Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [176,5,Mod(17,176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(176, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 9]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("176.17");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 176 = 2^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 176.n (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.1931135028\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{16} - 4 x^{15} + 138 x^{14} - 428 x^{13} + 7783 x^{12} - 18620 x^{11} + 235604 x^{10} + \cdots + 1499670491 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 11^{2} \) |
Twist minimal: | no (minimal twist has level 22) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 17.3 | ||
Root | \(0.809017 - 5.77971i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 176.17 |
Dual form | 176.5.n.c.145.3 |
$q$-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 \(\left(\mathbb{Z}/176\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(133\) | \(145\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) |
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 | ||||||||
\(3\) | 3.20187 | + | 2.32629i | 0.355763 | + | 0.258477i | 0.751283 | − | 0.659980i | \(-0.229435\pi\) |
−0.395520 | + | 0.918458i | \(0.629435\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 13.3838 | − | 41.1910i | 0.535350 | − | 1.64764i | −0.207540 | − | 0.978226i | \(-0.566546\pi\) |
0.742891 | − | 0.669413i | \(-0.233454\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.80030 | + | 10.7362i | 0.159190 | + | 0.219106i | 0.881160 | − | 0.472818i | \(-0.156763\pi\) |
−0.721970 | + | 0.691924i | \(0.756763\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −20.1901 | − | 62.1386i | −0.249260 | − | 0.767143i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −90.5882 | − | 80.2170i | −0.748663 | − | 0.662951i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −170.407 | + | 55.3685i | −1.00832 | + | 0.327624i | −0.766187 | − | 0.642618i | \(-0.777848\pi\) |
−0.242137 | + | 0.970242i | \(0.577848\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 138.675 | − | 100.754i | 0.616335 | − | 0.447794i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 167.901 | + | 54.5543i | 0.580972 | + | 0.188769i | 0.584736 | − | 0.811224i | \(-0.301198\pi\) |
−0.00376408 | + | 0.999993i | \(0.501198\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −213.240 | + | 293.500i | −0.590693 | + | 0.813019i | −0.994817 | − | 0.101685i | \(-0.967577\pi\) |
0.404123 | + | 0.914704i | \(0.367577\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 52.5217i | 0.119097i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −564.946 | −1.06795 | −0.533975 | − | 0.845500i | \(-0.679302\pi\) | ||||
−0.533975 | + | 0.845500i | \(0.679302\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1011.94 | − | 735.215i | −1.61910 | − | 1.17634i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 178.970 | − | 550.813i | 0.245501 | − | 0.755574i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 505.658 | + | 695.978i | 0.601258 | + | 0.827560i | 0.995823 | − | 0.0913079i | \(-0.0291048\pi\) |
−0.394565 | + | 0.918868i | \(0.629105\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −276.141 | − | 849.875i | −0.287348 | − | 0.884365i | −0.985685 | − | 0.168596i | \(-0.946077\pi\) |
0.698338 | − | 0.715769i | \(-0.253923\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −103.443 | − | 467.579i | −0.0949893 | − | 0.429366i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 546.632 | − | 177.611i | 0.446230 | − | 0.144989i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −164.418 | + | 119.457i | −0.120101 | + | 0.0872585i | −0.646214 | − | 0.763156i | \(-0.723649\pi\) |
0.526113 | + | 0.850415i | \(0.323649\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −674.423 | − | 219.133i | −0.443408 | − | 0.144072i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1540.12 | − | 2119.80i | 0.916196 | − | 1.26103i | −0.0488107 | − | 0.998808i | \(-0.515543\pi\) |
0.965006 | − | 0.262227i | \(-0.0844569\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2603.62i | − | 1.40812i | −0.710140 | − | 0.704061i | \(-0.751368\pi\) | ||
0.710140 | − | 0.704061i | \(-0.248632\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2829.77 | −1.39742 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1250.87 | + | 908.812i | 0.566262 | + | 0.411413i | 0.833745 | − | 0.552149i | \(-0.186192\pi\) |
−0.267484 | + | 0.963562i | \(0.586192\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 687.529 | − | 2116.00i | 0.286351 | − | 0.881298i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 410.687 | + | 565.262i | 0.157896 | + | 0.217325i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −454.551 | − | 1398.97i | −0.161820 | − | 0.498030i | 0.836968 | − | 0.547251i | \(-0.184326\pi\) |
−0.998788 | + | 0.0492218i | \(0.984326\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4516.63 | + | 2657.81i | −1.49310 | + | 0.878616i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1365.53 | + | 443.689i | −0.420294 | + | 0.136562i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3977.33 | + | 2889.70i | −1.14258 | + | 0.830135i | −0.987477 | − | 0.157762i | \(-0.949572\pi\) |
−0.155106 | + | 0.987898i | \(0.549572\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1508.75 | − | 490.221i | −0.405468 | − | 0.131745i | 0.0991805 | − | 0.995069i | \(-0.468378\pi\) |
−0.504648 | + | 0.863325i | \(0.668378\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 509.644 | − | 701.464i | 0.128406 | − | 0.176736i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7760.26i | 1.83675i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3004.99 | 0.669413 | 0.334706 | − | 0.942323i | \(-0.391363\pi\) | ||||
0.334706 | + | 0.942323i | \(0.391363\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1808.88 | − | 1314.23i | −0.379937 | − | 0.276041i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2625.89 | − | 8081.67i | 0.520907 | − | 1.60319i | −0.251362 | − | 0.967893i | \(-0.580879\pi\) |
0.772270 | − | 0.635295i | \(-0.219121\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2674.58 | + | 3681.24i | 0.501891 | + | 0.690793i | 0.982526 | − | 0.186127i | \(-0.0595937\pi\) |
−0.480635 | + | 0.876921i | \(0.659594\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1529.76 | − | 4708.12i | −0.271958 | − | 0.836999i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 154.610 | − | 1598.29i | 0.0260769 | − | 0.269572i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2009.88 | + | 653.050i | −0.322045 | + | 0.104639i | −0.465578 | − | 0.885007i | \(-0.654154\pi\) |
0.143533 | + | 0.989645i | \(0.454154\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2427.13 | + | 1763.41i | −0.369932 | + | 0.268772i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8994.67 | + | 2922.55i | 1.30566 | + | 0.424234i | 0.877546 | − | 0.479493i | \(-0.159179\pi\) |
0.428111 | + | 0.903726i | \(0.359179\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4494.29 | − | 6185.86i | 0.622047 | − | 0.856174i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3404.74i | 0.449827i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14557.2 | 1.83779 | 0.918896 | − | 0.394499i | \(-0.129082\pi\) | ||||
0.918896 | + | 0.394499i | \(0.129082\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1923.67 | − | 1397.63i | −0.232299 | − | 0.168775i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1092.89 | − | 3363.57i | 0.126360 | − | 0.388897i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9235.60 | + | 12711.7i | 1.02333 | + | 1.40850i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2097.12 | + | 6454.28i | 0.222885 | + | 0.685969i | 0.998499 | + | 0.0547624i | \(0.0174401\pi\) |
−0.775614 | + | 0.631207i | \(0.782560\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3155.59 | + | 7248.61i | −0.321966 | + | 0.739579i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12997.2 | + | 4223.06i | −1.27411 | + | 0.413985i | −0.866504 | − | 0.499171i | \(-0.833638\pi\) |
