Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 271.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.271 |
Dual form | 405.2.e.h.136.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.707107 | + | 1.22474i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.50000 | + | 2.59808i | 0.566947 | + | 0.981981i | 0.996866 | + | 0.0791130i | \(0.0252088\pi\) |
−0.429919 | + | 0.902867i | \(0.641458\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | 0.632456 | ||||||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.50000 | − | 4.33013i | 0.693375 | − | 1.20096i | −0.277350 | − | 0.960769i | \(-0.589456\pi\) |
0.970725 | − | 0.240192i | \(-0.0772105\pi\) | |||||||
\(14\) | −3.00000 | + | 5.19615i | −0.801784 | + | 1.38873i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | −8.00000 | −1.94029 | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||||
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 1.00000 | + | 1.73205i | 0.223607 | + | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | + | 3.46410i | −0.426401 | + | 0.738549i | ||||
\(23\) | −3.00000 | + | 5.19615i | −0.625543 | + | 1.08347i | 0.362892 | + | 0.931831i | \(0.381789\pi\) |
−0.988436 | + | 0.151642i | \(0.951544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 10.0000 | 1.96116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.00000 | −1.13389 | ||||||||
\(29\) | −1.00000 | − | 1.73205i | −0.185695 | − | 0.321634i | 0.758115 | − | 0.652121i | \(-0.226120\pi\) |
−0.943811 | + | 0.330487i | \(0.892787\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(32\) | −4.00000 | + | 6.92820i | −0.707107 | + | 1.22474i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.00000 | − | 13.8564i | −1.37199 | − | 2.37635i | ||||
\(35\) | 3.00000 | 0.507093 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000 | 0.821995 | 0.410997 | − | 0.911636i | \(-0.365181\pi\) | ||||
0.410997 | + | 0.911636i | \(0.365181\pi\) | |||||||
\(38\) | 1.00000 | + | 1.73205i | 0.162221 | + | 0.280976i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.00000 | − | 8.66025i | 0.780869 | − | 1.35250i | −0.150567 | − | 0.988600i | \(-0.548110\pi\) |
0.931436 | − | 0.363905i | \(-0.118557\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | − | 3.46410i | −0.304997 | − | 0.528271i | 0.672264 | − | 0.740312i | \(-0.265322\pi\) |
−0.977261 | + | 0.212041i | \(0.931989\pi\) | |||||||
\(44\) | −4.00000 | −0.603023 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.0000 | −1.76930 | ||||||||
\(47\) | −2.00000 | − | 3.46410i | −0.291730 | − | 0.505291i | 0.682489 | − | 0.730896i | \(-0.260898\pi\) |
−0.974219 | + | 0.225605i | \(0.927564\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | + | 1.73205i | −0.142857 | + | 0.247436i | ||||
\(50\) | 1.00000 | − | 1.73205i | 0.141421 | − | 0.244949i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.00000 | + | 8.66025i | 0.693375 | + | 1.20096i | ||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.00000 | − | 3.46410i | 0.262613 | − | 0.454859i | ||||
\(59\) | 4.00000 | − | 6.92820i | 0.520756 | − | 0.901975i | −0.478953 | − | 0.877841i | \(-0.658984\pi\) |
0.999709 | − | 0.0241347i | \(-0.00768307\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.50000 | − | 6.06218i | −0.448129 | − | 0.776182i | 0.550135 | − | 0.835076i | \(-0.314576\pi\) |
−0.998264 | + | 0.0588933i | \(0.981243\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −2.50000 | − | 4.33013i | −0.310087 | − | 0.537086i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.50000 | − | 7.79423i | 0.549762 | − | 0.952217i | −0.448528 | − | 0.893769i | \(-0.648052\pi\) |
0.998290 | − | 0.0584478i | \(-0.0186151\pi\) | |||||||
\(68\) | 8.00000 | − | 13.8564i | 0.970143 | − | 1.68034i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.00000 | + | 5.19615i | 0.358569 | + | 0.621059i | ||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.00000 | −0.585206 | −0.292603 | − | 0.956234i | \(-0.594521\pi\) | ||||
−0.292603 | + | 0.956234i | \(0.594521\pi\) | |||||||
\(74\) | 5.00000 | + | 8.66025i | 0.581238 | + | 1.00673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | + | 1.73205i | −0.114708 | + | 0.198680i | ||||
\(77\) | −3.00000 | + | 5.19615i | −0.341882 | + | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.50000 | + | 2.59808i | 0.168763 | + | 0.292306i | 0.937985 | − | 0.346675i | \(-0.112689\pi\) |
−0.769222 | + | 0.638982i | \(0.779356\pi\) | |||||||
\(80\) | 4.00000 | 0.447214 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 20.0000 | 2.20863 | ||||||||
\(83\) | −3.00000 | − | 5.19615i | −0.329293 | − | 0.570352i | 0.653079 | − | 0.757290i | \(-0.273477\pi\) |
−0.982372 | + | 0.186938i | \(0.940144\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | + | 6.92820i | −0.433861 | + | 0.751469i | ||||
\(86\) | 4.00000 | − | 6.92820i | 0.431331 | − | 0.747087i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.0000 | −1.27200 | −0.635999 | − | 0.771690i | \(-0.719412\pi\) | ||||
−0.635999 | + | 0.771690i | \(0.719412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.0000 | 1.57243 | ||||||||
\(92\) | −6.00000 | − | 10.3923i | −0.625543 | − | 1.08347i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.00000 | − | 6.92820i | 0.412568 | − | 0.714590i | ||||
\(95\) | 0.500000 | − | 0.866025i | 0.0512989 | − | 0.0888523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.50000 | + | 11.2583i | 0.659975 | + | 1.14311i | 0.980622 | + | 0.195911i | \(0.0627665\pi\) |
−0.320647 | + | 0.947199i | \(0.603900\pi\) | |||||||
\(98\) | −4.00000 | −0.404061 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.00000 | 0.200000 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.50000 | + | 14.7224i | −0.837530 | + | 1.45064i | 0.0544240 | + | 0.998518i | \(0.482668\pi\) |
−0.891954 | + | 0.452126i | \(0.850666\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | − | 3.46410i | −0.194257 | − | 0.336463i | ||||
\(107\) | 6.00000 | 0.580042 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 2.00000 | + | 3.46410i | 0.190693 | + | 0.330289i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.00000 | + | 10.3923i | −0.566947 | + | 0.981981i | ||||
\(113\) | −5.00000 | + | 8.66025i | −0.470360 | + | 0.814688i | −0.999425 | − | 0.0338931i | \(-0.989209\pi\) |
0.529065 | + | 0.848581i | \(0.322543\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.00000 | + | 5.19615i | 0.279751 | + | 0.484544i | ||||
\(116\) | 4.00000 | 0.371391 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 16.0000 | 1.47292 | ||||||||
\(119\) | −12.0000 | − | 20.7846i | −1.10004 | − | 1.90532i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 7.00000 | − | 12.1244i | 0.633750 | − | 1.09769i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.00000 | − | 8.66025i | 0.438529 | − | 0.759555i | ||||
\(131\) | −6.00000 | + | 10.3923i | −0.524222 | + | 0.907980i | 0.475380 | + | 0.879781i | \(0.342311\pi\) |
−0.999602 | + | 0.0281993i | \(0.991023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.50000 | + | 2.59808i | 0.130066 | + | 0.225282i | ||||
\(134\) | 18.0000 | 1.55496 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.00000 | + | 5.19615i | 0.256307 | + | 0.443937i | 0.965250 | − | 0.261329i | \(-0.0841608\pi\) |
−0.708942 | + | 0.705266i | \(0.750827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.50000 | − | 11.2583i | 0.551323 | − | 0.954919i | −0.446857 | − | 0.894606i | \(-0.647457\pi\) |
