Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [70,2,Mod(9,70)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(70, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("70.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 70 = 2 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 70.i (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.558952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 9.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 70.9 |
Dual form | 70.2.i.a.39.2 |
$q$-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 \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(57\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −2.59808 | + | 1.50000i | −1.50000 | + | 0.866025i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.23205 | + | 1.86603i | 0.550990 | + | 0.834512i | ||||
\(6\) | −3.00000 | −1.22474 | ||||||||
\(7\) | 0.866025 | − | 2.50000i | 0.327327 | − | 0.944911i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 3.00000 | − | 5.19615i | 1.00000 | − | 1.73205i | ||||
\(10\) | 0.133975 | + | 2.23205i | 0.0423665 | + | 0.705836i | ||||
\(11\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | −2.59808 | − | 1.50000i | −0.750000 | − | 0.433013i | ||||
\(13\) | − | 2.00000i | − | 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | 2.00000 | − | 1.73205i | 0.534522 | − | 0.462910i | ||||
\(15\) | −6.00000 | − | 3.00000i | −1.54919 | − | 0.774597i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.73205 | − | 1.00000i | 0.420084 | − | 0.242536i | −0.275029 | − | 0.961436i | \(-0.588688\pi\) |
0.695113 | + | 0.718900i | \(0.255354\pi\) | |||||||
\(18\) | 5.19615 | − | 3.00000i | 1.22474 | − | 0.707107i | ||||
\(19\) | −1.00000 | + | 1.73205i | −0.229416 | + | 0.397360i | −0.957635 | − | 0.287984i | \(-0.907015\pi\) |
0.728219 | + | 0.685344i | \(0.240348\pi\) | |||||||
\(20\) | −1.00000 | + | 2.00000i | −0.223607 | + | 0.447214i | ||||
\(21\) | 1.50000 | + | 7.79423i | 0.327327 | + | 1.70084i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.866025 | + | 0.500000i | 0.180579 | + | 0.104257i | 0.587565 | − | 0.809177i | \(-0.300087\pi\) |
−0.406986 | + | 0.913434i | \(0.633420\pi\) | |||||||
\(24\) | −1.50000 | − | 2.59808i | −0.306186 | − | 0.530330i | ||||
\(25\) | −1.96410 | + | 4.59808i | −0.392820 | + | 0.919615i | ||||
\(26\) | 1.00000 | − | 1.73205i | 0.196116 | − | 0.339683i | ||||
\(27\) | 9.00000i | 1.73205i | ||||||||
\(28\) | 2.59808 | − | 0.500000i | 0.490990 | − | 0.0944911i | ||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | −3.69615 | − | 5.59808i | −0.674822 | − | 1.02206i | ||||
\(31\) | −5.00000 | − | 8.66025i | −0.898027 | − | 1.55543i | −0.830014 | − | 0.557743i | \(-0.811667\pi\) |
−0.0680129 | − | 0.997684i | \(-0.521666\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 5.73205 | − | 1.46410i | 0.968893 | − | 0.247478i | ||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | −6.92820 | − | 4.00000i | −1.13899 | − | 0.657596i | −0.192809 | − | 0.981236i | \(-0.561760\pi\) |
−0.946180 | + | 0.323640i | \(0.895093\pi\) | |||||||
\(38\) | −1.73205 | + | 1.00000i | −0.280976 | + | 0.162221i | ||||
\(39\) | 3.00000 | + | 5.19615i | 0.480384 | + | 0.832050i | ||||
\(40\) | −1.86603 | + | 1.23205i | −0.295045 | + | 0.194804i | ||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | −2.59808 | + | 7.50000i | −0.400892 | + | 1.15728i | ||||
\(43\) | 5.00000i | 0.762493i | 0.924473 | + | 0.381246i | \(0.124505\pi\) | ||||
−0.924473 | + | 0.381246i | \(0.875495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13.3923 | − | 0.803848i | 1.99641 | − | 0.119831i | ||||
\(46\) | 0.500000 | + | 0.866025i | 0.0737210 | + | 0.127688i | ||||
\(47\) | 6.92820 | + | 4.00000i | 1.01058 | + | 0.583460i | 0.911362 | − | 0.411606i | \(-0.135032\pi\) |
0.0992202 | + | 0.995066i | \(0.468365\pi\) | |||||||
\(48\) | − | 3.00000i | − | 0.433013i | ||||||
\(49\) | −5.50000 | − | 4.33013i | −0.785714 | − | 0.618590i | ||||
\(50\) | −4.00000 | + | 3.00000i | −0.565685 | + | 0.424264i | ||||
\(51\) | −3.00000 | + | 5.19615i | −0.420084 | + | 0.727607i | ||||
\(52\) | 1.73205 | − | 1.00000i | 0.240192 | − | 0.138675i | ||||
\(53\) | −5.19615 | + | 3.00000i | −0.713746 | + | 0.412082i | −0.812447 | − | 0.583036i | \(-0.801865\pi\) |
0.0987002 | + | 0.995117i | \(0.468532\pi\) | |||||||
\(54\) | −4.50000 | + | 7.79423i | −0.612372 | + | 1.06066i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.50000 | + | 0.866025i | 0.334077 | + | 0.115728i | ||||
\(57\) | − | 6.00000i | − | 0.794719i | ||||||
\(58\) | 0.866025 | + | 0.500000i | 0.113715 | + | 0.0656532i | ||||
\(59\) | 1.00000 | + | 1.73205i | 0.130189 | + | 0.225494i | 0.923749 | − | 0.382998i | \(-0.125108\pi\) |
−0.793560 | + | 0.608492i | \(0.791775\pi\) | |||||||
\(60\) | −0.401924 | − | 6.69615i | −0.0518881 | − | 0.864470i | ||||
\(61\) | 4.50000 | − | 7.79423i | 0.576166 | − | 0.997949i | −0.419748 | − | 0.907641i | \(-0.637882\pi\) |
0.995914 | − | 0.0903080i | \(-0.0287851\pi\) | |||||||
\(62\) | − | 10.0000i | − | 1.27000i | ||||||
\(63\) | −10.3923 | − | 12.0000i | −1.30931 | − | 1.51186i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.73205 | − | 2.46410i | 0.462904 | − | 0.305634i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.06218 | − | 3.50000i | 0.740613 | − | 0.427593i | −0.0816792 | − | 0.996659i | \(-0.526028\pi\) |
0.822292 | + | 0.569066i | \(0.192695\pi\) | |||||||
\(68\) | 1.73205 | + | 1.00000i | 0.210042 | + | 0.121268i | ||||
\(69\) | −3.00000 | −0.361158 | ||||||||
\(70\) | 5.69615 | + | 1.59808i | 0.680820 | + | 0.191007i | ||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 5.19615 | + | 3.00000i | 0.612372 | + | 0.353553i | ||||
\(73\) | −8.66025 | + | 5.00000i | −1.01361 | + | 0.585206i | −0.912245 | − | 0.409644i | \(-0.865653\pi\) |
−0.101361 | + | 0.994850i | \(0.532320\pi\) | |||||||
\(74\) | −4.00000 | − | 6.92820i | −0.464991 | − | 0.805387i | ||||
\(75\) | −1.79423 | − | 14.8923i | −0.207180 | − | 1.71962i | ||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.00000i | 0.679366i | ||||||||
\(79\) | −5.00000 | + | 8.66025i | −0.562544 | + | 0.974355i | 0.434730 | + | 0.900561i | \(0.356844\pi\) |
−0.997274 | + | 0.0737937i | \(0.976489\pi\) | |||||||
\(80\) | −2.23205 | + | 0.133975i | −0.249551 | + | 0.0149788i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | −2.59808 | − | 1.50000i | −0.286910 | − | 0.165647i | ||||
\(83\) | − | 9.00000i | − | 0.987878i | −0.869496 | − | 0.493939i | \(-0.835557\pi\) | ||
0.869496 | − | 0.493939i | \(-0.164443\pi\) | |||||||
\(84\) | −6.00000 | + | 5.19615i | −0.654654 | + | 0.566947i | ||||
\(85\) | 4.00000 | + | 2.00000i | 0.433861 | + | 0.216930i | ||||
\(86\) | −2.50000 | + | 4.33013i | −0.269582 | + | 0.466930i | ||||
\(87\) | −2.59808 | + | 1.50000i | −0.278543 | + | 0.160817i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.50000 | + | 6.06218i | −0.370999 | + | 0.642590i | −0.989720 | − | 0.143022i | \(-0.954318\pi\) |
0.618720 | + | 0.785611i | \(0.287651\pi\) | |||||||
\(90\) | 12.0000 | + | 6.00000i | 1.26491 | + | 0.632456i | ||||
\(91\) | −5.00000 | − | 1.73205i | −0.524142 | − | 0.181568i | ||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | 25.9808 | + | 15.0000i | 2.69408 | + | 1.55543i | ||||
\(94\) | 4.00000 | + | 6.92820i | 0.412568 | + | 0.714590i | ||||
\(95\) | −4.46410 | + | 0.267949i | −0.458007 | + | 0.0274910i | ||||
\(96\) | 1.50000 | − | 2.59808i | 0.153093 | − | 0.265165i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | −2.59808 | − | 6.50000i | −0.262445 | − | 0.656599i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.96410 | + | 0.598076i | −0.496410 | + | 0.0598076i | ||||
\(101\) | 7.50000 | + | 12.9904i | 0.746278 | + | 1.29259i | 0.949595 | + | 0.313478i | \(0.101494\pi\) |
−0.203317 | + | 0.979113i | \(0.565172\pi\) | |||||||
\(102\) | −5.19615 | + | 3.00000i | −0.514496 | + | 0.297044i | ||||
\(103\) | 9.52628 | + | 5.50000i | 0.938652 | + | 0.541931i | 0.889538 | − | 0.456862i | \(-0.151027\pi\) |
0.0491146 | + | 0.998793i | \(0.484360\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | −12.6962 | + | 12.4019i | −1.23902 | + | 1.21030i | ||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −6.06218 | − | 3.50000i | −0.586053 | − | 0.338358i | 0.177482 | − | 0.984124i | \(-0.443205\pi\) |
−0.763535 | + | 0.645766i | \(0.776538\pi\) | |||||||
\(108\) | −7.79423 | + | 4.50000i | −0.750000 | + | 0.433013i | ||||
\(109\) | 2.50000 | + | 4.33013i | 0.239457 | + | 0.414751i | 0.960558 | − | 0.278078i | \(-0.0896974\pi\) |
−0.721102 | + | 0.692829i | \(0.756364\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 24.0000 | 2.27798 | ||||||||
\(112\) | 1.73205 | + | 2.00000i | 0.163663 | + | 0.188982i | ||||
\(113\) | − | 10.0000i | − | 0.940721i | −0.882474 | − | 0.470360i | \(-0.844124\pi\) | ||
0.882474 | − | 0.470360i | \(-0.155876\pi\) | |||||||
\(114\) | 3.00000 | − | 5.19615i | 0.280976 | − | 0.486664i | ||||
\(115\) | 0.133975 | + | 2.23205i | 0.0124932 | + | 0.208140i | ||||
\(116\) | 0.500000 | + | 0.866025i | 0.0464238 | + | 0.0804084i | ||||
\(117\) | −10.3923 | − | 6.00000i | −0.960769 | − | 0.554700i | ||||
\(118\) | 2.00000i | 0.184115i | ||||||||
\(119\) | −1.00000 | − | 5.19615i | −0.0916698 | − | 0.476331i | ||||
\(120\) | 3.00000 | − | 6.00000i | 0.273861 | − | 0.547723i | ||||
\(121\) | 5.50000 | − | 9.52628i | 0.500000 | − | 0.866025i | ||||
\(122\) | 7.79423 | − | 4.50000i | 0.705656 | − | 0.407411i | ||||
\(123\) | 7.79423 | − | 4.50000i | 0.702782 | − | 0.405751i | ||||
