Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(77,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 6, 10, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.br (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 317.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.317 |
Dual form | 360.2.br.d.293.1 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | − | 1.36603i | 0.258819 | − | 0.965926i | ||||
\(3\) | 0.866025 | + | 1.50000i | 0.500000 | + | 0.866025i | ||||
\(4\) | −1.73205 | − | 1.00000i | −0.866025 | − | 0.500000i | ||||
\(5\) | −1.23205 | + | 1.86603i | −0.550990 | + | 0.834512i | ||||
\(6\) | 2.36603 | − | 0.633975i | 0.965926 | − | 0.258819i | ||||
\(7\) | −4.23205 | + | 1.13397i | −1.59956 | + | 0.428602i | −0.944911 | − | 0.327327i | \(-0.893852\pi\) |
−0.654654 | + | 0.755929i | \(0.727186\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.707107 | + | 0.707107i | ||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | 2.09808 | + | 2.36603i | 0.663470 | + | 0.748203i | ||||
\(11\) | 1.00000 | − | 1.73205i | 0.301511 | − | 0.522233i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
0.976478 | + | 0.215615i | \(0.0691756\pi\) | |||||||
\(12\) | − | 3.46410i | − | 1.00000i | ||||||
\(13\) | −0.464102 | + | 1.73205i | −0.128719 | + | 0.480384i | −0.999945 | − | 0.0104972i | \(-0.996659\pi\) |
0.871226 | + | 0.490882i | \(0.163325\pi\) | |||||||
\(14\) | 6.19615i | 1.65599i | ||||||||
\(15\) | −3.86603 | − | 0.232051i | −0.998203 | − | 0.0599153i | ||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | −3.00000 | + | 3.00000i | −0.727607 | + | 0.727607i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) |
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 3.00000 | + | 3.00000i | 0.707107 | + | 0.707107i | ||||
\(19\) | 4.73205 | 1.08561 | 0.542803 | − | 0.839860i | \(-0.317363\pi\) | ||||
0.542803 | + | 0.839860i | \(0.317363\pi\) | |||||||
\(20\) | 4.00000 | − | 2.00000i | 0.894427 | − | 0.447214i | ||||
\(21\) | −5.36603 | − | 5.36603i | −1.17096 | − | 1.17096i | ||||
\(22\) | −2.00000 | − | 2.00000i | −0.426401 | − | 0.426401i | ||||
\(23\) | 0.232051 | − | 0.866025i | 0.0483859 | − | 0.180579i | −0.937504 | − | 0.347975i | \(-0.886869\pi\) |
0.985890 | + | 0.167396i | \(0.0535360\pi\) | |||||||
\(24\) | −4.73205 | − | 1.26795i | −0.965926 | − | 0.258819i | ||||
\(25\) | −1.96410 | − | 4.59808i | −0.392820 | − | 0.919615i | ||||
\(26\) | 2.19615 | + | 1.26795i | 0.430701 | + | 0.248665i | ||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 8.46410 | + | 2.26795i | 1.59956 | + | 0.428602i | ||||
\(29\) | −2.76795 | − | 1.59808i | −0.513995 | − | 0.296755i | 0.220479 | − | 0.975392i | \(-0.429238\pi\) |
−0.734474 | + | 0.678636i | \(0.762571\pi\) | |||||||
\(30\) | −1.73205 | + | 5.19615i | −0.316228 | + | 0.948683i | ||||
\(31\) | 4.09808 | + | 7.09808i | 0.736036 | + | 1.27485i | 0.954267 | + | 0.298955i | \(0.0966380\pi\) |
−0.218231 | + | 0.975897i | \(0.570029\pi\) | |||||||
\(32\) | 5.46410 | − | 1.46410i | 0.965926 | − | 0.258819i | ||||
\(33\) | 3.46410 | 0.603023 | ||||||||
\(34\) | 3.00000 | + | 5.19615i | 0.514496 | + | 0.891133i | ||||
\(35\) | 3.09808 | − | 9.29423i | 0.523670 | − | 1.57101i | ||||
\(36\) | 5.19615 | − | 3.00000i | 0.866025 | − | 0.500000i | ||||
\(37\) | 0.464102 | − | 0.464102i | 0.0762978 | − | 0.0762978i | −0.667928 | − | 0.744226i | \(-0.732819\pi\) |
0.744226 | + | 0.667928i | \(0.232819\pi\) | |||||||
\(38\) | 1.73205 | − | 6.46410i | 0.280976 | − | 1.04862i | ||||
\(39\) | −3.00000 | + | 0.803848i | −0.480384 | + | 0.128719i | ||||
\(40\) | −1.26795 | − | 6.19615i | −0.200480 | − | 0.979698i | ||||
\(41\) | −5.59808 | + | 3.23205i | −0.874273 | + | 0.504762i | −0.868766 | − | 0.495223i | \(-0.835086\pi\) |
−0.00550690 | + | 0.999985i | \(0.501753\pi\) | |||||||
\(42\) | −9.29423 | + | 5.36603i | −1.43413 | + | 0.827996i | ||||
\(43\) | 8.83013 | − | 2.36603i | 1.34658 | − | 0.360815i | 0.487710 | − | 0.873006i | \(-0.337832\pi\) |
0.858872 | + | 0.512190i | \(0.171166\pi\) | |||||||
\(44\) | −3.46410 | + | 2.00000i | −0.522233 | + | 0.301511i | ||||
\(45\) | −3.00000 | − | 6.00000i | −0.447214 | − | 0.894427i | ||||
\(46\) | −1.09808 | − | 0.633975i | −0.161903 | − | 0.0934745i | ||||
\(47\) | −0.401924 | − | 1.50000i | −0.0586266 | − | 0.218797i | 0.930397 | − | 0.366552i | \(-0.119462\pi\) |
−0.989024 | + | 0.147755i | \(0.952795\pi\) | |||||||
\(48\) | −3.46410 | + | 6.00000i | −0.500000 | + | 0.866025i | ||||
\(49\) | 10.5622 | − | 6.09808i | 1.50888 | − | 0.871154i | ||||
\(50\) | −7.00000 | + | 1.00000i | −0.989949 | + | 0.141421i | ||||
\(51\) | −7.09808 | − | 1.90192i | −0.993929 | − | 0.266323i | ||||
\(52\) | 2.53590 | − | 2.53590i | 0.351666 | − | 0.351666i | ||||
\(53\) | −5.19615 | + | 5.19615i | −0.713746 | + | 0.713746i | −0.967317 | − | 0.253570i | \(-0.918395\pi\) |
0.253570 | + | 0.967317i | \(0.418395\pi\) | |||||||
\(54\) | −1.90192 | + | 7.09808i | −0.258819 | + | 0.965926i | ||||
\(55\) | 2.00000 | + | 4.00000i | 0.269680 | + | 0.539360i | ||||
\(56\) | 6.19615 | − | 10.7321i | 0.827996 | − | 1.43413i | ||||
\(57\) | 4.09808 | + | 7.09808i | 0.542803 | + | 0.940163i | ||||
\(58\) | −3.19615 | + | 3.19615i | −0.419675 | + | 0.419675i | ||||
\(59\) | −1.56218 | + | 0.901924i | −0.203378 | + | 0.117420i | −0.598230 | − | 0.801324i | \(-0.704129\pi\) |
0.394852 | + | 0.918745i | \(0.370796\pi\) | |||||||
\(60\) | 6.46410 | + | 4.26795i | 0.834512 | + | 0.550990i | ||||
\(61\) | 12.6962 | + | 7.33013i | 1.62558 | + | 0.938527i | 0.985391 | + | 0.170305i | \(0.0544754\pi\) |
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | 11.1962 | − | 3.00000i | 1.42191 | − | 0.381000i | ||||
\(63\) | 3.40192 | − | 12.6962i | 0.428602 | − | 1.59956i | ||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | −2.66025 | − | 3.00000i | −0.329964 | − | 0.372104i | ||||
\(66\) | 1.26795 | − | 4.73205i | 0.156074 | − | 0.582475i | ||||
\(67\) | 7.33013 | + | 1.96410i | 0.895518 | + | 0.239953i | 0.677090 | − | 0.735900i | \(-0.263241\pi\) |
0.218427 | + | 0.975853i | \(0.429907\pi\) | |||||||
\(68\) | 8.19615 | − | 2.19615i | 0.993929 | − | 0.266323i | ||||
\(69\) | 1.50000 | − | 0.401924i | 0.180579 | − | 0.0483859i | ||||
\(70\) | −11.5622 | − | 7.63397i | −1.38194 | − | 0.912434i | ||||
\(71\) | − | 12.0000i | − | 1.42414i | −0.702109 | − | 0.712069i | \(-0.747758\pi\) | ||
0.702109 | − | 0.712069i | \(-0.252242\pi\) | |||||||
\(72\) | −2.19615 | − | 8.19615i | −0.258819 | − | 0.965926i | ||||
\(73\) | −10.1962 | + | 10.1962i | −1.19337 | + | 1.19337i | −0.217254 | + | 0.976115i | \(0.569710\pi\) |
−0.976115 | + | 0.217254i | \(0.930290\pi\) | |||||||
\(74\) | −0.464102 | − | 0.803848i | −0.0539507 | − | 0.0934454i | ||||
\(75\) | 5.19615 | − | 6.92820i | 0.600000 | − | 0.800000i | ||||
\(76\) | −8.19615 | − | 4.73205i | −0.940163 | − | 0.542803i | ||||
\(77\) | −2.26795 | + | 8.46410i | −0.258457 | + | 0.964574i | ||||
\(78\) | 4.39230i | 0.497331i | ||||||||
\(79\) | −1.90192 | − | 1.09808i | −0.213983 | − | 0.123543i | 0.389178 | − | 0.921163i | \(-0.372759\pi\) |
−0.603161 | + | 0.797619i | \(0.706092\pi\) | |||||||
\(80\) | −8.92820 | − | 0.535898i | −0.998203 | − | 0.0599153i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 2.36603 | + | 8.83013i | 0.261284 | + | 0.975124i | ||||
\(83\) | 3.03590 | + | 11.3301i | 0.333233 | + | 1.24364i | 0.905772 | + | 0.423765i | \(0.139292\pi\) |
−0.572539 | + | 0.819878i | \(0.694041\pi\) | |||||||
\(84\) | 3.92820 | + | 14.6603i | 0.428602 | + | 1.59956i | ||||
\(85\) | −1.90192 | − | 9.29423i | −0.206293 | − | 1.00810i | ||||
\(86\) | − | 12.9282i | − | 1.39408i | ||||||
\(87\) | − | 5.53590i | − | 0.593511i | ||||||
\(88\) | 1.46410 | + | 5.46410i | 0.156074 | + | 0.582475i | ||||
\(89\) | −2.66025 | −0.281986 | −0.140993 | − | 0.990011i | \(-0.545030\pi\) | ||||
−0.140993 | + | 0.990011i | \(0.545030\pi\) | |||||||
\(90\) | −9.29423 | + | 1.90192i | −0.979698 | + | 0.200480i | ||||
\(91\) | − | 7.85641i | − | 0.823575i | ||||||
\(92\) | −1.26795 | + | 1.26795i | −0.132193 | + | 0.132193i | ||||
\(93\) | −7.09808 | + | 12.2942i | −0.736036 | + | 1.27485i | ||||
\(94\) | −2.19615 | −0.226516 | ||||||||
\(95\) | −5.83013 | + | 8.83013i | −0.598158 | + | 0.905952i | ||||
\(96\) | 6.92820 | + | 6.92820i | 0.707107 | + | 0.707107i | ||||
\(97\) | −6.83013 | + | 1.83013i | −0.693494 | + | 0.185821i | −0.588315 | − | 0.808632i | \(-0.700208\pi\) |
−0.105180 | + | 0.994453i | \(0.533542\pi\) | |||||||
\(98\) | −4.46410 | − | 16.6603i | −0.450942 | − | 1.68294i | ||||
\(99\) | 3.00000 | + | 5.19615i | 0.301511 | + | 0.522233i | ||||
\(100\) | −1.19615 | + | 9.92820i | −0.119615 | + | 0.992820i | ||||
\(101\) | −1.00000 | + | 1.73205i | −0.0995037 | + | 0.172345i | −0.911479 | − | 0.411346i | \(-0.865059\pi\) |
0.811976 | + | 0.583691i | \(0.198392\pi\) | |||||||
\(102\) | −5.19615 | + | 9.00000i | −0.514496 | + | 0.891133i | ||||
\(103\) | −15.5622 | − | 4.16987i | −1.53339 | − | 0.410870i | −0.609265 | − | 0.792967i | \(-0.708535\pi\) |
−0.924122 | + | 0.382097i | \(0.875202\pi\) | |||||||
\(104\) | −2.53590 | − | 4.39230i | −0.248665 | − | 0.430701i | ||||
\(105\) | 16.6244 | − | 3.40192i | 1.62237 | − | 0.331994i | ||||
\(106\) | 5.19615 | + | 9.00000i | 0.504695 | + | 0.874157i | ||||
\(107\) | −6.09808 | − | 6.09808i | −0.589523 | − | 0.589523i | 0.347979 | − | 0.937502i | \(-0.386868\pi\) |
−0.937502 | + | 0.347979i | \(0.886868\pi\) | |||||||
\(108\) | 9.00000 | + | 5.19615i | 0.866025 | + | 0.500000i | ||||
\(109\) | −8.66025 | −0.829502 | −0.414751 | − | 0.909935i | \(-0.636131\pi\) | ||||
−0.414751 | + | 0.909935i | \(0.636131\pi\) | |||||||
\(110\) | 6.19615 | − | 1.26795i | 0.590780 | − | 0.120894i | ||||
\(111\) | 1.09808 | + | 0.294229i | 0.104225 | + | 0.0279269i | ||||
\(112\) | −12.3923 | − | 12.3923i | −1.17096 | − | 1.17096i | ||||
\(113\) | 0.464102 | − | 1.73205i | 0.0436590 | − | 0.162938i | −0.940655 | − | 0.339366i | \(-0.889788\pi\) |
0.984314 | + | 0.176428i | \(0.0564543\pi\) | |||||||
\(114\) | 11.1962 | − | 3.00000i | 1.04862 | − | 0.280976i | ||||