−0.407611 | + | 0.913156i | \(0.633638\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 995.164 | − | 723.029i | 0.0938038 | − | 0.0681524i | −0.539895 | − | 0.841733i | \(-0.681536\pi\) |
0.633699 | + | 0.773580i | \(0.281536\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2163.42 | + | 702.937i | 0.196228 | + | 0.0637585i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4974.60 | − | 6846.95i | 0.434501 | − | 0.598040i | −0.534478 | − | 0.845182i | \(-0.679492\pi\) |
0.968979 | + | 0.247143i | \(0.0794917\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7648.65i | − | 0.643771i | −0.946779 | − | 0.321886i | \(-0.895683\pi\) | ||
0.946779 | − | 0.321886i | \(-0.104317\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −804.338 | −0.0652819 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7345.60 | + | 5336.89i | 0.575269 | + | 0.417957i | 0.837015 | − | 0.547180i | \(-0.184298\pi\) |
−0.261747 | + | 0.965137i | \(0.584298\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7561.10 | + | 23270.7i | −0.571728 | + | 1.75960i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6881.04 | + | 9470.94i | 0.502670 | + | 0.691865i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 723.972 | + | 2228.16i | 0.0511243 | + | 0.157345i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1771.46 | + | 14533.4i | 0.120993 | + | 0.992653i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9862.55 | − | 3204.54i | 0.651897 | − | 0.211814i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −21928.3 | + | 15931.8i | −1.40341 | + | 1.01964i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6550.78 | + | 2128.48i | 0.406149 | + | 0.131966i | 0.504965 | − | 0.863140i | \(-0.331505\pi\) |
−0.0988156 | + | 0.995106i | \(0.531505\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6056.78 | − | 8336.44i | 0.363967 | − | 0.500958i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1471.01i | − | 0.0857182i | −0.999081 | − | 0.0428591i | \(-0.986353\pi\) | ||
0.999081 | − | 0.0428591i | \(-0.0136467\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4814.41 | −0.272170 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −20293.3 | − | 14743.9i | −1.11348 | − | 0.808994i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5600.55 | − | 17236.7i | 0.298394 | − | 0.918361i | −0.683667 | − | 0.729794i | \(-0.739616\pi\) |
0.982060 | − | 0.188567i | \(-0.0603841\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5984.50 | − | 8236.96i | −0.309741 | − | 0.426322i | 0.625559 | − | 0.780176i | \(-0.284871\pi\) |
−0.935300 | + | 0.353855i | \(0.884871\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1890.97 | + | 5819.79i | 0.0951142 | + | 0.292731i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19878.3 | + | 8653.78i | 0.972094 | + | 0.423189i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 35435.6 | − | 11513.7i | 1.68540 | − | 0.547621i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7123.80 | − | 5175.75i | 0.329668 | − | 0.239518i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −25251.0 | − | 8204.56i | −1.13738 | − | 0.369558i | −0.321006 | − | 0.947077i | \(-0.604021\pi\) |
−0.816377 | + | 0.577519i | \(0.804021\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11161.2 | − | 15362.0i | 0.489503 | − | 0.673744i | −0.490793 | − | 0.871276i | \(-0.663293\pi\) |
0.980296 | + | 0.197533i | \(0.0632928\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 11534.6i | − | 0.492741i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −38703.0 | −1.61095 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2755.25 | + | 2001.81i | 0.111779 | + | 0.0812124i | 0.642271 | − | 0.766478i | \(-0.277993\pi\) |
−0.530491 | + | 0.847690i | \(0.677993\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1798.99 | − | 5536.72i | 0.0711598 | − | 0.219007i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4406.74 | − | 6065.36i | −0.170007 | − | 0.233994i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2632.77 | − | 8102.84i | −0.0990918 | − | 0.304973i | 0.889207 | − | 0.457506i | \(-0.151257\pi\) |
−0.988298 | + | 0.152533i | \(0.951257\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −20644.5 | − | 1997.04i | −0.758292 | − | 0.0733530i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12611.3 | + | 4097.65i | −0.452196 | + | 0.146927i | −0.526255 | − | 0.850327i | \(-0.676404\pi\) |
0.0740598 | + | 0.997254i | \(0.476404\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2866.45 | − | 2082.59i | 0.100362 | − | 0.0729174i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22543.0 | + | 7324.67i | 0.770939 | + | 0.250493i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12984.4 | + | 17871.4i | −0.433839 | + | 0.597128i | −0.968829 | − | 0.247730i | \(-0.920315\pi\) |
0.534990 | + | 0.844858i | \(0.320315\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 16599.2i | − | 0.542016i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19457.2 | −0.621060 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6760.86 | − | 4912.05i | −0.211006 | − | 0.153305i | 0.477263 | − | 0.878761i | \(-0.341629\pi\) |
−0.688269 | + | 0.725456i | \(0.741629\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3111.80 | − | 9577.13i | 0.0949848 | − | 0.292333i | −0.892265 | − | 0.451512i | \(-0.850885\pi\) |
0.987250 | + | 0.159179i | \(0.0508847\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3690.41 | − | 5079.41i | −0.110198 | − | 0.151674i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2720.01 | + | 8371.34i | 0.0794744 | + | 0.244597i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10833.7 | − | 18410.5i | −0.309808 | − | 0.526480i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7309.66 | − | 2375.05i | 0.204632 | − | 0.0664890i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −28569.5 | + | 20757.0i | −0.783134 | + | 0.568980i | −0.905918 | − | 0.423453i | \(-0.860818\pi\) |
0.122784 | + | 0.992433i | \(0.460818\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7441.19 | − | 2417.79i | −0.199769 | − | 0.0649088i | 0.207424 | − | 0.978251i | \(-0.433492\pi\) |
−0.407192 | + | 0.913342i | \(0.633492\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −18052.6 | + | 24847.3i | −0.474757 | + | 0.653447i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1473.23i | 0.0379610i | 0.999820 | + | 0.0189805i | \(0.00604205\pi\) | ||||
−0.999820 | + | 0.0189805i | \(0.993958\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26096.6 | 0.658987 | 0.329494 | − | 0.944158i | \(-0.393122\pi\) | ||||
0.329494 | + | 0.944158i | \(0.393122\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9621.59 | + | 6990.49i | 0.238152 | + | 0.173028i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3527.87 | + | 10857.7i | −0.0856093 | + | 0.263478i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −66704.0 | − | 91810.1i | −1.58725 | − | 2.18466i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11406.3 | + | 35104.9i | 0.266197 | + | 0.819271i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 42860.8 | − | 9482.15i | 0.981222 | − | 0.217077i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 68859.0 | − | 22373.6i | 1.54666 | − | 0.502541i | 0.593458 | − | 0.804865i | \(-0.297762\pi\) |
0.953205 | + | 0.302323i | \(0.0977622\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 27208.1 | − | 19767.8i | 0.599707 | − | 0.435713i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −107246. | − | 34846.2i | −2.32008 | − | 0.753839i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6970.43 | − | 9593.98i | 0.148027 | − | 0.203741i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18008.7i | 0.375486i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −31632.0 | −0.647653 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22887.6 | + | 16628.8i | 0.460246 | + | 0.334388i | 0.793628 | − | 0.608404i | \(-0.208190\pi\) |
−0.333382 | + | 0.942792i | \(0.608190\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25254.2 | + | 77724.3i | −0.498848 | + | 1.53530i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −42352.4 | − | 58293.1i | −0.821913 | − | 1.13127i | −0.989375 | − | 0.145388i | \(-0.953557\pi\) |
0.167461 | − | 0.985879i | \(-0.446443\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2762.09 | + | 8500.84i | 0.0526704 | + | 0.162103i | 0.973932 | − | 0.226841i | \(-0.0728399\pi\) |