\(124\) | 5.00000 | − | 8.66025i | 0.449013 | − | 0.777714i | ||||
\(125\) | −11.0000 | + | 2.00000i | −0.983870 | + | 0.178885i | ||||
\(126\) | −3.00000 | − | 15.5885i | −0.267261 | − | 1.38873i | ||||
\(127\) | 8.00000i | 0.709885i | 0.934888 | + | 0.354943i | \(0.115500\pi\) | ||||
−0.934888 | + | 0.354943i | \(0.884500\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −7.50000 | − | 12.9904i | −0.660338 | − | 1.14374i | ||||
\(130\) | 4.46410 | − | 0.267949i | 0.391528 | − | 0.0235007i | ||||
\(131\) | −10.0000 | + | 17.3205i | −0.873704 | + | 1.51330i | −0.0155672 | + | 0.999879i | \(0.504955\pi\) |
−0.858137 | + | 0.513421i | \(0.828378\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.46410 | + | 4.00000i | 0.300376 | + | 0.346844i | ||||
\(134\) | 7.00000 | 0.604708 | ||||||||
\(135\) | −16.7942 | + | 11.0885i | −1.44542 | + | 0.954342i | ||||
\(136\) | 1.00000 | + | 1.73205i | 0.0857493 | + | 0.148522i | ||||
\(137\) | −13.8564 | + | 8.00000i | −1.18383 | + | 0.683486i | −0.956898 | − | 0.290424i | \(-0.906204\pi\) |
−0.226935 | + | 0.973910i | \(0.572870\pi\) | |||||||
\(138\) | −2.59808 | − | 1.50000i | −0.221163 | − | 0.127688i | ||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | 4.13397 | + | 4.23205i | 0.349385 | + | 0.357674i | ||||
\(141\) | −24.0000 | −2.02116 | ||||||||
\(142\) | 5.19615 | + | 3.00000i | 0.436051 | + | 0.251754i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.00000 | + | 5.19615i | 0.250000 | + | 0.433013i | ||||
\(145\) | 1.23205 | + | 1.86603i | 0.102316 | + | 0.154965i | ||||
\(146\) | −10.0000 | −0.827606 | ||||||||
\(147\) | 20.7846 | + | 3.00000i | 1.71429 | + | 0.247436i | ||||
\(148\) | − | 8.00000i | − | 0.657596i | ||||||
\(149\) | −7.50000 | + | 12.9904i | −0.614424 | + | 1.06421i | 0.376061 | + | 0.926595i | \(0.377278\pi\) |
−0.990485 | + | 0.137619i | \(0.956055\pi\) | |||||||
\(150\) | 5.89230 | − | 13.7942i | 0.481105 | − | 1.12629i | ||||
\(151\) | −3.00000 | − | 5.19615i | −0.244137 | − | 0.422857i | 0.717752 | − | 0.696299i | \(-0.245171\pi\) |
−0.961888 | + | 0.273442i | \(0.911838\pi\) | |||||||
\(152\) | −1.73205 | − | 1.00000i | −0.140488 | − | 0.0811107i | ||||
\(153\) | − | 12.0000i | − | 0.970143i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.0000 | − | 20.0000i | 0.803219 | − | 1.60644i | ||||
\(156\) | −3.00000 | + | 5.19615i | −0.240192 | + | 0.416025i | ||||
\(157\) | 10.3923 | − | 6.00000i | 0.829396 | − | 0.478852i | −0.0242497 | − | 0.999706i | \(-0.507720\pi\) |
0.853646 | + | 0.520854i | \(0.174386\pi\) | |||||||
\(158\) | −8.66025 | + | 5.00000i | −0.688973 | + | 0.397779i | ||||
\(159\) | 9.00000 | − | 15.5885i | 0.713746 | − | 1.23625i | ||||
\(160\) | −2.00000 | − | 1.00000i | −0.158114 | − | 0.0790569i | ||||
\(161\) | 2.00000 | − | 1.73205i | 0.157622 | − | 0.136505i | ||||
\(162\) | − | 9.00000i | − | 0.707107i | ||||||
\(163\) | −10.3923 | − | 6.00000i | −0.813988 | − | 0.469956i | 0.0343508 | − | 0.999410i | \(-0.489064\pi\) |
−0.848339 | + | 0.529454i | \(0.822397\pi\) | |||||||
\(164\) | −1.50000 | − | 2.59808i | −0.117130 | − | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.50000 | − | 7.79423i | 0.349268 | − | 0.604949i | ||||
\(167\) | 9.00000i | 0.696441i | 0.937413 | + | 0.348220i | \(0.113214\pi\) | ||||
−0.937413 | + | 0.348220i | \(0.886786\pi\) | |||||||
\(168\) | −7.79423 | + | 1.50000i | −0.601338 | + | 0.115728i | ||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 2.46410 | + | 3.73205i | 0.188988 | + | 0.286235i | ||||
\(171\) | 6.00000 | + | 10.3923i | 0.458831 | + | 0.794719i | ||||
\(172\) | −4.33013 | + | 2.50000i | −0.330169 | + | 0.190623i | ||||
\(173\) | −10.3923 | − | 6.00000i | −0.790112 | − | 0.456172i | 0.0498898 | − | 0.998755i | \(-0.484113\pi\) |
−0.840002 | + | 0.542583i | \(0.817446\pi\) | |||||||
\(174\) | −3.00000 | −0.227429 | ||||||||
\(175\) | 9.79423 | + | 8.89230i | 0.740374 | + | 0.672195i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.19615 | − | 3.00000i | −0.390567 | − | 0.225494i | ||||
\(178\) | −6.06218 | + | 3.50000i | −0.454379 | + | 0.262336i | ||||
\(179\) | −13.0000 | − | 22.5167i | −0.971666 | − | 1.68297i | −0.690526 | − | 0.723307i | \(-0.742621\pi\) |
−0.281139 | − | 0.959667i | \(-0.590712\pi\) | |||||||
\(180\) | 7.39230 | + | 11.1962i | 0.550990 | + | 0.834512i | ||||
\(181\) | 5.00000 | 0.371647 | 0.185824 | − | 0.982583i | \(-0.440505\pi\) | ||||
0.185824 | + | 0.982583i | \(0.440505\pi\) | |||||||
\(182\) | −3.46410 | − | 4.00000i | −0.256776 | − | 0.296500i | ||||
\(183\) | 27.0000i | 1.99590i | ||||||||
\(184\) | −0.500000 | + | 0.866025i | −0.0368605 | + | 0.0638442i | ||||
\(185\) | −1.07180 | − | 17.8564i | −0.0788001 | − | 1.31283i | ||||
\(186\) | 15.0000 | + | 25.9808i | 1.09985 | + | 1.90500i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8.00000i | 0.583460i | ||||||||
\(189\) | 22.5000 | + | 7.79423i | 1.63663 | + | 0.566947i | ||||
\(190\) | −4.00000 | − | 2.00000i | −0.290191 | − | 0.145095i | ||||
\(191\) | 10.0000 | − | 17.3205i | 0.723575 | − | 1.25327i | −0.235983 | − | 0.971757i | \(-0.575831\pi\) |
0.959558 | − | 0.281511i | \(-0.0908356\pi\) | |||||||
\(192\) | 2.59808 | − | 1.50000i | 0.187500 | − | 0.108253i | ||||
\(193\) | 17.3205 | − | 10.0000i | 1.24676 | − | 0.719816i | 0.276296 | − | 0.961073i | \(-0.410893\pi\) |
0.970461 | + | 0.241257i | \(0.0775596\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.00000 | + | 12.0000i | −0.429669 | + | 0.859338i | ||||
\(196\) | 1.00000 | − | 6.92820i | 0.0714286 | − | 0.494872i | ||||
\(197\) | 8.00000i | 0.569976i | 0.958531 | + | 0.284988i | \(0.0919897\pi\) | ||||
−0.958531 | + | 0.284988i | \(0.908010\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.00000 | + | 10.3923i | 0.425329 | + | 0.736691i | 0.996451 | − | 0.0841740i | \(-0.0268252\pi\) |
−0.571122 | + | 0.820865i | \(0.693492\pi\) | |||||||
\(200\) | −4.59808 | − | 1.96410i | −0.325133 | − | 0.138883i | ||||
\(201\) | −10.5000 | + | 18.1865i | −0.740613 | + | 1.28278i | ||||
\(202\) | 15.0000i | 1.05540i | ||||||||
\(203\) | 0.866025 | − | 2.50000i | 0.0607831 | − | 0.175466i | ||||
\(204\) | −6.00000 | −0.420084 | ||||||||
\(205\) | −3.69615 | − | 5.59808i | −0.258150 | − | 0.390987i | ||||
\(206\) | 5.50000 | + | 9.52628i | 0.383203 | + | 0.663727i | ||||
\(207\) | 5.19615 | − | 3.00000i | 0.361158 | − | 0.208514i | ||||
\(208\) | 1.73205 | + | 1.00000i | 0.120096 | + | 0.0693375i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −17.1962 | + | 4.39230i | −1.18665 | + | 0.303098i | ||||
\(211\) | −18.0000 | −1.23917 | −0.619586 | − | 0.784929i | \(-0.712699\pi\) | ||||
−0.619586 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(212\) | −5.19615 | − | 3.00000i | −0.356873 | − | 0.206041i | ||||
\(213\) | −15.5885 | + | 9.00000i | −1.06810 | + | 0.616670i | ||||
\(214\) | −3.50000 | − | 6.06218i | −0.239255 | − | 0.414402i | ||||
\(215\) | −9.33013 | + | 6.16025i | −0.636309 | + | 0.420126i | ||||
\(216\) | −9.00000 | −0.612372 | ||||||||
\(217\) | −25.9808 | + | 5.00000i | −1.76369 | + | 0.339422i | ||||
\(218\) | 5.00000i | 0.338643i | ||||||||
\(219\) | 15.0000 | − | 25.9808i | 1.01361 | − | 1.75562i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.00000 | − | 3.46410i | −0.134535 | − | 0.233021i | ||||
\(222\) | 20.7846 | + | 12.0000i | 1.39497 | + | 0.805387i | ||||
\(223\) | − | 8.00000i | − | 0.535720i | −0.963458 | − | 0.267860i | \(-0.913684\pi\) | ||
0.963458 | − | 0.267860i | \(-0.0863164\pi\) | |||||||
\(224\) | 0.500000 | + | 2.59808i | 0.0334077 | + | 0.173591i | ||||
\(225\) | 18.0000 | + | 24.0000i | 1.20000 | + | 1.60000i | ||||
\(226\) | 5.00000 | − | 8.66025i | 0.332595 | − | 0.576072i | ||||
\(227\) | −10.3923 | + | 6.00000i | −0.689761 | + | 0.398234i | −0.803523 | − | 0.595274i | \(-0.797043\pi\) |
0.113761 | + | 0.993508i | \(0.463710\pi\) | |||||||
\(228\) | 5.19615 | − | 3.00000i | 0.344124 | − | 0.198680i | ||||
\(229\) | 5.00000 | − | 8.66025i | 0.330409 | − | 0.572286i | −0.652183 | − | 0.758062i | \(-0.726147\pi\) |
0.982592 | + | 0.185776i | \(0.0594799\pi\) | |||||||
\(230\) | −1.00000 | + | 2.00000i | −0.0659380 | + | 0.131876i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.00000i | 0.0656532i | ||||||||
\(233\) | 12.1244 | + | 7.00000i | 0.794293 | + | 0.458585i | 0.841472 | − | 0.540301i | \(-0.181690\pi\) |
−0.0471787 | + | 0.998886i | \(0.515023\pi\) | |||||||
\(234\) | −6.00000 | − | 10.3923i | −0.392232 | − | 0.679366i | ||||
\(235\) | 1.07180 | + | 17.8564i | 0.0699163 | + | 1.16482i | ||||
\(236\) | −1.00000 | + | 1.73205i | −0.0650945 | + | 0.112747i | ||||
\(237\) | − | 30.0000i | − | 1.94871i | ||||||
\(238\) | 1.73205 | − | 5.00000i | 0.112272 | − | 0.324102i | ||||
\(239\) | 10.0000 | 0.646846 | 0.323423 | − | 0.946254i | \(-0.395166\pi\) | ||||
0.323423 | + | 0.946254i | \(0.395166\pi\) | |||||||
\(240\) | 5.59808 | − | 3.69615i | 0.361354 | − | 0.238586i | ||||
\(241\) | −9.00000 | − | 15.5885i | −0.579741 | − | 1.00414i | −0.995509 | − | 0.0946700i | \(-0.969820\pi\) |
0.415768 | − | 0.909471i | \(-0.363513\pi\) | |||||||
\(242\) | 9.52628 | − | 5.50000i | 0.612372 | − | 0.353553i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.00000 | 0.576166 | ||||||||
\(245\) | 1.30385 | − | 15.5981i | 0.0832998 | − | 0.996525i | ||||
\(246\) | 9.00000 | 0.573819 | ||||||||
\(247\) | 3.46410 | + | 2.00000i | 0.220416 | + | 0.127257i | ||||
\(248\) | 8.66025 | − | 5.00000i | 0.549927 | − | 0.317500i | ||||
\(249\) | 13.5000 | + | 23.3827i | 0.855528 | + | 1.48182i | ||||
