Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(246,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("637.246");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.c (of order \(2\), degree \(1\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10x^{14} + 121x^{12} + 296x^{10} + 3468x^{8} - 1748x^{6} + 40192x^{4} - 65056x^{2} + 228484 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 246.12 | ||
Root | \(1.41421 + 1.52340i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.246 |
Dual form | 637.2.c.g.246.6 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.52340i | 1.07720i | 0.842561 | + | 0.538602i | \(0.181047\pi\) | ||||
−0.842561 | + | 0.538602i | \(0.818953\pi\) | |||||||
\(3\) | 2.99510 | 1.72922 | 0.864611 | − | 0.502442i | \(-0.167565\pi\) | ||||
0.864611 | + | 0.502442i | \(0.167565\pi\) | |||||||
\(4\) | −0.320733 | −0.160367 | ||||||||
\(5\) | − | 2.94606i | − | 1.31752i | −0.752354 | − | 0.658759i | \(-0.771082\pi\) | ||
0.752354 | − | 0.658759i | \(-0.228918\pi\) | |||||||
\(6\) | 4.56272i | 1.86272i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.55819i | 0.904456i | ||||||||
\(9\) | 5.97063 | 1.99021 | ||||||||
\(10\) | 4.48801 | 1.41923 | ||||||||
\(11\) | 2.37108i | 0.714908i | 0.933931 | + | 0.357454i | \(0.116355\pi\) | ||||
−0.933931 | + | 0.357454i | \(0.883645\pi\) | |||||||
\(12\) | −0.960628 | −0.277309 | ||||||||
\(13\) | 2.32734 | − | 2.75381i | 0.645489 | − | 0.763770i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 8.82374i | − | 2.27828i | ||||||
\(16\) | −4.53860 | −1.13465 | ||||||||
\(17\) | −5.36994 | −1.30240 | −0.651201 | − | 0.758905i | \(-0.725735\pi\) | ||||
−0.651201 | + | 0.758905i | \(0.725735\pi\) | |||||||
\(18\) | 9.09563i | 2.14386i | ||||||||
\(19\) | − | 5.35438i | − | 1.22838i | −0.789159 | − | 0.614189i | \(-0.789483\pi\) | ||
0.789159 | − | 0.614189i | \(-0.210517\pi\) | |||||||
\(20\) | 0.944899i | 0.211286i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.61209 | −0.770101 | ||||||||
\(23\) | −2.79056 | −0.581873 | −0.290936 | − | 0.956742i | \(-0.593967\pi\) | ||||
−0.290936 | + | 0.956742i | \(0.593967\pi\) | |||||||
\(24\) | 7.66203i | 1.56400i | ||||||||
\(25\) | −3.67927 | −0.735853 | ||||||||
\(26\) | 4.19514 | + | 3.54546i | 0.822735 | + | 0.695323i | ||||
\(27\) | 8.89733 | 1.71229 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.585818 | 0.108784 | 0.0543918 | − | 0.998520i | \(-0.482678\pi\) | ||||
0.0543918 | + | 0.998520i | \(0.482678\pi\) | |||||||
\(30\) | 13.4421 | 2.45417 | ||||||||
\(31\) | 8.33379i | 1.49679i | 0.663252 | + | 0.748397i | \(0.269176\pi\) | ||||
−0.663252 | + | 0.748397i | \(0.730824\pi\) | |||||||
\(32\) | − | 1.79770i | − | 0.317792i | ||||||
\(33\) | 7.10163i | 1.23623i | ||||||||
\(34\) | − | 8.18054i | − | 1.40295i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.91498 | −0.319163 | ||||||||
\(37\) | − | 0.675710i | − | 0.111086i | −0.998456 | − | 0.0555430i | \(-0.982311\pi\) | ||
0.998456 | − | 0.0555430i | \(-0.0176890\pi\) | |||||||
\(38\) | 8.15683 | 1.32321 | ||||||||
\(39\) | 6.97063 | − | 8.24794i | 1.11619 | − | 1.32073i | ||||
\(40\) | 7.53657 | 1.19164 | ||||||||
\(41\) | 11.2799i | 1.76162i | 0.473473 | + | 0.880808i | \(0.343000\pi\) | ||||
−0.473473 | + | 0.880808i | \(0.657000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.5271 | −1.60536 | −0.802682 | − | 0.596408i | \(-0.796594\pi\) | ||||
−0.802682 | + | 0.596408i | \(0.796594\pi\) | |||||||
\(44\) | − | 0.760484i | − | 0.114647i | ||||||
\(45\) | − | 17.5898i | − | 2.62214i | ||||||
\(46\) | − | 4.25113i | − | 0.626795i | ||||||
\(47\) | − | 0.537744i | − | 0.0784380i | −0.999231 | − | 0.0392190i | \(-0.987513\pi\) | ||
0.999231 | − | 0.0392190i | \(-0.0124870\pi\) | |||||||
\(48\) | −13.5936 | −1.96206 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 5.60498i | − | 0.792664i | ||||||
\(51\) | −16.0835 | −2.25214 | ||||||||
\(52\) | −0.746456 | + | 0.883239i | −0.103515 | + | 0.122483i | ||||
\(53\) | 7.90345 | 1.08562 | 0.542811 | − | 0.839855i | \(-0.317360\pi\) | ||||
0.542811 | + | 0.839855i | \(0.317360\pi\) | |||||||
\(54\) | 13.5541i | 1.84449i | ||||||||
\(55\) | 6.98535 | 0.941904 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 16.0369i | − | 2.12414i | ||||||
\(58\) | 0.892432i | 0.117182i | ||||||||
\(59\) | 6.14603i | 0.800145i | 0.916484 | + | 0.400072i | \(0.131015\pi\) | ||||
−0.916484 | + | 0.400072i | \(0.868985\pi\) | |||||||
\(60\) | 2.83007i | 0.365360i | ||||||||
\(61\) | −2.78689 | −0.356824 | −0.178412 | − | 0.983956i | \(-0.557096\pi\) | ||||
−0.178412 | + | 0.983956i | \(0.557096\pi\) | |||||||
\(62\) | −12.6957 | −1.61235 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.33858 | −0.792323 | ||||||||
\(65\) | −8.11289 | − | 6.85649i | −1.00628 | − | 0.850443i | ||||
\(66\) | −10.8186 | −1.33168 | ||||||||
\(67\) | 4.21353i | 0.514765i | 0.966310 | + | 0.257382i | \(0.0828600\pi\) | ||||
−0.966310 | + | 0.257382i | \(0.917140\pi\) | |||||||
\(68\) | 1.72232 | 0.208862 | ||||||||
\(69\) | −8.35802 | −1.00619 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.25151i | 0.148527i | 0.997239 | + | 0.0742637i | \(0.0236607\pi\) | ||||
−0.997239 | + | 0.0742637i | \(0.976339\pi\) | |||||||
\(72\) | 15.2740i | 1.80006i | ||||||||
\(73\) | − | 10.8620i | − | 1.27130i | −0.771977 | − | 0.635650i | \(-0.780732\pi\) | ||
0.771977 | − | 0.635650i | \(-0.219268\pi\) | |||||||
\(74\) | 1.02937 | 0.119662 | ||||||||
\(75\) | −11.0198 | −1.27245 | ||||||||
\(76\) | 1.71733i | 0.196991i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 12.5649 | + | 10.6190i | 1.42269 | + | 1.20237i | ||||
\(79\) | 6.29136 | 0.707833 | 0.353917 | − | 0.935277i | \(-0.384850\pi\) | ||||
0.353917 | + | 0.935277i | \(0.384850\pi\) | |||||||
\(80\) | 13.3710i | 1.49492i | ||||||||
\(81\) | 8.73651 | 0.970723 | ||||||||
\(82\) | −17.1837 | −1.89762 | ||||||||
\(83\) | − | 1.74725i | − | 0.191786i | −0.995392 | − | 0.0958928i | \(-0.969429\pi\) | ||
0.995392 | − | 0.0958928i | \(-0.0305706\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.8202i | 1.71594i | ||||||||
\(86\) | − | 16.0369i | − | 1.72930i | ||||||
\(87\) | 1.75458 | 0.188111 | ||||||||
\(88\) | −6.06567 | −0.646602 | ||||||||
\(89\) | − | 10.2343i | − | 1.08483i | −0.840110 | − | 0.542416i | \(-0.817510\pi\) | ||
0.840110 | − | 0.542416i | \(-0.182490\pi\) | |||||||
\(90\) | 26.7963 | 2.82457 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.895027 | 0.0933130 | ||||||||
\(93\) | 24.9605i | 2.58829i | ||||||||
\(94\) | 0.819196 | 0.0844936 | ||||||||
\(95\) | −15.7743 | −1.61841 | ||||||||
\(96\) | − | 5.38430i | − | 0.549533i | ||||||
\(97\) | − | 9.90640i | − | 1.00584i | −0.864332 | − | 0.502921i | \(-0.832259\pi\) | ||
0.864332 | − | 0.502921i | \(-0.167741\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.1568i | 1.42282i | ||||||||
\(100\) | 1.18006 | 0.118006 | ||||||||
\(101\) | 2.05077 | 0.204059 | 0.102030 | − | 0.994781i | \(-0.467466\pi\) | ||||
0.102030 | + | 0.994781i | \(0.467466\pi\) | |||||||
\(102\) | − | 24.5016i | − | 2.42602i | ||||||
\(103\) | 3.02962 | 0.298517 | 0.149259 | − | 0.988798i | \(-0.452311\pi\) | ||||
0.149259 | + | 0.988798i | \(0.452311\pi\) | |||||||
\(104\) | 7.04476 | + | 5.95378i | 0.690796 | + | 0.583816i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.0401i | 1.16944i | ||||||||
\(107\) | −12.4305 | −1.20170 | −0.600852 | − | 0.799360i | \(-0.705172\pi\) | ||||
−0.600852 | + | 0.799360i | \(0.705172\pi\) | |||||||
\(108\) | −2.85367 | −0.274594 | ||||||||
