Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [416,2,Mod(225,416)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(416, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("416.225");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 416 = 2^{5} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 416.w (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: | \(3.32177672409\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.56070144.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 257.2 | ||
Root | \(0.500000 + 1.19293i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 416.257 |
Dual form | 416.2.w.c.225.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/416\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(287\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −0.619657 | − | 1.07328i | −0.357759 | − | 0.619657i | 0.629827 | − | 0.776735i | \(-0.283126\pi\) |
−0.987586 | + | 0.157079i | \(0.949792\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.00000i | − | 0.894427i | −0.894427 | − | 0.447214i | \(-0.852416\pi\) | ||
0.894427 | − | 0.447214i | \(-0.147584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.00552 | + | 2.31259i | 1.51395 | + | 0.874077i | 0.999867 | + | 0.0163346i | \(0.00519970\pi\) |
0.514079 | + | 0.857743i | \(0.328134\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.732051 | − | 1.26795i | 0.244017 | − | 0.422650i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.85897 | + | 1.07328i | −0.560501 | + | 0.323605i | −0.753346 | − | 0.657624i | \(-0.771562\pi\) |
0.192846 | + | 0.981229i | \(0.438228\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | − | 3.46410i | −0.277350 | − | 0.960769i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.14655 | + | 1.23931i | −0.554238 | + | 0.319989i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.232051 | − | 0.401924i | 0.0562806 | − | 0.0974808i | −0.836512 | − | 0.547948i | \(-0.815409\pi\) |
0.892793 | + | 0.450467i | \(0.148743\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00552 | + | 2.31259i | 0.918930 | + | 0.530545i | 0.883294 | − | 0.468820i | \(-0.155321\pi\) |
0.0356367 | + | 0.999365i | \(0.488654\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 5.73205i | − | 1.25084i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.76621 | − | 4.79122i | −0.576795 | − | 0.999038i | −0.995844 | − | 0.0910745i | \(-0.970970\pi\) |
0.419049 | − | 0.907964i | \(-0.362363\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.53242 | −1.06472 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50000 | − | 2.59808i | −0.278543 | − | 0.482451i | 0.692480 | − | 0.721437i | \(-0.256518\pi\) |
−0.971023 | + | 0.238987i | \(0.923185\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.25036i | − | 1.66141i | −0.556710 | − | 0.830707i | \(-0.687936\pi\) | ||
0.556710 | − | 0.830707i | \(-0.312064\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.30385 | + | 1.33013i | 0.401048 | + | 0.231545i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.62518 | − | 8.01105i | 0.781798 | − | 1.35411i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.69615 | − | 3.86603i | 1.10084 | − | 0.635571i | 0.164399 | − | 0.986394i | \(-0.447432\pi\) |
0.936442 | + | 0.350823i | \(0.114098\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.09828 | + | 3.21983i | −0.496123 | + | 0.515586i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.23205 | + | 3.59808i | −0.973283 | + | 0.561925i | −0.900235 | − | 0.435403i | \(-0.856606\pi\) |
−0.0730473 | + | 0.997328i | \(0.523272\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.85897 | + | 3.21983i | −0.283490 | + | 0.491020i | −0.972242 | − | 0.233978i | \(-0.924826\pi\) |
0.688752 | + | 0.724997i | \(0.258159\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.53590 | − | 1.46410i | −0.378029 | − | 0.218255i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.7290i | 1.71085i | 0.517927 | + | 0.855425i | \(0.326704\pi\) | ||||
−0.517927 | + | 0.855425i | \(0.673296\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.19615 | + | 12.4641i | 1.02802 | + | 1.78059i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.575167 | −0.0805396 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.53590 | 0.348332 | 0.174166 | − | 0.984716i | \(-0.444277\pi\) | ||||
0.174166 | + | 0.984716i | \(0.444277\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.14655 | + | 3.71794i | 0.289441 | + | 0.501327i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.73205i | − | 0.759229i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.29863 | + | 4.79122i | 1.08039 | + | 0.623763i | 0.931002 | − | 0.365015i | \(-0.118936\pi\) |
0.149388 | + | 0.988779i | \(0.452270\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.50000 | + | 2.59808i | −0.192055 | + | 0.332650i | −0.945931 | − | 0.324367i | \(-0.894849\pi\) |
0.753876 | + | 0.657017i | \(0.228182\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.86450 | − | 3.38587i | 0.738857 | − | 0.426579i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.92820 | + | 2.00000i | −0.859338 | + | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00552 | + | 2.31259i | −0.489353 | + | 0.282528i | −0.724306 | − | 0.689479i | \(-0.757840\pi\) |
0.234953 | + | 0.972007i | \(0.424506\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.42820 | + | 5.93782i | −0.412707 | + | 0.714830i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.57691 | − | 3.21983i | −0.661858 | − | 0.382124i | 0.131127 | − | 0.991366i | \(-0.458141\pi\) |
−0.792984 | + | 0.609242i | \(0.791474\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000i | 0.702247i | 0.936329 | + | 0.351123i | \(0.114200\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.619657 | − | 1.07328i | −0.0715518 | − | 0.123931i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.92820 | −1.13142 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.29311 | 0.483012 | 0.241506 | − | 0.970399i | \(-0.422359\pi\) | ||||
0.241506 | + | 0.970399i | \(0.422359\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.23205 | + | 2.13397i | 0.136895 | + | 0.237108i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.29311i | 0.471230i | 0.971846 | + | 0.235615i | \(0.0757104\pi\) | ||||
−0.971846 | + | 0.235615i | \(0.924290\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.803848 | − | 0.464102i | −0.0871895 | − | 0.0503389i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.85897 | + | 3.21983i | −0.199303 | + | 0.345202i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.03590 | + | 0.598076i | −0.109805 | + | 0.0633960i | −0.553897 | − | 0.832585i | \(-0.686860\pi\) |
0.444092 | + | 0.895981i | \(0.353526\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00552 | − | 16.1881i | 0.419893 | − | 1.69698i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.92820 | + | 5.73205i | −1.02951 | + | 0.594386i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.62518 | − | 8.01105i | 0.474534 | − | 0.821916i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.8923 | + | 6.86603i | 1.20748 | + | 0.697139i | 0.962208 | − | 0.272315i | \(-0.0877893\pi\) |
0.245272 | + | 0.969454i | \(0.421123\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.14277i | 0.315861i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.69615 | + | 16.7942i | 0.964803 | + | 1.67109i | 0.710143 | + | 0.704058i | \(0.248630\pi\) |
0.254660 | + | 0.967031i | \(0.418036\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.58622 | −0.846025 | −0.423013 | − | 0.906124i | \(-0.639027\pi\) | ||||
−0.423013 | + | 0.906124i | \(0.639027\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.4641 | −1.11878 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.85897 | + | 3.21983i | 0.179713 | + | 0.311273i | 0.941782 | − | 0.336223i | \(-0.109150\pi\) |
