Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(61,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.bf (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: | \(2.87461447277\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 301.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.301 |
Dual form | 360.2.bf.a.61.2 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | − | 1.36603i | 0.258819 | − | 0.965926i | ||||
\(3\) | 0.866025 | + | 1.50000i | 0.500000 | + | 0.866025i | ||||
\(4\) | −1.73205 | − | 1.00000i | −0.866025 | − | 0.500000i | ||||
\(5\) | −0.866025 | − | 0.500000i | −0.387298 | − | 0.223607i | ||||
\(6\) | 2.36603 | − | 0.633975i | 0.965926 | − | 0.258819i | ||||
\(7\) | 2.00000 | + | 3.46410i | 0.755929 | + | 1.30931i | 0.944911 | + | 0.327327i | \(0.106148\pi\) |
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.707107 | + | 0.707107i | ||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | −1.00000 | + | 1.00000i | −0.316228 | + | 0.316228i | ||||
\(11\) | 4.33013 | − | 2.50000i | 1.30558 | − | 0.753778i | 0.324227 | − | 0.945979i | \(-0.394896\pi\) |
0.981356 | + | 0.192201i | \(0.0615626\pi\) | |||||||
\(12\) | − | 3.46410i | − | 1.00000i | ||||||
\(13\) | 5.19615 | + | 3.00000i | 1.44115 | + | 0.832050i | 0.997927 | − | 0.0643593i | \(-0.0205004\pi\) |
0.443227 | + | 0.896410i | \(0.353834\pi\) | |||||||
\(14\) | 5.46410 | − | 1.46410i | 1.46034 | − | 0.391298i | ||||
\(15\) | − | 1.73205i | − | 0.447214i | ||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | 3.00000 | + | 3.00000i | 0.707107 | + | 0.707107i | ||||
\(19\) | − | 7.00000i | − | 1.60591i | −0.596040 | − | 0.802955i | \(-0.703260\pi\) | ||
0.596040 | − | 0.802955i | \(-0.296740\pi\) | |||||||
\(20\) | 1.00000 | + | 1.73205i | 0.223607 | + | 0.387298i | ||||
\(21\) | −3.46410 | + | 6.00000i | −0.755929 | + | 1.30931i | ||||
\(22\) | −1.83013 | − | 6.83013i | −0.390184 | − | 1.45619i | ||||
\(23\) | −1.00000 | + | 1.73205i | −0.208514 | + | 0.361158i | −0.951247 | − | 0.308431i | \(-0.900196\pi\) |
0.742732 | + | 0.669588i | \(0.233529\pi\) | |||||||
\(24\) | −4.73205 | − | 1.26795i | −0.965926 | − | 0.258819i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 6.00000 | − | 6.00000i | 1.17670 | − | 1.17670i | ||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | − | 8.00000i | − | 1.51186i | ||||||
\(29\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(30\) | −2.36603 | − | 0.633975i | −0.431975 | − | 0.115747i | ||||
\(31\) | −2.00000 | + | 3.46410i | −0.359211 | + | 0.622171i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 5.46410 | − | 1.46410i | 0.965926 | − | 0.258819i | ||||
\(33\) | 7.50000 | + | 4.33013i | 1.30558 | + | 0.753778i | ||||
\(34\) | −1.09808 | + | 4.09808i | −0.188319 | + | 0.702814i | ||||
\(35\) | − | 4.00000i | − | 0.676123i | ||||||
