Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [880,2,Mod(81,880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(880, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("880.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 880 = 2^{4} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 880.bo (of order \(5\), degree \(4\), 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: | \(7.02683537787\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 110) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 81.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 880.81 |
Dual form | 880.2.bo.a.641.1 |
$q$-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 \(\left(\mathbb{Z}/880\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(177\) | \(321\) | \(661\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | + | 3.07768i | −0.577350 | + | 1.77690i | 0.0506828 | + | 0.998715i | \(0.483860\pi\) |
−0.628033 | + | 0.778187i | \(0.716140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.809017 | − | 0.587785i | 0.361803 | − | 0.262866i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.809017 | − | 2.48990i | −0.305780 | − | 0.941093i | −0.979385 | − | 0.202002i | \(-0.935255\pi\) |
0.673605 | − | 0.739091i | \(-0.264745\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.04508 | − | 4.39201i | −2.01503 | − | 1.46400i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.54508 | − | 2.12663i | 0.767372 | − | 0.641202i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.30902 | + | 0.951057i | 0.363056 | + | 0.263776i | 0.754326 | − | 0.656500i | \(-0.227964\pi\) |
−0.391270 | + | 0.920276i | \(0.627964\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | + | 3.07768i | 0.258199 | + | 0.794654i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.23607 | − | 3.07768i | 1.02740 | − | 0.746448i | 0.0596113 | − | 0.998222i | \(-0.481014\pi\) |
0.967786 | + | 0.251774i | \(0.0810139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.26393 | − | 3.88998i | 0.289966 | − | 0.892423i | −0.694900 | − | 0.719106i | \(-0.744551\pi\) |
0.984866 | − | 0.173317i | \(-0.0554485\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.47214 | 1.84877 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.145898 | −0.0304218 | −0.0152109 | − | 0.999884i | \(-0.504842\pi\) | ||||
−0.0152109 | + | 0.999884i | \(0.504842\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.309017 | − | 0.951057i | 0.0618034 | − | 0.190211i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11.7082 | − | 8.50651i | 2.25324 | − | 1.63708i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.381966 | − | 1.17557i | −0.0709293 | − | 0.218298i | 0.909308 | − | 0.416124i | \(-0.136612\pi\) |
−0.980237 | + | 0.197826i | \(0.936612\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.85410 | − | 4.25325i | −1.05143 | − | 0.763907i | −0.0789443 | − | 0.996879i | \(-0.525155\pi\) |
−0.972483 | + | 0.232972i | \(0.925155\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.00000 | + | 9.95959i | 0.696311 | + | 1.73374i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.11803 | − | 1.53884i | −0.358013 | − | 0.260112i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.263932 | − | 0.812299i | −0.0433902 | − | 0.133541i | 0.927015 | − | 0.375025i | \(-0.122366\pi\) |
−0.970405 | + | 0.241484i | \(0.922366\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.23607 | + | 3.07768i | −0.678314 | + | 0.492824i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.572949 | + | 1.76336i | −0.0894796 | + | 0.275390i | −0.985776 | − | 0.168066i | \(-0.946248\pi\) |
0.896296 | + | 0.443456i | \(0.146248\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.23607 | 1.40849 | 0.704244 | − | 0.709958i | \(-0.251286\pi\) | ||||
0.704244 | + | 0.709958i | \(0.251286\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.47214 | −1.11388 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.50000 | + | 10.7719i | −0.510527 | + | 1.57124i | 0.280748 | + | 0.959782i | \(0.409418\pi\) |
−0.791275 | + | 0.611460i | \(0.790582\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.118034 | − | 0.0857567i | 0.0168620 | − | 0.0122510i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.23607 | + | 16.1150i | 0.733196 | + | 2.25655i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.736068 | − | 0.534785i | −0.101107 | − | 0.0734583i | 0.536083 | − | 0.844165i | \(-0.319903\pi\) |
−0.637190 | + | 0.770707i | \(0.719903\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.809017 | − | 3.21644i | 0.109088 | − | 0.433705i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.7082 | + | 7.77997i | 1.41834 | + | 1.03048i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.736068 | − | 2.26538i | −0.0958279 | − | 0.294928i | 0.891641 | − | 0.452744i | \(-0.149555\pi\) |
−0.987469 | + | 0.157816i | \(0.949555\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.23607 | + | 5.25731i | −0.926484 | + | 0.673130i | −0.945129 | − | 0.326696i | \(-0.894065\pi\) |
0.0186458 | + | 0.999826i | \(0.494065\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.04508 | + | 18.6049i | −0.761609 | + | 2.34399i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.61803 | 0.200692 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.763932 | −0.0933292 | −0.0466646 | − | 0.998911i | \(-0.514859\pi\) | ||||
−0.0466646 | + | 0.998911i | \(0.514859\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.145898 | − | 0.449028i | 0.0175641 | − | 0.0540566i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.7082 | − | 7.77997i | 1.27083 | − | 0.923312i | 0.271595 | − | 0.962412i | \(-0.412449\pi\) |
0.999235 | + | 0.0390997i | \(0.0124490\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.527864 | − | 1.62460i | −0.0617818 | − | 0.190145i | 0.915402 | − | 0.402542i | \(-0.131873\pi\) |
−0.977184 | + | 0.212397i | \(0.931873\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.61803 | + | 1.90211i | 0.302305 | + | 0.219637i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.35410 | − | 4.61653i | −0.838078 | − | 0.526102i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.23607 | − | 0.898056i | −0.139069 | − | 0.101039i | 0.516076 | − | 0.856543i | \(-0.327392\pi\) |
−0.655144 | + | 0.755504i | \(0.727392\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.54508 | + | 23.2214i | 0.838343 | + | 2.58015i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.7082 | − | 9.23305i | 1.39491 | − | 1.01346i | 0.399600 | − | 0.916690i | \(-0.369149\pi\) |
0.995307 | − | 0.0967693i | \(-0.0308509\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.61803 | − | 4.97980i | 0.175500 | − | 0.540135i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.00000 | 0.428845 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.0344 | −1.27565 | −0.637824 | − | 0.770182i | \(-0.720165\pi\) | ||||
−0.637824 | + | 0.770182i | \(0.720165\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.30902 | − | 4.02874i | 0.137222 | − | 0.422327i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.9443 | − | 13.7638i | 1.96443 | − | 1.42724i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.26393 | − | 3.88998i | −0.129677 | − | 0.399104i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.70820 | + | 7.05342i | 0.985719 | + | 0.716167i | 0.958979 | − | 0.283476i | \(-0.0914876\pi\) |
0.0267394 | + | 0.999642i | \(0.491488\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −24.7254 | + | 1.67760i | −2.48500 | + | 0.168605i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.00000 | − | 2.17963i | −0.298511 | − | 0.216881i | 0.428440 | − | 0.903570i | \(-0.359063\pi\) |
−0.726951 | + | 0.686689i | \(0.759063\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.50000 | + | 10.7719i | 0.344865 | + | 1.06139i | 0.961656 | + | 0.274259i | \(0.0884325\pi\) |
−0.616791 | + | 0.787127i | \(0.711567\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.85410 | − | 4.97980i | 0.668892 | − | 0.485978i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.32624 | − | 7.15942i | 0.224886 | − | 0.692128i | −0.773417 | − | 0.633897i | \(-0.781454\pi\) |
