Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [121,2,Mod(3,121)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(121, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("121.3");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 121 = 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 121.c (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: | \(0.966189864457\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 81.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 121.81 |
Dual form | 121.2.c.d.3.1 |
$q$-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 \(\left(\mathbb{Z}/121\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | + | 0.587785i | 0.572061 | + | 0.415627i | 0.835853 | − | 0.548953i | \(-0.184973\pi\) |
−0.263792 | + | 0.964580i | \(0.584973\pi\) | |||||||
\(3\) | 0.618034 | − | 1.90211i | 0.356822 | − | 1.09819i | −0.598123 | − | 0.801404i | \(-0.704087\pi\) |
0.954945 | − | 0.296781i | \(-0.0959133\pi\) | |||||||
\(4\) | −0.309017 | − | 0.951057i | −0.154508 | − | 0.475528i | ||||
\(5\) | −0.809017 | + | 0.587785i | −0.361803 | + | 0.262866i | −0.753804 | − | 0.657099i | \(-0.771783\pi\) |
0.392000 | + | 0.919965i | \(0.371783\pi\) | |||||||
\(6\) | 1.61803 | − | 1.17557i | 0.660560 | − | 0.479925i | ||||
\(7\) | 0.618034 | + | 1.90211i | 0.233595 | + | 0.718931i | 0.997305 | + | 0.0733714i | \(0.0233759\pi\) |
−0.763710 | + | 0.645560i | \(0.776624\pi\) | |||||||
\(8\) | 0.927051 | − | 2.85317i | 0.327762 | − | 1.00875i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.00000 | −0.577350 | ||||||||
\(13\) | 0.809017 | + | 0.587785i | 0.224381 | + | 0.163022i | 0.694297 | − | 0.719689i | \(-0.255716\pi\) |
−0.469916 | + | 0.882711i | \(0.655716\pi\) | |||||||
\(14\) | −0.618034 | + | 1.90211i | −0.165177 | + | 0.508361i | ||||
\(15\) | 0.618034 | + | 1.90211i | 0.159576 | + | 0.491123i | ||||
\(16\) | 0.809017 | − | 0.587785i | 0.202254 | − | 0.146946i | ||||
\(17\) | −4.04508 | + | 2.93893i | −0.981077 | + | 0.712794i | −0.957949 | − | 0.286938i | \(-0.907363\pi\) |
−0.0231281 | + | 0.999733i | \(0.507363\pi\) | |||||||
\(18\) | −0.309017 | − | 0.951057i | −0.0728360 | − | 0.224166i | ||||
\(19\) | −1.85410 | + | 5.70634i | −0.425360 | + | 1.30912i | 0.477289 | + | 0.878746i | \(0.341620\pi\) |
−0.902649 | + | 0.430377i | \(0.858380\pi\) | |||||||
\(20\) | 0.809017 | + | 0.587785i | 0.180902 | + | 0.131433i | ||||
\(21\) | 4.00000 | 0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | 0.417029 | 0.208514 | − | 0.978019i | \(-0.433137\pi\) | ||||
0.208514 | + | 0.978019i | \(0.433137\pi\) | |||||||
\(24\) | −4.85410 | − | 3.52671i | −0.990839 | − | 0.719887i | ||||
\(25\) | −1.23607 | + | 3.80423i | −0.247214 | + | 0.760845i | ||||
\(26\) | 0.309017 | + | 0.951057i | 0.0606032 | + | 0.186518i | ||||
\(27\) | 3.23607 | − | 2.35114i | 0.622782 | − | 0.452477i | ||||
\(28\) | 1.61803 | − | 1.17557i | 0.305780 | − | 0.222162i | ||||
\(29\) | −2.78115 | − | 8.55951i | −0.516447 | − | 1.58946i | −0.780633 | − | 0.624989i | \(-0.785103\pi\) |
0.264186 | − | 0.964472i | \(-0.414897\pi\) | |||||||
\(30\) | −0.618034 | + | 1.90211i | −0.112837 | + | 0.347277i | ||||
\(31\) | 1.61803 | + | 1.17557i | 0.290607 | + | 0.211139i | 0.723531 | − | 0.690292i | \(-0.242518\pi\) |
−0.432923 | + | 0.901431i | \(0.642518\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.00000 | −0.857493 | ||||||||
\(35\) | −1.61803 | − | 1.17557i | −0.273498 | − | 0.198708i | ||||
\(36\) | −0.309017 | + | 0.951057i | −0.0515028 | + | 0.158509i | ||||
\(37\) | −0.927051 | − | 2.85317i | −0.152406 | − | 0.469058i | 0.845483 | − | 0.534003i | \(-0.179313\pi\) |
−0.997889 | + | 0.0649448i | \(0.979313\pi\) | |||||||
\(38\) | −4.85410 | + | 3.52671i | −0.787439 | + | 0.572108i | ||||
\(39\) | 1.61803 | − | 1.17557i | 0.259093 | − | 0.188242i | ||||
\(40\) | 0.927051 | + | 2.85317i | 0.146580 | + | 0.451126i | ||||
\(41\) | 1.54508 | − | 4.75528i | 0.241302 | − | 0.742650i | −0.754921 | − | 0.655816i | \(-0.772325\pi\) |
0.996223 | − | 0.0868346i | \(-0.0276752\pi\) | |||||||
\(42\) | 3.23607 | + | 2.35114i | 0.499336 | + | 0.362789i | ||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 1.61803 | + | 1.17557i | 0.238566 | + | 0.173328i | ||||
\(47\) | 0.618034 | − | 1.90211i | 0.0901495 | − | 0.277452i | −0.895810 | − | 0.444438i | \(-0.853403\pi\) |
0.985959 | + | 0.166986i | \(0.0534035\pi\) | |||||||
\(48\) | −0.618034 | − | 1.90211i | −0.0892055 | − | 0.274546i | ||||
\(49\) | 2.42705 | − | 1.76336i | 0.346722 | − | 0.251908i | ||||
\(50\) | −3.23607 | + | 2.35114i | −0.457649 | + | 0.332502i | ||||
\(51\) | 3.09017 | + | 9.51057i | 0.432710 | + | 1.33175i | ||||
\(52\) | 0.309017 | − | 0.951057i | 0.0428529 | − | 0.131888i | ||||
\(53\) | −7.28115 | − | 5.29007i | −1.00014 | − | 0.726647i | −0.0380244 | − | 0.999277i | \(-0.512106\pi\) |
−0.962119 | + | 0.272630i | \(0.912106\pi\) | |||||||
\(54\) | 4.00000 | 0.544331 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.00000 | 0.801784 | ||||||||
\(57\) | 9.70820 | + | 7.05342i | 1.28588 | + | 0.934249i | ||||
\(58\) | 2.78115 | − | 8.55951i | 0.365183 | − | 1.12392i | ||||
\(59\) | 2.47214 | + | 7.60845i | 0.321845 | + | 0.990536i | 0.972845 | + | 0.231458i | \(0.0743497\pi\) |
−0.651000 | + | 0.759078i | \(0.725650\pi\) | |||||||
\(60\) | 1.61803 | − | 1.17557i | 0.208887 | − | 0.151765i | ||||
\(61\) | 4.85410 | − | 3.52671i | 0.621504 | − | 0.451549i | −0.231942 | − | 0.972730i | \(-0.574508\pi\) |
0.853447 | + | 0.521180i | \(0.174508\pi\) | |||||||
\(62\) | 0.618034 | + | 1.90211i | 0.0784904 | + | 0.241569i | ||||
\(63\) | 0.618034 | − | 1.90211i | 0.0778650 | − | 0.239644i | ||||
\(64\) | −5.66312 | − | 4.11450i | −0.707890 | − | 0.514312i | ||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | 0.244339 | 0.122169 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122169 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(68\) | 4.04508 | + | 2.93893i | 0.490539 | + | 0.356397i | ||||
\(69\) | 1.23607 | − | 3.80423i | 0.148805 | − | 0.457975i | ||||
\(70\) | −0.618034 | − | 1.90211i | −0.0738692 | − | 0.227346i | ||||
\(71\) | −9.70820 | + | 7.05342i | −1.15215 | + | 0.837087i | −0.988766 | − | 0.149475i | \(-0.952242\pi\) |
−0.163386 | + | 0.986562i | \(0.552242\pi\) | |||||||
\(72\) | −2.42705 | + | 1.76336i | −0.286031 | + | 0.207813i | ||||
\(73\) | 0.618034 | + | 1.90211i | 0.0723354 | + | 0.222625i | 0.980688 | − | 0.195580i | \(-0.0626591\pi\) |
−0.908352 | + | 0.418206i | \(0.862659\pi\) | |||||||
\(74\) | 0.927051 | − | 2.85317i | 0.107767 | − | 0.331674i | ||||
\(75\) | 6.47214 | + | 4.70228i | 0.747338 | + | 0.542973i | ||||
\(76\) | 6.00000 | 0.688247 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.00000 | 0.226455 | ||||||||
\(79\) | −8.09017 | − | 5.87785i | −0.910215 | − | 0.661310i | 0.0308541 | − | 0.999524i | \(-0.490177\pi\) |
−0.941069 | + | 0.338214i | \(0.890177\pi\) | |||||||
\(80\) | −0.309017 | + | 0.951057i | −0.0345492 | + | 0.106331i | ||||
\(81\) | −3.39919 | − | 10.4616i | −0.377687 | − | 1.16240i | ||||
\(82\) | 4.04508 | − | 2.93893i | 0.446705 | − | 0.324550i | ||||
\(83\) | 4.85410 | − | 3.52671i | 0.532807 | − | 0.387107i | −0.288600 | − | 0.957450i | \(-0.593190\pi\) |
0.821407 | + | 0.570343i | \(0.193190\pi\) | |||||||
\(84\) | −1.23607 | − | 3.80423i | −0.134866 | − | 0.415075i | ||||
\(85\) | 1.54508 | − | 4.75528i | 0.167588 | − | 0.515783i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18.0000 | −1.92980 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | 0.809017 | + | 0.587785i | 0.0852779 | + | 0.0619580i | ||||
\(91\) | −0.618034 | + | 1.90211i | −0.0647876 | + | 0.199396i | ||||
\(92\) | −0.618034 | − | 1.90211i | −0.0644345 | − | 0.198309i | ||||
\(93\) | 3.23607 | − | 2.35114i | 0.335565 | − | 0.243802i | ||||
\(94\) | 1.61803 | − | 1.17557i | 0.166887 | − | 0.121251i | ||||
\(95\) | −1.85410 | − | 5.70634i | −0.190227 | − | 0.585458i | ||||
\(96\) | −3.09017 | + | 9.51057i | −0.315389 | + | 0.970668i | ||||
\(97\) | 10.5172 | + | 7.64121i | 1.06786 | + | 0.775847i | 0.975527 | − | 0.219881i | \(-0.0705669\pi\) |
0.0923353 | + | 0.995728i | \(0.470567\pi\) | |||||||
\(98\) | 3.00000 | 0.303046 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | −8.09017 | − | 5.87785i | −0.805002 | − | 0.584868i | 0.107375 | − | 0.994219i | \(-0.465755\pi\) |
−0.912377 | + | 0.409350i | \(0.865755\pi\) | |||||||
\(102\) | −3.09017 | + | 9.51057i | −0.305972 | + | 0.941686i | ||||
\(103\) | 2.47214 | + | 7.60845i | 0.243587 | + | 0.749683i | 0.995866 | + | 0.0908382i | \(0.0289546\pi\) |
−0.752279 | + | 0.658845i | \(0.771045\pi\) | |||||||
\(104\) | 2.42705 | − | 1.76336i | 0.237992 | − | 0.172911i | ||||
\(105\) | −3.23607 | + | 2.35114i | −0.315808 | + | 0.229448i | ||||
\(106\) | −2.78115 | − | 8.55951i | −0.270129 | − | 0.831373i | ||||
\(107\) | −1.85410 | + | 5.70634i | −0.179243 | + | 0.551653i | −0.999802 | − | 0.0199092i | \(-0.993662\pi\) |
0.820559 | + | 0.571562i | \(0.193662\pi\) | |||||||
\(108\) | −3.23607 | − | 2.35114i | −0.311391 | − | 0.226239i | ||||
\(109\) | 11.0000 | 1.05361 | 0.526804 | − | 0.849987i | \(-0.323390\pi\) | ||||
0.526804 | + | 0.849987i | \(0.323390\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | −0.569495 | ||||||||
\(112\) | 1.61803 | + | 1.17557i | 0.152890 | + | 0.111081i | ||||
\(113\) | −2.78115 | + | 8.55951i | −0.261629 | + | 0.805211i | 0.730822 | + | 0.682568i | \(0.239137\pi\) |
−0.992451 | + | 0.122643i | \(0.960863\pi\) | |||||||
\(114\) | 3.70820 | + | 11.4127i | 0.347305 | + | 1.06890i | ||||