\(36\) | 5.19615 | − | 3.00000i | 0.866025 | − | 0.500000i | ||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | −9.56218 | − | 2.56218i | −1.55119 | − | 0.415640i | ||||
\(39\) | 10.3923i | 1.66410i | ||||||||
\(40\) | 2.73205 | − | 0.732051i | 0.431975 | − | 0.115747i | ||||
\(41\) | 2.50000 | − | 4.33013i | 0.390434 | − | 0.676252i | −0.602072 | − | 0.798441i | \(-0.705658\pi\) |
0.992507 | + | 0.122189i | \(0.0389915\pi\) | |||||||
\(42\) | 6.92820 | + | 6.92820i | 1.06904 | + | 1.06904i | ||||
\(43\) | −4.33013 | + | 2.50000i | −0.660338 | + | 0.381246i | −0.792406 | − | 0.609994i | \(-0.791172\pi\) |
0.132068 | + | 0.991241i | \(0.457838\pi\) | |||||||
\(44\) | −10.0000 | −1.50756 | ||||||||
\(45\) | 2.59808 | − | 1.50000i | 0.387298 | − | 0.223607i | ||||
\(46\) | 2.00000 | + | 2.00000i | 0.294884 | + | 0.294884i | ||||
\(47\) | −1.00000 | − | 1.73205i | −0.145865 | − | 0.252646i | 0.783830 | − | 0.620975i | \(-0.213263\pi\) |
−0.929695 | + | 0.368329i | \(0.879930\pi\) | |||||||
\(48\) | −3.46410 | + | 6.00000i | −0.500000 | + | 0.866025i | ||||
\(49\) | −4.50000 | + | 7.79423i | −0.642857 | + | 1.11346i | ||||
\(50\) | 1.36603 | − | 0.366025i | 0.193185 | − | 0.0517638i | ||||
\(51\) | −2.59808 | − | 4.50000i | −0.363803 | − | 0.630126i | ||||
\(52\) | −6.00000 | − | 10.3923i | −0.832050 | − | 1.44115i | ||||
\(53\) | − | 8.00000i | − | 1.09888i | −0.835532 | − | 0.549442i | \(-0.814840\pi\) | ||
0.835532 | − | 0.549442i | \(-0.185160\pi\) | |||||||
\(54\) | −1.90192 | + | 7.09808i | −0.258819 | + | 0.965926i | ||||
\(55\) | −5.00000 | −0.674200 | ||||||||
\(56\) | −10.9282 | − | 2.92820i | −1.46034 | − | 0.391298i | ||||
\(57\) | 10.5000 | − | 6.06218i | 1.39076 | − | 0.802955i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.06218 | − | 3.50000i | −0.789228 | − | 0.455661i | 0.0504625 | − | 0.998726i | \(-0.483930\pi\) |
−0.839691 | + | 0.543065i | \(0.817264\pi\) | |||||||
\(60\) | −1.73205 | + | 3.00000i | −0.223607 | + | 0.387298i | ||||
\(61\) | −3.46410 | + | 2.00000i | −0.443533 | + | 0.256074i | −0.705095 | − | 0.709113i | \(-0.749096\pi\) |
0.261562 | + | 0.965187i | \(0.415762\pi\) | |||||||
\(62\) | 4.00000 | + | 4.00000i | 0.508001 | + | 0.508001i | ||||
\(63\) | −12.0000 | −1.51186 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | −3.00000 | − | 5.19615i | −0.372104 | − | 0.644503i | ||||
\(66\) | 8.66025 | − | 8.66025i | 1.06600 | − | 1.06600i | ||||
\(67\) | −2.59808 | − | 1.50000i | −0.317406 | − | 0.183254i | 0.332830 | − | 0.942987i | \(-0.391996\pi\) |
−0.650236 | + | 0.759733i | \(0.725330\pi\) | |||||||
\(68\) | 5.19615 | + | 3.00000i | 0.630126 | + | 0.363803i | ||||
\(69\) | −3.46410 | −0.417029 | ||||||||
\(70\) | −5.46410 | − | 1.46410i | −0.653085 | − | 0.174994i | ||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | −2.19615 | − | 8.19615i | −0.258819 | − | 0.965926i | ||||
\(73\) | 1.00000 | 0.117041 | 0.0585206 | − | 0.998286i | \(-0.481362\pi\) | ||||
