Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,2,Mod(61,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.m (of order \(5\), degree \(4\), 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: | \(2.39551206064\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\Q(\zeta_{15})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 241.1 | ||
Root | \(0.913545 - 0.406737i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.241 |
Dual form | 300.2.m.a.61.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 | 0 | ||||||||
\(3\) | 0.309017 | + | 0.951057i | 0.178411 | + | 0.549093i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.49622 | + | 1.66172i | −0.669131 | + | 0.743145i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.78339 | −1.80795 | −0.903975 | − | 0.427585i | \(-0.859364\pi\) | ||||
−0.903975 | + | 0.427585i | \(0.859364\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.58268 | − | 1.14988i | −0.477195 | − | 0.346702i | 0.323044 | − | 0.946384i | \(-0.395294\pi\) |
−0.800239 | + | 0.599682i | \(0.795294\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.873619 | + | 0.634721i | −0.242298 | + | 0.176040i | −0.702307 | − | 0.711875i | \(-0.747846\pi\) |
0.460008 | + | 0.887915i | \(0.347846\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.04275 | − | 0.909491i | −0.527436 | − | 0.234830i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.17603 | + | 3.61946i | −0.285230 | + | 0.877848i | 0.701099 | + | 0.713064i | \(0.252693\pi\) |
−0.986330 | + | 0.164785i | \(0.947307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.31359 | − | 4.04280i | 0.301357 | − | 0.927482i | −0.679654 | − | 0.733533i | \(-0.737870\pi\) |
0.981012 | − | 0.193949i | \(-0.0621298\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.47815 | − | 4.54927i | −0.322558 | − | 0.992732i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.74346 | + | 3.44633i | 0.989080 | + | 0.718608i | 0.959719 | − | 0.280960i | \(-0.0906530\pi\) |
0.0293604 | + | 0.999569i | \(0.490653\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.522642 | − | 4.97261i | −0.104528 | − | 0.994522i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.809017 | − | 0.587785i | −0.155695 | − | 0.113119i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.26015 | + | 10.0337i | 0.605395 | + | 1.86322i | 0.494050 | + | 0.869433i | \(0.335516\pi\) |
0.111345 | + | 0.993782i | \(0.464484\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.33369 | + | 4.10468i | −0.239538 | + | 0.737223i | 0.756949 | + | 0.653474i | \(0.226689\pi\) |
−0.996487 | + | 0.0837487i | \(0.973311\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.604528 | − | 1.86055i | 0.105235 | − | 0.323880i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.15701 | − | 7.94866i | 1.20975 | − | 1.34357i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.57890 | + | 3.32676i | −0.752766 | + | 0.546917i | −0.896683 | − | 0.442673i | \(-0.854030\pi\) |
0.143917 | + | 0.989590i | \(0.454030\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.873619 | − | 0.634721i | −0.139891 | − | 0.101637i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.694596 | + | 0.504654i | −0.108478 | + | 0.0788137i | −0.640702 | − | 0.767790i | \(-0.721356\pi\) |
0.532224 | + | 0.846604i | \(0.321356\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.8764 | −1.65864 | −0.829321 | − | 0.558773i | \(-0.811272\pi\) | ||||
−0.829321 | + | 0.558773i | \(0.811272\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.233733 | − | 2.22382i | 0.0348428 | − | 0.331507i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.927539 | + | 2.85467i | 0.135295 | + | 0.416397i | 0.995636 | − | 0.0933233i | \(-0.0297490\pi\) |
−0.860340 | + | 0.509720i | \(0.829749\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.8808 | 2.26868 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.80573 | −0.532908 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.30524 | + | 4.01711i | 0.179288 | + | 0.551793i | 0.999803 | − | 0.0198323i | \(-0.00631324\pi\) |
−0.820515 | + | 0.571625i | \(0.806313\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.27882 | − | 0.909491i | 0.576956 | − | 0.122636i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.25085 | 0.563039 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.85916 | − | 2.80384i | 0.502420 | − | 0.365029i | −0.307521 | − | 0.951541i | \(-0.599499\pi\) |
0.809940 | + | 0.586512i | \(0.199499\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.93822 | − | 2.13474i | −0.376201 | − | 0.273326i | 0.383577 | − | 0.923509i | \(-0.374692\pi\) |
−0.759777 | + | 0.650183i | \(0.774692\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.86984 | − | 2.81160i | 0.487554 | − | 0.354229i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.252397 | − | 2.40140i | 0.0313060 | − | 0.297857i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.14163 | − | 6.59126i | 0.261642 | − | 0.805251i | −0.730806 | − | 0.682585i | \(-0.760856\pi\) |
0.992448 | − | 0.122666i | \(-0.0391444\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.81184 | + | 5.57627i | −0.218120 | + | 0.671304i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.70731 | − | 11.4099i | −0.439977 | − | 1.35411i | −0.887899 | − | 0.460038i | \(-0.847836\pi\) |
0.447922 | − | 0.894072i | \(-0.352164\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.7177 | + | 9.96647i | 1.60553 | + | 1.16649i | 0.875695 | + | 0.482864i | \(0.160404\pi\) |
0.729836 | + | 0.683622i | \(0.239596\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.56773 | − | 2.03368i | 0.527436 | − | 0.234830i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.57055 | + | 5.50033i | 0.862744 | + | 0.626820i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.04587 | − | 6.29656i | −0.230179 | − | 0.708418i | −0.997724 | − | 0.0674234i | \(-0.978522\pi\) |
0.767546 | − | 0.640994i | \(-0.221478\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.797847 | + | 2.45552i | −0.0875751 | + | 0.269528i | −0.985248 | − | 0.171135i | \(-0.945257\pi\) |
0.897673 | + | 0.440663i | \(0.145257\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.25493 | − | 7.36976i | −0.461512 | − | 0.799362i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.53519 | + | 6.20118i | −0.915069 | + | 0.664836i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.673699 | + | 0.489471i | 0.0714120 | + | 0.0518838i | 0.622918 | − | 0.782287i | \(-0.285947\pi\) |
−0.551507 | + | 0.834171i | \(0.685947\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.17886 | − | 3.03612i | 0.438063 | − | 0.318272i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.31592 | −0.447540 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.75260 | + | 8.23174i | 0.487606 | + | 0.844559i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.81730 | − | 8.67076i | −0.286054 | − | 0.880382i | −0.986081 | − | 0.166266i | \(-0.946829\pi\) |
0.700027 | − | 0.714116i | \(-0.253171\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.95630 | 0.196615 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.49541 | 0.148799 | 0.0743994 | − | 0.997229i | \(-0.476296\pi\) | ||||
0.0743994 | + | 0.997229i | \(0.476296\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.35664 | + | 10.3307i | 0.330739 | + | 1.01791i | 0.968783 | + | 0.247911i | \(0.0797439\pi\) |
−0.638044 | + | 0.770000i | \(0.720256\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.77126 | + | 4.35045i | 0.953577 | + | 0.424560i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.8390 | −1.91791 | −0.958954 | − | 0.283563i | \(-0.908484\pi\) | ||||
−0.958954 | + | 0.283563i | \(0.908484\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.89626 | − | 1.37771i | 0.181629 | − | 0.131961i | −0.493256 | − | 0.869884i | \(-0.664193\pi\) |
0.674885 | + | 0.737923i | \(0.264193\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.57890 | − | 3.32676i | −0.434610 | − | 0.315762i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.61192 | − | 1.89767i | 0.245709 | − | 0.178518i | −0.458114 | − | 0.888893i | \(-0.651475\pi\) |