\(115\) | 1.33013 | + | 1.50000i | 0.124035 | + | 0.139876i | ||||
\(116\) | 3.19615 | + | 5.53590i | 0.296755 | + | 0.513995i | ||||
\(117\) | −3.80385 | − | 3.80385i | −0.351666 | − | 0.351666i | ||||
\(118\) | 0.660254 | + | 2.46410i | 0.0607813 | + | 0.226839i | ||||
\(119\) | 9.29423 | − | 16.0981i | 0.852001 | − | 1.47571i | ||||
\(120\) | 8.19615 | − | 7.26795i | 0.748203 | − | 0.663470i | ||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 14.6603 | − | 14.6603i | 1.32728 | − | 1.32728i | ||||
\(123\) | −9.69615 | − | 5.59808i | −0.874273 | − | 0.504762i | ||||
\(124\) | − | 16.3923i | − | 1.47207i | ||||||
\(125\) | 11.0000 | + | 2.00000i | 0.983870 | + | 0.178885i | ||||
\(126\) | −16.0981 | − | 9.29423i | −1.43413 | − | 0.827996i | ||||
\(127\) | 5.90192 | + | 5.90192i | 0.523711 | + | 0.523711i | 0.918690 | − | 0.394979i | \(-0.129248\pi\) |
−0.394979 | + | 0.918690i | \(0.629248\pi\) | |||||||
\(128\) | −10.9282 | − | 2.92820i | −0.965926 | − | 0.258819i | ||||
\(129\) | 11.1962 | + | 11.1962i | 0.985766 | + | 0.985766i | ||||
\(130\) | −5.07180 | + | 2.53590i | −0.444826 | + | 0.222413i | ||||
\(131\) | 3.90192 | + | 6.75833i | 0.340913 | + | 0.590478i | 0.984602 | − | 0.174808i | \(-0.0559306\pi\) |
−0.643690 | + | 0.765287i | \(0.722597\pi\) | |||||||
\(132\) | −6.00000 | − | 3.46410i | −0.522233 | − | 0.301511i | ||||
\(133\) | −20.0263 | + | 5.36603i | −1.73650 | + | 0.465293i | ||||
\(134\) | 5.36603 | − | 9.29423i | 0.463554 | − | 0.802899i | ||||
\(135\) | 6.40192 | − | 9.69615i | 0.550990 | − | 0.834512i | ||||
\(136\) | − | 12.0000i | − | 1.02899i | ||||||
\(137\) | 3.46410 | + | 12.9282i | 0.295958 | + | 1.10453i | 0.940453 | + | 0.339923i | \(0.110401\pi\) |
−0.644495 | + | 0.764608i | \(0.722932\pi\) | |||||||
\(138\) | − | 2.19615i | − | 0.186949i | ||||||
\(139\) | 3.46410 | + | 6.00000i | 0.293821 | + | 0.508913i | 0.974710 | − | 0.223474i | \(-0.0717396\pi\) |
−0.680889 | + | 0.732387i | \(0.738406\pi\) | |||||||
\(140\) | −14.6603 | + | 13.0000i | −1.23902 | + | 1.09870i | ||||
\(141\) | 1.90192 | − | 1.90192i | 0.160171 | − | 0.160171i | ||||
\(142\) | −16.3923 | − | 4.39230i | −1.37561 | − | 0.368594i | ||||
\(143\) | 2.53590 | + | 2.53590i | 0.212062 | + | 0.212062i | ||||
\(144\) | −12.0000 | −1.00000 | ||||||||
\(145\) | 6.39230 | − | 3.19615i | 0.530852 | − | 0.265426i | ||||
\(146\) | 10.1962 | + | 17.6603i | 0.843840 | + | 1.46157i | ||||
\(147\) | 18.2942 | + | 10.5622i | 1.50888 | + | 0.871154i | ||||
\(148\) | −1.26795 | + | 0.339746i | −0.104225 | + | 0.0279269i | ||||
\(149\) | 6.06218 | − | 3.50000i | 0.496633 | − | 0.286731i | −0.230689 | − | 0.973028i | \(-0.574098\pi\) |
0.727322 | + | 0.686296i | \(0.240765\pi\) | |||||||
\(150\) | −7.56218 | − | 9.63397i | −0.617449 | − | 0.786611i | ||||
\(151\) | 8.00000 | − | 13.8564i | 0.651031 | − | 1.12762i | −0.331842 | − | 0.943335i | \(-0.607670\pi\) |
0.982873 | − | 0.184284i | \(-0.0589965\pi\) | |||||||
\(152\) | −9.46410 | + | 9.46410i | −0.767640 | + | 0.767640i | ||||
\(153\) | −3.29423 | − | 12.2942i | −0.266323 | − | 0.993929i | ||||
\(154\) | 10.7321 | + | 6.19615i | 0.864813 | + | 0.499300i | ||||
\(155\) | −18.2942 | − | 1.09808i | −1.46943 | − | 0.0881996i | ||||
\(156\) | 6.00000 | + | 1.60770i | 0.480384 | + | 0.128719i | ||||
\(157\) | 12.2942 | + | 3.29423i | 0.981186 | + | 0.262908i | 0.713544 | − | 0.700610i | \(-0.247089\pi\) |
0.267642 | + | 0.963518i | \(0.413756\pi\) | |||||||
\(158\) | −2.19615 | + | 2.19615i | −0.174717 | + | 0.174717i | ||||
\(159\) | −12.2942 | − | 3.29423i | −0.974996 | − | 0.261249i | ||||
\(160\) | −4.00000 | + | 12.0000i | −0.316228 | + | 0.948683i | ||||
\(161\) | 3.92820i | 0.309586i | ||||||||
\(162\) | −12.2942 | + | 3.29423i | −0.965926 | + | 0.258819i | ||||
\(163\) | −6.46410 | − | 6.46410i | −0.506308 | − | 0.506308i | 0.407083 | − | 0.913391i | \(-0.366546\pi\) |
−0.913391 | + | 0.407083i | \(0.866546\pi\) | |||||||
\(164\) | 12.9282 | 1.00952 | ||||||||
\(165\) | −4.26795 | + | 6.46410i | −0.332259 | + | 0.503230i | ||||
\(166\) | 16.5885 | 1.28751 | ||||||||
\(167\) | 17.8923 | + | 4.79423i | 1.38455 | + | 0.370989i | 0.872771 | − | 0.488130i | \(-0.162321\pi\) |
0.511777 | + | 0.859118i | \(0.328987\pi\) | |||||||
\(168\) | 21.4641 | 1.65599 | ||||||||
\(169\) | 8.47372 | + | 4.89230i | 0.651825 | + | 0.376331i | ||||
\(170\) | −13.3923 | − | 0.803848i | −1.02714 | − | 0.0616523i | ||||
\(171\) | −7.09808 | + | 12.2942i | −0.542803 | + | 0.940163i | ||||
\(172\) | −17.6603 | − | 4.73205i | −1.34658 | − | 0.360815i | ||||
\(173\) | −0.732051 | − | 2.73205i | −0.0556568 | − | 0.207714i | 0.932498 | − | 0.361176i | \(-0.117625\pi\) |
−0.988155 | + | 0.153462i | \(0.950958\pi\) | |||||||
\(174\) | −7.56218 | − | 2.02628i | −0.573287 | − | 0.153612i | ||||
\(175\) | 13.5263 | + | 17.2321i | 1.02249 | + | 1.30262i | ||||
\(176\) | 8.00000 | 0.603023 | ||||||||
\(177\) | −2.70577 | − | 1.56218i | −0.203378 | − | 0.117420i | ||||
\(178\) | −0.973721 | + | 3.63397i | −0.0729834 | + | 0.272378i | ||||
\(179\) | 6.39230i | 0.477783i | 0.971046 | + | 0.238892i | \(0.0767841\pi\) | ||||
−0.971046 | + | 0.238892i | \(0.923216\pi\) | |||||||
\(180\) | −0.803848 | + | 13.3923i | −0.0599153 | + | 0.998203i | ||||
\(181\) | − | 3.00000i | − | 0.222988i | −0.993765 | − | 0.111494i | \(-0.964436\pi\) | ||
0.993765 | − | 0.111494i | \(-0.0355636\pi\) | |||||||
\(182\) | −10.7321 | − | 2.87564i | −0.795513 | − | 0.213157i | ||||
\(183\) | 25.3923i | 1.87705i | ||||||||
\(184\) | 1.26795 | + | 2.19615i | 0.0934745 | + | 0.161903i | ||||
\(185\) | 0.294229 | + | 1.43782i | 0.0216321 | + | 0.105711i | ||||
\(186\) | 14.1962 | + | 14.1962i | 1.04091 | + | 1.04091i | ||||
\(187\) | 2.19615 | + | 8.19615i | 0.160599 | + | 0.599362i | ||||
\(188\) | −0.803848 | + | 3.00000i | −0.0586266 | + | 0.218797i | ||||
\(189\) | 21.9904 | − | 5.89230i | 1.59956 | − | 0.428602i | ||||
\(190\) | 9.92820 | + | 11.1962i | 0.720268 | + | 0.812254i | ||||
\(191\) | −16.0981 | − | 9.29423i | −1.16482 | − | 0.672507i | −0.212362 | − | 0.977191i | \(-0.568116\pi\) |
−0.952453 | + | 0.304684i | \(0.901449\pi\) | |||||||
\(192\) | 12.0000 | − | 6.92820i | 0.866025 | − | 0.500000i | ||||
\(193\) | 13.6603 | + | 3.66025i | 0.983287 | + | 0.263471i | 0.714428 | − | 0.699709i | \(-0.246687\pi\) |
0.268858 | + | 0.963180i | \(0.413354\pi\) | |||||||
\(194\) | 10.0000i | 0.717958i | ||||||||
\(195\) | 2.19615 | − | 6.58846i | 0.157270 | − | 0.471809i | ||||
\(196\) | −24.3923 | −1.74231 | ||||||||
\(197\) | 12.0000 | + | 12.0000i | 0.854965 | + | 0.854965i | 0.990740 | − | 0.135775i | \(-0.0433525\pi\) |
−0.135775 | + | 0.990740i | \(0.543352\pi\) | |||||||
\(198\) | 8.19615 | − | 2.19615i | 0.582475 | − | 0.156074i | ||||
\(199\) | 4.19615i | 0.297457i | 0.988878 | + | 0.148729i | \(0.0475181\pi\) | ||||
−0.988878 | + | 0.148729i | \(0.952482\pi\) | |||||||
\(200\) | 13.1244 | + | 5.26795i | 0.928032 | + | 0.372500i | ||||
\(201\) | 3.40192 | + | 12.6962i | 0.239953 | + | 0.895518i | ||||
\(202\) | 2.00000 | + | 2.00000i | 0.140720 | + | 0.140720i | ||||
\(203\) | 13.5263 | + | 3.62436i | 0.949359 | + | 0.254380i | ||||
\(204\) | 10.3923 | + | 10.3923i | 0.727607 | + | 0.727607i | ||||
\(205\) | 0.866025 | − | 14.4282i | 0.0604858 | − | 1.00771i | ||||
\(206\) | −11.3923 | + | 19.7321i | −0.793739 | + | 1.37480i | ||||
\(207\) | 1.90192 | + | 1.90192i | 0.132193 | + | 0.132193i | ||||
\(208\) | −6.92820 | + | 1.85641i | −0.480384 | + | 0.128719i | ||||
\(209\) | 4.73205 | − | 8.19615i | 0.327323 | − | 0.566940i | ||||
\(210\) | 1.43782 | − | 23.9545i | 0.0992192 | − | 1.65302i | ||||
\(211\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(212\) | 14.1962 | − | 3.80385i | 0.974996 | − | 0.261249i | ||||
\(213\) | 18.0000 | − | 10.3923i | 1.23334 | − | 0.712069i | ||||
\(214\) | −10.5622 | + | 6.09808i | −0.722016 | + | 0.416856i | ||||
\(215\) | −6.46410 | + | 19.3923i | −0.440848 | + | 1.32254i | ||||
\(216\) | 10.3923 | − | 10.3923i | 0.707107 | − | 0.707107i | ||||
\(217\) | −25.3923 | − | 25.3923i | −1.72374 | − | 1.72374i | ||||
\(218\) | −3.16987 | + | 11.8301i | −0.214691 | + | 0.801237i | ||||
\(219\) | −24.1244 | − | 6.46410i | −1.63017 | − | 0.436804i | ||||
\(220\) | 0.535898 | − | 8.92820i | 0.0361303 | − | 0.601939i | ||||
\(221\) | −3.80385 | − | 6.58846i | −0.255874 | − | 0.443188i | ||||
\(222\) | 0.803848 | − | 1.39230i | 0.0539507 | − | 0.0934454i | ||||
\(223\) | 4.42820 | + | 16.5263i | 0.296534 | + | 1.10668i | 0.939991 | + | 0.341199i | \(0.110833\pi\) |
−0.643457 | + | 0.765483i | \(0.722500\pi\) | |||||||
\(224\) | −21.4641 | + | 12.3923i | −1.43413 | + | 0.827996i | ||||
\(225\) | 14.8923 | + | 1.79423i | 0.992820 | + | 0.119615i | ||||
\(226\) | −2.19615 | − | 1.26795i | −0.146086 | − | 0.0843427i | ||||
\(227\) | 10.0981 | − | 2.70577i | 0.670233 | − | 0.179588i | 0.0923731 | − | 0.995724i | \(-0.470555\pi\) |
0.577860 | + | 0.816136i | \(0.303888\pi\) | |||||||
\(228\) | − | 16.3923i | − | 1.08561i | ||||||
\(229\) | −5.76795 | − | 9.99038i | −0.381157 | − | 0.660183i | 0.610071 | − | 0.792347i | \(-0.291141\pi\) |
−0.991228 | + | 0.132164i | \(0.957808\pi\) | |||||||
\(230\) | 2.53590 | − | 1.26795i | 0.167212 | − | 0.0836061i | ||||
\(231\) | −14.6603 | + | 3.92820i | −0.964574 | + | 0.258457i | ||||
\(232\) | 8.73205 | − | 2.33975i | 0.573287 | − | 0.153612i | ||||
\(233\) | −18.1244 | − | 18.1244i | −1.18737 | − | 1.18737i | −0.977793 | − | 0.209573i | \(-0.932793\pi\) |
−0.209573 | − | 0.977793i | \(-0.567207\pi\) | |||||||
\(234\) | −6.58846 | + | 3.80385i | −0.430701 | + | 0.248665i | ||||
\(235\) | 3.29423 | + | 1.09808i | 0.214892 | + | 0.0716306i | ||||
\(236\) | 3.60770 | 0.234841 | ||||||||
\(237\) | − | 3.80385i | − | 0.247086i | ||||||
\(238\) | −18.5885 | − | 18.5885i | −1.20491 | − | 1.20491i | ||||
\(239\) | 9.46410 | + | 16.3923i | 0.612182 | + | 1.06033i | 0.990872 | + | 0.134807i | \(0.0430413\pi\) |
−0.378690 | + | 0.925524i | \(0.623625\pi\) | |||||||
\(240\) | −6.92820 | − | 13.8564i | −0.447214 | − | 0.894427i | ||||
\(241\) | 9.40192 | − | 16.2846i | 0.605631 | − | 1.04898i | −0.386320 | − | 0.922365i | \(-0.626254\pi\) |