0.0585206 | + | 0.998286i | \(0.481362\pi\) | |||||||
\(74\) | 2.73205 | + | 0.732051i | 0.317594 | + | 0.0850992i | ||||
\(75\) | −0.866025 | + | 1.50000i | −0.100000 | + | 0.173205i | ||||
\(76\) | −7.00000 | + | 12.1244i | −0.802955 | + | 1.39076i | ||||
\(77\) | 17.3205 | + | 10.0000i | 1.97386 | + | 1.13961i | ||||
\(78\) | 14.1962 | + | 3.80385i | 1.60740 | + | 0.430701i | ||||
\(79\) | −5.00000 | − | 8.66025i | −0.562544 | − | 0.974355i | −0.997274 | − | 0.0737937i | \(-0.976489\pi\) |
0.434730 | − | 0.900561i | \(-0.356844\pi\) | |||||||
\(80\) | − | 4.00000i | − | 0.447214i | ||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | −5.00000 | − | 5.00000i | −0.552158 | − | 0.552158i | ||||
\(83\) | 10.3923 | − | 6.00000i | 1.14070 | − | 0.658586i | 0.194099 | − | 0.980982i | \(-0.437822\pi\) |
0.946605 | + | 0.322396i | \(0.104488\pi\) | |||||||
\(84\) | 12.0000 | − | 6.92820i | 1.30931 | − | 0.755929i | ||||
\(85\) | 2.59808 | + | 1.50000i | 0.281801 | + | 0.162698i | ||||
\(86\) | 1.83013 | + | 6.83013i | 0.197348 | + | 0.736512i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.66025 | + | 13.6603i | −0.390184 | + | 1.45619i | ||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | −1.09808 | − | 4.09808i | −0.115747 | − | 0.431975i | ||||
\(91\) | 24.0000i | 2.51588i | ||||||||
\(92\) | 3.46410 | − | 2.00000i | 0.361158 | − | 0.208514i | ||||
\(93\) | −6.92820 | −0.718421 | ||||||||
\(94\) | −2.73205 | + | 0.732051i | −0.281790 | + | 0.0755053i | ||||
\(95\) | −3.50000 | + | 6.06218i | −0.359092 | + | 0.621966i | ||||
\(96\) | 6.92820 | + | 6.92820i | 0.707107 | + | 0.707107i | ||||
\(97\) | 3.50000 | + | 6.06218i | 0.355371 | + | 0.615521i | 0.987181 | − | 0.159602i | \(-0.0510211\pi\) |
−0.631810 | + | 0.775123i | \(0.717688\pi\) | |||||||
\(98\) | 9.00000 | + | 9.00000i | 0.909137 | + | 0.909137i | ||||
\(99\) | 15.0000i | 1.50756i | ||||||||
\(100\) | − | 2.00000i | − | 0.200000i | ||||||
\(101\) | −12.1244 | + | 7.00000i | −1.20642 | + | 0.696526i | −0.961975 | − | 0.273138i | \(-0.911939\pi\) |
−0.244443 | + | 0.969664i | \(0.578605\pi\) | |||||||
\(102\) | −7.09808 | + | 1.90192i | −0.702814 | + | 0.188319i | ||||
\(103\) | 7.00000 | − | 12.1244i | 0.689730 | − | 1.19465i | −0.282194 | − | 0.959357i | \(-0.591062\pi\) |
0.971925 | − | 0.235291i | \(-0.0756043\pi\) | |||||||
\(104\) | −16.3923 | + | 4.39230i | −1.60740 | + | 0.430701i | ||||
\(105\) | 6.00000 | − | 3.46410i | 0.585540 | − | 0.338062i | ||||
\(106\) | −10.9282 | − | 2.92820i | −1.06144 | − | 0.284412i | ||||
\(107\) | − | 13.0000i | − | 1.25676i | −0.777908 | − | 0.628379i | \(-0.783719\pi\) | ||
0.777908 | − | 0.628379i | \(-0.216281\pi\) | |||||||
\(108\) | 9.00000 | + | 5.19615i | 0.866025 | + | 0.500000i | ||||
\(109\) | − | 4.00000i | − | 0.383131i | −0.981480 | − | 0.191565i | \(-0.938644\pi\) | ||
0.981480 | − | 0.191565i | \(-0.0613564\pi\) | |||||||
