Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [550,2,Mod(201,550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(550, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("550.201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 550 = 2 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 550.h (of order \(5\), degree \(4\), 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: | \(4.39177211117\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 110) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 301.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 550.301 |
Dual form | 550.2.h.f.201.1 |
$q$-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 \(\left(\mathbb{Z}/550\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | + | 0.587785i | 0.572061 | + | 0.415627i | ||||
\(3\) | −1.00000 | + | 3.07768i | −0.577350 | + | 1.77690i | 0.0506828 | + | 0.998715i | \(0.483860\pi\) |
−0.628033 | + | 0.778187i | \(0.716140\pi\) | |||||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.61803 | + | 1.90211i | −1.06881 | + | 0.776534i | ||||
\(7\) | −0.809017 | − | 2.48990i | −0.305780 | − | 0.941093i | −0.979385 | − | 0.202002i | \(-0.935255\pi\) |
0.673605 | − | 0.739091i | \(-0.264745\pi\) | |||||||
\(8\) | −0.309017 | + | 0.951057i | −0.109254 | + | 0.336249i | ||||
\(9\) | −6.04508 | − | 4.39201i | −2.01503 | − | 1.46400i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.54508 | + | 2.12663i | −0.767372 | + | 0.641202i | ||||
\(12\) | −3.23607 | −0.934172 | ||||||||
\(13\) | −1.30902 | − | 0.951057i | −0.363056 | − | 0.263776i | 0.391270 | − | 0.920276i | \(-0.372036\pi\) |
−0.754326 | + | 0.656500i | \(0.772036\pi\) | |||||||
\(14\) | 0.809017 | − | 2.48990i | 0.216219 | − | 0.665453i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | −4.23607 | + | 3.07768i | −1.02740 | + | 0.746448i | −0.967786 | − | 0.251774i | \(-0.918986\pi\) |
−0.0596113 | + | 0.998222i | \(0.518986\pi\) | |||||||
\(18\) | −2.30902 | − | 7.10642i | −0.544241 | − | 1.67500i | ||||
\(19\) | −1.26393 | + | 3.88998i | −0.289966 | + | 0.892423i | 0.694900 | + | 0.719106i | \(0.255449\pi\) |
−0.984866 | + | 0.173317i | \(0.944551\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.47214 | 1.84877 | ||||||||
\(22\) | −3.30902 | + | 0.224514i | −0.705485 | + | 0.0478665i | ||||
\(23\) | −0.145898 | −0.0304218 | −0.0152109 | − | 0.999884i | \(-0.504842\pi\) | ||||
−0.0152109 | + | 0.999884i | \(0.504842\pi\) | |||||||
\(24\) | −2.61803 | − | 1.90211i | −0.534404 | − | 0.388267i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.500000 | − | 1.53884i | −0.0980581 | − | 0.301792i | ||||
\(27\) | 11.7082 | − | 8.50651i | 2.25324 | − | 1.63708i | ||||
\(28\) | 2.11803 | − | 1.53884i | 0.400271 | − | 0.290814i | ||||
\(29\) | −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 | 0.972483 | − | 0.232972i | \(-0.0748451\pi\) |
0.0789443 | + | 0.996879i | \(0.474845\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.00000 | − | 9.95959i | −0.696311 | − | 1.73374i | ||||
\(34\) | −5.23607 | −0.897978 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.30902 | − | 7.10642i | 0.384836 | − | 1.18440i | ||||
\(37\) | 0.263932 | + | 0.812299i | 0.0433902 | + | 0.133541i | 0.970405 | − | 0.241484i | \(-0.0776341\pi\) |
−0.927015 | + | 0.375025i | \(0.877634\pi\) | |||||||
\(38\) | −3.30902 | + | 2.40414i | −0.536793 | + | 0.390003i | ||||
\(39\) | 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 | \(0.146248\pi\) | |||||||
\(42\) | 6.85410 | + | 4.97980i | 1.05761 | + | 0.768399i | ||||
\(43\) | 9.23607 | 1.40849 | 0.704244 | − | 0.709958i | \(-0.251286\pi\) | ||||
0.704244 | + | 0.709958i | \(0.251286\pi\) | |||||||
\(44\) | −2.80902 | − | 1.76336i | −0.423475 | − | 0.265836i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.118034 | − | 0.0857567i | −0.0174032 | − | 0.0126441i | ||||
\(47\) | −3.50000 | + | 10.7719i | −0.510527 | + | 1.57124i | 0.280748 | + | 0.959782i | \(0.409418\pi\) |
−0.791275 | + | 0.611460i | \(0.790582\pi\) | |||||||
\(48\) | −1.00000 | − | 3.07768i | −0.144338 | − | 0.444225i | ||||
\(49\) | 0.118034 | − | 0.0857567i | 0.0168620 | − | 0.0122510i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.23607 | − | 16.1150i | −0.733196 | − | 2.25655i | ||||
\(52\) | 0.500000 | − | 1.53884i | 0.0693375 | − | 0.213399i | ||||
\(53\) | 0.736068 | + | 0.534785i | 0.101107 | + | 0.0734583i | 0.637190 | − | 0.770707i | \(-0.280097\pi\) |
−0.536083 | + | 0.844165i | \(0.680097\pi\) | |||||||
\(54\) | 14.4721 | 1.96941 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.61803 | 0.349850 | ||||||||
\(57\) | −10.7082 | − | 7.77997i | −1.41834 | − | 1.03048i | ||||
\(58\) | 0.381966 | − | 1.17557i | 0.0501546 | − | 0.154360i | ||||
\(59\) | 0.736068 | + | 2.26538i | 0.0958279 | + | 0.294928i | 0.987469 | − | 0.157816i | \(-0.0504452\pi\) |
−0.891641 | + | 0.452744i | \(0.850445\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.23607 | + | 5.25731i | −0.926484 | + | 0.673130i | −0.945129 | − | 0.326696i | \(-0.894065\pi\) |
0.0186458 | + | 0.999826i | \(0.494065\pi\) | |||||||
\(62\) | 2.23607 | + | 6.88191i | 0.283981 | + | 0.874003i | ||||
\(63\) | −6.04508 | + | 18.6049i | −0.761609 | + | 2.34399i | ||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.61803 | − | 10.4086i | 0.322258 | − | 1.28121i | ||||
\(67\) | −0.763932 | −0.0933292 | −0.0466646 | − | 0.998911i | \(-0.514859\pi\) | ||||
−0.0466646 | + | 0.998911i | \(0.514859\pi\) | |||||||
\(68\) | −4.23607 | − | 3.07768i | −0.513699 | − | 0.373224i | ||||
\(69\) | 0.145898 | − | 0.449028i | 0.0175641 | − | 0.0540566i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.7082 | + | 7.77997i | −1.27083 | + | 0.923312i | −0.999235 | − | 0.0390997i | \(-0.987551\pi\) |
−0.271595 | + | 0.962412i | \(0.587551\pi\) | |||||||
\(72\) | 6.04508 | − | 4.39201i | 0.712420 | − | 0.517603i | ||||
\(73\) | 0.527864 | + | 1.62460i | 0.0617818 | + | 0.190145i | 0.977184 | − | 0.212397i | \(-0.0681269\pi\) |
−0.915402 | + | 0.402542i | \(0.868127\pi\) | |||||||
\(74\) | −0.263932 | + | 0.812299i | −0.0306815 | + | 0.0944279i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.09017 | −0.469175 | ||||||||
\(77\) | 7.35410 | + | 4.61653i | 0.838078 | + | 0.526102i | ||||
\(78\) | 5.23607 | 0.592868 | ||||||||
\(79\) | 1.23607 | + | 0.898056i | 0.139069 | + | 0.101039i | 0.655144 | − | 0.755504i | \(-0.272608\pi\) |
−0.516076 | + | 0.856543i | \(0.672608\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.54508 | + | 23.2214i | 0.838343 | + | 2.58015i | ||||
\(82\) | −1.50000 | + | 1.08981i | −0.165647 | + | 0.120350i | ||||
\(83\) | 12.7082 | − | 9.23305i | 1.39491 | − | 1.01346i | 0.399600 | − | 0.916690i | \(-0.369149\pi\) |
0.995307 | − | 0.0967693i | \(-0.0308509\pi\) | |||||||
\(84\) | 2.61803 | + | 8.05748i | 0.285651 | + | 0.879143i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.47214 | + | 5.42882i | 0.805741 | + | 0.585405i | ||||
\(87\) | 4.00000 | 0.428845 | ||||||||
\(88\) | −1.23607 | − | 3.07768i | −0.131765 | − | 0.328082i | ||||
\(89\) | −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 | ||||
\(92\) | −0.0450850 | − | 0.138757i | −0.00470043 | − | 0.0144664i | ||||
\(93\) | −18.9443 | + | 13.7638i | −1.96443 | + | 1.42724i | ||||
\(94\) | −9.16312 | + | 6.65740i | −0.945104 | + | 0.686658i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | − | 3.07768i | 0.102062 | − | 0.314115i | ||||
\(97\) | −9.70820 | − | 7.05342i | −0.985719 | − | 0.716167i | −0.0267394 | − | 0.999642i | \(-0.508512\pi\) |
−0.958979 | + | 0.283476i | \(0.908512\pi\) | |||||||
\(98\) | 0.145898 | 0.0147379 | ||||||||
\(99\) | 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 | \(0.759063\pi\) | |||||||
\(102\) | 5.23607 | − | 16.1150i | 0.518448 | − | 1.59562i | ||||
\(103\) | 3.50000 | + | 10.7719i | 0.344865 | + | 1.06139i | 0.961656 | + | 0.274259i | \(0.0884325\pi\) |
−0.616791 | + | 0.787127i | \(0.711567\pi\) | |||||||
\(104\) | 1.30902 | − | 0.951057i | 0.128360 | − | 0.0932588i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.281153 | + | 0.865300i | 0.0273080 | + | 0.0840453i | ||||
\(107\) | 2.32624 | − | 7.15942i | 0.224886 | − | 0.692128i | −0.773417 | − | 0.633897i | \(-0.781454\pi\) |
0.998303 | − | 0.0582304i | \(-0.0185458\pi\) | |||||||
\(108\) | 11.7082 | + | 8.50651i | 1.12662 | + | 0.818539i | ||||
\(109\) | 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 | ||||||||
\(112\) | 2.11803 | + | 1.53884i | 0.200135 | + | 0.145407i | ||||
\(113\) | −1.94427 | + | 5.98385i | −0.182902 | + | 0.562914i | −0.999906 | − | 0.0137181i | \(-0.995633\pi\) |
0.817004 | + | 0.576632i | \(0.195633\pi\) | |||||||
