Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [297,2,Mod(37,297)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(297, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([10, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("297.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 297 = 3^{3} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 297.n (of order \(15\), degree \(8\), 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: | \(2.37155694003\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{15})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{15}]$ |
Embedding invariants
Embedding label | 64.1 | ||
Root | \(0.669131 + 0.743145i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 297.64 |
Dual form | 297.2.n.a.181.1 |
$q$-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 \(\left(\mathbb{Z}/297\mathbb{Z}\right)^\times\).
\(n\) | \(56\) | \(244\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.373619 | + | 0.0794152i | −0.264189 | + | 0.0561550i | −0.338101 | − | 0.941110i | \(-0.609785\pi\) |
0.0739128 | + | 0.997265i | \(0.476451\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.69381 | + | 0.754131i | −0.846903 | + | 0.377066i | ||||
\(5\) | −1.20906 | − | 0.256993i | −0.540707 | − | 0.114931i | −0.0705409 | − | 0.997509i | \(-0.522473\pi\) |
−0.470166 | + | 0.882578i | \(0.655806\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.104528 | − | 0.994522i | 0.0395080 | − | 0.375894i | −0.956847 | − | 0.290592i | \(-0.906148\pi\) |
0.996355 | − | 0.0853021i | \(-0.0271855\pi\) | |||||||
\(8\) | 1.19098 | − | 0.865300i | 0.421076 | − | 0.305930i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.472136 | 0.149302 | ||||||||
\(11\) | 3.01430 | − | 1.38348i | 0.908844 | − | 0.417136i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.33070 | − | 4.80973i | −1.20112 | − | 1.33398i | −0.928262 | − | 0.371926i | \(-0.878697\pi\) |
−0.272859 | − | 0.962054i | \(-0.587969\pi\) | |||||||
\(14\) | 0.0399263 | + | 0.379874i | 0.0106708 | + | 0.101525i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.10502 | − | 2.33786i | 0.526254 | − | 0.584464i | ||||
\(17\) | −1.50000 | − | 4.61653i | −0.363803 | − | 1.11967i | −0.950727 | − | 0.310029i | \(-0.899661\pi\) |
0.586924 | − | 0.809642i | \(-0.300339\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.809017 | + | 0.587785i | −0.185601 | + | 0.134847i | −0.676706 | − | 0.736253i | \(-0.736593\pi\) |
0.491105 | + | 0.871100i | \(0.336593\pi\) | |||||||
\(20\) | 2.24171 | − | 0.476491i | 0.501263 | − | 0.106547i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.01633 | + | 0.756276i | −0.216682 | + | 0.161239i | ||||
\(23\) | 2.30902 | − | 3.99933i | 0.481463 | − | 0.833919i | −0.518310 | − | 0.855193i | \(-0.673439\pi\) |
0.999774 | + | 0.0212736i | \(0.00677212\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.17195 | − | 1.41224i | −0.634391 | − | 0.282449i | ||||
\(26\) | 2.00000 | + | 1.45309i | 0.392232 | + | 0.284973i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.572949 | + | 1.76336i | 0.108277 | + | 0.333243i | ||||
\(29\) | −0.507392 | + | 4.82751i | −0.0942203 | + | 0.896446i | 0.840679 | + | 0.541534i | \(0.182156\pi\) |
−0.934899 | + | 0.354913i | \(0.884511\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.413545 | + | 0.459289i | 0.0742750 | + | 0.0824907i | 0.779137 | − | 0.626854i | \(-0.215658\pi\) |
−0.704862 | + | 0.709345i | \(0.748991\pi\) | |||||||
\(32\) | −2.07295 | + | 3.59045i | −0.366449 | + | 0.634708i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.927051 | + | 1.60570i | 0.158988 | + | 0.275375i | ||||
\(35\) | −0.381966 | + | 1.17557i | −0.0645640 | + | 0.198708i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.11803 | + | 2.99193i | 0.677001 | + | 0.491870i | 0.872361 | − | 0.488862i | \(-0.162588\pi\) |
−0.195361 | + | 0.980731i | \(0.562588\pi\) | |||||||
\(38\) | 0.255585 | − | 0.283856i | 0.0414614 | − | 0.0460475i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.66234 | + | 0.740122i | −0.262839 | + | 0.117024i | ||||
\(41\) | −0.264234 | − | 2.51402i | −0.0412664 | − | 0.392623i | −0.995587 | − | 0.0938399i | \(-0.970086\pi\) |
0.954321 | − | 0.298783i | \(-0.0965808\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.927051 | − | 1.60570i | −0.141374 | − | 0.244867i | 0.786640 | − | 0.617412i | \(-0.211819\pi\) |
−0.928014 | + | 0.372545i | \(0.878485\pi\) | |||||||
\(44\) | −4.06231 | + | 4.61653i | −0.612416 | + | 0.695967i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.545085 | + | 1.67760i | −0.0803684 | + | 0.247348i | ||||
\(47\) | −10.9116 | − | 4.85817i | −1.59163 | − | 0.708637i | −0.596081 | − | 0.802925i | \(-0.703276\pi\) |
−0.995545 | + | 0.0942873i | \(0.969943\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.86889 | + | 1.24747i | 0.838412 | + | 0.178210i | ||||
\(50\) | 1.29726 | + | 0.275740i | 0.183460 | + | 0.0389956i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.9625 | + | 4.88084i | 1.52023 | + | 0.676851i | ||||
\(53\) | −1.26393 | + | 3.88998i | −0.173614 | + | 0.534330i | −0.999567 | − | 0.0294087i | \(-0.990638\pi\) |
0.825953 | + | 0.563739i | \(0.190638\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | + | 0.898056i | −0.539360 | + | 0.121094i | ||||
\(56\) | −0.736068 | − | 1.27491i | −0.0983612 | − | 0.170367i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.193806 | − | 1.84395i | −0.0254480 | − | 0.242122i | ||||
\(59\) | −1.47815 | + | 0.658114i | −0.192438 | + | 0.0856791i | −0.500694 | − | 0.865625i | \(-0.666922\pi\) |
0.308255 | + | 0.951304i | \(0.400255\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.26281 | − | 8.06617i | 0.929908 | − | 1.03277i | −0.0694731 | − | 0.997584i | \(-0.522132\pi\) |
0.999381 | − | 0.0351834i | \(-0.0112015\pi\) | |||||||
\(62\) | −0.190983 | − | 0.138757i | −0.0242549 | − | 0.0176222i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.45492 | + | 4.47777i | −0.181864 | + | 0.559721i | ||||
\(65\) | 4.00000 | + | 6.92820i | 0.496139 | + | 0.859338i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.00000 | + | 5.19615i | −0.366508 | + | 0.634811i | −0.989017 | − | 0.147802i | \(-0.952780\pi\) |
0.622509 | + | 0.782613i | \(0.286114\pi\) | |||||||
\(68\) | 6.02218 | + | 6.68830i | 0.730296 | + | 0.811076i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0493516 | − | 0.469550i | 0.00589865 | − | 0.0561219i | ||||
\(71\) | 0.899187 | + | 2.76741i | 0.106714 | + | 0.328431i | 0.990129 | − | 0.140160i | \(-0.0447617\pi\) |
−0.883415 | + | 0.468591i | \(0.844762\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.118034 | + | 0.0857567i | 0.0138148 | + | 0.0100371i | 0.594671 | − | 0.803969i | \(-0.297282\pi\) |
−0.580856 | + | 0.814006i | \(0.697282\pi\) | |||||||
\(74\) | −1.77618 | − | 0.790807i | −0.206477 | − | 0.0919294i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.927051 | − | 1.60570i | 0.106340 | − | 0.184186i | ||||
\(77\) | −1.06082 | − | 3.14240i | −0.120892 | − | 0.358109i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.3315 | + | 2.19603i | −1.16238 | + | 0.247072i | −0.748423 | − | 0.663222i | \(-0.769188\pi\) |
−0.413961 | + | 0.910294i | \(0.635855\pi\) | |||||||
\(80\) | −3.14590 | + | 2.28563i | −0.351722 | + | 0.255541i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.298374 | + | 0.918300i | 0.0329499 | + | 0.101409i | ||||
\(83\) | 6.53335 | − | 7.25602i | 0.717128 | − | 0.796451i | −0.268876 | − | 0.963175i | \(-0.586652\pi\) |
0.986004 | + | 0.166724i | \(0.0533188\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.627171 | + | 5.96713i | 0.0680262 | + | 0.647226i | ||||
\(86\) | 0.473881 | + | 0.526298i | 0.0510999 | + | 0.0567522i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.39285 | − | 4.25597i | 0.255078 | − | 0.453688i | ||||
\(89\) | 6.76393 | 0.716975 | 0.358488 | − | 0.933534i | \(-0.383293\pi\) | ||||
0.358488 | + | 0.933534i | \(0.383293\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.23607 | + | 3.80423i | −0.548889 | + | 0.398791i | ||||
\(92\) | −0.895005 | + | 8.51540i | −0.0933107 | + | 0.887792i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.46261 | + | 0.948557i | 0.460283 | + | 0.0978362i | ||||
\(95\) | 1.12920 | − | 0.502754i | 0.115854 | − | 0.0515815i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.86889 | + | 1.24747i | −0.595895 | + | 0.126661i | −0.495979 | − | 0.868334i | \(-0.665191\pi\) |
−0.0999160 | + | 0.994996i | \(0.531857\pi\) | |||||||
\(98\) | −2.29180 | −0.231506 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.43769 | 0.643769 | ||||||||
\(101\) | −8.28700 | + | 1.76146i | −0.824587 | + | 0.175271i | −0.600833 | − | 0.799374i | \(-0.705165\pi\) |
−0.223754 | + | 0.974646i | \(0.571831\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.35111 | + | 4.16338i | −0.921393 | + | 0.410230i | −0.811926 | − | 0.583760i | \(-0.801581\pi\) |
−0.109466 | + | 0.993990i | \(0.534914\pi\) | |||||||
\(104\) | −9.31966 | − | 1.98095i | −0.913868 | − | 0.194249i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.163305 | − | 1.55375i | 0.0158616 | − | 0.150913i | ||||
\(107\) | 11.3541 | − | 8.24924i | 1.09764 | − | 0.797484i | 0.116969 | − | 0.993136i | \(-0.462682\pi\) |
