Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,3,Mod(145,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.be (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.8502001097\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 6.0.92607408.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 57) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.2 | ||
Root | \(0.500000 - 2.69511i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.145 |
Dual form | 912.3.be.f.673.2 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50000 | − | 0.866025i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.32722 | + | 4.03087i | 0.465445 | + | 0.806174i | 0.999221 | − | 0.0394517i | \(-0.0125611\pi\) |
−0.533777 | + | 0.845625i | \(0.679228\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.6817 | 1.52596 | 0.762978 | − | 0.646424i | \(-0.223736\pi\) | ||||
0.762978 | + | 0.646424i | \(0.223736\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.37280 | 0.579346 | 0.289673 | − | 0.957126i | \(-0.406453\pi\) | ||||
0.289673 | + | 0.957126i | \(0.406453\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.3770 | + | 8.87792i | 1.18285 | + | 0.682917i | 0.956671 | − | 0.291170i | \(-0.0940444\pi\) |
0.226176 | + | 0.974087i | \(0.427378\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.98167 | + | 4.03087i | 0.465445 | + | 0.268725i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.84976 | − | 10.1321i | −0.344104 | − | 0.596005i | 0.641087 | − | 0.767468i | \(-0.278484\pi\) |
−0.985191 | + | 0.171463i | \(0.945151\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.88643 | − | 18.5983i | 0.204549 | − | 0.978856i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 16.0225 | − | 9.25062i | 0.762978 | − | 0.440506i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −13.9817 | + | 24.2170i | −0.607899 | + | 1.05291i | 0.383688 | + | 0.923463i | \(0.374654\pi\) |
−0.991586 | + | 0.129448i | \(0.958679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.66807 | − | 2.88918i | 0.0667228 | − | 0.115567i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −33.2498 | − | 19.1968i | −1.14655 | − | 0.661958i | −0.198502 | − | 0.980100i | \(-0.563608\pi\) |
−0.948043 | + | 0.318142i | \(0.896941\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 42.9440i | 1.38529i | 0.721278 | + | 0.692645i | \(0.243555\pi\) | ||||
−0.721278 | + | 0.692645i | \(0.756445\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.55920 | − | 5.51901i | 0.289673 | − | 0.167243i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 24.8587 | + | 43.0565i | 0.710248 | + | 1.23019i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 33.9790i | 0.918351i | 0.888346 | + | 0.459176i | \(0.151855\pi\) | ||||
−0.888346 | + | 0.459176i | \(0.848145\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 30.7540 | 0.788565 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16.3728 | − | 9.45284i | 0.399337 | − | 0.230557i | −0.286861 | − | 0.957972i | \(-0.592612\pi\) |
0.686198 | + | 0.727415i | \(0.259278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −26.5089 | − | 45.9148i | −0.616486 | − | 1.06779i | −0.990122 | − | 0.140210i | \(-0.955222\pi\) |
0.373635 | − | 0.927576i | \(-0.378111\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13.9633 | 0.310296 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.0272 | − | 20.8318i | 0.255899 | − | 0.443230i | −0.709240 | − | 0.704967i | \(-0.750962\pi\) |
0.965139 | + | 0.261737i | \(0.0842952\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 65.0986 | 1.32854 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −17.5493 | − | 10.1321i | −0.344104 | − | 0.198668i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.3224 | − | 7.69168i | −0.251366 | − | 0.145126i | 0.369024 | − | 0.929420i | \(-0.379692\pi\) |
−0.620389 | + | 0.784294i | \(0.713025\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.8309 | + | 25.6879i | 0.269653 | + | 0.467053i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.2769 | − | 31.2632i | −0.180297 | − | 0.548476i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −25.6539 | + | 14.8113i | −0.434813 | + | 0.251039i | −0.701395 | − | 0.712773i | \(-0.747439\pi\) |
0.266582 | + | 0.963812i | \(0.414106\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −21.3403 | + | 36.9626i | −0.349842 | + | 0.605944i | −0.986221 | − | 0.165433i | \(-0.947098\pi\) |
0.636379 | + | 0.771376i | \(0.280431\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 16.0225 | − | 27.7519i | 0.254326 | − | 0.440506i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 82.6436i | 1.27144i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.1585 | + | 8.75178i | 0.226247 | + | 0.130624i | 0.608839 | − | 0.793294i | \(-0.291635\pi\) |
−0.382593 | + | 0.923917i | \(0.624969\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 48.4339i | 0.701941i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 74.6028 | − | 43.0719i | 1.05074 | − | 0.606647i | 0.127886 | − | 0.991789i | \(-0.459181\pi\) |
0.922857 | + | 0.385142i | \(0.125847\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 46.2352 | + | 80.0817i | 0.633359 | + | 1.09701i | 0.986860 | + | 0.161576i | \(0.0516576\pi\) |
−0.353502 | + | 0.935434i | \(0.615009\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 5.77836i | − | 0.0770448i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 68.0723 | 0.884056 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 26.3908 | − | 15.2367i | 0.334060 | − | 0.192870i | −0.323582 | − | 0.946200i | \(-0.604887\pi\) |
0.657642 | + | 0.753330i | \(0.271554\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −77.1154 | −0.929101 | −0.464551 | − | 0.885547i | \(-0.653784\pi\) | ||||
−0.464551 | + | 0.885547i | \(0.653784\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 27.2274 | − | 47.1592i | 0.320322 | − | 0.554815i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −66.4996 | −0.764364 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −76.8129 | − | 44.3479i | −0.863066 | − | 0.498291i | 0.00197195 | − | 0.999998i | \(-0.499372\pi\) |
−0.865038 | + | 0.501707i | \(0.832706\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 164.253 | + | 94.8312i | 1.80497 | + | 1.04210i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 37.1906 | + | 64.4160i | 0.399899 | + | 0.692645i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 84.0118 | − | 27.6166i | 0.884334 | − | 0.290702i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.82351 | + | 1.05281i | −0.0187991 | + | 0.0108537i | −0.509370 | − | 0.860548i | \(-0.670122\pi\) |
0.490571 | + | 0.871401i | \(0.336788\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.55920 | − | 16.5570i | 0.0965576 | − | 0.167243i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.7690 | + | 23.8486i | −0.136327 | + | 0.236125i | −0.926104 | − | 0.377269i | \(-0.876863\pi\) |
0.789777 | + | 0.613395i | \(0.210196\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 102.351i | − | 0.993696i | −0.867837 | − | 0.496848i | \(-0.834491\pi\) | ||
0.867837 | − | 0.496848i | \(-0.165509\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 74.5760 | + | 43.0565i | 0.710248 | + | 0.410062i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 0.549592i | − | 0.00513638i | −0.999997 | − | 0.00256819i | \(-0.999183\pi\) | ||
0.999997 | − | 0.00256819i | \(-0.000817481\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 80.7219 | − | 46.6048i | 0.740568 | − | 0.427567i | −0.0817076 | − | 0.996656i | \(-0.526037\pi\) |
0.822276 | + | 0.569089i | \(0.192704\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 29.4267 | + | 50.9685i | 0.265105 | + | 0.459176i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 55.4186i | − | 0.490430i | −0.969469 | − | 0.245215i | \(-0.921141\pi\) | ||