\(115\) | −1.61803 | + | 1.17557i | −0.150882 | + | 0.109623i | ||||
\(116\) | −7.28115 | + | 5.29007i | −0.676038 | + | 0.491170i | ||||
\(117\) | −0.309017 | − | 0.951057i | −0.0285686 | − | 0.0879252i | ||||
\(118\) | −2.47214 | + | 7.60845i | −0.227579 | + | 0.700415i | ||||
\(119\) | −8.09017 | − | 5.87785i | −0.741625 | − | 0.538822i | ||||
\(120\) | 6.00000 | 0.547723 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 6.00000 | 0.543214 | ||||||||
\(123\) | −8.09017 | − | 5.87785i | −0.729466 | − | 0.529988i | ||||
\(124\) | 0.618034 | − | 1.90211i | 0.0555011 | − | 0.170815i | ||||
\(125\) | −2.78115 | − | 8.55951i | −0.248754 | − | 0.765586i | ||||
\(126\) | 1.61803 | − | 1.17557i | 0.144146 | − | 0.104728i | ||||
\(127\) | −12.9443 | + | 9.40456i | −1.14862 | + | 0.834520i | −0.988297 | − | 0.152545i | \(-0.951253\pi\) |
−0.160322 | + | 0.987065i | \(0.551253\pi\) | |||||||
\(128\) | 0.927051 | + | 2.85317i | 0.0819405 | + | 0.252187i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.809017 | − | 0.587785i | −0.0709555 | − | 0.0515522i | ||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.0000 | −1.04053 | ||||||||
\(134\) | 1.61803 | + | 1.17557i | 0.139777 | + | 0.101554i | ||||
\(135\) | −1.23607 | + | 3.80423i | −0.106384 | + | 0.327416i | ||||
\(136\) | 4.63525 | + | 14.2658i | 0.397470 | + | 1.22329i | ||||
\(137\) | 8.09017 | − | 5.87785i | 0.691190 | − | 0.502179i | −0.185861 | − | 0.982576i | \(-0.559507\pi\) |
0.877051 | + | 0.480397i | \(0.159507\pi\) | |||||||
\(138\) | 3.23607 | − | 2.35114i | 0.275472 | − | 0.200142i | ||||
\(139\) | 0.618034 | + | 1.90211i | 0.0524210 | + | 0.161335i | 0.973840 | − | 0.227236i | \(-0.0729688\pi\) |
−0.921419 | + | 0.388571i | \(0.872969\pi\) | |||||||
\(140\) | −0.618034 | + | 1.90211i | −0.0522334 | + | 0.160758i | ||||
\(141\) | −3.23607 | − | 2.35114i | −0.272526 | − | 0.198002i | ||||
\(142\) | −12.0000 | −1.00702 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 7.28115 | + | 5.29007i | 0.604667 | + | 0.439316i | ||||
\(146\) | −0.618034 | + | 1.90211i | −0.0511489 | + | 0.157420i | ||||
\(147\) | −1.85410 | − | 5.70634i | −0.152924 | − | 0.470651i | ||||
\(148\) | −2.42705 | + | 1.76336i | −0.199502 | + | 0.144947i | ||||
\(149\) | 13.7533 | − | 9.99235i | 1.12671 | − | 0.818605i | 0.141500 | − | 0.989938i | \(-0.454807\pi\) |
0.985213 | + | 0.171333i | \(0.0548074\pi\) | |||||||
\(150\) | 2.47214 | + | 7.60845i | 0.201849 | + | 0.621228i | ||||
\(151\) | 4.94427 | − | 15.2169i | 0.402359 | − | 1.23833i | −0.520721 | − | 0.853727i | \(-0.674337\pi\) |
0.923080 | − | 0.384607i | \(-0.125663\pi\) | |||||||
\(152\) | 14.5623 | + | 10.5801i | 1.18116 | + | 0.858162i | ||||
\(153\) | 5.00000 | 0.404226 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | −0.160644 | ||||||||
\(156\) | −1.61803 | − | 1.17557i | −0.129546 | − | 0.0941210i | ||||
\(157\) | 0.618034 | − | 1.90211i | 0.0493245 | − | 0.151805i | −0.923361 | − | 0.383934i | \(-0.874569\pi\) |
0.972685 | + | 0.232129i | \(0.0745691\pi\) | |||||||
\(158\) | −3.09017 | − | 9.51057i | −0.245841 | − | 0.756620i | ||||
\(159\) | −14.5623 | + | 10.5801i | −1.15487 | + | 0.839059i | ||||
\(160\) | 4.04508 | − | 2.93893i | 0.319792 | − | 0.232343i | ||||
\(161\) | 1.23607 | + | 3.80423i | 0.0974158 | + | 0.299815i | ||||
\(162\) | 3.39919 | − | 10.4616i | 0.267065 | − | 0.821943i | ||||
\(163\) | 1.61803 | + | 1.17557i | 0.126734 | + | 0.0920778i | 0.649347 | − | 0.760493i | \(-0.275042\pi\) |
−0.522612 | + | 0.852570i | \(0.675042\pi\) | |||||||
\(164\) | −5.00000 | −0.390434 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | 0.465690 | ||||||||
\(167\) | 9.70820 | + | 7.05342i | 0.751243 | + | 0.545810i | 0.896212 | − | 0.443626i | \(-0.146308\pi\) |
−0.144969 | + | 0.989436i | \(0.546308\pi\) | |||||||
\(168\) | 3.70820 | − | 11.4127i | 0.286094 | − | 0.880507i | ||||
\(169\) | −3.70820 | − | 11.4127i | −0.285246 | − | 0.877898i | ||||
\(170\) | 4.04508 | − | 2.93893i | 0.310244 | − | 0.225405i | ||||
\(171\) | 4.85410 | − | 3.52671i | 0.371202 | − | 0.269694i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.85410 | + | 5.70634i | −0.140965 | + | 0.433845i | −0.996470 | − | 0.0839492i | \(-0.973247\pi\) |
0.855505 | + | 0.517794i | \(0.173247\pi\) | |||||||
\(174\) | −14.5623 | − | 10.5801i | −1.10397 | − | 0.802078i | ||||
\(175\) | −8.00000 | −0.604743 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.0000 | 1.20263 | ||||||||
\(178\) | −7.28115 | − | 5.29007i | −0.545745 | − | 0.396507i | ||||
\(179\) | 7.41641 | − | 22.8254i | 0.554328 | − | 1.70605i | −0.143382 | − | 0.989667i | \(-0.545798\pi\) |
0.697710 | − | 0.716380i | \(-0.254202\pi\) | |||||||
\(180\) | −0.309017 | − | 0.951057i | −0.0230328 | − | 0.0708876i | ||||
\(181\) | −0.809017 | + | 0.587785i | −0.0601338 | + | 0.0436897i | −0.617446 | − | 0.786613i | \(-0.711833\pi\) |
0.557312 | + | 0.830303i | \(0.311833\pi\) | |||||||
\(182\) | −1.61803 | + | 1.17557i | −0.119937 | + | 0.0871391i | ||||
\(183\) | −3.70820 | − | 11.4127i | −0.274118 | − | 0.843649i | ||||
\(184\) | 1.85410 | − | 5.70634i | 0.136686 | − | 0.420677i | ||||
\(185\) | 2.42705 | + | 1.76336i | 0.178440 | + | 0.129644i | ||||
\(186\) | 4.00000 | 0.293294 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2.00000 | −0.145865 | ||||||||
\(189\) | 6.47214 | + | 4.70228i | 0.470779 | + | 0.342041i | ||||
\(190\) | 1.85410 | − | 5.70634i | 0.134511 | − | 0.413981i | ||||
\(191\) | 2.47214 | + | 7.60845i | 0.178877 | + | 0.550528i | 0.999789 | − | 0.0205267i | \(-0.00653431\pi\) |
−0.820912 | + | 0.571055i | \(0.806534\pi\) | |||||||
\(192\) | −11.3262 | + | 8.22899i | −0.817401 | + | 0.593876i | ||||
\(193\) | −4.04508 | + | 2.93893i | −0.291172 | + | 0.211549i | −0.723775 | − | 0.690036i | \(-0.757595\pi\) |
0.432604 | + | 0.901584i | \(0.357595\pi\) | |||||||
\(194\) | 4.01722 | + | 12.3637i | 0.288420 | + | 0.887664i | ||||
\(195\) | −0.618034 | + | 1.90211i | −0.0442583 | + | 0.136213i | ||||
\(196\) | −2.42705 | − | 1.76336i | −0.173361 | − | 0.125954i | ||||
\(197\) | 11.0000 | 0.783718 | 0.391859 | − | 0.920025i | \(-0.371832\pi\) | ||||
0.391859 | + | 0.920025i | \(0.371832\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0000 | 1.70131 | 0.850657 | − | 0.525720i | \(-0.176204\pi\) | ||||
0.850657 | + | 0.525720i | \(0.176204\pi\) | |||||||
\(200\) | 9.70820 | + | 7.05342i | 0.686474 | + | 0.498752i | ||||
\(201\) | 1.23607 | − | 3.80423i | 0.0871855 | − | 0.268329i | ||||
\(202\) | −3.09017 | − | 9.51057i | −0.217424 | − | 0.669161i | ||||
\(203\) | 14.5623 | − | 10.5801i | 1.02207 | − | 0.742580i | ||||
\(204\) | 8.09017 | − | 5.87785i | 0.566425 | − | 0.411532i | ||||
\(205\) | 1.54508 | + | 4.75528i | 0.107913 | + | 0.332123i | ||||
\(206\) | −2.47214 | + | 7.60845i | −0.172242 | + | 0.530106i | ||||
\(207\) | −1.61803 | − | 1.17557i | −0.112461 | − | 0.0817078i | ||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −4.00000 | −0.276026 | ||||||||
\(211\) | 9.70820 | + | 7.05342i | 0.668340 | + | 0.485578i | 0.869469 | − | 0.493987i | \(-0.164461\pi\) |
−0.201129 | + | 0.979565i | \(0.564461\pi\) | |||||||
\(212\) | −2.78115 | + | 8.55951i | −0.191010 | + | 0.587869i | ||||
\(213\) | 7.41641 | + | 22.8254i | 0.508164 | + | 1.56397i | ||||
\(214\) | −4.85410 | + | 3.52671i | −0.331820 | + | 0.241081i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.70820 | − | 11.4127i | −0.252311 | − | 0.776534i | ||||
\(217\) | −1.23607 | + | 3.80423i | −0.0839098 | + | 0.258248i | ||||
\(218\) | 8.89919 | + | 6.46564i | 0.602729 | + | 0.437908i | ||||
\(219\) | 4.00000 | 0.270295 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.00000 | −0.336336 | ||||||||
\(222\) | −4.85410 | − | 3.52671i | −0.325786 | − | 0.236697i | ||||
\(223\) | −6.18034 | + | 19.0211i | −0.413866 | + | 1.27375i | 0.499395 | + | 0.866374i | \(0.333556\pi\) |
−0.913261 | + | 0.407375i | \(0.866444\pi\) | |||||||
\(224\) | −3.09017 | − | 9.51057i | −0.206471 | − | 0.635451i | ||||
\(225\) | 3.23607 | − | 2.35114i | 0.215738 | − | 0.156743i | ||||
\(226\) | −7.28115 | + | 5.29007i | −0.484335 | + | 0.351890i | ||||
\(227\) | 7.41641 | + | 22.8254i | 0.492244 | + | 1.51497i | 0.821208 | + | 0.570629i | \(0.193301\pi\) |
−0.328963 | + | 0.944343i | \(0.606699\pi\) | |||||||
\(228\) | 3.70820 | − | 11.4127i | 0.245582 | − | 0.755823i | ||||
\(229\) | −7.28115 | − | 5.29007i | −0.481152 | − | 0.349577i | 0.320619 | − | 0.947208i | \(-0.396109\pi\) |
−0.801772 | + | 0.597631i | \(0.796109\pi\) | |||||||
\(230\) | −2.00000 | −0.131876 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −27.0000 | −1.77264 | ||||||||
\(233\) | −16.9894 | − | 12.3435i | −1.11301 | − | 0.808649i | −0.129875 | − | 0.991530i | \(-0.541458\pi\) |
−0.983135 | + | 0.182881i | \(0.941458\pi\) | |||||||
\(234\) | 0.309017 | − | 0.951057i | 0.0202011 | − | 0.0621725i | ||||
\(235\) | 0.618034 | + | 1.90211i | 0.0403161 | + | 0.124080i | ||||
\(236\) | 6.47214 | − | 4.70228i | 0.421300 | − | 0.306092i | ||||
\(237\) | −16.1803 | + | 11.7557i | −1.05103 | + | 0.763615i | ||||
\(238\) | −3.09017 | − | 9.51057i | −0.200306 | − | 0.616478i | ||||
\(239\) | −1.85410 | + | 5.70634i | −0.119932 | + | 0.369112i | −0.992944 | − | 0.118587i | \(-0.962164\pi\) |
0.873012 | + | 0.487699i | \(0.162164\pi\) | |||||||
\(240\) | 1.61803 | + | 1.17557i | 0.104444 | + | 0.0758827i | ||||
\(241\) | −22.0000 | −1.41714 | −0.708572 | − | 0.705638i | \(-0.750660\pi\) | ||||
−0.708572 | + | 0.705638i | \(0.750660\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.0000 | −0.641500 | ||||||||
