Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (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: | \(6.76332905120\) |
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 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 323.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.323 |
Dual form | 847.2.f.k.729.1 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 | ||||
\(5\) | 1.61803 | − | 1.17557i | 0.723607 | − | 0.525731i | −0.163928 | − | 0.986472i | \(-0.552416\pi\) |
0.887535 | + | 0.460741i | \(0.152416\pi\) | |||||||
\(6\) | 1.61803 | − | 1.17557i | 0.660560 | − | 0.479925i | ||||
\(7\) | 0.309017 | + | 0.951057i | 0.116797 | + | 0.359466i | ||||
\(8\) | 0.927051 | − | 2.85317i | 0.327762 | − | 1.00875i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | 2.00000 | 0.632456 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.00000 | −0.577350 | ||||||||
\(13\) | 3.23607 | + | 2.35114i | 0.897524 | + | 0.652089i | 0.937829 | − | 0.347098i | \(-0.112833\pi\) |
−0.0403050 | + | 0.999187i | \(0.512833\pi\) | |||||||
\(14\) | −0.309017 | + | 0.951057i | −0.0825883 | + | 0.254181i | ||||
\(15\) | −1.23607 | − | 3.80423i | −0.319151 | − | 0.982247i | ||||
\(16\) | 0.809017 | − | 0.587785i | 0.202254 | − | 0.146946i | ||||
\(17\) | 3.23607 | − | 2.35114i | 0.784862 | − | 0.570235i | −0.121572 | − | 0.992583i | \(-0.538794\pi\) |
0.906434 | + | 0.422347i | \(0.138794\pi\) | |||||||
\(18\) | −0.309017 | − | 0.951057i | −0.0728360 | − | 0.224166i | ||||
\(19\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(20\) | −1.61803 | − | 1.17557i | −0.361803 | − | 0.262866i | ||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | −4.85410 | − | 3.52671i | −0.990839 | − | 0.719887i | ||||
\(25\) | −0.309017 | + | 0.951057i | −0.0618034 | + | 0.190211i | ||||
\(26\) | 1.23607 | + | 3.80423i | 0.242413 | + | 0.746070i | ||||
\(27\) | 3.23607 | − | 2.35114i | 0.622782 | − | 0.452477i | ||||
\(28\) | 0.809017 | − | 0.587785i | 0.152890 | − | 0.111081i | ||||
\(29\) | 1.85410 | + | 5.70634i | 0.344298 | + | 1.05964i | 0.961958 | + | 0.273196i | \(0.0880806\pi\) |
−0.617660 | + | 0.786445i | \(0.711919\pi\) | |||||||
\(30\) | 1.23607 | − | 3.80423i | 0.225674 | − | 0.694553i | ||||
\(31\) | −8.09017 | − | 5.87785i | −1.45304 | − | 1.05569i | −0.985110 | − | 0.171927i | \(-0.945001\pi\) |
−0.467928 | − | 0.883767i | \(-0.654999\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 1.61803 | + | 1.17557i | 0.273498 | + | 0.198708i | ||||
\(36\) | −0.309017 | + | 0.951057i | −0.0515028 | + | 0.158509i | ||||
\(37\) | −1.85410 | − | 5.70634i | −0.304812 | − | 0.938116i | −0.979747 | − | 0.200239i | \(-0.935828\pi\) |
0.674935 | − | 0.737878i | \(-0.264172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.47214 | − | 4.70228i | 1.03637 | − | 0.752968i | ||||
\(40\) | −1.85410 | − | 5.70634i | −0.293159 | − | 0.902251i | ||||
\(41\) | −1.23607 | + | 3.80423i | −0.193041 | + | 0.594120i | 0.806952 | + | 0.590616i | \(0.201115\pi\) |
−0.999994 | + | 0.00350392i | \(0.998885\pi\) | |||||||
\(42\) | 1.61803 | + | 1.17557i | 0.249668 | + | 0.181394i | ||||
\(43\) | −12.0000 | −1.82998 | −0.914991 | − | 0.403473i | \(-0.867803\pi\) | ||||
−0.914991 | + | 0.403473i | \(0.867803\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.00000 | −0.298142 | ||||||||
\(46\) | −3.23607 | − | 2.35114i | −0.477132 | − | 0.346657i | ||||
\(47\) | −3.09017 | + | 9.51057i | −0.450748 | + | 1.38726i | 0.425308 | + | 0.905049i | \(0.360166\pi\) |
−0.876056 | + | 0.482210i | \(0.839834\pi\) | |||||||
\(48\) | −0.618034 | − | 1.90211i | −0.0892055 | − | 0.274546i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | −0.809017 | + | 0.587785i | −0.114412 | + | 0.0831254i | ||||
\(51\) | −2.47214 | − | 7.60845i | −0.346168 | − | 1.06540i | ||||
\(52\) | 1.23607 | − | 3.80423i | 0.171412 | − | 0.527551i | ||||
\(53\) | 4.85410 | + | 3.52671i | 0.666762 | + | 0.484431i | 0.868940 | − | 0.494918i | \(-0.164802\pi\) |
−0.202178 | + | 0.979349i | \(0.564802\pi\) | |||||||
\(54\) | 4.00000 | 0.544331 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.85410 | + | 5.70634i | −0.243456 | + | 0.749279i | ||||
\(59\) | 0.618034 | + | 1.90211i | 0.0804612 | + | 0.247634i | 0.983193 | − | 0.182570i | \(-0.0584416\pi\) |
−0.902732 | + | 0.430204i | \(0.858442\pi\) | |||||||
\(60\) | −3.23607 | + | 2.35114i | −0.417775 | + | 0.303531i | ||||
\(61\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(62\) | −3.09017 | − | 9.51057i | −0.392452 | − | 1.20784i | ||||
\(63\) | 0.309017 | − | 0.951057i | 0.0389325 | − | 0.119822i | ||||
\(64\) | −5.66312 | − | 4.11450i | −0.707890 | − | 0.514312i | ||||
\(65\) | 8.00000 | 0.992278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | −3.23607 | − | 2.35114i | −0.392431 | − | 0.285118i | ||||
\(69\) | −2.47214 | + | 7.60845i | −0.297610 | + | 0.915950i | ||||
\(70\) | 0.618034 | + | 1.90211i | 0.0738692 | + | 0.227346i | ||||
\(71\) | 9.70820 | − | 7.05342i | 1.15215 | − | 0.837087i | 0.163386 | − | 0.986562i | \(-0.447758\pi\) |
0.988766 | + | 0.149475i | \(0.0477583\pi\) | |||||||
\(72\) | −2.42705 | + | 1.76336i | −0.286031 | + | 0.207813i | ||||
\(73\) | 2.47214 | + | 7.60845i | 0.289342 | + | 0.890502i | 0.985064 | + | 0.172191i | \(0.0550846\pi\) |
−0.695722 | + | 0.718311i | \(0.744915\pi\) | |||||||
\(74\) | 1.85410 | − | 5.70634i | 0.215535 | − | 0.663348i | ||||
\(75\) | 1.61803 | + | 1.17557i | 0.186834 | + | 0.135743i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 8.00000 | 0.905822 | ||||||||
\(79\) | 6.47214 | + | 4.70228i | 0.728172 | + | 0.529048i | 0.888985 | − | 0.457937i | \(-0.151411\pi\) |
−0.160813 | + | 0.986985i | \(0.551411\pi\) | |||||||
\(80\) | 0.618034 | − | 1.90211i | 0.0690983 | − | 0.212663i | ||||
\(81\) | −3.39919 | − | 10.4616i | −0.377687 | − | 1.16240i | ||||
\(82\) | −3.23607 | + | 2.35114i | −0.357364 | + | 0.259640i | ||||
\(83\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(84\) | −0.618034 | − | 1.90211i | −0.0674330 | − | 0.207538i | ||||
\(85\) | 2.47214 | − | 7.60845i | 0.268141 | − | 0.825253i | ||||
\(86\) | −9.70820 | − | 7.05342i | −1.04686 | − | 0.760590i | ||||
\(87\) | 12.0000 | 1.28654 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | −1.61803 | − | 1.17557i | −0.170556 | − | 0.123916i | ||||
\(91\) | −1.23607 | + | 3.80423i | −0.129575 | + | 0.398791i | ||||
\(92\) | 1.23607 | + | 3.80423i | 0.128869 | + | 0.396618i | ||||
\(93\) | −16.1803 | + | 11.7557i | −1.67782 | + | 1.21901i | ||||
\(94\) | −8.09017 | + | 5.87785i | −0.834437 | + | 0.606254i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.09017 | + | 9.51057i | −0.315389 | + | 0.970668i | ||||
\(97\) | 8.09017 | + | 5.87785i | 0.821432 | + | 0.596806i | 0.917122 | − | 0.398606i | \(-0.130506\pi\) |
−0.0956901 | + | 0.995411i | \(0.530506\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −3.23607 | − | 2.35114i | −0.322001 | − | 0.233947i | 0.415028 | − | 0.909809i | \(-0.363772\pi\) |
−0.737029 | + | 0.675861i | \(0.763772\pi\) | |||||||
\(102\) | 2.47214 | − | 7.60845i | 0.244778 | − | 0.753349i | ||||
\(103\) | 4.32624 | + | 13.3148i | 0.426277 | + | 1.31195i | 0.901766 | + | 0.432224i | \(0.142271\pi\) |
−0.475489 | + | 0.879721i | \(0.657729\pi\) | |||||||
\(104\) | 9.70820 | − | 7.05342i | 0.951968 | − | 0.691645i | ||||
\(105\) | 3.23607 | − | 2.35114i | 0.315808 | − | 0.229448i | ||||
\(106\) | 1.85410 | + | 5.70634i | 0.180086 | + | 0.554249i | ||||
\(107\) | −3.70820 | + | 11.4127i | −0.358486 | + | 1.10331i | 0.595475 | + | 0.803374i | \(0.296964\pi\) |
−0.953961 | + | 0.299932i | \(0.903036\pi\) | |||||||
\(108\) | −3.23607 | − | 2.35114i | −0.311391 | − | 0.226239i | ||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.0000 | −1.13899 | ||||||||
\(112\) | 0.809017 | + | 0.587785i | 0.0764449 | + | 0.0555405i | ||||
\(113\) | 5.56231 | − | 17.1190i | 0.523258 | − | 1.61042i | −0.244478 | − | 0.969655i | \(-0.578617\pi\) |
0.767736 | − | 0.640767i | \(-0.221383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.47214 | + | 4.70228i | −0.603530 | + | 0.438490i | ||||
\(116\) | 4.85410 | − | 3.52671i | 0.450692 | − | 0.327447i | ||||
\(117\) | −1.23607 | − | 3.80423i | −0.114275 | − | 0.351701i | ||||
\(118\) | −0.618034 | + | 1.90211i | −0.0568946 | + | 0.175104i | ||||
\(119\) | 3.23607 | + | 2.35114i | 0.296650 | + | 0.215529i | ||||
\(120\) | −12.0000 | −1.09545 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.47214 | + | 4.70228i | 0.583573 | + | 0.423990i | ||||
\(124\) | −3.09017 | + | 9.51057i | −0.277505 | + | 0.854074i | ||||
\(125\) | 3.70820 | + | 11.4127i | 0.331672 | + | 1.02078i | ||||
\(126\) | 0.809017 | − | 0.587785i | 0.0720730 | − | 0.0523641i | ||||
\(127\) | 6.47214 | − | 4.70228i | 0.574309 | − | 0.417260i | −0.262359 | − | 0.964970i | \(-0.584500\pi\) |
0.836668 | + | 0.547710i | \(0.184500\pi\) | |||||||