0.998303 | − | 0.0582304i | \(-0.0185458\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.52786 | 0.721039 | 0.360519 | − | 0.932752i | \(-0.382599\pi\) | ||||
0.360519 | + | 0.932752i | \(0.382599\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.76393 | 0.262341 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.94427 | − | 5.98385i | 0.182902 | − | 0.562914i | −0.817004 | − | 0.576632i | \(-0.804367\pi\) |
0.999906 | + | 0.0137181i | \(0.00436676\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.118034 | + | 0.0857567i | −0.0110067 | + | 0.00799685i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.73607 | − | 11.4984i | −0.345400 | − | 1.06303i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.0902 | − | 8.05748i | −1.01663 | − | 0.738628i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.95492 | − | 10.8249i | 0.177720 | − | 0.984081i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.85410 | − | 3.52671i | −0.437680 | − | 0.317993i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.309017 | − | 0.951057i | −0.0276393 | − | 0.0850651i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.92705 | + | 1.40008i | −0.170998 | + | 0.124237i | −0.669993 | − | 0.742368i | \(-0.733703\pi\) |
0.498995 | + | 0.866605i | \(0.333703\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.23607 | + | 28.4257i | −0.813190 | + | 2.50274i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.4164 | −0.997456 | −0.498728 | − | 0.866758i | \(-0.666199\pi\) | ||||
−0.498728 | + | 0.866758i | \(0.666199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.7082 | −0.928519 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.47214 | − | 13.7638i | 0.384900 | − | 1.18460i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.23607 | − | 3.07768i | 0.361912 | − | 0.262944i | −0.391937 | − | 0.919992i | \(-0.628195\pi\) |
0.753849 | + | 0.657048i | \(0.228195\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.51722 | + | 7.74721i | 0.213508 | + | 0.657110i | 0.999256 | + | 0.0385633i | \(0.0122781\pi\) |
−0.785748 | + | 0.618546i | \(0.787722\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −29.6525 | − | 21.5438i | −2.49719 | − | 1.81431i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.35410 | − | 0.363271i | 0.447732 | − | 0.0303783i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.00000 | − | 0.726543i | −0.0830455 | − | 0.0603361i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.145898 | + | 0.449028i | 0.0120335 | + | 0.0370352i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.23607 | − | 2.35114i | 0.265109 | − | 0.192613i | −0.447287 | − | 0.894390i | \(-0.647610\pi\) |
0.712396 | + | 0.701777i | \(0.247610\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.90983 | + | 12.0332i | −0.318177 | + | 0.979250i | 0.656249 | + | 0.754544i | \(0.272142\pi\) |
−0.974427 | + | 0.224705i | \(0.927858\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −39.1246 | −3.16304 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.23607 | −0.581215 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.66312 | − | 8.19624i | 0.212540 | − | 0.654131i | −0.786779 | − | 0.617235i | \(-0.788253\pi\) |
0.999319 | − | 0.0368962i | \(-0.0117471\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.38197 | − | 1.73060i | 0.188902 | − | 0.137245i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.118034 | + | 0.363271i | 0.00930238 | + | 0.0286298i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.85410 | − | 4.25325i | −0.458529 | − | 0.333141i | 0.334425 | − | 0.942422i | \(-0.391458\pi\) |
−0.792954 | + | 0.609282i | \(0.791458\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.09017 | + | 5.70634i | 0.707669 | + | 0.444238i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.39919 | + | 4.64928i | 0.495184 | + | 0.359772i | 0.807174 | − | 0.590313i | \(-0.200996\pi\) |
−0.311990 | + | 0.950085i | \(0.600996\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.20820 | − | 9.87384i | −0.246785 | − | 0.759526i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.7254 | + | 17.9641i | −1.89080 | + | 1.37375i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.89919 | + | 12.0005i | −0.296450 | + | 0.912378i | 0.686281 | + | 0.727337i | \(0.259242\pi\) |
−0.982731 | + | 0.185042i | \(0.940758\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.61803 | −0.197905 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.70820 | 0.579384 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.899187 | − | 2.76741i | 0.0672084 | − | 0.206846i | −0.911812 | − | 0.410607i | \(-0.865317\pi\) |
0.979021 | + | 0.203761i | \(0.0653167\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.5623 | − | 12.0332i | 1.23107 | − | 0.894422i | 0.234097 | − | 0.972213i | \(-0.424787\pi\) |
0.996970 | + | 0.0777911i | \(0.0247867\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.94427 | − | 27.5276i | −0.661180 | − | 2.03490i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.690983 | − | 0.502029i | −0.0508021 | − | 0.0369099i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.23607 | − | 16.8415i | 0.309772 | − | 1.23157i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −30.6525 | − | 22.2703i | −2.22964 | − | 1.61993i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.85410 | − | 24.1724i | −0.568303 | − | 1.74906i | −0.657928 | − | 0.753081i | \(-0.728567\pi\) |
0.0896251 | − | 0.995976i | \(-0.471433\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.38197 | − | 3.18368i | 0.315421 | − | 0.229167i | −0.418798 | − | 0.908079i | \(-0.637549\pi\) |
0.734219 | + | 0.678913i | \(0.237549\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.61803 | + | 4.97980i | −0.115870 | + | 0.356611i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.90983 | −0.349811 | −0.174905 | − | 0.984585i | \(-0.555962\pi\) | ||||
−0.174905 | + | 0.984585i | \(0.555962\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.70820 | −0.121091 | −0.0605457 | − | 0.998165i | \(-0.519284\pi\) | ||||
−0.0605457 | + | 0.998165i | \(0.519284\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.763932 | − | 2.35114i | 0.0538836 | − | 0.165837i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.61803 | + | 1.90211i | −0.183750 | + | 0.133502i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.572949 | + | 1.76336i | 0.0400165 | + | 0.123158i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.881966 | + | 0.640786i | 0.0613009 | + | 0.0445377i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.05573 | − | 12.5882i | −0.349712 | − | 0.870747i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.9443 | + | 12.3107i | 1.16649 | + | 0.847506i | 0.990585 | − | 0.136901i | \(-0.0437142\pi\) |
0.175907 | + | 0.984407i | \(0.443714\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.2361 | + | 40.7364i | 0.906920 | + | 2.79121i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.47214 | − | 5.42882i | 0.509595 | − | 0.370243i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.85410 | + | 18.0171i | −0.397402 | + | 1.22308i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.52786 | 0.373538 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.47214 | 0.569898 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.98936 | + | 9.20029i | −0.200182 | + | 0.616097i | 0.799695 | + | 0.600407i | \(0.204995\pi\) |
−0.999877 | + | 0.0156905i | \(0.995005\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.04508 | + | 4.39201i | −0.403006 | + | 0.292801i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.09017 | + | 15.6659i | 0.337846 | + | 1.03978i | 0.965303 | + | 0.261133i | \(0.0840960\pi\) |
−0.627456 | + | 0.778652i | \(0.715904\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.7984 | + | 16.5640i | 1.50656 | + | 1.09458i | 0.967675 | + | 0.252199i | \(0.0811537\pi\) |
0.538884 | + | 0.842380i | \(0.318846\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21.5623 | − | 18.0171i | 1.41870 | − | 1.18544i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.3262 | − | 8.95554i | −0.807519 | − | 0.586697i | 0.105591 | − | 0.994410i | \(-0.466326\pi\) |