0.980673 | + | 0.195652i | \(0.0626822\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.14590 | 0.684453 | 0.342226 | − | 0.939618i | \(-0.388819\pi\) | ||||
0.342226 | + | 0.939618i | \(0.388819\pi\) | |||||||
\(110\) | 1.42316 | − | 0.653192i | 0.135693 | − | 0.0622794i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.10502 | − | 2.33786i | −0.198905 | − | 0.220907i | ||||
\(113\) | 1.80166 | + | 17.1416i | 0.169486 | + | 1.61255i | 0.666975 | + | 0.745080i | \(0.267589\pi\) |
−0.497489 | + | 0.867470i | \(0.665745\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.81953 | + | 4.24202i | −0.356173 | + | 0.395571i | ||||
\(116\) | −2.78115 | − | 8.55951i | −0.258224 | − | 0.794730i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.500000 | − | 0.363271i | 0.0460287 | − | 0.0334418i | ||||
\(119\) | −4.74803 | + | 1.00922i | −0.435251 | + | 0.0925155i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.17195 | − | 8.34045i | 0.651996 | − | 0.758223i | ||||
\(122\) | −2.07295 | + | 3.59045i | −0.187676 | + | 0.325064i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.04683 | − | 0.466079i | −0.0940081 | − | 0.0418551i | ||||
\(125\) | 8.47214 | + | 6.15537i | 0.757771 | + | 0.550553i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.26393 | − | 10.0453i | −0.289627 | − | 0.891381i | −0.984973 | − | 0.172706i | \(-0.944749\pi\) |
0.695346 | − | 0.718675i | \(-0.255251\pi\) | |||||||
\(128\) | 1.05471 | − | 10.0349i | 0.0932241 | − | 0.886968i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.04468 | − | 2.27085i | −0.179330 | − | 0.199167i | ||||
\(131\) | 10.6180 | − | 18.3910i | 0.927702 | − | 1.60683i | 0.140545 | − | 0.990074i | \(-0.455115\pi\) |
0.787157 | − | 0.616753i | \(-0.211552\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.500000 | + | 0.866025i | 0.0433555 | + | 0.0750939i | ||||
\(134\) | 0.708204 | − | 2.17963i | 0.0611795 | − | 0.188291i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.78115 | − | 4.20025i | −0.495730 | − | 0.360169i | ||||
\(137\) | 5.76659 | − | 6.40445i | 0.492673 | − | 0.547169i | −0.444616 | − | 0.895721i | \(-0.646660\pi\) |
0.937289 | + | 0.348552i | \(0.113327\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.86889 | − | 3.94868i | 0.752249 | − | 0.334923i | 0.00546112 | − | 0.999985i | \(-0.498262\pi\) |
0.746788 | + | 0.665062i | \(0.231595\pi\) | |||||||
\(140\) | −0.239558 | − | 2.27924i | −0.0202463 | − | 0.192631i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.555728 | − | 0.962549i | −0.0466357 | − | 0.0807753i | ||||
\(143\) | −19.7082 | − | 8.50651i | −1.64808 | − | 0.711350i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.85410 | − | 5.70634i | 0.153975 | − | 0.473886i | ||||
\(146\) | −0.0509101 | − | 0.0226667i | −0.00421335 | − | 0.00187591i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.23146 | − | 1.96221i | −0.758821 | − | 0.161292i | ||||
\(149\) | −14.8486 | − | 3.15617i | −1.21645 | − | 0.258564i | −0.445393 | − | 0.895335i | \(-0.646936\pi\) |
−0.771053 | + | 0.636772i | \(0.780269\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.95222 | + | 1.75964i | 0.321627 | + | 0.143197i | 0.561199 | − | 0.827681i | \(-0.310340\pi\) |
−0.239572 | + | 0.970879i | \(0.577007\pi\) | |||||||
\(152\) | −0.454915 | + | 1.40008i | −0.0368985 | + | 0.113562i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.645898 | + | 1.08981i | 0.0520479 | + | 0.0878197i | ||||
\(155\) | −0.381966 | − | 0.661585i | −0.0306802 | − | 0.0531397i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.746950 | − | 7.10675i | −0.0596131 | − | 0.567181i | −0.983038 | − | 0.183402i | \(-0.941289\pi\) |
0.923425 | − | 0.383779i | \(-0.125378\pi\) | |||||||
\(158\) | 3.68565 | − | 1.64096i | 0.293214 | − | 0.130547i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.42903 | − | 3.80833i | 0.271089 | − | 0.301075i | ||||
\(161\) | −3.73607 | − | 2.71441i | −0.294443 | − | 0.213926i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.39919 | − | 19.6947i | 0.501223 | − | 1.54261i | −0.305806 | − | 0.952094i | \(-0.598926\pi\) |
0.807029 | − | 0.590512i | \(-0.201074\pi\) | |||||||
\(164\) | 2.34346 | + | 4.05899i | 0.182993 | + | 0.316954i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.86475 | + | 3.22983i | −0.144732 | + | 0.250684i | ||||
\(167\) | 3.85682 | + | 4.28344i | 0.298450 | + | 0.331462i | 0.873654 | − | 0.486548i | \(-0.161744\pi\) |
−0.575204 | + | 0.818010i | \(0.695077\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.01968 | + | 28.7303i | −0.232283 | + | 2.21002i | ||||
\(170\) | −0.708204 | − | 2.17963i | −0.0543168 | − | 0.167170i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.78115 | + | 2.02063i | 0.212061 | + | 0.154071i | ||||
\(173\) | 21.0939 | + | 9.39162i | 1.60374 | + | 0.714032i | 0.996741 | − | 0.0806702i | \(-0.0257060\pi\) |
0.607000 | + | 0.794702i | \(0.292373\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.73607 | + | 3.00696i | −0.131234 | + | 0.227305i | ||||
\(176\) | 3.11076 | − | 9.95925i | 0.234482 | − | 0.750707i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.52713 | + | 0.537159i | −0.189417 | + | 0.0402618i | ||||
\(179\) | −4.09017 | + | 2.97168i | −0.305714 | + | 0.222114i | −0.730055 | − | 0.683388i | \(-0.760506\pi\) |
0.424341 | + | 0.905502i | \(0.360506\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.06231 | − | 9.42481i | −0.227619 | − | 0.700540i | −0.998015 | − | 0.0629745i | \(-0.979941\pi\) |
0.770396 | − | 0.637566i | \(-0.220059\pi\) | |||||||
\(182\) | 1.65418 | − | 1.83716i | 0.122616 | − | 0.136179i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.710624 | − | 6.76113i | −0.0523879 | − | 0.498437i | ||||
\(185\) | −4.21003 | − | 4.67572i | −0.309528 | − | 0.343765i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.9083 | − | 11.8403i | −0.797696 | − | 0.865852i | ||||
\(188\) | 22.1459 | 1.61516 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.381966 | + | 0.277515i | −0.0277107 | + | 0.0201330i | ||||
\(191\) | 0.621346 | − | 5.91171i | 0.0449590 | − | 0.427756i | −0.948772 | − | 0.315961i | \(-0.897673\pi\) |
0.993731 | − | 0.111795i | \(-0.0356601\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.7596 | + | 2.28703i | 0.774495 | + | 0.164624i | 0.578171 | − | 0.815915i | \(-0.303766\pi\) |
0.196323 | + | 0.980539i | \(0.437100\pi\) | |||||||
\(194\) | 2.09366 | − | 0.932157i | 0.150316 | − | 0.0669250i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.8815 | + | 2.31294i | −0.777251 | + | 0.165210i | ||||
\(197\) | −8.23607 | −0.586796 | −0.293398 | − | 0.955990i | \(-0.594786\pi\) | ||||
−0.293398 | + | 0.955990i | \(0.594786\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.14590 | −0.506559 | −0.253280 | − | 0.967393i | \(-0.581509\pi\) | ||||
−0.253280 | + | 0.967393i | \(0.581509\pi\) | |||||||
\(200\) | −4.99976 | + | 1.06273i | −0.353536 | + | 0.0751465i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.95630 | − | 1.31623i | 0.208004 | − | 0.0926094i | ||||
\(203\) | 4.74803 | + | 1.00922i | 0.333246 | + | 0.0708337i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.326611 | + | 3.10749i | −0.0228115 | + | 0.217037i | ||||
\(206\) | 3.16312 | − | 2.29814i | 0.220385 | − | 0.160119i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −20.3607 | −1.41176 | ||||||||
\(209\) | −1.62543 | + | 2.89102i | −0.112433 | + | 0.199976i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.6985 | + | 15.2138i | 0.943046 | + | 1.04736i | 0.998803 | + | 0.0489142i | \(0.0155761\pi\) |
−0.0557571 | + | 0.998444i | \(0.517757\pi\) | |||||||
\(212\) | −0.792701 | − | 7.54205i | −0.0544429 | − | 0.517990i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.58699 | + | 3.98376i | −0.245202 | + | 0.272324i | ||||
\(215\) | 0.708204 | + | 2.17963i | 0.0482991 | + | 0.148649i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.500000 | − | 0.363271i | 0.0339422 | − | 0.0246605i | ||||
\(218\) | −2.66984 | + | 0.567493i | −0.180825 | + | 0.0384355i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.09797 | − | 4.53766i | 0.411125 | − | 0.305929i | ||||
\(221\) | −15.7082 | + | 27.2074i | −1.05665 | + | 1.83017i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.1660 | − | 6.30709i | −0.948623 | − | 0.422354i | −0.126693 | − | 0.991942i | \(-0.540436\pi\) |
−0.821930 | + | 0.569588i | \(0.807103\pi\) | |||||||
\(224\) | 3.35410 | + | 2.43690i | 0.224105 | + | 0.162822i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.03444 | − | 6.26137i | −0.135329 | − | 0.416500i | ||||
\(227\) | −1.73706 | + | 16.5270i | −0.115293 | + | 1.09694i | 0.771966 | + | 0.635664i | \(0.219273\pi\) |
−0.887259 | + | 0.461272i | \(0.847393\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.81198 | + | 7.56547i | 0.450148 | + | 0.499940i | 0.924916 | − | 0.380171i | \(-0.124135\pi\) |
−0.474768 | + | 0.880111i | \(0.657468\pi\) | |||||||
\(230\) | 1.09017 | − | 1.88823i | 0.0718837 | − | 0.124506i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.57295 | + | 6.18853i | 0.234576 | + | 0.406297i | ||||
\(233\) | 3.43769 | − | 10.5801i | 0.225211 | − | 0.693128i | −0.773059 | − | 0.634334i | \(-0.781275\pi\) |
