0.722073i | \(-0.743190\pi\) |
0.722073 | + | 0.691817i | \(0.243190\pi\) | |||||||
\(684\) | −3.46136 | − | 9.34427i | −0.132349 | − | 0.357287i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −37.9549 | − | 52.2404i | −1.44912 | − | 1.99455i | ||||
\(687\) | −0.262286 | + | 0.866708i | −0.0100068 | + | 0.0330670i | ||||
\(688\) | −18.7819 | + | 9.56985i | −0.716053 | + | 0.364847i | ||||
\(689\) | −3.29250 | + | 2.39214i | −0.125434 | + | 0.0911332i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.96578 | + | 27.5938i | 0.341074 | + | 1.04972i | 0.963652 | + | 0.267161i | \(0.0860855\pi\) |
−0.622578 | + | 0.782558i | \(0.713914\pi\) | |||||||
\(692\) | 3.95937 | + | 3.95937i | 0.150513 | + | 0.150513i | ||||
\(693\) | 43.0891 | + | 25.3072i | 1.63682 | + | 0.961342i | ||||
\(694\) | − | 12.1522i | − | 0.461290i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.40004 | − | 41.2807i | −0.280498 | − | 1.56474i | ||||
\(697\) | 0.499612 | − | 3.15442i | 0.0189241 | − | 0.119482i | ||||
\(698\) | −2.03989 | − | 4.00351i | −0.0772110 | − | 0.151535i | ||||
\(699\) | −27.6877 | + | 14.8230i | −1.04725 | + | 0.560658i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.2636 | + | 30.6433i | −0.840886 | + | 1.15738i | 0.144912 | + | 0.989445i | \(0.453710\pi\) |
−0.985798 | + | 0.167936i | \(0.946290\pi\) | |||||||
\(702\) | −3.32792 | − | 8.45319i | −0.125604 | − | 0.319045i | ||||
\(703\) | −8.69473 | − | 8.69473i | −0.327928 | − | 0.327928i | ||||
\(704\) | 25.9062 | + | 11.4004i | 0.976376 | + | 0.429671i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.0519 | − | 40.1695i | −0.491213 | − | 1.51180i | ||||
\(707\) | 10.5623 | + | 66.6878i | 0.397237 | + | 2.50805i | ||||
\(708\) | −3.96878 | + | 3.00843i | −0.149156 | + | 0.113064i | ||||
\(709\) | −13.2635 | − | 4.30956i | −0.498120 | − | 0.161849i | 0.0491728 | − | 0.998790i | \(-0.484342\pi\) |
−0.547293 | + | 0.836941i | \(0.684342\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.7509 | + | 24.9857i | 0.740717 | + | 0.937037i | ||||
\(712\) | 49.8504 | − | 7.89552i | 1.86822 | − | 0.295897i | ||||
\(713\) | −10.4440 | − | 5.32150i | −0.391132 | − | 0.199292i | ||||
\(714\) | 7.58410 | − | 7.89841i | 0.283828 | − | 0.295591i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 6.51348i | − | 0.243420i | ||||||
\(717\) | 14.3492 | − | 4.98652i | 0.535880 | − | 0.186225i | ||||
\(718\) | −2.16599 | − | 13.6755i | −0.0808341 | − | 0.510367i | ||||
\(719\) | −16.1823 | + | 11.7572i | −0.603500 | + | 0.438468i | −0.847119 | − | 0.531403i | \(-0.821665\pi\) |
0.243620 | + | 0.969871i | \(0.421665\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.398733 | + | 1.22717i | −0.0148496 | + | 0.0457023i | ||||
\(722\) | −4.89921 | − | 0.775958i | −0.182330 | − | 0.0288782i | ||||
\(723\) | −9.70555 | + | 13.9452i | −0.360953 | + | 0.518629i | ||||
\(724\) | 3.40043 | − | 1.10487i | 0.126376 | − | 0.0410621i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 17.9533 | − | 12.4118i | 0.666308 | − | 0.460644i | ||||
\(727\) | −30.1567 | + | 30.1567i | −1.11845 | + | 1.11845i | −0.126479 | + | 0.991969i | \(0.540368\pi\) |