\(250\) | −10.5263 | − | 3.76795i | −0.665740 | − | 0.238306i | ||||
\(251\) | −10.0000 | −0.631194 | −0.315597 | − | 0.948893i | \(-0.602205\pi\) | ||||
−0.315597 | + | 0.948893i | \(0.602205\pi\) | |||||||
\(252\) | 5.19615 | − | 15.0000i | 0.327327 | − | 0.944911i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −4.00000 | + | 6.92820i | −0.250982 | + | 0.434714i | ||||
\(255\) | −13.3923 | + | 0.803848i | −0.838659 | + | 0.0503389i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 10.3923 | + | 6.00000i | 0.648254 | + | 0.374270i | 0.787787 | − | 0.615948i | \(-0.211227\pi\) |
−0.139533 | + | 0.990217i | \(0.544560\pi\) | |||||||
\(258\) | − | 15.0000i | − | 0.933859i | ||||||
\(259\) | −16.0000 | + | 13.8564i | −0.994192 | + | 0.860995i | ||||
\(260\) | 4.00000 | + | 2.00000i | 0.248069 | + | 0.124035i | ||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | −17.3205 | + | 10.0000i | −1.07006 | + | 0.617802i | ||||
\(263\) | 18.1865 | − | 10.5000i | 1.12143 | − | 0.647458i | 0.179664 | − | 0.983728i | \(-0.442499\pi\) |
0.941766 | + | 0.336270i | \(0.109166\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | − | 6.00000i | −0.737154 | − | 0.368577i | ||||
\(266\) | 1.00000 | + | 5.19615i | 0.0613139 | + | 0.318597i | ||||
\(267\) | − | 21.0000i | − | 1.28518i | ||||||
\(268\) | 6.06218 | + | 3.50000i | 0.370306 | + | 0.213797i | ||||
\(269\) | 2.50000 | + | 4.33013i | 0.152428 | + | 0.264013i | 0.932119 | − | 0.362151i | \(-0.117958\pi\) |
−0.779692 | + | 0.626164i | \(0.784624\pi\) | |||||||
\(270\) | −20.0885 | + | 1.20577i | −1.22254 | + | 0.0733809i | ||||
\(271\) | −3.00000 | + | 5.19615i | −0.182237 | + | 0.315644i | −0.942642 | − | 0.333805i | \(-0.891667\pi\) |
0.760405 | + | 0.649449i | \(0.225000\pi\) | |||||||
\(272\) | 2.00000i | 0.121268i | ||||||||
\(273\) | 15.5885 | − | 3.00000i | 0.943456 | − | 0.181568i | ||||
\(274\) | −16.0000 | −0.966595 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.50000 | − | 2.59808i | −0.0902894 | − | 0.156386i | ||||
\(277\) | 22.5167 | − | 13.0000i | 1.35290 | − | 0.781094i | 0.364241 | − | 0.931305i | \(-0.381328\pi\) |
0.988654 | + | 0.150210i | \(0.0479951\pi\) | |||||||
\(278\) | 6.92820 | + | 4.00000i | 0.415526 | + | 0.239904i | ||||
\(279\) | −60.0000 | −3.59211 | ||||||||
\(280\) | 1.46410 | + | 5.73205i | 0.0874968 | + | 0.342556i | ||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | −20.7846 | − | 12.0000i | −1.23771 | − | 0.714590i | ||||
\(283\) | 6.92820 | − | 4.00000i | 0.411839 | − | 0.237775i | −0.279741 | − | 0.960076i | \(-0.590248\pi\) |
0.691580 | + | 0.722300i | \(0.256915\pi\) | |||||||
\(284\) | 3.00000 | + | 5.19615i | 0.178017 | + | 0.308335i | ||||
\(285\) | 11.1962 | − | 7.39230i | 0.663203 | − | 0.437882i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.59808 | + | 7.50000i | −0.153360 | + | 0.442711i | ||||
\(288\) | 6.00000i | 0.353553i | ||||||||
\(289\) | −6.50000 | + | 11.2583i | −0.382353 | + | 0.662255i | ||||
\(290\) | 0.133975 | + | 2.23205i | 0.00786726 | + | 0.131071i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.66025 | − | 5.00000i | −0.506803 | − | 0.292603i | ||||
\(293\) | 24.0000i | 1.40209i | 0.713115 | + | 0.701047i | \(0.247284\pi\) | ||||
−0.713115 | + | 0.701047i | \(0.752716\pi\) | |||||||
\(294\) | 16.5000 | + | 12.9904i | 0.962300 | + | 0.757614i | ||||
\(295\) | −2.00000 | + | 4.00000i | −0.116445 | + | 0.232889i | ||||
\(296\) | 4.00000 | − | 6.92820i | 0.232495 | − | 0.402694i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.9904 | + | 7.50000i | −0.752513 | + | 0.434463i | ||||
\(299\) | 1.00000 | − | 1.73205i | 0.0578315 | − | 0.100167i | ||||
\(300\) | 12.0000 | − | 9.00000i | 0.692820 | − | 0.519615i | ||||
\(301\) | 12.5000 | + | 4.33013i | 0.720488 | + | 0.249584i | ||||
\(302\) | − | 6.00000i | − | 0.345261i | ||||||
\(303\) | −38.9711 | − | 22.5000i | −2.23883 | − | 1.29259i | ||||
\(304\) | −1.00000 | − | 1.73205i | −0.0573539 | − | 0.0993399i | ||||
\(305\) | 20.0885 | − | 1.20577i | 1.15026 | − | 0.0690423i | ||||
\(306\) | 6.00000 | − | 10.3923i | 0.342997 | − | 0.594089i | ||||
\(307\) | 19.0000i | 1.08439i | 0.840254 | + | 0.542194i | \(0.182406\pi\) | ||||
−0.840254 | + | 0.542194i | \(0.817594\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −33.0000 | −1.87730 | ||||||||
\(310\) | 18.6603 | − | 12.3205i | 1.05983 | − | 0.699758i | ||||
\(311\) | −3.00000 | − | 5.19615i | −0.170114 | − | 0.294647i | 0.768345 | − | 0.640036i | \(-0.221080\pi\) |
−0.938460 | + | 0.345389i | \(0.887747\pi\) | |||||||
\(312\) | −5.19615 | + | 3.00000i | −0.294174 | + | 0.169842i | ||||
\(313\) | −6.92820 | − | 4.00000i | −0.391605 | − | 0.226093i | 0.291250 | − | 0.956647i | \(-0.405929\pi\) |
−0.682855 | + | 0.730554i | \(0.739262\pi\) | |||||||
\(314\) | 12.0000 | 0.677199 | ||||||||
\(315\) | 9.58846 | − | 34.1769i | 0.540248 | − | 1.92565i | ||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | 19.0526 | + | 11.0000i | 1.07010 | + | 0.617822i | 0.928208 | − | 0.372061i | \(-0.121349\pi\) |
0.141890 | + | 0.989882i | \(0.454682\pi\) | |||||||
\(318\) | 15.5885 | − | 9.00000i | 0.874157 | − | 0.504695i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.23205 | − | 1.86603i | −0.0688737 | − | 0.104314i | ||||
\(321\) | 21.0000 | 1.17211 | ||||||||
\(322\) | 2.59808 | − | 0.500000i | 0.144785 | − | 0.0278639i | ||||
\(323\) | 4.00000i | 0.222566i | ||||||||
\(324\) | 4.50000 | − | 7.79423i | 0.250000 | − | 0.433013i | ||||
\(325\) | 9.19615 | + | 3.92820i | 0.510111 | + | 0.217898i | ||||
\(326\) | −6.00000 | − | 10.3923i | −0.332309 | − | 0.575577i | ||||
\(327\) | −12.9904 | − | 7.50000i | −0.718370 | − | 0.414751i | ||||
\(328\) | − | 3.00000i | − | 0.165647i | ||||||
\(329\) | 16.0000 | − | 13.8564i | 0.882109 | − | 0.763928i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.00000 | + | 12.1244i | −0.384755 | + | 0.666415i | −0.991735 | − | 0.128302i | \(-0.959047\pi\) |
0.606980 | + | 0.794717i | \(0.292381\pi\) | |||||||
\(332\) | 7.79423 | − | 4.50000i | 0.427764 | − | 0.246970i | ||||
\(333\) | −41.5692 | + | 24.0000i | −2.27798 | + | 1.31519i | ||||
\(334\) | −4.50000 | + | 7.79423i | −0.246229 | + | 0.426481i | ||||
\(335\) | 14.0000 | + | 7.00000i | 0.764902 | + | 0.382451i | ||||
\(336\) | −7.50000 | − | 2.59808i | −0.409159 | − | 0.141737i | ||||
\(337\) | 2.00000i | 0.108947i | 0.998515 | + | 0.0544735i | \(0.0173480\pi\) | ||||
−0.998515 | + | 0.0544735i | \(0.982652\pi\) | |||||||
\(338\) | 7.79423 | + | 4.50000i | 0.423950 | + | 0.244768i | ||||
\(339\) | 15.0000 | + | 25.9808i | 0.814688 | + | 1.41108i | ||||
\(340\) | 0.267949 | + | 4.46410i | 0.0145316 | + | 0.242100i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 12.0000i | 0.648886i | ||||||||
\(343\) | −15.5885 | + | 10.0000i | −0.841698 | + | 0.539949i | ||||
\(344\) | −5.00000 | −0.269582 | ||||||||
\(345\) | −3.69615 | − | 5.59808i | −0.198994 | − | 0.301390i | ||||
\(346\) | −6.00000 | − | 10.3923i | −0.322562 | − | 0.558694i | ||||
\(347\) | −18.1865 | + | 10.5000i | −0.976304 | + | 0.563670i | −0.901152 | − | 0.433503i | \(-0.857278\pi\) |
−0.0751519 | + | 0.997172i | \(0.523944\pi\) | |||||||
\(348\) | −2.59808 | − | 1.50000i | −0.139272 | − | 0.0804084i | ||||
\(349\) | 9.00000 | 0.481759 | 0.240879 | − | 0.970555i | \(-0.422564\pi\) | ||||
0.240879 | + | 0.970555i | \(0.422564\pi\) | |||||||
\(350\) | 4.03590 | + | 12.5981i | 0.215728 | + | 0.673395i | ||||
\(351\) | 18.0000 | 0.960769 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.19615 | + | 3.00000i | −0.276563 | + | 0.159674i | −0.631867 | − | 0.775077i | \(-0.717711\pi\) |
0.355303 | + | 0.934751i | \(0.384378\pi\) | |||||||
\(354\) | −3.00000 | − | 5.19615i | −0.159448 | − | 0.276172i | ||||
\(355\) | 7.39230 | + | 11.1962i | 0.392343 | + | 0.594230i | ||||
\(356\) | −7.00000 | −0.370999 | ||||||||
\(357\) | 10.3923 | + | 12.0000i | 0.550019 | + | 0.635107i | ||||
\(358\) | − | 26.0000i | − | 1.37414i | ||||||
\(359\) | −7.00000 | + | 12.1244i | −0.369446 | + | 0.639899i | −0.989479 | − | 0.144677i | \(-0.953786\pi\) |
0.620033 | + | 0.784576i | \(0.287119\pi\) | |||||||
\(360\) | 0.803848 | + | 13.3923i | 0.0423665 | + | 0.705836i | ||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | 4.33013 | + | 2.50000i | 0.227586 | + | 0.131397i | ||||
\(363\) | 33.0000i | 1.73205i | ||||||||
\(364\) | −1.00000 | − | 5.19615i | −0.0524142 | − | 0.272352i | ||||
\(365\) | −20.0000 | − | 10.0000i | −1.04685 | − | 0.523424i | ||||
\(366\) | −13.5000 | + | 23.3827i | −0.705656 | + | 1.22223i | ||||
\(367\) | 19.9186 | − | 11.5000i | 1.03974 | − | 0.600295i | 0.119982 | − | 0.992776i | \(-0.461716\pi\) |
0.919760 | + | 0.392481i | \(0.128383\pi\) | |||||||
\(368\) | −0.866025 | + | 0.500000i | −0.0451447 | + | 0.0260643i | ||||
\(369\) | −9.00000 | + | 15.5885i | −0.468521 | + | 0.811503i | ||||
\(370\) | 8.00000 | − | 16.0000i | 0.415900 | − | 0.831800i | ||||
\(371\) | 3.00000 | + | 15.5885i | 0.155752 | + | 0.809312i | ||||
\(372\) | 30.0000i | 1.55543i | ||||||||
\(373\) | −6.92820 | − | 4.00000i | −0.358729 | − | 0.207112i | 0.309794 | − | 0.950804i | \(-0.399740\pi\) |
−0.668523 | + | 0.743691i | \(0.733073\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.5788 | − | 21.6962i | 1.32089 | − | 1.12038i | ||||
\(376\) | −4.00000 | + | 6.92820i | −0.206284 | + | 0.357295i | ||||
\(377\) | − | 2.00000i | − | 0.103005i | ||||||
\(378\) | 15.5885 | + | 18.0000i | 0.801784 | + | 0.925820i | ||||
\(379\) | 2.00000 | 0.102733 | 0.0513665 | − | 0.998680i | \(-0.483642\pi\) | ||||