0.998270 | − | 0.0587939i | \(-0.0187255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.9443 | + | 8.67802i | 0.779158 | + | 0.566092i | ||||
\(236\) | 2.00739 | − | 2.22943i | 0.130670 | − | 0.145124i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.69381 | − | 0.754131i | 0.109793 | − | 0.0488831i | ||||
\(239\) | 1.09464 | + | 10.4148i | 0.0708061 | + | 0.673675i | 0.971146 | + | 0.238487i | \(0.0766515\pi\) |
−0.900340 | + | 0.435188i | \(0.856682\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.4164 | + | 23.2379i | 0.864227 | + | 1.49688i | 0.867813 | + | 0.496891i | \(0.165525\pi\) |
−0.00358606 | + | 0.999994i | \(0.501141\pi\) | |||||||
\(242\) | −2.01722 | + | 3.68571i | −0.129672 | + | 0.236927i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.21885 | + | 19.1396i | −0.398121 | + | 1.22529i | ||||
\(245\) | −6.77523 | − | 3.01652i | −0.432853 | − | 0.192719i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.33070 | + | 1.34563i | 0.402813 | + | 0.0856206i | ||||
\(248\) | 0.889948 | + | 0.189164i | 0.0565118 | + | 0.0120119i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.65418 | − | 1.62695i | −0.231111 | − | 0.102897i | ||||
\(251\) | −6.35410 | + | 19.5559i | −0.401067 | + | 1.23436i | 0.523067 | + | 0.852291i | \(0.324788\pi\) |
−0.924135 | + | 0.382067i | \(0.875212\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.42705 | − | 15.2497i | 0.0897179 | − | 0.958738i | ||||
\(254\) | 2.01722 | + | 3.49393i | 0.126572 | + | 0.219229i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.581419 | − | 5.53184i | −0.0363387 | − | 0.345740i | ||||
\(257\) | 13.6208 | − | 6.06437i | 0.849643 | − | 0.378285i | 0.0647383 | − | 0.997902i | \(-0.479379\pi\) |
0.784904 | + | 0.619617i | \(0.212712\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.40599 | − | 3.78273i | 0.211638 | − | 0.235048i | ||||
\(260\) | −12.0000 | − | 8.71851i | −0.744208 | − | 0.540699i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.50658 | + | 7.71445i | −0.154857 | + | 0.476601i | ||||
\(263\) | −6.35410 | − | 11.0056i | −0.391811 | − | 0.678636i | 0.600878 | − | 0.799341i | \(-0.294818\pi\) |
−0.992688 | + | 0.120705i | \(0.961485\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.52786 | − | 4.37839i | 0.155285 | − | 0.268962i | ||||
\(266\) | −0.255585 | − | 0.283856i | −0.0156709 | − | 0.0174043i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.16284 | − | 11.0637i | 0.0710317 | − | 0.675821i | ||||
\(269\) | 6.57295 | + | 20.2295i | 0.400760 | + | 1.23341i | 0.924384 | + | 0.381463i | \(0.124579\pi\) |
−0.523625 | + | 0.851949i | \(0.675421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.70820 | − | 6.32688i | −0.528986 | − | 0.384331i | 0.290993 | − | 0.956725i | \(-0.406015\pi\) |
−0.819978 | + | 0.572395i | \(0.806015\pi\) | |||||||
\(272\) | −13.9503 | − | 6.21108i | −0.845861 | − | 0.376602i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.64590 | + | 2.85078i | −0.0994323 | + | 0.172222i | ||||
\(275\) | −11.5150 | + | 0.131418i | −0.694382 | + | 0.00792483i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.8157 | − | 3.99940i | 1.13053 | − | 0.240301i | 0.395584 | − | 0.918430i | \(-0.370542\pi\) |
0.734943 | + | 0.678129i | \(0.237209\pi\) | |||||||
\(278\) | −3.00000 | + | 2.17963i | −0.179928 | + | 0.130725i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.562306 | + | 1.73060i | 0.0336042 | + | 0.103423i | ||||
\(281\) | 6.24047 | − | 6.93075i | 0.372275 | − | 0.413454i | −0.527675 | − | 0.849446i | \(-0.676936\pi\) |
0.899950 | + | 0.435993i | \(0.143603\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.77698 | + | 16.9069i | 0.105631 | + | 1.00501i | 0.911048 | + | 0.412301i | \(0.135275\pi\) |
−0.805417 | + | 0.592708i | \(0.798059\pi\) | |||||||
\(284\) | −3.61004 | − | 4.00936i | −0.214217 | − | 0.237912i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.03891 | + | 1.61306i | 0.475351 | + | 0.0953824i | ||||
\(287\) | −2.52786 | −0.149215 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.30902 | + | 3.85723i | −0.312295 | + | 0.226896i | ||||
\(290\) | −0.239558 | + | 2.27924i | −0.0140673 | + | 0.133842i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.264599 | − | 0.0562422i | −0.0154845 | − | 0.00329132i | ||||
\(293\) | 26.6576 | − | 11.8687i | 1.55735 | − | 0.693378i | 0.565975 | − | 0.824422i | \(-0.308500\pi\) |
0.991376 | + | 0.131045i | \(0.0418331\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.95630 | − | 0.415823i | 0.113900 | − | 0.0242102i | ||||
\(296\) | 7.49342 | 0.435546 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.79837 | 0.335891 | ||||||||
\(299\) | −29.2354 | + | 6.21418i | −1.69073 | + | 0.359375i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.69381 | + | 0.754131i | −0.0976294 | + | 0.0434674i | ||||
\(302\) | −1.61637 | − | 0.343569i | −0.0930114 | − | 0.0197702i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.328836 | + | 3.12866i | −0.0188600 | + | 0.179441i | ||||
\(305\) | −10.8541 | + | 7.88597i | −0.621504 | + | 0.451549i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.85410 | 0.448257 | 0.224129 | − | 0.974560i | \(-0.428046\pi\) | ||||
0.224129 | + | 0.974560i | \(0.428046\pi\) | |||||||
\(308\) | 4.16661 | + | 4.52261i | 0.237415 | + | 0.257700i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.195250 | + | 0.216847i | 0.0110894 | + | 0.0123161i | ||||
\(311\) | 1.58678 | + | 15.0972i | 0.0899779 | + | 0.856083i | 0.942683 | + | 0.333690i | \(0.108294\pi\) |
−0.852705 | + | 0.522393i | \(0.825040\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.32331 | − | 2.58030i | 0.131321 | − | 0.145847i | −0.673898 | − | 0.738825i | \(-0.735381\pi\) |
0.805219 | + | 0.592978i | \(0.202048\pi\) | |||||||
\(314\) | 0.843459 | + | 2.59590i | 0.0475991 | + | 0.146495i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.8435 | − | 11.5109i | 0.891264 | − | 0.647541i | ||||
\(317\) | 20.4866 | − | 4.35456i | 1.15064 | − | 0.244576i | 0.407175 | − | 0.913350i | \(-0.366514\pi\) |
0.743466 | + | 0.668774i | \(0.233180\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.14935 | + | 15.2535i | 0.288308 | + | 0.854033i | ||||
\(320\) | 2.90983 | − | 5.03997i | 0.162664 | − | 0.281743i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.61143 | + | 0.717456i | 0.0898016 | + | 0.0399822i | ||||
\(323\) | 3.92705 | + | 2.85317i | 0.218507 | + | 0.158755i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.94427 | + | 21.3723i | 0.385199 | + | 1.18552i | ||||
\(326\) | −0.826802 | + | 7.86650i | −0.0457923 | + | 0.435685i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.49008 | − | 2.76551i | −0.137491 | − | 0.152700i | ||||
\(329\) | −5.97214 | + | 10.3440i | −0.329255 | + | 0.570286i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.20820 | − | 12.4850i | −0.396199 | − | 0.686236i | 0.597055 | − | 0.802201i | \(-0.296338\pi\) |
−0.993253 | + | 0.115964i | \(0.963004\pi\) | |||||||
\(332\) | −5.59424 | + | 17.2173i | −0.307024 | + | 0.944921i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.78115 | − | 1.29408i | −0.0974604 | − | 0.0708091i | ||||
\(335\) | 4.96255 | − | 5.51147i | 0.271133 | − | 0.301124i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.4803 | + | 4.66614i | −0.570899 | + | 0.254181i | −0.671821 | − | 0.740714i | \(-0.734488\pi\) |
0.100922 | + | 0.994894i | \(0.467821\pi\) | |||||||
\(338\) | −1.15341 | − | 10.9740i | −0.0627374 | − | 0.596907i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.56231 | − | 9.63420i | −0.301658 | − | 0.522488i | ||||
\(341\) | 1.88197 | + | 0.812299i | 0.101914 | + | 0.0439885i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.01722 | − | 12.3637i | 0.216910 | − | 0.667579i | ||||
\(344\) | −2.49351 | − | 1.11018i | −0.134441 | − | 0.0598571i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.62693 | − | 1.83371i | −0.463787 | − | 0.0985809i | ||||
\(347\) | −8.69431 | − | 1.84803i | −0.466735 | − | 0.0992076i | −0.0314597 | − | 0.999505i | \(-0.510016\pi\) |
−0.435275 | + | 0.900297i | \(0.643349\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.78747 | − | 1.68629i | −0.202738 | − | 0.0902650i | 0.302856 | − | 0.953036i | \(-0.402060\pi\) |
−0.505594 | + | 0.862771i | \(0.668727\pi\) | |||||||
\(350\) | 0.409830 | − | 1.26133i | 0.0219063 | − | 0.0674208i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.28115 | + | 13.6906i | −0.0682857 | + | 0.729710i | ||||
\(353\) | −8.20820 | − | 14.2170i | −0.436879 | − | 0.756696i | 0.560568 | − | 0.828108i | \(-0.310583\pi\) |
−0.997447 | + | 0.0714123i | \(0.977249\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.375963 | − | 3.57704i | −0.0199540 | − | 0.189850i | ||||
\(356\) | −11.4568 | + | 5.10089i | −0.607209 | + | 0.270347i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.29217 | − | 1.43510i | 0.0682933 | − | 0.0758473i | ||||
\(359\) | −18.4894 | − | 13.4333i | −0.975831 | − | 0.708983i | −0.0190579 | − | 0.999818i | \(-0.506067\pi\) |
−0.956773 | + | 0.290836i | \(0.906067\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.56231 | + | 17.1190i | −0.292753 | + | 0.901001i | ||||
\(362\) | 1.89261 | + | 3.27810i | 0.0994733 | + | 0.172293i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.00000 | − | 10.3923i | 0.314485 | − | 0.544705i | ||||