−0.913110 | + | 0.407713i | \(0.866326\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.50000 | + | 10.7719i | 0.228315 | + | 0.702681i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.00000 | − | 2.90617i | 0.259828 | − | 0.188776i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.94427 | + | 9.06154i | −0.190449 | + | 0.586142i | −1.00000 | 0.000908170i | \(-0.999711\pi\) | |
0.809550 | + | 0.587050i | \(0.199711\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.85410 | −0.119433 | −0.0597166 | − | 0.998215i | \(-0.519020\pi\) | ||||
−0.0597166 | + | 0.998215i | \(0.519020\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −35.5967 | −2.28353 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.0450850 | − | 0.138757i | 0.00288037 | − | 0.00886488i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.35410 | − | 3.88998i | 0.340673 | − | 0.247514i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.7082 | + | 48.3449i | 0.995467 | + | 3.06373i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.11803 | − | 5.89810i | −0.512406 | − | 0.372285i | 0.301330 | − | 0.953520i | \(-0.402570\pi\) |
−0.813735 | + | 0.581235i | \(0.802570\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.371323 | + | 0.310271i | −0.0233449 | + | 0.0195066i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.7082 | + | 9.95959i | 0.858441 | + | 0.623694i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.70820 | − | 11.4127i | −0.231311 | − | 0.711903i | −0.997589 | − | 0.0693940i | \(-0.977893\pi\) |
0.766278 | − | 0.642509i | \(-0.222107\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.80902 | + | 1.31433i | −0.112407 | + | 0.0816684i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.85410 | + | 8.78402i | −0.176664 | + | 0.543717i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.7984 | −1.59080 | −0.795398 | − | 0.606088i | \(-0.792738\pi\) | ||||
−0.795398 | + | 0.606088i | \(0.792738\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.909830 | −0.0558904 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.0344 | − | 37.0382i | 0.736496 | − | 2.26670i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.2361 | + | 10.3431i | −0.867988 | + | 0.630630i | −0.930046 | − | 0.367442i | \(-0.880234\pi\) |
0.0620580 | + | 0.998073i | \(0.480234\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.14590 | − | 12.7598i | −0.251845 | − | 0.775100i | −0.994435 | − | 0.105353i | \(-0.966403\pi\) |
0.742589 | − | 0.669747i | \(-0.233597\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.0902 | + | 8.05748i | 0.671208 | + | 0.487661i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.23607 | − | 3.07768i | −0.0745377 | − | 0.185591i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.500000 | + | 0.363271i | 0.0300421 | + | 0.0218269i | 0.602705 | − | 0.797964i | \(-0.294090\pi\) |
−0.572663 | + | 0.819791i | \(0.694090\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.7082 | + | 51.4226i | 1.00029 | + | 3.07859i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.5623 | + | 10.5801i | −0.868714 | + | 0.631158i | −0.930242 | − | 0.366947i | \(-0.880403\pi\) |
0.0615273 | + | 0.998105i | \(0.480403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.67376 | + | 23.6174i | −0.456158 | + | 1.40391i | 0.413613 | + | 0.910453i | \(0.364267\pi\) |
−0.869771 | + | 0.493456i | \(0.835733\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.2361 | 0.784037 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.85410 | 0.286529 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.21885 | − | 9.90659i | 0.189344 | − | 0.582741i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −31.4164 | + | 22.8254i | −1.84166 | + | 1.33805i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.33688 | − | 22.5806i | −0.428625 | − | 1.31917i | −0.899480 | − | 0.436962i | \(-0.856054\pi\) |
0.470855 | − | 0.882211i | \(-0.343946\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.92705 | − | 1.40008i | −0.112197 | − | 0.0815161i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.7082 | − | 46.5488i | 0.679379 | − | 2.70103i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.190983 | − | 0.138757i | −0.0110448 | − | 0.00802454i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.47214 | − | 22.9969i | −0.430687 | − | 1.32552i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.70820 | − | 7.05342i | 0.557722 | − | 0.405209i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.76393 | + | 8.50651i | −0.158262 | + | 0.487081i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.9443 | 1.53779 | 0.768895 | − | 0.639375i | \(-0.220807\pi\) | ||||
0.768895 | + | 0.639375i | \(0.220807\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −36.6525 | −2.08509 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.763932 | − | 2.35114i | 0.0433186 | − | 0.133321i | −0.927058 | − | 0.374917i | \(-0.877671\pi\) |
0.970377 | + | 0.241597i | \(0.0776710\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.1803 | + | 16.1150i | −1.25371 | + | 0.910871i | −0.998431 | − | 0.0559968i | \(-0.982166\pi\) |
−0.255276 | + | 0.966868i | \(0.582166\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.04508 | + | 18.6049i | 0.340602 | + | 1.04827i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.01722 | − | 3.64522i | −0.281795 | − | 0.204736i | 0.437905 | − | 0.899021i | \(-0.355721\pi\) |
−0.719700 | + | 0.694285i | \(0.755721\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.47214 | − | 2.17963i | −0.194402 | − | 0.122036i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.7082 | + | 14.3188i | 1.10000 | + | 0.799200i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.61803 | − | 20.3682i | −0.368237 | − | 1.13332i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.30902 | − | 0.951057i | 0.0726112 | − | 0.0527551i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.52786 | + | 23.1684i | −0.416292 | + | 1.28121i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 29.6525 | 1.63479 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.3820 | 0.790504 | 0.395252 | − | 0.918573i | \(-0.370657\pi\) | ||||
0.395252 | + | 0.918573i | \(0.370657\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.97214 | + | 6.06961i | −0.108072 | + | 0.332613i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.618034 | + | 0.449028i | −0.0337668 | + | 0.0245330i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.9443 | + | 33.6830i | 0.596172 | + | 1.83483i | 0.548801 | + | 0.835953i | \(0.315084\pi\) |
0.0473712 | + | 0.998877i | \(0.484916\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.4721 | + | 11.9677i | 0.894644 | + | 0.649997i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.9443 | + | 1.62460i | −1.29666 | + | 0.0879769i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.1353 | − | 10.9964i | −0.817227 | − | 0.593750i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.145898 | − | 0.449028i | −0.00785489 | − | 0.0241749i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.9443 | + | 15.9434i | −1.17803 | + | 0.855889i | −0.991948 | − | 0.126645i | \(-0.959579\pi\) |
−0.186082 | + | 0.982534i | \(0.559579\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.56231 | − | 29.4298i | 0.511858 | − | 1.57534i | −0.277068 | − | 0.960850i | \(-0.589363\pi\) |
0.788926 | − | 0.614488i | \(-0.210637\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.4164 | 1.24988 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.7082 | 0.623165 | 0.311582 | − | 0.950219i | \(-0.399141\pi\) | ||||
0.311582 | + | 0.950219i | \(0.399141\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.09017 | − | 12.5882i | 0.217084 | − | 0.668115i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 35.8885 | − | 26.0746i | 1.89942 | − | 1.38001i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.41641 | + | 28.9807i | 0.496979 | + | 1.52954i | 0.813850 | + | 0.581075i | \(0.197368\pi\) |
−0.316871 | + | 0.948469i | \(0.602632\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.83688 | + | 1.33457i | 0.0966779 | + | 0.0702406i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 31.3607 | + | 16.8415i | 1.64601 | + | 0.883950i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.38197 | − | 1.00406i | −0.0723354 | − | 0.0525547i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.23607 | − | 9.95959i | −0.168921 | − | 0.519887i | 0.830382 | − | 0.557194i | \(-0.188122\pi\) |
