Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1500,2,Mod(49,1500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1500, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1500.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1500.o (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: | \(11.9775603032\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 349.2 | ||
Character | \(\chi\) | \(=\) | 1500.349 |
Dual form | 1500.2.o.c.649.2 |
$q$-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 \(\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times\).
\(n\) | \(751\) | \(877\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.587785 | − | 0.809017i | −0.339358 | − | 0.467086i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.13266i | 1.56200i | 0.624532 | + | 0.780999i | \(0.285290\pi\) | ||||
−0.624532 | + | 0.780999i | \(0.714710\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.309017 | + | 0.951057i | −0.103006 | + | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.16386 | − | 3.58198i | −0.350916 | − | 1.08001i | −0.958340 | − | 0.285630i | \(-0.907797\pi\) |
0.607424 | − | 0.794378i | \(-0.292203\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.664470 | − | 0.215899i | −0.184291 | − | 0.0598797i | 0.215418 | − | 0.976522i | \(-0.430889\pi\) |
−0.399709 | + | 0.916642i | \(0.630889\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.11086 | − | 4.28173i | 0.754494 | − | 1.03847i | −0.243159 | − | 0.969987i | \(-0.578184\pi\) |
0.997652 | − | 0.0684847i | \(-0.0218164\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.63966 | + | 3.37091i | 1.06441 | + | 0.773340i | 0.974899 | − | 0.222646i | \(-0.0714692\pi\) |
0.0895120 | + | 0.995986i | \(0.471469\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.34339 | − | 2.42912i | 0.729588 | − | 0.530077i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.19894 | + | 1.68924i | −1.08405 | + | 0.352231i | −0.795946 | − | 0.605367i | \(-0.793026\pi\) |
−0.288108 | + | 0.957598i | \(0.593026\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.951057 | − | 0.309017i | 0.183031 | − | 0.0594703i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.68284 | + | 4.12883i | −1.05528 | + | 0.766704i | −0.973209 | − | 0.229923i | \(-0.926153\pi\) |
−0.0820685 | + | 0.996627i | \(0.526153\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.16460 | + | 5.93193i | 1.46641 | + | 1.06541i | 0.981636 | + | 0.190764i | \(0.0610964\pi\) |
0.484769 | + | 0.874642i | \(0.338904\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.21379 | + | 3.04701i | −0.385371 | + | 0.530417i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.50175 | − | 1.78763i | −0.904482 | − | 0.293884i | −0.180396 | − | 0.983594i | \(-0.557738\pi\) |
−0.724086 | + | 0.689710i | \(0.757738\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.215899 | + | 0.664470i | 0.0345716 | + | 0.106400i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.03813 | + | 6.27271i | −0.318302 | + | 0.979633i | 0.656072 | + | 0.754698i | \(0.272217\pi\) |
−0.974374 | + | 0.224935i | \(0.927783\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.79668i | 0.731488i | 0.930716 | + | 0.365744i | \(0.119185\pi\) | ||||
−0.930716 | + | 0.365744i | \(0.880815\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.68611 | + | 7.82626i | 0.829405 | + | 1.14158i | 0.988033 | + | 0.154239i | \(0.0492927\pi\) |
−0.158629 | + | 0.987338i | \(0.550707\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.0789 | −1.43984 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.29251 | −0.741099 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.99634 | + | 2.74773i | 0.274219 | + | 0.377429i | 0.923808 | − | 0.382856i | \(-0.125059\pi\) |
−0.649590 | + | 0.760285i | \(0.725059\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.73494i | − | 0.759611i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.230309 | + | 0.708820i | −0.0299837 | + | 0.0922804i | −0.964928 | − | 0.262513i | \(-0.915449\pi\) |
0.934945 | + | 0.354793i | \(0.115449\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.64886 | + | 11.2300i | 0.467188 | + | 1.43786i | 0.856210 | + | 0.516629i | \(0.172813\pi\) |
−0.389021 | + | 0.921229i | \(0.627187\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.93039 | − | 1.27706i | −0.495183 | − | 0.160895i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.81995 | − | 3.88133i | 0.344512 | − | 0.474180i | −0.601241 | − | 0.799068i | \(-0.705327\pi\) |
0.945752 | + | 0.324888i | \(0.105327\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.42248 | + | 3.21312i | 0.532405 | + | 0.386815i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.54239 | − | 1.84715i | 0.301726 | − | 0.219217i | −0.426612 | − | 0.904435i | \(-0.640293\pi\) |
0.728338 | + | 0.685218i | \(0.240293\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2213 | + | 3.32110i | −1.19631 | + | 0.388706i | −0.838403 | − | 0.545051i | \(-0.816510\pi\) |
−0.357910 | + | 0.933756i | \(0.616510\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.8031 | − | 4.80982i | 1.68697 | − | 0.548130i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.38222 | + | 5.36349i | −0.830564 | + | 0.603440i | −0.919719 | − | 0.392578i | \(-0.871583\pi\) |
0.0891546 | + | 0.996018i | \(0.471583\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.96148 | − | 6.82889i | 0.544593 | − | 0.749569i | −0.444673 | − | 0.895693i | \(-0.646680\pi\) |
0.989266 | + | 0.146125i | \(0.0466800\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.68058 | + | 2.17065i | 0.716234 | + | 0.232718i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.04690 | + | 3.22202i | 0.110971 | + | 0.341533i | 0.991085 | − | 0.133228i | \(-0.0425343\pi\) |
−0.880114 | + | 0.474761i | \(0.842534\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.892239 | − | 2.74603i | 0.0935321 | − | 0.287862i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 10.0920i | − | 1.04649i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.13358 | + | 8.44215i | 0.622771 | + | 0.857170i | 0.997551 | − | 0.0699435i | \(-0.0222819\pi\) |
−0.374780 | + | 0.927114i | \(0.622282\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.76632 | 0.378529 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.10799 | 0.707272 | 0.353636 | − | 0.935383i | \(-0.384945\pi\) | ||||
0.353636 | + | 0.935383i | \(0.384945\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.17630 | + | 9.87733i | 0.707102 | + | 0.973243i | 0.999855 | + | 0.0170543i | \(0.00542883\pi\) |
−0.292752 | + | 0.956188i | \(0.594571\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 4.04303i | − | 0.390855i | −0.980718 | − | 0.195427i | \(-0.937391\pi\) | ||
0.980718 | − | 0.195427i | \(-0.0626094\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.239122 | − | 0.735942i | 0.0229037 | − | 0.0704904i | −0.938951 | − | 0.344050i | \(-0.888201\pi\) |