0.991951 | − | 0.126619i | \(-0.0404126\pi\) | |||||||
\(242\) | 9.56218 | − | 2.56218i | 0.614680 | − | 0.164703i | ||||
\(243\) | 7.79423 | − | 13.5000i | 0.500000 | − | 0.866025i | ||||
\(244\) | −14.6603 | − | 25.3923i | −0.938527 | − | 1.62558i | ||||
\(245\) | −1.63397 | + | 27.2224i | −0.104391 | + | 1.73918i | ||||
\(246\) | −11.1962 | + | 11.1962i | −0.713841 | + | 0.713841i | ||||
\(247\) | −2.19615 | + | 8.19615i | −0.139738 | + | 0.521509i | ||||
\(248\) | −22.3923 | − | 6.00000i | −1.42191 | − | 0.381000i | ||||
\(249\) | −14.3660 | + | 14.3660i | −0.910410 | + | 0.910410i | ||||
\(250\) | 6.75833 | − | 14.2942i | 0.427434 | − | 0.904046i | ||||
\(251\) | −26.5885 | −1.67825 | −0.839124 | − | 0.543940i | \(-0.816932\pi\) | ||||
−0.839124 | + | 0.543940i | \(0.816932\pi\) | |||||||
\(252\) | −18.5885 | + | 18.5885i | −1.17096 | + | 1.17096i | ||||
\(253\) | −1.26795 | − | 1.26795i | −0.0797153 | − | 0.0797153i | ||||
\(254\) | 10.2224 | − | 5.90192i | 0.641412 | − | 0.370320i | ||||
\(255\) | 12.2942 | − | 10.9019i | 0.769894 | − | 0.682705i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −15.7583 | − | 4.22243i | −0.982978 | − | 0.263388i | −0.268680 | − | 0.963230i | \(-0.586587\pi\) |
−0.714298 | + | 0.699842i | \(0.753254\pi\) | |||||||
\(258\) | 19.3923 | − | 11.1962i | 1.20731 | − | 0.697042i | ||||
\(259\) | −1.43782 | + | 2.49038i | −0.0893419 | + | 0.154745i | ||||
\(260\) | 1.60770 | + | 7.85641i | 0.0997050 | + | 0.487234i | ||||
\(261\) | 8.30385 | − | 4.79423i | 0.513995 | − | 0.296755i | ||||
\(262\) | 10.6603 | − | 2.85641i | 0.658593 | − | 0.176469i | ||||
\(263\) | 13.5622 | − | 3.63397i | 0.836280 | − | 0.224080i | 0.184828 | − | 0.982771i | \(-0.440827\pi\) |
0.651451 | + | 0.758690i | \(0.274160\pi\) | |||||||
\(264\) | −6.92820 | + | 6.92820i | −0.426401 | + | 0.426401i | ||||
\(265\) | −3.29423 | − | 16.0981i | −0.202363 | − | 0.988897i | ||||
\(266\) | 29.3205i | 1.79776i | ||||||||
\(267\) | −2.30385 | − | 3.99038i | −0.140993 | − | 0.244207i | ||||
\(268\) | −10.7321 | − | 10.7321i | −0.655564 | − | 0.655564i | ||||
\(269\) | − | 1.00000i | − | 0.0609711i | −0.999535 | − | 0.0304855i | \(-0.990295\pi\) | ||
0.999535 | − | 0.0304855i | \(-0.00970535\pi\) | |||||||
\(270\) | −10.9019 | − | 12.2942i | −0.663470 | − | 0.748203i | ||||
\(271\) | 4.58846 | 0.278729 | 0.139364 | − | 0.990241i | \(-0.455494\pi\) | ||||
0.139364 | + | 0.990241i | \(0.455494\pi\) | |||||||
\(272\) | −16.3923 | − | 4.39230i | −0.993929 | − | 0.266323i | ||||
\(273\) | 11.7846 | − | 6.80385i | 0.713237 | − | 0.411788i | ||||
\(274\) | 18.9282 | 1.14349 | ||||||||
\(275\) | −9.92820 | − | 1.19615i | −0.598693 | − | 0.0721307i | ||||
\(276\) | −3.00000 | − | 0.803848i | −0.180579 | − | 0.0483859i | ||||
\(277\) | 2.36603 | + | 8.83013i | 0.142161 | + | 0.530551i | 0.999865 | + | 0.0164083i | \(0.00522314\pi\) |
−0.857705 | + | 0.514143i | \(0.828110\pi\) | |||||||
\(278\) | 9.46410 | − | 2.53590i | 0.567619 | − | 0.152093i | ||||
\(279\) | −24.5885 | −1.47207 | ||||||||
\(280\) | 12.3923 | + | 24.7846i | 0.740582 | + | 1.48116i | ||||
\(281\) | −1.79423 | − | 1.03590i | −0.107035 | − | 0.0617965i | 0.445527 | − | 0.895268i | \(-0.353016\pi\) |
−0.552562 | + | 0.833472i | \(0.686350\pi\) | |||||||
\(282\) | −1.90192 | − | 3.29423i | −0.113258 | − | 0.196168i | ||||
\(283\) | −1.20577 | + | 4.50000i | −0.0716757 | + | 0.267497i | −0.992459 | − | 0.122577i | \(-0.960884\pi\) |
0.920783 | + | 0.390074i | \(0.127551\pi\) | |||||||
\(284\) | −12.0000 | + | 20.7846i | −0.712069 | + | 1.23334i | ||||
\(285\) | −18.2942 | − | 1.09808i | −1.08366 | − | 0.0650444i | ||||
\(286\) | 4.39230 | − | 2.53590i | 0.259722 | − | 0.149951i | ||||
\(287\) | 20.0263 | − | 20.0263i | 1.18211 | − | 1.18211i | ||||
\(288\) | −4.39230 | + | 16.3923i | −0.258819 | + | 0.965926i | ||||
\(289\) | − | 1.00000i | − | 0.0588235i | ||||||
\(290\) | −2.02628 | − | 9.90192i | −0.118987 | − | 0.581461i | ||||
\(291\) | −8.66025 | − | 8.66025i | −0.507673 | − | 0.507673i | ||||
\(292\) | 27.8564 | − | 7.46410i | 1.63017 | − | 0.436804i | ||||
\(293\) | 1.09808 | + | 0.294229i | 0.0641503 | + | 0.0171890i | 0.290751 | − | 0.956799i | \(-0.406095\pi\) |
−0.226601 | + | 0.973988i | \(0.572761\pi\) | |||||||
\(294\) | 21.1244 | − | 21.1244i | 1.23200 | − | 1.23200i | ||||
\(295\) | 0.241670 | − | 4.02628i | 0.0140706 | − | 0.234419i | ||||
\(296\) | 1.85641i | 0.107901i | ||||||||
\(297\) | −5.19615 | + | 9.00000i | −0.301511 | + | 0.522233i | ||||
\(298\) | −2.56218 | − | 9.56218i | −0.148423 | − | 0.553922i | ||||
\(299\) | 1.39230 | + | 0.803848i | 0.0805191 | + | 0.0464877i | ||||
\(300\) | −15.9282 | + | 6.80385i | −0.919615 | + | 0.392820i | ||||
\(301\) | −34.6865 | + | 20.0263i | −1.99930 | + | 1.15430i | ||||
\(302\) | −16.0000 | − | 16.0000i | −0.920697 | − | 0.920697i | ||||
\(303\) | −3.46410 | −0.199007 | ||||||||
\(304\) | 9.46410 | + | 16.3923i | 0.542803 | + | 0.940163i | ||||
\(305\) | −29.3205 | + | 14.6603i | −1.67889 | + | 0.839444i | ||||
\(306\) | −18.0000 | −1.02899 | ||||||||
\(307\) | 14.3660 | − | 14.3660i | 0.819912 | − | 0.819912i | −0.166183 | − | 0.986095i | \(-0.553144\pi\) |
0.986095 | + | 0.166183i | \(0.0531441\pi\) | |||||||
\(308\) | 12.3923 | − | 12.3923i | 0.706117 | − | 0.706117i | ||||
\(309\) | −7.22243 | − | 26.9545i | −0.410870 | − | 1.53339i | ||||
\(310\) | −8.19615 | + | 24.5885i | −0.465510 | + | 1.39653i | ||||
\(311\) | 12.2942 | − | 7.09808i | 0.697142 | − | 0.402495i | −0.109140 | − | 0.994026i | \(-0.534810\pi\) |
0.806282 | + | 0.591531i | \(0.201476\pi\) | |||||||
\(312\) | 4.39230 | − | 7.60770i | 0.248665 | − | 0.430701i | ||||
\(313\) | −3.87564 | − | 14.4641i | −0.219064 | − | 0.817559i | −0.984696 | − | 0.174280i | \(-0.944240\pi\) |
0.765632 | − | 0.643279i | \(-0.222427\pi\) | |||||||
\(314\) | 9.00000 | − | 15.5885i | 0.507899 | − | 0.879708i | ||||
\(315\) | 19.5000 | + | 21.9904i | 1.09870 | + | 1.23902i | ||||
\(316\) | 2.19615 | + | 3.80385i | 0.123543 | + | 0.213983i | ||||
\(317\) | −13.6603 | + | 3.66025i | −0.767236 | + | 0.205580i | −0.621150 | − | 0.783692i | \(-0.713334\pi\) |
−0.146086 | + | 0.989272i | \(0.546668\pi\) | |||||||
\(318\) | −9.00000 | + | 15.5885i | −0.504695 | + | 0.874157i | ||||
\(319\) | −5.53590 | + | 3.19615i | −0.309951 | + | 0.178950i | ||||
\(320\) | 14.9282 | + | 9.85641i | 0.834512 | + | 0.550990i | ||||
\(321\) | 3.86603 | − | 14.4282i | 0.215780 | − | 0.805304i | ||||
\(322\) | 5.36603 | + | 1.43782i | 0.299037 | + | 0.0801267i | ||||
\(323\) | −14.1962 | + | 14.1962i | −0.789895 | + | 0.789895i | ||||
\(324\) | 18.0000i | 1.00000i | ||||||||
\(325\) | 8.87564 | − | 1.26795i | 0.492332 | − | 0.0703332i | ||||
\(326\) | −11.1962 | + | 6.46410i | −0.620098 | + | 0.358013i | ||||
\(327\) | −7.50000 | − | 12.9904i | −0.414751 | − | 0.718370i | ||||
\(328\) | 4.73205 | − | 17.6603i | 0.261284 | − | 0.975124i | ||||
\(329\) | 3.40192 | + | 5.89230i | 0.187554 | + | 0.324853i | ||||
\(330\) | 7.26795 | + | 8.19615i | 0.400087 | + | 0.451183i | ||||
\(331\) | 0.509619 | + | 0.294229i | 0.0280112 | + | 0.0161723i | 0.513940 | − | 0.857826i | \(-0.328185\pi\) |
−0.485929 | + | 0.873998i | \(0.661519\pi\) | |||||||
\(332\) | 6.07180 | − | 22.6603i | 0.333233 | − | 1.24364i | ||||
\(333\) | 0.509619 | + | 1.90192i | 0.0279269 | + | 0.104225i | ||||
\(334\) | 13.0981 | − | 22.6865i | 0.716695 | − | 1.24135i | ||||
\(335\) | −12.6962 | + | 11.2583i | −0.693665 | + | 0.615108i | ||||
\(336\) | 7.85641 | − | 29.3205i | 0.428602 | − | 1.59956i | ||||
\(337\) | 0.0717968 | − | 0.267949i | 0.00391102 | − | 0.0145961i | −0.963943 | − | 0.266110i | \(-0.914262\pi\) |
0.967854 | + | 0.251514i | \(0.0809283\pi\) | |||||||
\(338\) | 9.78461 | − | 9.78461i | 0.532213 | − | 0.532213i | ||||
\(339\) | 3.00000 | − | 0.803848i | 0.162938 | − | 0.0436590i | ||||
\(340\) | −6.00000 | + | 18.0000i | −0.325396 | + | 0.976187i | ||||
\(341\) | 16.3923 | 0.887693 | ||||||||
\(342\) | 14.1962 | + | 14.1962i | 0.767640 | + | 0.767640i | ||||
\(343\) | −16.0981 | + | 16.0981i | −0.869214 | + | 0.869214i | ||||
\(344\) | −12.9282 | + | 22.3923i | −0.697042 | + | 1.20731i | ||||
\(345\) | −1.09808 | + | 3.29423i | −0.0591184 | + | 0.177355i | ||||
\(346\) | −4.00000 | −0.215041 | ||||||||
\(347\) | 1.90192 | − | 7.09808i | 0.102101 | − | 0.381045i | −0.895899 | − | 0.444257i | \(-0.853468\pi\) |
0.998000 | + | 0.0632121i | \(0.0201345\pi\) | |||||||
\(348\) | −5.53590 | + | 9.58846i | −0.296755 | + | 0.513995i | ||||
\(349\) | 18.2321 | − | 31.5788i | 0.975939 | − | 1.69038i | 0.299139 | − | 0.954209i | \(-0.403300\pi\) |
0.676800 | − | 0.736167i | \(-0.263366\pi\) | |||||||
\(350\) | 28.4904 | − | 12.1699i | 1.52287 | − | 0.650507i | ||||
\(351\) | 2.41154 | − | 9.00000i | 0.128719 | − | 0.480384i | ||||
\(352\) | 2.92820 | − | 10.9282i | 0.156074 | − | 0.582475i | ||||
\(353\) | 12.9282 | − | 3.46410i | 0.688099 | − | 0.184376i | 0.102205 | − | 0.994763i | \(-0.467410\pi\) |
0.585894 | + | 0.810388i | \(0.300744\pi\) | |||||||
\(354\) | −3.12436 | + | 3.12436i | −0.166058 | + | 0.166058i | ||||
\(355\) | 22.3923 | + | 14.7846i | 1.18846 | + | 0.784686i | ||||
\(356\) | 4.60770 | + | 2.66025i | 0.244207 | + | 0.140993i | ||||
\(357\) | 32.1962 | 1.70400 | ||||||||
\(358\) | 8.73205 | + | 2.33975i | 0.461503 | + | 0.123659i | ||||
\(359\) | 2.19615 | 0.115908 | 0.0579542 | − | 0.998319i | \(-0.481542\pi\) | ||||
0.0579542 | + | 0.998319i | \(0.481542\pi\) | |||||||
\(360\) | 18.0000 | + | 6.00000i | 0.948683 | + | 0.316228i | ||||
\(361\) | 3.39230 | 0.178542 | ||||||||
\(362\) | −4.09808 | − | 1.09808i | −0.215390 | − | 0.0577136i | ||||
\(363\) | −6.06218 | + | 10.5000i | −0.318182 | + | 0.551107i | ||||
\(364\) | −7.85641 | + | 13.6077i | −0.411788 | + | 0.713237i | ||||
\(365\) | −6.46410 | − | 31.5885i | −0.338347 | − | 1.65342i | ||||
\(366\) | 34.6865 | + | 9.29423i | 1.81309 | + | 0.485817i | ||||
\(367\) | −9.56218 | + | 2.56218i | −0.499142 | + | 0.133745i | −0.499602 | − | 0.866255i | \(-0.666520\pi\) |
0.000459976 | 1.00000i | \(0.499854\pi\) | ||||||||
