Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [124,4,Mod(5,124)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(124, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("124.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 124 = 2^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 124.e (of order \(3\), degree \(2\), 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: | \(7.31623684071\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.250722553392.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 46x^{4} - 24x^{3} + 2116x^{2} - 552x + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 25.1 | ||
Root | \(-3.45459 + 5.98353i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 124.25 |
Dual form | 124.4.e.b.5.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).
\(n\) | \(63\) | \(65\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −4.95459 | − | 8.58160i | −0.953512 | − | 1.65153i | −0.737738 | − | 0.675087i | \(-0.764106\pi\) |
−0.215774 | − | 0.976443i | \(-0.569227\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.40918 | + | 12.8331i | −0.662698 | + | 1.14783i | 0.317207 | + | 0.948356i | \(0.397255\pi\) |
−0.979904 | + | 0.199469i | \(0.936078\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.04541 | + | 7.00685i | 0.218432 | + | 0.378334i | 0.954329 | − | 0.298759i | \(-0.0965726\pi\) |
−0.735897 | + | 0.677093i | \(0.763239\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −35.5960 | + | 61.6540i | −1.31837 | + | 2.28348i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.9045 | − | 32.7436i | 0.518176 | − | 0.897507i | −0.481601 | − | 0.876391i | \(-0.659945\pi\) |
0.999777 | − | 0.0211166i | \(-0.00672212\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.5500 | − | 23.4694i | 0.289085 | − | 0.500710i | −0.684507 | − | 0.729007i | \(-0.739982\pi\) |
0.973592 | + | 0.228297i | \(0.0733156\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 146.838 | 2.52756 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 39.1960 | + | 67.8895i | 0.559202 | + | 0.968567i | 0.997563 | + | 0.0697676i | \(0.0222258\pi\) |
−0.438361 | + | 0.898799i | \(0.644441\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 72.0742 | + | 124.836i | 0.870261 | + | 1.50734i | 0.861727 | + | 0.507373i | \(0.169383\pi\) |
0.00853467 | + | 0.999964i | \(0.497283\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 40.0867 | − | 69.4322i | 0.416554 | − | 0.721493i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −114.058 | −1.03403 | −0.517014 | − | 0.855977i | \(-0.672957\pi\) | ||||
−0.517014 | + | 0.855977i | \(0.672957\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −47.2920 | − | 81.9122i | −0.378336 | − | 0.655297i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 437.906 | 3.12130 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −86.1021 | −0.551337 | −0.275668 | − | 0.961253i | \(-0.588899\pi\) | ||||
−0.275668 | + | 0.961253i | \(0.588899\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −157.260 | + | 71.1346i | −0.911123 | + | 0.412134i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −374.657 | −1.97635 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −119.893 | −0.579016 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 170.656 | + | 295.585i | 0.758261 | + | 1.31335i | 0.943737 | + | 0.330698i | \(0.107284\pi\) |
−0.185476 | + | 0.982649i | \(0.559383\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −268.540 | −1.10258 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −157.996 | + | 273.657i | −0.601825 | + | 1.04239i | 0.390720 | + | 0.920510i | \(0.372226\pi\) |
−0.992545 | + | 0.121881i | \(0.961107\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 163.129 | + | 282.548i | 0.578533 | + | 1.00205i | 0.995648 | + | 0.0931953i | \(0.0297081\pi\) |
−0.417114 | + | 0.908854i | \(0.636959\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −527.474 | − | 913.612i | −1.74736 | − | 3.02652i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 58.1466 | 0.180459 | 0.0902293 | − | 0.995921i | \(-0.471240\pi\) | ||||
0.0902293 | + | 0.995921i | \(0.471240\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 138.769 | − | 240.356i | 0.404575 | − | 0.700745i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 388.401 | − | 672.730i | 1.06641 | − | 1.84708i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −133.540 | + | 231.298i | −0.346096 | + | 0.599456i | −0.985552 | − | 0.169371i | \(-0.945826\pi\) |
0.639456 | + | 0.768828i | \(0.279160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 280.135 | + | 485.207i | 0.686788 | + | 1.18955i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 714.197 | − | 1237.03i | 1.65961 | − | 2.87453i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −279.244 | − | 483.665i | −0.616177 | − | 1.06725i | −0.990177 | − | 0.139821i | \(-0.955347\pi\) |
0.373999 | − | 0.927429i | \(-0.377986\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −234.587 | −0.492391 | −0.246195 | − | 0.969220i | \(-0.579180\pi\) | ||||
−0.246195 | + | 0.969220i | \(0.579180\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −576.001 | −1.15189 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 200.790 | + | 347.778i | 0.383152 | + | 0.663639i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −107.555 | + | 186.292i | −0.196119 | + | 0.339689i | −0.947267 | − | 0.320446i | \(-0.896167\pi\) |
0.751148 | + | 0.660134i | \(0.229501\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 565.109 | + | 978.798i | 0.985959 | + | 1.70773i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −399.541 | + | 692.026i | −0.667843 | + | 1.15674i | 0.310663 | + | 0.950520i | \(0.399449\pi\) |
−0.978506 | + | 0.206218i | \(0.933884\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 193.956 | − | 335.942i | 0.310971 | − | 0.538617i | −0.667602 | − | 0.744518i | \(-0.732679\pi\) |
0.978573 | + | 0.205901i | \(0.0660125\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −468.625 | + | 811.683i | −0.721496 | + | 1.24967i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 305.906 | 0.452744 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −73.5118 | − | 127.326i | −0.104693 | − | 0.181333i | 0.808920 | − | 0.587919i | \(-0.200053\pi\) |
−0.913613 | + | 0.406586i | \(0.866719\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1208.55 | − | 2093.28i | −1.65782 | − | 2.87144i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 429.550 | − | 744.003i | 0.568063 | − | 0.983914i | −0.428694 | − | 0.903450i | \(-0.641026\pi\) |
0.996757 | − | 0.0804647i | \(-0.0256404\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1161.64 | −1.48233 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 426.601 | + | 738.894i | 0.525706 | + | 0.910549i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −284.219 | −0.338507 | −0.169254 | − | 0.985573i | \(-0.554136\pi\) | ||||
−0.169254 | + | 0.985573i | \(0.554136\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 219.262 | 0.252581 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1389.61 | + | 997.104i | 1.54942 | + | 1.11177i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2136.04 | −2.30688 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −59.2991 | −0.0620712 | −0.0310356 | − | 0.999518i | \(-0.509881\pi\) | ||||
−0.0310356 | + | 0.999518i | \(0.509881\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1345.85 | + | 2331.08i | 1.36629 | + | 2.36649i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 163.729 | 0.161303 | 0.0806517 | − | 0.996742i | \(-0.474300\pi\) | ||||
0.0806517 | + | 0.996742i | \(0.474300\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 650.644 | − | 1126.95i | 0.622426 | − | 1.07807i | −0.366607 | − | 0.930376i | \(-0.619481\pi\) |