\(365\) | −0.120671 | − | 0.134019i | −0.00631621 | − | 0.00701486i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.32837 | − | 12.6386i | 0.0693403 | − | 0.659729i | −0.903553 | − | 0.428476i | \(-0.859051\pi\) |
0.972894 | − | 0.231253i | \(-0.0742826\pi\) | |||||||
\(368\) | −4.48936 | − | 13.8168i | −0.234024 | − | 0.720252i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.94427 | + | 1.41260i | 0.101078 | + | 0.0734374i | ||||
\(371\) | 3.73656 | + | 1.66362i | 0.193992 | + | 0.0863710i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.82624 | − | 4.89519i | 0.146337 | − | 0.253463i | −0.783534 | − | 0.621349i | \(-0.786585\pi\) |
0.929871 | + | 0.367886i | \(0.119918\pi\) | |||||||
\(374\) | 5.01586 | + | 3.55749i | 0.259364 | + | 0.183954i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.1993 | + | 3.65583i | −0.886989 | + | 0.188535i | ||||
\(377\) | 25.4164 | − | 18.4661i | 1.30901 | − | 0.951053i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.88197 | + | 15.0251i | 0.250770 | + | 0.771790i | 0.994634 | + | 0.103459i | \(0.0329910\pi\) |
−0.743864 | + | 0.668331i | \(0.767009\pi\) | |||||||
\(380\) | −1.53351 | + | 1.70314i | −0.0786674 | + | 0.0873691i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.237333 | + | 2.25807i | 0.0121430 | + | 0.115533i | ||||
\(383\) | −13.2850 | − | 14.7545i | −0.678831 | − | 0.753918i | 0.301026 | − | 0.953616i | \(-0.402671\pi\) |
−0.979858 | + | 0.199697i | \(0.936004\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.475022 | + | 4.07196i | 0.0242094 | + | 0.207526i | ||||
\(386\) | −4.20163 | −0.213857 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.00000 | − | 6.53888i | 0.456906 | − | 0.331961i | ||||
\(389\) | −2.36783 | + | 22.5284i | −0.120054 | + | 1.14223i | 0.754159 | + | 0.656692i | \(0.228045\pi\) |
−0.874213 | + | 0.485543i | \(0.838622\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.9266 | − | 4.66063i | −1.10887 | − | 0.235698i | ||||
\(392\) | 8.06918 | − | 3.59263i | 0.407555 | − | 0.181455i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.07715 | − | 0.654069i | 0.155025 | − | 0.0329515i | ||||
\(395\) | 13.0557 | 0.656905 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.12461 | −0.106631 | −0.0533156 | − | 0.998578i | \(-0.516979\pi\) | ||||
−0.0533156 | + | 0.998578i | \(0.516979\pi\) | |||||||
\(398\) | 2.66984 | − | 0.567493i | 0.133827 | − | 0.0284458i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.97864 | + | 4.44278i | −0.498932 | + | 0.222139i | ||||
\(401\) | 14.2441 | + | 3.02767i | 0.711316 | + | 0.151195i | 0.549339 | − | 0.835600i | \(-0.314880\pi\) |
0.161977 | + | 0.986795i | \(0.448213\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.418114 | − | 3.97809i | 0.0208277 | − | 0.198163i | ||||
\(404\) | 12.7082 | − | 9.23305i | 0.632257 | − | 0.459361i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.85410 | −0.0920175 | ||||||||
\(407\) | 16.5522 | + | 3.32132i | 0.820465 | + | 0.164632i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.5782 | − | 25.0757i | −1.11642 | − | 1.23991i | −0.967990 | − | 0.250990i | \(-0.919244\pi\) |
−0.148432 | − | 0.988923i | \(-0.547423\pi\) | |||||||
\(410\) | −0.124754 | − | 1.18696i | −0.00616117 | − | 0.0586196i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.6992 | − | 14.1039i | 0.625647 | − | 0.694851i | ||||
\(413\) | 0.500000 | + | 1.53884i | 0.0246034 | + | 0.0757215i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.76393 | + | 7.09391i | −0.479293 | + | 0.348226i | ||||
\(416\) | 26.2465 | − | 5.57886i | 1.28684 | − | 0.273526i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.377699 | − | 1.20922i | 0.0184739 | − | 0.0591451i | ||||
\(419\) | 4.04508 | − | 7.00629i | 0.197615 | − | 0.342280i | −0.750139 | − | 0.661280i | \(-0.770014\pi\) |
0.947755 | + | 0.319000i | \(0.103347\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.35111 | + | 4.16338i | 0.455745 | + | 0.202911i | 0.621753 | − | 0.783214i | \(-0.286421\pi\) |
−0.166007 | + | 0.986125i | \(0.553088\pi\) | |||||||
\(422\) | −6.32624 | − | 4.59628i | −0.307956 | − | 0.223743i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.86068 | + | 5.72658i | 0.0903626 | + | 0.278107i | ||||
\(425\) | −1.76173 | + | 16.7618i | −0.0854566 | + | 0.813065i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.26281 | − | 8.06617i | −0.351472 | − | 0.390349i | ||||
\(428\) | −13.0106 | + | 22.5351i | −0.628893 | + | 1.08927i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.437694 | − | 0.758108i | −0.0211075 | − | 0.0365592i | ||||
\(431\) | 10.5279 | − | 32.4014i | 0.507109 | − | 1.56072i | −0.290086 | − | 0.957001i | \(-0.593684\pi\) |
0.797195 | − | 0.603722i | \(-0.206316\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.9271 | − | 8.66551i | −0.573177 | − | 0.416438i | 0.263081 | − | 0.964774i | \(-0.415261\pi\) |
−0.836258 | + | 0.548336i | \(0.815261\pi\) | |||||||
\(434\) | −0.157960 | + | 0.175433i | −0.00758234 | + | 0.00842104i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.1038 | + | 5.38894i | −0.579665 | + | 0.258084i | ||||
\(437\) | 0.482716 | + | 4.59274i | 0.0230914 | + | 0.219700i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.354102 | + | 0.613323i | 0.0169004 | + | 0.0292723i | 0.874352 | − | 0.485292i | \(-0.161287\pi\) |
−0.857452 | + | 0.514565i | \(0.827954\pi\) | |||||||
\(440\) | −3.98684 | + | 4.53077i | −0.190065 | + | 0.215996i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.70820 | − | 11.4127i | 0.176381 | − | 0.542846i | ||||
\(443\) | 1.12920 | + | 0.502754i | 0.0536501 | + | 0.0238866i | 0.433386 | − | 0.901208i | \(-0.357319\pi\) |
−0.379736 | + | 0.925095i | \(0.623985\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.17798 | − | 1.73828i | −0.387673 | − | 0.0824025i | ||||
\(446\) | 5.79355 | + | 1.23146i | 0.274333 | + | 0.0583112i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.30116 | + | 1.91500i | 0.203211 | + | 0.0904752i | ||||
\(449\) | −2.30902 | + | 7.10642i | −0.108969 | + | 0.335373i | −0.990642 | − | 0.136489i | \(-0.956418\pi\) |
0.881672 | + | 0.471862i | \(0.156418\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.27458 | − | 7.21242i | −0.201282 | − | 0.339620i | ||||
\(452\) | −15.9787 | − | 27.6759i | −0.751575 | − | 1.30177i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.663497 | − | 6.31275i | −0.0311395 | − | 0.296272i | ||||
\(455\) | 7.30836 | − | 3.25389i | 0.342621 | − | 0.152545i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.669131 | + | 0.743145i | −0.0313006 | + | 0.0347628i | −0.758592 | − | 0.651566i | \(-0.774112\pi\) |
0.727291 | + | 0.686329i | \(0.240779\pi\) | |||||||
\(458\) | −3.14590 | − | 2.28563i | −0.146998 | − | 0.106800i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.27051 | − | 10.0656i | 0.152488 | − | 0.469311i | ||||
\(461\) | −8.07295 | − | 13.9828i | −0.375995 | − | 0.651242i | 0.614481 | − | 0.788932i | \(-0.289366\pi\) |
−0.990475 | + | 0.137690i | \(0.956032\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.50000 | + | 14.7224i | −0.395029 | + | 0.684209i | −0.993105 | − | 0.117230i | \(-0.962599\pi\) |
0.598076 | + | 0.801439i | \(0.295932\pi\) | |||||||
\(464\) | 10.2180 | + | 11.3482i | 0.474357 | + | 0.526827i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.444165 | + | 4.22595i | −0.0205755 | + | 0.195763i | ||||
\(467\) | 0.236068 | + | 0.726543i | 0.0109239 | + | 0.0336204i | 0.956370 | − | 0.292159i | \(-0.0943735\pi\) |
−0.945446 | + | 0.325779i | \(0.894373\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.85410 | + | 3.52671i | 0.224142 | + | 0.162848i | ||||
\(470\) | −5.15178 | − | 2.29372i | −0.237634 | − | 0.105801i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.19098 | + | 2.06284i | −0.0548194 | + | 0.0949500i | ||||
\(473\) | −5.01586 | − | 3.55749i | −0.230630 | − | 0.163574i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.39626 | − | 0.721898i | 0.155831 | − | 0.0331229i | ||||
\(476\) | 7.28115 | − | 5.29007i | 0.333731 | − | 0.242470i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.23607 | − | 3.80423i | −0.0565364 | − | 0.174001i | ||||
\(479\) | 7.87161 | − | 8.74231i | 0.359663 | − | 0.399446i | −0.535972 | − | 0.844236i | \(-0.680055\pi\) |
0.895635 | + | 0.444789i | \(0.146722\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.44361 | − | 32.7638i | −0.157015 | − | 1.49390i | ||||
\(482\) | −6.85807 | − | 7.61666i | −0.312376 | − | 0.346929i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.85811 | + | 19.5357i | −0.266278 | + | 0.887986i | ||||
\(485\) | 7.41641 | 0.336762 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.5000 | − | 7.62870i | 0.475800 | − | 0.345689i | −0.323897 | − | 0.946092i | \(-0.604993\pi\) |
0.799698 | + | 0.600403i | \(0.204993\pi\) | |||||||
\(488\) | 1.67023 | − | 15.8912i | 0.0756078 | − | 0.719360i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.77091 | + | 0.588976i | 0.125177 | + | 0.0266072i | ||||
\(491\) | −6.69285 | + | 2.97985i | −0.302044 | + | 0.134479i | −0.552162 | − | 0.833737i | \(-0.686197\pi\) |
0.250118 | + | 0.968215i | \(0.419531\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.0474 | − | 4.89888i | 1.03800 | − | 0.220634i | ||||