0.961855 | + | 0.273560i | \(0.0882010\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.78763 | + | 5.50175i | 0.169674 | + | 0.522203i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.08366 | + | 0.352104i | 0.101943 | + | 0.0331231i | 0.359544 | − | 0.933128i | \(-0.382932\pi\) |
−0.257602 | + | 0.966251i | \(0.582932\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.410665 | − | 0.565232i | 0.0379660 | − | 0.0522557i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.6949 | + | 12.8561i | 1.62209 | + | 1.17852i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.57684 | + | 1.87218i | −0.234258 | + | 0.170198i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.27271 | − | 2.03813i | 0.565591 | − | 0.183772i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.511543 | + | 0.166210i | −0.0453921 | + | 0.0147488i | −0.331625 | − | 0.943411i | \(-0.607597\pi\) |
0.286233 | + | 0.958160i | \(0.407597\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.88060 | − | 2.81942i | 0.341668 | − | 0.248236i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.43855 | + | 3.95134i | 0.475169 | + | 0.345230i | 0.799452 | − | 0.600730i | \(-0.205123\pi\) |
−0.324284 | + | 0.945960i | \(0.605123\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.9308 | + | 19.1741i | −1.20796 | + | 1.66261i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.174404 | + | 0.0566672i | 0.0149003 | + | 0.00484140i | 0.316458 | − | 0.948607i | \(-0.397506\pi\) |
−0.301557 | + | 0.953448i | \(0.597506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.54014 | − | 7.81775i | −0.215452 | − | 0.663093i | −0.999121 | − | 0.0419144i | \(-0.986654\pi\) |
0.783669 | − | 0.621178i | \(-0.213346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.98937 | − | 9.20032i | 0.251750 | − | 0.774807i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.63140i | 0.220048i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.92421 | + | 8.15398i | 0.488621 | + | 0.672529i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.53790 | −0.453682 | −0.226841 | − | 0.973932i | \(-0.572840\pi\) | ||||
−0.226841 | + | 0.973932i | \(0.572840\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.8736 | 1.04764 | 0.523821 | − | 0.851828i | \(-0.324506\pi\) | ||||
0.523821 | + | 0.851828i | \(0.324506\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.11086 | + | 4.28173i | 0.251498 | + | 0.346157i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 14.6395i | − | 1.16836i | −0.811625 | − | 0.584179i | \(-0.801417\pi\) | ||
0.811625 | − | 0.584179i | \(-0.198583\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.04954 | − | 3.23015i | 0.0832338 | − | 0.256167i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.98105 | − | 21.4855i | −0.550184 | − | 1.69329i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.22672 | + | 1.37334i | 0.331062 | + | 0.107569i | 0.469832 | − | 0.882756i | \(-0.344315\pi\) |
−0.138769 | + | 0.990325i | \(0.544315\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.9690 | + | 19.2267i | −1.08095 | + | 1.48780i | −0.222487 | + | 0.974936i | \(0.571417\pi\) |
−0.858467 | + | 0.512869i | \(0.828583\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1223 | − | 7.35429i | −0.778639 | − | 0.565715i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.63966 | + | 3.37091i | −0.354804 | + | 0.257780i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.3484 | + | 4.66207i | −1.09089 | + | 0.354451i | −0.798589 | − | 0.601877i | \(-0.794420\pi\) |
−0.292298 | + | 0.956327i | \(0.594420\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.708820 | − | 0.230309i | 0.0532781 | − | 0.0173111i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.5238 | − | 9.82561i | 1.01082 | − | 0.734401i | 0.0464356 | − | 0.998921i | \(-0.485214\pi\) |
0.964380 | + | 0.264521i | \(0.0852138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.40755 | − | 6.10844i | −0.624928 | − | 0.454037i | 0.229711 | − | 0.973259i | \(-0.426222\pi\) |
−0.854639 | + | 0.519222i | \(0.826222\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.94054 | − | 9.55283i | 0.513059 | − | 0.706166i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.9576 | − | 6.15971i | −1.38632 | − | 0.450443i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.27706 | + | 3.93039i | 0.0928926 | + | 0.285894i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.10485 | + | 18.7888i | −0.441732 | + | 1.35951i | 0.444297 | + | 0.895880i | \(0.353454\pi\) |
−0.886029 | + | 0.463631i | \(0.846546\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.23549i | 0.160914i | 0.996758 | + | 0.0804571i | \(0.0256380\pi\) | ||||
−0.996758 | + | 0.0804571i | \(0.974362\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.3761 | − | 18.4106i | −0.953008 | − | 1.31170i | −0.950178 | − | 0.311706i | \(-0.899099\pi\) |
−0.00282909 | − | 0.999996i | \(-0.500901\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.8171 | −1.61746 | −0.808731 | − | 0.588179i | \(-0.799845\pi\) | ||||
−0.808731 | + | 0.588179i | \(0.799845\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.79759 | −0.338396 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.0630 | − | 23.4853i | −1.19759 | − | 1.64834i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 5.46649i | − | 0.379947i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.67464 | − | 20.5424i | 0.461695 | − | 1.42095i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.21019 | + | 19.1130i | 0.427527 | + | 1.31579i | 0.900554 | + | 0.434745i | \(0.143161\pi\) |
−0.473027 | + | 0.881048i | \(0.656839\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.98875 | − | 0.971105i | −0.204786 | − | 0.0665390i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.5146 | + | 33.7415i | −1.66416 | + | 2.29052i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.69476 | + | 6.31711i | 0.587537 | + | 0.426871i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.99149 | + | 2.17345i | −0.201230 | + | 0.146202i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.7621 | − | 4.14665i | 0.854612 | − | 0.277680i | 0.151236 | − | 0.988498i | \(-0.451675\pi\) |
0.703377 | + | 0.710817i | \(0.251675\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.5862 | − | 5.71411i | 1.16724 | − | 0.379259i | 0.339628 | − | 0.940560i | \(-0.389699\pi\) |
0.827612 | + | 0.561301i | \(0.189699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.7050 | + | 11.4104i | −1.03782 | + | 0.754017i | −0.969858 | − | 0.243671i | \(-0.921648\pi\) |
−0.0679579 | + | 0.997688i | \(0.521648\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.5923 | − | 9.14882i | −0.828511 | − | 0.601948i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.16114 | − | 9.85646i | 0.469142 | − | 0.645718i | −0.507231 | − | 0.861810i | \(-0.669331\pi\) |