0.989033 | − | 0.147697i | \(-0.0471861\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 594.019 | + | 1028.87i | 0.552099 | + | 0.956263i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 770.368 | + | 1334.32i | 0.696021 | + | 1.20554i | 0.969835 | + | 0.243761i | \(0.0783814\pi\) |
−0.273814 | + | 0.961783i | \(0.588285\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −592.520 | −0.520671 | −0.260335 | − | 0.965518i | \(-0.583833\pi\) | ||||
−0.260335 | + | 0.965518i | \(0.583833\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1691.06 | − | 2929.00i | 1.44602 | − | 2.50458i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −775.271 | + | 1342.81i | −0.645410 | + | 1.11788i | 0.338797 | + | 0.940860i | \(0.389980\pi\) |
−0.984207 | + | 0.177023i | \(0.943353\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 845.074 | − | 1463.71i | 0.685248 | − | 1.18688i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 964.654 | + | 1670.83i | 0.762241 | + | 1.32024i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −317.128 | + | 549.282i | −0.244295 | + | 0.423131i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −49.2640 | − | 85.3278i | −0.0370128 | − | 0.0641080i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3131.22 | 2.29539 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −450.715 | −0.322506 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −74.1212 | − | 128.382i | −0.0517889 | − | 0.0897011i | 0.838969 | − | 0.544180i | \(-0.183159\pi\) |
−0.890758 | + | 0.454478i | \(0.849826\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1616.48 | − | 2799.82i | 1.10328 | − | 1.91093i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −132.170 | − | 228.924i | −0.0881504 | − | 0.152681i | 0.818579 | − | 0.574394i | \(-0.194762\pi\) |
−0.906729 | + | 0.421713i | \(0.861429\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −583.139 | + | 1010.03i | −0.380185 | + | 0.658500i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3244.52 | + | 5619.68i | −2.06848 | + | 3.58271i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −112.868 | + | 195.494i | −0.0703868 | + | 0.121913i | −0.899071 | − | 0.437803i | \(-0.855757\pi\) |
0.828684 | + | 0.559717i | \(0.189090\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2986.61 | 1.82245 | 0.911225 | − | 0.411909i | \(-0.135138\pi\) | ||||
0.911225 | + | 0.411909i | \(0.135138\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −288.093 | − | 498.991i | −0.172069 | − | 0.298033i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −512.315 | − | 887.355i | −0.299594 | − | 0.518912i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 637.946 | − | 1104.96i | 0.365369 | − | 0.632838i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2750.18 | −1.54307 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −962.109 | − | 1666.42i | −0.528987 | − | 0.916232i | −0.999429 | − | 0.0338012i | \(-0.989239\pi\) |
0.470442 | − | 0.882431i | \(-0.344095\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2227.25 | −1.20034 | −0.600169 | − | 0.799874i | \(-0.704900\pi\) | ||||
−0.600169 | + | 0.799874i | \(0.704900\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5580.88 | −2.94894 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 252.295 | − | 2545.19i | 0.130741 | − | 1.31893i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 428.582 | 0.217863 | 0.108932 | − | 0.994049i | \(-0.465257\pi\) | ||||
0.108932 | + | 0.994049i | \(0.465257\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2646.54 | 1.32003 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −461.410 | − | 799.185i | −0.225864 | − | 0.391209i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2992.70 | 1.43807 | 0.719037 | − | 0.694972i | \(-0.244583\pi\) | ||||
0.719037 | + | 0.694972i | \(0.244583\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2775.90 | − | 4808.01i | 1.30972 | − | 2.26850i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 500.005 | + | 866.034i | 0.231686 | + | 0.401292i | 0.958304 | − | 0.285749i | \(-0.0922425\pi\) |
−0.726618 | + | 0.687041i | \(0.758909\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 731.293 | + | 1266.64i | 0.332860 | + | 0.576530i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10262.2 | −4.58930 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −981.140 | + | 1699.38i | −0.431183 | + | 0.746831i | −0.996975 | − | 0.0777167i | \(-0.975237\pi\) |
0.565792 | + | 0.824548i | \(0.308570\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 382.631 | − | 662.736i | 0.165281 | − | 0.286275i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2767.08 | + | 4792.72i | −1.17506 | + | 2.03527i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1791.98 | − | 3103.80i | −0.748262 | − | 1.29603i | −0.948655 | − | 0.316313i | \(-0.897555\pi\) |
0.200392 | − | 0.979716i | \(-0.435778\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1922.87 | − | 3330.51i | 0.789646 | − | 1.36771i | −0.136537 | − | 0.990635i | \(-0.543597\pi\) |
0.926184 | − | 0.377073i | \(-0.123069\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1162.28 | + | 2013.14i | 0.469500 | + | 0.813198i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5057.68 | −2.00999 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2963.93 | 1.15906 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1771.51 | + | 3068.34i | 0.681790 | + | 1.18089i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1676.89 | − | 2904.46i | 0.635265 | − | 1.10031i | −0.351194 | − | 0.936303i | \(-0.614224\pi\) |
0.986459 | − | 0.164009i | \(-0.0524425\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2084.12 | + | 3609.80i | 0.777297 | + | 1.34632i | 0.933495 | + | 0.358592i | \(0.116743\pi\) |
−0.156198 | + | 0.987726i | \(0.549924\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1989.66 | − | 3446.19i | 0.730680 | − | 1.26557i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1913.93 | + | 3315.02i | −0.692191 | + | 1.19891i | 0.278927 | + | 0.960312i | \(0.410021\pi\) |
−0.971118 | + | 0.238598i | \(0.923312\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −874.649 | + | 1514.94i | −0.311569 | + | 0.539653i | −0.978702 | − | 0.205285i | \(-0.934188\pi\) |
0.667133 | + | 0.744938i | \(0.267521\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2131.57 | 0.748008 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −348.318 | − | 603.305i | −0.120429 | − | 0.208590i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2341.24 | − | 4055.15i | −0.797655 | − | 1.38158i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4059.99 | − | 7032.11i | 1.36323 | − | 2.36119i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5450.12 | 1.80379 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −176.325 | − | 305.404i | −0.0575295 | − | 0.0996440i | 0.835826 | − | 0.548994i | \(-0.184989\pi\) |
−0.893356 | + | 0.449350i | \(0.851656\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7918.26 | 2.54718 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4834.61 | −1.53357 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1134.61 | − | 814.133i | −0.354943 | − | 0.254686i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3843.90 | −1.18606 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2124.43 | 0.646628 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2738.81 | − | 4743.75i | −0.822439 | − | 1.42451i | −0.903861 | − | 0.427827i | \(-0.859279\pi\) |
0.0814212 | − | 0.996680i | \(-0.474054\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6733.62 | 1.99515 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −385.602 | + | 667.883i | −0.112746 | + | 0.195282i | −0.916876 | − | 0.399171i | \(-0.869298\pi\) |
0.804131 | + | 0.594453i | \(0.202631\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2169.44 | + | 3757.58i | 0.626028 | + | 1.08431i | 0.988341 | + | 0.152256i | \(0.0486539\pi\) |
