Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [726,2,Mod(487,726)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(726, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("726.487");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 726 = 2 \cdot 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 726.e (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: | \(5.79713918674\) |
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 66) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 511.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 726.511 |
Dual form | 726.2.e.f.493.1 |
$q$-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 \(\left(\mathbb{Z}/726\mathbb{Z}\right)^\times\).
\(n\) | \(485\) | \(607\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | + | 0.951057i | 0.218508 | + | 0.672499i | ||||
\(3\) | 0.809017 | + | 0.587785i | 0.467086 | + | 0.339358i | ||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | −1.19098 | + | 3.66547i | −0.532624 | + | 1.63925i | 0.216104 | + | 0.976370i | \(0.430665\pi\) |
−0.748728 | + | 0.662877i | \(0.769335\pi\) | |||||||
\(6\) | −0.309017 | + | 0.951057i | −0.126156 | + | 0.388267i | ||||
\(7\) | −1.92705 | + | 1.40008i | −0.728357 | + | 0.529182i | −0.889043 | − | 0.457823i | \(-0.848629\pi\) |
0.160686 | + | 0.987006i | \(0.448629\pi\) | |||||||
\(8\) | −0.809017 | − | 0.587785i | −0.286031 | − | 0.207813i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | −3.85410 | −1.21877 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0.381966 | + | 1.17557i | 0.105938 | + | 0.326045i | 0.989950 | − | 0.141421i | \(-0.0451671\pi\) |
−0.884011 | + | 0.467466i | \(0.845167\pi\) | |||||||
\(14\) | −1.92705 | − | 1.40008i | −0.515026 | − | 0.374188i | ||||
\(15\) | −3.11803 | + | 2.26538i | −0.805073 | + | 0.584920i | ||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | 2.00000 | − | 6.15537i | 0.485071 | − | 1.49290i | −0.346806 | − | 0.937937i | \(-0.612734\pi\) |
0.831878 | − | 0.554959i | \(-0.187266\pi\) | |||||||
\(18\) | −0.809017 | + | 0.587785i | −0.190687 | + | 0.138542i | ||||
\(19\) | −1.00000 | − | 0.726543i | −0.229416 | − | 0.166680i | 0.467139 | − | 0.884184i | \(-0.345285\pi\) |
−0.696555 | + | 0.717504i | \(0.745285\pi\) | |||||||
\(20\) | −1.19098 | − | 3.66547i | −0.266312 | − | 0.819624i | ||||
\(21\) | −2.38197 | −0.519788 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.23607 | 0.257738 | 0.128869 | − | 0.991662i | \(-0.458865\pi\) | ||||
0.128869 | + | 0.991662i | \(0.458865\pi\) | |||||||
\(24\) | −0.309017 | − | 0.951057i | −0.0630778 | − | 0.194134i | ||||
\(25\) | −7.97214 | − | 5.79210i | −1.59443 | − | 1.15842i | ||||
\(26\) | −1.00000 | + | 0.726543i | −0.196116 | + | 0.142487i | ||||
\(27\) | −0.309017 | + | 0.951057i | −0.0594703 | + | 0.183031i | ||||
\(28\) | 0.736068 | − | 2.26538i | 0.139104 | − | 0.428117i | ||||
\(29\) | 2.11803 | − | 1.53884i | 0.393309 | − | 0.285756i | −0.373501 | − | 0.927630i | \(-0.621843\pi\) |
0.766810 | + | 0.641874i | \(0.221843\pi\) | |||||||
\(30\) | −3.11803 | − | 2.26538i | −0.569273 | − | 0.413601i | ||||
\(31\) | 1.97214 | + | 6.06961i | 0.354206 | + | 1.09013i | 0.956468 | + | 0.291836i | \(0.0942661\pi\) |
−0.602262 | + | 0.798298i | \(0.705734\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.47214 | 1.10996 | ||||||||
\(35\) | −2.83688 | − | 8.73102i | −0.479520 | − | 1.47581i | ||||
\(36\) | −0.809017 | − | 0.587785i | −0.134836 | − | 0.0979642i | ||||
\(37\) | −8.47214 | + | 6.15537i | −1.39281 | + | 1.01194i | −0.397260 | + | 0.917706i | \(0.630039\pi\) |
−0.995550 | + | 0.0942301i | \(0.969961\pi\) | |||||||
\(38\) | 0.381966 | − | 1.17557i | 0.0619631 | − | 0.190703i | ||||
\(39\) | −0.381966 | + | 1.17557i | −0.0611635 | + | 0.188242i | ||||
\(40\) | 3.11803 | − | 2.26538i | 0.493004 | − | 0.358189i | ||||
\(41\) | −1.00000 | − | 0.726543i | −0.156174 | − | 0.113467i | 0.506954 | − | 0.861973i | \(-0.330771\pi\) |
−0.663128 | + | 0.748506i | \(0.730771\pi\) | |||||||
\(42\) | −0.736068 | − | 2.26538i | −0.113578 | − | 0.349556i | ||||
\(43\) | 1.23607 | 0.188499 | 0.0942493 | − | 0.995549i | \(-0.469955\pi\) | ||||
0.0942493 | + | 0.995549i | \(0.469955\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.85410 | −0.574536 | ||||||||
\(46\) | 0.381966 | + | 1.17557i | 0.0563178 | + | 0.173328i | ||||
\(47\) | 5.23607 | + | 3.80423i | 0.763759 | + | 0.554903i | 0.900061 | − | 0.435764i | \(-0.143522\pi\) |
−0.136302 | + | 0.990667i | \(0.543522\pi\) | |||||||
\(48\) | 0.809017 | − | 0.587785i | 0.116772 | − | 0.0848395i | ||||
\(49\) | −0.409830 | + | 1.26133i | −0.0585472 | + | 0.180190i | ||||
\(50\) | 3.04508 | − | 9.37181i | 0.430640 | − | 1.32537i | ||||
\(51\) | 5.23607 | − | 3.80423i | 0.733196 | − | 0.532698i | ||||
\(52\) | −1.00000 | − | 0.726543i | −0.138675 | − | 0.100753i | ||||
\(53\) | 0.881966 | + | 2.71441i | 0.121147 | + | 0.372853i | 0.993179 | − | 0.116595i | \(-0.0371981\pi\) |
−0.872032 | + | 0.489449i | \(0.837198\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.38197 | 0.318304 | ||||||||
\(57\) | −0.381966 | − | 1.17557i | −0.0505926 | − | 0.155708i | ||||
\(58\) | 2.11803 | + | 1.53884i | 0.278111 | + | 0.202060i | ||||
\(59\) | −2.30902 | + | 1.67760i | −0.300608 | + | 0.218405i | −0.727856 | − | 0.685730i | \(-0.759483\pi\) |
0.427248 | + | 0.904135i | \(0.359483\pi\) | |||||||
\(60\) | 1.19098 | − | 3.66547i | 0.153755 | − | 0.473210i | ||||
\(61\) | −3.47214 | + | 10.6861i | −0.444561 | + | 1.36822i | 0.438403 | + | 0.898779i | \(0.355544\pi\) |
−0.882964 | + | 0.469441i | \(0.844456\pi\) | |||||||
\(62\) | −5.16312 | + | 3.75123i | −0.655717 | + | 0.476406i | ||||
\(63\) | −1.92705 | − | 1.40008i | −0.242786 | − | 0.176394i | ||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | −4.76393 | −0.590893 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 2.00000 | + | 6.15537i | 0.242536 | + | 0.746448i | ||||
\(69\) | 1.00000 | + | 0.726543i | 0.120386 | + | 0.0874654i | ||||
\(70\) | 7.42705 | − | 5.39607i | 0.887702 | − | 0.644954i | ||||
\(71\) | 1.09017 | − | 3.35520i | 0.129379 | − | 0.398189i | −0.865294 | − | 0.501264i | \(-0.832868\pi\) |
0.994674 | + | 0.103076i | \(0.0328684\pi\) | |||||||
\(72\) | 0.309017 | − | 0.951057i | 0.0364180 | − | 0.112083i | ||||
\(73\) | −3.50000 | + | 2.54290i | −0.409644 | + | 0.297624i | −0.773458 | − | 0.633848i | \(-0.781474\pi\) |
0.363814 | + | 0.931472i | \(0.381474\pi\) | |||||||
\(74\) | −8.47214 | − | 6.15537i | −0.984866 | − | 0.715547i | ||||
\(75\) | −3.04508 | − | 9.37181i | −0.351616 | − | 1.08216i | ||||
\(76\) | 1.23607 | 0.141787 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.23607 | −0.139957 | ||||||||
\(79\) | 1.95492 | + | 6.01661i | 0.219945 | + | 0.676921i | 0.998765 | + | 0.0496744i | \(0.0158184\pi\) |
−0.778820 | + | 0.627247i | \(0.784182\pi\) | |||||||
\(80\) | 3.11803 | + | 2.26538i | 0.348607 | + | 0.253278i | ||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 0.381966 | − | 1.17557i | 0.0421811 | − | 0.129820i | ||||
\(83\) | −5.04508 | + | 15.5272i | −0.553770 | + | 1.70433i | 0.145400 | + | 0.989373i | \(0.453553\pi\) |
−0.699170 | + | 0.714956i | \(0.746447\pi\) | |||||||
\(84\) | 1.92705 | − | 1.40008i | 0.210258 | − | 0.152762i | ||||
\(85\) | 20.1803 | + | 14.6619i | 2.18887 | + | 1.59030i | ||||
\(86\) | 0.381966 | + | 1.17557i | 0.0411885 | + | 0.126765i | ||||
\(87\) | 2.61803 | 0.280683 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.70820 | 0.181069 | 0.0905346 | − | 0.995893i | \(-0.471142\pi\) | ||||
0.0905346 | + | 0.995893i | \(0.471142\pi\) | |||||||
\(90\) | −1.19098 | − | 3.66547i | −0.125541 | − | 0.386374i | ||||
\(91\) | −2.38197 | − | 1.73060i | −0.249698 | − | 0.181416i | ||||
\(92\) | −1.00000 | + | 0.726543i | −0.104257 | + | 0.0757473i | ||||
\(93\) | −1.97214 | + | 6.06961i | −0.204501 | + | 0.629389i | ||||
\(94\) | −2.00000 | + | 6.15537i | −0.206284 | + | 0.634878i | ||||
\(95\) | 3.85410 | − | 2.80017i | 0.395423 | − | 0.287291i | ||||
\(96\) | 0.809017 | + | 0.587785i | 0.0825700 | + | 0.0599906i | ||||
\(97\) | −1.33688 | − | 4.11450i | −0.135740 | − | 0.417764i | 0.859965 | − | 0.510354i | \(-0.170485\pi\) |
−0.995704 | + | 0.0925898i | \(0.970485\pi\) | |||||||
\(98\) | −1.32624 | −0.133970 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.85410 | 0.985410 | ||||||||
\(101\) | −4.51722 | − | 13.9026i | −0.449480 | − | 1.38336i | −0.877495 | − | 0.479586i | \(-0.840787\pi\) |
0.428014 | − | 0.903772i | \(-0.359213\pi\) | |||||||
\(102\) | 5.23607 | + | 3.80423i | 0.518448 | + | 0.376675i | ||||
\(103\) | 13.7812 | − | 10.0126i | 1.35790 | − | 0.986570i | 0.359322 | − | 0.933214i | \(-0.383008\pi\) |
0.998576 | − | 0.0533565i | \(-0.0169920\pi\) | |||||||
\(104\) | 0.381966 | − | 1.17557i | 0.0374548 | − | 0.115274i | ||||
\(105\) | 2.83688 | − | 8.73102i | 0.276851 | − | 0.852061i | ||||
\(106\) | −2.30902 | + | 1.67760i | −0.224272 | + | 0.162943i | ||||
\(107\) | −6.16312 | − | 4.47777i | −0.595811 | − | 0.432882i | 0.248578 | − | 0.968612i | \(-0.420037\pi\) |
−0.844390 | + | 0.535730i | \(0.820037\pi\) | |||||||
\(108\) | −0.309017 | − | 0.951057i | −0.0297352 | − | 0.0915155i | ||||
\(109\) | −9.41641 | −0.901928 | −0.450964 | − | 0.892542i | \(-0.648920\pi\) | ||||
−0.450964 | + | 0.892542i | \(0.648920\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.4721 | −0.993971 | ||||||||
\(112\) | 0.736068 | + | 2.26538i | 0.0695519 | + | 0.214059i | ||||
\(113\) | 2.85410 | + | 2.07363i | 0.268491 | + | 0.195070i | 0.713882 | − | 0.700266i | \(-0.246935\pi\) |
−0.445391 | + | 0.895336i | \(0.646935\pi\) | |||||||
\(114\) | 1.00000 | − | 0.726543i | 0.0936586 | − | 0.0680469i | ||||
