Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(33,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.33");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.s (of order \(6\), 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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 26 x^{14} - 16 x^{13} + 469 x^{12} + 144 x^{11} - 4526 x^{10} + 4440 x^{9} + 32608 x^{8} + \cdots + 208849 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{20}\cdot 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 129.6 | ||
Root | \(-1.90990 + 0.286185i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.129 |
Dual form | 224.3.s.b.33.6 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 2.20101 | + | 1.27075i | 0.733669 | + | 0.423584i | 0.819763 | − | 0.572703i | \(-0.194105\pi\) |
−0.0860939 | + | 0.996287i | \(0.527439\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.56697 | − | 2.05939i | 0.713393 | − | 0.411878i | −0.0989230 | − | 0.995095i | \(-0.531540\pi\) |
0.812316 | + | 0.583217i | \(0.198206\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.98814 | + | 0.407289i | 0.998306 | + | 0.0581841i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.27038 | − | 2.20036i | −0.141153 | − | 0.244485i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.63392 | − | 2.83003i | 0.148538 | − | 0.257275i | −0.782149 | − | 0.623091i | \(-0.785877\pi\) |
0.930687 | + | 0.365816i | \(0.119210\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.88759i | 0.452892i | 0.974024 | + | 0.226446i | \(0.0727107\pi\) | ||||
−0.974024 | + | 0.226446i | \(0.927289\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.4679 | 0.697859 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −12.0204 | − | 6.93999i | −0.707083 | − | 0.408234i | 0.102897 | − | 0.994692i | \(-0.467189\pi\) |
−0.809980 | + | 0.586458i | \(0.800522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13.7058 | − | 7.91304i | 0.721357 | − | 0.416476i | −0.0938951 | − | 0.995582i | \(-0.529932\pi\) |
0.815252 | + | 0.579107i | \(0.196598\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.8634 | + | 9.77664i | 0.707780 | + | 0.465554i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 18.2518 | + | 31.6131i | 0.793557 | + | 1.37448i | 0.923751 | + | 0.382993i | \(0.125106\pi\) |
−0.130194 | + | 0.991488i | \(0.541560\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.01784 | + | 6.95910i | −0.160713 | + | 0.278364i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 29.3309i | − | 1.08633i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −28.4655 | −0.981568 | −0.490784 | − | 0.871281i | \(-0.663290\pi\) | ||||
−0.490784 | + | 0.871281i | \(0.663290\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 36.2014 | + | 20.9009i | 1.16779 | + | 0.674222i | 0.953158 | − | 0.302474i | \(-0.0978126\pi\) |
0.214629 | + | 0.976696i | \(0.431146\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.19253 | − | 4.15261i | 0.217955 | − | 0.125837i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 25.7652 | − | 12.9385i | 0.736149 | − | 0.369672i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.14285 | − | 12.3718i | −0.193050 | − | 0.334372i | 0.753210 | − | 0.657781i | \(-0.228505\pi\) |
−0.946260 | + | 0.323408i | \(0.895171\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.48167 | + | 12.9586i | −0.191838 | + | 0.332273i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 21.3515i | 0.520769i | 0.965505 | + | 0.260385i | \(0.0838493\pi\) | ||||
−0.965505 | + | 0.260385i | \(0.916151\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −55.3992 | −1.28835 | −0.644177 | − | 0.764877i | \(-0.722800\pi\) | ||||
−0.644177 | + | 0.764877i | \(0.722800\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.06280 | − | 5.23241i | −0.201395 | − | 0.116276i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −29.3178 | + | 16.9266i | −0.623783 | + | 0.360141i | −0.778340 | − | 0.627843i | \(-0.783938\pi\) |
0.154558 | + | 0.987984i | \(0.450605\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.6682 | + | 5.69238i | 0.993229 | + | 0.116171i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −17.6380 | − | 30.5499i | −0.345843 | − | 0.599018i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 42.4271 | − | 73.4859i | 0.800512 | − | 1.38653i | −0.118768 | − | 0.992922i | \(-0.537894\pi\) |
0.919280 | − | 0.393605i | \(-0.128772\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 13.4595i | − | 0.244718i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 40.2220 | 0.705649 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −58.5062 | − | 33.7786i | −0.991631 | − | 0.572518i | −0.0858695 | − | 0.996306i | \(-0.527367\pi\) |
−0.905761 | + | 0.423788i | \(0.860700\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −25.6135 | + | 14.7879i | −0.419893 | + | 0.242425i | −0.695032 | − | 0.718979i | \(-0.744610\pi\) |
0.275139 | + | 0.961405i | \(0.411276\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.98140 | − | 15.8938i | −0.126689 | − | 0.252283i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.1248 | + | 21.0008i | 0.186536 | + | 0.323090i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −27.4789 | + | 47.5949i | −0.410133 | + | 0.710371i | −0.994904 | − | 0.100827i | \(-0.967851\pi\) |
0.584771 | + | 0.811198i | \(0.301184\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 92.7741i | 1.34455i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −83.8102 | −1.18043 | −0.590213 | − | 0.807248i | \(-0.700956\pi\) | ||||
−0.590213 | + | 0.807248i | \(0.700956\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −108.784 | − | 62.8065i | −1.49019 | − | 0.860363i | −0.490255 | − | 0.871579i | \(-0.663096\pi\) |
−0.999937 | + | 0.0112159i | \(0.996430\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −17.6866 | + | 10.2113i | −0.235821 | + | 0.136151i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.5707 | − | 19.1112i | 0.163256 | − | 0.248197i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 35.1955 | + | 60.9604i | 0.445512 | + | 0.771650i | 0.998088 | − | 0.0618128i | \(-0.0196882\pi\) |
−0.552575 | + | 0.833463i | \(0.686355\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 25.8389 | − | 44.7542i | 0.318998 | − | 0.552521i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 27.1264i | − | 0.326824i | −0.986558 | − | 0.163412i | \(-0.947750\pi\) | ||
0.986558 | − | 0.163412i | \(-0.0522500\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −57.1685 | −0.672571 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −62.6527 | − | 36.1726i | −0.720146 | − | 0.415777i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −126.553 | + | 73.0654i | −1.42194 | + | 0.820959i | −0.996465 | − | 0.0840094i | \(-0.973227\pi\) |
−0.425478 | + | 0.904969i | \(0.639894\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.39795 | + | 41.1433i | −0.0263511 | + | 0.452125i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 53.1196 | + | 92.0059i | 0.571179 | + | 0.989311i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 32.5920 | − | 56.4511i | 0.343074 | − | 0.594222i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 11.3574i | − | 0.117086i | −0.998285 | − | 0.0585431i | \(-0.981354\pi\) | ||
0.998285 | − | 0.0585431i | \(-0.0186455\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.30278 | −0.0838664 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −36.2851 | − | 20.9492i | −0.359258 | − | 0.207418i | 0.309497 | − | 0.950900i | \(-0.399839\pi\) |
−0.668755 | + | 0.743482i | \(0.733173\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −84.1601 | + | 48.5899i | −0.817089 | + | 0.471746i | −0.849412 | − | 0.527731i | \(-0.823043\pi\) |
0.0323227 | + | 0.999477i | \(0.489710\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 73.1511 | + | 4.26345i | 0.696677 | + | 0.0406043i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −41.7218 | − | 72.2643i | −0.389924 | − | 0.675368i | 0.602515 | − | 0.798107i | \(-0.294165\pi\) |