−0.921261 | + | 0.388944i | \(0.872840\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4213.13 | − | 4757.84i | 0.0789552 | − | 0.0891633i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 46046.9 | − | 14961.6i | 0.848182 | − | 0.275591i | 0.147497 | − | 0.989062i | \(-0.452878\pi\) |
0.700684 | + | 0.713472i | \(0.252878\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 54176.2 | − | 39361.3i | 0.981009 | − | 0.712745i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7954.57 | − | 2584.59i | −0.141618 | − | 0.0460146i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 31831.6 | − | 43812.5i | 0.557266 | − | 0.767011i | −0.433709 | − | 0.901053i | \(-0.642796\pi\) |
0.990976 | + | 0.134041i | \(0.0427955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 54166.9i | 0.932610i | 0.884624 | + | 0.466305i | \(0.154415\pi\) | ||||
−0.884624 | + | 0.466305i | \(0.845585\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −58785.5 | −0.995537 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −77958.2 | − | 56640.0i | −1.29876 | − | 0.943606i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20086.9 | − | 61821.2i | 0.329245 | − | 1.01331i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 22001.0 | + | 30281.8i | 0.354850 | + | 0.488409i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4416.42 | − | 13592.3i | −0.0701008 | − | 0.215748i | 0.909868 | − | 0.414897i | \(-0.136182\pi\) |
−0.979969 | + | 0.199149i | \(0.936182\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 51177.4 | + | 45318.2i | 0.799535 | + | 0.707998i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 28780.2 | − | 9351.27i | 0.442603 | − | 0.143810i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 31133.7 | − | 22619.9i | 0.471372 | − | 0.342472i | −0.326604 | − | 0.945161i | \(-0.605904\pi\) |
0.797976 | + | 0.602689i | \(0.205904\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2565.02 | − | 833.427i | −0.0382377 | − | 0.0124242i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 33037.8 | − | 45472.7i | 0.484988 | − | 0.667528i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 130054.i | 1.88024i | 0.340841 | + | 0.940121i | \(0.389288\pi\) | ||||
−0.340841 | + | 0.940121i | \(0.610712\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −63708.4 | −0.907203 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 46610.1 | + | 33864.2i | 0.653819 | + | 0.475027i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21831.7 | + | 67190.9i | −0.301705 | + | 0.928552i | 0.679182 | + | 0.733970i | \(0.262335\pi\) |
−0.980886 | + | 0.194582i | \(0.937665\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −46867.1 | − | 64507.0i | −0.638160 | − | 0.878352i | 0.360356 | − | 0.932815i | \(-0.382655\pi\) |
−0.998516 | + | 0.0544632i | \(0.982655\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2908.05 | − | 8950.04i | −0.0390190 | − | 0.120088i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 32692.8 | + | 147776.i | 0.432301 | + | 1.95407i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 42143.0 | − | 13693.1i | 0.549245 | − | 0.178461i | −0.0212312 | − | 0.999775i | \(-0.506759\pi\) |
0.570476 | + | 0.821314i | \(0.306759\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −47234.7 | + | 34318.0i | −0.606810 | + | 0.440874i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 74439.7 | + | 24186.9i | 0.942740 | + | 0.306315i | 0.739762 | − | 0.672868i | \(-0.234938\pi\) |
0.202978 | + | 0.979183i | \(0.434938\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −52782.1 | + | 72648.4i | −0.659043 | + | 0.907095i | −0.999449 | − | 0.0331832i | \(-0.989436\pi\) |
0.340406 | + | 0.940279i | \(0.389436\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 62185.9i | 0.765601i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 34772.0 | 0.422149 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −42355.4 | − | 30773.0i | −0.507123 | − | 0.368446i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8299.84 | + | 25544.3i | −0.0980131 | + | 0.301653i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12058.9 | + | 16597.6i | 0.140466 | + | 0.193335i | 0.873454 | − | 0.486907i | \(-0.161875\pi\) |
−0.732988 | + | 0.680242i | \(0.761875\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 65798.0 | + | 202505.i | 0.756081 | + | 2.32698i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −60397.2 | + | 35540.8i | −0.684706 | + | 0.402915i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 96270.5 | − | 31280.2i | 1.07684 | − | 0.349886i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27952.9 | − | 20309.0i | 0.308528 | − | 0.224159i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −51439.5 | − | 16713.7i | −0.560289 | − | 0.182049i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −40385.4 | + | 55585.7i | −0.434135 | + | 0.597535i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 133825.i | − | 1.41991i | −0.704248 | − | 0.709954i | \(-0.748716\pi\) | ||
0.704248 | − | 0.709954i | \(-0.251284\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4868.36 | 0.0509878 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 34207.5 | + | 24853.2i | 0.353672 | + | 0.256958i | 0.750408 | − | 0.660975i | \(-0.229857\pi\) |
−0.396736 | + | 0.917933i | \(0.629857\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 53394.1 | − | 164330.i | 0.545011 | − | 1.67737i | −0.175954 | − | 0.984398i | \(-0.556301\pi\) |
0.720965 | − | 0.692972i | \(-0.243699\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −22073.0 | − | 30380.9i | −0.222455 | − | 0.306182i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26059.8 | + | 80203.7i | 0.259329 | + | 0.798134i | 0.992946 | + | 0.118570i | \(0.0378310\pi\) |
−0.733616 | + | 0.679564i | \(0.762169\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10022.6 | − | 103610.i | 0.0984920 | − | 1.01817i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 31856.1 | − | 10350.7i | 0.309159 | − | 0.100452i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −51814.9 | + | 37645.7i | −0.496649 | + | 0.360837i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 213149. | + | 69256.1i | 2.01797 | + | 0.655679i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17793.0 | − | 24490.0i | 0.166400 | − | 0.229030i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20518.6i | 0.189564i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 130067. | 1.18717 | 0.593583 | − | 0.804773i | \(-0.297713\pi\) | ||||
0.593583 | + | 0.804773i | \(0.297713\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10742.5 | + | 7804.89i | 0.0968762 | + | 0.0703847i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 40218.1 | − | 123779.i | 0.358370 | − | 1.10295i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −48084.9 | − | 66183.1i | −0.423398 | − | 0.582757i | 0.543024 | − | 0.839717i | \(-0.317279\pi\) |
−0.966422 | + | 0.256960i | \(0.917279\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11104.5 | + | 34176.1i | 0.0966270 | + | 0.297387i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −43159.3 | + | 99139.9i | −0.371164 | + | 0.852589i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 58384.0 | − | 18970.1i | 0.496256 | − | 0.161243i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −78344.0 | + | 56920.3i | −0.658215 | + | 0.478221i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 219762. | + | 71404.9i | 1.82513 | + | 0.593019i | 0.999589 | + | 0.0286715i | \(0.00912768\pi\) |
0.825537 | + | 0.564348i | \(0.190872\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7604.61 | + | 10466.9i | −0.0624347 | + | 0.0859340i | −0.839093 | − | 0.543989i | \(-0.816913\pi\) |
0.776658 | + | 0.629923i | \(0.216913\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 103772.i | 0.842295i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 59097.3 | 0.474262 | 0.237131 | − | 0.971478i | \(-0.423793\pi\) | ||||
0.237131 | + | 0.971478i | \(0.423793\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −297748. | − | 216326.i | −2.36261 | − | 1.71654i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2865.28 | + | 8818.43i | −0.0224818 | + | 0.0691918i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32828.5 | + | 45184.6i | 0.254720 | + | 0.350591i | 0.917157 | − | 0.398526i | \(-0.130478\pi\) |