\(128\) | 0.927051 | + | 2.85317i | 0.0819405 | + | 0.252187i | ||||
\(129\) | −7.41641 | + | 22.8254i | −0.652978 | + | 2.00966i | ||||
\(130\) | 6.47214 | + | 4.70228i | 0.567644 | + | 0.412417i | ||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.47214 | + | 4.70228i | 0.559107 | + | 0.406215i | ||||
\(135\) | 2.47214 | − | 7.60845i | 0.212768 | − | 0.654831i | ||||
\(136\) | −3.70820 | − | 11.4127i | −0.317976 | − | 0.978629i | ||||
\(137\) | 8.09017 | − | 5.87785i | 0.691190 | − | 0.502179i | −0.185861 | − | 0.982576i | \(-0.559507\pi\) |
0.877051 | + | 0.480397i | \(0.159507\pi\) | |||||||
\(138\) | −6.47214 | + | 4.70228i | −0.550945 | + | 0.400285i | ||||
\(139\) | 2.47214 | + | 7.60845i | 0.209684 | + | 0.645340i | 0.999488 | + | 0.0319820i | \(0.0101819\pi\) |
−0.789805 | + | 0.613359i | \(0.789818\pi\) | |||||||
\(140\) | 0.618034 | − | 1.90211i | 0.0522334 | − | 0.160758i | ||||
\(141\) | 16.1803 | + | 11.7557i | 1.36263 | + | 0.990009i | ||||
\(142\) | 12.0000 | 1.00702 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 9.70820 | + | 7.05342i | 0.806222 | + | 0.585755i | ||||
\(146\) | −2.47214 | + | 7.60845i | −0.204595 | + | 0.629680i | ||||
\(147\) | 0.618034 | + | 1.90211i | 0.0509746 | + | 0.156884i | ||||
\(148\) | −4.85410 | + | 3.52671i | −0.399005 | + | 0.289894i | ||||
\(149\) | −8.09017 | + | 5.87785i | −0.662773 | + | 0.481532i | −0.867598 | − | 0.497266i | \(-0.834337\pi\) |
0.204826 | + | 0.978798i | \(0.434337\pi\) | |||||||
\(150\) | 0.618034 | + | 1.90211i | 0.0504623 | + | 0.155307i | ||||
\(151\) | 4.94427 | − | 15.2169i | 0.402359 | − | 1.23833i | −0.520721 | − | 0.853727i | \(-0.674337\pi\) |
0.923080 | − | 0.384607i | \(-0.125663\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.0000 | −1.60644 | ||||||||
\(156\) | −6.47214 | − | 4.70228i | −0.518186 | − | 0.376484i | ||||
\(157\) | 4.32624 | − | 13.3148i | 0.345271 | − | 1.06264i | −0.616167 | − | 0.787616i | \(-0.711315\pi\) |
0.961438 | − | 0.275020i | \(-0.0886846\pi\) | |||||||
\(158\) | 2.47214 | + | 7.60845i | 0.196673 | + | 0.605296i | ||||
\(159\) | 9.70820 | − | 7.05342i | 0.769911 | − | 0.559373i | ||||
\(160\) | −8.09017 | + | 5.87785i | −0.639584 | + | 0.464685i | ||||
\(161\) | −1.23607 | − | 3.80423i | −0.0974158 | − | 0.299815i | ||||
\(162\) | 3.39919 | − | 10.4616i | 0.267065 | − | 0.821943i | ||||
\(163\) | 6.47214 | + | 4.70228i | 0.506937 | + | 0.368311i | 0.811660 | − | 0.584130i | \(-0.198564\pi\) |
−0.304724 | + | 0.952441i | \(0.598564\pi\) | |||||||
\(164\) | 4.00000 | 0.312348 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(168\) | 1.85410 | − | 5.70634i | 0.143047 | − | 0.440254i | ||||
\(169\) | 0.927051 | + | 2.85317i | 0.0713116 | + | 0.219475i | ||||
\(170\) | 6.47214 | − | 4.70228i | 0.496390 | − | 0.360649i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.70820 | + | 11.4127i | 0.282748 | + | 0.870209i | ||||
\(173\) | −3.70820 | + | 11.4127i | −0.281930 | + | 0.867690i | 0.705373 | + | 0.708837i | \(0.250780\pi\) |
−0.987302 | + | 0.158853i | \(0.949220\pi\) | |||||||
\(174\) | 9.70820 | + | 7.05342i | 0.735977 | + | 0.534719i | ||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.00000 | 0.300658 | ||||||||
\(178\) | −4.85410 | − | 3.52671i | −0.363830 | − | 0.264338i | ||||
\(179\) | 3.70820 | − | 11.4127i | 0.277164 | − | 0.853024i | −0.711474 | − | 0.702712i | \(-0.751972\pi\) |
0.988639 | − | 0.150312i | \(-0.0480277\pi\) | |||||||
\(180\) | 0.618034 | + | 1.90211i | 0.0460655 | + | 0.141775i | ||||
\(181\) | −8.09017 | + | 5.87785i | −0.601338 | + | 0.436897i | −0.846353 | − | 0.532622i | \(-0.821207\pi\) |
0.245016 | + | 0.969519i | \(0.421207\pi\) | |||||||
\(182\) | −3.23607 | + | 2.35114i | −0.239873 | + | 0.174278i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.70820 | + | 11.4127i | −0.273372 | + | 0.841354i | ||||
\(185\) | −9.70820 | − | 7.05342i | −0.713761 | − | 0.518578i | ||||
\(186\) | −20.0000 | −1.46647 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 10.0000 | 0.729325 | ||||||||
\(189\) | 3.23607 | + | 2.35114i | 0.235389 | + | 0.171020i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 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 | ||||
\(193\) | −11.3262 | + | 8.22899i | −0.815280 | + | 0.592336i | −0.915357 | − | 0.402644i | \(-0.868091\pi\) |
0.100076 | + | 0.994980i | \(0.468091\pi\) | |||||||
\(194\) | 3.09017 | + | 9.51057i | 0.221861 | + | 0.682819i | ||||
\(195\) | 4.94427 | − | 15.2169i | 0.354067 | − | 1.08971i | ||||
\(196\) | 0.809017 | + | 0.587785i | 0.0577869 | + | 0.0419847i | ||||
\(197\) | −22.0000 | −1.56744 | −0.783718 | − | 0.621117i | \(-0.786679\pi\) | ||||
−0.783718 | + | 0.621117i | \(0.786679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.0000 | −1.27599 | −0.637993 | − | 0.770042i | \(-0.720235\pi\) | ||||
−0.637993 | + | 0.770042i | \(0.720235\pi\) | |||||||
\(200\) | 2.42705 | + | 1.76336i | 0.171618 | + | 0.124688i | ||||
\(201\) | 4.94427 | − | 15.2169i | 0.348742 | − | 1.07332i | ||||
\(202\) | −1.23607 | − | 3.80423i | −0.0869694 | − | 0.267664i | ||||
\(203\) | −4.85410 | + | 3.52671i | −0.340691 | + | 0.247527i | ||||
\(204\) | −6.47214 | + | 4.70228i | −0.453140 | + | 0.329226i | ||||
\(205\) | 2.47214 | + | 7.60845i | 0.172661 | + | 0.531397i | ||||
\(206\) | −4.32624 | + | 13.3148i | −0.301423 | + | 0.927685i | ||||
\(207\) | 3.23607 | + | 2.35114i | 0.224922 | + | 0.163416i | ||||
\(208\) | 4.00000 | 0.277350 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.00000 | 0.276026 | ||||||||
\(211\) | −9.70820 | − | 7.05342i | −0.668340 | − | 0.485578i | 0.201129 | − | 0.979565i | \(-0.435539\pi\) |
−0.869469 | + | 0.493987i | \(0.835539\pi\) | |||||||
\(212\) | 1.85410 | − | 5.70634i | 0.127340 | − | 0.391913i | ||||
\(213\) | −7.41641 | − | 22.8254i | −0.508164 | − | 1.56397i | ||||
\(214\) | −9.70820 | + | 7.05342i | −0.663639 | + | 0.482162i | ||||
\(215\) | −19.4164 | + | 14.1068i | −1.32419 | + | 0.962079i | ||||
\(216\) | −3.70820 | − | 11.4127i | −0.252311 | − | 0.776534i | ||||
\(217\) | 3.09017 | − | 9.51057i | 0.209774 | − | 0.645619i | ||||
\(218\) | 11.3262 | + | 8.22899i | 0.767110 | + | 0.557338i | ||||
\(219\) | 16.0000 | 1.08118 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.0000 | 1.07628 | ||||||||
\(222\) | −9.70820 | − | 7.05342i | −0.651572 | − | 0.473395i | ||||
\(223\) | 6.79837 | − | 20.9232i | 0.455253 | − | 1.40112i | −0.415585 | − | 0.909554i | \(-0.636423\pi\) |
0.870838 | − | 0.491570i | \(-0.163577\pi\) | |||||||
\(224\) | −1.54508 | − | 4.75528i | −0.103235 | − | 0.317726i | ||||
\(225\) | 0.809017 | − | 0.587785i | 0.0539345 | − | 0.0391857i | ||||
\(226\) | 14.5623 | − | 10.5801i | 0.968670 | − | 0.703780i | ||||
\(227\) | −3.70820 | − | 11.4127i | −0.246122 | − | 0.757486i | −0.995450 | − | 0.0952867i | \(-0.969623\pi\) |
0.749328 | − | 0.662199i | \(-0.230377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.5623 | − | 10.5801i | −0.962304 | − | 0.699155i | −0.00861950 | − | 0.999963i | \(-0.502744\pi\) |
−0.953685 | + | 0.300808i | \(0.902744\pi\) | |||||||
\(230\) | −8.00000 | −0.527504 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.0000 | 1.18176 | ||||||||
\(233\) | −14.5623 | − | 10.5801i | −0.954008 | − | 0.693128i | −0.00225687 | − | 0.999997i | \(-0.500718\pi\) |
−0.951752 | + | 0.306870i | \(0.900718\pi\) | |||||||
\(234\) | 1.23607 | − | 3.80423i | 0.0808043 | − | 0.248690i | ||||
\(235\) | 6.18034 | + | 19.0211i | 0.403161 | + | 1.24080i | ||||
\(236\) | 1.61803 | − | 1.17557i | 0.105325 | − | 0.0765231i | ||||
\(237\) | 12.9443 | − | 9.40456i | 0.840821 | − | 0.610892i | ||||
\(238\) | 1.23607 | + | 3.80423i | 0.0801224 | + | 0.246591i | ||||
\(239\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(240\) | −3.23607 | − | 2.35114i | −0.208887 | − | 0.151765i | ||||
\(241\) | 20.0000 | 1.28831 | 0.644157 | − | 0.764894i | \(-0.277208\pi\) | ||||
0.644157 | + | 0.764894i | \(0.277208\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.0000 | −0.641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.618034 | + | 1.90211i | −0.0394847 | + | 0.121522i | ||||
\(246\) | 2.47214 | + | 7.60845i | 0.157618 | + | 0.485097i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −24.2705 | + | 17.6336i | −1.54118 | + | 1.11973i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.70820 | + | 11.4127i | −0.234527 | + | 0.721801i | ||||
\(251\) | 1.61803 | + | 1.17557i | 0.102129 | + | 0.0742014i | 0.637678 | − | 0.770303i | \(-0.279895\pi\) |
−0.535548 | + | 0.844504i | \(0.679895\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 8.00000 | 0.501965 | ||||||||
\(255\) | −12.9443 | − | 9.40456i | −0.810602 | − | 0.588937i | ||||
\(256\) | −5.25329 | + | 16.1680i | −0.328331 | + | 1.01050i | ||||
\(257\) | −4.32624 | − | 13.3148i | −0.269863 | − | 0.830554i | −0.990533 | − | 0.137275i | \(-0.956166\pi\) |
0.720670 | − | 0.693279i | \(-0.243834\pi\) | |||||||