\(109\) | − | 3.53782i | − | 0.338862i | −0.985542 | − | 0.169431i | \(-0.945807\pi\) | ||
0.985542 | − | 0.169431i | \(-0.0541929\pi\) | |||||||
\(110\) | 10.6414i | 1.01462i | ||||||||
\(111\) | − | 2.02382i | − | 0.192092i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.3848 | 0.976921 | 0.488460 | − | 0.872586i | \(-0.337559\pi\) | ||||
0.488460 | + | 0.872586i | \(0.337559\pi\) | |||||||
\(114\) | 24.4305 | 2.28813 | ||||||||
\(115\) | 8.22117i | 0.766628i | ||||||||
\(116\) | −0.187891 | −0.0174453 | ||||||||
\(117\) | 13.8957 | − | 16.4420i | 1.28466 | − | 1.52006i | ||||
\(118\) | −9.36283 | −0.861918 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 22.5728 | 2.06060 | ||||||||
\(121\) | 5.37797 | 0.488907 | ||||||||
\(122\) | − | 4.24553i | − | 0.384372i | ||||||
\(123\) | 33.7843i | 3.04623i | ||||||||
\(124\) | − | 2.67292i | − | 0.240036i | ||||||
\(125\) | − | 3.89096i | − | 0.348018i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.09504 | −0.452112 | −0.226056 | − | 0.974114i | \(-0.572583\pi\) | ||||
−0.226056 | + | 0.974114i | \(0.572583\pi\) | |||||||
\(128\) | − | 13.2516i | − | 1.17128i | ||||||
\(129\) | −31.5296 | −2.77603 | ||||||||
\(130\) | 10.4451 | − | 12.3591i | 0.916100 | − | 1.08397i | ||||
\(131\) | −22.5443 | −1.96971 | −0.984854 | − | 0.173386i | \(-0.944529\pi\) | ||||
−0.984854 | + | 0.173386i | \(0.944529\pi\) | |||||||
\(132\) | − | 2.27773i | − | 0.198251i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.41887 | −0.554506 | ||||||||
\(135\) | − | 26.2121i | − | 2.25597i | ||||||
\(136\) | − | 13.7373i | − | 1.17797i | ||||||
\(137\) | − | 1.03479i | − | 0.0884082i | −0.999023 | − | 0.0442041i | \(-0.985925\pi\) | ||
0.999023 | − | 0.0442041i | \(-0.0140752\pi\) | |||||||
\(138\) | − | 12.7326i | − | 1.08387i | ||||||
\(139\) | −8.49456 | −0.720499 | −0.360249 | − | 0.932856i | \(-0.617308\pi\) | ||||
−0.360249 | + | 0.932856i | \(0.617308\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 1.61060i | − | 0.135637i | ||||||
\(142\) | −1.90655 | −0.159994 | ||||||||
\(143\) | 6.52951 | + | 5.51832i | 0.546025 | + | 0.461465i | ||||
\(144\) | −27.0983 | −2.25819 | ||||||||
\(145\) | − | 1.72585i | − | 0.143324i | ||||||
\(146\) | 16.5471 | 1.36945 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.216723i | 0.0178145i | ||||||||
\(149\) | 4.31343i | 0.353370i | 0.984267 | + | 0.176685i | \(0.0565374\pi\) | ||||
−0.984267 | + | 0.176685i | \(0.943463\pi\) | |||||||
\(150\) | − | 16.7875i | − | 1.37069i | ||||||
\(151\) | − | 12.2447i | − | 0.996463i | −0.867044 | − | 0.498232i | \(-0.833983\pi\) | ||
0.867044 | − | 0.498232i | \(-0.166017\pi\) | |||||||
\(152\) | 13.6975 | 1.11101 | ||||||||
\(153\) | −32.0619 | −2.59205 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 24.5518 | 1.97205 | ||||||||
\(156\) | −2.23571 | + | 2.64539i | −0.179000 | + | 0.211801i | ||||
\(157\) | 22.2040 | 1.77207 | 0.886035 | − | 0.463619i | \(-0.153449\pi\) | ||||
0.886035 | + | 0.463619i | \(0.153449\pi\) | |||||||
\(158\) | 9.58423i | 0.762480i | ||||||||
\(159\) | 23.6716 | 1.87728 | ||||||||
\(160\) | −5.29614 | −0.418697 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 13.3092i | 1.04567i | ||||||||
\(163\) | − | 11.3644i | − | 0.890127i | −0.895499 | − | 0.445063i | \(-0.853181\pi\) | ||
0.895499 | − | 0.445063i | \(-0.146819\pi\) | |||||||
\(164\) | − | 3.61782i | − | 0.282505i | ||||||
\(165\) | 20.9218 | 1.62876 | ||||||||
\(166\) | 2.66175 | 0.206592 | ||||||||
\(167\) | − | 1.88127i | − | 0.145577i | −0.997347 | − | 0.0727885i | \(-0.976810\pi\) | ||
0.997347 | − | 0.0727885i | \(-0.0231898\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.16695 | − | 12.8181i | −0.166688 | − | 0.986010i | ||||
\(170\) | −24.1004 | −1.84841 | ||||||||
\(171\) | − | 31.9690i | − | 2.44473i | ||||||
\(172\) | 3.37638 | 0.257447 | ||||||||
\(173\) | −5.57113 | −0.423565 | −0.211783 | − | 0.977317i | \(-0.567927\pi\) | ||||
−0.211783 | + | 0.977317i | \(0.567927\pi\) | |||||||
\(174\) | 2.67292i | 0.202634i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 10.7614i | − | 0.811170i | ||||||
\(177\) | 18.4080i | 1.38363i | ||||||||
\(178\) | 15.5909 | 1.16858 | ||||||||
\(179\) | 4.66142 | 0.348411 | 0.174205 | − | 0.984709i | \(-0.444264\pi\) | ||||
0.174205 | + | 0.984709i | \(0.444264\pi\) | |||||||
\(180\) | 5.64164i | 0.420503i | ||||||||
\(181\) | 12.5360 | 0.931794 | 0.465897 | − | 0.884839i | \(-0.345732\pi\) | ||||
0.465897 | + | 0.884839i | \(0.345732\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.34701 | −0.617029 | ||||||||
\(184\) | − | 7.13879i | − | 0.526278i | ||||||
\(185\) | −1.99068 | −0.146358 | ||||||||
\(186\) | −38.0248 | −2.78811 | ||||||||
\(187\) | − | 12.7326i | − | 0.931098i | ||||||
\(188\) | 0.172472i | 0.0125788i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 24.0305i | − | 1.74336i | ||||||
\(191\) | −1.31764 | −0.0953408 | −0.0476704 | − | 0.998863i | \(-0.515180\pi\) | ||||
−0.0476704 | + | 0.998863i | \(0.515180\pi\) | |||||||
\(192\) | −18.9847 | −1.37010 | ||||||||
\(193\) | 15.1445i | 1.09012i | 0.838396 | + | 0.545061i | \(0.183494\pi\) | ||||
−0.838396 | + | 0.545061i | \(0.816506\pi\) | |||||||
\(194\) | 15.0914 | 1.08350 | ||||||||
\(195\) | −24.2989 | − | 20.5359i | −1.74008 | − | 1.47061i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.90571i | 0.705753i | 0.935670 | + | 0.352876i | \(0.114796\pi\) | ||||
−0.935670 | + | 0.352876i | \(0.885204\pi\) | |||||||
\(198\) | −21.5665 | −1.53266 | ||||||||
\(199\) | −8.57326 | −0.607742 | −0.303871 | − | 0.952713i | \(-0.598279\pi\) | ||||
−0.303871 | + | 0.952713i | \(0.598279\pi\) | |||||||
\(200\) | − | 9.41225i | − | 0.665547i | ||||||
\(201\) | 12.6199i | 0.890142i | ||||||||
\(202\) | 3.12413i | 0.219813i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.15852 | 0.361169 | ||||||||
\(205\) | 33.2311 | 2.32096 | ||||||||
\(206\) | 4.61530i | 0.321564i | ||||||||
\(207\) | −16.6614 | −1.15805 | ||||||||
\(208\) | −10.5629 | + | 12.4984i | −0.732403 | + | 0.866611i | ||||
\(209\) | 12.6957 | 0.878177 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.44515 | −0.0994881 | −0.0497440 | − | 0.998762i | \(-0.515841\pi\) | ||||
−0.0497440 | + | 0.998762i | \(0.515841\pi\) | |||||||
\(212\) | −2.53490 | −0.174098 | ||||||||
\(213\) | 3.74841i | 0.256837i | ||||||||
\(214\) | − | 18.9366i | − | 1.29448i | ||||||
\(215\) | 31.0134i | 2.11510i | ||||||||
\(216\) | 22.7610i | 1.54869i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.38950 | 0.365023 | ||||||||
\(219\) | − | 32.5328i | − | 2.19836i | ||||||
\(220\) | −2.24043 | −0.151050 | ||||||||
\(221\) | −12.4977 | + | 14.7878i | −0.840686 | + | 0.994735i | ||||
\(222\) | 3.08307 | 0.206922 | ||||||||
\(223\) | − | 14.9949i | − | 1.00413i | −0.864829 | − | 0.502067i | \(-0.832573\pi\) | ||
0.864829 | − | 0.502067i | \(-0.167427\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −21.9675 | −1.46450 | ||||||||
\(226\) | 15.8202i | 1.05234i | ||||||||
\(227\) | − | 1.14220i | − | 0.0758105i | −0.999281 | − | 0.0379052i | \(-0.987932\pi\) | ||
0.999281 | − | 0.0379052i | \(-0.0120685\pi\) | |||||||
\(228\) | 5.14356i | 0.340641i | ||||||||
\(229\) | 6.26935i | 0.414290i | 0.978310 | + | 0.207145i | \(0.0664172\pi\) | ||||
−0.978310 | + | 0.207145i | \(0.933583\pi\) | |||||||
\(230\) | −12.5241 | −0.825814 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.49863i | 0.0983900i | ||||||||
\(233\) | 6.16695 | 0.404010 | 0.202005 | − | 0.979384i | \(-0.435254\pi\) | ||||
0.202005 | + | 0.979384i | \(0.435254\pi\) | |||||||