−0.991969 | + | 0.126479i | \(0.959632\pi\) | |||||||
\(728\) | −21.0276 | − | 10.7141i | −0.779334 | − | 0.397091i | ||||
\(729\) | 23.6097 | + | 13.0990i | 0.874433 | + | 0.485147i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.2379 | − | 3.32650i | −0.378663 | − | 0.123035i | ||||
\(732\) | 0.128508 | − | 0.424646i | 0.00474978 | − | 0.0156954i | ||||
\(733\) | 36.5897 | + | 5.79524i | 1.35147 | + | 0.214052i | 0.789828 | − | 0.613328i | \(-0.210170\pi\) |
0.561642 | + | 0.827380i | \(0.310170\pi\) | |||||||
\(734\) | −14.4878 | − | 10.5260i | −0.534753 | − | 0.388521i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.8427 | −0.473386 | ||||||||
\(737\) | −7.75179 | + | 0.439812i | −0.285541 | + | 0.0162007i | ||||
\(738\) | −6.77058 | + | 7.34388i | −0.249229 | + | 0.270332i | ||||
\(739\) | 22.9863 | − | 7.46870i | 0.845565 | − | 0.274741i | 0.145978 | − | 0.989288i | \(-0.453367\pi\) |
0.699587 | + | 0.714547i | \(0.253367\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.6489 | + | 1.74100i | 0.464667 | + | 0.0639573i | ||||
\(742\) | 6.96510 | + | 13.6698i | 0.255697 | + | 0.501833i | ||||
\(743\) | 18.0674 | + | 35.4592i | 0.662828 | + | 1.30087i | 0.940368 | + | 0.340159i | \(0.110481\pi\) |
−0.277540 | + | 0.960714i | \(0.589519\pi\) | |||||||
\(744\) | 17.8066 | + | 2.45092i | 0.652821 | + | 0.0898551i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.73948 | + | 0.565191i | −0.0636869 | + | 0.0206931i | ||||
\(747\) | −31.9334 | + | 34.6374i | −1.16838 | + | 1.26732i | ||||
\(748\) | 0.908237 | + | 2.33585i | 0.0332084 | + | 0.0854073i | ||||
\(749\) | −48.9656 | −1.78916 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.1678 | + | 17.5589i | 0.881894 | + | 0.640733i | 0.933752 | − | 0.357921i | \(-0.116514\pi\) |
−0.0518579 | + | 0.998654i | \(0.516514\pi\) | |||||||
\(752\) | 11.6949 | + | 1.85229i | 0.426469 | + | 0.0675460i | ||||
\(753\) | −3.29260 | + | 10.8802i | −0.119989 | + | 0.396497i | ||||
\(754\) | 13.0765 | + | 4.24881i | 0.476218 | + | 0.154733i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 17.5216 | − | 3.88089i | 0.637253 | − | 0.141147i | ||||
\(757\) | 48.0604 | + | 24.4880i | 1.74678 | + | 0.890031i | 0.963217 | + | 0.268725i | \(0.0866022\pi\) |
0.783568 | + | 0.621307i | \(0.213398\pi\) | |||||||
\(758\) | −19.7910 | + | 19.7910i | −0.718841 | + | 0.718841i | ||||
\(759\) | −10.4650 | + | 17.0174i | −0.379855 | + | 0.617694i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.5187 | − | 11.5407i | 1.28755 | − | 0.418351i | 0.416318 | − | 0.909219i | \(-0.363320\pi\) |
0.871234 | + | 0.490868i | \(0.163320\pi\) | |||||||
\(762\) | 14.6744 | − | 21.0846i | 0.531596 | − | 0.763814i | ||||
\(763\) | 77.4356 | + | 12.2646i | 2.80336 | + | 0.444008i | ||||
\(764\) | −0.650542 | + | 2.00216i | −0.0235358 | + | 0.0724357i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.2589 | − | 13.9924i | 0.695851 | − | 0.505566i | ||||
\(767\) | −0.998238 | − | 6.30263i | −0.0360443 | − | 0.227575i | ||||
\(768\) | 23.4441 | − | 8.14713i | 0.845967 | − | 0.293984i | ||||
\(769\) | 36.6929i | 1.32318i | 0.749867 | + | 0.661589i | \(0.230118\pi\) | ||||