0.703823 | + | 0.710376i | \(0.251475\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.8241 | + | 2.72585i | −1.19585 | + | 0.254187i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.333693 | − | 1.02700i | 0.0308499 | − | 0.0949463i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.62543 | − | 17.3133i | 0.515682 | − | 1.58711i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.21655 | − | 6.82184i | −0.201505 | − | 0.620167i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.694596 | − | 0.504654i | −0.0626296 | − | 0.0455031i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.04508 | + | 6.57164i | 0.809017 | + | 0.587785i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.97565 | − | 4.34156i | −0.530253 | − | 0.385251i | 0.290199 | − | 0.956966i | \(-0.406278\pi\) |
−0.820452 | + | 0.571715i | \(0.806278\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.36101 | − | 10.3441i | −0.295920 | − | 0.910748i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.21740 | + | 16.0575i | −0.455847 | + | 1.40295i | 0.414292 | + | 0.910144i | \(0.364029\pi\) |
−0.870138 | + | 0.492808i | \(0.835971\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.28339 | + | 19.3383i | −0.544839 | + | 1.67684i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.18720 | − | 0.464905i | 0.188245 | − | 0.0400126i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.679023 | + | 0.493339i | −0.0580128 | + | 0.0421488i | −0.616414 | − | 0.787422i | \(-0.711415\pi\) |
0.558401 | + | 0.829571i | \(0.311415\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.02701 | + | 6.55851i | 0.765661 | + | 0.556285i | 0.900641 | − | 0.434563i | \(-0.143097\pi\) |
−0.134980 | + | 0.990848i | \(0.543097\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.42833 | + | 1.76428i | −0.204502 | + | 0.148580i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.11251 | 0.176657 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.5512 | − | 9.59520i | −1.78973 | − | 0.796838i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.90743 | + | 15.1035i | 0.404758 | + | 1.24572i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.0277 | −1.80458 | −0.902288 | − | 0.431134i | \(-0.858114\pi\) | ||||
−0.902288 | + | 0.431134i | \(0.858114\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.7890 | 0.959378 | 0.479689 | − | 0.877439i | \(-0.340750\pi\) | ||||
0.479689 | + | 0.877439i | \(0.340750\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.17603 | − | 3.61946i | −0.0950767 | − | 0.292616i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.82535 | − | 8.35774i | −0.387581 | − | 0.671310i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.2769 | 0.899994 | 0.449997 | − | 0.893030i | \(-0.351425\pi\) | ||||
0.449997 | + | 0.893030i | \(0.351425\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.41716 | + | 2.48271i | −0.270998 | + | 0.196892i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.6898 | − | 16.4851i | −1.78821 | − | 1.29921i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.00627 | + | 5.81690i | −0.627100 | + | 0.455615i | −0.855394 | − | 0.517978i | \(-0.826685\pi\) |
0.228295 | + | 0.973592i | \(0.426685\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.18720 | + | 3.78835i | 0.170274 | + | 0.294923i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.32246 | + | 7.14780i | −0.179717 | + | 0.553113i | −0.999817 | − | 0.0191070i | \(-0.993918\pi\) |
0.820100 | + | 0.572220i | \(0.193918\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.65688 | + | 11.2547i | −0.281299 | + | 0.865748i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.31359 | + | 4.04280i | 0.100452 | + | 0.309161i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.93332 | − | 7.21698i | −0.755217 | − | 0.548697i | 0.142223 | − | 0.989835i | \(-0.454575\pi\) |
−0.897439 | + | 0.441138i | \(0.854575\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.50000 | + | 23.7859i | 0.188982 | + | 1.79805i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.85916 | + | 2.80384i | 0.290072 | + | 0.210750i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.69982 | + | 14.4646i | 0.351281 | + | 1.08113i | 0.958135 | + | 0.286318i | \(0.0924314\pi\) |
−0.606854 | + | 0.794813i | \(0.707569\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.45087 | + | 19.8537i | −0.479490 | + | 1.47572i | 0.360316 | + | 0.932830i | \(0.382669\pi\) |
−0.839806 | + | 0.542887i | \(0.817331\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.12230 | − | 3.45409i | 0.0829629 | − | 0.255333i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.32289 | − | 12.5864i | 0.0972606 | − | 0.925373i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.02323 | − | 4.37613i | 0.440462 | − | 0.320015i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.86984 | + | 2.81160i | 0.281489 | + | 0.204514i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.24803 | − | 3.08637i | 0.307377 | − | 0.223322i | −0.423393 | − | 0.905946i | \(-0.639161\pi\) |
0.730770 | + | 0.682624i | \(0.239161\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.94565 | 0.571940 | 0.285970 | − | 0.958239i | \(-0.407684\pi\) | ||||
0.285970 | + | 0.958239i | \(0.407684\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.36186 | − | 0.502029i | 0.169136 | − | 0.0359510i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.01905 | − | 12.3694i | −0.286345 | − | 0.881281i | −0.985992 | − | 0.166792i | \(-0.946659\pi\) |
0.699647 | − | 0.714489i | \(-0.253341\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.06434 | 0.0754490 | 0.0377245 | − | 0.999288i | \(-0.487989\pi\) | ||||
0.0377245 | + | 0.999288i | \(0.487989\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.93046 | 0.488837 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.5946 | − | 47.9952i | −1.09452 | − | 3.36860i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.200676 | − | 1.90930i | 0.0140158 | − | 0.133351i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.86324 | −0.407523 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.72772 | + | 4.88798i | −0.465366 | + | 0.338108i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.5791 | + | 12.0454i | 1.14135 | + | 0.829239i | 0.987307 | − | 0.158825i | \(-0.0507707\pi\) |
0.154043 | + | 0.988064i | \(0.450771\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.70587 | − | 7.05173i | 0.665035 | − | 0.483176i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.2736 | − | 18.0736i | 1.10985 | − | 1.23261i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.37957 | − | 19.6343i | 0.433073 | − | 1.33286i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.23968 | + | 16.1261i | −0.354065 | + | 1.08970i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.26994 | − | 3.90848i | −0.0854257 | − | 0.262913i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.34266 | − | 6.06130i | −0.558666 | − | 0.405895i | 0.272304 | − | 0.962211i | \(-0.412214\pi\) |
−0.830971 | + | 0.556316i | \(0.812214\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.34565 | + | 3.71572i | 0.223044 | + | 0.247715i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.6763 | + | 10.6630i | 0.974100 | + | 0.707725i | 0.956382 | − | 0.292118i | \(-0.0943600\pi\) |
0.0177176 | + | 0.999843i | \(0.494360\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.00311 | − | 9.24263i | −0.198451 | − | 0.610770i | −0.999919 | − | 0.0127320i | \(-0.995947\pi\) |
0.801468 | − | 0.598038i | \(-0.204053\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.89169 | + | 8.89972i | −0.190259 | + | 0.585558i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.86586 | + | 21.1310i | −0.449798 | + | 1.38433i | 0.427338 | + | 0.904092i | \(0.359451\pi\) |
−0.877136 | + | 0.480243i | \(0.840549\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.13148 | − | 2.72991i | −0.399973 | − | 0.178080i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.35617 | − | 3.89149i | 0.347921 | − | 0.252779i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.8871 | − | 9.36300i | −0.833595 | − | 0.605642i | 0.0869793 | − | 0.996210i | \(-0.472279\pi\) |