0.0513665 | + | 0.998680i | \(0.483642\pi\) | |||||||
\(380\) | −2.46410 | − | 3.73205i | −0.126406 | − | 0.191450i | ||||
\(381\) | −12.0000 | − | 20.7846i | −0.614779 | − | 1.06483i | ||||
\(382\) | 17.3205 | − | 10.0000i | 0.886194 | − | 0.511645i | ||||
\(383\) | 7.79423 | + | 4.50000i | 0.398266 | + | 0.229939i | 0.685736 | − | 0.727851i | \(-0.259481\pi\) |
−0.287469 | + | 0.957790i | \(0.592814\pi\) | |||||||
\(384\) | 3.00000 | 0.153093 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.0000 | 1.01797 | ||||||||
\(387\) | 25.9808 | + | 15.0000i | 1.32068 | + | 0.762493i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.00000 | − | 15.5885i | −0.456318 | − | 0.790366i | 0.542445 | − | 0.840091i | \(-0.317499\pi\) |
−0.998763 | + | 0.0497253i | \(0.984165\pi\) | |||||||
\(390\) | −11.1962 | + | 7.39230i | −0.566939 | + | 0.374324i | ||||
\(391\) | 2.00000 | 0.101144 | ||||||||
\(392\) | 4.33013 | − | 5.50000i | 0.218704 | − | 0.277792i | ||||
\(393\) | − | 60.0000i | − | 3.02660i | ||||||
\(394\) | −4.00000 | + | 6.92820i | −0.201517 | + | 0.349038i | ||||
\(395\) | −22.3205 | + | 1.33975i | −1.12307 | + | 0.0674099i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.7128 | − | 16.0000i | −1.39087 | − | 0.803017i | −0.397455 | − | 0.917622i | \(-0.630107\pi\) |
−0.993411 | + | 0.114605i | \(0.963440\pi\) | |||||||
\(398\) | 12.0000i | 0.601506i | ||||||||
\(399\) | −15.0000 | − | 5.19615i | −0.750939 | − | 0.260133i | ||||
\(400\) | −3.00000 | − | 4.00000i | −0.150000 | − | 0.200000i | ||||
\(401\) | −1.50000 | + | 2.59808i | −0.0749064 | + | 0.129742i | −0.901046 | − | 0.433724i | \(-0.857199\pi\) |
0.826139 | + | 0.563466i | \(0.190532\pi\) | |||||||
\(402\) | −18.1865 | + | 10.5000i | −0.907062 | + | 0.523692i | ||||
\(403\) | −17.3205 | + | 10.0000i | −0.862796 | + | 0.498135i | ||||
\(404\) | −7.50000 | + | 12.9904i | −0.373139 | + | 0.646296i | ||||
\(405\) | 9.00000 | − | 18.0000i | 0.447214 | − | 0.894427i | ||||
\(406\) | 2.00000 | − | 1.73205i | 0.0992583 | − | 0.0859602i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −5.19615 | − | 3.00000i | −0.257248 | − | 0.148522i | ||||
\(409\) | −8.50000 | − | 14.7224i | −0.420298 | − | 0.727977i | 0.575670 | − | 0.817682i | \(-0.304741\pi\) |
−0.995968 | + | 0.0897044i | \(0.971408\pi\) | |||||||
\(410\) | −0.401924 | − | 6.69615i | −0.0198496 | − | 0.330699i | ||||
\(411\) | 24.0000 | − | 41.5692i | 1.18383 | − | 2.05046i | ||||
\(412\) | 11.0000i | 0.541931i | ||||||||
\(413\) | 5.19615 | − | 1.00000i | 0.255686 | − | 0.0492068i | ||||
\(414\) | 6.00000 | 0.294884 | ||||||||
\(415\) | 16.7942 | − | 11.0885i | 0.824396 | − | 0.544311i | ||||
\(416\) | 1.00000 | + | 1.73205i | 0.0490290 | + | 0.0849208i | ||||
\(417\) | −20.7846 | + | 12.0000i | −1.01783 | + | 0.587643i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 40.0000 | 1.95413 | 0.977064 | − | 0.212946i | \(-0.0683059\pi\) | ||||
0.977064 | + | 0.212946i | \(0.0683059\pi\) | |||||||
\(420\) | −17.0885 | − | 4.79423i | −0.833831 | − | 0.233934i | ||||
\(421\) | 31.0000 | 1.51085 | 0.755424 | − | 0.655237i | \(-0.227431\pi\) | ||||
0.755424 | + | 0.655237i | \(0.227431\pi\) | |||||||
\(422\) | −15.5885 | − | 9.00000i | −0.758834 | − | 0.438113i | ||||
\(423\) | 41.5692 | − | 24.0000i | 2.02116 | − | 1.16692i | ||||
\(424\) | −3.00000 | − | 5.19615i | −0.145693 | − | 0.252347i | ||||
\(425\) | 1.19615 | + | 9.92820i | 0.0580219 | + | 0.481589i | ||||
\(426\) | −18.0000 | −0.872103 | ||||||||
\(427\) | −15.5885 | − | 18.0000i | −0.754378 | − | 0.871081i | ||||
\(428\) | − | 7.00000i | − | 0.338358i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.1603 | + | 0.669873i | −0.538195 | + | 0.0323041i | ||||
\(431\) | −16.0000 | − | 27.7128i | −0.770693 | − | 1.33488i | −0.937184 | − | 0.348836i | \(-0.886577\pi\) |
0.166491 | − | 0.986043i | \(-0.446756\pi\) | |||||||
\(432\) | −7.79423 | − | 4.50000i | −0.375000 | − | 0.216506i | ||||
\(433\) | − | 14.0000i | − | 0.672797i | −0.941720 | − | 0.336399i | \(-0.890791\pi\) | ||
0.941720 | − | 0.336399i | \(-0.109209\pi\) | |||||||
\(434\) | −25.0000 | − | 8.66025i | −1.20004 | − | 0.415705i | ||||
\(435\) | −6.00000 | − | 3.00000i | −0.287678 | − | 0.143839i | ||||
\(436\) | −2.50000 | + | 4.33013i | −0.119728 | + | 0.207375i | ||||
\(437\) | −1.73205 | + | 1.00000i | −0.0828552 | + | 0.0478365i | ||||
\(438\) | 25.9808 | − | 15.0000i | 1.24141 | − | 0.716728i | ||||
\(439\) | 4.00000 | − | 6.92820i | 0.190910 | − | 0.330665i | −0.754642 | − | 0.656136i | \(-0.772190\pi\) |
0.945552 | + | 0.325471i | \(0.105523\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −39.0000 | + | 15.5885i | −1.85714 | + | 0.742307i | ||||
\(442\) | − | 4.00000i | − | 0.190261i | ||||||
\(443\) | 2.59808 | + | 1.50000i | 0.123438 | + | 0.0712672i | 0.560448 | − | 0.828190i | \(-0.310629\pi\) |
−0.437009 | + | 0.899457i | \(0.643962\pi\) | |||||||
\(444\) | 12.0000 | + | 20.7846i | 0.569495 | + | 0.986394i | ||||
\(445\) | −15.6244 | + | 0.937822i | −0.740665 | + | 0.0444570i | ||||
\(446\) | 4.00000 | − | 6.92820i | 0.189405 | − | 0.328060i | ||||
\(447\) | − | 45.0000i | − | 2.12843i | ||||||
\(448\) | −0.866025 | + | 2.50000i | −0.0409159 | + | 0.118114i | ||||
\(449\) | −23.0000 | −1.08544 | −0.542719 | − | 0.839915i | \(-0.682605\pi\) | ||||
−0.542719 | + | 0.839915i | \(0.682605\pi\) | |||||||
\(450\) | 3.58846 | + | 29.7846i | 0.169161 | + | 1.40406i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 8.66025 | − | 5.00000i | 0.407344 | − | 0.235180i | ||||
\(453\) | 15.5885 | + | 9.00000i | 0.732410 | + | 0.422857i | ||||
\(454\) | −12.0000 | −0.563188 | ||||||||
\(455\) | −2.92820 | − | 11.4641i | −0.137276 | − | 0.537445i | ||||
\(456\) | 6.00000 | 0.280976 | ||||||||
\(457\) | 27.7128 | + | 16.0000i | 1.29635 | + | 0.748448i | 0.979772 | − | 0.200118i | \(-0.0641325\pi\) |
0.316579 | + | 0.948566i | \(0.397466\pi\) | |||||||
\(458\) | 8.66025 | − | 5.00000i | 0.404667 | − | 0.233635i | ||||
\(459\) | 9.00000 | + | 15.5885i | 0.420084 | + | 0.727607i | ||||
\(460\) | −1.86603 | + | 1.23205i | −0.0870039 | + | 0.0574447i | ||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.0000i | 1.16185i | 0.813958 | + | 0.580924i | \(0.197309\pi\) | ||||
−0.813958 | + | 0.580924i | \(0.802691\pi\) | |||||||
\(464\) | −0.500000 | + | 0.866025i | −0.0232119 | + | 0.0402042i | ||||
\(465\) | 4.01924 | + | 66.9615i | 0.186388 | + | 3.10527i | ||||
\(466\) | 7.00000 | + | 12.1244i | 0.324269 | + | 0.561650i | ||||
\(467\) | 0.866025 | + | 0.500000i | 0.0400749 | + | 0.0231372i | 0.519904 | − | 0.854225i | \(-0.325968\pi\) |
−0.479829 | + | 0.877362i | \(0.659301\pi\) | |||||||
\(468\) | − | 12.0000i | − | 0.554700i | ||||||
\(469\) | −3.50000 | − | 18.1865i | −0.161615 | − | 0.839776i | ||||
\(470\) | −8.00000 | + | 16.0000i | −0.369012 | + | 0.738025i | ||||
\(471\) | −18.0000 | + | 31.1769i | −0.829396 | + | 1.43656i | ||||
\(472\) | −1.73205 | + | 1.00000i | −0.0797241 | + | 0.0460287i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 15.0000 | − | 25.9808i | 0.688973 | − | 1.19334i | ||||
\(475\) | −6.00000 | − | 8.00000i | −0.275299 | − | 0.367065i | ||||
\(476\) | 4.00000 | − | 3.46410i | 0.183340 | − | 0.158777i | ||||
\(477\) | 36.0000i | 1.64833i | ||||||||
\(478\) | 8.66025 | + | 5.00000i | 0.396111 | + | 0.228695i | ||||
\(479\) | 9.00000 | + | 15.5885i | 0.411220 | + | 0.712255i | 0.995023 | − | 0.0996406i | \(-0.0317693\pi\) |
−0.583803 | + | 0.811895i | \(0.698436\pi\) | |||||||
\(480\) | 6.69615 | − | 0.401924i | 0.305636 | − | 0.0183452i | ||||
\(481\) | −8.00000 | + | 13.8564i | −0.364769 | + | 0.631798i | ||||
\(482\) | − | 18.0000i | − | 0.819878i | ||||||
\(483\) | −2.59808 | + | 7.50000i | −0.118217 | + | 0.341262i | ||||
\(484\) | 11.0000 | 0.500000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.46410 | + | 2.00000i | −0.156973 | + | 0.0906287i | −0.576429 | − | 0.817147i | \(-0.695554\pi\) |
0.419456 | + | 0.907776i | \(0.362221\pi\) | |||||||
\(488\) | 7.79423 | + | 4.50000i | 0.352828 | + | 0.203705i | ||||
\(489\) | 36.0000 | 1.62798 | ||||||||
\(490\) | 8.92820 | − | 12.8564i | 0.403335 | − | 0.580793i | ||||
\(491\) | −18.0000 | −0.812329 | −0.406164 | − | 0.913800i | \(-0.633134\pi\) | ||||
−0.406164 | + | 0.913800i | \(0.633134\pi\) | |||||||
\(492\) | 7.79423 | + | 4.50000i | 0.351391 | + | 0.202876i | ||||
\(493\) | 1.73205 | − | 1.00000i | 0.0780076 | − | 0.0450377i | ||||
\(494\) | 2.00000 | + | 3.46410i | 0.0899843 | + | 0.155857i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.0000 | 0.449013 | ||||||||
\(497\) | 5.19615 | − | 15.0000i | 0.233079 | − | 0.672842i | ||||
\(498\) | 27.0000i | 1.20990i | ||||||||
\(499\) | 8.00000 | − | 13.8564i | 0.358129 | − | 0.620298i | −0.629519 | − | 0.776985i | \(-0.716748\pi\) |
0.987648 | + | 0.156687i | \(0.0500814\pi\) | |||||||
\(500\) | −7.23205 | − | 8.52628i | −0.323427 | − | 0.381307i | ||||
\(501\) | −13.5000 | − | 23.3827i | −0.603136 | − | 1.04466i | ||||
\(502\) | −8.66025 | − | 5.00000i | −0.386526 | − | 0.223161i | ||||
\(503\) | − | 5.00000i | − | 0.222939i | −0.993768 | − | 0.111469i | \(-0.964444\pi\) | ||
0.993768 | − | 0.111469i | \(-0.0355557\pi\) | |||||||
\(504\) | 12.0000 | − | 10.3923i | 0.534522 | − | 0.462910i | ||||
\(505\) | −15.0000 | + | 30.0000i | −0.667491 | + | 1.33498i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.3827 | + | 13.5000i | −1.03846 | + | 0.599556i | ||||
\(508\) | −6.92820 | + | 4.00000i | −0.307389 | + | 0.177471i | ||||
\(509\) | 17.5000 | − | 30.3109i | 0.775674 | − | 1.34351i | −0.158741 | − | 0.987320i | \(-0.550744\pi\) |