0.976373 | + | 0.216092i | \(0.0693311\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.67832 | + | 2.81976i | 0.563717 | + | 0.183163i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.39823 | − | 4.30330i | −0.0904438 | − | 0.278357i | 0.895596 | − | 0.444869i | \(-0.146750\pi\) |
−0.986040 | + | 0.166512i | \(0.946750\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.78479 | − | 8.57071i | 0.179384 | − | 0.552088i | −0.820422 | − | 0.571758i | \(-0.806262\pi\) |
0.999807 | + | 0.0196702i | \(0.00626163\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.35514 | − | 3.24157i | −0.149854 | − | 0.206256i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.44098 | −0.534925 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.16965 | 0.200066 | 0.100033 | − | 0.994984i | \(-0.468105\pi\) | ||||
0.100033 | + | 0.994984i | \(0.468105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.1016 | + | 16.6565i | 0.760824 | + | 1.04718i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.25241i | 0.202880i | 0.994842 | + | 0.101440i | \(0.0323450\pi\) | ||||
−0.994842 | + | 0.101440i | \(0.967655\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.38766 | − | 22.7369i | 0.459047 | − | 1.41280i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.17065 | − | 6.68058i | −0.134360 | − | 0.413518i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.5187 | + | 3.41774i | 0.648612 | + | 0.210747i | 0.614802 | − | 0.788682i | \(-0.289236\pi\) |
0.0338097 | + | 0.999428i | \(0.489236\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.99132 | − | 2.74081i | 0.121867 | − | 0.167735i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.0279 | + | 14.5511i | 1.22112 | + | 0.887197i | 0.996193 | − | 0.0871780i | \(-0.0277849\pi\) |
0.224929 | + | 0.974375i | \(0.427785\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.202420 | + | 0.147067i | −0.0122962 | + | 0.00893369i | −0.593916 | − | 0.804527i | \(-0.702419\pi\) |
0.581620 | + | 0.813460i | \(0.302419\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.74603 | + | 0.892239i | −0.166197 | + | 0.0540008i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.43658 | + | 2.74121i | −0.506905 | + | 0.164703i | −0.551294 | − | 0.834311i | \(-0.685866\pi\) |
0.0443894 | + | 0.999014i | \(0.485866\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.16460 | + | 5.93193i | −0.488802 | + | 0.355135i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.9683 | − | 11.6016i | −0.952588 | − | 0.692096i | −0.00117050 | − | 0.999999i | \(-0.500373\pi\) |
−0.951418 | + | 0.307904i | \(0.900373\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5421 | − | 21.3919i | 0.923882 | − | 1.27162i | −0.0383159 | − | 0.999266i | \(-0.512199\pi\) |
0.962198 | − | 0.272349i | \(-0.0878007\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.9230 | − | 8.42289i | −1.53019 | − | 0.497187i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.40247 | − | 10.4717i | −0.200145 | − | 0.615983i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.22461 | − | 9.92434i | 0.189030 | − | 0.581775i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 19.1882i | − | 1.12099i | −0.828158 | − | 0.560494i | \(-0.810611\pi\) | ||
0.828158 | − | 0.560494i | \(-0.189389\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.21379 | − | 3.04701i | −0.128457 | − | 0.176806i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.81925 | 0.220873 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.8231 | −1.14258 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.17797 | − | 5.75049i | −0.240018 | − | 0.330357i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.26979i | − | 0.529055i | −0.964378 | − | 0.264527i | \(-0.914784\pi\) | ||
0.964378 | − | 0.264527i | \(-0.0852160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.77281 | − | 11.6115i | 0.214627 | − | 0.660555i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.69255 | − | 23.6752i | −0.436204 | − | 1.34250i | −0.891847 | − | 0.452336i | \(-0.850591\pi\) |
0.455643 | − | 0.890163i | \(-0.349409\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.75115 | − | 1.86866i | −0.325074 | − | 0.105623i | 0.141934 | − | 0.989876i | \(-0.454668\pi\) |
−0.467008 | + | 0.884253i | \(0.654668\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.45614 | − | 11.6389i | 0.474944 | − | 0.653705i | −0.502579 | − | 0.864531i | \(-0.667616\pi\) |
0.977523 | + | 0.210827i | \(0.0676155\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.4034 | + | 15.5505i | 1.19836 | + | 0.870659i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.27088 | + | 2.37644i | −0.182563 | + | 0.132640i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28.8666 | − | 9.37934i | 1.60618 | − | 0.521881i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.735942 | + | 0.239122i | −0.0406977 | + | 0.0132235i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −32.3433 | + | 23.4988i | −1.78314 | + | 1.29553i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.863126 | − | 0.627098i | −0.0474417 | − | 0.0344684i | 0.563812 | − | 0.825903i | \(-0.309334\pi\) |
−0.611253 | + | 0.791435i | \(0.709334\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.40027 | − | 4.68007i | 0.186334 | − | 0.256466i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.8873 | + | 4.51226i | 0.756490 | + | 0.245799i | 0.661772 | − | 0.749705i | \(-0.269805\pi\) |
0.0947186 | + | 0.995504i | \(0.469805\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.352104 | − | 1.08366i | −0.0191236 | − | 0.0588565i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.7456 | − | 36.1493i | 0.636062 | − | 1.95760i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 12.7239i | − | 0.687029i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.48995 | + | 13.0618i | 0.509447 | + | 0.701194i | 0.983826 | − | 0.179127i | \(-0.0573273\pi\) |
−0.474379 | + | 0.880321i | \(0.657327\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.2622 | 1.19167 | 0.595834 | − | 0.803108i | \(-0.296822\pi\) | ||||
0.595834 | + | 0.803108i | \(0.296822\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.698665 | −0.0372920 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.60158 | + | 7.70991i | 0.298142 | + | 0.410357i | 0.931637 | − | 0.363389i | \(-0.118381\pi\) |
−0.633496 | + | 0.773746i | \(0.718381\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 21.8721i | − | 1.15760i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.18753 | − | 15.9656i | 0.273788 | − | 0.842632i | −0.715750 | − | 0.698357i | \(-0.753915\pi\) |
0.989538 | − | 0.144275i | \(-0.0460850\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.29210 | + | 13.2097i | 0.225900 | + | 0.695248i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.02925 | + | 0.984264i | 0.158995 | + | 0.0516604i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.0893 | + | 26.2741i | −0.996452 | + | 1.37150i | −0.0689751 | + | 0.997618i | \(0.521973\pi\) |