−0.362313 | + | 0.932057i | \(0.618013\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1515.64 | − | 2625.17i | −0.431697 | − | 0.747720i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5612.89 | −1.57816 | −0.789082 | − | 0.614287i | \(-0.789444\pi\) | ||||
−0.789082 | + | 0.614287i | \(0.789444\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −430.819 | + | 746.200i | −0.119589 | + | 0.207135i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −728.442 | + | 1261.70i | −0.199651 | + | 0.345806i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2631.53 | + | 4557.95i | −0.712217 | + | 1.23360i | 0.251807 | + | 0.967778i | \(0.418975\pi\) |
−0.964023 | + | 0.265818i | \(0.914358\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1598.96 | + | 2769.48i | 0.427378 | + | 0.740240i | 0.996639 | − | 0.0819163i | \(-0.0261040\pi\) |
−0.569261 | + | 0.822157i | \(0.692771\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6064.05 | + | 10503.2i | −1.60086 | + | 2.77277i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2056.34 | + | 3561.68i | 0.536222 | + | 0.928764i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3906.44 | 1.00632 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8512.98 | −2.16662 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1007.35 | − | 1744.78i | −0.253320 | − | 0.438763i | 0.711118 | − | 0.703073i | \(-0.248189\pi\) |
−0.964438 | + | 0.264310i | \(0.914856\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2156.21 | + | 3734.66i | −0.535809 | + | 0.928048i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5755.47 | + | 9968.76i | 1.41342 | + | 2.44811i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1632.81 | − | 2828.10i | 0.396310 | − | 0.686428i | −0.596958 | − | 0.802273i | \(-0.703624\pi\) |
0.993267 | + | 0.115844i | \(0.0369573\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1380.75 | + | 2391.52i | −0.331256 | + | 0.573752i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3064.89 | − | 5308.54i | 0.726865 | − | 1.25897i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1694.90 | 0.397384 | 0.198692 | − | 0.980062i | \(-0.436331\pi\) | ||||
0.198692 | + | 0.980062i | \(0.436331\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1978.84 | − | 3427.45i | −0.458714 | − | 0.794516i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1408.19 | + | 2439.06i | 0.322771 | + | 0.559055i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2938.67 | − | 5089.93i | 0.666075 | − | 1.15368i | −0.312918 | − | 0.949780i | \(-0.601307\pi\) |
0.978993 | − | 0.203895i | \(-0.0653601\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6034.41 | −1.35264 | −0.676318 | − | 0.736610i | \(-0.736425\pi\) | ||||
−0.676318 | + | 0.736610i | \(0.736425\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1086.35 | − | 1881.62i | −0.240839 | − | 0.417145i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3576.14 | −0.784179 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5538.88 | 1.20144 | 0.600720 | − | 0.799460i | \(-0.294881\pi\) | ||||
0.600720 | + | 0.799460i | \(0.294881\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1212.10 | − | 12227.8i | 0.260096 | − | 2.62388i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 981.401 | 0.208347 | 0.104173 | − | 0.994559i | \(-0.466780\pi\) | ||||
0.104173 | + | 0.994559i | \(0.466780\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1032.18 | 0.216809 | 0.108404 | − | 0.994107i | \(-0.465426\pi\) | ||||
0.108404 | + | 0.994107i | \(0.465426\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10583.2 | + | 18330.7i | 2.19964 | + | 3.80988i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2556.63 | −0.525830 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −616.160 | + | 1067.22i | −0.125414 | + | 0.217224i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 293.803 | + | 508.881i | 0.0591856 | + | 0.102512i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3222.20 | + | 5581.02i | 0.642468 | + | 1.11279i | 0.984880 | + | 0.173238i | \(0.0554228\pi\) |
−0.342412 | + | 0.939550i | \(0.611244\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8275.88 | 1.63336 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8278.41 | − | 14338.6i | 1.61738 | − | 2.80139i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1545.49 | + | 2676.86i | −0.298922 | + | 0.517749i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1319.85 | + | 2286.04i | −0.252740 | + | 0.437758i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −811.210 | − | 1405.06i | −0.153805 | − | 0.266398i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1738.10 | − | 3010.48i | 0.326306 | − | 0.565179i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2353.34 | − | 4076.10i | −0.437499 | − | 0.757770i | 0.559997 | − | 0.828495i | \(-0.310802\pi\) |
−0.997496 | + | 0.0707242i | \(0.977469\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12894.7 | −2.37396 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6549.04 | 1.19409 | 0.597045 | − | 0.802208i | \(-0.296341\pi\) | ||||
0.597045 | + | 0.802208i | \(0.296341\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.0379 | + | 27.7785i | 0.00289622 | + | 0.00501640i | 0.867470 | − | 0.497490i | \(-0.165745\pi\) |
−0.864574 | + | 0.502506i | \(0.832411\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4267.70 | − | 7391.87i | 0.763357 | − | 1.32217i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1624.24 | + | 2813.26i | 0.287780 | + | 0.498450i | 0.973280 | − | 0.229623i | \(-0.0737494\pi\) |
−0.685499 | + | 0.728073i | \(0.740416\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1627.72 | + | 2819.30i | −0.285689 | + | 0.494829i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7633.72 | − | 13222.0i | 1.32733 | − | 2.29900i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5650.05 | + | 9786.17i | −0.973304 | + | 1.68581i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2563.23 | −0.437485 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2935.69 | + | 5084.77i | 0.496465 | + | 0.859903i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 235.227 | + | 407.425i | 0.0394178 | + | 0.0682737i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1217.92 | − | 2109.50i | 0.202245 | − | 0.350298i | −0.747007 | − | 0.664816i | \(-0.768510\pi\) |
0.949251 | + | 0.314519i | \(0.101843\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −24298.6 | −3.99867 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1593.80 | − | 2760.54i | −0.259936 | − | 0.450222i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2602.95 | −0.420746 | −0.210373 | − | 0.977621i | \(-0.567468\pi\) | ||||
−0.210373 | + | 0.977621i | \(0.567468\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15364.6 | 2.46162 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −643.732 | + | 6494.05i | −0.102229 | + | 1.03130i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5020.66 | 0.790351 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16748.0 | −2.61357 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1041.96 | − | 1804.72i | −0.161197 | − | 0.279201i | 0.774101 | − | 0.633062i | \(-0.218202\pi\) |
−0.935298 | + | 0.353861i | \(0.884869\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8972.63 | −1.37620 | −0.688100 | − | 0.725616i | \(-0.741555\pi\) | ||||
−0.688100 | + | 0.725616i | \(0.741555\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5933.64 | − | 10277.4i | 0.902320 | − | 1.56286i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −161.687 | − | 280.051i | −0.0243789 | − | 0.0422255i | 0.853579 | − | 0.520964i | \(-0.174427\pi\) |
−0.877957 | + | 0.478739i | \(0.841094\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5920.55 | − | 10254.7i | −0.885156 | − | 1.53313i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6284.96 | 0.931752 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3176.90 | + | 5502.56i | −0.467049 | + | 0.808953i | −0.999291 | − | 0.0376394i | \(-0.988016\pi\) |