−0.999304 | + | 0.0373073i | \(0.988122\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.2082 | − | 8.14324i | 0.583476 | − | 0.423920i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.736068 | + | 2.26538i | −0.0382147 | + | 0.117613i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.96556 | 0.360663 | 0.180331 | − | 0.983606i | \(-0.442283\pi\) | ||||
0.180331 | + | 0.983606i | \(0.442283\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.23607 | 0.167110 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.618034 | − | 1.90211i | 0.0318304 | − | 0.0979638i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.35410 | + | 6.06961i | −0.429121 | + | 0.311775i | −0.781297 | − | 0.624159i | \(-0.785442\pi\) |
0.352176 | + | 0.935934i | \(0.385442\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.38197 | − | 7.33094i | −0.122032 | − | 0.375575i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.8262 | − | 9.31881i | −0.655390 | − | 0.476169i | 0.209713 | − | 0.977763i | \(-0.432747\pi\) |
−0.865103 | + | 0.501594i | \(0.832747\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.66312 | + | 0.587785i | −0.441513 | + | 0.0299563i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −55.8328 | − | 40.5649i | −2.83814 | − | 2.06203i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.76393 | + | 11.5842i | 0.190839 | + | 0.587342i | 1.00000 | 0.000245108i | \(-7.80203e-5\pi\) | |
−0.809161 | + | 0.587587i | \(0.800078\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.618034 | + | 0.449028i | −0.0312553 | + | 0.0227083i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.4164 | − | 35.1361i | 0.575882 | − | 1.77238i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.52786 | −0.0768752 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.79837 | 0.341201 | 0.170600 | − | 0.985340i | \(-0.445429\pi\) | ||||
0.170600 | + | 0.985340i | \(0.445429\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.7082 | − | 32.9565i | 0.536081 | − | 1.64989i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.69098 | − | 6.31437i | 0.434007 | − | 0.315325i | −0.349242 | − | 0.937033i | \(-0.613561\pi\) |
0.783249 | + | 0.621708i | \(0.213561\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.61803 | − | 11.1352i | −0.180227 | − | 0.554682i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 19.7533 | + | 14.3516i | 0.981549 | + | 0.713137i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.39919 | − | 1.50609i | −0.118923 | − | 0.0746539i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.8713 | + | 13.7108i | 0.933127 | + | 0.677956i | 0.946756 | − | 0.321951i | \(-0.104339\pi\) |
−0.0136296 | + | 0.999907i | \(0.504339\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.23607 | + | 16.1150i | 0.258276 | + | 0.794892i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.04508 | + | 3.66547i | −0.248252 | + | 0.180366i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.85410 | − | 14.9394i | 0.238278 | − | 0.733346i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.3607 | −1.29089 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.61803 | 0.0790461 | 0.0395231 | − | 0.999219i | \(-0.487416\pi\) | ||||
0.0395231 | + | 0.999219i | \(0.487416\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.76393 | + | 17.7396i | −0.280917 | + | 0.864573i | 0.706676 | + | 0.707537i | \(0.250194\pi\) |
−0.987593 | + | 0.157036i | \(0.949806\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 68.4681 | − | 49.7450i | 3.32903 | − | 2.41868i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.61803 | − | 4.97980i | −0.0784862 | − | 0.241556i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.9443 | + | 13.7638i | 0.916778 | + | 0.666078i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.23607 | + | 16.8415i | −0.204519 | + | 0.813115i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.1803 | − | 15.3884i | −1.02022 | − | 0.741234i | −0.0538929 | − | 0.998547i | \(-0.517163\pi\) |
−0.966328 | + | 0.257313i | \(0.917163\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.94427 | + | 9.06154i | 0.141493 | + | 0.435470i | 0.996543 | − | 0.0830748i | \(-0.0264741\pi\) |
−0.855051 | + | 0.518545i | \(0.826474\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.23607 | − | 2.35114i | 0.155158 | − | 0.112729i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.184405 | + | 0.567541i | −0.00882130 | + | 0.0271492i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.1246 | 0.626404 | 0.313202 | − | 0.949687i | \(-0.398598\pi\) | ||||
0.313202 | + | 0.949687i | \(0.398598\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.09017 | −0.0519129 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.416408 | + | 1.28157i | −0.0197841 | + | 0.0608893i | −0.960461 | − | 0.278414i | \(-0.910191\pi\) |
0.940677 | + | 0.339303i | \(0.110191\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.73607 | + | 7.07367i | −0.461534 | + | 0.335324i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.00000 | + | 12.3107i | 0.189194 | + | 0.582278i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.54508 | − | 1.84911i | −0.120110 | − | 0.0872650i | 0.526109 | − | 0.850417i | \(-0.323651\pi\) |
−0.646219 | + | 0.763152i | \(0.723651\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.29180 | + | 5.70634i | 0.107916 | + | 0.268701i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −33.1246 | − | 24.0664i | −1.55633 | − | 1.13074i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.30902 | − | 4.02874i | −0.0613677 | − | 0.188870i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.3262 | + | 19.1271i | −1.23149 | + | 0.894729i | −0.997001 | − | 0.0773894i | \(-0.975342\pi\) |
−0.234489 | + | 0.972119i | \(0.575342\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 23.4164 | − | 72.0683i | 1.09298 | − | 3.36386i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.5410 | 1.32929 | 0.664644 | − | 0.747160i | \(-0.268583\pi\) | ||||
0.664644 | + | 0.747160i | \(0.268583\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.5066 | −0.720652 | −0.360326 | − | 0.932826i | \(-0.617335\pi\) | ||||
−0.360326 | + | 0.932826i | \(0.617335\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.23607 | − | 22.2703i | 0.335565 | − | 1.03276i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.9443 | − | 10.1311i | 0.645264 | − | 0.468812i | −0.216391 | − | 0.976307i | \(-0.569428\pi\) |
0.861655 | + | 0.507495i | \(0.169428\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.618034 | + | 1.90211i | 0.0285382 | + | 0.0878314i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.5623 | + | 16.3925i | 1.03962 | + | 0.755325i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23.5066 | − | 19.6417i | 1.08083 | − | 0.903125i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.30902 | − | 2.40414i | −0.151828 | − | 0.110310i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.10081 | + | 6.46564i | 0.0961896 | + | 0.296041i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −23.9443 | + | 17.3965i | −1.09404 | + | 0.794868i | −0.980077 | − | 0.198617i | \(-0.936355\pi\) |
−0.113965 | + | 0.993485i | \(0.536355\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.427051 | − | 1.31433i | 0.0194718 | − | 0.0599282i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.23607 | −0.0562430 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.0000 | 0.544892 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.4164 | + | 35.1361i | −0.517327 | + | 1.59217i | 0.261681 | + | 0.965154i | \(0.415723\pi\) |
−0.779008 | + | 0.627014i | \(0.784277\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.9443 | − | 13.7638i | 0.856690 | − | 0.622421i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.2639 | − | 34.6668i | −0.508334 | − | 1.56449i | −0.795092 | − | 0.606489i | \(-0.792578\pi\) |