0.969469 | − | 0.245215i | \(-0.0788586\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −130.154 | −1.13177 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 46.1310 | − | 26.6338i | 0.394282 | − | 0.227639i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −62.4854 | − | 108.228i | −0.525087 | − | 0.909478i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −80.3874 | −0.664359 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.3728 | − | 28.3585i | 0.133112 | − | 0.230557i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 131.889 | 1.05511 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 82.7181 | + | 47.7573i | 0.651324 | + | 0.376042i | 0.788963 | − | 0.614441i | \(-0.210618\pi\) |
−0.137640 | + | 0.990482i | \(0.543952\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −79.5267 | − | 45.9148i | −0.616486 | − | 0.355929i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 84.0762 | + | 145.624i | 0.641803 | + | 1.11164i | 0.985030 | + | 0.172383i | \(0.0551466\pi\) |
−0.343227 | + | 0.939252i | \(0.611520\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 41.5136 | − | 198.661i | 0.312133 | − | 1.49369i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 20.9450 | − | 12.0926i | 0.155148 | − | 0.0895748i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 59.3774 | − | 102.845i | 0.433412 | − | 0.750691i | −0.563753 | − | 0.825943i | \(-0.690643\pi\) |
0.997165 | + | 0.0752526i | \(0.0239763\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 55.1822 | − | 95.5784i | 0.396994 | − | 0.687614i | −0.596359 | − | 0.802718i | \(-0.703387\pi\) |
0.993354 | + | 0.115104i | \(0.0367200\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 41.6636i | − | 0.295487i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 97.9947 | + | 56.5772i | 0.685277 | + | 0.395645i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 178.701i | − | 1.23242i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 97.6479 | − | 56.3770i | 0.664271 | − | 0.383517i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 28.8719 | + | 50.0077i | 0.193771 | + | 0.335622i | 0.946497 | − | 0.322712i | \(-0.104595\pi\) |
−0.752726 | + | 0.658334i | \(0.771261\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 205.459i | 1.36066i | 0.732908 | + | 0.680328i | \(0.238163\pi\) | ||||
−0.732908 | + | 0.680328i | \(0.761837\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −35.0986 | −0.229402 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −173.102 | + | 99.9403i | −1.11678 | + | 0.644776i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −55.6080 | − | 96.3159i | −0.354191 | − | 0.613477i | 0.632788 | − | 0.774325i | \(-0.281910\pi\) |
−0.986979 | + | 0.160848i | \(0.948577\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −26.6448 | −0.167577 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −149.348 | + | 258.678i | −0.927627 | + | 1.60670i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −69.1905 | −0.424481 | −0.212241 | − | 0.977217i | \(-0.568076\pi\) | ||||
−0.212241 | + | 0.977217i | \(0.568076\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 44.4928 | + | 25.6879i | 0.269653 | + | 0.155684i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −181.817 | − | 104.972i | −1.08873 | − | 0.628577i | −0.155490 | − | 0.987837i | \(-0.549696\pi\) |
−0.933237 | + | 0.359261i | \(0.883029\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 73.1350 | + | 126.674i | 0.432751 | + | 0.749547i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −42.4901 | − | 37.9946i | −0.248480 | − | 0.222191i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −264.781 | + | 152.871i | −1.53053 | + | 0.883649i | −0.531188 | + | 0.847254i | \(0.678254\pi\) |
−0.999337 | + | 0.0363949i | \(0.988413\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.8178 | − | 30.8613i | 0.101816 | − | 0.176351i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −25.6539 | + | 44.4339i | −0.144938 | + | 0.251039i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 303.001i | 1.69274i | 0.532593 | + | 0.846371i | \(0.321218\pi\) | ||||
−0.532593 | + | 0.846371i | \(0.678782\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −62.8763 | − | 36.3016i | −0.347383 | − | 0.200561i | 0.316149 | − | 0.948709i | \(-0.397610\pi\) |
−0.663532 | + | 0.748148i | \(0.730943\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 73.9251i | 0.403962i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −136.965 | + | 79.0767i | −0.740350 | + | 0.427442i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −37.2794 | − | 64.5698i | −0.199355 | − | 0.345293i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 55.5037i | − | 0.293670i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 48.5734 | 0.254311 | 0.127156 | − | 0.991883i | \(-0.459415\pi\) | ||||
0.127156 | + | 0.991883i | \(0.459415\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.48401 | − | 5.47559i | 0.0491399 | − | 0.0283710i | −0.475229 | − | 0.879862i | \(-0.657635\pi\) |
0.524369 | + | 0.851491i | \(0.324301\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 71.5715 | + | 123.965i | 0.367033 | + | 0.635720i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 104.442 | 0.530163 | 0.265082 | − | 0.964226i | \(-0.414601\pi\) | ||||
0.265082 | + | 0.964226i | \(0.414601\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 140.643 | − | 243.602i | 0.706751 | − | 1.22413i | −0.259305 | − | 0.965795i | \(-0.583494\pi\) |
0.966056 | − | 0.258333i | \(-0.0831731\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 30.3171 | 0.150831 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −355.164 | − | 205.054i | −1.74958 | − | 1.01012i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 76.2063 | + | 43.9977i | 0.371738 | + | 0.214623i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 41.9450 | + | 72.6509i | 0.202633 | + | 0.350970i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.7674 | − | 118.523i | 0.118504 | − | 0.567096i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −89.2808 | + | 51.5463i | −0.423132 | + | 0.244295i | −0.696416 | − | 0.717638i | \(-0.745223\pi\) |
0.273285 | + | 0.961933i | \(0.411890\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 74.6028 | − | 129.216i | 0.350248 | − | 0.606647i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 123.384 | − | 213.708i | 0.573880 | − | 0.993990i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 458.715i | 2.11389i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 138.706 | + | 80.0817i | 0.633359 | + | 0.365670i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 207.735i | − | 0.939977i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 68.9560 | − | 39.8118i | 0.309220 | − | 0.178528i | −0.337357 | − | 0.941377i | \(-0.609533\pi\) |
0.646577 | + | 0.762848i | \(0.276200\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.00421 | − | 8.66754i | −0.0222409 | − | 0.0385224i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 131.031i | 0.577228i | 0.957446 | + | 0.288614i | \(0.0931944\pi\) | ||||
−0.957446 | + | 0.288614i | \(0.906806\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 30.3537 | 0.132549 | 0.0662745 | − | 0.997801i | \(-0.478889\pi\) | ||||
0.0662745 | + | 0.997801i | \(0.478889\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 102.108 | − | 58.9524i | 0.442028 | − | 0.255205i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −47.0484 | − | 81.4902i | −0.201924 | − | 0.349743i | 0.747224 | − | 0.664572i | \(-0.231386\pi\) |
−0.949148 | + | 0.314829i | \(0.898053\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 111.960 | 0.476427 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 26.3908 | − | 45.7101i | 0.111353 | − | 0.192870i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −375.297 | −1.57028 | −0.785141 | − | 0.619317i | \(-0.787409\pi\) | ||||
