Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [722,2,Mod(99,722)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(722, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("722.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 722 = 2 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 722.e (of order \(9\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.76519902594\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 423.1 | ||
Root | \(-0.173648 + 0.984808i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 722.423 |
Dual form | 722.2.e.h.99.1 |
$q$-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 \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).
\(n\) | \(363\) |
\(\chi(n)\) | \(e\left(\frac{8}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.939693 | − | 0.342020i | 0.664463 | − | 0.241845i | ||||
\(3\) | −0.520945 | + | 2.95442i | −0.300767 | + | 1.70574i | 0.342020 | + | 0.939693i | \(0.388889\pi\) |
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(4\) | 0.766044 | − | 0.642788i | 0.383022 | − | 0.321394i | ||||
\(5\) | 1.53209 | + | 1.28558i | 0.685171 | + | 0.574927i | 0.917512 | − | 0.397708i | \(-0.130194\pi\) |
−0.232341 | + | 0.972634i | \(0.574639\pi\) | |||||||
\(6\) | 0.520945 | + | 2.95442i | 0.212675 | + | 1.20614i | ||||
\(7\) | 1.50000 | + | 2.59808i | 0.566947 | + | 0.981981i | 0.996866 | + | 0.0791130i | \(0.0252088\pi\) |
−0.429919 | + | 0.902867i | \(0.641458\pi\) | |||||||
\(8\) | 0.500000 | − | 0.866025i | 0.176777 | − | 0.306186i | ||||
\(9\) | −5.63816 | − | 2.05212i | −1.87939 | − | 0.684040i | ||||
\(10\) | 1.87939 | + | 0.684040i | 0.594314 | + | 0.216313i | ||||
\(11\) | 1.00000 | − | 1.73205i | 0.301511 | − | 0.522233i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
0.976478 | + | 0.215615i | \(0.0691756\pi\) | |||||||
\(12\) | 1.50000 | + | 2.59808i | 0.433013 | + | 0.750000i | ||||
\(13\) | 0.520945 | + | 2.95442i | 0.144484 | + | 0.819410i | 0.967780 | + | 0.251797i | \(0.0810216\pi\) |
−0.823296 | + | 0.567612i | \(0.807867\pi\) | |||||||
\(14\) | 2.29813 | + | 1.92836i | 0.614202 | + | 0.515377i | ||||
\(15\) | −4.59627 | + | 3.85673i | −1.18675 | + | 0.995802i | ||||
\(16\) | 0.173648 | − | 0.984808i | 0.0434120 | − | 0.246202i | ||||
\(17\) | 0.939693 | − | 0.342020i | 0.227909 | − | 0.0829521i | −0.225542 | − | 0.974234i | \(-0.572415\pi\) |
0.453450 | + | 0.891281i | \(0.350193\pi\) | |||||||
\(18\) | −6.00000 | −1.41421 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 2.00000 | 0.447214 | ||||||||
\(21\) | −8.45723 | + | 3.07818i | −1.84552 | + | 0.671714i | ||||
\(22\) | 0.347296 | − | 1.96962i | 0.0740438 | − | 0.419923i | ||||
\(23\) | 3.83022 | − | 3.21394i | 0.798657 | − | 0.670152i | −0.149215 | − | 0.988805i | \(-0.547675\pi\) |
0.947872 | + | 0.318652i | \(0.103230\pi\) | |||||||
\(24\) | 2.29813 | + | 1.92836i | 0.469105 | + | 0.393625i | ||||
\(25\) | −0.173648 | − | 0.984808i | −0.0347296 | − | 0.196962i | ||||
\(26\) | 1.50000 | + | 2.59808i | 0.294174 | + | 0.509525i | ||||
\(27\) | 4.50000 | − | 7.79423i | 0.866025 | − | 1.50000i | ||||
\(28\) | 2.81908 | + | 1.02606i | 0.532756 | + | 0.193907i | ||||
\(29\) | −2.81908 | − | 1.02606i | −0.523490 | − | 0.190535i | 0.0667395 | − | 0.997770i | \(-0.478740\pi\) |
−0.590229 | + | 0.807236i | \(0.700963\pi\) | |||||||
\(30\) | −3.00000 | + | 5.19615i | −0.547723 | + | 0.948683i | ||||
\(31\) | −3.00000 | − | 5.19615i | −0.538816 | − | 0.933257i | −0.998968 | − | 0.0454165i | \(-0.985539\pi\) |
0.460152 | − | 0.887840i | \(-0.347795\pi\) | |||||||
\(32\) | −0.173648 | − | 0.984808i | −0.0306970 | − | 0.174091i | ||||
\(33\) | 4.59627 | + | 3.85673i | 0.800107 | + | 0.671370i | ||||
\(34\) | 0.766044 | − | 0.642788i | 0.131376 | − | 0.110237i | ||||
\(35\) | −1.04189 | + | 5.90885i | −0.176111 | + | 0.998777i | ||||
\(36\) | −5.63816 | + | 2.05212i | −0.939693 | + | 0.342020i | ||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.00000 | −1.44115 | ||||||||
\(40\) | 1.87939 | − | 0.684040i | 0.297157 | − | 0.108156i | ||||
\(41\) | −2.08378 | + | 11.8177i | −0.325431 | + | 1.84561i | 0.181194 | + | 0.983447i | \(0.442004\pi\) |
−0.506626 | + | 0.862166i | \(0.669107\pi\) | |||||||
\(42\) | −6.89440 | + | 5.78509i | −1.06383 | + | 0.892659i | ||||
\(43\) | −7.66044 | − | 6.42788i | −1.16821 | − | 0.980242i | −0.168222 | − | 0.985749i | \(-0.553803\pi\) |
−0.999985 | + | 0.00550722i | \(0.998247\pi\) | |||||||
\(44\) | −0.347296 | − | 1.96962i | −0.0523569 | − | 0.296931i | ||||
\(45\) | −6.00000 | − | 10.3923i | −0.894427 | − | 1.54919i | ||||
\(46\) | 2.50000 | − | 4.33013i | 0.368605 | − | 0.638442i | ||||
\(47\) | 7.51754 | + | 2.73616i | 1.09655 | + | 0.399110i | 0.826042 | − | 0.563609i | \(-0.190587\pi\) |
0.270504 | + | 0.962719i | \(0.412810\pi\) | |||||||
\(48\) | 2.81908 | + | 1.02606i | 0.406899 | + | 0.148099i | ||||
\(49\) | −1.00000 | + | 1.73205i | −0.142857 | + | 0.247436i | ||||
\(50\) | −0.500000 | − | 0.866025i | −0.0707107 | − | 0.122474i | ||||
\(51\) | 0.520945 | + | 2.95442i | 0.0729468 | + | 0.413702i | ||||
\(52\) | 2.29813 | + | 1.92836i | 0.318694 | + | 0.267416i | ||||
\(53\) | 2.29813 | − | 1.92836i | 0.315673 | − | 0.264881i | −0.471159 | − | 0.882048i | \(-0.656164\pi\) |
0.786832 | + | 0.617167i | \(0.211720\pi\) | |||||||
\(54\) | 1.56283 | − | 8.86327i | 0.212675 | − | 1.20614i | ||||
\(55\) | 3.75877 | − | 1.36808i | 0.506833 | − | 0.184472i | ||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.00000 | −0.393919 | ||||||||
\(59\) | 2.81908 | − | 1.02606i | 0.367013 | − | 0.133582i | −0.151929 | − | 0.988391i | \(-0.548548\pi\) |
0.518942 | + | 0.854810i | \(0.326326\pi\) | |||||||
\(60\) | −1.04189 | + | 5.90885i | −0.134507 | + | 0.762829i | ||||
\(61\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(62\) | −4.59627 | − | 3.85673i | −0.583726 | − | 0.489805i | ||||
\(63\) | −3.12567 | − | 17.7265i | −0.393797 | − | 2.23333i | ||||
\(64\) | −0.500000 | − | 0.866025i | −0.0625000 | − | 0.108253i | ||||
\(65\) | −3.00000 | + | 5.19615i | −0.372104 | + | 0.644503i | ||||
\(66\) | 5.63816 | + | 2.05212i | 0.694009 | + | 0.252599i | ||||
\(67\) | 14.0954 | + | 5.13030i | 1.72203 | + | 0.626766i | 0.998012 | − | 0.0630195i | \(-0.0200730\pi\) |
0.724014 | + | 0.689786i | \(0.242295\pi\) | |||||||
\(68\) | 0.500000 | − | 0.866025i | 0.0606339 | − | 0.105021i | ||||
\(69\) | 7.50000 | + | 12.9904i | 0.902894 | + | 1.56386i | ||||
\(70\) | 1.04189 | + | 5.90885i | 0.124530 | + | 0.706242i | ||||
\(71\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(72\) | −4.59627 | + | 3.85673i | −0.541675 | + | 0.454519i | ||||
\(73\) | −1.91013 | + | 10.8329i | −0.223564 | + | 1.26789i | 0.641848 | + | 0.766832i | \(0.278168\pi\) |
−0.865412 | + | 0.501061i | \(0.832943\pi\) | |||||||
\(74\) | −5.63816 | + | 2.05212i | −0.655422 | + | 0.238554i | ||||
\(75\) | 3.00000 | 0.346410 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.00000 | 0.683763 | ||||||||
\(78\) | −8.45723 | + | 3.07818i | −0.957593 | + | 0.348535i | ||||
\(79\) | 2.08378 | − | 11.8177i | 0.234443 | − | 1.32959i | −0.609339 | − | 0.792909i | \(-0.708565\pi\) |
0.843783 | − | 0.536685i | \(-0.180324\pi\) | |||||||
\(80\) | 1.53209 | − | 1.28558i | 0.171293 | − | 0.143732i | ||||
\(81\) | 6.89440 | + | 5.78509i | 0.766044 | + | 0.642788i | ||||
\(82\) | 2.08378 | + | 11.8177i | 0.230115 | + | 1.30505i | ||||
\(83\) | −1.00000 | − | 1.73205i | −0.109764 | − | 0.190117i | 0.805910 | − | 0.592037i | \(-0.201676\pi\) |
−0.915675 | + | 0.401920i | \(0.868343\pi\) | |||||||
\(84\) | −4.50000 | + | 7.79423i | −0.490990 | + | 0.850420i | ||||
\(85\) | 1.87939 | + | 0.684040i | 0.203848 | + | 0.0741946i | ||||
\(86\) | −9.39693 | − | 3.42020i | −1.01330 | − | 0.368810i | ||||
\(87\) | 4.50000 | − | 7.79423i | 0.482451 | − | 0.835629i | ||||
\(88\) | −1.00000 | − | 1.73205i | −0.106600 | − | 0.184637i | ||||
\(89\) | −1.04189 | − | 5.90885i | −0.110440 | − | 0.626336i | −0.988907 | − | 0.148534i | \(-0.952545\pi\) |
0.878467 | − | 0.477803i | \(-0.158567\pi\) | |||||||
\(90\) | −9.19253 | − | 7.71345i | −0.968978 | − | 0.813069i | ||||
\(91\) | −6.89440 | + | 5.78509i | −0.722729 | + | 0.606442i | ||||
\(92\) | 0.868241 | − | 4.92404i | 0.0905204 | − | 0.513367i | ||||
\(93\) | 16.9145 | − | 6.15636i | 1.75395 | − | 0.638385i | ||||
\(94\) | 8.00000 | 0.825137 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.00000 | 0.306186 | ||||||||
\(97\) | 11.2763 | − | 4.10424i | 1.14494 | − | 0.416723i | 0.301242 | − | 0.953548i | \(-0.402599\pi\) |
0.843694 | + | 0.536825i | \(0.180376\pi\) | |||||||
\(98\) | −0.347296 | + | 1.96962i | −0.0350822 | + | 0.198961i | ||||
\(99\) | −9.19253 | + | 7.71345i | −0.923884 | + | 0.775231i | ||||
\(100\) | −0.766044 | − | 0.642788i | −0.0766044 | − | 0.0642788i | ||||
\(101\) | 1.73648 | + | 9.84808i | 0.172786 | + | 0.979920i | 0.940668 | + | 0.339328i | \(0.110200\pi\) |
−0.767882 | + | 0.640592i | \(0.778689\pi\) | |||||||
\(102\) | 1.50000 | + | 2.59808i | 0.148522 | + | 0.257248i | ||||
\(103\) | 3.00000 | − | 5.19615i | 0.295599 | − | 0.511992i | −0.679525 | − | 0.733652i | \(-0.737814\pi\) |
0.975124 | + | 0.221660i | \(0.0711475\pi\) | |||||||
\(104\) | 2.81908 | + | 1.02606i | 0.276433 | + | 0.100614i | ||||
\(105\) | −16.9145 | − | 6.15636i | −1.65068 | − | 0.600799i | ||||
\(106\) | 1.50000 | − | 2.59808i | 0.145693 | − | 0.252347i | ||||
\(107\) | −1.50000 | − | 2.59808i | −0.145010 | − | 0.251166i | 0.784366 | − | 0.620298i | \(-0.212988\pi\) |
−0.929377 | + | 0.369132i | \(0.879655\pi\) | |||||||
\(108\) | −1.56283 | − | 8.86327i | −0.150384 | − | 0.852869i | ||||
\(109\) | −2.29813 | − | 1.92836i | −0.220121 | − | 0.184704i | 0.526058 | − | 0.850449i | \(-0.323669\pi\) |
−0.746179 | + | 0.665745i | \(0.768114\pi\) | |||||||
\(110\) | 3.06418 | − | 2.57115i | 0.292158 | − | 0.245150i | ||||