\(114\) | −4.09017 | − | 12.5882i | −0.383080 | − | 1.17900i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.00000 | − | 0.726543i | 0.0928477 | − | 0.0674578i | ||||
\(117\) | 3.73607 | + | 11.4984i | 0.345400 | + | 1.06303i | ||||
\(118\) | −0.736068 | + | 2.26538i | −0.0677605 | + | 0.208546i | ||||
\(119\) | 11.0902 | + | 8.05748i | 1.01663 | + | 0.738628i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.95492 | − | 10.8249i | 0.177720 | − | 0.984081i | ||||
\(122\) | −8.94427 | −0.809776 | ||||||||
\(123\) | −4.85410 | − | 3.52671i | −0.437680 | − | 0.317993i | ||||
\(124\) | −2.23607 | + | 6.88191i | −0.200805 | + | 0.618014i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −15.8262 | + | 11.4984i | −1.40991 | + | 1.02436i | ||||
\(127\) | −1.92705 | + | 1.40008i | −0.170998 | + | 0.124237i | −0.669993 | − | 0.742368i | \(-0.733703\pi\) |
0.498995 | + | 0.866605i | \(0.333703\pi\) | |||||||
\(128\) | −0.309017 | − | 0.951057i | −0.0273135 | − | 0.0840623i | ||||
\(129\) | −9.23607 | + | 28.4257i | −0.813190 | + | 2.50274i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.4164 | 0.997456 | 0.498728 | − | 0.866758i | \(-0.333801\pi\) | ||||
0.498728 | + | 0.866758i | \(0.333801\pi\) | |||||||
\(132\) | 8.23607 | − | 6.88191i | 0.716858 | − | 0.598993i | ||||
\(133\) | 10.7082 | 0.928519 | ||||||||
\(134\) | −0.618034 | − | 0.449028i | −0.0533900 | − | 0.0387901i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.61803 | − | 4.97980i | −0.138745 | − | 0.427014i | ||||
\(137\) | −4.23607 | + | 3.07768i | −0.361912 | + | 0.262944i | −0.753849 | − | 0.657048i | \(-0.771805\pi\) |
0.391937 | + | 0.919992i | \(0.371805\pi\) | |||||||
\(138\) | 0.381966 | − | 0.277515i | 0.0325151 | − | 0.0236236i | ||||
\(139\) | −2.51722 | − | 7.74721i | −0.213508 | − | 0.657110i | −0.999256 | − | 0.0385633i | \(-0.987722\pi\) |
0.785748 | − | 0.618546i | \(-0.212278\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −29.6525 | − | 21.5438i | −2.49719 | − | 1.81431i | ||||
\(142\) | −13.2361 | −1.11075 | ||||||||
\(143\) | 5.35410 | − | 0.363271i | 0.447732 | − | 0.0303783i | ||||
\(144\) | 7.47214 | 0.622678 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.527864 | + | 1.62460i | −0.0436863 | + | 0.134453i | ||||
\(147\) | 0.145898 | + | 0.449028i | 0.0120335 | + | 0.0370352i | ||||
\(148\) | −0.690983 | + | 0.502029i | −0.0567985 | + | 0.0412665i | ||||
\(149\) | 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 | \(-0.727858\pi\) |
0.974427 | − | 0.224705i | \(-0.0721420\pi\) | |||||||
\(152\) | −3.30902 | − | 2.40414i | −0.268397 | − | 0.195002i | ||||
\(153\) | 39.1246 | 3.16304 | ||||||||
\(154\) | 3.23607 | + | 8.05748i | 0.260770 | + | 0.649290i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.23607 | + | 3.07768i | 0.339157 | + | 0.246412i | ||||
\(157\) | −2.66312 | + | 8.19624i | −0.212540 | + | 0.654131i | 0.786779 | + | 0.617235i | \(0.211747\pi\) |
−0.999319 | + | 0.0368962i | \(0.988253\pi\) | |||||||
\(158\) | 0.472136 | + | 1.45309i | 0.0375611 | + | 0.115601i | ||||
\(159\) | −2.38197 | + | 1.73060i | −0.188902 | + | 0.137245i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.118034 | + | 0.363271i | 0.00930238 | + | 0.0286298i | ||||
\(162\) | −7.54508 | + | 23.2214i | −0.592798 | + | 1.82444i | ||||
\(163\) | −5.85410 | − | 4.25325i | −0.458529 | − | 0.333141i | 0.334425 | − | 0.942422i | \(-0.391458\pi\) |
−0.792954 | + | 0.609282i | \(0.791458\pi\) | |||||||
\(164\) | −1.85410 | −0.144781 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.7082 | 1.21919 | ||||||||
\(167\) | 6.39919 | + | 4.64928i | 0.495184 | + | 0.359772i | 0.807174 | − | 0.590313i | \(-0.200996\pi\) |
−0.311990 | + | 0.950085i | \(0.600996\pi\) | |||||||
\(168\) | −2.61803 | + | 8.05748i | −0.201986 | + | 0.621648i | ||||
\(169\) | −3.20820 | − | 9.87384i | −0.246785 | − | 0.759526i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.7254 | − | 17.9641i | 1.89080 | − | 1.37375i | ||||
\(172\) | 2.85410 | + | 8.78402i | 0.217623 | + | 0.669775i | ||||
\(173\) | 3.89919 | − | 12.0005i | 0.296450 | − | 0.912378i | −0.686281 | − | 0.727337i | \(-0.740758\pi\) |
0.982731 | − | 0.185042i | \(-0.0592421\pi\) | |||||||
\(174\) | 3.23607 | + | 2.35114i | 0.245326 | + | 0.178240i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.809017 | − | 3.21644i | 0.0609820 | − | 0.242448i | ||||
\(177\) | −7.70820 | −0.579384 | ||||||||
\(178\) | −9.73607 | − | 7.07367i | −0.729749 | − | 0.530194i | ||||
\(179\) | −0.899187 | + | 2.76741i | −0.0672084 | + | 0.206846i | −0.979021 | − | 0.203761i | \(-0.934683\pi\) |
0.911812 | + | 0.410607i | \(0.134683\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.5623 | − | 12.0332i | 1.23107 | − | 0.894422i | 0.234097 | − | 0.972213i | \(-0.424787\pi\) |
0.996970 | + | 0.0777911i | \(0.0247867\pi\) | |||||||
\(182\) | −3.42705 | + | 2.48990i | −0.254030 | + | 0.184564i | ||||
\(183\) | −8.94427 | − | 27.5276i | −0.661180 | − | 2.03490i | ||||
\(184\) | 0.0450850 | − | 0.138757i | 0.00332371 | − | 0.0102293i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −23.4164 | −1.71697 | ||||||||
\(187\) | 4.23607 | − | 16.8415i | 0.309772 | − | 1.23157i | ||||
\(188\) | −11.3262 | −0.826051 | ||||||||
\(189\) | −30.6525 | − | 22.2703i | −2.22964 | − | 1.61993i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.85410 | + | 24.1724i | 0.568303 | + | 1.74906i | 0.657928 | + | 0.753081i | \(0.271433\pi\) |
−0.0896251 | + | 0.995976i | \(0.528567\pi\) | |||||||
\(192\) | 2.61803 | − | 1.90211i | 0.188940 | − | 0.137273i | ||||
\(193\) | −4.38197 | + | 3.18368i | −0.315421 | + | 0.229167i | −0.734219 | − | 0.678913i | \(-0.762451\pi\) |
0.418798 | + | 0.908079i | \(0.362451\pi\) | |||||||
\(194\) | −3.70820 | − | 11.4127i | −0.266234 | − | 0.819383i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.118034 | + | 0.0857567i | 0.00843100 | + | 0.00612548i | ||||
\(197\) | 4.90983 | 0.349811 | 0.174905 | − | 0.984585i | \(-0.444038\pi\) | ||||
0.174905 | + | 0.984585i | \(0.444038\pi\) | |||||||
\(198\) | 20.9894 | + | 13.1760i | 1.49165 | + | 0.936380i | ||||
\(199\) | 1.70820 | 0.121091 | 0.0605457 | − | 0.998165i | \(-0.480716\pi\) | ||||
0.0605457 | + | 0.998165i | \(0.480716\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.763932 | − | 2.35114i | 0.0538836 | − | 0.165837i | ||||
\(202\) | −1.14590 | − | 3.52671i | −0.0806251 | − | 0.248139i | ||||
\(203\) | −2.61803 | + | 1.90211i | −0.183750 | + | 0.133502i | ||||
\(204\) | 13.7082 | − | 9.95959i | 0.959766 | − | 0.697311i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.50000 | + | 10.7719i | −0.243857 | + | 0.750513i | ||||
\(207\) | 0.881966 | + | 0.640786i | 0.0613009 | + | 0.0445377i | ||||
\(208\) | 1.61803 | 0.112190 | ||||||||
\(209\) | −5.05573 | − | 12.5882i | −0.349712 | − | 0.870747i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.9443 | − | 12.3107i | −1.16649 | − | 0.847506i | −0.175907 | − | 0.984407i | \(-0.556286\pi\) |
−0.990585 | + | 0.136901i | \(0.956286\pi\) | |||||||
\(212\) | −0.281153 | + | 0.865300i | −0.0193097 | + | 0.0594290i | ||||
\(213\) | −13.2361 | − | 40.7364i | −0.906920 | − | 2.79121i | ||||
\(214\) | 6.09017 | − | 4.42477i | 0.416315 | − | 0.302471i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.47214 | + | 13.7638i | 0.304290 | + | 0.936509i | ||||
\(217\) | 5.85410 | − | 18.0171i | 0.397402 | − | 1.22308i | ||||
\(218\) | 6.09017 | + | 4.42477i | 0.412478 | + | 0.299683i | ||||
\(219\) | −5.52786 | −0.373538 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.47214 | 0.569898 | ||||||||
\(222\) | −2.23607 | − | 1.62460i | −0.150075 | − | 0.109036i | ||||
\(223\) | −2.98936 | + | 9.20029i | −0.200182 | + | 0.616097i | 0.799695 | + | 0.600407i | \(0.204995\pi\) |
−0.999877 | + | 0.0156905i | \(0.995005\pi\) | |||||||
\(224\) | 0.809017 | + | 2.48990i | 0.0540547 | + | 0.166363i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.09017 | + | 3.69822i | −0.338593 | + | 0.246002i | ||||
\(227\) | 5.09017 | + | 15.6659i | 0.337846 | + | 1.03978i | 0.965303 | + | 0.261133i | \(0.0840960\pi\) |
−0.627456 | + | 0.778652i | \(0.715904\pi\) | |||||||
\(228\) | 4.09017 | − | 12.5882i | 0.270878 | − | 0.833677i | ||||
\(229\) | 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 | ||||
\(232\) | 1.23607 | 0.0811518 | ||||||||
\(233\) | 12.3262 | + | 8.95554i | 0.807519 | + | 0.586697i | 0.913110 | − | 0.407713i | \(-0.133674\pi\) |
−0.105591 | + | 0.994410i | \(0.533674\pi\) | |||||||
\(234\) | −3.73607 | + | 11.4984i | −0.244234 | + | 0.751676i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.92705 | + | 1.40008i | −0.125440 | + | 0.0911377i | ||||
\(237\) | −4.00000 | + | 2.90617i | −0.259828 | + | 0.188776i | ||||
\(238\) | 4.23607 | + | 13.0373i | 0.274584 | + | 0.845081i | ||||