\(234\) | 25.0476 | + | 21.1686i | 1.63741 | + | 1.38384i | ||||
\(235\) | −1.58423 | −0.103343 | ||||||||
\(236\) | − | 1.97124i | − | 0.128317i | ||||||
\(237\) | 18.8433 | 1.22400 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.4589i | 1.77617i | 0.459684 | + | 0.888083i | \(0.347963\pi\) | ||||
−0.459684 | + | 0.888083i | \(0.652037\pi\) | |||||||
\(240\) | 40.0474i | 2.58505i | ||||||||
\(241\) | − | 9.79378i | − | 0.630873i | −0.948947 | − | 0.315436i | \(-0.897849\pi\) | ||
0.948947 | − | 0.315436i | \(-0.102151\pi\) | |||||||
\(242\) | 8.19278i | 0.526652i | ||||||||
\(243\) | −0.525262 | −0.0336956 | ||||||||
\(244\) | 0.893848 | 0.0572227 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −51.4668 | −3.28140 | ||||||||
\(247\) | −14.7449 | − | 12.4615i | −0.938198 | − | 0.792904i | ||||
\(248\) | −21.3194 | −1.35378 | ||||||||
\(249\) | − | 5.23319i | − | 0.331640i | ||||||
\(250\) | 5.92747 | 0.374886 | ||||||||
\(251\) | 12.4945 | 0.788644 | 0.394322 | − | 0.918972i | \(-0.370979\pi\) | ||||
0.394322 | + | 0.918972i | \(0.370979\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6.61665i | − | 0.415985i | ||||||
\(254\) | − | 7.76176i | − | 0.487016i | ||||||
\(255\) | 47.3830i | 2.96724i | ||||||||
\(256\) | 7.51022 | 0.469389 | ||||||||
\(257\) | 19.1929 | 1.19722 | 0.598610 | − | 0.801040i | \(-0.295720\pi\) | ||||
0.598610 | + | 0.801040i | \(0.295720\pi\) | |||||||
\(258\) | − | 48.0321i | − | 2.99035i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.60207 | + | 2.19910i | 0.161374 | + | 0.136383i | ||||
\(261\) | 3.49770 | 0.216502 | ||||||||
\(262\) | − | 34.3439i | − | 2.12178i | ||||||
\(263\) | 28.8153 | 1.77683 | 0.888415 | − | 0.459041i | \(-0.151807\pi\) | ||||
0.888415 | + | 0.459041i | \(0.151807\pi\) | |||||||
\(264\) | −18.1673 | −1.11812 | ||||||||
\(265\) | − | 23.2840i | − | 1.43033i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 30.6527i | − | 1.87592i | ||||||
\(268\) | − | 1.35142i | − | 0.0825511i | ||||||
\(269\) | −8.15419 | −0.497170 | −0.248585 | − | 0.968610i | \(-0.579965\pi\) | ||||
−0.248585 | + | 0.968610i | \(0.579965\pi\) | |||||||
\(270\) | 39.9313 | 2.43014 | ||||||||
\(271\) | − | 18.5788i | − | 1.12858i | −0.825577 | − | 0.564290i | \(-0.809150\pi\) | ||
0.825577 | − | 0.564290i | \(-0.190850\pi\) | |||||||
\(272\) | 24.3720 | 1.47777 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.57640 | 0.0952336 | ||||||||
\(275\) | − | 8.72384i | − | 0.526067i | ||||||
\(276\) | 2.68069 | 0.161359 | ||||||||
\(277\) | 17.2342 | 1.03550 | 0.517752 | − | 0.855531i | \(-0.326769\pi\) | ||||
0.517752 | + | 0.855531i | \(0.326769\pi\) | |||||||
\(278\) | − | 12.9406i | − | 0.776124i | ||||||
\(279\) | 49.7580i | 2.97893i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 11.4691i | − | 0.684191i | −0.939665 | − | 0.342096i | \(-0.888863\pi\) | ||
0.939665 | − | 0.342096i | \(-0.111137\pi\) | |||||||
\(282\) | 2.45358 | 0.146108 | ||||||||
\(283\) | 1.45575 | 0.0865355 | 0.0432678 | − | 0.999064i | \(-0.486223\pi\) | ||||
0.0432678 | + | 0.999064i | \(0.486223\pi\) | |||||||
\(284\) | − | 0.401402i | − | 0.0238188i | ||||||
\(285\) | −47.2456 | −2.79859 | ||||||||
\(286\) | −8.40658 | + | 9.94702i | −0.497092 | + | 0.588180i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 10.7334i | − | 0.632472i | ||||||
\(289\) | 11.8363 | 0.696252 | ||||||||
\(290\) | 2.62916 | 0.154389 | ||||||||
\(291\) | − | 29.6707i | − | 1.73932i | ||||||
\(292\) | 3.48380i | 0.203874i | ||||||||
\(293\) | 30.6962i | 1.79329i | 0.442750 | + | 0.896645i | \(0.354003\pi\) | ||||
−0.442750 | + | 0.896645i | \(0.645997\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.1066 | 1.05421 | ||||||||
\(296\) | 1.72859 | 0.100472 | ||||||||
\(297\) | 21.0963i | 1.22413i | ||||||||
\(298\) | −6.57107 | −0.380652 | ||||||||
\(299\) | −6.49460 | + | 7.68469i | −0.375592 | + | 0.444417i | ||||
\(300\) | 3.53441 | 0.204059 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 18.6536 | 1.07339 | ||||||||
\(303\) | 6.14226 | 0.352864 | ||||||||
\(304\) | 24.3013i | 1.39378i | ||||||||
\(305\) | 8.21034i | 0.470123i | ||||||||
\(306\) | − | 48.8430i | − | 2.79217i | ||||||
\(307\) | 21.2602i | 1.21339i | 0.794936 | + | 0.606693i | \(0.207504\pi\) | ||||
−0.794936 | + | 0.606693i | \(0.792496\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.07401 | 0.516202 | ||||||||
\(310\) | 37.4022i | 2.12430i | ||||||||
\(311\) | 4.44647 | 0.252136 | 0.126068 | − | 0.992022i | \(-0.459764\pi\) | ||||
0.126068 | + | 0.992022i | \(0.459764\pi\) | |||||||
\(312\) | 21.0998 | + | 17.8322i | 1.19454 | + | 1.00955i | ||||
\(313\) | 2.28687 | 0.129261 | 0.0646307 | − | 0.997909i | \(-0.479413\pi\) | ||||
0.0646307 | + | 0.997909i | \(0.479413\pi\) | |||||||
\(314\) | 33.8254i | 1.90888i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.01785 | −0.113513 | ||||||||
\(317\) | 8.10086i | 0.454990i | 0.973779 | + | 0.227495i | \(0.0730535\pi\) | ||||
−0.973779 | + | 0.227495i | \(0.926947\pi\) | |||||||
\(318\) | 36.0613i | 2.02222i | ||||||||
\(319\) | 1.38902i | 0.0777703i | ||||||||
\(320\) | 18.6738i | 1.04390i | ||||||||
\(321\) | −37.2307 | −2.07801 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28.7527i | 1.59984i | ||||||||
\(324\) | −2.80209 | −0.155672 | ||||||||
\(325\) | −8.56292 | + | 10.1320i | −0.474985 | + | 0.562022i | ||||
\(326\) | 17.3124 | 0.958847 | ||||||||
\(327\) | − | 10.5961i | − | 0.585967i | ||||||
\(328\) | −28.8560 | −1.59330 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 31.8722i | 1.75451i | ||||||||
\(331\) | 11.7858i | 0.647804i | 0.946091 | + | 0.323902i | \(0.104995\pi\) | ||||
−0.946091 | + | 0.323902i | \(0.895005\pi\) | |||||||
\(332\) | 0.560401i | 0.0307560i | ||||||||
\(333\) | − | 4.03441i | − | 0.221084i | ||||||
\(334\) | 2.86592 | 0.156816 | ||||||||
\(335\) | 12.4133 | 0.678212 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.63045 | −0.143290 | −0.0716450 | − | 0.997430i | \(-0.522825\pi\) | ||||
−0.0716450 | + | 0.997430i | \(0.522825\pi\) | |||||||
\(338\) | 19.5271 | − | 3.30112i | 1.06213 | − | 0.179557i | ||||
\(339\) | 31.1035 | 1.68931 | ||||||||
\(340\) | − | 5.07405i | − | 0.275179i | ||||||
\(341\) | −19.7601 | −1.07007 | ||||||||
\(342\) | 48.7014 | 2.63347 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 26.9302i | − | 1.45198i | ||||||
\(345\) | 24.6232i | 1.32567i | ||||||||
\(346\) | − | 8.48704i | − | 0.456266i | ||||||
\(347\) | 4.82463 | 0.259000 | 0.129500 | − | 0.991579i | \(-0.458663\pi\) | ||||
0.129500 | + | 0.991579i | \(0.458663\pi\) | |||||||
\(348\) | −0.562753 | −0.0301667 | ||||||||
\(349\) | 17.5231i | 0.937991i | 0.883201 | + | 0.468995i | \(0.155384\pi\) | ||||
−0.883201 | + | 0.468995i | \(0.844616\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.7071 | − | 24.5016i | 1.10527 | − | 1.30780i | ||||
\(352\) | 4.26250 | 0.227192 | ||||||||
\(353\) | − | 6.59724i | − | 0.351136i | −0.984467 | − | 0.175568i | \(-0.943824\pi\) | ||
0.984467 | − | 0.175568i | \(-0.0561761\pi\) | |||||||
\(354\) | −28.0426 | −1.49045 | ||||||||
\(355\) | 3.68704 | 0.195688 | ||||||||
\(356\) | 3.28248i | 0.173971i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.10118i | 0.375309i | ||||||||
\(359\) | 23.0484i | 1.21645i | 0.793764 | + | 0.608225i | \(0.208118\pi\) | ||||
−0.793764 | + | 0.608225i | \(0.791882\pi\) | |||||||
\(360\) | 44.9981 | 2.37161 | ||||||||
\(361\) | −9.66934 | −0.508912 | ||||||||
\(362\) | 19.0973i | 1.00373i | ||||||||
\(363\) | 16.1076 | 0.845428 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −32.0001 | −1.67496 | ||||||||