\(111\) | 3.12567 | − | 17.7265i | 0.296675 | − | 1.68253i | ||||
\(112\) | 2.81908 | − | 1.02606i | 0.266378 | − | 0.0969536i | ||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.0000 | 0.932505 | ||||||||
\(116\) | −2.81908 | + | 1.02606i | −0.261745 | + | 0.0952673i | ||||
\(117\) | 3.12567 | − | 17.7265i | 0.288968 | − | 1.63882i | ||||
\(118\) | 2.29813 | − | 1.92836i | 0.211560 | − | 0.177520i | ||||
\(119\) | 2.29813 | + | 1.92836i | 0.210670 | + | 0.176773i | ||||
\(120\) | 1.04189 | + | 5.90885i | 0.0951110 | + | 0.539401i | ||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −33.8289 | − | 12.3127i | −3.05025 | − | 1.11020i | ||||
\(124\) | −5.63816 | − | 2.05212i | −0.506321 | − | 0.184286i | ||||
\(125\) | 6.00000 | − | 10.3923i | 0.536656 | − | 0.929516i | ||||
\(126\) | −9.00000 | − | 15.5885i | −0.801784 | − | 1.38873i | ||||
\(127\) | −2.08378 | − | 11.8177i | −0.184905 | − | 1.04865i | −0.926077 | − | 0.377335i | \(-0.876841\pi\) |
0.741171 | − | 0.671316i | \(-0.234271\pi\) | |||||||
\(128\) | −0.766044 | − | 0.642788i | −0.0677094 | − | 0.0568149i | ||||
\(129\) | 22.9813 | − | 19.2836i | 2.02339 | − | 1.69783i | ||||
\(130\) | −1.04189 | + | 5.90885i | −0.0913797 | + | 0.518240i | ||||
\(131\) | −13.1557 | + | 4.78828i | −1.14942 | + | 0.418354i | −0.845306 | − | 0.534282i | \(-0.820582\pi\) |
−0.304112 | + | 0.952636i | \(0.598360\pi\) | |||||||
\(132\) | 6.00000 | 0.522233 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 15.0000 | 1.29580 | ||||||||
\(135\) | 16.9145 | − | 6.15636i | 1.45577 | − | 0.529855i | ||||
\(136\) | 0.173648 | − | 0.984808i | 0.0148902 | − | 0.0844466i | ||||
\(137\) | 14.5548 | − | 12.2130i | 1.24350 | − | 1.04342i | 0.246262 | − | 0.969203i | \(-0.420797\pi\) |
0.997242 | − | 0.0742208i | \(-0.0236470\pi\) | |||||||
\(138\) | 11.4907 | + | 9.64181i | 0.978151 | + | 0.820766i | ||||
\(139\) | 1.04189 | + | 5.90885i | 0.0883719 | + | 0.501182i | 0.996578 | + | 0.0826585i | \(0.0263411\pi\) |
−0.908206 | + | 0.418523i | \(0.862548\pi\) | |||||||
\(140\) | 3.00000 | + | 5.19615i | 0.253546 | + | 0.439155i | ||||
\(141\) | −12.0000 | + | 20.7846i | −1.01058 | + | 1.75038i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.63816 | + | 2.05212i | 0.471486 | + | 0.171607i | ||||
\(144\) | −3.00000 | + | 5.19615i | −0.250000 | + | 0.433013i | ||||
\(145\) | −3.00000 | − | 5.19615i | −0.249136 | − | 0.431517i | ||||
\(146\) | 1.91013 | + | 10.8329i | 0.158083 | + | 0.896536i | ||||
\(147\) | −4.59627 | − | 3.85673i | −0.379094 | − | 0.318097i | ||||
\(148\) | −4.59627 | + | 3.85673i | −0.377811 | + | 0.317021i | ||||
\(149\) | −1.38919 | + | 7.87846i | −0.113807 | + | 0.645429i | 0.873528 | + | 0.486774i | \(0.161827\pi\) |
−0.987334 | + | 0.158654i | \(0.949284\pi\) | |||||||
\(150\) | 2.81908 | − | 1.02606i | 0.230177 | − | 0.0837775i | ||||
\(151\) | 18.0000 | 1.46482 | 0.732410 | − | 0.680864i | \(-0.238396\pi\) | ||||
0.732410 | + | 0.680864i | \(0.238396\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | 5.63816 | − | 2.05212i | 0.454336 | − | 0.165365i | ||||
\(155\) | 2.08378 | − | 11.8177i | 0.167373 | − | 0.949220i | ||||
\(156\) | −6.89440 | + | 5.78509i | −0.551994 | + | 0.463178i | ||||
\(157\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(158\) | −2.08378 | − | 11.8177i | −0.165776 | − | 0.940165i | ||||
\(159\) | 4.50000 | + | 7.79423i | 0.356873 | + | 0.618123i | ||||
\(160\) | 1.00000 | − | 1.73205i | 0.0790569 | − | 0.136931i | ||||
\(161\) | 14.0954 | + | 5.13030i | 1.11087 | + | 0.404324i | ||||
\(162\) | 8.45723 | + | 3.07818i | 0.664463 | + | 0.241845i | ||||
\(163\) | 3.00000 | − | 5.19615i | 0.234978 | − | 0.406994i | −0.724288 | − | 0.689497i | \(-0.757831\pi\) |
0.959266 | + | 0.282503i | \(0.0911648\pi\) | |||||||
\(164\) | 6.00000 | + | 10.3923i | 0.468521 | + | 0.811503i | ||||
\(165\) | 2.08378 | + | 11.8177i | 0.162222 | + | 0.920006i | ||||
\(166\) | −1.53209 | − | 1.28558i | −0.118913 | − | 0.0997800i | ||||
\(167\) | 9.19253 | − | 7.71345i | 0.711340 | − | 0.596885i | −0.213635 | − | 0.976914i | \(-0.568530\pi\) |
0.924975 | + | 0.380029i | \(0.124086\pi\) | |||||||
\(168\) | −1.56283 | + | 8.86327i | −0.120575 | + | 0.683816i | ||||
\(169\) | 3.75877 | − | 1.36808i | 0.289136 | − | 0.105237i | ||||
\(170\) | 2.00000 | 0.153393 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.0000 | −0.762493 | ||||||||
\(173\) | −16.9145 | + | 6.15636i | −1.28598 | + | 0.468060i | −0.892407 | − | 0.451232i | \(-0.850985\pi\) |
−0.393577 | + | 0.919292i | \(0.628762\pi\) | |||||||
\(174\) | 1.56283 | − | 8.86327i | 0.118478 | − | 0.671923i | ||||
\(175\) | 2.29813 | − | 1.92836i | 0.173723 | − | 0.145771i | ||||
\(176\) | −1.53209 | − | 1.28558i | −0.115486 | − | 0.0969039i | ||||
\(177\) | 1.56283 | + | 8.86327i | 0.117470 | + | 0.666204i | ||||
\(178\) | −3.00000 | − | 5.19615i | −0.224860 | − | 0.389468i | ||||
\(179\) | −6.00000 | + | 10.3923i | −0.448461 | + | 0.776757i | −0.998286 | − | 0.0585225i | \(-0.981361\pi\) |
0.549825 | + | 0.835280i | \(0.314694\pi\) | |||||||
\(180\) | −11.2763 | − | 4.10424i | −0.840487 | − | 0.305912i | ||||
\(181\) | 16.9145 | + | 6.15636i | 1.25724 | + | 0.457599i | 0.882843 | − | 0.469669i | \(-0.155627\pi\) |
0.374400 | + | 0.927267i | \(0.377849\pi\) | |||||||
\(182\) | −4.50000 | + | 7.79423i | −0.333562 | + | 0.577747i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.868241 | − | 4.92404i | −0.0640076 | − | 0.363005i | ||||
\(185\) | −9.19253 | − | 7.71345i | −0.675848 | − | 0.567104i | ||||
\(186\) | 13.7888 | − | 11.5702i | 1.01104 | − | 0.848367i | ||||
\(187\) | 0.347296 | − | 1.96962i | 0.0253968 | − | 0.144033i | ||||
\(188\) | 7.51754 | − | 2.73616i | 0.548273 | − | 0.199555i | ||||
\(189\) | 27.0000 | 1.96396 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.0000 | −0.795932 | −0.397966 | − | 0.917400i | \(-0.630284\pi\) | ||||
−0.397966 | + | 0.917400i | \(0.630284\pi\) | |||||||
\(192\) | 2.81908 | − | 1.02606i | 0.203449 | − | 0.0740495i | ||||
\(193\) | −1.04189 | + | 5.90885i | −0.0749968 | + | 0.425328i | 0.924073 | + | 0.382215i | \(0.124839\pi\) |
−0.999070 | + | 0.0431130i | \(0.986272\pi\) | |||||||
\(194\) | 9.19253 | − | 7.71345i | 0.659985 | − | 0.553794i | ||||
\(195\) | −13.7888 | − | 11.5702i | −0.987436 | − | 0.828558i | ||||
\(196\) | 0.347296 | + | 1.96962i | 0.0248069 | + | 0.140687i | ||||
\(197\) | −2.00000 | − | 3.46410i | −0.142494 | − | 0.246807i | 0.785941 | − | 0.618301i | \(-0.212179\pi\) |
−0.928435 | + | 0.371494i | \(0.878846\pi\) | |||||||
\(198\) | −6.00000 | + | 10.3923i | −0.426401 | + | 0.738549i | ||||
\(199\) | 6.57785 | + | 2.39414i | 0.466291 | + | 0.169716i | 0.564472 | − | 0.825452i | \(-0.309080\pi\) |
−0.0981803 | + | 0.995169i | \(0.531302\pi\) | |||||||
\(200\) | −0.939693 | − | 0.342020i | −0.0664463 | − | 0.0241845i | ||||
\(201\) | −22.5000 | + | 38.9711i | −1.58703 | + | 2.74881i | ||||
\(202\) | 5.00000 | + | 8.66025i | 0.351799 | + | 0.609333i | ||||
\(203\) | −1.56283 | − | 8.86327i | −0.109689 | − | 0.622080i | ||||
\(204\) | 2.29813 | + | 1.92836i | 0.160902 | + | 0.135012i | ||||
\(205\) | −18.3851 | + | 15.4269i | −1.28407 | + | 1.07746i | ||||
\(206\) | 1.04189 | − | 5.90885i | 0.0725919 | − | 0.411689i | ||||
\(207\) | −28.1908 | + | 10.2606i | −1.95939 | + | 0.713161i | ||||
\(208\) | 3.00000 | 0.208013 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −18.0000 | −1.24212 | ||||||||
\(211\) | 2.81908 | − | 1.02606i | 0.194073 | − | 0.0706369i | −0.243155 | − | 0.969987i | \(-0.578182\pi\) |
0.437228 | + | 0.899351i | \(0.355960\pi\) | |||||||
\(212\) | 0.520945 | − | 2.95442i | 0.0357786 | − | 0.202911i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.29813 | − | 1.92836i | −0.157097 | − | 0.131820i | ||||
\(215\) | −3.47296 | − | 19.6962i | −0.236854 | − | 1.34327i | ||||
\(216\) | −4.50000 | − | 7.79423i | −0.306186 | − | 0.530330i | ||||
\(217\) | 9.00000 | − | 15.5885i | 0.610960 | − | 1.05821i | ||||
\(218\) | −2.81908 | − | 1.02606i | −0.190932 | − | 0.0694936i | ||||
\(219\) | −31.0099 | − | 11.2867i | −2.09545 | − | 0.762682i | ||||
\(220\) | 2.00000 | − | 3.46410i | 0.134840 | − | 0.233550i | ||||
\(221\) | 1.50000 | + | 2.59808i | 0.100901 | + | 0.174766i | ||||
\(222\) | −3.12567 | − | 17.7265i | −0.209781 | − | 1.18973i | ||||
\(223\) | −13.7888 | − | 11.5702i | −0.923366 | − | 0.774796i | 0.0512482 | − | 0.998686i | \(-0.483680\pi\) |
−0.974615 | + | 0.223890i | \(0.928124\pi\) | |||||||
\(224\) | 2.29813 | − | 1.92836i | 0.153550 | − | 0.128844i | ||||
\(225\) | −1.04189 | + | 5.90885i | −0.0694593 | + | 0.393923i | ||||
\(226\) | −11.2763 | + | 4.10424i | −0.750089 | + | 0.273010i | ||||
\(227\) | −3.00000 | −0.199117 | −0.0995585 | − | 0.995032i | \(-0.531743\pi\) | ||||
−0.0995585 | + | 0.995032i | \(0.531743\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.0000 | −0.792982 | −0.396491 | − | 0.918039i | \(-0.629772\pi\) | ||||
−0.396491 | + | 0.918039i | \(0.629772\pi\) | |||||||
\(230\) | 9.39693 | − | 3.42020i | 0.619615 | − | 0.225521i | ||||
\(231\) | −3.12567 | + | 17.7265i | −0.205654 | + | 1.16632i | ||||
\(232\) | −2.29813 | + | 1.92836i | −0.150880 | + | 0.126603i | ||||
\(233\) | 10.7246 | + | 8.99903i | 0.702593 | + | 0.589546i | 0.922510 | − | 0.385973i | \(-0.126134\pi\) |
−0.219917 | + | 0.975519i | \(0.570579\pi\) | |||||||
\(234\) | −3.12567 | − | 17.7265i | −0.204331 | − | 1.15882i | ||||
\(235\) | 8.00000 | + | 13.8564i | 0.521862 | + | 0.903892i | ||||
\(236\) | 1.50000 | − | 2.59808i | 0.0976417 | − | 0.169120i | ||||
\(237\) | 33.8289 | + | 12.3127i | 2.19743 | + | 0.799797i | ||||
\(238\) | 2.81908 | + | 1.02606i | 0.182734 | + | 0.0665096i | ||||
\(239\) | −0.500000 | + | 0.866025i | −0.0323423 | + | 0.0560185i | −0.881743 | − | 0.471729i | \(-0.843630\pi\) |
0.849401 | + | 0.527748i | \(0.176963\pi\) | |||||||
\(240\) | 3.00000 | + | 5.19615i | 0.193649 | + | 0.335410i | ||||