−0.762069 | + | 0.647496i | \(0.775816\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.00000i | 0.574696i | 0.957826 | + | 0.287348i | \(0.0927736\pi\) | ||||
−0.957826 | + | 0.287348i | \(0.907226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.29863 | − | 4.79122i | −0.787671 | − | 0.454762i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.23205 | − | 10.7942i | 0.586262 | − | 1.01544i | −0.408455 | − | 0.912779i | \(-0.633932\pi\) |
0.994717 | − | 0.102657i | \(-0.0327344\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.58244 | + | 5.53242i | −0.893567 | + | 0.515901i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.12436 | − | 1.26795i | −0.473747 | − | 0.117222i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.85897 | − | 1.07328i | 0.170412 | − | 0.0983872i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.19615 | + | 5.53590i | −0.290559 | + | 0.503263i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.72347 | + | 4.45915i | 0.696401 | + | 0.402068i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.0000i | − | 1.07331i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.85897 | + | 3.21983i | 0.164957 | + | 0.285714i | 0.936640 | − | 0.350293i | \(-0.113918\pi\) |
−0.771683 | + | 0.636007i | \(0.780585\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.60770 | 0.405685 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.6962 | + | 18.5263i | 0.927474 | + | 1.60643i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.0648i | 0.952310i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.4282 | − | 6.59808i | −0.976377 | − | 0.563712i | −0.0752028 | − | 0.997168i | \(-0.523960\pi\) |
−0.901174 | + | 0.433457i | \(0.857294\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00552 | + | 6.93777i | −0.339744 | + | 0.588454i | −0.984384 | − | 0.176032i | \(-0.943674\pi\) |
0.644640 | + | 0.764486i | \(0.277007\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.5885 | − | 7.26795i | 1.06014 | − | 0.612072i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.57691 | + | 5.36639i | 0.466365 | + | 0.448760i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.19615 | + | 3.00000i | −0.431517 | + | 0.249136i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.91829 | − | 15.4469i | 0.735568 | − | 1.27404i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.0359 | + | 5.79423i | 0.822173 | + | 0.474682i | 0.851165 | − | 0.524898i | \(-0.175897\pi\) |
−0.0289923 | + | 0.999580i | \(0.509230\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 9.25036i | − | 0.752784i | −0.926461 | − | 0.376392i | \(-0.877165\pi\) | ||
0.926461 | − | 0.376392i | \(-0.122835\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.339746 | − | 0.588457i | −0.0274668 | − | 0.0475740i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.5007 | −1.48601 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.39230 | 0.350544 | 0.175272 | − | 0.984520i | \(-0.443920\pi\) | ||||
0.175272 | + | 0.984520i | \(0.443920\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.57139 | − | 2.72172i | −0.124619 | − | 0.215847i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 25.5885i | − | 2.01665i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.5990 | − | 12.4702i | −1.69177 | − | 0.976741i | −0.953094 | − | 0.302675i | \(-0.902120\pi\) |
−0.738671 | − | 0.674066i | \(-0.764546\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.66025 | − | 4.60770i | 0.207100 | − | 0.358709i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.4525 | − | 11.2309i | 1.50528 | − | 0.869072i | 0.505295 | − | 0.862947i | \(-0.331384\pi\) |
0.999981 | − | 0.00612500i | \(-0.00194966\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | + | 6.92820i | −0.846154 | + | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.86450 | − | 3.38587i | 0.448469 | − | 0.258924i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.96410 | + | 8.59808i | −0.377414 | + | 0.653700i | −0.990685 | − | 0.136173i | \(-0.956520\pi\) |
0.613271 | + | 0.789872i | \(0.289853\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.00552 | + | 2.31259i | 0.302789 | + | 0.174815i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 11.8756i | − | 0.892628i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.85897 | + | 3.21983i | 0.138946 | + | 0.240661i | 0.927098 | − | 0.374819i | \(-0.122295\pi\) |
−0.788152 | + | 0.615481i | \(0.788962\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.3923 | −1.21843 | −0.609215 | − | 0.793005i | \(-0.708515\pi\) | ||||
−0.609215 | + | 0.793005i | \(0.708515\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.71794 | 0.274838 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.73205 | − | 13.3923i | −0.568472 | − | 0.984622i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.996219i | 0.0728508i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −22.1603 | − | 12.7942i | −1.61192 | − | 0.930643i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.48415 | + | 11.2309i | −0.469177 | + | 0.812638i | −0.999379 | − | 0.0352331i | \(-0.988783\pi\) |
0.530202 | + | 0.847871i | \(0.322116\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.0885 | − | 9.86603i | 1.23005 | − | 0.710172i | 0.263013 | − | 0.964792i | \(-0.415284\pi\) |
0.967041 | + | 0.254620i | \(0.0819505\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.43966 | + | 6.19657i | 0.461154 | + | 0.443745i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.4282 | − | 11.7942i | 1.45545 | − | 0.840304i | 0.456667 | − | 0.889638i | \(-0.349043\pi\) |
0.998782 | + | 0.0493338i | \(0.0157098\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.15208 | + | 10.6557i | −0.436109 | + | 0.755363i | −0.997385 | − | 0.0722651i | \(-0.976977\pi\) |
0.561276 | + | 0.827629i | \(0.310311\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.96410 | + | 2.86603i | 0.350141 | + | 0.202154i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 13.8755i | − | 0.973872i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.19615 | + | 12.4641i | 0.502601 | + | 0.870531i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.10003 | −0.562991 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.92820 | −0.686748 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.5880 | + | 23.5350i | 0.935434 | + | 1.62022i | 0.773859 | + | 0.633359i | \(0.218324\pi\) |
0.161575 | + | 0.986860i | \(0.448343\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.98076i | 0.546833i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.43966 | + | 3.71794i | 0.439181 | + | 0.253561i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.3923 | − | 37.0526i | 1.45220 | − | 2.51529i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.43966 | − | 3.71794i | 0.435152 | − | 0.251235i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.62436 | − | 0.401924i | −0.109266 | − | 0.0270363i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00552 | + | 2.31259i | −0.268230 | + | 0.154863i | −0.628083 | − | 0.778146i | \(-0.716160\pi\) |
0.359853 | + | 0.933009i | \(0.382827\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.732051 | − | 1.26795i | 0.0488034 | − | 0.0845299i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.0166 | − | 6.93777i | −0.797568 | − | 0.460476i | 0.0450520 | − | 0.998985i | \(-0.485655\pi\) |
−0.842620 | + | 0.538509i | \(0.818988\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 0.928203i | − | 0.0613374i | −0.999530 | − | 0.0306687i | \(-0.990236\pi\) | ||
0.999530 | − | 0.0306687i | \(-0.00976368\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.15208 | + | 10.6557i | 0.404777 | + | 0.701094i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.5359 | −0.952278 | −0.476139 | − | 0.879370i | \(-0.657964\pi\) | ||||