−0.992439 | + | 0.122740i | \(0.960832\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 80.9965 | − | 140.290i | 0.743088 | − | 1.28707i | −0.207995 | − | 0.978130i | \(-0.566694\pi\) |
0.951083 | − | 0.308936i | \(-0.0999728\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 36.3072i | − | 0.327092i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 27.2503 | 0.241153 | 0.120576 | − | 0.992704i | \(-0.461526\pi\) | ||||
0.120576 | + | 0.992704i | \(0.461526\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 130.207 | + | 75.1751i | 1.13224 | + | 0.653697i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.9548 | − | 7.47948i | 0.110725 | − | 0.0639271i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −81.1737 | − | 53.3934i | −0.682132 | − | 0.448684i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 55.1606 | + | 95.5410i | 0.455873 | + | 0.789595i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −27.1325 | + | 46.9949i | −0.220589 | + | 0.382072i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 136.067i | 1.08853i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 232.457 | 1.83037 | 0.915183 | − | 0.403038i | \(-0.132046\pi\) | ||||
0.915183 | + | 0.403038i | \(0.132046\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −121.934 | − | 70.3986i | −0.945225 | − | 0.545726i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 152.509 | − | 88.0512i | 1.16419 | − | 0.672146i | 0.211887 | − | 0.977294i | \(-0.432039\pi\) |
0.952305 | + | 0.305148i | \(0.0987058\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 99.0008 | − | 49.7152i | 0.744367 | − | 0.373798i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −60.4037 | − | 104.622i | −0.447435 | − | 0.774980i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 132.462 | − | 229.432i | 0.966879 | − | 1.67468i | 0.262400 | − | 0.964959i | \(-0.415486\pi\) |
0.704479 | − | 0.709725i | \(-0.251181\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 267.680i | 1.92576i | 0.269935 | + | 0.962878i | \(0.412998\pi\) | ||||
−0.269935 | + | 0.962878i | \(0.587002\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −86.0382 | −0.610200 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.6621 | + | 9.61984i | 0.116518 | + | 0.0672716i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −101.535 | + | 58.6215i | −0.700244 | + | 0.404286i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 99.8855 | + | 74.3742i | 0.679493 | + | 0.505947i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.972701 | + | 1.68477i | 0.00652820 | + | 0.0113072i | 0.869271 | − | 0.494336i | \(-0.164589\pi\) |
−0.862743 | + | 0.505643i | \(0.831255\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 50.1524 | − | 86.8665i | 0.332135 | − | 0.575275i | −0.650795 | − | 0.759253i | \(-0.725564\pi\) |
0.982930 | + | 0.183978i | \(0.0588977\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 35.2656i | 0.230494i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 172.172 | 1.11079 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −117.153 | − | 67.6386i | −0.746200 | − | 0.430819i | 0.0781191 | − | 0.996944i | \(-0.475109\pi\) |
−0.824319 | + | 0.566125i | \(0.808442\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 186.765 | − | 107.829i | 1.17462 | − | 0.678168i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 114.671 | + | 228.350i | 0.712240 | + | 1.41832i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 127.353 | + | 220.582i | 0.781307 | + | 1.35326i | 0.931180 | + | 0.364559i | \(0.118780\pi\) |
−0.149873 | + | 0.988705i | \(0.547886\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 17.1037 | − | 29.6244i | 0.103659 | − | 0.179542i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 50.9246i | − | 0.304938i | −0.988308 | − | 0.152469i | \(-0.951278\pi\) | ||
0.988308 | − | 0.152469i | \(-0.0487224\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 134.336 | 0.794889 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −34.8231 | − | 20.1051i | −0.203644 | − | 0.117574i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 60.9855 | − | 35.2100i | 0.352517 | − | 0.203526i | −0.313276 | − | 0.949662i | \(-0.601427\pi\) |
0.665793 | + | 0.746136i | \(0.268093\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −30.9116 | + | 46.9947i | −0.176638 | + | 0.268541i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −85.8484 | − | 148.694i | −0.485019 | − | 0.840078i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 73.7202 | − | 127.687i | 0.411845 | − | 0.713336i | −0.583247 | − | 0.812295i | \(-0.698218\pi\) |
0.995092 | + | 0.0989591i | \(0.0315513\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 294.491i | 1.62702i | 0.581550 | + | 0.813511i | \(0.302447\pi\) | ||||
−0.581550 | + | 0.813511i | \(0.697553\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −75.1672 | −0.410750 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −50.9566 | − | 29.4198i | −0.275441 | − | 0.159026i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −39.2807 | + | 22.6787i | −0.210057 | + | 0.121277i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.9461 | − | 204.968i | 0.0632071 | − | 1.08449i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −56.2595 | − | 97.4444i | −0.294553 | − | 0.510180i | 0.680328 | − | 0.732908i | \(-0.261837\pi\) |
−0.974881 | + | 0.222728i | \(0.928504\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −63.7435 | + | 110.407i | −0.330277 | + | 0.572057i | −0.982566 | − | 0.185914i | \(-0.940475\pi\) |
0.652289 | + | 0.757970i | \(0.273809\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 61.6307i | 0.316055i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −293.140 | −1.48802 | −0.744011 | − | 0.668167i | \(-0.767079\pi\) | ||||
−0.744011 | + | 0.668167i | \(0.767079\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.43677 | + | 4.87097i | 0.0423958 | + | 0.0244772i | 0.521048 | − | 0.853527i | \(-0.325541\pi\) |
−0.478652 | + | 0.878005i | \(0.658875\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −120.963 | + | 69.8378i | −0.601804 | + | 0.347452i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −198.921 | − | 11.5937i | −0.979905 | − | 0.0571117i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 43.9711 | + | 76.1602i | 0.214493 | + | 0.371513i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 46.3734 | − | 80.3211i | 0.224026 | − | 0.388025i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 51.7170i | − | 0.247450i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 139.516 | 0.661214 | 0.330607 | − | 0.943769i | \(-0.392747\pi\) | ||||
0.330607 | + | 0.943769i | \(0.392747\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −184.467 | − | 106.502i | −0.866042 | − | 0.500009i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −197.607 | + | 114.088i | −0.919102 | + | 0.530644i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 244.468 | + | 160.803i | 1.12658 | + | 0.741026i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −159.623 | − | 276.475i | −0.728872 | − | 1.26244i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 40.8598 | − | 70.7713i | 0.184886 | − | 0.320232i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 273.426i | 1.22612i | 0.790035 | + | 0.613062i | \(0.210062\pi\) | ||||
−0.790035 | + | 0.613062i | \(0.789938\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 20.4167 | 0.0907409 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −58.4952 | − | 33.7722i | −0.257688 | − | 0.148776i | 0.365591 | − | 0.930775i | \(-0.380867\pi\) |
−0.623279 | + | 0.781999i | \(0.714200\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 166.765 | − | 96.2816i | 0.728230 | − | 0.420444i | −0.0895442 | − | 0.995983i | \(-0.528541\pi\) |
0.817774 | + | 0.575539i | \(0.195208\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 51.9537 | − | 26.0896i | 0.224908 | − | 0.112942i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −40.7024 | − | 70.4987i | −0.174689 | − | 0.302569i | 0.765365 | − | 0.643597i | \(-0.222559\pi\) |