\(366\) | − | 12.7158i | − | 0.664665i | ||||||
\(367\) | 15.9318 | 0.831631 | 0.415815 | − | 0.909449i | \(-0.363496\pi\) | ||||
0.415815 | + | 0.909449i | \(0.363496\pi\) | |||||||
\(368\) | 12.6652 | 0.660222 | ||||||||
\(369\) | 67.3478i | 3.50599i | ||||||||
\(370\) | − | 3.03259i | − | 0.157657i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 8.00568i | − | 0.415075i | ||||||
\(373\) | 23.4289 | 1.21310 | 0.606552 | − | 0.795044i | \(-0.292552\pi\) | ||||
0.606552 | + | 0.795044i | \(0.292552\pi\) | |||||||
\(374\) | 19.3967 | 1.00298 | ||||||||
\(375\) | − | 11.6538i | − | 0.601800i | ||||||
\(376\) | 1.37565 | 0.0709437 | ||||||||
\(377\) | 1.36340 | − | 1.61323i | 0.0702186 | − | 0.0830856i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.1041i | 1.54634i | 0.634196 | + | 0.773172i | \(0.281331\pi\) | ||||
−0.634196 | + | 0.773172i | \(0.718669\pi\) | |||||||
\(380\) | 5.05934 | 0.259539 | ||||||||
\(381\) | −15.2602 | −0.781802 | ||||||||
\(382\) | − | 2.00728i | − | 0.102701i | ||||||
\(383\) | 12.8597i | 0.657101i | 0.944486 | + | 0.328551i | \(0.106560\pi\) | ||||
−0.944486 | + | 0.328551i | \(0.893440\pi\) | |||||||
\(384\) | − | 39.6898i | − | 2.02541i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.0710 | −1.17428 | ||||||||
\(387\) | −62.8532 | −3.19501 | ||||||||
\(388\) | 3.17731i | 0.161304i | ||||||||
\(389\) | −36.8531 | −1.86853 | −0.934264 | − | 0.356582i | \(-0.883942\pi\) | ||||
−0.934264 | + | 0.356582i | \(0.883942\pi\) | |||||||
\(390\) | 31.2843 | − | 37.0169i | 1.58414 | − | 1.87442i | ||||
\(391\) | 14.9852 | 0.757833 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −67.5226 | −3.40606 | ||||||||
\(394\) | −15.0903 | −0.760239 | ||||||||
\(395\) | − | 18.5347i | − | 0.932583i | ||||||
\(396\) | − | 4.54057i | − | 0.228172i | ||||||
\(397\) | − | 20.3087i | − | 1.01926i | −0.860393 | − | 0.509631i | \(-0.829782\pi\) | ||
0.860393 | − | 0.509631i | \(-0.170218\pi\) | |||||||
\(398\) | − | 13.0605i | − | 0.654662i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.6987 | 0.834935 | ||||||||
\(401\) | − | 19.6699i | − | 0.982268i | −0.871084 | − | 0.491134i | \(-0.836583\pi\) | ||
0.871084 | − | 0.491134i | \(-0.163417\pi\) | |||||||
\(402\) | −19.2252 | −0.958864 | ||||||||
\(403\) | 22.9497 | + | 19.3956i | 1.14321 | + | 0.966163i | ||||
\(404\) | −0.657750 | −0.0327243 | ||||||||
\(405\) | − | 25.7383i | − | 1.27895i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.60216 | 0.0794162 | ||||||||
\(408\) | − | 41.1446i | − | 2.03696i | ||||||
\(409\) | − | 23.1755i | − | 1.14595i | −0.819572 | − | 0.572976i | \(-0.805789\pi\) | ||
0.819572 | − | 0.572976i | \(-0.194211\pi\) | |||||||
\(410\) | 50.6241i | 2.50015i | ||||||||
\(411\) | − | 3.09931i | − | 0.152877i | ||||||
\(412\) | −0.971699 | −0.0478722 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 25.3819i | − | 1.24745i | ||||||
\(415\) | −5.14750 | −0.252681 | ||||||||
\(416\) | −4.95053 | − | 4.18387i | −0.242720 | − | 0.205131i | ||||
\(417\) | −25.4421 | −1.24590 | ||||||||
\(418\) | 19.3405i | 0.945975i | ||||||||
\(419\) | −28.6478 | −1.39953 | −0.699767 | − | 0.714371i | \(-0.746713\pi\) | ||||
−0.699767 | + | 0.714371i | \(0.746713\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 36.3249i | − | 1.77037i | −0.465241 | − | 0.885184i | \(-0.654032\pi\) | ||
0.465241 | − | 0.885184i | \(-0.345968\pi\) | |||||||
\(422\) | − | 2.20153i | − | 0.107169i | ||||||
\(423\) | − | 3.21067i | − | 0.156108i | ||||||
\(424\) | 20.2185i | 0.981898i | ||||||||
\(425\) | 19.7575 | 0.958377 | ||||||||
\(426\) | −5.71031 | −0.276666 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.98688 | 0.192713 | ||||||||
\(429\) | 19.5565 | + | 16.5279i | 0.944198 | + | 0.797976i | ||||
\(430\) | −47.2456 | −2.27839 | ||||||||
\(431\) | 7.93131i | 0.382038i | 0.981586 | + | 0.191019i | \(0.0611792\pi\) | ||||
−0.981586 | + | 0.191019i | \(0.938821\pi\) | |||||||
\(432\) | −40.3814 | −1.94285 | ||||||||
\(433\) | 9.60994 | 0.461824 | 0.230912 | − | 0.972975i | \(-0.425829\pi\) | ||||
0.230912 | + | 0.972975i | \(0.425829\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 5.16911i | − | 0.247840i | ||||||
\(436\) | 1.13470i | 0.0543421i | ||||||||
\(437\) | 14.9417i | 0.714760i | ||||||||
\(438\) | 49.5603 | 2.36808 | ||||||||
\(439\) | 3.46690 | 0.165466 | 0.0827332 | − | 0.996572i | \(-0.473635\pi\) | ||||
0.0827332 | + | 0.996572i | \(0.473635\pi\) | |||||||
\(440\) | 17.8698i | 0.851910i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −22.5277 | − | 19.0389i | −1.07153 | − | 0.905590i | ||||
\(443\) | 2.45667 | 0.116720 | 0.0583600 | − | 0.998296i | \(-0.481413\pi\) | ||||
0.0583600 | + | 0.998296i | \(0.481413\pi\) | |||||||
\(444\) | 0.649106i | 0.0308052i | ||||||||
\(445\) | −30.1508 | −1.42929 | ||||||||
\(446\) | 22.8432 | 1.08166 | ||||||||
\(447\) | 12.9192i | 0.611056i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.7487i | 1.07358i | 0.843716 | + | 0.536790i | \(0.180363\pi\) | ||||
−0.843716 | + | 0.536790i | \(0.819637\pi\) | |||||||
\(450\) | − | 33.4652i | − | 1.57757i | ||||||
\(451\) | −26.7454 | −1.25939 | ||||||||
\(452\) | −3.33075 | −0.156665 | ||||||||
\(453\) | − | 36.6742i | − | 1.72311i | ||||||
\(454\) | 1.74002 | 0.0816633 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 41.0254 | 1.92119 | ||||||||
\(457\) | 12.2568i | 0.573349i | 0.958028 | + | 0.286675i | \(0.0925499\pi\) | ||||
−0.958028 | + | 0.286675i | \(0.907450\pi\) | |||||||
\(458\) | −9.55070 | −0.446275 | ||||||||
\(459\) | −47.7781 | −2.23009 | ||||||||
\(460\) | − | 2.63680i | − | 0.122942i | ||||||
\(461\) | − | 24.0650i | − | 1.12082i | −0.828216 | − | 0.560409i | \(-0.810644\pi\) | ||
0.828216 | − | 0.560409i | \(-0.189356\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 19.3956i | − | 0.901390i | −0.892678 | − | 0.450695i | \(-0.851176\pi\) | ||
0.892678 | − | 0.450695i | \(-0.148824\pi\) | |||||||
\(464\) | −2.65879 | −0.123431 | ||||||||
\(465\) | 73.5352 | 3.41012 | ||||||||
\(466\) | 9.39470i | 0.435201i | ||||||||
\(467\) | 17.8782 | 0.827307 | 0.413653 | − | 0.910434i | \(-0.364253\pi\) | ||||
0.413653 | + | 0.910434i | \(0.364253\pi\) | |||||||
\(468\) | −4.45681 | + | 5.27349i | −0.206016 | + | 0.243767i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 2.41340i | − | 0.111322i | ||||||
\(471\) | 66.5031 | 3.06430 | ||||||||
\(472\) | −15.7227 | −0.723696 | ||||||||
\(473\) | − | 24.9605i | − | 1.14769i | ||||||
\(474\) | 28.7057i | 1.31850i | ||||||||
\(475\) | 19.7002i | 0.903906i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 47.1886 | 2.16062 | ||||||||
\(478\) | −41.8307 | −1.91329 | ||||||||
\(479\) | − | 20.7671i | − | 0.948875i | −0.880289 | − | 0.474437i | \(-0.842652\pi\) | ||
0.880289 | − | 0.474437i | \(-0.157348\pi\) | |||||||
\(480\) | −15.8625 | −0.724019 | ||||||||
\(481\) | −1.86078 | − | 1.57261i | −0.0848441 | − | 0.0717048i | ||||
\(482\) | 14.9198 | 0.679578 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.72490 | −0.0784043 | ||||||||
\(485\) | −29.1848 | −1.32522 | ||||||||
\(486\) | − | 0.800181i | − | 0.0362970i | ||||||
\(487\) | − | 19.1987i | − | 0.869977i | −0.900436 | − | 0.434988i | \(-0.856752\pi\) | ||
0.900436 | − | 0.434988i | \(-0.143248\pi\) | |||||||
\(488\) | − | 7.12938i | − | 0.322732i | ||||||
\(489\) | − | 34.0374i | − | 1.53923i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.91648 | −0.357266 | −0.178633 | − | 0.983916i | \(-0.557167\pi\) | ||||
−0.178633 | + | 0.983916i | \(0.557167\pi\) | |||||||
\(492\) | − | 10.8357i | − | 0.488513i | ||||||