−0.920574 | + | 0.390568i | \(0.872279\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.98964 | − | 2.89864i | 0.256995 | − | 0.186718i | −0.451826 | − | 0.892106i | \(-0.649227\pi\) |
0.708821 | + | 0.705388i | \(0.249227\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −23.7612 | + | 26.3895i | −1.51805 | + | 1.68596i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.41848 | + | 4.36563i | 0.0902556 | + | 0.277778i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.58189 | −0.163620 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.4351 | 0.974252 | 0.487126 | − | 0.873332i | \(-0.338045\pi\) | ||||
0.487126 | + | 0.873332i | \(0.338045\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.54449 | − | 10.9088i | −0.222840 | − | 0.685832i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.69421 | − | 6.32406i | 0.356585 | − | 0.396028i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.1828 | 1.32134 | 0.660672 | − | 0.750674i | \(-0.270271\pi\) | ||||
0.660672 | + | 0.750674i | \(0.270271\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.9026 | − | 15.9132i | 1.36096 | − | 0.988798i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.53519 | − | 6.20118i | −0.528315 | − | 0.383843i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.9298 | − | 12.3002i | 1.04394 | − | 0.758465i | 0.0728867 | − | 0.997340i | \(-0.476779\pi\) |
0.971050 | + | 0.238876i | \(0.0767788\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.62825 | − | 3.84154i | −0.530029 | − | 0.235984i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.257330 | + | 0.791981i | −0.0157483 | + | 0.0484684i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.25938 | + | 13.1090i | −0.259699 | + | 0.799272i | 0.733168 | + | 0.680048i | \(0.238041\pi\) |
−0.992867 | + | 0.119225i | \(0.961959\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.25998 | + | 10.0332i | 0.198029 | + | 0.609472i | 0.999928 | + | 0.0120115i | \(0.00382346\pi\) |
−0.801898 | + | 0.597460i | \(0.796177\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.17886 | + | 3.03612i | 0.252916 | + | 0.183754i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.89074 | + | 8.47101i | −0.294923 | + | 0.510821i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.5317 | − | 10.5579i | −0.873127 | − | 0.634364i | 0.0582969 | − | 0.998299i | \(-0.481433\pi\) |
−0.931424 | + | 0.363935i | \(0.881433\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.33369 | − | 4.10468i | −0.0798461 | − | 0.245741i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.286375 | + | 0.881371i | −0.0170837 | + | 0.0525782i | −0.959235 | − | 0.282610i | \(-0.908800\pi\) |
0.942151 | + | 0.335188i | \(0.108800\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.03256 | + | 6.25556i | −0.120823 | + | 0.371855i | −0.993117 | − | 0.117127i | \(-0.962632\pi\) |
0.872294 | + | 0.488982i | \(0.162632\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.36022 | + | 7.06374i | −0.376747 | + | 0.418420i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.32252 | − | 2.41395i | 0.196122 | − | 0.142491i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.03585 | + | 1.47913i | 0.119756 | + | 0.0870076i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.37579 | − | 5.35882i | 0.432376 | − | 0.314140i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.6208 | 1.49678 | 0.748391 | − | 0.663257i | \(-0.230827\pi\) | ||||
0.748391 | + | 0.663257i | \(0.230827\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.11495 | + | 10.6080i | −0.0649148 | + | 0.617623i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.604528 | + | 1.86055i | 0.0350783 | + | 0.107960i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.33143 | −0.366156 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 52.0262 | 2.99874 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.462107 | + | 1.42222i | 0.0265474 | + | 0.0817044i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.94358 | − | 1.68846i | 0.454848 | − | 0.0966809i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.18420 | −0.352951 | −0.176476 | − | 0.984305i | \(-0.556470\pi\) | ||||
−0.176476 | + | 0.984305i | \(0.556470\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.78779 | + | 6.38470i | −0.499920 | + | 0.363213i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.6091 | + | 14.2468i | 1.11193 | + | 0.807864i | 0.982966 | − | 0.183785i | \(-0.0588351\pi\) |
0.128963 | + | 0.991649i | \(0.458835\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.2392 | − | 17.6108i | 1.37008 | − | 0.995420i | 0.372347 | − | 0.928094i | \(-0.378553\pi\) |
0.997731 | − | 0.0673262i | \(-0.0214468\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.11803 | + | 10.6374i | −0.0629941 | + | 0.599349i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.761007 | − | 2.34214i | 0.0427424 | − | 0.131548i | −0.927408 | − | 0.374051i | \(-0.877969\pi\) |
0.970151 | + | 0.242503i | \(0.0779685\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.37782 | − | 19.6289i | 0.357090 | − | 1.09901i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.13058 | − | 18.8680i | −0.342176 | − | 1.05311i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.0879 | + | 9.50894i | 0.728232 | + | 0.529092i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.61281 | + | 4.01243i | 0.200403 | + | 0.222570i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.89626 | + | 1.37771i | 0.104863 | + | 0.0761878i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.43678 | − | 13.6550i | −0.244607 | − | 0.752824i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.27755 | + | 25.4757i | −0.454975 | + | 1.40027i | 0.416189 | + | 0.909278i | \(0.363366\pi\) |
−0.871164 | + | 0.490992i | \(0.836634\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.74898 | − | 5.38282i | 0.0958437 | − | 0.294977i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.74850 | + | 13.4208i | 0.423346 | + | 0.733256i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.97124 | + | 1.43219i | −0.107381 | + | 0.0780165i | −0.640180 | − | 0.768225i | \(-0.721140\pi\) |
0.532799 | + | 0.846242i | \(0.321140\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.61192 | + | 1.89767i | 0.141860 | + | 0.103067i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.83070 | − | 4.96280i | 0.369903 | − | 0.268751i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −42.4802 | −2.29372 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.55530 | − | 11.3541i | −0.352925 | − | 0.611285i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.36011 | − | 7.26368i | −0.126698 | − | 0.389935i | 0.867509 | − | 0.497421i | \(-0.165720\pi\) |
−0.994207 | + | 0.107487i | \(0.965720\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.2283 | −1.08280 | −0.541398 | − | 0.840766i | \(-0.682105\pi\) | ||||
−0.541398 | + | 0.840766i | \(0.682105\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.07985 | 0.0576383 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.74279 | − | 26.9075i | −0.465331 | − | 1.43214i | −0.858565 | − | 0.512705i | \(-0.828644\pi\) |
0.393234 | − | 0.919439i | \(-0.371356\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.5071 | + | 10.9113i | 1.30070 | + | 0.579110i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.2043 | 0.963472 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.4713 | + | 13.4202i | −0.974880 | + | 0.708292i | −0.956559 | − | 0.291540i | \(-0.905832\pi\) |
−0.0183215 | + | 0.999832i | \(0.505832\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.752597 | + | 0.546793i | 0.0396103 | + | 0.0287786i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.80301 | − | 4.21613i | 0.304579 | − | 0.221289i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −37.0862 | + | 7.88291i | −1.94118 | + | 0.412610i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.778091 | + | 2.39472i | −0.0406160 | + | 0.125003i | −0.969309 | − | 0.245847i | \(-0.920934\pi\) |