−0.785141 | + | 0.619317i | \(0.787409\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.482424 | + | 0.278528i | 0.00200176 | + | 0.00115572i | 0.501001 | − | 0.865447i | \(-0.332965\pi\) |
−0.498999 | + | 0.866603i | \(0.666299\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5000 | − | 7.79423i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 151.499 | + | 262.404i | 0.618363 | + | 1.07104i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 224.876 | − | 251.482i | 0.910428 | − | 1.01815i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −115.673 | + | 66.7839i | −0.464551 | + | 0.268208i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −117.309 | + | 203.185i | −0.467367 | + | 0.809504i | −0.999305 | − | 0.0372799i | \(-0.988131\pi\) |
0.531938 | + | 0.846783i | \(0.321464\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −89.1024 | + | 154.330i | −0.352183 | + | 0.610000i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 94.3185i | − | 0.369876i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.0702 | − | 6.39141i | −0.0430749 | − | 0.0248693i | 0.478308 | − | 0.878192i | \(-0.341250\pi\) |
−0.521383 | + | 0.853323i | \(0.674584\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 362.953i | 1.40136i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −99.7494 | + | 57.5904i | −0.382182 | + | 0.220653i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −106.457 | − | 184.389i | −0.404780 | − | 0.701099i | 0.589516 | − | 0.807757i | \(-0.299319\pi\) |
−0.994296 | + | 0.106657i | \(0.965985\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 71.6010i | − | 0.270193i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −153.626 | −0.575377 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −438.717 | + | 253.293i | −1.63092 | + | 0.941610i | −0.647106 | + | 0.762400i | \(0.724021\pi\) |
−0.983811 | + | 0.179211i | \(0.942646\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −110.063 | − | 190.635i | −0.406136 | − | 0.703449i | 0.588317 | − | 0.808631i | \(-0.299791\pi\) |
−0.994453 | + | 0.105182i | \(0.966457\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 328.505 | 1.20332 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.6303 | − | 18.4122i | 0.0386556 | − | 0.0669534i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 262.083 | 0.946148 | 0.473074 | − | 0.881023i | \(-0.343144\pi\) | ||||
0.473074 | + | 0.881023i | \(0.343144\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 111.572 | + | 64.4160i | 0.399899 | + | 0.230882i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −346.203 | − | 199.880i | −1.23204 | − | 0.711317i | −0.264583 | − | 0.964363i | \(-0.585234\pi\) |
−0.967454 | + | 0.253046i | \(0.918568\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −41.2358 | − | 71.4225i | −0.145710 | − | 0.252376i | 0.783928 | − | 0.620852i | \(-0.213213\pi\) |
−0.929637 | + | 0.368475i | \(0.879880\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 102.101 | − | 114.181i | 0.358249 | − | 0.400636i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 174.889 | − | 100.972i | 0.609370 | − | 0.351820i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 76.0605 | − | 131.741i | 0.263185 | − | 0.455850i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.82351 | + | 3.15842i | −0.00626637 | + | 0.0108537i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 223.552i | 0.762977i | 0.924374 | + | 0.381489i | \(0.124588\pi\) | ||||
−0.924374 | + | 0.381489i | \(0.875412\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −119.405 | − | 68.9384i | −0.404762 | − | 0.233690i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 33.1141i | − | 0.111495i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −429.993 | + | 248.256i | −1.43810 | + | 0.830289i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −283.160 | − | 490.448i | −0.940731 | − | 1.62939i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 47.6973i | 0.157417i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −198.655 | −0.651328 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −339.034 | + | 195.741i | −1.10434 | + | 0.637594i | −0.937359 | − | 0.348366i | \(-0.886737\pi\) |
−0.166986 | + | 0.985959i | \(0.553403\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −88.6383 | − | 153.526i | −0.286855 | − | 0.496848i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −375.828 | −1.20845 | −0.604224 | − | 0.796814i | \(-0.706517\pi\) | ||||
−0.604224 | + | 0.796814i | \(0.706517\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 75.3935 | − | 130.585i | 0.240874 | − | 0.417206i | −0.720090 | − | 0.693881i | \(-0.755899\pi\) |
0.960963 | + | 0.276675i | \(0.0892327\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 149.152 | 0.473499 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −438.163 | − | 252.973i | −1.38222 | − | 0.798024i | −0.389796 | − | 0.920901i | \(-0.627454\pi\) |
−0.992422 | + | 0.122878i | \(0.960788\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −211.895 | − | 122.337i | −0.664246 | − | 0.383503i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.475961 | − | 0.824389i | −0.00148274 | − | 0.00256819i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −211.174 | + | 69.4179i | −0.653789 | + | 0.214916i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 51.2998 | − | 29.6180i | 0.157846 | − | 0.0911322i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 80.7219 | − | 139.814i | 0.246856 | − | 0.427567i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 128.471 | − | 222.519i | 0.390491 | − | 0.676349i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 443.028i | − | 1.33845i | −0.743058 | − | 0.669227i | \(-0.766626\pi\) | ||
0.743058 | − | 0.669227i | \(-0.233374\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 88.2800 | + | 50.9685i | 0.265105 | + | 0.153059i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 81.4694i | 0.243192i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 168.764 | − | 97.4357i | 0.500782 | − | 0.289127i | −0.228254 | − | 0.973602i | \(-0.573302\pi\) |
0.729037 | + | 0.684475i | \(0.239968\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −47.9939 | − | 83.1279i | −0.141575 | − | 0.245215i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 273.674i | 0.802562i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 171.960 | 0.501341 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −195.231 | + | 112.717i | −0.565886 | + | 0.326715i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −262.446 | − | 454.570i | −0.756329 | − | 1.31000i | −0.944711 | − | 0.327905i | \(-0.893658\pi\) |
0.188382 | − | 0.982096i | \(-0.439676\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −369.064 | −1.05749 | −0.528745 | − | 0.848781i | \(-0.677337\pi\) | ||||
−0.528745 | + | 0.848781i | \(0.677337\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 46.1310 | − | 79.9013i | 0.131427 | − | 0.227639i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 323.725 | 0.917067 | 0.458533 | − | 0.888677i | \(-0.348375\pi\) | ||||
0.458533 | + | 0.888677i | \(0.348375\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 347.235 | + | 200.476i | 0.978126 | + | 0.564721i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −187.456 | − | 108.228i | −0.525087 | − | 0.303159i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.25614 | + | 10.8359i | 0.0174266 | + | 0.0301837i | 0.874607 | − | 0.484832i | \(-0.161119\pi\) |
−0.857181 | + | 0.515016i | \(0.827786\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −330.791 | − | 144.562i | −0.916320 | − | 0.400448i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −120.581 | + | 69.6175i | −0.332179 | + | 0.191784i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −215.199 | + | 372.736i | −0.589587 | + | 1.02119i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 44.3159 | − | 76.7574i | 0.120752 | − | 0.209148i | −0.799313 | − | 0.600916i | \(-0.794803\pi\) |