\(115\) | −1.47214 | + | 4.53077i | −0.137277 | + | 0.422496i | ||||
\(116\) | −0.809017 | + | 2.48990i | −0.0751153 | + | 0.231181i | ||||
\(117\) | −1.00000 | + | 0.726543i | −0.0924500 | + | 0.0671689i | ||||
\(118\) | −2.30902 | − | 1.67760i | −0.212562 | − | 0.154436i | ||||
\(119\) | 4.76393 | + | 14.6619i | 0.436709 | + | 1.34405i | ||||
\(120\) | 3.85410 | 0.351830 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −11.2361 | −1.01727 | ||||||||
\(123\) | −0.381966 | − | 1.17557i | −0.0344407 | − | 0.105998i | ||||
\(124\) | −5.16312 | − | 3.75123i | −0.463662 | − | 0.336870i | ||||
\(125\) | 15.1353 | − | 10.9964i | 1.35374 | − | 0.983548i | ||||
\(126\) | 0.736068 | − | 2.26538i | 0.0655741 | − | 0.201816i | ||||
\(127\) | 3.70820 | − | 11.4127i | 0.329050 | − | 1.01271i | −0.640529 | − | 0.767934i | \(-0.721285\pi\) |
0.969579 | − | 0.244778i | \(-0.0787150\pi\) | |||||||
\(128\) | −0.809017 | + | 0.587785i | −0.0715077 | + | 0.0519534i | ||||
\(129\) | 1.00000 | + | 0.726543i | 0.0880451 | + | 0.0639685i | ||||
\(130\) | −1.47214 | − | 4.53077i | −0.129115 | − | 0.397375i | ||||
\(131\) | 18.2705 | 1.59630 | 0.798151 | − | 0.602458i | \(-0.205812\pi\) | ||||
0.798151 | + | 0.602458i | \(0.205812\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.94427 | 0.255301 | ||||||||
\(134\) | 1.23607 | + | 3.80423i | 0.106780 | + | 0.328635i | ||||
\(135\) | −3.11803 | − | 2.26538i | −0.268358 | − | 0.194973i | ||||
\(136\) | −5.23607 | + | 3.80423i | −0.448989 | + | 0.326210i | ||||
\(137\) | 5.29180 | − | 16.2865i | 0.452109 | − | 1.39145i | −0.422388 | − | 0.906415i | \(-0.638808\pi\) |
0.874496 | − | 0.485032i | \(-0.161192\pi\) | |||||||
\(138\) | −0.381966 | + | 1.17557i | −0.0325151 | + | 0.100071i | ||||
\(139\) | −7.09017 | + | 5.15131i | −0.601380 | + | 0.436928i | −0.846369 | − | 0.532598i | \(-0.821216\pi\) |
0.244988 | + | 0.969526i | \(0.421216\pi\) | |||||||
\(140\) | 7.42705 | + | 5.39607i | 0.627700 | + | 0.456051i | ||||
\(141\) | 2.00000 | + | 6.15537i | 0.168430 | + | 0.518375i | ||||
\(142\) | 3.52786 | 0.296052 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.11803 | + | 9.59632i | 0.258939 | + | 0.796931i | ||||
\(146\) | −3.50000 | − | 2.54290i | −0.289662 | − | 0.210452i | ||||
\(147\) | −1.07295 | + | 0.779543i | −0.0884953 | + | 0.0642956i | ||||
\(148\) | 3.23607 | − | 9.95959i | 0.266003 | − | 0.818674i | ||||
\(149\) | 1.11803 | − | 3.44095i | 0.0915929 | − | 0.281894i | −0.894758 | − | 0.446552i | \(-0.852652\pi\) |
0.986351 | + | 0.164658i | \(0.0526519\pi\) | |||||||
\(150\) | 7.97214 | − | 5.79210i | 0.650922 | − | 0.472923i | ||||
\(151\) | 5.11803 | + | 3.71847i | 0.416500 | + | 0.302605i | 0.776228 | − | 0.630452i | \(-0.217131\pi\) |
−0.359728 | + | 0.933057i | \(0.617131\pi\) | |||||||
\(152\) | 0.381966 | + | 1.17557i | 0.0309815 | + | 0.0953514i | ||||
\(153\) | 6.47214 | 0.523241 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −24.5967 | −1.97566 | ||||||||
\(156\) | −0.381966 | − | 1.17557i | −0.0305818 | − | 0.0941210i | ||||
\(157\) | 3.61803 | + | 2.62866i | 0.288751 | + | 0.209790i | 0.722725 | − | 0.691136i | \(-0.242889\pi\) |
−0.433975 | + | 0.900925i | \(0.642889\pi\) | |||||||
\(158\) | −5.11803 | + | 3.71847i | −0.407169 | + | 0.295826i | ||||
\(159\) | −0.881966 | + | 2.71441i | −0.0699445 | + | 0.215267i | ||||
\(160\) | −1.19098 | + | 3.66547i | −0.0941555 | + | 0.289781i | ||||
\(161\) | −2.38197 | + | 1.73060i | −0.187725 | + | 0.136390i | ||||
\(162\) | −0.809017 | − | 0.587785i | −0.0635624 | − | 0.0461808i | ||||
\(163\) | 4.14590 | + | 12.7598i | 0.324732 | + | 0.999422i | 0.971562 | + | 0.236787i | \(0.0760944\pi\) |
−0.646830 | + | 0.762634i | \(0.723906\pi\) | |||||||
\(164\) | 1.23607 | 0.0965207 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.3262 | −1.26716 | ||||||||
\(167\) | 0.854102 | + | 2.62866i | 0.0660924 | + | 0.203411i | 0.978649 | − | 0.205539i | \(-0.0658948\pi\) |
−0.912556 | + | 0.408951i | \(0.865895\pi\) | |||||||
\(168\) | 1.92705 | + | 1.40008i | 0.148675 | + | 0.108019i | ||||
\(169\) | 9.28115 | − | 6.74315i | 0.713935 | − | 0.518704i | ||||
\(170\) | −7.70820 | + | 23.7234i | −0.591192 | + | 1.81950i | ||||
\(171\) | 0.381966 | − | 1.17557i | 0.0292097 | − | 0.0898981i | ||||
\(172\) | −1.00000 | + | 0.726543i | −0.0762493 | + | 0.0553983i | ||||
\(173\) | 8.78115 | + | 6.37988i | 0.667619 | + | 0.485053i | 0.869227 | − | 0.494413i | \(-0.164617\pi\) |
−0.201609 | + | 0.979466i | \(0.564617\pi\) | |||||||
\(174\) | 0.809017 | + | 2.48990i | 0.0613314 | + | 0.188759i | ||||
\(175\) | 23.4721 | 1.77433 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.85410 | −0.214527 | ||||||||
\(178\) | 0.527864 | + | 1.62460i | 0.0395651 | + | 0.121769i | ||||
\(179\) | 6.97214 | + | 5.06555i | 0.521122 | + | 0.378617i | 0.817026 | − | 0.576600i | \(-0.195621\pi\) |
−0.295904 | + | 0.955218i | \(0.595621\pi\) | |||||||
\(180\) | 3.11803 | − | 2.26538i | 0.232405 | − | 0.168852i | ||||
\(181\) | −2.32624 | + | 7.15942i | −0.172908 | + | 0.532156i | −0.999532 | − | 0.0305991i | \(-0.990258\pi\) |
0.826624 | + | 0.562755i | \(0.190258\pi\) | |||||||
\(182\) | 0.909830 | − | 2.80017i | 0.0674411 | − | 0.207562i | ||||
\(183\) | −9.09017 | + | 6.60440i | −0.671965 | + | 0.488211i | ||||
\(184\) | −1.00000 | − | 0.726543i | −0.0737210 | − | 0.0535614i | ||||
\(185\) | −12.4721 | − | 38.3853i | −0.916970 | − | 2.82214i | ||||
\(186\) | −6.38197 | −0.467948 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.47214 | −0.472029 | ||||||||
\(189\) | −0.736068 | − | 2.26538i | −0.0535411 | − | 0.164782i | ||||
\(190\) | 3.85410 | + | 2.80017i | 0.279606 | + | 0.203146i | ||||
\(191\) | −10.9443 | + | 7.95148i | −0.791900 | + | 0.575349i | −0.908527 | − | 0.417827i | \(-0.862792\pi\) |
0.116627 | + | 0.993176i | \(0.462792\pi\) | |||||||
\(192\) | −0.309017 | + | 0.951057i | −0.0223014 | + | 0.0686366i | ||||
\(193\) | −4.73607 | + | 14.5761i | −0.340910 | + | 1.04921i | 0.622828 | + | 0.782359i | \(0.285984\pi\) |
−0.963737 | + | 0.266853i | \(0.914016\pi\) | |||||||
\(194\) | 3.50000 | − | 2.54290i | 0.251285 | − | 0.182569i | ||||
\(195\) | −3.85410 | − | 2.80017i | −0.275998 | − | 0.200524i | ||||
\(196\) | −0.409830 | − | 1.26133i | −0.0292736 | − | 0.0900948i | ||||
\(197\) | −5.09017 | −0.362660 | −0.181330 | − | 0.983422i | \(-0.558040\pi\) | ||||
−0.181330 | + | 0.983422i | \(0.558040\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.8541 | 1.40742 | 0.703710 | − | 0.710487i | \(-0.251525\pi\) | ||||
0.703710 | + | 0.710487i | \(0.251525\pi\) | |||||||
\(200\) | 3.04508 | + | 9.37181i | 0.215320 | + | 0.662687i | ||||
\(201\) | 3.23607 | + | 2.35114i | 0.228255 | + | 0.165837i | ||||
\(202\) | 11.8262 | − | 8.59226i | 0.832091 | − | 0.604550i | ||||
\(203\) | −1.92705 | + | 5.93085i | −0.135252 | + | 0.416264i | ||||
\(204\) | −2.00000 | + | 6.15537i | −0.140028 | + | 0.430962i | ||||
\(205\) | 3.85410 | − | 2.80017i | 0.269182 | − | 0.195572i | ||||
\(206\) | 13.7812 | + | 10.0126i | 0.960178 | + | 0.697610i | ||||
\(207\) | 0.381966 | + | 1.17557i | 0.0265485 | + | 0.0817078i | ||||
\(208\) | 1.23607 | 0.0857059 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 9.18034 | 0.633504 | ||||||||
\(211\) | 8.23607 | + | 25.3480i | 0.566994 | + | 1.74503i | 0.661950 | + | 0.749548i | \(0.269729\pi\) |
−0.0949562 | + | 0.995481i | \(0.530271\pi\) | |||||||
\(212\) | −2.30902 | − | 1.67760i | −0.158584 | − | 0.115218i | ||||
\(213\) | 2.85410 | − | 2.07363i | 0.195560 | − | 0.142083i | ||||
\(214\) | 2.35410 | − | 7.24518i | 0.160923 | − | 0.495270i | ||||
\(215\) | −1.47214 | + | 4.53077i | −0.100399 | + | 0.308996i | ||||
\(216\) | 0.809017 | − | 0.587785i | 0.0550466 | − | 0.0399937i | ||||
\(217\) | −12.2984 | − | 8.93529i | −0.834868 | − | 0.606567i | ||||
\(218\) | −2.90983 | − | 8.95554i | −0.197079 | − | 0.606545i | ||||
\(219\) | −4.32624 | −0.292340 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.00000 | 0.538138 | ||||||||
\(222\) | −3.23607 | − | 9.95959i | −0.217191 | − | 0.668444i | ||||
\(223\) | 10.5902 | + | 7.69421i | 0.709170 | + | 0.515242i | 0.882906 | − | 0.469550i | \(-0.155584\pi\) |
−0.173736 | + | 0.984792i | \(0.555584\pi\) | |||||||
\(224\) | −1.92705 | + | 1.40008i | −0.128757 | + | 0.0935471i | ||||
\(225\) | 3.04508 | − | 9.37181i | 0.203006 | − | 0.624787i | ||||
\(226\) | −1.09017 | + | 3.35520i | −0.0725170 | + | 0.223184i | ||||
\(227\) | 11.2082 | − | 8.14324i | 0.743915 | − | 0.540486i | −0.150020 | − | 0.988683i | \(-0.547934\pi\) |
0.893935 | + | 0.448197i | \(0.147934\pi\) | |||||||
\(228\) | 1.00000 | + | 0.726543i | 0.0662266 | + | 0.0481165i | ||||
\(229\) | 1.56231 | + | 4.80828i | 0.103240 | + | 0.317740i | 0.989313 | − | 0.145805i | \(-0.0465772\pi\) |
−0.886073 | + | 0.463545i | \(0.846577\pi\) | |||||||
\(230\) | −4.76393 | −0.314124 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.61803 | −0.171882 | ||||||||
\(233\) | 2.76393 | + | 8.50651i | 0.181071 | + | 0.557280i | 0.999859 | − | 0.0168170i | \(-0.00535327\pi\) |
−0.818787 | + | 0.574097i | \(0.805353\pi\) | |||||||
\(234\) | −1.00000 | − | 0.726543i | −0.0653720 | − | 0.0474956i | ||||
\(235\) | −20.1803 | + | 14.6619i | −1.31642 | + | 0.956435i | ||||
\(236\) | 0.881966 | − | 2.71441i | 0.0574111 | − | 0.176693i | ||||
\(237\) | −1.95492 | + | 6.01661i | −0.126985 | + | 0.390821i | ||||
\(238\) | −12.4721 | + | 9.06154i | −0.808448 | + | 0.587372i | ||||
\(239\) | 6.09017 | + | 4.42477i | 0.393940 | + | 0.286214i | 0.767068 | − | 0.641565i | \(-0.221715\pi\) |
−0.373128 | + | 0.927780i | \(0.621715\pi\) | |||||||
\(240\) | 1.19098 | + | 3.66547i | 0.0768776 | + | 0.236605i | ||||