−0.476139 | + | 0.879370i | \(0.657964\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.4580 | 1.53023 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.66025 | − | 4.60770i | −0.172802 | − | 0.299302i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4.29311i | − | 0.277698i | −0.990314 | − | 0.138849i | \(-0.955660\pi\) | ||
0.990314 | − | 0.138849i | \(-0.0443403\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.6962 | + | 10.7942i | 1.20433 | + | 0.695317i | 0.961514 | − | 0.274756i | \(-0.0885971\pi\) |
0.242811 | + | 0.970074i | \(0.421930\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.77174 | + | 11.7290i | −0.434407 | + | 0.752415i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 24.9282 | − | 14.3923i | 1.59260 | − | 0.919491i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00552 | − | 16.1881i | 0.254865 | − | 1.03003i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.60770 | − | 2.66025i | 0.292001 | − | 0.168587i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.9238 | + | 22.3847i | −0.815744 | + | 1.41291i | 0.0930485 | + | 0.995662i | \(0.470339\pi\) |
−0.908792 | + | 0.417248i | \(0.862995\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.2846 | + | 5.93782i | 0.646588 | + | 0.373308i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.15033i | 0.0720368i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.232051 | + | 0.401924i | 0.0144749 | + | 0.0250713i | 0.873172 | − | 0.487412i | \(-0.162059\pi\) |
−0.858697 | + | 0.512483i | \(0.828726\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 35.7621 | 2.22215 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.39230 | −0.271877 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0166 | − | 20.8133i | −0.740974 | − | 1.28340i | −0.952052 | − | 0.305935i | \(-0.901031\pi\) |
0.211079 | − | 0.977469i | \(-0.432302\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.07180i | − | 0.311558i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.28380 | + | 0.741204i | 0.0785675 | + | 0.0453609i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.30385 | + | 3.99038i | −0.140468 | + | 0.243298i | −0.927673 | − | 0.373394i | \(-0.878194\pi\) |
0.787205 | + | 0.616692i | \(0.211527\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.0276 | + | 11.5630i | −1.21659 | + | 0.702399i | −0.964187 | − | 0.265222i | \(-0.914555\pi\) |
−0.252404 | + | 0.967622i | \(0.581221\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −19.8564 | + | 5.73205i | −1.20176 | + | 0.346919i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.85897 | + | 1.07328i | −0.112100 | + | 0.0647210i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.69615 | − | 2.93782i | 0.101912 | − | 0.176517i | −0.810560 | − | 0.585655i | \(-0.800837\pi\) |
0.912472 | + | 0.409138i | \(0.134171\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.7290 | − | 6.77174i | −0.702196 | − | 0.405413i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.0000i | − | 0.596550i | −0.954480 | − | 0.298275i | \(-0.903589\pi\) | ||
0.954480 | − | 0.298275i | \(-0.0964112\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.87002 | − | 17.0954i | −0.586712 | − | 1.01621i | −0.994660 | − | 0.103209i | \(-0.967089\pi\) |
0.407948 | − | 0.913005i | \(-0.366245\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −11.4641 | −0.679075 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −33.2835 | −1.96466 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.39230 | + | 14.5359i | 0.493665 | + | 0.855053i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 17.0183i | − | 0.997631i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.8205 | − | 12.5981i | −1.27477 | − | 0.735987i | −0.298886 | − | 0.954289i | \(-0.596615\pi\) |
−0.975881 | + | 0.218301i | \(0.929948\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.58244 | − | 16.5973i | 0.557911 | − | 0.966330i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.2846 | − | 5.93782i | 0.596774 | − | 0.344547i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.8311 | + | 14.3737i | −0.799871 | + | 0.831250i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.8923 | + | 8.59808i | −0.858378 | + | 0.495585i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.0166 | − | 20.8133i | 0.690334 | − | 1.19569i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.19615 | + | 3.00000i | 0.297531 | + | 0.171780i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5.62140i | − | 0.320830i | −0.987050 | − | 0.160415i | \(-0.948717\pi\) | ||
0.987050 | − | 0.160415i | \(-0.0512833\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.32051 | + | 9.21539i | 0.302673 | + | 0.524245i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.5007 | 1.04908 | 0.524540 | − | 0.851386i | \(-0.324237\pi\) | ||||
0.524540 | + | 0.851386i | \(0.324237\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.39230 | −0.474361 | −0.237181 | − | 0.971466i | \(-0.576223\pi\) | ||||
−0.237181 | + | 0.971466i | \(0.576223\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.77174 | − | 11.7290i | −0.381544 | − | 0.660854i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 4.00000i | − | 0.224662i | −0.993671 | − | 0.112331i | \(-0.964168\pi\) | ||
0.993671 | − | 0.112331i | \(-0.0358318\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.57691 | + | 3.21983i | 0.312247 | + | 0.180276i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.30385 | − | 3.99038i | 0.128588 | − | 0.222721i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.85897 | − | 1.07328i | 0.103436 | − | 0.0597187i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | − | 3.46410i | −0.0554700 | − | 0.192154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.43966 | − | 3.71794i | 0.356114 | − | 0.205603i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.1244 | + | 46.9808i | −1.49541 | + | 2.59013i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.43414 | − | 1.40535i | −0.133792 | − | 0.0772450i | 0.431610 | − | 0.902060i | \(-0.357946\pi\) |
−0.565402 | + | 0.824815i | \(0.691279\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 11.3205i | − | 0.620360i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.62518 | + | 8.01105i | 0.252701 | + | 0.437690i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.392305 | −0.0213702 | −0.0106851 | − | 0.999943i | \(-0.503401\pi\) | ||||
−0.0106851 | + | 0.999943i | \(0.503401\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.4469 | −0.838962 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.92820 | + | 17.1962i | 0.537642 | + | 0.931224i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 34.1908i | 1.84613i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.8756 | + | 6.85641i | 0.639363 | + | 0.369137i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.39139 | − | 12.8023i | 0.396791 | − | 0.687262i | −0.596537 | − | 0.802585i | \(-0.703457\pi\) |
0.993328 | + | 0.115324i | \(0.0367905\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.30385 | − | 4.79423i | 0.444495 | − | 0.256629i | −0.261008 | − | 0.965337i | \(-0.584055\pi\) |
0.705502 | + | 0.708708i | \(0.250721\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.53242 | + | 19.1649i | 0.295299 | + | 1.02295i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.96410 | + | 4.59808i | −0.423886 | + | 0.244731i | −0.696739 | − | 0.717325i | \(-0.745366\pi\) |
0.272852 | + | 0.962056i | \(0.412033\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.43966 | + | 11.1538i | −0.341782 | + | 0.591983i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.30385 | − | 1.33013i | −0.121933 | − | 0.0703978i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.29311i | 0.226582i | 0.993562 | + | 0.113291i | \(0.0361392\pi\) | ||||