0.920064 | + | 0.391767i | \(0.128136\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 56.7171i | − | 0.153705i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −142.306 | − | 82.1602i | −0.383573 | − | 0.221456i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 406.489i | 1.08978i | 0.838507 | + | 0.544892i | \(0.183429\pi\) | ||||
−0.838507 | + | 0.544892i | \(0.816571\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 197.834 | − | 114.219i | 0.527556 | − | 0.304585i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −340.855 | − | 590.378i | −0.904125 | − | 1.56599i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 433.800i | 1.14459i | 0.820047 | + | 0.572296i | \(0.193947\pi\) | ||||
−0.820047 | + | 0.572296i | \(0.806053\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 165.436 | 0.434216 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 355.819 | − | 205.432i | 0.929031 | − | 0.536377i | 0.0425263 | − | 0.999095i | \(-0.486459\pi\) |
0.886505 | + | 0.462719i | \(0.153126\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 158.419 | + | 274.391i | 0.411479 | + | 0.712703i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −159.053 | −0.410991 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −94.6013 | + | 163.854i | −0.243191 | + | 0.421219i | −0.961621 | − | 0.274380i | \(-0.911528\pi\) |
0.718430 | + | 0.695599i | \(0.244861\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 327.158 | 0.836721 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 252.228 | + | 145.624i | 0.641803 | + | 0.370545i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 122.834 | + | 70.9185i | 0.310973 | + | 0.179540i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −220.839 | − | 382.504i | −0.556269 | − | 0.963487i | −0.997804 | − | 0.0662425i | \(-0.978899\pi\) |
0.441534 | − | 0.897244i | \(-0.354434\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −109.775 | − | 333.943i | −0.275125 | − | 0.836951i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 320.526 | − | 185.056i | 0.799316 | − | 0.461485i | −0.0439159 | − | 0.999035i | \(-0.513983\pi\) |
0.843232 | + | 0.537550i | \(0.180650\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −381.254 | + | 660.351i | −0.946039 | + | 1.63859i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.9450 | − | 36.2778i | 0.0517161 | − | 0.0895748i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 216.541i | 0.532043i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 418.387 | + | 241.556i | 1.02295 | + | 0.590602i | 0.914958 | − | 0.403550i | \(-0.132224\pi\) |
0.107995 | + | 0.994151i | \(0.465557\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 205.689i | − | 0.500461i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −274.028 | + | 158.210i | −0.663505 | + | 0.383075i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −179.465 | − | 310.842i | −0.432445 | − | 0.749017i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 191.157i | − | 0.458409i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 295.264 | 0.704687 | 0.352344 | − | 0.935871i | \(-0.385385\pi\) | ||||
0.352344 | + | 0.935871i | \(0.385385\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −449.581 | + | 259.566i | −1.06789 | + | 0.616545i | −0.927604 | − | 0.373566i | \(-0.878135\pi\) |
−0.140284 | + | 0.990111i | \(0.544802\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −36.0817 | − | 62.4954i | −0.0852996 | − | 0.147743i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −39.0312 | −0.0918382 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −227.951 | + | 394.823i | −0.533843 | + | 0.924644i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 195.989 | 0.456852 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 195.895 | + | 113.100i | 0.454514 | + | 0.262414i | 0.709735 | − | 0.704469i | \(-0.248815\pi\) |
−0.255221 | + | 0.966883i | \(0.582148\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −251.769 | − | 145.359i | −0.581452 | − | 0.335702i | 0.180258 | − | 0.983619i | \(-0.442307\pi\) |
−0.761710 | + | 0.647918i | \(0.775640\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −154.759 | − | 268.051i | −0.355769 | − | 0.616210i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 396.055 | + | 354.152i | 0.906304 | + | 0.810417i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −251.921 | + | 145.447i | −0.573852 | + | 0.331314i | −0.758686 | − | 0.651456i | \(-0.774158\pi\) |
0.184834 | + | 0.982770i | \(0.440825\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 97.6479 | − | 169.131i | 0.221424 | − | 0.383517i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 217.722 | − | 377.106i | 0.491473 | − | 0.851256i | −0.508479 | − | 0.861074i | \(-0.669792\pi\) |
0.999952 | + | 0.00981853i | \(0.00312539\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 412.830i | − | 0.927708i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 86.6158 | + | 50.0077i | 0.193771 | + | 0.111874i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 263.736i | − | 0.587385i | −0.955900 | − | 0.293692i | \(-0.905116\pi\) | ||
0.955900 | − | 0.293692i | \(-0.0948842\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 104.341 | − | 60.2411i | 0.231354 | − | 0.133572i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 177.933 | + | 308.189i | 0.392788 | + | 0.680328i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 882.774i | 1.94016i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 641.042 | 1.40272 | 0.701359 | − | 0.712809i | \(-0.252577\pi\) | ||||
0.701359 | + | 0.712809i | \(0.252577\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −52.6479 | + | 30.3963i | −0.114701 | + | 0.0662228i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −323.490 | − | 560.302i | −0.701714 | − | 1.21540i | −0.967864 | − | 0.251473i | \(-0.919085\pi\) |
0.266150 | − | 0.963932i | \(-0.414248\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 407.362 | 0.879831 | 0.439916 | − | 0.898039i | \(-0.355008\pi\) | ||||
0.439916 | + | 0.898039i | \(0.355008\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −173.102 | + | 299.821i | −0.372262 | + | 0.644776i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −146.962 | −0.314694 | −0.157347 | − | 0.987543i | \(-0.550294\pi\) | ||||
−0.157347 | + | 0.987543i | \(0.550294\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 161.919 | + | 93.4838i | 0.345242 | + | 0.199326i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −166.824 | − | 96.3159i | −0.354191 | − | 0.204492i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −168.936 | − | 292.606i | −0.357159 | − | 0.618617i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −47.2509 | − | 42.2518i | −0.0994757 | − | 0.0889512i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −39.9672 | + | 23.0751i | −0.0837886 | + | 0.0483754i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 309.698 | − | 536.413i | 0.646552 | − | 1.11986i | −0.337389 | − | 0.941365i | \(-0.609544\pi\) |
0.983941 | − | 0.178495i | \(-0.0571230\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −301.663 | + | 522.495i | −0.627158 | + | 1.08627i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 517.356i | 1.07113i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.48745 | − | 4.90023i | −0.0174999 | − | 0.0101036i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 343.861i | 0.706080i | 0.935608 | + | 0.353040i | \(0.114852\pi\) | ||||
−0.935608 | + | 0.353040i | \(0.885148\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −103.786 | + | 59.9207i | −0.212241 | + | 0.122537i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 250.993 | + | 434.733i | 0.511187 | + | 0.885402i | 0.999916 | + | 0.0129665i | \(0.00412747\pi\) |