0.928693 | + | 0.370851i | \(0.120934\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.265312 | − | 0.816547i | 0.0138116 | − | 0.0425077i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.24346 | − | 19.2154i | −0.324144 | − | 0.997614i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.57416 | − | 3.32332i | −0.236841 | − | 0.172075i | 0.463034 | − | 0.886341i | \(-0.346761\pi\) |
−0.699875 | + | 0.714265i | \(0.746761\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.45492 | + | 10.6331i | −0.178411 | + | 0.549093i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.21675 | − | 6.69636i | −0.474687 | − | 0.344880i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.44729 | − | 13.6874i | −0.228442 | − | 0.703073i | −0.997924 | − | 0.0644039i | \(-0.979485\pi\) |
0.769482 | − | 0.638669i | \(-0.220515\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.28249 | − | 7.02479i | 0.116936 | − | 0.359891i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.53391 | + | 7.79859i | −0.129477 | + | 0.398489i | −0.994690 | − | 0.102915i | \(-0.967183\pi\) |
0.865213 | + | 0.501404i | \(0.167183\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.4672 | + | 4.35045i | −1.04311 | + | 0.221719i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.79923 | − | 6.39301i | 0.447290 | − | 0.324975i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.82719 | − | 2.78062i | −0.194046 | − | 0.140983i | 0.486520 | − | 0.873670i | \(-0.338266\pi\) |
−0.680566 | + | 0.732687i | \(0.738266\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0523 | + | 13.1158i | −0.912945 | + | 0.663293i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.8839 | −0.851679 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.5242 | + | 6.02137i | 0.680477 | + | 0.302968i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.34336 | − | 7.21211i | −0.117610 | − | 0.361965i | 0.874873 | − | 0.484353i | \(-0.160945\pi\) |
−0.992482 | + | 0.122387i | \(0.960945\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.3335 | −1.01795 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.1128 | 0.505011 | 0.252506 | − | 0.967595i | \(-0.418745\pi\) | ||||
0.252506 | + | 0.967595i | \(0.418745\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.44019 | − | 4.43245i | −0.0717411 | − | 0.220796i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.11803 | + | 1.93649i | 0.0555556 | + | 0.0962250i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.0723 | 0.548833 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.21927 | + | 2.33894i | −0.159183 | + | 0.115653i | −0.664525 | − | 0.747266i | \(-0.731366\pi\) |
0.505342 | + | 0.862919i | \(0.331366\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.679023 | − | 0.493339i | −0.0334937 | − | 0.0243346i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.4598 | + | 13.4119i | −0.908350 | + | 0.659955i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.88664 | − | 4.99980i | −0.141699 | − | 0.245431i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.44801 | + | 10.6119i | −0.168850 | + | 0.519666i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.555164 | − | 1.70862i | 0.0271215 | − | 0.0834714i | −0.936580 | − | 0.350455i | \(-0.886027\pi\) |
0.963701 | + | 0.266984i | \(0.0860269\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.84234 | + | 14.9032i | 0.236001 | + | 0.726337i | 0.996987 | + | 0.0775686i | \(0.0247157\pi\) |
−0.760986 | + | 0.648769i | \(0.775284\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.42833 | − | 1.76428i | −0.118069 | − | 0.0857824i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.6128 | + | 3.95628i | 0.902854 | + | 0.191908i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.0546 | + | 10.2113i | 0.680152 | + | 0.494159i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.652802 | + | 2.00912i | 0.0315176 | + | 0.0970011i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.9206 | + | 36.6880i | −0.574197 | + | 1.76720i | 0.0646985 | + | 0.997905i | \(0.479391\pi\) |
−0.638896 | + | 0.769293i | \(0.720609\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.83353 | − | 8.72070i | 0.136171 | − | 0.419090i | −0.859600 | − | 0.510968i | \(-0.829287\pi\) |
0.995770 | + | 0.0918780i | \(0.0292870\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.46590 | − | 23.4615i | 0.118231 | − | 1.12489i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.1637 | − | 14.6498i | 0.964563 | − | 0.700796i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.3101 | − | 10.3969i | −0.682982 | − | 0.496216i | 0.191363 | − | 0.981519i | \(-0.438709\pi\) |
−0.874346 | + | 0.485304i | \(0.838709\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.8478 | + | 9.33449i | −0.611801 | + | 0.444500i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.6673 | −0.886912 | −0.443456 | − | 0.896296i | \(-0.646248\pi\) | ||||
−0.443456 | + | 0.896296i | \(0.646248\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.82137 | + | 0.387144i | −0.0863411 | + | 0.0183524i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.80692 | − | 20.9495i | −0.321956 | − | 0.990880i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 41.2111 | 1.94487 | 0.972436 | − | 0.233171i | \(-0.0749102\pi\) | ||||
0.972436 | + | 0.233171i | \(0.0749102\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.67961 | 0.0790899 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.64301 | + | 11.2120i | 0.171164 | + | 0.526787i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.20731 | + | 11.4868i | −0.0565997 | + | 0.538510i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.56092 | −0.260129 | −0.130064 | − | 0.991506i | \(-0.541518\pi\) | ||||
−0.130064 | + | 0.991506i | \(0.541518\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.07890 | − | 2.23695i | 0.143711 | − | 0.104412i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.1210 | − | 12.4391i | −0.797404 | − | 0.579348i | 0.112747 | − | 0.993624i | \(-0.464035\pi\) |
−0.910151 | + | 0.414276i | \(0.864035\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.26637 | − | 4.55278i | 0.291223 | − | 0.211586i | −0.432575 | − | 0.901598i | \(-0.642395\pi\) |
0.723798 | + | 0.690012i | \(0.242395\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.45757 | − | 7.17186i | 0.299463 | − | 0.332587i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.751544 | + | 2.31301i | −0.0347773 | + | 0.107034i | −0.966938 | − | 0.255011i | \(-0.917921\pi\) |
0.932161 | + | 0.362044i | \(0.117921\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.2442 | + | 31.5286i | −0.473036 | + | 1.45585i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.48475 | + | 10.7250i | 0.160569 | + | 0.494180i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.2139 | + | 12.5066i | 0.791495 | + | 0.575055i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.7898 | − | 4.41901i | −0.953902 | − | 0.202758i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.41716 | − | 2.48271i | −0.156461 | − | 0.113676i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.5465 | + | 32.4587i | 0.481880 | + | 1.48308i | 0.836449 | + | 0.548045i | \(0.184628\pi\) |
−0.354569 | + | 0.935030i | \(0.615372\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.88864 | − | 5.81265i | 0.0861148 | − | 0.265034i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.66673 | − | 26.6735i | 0.394350 | − | 1.21368i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.6237 | + | 8.29181i | 0.845659 | + | 0.376512i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.9175 | − | 18.8302i | 1.17443 | − | 0.853277i | 0.182902 | − | 0.983131i | \(-0.441451\pi\) |
0.991533 | + | 0.129854i | \(0.0414509\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.00627 | − | 5.81690i | −0.362056 | − | 0.263049i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.7860 | + | 17.2815i | −1.07345 | + | 0.779904i | −0.976529 | − | 0.215388i | \(-0.930898\pi\) |