\(110\) | −1.83013 | + | 6.83013i | −0.174496 | + | 0.651227i | ||||
\(111\) | −3.00000 | + | 1.73205i | −0.284747 | + | 0.164399i | ||||
\(112\) | −8.00000 | + | 13.8564i | −0.755929 | + | 1.30931i | ||||
\(113\) | −3.00000 | + | 5.19615i | −0.282216 | + | 0.488813i | −0.971930 | − | 0.235269i | \(-0.924403\pi\) |
0.689714 | + | 0.724082i | \(0.257736\pi\) | |||||||
\(114\) | −4.43782 | − | 16.5622i | −0.415640 | − | 1.55119i | ||||
\(115\) | 1.73205 | − | 1.00000i | 0.161515 | − | 0.0932505i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.5885 | + | 9.00000i | −1.44115 | + | 0.832050i | ||||
\(118\) | −7.00000 | + | 7.00000i | −0.644402 | + | 0.644402i | ||||
\(119\) | −6.00000 | − | 10.3923i | −0.550019 | − | 0.952661i | ||||
\(120\) | 3.46410 | + | 3.46410i | 0.316228 | + | 0.316228i | ||||
\(121\) | 7.00000 | − | 12.1244i | 0.636364 | − | 1.10221i | ||||
\(122\) | 1.46410 | + | 5.46410i | 0.132554 | + | 0.494697i | ||||
\(123\) | 8.66025 | 0.780869 | ||||||||
\(124\) | 6.92820 | − | 4.00000i | 0.622171 | − | 0.359211i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −4.39230 | + | 16.3923i | −0.391298 | + | 1.46034i | ||||
\(127\) | −18.0000 | −1.59724 | −0.798621 | − | 0.601834i | \(-0.794437\pi\) | ||||
−0.798621 | + | 0.601834i | \(0.794437\pi\) | |||||||
\(128\) | −10.9282 | − | 2.92820i | −0.965926 | − | 0.258819i | ||||
\(129\) | −7.50000 | − | 4.33013i | −0.660338 | − | 0.381246i | ||||
\(130\) | −8.19615 | + | 2.19615i | −0.718850 | + | 0.192615i | ||||
\(131\) | −10.3923 | − | 6.00000i | −0.907980 | − | 0.524222i | −0.0281993 | − | 0.999602i | \(-0.508977\pi\) |
−0.879781 | + | 0.475380i | \(0.842311\pi\) | |||||||
\(132\) | −8.66025 | − | 15.0000i | −0.753778 | − | 1.30558i | ||||
\(133\) | 24.2487 | − | 14.0000i | 2.10263 | − | 1.21395i | ||||
\(134\) | −3.00000 | + | 3.00000i | −0.259161 | + | 0.259161i | ||||
\(135\) | 4.50000 | + | 2.59808i | 0.387298 | + | 0.223607i | ||||
\(136\) | 6.00000 | − | 6.00000i | 0.514496 | − | 0.514496i | ||||
\(137\) | 8.50000 | + | 14.7224i | 0.726204 | + | 1.25782i | 0.958477 | + | 0.285171i | \(0.0920506\pi\) |
−0.232273 | + | 0.972651i | \(0.574616\pi\) | |||||||
\(138\) | −1.26795 | + | 4.73205i | −0.107935 | + | 0.402819i | ||||
\(139\) | 9.52628 | + | 5.50000i | 0.808008 | + | 0.466504i | 0.846264 | − | 0.532764i | \(-0.178847\pi\) |
−0.0382553 | + | 0.999268i | \(0.512180\pi\) | |||||||
\(140\) | −4.00000 | + | 6.92820i | −0.338062 | + | 0.585540i | ||||
\(141\) | 1.73205 | − | 3.00000i | 0.145865 | − | 0.252646i | ||||
\(142\) | 0.732051 | − | 2.73205i | 0.0614323 | − | 0.229269i | ||||
\(143\) | 30.0000 | 2.50873 | ||||||||
\(144\) | −12.0000 | −1.00000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.366025 | − | 1.36603i | 0.0302925 | − | 0.113053i | ||||
\(147\) | −15.5885 | −1.28571 | ||||||||
\(148\) | 2.00000 | − | 3.46410i | 0.164399 | − | 0.284747i | ||||