\(258\) | −19.4164 | + | 14.1068i | −1.20881 | + | 0.878254i | ||||
\(259\) | 4.85410 | − | 3.52671i | 0.301619 | − | 0.219139i | ||||
\(260\) | −2.47214 | − | 7.60845i | −0.153315 | − | 0.471856i | ||||
\(261\) | 1.85410 | − | 5.70634i | 0.114766 | − | 0.353214i | ||||
\(262\) | −9.70820 | − | 7.05342i | −0.599775 | − | 0.435762i | ||||
\(263\) | −8.00000 | −0.493301 | −0.246651 | − | 0.969104i | \(-0.579330\pi\) | ||||
−0.246651 | + | 0.969104i | \(0.579330\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.0000 | 0.737154 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.70820 | + | 11.4127i | −0.226938 | + | 0.698445i | ||||
\(268\) | −2.47214 | − | 7.60845i | −0.151010 | − | 0.464760i | ||||
\(269\) | −8.09017 | + | 5.87785i | −0.493266 | + | 0.358379i | −0.806439 | − | 0.591317i | \(-0.798608\pi\) |
0.313173 | + | 0.949696i | \(0.398608\pi\) | |||||||
\(270\) | 6.47214 | − | 4.70228i | 0.393882 | − | 0.286172i | ||||
\(271\) | 1.23607 | + | 3.80423i | 0.0750858 | + | 0.231090i | 0.981554 | − | 0.191183i | \(-0.0612323\pi\) |
−0.906469 | + | 0.422273i | \(0.861232\pi\) | |||||||
\(272\) | 1.23607 | − | 3.80423i | 0.0749476 | − | 0.230665i | ||||
\(273\) | 6.47214 | + | 4.70228i | 0.391711 | + | 0.284595i | ||||
\(274\) | 10.0000 | 0.604122 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.00000 | 0.481543 | ||||||||
\(277\) | 17.7984 | + | 12.9313i | 1.06940 | + | 0.776965i | 0.975804 | − | 0.218645i | \(-0.0701637\pi\) |
0.0935962 | + | 0.995610i | \(0.470164\pi\) | |||||||
\(278\) | −2.47214 | + | 7.60845i | −0.148269 | + | 0.456325i | ||||
\(279\) | 3.09017 | + | 9.51057i | 0.185004 | + | 0.569383i | ||||
\(280\) | 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 | \(0.242725\pi\) | |||||||
\(282\) | 6.18034 | + | 19.0211i | 0.368034 | + | 1.13269i | ||||
\(283\) | −1.23607 | + | 3.80423i | −0.0734766 | + | 0.226138i | −0.981050 | − | 0.193756i | \(-0.937933\pi\) |
0.907573 | + | 0.419894i | \(0.137933\pi\) | |||||||
\(284\) | −9.70820 | − | 7.05342i | −0.576076 | − | 0.418544i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | 4.04508 | + | 2.93893i | 0.238359 | + | 0.173178i | ||||
\(289\) | −0.309017 | + | 0.951057i | −0.0181775 | + | 0.0559445i | ||||
\(290\) | 3.70820 | + | 11.4127i | 0.217753 | + | 0.670176i | ||||
\(291\) | 16.1803 | − | 11.7557i | 0.948508 | − | 0.689132i | ||||
\(292\) | 6.47214 | − | 4.70228i | 0.378753 | − | 0.275180i | ||||
\(293\) | 7.41641 | + | 22.8254i | 0.433271 | + | 1.33347i | 0.894848 | + | 0.446371i | \(0.147284\pi\) |
−0.461577 | + | 0.887100i | \(0.652716\pi\) | |||||||
\(294\) | −0.618034 | + | 1.90211i | −0.0360445 | + | 0.110933i | ||||
\(295\) | 3.23607 | + | 2.35114i | 0.188411 | + | 0.136889i | ||||
\(296\) | −18.0000 | −1.04623 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.0000 | −0.579284 | ||||||||
\(299\) | −12.9443 | − | 9.40456i | −0.748587 | − | 0.543880i | ||||
\(300\) | 0.618034 | − | 1.90211i | 0.0356822 | − | 0.109819i | ||||
\(301\) | −3.70820 | − | 11.4127i | −0.213737 | − | 0.657816i | ||||
\(302\) | 12.9443 | − | 9.40456i | 0.744859 | − | 0.541172i | ||||
\(303\) | −6.47214 | + | 4.70228i | −0.371814 | + | 0.270139i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.23607 | − | 2.35114i | −0.184994 | − | 0.134406i | ||||
\(307\) | −20.0000 | −1.14146 | −0.570730 | − | 0.821138i | \(-0.693340\pi\) | ||||
−0.570730 | + | 0.821138i | \(0.693340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28.0000 | 1.59286 | ||||||||
\(310\) | −16.1803 | − | 11.7557i | −0.918982 | − | 0.667679i | ||||
\(311\) | −5.56231 | + | 17.1190i | −0.315409 | + | 0.970730i | 0.660176 | + | 0.751111i | \(0.270482\pi\) |
−0.975586 | + | 0.219620i | \(0.929518\pi\) | |||||||
\(312\) | −7.41641 | − | 22.8254i | −0.419871 | − | 1.29223i | ||||
\(313\) | −1.61803 | + | 1.17557i | −0.0914567 | + | 0.0664472i | −0.632574 | − | 0.774500i | \(-0.718002\pi\) |
0.541117 | + | 0.840947i | \(0.318002\pi\) | |||||||
\(314\) | 11.3262 | − | 8.22899i | 0.639177 | − | 0.464389i | ||||
\(315\) | −0.618034 | − | 1.90211i | −0.0348223 | − | 0.107172i | ||||
\(316\) | 2.47214 | − | 7.60845i | 0.139069 | − | 0.428009i | ||||
\(317\) | 1.61803 | + | 1.17557i | 0.0908778 | + | 0.0660266i | 0.632296 | − | 0.774727i | \(-0.282113\pi\) |
−0.541418 | + | 0.840753i | \(0.682113\pi\) | |||||||
\(318\) | 12.0000 | 0.672927 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −14.0000 | −0.782624 | ||||||||
\(321\) | 19.4164 | + | 14.1068i | 1.08372 | + | 0.787367i | ||||
\(322\) | 1.23607 | − | 3.80423i | 0.0688834 | − | 0.212001i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −8.89919 | + | 6.46564i | −0.494399 | + | 0.359202i | ||||
\(325\) | −3.23607 | + | 2.35114i | −0.179505 | + | 0.130418i | ||||
\(326\) | 2.47214 | + | 7.60845i | 0.136919 | + | 0.421393i | ||||
\(327\) | 8.65248 | − | 26.6296i | 0.478483 | − | 1.47262i | ||||
\(328\) | 9.70820 | + | 7.05342i | 0.536046 | + | 0.389460i | ||||
\(329\) | −10.0000 | −0.551318 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0000 | −1.09930 | −0.549650 | − | 0.835395i | \(-0.685239\pi\) | ||||
−0.549650 | + | 0.835395i | \(0.685239\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.85410 | + | 5.70634i | −0.101604 | + | 0.312705i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.9443 | − | 9.40456i | 0.707221 | − | 0.513826i | ||||
\(336\) | 1.61803 | − | 1.17557i | 0.0882710 | − | 0.0641326i | ||||
\(337\) | −4.32624 | − | 13.3148i | −0.235665 | − | 0.725303i | −0.997032 | − | 0.0769821i | \(-0.975472\pi\) |
0.761367 | − | 0.648321i | \(-0.224528\pi\) | |||||||
\(338\) | −0.927051 | + | 2.85317i | −0.0504249 | + | 0.155192i | ||||
\(339\) | −29.1246 | − | 21.1603i | −1.58183 | − | 1.14927i | ||||
\(340\) | −8.00000 | −0.433861 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.809017 | − | 0.587785i | −0.0436828 | − | 0.0317374i | ||||
\(344\) | −11.1246 | + | 34.2380i | −0.599799 | + | 1.84599i | ||||
\(345\) | 4.94427 | + | 15.2169i | 0.266191 | + | 0.819251i | ||||
\(346\) | −9.70820 | + | 7.05342i | −0.521916 | + | 0.379194i | ||||
\(347\) | 3.23607 | − | 2.35114i | 0.173721 | − | 0.126216i | −0.497527 | − | 0.867448i | \(-0.665758\pi\) |
0.671248 | + | 0.741233i | \(0.265758\pi\) | |||||||
\(348\) | −3.70820 | − | 11.4127i | −0.198781 | − | 0.611784i | ||||
\(349\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(350\) | −0.809017 | − | 0.587785i | −0.0432438 | − | 0.0314184i | ||||
\(351\) | 16.0000 | 0.854017 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.0000 | −1.59674 | −0.798369 | − | 0.602168i | \(-0.794304\pi\) | ||||
−0.798369 | + | 0.602168i | \(0.794304\pi\) | |||||||
\(354\) | 3.23607 | + | 2.35114i | 0.171995 | + | 0.124962i | ||||
\(355\) | 7.41641 | − | 22.8254i | 0.393622 | − | 1.21144i | ||||
\(356\) | 1.85410 | + | 5.70634i | 0.0982672 | + | 0.302435i | ||||
\(357\) | 6.47214 | − | 4.70228i | 0.342542 | − | 0.248871i | ||||
\(358\) | 9.70820 | − | 7.05342i | 0.513095 | − | 0.372785i | ||||
\(359\) | −4.94427 | − | 15.2169i | −0.260949 | − | 0.803117i | −0.992599 | − | 0.121437i | \(-0.961250\pi\) |
0.731650 | − | 0.681680i | \(-0.238750\pi\) | |||||||
\(360\) | −1.85410 | + | 5.70634i | −0.0977198 | + | 0.300750i | ||||
\(361\) | 15.3713 | + | 11.1679i | 0.809017 | + | 0.587785i | ||||
\(362\) | −10.0000 | −0.525588 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.00000 | 0.209657 | ||||||||
\(365\) | 12.9443 | + | 9.40456i | 0.677534 | + | 0.492257i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.79837 | + | 20.9232i | 0.354872 | + | 1.09218i | 0.956084 | + | 0.293094i | \(0.0946850\pi\) |
−0.601211 | + | 0.799090i | \(0.705315\pi\) | |||||||
\(368\) | −3.23607 | + | 2.35114i | −0.168692 | + | 0.122562i | ||||
\(369\) | 3.23607 | − | 2.35114i | 0.168463 | − | 0.122396i | ||||
\(370\) | −3.70820 | − | 11.4127i | −0.192780 | − | 0.593317i | ||||
\(371\) | −1.85410 | + | 5.70634i | −0.0962602 | + | 0.296258i | ||||
\(372\) | 16.1803 | + | 11.7557i | 0.838912 | + | 0.609505i | ||||
\(373\) | 26.0000 | 1.34623 | 0.673114 | − | 0.739538i | \(-0.264956\pi\) | ||||
0.673114 | + | 0.739538i | \(0.264956\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.0000 | 1.23935 | ||||||||
\(376\) | 24.2705 | + | 17.6336i | 1.25166 | + | 0.909381i | ||||
\(377\) | −7.41641 | + | 22.8254i | −0.381964 | + | 1.17557i | ||||
\(378\) | 1.23607 | + | 3.80423i | 0.0635765 | + | 0.195668i | ||||
\(379\) | 6.47214 | − | 4.70228i | 0.332451 | − | 0.241540i | −0.409019 | − | 0.912526i | \(-0.634129\pi\) |
0.741470 | + | 0.670986i | \(0.234129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.94427 | − | 15.2169i | −0.253303 | − | 0.779586i | ||||
\(382\) | −2.47214 | + | 7.60845i | −0.126485 | + | 0.389282i | ||||
\(383\) | −1.61803 | − | 1.17557i | −0.0826777 | − | 0.0600688i | 0.545679 | − | 0.837995i | \(-0.316272\pi\) |
−0.628356 | + | 0.777926i | \(0.716272\pi\) | |||||||