0.934415 | − | 0.356186i | \(-0.115923\pi\) | |||||||
\(510\) | −12.0000 | − | 6.00000i | −0.531369 | − | 0.265684i | ||||
\(511\) | 5.00000 | + | 25.9808i | 0.221187 | + | 1.14932i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −15.5885 | − | 9.00000i | −0.688247 | − | 0.397360i | ||||
\(514\) | 6.00000 | + | 10.3923i | 0.264649 | + | 0.458385i | ||||
\(515\) | 1.47372 | + | 24.5526i | 0.0649399 | + | 1.08192i | ||||
\(516\) | 7.50000 | − | 12.9904i | 0.330169 | − | 0.571870i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −20.7846 | + | 4.00000i | −0.913223 | + | 0.175750i | ||||
\(519\) | 36.0000 | 1.58022 | ||||||||
\(520\) | 2.46410 | + | 3.73205i | 0.108058 | + | 0.163661i | ||||
\(521\) | 9.00000 | + | 15.5885i | 0.394297 | + | 0.682943i | 0.993011 | − | 0.118020i | \(-0.0376547\pi\) |
−0.598714 | + | 0.800963i | \(0.704321\pi\) | |||||||
\(522\) | 5.19615 | − | 3.00000i | 0.227429 | − | 0.131306i | ||||
\(523\) | −3.46410 | − | 2.00000i | −0.151475 | − | 0.0874539i | 0.422347 | − | 0.906434i | \(-0.361206\pi\) |
−0.573822 | + | 0.818980i | \(0.694540\pi\) | |||||||
\(524\) | −20.0000 | −0.873704 | ||||||||
\(525\) | −38.7846 | − | 8.41154i | −1.69270 | − | 0.367110i | ||||
\(526\) | 21.0000 | 0.915644 | ||||||||
\(527\) | −17.3205 | − | 10.0000i | −0.754493 | − | 0.435607i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0000 | − | 19.0526i | −0.478261 | − | 0.828372i | ||||
\(530\) | −7.39230 | − | 11.1962i | −0.321101 | − | 0.486330i | ||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | −1.73205 | + | 5.00000i | −0.0750939 | + | 0.216777i | ||||
\(533\) | 6.00000i | 0.259889i | ||||||||
\(534\) | 10.5000 | − | 18.1865i | 0.454379 | − | 0.787008i | ||||
\(535\) | −0.937822 | − | 15.6244i | −0.0405456 | − | 0.675500i | ||||
\(536\) | 3.50000 | + | 6.06218i | 0.151177 | + | 0.261846i | ||||
\(537\) | 67.5500 | + | 39.0000i | 2.91500 | + | 1.68297i | ||||
\(538\) | 5.00000i | 0.215565i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −18.0000 | − | 9.00000i | −0.774597 | − | 0.387298i | ||||
\(541\) | −2.50000 | + | 4.33013i | −0.107483 | + | 0.186167i | −0.914750 | − | 0.404020i | \(-0.867613\pi\) |
0.807267 | + | 0.590187i | \(0.200946\pi\) | |||||||
\(542\) | −5.19615 | + | 3.00000i | −0.223194 | + | 0.128861i | ||||
\(543\) | −12.9904 | + | 7.50000i | −0.557471 | + | 0.321856i | ||||
\(544\) | −1.00000 | + | 1.73205i | −0.0428746 | + | 0.0742611i | ||||
\(545\) | −5.00000 | + | 10.0000i | −0.214176 | + | 0.428353i | ||||
\(546\) | 15.0000 | + | 5.19615i | 0.641941 | + | 0.222375i | ||||
\(547\) | − | 37.0000i | − | 1.58201i | −0.611812 | − | 0.791003i | \(-0.709559\pi\) | ||
0.611812 | − | 0.791003i | \(-0.290441\pi\) | |||||||
\(548\) | −13.8564 | − | 8.00000i | −0.591916 | − | 0.341743i | ||||
\(549\) | −27.0000 | − | 46.7654i | −1.15233 | − | 1.99590i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.00000 | + | 1.73205i | −0.0426014 | + | 0.0737878i | ||||
\(552\) | − | 3.00000i | − | 0.127688i | ||||||
\(553\) | 17.3205 | + | 20.0000i | 0.736543 | + | 0.850487i | ||||
\(554\) | 26.0000 | 1.10463 | ||||||||
\(555\) | 29.5692 | + | 44.7846i | 1.25514 | + | 1.90100i | ||||
\(556\) | 4.00000 | + | 6.92820i | 0.169638 | + | 0.293821i | ||||
\(557\) | 3.46410 | − | 2.00000i | 0.146779 | − | 0.0847427i | −0.424812 | − | 0.905282i | \(-0.639660\pi\) |
0.571591 | + | 0.820539i | \(0.306326\pi\) | |||||||
\(558\) | −51.9615 | − | 30.0000i | −2.19971 | − | 1.27000i | ||||
\(559\) | 10.0000 | 0.422955 | ||||||||
\(560\) | −1.59808 | + | 5.69615i | −0.0675310 | + | 0.240706i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.5885 | + | 9.00000i | 0.657559 | + | 0.379642i | ||||
\(563\) | 9.52628 | − | 5.50000i | 0.401485 | − | 0.231797i | −0.285640 | − | 0.958337i | \(-0.592206\pi\) |
0.687124 | + | 0.726540i | \(0.258873\pi\) | |||||||
\(564\) | −12.0000 | − | 20.7846i | −0.505291 | − | 0.875190i | ||||
\(565\) | 18.6603 | − | 12.3205i | 0.785043 | − | 0.518328i | ||||
\(566\) | 8.00000 | 0.336265 | ||||||||
\(567\) | −23.3827 | + | 4.50000i | −0.981981 | + | 0.188982i | ||||
\(568\) | 6.00000i | 0.251754i | ||||||||
\(569\) | −9.00000 | + | 15.5885i | −0.377300 | + | 0.653502i | −0.990668 | − | 0.136295i | \(-0.956481\pi\) |
0.613369 | + | 0.789797i | \(0.289814\pi\) | |||||||
\(570\) | 13.3923 | − | 0.803848i | 0.560942 | − | 0.0336695i | ||||
\(571\) | 5.00000 | + | 8.66025i | 0.209243 | + | 0.362420i | 0.951476 | − | 0.307722i | \(-0.0995665\pi\) |
−0.742233 | + | 0.670142i | \(0.766233\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 60.0000i | 2.50654i | ||||||||
\(574\) | −6.00000 | + | 5.19615i | −0.250435 | + | 0.216883i | ||||
\(575\) | −4.00000 | + | 3.00000i | −0.166812 | + | 0.125109i | ||||
\(576\) | −3.00000 | + | 5.19615i | −0.125000 | + | 0.216506i | ||||
\(577\) | 13.8564 | − | 8.00000i | 0.576850 | − | 0.333044i | −0.183031 | − | 0.983107i | \(-0.558591\pi\) |
0.759880 | + | 0.650063i | \(0.225257\pi\) | |||||||
\(578\) | −11.2583 | + | 6.50000i | −0.468285 | + | 0.270364i | ||||
\(579\) | −30.0000 | + | 51.9615i | −1.24676 | + | 2.15945i | ||||
\(580\) | −1.00000 | + | 2.00000i | −0.0415227 | + | 0.0830455i | ||||
\(581\) | −22.5000 | − | 7.79423i | −0.933457 | − | 0.323359i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −5.00000 | − | 8.66025i | −0.206901 | − | 0.358364i | ||||
\(585\) | −1.60770 | − | 26.7846i | −0.0664700 | − | 1.10741i | ||||
\(586\) | −12.0000 | + | 20.7846i | −0.495715 | + | 0.858604i | ||||
\(587\) | − | 28.0000i | − | 1.15568i | −0.816149 | − | 0.577842i | \(-0.803895\pi\) | ||
0.816149 | − | 0.577842i | \(-0.196105\pi\) | |||||||
\(588\) | 7.79423 | + | 19.5000i | 0.321429 | + | 0.804166i | ||||
\(589\) | 20.0000 | 0.824086 | ||||||||
\(590\) | −3.73205 | + | 2.46410i | −0.153646 | + | 0.101445i | ||||
\(591\) | −12.0000 | − | 20.7846i | −0.493614 | − | 0.854965i | ||||
\(592\) | 6.92820 | − | 4.00000i | 0.284747 | − | 0.164399i | ||||
\(593\) | −36.3731 | − | 21.0000i | −1.49366 | − | 0.862367i | −0.493689 | − | 0.869638i | \(-0.664352\pi\) |
−0.999974 | + | 0.00727173i | \(0.997685\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.46410 | − | 8.26795i | 0.346994 | − | 0.338953i | ||||
\(596\) | −15.0000 | −0.614424 | ||||||||
\(597\) | −31.1769 | − | 18.0000i | −1.27599 | − | 0.736691i | ||||
\(598\) | 1.73205 | − | 1.00000i | 0.0708288 | − | 0.0408930i | ||||
\(599\) | 18.0000 | + | 31.1769i | 0.735460 | + | 1.27385i | 0.954521 | + | 0.298143i | \(0.0963673\pi\) |
−0.219061 | + | 0.975711i | \(0.570299\pi\) | |||||||
\(600\) | 14.8923 | − | 1.79423i | 0.607976 | − | 0.0732491i | ||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 8.66025 | + | 10.0000i | 0.352966 | + | 0.407570i | ||||
\(603\) | − | 42.0000i | − | 1.71037i | ||||||
\(604\) | 3.00000 | − | 5.19615i | 0.122068 | − | 0.211428i | ||||
\(605\) | 24.5526 | − | 1.47372i | 0.998203 | − | 0.0599153i | ||||
\(606\) | −22.5000 | − | 38.9711i | −0.914000 | − | 1.58309i | ||||
\(607\) | 4.33013 | + | 2.50000i | 0.175754 | + | 0.101472i | 0.585296 | − | 0.810819i | \(-0.300978\pi\) |
−0.409542 | + | 0.912291i | \(0.634311\pi\) | |||||||
\(608\) | − | 2.00000i | − | 0.0811107i | ||||||
\(609\) | 1.50000 | + | 7.79423i | 0.0607831 | + | 0.315838i | ||||
\(610\) | 18.0000 | + | 9.00000i | 0.728799 | + | 0.364399i | ||||
\(611\) | 8.00000 | − | 13.8564i | 0.323645 | − | 0.560570i | ||||
\(612\) | 10.3923 | − | 6.00000i | 0.420084 | − | 0.242536i | ||||
\(613\) | 15.5885 | − | 9.00000i | 0.629612 | − | 0.363507i | −0.150990 | − | 0.988535i | \(-0.548246\pi\) |
0.780602 | + | 0.625029i | \(0.214913\pi\) | |||||||
\(614\) | −9.50000 | + | 16.4545i | −0.383389 | + | 0.664049i | ||||
\(615\) | 18.0000 | + | 9.00000i | 0.725830 | + | 0.362915i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 20.0000i | − | 0.805170i | −0.915383 | − | 0.402585i | \(-0.868112\pi\) | ||
0.915383 | − | 0.402585i | \(-0.131888\pi\) | |||||||
\(618\) | −28.5788 | − | 16.5000i | −1.14961 | − | 0.663727i | ||||
\(619\) | −10.0000 | − | 17.3205i | −0.401934 | − | 0.696170i | 0.592025 | − | 0.805919i | \(-0.298329\pi\) |
−0.993959 | + | 0.109749i | \(0.964995\pi\) | |||||||
\(620\) | 22.3205 | − | 1.33975i | 0.896413 | − | 0.0538055i | ||||
\(621\) | −4.50000 | + | 7.79423i | −0.180579 | + | 0.312772i | ||||
\(622\) | − | 6.00000i | − | 0.240578i | ||||||
\(623\) | 12.1244 | + | 14.0000i | 0.485752 | + | 0.560898i | ||||
\(624\) | −6.00000 | −0.240192 | ||||||||
\(625\) | −17.2846 | − | 18.0622i | −0.691384 | − | 0.722487i | ||||
\(626\) | −4.00000 | − | 6.92820i | −0.159872 | − | 0.276907i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.3923 | + | 6.00000i | 0.414698 | + | 0.239426i | ||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 25.3923 | − | 24.8038i | 1.01165 | − | 0.988209i | ||||
\(631\) | −24.0000 | −0.955425 | −0.477712 | − | 0.878516i | \(-0.658534\pi\) | ||||
−0.477712 | + | 0.878516i | \(0.658534\pi\) | |||||||
\(632\) | −8.66025 | − | 5.00000i | −0.344486 | − | 0.198889i | ||||
\(633\) | 46.7654 | − | 27.0000i | 1.85876 | − | 1.07315i | ||||
\(634\) | 11.0000 | + | 19.0526i | 0.436866 | + | 0.756674i | ||||
\(635\) | −14.9282 | + | 9.85641i | −0.592408 | + | 0.391140i | ||||
\(636\) | 18.0000 | 0.713746 | ||||||||
\(637\) | −8.66025 | + | 11.0000i | −0.343132 | + | 0.435836i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.0000 | − | 31.1769i | 0.712069 | − | 1.23334i | ||||
\(640\) | −0.133975 | − | 2.23205i | −0.00529581 | − | 0.0882296i | ||||