\(241\) | −22.5623 | −1.45337 | −0.726683 | − | 0.686973i | \(-0.758939\pi\) | ||||
−0.726683 | + | 0.686973i | \(0.758939\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.47214 | − | 10.6861i | −0.222281 | − | 0.684110i | ||||
\(245\) | −4.13525 | − | 3.00444i | −0.264192 | − | 0.191947i | ||||
\(246\) | 1.00000 | − | 0.726543i | 0.0637577 | − | 0.0463227i | ||||
\(247\) | 0.472136 | − | 1.45309i | 0.0300413 | − | 0.0924576i | ||||
\(248\) | 1.97214 | − | 6.06961i | 0.125231 | − | 0.385421i | ||||
\(249\) | −13.2082 | + | 9.59632i | −0.837036 | + | 0.608142i | ||||
\(250\) | 15.1353 | + | 10.9964i | 0.957238 | + | 0.695474i | ||||
\(251\) | −1.13525 | − | 3.49396i | −0.0716567 | − | 0.220537i | 0.908814 | − | 0.417201i | \(-0.136989\pi\) |
−0.980471 | + | 0.196665i | \(0.936989\pi\) | |||||||
\(252\) | 2.38197 | 0.150050 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 12.0000 | 0.752947 | ||||||||
\(255\) | 7.70820 | + | 23.7234i | 0.482706 | + | 1.48562i | ||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 19.5623 | − | 14.2128i | 1.22026 | − | 0.886573i | 0.224141 | − | 0.974557i | \(-0.428042\pi\) |
0.996122 | + | 0.0879836i | \(0.0280423\pi\) | |||||||
\(258\) | −0.381966 | + | 1.17557i | −0.0237802 | + | 0.0731878i | ||||
\(259\) | 7.70820 | − | 23.7234i | 0.478964 | − | 1.47410i | ||||
\(260\) | 3.85410 | − | 2.80017i | 0.239021 | − | 0.173659i | ||||
\(261\) | 2.11803 | + | 1.53884i | 0.131103 | + | 0.0952519i | ||||
\(262\) | 5.64590 | + | 17.3763i | 0.348805 | + | 1.07351i | ||||
\(263\) | −5.70820 | −0.351983 | −0.175991 | − | 0.984392i | \(-0.556313\pi\) | ||||
−0.175991 | + | 0.984392i | \(0.556313\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.0000 | −0.675725 | ||||||||
\(266\) | 0.909830 | + | 2.80017i | 0.0557853 | + | 0.171689i | ||||
\(267\) | 1.38197 | + | 1.00406i | 0.0845749 | + | 0.0614473i | ||||
\(268\) | −3.23607 | + | 2.35114i | −0.197674 | + | 0.143619i | ||||
\(269\) | 4.61803 | − | 14.2128i | 0.281567 | − | 0.866573i | −0.705840 | − | 0.708371i | \(-0.749430\pi\) |
0.987407 | − | 0.158202i | \(-0.0505696\pi\) | |||||||
\(270\) | 1.19098 | − | 3.66547i | 0.0724809 | − | 0.223073i | ||||
\(271\) | 2.76393 | − | 2.00811i | 0.167897 | − | 0.121984i | −0.500664 | − | 0.865642i | \(-0.666911\pi\) |
0.668561 | + | 0.743658i | \(0.266911\pi\) | |||||||
\(272\) | −5.23607 | − | 3.80423i | −0.317483 | − | 0.230665i | ||||
\(273\) | −0.909830 | − | 2.80017i | −0.0550654 | − | 0.169474i | ||||
\(274\) | 17.1246 | 1.03454 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.23607 | −0.0744025 | ||||||||
\(277\) | −9.00000 | − | 27.6992i | −0.540758 | − | 1.66428i | −0.730869 | − | 0.682518i | \(-0.760885\pi\) |
0.190111 | − | 0.981763i | \(-0.439115\pi\) | |||||||
\(278\) | −7.09017 | − | 5.15131i | −0.425240 | − | 0.308955i | ||||
\(279\) | −5.16312 | + | 3.75123i | −0.309108 | + | 0.224580i | ||||
\(280\) | −2.83688 | + | 8.73102i | −0.169536 | + | 0.521778i | ||||
\(281\) | −5.29180 | + | 16.2865i | −0.315682 | + | 0.971570i | 0.659791 | + | 0.751449i | \(0.270645\pi\) |
−0.975473 | + | 0.220120i | \(0.929355\pi\) | |||||||
\(282\) | −5.23607 | + | 3.80423i | −0.311803 | + | 0.226538i | ||||
\(283\) | −9.61803 | − | 6.98791i | −0.571733 | − | 0.415388i | 0.264001 | − | 0.964522i | \(-0.414958\pi\) |
−0.835734 | + | 0.549134i | \(0.814958\pi\) | |||||||
\(284\) | 1.09017 | + | 3.35520i | 0.0646897 | + | 0.199094i | ||||
\(285\) | 4.76393 | 0.282191 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.94427 | 0.173795 | ||||||||
\(288\) | 0.309017 | + | 0.951057i | 0.0182090 | + | 0.0560415i | ||||
\(289\) | −20.1353 | − | 14.6291i | −1.18443 | − | 0.860536i | ||||
\(290\) | −8.16312 | + | 5.93085i | −0.479355 | + | 0.348272i | ||||
\(291\) | 1.33688 | − | 4.11450i | 0.0783694 | − | 0.241196i | ||||
\(292\) | 1.33688 | − | 4.11450i | 0.0782350 | − | 0.240783i | ||||
\(293\) | 19.3992 | − | 14.0943i | 1.13331 | − | 0.823400i | 0.147139 | − | 0.989116i | \(-0.452994\pi\) |
0.986174 | + | 0.165716i | \(0.0529935\pi\) | |||||||
\(294\) | −1.07295 | − | 0.779543i | −0.0625757 | − | 0.0454639i | ||||
\(295\) | −3.39919 | − | 10.4616i | −0.197908 | − | 0.609099i | ||||
\(296\) | 10.4721 | 0.608681 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.61803 | 0.209587 | ||||||||
\(299\) | 0.472136 | + | 1.45309i | 0.0273043 | + | 0.0840341i | ||||
\(300\) | 7.97214 | + | 5.79210i | 0.460271 | + | 0.334407i | ||||
\(301\) | −2.38197 | + | 1.73060i | −0.137294 | + | 0.0997501i | ||||
\(302\) | −1.95492 | + | 6.01661i | −0.112493 | + | 0.346217i | ||||
\(303\) | 4.51722 | − | 13.9026i | 0.259508 | − | 0.798682i | ||||
\(304\) | −1.00000 | + | 0.726543i | −0.0573539 | + | 0.0416701i | ||||
\(305\) | −35.0344 | − | 25.4540i | −2.00607 | − | 1.45749i | ||||
\(306\) | 2.00000 | + | 6.15537i | 0.114332 | + | 0.351879i | ||||
\(307\) | 14.6525 | 0.836261 | 0.418130 | − | 0.908387i | \(-0.362685\pi\) | ||||
0.418130 | + | 0.908387i | \(0.362685\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.0344 | 0.969056 | ||||||||
\(310\) | −7.60081 | − | 23.3929i | −0.431697 | − | 1.32863i | ||||
\(311\) | −9.61803 | − | 6.98791i | −0.545389 | − | 0.396248i | 0.280694 | − | 0.959797i | \(-0.409435\pi\) |
−0.826082 | + | 0.563549i | \(0.809435\pi\) | |||||||
\(312\) | 1.00000 | − | 0.726543i | 0.0566139 | − | 0.0411324i | ||||
\(313\) | 6.75329 | − | 20.7845i | 0.381718 | − | 1.17481i | −0.557114 | − | 0.830436i | \(-0.688092\pi\) |
0.938833 | − | 0.344373i | \(-0.111908\pi\) | |||||||
\(314\) | −1.38197 | + | 4.25325i | −0.0779889 | + | 0.240025i | ||||
\(315\) | 7.42705 | − | 5.39607i | 0.418467 | − | 0.304034i | ||||
\(316\) | −5.11803 | − | 3.71847i | −0.287912 | − | 0.209180i | ||||
\(317\) | 4.90983 | + | 15.1109i | 0.275764 | + | 0.848713i | 0.989016 | + | 0.147806i | \(0.0472211\pi\) |
−0.713253 | + | 0.700907i | \(0.752779\pi\) | |||||||
\(318\) | −2.85410 | −0.160050 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −3.85410 | −0.215451 | ||||||||
\(321\) | −2.35410 | − | 7.24518i | −0.131393 | − | 0.404387i | ||||
\(322\) | −2.38197 | − | 1.73060i | −0.132742 | − | 0.0964425i | ||||
\(323\) | −6.47214 | + | 4.70228i | −0.360119 | + | 0.261642i | ||||
\(324\) | 0.309017 | − | 0.951057i | 0.0171676 | − | 0.0528365i | ||||
\(325\) | 3.76393 | − | 11.5842i | 0.208785 | − | 0.642575i | ||||
\(326\) | −10.8541 | + | 7.88597i | −0.601153 | + | 0.436763i | ||||
\(327\) | −7.61803 | − | 5.53483i | −0.421278 | − | 0.306077i | ||||
\(328\) | 0.381966 | + | 1.17557i | 0.0210905 | + | 0.0649100i | ||||
\(329\) | −15.4164 | −0.849934 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.94427 | −0.491622 | −0.245811 | − | 0.969318i | \(-0.579054\pi\) | ||||
−0.245811 | + | 0.969318i | \(0.579054\pi\) | |||||||
\(332\) | −5.04508 | − | 15.5272i | −0.276885 | − | 0.852164i | ||||
\(333\) | −8.47214 | − | 6.15537i | −0.464270 | − | 0.337312i | ||||
\(334\) | −2.23607 | + | 1.62460i | −0.122352 | + | 0.0888941i | ||||
\(335\) | −4.76393 | + | 14.6619i | −0.260281 | + | 0.801064i | ||||
\(336\) | −0.736068 | + | 2.26538i | −0.0401558 | + | 0.123587i | ||||
\(337\) | 8.85410 | − | 6.43288i | 0.482314 | − | 0.350421i | −0.319907 | − | 0.947449i | \(-0.603652\pi\) |
0.802221 | + | 0.597028i | \(0.203652\pi\) | |||||||
\(338\) | 9.28115 | + | 6.74315i | 0.504828 | + | 0.366779i | ||||
\(339\) | 1.09017 | + | 3.35520i | 0.0592099 | + | 0.182229i | ||||
\(340\) | −24.9443 | −1.35279 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.23607 | 0.0668389 | ||||||||
\(343\) | −6.12868 | − | 18.8621i | −0.330917 | − | 1.01846i | ||||
\(344\) | −1.00000 | − | 0.726543i | −0.0539164 | − | 0.0391725i | ||||
\(345\) | −3.85410 | + | 2.80017i | −0.207498 | + | 0.150756i | ||||
\(346\) | −3.35410 | + | 10.3229i | −0.180318 | + | 0.554961i | ||||
\(347\) | 1.59017 | − | 4.89404i | 0.0853648 | − | 0.262726i | −0.899258 | − | 0.437418i | \(-0.855893\pi\) |
0.984623 | + | 0.174692i | \(0.0558930\pi\) | |||||||
\(348\) | −2.11803 | + | 1.53884i | −0.113539 | + | 0.0824906i | ||||
\(349\) | 7.09017 | + | 5.15131i | 0.379528 | + | 0.275743i | 0.761151 | − | 0.648575i | \(-0.224635\pi\) |
−0.381623 | + | 0.924318i | \(0.624635\pi\) | |||||||
\(350\) | 7.25329 | + | 22.3233i | 0.387705 | + | 1.19323i | ||||
\(351\) | −1.23607 | −0.0659764 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.5967 | 1.46883 | 0.734413 | − | 0.678702i | \(-0.237457\pi\) | ||||
0.734413 | + | 0.678702i | \(0.237457\pi\) | |||||||
\(354\) | −0.881966 | − | 2.71441i | −0.0468760 | − | 0.144269i | ||||
\(355\) | 11.0000 | + | 7.99197i | 0.583819 | + | 0.424170i | ||||
\(356\) | −1.38197 | + | 1.00406i | −0.0732441 | + | 0.0532149i | ||||
\(357\) | −4.76393 | + | 14.6619i | −0.252134 | + | 0.775989i | ||||
\(358\) | −2.66312 | + | 8.19624i | −0.140750 | + | 0.433185i | ||||
\(359\) | −13.9443 | + | 10.1311i | −0.735951 | + | 0.534699i | −0.891440 | − | 0.453138i | \(-0.850304\pi\) |
0.155490 | + | 0.987838i | \(0.450304\pi\) | |||||||
\(360\) | 3.11803 | + | 2.26538i | 0.164335 | + | 0.119396i | ||||
\(361\) | −5.39919 | − | 16.6170i | −0.284168 | − | 0.874578i | ||||
\(362\) | −7.52786 | −0.395656 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.94427 | 0.154322 | ||||||||
\(365\) | −5.15248 | − | 15.8577i | −0.269693 | − | 0.830029i | ||||
\(366\) | −9.09017 | − | 6.60440i | −0.475151 | − | 0.345217i | ||||
\(367\) | −0.409830 | + | 0.297759i | −0.0213930 | + | 0.0155429i | −0.598430 | − | 0.801175i | \(-0.704209\pi\) |
0.577037 | + | 0.816718i | \(0.304209\pi\) | |||||||
\(368\) | 0.381966 | − | 1.17557i | 0.0199114 | − | 0.0612808i | ||||
\(369\) | 0.381966 | − | 1.17557i | 0.0198844 | − | 0.0611978i | ||||
\(370\) | 32.6525 | − | 23.7234i | 1.69752 | − | 1.23332i | ||||