\(239\) | 2.94427 | − | 9.06154i | 0.190449 | − | 0.586142i | −0.809550 | − | 0.587050i | \(-0.800289\pi\) |
1.00000 | 0.000908170i | \(0.000289080\pi\) | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.85410 | −0.119433 | −0.0597166 | − | 0.998215i | \(-0.519020\pi\) | ||||
−0.0597166 | + | 0.998215i | \(0.519020\pi\) | |||||||
\(242\) | 7.94427 | − | 7.60845i | 0.510677 | − | 0.489090i | ||||
\(243\) | −35.5967 | −2.28353 | ||||||||
\(244\) | −7.23607 | − | 5.25731i | −0.463242 | − | 0.336565i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.85410 | − | 5.70634i | −0.118213 | − | 0.363823i | ||||
\(247\) | 5.35410 | − | 3.88998i | 0.340673 | − | 0.247514i | ||||
\(248\) | −5.85410 | + | 4.25325i | −0.371736 | + | 0.270082i | ||||
\(249\) | 15.7082 | + | 48.3449i | 0.995467 | + | 3.06373i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.11803 | + | 5.89810i | 0.512406 | + | 0.372285i | 0.813735 | − | 0.581235i | \(-0.197430\pi\) |
−0.301330 | + | 0.953520i | \(0.597430\pi\) | |||||||
\(252\) | −19.5623 | −1.23231 | ||||||||
\(253\) | 0.371323 | − | 0.310271i | 0.0233449 | − | 0.0195066i | ||||
\(254\) | −2.38197 | −0.149458 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | 3.70820 | + | 11.4127i | 0.231311 | + | 0.711903i | 0.997589 | + | 0.0693940i | \(0.0221066\pi\) |
−0.766278 | + | 0.642509i | \(0.777893\pi\) | |||||||
\(258\) | −24.1803 | + | 17.5680i | −1.50540 | + | 1.09374i | ||||
\(259\) | 1.80902 | − | 1.31433i | 0.112407 | − | 0.0816684i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.85410 | + | 8.78402i | −0.176664 | + | 0.543717i | ||||
\(262\) | 9.23607 | + | 6.71040i | 0.570606 | + | 0.414570i | ||||
\(263\) | −25.7984 | −1.59080 | −0.795398 | − | 0.606088i | \(-0.792738\pi\) | ||||
−0.795398 | + | 0.606088i | \(0.792738\pi\) | |||||||
\(264\) | 10.7082 | − | 0.726543i | 0.659044 | − | 0.0447156i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.66312 | + | 6.29412i | 0.531170 | + | 0.385918i | ||||
\(267\) | 12.0344 | − | 37.0382i | 0.736496 | − | 2.26670i | ||||
\(268\) | −0.236068 | − | 0.726543i | −0.0144201 | − | 0.0443806i | ||||
\(269\) | −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 | \(0.0335974\pi\) |
−0.742589 | + | 0.669747i | \(0.766403\pi\) | |||||||
\(272\) | 1.61803 | − | 4.97980i | 0.0981077 | − | 0.301945i | ||||
\(273\) | −11.0902 | − | 8.05748i | −0.671208 | − | 0.487661i | ||||
\(274\) | −5.23607 | −0.316322 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.472136 | 0.0284192 | ||||||||
\(277\) | −0.500000 | − | 0.363271i | −0.0300421 | − | 0.0218269i | 0.572663 | − | 0.819791i | \(-0.305910\pi\) |
−0.602705 | + | 0.797964i | \(0.705910\pi\) | |||||||
\(278\) | 2.51722 | − | 7.74721i | 0.150973 | − | 0.464647i | ||||
\(279\) | −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 | \(0.480403\pi\) | |||||||
\(282\) | −11.3262 | − | 34.8586i | −0.674468 | − | 2.07580i | ||||
\(283\) | −7.67376 | + | 23.6174i | −0.456158 | + | 1.40391i | 0.413613 | + | 0.910453i | \(0.364267\pi\) |
−0.869771 | + | 0.493456i | \(0.835733\pi\) | |||||||
\(284\) | −10.7082 | − | 7.77997i | −0.635415 | − | 0.461656i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.54508 | + | 2.85317i | 0.268757 | + | 0.168711i | ||||
\(287\) | 4.85410 | 0.286529 | ||||||||
\(288\) | 6.04508 | + | 4.39201i | 0.356210 | + | 0.258802i | ||||
\(289\) | 3.21885 | − | 9.90659i | 0.189344 | − | 0.582741i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 31.4164 | − | 22.8254i | 1.84166 | − | 1.33805i | ||||
\(292\) | −1.38197 | + | 1.00406i | −0.0808734 | + | 0.0587580i | ||||
\(293\) | 7.33688 | + | 22.5806i | 0.428625 | + | 1.31917i | 0.899480 | + | 0.436962i | \(0.143946\pi\) |
−0.470855 | + | 0.882211i | \(0.656054\pi\) | |||||||
\(294\) | −0.145898 | + | 0.449028i | −0.00850895 | + | 0.0261878i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.854102 | −0.0496437 | ||||||||
\(297\) | −11.7082 | + | 46.5488i | −0.679379 | + | 2.70103i | ||||
\(298\) | 4.00000 | 0.231714 | ||||||||
\(299\) | 0.190983 | + | 0.138757i | 0.0110448 | + | 0.00802454i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.47214 | − | 22.9969i | −0.430687 | − | 1.32552i | ||||
\(302\) | 10.2361 | − | 7.43694i | 0.589020 | − | 0.427948i | ||||
\(303\) | 9.70820 | − | 7.05342i | 0.557722 | − | 0.405209i | ||||
\(304\) | −1.26393 | − | 3.88998i | −0.0724915 | − | 0.223106i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 31.6525 | + | 22.9969i | 1.80945 | + | 1.31464i | ||||
\(307\) | 26.9443 | 1.53779 | 0.768895 | − | 0.639375i | \(-0.220807\pi\) | ||||
0.768895 | + | 0.639375i | \(0.220807\pi\) | |||||||
\(308\) | −2.11803 | + | 8.42075i | −0.120686 | + | 0.479817i | ||||
\(309\) | −36.6525 | −2.08509 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.763932 | + | 2.35114i | −0.0433186 | + | 0.133321i | −0.970377 | − | 0.241597i | \(-0.922329\pi\) |
0.927058 | + | 0.374917i | \(0.122329\pi\) | |||||||
\(312\) | 1.61803 | + | 4.97980i | 0.0916031 | + | 0.281925i | ||||
\(313\) | 22.1803 | − | 16.1150i | 1.25371 | − | 0.910871i | 0.255276 | − | 0.966868i | \(-0.417834\pi\) |
0.998431 | + | 0.0559968i | \(0.0178337\pi\) | |||||||
\(314\) | −6.97214 | + | 5.06555i | −0.393460 | + | 0.285866i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.472136 | + | 1.45309i | −0.0265597 | + | 0.0817424i | ||||
\(317\) | 5.01722 | + | 3.64522i | 0.281795 | + | 0.204736i | 0.719700 | − | 0.694285i | \(-0.244279\pi\) |
−0.437905 | + | 0.899021i | \(0.644279\pi\) | |||||||
\(318\) | −2.94427 | −0.165107 | ||||||||
\(319\) | 3.47214 | + | 2.17963i | 0.194402 | + | 0.122036i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.7082 | + | 14.3188i | 1.10000 | + | 0.799200i | ||||
\(322\) | −0.118034 | + | 0.363271i | −0.00657778 | + | 0.0202443i | ||||
\(323\) | −6.61803 | − | 20.3682i | −0.368237 | − | 1.13332i | ||||
\(324\) | −19.7533 | + | 14.3516i | −1.09740 | + | 0.797311i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.23607 | − | 6.88191i | −0.123844 | − | 0.381154i | ||||
\(327\) | −7.52786 | + | 23.1684i | −0.416292 | + | 1.28121i | ||||
\(328\) | −1.50000 | − | 1.08981i | −0.0828236 | − | 0.0601749i | ||||
\(329\) | 29.6525 | 1.63479 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.3820 | −0.790504 | −0.395252 | − | 0.918573i | \(-0.629343\pi\) | ||||
−0.395252 | + | 0.918573i | \(0.629343\pi\) | |||||||
\(332\) | 12.7082 | + | 9.23305i | 0.697453 | + | 0.506729i | ||||
\(333\) | 1.97214 | − | 6.06961i | 0.108072 | − | 0.332613i | ||||
\(334\) | 2.44427 | + | 7.52270i | 0.133745 | + | 0.411624i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.85410 | + | 4.97980i | −0.373922 | + | 0.271670i | ||||
\(337\) | −10.9443 | − | 33.6830i | −0.596172 | − | 1.83483i | −0.548801 | − | 0.835953i | \(-0.684916\pi\) |
−0.0473712 | − | 0.998877i | \(-0.515084\pi\) | |||||||
\(338\) | 3.20820 | − | 9.87384i | 0.174503 | − | 0.537066i | ||||
\(339\) | −16.4721 | − | 11.9677i | −0.894644 | − | 0.649997i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.9443 | + | 1.62460i | −1.29666 | + | 0.0879769i | ||||
\(342\) | 30.5623 | 1.65262 | ||||||||
\(343\) | −15.1353 | − | 10.9964i | −0.817227 | − | 0.593750i | ||||
\(344\) | −2.85410 | + | 8.78402i | −0.153883 | + | 0.473603i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.2082 | − | 7.41669i | 0.548796 | − | 0.398724i | ||||
\(347\) | −21.9443 | + | 15.9434i | −1.17803 | + | 0.855889i | −0.991948 | − | 0.126645i | \(-0.959579\pi\) |
−0.186082 | + | 0.982534i | \(0.559579\pi\) | |||||||
\(348\) | 1.23607 | + | 3.80423i | 0.0662602 | + | 0.203928i | ||||
\(349\) | 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 | ||||||||
\(352\) | 2.54508 | − | 2.12663i | 0.135653 | − | 0.113350i | ||||
\(353\) | −11.7082 | −0.623165 | −0.311582 | − | 0.950219i | \(-0.600859\pi\) | ||||
−0.311582 | + | 0.950219i | \(0.600859\pi\) | |||||||
\(354\) | −6.23607 | − | 4.53077i | −0.331443 | − | 0.240808i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.71885 | − | 11.4454i | −0.197098 | − | 0.606607i | ||||
\(357\) | −35.8885 | + | 26.0746i | −1.89942 | + | 1.38001i | ||||
\(358\) | −2.35410 | + | 1.71036i | −0.124418 | + | 0.0903951i | ||||
\(359\) | −9.41641 | − | 28.9807i | −0.496979 | − | 1.52954i | −0.813850 | − | 0.581075i | \(-0.802632\pi\) |
0.316871 | − | 0.948469i | \(-0.397368\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.83688 | + | 1.33457i | 0.0966779 | + | 0.0702406i | ||||
\(362\) | 20.4721 | 1.07599 | ||||||||
\(363\) | 31.3607 | + | 16.8415i | 1.64601 | + | 0.883950i | ||||
\(364\) | −4.23607 | −0.222030 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8.94427 | − | 27.5276i | 0.467525 | − | 1.43889i | ||||
\(367\) | −3.23607 | − | 9.95959i | −0.168921 | − | 0.519887i | 0.830382 | − | 0.557194i | \(-0.188122\pi\) |