0.998179 | − | 0.0603135i | \(-0.0192101\pi\) | |||||||
\(140\) | −3.00000 | + | 5.19615i | −0.253546 | + | 0.439155i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.00000 | + | 3.46410i | 0.167836 | + | 0.290701i | ||||
\(143\) | 10.0000 | 0.836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | −5.00000 | − | 8.66025i | −0.413803 | − | 0.716728i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.00000 | + | 8.66025i | −0.410997 | + | 0.711868i | ||||
\(149\) | 2.00000 | − | 3.46410i | 0.163846 | − | 0.283790i | −0.772399 | − | 0.635138i | \(-0.780943\pi\) |
0.936245 | + | 0.351348i | \(0.114277\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.500000 | − | 0.866025i | −0.0406894 | − | 0.0704761i | 0.844963 | − | 0.534824i | \(-0.179622\pi\) |
−0.885653 | + | 0.464348i | \(0.846289\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12.0000 | −0.966988 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.00000 | + | 1.73205i | −0.0798087 | + | 0.138233i | −0.903167 | − | 0.429289i | \(-0.858764\pi\) |
0.823359 | + | 0.567521i | \(0.192098\pi\) | |||||||
\(158\) | −3.00000 | + | 5.19615i | −0.238667 | + | 0.413384i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.00000 | + | 6.92820i | 0.316228 | + | 0.547723i | ||||
\(161\) | −18.0000 | −1.41860 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.0000 | −1.48819 | −0.744097 | − | 0.668071i | \(-0.767120\pi\) | ||||
−0.744097 | + | 0.668071i | \(0.767120\pi\) | |||||||
\(164\) | 10.0000 | + | 17.3205i | 0.780869 | + | 1.35250i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | − | 10.3923i | 0.465690 | − | 0.806599i | ||||
\(167\) | 6.00000 | − | 10.3923i | 0.464294 | − | 0.804181i | −0.534875 | − | 0.844931i | \(-0.679641\pi\) |
0.999169 | + | 0.0407502i | \(0.0129748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | − | 10.3923i | −0.461538 | − | 0.799408i | ||||
\(170\) | −16.0000 | −1.22714 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | 6.00000 | + | 10.3923i | 0.456172 | + | 0.790112i | 0.998755 | − | 0.0498898i | \(-0.0158870\pi\) |
−0.542583 | + | 0.840002i | \(0.682554\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.50000 | − | 2.59808i | 0.113389 | − | 0.196396i | ||||
\(176\) | −4.00000 | + | 6.92820i | −0.301511 | + | 0.522233i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.0000 | − | 20.7846i | −0.899438 | − | 1.55787i | ||||
\(179\) | 22.0000 | 1.64436 | 0.822179 | − | 0.569230i | \(-0.192758\pi\) | ||||
0.822179 | + | 0.569230i | \(0.192758\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.00000 | 0.371647 | 0.185824 | − | 0.982583i | \(-0.440505\pi\) | ||||
0.185824 | + | 0.982583i | \(0.440505\pi\) | |||||||
\(182\) | 15.0000 | + | 25.9808i | 1.11187 | + | 1.92582i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.50000 | − | 4.33013i | 0.183804 | − | 0.318357i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.00000 | − | 13.8564i | −0.585018 | − | 1.01328i | ||||
\(188\) | 8.00000 | 0.583460 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.00000 | 0.145095 | ||||||||
\(191\) | 2.00000 | + | 3.46410i | 0.144715 | + | 0.250654i | 0.929267 | − | 0.369410i | \(-0.120440\pi\) |
−0.784552 | + | 0.620063i | \(0.787107\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.50000 | + | 4.33013i | −0.179954 | + | 0.311689i | −0.941865 | − | 0.335993i | \(-0.890928\pi\) |
0.761911 | + | 0.647682i | \(0.224262\pi\) | |||||||
\(194\) | −13.0000 | + | 22.5167i | −0.933346 | + | 1.61660i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.00000 | − | 3.46410i | −0.142857 | − | 0.247436i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.0000 | −1.20510 | −0.602549 | − | 0.798082i | \(-0.705848\pi\) | ||||
−0.602549 | + | 0.798082i | \(0.705848\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.00000 | − | 5.19615i | 0.210559 | − | 0.364698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.00000 | − | 8.66025i | −0.349215 | − | 0.604858i | ||||
\(206\) | −34.0000 | −2.36889 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20.0000 | 1.38675 | ||||||||
\(209\) | 1.00000 | + | 1.73205i | 0.0691714 | + | 0.119808i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.5000 | + | 19.9186i | −0.791693 | + | 1.37125i | 0.133226 | + | 0.991086i | \(0.457467\pi\) |
−0.924918 | + | 0.380166i | \(0.875867\pi\) | |||||||
\(212\) | 2.00000 | − | 3.46410i | 0.137361 | − | 0.237915i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.00000 | + | 10.3923i | 0.410152 | + | 0.710403i | ||||
\(215\) | −4.00000 | −0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.0000 | − | 17.3205i | −0.677285 | − | 1.17309i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.00000 | + | 3.46410i | −0.134840 | + | 0.233550i | ||||
\(221\) | −20.0000 | + | 34.6410i | −1.34535 | + | 2.33021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | − | 6.92820i | −0.267860 | − | 0.463947i | 0.700449 | − | 0.713702i | \(-0.252983\pi\) |
−0.968309 | + | 0.249756i | \(0.919650\pi\) | |||||||
\(224\) | −24.0000 | −1.60357 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.0000 | −1.33038 | ||||||||
\(227\) | 5.00000 | + | 8.66025i | 0.331862 | + | 0.574801i | 0.982877 | − | 0.184263i | \(-0.0589899\pi\) |
−0.651015 | + | 0.759065i | \(0.725657\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.00000 | + | 5.19615i | −0.198246 | + | 0.343371i | −0.947960 | − | 0.318390i | \(-0.896858\pi\) |
0.749714 | + | 0.661762i | \(0.230191\pi\) | |||||||
\(230\) | −6.00000 | + | 10.3923i | −0.395628 | + | 0.685248i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.0000 | −1.57229 | −0.786146 | − | 0.618041i | \(-0.787927\pi\) | ||||
−0.786146 | + | 0.618041i | \(0.787927\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | −0.260931 | ||||||||
\(236\) | 8.00000 | + | 13.8564i | 0.520756 | + | 0.901975i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 24.0000 | − | 41.5692i | 1.55569 | − | 2.69453i | ||||
\(239\) | 13.0000 | − | 22.5167i | 0.840900 | − | 1.45648i | −0.0482346 | − | 0.998836i | \(-0.515360\pi\) |
0.889135 | − | 0.457646i | \(-0.151307\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.500000 | − | 0.866025i | −0.0322078 | − | 0.0557856i | 0.849472 | − | 0.527633i | \(-0.176921\pi\) |
−0.881680 | + | 0.471848i | \(0.843587\pi\) | |||||||
\(242\) | 14.0000 | 0.899954 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.0000 | 0.896258 | ||||||||
\(245\) | 1.00000 | + | 1.73205i | 0.0638877 | + | 0.110657i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.50000 | − | 4.33013i | 0.159071 | − | 0.275519i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | − | 1.73205i | −0.0632456 | − | 0.109545i | ||||
\(251\) | 6.00000 | 0.378717 | 0.189358 | − | 0.981908i | \(-0.439359\pi\) | ||||
0.189358 | + | 0.981908i | \(0.439359\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | −8.00000 | − | 13.8564i | −0.501965 | − | 0.869428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.50000 | + | 12.9904i | 0.466027 | + | 0.807183i | ||||
\(260\) | 10.0000 | 0.620174 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −24.0000 | −1.48272 | ||||||||
\(263\) | 14.0000 | + | 24.2487i | 0.863277 | + | 1.49524i | 0.868748 | + | 0.495255i | \(0.164925\pi\) |
−0.00547092 | + | 0.999985i | \(0.501741\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.00000 | + | 1.73205i | −0.0614295 | + | 0.106399i | ||||