\(244\) | −4.85410 | − | 3.52671i | −0.310752 | − | 0.225775i | ||||
\(245\) | −0.927051 | + | 2.85317i | −0.0592271 | + | 0.182282i | ||||
\(246\) | −3.09017 | − | 9.51057i | −0.197022 | − | 0.606371i | ||||
\(247\) | −4.85410 | + | 3.52671i | −0.308859 | + | 0.224399i | ||||
\(248\) | 4.85410 | − | 3.52671i | 0.308236 | − | 0.223946i | ||||
\(249\) | −3.70820 | − | 11.4127i | −0.234998 | − | 0.723249i | ||||
\(250\) | 2.78115 | − | 8.55951i | 0.175896 | − | 0.541351i | ||||
\(251\) | 1.61803 | + | 1.17557i | 0.102129 | + | 0.0742014i | 0.637678 | − | 0.770303i | \(-0.279895\pi\) |
−0.535548 | + | 0.844504i | \(0.679895\pi\) | |||||||
\(252\) | −2.00000 | −0.125988 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −16.0000 | −1.00393 | ||||||||
\(255\) | −8.09017 | − | 5.87785i | −0.506626 | − | 0.368085i | ||||
\(256\) | −5.25329 | + | 16.1680i | −0.328331 | + | 1.01050i | ||||
\(257\) | 5.87132 | + | 18.0701i | 0.366243 | + | 1.12718i | 0.949199 | + | 0.314676i | \(0.101896\pi\) |
−0.582956 | + | 0.812504i | \(0.698104\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.85410 | − | 3.52671i | 0.301619 | − | 0.219139i | ||||
\(260\) | 0.309017 | + | 0.951057i | 0.0191644 | + | 0.0589820i | ||||
\(261\) | −2.78115 | + | 8.55951i | −0.172149 | + | 0.529820i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.0000 | 1.35658 | 0.678289 | − | 0.734795i | \(-0.262722\pi\) | ||||
0.678289 | + | 0.734795i | \(0.262722\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | 0.552866 | ||||||||
\(266\) | −9.70820 | − | 7.05342i | −0.595248 | − | 0.432473i | ||||
\(267\) | −5.56231 | + | 17.1190i | −0.340408 | + | 1.04767i | ||||
\(268\) | −0.618034 | − | 1.90211i | −0.0377524 | − | 0.116190i | ||||
\(269\) | −0.809017 | + | 0.587785i | −0.0493266 | + | 0.0358379i | −0.612175 | − | 0.790722i | \(-0.709705\pi\) |
0.562849 | + | 0.826560i | \(0.309705\pi\) | |||||||
\(270\) | −3.23607 | + | 2.35114i | −0.196941 | + | 0.143086i | ||||
\(271\) | −6.18034 | − | 19.0211i | −0.375429 | − | 1.15545i | −0.943189 | − | 0.332257i | \(-0.892190\pi\) |
0.567760 | − | 0.823194i | \(-0.307810\pi\) | |||||||
\(272\) | −1.54508 | + | 4.75528i | −0.0936845 | + | 0.288331i | ||||
\(273\) | 3.23607 | + | 2.35114i | 0.195856 | + | 0.142298i | ||||
\(274\) | 10.0000 | 0.604122 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.00000 | −0.240772 | ||||||||
\(277\) | 0.809017 | + | 0.587785i | 0.0486091 | + | 0.0353166i | 0.611825 | − | 0.790994i | \(-0.290436\pi\) |
−0.563215 | + | 0.826310i | \(0.690436\pi\) | |||||||
\(278\) | −0.618034 | + | 1.90211i | −0.0370672 | + | 0.114081i | ||||
\(279\) | −0.618034 | − | 1.90211i | −0.0370007 | − | 0.113877i | ||||
\(280\) | −4.85410 | + | 3.52671i | −0.290088 | + | 0.210761i | ||||
\(281\) | 4.85410 | − | 3.52671i | 0.289571 | − | 0.210386i | −0.433510 | − | 0.901149i | \(-0.642725\pi\) |
0.723081 | + | 0.690763i | \(0.242725\pi\) | |||||||
\(282\) | −1.23607 | − | 3.80423i | −0.0736068 | − | 0.226538i | ||||
\(283\) | −8.65248 | + | 26.6296i | −0.514336 | + | 1.58296i | 0.270150 | + | 0.962818i | \(0.412927\pi\) |
−0.784486 | + | 0.620146i | \(0.787073\pi\) | |||||||
\(284\) | 9.70820 | + | 7.05342i | 0.576076 | + | 0.418544i | ||||
\(285\) | −12.0000 | −0.710819 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.0000 | 0.590281 | ||||||||
\(288\) | 4.04508 | + | 2.93893i | 0.238359 | + | 0.173178i | ||||
\(289\) | 2.47214 | − | 7.60845i | 0.145420 | − | 0.447556i | ||||
\(290\) | 2.78115 | + | 8.55951i | 0.163315 | + | 0.502632i | ||||
\(291\) | 21.0344 | − | 15.2824i | 1.23306 | − | 0.895871i | ||||
\(292\) | 1.61803 | − | 1.17557i | 0.0946883 | − | 0.0687951i | ||||
\(293\) | −2.78115 | − | 8.55951i | −0.162477 | − | 0.500052i | 0.836365 | − | 0.548173i | \(-0.184677\pi\) |
−0.998841 | + | 0.0481214i | \(0.984677\pi\) | |||||||
\(294\) | 1.85410 | − | 5.70634i | 0.108133 | − | 0.332800i | ||||
\(295\) | −6.47214 | − | 4.70228i | −0.376822 | − | 0.273777i | ||||
\(296\) | −9.00000 | −0.523114 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 17.0000 | 0.984784 | ||||||||
\(299\) | 1.61803 | + | 1.17557i | 0.0935733 | + | 0.0679850i | ||||
\(300\) | 2.47214 | − | 7.60845i | 0.142729 | − | 0.439274i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12.9443 | − | 9.40456i | 0.744859 | − | 0.541172i | ||||
\(303\) | −16.1803 | + | 11.7557i | −0.929536 | + | 0.675348i | ||||
\(304\) | 1.85410 | + | 5.70634i | 0.106340 | + | 0.327281i | ||||
\(305\) | −1.85410 | + | 5.70634i | −0.106166 | + | 0.326744i | ||||
\(306\) | 4.04508 | + | 2.93893i | 0.231242 | + | 0.168007i | ||||
\(307\) | 22.0000 | 1.25561 | 0.627803 | − | 0.778372i | \(-0.283954\pi\) | ||||
0.627803 | + | 0.778372i | \(0.283954\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.0000 | 0.910208 | ||||||||
\(310\) | −1.61803 | − | 1.17557i | −0.0918982 | − | 0.0667679i | ||||
\(311\) | 7.41641 | − | 22.8254i | 0.420546 | − | 1.29431i | −0.486649 | − | 0.873597i | \(-0.661781\pi\) |
0.907195 | − | 0.420710i | \(-0.138219\pi\) | |||||||
\(312\) | −1.85410 | − | 5.70634i | −0.104968 | − | 0.323058i | ||||
\(313\) | −18.6074 | + | 13.5191i | −1.05175 | + | 0.764142i | −0.972545 | − | 0.232716i | \(-0.925239\pi\) |
−0.0792071 | + | 0.996858i | \(0.525239\pi\) | |||||||
\(314\) | 1.61803 | − | 1.17557i | 0.0913109 | − | 0.0663413i | ||||
\(315\) | 0.618034 | + | 1.90211i | 0.0348223 | + | 0.107172i | ||||
\(316\) | −3.09017 | + | 9.51057i | −0.173836 | + | 0.535011i | ||||
\(317\) | 1.61803 | + | 1.17557i | 0.0908778 | + | 0.0660266i | 0.632296 | − | 0.774727i | \(-0.282113\pi\) |
−0.541418 | + | 0.840753i | \(0.682113\pi\) | |||||||
\(318\) | −18.0000 | −1.00939 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 7.00000 | 0.391312 | ||||||||
\(321\) | 9.70820 | + | 7.05342i | 0.541859 | + | 0.393684i | ||||
\(322\) | −1.23607 | + | 3.80423i | −0.0688834 | + | 0.212001i | ||||
\(323\) | −9.27051 | − | 28.5317i | −0.515825 | − | 1.58755i | ||||
\(324\) | −8.89919 | + | 6.46564i | −0.494399 | + | 0.359202i | ||||
\(325\) | −3.23607 | + | 2.35114i | −0.179505 | + | 0.130418i | ||||
\(326\) | 0.618034 | + | 1.90211i | 0.0342297 | + | 0.105348i | ||||
\(327\) | 6.79837 | − | 20.9232i | 0.375951 | − | 1.15706i | ||||
\(328\) | −12.1353 | − | 8.81678i | −0.670057 | − | 0.486825i | ||||
\(329\) | 4.00000 | 0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0000 | −1.09930 | −0.549650 | − | 0.835395i | \(-0.685239\pi\) | ||||
−0.549650 | + | 0.835395i | \(0.685239\pi\) | |||||||
\(332\) | −4.85410 | − | 3.52671i | −0.266403 | − | 0.193553i | ||||
\(333\) | −0.927051 | + | 2.85317i | −0.0508021 | + | 0.156353i | ||||
\(334\) | 3.70820 | + | 11.4127i | 0.202904 | + | 0.624474i | ||||
\(335\) | −1.61803 | + | 1.17557i | −0.0884026 | + | 0.0642283i | ||||
\(336\) | 3.23607 | − | 2.35114i | 0.176542 | − | 0.128265i | ||||
\(337\) | 4.01722 | + | 12.3637i | 0.218832 | + | 0.673496i | 0.998859 | + | 0.0477501i | \(0.0152051\pi\) |
−0.780027 | + | 0.625745i | \(0.784795\pi\) | |||||||
\(338\) | 3.70820 | − | 11.4127i | 0.201700 | − | 0.620768i | ||||
\(339\) | 14.5623 | + | 10.5801i | 0.790916 | + | 0.574634i | ||||
\(340\) | −5.00000 | −0.271163 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 6.00000 | 0.324443 | ||||||||
\(343\) | 16.1803 | + | 11.7557i | 0.873656 | + | 0.634748i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.23607 | + | 3.80423i | 0.0665477 | + | 0.204813i | ||||
\(346\) | −4.85410 | + | 3.52671i | −0.260958 | + | 0.189597i | ||||
\(347\) | 22.6525 | − | 16.4580i | 1.21605 | − | 0.883511i | 0.220283 | − | 0.975436i | \(-0.429302\pi\) |
0.995766 | + | 0.0919250i | \(0.0293020\pi\) | |||||||
\(348\) | 5.56231 | + | 17.1190i | 0.298171 | + | 0.917676i | ||||
\(349\) | 8.34346 | − | 25.6785i | 0.446615 | − | 1.37454i | −0.434088 | − | 0.900871i | \(-0.642929\pi\) |
0.880703 | − | 0.473669i | \(-0.157071\pi\) | |||||||
\(350\) | −6.47214 | − | 4.70228i | −0.345950 | − | 0.251348i | ||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.00000 | −0.479022 | −0.239511 | − | 0.970894i | \(-0.576987\pi\) | ||||
−0.239511 | + | 0.970894i | \(0.576987\pi\) | |||||||
\(354\) | 12.9443 | + | 9.40456i | 0.687980 | + | 0.499847i | ||||
\(355\) | 3.70820 | − | 11.4127i | 0.196811 | − | 0.605722i | ||||
\(356\) | 2.78115 | + | 8.55951i | 0.147401 | + | 0.453653i | ||||
\(357\) | −16.1803 | + | 11.7557i | −0.856354 | + | 0.622178i | ||||
\(358\) | 19.4164 | − | 14.1068i | 1.02619 | − | 0.745570i | ||||
\(359\) | 0.618034 | + | 1.90211i | 0.0326186 | + | 0.100390i | 0.966040 | − | 0.258391i | \(-0.0831924\pi\) |
−0.933422 | + | 0.358781i | \(0.883192\pi\) | |||||||
\(360\) | 0.927051 | − | 2.85317i | 0.0488599 | − | 0.150375i | ||||
\(361\) | −13.7533 | − | 9.99235i | −0.723857 | − | 0.525913i | ||||
\(362\) | −1.00000 | −0.0525588 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | −1.61803 | − | 1.17557i | −0.0846918 | − | 0.0615322i | ||||
\(366\) | 3.70820 | − | 11.4127i | 0.193831 | − | 0.596550i | ||||
\(367\) | −4.32624 | − | 13.3148i | −0.225828 | − | 0.695026i | −0.998207 | − | 0.0598642i | \(-0.980933\pi\) |
0.772379 | − | 0.635162i | \(-0.219067\pi\) | |||||||
\(368\) | 1.61803 | − | 1.17557i | 0.0843459 | − | 0.0612808i | ||||
\(369\) | −4.04508 | + | 2.93893i | −0.210579 | + | 0.152994i | ||||
\(370\) | 0.927051 | + | 2.85317i | 0.0481951 | + | 0.148329i | ||||
\(371\) | 5.56231 | − | 17.1190i | 0.288781 | − | 0.888775i | ||||
\(372\) | −3.23607 | − | 2.35114i | −0.167782 | − | 0.121901i | ||||