0.532242 | + | 0.846592i | \(0.321350\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6959.89 | + | 12054.9i | −1.01471 | + | 1.75753i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −488.166 | + | 845.528i | −0.0705842 | + | 0.122255i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2874.12 | + | 4978.11i | 0.412159 | + | 0.713881i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −530.123 | + | 918.199i | −0.0754010 | + | 0.130598i | −0.901261 | − | 0.433277i | \(-0.857357\pi\) |
0.825860 | + | 0.563876i | \(0.190690\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11248.0 | − | 19482.2i | −1.58685 | − | 2.74851i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2160.89 | −0.302393 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1475.27 | −0.204790 | −0.102395 | − | 0.994744i | \(-0.532651\pi\) | ||||
−0.102395 | + | 0.994744i | \(0.532651\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2233.11 | + | 3867.86i | 0.307513 | + | 0.532628i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1166.69 | + | 2020.76i | −0.159383 | + | 0.276060i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1803.47 | − | 3123.70i | −0.244427 | − | 0.423361i | 0.717543 | − | 0.696514i | \(-0.245267\pi\) |
−0.961970 | + | 0.273154i | \(0.911933\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −734.481 | + | 1272.16i | −0.0987627 | + | 0.171062i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1888.86 | − | 3271.61i | 0.252001 | − | 0.436478i | −0.712076 | − | 0.702103i | \(-0.752245\pi\) |
0.964077 | + | 0.265624i | \(0.0855781\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2266.52 | + | 3925.72i | −0.300032 | + | 0.519671i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −23226.9 | −3.05088 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3208.07 | − | 5556.54i | −0.418138 | − | 0.724236i | 0.577614 | − | 0.816310i | \(-0.303984\pi\) |
−0.995752 | + | 0.0920738i | \(0.970650\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4470.61 | − | 7743.32i | −0.578231 | − | 1.00153i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1309.69 | + | 2268.45i | −0.168105 | + | 0.291166i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2178.65 | 0.277518 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2568.18 | − | 4448.22i | −0.324668 | − | 0.562342i | 0.656777 | − | 0.754085i | \(-0.271919\pi\) |
−0.981445 | + | 0.191743i | \(0.938586\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11556.9 | 1.45004 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2245.96 | 0.279695 | 0.139847 | − | 0.990173i | \(-0.455339\pi\) | ||||
0.139847 | + | 0.990173i | \(0.455339\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −461.402 | + | 4654.68i | −0.0570324 | + | 0.575350i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 35817.6 | 4.39454 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12904.7 | 1.57165 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2770.52 | + | 4798.68i | 0.334947 | + | 0.580145i | 0.983475 | − | 0.181046i | \(-0.0579483\pi\) |
−0.648528 | + | 0.761191i | \(0.724615\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2236.86 | 0.268458 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2259.31 | − | 3913.24i | 0.269185 | − | 0.466242i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6365.23 | + | 11024.9i | 0.752908 | + | 1.30408i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14797.4 | − | 25629.9i | −1.73773 | − | 3.00983i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9559.85 | 1.11463 | 0.557314 | − | 0.830302i | \(-0.311832\pi\) | ||||
0.557314 | + | 0.830302i | \(0.311832\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 798.547 | − | 1383.12i | 0.0924437 | − | 0.160117i | −0.816095 | − | 0.577918i | \(-0.803866\pi\) |
0.908539 | + | 0.417800i | \(0.137199\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2069.78 | + | 3584.97i | −0.237911 | + | 0.412074i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3707.32 | − | 6421.26i | 0.423133 | − | 0.732887i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −949.002 | − | 1643.72i | −0.107554 | − | 0.186288i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5076.62 | + | 8792.97i | −0.571332 | + | 0.989577i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2431.24 | + | 4211.03i | 0.271714 | + | 0.470622i | 0.969301 | − | 0.245878i | \(-0.0790763\pi\) |
−0.697587 | + | 0.716500i | \(0.745743\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8991.51 | 0.997932 | 0.498966 | − | 0.866622i | \(-0.333713\pi\) | ||||
0.498966 | + | 0.866622i | \(0.333713\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12643.1 | −1.39354 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8220.62 | − | 14238.5i | −0.899875 | − | 1.55863i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3439.44 | + | 5957.29i | −0.373931 | + | 0.647667i | −0.990166 | − | 0.139895i | \(-0.955324\pi\) |
0.616236 | + | 0.787562i | \(0.288657\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9879.26 | + | 17111.4i | 1.06676 | + | 1.84768i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7587.15 | − | 13141.3i | 0.813716 | − | 1.40940i | −0.0965298 | − | 0.995330i | \(-0.530774\pi\) |
0.910246 | − | 0.414068i | \(-0.135892\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2105.83 | − | 3647.41i | 0.224328 | − | 0.388548i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9533.72 | + | 16512.9i | −1.00879 | + | 1.74728i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7703.39 | 0.809678 | 0.404839 | − | 0.914388i | \(-0.367328\pi\) | ||||
0.404839 | + | 0.914388i | \(0.367328\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5973.68 | + | 10346.7i | 0.623702 | + | 1.08028i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11035.1 | + | 19113.4i | 1.14454 | + | 1.98239i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1624.55 | + | 2813.80i | −0.167385 | + | 0.289919i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1834.21 | −0.187747 | −0.0938736 | − | 0.995584i | \(-0.529925\pi\) | ||||
−0.0938736 | + | 0.995584i | \(0.529925\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17164.2 | + | 29729.2i | 1.74544 | + | 3.02318i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6434.20 | 0.650045 | 0.325022 | − | 0.945706i | \(-0.394628\pi\) | ||||
0.325022 | + | 0.945706i | \(0.394628\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2211.28 | 0.221959 | 0.110979 | − | 0.993823i | \(-0.464601\pi\) | ||||
0.110979 | + | 0.993823i | \(0.464601\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −23091.8 | + | 10445.3i | −2.30292 | + | 1.04169i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3041.83 | −0.301411 | −0.150706 | − | 0.988579i | \(-0.548155\pi\) | ||||
−0.150706 | + | 0.988579i | \(0.548155\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1740.42 | −0.171355 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2123.45 | − | 3677.92i | −0.207735 | − | 0.359808i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12335.5 | 1.19913 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6817.07 | − | 11807.5i | 0.658502 | − | 1.14056i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9506.95 | − | 16466.5i | −0.912565 | − | 1.58061i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 489.900 | + | 848.532i | 0.0467309 | + | 0.0809404i | 0.888445 | − | 0.458984i | \(-0.151786\pi\) |
−0.841714 | + | 0.539924i | \(0.818453\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9249.58 | 0.876807 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4572.19 | + | 7919.27i | −0.430729 | + | 0.746044i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 439.358 | − | 760.990i | 0.0411344 | − | 0.0712469i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1499.08 | − | 2596.47i | 0.139486 | − | 0.241596i | −0.787816 | − | 0.615910i | \(-0.788788\pi\) |