\(494\) | −2.47214 | −0.111227 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.94427 | 0.0873004 | ||||||||
\(497\) | 2.84624 | − | 0.604988i | 0.127671 | − | 0.0271374i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.0951 | − | 15.6254i | 1.57107 | − | 0.699487i | 0.577898 | − | 0.816109i | \(-0.303873\pi\) |
0.993176 | + | 0.116622i | \(0.0372066\pi\) | |||||||
\(500\) | −18.9921 | − | 4.03690i | −0.849353 | − | 0.180536i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.820977 | − | 7.81108i | 0.0366420 | − | 0.348625i | ||||
\(503\) | −7.70820 | + | 5.60034i | −0.343692 | + | 0.249707i | −0.746218 | − | 0.665702i | \(-0.768132\pi\) |
0.402526 | + | 0.915409i | \(0.368132\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.4721 | 0.466004 | ||||||||
\(506\) | 0.677881 | + | 5.81089i | 0.0301355 | + | 0.258326i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.1040 | + | 14.5534i | 0.581395 | + | 0.645705i | ||||
\(509\) | −2.84112 | − | 27.0314i | −0.125930 | − | 1.19815i | −0.856807 | − | 0.515638i | \(-0.827555\pi\) |
0.730876 | − | 0.682510i | \(-0.239112\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.0976248 | − | 0.108423i | 0.00431867 | − | 0.00479637i | ||||
\(512\) | 6.89261 | + | 21.2133i | 0.304613 | + | 0.937503i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.60739 | + | 3.34747i | −0.203223 | + | 0.147650i | ||||
\(515\) | 12.3760 | − | 2.63060i | 0.545351 | − | 0.115918i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −39.6121 | + | 0.452084i | −1.74214 | + | 0.0198826i | ||||
\(518\) | −0.972136 | + | 1.68379i | −0.0427132 | + | 0.0739814i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.7589 | + | 4.79017i | 0.471809 | + | 0.210063i | ||||
\(521\) | −32.6525 | − | 23.7234i | −1.43053 | − | 1.03934i | −0.989918 | − | 0.141645i | \(-0.954761\pi\) |
−0.440613 | − | 0.897697i | \(-0.645239\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(524\) | −4.11569 | + | 39.1581i | −0.179795 | + | 1.71063i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.24803 | + | 3.60730i | 0.141621 | + | 0.157286i | ||||
\(527\) | 1.50000 | − | 2.59808i | 0.0653410 | − | 0.113174i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.836881 | + | 1.44952i | 0.0363861 | + | 0.0630226i | ||||
\(530\) | −0.596748 | + | 1.83660i | −0.0259211 | + | 0.0797768i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.50000 | − | 1.08981i | −0.0650332 | − | 0.0472494i | ||||
\(533\) | −10.9474 | + | 12.1584i | −0.474186 | + | 0.526637i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.8478 | + | 7.05587i | −0.685158 | + | 0.305052i | ||||
\(536\) | 0.923281 | + | 8.78443i | 0.0398797 | + | 0.379430i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.06231 | − | 7.03612i | −0.175138 | − | 0.303349i | ||||
\(539\) | 19.4164 | − | 4.35926i | 0.836324 | − | 0.187766i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.68034 | + | 11.3269i | −0.158230 | + | 0.486982i | −0.998474 | − | 0.0552266i | \(-0.982412\pi\) |
0.840244 | + | 0.542209i | \(0.182412\pi\) | |||||||
\(542\) | 3.75600 | + | 1.67228i | 0.161334 | + | 0.0718306i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 19.6848 | + | 4.18414i | 0.843981 | + | 0.179394i | ||||
\(545\) | −8.63980 | − | 1.83645i | −0.370088 | − | 0.0786647i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.5315 | − | 13.1483i | −1.26268 | − | 0.562179i | −0.337359 | − | 0.941376i | \(-0.609534\pi\) |
−0.925316 | + | 0.379197i | \(0.876200\pi\) | |||||||
\(548\) | −4.93769 | + | 15.1967i | −0.210928 | + | 0.649169i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.29180 | − | 0.963568i | 0.183003 | − | 0.0410867i | ||||
\(551\) | −2.42705 | − | 4.20378i | −0.103396 | − | 0.179087i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.10406 | + | 10.5044i | 0.0469495 | + | 0.446694i | ||||
\(554\) | −6.71230 | + | 2.98851i | −0.285178 | + | 0.126970i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.0444 | + | 13.3766i | −0.510794 | + | 0.567294i | ||||
\(557\) | −0.527864 | − | 0.383516i | −0.0223663 | − | 0.0162501i | 0.576546 | − | 0.817065i | \(-0.304400\pi\) |
−0.598912 | + | 0.800815i | \(0.704400\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.70820 | + | 11.4127i | −0.156840 | + | 0.482705i | ||||
\(560\) | 1.94427 | + | 3.36758i | 0.0821605 | + | 0.142306i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.78115 | + | 3.08505i | −0.0751334 | + | 0.130135i | ||||
\(563\) | 13.5867 | + | 15.0895i | 0.572610 | + | 0.635947i | 0.957987 | − | 0.286812i | \(-0.0925954\pi\) |
−0.385377 | + | 0.922759i | \(0.625929\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.22697 | − | 21.1882i | 0.0936895 | − | 0.891396i | ||||
\(566\) | −2.00658 | − | 6.17561i | −0.0843428 | − | 0.259580i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.46556 | + | 2.51788i | 0.145412 | + | 0.105648i | ||||
\(569\) | −35.4441 | − | 15.7807i | −1.48589 | − | 0.661562i | −0.506264 | − | 0.862378i | \(-0.668974\pi\) |
−0.979629 | + | 0.200816i | \(0.935641\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.26393 | − | 16.0456i | 0.387683 | − | 0.671488i | −0.604454 | − | 0.796640i | \(-0.706609\pi\) |
0.992138 | + | 0.125153i | \(0.0399420\pi\) | |||||||
\(572\) | 39.7969 | − | 0.454194i | 1.66399 | − | 0.0189908i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.944458 | − | 0.200751i | 0.0394209 | − | 0.00837918i | ||||
\(575\) | −12.9721 | + | 9.42481i | −0.540975 | + | 0.393042i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.9443 | + | 33.6830i | 0.455616 | + | 1.40224i | 0.870410 | + | 0.492327i | \(0.163853\pi\) |
−0.414794 | + | 0.909915i | \(0.636147\pi\) | |||||||
\(578\) | 1.67723 | − | 1.86275i | 0.0697635 | − | 0.0774802i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.16284 | + | 11.0637i | 0.0482842 | + | 0.459394i | ||||
\(581\) | −6.53335 | − | 7.25602i | −0.271049 | − | 0.301030i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.57186 | + | 13.4742i | 0.0650997 | + | 0.558044i | ||||
\(584\) | 0.214782 | 0.00888773 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.01722 | + | 6.55139i | −0.372498 | + | 0.270636i | ||||
\(587\) | 1.40240 | − | 13.3429i | 0.0578831 | − | 0.550721i | −0.926700 | − | 0.375802i | \(-0.877367\pi\) |
0.984583 | − | 0.174918i | \(-0.0559662\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.604528 | − | 0.128496i | −0.0249092 | − | 0.00529461i | ||||
\(590\) | −0.697887 | + | 0.310719i | −0.0287315 | + | 0.0127921i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 15.6632 | − | 3.32932i | 0.643755 | − | 0.136834i | ||||
\(593\) | 10.9443 | 0.449427 | 0.224714 | − | 0.974425i | \(-0.427855\pi\) | ||||
0.224714 | + | 0.974425i | \(0.427855\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.00000 | 0.245976 | ||||||||
\(596\) | 27.5308 | − | 5.85186i | 1.12771 | − | 0.239702i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.4294 | − | 4.64347i | 0.426490 | − | 0.189886i | ||||
\(599\) | −13.0687 | − | 2.77784i | −0.533973 | − | 0.113500i | −0.0669698 | − | 0.997755i | \(-0.521333\pi\) |
−0.467003 | + | 0.884255i | \(0.654666\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.82634 | − | 17.3764i | 0.0744978 | − | 0.708799i | −0.891985 | − | 0.452066i | \(-0.850687\pi\) |
0.966482 | − | 0.256733i | \(-0.0826461\pi\) | |||||||
\(602\) | 0.572949 | − | 0.416272i | 0.0233517 | − | 0.0169660i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.02129 | −0.326382 | ||||||||
\(605\) | −10.8147 | + | 8.24093i | −0.439682 | + | 0.335042i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.39789 | − | 2.66313i | −0.0973274 | − | 0.108093i | 0.692513 | − | 0.721405i | \(-0.256503\pi\) |
−0.789841 | + | 0.613312i | \(0.789837\pi\) | |||||||
\(608\) | −0.433364 | − | 4.12319i | −0.0175752 | − | 0.167217i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.42903 | − | 3.80833i | 0.138838 | − | 0.154195i | ||||
\(611\) | 23.8885 | + | 73.5214i | 0.966427 | + | 2.97436i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.0623 | + | 11.6699i | −0.648750 | + | 0.471345i | −0.862845 | − | 0.505468i | \(-0.831320\pi\) |
0.214095 | + | 0.976813i | \(0.431320\pi\) | |||||||
\(614\) | −2.93444 | + | 0.623735i | −0.118424 | + | 0.0251719i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.98254 | − | 2.82461i | −0.160461 | − | 0.113807i | ||||
\(617\) | −13.5795 | + | 23.5204i | −0.546691 | + | 0.946897i | 0.451807 | + | 0.892116i | \(0.350779\pi\) |
−0.998498 | + | 0.0547813i | \(0.982554\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.1794 | + | 11.2106i | 1.01205 | + | 0.450592i | 0.844662 | − | 0.535300i | \(-0.179801\pi\) |
0.167384 | + | 0.985892i | \(0.446468\pi\) | |||||||
\(620\) | 1.14590 | + | 0.832544i | 0.0460204 | + | 0.0334358i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.79180 | − | 5.51458i | −0.0718445 | − | 0.221115i | ||||
\(623\) | 0.707023 | − | 6.72688i | 0.0283263 | − | 0.269507i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.95515 | + | 3.28203i | 0.118206 | + | 0.131281i | ||||
\(626\) | −0.663119 | + | 1.14856i | −0.0265036 | + | 0.0459055i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.62461 | + | 11.4742i | 0.264351 | + | 0.457869i | ||||