\(373\) | −22.0000 | −1.13912 | −0.569558 | − | 0.821951i | \(-0.692886\pi\) | ||||
−0.569558 | + | 0.821951i | \(0.692886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.0000 | −0.929516 | ||||||||
\(376\) | −4.85410 | − | 3.52671i | −0.250331 | − | 0.181876i | ||||
\(377\) | 2.78115 | − | 8.55951i | 0.143237 | − | 0.440837i | ||||
\(378\) | 2.47214 | + | 7.60845i | 0.127153 | + | 0.391337i | ||||
\(379\) | 25.8885 | − | 18.8091i | 1.32981 | − | 0.966160i | 0.330052 | − | 0.943963i | \(-0.392934\pi\) |
0.999754 | − | 0.0221971i | \(-0.00706614\pi\) | |||||||
\(380\) | −4.85410 | + | 3.52671i | −0.249010 | + | 0.180916i | ||||
\(381\) | 9.88854 | + | 30.4338i | 0.506605 | + | 1.55917i | ||||
\(382\) | −2.47214 | + | 7.60845i | −0.126485 | + | 0.389282i | ||||
\(383\) | −16.1803 | − | 11.7557i | −0.826777 | − | 0.600688i | 0.0918688 | − | 0.995771i | \(-0.470716\pi\) |
−0.918646 | + | 0.395083i | \(0.870716\pi\) | |||||||
\(384\) | 6.00000 | 0.306186 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.00000 | −0.254493 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.01722 | − | 12.3637i | 0.203943 | − | 0.627674i | ||||
\(389\) | −0.927051 | − | 2.85317i | −0.0470034 | − | 0.144661i | 0.924800 | − | 0.380453i | \(-0.124232\pi\) |
−0.971804 | + | 0.235791i | \(0.924232\pi\) | |||||||
\(390\) | −1.61803 | + | 1.17557i | −0.0819323 | + | 0.0595273i | ||||
\(391\) | −8.09017 | + | 5.87785i | −0.409137 | + | 0.297256i | ||||
\(392\) | −2.78115 | − | 8.55951i | −0.140469 | − | 0.432320i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.89919 | + | 6.46564i | 0.448335 | + | 0.325734i | ||||
\(395\) | 10.0000 | 0.503155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.0000 | 0.652451 | 0.326226 | − | 0.945292i | \(-0.394223\pi\) | ||||
0.326226 | + | 0.945292i | \(0.394223\pi\) | |||||||
\(398\) | 19.4164 | + | 14.1068i | 0.973257 | + | 0.707112i | ||||
\(399\) | −7.41641 | + | 22.8254i | −0.371285 | + | 1.14270i | ||||
\(400\) | 1.23607 | + | 3.80423i | 0.0618034 | + | 0.190211i | ||||
\(401\) | −18.6074 | + | 13.5191i | −0.929209 | + | 0.675110i | −0.945799 | − | 0.324753i | \(-0.894719\pi\) |
0.0165902 | + | 0.999862i | \(0.494719\pi\) | |||||||
\(402\) | 3.23607 | − | 2.35114i | 0.161400 | − | 0.117264i | ||||
\(403\) | 0.618034 | + | 1.90211i | 0.0307865 | + | 0.0947510i | ||||
\(404\) | −3.09017 | + | 9.51057i | −0.153742 | + | 0.473168i | ||||
\(405\) | 8.89919 | + | 6.46564i | 0.442204 | + | 0.321280i | ||||
\(406\) | 18.0000 | 0.893325 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 30.0000 | 1.48522 | ||||||||
\(409\) | −16.9894 | − | 12.3435i | −0.840070 | − | 0.610346i | 0.0823205 | − | 0.996606i | \(-0.473767\pi\) |
−0.922390 | + | 0.386260i | \(0.873767\pi\) | |||||||
\(410\) | −1.54508 | + | 4.75528i | −0.0763063 | + | 0.234847i | ||||
\(411\) | −6.18034 | − | 19.0211i | −0.304854 | − | 0.938243i | ||||
\(412\) | 6.47214 | − | 4.70228i | 0.318859 | − | 0.231665i | ||||
\(413\) | −12.9443 | + | 9.40456i | −0.636946 | + | 0.462768i | ||||
\(414\) | −0.618034 | − | 1.90211i | −0.0303747 | − | 0.0934838i | ||||
\(415\) | −1.85410 | + | 5.70634i | −0.0910143 | + | 0.280113i | ||||
\(416\) | −4.04508 | − | 2.93893i | −0.198327 | − | 0.144093i | ||||
\(417\) | 4.00000 | 0.195881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.00000 | 0.0977064 | 0.0488532 | − | 0.998806i | \(-0.484443\pi\) | ||||
0.0488532 | + | 0.998806i | \(0.484443\pi\) | |||||||
\(420\) | 3.23607 | + | 2.35114i | 0.157904 | + | 0.114724i | ||||
\(421\) | 4.01722 | − | 12.3637i | 0.195787 | − | 0.602572i | −0.804179 | − | 0.594387i | \(-0.797395\pi\) |
0.999967 | − | 0.00818455i | \(-0.00260525\pi\) | |||||||
\(422\) | 3.70820 | + | 11.4127i | 0.180513 | + | 0.555560i | ||||
\(423\) | −1.61803 | + | 1.17557i | −0.0786715 | + | 0.0571582i | ||||
\(424\) | −21.8435 | + | 15.8702i | −1.06081 | + | 0.770725i | ||||
\(425\) | −6.18034 | − | 19.0211i | −0.299791 | − | 0.922660i | ||||
\(426\) | −7.41641 | + | 22.8254i | −0.359326 | + | 1.10589i | ||||
\(427\) | 9.70820 | + | 7.05342i | 0.469813 | + | 0.341339i | ||||
\(428\) | 6.00000 | 0.290021 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.70820 | + | 7.05342i | 0.467628 | + | 0.339751i | 0.796516 | − | 0.604617i | \(-0.206674\pi\) |
−0.328888 | + | 0.944369i | \(0.606674\pi\) | |||||||
\(432\) | 1.23607 | − | 3.80423i | 0.0594703 | − | 0.183031i | ||||
\(433\) | 5.87132 | + | 18.0701i | 0.282158 | + | 0.868392i | 0.987236 | + | 0.159263i | \(0.0509118\pi\) |
−0.705078 | + | 0.709129i | \(0.749088\pi\) | |||||||
\(434\) | −3.23607 | + | 2.35114i | −0.155336 | + | 0.112858i | ||||
\(435\) | 14.5623 | − | 10.5801i | 0.698209 | − | 0.507279i | ||||
\(436\) | −3.39919 | − | 10.4616i | −0.162792 | − | 0.501021i | ||||
\(437\) | −3.70820 | + | 11.4127i | −0.177387 | + | 0.545942i | ||||
\(438\) | 3.23607 | + | 2.35114i | 0.154625 | + | 0.112342i | ||||
\(439\) | −22.0000 | −1.05000 | −0.525001 | − | 0.851101i | \(-0.675935\pi\) | ||||
−0.525001 | + | 0.851101i | \(0.675935\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | −4.04508 | − | 2.93893i | −0.192405 | − | 0.139790i | ||||
\(443\) | −6.18034 | + | 19.0211i | −0.293637 | + | 0.903721i | 0.690039 | + | 0.723772i | \(0.257593\pi\) |
−0.983676 | + | 0.179949i | \(0.942407\pi\) | |||||||
\(444\) | 1.85410 | + | 5.70634i | 0.0879918 | + | 0.270811i | ||||
\(445\) | 7.28115 | − | 5.29007i | 0.345160 | − | 0.250773i | ||||
\(446\) | −16.1803 | + | 11.7557i | −0.766161 | + | 0.556649i | ||||
\(447\) | −10.5066 | − | 32.3359i | −0.496944 | − | 1.52944i | ||||
\(448\) | 4.32624 | − | 13.3148i | 0.204396 | − | 0.629065i | ||||
\(449\) | 10.5172 | + | 7.64121i | 0.496338 | + | 0.360611i | 0.807617 | − | 0.589708i | \(-0.200757\pi\) |
−0.311278 | + | 0.950319i | \(0.600757\pi\) | |||||||
\(450\) | 4.00000 | 0.188562 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 9.00000 | 0.423324 | ||||||||
\(453\) | −25.8885 | − | 18.8091i | −1.21635 | − | 0.883730i | ||||
\(454\) | −7.41641 | + | 22.8254i | −0.348069 | + | 1.07125i | ||||
\(455\) | −0.618034 | − | 1.90211i | −0.0289739 | − | 0.0891724i | ||||
\(456\) | 29.1246 | − | 21.1603i | 1.36388 | − | 0.990920i | ||||
\(457\) | 31.5517 | − | 22.9236i | 1.47592 | − | 1.07232i | 0.497083 | − | 0.867703i | \(-0.334405\pi\) |
0.978842 | − | 0.204619i | \(-0.0655955\pi\) | |||||||
\(458\) | −2.78115 | − | 8.55951i | −0.129955 | − | 0.399960i | ||||
\(459\) | −6.18034 | + | 19.0211i | −0.288474 | + | 0.887830i | ||||
\(460\) | 1.61803 | + | 1.17557i | 0.0754412 | + | 0.0548113i | ||||
\(461\) | −33.0000 | −1.53696 | −0.768482 | − | 0.639872i | \(-0.778987\pi\) | ||||
−0.768482 | + | 0.639872i | \(0.778987\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.0000 | −0.929479 | −0.464739 | − | 0.885448i | \(-0.653852\pi\) | ||||
−0.464739 | + | 0.885448i | \(0.653852\pi\) | |||||||
\(464\) | −7.28115 | − | 5.29007i | −0.338019 | − | 0.245585i | ||||
\(465\) | −1.23607 | + | 3.80423i | −0.0573213 | + | 0.176417i | ||||
\(466\) | −6.48936 | − | 19.9722i | −0.300614 | − | 0.925194i | ||||
\(467\) | −9.70820 | + | 7.05342i | −0.449242 | + | 0.326393i | −0.789296 | − | 0.614012i | \(-0.789555\pi\) |
0.340054 | + | 0.940406i | \(0.389555\pi\) | |||||||
\(468\) | −0.809017 | + | 0.587785i | −0.0373968 | + | 0.0271704i | ||||
\(469\) | 1.23607 | + | 3.80423i | 0.0570763 | + | 0.175663i | ||||
\(470\) | −0.618034 | + | 1.90211i | −0.0285078 | + | 0.0877379i | ||||
\(471\) | −3.23607 | − | 2.35114i | −0.149110 | − | 0.108335i | ||||
\(472\) | 24.0000 | 1.10469 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −20.0000 | −0.918630 | ||||||||
\(475\) | −19.4164 | − | 14.1068i | −0.890886 | − | 0.647266i | ||||
\(476\) | −3.09017 | + | 9.51057i | −0.141638 | + | 0.435916i | ||||
\(477\) | 2.78115 | + | 8.55951i | 0.127340 | + | 0.391913i | ||||
\(478\) | −4.85410 | + | 3.52671i | −0.222021 | + | 0.161308i | ||||
\(479\) | −12.9443 | + | 9.40456i | −0.591439 | + | 0.429705i | −0.842830 | − | 0.538180i | \(-0.819112\pi\) |
0.251391 | + | 0.967886i | \(0.419112\pi\) | |||||||
\(480\) | −3.09017 | − | 9.51057i | −0.141046 | − | 0.434096i | ||||
\(481\) | 0.927051 | − | 2.85317i | 0.0422699 | − | 0.130093i | ||||
\(482\) | −17.7984 | − | 12.9313i | −0.810694 | − | 0.589003i | ||||
\(483\) | 8.00000 | 0.364013 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.0000 | −0.590300 | ||||||||
\(486\) | −8.09017 | − | 5.87785i | −0.366978 | − | 0.266625i | ||||
\(487\) | 0.618034 | − | 1.90211i | 0.0280058 | − | 0.0861930i | −0.936077 | − | 0.351796i | \(-0.885571\pi\) |
0.964082 | + | 0.265603i | \(0.0855711\pi\) | |||||||
\(488\) | −5.56231 | − | 17.1190i | −0.251794 | − | 0.774942i | ||||
\(489\) | 3.23607 | − | 2.35114i | 0.146340 | − | 0.106322i | ||||
\(490\) | −2.42705 | + | 1.76336i | −0.109643 | + | 0.0796603i | ||||
\(491\) | 0.618034 | + | 1.90211i | 0.0278915 | + | 0.0858412i | 0.964033 | − | 0.265782i | \(-0.0856300\pi\) |
−0.936142 | + | 0.351623i | \(0.885630\pi\) | |||||||
\(492\) | −3.09017 | + | 9.51057i | −0.139316 | + | 0.428769i | ||||
\(493\) | 36.4058 | + | 26.4503i | 1.63963 | + | 1.19126i | ||||
\(494\) | −6.00000 | −0.269953 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −19.4164 | − | 14.1068i | −0.870945 | − | 0.632779i | ||||
\(498\) | 3.70820 | − | 11.4127i | 0.166169 | − | 0.511414i | ||||
\(499\) | 2.47214 | + | 7.60845i | 0.110668 | + | 0.340601i | 0.991019 | − | 0.133722i | \(-0.0426929\pi\) |
−0.880351 | + | 0.474323i | \(0.842693\pi\) | |||||||
\(500\) | −7.28115 | + | 5.29007i | −0.325623 | + | 0.236579i | ||||