0.927302 | + | 0.374314i | \(0.122122\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14827.6 | − | 25682.1i | −1.37122 | − | 2.37502i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2986.00 | + | 5171.90i | −0.274452 | + | 0.475366i | −0.969997 | − | 0.243118i | \(-0.921830\pi\) |
0.695544 | + | 0.718483i | \(0.255163\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3374.86 | − | 5845.43i | −0.308309 | − | 0.534006i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −39886.6 | −3.62176 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6465.23 | −0.583512 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1881.74 | + | 3259.28i | 0.168815 | + | 0.292395i | 0.938003 | − | 0.346626i | \(-0.112673\pi\) |
−0.769189 | + | 0.639022i | \(0.779339\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4954.64 | − | 8581.69i | 0.441831 | − | 0.765273i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6698.12 | − | 11601.5i | −0.593747 | − | 1.02840i | −0.993722 | − | 0.111874i | \(-0.964315\pi\) |
0.399976 | − | 0.916526i | \(-0.369019\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1213.10 | + | 2101.15i | −0.106895 | + | 0.185148i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7246.51 | − | 12551.3i | 0.634771 | − | 1.09946i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6735.53 | − | 11666.3i | 0.586536 | − | 1.01591i | −0.408146 | − | 0.912917i | \(-0.633824\pi\) |
0.994682 | − | 0.102994i | \(-0.0328422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3138.53 | 0.271703 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 31561.7 | + | 54666.5i | 2.71634 | + | 4.70485i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9641.48 | + | 16699.5i | 0.824960 | + | 1.42887i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1099.24 | − | 1903.93i | 0.0935093 | − | 0.161963i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19444.6 | 1.64455 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4236.78 | − | 7338.33i | −0.356270 | − | 0.617078i | 0.631064 | − | 0.775731i | \(-0.282618\pi\) |
−0.987335 | + | 0.158652i | \(0.949285\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20087.3 | −1.67946 | −0.839730 | − | 0.543004i | \(-0.817287\pi\) | ||||
−0.839730 | + | 0.543004i | \(0.817287\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7583.12 | −0.630390 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10993.3 | − | 7888.15i | −0.908681 | − | 0.652017i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 842.147 | 0.0692157 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 39759.8 | 3.24940 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4281.70 | + | 7416.12i | 0.347957 | + | 0.602679i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22831.2 | −1.84501 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17757.1 | + | 30756.2i | −1.42695 | + | 2.47156i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5246.74 | − | 9087.63i | −0.419282 | − | 0.726219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11473.0 | + | 19871.8i | 0.911760 | + | 1.57922i | 0.811576 | + | 0.584247i | \(0.198610\pi\) |
0.100184 | + | 0.994969i | \(0.468057\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −38108.2 | −3.01175 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4390.09 | − | 7603.85i | 0.345047 | − | 0.597639i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5347.88 | + | 9262.80i | −0.418023 | + | 0.724038i | −0.995741 | − | 0.0921994i | \(-0.970610\pi\) |
0.577717 | + | 0.816237i | \(0.303944\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8350.36 | − | 14463.3i | 0.649153 | − | 1.12437i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6205.74 | − | 10748.7i | −0.479807 | − | 0.831050i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 594.771 | − | 1030.17i | 0.0457364 | − | 0.0792177i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 25058.8 | + | 43403.0i | 1.91655 | + | 3.31956i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21326.4 | 1.62231 | 0.811157 | − | 0.584828i | \(-0.198838\pi\) | ||||
0.811157 | + | 0.584828i | \(0.198838\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8841.62 | 0.668981 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14685.1 | − | 25435.3i | −1.10518 | − | 1.91422i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −284.862 | + | 493.396i | −0.0213242 | + | 0.0369346i | −0.876491 | − | 0.481419i | \(-0.840122\pi\) |
0.855166 | + | 0.518354i | \(0.173455\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11488.2 | − | 19898.2i | −0.855423 | − | 1.48164i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9778.19 | − | 16936.3i | 0.724242 | − | 1.25442i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8017.16 | − | 13886.1i | 0.590680 | − | 1.02309i | −0.403461 | − | 0.914997i | \(-0.632193\pi\) |
0.994141 | − | 0.108091i | \(-0.0344736\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12821.7 | − | 22207.8i | 0.939702 | − | 1.62761i | 0.173675 | − | 0.984803i | \(-0.444436\pi\) |
0.766027 | − | 0.642809i | \(-0.222231\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −33233.3 | −2.42293 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5394.01 | + | 9342.71i | 0.391210 | + | 0.677596i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −320.446 | − | 555.029i | −0.0231202 | − | 0.0400454i | 0.854234 | − | 0.519889i | \(-0.174027\pi\) |
−0.877354 | + | 0.479844i | \(0.840693\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20651.9 | − | 35770.2i | 1.48232 | − | 2.56746i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6950.82 | 0.496332 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5049.02 | + | 8745.16i | 0.358677 | + | 0.621248i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −28589.2 | −2.02054 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5647.21 | −0.397079 | −0.198540 | − | 0.980093i | \(-0.563620\pi\) | ||||
−0.198540 | + | 0.980093i | \(0.563620\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20214.6 | − | 14504.8i | −1.41414 | − | 1.01471i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 37930.9 | 2.64005 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27731.1 | 1.92037 | 0.960184 | − | 0.279370i | \(-0.0901255\pi\) | ||||
0.960184 | + | 0.279370i | \(0.0901255\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4699.32 | − | 8139.46i | −0.323787 | − | 0.560816i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17334.1 | 1.18834 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4433.20 | + | 7678.53i | −0.302397 | + | 0.523767i | −0.976678 | − | 0.214708i | \(-0.931120\pi\) |
0.674281 | + | 0.738475i | \(0.264453\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3540.20 | + | 6131.81i | 0.240279 | + | 0.416176i | 0.960794 | − | 0.277264i | \(-0.0894276\pi\) |
−0.720514 | + | 0.693440i | \(0.756094\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7657.08 | − | 13262.5i | −0.517115 | − | 0.895670i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1460.02 | 0.0981131 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1928.06 | + | 3339.51i | −0.128925 | + | 0.223305i | −0.923261 | − | 0.384174i | \(-0.874486\pi\) |
0.794335 | + | 0.607480i | \(0.207819\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3451.55 | + | 5978.26i | −0.229661 | + | 0.397785i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 787.889 | − | 1364.66i | 0.0521679 | − | 0.0903574i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3122.69 | − | 5408.66i | −0.205749 | − | 0.356368i | 0.744622 | − | 0.667487i | \(-0.232630\pi\) |