\(368\) | 3.46410 | − | 0.928203i | 0.180579 | − | 0.0483859i | ||||
\(369\) | − | 19.3923i | − | 1.00952i | ||||||
\(370\) | 2.07180 | + | 0.124356i | 0.107708 | + | 0.00646494i | ||||
\(371\) | 16.0981 | − | 27.8827i | 0.835770 | − | 1.44760i | ||||
\(372\) | 24.5885 | − | 14.1962i | 1.27485 | − | 0.736036i | ||||
\(373\) | −0.973721 | + | 3.63397i | −0.0504173 | + | 0.188160i | −0.986542 | − | 0.163508i | \(-0.947719\pi\) |
0.936125 | + | 0.351669i | \(0.114386\pi\) | |||||||
\(374\) | 12.0000 | 0.620505 | ||||||||
\(375\) | 6.52628 | + | 18.2321i | 0.337016 | + | 0.941499i | ||||
\(376\) | 3.80385 | + | 2.19615i | 0.196168 | + | 0.113258i | ||||
\(377\) | 4.05256 | − | 4.05256i | 0.208717 | − | 0.208717i | ||||
\(378\) | − | 32.1962i | − | 1.65599i | ||||||
\(379\) | −33.1244 | −1.70148 | −0.850742 | − | 0.525584i | \(-0.823847\pi\) | ||||
−0.850742 | + | 0.525584i | \(0.823847\pi\) | |||||||
\(380\) | 18.9282 | − | 9.46410i | 0.970996 | − | 0.485498i | ||||
\(381\) | −3.74167 | + | 13.9641i | −0.191692 | + | 0.715403i | ||||
\(382\) | −18.5885 | + | 18.5885i | −0.951068 | + | 0.951068i | ||||
\(383\) | 7.43782 | − | 27.7583i | 0.380055 | − | 1.41838i | −0.465761 | − | 0.884910i | \(-0.654220\pi\) |
0.845816 | − | 0.533474i | \(-0.179114\pi\) | |||||||
\(384\) | −5.07180 | − | 18.9282i | −0.258819 | − | 0.965926i | ||||
\(385\) | −13.0000 | − | 14.6603i | −0.662541 | − | 0.747156i | ||||
\(386\) | 10.0000 | − | 17.3205i | 0.508987 | − | 0.881591i | ||||
\(387\) | −7.09808 | + | 26.4904i | −0.360815 | + | 1.34658i | ||||
\(388\) | 13.6603 | + | 3.66025i | 0.693494 | + | 0.185821i | ||||
\(389\) | 15.0622 | + | 8.69615i | 0.763683 | + | 0.440912i | 0.830616 | − | 0.556845i | \(-0.187988\pi\) |
−0.0669337 | + | 0.997757i | \(0.521322\pi\) | |||||||
\(390\) | −8.19615 | − | 5.41154i | −0.415028 | − | 0.274024i | ||||
\(391\) | 1.90192 | + | 3.29423i | 0.0961844 | + | 0.166596i | ||||
\(392\) | −8.92820 | + | 33.3205i | −0.450942 | + | 1.68294i | ||||
\(393\) | −6.75833 | + | 11.7058i | −0.340913 | + | 0.590478i | ||||
\(394\) | 20.7846 | − | 12.0000i | 1.04711 | − | 0.604551i | ||||
\(395\) | 4.39230 | − | 2.19615i | 0.221001 | − | 0.110500i | ||||
\(396\) | − | 12.0000i | − | 0.603023i | ||||||
\(397\) | −0.803848 | + | 0.803848i | −0.0403440 | + | 0.0403440i | −0.726991 | − | 0.686647i | \(-0.759082\pi\) |
0.686647 | + | 0.726991i | \(0.259082\pi\) | |||||||
\(398\) | 5.73205 | + | 1.53590i | 0.287322 | + | 0.0769876i | ||||
\(399\) | −25.3923 | − | 25.3923i | −1.27121 | − | 1.27121i | ||||
\(400\) | 12.0000 | − | 16.0000i | 0.600000 | − | 0.800000i | ||||
\(401\) | −31.3923 | + | 18.1244i | −1.56766 | + | 0.905087i | −0.571215 | + | 0.820800i | \(0.693528\pi\) |
−0.996442 | + | 0.0842869i | \(0.973139\pi\) | |||||||
\(402\) | 18.5885 | 0.927108 | ||||||||
\(403\) | −14.1962 | + | 3.80385i | −0.707161 | + | 0.189483i | ||||
\(404\) | 3.46410 | − | 2.00000i | 0.172345 | − | 0.0995037i | ||||
\(405\) | 20.0885 | + | 1.20577i | 0.998203 | + | 0.0599153i | ||||
\(406\) | 9.90192 | − | 17.1506i | 0.491424 | − | 0.851172i | ||||
\(407\) | −0.339746 | − | 1.26795i | −0.0168406 | − | 0.0628499i | ||||
\(408\) | 18.0000 | − | 10.3923i | 0.891133 | − | 0.514496i | ||||
\(409\) | −5.19615 | + | 3.00000i | −0.256933 | + | 0.148340i | −0.622935 | − | 0.782274i | \(-0.714060\pi\) |
0.366002 | + | 0.930614i | \(0.380726\pi\) | |||||||
\(410\) | −19.3923 | − | 6.46410i | −0.957718 | − | 0.319239i | ||||
\(411\) | −16.3923 | + | 16.3923i | −0.808573 | + | 0.808573i | ||||
\(412\) | 22.7846 | + | 22.7846i | 1.12252 | + | 1.12252i | ||||
\(413\) | 5.58846 | − | 5.58846i | 0.274990 | − | 0.274990i | ||||
\(414\) | 3.29423 | − | 1.90192i | 0.161903 | − | 0.0934745i | ||||
\(415\) | −24.8827 | − | 8.29423i | −1.22144 | − | 0.407148i | ||||
\(416\) | 10.1436i | 0.497331i | ||||||||
\(417\) | −6.00000 | + | 10.3923i | −0.293821 | + | 0.508913i | ||||
\(418\) | −9.46410 | − | 9.46410i | −0.462904 | − | 0.462904i | ||||
\(419\) | −10.7321 | + | 6.19615i | −0.524295 | + | 0.302702i | −0.738690 | − | 0.674045i | \(-0.764555\pi\) |
0.214395 | + | 0.976747i | \(0.431222\pi\) | |||||||
\(420\) | −32.1962 | − | 10.7321i | −1.57101 | − | 0.523670i | ||||
\(421\) | 4.60770 | + | 2.66025i | 0.224565 | + | 0.129653i | 0.608062 | − | 0.793889i | \(-0.291947\pi\) |
−0.383497 | + | 0.923542i | \(0.625280\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.50000 | + | 1.20577i | 0.218797 | + | 0.0586266i | ||||
\(424\) | − | 20.7846i | − | 1.00939i | ||||||
\(425\) | 19.6865 | + | 7.90192i | 0.954937 | + | 0.383300i | ||||
\(426\) | −7.60770 | − | 28.3923i | −0.368594 | − | 1.37561i | ||||
\(427\) | −62.0429 | − | 16.6244i | −3.00247 | − | 0.804509i | ||||
\(428\) | 4.46410 | + | 16.6603i | 0.215780 | + | 0.805304i | ||||
\(429\) | −1.60770 | + | 6.00000i | −0.0776203 | + | 0.289683i | ||||
\(430\) | 24.1244 | + | 15.9282i | 1.16338 | + | 0.768126i | ||||
\(431\) | 22.0526i | 1.06223i | 0.847298 | + | 0.531117i | \(0.178228\pi\) | ||||
−0.847298 | + | 0.531117i | \(0.821772\pi\) | |||||||
\(432\) | −10.3923 | − | 18.0000i | −0.500000 | − | 0.866025i | ||||
\(433\) | −15.3923 | + | 15.3923i | −0.739707 | + | 0.739707i | −0.972521 | − | 0.232814i | \(-0.925207\pi\) |
0.232814 | + | 0.972521i | \(0.425207\pi\) | |||||||
\(434\) | −43.9808 | + | 25.3923i | −2.11114 | + | 1.21887i | ||||
\(435\) | 10.3301 | + | 6.82051i | 0.495292 | + | 0.327018i | ||||
\(436\) | 15.0000 | + | 8.66025i | 0.718370 | + | 0.414751i | ||||
\(437\) | 1.09808 | − | 4.09808i | 0.0525281 | − | 0.196038i | ||||
\(438\) | −17.6603 | + | 30.5885i | −0.843840 | + | 1.46157i | ||||
\(439\) | −16.2679 | − | 9.39230i | −0.776427 | − | 0.448270i | 0.0587356 | − | 0.998274i | \(-0.481293\pi\) |
−0.835162 | + | 0.550003i | \(0.814626\pi\) | |||||||
\(440\) | −12.0000 | − | 4.00000i | −0.572078 | − | 0.190693i | ||||
\(441\) | 36.5885i | 1.74231i | ||||||||
\(442\) | −10.3923 | + | 2.78461i | −0.494312 | + | 0.132450i | ||||
\(443\) | −9.99038 | − | 37.2846i | −0.474657 | − | 1.77145i | −0.622696 | − | 0.782464i | \(-0.713963\pi\) |
0.148039 | − | 0.988982i | \(-0.452704\pi\) | |||||||
\(444\) | −1.60770 | − | 1.60770i | −0.0762978 | − | 0.0762978i | ||||
\(445\) | 3.27757 | − | 4.96410i | 0.155372 | − | 0.235321i | ||||
\(446\) | 24.1962 | 1.14572 | ||||||||
\(447\) | 10.5000 | + | 6.06218i | 0.496633 | + | 0.286731i | ||||
\(448\) | 9.07180 | + | 33.8564i | 0.428602 | + | 1.59956i | ||||
\(449\) | 32.7846 | 1.54720 | 0.773601 | − | 0.633673i | \(-0.218454\pi\) | ||||
0.773601 | + | 0.633673i | \(0.218454\pi\) | |||||||
\(450\) | 7.90192 | − | 19.6865i | 0.372500 | − | 0.928032i | ||||
\(451\) | 12.9282i | 0.608765i | ||||||||
\(452\) | −2.53590 | + | 2.53590i | −0.119279 | + | 0.119279i | ||||
\(453\) | 27.7128 | 1.30206 | ||||||||
\(454\) | − | 14.7846i | − | 0.693876i | ||||||
\(455\) | 14.6603 | + | 9.67949i | 0.687283 | + | 0.453782i | ||||
\(456\) | −22.3923 | − | 6.00000i | −1.04862 | − | 0.280976i | ||||
\(457\) | 9.83013 | − | 2.63397i | 0.459834 | − | 0.123212i | −0.0214632 | − | 0.999770i | \(-0.506832\pi\) |
0.481297 | + | 0.876558i | \(0.340166\pi\) | |||||||
\(458\) | −15.7583 | + | 4.22243i | −0.736338 | + | 0.197301i | ||||
\(459\) | 15.5885 | − | 15.5885i | 0.727607 | − | 0.727607i | ||||
\(460\) | −0.803848 | − | 3.92820i | −0.0374796 | − | 0.183153i | ||||
\(461\) | 6.79423 | − | 11.7679i | 0.316439 | − | 0.548088i | −0.663304 | − | 0.748350i | \(-0.730846\pi\) |
0.979742 | + | 0.200262i | \(0.0641795\pi\) | |||||||
\(462\) | 21.4641i | 0.998600i | ||||||||
\(463\) | 6.56218 | + | 1.75833i | 0.304970 | + | 0.0817165i | 0.408059 | − | 0.912956i | \(-0.366206\pi\) |
−0.103089 | + | 0.994672i | \(0.532873\pi\) | |||||||
\(464\) | − | 12.7846i | − | 0.593511i | ||||||
\(465\) | −14.1962 | − | 28.3923i | −0.658331 | − | 1.31666i | ||||
\(466\) | −31.3923 | + | 18.1244i | −1.45422 | + | 0.839595i | ||||
\(467\) | −8.60770 | − | 8.60770i | −0.398317 | − | 0.398317i | 0.479322 | − | 0.877639i | \(-0.340882\pi\) |
−0.877639 | + | 0.479322i | \(0.840882\pi\) | |||||||
\(468\) | 2.78461 | + | 10.3923i | 0.128719 | + | 0.480384i | ||||
\(469\) | −33.2487 | −1.53528 | ||||||||
\(470\) | 2.70577 | − | 4.09808i | 0.124808 | − | 0.189030i | ||||
\(471\) | 5.70577 | + | 21.2942i | 0.262908 | + | 0.981186i | ||||
\(472\) | 1.32051 | − | 4.92820i | 0.0607813 | − | 0.226839i | ||||
\(473\) | 4.73205 | − | 17.6603i | 0.217580 | − | 0.812019i | ||||
\(474\) | −5.19615 | − | 1.39230i | −0.238667 | − | 0.0639507i | ||||
\(475\) | −9.29423 | − | 21.7583i | −0.426448 | − | 0.998341i | ||||
\(476\) | −32.1962 | + | 18.5885i | −1.47571 | + | 0.852001i | ||||
\(477\) | −5.70577 | − | 21.2942i | −0.261249 | − | 0.974996i | ||||
\(478\) | 25.8564 | − | 6.92820i | 1.18264 | − | 0.316889i | ||||
\(479\) | −10.5622 | + | 18.2942i | −0.482598 | + | 0.835885i | −0.999800 | − | 0.0199786i | \(-0.993640\pi\) |
0.517202 | + | 0.855863i | \(0.326974\pi\) | |||||||
\(480\) | −21.4641 | + | 4.39230i | −0.979698 | + | 0.200480i | ||||
\(481\) | 0.588457 | + | 1.01924i | 0.0268313 | + | 0.0464732i | ||||
\(482\) | −18.8038 | − | 18.8038i | −0.856492 | − | 0.856492i | ||||
\(483\) | −5.89230 | + | 3.40192i | −0.268109 | + | 0.154793i | ||||
\(484\) | − | 14.0000i | − | 0.636364i | ||||||
\(485\) | 5.00000 | − | 15.0000i | 0.227038 | − | 0.681115i | ||||
\(486\) | −15.5885 | − | 15.5885i | −0.707107 | − | 0.707107i | ||||
\(487\) | 3.39230 | + | 3.39230i | 0.153720 | + | 0.153720i | 0.779777 | − | 0.626057i | \(-0.215332\pi\) |
−0.626057 | + | 0.779777i | \(0.715332\pi\) | |||||||
\(488\) | −40.0526 | + | 10.7321i | −1.81309 | + | 0.485817i | ||||
\(489\) | 4.09808 | − | 15.2942i | 0.185321 | − | 0.691629i | ||||
\(490\) | 36.5885 | + | 12.1962i | 1.65290 | + | 0.550966i | ||||
\(491\) | 12.3923 | + | 21.4641i | 0.559257 | + | 0.968661i | 0.997559 | + | 0.0698335i | \(0.0222468\pi\) |
−0.438302 | + | 0.898828i | \(0.644420\pi\) | |||||||
\(492\) | 11.1962 | + | 19.3923i | 0.504762 | + | 0.874273i | ||||
\(493\) | 13.0981 | − | 3.50962i | 0.589908 | − | 0.158065i | ||||
\(494\) | 10.3923 | + | 6.00000i | 0.467572 | + | 0.269953i | ||||
\(495\) | −13.3923 | − | 0.803848i | −0.601939 | − | 0.0361303i | ||||