\(371\) | −5.50000 | − | 3.99598i | −0.285546 | − | 0.207461i | ||||
\(372\) | −1.97214 | − | 6.06961i | −0.102250 | − | 0.314695i | ||||
\(373\) | −18.4721 | −0.956451 | −0.478225 | − | 0.878237i | \(-0.658720\pi\) | ||||
−0.478225 | + | 0.878237i | \(0.658720\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.7082 | 0.966087 | ||||||||
\(376\) | −2.00000 | − | 6.15537i | −0.103142 | − | 0.317439i | ||||
\(377\) | 2.61803 | + | 1.90211i | 0.134836 | + | 0.0979638i | ||||
\(378\) | 1.92705 | − | 1.40008i | 0.0991168 | − | 0.0720126i | ||||
\(379\) | −3.00000 | + | 9.23305i | −0.154100 | + | 0.474270i | −0.998069 | − | 0.0621221i | \(-0.980213\pi\) |
0.843969 | + | 0.536392i | \(0.180213\pi\) | |||||||
\(380\) | −1.47214 | + | 4.53077i | −0.0755190 | + | 0.232424i | ||||
\(381\) | 9.70820 | − | 7.05342i | 0.497366 | − | 0.361358i | ||||
\(382\) | −10.9443 | − | 7.95148i | −0.559958 | − | 0.406833i | ||||
\(383\) | 2.70820 | + | 8.33499i | 0.138383 | + | 0.425898i | 0.996101 | − | 0.0882220i | \(-0.0281185\pi\) |
−0.857718 | + | 0.514120i | \(0.828118\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.3262 | −0.780085 | ||||||||
\(387\) | 0.381966 | + | 1.17557i | 0.0194164 | + | 0.0597576i | ||||
\(388\) | 3.50000 | + | 2.54290i | 0.177686 | + | 0.129096i | ||||
\(389\) | −17.0344 | + | 12.3762i | −0.863680 | + | 0.627501i | −0.928884 | − | 0.370371i | \(-0.879230\pi\) |
0.0652033 | + | 0.997872i | \(0.479230\pi\) | |||||||
\(390\) | 1.47214 | − | 4.53077i | 0.0745445 | − | 0.229424i | ||||
\(391\) | 2.47214 | − | 7.60845i | 0.125021 | − | 0.384776i | ||||
\(392\) | 1.07295 | − | 0.779543i | 0.0541921 | − | 0.0393729i | ||||
\(393\) | 14.7812 | + | 10.7391i | 0.745611 | + | 0.541718i | ||||
\(394\) | −1.57295 | − | 4.84104i | −0.0792440 | − | 0.243888i | ||||
\(395\) | −24.3820 | −1.22679 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.8885 | −1.29931 | −0.649654 | − | 0.760230i | \(-0.725086\pi\) | ||||
−0.649654 | + | 0.760230i | \(0.725086\pi\) | |||||||
\(398\) | 6.13525 | + | 18.8824i | 0.307533 | + | 0.946488i | ||||
\(399\) | 2.38197 | + | 1.73060i | 0.119247 | + | 0.0866383i | ||||
\(400\) | −7.97214 | + | 5.79210i | −0.398607 | + | 0.289605i | ||||
\(401\) | 7.32624 | − | 22.5478i | 0.365855 | − | 1.12599i | −0.583589 | − | 0.812049i | \(-0.698352\pi\) |
0.949444 | − | 0.313936i | \(-0.101648\pi\) | |||||||
\(402\) | −1.23607 | + | 3.80423i | −0.0616495 | + | 0.189738i | ||||
\(403\) | −6.38197 | + | 4.63677i | −0.317908 | + | 0.230974i | ||||
\(404\) | 11.8262 | + | 8.59226i | 0.588377 | + | 0.427481i | ||||
\(405\) | −1.19098 | − | 3.66547i | −0.0591804 | − | 0.182139i | ||||
\(406\) | −6.23607 | −0.309491 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −6.47214 | −0.320418 | ||||||||
\(409\) | −0.281153 | − | 0.865300i | −0.0139021 | − | 0.0427863i | 0.943865 | − | 0.330332i | \(-0.107161\pi\) |
−0.957767 | + | 0.287546i | \(0.907161\pi\) | |||||||
\(410\) | 3.85410 | + | 2.80017i | 0.190341 | + | 0.138290i | ||||
\(411\) | 13.8541 | − | 10.0656i | 0.683372 | − | 0.496499i | ||||
\(412\) | −5.26393 | + | 16.2007i | −0.259335 | + | 0.798152i | ||||
\(413\) | 2.10081 | − | 6.46564i | 0.103374 | − | 0.318153i | ||||
\(414\) | −1.00000 | + | 0.726543i | −0.0491473 | + | 0.0357076i | ||||
\(415\) | −50.9058 | − | 36.9852i | −2.49887 | − | 1.81553i | ||||
\(416\) | 0.381966 | + | 1.17557i | 0.0187274 | + | 0.0576371i | ||||
\(417\) | −8.76393 | −0.429172 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.9787 | 1.41570 | 0.707851 | − | 0.706361i | \(-0.249665\pi\) | ||||
0.707851 | + | 0.706361i | \(0.249665\pi\) | |||||||
\(420\) | 2.83688 | + | 8.73102i | 0.138426 | + | 0.426030i | ||||
\(421\) | 4.14590 | + | 3.01217i | 0.202059 | + | 0.146804i | 0.684213 | − | 0.729282i | \(-0.260146\pi\) |
−0.482155 | + | 0.876086i | \(0.660146\pi\) | |||||||
\(422\) | −21.5623 | + | 15.6659i | −1.04964 | + | 0.762606i | ||||
\(423\) | −2.00000 | + | 6.15537i | −0.0972433 | + | 0.299284i | ||||
\(424\) | 0.881966 | − | 2.71441i | 0.0428321 | − | 0.131824i | ||||
\(425\) | −51.5967 | + | 37.4872i | −2.50281 | + | 1.81840i | ||||
\(426\) | 2.85410 | + | 2.07363i | 0.138282 | + | 0.100468i | ||||
\(427\) | −8.27051 | − | 25.4540i | −0.400238 | − | 1.23181i | ||||
\(428\) | 7.61803 | 0.368232 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.76393 | −0.229737 | ||||||||
\(431\) | −0.854102 | − | 2.62866i | −0.0411406 | − | 0.126618i | 0.928377 | − | 0.371641i | \(-0.121205\pi\) |
−0.969517 | + | 0.245023i | \(0.921205\pi\) | |||||||
\(432\) | 0.809017 | + | 0.587785i | 0.0389238 | + | 0.0282798i | ||||
\(433\) | 2.69098 | − | 1.95511i | 0.129320 | − | 0.0939568i | −0.521245 | − | 0.853407i | \(-0.674532\pi\) |
0.650565 | + | 0.759451i | \(0.274532\pi\) | |||||||
\(434\) | 4.69756 | − | 14.4576i | 0.225490 | − | 0.693987i | ||||
\(435\) | −3.11803 | + | 9.59632i | −0.149498 | + | 0.460108i | ||||
\(436\) | 7.61803 | − | 5.53483i | 0.364838 | − | 0.265070i | ||||
\(437\) | −1.23607 | − | 0.898056i | −0.0591292 | − | 0.0429598i | ||||
\(438\) | −1.33688 | − | 4.11450i | −0.0638786 | − | 0.196598i | ||||
\(439\) | −13.0344 | −0.622100 | −0.311050 | − | 0.950394i | \(-0.600681\pi\) | ||||
−0.311050 | + | 0.950394i | \(0.600681\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.32624 | −0.0631542 | ||||||||
\(442\) | 2.47214 | + | 7.60845i | 0.117588 | + | 0.361897i | ||||
\(443\) | 14.0172 | + | 10.1841i | 0.665978 | + | 0.483862i | 0.868677 | − | 0.495380i | \(-0.164971\pi\) |
−0.202698 | + | 0.979241i | \(0.564971\pi\) | |||||||
\(444\) | 8.47214 | − | 6.15537i | 0.402070 | − | 0.292121i | ||||
\(445\) | −2.03444 | + | 6.26137i | −0.0964418 | + | 0.296817i | ||||
\(446\) | −4.04508 | + | 12.4495i | −0.191540 | + | 0.589501i | ||||
\(447\) | 2.92705 | − | 2.12663i | 0.138445 | − | 0.100586i | ||||
\(448\) | −1.92705 | − | 1.40008i | −0.0910446 | − | 0.0661478i | ||||
\(449\) | 0.0344419 | + | 0.106001i | 0.00162541 | + | 0.00500250i | 0.951866 | − | 0.306515i | \(-0.0991629\pi\) |
−0.950241 | + | 0.311517i | \(0.899163\pi\) | |||||||
\(450\) | 9.85410 | 0.464527 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −3.52786 | −0.165937 | ||||||||
\(453\) | 1.95492 | + | 6.01661i | 0.0918499 | + | 0.282685i | ||||
\(454\) | 11.2082 | + | 8.14324i | 0.526027 | + | 0.382181i | ||||
\(455\) | 9.18034 | − | 6.66991i | 0.430381 | − | 0.312690i | ||||
\(456\) | −0.381966 | + | 1.17557i | −0.0178872 | + | 0.0550511i | ||||
\(457\) | 7.71885 | − | 23.7562i | 0.361072 | − | 1.11127i | −0.591332 | − | 0.806428i | \(-0.701398\pi\) |
0.952404 | − | 0.304838i | \(-0.0986024\pi\) | |||||||
\(458\) | −4.09017 | + | 2.97168i | −0.191121 | + | 0.138858i | ||||
\(459\) | 5.23607 | + | 3.80423i | 0.244399 | + | 0.177566i | ||||
\(460\) | −1.47214 | − | 4.53077i | −0.0686387 | − | 0.211248i | ||||
\(461\) | −12.8328 | −0.597684 | −0.298842 | − | 0.954303i | \(-0.596600\pi\) | ||||
−0.298842 | + | 0.954303i | \(0.596600\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.90983 | 0.367601 | 0.183800 | − | 0.982964i | \(-0.441160\pi\) | ||||
0.183800 | + | 0.982964i | \(0.441160\pi\) | |||||||
\(464\) | −0.809017 | − | 2.48990i | −0.0375577 | − | 0.115591i | ||||
\(465\) | −19.8992 | − | 14.4576i | −0.922803 | − | 0.670455i | ||||
\(466\) | −7.23607 | + | 5.25731i | −0.335204 | + | 0.243540i | ||||
\(467\) | −0.173762 | + | 0.534785i | −0.00804075 | + | 0.0247469i | −0.954996 | − | 0.296617i | \(-0.904141\pi\) |
0.946956 | + | 0.321364i | \(0.104141\pi\) | |||||||
\(468\) | 0.381966 | − | 1.17557i | 0.0176564 | − | 0.0543408i | ||||
\(469\) | −7.70820 | + | 5.60034i | −0.355932 | + | 0.258600i | ||||
\(470\) | −20.1803 | − | 14.6619i | −0.930850 | − | 0.676302i | ||||
\(471\) | 1.38197 | + | 4.25325i | 0.0636776 | + | 0.195980i | ||||
\(472\) | 2.85410 | 0.131371 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −6.32624 | −0.290574 | ||||||||
\(475\) | 3.76393 | + | 11.5842i | 0.172701 | + | 0.531519i | ||||
\(476\) | −12.4721 | − | 9.06154i | −0.571659 | − | 0.415335i | ||||
\(477\) | −2.30902 | + | 1.67760i | −0.105723 | + | 0.0768120i | ||||
\(478\) | −2.32624 | + | 7.15942i | −0.106400 | + | 0.327464i | ||||
\(479\) | −0.854102 | + | 2.62866i | −0.0390249 | + | 0.120106i | −0.968671 | − | 0.248347i | \(-0.920113\pi\) |
0.929646 | + | 0.368454i | \(0.120113\pi\) | |||||||
\(480\) | −3.11803 | + | 2.26538i | −0.142318 | + | 0.103400i | ||||
\(481\) | −10.4721 | − | 7.60845i | −0.477488 | − | 0.346916i | ||||
\(482\) | −6.97214 | − | 21.4580i | −0.317572 | − | 0.977386i | ||||
\(483\) | −2.94427 | −0.133969 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.6738 | 0.757117 | ||||||||
\(486\) | −0.309017 | − | 0.951057i | −0.0140173 | − | 0.0431408i | ||||
\(487\) | 17.7812 | + | 12.9188i | 0.805741 | + | 0.585405i | 0.912593 | − | 0.408870i | \(-0.134077\pi\) |
−0.106852 | + | 0.994275i | \(0.534077\pi\) | |||||||
\(488\) | 9.09017 | − | 6.60440i | 0.411493 | − | 0.298967i | ||||
\(489\) | −4.14590 | + | 12.7598i | −0.187484 | + | 0.577016i | ||||
\(490\) | 1.57953 | − | 4.86128i | 0.0713557 | − | 0.219610i | ||||
\(491\) | 30.9443 | − | 22.4823i | 1.39650 | − | 1.01461i | 0.401378 | − | 0.915912i | \(-0.368531\pi\) |
0.995117 | − | 0.0987010i | \(-0.0314687\pi\) | |||||||
\(492\) | 1.00000 | + | 0.726543i | 0.0450835 | + | 0.0327551i | ||||
\(493\) | −5.23607 | − | 16.1150i | −0.235821 | − | 0.725781i | ||||
\(494\) | 1.52786 | 0.0687419 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.38197 | 0.286559 | ||||||||
\(497\) | 2.59675 | + | 7.99197i | 0.116480 | + | 0.358489i | ||||
\(498\) | −13.2082 | − | 9.59632i | −0.591874 | − | 0.430021i | ||||
\(499\) | −15.7082 | + | 11.4127i | −0.703196 | + | 0.510902i | −0.880971 | − | 0.473169i | \(-0.843110\pi\) |