−0.662438 | + | 0.749117i | \(0.730478\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −399.455 | − | 1229.40i | −0.00306517 | − | 0.00943361i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −28137.1 | + | 50655.1i | −0.213533 | + | 0.384423i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 187430. | − | 60899.6i | 1.40687 | − | 0.457118i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −128062. | + | 93042.3i | −0.950796 | + | 0.690793i | −0.950995 | − | 0.309207i | \(-0.899937\pi\) |
0.000199318 | 1.00000i | \(0.499937\pi\) | ||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −162817. | − | 52902.3i | −1.19577 | − | 0.388528i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11473.9 | − | 15792.5i | 0.0833612 | − | 0.114737i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 133744.i | − | 0.961297i | −0.876913 | − | 0.480649i | \(-0.840401\pi\) | ||
0.876913 | − | 0.480649i | \(-0.159599\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −107274. | −0.762834 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −124703. | − | 90601.8i | −0.877391 | − | 0.637462i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16655.2 | − | 51259.4i | 0.115950 | − | 0.356858i | −0.876194 | − | 0.481959i | \(-0.839925\pi\) |
0.992144 | + | 0.125101i | \(0.0399255\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16023.3 | + | 22054.1i | 0.110383 | + | 0.151929i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15091.9 | − | 46448.1i | −0.102884 | − | 0.316643i | 0.886344 | − | 0.463027i | \(-0.153237\pi\) |
−0.989228 | + | 0.146383i | \(0.953237\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −63765.9 | − | 27759.7i | −0.430196 | − | 0.187281i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −161785. | + | 52567.2i | −1.08023 | + | 0.350988i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −221746. | + | 161108.i | −1.46540 | + | 1.06468i | −0.483491 | + | 0.875349i | \(0.660631\pi\) |
−0.981914 | + | 0.189329i | \(0.939369\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −94854.8 | − | 30820.2i | −0.620449 | − | 0.201596i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3422.00 | − | 4709.98i | 0.0221562 | − | 0.0304954i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 91529.3i | 0.586632i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 49313.3 | 0.312884 | 0.156442 | − | 0.987687i | \(-0.449998\pi\) | ||||
0.156442 | + | 0.987687i | \(0.449998\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15415.1 | − | 11199.7i | −0.0968280 | − | 0.0703496i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2341.63 | − | 7206.79i | 0.0145623 | − | 0.0448181i | −0.943511 | − | 0.331340i | \(-0.892499\pi\) |
0.958074 | + | 0.286522i | \(0.0924992\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 94112.6 | + | 129535.i | 0.579479 | + | 0.797584i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 40152.5 | + | 123577.i | 0.244795 | + | 0.753402i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24476.8 | + | 2367.76i | 0.147763 | + | 0.0142938i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13724.0 | + | 4459.20i | −0.0820417 | + | 0.0266570i | −0.349750 | − | 0.936843i | \(-0.613734\pi\) |
0.267709 | + | 0.963500i | \(0.413734\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 58029.9 | − | 42161.2i | 0.343533 | − | 0.249591i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −62048.8 | − | 20160.9i | −0.363775 | − | 0.118198i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 240765. | − | 331385.i | 1.39797 | − | 1.92414i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 40295.4i | − | 0.231731i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −229500. | −1.30724 | −0.653619 | − | 0.756824i | \(-0.726750\pi\) | ||||
−0.653619 | + | 0.756824i | \(0.726750\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9854.14 | − | 7159.45i | −0.0555974 | − | 0.0403939i | 0.559639 | − | 0.828736i | \(-0.310940\pi\) |
−0.615237 | + | 0.788342i | \(0.710940\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 31217.1 | − | 96076.4i | 0.174467 | − | 0.536953i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −129796. | − | 178649.i | −0.718593 | − | 0.989058i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6505.56 | − | 20022.1i | −0.0356803 | − | 0.109813i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 43516.6 | + | 73951.1i | 0.236451 | + | 0.401819i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 40180.7 | − | 13055.5i | 0.216303 | − | 0.0702813i | −0.198861 | − | 0.980028i | \(-0.563724\pi\) |
0.415164 | + | 0.909747i | \(0.363724\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −53631.9 | + | 38965.8i | −0.286053 | + | 0.207830i | −0.721553 | − | 0.692359i | \(-0.756572\pi\) |
0.435500 | + | 0.900189i | \(0.356572\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 140244. | + | 45568.2i | 0.741152 | + | 0.240815i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 120469. | − | 165812.i | 0.630831 | − | 0.868264i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 212489.i | 1.10257i | 0.834316 | + | 0.551287i | \(0.185863\pi\) | ||||
−0.834316 | + | 0.551287i | \(0.814137\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −145366. | −0.747457 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −289268. | − | 210166.i | −1.47399 | − | 1.07091i | −0.979434 | − | 0.201766i | \(-0.935332\pi\) |
−0.494553 | − | 0.869148i | \(-0.664668\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 194829. | − | 599624.i | 0.983863 | − | 3.02802i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −61764.3 | − | 85011.3i | −0.309117 | − | 0.425463i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11170.1 | + | 34378.0i | 0.0554069 | + | 0.170525i | 0.974930 | − | 0.222510i | \(-0.0714251\pi\) |
−0.919523 | + | 0.393035i | \(0.871425\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −309561. | + | 68484.7i | −1.52193 | + | 0.336698i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 71473.2 | − | 23223.0i | 0.348295 | − | 0.113168i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −83315.6 | + | 60532.3i | −0.402442 | + | 0.292391i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23357.6 | + | 7589.34i | 0.111840 | + | 0.0363389i | 0.364402 | − | 0.931242i | \(-0.381273\pi\) |
−0.252563 | + | 0.967581i | \(0.581273\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 60098.5 | − | 82718.4i | 0.285258 | − | 0.392624i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41038.8i | 0.193105i | 0.995328 | + | 0.0965523i | \(0.0307815\pi\) | ||||
−0.995328 | + | 0.0965523i | \(0.969218\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 263948. | 1.23128 | 0.615640 | − | 0.788027i | \(-0.288897\pi\) | ||||
0.615640 | + | 0.788027i | \(0.288897\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −123922. | − | 90034.5i | −0.573115 | − | 0.416393i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7002.66 | − | 21552.0i | 0.0321092 | − | 0.0988219i | −0.933718 | − | 0.358011i | \(-0.883455\pi\) |
0.965827 | + | 0.259189i | \(0.0834552\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23439.8 | + | 32262.2i | 0.106564 | + | 0.146672i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4165.16 | + | 12819.0i | 0.0187754 | + | 0.0577848i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −208854. | + | 235857.i | −0.933515 | + | 1.05421i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 431571. | − | 140226.i | 1.91278 | − | 0.621500i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −77752.3 | + | 56490.4i | −0.341725 | + | 0.248278i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −63206.4 | − | 20537.0i | −0.275480 | − | 0.0895089i | 0.168019 | − | 0.985784i | \(-0.446263\pi\) |
−0.443499 | + | 0.896275i | \(0.646263\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21403.8 | − | 29459.9i | 0.0925127 | − | 0.127333i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 29671.9i | − | 0.127189i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 293926. | 1.24955 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −329613. | − | 239478.i | −1.38978 | − | 1.00973i | −0.995890 | − | 0.0905764i | \(-0.971129\pi\) |