0.286758 | − | 0.958003i | \(-0.407422\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.23607 | − | 3.80423i | −0.235821 | − | 0.171334i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19.0172 | + | 15.8904i | −0.854761 | + | 0.714222i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −28.0344 | − | 20.3682i | −1.25752 | − | 0.913639i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.95492 | + | 12.1720i | 0.177046 | + | 0.544893i | 0.999721 | − | 0.0236199i | \(-0.00751914\pi\) |
−0.822675 | + | 0.568512i | \(0.807519\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.7082 | + | 15.0454i | −0.925174 | + | 0.672178i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.31966 | + | 7.13918i | −0.103429 | + | 0.318320i | −0.989358 | − | 0.145499i | \(-0.953521\pi\) |
0.885930 | + | 0.463819i | \(0.153521\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.70820 | −0.165013 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 33.5967 | 1.49208 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.61803 | + | 29.6013i | −0.426312 | + | 1.31205i | 0.475421 | + | 0.879759i | \(0.342296\pi\) |
−0.901733 | + | 0.432294i | \(0.857704\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.61803 | + | 2.62866i | −0.160052 | + | 0.116285i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.2918 | − | 56.2964i | −0.807603 | − | 2.48554i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.16312 | + | 6.65740i | 0.403775 | + | 0.293360i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.0000 | + | 34.8586i | 0.615719 | + | 1.53308i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −33.0344 | − | 24.0009i | −1.45005 | − | 1.05352i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.66312 | − | 8.19624i | −0.116673 | − | 0.359084i | 0.875619 | − | 0.483002i | \(-0.160454\pi\) |
−0.992292 | + | 0.123919i | \(0.960454\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.94427 | + | 4.31877i | −0.259925 | + | 0.188846i | −0.710114 | − | 0.704087i | \(-0.751357\pi\) |
0.450189 | + | 0.892933i | \(0.351357\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.61803 | − | 8.05748i | 0.114260 | − | 0.351657i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −37.8885 | −1.65045 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9787 | −0.999075 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.50000 | + | 16.9273i | −0.238680 | + | 0.734580i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.42705 | + | 1.76336i | −0.105127 | + | 0.0763794i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.32624 | − | 7.15942i | −0.100572 | − | 0.309529i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.61803 | + | 5.53483i | 0.328742 | + | 0.238845i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.118034 | − | 0.469272i | 0.00508408 | − | 0.0202130i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.47214 | + | 4.70228i | 0.278259 | + | 0.202167i | 0.718158 | − | 0.695880i | \(-0.244986\pi\) |
−0.439899 | + | 0.898047i | \(0.644986\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.4721 | + | 63.0068i | 0.878543 | + | 2.70388i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.09017 | − | 4.42477i | 0.260874 | − | 0.189536i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.81966 | − | 14.8334i | 0.206074 | − | 0.634230i | −0.793594 | − | 0.608448i | \(-0.791792\pi\) |
0.999668 | − | 0.0257820i | \(-0.00820757\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 66.8328 | 2.85236 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.05573 | −0.215381 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.23607 | + | 3.80423i | −0.0525630 | + | 0.161772i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.23607 | − | 1.62460i | 0.0949158 | − | 0.0689604i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.2639 | + | 31.5891i | 0.434897 | + | 1.33847i | 0.893192 | + | 0.449675i | \(0.148460\pi\) |
−0.458296 | + | 0.888800i | \(0.651540\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.0902 | + | 8.78402i | 0.511360 | + | 0.371525i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 47.5967 | + | 29.8788i | 2.00954 | + | 1.26148i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.3262 | + | 14.0413i | 0.814504 | + | 0.591772i | 0.915133 | − | 0.403152i | \(-0.132086\pi\) |
−0.100629 | + | 0.994924i | \(0.532086\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.94427 | − | 5.98385i | −0.0817961 | − | 0.251743i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 51.7148 | − | 37.5730i | 2.17182 | − | 1.57792i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.57295 | − | 7.91872i | 0.107864 | − | 0.331970i | −0.882528 | − | 0.470259i | \(-0.844160\pi\) |
0.990392 | + | 0.138289i | \(0.0441604\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.0902 | 1.21739 | 0.608693 | − | 0.793406i | \(-0.291694\pi\) | ||||
0.608693 | + | 0.793406i | \(0.291694\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 82.2492 | 3.43601 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.0450850 | + | 0.138757i | −0.00188017 | + | 0.00578658i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.0902 | + | 8.78402i | −0.503320 | + | 0.365684i | −0.810284 | − | 0.586038i | \(-0.800687\pi\) |
0.306963 | + | 0.951721i | \(0.400687\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.41641 | + | 16.6700i | 0.225098 | + | 0.692781i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33.2705 | − | 24.1724i | −1.38029 | − | 1.00284i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.01064 | + | 0.204270i | −0.124688 | + | 0.00845998i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.78115 | − | 7.10642i | −0.404401 | − | 0.293814i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.41641 | + | 19.7477i | 0.264833 | + | 0.815074i | 0.991732 | + | 0.128328i | \(0.0409612\pi\) |
−0.726898 | + | 0.686745i | \(0.759039\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.9443 | + | 17.3965i | −0.986607 | + | 0.716812i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.90983 | − | 15.1109i | 0.201963 | − | 0.621579i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.7082 | −0.809319 | −0.404659 | − | 0.914467i | \(-0.632610\pi\) | ||||
−0.404659 | + | 0.914467i | \(0.632610\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.7082 | −0.561982 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.70820 | − | 5.25731i | 0.0699121 | − | 0.215167i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.3262 | − | 9.68208i | 0.544495 | − | 0.395599i | −0.281257 | − | 0.959633i | \(-0.590751\pi\) |
0.825752 | + | 0.564034i | \(0.190751\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.97214 | + | 21.4580i | 0.284399 | + | 0.875291i | 0.986578 | + | 0.163290i | \(0.0522108\pi\) |
−0.702179 | + | 0.712001i | \(0.747789\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.61803 | + | 3.35520i | 0.188061 | + | 0.136634i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.78115 | − | 9.90659i | −0.194382 | − | 0.402760i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.1803 | + | 19.0211i | 1.06263 | + | 0.772044i | 0.974573 | − | 0.224072i | \(-0.0719350\pi\) |
0.0880546 | + | 0.996116i | \(0.471935\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.23607 | − | 9.95959i | −0.131132 | − | 0.403583i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.8262 | + | 10.7719i | −0.599805 | + | 0.435784i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.56231 | − | 10.9637i | 0.143880 | − | 0.442818i | −0.852985 | − | 0.521935i | \(-0.825210\pi\) |
0.996865 | + | 0.0791176i | \(0.0252103\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.00000 | −0.241943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.9443 | 1.32629 | 0.663143 | − | 0.748493i | \(-0.269222\pi\) | ||||
0.663143 | + | 0.748493i | \(0.269222\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.02786 | + | 21.6295i | −0.282474 | + | 0.869365i | 0.704671 | + | 0.709534i | \(0.251095\pi\) |
−0.987145 | + | 0.159830i | \(0.948905\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.70820 | + | 1.24108i | −0.0685479 | + | 0.0498029i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.73607 | + | 29.9645i | 0.390067 | + | 1.20050i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.809017 | − | 0.587785i | −0.0323607 | − | 0.0235114i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 43.7984 | − | 2.97168i | 1.74914 | − | 0.118678i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.61803 | − | 2.62866i | −0.144260 | − | 0.104811i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.29180 | − | 7.05342i | −0.0912350 | − | 0.280792i | 0.895019 | − | 0.446028i | \(-0.147162\pi\) |