\(384\) | 6.00000 | 0.306186 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.0000 | −0.712581 | ||||||||
\(387\) | 9.70820 | + | 7.05342i | 0.493496 | + | 0.358546i | ||||
\(388\) | 3.09017 | − | 9.51057i | 0.156880 | − | 0.482826i | ||||
\(389\) | 1.85410 | + | 5.70634i | 0.0940067 | + | 0.289323i | 0.986994 | − | 0.160760i | \(-0.0513945\pi\) |
−0.892987 | + | 0.450083i | \(0.851394\pi\) | |||||||
\(390\) | 12.9443 | − | 9.40456i | 0.655459 | − | 0.476219i | ||||
\(391\) | −12.9443 | + | 9.40456i | −0.654620 | + | 0.475609i | ||||
\(392\) | 0.927051 | + | 2.85317i | 0.0468231 | + | 0.144107i | ||||
\(393\) | −7.41641 | + | 22.8254i | −0.374108 | + | 1.15139i | ||||
\(394\) | −17.7984 | − | 12.9313i | −0.896669 | − | 0.651468i | ||||
\(395\) | 16.0000 | 0.805047 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.0000 | 1.10415 | 0.552074 | − | 0.833795i | \(-0.313837\pi\) | ||||
0.552074 | + | 0.833795i | \(0.313837\pi\) | |||||||
\(398\) | −14.5623 | − | 10.5801i | −0.729942 | − | 0.530334i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.309017 | + | 0.951057i | 0.0154508 | + | 0.0475528i | ||||
\(401\) | 17.7984 | − | 12.9313i | 0.888808 | − | 0.645757i | −0.0467587 | − | 0.998906i | \(-0.514889\pi\) |
0.935567 | + | 0.353149i | \(0.114889\pi\) | |||||||
\(402\) | 12.9443 | − | 9.40456i | 0.645602 | − | 0.469057i | ||||
\(403\) | −12.3607 | − | 38.0423i | −0.615729 | − | 1.89502i | ||||
\(404\) | −1.23607 | + | 3.80423i | −0.0614967 | + | 0.189267i | ||||
\(405\) | −17.7984 | − | 12.9313i | −0.884408 | − | 0.642560i | ||||
\(406\) | −6.00000 | −0.297775 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −24.0000 | −1.18818 | ||||||||
\(409\) | 19.4164 | + | 14.1068i | 0.960080 | + | 0.697539i | 0.953169 | − | 0.302437i | \(-0.0978003\pi\) |
0.00691035 | + | 0.999976i | \(0.497800\pi\) | |||||||
\(410\) | −2.47214 | + | 7.60845i | −0.122090 | + | 0.375755i | ||||
\(411\) | −6.18034 | − | 19.0211i | −0.304854 | − | 0.938243i | ||||
\(412\) | 11.3262 | − | 8.22899i | 0.558004 | − | 0.405413i | ||||
\(413\) | −1.61803 | + | 1.17557i | −0.0796182 | + | 0.0578460i | ||||
\(414\) | 1.23607 | + | 3.80423i | 0.0607494 | + | 0.186968i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16.1803 | − | 11.7557i | −0.793306 | − | 0.576371i | ||||
\(417\) | 16.0000 | 0.783523 | ||||||||
\(418\) | 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 | ||||
\(421\) | −4.32624 | + | 13.3148i | −0.210848 | + | 0.648923i | 0.788574 | + | 0.614939i | \(0.210819\pi\) |
−0.999422 | + | 0.0339839i | \(0.989181\pi\) | |||||||
\(422\) | −3.70820 | − | 11.4127i | −0.180513 | − | 0.555560i | ||||
\(423\) | 8.09017 | − | 5.87785i | 0.393358 | − | 0.285791i | ||||
\(424\) | 14.5623 | − | 10.5801i | 0.707208 | − | 0.513817i | ||||
\(425\) | 1.23607 | + | 3.80423i | 0.0599581 | + | 0.184532i | ||||
\(426\) | 7.41641 | − | 22.8254i | 0.359326 | − | 1.10589i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −24.0000 | −1.15738 | ||||||||
\(431\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(432\) | 1.23607 | − | 3.80423i | 0.0594703 | − | 0.183031i | ||||
\(433\) | −8.03444 | − | 24.7275i | −0.386111 | − | 1.18833i | −0.935671 | − | 0.352873i | \(-0.885205\pi\) |
0.549561 | − | 0.835454i | \(-0.314795\pi\) | |||||||
\(434\) | 8.09017 | − | 5.87785i | 0.388341 | − | 0.282146i | ||||
\(435\) | 19.4164 | − | 14.1068i | 0.930946 | − | 0.676371i | ||||
\(436\) | −4.32624 | − | 13.3148i | −0.207189 | − | 0.637663i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 12.9443 | + | 9.40456i | 0.618501 | + | 0.449367i | ||||
\(439\) | 20.0000 | 0.954548 | 0.477274 | − | 0.878755i | \(-0.341625\pi\) | ||||
0.477274 | + | 0.878755i | \(0.341625\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 12.9443 | + | 9.40456i | 0.615696 | + | 0.447329i | ||||
\(443\) | 1.23607 | − | 3.80423i | 0.0587274 | − | 0.180744i | −0.917389 | − | 0.397991i | \(-0.869708\pi\) |
0.976117 | + | 0.217247i | \(0.0697076\pi\) | |||||||
\(444\) | 3.70820 | + | 11.4127i | 0.175984 | + | 0.541622i | ||||
\(445\) | −9.70820 | + | 7.05342i | −0.460213 | + | 0.334364i | ||||
\(446\) | 17.7984 | − | 12.9313i | 0.842777 | − | 0.612314i | ||||
\(447\) | 6.18034 | + | 19.0211i | 0.292320 | + | 0.899669i | ||||
\(448\) | 2.16312 | − | 6.65740i | 0.102198 | − | 0.314532i | ||||
\(449\) | 8.09017 | + | 5.87785i | 0.381799 | + | 0.277393i | 0.762087 | − | 0.647475i | \(-0.224175\pi\) |
−0.380288 | + | 0.924868i | \(0.624175\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −18.0000 | −0.846649 | ||||||||
\(453\) | −25.8885 | − | 18.8091i | −1.21635 | − | 0.883730i | ||||
\(454\) | 3.70820 | − | 11.4127i | 0.174035 | − | 0.535624i | ||||
\(455\) | 2.47214 | + | 7.60845i | 0.115896 | + | 0.356690i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5623 | − | 10.5801i | 0.681196 | − | 0.494918i | −0.192558 | − | 0.981286i | \(-0.561678\pi\) |
0.873754 | + | 0.486368i | \(0.161678\pi\) | |||||||
\(458\) | −5.56231 | − | 17.1190i | −0.259909 | − | 0.799919i | ||||
\(459\) | 4.94427 | − | 15.2169i | 0.230779 | − | 0.710264i | ||||
\(460\) | 6.47214 | + | 4.70228i | 0.301765 | + | 0.219245i | ||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000 | 0.185896 | 0.0929479 | − | 0.995671i | \(-0.470371\pi\) | ||||
0.0929479 | + | 0.995671i | \(0.470371\pi\) | |||||||
\(464\) | 4.85410 | + | 3.52671i | 0.225346 | + | 0.163723i | ||||
\(465\) | −12.3607 | + | 38.0423i | −0.573213 | + | 1.76417i | ||||
\(466\) | −5.56231 | − | 17.1190i | −0.257669 | − | 0.793023i | ||||
\(467\) | −24.2705 | + | 17.6336i | −1.12311 | + | 0.815984i | −0.984677 | − | 0.174389i | \(-0.944205\pi\) |
−0.138428 | + | 0.990372i | \(0.544205\pi\) | |||||||
\(468\) | −3.23607 | + | 2.35114i | −0.149587 | + | 0.108682i | ||||
\(469\) | 2.47214 | + | 7.60845i | 0.114153 | + | 0.351326i | ||||
\(470\) | −6.18034 | + | 19.0211i | −0.285078 | + | 0.877379i | ||||
\(471\) | −22.6525 | − | 16.4580i | −1.04377 | − | 0.758344i | ||||
\(472\) | 6.00000 | 0.276172 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 16.0000 | 0.734904 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.23607 | − | 3.80423i | 0.0566551 | − | 0.174366i | ||||
\(477\) | −1.85410 | − | 5.70634i | −0.0848935 | − | 0.261275i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.23607 | + | 2.35114i | −0.147860 | + | 0.107426i | −0.659256 | − | 0.751919i | \(-0.729129\pi\) |
0.511396 | + | 0.859345i | \(0.329129\pi\) | |||||||
\(480\) | 6.18034 | + | 19.0211i | 0.282093 | + | 0.868192i | ||||
\(481\) | 7.41641 | − | 22.8254i | 0.338159 | − | 1.04075i | ||||
\(482\) | 16.1803 | + | 11.7557i | 0.736994 | + | 0.535458i | ||||
\(483\) | −8.00000 | −0.364013 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.0000 | 0.908153 | ||||||||
\(486\) | −8.09017 | − | 5.87785i | −0.366978 | − | 0.266625i | ||||
\(487\) | −8.65248 | + | 26.6296i | −0.392081 | + | 1.20670i | 0.539130 | + | 0.842222i | \(0.318753\pi\) |
−0.931212 | + | 0.364479i | \(0.881247\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.9443 | − | 9.40456i | 0.585360 | − | 0.425289i | ||||
\(490\) | −1.61803 | + | 1.17557i | −0.0730953 | + | 0.0531069i | ||||
\(491\) | −8.65248 | − | 26.6296i | −0.390481 | − | 1.20178i | −0.932426 | − | 0.361362i | \(-0.882312\pi\) |
0.541945 | − | 0.840414i | \(-0.317688\pi\) | |||||||
\(492\) | 2.47214 | − | 7.60845i | 0.111452 | − | 0.343016i | ||||
\(493\) | 19.4164 | + | 14.1068i | 0.874471 | + | 0.635340i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.0000 | −0.449013 | ||||||||
\(497\) | 9.70820 | + | 7.05342i | 0.435472 | + | 0.316389i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.94427 | − | 15.2169i | −0.221336 | − | 0.681202i | −0.998643 | − | 0.0520806i | \(-0.983415\pi\) |
0.777307 | − | 0.629122i | \(-0.216585\pi\) | |||||||
\(500\) | 9.70820 | − | 7.05342i | 0.434164 | − | 0.315439i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.618034 | + | 1.90211i | 0.0275842 | + | 0.0848955i | ||||
\(503\) | −1.23607 | + | 3.80423i | −0.0551135 | + | 0.169622i | −0.974824 | − | 0.222975i | \(-0.928423\pi\) |
0.919711 | + | 0.392597i | \(0.128423\pi\) | |||||||
\(504\) | −2.42705 | − | 1.76336i | −0.108109 | − | 0.0785461i | ||||
\(505\) | −8.00000 | −0.355995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.00000 | 0.266469 | ||||||||
\(508\) | −6.47214 | − | 4.70228i | −0.287155 | − | 0.208630i | ||||
\(509\) | 5.56231 | − | 17.1190i | 0.246545 | − | 0.758787i | −0.748834 | − | 0.662758i | \(-0.769386\pi\) |
0.995379 | − | 0.0960291i | \(-0.0306142\pi\) | |||||||
\(510\) | −4.94427 | − | 15.2169i | −0.218936 | − | 0.673816i | ||||
\(511\) | −6.47214 | + | 4.70228i | −0.286310 | + | 0.208017i | ||||
\(512\) | −8.89919 | + | 6.46564i | −0.393292 | + | 0.285744i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.32624 | − | 13.3148i | 0.190822 | − | 0.587290i | ||||
\(515\) | 22.6525 | + | 16.4580i | 0.998187 | + | 0.725226i | ||||