−0.749867 | + | 0.661589i | \(0.769882\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.06930 | + | 7.36227i | −0.254595 | + | 0.265146i | ||||
\(772\) | −10.6562 | − | 5.42960i | −0.383524 | − | 0.195415i | ||||
\(773\) | −41.2415 | + | 6.53201i | −1.48335 | + | 0.234940i | −0.844984 | − | 0.534791i | \(-0.820390\pi\) |
−0.638368 | + | 0.769731i | \(0.720390\pi\) | |||||||
\(774\) | 20.8784 | + | 26.4121i | 0.750460 | + | 0.949362i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −26.9358 | − | 8.75196i | −0.966937 | − | 0.314177i | ||||
\(777\) | 17.6478 | − | 13.3775i | 0.633113 | − | 0.479914i | ||||
\(778\) | 2.36237 | + | 14.9154i | 0.0846952 | + | 0.534745i | ||||
\(779\) | −4.33817 | − | 13.3515i | −0.155431 | − | 0.478367i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.4964 | − | 36.8645i | −0.769201 | − | 1.31911i | ||||
\(782\) | 3.09547 | + | 3.09547i | 0.110694 | + | 0.110694i | ||||
\(783\) | −38.0233 | + | 14.9693i | −1.35884 | + | 0.534960i | ||||
\(784\) | −23.0482 | + | 31.7231i | −0.823150 | + | 1.13297i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −21.9021 | + | 11.7256i | −0.781223 | + | 0.418239i | ||||
\(787\) | −4.19956 | − | 8.24210i | −0.149698 | − | 0.293799i | 0.803964 | − | 0.594677i | \(-0.202720\pi\) |
−0.953663 | + | 0.300878i | \(0.902720\pi\) | |||||||
\(788\) | 2.16038 | − | 13.6401i | 0.0769604 | − | 0.485909i | ||||
\(789\) | 1.20145 | + | 6.70223i | 0.0427728 | + | 0.238606i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 69.3498i | − | 2.46580i | ||||||
\(792\) | 6.59233 | − | 29.9171i | 0.234248 | − | 1.06306i | ||||
\(793\) | 0.401976 | + | 0.401976i | 0.0142746 | + | 0.0142746i | ||||
\(794\) | −1.81586 | − | 5.58864i | −0.0644424 | − | 0.198333i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.31594 | − | 0.956085i | 0.0466422 | − | 0.0338875i | ||||
\(797\) | −13.1056 | + | 6.67761i | −0.464223 | + | 0.236533i | −0.670427 | − | 0.741976i | \(-0.733889\pi\) |
0.206204 | + | 0.978509i | \(0.433889\pi\) | |||||||
\(798\) | 13.9416 | − | 46.0693i | 0.493528 | − | 1.63084i | ||||
\(799\) | 3.55420 | + | 4.89193i | 0.125738 | + | 0.173064i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.0826 | − | 46.1159i | −0.603583 | − | 1.62943i | ||||
\(802\) | 3.45987 | − | 3.45987i | 0.122172 | − | 0.122172i | ||||
\(803\) | −6.46409 | − | 7.91242i | −0.228113 | − | 0.279223i | ||||
\(804\) | −1.93126 | + | 2.01130i | −0.0681103 | + | 0.0709329i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.46374 | + | 4.76742i | −0.122005 | + | 0.167925i | ||||
\(807\) | −16.3680 | − | 21.5931i | −0.576183 | − | 0.760112i | ||||
\(808\) | 36.8810 | − | 18.7918i | 1.29747 | − | 0.661093i | ||||
\(809\) | 4.82410 | − | 14.8470i | 0.169606 | − | 0.521994i | −0.829740 | − | 0.558150i | \(-0.811511\pi\) |
0.999346 | + | 0.0361560i | \(0.0115113\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.2062 | + | 13.2276i | 0.639307 | + | 0.464483i | 0.859612 | − | 0.510948i | \(-0.170705\pi\) |
−0.220305 | + | 0.975431i | \(0.570705\pi\) | |||||||
\(812\) | −12.3309 | + | 24.2007i | −0.432729 | + | 0.849279i | ||||
\(813\) | −0.126307 | − | 6.22181i | −0.00442979 | − | 0.218208i | ||||