−0.0969178 | + | 0.995292i | \(0.530898\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −40.1507 | −1.80830 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.92705 | + | 3.25082i | −0.131561 | + | 0.146113i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.7335 | + | 54.5781i | 0.795456 | + | 2.44816i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.04298 | −0.404819 | −0.202410 | − | 0.979301i | \(-0.564877\pi\) | ||||
−0.202410 | + | 0.979301i | \(0.564877\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.51564 | −0.335774 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.950848 | + | 2.92641i | 0.0423962 | + | 0.130482i | 0.970014 | − | 0.243048i | \(-0.0781473\pi\) |
−0.927618 | + | 0.373530i | \(0.878147\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.23747 | + | 2.48496i | −0.0995659 | + | 0.110579i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.8339 | −0.525563 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.2410 | + | 15.4325i | −0.941491 | + | 0.684033i | −0.948779 | − | 0.315940i | \(-0.897680\pi\) |
0.00728833 | + | 0.999973i | \(0.497680\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −65.6169 | − | 47.6735i | −2.90272 | − | 2.10895i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.43901 | + | 2.49859i | −0.151836 | + | 0.110315i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.1890 | − | 9.87917i | −0.977763 | − | 0.435328i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.81454 | − | 5.58458i | 0.0798034 | − | 0.245610i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.79419 | − | 11.6773i | 0.166547 | − | 0.512578i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.41127 | + | 19.7319i | 0.280883 | + | 0.864469i | 0.987603 | + | 0.156975i | \(0.0501742\pi\) |
−0.706720 | + | 0.707494i | \(0.749826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.1623 | + | 13.1957i | 0.794182 | + | 0.577007i | 0.909202 | − | 0.416356i | \(-0.136693\pi\) |
−0.115020 | + | 0.993363i | \(0.536693\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −21.8492 | + | 9.72789i | −0.953577 | + | 0.424560i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.2883 | − | 9.65450i | −0.578846 | − | 0.420557i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.51586 | + | 10.8207i | 0.152864 | + | 0.470466i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.47407 | + | 4.53671i | −0.0639691 | + | 0.196877i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.286498 | − | 0.881750i | 0.0124096 | − | 0.0381928i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.6835 | − | 32.9669i | 1.28333 | − | 1.42528i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.3043 | + | 8.93959i | −0.530969 | + | 0.385772i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.1341 | − | 18.2610i | −1.08260 | − | 0.786558i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.4954 | − | 14.8908i | 0.881166 | − | 0.640205i | −0.0523936 | − | 0.998627i | \(-0.516685\pi\) |
0.933560 | + | 0.358422i | \(0.116685\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.8755 | −0.895852 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.547848 | + | 5.21243i | −0.0234672 | + | 0.223276i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.64866 | − | 11.2294i | −0.156005 | − | 0.480135i | 0.842256 | − | 0.539078i | \(-0.181227\pi\) |
−0.998261 | + | 0.0589426i | \(0.981227\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.63184 | 0.155003 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 44.8468 | 1.91054 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.78621 | + | 30.1189i | 0.416152 | + | 1.28078i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.3792 | − | 2.63128i | 0.525468 | − | 0.111692i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.93356 | 0.251413 | 0.125706 | − | 0.992067i | \(-0.459880\pi\) | ||||
0.125706 | + | 0.992067i | \(0.459880\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.50187 | − | 6.90351i | 0.401886 | − | 0.291987i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.02323 | + | 4.37613i | 0.254301 | + | 0.184761i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.1180 | + | 8.07772i | −0.468569 | + | 0.340435i | −0.796883 | − | 0.604133i | \(-0.793520\pi\) |
0.328314 | + | 0.944569i | \(0.393520\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.754609 | + | 7.17962i | −0.0317466 | + | 0.302049i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.47815 | + | 4.54927i | −0.0620764 | + | 0.191051i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.2309 | − | 31.4874i | 0.428900 | − | 1.32002i | −0.470309 | − | 0.882502i | \(-0.655858\pi\) |
0.899210 | − | 0.437518i | \(-0.144142\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.91367 | − | 24.3558i | −0.331177 | − | 1.01926i | −0.968575 | − | 0.248722i | \(-0.919989\pi\) |
0.637398 | − | 0.770535i | \(-0.280011\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.24803 | + | 3.08637i | 0.177464 | + | 0.128935i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.6581 | − | 25.3886i | 0.611285 | − | 1.05878i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.82151 | − | 2.04995i | −0.117461 | − | 0.0853405i | 0.527504 | − | 0.849553i | \(-0.323128\pi\) |
−0.644965 | + | 0.764212i | \(0.723128\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.45534 | + | 7.55676i | 0.102040 | + | 0.314048i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.81641 | − | 11.7457i | 0.158331 | − | 0.487294i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.55343 | − | 7.85866i | 0.105752 | − | 0.325472i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.20731 | + | 2.09113i | 0.0499162 | + | 0.0864574i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.8690 | + | 20.2480i | −1.15028 | + | 0.835724i | −0.988517 | − | 0.151107i | \(-0.951716\pi\) |
−0.161758 | + | 0.986831i | \(0.551716\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.8425 | + | 10.7837i | 0.611575 | + | 0.444335i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.5220 | − | 7.64469i | 0.432818 | − | 0.314460i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.7248 | 1.46704 | 0.733522 | − | 0.679666i | \(-0.237875\pi\) | ||||
0.733522 | + | 0.679666i | \(0.237875\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.3530 | + | 35.2524i | 0.834391 | + | 1.44521i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.328899 | + | 1.01225i | 0.0134609 | + | 0.0414285i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.7697 | 1.62495 | 0.812473 | − | 0.582998i | \(-0.198121\pi\) | ||||
0.812473 | + | 0.582998i | \(0.198121\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.5134 | −0.632805 | −0.316402 | − | 0.948625i | \(-0.602475\pi\) | ||||
−0.316402 | + | 0.948625i | \(0.602475\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.14163 | + | 6.59126i | 0.0872140 | + | 0.268417i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.6525 | + | 6.52369i | 0.595707 | + | 0.265226i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.1855 | 0.616358 | 0.308179 | − | 0.951328i | \(-0.400280\pi\) | ||||
0.308179 | + | 0.951328i | \(0.400280\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 40.8271 | − | 29.6626i | 1.65440 | − | 1.20199i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.62224 | − | 1.90517i | −0.106084 | − | 0.0770748i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.9974 | − | 18.8882i | 1.05002 | − | 0.762887i | 0.0778070 | − | 0.996968i | \(-0.475208\pi\) |
0.972217 | + | 0.234081i | \(0.0752082\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.87786 | − | 0.399152i | 0.0757228 | − | 0.0160954i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.33569 | − | 4.11082i | 0.0537727 | − | 0.165495i | −0.920564 | − | 0.390593i | \(-0.872270\pi\) |
0.974336 | + | 0.225097i | \(0.0722700\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.3201 | − | 31.7621i | 0.414801 | − | 1.27663i | −0.497627 | − | 0.867391i | \(-0.665795\pi\) |