\(516\) | 24.0000 | 1.05654 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 6.00000 | 0.263625 | ||||||||
\(519\) | 19.4164 | + | 14.1068i | 0.852286 | + | 0.619222i | ||||
\(520\) | 7.41641 | − | 22.8254i | 0.325231 | − | 1.00096i | ||||
\(521\) | 1.85410 | + | 5.70634i | 0.0812297 | + | 0.249999i | 0.983421 | − | 0.181337i | \(-0.0580424\pi\) |
−0.902191 | + | 0.431336i | \(0.858042\pi\) | |||||||
\(522\) | 4.85410 | − | 3.52671i | 0.212458 | − | 0.154360i | ||||
\(523\) | 16.1803 | − | 11.7557i | 0.707517 | − | 0.514041i | −0.174855 | − | 0.984594i | \(-0.555946\pi\) |
0.882372 | + | 0.470553i | \(0.155946\pi\) | |||||||
\(524\) | 3.70820 | + | 11.4127i | 0.161994 | + | 0.498565i | ||||
\(525\) | −0.618034 | + | 1.90211i | −0.0269732 | + | 0.0830150i | ||||
\(526\) | −6.47214 | − | 4.70228i | −0.282199 | − | 0.205029i | ||||
\(527\) | −40.0000 | −1.74243 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 9.70820 | + | 7.05342i | 0.421697 | + | 0.306381i | ||||
\(531\) | 0.618034 | − | 1.90211i | 0.0268204 | − | 0.0825447i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.9443 | + | 9.40456i | −0.560679 | + | 0.407357i | ||||
\(534\) | −9.70820 | + | 7.05342i | −0.420115 | + | 0.305231i | ||||
\(535\) | 7.41641 | + | 22.8254i | 0.320639 | + | 0.986826i | ||||
\(536\) | 7.41641 | − | 22.8254i | 0.320340 | − | 0.985905i | ||||
\(537\) | −19.4164 | − | 14.1068i | −0.837880 | − | 0.608755i | ||||
\(538\) | −10.0000 | −0.431131 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −8.00000 | −0.344265 | ||||||||
\(541\) | −21.0344 | − | 15.2824i | −0.904341 | − | 0.657042i | 0.0352361 | − | 0.999379i | \(-0.488782\pi\) |
−0.939577 | + | 0.342337i | \(0.888782\pi\) | |||||||
\(542\) | −1.23607 | + | 3.80423i | −0.0530937 | + | 0.163406i | ||||
\(543\) | 6.18034 | + | 19.0211i | 0.265224 | + | 0.816275i | ||||
\(544\) | −16.1803 | + | 11.7557i | −0.693726 | + | 0.504022i | ||||
\(545\) | 22.6525 | − | 16.4580i | 0.970325 | − | 0.704983i | ||||
\(546\) | 2.47214 | + | 7.60845i | 0.105798 | + | 0.325612i | ||||
\(547\) | 8.65248 | − | 26.6296i | 0.369953 | − | 1.13860i | −0.576868 | − | 0.816838i | \(-0.695725\pi\) |
0.946821 | − | 0.321761i | \(-0.104275\pi\) | |||||||
\(548\) | −8.09017 | − | 5.87785i | −0.345595 | − | 0.251089i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 19.4164 | + | 14.1068i | 0.826417 | + | 0.600427i | ||||
\(553\) | −2.47214 | + | 7.60845i | −0.105126 | + | 0.323544i | ||||
\(554\) | 6.79837 | + | 20.9232i | 0.288835 | + | 0.888943i | ||||
\(555\) | −19.4164 | + | 14.1068i | −0.824181 | + | 0.598802i | ||||
\(556\) | 6.47214 | − | 4.70228i | 0.274480 | − | 0.199421i | ||||
\(557\) | −6.79837 | − | 20.9232i | −0.288056 | − | 0.886546i | −0.985466 | − | 0.169873i | \(-0.945664\pi\) |
0.697410 | − | 0.716673i | \(-0.254336\pi\) | |||||||
\(558\) | −3.09017 | + | 9.51057i | −0.130817 | + | 0.402614i | ||||
\(559\) | −38.8328 | − | 28.2137i | −1.64245 | − | 1.19331i | ||||
\(560\) | 2.00000 | 0.0845154 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00000 | 0.253095 | ||||||||
\(563\) | −25.8885 | − | 18.8091i | −1.09107 | − | 0.792710i | −0.111492 | − | 0.993765i | \(-0.535563\pi\) |
−0.979580 | + | 0.201055i | \(0.935563\pi\) | |||||||
\(564\) | 6.18034 | − | 19.0211i | 0.260239 | − | 0.800934i | ||||
\(565\) | −11.1246 | − | 34.2380i | −0.468016 | − | 1.44040i | ||||
\(566\) | −3.23607 | + | 2.35114i | −0.136022 | + | 0.0988258i | ||||
\(567\) | 8.89919 | − | 6.46564i | 0.373731 | − | 0.271531i | ||||
\(568\) | −11.1246 | − | 34.2380i | −0.466778 | − | 1.43660i | ||||
\(569\) | −9.27051 | + | 28.5317i | −0.388640 | + | 1.19611i | 0.545165 | + | 0.838329i | \(0.316467\pi\) |
−0.933805 | + | 0.357782i | \(0.883533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.0000 | 0.668410 | ||||||||
\(574\) | −3.23607 | − | 2.35114i | −0.135071 | − | 0.0981347i | ||||
\(575\) | 1.23607 | − | 3.80423i | 0.0515476 | − | 0.158647i | ||||
\(576\) | 2.16312 | + | 6.65740i | 0.0901300 | + | 0.277391i | ||||
\(577\) | 14.5623 | − | 10.5801i | 0.606237 | − | 0.440457i | −0.241850 | − | 0.970314i | \(-0.577754\pi\) |
0.848087 | + | 0.529857i | \(0.177754\pi\) | |||||||
\(578\) | −0.809017 | + | 0.587785i | −0.0336507 | + | 0.0244486i | ||||
\(579\) | 8.65248 | + | 26.6296i | 0.359585 | + | 1.10669i | ||||
\(580\) | 3.70820 | − | 11.4127i | 0.153975 | − | 0.473886i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 20.0000 | 0.829027 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 24.0000 | 0.993127 | ||||||||
\(585\) | −6.47214 | − | 4.70228i | −0.267590 | − | 0.194415i | ||||
\(586\) | −7.41641 | + | 22.8254i | −0.306369 | + | 0.942907i | ||||
\(587\) | −0.618034 | − | 1.90211i | −0.0255090 | − | 0.0785086i | 0.937492 | − | 0.348008i | \(-0.113142\pi\) |
−0.963001 | + | 0.269499i | \(0.913142\pi\) | |||||||
\(588\) | 1.61803 | − | 1.17557i | 0.0667266 | − | 0.0484797i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.23607 | + | 3.80423i | 0.0508881 | + | 0.156618i | ||||
\(591\) | −13.5967 | + | 41.8465i | −0.559295 | + | 1.72133i | ||||
\(592\) | −4.85410 | − | 3.52671i | −0.199502 | − | 0.144947i | ||||
\(593\) | −32.0000 | −1.31408 | −0.657041 | − | 0.753855i | \(-0.728192\pi\) | ||||
−0.657041 | + | 0.753855i | \(0.728192\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.00000 | 0.327968 | ||||||||
\(596\) | 8.09017 | + | 5.87785i | 0.331386 | + | 0.240766i | ||||
\(597\) | −11.1246 | + | 34.2380i | −0.455300 | + | 1.40127i | ||||
\(598\) | −4.94427 | − | 15.2169i | −0.202186 | − | 0.622265i | ||||
\(599\) | 16.1803 | − | 11.7557i | 0.661111 | − | 0.480325i | −0.205927 | − | 0.978567i | \(-0.566021\pi\) |
0.867038 | + | 0.498242i | \(0.166021\pi\) | |||||||
\(600\) | 4.85410 | − | 3.52671i | 0.198168 | − | 0.143977i | ||||
\(601\) | 8.65248 | + | 26.6296i | 0.352942 | + | 1.08624i | 0.957193 | + | 0.289450i | \(0.0934723\pi\) |
−0.604251 | + | 0.796794i | \(0.706528\pi\) | |||||||
\(602\) | 3.70820 | − | 11.4127i | 0.151135 | − | 0.465146i | ||||
\(603\) | −6.47214 | − | 4.70228i | −0.263566 | − | 0.191492i | ||||
\(604\) | −16.0000 | −0.651031 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.00000 | −0.324978 | ||||||||
\(607\) | −32.3607 | − | 23.5114i | −1.31348 | − | 0.954299i | −0.999989 | − | 0.00470738i | \(-0.998502\pi\) |
−0.313491 | − | 0.949591i | \(-0.601498\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.70820 | + | 11.4127i | 0.150264 | + | 0.462465i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.3607 | + | 23.5114i | −1.30917 | + | 0.951170i | ||||
\(612\) | 1.23607 | + | 3.80423i | 0.0499651 | + | 0.153777i | ||||
\(613\) | −8.03444 | + | 24.7275i | −0.324508 | + | 0.998733i | 0.647154 | + | 0.762359i | \(0.275959\pi\) |
−0.971662 | + | 0.236374i | \(0.924041\pi\) | |||||||
\(614\) | −16.1803 | − | 11.7557i | −0.652985 | − | 0.474422i | ||||
\(615\) | 16.0000 | 0.645182 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | 22.6525 | + | 16.4580i | 0.911216 | + | 0.662037i | ||||
\(619\) | 4.32624 | − | 13.3148i | 0.173886 | − | 0.535167i | −0.825695 | − | 0.564117i | \(-0.809217\pi\) |
0.999581 | + | 0.0289507i | \(0.00921657\pi\) | |||||||
\(620\) | 6.18034 | + | 19.0211i | 0.248208 | + | 0.763907i | ||||
\(621\) | −12.9443 | + | 9.40456i | −0.519436 | + | 0.377392i | ||||
\(622\) | −14.5623 | + | 10.5801i | −0.583895 | + | 0.424225i | ||||
\(623\) | −1.85410 | − | 5.70634i | −0.0742830 | − | 0.228620i | ||||
\(624\) | 2.47214 | − | 7.60845i | 0.0989646 | − | 0.304582i | ||||
\(625\) | 15.3713 | + | 11.1679i | 0.614853 | + | 0.446717i | ||||
\(626\) | −2.00000 | −0.0799361 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.0000 | −0.558661 | ||||||||
\(629\) | −19.4164 | − | 14.1068i | −0.774183 | − | 0.562477i | ||||
\(630\) | 0.618034 | − | 1.90211i | 0.0246231 | − | 0.0757820i | ||||
\(631\) | −2.47214 | − | 7.60845i | −0.0984142 | − | 0.302888i | 0.889714 | − | 0.456518i | \(-0.150904\pi\) |
−0.988128 | + | 0.153630i | \(0.950904\pi\) | |||||||
\(632\) | 19.4164 | − | 14.1068i | 0.772343 | − | 0.561140i | ||||
\(633\) | −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 | ||||
\(636\) | −9.70820 | − | 7.05342i | −0.384955 | − | 0.279686i | ||||
\(637\) | −4.00000 | −0.158486 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.0000 | −0.474713 | ||||||||
\(640\) | 4.85410 | + | 3.52671i | 0.191875 | + | 0.139406i | ||||
\(641\) | −5.56231 | + | 17.1190i | −0.219698 | + | 0.676161i | 0.779089 | + | 0.626914i | \(0.215682\pi\) |
−0.998787 | + | 0.0492469i | \(0.984318\pi\) | |||||||
\(642\) | 7.41641 | + | 22.8254i | 0.292702 | + | 0.900845i | ||||
\(643\) | −11.3262 | + | 8.22899i | −0.446663 | + | 0.324520i | −0.788277 | − | 0.615321i | \(-0.789027\pi\) |
0.341614 | + | 0.939840i | \(0.389027\pi\) | |||||||
\(644\) | −3.23607 | + | 2.35114i | −0.127519 | + | 0.0926479i | ||||