−0.488729 | + | 0.872436i | \(0.662539\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 449.187i | 0.911129i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 88.9856 | 0.179769 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 796.884 | − | 460.081i | 1.60339 | − | 0.925717i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −453.717 | − | 785.861i | −0.909253 | − | 1.57487i | −0.815105 | − | 0.579314i | \(-0.803321\pi\) |
−0.0941479 | − | 0.995558i | \(-0.530013\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −363.635 | −0.725818 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −183.800 | + | 318.352i | −0.365408 | + | 0.632906i | −0.988842 | − | 0.148971i | \(-0.952404\pi\) |
0.623433 | + | 0.781877i | \(0.285737\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −128.174 | −0.253810 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 219.405 | + | 126.674i | 0.432751 | + | 0.249849i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 406.585 | + | 234.742i | 0.798791 | + | 0.461182i | 0.843048 | − | 0.537838i | \(-0.180759\pi\) |
−0.0442573 | + | 0.999020i | \(0.514092\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 493.870 | + | 855.408i | 0.966478 | + | 1.67399i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −96.6395 | − | 20.1945i | −0.188381 | − | 0.0393654i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 412.562 | − | 238.193i | 0.801092 | − | 0.462511i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 76.6473 | − | 132.757i | 0.148254 | − | 0.256783i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −264.781 | + | 458.614i | −0.510175 | + | 0.883649i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 691.695i | 1.32763i | 0.747897 | + | 0.663815i | \(0.231064\pi\) | ||||
−0.747897 | + | 0.663815i | \(0.768936\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 70.7545 | + | 40.8501i | 0.135286 | + | 0.0781073i | 0.566115 | − | 0.824326i | \(-0.308446\pi\) |
−0.430830 | + | 0.902433i | \(0.641779\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 61.7227i | − | 0.117567i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 435.113 | − | 251.212i | 0.825640 | − | 0.476684i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −126.474 | − | 219.060i | −0.239081 | − | 0.414101i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 88.8679i | 0.167359i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 335.686 | 0.629806 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.21533 | − | 1.27902i | 0.00414081 | − | 0.00239070i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 262.406 | + | 454.501i | 0.488653 | + | 0.846371i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 414.860 | 0.769685 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 373.182 | − | 646.370i | 0.689800 | − | 1.19477i | −0.282102 | − | 0.959384i | \(-0.591032\pi\) |
0.971902 | − | 0.235384i | \(-0.0756349\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −125.753 | −0.231588 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 375.716 | + | 216.920i | 0.689387 | + | 0.398018i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −404.687 | − | 233.646i | −0.739830 | − | 0.427141i | 0.0821772 | − | 0.996618i | \(-0.473813\pi\) |
−0.822008 | + | 0.569476i | \(0.807146\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 64.0210 | + | 110.888i | 0.116614 | + | 0.201981i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −486.250 | + | 543.782i | −0.882487 | + | 0.986900i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 281.898 | − | 162.754i | 0.509761 | − | 0.294311i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −136.965 | + | 237.230i | −0.246783 | + | 0.427442i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 386.099 | − | 668.743i | 0.693175 | − | 1.20061i | −0.277617 | − | 0.960692i | \(-0.589544\pi\) |
0.970792 | − | 0.239923i | \(-0.0771222\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 941.376i | − | 1.68404i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −111.838 | − | 64.5698i | −0.199355 | − | 0.115098i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 195.273i | − | 0.346844i | −0.984848 | − | 0.173422i | \(-0.944518\pi\) | ||
0.984848 | − | 0.173422i | \(-0.0554825\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 223.385 | − | 128.971i | 0.395372 | − | 0.228268i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −48.0676 | − | 83.2556i | −0.0847753 | − | 0.146835i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 579.517i | 1.01848i | 0.860624 | + | 0.509242i | \(0.170074\pi\) | ||||
−0.860624 | + | 0.509242i | \(0.829926\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 145.886 | 0.255492 | 0.127746 | − | 0.991807i | \(-0.459226\pi\) | ||||
0.127746 | + | 0.991807i | \(0.459226\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 72.8602 | − | 42.0658i | 0.127156 | − | 0.0734133i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 46.6448 | + | 80.7911i | 0.0811214 | + | 0.140506i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1037.54 | −1.79817 | −0.899084 | − | 0.437777i | \(-0.855766\pi\) | ||||
−0.899084 | + | 0.437777i | \(0.855766\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.48401 | − | 16.4268i | 0.0163800 | − | 0.0283710i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −823.723 | −1.41777 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −84.9009 | − | 49.0176i | −0.145628 | − | 0.0840782i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 214.714 | + | 123.965i | 0.367033 | + | 0.211907i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −441.521 | − | 764.737i | −0.752165 | − | 1.30279i | −0.946771 | − | 0.321907i | \(-0.895676\pi\) |
0.194606 | − | 0.980882i | \(-0.437657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 798.684 | + | 166.899i | 1.35600 | + | 0.283360i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 156.663 | − | 90.4495i | 0.265082 | − | 0.153045i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 119.583 | − | 207.125i | 0.201658 | − | 0.349283i | −0.747404 | − | 0.664369i | \(-0.768700\pi\) |
0.949063 | + | 0.315087i | \(0.102034\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 290.835 | − | 503.741i | 0.488798 | − | 0.846623i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 487.203i | − | 0.816086i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 793.604 | + | 458.187i | 1.32488 | + | 0.764920i | 0.984503 | − | 0.175368i | \(-0.0561116\pi\) |
0.340378 | + | 0.940289i | \(0.389445\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 789.891i | 1.31429i | 0.753762 | + | 0.657147i | \(0.228237\pi\) | ||||
−0.753762 | + | 0.657147i | \(0.771763\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 45.4756 | − | 26.2553i | 0.0754155 | − | 0.0435412i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −187.079 | − | 324.031i | −0.309222 | − | 0.535588i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 653.712i | − | 1.07696i | −0.842640 | − | 0.538478i | \(-0.819000\pi\) | ||
0.842640 | − | 0.538478i | \(-0.181000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −710.329 | −1.16639 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 369.886 | − | 213.554i | 0.605379 | − | 0.349515i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 528.343 | + | 915.118i | 0.861898 | + | 1.49285i | 0.870095 | + | 0.492885i | \(0.164057\pi\) |
−0.00819687 | + | 0.999966i | \(0.502609\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 152.413 | 0.247825 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −501.032 | + | 867.813i | −0.812045 | + | 1.40650i | 0.0993850 | + | 0.995049i | \(0.468312\pi\) |
−0.911430 | + | 0.411455i | \(0.865021\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −252.948 | −0.408640 | −0.204320 | − | 0.978904i | \(-0.565498\pi\) | ||||