−0.927477 | + | 0.373880i | \(0.878027\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.33589 | − | 3.87675i | −0.277775 | − | 0.201815i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.3554 | + | 8.25020i | −0.589544 | + | 0.428329i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.5918 | − | 4.41623i | 0.703755 | − | 0.228664i | 0.0647890 | − | 0.997899i | \(-0.479363\pi\) |
0.638966 | + | 0.769235i | \(0.279363\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.66749 | − | 1.51656i | 0.240388 | − | 0.0781068i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.60155 | + | 1.89014i | −0.133633 | + | 0.0970897i | −0.652593 | − | 0.757708i | \(-0.726319\pi\) |
0.518961 | + | 0.854798i | \(0.326319\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.435145 | + | 0.316151i | 0.0222931 | + | 0.0161969i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.26491 | + | 9.99929i | −0.371220 | + | 0.510940i | −0.953232 | − | 0.302240i | \(-0.902266\pi\) |
0.582012 | + | 0.813180i | \(0.302266\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.56192 | − | 1.48226i | −0.231895 | − | 0.0753474i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.14594 | − | 21.9930i | −0.362314 | − | 1.11509i | −0.951646 | − | 0.307196i | \(-0.900609\pi\) |
0.589332 | − | 0.807891i | \(-0.299391\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.94031 | + | 27.5154i | −0.452131 | + | 1.39152i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 6.72242i | − | 0.339101i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.25095 | + | 1.72179i | 0.0627834 | + | 0.0864140i | 0.839254 | − | 0.543739i | \(-0.182992\pi\) |
−0.776471 | + | 0.630153i | \(0.782992\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 23.7005 | 1.18651 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.8250 | −1.68914 | −0.844569 | − | 0.535447i | \(-0.820143\pi\) | ||||
−0.844569 | + | 0.535447i | \(0.820143\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.14443 | − | 5.70432i | −0.206449 | − | 0.284153i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.7877i | 1.07998i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.7434 | − | 33.0647i | 0.531226 | − | 1.63495i | −0.220439 | − | 0.975401i | \(-0.570749\pi\) |
0.751665 | − | 0.659545i | \(-0.229251\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0566672 | − | 0.174404i | −0.00279518 | − | 0.00860269i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.92931 | − | 0.951790i | −0.144142 | − | 0.0468345i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.83163 | + | 6.65017i | −0.236606 | + | 0.325660i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.49925 | − | 3.99544i | −0.268656 | − | 0.195190i | 0.445298 | − | 0.895382i | \(-0.353098\pi\) |
−0.713954 | + | 0.700192i | \(0.753098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.75730 | − | 6.36255i | 0.426805 | − | 0.310092i | −0.353565 | − | 0.935410i | \(-0.615031\pi\) |
0.780370 | + | 0.625318i | \(0.215031\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.20032 | + | 2.98937i | −0.447335 | + | 0.145348i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −46.4099 | + | 15.0795i | −2.24593 | + | 0.729747i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.12884 | − | 1.54670i | 0.102782 | − | 0.0746752i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.40317 | + | 6.10526i | 0.404767 | + | 0.294080i | 0.771480 | − | 0.636254i | \(-0.219517\pi\) |
−0.366713 | + | 0.930334i | \(0.619517\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.20630 | + | 12.6714i | −0.442427 | + | 0.608948i | −0.970749 | − | 0.240096i | \(-0.922821\pi\) |
0.528323 | + | 0.849044i | \(0.322821\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −29.8156 | − | 9.68768i | −1.42627 | − | 0.463425i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.80071 | − | 20.9304i | −0.324580 | − | 0.998955i | −0.971630 | − | 0.236507i | \(-0.923997\pi\) |
0.647050 | − | 0.762448i | \(-0.276003\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.11454 | − | 9.58558i | 0.148312 | − | 0.456456i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.4447i | 1.39896i | 0.714652 | + | 0.699480i | \(0.246585\pi\) | ||||
−0.714652 | + | 0.699480i | \(0.753415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.25509 | + | 4.48025i | 0.153961 | + | 0.211909i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.3445 | −1.29047 | −0.645234 | − | 0.763985i | \(-0.723240\pi\) | ||||
−0.645234 | + | 0.763985i | \(0.723240\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.8408 | 1.16971 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.56693 | − | 10.4150i | −0.355526 | − | 0.489339i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 33.6394i | − | 1.57359i | −0.617217 | − | 0.786793i | \(-0.711740\pi\) | ||
0.617217 | − | 0.786793i | \(-0.288260\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.63547 | − | 5.03347i | 0.0763374 | − | 0.234942i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.86199 | + | 24.1967i | 0.366169 | + | 1.12695i | 0.949246 | + | 0.314536i | \(0.101849\pi\) |
−0.583076 | + | 0.812417i | \(0.698151\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.45749 | + | 2.42308i | 0.346579 | + | 0.112610i | 0.477134 | − | 0.878831i | \(-0.341676\pi\) |
−0.130555 | + | 0.991441i | \(0.541676\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.34847 | − | 8.73792i | 0.293772 | − | 0.404343i | −0.636463 | − | 0.771307i | \(-0.719603\pi\) |
0.930235 | + | 0.366965i | \(0.119603\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.0402 | + | 11.6539i | 0.740668 | + | 0.538127i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.8436 | + | 8.60487i | −0.545724 | + | 0.396491i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.1816 | − | 5.58265i | 0.790012 | − | 0.256691i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.23015 | + | 1.04954i | −0.147898 | + | 0.0480551i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.3447 | − | 13.3282i | 0.838191 | − | 0.608981i | −0.0836740 | − | 0.996493i | \(-0.526665\pi\) |
0.921865 | + | 0.387512i | \(0.126665\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.26980 | + | 2.37565i | 0.149090 | + | 0.108320i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.2787 | + | 18.2766i | −0.604204 | + | 0.831615i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.74184 | − | 1.54072i | −0.214873 | − | 0.0698166i | 0.199602 | − | 0.979877i | \(-0.436035\pi\) |
−0.414476 | + | 0.910060i | \(0.636035\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.37334 | − | 4.22672i | −0.0621048 | − | 0.191139i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.17443 | + | 25.1583i | −0.368907 | + | 1.13538i | 0.578592 | + | 0.815617i | \(0.303603\pi\) |