−0.393890 | − | 0.919158i | \(-0.628871\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10419.8 | − | 32068.8i | 0.0435754 | − | 0.134111i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20767.7 | − | 28584.3i | −0.0861442 | − | 0.118567i | 0.763770 | − | 0.645489i | \(-0.223346\pi\) |
−0.849914 | + | 0.526921i | \(0.823346\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 46931.8 | + | 144441.i | 0.193096 | + | 0.594288i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 256344. | + | 226996.i | 1.04619 | + | 0.926418i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 107249. | − | 34847.4i | 0.434191 | − | 0.141077i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24801.7 | − | 18019.5i | 0.0996046 | − | 0.0723670i | −0.536868 | − | 0.843666i | \(-0.680393\pi\) |
0.636473 | + | 0.771299i | \(0.280393\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −49912.0 | − | 16217.4i | −0.198852 | − | 0.0646109i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −164396. | + | 226272.i | −0.649764 | + | 0.894323i | −0.999089 | − | 0.0426785i | \(-0.986411\pi\) |
0.349325 | + | 0.937002i | \(0.386411\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 591890.i | 2.32091i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14022.7 | 0.0545527 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −122810. | − | 89227.0i | −0.474024 | − | 0.344398i | 0.324984 | − | 0.945720i | \(-0.394641\pi\) |
−0.799007 | + | 0.601321i | \(0.794641\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18660.0 | + | 57429.5i | −0.0714611 | + | 0.219935i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 123500. | + | 169983.i | 0.469281 | + | 0.645909i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16463.2 | − | 50668.6i | −0.0620727 | − | 0.191040i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −40412.1 | − | 182669.i | −0.151193 | − | 0.683414i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −83148.4 | + | 27016.6i | −0.308688 | + | 0.100299i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1689.60 | − | 1227.57i | 0.00622455 | − | 0.00452240i | −0.584669 | − | 0.811272i | \(-0.698775\pi\) |
0.590893 | + | 0.806750i | \(0.298775\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 290679. | + | 94447.4i | 1.06270 | + | 0.345292i | 0.787641 | − | 0.616135i | \(-0.211302\pi\) |
0.275060 | + | 0.961427i | \(0.411302\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 38614.7 | − | 53148.6i | 0.140099 | − | 0.192829i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 157759.i | − | 0.568033i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 39322.4 | 0.140517 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 259865. | + | 188803.i | 0.921633 | + | 0.669606i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −145077. | + | 446503.i | −0.510676 | + | 1.57170i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −215454. | − | 296547.i | −0.752743 | − | 1.03606i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10220.5 | − | 31455.5i | −0.0354424 | − | 0.109081i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −232021. | + | 136533.i | −0.798637 | + | 0.469959i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −120348. | + | 39103.4i | −0.411192 | + | 0.133604i | −0.507306 | − | 0.861766i | \(-0.669359\pi\) |
0.0961142 | + | 0.995370i | \(0.469359\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 32242.8 | − | 23425.8i | 0.109354 | − | 0.0794500i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −315055. | − | 102368.i | −1.06070 | − | 0.344643i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −208238. | + | 286615.i | −0.695961 | + | 0.957908i | 0.304025 | + | 0.952664i | \(0.401669\pi\) |
−0.999986 | + | 0.00524442i | \(0.998331\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 103649.i | 0.343891i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −312096. | −1.02798 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22689.0 | − | 16484.5i | −0.0741932 | − | 0.0539045i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10765.1 | + | 33131.5i | −0.0349487 | + | 0.107561i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18181.9 | + | 25025.2i | 0.0586042 | + | 0.0806618i | 0.837313 | − | 0.546724i | \(-0.184125\pi\) |
−0.778709 | + | 0.627385i | \(0.784125\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 144158. | + | 443674.i | 0.461335 | + | 1.41984i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8140.23 | − | 84150.2i | 0.0258649 | − | 0.267380i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 338262. | − | 109908.i | 1.06718 | − | 0.346747i | 0.277789 | − | 0.960642i | \(-0.410398\pi\) |
0.789387 | + | 0.613896i | \(0.210398\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 318144. | − | 231145.i | 0.996613 | − | 0.724082i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −37864.6 | − | 12303.0i | −0.117779 | − | 0.0382687i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 257141. | − | 353925.i | 0.794232 | − | 1.09317i | −0.199337 | − | 0.979931i | \(-0.563879\pi\) |
0.993568 | − | 0.113235i | \(-0.0361213\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1830.95i | − | 0.00561570i | −0.999996 | − | 0.00280785i | \(-0.999106\pi\) | ||
0.999996 | − | 0.00280785i | \(-0.000893767\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −139763. | −0.425679 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 571689. | + | 415356.i | 1.72912 | + | 1.25628i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 71653.2 | − | 220526.i | 0.215221 | − | 0.662381i | −0.783917 | − | 0.620865i | \(-0.786781\pi\) |
0.999138 | − | 0.0415155i | \(-0.0132186\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18201.2 | − | 25051.8i | −0.0542930 | − | 0.0747278i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38784.1 | + | 119365.i | 0.114895 | + | 0.353611i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −71043.8 | + | 163193.i | −0.209021 | + | 0.480135i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 482212. | − | 156680.i | 1.40905 | − | 0.457828i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41941.6 | − | 30472.3i | 0.121722 | − | 0.0884361i | −0.525259 | − | 0.850943i | \(-0.676031\pi\) |
0.646981 | + | 0.762506i | \(0.276031\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 308323. | + | 100180.i | 0.888740 | + | 0.288769i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3427.16 | + | 4717.09i | −0.00981205 | + | 0.0135051i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 94653.9i | − | 0.269171i | −0.990902 | − | 0.134586i | \(-0.957030\pi\) | ||
0.990902 | − | 0.134586i | \(-0.0429704\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 101469. | 0.286616 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 83557.7 | + | 60708.2i | 0.234443 | + | 0.170333i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35391.5 | + | 108924.i | −0.0986382 | + | 0.303577i | −0.988185 | − | 0.153267i | \(-0.951020\pi\) |
0.889547 | + | 0.456844i | \(0.151020\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −190529. | − | 262240.i | −0.527486 | − | 0.726023i | 0.459258 | − | 0.888303i | \(-0.348115\pi\) |
−0.986745 | + | 0.162280i | \(0.948115\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −60671.0 | − | 186726.i | −0.166858 | − | 0.513535i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 622355. | + | 121544.i | 1.70031 | + | 0.332064i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 666226. | − | 216470.i | 1.80819 | − | 0.587517i | 0.808191 | − | 0.588920i | \(-0.200447\pi\) |
0.999999 | + | 0.00140328i | \(0.000446679\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −36553.9 | + | 26558.0i | −0.0985597 | + | 0.0716078i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −263477. | − | 85608.7i | −0.705764 | − | 0.229317i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −351341. | + | 483580.i | −0.934992 | + | 1.28691i | 0.0228878 | + | 0.999738i | \(0.492714\pi\) |
−0.957880 | + | 0.287168i | \(0.907286\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 449137.i | − | 1.18749i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −704195. | −1.84979 | −0.924896 | − | 0.380221i | \(-0.875848\pi\) | ||||