\(241\) | −4.16756 | − | 23.6354i | −0.268456 | − | 1.52249i | −0.759010 | − | 0.651079i | \(-0.774317\pi\) |
0.490554 | − | 0.871411i | \(-0.336794\pi\) | |||||||
\(242\) | 5.36231 | + | 4.49951i | 0.344702 | + | 0.289240i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.75877 | + | 1.36808i | −0.240139 | + | 0.0874035i | ||||
\(246\) | −36.0000 | −2.29528 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.00000 | −0.381000 | ||||||||
\(249\) | 5.63816 | − | 2.05212i | 0.357304 | − | 0.130048i | ||||
\(250\) | 2.08378 | − | 11.8177i | 0.131790 | − | 0.747417i | ||||
\(251\) | −15.3209 | + | 12.8558i | −0.967046 | + | 0.811448i | −0.982085 | − | 0.188439i | \(-0.939657\pi\) |
0.0150390 | + | 0.999887i | \(0.495213\pi\) | |||||||
\(252\) | −13.7888 | − | 11.5702i | −0.868613 | − | 0.728853i | ||||
\(253\) | −1.73648 | − | 9.84808i | −0.109172 | − | 0.619143i | ||||
\(254\) | −6.00000 | − | 10.3923i | −0.376473 | − | 0.652071i | ||||
\(255\) | −3.00000 | + | 5.19615i | −0.187867 | + | 0.325396i | ||||
\(256\) | −0.939693 | − | 0.342020i | −0.0587308 | − | 0.0213763i | ||||
\(257\) | −16.9145 | − | 6.15636i | −1.05510 | − | 0.384023i | −0.244512 | − | 0.969646i | \(-0.578628\pi\) |
−0.810584 | + | 0.585623i | \(0.800850\pi\) | |||||||
\(258\) | 15.0000 | − | 25.9808i | 0.933859 | − | 1.61749i | ||||
\(259\) | −9.00000 | − | 15.5885i | −0.559233 | − | 0.968620i | ||||
\(260\) | 1.04189 | + | 5.90885i | 0.0646152 | + | 0.366451i | ||||
\(261\) | 13.7888 | + | 11.5702i | 0.853505 | + | 0.716176i | ||||
\(262\) | −10.7246 | + | 8.99903i | −0.662569 | + | 0.555962i | ||||
\(263\) | −1.38919 | + | 7.87846i | −0.0856608 | + | 0.485807i | 0.911551 | + | 0.411187i | \(0.134886\pi\) |
−0.997212 | + | 0.0746202i | \(0.976226\pi\) | |||||||
\(264\) | 5.63816 | − | 2.05212i | 0.347004 | − | 0.126299i | ||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.0000 | 1.10158 | ||||||||
\(268\) | 14.0954 | − | 5.13030i | 0.861013 | − | 0.313383i | ||||
\(269\) | 1.04189 | − | 5.90885i | 0.0635251 | − | 0.360269i | −0.936431 | − | 0.350853i | \(-0.885892\pi\) |
0.999956 | − | 0.00941580i | \(-0.00299719\pi\) | |||||||
\(270\) | 13.7888 | − | 11.5702i | 0.839160 | − | 0.704139i | ||||
\(271\) | −8.42649 | − | 7.07066i | −0.511873 | − | 0.429512i | 0.349915 | − | 0.936782i | \(-0.386211\pi\) |
−0.861788 | + | 0.507269i | \(0.830655\pi\) | |||||||
\(272\) | −0.173648 | − | 0.984808i | −0.0105290 | − | 0.0597127i | ||||
\(273\) | −13.5000 | − | 23.3827i | −0.817057 | − | 1.41518i | ||||
\(274\) | 9.50000 | − | 16.4545i | 0.573916 | − | 0.994052i | ||||
\(275\) | −1.87939 | − | 0.684040i | −0.113331 | − | 0.0412492i | ||||
\(276\) | 14.0954 | + | 5.13030i | 0.848443 | + | 0.308808i | ||||
\(277\) | −15.0000 | + | 25.9808i | −0.901263 | + | 1.56103i | −0.0754058 | + | 0.997153i | \(0.524025\pi\) |
−0.825857 | + | 0.563880i | \(0.809308\pi\) | |||||||
\(278\) | 3.00000 | + | 5.19615i | 0.179928 | + | 0.311645i | ||||
\(279\) | 6.25133 | + | 35.4531i | 0.374258 | + | 2.12252i | ||||
\(280\) | 4.59627 | + | 3.85673i | 0.274679 | + | 0.230483i | ||||
\(281\) | −9.19253 | + | 7.71345i | −0.548381 | + | 0.460146i | −0.874392 | − | 0.485220i | \(-0.838740\pi\) |
0.326012 | + | 0.945366i | \(0.394295\pi\) | |||||||
\(282\) | −4.16756 | + | 23.6354i | −0.248174 | + | 1.40747i | ||||
\(283\) | 13.1557 | − | 4.78828i | 0.782025 | − | 0.284634i | 0.0800082 | − | 0.996794i | \(-0.474505\pi\) |
0.702017 | + | 0.712160i | \(0.252283\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.00000 | 0.354787 | ||||||||
\(287\) | −33.8289 | + | 12.3127i | −1.99686 | + | 0.726797i | ||||
\(288\) | −1.04189 | + | 5.90885i | −0.0613939 | + | 0.348182i | ||||
\(289\) | −12.2567 | + | 10.2846i | −0.720983 | + | 0.604977i | ||||
\(290\) | −4.59627 | − | 3.85673i | −0.269902 | − | 0.226475i | ||||
\(291\) | 6.25133 | + | 35.4531i | 0.366460 | + | 2.07830i | ||||
\(292\) | 5.50000 | + | 9.52628i | 0.321863 | + | 0.557483i | ||||
\(293\) | −4.50000 | + | 7.79423i | −0.262893 | + | 0.455344i | −0.967009 | − | 0.254741i | \(-0.918010\pi\) |
0.704117 | + | 0.710084i | \(0.251343\pi\) | |||||||
\(294\) | −5.63816 | − | 2.05212i | −0.328824 | − | 0.119682i | ||||
\(295\) | 5.63816 | + | 2.05212i | 0.328266 | + | 0.119479i | ||||
\(296\) | −3.00000 | + | 5.19615i | −0.174371 | + | 0.302020i | ||||
\(297\) | −9.00000 | − | 15.5885i | −0.522233 | − | 0.904534i | ||||
\(298\) | 1.38919 | + | 7.87846i | 0.0804734 | + | 0.456387i | ||||
\(299\) | 11.4907 | + | 9.64181i | 0.664522 | + | 0.557601i | ||||
\(300\) | 2.29813 | − | 1.92836i | 0.132683 | − | 0.111334i | ||||
\(301\) | 5.20945 | − | 29.5442i | 0.300267 | − | 1.70290i | ||||
\(302\) | 16.9145 | − | 6.15636i | 0.973318 | − | 0.354259i | ||||
\(303\) | −30.0000 | −1.72345 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.63816 | + | 2.05212i | −0.322312 | + | 0.117312i | ||||
\(307\) | −2.08378 | + | 11.8177i | −0.118927 | + | 0.674471i | 0.865803 | + | 0.500385i | \(0.166808\pi\) |
−0.984730 | + | 0.174086i | \(0.944303\pi\) | |||||||
\(308\) | 4.59627 | − | 3.85673i | 0.261897 | − | 0.219757i | ||||
\(309\) | 13.7888 | + | 11.5702i | 0.784417 | + | 0.658204i | ||||
\(310\) | −2.08378 | − | 11.8177i | −0.118351 | − | 0.671200i | ||||
\(311\) | 5.50000 | + | 9.52628i | 0.311876 | + | 0.540186i | 0.978769 | − | 0.204968i | \(-0.0657092\pi\) |
−0.666892 | + | 0.745154i | \(0.732376\pi\) | |||||||
\(312\) | −4.50000 | + | 7.79423i | −0.254762 | + | 0.441261i | ||||
\(313\) | −19.7335 | − | 7.18242i | −1.11541 | − | 0.405975i | −0.282432 | − | 0.959287i | \(-0.591141\pi\) |
−0.832974 | + | 0.553313i | \(0.813363\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 18.0000 | − | 31.1769i | 1.01419 | − | 1.75662i | ||||
\(316\) | −6.00000 | − | 10.3923i | −0.337526 | − | 0.584613i | ||||
\(317\) | 5.73039 | + | 32.4987i | 0.321851 | + | 1.82531i | 0.530940 | + | 0.847410i | \(0.321839\pi\) |
−0.209089 | + | 0.977897i | \(0.567050\pi\) | |||||||
\(318\) | 6.89440 | + | 5.78509i | 0.386619 | + | 0.324412i | ||||
\(319\) | −4.59627 | + | 3.85673i | −0.257342 | + | 0.215935i | ||||
\(320\) | 0.347296 | − | 1.96962i | 0.0194145 | − | 0.110105i | ||||
\(321\) | 8.45723 | − | 3.07818i | 0.472037 | − | 0.171807i | ||||
\(322\) | 15.0000 | 0.835917 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | 2.81908 | − | 1.02606i | 0.156374 | − | 0.0569156i | ||||
\(326\) | 1.04189 | − | 5.90885i | 0.0577049 | − | 0.327261i | ||||
\(327\) | 6.89440 | − | 5.78509i | 0.381261 | − | 0.319916i | ||||
\(328\) | 9.19253 | + | 7.71345i | 0.507573 | + | 0.425904i | ||||
\(329\) | 4.16756 | + | 23.6354i | 0.229765 | + | 1.30306i | ||||
\(330\) | 6.00000 | + | 10.3923i | 0.330289 | + | 0.572078i | ||||
\(331\) | 4.50000 | − | 7.79423i | 0.247342 | − | 0.428410i | −0.715445 | − | 0.698669i | \(-0.753776\pi\) |
0.962788 | + | 0.270259i | \(0.0871094\pi\) | |||||||
\(332\) | −1.87939 | − | 0.684040i | −0.103145 | − | 0.0375416i | ||||
\(333\) | 33.8289 | + | 12.3127i | 1.85381 | + | 0.674733i | ||||
\(334\) | 6.00000 | − | 10.3923i | 0.328305 | − | 0.568642i | ||||
\(335\) | 15.0000 | + | 25.9808i | 0.819538 | + | 1.41948i | ||||
\(336\) | 1.56283 | + | 8.86327i | 0.0852596 | + | 0.483531i | ||||
\(337\) | −13.7888 | − | 11.5702i | −0.751124 | − | 0.630268i | 0.184676 | − | 0.982799i | \(-0.440876\pi\) |
−0.935800 | + | 0.352532i | \(0.885321\pi\) | |||||||
\(338\) | 3.06418 | − | 2.57115i | 0.166669 | − | 0.139852i | ||||
\(339\) | 6.25133 | − | 35.4531i | 0.339526 | − | 1.92555i | ||||
\(340\) | 1.87939 | − | 0.684040i | 0.101924 | − | 0.0370973i | ||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | −9.39693 | + | 3.42020i | −0.506648 | + | 0.184405i | ||||
\(345\) | −5.20945 | + | 29.5442i | −0.280467 | + | 1.59061i | ||||
\(346\) | −13.7888 | + | 11.5702i | −0.741290 | + | 0.622017i | ||||
\(347\) | 12.2567 | + | 10.2846i | 0.657975 | + | 0.552106i | 0.909479 | − | 0.415750i | \(-0.136481\pi\) |
−0.251504 | + | 0.967856i | \(0.580925\pi\) | |||||||
\(348\) | −1.56283 | − | 8.86327i | −0.0837767 | − | 0.475121i | ||||
\(349\) | −14.0000 | − | 24.2487i | −0.749403 | − | 1.29800i | −0.948109 | − | 0.317945i | \(-0.897007\pi\) |
0.198706 | − | 0.980059i | \(-0.436326\pi\) | |||||||
\(350\) | 1.50000 | − | 2.59808i | 0.0801784 | − | 0.138873i | ||||
\(351\) | 25.3717 | + | 9.23454i | 1.35424 | + | 0.492903i | ||||
\(352\) | −1.87939 | − | 0.684040i | −0.100172 | − | 0.0364595i | ||||
\(353\) | 15.5000 | − | 26.8468i | 0.824982 | − | 1.42891i | −0.0769515 | − | 0.997035i | \(-0.524519\pi\) |
0.901933 | − | 0.431875i | \(-0.142148\pi\) | |||||||
\(354\) | 4.50000 | + | 7.79423i | 0.239172 | + | 0.414259i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.59627 | − | 3.85673i | −0.243602 | − | 0.204406i | ||||
\(357\) | −6.89440 | + | 5.78509i | −0.364890 | + | 0.306179i | ||||
\(358\) | −2.08378 | + | 11.8177i | −0.110131 | + | 0.624584i | ||||
\(359\) | −17.8542 | + | 6.49838i | −0.942307 | + | 0.342972i | −0.767076 | − | 0.641556i | \(-0.778289\pi\) |
−0.175230 | + | 0.984527i | \(0.556067\pi\) | |||||||
\(360\) | −12.0000 | −0.632456 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 18.0000 | 0.946059 | ||||||||
\(363\) | −19.7335 | + | 7.18242i | −1.03574 | + | 0.376979i | ||||
\(364\) | −1.56283 | + | 8.86327i | −0.0819147 | + | 0.464562i | ||||
\(365\) | −16.8530 | + | 14.1413i | −0.882125 | + | 0.740191i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.38919 | + | 7.87846i | 0.0725149 | + | 0.411252i | 0.999359 | + | 0.0358054i | \(0.0113997\pi\) |
−0.926844 | + | 0.375447i | \(0.877489\pi\) | |||||||
\(368\) | −2.50000 | − | 4.33013i | −0.130322 | − | 0.225723i | ||||
\(369\) | 36.0000 | − | 62.3538i | 1.87409 | − | 3.24601i | ||||
\(370\) | −11.2763 | − | 4.10424i | −0.586228 | − | 0.213369i | ||||
\(371\) | 8.45723 | + | 3.07818i | 0.439078 | + | 0.159811i | ||||
\(372\) | 9.00000 | − | 15.5885i | 0.466628 | − | 0.808224i | ||||