\(641\) | 17.5000 | + | 30.3109i | 0.691208 | + | 1.19721i | 0.971442 | + | 0.237276i | \(0.0762547\pi\) |
−0.280234 | + | 0.959932i | \(0.590412\pi\) | |||||||
\(642\) | 18.1865 | + | 10.5000i | 0.717765 | + | 0.414402i | ||||
\(643\) | − | 20.0000i | − | 0.788723i | −0.918955 | − | 0.394362i | \(-0.870966\pi\) | ||
0.918955 | − | 0.394362i | \(-0.129034\pi\) | |||||||
\(644\) | 2.50000 | + | 0.866025i | 0.0985138 | + | 0.0341262i | ||||
\(645\) | 15.0000 | − | 30.0000i | 0.590624 | − | 1.18125i | ||||
\(646\) | −2.00000 | + | 3.46410i | −0.0786889 | + | 0.136293i | ||||
\(647\) | −18.1865 | + | 10.5000i | −0.714986 | + | 0.412798i | −0.812905 | − | 0.582397i | \(-0.802115\pi\) |
0.0979182 | + | 0.995194i | \(0.468782\pi\) | |||||||
\(648\) | 7.79423 | − | 4.50000i | 0.306186 | − | 0.176777i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 6.00000 | + | 8.00000i | 0.235339 | + | 0.313786i | ||||
\(651\) | 60.0000 | − | 51.9615i | 2.35159 | − | 2.03653i | ||||
\(652\) | − | 12.0000i | − | 0.469956i | ||||||
\(653\) | −36.3731 | − | 21.0000i | −1.42339 | − | 0.821794i | −0.426801 | − | 0.904345i | \(-0.640360\pi\) |
−0.996587 | + | 0.0825519i | \(0.973693\pi\) | |||||||
\(654\) | −7.50000 | − | 12.9904i | −0.293273 | − | 0.507964i | ||||
\(655\) | −44.6410 | + | 2.67949i | −1.74427 | + | 0.104696i | ||||
\(656\) | 1.50000 | − | 2.59808i | 0.0585652 | − | 0.101438i | ||||
\(657\) | 60.0000i | 2.34082i | ||||||||
\(658\) | 20.7846 | − | 4.00000i | 0.810268 | − | 0.155936i | ||||
\(659\) | −30.0000 | −1.16863 | −0.584317 | − | 0.811525i | \(-0.698638\pi\) | ||||
−0.584317 | + | 0.811525i | \(0.698638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.5000 | + | 35.5070i | 0.797358 | + | 1.38106i | 0.921331 | + | 0.388778i | \(0.127103\pi\) |
−0.123974 | + | 0.992286i | \(0.539564\pi\) | |||||||
\(662\) | −12.1244 | + | 7.00000i | −0.471226 | + | 0.272063i | ||||
\(663\) | 10.3923 | + | 6.00000i | 0.403604 | + | 0.233021i | ||||
\(664\) | 9.00000 | 0.349268 | ||||||||
\(665\) | −3.19615 | + | 11.3923i | −0.123941 | + | 0.441775i | ||||
\(666\) | −48.0000 | −1.85996 | ||||||||
\(667\) | 0.866025 | + | 0.500000i | 0.0335326 | + | 0.0193601i | ||||
\(668\) | −7.79423 | + | 4.50000i | −0.301568 | + | 0.174110i | ||||
\(669\) | 12.0000 | + | 20.7846i | 0.463947 | + | 0.803579i | ||||
\(670\) | 8.62436 | + | 13.0622i | 0.333188 | + | 0.504636i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −5.19615 | − | 6.00000i | −0.200446 | − | 0.231455i | ||||
\(673\) | 20.0000i | 0.770943i | 0.922720 | + | 0.385472i | \(0.125961\pi\) | ||||
−0.922720 | + | 0.385472i | \(0.874039\pi\) | |||||||
\(674\) | −1.00000 | + | 1.73205i | −0.0385186 | + | 0.0667161i | ||||
\(675\) | −41.3827 | − | 17.6769i | −1.59282 | − | 0.680385i | ||||
\(676\) | 4.50000 | + | 7.79423i | 0.173077 | + | 0.299778i | ||||
\(677\) | −1.73205 | − | 1.00000i | −0.0665681 | − | 0.0384331i | 0.466347 | − | 0.884602i | \(-0.345570\pi\) |
−0.532915 | + | 0.846169i | \(0.678903\pi\) | |||||||
\(678\) | 30.0000i | 1.15214i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.00000 | + | 4.00000i | −0.0766965 | + | 0.153393i | ||||
\(681\) | 18.0000 | − | 31.1769i | 0.689761 | − | 1.19470i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.6506 | − | 12.5000i | 0.828439 | − | 0.478299i | −0.0248792 | − | 0.999690i | \(-0.507920\pi\) |
0.853318 | + | 0.521391i | \(0.174587\pi\) | |||||||
\(684\) | −6.00000 | + | 10.3923i | −0.229416 | + | 0.397360i | ||||
\(685\) | −32.0000 | − | 16.0000i | −1.22266 | − | 0.611329i | ||||
\(686\) | −18.5000 | + | 0.866025i | −0.706333 | + | 0.0330650i | ||||
\(687\) | 30.0000i | 1.14457i | ||||||||
\(688\) | −4.33013 | − | 2.50000i | −0.165085 | − | 0.0953116i | ||||
\(689\) | 6.00000 | + | 10.3923i | 0.228582 | + | 0.395915i | ||||
\(690\) | −0.401924 | − | 6.69615i | −0.0153010 | − | 0.254918i | ||||
\(691\) | 10.0000 | − | 17.3205i | 0.380418 | − | 0.658903i | −0.610704 | − | 0.791859i | \(-0.709113\pi\) |
0.991122 | + | 0.132956i | \(0.0424468\pi\) | |||||||
\(692\) | − | 12.0000i | − | 0.456172i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.0000 | −0.797149 | ||||||||
\(695\) | 9.85641 | + | 14.9282i | 0.373875 | + | 0.566259i | ||||
\(696\) | −1.50000 | − | 2.59808i | −0.0568574 | − | 0.0984798i | ||||
\(697\) | −5.19615 | + | 3.00000i | −0.196818 | + | 0.113633i | ||||
\(698\) | 7.79423 | + | 4.50000i | 0.295016 | + | 0.170328i | ||||
\(699\) | −42.0000 | −1.58859 | ||||||||
\(700\) | −2.80385 | + | 12.9282i | −0.105975 | + | 0.488640i | ||||
\(701\) | −1.00000 | −0.0377695 | −0.0188847 | − | 0.999822i | \(-0.506012\pi\) | ||||
−0.0188847 | + | 0.999822i | \(0.506012\pi\) | |||||||
\(702\) | 15.5885 | + | 9.00000i | 0.588348 | + | 0.339683i | ||||
\(703\) | 13.8564 | − | 8.00000i | 0.522604 | − | 0.301726i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −29.5692 | − | 44.7846i | −1.11364 | − | 1.68669i | ||||
\(706\) | −6.00000 | −0.225813 | ||||||||
\(707\) | 38.9711 | − | 7.50000i | 1.46566 | − | 0.282067i | ||||
\(708\) | − | 6.00000i | − | 0.225494i | ||||||
\(709\) | −4.50000 | + | 7.79423i | −0.169001 | + | 0.292718i | −0.938069 | − | 0.346449i | \(-0.887387\pi\) |
0.769068 | + | 0.639167i | \(0.220721\pi\) | |||||||
\(710\) | 0.803848 | + | 13.3923i | 0.0301679 | + | 0.502604i | ||||
\(711\) | 30.0000 | + | 51.9615i | 1.12509 | + | 1.94871i | ||||
\(712\) | −6.06218 | − | 3.50000i | −0.227190 | − | 0.131168i | ||||
\(713\) | − | 10.0000i | − | 0.374503i | ||||||
\(714\) | 3.00000 | + | 15.5885i | 0.112272 | + | 0.583383i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.0000 | − | 22.5167i | 0.485833 | − | 0.841487i | ||||
\(717\) | −25.9808 | + | 15.0000i | −0.970269 | + | 0.560185i | ||||
\(718\) | −12.1244 | + | 7.00000i | −0.452477 | + | 0.261238i | ||||
\(719\) | 10.0000 | − | 17.3205i | 0.372937 | − | 0.645946i | −0.617079 | − | 0.786901i | \(-0.711684\pi\) |
0.990016 | + | 0.140955i | \(0.0450174\pi\) | |||||||
\(720\) | −6.00000 | + | 12.0000i | −0.223607 | + | 0.447214i | ||||
\(721\) | 22.0000 | − | 19.0526i | 0.819323 | − | 0.709554i | ||||
\(722\) | 15.0000i | 0.558242i | ||||||||
\(723\) | 46.7654 | + | 27.0000i | 1.73922 | + | 1.00414i | ||||
\(724\) | 2.50000 | + | 4.33013i | 0.0929118 | + | 0.160928i | ||||
\(725\) | −1.96410 | + | 4.59808i | −0.0729449 | + | 0.170768i | ||||
\(726\) | −16.5000 | + | 28.5788i | −0.612372 | + | 1.06066i | ||||
\(727\) | 29.0000i | 1.07555i | 0.843088 | + | 0.537775i | \(0.180735\pi\) | ||||
−0.843088 | + | 0.537775i | \(0.819265\pi\) | |||||||
\(728\) | 1.73205 | − | 5.00000i | 0.0641941 | − | 0.185312i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −12.3205 | − | 18.6603i | −0.456002 | − | 0.690647i | ||||
\(731\) | 5.00000 | + | 8.66025i | 0.184932 | + | 0.320311i | ||||
\(732\) | −23.3827 | + | 13.5000i | −0.864249 | + | 0.498974i | ||||
\(733\) | 13.8564 | + | 8.00000i | 0.511798 | + | 0.295487i | 0.733572 | − | 0.679611i | \(-0.237852\pi\) |
−0.221774 | + | 0.975098i | \(0.571185\pi\) | |||||||
\(734\) | 23.0000 | 0.848945 | ||||||||
\(735\) | 20.0096 | + | 42.4808i | 0.738066 | + | 1.56693i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −15.5885 | + | 9.00000i | −0.573819 | + | 0.331295i | ||||
\(739\) | −16.0000 | − | 27.7128i | −0.588570 | − | 1.01943i | −0.994420 | − | 0.105493i | \(-0.966358\pi\) |
0.405851 | − | 0.913939i | \(-0.366975\pi\) | |||||||
\(740\) | 14.9282 | − | 9.85641i | 0.548772 | − | 0.362329i | ||||
\(741\) | −12.0000 | −0.440831 | ||||||||
\(742\) | −5.19615 | + | 15.0000i | −0.190757 | + | 0.550667i | ||||
\(743\) | − | 3.00000i | − | 0.110059i | −0.998485 | − | 0.0550297i | \(-0.982475\pi\) | ||
0.998485 | − | 0.0550297i | \(-0.0175253\pi\) | |||||||
\(744\) | −15.0000 | + | 25.9808i | −0.549927 | + | 0.952501i | ||||
\(745\) | −33.4808 | + | 2.00962i | −1.22664 | + | 0.0736267i | ||||
\(746\) | −4.00000 | − | 6.92820i | −0.146450 | − | 0.253660i | ||||
\(747\) | −46.7654 | − | 27.0000i | −1.71106 | − | 0.987878i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.0000 | + | 12.1244i | −0.511549 | + | 0.443014i | ||||
\(750\) | 33.0000 | − | 6.00000i | 1.20499 | − | 0.219089i | ||||
\(751\) | −2.00000 | + | 3.46410i | −0.0729810 | + | 0.126407i | −0.900207 | − | 0.435463i | \(-0.856585\pi\) |
0.827225 | + | 0.561870i | \(0.189918\pi\) | |||||||
\(752\) | −6.92820 | + | 4.00000i | −0.252646 | + | 0.145865i | ||||
\(753\) | 25.9808 | − | 15.0000i | 0.946792 | − | 0.546630i | ||||
\(754\) | 1.00000 | − | 1.73205i | 0.0364179 | − | 0.0630776i | ||||
\(755\) | 6.00000 | − | 12.0000i | 0.218362 | − | 0.436725i | ||||
\(756\) | 4.50000 | + | 23.3827i | 0.163663 | + | 0.850420i | ||||
\(757\) | 6.00000i | 0.218074i | 0.994038 | + | 0.109037i | \(0.0347767\pi\) | ||||
−0.994038 | + | 0.109037i | \(0.965223\pi\) | |||||||
\(758\) | 1.73205 | + | 1.00000i | 0.0629109 | + | 0.0363216i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.267949 | − | 4.46410i | −0.00971954 | − | 0.161930i | ||||
\(761\) | 25.0000 | − | 43.3013i | 0.906249 | − | 1.56967i | 0.0870179 | − | 0.996207i | \(-0.472266\pi\) |
0.819231 | − | 0.573463i | \(-0.194400\pi\) | |||||||
\(762\) | − | 24.0000i | − | 0.869428i | ||||||
\(763\) | 12.9904 | − | 2.50000i | 0.470283 | − | 0.0905061i | ||||
\(764\) | 20.0000 | 0.723575 | ||||||||
\(765\) | 22.3923 | − | 14.7846i | 0.809595 | − | 0.534539i | ||||
\(766\) | 4.50000 | + | 7.79423i | 0.162592 | + | 0.281617i | ||||
\(767\) | 3.46410 | − | 2.00000i | 0.125081 | − | 0.0722158i | ||||
\(768\) | 2.59808 | + | 1.50000i | 0.0937500 | + | 0.0541266i | ||||