\(501\) | 19.4164 | − | 14.1068i | 0.867461 | − | 0.630247i | ||||
\(502\) | 0.618034 | + | 1.90211i | 0.0275842 | + | 0.0848955i | ||||
\(503\) | 11.7426 | − | 36.1401i | 0.523579 | − | 1.61141i | −0.243531 | − | 0.969893i | \(-0.578306\pi\) |
0.767109 | − | 0.641516i | \(-0.221694\pi\) | |||||||
\(504\) | −4.85410 | − | 3.52671i | −0.216219 | − | 0.157092i | ||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24.0000 | −1.06588 | ||||||||
\(508\) | 12.9443 | + | 9.40456i | 0.574309 | + | 0.417260i | ||||
\(509\) | −12.9787 | + | 39.9444i | −0.575271 | + | 1.77050i | 0.0599820 | + | 0.998199i | \(0.480896\pi\) |
−0.635253 | + | 0.772304i | \(0.719104\pi\) | |||||||
\(510\) | −3.09017 | − | 9.51057i | −0.136835 | − | 0.421135i | ||||
\(511\) | −3.23607 | + | 2.35114i | −0.143155 | + | 0.104008i | ||||
\(512\) | −8.89919 | + | 6.46564i | −0.393292 | + | 0.285744i | ||||
\(513\) | 7.41641 | + | 22.8254i | 0.327442 | + | 1.00776i | ||||
\(514\) | −5.87132 | + | 18.0701i | −0.258973 | + | 0.797037i | ||||
\(515\) | −6.47214 | − | 4.70228i | −0.285196 | − | 0.207207i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 6.00000 | 0.263625 | ||||||||
\(519\) | 9.70820 | + | 7.05342i | 0.426143 | + | 0.309611i | ||||
\(520\) | −0.927051 | + | 2.85317i | −0.0406539 | + | 0.125120i | ||||
\(521\) | 9.27051 | + | 28.5317i | 0.406148 | + | 1.25000i | 0.919933 | + | 0.392077i | \(0.128243\pi\) |
−0.513784 | + | 0.857920i | \(0.671757\pi\) | |||||||
\(522\) | −7.28115 | + | 5.29007i | −0.318687 | + | 0.231540i | ||||
\(523\) | −12.9443 | + | 9.40456i | −0.566013 | + | 0.411233i | −0.833655 | − | 0.552286i | \(-0.813756\pi\) |
0.267641 | + | 0.963519i | \(0.413756\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.94427 | + | 15.2169i | −0.215786 | + | 0.664120i | ||||
\(526\) | 17.7984 | + | 12.9313i | 0.776046 | + | 0.563830i | ||||
\(527\) | −10.0000 | −0.435607 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 7.28115 | + | 5.29007i | 0.316273 | + | 0.229786i | ||||
\(531\) | 2.47214 | − | 7.60845i | 0.107282 | − | 0.330179i | ||||
\(532\) | 3.70820 | + | 11.4127i | 0.160771 | + | 0.494802i | ||||
\(533\) | 4.04508 | − | 2.93893i | 0.175212 | − | 0.127299i | ||||
\(534\) | −14.5623 | + | 10.5801i | −0.630173 | + | 0.457847i | ||||
\(535\) | −1.85410 | − | 5.70634i | −0.0801598 | − | 0.246707i | ||||
\(536\) | 1.85410 | − | 5.70634i | 0.0800850 | − | 0.246476i | ||||
\(537\) | −38.8328 | − | 28.2137i | −1.67576 | − | 1.21751i | ||||
\(538\) | −1.00000 | −0.0431131 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.00000 | 0.172133 | ||||||||
\(541\) | 27.5066 | + | 19.9847i | 1.18260 | + | 0.859209i | 0.992463 | − | 0.122548i | \(-0.0391066\pi\) |
0.190138 | + | 0.981757i | \(0.439107\pi\) | |||||||
\(542\) | 6.18034 | − | 19.0211i | 0.265468 | − | 0.817028i | ||||
\(543\) | 0.618034 | + | 1.90211i | 0.0265224 | + | 0.0816275i | ||||
\(544\) | 20.2254 | − | 14.6946i | 0.867158 | − | 0.630027i | ||||
\(545\) | −8.89919 | + | 6.46564i | −0.381199 | + | 0.276957i | ||||
\(546\) | 1.23607 | + | 3.80423i | 0.0528988 | + | 0.162806i | ||||
\(547\) | 4.94427 | − | 15.2169i | 0.211402 | − | 0.650628i | −0.787988 | − | 0.615691i | \(-0.788877\pi\) |
0.999390 | − | 0.0349369i | \(-0.0111230\pi\) | |||||||
\(548\) | −8.09017 | − | 5.87785i | −0.345595 | − | 0.251089i | ||||
\(549\) | −6.00000 | −0.256074 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 54.0000 | 2.30048 | ||||||||
\(552\) | −9.70820 | − | 7.05342i | −0.413209 | − | 0.300214i | ||||
\(553\) | 6.18034 | − | 19.0211i | 0.262815 | − | 0.808861i | ||||
\(554\) | 0.309017 | + | 0.951057i | 0.0131289 | + | 0.0404065i | ||||
\(555\) | 4.85410 | − | 3.52671i | 0.206045 | − | 0.149701i | ||||
\(556\) | 1.61803 | − | 1.17557i | 0.0686199 | − | 0.0498553i | ||||
\(557\) | 0.618034 | + | 1.90211i | 0.0261869 | + | 0.0805951i | 0.963296 | − | 0.268442i | \(-0.0865087\pi\) |
−0.937109 | + | 0.349037i | \(0.886509\pi\) | |||||||
\(558\) | 0.618034 | − | 1.90211i | 0.0261635 | − | 0.0805229i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.00000 | −0.0845154 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00000 | 0.253095 | ||||||||
\(563\) | 27.5066 | + | 19.9847i | 1.15926 | + | 0.842255i | 0.989685 | − | 0.143262i | \(-0.0457591\pi\) |
0.169579 | + | 0.985517i | \(0.445759\pi\) | |||||||
\(564\) | −1.23607 | + | 3.80423i | −0.0520479 | + | 0.160187i | ||||
\(565\) | −2.78115 | − | 8.55951i | −0.117004 | − | 0.360101i | ||||
\(566\) | −22.6525 | + | 16.4580i | −0.952155 | + | 0.691781i | ||||
\(567\) | 17.7984 | − | 12.9313i | 0.747461 | − | 0.543063i | ||||
\(568\) | 11.1246 | + | 34.2380i | 0.466778 | + | 1.43660i | ||||
\(569\) | −1.85410 | + | 5.70634i | −0.0777280 | + | 0.239222i | −0.982369 | − | 0.186952i | \(-0.940139\pi\) |
0.904641 | + | 0.426174i | \(0.140139\pi\) | |||||||
\(570\) | −9.70820 | − | 7.05342i | −0.406632 | − | 0.295435i | ||||
\(571\) | 22.0000 | 0.920671 | 0.460336 | − | 0.887745i | \(-0.347729\pi\) | ||||
0.460336 | + | 0.887745i | \(0.347729\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.0000 | 0.668410 | ||||||||
\(574\) | 8.09017 | + | 5.87785i | 0.337677 | + | 0.245337i | ||||
\(575\) | −2.47214 | + | 7.60845i | −0.103095 | + | 0.317294i | ||||
\(576\) | 2.16312 | + | 6.65740i | 0.0901300 | + | 0.277391i | ||||
\(577\) | 16.9894 | − | 12.3435i | 0.707276 | − | 0.513866i | −0.175018 | − | 0.984565i | \(-0.555998\pi\) |
0.882294 | + | 0.470699i | \(0.155998\pi\) | |||||||
\(578\) | 6.47214 | − | 4.70228i | 0.269205 | − | 0.195589i | ||||
\(579\) | 3.09017 | + | 9.51057i | 0.128423 | + | 0.395246i | ||||
\(580\) | 2.78115 | − | 8.55951i | 0.115481 | − | 0.355414i | ||||
\(581\) | 9.70820 | + | 7.05342i | 0.402764 | + | 0.292625i | ||||
\(582\) | 26.0000 | 1.07773 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | 0.809017 | + | 0.587785i | 0.0334487 | + | 0.0243019i | ||||
\(586\) | 2.78115 | − | 8.55951i | 0.114888 | − | 0.353590i | ||||
\(587\) | −4.32624 | − | 13.3148i | −0.178563 | − | 0.549560i | 0.821215 | − | 0.570618i | \(-0.193296\pi\) |
−0.999778 | + | 0.0210582i | \(0.993296\pi\) | |||||||
\(588\) | −4.85410 | + | 3.52671i | −0.200180 | + | 0.145439i | ||||
\(589\) | −9.70820 | + | 7.05342i | −0.400020 | + | 0.290631i | ||||
\(590\) | −2.47214 | − | 7.60845i | −0.101776 | − | 0.313235i | ||||
\(591\) | 6.79837 | − | 20.9232i | 0.279648 | − | 0.860667i | ||||
\(592\) | −2.42705 | − | 1.76336i | −0.0997512 | − | 0.0724735i | ||||
\(593\) | −11.0000 | −0.451716 | −0.225858 | − | 0.974160i | \(-0.572519\pi\) | ||||
−0.225858 | + | 0.974160i | \(0.572519\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.0000 | 0.409960 | ||||||||
\(596\) | −13.7533 | − | 9.99235i | −0.563357 | − | 0.409303i | ||||
\(597\) | 14.8328 | − | 45.6507i | 0.607067 | − | 1.86836i | ||||
\(598\) | 0.618034 | + | 1.90211i | 0.0252733 | + | 0.0777832i | ||||
\(599\) | −27.5066 | + | 19.9847i | −1.12389 | + | 0.816553i | −0.984794 | − | 0.173726i | \(-0.944419\pi\) |
−0.139094 | + | 0.990279i | \(0.544419\pi\) | |||||||
\(600\) | 19.4164 | − | 14.1068i | 0.792672 | − | 0.575910i | ||||
\(601\) | 4.01722 | + | 12.3637i | 0.163866 | + | 0.504327i | 0.998951 | − | 0.0457936i | \(-0.0145816\pi\) |
−0.835085 | + | 0.550121i | \(0.814582\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.61803 | − | 1.17557i | −0.0658914 | − | 0.0478729i | ||||
\(604\) | −16.0000 | −0.651031 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −20.0000 | −0.812444 | ||||||||
\(607\) | −8.09017 | − | 5.87785i | −0.328370 | − | 0.238575i | 0.411369 | − | 0.911469i | \(-0.365051\pi\) |
−0.739739 | + | 0.672894i | \(0.765051\pi\) | |||||||
\(608\) | 9.27051 | − | 28.5317i | 0.375969 | − | 1.15711i | ||||
\(609\) | −11.1246 | − | 34.2380i | −0.450792 | − | 1.38740i | ||||
\(610\) | −4.85410 | + | 3.52671i | −0.196537 | + | 0.142792i | ||||
\(611\) | 1.61803 | − | 1.17557i | 0.0654586 | − | 0.0475585i | ||||
\(612\) | −1.54508 | − | 4.75528i | −0.0624564 | − | 0.192221i | ||||
\(613\) | −5.25329 | + | 16.1680i | −0.212178 | + | 0.653018i | 0.787164 | + | 0.616744i | \(0.211549\pi\) |
−0.999342 | + | 0.0362735i | \(0.988451\pi\) | |||||||
\(614\) | 17.7984 | + | 12.9313i | 0.718284 | + | 0.521864i | ||||
\(615\) | 10.0000 | 0.403239 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.00000 | −0.362326 | −0.181163 | − | 0.983453i | \(-0.557986\pi\) | ||||
−0.181163 | + | 0.983453i | \(0.557986\pi\) | |||||||
\(618\) | 12.9443 | + | 9.40456i | 0.520695 | + | 0.378307i | ||||
\(619\) | 0.618034 | − | 1.90211i | 0.0248409 | − | 0.0764524i | −0.937868 | − | 0.346993i | \(-0.887203\pi\) |
0.962708 | + | 0.270541i | \(0.0872026\pi\) | |||||||
\(620\) | 0.618034 | + | 1.90211i | 0.0248208 | + | 0.0763907i | ||||
\(621\) | 6.47214 | − | 4.70228i | 0.259718 | − | 0.188696i | ||||
\(622\) | 19.4164 | − | 14.1068i | 0.778527 | − | 0.565633i | ||||
\(623\) | −5.56231 | − | 17.1190i | −0.222849 | − | 0.685859i | ||||
\(624\) | 0.618034 | − | 1.90211i | 0.0247412 | − | 0.0761455i | ||||
\(625\) | −8.89919 | − | 6.46564i | −0.355967 | − | 0.258626i | ||||
\(626\) | −23.0000 | −0.919265 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.00000 | −0.0798087 | ||||||||
\(629\) | 12.1353 | + | 8.81678i | 0.483864 | + | 0.351548i | ||||
\(630\) | −0.618034 | + | 1.90211i | −0.0246231 | + | 0.0757820i | ||||
\(631\) | −4.32624 | − | 13.3148i | −0.172225 | − | 0.530053i | 0.827271 | − | 0.561803i | \(-0.189892\pi\) |
−0.999496 | + | 0.0317495i | \(0.989892\pi\) | |||||||
\(632\) | −24.2705 | + | 17.6336i | −0.965429 | + | 0.701425i | ||||