−0.924896 | + | 0.380221i | \(0.875848\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31537.5 | + | 22913.3i | 0.0823087 | + | 0.0598008i | 0.628179 | − | 0.778069i | \(-0.283801\pi\) |
−0.545870 | + | 0.837870i | \(0.683801\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −101108. | + | 311180.i | −0.262183 | + | 0.806915i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 113550. | + | 156288.i | 0.292558 | + | 0.402671i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 121186. | + | 372973.i | 0.310237 | + | 0.954811i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 159293. | + | 69346.1i | 0.405192 | + | 0.176395i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34122.9 | + | 11087.2i | −0.0862471 | + | 0.0280234i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15476.7 | + | 11244.5i | −0.0388706 | + | 0.0282411i | −0.607051 | − | 0.794663i | \(-0.707648\pi\) |
0.568180 | + | 0.822904i | \(0.307648\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 272525. | + | 88548.8i | 0.680141 | + | 0.220991i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 175348. | − | 241346.i | 0.434864 | − | 0.598540i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 398647.i | 0.982449i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −555201. | −1.35972 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 277946. | + | 201939.i | 0.676462 | + | 0.491479i | 0.872182 | − | 0.489181i | \(-0.162704\pi\) |
−0.195720 | + | 0.980660i | \(0.562704\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22016.3 | − | 67759.1i | 0.0532503 | − | 0.163887i | −0.920895 | − | 0.389812i | \(-0.872540\pi\) |
0.974145 | + | 0.225924i | \(0.0725401\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −262324. | − | 361058.i | −0.630548 | − | 0.867875i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42270.7 | − | 130096.i | −0.100979 | − | 0.310781i | 0.887787 | − | 0.460255i | \(-0.152242\pi\) |
−0.988766 | + | 0.149474i | \(0.952242\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 592103. | + | 57276.8i | 1.40575 | + | 0.135984i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 44636.8 | − | 14503.4i | 0.105325 | − | 0.0342222i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −439262. | + | 319143.i | −1.03014 | + | 0.748443i | −0.968337 | − | 0.249646i | \(-0.919686\pi\) |
−0.0618056 | + | 0.998088i | \(0.519686\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −60592.4 | − | 19687.7i | −0.141233 | − | 0.0458893i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 174747. | − | 240519.i | 0.404836 | − | 0.557209i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 702060.i | 1.61660i | 0.588768 | + | 0.808302i | \(0.299613\pi\) | ||||
−0.588768 | + | 0.808302i | \(0.700387\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −226372. | −0.518108 | −0.259054 | − | 0.965863i | \(-0.583411\pi\) | ||||
−0.259054 | + | 0.965863i | \(0.583411\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −101282. | − | 73585.4i | −0.230411 | − | 0.167403i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −64434.9 | + | 198310.i | −0.145706 | + | 0.448438i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −285669. | − | 393190.i | −0.642113 | − | 0.883793i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 34599.5 | + | 106486.i | 0.0773069 | + | 0.237926i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 97350.6 | + | 165435.i | 0.216219 | + | 0.367437i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41554.0 | + | 13501.7i | −0.0917450 | + | 0.0298097i | −0.354530 | − | 0.935045i | \(-0.615359\pi\) |
0.262785 | + | 0.964854i | \(0.415359\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −586073. | + | 425807.i | −1.28630 | + | 0.934555i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −488471. | − | 158714.i | −1.06577 | − | 0.346288i | −0.276929 | − | 0.960891i | \(-0.589317\pi\) |
−0.788837 | + | 0.614602i | \(0.789317\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −52936.2 | + | 72860.5i | −0.114819 | + | 0.158035i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 285171.i | − | 0.614909i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 289751. | 0.621131 | 0.310566 | − | 0.950552i | \(-0.399482\pi\) | ||||
0.310566 | + | 0.950552i | \(0.399482\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −635041. | − | 461384.i | −1.35338 | − | 0.983290i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10931.6 | + | 33644.0i | −0.0231617 | + | 0.0712844i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 154917. | + | 213225.i | 0.326333 | + | 0.449159i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 148192. | + | 456087.i | 0.310361 | + | 0.955194i | 0.977622 | + | 0.210370i | \(0.0674667\pi\) |
−0.667261 | + | 0.744824i | \(0.732533\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −102437. | + | 22662.3i | −0.213300 | + | 0.0471887i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −419384. | + | 136266.i | −0.868245 | + | 0.282110i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 374232. | − | 271896.i | 0.770328 | − | 0.559676i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 182241. | + | 59213.7i | 0.372986 | + | 0.121190i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 397842. | − | 547582.i | 0.809607 | − | 1.11433i | −0.181777 | − | 0.983340i | \(-0.558185\pi\) |
0.991384 | − | 0.130989i | \(-0.0418152\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 73729.8i | − | 0.149188i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 265031. | 0.533235 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −146722. | − | 106600.i | −0.293533 | − | 0.213264i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −69762.5 | + | 214707.i | −0.138781 | + | 0.427124i | −0.996159 | − | 0.0875635i | \(-0.972092\pi\) |
0.857378 | + | 0.514687i | \(0.172092\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 81159.3 | + | 111706.i | 0.160546 | + | 0.220972i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 156005. | + | 480133.i | 0.306873 | + | 0.944457i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 622505. | − | 702988.i | 1.21767 | − | 1.37511i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 203841. | − | 66232.0i | 0.396510 | − | 0.128834i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 752504. | − | 546726.i | 1.45563 | − | 1.05758i | 0.471155 | − | 0.882050i | \(-0.343837\pi\) |
0.984475 | − | 0.175527i | \(-0.0561629\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15525.2 | + | 5044.43i | 0.0298652 | + | 0.00970379i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −126008. | + | 173435.i | −0.241058 | + | 0.331788i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1.07605e6i | − | 2.04719i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −141940. | −0.268556 | −0.134278 | − | 0.990944i | \(-0.542872\pi\) | ||||
−0.134278 | + | 0.990944i | \(0.542872\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8373.95 | + | 6084.03i | 0.0157571 | + | 0.0114482i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 142039. | − | 437150.i | 0.265810 | − | 0.818079i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −599214. | − | 824747.i | −1.11525 | − | 1.53502i | −0.813441 | − | 0.581648i | \(-0.802408\pi\) |
−0.301813 | − | 0.953367i | \(-0.597592\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −117851. | − | 362707.i | −0.218151 | − | 0.671401i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −272217. | − | 241052.i | −0.501165 | − | 0.443787i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −902735. | + | 293316.i | −1.65299 | + | 0.537091i | −0.979386 | − | 0.201997i | \(-0.935257\pi\) |
−0.673609 | + | 0.739088i | \(0.735257\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 208130. | − | 151215.i | 0.379051 | − | 0.275397i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −432128. | − | 140407.i | −0.782771 | − | 0.254338i | −0.109748 | − | 0.993959i | \(-0.535004\pi\) |