\(266\) | −3.00000 | + | 5.19615i | −0.183942 | + | 0.318597i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.00000 | + | 15.5885i | 0.549762 | + | 0.952217i | ||||
\(269\) | 16.0000 | 0.975537 | 0.487769 | − | 0.872973i | \(-0.337811\pi\) | ||||
0.487769 | + | 0.872973i | \(0.337811\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.0000 | 0.789694 | 0.394847 | − | 0.918747i | \(-0.370798\pi\) | ||||
0.394847 | + | 0.918747i | \(0.370798\pi\) | |||||||
\(272\) | −16.0000 | − | 27.7128i | −0.970143 | − | 1.68034i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.00000 | + | 10.3923i | −0.362473 | + | 0.627822i | ||||
\(275\) | 1.00000 | − | 1.73205i | 0.0603023 | − | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.0000 | + | 25.9808i | 0.901263 | + | 1.56103i | 0.825857 | + | 0.563880i | \(0.190692\pi\) |
0.0754058 | + | 0.997153i | \(0.475975\pi\) | |||||||
\(278\) | 26.0000 | 1.55938 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.00000 | + | 10.3923i | −0.356663 | + | 0.617758i | −0.987401 | − | 0.158237i | \(-0.949419\pi\) |
0.630738 | + | 0.775996i | \(0.282752\pi\) | |||||||
\(284\) | −2.00000 | + | 3.46410i | −0.118678 | + | 0.205557i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.0000 | + | 17.3205i | 0.591312 | + | 1.02418i | ||||
\(287\) | 30.0000 | 1.77084 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 47.0000 | 2.76471 | ||||||||
\(290\) | −2.00000 | − | 3.46410i | −0.117444 | − | 0.203419i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.00000 | − | 8.66025i | 0.292603 | − | 0.506803i | ||||
\(293\) | −9.00000 | + | 15.5885i | −0.525786 | + | 0.910687i | 0.473763 | + | 0.880652i | \(0.342895\pi\) |
−0.999549 | + | 0.0300351i | \(0.990438\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | − | 6.92820i | −0.232889 | − | 0.403376i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.00000 | 0.463428 | ||||||||
\(299\) | 15.0000 | + | 25.9808i | 0.867472 | + | 1.50251i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | − | 10.3923i | 0.345834 | − | 0.599002i | ||||
\(302\) | 1.00000 | − | 1.73205i | 0.0575435 | − | 0.0996683i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | + | 3.46410i | 0.114708 | + | 0.198680i | ||||
\(305\) | −7.00000 | −0.400819 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0000 | 0.913168 | 0.456584 | − | 0.889680i | \(-0.349073\pi\) | ||||
0.456584 | + | 0.889680i | \(0.349073\pi\) | |||||||
\(308\) | −6.00000 | − | 10.3923i | −0.341882 | − | 0.592157i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | − | 20.7846i | 0.680458 | − | 1.17859i | −0.294384 | − | 0.955687i | \(-0.595114\pi\) |
0.974841 | − | 0.222900i | \(-0.0715523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.50000 | + | 6.06218i | 0.197832 | + | 0.342655i | 0.947825 | − | 0.318791i | \(-0.103277\pi\) |
−0.749993 | + | 0.661445i | \(0.769943\pi\) | |||||||
\(314\) | −4.00000 | −0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.00000 | −0.337526 | ||||||||
\(317\) | −10.0000 | − | 17.3205i | −0.561656 | − | 0.972817i | −0.997352 | − | 0.0727229i | \(-0.976831\pi\) |
0.435696 | − | 0.900094i | \(-0.356502\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.00000 | − | 3.46410i | 0.111979 | − | 0.193952i | ||||
\(320\) | −4.00000 | + | 6.92820i | −0.223607 | + | 0.387298i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −18.0000 | − | 31.1769i | −1.00310 | − | 1.73742i | ||||
\(323\) | −8.00000 | −0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.00000 | −0.277350 | ||||||||
\(326\) | −19.0000 | − | 32.9090i | −1.05231 | − | 1.82266i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.00000 | − | 10.3923i | 0.330791 | − | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.5000 | + | 18.1865i | 0.577132 | + | 0.999622i | 0.995806 | + | 0.0914858i | \(0.0291616\pi\) |
−0.418674 | + | 0.908137i | \(0.637505\pi\) | |||||||
\(332\) | 12.0000 | 0.658586 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 24.0000 | 1.31322 | ||||||||
\(335\) | −4.50000 | − | 7.79423i | −0.245861 | − | 0.425844i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.50000 | + | 6.06218i | −0.190657 | + | 0.330228i | −0.945468 | − | 0.325714i | \(-0.894395\pi\) |
0.754811 | + | 0.655942i | \(0.227729\pi\) | |||||||
\(338\) | 12.0000 | − | 20.7846i | 0.652714 | − | 1.13053i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.00000 | − | 13.8564i | −0.433861 | − | 0.751469i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.0000 | + | 20.7846i | −0.645124 | + | 1.11739i | ||||
\(347\) | −5.00000 | + | 8.66025i | −0.268414 | + | 0.464907i | −0.968452 | − | 0.249198i | \(-0.919833\pi\) |
0.700038 | + | 0.714105i | \(0.253166\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.50000 | − | 16.4545i | −0.508523 | − | 0.880788i | −0.999951 | − | 0.00987003i | \(-0.996858\pi\) |
0.491428 | − | 0.870918i | \(-0.336475\pi\) | |||||||
\(350\) | 6.00000 | 0.320713 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −16.0000 | −0.852803 | ||||||||
\(353\) | 6.00000 | + | 10.3923i | 0.319348 | + | 0.553127i | 0.980352 | − | 0.197256i | \(-0.0632029\pi\) |
−0.661004 | + | 0.750382i | \(0.729870\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.00000 | − | 1.73205i | 0.0530745 | − | 0.0919277i | ||||
\(356\) | 12.0000 | − | 20.7846i | 0.635999 | − | 1.10158i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.0000 | + | 38.1051i | 1.16274 | + | 2.01392i | ||||
\(359\) | −18.0000 | −0.950004 | −0.475002 | − | 0.879985i | \(-0.657553\pi\) | ||||
−0.475002 | + | 0.879985i | \(0.657553\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 5.00000 | + | 8.66025i | 0.262794 | + | 0.455173i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −15.0000 | + | 25.9808i | −0.786214 | + | 1.36176i | ||||
\(365\) | −2.50000 | + | 4.33013i | −0.130856 | + | 0.226649i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.5000 | − | 18.1865i | −0.548096 | − | 0.949329i | −0.998405 | − | 0.0564568i | \(-0.982020\pi\) |
0.450310 | − | 0.892873i | \(-0.351314\pi\) | |||||||
\(368\) | −24.0000 | −1.25109 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.0000 | 0.519875 | ||||||||
\(371\) | −3.00000 | − | 5.19615i | −0.155752 | − | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.50000 | − | 9.52628i | 0.284779 | − | 0.493252i | −0.687776 | − | 0.725923i | \(-0.741413\pi\) |
0.972556 | + | 0.232671i | \(0.0747464\pi\) | |||||||
\(374\) | 16.0000 | − | 27.7128i | 0.827340 | − | 1.43300i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.0000 | −0.515026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.0000 | −0.565032 | −0.282516 | − | 0.959263i | \(-0.591169\pi\) | ||||
−0.282516 | + | 0.959263i | \(0.591169\pi\) | |||||||
\(380\) | 1.00000 | + | 1.73205i | 0.0512989 | + | 0.0888523i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.00000 | + | 6.92820i | −0.204658 | + | 0.354478i | ||||
\(383\) | 12.0000 | − | 20.7846i | 0.613171 | − | 1.06204i | −0.377531 | − | 0.925997i | \(-0.623227\pi\) |
0.990702 | − | 0.136047i | \(-0.0434398\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.00000 | + | 5.19615i | 0.152894 | + | 0.264820i | ||||
\(386\) | −10.0000 | −0.508987 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −26.0000 | −1.31995 | ||||||||
\(389\) | −12.0000 | − | 20.7846i | −0.608424 | − | 1.05382i | −0.991500 | − | 0.130105i | \(-0.958469\pi\) |