\(493\) | −3.14581 | −0.141680 | ||||||||
\(494\) | 18.9837 | − | 22.4624i | 0.854119 | − | 1.01063i | ||||
\(495\) | 41.7069 | 1.87459 | ||||||||
\(496\) | − | 37.8237i | − | 1.69833i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.97222 | 0.357244 | ||||||||
\(499\) | 39.1750i | 1.75371i | 0.480753 | + | 0.876856i | \(0.340363\pi\) | ||||
−0.480753 | + | 0.876856i | \(0.659637\pi\) | |||||||
\(500\) | 1.24796i | 0.0558105i | ||||||||
\(501\) | − | 5.63459i | − | 0.251735i | ||||||
\(502\) | 19.0340i | 0.849530i | ||||||||
\(503\) | 16.1533 | 0.720239 | 0.360120 | − | 0.932906i | \(-0.382736\pi\) | ||||
0.360120 | + | 0.932906i | \(0.382736\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 6.04169i | − | 0.268852i | ||||||
\(506\) | 10.0798 | 0.448101 | ||||||||
\(507\) | −6.49022 | − | 38.3916i | −0.288241 | − | 1.70503i | ||||
\(508\) | 1.63415 | 0.0725036 | ||||||||
\(509\) | − | 24.3177i | − | 1.07786i | −0.842350 | − | 0.538930i | \(-0.818829\pi\) | ||
0.842350 | − | 0.538930i | \(-0.181171\pi\) | |||||||
\(510\) | −72.1830 | −3.19632 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 15.0621i | − | 0.665658i | ||||||
\(513\) | − | 47.6396i | − | 2.10334i | ||||||
\(514\) | 29.2384i | 1.28965i | ||||||||
\(515\) | − | 8.92543i | − | 0.393302i | ||||||
\(516\) | 10.1126 | 0.445183 | ||||||||
\(517\) | 1.27503 | 0.0560759 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.6861 | −0.732439 | ||||||||
\(520\) | 17.5402 | − | 20.7543i | 0.769188 | − | 0.910136i | ||||
\(521\) | −34.4550 | −1.50950 | −0.754750 | − | 0.656012i | \(-0.772242\pi\) | ||||
−0.754750 | + | 0.656012i | \(0.772242\pi\) | |||||||
\(522\) | 5.32838i | 0.233217i | ||||||||
\(523\) | 34.6865 | 1.51674 | 0.758368 | − | 0.651827i | \(-0.225997\pi\) | ||||
0.758368 | + | 0.651827i | \(0.225997\pi\) | |||||||
\(524\) | 7.23072 | 0.315875 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 43.8971i | 1.91401i | ||||||||
\(527\) | − | 44.7520i | − | 1.94943i | ||||||
\(528\) | − | 32.2314i | − | 1.40269i | ||||||
\(529\) | −15.2128 | −0.661424 | ||||||||
\(530\) | 35.4708 | 1.54075 | ||||||||
\(531\) | 36.6956i | 1.59246i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.0626 | + | 26.2521i | 1.34547 | + | 1.13710i | ||||
\(534\) | 46.6962 | 2.02074 | ||||||||
\(535\) | 36.6211i | 1.58327i | ||||||||
\(536\) | −10.7790 | −0.465582 | ||||||||
\(537\) | 13.9614 | 0.602480 | ||||||||
\(538\) | − | 12.4221i | − | 0.535553i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.40708i | 0.361783i | ||||||||
\(541\) | 12.2568i | 0.526961i | 0.964665 | + | 0.263481i | \(0.0848705\pi\) | ||||
−0.964665 | + | 0.263481i | \(0.915129\pi\) | |||||||
\(542\) | 28.3028 | 1.21571 | ||||||||
\(543\) | 37.5466 | 1.61128 | ||||||||
\(544\) | 9.65356i | 0.413893i | ||||||||
\(545\) | −10.4226 | −0.446456 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.4110 | −0.701686 | −0.350843 | − | 0.936434i | \(-0.614105\pi\) | ||||
−0.350843 | + | 0.936434i | \(0.614105\pi\) | |||||||
\(548\) | 0.331892i | 0.0141777i | ||||||||
\(549\) | −16.6395 | −0.710155 | ||||||||
\(550\) | 13.2899 | 0.566681 | ||||||||
\(551\) | − | 3.13669i | − | 0.133627i | ||||||
\(552\) | − | 21.3814i | − | 0.910052i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 26.2545i | 1.11545i | ||||||||
\(555\) | −5.96229 | −0.253085 | ||||||||
\(556\) | 2.72449 | 0.115544 | ||||||||
\(557\) | − | 35.6541i | − | 1.51071i | −0.655315 | − | 0.755356i | \(-0.727464\pi\) | ||
0.655315 | − | 0.755356i | \(-0.272536\pi\) | |||||||
\(558\) | −75.8010 | −3.20891 | ||||||||
\(559\) | −24.5001 | + | 28.9896i | −1.03624 | + | 1.22613i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 38.1353i | − | 1.61007i | ||||||
\(562\) | 17.4720 | 0.737013 | ||||||||
\(563\) | −10.7748 | −0.454103 | −0.227052 | − | 0.973883i | \(-0.572909\pi\) | ||||
−0.227052 | + | 0.973883i | \(0.572909\pi\) | |||||||
\(564\) | 0.516572i | 0.0217516i | ||||||||
\(565\) | − | 30.5943i | − | 1.28711i | ||||||
\(566\) | 2.21769i | 0.0932163i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.20161 | −0.134336 | ||||||||
\(569\) | −20.9328 | −0.877550 | −0.438775 | − | 0.898597i | \(-0.644587\pi\) | ||||
−0.438775 | + | 0.898597i | \(0.644587\pi\) | |||||||
\(570\) | − | 71.9738i | − | 3.01465i | ||||||
\(571\) | −32.2668 | −1.35032 | −0.675161 | − | 0.737670i | \(-0.735926\pi\) | ||||
−0.675161 | + | 0.737670i | \(0.735926\pi\) | |||||||
\(572\) | −2.09423 | − | 1.76991i | −0.0875642 | − | 0.0740036i | ||||
\(573\) | −3.94645 | −0.164865 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.2672 | 0.428173 | ||||||||
\(576\) | −37.8453 | −1.57689 | ||||||||
\(577\) | 0.197896i | 0.00823851i | 0.999992 | + | 0.00411925i | \(0.00131120\pi\) | ||||
−0.999992 | + | 0.00411925i | \(0.998689\pi\) | |||||||
\(578\) | 18.0313i | 0.750005i | ||||||||
\(579\) | 45.3592i | 1.88506i | ||||||||
\(580\) | 0.553539i | 0.0229844i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 45.2001 | 1.87361 | ||||||||
\(583\) | 18.7397i | 0.776120i | ||||||||
\(584\) | 27.7870 | 1.14984 | ||||||||
\(585\) | −48.4390 | − | 40.9376i | −2.00271 | − | 1.69256i | ||||
\(586\) | −46.7624 | −1.93174 | ||||||||
\(587\) | 10.1251i | 0.417907i | 0.977926 | + | 0.208954i | \(0.0670058\pi\) | ||||
−0.977926 | + | 0.208954i | \(0.932994\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.6222 | 1.83863 | ||||||||
\(590\) | 27.5835i | 1.13559i | ||||||||
\(591\) | 29.6686i | 1.22040i | ||||||||
\(592\) | 3.06677i | 0.126044i | ||||||||
\(593\) | − | 29.9345i | − | 1.22926i | −0.788815 | − | 0.614631i | \(-0.789305\pi\) | ||
0.788815 | − | 0.614631i | \(-0.210695\pi\) | |||||||
\(594\) | −32.1380 | −1.31864 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 1.38346i | − | 0.0566688i | ||||||
\(597\) | −25.6778 | −1.05092 | ||||||||
\(598\) | −11.7068 | − | 9.89384i | −0.478727 | − | 0.404589i | ||||
\(599\) | 26.8872 | 1.09858 | 0.549291 | − | 0.835631i | \(-0.314898\pi\) | ||||
0.549291 | + | 0.835631i | \(0.314898\pi\) | |||||||
\(600\) | − | 28.1906i | − | 1.15088i | ||||||
\(601\) | 24.7432 | 1.00930 | 0.504649 | − | 0.863325i | \(-0.331622\pi\) | ||||
0.504649 | + | 0.863325i | \(0.331622\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.1574i | 1.02449i | ||||||||
\(604\) | 3.92730i | 0.159799i | ||||||||
\(605\) | − | 15.8438i | − | 0.644143i | ||||||
\(606\) | 9.35709i | 0.380106i | ||||||||
\(607\) | −3.09235 | −0.125515 | −0.0627573 | − | 0.998029i | \(-0.519989\pi\) | ||||
−0.0627573 | + | 0.998029i | \(0.519989\pi\) | |||||||
\(608\) | −9.62557 | −0.390369 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.5076 | −0.506417 | ||||||||
\(611\) | −1.48084 | − | 1.25151i | −0.0599086 | − | 0.0506308i | ||||
\(612\) | 10.2833 | 0.415679 | ||||||||
\(613\) | 31.3605i | 1.26664i | 0.773891 | + | 0.633319i | \(0.218308\pi\) | ||||
−0.773891 | + | 0.633319i | \(0.781692\pi\) | |||||||
\(614\) | −32.3877 | −1.30706 | ||||||||
\(615\) | 99.5305 | 4.01346 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.5311i | 0.504484i | 0.967664 | + | 0.252242i | \(0.0811678\pi\) | ||||
−0.967664 | + | 0.252242i | \(0.918832\pi\) | |||||||
\(618\) | 13.8233i | 0.556055i | ||||||||
\(619\) | − | 11.6112i | − | 0.466692i | −0.972394 | − | 0.233346i | \(-0.925032\pi\) | ||
0.972394 | − | 0.233346i | \(-0.0749675\pi\) | |||||||
\(620\) | −7.87459 | −0.316251 | ||||||||
\(621\) | −24.8286 | −0.996336 | ||||||||
\(622\) | 6.77374i | 0.271602i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −31.6369 | + | 37.4341i | −1.26649 | + | 1.49856i | ||||