−0.673023 | + | 0.739622i | \(0.735004\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −675908. | + | 930308.i | −1.21780 | + | 1.67615i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 617923.i | − | 1.10737i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 112314. | 0.200202 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −337489. | − | 245200.i | −0.598383 | − | 0.434751i | 0.246921 | − | 0.969036i | \(-0.420581\pi\) |
−0.845305 | + | 0.534285i | \(0.820581\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17479.0 | − | 53794.8i | 0.0308266 | − | 0.0948747i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −483399. | − | 665341.i | −0.848031 | − | 1.16721i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −344073. | − | 1.05895e6i | −0.600425 | − | 1.84792i | −0.525620 | − | 0.850719i | \(-0.676167\pi\) |
−0.0748048 | − | 0.997198i | \(-0.523833\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 58439.8 | + | 264157.i | 0.101444 | + | 0.458541i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 230550. | − | 74910.2i | 0.398103 | − | 0.129352i | −0.103121 | − | 0.994669i | \(-0.532883\pi\) |
0.501225 | + | 0.865317i | \(0.332883\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 82117.3 | − | 59661.7i | 0.141054 | − | 0.102482i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −475121. | − | 154376.i | −0.811860 | − | 0.263789i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 517766. | − | 712643.i | 0.880121 | − | 1.21138i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 502205.i | 0.849235i | 0.905373 | + | 0.424618i | \(0.139591\pi\) | ||||
−0.905373 | + | 0.424618i | \(0.860409\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 152306. | 0.256218 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 514266. | + | 373636.i | 0.860654 | + | 0.625302i | 0.928063 | − | 0.372423i | \(-0.121473\pi\) |
−0.0674085 | + | 0.997725i | \(0.521473\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −345403. | + | 1.06304e6i | −0.575073 | + | 1.76989i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6274.08 | − | 8635.52i | −0.0103922 | − | 0.0143036i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 293745. | + | 904053.i | 0.484055 | + | 1.48977i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −886163. | + | 521463.i | −1.45282 | + | 0.854912i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 473852. | − | 153964.i | 0.772892 | − | 0.251128i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 119332. | − | 86699.7i | 0.193650 | − | 0.140695i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −573732. | − | 186417.i | −0.926317 | − | 0.300979i | −0.193262 | − | 0.981147i | \(-0.561907\pi\) |
−0.733056 | + | 0.680168i | \(0.761907\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −302545. | + | 416417.i | −0.485999 | + | 0.668921i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 120493.i | 0.192579i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 284243. | 0.452006 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −203986. | − | 148204.i | −0.322750 | − | 0.234491i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 268673. | − | 826889.i | 0.422967 | − | 1.30176i | −0.481960 | − | 0.876193i | \(-0.660075\pi\) |
0.904927 | − | 0.425566i | \(-0.139925\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 160443. | + | 220831.i | 0.251320 | + | 0.345912i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −293910. | − | 904561.i | −0.458088 | − | 1.40985i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 53012.8 | − | 548023.i | 0.0822147 | − | 0.849900i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −308817. | + | 100341.i | −0.476551 | + | 0.154841i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −226208. | + | 164350.i | −0.347345 | + | 0.252361i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 344281. | + | 111864.i | 0.526036 | + | 0.170920i | 0.559983 | − | 0.828504i | \(-0.310808\pi\) |
−0.0339467 | + | 0.999424i | \(0.510808\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −332769. | + | 458018.i | −0.505943 | + | 0.696371i | −0.983229 | − | 0.182377i | \(-0.941621\pi\) |
0.477285 | + | 0.878748i | \(0.341621\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 315570.i | − | 0.477435i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −369000. | −0.555535 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 764162. | + | 555196.i | 1.14483 | + | 0.831768i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −48007.7 | + | 147752.i | −0.0715719 | + | 0.220276i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 426408. | + | 586901.i | 0.632615 | + | 0.870720i | 0.998195 | − | 0.0600604i | \(-0.0191293\pi\) |
−0.365580 | + | 0.930780i | \(0.619129\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −291256. | − | 896394.i | −0.430007 | − | 1.32343i | −0.898118 | − | 0.439756i | \(-0.855065\pi\) |
0.468110 | − | 0.883670i | \(-0.344935\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −239093. | + | 549213.i | −0.351285 | + | 0.806925i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −303169. | + | 98505.6i | −0.443276 | + | 0.144029i | −0.522146 | − | 0.852856i | \(-0.674869\pi\) |
0.0788708 | + | 0.996885i | \(0.474869\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −793128. | + | 576241.i | −1.15408 | + | 0.838485i | −0.989017 | − | 0.147799i | \(-0.952781\pi\) |
−0.165058 | + | 0.986284i | \(0.552781\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 166791. | + | 54193.6i | 0.241529 | + | 0.0784776i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 230873. | − | 317770.i | 0.332724 | − | 0.457955i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 574313.i | 0.823713i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −517543. | −0.738747 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 423441. | + | 307648.i | 0.601546 | + | 0.437048i | 0.846427 | − | 0.532505i | \(-0.178749\pi\) |
−0.244882 | + | 0.969553i | \(0.578749\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10133.9 | + | 31188.9i | −0.0143280 | + | 0.0440969i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 182080. | + | 250612.i | 0.256217 | + | 0.352652i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −47420.3 | − | 145945.i | −0.0664127 | − | 0.204397i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −142216. | + | 132384.i | −0.198235 | + | 0.184531i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −338003. | + | 109824.i | −0.468927 | + | 0.152364i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 92887.4 | − | 67486.7i | 0.128262 | − | 0.0931877i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 328116. | + | 106611.i | 0.450951 | + | 0.146523i | 0.525683 | − | 0.850681i | \(-0.323810\pi\) |
−0.0747314 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 603421. | − | 830537.i | 0.825445 | − | 1.13613i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 652071.i | − | 0.887837i | −0.896067 | − | 0.443919i | \(-0.853588\pi\) | ||
0.896067 | − | 0.443919i | \(-0.146412\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 559418. | 0.758142 | 0.379071 | − | 0.925368i | \(-0.376244\pi\) | ||||
0.379071 | + | 0.925368i | \(0.376244\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 111335. | + | 80889.9i | 0.150185 | + | 0.109116i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 116919. | − | 359840.i | 0.156987 | − | 0.483157i | −0.841370 | − | 0.540460i | \(-0.818250\pi\) |
0.998357 | + | 0.0573033i | \(0.0182502\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 562363. | + | 774026.i | 0.751596 | + | 1.03448i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −64029.4 | − | 197062.i | −0.0851806 | − | 0.262159i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 234457. | + | 102068.i | 0.310474 | + | 0.135161i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −512071. | + | 166382.i | −0.674985 | + | 0.219316i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 358719. | − | 260625.i | 0.470680 | − | 0.341969i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −342094. | − | 111153.i | −0.446817 | − | 0.145180i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 133607. | − | 183894.i | 0.173712 | − | 0.239094i | −0.713280 | − | 0.700880i | \(-0.752791\pi\) |
0.886992 | + | 0.461785i | \(0.152791\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 81196.0i | 0.105089i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 721351. | 0.929383 | 0.464692 | − | 0.885473i | \(-0.346165\pi\) | ||||