\(373\) | −10.5000 | − | 18.1865i | −0.543669 | − | 0.941663i | −0.998689 | − | 0.0511818i | \(-0.983701\pi\) |
0.455020 | − | 0.890481i | \(-0.349632\pi\) | |||||||
\(374\) | −0.347296 | − | 1.96962i | −0.0179583 | − | 0.101846i | ||||
\(375\) | 27.5776 | + | 23.1404i | 1.42410 | + | 1.19496i | ||||
\(376\) | 6.12836 | − | 5.14230i | 0.316046 | − | 0.265194i | ||||
\(377\) | 1.56283 | − | 8.86327i | 0.0804900 | − | 0.456482i | ||||
\(378\) | 25.3717 | − | 9.23454i | 1.30498 | − | 0.474974i | ||||
\(379\) | −3.00000 | −0.154100 | −0.0770498 | − | 0.997027i | \(-0.524550\pi\) | ||||
−0.0770498 | + | 0.997027i | \(0.524550\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 36.0000 | 1.84434 | ||||||||
\(382\) | −10.3366 | + | 3.76222i | −0.528867 | + | 0.192492i | ||||
\(383\) | −3.12567 | + | 17.7265i | −0.159714 | + | 0.905784i | 0.794634 | + | 0.607088i | \(0.207663\pi\) |
−0.954348 | + | 0.298696i | \(0.903449\pi\) | |||||||
\(384\) | 2.29813 | − | 1.92836i | 0.117276 | − | 0.0984064i | ||||
\(385\) | 9.19253 | + | 7.71345i | 0.468495 | + | 0.393114i | ||||
\(386\) | 1.04189 | + | 5.90885i | 0.0530308 | + | 0.300752i | ||||
\(387\) | 30.0000 | + | 51.9615i | 1.52499 | + | 2.64135i | ||||
\(388\) | 6.00000 | − | 10.3923i | 0.304604 | − | 0.527589i | ||||
\(389\) | −24.4320 | − | 8.89252i | −1.23875 | − | 0.450869i | −0.362166 | − | 0.932114i | \(-0.617963\pi\) |
−0.876586 | + | 0.481245i | \(0.840185\pi\) | |||||||
\(390\) | −16.9145 | − | 6.15636i | −0.856497 | − | 0.311740i | ||||
\(391\) | 2.50000 | − | 4.33013i | 0.126430 | − | 0.218984i | ||||
\(392\) | 1.00000 | + | 1.73205i | 0.0505076 | + | 0.0874818i | ||||
\(393\) | −7.29322 | − | 41.3619i | −0.367894 | − | 2.08643i | ||||
\(394\) | −3.06418 | − | 2.57115i | −0.154371 | − | 0.129533i | ||||
\(395\) | 18.3851 | − | 15.4269i | 0.925053 | − | 0.776212i | ||||
\(396\) | −2.08378 | + | 11.8177i | −0.104714 | + | 0.593861i | ||||
\(397\) | −1.87939 | + | 0.684040i | −0.0943236 | + | 0.0343310i | −0.388751 | − | 0.921343i | \(-0.627093\pi\) |
0.294427 | + | 0.955674i | \(0.404871\pi\) | |||||||
\(398\) | 7.00000 | 0.350878 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 33.8289 | − | 12.3127i | 1.68934 | − | 0.614868i | 0.694795 | − | 0.719208i | \(-0.255495\pi\) |
0.994542 | + | 0.104340i | \(0.0332730\pi\) | |||||||
\(402\) | −7.81417 | + | 44.3163i | −0.389735 | + | 2.21030i | ||||
\(403\) | 13.7888 | − | 11.5702i | 0.686869 | − | 0.576352i | ||||
\(404\) | 7.66044 | + | 6.42788i | 0.381121 | + | 0.319799i | ||||
\(405\) | 3.12567 | + | 17.7265i | 0.155316 | + | 0.880839i | ||||
\(406\) | −4.50000 | − | 7.79423i | −0.223331 | − | 0.386821i | ||||
\(407\) | −6.00000 | + | 10.3923i | −0.297409 | + | 0.515127i | ||||
\(408\) | 2.81908 | + | 1.02606i | 0.139565 | + | 0.0507976i | ||||
\(409\) | 5.63816 | + | 2.05212i | 0.278789 | + | 0.101471i | 0.477631 | − | 0.878561i | \(-0.341496\pi\) |
−0.198842 | + | 0.980032i | \(0.563718\pi\) | |||||||
\(410\) | −12.0000 | + | 20.7846i | −0.592638 | + | 1.02648i | ||||
\(411\) | 28.5000 | + | 49.3634i | 1.40580 | + | 2.43492i | ||||
\(412\) | −1.04189 | − | 5.90885i | −0.0513302 | − | 0.291108i | ||||
\(413\) | 6.89440 | + | 5.78509i | 0.339251 | + | 0.284666i | ||||
\(414\) | −22.9813 | + | 19.2836i | −1.12947 | + | 0.947739i | ||||
\(415\) | 0.694593 | − | 3.93923i | 0.0340962 | − | 0.193369i | ||||
\(416\) | 2.81908 | − | 1.02606i | 0.138217 | − | 0.0503068i | ||||
\(417\) | −18.0000 | −0.881464 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.0000 | −0.683945 | −0.341972 | − | 0.939710i | \(-0.611095\pi\) | ||||
−0.341972 | + | 0.939710i | \(0.611095\pi\) | |||||||
\(420\) | −16.9145 | + | 6.15636i | −0.825341 | + | 0.300400i | ||||
\(421\) | 4.68850 | − | 26.5898i | 0.228504 | − | 1.29591i | −0.627369 | − | 0.778722i | \(-0.715868\pi\) |
0.855873 | − | 0.517186i | \(-0.173021\pi\) | |||||||
\(422\) | 2.29813 | − | 1.92836i | 0.111871 | − | 0.0938712i | ||||
\(423\) | −36.7701 | − | 30.8538i | −1.78783 | − | 1.50016i | ||||
\(424\) | −0.520945 | − | 2.95442i | −0.0252993 | − | 0.143479i | ||||
\(425\) | −0.500000 | − | 0.866025i | −0.0242536 | − | 0.0420084i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.81908 | − | 1.02606i | −0.136265 | − | 0.0495965i | ||||
\(429\) | −9.00000 | + | 15.5885i | −0.434524 | + | 0.752618i | ||||
\(430\) | −10.0000 | − | 17.3205i | −0.482243 | − | 0.835269i | ||||
\(431\) | −4.16756 | − | 23.6354i | −0.200744 | − | 1.13848i | −0.903998 | − | 0.427537i | \(-0.859381\pi\) |
0.703254 | − | 0.710939i | \(-0.251730\pi\) | |||||||
\(432\) | −6.89440 | − | 5.78509i | −0.331707 | − | 0.278335i | ||||
\(433\) | −22.9813 | + | 19.2836i | −1.10441 | + | 0.926712i | −0.997714 | − | 0.0675794i | \(-0.978472\pi\) |
−0.106698 | + | 0.994291i | \(0.534028\pi\) | |||||||
\(434\) | 3.12567 | − | 17.7265i | 0.150037 | − | 0.850901i | ||||
\(435\) | 16.9145 | − | 6.15636i | 0.810987 | − | 0.295175i | ||||
\(436\) | −3.00000 | −0.143674 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −33.0000 | −1.57680 | ||||||||
\(439\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(440\) | 0.694593 | − | 3.93923i | 0.0331134 | − | 0.187795i | ||||
\(441\) | 9.19253 | − | 7.71345i | 0.437740 | − | 0.367307i | ||||
\(442\) | 2.29813 | + | 1.92836i | 0.109311 | + | 0.0917229i | ||||
\(443\) | −3.82026 | − | 21.6658i | −0.181506 | − | 1.02937i | −0.930363 | − | 0.366640i | \(-0.880508\pi\) |
0.748857 | − | 0.662732i | \(-0.230603\pi\) | |||||||
\(444\) | −9.00000 | − | 15.5885i | −0.427121 | − | 0.739795i | ||||
\(445\) | 6.00000 | − | 10.3923i | 0.284427 | − | 0.492642i | ||||
\(446\) | −16.9145 | − | 6.15636i | −0.800923 | − | 0.291512i | ||||
\(447\) | −22.5526 | − | 8.20848i | −1.06670 | − | 0.388248i | ||||
\(448\) | 1.50000 | − | 2.59808i | 0.0708683 | − | 0.122748i | ||||
\(449\) | 3.00000 | + | 5.19615i | 0.141579 | + | 0.245222i | 0.928091 | − | 0.372353i | \(-0.121449\pi\) |
−0.786513 | + | 0.617574i | \(0.788115\pi\) | |||||||
\(450\) | 1.04189 | + | 5.90885i | 0.0491151 | + | 0.278546i | ||||
\(451\) | 18.3851 | + | 15.4269i | 0.865719 | + | 0.726424i | ||||
\(452\) | −9.19253 | + | 7.71345i | −0.432380 | + | 0.362810i | ||||
\(453\) | −9.37700 | + | 53.1796i | −0.440570 | + | 2.49860i | ||||
\(454\) | −2.81908 | + | 1.02606i | −0.132306 | + | 0.0481554i | ||||
\(455\) | −18.0000 | −0.843853 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.00000 | 0.0467780 | 0.0233890 | − | 0.999726i | \(-0.492554\pi\) | ||||
0.0233890 | + | 0.999726i | \(0.492554\pi\) | |||||||
\(458\) | −11.2763 | + | 4.10424i | −0.526907 | + | 0.191779i | ||||
\(459\) | 1.56283 | − | 8.86327i | 0.0729468 | − | 0.413702i | ||||
\(460\) | 7.66044 | − | 6.42788i | 0.357170 | − | 0.299701i | ||||
\(461\) | 3.06418 | + | 2.57115i | 0.142713 | + | 0.119750i | 0.711349 | − | 0.702839i | \(-0.248084\pi\) |
−0.568636 | + | 0.822589i | \(0.692529\pi\) | |||||||
\(462\) | 3.12567 | + | 17.7265i | 0.145419 | + | 0.824713i | ||||
\(463\) | −16.0000 | − | 27.7128i | −0.743583 | − | 1.28792i | −0.950854 | − | 0.309640i | \(-0.899791\pi\) |
0.207271 | − | 0.978284i | \(-0.433542\pi\) | |||||||
\(464\) | −1.50000 | + | 2.59808i | −0.0696358 | + | 0.120613i | ||||
\(465\) | 33.8289 | + | 12.3127i | 1.56878 | + | 0.570989i | ||||
\(466\) | 13.1557 | + | 4.78828i | 0.609426 | + | 0.221813i | ||||
\(467\) | −4.00000 | + | 6.92820i | −0.185098 | + | 0.320599i | −0.943610 | − | 0.331061i | \(-0.892594\pi\) |
0.758512 | + | 0.651660i | \(0.225927\pi\) | |||||||
\(468\) | −9.00000 | − | 15.5885i | −0.416025 | − | 0.720577i | ||||
\(469\) | 7.81417 | + | 44.3163i | 0.360825 | + | 2.04634i | ||||
\(470\) | 12.2567 | + | 10.2846i | 0.565360 | + | 0.474393i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.520945 | − | 2.95442i | 0.0239784 | − | 0.135988i | ||||
\(473\) | −18.7939 | + | 6.84040i | −0.864142 | + | 0.314522i | ||||
\(474\) | 36.0000 | 1.65353 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.00000 | 0.137505 | ||||||||
\(477\) | −16.9145 | + | 6.15636i | −0.774460 | + | 0.281880i | ||||
\(478\) | −0.173648 | + | 0.984808i | −0.00794248 | + | 0.0450441i | ||||
\(479\) | −30.6418 | + | 25.7115i | −1.40006 | + | 1.17479i | −0.438986 | + | 0.898494i | \(0.644662\pi\) |
−0.961073 | + | 0.276294i | \(0.910893\pi\) | |||||||
\(480\) | 4.59627 | + | 3.85673i | 0.209790 | + | 0.176035i | ||||
\(481\) | −3.12567 | − | 17.7265i | −0.142518 | − | 0.808261i | ||||
\(482\) | −12.0000 | − | 20.7846i | −0.546585 | − | 0.946713i | ||||
\(483\) | −22.5000 | + | 38.9711i | −1.02379 | + | 1.77325i | ||||
\(484\) | 6.57785 | + | 2.39414i | 0.298993 | + | 0.108825i | ||||
\(485\) | 22.5526 | + | 8.20848i | 1.02406 | + | 0.372728i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.00000 | − | 15.5885i | −0.407829 | − | 0.706380i | 0.586817 | − | 0.809719i | \(-0.300381\pi\) |
−0.994646 | + | 0.103339i | \(0.967047\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.7888 | + | 11.5702i | 0.623551 | + | 0.523221i | ||||
\(490\) | −3.06418 | + | 2.57115i | −0.138425 | + | 0.116153i | ||||
\(491\) | 1.38919 | − | 7.87846i | 0.0626931 | − | 0.355550i | −0.937283 | − | 0.348570i | \(-0.886667\pi\) |
0.999976 | − | 0.00697956i | \(-0.00222168\pi\) | |||||||
\(492\) | −33.8289 | + | 12.3127i | −1.52513 | + | 0.555101i | ||||
\(493\) | −3.00000 | −0.135113 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −24.0000 | −1.07872 | ||||||||
\(496\) | −5.63816 | + | 2.05212i | −0.253161 | + | 0.0921429i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.59627 | − | 3.85673i | 0.205964 | − | 0.172824i | ||||
\(499\) | 13.7888 | + | 11.5702i | 0.617271 | + | 0.517952i | 0.896945 | − | 0.442143i | \(-0.145782\pi\) |
−0.279673 | + | 0.960095i | \(0.590226\pi\) | |||||||
\(500\) | −2.08378 | − | 11.8177i | −0.0931894 | − | 0.528503i | ||||
\(501\) | 18.0000 | + | 31.1769i | 0.804181 | + | 1.39288i | ||||