\(769\) | −34.0000 | −1.22607 | −0.613036 | − | 0.790055i | \(-0.710052\pi\) | ||||
−0.613036 | + | 0.790055i | \(0.710052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −36.0000 | −1.29651 | ||||||||
\(772\) | 17.3205 | + | 10.0000i | 0.623379 | + | 0.359908i | ||||
\(773\) | −15.5885 | + | 9.00000i | −0.560678 | + | 0.323708i | −0.753418 | − | 0.657542i | \(-0.771596\pi\) |
0.192740 | + | 0.981250i | \(0.438263\pi\) | |||||||
\(774\) | 15.0000 | + | 25.9808i | 0.539164 | + | 0.933859i | ||||
\(775\) | 49.6410 | − | 5.98076i | 1.78316 | − | 0.214835i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20.7846 | − | 60.0000i | 0.745644 | − | 2.15249i | ||||
\(778\) | − | 18.0000i | − | 0.645331i | ||||||
\(779\) | 3.00000 | − | 5.19615i | 0.107486 | − | 0.186171i | ||||
\(780\) | −13.3923 | + | 0.803848i | −0.479521 | + | 0.0287824i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.73205 | + | 1.00000i | 0.0619380 | + | 0.0357599i | ||||
\(783\) | 9.00000i | 0.321634i | ||||||||
\(784\) | 6.50000 | − | 2.59808i | 0.232143 | − | 0.0927884i | ||||
\(785\) | 24.0000 | + | 12.0000i | 0.856597 | + | 0.428298i | ||||
\(786\) | 30.0000 | − | 51.9615i | 1.07006 | − | 1.85341i | ||||
\(787\) | −18.1865 | + | 10.5000i | −0.648280 | + | 0.374285i | −0.787797 | − | 0.615935i | \(-0.788778\pi\) |
0.139517 | + | 0.990220i | \(0.455445\pi\) | |||||||
\(788\) | −6.92820 | + | 4.00000i | −0.246807 | + | 0.142494i | ||||
\(789\) | −31.5000 | + | 54.5596i | −1.12143 | + | 1.94237i | ||||
\(790\) | −20.0000 | − | 10.0000i | −0.711568 | − | 0.355784i | ||||
\(791\) | −25.0000 | − | 8.66025i | −0.888898 | − | 0.307923i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.5885 | − | 9.00000i | −0.553562 | − | 0.319599i | ||||
\(794\) | −16.0000 | − | 27.7128i | −0.567819 | − | 0.983491i | ||||
\(795\) | 40.1769 | − | 2.41154i | 1.42493 | − | 0.0855286i | ||||
\(796\) | −6.00000 | + | 10.3923i | −0.212664 | + | 0.368345i | ||||
\(797\) | 8.00000i | 0.283375i | 0.989911 | + | 0.141687i | \(0.0452527\pi\) | ||||
−0.989911 | + | 0.141687i | \(0.954747\pi\) | |||||||
\(798\) | −10.3923 | − | 12.0000i | −0.367884 | − | 0.424795i | ||||
\(799\) | 16.0000 | 0.566039 | ||||||||
\(800\) | −0.598076 | − | 4.96410i | −0.0211452 | − | 0.175507i | ||||
\(801\) | 21.0000 | + | 36.3731i | 0.741999 | + | 1.28518i | ||||
\(802\) | −2.59808 | + | 1.50000i | −0.0917413 | + | 0.0529668i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −21.0000 | −0.740613 | ||||||||
\(805\) | 5.69615 | + | 1.59808i | 0.200763 | + | 0.0563248i | ||||
\(806\) | −20.0000 | −0.704470 | ||||||||
\(807\) | −12.9904 | − | 7.50000i | −0.457283 | − | 0.264013i | ||||
\(808\) | −12.9904 | + | 7.50000i | −0.457000 | + | 0.263849i | ||||
\(809\) | 12.5000 | + | 21.6506i | 0.439477 | + | 0.761196i | 0.997649 | − | 0.0685291i | \(-0.0218306\pi\) |
−0.558173 | + | 0.829725i | \(0.688497\pi\) | |||||||
\(810\) | 16.7942 | − | 11.0885i | 0.590089 | − | 0.389609i | ||||
\(811\) | 6.00000 | 0.210688 | 0.105344 | − | 0.994436i | \(-0.466406\pi\) | ||||
0.105344 | + | 0.994436i | \(0.466406\pi\) | |||||||
\(812\) | 2.59808 | − | 0.500000i | 0.0911746 | − | 0.0175466i | ||||
\(813\) | − | 18.0000i | − | 0.631288i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.60770 | − | 26.7846i | −0.0563151 | − | 0.938224i | ||||
\(816\) | −3.00000 | − | 5.19615i | −0.105021 | − | 0.181902i | ||||
\(817\) | −8.66025 | − | 5.00000i | −0.302984 | − | 0.174928i | ||||
\(818\) | − | 17.0000i | − | 0.594391i | ||||||
\(819\) | −24.0000 | + | 20.7846i | −0.838628 | + | 0.726273i | ||||
\(820\) | 3.00000 | − | 6.00000i | 0.104765 | − | 0.209529i | ||||
\(821\) | 21.0000 | − | 36.3731i | 0.732905 | − | 1.26943i | −0.222731 | − | 0.974880i | \(-0.571497\pi\) |
0.955636 | − | 0.294549i | \(-0.0951694\pi\) | |||||||
\(822\) | 41.5692 | − | 24.0000i | 1.44989 | − | 0.837096i | ||||
\(823\) | −38.9711 | + | 22.5000i | −1.35845 | + | 0.784301i | −0.989415 | − | 0.145115i | \(-0.953645\pi\) |
−0.369034 | + | 0.929416i | \(0.620311\pi\) | |||||||
\(824\) | −5.50000 | + | 9.52628i | −0.191602 | + | 0.331864i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.00000 | + | 1.73205i | 0.173972 | + | 0.0602658i | ||||
\(827\) | 37.0000i | 1.28662i | 0.765607 | + | 0.643308i | \(0.222439\pi\) | ||||
−0.765607 | + | 0.643308i | \(0.777561\pi\) | |||||||
\(828\) | 5.19615 | + | 3.00000i | 0.180579 | + | 0.104257i | ||||
\(829\) | 17.0000 | + | 29.4449i | 0.590434 | + | 1.02266i | 0.994174 | + | 0.107788i | \(0.0343769\pi\) |
−0.403739 | + | 0.914874i | \(0.632290\pi\) | |||||||
\(830\) | 20.0885 | − | 1.20577i | 0.697281 | − | 0.0418529i | ||||
\(831\) | −39.0000 | + | 67.5500i | −1.35290 | + | 2.34328i | ||||
\(832\) | 2.00000i | 0.0693375i | ||||||||
\(833\) | −13.8564 | − | 2.00000i | −0.480096 | − | 0.0692959i | ||||
\(834\) | −24.0000 | −0.831052 | ||||||||
\(835\) | −16.7942 | + | 11.0885i | −0.581188 | + | 0.383732i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 77.9423 | − | 45.0000i | 2.69408 | − | 1.55543i | ||||
\(838\) | 34.6410 | + | 20.0000i | 1.19665 | + | 0.690889i | ||||
\(839\) | −32.0000 | −1.10476 | −0.552381 | − | 0.833592i | \(-0.686281\pi\) | ||||
−0.552381 | + | 0.833592i | \(0.686281\pi\) | |||||||
\(840\) | −12.4019 | − | 12.6962i | −0.427907 | − | 0.438059i | ||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 26.8468 | + | 15.5000i | 0.925201 | + | 0.534165i | ||||
\(843\) | −46.7654 | + | 27.0000i | −1.61068 | + | 0.929929i | ||||
\(844\) | −9.00000 | − | 15.5885i | −0.309793 | − | 0.536577i | ||||
\(845\) | 11.0885 | + | 16.7942i | 0.381455 | + | 0.577739i | ||||
\(846\) | 48.0000 | 1.65027 | ||||||||
\(847\) | −19.0526 | − | 22.0000i | −0.654654 | − | 0.755929i | ||||
\(848\) | − | 6.00000i | − | 0.206041i | ||||||
\(849\) | −12.0000 | + | 20.7846i | −0.411839 | + | 0.713326i | ||||
\(850\) | −3.92820 | + | 9.19615i | −0.134736 | + | 0.315425i | ||||
\(851\) | −4.00000 | − | 6.92820i | −0.137118 | − | 0.237496i | ||||
\(852\) | −15.5885 | − | 9.00000i | −0.534052 | − | 0.308335i | ||||
\(853\) | − | 10.0000i | − | 0.342393i | −0.985237 | − | 0.171197i | \(-0.945237\pi\) | ||
0.985237 | − | 0.171197i | \(-0.0547634\pi\) | |||||||
\(854\) | −4.50000 | − | 23.3827i | −0.153987 | − | 0.800139i | ||||
\(855\) | −12.0000 | + | 24.0000i | −0.410391 | + | 0.820783i | ||||
\(856\) | 3.50000 | − | 6.06218i | 0.119628 | − | 0.207201i | ||||
\(857\) | 3.46410 | − | 2.00000i | 0.118331 | − | 0.0683187i | −0.439666 | − | 0.898161i | \(-0.644903\pi\) |
0.557998 | + | 0.829843i | \(0.311570\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(860\) | −10.0000 | − | 5.00000i | −0.340997 | − | 0.170499i | ||||
\(861\) | −4.50000 | − | 23.3827i | −0.153360 | − | 0.796880i | ||||
\(862\) | − | 32.0000i | − | 1.08992i | ||||||
\(863\) | 9.52628 | + | 5.50000i | 0.324278 | + | 0.187222i | 0.653298 | − | 0.757101i | \(-0.273385\pi\) |
−0.329020 | + | 0.944323i | \(0.606718\pi\) | |||||||
\(864\) | −4.50000 | − | 7.79423i | −0.153093 | − | 0.265165i | ||||
\(865\) | −1.60770 | − | 26.7846i | −0.0546633 | − | 0.910704i | ||||
\(866\) | 7.00000 | − | 12.1244i | 0.237870 | − | 0.412002i | ||||
\(867\) | − | 39.0000i | − | 1.32451i | ||||||
\(868\) | −17.3205 | − | 20.0000i | −0.587896 | − | 0.678844i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −3.69615 | − | 5.59808i | −0.125311 | − | 0.189793i | ||||
\(871\) | −7.00000 | − | 12.1244i | −0.237186 | − | 0.410818i | ||||
\(872\) | −4.33013 | + | 2.50000i | −0.146637 | + | 0.0846607i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.00000 | −0.0676510 | ||||||||
\(875\) | −4.52628 | + | 29.2321i | −0.153016 | + | 0.988224i | ||||
\(876\) | 30.0000 | 1.01361 | ||||||||
\(877\) | −12.1244 | − | 7.00000i | −0.409410 | − | 0.236373i | 0.281126 | − | 0.959671i | \(-0.409292\pi\) |
−0.690536 | + | 0.723298i | \(0.742625\pi\) | |||||||
\(878\) | 6.92820 | − | 4.00000i | 0.233816 | − | 0.134993i | ||||
\(879\) | −36.0000 | − | 62.3538i | −1.21425 | − | 2.10314i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.00000 | −0.101073 | −0.0505363 | − | 0.998722i | \(-0.516093\pi\) | ||||
−0.0505363 | + | 0.998722i | \(0.516093\pi\) | |||||||
\(882\) | −41.5692 | − | 6.00000i | −1.39971 | − | 0.202031i | ||||
\(883\) | 4.00000i | 0.134611i | 0.997732 | + | 0.0673054i | \(0.0214402\pi\) | ||||
−0.997732 | + | 0.0673054i | \(0.978560\pi\) | |||||||
\(884\) | 2.00000 | − | 3.46410i | 0.0672673 | − | 0.116510i | ||||
\(885\) | −0.803848 | − | 13.3923i | −0.0270210 | − | 0.450177i | ||||
\(886\) | 1.50000 | + | 2.59808i | 0.0503935 | + | 0.0872841i | ||||
\(887\) | 7.79423 | + | 4.50000i | 0.261705 | + | 0.151095i | 0.625112 | − | 0.780535i | \(-0.285053\pi\) |
−0.363407 | + | 0.931630i | \(0.618387\pi\) | |||||||
\(888\) | 24.0000i | 0.805387i | ||||||||
\(889\) | 20.0000 | + | 6.92820i | 0.670778 | + | 0.232364i | ||||
\(890\) | −14.0000 | − | 7.00000i | −0.469281 | − | 0.234641i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.92820 | − | 4.00000i | 0.231973 | − | 0.133930i | ||||
\(893\) | −13.8564 | + | 8.00000i | −0.463687 | + | 0.267710i | ||||
\(894\) | 22.5000 | − | 38.9711i | 0.752513 | − | 1.30339i | ||||
\(895\) | 26.0000 | − | 52.0000i | 0.869084 | − | 1.73817i | ||||
\(896\) | −2.00000 | + | 1.73205i | −0.0668153 | + | 0.0578638i | ||||
\(897\) | 6.00000i | 0.200334i | ||||||||
\(898\) | −19.9186 | − | 11.5000i | −0.664692 | − | 0.383760i | ||||
\(899\) | −5.00000 | − | 8.66025i | −0.166759 | − | 0.288836i | ||||
\(900\) | −11.7846 | + | 27.5885i | −0.392820 | + | 0.919615i | ||||