0.177776 | + | 0.984071i | \(0.443110\pi\) | |||||||
\(500\) | −5.78115 | + | 17.7926i | −0.258541 | + | 0.795707i | ||||
\(501\) | −0.854102 | + | 2.62866i | −0.0381585 | + | 0.117440i | ||||
\(502\) | 2.97214 | − | 2.15938i | 0.132653 | − | 0.0963780i | ||||
\(503\) | 32.6525 | + | 23.7234i | 1.45590 | + | 1.05777i | 0.984407 | + | 0.175906i | \(0.0562855\pi\) |
0.471495 | + | 0.881869i | \(0.343715\pi\) | |||||||
\(504\) | 0.736068 | + | 2.26538i | 0.0327871 | + | 0.100908i | ||||
\(505\) | 56.3394 | 2.50707 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.4721 | 0.509495 | ||||||||
\(508\) | 3.70820 | + | 11.4127i | 0.164525 | + | 0.506356i | ||||
\(509\) | −22.4894 | − | 16.3395i | −0.996823 | − | 0.724234i | −0.0354185 | − | 0.999373i | \(-0.511276\pi\) |
−0.961405 | + | 0.275138i | \(0.911276\pi\) | |||||||
\(510\) | −20.1803 | + | 14.6619i | −0.893600 | + | 0.649239i | ||||
\(511\) | 3.18441 | − | 9.80059i | 0.140870 | − | 0.433553i | ||||
\(512\) | 0.309017 | − | 0.951057i | 0.0136568 | − | 0.0420312i | ||||
\(513\) | 1.00000 | − | 0.726543i | 0.0441511 | − | 0.0320776i | ||||
\(514\) | 19.5623 | + | 14.2128i | 0.862856 | + | 0.626902i | ||||
\(515\) | 20.2877 | + | 62.4392i | 0.893984 | + | 2.75140i | ||||
\(516\) | −1.23607 | −0.0544149 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 24.9443 | 1.09599 | ||||||||
\(519\) | 3.35410 | + | 10.3229i | 0.147229 | + | 0.453123i | ||||
\(520\) | 3.85410 | + | 2.80017i | 0.169014 | + | 0.122796i | ||||
\(521\) | −3.70820 | + | 2.69417i | −0.162459 | + | 0.118034i | −0.666045 | − | 0.745912i | \(-0.732014\pi\) |
0.503585 | + | 0.863946i | \(0.332014\pi\) | |||||||
\(522\) | −0.809017 | + | 2.48990i | −0.0354097 | + | 0.108980i | ||||
\(523\) | −9.14590 | + | 28.1482i | −0.399922 | + | 1.23083i | 0.525139 | + | 0.851016i | \(0.324013\pi\) |
−0.925061 | + | 0.379818i | \(0.875987\pi\) | |||||||
\(524\) | −14.7812 | + | 10.7391i | −0.645718 | + | 0.469141i | ||||
\(525\) | 18.9894 | + | 13.7966i | 0.828763 | + | 0.602132i | ||||
\(526\) | −1.76393 | − | 5.42882i | −0.0769111 | − | 0.236708i | ||||
\(527\) | 41.3050 | 1.79927 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.4721 | −0.933571 | ||||||||
\(530\) | −3.39919 | − | 10.4616i | −0.147651 | − | 0.454424i | ||||
\(531\) | −2.30902 | − | 1.67760i | −0.100203 | − | 0.0728016i | ||||
\(532\) | −2.38197 | + | 1.73060i | −0.103271 | + | 0.0750310i | ||||
\(533\) | 0.472136 | − | 1.45309i | 0.0204505 | − | 0.0629401i | ||||
\(534\) | −0.527864 | + | 1.62460i | −0.0228429 | + | 0.0703033i | ||||
\(535\) | 23.7533 | − | 17.2578i | 1.02694 | − | 0.746119i | ||||
\(536\) | −3.23607 | − | 2.35114i | −0.139777 | − | 0.101554i | ||||
\(537\) | 2.66312 | + | 8.19624i | 0.114922 | + | 0.353694i | ||||
\(538\) | 14.9443 | 0.644293 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.85410 | 0.165854 | ||||||||
\(541\) | 5.09017 | + | 15.6659i | 0.218843 | + | 0.673531i | 0.998858 | + | 0.0477700i | \(0.0152115\pi\) |
−0.780015 | + | 0.625761i | \(0.784789\pi\) | |||||||
\(542\) | 2.76393 | + | 2.00811i | 0.118721 | + | 0.0862559i | ||||
\(543\) | −6.09017 | + | 4.42477i | −0.261354 | + | 0.189885i | ||||
\(544\) | 2.00000 | − | 6.15537i | 0.0857493 | − | 0.263909i | ||||
\(545\) | 11.2148 | − | 34.5155i | 0.480388 | − | 1.47848i | ||||
\(546\) | 2.38197 | − | 1.73060i | 0.101939 | − | 0.0740628i | ||||
\(547\) | 3.38197 | + | 2.45714i | 0.144602 | + | 0.105060i | 0.657734 | − | 0.753250i | \(-0.271515\pi\) |
−0.513132 | + | 0.858310i | \(0.671515\pi\) | |||||||
\(548\) | 5.29180 | + | 16.2865i | 0.226054 | + | 0.695724i | ||||
\(549\) | −11.2361 | −0.479544 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.23607 | −0.137861 | ||||||||
\(552\) | −0.381966 | − | 1.17557i | −0.0162576 | − | 0.0500356i | ||||
\(553\) | −12.1910 | − | 8.85727i | −0.518413 | − | 0.376649i | ||||
\(554\) | 23.5623 | − | 17.1190i | 1.00107 | − | 0.727317i | ||||
\(555\) | 12.4721 | − | 38.3853i | 0.529413 | − | 1.62936i | ||||
\(556\) | 2.70820 | − | 8.33499i | 0.114853 | − | 0.353483i | ||||
\(557\) | 10.4894 | − | 7.62096i | 0.444448 | − | 0.322911i | −0.342952 | − | 0.939353i | \(-0.611427\pi\) |
0.787400 | + | 0.616442i | \(0.211427\pi\) | |||||||
\(558\) | −5.16312 | − | 3.75123i | −0.218572 | − | 0.158802i | ||||
\(559\) | 0.472136 | + | 1.45309i | 0.0199692 | + | 0.0614589i | ||||
\(560\) | −9.18034 | −0.387940 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.1246 | −0.722358 | ||||||||
\(563\) | 2.11146 | + | 6.49839i | 0.0889873 | + | 0.273875i | 0.985640 | − | 0.168860i | \(-0.0540085\pi\) |
−0.896653 | + | 0.442734i | \(0.854008\pi\) | |||||||
\(564\) | −5.23607 | − | 3.80423i | −0.220478 | − | 0.160187i | ||||
\(565\) | −11.0000 | + | 7.99197i | −0.462773 | + | 0.336225i | ||||
\(566\) | 3.67376 | − | 11.3067i | 0.154420 | − | 0.475255i | ||||
\(567\) | 0.736068 | − | 2.26538i | 0.0309119 | − | 0.0951372i | ||||
\(568\) | −2.85410 | + | 2.07363i | −0.119755 | + | 0.0870074i | ||||
\(569\) | 13.6180 | + | 9.89408i | 0.570898 | + | 0.414781i | 0.835431 | − | 0.549595i | \(-0.185218\pi\) |
−0.264534 | + | 0.964376i | \(0.585218\pi\) | |||||||
\(570\) | 1.47214 | + | 4.53077i | 0.0616610 | + | 0.189773i | ||||
\(571\) | −39.5967 | −1.65707 | −0.828536 | − | 0.559936i | \(-0.810826\pi\) | ||||
−0.828536 | + | 0.559936i | \(0.810826\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.5279 | −0.565135 | ||||||||
\(574\) | 0.909830 | + | 2.80017i | 0.0379756 | + | 0.116877i | ||||
\(575\) | −9.85410 | − | 7.15942i | −0.410944 | − | 0.298569i | ||||
\(576\) | −0.809017 | + | 0.587785i | −0.0337090 | + | 0.0244911i | ||||
\(577\) | −1.26393 | + | 3.88998i | −0.0526182 | + | 0.161942i | −0.973912 | − | 0.226924i | \(-0.927133\pi\) |
0.921294 | + | 0.388866i | \(0.127133\pi\) | |||||||
\(578\) | 7.69098 | − | 23.6704i | 0.319903 | − | 0.984559i | ||||
\(579\) | −12.3992 | + | 9.00854i | −0.515293 | + | 0.374382i | ||||
\(580\) | −8.16312 | − | 5.93085i | −0.338955 | − | 0.246265i | ||||
\(581\) | −12.0172 | − | 36.9852i | −0.498558 | − | 1.53440i | ||||
\(582\) | 4.32624 | 0.179328 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.32624 | 0.179021 | ||||||||
\(585\) | −1.47214 | − | 4.53077i | −0.0608653 | − | 0.187324i | ||||
\(586\) | 19.3992 | + | 14.0943i | 0.801373 | + | 0.582232i | ||||
\(587\) | 10.4443 | − | 7.58821i | 0.431081 | − | 0.313199i | −0.351000 | − | 0.936376i | \(-0.614158\pi\) |
0.782081 | + | 0.623177i | \(0.214158\pi\) | |||||||
\(588\) | 0.409830 | − | 1.26133i | 0.0169011 | − | 0.0520163i | ||||
\(589\) | 2.43769 | − | 7.50245i | 0.100443 | − | 0.309133i | ||||
\(590\) | 8.89919 | − | 6.46564i | 0.366374 | − | 0.266186i | ||||
\(591\) | −4.11803 | − | 2.99193i | −0.169393 | − | 0.123071i | ||||
\(592\) | 3.23607 | + | 9.95959i | 0.133002 | + | 0.409337i | ||||
\(593\) | 15.5279 | 0.637653 | 0.318826 | − | 0.947813i | \(-0.396711\pi\) | ||||
0.318826 | + | 0.947813i | \(0.396711\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −59.4164 | −2.43584 | ||||||||
\(596\) | 1.11803 | + | 3.44095i | 0.0457965 | + | 0.140947i | ||||
\(597\) | 16.0623 | + | 11.6699i | 0.657386 | + | 0.477619i | ||||
\(598\) | −1.23607 | + | 0.898056i | −0.0505466 | + | 0.0367242i | ||||
\(599\) | −11.2361 | + | 34.5811i | −0.459093 | + | 1.41294i | 0.407168 | + | 0.913353i | \(0.366516\pi\) |
−0.866262 | + | 0.499591i | \(0.833484\pi\) | |||||||
\(600\) | −3.04508 | + | 9.37181i | −0.124315 | + | 0.382602i | ||||
\(601\) | −15.1631 | + | 11.0167i | −0.618517 | + | 0.449379i | −0.852403 | − | 0.522885i | \(-0.824856\pi\) |
0.233886 | + | 0.972264i | \(0.424856\pi\) | |||||||
\(602\) | −2.38197 | − | 1.73060i | −0.0970817 | − | 0.0705340i | ||||
\(603\) | 1.23607 | + | 3.80423i | 0.0503366 | + | 0.154920i | ||||
\(604\) | −6.32624 | −0.257411 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 14.6180 | 0.593817 | ||||||||
\(607\) | −14.7639 | − | 45.4387i | −0.599250 | − | 1.84430i | −0.532321 | − | 0.846543i | \(-0.678680\pi\) |
−0.0669285 | − | 0.997758i | \(-0.521320\pi\) | |||||||
\(608\) | −1.00000 | − | 0.726543i | −0.0405554 | − | 0.0294652i | ||||
\(609\) | −5.04508 | + | 3.66547i | −0.204437 | + | 0.148532i | ||||
\(610\) | 13.3820 | − | 41.1855i | 0.541820 | − | 1.66755i | ||||
\(611\) | −2.47214 | + | 7.60845i | −0.100012 | + | 0.307805i | ||||
\(612\) | −5.23607 | + | 3.80423i | −0.211656 | + | 0.153777i | ||||
\(613\) | 22.4164 | + | 16.2865i | 0.905390 | + | 0.657804i | 0.939845 | − | 0.341602i | \(-0.110969\pi\) |
−0.0344546 | + | 0.999406i | \(0.510969\pi\) | |||||||
\(614\) | 4.52786 | + | 13.9353i | 0.182730 | + | 0.562384i | ||||
\(615\) | 4.76393 | 0.192100 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.7082 | −1.75963 | −0.879813 | − | 0.475320i | \(-0.842332\pi\) | ||||
−0.879813 | + | 0.475320i | \(0.842332\pi\) | |||||||
\(618\) | 5.26393 | + | 16.2007i | 0.211746 | + | 0.651688i | ||||
\(619\) | −30.1803 | − | 21.9273i | −1.21305 | − | 0.881333i | −0.217546 | − | 0.976050i | \(-0.569805\pi\) |
−0.995504 | + | 0.0947174i | \(0.969805\pi\) | |||||||
\(620\) | 19.8992 | − | 14.4576i | 0.799171 | − | 0.580631i | ||||
\(621\) | −0.381966 | + | 1.17557i | −0.0153278 | + | 0.0471740i | ||||
\(622\) | 3.67376 | − | 11.3067i | 0.147304 | − | 0.453356i | ||||
\(623\) | −3.29180 | + | 2.39163i | −0.131883 | + | 0.0958186i | ||||
\(624\) | 1.00000 | + | 0.726543i | 0.0400320 | + | 0.0290850i | ||||
\(625\) | 7.05573 | + | 21.7153i | 0.282229 | + | 0.868612i | ||||
\(626\) | 21.8541 | 0.873466 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.47214 | −0.178458 | ||||||||
\(629\) | 20.9443 | + | 64.4598i | 0.835103 | + | 2.57018i | ||||