0.912428 | − | 0.409236i | \(-0.134205\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.81184 | − | 5.57627i | −0.0727067 | − | 0.223768i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.22256 | − | 2.34133i | −0.129109 | − | 0.0938034i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.4537 | + | 5.19779i | −0.978148 | + | 0.207912i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.72772 | − | 4.88798i | −0.268679 | − | 0.195207i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.65615 | − | 20.4855i | −0.265398 | − | 0.816812i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.39726 | − | 10.4557i | 0.135243 | − | 0.416234i | −0.860385 | − | 0.509645i | \(-0.829777\pi\) |
0.995628 | + | 0.0934106i | \(0.0297769\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.33264 | + | 19.4898i | −0.251700 | + | 0.774652i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.1554 | − | 3.43393i | 0.641106 | − | 0.136271i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.8738 | + | 10.0799i | −0.549698 | + | 0.399379i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.70587 | + | 7.05173i | 0.383958 | + | 0.278962i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.55031 | − | 4.03253i | 0.219224 | − | 0.159276i | −0.472753 | − | 0.881195i | \(-0.656740\pi\) |
0.691977 | + | 0.721919i | \(0.256740\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.1923 | 0.914615 | 0.457308 | − | 0.889309i | \(-0.348814\pi\) | ||||
0.457308 | + | 0.889309i | \(0.348814\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 22.2179 | + | 9.89202i | 0.874827 | + | 0.389498i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.51298 | − | 29.2779i | −0.373994 | − | 1.15103i | −0.944155 | − | 0.329502i | \(-0.893119\pi\) |
0.570161 | − | 0.821533i | \(-0.306881\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.33188 | −0.366309 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.6447 | 0.809130 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.41245 | − | 7.42477i | −0.0944066 | − | 0.290554i | 0.892692 | − | 0.450667i | \(-0.148814\pi\) |
−0.987099 | + | 0.160114i | \(0.948814\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.8767 | − | 32.6955i | −0.737575 | − | 1.27752i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.9560 | −0.661515 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.26388 | + | 3.09789i | −0.166097 | + | 0.120677i | −0.667729 | − | 0.744405i | \(-0.732733\pi\) |
0.501632 | + | 0.865081i | \(0.332733\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.8490 | + | 21.6865i | 1.16099 | + | 0.843509i | 0.989903 | − | 0.141747i | \(-0.0452719\pi\) |
0.171088 | + | 0.985256i | \(0.445272\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.32476 | − | 2.41558i | 0.129123 | − | 0.0938132i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.7335 | − | 39.3756i | −0.881567 | − | 1.52692i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.1151 | + | 58.8301i | −0.740138 | + | 2.27791i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.18661 | − | 9.80739i | 0.123202 | − | 0.379176i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.19555 | + | 6.75721i | 0.0847583 | + | 0.260859i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.4227 | + | 26.4626i | 1.40399 | + | 1.02006i | 0.994162 | + | 0.107897i | \(0.0344116\pi\) |
0.409829 | + | 0.912162i | \(0.365588\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.50000 | + | 4.33013i | −0.0962250 | + | 0.166667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.5161 | − | 18.5385i | −0.980662 | − | 0.712493i | −0.0228056 | − | 0.999740i | \(-0.507260\pi\) |
−0.957856 | + | 0.287247i | \(0.907260\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.4762 | + | 41.4756i | 0.517171 | + | 1.59169i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.60585 | + | 17.2530i | −0.214816 | + | 0.661137i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.39320 | + | 19.6762i | −0.244629 | + | 0.752891i | 0.751068 | + | 0.660225i | \(0.229539\pi\) |
−0.995697 | + | 0.0926660i | \(0.970461\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.196176 | − | 1.86649i | 0.00749551 | − | 0.0713150i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.86225 | − | 5.71226i | 0.299964 | − | 0.217936i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.69003 | − | 2.68096i | −0.140579 | − | 0.102137i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.6523 | − | 20.0906i | 1.05194 | − | 0.764282i | 0.0793624 | − | 0.996846i | \(-0.474712\pi\) |
0.972581 | + | 0.232564i | \(0.0747116\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.35772 | −0.355470 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24.4048 | + | 5.18741i | −0.925728 | + | 0.196770i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.00971 | − | 3.10755i | −0.0382453 | − | 0.117707i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.2184 | −0.840377 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.6859 | −0.630216 | −0.315108 | − | 0.949056i | \(-0.602041\pi\) | ||||
−0.315108 | + | 0.949056i | \(0.602041\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.43467 | + | 22.8816i | 0.280404 | + | 0.862994i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.701568 | − | 6.67497i | 0.0264226 | − | 0.251394i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.15312 | −0.269021 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.2796 | + | 27.8118i | −1.43762 | + | 1.04449i | −0.449089 | + | 0.893487i | \(0.648251\pi\) |
−0.988533 | + | 0.151007i | \(0.951749\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.35617 | + | 3.89149i | 0.200872 | + | 0.145942i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.4724 | + | 14.8741i | −0.766697 | + | 0.557038i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.16078 | + | 3.51041i | −0.118207 | + | 0.131282i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.92242 | − | 15.1496i | 0.183831 | − | 0.565774i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.73431 | − | 5.33767i | 0.0646790 | − | 0.199062i | −0.913495 | − | 0.406851i | \(-0.866627\pi\) |
0.978174 | + | 0.207789i | \(0.0666268\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.0561 | − | 49.4156i | −0.597960 | − | 1.84033i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.98964 | + | 2.89864i | 0.148376 | + | 0.107802i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 48.1899 | − | 21.4555i | 1.78973 | − | 0.796838i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.8412 | + | 8.60317i | 0.439167 | + | 0.319074i | 0.785304 | − | 0.619110i | \(-0.212507\pi\) |
−0.346137 | + | 0.938184i | \(0.612507\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.7911 | − | 39.3669i | 0.473095 | − | 1.45604i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.96818 | − | 30.6789i | 0.368183 | − | 1.13315i | −0.579781 | − | 0.814773i | \(-0.696862\pi\) |
0.947964 | − | 0.318378i | \(-0.103138\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −32.4405 | − | 14.4434i | −1.19658 | − | 0.532754i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.9687 | + | 7.96921i | −0.404037 | + | 0.293550i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.2956 | + | 14.0191i | 0.709800 | + | 0.515700i | 0.883109 | − | 0.469168i | \(-0.155446\pi\) |
−0.173309 | + | 0.984867i | \(0.555446\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.71363 | + | 2.69811i | −0.136423 | + | 0.0991174i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.48188 | 0.274483 | 0.137242 | − | 0.990538i | \(-0.456176\pi\) | ||||
0.137242 | + | 0.990538i | \(0.456176\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.9583 | − | 36.6039i | 1.20750 | − | 1.34106i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.797847 | − | 2.45552i | −0.0291917 | − | 0.0898428i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 94.8975 | 3.46748 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.3687 | −1.18115 | −0.590576 | − | 0.806982i | \(-0.701099\pi\) | ||||
−0.590576 | + | 0.806982i | \(0.701099\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.76969 | + | 14.6796i | 0.173817 | + | 0.534955i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.6390 | + | 19.5901i | −0.641949 | + | 0.712957i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.2847 | −0.373804 | −0.186902 | − | 0.982379i | \(-0.559845\pi\) | ||||