−0.204320 | + | 0.978904i | \(0.565498\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 125.835 | + | 72.6509i | 0.202633 | + | 0.116990i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −820.491 | − | 473.711i | −1.31700 | − | 0.760371i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 265.233 | + | 459.398i | 0.424373 | + | 0.735036i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −65.4929 | − | 199.234i | −0.104454 | − | 0.317757i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 344.278 | − | 198.769i | 0.547342 | − | 0.316008i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 605.640 | − | 1049.00i | 0.959809 | − | 1.66244i | 0.236853 | − | 0.971546i | \(-0.423884\pi\) |
0.722957 | − | 0.690893i | \(-0.242783\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −89.2808 | + | 154.639i | −0.141044 | + | 0.244295i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 444.568i | 0.700107i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1001.02 | + | 577.940i | 1.57146 | + | 0.907284i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 258.432i | − | 0.404431i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 89.1040 | − | 51.4442i | 0.139008 | − | 0.0802562i | −0.428883 | − | 0.903360i | \(-0.641093\pi\) |
0.567891 | + | 0.823104i | \(0.307759\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 384.990 | + | 666.822i | 0.598740 | + | 1.03705i | 0.993007 | + | 0.118052i | \(0.0376650\pi\) |
−0.394267 | + | 0.918996i | \(0.629002\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 427.416i | − | 0.662660i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 790.984 | 1.22254 | 0.611270 | − | 0.791422i | \(-0.290659\pi\) | ||||
0.611270 | + | 0.791422i | \(0.290659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −163.488 | + | 94.3896i | −0.251907 | + | 0.145438i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 397.259 | + | 688.072i | 0.610228 | + | 1.05695i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 320.503 | 0.490816 | 0.245408 | − | 0.969420i | \(-0.421078\pi\) | ||||
0.245408 | + | 0.969420i | \(0.421078\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −391.328 | + | 677.800i | −0.597447 | + | 1.03481i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 277.411 | 0.422239 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 616.112 | + | 355.713i | 0.934920 | + | 0.539776i | 0.888364 | − | 0.459139i | \(-0.151842\pi\) |
0.0465558 | + | 0.998916i | \(0.485175\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −410.779 | − | 237.163i | −0.621451 | − | 0.358795i | 0.155983 | − | 0.987760i | \(-0.450146\pi\) |
−0.777434 | + | 0.628965i | \(0.783479\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −179.904 | − | 311.602i | −0.271348 | − | 0.469989i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 897.388 | − | 294.993i | 1.34946 | − | 0.443598i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 929.776 | − | 536.806i | 1.39397 | − | 0.804807i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 68.9560 | − | 119.435i | 0.103073 | − | 0.178528i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −135.998 | + | 235.555i | −0.202679 | + | 0.351051i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 648.662i | − | 0.963836i | −0.876216 | − | 0.481918i | \(-0.839940\pi\) | ||
0.876216 | − | 0.481918i | \(-0.160060\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15.0126 | − | 8.66754i | −0.0222409 | − | 0.0128408i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 860.699i | 1.27134i | 0.771960 | + | 0.635671i | \(0.219277\pi\) | ||||
−0.771960 | + | 0.635671i | \(0.780723\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.4782 | + | 11.2458i | −0.0286866 | + | 0.0165622i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 113.476 | + | 196.546i | 0.166631 | + | 0.288614i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 194.789i | − | 0.285196i | −0.989781 | − | 0.142598i | \(-0.954454\pi\) | ||
0.989781 | − | 0.142598i | \(-0.0455456\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 552.738 | 0.806916 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 45.5306 | − | 26.2871i | 0.0662745 | − | 0.0382636i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −136.572 | − | 236.550i | −0.198218 | − | 0.343324i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −719.067 | −1.04062 | −0.520309 | − | 0.853978i | \(-0.674183\pi\) | ||||
−0.520309 | + | 0.853978i | \(0.674183\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 102.108 | − | 176.857i | 0.147343 | − | 0.255205i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 513.685 | 0.739115 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −191.554 | − | 110.594i | −0.274826 | − | 0.158671i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −141.145 | − | 81.4902i | −0.201924 | − | 0.116581i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 242.353 | + | 419.767i | 0.345724 | + | 0.598812i | 0.985485 | − | 0.169762i | \(-0.0542999\pi\) |
−0.639761 | + | 0.768574i | \(0.720967\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 631.951 | + | 132.057i | 0.898934 | + | 0.187848i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 167.941 | − | 96.9605i | 0.238213 | − | 0.137533i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −147.076 | + | 254.744i | −0.208029 | + | 0.360317i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 620.485 | − | 1074.71i | 0.875156 | − | 1.51581i | 0.0185591 | − | 0.999828i | \(-0.494092\pi\) |
0.856597 | − | 0.515987i | \(-0.172575\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 91.4203i | − | 0.128580i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1039.97 | − | 600.429i | −1.45859 | − | 0.842116i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 526.671i | 0.736603i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −562.946 | + | 325.017i | −0.785141 | + | 0.453301i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −65.3191 | − | 113.136i | −0.0908471 | − | 0.157352i | 0.817021 | − | 0.576608i | \(-0.195624\pi\) |
−0.907868 | + | 0.419256i | \(0.862291\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 1093.28i | − | 1.51634i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.964848 | 0.00133451 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −110.926 | + | 64.0432i | −0.153001 | + | 0.0883354i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 566.505 | + | 981.216i | 0.779237 | + | 1.34968i | 0.932382 | + | 0.361475i | \(0.117727\pi\) |
−0.153145 | + | 0.988204i | \(0.548940\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −310.142 | + | 537.181i | −0.424271 | + | 0.734858i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −837.144 | −1.14208 | −0.571040 | − | 0.820922i | \(-0.693460\pi\) | ||||
−0.571040 | + | 0.820922i | \(0.693460\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 454.497 | + | 262.404i | 0.618363 | + | 0.357012i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 96.6023 | + | 55.7734i | 0.131075 | + | 0.0756762i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −144.463 | − | 250.216i | −0.195484 | − | 0.338588i | 0.751575 | − | 0.659647i | \(-0.229294\pi\) |
−0.947059 | + | 0.321060i | \(0.895961\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 119.523 | − | 571.972i | 0.161300 | − | 0.771892i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 66.4928 | − | 38.3896i | 0.0894923 | − | 0.0516684i | −0.454586 | − | 0.890703i | \(-0.650213\pi\) |
0.544078 | + | 0.839034i | \(0.316879\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −134.383 | + | 232.758i | −0.180380 | + | 0.312427i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −115.673 | + | 200.352i | −0.154850 | + | 0.268208i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 5.87058i | − | 0.00783789i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −923.318 | − | 533.078i | −1.22945 | − | 0.709824i | −0.262536 | − | 0.964922i | \(-0.584559\pi\) |