0.383076 | − | 0.923717i | \(-0.374865\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | − | 41.5692i | 1.21373 | − | 2.10225i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.00000 | 0.150946 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.00000 | −0.100377 | −0.0501886 | − | 0.998740i | \(-0.515982\pi\) | ||||
−0.0501886 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(398\) | −17.0000 | − | 29.4449i | −0.852133 | − | 1.47594i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.00000 | − | 3.46410i | 0.100000 | − | 0.173205i | ||||
\(401\) | −3.00000 | + | 5.19615i | −0.149813 | + | 0.259483i | −0.931158 | − | 0.364615i | \(-0.881200\pi\) |
0.781345 | + | 0.624099i | \(0.214534\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.0000 | 0.595550 | ||||||||
\(407\) | 5.00000 | + | 8.66025i | 0.247841 | + | 0.429273i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.50000 | − | 6.06218i | 0.173064 | − | 0.299755i | −0.766426 | − | 0.642333i | \(-0.777967\pi\) |
0.939490 | + | 0.342578i | \(0.111300\pi\) | |||||||
\(410\) | 10.0000 | − | 17.3205i | 0.493865 | − | 0.855399i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.0000 | − | 29.4449i | −0.837530 | − | 1.45064i | ||||
\(413\) | 24.0000 | 1.18096 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.00000 | −0.294528 | ||||||||
\(416\) | 20.0000 | + | 34.6410i | 0.980581 | + | 1.69842i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.00000 | + | 3.46410i | −0.0978232 | + | 0.169435i | ||||
\(419\) | −16.0000 | + | 27.7128i | −0.781651 | + | 1.35386i | 0.149328 | + | 0.988788i | \(0.452289\pi\) |
−0.930979 | + | 0.365072i | \(0.881044\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.500000 | − | 0.866025i | −0.0243685 | − | 0.0422075i | 0.853584 | − | 0.520955i | \(-0.174424\pi\) |
−0.877952 | + | 0.478748i | \(0.841091\pi\) | |||||||
\(422\) | −46.0000 | −2.23924 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.00000 | + | 6.92820i | 0.194029 | + | 0.336067i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.5000 | − | 18.1865i | 0.508131 | − | 0.880108i | ||||
\(428\) | −6.00000 | + | 10.3923i | −0.290021 | + | 0.502331i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.00000 | − | 6.92820i | −0.192897 | − | 0.334108i | ||||
\(431\) | 30.0000 | 1.44505 | 0.722525 | − | 0.691345i | \(-0.242982\pi\) | ||||
0.722525 | + | 0.691345i | \(0.242982\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.0000 | −1.82616 | −0.913082 | − | 0.407777i | \(-0.866304\pi\) | ||||
−0.913082 | + | 0.407777i | \(0.866304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.0000 | − | 17.3205i | 0.478913 | − | 0.829502i | ||||
\(437\) | −3.00000 | + | 5.19615i | −0.143509 | + | 0.248566i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000 | + | 27.7128i | 0.763638 | + | 1.32266i | 0.940963 | + | 0.338508i | \(0.109922\pi\) |
−0.177325 | + | 0.984152i | \(0.556744\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −80.0000 | −3.80521 | ||||||||
\(443\) | 6.00000 | + | 10.3923i | 0.285069 | + | 0.493753i | 0.972626 | − | 0.232377i | \(-0.0746503\pi\) |
−0.687557 | + | 0.726130i | \(0.741317\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.00000 | + | 10.3923i | −0.284427 | + | 0.492642i | ||||
\(446\) | 8.00000 | − | 13.8564i | 0.378811 | − | 0.656120i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −12.0000 | − | 20.7846i | −0.566947 | − | 0.981981i | ||||
\(449\) | 4.00000 | 0.188772 | 0.0943858 | − | 0.995536i | \(-0.469911\pi\) | ||||
0.0943858 | + | 0.995536i | \(0.469911\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.0000 | 0.941763 | ||||||||
\(452\) | −10.0000 | − | 17.3205i | −0.470360 | − | 0.814688i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.0000 | + | 17.3205i | −0.469323 | + | 0.812892i | ||||
\(455\) | 7.50000 | − | 12.9904i | 0.351605 | − | 0.608998i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0000 | − | 19.0526i | −0.514558 | − | 0.891241i | −0.999857 | − | 0.0168929i | \(-0.994623\pi\) |
0.485299 | − | 0.874348i | \(-0.338711\pi\) | |||||||
\(458\) | −12.0000 | −0.560723 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.0000 | −0.559503 | ||||||||
\(461\) | 6.00000 | + | 10.3923i | 0.279448 | + | 0.484018i | 0.971248 | − | 0.238071i | \(-0.0765153\pi\) |
−0.691800 | + | 0.722089i | \(0.743182\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.5000 | + | 28.5788i | −0.766820 | + | 1.32817i | 0.172459 | + | 0.985017i | \(0.444829\pi\) |
−0.939279 | + | 0.343155i | \(0.888505\pi\) | |||||||
\(464\) | 4.00000 | − | 6.92820i | 0.185695 | − | 0.321634i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.0000 | − | 41.5692i | −1.11178 | − | 1.92566i | ||||
\(467\) | −28.0000 | −1.29569 | −0.647843 | − | 0.761774i | \(-0.724329\pi\) | ||||
−0.647843 | + | 0.761774i | \(0.724329\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.0000 | 1.24674 | ||||||||
\(470\) | −4.00000 | − | 6.92820i | −0.184506 | − | 0.319574i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.00000 | − | 6.92820i | 0.183920 | − | 0.318559i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.500000 | − | 0.866025i | −0.0229416 | − | 0.0397360i | ||||
\(476\) | 48.0000 | 2.20008 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 52.0000 | 2.37842 | ||||||||
\(479\) | −3.00000 | − | 5.19615i | −0.137073 | − | 0.237418i | 0.789314 | − | 0.613990i | \(-0.210436\pi\) |
−0.926388 | + | 0.376571i | \(0.877103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.5000 | − | 21.6506i | 0.569951 | − | 0.987184i | ||||
\(482\) | 1.00000 | − | 1.73205i | 0.0455488 | − | 0.0788928i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | + | 12.1244i | 0.318182 | + | 0.551107i | ||||
\(485\) | 13.0000 | 0.590300 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.00000 | 0.226572 | 0.113286 | − | 0.993562i | \(-0.463862\pi\) | ||||
0.113286 | + | 0.993562i | \(0.463862\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.00000 | + | 3.46410i | −0.0903508 | + | 0.156492i | ||||
\(491\) | 11.0000 | − | 19.0526i | 0.496423 | − | 0.859830i | −0.503568 | − | 0.863955i | \(-0.667980\pi\) |
0.999991 | + | 0.00412539i | \(0.00131316\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.00000 | + | 13.8564i | 0.360302 | + | 0.624061i | ||||
\(494\) | 10.0000 | 0.449921 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.00000 | + | 5.19615i | 0.134568 | + | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.00000 | + | 13.8564i | −0.358129 | + | 0.620298i | −0.987648 | − | 0.156687i | \(-0.949919\pi\) |
0.629519 | + | 0.776985i | \(0.283252\pi\) | |||||||
\(500\) | 1.00000 | − | 1.73205i | 0.0447214 | − | 0.0774597i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.00000 | + | 10.3923i | 0.267793 | + | 0.463831i | ||||
\(503\) | 26.0000 | 1.15928 | 0.579641 | − | 0.814872i | \(-0.303193\pi\) | ||||
0.579641 | + | 0.814872i | \(0.303193\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −12.0000 | − | 20.7846i | −0.533465 | − | 0.923989i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.00000 | − | 13.8564i | 0.354943 | − | 0.614779i | ||||
\(509\) | −17.0000 | + | 29.4449i | −0.753512 | + | 1.30512i | 0.192599 | + | 0.981278i | \(0.438308\pi\) |
−0.946111 | + | 0.323843i | \(0.895025\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.50000 | − | 12.9904i | −0.331780 | − | 0.574661i | ||||
\(512\) | −32.0000 | −1.41421 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.50000 | + | 14.7224i | 0.374555 | + | 0.648748i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.00000 | − | 6.92820i | 0.175920 | − | 0.304702i | ||||