−0.999304 | + | 0.0373073i | \(0.988122\pi\) | |||||||
\(368\) | 0.118034 | − | 0.0857567i | 0.00615295 | − | 0.00447038i | ||||
\(369\) | 11.2082 | − | 8.14324i | 0.583476 | − | 0.423920i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.736068 | − | 2.26538i | 0.0382147 | − | 0.117613i | ||||
\(372\) | −18.9443 | − | 13.7638i | −0.982215 | − | 0.713621i | ||||
\(373\) | −6.96556 | −0.360663 | −0.180331 | − | 0.983606i | \(-0.557717\pi\) | ||||
−0.180331 | + | 0.983606i | \(0.557717\pi\) | |||||||
\(374\) | 13.3262 | − | 11.1352i | 0.689083 | − | 0.575786i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.16312 | − | 6.65740i | −0.472552 | − | 0.343329i | ||||
\(377\) | −0.618034 | + | 1.90211i | −0.0318304 | + | 0.0979638i | ||||
\(378\) | −11.7082 | − | 36.0341i | −0.602205 | − | 1.85340i | ||||
\(379\) | 8.35410 | − | 6.06961i | 0.429121 | − | 0.311775i | −0.352176 | − | 0.935934i | \(-0.614558\pi\) |
0.781297 | + | 0.624159i | \(0.214558\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.38197 | − | 7.33094i | −0.122032 | − | 0.375575i | ||||
\(382\) | −7.85410 | + | 24.1724i | −0.401851 | + | 1.23677i | ||||
\(383\) | −12.8262 | − | 9.31881i | −0.655390 | − | 0.476169i | 0.209713 | − | 0.977763i | \(-0.432747\pi\) |
−0.865103 | + | 0.501594i | \(0.832747\pi\) | |||||||
\(384\) | 3.23607 | 0.165140 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.41641 | −0.275688 | ||||||||
\(387\) | −55.8328 | − | 40.5649i | −2.83814 | − | 2.06203i | ||||
\(388\) | 3.70820 | − | 11.4127i | 0.188256 | − | 0.579391i | ||||
\(389\) | 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 | ||||
\(392\) | 0.0450850 | + | 0.138757i | 0.00227713 | + | 0.00700830i | ||||
\(393\) | −11.4164 | + | 35.1361i | −0.575882 | + | 1.77238i | ||||
\(394\) | 3.97214 | + | 2.88593i | 0.200113 | + | 0.145391i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.23607 | + | 22.9969i | 0.464130 | + | 1.15564i | ||||
\(397\) | −6.79837 | −0.341201 | −0.170600 | − | 0.985340i | \(-0.554571\pi\) | ||||
−0.170600 | + | 0.985340i | \(0.554571\pi\) | |||||||
\(398\) | 1.38197 | + | 1.00406i | 0.0692717 | + | 0.0503288i | ||||
\(399\) | −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 | \(0.213561\pi\) | |||||||
\(402\) | 2.00000 | − | 1.45309i | 0.0997509 | − | 0.0724733i | ||||
\(403\) | −3.61803 | − | 11.1352i | −0.180227 | − | 0.554682i | ||||
\(404\) | 1.14590 | − | 3.52671i | 0.0570106 | − | 0.175460i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.23607 | −0.160603 | ||||||||
\(407\) | −2.39919 | − | 1.50609i | −0.118923 | − | 0.0746539i | ||||
\(408\) | 16.9443 | 0.838866 | ||||||||
\(409\) | 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 | ||||
\(412\) | −9.16312 | + | 6.65740i | −0.451434 | + | 0.327986i | ||||
\(413\) | 5.04508 | − | 3.66547i | 0.248252 | − | 0.180366i | ||||
\(414\) | 0.336881 | + | 1.03681i | 0.0165568 | + | 0.0509566i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.30902 | + | 0.951057i | 0.0641798 | + | 0.0466294i | ||||
\(417\) | 26.3607 | 1.29089 | ||||||||
\(418\) | 3.30902 | − | 13.1558i | 0.161849 | − | 0.643471i | ||||
\(419\) | −1.61803 | −0.0790461 | −0.0395231 | − | 0.999219i | \(-0.512584\pi\) | ||||
−0.0395231 | + | 0.999219i | \(0.512584\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.76393 | + | 17.7396i | −0.280917 | + | 0.864573i | 0.706676 | + | 0.707537i | \(0.250194\pi\) |
−0.987593 | + | 0.157036i | \(0.949806\pi\) | |||||||
\(422\) | −6.47214 | − | 19.9192i | −0.315059 | − | 0.969651i | ||||
\(423\) | 68.4681 | − | 49.7450i | 3.32903 | − | 2.41868i | ||||
\(424\) | −0.736068 | + | 0.534785i | −0.0357466 | + | 0.0259714i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 13.2361 | − | 40.7364i | 0.641290 | − | 1.97369i | ||||
\(427\) | 18.9443 | + | 13.7638i | 0.916778 | + | 0.666078i | ||||
\(428\) | 7.52786 | 0.363873 | ||||||||
\(429\) | −4.23607 | + | 16.8415i | −0.204519 | + | 0.813115i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.1803 | + | 15.3884i | 1.02022 | + | 0.741234i | 0.966328 | − | 0.257313i | \(-0.0828370\pi\) |
0.0538929 | + | 0.998547i | \(0.482837\pi\) | |||||||
\(432\) | −4.47214 | + | 13.7638i | −0.215166 | + | 0.662212i | ||||
\(433\) | −2.94427 | − | 9.06154i | −0.141493 | − | 0.435470i | 0.855051 | − | 0.518545i | \(-0.173526\pi\) |
−0.996543 | + | 0.0830748i | \(0.973526\pi\) | |||||||
\(434\) | 15.3262 | − | 11.1352i | 0.735683 | − | 0.534505i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.32624 | + | 7.15942i | 0.111407 | + | 0.342874i | ||||
\(437\) | 0.184405 | − | 0.567541i | 0.00882130 | − | 0.0271492i | ||||
\(438\) | −4.47214 | − | 3.24920i | −0.213687 | − | 0.155253i | ||||
\(439\) | −13.1246 | −0.626404 | −0.313202 | − | 0.949687i | \(-0.601402\pi\) | ||||
−0.313202 | + | 0.949687i | \(0.601402\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.09017 | −0.0519129 | ||||||||
\(442\) | 6.85410 | + | 4.97980i | 0.326016 | + | 0.236865i | ||||
\(443\) | −0.416408 | + | 1.28157i | −0.0197841 | + | 0.0608893i | −0.960461 | − | 0.278414i | \(-0.910191\pi\) |
0.940677 | + | 0.339303i | \(0.110191\pi\) | |||||||
\(444\) | −0.854102 | − | 2.62866i | −0.0405339 | − | 0.124750i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.82624 | + | 5.68609i | −0.370583 | + | 0.269244i | ||||
\(447\) | 4.00000 | + | 12.3107i | 0.189194 | + | 0.582278i | ||||
\(448\) | −0.809017 | + | 2.48990i | −0.0382225 | + | 0.117637i | ||||
\(449\) | −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 | ||||
\(452\) | −6.29180 | −0.295941 | ||||||||
\(453\) | 33.1246 | + | 24.0664i | 1.55633 | + | 1.13074i | ||||
\(454\) | −5.09017 | + | 15.6659i | −0.238894 | + | 0.735239i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.7082 | − | 7.77997i | 0.501458 | − | 0.364330i | ||||
\(457\) | 26.3262 | − | 19.1271i | 1.23149 | − | 0.894729i | 0.234489 | − | 0.972119i | \(-0.424658\pi\) |
0.997001 | + | 0.0773894i | \(0.0246585\pi\) | |||||||
\(458\) | 8.70820 | + | 26.8011i | 0.406908 | + | 1.25233i | ||||
\(459\) | −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 | \(0.268583\pi\) | |||||||
\(462\) | −28.0344 | + | 1.90211i | −1.30428 | + | 0.0884943i | ||||
\(463\) | −15.5066 | −0.720652 | −0.360326 | − | 0.932826i | \(-0.617335\pi\) | ||||
−0.360326 | + | 0.932826i | \(0.617335\pi\) | |||||||
\(464\) | 1.00000 | + | 0.726543i | 0.0464238 | + | 0.0337289i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.70820 | + | 14.4904i | 0.218103 | + | 0.671253i | ||||
\(467\) | 13.9443 | − | 10.1311i | 0.645264 | − | 0.468812i | −0.216391 | − | 0.976307i | \(-0.569428\pi\) |
0.861655 | + | 0.507495i | \(0.169428\pi\) | |||||||
\(468\) | −9.78115 | + | 7.10642i | −0.452134 | + | 0.328495i | ||||
\(469\) | 0.618034 | + | 1.90211i | 0.0285382 | + | 0.0878314i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.5623 | − | 16.3925i | −1.03962 | − | 0.755325i | ||||
\(472\) | −2.38197 | −0.109639 | ||||||||
\(473\) | −23.5066 | + | 19.6417i | −1.08083 | + | 0.903125i | ||||
\(474\) | −4.94427 | −0.227098 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.23607 | + | 13.0373i | −0.194160 | + | 0.597563i | ||||
\(477\) | −2.10081 | − | 6.46564i | −0.0961896 | − | 0.296041i | ||||
\(478\) | 7.70820 | − | 5.60034i | 0.352565 | − | 0.256153i | ||||
\(479\) | 23.9443 | − | 17.3965i | 1.09404 | − | 0.794868i | 0.113965 | − | 0.993485i | \(-0.463645\pi\) |
0.980077 | + | 0.198617i | \(0.0636450\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.427051 | − | 1.31433i | 0.0194718 | − | 0.0599282i | ||||
\(482\) | −1.50000 | − | 1.08981i | −0.0683231 | − | 0.0496397i | ||||
\(483\) | −1.23607 | −0.0562430 | ||||||||
\(484\) | 10.8992 | − | 1.48584i | 0.495418 | − | 0.0675382i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −28.7984 | − | 20.9232i | −1.30632 | − | 0.949098i | ||||
\(487\) | −11.4164 | + | 35.1361i | −0.517327 | + | 1.59217i | 0.261681 | + | 0.965154i | \(0.415723\pi\) |
−0.779008 | + | 0.627014i | \(0.784277\pi\) | |||||||
\(488\) | −2.76393 | − | 8.50651i | −0.125117 | − | 0.385072i | ||||
\(489\) | 18.9443 | − | 13.7638i | 0.856690 | − | 0.622421i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.2639 | + | 34.6668i | 0.508334 | + | 1.56449i | 0.795092 | + | 0.606489i | \(0.207422\pi\) |
−0.286758 | + | 0.958003i | \(0.592578\pi\) | |||||||
\(492\) | 1.85410 | − | 5.70634i | 0.0835894 | − | 0.257262i | ||||
\(493\) | 5.23607 | + | 3.80423i | 0.235821 | + | 0.171334i | ||||
\(494\) | 6.61803 | 0.297759 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.23607 | −0.324909 | ||||||||
\(497\) | 28.0344 | + | 20.3682i | 1.25752 | + | 0.913639i | ||||
\(498\) | −15.7082 | + | 48.3449i | −0.703901 | + | 2.16639i | ||||
\(499\) | −3.95492 | − | 12.1720i | −0.177046 | − | 0.544893i | 0.822675 | − | 0.568512i | \(-0.192481\pi\) |