\(149\) | 5.19615 | + | 3.00000i | 0.425685 | + | 0.245770i | 0.697507 | − | 0.716578i | \(-0.254293\pi\) |
−0.271821 | + | 0.962348i | \(0.587626\pi\) | |||||||
\(150\) | 1.73205 | + | 1.73205i | 0.141421 | + | 0.141421i | ||||
\(151\) | −5.00000 | − | 8.66025i | −0.406894 | − | 0.704761i | 0.587646 | − | 0.809118i | \(-0.300055\pi\) |
−0.994540 | + | 0.104357i | \(0.966722\pi\) | |||||||
\(152\) | 14.0000 | + | 14.0000i | 1.13555 | + | 1.13555i | ||||
\(153\) | 4.50000 | − | 7.79423i | 0.363803 | − | 0.630126i | ||||
\(154\) | 20.0000 | − | 20.0000i | 1.61165 | − | 1.61165i | ||||
\(155\) | 3.46410 | − | 2.00000i | 0.278243 | − | 0.160644i | ||||
\(156\) | 10.3923 | − | 18.0000i | 0.832050 | − | 1.44115i | ||||
\(157\) | 17.3205 | + | 10.0000i | 1.38233 | + | 0.798087i | 0.992435 | − | 0.122774i | \(-0.0391789\pi\) |
0.389892 | + | 0.920860i | \(0.372512\pi\) | |||||||
\(158\) | −13.6603 | + | 3.66025i | −1.08675 | + | 0.291194i | ||||
\(159\) | 12.0000 | − | 6.92820i | 0.951662 | − | 0.549442i | ||||
\(160\) | −5.46410 | − | 1.46410i | −0.431975 | − | 0.115747i | ||||
\(161\) | −8.00000 | −0.630488 | ||||||||
\(162\) | −12.2942 | + | 3.29423i | −0.965926 | + | 0.258819i | ||||
\(163\) | − | 20.0000i | − | 1.56652i | −0.621694 | − | 0.783260i | \(-0.713555\pi\) | ||
0.621694 | − | 0.783260i | \(-0.286445\pi\) | |||||||
\(164\) | −8.66025 | + | 5.00000i | −0.676252 | + | 0.390434i | ||||
\(165\) | −4.33013 | − | 7.50000i | −0.337100 | − | 0.583874i | ||||
\(166\) | −4.39230 | − | 16.3923i | −0.340909 | − | 1.27229i | ||||
\(167\) | −3.00000 | + | 5.19615i | −0.232147 | + | 0.402090i | −0.958440 | − | 0.285295i | \(-0.907908\pi\) |
0.726293 | + | 0.687386i | \(0.241242\pi\) | |||||||
\(168\) | −5.07180 | − | 18.9282i | −0.391298 | − | 1.46034i | ||||
\(169\) | 11.5000 | + | 19.9186i | 0.884615 | + | 1.53220i | ||||
\(170\) | 3.00000 | − | 3.00000i | 0.230089 | − | 0.230089i | ||||
\(171\) | 18.1865 | + | 10.5000i | 1.39076 | + | 0.802955i | ||||
\(172\) | 10.0000 | 0.762493 | ||||||||
\(173\) | −6.92820 | + | 4.00000i | −0.526742 | + | 0.304114i | −0.739689 | − | 0.672949i | \(-0.765027\pi\) |
0.212947 | + | 0.977064i | \(0.431694\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | + | 3.46410i | −0.151186 | + | 0.261861i | ||||
\(176\) | 17.3205 | + | 10.0000i | 1.30558 | + | 0.753778i | ||||
\(177\) | − | 12.1244i | − | 0.911322i | ||||||
\(178\) | 0.732051 | − | 2.73205i | 0.0548695 | − | 0.204776i | ||||
\(179\) | − | 12.0000i | − | 0.896922i | −0.893802 | − | 0.448461i | \(-0.851972\pi\) | ||
0.893802 | − | 0.448461i | \(-0.148028\pi\) | |||||||
\(180\) | −6.00000 | −0.447214 | ||||||||
\(181\) | 2.00000i | 0.148659i | 0.997234 | + | 0.0743294i | \(0.0236816\pi\) | ||||
−0.997234 | + | 0.0743294i | \(0.976318\pi\) | |||||||
\(182\) | 32.7846 | + | 8.78461i | 2.43016 | + | 0.651159i | ||||
\(183\) | −6.00000 | − | 3.46410i | −0.443533 | − | 0.256074i | ||||