−0.950371 | + | 0.311118i | \(0.899296\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −23199.8 | + | 40183.2i | −1.52115 | + | 2.63470i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1722.12 | + | 2982.80i | 0.112366 | + | 0.194624i | 0.916724 | − | 0.399521i | \(-0.130824\pi\) |
−0.804358 | + | 0.594146i | \(0.797490\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12428.1 | −0.806990 | −0.403495 | − | 0.914982i | \(-0.632205\pi\) | ||||
−0.403495 | + | 0.914982i | \(0.632205\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −49946.5 | −3.22751 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1149.78 | − | 1991.48i | −0.0739407 | − | 0.128069i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9250.93 | − | 16023.1i | 0.592060 | − | 1.02548i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −27003.1 | − | 46770.8i | −1.71994 | − | 2.97902i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13378.1 | + | 23171.5i | −0.848042 | + | 1.46885i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2140.54 | + | 3707.53i | −0.135045 | + | 0.233905i | −0.925615 | − | 0.378467i | \(-0.876451\pi\) |
0.790569 | + | 0.612372i | \(0.209785\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1747.24 | + | 3026.31i | −0.109710 | + | 0.190023i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2196.71 | 0.137282 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3760.66 | − | 6513.66i | −0.233913 | − | 0.405150i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −28444.1 | − | 49266.7i | −1.76093 | − | 3.05001i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4000.08 | + | 6928.34i | −0.246480 | + | 0.426915i | −0.962547 | − | 0.271116i | \(-0.912607\pi\) |
0.716067 | + | 0.698032i | \(0.245941\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5658.50 | 0.347044 | 0.173522 | − | 0.984830i | \(-0.444485\pi\) | ||||
0.173522 | + | 0.984830i | \(0.444485\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 23953.5 | + | 41488.7i | 1.46228 | + | 2.53274i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28240.7 | 1.71600 | 0.858002 | − | 0.513646i | \(-0.171706\pi\) | ||||
0.858002 | + | 0.513646i | \(0.171706\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21115.9 | −1.27715 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1365.02 | + | 13770.5i | −0.0821803 | + | 0.829045i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21480.5 | 1.28729 | 0.643643 | − | 0.765326i | \(-0.277422\pi\) | ||||
0.643643 | + | 0.765326i | \(0.277422\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3917.07 | 0.233668 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13808.1 | + | 23916.4i | 0.819949 | + | 1.42019i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9927.81 | −0.586847 | −0.293424 | − | 0.955982i | \(-0.594795\pi\) | ||||
−0.293424 | + | 0.955982i | \(0.594795\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3150.45 | − | 5456.74i | 0.185383 | − | 0.321093i | −0.758322 | − | 0.651880i | \(-0.773981\pi\) |
0.943706 | + | 0.330786i | \(0.107314\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10525.7 | − | 18231.0i | −0.616567 | − | 1.06793i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8641.17 | − | 14967.0i | −0.503895 | − | 0.872772i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9820.61 | 0.570098 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27139.3 | + | 47006.7i | −1.56841 | + | 2.71657i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4434.77 | + | 7681.24i | −0.255145 | + | 0.441924i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1488.29 | + | 2577.79i | −0.0852441 | + | 0.147647i | −0.905495 | − | 0.424356i | \(-0.860500\pi\) |
0.820251 | + | 0.572004i | \(0.193834\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20709.4 | − | 35869.8i | −1.18090 | − | 2.04538i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6191.39 | − | 10723.8i | 0.351484 | − | 0.608788i | −0.635026 | − | 0.772491i | \(-0.719011\pi\) |
0.986510 | + | 0.163703i | \(0.0523439\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −239.889 | − | 415.500i | −0.0135583 | − | 0.0234837i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7642.01 | 0.430018 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1543.16 | 0.0864531 | 0.0432265 | − | 0.999065i | \(-0.486236\pi\) | ||||
0.0432265 | + | 0.999065i | \(0.486236\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1672.52 | − | 2896.90i | −0.0932903 | − | 0.161583i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21497.4 | − | 37234.5i | 1.19385 | − | 2.06781i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3618.94 | + | 6268.19i | 0.200102 | + | 0.346588i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13856.7 | − | 24000.5i | 0.762856 | − | 1.32130i | −0.178517 | − | 0.983937i | \(-0.557130\pi\) |
0.941373 | − | 0.337368i | \(-0.109537\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10889.0 | + | 18860.4i | −0.596883 | + | 1.03383i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22128.3 | + | 38327.4i | −1.20773 | + | 2.09186i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24771.3 | −1.34617 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27809.6 | + | 48167.6i | 1.50480 | + | 2.60639i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8589.04 | − | 14876.6i | −0.462772 | − | 0.801545i | 0.536326 | − | 0.844011i | \(-0.319812\pi\) |
−0.999098 | + | 0.0424659i | \(0.986479\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24599.8 | + | 42608.1i | −1.31977 | + | 2.28591i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8538.13 | 0.456120 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 662.351 | + | 1147.23i | 0.0352338 | + | 0.0610266i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16812.4 | −0.890556 | −0.445278 | − | 0.895392i | \(-0.646895\pi\) | ||||
−0.445278 | + | 0.895392i | \(0.646895\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10466.9 | 0.552095 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17936.8 | − | 8113.45i | 0.942128 | − | 0.426159i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15183.3 | 0.794160 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 52152.7 | 2.71643 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4488.07 | + | 7773.56i | 0.232791 | + | 0.403206i | 0.958628 | − | 0.284660i | \(-0.0918809\pi\) |
−0.725837 | + | 0.687866i | \(0.758548\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10528.5 | 0.543830 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15844.4 | − | 27443.3i | 0.815020 | − | 1.41166i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4071.94 | + | 7052.81i | 0.208591 | + | 0.361289i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7195.10 | + | 12462.3i | 0.367058 | + | 0.635764i | 0.989104 | − | 0.147217i | \(-0.0470316\pi\) |
−0.622046 | + | 0.782981i | \(0.713698\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 54917.7 | 2.79011 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12788.0 | + | 22149.5i | −0.647034 | + | 1.12070i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1958.83 | − | 3392.80i | 0.0987056 | − | 0.170963i | −0.812444 | − | 0.583040i | \(-0.801863\pi\) |
0.911149 | + | 0.412077i | \(0.135196\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 20376.6 | − | 35293.3i | 1.02259 | − | 1.77117i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4066.58 | + | 7043.52i | 0.203249 | + | 0.352037i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5695.58 | + | 9865.03i | −0.283512 | + | 0.491057i | −0.972247 | − | 0.233956i | \(-0.924833\pi\) |
0.688735 | + | 0.725013i | \(0.258166\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19354.8 | − | 33523.5i | −0.959536 | − | 1.66196i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22717.2 | −1.12169 | −0.560844 | − | 0.827921i | \(-0.689523\pi\) | ||||