−0.999721 | + | 0.0236199i | \(0.992481\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.7082 | + | 15.0454i | −0.925174 | + | 0.672178i | ||||
\(502\) | 3.10081 | + | 9.54332i | 0.138396 | + | 0.425939i | ||||
\(503\) | −2.31966 | + | 7.13918i | −0.103429 | + | 0.318320i | −0.989358 | − | 0.145499i | \(-0.953521\pi\) |
0.885930 | + | 0.463819i | \(0.153521\pi\) | |||||||
\(504\) | −15.8262 | − | 11.4984i | −0.704957 | − | 0.512181i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.482779 | − | 0.0327561i | 0.0214621 | − | 0.00145619i | ||||
\(507\) | 33.5967 | 1.49208 | ||||||||
\(508\) | −1.92705 | − | 1.40008i | −0.0854991 | − | 0.0621187i | ||||
\(509\) | −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 | ||||
\(512\) | 0.809017 | − | 0.587785i | 0.0357538 | − | 0.0259767i | ||||
\(513\) | 18.2918 | + | 56.2964i | 0.807603 | + | 2.48554i | ||||
\(514\) | −3.70820 | + | 11.4127i | −0.163562 | + | 0.503392i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −29.8885 | −1.31577 | ||||||||
\(517\) | −14.0000 | − | 34.8586i | −0.615719 | − | 1.53308i | ||||
\(518\) | 2.23607 | 0.0982472 | ||||||||
\(519\) | 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 | \(0.960454\pi\) | |||||||
\(522\) | −7.47214 | + | 5.42882i | −0.327047 | + | 0.237613i | ||||
\(523\) | −5.94427 | + | 4.31877i | −0.259925 | + | 0.188846i | −0.710114 | − | 0.704087i | \(-0.751357\pi\) |
0.450189 | + | 0.892933i | \(0.351357\pi\) | |||||||
\(524\) | 3.52786 | + | 10.8576i | 0.154115 | + | 0.474319i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.8713 | − | 15.1639i | −0.910033 | − | 0.661178i | ||||
\(527\) | −37.8885 | −1.65045 | ||||||||
\(528\) | 9.09017 | + | 5.70634i | 0.395599 | + | 0.248337i | ||||
\(529\) | −22.9787 | −0.999075 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.50000 | − | 16.9273i | 0.238680 | − | 0.734580i | ||||
\(532\) | 3.30902 | + | 10.1841i | 0.143464 | + | 0.441537i | ||||
\(533\) | 2.42705 | − | 1.76336i | 0.105127 | − | 0.0763794i | ||||
\(534\) | 31.5066 | − | 22.8909i | 1.36342 | − | 0.990585i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.236068 | − | 0.726543i | 0.0101966 | − | 0.0313819i | ||||
\(537\) | −7.61803 | − | 5.53483i | −0.328742 | − | 0.238845i | ||||
\(538\) | −17.5967 | −0.758650 | ||||||||
\(539\) | −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 | \(0.644986\pi\) | |||||||
\(542\) | −4.14590 | + | 12.7598i | −0.178082 | + | 0.548079i | ||||
\(543\) | 20.4721 | + | 63.0068i | 0.878543 | + | 2.70388i | ||||
\(544\) | 4.23607 | − | 3.07768i | 0.181620 | − | 0.131955i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.23607 | − | 13.0373i | −0.181287 | − | 0.557944i | ||||
\(547\) | 4.81966 | − | 14.8334i | 0.206074 | − | 0.634230i | −0.793594 | − | 0.608448i | \(-0.791792\pi\) |
0.999668 | − | 0.0257820i | \(-0.00820757\pi\) | |||||||
\(548\) | −4.23607 | − | 3.07768i | −0.180956 | − | 0.131472i | ||||
\(549\) | 66.8328 | 2.85236 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.05573 | 0.215381 | ||||||||
\(552\) | 0.381966 | + | 0.277515i | 0.0162576 | + | 0.0118118i | ||||
\(553\) | 1.23607 | − | 3.80423i | 0.0525630 | − | 0.161772i | ||||
\(554\) | −0.190983 | − | 0.587785i | −0.00811409 | − | 0.0249726i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.59017 | − | 4.78804i | 0.279485 | − | 0.203058i | ||||
\(557\) | −10.2639 | − | 31.5891i | −0.434897 | − | 1.33847i | −0.893192 | − | 0.449675i | \(-0.851540\pi\) |
0.458296 | − | 0.888800i | \(-0.348460\pi\) | |||||||
\(558\) | 16.7082 | − | 51.4226i | 0.707315 | − | 2.17689i | ||||
\(559\) | −12.0902 | − | 8.78402i | −0.511360 | − | 0.371525i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 47.5967 | + | 29.8788i | 2.00954 | + | 1.26148i | ||||
\(562\) | −18.0000 | −0.759284 | ||||||||
\(563\) | 19.3262 | + | 14.0413i | 0.814504 | + | 0.591772i | 0.915133 | − | 0.403152i | \(-0.132086\pi\) |
−0.100629 | + | 0.994924i | \(0.532086\pi\) | |||||||
\(564\) | 11.3262 | − | 34.8586i | 0.476921 | − | 1.46781i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −20.0902 | + | 14.5964i | −0.844453 | + | 0.613531i | ||||
\(567\) | 51.7148 | − | 37.5730i | 2.17182 | − | 1.57792i | ||||
\(568\) | −4.09017 | − | 12.5882i | −0.171620 | − | 0.528191i | ||||
\(569\) | 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 | \(-0.708306\pi\) | ||||
−0.608693 | + | 0.793406i | \(0.708306\pi\) | |||||||
\(572\) | 2.00000 | + | 4.97980i | 0.0836242 | + | 0.208216i | ||||
\(573\) | −82.2492 | −3.43601 | ||||||||
\(574\) | 3.92705 | + | 2.85317i | 0.163912 | + | 0.119089i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.30902 | + | 7.10642i | 0.0962090 | + | 0.296101i | ||||
\(577\) | 12.0902 | − | 8.78402i | 0.503320 | − | 0.365684i | −0.306963 | − | 0.951721i | \(-0.599313\pi\) |
0.810284 | + | 0.586038i | \(0.199313\pi\) | |||||||
\(578\) | 8.42705 | − | 6.12261i | 0.350519 | − | 0.254667i | ||||
\(579\) | −5.41641 | − | 16.6700i | −0.225098 | − | 0.692781i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33.2705 | − | 24.1724i | −1.38029 | − | 1.00284i | ||||
\(582\) | 38.8328 | 1.60967 | ||||||||
\(583\) | −3.01064 | + | 0.204270i | −0.124688 | + | 0.00845998i | ||||
\(584\) | −1.70820 | −0.0706860 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.33688 | + | 22.5806i | −0.303084 | + | 0.932796i | ||||
\(587\) | 6.41641 | + | 19.7477i | 0.264833 | + | 0.815074i | 0.991732 | + | 0.128328i | \(0.0409612\pi\) |
−0.726898 | + | 0.686745i | \(0.759039\pi\) | |||||||
\(588\) | −0.381966 | + | 0.277515i | −0.0157520 | + | 0.0114445i | ||||
\(589\) | −23.9443 | + | 17.3965i | −0.986607 | + | 0.716812i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.90983 | + | 15.1109i | −0.201963 | + | 0.621579i | ||||
\(592\) | −0.690983 | − | 0.502029i | −0.0283992 | − | 0.0206332i | ||||
\(593\) | 19.7082 | 0.809319 | 0.404659 | − | 0.914467i | \(-0.367390\pi\) | ||||
0.404659 | + | 0.914467i | \(0.367390\pi\) | |||||||
\(594\) | −36.8328 | + | 30.7768i | −1.51127 | + | 1.26279i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.23607 | + | 2.35114i | 0.132555 | + | 0.0963065i | ||||
\(597\) | −1.70820 | + | 5.25731i | −0.0699121 | + | 0.215167i | ||||
\(598\) | 0.0729490 | + | 0.224514i | 0.00298311 | + | 0.00918106i | ||||
\(599\) | −13.3262 | + | 9.68208i | −0.544495 | + | 0.395599i | −0.825752 | − | 0.564034i | \(-0.809249\pi\) |
0.281257 | + | 0.959633i | \(0.409249\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.97214 | + | 21.4580i | 0.284399 | + | 0.875291i | 0.986578 | + | 0.163290i | \(0.0522108\pi\) |
−0.702179 | + | 0.712001i | \(0.747789\pi\) | |||||||
\(602\) | 7.47214 | − | 22.9969i | 0.304542 | − | 0.937282i | ||||
\(603\) | 4.61803 | + | 3.35520i | 0.188061 | + | 0.136634i | ||||
\(604\) | 12.6525 | 0.514822 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 12.0000 | 0.487467 | ||||||||
\(607\) | 26.1803 | + | 19.0211i | 1.06263 | + | 0.772044i | 0.974573 | − | 0.224072i | \(-0.0719350\pi\) |
0.0880546 | + | 0.996116i | \(0.471935\pi\) | |||||||
\(608\) | 1.26393 | − | 3.88998i | 0.0512592 | − | 0.157760i | ||||
\(609\) | −3.23607 | − | 9.95959i | −0.131132 | − | 0.403583i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.8262 | − | 10.7719i | 0.599805 | − | 0.435784i | ||||
\(612\) | 12.0902 | + | 37.2097i | 0.488716 | + | 1.50411i | ||||
\(613\) | −3.56231 | + | 10.9637i | −0.143880 | + | 0.442818i | −0.996865 | − | 0.0791176i | \(-0.974790\pi\) |
0.852985 | + | 0.521935i | \(0.174790\pi\) | |||||||
\(614\) | 21.7984 | + | 15.8374i | 0.879711 | + | 0.639147i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.66312 | + | 5.56758i | −0.268465 | + | 0.224324i | ||||
\(617\) | −32.9443 | −1.32629 | −0.663143 | − | 0.748493i | \(-0.730778\pi\) | ||||
−0.663143 | + | 0.748493i | \(0.730778\pi\) | |||||||
\(618\) | −29.6525 | − | 21.5438i | −1.19280 | − | 0.866618i | ||||
\(619\) | 7.02786 | − | 21.6295i | 0.282474 | − | 0.869365i | −0.704671 | − | 0.709534i | \(-0.748905\pi\) |
0.987145 | − | 0.159830i | \(-0.0510947\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.70820 | + | 1.24108i | −0.0685479 | + | 0.0498029i | ||||
\(622\) | −2.00000 | + | 1.45309i | −0.0801927 | + | 0.0582634i | ||||
\(623\) | 9.73607 | + | 29.9645i | 0.390067 | + | 1.20050i | ||||
\(624\) | −1.61803 | + | 4.97980i | −0.0647732 | + | 0.199351i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 27.4164 | 1.09578 | ||||||||
\(627\) | 43.7984 | − | 2.97168i | 1.74914 | − | 0.118678i | ||||
\(628\) | −8.61803 | −0.343897 | ||||||||
\(629\) | −3.61803 | − | 2.62866i | −0.144260 | − | 0.104811i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.29180 | + | 7.05342i | 0.0912350 | + | 0.280792i | 0.986254 | − | 0.165235i | \(-0.0528383\pi\) |