\(645\) | 14.8328 | + | 45.6507i | 0.584042 | + | 1.79750i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.7984 | + | 12.9313i | 0.699726 | + | 0.508381i | 0.879843 | − | 0.475264i | \(-0.157648\pi\) |
−0.180117 | + | 0.983645i | \(0.557648\pi\) | |||||||
\(648\) | −33.0000 | −1.29636 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.00000 | −0.156893 | ||||||||
\(651\) | −16.1803 | − | 11.7557i | −0.634158 | − | 0.460742i | ||||
\(652\) | 2.47214 | − | 7.60845i | 0.0968163 | − | 0.297970i | ||||
\(653\) | −8.03444 | − | 24.7275i | −0.314412 | − | 0.967661i | −0.975996 | − | 0.217789i | \(-0.930115\pi\) |
0.661584 | − | 0.749871i | \(-0.269885\pi\) | |||||||
\(654\) | 22.6525 | − | 16.4580i | 0.885782 | − | 0.643558i | ||||
\(655\) | −19.4164 | + | 14.1068i | −0.758662 | + | 0.551200i | ||||
\(656\) | 1.23607 | + | 3.80423i | 0.0482603 | + | 0.148530i | ||||
\(657\) | 2.47214 | − | 7.60845i | 0.0964472 | − | 0.296834i | ||||
\(658\) | −8.09017 | − | 5.87785i | −0.315388 | − | 0.229143i | ||||
\(659\) | −4.00000 | −0.155818 | −0.0779089 | − | 0.996960i | \(-0.524824\pi\) | ||||
−0.0779089 | + | 0.996960i | \(0.524824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | −16.1803 | − | 11.7557i | −0.628867 | − | 0.456898i | ||||
\(663\) | 9.88854 | − | 30.4338i | 0.384039 | − | 1.18195i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.85410 | + | 3.52671i | −0.188093 | + | 0.136657i | ||||
\(667\) | −7.41641 | − | 22.8254i | −0.287164 | − | 0.883801i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −35.5967 | − | 25.8626i | −1.37625 | − | 0.999904i | ||||
\(670\) | 16.0000 | 0.618134 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −10.0000 | −0.385758 | ||||||||
\(673\) | −27.5066 | − | 19.9847i | −1.06030 | − | 0.770354i | −0.0861567 | − | 0.996282i | \(-0.527459\pi\) |
−0.974144 | + | 0.225928i | \(0.927459\pi\) | |||||||
\(674\) | 4.32624 | − | 13.3148i | 0.166640 | − | 0.512867i | ||||
\(675\) | 1.23607 | + | 3.80423i | 0.0475763 | + | 0.146425i | ||||
\(676\) | 2.42705 | − | 1.76336i | 0.0933481 | − | 0.0678214i | ||||
\(677\) | −9.70820 | + | 7.05342i | −0.373117 | + | 0.271085i | −0.758502 | − | 0.651671i | \(-0.774068\pi\) |
0.385386 | + | 0.922756i | \(0.374068\pi\) | |||||||
\(678\) | −11.1246 | − | 34.2380i | −0.427238 | − | 1.31490i | ||||
\(679\) | −3.09017 | + | 9.51057i | −0.118590 | + | 0.364982i | ||||
\(680\) | −19.4164 | − | 14.1068i | −0.744585 | − | 0.540973i | ||||
\(681\) | −24.0000 | −0.919682 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.00000 | −0.153056 | −0.0765279 | − | 0.997067i | \(-0.524383\pi\) | ||||
−0.0765279 | + | 0.997067i | \(0.524383\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.18034 | − | 19.0211i | 0.236139 | − | 0.726760i | ||||
\(686\) | −0.309017 | − | 0.951057i | −0.0117983 | − | 0.0363115i | ||||
\(687\) | −29.1246 | + | 21.1603i | −1.11117 | + | 0.807315i | ||||
\(688\) | −9.70820 | + | 7.05342i | −0.370122 | + | 0.268909i | ||||
\(689\) | 7.41641 | + | 22.8254i | 0.282543 | + | 0.869577i | ||||
\(690\) | −4.94427 | + | 15.2169i | −0.188225 | + | 0.579298i | ||||
\(691\) | 37.2148 | + | 27.0381i | 1.41572 | + | 1.02858i | 0.992460 | + | 0.122569i | \(0.0391133\pi\) |
0.423257 | + | 0.906010i | \(0.360887\pi\) | |||||||
\(692\) | 12.0000 | 0.456172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.00000 | 0.151838 | ||||||||
\(695\) | 12.9443 | + | 9.40456i | 0.491004 | + | 0.356735i | ||||
\(696\) | 11.1246 | − | 34.2380i | 0.421677 | − | 1.29779i | ||||
\(697\) | 4.94427 | + | 15.2169i | 0.187278 | + | 0.576381i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −29.1246 | + | 21.1603i | −1.10159 | + | 0.800355i | ||||
\(700\) | 0.309017 | + | 0.951057i | 0.0116797 | + | 0.0359466i | ||||
\(701\) | 6.79837 | − | 20.9232i | 0.256771 | − | 0.790260i | −0.736705 | − | 0.676215i | \(-0.763619\pi\) |
0.993476 | − | 0.114045i | \(-0.0363809\pi\) | |||||||
\(702\) | 12.9443 | + | 9.40456i | 0.488550 | + | 0.354952i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 40.0000 | 1.50649 | ||||||||
\(706\) | −24.2705 | − | 17.6336i | −0.913433 | − | 0.663648i | ||||
\(707\) | 1.23607 | − | 3.80423i | 0.0464871 | − | 0.143073i | ||||
\(708\) | −1.23607 | − | 3.80423i | −0.0464543 | − | 0.142972i | ||||
\(709\) | 27.5066 | − | 19.9847i | 1.03303 | − | 0.750541i | 0.0641181 | − | 0.997942i | \(-0.479577\pi\) |
0.968913 | + | 0.247401i | \(0.0795766\pi\) | |||||||
\(710\) | 19.4164 | − | 14.1068i | 0.728685 | − | 0.529420i | ||||
\(711\) | −2.47214 | − | 7.60845i | −0.0927123 | − | 0.285339i | ||||
\(712\) | −5.56231 | + | 17.1190i | −0.208456 | + | 0.641562i | ||||
\(713\) | 32.3607 | + | 23.5114i | 1.21192 | + | 0.880509i | ||||
\(714\) | 8.00000 | 0.299392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.94427 | − | 15.2169i | 0.184519 | − | 0.567890i | ||||
\(719\) | −1.85410 | − | 5.70634i | −0.0691463 | − | 0.212811i | 0.910512 | − | 0.413482i | \(-0.135688\pi\) |
−0.979659 | + | 0.200672i | \(0.935688\pi\) | |||||||
\(720\) | −1.61803 | + | 1.17557i | −0.0603006 | + | 0.0438109i | ||||
\(721\) | −11.3262 | + | 8.22899i | −0.421811 | + | 0.306464i | ||||
\(722\) | 5.87132 | + | 18.0701i | 0.218508 | + | 0.672499i | ||||
\(723\) | 12.3607 | − | 38.0423i | 0.459699 | − | 1.41481i | ||||
\(724\) | 8.09017 | + | 5.87785i | 0.300669 | + | 0.218449i | ||||
\(725\) | −6.00000 | −0.222834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.0000 | 0.667583 | 0.333792 | − | 0.942647i | \(-0.391672\pi\) | ||||
0.333792 | + | 0.942647i | \(0.391672\pi\) | |||||||
\(728\) | 9.70820 | + | 7.05342i | 0.359810 | + | 0.261417i | ||||
\(729\) | 4.01722 | − | 12.3637i | 0.148786 | − | 0.457916i | ||||
\(730\) | 4.94427 | + | 15.2169i | 0.182996 | + | 0.563203i | ||||
\(731\) | −38.8328 | + | 28.2137i | −1.43628 | + | 1.04352i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(734\) | −6.79837 | + | 20.9232i | −0.250933 | + | 0.772291i | ||||
\(735\) | 3.23607 | + | 2.35114i | 0.119364 | + | 0.0867231i | ||||
\(736\) | 20.0000 | 0.737210 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 4.00000 | 0.147242 | ||||||||
\(739\) | −3.23607 | − | 2.35114i | −0.119041 | − | 0.0864881i | 0.526672 | − | 0.850069i | \(-0.323440\pi\) |
−0.645713 | + | 0.763580i | \(0.723440\pi\) | |||||||
\(740\) | −3.70820 | + | 11.4127i | −0.136316 | + | 0.419538i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.85410 | + | 3.52671i | −0.178200 | + | 0.129470i | ||||
\(743\) | −6.47214 | + | 4.70228i | −0.237440 | + | 0.172510i | −0.700142 | − | 0.714004i | \(-0.746880\pi\) |
0.462702 | + | 0.886514i | \(0.346880\pi\) | |||||||
\(744\) | 18.5410 | + | 57.0634i | 0.679747 | + | 2.09205i | ||||
\(745\) | −6.18034 | + | 19.0211i | −0.226430 | + | 0.696880i | ||||
\(746\) | 21.0344 | + | 15.2824i | 0.770126 | + | 0.559529i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0000 | −0.438470 | ||||||||
\(750\) | 19.4164 | + | 14.1068i | 0.708987 | + | 0.515109i | ||||
\(751\) | −6.18034 | + | 19.0211i | −0.225524 | + | 0.694091i | 0.772714 | + | 0.634754i | \(0.218899\pi\) |
−0.998238 | + | 0.0593368i | \(0.981101\pi\) | |||||||
\(752\) | 3.09017 | + | 9.51057i | 0.112687 | + | 0.346815i | ||||
\(753\) | 3.23607 | − | 2.35114i | 0.117929 | − | 0.0856803i | ||||
\(754\) | −19.4164 | + | 14.1068i | −0.707104 | + | 0.513741i | ||||
\(755\) | −9.88854 | − | 30.4338i | −0.359881 | − | 1.10760i | ||||
\(756\) | 1.23607 | − | 3.80423i | 0.0449554 | − | 0.138358i | ||||
\(757\) | 8.09017 | + | 5.87785i | 0.294042 | + | 0.213634i | 0.725019 | − | 0.688729i | \(-0.241831\pi\) |
−0.430977 | + | 0.902363i | \(0.641831\pi\) | |||||||
\(758\) | 8.00000 | 0.290573 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.8328 | + | 28.2137i | 1.40769 | + | 1.02275i | 0.993653 | + | 0.112485i | \(0.0358809\pi\) |
0.414035 | + | 0.910261i | \(0.364119\pi\) | |||||||
\(762\) | 4.94427 | − | 15.2169i | 0.179112 | − | 0.551250i | ||||
\(763\) | 4.32624 | + | 13.3148i | 0.156620 | + | 0.482028i | ||||
\(764\) | 6.47214 | − | 4.70228i | 0.234154 | − | 0.170123i | ||||
\(765\) | −6.47214 | + | 4.70228i | −0.234001 | + | 0.170011i | ||||
\(766\) | −0.618034 | − | 1.90211i | −0.0223305 | − | 0.0687261i | ||||
\(767\) | −2.47214 | + | 7.60845i | −0.0892637 | + | 0.274725i | ||||
\(768\) | 27.5066 | + | 19.9847i | 0.992558 | + | 0.721136i | ||||
\(769\) | −32.0000 | −1.15395 | −0.576975 | − | 0.816762i | \(-0.695767\pi\) | ||||
−0.576975 | + | 0.816762i | \(0.695767\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.0000 | −1.00840 | ||||||||
\(772\) | 11.3262 | + | 8.22899i | 0.407640 | + | 0.296168i | ||||
\(773\) | −9.27051 | + | 28.5317i | −0.333437 | + | 1.02621i | 0.634050 | + | 0.773292i | \(0.281391\pi\) |
−0.967487 | + | 0.252921i | \(0.918609\pi\) | |||||||
\(774\) | 3.70820 | + | 11.4127i | 0.133289 | + | 0.410220i | ||||
\(775\) | 8.09017 | − | 5.87785i | 0.290607 | − | 0.211139i | ||||
\(776\) | 24.2705 | − | 17.6336i | 0.871261 | − | 0.633008i | ||||