−0.986254 | + | 0.165235i | \(0.947162\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −54.8328 | + | 39.8384i | −2.17941 | + | 1.58343i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.736068 | + | 2.26538i | −0.0292100 | + | 0.0898990i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.236068 | 0.00935335 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −98.9017 | −3.91249 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.7918 | − | 36.2914i | 0.465748 | − | 1.43342i | −0.392291 | − | 0.919841i | \(-0.628318\pi\) |
0.858039 | − | 0.513584i | \(-0.171682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.8541 | + | 7.88597i | −0.428044 | + | 0.310992i | −0.780866 | − | 0.624698i | \(-0.785222\pi\) |
0.352822 | + | 0.935690i | \(0.385222\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.23607 | + | 28.4257i | 0.363670 | + | 1.11926i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.70820 | − | 4.14725i | −0.224413 | − | 0.163045i | 0.469898 | − | 0.882721i | \(-0.344291\pi\) |
−0.694311 | + | 0.719675i | \(0.744291\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.69098 | − | 4.20025i | −0.262644 | − | 0.164874i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −49.5967 | − | 36.0341i | −1.94385 | − | 1.41229i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.97214 | + | 24.5357i | 0.311974 | + | 0.960157i | 0.976982 | + | 0.213321i | \(0.0684279\pi\) |
−0.665008 | + | 0.746836i | \(0.731572\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.23607 | + | 6.71040i | −0.360883 | + | 0.262197i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.94427 | + | 12.1392i | −0.153881 | + | 0.473596i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.3820 | 0.521287 | 0.260644 | − | 0.965435i | \(-0.416065\pi\) | ||||
0.260644 | + | 0.965435i | \(0.416065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.18034 | 0.0848054 | 0.0424027 | − | 0.999101i | \(-0.486499\pi\) | ||||
0.0424027 | + | 0.999101i | \(0.486499\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.47214 | + | 26.0746i | −0.329030 | + | 1.01265i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.66312 | + | 6.29412i | −0.335941 | + | 0.244076i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.0557281 | + | 0.171513i | 0.00215780 | + | 0.00664103i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.3262 | − | 18.4006i | −0.979169 | − | 0.711408i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.23607 | + | 28.7687i | −0.279345 | + | 1.11060i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.23607 | + | 2.35114i | 0.124741 | + | 0.0906298i | 0.648407 | − | 0.761294i | \(-0.275436\pi\) |
−0.523665 | + | 0.851924i | \(0.675436\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.47214 | − | 13.7638i | −0.172133 | − | 0.529770i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.09017 | − | 5.87785i | 0.310930 | − | 0.225904i | −0.421365 | − | 0.906891i | \(-0.638449\pi\) |
0.732296 | + | 0.680987i | \(0.238449\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.70820 | − | 29.8788i | 0.372567 | − | 1.14664i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −53.3050 | −2.04265 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 47.0132 | 1.79891 | 0.899454 | − | 0.437015i | \(-0.143964\pi\) | ||||
0.899454 | + | 0.437015i | \(0.143964\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.61803 | − | 4.97980i | 0.0618219 | − | 0.190268i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −73.7771 | + | 53.6022i | −2.81477 | + | 2.04505i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.454915 | − | 1.40008i | −0.0173309 | − | 0.0533390i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.1180 | + | 8.07772i | 0.422950 | + | 0.307291i | 0.778824 | − | 0.627243i | \(-0.215817\pi\) |
−0.355874 | + | 0.934534i | \(0.615817\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 24.1803 | + | 60.2066i | 0.918535 | + | 2.28706i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.59017 | + | 4.78804i | 0.249979 | + | 0.181621i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.00000 | + | 9.23305i | 0.113633 | + | 0.349727i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 39.8885 | − | 28.9807i | 1.50872 | − | 1.09615i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.79837 | − | 5.53483i | 0.0679236 | − | 0.209047i | −0.911334 | − | 0.411669i | \(-0.864946\pi\) |
0.979257 | + | 0.202621i | \(0.0649461\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.49342 | −0.131757 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −36.6525 | −1.38041 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.00000 | + | 9.23305i | −0.112827 | + | 0.347245i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.79837 | + | 6.39239i | −0.330430 | + | 0.240071i | −0.740613 | − | 0.671932i | \(-0.765465\pi\) |
0.410183 | + | 0.912003i | \(0.365465\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.52786 | + | 10.8576i | 0.132305 | + | 0.407194i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.854102 | + | 0.620541i | 0.0319864 | + | 0.0232395i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.11803 | − | 3.44095i | 0.154006 | − | 0.128684i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.9443 | − | 18.1231i | −0.931561 | − | 0.676819i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.36068 | − | 22.6538i | −0.274507 | − | 0.844846i | −0.989349 | − | 0.145560i | \(-0.953502\pi\) |
0.714842 | − | 0.699286i | \(-0.246498\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.9894 | − | 17.4293i | 0.893410 | − | 0.649101i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.85410 | − | 5.70634i | 0.0689548 | − | 0.212221i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.23607 | −0.0459064 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.79837 | 0.326314 | 0.163157 | − | 0.986600i | \(-0.447832\pi\) | ||||
0.163157 | + | 0.986600i | \(0.447832\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.9615 | − | 39.8914i | 0.480055 | − | 1.47746i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.1246 | − | 28.4257i | 1.44708 | − | 1.05136i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.2016 | + | 34.4751i | 0.413742 | + | 1.27337i | 0.913372 | + | 0.407127i | \(0.133469\pi\) |
−0.499630 | + | 0.866239i | \(0.666531\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.381966 | + | 0.277515i | 0.0140890 | + | 0.0102363i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.94427 | + | 1.62460i | −0.0716182 | + | 0.0598429i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.7705 | − | 18.7234i | −0.947984 | − | 0.688750i | 0.00234556 | − | 0.999997i | \(-0.499253\pi\) |
−0.950329 | + | 0.311247i | \(0.899253\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.61803 | + | 20.3682i | 0.243120 | + | 0.748245i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.3541 | + | 10.4289i | −0.526601 | + | 0.382598i | −0.819085 | − | 0.573672i | \(-0.805518\pi\) |
0.292484 | + | 0.956270i | \(0.405518\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.23607 | − | 3.80423i | 0.0452860 | − | 0.139376i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −117.374 | −4.29448 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.7082 | −0.720122 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.38197 | − | 10.4086i | 0.123410 | − | 0.379816i | −0.870198 | − | 0.492702i | \(-0.836009\pi\) |
0.993608 | + | 0.112886i | \(0.0360094\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.2705 | − | 19.0866i | 0.957351 | − | 0.695556i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.90983 | + | 12.0332i | 0.142293 | + | 0.437934i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.9615 | − | 13.0498i | −0.652822 | − | 0.474303i | 0.211410 | − | 0.977398i | \(-0.432195\pi\) |
−0.864231 | + | 0.503095i | \(0.832195\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.583592 | − | 1.45309i | −0.0211831 | − | 0.0527436i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.32624 | − | 3.86974i | −0.193076 | − | 0.140278i | 0.487048 | − | 0.873375i | \(-0.338074\pi\) |