−0.895019 | + | 0.446028i | \(0.852838\pi\) | |||||||
\(632\) | −1.23607 | + | 0.898056i | −0.0491681 | + | 0.0357227i | ||||
\(633\) | 54.8328 | − | 39.8384i | 2.17941 | − | 1.58343i | ||||
\(634\) | 1.91641 | + | 5.89810i | 0.0761103 | + | 0.234243i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.38197 | − | 1.73060i | −0.0944511 | − | 0.0686227i | ||||
\(637\) | −0.236068 | −0.00935335 | ||||||||
\(638\) | 1.52786 | + | 3.80423i | 0.0604887 | + | 0.150611i | ||||
\(639\) | 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 | \(-0.171682\pi\) | |||||||
\(642\) | 7.52786 | + | 23.1684i | 0.297101 | + | 0.914383i | ||||
\(643\) | −10.8541 | + | 7.88597i | −0.428044 | + | 0.310992i | −0.780866 | − | 0.624698i | \(-0.785222\pi\) |
0.352822 | + | 0.935690i | \(0.385222\pi\) | |||||||
\(644\) | −0.309017 | + | 0.224514i | −0.0121770 | + | 0.00884709i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.61803 | − | 20.3682i | 0.260383 | − | 0.801377i | ||||
\(647\) | −5.70820 | − | 4.14725i | −0.224413 | − | 0.163045i | 0.469898 | − | 0.882721i | \(-0.344291\pi\) |
−0.694311 | + | 0.719675i | \(0.744291\pi\) | |||||||
\(648\) | −24.4164 | −0.959167 | ||||||||
\(649\) | −6.69098 | − | 4.20025i | −0.262644 | − | 0.164874i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 49.5967 | + | 36.0341i | 1.94385 | + | 1.41229i | ||||
\(652\) | 2.23607 | − | 6.88191i | 0.0875712 | − | 0.269516i | ||||
\(653\) | −7.97214 | − | 24.5357i | −0.311974 | − | 0.960157i | −0.976982 | − | 0.213321i | \(-0.931572\pi\) |
0.665008 | − | 0.746836i | \(-0.268428\pi\) | |||||||
\(654\) | −19.7082 | + | 14.3188i | −0.770652 | + | 0.559911i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.572949 | − | 1.76336i | −0.0223699 | − | 0.0688475i | ||||
\(657\) | 3.94427 | − | 12.1392i | 0.153881 | − | 0.473596i | ||||
\(658\) | 23.9894 | + | 17.4293i | 0.935202 | + | 0.679464i | ||||
\(659\) | −13.3820 | −0.521287 | −0.260644 | − | 0.965435i | \(-0.583935\pi\) | ||||
−0.260644 | + | 0.965435i | \(0.583935\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.18034 | 0.0848054 | 0.0424027 | − | 0.999101i | \(-0.486499\pi\) | ||||
0.0424027 | + | 0.999101i | \(0.486499\pi\) | |||||||
\(662\) | −11.6353 | − | 8.45351i | −0.452217 | − | 0.328555i | ||||
\(663\) | −8.47214 | + | 26.0746i | −0.329030 | + | 1.01265i | ||||
\(664\) | 4.85410 | + | 14.9394i | 0.188376 | + | 0.579761i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.16312 | − | 3.75123i | 0.200067 | − | 0.145357i | ||||
\(667\) | 0.0557281 | + | 0.171513i | 0.00215780 | + | 0.00664103i | ||||
\(668\) | −2.44427 | + | 7.52270i | −0.0945717 | + | 0.291062i | ||||
\(669\) | −25.3262 | − | 18.4006i | −0.979169 | − | 0.711408i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.23607 | − | 28.7687i | 0.279345 | − | 1.11060i | ||||
\(672\) | −8.47214 | −0.326820 | ||||||||
\(673\) | −3.23607 | − | 2.35114i | −0.124741 | − | 0.0906298i | 0.523665 | − | 0.851924i | \(-0.324564\pi\) |
−0.648407 | + | 0.761294i | \(0.724564\pi\) | |||||||
\(674\) | 10.9443 | − | 33.6830i | 0.421558 | − | 1.29742i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.39919 | − | 6.10237i | 0.323046 | − | 0.234706i | ||||
\(677\) | −8.09017 | + | 5.87785i | −0.310930 | + | 0.225904i | −0.732296 | − | 0.680987i | \(-0.761551\pi\) |
0.421365 | + | 0.906891i | \(0.361551\pi\) | |||||||
\(678\) | −6.29180 | − | 19.3642i | −0.241635 | − | 0.743676i | ||||
\(679\) | −9.70820 | + | 29.8788i | −0.372567 | + | 1.14664i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −53.3050 | −2.04265 | ||||||||
\(682\) | −20.3262 | − | 12.7598i | −0.778332 | − | 0.488597i | ||||
\(683\) | 47.0132 | 1.79891 | 0.899454 | − | 0.437015i | \(-0.143964\pi\) | ||||
0.899454 | + | 0.437015i | \(0.143964\pi\) | |||||||
\(684\) | 24.7254 | + | 17.9641i | 0.945400 | + | 0.686873i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.78115 | − | 17.7926i | −0.220725 | − | 0.679323i | ||||
\(687\) | −73.7771 | + | 53.6022i | −2.81477 | + | 2.04505i | ||||
\(688\) | −7.47214 | + | 5.42882i | −0.284873 | + | 0.206972i | ||||
\(689\) | −0.454915 | − | 1.40008i | −0.0173309 | − | 0.0533390i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.1180 | − | 8.07772i | −0.422950 | − | 0.307291i | 0.355874 | − | 0.934534i | \(-0.384183\pi\) |
−0.778824 | + | 0.627243i | \(0.784183\pi\) | |||||||
\(692\) | 12.6180 | 0.479666 | ||||||||
\(693\) | −24.1803 | − | 60.2066i | −0.918535 | − | 2.28706i | ||||
\(694\) | −27.1246 | −1.02964 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.23607 | + | 3.80423i | −0.0468530 | + | 0.144199i | ||||
\(697\) | −3.00000 | − | 9.23305i | −0.113633 | − | 0.349727i | ||||
\(698\) | 25.0344 | − | 18.1886i | 0.947568 | − | 0.688448i | ||||
\(699\) | −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 | \(0.0649461\pi\) | |||||||
\(702\) | −18.9443 | − | 13.7638i | −0.715005 | − | 0.519482i | ||||
\(703\) | −3.49342 | −0.131757 | ||||||||
\(704\) | 3.30902 | − | 0.224514i | 0.124713 | − | 0.00846169i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.47214 | − | 6.88191i | −0.356489 | − | 0.259004i | ||||
\(707\) | −3.00000 | + | 9.23305i | −0.112827 | + | 0.347245i | ||||
\(708\) | −2.38197 | − | 7.33094i | −0.0895198 | − | 0.275514i | ||||
\(709\) | −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 | ||||
\(712\) | 3.71885 | − | 11.4454i | 0.139370 | − | 0.428936i | ||||
\(713\) | −0.854102 | − | 0.620541i | −0.0319864 | − | 0.0232395i | ||||
\(714\) | −44.3607 | −1.66016 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.90983 | −0.108745 | ||||||||
\(717\) | 24.9443 | + | 18.1231i | 0.931561 | + | 0.676819i | ||||
\(718\) | 9.41641 | − | 28.9807i | 0.351417 | − | 1.08155i | ||||
\(719\) | 7.36068 | + | 22.6538i | 0.274507 | + | 0.844846i | 0.989349 | + | 0.145560i | \(0.0464984\pi\) |
−0.714842 | + | 0.699286i | \(0.753502\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.9894 | − | 17.4293i | 0.893410 | − | 0.649101i | ||||
\(722\) | 0.701626 | + | 2.15938i | 0.0261118 | + | 0.0803639i | ||||
\(723\) | 1.85410 | − | 5.70634i | 0.0689548 | − | 0.212221i | ||||
\(724\) | 16.5623 | + | 12.0332i | 0.615533 | + | 0.447211i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 15.4721 | + | 32.0584i | 0.574225 | + | 1.18980i | ||||
\(727\) | 8.79837 | 0.326314 | 0.163157 | − | 0.986600i | \(-0.447832\pi\) | ||||
0.163157 | + | 0.986600i | \(0.447832\pi\) | |||||||
\(728\) | −3.42705 | − | 2.48990i | −0.127015 | − | 0.0922818i | ||||
\(729\) | 12.9615 | − | 39.8914i | 0.480055 | − | 1.47746i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −39.1246 | + | 28.4257i | −1.44708 | + | 1.05136i | ||||
\(732\) | 23.4164 | − | 17.0130i | 0.865495 | − | 0.628819i | ||||
\(733\) | −11.2016 | − | 34.4751i | −0.413742 | − | 1.27337i | −0.913372 | − | 0.407127i | \(-0.866531\pi\) |
0.499630 | − | 0.866239i | \(-0.333469\pi\) | |||||||
\(734\) | 3.23607 | − | 9.95959i | 0.119445 | − | 0.367615i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.145898 | 0.00537787 | ||||||||
\(737\) | 1.94427 | − | 1.62460i | 0.0716182 | − | 0.0598429i | ||||
\(738\) | 13.8541 | 0.509977 | ||||||||
\(739\) | 25.7705 | + | 18.7234i | 0.947984 | + | 0.688750i | 0.950329 | − | 0.311247i | \(-0.100747\pi\) |
−0.00234556 | + | 0.999997i | \(0.500747\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.61803 | + | 20.3682i | 0.243120 | + | 0.748245i | ||||
\(742\) | 1.92705 | − | 1.40008i | 0.0707443 | − | 0.0513987i | ||||
\(743\) | −14.3541 | + | 10.4289i | −0.526601 | + | 0.382598i | −0.819085 | − | 0.573672i | \(-0.805518\pi\) |
0.292484 | + | 0.956270i | \(0.405518\pi\) | |||||||
\(744\) | −7.23607 | − | 22.2703i | −0.265287 | − | 0.816470i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.63525 | − | 4.09425i | −0.206321 | − | 0.149901i | ||||
\(747\) | −117.374 | −4.29448 | ||||||||
\(748\) | 17.3262 | − | 1.17557i | 0.633510 | − | 0.0429831i | ||||
\(749\) | −19.7082 | −0.720122 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.38197 | + | 10.4086i | −0.123410 | + | 0.379816i | −0.993608 | − | 0.112886i | \(-0.963991\pi\) |
0.870198 | + | 0.492702i | \(0.163991\pi\) | |||||||
\(752\) | −3.50000 | − | 10.7719i | −0.127632 | − | 0.392810i | ||||
\(753\) | −26.2705 | + | 19.0866i | −0.957351 | + | 0.695556i | ||||
\(754\) | −1.61803 | + | 1.17557i | −0.0589253 | + | 0.0428118i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 11.7082 | − | 36.0341i | 0.425823 | − | 1.31055i | ||||
\(757\) | 17.9615 | + | 13.0498i | 0.652822 | + | 0.474303i | 0.864231 | − | 0.503095i | \(-0.167805\pi\) |
−0.211410 | + | 0.977398i | \(0.567805\pi\) | |||||||
\(758\) | 10.3262 | 0.375066 | ||||||||
\(759\) | 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 | \(0.738074\pi\) | |||||||