\(625\) | −29.8593 | −1.19437 | ||||||||
\(626\) | 3.48380i | 0.139241i | ||||||||
\(627\) | 38.0248 | 1.51856 | ||||||||
\(628\) | −7.12155 | −0.284181 | ||||||||
\(629\) | 3.62852i | 0.144679i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.7037i | 0.505728i | 0.967502 | + | 0.252864i | \(0.0813725\pi\) | ||||
−0.967502 | + | 0.252864i | \(0.918628\pi\) | |||||||
\(632\) | 16.0945i | 0.640204i | ||||||||
\(633\) | −4.32836 | −0.172037 | ||||||||
\(634\) | −12.3408 | −0.490116 | ||||||||
\(635\) | 15.0103i | 0.595665i | ||||||||
\(636\) | −7.59228 | −0.301054 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.11603 | −0.0837744 | ||||||||
\(639\) | 7.47233i | 0.295601i | ||||||||
\(640\) | −39.0399 | −1.54319 | ||||||||
\(641\) | 40.3015 | 1.59181 | 0.795906 | − | 0.605420i | \(-0.206995\pi\) | ||||
0.795906 | + | 0.605420i | \(0.206995\pi\) | |||||||
\(642\) | − | 56.7170i | − | 2.23844i | ||||||
\(643\) | − | 11.6643i | − | 0.459997i | −0.973191 | − | 0.229998i | \(-0.926128\pi\) | ||
0.973191 | − | 0.229998i | \(-0.0738721\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 92.8882i | 3.65747i | ||||||||
\(646\) | −43.8017 | −1.72336 | ||||||||
\(647\) | −11.0387 | −0.433977 | −0.216988 | − | 0.976174i | \(-0.569623\pi\) | ||||
−0.216988 | + | 0.976174i | \(0.569623\pi\) | |||||||
\(648\) | 22.3496i | 0.877976i | ||||||||
\(649\) | −14.5727 | −0.572030 | ||||||||
\(650\) | −15.4350 | − | 13.0447i | −0.605412 | − | 0.511656i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.64493i | 0.142747i | ||||||||
\(653\) | 19.1260 | 0.748458 | 0.374229 | − | 0.927336i | \(-0.377907\pi\) | ||||
0.374229 | + | 0.927336i | \(0.377907\pi\) | |||||||
\(654\) | 16.1421 | 0.631206 | ||||||||
\(655\) | 66.4170i | 2.59513i | ||||||||
\(656\) | − | 51.1947i | − | 1.99882i | ||||||
\(657\) | − | 64.8529i | − | 2.53015i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.8233 | 1.12279 | 0.561397 | − | 0.827546i | \(-0.310264\pi\) | ||||
0.561397 | + | 0.827546i | \(0.310264\pi\) | |||||||
\(660\) | −6.71032 | −0.261199 | ||||||||
\(661\) | 48.2385i | 1.87626i | 0.346281 | + | 0.938131i | \(0.387444\pi\) | ||||
−0.346281 | + | 0.938131i | \(0.612556\pi\) | |||||||
\(662\) | −17.9544 | −0.697816 | ||||||||
\(663\) | −37.4319 | + | 44.2910i | −1.45373 | + | 1.72012i | ||||
\(664\) | 4.46979 | 0.173462 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.14600 | 0.238153 | ||||||||
\(667\) | −1.63476 | −0.0632982 | ||||||||
\(668\) | 0.603386i | 0.0233457i | ||||||||
\(669\) | − | 44.9112i | − | 1.73637i | ||||||
\(670\) | 18.9104i | 0.730572i | ||||||||
\(671\) | − | 6.60794i | − | 0.255097i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.0426 | 1.27370 | 0.636849 | − | 0.770989i | \(-0.280238\pi\) | ||||
0.636849 | + | 0.770989i | \(0.280238\pi\) | |||||||
\(674\) | − | 4.00722i | − | 0.154352i | ||||||
\(675\) | −32.7356 | −1.26000 | ||||||||
\(676\) | 0.695012 | + | 4.11120i | 0.0267312 | + | 0.158123i | ||||
\(677\) | −15.7186 | −0.604117 | −0.302058 | − | 0.953289i | \(-0.597674\pi\) | ||||
−0.302058 | + | 0.953289i | \(0.597674\pi\) | |||||||
\(678\) | 47.3830i | 1.81973i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −40.4710 | −1.55199 | ||||||||
\(681\) | − | 3.42100i | − | 0.131093i | ||||||
\(682\) | − | 30.1024i | − | 1.15268i | ||||||
\(683\) | − | 33.3629i | − | 1.27660i | −0.769789 | − | 0.638298i | \(-0.779639\pi\) | ||
0.769789 | − | 0.638298i | \(-0.220361\pi\) | |||||||
\(684\) | 10.2535i | 0.392053i | ||||||||
\(685\) | −3.04856 | −0.116479 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.7773i | 0.716400i | ||||||||
\(688\) | 47.7781 | 1.82152 | ||||||||
\(689\) | 18.3941 | − | 21.7646i | 0.700758 | − | 0.829166i | ||||
\(690\) | −37.5109 | −1.42802 | ||||||||
\(691\) | 45.3507i | 1.72522i | 0.505869 | + | 0.862610i | \(0.331172\pi\) | ||||
−0.505869 | + | 0.862610i | \(0.668828\pi\) | |||||||
\(692\) | 1.78685 | 0.0679257 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.34981i | 0.278995i | ||||||||
\(695\) | 25.0255i | 0.949270i | ||||||||
\(696\) | 4.48855i | 0.170138i | ||||||||
\(697\) | − | 60.5721i | − | 2.29433i | ||||||
\(698\) | −26.6946 | −1.01041 | ||||||||
\(699\) | 18.4706 | 0.698623 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.5681 | −0.890155 | −0.445077 | − | 0.895492i | \(-0.646824\pi\) | ||||
−0.445077 | + | 0.895492i | \(0.646824\pi\) | |||||||
\(702\) | 37.3256 | + | 31.5452i | 1.40876 | + | 1.19060i | ||||
\(703\) | −3.61800 | −0.136456 | ||||||||
\(704\) | − | 15.0293i | − | 0.566438i | ||||||
\(705\) | −4.74491 | −0.178704 | ||||||||
\(706\) | 10.0502 | 0.378244 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 5.90405i | − | 0.221888i | ||||||
\(709\) | − | 8.66932i | − | 0.325583i | −0.986660 | − | 0.162792i | \(-0.947950\pi\) | ||
0.986660 | − | 0.162792i | \(-0.0520498\pi\) | |||||||
\(710\) | 5.61681i | 0.210795i | ||||||||
\(711\) | 37.5634 | 1.40874 | ||||||||
\(712\) | 26.1812 | 0.981183 | ||||||||
\(713\) | − | 23.2560i | − | 0.870943i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.2573 | − | 19.2363i | 0.607988 | − | 0.719398i | ||||
\(716\) | −1.49507 | −0.0558735 | ||||||||
\(717\) | 82.2420i | 3.07138i | ||||||||
\(718\) | −35.1119 | −1.31036 | ||||||||
\(719\) | 11.0038 | 0.410373 | 0.205186 | − | 0.978723i | \(-0.434220\pi\) | ||||
0.205186 | + | 0.978723i | \(0.434220\pi\) | |||||||
\(720\) | 79.8331i | 2.97520i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 14.7302i | − | 0.548202i | ||||||
\(723\) | − | 29.3333i | − | 1.09092i | ||||||
\(724\) | −4.02071 | −0.149429 | ||||||||
\(725\) | −2.15538 | −0.0800488 | ||||||||
\(726\) | 24.5382i | 0.910698i | ||||||||
\(727\) | −40.7049 | −1.50966 | −0.754831 | − | 0.655919i | \(-0.772281\pi\) | ||||
−0.754831 | + | 0.655919i | \(0.772281\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.7827 | −1.02899 | ||||||||
\(730\) | − | 48.7488i | − | 1.80427i | ||||||
\(731\) | 56.5298 | 2.09083 | ||||||||
\(732\) | 2.67716 | 0.0989508 | ||||||||
\(733\) | 10.3536i | 0.382418i | 0.981549 | + | 0.191209i | \(0.0612409\pi\) | ||||
−0.981549 | + | 0.191209i | \(0.938759\pi\) | |||||||
\(734\) | 24.2704i | 0.895835i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.01660i | 0.184914i | ||||||||
\(737\) | −9.99062 | −0.368009 | ||||||||
\(738\) | −102.597 | −3.77666 | ||||||||
\(739\) | 48.5321i | 1.78528i | 0.450770 | + | 0.892640i | \(0.351150\pi\) | ||||
−0.450770 | + | 0.892640i | \(0.648850\pi\) | |||||||
\(740\) | 0.638477 | 0.0234709 | ||||||||
\(741\) | −44.1626 | − | 37.3234i | −1.62235 | − | 1.37111i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 24.5215i | − | 0.899608i | −0.893127 | − | 0.449804i | \(-0.851494\pi\) | ||
0.893127 | − | 0.449804i | \(-0.148506\pi\) | |||||||
\(744\) | −63.8537 | −2.34099 | ||||||||
\(745\) | 12.7076 | 0.465572 | ||||||||
\(746\) | 35.6915i | 1.30676i | ||||||||
\(747\) | − | 10.4322i | − | 0.381694i | ||||||
\(748\) | 4.08376i | 0.149317i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 17.7534 | 0.648261 | ||||||||
\(751\) | 28.0663 | 1.02415 | 0.512077 | − | 0.858939i | \(-0.328876\pi\) | ||||
0.512077 | + | 0.858939i | \(0.328876\pi\) | |||||||
\(752\) | 2.44060i | 0.0889996i | ||||||||
\(753\) | 37.4222 | 1.36374 | ||||||||
\(754\) | 2.45759 | + | 2.07700i | 0.0895001 | + | 0.0756397i | ||||
\(755\) | −36.0738 | −1.31286 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.70864 | 0.207484 | 0.103742 | − | 0.994604i | \(-0.466918\pi\) | ||||
0.103742 | + | 0.994604i | \(0.466918\pi\) | |||||||
\(758\) | −45.8605 | −1.66573 | ||||||||