\(814\) | −2.05180 | − | 9.45216i | −0.0719155 | − | 0.331298i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.68589 | − | 1.78477i | −0.129032 | − | 0.0624793i | ||||
\(817\) | −46.7357 | + | 7.40220i | −1.63507 | + | 0.258970i | ||||
\(818\) | 0.932564 | − | 5.88798i | 0.0326063 | − | 0.205868i | ||||
\(819\) | −6.21241 | + | 22.1399i | −0.217079 | + | 0.773629i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.36504 | − | 6.00796i | −0.152341 | − | 0.209679i | 0.726025 | − | 0.687669i | \(-0.241366\pi\) |
−0.878366 | + | 0.477989i | \(0.841366\pi\) | |||||||
\(822\) | −27.9829 | − | 19.4755i | −0.976017 | − | 0.679285i | ||||
\(823\) | 8.47092 | − | 16.6251i | 0.295278 | − | 0.579515i | −0.694937 | − | 0.719071i | \(-0.744568\pi\) |
0.990214 | + | 0.139556i | \(0.0445676\pi\) | |||||||
\(824\) | 0.791032 | 0.0275569 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.0555 | −0.836999 | ||||||||
\(827\) | −11.1556 | + | 21.8940i | −0.387917 | + | 0.761329i | −0.999556 | − | 0.0298079i | \(-0.990510\pi\) |
0.611639 | + | 0.791137i | \(0.290510\pi\) | |||||||
\(828\) | 1.40903 | + | 7.03489i | 0.0489671 | + | 0.244479i | ||||
\(829\) | 3.85643 | + | 5.30792i | 0.133939 | + | 0.184352i | 0.870719 | − | 0.491782i | \(-0.163654\pi\) |
−0.736779 | + | 0.676134i | \(0.763654\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.98645 | − | 3.74029i | 0.242357 | − | 0.129749i | ||||
\(832\) | −2.03746 | + | 12.8640i | −0.0706361 | + | 0.445979i | ||||
\(833\) | −19.7781 | + | 3.13254i | −0.685270 | + | 0.108536i | ||||
\(834\) | 8.70312 | − | 17.9736i | 0.301364 | − | 0.622376i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.21856 | + | 7.33604i | 0.284245 | + | 0.253722i | ||||
\(837\) | −1.06582 | − | 17.4813i | −0.0368402 | − | 0.604243i | ||||
\(838\) | 12.8614 | − | 25.2420i | 0.444291 | − | 0.871971i | ||||
\(839\) | −27.7296 | − | 20.1467i | −0.957331 | − | 0.695542i | −0.00480151 | − | 0.999988i | \(-0.501528\pi\) |
−0.952529 | + | 0.304447i | \(0.901528\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.1501 | − | 31.2387i | 0.350003 | − | 1.07720i | ||||
\(842\) | −34.9254 | + | 17.7954i | −1.20361 | + | 0.613270i | ||||
\(843\) | −9.08580 | + | 6.88725i | −0.312931 | + | 0.237209i | ||||
\(844\) | −5.80538 | + | 7.99042i | −0.199829 | + | 0.275042i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.767524 | − | 18.8961i | −0.0263880 | − | 0.649661i | ||||
\(847\) | −55.1925 | − | 2.41497i | −1.89644 | − | 0.0829794i | ||||
\(848\) | 4.05724 | − | 4.05724i | 0.139326 | − | 0.139326i | ||||
\(849\) | −14.8959 | − | 7.21282i | −0.511225 | − | 0.247543i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.20381 | + | 7.16243i | 0.178384 | + | 0.245525i | ||||
\(852\) | −14.6686 | − | 4.43906i | −0.502539 | − | 0.152080i | ||||
\(853\) | −16.9268 | + | 8.62463i | −0.579562 | + | 0.295302i | −0.719091 | − | 0.694916i | \(-0.755441\pi\) |
0.139528 | + | 0.990218i | \(0.455441\pi\) | |||||||
\(854\) | 1.73375 | − | 1.25964i | 0.0593276 | − | 0.0431040i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.27617 | + | 28.5491i | 0.317053 | + | 0.975789i | ||||