−0.947498 | + | 0.319761i | \(0.896397\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.1766i | 1.67435i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.63365 | + | 10.5068i | 0.342416 | + | 0.471295i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.0875 | −1.70503 | −0.852516 | − | 0.522702i | \(-0.824924\pi\) | ||||
−0.852516 | + | 0.522702i | \(0.824924\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.7655 | 1.06176 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.38481 | + | 1.90603i | 0.0617456 | + | 0.0849856i | 0.838773 | − | 0.544481i | \(-0.183273\pi\) |
−0.777027 | + | 0.629467i | \(0.783273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.5119i | 0.555672i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.02282 | − | 27.7694i | 0.399929 | − | 1.23086i | −0.525126 | − | 0.851024i | \(-0.675982\pi\) |
0.925056 | − | 0.379832i | \(-0.124018\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.7250 | − | 42.2412i | −0.607158 | − | 1.86864i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.45425 | + | 1.77219i | 0.240811 | + | 0.0782442i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.4157 | − | 29.4762i | 0.941862 | − | 1.29636i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.2055 | + | 8.86778i | 0.535760 | + | 0.389252i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.4787 | − | 25.0503i | 1.51054 | − | 1.09747i | 0.544604 | − | 0.838693i | \(-0.316680\pi\) |
0.965937 | − | 0.258779i | \(-0.0833200\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.6631 | + | 6.38893i | −0.859808 | + | 0.279368i | −0.705548 | − | 0.708662i | \(-0.749299\pi\) |
−0.154259 | + | 0.988030i | \(0.549299\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 50.7978 | − | 16.5052i | 2.21279 | − | 0.718978i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.56809 | − | 4.04545i | 0.242091 | − | 0.175889i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.602958 | − | 0.438075i | −0.0261661 | − | 0.0190108i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.70855 | − | 3.72800i | 0.117320 | − | 0.161478i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.8982 | − | 5.16563i | −0.686057 | − | 0.222913i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.7304 | + | 36.1023i | 0.505262 | + | 1.55504i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.69426 | − | 11.3698i | 0.158829 | − | 0.488824i | −0.839700 | − | 0.543050i | \(-0.817269\pi\) |
0.998529 | + | 0.0542264i | \(0.0172693\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3923i | 0.445976i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.6366 | + | 21.5220i | 0.668575 | + | 0.920214i | 0.999727 | − | 0.0233630i | \(-0.00743737\pi\) |
−0.331152 | + | 0.943577i | \(0.607437\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.8079 | −0.503951 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −40.2844 | −1.71617 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.1655 | − | 30.5082i | −0.942573 | − | 1.29734i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.3420i | 1.20089i | 0.799667 | + | 0.600444i | \(0.205010\pi\) | ||||
−0.799667 | + | 0.600444i | \(0.794990\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.03560 | − | 3.18725i | 0.0438013 | − | 0.134806i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.15971 | + | 18.9576i | 0.260063 | + | 0.800393i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.85764 | + | 1.25342i | 0.162580 | + | 0.0528255i | 0.389176 | − | 0.921163i | \(-0.372760\pi\) |
−0.226596 | + | 0.973989i | \(0.572760\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.42912 | − | 3.34339i | 0.102013 | − | 0.140409i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.59124 | + | 1.15610i | 0.0667081 | + | 0.0484663i | 0.620640 | − | 0.784096i | \(-0.286873\pi\) |
−0.553931 | + | 0.832562i | \(0.686873\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.17273 | + | 3.03167i | −0.174623 | + | 0.126871i | −0.671664 | − | 0.740856i | \(-0.734420\pi\) |
0.497040 | + | 0.867727i | \(0.334420\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.7888 | − | 6.10485i | 0.784914 | − | 0.255034i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.7286 | − | 11.9338i | 1.52903 | − | 0.496812i | 0.580706 | − | 0.814113i | \(-0.302776\pi\) |
0.948325 | + | 0.317301i | \(0.102776\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.80855 | − | 1.31399i | 0.0751608 | − | 0.0546075i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.2215 | + | 20.5041i | 1.17083 | + | 0.850654i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.51885 | − | 10.3488i | 0.311399 | − | 0.428604i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.8420 | − | 8.39659i | −1.06662 | − | 0.346564i | −0.277447 | − | 0.960741i | \(-0.589488\pi\) |
−0.789168 | + | 0.614177i | \(0.789488\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.8850 | + | 55.0443i | 0.736937 | + | 2.26806i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.03223 | + | 21.6430i | −0.289267 | + | 0.890273i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 30.3486i | − | 1.24627i | −0.782114 | − | 0.623135i | \(-0.785859\pi\) | ||
0.782114 | − | 0.623135i | \(-0.214141\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.4116 | + | 18.4594i | 0.548899 | + | 0.755494i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.9205 | 1.09994 | 0.549971 | − | 0.835184i | \(-0.314639\pi\) | ||||
0.549971 | + | 0.835184i | \(0.314639\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.9133 | −0.689910 | −0.344955 | − | 0.938619i | \(-0.612106\pi\) | ||||
−0.344955 | + | 0.938619i | \(0.612106\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.81995 | + | 3.88133i | 0.114837 | + | 0.158060i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 18.9715i | − | 0.770028i | −0.922911 | − | 0.385014i | \(-0.874197\pi\) | ||
0.922911 | − | 0.385014i | \(-0.125803\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.97057 | + | 27.6086i | −0.363506 | + | 1.11876i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.08857 | − | 6.42795i | −0.0844944 | − | 0.260047i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.19102 | + | 1.68666i | 0.209663 | + | 0.0681237i | 0.411966 | − | 0.911199i | \(-0.364842\pi\) |
−0.202302 | + | 0.979323i | \(0.564842\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.99287 | + | 9.62485i | −0.281522 | + | 0.387482i | −0.926237 | − | 0.376941i | \(-0.876976\pi\) |
0.644715 | + | 0.764423i | \(0.276976\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.6888 | − | 7.76586i | −0.429619 | − | 0.312136i | 0.351878 | − | 0.936046i | \(-0.385543\pi\) |