\(633\) | 19.4164 | − | 14.1068i | 0.771733 | − | 0.560697i | ||||
\(634\) | 0.618034 | + | 1.90211i | 0.0245453 | + | 0.0755426i | ||||
\(635\) | 4.94427 | − | 15.2169i | 0.196207 | − | 0.603864i | ||||
\(636\) | 14.5623 | + | 10.5801i | 0.577433 | + | 0.419530i | ||||
\(637\) | 3.00000 | 0.118864 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | 0.474713 | ||||||||
\(640\) | −2.42705 | − | 1.76336i | −0.0959376 | − | 0.0697028i | ||||
\(641\) | −2.78115 | + | 8.55951i | −0.109849 | + | 0.338080i | −0.990838 | − | 0.135057i | \(-0.956878\pi\) |
0.880989 | + | 0.473137i | \(0.156878\pi\) | |||||||
\(642\) | 3.70820 | + | 11.4127i | 0.146351 | + | 0.450422i | ||||
\(643\) | 8.09017 | − | 5.87785i | 0.319045 | − | 0.231800i | −0.416723 | − | 0.909034i | \(-0.636821\pi\) |
0.735768 | + | 0.677234i | \(0.236821\pi\) | |||||||
\(644\) | 3.23607 | − | 2.35114i | 0.127519 | − | 0.0926479i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.27051 | − | 28.5317i | 0.364743 | − | 1.12256i | ||||
\(647\) | −16.1803 | − | 11.7557i | −0.636115 | − | 0.462164i | 0.222398 | − | 0.974956i | \(-0.428611\pi\) |
−0.858513 | + | 0.512791i | \(0.828611\pi\) | |||||||
\(648\) | −33.0000 | −1.29636 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.00000 | −0.156893 | ||||||||
\(651\) | 6.47214 | + | 4.70228i | 0.253663 | + | 0.184297i | ||||
\(652\) | 0.618034 | − | 1.90211i | 0.0242041 | − | 0.0744925i | ||||
\(653\) | −4.32624 | − | 13.3148i | −0.169299 | − | 0.521048i | 0.830029 | − | 0.557721i | \(-0.188324\pi\) |
−0.999327 | + | 0.0366729i | \(0.988324\pi\) | |||||||
\(654\) | 17.7984 | − | 12.9313i | 0.695971 | − | 0.505653i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.54508 | − | 4.75528i | −0.0603254 | − | 0.185663i | ||||
\(657\) | 0.618034 | − | 1.90211i | 0.0241118 | − | 0.0742085i | ||||
\(658\) | 3.23607 | + | 2.35114i | 0.126155 | + | 0.0916570i | ||||
\(659\) | −22.0000 | −0.856998 | −0.428499 | − | 0.903542i | \(-0.640958\pi\) | ||||
−0.428499 | + | 0.903542i | \(0.640958\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.0000 | 0.505641 | 0.252821 | − | 0.967513i | \(-0.418642\pi\) | ||||
0.252821 | + | 0.967513i | \(0.418642\pi\) | |||||||
\(662\) | −16.1803 | − | 11.7557i | −0.628867 | − | 0.456898i | ||||
\(663\) | −3.09017 | + | 9.51057i | −0.120012 | + | 0.369360i | ||||
\(664\) | −5.56231 | − | 17.1190i | −0.215859 | − | 0.664347i | ||||
\(665\) | 9.70820 | − | 7.05342i | 0.376468 | − | 0.273520i | ||||
\(666\) | −2.42705 | + | 1.76336i | −0.0940463 | + | 0.0683286i | ||||
\(667\) | −5.56231 | − | 17.1190i | −0.215373 | − | 0.662851i | ||||
\(668\) | 3.70820 | − | 11.4127i | 0.143475 | − | 0.441570i | ||||
\(669\) | 32.3607 | + | 23.5114i | 1.25114 | + | 0.909004i | ||||
\(670\) | −2.00000 | −0.0772667 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −20.0000 | −0.771517 | ||||||||
\(673\) | −8.09017 | − | 5.87785i | −0.311853 | − | 0.226575i | 0.420838 | − | 0.907136i | \(-0.361736\pi\) |
−0.732691 | + | 0.680561i | \(0.761736\pi\) | |||||||
\(674\) | −4.01722 | + | 12.3637i | −0.154738 | + | 0.476233i | ||||
\(675\) | 4.94427 | + | 15.2169i | 0.190305 | + | 0.585699i | ||||
\(676\) | −9.70820 | + | 7.05342i | −0.373392 | + | 0.271286i | ||||
\(677\) | −21.8435 | + | 15.8702i | −0.839512 | + | 0.609941i | −0.922234 | − | 0.386631i | \(-0.873639\pi\) |
0.0827221 | + | 0.996573i | \(0.473639\pi\) | |||||||
\(678\) | 5.56231 | + | 17.1190i | 0.213619 | + | 0.657452i | ||||
\(679\) | −8.03444 | + | 24.7275i | −0.308334 | + | 0.948953i | ||||
\(680\) | −12.1353 | − | 8.81678i | −0.465366 | − | 0.338108i | ||||
\(681\) | 48.0000 | 1.83936 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.00000 | 0.0765279 | 0.0382639 | − | 0.999268i | \(-0.487817\pi\) | ||||
0.0382639 | + | 0.999268i | \(0.487817\pi\) | |||||||
\(684\) | −4.85410 | − | 3.52671i | −0.185601 | − | 0.134847i | ||||
\(685\) | −3.09017 | + | 9.51057i | −0.118069 | + | 0.363380i | ||||
\(686\) | 6.18034 | + | 19.0211i | 0.235966 | + | 0.726230i | ||||
\(687\) | −14.5623 | + | 10.5801i | −0.555587 | + | 0.403657i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.78115 | − | 8.55951i | −0.105953 | − | 0.326091i | ||||
\(690\) | −1.23607 | + | 3.80423i | −0.0470563 | + | 0.144824i | ||||
\(691\) | −16.1803 | − | 11.7557i | −0.615529 | − | 0.447208i | 0.235828 | − | 0.971795i | \(-0.424220\pi\) |
−0.851357 | + | 0.524587i | \(0.824220\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.0000 | 1.06287 | ||||||||
\(695\) | −1.61803 | − | 1.17557i | −0.0613755 | − | 0.0445919i | ||||
\(696\) | −16.6869 | + | 51.3571i | −0.632516 | + | 1.94668i | ||||
\(697\) | 7.72542 | + | 23.7764i | 0.292621 | + | 0.900596i | ||||
\(698\) | 21.8435 | − | 15.8702i | 0.826787 | − | 0.600696i | ||||
\(699\) | −33.9787 | + | 24.6870i | −1.28519 | + | 0.933747i | ||||
\(700\) | 2.47214 | + | 7.60845i | 0.0934380 | + | 0.287572i | ||||
\(701\) | −5.25329 | + | 16.1680i | −0.198414 | + | 0.610655i | 0.801506 | + | 0.597987i | \(0.204033\pi\) |
−0.999920 | + | 0.0126684i | \(0.995967\pi\) | |||||||
\(702\) | 3.23607 | + | 2.35114i | 0.122138 | + | 0.0887381i | ||||
\(703\) | 18.0000 | 0.678883 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.00000 | 0.150649 | ||||||||
\(706\) | −7.28115 | − | 5.29007i | −0.274030 | − | 0.199094i | ||||
\(707\) | 6.18034 | − | 19.0211i | 0.232436 | − | 0.715363i | ||||
\(708\) | −4.94427 | − | 15.2169i | −0.185817 | − | 0.571886i | ||||
\(709\) | 8.09017 | − | 5.87785i | 0.303833 | − | 0.220747i | −0.425413 | − | 0.904999i | \(-0.639871\pi\) |
0.729246 | + | 0.684252i | \(0.239871\pi\) | |||||||
\(710\) | 9.70820 | − | 7.05342i | 0.364342 | − | 0.264710i | ||||
\(711\) | 3.09017 | + | 9.51057i | 0.115890 | + | 0.356674i | ||||
\(712\) | −8.34346 | + | 25.6785i | −0.312684 | + | 0.962343i | ||||
\(713\) | 3.23607 | + | 2.35114i | 0.121192 | + | 0.0880509i | ||||
\(714\) | −20.0000 | −0.748481 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.0000 | −0.896922 | ||||||||
\(717\) | 9.70820 | + | 7.05342i | 0.362560 | + | 0.263415i | ||||
\(718\) | −0.618034 | + | 1.90211i | −0.0230648 | + | 0.0709862i | ||||
\(719\) | 9.27051 | + | 28.5317i | 0.345732 | + | 1.06405i | 0.961191 | + | 0.275884i | \(0.0889706\pi\) |
−0.615459 | + | 0.788169i | \(0.711029\pi\) | |||||||
\(720\) | 0.809017 | − | 0.587785i | 0.0301503 | − | 0.0219055i | ||||
\(721\) | −12.9443 | + | 9.40456i | −0.482070 | + | 0.350244i | ||||
\(722\) | −5.25329 | − | 16.1680i | −0.195507 | − | 0.601709i | ||||
\(723\) | −13.5967 | + | 41.8465i | −0.505668 | + | 1.55629i | ||||
\(724\) | 0.809017 | + | 0.587785i | 0.0300669 | + | 0.0218449i | ||||
\(725\) | 36.0000 | 1.33701 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.0000 | −1.55769 | −0.778847 | − | 0.627214i | \(-0.784195\pi\) | ||||
−0.778847 | + | 0.627214i | \(0.784195\pi\) | |||||||
\(728\) | 4.85410 | + | 3.52671i | 0.179905 | + | 0.130709i | ||||
\(729\) | 4.01722 | − | 12.3637i | 0.148786 | − | 0.457916i | ||||
\(730\) | −0.618034 | − | 1.90211i | −0.0228745 | − | 0.0704004i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −9.70820 | + | 7.05342i | −0.358826 | + | 0.260702i | ||||
\(733\) | −2.78115 | − | 8.55951i | −0.102724 | − | 0.316153i | 0.886465 | − | 0.462795i | \(-0.153153\pi\) |
−0.989190 | + | 0.146642i | \(0.953153\pi\) | |||||||
\(734\) | 4.32624 | − | 13.3148i | 0.159684 | − | 0.491458i | ||||
\(735\) | 4.85410 | + | 3.52671i | 0.179046 | + | 0.130085i | ||||
\(736\) | −10.0000 | −0.368605 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −5.00000 | −0.184053 | ||||||||
\(739\) | −8.09017 | − | 5.87785i | −0.297602 | − | 0.216220i | 0.428957 | − | 0.903325i | \(-0.358881\pi\) |
−0.726558 | + | 0.687105i | \(0.758881\pi\) | |||||||
\(740\) | 0.927051 | − | 2.85317i | 0.0340791 | − | 0.104885i | ||||
\(741\) | 3.70820 | + | 11.4127i | 0.136224 | + | 0.419255i | ||||
\(742\) | 14.5623 | − | 10.5801i | 0.534599 | − | 0.388409i | ||||
\(743\) | −30.7426 | + | 22.3358i | −1.12784 | + | 0.819422i | −0.985379 | − | 0.170378i | \(-0.945501\pi\) |
−0.142460 | + | 0.989801i | \(0.545501\pi\) | |||||||
\(744\) | −3.70820 | − | 11.4127i | −0.135949 | − | 0.418409i | ||||
\(745\) | −5.25329 | + | 16.1680i | −0.192466 | + | 0.592348i | ||||
\(746\) | −17.7984 | − | 12.9313i | −0.651645 | − | 0.473448i | ||||
\(747\) | −6.00000 | −0.219529 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0000 | −0.438470 | ||||||||
\(750\) | −14.5623 | − | 10.5801i | −0.531740 | − | 0.386332i | ||||
\(751\) | −6.18034 | + | 19.0211i | −0.225524 | + | 0.694091i | 0.772714 | + | 0.634754i | \(0.218899\pi\) |
−0.998238 | + | 0.0593368i | \(0.981101\pi\) | |||||||
\(752\) | −0.618034 | − | 1.90211i | −0.0225374 | − | 0.0693629i | ||||
\(753\) | 3.23607 | − | 2.35114i | 0.117929 | − | 0.0856803i | ||||
\(754\) | 7.28115 | − | 5.29007i | 0.265164 | − | 0.192653i | ||||
\(755\) | 4.94427 | + | 15.2169i | 0.179940 | + | 0.553800i | ||||
\(756\) | 2.47214 | − | 7.60845i | 0.0899107 | − | 0.276717i | ||||
\(757\) | −42.8779 | − | 31.1526i | −1.55842 | − | 1.13226i | −0.937287 | − | 0.348559i | \(-0.886671\pi\) |
−0.621137 | − | 0.783702i | \(-0.713329\pi\) | |||||||
\(758\) | 32.0000 | 1.16229 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −18.0000 | −0.652929 | ||||||||
\(761\) | −16.9894 | − | 12.3435i | −0.615864 | − | 0.447451i | 0.235611 | − | 0.971848i | \(-0.424291\pi\) |
−0.851474 | + | 0.524396i | \(0.824291\pi\) | |||||||
\(762\) | −9.88854 | + | 30.4338i | −0.358224 | + | 1.10250i | ||||
\(763\) | 6.79837 | + | 20.9232i | 0.246118 | + | 0.757472i | ||||