\(518\) | −15.0000 | + | 25.9808i | −0.659062 | + | 1.14153i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.0000 | 1.66481 | 0.832405 | − | 0.554168i | \(-0.186963\pi\) | ||||
0.832405 | + | 0.554168i | \(0.186963\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.0000 | 0.830812 | 0.415406 | − | 0.909636i | \(-0.363640\pi\) | ||||
0.415406 | + | 0.909636i | \(0.363640\pi\) | |||||||
\(524\) | −12.0000 | − | 20.7846i | −0.524222 | − | 0.907980i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.0000 | + | 48.4974i | −1.22086 | + | 2.11459i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | −4.00000 | −0.173749 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.00000 | −0.260133 | ||||||||
\(533\) | −25.0000 | − | 43.3013i | −1.08287 | − | 1.87559i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.00000 | − | 5.19615i | 0.129701 | − | 0.224649i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.0000 | + | 27.7128i | 0.689809 | + | 1.19478i | ||||
\(539\) | −4.00000 | −0.172292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.0000 | 1.41878 | 0.709390 | − | 0.704816i | \(-0.248970\pi\) | ||||
0.709390 | + | 0.704816i | \(0.248970\pi\) | |||||||
\(542\) | 13.0000 | + | 22.5167i | 0.558398 | + | 0.967173i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 32.0000 | − | 55.4256i | 1.37199 | − | 2.37635i | ||||
\(545\) | −5.00000 | + | 8.66025i | −0.214176 | + | 0.370965i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.5000 | − | 32.0429i | −0.791003 | − | 1.37006i | −0.925347 | − | 0.379122i | \(-0.876226\pi\) |
0.134344 | − | 0.990935i | \(-0.457107\pi\) | |||||||
\(548\) | −12.0000 | −0.512615 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.00000 | 0.170561 | ||||||||
\(551\) | −1.00000 | − | 1.73205i | −0.0426014 | − | 0.0737878i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.50000 | + | 7.79423i | −0.191359 | + | 0.331444i | ||||
\(554\) | −30.0000 | + | 51.9615i | −1.27458 | + | 2.20763i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.0000 | + | 22.5167i | 0.551323 | + | 0.954919i | ||||
\(557\) | 12.0000 | 0.508456 | 0.254228 | − | 0.967144i | \(-0.418179\pi\) | ||||
0.254228 | + | 0.967144i | \(0.418179\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.0000 | −0.845910 | ||||||||
\(560\) | 6.00000 | + | 10.3923i | 0.253546 | + | 0.439155i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.0000 | + | 31.1769i | −0.758610 | + | 1.31395i | 0.184950 | + | 0.982748i | \(0.440788\pi\) |
−0.943560 | + | 0.331202i | \(0.892546\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.00000 | + | 8.66025i | 0.210352 | + | 0.364340i | ||||
\(566\) | −24.0000 | −1.00880 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.50000 | + | 4.33013i | −0.104622 | + | 0.181210i | −0.913584 | − | 0.406651i | \(-0.866697\pi\) |
0.808962 | + | 0.587861i | \(0.200030\pi\) | |||||||
\(572\) | −10.0000 | + | 17.3205i | −0.418121 | + | 0.724207i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 30.0000 | + | 51.9615i | 1.25218 | + | 2.16883i | ||||
\(575\) | 6.00000 | 0.250217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.0000 | 0.707719 | 0.353860 | − | 0.935299i | \(-0.384869\pi\) | ||||
0.353860 | + | 0.935299i | \(0.384869\pi\) | |||||||
\(578\) | 47.0000 | + | 81.4064i | 1.95494 | + | 3.38606i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.00000 | − | 3.46410i | 0.0830455 | − | 0.143839i | ||||
\(581\) | 9.00000 | − | 15.5885i | 0.373383 | − | 0.646718i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.00000 | − | 3.46410i | −0.0828315 | − | 0.143468i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −36.0000 | −1.48715 | ||||||||
\(587\) | 9.00000 | + | 15.5885i | 0.371470 | + | 0.643404i | 0.989792 | − | 0.142520i | \(-0.0455206\pi\) |
−0.618322 | + | 0.785925i | \(0.712187\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 8.00000 | − | 13.8564i | 0.329355 | − | 0.570459i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.0000 | + | 17.3205i | 0.410997 | + | 0.711868i | ||||
\(593\) | −22.0000 | −0.903432 | −0.451716 | − | 0.892162i | \(-0.649188\pi\) | ||||
−0.451716 | + | 0.892162i | \(0.649188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.0000 | −0.983904 | ||||||||
\(596\) | 4.00000 | + | 6.92820i | 0.163846 | + | 0.283790i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −30.0000 | + | 51.9615i | −1.22679 | + | 2.12486i | ||||
\(599\) | 5.00000 | − | 8.66025i | 0.204294 | − | 0.353848i | −0.745613 | − | 0.666379i | \(-0.767843\pi\) |
0.949908 | + | 0.312531i | \(0.101177\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.0000 | + | 29.4449i | 0.693444 | + | 1.20108i | 0.970702 | + | 0.240285i | \(0.0772411\pi\) |
−0.277258 | + | 0.960796i | \(0.589426\pi\) | |||||||
\(602\) | 24.0000 | 0.978167 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.00000 | 0.0813788 | ||||||||
\(605\) | −3.50000 | − | 6.06218i | −0.142295 | − | 0.246463i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.500000 | + | 0.866025i | −0.0202944 | + | 0.0351509i | −0.875994 | − | 0.482322i | \(-0.839794\pi\) |
0.855700 | + | 0.517472i | \(0.173127\pi\) | |||||||
\(608\) | −4.00000 | + | 6.92820i | −0.162221 | + | 0.280976i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.00000 | − | 12.1244i | −0.283422 | − | 0.490901i | ||||
\(611\) | −20.0000 | −0.809113 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.00000 | 0.0403896 | 0.0201948 | − | 0.999796i | \(-0.493571\pi\) | ||||
0.0201948 | + | 0.999796i | \(0.493571\pi\) | |||||||
\(614\) | 16.0000 | + | 27.7128i | 0.645707 | + | 1.11840i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.00000 | + | 15.5885i | −0.362326 | + | 0.627568i | −0.988343 | − | 0.152242i | \(-0.951351\pi\) |
0.626017 | + | 0.779809i | \(0.284684\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.50000 | + | 16.4545i | 0.381837 | + | 0.661361i | 0.991325 | − | 0.131434i | \(-0.0419582\pi\) |
−0.609488 | + | 0.792796i | \(0.708625\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 48.0000 | 1.92462 | ||||||||
\(623\) | −18.0000 | − | 31.1769i | −0.721155 | − | 1.24908i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −7.00000 | + | 12.1244i | −0.279776 | + | 0.484587i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.00000 | − | 3.46410i | −0.0798087 | − | 0.138233i | ||||
\(629\) | −40.0000 | −1.59490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.0000 | −0.437903 | −0.218952 | − | 0.975736i | \(-0.570264\pi\) | ||||
−0.218952 | + | 0.975736i | \(0.570264\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20.0000 | − | 34.6410i | 0.794301 | − | 1.37577i | ||||
\(635\) | −4.00000 | + | 6.92820i | −0.158735 | + | 0.274937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.00000 | + | 8.66025i | 0.198107 | + | 0.343132i | ||||
\(638\) | 8.00000 | 0.316723 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.00000 | − | 10.3923i | 0.236617 | − | 0.409832i | −0.723124 | − | 0.690718i | \(-0.757295\pi\) |
0.959741 | + | 0.280885i | \(0.0906280\pi\) | |||||||
\(644\) | 18.0000 | − | 31.1769i | 0.709299 | − | 1.22854i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.00000 | − | 13.8564i | −0.314756 | − | 0.545173i | ||||
\(647\) | −38.0000 | −1.49393 | −0.746967 | − | 0.664861i | \(-0.768491\pi\) | ||||
−0.746967 | + | 0.664861i | \(0.768491\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.0000 | 0.628055 | ||||||||