\(901\) | −6.00000 | + | 10.3923i | −0.199889 | + | 0.346218i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −38.9711 | + | 7.50000i | −1.29688 | + | 0.249584i | ||||
\(904\) | 10.0000 | 0.332595 | ||||||||
\(905\) | 6.16025 | + | 9.33013i | 0.204774 | + | 0.310144i | ||||
\(906\) | 9.00000 | + | 15.5885i | 0.299005 | + | 0.517892i | ||||
\(907\) | 21.6506 | − | 12.5000i | 0.718898 | − | 0.415056i | −0.0954492 | − | 0.995434i | \(-0.530429\pi\) |
0.814347 | + | 0.580379i | \(0.197095\pi\) | |||||||
\(908\) | −10.3923 | − | 6.00000i | −0.344881 | − | 0.199117i | ||||
\(909\) | 90.0000 | 2.98511 | ||||||||
\(910\) | 3.19615 | − | 11.3923i | 0.105951 | − | 0.377651i | ||||
\(911\) | 8.00000 | 0.265052 | 0.132526 | − | 0.991180i | \(-0.457691\pi\) | ||||
0.132526 | + | 0.991180i | \(0.457691\pi\) | |||||||
\(912\) | 5.19615 | + | 3.00000i | 0.172062 | + | 0.0993399i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 16.0000 | + | 27.7128i | 0.529233 | + | 0.916658i | ||||
\(915\) | −50.3827 | + | 33.2654i | −1.66560 | + | 1.09972i | ||||
\(916\) | 10.0000 | 0.330409 | ||||||||
\(917\) | 34.6410 | + | 40.0000i | 1.14395 | + | 1.32092i | ||||
\(918\) | 18.0000i | 0.594089i | ||||||||
\(919\) | 13.0000 | − | 22.5167i | 0.428830 | − | 0.742756i | −0.567939 | − | 0.823071i | \(-0.692259\pi\) |
0.996770 | + | 0.0803145i | \(0.0255924\pi\) | |||||||
\(920\) | −2.23205 | + | 0.133975i | −0.0735885 | + | 0.00441701i | ||||
\(921\) | −28.5000 | − | 49.3634i | −0.939107 | − | 1.62658i | ||||
\(922\) | −12.1244 | − | 7.00000i | −0.399294 | − | 0.230533i | ||||
\(923\) | − | 12.0000i | − | 0.394985i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.0000 | − | 24.0000i | 1.05215 | − | 0.789115i | ||||
\(926\) | −12.5000 | + | 21.6506i | −0.410775 | + | 0.711484i | ||||
\(927\) | 57.1577 | − | 33.0000i | 1.87730 | − | 1.08386i | ||||
\(928\) | −0.866025 | + | 0.500000i | −0.0284287 | + | 0.0164133i | ||||
\(929\) | 13.5000 | − | 23.3827i | 0.442921 | − | 0.767161i | −0.554984 | − | 0.831861i | \(-0.687276\pi\) |
0.997905 | + | 0.0646999i | \(0.0206090\pi\) | |||||||
\(930\) | −30.0000 | + | 60.0000i | −0.983739 | + | 1.96748i | ||||
\(931\) | 13.0000 | − | 5.19615i | 0.426058 | − | 0.170297i | ||||
\(932\) | 14.0000i | 0.458585i | ||||||||
\(933\) | 15.5885 | + | 9.00000i | 0.510343 | + | 0.294647i | ||||
\(934\) | 0.500000 | + | 0.866025i | 0.0163605 | + | 0.0283372i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.00000 | − | 10.3923i | 0.196116 | − | 0.339683i | ||||
\(937\) | 56.0000i | 1.82944i | 0.404088 | + | 0.914720i | \(0.367589\pi\) | ||||
−0.404088 | + | 0.914720i | \(0.632411\pi\) | |||||||
\(938\) | 6.06218 | − | 17.5000i | 0.197937 | − | 0.571395i | ||||
\(939\) | 24.0000 | 0.783210 | ||||||||
\(940\) | −14.9282 | + | 9.85641i | −0.486904 | + | 0.321481i | ||||
\(941\) | −7.00000 | − | 12.1244i | −0.228193 | − | 0.395243i | 0.729079 | − | 0.684429i | \(-0.239949\pi\) |
−0.957273 | + | 0.289187i | \(0.906615\pi\) | |||||||
\(942\) | −31.1769 | + | 18.0000i | −1.01580 | + | 0.586472i | ||||
\(943\) | −2.59808 | − | 1.50000i | −0.0846050 | − | 0.0488467i | ||||
\(944\) | −2.00000 | −0.0650945 | ||||||||
\(945\) | 13.1769 | + | 51.5885i | 0.428645 | + | 1.67817i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.59808 | − | 1.50000i | −0.0844261 | − | 0.0487435i | 0.457193 | − | 0.889368i | \(-0.348855\pi\) |
−0.541619 | + | 0.840624i | \(0.682188\pi\) | |||||||
\(948\) | 25.9808 | − | 15.0000i | 0.843816 | − | 0.487177i | ||||
\(949\) | 10.0000 | + | 17.3205i | 0.324614 | + | 0.562247i | ||||
\(950\) | −1.19615 | − | 9.92820i | −0.0388083 | − | 0.322113i | ||||
\(951\) | −66.0000 | −2.14020 | ||||||||
\(952\) | 5.19615 | − | 1.00000i | 0.168408 | − | 0.0324102i | ||||
\(953\) | 36.0000i | 1.16615i | 0.812417 | + | 0.583077i | \(0.198151\pi\) | ||||
−0.812417 | + | 0.583077i | \(0.801849\pi\) | |||||||
\(954\) | −18.0000 | + | 31.1769i | −0.582772 | + | 1.00939i | ||||
\(955\) | 44.6410 | − | 2.67949i | 1.44455 | − | 0.0867063i | ||||
\(956\) | 5.00000 | + | 8.66025i | 0.161712 | + | 0.280093i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.0000i | 0.581554i | ||||||||
\(959\) | 8.00000 | + | 41.5692i | 0.258333 | + | 1.34234i | ||||
\(960\) | 6.00000 | + | 3.00000i | 0.193649 | + | 0.0968246i | ||||
\(961\) | −34.5000 | + | 59.7558i | −1.11290 | + | 1.92760i | ||||
\(962\) | −13.8564 | + | 8.00000i | −0.446748 | + | 0.257930i | ||||
\(963\) | −36.3731 | + | 21.0000i | −1.17211 | + | 0.676716i | ||||
\(964\) | 9.00000 | − | 15.5885i | 0.289870 | − | 0.502070i | ||||
\(965\) | 40.0000 | + | 20.0000i | 1.28765 | + | 0.643823i | ||||
\(966\) | −6.00000 | + | 5.19615i | −0.193047 | + | 0.167183i | ||||
\(967\) | − | 17.0000i | − | 0.546683i | −0.961917 | − | 0.273342i | \(-0.911871\pi\) | ||
0.961917 | − | 0.273342i | \(-0.0881289\pi\) | |||||||
\(968\) | 9.52628 | + | 5.50000i | 0.306186 | + | 0.176777i | ||||
\(969\) | −6.00000 | − | 10.3923i | −0.192748 | − | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.92820 | − | 20.0000i | 0.222108 | − | 0.641171i | ||||
\(974\) | −4.00000 | −0.128168 | ||||||||
\(975\) | −29.7846 | + | 3.58846i | −0.953871 | + | 0.114923i | ||||
\(976\) | 4.50000 | + | 7.79423i | 0.144041 | + | 0.249487i | ||||
\(977\) | −31.1769 | + | 18.0000i | −0.997438 | + | 0.575871i | −0.907489 | − | 0.420075i | \(-0.862004\pi\) |
−0.0899487 | + | 0.995946i | \(0.528670\pi\) | |||||||
\(978\) | 31.1769 | + | 18.0000i | 0.996928 | + | 0.575577i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 14.1603 | − | 6.66987i | 0.452333 | − | 0.213061i | ||||
\(981\) | 30.0000 | 0.957826 | ||||||||
\(982\) | −15.5885 | − | 9.00000i | −0.497448 | − | 0.287202i | ||||
\(983\) | 21.6506 | − | 12.5000i | 0.690548 | − | 0.398688i | −0.113269 | − | 0.993564i | \(-0.536132\pi\) |
0.803817 | + | 0.594876i | \(0.202799\pi\) | |||||||
\(984\) | 4.50000 | + | 7.79423i | 0.143455 | + | 0.248471i | ||||
\(985\) | −14.9282 | + | 9.85641i | −0.475652 | + | 0.314051i | ||||
\(986\) | 2.00000 | 0.0636930 | ||||||||
\(987\) | −20.7846 | + | 60.0000i | −0.661581 | + | 1.90982i | ||||
\(988\) | 4.00000i | 0.127257i | ||||||||
\(989\) | −2.50000 | + | 4.33013i | −0.0794954 | + | 0.137690i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.0000 | + | 22.5167i | 0.412959 | + | 0.715265i | 0.995212 | − | 0.0977423i | \(-0.0311621\pi\) |
−0.582253 | + | 0.813008i | \(0.697829\pi\) | |||||||
\(992\) | 8.66025 | + | 5.00000i | 0.274963 | + | 0.158750i | ||||
\(993\) | − | 42.0000i | − | 1.33283i | ||||||
\(994\) | 12.0000 | − | 10.3923i | 0.380617 | − | 0.329624i | ||||
\(995\) | −12.0000 | + | 24.0000i | −0.380426 | + | 0.760851i | ||||
\(996\) | −13.5000 | + | 23.3827i | −0.427764 | + | 0.740909i | ||||
\(997\) | −29.4449 | + | 17.0000i | −0.932528 | + | 0.538395i | −0.887610 | − | 0.460595i | \(-0.847636\pi\) |
−0.0449179 | + | 0.998991i | \(0.514303\pi\) | |||||||
\(998\) | 13.8564 | − | 8.00000i | 0.438617 | − | 0.253236i | ||||
\(999\) | 36.0000 | − | 62.3538i | 1.13899 | − | 1.97279i |
(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 | 70.2.i.a.9.2 | yes | 4 | |
3.2 | odd | 2 | 630.2.u.b.289.1 | 4 | |||
4.3 | odd | 2 | 560.2.bw.c.289.2 | 4 | |||
5.2 | odd | 4 | 350.2.e.f.51.1 | 2 | |||
5.3 | odd | 4 | 350.2.e.g.51.1 | 2 | |||
5.4 | even | 2 | inner | 70.2.i.a.9.1 | ✓ | 4 | |
7.2 | even | 3 | 490.2.c.c.99.1 | 2 | |||
7.3 | odd | 6 | 490.2.i.b.459.1 | 4 | |||
7.4 | even | 3 | inner | 70.2.i.a.39.1 | yes | 4 | |
7.5 | odd | 6 | 490.2.c.b.99.1 | 2 | |||
7.6 | odd | 2 | 490.2.i.b.79.2 | 4 | |||
15.14 | odd | 2 | 630.2.u.b.289.2 | 4 | |||
20.19 | odd | 2 | 560.2.bw.c.289.1 | 4 | |||
21.11 | odd | 6 | 630.2.u.b.109.2 | 4 | |||
28.11 | odd | 6 | 560.2.bw.c.529.1 | 4 | |||
35.2 | odd | 12 | 2450.2.a.s.1.1 | 1 | |||
35.4 | even | 6 | inner | 70.2.i.a.39.2 | yes | 4 | |
35.9 | even | 6 | 490.2.c.c.99.2 | 2 | |||
35.12 | even | 12 | 2450.2.a.bh.1.1 | 1 | |||
35.18 | odd | 12 | 350.2.e.g.151.1 | 2 | |||
35.19 | odd | 6 | 490.2.c.b.99.2 | 2 | |||
35.23 | odd | 12 | 2450.2.a.r.1.1 | 1 | |||
35.24 | odd | 6 | 490.2.i.b.459.2 | 4 | |||
35.32 | odd | 12 | 350.2.e.f.151.1 | 2 | |||
35.33 | even | 12 | 2450.2.a.c.1.1 | 1 | |||
35.34 | odd | 2 | 490.2.i.b.79.1 | 4 | |||
105.74 | odd | 6 | 630.2.u.b.109.1 | 4 | |||
140.39 | odd | 6 | 560.2.bw.c.529.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.i.a.9.1 | ✓ | 4 | 5.4 | even | 2 | inner | |
70.2.i.a.9.2 | yes | 4 | 1.1 | even | 1 | trivial | |
70.2.i.a.39.1 | yes | 4 | 7.4 | even | 3 | inner | |
70.2.i.a.39.2 | yes | 4 | 35.4 | even | 6 | inner | |
350.2.e.f.51.1 | 2 | 5.2 | odd | 4 | |||
350.2.e.f.151.1 | 2 | 35.32 | odd | 12 | |||
350.2.e.g.51.1 | 2 | 5.3 | odd | 4 | |||
350.2.e.g.151.1 | 2 | 35.18 | odd | 12 | |||
490.2.c.b.99.1 | 2 | 7.5 | odd | 6 | |||
490.2.c.b.99.2 | 2 | 35.19 | odd | 6 | |||
490.2.c.c.99.1 | 2 | 7.2 | even | 3 | |||
490.2.c.c.99.2 | 2 | 35.9 | even | 6 | |||
490.2.i.b.79.1 | 4 | 35.34 | odd | 2 | |||
490.2.i.b.79.2 | 4 | 7.6 | odd | 2 | |||
490.2.i.b.459.1 | 4 | 7.3 | odd | 6 | |||
490.2.i.b.459.2 | 4 | 35.24 | odd | 6 | |||
560.2.bw.c.289.1 | 4 | 20.19 | odd | 2 | |||
560.2.bw.c.289.2 | 4 | 4.3 | odd | 2 | |||
560.2.bw.c.529.1 | 4 | 28.11 | odd | 6 | |||
560.2.bw.c.529.2 | 4 | 140.39 | odd | 6 | |||
630.2.u.b.109.1 | 4 | 105.74 | odd | 6 | |||
630.2.u.b.109.2 | 4 | 21.11 | odd | 6 | |||
630.2.u.b.289.1 | 4 | 3.2 | odd | 2 | |||
630.2.u.b.289.2 | 4 | 15.14 | odd | 2 | |||
2450.2.a.c.1.1 | 1 | 35.33 | even | 12 | |||
2450.2.a.r.1.1 | 1 | 35.23 | odd | 12 | |||
2450.2.a.s.1.1 | 1 | 35.2 | odd | 12 | |||
2450.2.a.bh.1.1 | 1 | 35.12 | even | 12 |