0.464692 | + | 0.885473i | \(0.346165\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 173179. | + | 125822.i | 0.222113 | + | 0.161374i | 0.693277 | − | 0.720671i | \(-0.256166\pi\) |
−0.471165 | + | 0.882045i | \(0.656166\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −260410. | + | 801461.i | −0.332485 | + | 1.02328i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 720290. | + | 991394.i | 0.915504 | + | 1.26008i | 0.965252 | + | 0.261322i | \(0.0841583\pi\) |
−0.0497477 | + | 0.998762i | \(0.515842\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28246.3 | + | 86933.2i | 0.0357403 | + | 0.109997i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 361325. | + | 34952.6i | 0.455137 | + | 0.0440275i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −533473. | + | 173336.i | −0.668974 | + | 0.217363i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −292818. | + | 212745.i | −0.365554 | + | 0.265591i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 381012. | + | 123798.i | 0.473537 | + | 0.153862i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 451861. | − | 621934.i | 0.559095 | − | 0.769528i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 259685.i | − | 0.319888i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 136746. | 0.167703 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −352844. | − | 256356.i | −0.430810 | − | 0.313001i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 313569. | − | 965067.i | 0.381170 | − | 1.17312i | −0.558050 | − | 0.829807i | \(-0.688450\pi\) |
0.939221 | − | 0.343314i | \(-0.111550\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 524830. | + | 722367.i | 0.635172 | + | 0.874239i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −369150. | − | 1.13613e6i | −0.444802 | − | 1.36896i | −0.882701 | − | 0.469935i | \(-0.844277\pi\) |
0.437899 | − | 0.899024i | \(-0.355723\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −580373. | − | 986274.i | −0.696251 | − | 1.18319i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −258617. | + | 84029.9i | −0.308898 | + | 0.100367i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15793.0 | − | 11474.3i | 0.0187814 | − | 0.0136455i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.42102e6 | + | 461717.i | 1.68255 | + | 0.546695i | 0.985404 | − | 0.170230i | \(-0.0544512\pi\) |
0.697150 | + | 0.716925i | \(0.254451\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 311316. | − | 428490.i | 0.367014 | − | 0.505151i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.52256e6i | 1.78719i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 254207. | 0.297101 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −65020.5 | − | 47240.1i | −0.0756642 | − | 0.0549733i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −147042. | + | 452547.i | −0.170376 | + | 0.524364i | −0.999392 | − | 0.0348610i | \(-0.988901\pi\) |
0.829016 | + | 0.559225i | \(0.188901\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 474436. | + | 653005.i | 0.547367 | + | 0.753385i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 51712.0 | + | 159153.i | 0.0594057 | + | 0.182832i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −903341. | + | 199848.i | −1.03330 | + | 0.228600i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 869952. | − | 282665.i | 0.990869 | − | 0.321953i | 0.231658 | − | 0.972797i | \(-0.425585\pi\) |
0.759211 | + | 0.650845i | \(0.225585\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 553241. | − | 401953.i | 0.627456 | − | 0.455874i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 790180. | + | 256745.i | 0.892374 | + | 0.289950i | 0.719086 | − | 0.694921i | \(-0.244561\pi\) |
0.173288 | + | 0.984871i | \(0.444561\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −870087. | + | 1.19757e6i | −0.978451 | + | 1.34672i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 332879.i | − | 0.372755i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 322279. | 0.359362 | 0.179681 | − | 0.983725i | \(-0.442494\pi\) | ||||
0.179681 | + | 0.983725i | \(0.442494\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −659590. | − | 479220.i | −0.732389 | − | 0.532112i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −103137. | + | 317424.i | −0.114039 | + | 0.350977i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −182953. | − | 251813.i | −0.201444 | − | 0.277263i | 0.696329 | − | 0.717723i | \(-0.254816\pi\) |
−0.897772 | + | 0.440459i | \(0.854816\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 472632. | + | 1.45461e6i | 0.518223 | + | 1.59493i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 273118. | − | 308429.i | 0.298213 | − | 0.336769i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 228743. | − | 74323.0i | 0.248720 | − | 0.0808139i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 101111. | − | 73461.5i | 0.109484 | − | 0.0795450i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −525898. | − | 170875.i | −0.567086 | − | 0.184257i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −199182. | + | 274151.i | −0.213893 | + | 0.294398i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 852868.i | − | 0.912072i | −0.889961 | − | 0.456036i | \(-0.849269\pi\) | ||
0.889961 | − | 0.456036i | \(-0.150731\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −253480. | −0.269957 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 372880. | + | 270914.i | 0.395486 | + | 0.287337i | 0.767700 | − | 0.640810i | \(-0.221401\pi\) |
−0.372214 | + | 0.928147i | \(0.621401\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 41752.7 | − | 128502.i | 0.0441021 | − | 0.135732i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 521363. | + | 717595.i | 0.548443 | + | 0.754867i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −252268. | − | 776402.i | −0.264285 | − | 0.813387i | −0.991857 | − | 0.127355i | \(-0.959351\pi\) |
0.727572 | − | 0.686032i | \(-0.240649\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.31871e6 | − | 1.16773e6i | −1.37589 | − | 1.21837i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −475276. | + | 154427.i | −0.493865 | + | 0.160466i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.31752e6 | + | 957232.i | −1.36348 | + | 0.990627i | −0.365267 | + | 0.930903i | \(0.619022\pi\) |
−0.998215 | + | 0.0597245i | \(0.980978\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 60683.8 | + | 19717.4i | 0.0625461 | + | 0.0203225i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −47732.3 | + | 65697.9i | −0.0489980 | + | 0.0674399i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.47090e6i | 1.50380i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 552727. | 0.562812 | 0.281406 | − | 0.959589i | \(-0.409199\pi\) | ||||
0.281406 | + | 0.959589i | \(0.409199\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 416457. | + | 302574.i | 0.422350 | + | 0.306855i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 349270. | − | 1.07494e6i | 0.352789 | − | 1.08577i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 701494. | + | 965524.i | 0.705722 | + | 0.971344i | 0.999879 | + | 0.0155861i | \(0.00496143\pi\) |
−0.294156 | + | 0.955757i | \(0.595039\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 36372.5 | + | 111943.i | 0.0364454 | + | 0.112167i |
(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 | 176.5.n.c.17.3 | 16 | ||
4.3 | odd | 2 | 22.5.d.a.17.1 | yes | 16 | ||
11.2 | odd | 10 | inner | 176.5.n.c.145.3 | 16 | ||
12.11 | even | 2 | 198.5.j.a.127.3 | 16 | |||
44.3 | odd | 10 | 242.5.b.e.241.13 | 16 | |||
44.19 | even | 10 | 242.5.b.e.241.5 | 16 | |||
44.35 | even | 10 | 22.5.d.a.13.1 | ✓ | 16 | ||
132.35 | odd | 10 | 198.5.j.a.145.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.5.d.a.13.1 | ✓ | 16 | 44.35 | even | 10 | ||
22.5.d.a.17.1 | yes | 16 | 4.3 | odd | 2 | ||
176.5.n.c.17.3 | 16 | 1.1 | even | 1 | trivial | ||
176.5.n.c.145.3 | 16 | 11.2 | odd | 10 | inner | ||
198.5.j.a.127.3 | 16 | 12.11 | even | 2 | |||
198.5.j.a.145.3 | 16 | 132.35 | odd | 10 | |||
242.5.b.e.241.5 | 16 | 44.19 | even | 10 | |||
242.5.b.e.241.13 | 16 | 44.3 | odd | 10 |