−0.966915 | + | 0.255098i | \(0.917892\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 406.371i | 0.539669i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −828.179 | + | 478.149i | −1.09693 | + | 0.633310i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.94030 | + | 8.55684i | 0.00652615 | + | 0.0113036i | 0.869270 | − | 0.494338i | \(-0.164589\pi\) |
−0.862744 | + | 0.505641i | \(0.831256\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 308.660i | 0.406666i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1147.50 | 1.50788 | 0.753940 | − | 0.656944i | \(-0.228151\pi\) | ||||
0.753940 | + | 0.656944i | \(0.228151\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 862.247 | − | 497.819i | 1.13007 | − | 0.652449i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −81.6822 | − | 141.478i | −0.106774 | − | 0.184938i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −525.975 | −0.685756 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 299.227 | − | 518.276i | 0.389112 | − | 0.673961i | −0.603218 | − | 0.797576i | \(-0.706115\pi\) |
0.992330 | + | 0.123615i | \(0.0394486\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.1405 | −0.0287166 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 858.414 | + | 495.605i | 1.11050 | + | 0.641145i | 0.938958 | − | 0.344032i | \(-0.111793\pi\) |
0.171538 | + | 0.985177i | \(0.445126\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 124.073 | + | 71.6336i | 0.160094 | + | 0.0924305i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 314.327 | + | 544.430i | 0.404539 | + | 0.700682i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −112.175 | − | 341.244i | −0.143998 | − | 0.438053i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 475.429 | − | 274.489i | 0.608744 | − | 0.351458i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −99.7494 | + | 172.771i | −0.127394 | + | 0.220653i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 258.824 | − | 448.297i | 0.329713 | − | 0.571079i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1226.83i | 1.55887i | 0.626480 | + | 0.779437i | \(0.284495\pi\) | ||||
−0.626480 | + | 0.779437i | \(0.715505\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −319.371 | − | 184.389i | −0.404780 | − | 0.233700i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 591.965i | − | 0.748375i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −656.302 | + | 378.916i | −0.827619 | + | 0.477826i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −62.0083 | − | 107.402i | −0.0779979 | − | 0.135096i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 788.636i | − | 0.989506i | −0.869034 | − | 0.494753i | \(-0.835259\pi\) | ||
0.869034 | − | 0.494753i | \(-0.164741\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −281.426 | −0.352223 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −230.439 | + | 133.044i | −0.287689 | + | 0.166097i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 294.648 | + | 510.345i | 0.366934 | + | 0.635548i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1390.26 | −1.72704 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −438.717 | + | 759.880i | −0.543639 | + | 0.941610i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 640.524 | 0.791748 | 0.395874 | − | 0.918305i | \(-0.370442\pi\) | ||||
0.395874 | + | 0.918305i | \(0.370442\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 811.945 | + | 468.777i | 1.00117 | + | 0.578023i | 0.908593 | − | 0.417683i | \(-0.137158\pi\) |
0.0925727 | + | 0.995706i | \(0.470491\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −330.189 | − | 190.635i | −0.406136 | − | 0.234483i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −161.022 | − | 278.898i | −0.197573 | − | 0.342206i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −956.961 | + | 314.576i | −1.17131 | + | 0.385037i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 492.758 | − | 284.494i | 0.601658 | − | 0.347367i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −671.718 | + | 1163.45i | −0.818170 | + | 1.41711i | 0.0888591 | + | 0.996044i | \(0.471678\pi\) |
−0.907029 | + | 0.421068i | \(0.861655\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −435.019 | + | 753.475i | −0.528577 | + | 0.915522i | 0.470868 | + | 0.882204i | \(0.343941\pi\) |
−0.999445 | + | 0.0333184i | \(0.989392\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 36.8244i | − | 0.0446356i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −583.285 | − | 336.760i | −0.705303 | − | 0.407207i | 0.104017 | − | 0.994576i | \(-0.466830\pi\) |
−0.809319 | + | 0.587369i | \(0.800164\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 516.908i | − | 0.623532i | −0.950159 | − | 0.311766i | \(-0.899080\pi\) | ||
0.950159 | − | 0.311766i | \(-0.100920\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 393.125 | − | 226.971i | 0.473074 | − | 0.273129i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −380.811 | − | 659.584i | −0.457156 | − | 0.791818i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 977.176i | − | 1.17027i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 223.144 | 0.266599 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1050.53 | − | 606.526i | 1.25213 | − | 0.722915i | 0.280595 | − | 0.959826i | \(-0.409468\pi\) |
0.971531 | + | 0.236911i | \(0.0761350\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 316.533 | + | 548.252i | 0.376377 | + | 0.651905i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −692.405 | −0.821358 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −340.403 | + | 589.595i | −0.402844 | + | 0.697745i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −858.673 | −1.01378 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −123.707 | − | 71.4225i | −0.145710 | − | 0.0841255i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −822.868 | − | 475.083i | −0.966942 | − | 0.558264i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −267.766 | − | 463.785i | −0.313911 | − | 0.543710i | 0.665294 | − | 0.746581i | \(-0.268306\pi\) |
−0.979205 | + | 0.202871i | \(0.934973\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 54.2675 | − | 259.694i | 0.0634707 | − | 0.303736i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 655.156 | − | 378.254i | 0.764476 | − | 0.441370i | −0.0664245 | − | 0.997791i | \(-0.521159\pi\) |
0.830901 | + | 0.556421i | \(0.187826\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −538.135 | + | 932.077i | −0.626466 | + | 1.08507i | 0.361789 | + | 0.932260i | \(0.382166\pi\) |
−0.988255 | + | 0.152812i | \(0.951167\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 174.889 | − | 302.917i | 0.203123 | − | 0.351820i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 939.206i | 1.08830i | 0.838987 | + | 0.544152i | \(0.183148\pi\) | ||||
−0.838987 | + | 0.544152i | \(0.816852\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1232.41 | − | 711.531i | −1.42475 | − | 0.822579i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 263.481i | − | 0.303900i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 168.183 | − | 97.1006i | 0.193536 | − | 0.111738i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 155.395 | + | 269.152i | 0.178410 | + | 0.309015i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.31684i | 0.00723578i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1408.80 | 1.61005 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1011.30 | + | 583.873i | −1.15313 | + | 0.665761i | −0.949649 | − | 0.313317i | \(-0.898560\pi\) |