\(764\) | 6.47214 | − | 4.70228i | 0.234154 | − | 0.170123i | ||||
\(765\) | −4.04508 | + | 2.93893i | −0.146250 | + | 0.106257i | ||||
\(766\) | −6.18034 | − | 19.0211i | −0.223305 | − | 0.687261i | ||||
\(767\) | −2.47214 | + | 7.60845i | −0.0892637 | + | 0.274725i | ||||
\(768\) | 27.5066 | + | 19.9847i | 0.992558 | + | 0.721136i | ||||
\(769\) | −11.0000 | −0.396670 | −0.198335 | − | 0.980134i | \(-0.563553\pi\) | ||||
−0.198335 | + | 0.980134i | \(0.563553\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 38.0000 | 1.36854 | ||||||||
\(772\) | 4.04508 | + | 2.93893i | 0.145586 | + | 0.105774i | ||||
\(773\) | −12.9787 | + | 39.9444i | −0.466812 | + | 1.43670i | 0.389878 | + | 0.920867i | \(0.372517\pi\) |
−0.856689 | + | 0.515833i | \(0.827483\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.47214 | + | 4.70228i | −0.232486 | + | 0.168911i | ||||
\(776\) | 31.5517 | − | 22.9236i | 1.13264 | − | 0.822910i | ||||
\(777\) | −3.70820 | − | 11.4127i | −0.133031 | − | 0.409428i | ||||
\(778\) | 0.927051 | − | 2.85317i | 0.0332364 | − | 0.102291i | ||||
\(779\) | 24.2705 | + | 17.6336i | 0.869581 | + | 0.631788i | ||||
\(780\) | 2.00000 | 0.0716115 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −10.0000 | −0.357599 | ||||||||
\(783\) | −29.1246 | − | 21.1603i | −1.04083 | − | 0.756206i | ||||
\(784\) | 0.927051 | − | 2.85317i | 0.0331090 | − | 0.101899i | ||||
\(785\) | 0.618034 | + | 1.90211i | 0.0220586 | + | 0.0678893i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.6525 | − | 16.4580i | 0.807474 | − | 0.586664i | −0.105623 | − | 0.994406i | \(-0.533684\pi\) |
0.913097 | + | 0.407742i | \(0.133684\pi\) | |||||||
\(788\) | −3.39919 | − | 10.4616i | −0.121091 | − | 0.372680i | ||||
\(789\) | 13.5967 | − | 41.8465i | 0.484057 | − | 1.48977i | ||||
\(790\) | 8.09017 | + | 5.87785i | 0.287835 | + | 0.209125i | ||||
\(791\) | −18.0000 | −0.640006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.00000 | 0.213066 | ||||||||
\(794\) | 10.5172 | + | 7.64121i | 0.373242 | + | 0.271176i | ||||
\(795\) | 5.56231 | − | 17.1190i | 0.197275 | − | 0.607149i | ||||
\(796\) | −7.41641 | − | 22.8254i | −0.262868 | − | 0.809023i | ||||
\(797\) | 8.09017 | − | 5.87785i | 0.286569 | − | 0.208204i | −0.435209 | − | 0.900330i | \(-0.643325\pi\) |
0.721777 | + | 0.692125i | \(0.243325\pi\) | |||||||
\(798\) | −19.4164 | + | 14.1068i | −0.687333 | + | 0.499377i | ||||
\(799\) | 3.09017 | + | 9.51057i | 0.109322 | + | 0.336460i | ||||
\(800\) | 6.18034 | − | 19.0211i | 0.218508 | − | 0.672499i | ||||
\(801\) | 7.28115 | + | 5.29007i | 0.257267 | + | 0.186915i | ||||
\(802\) | −23.0000 | −0.812158 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −4.00000 | −0.141069 | ||||||||
\(805\) | −3.23607 | − | 2.35114i | −0.114056 | − | 0.0828668i | ||||
\(806\) | −0.618034 | + | 1.90211i | −0.0217693 | + | 0.0669991i | ||||
\(807\) | 0.618034 | + | 1.90211i | 0.0217558 | + | 0.0669575i | ||||
\(808\) | −24.2705 | + | 17.6336i | −0.853834 | + | 0.620346i | ||||
\(809\) | 4.85410 | − | 3.52671i | 0.170661 | − | 0.123993i | −0.499176 | − | 0.866501i | \(-0.666364\pi\) |
0.669837 | + | 0.742508i | \(0.266364\pi\) | |||||||
\(810\) | 3.39919 | + | 10.4616i | 0.119435 | + | 0.367584i | ||||
\(811\) | −8.65248 | + | 26.6296i | −0.303830 | + | 0.935091i | 0.676282 | + | 0.736643i | \(0.263590\pi\) |
−0.980111 | + | 0.198448i | \(0.936410\pi\) | |||||||
\(812\) | −14.5623 | − | 10.5801i | −0.511037 | − | 0.371290i | ||||
\(813\) | −40.0000 | −1.40286 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.00000 | −0.0700569 | ||||||||
\(816\) | 8.09017 | + | 5.87785i | 0.283213 | + | 0.205766i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −6.48936 | − | 19.9722i | −0.226895 | − | 0.698311i | ||||
\(819\) | 1.61803 | − | 1.17557i | 0.0565387 | − | 0.0410778i | ||||
\(820\) | 4.04508 | − | 2.93893i | 0.141260 | − | 0.102632i | ||||
\(821\) | 0.618034 | + | 1.90211i | 0.0215695 | + | 0.0663842i | 0.961262 | − | 0.275637i | \(-0.0888887\pi\) |
−0.939692 | + | 0.342021i | \(0.888889\pi\) | |||||||
\(822\) | 6.18034 | − | 19.0211i | 0.215564 | − | 0.663438i | ||||
\(823\) | 19.4164 | + | 14.1068i | 0.676813 | + | 0.491734i | 0.872299 | − | 0.488973i | \(-0.162628\pi\) |
−0.195486 | + | 0.980707i | \(0.562628\pi\) | |||||||
\(824\) | 24.0000 | 0.836080 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.0000 | −0.556711 | ||||||||
\(827\) | −8.09017 | − | 5.87785i | −0.281323 | − | 0.204393i | 0.438171 | − | 0.898891i | \(-0.355626\pi\) |
−0.719494 | + | 0.694498i | \(0.755626\pi\) | |||||||
\(828\) | −0.618034 | + | 1.90211i | −0.0214782 | + | 0.0661030i | ||||
\(829\) | −14.5238 | − | 44.6997i | −0.504432 | − | 1.55248i | −0.801723 | − | 0.597696i | \(-0.796083\pi\) |
0.297290 | − | 0.954787i | \(-0.403917\pi\) | |||||||
\(830\) | −4.85410 | + | 3.52671i | −0.168488 | + | 0.122414i | ||||
\(831\) | 1.61803 | − | 1.17557i | 0.0561290 | − | 0.0407801i | ||||
\(832\) | −2.16312 | − | 6.65740i | −0.0749927 | − | 0.230804i | ||||
\(833\) | −4.63525 | + | 14.2658i | −0.160602 | + | 0.494282i | ||||
\(834\) | 3.23607 | + | 2.35114i | 0.112056 | + | 0.0814134i | ||||
\(835\) | −12.0000 | −0.415277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.00000 | 0.276520 | ||||||||
\(838\) | 1.61803 | + | 1.17557i | 0.0558941 | + | 0.0406094i | ||||
\(839\) | 14.2148 | − | 43.7486i | 0.490749 | − | 1.51037i | −0.332730 | − | 0.943022i | \(-0.607970\pi\) |
0.823479 | − | 0.567347i | \(-0.192030\pi\) | |||||||
\(840\) | 3.70820 | + | 11.4127i | 0.127945 | + | 0.393775i | ||||
\(841\) | −42.0689 | + | 30.5648i | −1.45065 | + | 1.05396i | ||||
\(842\) | 10.5172 | − | 7.64121i | 0.362447 | − | 0.263333i | ||||
\(843\) | −3.70820 | − | 11.4127i | −0.127717 | − | 0.393074i | ||||
\(844\) | 3.70820 | − | 11.4127i | 0.127642 | − | 0.392841i | ||||
\(845\) | 9.70820 | + | 7.05342i | 0.333972 | + | 0.242645i | ||||
\(846\) | −2.00000 | −0.0687614 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.00000 | −0.309061 | ||||||||
\(849\) | 45.3050 | + | 32.9160i | 1.55486 | + | 1.12967i | ||||
\(850\) | 6.18034 | − | 19.0211i | 0.211984 | − | 0.652419i | ||||
\(851\) | −1.85410 | − | 5.70634i | −0.0635578 | − | 0.195611i | ||||
\(852\) | 19.4164 | − | 14.1068i | 0.665195 | − | 0.483293i | ||||
\(853\) | 13.7533 | − | 9.99235i | 0.470904 | − | 0.342132i | −0.326890 | − | 0.945062i | \(-0.606001\pi\) |
0.797793 | + | 0.602931i | \(0.206001\pi\) | |||||||
\(854\) | 3.70820 | + | 11.4127i | 0.126892 | + | 0.390534i | ||||
\(855\) | −1.85410 | + | 5.70634i | −0.0634089 | + | 0.195153i | ||||
\(856\) | 14.5623 | + | 10.5801i | 0.497729 | + | 0.361622i | ||||
\(857\) | 22.0000 | 0.751506 | 0.375753 | − | 0.926720i | \(-0.377384\pi\) | ||||
0.375753 | + | 0.926720i | \(0.377384\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.0000 | 0.818869 | 0.409435 | − | 0.912339i | \(-0.365726\pi\) | ||||
0.409435 | + | 0.912339i | \(0.365726\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.18034 | − | 19.0211i | 0.210625 | − | 0.648238i | ||||
\(862\) | 3.70820 | + | 11.4127i | 0.126302 | + | 0.388717i | ||||
\(863\) | 43.6869 | − | 31.7404i | 1.48712 | − | 1.08046i | 0.511946 | − | 0.859018i | \(-0.328925\pi\) |
0.975174 | − | 0.221438i | \(-0.0710750\pi\) | |||||||
\(864\) | −16.1803 | + | 11.7557i | −0.550466 | + | 0.399937i | ||||
\(865\) | −1.85410 | − | 5.70634i | −0.0630414 | − | 0.194021i | ||||
\(866\) | −5.87132 | + | 18.0701i | −0.199516 | + | 0.614046i | ||||
\(867\) | −12.9443 | − | 9.40456i | −0.439611 | − | 0.319396i | ||||
\(868\) | 4.00000 | 0.135769 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 18.0000 | 0.610257 | ||||||||
\(871\) | 1.61803 | + | 1.17557i | 0.0548250 | + | 0.0398327i | ||||
\(872\) | 10.1976 | − | 31.3849i | 0.345333 | − | 1.06283i | ||||
\(873\) | −4.01722 | − | 12.3637i | −0.135962 | − | 0.418449i | ||||
\(874\) | −9.70820 | + | 7.05342i | −0.328385 | + | 0.238586i | ||||
\(875\) | 14.5623 | − | 10.5801i | 0.492296 | − | 0.357674i | ||||
\(876\) | −1.23607 | − | 3.80423i | −0.0417629 | − | 0.128533i | ||||
\(877\) | 8.34346 | − | 25.6785i | 0.281739 | − | 0.867102i | −0.705619 | − | 0.708592i | \(-0.749331\pi\) |
0.987357 | − | 0.158510i | \(-0.0506692\pi\) | |||||||
\(878\) | −17.7984 | − | 12.9313i | −0.600666 | − | 0.436409i | ||||
\(879\) | −18.0000 | −0.607125 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.0000 | 1.17918 | 0.589590 | − | 0.807703i | \(-0.299289\pi\) | ||||
0.589590 | + | 0.807703i | \(0.299289\pi\) | |||||||
\(882\) | −2.42705 | − | 1.76336i | −0.0817231 | − | 0.0593753i | ||||
\(883\) | −6.18034 | + | 19.0211i | −0.207985 | + | 0.640112i | 0.791593 | + | 0.611049i | \(0.209252\pi\) |
−0.999578 | + | 0.0290628i | \(0.990748\pi\) | |||||||
\(884\) | 1.54508 | + | 4.75528i | 0.0519668 | + | 0.159937i | ||||
\(885\) | −12.9443 | + | 9.40456i | −0.435117 | + | 0.316131i | ||||
\(886\) | −16.1803 | + | 11.7557i | −0.543589 | + | 0.394941i | ||||
\(887\) | 14.2148 | + | 43.7486i | 0.477286 | + | 1.46893i | 0.842850 | + | 0.538148i | \(0.180876\pi\) |
−0.365565 | + | 0.930786i | \(0.619124\pi\) | |||||||
\(888\) | −5.56231 | + | 17.1190i | −0.186659 | + | 0.574477i | ||||
\(889\) | −25.8885 | − | 18.8091i | −0.868274 | − | 0.630838i | ||||
\(890\) | 9.00000 | 0.301681 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.0000 | 0.669650 | ||||||||
\(893\) | 9.70820 | + | 7.05342i | 0.324873 | + | 0.236034i | ||||
\(894\) | 10.5066 | − | 32.3359i | 0.351393 | − | 1.08147i | ||||
\(895\) | 7.41641 | + | 22.8254i | 0.247903 | + | 0.762968i | ||||