\(496\) | −16.3923 | + | 28.3923i | −0.736036 | + | 1.27485i | ||||
\(497\) | 13.6077 | + | 50.7846i | 0.610389 | + | 2.27800i | ||||
\(498\) | 14.3660 | + | 24.8827i | 0.643757 | + | 1.11502i | ||||
\(499\) | 13.3923 | + | 23.1962i | 0.599522 | + | 1.03840i | 0.992892 | + | 0.119022i | \(0.0379759\pi\) |
−0.393370 | + | 0.919380i | \(0.628691\pi\) | |||||||
\(500\) | −17.0526 | − | 14.4641i | −0.762614 | − | 0.646854i | ||||
\(501\) | 8.30385 | + | 30.9904i | 0.370989 | + | 1.38455i | ||||
\(502\) | −9.73205 | + | 36.3205i | −0.434363 | + | 1.62106i | ||||
\(503\) | 3.97372 | + | 3.97372i | 0.177179 | + | 0.177179i | 0.790125 | − | 0.612946i | \(-0.210016\pi\) |
−0.612946 | + | 0.790125i | \(0.710016\pi\) | |||||||
\(504\) | 18.5885 | + | 32.1962i | 0.827996 | + | 1.43413i | ||||
\(505\) | −2.00000 | − | 4.00000i | −0.0889988 | − | 0.177998i | ||||
\(506\) | −2.19615 | + | 1.26795i | −0.0976309 | + | 0.0563672i | ||||
\(507\) | 16.9474i | 0.752662i | ||||||||
\(508\) | −4.32051 | − | 16.1244i | −0.191692 | − | 0.715403i | ||||
\(509\) | 6.57180 | − | 3.79423i | 0.291290 | − | 0.168176i | −0.347234 | − | 0.937779i | \(-0.612879\pi\) |
0.638523 | + | 0.769602i | \(0.279546\pi\) | |||||||
\(510\) | −10.3923 | − | 20.7846i | −0.460179 | − | 0.920358i | ||||
\(511\) | 31.5885 | − | 54.7128i | 1.39739 | − | 2.42035i | ||||
\(512\) | 16.0000 | + | 16.0000i | 0.707107 | + | 0.707107i | ||||
\(513\) | −24.5885 | −1.08561 | ||||||||
\(514\) | −11.5359 | + | 19.9808i | −0.508827 | + | 0.881314i | ||||
\(515\) | 26.9545 | − | 23.9019i | 1.18776 | − | 1.05324i | ||||
\(516\) | −8.19615 | − | 30.5885i | −0.360815 | − | 1.34658i | ||||
\(517\) | −3.00000 | − | 0.803848i | −0.131940 | − | 0.0353532i | ||||
\(518\) | 2.87564 | + | 2.87564i | 0.126349 | + | 0.126349i | ||||
\(519\) | 3.46410 | − | 3.46410i | 0.152057 | − | 0.152057i | ||||
\(520\) | 11.3205 | + | 0.679492i | 0.496437 | + | 0.0297977i | ||||
\(521\) | − | 14.6603i | − | 0.642277i | −0.947032 | − | 0.321139i | \(-0.895934\pi\) | ||
0.947032 | − | 0.321139i | \(-0.104066\pi\) | |||||||
\(522\) | −3.50962 | − | 13.0981i | −0.153612 | − | 0.573287i | ||||
\(523\) | −1.56218 | − | 1.56218i | −0.0683093 | − | 0.0683093i | 0.672127 | − | 0.740436i | \(-0.265381\pi\) |
−0.740436 | + | 0.672127i | \(0.765381\pi\) | |||||||
\(524\) | − | 15.6077i | − | 0.681825i | ||||||
\(525\) | −14.1340 | + | 35.2128i | −0.616857 | + | 1.53681i | ||||
\(526\) | − | 19.8564i | − | 0.865780i | ||||||
\(527\) | −33.5885 | − | 9.00000i | −1.46314 | − | 0.392046i | ||||
\(528\) | 6.92820 | + | 12.0000i | 0.301511 | + | 0.522233i | ||||
\(529\) | 19.2224 | + | 11.0981i | 0.835758 | + | 0.482525i | ||||
\(530\) | −23.1962 | − | 1.39230i | −1.00758 | − | 0.0604779i | ||||
\(531\) | − | 5.41154i | − | 0.234841i | ||||||
\(532\) | 40.0526 | + | 10.7321i | 1.73650 | + | 0.465293i | ||||
\(533\) | −3.00000 | − | 11.1962i | −0.129944 | − | 0.484959i | ||||
\(534\) | −6.29423 | + | 1.68653i | −0.272378 | + | 0.0729834i | ||||
\(535\) | 18.8923 | − | 3.86603i | 0.816786 | − | 0.167143i | ||||
\(536\) | −18.5885 | + | 10.7321i | −0.802899 | + | 0.463554i | ||||
\(537\) | −9.58846 | + | 5.53590i | −0.413772 | + | 0.238892i | ||||
\(538\) | −1.36603 | − | 0.366025i | −0.0588935 | − | 0.0157805i | ||||
\(539\) | − | 24.3923i | − | 1.05065i | ||||||
\(540\) | −20.7846 | + | 10.3923i | −0.894427 | + | 0.447214i | ||||
\(541\) | 12.4641i | 0.535874i | 0.963436 | + | 0.267937i | \(0.0863418\pi\) | ||||
−0.963436 | + | 0.267937i | \(0.913658\pi\) | |||||||
\(542\) | 1.67949 | − | 6.26795i | 0.0721404 | − | 0.269231i | ||||
\(543\) | 4.50000 | − | 2.59808i | 0.193113 | − | 0.111494i | ||||
\(544\) | −12.0000 | + | 20.7846i | −0.514496 | + | 0.891133i | ||||
\(545\) | 10.6699 | − | 16.1603i | 0.457047 | − | 0.692229i | ||||
\(546\) | −4.98076 | − | 18.5885i | −0.213157 | − | 0.795513i | ||||
\(547\) | −7.11474 | − | 26.5526i | −0.304204 | − | 1.13531i | −0.933628 | − | 0.358243i | \(-0.883376\pi\) |
0.629424 | − | 0.777062i | \(-0.283291\pi\) | |||||||
\(548\) | 6.92820 | − | 25.8564i | 0.295958 | − | 1.10453i | ||||
\(549\) | −38.0885 | + | 21.9904i | −1.62558 | + | 0.938527i | ||||
\(550\) | −5.26795 | + | 13.1244i | −0.224626 | + | 0.559624i | ||||
\(551\) | −13.0981 | − | 7.56218i | −0.557997 | − | 0.322160i | ||||
\(552\) | −2.19615 | + | 3.80385i | −0.0934745 | + | 0.161903i | ||||
\(553\) | 9.29423 | + | 2.49038i | 0.395231 | + | 0.105902i | ||||
\(554\) | 12.9282 | 0.549267 | ||||||||
\(555\) | −1.90192 | + | 1.68653i | −0.0807322 | + | 0.0715894i | ||||
\(556\) | − | 13.8564i | − | 0.587643i | ||||||
\(557\) | 0.803848 | + | 0.803848i | 0.0340601 | + | 0.0340601i | 0.723932 | − | 0.689872i | \(-0.242333\pi\) |
−0.689872 | + | 0.723932i | \(0.742333\pi\) | |||||||
\(558\) | −9.00000 | + | 33.5885i | −0.381000 | + | 1.42191i | ||||
\(559\) | 16.3923i | 0.693321i | ||||||||
\(560\) | 38.3923 | − | 7.85641i | 1.62237 | − | 0.331994i | ||||
\(561\) | −10.3923 | + | 10.3923i | −0.438763 | + | 0.438763i | ||||
\(562\) | −2.07180 | + | 2.07180i | −0.0873935 | + | 0.0873935i | ||||
\(563\) | 32.0885 | + | 8.59808i | 1.35237 | + | 0.362366i | 0.861008 | − | 0.508591i | \(-0.169834\pi\) |
0.491359 | + | 0.870957i | \(0.336500\pi\) | |||||||
\(564\) | −5.19615 | + | 1.39230i | −0.218797 | + | 0.0586266i | ||||
\(565\) | 2.66025 | + | 3.00000i | 0.111918 | + | 0.126211i | ||||
\(566\) | 5.70577 | + | 3.29423i | 0.239831 | + | 0.138467i | ||||
\(567\) | 27.8827 | + | 27.8827i | 1.17096 | + | 1.17096i | ||||
\(568\) | 24.0000 | + | 24.0000i | 1.00702 | + | 1.00702i | ||||
\(569\) | 1.26795 | − | 2.19615i | 0.0531552 | − | 0.0920675i | −0.838223 | − | 0.545327i | \(-0.816406\pi\) |
0.891379 | + | 0.453259i | \(0.149739\pi\) | |||||||
\(570\) | −8.19615 | + | 24.5885i | −0.343299 | + | 1.02990i | ||||
\(571\) | 3.00000 | − | 1.73205i | 0.125546 | − | 0.0724841i | −0.435912 | − | 0.899989i | \(-0.643574\pi\) |
0.561458 | + | 0.827505i | \(0.310241\pi\) | |||||||
\(572\) | −1.85641 | − | 6.92820i | −0.0776203 | − | 0.289683i | ||||
\(573\) | − | 32.1962i | − | 1.34501i | ||||||
\(574\) | −20.0263 | − | 34.6865i | −0.835881 | − | 1.44779i | ||||
\(575\) | −4.43782 | + | 0.633975i | −0.185070 | + | 0.0264386i | ||||
\(576\) | 20.7846 | + | 12.0000i | 0.866025 | + | 0.500000i | ||||
\(577\) | 5.39230 | + | 5.39230i | 0.224485 | + | 0.224485i | 0.810384 | − | 0.585899i | \(-0.199259\pi\) |
−0.585899 | + | 0.810384i | \(0.699259\pi\) | |||||||
\(578\) | −1.36603 | − | 0.366025i | −0.0568192 | − | 0.0152246i | ||||
\(579\) | 6.33975 | + | 23.6603i | 0.263471 | + | 0.983287i | ||||
\(580\) | −14.2679 | − | 0.856406i | −0.592444 | − | 0.0355603i | ||||
\(581\) | −25.6962 | − | 44.5070i | −1.06606 | − | 1.84646i | ||||
\(582\) | −15.0000 | + | 8.66025i | −0.621770 | + | 0.358979i | ||||
\(583\) | 3.80385 | + | 14.1962i | 0.157539 | + | 0.587945i | ||||
\(584\) | − | 40.7846i | − | 1.68768i | ||||||
\(585\) | 11.7846 | − | 2.41154i | 0.487234 | − | 0.0997050i | ||||
\(586\) | 0.803848 | − | 1.39230i | 0.0332066 | − | 0.0575156i | ||||
\(587\) | 32.6506 | − | 8.74871i | 1.34764 | − | 0.361098i | 0.488374 | − | 0.872634i | \(-0.337590\pi\) |
0.859262 | + | 0.511536i | \(0.170923\pi\) | |||||||
\(588\) | −21.1244 | − | 36.5885i | −0.871154 | − | 1.50888i | ||||
\(589\) | 19.3923 | + | 33.5885i | 0.799046 | + | 1.38399i | ||||
\(590\) | −5.41154 | − | 1.80385i | −0.222790 | − | 0.0742632i | ||||
\(591\) | −7.60770 | + | 28.3923i | −0.312939 | + | 1.16790i | ||||
\(592\) | 2.53590 | + | 0.679492i | 0.104225 | + | 0.0279269i | ||||
\(593\) | 14.6603 | + | 14.6603i | 0.602024 | + | 0.602024i | 0.940849 | − | 0.338825i | \(-0.110029\pi\) |
−0.338825 | + | 0.940849i | \(0.610029\pi\) | |||||||
\(594\) | 10.3923 | + | 10.3923i | 0.426401 | + | 0.426401i | ||||
\(595\) | 18.5885 | + | 37.1769i | 0.762052 | + | 1.52410i | ||||
\(596\) | −14.0000 | −0.573462 | ||||||||
\(597\) | −6.29423 | + | 3.63397i | −0.257606 | + | 0.148729i | ||||
\(598\) | 1.60770 | − | 1.60770i | 0.0657435 | − | 0.0657435i | ||||
\(599\) | −15.2942 | − | 26.4904i | −0.624905 | − | 1.08237i | −0.988559 | − | 0.150834i | \(-0.951804\pi\) |
0.363654 | − | 0.931534i | \(-0.381529\pi\) | |||||||
\(600\) | 3.46410 | + | 24.2487i | 0.141421 | + | 0.989949i | ||||
\(601\) | −21.1962 | + | 36.7128i | −0.864609 | + | 1.49755i | 0.00282571 | + | 0.999996i | \(0.499101\pi\) |
−0.867435 | + | 0.497551i | \(0.834233\pi\) | |||||||
\(602\) | 14.6603 | + | 54.7128i | 0.597507 | + | 2.22993i | ||||
\(603\) | −16.0981 | + | 16.0981i | −0.655564 | + | 0.655564i | ||||
\(604\) | −27.7128 | + | 16.0000i | −1.12762 | + | 0.651031i | ||||
\(605\) | −15.6244 | − | 0.937822i | −0.635220 | − | 0.0381279i | ||||
\(606\) | −1.26795 | + | 4.73205i | −0.0515069 | + | 0.192226i | ||||
\(607\) | 7.57180 | − | 28.2583i | 0.307330 | − | 1.14697i | −0.623592 | − | 0.781750i | \(-0.714327\pi\) |
0.930921 | − | 0.365220i | \(-0.119006\pi\) | |||||||
\(608\) | 25.8564 | − | 6.92820i | 1.04862 | − | 0.280976i | ||||
\(609\) | 6.27757 | + | 23.4282i | 0.254380 | + | 0.949359i | ||||
\(610\) | 9.29423 | + | 45.4186i | 0.376312 | + | 1.83894i | ||||
\(611\) | 2.78461 | 0.112653 | ||||||||
\(612\) | −6.58846 | + | 24.5885i | −0.266323 | + | 0.993929i | ||||
\(613\) | 23.7846 | + | 23.7846i | 0.960651 | + | 0.960651i | 0.999255 | − | 0.0386033i | \(-0.0122909\pi\) |
−0.0386033 | + | 0.999255i | \(0.512291\pi\) | |||||||
\(614\) | −14.3660 | − | 24.8827i | −0.579766 | − | 1.00418i | ||||
\(615\) | 22.3923 | − | 11.1962i | 0.902945 | − | 0.451472i | ||||
\(616\) | −12.3923 | − | 21.4641i | −0.499300 | − | 0.864813i | ||||
\(617\) | 28.0526 | + | 7.51666i | 1.12935 | + | 0.302609i | 0.774663 | − | 0.632374i | \(-0.217920\pi\) |
0.354691 | + | 0.934984i | \(0.384586\pi\) | |||||||
\(618\) | −39.4641 | −1.58748 | ||||||||
\(619\) | −1.90192 | + | 3.29423i | −0.0764448 | + | 0.132406i | −0.901714 | − | 0.432334i | \(-0.857690\pi\) |
0.825269 | + | 0.564740i | \(0.191024\pi\) | |||||||
\(620\) | 30.5885 | + | 20.1962i | 1.22846 | + | 0.811097i | ||||
\(621\) | −1.20577 | + | 4.50000i | −0.0483859 | + | 0.180579i | ||||