\(857\) | 13.1921 | + | 13.1921i | 0.450633 | + | 0.450633i | 0.895564 | − | 0.444932i | \(-0.146772\pi\) |
−0.444932 | + | 0.895564i | \(0.646772\pi\) | |||||||
\(858\) | 7.62691 | + | 6.53468i | 0.260379 | + | 0.223090i | ||||
\(859\) | 27.5227i | 0.939062i | 0.882916 | + | 0.469531i | \(0.155577\pi\) | ||||
−0.882916 | + | 0.469531i | \(0.844423\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.8864 | − | 4.46117i | 0.848125 | − | 0.152036i | ||||
\(862\) | −1.59156 | + | 10.0487i | −0.0542088 | + | 0.342261i | ||||
\(863\) | −13.9133 | − | 27.3064i | −0.473615 | − | 0.929521i | −0.996998 | − | 0.0774238i | \(-0.975331\pi\) |
0.523384 | − | 0.852097i | \(-0.324669\pi\) | |||||||
\(864\) | −9.73586 | − | 16.5355i | −0.331221 | − | 0.562549i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.15393 | + | 4.34101i | −0.107175 | + | 0.147514i | ||||
\(867\) | 8.97897 | + | 25.8378i | 0.304942 | + | 0.877498i | ||||
\(868\) | −8.23140 | − | 8.23140i | −0.279392 | − | 0.279392i | ||||
\(869\) | −32.2282 | − | 14.1826i | −1.09327 | − | 0.481110i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.10406 | − | 3.39796i | −0.0374098 | − | 0.115136i | ||||
\(872\) | −7.51879 | − | 47.4718i | −0.254619 | − | 1.60760i | ||||
\(873\) | −3.20723 | + | 27.4090i | −0.108548 | + | 0.927655i | ||||
\(874\) | 18.3009 | + | 5.94632i | 0.619036 | + | 0.201137i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.63503 | − | 0.500330i | −0.122816 | − | 0.0169046i | ||||
\(877\) | 6.21947 | − | 0.985067i | 0.210016 | − | 0.0332633i | −0.0505396 | − | 0.998722i | \(-0.516094\pi\) |
0.260556 | + | 0.965459i | \(0.416094\pi\) | |||||||
\(878\) | 8.08975 | + | 4.12193i | 0.273016 | + | 0.139109i | ||||
\(879\) | −30.7133 | − | 29.4911i | −1.03593 | − | 0.994709i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.50803i | − | 0.0844976i | −0.999107 | − | 0.0422488i | \(-0.986548\pi\) | ||
0.999107 | − | 0.0422488i | \(-0.0134522\pi\) | |||||||
\(882\) | 56.9103 | + | 26.1446i | 1.91627 | + | 0.880334i | ||||
\(883\) | 5.41318 | + | 34.1775i | 0.182168 | + | 1.15016i | 0.894084 | + | 0.447899i | \(0.147827\pi\) |
−0.711916 | + | 0.702264i | \(0.752173\pi\) | |||||||
\(884\) | −0.933014 | + | 0.677874i | −0.0313806 | + | 0.0227994i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.47500 | − | 26.0834i | 0.284723 | − | 0.876288i | ||||
\(887\) | −11.9872 | − | 1.89858i | −0.402489 | − | 0.0637481i | −0.0480919 | − | 0.998843i | \(-0.515314\pi\) |
−0.354398 | + | 0.935095i | \(0.615314\pi\) | |||||||
\(888\) | −11.1429 | − | 7.75521i | −0.373932 | − | 0.260248i | ||||
\(889\) | −61.8396 | + | 20.0929i | −2.07403 | + | 0.673894i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29.8441 | − | 0.573432i | −0.999815 | − | 0.0192107i | ||||
\(892\) | −10.7756 | + | 10.7756i | −0.360795 | + | 0.360795i | ||||
\(893\) | 23.6825 | + | 12.0668i | 0.792504 | + | 0.403801i | ||||
\(894\) | 8.84417 | − | 1.58542i | 0.295793 | − | 0.0530244i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11.4175 | + | 3.70976i | 0.381431 | + | 0.123934i | ||||
\(897\) | −8.79894 | − | 2.66276i | −0.293788 | − | 0.0889070i | ||||