−0.940053 | + | 0.341027i | \(0.889225\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −69.7170 | + | 120.753i | −0.296668 | + | 0.513844i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 178.899i | 0.754848i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.6152 | −0.0946244 | −0.0473122 | − | 0.998880i | \(-0.515066\pi\) | ||||
−0.0473122 | + | 0.998880i | \(0.515066\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −81.5504 | − | 47.0832i | −0.338384 | − | 0.195366i | 0.321173 | − | 0.947020i | \(-0.395923\pi\) |
−0.659557 | + | 0.751655i | \(0.729256\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −114.869 | + | 66.3194i | −0.472710 | + | 0.272919i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 185.321 | − | 79.9223i | 0.756411 | − | 0.326213i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 46.5887 | + | 80.6941i | 0.188618 | + | 0.326697i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 34.4710 | − | 59.7054i | 0.138438 | − | 0.239781i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 316.694i | − | 1.26173i | −0.775892 | − | 0.630865i | \(-0.782700\pi\) | ||
0.775892 | − | 0.630865i | \(-0.217300\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 119.288 | 0.471493 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −125.828 | − | 72.6470i | −0.493444 | − | 0.284890i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 40.7550 | − | 23.5299i | 0.158580 | − | 0.0915560i | −0.418610 | − | 0.908166i | \(-0.637483\pi\) |
0.577190 | + | 0.816610i | \(0.304149\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −44.8764 | − | 89.3649i | −0.173268 | − | 0.345038i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 36.1619 | + | 62.6343i | 0.138551 | + | 0.239978i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −203.252 | + | 352.043i | −0.772822 | + | 1.33857i | 0.163189 | + | 0.986595i | \(0.447822\pi\) |
−0.936011 | + | 0.351972i | \(0.885511\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 349.496i | − | 1.31885i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −371.392 | −1.39098 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 287.957 | + | 166.252i | 1.07047 | + | 0.618038i | 0.928311 | − | 0.371806i | \(-0.121261\pi\) |
0.142162 | + | 0.989843i | \(0.454595\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 61.7686 | − | 35.6621i | 0.227928 | − | 0.131595i | −0.381688 | − | 0.924291i | \(-0.624657\pi\) |
0.609616 | + | 0.792697i | \(0.291324\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −57.5609 | + | 87.5096i | −0.210846 | + | 0.320548i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.1296 | + | 22.7412i | 0.0477441 | + | 0.0826952i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.8574 | − | 25.7337i | 0.0536367 | − | 0.0929015i | −0.837960 | − | 0.545731i | \(-0.816252\pi\) |
0.891597 | + | 0.452829i | \(0.149585\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 106.208i | − | 0.380674i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.06447 | 0.0322579 | 0.0161289 | − | 0.999870i | \(-0.494866\pi\) | ||||
0.0161289 | + | 0.999870i | \(0.494866\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −159.988 | − | 92.3689i | −0.565327 | − | 0.326392i | 0.189954 | − | 0.981793i | \(-0.439166\pi\) |
−0.755281 | + | 0.655401i | \(0.772500\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 143.471 | − | 82.8328i | 0.503406 | − | 0.290641i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.69624 | + | 149.208i | −0.0303005 | + | 0.519887i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −48.1732 | − | 83.4384i | −0.166689 | − | 0.288714i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.4324 | − | 24.9976i | 0.0495959 | − | 0.0859026i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 300.389i | 1.02522i | 0.858622 | + | 0.512609i | \(0.171321\pi\) | ||||
−0.858622 | + | 0.512609i | \(0.828679\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −278.253 | −0.943230 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −83.0072 | − | 47.9242i | −0.279486 | − | 0.161361i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −186.125 | + | 107.459i | −0.622491 | + | 0.359395i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −387.137 | − | 22.5635i | −1.28617 | − | 0.0749617i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −53.2425 | − | 92.2187i | −0.175718 | − | 0.304352i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −60.9083 | + | 105.496i | −0.199699 | + | 0.345889i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 390.385i | − | 1.27161i | −0.771848 | − | 0.635807i | \(-0.780667\pi\) | ||
0.771848 | − | 0.635807i | \(-0.219333\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −246.983 | −0.799297 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 83.2050 | + | 48.0384i | 0.267540 | + | 0.154464i | 0.627769 | − | 0.778400i | \(-0.283968\pi\) |
−0.360229 | + | 0.932864i | \(0.617301\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −419.921 | + | 242.442i | −1.34160 | + | 0.774574i | −0.987042 | − | 0.160460i | \(-0.948702\pi\) |
−0.354559 | + | 0.935034i | \(0.615369\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −61.2010 | − | 40.2560i | −0.194289 | − | 0.127797i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −33.9714 | − | 58.8401i | −0.107165 | − | 0.185616i | 0.807456 | − | 0.589928i | \(-0.200844\pi\) |
−0.914621 | + | 0.404313i | \(0.867511\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −46.5102 | + | 80.5581i | −0.145800 | + | 0.252533i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 212.072i | − | 0.660662i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −219.665 | −0.680079 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −40.9723 | − | 23.6554i | −0.126069 | − | 0.0727858i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 356.548 | − | 205.853i | 1.09036 | − | 0.629520i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −211.771 | + | 106.345i | −0.643680 | + | 0.323237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 132.634 | + | 229.729i | 0.400707 | + | 0.694046i | 0.993811 | − | 0.111080i | \(-0.0354311\pi\) |
−0.593104 | + | 0.805126i | \(0.702098\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −18.1483 | + | 31.4337i | −0.0544993 | + | 0.0943955i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 226.359i | 0.675699i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 549.980 | 1.63199 | 0.815993 | − | 0.578061i | \(-0.196191\pi\) | ||||
0.815993 | + | 0.578061i | \(0.196191\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 59.9780 | + | 34.6283i | 0.176926 | + | 0.102148i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 118.300 | − | 68.3006i | 0.346921 | − | 0.200295i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 337.782 | + | 59.6012i | 0.984787 | + | 0.173764i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 191.058 | + | 330.922i | 0.553791 | + | 0.959194i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 339.375 | − | 587.815i | 0.978026 | − | 1.69399i | 0.308463 | − | 0.951236i | \(-0.400185\pi\) |
0.669563 | − | 0.742755i | \(-0.266481\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 170.081i | − | 0.487339i | −0.969858 | − | 0.243669i | \(-0.921649\pi\) | ||
0.969858 | − | 0.243669i | \(-0.0783511\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 172.688 | 0.491990 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 204.423 | + | 118.024i | 0.579102 | + | 0.334345i | 0.760776 | − | 0.649014i | \(-0.224818\pi\) |
−0.181675 | + | 0.983359i | \(0.558152\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −298.948 | + | 172.598i | −0.842108 | + | 0.486191i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −110.814 | − | 220.671i | −0.310404 | − | 0.618126i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 229.058 | + | 396.740i | 0.638044 | + | 1.10512i | 0.985861 | + | 0.167562i | \(0.0535895\pi\) |