\(622\) | −5.19615 | − | 19.3923i | −0.208347 | − | 0.777561i | ||||
\(623\) | 11.2583 | − | 3.01666i | 0.451055 | − | 0.120860i | ||||
\(624\) | −8.78461 | − | 8.78461i | −0.351666 | − | 0.351666i | ||||
\(625\) | −17.2846 | + | 18.0622i | −0.691384 | + | 0.722487i | ||||
\(626\) | −21.1769 | −0.846400 | ||||||||
\(627\) | 16.3923 | 0.654646 | ||||||||
\(628\) | −18.0000 | − | 18.0000i | −0.718278 | − | 0.718278i | ||||
\(629\) | 2.78461i | 0.111030i | ||||||||
\(630\) | 37.1769 | − | 18.5885i | 1.48116 | − | 0.740582i | ||||
\(631\) | −18.0000 | −0.716569 | −0.358284 | − | 0.933613i | \(-0.616638\pi\) | ||||
−0.358284 | + | 0.933613i | \(0.616638\pi\) | |||||||
\(632\) | 6.00000 | − | 1.60770i | 0.238667 | − | 0.0639507i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20.0000i | 0.794301i | ||||||||
\(635\) | −18.2846 | + | 3.74167i | −0.725603 | + | 0.148484i | ||||
\(636\) | 18.0000 | + | 18.0000i | 0.713746 | + | 0.713746i | ||||
\(637\) | 5.66025 | + | 21.1244i | 0.224267 | + | 0.836977i | ||||
\(638\) | 2.33975 | + | 8.73205i | 0.0926314 | + | 0.345705i | ||||
\(639\) | 31.1769 | + | 18.0000i | 1.23334 | + | 0.712069i | ||||
\(640\) | 18.9282 | − | 16.7846i | 0.748203 | − | 0.663470i | ||||
\(641\) | −36.1865 | − | 20.8923i | −1.42928 | − | 0.825196i | −0.432218 | − | 0.901769i | \(-0.642269\pi\) |
−0.997064 | + | 0.0765727i | \(0.975602\pi\) | |||||||
\(642\) | −18.2942 | − | 10.5622i | −0.722016 | − | 0.416856i | ||||
\(643\) | 6.91154 | − | 25.7942i | 0.272565 | − | 1.01723i | −0.684891 | − | 0.728645i | \(-0.740150\pi\) |
0.957456 | − | 0.288580i | \(-0.0931830\pi\) | |||||||
\(644\) | 3.92820 | − | 6.80385i | 0.154793 | − | 0.268109i | ||||
\(645\) | −34.6865 | + | 7.09808i | −1.36578 | + | 0.279486i | ||||
\(646\) | 14.1962 | + | 24.5885i | 0.558540 | + | 0.967420i | ||||
\(647\) | −19.6865 | + | 19.6865i | −0.773957 | + | 0.773957i | −0.978796 | − | 0.204838i | \(-0.934333\pi\) |
0.204838 | + | 0.978796i | \(0.434333\pi\) | |||||||
\(648\) | 24.5885 | + | 6.58846i | 0.965926 | + | 0.258819i | ||||
\(649\) | 3.60770i | 0.141614i | ||||||||
\(650\) | 1.51666 | − | 12.5885i | 0.0594883 | − | 0.493760i | ||||
\(651\) | 16.0981 | − | 60.0788i | 0.630933 | − | 2.35468i | ||||
\(652\) | 4.73205 | + | 17.6603i | 0.185321 | + | 0.691629i | ||||
\(653\) | −29.2224 | − | 7.83013i | −1.14356 | − | 0.306417i | −0.363180 | − | 0.931719i | \(-0.618309\pi\) |
−0.780382 | + | 0.625303i | \(0.784976\pi\) | |||||||
\(654\) | −20.4904 | + | 5.49038i | −0.801237 | + | 0.214691i | ||||
\(655\) | −17.4186 | − | 1.04552i | −0.680600 | − | 0.0408517i | ||||
\(656\) | −22.3923 | − | 12.9282i | −0.874273 | − | 0.504762i | ||||
\(657\) | −11.1962 | − | 41.7846i | −0.436804 | − | 1.63017i | ||||
\(658\) | 9.29423 | − | 2.49038i | 0.362327 | − | 0.0970852i | ||||
\(659\) | 10.7321 | + | 6.19615i | 0.418061 | + | 0.241368i | 0.694248 | − | 0.719736i | \(-0.255737\pi\) |
−0.276186 | + | 0.961104i | \(0.589071\pi\) | |||||||
\(660\) | 13.8564 | − | 6.92820i | 0.539360 | − | 0.269680i | ||||
\(661\) | −6.00000 | + | 3.46410i | −0.233373 | + | 0.134738i | −0.612127 | − | 0.790759i | \(-0.709686\pi\) |
0.378754 | + | 0.925497i | \(0.376353\pi\) | |||||||
\(662\) | 0.588457 | − | 0.588457i | 0.0228710 | − | 0.0228710i | ||||
\(663\) | 6.58846 | − | 11.4115i | 0.255874 | − | 0.443188i | ||||
\(664\) | −28.7321 | − | 16.5885i | −1.11502 | − | 0.643757i | ||||
\(665\) | 14.6603 | − | 43.9808i | 0.568500 | − | 1.70550i | ||||
\(666\) | 2.78461 | 0.107901 | ||||||||
\(667\) | −2.02628 | + | 2.02628i | −0.0784579 | + | 0.0784579i | ||||
\(668\) | −26.1962 | − | 26.1962i | −1.01356 | − | 1.01356i | ||||
\(669\) | −20.9545 | + | 20.9545i | −0.810147 | + | 0.810147i | ||||
\(670\) | 10.7321 | + | 21.4641i | 0.414615 | + | 0.829231i | ||||
\(671\) | 25.3923 | − | 14.6603i | 0.980259 | − | 0.565953i | ||||
\(672\) | −37.1769 | − | 21.4641i | −1.43413 | − | 0.827996i | ||||
\(673\) | −1.24871 | − | 4.66025i | −0.0481343 | − | 0.179640i | 0.937674 | − | 0.347517i | \(-0.112975\pi\) |
−0.985808 | + | 0.167878i | \(0.946309\pi\) | |||||||
\(674\) | −0.339746 | − | 0.196152i | −0.0130865 | − | 0.00755551i | ||||
\(675\) | 10.2058 | + | 23.8923i | 0.392820 | + | 0.919615i | ||||
\(676\) | −9.78461 | − | 16.9474i | −0.376331 | − | 0.651825i | ||||
\(677\) | −39.3205 | + | 10.5359i | −1.51121 | + | 0.404927i | −0.916837 | − | 0.399262i | \(-0.869266\pi\) |
−0.594373 | + | 0.804189i | \(0.702600\pi\) | |||||||
\(678\) | − | 4.39230i | − | 0.168685i | ||||||
\(679\) | 26.8301 | − | 15.4904i | 1.02965 | − | 0.594466i | ||||
\(680\) | 22.3923 | + | 14.7846i | 0.858706 | + | 0.566964i | ||||
\(681\) | 12.8038 | + | 12.8038i | 0.490645 | + | 0.490645i | ||||
\(682\) | 6.00000 | − | 22.3923i | 0.229752 | − | 0.857446i | ||||
\(683\) | −7.00000 | + | 7.00000i | −0.267848 | + | 0.267848i | −0.828232 | − | 0.560385i | \(-0.810653\pi\) |
0.560385 | + | 0.828232i | \(0.310653\pi\) | |||||||
\(684\) | 24.5885 | − | 14.1962i | 0.940163 | − | 0.542803i | ||||
\(685\) | −28.3923 | − | 9.46410i | −1.08481 | − | 0.361605i | ||||
\(686\) | 16.0981 | + | 27.8827i | 0.614627 | + | 1.06457i | ||||
\(687\) | 9.99038 | − | 17.3038i | 0.381157 | − | 0.660183i | ||||
\(688\) | 25.8564 | + | 25.8564i | 0.985766 | + | 0.985766i | ||||
\(689\) | −6.58846 | − | 11.4115i | −0.251000 | − | 0.434745i | ||||
\(690\) | 4.09808 | + | 2.70577i | 0.156011 | + | 0.103007i | ||||
\(691\) | 40.4711 | + | 23.3660i | 1.53959 | + | 0.888885i | 0.998862 | + | 0.0476910i | \(0.0151863\pi\) |
0.540733 | + | 0.841194i | \(0.318147\pi\) | |||||||
\(692\) | −1.46410 | + | 5.46410i | −0.0556568 | + | 0.207714i | ||||
\(693\) | −18.5885 | − | 18.5885i | −0.706117 | − | 0.706117i | ||||
\(694\) | −9.00000 | − | 5.19615i | −0.341635 | − | 0.197243i | ||||
\(695\) | −15.4641 | − | 0.928203i | −0.586587 | − | 0.0352088i | ||||
\(696\) | 11.0718 | + | 11.0718i | 0.419675 | + | 0.419675i | ||||
\(697\) | 7.09808 | − | 26.4904i | 0.268859 | − | 1.00339i | ||||
\(698\) | −36.4641 | − | 36.4641i | −1.38019 | − | 1.38019i | ||||
\(699\) | 11.4904 | − | 42.8827i | 0.434606 | − | 1.62197i | ||||
\(700\) | −6.19615 | − | 43.3731i | −0.234193 | − | 1.63935i | ||||
\(701\) | 50.1769 | 1.89516 | 0.947578 | − | 0.319525i | \(-0.103523\pi\) | ||||
0.947578 | + | 0.319525i | \(0.103523\pi\) | |||||||
\(702\) | −11.4115 | − | 6.58846i | −0.430701 | − | 0.248665i | ||||
\(703\) | 2.19615 | − | 2.19615i | 0.0828295 | − | 0.0828295i | ||||
\(704\) | −13.8564 | − | 8.00000i | −0.522233 | − | 0.301511i | ||||
\(705\) | 1.20577 | + | 5.89230i | 0.0454120 | + | 0.221917i | ||||
\(706\) | − | 18.9282i | − | 0.712372i | ||||||
\(707\) | 2.26795 | − | 8.46410i | 0.0852950 | − | 0.318325i | ||||
\(708\) | 3.12436 | + | 5.41154i | 0.117420 | + | 0.203378i | ||||
\(709\) | −9.57180 | + | 16.5788i | −0.359476 | + | 0.622631i | −0.987873 | − | 0.155261i | \(-0.950378\pi\) |
0.628397 | + | 0.777893i | \(0.283711\pi\) | |||||||
\(710\) | 28.3923 | − | 25.1769i | 1.06554 | − | 0.944873i | ||||
\(711\) | 5.70577 | − | 3.29423i | 0.213983 | − | 0.123543i | ||||
\(712\) | 5.32051 | − | 5.32051i | 0.199394 | − | 0.199394i | ||||
\(713\) | 7.09808 | − | 1.90192i | 0.265825 | − | 0.0712276i | ||||
\(714\) | 11.7846 | − | 43.9808i | 0.441028 | − | 1.64594i | ||||
\(715\) | −7.85641 | + | 1.60770i | −0.293813 | + | 0.0601244i | ||||
\(716\) | 6.39230 | − | 11.0718i | 0.238892 | − | 0.413772i | ||||
\(717\) | −16.3923 | + | 28.3923i | −0.612182 | + | 1.06033i | ||||
\(718\) | 0.803848 | − | 3.00000i | 0.0299993 | − | 0.111959i | ||||
\(719\) | 1.51666 | 0.0565619 | 0.0282809 | − | 0.999600i | \(-0.490997\pi\) | ||||
0.0282809 | + | 0.999600i | \(0.490997\pi\) | |||||||
\(720\) | 14.7846 | − | 22.3923i | 0.550990 | − | 0.834512i | ||||
\(721\) | 70.5885 | 2.62885 | ||||||||
\(722\) | 1.24167 | − | 4.63397i | 0.0462102 | − | 0.172459i | ||||
\(723\) | 32.5692 | 1.21126 | ||||||||
\(724\) | −3.00000 | + | 5.19615i | −0.111494 | + | 0.193113i | ||||
\(725\) | −1.91154 | + | 15.8660i | −0.0709929 | + | 0.589249i | ||||
\(726\) | 12.1244 | + | 12.1244i | 0.449977 | + | 0.449977i | ||||
\(727\) | 2.86603 | − | 0.767949i | 0.106295 | − | 0.0284817i | −0.205279 | − | 0.978703i | \(-0.565810\pi\) |
0.311574 | + | 0.950222i | \(0.399144\pi\) | |||||||
\(728\) | 15.7128 | + | 15.7128i | 0.582356 | + | 0.582356i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −45.5167 | − | 2.73205i | −1.68465 | − | 0.101118i | ||||
\(731\) | −19.3923 | + | 33.5885i | −0.717250 | + | 1.24231i | ||||
\(732\) | 25.3923 | − | 43.9808i | 0.938527 | − | 1.62558i | ||||
\(733\) | 2.83013 | − | 10.5622i | 0.104533 | − | 0.390123i | −0.893759 | − | 0.448548i | \(-0.851941\pi\) |
0.998292 | + | 0.0584252i | \(0.0186079\pi\) | |||||||
\(734\) | 14.0000i | 0.516749i | ||||||||
\(735\) | −42.2487 | + | 21.1244i | −1.55837 | + | 0.779184i | ||||
\(736\) | − | 5.07180i | − | 0.186949i | ||||||
\(737\) | 10.7321 | − | 10.7321i | 0.395320 | − | 0.395320i | ||||
\(738\) | −26.4904 | − | 7.09808i | −0.975124 | − | 0.261284i | ||||
\(739\) | 22.7321 | 0.836212 | 0.418106 | − | 0.908398i | \(-0.362694\pi\) | ||||
0.418106 | + | 0.908398i | \(0.362694\pi\) | |||||||
\(740\) | 0.928203 | − | 2.78461i | 0.0341214 | − | 0.102364i | ||||
\(741\) | −14.1962 | + | 3.80385i | −0.521509 | + | 0.139738i | ||||
\(742\) | −32.1962 | − | 32.1962i | −1.18196 | − | 1.18196i | ||||
\(743\) | −6.82051 | + | 25.4545i | −0.250220 | + | 0.933834i | 0.720467 | + | 0.693489i | \(0.243927\pi\) |
−0.970687 | + | 0.240345i | \(0.922739\pi\) | |||||||
\(744\) | −10.3923 | − | 38.7846i | −0.381000 | − | 1.42191i | ||||
\(745\) | −0.937822 | + | 15.6244i | −0.0343591 | + | 0.572432i | ||||
\(746\) | 4.60770 | + | 2.66025i | 0.168700 | + | 0.0973988i | ||||
\(747\) | −33.9904 | − | 9.10770i | −1.24364 | − | 0.333233i | ||||
\(748\) | 4.39230 | − | 16.3923i | 0.160599 | − | 0.599362i | ||||
\(749\) | 32.7224 | + | 18.8923i | 1.19565 | + | 0.690310i | ||||
\(750\) | 27.2942 | − | 2.24167i | 0.996644 | − | 0.0818542i | ||||
\(751\) | −6.80385 | − | 11.7846i | −0.248276 | − | 0.430027i | 0.714772 | − | 0.699358i | \(-0.246531\pi\) |