−0.680123 | + | 0.733098i | \(0.738074\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.09017 | − | 18.7436i | −0.220479 | − | 0.678564i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −31.6525 | + | 22.9969i | −1.14440 | + | 0.831454i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.19098 | − | 3.66547i | 0.0430039 | − | 0.132352i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.0902 | −1.15720 | −0.578601 | − | 0.815611i | \(-0.696401\pi\) | ||||
−0.578601 | + | 0.815611i | \(0.696401\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 38.8328 | 1.39853 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.6074 | + | 35.7239i | −0.417489 | + | 1.28490i | 0.492517 | + | 0.870303i | \(0.336077\pi\) |
−0.910006 | + | 0.414596i | \(0.863923\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.85410 | + | 4.25325i | −0.210286 | + | 0.152781i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.23607 | − | 6.88191i | −0.0802185 | − | 0.246887i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.13525 | + | 4.45752i | 0.219818 | + | 0.159707i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.7082 | − | 42.5730i | 0.383170 | − | 1.52338i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14.4721 | − | 10.5146i | −0.517192 | − | 0.375762i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.66312 | − | 8.19624i | −0.0950508 | − | 0.292536i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.1246 | + | 21.1603i | −1.03818 | + | 0.754282i | −0.969929 | − | 0.243386i | \(-0.921742\pi\) |
−0.0682508 | + | 0.997668i | \(0.521742\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.7984 | − | 79.3992i | 0.918446 | − | 2.82669i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.4721 | −0.585682 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.4721 | −0.513921 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.909830 | − | 2.80017i | 0.0322683 | − | 0.0993118i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.9615 | + | 21.7683i | −1.06129 | + | 0.771073i | −0.974327 | − | 0.225139i | \(-0.927716\pi\) |
−0.0869638 | + | 0.996211i | \(0.527716\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.3262 | + | 56.4024i | 0.648336 | + | 1.99537i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 72.7492 | + | 52.8554i | 2.57047 | + | 1.86755i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.79837 | − | 3.01217i | −0.169331 | − | 0.106297i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.309017 | + | 0.224514i | 0.0108914 | + | 0.00791308i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.5967 | − | 54.1572i | −0.619435 | − | 1.90642i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.30902 | − | 5.31031i | 0.256971 | − | 0.186701i | −0.451839 | − | 0.892099i | \(-0.649232\pi\) |
0.708811 | + | 0.705399i | \(0.249232\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.4058 | − | 44.3364i | 0.505855 | − | 1.55686i | −0.293474 | − | 0.955967i | \(-0.594811\pi\) |
0.799329 | − | 0.600894i | \(-0.205189\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 43.4164 | 1.52268 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.23607 | −0.253468 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.6738 | − | 35.9281i | 0.408413 | − | 1.25697i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −25.6074 | + | 18.6049i | −0.894795 | + | 0.650106i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.52786 | − | 23.1684i | −0.262724 | − | 0.808582i | −0.992209 | − | 0.124585i | \(-0.960240\pi\) |
0.729485 | − | 0.683997i | \(-0.239760\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.7812 | − | 10.0126i | −0.480381 | − | 0.349017i | 0.321092 | − | 0.947048i | \(-0.395950\pi\) |
−0.801473 | + | 0.598031i | \(0.795950\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.7082 | − | 0.726543i | 0.372812 | − | 0.0252950i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.7984 | + | 12.9313i | 0.618910 | + | 0.449665i | 0.852541 | − | 0.522661i | \(-0.175061\pi\) |
−0.233631 | + | 0.972325i | \(0.575061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.00000 | − | 12.3107i | −0.138926 | − | 0.427569i | 0.857254 | − | 0.514893i | \(-0.172168\pi\) |
−0.996180 | + | 0.0873239i | \(0.972168\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.61803 | + | 1.17557i | −0.0561290 | + | 0.0407801i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.236068 | − | 0.726543i | 0.00817927 | − | 0.0251732i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.90983 | 0.273731 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −104.721 | −3.61970 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.2361 | − | 49.9695i | 0.560531 | − | 1.72514i | −0.120338 | − | 0.992733i | \(-0.538398\pi\) |
0.680869 | − | 0.732405i | \(-0.261602\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.2254 | − | 16.1477i | 0.766394 | − | 0.556818i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.0000 | − | 55.3983i | −0.619953 | − | 1.90802i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.39919 | − | 6.10237i | −0.288941 | − | 0.209928i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.5344 | + | 3.88998i | −0.980455 | + | 0.133661i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −65.0132 | − | 47.2348i | −2.23125 | − | 1.62109i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.0385072 | + | 0.118513i | 0.00132001 | + | 0.00406257i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.9164 | + | 9.38432i | −0.442249 | + | 0.321313i | −0.786528 | − | 0.617555i | \(-0.788123\pi\) |
0.344279 | + | 0.938867i | \(0.388123\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.44427 | + | 29.0665i | −0.322987 | + | 0.994053i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.0000 | 0.751506 | 0.375753 | − | 0.926720i | \(-0.377384\pi\) | ||||
0.375753 | + | 0.926720i | \(0.377384\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.9098 | 1.05463 | 0.527315 | − | 0.849670i | \(-0.323199\pi\) | ||||
0.527315 | + | 0.849670i | \(0.323199\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.85410 | + | 14.9394i | −0.165427 | + | 0.509133i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.01722 | + | 3.64522i | −0.170788 | + | 0.124085i | −0.669896 | − | 0.742455i | \(-0.733661\pi\) |
0.499108 | + | 0.866540i | \(0.333661\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.89919 | + | 12.0005i | 0.132576 | + | 0.408028i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 27.2705 | + | 19.8132i | 0.926155 | + | 0.672891i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.05573 | + | 0.343027i | −0.171504 | + | 0.0116364i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.00000 | − | 0.726543i | −0.0338837 | − | 0.0246180i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −27.7082 | − | 85.2771i | −0.937781 | − | 2.88619i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.11803 | + | 1.53884i | −0.0716026 | + | 0.0520223i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.736068 | − | 2.26538i | 0.0248552 | − | 0.0764966i | −0.937859 | − | 0.347015i | \(-0.887195\pi\) |
0.962715 | + | 0.270519i | \(0.0871952\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 76.8328 | 2.59151 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.4508 | −0.924843 | −0.462421 | − | 0.886660i | \(-0.653019\pi\) | ||||
−0.462421 | + | 0.886660i | \(0.653019\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.47214 | + | 29.1522i | −0.318763 | + | 0.981051i | 0.655415 | + | 0.755269i | \(0.272494\pi\) |
−0.974178 | + | 0.225782i | \(0.927506\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.23607 | − | 4.53077i | 0.209623 | − | 0.152300i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.6074 | − | 44.9569i | −0.490468 | − | 1.50951i | −0.823902 | − | 0.566732i | \(-0.808207\pi\) |