\(759\) | − | 19.8175i | − | 0.719331i | ||||||
\(760\) | − | 40.3536i | − | 1.46378i | ||||||
\(761\) | 7.69598i | 0.278979i | 0.990224 | + | 0.139490i | \(0.0445462\pi\) | ||||
−0.990224 | + | 0.139490i | \(0.955454\pi\) | |||||||
\(762\) | − | 23.2473i | − | 0.842159i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.422610 | 0.0152895 | ||||||||
\(765\) | 94.4563i | 3.41508i | ||||||||
\(766\) | −19.5904 | −0.707832 | ||||||||
\(767\) | 16.9250 | + | 14.3039i | 0.611126 | + | 0.516485i | ||||
\(768\) | 22.4939 | 0.811677 | ||||||||
\(769\) | 15.0754i | 0.543634i | 0.962349 | + | 0.271817i | \(0.0876245\pi\) | ||||
−0.962349 | + | 0.271817i | \(0.912375\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 57.4847 | 2.07026 | ||||||||
\(772\) | − | 4.85733i | − | 0.174819i | ||||||
\(773\) | 21.2624i | 0.764755i | 0.924006 | + | 0.382378i | \(0.124895\pi\) | ||||
−0.924006 | + | 0.382378i | \(0.875105\pi\) | |||||||
\(774\) | − | 95.7503i | − | 3.44167i | ||||||
\(775\) | − | 30.6622i | − | 1.10142i | ||||||
\(776\) | 25.3424 | 0.909740 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 56.1419i | − | 2.01278i | ||||||
\(779\) | 60.3966 | 2.16393 | ||||||||
\(780\) | 7.79347 | + | 6.58654i | 0.279051 | + | 0.235836i | ||||
\(781\) | −2.96744 | −0.106183 | ||||||||
\(782\) | 22.8283i | 0.816340i | ||||||||
\(783\) | 5.21221 | 0.186269 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 65.4142i | − | 2.33473i | ||||||
\(786\) | − | 102.864i | − | 3.66902i | ||||||
\(787\) | − | 9.28939i | − | 0.331131i | −0.986199 | − | 0.165565i | \(-0.947055\pi\) | ||
0.986199 | − | 0.165565i | \(-0.0529449\pi\) | |||||||
\(788\) | − | 3.17709i | − | 0.113179i | ||||||
\(789\) | 86.3048 | 3.07253 | ||||||||
\(790\) | 28.2357 | 1.00458 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −36.2158 | −1.28687 | ||||||||
\(793\) | −6.48604 | + | 7.67456i | −0.230326 | + | 0.272532i | ||||
\(794\) | 30.9381 | 1.09795 | ||||||||
\(795\) | − | 69.7381i | − | 2.47335i | ||||||
\(796\) | 2.74973 | 0.0974615 | ||||||||
\(797\) | −49.7686 | −1.76289 | −0.881447 | − | 0.472283i | \(-0.843430\pi\) | ||||
−0.881447 | + | 0.472283i | \(0.843430\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.88765i | 0.102158i | ||||||||
\(800\) | 6.61423i | 0.233848i | ||||||||
\(801\) | − | 61.1051i | − | 2.15904i | ||||||
\(802\) | 29.9650 | 1.05810 | ||||||||
\(803\) | 25.7547 | 0.908863 | ||||||||
\(804\) | − | 4.04764i | − | 0.142749i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −29.5472 | + | 34.9614i | −1.04075 | + | 1.23146i | ||||
\(807\) | −24.4226 | −0.859717 | ||||||||
\(808\) | 5.24625i | 0.184563i | ||||||||
\(809\) | −9.59433 | −0.337319 | −0.168659 | − | 0.985674i | \(-0.553944\pi\) | ||||
−0.168659 | + | 0.985674i | \(0.553944\pi\) | |||||||
\(810\) | 39.2096 | 1.37768 | ||||||||
\(811\) | − | 35.6060i | − | 1.25030i | −0.780506 | − | 0.625148i | \(-0.785038\pi\) | ||
0.780506 | − | 0.625148i | \(-0.214962\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 55.6453i | − | 1.95157i | ||||||
\(814\) | 2.44073i | 0.0855474i | ||||||||
\(815\) | −33.4801 | −1.17276 | ||||||||
\(816\) | 72.9966 | 2.55539 | ||||||||
\(817\) | 56.3659i | 1.97199i | ||||||||
\(818\) | 35.3054 | 1.23442 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.6583 | −0.372205 | ||||||||
\(821\) | 0.296780i | 0.0103577i | 0.999987 | + | 0.00517884i | \(0.00164848\pi\) | ||||
−0.999987 | + | 0.00517884i | \(0.998352\pi\) | |||||||
\(822\) | 4.72147 | 0.164680 | ||||||||
\(823\) | −22.9119 | −0.798658 | −0.399329 | − | 0.916808i | \(-0.630757\pi\) | ||||
−0.399329 | + | 0.916808i | \(0.630757\pi\) | |||||||
\(824\) | 7.75033i | 0.269995i | ||||||||
\(825\) | − | 26.1288i | − | 0.909687i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.50142i | 0.295623i | 0.989016 | + | 0.147812i | \(0.0472230\pi\) | ||||
−0.989016 | + | 0.147812i | \(0.952777\pi\) | |||||||
\(828\) | 5.34387 | 0.185712 | ||||||||
\(829\) | 54.3605 | 1.88802 | 0.944009 | − | 0.329919i | \(-0.107022\pi\) | ||||
0.944009 | + | 0.329919i | \(0.107022\pi\) | |||||||
\(830\) | − | 7.84168i | − | 0.272189i | ||||||
\(831\) | 51.6182 | 1.79061 | ||||||||
\(832\) | −14.7521 | + | 17.4553i | −0.511436 | + | 0.605152i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 38.7583i | − | 1.34209i | ||||||
\(835\) | −5.54233 | −0.191800 | ||||||||
\(836\) | −4.07192 | −0.140830 | ||||||||
\(837\) | 74.1485i | 2.56295i | ||||||||
\(838\) | − | 43.6419i | − | 1.50758i | ||||||
\(839\) | − | 17.0486i | − | 0.588585i | −0.955715 | − | 0.294292i | \(-0.904916\pi\) | ||
0.955715 | − | 0.294292i | \(-0.0950839\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6568 | −0.988166 | ||||||||
\(842\) | 55.3372 | 1.90705 | ||||||||
\(843\) | − | 34.3512i | − | 1.18312i | ||||||
\(844\) | 0.463507 | 0.0159546 | ||||||||
\(845\) | −37.7630 | + | 6.38395i | −1.29909 | + | 0.219615i | ||||
\(846\) | 4.89112 | 0.168160 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −35.8706 | −1.23180 | ||||||||
\(849\) | 4.36013 | 0.149639 | ||||||||
\(850\) | 30.0984i | 1.03237i | ||||||||
\(851\) | 1.88561i | 0.0646379i | ||||||||
\(852\) | − | 1.20224i | − | 0.0411881i | ||||||
\(853\) | 45.0401i | 1.54214i | 0.636747 | + | 0.771072i | \(0.280279\pi\) | ||||
−0.636747 | + | 0.771072i | \(0.719721\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −94.1825 | −3.22097 | ||||||||
\(856\) | − | 31.7996i | − | 1.08689i | ||||||
\(857\) | −39.7927 | −1.35929 | −0.679646 | − | 0.733541i | \(-0.737866\pi\) | ||||
−0.679646 | + | 0.733541i | \(0.737866\pi\) | |||||||
\(858\) | −25.1786 | + | 29.7923i | −0.859582 | + | 1.01709i | ||||
\(859\) | −22.3379 | −0.762158 | −0.381079 | − | 0.924542i | \(-0.624447\pi\) | ||||
−0.381079 | + | 0.924542i | \(0.624447\pi\) | |||||||
\(860\) | − | 9.94702i | − | 0.339191i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.0825 | −0.411532 | ||||||||
\(863\) | − | 14.1624i | − | 0.482094i | −0.970513 | − | 0.241047i | \(-0.922509\pi\) | ||
0.970513 | − | 0.241047i | \(-0.0774908\pi\) | |||||||
\(864\) | − | 15.9947i | − | 0.544152i | ||||||
\(865\) | 16.4129i | 0.558055i | ||||||||
\(866\) | 14.6397i | 0.497479i | ||||||||
\(867\) | 35.4509 | 1.20397 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.9173i | 0.506036i | ||||||||
\(870\) | 7.87459 | 0.266974 | ||||||||
\(871\) | 11.6033 | + | 9.80633i | 0.393162 | + | 0.332275i | ||||
\(872\) | 9.05041 | 0.306485 | ||||||||
\(873\) | − | 59.1474i | − | 2.00184i | ||||||
\(874\) | −22.7622 | −0.769941 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.4343i | 0.352544i | ||||||||
\(877\) | − | 43.9546i | − | 1.48424i | −0.670266 | − | 0.742121i | \(-0.733820\pi\) | ||
0.670266 | − | 0.742121i | \(-0.266180\pi\) | |||||||
\(878\) | 5.28147i | 0.178241i | ||||||||
\(879\) | 91.9382i | 3.10100i | ||||||||
\(880\) | −31.7037 | −1.06873 | ||||||||
\(881\) | 15.3849 | 0.518331 | 0.259165 | − | 0.965833i | \(-0.416553\pi\) | ||||
0.259165 | + | 0.965833i | \(0.416553\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.5262 | 1.49842 | 0.749212 | − | 0.662330i | \(-0.230432\pi\) | ||||
0.749212 | + | 0.662330i | \(0.230432\pi\) | |||||||
\(884\) | 4.00843 | − | 4.74294i | 0.134818 | − | 0.159522i | ||||
\(885\) | 54.2310 | 1.82295 | ||||||||
\(886\) | 3.74248i | 0.125731i | ||||||||
\(887\) | −16.1072 | −0.540826 | −0.270413 | − | 0.962744i | \(-0.587160\pi\) | ||||
−0.270413 | + | 0.962744i | \(0.587160\pi\) | |||||||
\(888\) | 5.17731 | 0.173739 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 45.9316i | − | 1.53963i | ||||||