\(762\) | 2.38197 | − | 7.33094i | 0.0862895 | − | 0.265572i | ||||
\(763\) | −6.09017 | − | 18.7436i | −0.220479 | − | 0.678564i | ||||
\(764\) | −20.5623 | + | 14.9394i | −0.743918 | + | 0.540488i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.89919 | − | 15.0781i | −0.177015 | − | 0.544796i | ||||
\(767\) | 1.19098 | − | 3.66547i | 0.0430039 | − | 0.132352i | ||||
\(768\) | 2.61803 | + | 1.90211i | 0.0944702 | + | 0.0686366i | ||||
\(769\) | −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 | ||||||||
\(772\) | −4.38197 | − | 3.18368i | −0.157710 | − | 0.114583i | ||||
\(773\) | 11.6074 | − | 35.7239i | 0.417489 | − | 1.28490i | −0.492517 | − | 0.870303i | \(-0.663923\pi\) |
0.910006 | − | 0.414596i | \(-0.136077\pi\) | |||||||
\(774\) | −21.3262 | − | 65.6354i | −0.766556 | − | 2.35922i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.70820 | − | 7.05342i | 0.348504 | − | 0.253203i | ||||
\(777\) | 2.23607 | + | 6.88191i | 0.0802185 | + | 0.246887i | ||||
\(778\) | −3.76393 | + | 11.5842i | −0.134944 | + | 0.415313i | ||||
\(779\) | −6.13525 | − | 4.45752i | −0.219818 | − | 0.159707i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.7082 | − | 42.5730i | 0.383170 | − | 1.52338i | ||||
\(782\) | 0.763932 | 0.0273182 | ||||||||
\(783\) | −14.4721 | − | 10.5146i | −0.517192 | − | 0.375762i | ||||
\(784\) | −0.0450850 | + | 0.138757i | −0.00161018 | + | 0.00495562i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −29.8885 | + | 21.7153i | −1.06609 | + | 0.774559i | ||||
\(787\) | −29.1246 | + | 21.1603i | −1.03818 | + | 0.754282i | −0.969929 | − | 0.243386i | \(-0.921742\pi\) |
−0.0682508 | + | 0.997668i | \(0.521742\pi\) | |||||||
\(788\) | 1.51722 | + | 4.66953i | 0.0540488 | + | 0.166345i | ||||
\(789\) | 25.7984 | − | 79.3992i | 0.918446 | − | 2.82669i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.4721 | 0.585682 | ||||||||
\(792\) | −6.04508 | + | 24.0337i | −0.214803 | + | 0.854000i | ||||
\(793\) | 14.4721 | 0.513921 | ||||||||
\(794\) | −5.50000 | − | 3.99598i | −0.195188 | − | 0.141812i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.527864 | + | 1.62460i | 0.0187096 | + | 0.0575824i | ||||
\(797\) | 29.9615 | − | 21.7683i | 1.06129 | − | 0.771073i | 0.0869638 | − | 0.996211i | \(-0.472284\pi\) |
0.974327 | + | 0.225139i | \(0.0722835\pi\) | |||||||
\(798\) | −28.0344 | + | 20.3682i | −0.992408 | + | 0.721027i | ||||
\(799\) | −18.3262 | − | 56.4024i | −0.648336 | − | 1.99537i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 72.7492 | + | 52.8554i | 2.57047 | + | 1.86755i | ||||
\(802\) | 10.7426 | 0.379336 | ||||||||
\(803\) | −4.79837 | − | 3.01217i | −0.169331 | − | 0.106297i | ||||
\(804\) | 2.47214 | 0.0871855 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.61803 | − | 11.1352i | 0.127440 | − | 0.392219i | ||||
\(807\) | −17.5967 | − | 54.1572i | −0.619435 | − | 1.90642i | ||||
\(808\) | 3.00000 | − | 2.17963i | 0.105540 | − | 0.0766790i | ||||
\(809\) | 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 | \(0.405189\pi\) |
−0.799329 | + | 0.600894i | \(0.794811\pi\) | |||||||
\(812\) | −2.61803 | − | 1.90211i | −0.0918750 | − | 0.0667511i | ||||
\(813\) | −43.4164 | −1.52268 | ||||||||
\(814\) | −1.05573 | − | 2.62866i | −0.0370033 | − | 0.0921343i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 13.7082 | + | 9.95959i | 0.479883 | + | 0.348655i | ||||
\(817\) | −11.6738 | + | 35.9281i | −0.408413 | + | 1.25697i | ||||
\(818\) | 7.20820 | + | 22.1846i | 0.252029 | + | 0.775665i | ||||
\(819\) | 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 | \(-0.239760\pi\) | |||||||
\(822\) | 5.23607 | − | 16.1150i | 0.182629 | − | 0.562074i | ||||
\(823\) | −13.7812 | − | 10.0126i | −0.480381 | − | 0.349017i | 0.321092 | − | 0.947048i | \(-0.395950\pi\) |
−0.801473 | + | 0.598031i | \(0.795950\pi\) | |||||||
\(824\) | −11.3262 | −0.394568 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.23607 | 0.216981 | ||||||||
\(827\) | 17.7984 | + | 12.9313i | 0.618910 | + | 0.449665i | 0.852541 | − | 0.522661i | \(-0.175061\pi\) |
−0.233631 | + | 0.972325i | \(0.575061\pi\) | |||||||
\(828\) | −0.336881 | + | 1.03681i | −0.0117074 | + | 0.0360318i | ||||
\(829\) | −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 | ||||
\(832\) | 0.500000 | + | 1.53884i | 0.0173344 | + | 0.0533497i | ||||
\(833\) | −0.236068 | + | 0.726543i | −0.00817927 | + | 0.0251732i | ||||
\(834\) | 21.3262 | + | 15.4944i | 0.738467 | + | 0.536528i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 10.4098 | − | 8.69827i | 0.360032 | − | 0.300836i | ||||
\(837\) | 104.721 | 3.61970 | ||||||||
\(838\) | −1.30902 | − | 0.951057i | −0.0452192 | − | 0.0328537i | ||||
\(839\) | −16.2361 | + | 49.9695i | −0.560531 | + | 1.72514i | 0.120338 | + | 0.992733i | \(0.461602\pi\) |
−0.680869 | + | 0.732405i | \(0.738398\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.2254 | − | 16.1477i | 0.766394 | − | 0.556818i | ||||
\(842\) | −15.0902 | + | 10.9637i | −0.520042 | + | 0.377832i | ||||
\(843\) | −18.0000 | − | 55.3983i | −0.619953 | − | 1.90802i | ||||
\(844\) | 6.47214 | − | 19.9192i | 0.222780 | − | 0.685647i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 84.6312 | 2.90968 | ||||||||
\(847\) | −28.5344 | + | 3.88998i | −0.980455 | + | 0.133661i | ||||
\(848\) | −0.909830 | −0.0312437 | ||||||||
\(849\) | −65.0132 | − | 47.2348i | −2.23125 | − | 1.62109i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.0385072 | − | 0.118513i | −0.00132001 | − | 0.00406257i | ||||
\(852\) | 34.6525 | − | 25.1765i | 1.18717 | − | 0.862533i | ||||
\(853\) | 12.9164 | − | 9.38432i | 0.442249 | − | 0.321313i | −0.344279 | − | 0.938867i | \(-0.611877\pi\) |
0.786528 | + | 0.617555i | \(0.211877\pi\) | |||||||
\(854\) | 7.23607 | + | 22.2703i | 0.247613 | + | 0.762075i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.09017 | + | 4.42477i | 0.208158 | + | 0.151235i | ||||
\(857\) | −22.0000 | −0.751506 | −0.375753 | − | 0.926720i | \(-0.622616\pi\) | ||||
−0.375753 | + | 0.926720i | \(0.622616\pi\) | |||||||
\(858\) | −13.3262 | + | 11.1352i | −0.454950 | + | 0.380148i | ||||
\(859\) | −30.9098 | −1.05463 | −0.527315 | − | 0.849670i | \(-0.676801\pi\) | ||||
−0.527315 | + | 0.849670i | \(0.676801\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.85410 | + | 14.9394i | −0.165427 | + | 0.509133i | ||||
\(862\) | 8.09017 | + | 24.8990i | 0.275552 | + | 0.848063i | ||||
\(863\) | −5.01722 | + | 3.64522i | −0.170788 | + | 0.124085i | −0.669896 | − | 0.742455i | \(-0.733661\pi\) |
0.499108 | + | 0.866540i | \(0.333661\pi\) | |||||||
\(864\) | −11.7082 | + | 8.50651i | −0.398321 | + | 0.289397i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.94427 | − | 9.06154i | 0.100050 | − | 0.307924i | ||||
\(867\) | 27.2705 | + | 19.8132i | 0.926155 | + | 0.672891i | ||||
\(868\) | 18.9443 | 0.643010 | ||||||||
\(869\) | −5.05573 | + | 0.343027i | −0.171504 | + | 0.0116364i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.00000 | + | 0.726543i | 0.0338837 | + | 0.0246180i | ||||
\(872\) | −2.32624 | + | 7.15942i | −0.0787764 | + | 0.242449i | ||||
\(873\) | 27.7082 | + | 85.2771i | 0.937781 | + | 2.88619i | ||||
\(874\) | 0.482779 | − | 0.350760i | 0.0163302 | − | 0.0118646i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.70820 | − | 5.25731i | −0.0577149 | − | 0.177628i | ||||
\(877\) | −0.736068 | + | 2.26538i | −0.0248552 | + | 0.0764966i | −0.962715 | − | 0.270519i | \(-0.912805\pi\) |
0.937859 | + | 0.347015i | \(0.112805\pi\) | |||||||
\(878\) | −10.6180 | − | 7.71445i | −0.358341 | − | 0.260350i | ||||
\(879\) | −76.8328 | −2.59151 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.4508 | −0.924843 | −0.462421 | − | 0.886660i | \(-0.653019\pi\) | ||||
−0.462421 | + | 0.886660i | \(0.653019\pi\) | |||||||
\(882\) | −0.881966 | − | 0.640786i | −0.0296973 | − | 0.0215764i | ||||
\(883\) | −9.47214 | + | 29.1522i | −0.318763 | + | 0.981051i | 0.655415 | + | 0.755269i | \(0.272494\pi\) |
−0.974178 | + | 0.225782i | \(0.927506\pi\) | |||||||
\(884\) | 2.61803 | + | 8.05748i | 0.0880540 | + | 0.271002i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.09017 | + | 0.792055i | −0.0366250 | + | 0.0266096i | ||||
\(887\) | −14.6074 | − | 44.9569i | −0.490468 | − | 1.50951i | −0.823902 | − | 0.566732i | \(-0.808207\pi\) |
0.333434 | − | 0.942774i | \(-0.391793\pi\) | |||||||
\(888\) | 0.854102 | − | 2.62866i | 0.0286618 | − | 0.0882119i | ||||
\(889\) | 5.04508 | + | 3.66547i | 0.169207 | + | 0.122936i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −68.5861 | − | 43.0548i | −2.29772 | − | 1.44239i | ||||
\(892\) | −9.67376 | −0.323902 | ||||||||
\(893\) | −37.4787 | − | 27.2299i | −1.25418 | − | 0.911213i | ||||