\(629\) | 7.63525 | − | 23.4989i | 0.304438 | − | 0.936962i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.80902 | + | 6.40013i | 0.350681 | + | 0.254785i | 0.749155 | − | 0.662395i | \(-0.230460\pi\) |
−0.398473 | + | 0.917180i | \(0.630460\pi\) | |||||||
\(632\) | −10.4044 | + | 11.5553i | −0.413865 | + | 0.459644i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.30836 | + | 3.25389i | −0.290252 | + | 0.129229i | ||||
\(635\) | 1.36470 | + | 12.9842i | 0.0541563 | + | 0.515263i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.4164 | − | 33.6302i | −0.769306 | − | 1.33248i | ||||
\(638\) | −3.13525 | − | 5.29007i | −0.124126 | − | 0.209436i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.85410 | + | 11.8617i | −0.152347 | + | 0.468875i | ||||
\(641\) | 18.6828 | + | 8.31811i | 0.737925 | + | 0.328546i | 0.741050 | − | 0.671450i | \(-0.234328\pi\) |
−0.00312481 | + | 0.999995i | \(0.500995\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.70432 | + | 1.42505i | 0.264393 | + | 0.0561984i | 0.338200 | − | 0.941074i | \(-0.390182\pi\) |
−0.0738078 | + | 0.997272i | \(0.523515\pi\) | |||||||
\(644\) | 8.37520 | + | 1.78020i | 0.330029 | + | 0.0701498i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.69381 | − | 0.754131i | −0.0666419 | − | 0.0296709i | ||||
\(647\) | 1.29180 | − | 3.97574i | 0.0507857 | − | 0.156302i | −0.922447 | − | 0.386123i | \(-0.873814\pi\) |
0.973233 | + | 0.229821i | \(0.0738140\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.54508 | + | 4.02874i | −0.139157 | + | 0.158142i | ||||
\(650\) | −4.29180 | − | 7.43361i | −0.168338 | − | 0.291570i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.01338 | + | 38.1848i | 0.157176 | + | 1.49543i | ||||
\(653\) | 1.24304 | − | 0.553438i | 0.0486440 | − | 0.0216577i | −0.382270 | − | 0.924050i | \(-0.624858\pi\) |
0.430914 | + | 0.902393i | \(0.358191\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.5642 | + | 19.5070i | −0.686288 | + | 0.762201i | ||||
\(656\) | −6.43363 | − | 4.67430i | −0.251191 | − | 0.182501i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.40983 | − | 4.33901i | 0.0549609 | − | 0.169152i | ||||
\(659\) | 4.98936 | + | 8.64182i | 0.194358 | + | 0.336637i | 0.946690 | − | 0.322147i | \(-0.104404\pi\) |
−0.752332 | + | 0.658784i | \(0.771071\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.14590 | − | 3.71680i | 0.0834658 | − | 0.144567i | −0.821271 | − | 0.570539i | \(-0.806734\pi\) |
0.904736 | + | 0.425972i | \(0.140068\pi\) | |||||||
\(662\) | 3.68462 | + | 4.09218i | 0.143207 | + | 0.159047i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.50247 | − | 14.2951i | 0.0583073 | − | 0.554757i | ||||
\(665\) | −0.381966 | − | 1.17557i | −0.0148120 | − | 0.0455867i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.1353 | + | 13.1760i | 0.702200 | + | 0.510178i | ||||
\(668\) | −9.76299 | − | 4.34676i | −0.377741 | − | 0.168181i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.41641 | + | 2.45329i | −0.0547206 | + | 0.0947789i | ||||
\(671\) | 10.7329 | − | 34.3618i | 0.414337 | − | 1.32652i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.9163 | − | 6.14635i | 1.11464 | − | 0.236924i | 0.386458 | − | 0.922307i | \(-0.373698\pi\) |
0.728183 | + | 0.685383i | \(0.240365\pi\) | |||||||
\(674\) | 3.54508 | − | 2.57565i | 0.136552 | − | 0.0992105i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.5517 | − | 50.9408i | −0.636602 | − | 1.95926i | ||||
\(677\) | −4.05207 | + | 4.50028i | −0.155734 | + | 0.172960i | −0.815963 | − | 0.578105i | \(-0.803793\pi\) |
0.660229 | + | 0.751064i | \(0.270459\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.627171 | + | 5.96713i | 0.0240686 | + | 0.228997i | ||||
\(680\) | 5.91031 | + | 6.56406i | 0.226650 | + | 0.251720i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.767647 | − | 0.154034i | −0.0293947 | − | 0.00589826i | ||||
\(683\) | 5.52786 | 0.211518 | 0.105759 | − | 0.994392i | \(-0.466273\pi\) | ||||
0.105759 | + | 0.994392i | \(0.466273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.61803 | + | 6.26137i | −0.329278 | + | 0.239235i | ||||
\(686\) | −0.519042 | + | 4.93836i | −0.0198171 | + | 0.188547i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.70535 | − | 1.21271i | −0.217515 | − | 0.0462342i | ||||
\(689\) | 24.1835 | − | 10.7672i | 0.921318 | − | 0.410197i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.2778 | + | 3.03483i | −0.543152 | + | 0.115451i | −0.471314 | − | 0.881966i | \(-0.656220\pi\) |
−0.0718386 | + | 0.997416i | \(0.522887\pi\) | |||||||
\(692\) | −42.8115 | −1.62745 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.39512 | 0.128877 | ||||||||
\(695\) | −11.7378 | + | 2.49494i | −0.445239 | + | 0.0946385i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.2097 | + | 4.99087i | −0.424596 | + | 0.189043i | ||||
\(698\) | 1.54899 | + | 0.329247i | 0.0586300 | + | 0.0124622i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.672922 | − | 6.40243i | 0.0254341 | − | 0.241989i | ||||
\(701\) | −38.6074 | + | 28.0499i | −1.45818 | + | 1.05943i | −0.474349 | + | 0.880337i | \(0.657317\pi\) |
−0.983832 | + | 0.179094i | \(0.942683\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.09017 | −0.191979 | ||||||||
\(704\) | 1.80937 | + | 15.5102i | 0.0681931 | + | 0.584561i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.19579 | + | 4.65990i | 0.157911 | + | 0.175378i | ||||
\(707\) | 0.885579 | + | 8.42572i | 0.0333056 | + | 0.316882i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.2394 | + | 19.1463i | −0.647441 | + | 0.719056i | −0.974108 | − | 0.226084i | \(-0.927408\pi\) |
0.326667 | + | 0.945139i | \(0.394074\pi\) | |||||||
\(710\) | 0.424538 | + | 1.30660i | 0.0159326 | + | 0.0490356i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.05573 | − | 5.85283i | 0.301901 | − | 0.219344i | ||||
\(713\) | 2.79173 | − | 0.593401i | 0.104551 | − | 0.0222230i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.6422 | + | 15.3497i | 0.809373 | + | 0.574047i | ||||
\(716\) | 4.68692 | − | 8.11798i | 0.175158 | − | 0.303383i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.97479 | + | 3.55060i | 0.297616 | + | 0.132507i | ||||
\(719\) | −15.8541 | − | 11.5187i | −0.591258 | − | 0.429574i | 0.251507 | − | 0.967855i | \(-0.419074\pi\) |
−0.842765 | + | 0.538281i | \(0.819074\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.16312 | + | 9.73508i | 0.117801 | + | 0.362553i | ||||
\(722\) | 0.718674 | − | 6.83772i | 0.0267463 | − | 0.254474i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.2945 | + | 13.6544i | 0.456921 | + | 0.507463i | ||||
\(725\) | 8.42705 | − | 14.5961i | 0.312973 | − | 0.542085i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.41641 | − | 16.3097i | −0.349235 | − | 0.604893i | 0.636879 | − | 0.770964i | \(-0.280225\pi\) |
−0.986114 | + | 0.166071i | \(0.946892\pi\) | |||||||
\(728\) | −2.94427 | + | 9.06154i | −0.109122 | + | 0.335843i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.0557281 | + | 0.0404888i | 0.00206259 | + | 0.00149856i | ||||
\(731\) | −6.02218 | + | 6.68830i | −0.222738 | + | 0.247376i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.2815 | − | 19.7154i | 1.63557 | − | 0.728205i | 0.636502 | − | 0.771275i | \(-0.280381\pi\) |
0.999072 | + | 0.0430700i | \(0.0137138\pi\) | |||||||
\(734\) | 0.507392 | + | 4.82751i | 0.0187282 | + | 0.178187i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.57295 | + | 16.5808i | 0.352864 | + | 0.611178i | ||||
\(737\) | −1.85410 | + | 19.8132i | −0.0682967 | + | 0.729828i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.1459 | − | 40.4589i | 0.483580 | − | 1.48831i | −0.350448 | − | 0.936582i | \(-0.613971\pi\) |
0.834027 | − | 0.551723i | \(-0.186029\pi\) | |||||||
\(740\) | 10.6571 | + | 4.74484i | 0.391762 | + | 0.174424i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.52817 | − | 0.324822i | −0.0561007 | − | 0.0119246i | ||||
\(743\) | −41.4350 | − | 8.80728i | −1.52010 | − | 0.323108i | −0.629179 | − | 0.777261i | \(-0.716609\pi\) |
−0.890924 | + | 0.454153i | \(0.849942\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.1417 | + | 7.63198i | 0.628023 | + | 0.279614i | ||||
\(746\) | −0.667184 | + | 2.05338i | −0.0244274 | + | 0.0751797i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 27.4058 | + | 11.8290i | 1.00205 | + | 0.432509i | ||||
\(749\) | −7.01722 | − | 12.1542i | −0.256404 | − | 0.444104i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.26643 | + | 31.0780i | 0.119194 | + | 1.13405i | 0.876637 | + | 0.481152i | \(0.159782\pi\) |
−0.757443 | + | 0.652901i | \(0.773552\pi\) | |||||||
\(752\) | −34.3269 | + | 15.2833i | −1.25177 | + | 0.557325i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.02957 | + | 8.91774i | −0.292420 | + | 0.324765i | ||||
\(755\) | −4.32624 | − | 3.14320i | −0.157448 | − | 0.114393i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.39919 | − | 10.4616i | 0.123546 | − | 0.380234i | −0.870088 | − | 0.492897i | \(-0.835938\pi\) |
0.993633 | + | 0.112663i | \(0.0359380\pi\) | |||||||
\(758\) | −3.01722 | − | 5.22598i | −0.109590 | − | 0.189816i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.909830 | − | 1.57587i | 0.0330030 | − | 0.0571629i | ||||