\(891\) | 20.7150i | 0.693978i | ||||||||
\(892\) | 4.80936i | 0.161029i | ||||||||
\(893\) | −2.87928 | −0.0963515 | ||||||||
\(894\) | −19.6810 | −0.658231 | ||||||||
\(895\) | − | 13.7328i | − | 0.459037i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.4520 | + | 23.0164i | −0.649483 | + | 0.768495i | ||||
\(898\) | −34.6553 | −1.15646 | ||||||||
\(899\) | 4.88208i | 0.162827i | ||||||||
\(900\) | 7.04572 | 0.234857 | ||||||||
\(901\) | −42.4411 | −1.41392 | ||||||||
\(902\) | − | 40.7439i | − | 1.35662i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 26.5663i | 0.883582i | ||||||||
\(905\) | − | 36.9318i | − | 1.22766i | ||||||
\(906\) | 55.8694 | 1.85614 | ||||||||
\(907\) | −18.6037 | −0.617725 | −0.308862 | − | 0.951107i | \(-0.599948\pi\) | ||||
−0.308862 | + | 0.951107i | \(0.599948\pi\) | |||||||
\(908\) | 0.366341i | 0.0121575i | ||||||||
\(909\) | 12.2444 | 0.406121 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.1801 | 1.26496 | 0.632481 | − | 0.774576i | \(-0.282037\pi\) | ||||
0.632481 | + | 0.774576i | \(0.282037\pi\) | |||||||
\(912\) | 72.7850i | 2.41015i | ||||||||
\(913\) | 4.14287 | 0.137109 | ||||||||
\(914\) | −18.6720 | −0.617614 | ||||||||
\(915\) | 24.5908i | 0.812946i | ||||||||
\(916\) | − | 2.01079i | − | 0.0664383i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 72.7850i | − | 2.40226i | ||||||
\(919\) | −16.7629 | −0.552956 | −0.276478 | − | 0.961020i | \(-0.589167\pi\) | ||||
−0.276478 | + | 0.961020i | \(0.589167\pi\) | |||||||
\(920\) | −21.0313 | −0.693381 | ||||||||
\(921\) | 63.6765i | 2.09821i | ||||||||
\(922\) | 36.6605 | 1.20735 | ||||||||
\(923\) | 3.44643 | + | 2.91270i | 0.113441 | + | 0.0958728i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.48612i | 0.0817430i | ||||||||
\(926\) | 29.5472 | 0.970980 | ||||||||
\(927\) | 18.0887 | 0.594111 | ||||||||
\(928\) | − | 1.05313i | − | 0.0345706i | ||||||
\(929\) | 6.58871i | 0.216169i | 0.994142 | + | 0.108084i | \(0.0344716\pi\) | ||||
−0.994142 | + | 0.108084i | \(0.965528\pi\) | |||||||
\(930\) | 112.023i | 3.67339i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.97794 | −0.0647897 | ||||||||
\(933\) | 13.3176 | 0.436000 | ||||||||
\(934\) | 27.2356i | 0.891177i | ||||||||
\(935\) | −37.5109 | −1.22674 | ||||||||
\(936\) | 42.0617 | + | 35.5478i | 1.37483 | + | 1.16192i | ||||
\(937\) | −39.0958 | −1.27721 | −0.638603 | − | 0.769537i | \(-0.720487\pi\) | ||||
−0.638603 | + | 0.769537i | \(0.720487\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.84940 | 0.223522 | ||||||||
\(940\) | 0.508114 | 0.0165728 | ||||||||
\(941\) | − | 13.2351i | − | 0.431452i | −0.976454 | − | 0.215726i | \(-0.930788\pi\) | ||
0.976454 | − | 0.215726i | \(-0.0692118\pi\) | |||||||
\(942\) | 101.311i | 3.30088i | ||||||||
\(943\) | − | 31.4771i | − | 1.02504i | ||||||
\(944\) | − | 27.8943i | − | 0.907884i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 38.0248 | 1.23629 | ||||||||
\(947\) | 50.1427i | 1.62942i | 0.579870 | + | 0.814709i | \(0.303103\pi\) | ||||
−0.579870 | + | 0.814709i | \(0.696897\pi\) | |||||||
\(948\) | −6.04366 | −0.196289 | ||||||||
\(949\) | −29.9119 | − | 25.2796i | −0.970981 | − | 0.820610i | ||||
\(950\) | −30.0112 | −0.973690 | ||||||||
\(951\) | 24.2629i | 0.786778i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.9832 | −0.971252 | −0.485626 | − | 0.874167i | \(-0.661408\pi\) | ||||
−0.485626 | + | 0.874167i | \(0.661408\pi\) | |||||||
\(954\) | 71.8869i | 2.32742i | ||||||||
\(955\) | 3.88184i | 0.125613i | ||||||||
\(956\) | − | 8.80697i | − | 0.284838i | ||||||
\(957\) | 4.16026i | 0.134482i | ||||||||
\(958\) | 31.6366 | 1.02213 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 55.9300i | 1.80513i | ||||||||
\(961\) | −38.4521 | −1.24039 | ||||||||
\(962\) | 2.39570 | − | 2.83470i | 0.0772406 | − | 0.0913943i | ||||
\(963\) | −74.2180 | −2.39164 | ||||||||
\(964\) | 3.14119i | 0.101171i | ||||||||
\(965\) | 44.6165 | 1.43626 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 37.8356i | − | 1.21671i | −0.793665 | − | 0.608356i | \(-0.791829\pi\) | ||
0.793665 | − | 0.608356i | \(-0.208171\pi\) | |||||||
\(968\) | 13.7579i | 0.442195i | ||||||||
\(969\) | 86.1172i | 2.76648i | ||||||||
\(970\) | − | 44.4600i | − | 1.42753i | ||||||
\(971\) | 15.3432 | 0.492388 | 0.246194 | − | 0.969221i | \(-0.420820\pi\) | ||||
0.246194 | + | 0.969221i | \(0.420820\pi\) | |||||||
\(972\) | 0.168469 | 0.00540364 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 29.2472 | 0.937142 | ||||||||
\(975\) | −25.6468 | + | 30.3464i | −0.821355 | + | 0.971862i | ||||
\(976\) | 12.6486 | 0.404871 | ||||||||
\(977\) | − | 26.5487i | − | 0.849367i | −0.905342 | − | 0.424684i | \(-0.860385\pi\) | ||
0.905342 | − | 0.424684i | \(-0.139615\pi\) | |||||||
\(978\) | 51.8525 | 1.65806 | ||||||||
\(979\) | 24.2663 | 0.775555 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 21.1230i | − | 0.674406i | ||||||
\(982\) | − | 12.0599i | − | 0.384848i | ||||||
\(983\) | − | 8.02003i | − | 0.255799i | −0.991787 | − | 0.127900i | \(-0.959176\pi\) | ||
0.991787 | − | 0.127900i | \(-0.0408235\pi\) | |||||||
\(984\) | −86.4265 | −2.75518 | ||||||||
\(985\) | 29.1828 | 0.929842 | ||||||||
\(986\) | − | 4.79231i | − | 0.152618i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.72919 | + | 3.99681i | 0.150456 | + | 0.127155i | ||||
\(989\) | 29.3765 | 0.934117 | ||||||||
\(990\) | 63.5361i | 2.01931i | ||||||||
\(991\) | 49.0958 | 1.55958 | 0.779789 | − | 0.626042i | \(-0.215326\pi\) | ||||
0.779789 | + | 0.626042i | \(0.215326\pi\) | |||||||
\(992\) | 14.9817 | 0.475669 | ||||||||
\(993\) | 35.2995i | 1.12020i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.2573i | 0.800711i | ||||||||
\(996\) | 1.67846i | 0.0531840i | ||||||||
\(997\) | 19.9476 | 0.631746 | 0.315873 | − | 0.948801i | \(-0.397703\pi\) | ||||
0.315873 | + | 0.948801i | \(0.397703\pi\) | |||||||
\(998\) | −59.6790 | −1.88910 | ||||||||
\(999\) | − | 6.01201i | − | 0.190212i |
(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 | 637.2.c.g.246.12 | yes | 16 | |
7.2 | even | 3 | 637.2.r.g.116.11 | 32 | |||
7.3 | odd | 6 | 637.2.r.g.324.6 | 32 | |||
7.4 | even | 3 | 637.2.r.g.324.5 | 32 | |||
7.5 | odd | 6 | 637.2.r.g.116.12 | 32 | |||
7.6 | odd | 2 | inner | 637.2.c.g.246.11 | yes | 16 | |
13.5 | odd | 4 | 8281.2.a.cs.1.12 | 16 | |||
13.8 | odd | 4 | 8281.2.a.cs.1.6 | 16 | |||
13.12 | even | 2 | inner | 637.2.c.g.246.6 | yes | 16 | |
91.12 | odd | 6 | 637.2.r.g.116.6 | 32 | |||
91.25 | even | 6 | 637.2.r.g.324.11 | 32 | |||
91.34 | even | 4 | 8281.2.a.cs.1.5 | 16 | |||
91.38 | odd | 6 | 637.2.r.g.324.12 | 32 | |||
91.51 | even | 6 | 637.2.r.g.116.5 | 32 | |||
91.83 | even | 4 | 8281.2.a.cs.1.11 | 16 | |||
91.90 | odd | 2 | inner | 637.2.c.g.246.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.c.g.246.5 | ✓ | 16 | 91.90 | odd | 2 | inner | |
637.2.c.g.246.6 | yes | 16 | 13.12 | even | 2 | inner | |
637.2.c.g.246.11 | yes | 16 | 7.6 | odd | 2 | inner | |
637.2.c.g.246.12 | yes | 16 | 1.1 | even | 1 | trivial | |
637.2.r.g.116.5 | 32 | 91.51 | even | 6 | |||
637.2.r.g.116.6 | 32 | 91.12 | odd | 6 | |||
637.2.r.g.116.11 | 32 | 7.2 | even | 3 | |||
637.2.r.g.116.12 | 32 | 7.5 | odd | 6 | |||
637.2.r.g.324.5 | 32 | 7.4 | even | 3 | |||
637.2.r.g.324.6 | 32 | 7.3 | odd | 6 | |||
637.2.r.g.324.11 | 32 | 91.25 | even | 6 | |||
637.2.r.g.324.12 | 32 | 91.38 | odd | 6 | |||
8281.2.a.cs.1.5 | 16 | 91.34 | even | 4 | |||
8281.2.a.cs.1.6 | 16 | 13.8 | odd | 4 | |||
8281.2.a.cs.1.11 | 16 | 91.83 | even | 4 | |||
8281.2.a.cs.1.12 | 16 | 13.5 | odd | 4 |