−0.993562 | + | 0.113291i | \(0.963861\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.19615 | + | 2.07180i | 0.0629554 | + | 0.109042i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.92207 | 0.415801 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.0000 | 0.628109 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.287584 | − | 0.498110i | −0.0150117 | − | 0.0260011i | 0.858422 | − | 0.512944i | \(-0.171445\pi\) |
−0.873434 | + | 0.486943i | \(0.838112\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.5359i | 0.548477i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.1576 | + | 5.86450i | 0.527357 | + | 0.304469i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.69615 | + | 8.13397i | −0.243158 | + | 0.421161i | −0.961612 | − | 0.274413i | \(-0.911517\pi\) |
0.718454 | + | 0.695574i | \(0.244850\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.8793 | + | 7.43588i | −0.665086 | + | 0.383987i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.50000 | + | 7.79423i | −0.386270 | + | 0.401423i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.43414 | − | 1.40535i | 0.125033 | − | 0.0721880i | −0.436179 | − | 0.899860i | \(-0.643669\pi\) |
0.561212 | + | 0.827672i | \(0.310335\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.30385 | − | 3.99038i | 0.118030 | − | 0.204433i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.1704 | + | 13.3774i | 1.18395 | + | 0.683555i | 0.956926 | − | 0.290334i | \(-0.0937663\pi\) |
0.227026 | + | 0.973889i | \(0.427100\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.8564i | 1.01198i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.72172 | + | 4.71416i | 0.138353 | + | 0.239634i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.56761 | −0.129849 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 8.58622i | − | 0.432019i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.6962 | − | 12.5263i | −1.08890 | − | 0.628676i | −0.155616 | − | 0.987818i | \(-0.549736\pi\) |
−0.933283 | + | 0.359142i | \(0.883069\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.2559 | − | 22.9599i | 0.663624 | − | 1.14943i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.1603 | + | 17.9904i | −1.55607 | + | 0.898397i | −0.558442 | + | 0.829544i | \(0.688601\pi\) |
−0.997627 | + | 0.0688532i | \(0.978066\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.0442 | + | 9.25036i | −1.59624 | + | 0.460793i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.26795 | − | 2.46410i | 0.212076 | − | 0.122442i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.29863 | + | 14.3737i | −0.411348 | + | 0.712476i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.6962 | + | 14.2583i | 1.22115 | + | 0.705029i | 0.965162 | − | 0.261652i | \(-0.0842673\pi\) |
0.255984 | + | 0.966681i | \(0.417601\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.3542i | 0.806692i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.1603 | + | 38.3827i | 1.09043 | + | 1.88869i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.58622 | 0.421481 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.92820 | 0.486186 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0166 | − | 20.8133i | −0.587048 | − | 1.01680i | −0.994617 | − | 0.103623i | \(-0.966957\pi\) |
0.407569 | − | 0.913175i | \(-0.366377\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.928203i | 0.0452379i | 0.999744 | + | 0.0226189i | \(0.00720044\pi\) | ||||
−0.999744 | + | 0.0226189i | \(0.992800\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.8718 | + | 8.58622i | 0.723090 | + | 0.417476i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.232051 | − | 0.401924i | 0.0112561 | − | 0.0194962i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.0166 | + | 6.93777i | −0.581523 | + | 0.335742i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.30385 | − | 9.31089i | 0.111231 | − | 0.449534i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.4562 | − | 10.6557i | 0.889006 | − | 0.513268i | 0.0153885 | − | 0.999882i | \(-0.495101\pi\) |
0.873617 | + | 0.486614i | \(0.161768\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.69615 | + | 11.5981i | −0.321797 | + | 0.557368i | −0.980859 | − | 0.194720i | \(-0.937620\pi\) |
0.659062 | + | 0.752088i | \(0.270953\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.43966 | + | 3.71794i | 0.308758 | + | 0.178262i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 25.5885i | − | 1.22406i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.87002 | − | 17.0954i | −0.471070 | − | 0.815918i | 0.528382 | − | 0.849007i | \(-0.322799\pi\) |
−0.999452 | + | 0.0330889i | \(0.989466\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.0718 | 1.00342 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 40.6304 | 1.93041 | 0.965205 | − | 0.261496i | \(-0.0842157\pi\) | ||||
0.965205 | + | 0.261496i | \(0.0842157\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.19615 | + | 2.07180i | 0.0567031 | + | 0.0982126i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 14.3617i | − | 0.679287i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.5526 | + | 18.7942i | 1.53625 | + | 0.886954i | 0.999054 | + | 0.0434975i | \(0.0138501\pi\) |
0.537197 | + | 0.843457i | \(0.319483\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.72347 | − | 13.3774i | 0.363684 | − | 0.629919i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.92820 | + | 5.73205i | −0.466468 | + | 0.269315i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −32.3763 | − | 8.01105i | −1.51782 | − | 0.375564i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.8923 | + | 12.0622i | −0.977301 | + | 0.564245i | −0.901454 | − | 0.432875i | \(-0.857499\pi\) |
−0.0758467 | + | 0.997119i | \(0.524166\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.28380 | + | 2.22361i | −0.0599228 | + | 0.103789i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.76795 | − | 1.59808i | −0.128916 | − | 0.0744298i | 0.434155 | − | 0.900838i | \(-0.357047\pi\) |
−0.563071 | + | 0.826408i | \(0.690380\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 31.3801i | − | 1.45835i | −0.684325 | − | 0.729177i | \(-0.739903\pi\) | ||
0.684325 | − | 0.729177i | \(-0.260097\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.4641 | + | 19.8564i | 0.531635 | + | 0.920819i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.25036 | 0.428056 | 0.214028 | − | 0.976828i | \(-0.431342\pi\) | ||||
0.214028 | + | 0.976828i | \(0.431342\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.3923 | −0.987805 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.72172 | − | 4.71416i | −0.125410 | − | 0.217217i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 7.98076i | − | 0.366956i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00552 | + | 2.31259i | 0.183786 | + | 0.106109i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.85641 | − | 3.21539i | 0.0849990 | − | 0.147223i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.29485 | + | 5.36639i | −0.424693 | + | 0.245196i | −0.697083 | − | 0.716990i | \(-0.745519\pi\) |
0.272390 | + | 0.962187i | \(0.412186\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0885 | − | 19.3301i | −0.915955 | − | 0.881378i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −27.4635 | + | 15.8561i | −1.24963 | + | 0.721476i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.7321 | − | 23.7846i | 0.623540 | − | 1.08000i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.43414 | − | 1.40535i | −0.110301 | − | 0.0636825i | 0.443834 | − | 0.896109i | \(-0.353618\pi\) |
−0.554136 | + | 0.832426i | \(0.686951\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 30.9090i | 1.39775i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.48415 | + | 11.2309i | 0.292626 | + | 0.506843i | 0.974430 | − | 0.224692i | \(-0.0721377\pi\) |