\(777\) | −3.70820 | − | 11.4127i | −0.133031 | − | 0.409428i | ||||
\(778\) | −1.85410 | + | 5.70634i | −0.0664728 | + | 0.204582i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −16.0000 | −0.572892 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −16.0000 | −0.572159 | ||||||||
\(783\) | 19.4164 | + | 14.1068i | 0.693886 | + | 0.504138i | ||||
\(784\) | −0.309017 | + | 0.951057i | −0.0110363 | + | 0.0339663i | ||||
\(785\) | −8.65248 | − | 26.6296i | −0.308820 | − | 0.950451i | ||||
\(786\) | −19.4164 | + | 14.1068i | −0.692560 | + | 0.503175i | ||||
\(787\) | 12.9443 | − | 9.40456i | 0.461413 | − | 0.335237i | −0.332672 | − | 0.943043i | \(-0.607950\pi\) |
0.794085 | + | 0.607806i | \(0.207950\pi\) | |||||||
\(788\) | 6.79837 | + | 20.9232i | 0.242182 | + | 0.745360i | ||||
\(789\) | −4.94427 | + | 15.2169i | −0.176021 | + | 0.541736i | ||||
\(790\) | 12.9443 | + | 9.40456i | 0.460537 | + | 0.334599i | ||||
\(791\) | 18.0000 | 0.640006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 17.7984 | + | 12.9313i | 0.631641 | + | 0.458914i | ||||
\(795\) | 7.41641 | − | 22.8254i | 0.263033 | − | 0.809532i | ||||
\(796\) | 5.56231 | + | 17.1190i | 0.197151 | + | 0.606767i | ||||
\(797\) | −11.3262 | + | 8.22899i | −0.401196 | + | 0.291486i | −0.770028 | − | 0.638010i | \(-0.779758\pi\) |
0.368832 | + | 0.929496i | \(0.379758\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.3607 | + | 38.0423i | 0.437289 | + | 1.34584i | ||||
\(800\) | 1.54508 | − | 4.75528i | 0.0546270 | − | 0.168125i | ||||
\(801\) | 4.85410 | + | 3.52671i | 0.171511 | + | 0.124610i | ||||
\(802\) | 22.0000 | 0.776847 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −16.0000 | −0.564276 | ||||||||
\(805\) | −6.47214 | − | 4.70228i | −0.228113 | − | 0.165734i | ||||
\(806\) | 12.3607 | − | 38.0423i | 0.435386 | − | 1.33998i | ||||
\(807\) | 6.18034 | + | 19.0211i | 0.217558 | + | 0.669575i | ||||
\(808\) | −9.70820 | + | 7.05342i | −0.341533 | + | 0.248139i | ||||
\(809\) | −24.2705 | + | 17.6336i | −0.853306 | + | 0.619963i | −0.926055 | − | 0.377387i | \(-0.876823\pi\) |
0.0727498 | + | 0.997350i | \(0.476823\pi\) | |||||||
\(810\) | −6.79837 | − | 20.9232i | −0.238871 | − | 0.735168i | ||||
\(811\) | −8.65248 | + | 26.6296i | −0.303830 | + | 0.935091i | 0.676282 | + | 0.736643i | \(0.263590\pi\) |
−0.980111 | + | 0.198448i | \(0.936410\pi\) | |||||||
\(812\) | 4.85410 | + | 3.52671i | 0.170346 | + | 0.123763i | ||||
\(813\) | 8.00000 | 0.280572 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.0000 | 0.560456 | ||||||||
\(816\) | −6.47214 | − | 4.70228i | −0.226570 | − | 0.164613i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 7.41641 | + | 22.8254i | 0.259309 | + | 0.798070i | ||||
\(819\) | 3.23607 | − | 2.35114i | 0.113077 | − | 0.0821555i | ||||
\(820\) | 6.47214 | − | 4.70228i | 0.226017 | − | 0.164211i | ||||
\(821\) | −14.2148 | − | 43.7486i | −0.496099 | − | 1.52684i | −0.815237 | − | 0.579128i | \(-0.803393\pi\) |
0.319137 | − | 0.947709i | \(-0.396607\pi\) | |||||||
\(822\) | 6.18034 | − | 19.0211i | 0.215564 | − | 0.663438i | ||||
\(823\) | −19.4164 | − | 14.1068i | −0.676813 | − | 0.491734i | 0.195486 | − | 0.980707i | \(-0.437372\pi\) |
−0.872299 | + | 0.488973i | \(0.837372\pi\) | |||||||
\(824\) | 42.0000 | 1.46314 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.00000 | −0.0695889 | ||||||||
\(827\) | −22.6525 | − | 16.4580i | −0.787704 | − | 0.572300i | 0.119577 | − | 0.992825i | \(-0.461846\pi\) |
−0.907281 | + | 0.420525i | \(0.861846\pi\) | |||||||
\(828\) | 1.23607 | − | 3.80423i | 0.0429563 | − | 0.132206i | ||||
\(829\) | −0.618034 | − | 1.90211i | −0.0214652 | − | 0.0660631i | 0.939750 | − | 0.341862i | \(-0.111058\pi\) |
−0.961215 | + | 0.275799i | \(0.911058\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 35.5967 | − | 25.8626i | 1.23484 | − | 0.897162i | ||||
\(832\) | −8.65248 | − | 26.6296i | −0.299971 | − | 0.923215i | ||||
\(833\) | −1.23607 | + | 3.80423i | −0.0428272 | + | 0.131809i | ||||
\(834\) | 12.9443 | + | 9.40456i | 0.448223 | + | 0.325653i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −40.0000 | −1.38260 | ||||||||
\(838\) | 1.61803 | + | 1.17557i | 0.0558941 | + | 0.0406094i | ||||
\(839\) | 10.5066 | − | 32.3359i | 0.362727 | − | 1.11636i | −0.588665 | − | 0.808377i | \(-0.700346\pi\) |
0.951392 | − | 0.307983i | \(-0.0996539\pi\) | |||||||
\(840\) | −3.70820 | − | 11.4127i | −0.127945 | − | 0.393775i | ||||
\(841\) | −5.66312 | + | 4.11450i | −0.195280 | + | 0.141879i | ||||
\(842\) | −11.3262 | + | 8.22899i | −0.390328 | + | 0.283590i | ||||
\(843\) | −3.70820 | − | 11.4127i | −0.127717 | − | 0.393074i | ||||
\(844\) | −3.70820 | + | 11.4127i | −0.127642 | + | 0.392841i | ||||
\(845\) | 4.85410 | + | 3.52671i | 0.166986 | + | 0.121323i | ||||
\(846\) | 10.0000 | 0.343807 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 6.47214 | + | 4.70228i | 0.222123 | + | 0.161382i | ||||
\(850\) | −1.23607 | + | 3.80423i | −0.0423968 | + | 0.130484i | ||||
\(851\) | 7.41641 | + | 22.8254i | 0.254231 | + | 0.782443i | ||||
\(852\) | −19.4164 | + | 14.1068i | −0.665195 | + | 0.483293i | ||||
\(853\) | 35.5967 | − | 25.8626i | 1.21881 | − | 0.885517i | 0.222809 | − | 0.974862i | \(-0.428477\pi\) |
0.996001 | + | 0.0893453i | \(0.0284775\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.1246 | + | 21.1603i | 0.995459 | + | 0.723243i | ||||
\(857\) | −56.0000 | −1.91292 | −0.956462 | − | 0.291858i | \(-0.905727\pi\) | ||||
−0.956462 | + | 0.291858i | \(0.905727\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.00000 | 0.204717 | 0.102359 | − | 0.994748i | \(-0.467361\pi\) | ||||
0.102359 | + | 0.994748i | \(0.467361\pi\) | |||||||
\(860\) | 19.4164 | + | 14.1068i | 0.662094 | + | 0.481039i | ||||
\(861\) | −2.47214 | + | 7.60845i | −0.0842502 | + | 0.259295i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.4164 | + | 14.1068i | −0.660942 | + | 0.480203i | −0.866981 | − | 0.498341i | \(-0.833943\pi\) |
0.206039 | + | 0.978544i | \(0.433943\pi\) | |||||||
\(864\) | −16.1803 | + | 11.7557i | −0.550466 | + | 0.399937i | ||||
\(865\) | 7.41641 | + | 22.8254i | 0.252165 | + | 0.776085i | ||||
\(866\) | 8.03444 | − | 24.7275i | 0.273021 | − | 0.840274i | ||||
\(867\) | 1.61803 | + | 1.17557i | 0.0549513 | + | 0.0399245i | ||||
\(868\) | −10.0000 | −0.339422 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 24.0000 | 0.813676 | ||||||||
\(871\) | 25.8885 | + | 18.8091i | 0.877200 | + | 0.637323i | ||||
\(872\) | 12.9787 | − | 39.9444i | 0.439515 | − | 1.35269i | ||||
\(873\) | −3.09017 | − | 9.51057i | −0.104586 | − | 0.321884i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.70820 | + | 7.05342i | −0.328197 | + | 0.238449i | ||||
\(876\) | −4.94427 | − | 15.2169i | −0.167051 | − | 0.514132i | ||||
\(877\) | −12.9787 | + | 39.9444i | −0.438260 | + | 1.34883i | 0.451449 | + | 0.892297i | \(0.350907\pi\) |
−0.889709 | + | 0.456529i | \(0.849093\pi\) | |||||||
\(878\) | 16.1803 | + | 11.7557i | 0.546060 | + | 0.396736i | ||||
\(879\) | 48.0000 | 1.61900 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.0000 | −1.14549 | −0.572745 | − | 0.819734i | \(-0.694121\pi\) | ||||
−0.572745 | + | 0.819734i | \(0.694121\pi\) | |||||||
\(882\) | 0.809017 | + | 0.587785i | 0.0272410 | + | 0.0197918i | ||||
\(883\) | 8.65248 | − | 26.6296i | 0.291179 | − | 0.896157i | −0.693299 | − | 0.720650i | \(-0.743844\pi\) |
0.984478 | − | 0.175507i | \(-0.0561564\pi\) | |||||||
\(884\) | −4.94427 | − | 15.2169i | −0.166294 | − | 0.511800i | ||||
\(885\) | 6.47214 | − | 4.70228i | 0.217558 | − | 0.158065i | ||||
\(886\) | 3.23607 | − | 2.35114i | 0.108718 | − | 0.0789881i | ||||
\(887\) | 8.65248 | + | 26.6296i | 0.290522 | + | 0.894134i | 0.984689 | + | 0.174320i | \(0.0557728\pi\) |
−0.694167 | + | 0.719814i | \(0.744227\pi\) | |||||||
\(888\) | −11.1246 | + | 34.2380i | −0.373318 | + | 1.14895i | ||||
\(889\) | 6.47214 | + | 4.70228i | 0.217068 | + | 0.157709i | ||||
\(890\) | −12.0000 | −0.402241 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −22.0000 | −0.736614 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −6.18034 | + | 19.0211i | −0.206701 | + | 0.636162i | ||||
\(895\) | −7.41641 | − | 22.8254i | −0.247903 | − | 0.762968i | ||||
\(896\) | −2.42705 | + | 1.76336i | −0.0810821 | + | 0.0589096i | ||||
\(897\) | −25.8885 | + | 18.8091i | −0.864393 | + | 0.628019i | ||||
\(898\) | 3.09017 | + | 9.51057i | 0.103120 | + | 0.317372i | ||||
\(899\) | 18.5410 | − | 57.0634i | 0.618378 | − | 1.90317i | ||||
\(900\) | −0.809017 | − | 0.587785i | −0.0269672 | − | 0.0195928i | ||||
\(901\) | 24.0000 | 0.799556 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.0000 | −0.798670 | ||||||||
\(904\) | −43.6869 | − | 31.7404i | −1.45301 | − | 1.05567i | ||||
\(905\) | −6.18034 | + | 19.0211i | −0.205441 | + | 0.632284i | ||||