\(502\) | −10.0000 | + | 17.3205i | −0.446322 | + | 0.773052i | ||||
\(503\) | −0.939693 | − | 0.342020i | −0.0418988 | − | 0.0152499i | 0.320986 | − | 0.947084i | \(-0.395986\pi\) |
−0.362885 | + | 0.931834i | \(0.618208\pi\) | |||||||
\(504\) | −16.9145 | − | 6.15636i | −0.753430 | − | 0.274226i | ||||
\(505\) | −10.0000 | + | 17.3205i | −0.444994 | + | 0.770752i | ||||
\(506\) | −5.00000 | − | 8.66025i | −0.222277 | − | 0.384995i | ||||
\(507\) | 2.08378 | + | 11.8177i | 0.0925438 | + | 0.524842i | ||||
\(508\) | −9.19253 | − | 7.71345i | −0.407853 | − | 0.342229i | ||||
\(509\) | −13.7888 | + | 11.5702i | −0.611178 | + | 0.512839i | −0.895017 | − | 0.446033i | \(-0.852836\pi\) |
0.283839 | + | 0.958872i | \(0.408392\pi\) | |||||||
\(510\) | −1.04189 | + | 5.90885i | −0.0461356 | + | 0.261648i | ||||
\(511\) | −31.0099 | + | 11.2867i | −1.37180 | + | 0.499293i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.0000 | −0.793946 | ||||||||
\(515\) | 11.2763 | − | 4.10424i | 0.496894 | − | 0.180854i | ||||
\(516\) | 5.20945 | − | 29.5442i | 0.229333 | − | 1.30061i | ||||
\(517\) | 12.2567 | − | 10.2846i | 0.539050 | − | 0.452316i | ||||
\(518\) | −13.7888 | − | 11.5702i | −0.605845 | − | 0.508364i | ||||
\(519\) | −9.37700 | − | 53.1796i | −0.411605 | − | 2.33433i | ||||
\(520\) | 3.00000 | + | 5.19615i | 0.131559 | + | 0.227866i | ||||
\(521\) | −6.00000 | + | 10.3923i | −0.262865 | + | 0.455295i | −0.967002 | − | 0.254769i | \(-0.918001\pi\) |
0.704137 | + | 0.710064i | \(0.251334\pi\) | |||||||
\(522\) | 16.9145 | + | 6.15636i | 0.740326 | + | 0.269457i | ||||
\(523\) | 8.45723 | + | 3.07818i | 0.369809 | + | 0.134599i | 0.520238 | − | 0.854021i | \(-0.325843\pi\) |
−0.150429 | + | 0.988621i | \(0.548065\pi\) | |||||||
\(524\) | −7.00000 | + | 12.1244i | −0.305796 | + | 0.529655i | ||||
\(525\) | 4.50000 | + | 7.79423i | 0.196396 | + | 0.340168i | ||||
\(526\) | 1.38919 | + | 7.87846i | 0.0605714 | + | 0.343517i | ||||
\(527\) | −4.59627 | − | 3.85673i | −0.200217 | − | 0.168002i | ||||
\(528\) | 4.59627 | − | 3.85673i | 0.200027 | − | 0.167842i | ||||
\(529\) | 0.347296 | − | 1.96962i | 0.0150998 | − | 0.0856355i | ||||
\(530\) | 5.63816 | − | 2.05212i | 0.244906 | − | 0.0891384i | ||||
\(531\) | −18.0000 | −0.781133 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.0000 | −1.55933 | ||||||||
\(534\) | 16.9145 | − | 6.15636i | 0.731961 | − | 0.266412i | ||||
\(535\) | 1.04189 | − | 5.90885i | 0.0450448 | − | 0.255462i | ||||
\(536\) | 11.4907 | − | 9.64181i | 0.496321 | − | 0.416463i | ||||
\(537\) | −27.5776 | − | 23.1404i | −1.19006 | − | 0.998580i | ||||
\(538\) | −1.04189 | − | 5.90885i | −0.0449190 | − | 0.254748i | ||||
\(539\) | 2.00000 | + | 3.46410i | 0.0861461 | + | 0.149209i | ||||
\(540\) | 9.00000 | − | 15.5885i | 0.387298 | − | 0.670820i | ||||
\(541\) | −1.87939 | − | 0.684040i | −0.0808011 | − | 0.0294092i | 0.301303 | − | 0.953528i | \(-0.402578\pi\) |
−0.382104 | + | 0.924119i | \(0.624801\pi\) | |||||||
\(542\) | −10.3366 | − | 3.76222i | −0.443996 | − | 0.161601i | ||||
\(543\) | −27.0000 | + | 46.7654i | −1.15868 | + | 2.00689i | ||||
\(544\) | −0.500000 | − | 0.866025i | −0.0214373 | − | 0.0371305i | ||||
\(545\) | −1.04189 | − | 5.90885i | −0.0446296 | − | 0.253107i | ||||
\(546\) | −20.6832 | − | 17.3553i | −0.885159 | − | 0.742737i | ||||
\(547\) | 27.5776 | − | 23.1404i | 1.17913 | − | 0.989410i | 0.179149 | − | 0.983822i | \(-0.442666\pi\) |
0.999984 | − | 0.00558807i | \(-0.00177875\pi\) | |||||||
\(548\) | 3.29932 | − | 18.7113i | 0.140940 | − | 0.799309i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.00000 | −0.0852803 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 15.0000 | 0.638442 | ||||||||
\(553\) | 33.8289 | − | 12.3127i | 1.43855 | − | 0.523590i | ||||
\(554\) | −5.20945 | + | 29.5442i | −0.221328 | + | 1.25521i | ||||
\(555\) | 27.5776 | − | 23.1404i | 1.17060 | − | 0.982253i | ||||
\(556\) | 4.59627 | + | 3.85673i | 0.194925 | + | 0.163562i | ||||
\(557\) | 3.82026 | + | 21.6658i | 0.161870 | + | 0.918008i | 0.952234 | + | 0.305371i | \(0.0987803\pi\) |
−0.790364 | + | 0.612638i | \(0.790109\pi\) | |||||||
\(558\) | 18.0000 | + | 31.1769i | 0.762001 | + | 1.31982i | ||||
\(559\) | 15.0000 | − | 25.9808i | 0.634432 | − | 1.09887i | ||||
\(560\) | 5.63816 | + | 2.05212i | 0.238256 | + | 0.0867179i | ||||
\(561\) | 5.63816 | + | 2.05212i | 0.238043 | + | 0.0866406i | ||||
\(562\) | −6.00000 | + | 10.3923i | −0.253095 | + | 0.438373i | ||||
\(563\) | −12.0000 | − | 20.7846i | −0.505740 | − | 0.875967i | −0.999978 | − | 0.00664037i | \(-0.997886\pi\) |
0.494238 | − | 0.869326i | \(-0.335447\pi\) | |||||||
\(564\) | 4.16756 | + | 23.6354i | 0.175486 | + | 0.995229i | ||||
\(565\) | −18.3851 | − | 15.4269i | −0.773466 | − | 0.649015i | ||||
\(566\) | 10.7246 | − | 8.99903i | 0.450789 | − | 0.378257i | ||||
\(567\) | −4.68850 | + | 26.5898i | −0.196899 | + | 1.11667i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.0000 | 1.00613 | 0.503066 | − | 0.864248i | \(-0.332205\pi\) | ||||
0.503066 | + | 0.864248i | \(0.332205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.0000 | −1.33916 | −0.669579 | − | 0.742741i | \(-0.733526\pi\) | ||||
−0.669579 | + | 0.742741i | \(0.733526\pi\) | |||||||
\(572\) | 5.63816 | − | 2.05212i | 0.235743 | − | 0.0858035i | ||||
\(573\) | 5.73039 | − | 32.4987i | 0.239390 | − | 1.35765i | ||||
\(574\) | −27.5776 | + | 23.1404i | −1.15107 | + | 0.965860i | ||||
\(575\) | −3.83022 | − | 3.21394i | −0.159731 | − | 0.134030i | ||||
\(576\) | 1.04189 | + | 5.90885i | 0.0434120 | + | 0.246202i | ||||
\(577\) | −7.50000 | − | 12.9904i | −0.312229 | − | 0.540797i | 0.666616 | − | 0.745402i | \(-0.267742\pi\) |
−0.978845 | + | 0.204605i | \(0.934409\pi\) | |||||||
\(578\) | −8.00000 | + | 13.8564i | −0.332756 | + | 0.576351i | ||||
\(579\) | −16.9145 | − | 6.15636i | −0.702941 | − | 0.255850i | ||||
\(580\) | −5.63816 | − | 2.05212i | −0.234112 | − | 0.0852097i | ||||
\(581\) | 3.00000 | − | 5.19615i | 0.124461 | − | 0.215573i | ||||
\(582\) | 18.0000 | + | 31.1769i | 0.746124 | + | 1.29232i | ||||
\(583\) | −1.04189 | − | 5.90885i | −0.0431506 | − | 0.244719i | ||||
\(584\) | 8.42649 | + | 7.07066i | 0.348691 | + | 0.292586i | ||||
\(585\) | 27.5776 | − | 23.1404i | 1.14019 | − | 0.956736i | ||||
\(586\) | −1.56283 | + | 8.86327i | −0.0645601 | + | 0.366138i | ||||
\(587\) | 26.3114 | − | 9.57656i | 1.08599 | − | 0.395267i | 0.263854 | − | 0.964563i | \(-0.415006\pi\) |
0.822133 | + | 0.569295i | \(0.192784\pi\) | |||||||
\(588\) | −6.00000 | −0.247436 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 6.00000 | 0.247016 | ||||||||
\(591\) | 11.2763 | − | 4.10424i | 0.463845 | − | 0.168826i | ||||
\(592\) | −1.04189 | + | 5.90885i | −0.0428214 | + | 0.242852i | ||||
\(593\) | −1.53209 | + | 1.28558i | −0.0629153 | + | 0.0527922i | −0.673703 | − | 0.739002i | \(-0.735297\pi\) |
0.610788 | + | 0.791794i | \(0.290853\pi\) | |||||||
\(594\) | −13.7888 | − | 11.5702i | −0.565761 | − | 0.474730i | ||||
\(595\) | 1.04189 | + | 5.90885i | 0.0427133 | + | 0.242239i | ||||
\(596\) | 4.00000 | + | 6.92820i | 0.163846 | + | 0.283790i | ||||
\(597\) | −10.5000 | + | 18.1865i | −0.429736 | + | 0.744325i | ||||
\(598\) | 14.0954 | + | 5.13030i | 0.576403 | + | 0.209794i | ||||
\(599\) | −33.8289 | − | 12.3127i | −1.38221 | − | 0.503084i | −0.459364 | − | 0.888248i | \(-0.651923\pi\) |
−0.922848 | + | 0.385164i | \(0.874145\pi\) | |||||||
\(600\) | 1.50000 | − | 2.59808i | 0.0612372 | − | 0.106066i | ||||
\(601\) | −3.00000 | − | 5.19615i | −0.122373 | − | 0.211955i | 0.798330 | − | 0.602220i | \(-0.205717\pi\) |
−0.920703 | + | 0.390264i | \(0.872384\pi\) | |||||||
\(602\) | −5.20945 | − | 29.5442i | −0.212321 | − | 1.20413i | ||||
\(603\) | −68.9440 | − | 57.8509i | −2.80762 | − | 2.35587i | ||||
\(604\) | 13.7888 | − | 11.5702i | 0.561058 | − | 0.470784i | ||||
\(605\) | −2.43107 | + | 13.7873i | −0.0988372 | + | 0.560534i | ||||
\(606\) | −28.1908 | + | 10.2606i | −1.14517 | + | 0.416809i | ||||
\(607\) | 12.0000 | 0.487065 | 0.243532 | − | 0.969893i | \(-0.421694\pi\) | ||||
0.243532 | + | 0.969893i | \(0.421694\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.0000 | 1.09410 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.16756 | + | 23.6354i | −0.168601 | + | 0.956185i | ||||
\(612\) | −4.59627 | + | 3.85673i | −0.185793 | + | 0.155899i | ||||
\(613\) | 13.7888 | + | 11.5702i | 0.556924 | + | 0.467315i | 0.877278 | − | 0.479983i | \(-0.159357\pi\) |
−0.320353 | + | 0.947298i | \(0.603802\pi\) | |||||||
\(614\) | 2.08378 | + | 11.8177i | 0.0840944 | + | 0.476923i | ||||
\(615\) | −36.0000 | − | 62.3538i | −1.45166 | − | 2.51435i | ||||
\(616\) | 3.00000 | − | 5.19615i | 0.120873 | − | 0.209359i | ||||
\(617\) | −9.39693 | − | 3.42020i | −0.378306 | − | 0.137692i | 0.145866 | − | 0.989304i | \(-0.453403\pi\) |
−0.524172 | + | 0.851612i | \(0.675625\pi\) | |||||||
\(618\) | 16.9145 | + | 6.15636i | 0.680400 | + | 0.247645i | ||||
\(619\) | 12.0000 | − | 20.7846i | 0.482321 | − | 0.835404i | −0.517473 | − | 0.855699i | \(-0.673127\pi\) |
0.999794 | + | 0.0202954i | \(0.00646066\pi\) | |||||||
\(620\) | −6.00000 | − | 10.3923i | −0.240966 | − | 0.417365i | ||||
\(621\) | −7.81417 | − | 44.3163i | −0.313572 | − | 1.77835i | ||||
\(622\) | 8.42649 | + | 7.07066i | 0.337871 | + | 0.283508i | ||||
\(623\) | 13.7888 | − | 11.5702i | 0.552437 | − | 0.463549i | ||||
\(624\) | −1.56283 | + | 8.86327i | −0.0625634 | + | 0.354815i | ||||
\(625\) | 17.8542 | − | 6.49838i | 0.714166 | − | 0.259935i | ||||
\(626\) | −21.0000 | −0.839329 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.63816 | + | 2.05212i | −0.224808 | + | 0.0818234i | ||||
\(630\) | 6.25133 | − | 35.4531i | 0.249059 | − | 1.41248i | ||||
\(631\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(632\) | −9.19253 | − | 7.71345i | −0.365659 | − | 0.306825i | ||||