\(630\) | 7.42705 | + | 5.39607i | 0.295901 | + | 0.214985i | ||||
\(631\) | 19.2984 | − | 14.0211i | 0.768256 | − | 0.558171i | −0.133175 | − | 0.991092i | \(-0.542517\pi\) |
0.901432 | + | 0.432922i | \(0.142517\pi\) | |||||||
\(632\) | 1.95492 | − | 6.01661i | 0.0777623 | − | 0.239328i | ||||
\(633\) | −8.23607 | + | 25.3480i | −0.327354 | + | 1.00749i | ||||
\(634\) | −12.8541 | + | 9.33905i | −0.510502 | + | 0.370901i | ||||
\(635\) | 37.4164 | + | 27.1846i | 1.48482 | + | 1.07879i | ||||
\(636\) | −0.881966 | − | 2.71441i | −0.0349722 | − | 0.107633i | ||||
\(637\) | −1.63932 | −0.0649522 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.52786 | 0.139560 | ||||||||
\(640\) | −1.19098 | − | 3.66547i | −0.0470777 | − | 0.144890i | ||||
\(641\) | −5.56231 | − | 4.04125i | −0.219698 | − | 0.159620i | 0.472493 | − | 0.881335i | \(-0.343354\pi\) |
−0.692191 | + | 0.721715i | \(0.743354\pi\) | |||||||
\(642\) | 6.16312 | − | 4.47777i | 0.243239 | − | 0.176723i | ||||
\(643\) | −2.14590 | + | 6.60440i | −0.0846260 | + | 0.260452i | −0.984412 | − | 0.175880i | \(-0.943723\pi\) |
0.899786 | + | 0.436332i | \(0.143723\pi\) | |||||||
\(644\) | 0.909830 | − | 2.80017i | 0.0358523 | − | 0.110342i | ||||
\(645\) | −3.85410 | + | 2.80017i | −0.151755 | + | 0.110257i | ||||
\(646\) | −6.47214 | − | 4.70228i | −0.254643 | − | 0.185009i | ||||
\(647\) | −13.3262 | − | 41.0139i | −0.523908 | − | 1.61242i | −0.766464 | − | 0.642287i | \(-0.777986\pi\) |
0.242556 | − | 0.970137i | \(-0.422014\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 12.1803 | 0.477752 | ||||||||
\(651\) | −4.69756 | − | 14.4576i | −0.184112 | − | 0.566638i | ||||
\(652\) | −10.8541 | − | 7.88597i | −0.425079 | − | 0.308838i | ||||
\(653\) | 22.5344 | − | 16.3722i | 0.881841 | − | 0.640695i | −0.0518970 | − | 0.998652i | \(-0.516527\pi\) |
0.933738 | + | 0.357958i | \(0.116527\pi\) | |||||||
\(654\) | 2.90983 | − | 8.95554i | 0.113783 | − | 0.350189i | ||||
\(655\) | −21.7599 | + | 66.9700i | −0.850228 | + | 2.61673i | ||||
\(656\) | −1.00000 | + | 0.726543i | −0.0390434 | + | 0.0283667i | ||||
\(657\) | −3.50000 | − | 2.54290i | −0.136548 | − | 0.0992079i | ||||
\(658\) | −4.76393 | − | 14.6619i | −0.185717 | − | 0.571579i | ||||
\(659\) | 49.8541 | 1.94204 | 0.971020 | − | 0.238998i | \(-0.0768190\pi\) | ||||
0.971020 | + | 0.238998i | \(0.0768190\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.1803 | 1.09609 | 0.548044 | − | 0.836449i | \(-0.315373\pi\) | ||||
0.548044 | + | 0.836449i | \(0.315373\pi\) | |||||||
\(662\) | −2.76393 | − | 8.50651i | −0.107423 | − | 0.330615i | ||||
\(663\) | 6.47214 | + | 4.70228i | 0.251357 | + | 0.182622i | ||||
\(664\) | 13.2082 | − | 9.59632i | 0.512578 | − | 0.372410i | ||||
\(665\) | −3.50658 | + | 10.7921i | −0.135979 | + | 0.418501i | ||||
\(666\) | 3.23607 | − | 9.95959i | 0.125395 | − | 0.385926i | ||||
\(667\) | 2.61803 | − | 1.90211i | 0.101371 | − | 0.0736501i | ||||
\(668\) | −2.23607 | − | 1.62460i | −0.0865161 | − | 0.0628576i | ||||
\(669\) | 4.04508 | + | 12.4495i | 0.156392 | + | 0.481325i | ||||
\(670\) | −15.4164 | −0.595588 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.38197 | −0.0918863 | ||||||||
\(673\) | −11.1353 | − | 34.2708i | −0.429233 | − | 1.32104i | −0.898883 | − | 0.438189i | \(-0.855620\pi\) |
0.469650 | − | 0.882853i | \(-0.344380\pi\) | |||||||
\(674\) | 8.85410 | + | 6.43288i | 0.341047 | + | 0.247785i | ||||
\(675\) | 7.97214 | − | 5.79210i | 0.306848 | − | 0.222938i | ||||
\(676\) | −3.54508 | + | 10.9106i | −0.136349 | + | 0.419640i | ||||
\(677\) | −0.770510 | + | 2.37139i | −0.0296131 | + | 0.0911397i | −0.964771 | − | 0.263092i | \(-0.915258\pi\) |
0.935158 | + | 0.354232i | \(0.115258\pi\) | |||||||
\(678\) | −2.85410 | + | 2.07363i | −0.109611 | + | 0.0796371i | ||||
\(679\) | 8.33688 | + | 6.05710i | 0.319940 | + | 0.232450i | ||||
\(680\) | −7.70820 | − | 23.7234i | −0.295596 | − | 0.909751i | ||||
\(681\) | 13.8541 | 0.530890 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.25735 | 0.124639 | 0.0623196 | − | 0.998056i | \(-0.480150\pi\) | ||||
0.0623196 | + | 0.998056i | \(0.480150\pi\) | |||||||
\(684\) | 0.381966 | + | 1.17557i | 0.0146048 | + | 0.0449491i | ||||
\(685\) | 53.3951 | + | 38.7938i | 2.04012 | + | 1.48224i | ||||
\(686\) | 16.0451 | − | 11.6574i | 0.612604 | − | 0.445083i | ||||
\(687\) | −1.56231 | + | 4.80828i | −0.0596057 | + | 0.183447i | ||||
\(688\) | 0.381966 | − | 1.17557i | 0.0145623 | − | 0.0448182i | ||||
\(689\) | −2.85410 | + | 2.07363i | −0.108733 | + | 0.0789989i | ||||
\(690\) | −3.85410 | − | 2.80017i | −0.146723 | − | 0.106601i | ||||
\(691\) | −4.23607 | − | 13.0373i | −0.161148 | − | 0.495961i | 0.837584 | − | 0.546308i | \(-0.183967\pi\) |
−0.998732 | + | 0.0503469i | \(0.983967\pi\) | |||||||
\(692\) | −10.8541 | −0.412611 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.14590 | 0.195336 | ||||||||
\(695\) | −10.4377 | − | 32.1239i | −0.395924 | − | 1.21853i | ||||
\(696\) | −2.11803 | − | 1.53884i | −0.0802839 | − | 0.0583296i | ||||
\(697\) | −6.47214 | + | 4.70228i | −0.245150 | + | 0.178112i | ||||
\(698\) | −2.70820 | + | 8.33499i | −0.102507 | + | 0.315484i | ||||
\(699\) | −2.76393 | + | 8.50651i | −0.104542 | + | 0.321746i | ||||
\(700\) | −18.9894 | + | 13.7966i | −0.717730 | + | 0.521462i | ||||
\(701\) | −15.3262 | − | 11.1352i | −0.578864 | − | 0.420569i | 0.259450 | − | 0.965756i | \(-0.416459\pi\) |
−0.838314 | + | 0.545187i | \(0.816459\pi\) | |||||||
\(702\) | −0.381966 | − | 1.17557i | −0.0144164 | − | 0.0443690i | ||||
\(703\) | 12.9443 | 0.488202 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24.9443 | −0.939456 | ||||||||
\(706\) | 8.52786 | + | 26.2461i | 0.320950 | + | 0.987784i | ||||
\(707\) | 28.1697 | + | 20.4665i | 1.05943 | + | 0.769721i | ||||
\(708\) | 2.30902 | − | 1.67760i | 0.0867782 | − | 0.0630480i | ||||
\(709\) | −12.6738 | + | 39.0058i | −0.475973 | + | 1.46489i | 0.368668 | + | 0.929561i | \(0.379814\pi\) |
−0.844641 | + | 0.535333i | \(0.820186\pi\) | |||||||
\(710\) | −4.20163 | + | 12.9313i | −0.157684 | + | 0.485302i | ||||
\(711\) | −5.11803 | + | 3.71847i | −0.191941 | + | 0.139453i | ||||
\(712\) | −1.38197 | − | 1.00406i | −0.0517914 | − | 0.0376286i | ||||
\(713\) | 2.43769 | + | 7.50245i | 0.0912924 | + | 0.280969i | ||||
\(714\) | −15.4164 | −0.576945 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.61803 | −0.322071 | ||||||||
\(717\) | 2.32624 | + | 7.15942i | 0.0868749 | + | 0.267374i | ||||
\(718\) | −13.9443 | − | 10.1311i | −0.520396 | − | 0.378090i | ||||
\(719\) | 5.61803 | − | 4.08174i | 0.209517 | − | 0.152223i | −0.478078 | − | 0.878317i | \(-0.658666\pi\) |
0.687595 | + | 0.726094i | \(0.258666\pi\) | |||||||
\(720\) | −1.19098 | + | 3.66547i | −0.0443853 | + | 0.136604i | ||||
\(721\) | −12.5385 | + | 38.5896i | −0.466958 | + | 1.43715i | ||||
\(722\) | 14.1353 | − | 10.2699i | 0.526060 | − | 0.382205i | ||||
\(723\) | −18.2533 | − | 13.2618i | −0.678847 | − | 0.493211i | ||||
\(724\) | −2.32624 | − | 7.15942i | −0.0864540 | − | 0.266078i | ||||
\(725\) | −25.7984 | −0.958128 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.4164 | −0.868466 | −0.434233 | − | 0.900800i | \(-0.642981\pi\) | ||||
−0.434233 | + | 0.900800i | \(0.642981\pi\) | |||||||
\(728\) | 0.909830 | + | 2.80017i | 0.0337205 | + | 0.103781i | ||||
\(729\) | −0.809017 | − | 0.587785i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | 13.4894 | − | 9.80059i | 0.499263 | − | 0.362736i | ||||
\(731\) | 2.47214 | − | 7.60845i | 0.0914353 | − | 0.281409i | ||||
\(732\) | 3.47214 | − | 10.6861i | 0.128334 | − | 0.394971i | ||||
\(733\) | 24.5066 | − | 17.8051i | 0.905171 | − | 0.657645i | −0.0346179 | − | 0.999401i | \(-0.511021\pi\) |
0.939789 | + | 0.341755i | \(0.111021\pi\) | |||||||
\(734\) | −0.409830 | − | 0.297759i | −0.0151271 | − | 0.0109905i | ||||
\(735\) | −1.57953 | − | 4.86128i | −0.0582617 | − | 0.179311i | ||||
\(736\) | 1.23607 | 0.0455621 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 1.23607 | 0.0455003 | ||||||||
\(739\) | 10.1803 | + | 31.3319i | 0.374490 | + | 1.15256i | 0.943822 | + | 0.330454i | \(0.107202\pi\) |
−0.569332 | + | 0.822107i | \(0.692798\pi\) | |||||||
\(740\) | 32.6525 | + | 23.7234i | 1.20033 | + | 0.872090i | ||||
\(741\) | 1.23607 | − | 0.898056i | 0.0454081 | − | 0.0329909i | ||||
\(742\) | 2.10081 | − | 6.46564i | 0.0771233 | − | 0.237361i | ||||
\(743\) | 10.4377 | − | 32.1239i | 0.382922 | − | 1.17851i | −0.555055 | − | 0.831814i | \(-0.687303\pi\) |
0.937977 | − | 0.346698i | \(-0.112697\pi\) | |||||||
\(744\) | 5.16312 | − | 3.75123i | 0.189289 | − | 0.137527i | ||||
\(745\) | 11.2812 | + | 8.19624i | 0.413309 | + | 0.300287i | ||||
\(746\) | −5.70820 | − | 17.5680i | −0.208992 | − | 0.643212i | ||||
\(747\) | −16.3262 | −0.597346 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.1459 | 0.663037 | ||||||||
\(750\) | 5.78115 | + | 17.7926i | 0.211098 | + | 0.649692i | ||||
\(751\) | 37.1246 | + | 26.9726i | 1.35470 | + | 0.984244i | 0.998763 | + | 0.0497333i | \(0.0158371\pi\) |
0.355934 | + | 0.934511i | \(0.384163\pi\) | |||||||
\(752\) | 5.23607 | − | 3.80423i | 0.190940 | − | 0.138726i | ||||
\(753\) | 1.13525 | − | 3.49396i | 0.0413710 | − | 0.127327i | ||||
\(754\) | −1.00000 | + | 3.07768i | −0.0364179 | + | 0.112083i | ||||
\(755\) | −19.7254 | + | 14.3314i | −0.717882 | + | 0.521572i | ||||
\(756\) | 1.92705 | + | 1.40008i | 0.0700862 | + | 0.0509206i | ||||
\(757\) | 11.2918 | + | 34.7526i | 0.410407 | + | 1.26310i | 0.916295 | + | 0.400504i | \(0.131165\pi\) |
−0.505888 | + | 0.862599i | \(0.668835\pi\) | |||||||
\(758\) | −9.70820 | −0.352618 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.76393 | −0.172806 | ||||||||