−0.186902 | + | 0.982379i | \(0.559845\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.27961 | − | 6.74203i | 0.336828 | − | 0.244720i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.3033 | − | 16.9308i | −0.844743 | − | 0.613742i | 0.0789487 | − | 0.996879i | \(-0.474844\pi\) |
−0.923691 | + | 0.383137i | \(0.874844\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.07055 | + | 6.59014i | −0.328376 | + | 0.238579i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.77415 | + | 3.46127i | 0.281075 | + | 0.125143i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.59178 | + | 4.89898i | −0.0574757 | + | 0.176892i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.1673 | + | 37.4472i | −0.438765 | + | 1.35038i | 0.450414 | + | 0.892820i | \(0.351276\pi\) |
−0.889179 | + | 0.457560i | \(0.848724\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.54584 | + | 20.1460i | 0.235743 | + | 0.725541i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.09692 | − | 2.97658i | −0.147356 | − | 0.107060i | 0.511665 | − | 0.859185i | \(-0.329029\pi\) |
−0.659021 | + | 0.752125i | \(0.729029\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.1080 | + | 4.48665i | 0.758223 | + | 0.161165i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.9026 | + | 15.9132i | 0.785753 | + | 0.570883i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.12780 | + | 3.47102i | 0.0404077 | + | 0.124362i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.25260 | + | 22.3212i | −0.259518 | + | 0.798715i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.26015 | − | 10.0337i | 0.116508 | − | 0.358576i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.8727 | + | 18.7391i | −0.602213 | + | 0.668826i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.31328 | + | 3.13378i | −0.153752 | + | 0.111707i | −0.662001 | − | 0.749503i | \(-0.730293\pi\) |
0.508250 | + | 0.861210i | \(0.330293\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.9298 | + | 12.3002i | 0.602717 | + | 0.437900i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.4938 | + | 9.07729i | −0.444229 | + | 0.322751i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.92185 | 0.139269 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.987250 | − | 9.39306i | 0.0350141 | − | 0.333137i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.92980 | + | 21.3277i | 0.245466 | + | 0.755467i | 0.995559 | + | 0.0941349i | \(0.0300085\pi\) |
−0.750093 | + | 0.661332i | \(0.769991\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.4232 | −0.404124 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.832738 | −0.0294233 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.2504 | − | 31.5474i | −0.361727 | − | 1.11328i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 61.3426 | − | 13.0388i | 2.16204 | − | 0.459557i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.7837 | −0.485208 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.76605 | + | 7.09545i | −0.343356 | + | 0.249463i | −0.746076 | − | 0.665860i | \(-0.768065\pi\) |
0.402721 | + | 0.915323i | \(0.368065\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.4731 | − | 15.6011i | −0.754023 | − | 0.547830i | 0.143048 | − | 0.989716i | \(-0.454310\pi\) |
−0.897071 | + | 0.441886i | \(0.854310\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.53473 | + | 6.20084i | −0.299326 | + | 0.217473i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.31309 | − | 22.0076i | 0.0810240 | − | 0.770891i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.2871 | + | 43.9713i | −0.499844 | + | 1.53836i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.59618 | + | 4.91254i | −0.0557751 | + | 0.171658i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.554306 | − | 1.70598i | −0.0193454 | − | 0.0595391i | 0.940918 | − | 0.338635i | \(-0.109965\pi\) |
−0.960263 | + | 0.279096i | \(0.909965\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.7913 | − | 20.9181i | −1.00360 | − | 0.729160i | −0.0407453 | − | 0.999170i | \(-0.512973\pi\) |
−0.962858 | + | 0.270009i | \(0.912973\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.56773 | − | 2.03368i | −0.333106 | − | 0.0708038i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.2013 | − | 16.1302i | −0.772016 | − | 0.560902i | 0.130556 | − | 0.991441i | \(-0.458324\pi\) |
−0.902572 | + | 0.430539i | \(0.858324\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.7501 | − | 36.1631i | −0.408098 | − | 1.25600i | −0.918281 | − | 0.395930i | \(-0.870422\pi\) |
0.510183 | − | 0.860066i | \(-0.329578\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.55063 | − | 17.0831i | 0.192549 | − | 0.592606i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.6763 | + | 57.4799i | −0.647097 | + | 1.99156i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.40274 | − | 14.5540i | −0.290789 | − | 0.503661i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.49165 | − | 2.53683i | 0.120689 | − | 0.0876858i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.2065 | + | 21.2197i | 1.00832 | + | 0.732586i | 0.963856 | − | 0.266425i | \(-0.0858423\pi\) |
0.0444629 | + | 0.999011i | \(0.485842\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −66.5855 | + | 48.3772i | −2.29605 | + | 1.66818i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.926728 | −0.0319182 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.2307 | − | 22.9163i | −0.455151 | − | 0.788344i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.6026 | + | 32.6315i | 0.364310 | + | 1.12123i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.57749 | −0.225739 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33.1849 | −1.13756 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.1818 | − | 31.3363i | −0.348617 | − | 1.07293i | −0.959619 | − | 0.281304i | \(-0.909233\pi\) |
0.611001 | − | 0.791630i | \(-0.290767\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.68343 | − | 3.86611i | −0.296967 | − | 0.132218i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.9514 | −0.476572 | −0.238286 | − | 0.971195i | \(-0.576586\pi\) | ||||
−0.238286 | + | 0.971195i | \(0.576586\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.2696 | − | 22.7187i | 1.06691 | − | 0.775152i | 0.0915521 | − | 0.995800i | \(-0.470817\pi\) |
0.975354 | + | 0.220648i | \(0.0708172\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.32252 | + | 2.41395i | 0.113231 | + | 0.0822673i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.89284 | − | 2.10177i | 0.0984734 | − | 0.0715451i | −0.537459 | − | 0.843290i | \(-0.680616\pi\) |
0.635932 | + | 0.771745i | \(0.280616\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.8551 | − | 5.70822i | 0.913100 | − | 0.194085i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.777624 | + | 2.39328i | −0.0264095 | + | 0.0812801i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.00234 | + | 12.3179i | −0.135770 | + | 0.417857i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.31265 | + | 7.11759i | 0.0783610 | + | 0.241170i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.37579 | + | 5.35882i | 0.249633 | + | 0.181369i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −43.2661 | − | 31.4347i | −1.46266 | − | 1.06269i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.08491 | + | 4.42095i | 0.205473 | + | 0.149285i | 0.685763 | − | 0.727825i | \(-0.259469\pi\) |
−0.480290 | + | 0.877110i | \(0.659469\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.91726 | + | 24.3668i | 0.267043 | + | 0.821873i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.14735 | + | 25.0750i | −0.274491 | + | 0.844797i | 0.714862 | + | 0.699265i | \(0.246489\pi\) |
−0.989354 | + | 0.145532i | \(0.953511\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.127210 | + | 0.391511i | −0.00428095 | + | 0.0131754i | −0.953174 | − | 0.302422i | \(-0.902205\pi\) |
0.948893 | + | 0.315597i | \(0.102205\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.4334 | + | 2.21768i | −0.350714 | + | 0.0745465i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.3008 | + | 16.9290i | −0.782363 | + | 0.568420i | −0.905687 | − | 0.423946i | \(-0.860645\pi\) |