0.333434 | − | 0.942774i | \(-0.391793\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.04508 | + | 3.66547i | 0.169207 | + | 0.122936i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 68.5861 | + | 43.0548i | 2.29772 | + | 1.44239i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 37.4787 | + | 27.2299i | 1.25418 | + | 0.911213i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.899187 | − | 2.76741i | −0.0300565 | − | 0.0925044i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.618034 | − | 0.449028i | 0.0206356 | − | 0.0149926i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.76393 | + | 8.50651i | −0.0921823 | + | 0.283708i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.76393 | −0.158710 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 78.2492 | 2.60397 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.32624 | − | 19.4702i | 0.210291 | − | 0.647210i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.2361 | + | 7.43694i | −0.339883 | + | 0.246939i | −0.744612 | − | 0.667497i | \(-0.767366\pi\) |
0.404729 | + | 0.914436i | \(0.367366\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.56231 | + | 26.3521i | 0.283994 | + | 0.874043i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.9443 | − | 12.3107i | −0.561389 | − | 0.407873i | 0.270578 | − | 0.962698i | \(-0.412785\pi\) |
−0.831967 | + | 0.554825i | \(0.812785\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.7082 | − | 50.5245i | 0.420580 | − | 1.67212i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23.4164 | − | 17.0130i | −0.774123 | − | 0.562433i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.23607 | + | 28.4257i | 0.305002 | + | 0.938699i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.70820 | + | 7.05342i | −0.320244 | + | 0.232671i | −0.736280 | − | 0.676677i | \(-0.763419\pi\) |
0.416036 | + | 0.909348i | \(0.363419\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.9443 | + | 82.9259i | −0.887844 | + | 2.73250i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.4164 | 0.704930 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.854102 | −0.0280827 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.1525 | − | 80.4890i | 0.858960 | − | 2.64361i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −43.0967 | + | 31.3116i | −1.41396 | + | 1.02730i | −0.421226 | + | 0.906956i | \(0.638400\pi\) |
−0.992732 | + | 0.120345i | \(0.961600\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.184405 | − | 0.567541i | −0.00604364 | − | 0.0186004i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.47214 | + | 4.70228i | 0.211888 | + | 0.153946i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.47214 | − | 16.1150i | −0.211661 | − | 0.527016i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.9787 | + | 28.3197i | 1.27338 | + | 0.925164i | 0.999332 | − | 0.0365522i | \(-0.0116375\pi\) |
0.274047 | + | 0.961716i | \(0.411638\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.4164 | − | 84.3790i | −0.894701 | − | 2.75361i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45.3607 | + | 32.9565i | −1.47872 | + | 1.07435i | −0.500748 | + | 0.865593i | \(0.666942\pi\) |
−0.977968 | + | 0.208757i | \(0.933058\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.0835921 | − | 0.257270i | 0.00272213 | − | 0.00837787i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −37.8885 | −1.23251 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −49.9574 | −1.62340 | −0.811699 | − | 0.584076i | \(-0.801457\pi\) | ||||
−0.811699 | + | 0.584076i | \(0.801457\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.854102 | − | 2.62866i | 0.0277253 | − | 0.0853298i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.2361 | − | 11.7962i | 0.526491 | − | 0.382518i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.85410 | + | 14.9394i | 0.157240 | + | 0.483934i | 0.998381 | − | 0.0568813i | \(-0.0181157\pi\) |
−0.841141 | + | 0.540816i | \(0.818116\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.5623 | − | 14.9394i | −0.665381 | − | 0.483427i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.1803 | − | 8.50651i | 0.329084 | − | 0.274976i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.0902 | − | 8.05748i | −0.358120 | − | 0.260190i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.60081 | + | 20.3152i | 0.212929 | + | 0.655329i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −45.5066 | + | 33.0625i | −1.46643 | + | 1.06542i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.67376 | − | 5.15131i | 0.0538803 | − | 0.165827i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.90983 | −0.125732 | −0.0628658 | − | 0.998022i | \(-0.520024\pi\) | ||||
−0.0628658 | + | 0.998022i | \(0.520024\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 69.3050 | 2.22640 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.1565 | + | 37.4140i | −0.390122 | + | 1.20067i | 0.542574 | + | 0.840008i | \(0.317450\pi\) |
−0.932696 | + | 0.360664i | \(0.882550\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.2533 | − | 12.5352i | 0.553115 | − | 0.401862i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.61803 | + | 4.97980i | 0.0518186 | + | 0.159481i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.38197 | + | 2.45714i | 0.108199 | + | 0.0786109i | 0.640569 | − | 0.767901i | \(-0.278699\pi\) |
−0.532370 | + | 0.846512i | \(0.678699\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.6287 | + | 25.5928i | −0.978897 | + | 0.817948i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −45.5066 | − | 33.0625i | −1.45291 | − | 1.05560i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.10081 | − | 9.54332i | −0.0989006 | − | 0.304385i | 0.889350 | − | 0.457227i | \(-0.151157\pi\) |
−0.988251 | + | 0.152842i | \(0.951157\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.97214 | + | 2.88593i | −0.126563 | + | 0.0919532i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −29.6525 | + | 91.2609i | −0.943849 | + | 2.90487i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.34752 | −0.0428488 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.7214 | −1.73828 | −0.869141 | − | 0.494565i | \(-0.835327\pi\) | ||||
−0.869141 | + | 0.494565i | \(0.835327\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.3820 | + | 44.2631i | −0.456398 | + | 1.40465i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.38197 | + | 1.00406i | −0.0438113 | + | 0.0318307i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.2148 | − | 49.9040i | −0.513527 | − | 1.58047i | −0.785946 | − | 0.618296i | \(-0.787823\pi\) |
0.272418 | − | 0.962179i | \(-0.412177\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.0000 | − | 7.26543i | −0.316386 | − | 0.229868i |
(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 | 880.2.bo.a.81.1 | 4 | ||
4.3 | odd | 2 | 110.2.g.a.81.1 | ✓ | 4 | ||
11.3 | even | 5 | inner | 880.2.bo.a.641.1 | 4 | ||
11.5 | even | 5 | 9680.2.a.bh.1.1 | 2 | |||
11.6 | odd | 10 | 9680.2.a.bi.1.1 | 2 | |||
12.11 | even | 2 | 990.2.n.f.631.1 | 4 | |||
20.3 | even | 4 | 550.2.ba.a.499.1 | 8 | |||
20.7 | even | 4 | 550.2.ba.a.499.2 | 8 | |||
20.19 | odd | 2 | 550.2.h.f.301.1 | 4 | |||
44.3 | odd | 10 | 110.2.g.a.91.1 | yes | 4 | ||
44.27 | odd | 10 | 1210.2.a.t.1.2 | 2 | |||
44.39 | even | 10 | 1210.2.a.p.1.2 | 2 | |||
132.47 | even | 10 | 990.2.n.f.91.1 | 4 | |||
220.3 | even | 20 | 550.2.ba.a.399.2 | 8 | |||
220.39 | even | 10 | 6050.2.a.cm.1.1 | 2 | |||
220.47 | even | 20 | 550.2.ba.a.399.1 | 8 | |||
220.159 | odd | 10 | 6050.2.a.bu.1.1 | 2 | |||
220.179 | odd | 10 | 550.2.h.f.201.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
110.2.g.a.81.1 | ✓ | 4 | 4.3 | odd | 2 | ||
110.2.g.a.91.1 | yes | 4 | 44.3 | odd | 10 | ||
550.2.h.f.201.1 | 4 | 220.179 | odd | 10 | |||
550.2.h.f.301.1 | 4 | 20.19 | odd | 2 | |||
550.2.ba.a.399.1 | 8 | 220.47 | even | 20 | |||
550.2.ba.a.399.2 | 8 | 220.3 | even | 20 | |||
550.2.ba.a.499.1 | 8 | 20.3 | even | 4 | |||
550.2.ba.a.499.2 | 8 | 20.7 | even | 4 | |||
880.2.bo.a.81.1 | 4 | 1.1 | even | 1 | trivial | ||
880.2.bo.a.641.1 | 4 | 11.3 | even | 5 | inner | ||
990.2.n.f.91.1 | 4 | 132.47 | even | 10 | |||
990.2.n.f.631.1 | 4 | 12.11 | even | 2 | |||
1210.2.a.p.1.2 | 2 | 44.39 | even | 10 | |||
1210.2.a.t.1.2 | 2 | 44.27 | odd | 10 | |||
6050.2.a.bu.1.1 | 2 | 220.159 | odd | 10 | |||
6050.2.a.cm.1.1 | 2 | 220.39 | even | 10 | |||
9680.2.a.bh.1.1 | 2 | 11.5 | even | 5 | |||
9680.2.a.bi.1.1 | 2 | 11.6 | odd | 10 |