−0.681804 | + | 0.731535i | \(0.738804\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.39230 | −0.0627063 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.28555 | 0.282514 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.8923 | − | 25.7942i | −0.668011 | − | 1.15703i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 9.25036i | − | 0.414103i | −0.978330 | − | 0.207052i | \(-0.933613\pi\) | ||
0.978330 | − | 0.207052i | \(-0.0663868\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.1077 | − | 13.9186i | −1.07705 | − | 0.621836i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.7345 | + | 27.2530i | −0.701567 | + | 1.21515i | 0.266349 | + | 0.963877i | \(0.414183\pi\) |
−0.967916 | + | 0.251274i | \(0.919151\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33.5885 | − | 19.3923i | 1.49467 | − | 0.862946i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.2521 | + | 7.51294i | 0.632958 | + | 0.333661i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.5526 | + | 13.5981i | −1.04395 | + | 0.602724i | −0.920949 | − | 0.389683i | \(-0.872585\pi\) |
−0.123000 | + | 0.992407i | \(0.539251\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.8755 | + | 24.0331i | −0.613818 | + | 1.06316i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −22.1603 | − | 12.7942i | −0.978399 | − | 0.564879i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.1724i | 0.756708i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.5885 | − | 21.8038i | −0.553640 | − | 0.958932i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.3042 | 0.540093 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.24871 | 0.273761 | 0.136881 | − | 0.990588i | \(-0.456292\pi\) | ||||
0.136881 | + | 0.990588i | \(0.456292\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.43036 | − | 5.94155i | −0.149999 | − | 0.259806i | 0.781228 | − | 0.624246i | \(-0.214594\pi\) |
−0.931227 | + | 0.364440i | \(0.881260\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 5.73205i | − | 0.250167i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.71794 | − | 2.14655i | −0.161956 | − | 0.0935054i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.80385 | + | 6.58846i | −0.165385 | + | 0.286455i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.1500 | − | 7.01483i | 0.527267 | − | 0.304418i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.6962 | + | 17.9904i | 0.809820 | + | 0.779250i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.43966 | − | 3.71794i | 0.278411 | − | 0.160741i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.30385 | − | 3.99038i | 0.0994184 | − | 0.172198i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.7549 | − | 15.4469i | −1.15241 | − | 0.665346i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 6.92820i | − | 0.297867i | −0.988847 | − | 0.148933i | \(-0.952416\pi\) | ||
0.988847 | − | 0.148933i | \(-0.0475840\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.1576 | + | 17.5935i | 0.435905 | + | 0.755009i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.0000 | 0.514024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.58622 | −0.367120 | −0.183560 | − | 0.983008i | \(-0.558762\pi\) | ||||
−0.183560 | + | 0.983008i | \(0.558762\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.19615 | + | 3.80385i | 0.0937295 | + | 0.162344i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 13.8755i | − | 0.591118i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.1962 | + | 9.92820i | 0.731255 | + | 0.422190i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.58244 | + | 16.5973i | −0.406752 | + | 0.704515i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.7487 | − | 11.4019i | 0.836780 | − | 0.483115i | −0.0193886 | − | 0.999812i | \(-0.506172\pi\) |
0.856168 | + | 0.516697i | \(0.172839\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.0128 | + | 3.21983i | 0.550383 | + | 0.136184i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.06922 | − | 0.617314i | 0.0451425 | − | 0.0260630i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.4525 | − | 33.6926i | 0.819823 | − | 1.41998i | −0.0859889 | − | 0.996296i | \(-0.527405\pi\) |
0.905812 | − | 0.423679i | \(-0.139262\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.5885 | − | 12.4641i | −0.908233 | − | 0.524369i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.3969i | 0.478626i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.96410 | − | 8.59808i | −0.208106 | − | 0.360450i | 0.743012 | − | 0.669278i | \(-0.233397\pi\) |
−0.951118 | + | 0.308828i | \(0.900063\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.4580 | −0.981686 | −0.490843 | − | 0.871248i | \(-0.663311\pi\) | ||||
−0.490843 | + | 0.871248i | \(0.663311\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.0718 | 0.671409 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.76621 | − | 4.79122i | −0.115359 | − | 0.199808i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 43.8564i | − | 1.82577i | −0.408221 | − | 0.912883i | \(-0.633851\pi\) | ||
0.408221 | − | 0.912883i | \(-0.366149\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.1780 | − | 12.2271i | −0.880126 | − | 0.508141i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.92820 | + | 17.1962i | −0.411891 | + | 0.713417i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.71416 | + | 2.72172i | −0.195241 | + | 0.112722i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.53590 | + | 10.2487i | −0.104846 | + | 0.423732i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.4525 | − | 11.2309i | 0.802889 | − | 0.463548i | −0.0415915 | − | 0.999135i | \(-0.513243\pi\) |
0.844480 | + | 0.535587i | \(0.179909\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.3923 | − | 37.0526i | 0.881455 | − | 1.52672i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.3170 | − | 14.6167i | −1.04140 | − | 0.601253i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 22.7846i | − | 0.935652i | −0.883821 | − | 0.467826i | \(-0.845037\pi\) | ||
0.883821 | − | 0.467826i | \(-0.154963\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.14655 | − | 3.71794i | −0.0880001 | − | 0.152421i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.2487 | 0.624088 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.8793 | 0.526235 | 0.263117 | − | 0.964764i | \(-0.415249\pi\) | ||||
0.263117 | + | 0.964764i | \(0.415249\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.69615 | − | 4.66987i | −0.109978 | − | 0.190488i | 0.805783 | − | 0.592211i | \(-0.201745\pi\) |
−0.915761 | + | 0.401723i | \(0.868411\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.77174i | 0.275766i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.0718 | + | 6.39230i | 0.450133 | + | 0.259884i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.43414 | − | 4.21605i | 0.0987986 | − | 0.171124i | −0.812389 | − | 0.583116i | \(-0.801833\pi\) |
0.911188 | + | 0.411992i | \(0.135167\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.8923 | + | 8.59808i | −0.603467 | + | 0.348412i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 40.6304 | − | 11.7290i | 1.64373 | − | 0.474504i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.696152 | − | 0.401924i | 0.0281173 | − | 0.0162335i | −0.485875 | − | 0.874028i | \(-0.661499\pi\) |
0.513993 | + | 0.857795i | \(0.328166\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.91829 | − | 15.4469i | 0.359620 | − | 0.622880i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.0359 | + | 5.79423i | 0.404030 | + | 0.233267i | 0.688221 | − | 0.725501i | \(-0.258392\pi\) |
−0.284191 | + | 0.958768i | \(0.591725\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 9.25036i | − | 0.371803i | −0.982568 | − | 0.185902i | \(-0.940479\pi\) | ||