\(650\) | −5.00000 | − | 8.66025i | −0.196116 | − | 0.339683i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19.0000 | − | 32.9090i | 0.744097 | − | 1.28881i | ||||
\(653\) | 2.00000 | − | 3.46410i | 0.0782660 | − | 0.135561i | −0.824236 | − | 0.566247i | \(-0.808395\pi\) |
0.902502 | + | 0.430686i | \(0.141728\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.00000 | + | 10.3923i | 0.234439 | + | 0.406061i | ||||
\(656\) | 40.0000 | 1.56174 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24.0000 | 0.935617 | ||||||||
\(659\) | 16.0000 | + | 27.7128i | 0.623272 | + | 1.07954i | 0.988872 | + | 0.148766i | \(0.0475302\pi\) |
−0.365601 | + | 0.930772i | \(0.619136\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.50000 | + | 6.06218i | −0.136134 | + | 0.235791i | −0.926030 | − | 0.377450i | \(-0.876801\pi\) |
0.789896 | + | 0.613241i | \(0.210135\pi\) | |||||||
\(662\) | −21.0000 | + | 36.3731i | −0.816188 | + | 1.41368i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.00000 | 0.116335 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0000 | 0.464642 | ||||||||
\(668\) | 12.0000 | + | 20.7846i | 0.464294 | + | 0.804181i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.00000 | − | 15.5885i | 0.347700 | − | 0.602235i | ||||
\(671\) | 7.00000 | − | 12.1244i | 0.270232 | − | 0.468056i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.5000 | − | 28.5788i | −0.636028 | − | 1.10163i | −0.986296 | − | 0.164984i | \(-0.947243\pi\) |
0.350268 | − | 0.936650i | \(-0.386091\pi\) | |||||||
\(674\) | −14.0000 | −0.539260 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 24.0000 | 0.923077 | ||||||||
\(677\) | −6.00000 | − | 10.3923i | −0.230599 | − | 0.399409i | 0.727386 | − | 0.686229i | \(-0.240735\pi\) |
−0.957984 | + | 0.286820i | \(0.907402\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.5000 | + | 33.7750i | −0.748341 | + | 1.29617i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.0000 | −0.688751 | −0.344375 | − | 0.938832i | \(-0.611909\pi\) | ||||
−0.344375 | + | 0.938832i | \(0.611909\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.00000 | 0.229248 | ||||||||
\(686\) | 15.0000 | + | 25.9808i | 0.572703 | + | 0.991950i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.00000 | − | 13.8564i | 0.304997 | − | 0.528271i | ||||
\(689\) | −5.00000 | + | 8.66025i | −0.190485 | + | 0.329929i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0000 | + | 17.3205i | 0.380418 | + | 0.658903i | 0.991122 | − | 0.132956i | \(-0.0424468\pi\) |
−0.610704 | + | 0.791859i | \(0.709113\pi\) | |||||||
\(692\) | −24.0000 | −0.912343 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.0000 | −0.759190 | ||||||||
\(695\) | −6.50000 | − | 11.2583i | −0.246559 | − | 0.427053i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −40.0000 | + | 69.2820i | −1.51511 | + | 2.62424i | ||||
\(698\) | 19.0000 | − | 32.9090i | 0.719161 | − | 1.24562i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.00000 | + | 5.19615i | 0.113389 | + | 0.196396i | ||||
\(701\) | −34.0000 | −1.28416 | −0.642081 | − | 0.766637i | \(-0.721929\pi\) | ||||
−0.642081 | + | 0.766637i | \(0.721929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.00000 | 0.188579 | ||||||||
\(704\) | −8.00000 | − | 13.8564i | −0.301511 | − | 0.522233i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.0000 | + | 20.7846i | −0.451626 | + | 0.782239i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.5000 | − | 21.6506i | −0.469447 | − | 0.813107i | 0.529943 | − | 0.848034i | \(-0.322213\pi\) |
−0.999390 | + | 0.0349269i | \(0.988880\pi\) | |||||||
\(710\) | 4.00000 | 0.150117 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.00000 | − | 8.66025i | 0.186989 | − | 0.323875i | ||||
\(716\) | −22.0000 | + | 38.1051i | −0.822179 | + | 1.42406i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18.0000 | − | 31.1769i | −0.671754 | − | 1.16351i | ||||
\(719\) | 30.0000 | 1.11881 | 0.559406 | − | 0.828894i | \(-0.311029\pi\) | ||||
0.559406 | + | 0.828894i | \(0.311029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −51.0000 | −1.89934 | ||||||||
\(722\) | −18.0000 | − | 31.1769i | −0.669891 | − | 1.16028i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.00000 | + | 8.66025i | −0.185824 | + | 0.321856i | ||||
\(725\) | −1.00000 | + | 1.73205i | −0.0371391 | + | 0.0643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.00000 | + | 13.8564i | 0.296704 | + | 0.513906i | 0.975380 | − | 0.220532i | \(-0.0707793\pi\) |
−0.678676 | + | 0.734438i | \(0.737446\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.0000 | −0.370117 | ||||||||
\(731\) | 16.0000 | + | 27.7128i | 0.591781 | + | 1.02500i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.0000 | − | 19.0526i | 0.406294 | − | 0.703722i | −0.588177 | − | 0.808732i | \(-0.700154\pi\) |
0.994471 | + | 0.105010i | \(0.0334875\pi\) | |||||||
\(734\) | 21.0000 | − | 36.3731i | 0.775124 | − | 1.34255i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24.0000 | − | 41.5692i | −0.884652 | − | 1.53226i | ||||
\(737\) | 18.0000 | 0.663039 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.0000 | −0.735712 | −0.367856 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367856 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(740\) | 5.00000 | + | 8.66025i | 0.183804 | + | 0.318357i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.00000 | − | 10.3923i | 0.220267 | − | 0.381514i | ||||
\(743\) | 16.0000 | − | 27.7128i | 0.586983 | − | 1.01668i | −0.407642 | − | 0.913142i | \(-0.633649\pi\) |
0.994625 | − | 0.103543i | \(-0.0330178\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.00000 | − | 3.46410i | −0.0732743 | − | 0.126915i | ||||
\(746\) | 22.0000 | 0.805477 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 32.0000 | 1.17004 | ||||||||
\(749\) | 9.00000 | + | 15.5885i | 0.328853 | + | 0.569590i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.5000 | + | 21.6506i | −0.456131 | + | 0.790043i | −0.998752 | − | 0.0499348i | \(-0.984099\pi\) |
0.542621 | + | 0.839978i | \(0.317432\pi\) | |||||||
\(752\) | 8.00000 | − | 13.8564i | 0.291730 | − | 0.505291i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.0000 | − | 17.3205i | −0.364179 | − | 0.630776i | ||||
\(755\) | −1.00000 | −0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −53.0000 | −1.92632 | −0.963159 | − | 0.268933i | \(-0.913329\pi\) | ||||
−0.963159 | + | 0.268933i | \(0.913329\pi\) | |||||||
\(758\) | −11.0000 | − | 19.0526i | −0.399538 | − | 0.692020i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.00000 | − | 15.5885i | 0.326250 | − | 0.565081i | −0.655515 | − | 0.755182i | \(-0.727548\pi\) |
0.981764 | + | 0.190101i | \(0.0608816\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.0000 | − | 25.9808i | −0.543036 | − | 0.940567i | ||||
\(764\) | −8.00000 | −0.289430 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 48.0000 | 1.73431 | ||||||||
\(767\) | −20.0000 | − | 34.6410i | −0.722158 | − | 1.25081i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.5000 | − | 32.0429i | 0.667127 | − | 1.15550i | −0.311577 | − | 0.950221i | \(-0.600857\pi\) |
0.978704 | − | 0.205277i | \(-0.0658095\pi\) | |||||||
\(770\) | −6.00000 | + | 10.3923i | −0.216225 | + | 0.374513i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.00000 | − | 8.66025i | −0.179954 | − | 0.311689i | ||||
\(773\) | 18.0000 | 0.647415 | 0.323708 | − | 0.946157i | \(-0.395071\pi\) | ||||