−0.347818 | + | 0.937562i | \(0.613077\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −55.2677 | + | 95.7266i | −0.153096 | + | 0.265170i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 280.382i | 0.772402i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −517.372 | −1.41746 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 356.315 | + | 205.718i | 0.970885 | + | 0.560541i | 0.899506 | − | 0.436909i | \(-0.143927\pi\) |
0.0713791 | + | 0.997449i | \(0.477260\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 46.9811 | − | 27.1245i | 0.127320 | − | 0.0735082i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 326.417 | − | 496.250i | 0.879829 | − | 1.33760i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.89853 | − | 13.6807i | −0.0211757 | − | 0.0366774i | 0.855243 | − | 0.518227i | \(-0.173408\pi\) |
−0.876419 | + | 0.481549i | \(0.840074\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −172.907 | + | 299.483i | −0.461085 | + | 0.798623i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 167.593i | − | 0.444544i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 455.384 | 1.20154 | 0.600770 | − | 0.799422i | \(-0.294861\pi\) | ||||
0.600770 | + | 0.799422i | \(0.294861\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 511.639 | + | 295.395i | 1.34288 | + | 0.775314i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −158.732 | + | 91.6439i | −0.414443 | + | 0.239279i | −0.692697 | − | 0.721229i | \(-0.743578\pi\) |
0.278254 | + | 0.960508i | \(0.410244\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.48190 | − | 94.0568i | 0.0142387 | − | 0.244303i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 70.3780 | + | 121.898i | 0.181855 | + | 0.314982i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 92.7471 | − | 160.643i | 0.238424 | − | 0.412963i | −0.721838 | − | 0.692062i | \(-0.756702\pi\) |
0.960262 | + | 0.279099i | \(0.0900357\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 506.669i | − | 1.29583i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 447.565 | 1.13884 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 251.082 | + | 144.962i | 0.635651 | + | 0.366993i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −39.5520 | + | 22.8353i | −0.0996271 | + | 0.0575197i | −0.548986 | − | 0.835832i | \(-0.684986\pi\) |
0.449359 | + | 0.893351i | \(0.351653\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 281.077 | + | 16.3820i | 0.704454 | + | 0.0410576i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.2312 | − | 33.3094i | −0.0479580 | − | 0.0830657i | 0.841050 | − | 0.540958i | \(-0.181938\pi\) |
−0.889008 | + | 0.457892i | \(0.848605\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −123.056 | + | 213.139i | −0.305349 | + | 0.528881i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 212.849i | − | 0.525553i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −46.6833 | −0.114701 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −145.264 | − | 83.8684i | −0.355169 | − | 0.205057i | 0.311790 | − | 0.950151i | \(-0.399071\pi\) |
−0.666960 | + | 0.745094i | \(0.732405\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 583.102 | − | 336.654i | 1.41874 | − | 0.819109i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −395.092 | − | 259.878i | −0.956640 | − | 0.629246i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −55.8639 | − | 96.7590i | −0.134612 | − | 0.233154i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −340.155 | + | 589.166i | −0.815720 | + | 1.41287i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 300.318i | − | 0.716751i | −0.933578 | − | 0.358375i | \(-0.883331\pi\) | ||
0.933578 | − | 0.358375i | \(-0.116669\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 280.567 | 0.666430 | 0.333215 | − | 0.942851i | \(-0.391867\pi\) | ||||
0.333215 | + | 0.942851i | \(0.391867\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 74.4894 | + | 43.0065i | 0.176098 | + | 0.101670i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 96.5920 | − | 55.7674i | 0.227275 | − | 0.131218i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −185.014 | + | 92.9082i | −0.433287 | + | 0.217584i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 24.4489 | + | 42.3467i | 0.0569904 | + | 0.0987102i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 112.382 | − | 194.651i | 0.260747 | − | 0.451627i | −0.705693 | − | 0.708517i | \(-0.749364\pi\) |
0.966441 | + | 0.256890i | \(0.0826977\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 731.236i | − | 1.68877i | −0.535739 | − | 0.844383i | \(-0.679967\pi\) | ||
0.535739 | − | 0.844383i | \(-0.320033\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −297.973 | −0.684996 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 500.311 | + | 288.854i | 1.14488 | + | 0.660994i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 259.322 | − | 149.720i | 0.590711 | − | 0.341047i | −0.174668 | − | 0.984627i | \(-0.555885\pi\) |
0.765379 | + | 0.643580i | \(0.222552\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −49.3018 | − | 114.319i | −0.111795 | − | 0.259227i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 198.077 | + | 343.080i | 0.447127 | + | 0.774447i | 0.998198 | − | 0.0600116i | \(-0.0191138\pi\) |
−0.551070 | + | 0.834459i | \(0.685780\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −300.940 | + | 521.243i | −0.676270 | + | 1.17133i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.94425i | 0.0110610i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 128.183 | 0.285486 | 0.142743 | − | 0.989760i | \(-0.454408\pi\) | ||||
0.142743 | + | 0.989760i | \(0.454408\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 60.4254 | + | 34.8866i | 0.133981 | + | 0.0773540i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 220.772 | − | 127.463i | 0.487354 | − | 0.281374i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 76.1767 | + | 151.695i | 0.167421 | + | 0.333396i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −202.574 | − | 350.868i | −0.443268 | − | 0.767763i | 0.554661 | − | 0.832076i | \(-0.312848\pi\) |
−0.997930 | + | 0.0643128i | \(0.979514\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −203.556 | + | 352.569i | −0.443477 | + | 0.768124i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 312.620i | − | 0.678134i | −0.940762 | − | 0.339067i | \(-0.889889\pi\) | ||
0.940762 | − | 0.339067i | \(-0.110111\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −246.396 | −0.532173 | −0.266087 | − | 0.963949i | \(-0.585731\pi\) | ||||
−0.266087 | + | 0.963949i | \(0.585731\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 378.952 | + | 218.788i | 0.814950 | + | 0.470512i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.8539 | + | 10.8853i | −0.0403723 | + | 0.0233090i | −0.520050 | − | 0.854136i | \(-0.674087\pi\) |
0.479678 | + | 0.877445i | \(0.340753\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −211.411 | + | 321.408i | −0.450770 | + | 0.685304i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −171.904 | − | 297.746i | −0.364976 | − | 0.632157i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −90.5177 | + | 156.781i | −0.191369 | + | 0.331461i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 127.173i | 0.267733i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −215.594 | −0.451979 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −452.490 | − | 261.245i | −0.944656 | − | 0.545397i | −0.0532389 | − | 0.998582i | \(-0.516954\pi\) |
−0.891417 | + | 0.453185i | \(0.850288\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 72.8400 | − | 42.0542i | 0.151435 | − | 0.0874308i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −37.7858 | + | 648.318i | −0.0782316 | + | 1.34227i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.3892 | − | 40.5113i | −0.0482252 | − | 0.0835285i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 409.067 | − | 708.525i | 0.839974 | − | 1.45488i | −0.0499421 | − | 0.998752i | \(-0.515904\pi\) |
0.889916 | − | 0.456125i | \(-0.150763\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 647.337i | 1.32380i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 762.002 | 1.55194 | 0.775969 | − | 0.630771i | \(-0.217261\pi\) | ||||