\(761\) | 7.32624 | + | 22.5478i | 0.265576 | + | 0.817359i | 0.991560 | + | 0.129647i | \(0.0413845\pi\) |
−0.725984 | + | 0.687711i | \(0.758615\pi\) | |||||||
\(762\) | 9.70820 | + | 7.05342i | 0.351691 | + | 0.255519i | ||||
\(763\) | 18.1459 | − | 13.1838i | 0.656926 | − | 0.477284i | ||||
\(764\) | 4.18034 | − | 12.8658i | 0.151239 | − | 0.465467i | ||||
\(765\) | −7.70820 | + | 23.7234i | −0.278691 | + | 0.857722i | ||||
\(766\) | −7.09017 | + | 5.15131i | −0.256178 | + | 0.186124i | ||||
\(767\) | −2.85410 | − | 2.07363i | −0.103056 | − | 0.0748743i | ||||
\(768\) | −0.309017 | − | 0.951057i | −0.0111507 | − | 0.0343183i | ||||
\(769\) | 29.2705 | 1.05552 | 0.527761 | − | 0.849393i | \(-0.323032\pi\) | ||||
0.527761 | + | 0.849393i | \(0.323032\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.1803 | 0.870834 | ||||||||
\(772\) | −4.73607 | − | 14.5761i | −0.170455 | − | 0.524606i | ||||
\(773\) | 23.0623 | + | 16.7557i | 0.829493 | + | 0.602662i | 0.919416 | − | 0.393286i | \(-0.128662\pi\) |
−0.0899225 | + | 0.995949i | \(0.528662\pi\) | |||||||
\(774\) | −1.00000 | + | 0.726543i | −0.0359443 | + | 0.0261150i | ||||
\(775\) | 19.4336 | − | 59.8106i | 0.698077 | − | 2.14846i | ||||
\(776\) | −1.33688 | + | 4.11450i | −0.0479912 | + | 0.147702i | ||||
\(777\) | 20.1803 | − | 14.6619i | 0.723966 | − | 0.525992i | ||||
\(778\) | −17.0344 | − | 12.3762i | −0.610714 | − | 0.443710i | ||||
\(779\) | 0.472136 | + | 1.45309i | 0.0169160 | + | 0.0520622i | ||||
\(780\) | 4.76393 | 0.170576 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 8.00000 | 0.286079 | ||||||||
\(783\) | 0.809017 | + | 2.48990i | 0.0289119 | + | 0.0889817i | ||||
\(784\) | 1.07295 | + | 0.779543i | 0.0383196 | + | 0.0278408i | ||||
\(785\) | −13.9443 | + | 10.1311i | −0.497692 | + | 0.361595i | ||||
\(786\) | −5.64590 | + | 17.3763i | −0.201383 | + | 0.619792i | ||||
\(787\) | 14.6738 | − | 45.1612i | 0.523063 | − | 1.60982i | −0.245051 | − | 0.969510i | \(-0.578805\pi\) |
0.768114 | − | 0.640313i | \(-0.221195\pi\) | |||||||
\(788\) | 4.11803 | − | 2.99193i | 0.146699 | − | 0.106583i | ||||
\(789\) | −4.61803 | − | 3.35520i | −0.164406 | − | 0.119448i | ||||
\(790\) | −7.53444 | − | 23.1886i | −0.268063 | − | 0.825014i | ||||
\(791\) | −8.40325 | −0.298785 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.8885 | −0.493197 | ||||||||
\(794\) | −8.00000 | − | 24.6215i | −0.283909 | − | 0.873783i | ||||
\(795\) | −8.89919 | − | 6.46564i | −0.315622 | − | 0.229313i | ||||
\(796\) | −16.0623 | + | 11.6699i | −0.569313 | + | 0.413630i | ||||
\(797\) | −6.29837 | + | 19.3844i | −0.223100 | + | 0.686631i | 0.775379 | + | 0.631496i | \(0.217559\pi\) |
−0.998479 | + | 0.0551347i | \(0.982441\pi\) | |||||||
\(798\) | −0.909830 | + | 2.80017i | −0.0322076 | + | 0.0991249i | ||||
\(799\) | 33.8885 | − | 24.6215i | 1.19889 | − | 0.871045i | ||||
\(800\) | −7.97214 | − | 5.79210i | −0.281858 | − | 0.204782i | ||||
\(801\) | 0.527864 | + | 1.62460i | 0.0186512 | + | 0.0574024i | ||||
\(802\) | 23.7082 | 0.837166 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −4.00000 | −0.141069 | ||||||||
\(805\) | −3.50658 | − | 10.7921i | −0.123591 | − | 0.380373i | ||||
\(806\) | −6.38197 | − | 4.63677i | −0.224795 | − | 0.163323i | ||||
\(807\) | 12.0902 | − | 8.78402i | 0.425594 | − | 0.309212i | ||||
\(808\) | −4.51722 | + | 13.9026i | −0.158915 | + | 0.489091i | ||||
\(809\) | −15.5279 | + | 47.7899i | −0.545931 | + | 1.68020i | 0.172836 | + | 0.984951i | \(0.444707\pi\) |
−0.718767 | + | 0.695251i | \(0.755293\pi\) | |||||||
\(810\) | 3.11803 | − | 2.26538i | 0.109557 | − | 0.0795975i | ||||
\(811\) | 36.5967 | + | 26.5891i | 1.28509 | + | 0.933669i | 0.999694 | − | 0.0247416i | \(-0.00787630\pi\) |
0.285392 | + | 0.958411i | \(0.407876\pi\) | |||||||
\(812\) | −1.92705 | − | 5.93085i | −0.0676262 | − | 0.208132i | ||||
\(813\) | 3.41641 | 0.119819 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −51.7082 | −1.81126 | ||||||||
\(816\) | −2.00000 | − | 6.15537i | −0.0700140 | − | 0.215481i | ||||
\(817\) | −1.23607 | − | 0.898056i | −0.0432445 | − | 0.0314190i | ||||
\(818\) | 0.736068 | − | 0.534785i | 0.0257360 | − | 0.0186983i | ||||
\(819\) | 0.909830 | − | 2.80017i | 0.0317920 | − | 0.0978458i | ||||
\(820\) | −1.47214 | + | 4.53077i | −0.0514092 | + | 0.158221i | ||||
\(821\) | −8.01722 | + | 5.82485i | −0.279803 | + | 0.203289i | −0.718831 | − | 0.695184i | \(-0.755323\pi\) |
0.439029 | + | 0.898473i | \(0.355323\pi\) | |||||||
\(822\) | 13.8541 | + | 10.0656i | 0.483217 | + | 0.351078i | ||||
\(823\) | 14.8992 | + | 45.8550i | 0.519353 | + | 1.59840i | 0.775219 | + | 0.631692i | \(0.217639\pi\) |
−0.255866 | + | 0.966712i | \(0.582361\pi\) | |||||||
\(824\) | −17.0344 | −0.593423 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.79837 | 0.236546 | ||||||||
\(827\) | −15.3541 | − | 47.2551i | −0.533914 | − | 1.64322i | −0.745983 | − | 0.665965i | \(-0.768020\pi\) |
0.212069 | − | 0.977255i | \(-0.431980\pi\) | |||||||
\(828\) | −1.00000 | − | 0.726543i | −0.0347524 | − | 0.0252491i | ||||
\(829\) | 44.7426 | − | 32.5074i | 1.55398 | − | 1.12903i | 0.613237 | − | 0.789899i | \(-0.289867\pi\) |
0.940739 | − | 0.339131i | \(-0.110133\pi\) | |||||||
\(830\) | 19.4443 | − | 59.8433i | 0.674921 | − | 2.07719i | ||||
\(831\) | 9.00000 | − | 27.6992i | 0.312207 | − | 0.960873i | ||||
\(832\) | −1.00000 | + | 0.726543i | −0.0346688 | + | 0.0251883i | ||||
\(833\) | 6.94427 | + | 5.04531i | 0.240605 | + | 0.174810i | ||||
\(834\) | −2.70820 | − | 8.33499i | −0.0937774 | − | 0.288617i | ||||
\(835\) | −10.6525 | −0.368644 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.38197 | −0.220593 | ||||||||
\(838\) | 8.95492 | + | 27.5604i | 0.309342 | + | 0.952058i | ||||
\(839\) | −30.0344 | − | 21.8213i | −1.03690 | − | 0.753355i | −0.0672253 | − | 0.997738i | \(-0.521415\pi\) |
−0.969679 | + | 0.244383i | \(0.921415\pi\) | |||||||
\(840\) | −7.42705 | + | 5.39607i | −0.256258 | + | 0.186182i | ||||
\(841\) | −6.84346 | + | 21.0620i | −0.235981 | + | 0.726276i | ||||
\(842\) | −1.58359 | + | 4.87380i | −0.0545742 | + | 0.167962i | ||||
\(843\) | −13.8541 | + | 10.0656i | −0.477161 | + | 0.346677i | ||||
\(844\) | −21.5623 | − | 15.6659i | −0.742205 | − | 0.539244i | ||||
\(845\) | 13.6631 | + | 42.0508i | 0.470026 | + | 1.44659i | ||||
\(846\) | −6.47214 | −0.222517 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.85410 | 0.0980103 | ||||||||
\(849\) | −3.67376 | − | 11.3067i | −0.126083 | − | 0.388044i | ||||
\(850\) | −51.5967 | − | 37.4872i | −1.76975 | − | 1.28580i | ||||
\(851\) | −10.4721 | + | 7.60845i | −0.358980 | + | 0.260814i | ||||
\(852\) | −1.09017 | + | 3.35520i | −0.0373486 | + | 0.114947i | ||||
\(853\) | 10.1803 | − | 31.3319i | 0.348568 | − | 1.07278i | −0.611078 | − | 0.791571i | \(-0.709264\pi\) |
0.959646 | − | 0.281212i | \(-0.0907364\pi\) | |||||||
\(854\) | 21.6525 | − | 15.7314i | 0.740932 | − | 0.538319i | ||||
\(855\) | 3.85410 | + | 2.80017i | 0.131808 | + | 0.0957638i | ||||
\(856\) | 2.35410 | + | 7.24518i | 0.0804615 | + | 0.247635i | ||||
\(857\) | 13.2361 | 0.452135 | 0.226068 | − | 0.974112i | \(-0.427413\pi\) | ||||
0.226068 | + | 0.974112i | \(0.427413\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.5967 | 1.82870 | 0.914349 | − | 0.404928i | \(-0.132703\pi\) | ||||
0.914349 | + | 0.404928i | \(0.132703\pi\) | |||||||
\(860\) | −1.47214 | − | 4.53077i | −0.0501994 | − | 0.154498i | ||||
\(861\) | 2.38197 | + | 1.73060i | 0.0811772 | + | 0.0589787i | ||||
\(862\) | 2.23607 | − | 1.62460i | 0.0761608 | − | 0.0553340i | ||||
\(863\) | 2.23607 | − | 6.88191i | 0.0761166 | − | 0.234263i | −0.905758 | − | 0.423796i | \(-0.860697\pi\) |
0.981874 | + | 0.189533i | \(0.0606974\pi\) | |||||||
\(864\) | −0.309017 | + | 0.951057i | −0.0105130 | + | 0.0323556i | ||||
\(865\) | −33.8435 | + | 24.5887i | −1.15071 | + | 0.836041i | ||||
\(866\) | 2.69098 | + | 1.95511i | 0.0914433 | + | 0.0664375i | ||||
\(867\) | −7.69098 | − | 23.6704i | −0.261199 | − | 0.803889i | ||||
\(868\) | 15.2016 | 0.515977 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −10.0902 | −0.342089 | ||||||||
\(871\) | 1.52786 | + | 4.70228i | 0.0517697 | + | 0.159331i | ||||
\(872\) | 7.61803 | + | 5.53483i | 0.257979 | + | 0.187433i | ||||
\(873\) | 3.50000 | − | 2.54290i | 0.118457 | − | 0.0860641i | ||||
\(874\) | 0.472136 | − | 1.45309i | 0.0159702 | − | 0.0491513i | ||||
\(875\) | −13.7705 | + | 42.3813i | −0.465528 | + | 1.43275i | ||||
\(876\) | 3.50000 | − | 2.54290i | 0.118254 | − | 0.0859166i | ||||
\(877\) | −11.6180 | − | 8.44100i | −0.392313 | − | 0.285032i | 0.374090 | − | 0.927393i | \(-0.377955\pi\) |
−0.766403 | + | 0.642360i | \(0.777955\pi\) | |||||||
\(878\) | −4.02786 | − | 12.3965i | −0.135934 | − | 0.418361i | ||||
\(879\) | 23.9787 | 0.808782 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.7082 | −0.866131 | −0.433066 | − | 0.901362i | \(-0.642568\pi\) | ||||
−0.433066 | + | 0.901362i | \(0.642568\pi\) | |||||||
\(882\) | −0.409830 | − | 1.26133i | −0.0137997 | − | 0.0424711i | ||||
\(883\) | −40.5967 | − | 29.4953i | −1.36619 | − | 0.992595i | −0.998024 | − | 0.0628343i | \(-0.979986\pi\) |
−0.368165 | − | 0.929760i | \(-0.620014\pi\) | |||||||
\(884\) | −6.47214 | + | 4.70228i | −0.217681 | + | 0.158155i | ||||
\(885\) | 3.39919 | − | 10.4616i | 0.114262 | − | 0.351664i | ||||
\(886\) | −5.35410 | + | 16.4782i | −0.179875 | + | 0.553597i | ||||
\(887\) | −31.1803 | + | 22.6538i | −1.04693 | + | 0.760642i | −0.971627 | − | 0.236519i | \(-0.923994\pi\) |
−0.0753064 | + | 0.997160i | \(0.523994\pi\) | |||||||
\(888\) | 8.47214 | + | 6.15537i | 0.284306 | + | 0.206561i | ||||