\(761\) | −4.66967 | − | 5.18620i | −0.169275 | − | 0.187999i | 0.652538 | − | 0.757756i | \(-0.273704\pi\) |
−0.821814 | + | 0.569756i | \(0.807038\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.746950 | − | 7.10675i | 0.0270414 | − | 0.257282i | ||||
\(764\) | 3.40576 | + | 10.4819i | 0.123216 | + | 0.379221i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.13525 | + | 4.45752i | 0.221676 | + | 0.161057i | ||||
\(767\) | 9.56677 | + | 4.25940i | 0.345436 | + | 0.153798i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.89919 | − | 13.6818i | 0.284852 | − | 0.493378i | −0.687721 | − | 0.725975i | \(-0.741389\pi\) |
0.972573 | + | 0.232597i | \(0.0747222\pi\) | |||||||
\(770\) | −0.500853 | − | 1.48364i | −0.0180495 | − | 0.0534666i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −19.9494 | + | 4.24038i | −0.717996 | + | 0.152615i | ||||
\(773\) | 19.1353 | − | 13.9026i | 0.688247 | − | 0.500041i | −0.187836 | − | 0.982200i | \(-0.560147\pi\) |
0.876083 | + | 0.482159i | \(0.160147\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.663119 | − | 2.04087i | −0.0238199 | − | 0.0733102i | ||||
\(776\) | −5.91031 | + | 6.56406i | −0.212168 | + | 0.235636i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.904430 | − | 8.60508i | −0.0324254 | − | 0.308507i | ||||
\(779\) | 1.69147 | + | 1.87857i | 0.0606032 | + | 0.0673067i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.53908 | + | 7.09779i | 0.233987 | + | 0.253979i | ||||
\(782\) | 8.56231 | 0.306187 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 15.2705 | − | 11.0947i | 0.545375 | − | 0.396238i | ||||
\(785\) | −0.923281 | + | 8.78443i | −0.0329533 | + | 0.313530i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.2133 | − | 7.48482i | −1.25522 | − | 0.266805i | −0.468138 | − | 0.883655i | \(-0.655075\pi\) |
−0.787081 | + | 0.616850i | \(0.788408\pi\) | |||||||
\(788\) | 13.9503 | − | 6.21108i | 0.496959 | − | 0.221260i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.87787 | + | 1.03682i | −0.173547 | + | 0.0368885i | ||||
\(791\) | 17.2361 | 0.612844 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −70.2492 | −2.49462 | ||||||||
\(794\) | 0.793796 | − | 0.168726i | 0.0281708 | − | 0.00598788i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.1038 | − | 5.38894i | 0.429007 | − | 0.191006i | ||||
\(797\) | 23.7401 | + | 5.04612i | 0.840919 | + | 0.178743i | 0.608183 | − | 0.793797i | \(-0.291899\pi\) |
0.232736 | + | 0.972540i | \(0.425232\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.06043 | + | 57.6611i | −0.214402 | + | 2.03990i | ||||
\(800\) | 11.6459 | − | 8.46124i | 0.411745 | − | 0.299150i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.56231 | −0.196412 | ||||||||
\(803\) | 0.474432 | + | 0.0951981i | 0.0167423 | + | 0.00335947i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.81953 | + | 4.24202i | 0.134621 | + | 0.149512i | ||||
\(806\) | 0.159705 | + | 1.51949i | 0.00562538 | + | 0.0535219i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.34549 | + | 9.26860i | −0.293593 | + | 0.326068i | ||||
\(809\) | 5.59017 | + | 17.2048i | 0.196540 | + | 0.604888i | 0.999955 | + | 0.00946853i | \(0.00301397\pi\) |
−0.803415 | + | 0.595419i | \(0.796986\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.02786 | + | 5.10604i | −0.246782 | + | 0.179297i | −0.704299 | − | 0.709903i | \(-0.748739\pi\) |
0.457518 | + | 0.889201i | \(0.348739\pi\) | |||||||
\(812\) | −8.80333 | + | 1.87121i | −0.308936 | + | 0.0656664i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.44800 | + | 0.0735897i | −0.226002 | + | 0.00257932i | ||||
\(815\) | −12.7984 | + | 22.1674i | −0.448307 | + | 0.776491i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.69381 | + | 0.754131i | 0.0592588 | + | 0.0263837i | ||||
\(818\) | 10.4271 | + | 7.57570i | 0.364573 | + | 0.264878i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.79024 | − | 5.50980i | −0.0625180 | − | 0.192411i | ||||
\(821\) | 3.99453 | − | 38.0054i | 0.139410 | − | 1.32640i | −0.671402 | − | 0.741093i | \(-0.734308\pi\) |
0.810813 | − | 0.585306i | \(-0.199026\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.2987 | − | 31.4289i | −0.986432 | − | 1.09554i | −0.995421 | − | 0.0955840i | \(-0.969528\pi\) |
0.00898947 | − | 0.999960i | \(-0.497139\pi\) | |||||||
\(824\) | −7.53444 | + | 13.0500i | −0.262475 | + | 0.454620i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.309017 | − | 0.535233i | −0.0107521 | − | 0.0186231i | ||||
\(827\) | 17.6246 | − | 54.2430i | 0.612868 | − | 1.88621i | 0.183721 | − | 0.982978i | \(-0.441186\pi\) |
0.429147 | − | 0.903235i | \(-0.358814\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.2254 | − | 25.5928i | −1.22343 | − | 0.888874i | −0.227049 | − | 0.973883i | \(-0.572908\pi\) |
−0.996380 | + | 0.0850096i | \(0.972908\pi\) | |||||||
\(830\) | 3.08463 | − | 3.42583i | 0.107069 | − | 0.118912i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 27.8377 | − | 12.3941i | 0.965098 | − | 0.429689i | ||||
\(833\) | −3.04435 | − | 28.9651i | −0.105481 | − | 1.00358i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.56231 | − | 6.17009i | −0.123279 | − | 0.213525i | ||||
\(836\) | 0.572949 | − | 6.12261i | 0.0198159 | − | 0.211755i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.954915 | + | 2.93893i | −0.0329870 | + | 0.101524i | ||||
\(839\) | 15.7968 | + | 7.03321i | 0.545368 | + | 0.242813i | 0.660878 | − | 0.750493i | \(-0.270184\pi\) |
−0.115511 | + | 0.993306i | \(0.536851\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.31887 | + | 1.13056i | 0.183409 | + | 0.0389848i | ||||
\(842\) | −3.82439 | − | 0.812899i | −0.131797 | − | 0.0280144i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −34.6758 | − | 15.4387i | −1.19359 | − | 0.531421i | ||||
\(845\) | 11.0344 | − | 33.9605i | 0.379596 | − | 1.16828i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.54508 | − | 8.00448i | −0.259252 | − | 0.275037i | ||||
\(848\) | 6.43363 | + | 11.1434i | 0.220932 | + | 0.382665i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.672922 | − | 6.40243i | −0.0230810 | − | 0.219601i | ||||
\(851\) | 21.4743 | − | 9.56099i | 0.736130 | − | 0.327746i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.7124 | + | 26.3353i | −0.811899 | + | 0.901705i | −0.996708 | − | 0.0810695i | \(-0.974166\pi\) |
0.184810 | + | 0.982774i | \(0.440833\pi\) | |||||||
\(854\) | 3.35410 | + | 2.43690i | 0.114775 | + | 0.0833889i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.38448 | − | 19.6494i | 0.218217 | − | 0.671603i | ||||
\(857\) | 12.6803 | + | 21.9630i | 0.433152 | + | 0.750242i | 0.997143 | − | 0.0755396i | \(-0.0240679\pi\) |
−0.563991 | + | 0.825781i | \(0.690735\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.2812 | − | 28.1998i | 0.555506 | − | 0.962164i | −0.442358 | − | 0.896838i | \(-0.645858\pi\) |
0.997864 | − | 0.0653258i | \(-0.0208087\pi\) | |||||||
\(860\) | −2.84329 | − | 3.15779i | −0.0969552 | − | 0.107680i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.36025 | + | 12.9419i | −0.0463301 | + | 0.440802i | ||||
\(863\) | −4.46556 | − | 13.7436i | −0.152009 | − | 0.467837i | 0.845836 | − | 0.533443i | \(-0.179102\pi\) |
−0.997846 | + | 0.0656059i | \(0.979102\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.0902 | − | 16.7760i | −0.785089 | − | 0.570401i | ||||
\(866\) | 5.14435 | + | 2.29041i | 0.174812 | + | 0.0778313i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.572949 | + | 0.992377i | −0.0194472 | + | 0.0336835i | ||||
\(869\) | −28.1040 | + | 20.9129i | −0.953363 | + | 0.709422i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.9842 | − | 8.07380i | 1.28705 | − | 0.273570i | ||||
\(872\) | 8.51064 | − | 6.18334i | 0.288207 | − | 0.209394i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.545085 | − | 1.67760i | −0.0184378 | − | 0.0567456i | ||||
\(875\) | 7.00723 | − | 7.78231i | 0.236887 | − | 0.263090i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.21219 | − | 11.5332i | −0.0409328 | − | 0.389449i | −0.995739 | − | 0.0922193i | \(-0.970604\pi\) |
0.954806 | − | 0.297230i | \(-0.0960628\pi\) | |||||||
\(878\) | −0.181006 | − | 0.201028i | −0.00610867 | − | 0.00678437i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.32054 | + | 11.2419i | −0.213065 | + | 0.378963i | ||||
\(881\) | −1.81966 | −0.0613059 | −0.0306530 | − | 0.999530i | \(-0.509759\pi\) | ||||
−0.0306530 | + | 0.999530i | \(0.509759\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.8435 | − | 20.9560i | 0.970660 | − | 0.705226i | 0.0150579 | − | 0.999887i | \(-0.495207\pi\) |
0.955602 | + | 0.294661i | \(0.0952068\pi\) | |||||||
\(884\) | 6.08870 | − | 57.9301i | 0.204785 | − | 1.94840i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.461819 | − | 0.0981626i | −0.0155151 | − | 0.00329784i | ||||
\(887\) | 3.68565 | − | 1.64096i | 0.123752 | − | 0.0550979i | −0.343927 | − | 0.938997i | \(-0.611757\pi\) |
0.467679 | + | 0.883899i | \(0.345090\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.3315 | + | 2.19603i | −0.346507 | + | 0.0736524i | ||||
\(890\) | 3.19350 | 0.107046 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 28.7508 | 0.962647 | ||||||||