0.775969 | + | 0.630771i | \(0.217261\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 342.167 | + | 197.550i | 0.694050 | + | 0.400710i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −29.6157 | + | 17.0986i | −0.0598297 | + | 0.0345427i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −585.678 | − | 34.1350i | −1.17843 | − | 0.0686820i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.4935 | − | 44.1560i | −0.0510891 | − | 0.0884889i | 0.839350 | − | 0.543592i | \(-0.182936\pi\) |
−0.890439 | + | 0.455103i | \(0.849603\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 64.7126 | − | 112.086i | 0.129167 | − | 0.223724i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 305.233i | 0.606825i | 0.952859 | + | 0.303413i | \(0.0981260\pi\) | ||||
−0.952859 | + | 0.303413i | \(0.901874\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −172.570 | −0.341723 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 295.675 | + | 170.708i | 0.583185 | + | 0.336702i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 156.536 | − | 90.3761i | 0.307536 | − | 0.177556i | −0.338287 | − | 0.941043i | \(-0.609848\pi\) |
0.645823 | + | 0.763487i | \(0.276514\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −734.618 | − | 483.207i | −1.43761 | − | 0.945611i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −232.096 | − | 402.003i | −0.452429 | − | 0.783631i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −200.131 | + | 346.637i | −0.388604 | + | 0.673081i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 110.627i | 0.213978i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 178.973 | 0.344841 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −312.767 | − | 180.576i | −0.600321 | − | 0.346595i | 0.168847 | − | 0.985642i | \(-0.445996\pi\) |
−0.769168 | + | 0.639047i | \(0.779329\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −566.506 | + | 327.072i | −1.08318 | + | 0.625377i | −0.931754 | − | 0.363091i | \(-0.881721\pi\) |
−0.151431 | + | 0.988468i | \(0.548388\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −127.755 | + | 64.1548i | −0.243343 | + | 0.122200i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −290.103 | − | 502.474i | −0.550481 | − | 0.953461i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −401.757 | + | 695.864i | −0.759465 | + | 1.31543i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 171.646i | 0.323251i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −125.709 | −0.235852 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −297.641 | − | 171.843i | −0.556338 | − | 0.321202i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 324.517 | − | 187.360i | 0.604315 | − | 0.348902i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 95.6295 | − | 128.432i | 0.177420 | − | 0.238277i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −301.642 | − | 522.459i | −0.557564 | − | 0.965729i | −0.997699 | − | 0.0677973i | \(-0.978403\pi\) |
0.440135 | − | 0.897931i | \(-0.354930\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −374.225 | + | 648.177i | −0.689180 | + | 1.19370i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 667.214i | − | 1.22424i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −686.167 | −1.25442 | −0.627209 | − | 0.778851i | \(-0.715803\pi\) | ||||
−0.627209 | + | 0.778851i | \(0.715803\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 65.0776 | + | 37.5726i | 0.118538 | + | 0.0684382i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −390.142 | + | 225.248i | −0.708061 | + | 0.408799i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 221.123 | + | 440.334i | 0.399860 | + | 0.796265i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −74.7706 | − | 129.506i | −0.134722 | − | 0.233345i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −392.661 | + | 680.108i | −0.704956 | + | 1.22102i | 0.261751 | + | 0.965135i | \(0.415700\pi\) |
−0.966707 | + | 0.255885i | \(0.917633\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 326.168i | − | 0.583485i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −115.276 | −0.205483 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −393.226 | − | 227.029i | −0.698447 | − | 0.403249i | 0.108321 | − | 0.994116i | \(-0.465452\pi\) |
−0.806769 | + | 0.590867i | \(0.798786\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 97.2007 | − | 56.1189i | 0.172037 | − | 0.0993254i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 198.794 | − | 302.225i | 0.350606 | − | 0.533025i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.7137 | + | 61.8580i | 0.0627658 | + | 0.108713i | 0.895701 | − | 0.444657i | \(-0.146675\pi\) |
−0.832935 | + | 0.553371i | \(0.813341\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 359.033 | − | 621.864i | 0.628780 | − | 1.08908i | −0.359017 | − | 0.933331i | \(-0.616888\pi\) |
0.987797 | − | 0.155748i | \(-0.0497787\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 285.968i | − | 0.499071i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −293.331 | −0.510141 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 786.338 | + | 453.993i | 1.36280 | + | 0.786815i | 0.989996 | − | 0.141093i | \(-0.0450617\pi\) |
0.372808 | + | 0.927909i | \(0.378395\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −280.600 | + | 162.004i | −0.484628 | + | 0.279800i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.0483 | − | 189.563i | 0.0190160 | − | 0.326271i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −138.645 | − | 240.140i | −0.237813 | − | 0.411904i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 30.8063 | − | 53.3581i | 0.0526603 | − | 0.0912104i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 862.870i | 1.46997i | 0.678086 | + | 0.734983i | \(0.262810\pi\) | ||||
−0.678086 | + | 0.734983i | \(0.737190\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 661.557 | 1.12319 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −645.204 | − | 372.509i | −1.09172 | − | 0.630302i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 470.127 | − | 271.428i | 0.792794 | − | 0.457720i | −0.0481510 | − | 0.998840i | \(-0.515333\pi\) |
0.840945 | + | 0.541120i | \(0.182000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −399.502 | − | 23.2841i | −0.671431 | − | 0.0391329i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.3796 | + | 21.4421i | 0.0207363 | + | 0.0359164i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.3074 | − | 68.0824i | 0.0656216 | − | 0.113660i | −0.831348 | − | 0.555752i | \(-0.812430\pi\) |
0.896970 | + | 0.442092i | \(0.145764\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 851.603i | − | 1.41698i | −0.705722 | − | 0.708489i | \(-0.749377\pi\) | ||
0.705722 | − | 0.708489i | \(-0.250623\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 139.635 | 0.231566 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 393.512 | + | 227.194i | 0.650433 | + | 0.375528i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −202.282 | + | 116.788i | −0.333249 | + | 0.192401i | −0.657282 | − | 0.753644i | \(-0.728294\pi\) |
0.324034 | + | 0.946045i | \(0.394961\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −423.093 | − | 278.297i | −0.694734 | − | 0.456973i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −99.6571 | − | 172.611i | −0.163105 | − | 0.282506i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −40.5620 | + | 70.2555i | −0.0661697 | + | 0.114609i | −0.897212 | − | 0.441600i | \(-0.854411\pi\) |
0.831043 | + | 0.556209i | \(0.187745\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 223.505i | 0.363424i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.2962 | 0.0766552 | 0.0383276 | − | 0.999265i | \(-0.487797\pi\) | ||||
0.0383276 | + | 0.999265i | \(0.487797\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −569.331 | − | 328.703i | −0.919759 | − | 0.531023i | −0.0362006 | − | 0.999345i | \(-0.511526\pi\) |