−0.560844 | + | 0.827921i | \(0.689523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28513.8 | 1.40223 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30580.5 | + | 52967.0i | 1.49783 | + | 2.59432i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6232.90 | + | 10795.7i | −0.304066 | + | 0.526658i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5162.14 | − | 8941.09i | −0.250824 | − | 0.434441i | 0.712929 | − | 0.701237i | \(-0.247368\pi\) |
−0.963753 | + | 0.266796i | \(0.914035\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9982.01 | + | 17289.3i | −0.483087 | + | 0.836731i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16502.1 | − | 28582.5i | 0.795460 | − | 1.37778i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2235.86 | − | 3872.62i | 0.107350 | − | 0.185935i | −0.807346 | − | 0.590078i | \(-0.799097\pi\) |
0.914696 | + | 0.404143i | \(0.132430\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 42732.5 | 2.04360 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8215.06 | − | 14228.9i | −0.391322 | − | 0.677789i | 0.601302 | − | 0.799021i | \(-0.294649\pi\) |
−0.992624 | + | 0.121232i | \(0.961315\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2396.98 | − | 4151.70i | −0.113731 | − | 0.196988i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 41349.8 | − | 71619.9i | 1.95425 | − | 3.38487i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15135.1 | −0.712511 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5951.89 | + | 10309.0i | 0.279104 | + | 0.483422i | 0.971162 | − | 0.238420i | \(-0.0766294\pi\) |
−0.692059 | + | 0.721841i | \(0.743296\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −32359.5 | −1.51154 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 487.871 | 0.0227005 | 0.0113503 | − | 0.999936i | \(-0.496387\pi\) | ||||
0.0113503 | + | 0.999936i | \(0.496387\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13264.0 | + | 9517.45i | 0.614781 | + | 0.441131i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 27364.1 | 1.26343 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −45549.7 | −2.09498 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15106.3 | + | 26164.9i | 0.692120 | + | 1.19879i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −37704.6 | −1.72089 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3175.44 | + | 5500.02i | −0.144377 | + | 0.250069i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9922.08 | + | 17185.5i | 0.449408 | + | 0.778397i | 0.998348 | − | 0.0574648i | \(-0.0183017\pi\) |
−0.548940 | + | 0.835862i | \(0.684968\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8397.53 | − | 14545.0i | −0.378910 | − | 0.656292i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12545.1 | −0.563911 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3178.67 | + | 5505.61i | −0.142343 | + | 0.246545i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19608.7 | + | 33963.3i | −0.874779 | + | 1.51516i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10767.3 | − | 18649.5i | 0.478540 | − | 0.828856i | −0.521157 | − | 0.853461i | \(-0.674499\pi\) |
0.999697 | + | 0.0246049i | \(0.00783278\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2279.12 | + | 3947.55i | 0.100913 | + | 0.174786i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10117.1 | − | 17523.2i | 0.446278 | − | 0.772976i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7333.31 | − | 12701.7i | −0.322275 | − | 0.558197i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13674.7 | 0.598719 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −58239.7 | −2.54044 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4950.09 | + | 8573.81i | 0.215125 | + | 0.372607i | 0.953311 | − | 0.301990i | \(-0.0976508\pi\) |
−0.738186 | + | 0.674597i | \(0.764317\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1926.18 | + | 3336.23i | −0.0833997 | + | 0.144453i | −0.904708 | − | 0.426032i | \(-0.859911\pi\) |
0.821308 | + | 0.570484i | \(0.193244\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29898.0 | + | 51784.9i | 1.28975 | + | 2.23392i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22173.4 | + | 38405.5i | −0.953008 | + | 1.65066i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23514.8 | + | 40728.8i | −1.00695 | + | 1.74409i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7804.83 | + | 13518.4i | −0.332995 | + | 0.576764i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2385.49 | −0.101406 | −0.0507029 | − | 0.998714i | \(-0.516146\pi\) | ||||
−0.0507029 | + | 0.998714i | \(0.516146\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20672.1 | + | 35805.2i | 0.875559 | + | 1.51651i | 0.856167 | + | 0.516700i | \(0.172840\pi\) |
0.0193921 | + | 0.999812i | \(0.493827\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17718.3 | + | 30689.0i | 0.747723 | + | 1.29510i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −339.085 | + | 587.312i | −0.0142577 | + | 0.0246951i | −0.873066 | − | 0.487602i | \(-0.837872\pi\) |
0.858809 | + | 0.512297i | \(0.171205\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32565.9 | −1.36437 | −0.682183 | − | 0.731182i | \(-0.738969\pi\) | ||||
−0.682183 | + | 0.731182i | \(0.738969\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27442.9 | − | 47532.4i | −1.14559 | − | 1.98421i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21756.8 | 0.904958 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14818.5 | −0.614151 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −68865.3 | + | 31150.3i | −2.84389 | + | 1.28639i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3007.55 | −0.123757 | −0.0618785 | − | 0.998084i | \(-0.519709\pi\) | ||||
−0.0618785 | + | 0.998084i | \(0.519709\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16975.4 | −0.696028 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4862.44 | − | 8421.99i | −0.198661 | − | 0.344091i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21673.1 | −0.882341 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 398.586 | − | 690.371i | 0.0161695 | − | 0.0280064i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5114.04 | − | 8857.77i | −0.206730 | − | 0.358066i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19464.6 | − | 33713.7i | −0.784064 | − | 1.35804i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14097.7 | 0.565882 | 0.282941 | − | 0.959137i | \(-0.408690\pi\) | ||||
0.282941 | + | 0.959137i | \(0.408690\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 76034.6 | − | 131696.i | 3.04132 | − | 5.26772i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3126.51 | − | 5415.28i | 0.124620 | − | 0.215849i | −0.796964 | − | 0.604027i | \(-0.793562\pi\) |
0.921584 | + | 0.388178i | \(0.126895\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2224.24 | + | 3852.49i | −0.0883469 | + | 0.153021i | −0.906812 | − | 0.421534i | \(-0.861492\pi\) |
0.818466 | + | 0.574556i | \(0.194825\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12667.1 | + | 21940.0i | 0.501385 | + | 0.868424i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 949.854 | − | 1645.20i | 0.0374663 | − | 0.0648935i | −0.846684 | − | 0.532096i | \(-0.821405\pi\) |
0.884151 | + | 0.467202i | \(0.154738\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14538.9 | − | 25182.1i | −0.571488 | − | 0.989846i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12211.3 | 0.478335 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5558.83 | −0.216997 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2914.76 | + | 5048.52i | 0.113390 | + | 0.196398i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2110.81 | − | 3656.02i | 0.0818327 | − | 0.141738i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1823.33 | − | 3158.10i | −0.0704454 | − | 0.122015i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24776.5 | − | 42914.1i | 0.953983 | − | 1.65235i | 0.217303 | − | 0.976104i | \(-0.430274\pi\) |