−0.963048 | + | 0.269331i | \(0.913197\pi\) | |||||||
\(752\) | 4.39230 | − | 4.39230i | 0.160171 | − | 0.160171i | ||||
\(753\) | −23.0263 | − | 39.8827i | −0.839124 | − | 1.45341i | ||||
\(754\) | −4.05256 | − | 7.01924i | −0.147585 | − | 0.255626i | ||||
\(755\) | 16.0000 | + | 32.0000i | 0.582300 | + | 1.16460i | ||||
\(756\) | −43.9808 | − | 11.7846i | −1.59956 | − | 0.428602i | ||||
\(757\) | 34.0526 | − | 34.0526i | 1.23766 | − | 1.23766i | 0.276707 | − | 0.960954i | \(-0.410757\pi\) |
0.960954 | − | 0.276707i | \(-0.0892431\pi\) | |||||||
\(758\) | −12.1244 | + | 45.2487i | −0.440376 | + | 1.64351i | ||||
\(759\) | 0.803848 | − | 3.00000i | 0.0291778 | − | 0.108893i | ||||
\(760\) | −6.00000 | − | 29.3205i | −0.217643 | − | 1.06357i | ||||
\(761\) | 21.4808 | − | 12.4019i | 0.778677 | − | 0.449569i | −0.0572842 | − | 0.998358i | \(-0.518244\pi\) |
0.835961 | + | 0.548789i | \(0.184911\pi\) | |||||||
\(762\) | 17.7058 | + | 10.2224i | 0.641412 | + | 0.370320i | ||||
\(763\) | 36.6506 | − | 9.82051i | 1.32684 | − | 0.355526i | ||||
\(764\) | 18.5885 | + | 32.1962i | 0.672507 | + | 1.16482i | ||||
\(765\) | 27.0000 | + | 9.00000i | 0.976187 | + | 0.325396i | ||||
\(766\) | −35.1962 | − | 20.3205i | −1.27169 | − | 0.734210i | ||||
\(767\) | −0.837169 | − | 3.12436i | −0.0302284 | − | 0.112814i | ||||
\(768\) | −27.7128 | −1.00000 | ||||||||
\(769\) | −29.9378 | + | 17.2846i | −1.07959 | + | 0.623299i | −0.930785 | − | 0.365568i | \(-0.880875\pi\) |
−0.148801 | + | 0.988867i | \(0.547541\pi\) | |||||||
\(770\) | −24.7846 | + | 12.3923i | −0.893175 | + | 0.446588i | ||||
\(771\) | −7.31347 | − | 27.2942i | −0.263388 | − | 0.982978i | ||||
\(772\) | −20.0000 | − | 20.0000i | −0.719816 | − | 0.719816i | ||||
\(773\) | −16.1962 | + | 16.1962i | −0.582535 | + | 0.582535i | −0.935599 | − | 0.353064i | \(-0.885140\pi\) |
0.353064 | + | 0.935599i | \(0.385140\pi\) | |||||||
\(774\) | 33.5885 | + | 19.3923i | 1.20731 | + | 0.697042i | ||||
\(775\) | 24.5885 | − | 32.7846i | 0.883243 | − | 1.17766i | ||||
\(776\) | 10.0000 | − | 17.3205i | 0.358979 | − | 0.621770i | ||||
\(777\) | −4.98076 | −0.178684 | ||||||||
\(778\) | 17.3923 | − | 17.3923i | 0.623544 | − | 0.623544i | ||||
\(779\) | −26.4904 | + | 15.2942i | −0.949116 | + | 0.547973i | ||||
\(780\) | −10.3923 | + | 9.21539i | −0.372104 | + | 0.329964i | ||||
\(781\) | −20.7846 | − | 12.0000i | −0.743732 | − | 0.429394i | ||||
\(782\) | 5.19615 | − | 1.39230i | 0.185814 | − | 0.0497887i | ||||
\(783\) | 14.3827 | + | 8.30385i | 0.513995 | + | 0.296755i | ||||
\(784\) | 42.2487 | + | 24.3923i | 1.50888 | + | 0.871154i | ||||
\(785\) | −21.2942 | + | 18.8827i | −0.760024 | + | 0.673952i | ||||
\(786\) | 13.5167 | + | 13.5167i | 0.482123 | + | 0.482123i | ||||
\(787\) | −38.9545 | − | 10.4378i | −1.38858 | − | 0.372068i | −0.514348 | − | 0.857582i | \(-0.671966\pi\) |
−0.874229 | + | 0.485513i | \(0.838633\pi\) | |||||||
\(788\) | −8.78461 | − | 32.7846i | −0.312939 | − | 1.16790i | ||||
\(789\) | 17.1962 | + | 17.1962i | 0.612199 | + | 0.612199i | ||||
\(790\) | −1.39230 | − | 6.80385i | −0.0495360 | − | 0.242070i | ||||
\(791\) | 7.85641i | 0.279342i | ||||||||
\(792\) | −16.3923 | − | 4.39230i | −0.582475 | − | 0.156074i | ||||
\(793\) | −18.5885 | + | 18.5885i | −0.660095 | + | 0.660095i | ||||
\(794\) | 0.803848 | + | 1.39230i | 0.0285275 | + | 0.0494111i | ||||
\(795\) | 21.2942 | − | 18.8827i | 0.755228 | − | 0.669700i | ||||
\(796\) | 4.19615 | − | 7.26795i | 0.148729 | − | 0.257606i | ||||
\(797\) | −5.92820 | + | 22.1244i | −0.209988 | + | 0.783685i | 0.777883 | + | 0.628409i | \(0.216293\pi\) |
−0.987871 | + | 0.155276i | \(0.950373\pi\) | |||||||
\(798\) | −43.9808 | + | 25.3923i | −1.55690 | + | 0.898878i | ||||
\(799\) | 5.70577 | + | 3.29423i | 0.201856 | + | 0.116541i | ||||
\(800\) | −17.4641 | − | 22.2487i | −0.617449 | − | 0.786611i | ||||
\(801\) | 3.99038 | − | 6.91154i | 0.140993 | − | 0.244207i | ||||
\(802\) | 13.2679 | + | 49.5167i | 0.468508 | + | 1.74849i | ||||
\(803\) | 7.46410 | + | 27.8564i | 0.263402 | + | 0.983031i | ||||
\(804\) | 6.80385 | − | 25.3923i | 0.239953 | − | 0.895518i | ||||
\(805\) | −7.33013 | − | 4.83975i | −0.258353 | − | 0.170579i | ||||
\(806\) | 20.7846i | 0.732107i | ||||||||
\(807\) | 1.50000 | − | 0.866025i | 0.0528025 | − | 0.0304855i | ||||
\(808\) | −1.46410 | − | 5.46410i | −0.0515069 | − | 0.192226i | ||||
\(809\) | 45.7128 | 1.60718 | 0.803588 | − | 0.595185i | \(-0.202921\pi\) | ||||
0.803588 | + | 0.595185i | \(0.202921\pi\) | |||||||
\(810\) | 9.00000 | − | 27.0000i | 0.316228 | − | 0.948683i | ||||
\(811\) | 16.7321i | 0.587542i | 0.955876 | + | 0.293771i | \(0.0949103\pi\) | ||||
−0.955876 | + | 0.293771i | \(0.905090\pi\) | |||||||
\(812\) | −19.8038 | − | 19.8038i | −0.694979 | − | 0.694979i | ||||
\(813\) | 3.97372 | + | 6.88269i | 0.139364 | + | 0.241386i | ||||
\(814\) | −1.85641 | −0.0650670 | ||||||||
\(815\) | 20.0263 | − | 4.09808i | 0.701490 | − | 0.143549i | ||||
\(816\) | −7.60770 | − | 28.3923i | −0.266323 | − | 0.993929i | ||||
\(817\) | 41.7846 | − | 11.1962i | 1.46186 | − | 0.391704i | ||||
\(818\) | 2.19615 | + | 8.19615i | 0.0767867 | + | 0.286572i | ||||
\(819\) | 20.4115 | + | 11.7846i | 0.713237 | + | 0.411788i | ||||
\(820\) | −15.9282 | + | 24.1244i | −0.556237 | + | 0.842459i | ||||
\(821\) | 14.2846 | − | 24.7417i | 0.498536 | − | 0.863490i | −0.501462 | − | 0.865180i | \(-0.667204\pi\) |
0.999999 | + | 0.00168929i | \(0.000537719\pi\) | |||||||
\(822\) | 16.3923 | + | 28.3923i | 0.571747 | + | 0.990295i | ||||
\(823\) | −11.0622 | − | 2.96410i | −0.385603 | − | 0.103322i | 0.0608092 | − | 0.998149i | \(-0.480632\pi\) |
−0.446412 | + | 0.894827i | \(0.647299\pi\) | |||||||
\(824\) | 39.4641 | − | 22.7846i | 1.37480 | − | 0.793739i | ||||
\(825\) | −6.80385 | − | 15.9282i | −0.236880 | − | 0.554549i | ||||
\(826\) | −5.58846 | − | 9.67949i | −0.194447 | − | 0.336793i | ||||
\(827\) | −9.29423 | − | 9.29423i | −0.323192 | − | 0.323192i | 0.526798 | − | 0.849990i | \(-0.323392\pi\) |
−0.849990 | + | 0.526798i | \(0.823392\pi\) | |||||||
\(828\) | −1.39230 | − | 5.19615i | −0.0483859 | − | 0.180579i | ||||
\(829\) | 25.0526 | 0.870111 | 0.435056 | − | 0.900404i | \(-0.356729\pi\) | ||||
0.435056 | + | 0.900404i | \(0.356729\pi\) | |||||||
\(830\) | −20.4378 | + | 30.9545i | −0.709407 | + | 1.07445i | ||||
\(831\) | −11.1962 | + | 11.1962i | −0.388390 | + | 0.388390i | ||||
\(832\) | 13.8564 | + | 3.71281i | 0.480384 | + | 0.128719i | ||||
\(833\) | −13.3923 | + | 49.9808i | −0.464016 | + | 1.73173i | ||||
\(834\) | 12.0000 | + | 12.0000i | 0.415526 | + | 0.415526i | ||||
\(835\) | −30.9904 | + | 27.4808i | −1.07247 | + | 0.951011i | ||||
\(836\) | −16.3923 | + | 9.46410i | −0.566940 | + | 0.327323i | ||||
\(837\) | −21.2942 | − | 36.8827i | −0.736036 | − | 1.27485i | ||||
\(838\) | 4.53590 | + | 16.9282i | 0.156690 | + | 0.584775i | ||||
\(839\) | −14.0263 | + | 24.2942i | −0.484241 | + | 0.838730i | −0.999836 | − | 0.0181024i | \(-0.994238\pi\) |
0.515595 | + | 0.856832i | \(0.327571\pi\) | |||||||
\(840\) | −26.4449 | + | 40.0526i | −0.912434 | + | 1.38194i | ||||
\(841\) | −9.39230 | − | 16.2679i | −0.323873 | − | 0.560964i | ||||
\(842\) | 5.32051 | − | 5.32051i | 0.183357 | − | 0.183357i | ||||
\(843\) | − | 3.58846i | − | 0.123593i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.5692 | + | 9.78461i | −0.673202 | + | 0.336601i | ||||
\(846\) | 3.29423 | − | 5.70577i | 0.113258 | − | 0.196168i | ||||
\(847\) | −21.6865 | − | 21.6865i | −0.745158 | − | 0.745158i | ||||
\(848\) | −28.3923 | − | 7.60770i | −0.974996 | − | 0.261249i | ||||
\(849\) | −7.79423 | + | 2.08846i | −0.267497 | + | 0.0716757i | ||||
\(850\) | 18.0000 | − | 24.0000i | 0.617395 | − | 0.823193i | ||||
\(851\) | −0.294229 | − | 0.509619i | −0.0100860 | − | 0.0174695i | ||||
\(852\) | −41.5692 | −1.42414 | ||||||||
\(853\) | −44.7846 | + | 12.0000i | −1.53340 | + | 0.410872i | −0.924125 | − | 0.382090i | \(-0.875204\pi\) |
−0.609271 | + | 0.792962i | \(0.708538\pi\) | |||||||
\(854\) | −45.4186 | + | 78.6673i | −1.55419 | + | 2.69194i | ||||
\(855\) | −14.1962 | − | 28.3923i | −0.485498 | − | 0.970996i | ||||
\(856\) | 24.3923 | 0.833712 | ||||||||
\(857\) | −7.48334 | − | 27.9282i | −0.255626 | − | 0.954009i | −0.967741 | − | 0.251947i | \(-0.918929\pi\) |
0.712115 | − | 0.702063i | \(-0.247737\pi\) | |||||||
\(858\) | 7.60770 | + | 4.39230i | 0.259722 | + | 0.149951i | ||||
\(859\) | 8.66025 | + | 15.0000i | 0.295484 | + | 0.511793i | 0.975097 | − | 0.221777i | \(-0.0711857\pi\) |
−0.679613 | + | 0.733571i | \(0.737852\pi\) | |||||||
\(860\) | 30.5885 | − | 27.1244i | 1.04306 | − | 0.924933i | ||||
\(861\) | 47.3827 | + | 12.6962i | 1.61480 | + | 0.432684i | ||||
\(862\) | 30.1244 | + | 8.07180i | 1.02604 | + | 0.274926i | ||||
\(863\) | 12.4186 | + | 12.4186i | 0.422734 | + | 0.422734i | 0.886144 | − | 0.463410i | \(-0.153374\pi\) |
−0.463410 | + | 0.886144i | \(0.653374\pi\) | |||||||
\(864\) | −28.3923 | + | 7.60770i | −0.965926 | + | 0.258819i | ||||
\(865\) | 6.00000 | + | 2.00000i | 0.204006 | + | 0.0680020i | ||||
\(866\) | 15.3923 | + | 26.6603i | 0.523052 | + | 0.905952i | ||||
\(867\) | 1.50000 | − | 0.866025i | 0.0509427 | − | 0.0294118i | ||||
\(868\) | 18.5885 | + | 69.3731i | 0.630933 | + | 2.35468i | ||||
\(869\) | −3.80385 | + | 2.19615i | −0.129037 | + | 0.0744994i | ||||
\(870\) | 13.0981 | − | 11.6147i | 0.444066 | − | 0.393776i | ||||
\(871\) | −6.80385 | + | 11.7846i | −0.230540 | + | 0.399306i | ||||
\(872\) | 17.3205 | − | 17.3205i | 0.586546 | − | 0.586546i | ||||
\(873\) | 5.49038 | − | 20.4904i | 0.185821 | − | 0.693494i | ||||
\(874\) | −5.19615 | − | 3.00000i | −0.175762 | − | 0.101477i | ||||
\(875\) | −48.8205 | + | 4.00962i | −1.65043 | + | 0.135550i | ||||
\(876\) | 35.3205 | + | 35.3205i | 1.19337 | + | 1.19337i | ||||
\(877\) | 24.1244 | + | 6.46410i | 0.814622 | + | 0.218277i | 0.641994 | − | 0.766710i | \(-0.278108\pi\) |
0.172628 | + | 0.984987i | \(0.444774\pi\) | |||||||
\(878\) | −18.7846 | + | 18.7846i | −0.633950 | + | 0.633950i | ||||
\(879\) | 0.509619 | + | 1.90192i | 0.0171890 | + | 0.0641503i | ||||