−0.883558 | + | 0.468322i | \(0.844859\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 927.239 | − | 535.342i | 1.49314 | − | 0.862064i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −914.129 | + | 459.048i | −1.46730 | + | 0.736834i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 179.768 | + | 311.367i | 0.287629 | + | 0.498188i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 65.7194 | − | 113.829i | 0.104816 | − | 0.181546i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 198.285i | 0.315239i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 270.276 | 0.428330 | 0.214165 | − | 0.976797i | \(-0.431297\pi\) | ||||
0.214165 | + | 0.976797i | \(0.431297\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 307.076 | + | 177.290i | 0.485112 | + | 0.280079i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 829.165 | − | 478.718i | 1.30577 | − | 0.753887i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.5144 | + | 286.539i | −0.0526129 | + | 0.449825i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 106.471 | + | 184.413i | 0.166621 | + | 0.288596i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −122.305 | + | 211.838i | −0.190803 | + | 0.330481i | −0.945517 | − | 0.325574i | \(-0.894443\pi\) |
0.754713 | + | 0.656055i | \(0.227776\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 358.233i | 0.557128i | 0.960418 | + | 0.278564i | \(0.0898584\pi\) | ||||
−0.960418 | + | 0.278564i | \(0.910142\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −579.913 | −0.899089 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1024.30 | + | 591.377i | 1.58315 | + | 0.914030i | 0.994397 | + | 0.105715i | \(0.0337130\pi\) |
0.588750 | + | 0.808315i | \(0.299620\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −191.189 | + | 110.383i | −0.294590 | + | 0.170081i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 333.735 | + | 664.585i | 0.512649 | + | 1.02087i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −107.647 | − | 186.451i | −0.164850 | − | 0.285529i | 0.771752 | − | 0.635924i | \(-0.219381\pi\) |
−0.936602 | + | 0.350395i | \(0.886047\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 362.663 | − | 628.151i | 0.553684 | − | 0.959009i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 319.152i | 0.485772i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 254.983 | 0.386925 | 0.193462 | − | 0.981108i | \(-0.438028\pi\) | ||||
0.193462 | + | 0.981108i | \(0.438028\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1077.04 | − | 621.830i | −1.62941 | − | 0.940741i | −0.984269 | − | 0.176679i | \(-0.943465\pi\) |
−0.645142 | − | 0.764062i | \(-0.723202\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 179.865 | − | 103.845i | 0.271290 | − | 0.156630i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 250.750 | − | 381.214i | 0.377067 | − | 0.573253i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −519.546 | − | 899.881i | −0.778930 | − | 1.34915i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −347.456 | + | 601.812i | −0.519367 | + | 0.899569i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 96.6491i | 0.144037i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −63.0354 | −0.0936633 | −0.0468317 | − | 0.998903i | \(-0.514912\pi\) | ||||
−0.0468317 | + | 0.998903i | \(0.514912\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 204.116 | + | 117.847i | 0.302395 | + | 0.174588i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −855.162 | + | 493.728i | −1.26316 | + | 0.729288i | −0.973685 | − | 0.227896i | \(-0.926815\pi\) |
−0.289479 | + | 0.957184i | \(0.593482\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.62573 | − | 79.3669i | 0.00681256 | − | 0.116888i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −85.8322 | − | 148.666i | −0.126038 | − | 0.218305i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −467.447 | + | 809.642i | −0.684403 | + | 1.18542i | 0.289221 | + | 0.957262i | \(0.406604\pi\) |
−0.973624 | + | 0.228159i | \(0.926730\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1091.17i | − | 1.59294i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 489.400 | 0.712373 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 432.655 | + | 249.794i | 0.627947 | + | 0.362545i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 842.192 | − | 486.240i | 1.21880 | − | 0.703676i | 0.254140 | − | 0.967167i | \(-0.418207\pi\) |
0.964662 | + | 0.263492i | \(0.0848741\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −58.0210 | − | 3.38163i | −0.0837243 | − | 0.00487969i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 551.258 | + | 954.806i | 0.793176 | + | 1.37382i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 148.179 | − | 256.654i | 0.212596 | − | 0.368227i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 206.891i | − | 0.295981i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 695.549 | 0.992224 | 0.496112 | − | 0.868259i | \(-0.334761\pi\) | ||||
0.496112 | + | 0.868259i | \(0.334761\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −195.797 | − | 113.043i | −0.278516 | − | 0.160801i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −306.895 | + | 177.186i | −0.435312 | + | 0.251328i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −245.033 | − | 161.175i | −0.346581 | − | 0.227970i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 78.6320 | + | 136.195i | 0.110905 | + | 0.192094i | 0.916136 | − | 0.400869i | \(-0.131292\pi\) |
−0.805230 | + | 0.592962i | \(0.797958\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 89.4232 | − | 154.886i | 0.125771 | − | 0.217842i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1525.91i | 2.14013i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 79.2440 | 0.110831 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −49.7763 | − | 28.7384i | −0.0694230 | − | 0.0400814i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −183.553 | + | 105.975i | −0.255290 | + | 0.147392i | −0.622184 | − | 0.782871i | \(-0.713754\pi\) |
0.366894 | + | 0.930263i | \(0.380421\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −607.913 | + | 305.275i | −0.843153 | + | 0.423406i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −119.662 | − | 207.261i | −0.165508 | − | 0.286668i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 114.370 | − | 198.094i | 0.157751 | − | 0.273233i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 271.507i | − | 0.373462i | −0.982411 | − | 0.186731i | \(-0.940211\pi\) | ||
0.982411 | − | 0.186731i | \(-0.0597893\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −802.202 | −1.10041 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 665.921 | + | 384.470i | 0.910972 | + | 0.525950i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −442.045 | + | 255.215i | −0.603062 | + | 0.348178i | −0.770245 | − | 0.637748i | \(-0.779866\pi\) |
0.167183 | + | 0.985926i | \(0.446533\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 509.454 | + | 59.5872i | 0.693134 | + | 0.0810711i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 89.7965 | + | 155.532i | 0.121841 | + | 0.211034i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −187.084 | + | 324.039i | −0.253158 | + | 0.438483i | −0.964394 | − | 0.264471i | \(-0.914803\pi\) |
0.711235 | + | 0.702954i | \(0.248136\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 236.811i | 0.319583i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 792.307 | 1.06636 | 0.533181 | − | 0.846001i | \(-0.320996\pi\) | ||||
0.533181 | + | 0.846001i | \(0.320996\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.93919 | + | 4.00634i | 0.00931434 | + | 0.00537764i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −59.6879 | + | 34.4608i | −0.0799035 | + | 0.0461323i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −262.126 | − | 521.986i | −0.349967 | − | 0.696911i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.1482 | − | 22.7733i | −0.0175076 | − | 0.0303240i | 0.857139 | − | 0.515085i | \(-0.172240\pi\) |