0.982568 | − | 0.185902i | \(-0.0595206\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.3038 | + | 26.5070i | 0.614122 | + | 1.06369i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.53242 | −0.221652 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.15208 | + | 10.6557i | 0.245690 | + | 0.425548i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 3.58846i | − | 0.143081i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.7418 | − | 14.2847i | −0.984955 | − | 0.568664i | −0.0811925 | − | 0.996698i | \(-0.525873\pi\) |
−0.903762 | + | 0.428034i | \(0.859206\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.8397 | − | 29.1673i | 0.669320 | − | 1.15930i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.43966 | − | 3.71794i | 0.255550 | − | 0.147542i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 35.9808 | − | 37.3923i | 1.42561 | − | 1.48154i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.16517 | + | 4.71416i | −0.323009 | + | 0.186489i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.69615 | − | 16.7942i | 0.382975 | − | 0.663332i | −0.608511 | − | 0.793545i | \(-0.708233\pi\) |
0.991486 | + | 0.130213i | \(0.0415662\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.4673 | + | 15.2809i | 1.04377 | + | 0.602620i | 0.920898 | − | 0.389803i | \(-0.127457\pi\) |
0.122870 | + | 0.992423i | \(0.460790\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 9.21539i | − | 0.362856i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.57691 | − | 9.65949i | −0.219251 | − | 0.379754i | 0.735328 | − | 0.677711i | \(-0.237028\pi\) |
−0.954579 | + | 0.297957i | \(0.903695\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.5692 | −0.807412 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −53.0236 | −2.07816 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.62436 | − | 13.2058i | −0.298364 | − | 0.516782i | 0.677398 | − | 0.735617i | \(-0.263108\pi\) |
−0.975762 | + | 0.218835i | \(0.929774\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.60770 | + | 4.39230i | 0.296804 | + | 0.171360i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.67345 | + | 6.36260i | −0.143097 | + | 0.247852i | −0.928661 | − | 0.370928i | \(-0.879040\pi\) |
0.785564 | + | 0.618780i | \(0.212373\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.3038 | + | 6.52628i | −0.439669 | + | 0.253843i | −0.703457 | − | 0.710738i | \(-0.748361\pi\) |
0.263788 | + | 0.964581i | \(0.415028\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.575167 | + | 1.99244i | 0.0223377 | + | 0.0773799i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 37.0526 | − | 21.3923i | 1.43684 | − | 0.829558i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.29863 | + | 14.3737i | −0.321324 | + | 0.556550i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.96410 | + | 2.86603i | 0.191923 | + | 0.110807i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 6.43966i | − | 0.248600i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.8923 | − | 20.5981i | −0.458415 | − | 0.793997i | 0.540463 | − | 0.841368i | \(-0.318249\pi\) |
−0.998877 | + | 0.0473705i | \(0.984916\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.53242 | −0.212943 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.46410 | 0.363735 | 0.181867 | − | 0.983323i | \(-0.441786\pi\) | ||||
0.181867 | + | 0.983323i | \(0.441786\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.7566 | + | 55.0041i | 1.21871 | + | 2.11086i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.1962i | 0.658958i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.29863 | + | 4.79122i | 0.317538 | + | 0.183331i | 0.650295 | − | 0.759682i | \(-0.274645\pi\) |
−0.332756 | + | 0.943013i | \(0.607979\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.1962 | + | 22.8564i | −0.504199 | + | 0.873298i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.996219 | + | 0.575167i | −0.0380081 | + | 0.0219440i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.53590 | − | 8.78461i | −0.0966100 | − | 0.334667i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.4783 | − | 19.9061i | 1.31162 | − | 0.757263i | 0.329254 | − | 0.944241i | \(-0.393203\pi\) |
0.982364 | + | 0.186979i | \(0.0598695\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.26795 | + | 12.5885i | −0.276087 | + | 0.478196i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.8755 | + | 8.01105i | 0.526329 | + | 0.303876i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.33975i | 0.126502i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.00727 | + | 15.6010i | 0.340686 | + | 0.590086i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.1051 | 1.21259 | 0.606297 | − | 0.795238i | \(-0.292654\pi\) | ||||
0.606297 | + | 0.795238i | \(0.292654\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.7621 | 1.34879 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.5359 | − | 25.1769i | −0.547454 | − | 0.948217i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 89.6929i | 3.37325i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.3038 | − | 13.4545i | −0.875194 | − | 0.505294i | −0.00612347 | − | 0.999981i | \(-0.501949\pi\) |
−0.869071 | + | 0.494688i | \(0.835283\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.14277 | − | 5.44344i | 0.117863 | − | 0.204145i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −44.3205 | + | 25.5885i | −1.65982 | + | 0.958295i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.7328 | − | 11.1538i | 0.401383 | − | 0.417129i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.60770 | + | 2.66025i | −0.172078 | + | 0.0993490i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.48415 | + | 11.2309i | −0.241818 | + | 0.418841i | −0.961232 | − | 0.275740i | \(-0.911077\pi\) |
0.719414 | + | 0.694581i | \(0.244410\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34.3923 | − | 19.8564i | −1.28084 | − | 0.739491i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 26.7549i | − | 0.995024i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.50000 | − | 2.59808i | −0.0557086 | − | 0.0964901i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.1724 | −0.636890 | −0.318445 | − | 0.947941i | \(-0.603161\pi\) | ||||
−0.318445 | + | 0.947941i | \(0.603161\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.1769 | 0.895441 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.862751 | + | 1.49433i | 0.0319100 | + | 0.0552698i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.7128i | 0.580366i | 0.956971 | + | 0.290183i | \(0.0937162\pi\) | ||||
−0.956971 | + | 0.290183i | \(0.906284\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −30.8939 | − | 17.8366i | −1.13954 | − | 0.657912i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.96410 | − | 8.59808i | 0.182855 | − | 0.316714i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.1814 | − | 18.0026i | 1.14703 | − | 0.662237i | 0.198867 | − | 0.980027i | \(-0.436274\pi\) |
0.948161 | + | 0.317790i | \(0.102941\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.8564 | + | 5.73205i | −0.729443 | + | 0.210572i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.0459 | + | 21.3885i | −1.35908 | + | 0.784667i | −0.989500 | − | 0.144530i | \(-0.953833\pi\) |
−0.369583 | + | 0.929198i | \(0.620500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.5885 | − | 20.0718i | 0.424568 | − | 0.735374i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.44344 | + | 3.14277i | 0.199165 | + | 0.114988i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.1962i | 0.628334i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.287584 | − | 0.498110i | −0.0104941 | − | 0.0181763i | 0.860731 | − | 0.509061i | \(-0.170007\pi\) |