\(633\) | 1.56283 | + | 8.86327i | 0.0621171 | + | 0.352283i | ||||
\(634\) | 16.5000 | + | 28.5788i | 0.655299 | + | 1.13501i | ||||
\(635\) | 12.0000 | − | 20.7846i | 0.476205 | − | 0.824812i | ||||
\(636\) | 8.45723 | + | 3.07818i | 0.335351 | + | 0.122058i | ||||
\(637\) | −5.63816 | − | 2.05212i | −0.223392 | − | 0.0813080i | ||||
\(638\) | −3.00000 | + | 5.19615i | −0.118771 | + | 0.205718i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.347296 | − | 1.96962i | −0.0137281 | − | 0.0778559i | ||||
\(641\) | −13.7888 | − | 11.5702i | −0.544625 | − | 0.456995i | 0.328491 | − | 0.944507i | \(-0.393460\pi\) |
−0.873116 | + | 0.487513i | \(0.837904\pi\) | |||||||
\(642\) | 6.89440 | − | 5.78509i | 0.272100 | − | 0.228319i | ||||
\(643\) | 5.55674 | − | 31.5138i | 0.219137 | − | 1.24278i | −0.654446 | − | 0.756109i | \(-0.727098\pi\) |
0.873582 | − | 0.486676i | \(-0.161791\pi\) | |||||||
\(644\) | 14.0954 | − | 5.13030i | 0.555436 | − | 0.202162i | ||||
\(645\) | 60.0000 | 2.36250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.0000 | −0.904223 | −0.452112 | − | 0.891961i | \(-0.649329\pi\) | ||||
−0.452112 | + | 0.891961i | \(0.649329\pi\) | |||||||
\(648\) | 8.45723 | − | 3.07818i | 0.332232 | − | 0.120922i | ||||
\(649\) | 1.04189 | − | 5.90885i | 0.0408977 | − | 0.231943i | ||||
\(650\) | 2.29813 | − | 1.92836i | 0.0901402 | − | 0.0756366i | ||||
\(651\) | 41.3664 | + | 34.7105i | 1.62128 | + | 1.36041i | ||||
\(652\) | −1.04189 | − | 5.90885i | −0.0408035 | − | 0.231408i | ||||
\(653\) | 5.00000 | + | 8.66025i | 0.195665 | + | 0.338902i | 0.947118 | − | 0.320884i | \(-0.103980\pi\) |
−0.751453 | + | 0.659786i | \(0.770647\pi\) | |||||||
\(654\) | 4.50000 | − | 7.79423i | 0.175964 | − | 0.304778i | ||||
\(655\) | −26.3114 | − | 9.57656i | −1.02807 | − | 0.374187i | ||||
\(656\) | 11.2763 | + | 4.10424i | 0.440266 | + | 0.160244i | ||||
\(657\) | 33.0000 | − | 57.1577i | 1.28745 | − | 2.22993i | ||||
\(658\) | 12.0000 | + | 20.7846i | 0.467809 | + | 0.810268i | ||||
\(659\) | 2.60472 | + | 14.7721i | 0.101466 | + | 0.575440i | 0.992573 | + | 0.121648i | \(0.0388179\pi\) |
−0.891108 | + | 0.453792i | \(0.850071\pi\) | |||||||
\(660\) | 9.19253 | + | 7.71345i | 0.357819 | + | 0.300246i | ||||
\(661\) | −11.4907 | + | 9.64181i | −0.446935 | + | 0.375023i | −0.838297 | − | 0.545214i | \(-0.816448\pi\) |
0.391362 | + | 0.920237i | \(0.372004\pi\) | |||||||
\(662\) | 1.56283 | − | 8.86327i | 0.0607413 | − | 0.344481i | ||||
\(663\) | −8.45723 | + | 3.07818i | −0.328452 | + | 0.119547i | ||||
\(664\) | −2.00000 | −0.0776151 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 36.0000 | 1.39497 | ||||||||
\(667\) | −14.0954 | + | 5.13030i | −0.545776 | + | 0.198646i | ||||
\(668\) | 2.08378 | − | 11.8177i | 0.0806238 | − | 0.457240i | ||||
\(669\) | 41.3664 | − | 34.7105i | 1.59932 | − | 1.34199i | ||||
\(670\) | 22.9813 | + | 19.2836i | 0.887846 | + | 0.744992i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 4.50000 | + | 7.79423i | 0.173591 | + | 0.300669i | ||||
\(673\) | −24.0000 | + | 41.5692i | −0.925132 | + | 1.60238i | −0.133783 | + | 0.991011i | \(0.542713\pi\) |
−0.791349 | + | 0.611365i | \(0.790621\pi\) | |||||||
\(674\) | −16.9145 | − | 6.15636i | −0.651521 | − | 0.237134i | ||||
\(675\) | −8.45723 | − | 3.07818i | −0.325519 | − | 0.118479i | ||||
\(676\) | 2.00000 | − | 3.46410i | 0.0769231 | − | 0.133235i | ||||
\(677\) | 1.50000 | + | 2.59808i | 0.0576497 | + | 0.0998522i | 0.893410 | − | 0.449242i | \(-0.148306\pi\) |
−0.835760 | + | 0.549095i | \(0.814973\pi\) | |||||||
\(678\) | −6.25133 | − | 35.4531i | −0.240081 | − | 1.36157i | ||||
\(679\) | 27.5776 | + | 23.1404i | 1.05833 | + | 0.888045i | ||||
\(680\) | 1.53209 | − | 1.28558i | 0.0587529 | − | 0.0492996i | ||||
\(681\) | 1.56283 | − | 8.86327i | 0.0598879 | − | 0.339641i | ||||
\(682\) | −11.2763 | + | 4.10424i | −0.431792 | + | 0.157160i | ||||
\(683\) | 36.0000 | 1.37750 | 0.688751 | − | 0.724998i | \(-0.258159\pi\) | ||||
0.688751 | + | 0.724998i | \(0.258159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 38.0000 | 1.45191 | ||||||||
\(686\) | 14.0954 | − | 5.13030i | 0.538164 | − | 0.195876i | ||||
\(687\) | 6.25133 | − | 35.4531i | 0.238503 | − | 1.35262i | ||||
\(688\) | −7.66044 | + | 6.42788i | −0.292052 | + | 0.245060i | ||||
\(689\) | 6.89440 | + | 5.78509i | 0.262656 | + | 0.220394i | ||||
\(690\) | 5.20945 | + | 29.5442i | 0.198320 | + | 1.12473i | ||||
\(691\) | 4.00000 | + | 6.92820i | 0.152167 | + | 0.263561i | 0.932024 | − | 0.362397i | \(-0.118041\pi\) |
−0.779857 | + | 0.625958i | \(0.784708\pi\) | |||||||
\(692\) | −9.00000 | + | 15.5885i | −0.342129 | + | 0.592584i | ||||
\(693\) | −33.8289 | − | 12.3127i | −1.28505 | − | 0.467722i | ||||
\(694\) | 15.0351 | + | 5.47232i | 0.570724 | + | 0.207727i | ||||
\(695\) | −6.00000 | + | 10.3923i | −0.227593 | + | 0.394203i | ||||
\(696\) | −4.50000 | − | 7.79423i | −0.170572 | − | 0.295439i | ||||
\(697\) | 2.08378 | + | 11.8177i | 0.0789287 | + | 0.447627i | ||||
\(698\) | −21.4492 | − | 17.9981i | −0.811866 | − | 0.681236i | ||||
\(699\) | −32.1739 | + | 26.9971i | −1.21693 | + | 1.02112i | ||||
\(700\) | 0.520945 | − | 2.95442i | 0.0196899 | − | 0.111667i | ||||
\(701\) | 37.5877 | − | 13.6808i | 1.41967 | − | 0.516717i | 0.485716 | − | 0.874116i | \(-0.338559\pi\) |
0.933952 | + | 0.357400i | \(0.116337\pi\) | |||||||
\(702\) | 27.0000 | 1.01905 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | −45.1052 | + | 16.4170i | −1.69876 | + | 0.618299i | ||||
\(706\) | 5.38309 | − | 30.5290i | 0.202595 | − | 1.14898i | ||||
\(707\) | −22.9813 | + | 19.2836i | −0.864302 | + | 0.725235i | ||||
\(708\) | 6.89440 | + | 5.78509i | 0.259107 | + | 0.217417i | ||||
\(709\) | −1.38919 | − | 7.87846i | −0.0521720 | − | 0.295882i | 0.947546 | − | 0.319619i | \(-0.103555\pi\) |
−0.999718 | + | 0.0237367i | \(0.992444\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −36.0000 | + | 62.3538i | −1.35011 | + | 2.33845i | ||||
\(712\) | −5.63816 | − | 2.05212i | −0.211299 | − | 0.0769065i | ||||
\(713\) | −28.1908 | − | 10.2606i | −1.05575 | − | 0.384263i | ||||
\(714\) | −4.50000 | + | 7.79423i | −0.168408 | + | 0.291692i | ||||
\(715\) | 6.00000 | + | 10.3923i | 0.224387 | + | 0.388650i | ||||
\(716\) | 2.08378 | + | 11.8177i | 0.0778744 | + | 0.441648i | ||||
\(717\) | −2.29813 | − | 1.92836i | −0.0858254 | − | 0.0720160i | ||||
\(718\) | −14.5548 | + | 12.2130i | −0.543182 | + | 0.455784i | ||||
\(719\) | −7.46687 | + | 42.3467i | −0.278467 | + | 1.57927i | 0.449261 | + | 0.893401i | \(0.351687\pi\) |
−0.727728 | + | 0.685866i | \(0.759424\pi\) | |||||||
\(720\) | −11.2763 | + | 4.10424i | −0.420243 | + | 0.152956i | ||||
\(721\) | 18.0000 | 0.670355 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 72.0000 | 2.67771 | ||||||||
\(724\) | 16.9145 | − | 6.15636i | 0.628621 | − | 0.228799i | ||||
\(725\) | −0.520945 | + | 2.95442i | −0.0193474 | + | 0.109725i | ||||
\(726\) | −16.0869 | + | 13.4985i | −0.597042 | + | 0.500978i | ||||
\(727\) | −26.8116 | − | 22.4976i | −0.994386 | − | 0.834389i | −0.00818884 | − | 0.999966i | \(-0.502607\pi\) |
−0.986197 | + | 0.165578i | \(0.947051\pi\) | |||||||
\(728\) | 1.56283 | + | 8.86327i | 0.0579225 | + | 0.328495i | ||||
\(729\) | 13.5000 | + | 23.3827i | 0.500000 | + | 0.866025i | ||||
\(730\) | −11.0000 | + | 19.0526i | −0.407128 | + | 0.705167i | ||||
\(731\) | −9.39693 | − | 3.42020i | −0.347558 | − | 0.126501i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.0000 | − | 19.0526i | 0.406294 | − | 0.703722i | −0.588177 | − | 0.808732i | \(-0.700154\pi\) |
0.994471 | + | 0.105010i | \(0.0334875\pi\) | |||||||
\(734\) | 4.00000 | + | 6.92820i | 0.147643 | + | 0.255725i | ||||
\(735\) | −2.08378 | − | 11.8177i | −0.0768613 | − | 0.435902i | ||||
\(736\) | −3.83022 | − | 3.21394i | −0.141184 | − | 0.118467i | ||||
\(737\) | 22.9813 | − | 19.2836i | 0.846528 | − | 0.710322i | ||||
\(738\) | 12.5027 | − | 70.9062i | 0.460230 | − | 2.61009i | ||||
\(739\) | 11.2763 | − | 4.10424i | 0.414806 | − | 0.150977i | −0.126183 | − | 0.992007i | \(-0.540273\pi\) |
0.540988 | + | 0.841030i | \(0.318050\pi\) | |||||||
\(740\) | −12.0000 | −0.441129 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.00000 | 0.330400 | ||||||||
\(743\) | 5.63816 | − | 2.05212i | 0.206844 | − | 0.0752850i | −0.236520 | − | 0.971627i | \(-0.576007\pi\) |
0.443364 | + | 0.896342i | \(0.353785\pi\) | |||||||
\(744\) | 3.12567 | − | 17.7265i | 0.114593 | − | 0.649886i | ||||
\(745\) | −12.2567 | + | 10.2846i | −0.449051 | + | 0.376799i | ||||
\(746\) | −16.0869 | − | 13.4985i | −0.588984 | − | 0.494217i | ||||
\(747\) | 2.08378 | + | 11.8177i | 0.0762415 | + | 0.432387i | ||||
\(748\) | −1.00000 | − | 1.73205i | −0.0365636 | − | 0.0633300i | ||||
\(749\) | 4.50000 | − | 7.79423i | 0.164426 | − | 0.284795i | ||||
\(750\) | 33.8289 | + | 12.3127i | 1.23526 | + | 0.449597i | ||||
\(751\) | 11.2763 | + | 4.10424i | 0.411478 | + | 0.149766i | 0.539461 | − | 0.842010i | \(-0.318628\pi\) |
−0.127983 | + | 0.991776i | \(0.540850\pi\) | |||||||
\(752\) | 4.00000 | − | 6.92820i | 0.145865 | − | 0.252646i | ||||
\(753\) | −30.0000 | − | 51.9615i | −1.09326 | − | 1.89358i | ||||
\(754\) | −1.56283 | − | 8.86327i | −0.0569150 | − | 0.322781i | ||||
\(755\) | 27.5776 | + | 23.1404i | 1.00365 | + | 0.842164i | ||||
\(756\) | 20.6832 | − | 17.3553i | 0.752241 | − | 0.631205i | ||||
\(757\) | 2.08378 | − | 11.8177i | 0.0757362 | − | 0.429521i | −0.923238 | − | 0.384230i | \(-0.874467\pi\) |
0.998974 | − | 0.0452918i | \(-0.0144218\pi\) | |||||||
\(758\) | −2.81908 | + | 1.02606i | −0.102394 | + | 0.0372682i | ||||
\(759\) | 30.0000 | 1.08893 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.0000 | −0.471250 | −0.235625 | − | 0.971844i | \(-0.575714\pi\) | ||||
−0.235625 | + | 0.971844i | \(0.575714\pi\) | |||||||
\(762\) | 33.8289 | − | 12.3127i | 1.22549 | − | 0.446043i | ||||