\(894\) | −4.00000 | + | 12.3107i | −0.133780 | + | 0.411733i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.11803 | + | 1.53884i | −0.0707585 | + | 0.0514091i | ||||
\(897\) | −0.618034 | + | 0.449028i | −0.0206356 | + | 0.0149926i | ||||
\(898\) | −0.972136 | − | 2.99193i | −0.0324406 | − | 0.0998419i | ||||
\(899\) | 2.76393 | − | 8.50651i | 0.0921823 | − | 0.283708i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.76393 | −0.158710 | ||||||||
\(902\) | 1.50000 | − | 5.96361i | 0.0499445 | − | 0.198566i | ||||
\(903\) | 78.2492 | 2.60397 | ||||||||
\(904\) | −5.09017 | − | 3.69822i | −0.169297 | − | 0.123001i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 12.6525 | + | 38.9403i | 0.420350 | + | 1.29371i | ||||
\(907\) | −10.2361 | + | 7.43694i | −0.339883 | + | 0.246939i | −0.744612 | − | 0.667497i | \(-0.767366\pi\) |
0.404729 | + | 0.914436i | \(0.367366\pi\) | |||||||
\(908\) | −13.3262 | + | 9.68208i | −0.442247 | + | 0.321311i | ||||
\(909\) | 8.56231 | + | 26.3521i | 0.283994 | + | 0.874043i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.9443 | + | 12.3107i | 0.561389 | + | 0.407873i | 0.831967 | − | 0.554825i | \(-0.187215\pi\) |
−0.270578 | + | 0.962698i | \(0.587215\pi\) | |||||||
\(912\) | 13.2361 | 0.438290 | ||||||||
\(913\) | −12.7082 | + | 50.5245i | −0.420580 | + | 1.67212i | ||||
\(914\) | 32.5410 | 1.07636 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.70820 | + | 26.8011i | −0.287727 | + | 0.885533i | ||||
\(917\) | −9.23607 | − | 28.4257i | −0.305002 | − | 0.938699i | ||||
\(918\) | −61.3050 | + | 44.5407i | −2.02336 | + | 1.47006i | ||||
\(919\) | 9.70820 | − | 7.05342i | 0.320244 | − | 0.232671i | −0.416036 | − | 0.909348i | \(-0.636581\pi\) |
0.736280 | + | 0.676677i | \(0.236581\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.9443 | + | 82.9259i | −0.887844 | + | 2.73250i | ||||
\(922\) | 23.0902 | + | 16.7760i | 0.760434 | + | 0.552488i | ||||
\(923\) | 21.4164 | 0.704930 | ||||||||
\(924\) | −23.7984 | − | 14.9394i | −0.782909 | − | 0.491470i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12.5451 | − | 9.11454i | −0.412257 | − | 0.299522i | ||||
\(927\) | 26.1525 | − | 80.4890i | 0.858960 | − | 2.64361i | ||||
\(928\) | 0.381966 | + | 1.17557i | 0.0125386 | + | 0.0385900i | ||||
\(929\) | −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 | ||||
\(932\) | −4.70820 | + | 14.4904i | −0.154222 | + | 0.474648i | ||||
\(933\) | −6.47214 | − | 4.70228i | −0.211888 | − | 0.153946i | ||||
\(934\) | 17.2361 | 0.563981 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.0902 | −0.395180 | ||||||||
\(937\) | −38.9787 | − | 28.3197i | −1.27338 | − | 0.925164i | −0.274047 | − | 0.961716i | \(-0.588362\pi\) |
−0.999332 | + | 0.0365522i | \(0.988362\pi\) | |||||||
\(938\) | −0.618034 | + | 1.90211i | −0.0201795 | + | 0.0621062i | ||||
\(939\) | 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 | \(0.933058\pi\) | |||||||
\(942\) | −8.61803 | − | 26.5236i | −0.280791 | − | 0.864185i | ||||
\(943\) | 0.0835921 | − | 0.257270i | 0.00272213 | − | 0.00837787i | ||||
\(944\) | −1.92705 | − | 1.40008i | −0.0627202 | − | 0.0455689i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −30.5623 | + | 2.07363i | −0.993666 | + | 0.0674194i | ||||
\(947\) | −49.9574 | −1.62340 | −0.811699 | − | 0.584076i | \(-0.801457\pi\) | ||||
−0.811699 | + | 0.584076i | \(0.801457\pi\) | |||||||
\(948\) | −4.00000 | − | 2.90617i | −0.129914 | − | 0.0943880i | ||||
\(949\) | 0.854102 | − | 2.62866i | 0.0277253 | − | 0.0853298i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.2361 | + | 11.7962i | −0.526491 | + | 0.382518i | ||||
\(952\) | −11.0902 | + | 8.05748i | −0.359434 | + | 0.261144i | ||||
\(953\) | −4.85410 | − | 14.9394i | −0.157240 | − | 0.483934i | 0.841141 | − | 0.540816i | \(-0.181884\pi\) |
−0.998381 | + | 0.0568813i | \(0.981884\pi\) | |||||||
\(954\) | 2.10081 | − | 6.46564i | 0.0680163 | − | 0.209333i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.52786 | 0.308153 | ||||||||
\(957\) | −10.1803 | + | 8.50651i | −0.329084 | + | 0.274976i | ||||
\(958\) | 29.5967 | 0.956228 | ||||||||
\(959\) | 11.0902 | + | 8.05748i | 0.358120 | + | 0.260190i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.60081 | + | 20.3152i | 0.212929 | + | 0.655329i | ||||
\(962\) | 1.11803 | − | 0.812299i | 0.0360469 | − | 0.0261896i | ||||
\(963\) | −45.5066 | + | 33.0625i | −1.46643 | + | 1.06542i | ||||
\(964\) | −0.572949 | − | 1.76336i | −0.0184534 | − | 0.0567939i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.00000 | − | 0.726543i | −0.0321745 | − | 0.0233761i | ||||
\(967\) | −3.90983 | −0.125732 | −0.0628658 | − | 0.998022i | \(-0.520024\pi\) | ||||
−0.0628658 | + | 0.998022i | \(0.520024\pi\) | |||||||
\(968\) | 9.69098 | + | 5.20431i | 0.311480 | + | 0.167273i | ||||
\(969\) | 69.3050 | 2.22640 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.1565 | − | 37.4140i | 0.390122 | − | 1.20067i | −0.542574 | − | 0.840008i | \(-0.682550\pi\) |
0.932696 | − | 0.360664i | \(-0.117450\pi\) | |||||||
\(972\) | −11.0000 | − | 33.8545i | −0.352825 | − | 1.08588i | ||||
\(973\) | −17.2533 | + | 12.5352i | −0.553115 | + | 0.401862i | ||||
\(974\) | −29.8885 | + | 21.7153i | −0.957691 | + | 0.695803i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.76393 | − | 8.50651i | 0.0884713 | − | 0.272287i | ||||
\(977\) | −3.38197 | − | 2.45714i | −0.108199 | − | 0.0786109i | 0.532370 | − | 0.846512i | \(-0.321301\pi\) |
−0.640569 | + | 0.767901i | \(0.721301\pi\) | |||||||
\(978\) | 23.4164 | 0.748774 | ||||||||
\(979\) | 30.6287 | − | 25.5928i | 0.978897 | − | 0.817948i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −45.5066 | − | 33.0625i | −1.45291 | − | 1.05560i | ||||
\(982\) | −11.2639 | + | 34.6668i | −0.359447 | + | 1.10626i | ||||
\(983\) | −3.10081 | − | 9.54332i | −0.0989006 | − | 0.304385i | 0.889350 | − | 0.457227i | \(-0.151157\pi\) |
−0.988251 | + | 0.152842i | \(0.951157\pi\) | |||||||
\(984\) | 4.85410 | − | 3.52671i | 0.154743 | − | 0.112427i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.00000 | + | 6.15537i | 0.0636930 | + | 0.196027i | ||||
\(987\) | −29.6525 | + | 91.2609i | −0.943849 | + | 2.90487i | ||||
\(988\) | 5.35410 | + | 3.88998i | 0.170337 | + | 0.123757i | ||||
\(989\) | −1.34752 | −0.0428488 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.7214 | 1.73828 | 0.869141 | − | 0.494565i | \(-0.164673\pi\) | ||||
0.869141 | + | 0.494565i | \(0.164673\pi\) | |||||||
\(992\) | −5.85410 | − | 4.25325i | −0.185868 | − | 0.135041i | ||||
\(993\) | 14.3820 | − | 44.2631i | 0.456398 | − | 1.40465i | ||||
\(994\) | 10.7082 | + | 32.9565i | 0.339644 | + | 1.04532i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −41.1246 | + | 29.8788i | −1.30308 | + | 0.946745i | ||||
\(997\) | 16.2148 | + | 49.9040i | 0.513527 | + | 1.58047i | 0.785946 | + | 0.618296i | \(0.212177\pi\) |
−0.272418 | + | 0.962179i | \(0.587823\pi\) | |||||||
\(998\) | 3.95492 | − | 12.1720i | 0.125191 | − | 0.385297i | ||||
\(999\) | 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 | 550.2.h.f.301.1 | 4 | ||
5.2 | odd | 4 | 550.2.ba.a.499.1 | 8 | |||
5.3 | odd | 4 | 550.2.ba.a.499.2 | 8 | |||
5.4 | even | 2 | 110.2.g.a.81.1 | ✓ | 4 | ||
11.3 | even | 5 | inner | 550.2.h.f.201.1 | 4 | ||
11.5 | even | 5 | 6050.2.a.bu.1.1 | 2 | |||
11.6 | odd | 10 | 6050.2.a.cm.1.1 | 2 | |||
15.14 | odd | 2 | 990.2.n.f.631.1 | 4 | |||
20.19 | odd | 2 | 880.2.bo.a.81.1 | 4 | |||
55.3 | odd | 20 | 550.2.ba.a.399.1 | 8 | |||
55.14 | even | 10 | 110.2.g.a.91.1 | yes | 4 | ||
55.39 | odd | 10 | 1210.2.a.p.1.2 | 2 | |||
55.47 | odd | 20 | 550.2.ba.a.399.2 | 8 | |||
55.49 | even | 10 | 1210.2.a.t.1.2 | 2 | |||
165.14 | odd | 10 | 990.2.n.f.91.1 | 4 | |||
220.39 | even | 10 | 9680.2.a.bi.1.1 | 2 | |||
220.159 | odd | 10 | 9680.2.a.bh.1.1 | 2 | |||
220.179 | odd | 10 | 880.2.bo.a.641.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
110.2.g.a.81.1 | ✓ | 4 | 5.4 | even | 2 | ||
110.2.g.a.91.1 | yes | 4 | 55.14 | even | 10 | ||
550.2.h.f.201.1 | 4 | 11.3 | even | 5 | inner | ||
550.2.h.f.301.1 | 4 | 1.1 | even | 1 | trivial | ||
550.2.ba.a.399.1 | 8 | 55.3 | odd | 20 | |||
550.2.ba.a.399.2 | 8 | 55.47 | odd | 20 | |||
550.2.ba.a.499.1 | 8 | 5.2 | odd | 4 | |||
550.2.ba.a.499.2 | 8 | 5.3 | odd | 4 | |||
880.2.bo.a.81.1 | 4 | 20.19 | odd | 2 | |||
880.2.bo.a.641.1 | 4 | 220.179 | odd | 10 | |||
990.2.n.f.91.1 | 4 | 165.14 | odd | 10 | |||
990.2.n.f.631.1 | 4 | 15.14 | odd | 2 | |||
1210.2.a.p.1.2 | 2 | 55.39 | odd | 10 | |||
1210.2.a.t.1.2 | 2 | 55.49 | even | 10 | |||
6050.2.a.bu.1.1 | 2 | 11.5 | even | 5 | |||
6050.2.a.cm.1.1 | 2 | 11.6 | odd | 10 | |||
9680.2.a.bh.1.1 | 2 | 220.159 | odd | 10 | |||
9680.2.a.bi.1.1 | 2 | 220.39 | even | 10 |