\(898\) | 5.69867 | + | 0.902580i | 0.190167 | + | 0.0301195i | ||||
\(899\) | 21.4443 | + | 15.5802i | 0.715209 | + | 0.519630i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.93017 | 0.0976180 | ||||||||
\(902\) | 2.81204 | − | 10.6788i | 0.0936308 | − | 0.355567i | ||||
\(903\) | −1.72964 | − | 85.2010i | −0.0575589 | − | 2.83531i | ||||
\(904\) | −40.4340 | + | 13.1378i | −1.34481 | + | 0.436957i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.01152 | + | 29.1448i | −0.133274 | + | 0.968270i | ||||
\(907\) | −11.1296 | − | 21.8430i | −0.369552 | − | 0.725286i | 0.629093 | − | 0.777330i | \(-0.283426\pi\) |
−0.998645 | + | 0.0520439i | \(0.983426\pi\) | |||||||
\(908\) | 3.61005 | + | 7.08512i | 0.119804 | + | 0.235128i | ||||
\(909\) | −25.0110 | − | 31.6400i | −0.829563 | − | 1.04943i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.2804 | + | 11.7882i | −1.20202 | + | 0.390561i | −0.840504 | − | 0.541805i | \(-0.817741\pi\) |
−0.361517 | + | 0.932365i | \(0.617741\pi\) | |||||||
\(912\) | −17.9976 | + | 0.365365i | −0.595961 | + | 0.0120984i | ||||
\(913\) | 13.2630 | − | 50.3667i | 0.438941 | − | 1.66689i | ||||
\(914\) | 11.2898 | 0.373434 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.290861 | − | 0.211323i | −0.00961033 | − | 0.00698231i | ||||
\(917\) | 62.1088 | + | 9.83707i | 2.05101 | + | 0.324849i | ||||
\(918\) | −1.63892 | + | 6.33220i | −0.0540925 | + | 0.208994i | ||||
\(919\) | 4.72724 | + | 1.53597i | 0.155937 | + | 0.0506670i | 0.385945 | − | 0.922522i | \(-0.373875\pi\) |
−0.230008 | + | 0.973189i | \(0.573875\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.40634 | − | 35.7374i | −0.211096 | − | 1.17759i | ||||
\(922\) | −26.1073 | − | 13.3024i | −0.859800 | − | 0.438090i | ||||
\(923\) | 13.8855 | − | 13.8855i | 0.457047 | − | 0.457047i | ||||
\(924\) | −15.1068 | + | 12.8616i | −0.496978 | + | 0.423115i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 21.5978 | − | 7.01754i | 0.709747 | − | 0.230611i | ||||
\(927\) | −0.151370 | − | 0.755748i | −0.00497163 | − | 0.0248220i | ||||
\(928\) | 28.6842 | + | 4.54313i | 0.941605 | + | 0.149136i | ||||
\(929\) | −14.9744 | + | 46.0863i | −0.491293 | + | 1.51204i | 0.331363 | + | 0.943504i | \(0.392492\pi\) |
−0.822655 | + | 0.568540i | \(0.807508\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −71.2108 | + | 51.7377i | −2.33384 | + | 1.69563i | ||||
\(932\) | −1.95062 | − | 12.3157i | −0.0638945 | − | 0.403414i | ||||
\(933\) | 7.14876 | + | 20.5712i | 0.234040 | + | 0.673471i | ||||
\(934\) | − | 8.80460i | − | 0.288095i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 14.0854 | − | 0.572123i | 0.460396 | − | 0.0187004i | ||||
\(937\) | 5.94379 | + | 3.02851i | 0.194175 | + | 0.0989372i | 0.548375 | − | 0.836233i | \(-0.315247\pi\) |
−0.354200 | + | 0.935170i | \(0.615247\pi\) | |||||||
\(938\) | −13.3029 | + | 2.10697i | −0.434354 | + | 0.0687949i | ||||
\(939\) | −8.08003 | + | 58.7036i | −0.263682 | + | 1.91572i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54.6261 | + | 17.7491i | 1.78076 | + | 0.578604i | 0.998989 | − | 0.0449628i | \(-0.0143169\pi\) |