−0.871225 | + | 0.490884i | \(0.836674\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 32.0333 | 1.16736 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.5007 | −0.673310 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.3038 | + | 19.5788i | 0.410845 | + | 0.711605i | 0.994982 | − | 0.100050i | \(-0.0319003\pi\) |
−0.584137 | + | 0.811655i | \(0.698567\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 14.7176i | − | 0.534217i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.76795 | − | 1.59808i | −0.100338 | − | 0.0579302i | 0.448991 | − | 0.893536i | \(-0.351783\pi\) |
−0.549329 | + | 0.835606i | \(0.685117\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.8755 | + | 24.0331i | −0.502328 | + | 0.870058i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.17691 | + | 0.679492i | −0.0425514 | + | 0.0245671i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.29863 | − | 33.5385i | 0.299646 | − | 1.21101i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.4808 | + | 21.0622i | −1.31553 | + | 0.759522i | −0.983006 | − | 0.183573i | \(-0.941234\pi\) |
−0.332524 | + | 0.943095i | \(0.607900\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.287584 | − | 0.498110i | 0.0103571 | − | 0.0179390i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.5526 | + | 8.40192i | 0.523419 | + | 0.302196i | 0.738332 | − | 0.674437i | \(-0.235614\pi\) |
−0.214913 | + | 0.976633i | \(0.568947\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 9.25036i | − | 0.332283i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −22.1603 | − | 38.3827i | −0.794995 | − | 1.37697i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −33.2835 | −1.19251 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8231 | 0.494629 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.29863 | + | 14.3737i | 0.296569 | + | 0.513673i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 8.78461i | − | 0.313536i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.3245 | + | 13.4664i | 0.831429 | + | 0.480026i | 0.854342 | − | 0.519712i | \(-0.173961\pi\) |
−0.0229126 | + | 0.999737i | \(0.507294\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.8923 | + | 25.7942i | −0.530180 | + | 0.918299i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 49.9253 | − | 28.8244i | 1.77514 | − | 1.02488i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.5000 | + | 2.59808i | 0.372866 | + | 0.0922604i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.44344 | + | 3.14277i | −0.193059 | + | 0.111463i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.3564 | + | 26.5981i | −0.543952 | + | 0.942152i | 0.454720 | + | 0.890634i | \(0.349739\pi\) |
−0.998672 | + | 0.0515179i | \(0.983594\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.71416 | + | 2.72172i | 0.166775 | + | 0.0962876i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.75129i | 0.0618787i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.43966 | − | 11.1538i | −0.227251 | − | 0.393610i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −51.1769 | −1.80375 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.71038 | 0.201015 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.76795 | + | 15.1865i | 0.308265 | + | 0.533930i | 0.977983 | − | 0.208685i | \(-0.0669184\pi\) |
−0.669718 | + | 0.742615i | \(0.733585\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 16.6862i | − | 0.585933i | −0.956123 | − | 0.292967i | \(-0.905358\pi\) | ||
0.956123 | − | 0.292967i | \(-0.0946425\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.8205 | + | 14.3301i | 0.870493 | + | 0.502579i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.9404 | + | 43.1980i | −0.873624 | + | 1.51316i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.8923 | + | 8.59808i | −0.521016 | + | 0.300809i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17.5935 | − | 16.9293i | −0.614766 | − | 0.591559i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.4282 | − | 22.1865i | 1.34115 | − | 0.774315i | 0.354177 | − | 0.935178i | \(-0.384761\pi\) |
0.986977 | + | 0.160863i | \(0.0514278\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.5990 | − | 37.4106i | 0.752894 | − | 1.30405i | −0.193520 | − | 0.981096i | \(-0.561991\pi\) |
0.946414 | − | 0.322955i | \(-0.104676\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.30385 | + | 1.33013i | 0.0802097 | + | 0.0463091i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 27.7511i | − | 0.965000i | −0.875896 | − | 0.482500i | \(-0.839729\pi\) | ||
0.875896 | − | 0.482500i | \(-0.160271\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.2846 | − | 38.5981i | −0.773976 | − | 1.34057i | −0.935368 | − | 0.353676i | \(-0.884932\pi\) |
0.161391 | − | 0.986890i | \(-0.448402\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.20413 | −0.145840 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.67949 | 0.231431 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.4618 | − | 38.9049i | −0.777321 | − | 1.34636i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 51.1769i | 1.76893i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.4562 | − | 10.6557i | −0.637180 | − | 0.367876i | 0.146347 | − | 0.989233i | \(-0.453248\pi\) |
−0.783527 | + | 0.621357i | \(0.786582\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | − | 17.3205i | 0.344828 | − | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.7328 | + | 6.19657i | −0.369656 | + | 0.213421i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.8564 | + | 22.0000i | 0.476675 | + | 0.756823i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.6045 | + | 14.7828i | −0.879782 | + | 0.507943i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.2321 | + | 21.1865i | −0.419803 | + | 0.727120i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.0459 | − | 21.3885i | −1.26992 | − | 0.733188i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.0718i | 1.20084i | 0.799687 | + | 0.600418i | \(0.204999\pi\) | ||||
−0.799687 | + | 0.600418i | \(0.795001\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.77174 | − | 11.7290i | −0.231588 | − | 0.401123i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.0333 | 1.33335 | 0.666676 | − | 0.745347i | \(-0.267716\pi\) | ||||
0.666676 | + | 0.745347i | \(0.267716\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.6244 | + | 35.7224i | 0.702876 | + | 1.21742i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 12.8793i | − | 0.438417i | −0.975678 | − | 0.219209i | \(-0.929652\pi\) | ||
0.975678 | − | 0.219209i | \(-0.0703475\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.1962 | + | 9.92820i | 0.584687 | + | 0.337569i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.4007 | − | 18.0145i | 0.353226 | − | 0.611806i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.98076 | + | 4.60770i | −0.270729 | + | 0.156305i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0166 | + | 11.5630i | 0.407166 | + | 0.391796i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.4115 | − | 10.0526i | 0.589291 | − | 0.340228i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27.7511 | − | 48.0663i | 0.938158 | − | 1.62494i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.6769 | − | 10.2058i | −0.596907 | − | 0.344624i | 0.170917 | − | 0.985285i | \(-0.445327\pi\) |
−0.767824 | + | 0.640661i | \(0.778660\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31.2259i | 1.05322i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.83975 | − | 8.38269i | −0.163055 | − | 0.282420i | 0.772908 | − | 0.634518i | \(-0.218802\pi\) |
−0.935963 | + | 0.352099i | \(0.885468\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.6304 | −1.36732 | −0.683661 | − | 0.729800i | \(-0.739613\pi\) | ||||