0.736680 | − | 0.676242i | \(-0.236393\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31929.4 | − | 55303.4i | 1.22520 | − | 2.12211i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8861.87 | + | 15349.2i | −0.338892 | + | 0.586979i | −0.984225 | − | 0.176923i | \(-0.943386\pi\) |
0.645332 | + | 0.763902i | \(0.276719\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26593.2 | 1.01352 | 0.506758 | − | 0.862089i | \(-0.330844\pi\) | ||||
0.506758 | + | 0.862089i | \(0.330844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −41003.6 | − | 71020.3i | −1.55742 | − | 2.69754i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11380.2 | + | 19711.1i | 0.430789 | + | 0.746149i | 0.996941 | − | 0.0781518i | \(-0.0249019\pi\) |
−0.566152 | + | 0.824301i | \(0.691569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 599.701 | − | 1038.71i | 0.0226247 | − | 0.0391871i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −91388.7 | −3.43618 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4190.87 | + | 7258.80i | 0.157046 | + | 0.272012i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 53108.5 | 1.98349 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 30629.0 | 1.14010 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13540.5 | − | 6124.84i | 0.502336 | − | 0.227225i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20936.9 | −0.774151 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 26157.2 | 0.963962 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28493.8 | + | 49352.8i | 1.04659 | + | 1.81275i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15569.5 | −0.569986 | −0.284993 | − | 0.958530i | \(-0.591991\pi\) | ||||
−0.284993 | + | 0.958530i | \(0.591991\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5828.09 | + | 10094.6i | −0.212657 | + | 0.368333i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4802.10 | − | 8317.49i | −0.174644 | − | 0.302492i | 0.765394 | − | 0.643562i | \(-0.222544\pi\) |
−0.940038 | + | 0.341070i | \(0.889211\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16240.9 | − | 28130.1i | −0.588713 | − | 1.01968i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −34446.3 | −1.24455 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1069.36 | − | 1852.18i | 0.0385097 | − | 0.0667007i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9386.88 | − | 16258.6i | 0.336937 | − | 0.583591i | −0.646918 | − | 0.762559i | \(-0.723943\pi\) |
0.983855 | + | 0.178968i | \(0.0572759\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23319.7 | + | 40390.9i | −0.834321 | + | 1.44509i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10827.6 | + | 18754.0i | 0.386127 | + | 0.668791i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16141.3 | − | 27957.6i | 0.573755 | − | 0.993773i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 46320.6 | + | 80229.6i | 1.64117 | + | 2.84260i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16277.5 | −0.574864 | −0.287432 | − | 0.957801i | \(-0.592802\pi\) | ||||
−0.287432 | + | 0.957801i | \(0.592802\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40006.8 | 1.40834 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −32447.8 | − | 56201.2i | −1.13858 | − | 1.97208i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21960.3 | + | 38036.4i | −0.768107 | + | 1.33040i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8870.66 | + | 15364.4i | 0.309276 | + | 0.535682i | 0.978204 | − | 0.207645i | \(-0.0665798\pi\) |
−0.668928 | + | 0.743327i | \(0.733247\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 158.923 | − | 275.262i | 0.00552316 | − | 0.00956639i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2598.71 | − | 4501.09i | 0.0900270 | − | 0.155931i | −0.817495 | − | 0.575935i | \(-0.804638\pi\) |
0.907522 | + | 0.420004i | \(0.137971\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18020.6 | − | 31212.7i | 0.622304 | − | 1.07786i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −52501.7 | −1.80728 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9149.42 | − | 15847.3i | −0.313956 | − | 0.543787i | 0.665259 | − | 0.746613i | \(-0.268321\pi\) |
−0.979215 | + | 0.202825i | \(0.934988\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5256.23 | − | 9104.06i | −0.179794 | − | 0.311412i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16094.9 | − | 27877.2i | 0.548804 | − | 0.950556i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9410.33 | −0.319864 | −0.159932 | − | 0.987128i | \(-0.551128\pi\) | ||||
−0.159932 | + | 0.987128i | \(0.551128\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24848.8 | + | 43039.4i | 0.841977 | + | 1.45835i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 32258.8 | 1.08963 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1826.39 | −0.0614987 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19670.7 | − | 22373.3i | 0.660291 | − | 0.751010i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −109688. | −3.67045 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −61766.5 | −2.06045 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.15592 | + | 3.73416i | 7.16956e−5 | + | 0.000124180i | 0.866061 | − | 0.499938i | \(-0.166644\pi\) |
−0.865990 | + | 0.500062i | \(0.833311\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 111975. | 3.71223 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6426.53 | − | 11131.1i | 0.212397 | − | 0.367882i | −0.740067 | − | 0.672533i | \(-0.765206\pi\) |
0.952464 | + | 0.304651i | \(0.0985397\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12082.0 | + | 20926.7i | 0.398081 | + | 0.689496i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12699.8 | + | 21996.7i | 0.417147 | + | 0.722520i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38951.1 | −1.27549 | −0.637746 | − | 0.770247i | \(-0.720133\pi\) | ||||
−0.637746 | + | 0.770247i | \(0.720133\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5373.03 | + | 9306.37i | −0.175406 | + | 0.303813i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21091.3 | − | 36531.2i | 0.686436 | − | 1.18894i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6573.07 | − | 11384.9i | 0.213274 | − | 0.369401i | −0.739463 | − | 0.673197i | \(-0.764921\pi\) |
0.952737 | + | 0.303795i | \(0.0982540\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28361.3 | − | 49123.2i | −0.917427 | − | 1.58903i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2330.90 | − | 4037.25i | 0.0751707 | − | 0.130200i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18606.1 | − | 32226.7i | −0.598220 | − | 1.03615i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23070.3 | −0.739509 | −0.369755 | − | 0.929129i | \(-0.620558\pi\) | ||||
−0.369755 | + | 0.929129i | \(0.620558\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24137.2 | −0.771370 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12960.9 | − | 22448.9i | −0.412952 | − | 0.715253i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21000.5 | + | 36374.0i | −0.667094 | + | 1.15544i | 0.311618 | + | 0.950207i | \(0.399129\pi\) |
−0.978713 | + | 0.205234i | \(0.934204\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 74731.2 | + | 129438.i | 2.36676 | + | 4.09934i |
(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 | 124.4.e.b.25.1 | yes | 6 | |
3.2 | odd | 2 | 1116.4.i.d.397.3 | 6 | |||
4.3 | odd | 2 | 496.4.i.b.273.3 | 6 | |||
31.5 | even | 3 | inner | 124.4.e.b.5.1 | ✓ | 6 | |
93.5 | odd | 6 | 1116.4.i.d.253.3 | 6 | |||
124.67 | odd | 6 | 496.4.i.b.129.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
124.4.e.b.5.1 | ✓ | 6 | 31.5 | even | 3 | inner | |
124.4.e.b.25.1 | yes | 6 | 1.1 | even | 1 | trivial | |
496.4.i.b.129.3 | 6 | 124.67 | odd | 6 | |||
496.4.i.b.273.3 | 6 | 4.3 | odd | 2 | |||
1116.4.i.d.253.3 | 6 | 93.5 | odd | 6 | |||
1116.4.i.d.397.3 | 6 | 3.2 | odd | 2 |