0.123324 | + | 0.992366i | \(0.460645\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.5838 | + | 20.7674i | 0.958671 | + | 0.696515i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.58268 | + | 1.14988i | −0.0530216 | + | 0.0385225i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.7593 | 0.426973 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.0680 | − | 13.8324i | −1.03849 | − | 0.462366i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.95652 | − | 6.02155i | −0.0653263 | − | 0.201054i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −45.5333 | −1.51862 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.0748 | −0.535529 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.0770 | + | 49.4799i | 0.535009 | + | 1.64659i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.3395 | − | 40.4252i | −0.775831 | − | 1.34378i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.80122 | −0.0598085 | −0.0299042 | − | 0.999553i | \(-0.509520\pi\) | ||||
−0.0299042 | + | 0.999553i | \(0.509520\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.20981 | + | 0.878980i | −0.0401269 | + | 0.0291539i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.50521 | − | 2.54669i | −0.116133 | − | 0.0843755i | 0.528203 | − | 0.849118i | \(-0.322866\pi\) |
−0.644336 | + | 0.764743i | \(0.722866\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.08629 | − | 2.96886i | 0.135236 | − | 0.0982550i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.06052 | + | 7.03303i | 0.134237 | + | 0.232505i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.9569 | − | 76.8093i | 0.824148 | − | 2.53647i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.40845 | + | 7.41244i | −0.0794473 | + | 0.244514i | −0.982889 | − | 0.184196i | \(-0.941032\pi\) |
0.903442 | + | 0.428710i | \(0.141032\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.91102 | − | 5.88153i | −0.0629704 | − | 0.193803i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.4809 | + | 7.61483i | 0.344983 | + | 0.250645i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.9358 | + | 21.0304i | 0.622606 | + | 0.691474i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.78779 | − | 6.38470i | −0.288629 | − | 0.209701i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.3076 | − | 31.7234i | −0.338180 | − | 1.04081i | −0.965134 | − | 0.261756i | \(-0.915699\pi\) |
0.626954 | − | 0.779056i | \(-0.284301\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.8608 | − | 64.2028i | 0.683684 | − | 2.10416i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.49001 | + | 23.0519i | −0.245212 | + | 0.754684i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.74017 | + | 16.5566i | −0.0569096 | + | 0.541459i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.7063 | + | 19.4033i | −0.872458 | + | 0.633878i | −0.931245 | − | 0.364393i | \(-0.881277\pi\) |
0.0587876 | + | 0.998271i | \(0.481277\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.2392 | + | 17.6108i | 0.791015 | + | 0.574706i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.4034 | − | 30.0813i | 1.34971 | − | 0.980624i | 0.350687 | − | 0.936493i | \(-0.385948\pi\) |
0.999026 | − | 0.0441311i | \(-0.0140519\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.03399 | −0.163929 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.4622 | + | 2.22382i | −0.340337 | + | 0.0723408i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.21428 | − | 6.81485i | −0.0719544 | − | 0.221453i | 0.908612 | − | 0.417642i | \(-0.137143\pi\) |
−0.980566 | + | 0.196189i | \(0.937143\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.3099 | −0.594366 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.46267 | 0.0798575 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.14180 | − | 12.7472i | −0.134166 | − | 0.412921i | 0.861293 | − | 0.508108i | \(-0.169655\pi\) |
−0.995459 | + | 0.0951872i | \(0.969655\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.22730 | + | 11.6769i | −0.0397144 | + | 0.377857i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.6391 | 0.667166 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.24803 | − | 2.35983i | 0.104884 | − | 0.0762029i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.0098 | + | 7.27257i | 0.322898 | + | 0.234599i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.0501 | − | 11.6611i | 0.517207 | − | 0.375773i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.8884 | + | 13.2035i | −0.382703 | + | 0.425034i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.58341 | + | 11.0286i | −0.115235 | + | 0.354656i | −0.991996 | − | 0.126270i | \(-0.959699\pi\) |
0.876761 | + | 0.480926i | \(0.159699\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.99915 | + | 15.3858i | −0.160596 | + | 0.494263i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.35477 | − | 7.24723i | −0.0755681 | − | 0.232575i | 0.906136 | − | 0.422986i | \(-0.139018\pi\) |
−0.981704 | + | 0.190411i | \(0.939018\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −43.1797 | − | 31.3719i | −1.38428 | − | 1.00574i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.69963 | + | 4.67590i | −0.0864574 | + | 0.149749i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.1197 | − | 25.5159i | −1.12358 | − | 0.816327i | −0.138830 | − | 0.990316i | \(-0.544334\pi\) |
−0.984748 | + | 0.173989i | \(0.944334\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.503414 | − | 1.54935i | −0.0160892 | − | 0.0495174i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.724307 | + | 2.22919i | −0.0231254 | + | 0.0711725i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.9339 | + | 52.1172i | −0.540107 | + | 1.66228i | 0.192240 | + | 0.981348i | \(0.438425\pi\) |
−0.732348 | + | 0.680931i | \(0.761575\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.5678 | + | 11.8288i | 0.846522 | + | 0.376896i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.6156 | − | 8.43925i | 0.369730 | − | 0.268624i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −51.5920 | − | 37.4838i | −1.64053 | − | 1.19191i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.7531 | + | 12.8984i | −0.563945 | + | 0.409730i | −0.832901 | − | 0.553422i | \(-0.813322\pi\) |
0.268956 | + | 0.963153i | \(0.413322\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.7867 | −0.850051 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.59249 | + | 1.76864i | −0.0504852 | + | 0.0560695i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.0781 | + | 37.1725i | 0.382516 | + | 1.17726i | 0.938266 | + | 0.345914i | \(0.112431\pi\) |
−0.555750 | + | 0.831350i | \(0.687569\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.65983 | 0.179069 |
(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 | 300.2.m.a.241.1 | yes | 8 | |
3.2 | odd | 2 | 900.2.n.a.541.2 | 8 | |||
5.2 | odd | 4 | 1500.2.o.a.49.3 | 16 | |||
5.3 | odd | 4 | 1500.2.o.a.49.2 | 16 | |||
5.4 | even | 2 | 1500.2.m.b.1201.2 | 8 | |||
25.2 | odd | 20 | 1500.2.o.a.949.1 | 16 | |||
25.6 | even | 5 | 7500.2.a.g.1.1 | 4 | |||
25.8 | odd | 20 | 7500.2.d.d.1249.8 | 8 | |||
25.11 | even | 5 | inner | 300.2.m.a.61.1 | ✓ | 8 | |
25.14 | even | 10 | 1500.2.m.b.301.2 | 8 | |||
25.17 | odd | 20 | 7500.2.d.d.1249.1 | 8 | |||
25.19 | even | 10 | 7500.2.a.d.1.4 | 4 | |||
25.23 | odd | 20 | 1500.2.o.a.949.4 | 16 | |||
75.11 | odd | 10 | 900.2.n.a.361.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.m.a.61.1 | ✓ | 8 | 25.11 | even | 5 | inner | |
300.2.m.a.241.1 | yes | 8 | 1.1 | even | 1 | trivial | |
900.2.n.a.361.2 | 8 | 75.11 | odd | 10 | |||
900.2.n.a.541.2 | 8 | 3.2 | odd | 2 | |||
1500.2.m.b.301.2 | 8 | 25.14 | even | 10 | |||
1500.2.m.b.1201.2 | 8 | 5.4 | even | 2 | |||
1500.2.o.a.49.2 | 16 | 5.3 | odd | 4 | |||
1500.2.o.a.49.3 | 16 | 5.2 | odd | 4 | |||
1500.2.o.a.949.1 | 16 | 25.2 | odd | 20 | |||
1500.2.o.a.949.4 | 16 | 25.23 | odd | 20 | |||
7500.2.a.d.1.4 | 4 | 25.19 | even | 10 | |||
7500.2.a.g.1.1 | 4 | 25.6 | even | 5 | |||
7500.2.d.d.1249.1 | 8 | 25.17 | odd | 20 | |||
7500.2.d.d.1249.8 | 8 | 25.8 | odd | 20 |