−0.781496 | + | 0.623910i | \(0.785543\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.42248 | + | 3.21312i | −0.177468 | + | 0.128938i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.3155 | + | 4.32647i | −0.533475 | + | 0.173336i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.5424 | + | 6.67464i | −0.820386 | + | 0.266560i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.7693 | + | 17.9959i | −0.987616 | + | 0.717545i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.39932 | + | 6.82900i | 0.374181 | + | 0.271858i | 0.758943 | − | 0.651158i | \(-0.225716\pi\) |
−0.384762 | + | 0.923016i | \(0.625716\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.8125 | − | 16.2585i | 0.469504 | − | 0.646217i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.69711 | + | 2.17602i | 0.265349 | + | 0.0862172i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.971105 | + | 2.98875i | 0.0384163 | + | 0.118233i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.7784 | + | 33.1725i | −0.425721 | + | 1.31023i | 0.476582 | + | 0.879130i | \(0.341876\pi\) |
−0.902303 | + | 0.431103i | \(0.858124\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.90629i | − | 0.114613i | −0.998357 | − | 0.0573065i | \(-0.981749\pi\) | ||
0.998357 | − | 0.0573065i | \(-0.0182512\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.13583 | − | 9.82163i | −0.280538 | − | 0.386128i | 0.645374 | − | 0.763867i | \(-0.276702\pi\) |
−0.925912 | + | 0.377739i | \(0.876702\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.80702 | 0.110185 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 41.7068 | 1.63462 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.3404 | + | 21.1143i | 0.600318 | + | 0.826266i | 0.995737 | − | 0.0922343i | \(-0.0294009\pi\) |
−0.395420 | + | 0.918500i | \(0.629401\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 10.7473i | − | 0.419293i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.59035 | + | 20.2830i | −0.256724 | + | 0.790114i | 0.736761 | + | 0.676153i | \(0.236354\pi\) |
−0.993485 | + | 0.113962i | \(0.963646\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.79161 | − | 30.1355i | −0.380850 | − | 1.17213i | −0.939447 | − | 0.342695i | \(-0.888660\pi\) |
0.558597 | − | 0.829439i | \(-0.311340\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.51671 | + | 1.14265i | 0.136578 | + | 0.0443768i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.5702 | − | 31.0652i | 0.873922 | − | 1.20285i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.8561 | − | 7.88740i | −0.419720 | − | 0.304945i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.9790 | − | 26.1403i | 1.38895 | − | 1.00913i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.88857 | − | 0.613635i | 0.0727992 | − | 0.0236539i | −0.272391 | − | 0.962187i | \(-0.587814\pi\) |
0.345190 | + | 0.938533i | \(0.387814\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 37.5057 | − | 12.1864i | 1.44146 | − | 0.468360i | 0.519110 | − | 0.854708i | \(-0.326264\pi\) |
0.922353 | + | 0.386348i | \(0.126264\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −34.8885 | + | 25.3480i | −1.33890 | + | 0.972767i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.9597 | − | 10.8689i | −0.573259 | − | 0.416497i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.22768 | + | 9.94805i | −0.276559 | + | 0.380651i | −0.924590 | − | 0.380962i | \(-0.875593\pi\) |
0.648031 | + | 0.761614i | \(0.275593\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.4623 | + | 5.99878i | 0.704382 | + | 0.228868i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.733276 | − | 2.25679i | −0.0279356 | − | 0.0859769i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.85334 | − | 14.9371i | 0.184630 | − | 0.568232i | −0.815312 | − | 0.579022i | \(-0.803435\pi\) |
0.999942 | + | 0.0107896i | \(0.00343451\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.5649i | 0.591262i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.5177 | + | 28.2402i | 0.777164 | + | 1.06967i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.1833 | −0.460813 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.4222 | −0.997953 | −0.498976 | − | 0.866616i | \(-0.666291\pi\) | ||||
−0.498976 | + | 0.866616i | \(0.666291\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.5003 | − | 26.8399i | −0.735469 | − | 1.01229i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.3749i | 1.10476i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.0638 | + | 46.3616i | −0.565733 | + | 1.74115i | 0.100030 | + | 0.994984i | \(0.468106\pi\) |
−0.665763 | + | 0.746163i | \(0.731894\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.81976 | − | 8.67832i | −0.105749 | − | 0.325462i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −52.4677 | − | 17.0478i | −1.96493 | − | 0.638445i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.65959 | + | 3.66061i | −0.0993241 | + | 0.136708i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.7117 | − | 20.1337i | −1.03347 | − | 0.750861i | −0.0644713 | − | 0.997920i | \(-0.520536\pi\) |
−0.969001 | + | 0.247058i | \(0.920536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.8197 | + | 29.6572i | −1.52020 | + | 1.10449i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.57071 | + | 2.78479i | −0.318748 | + | 0.103568i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.3168 | − | 6.60134i | 0.753510 | − | 0.244830i | 0.0930190 | − | 0.995664i | \(-0.470348\pi\) |
0.660491 | + | 0.750834i | \(0.270348\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.809017 | − | 0.587785i | 0.0299636 | − | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.5381 | + | 14.9218i | 0.759629 | + | 0.551903i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.3875 | + | 25.3083i | −0.679159 | + | 0.934782i | −0.999923 | − | 0.0123772i | \(-0.996060\pi\) |
0.320765 | + | 0.947159i | \(0.396060\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.1849 | − | 5.58370i | −0.633013 | − | 0.205678i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.406330 | − | 1.25056i | −0.0149471 | − | 0.0460025i | 0.943305 | − | 0.331928i | \(-0.107699\pi\) |
−0.958252 | + | 0.285925i | \(0.907699\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.23817 | + | 3.81070i | −0.0454853 | + | 0.139989i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8.76431i | − | 0.321531i | −0.986993 | − | 0.160766i | \(-0.948604\pi\) | ||
0.986993 | − | 0.160766i | \(-0.0513963\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.96148 | + | 6.82889i | 0.181531 | + | 0.249856i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.7085 | 0.610515 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.6570 | 1.62956 | 0.814779 | − | 0.579772i | \(-0.196858\pi\) | ||||
0.814779 | + | 0.579772i | \(0.196858\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.86307 | − | 2.56430i | −0.0678941 | − | 0.0934482i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.70729i | 0.280126i | 0.990143 | + | 0.140063i | \(0.0447305\pi\) | ||||