\(906\) | −9.88854 | − | 30.4338i | −0.328525 | − | 1.01110i | ||||
\(907\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(908\) | −9.70820 | + | 7.05342i | −0.322178 | + | 0.234076i | ||||
\(909\) | 1.23607 | + | 3.80423i | 0.0409978 | + | 0.126178i | ||||
\(910\) | −2.47214 | + | 7.60845i | −0.0819505 | + | 0.252218i | ||||
\(911\) | −29.1246 | − | 21.1603i | −0.964941 | − | 0.701071i | −0.0106483 | − | 0.999943i | \(-0.503390\pi\) |
−0.954293 | + | 0.298872i | \(0.903390\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 18.0000 | 0.595387 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.56231 | + | 17.1190i | −0.183784 | + | 0.565628i | ||||
\(917\) | −3.70820 | − | 11.4127i | −0.122456 | − | 0.376880i | ||||
\(918\) | 12.9443 | − | 9.40456i | 0.427225 | − | 0.310397i | ||||
\(919\) | 32.3607 | − | 23.5114i | 1.06748 | − | 0.775570i | 0.0920227 | − | 0.995757i | \(-0.470667\pi\) |
0.975458 | + | 0.220187i | \(0.0706668\pi\) | |||||||
\(920\) | 7.41641 | + | 22.8254i | 0.244512 | + | 0.752530i | ||||
\(921\) | −12.3607 | + | 38.0423i | −0.407298 | + | 1.25354i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 48.0000 | 1.57994 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 3.23607 | + | 2.35114i | 0.106344 | + | 0.0772633i | ||||
\(927\) | 4.32624 | − | 13.3148i | 0.142092 | − | 0.437315i | ||||
\(928\) | −9.27051 | − | 28.5317i | −0.304319 | − | 0.936599i | ||||
\(929\) | −4.85410 | + | 3.52671i | −0.159258 | + | 0.115708i | −0.664560 | − | 0.747235i | \(-0.731381\pi\) |
0.505302 | + | 0.862942i | \(0.331381\pi\) | |||||||
\(930\) | −32.3607 | + | 23.5114i | −1.06115 | + | 0.770970i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5.56231 | + | 17.1190i | −0.182199 | + | 0.560752i | ||||
\(933\) | 29.1246 | + | 21.1603i | 0.953497 | + | 0.692756i | ||||
\(934\) | −30.0000 | −0.981630 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.0000 | −0.392232 | ||||||||
\(937\) | −12.9443 | − | 9.40456i | −0.422871 | − | 0.307234i | 0.355921 | − | 0.934516i | \(-0.384167\pi\) |
−0.778792 | + | 0.627282i | \(0.784167\pi\) | |||||||
\(938\) | −2.47214 | + | 7.60845i | −0.0807181 | + | 0.248425i | ||||
\(939\) | 1.23607 | + | 3.80423i | 0.0403376 | + | 0.124146i | ||||
\(940\) | 16.1803 | − | 11.7557i | 0.527744 | − | 0.383429i | ||||
\(941\) | −19.4164 | + | 14.1068i | −0.632957 | + | 0.459870i | −0.857423 | − | 0.514612i | \(-0.827936\pi\) |
0.224467 | + | 0.974482i | \(0.427936\pi\) | |||||||
\(942\) | −8.65248 | − | 26.6296i | −0.281913 | − | 0.867639i | ||||
\(943\) | 4.94427 | − | 15.2169i | 0.161008 | − | 0.495531i | ||||
\(944\) | 1.61803 | + | 1.17557i | 0.0526625 | + | 0.0382616i | ||||
\(945\) | 8.00000 | 0.260240 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.0000 | −1.16984 | −0.584921 | − | 0.811090i | \(-0.698875\pi\) | ||||
−0.584921 | + | 0.811090i | \(0.698875\pi\) | |||||||
\(948\) | −12.9443 | − | 9.40456i | −0.420410 | − | 0.305446i | ||||
\(949\) | −9.88854 | + | 30.4338i | −0.320996 | + | 0.987923i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.23607 | − | 2.35114i | 0.104937 | − | 0.0762410i | ||||
\(952\) | 9.70820 | − | 7.05342i | 0.314645 | − | 0.228603i | ||||
\(953\) | −10.5066 | − | 32.3359i | −0.340341 | − | 1.04746i | −0.964031 | − | 0.265791i | \(-0.914367\pi\) |
0.623689 | − | 0.781672i | \(-0.285633\pi\) | |||||||
\(954\) | 1.85410 | − | 5.70634i | 0.0600288 | − | 0.184750i | ||||
\(955\) | 12.9443 | + | 9.40456i | 0.418867 | + | 0.304325i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.00000 | −0.129234 | ||||||||
\(959\) | 8.09017 | + | 5.87785i | 0.261245 | + | 0.189806i | ||||
\(960\) | −8.65248 | + | 26.6296i | −0.279257 | + | 0.859466i | ||||
\(961\) | 21.3222 | + | 65.6229i | 0.687812 | + | 2.11687i | ||||
\(962\) | 19.4164 | − | 14.1068i | 0.626010 | − | 0.454823i | ||||
\(963\) | 9.70820 | − | 7.05342i | 0.312842 | − | 0.227293i | ||||
\(964\) | −6.18034 | − | 19.0211i | −0.199055 | − | 0.612629i | ||||
\(965\) | −8.65248 | + | 26.6296i | −0.278533 | + | 0.857237i | ||||
\(966\) | −6.47214 | − | 4.70228i | −0.208238 | − | 0.151293i | ||||
\(967\) | −40.0000 | −1.28631 | −0.643157 | − | 0.765735i | \(-0.722376\pi\) | ||||
−0.643157 | + | 0.765735i | \(0.722376\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16.1803 | + | 11.7557i | 0.519519 | + | 0.377453i | ||||
\(971\) | 4.32624 | − | 13.3148i | 0.138836 | − | 0.427292i | −0.857331 | − | 0.514765i | \(-0.827879\pi\) |
0.996167 | + | 0.0874730i | \(0.0278792\pi\) | |||||||
\(972\) | 3.09017 | + | 9.51057i | 0.0991172 | + | 0.305052i | ||||
\(973\) | −6.47214 | + | 4.70228i | −0.207487 | + | 0.150748i | ||||
\(974\) | −22.6525 | + | 16.4580i | −0.725832 | + | 0.527348i | ||||
\(975\) | 2.47214 | + | 7.60845i | 0.0791717 | + | 0.243665i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.9787 | − | 24.6870i | −1.08708 | − | 0.789806i | −0.108172 | − | 0.994132i | \(-0.534500\pi\) |
−0.978903 | + | 0.204326i | \(0.934500\pi\) | |||||||
\(978\) | 16.0000 | 0.511624 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 2.00000 | 0.0638877 | ||||||||
\(981\) | −11.3262 | − | 8.22899i | −0.361619 | − | 0.262732i | ||||
\(982\) | 8.65248 | − | 26.6296i | 0.276112 | − | 0.849784i | ||||
\(983\) | 16.6869 | + | 51.3571i | 0.532230 | + | 1.63804i | 0.749559 | + | 0.661937i | \(0.230265\pi\) |
−0.217329 | + | 0.976098i | \(0.569735\pi\) | |||||||
\(984\) | 19.4164 | − | 14.1068i | 0.618972 | − | 0.449710i | ||||
\(985\) | −35.5967 | + | 25.8626i | −1.13421 | + | 0.824049i | ||||
\(986\) | 7.41641 | + | 22.8254i | 0.236187 | + | 0.726907i | ||||
\(987\) | −6.18034 | + | 19.0211i | −0.196722 | + | 0.605449i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.0000 | 1.52631 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.0000 | 1.65183 | 0.825917 | − | 0.563791i | \(-0.190658\pi\) | ||||
0.825917 | + | 0.563791i | \(0.190658\pi\) | |||||||
\(992\) | 40.4508 | + | 29.3893i | 1.28432 | + | 0.933110i | ||||
\(993\) | −12.3607 | + | 38.0423i | −0.392254 | + | 1.20723i | ||||
\(994\) | 3.70820 | + | 11.4127i | 0.117617 | + | 0.361988i | ||||
\(995\) | −29.1246 | + | 21.1603i | −0.923312 | + | 0.670826i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.18034 | − | 19.0211i | −0.195733 | − | 0.602405i | −0.999967 | − | 0.00809237i | \(-0.997424\pi\) |
0.804234 | − | 0.594313i | \(-0.202576\pi\) | |||||||
\(998\) | 4.94427 | − | 15.2169i | 0.156508 | − | 0.481683i | ||||
\(999\) | −19.4164 | − | 14.1068i | −0.614308 | − | 0.446321i |
(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 | 847.2.f.k.323.1 | 4 | ||
11.2 | odd | 10 | 847.2.f.e.148.1 | 4 | |||
11.3 | even | 5 | inner | 847.2.f.k.729.1 | 4 | ||
11.4 | even | 5 | inner | 847.2.f.k.372.1 | 4 | ||
11.5 | even | 5 | 847.2.a.a.1.1 | 1 | |||
11.6 | odd | 10 | 77.2.a.c.1.1 | ✓ | 1 | ||
11.7 | odd | 10 | 847.2.f.e.372.1 | 4 | |||
11.8 | odd | 10 | 847.2.f.e.729.1 | 4 | |||
11.9 | even | 5 | inner | 847.2.f.k.148.1 | 4 | ||
11.10 | odd | 2 | 847.2.f.e.323.1 | 4 | |||
33.5 | odd | 10 | 7623.2.a.n.1.1 | 1 | |||
33.17 | even | 10 | 693.2.a.a.1.1 | 1 | |||
44.39 | even | 10 | 1232.2.a.a.1.1 | 1 | |||
55.17 | even | 20 | 1925.2.b.d.1849.2 | 2 | |||
55.28 | even | 20 | 1925.2.b.d.1849.1 | 2 | |||
55.39 | odd | 10 | 1925.2.a.c.1.1 | 1 | |||
77.6 | even | 10 | 539.2.a.d.1.1 | 1 | |||
77.17 | even | 30 | 539.2.e.b.177.1 | 2 | |||
77.27 | odd | 10 | 5929.2.a.b.1.1 | 1 | |||
77.39 | odd | 30 | 539.2.e.a.177.1 | 2 | |||
77.61 | even | 30 | 539.2.e.b.67.1 | 2 | |||
77.72 | odd | 30 | 539.2.e.a.67.1 | 2 | |||
88.61 | odd | 10 | 4928.2.a.g.1.1 | 1 | |||
88.83 | even | 10 | 4928.2.a.bi.1.1 | 1 | |||
231.83 | odd | 10 | 4851.2.a.a.1.1 | 1 | |||
308.83 | odd | 10 | 8624.2.a.bc.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.a.c.1.1 | ✓ | 1 | 11.6 | odd | 10 | ||
539.2.a.d.1.1 | 1 | 77.6 | even | 10 | |||
539.2.e.a.67.1 | 2 | 77.72 | odd | 30 | |||
539.2.e.a.177.1 | 2 | 77.39 | odd | 30 | |||
539.2.e.b.67.1 | 2 | 77.61 | even | 30 | |||
539.2.e.b.177.1 | 2 | 77.17 | even | 30 | |||
693.2.a.a.1.1 | 1 | 33.17 | even | 10 | |||
847.2.a.a.1.1 | 1 | 11.5 | even | 5 | |||
847.2.f.e.148.1 | 4 | 11.2 | odd | 10 | |||
847.2.f.e.323.1 | 4 | 11.10 | odd | 2 | |||
847.2.f.e.372.1 | 4 | 11.7 | odd | 10 | |||
847.2.f.e.729.1 | 4 | 11.8 | odd | 10 | |||
847.2.f.k.148.1 | 4 | 11.9 | even | 5 | inner | ||
847.2.f.k.323.1 | 4 | 1.1 | even | 1 | trivial | ||
847.2.f.k.372.1 | 4 | 11.4 | even | 5 | inner | ||
847.2.f.k.729.1 | 4 | 11.3 | even | 5 | inner | ||
1232.2.a.a.1.1 | 1 | 44.39 | even | 10 | |||
1925.2.a.c.1.1 | 1 | 55.39 | odd | 10 | |||
1925.2.b.d.1849.1 | 2 | 55.28 | even | 20 | |||
1925.2.b.d.1849.2 | 2 | 55.17 | even | 20 | |||
4851.2.a.a.1.1 | 1 | 231.83 | odd | 10 | |||
4928.2.a.g.1.1 | 1 | 88.61 | odd | 10 | |||
4928.2.a.bi.1.1 | 1 | 88.83 | even | 10 | |||
5929.2.a.b.1.1 | 1 | 77.27 | odd | 10 | |||
7623.2.a.n.1.1 | 1 | 33.5 | odd | 10 | |||
8624.2.a.bc.1.1 | 1 | 308.83 | odd | 10 |