−0.203484 | + | 0.979078i | \(0.565226\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 193.602 | + | 335.328i | 0.220252 | + | 0.381489i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 68.2541 | 0.0774734 | 0.0387367 | − | 0.999249i | \(-0.487667\pi\) | ||||
0.0387367 | + | 0.999249i | \(0.487667\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 134.599 | − | 233.133i | 0.152434 | − | 0.264023i | −0.779688 | − | 0.626169i | \(-0.784622\pi\) |
0.932122 | + | 0.362145i | \(0.117956\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −238.810 | −0.269842 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −795.589 | − | 459.333i | −0.896943 | − | 0.517850i | −0.0207361 | − | 0.999785i | \(-0.506601\pi\) |
−0.876207 | + | 0.481935i | \(0.839934\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 883.569 | + | 510.129i | 0.993891 | + | 0.573823i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28.6776 | − | 49.6711i | −0.0321859 | − | 0.0557476i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −340.693 | − | 304.647i | −0.381515 | − | 0.341150i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1221.36 | + | 705.151i | −1.36464 | + | 0.787878i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −429.993 | + | 744.769i | −0.479367 | + | 0.830289i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 824.387 | − | 1427.88i | 0.917005 | − | 1.58830i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 179.978i | 0.199754i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −849.480 | − | 490.448i | −0.940731 | − | 0.543131i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 337.928i | − | 0.373401i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −654.944 | + | 378.132i | −0.722099 | + | 0.416904i | −0.815525 | − | 0.578722i | \(-0.803552\pi\) |
0.0934255 | + | 0.995626i | \(0.470218\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 41.3071 | + | 71.5459i | 0.0454423 | + | 0.0787084i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 945.788i | − | 1.03819i | −0.854718 | − | 0.519093i | \(-0.826270\pi\) | ||
0.854718 | − | 0.519093i | \(-0.173730\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −491.441 | −0.538271 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −297.982 | + | 172.040i | −0.325664 | + | 0.188022i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 898.076 | + | 1555.51i | 0.979363 | + | 1.69631i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1224.77 | −1.33272 | −0.666362 | − | 0.745628i | \(-0.732150\pi\) | ||||
−0.666362 | + | 0.745628i | \(0.732150\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −339.034 | + | 587.224i | −0.368115 | + | 0.637594i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1529.56 | 1.65716 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 98.1715 | + | 56.6793i | 0.106131 | + | 0.0612749i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −265.915 | − | 153.526i | −0.286855 | − | 0.165616i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −529.236 | − | 916.663i | −0.569683 | − | 0.986721i | −0.996597 | − | 0.0824281i | \(-0.973733\pi\) |
0.426914 | − | 0.904292i | \(-0.359601\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 253.001 | − | 1210.72i | 0.271752 | − | 1.30045i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −563.741 | + | 325.476i | −0.604224 | + | 0.348849i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 173.515 | − | 300.537i | 0.185577 | − | 0.321429i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −96.5921 | + | 167.302i | −0.103087 | + | 0.178551i | −0.912955 | − | 0.408061i | \(-0.866205\pi\) |
0.809868 | + | 0.586612i | \(0.199539\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 261.171i | − | 0.278137i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 178.549 | + | 103.085i | 0.189744 | + | 0.109549i | 0.591863 | − | 0.806039i | \(-0.298393\pi\) |
−0.402119 | + | 0.915587i | \(0.631726\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 528.666i | 0.560621i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 223.728 | − | 129.169i | 0.236749 | − | 0.136687i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −553.455 | − | 958.612i | −0.584430 | − | 1.01226i | −0.994946 | − | 0.100409i | \(-0.967985\pi\) |
0.410517 | − | 0.911853i | \(-0.365348\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1641.89i | 1.73013i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −876.326 | −0.921478 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 729.970 | − | 421.448i | 0.765970 | − | 0.442233i | −0.0654649 | − | 0.997855i | \(-0.520853\pi\) |
0.831435 | + | 0.555622i | \(0.187520\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 113.041 | + | 195.793i | 0.118368 | + | 0.205019i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −423.789 | −0.442831 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 634.251 | − | 1098.55i | 0.661367 | − | 1.14552i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −883.189 | −0.919031 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.42788 | − | 0.824389i | −0.00148274 | − | 0.000856063i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 44.1428 | + | 25.4859i | 0.0457438 | + | 0.0264102i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 404.649 | + | 700.873i | 0.418458 | + | 0.724791i | 0.995785 | − | 0.0917223i | \(-0.0292372\pi\) |
−0.577326 | + | 0.816514i | \(0.695904\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −256.643 | + | 287.009i | −0.264854 | + | 0.296191i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.7562 | − | 17.1798i | 0.0306449 | − | 0.0176929i | −0.484599 | − | 0.874736i | \(-0.661035\pi\) |
0.515244 | + | 0.857043i | \(0.327701\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 589.439 | − | 1020.94i | 0.605796 | − | 1.04927i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 51.2998 | − | 88.8539i | 0.0526152 | − | 0.0911322i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1293.09i | − | 1.32353i | −0.749711 | − | 0.661765i | \(-0.769808\pi\) | ||
0.749711 | − | 0.661765i | \(-0.230192\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −489.513 | − | 282.621i | −0.500013 | − | 0.288683i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 279.629i | − | 0.285045i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −405.649 | + | 234.202i | −0.412665 | + | 0.238252i | −0.691934 | − | 0.721961i | \(-0.743241\pi\) |
0.279269 | + | 0.960213i | \(0.409908\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 243.060 | + | 420.992i | 0.246762 | + | 0.427403i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 445.038i | − | 0.450900i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1482.56 | 1.49904 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1362.49 | + | 786.632i | −1.37486 | + | 0.793776i | −0.991535 | − | 0.129838i | \(-0.958554\pi\) |
−0.383325 | + | 0.923614i | \(0.625221\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −383.674 | − | 664.542i | −0.386378 | − | 0.669227i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1309.23 | 1.31581 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 121.379 | − | 210.235i | 0.121744 | − | 0.210867i | −0.798711 | − | 0.601714i | \(-0.794485\pi\) |
0.920456 | + | 0.390847i | \(0.127818\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 176.560 | 0.176737 |
(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 | 912.3.be.f.145.2 | 6 | ||
4.3 | odd | 2 | 57.3.g.b.31.3 | ✓ | 6 | ||
12.11 | even | 2 | 171.3.p.c.145.1 | 6 | |||
19.8 | odd | 6 | inner | 912.3.be.f.673.2 | 6 | ||
76.27 | even | 6 | 57.3.g.b.46.3 | yes | 6 | ||
228.179 | odd | 6 | 171.3.p.c.46.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.3.g.b.31.3 | ✓ | 6 | 4.3 | odd | 2 | ||
57.3.g.b.46.3 | yes | 6 | 76.27 | even | 6 | ||
171.3.p.c.46.1 | 6 | 228.179 | odd | 6 | |||
171.3.p.c.145.1 | 6 | 12.11 | even | 2 | |||
912.3.be.f.145.2 | 6 | 1.1 | even | 1 | trivial | ||
912.3.be.f.673.2 | 6 | 19.8 | odd | 6 | inner |