\(763\) | 1.56283 | − | 8.86327i | 0.0565784 | − | 0.320872i | ||||
\(764\) | −8.42649 | + | 7.07066i | −0.304860 | + | 0.255808i | ||||
\(765\) | −9.19253 | − | 7.71345i | −0.332357 | − | 0.278880i | ||||
\(766\) | 3.12567 | + | 17.7265i | 0.112935 | + | 0.640486i | ||||
\(767\) | 4.50000 | + | 7.79423i | 0.162486 | + | 0.281433i | ||||
\(768\) | 1.50000 | − | 2.59808i | 0.0541266 | − | 0.0937500i | ||||
\(769\) | 14.0954 | + | 5.13030i | 0.508293 | + | 0.185003i | 0.583420 | − | 0.812171i | \(-0.301714\pi\) |
−0.0751274 | + | 0.997174i | \(0.523936\pi\) | |||||||
\(770\) | 11.2763 | + | 4.10424i | 0.406370 | + | 0.147907i | ||||
\(771\) | 27.0000 | − | 46.7654i | 0.972381 | − | 1.68421i | ||||
\(772\) | 3.00000 | + | 5.19615i | 0.107972 | + | 0.187014i | ||||
\(773\) | −2.60472 | − | 14.7721i | −0.0936854 | − | 0.531316i | −0.995142 | − | 0.0984472i | \(-0.968612\pi\) |
0.901457 | − | 0.432869i | \(-0.142499\pi\) | |||||||
\(774\) | 45.9627 | + | 38.5673i | 1.65209 | + | 1.38627i | ||||
\(775\) | −4.59627 | + | 3.85673i | −0.165103 | + | 0.138538i | ||||
\(776\) | 2.08378 | − | 11.8177i | 0.0748033 | − | 0.424230i | ||||
\(777\) | 50.7434 | − | 18.4691i | 1.82041 | − | 0.662575i | ||||
\(778\) | −26.0000 | −0.932145 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −18.0000 | −0.644503 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.868241 | − | 4.92404i | 0.0310482 | − | 0.176083i | ||||
\(783\) | −20.6832 | + | 17.3553i | −0.739157 | + | 0.620227i | ||||
\(784\) | 1.53209 | + | 1.28558i | 0.0547175 | + | 0.0459134i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −21.0000 | − | 36.3731i | −0.749045 | − | 1.29738i | ||||
\(787\) | −4.50000 | + | 7.79423i | −0.160408 | + | 0.277834i | −0.935015 | − | 0.354608i | \(-0.884614\pi\) |
0.774607 | + | 0.632443i | \(0.217948\pi\) | |||||||
\(788\) | −3.75877 | − | 1.36808i | −0.133901 | − | 0.0487359i | ||||
\(789\) | −22.5526 | − | 8.20848i | −0.802895 | − | 0.292230i | ||||
\(790\) | 12.0000 | − | 20.7846i | 0.426941 | − | 0.739483i | ||||
\(791\) | −18.0000 | − | 31.1769i | −0.640006 | − | 1.10852i | ||||
\(792\) | 2.08378 | + | 11.8177i | 0.0740438 | + | 0.419923i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −1.53209 | + | 1.28558i | −0.0543718 | + | 0.0456234i | ||||
\(795\) | −3.12567 | + | 17.7265i | −0.110856 | + | 0.628696i | ||||
\(796\) | 6.57785 | − | 2.39414i | 0.233146 | − | 0.0848581i | ||||
\(797\) | −33.0000 | −1.16892 | −0.584460 | − | 0.811423i | \(-0.698694\pi\) | ||||
−0.584460 | + | 0.811423i | \(0.698694\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000 | 0.283020 | ||||||||
\(800\) | −0.939693 | + | 0.342020i | −0.0332232 | + | 0.0120922i | ||||
\(801\) | −6.25133 | + | 35.4531i | −0.220880 | + | 1.25267i | ||||
\(802\) | 27.5776 | − | 23.1404i | 0.973799 | − | 0.817114i | ||||
\(803\) | 16.8530 | + | 14.1413i | 0.594729 | + | 0.499037i | ||||
\(804\) | 7.81417 | + | 44.3163i | 0.275584 | + | 1.56292i | ||||
\(805\) | 15.0000 | + | 25.9808i | 0.528681 | + | 0.915702i | ||||
\(806\) | 9.00000 | − | 15.5885i | 0.317011 | − | 0.549080i | ||||
\(807\) | 16.9145 | + | 6.15636i | 0.595417 | + | 0.216714i | ||||
\(808\) | 9.39693 | + | 3.42020i | 0.330583 | + | 0.120322i | ||||
\(809\) | 5.50000 | − | 9.52628i | 0.193370 | − | 0.334926i | −0.752995 | − | 0.658026i | \(-0.771392\pi\) |
0.946365 | + | 0.323100i | \(0.104725\pi\) | |||||||
\(810\) | 9.00000 | + | 15.5885i | 0.316228 | + | 0.547723i | ||||
\(811\) | −5.73039 | − | 32.4987i | −0.201221 | − | 1.14118i | −0.903276 | − | 0.429059i | \(-0.858845\pi\) |
0.702055 | − | 0.712123i | \(-0.252266\pi\) | |||||||
\(812\) | −6.89440 | − | 5.78509i | −0.241946 | − | 0.203017i | ||||
\(813\) | 25.2795 | − | 21.2120i | 0.886590 | − | 0.743937i | ||||
\(814\) | −2.08378 | + | 11.8177i | −0.0730364 | + | 0.414210i | ||||
\(815\) | 11.2763 | − | 4.10424i | 0.394992 | − | 0.143765i | ||||
\(816\) | 3.00000 | 0.105021 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 6.00000 | 0.209785 | ||||||||
\(819\) | 50.7434 | − | 18.4691i | 1.77312 | − | 0.645362i | ||||
\(820\) | −4.16756 | + | 23.6354i | −0.145537 | + | 0.825383i | ||||
\(821\) | 1.53209 | − | 1.28558i | 0.0534703 | − | 0.0448669i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
0.669131 | + | 0.743144i | \(0.266666\pi\) | |||||||
\(822\) | 43.6645 | + | 36.6389i | 1.52298 | + | 1.27793i | ||||
\(823\) | 0.520945 | + | 2.95442i | 0.0181590 | + | 0.102985i | 0.992540 | − | 0.121918i | \(-0.0389046\pi\) |
−0.974381 | + | 0.224903i | \(0.927793\pi\) | |||||||
\(824\) | −3.00000 | − | 5.19615i | −0.104510 | − | 0.181017i | ||||
\(825\) | 3.00000 | − | 5.19615i | 0.104447 | − | 0.180907i | ||||
\(826\) | 8.45723 | + | 3.07818i | 0.294265 | + | 0.107104i | ||||
\(827\) | 14.0954 | + | 5.13030i | 0.490145 | + | 0.178398i | 0.575256 | − | 0.817973i | \(-0.304902\pi\) |
−0.0851114 | + | 0.996371i | \(0.527125\pi\) | |||||||
\(828\) | −15.0000 | + | 25.9808i | −0.521286 | + | 0.902894i | ||||
\(829\) | 25.5000 | + | 44.1673i | 0.885652 | + | 1.53399i | 0.844965 | + | 0.534822i | \(0.179621\pi\) |
0.0406866 | + | 0.999172i | \(0.487045\pi\) | |||||||
\(830\) | −0.694593 | − | 3.93923i | −0.0241097 | − | 0.136733i | ||||
\(831\) | −68.9440 | − | 57.8509i | −2.39164 | − | 2.00682i | ||||
\(832\) | 2.29813 | − | 1.92836i | 0.0796734 | − | 0.0668540i | ||||
\(833\) | −0.347296 | + | 1.96962i | −0.0120331 | + | 0.0682431i | ||||
\(834\) | −16.9145 | + | 6.15636i | −0.585700 | + | 0.213177i | ||||
\(835\) | 24.0000 | 0.830554 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −54.0000 | −1.86651 | ||||||||
\(838\) | −13.1557 | + | 4.78828i | −0.454456 | + | 0.165408i | ||||
\(839\) | 3.12567 | − | 17.7265i | 0.107910 | − | 0.611988i | −0.882108 | − | 0.471047i | \(-0.843876\pi\) |
0.990018 | − | 0.140941i | \(-0.0450128\pi\) | |||||||
\(840\) | −13.7888 | + | 11.5702i | −0.475759 | + | 0.399209i | ||||
\(841\) | −15.3209 | − | 12.8558i | −0.528307 | − | 0.443302i | ||||
\(842\) | −4.68850 | − | 26.5898i | −0.161576 | − | 0.916345i | ||||
\(843\) | −18.0000 | − | 31.1769i | −0.619953 | − | 1.07379i | ||||
\(844\) | 1.50000 | − | 2.59808i | 0.0516321 | − | 0.0894295i | ||||
\(845\) | 7.51754 | + | 2.73616i | 0.258611 | + | 0.0941268i | ||||
\(846\) | −45.1052 | − | 16.4170i | −1.55075 | − | 0.564427i | ||||
\(847\) | −10.5000 | + | 18.1865i | −0.360784 | + | 0.624897i | ||||
\(848\) | −1.50000 | − | 2.59808i | −0.0515102 | − | 0.0892183i | ||||
\(849\) | 7.29322 | + | 41.3619i | 0.250303 | + | 1.41954i | ||||
\(850\) | −0.766044 | − | 0.642788i | −0.0262751 | − | 0.0220474i | ||||
\(851\) | −22.9813 | + | 19.2836i | −0.787790 | + | 0.661034i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43.2259 | + | 15.7329i | −1.48003 | + | 0.538685i | −0.950802 | − | 0.309798i | \(-0.899739\pi\) |
−0.529223 | + | 0.848483i | \(0.677516\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.00000 | −0.102538 | ||||||||
\(857\) | 22.5526 | − | 8.20848i | 0.770383 | − | 0.280396i | 0.0732263 | − | 0.997315i | \(-0.476670\pi\) |
0.697157 | + | 0.716919i | \(0.254448\pi\) | |||||||
\(858\) | −3.12567 | + | 17.7265i | −0.106709 | + | 0.605174i | ||||
\(859\) | 41.3664 | − | 34.7105i | 1.41140 | − | 1.18431i | 0.455643 | − | 0.890163i | \(-0.349410\pi\) |
0.955761 | − | 0.294145i | \(-0.0950349\pi\) | |||||||
\(860\) | −15.3209 | − | 12.8558i | −0.522438 | − | 0.438378i | ||||
\(861\) | −18.7540 | − | 106.359i | −0.639135 | − | 3.62471i | ||||
\(862\) | −12.0000 | − | 20.7846i | −0.408722 | − | 0.707927i | ||||
\(863\) | 24.0000 | − | 41.5692i | 0.816970 | − | 1.41503i | −0.0909355 | − | 0.995857i | \(-0.528986\pi\) |
0.907905 | − | 0.419176i | \(-0.137681\pi\) | |||||||
\(864\) | −8.45723 | − | 3.07818i | −0.287721 | − | 0.104722i | ||||
\(865\) | −33.8289 | − | 12.3127i | −1.15022 | − | 0.418645i | ||||
\(866\) | −15.0000 | + | 25.9808i | −0.509721 | + | 0.882862i | ||||
\(867\) | −24.0000 | − | 41.5692i | −0.815083 | − | 1.41176i | ||||
\(868\) | −3.12567 | − | 17.7265i | −0.106092 | − | 0.601678i | ||||
\(869\) | −18.3851 | − | 15.4269i | −0.623671 | − | 0.523322i | ||||
\(870\) | 13.7888 | − | 11.5702i | 0.467484 | − | 0.392266i | ||||
\(871\) | −7.81417 | + | 44.3163i | −0.264773 | + | 1.50160i | ||||
\(872\) | −2.81908 | + | 1.02606i | −0.0954660 | + | 0.0347468i | ||||
\(873\) | −72.0000 | −2.43683 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.0000 | 1.21702 | ||||||||
\(876\) | −31.0099 | + | 11.2867i | −1.04773 | + | 0.381341i | ||||
\(877\) | −4.68850 | + | 26.5898i | −0.158319 | + | 0.897874i | 0.797369 | + | 0.603493i | \(0.206225\pi\) |
−0.955688 | + | 0.294381i | \(0.904886\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.6832 | − | 17.3553i | −0.697627 | − | 0.585379i | ||||
\(880\) | −0.694593 | − | 3.93923i | −0.0234147 | − | 0.132791i | ||||
\(881\) | −17.0000 | − | 29.4449i | −0.572745 | − | 0.992023i | −0.996283 | − | 0.0861444i | \(-0.972545\pi\) |
0.423538 | − | 0.905878i | \(-0.360788\pi\) | |||||||
\(882\) | 6.00000 | − | 10.3923i | 0.202031 | − | 0.349927i | ||||
\(883\) | 22.5526 | + | 8.20848i | 0.758956 | + | 0.276237i | 0.692369 | − | 0.721543i | \(-0.256567\pi\) |
0.0665867 | + | 0.997781i | \(0.478789\pi\) | |||||||
\(884\) | 2.81908 | + | 1.02606i | 0.0948158 | + | 0.0345101i | ||||
\(885\) | −9.00000 | + | 15.5885i | −0.302532 | + | 0.524000i | ||||
\(886\) | −11.0000 | − | 19.0526i | −0.369552 | − | 0.640083i | ||||
\(887\) | 4.16756 | + | 23.6354i | 0.139933 | + | 0.793599i | 0.971297 | + | 0.237870i | \(0.0764494\pi\) |
−0.831364 | + | 0.555728i | \(0.812440\pi\) | |||||||
\(888\) | −13.7888 | − | 11.5702i | −0.462722 | − | 0.388270i | ||||
\(889\) | 27.5776 | − | 23.1404i | 0.924923 | − | 0.776103i | ||||
\(890\) | 2.08378 | − | 11.8177i | 0.0698484 | − | 0.396130i | ||||
\(891\) | 16.9145 | − | 6.15636i | 0.566656 | − | 0.206246i | ||||