−0.990143 | + | 0.140063i | \(0.955269\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.36221 | − | 19.5809i | 0.230934 | − | 0.710740i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.2344 | + | 37.6537i | 0.443498 | + | 1.36495i | 0.884123 | + | 0.467254i | \(0.154757\pi\) |
−0.440625 | + | 0.897691i | \(0.645243\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.04140 | + | 0.988210i | 0.110106 | + | 0.0357756i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.306068 | − | 0.421266i | 0.0110515 | − | 0.0152110i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.7336 | + | 17.2435i | 0.855855 | + | 0.621815i | 0.926754 | − | 0.375668i | \(-0.122587\pi\) |
−0.0708991 | + | 0.997483i | \(0.522587\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.63126 | − | 1.91172i | 0.0947624 | − | 0.0688489i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.3762 | + | 3.37142i | −0.373205 | + | 0.121262i | −0.489613 | − | 0.871940i | \(-0.662862\pi\) |
0.116408 | + | 0.993201i | \(0.462862\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −22.7369 | + | 7.38766i | −0.815681 | + | 0.265031i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30.6010 | + | 22.2329i | −1.09639 | + | 0.796577i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.57543 | − | 6.95696i | −0.342636 | − | 0.248940i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.12883 | + | 5.68284i | −0.147552 | + | 0.203088i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.8619 | + | 11.6522i | 1.27834 | + | 0.415358i | 0.867995 | − | 0.496573i | \(-0.165409\pi\) |
0.410344 | + | 0.911931i | \(0.365409\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.41774 | − | 10.5187i | −0.121675 | − | 0.374476i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.45512 | + | 4.47841i | −0.0517383 | + | 0.159234i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 8.24980i | − | 0.292959i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.9432 | − | 39.8369i | −1.02522 | − | 1.41110i | −0.908477 | − | 0.417935i | \(-0.862754\pi\) |
−0.116745 | − | 0.993162i | \(-0.537246\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51.1986 | 1.81128 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.38783 | −0.119703 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.7922 | + | 32.7472i | 0.839610 | + | 1.15562i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 24.7558i | − | 0.871447i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.33675 | + | 25.6579i | −0.293105 | + | 0.902083i | 0.690747 | + | 0.723097i | \(0.257282\pi\) |
−0.983852 | + | 0.178987i | \(0.942718\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.52546 | + | 7.77257i | 0.0886809 | + | 0.272932i | 0.985555 | − | 0.169353i | \(-0.0541679\pi\) |
−0.896875 | + | 0.442285i | \(0.854168\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.237960 | + | 0.0773177i | 0.00834561 | + | 0.00271165i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.1692 | + | 22.2550i | −0.565689 | + | 0.778604i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.33591 | + | 1.69714i | 0.0816234 | + | 0.0593029i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.4256 | − | 25.7382i | 1.23636 | − | 0.898269i | 0.239011 | − | 0.971017i | \(-0.423177\pi\) |
0.997350 | + | 0.0727478i | \(0.0231768\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.6512 | + | 5.08540i | −0.545568 | + | 0.177266i | −0.568817 | − | 0.822464i | \(-0.692599\pi\) |
0.0232493 | + | 0.999730i | \(0.492599\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.82167 | + | 1.24174i | −0.132893 | + | 0.0431794i | −0.374708 | − | 0.927143i | \(-0.622257\pi\) |
0.241816 | + | 0.970322i | \(0.422257\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.3103 | − | 22.0217i | 1.05272 | − | 0.764847i | 0.0799935 | − | 0.996795i | \(-0.474510\pi\) |
0.972728 | + | 0.231948i | \(0.0745101\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.17658 | + | 5.21409i | 0.248953 | + | 0.180875i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −31.3539 | + | 43.1550i | −1.08635 | + | 1.49523i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.59806 | + | 3.11860i | 0.331758 | + | 0.107795i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.58335 | + | 11.0284i | 0.123711 | + | 0.380743i | 0.993664 | − | 0.112391i | \(-0.0358510\pi\) |
−0.869953 | + | 0.493135i | \(0.835851\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.28600 | − | 19.3463i | 0.216759 | − | 0.667114i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.7379i | 0.679809i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.73709 | − | 10.6492i | −0.265849 | − | 0.365910i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.4418 | −0.907481 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.6230 | 1.08402 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.777036 | − | 1.06950i | −0.0266052 | − | 0.0366189i | 0.795507 | − | 0.605944i | \(-0.207205\pi\) |
−0.822112 | + | 0.569325i | \(0.807205\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.5623i | 0.531598i | 0.964028 | + | 0.265799i | \(0.0856358\pi\) | ||||
−0.964028 | + | 0.265799i | \(0.914364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.46169 | − | 26.0424i | 0.288709 | − | 0.888556i | −0.696553 | − | 0.717505i | \(-0.745284\pi\) |
0.985262 | − | 0.171050i | \(-0.0547161\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.42289 | + | 25.9230i | 0.287051 | + | 0.883453i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.4617 | − | 9.89760i | −1.03693 | − | 0.336918i | −0.259402 | − | 0.965769i | \(-0.583525\pi\) |
−0.777526 | + | 0.628851i | \(0.783525\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.47188 | + | 8.90777i | −0.219796 | + | 0.302524i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27.8038 | + | 20.2006i | 0.943178 | + | 0.685259i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.71175 | + | 1.97020i | −0.0918842 | + | 0.0667578i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.92434 | + | 3.22461i | −0.335888 | + | 0.109137i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.08119 | − | 1.32606i | 0.137812 | − | 0.0447778i | −0.239299 | − | 0.970946i | \(-0.576918\pi\) |
0.377111 | + | 0.926168i | \(0.376918\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.5236 | + | 11.2786i | −0.523598 | + | 0.380416i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.7520 | + | 31.7877i | 1.47404 | + | 1.07095i | 0.979417 | + | 0.201848i | \(0.0646947\pi\) |
0.494625 | + | 0.869106i | \(0.335305\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.6340 | − | 25.6474i | 0.627083 | − | 0.863105i | −0.370762 | − | 0.928728i | \(-0.620903\pi\) |
0.997845 | + | 0.0656228i | \(0.0209034\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.11670 | − | 1.66252i | −0.171802 | − | 0.0558218i | 0.221853 | − | 0.975080i | \(-0.428789\pi\) |