0.323708 | + | 0.946157i | \(0.395071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.0000 | − | 41.5692i | 0.860442 | − | 1.49033i | ||||
\(779\) | 5.00000 | − | 8.66025i | 0.179144 | − | 0.310286i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00000 | + | 3.46410i | 0.0715656 | + | 0.123955i | ||||
\(782\) | 96.0000 | 3.43295 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.00000 | −0.285714 | ||||||||
\(785\) | 1.00000 | + | 1.73205i | 0.0356915 | + | 0.0618195i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.5000 | − | 35.5070i | 0.730746 | − | 1.26569i | −0.225819 | − | 0.974169i | \(-0.572506\pi\) |
0.956565 | − | 0.291520i | \(-0.0941610\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.00000 | + | 5.19615i | 0.106735 | + | 0.184871i | ||||
\(791\) | −30.0000 | −1.06668 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.0000 | −1.24289 | ||||||||
\(794\) | −2.00000 | − | 3.46410i | −0.0709773 | − | 0.122936i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.0000 | − | 29.4449i | 0.602549 | − | 1.04365i | ||||
\(797\) | 8.00000 | − | 13.8564i | 0.283375 | − | 0.490819i | −0.688839 | − | 0.724914i | \(-0.741879\pi\) |
0.972214 | + | 0.234095i | \(0.0752127\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.0000 | + | 27.7128i | 0.566039 | + | 0.980409i | ||||
\(800\) | 8.00000 | 0.282843 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.0000 | −0.423735 | ||||||||
\(803\) | −5.00000 | − | 8.66025i | −0.176446 | − | 0.305614i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.00000 | + | 15.5885i | −0.317208 | + | 0.549421i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.0000 | −0.562530 | −0.281265 | − | 0.959630i | \(-0.590754\pi\) | ||||
−0.281265 | + | 0.959630i | \(0.590754\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.0000 | −0.421377 | −0.210688 | − | 0.977553i | \(-0.567571\pi\) | ||||
−0.210688 | + | 0.977553i | \(0.567571\pi\) | |||||||
\(812\) | 6.00000 | + | 10.3923i | 0.210559 | + | 0.364698i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.0000 | + | 17.3205i | −0.350500 | + | 0.607083i | ||||
\(815\) | −9.50000 | + | 16.4545i | −0.332770 | + | 0.576375i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.00000 | − | 3.46410i | −0.0699711 | − | 0.121194i | ||||
\(818\) | 14.0000 | 0.489499 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.0000 | 0.698430 | ||||||||
\(821\) | −24.0000 | − | 41.5692i | −0.837606 | − | 1.45078i | −0.891891 | − | 0.452250i | \(-0.850621\pi\) |
0.0542853 | − | 0.998525i | \(-0.482712\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.50000 | + | 9.52628i | −0.191718 | + | 0.332065i | −0.945820 | − | 0.324692i | \(-0.894739\pi\) |
0.754102 | + | 0.656758i | \(0.228073\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.0000 | + | 41.5692i | 0.835067 | + | 1.44638i | ||||
\(827\) | 28.0000 | 0.973655 | 0.486828 | − | 0.873498i | \(-0.338154\pi\) | ||||
0.486828 | + | 0.873498i | \(0.338154\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.0000 | −1.77130 | −0.885652 | − | 0.464350i | \(-0.846288\pi\) | ||||
−0.885652 | + | 0.464350i | \(0.846288\pi\) | |||||||
\(830\) | −6.00000 | − | 10.3923i | −0.208263 | − | 0.360722i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.0000 | + | 34.6410i | −0.693375 | + | 1.20096i | ||||
\(833\) | 8.00000 | − | 13.8564i | 0.277184 | − | 0.480096i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.00000 | − | 10.3923i | −0.207639 | − | 0.359641i | ||||
\(836\) | −4.00000 | −0.138343 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −64.0000 | −2.21084 | ||||||||
\(839\) | 2.00000 | + | 3.46410i | 0.0690477 | + | 0.119594i | 0.898482 | − | 0.439010i | \(-0.144671\pi\) |
−0.829435 | + | 0.558604i | \(0.811337\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.5000 | − | 21.6506i | 0.431034 | − | 0.746574i | ||||
\(842\) | 1.00000 | − | 1.73205i | 0.0344623 | − | 0.0596904i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −23.0000 | − | 39.8372i | −0.791693 | − | 1.37125i | ||||
\(845\) | −12.0000 | −0.412813 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.0000 | 0.721569 | ||||||||
\(848\) | −4.00000 | − | 6.92820i | −0.137361 | − | 0.237915i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.00000 | + | 13.8564i | −0.274398 | + | 0.475271i | ||||
\(851\) | −15.0000 | + | 25.9808i | −0.514193 | + | 0.890609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.5000 | − | 18.1865i | −0.359513 | − | 0.622695i | 0.628366 | − | 0.777918i | \(-0.283724\pi\) |
−0.987880 | + | 0.155222i | \(0.950391\pi\) | |||||||
\(854\) | 42.0000 | 1.43721 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.0000 | + | 22.5167i | 0.444072 | + | 0.769154i | 0.997987 | − | 0.0634184i | \(-0.0202003\pi\) |
−0.553915 | + | 0.832573i | \(0.686867\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.50000 | + | 6.06218i | −0.119418 | + | 0.206839i | −0.919537 | − | 0.393003i | \(-0.871436\pi\) |
0.800119 | + | 0.599841i | \(0.204770\pi\) | |||||||
\(860\) | 4.00000 | − | 6.92820i | 0.136399 | − | 0.236250i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.0000 | + | 51.9615i | 1.02180 | + | 1.76982i | ||||
\(863\) | −4.00000 | −0.136162 | −0.0680808 | − | 0.997680i | \(-0.521688\pi\) | ||||
−0.0680808 | + | 0.997680i | \(0.521688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0000 | 0.408012 | ||||||||
\(866\) | −38.0000 | − | 65.8179i | −1.29129 | − | 2.23658i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.00000 | + | 5.19615i | −0.101768 | + | 0.176267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.5000 | − | 38.9711i | −0.762383 | − | 1.32049i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12.0000 | −0.405906 | ||||||||
\(875\) | −1.50000 | − | 2.59808i | −0.0507093 | − | 0.0878310i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.50000 | + | 7.79423i | −0.151954 | + | 0.263192i | −0.931946 | − | 0.362598i | \(-0.881890\pi\) |
0.779992 | + | 0.625790i | \(0.215223\pi\) | |||||||
\(878\) | −32.0000 | + | 55.4256i | −1.07995 | + | 1.87052i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.00000 | + | 6.92820i | 0.134840 | + | 0.233550i | ||||
\(881\) | −38.0000 | −1.28025 | −0.640126 | − | 0.768270i | \(-0.721118\pi\) | ||||
−0.640126 | + | 0.768270i | \(0.721118\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.0000 | −0.639401 | −0.319700 | − | 0.947519i | \(-0.603582\pi\) | ||||
−0.319700 | + | 0.947519i | \(0.603582\pi\) | |||||||
\(884\) | −40.0000 | − | 69.2820i | −1.34535 | − | 2.33021i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.0000 | + | 20.7846i | −0.403148 | + | 0.698273i | ||||
\(887\) | 24.0000 | − | 41.5692i | 0.805841 | − | 1.39576i | −0.109881 | − | 0.993945i | \(-0.535047\pi\) |
0.915722 | − | 0.401813i | \(-0.131620\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.0000 | − | 20.7846i | −0.402467 | − | 0.697093i | ||||
\(890\) | −24.0000 | −0.804482 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.0000 | 0.535720 | ||||||||
\(893\) | −2.00000 | − | 3.46410i | −0.0669274 | − | 0.115922i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.0000 | − | 19.0526i | 0.367689 | − | 0.636857i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.00000 | + | 6.92820i | 0.133482 | + | 0.231197i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.0000 | 0.533037 | ||||||||