0.781770 | + | 0.623566i | \(0.214317\pi\) | |||||||
\(942\) | −1.20497 | − | 1.58962i | −0.0392601 | − | 0.0517927i | ||||
\(943\) | 1.58120 | + | 9.98334i | 0.0514911 | + | 0.325102i | ||||
\(944\) | 2.78011 | + | 8.55631i | 0.0904850 | + | 0.278484i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34.0680 | − | 14.9922i | −1.10765 | − | 0.487439i | ||||
\(947\) | −21.7413 | − | 21.7413i | −0.706499 | − | 0.706499i | 0.259298 | − | 0.965797i | \(-0.416509\pi\) |
−0.965797 | + | 0.259298i | \(0.916509\pi\) | |||||||
\(948\) | −11.9446 | + | 4.15090i | −0.387942 | + | 0.134815i | ||||
\(949\) | 2.76352 | − | 3.80366i | 0.0897076 | − | 0.123472i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.5485 | + | 29.0428i | 0.504193 | + | 0.941777i | ||||
\(952\) | 7.71401 | + | 15.1396i | 0.250012 | + | 0.490677i | ||||
\(953\) | 3.67854 | − | 23.2254i | 0.119160 | − | 0.752344i | −0.853669 | − | 0.520816i | \(-0.825628\pi\) |
0.972828 | − | 0.231528i | \(-0.0743724\pi\) | |||||||
\(954\) | −7.62659 | − | 5.08131i | −0.246920 | − | 0.164513i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.03131i | 0.195067i | ||||||||
\(957\) | 29.3936 | − | 34.3066i | 0.950162 | − | 1.10898i | ||||
\(958\) | 26.2832 | + | 26.2832i | 0.849170 | + | 0.849170i | ||||
\(959\) | 26.6668 | + | 82.0720i | 0.861116 | + | 2.65024i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.8887 | − | 11.5438i | 0.512539 | − | 0.372382i | ||||
\(962\) | 3.96573 | − | 2.02064i | 0.127860 | − | 0.0651480i | ||||
\(963\) | 25.5006 | − | 14.3255i | 0.821746 | − | 0.461632i | ||||
\(964\) | −3.96502 | − | 5.45738i | −0.127705 | − | 0.175770i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −15.1033 | + | 31.1912i | −0.485940 | + | 1.00356i | ||||
\(967\) | 22.6755 | − | 22.6755i | 0.729196 | − | 0.729196i | −0.241263 | − | 0.970460i | \(-0.577562\pi\) |
0.970460 | + | 0.241263i | \(0.0775618\pi\) | |||||||
\(968\) | 9.04776 | + | 32.6371i | 0.290806 | + | 1.04900i | ||||
\(969\) | −6.63094 | − | 6.36707i | −0.213016 | − | 0.204540i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.52745 | + | 13.1134i | −0.305751 | + | 0.420830i | −0.934050 | − | 0.357142i | \(-0.883751\pi\) |
0.628300 | + | 0.777972i | \(0.283751\pi\) | |||||||
\(972\) | −7.98958 | + | 7.14725i | −0.256266 | + | 0.229248i | ||||
\(973\) | −45.0379 | + | 22.9480i | −1.44385 | + | 0.735678i | ||||
\(974\) | 0.492766 | − | 1.51658i | 0.0157892 | − | 0.0485943i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.648412 | − | 0.471099i | −0.0207552 | − | 0.0150795i | ||||
\(977\) | −14.3972 | + | 28.2561i | −0.460606 | + | 0.903991i | 0.537546 | + | 0.843234i | \(0.319351\pi\) |
−0.998153 | + | 0.0607568i | \(0.980649\pi\) | |||||||
\(978\) | −12.0887 | + | 0.245410i | −0.386555 | + | 0.00784735i | ||||
\(979\) | 40.5603 | + | 36.2049i | 1.29631 | + | 1.15711i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −43.9155 | + | 16.2675i | −1.40212 | + | 0.519381i | ||||
\(982\) | 26.5173 | − | 4.19993i | 0.846201 | − | 0.134025i | ||||
\(983\) | −2.25168 | + | 14.2166i | −0.0718175 | + | 0.453438i | 0.925406 | + | 0.378976i | \(0.123724\pi\) |