−0.393655 | + | 0.919258i | \(0.628789\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.686891 | − | 2.11403i | −0.0230376 | − | 0.0709024i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.16386 | + | 3.58198i | −0.0389906 | + | 0.120001i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 55.4786i | 1.85652i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.24490 | − | 3.08984i | −0.0749550 | − | 0.103167i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −70.8900 | −2.36432 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.9753 | 0.598846 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.6517 | + | 16.0372i | 0.387744 | + | 0.533684i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 45.7593i | − | 1.51941i | −0.650266 | − | 0.759706i | \(-0.725343\pi\) | ||
0.650266 | − | 0.759706i | \(-0.274657\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.19649 | + | 6.76010i | −0.0728530 | + | 0.224219i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.669870 | + | 2.06165i | 0.0221938 | + | 0.0683054i | 0.961540 | − | 0.274665i | \(-0.0885669\pi\) |
−0.939346 | + | 0.342970i | \(0.888567\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.2354 | − | 9.82408i | −1.00065 | − | 0.325130i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.3295 | + | 22.4757i | −0.539249 | + | 0.742213i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.9053 | − | 11.5559i | −0.524666 | − | 0.381192i | 0.293693 | − | 0.955900i | \(-0.405116\pi\) |
−0.818359 | + | 0.574708i | \(0.805116\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.49942 | + | 5.44865i | −0.247114 | + | 0.179539i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.08814 | + | 0.678477i | −0.0687319 | + | 0.0223324i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.6115 | + | 3.77281i | −0.381372 | + | 0.123915i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.2728 | − | 25.6272i | 1.15726 | − | 0.840800i | 0.167832 | − | 0.985816i | \(-0.446323\pi\) |
0.989429 | + | 0.145016i | \(0.0463233\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −46.7626 | − | 33.9750i | −1.53258 | − | 1.11349i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.6321 | + | 20.1393i | −0.479033 | + | 0.659333i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.0143 | + | 13.0014i | 1.30721 | + | 0.424738i | 0.878084 | − | 0.478506i | \(-0.158822\pi\) |
0.429126 | + | 0.903245i | \(0.358822\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.86866 | + | 5.75115i | 0.0609815 | + | 0.187682i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.1162 | − | 46.5228i | 0.492773 | − | 1.51660i | −0.327625 | − | 0.944808i | \(-0.606248\pi\) |
0.820399 | − | 0.571792i | \(-0.193752\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 36.0544i | − | 1.17409i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.18115 | + | 5.75486i | 0.135869 | + | 0.187008i | 0.871530 | − | 0.490342i | \(-0.163128\pi\) |
−0.735661 | + | 0.677350i | \(0.763128\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.50878 | 0.243745 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.3864 | −0.466512 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.0707 | − | 17.9903i | −0.423402 | − | 0.582762i | 0.543021 | − | 0.839719i | \(-0.317280\pi\) |
−0.966423 | + | 0.256957i | \(0.917280\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 26.4560i | − | 0.855202i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.234186 | + | 0.720751i | −0.00756226 | + | 0.0232743i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.8934 | + | 67.3809i | 0.706238 | + | 2.17358i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.84515 | + | 1.24937i | 0.123908 | + | 0.0402603i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.17914 | − | 11.2576i | 0.263023 | − | 0.362021i | −0.656996 | − | 0.753894i | \(-0.728173\pi\) |
0.920019 | + | 0.391874i | \(0.128173\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.5554 | − | 17.8406i | −0.788834 | − | 0.573122i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.6548 | + | 14.2801i | −0.630754 | + | 0.458270i | −0.856661 | − | 0.515879i | \(-0.827465\pi\) |
0.225907 | + | 0.974149i | \(0.427465\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.3081 | − | 10.4975i | 1.03575 | − | 0.336535i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −44.0637 | + | 14.3172i | −1.40972 | + | 0.458047i | −0.912322 | − | 0.409473i | \(-0.865713\pi\) |
−0.497402 | + | 0.867520i | \(0.665713\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.3228 | − | 7.49993i | 0.329917 | − | 0.239699i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.626030 | + | 0.454837i | 0.0199876 | + | 0.0145218i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.1334 | + | 33.2168i | −0.769736 | + | 1.05945i | 0.226605 | + | 0.973987i | \(0.427237\pi\) |
−0.996341 | + | 0.0854644i | \(0.972763\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 38.0218 | + | 12.3540i | 1.21025 | + | 0.393233i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.10275 | − | 24.9377i | −0.257652 | − | 0.792972i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.26579 | − | 19.2841i | 0.199039 | − | 0.612580i | −0.800866 | − | 0.598843i | \(-0.795627\pi\) |
0.999906 | − | 0.0137370i | \(-0.00437276\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.06688i | 0.0338565i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.3204 | + | 19.7104i | 0.453533 | + | 0.624234i | 0.973152 | − | 0.230164i | \(-0.0739262\pi\) |
−0.519619 | + | 0.854398i | \(0.673926\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.78488 | −0.183026 |
(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 | 1500.2.o.c.349.2 | 24 | ||
5.2 | odd | 4 | 1500.2.m.c.901.1 | 24 | |||
5.3 | odd | 4 | 1500.2.m.d.901.6 | 24 | |||
5.4 | even | 2 | 300.2.o.a.169.5 | ✓ | 24 | ||
15.14 | odd | 2 | 900.2.w.c.469.3 | 24 | |||
25.2 | odd | 20 | 7500.2.a.n.1.1 | 12 | |||
25.3 | odd | 20 | 1500.2.m.d.601.6 | 24 | |||
25.4 | even | 10 | inner | 1500.2.o.c.649.2 | 24 | ||
25.11 | even | 5 | 7500.2.d.g.1249.24 | 24 | |||
25.14 | even | 10 | 7500.2.d.g.1249.1 | 24 | |||
25.21 | even | 5 | 300.2.o.a.229.5 | yes | 24 | ||
25.22 | odd | 20 | 1500.2.m.c.601.1 | 24 | |||
25.23 | odd | 20 | 7500.2.a.m.1.12 | 12 | |||
75.71 | odd | 10 | 900.2.w.c.829.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.169.5 | ✓ | 24 | 5.4 | even | 2 | ||
300.2.o.a.229.5 | yes | 24 | 25.21 | even | 5 | ||
900.2.w.c.469.3 | 24 | 15.14 | odd | 2 | |||
900.2.w.c.829.3 | 24 | 75.71 | odd | 10 | |||
1500.2.m.c.601.1 | 24 | 25.22 | odd | 20 | |||
1500.2.m.c.901.1 | 24 | 5.2 | odd | 4 | |||
1500.2.m.d.601.6 | 24 | 25.3 | odd | 20 | |||
1500.2.m.d.901.6 | 24 | 5.3 | odd | 4 | |||
1500.2.o.c.349.2 | 24 | 1.1 | even | 1 | trivial | ||
1500.2.o.c.649.2 | 24 | 25.4 | even | 10 | inner | ||
7500.2.a.m.1.12 | 12 | 25.23 | odd | 20 | |||
7500.2.a.n.1.1 | 12 | 25.2 | odd | 20 | |||
7500.2.d.g.1249.1 | 24 | 25.14 | even | 10 | |||
7500.2.d.g.1249.24 | 24 | 25.11 | even | 5 |