\(902\) | 20.0000 | + | 34.6410i | 0.665927 | + | 1.15342i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.50000 | − | 4.33013i | 0.0831028 | − | 0.143938i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.5000 | + | 18.1865i | 0.348647 | + | 0.603874i | 0.986009 | − | 0.166690i | \(-0.0533080\pi\) |
−0.637363 | + | 0.770564i | \(0.719975\pi\) | |||||||
\(908\) | −20.0000 | −0.663723 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 30.0000 | 0.994490 | ||||||||
\(911\) | −20.0000 | − | 34.6410i | −0.662630 | − | 1.14771i | −0.979922 | − | 0.199380i | \(-0.936107\pi\) |
0.317293 | − | 0.948328i | \(-0.397226\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.00000 | − | 10.3923i | 0.198571 | − | 0.343935i | ||||
\(914\) | 22.0000 | − | 38.1051i | 0.727695 | − | 1.26041i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.00000 | − | 10.3923i | −0.198246 | − | 0.343371i | ||||
\(917\) | −36.0000 | −1.18882 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.0000 | 1.31948 | 0.659739 | − | 0.751495i | \(-0.270667\pi\) | ||||
0.659739 | + | 0.751495i | \(0.270667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.0000 | + | 20.7846i | −0.395199 | + | 0.684505i | ||||
\(923\) | 5.00000 | − | 8.66025i | 0.164577 | − | 0.285056i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.50000 | − | 4.33013i | −0.0821995 | − | 0.142374i | ||||
\(926\) | −66.0000 | −2.16889 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16.0000 | 0.525226 | ||||||||
\(929\) | 17.0000 | + | 29.4449i | 0.557752 | + | 0.966055i | 0.997684 | + | 0.0680235i | \(0.0216693\pi\) |
−0.439932 | + | 0.898031i | \(0.644997\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | + | 1.73205i | −0.0327737 | + | 0.0567657i | ||||
\(932\) | 24.0000 | − | 41.5692i | 0.786146 | − | 1.36165i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −28.0000 | − | 48.4974i | −0.916188 | − | 1.58688i | ||||
\(935\) | −16.0000 | −0.523256 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.0000 | 1.07806 | 0.539032 | − | 0.842286i | \(-0.318790\pi\) | ||||
0.539032 | + | 0.842286i | \(0.318790\pi\) | |||||||
\(938\) | 27.0000 | + | 46.7654i | 0.881581 | + | 1.52694i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.00000 | − | 6.92820i | 0.130466 | − | 0.225973i | ||||
\(941\) | 11.0000 | − | 19.0526i | 0.358590 | − | 0.621096i | −0.629136 | − | 0.777295i | \(-0.716591\pi\) |
0.987725 | + | 0.156200i | \(0.0499244\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.0000 | + | 51.9615i | 0.976934 | + | 1.69210i | ||||
\(944\) | 32.0000 | 1.04151 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.0000 | 0.520205 | ||||||||
\(947\) | −24.0000 | − | 41.5692i | −0.779895 | − | 1.35082i | −0.932002 | − | 0.362454i | \(-0.881939\pi\) |
0.152106 | − | 0.988364i | \(-0.451394\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.5000 | + | 21.6506i | −0.405767 | + | 0.702809i | ||||
\(950\) | 1.00000 | − | 1.73205i | 0.0324443 | − | 0.0561951i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.0000 | 1.29573 | 0.647864 | − | 0.761756i | \(-0.275663\pi\) | ||||
0.647864 | + | 0.761756i | \(0.275663\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.00000 | 0.129437 | ||||||||
\(956\) | 26.0000 | + | 45.0333i | 0.840900 | + | 1.45648i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.00000 | − | 10.3923i | 0.193851 | − | 0.335760i | ||||
\(959\) | −9.00000 | + | 15.5885i | −0.290625 | + | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5000 | + | 26.8468i | 0.500000 | + | 0.866025i | ||||
\(962\) | 50.0000 | 1.61206 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.00000 | 0.0644157 | ||||||||
\(965\) | 2.50000 | + | 4.33013i | 0.0804778 | + | 0.139392i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.50000 | − | 11.2583i | 0.209026 | − | 0.362043i | −0.742382 | − | 0.669977i | \(-0.766304\pi\) |
0.951408 | + | 0.307933i | \(0.0996374\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13.0000 | + | 22.5167i | 0.417405 | + | 0.722966i | ||||
\(971\) | −12.0000 | −0.385098 | −0.192549 | − | 0.981287i | \(-0.561675\pi\) | ||||
−0.192549 | + | 0.981287i | \(0.561675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.0000 | 1.25028 | ||||||||
\(974\) | 5.00000 | + | 8.66025i | 0.160210 | + | 0.277492i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.0000 | − | 24.2487i | 0.448129 | − | 0.776182i | ||||
\(977\) | 31.0000 | − | 53.6936i | 0.991778 | − | 1.71781i | 0.385063 | − | 0.922890i | \(-0.374180\pi\) |
0.606715 | − | 0.794919i | \(-0.292487\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.0000 | − | 20.7846i | −0.383522 | − | 0.664279i | ||||
\(980\) | −4.00000 | −0.127775 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 44.0000 | 1.40410 | ||||||||
\(983\) | −27.0000 | − | 46.7654i | −0.861166 | − | 1.49158i | −0.870804 | − | 0.491630i | \(-0.836401\pi\) |
0.00963785 | − | 0.999954i | \(-0.496932\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −16.0000 | + | 27.7128i | −0.509544 | + | 0.882556i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.00000 | + | 8.66025i | 0.159071 | + | 0.275519i | ||||
\(989\) | 24.0000 | 0.763156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.0000 | −0.794151 | −0.397076 | − | 0.917786i | \(-0.629975\pi\) | ||||
−0.397076 | + | 0.917786i | \(0.629975\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.00000 | + | 10.3923i | −0.190308 | + | 0.329624i | ||||
\(995\) | −8.50000 | + | 14.7224i | −0.269468 | + | 0.466732i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.0000 | + | 36.3731i | 0.665077 | + | 1.15195i | 0.979265 | + | 0.202586i | \(0.0649345\pi\) |
−0.314188 | + | 0.949361i | \(0.601732\pi\) | |||||||
\(998\) | −32.0000 | −1.01294 | ||||||||
\(999\) | 0 | 0 |
(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 | 405.2.e.h.271.1 | 2 | ||
3.2 | odd | 2 | 405.2.e.b.271.1 | 2 | |||
9.2 | odd | 6 | 405.2.e.b.136.1 | 2 | |||
9.4 | even | 3 | 135.2.a.a.1.1 | ✓ | 1 | ||
9.5 | odd | 6 | 135.2.a.b.1.1 | yes | 1 | ||
9.7 | even | 3 | inner | 405.2.e.h.136.1 | 2 | ||
36.23 | even | 6 | 2160.2.a.v.1.1 | 1 | |||
36.31 | odd | 6 | 2160.2.a.j.1.1 | 1 | |||
45.4 | even | 6 | 675.2.a.i.1.1 | 1 | |||
45.13 | odd | 12 | 675.2.b.a.649.2 | 2 | |||
45.14 | odd | 6 | 675.2.a.a.1.1 | 1 | |||
45.22 | odd | 12 | 675.2.b.a.649.1 | 2 | |||
45.23 | even | 12 | 675.2.b.b.649.1 | 2 | |||
45.32 | even | 12 | 675.2.b.b.649.2 | 2 | |||
63.13 | odd | 6 | 6615.2.a.a.1.1 | 1 | |||
63.41 | even | 6 | 6615.2.a.j.1.1 | 1 | |||
72.5 | odd | 6 | 8640.2.a.c.1.1 | 1 | |||
72.13 | even | 6 | 8640.2.a.bh.1.1 | 1 | |||
72.59 | even | 6 | 8640.2.a.bb.1.1 | 1 | |||
72.67 | odd | 6 | 8640.2.a.ce.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.2.a.a.1.1 | ✓ | 1 | 9.4 | even | 3 | ||
135.2.a.b.1.1 | yes | 1 | 9.5 | odd | 6 | ||
405.2.e.b.136.1 | 2 | 9.2 | odd | 6 | |||
405.2.e.b.271.1 | 2 | 3.2 | odd | 2 | |||
405.2.e.h.136.1 | 2 | 9.7 | even | 3 | inner | ||
405.2.e.h.271.1 | 2 | 1.1 | even | 1 | trivial | ||
675.2.a.a.1.1 | 1 | 45.14 | odd | 6 | |||
675.2.a.i.1.1 | 1 | 45.4 | even | 6 | |||
675.2.b.a.649.1 | 2 | 45.22 | odd | 12 | |||
675.2.b.a.649.2 | 2 | 45.13 | odd | 12 | |||
675.2.b.b.649.1 | 2 | 45.23 | even | 12 | |||
675.2.b.b.649.2 | 2 | 45.32 | even | 12 | |||
2160.2.a.j.1.1 | 1 | 36.31 | odd | 6 | |||
2160.2.a.v.1.1 | 1 | 36.23 | even | 6 | |||
6615.2.a.a.1.1 | 1 | 63.13 | odd | 6 | |||
6615.2.a.j.1.1 | 1 | 63.41 | even | 6 | |||
8640.2.a.c.1.1 | 1 | 72.5 | odd | 6 | |||
8640.2.a.bb.1.1 | 1 | 72.59 | even | 6 | |||
8640.2.a.bh.1.1 | 1 | 72.13 | even | 6 | |||
8640.2.a.ce.1.1 | 1 | 72.67 | odd | 6 |