\(893\) | 11.6833 | − | 2.48335i | 0.390965 | − | 0.0831023i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.70895 | − | 2.54179i | 0.190829 | − | 0.0849626i | ||||
\(896\) | −9.86968 | − | 2.09786i | −0.329723 | − | 0.0700847i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.298335 | − | 2.83847i | 0.00995556 | − | 0.0947209i | ||||
\(899\) | −2.42705 | + | 1.76336i | −0.0809467 | + | 0.0588112i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.8541 | 0.661436 | ||||||||
\(902\) | 2.16984 | + | 2.35523i | 0.0722477 | + | 0.0784207i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.9784 | + | 18.8564i | 0.564694 | + | 0.627156i | ||||
\(905\) | 1.28039 | + | 12.1821i | 0.0425617 | + | 0.404947i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.75833 | + | 10.8377i | −0.324020 | + | 0.359861i | −0.883043 | − | 0.469291i | \(-0.844509\pi\) |
0.559024 | + | 0.829152i | \(0.311176\pi\) | |||||||
\(908\) | −9.52129 | − | 29.3035i | −0.315975 | − | 0.972471i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.47214 | + | 1.79611i | −0.0819505 | + | 0.0595405i | ||||
\(911\) | −18.7612 | + | 3.98782i | −0.621586 | + | 0.132122i | −0.507931 | − | 0.861398i | \(-0.669589\pi\) |
−0.113656 | + | 0.993520i | \(0.536256\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.65487 | − | 30.9105i | 0.319529 | − | 1.02299i | ||||
\(914\) | 0.190983 | − | 0.330792i | 0.00631716 | − | 0.0109416i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.2435 | − | 7.67731i | −0.569742 | − | 0.253666i | ||||
\(917\) | −17.1803 | − | 12.4822i | −0.567345 | − | 0.412200i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.30244 | − | 25.5523i | −0.273872 | − | 0.842892i | −0.989516 | − | 0.144426i | \(-0.953866\pi\) |
0.715643 | − | 0.698466i | \(-0.246134\pi\) | |||||||
\(920\) | −0.878379 | + | 8.35722i | −0.0289593 | + | 0.275529i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.12665 | + | 4.58311i | 0.135904 | + | 0.150937i | ||||
\(923\) | 9.41641 | − | 16.3097i | 0.309945 | − | 0.536840i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.83688 | − | 15.3059i | −0.290555 | − | 0.503256i | ||||
\(926\) | 2.00658 | − | 6.17561i | 0.0659402 | − | 0.202943i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −16.2812 | − | 11.8290i | −0.534455 | − | 0.388304i | ||||
\(929\) | 32.2993 | − | 35.8720i | 1.05970 | − | 1.17692i | 0.0760042 | − | 0.997107i | \(-0.475784\pi\) |
0.983701 | − | 0.179814i | \(-0.0575496\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.48127 | + | 2.44042i | −0.179641 | + | 0.0799815i | ||||
\(932\) | 2.15602 | + | 20.5132i | 0.0706228 | + | 0.671931i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.145898 | − | 0.252703i | −0.00477393 | − | 0.00826869i | ||||
\(935\) | 10.1459 | + | 17.1190i | 0.331806 | + | 0.559852i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.11803 | + | 21.9071i | −0.232536 | + | 0.715672i | 0.764903 | + | 0.644146i | \(0.222787\pi\) |
−0.997439 | + | 0.0715265i | \(0.977213\pi\) | |||||||
\(938\) | −2.09366 | − | 0.932157i | −0.0683604 | − | 0.0304360i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −26.7757 | − | 5.69134i | −0.873325 | − | 0.185631i | ||||
\(941\) | 26.5656 | + | 5.64668i | 0.866013 | + | 0.184077i | 0.619436 | − | 0.785047i | \(-0.287361\pi\) |
0.246576 | + | 0.969123i | \(0.420694\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.6645 | − | 4.74815i | −0.347284 | − | 0.154621i | ||||
\(944\) | −1.57295 | + | 4.84104i | −0.0511951 | + | 0.157562i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.15654 | + | 0.930812i | 0.0701152 | + | 0.0302633i | ||||
\(947\) | 18.3541 | + | 31.7902i | 0.596428 | + | 1.03304i | 0.993344 | + | 0.115189i | \(0.0367473\pi\) |
−0.396915 | + | 0.917855i | \(0.629919\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.0987033 | − | 0.939099i | −0.00320404 | − | 0.0304844i | ||||
\(950\) | −1.21158 | + | 0.539430i | −0.0393088 | + | 0.0175014i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.78154 | + | 5.31044i | −0.154971 | + | 0.172112i | ||||
\(953\) | −7.68034 | − | 5.58009i | −0.248791 | − | 0.180757i | 0.456400 | − | 0.889775i | \(-0.349139\pi\) |
−0.705191 | + | 0.709018i | \(0.749139\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.27051 | + | 6.98791i | −0.0734720 | + | 0.226123i | ||||
\(956\) | −9.70820 | − | 16.8151i | −0.313986 | − | 0.543839i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.24671 | + | 3.89142i | −0.0725879 | + | 0.125726i | ||||
\(959\) | −5.76659 | − | 6.40445i | −0.186213 | − | 0.206810i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.20046 | − | 30.4503i | 0.103241 | − | 0.982268i | ||||
\(962\) | 3.88854 | + | 11.9677i | 0.125372 | + | 0.385854i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −40.2492 | − | 29.2428i | −1.29634 | − | 0.941846i | ||||
\(965\) | −12.4212 | − | 5.53030i | −0.399854 | − | 0.178027i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.2426 | + | 45.4536i | −0.843907 | + | 1.46169i | 0.0426608 | + | 0.999090i | \(0.486417\pi\) |
−0.886567 | + | 0.462599i | \(0.846917\pi\) | |||||||
\(968\) | 1.32469 | − | 16.1392i | 0.0425771 | − | 0.518734i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.77091 | + | 0.588976i | −0.0889686 | + | 0.0189109i | ||||
\(971\) | 7.50000 | − | 5.44907i | 0.240686 | − | 0.174869i | −0.460903 | − | 0.887451i | \(-0.652474\pi\) |
0.701589 | + | 0.712582i | \(0.252474\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.00000 | − | 9.23305i | −0.0961756 | − | 0.295998i | ||||
\(974\) | −3.31717 | + | 3.68409i | −0.106289 | + | 0.118046i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.56922 | − | 33.9588i | −0.114248 | − | 1.08700i | ||||
\(977\) | −10.5481 | − | 11.7149i | −0.337465 | − | 0.374792i | 0.550397 | − | 0.834903i | \(-0.314476\pi\) |
−0.887862 | + | 0.460111i | \(0.847810\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.3885 | − | 9.35778i | 0.651619 | − | 0.299076i | ||||
\(980\) | 13.7508 | 0.439252 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.26393 | − | 1.64484i | 0.0722450 | − | 0.0524890i | ||||
\(983\) | 0.967657 | − | 9.20664i | 0.0308635 | − | 0.293646i | −0.968193 | − | 0.250206i | \(-0.919502\pi\) |
0.999056 | − | 0.0434400i | \(-0.0138317\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.95788 | + | 2.11661i | 0.317284 | + | 0.0674409i | ||||
\(986\) | −8.22191 | + | 3.66063i | −0.261839 | + | 0.116578i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.7378 | + | 2.49494i | −0.373428 | + | 0.0793746i | ||||
\(989\) | −8.56231 | −0.272265 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.5967 | 0.654277 | 0.327139 | − | 0.944976i | \(-0.393916\pi\) | ||||
0.327139 | + | 0.944976i | \(0.393916\pi\) | |||||||
\(992\) | −2.50631 | + | 0.532733i | −0.0795755 | + | 0.0169143i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.01537 | + | 0.452070i | −0.0322054 | + | 0.0143388i | ||||
\(995\) | 8.63980 | + | 1.83645i | 0.273900 | + | 0.0582192i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.771626 | + | 7.34153i | −0.0244376 | + | 0.232508i | 0.975485 | + | 0.220066i | \(0.0706273\pi\) |
−0.999923 | + | 0.0124424i | \(0.996039\pi\) | |||||||
\(998\) | −11.8713 | + | 8.62502i | −0.375780 | + | 0.273020i | ||||
\(999\) | 0 | 0 |
(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 | 297.2.n.a.64.1 | 8 | ||
3.2 | odd | 2 | 99.2.m.a.31.1 | yes | 8 | ||
9.2 | odd | 6 | 99.2.m.a.97.1 | yes | 8 | ||
9.4 | even | 3 | 891.2.f.a.163.1 | 4 | |||
9.5 | odd | 6 | 891.2.f.b.163.1 | 4 | |||
9.7 | even | 3 | inner | 297.2.n.a.262.1 | 8 | ||
11.5 | even | 5 | inner | 297.2.n.a.280.1 | 8 | ||
33.5 | odd | 10 | 99.2.m.a.49.1 | yes | 8 | ||
33.26 | odd | 10 | 1089.2.e.g.364.1 | 4 | |||
33.29 | even | 10 | 1089.2.e.d.364.2 | 4 | |||
99.4 | even | 15 | 9801.2.a.bb.1.1 | 2 | |||
99.5 | odd | 30 | 891.2.f.b.82.1 | 4 | |||
99.16 | even | 15 | inner | 297.2.n.a.181.1 | 8 | ||
99.29 | even | 30 | 1089.2.e.d.727.2 | 4 | |||
99.38 | odd | 30 | 99.2.m.a.16.1 | ✓ | 8 | ||
99.40 | odd | 30 | 9801.2.a.m.1.2 | 2 | |||
99.49 | even | 15 | 891.2.f.a.82.1 | 4 | |||
99.59 | odd | 30 | 9801.2.a.n.1.2 | 2 | |||
99.92 | odd | 30 | 1089.2.e.g.727.1 | 4 | |||
99.95 | even | 30 | 9801.2.a.bc.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.m.a.16.1 | ✓ | 8 | 99.38 | odd | 30 | ||
99.2.m.a.31.1 | yes | 8 | 3.2 | odd | 2 | ||
99.2.m.a.49.1 | yes | 8 | 33.5 | odd | 10 | ||
99.2.m.a.97.1 | yes | 8 | 9.2 | odd | 6 | ||
297.2.n.a.64.1 | 8 | 1.1 | even | 1 | trivial | ||
297.2.n.a.181.1 | 8 | 99.16 | even | 15 | inner | ||
297.2.n.a.262.1 | 8 | 9.7 | even | 3 | inner | ||
297.2.n.a.280.1 | 8 | 11.5 | even | 5 | inner | ||
891.2.f.a.82.1 | 4 | 99.49 | even | 15 | |||
891.2.f.a.163.1 | 4 | 9.4 | even | 3 | |||
891.2.f.b.82.1 | 4 | 99.5 | odd | 30 | |||
891.2.f.b.163.1 | 4 | 9.5 | odd | 6 | |||
1089.2.e.d.364.2 | 4 | 33.29 | even | 10 | |||
1089.2.e.d.727.2 | 4 | 99.29 | even | 30 | |||
1089.2.e.g.364.1 | 4 | 33.26 | odd | 10 | |||
1089.2.e.g.727.1 | 4 | 99.92 | odd | 30 | |||
9801.2.a.m.1.2 | 2 | 99.40 | odd | 30 | |||
9801.2.a.n.1.2 | 2 | 99.59 | odd | 30 | |||
9801.2.a.bb.1.1 | 2 | 99.4 | even | 15 | |||
9801.2.a.bc.1.1 | 2 | 99.95 | even | 30 |