−0.683661 | + | 0.729800i | \(0.739613\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23.7513 | −0.798391 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.3597 | + | 35.2640i | 0.683612 | + | 1.18405i | 0.973871 | + | 0.227102i | \(0.0729251\pi\) |
−0.290259 | + | 0.956948i | \(0.593742\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.1962i | 0.576740i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.58069 | − | 2.64466i | −0.153459 | − | 0.0885996i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −27.1244 | + | 46.9808i | −0.907682 | + | 1.57215i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.43966 | − | 3.71794i | 0.215254 | − | 0.124277i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.9974 | + | 5.93782i | 0.801251 | + | 0.198258i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.0331 | + | 13.8755i | −0.801550 | + | 0.462775i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.588457 | − | 1.01924i | 0.0196044 | − | 0.0339557i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 18.4562 | + | 10.6557i | 0.614185 | + | 0.354600i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 32.7846i | 1.08980i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.8811 | + | 30.9709i | 0.593731 | + | 1.02837i | 0.993725 | + | 0.111855i | \(0.0356791\pi\) |
−0.399993 | + | 0.916518i | \(0.630988\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 28.3923 | 0.941713 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.0015 | 1.22591 | 0.612956 | − | 0.790117i | \(-0.289980\pi\) | ||||
0.612956 | + | 0.790117i | \(0.289980\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.60770 | − | 7.98076i | −0.152492 | − | 0.264125i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 7.43588i | − | 0.245823i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.287584 | − | 0.498110i | 0.00948651 | − | 0.0164311i | −0.861243 | − | 0.508193i | \(-0.830314\pi\) |
0.870730 | + | 0.491762i | \(0.163647\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.03332 | + | 3.48334i | −0.198805 | + | 0.114780i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.57691 | + | 22.5388i | −0.183566 | + | 0.741874i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.69615 | − | 3.86603i | 0.220168 | − | 0.127114i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.28555 | + | 10.8869i | −0.206444 | + | 0.357572i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.55256 | − | 3.20577i | −0.182174 | − | 0.105178i | 0.406140 | − | 0.913811i | \(-0.366875\pi\) |
−0.588313 | + | 0.808633i | \(0.700208\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 66.5670i | 2.18165i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.4641 | − | 19.8564i | −0.375318 | − | 0.650070i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.99244 | 0.0651597 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.1769 | −1.21452 | −0.607258 | − | 0.794504i | \(-0.707731\pi\) | ||||
−0.607258 | + | 0.794504i | \(0.707731\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.20035 | + | 9.00727i | 0.169707 | + | 0.293941i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.7846i | 1.19914i | 0.800321 | + | 0.599572i | \(0.204663\pi\) | ||||
−0.800321 | + | 0.599572i | \(0.795337\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.4783 | + | 19.9061i | 1.12277 | + | 0.648231i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −25.5885 | + | 44.3205i | −0.832393 | + | 1.44175i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.6101 | + | 17.0954i | −0.962198 | + | 0.555525i | −0.896849 | − | 0.442337i | \(-0.854149\pi\) |
−0.0653489 | + | 0.997862i | \(0.520816\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.7846 | − | 6.00000i | 0.674697 | − | 0.194768i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.29311 | + | 2.47863i | −0.139214 | + | 0.0803750i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.356406 | − | 0.617314i | 0.0115451 | − | 0.0199968i | −0.860195 | − | 0.509965i | \(-0.829658\pi\) |
0.871740 | + | 0.489968i | \(0.162992\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.4618 | + | 12.9683i | 0.726846 | + | 0.419644i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 7.98076i | − | 0.257981i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −30.5173 | − | 52.8575i | −0.985455 | − | 1.70686i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −54.5692 | −1.76030 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.44344 | 0.175413 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.7321 | − | 34.1769i | −0.635197 | − | 1.10019i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 16.5083i | − | 0.530871i | −0.964129 | − | 0.265435i | \(-0.914484\pi\) | ||
0.964129 | − | 0.265435i | \(-0.0855157\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.30385 | − | 1.33013i | −0.0740102 | − | 0.0427298i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.6418 | − | 28.8244i | 0.534059 | − | 0.925018i | −0.465149 | − | 0.885232i | \(-0.653999\pi\) |
0.999208 | − | 0.0397855i | \(-0.0126675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.0885 | + | 18.5263i | −1.02871 | + | 0.593925i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.09828 | + | 3.21983i | −0.0992245 | + | 0.103117i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.03590 | + | 0.598076i | −0.0331413 | + | 0.0191342i | −0.516479 | − | 0.856300i | \(-0.672758\pi\) |
0.483338 | + | 0.875434i | \(0.339424\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.28380 | − | 2.22361i | 0.0410305 | − | 0.0710670i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.60770 | + | 4.39230i | 0.242895 | + | 0.140236i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.5787i | 0.337407i | 0.985667 | + | 0.168703i | \(0.0539580\pi\) | ||||
−0.985667 | + | 0.168703i | \(0.946042\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.5885 | − | 40.8564i | −0.751591 | − | 1.30179i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 67.2312 | 2.13999 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.5692 | 0.654063 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.3059 | − | 29.9747i | −0.549740 | − | 0.952178i | −0.998292 | − | 0.0584210i | \(-0.981393\pi\) |
0.448552 | − | 0.893757i | \(-0.351940\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.48334i | 0.110540i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.3114 | + | 12.3042i | 0.675618 | + | 0.390068i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.5000 | − | 25.1147i | 0.459220 | − | 0.795392i | −0.539700 | − | 0.841857i | \(-0.681462\pi\) |
0.998920 | + | 0.0464655i | \(0.0147958\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −37.0459 | + | 21.3885i | −1.17208 | + | 0.676702i |
(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 | 416.2.w.c.257.2 | yes | 8 | |
4.3 | odd | 2 | inner | 416.2.w.c.257.3 | yes | 8 | |
8.3 | odd | 2 | 832.2.w.h.257.2 | 8 | |||
8.5 | even | 2 | 832.2.w.h.257.3 | 8 | |||
13.2 | odd | 12 | 5408.2.a.bg.1.3 | 4 | |||
13.4 | even | 6 | inner | 416.2.w.c.225.2 | ✓ | 8 | |
13.11 | odd | 12 | 5408.2.a.bk.1.3 | 4 | |||
52.11 | even | 12 | 5408.2.a.bk.1.2 | 4 | |||
52.15 | even | 12 | 5408.2.a.bg.1.2 | 4 | |||
52.43 | odd | 6 | inner | 416.2.w.c.225.3 | yes | 8 | |
104.43 | odd | 6 | 832.2.w.h.641.2 | 8 | |||
104.69 | even | 6 | 832.2.w.h.641.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
416.2.w.c.225.2 | ✓ | 8 | 13.4 | even | 6 | inner | |
416.2.w.c.225.3 | yes | 8 | 52.43 | odd | 6 | inner | |
416.2.w.c.257.2 | yes | 8 | 1.1 | even | 1 | trivial | |
416.2.w.c.257.3 | yes | 8 | 4.3 | odd | 2 | inner | |
832.2.w.h.257.2 | 8 | 8.3 | odd | 2 | |||
832.2.w.h.257.3 | 8 | 8.5 | even | 2 | |||
832.2.w.h.641.2 | 8 | 104.43 | odd | 6 | |||
832.2.w.h.641.3 | 8 | 104.69 | even | 6 | |||
5408.2.a.bg.1.2 | 4 | 52.15 | even | 12 | |||
5408.2.a.bg.1.3 | 4 | 13.2 | odd | 12 | |||
5408.2.a.bk.1.2 | 4 | 52.11 | even | 12 | |||
5408.2.a.bk.1.3 | 4 | 13.11 | odd | 12 |