−0.874646 | + | 0.484761i | \(0.838906\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 402.440 | − | 697.046i | 0.534449 | − | 0.925692i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 413.133i | − | 0.547196i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1287.30 | 1.70053 | 0.850264 | − | 0.526356i | \(-0.176442\pi\) | ||||
0.850264 | + | 0.526356i | \(0.176442\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 262.553 | + | 151.585i | 0.345920 | + | 0.199717i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 839.569 | − | 484.726i | 1.10324 | − | 0.636959i | 0.166174 | − | 0.986097i | \(-0.446859\pi\) |
0.937071 | + | 0.349138i | \(0.113525\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 623.154 | − | 947.378i | 0.816715 | − | 1.24165i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 72.6257 | + | 125.791i | 0.0949355 | + | 0.164433i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 198.875 | − | 344.461i | 0.259289 | − | 0.449102i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 499.204i | − | 0.649160i | −0.945858 | − | 0.324580i | \(-0.894777\pi\) | ||
0.945858 | − | 0.324580i | \(-0.105223\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 119.603 | 0.155127 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −125.870 | − | 72.6713i | −0.162834 | − | 0.0940120i | 0.416369 | − | 0.909196i | \(-0.363303\pi\) |
−0.579202 | + | 0.815184i | \(0.696636\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −290.902 | + | 167.953i | −0.375358 | + | 0.216713i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.7875 | − | 253.720i | 0.0190315 | − | 0.326537i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 168.955 | + | 292.639i | 0.216888 | + | 0.375660i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −136.939 | + | 237.185i | −0.175338 | + | 0.303694i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 834.918i | 1.06631i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −557.176 | −0.709779 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −333.132 | − | 192.334i | −0.423294 | − | 0.244389i | 0.273192 | − | 0.961960i | \(-0.411921\pi\) |
−0.696486 | + | 0.717571i | \(0.745254\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −894.719 | + | 516.566i | −1.13399 | + | 0.654710i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 190.429 | + | 11.0987i | 0.240744 | + | 0.0140313i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −87.0654 | − | 150.802i | −0.109792 | − | 0.190166i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 444.122 | − | 769.243i | 0.558645 | − | 0.967601i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.29571i | 0.0116634i | 0.999983 | + | 0.00583169i | \(0.00185629\pi\) | ||||
−0.999983 | + | 0.00583169i | \(0.998144\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 469.882 | 0.588088 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 321.540 | + | 185.641i | 0.401424 | + | 0.231762i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −355.488 | + | 205.241i | −0.442700 | + | 0.255593i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 879.288 | + | 578.366i | 1.09228 | + | 0.718468i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 422.530 | + | 731.844i | 0.523582 | + | 0.906870i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 407.696 | − | 706.149i | 0.503950 | − | 0.872867i | −0.496040 | − | 0.868300i | \(-0.665213\pi\) |
0.999990 | − | 0.00456703i | \(-0.00145374\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 762.398i | − | 0.940071i | −0.882647 | − | 0.470036i | \(-0.844241\pi\) | ||
0.882647 | − | 0.470036i | \(-0.155759\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 181.271 | 0.222965 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 908.528 | + | 524.539i | 1.11476 | + | 0.643606i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −759.289 | + | 438.376i | −0.929362 | + | 0.536568i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 93.5765 | − | 46.9913i | 0.114257 | − | 0.0573764i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 561.968 | + | 973.358i | 0.684493 | + | 1.18558i | 0.973596 | + | 0.228278i | \(0.0733095\pi\) |
−0.289103 | + | 0.957298i | \(0.593357\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −166.411 | + | 288.232i | −0.202200 | + | 0.350221i | −0.949237 | − | 0.314561i | \(-0.898143\pi\) |
0.747037 | + | 0.664783i | \(0.231476\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 66.7380i | 0.0808945i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −451.741 | −0.546241 | −0.273120 | − | 0.961980i | \(-0.588056\pi\) | ||||
−0.273120 | + | 0.961980i | \(0.588056\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 396.030 | + | 228.648i | 0.477720 | + | 0.275812i | 0.719466 | − | 0.694528i | \(-0.244387\pi\) |
−0.241746 | + | 0.970340i | \(0.577720\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 65.4024 | − | 37.7601i | 0.0787032 | − | 0.0454393i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −545.507 | − | 406.182i | −0.654870 | − | 0.487613i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −104.874 | − | 181.646i | −0.125597 | − | 0.217541i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 613.041 | − | 1061.82i | 0.732426 | − | 1.26860i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 97.6089i | 0.116340i | 0.998307 | + | 0.0581698i | \(0.0185265\pi\) | ||||
−0.998307 | + | 0.0581698i | \(0.981474\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.7167 | −0.0365240 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.9510 | + | 11.5187i | 0.0236666 | + | 0.0136639i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 479.173 | − | 276.651i | 0.567068 | − | 0.327397i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 346.557 | + | 690.120i | 0.409159 | + | 0.814782i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −234.756 | − | 406.609i | −0.276509 | − | 0.478927i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 260.740 | − | 451.615i | 0.306392 | − | 0.530687i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 832.329i | − | 0.975766i | −0.872909 | − | 0.487883i | \(-0.837769\pi\) | ||
0.872909 | − | 0.487883i | \(-0.162231\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −165.617 | −0.193704 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −846.076 | − | 488.482i | −0.987253 | − | 0.569991i | −0.0828008 | − | 0.996566i | \(-0.526387\pi\) |
−0.904452 | + | 0.426575i | \(0.859720\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 604.432 | − | 348.969i | 0.703646 | − | 0.406250i | −0.105058 | − | 0.994466i | \(-0.533503\pi\) |
0.808704 | + | 0.588216i | \(0.200169\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −208.746 | + | 317.356i | −0.242446 | + | 0.368590i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 421.518 | + | 730.091i | 0.488434 | + | 0.845992i | 0.999911 | − | 0.0133047i | \(-0.00423514\pi\) |
−0.511478 | + | 0.859296i | \(0.670902\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 145.022 | − | 251.186i | 0.167656 | − | 0.290388i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 244.865i | − | 0.282428i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 230.026 | 0.264702 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −280.219 | − | 161.785i | −0.321721 | − | 0.185746i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −24.9903 | + | 14.4282i | −0.0286258 | + | 0.0165271i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −55.4184 | + | 950.852i | −0.0633353 | + | 1.08669i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.0573 | − | 50.3287i | −0.0331326 | − | 0.0573873i | 0.848984 | − | 0.528419i | \(-0.177215\pi\) |
−0.882116 | + | 0.471032i | \(0.843882\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −381.720 | + | 661.158i | −0.434266 | + | 0.752171i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1034.35i | 1.17406i | 0.809565 | + | 0.587030i | \(0.199703\pi\) | ||||
−0.809565 | + | 0.587030i | \(0.800297\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −483.067 | −0.547075 | −0.273538 | − | 0.961861i | \(-0.588194\pi\) | ||||