\(892\) | −18.0000 | −0.602685 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −24.0000 | −0.802680 | ||||||||
\(895\) | −22.5526 | + | 8.20848i | −0.753851 | + | 0.274379i | ||||
\(896\) | 0.520945 | − | 2.95442i | 0.0174035 | − | 0.0987004i | ||||
\(897\) | −34.4720 | + | 28.9254i | −1.15099 | + | 0.965792i | ||||
\(898\) | 4.59627 | + | 3.85673i | 0.153379 | + | 0.128701i | ||||
\(899\) | 3.12567 | + | 17.7265i | 0.104247 | + | 0.591213i | ||||
\(900\) | 3.00000 | + | 5.19615i | 0.100000 | + | 0.173205i | ||||
\(901\) | 1.50000 | − | 2.59808i | 0.0499722 | − | 0.0865545i | ||||
\(902\) | 22.5526 | + | 8.20848i | 0.750920 | + | 0.273313i | ||||
\(903\) | 84.5723 | + | 30.7818i | 2.81439 | + | 1.02435i | ||||
\(904\) | −6.00000 | + | 10.3923i | −0.199557 | + | 0.345643i | ||||
\(905\) | 18.0000 | + | 31.1769i | 0.598340 | + | 1.03636i | ||||
\(906\) | 9.37700 | + | 53.1796i | 0.311530 | + | 1.76677i | ||||
\(907\) | 11.4907 | + | 9.64181i | 0.381541 | + | 0.320151i | 0.813307 | − | 0.581835i | \(-0.197665\pi\) |
−0.431766 | + | 0.901986i | \(0.642109\pi\) | |||||||
\(908\) | −2.29813 | + | 1.92836i | −0.0762662 | + | 0.0639950i | ||||
\(909\) | 10.4189 | − | 59.0885i | 0.345573 | − | 1.95984i | ||||
\(910\) | −16.9145 | + | 6.15636i | −0.560709 | + | 0.204081i | ||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.00000 | −0.132381 | ||||||||
\(914\) | 0.939693 | − | 0.342020i | 0.0310823 | − | 0.0113130i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.19253 | + | 7.71345i | −0.303730 | + | 0.254860i | ||||
\(917\) | −32.1739 | − | 26.9971i | −1.06247 | − | 0.891522i | ||||
\(918\) | −1.56283 | − | 8.86327i | −0.0515812 | − | 0.292531i | ||||
\(919\) | −7.50000 | − | 12.9904i | −0.247402 | − | 0.428513i | 0.715402 | − | 0.698713i | \(-0.246244\pi\) |
−0.962804 | + | 0.270200i | \(0.912910\pi\) | |||||||
\(920\) | 5.00000 | − | 8.66025i | 0.164845 | − | 0.285520i | ||||
\(921\) | −33.8289 | − | 12.3127i | −1.11470 | − | 0.405718i | ||||
\(922\) | 3.75877 | + | 1.36808i | 0.123789 | + | 0.0450553i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 9.00000 | + | 15.5885i | 0.296078 | + | 0.512823i | ||||
\(925\) | 1.04189 | + | 5.90885i | 0.0342571 | + | 0.194282i | ||||
\(926\) | −24.5134 | − | 20.5692i | −0.805561 | − | 0.675946i | ||||
\(927\) | −27.5776 | + | 23.1404i | −0.905767 | + | 0.760029i | ||||
\(928\) | −0.520945 | + | 2.95442i | −0.0171008 | + | 0.0969837i | ||||
\(929\) | −38.5274 | + | 14.0228i | −1.26404 | + | 0.460074i | −0.885124 | − | 0.465356i | \(-0.845926\pi\) |
−0.378919 | + | 0.925430i | \(0.623704\pi\) | |||||||
\(930\) | 36.0000 | 1.18049 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 14.0000 | 0.458585 | ||||||||
\(933\) | −31.0099 | + | 11.2867i | −1.01522 | + | 0.369509i | ||||
\(934\) | −1.38919 | + | 7.87846i | −0.0454555 | + | 0.257791i | ||||
\(935\) | 3.06418 | − | 2.57115i | 0.100209 | − | 0.0840856i | ||||
\(936\) | −13.7888 | − | 11.5702i | −0.450701 | − | 0.378183i | ||||
\(937\) | −8.16146 | − | 46.2860i | −0.266623 | − | 1.51210i | −0.764372 | − | 0.644775i | \(-0.776951\pi\) |
0.497749 | − | 0.867321i | \(-0.334160\pi\) | |||||||
\(938\) | 22.5000 | + | 38.9711i | 0.734651 | + | 1.27245i | ||||
\(939\) | 31.5000 | − | 54.5596i | 1.02796 | − | 1.78049i | ||||
\(940\) | 15.0351 | + | 5.47232i | 0.490390 | + | 0.178487i | ||||
\(941\) | −25.3717 | − | 9.23454i | −0.827094 | − | 0.301038i | −0.106428 | − | 0.994320i | \(-0.533941\pi\) |
−0.720666 | + | 0.693283i | \(0.756164\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.0000 | + | 51.9615i | 0.976934 | + | 1.69210i | ||||
\(944\) | −0.520945 | − | 2.95442i | −0.0169553 | − | 0.0961583i | ||||
\(945\) | 41.3664 | + | 34.7105i | 1.34565 | + | 1.12913i | ||||
\(946\) | −15.3209 | + | 12.8558i | −0.498125 | + | 0.417977i | ||||
\(947\) | −7.98782 | + | 45.3012i | −0.259569 | + | 1.47209i | 0.524497 | + | 0.851412i | \(0.324253\pi\) |
−0.784066 | + | 0.620677i | \(0.786858\pi\) | |||||||
\(948\) | 33.8289 | − | 12.3127i | 1.09871 | − | 0.399899i | ||||
\(949\) | −33.0000 | −1.07123 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −99.0000 | −3.21029 | ||||||||
\(952\) | 2.81908 | − | 1.02606i | 0.0913668 | − | 0.0332548i | ||||
\(953\) | 5.20945 | − | 29.5442i | 0.168750 | − | 0.957032i | −0.776362 | − | 0.630287i | \(-0.782937\pi\) |
0.945113 | − | 0.326745i | \(-0.105952\pi\) | |||||||
\(954\) | −13.7888 | + | 11.5702i | −0.446429 | + | 0.374598i | ||||
\(955\) | −16.8530 | − | 14.1413i | −0.545350 | − | 0.457603i | ||||
\(956\) | 0.173648 | + | 0.984808i | 0.00561618 | + | 0.0318510i | ||||
\(957\) | −9.00000 | − | 15.5885i | −0.290929 | − | 0.503903i | ||||
\(958\) | −20.0000 | + | 34.6410i | −0.646171 | + | 1.11920i | ||||
\(959\) | 53.5625 | + | 19.4951i | 1.72962 | + | 0.629531i | ||||
\(960\) | 5.63816 | + | 2.05212i | 0.181971 | + | 0.0662319i | ||||
\(961\) | −2.50000 | + | 4.33013i | −0.0806452 | + | 0.139682i | ||||
\(962\) | −9.00000 | − | 15.5885i | −0.290172 | − | 0.502592i | ||||
\(963\) | 3.12567 | + | 17.7265i | 0.100723 | + | 0.571230i | ||||
\(964\) | −18.3851 | − | 15.4269i | −0.592143 | − | 0.496867i | ||||
\(965\) | −9.19253 | + | 7.71345i | −0.295918 | + | 0.248305i | ||||
\(966\) | −7.81417 | + | 44.3163i | −0.251417 | + | 1.42586i | ||||
\(967\) | 22.5526 | − | 8.20848i | 0.725243 | − | 0.263967i | 0.0470934 | − | 0.998890i | \(-0.485004\pi\) |
0.678150 | + | 0.734923i | \(0.262782\pi\) | |||||||
\(968\) | 7.00000 | 0.224989 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 24.0000 | 0.770594 | ||||||||
\(971\) | −45.1052 | + | 16.4170i | −1.44750 | + | 0.526846i | −0.941891 | − | 0.335919i | \(-0.890953\pi\) |
−0.505605 | + | 0.862765i | \(0.668731\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.7888 | + | 11.5702i | −0.442049 | + | 0.370923i | ||||
\(974\) | −13.7888 | − | 11.5702i | −0.441822 | − | 0.370732i | ||||
\(975\) | 1.56283 | + | 8.86327i | 0.0500507 | + | 0.283852i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.0000 | + | 25.9808i | −0.479893 | + | 0.831198i | −0.999734 | − | 0.0230645i | \(-0.992658\pi\) |
0.519841 | + | 0.854263i | \(0.325991\pi\) | |||||||
\(978\) | 16.9145 | + | 6.15636i | 0.540865 | + | 0.196859i | ||||
\(979\) | −11.2763 | − | 4.10424i | −0.360392 | − | 0.131172i | ||||
\(980\) | −2.00000 | + | 3.46410i | −0.0638877 | + | 0.110657i | ||||
\(981\) | 9.00000 | + | 15.5885i | 0.287348 | + | 0.497701i | ||||
\(982\) | −1.38919 | − | 7.87846i | −0.0443307 | − | 0.251412i | ||||
\(983\) | 18.3851 | + | 15.4269i | 0.586393 | + | 0.492042i | 0.887039 | − | 0.461694i | \(-0.152758\pi\) |
−0.300647 | + | 0.953736i | \(0.597203\pi\) | |||||||
\(984\) | −27.5776 | + | 23.1404i | −0.879142 | + | 0.737688i | ||||
\(985\) | 1.38919 | − | 7.87846i | 0.0442631 | − | 0.251029i | ||||
\(986\) | −2.81908 | + | 1.02606i | −0.0897777 | + | 0.0326764i | ||||
\(987\) | −72.0000 | −2.29179 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −50.0000 | −1.58991 | ||||||||
\(990\) | −22.5526 | + | 8.20848i | −0.716769 | + | 0.260883i | ||||
\(991\) | −1.04189 | + | 5.90885i | −0.0330967 | + | 0.187701i | −0.996874 | − | 0.0790075i | \(-0.974825\pi\) |
0.963777 | + | 0.266708i | \(0.0859360\pi\) | |||||||
\(992\) | −4.59627 | + | 3.85673i | −0.145932 | + | 0.122451i | ||||
\(993\) | 20.6832 | + | 17.3553i | 0.656362 | + | 0.550753i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.00000 | + | 12.1244i | 0.221915 | + | 0.384368i | ||||
\(996\) | 3.00000 | − | 5.19615i | 0.0950586 | − | 0.164646i | ||||
\(997\) | −5.63816 | − | 2.05212i | −0.178562 | − | 0.0649913i | 0.251192 | − | 0.967937i | \(-0.419178\pi\) |
−0.429754 | + | 0.902946i | \(0.641400\pi\) | |||||||
\(998\) | 16.9145 | + | 6.15636i | 0.535418 | + | 0.194876i | ||||
\(999\) | −27.0000 | + | 46.7654i | −0.854242 | + | 1.47959i |
(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 | 722.2.e.h.423.1 | 6 | ||
19.2 | odd | 18 | 722.2.a.f.1.1 | yes | 1 | ||
19.3 | odd | 18 | 722.2.c.a.653.1 | 2 | |||
19.4 | even | 9 | inner | 722.2.e.h.99.1 | 6 | ||
19.5 | even | 9 | 722.2.c.g.429.1 | 2 | |||
19.6 | even | 9 | inner | 722.2.e.h.389.1 | 6 | ||
19.7 | even | 3 | inner | 722.2.e.h.245.1 | 6 | ||
19.8 | odd | 6 | 722.2.e.g.415.1 | 6 | |||
19.9 | even | 9 | inner | 722.2.e.h.595.1 | 6 | ||
19.10 | odd | 18 | 722.2.e.g.595.1 | 6 | |||
19.11 | even | 3 | inner | 722.2.e.h.415.1 | 6 | ||
19.12 | odd | 6 | 722.2.e.g.245.1 | 6 | |||
19.13 | odd | 18 | 722.2.e.g.389.1 | 6 | |||
19.14 | odd | 18 | 722.2.c.a.429.1 | 2 | |||
19.15 | odd | 18 | 722.2.e.g.99.1 | 6 | |||
19.16 | even | 9 | 722.2.c.g.653.1 | 2 | |||
19.17 | even | 9 | 722.2.a.a.1.1 | ✓ | 1 | ||
19.18 | odd | 2 | 722.2.e.g.423.1 | 6 | |||
57.2 | even | 18 | 6498.2.a.a.1.1 | 1 | |||
57.17 | odd | 18 | 6498.2.a.m.1.1 | 1 | |||
76.55 | odd | 18 | 5776.2.a.q.1.1 | 1 | |||
76.59 | even | 18 | 5776.2.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
722.2.a.a.1.1 | ✓ | 1 | 19.17 | even | 9 | ||
722.2.a.f.1.1 | yes | 1 | 19.2 | odd | 18 | ||
722.2.c.a.429.1 | 2 | 19.14 | odd | 18 | |||
722.2.c.a.653.1 | 2 | 19.3 | odd | 18 | |||
722.2.c.g.429.1 | 2 | 19.5 | even | 9 | |||
722.2.c.g.653.1 | 2 | 19.16 | even | 9 | |||
722.2.e.g.99.1 | 6 | 19.15 | odd | 18 | |||
722.2.e.g.245.1 | 6 | 19.12 | odd | 6 | |||
722.2.e.g.389.1 | 6 | 19.13 | odd | 18 | |||
722.2.e.g.415.1 | 6 | 19.8 | odd | 6 | |||
722.2.e.g.423.1 | 6 | 19.18 | odd | 2 | |||
722.2.e.g.595.1 | 6 | 19.10 | odd | 18 | |||
722.2.e.h.99.1 | 6 | 19.4 | even | 9 | inner | ||
722.2.e.h.245.1 | 6 | 19.7 | even | 3 | inner | ||
722.2.e.h.389.1 | 6 | 19.6 | even | 9 | inner | ||
722.2.e.h.415.1 | 6 | 19.11 | even | 3 | inner | ||
722.2.e.h.423.1 | 6 | 1.1 | even | 1 | trivial | ||
722.2.e.h.595.1 | 6 | 19.9 | even | 9 | inner | ||
5776.2.a.a.1.1 | 1 | 76.59 | even | 18 | |||
5776.2.a.q.1.1 | 1 | 76.55 | odd | 18 | |||
6498.2.a.a.1.1 | 1 | 57.2 | even | 18 | |||
6498.2.a.m.1.1 | 1 | 57.17 | odd | 18 |