\(889\) | 8.83282 | + | 27.1846i | 0.296243 | + | 0.911743i | ||||
\(890\) | −6.58359 | −0.220683 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.0902 | −0.438291 | ||||||||
\(893\) | −2.47214 | − | 7.60845i | −0.0827269 | − | 0.254607i | ||||
\(894\) | 2.92705 | + | 2.12663i | 0.0978952 | + | 0.0711250i | ||||
\(895\) | −26.8713 | + | 19.5232i | −0.898209 | + | 0.652587i | ||||
\(896\) | 0.736068 | − | 2.26538i | 0.0245903 | − | 0.0756812i | ||||
\(897\) | −0.472136 | + | 1.45309i | −0.0157642 | + | 0.0485171i | ||||
\(898\) | −0.0901699 | + | 0.0655123i | −0.00300901 | + | 0.00218617i | ||||
\(899\) | 13.5172 | + | 9.82084i | 0.450825 | + | 0.327543i | ||||
\(900\) | 3.04508 | + | 9.37181i | 0.101503 | + | 0.312394i | ||||
\(901\) | 18.4721 | 0.615396 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.94427 | −0.0979792 | ||||||||
\(904\) | −1.09017 | − | 3.35520i | −0.0362585 | − | 0.111592i | ||||
\(905\) | −23.4721 | − | 17.0535i | −0.780240 | − | 0.566878i | ||||
\(906\) | −5.11803 | + | 3.71847i | −0.170035 | + | 0.123538i | ||||
\(907\) | 4.38197 | − | 13.4863i | 0.145501 | − | 0.447805i | −0.851574 | − | 0.524234i | \(-0.824352\pi\) |
0.997075 | + | 0.0764286i | \(0.0243517\pi\) | |||||||
\(908\) | −4.28115 | + | 13.1760i | −0.142075 | + | 0.437262i | ||||
\(909\) | 11.8262 | − | 8.59226i | 0.392252 | − | 0.284987i | ||||
\(910\) | 9.18034 | + | 6.66991i | 0.304325 | + | 0.221105i | ||||
\(911\) | 9.36068 | + | 28.8092i | 0.310133 | + | 0.954492i | 0.977712 | + | 0.209952i | \(0.0673309\pi\) |
−0.667578 | + | 0.744539i | \(0.732669\pi\) | |||||||
\(912\) | −1.23607 | −0.0409303 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 24.9787 | 0.826222 | ||||||||
\(915\) | −13.3820 | − | 41.1855i | −0.442394 | − | 1.36155i | ||||
\(916\) | −4.09017 | − | 2.97168i | −0.135143 | − | 0.0981872i | ||||
\(917\) | −35.2082 | + | 25.5803i | −1.16268 | + | 0.844735i | ||||
\(918\) | −2.00000 | + | 6.15537i | −0.0660098 | + | 0.203157i | ||||
\(919\) | 5.16970 | − | 15.9107i | 0.170533 | − | 0.524845i | −0.828869 | − | 0.559443i | \(-0.811015\pi\) |
0.999401 | + | 0.0345978i | \(0.0110150\pi\) | |||||||
\(920\) | 3.85410 | − | 2.80017i | 0.127066 | − | 0.0923188i | ||||
\(921\) | 11.8541 | + | 8.61251i | 0.390606 | + | 0.283792i | ||||
\(922\) | −3.96556 | − | 12.2047i | −0.130599 | − | 0.401941i | ||||
\(923\) | 4.36068 | 0.143534 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 103.193 | 3.39298 | ||||||||
\(926\) | 2.44427 | + | 7.52270i | 0.0803238 | + | 0.247211i | ||||
\(927\) | 13.7812 | + | 10.0126i | 0.452632 | + | 0.328857i | ||||
\(928\) | 2.11803 | − | 1.53884i | 0.0695279 | − | 0.0505150i | ||||
\(929\) | 5.29180 | − | 16.2865i | 0.173618 | − | 0.534342i | −0.825949 | − | 0.563744i | \(-0.809360\pi\) |
0.999568 | + | 0.0294023i | \(0.00936039\pi\) | |||||||
\(930\) | 7.60081 | − | 23.3929i | 0.249240 | − | 0.767083i | ||||
\(931\) | 1.32624 | − | 0.963568i | 0.0434657 | − | 0.0315797i | ||||
\(932\) | −7.23607 | − | 5.25731i | −0.237025 | − | 0.172209i | ||||
\(933\) | −3.67376 | − | 11.3067i | −0.120274 | − | 0.370164i | ||||
\(934\) | −0.562306 | −0.0183992 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.23607 | 0.0404021 | ||||||||
\(937\) | −8.79180 | − | 27.0584i | −0.287215 | − | 0.883958i | −0.985726 | − | 0.168358i | \(-0.946153\pi\) |
0.698510 | − | 0.715600i | \(-0.253847\pi\) | |||||||
\(938\) | −7.70820 | − | 5.60034i | −0.251682 | − | 0.182858i | ||||
\(939\) | 17.6803 | − | 12.8455i | 0.576976 | − | 0.419198i | ||||
\(940\) | 7.70820 | − | 23.7234i | 0.251414 | − | 0.773772i | ||||
\(941\) | 13.8541 | − | 42.6385i | 0.451631 | − | 1.38998i | −0.423415 | − | 0.905936i | \(-0.639169\pi\) |
0.875045 | − | 0.484041i | \(-0.160831\pi\) | |||||||
\(942\) | −3.61803 | + | 2.62866i | −0.117882 | + | 0.0856462i | ||||
\(943\) | −1.23607 | − | 0.898056i | −0.0402519 | − | 0.0292447i | ||||
\(944\) | 0.881966 | + | 2.71441i | 0.0287055 | + | 0.0883466i | ||||
\(945\) | 9.18034 | 0.298636 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.3262 | −0.433045 | −0.216522 | − | 0.976278i | \(-0.569471\pi\) | ||||
−0.216522 | + | 0.976278i | \(0.569471\pi\) | |||||||
\(948\) | −1.95492 | − | 6.01661i | −0.0634927 | − | 0.195410i | ||||
\(949\) | −4.32624 | − | 3.14320i | −0.140436 | − | 0.102032i | ||||
\(950\) | −9.85410 | + | 7.15942i | −0.319709 | + | 0.232282i | ||||
\(951\) | −4.90983 | + | 15.1109i | −0.159212 | + | 0.490005i | ||||
\(952\) | 4.76393 | − | 14.6619i | 0.154400 | − | 0.475194i | ||||
\(953\) | 32.9443 | − | 23.9354i | 1.06717 | − | 0.775344i | 0.0917683 | − | 0.995780i | \(-0.470748\pi\) |
0.975401 | + | 0.220436i | \(0.0707481\pi\) | |||||||
\(954\) | −2.30902 | − | 1.67760i | −0.0747572 | − | 0.0543143i | ||||
\(955\) | −16.1115 | − | 49.5860i | −0.521354 | − | 1.60456i | ||||
\(956\) | −7.52786 | −0.243469 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.76393 | −0.0892986 | ||||||||
\(959\) | 12.6049 | + | 38.7938i | 0.407033 | + | 1.25272i | ||||
\(960\) | −3.11803 | − | 2.26538i | −0.100634 | − | 0.0731150i | ||||
\(961\) | −7.87132 | + | 5.71885i | −0.253914 | + | 0.184479i | ||||
\(962\) | 4.00000 | − | 12.3107i | 0.128965 | − | 0.396914i | ||||
\(963\) | 2.35410 | − | 7.24518i | 0.0758599 | − | 0.233473i | ||||
\(964\) | 18.2533 | − | 13.2618i | 0.587899 | − | 0.427134i | ||||
\(965\) | −47.7877 | − | 34.7198i | −1.53834 | − | 1.11767i | ||||
\(966\) | −0.909830 | − | 2.80017i | −0.0292733 | − | 0.0900940i | ||||
\(967\) | −46.6869 | −1.50135 | −0.750675 | − | 0.660672i | \(-0.770272\pi\) | ||||
−0.750675 | + | 0.660672i | \(0.770272\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.00000 | −0.256997 | ||||||||
\(970\) | 5.15248 | + | 15.8577i | 0.165436 | + | 0.509160i | ||||
\(971\) | −43.1246 | − | 31.3319i | −1.38393 | − | 1.00549i | −0.996500 | − | 0.0835901i | \(-0.973361\pi\) |
−0.387434 | − | 0.921897i | \(-0.626639\pi\) | |||||||
\(972\) | 0.809017 | − | 0.587785i | 0.0259492 | − | 0.0188532i | ||||
\(973\) | 6.45085 | − | 19.8537i | 0.206805 | − | 0.636480i | ||||
\(974\) | −6.79180 | + | 20.9030i | −0.217623 | + | 0.669775i | ||||
\(975\) | 9.85410 | − | 7.15942i | 0.315584 | − | 0.229285i | ||||
\(976\) | 9.09017 | + | 6.60440i | 0.290969 | + | 0.211402i | ||||
\(977\) | −12.7426 | − | 39.2178i | −0.407673 | − | 1.25469i | −0.918642 | − | 0.395090i | \(-0.870713\pi\) |
0.510969 | − | 0.859599i | \(-0.329287\pi\) | |||||||
\(978\) | −13.4164 | −0.429009 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 5.11146 | 0.163279 | ||||||||
\(981\) | −2.90983 | − | 8.95554i | −0.0929037 | − | 0.285928i | ||||
\(982\) | 30.9443 | + | 22.4823i | 0.987471 | + | 0.717440i | ||||
\(983\) | −25.1803 | + | 18.2946i | −0.803128 | + | 0.583507i | −0.911830 | − | 0.410568i | \(-0.865331\pi\) |
0.108702 | + | 0.994074i | \(0.465331\pi\) | |||||||
\(984\) | −0.381966 | + | 1.17557i | −0.0121766 | + | 0.0374758i | ||||
\(985\) | 6.06231 | − | 18.6579i | 0.193161 | − | 0.594489i | ||||
\(986\) | 13.7082 | − | 9.95959i | 0.436558 | − | 0.317178i | ||||
\(987\) | −12.4721 | − | 9.06154i | −0.396992 | − | 0.288432i | ||||
\(988\) | 0.472136 | + | 1.45309i | 0.0150206 | + | 0.0462288i | ||||
\(989\) | 1.52786 | 0.0485833 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.6869 | 0.466545 | 0.233273 | − | 0.972411i | \(-0.425057\pi\) | ||||
0.233273 | + | 0.972411i | \(0.425057\pi\) | |||||||
\(992\) | 1.97214 | + | 6.06961i | 0.0626154 | + | 0.192710i | ||||
\(993\) | −7.23607 | − | 5.25731i | −0.229630 | − | 0.166836i | ||||
\(994\) | −6.79837 | + | 4.93931i | −0.215631 | + | 0.156665i | ||||
\(995\) | −23.6459 | + | 72.7746i | −0.749625 | + | 2.30711i | ||||
\(996\) | 5.04508 | − | 15.5272i | 0.159860 | − | 0.491997i | ||||
\(997\) | 29.0902 | − | 21.1352i | 0.921295 | − | 0.669360i | −0.0225511 | − | 0.999746i | \(-0.507179\pi\) |
0.943846 | + | 0.330386i | \(0.107179\pi\) | |||||||
\(998\) | −15.7082 | − | 11.4127i | −0.497235 | − | 0.361262i | ||||
\(999\) | −3.23607 | − | 9.95959i | −0.102385 | − | 0.315108i |
(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 | 726.2.e.f.511.1 | 4 | ||
11.2 | odd | 10 | 726.2.e.n.493.1 | 4 | |||
11.3 | even | 5 | 726.2.a.l.1.1 | 2 | |||
11.4 | even | 5 | 66.2.e.a.25.1 | ✓ | 4 | ||
11.5 | even | 5 | 66.2.e.a.37.1 | yes | 4 | ||
11.6 | odd | 10 | 726.2.e.r.565.1 | 4 | |||
11.7 | odd | 10 | 726.2.e.r.487.1 | 4 | |||
11.8 | odd | 10 | 726.2.a.j.1.1 | 2 | |||
11.9 | even | 5 | inner | 726.2.e.f.493.1 | 4 | ||
11.10 | odd | 2 | 726.2.e.n.511.1 | 4 | |||
33.5 | odd | 10 | 198.2.f.c.37.1 | 4 | |||
33.8 | even | 10 | 2178.2.a.bb.1.2 | 2 | |||
33.14 | odd | 10 | 2178.2.a.t.1.2 | 2 | |||
33.26 | odd | 10 | 198.2.f.c.91.1 | 4 | |||
44.3 | odd | 10 | 5808.2.a.cb.1.1 | 2 | |||
44.15 | odd | 10 | 528.2.y.d.289.1 | 4 | |||
44.19 | even | 10 | 5808.2.a.cg.1.1 | 2 | |||
44.27 | odd | 10 | 528.2.y.d.433.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
66.2.e.a.25.1 | ✓ | 4 | 11.4 | even | 5 | ||
66.2.e.a.37.1 | yes | 4 | 11.5 | even | 5 | ||
198.2.f.c.37.1 | 4 | 33.5 | odd | 10 | |||
198.2.f.c.91.1 | 4 | 33.26 | odd | 10 | |||
528.2.y.d.289.1 | 4 | 44.15 | odd | 10 | |||
528.2.y.d.433.1 | 4 | 44.27 | odd | 10 | |||
726.2.a.j.1.1 | 2 | 11.8 | odd | 10 | |||
726.2.a.l.1.1 | 2 | 11.3 | even | 5 | |||
726.2.e.f.493.1 | 4 | 11.9 | even | 5 | inner | ||
726.2.e.f.511.1 | 4 | 1.1 | even | 1 | trivial | ||
726.2.e.n.493.1 | 4 | 11.2 | odd | 10 | |||
726.2.e.n.511.1 | 4 | 11.10 | odd | 2 | |||
726.2.e.r.487.1 | 4 | 11.7 | odd | 10 | |||
726.2.e.r.565.1 | 4 | 11.6 | odd | 10 | |||
2178.2.a.t.1.2 | 2 | 33.14 | odd | 10 | |||
2178.2.a.bb.1.2 | 2 | 33.8 | even | 10 | |||
5808.2.a.cb.1.1 | 2 | 44.3 | odd | 10 | |||
5808.2.a.cg.1.1 | 2 | 44.19 | even | 10 |