\(880\) | −9.85641 | + | 14.9282i | −0.332259 | + | 0.503230i | ||||
\(881\) | − | 2.07180i | − | 0.0698006i | −0.999391 | − | 0.0349003i | \(-0.988889\pi\) | ||
0.999391 | − | 0.0349003i | \(-0.0111114\pi\) | |||||||
\(882\) | 49.9808 | + | 13.3923i | 1.68294 | + | 0.450942i | ||||
\(883\) | −27.4186 | − | 27.4186i | −0.922709 | − | 0.922709i | 0.0745113 | − | 0.997220i | \(-0.476260\pi\) |
−0.997220 | + | 0.0745113i | \(0.976260\pi\) | |||||||
\(884\) | 15.2154i | 0.511749i | ||||||||
\(885\) | 6.24871 | − | 3.12436i | 0.210048 | − | 0.105024i | ||||
\(886\) | −54.5885 | −1.83394 | ||||||||
\(887\) | −1.56218 | − | 0.418584i | −0.0524528 | − | 0.0140547i | 0.232497 | − | 0.972597i | \(-0.425310\pi\) |
−0.284950 | + | 0.958542i | \(0.591977\pi\) | |||||||
\(888\) | −2.78461 | + | 1.60770i | −0.0934454 | + | 0.0539507i | ||||
\(889\) | −31.6699 | − | 18.2846i | −1.06217 | − | 0.613246i | ||||
\(890\) | −5.58142 | − | 6.29423i | −0.187089 | − | 0.210983i | ||||
\(891\) | −18.0000 | −0.603023 | ||||||||
\(892\) | 8.85641 | − | 33.0526i | 0.296534 | − | 1.10668i | ||||
\(893\) | −1.90192 | − | 7.09808i | −0.0636455 | − | 0.237528i | ||||
\(894\) | 12.1244 | − | 12.1244i | 0.405499 | − | 0.405499i | ||||
\(895\) | −11.9282 | − | 7.87564i | −0.398716 | − | 0.263254i | ||||
\(896\) | 49.5692 | 1.65599 | ||||||||
\(897\) | 2.78461i | 0.0929754i | ||||||||
\(898\) | 12.0000 | − | 44.7846i | 0.400445 | − | 1.49448i | ||||
\(899\) | − | 26.1962i | − | 0.873691i | ||||||
\(900\) | −24.0000 | − | 18.0000i | −0.800000 | − | 0.600000i | ||||
\(901\) | − | 31.1769i | − | 1.03865i | ||||||
\(902\) | 17.6603 | + | 4.73205i | 0.588022 | + | 0.157560i | ||||
\(903\) | −60.0788 | − | 34.6865i | −1.99930 | − | 1.15430i | ||||
\(904\) | 2.53590 | + | 4.39230i | 0.0843427 | + | 0.146086i | ||||
\(905\) | 5.59808 | + | 3.69615i | 0.186086 | + | 0.122864i | ||||
\(906\) | 10.1436 | − | 37.8564i | 0.336998 | − | 1.25769i | ||||
\(907\) | −0.944864 | − | 3.52628i | −0.0313737 | − | 0.117088i | 0.948463 | − | 0.316887i | \(-0.102638\pi\) |
−0.979837 | + | 0.199799i | \(0.935971\pi\) | |||||||
\(908\) | −20.1962 | − | 5.41154i | −0.670233 | − | 0.179588i | ||||
\(909\) | −3.00000 | − | 5.19615i | −0.0995037 | − | 0.172345i | ||||
\(910\) | 18.5885 | − | 16.4833i | 0.616201 | − | 0.546417i | ||||
\(911\) | 23.4904 | + | 13.5622i | 0.778271 | + | 0.449335i | 0.835817 | − | 0.549008i | \(-0.184994\pi\) |
−0.0575461 | + | 0.998343i | \(0.518328\pi\) | |||||||
\(912\) | −16.3923 | + | 28.3923i | −0.542803 | + | 0.940163i | ||||
\(913\) | 22.6603 | + | 6.07180i | 0.749945 | + | 0.200947i | ||||
\(914\) | − | 14.3923i | − | 0.476055i | ||||||
\(915\) | −47.3827 | − | 31.2846i | −1.56642 | − | 1.03424i | ||||
\(916\) | 23.0718i | 0.762314i | ||||||||
\(917\) | −24.1769 | − | 24.1769i | −0.798392 | − | 0.798392i | ||||
\(918\) | −15.5885 | − | 27.0000i | −0.514496 | − | 0.891133i | ||||
\(919\) | − | 20.1962i | − | 0.666210i | −0.942890 | − | 0.333105i | \(-0.891904\pi\) | ||
0.942890 | − | 0.333105i | \(-0.108096\pi\) | |||||||
\(920\) | −5.66025 | − | 0.339746i | −0.186613 | − | 0.0112011i | ||||
\(921\) | 33.9904 | + | 9.10770i | 1.12002 | + | 0.300109i | ||||
\(922\) | −13.5885 | − | 13.5885i | −0.447512 | − | 0.447512i | ||||
\(923\) | 20.7846 | + | 5.56922i | 0.684134 | + | 0.183313i | ||||
\(924\) | 29.3205 | + | 7.85641i | 0.964574 | + | 0.258457i | ||||
\(925\) | −3.04552 | − | 1.22243i | −0.100136 | − | 0.0401933i | ||||
\(926\) | 4.80385 | − | 8.32051i | 0.157864 | − | 0.273429i | ||||
\(927\) | 34.1769 | − | 34.1769i | 1.12252 | − | 1.12252i | ||||
\(928\) | −17.4641 | − | 4.67949i | −0.573287 | − | 0.153612i | ||||
\(929\) | −2.19615 | + | 3.80385i | −0.0720534 | + | 0.124800i | −0.899801 | − | 0.436300i | \(-0.856289\pi\) |
0.827748 | + | 0.561100i | \(0.189622\pi\) | |||||||
\(930\) | −43.9808 | + | 9.00000i | −1.44219 | + | 0.295122i | ||||
\(931\) | 49.9808 | − | 28.8564i | 1.63805 | − | 0.945731i | ||||
\(932\) | 13.2679 | + | 49.5167i | 0.434606 | + | 1.62197i | ||||
\(933\) | 21.2942 | + | 12.2942i | 0.697142 | + | 0.402495i | ||||
\(934\) | −14.9090 | + | 8.60770i | −0.487836 | + | 0.281652i | ||||
\(935\) | −18.0000 | − | 6.00000i | −0.588663 | − | 0.196221i | ||||
\(936\) | 15.2154 | 0.497331 | ||||||||
\(937\) | −4.58846 | − | 4.58846i | −0.149898 | − | 0.149898i | 0.628174 | − | 0.778073i | \(-0.283802\pi\) |
−0.778073 | + | 0.628174i | \(0.783802\pi\) | |||||||
\(938\) | −12.1699 | + | 45.4186i | −0.397360 | + | 1.48297i | ||||
\(939\) | 18.3397 | − | 18.3397i | 0.598495 | − | 0.598495i | ||||
\(940\) | −4.60770 | − | 5.19615i | −0.150286 | − | 0.169480i | ||||
\(941\) | 4.40192 | + | 7.62436i | 0.143499 | + | 0.248547i | 0.928812 | − | 0.370552i | \(-0.120831\pi\) |
−0.785313 | + | 0.619099i | \(0.787498\pi\) | |||||||
\(942\) | 31.1769 | 1.01580 | ||||||||
\(943\) | 1.50000 | + | 5.59808i | 0.0488467 | + | 0.182298i | ||||
\(944\) | −6.24871 | − | 3.60770i | −0.203378 | − | 0.117420i | ||||
\(945\) | −16.0981 | + | 48.2942i | −0.523670 | + | 1.57101i | ||||
\(946\) | −22.3923 | − | 12.9282i | −0.728037 | − | 0.420332i | ||||
\(947\) | 23.0885 | − | 6.18653i | 0.750274 | − | 0.201035i | 0.136634 | − | 0.990622i | \(-0.456371\pi\) |
0.613640 | + | 0.789586i | \(0.289705\pi\) | |||||||
\(948\) | −3.80385 | + | 6.58846i | −0.123543 | + | 0.213983i | ||||
\(949\) | −12.9282 | − | 22.3923i | −0.419667 | − | 0.726885i | ||||
\(950\) | −33.1244 | + | 4.73205i | −1.07470 | + | 0.153528i | ||||
\(951\) | −17.3205 | − | 17.3205i | −0.561656 | − | 0.561656i | ||||
\(952\) | 13.6077 | + | 50.7846i | 0.441028 | + | 1.64594i | ||||
\(953\) | 24.9282 | + | 24.9282i | 0.807504 | + | 0.807504i | 0.984255 | − | 0.176752i | \(-0.0565590\pi\) |
−0.176752 | + | 0.984255i | \(0.556559\pi\) | |||||||
\(954\) | −31.1769 | −1.00939 | ||||||||
\(955\) | 37.1769 | − | 18.5885i | 1.20302 | − | 0.601508i | ||||
\(956\) | − | 37.8564i | − | 1.22436i | ||||||
\(957\) | −9.58846 | − | 5.53590i | −0.309951 | − | 0.178950i | ||||
\(958\) | 21.1244 | + | 21.1244i | 0.682497 | + | 0.682497i | ||||
\(959\) | −29.3205 | − | 50.7846i | −0.946809 | − | 1.63992i | ||||
\(960\) | −1.85641 | + | 30.9282i | −0.0599153 | + | 0.998203i | ||||
\(961\) | −18.0885 | + | 31.3301i | −0.583499 | + | 1.01065i | ||||
\(962\) | 1.60770 | − | 0.430781i | 0.0518342 | − | 0.0138889i | ||||
\(963\) | 24.9904 | − | 6.69615i | 0.805304 | − | 0.215780i | ||||
\(964\) | −32.5692 | + | 18.8038i | −1.04898 | + | 0.605631i | ||||
\(965\) | −23.6603 | + | 20.9808i | −0.761651 | + | 0.675395i | ||||
\(966\) | 2.49038 | + | 9.29423i | 0.0801267 | + | 0.299037i | ||||
\(967\) | −4.27757 | + | 15.9641i | −0.137557 | + | 0.513371i | 0.862417 | + | 0.506199i | \(0.168950\pi\) |
−0.999974 | + | 0.00717234i | \(0.997717\pi\) | |||||||
\(968\) | −19.1244 | − | 5.12436i | −0.614680 | − | 0.164703i | ||||
\(969\) | −33.5885 | − | 9.00000i | −1.07902 | − | 0.289122i | ||||
\(970\) | −18.6603 | − | 12.3205i | −0.599145 | − | 0.395588i | ||||
\(971\) | 29.8038 | 0.956451 | 0.478225 | − | 0.878237i | \(-0.341280\pi\) | ||||
0.478225 | + | 0.878237i | \(0.341280\pi\) | |||||||
\(972\) | −27.0000 | + | 15.5885i | −0.866025 | + | 0.500000i | ||||
\(973\) | −21.4641 | − | 21.4641i | −0.688108 | − | 0.688108i | ||||
\(974\) | 5.87564 | − | 3.39230i | 0.188268 | − | 0.108696i | ||||
\(975\) | 9.58846 | + | 12.2154i | 0.307076 | + | 0.391206i | ||||
\(976\) | 58.6410i | 1.87705i | ||||||||
\(977\) | −40.0526 | − | 10.7321i | −1.28139 | − | 0.343349i | −0.447009 | − | 0.894529i | \(-0.647511\pi\) |
−0.834386 | + | 0.551181i | \(0.814177\pi\) | |||||||
\(978\) | −19.3923 | − | 11.1962i | −0.620098 | − | 0.358013i | ||||
\(979\) | −2.66025 | + | 4.60770i | −0.0850221 | + | 0.147263i | ||||
\(980\) | 30.0526 | − | 45.5167i | 0.959994 | − | 1.45398i | ||||
\(981\) | 12.9904 | − | 22.5000i | 0.414751 | − | 0.718370i | ||||
\(982\) | 33.8564 | − | 9.07180i | 1.08040 | − | 0.289493i | ||||
\(983\) | 13.3301 | − | 3.57180i | 0.425165 | − | 0.113923i | −0.0398907 | − | 0.999204i | \(-0.512701\pi\) |
0.465056 | + | 0.885281i | \(0.346034\pi\) | |||||||
\(984\) | 30.5885 | − | 8.19615i | 0.975124 | − | 0.261284i | ||||
\(985\) | −37.1769 | + | 7.60770i | −1.18455 | + | 0.242401i | ||||
\(986\) | − | 19.1769i | − | 0.610717i | ||||||
\(987\) | −5.89230 | + | 10.2058i | −0.187554 | + | 0.324853i | ||||
\(988\) | 12.0000 | − | 12.0000i | 0.381771 | − | 0.381771i | ||||
\(989\) | − | 8.19615i | − | 0.260622i | ||||||
\(990\) | −6.00000 | + | 18.0000i | −0.190693 | + | 0.572078i | ||||
\(991\) | 10.1962 | 0.323891 | 0.161946 | − | 0.986800i | \(-0.448223\pi\) | ||||
0.161946 | + | 0.986800i | \(0.448223\pi\) | |||||||
\(992\) | 32.7846 | + | 32.7846i | 1.04091 | + | 1.04091i | ||||
\(993\) | 1.01924i | 0.0323445i | ||||||||
\(994\) | 74.3538 | 2.35836 | ||||||||
\(995\) | −7.83013 | − | 5.16987i | −0.248232 | − | 0.163896i | ||||
\(996\) | 39.2487 | − | 10.5167i | 1.24364 | − | 0.333233i | ||||
\(997\) | −1.77757 | − | 6.63397i | −0.0562961 | − | 0.210100i | 0.932048 | − | 0.362334i | \(-0.118020\pi\) |
−0.988345 | + | 0.152234i | \(0.951353\pi\) | |||||||
\(998\) | 36.5885 | − | 9.80385i | 1.15819 | − | 0.310335i | ||||
\(999\) | −2.41154 | + | 2.41154i | −0.0762978 | + | 0.0762978i |
(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 | 360.2.br.d.317.1 | yes | 4 | |
5.3 | odd | 4 | 360.2.br.c.173.1 | yes | 4 | ||
8.5 | even | 2 | 360.2.br.a.317.1 | yes | 4 | ||
9.5 | odd | 6 | 360.2.br.b.77.1 | yes | 4 | ||
40.13 | odd | 4 | 360.2.br.b.173.1 | yes | 4 | ||
45.23 | even | 12 | 360.2.br.a.293.1 | ✓ | 4 | ||
72.5 | odd | 6 | 360.2.br.c.77.1 | yes | 4 | ||
360.293 | even | 12 | inner | 360.2.br.d.293.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.br.a.293.1 | ✓ | 4 | 45.23 | even | 12 | ||
360.2.br.a.317.1 | yes | 4 | 8.5 | even | 2 | ||
360.2.br.b.77.1 | yes | 4 | 9.5 | odd | 6 | ||
360.2.br.b.173.1 | yes | 4 | 40.13 | odd | 4 | ||
360.2.br.c.77.1 | yes | 4 | 72.5 | odd | 6 | ||
360.2.br.c.173.1 | yes | 4 | 5.3 | odd | 4 | ||
360.2.br.d.293.1 | yes | 4 | 360.293 | even | 12 | inner | |
360.2.br.d.317.1 | yes | 4 | 1.1 | even | 1 | trivial |