\(896\) | −4.85410 | + | 3.52671i | −0.162164 | + | 0.117819i | ||||
\(897\) | 3.23607 | − | 2.35114i | 0.108049 | − | 0.0785023i | ||||
\(898\) | 4.01722 | + | 12.3637i | 0.134056 | + | 0.412583i | ||||
\(899\) | 5.56231 | − | 17.1190i | 0.185513 | − | 0.570951i | ||||
\(900\) | −3.23607 | − | 2.35114i | −0.107869 | − | 0.0783714i | ||||
\(901\) | 45.0000 | 1.49917 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21.8435 | + | 15.8702i | 0.726503 | + | 0.527835i | ||||
\(905\) | 0.309017 | − | 0.951057i | 0.0102721 | − | 0.0316142i | ||||
\(906\) | −9.88854 | − | 30.4338i | −0.328525 | − | 1.01110i | ||||
\(907\) | −9.70820 | + | 7.05342i | −0.322356 | + | 0.234205i | −0.737180 | − | 0.675696i | \(-0.763843\pi\) |
0.414824 | + | 0.909902i | \(0.363843\pi\) | |||||||
\(908\) | 19.4164 | − | 14.1068i | 0.644356 | − | 0.468152i | ||||
\(909\) | 3.09017 | + | 9.51057i | 0.102494 | + | 0.315446i | ||||
\(910\) | 0.618034 | − | 1.90211i | 0.0204876 | − | 0.0630544i | ||||
\(911\) | 19.4164 | + | 14.1068i | 0.643294 | + | 0.467381i | 0.860980 | − | 0.508638i | \(-0.169851\pi\) |
−0.217686 | + | 0.976019i | \(0.569851\pi\) | |||||||
\(912\) | 12.0000 | 0.397360 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 39.0000 | 1.29001 | ||||||||
\(915\) | 9.70820 | + | 7.05342i | 0.320943 | + | 0.233179i | ||||
\(916\) | −2.78115 | + | 8.55951i | −0.0918919 | + | 0.282814i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −16.1803 | + | 11.7557i | −0.534031 | + | 0.387996i | ||||
\(919\) | 22.6525 | − | 16.4580i | 0.747236 | − | 0.542899i | −0.147733 | − | 0.989027i | \(-0.547198\pi\) |
0.894969 | + | 0.446128i | \(0.147198\pi\) | |||||||
\(920\) | 1.85410 | + | 5.70634i | 0.0611279 | + | 0.188132i | ||||
\(921\) | 13.5967 | − | 41.8465i | 0.448028 | − | 1.37889i | ||||
\(922\) | −26.6976 | − | 19.3969i | −0.879237 | − | 0.638803i | ||||
\(923\) | −12.0000 | −0.394985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.0000 | 0.394558 | ||||||||
\(926\) | −16.1803 | − | 11.7557i | −0.531719 | − | 0.386316i | ||||
\(927\) | 2.47214 | − | 7.60845i | 0.0811956 | − | 0.249894i | ||||
\(928\) | 13.9058 | + | 42.7975i | 0.456479 | + | 1.40490i | ||||
\(929\) | 16.9894 | − | 12.3435i | 0.557403 | − | 0.404977i | −0.273105 | − | 0.961984i | \(-0.588051\pi\) |
0.830507 | + | 0.557008i | \(0.188051\pi\) | |||||||
\(930\) | −3.23607 | + | 2.35114i | −0.106115 | + | 0.0770970i | ||||
\(931\) | 5.56231 | + | 17.1190i | 0.182297 | + | 0.561053i | ||||
\(932\) | −6.48936 | + | 19.9722i | −0.212566 | + | 0.654211i | ||||
\(933\) | −38.8328 | − | 28.2137i | −1.27133 | − | 0.923675i | ||||
\(934\) | −12.0000 | −0.392652 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.00000 | −0.0980581 | ||||||||
\(937\) | 18.6074 | + | 13.5191i | 0.607877 | + | 0.441648i | 0.848666 | − | 0.528929i | \(-0.177406\pi\) |
−0.240789 | + | 0.970577i | \(0.577406\pi\) | |||||||
\(938\) | −1.23607 | + | 3.80423i | −0.0403591 | + | 0.124212i | ||||
\(939\) | 14.2148 | + | 43.7486i | 0.463882 | + | 1.42768i | ||||
\(940\) | 1.61803 | − | 1.17557i | 0.0527744 | − | 0.0383429i | ||||
\(941\) | −21.8435 | + | 15.8702i | −0.712076 | + | 0.517354i | −0.883843 | − | 0.467784i | \(-0.845053\pi\) |
0.171766 | + | 0.985138i | \(0.445053\pi\) | |||||||
\(942\) | −1.23607 | − | 3.80423i | −0.0402733 | − | 0.123948i | ||||
\(943\) | 3.09017 | − | 9.51057i | 0.100630 | − | 0.309707i | ||||
\(944\) | 6.47214 | + | 4.70228i | 0.210650 | + | 0.153046i | ||||
\(945\) | −8.00000 | −0.260240 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.0000 | −1.36482 | −0.682408 | − | 0.730971i | \(-0.739067\pi\) | ||||
−0.682408 | + | 0.730971i | \(0.739067\pi\) | |||||||
\(948\) | 16.1803 | + | 11.7557i | 0.525513 | + | 0.381808i | ||||
\(949\) | −0.618034 | + | 1.90211i | −0.0200622 | + | 0.0617452i | ||||
\(950\) | −7.41641 | − | 22.8254i | −0.240620 | − | 0.740552i | ||||
\(951\) | 3.23607 | − | 2.35114i | 0.104937 | − | 0.0762410i | ||||
\(952\) | −24.2705 | + | 17.6336i | −0.786612 | + | 0.571507i | ||||
\(953\) | −9.57953 | − | 29.4828i | −0.310311 | − | 0.955040i | −0.977642 | − | 0.210278i | \(-0.932563\pi\) |
0.667330 | − | 0.744762i | \(-0.267437\pi\) | |||||||
\(954\) | −2.78115 | + | 8.55951i | −0.0900432 | + | 0.277124i | ||||
\(955\) | −6.47214 | − | 4.70228i | −0.209433 | − | 0.152162i | ||||
\(956\) | 6.00000 | 0.194054 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.0000 | −0.516937 | ||||||||
\(959\) | 16.1803 | + | 11.7557i | 0.522490 | + | 0.379612i | ||||
\(960\) | 4.32624 | − | 13.3148i | 0.139629 | − | 0.429733i | ||||
\(961\) | −8.34346 | − | 25.6785i | −0.269144 | − | 0.828340i | ||||
\(962\) | 2.42705 | − | 1.76336i | 0.0782513 | − | 0.0568529i | ||||
\(963\) | 4.85410 | − | 3.52671i | 0.156421 | − | 0.113647i | ||||
\(964\) | 6.79837 | + | 20.9232i | 0.218961 | + | 0.673892i | ||||
\(965\) | 1.54508 | − | 4.75528i | 0.0497380 | − | 0.153078i | ||||
\(966\) | 6.47214 | + | 4.70228i | 0.208238 | + | 0.151293i | ||||
\(967\) | −22.0000 | −0.707472 | −0.353736 | − | 0.935345i | \(-0.615089\pi\) | ||||
−0.353736 | + | 0.935345i | \(0.615089\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −60.0000 | −1.92748 | ||||||||
\(970\) | −10.5172 | − | 7.64121i | −0.337688 | − | 0.245344i | ||||
\(971\) | 0.618034 | − | 1.90211i | 0.0198337 | − | 0.0610417i | −0.940650 | − | 0.339379i | \(-0.889783\pi\) |
0.960483 | + | 0.278337i | \(0.0897832\pi\) | |||||||
\(972\) | 3.09017 | + | 9.51057i | 0.0991172 | + | 0.305052i | ||||
\(973\) | −3.23607 | + | 2.35114i | −0.103744 | + | 0.0753741i | ||||
\(974\) | 1.61803 | − | 1.17557i | 0.0518452 | − | 0.0376677i | ||||
\(975\) | 2.47214 | + | 7.60845i | 0.0791717 | + | 0.243665i | ||||
\(976\) | 1.85410 | − | 5.70634i | 0.0593484 | − | 0.182655i | ||||
\(977\) | 46.1140 | + | 33.5038i | 1.47532 | + | 1.07188i | 0.979029 | + | 0.203722i | \(0.0653039\pi\) |
0.496288 | + | 0.868158i | \(0.334696\pi\) | |||||||
\(978\) | 4.00000 | 0.127906 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 3.00000 | 0.0958315 | ||||||||
\(981\) | −8.89919 | − | 6.46564i | −0.284129 | − | 0.206432i | ||||
\(982\) | −0.618034 | + | 1.90211i | −0.0197223 | + | 0.0606989i | ||||
\(983\) | −11.1246 | − | 34.2380i | −0.354820 | − | 1.09202i | −0.956114 | − | 0.292996i | \(-0.905348\pi\) |
0.601294 | − | 0.799028i | \(-0.294652\pi\) | |||||||
\(984\) | −24.2705 | + | 17.6336i | −0.773716 | + | 0.562137i | ||||
\(985\) | −8.89919 | + | 6.46564i | −0.283552 | + | 0.206012i | ||||
\(986\) | 13.9058 | + | 42.7975i | 0.442850 | + | 1.36295i | ||||
\(987\) | 2.47214 | − | 7.60845i | 0.0786890 | − | 0.242180i | ||||
\(988\) | 4.85410 | + | 3.52671i | 0.154430 | + | 0.112200i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.0000 | −0.635321 | −0.317660 | − | 0.948205i | \(-0.602897\pi\) | ||||
−0.317660 | + | 0.948205i | \(0.602897\pi\) | |||||||
\(992\) | −8.09017 | − | 5.87785i | −0.256863 | − | 0.186622i | ||||
\(993\) | −12.3607 | + | 38.0423i | −0.392254 | + | 1.20723i | ||||
\(994\) | −7.41641 | − | 22.8254i | −0.235234 | − | 0.723976i | ||||
\(995\) | −19.4164 | + | 14.1068i | −0.615542 | + | 0.447217i | ||||
\(996\) | −9.70820 | + | 7.05342i | −0.307616 | + | 0.223496i | ||||
\(997\) | −16.3779 | − | 50.4060i | −0.518693 | − | 1.59637i | −0.776460 | − | 0.630167i | \(-0.782987\pi\) |
0.257767 | − | 0.966207i | \(-0.417013\pi\) | |||||||
\(998\) | −2.47214 | + | 7.60845i | −0.0782541 | + | 0.240841i | ||||
\(999\) | −9.70820 | − | 7.05342i | −0.307154 | − | 0.223160i |
(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 | 121.2.c.d.81.1 | 4 | ||
11.2 | odd | 10 | 121.2.c.b.27.1 | 4 | |||
11.3 | even | 5 | inner | 121.2.c.d.3.1 | 4 | ||
11.4 | even | 5 | inner | 121.2.c.d.9.1 | 4 | ||
11.5 | even | 5 | 121.2.a.a.1.1 | ✓ | 1 | ||
11.6 | odd | 10 | 121.2.a.c.1.1 | yes | 1 | ||
11.7 | odd | 10 | 121.2.c.b.9.1 | 4 | |||
11.8 | odd | 10 | 121.2.c.b.3.1 | 4 | |||
11.9 | even | 5 | inner | 121.2.c.d.27.1 | 4 | ||
11.10 | odd | 2 | 121.2.c.b.81.1 | 4 | |||
33.5 | odd | 10 | 1089.2.a.i.1.1 | 1 | |||
33.17 | even | 10 | 1089.2.a.c.1.1 | 1 | |||
44.27 | odd | 10 | 1936.2.a.a.1.1 | 1 | |||
44.39 | even | 10 | 1936.2.a.b.1.1 | 1 | |||
55.39 | odd | 10 | 3025.2.a.b.1.1 | 1 | |||
55.49 | even | 10 | 3025.2.a.e.1.1 | 1 | |||
77.6 | even | 10 | 5929.2.a.g.1.1 | 1 | |||
77.27 | odd | 10 | 5929.2.a.a.1.1 | 1 | |||
88.5 | even | 10 | 7744.2.a.f.1.1 | 1 | |||
88.27 | odd | 10 | 7744.2.a.be.1.1 | 1 | |||
88.61 | odd | 10 | 7744.2.a.c.1.1 | 1 | |||
88.83 | even | 10 | 7744.2.a.bf.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
121.2.a.a.1.1 | ✓ | 1 | 11.5 | even | 5 | ||
121.2.a.c.1.1 | yes | 1 | 11.6 | odd | 10 | ||
121.2.c.b.3.1 | 4 | 11.8 | odd | 10 | |||
121.2.c.b.9.1 | 4 | 11.7 | odd | 10 | |||
121.2.c.b.27.1 | 4 | 11.2 | odd | 10 | |||
121.2.c.b.81.1 | 4 | 11.10 | odd | 2 | |||
121.2.c.d.3.1 | 4 | 11.3 | even | 5 | inner | ||
121.2.c.d.9.1 | 4 | 11.4 | even | 5 | inner | ||
121.2.c.d.27.1 | 4 | 11.9 | even | 5 | inner | ||
121.2.c.d.81.1 | 4 | 1.1 | even | 1 | trivial | ||
1089.2.a.c.1.1 | 1 | 33.17 | even | 10 | |||
1089.2.a.i.1.1 | 1 | 33.5 | odd | 10 | |||
1936.2.a.a.1.1 | 1 | 44.27 | odd | 10 | |||
1936.2.a.b.1.1 | 1 | 44.39 | even | 10 | |||
3025.2.a.b.1.1 | 1 | 55.39 | odd | 10 | |||
3025.2.a.e.1.1 | 1 | 55.49 | even | 10 | |||
5929.2.a.a.1.1 | 1 | 77.27 | odd | 10 | |||
5929.2.a.g.1.1 | 1 | 77.6 | even | 10 | |||
7744.2.a.c.1.1 | 1 | 88.61 | odd | 10 | |||
7744.2.a.f.1.1 | 1 | 88.5 | even | 10 | |||
7744.2.a.be.1.1 | 1 | 88.27 | odd | 10 | |||
7744.2.a.bf.1.1 | 1 | 88.83 | even | 10 |