−0.273538 | + | 0.961861i | \(0.588194\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −612.437 | − | 353.590i | −0.692019 | − | 0.399537i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 381.611 | − | 220.323i | 0.430227 | − | 0.248392i | −0.269216 | − | 0.963080i | \(-0.586765\pi\) |
0.699443 | + | 0.714688i | \(0.253431\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1624.44 | + | 94.6770i | 1.82727 | + | 0.106498i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −84.4371 | − | 146.249i | −0.0947667 | − | 0.164141i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −267.882 | + | 463.985i | −0.299980 | + | 0.519580i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 607.274i | − | 0.678519i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −546.216 | −0.608937 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1030.49 | − | 594.953i | −1.14626 | − | 0.661795i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1019.98 | + | 588.887i | −1.13206 | + | 0.653593i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −823.419 | − | 541.618i | −0.911871 | − | 0.599798i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 606.471 | + | 1050.44i | 0.670134 | + | 1.16071i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −229.774 | + | 397.981i | −0.253334 | + | 0.438788i | −0.964442 | − | 0.264295i | \(-0.914861\pi\) |
0.711107 | + | 0.703083i | \(0.248194\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 106.454i | 0.117111i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1515.03 | −1.66304 | −0.831518 | − | 0.555498i | \(-0.812528\pi\) | ||||
−0.831518 | + | 0.555498i | \(0.812528\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −76.7685 | − | 44.3223i | −0.0840838 | − | 0.0485458i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −268.119 | + | 154.799i | −0.293026 | + | 0.169179i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1101.62 | − | 553.199i | 1.20133 | − | 0.603270i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51.6821 | − | 89.5160i | −0.0562373 | − | 0.0974058i | 0.836536 | − | 0.547912i | \(-0.184577\pi\) |
−0.892773 | + | 0.450506i | \(0.851244\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 496.083 | − | 859.241i | 0.538635 | − | 0.932944i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 493.441i | − | 0.534605i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 114.795 | 0.124103 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 213.831 | + | 123.455i | 0.230669 | + | 0.133177i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1171.77 | − | 676.521i | 1.26132 | − | 0.728225i | 0.287992 | − | 0.957633i | \(-0.407012\pi\) |
0.973330 | + | 0.229408i | \(0.0736791\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 712.080 | − | 307.095i | 0.764855 | − | 0.329855i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 122.090 | + | 211.466i | 0.130857 | + | 0.226651i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −93.4086 | + | 161.788i | −0.0999023 | + | 0.173036i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1443.67i | 1.54074i | 0.637600 | + | 0.770368i | \(0.279927\pi\) | ||||
−0.637600 | + | 0.770368i | \(0.720073\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1232.33 | −1.31239 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1097.89 | − | 633.869i | −1.16673 | − | 0.673612i | −0.213822 | − | 0.976873i | \(-0.568591\pi\) |
−0.952908 | + | 0.303261i | \(0.901925\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −674.987 | + | 389.704i | −0.715787 | + | 0.413260i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −379.498 | − | 755.717i | −0.401585 | − | 0.799700i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −200.712 | − | 347.643i | −0.211945 | − | 0.367099i | 0.740378 | − | 0.672190i | \(-0.234646\pi\) |
−0.952323 | + | 0.305091i | \(0.901313\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 369.779 | − | 640.476i | 0.389651 | − | 0.674896i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 172.677i | − | 0.181574i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1544.95 | −1.62115 | −0.810573 | − | 0.585637i | \(-0.800844\pi\) | ||||
−0.810573 | + | 0.585637i | \(0.800844\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −401.352 | − | 231.721i | −0.420264 | − | 0.242639i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −204.739 | + | 118.206i | −0.213938 | + | 0.123517i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1019.11 | − | 1549.35i | 1.06268 | − | 1.61559i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 393.193 | + | 681.030i | 0.409150 | + | 0.708668i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −106.005 | + | 183.606i | −0.110078 | + | 0.190661i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 525.090i | 0.544135i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1272.03 | −1.31544 | −0.657718 | − | 0.753264i | \(-0.728478\pi\) | ||||
−0.657718 | + | 0.753264i | \(0.728478\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −483.485 | − | 279.140i | −0.498953 | − | 0.288070i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −916.173 | + | 528.953i | −0.943536 | + | 0.544751i | −0.891067 | − | 0.453872i | \(-0.850042\pi\) |
−0.0524687 | + | 0.998623i | \(0.516709\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −109.023 | + | 1870.59i | −0.112048 | + | 1.92249i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −60.1203 | − | 104.131i | −0.0616618 | − | 0.106801i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −227.645 | + | 394.293i | −0.233004 | + | 0.403575i | −0.958691 | − | 0.284450i | \(-0.908189\pi\) |
0.725687 | + | 0.688025i | \(0.241522\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 477.531i | 0.487774i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −411.585 | −0.419557 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −938.128 | − | 541.628i | −0.954352 | − | 0.550995i | −0.0599216 | − | 0.998203i | \(-0.519085\pi\) |
−0.894430 | + | 0.447208i | \(0.852418\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1045.62 | + | 603.690i | −1.06154 | + | 0.612883i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −601.247 | − | 35.0424i | −0.609166 | − | 0.0355039i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1011.14 | − | 1751.34i | −1.02238 | − | 1.77082i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −555.040 | + | 961.358i | −0.560081 | + | 0.970088i | 0.437408 | + | 0.899263i | \(0.355897\pi\) |
−0.997489 | + | 0.0708253i | \(0.977437\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 674.180i | 0.678933i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 40.1249 | 0.0403265 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1332.56 | − | 769.353i | −1.33657 | − | 0.771668i | −0.350272 | − | 0.936648i | \(-0.613911\pi\) |
−0.986297 | + | 0.164980i | \(0.947244\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −362.875 | + | 209.506i | −0.363238 | + | 0.209716i |
(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 | 224.3.s.b.129.6 | yes | 16 | |
4.3 | odd | 2 | inner | 224.3.s.b.129.3 | yes | 16 | |
7.3 | odd | 6 | 1568.3.c.g.97.11 | 16 | |||
7.4 | even | 3 | 1568.3.c.g.97.6 | 16 | |||
7.5 | odd | 6 | inner | 224.3.s.b.33.6 | yes | 16 | |
8.3 | odd | 2 | 448.3.s.h.129.6 | 16 | |||
8.5 | even | 2 | 448.3.s.h.129.3 | 16 | |||
28.3 | even | 6 | 1568.3.c.g.97.5 | 16 | |||
28.11 | odd | 6 | 1568.3.c.g.97.12 | 16 | |||
28.19 | even | 6 | inner | 224.3.s.b.33.3 | ✓ | 16 | |
56.5 | odd | 6 | 448.3.s.h.257.3 | 16 | |||
56.19 | even | 6 | 448.3.s.h.257.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.s.b.33.3 | ✓ | 16 | 28.19 | even | 6 | inner | |
224.3.s.b.33.6 | yes | 16 | 7.5 | odd | 6 | inner | |
224.3.s.b.129.3 | yes | 16 | 4.3 | odd | 2 | inner | |
224.3.s.b.129.6 | yes | 16 | 1.1 | even | 1 | trivial | |
448.3.s.h.129.3 | 16 | 8.5 | even | 2 | |||
448.3.s.h.129.6 | 16 | 8.3 | odd | 2 | |||
448.3.s.h.257.3 | 16 | 56.5 | odd | 6 | |||
448.3.s.h.257.6 | 16 | 56.19 | even | 6 | |||
1568.3.c.g.97.5 | 16 | 28.3 | even | 6 | |||
1568.3.c.g.97.6 | 16 | 7.4 | even | 3 | |||
1568.3.c.g.97.11 | 16 | 7.3 | odd | 6 | |||
1568.3.c.g.97.12 | 16 | 28.11 | odd | 6 |