−0.997224 | + | 0.0744616i | \(0.976276\pi\) | |||||||
\(984\) | −7.31559 | − | 13.6647i | −0.233213 | − | 0.435615i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.81874 | − | 8.00880i | −0.185306 | − | 0.255052i | ||||
\(987\) | −27.3447 | + | 39.2897i | −0.870393 | + | 1.25061i | ||||
\(988\) | −2.30145 | + | 4.51684i | −0.0732188 | + | 0.143700i | ||||
\(989\) | 34.0691 | 1.08333 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.0019 | 0.603616 | 0.301808 | − | 0.953369i | \(-0.402410\pi\) | ||||
0.301808 | + | 0.953369i | \(0.402410\pi\) | |||||||
\(992\) | −5.65081 | + | 11.0903i | −0.179413 | + | 0.352119i | ||||
\(993\) | −8.58528 | + | 12.3356i | −0.272446 | + | 0.391458i | ||||
\(994\) | −43.5120 | − | 59.8891i | −1.38012 | − | 1.89957i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.82834 | − | 16.4904i | −0.279737 | − | 0.522517i | ||||
\(997\) | 3.87662 | − | 24.4760i | 0.122774 | − | 0.775162i | −0.847078 | − | 0.531468i | \(-0.821641\pi\) |
0.969852 | − | 0.243694i | \(-0.0783594\pi\) | |||||||
\(998\) | −47.1245 | + | 7.46378i | −1.49170 | + | 0.236262i | ||||
\(999\) | −5.27701 | + | 12.1299i | −0.166957 | + | 0.383773i |
(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 | 825.2.ct.c.368.21 | yes | 256 | |
3.2 | odd | 2 | inner | 825.2.ct.c.368.11 | yes | 256 | |
5.2 | odd | 4 | inner | 825.2.ct.c.632.21 | yes | 256 | |
5.3 | odd | 4 | inner | 825.2.ct.c.632.12 | yes | 256 | |
5.4 | even | 2 | inner | 825.2.ct.c.368.12 | yes | 256 | |
11.9 | even | 5 | inner | 825.2.ct.c.218.11 | ✓ | 256 | |
15.2 | even | 4 | inner | 825.2.ct.c.632.11 | yes | 256 | |
15.8 | even | 4 | inner | 825.2.ct.c.632.22 | yes | 256 | |
15.14 | odd | 2 | inner | 825.2.ct.c.368.22 | yes | 256 | |
33.20 | odd | 10 | inner | 825.2.ct.c.218.21 | yes | 256 | |
55.9 | even | 10 | inner | 825.2.ct.c.218.22 | yes | 256 | |
55.42 | odd | 20 | inner | 825.2.ct.c.482.11 | yes | 256 | |
55.53 | odd | 20 | inner | 825.2.ct.c.482.22 | yes | 256 | |
165.53 | even | 20 | inner | 825.2.ct.c.482.12 | yes | 256 | |
165.119 | odd | 10 | inner | 825.2.ct.c.218.12 | yes | 256 | |
165.152 | even | 20 | inner | 825.2.ct.c.482.21 | yes | 256 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.ct.c.218.11 | ✓ | 256 | 11.9 | even | 5 | inner | |
825.2.ct.c.218.12 | yes | 256 | 165.119 | odd | 10 | inner | |
825.2.ct.c.218.21 | yes | 256 | 33.20 | odd | 10 | inner | |
825.2.ct.c.218.22 | yes | 256 | 55.9 | even | 10 | inner | |
825.2.ct.c.368.11 | yes | 256 | 3.2 | odd | 2 | inner | |
825.2.ct.c.368.12 | yes | 256 | 5.4 | even | 2 | inner | |
825.2.ct.c.368.21 | yes | 256 | 1.1 | even | 1 | trivial | |
825.2.ct.c.368.22 | yes | 256 | 15.14 | odd | 2 | inner | |
825.2.ct.c.482.11 | yes | 256 | 55.42 | odd | 20 | inner | |
825.2.ct.c.482.12 | yes | 256 | 165.53 | even | 20 | inner | |
825.2.ct.c.482.21 | yes | 256 | 165.152 | even | 20 | inner | |
825.2.ct.c.482.22 | yes | 256 | 55.53 | odd | 20 | inner | |
825.2.ct.c.632.11 | yes | 256 | 15.2 | even | 4 | inner | |
825.2.ct.c.632.12 | yes | 256 | 5.3 | odd | 4 | inner | |
825.2.ct.c.632.21 | yes | 256 | 5.2 | odd | 4 | inner | |
825.2.ct.c.632.22 | yes | 256 | 15.8 | even | 4 | inner |