\(184\) | −1.46410 | − | 5.46410i | −0.107935 | − | 0.402819i | ||||
\(185\) | 1.00000 | − | 1.73205i | 0.0735215 | − | 0.127343i | ||||
\(186\) | −2.53590 | + | 9.46410i | −0.185941 | + | 0.693942i | ||||
\(187\) | −12.9904 | + | 7.50000i | −0.949951 | + | 0.548454i | ||||
\(188\) | 4.00000i | 0.291730i | ||||||||
\(189\) | −10.3923 | − | 18.0000i | −0.755929 | − | 1.30931i | ||||
\(190\) | 7.00000 | + | 7.00000i | 0.507833 | + | 0.507833i | ||||
\(191\) | 4.00000 | + | 6.92820i | 0.289430 | + | 0.501307i | 0.973674 | − | 0.227946i | \(-0.0732010\pi\) |
−0.684244 | + | 0.729253i | \(0.739868\pi\) | |||||||
\(192\) | 12.0000 | − | 6.92820i | 0.866025 | − | 0.500000i | ||||
\(193\) | 11.5000 | − | 19.9186i | 0.827788 | − | 1.43377i | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) |
0.899770 | − | 0.436365i | \(-0.143734\pi\) | |||||||
\(194\) | 9.56218 | − | 2.56218i | 0.686524 | − | 0.183954i | ||||
\(195\) | 5.19615 | − | 9.00000i | 0.372104 | − | 0.644503i | ||||
\(196\) | 15.5885 | − | 9.00000i | 1.11346 | − | 0.642857i | ||||
\(197\) | − | 8.00000i | − | 0.569976i | −0.958531 | − | 0.284988i | \(-0.908010\pi\) | ||
0.958531 | − | 0.284988i | \(-0.0919897\pi\) | |||||||
\(198\) | 20.4904 | + | 5.49038i | 1.45619 | + | 0.390184i | ||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | −2.73205 | − | 0.732051i | −0.193185 | − | 0.0517638i | ||||
\(201\) | − | 5.19615i | − | 0.366508i | ||||||
\(202\) | 5.12436 | + | 19.1244i | 0.360548 | + | 1.34558i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 10.3923i | 0.727607i | ||||||||
\(205\) | −4.33013 | + | 2.50000i | −0.302429 | + | 0.174608i | ||||
\(206\) | −14.0000 | − | 14.0000i | −0.975426 | − | 0.975426i | ||||
\(207\) | −3.00000 | − | 5.19615i | −0.208514 | − | 0.361158i | ||||
\(208\) | 24.0000i | 1.66410i | ||||||||
\(209\) | −17.5000 | − | 30.3109i | −1.21050 | − | 2.09665i | ||||
\(210\) | −2.53590 | − | 9.46410i | −0.174994 | − | 0.653085i | ||||
\(211\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(212\) | −8.00000 | + | 13.8564i | −0.549442 | + | 0.951662i | ||||
\(213\) | 1.73205 | + | 3.00000i | 0.118678 | + | 0.205557i | ||||
\(214\) | −17.7583 | − | 4.75833i | −1.21393 | − | 0.325273i | ||||
\(215\) | 5.00000 | 0.340997 | ||||||||
\(216\) | 10.3923 | − | 10.3923i | 0.707107 | − | 0.707107i | ||||
\(217\) | −16.0000 | −1.08615 | ||||||||
\(218\) | −5.46410 | − | 1.46410i | −0.370076 | − | 0.0991615i | ||||
\(219\) | 0.866025 | + | 1.50000i | 0.0585206 | + | 0.101361i | ||||
\(220\) | 8.66025 | + | 5.00000i | 0.583874 | + | 0.337100i | ||||
\(221\) | −15.5885 | − | 9.00000i | −1.04859 | − | 0.605406i | ||||
\(222\) | 1.26795 | + | 4.73205i | 0.0850992 | + | 0.317594i | ||||
\(223\) | 7.00000 | + | 12.1244i | 0.468755 | + | 0.811907i | 0.999362 | − | 0.0357107i | \(-0.0113695\pi\) |
−0.530607 | + | 0.847618i | \(0.678036\pi\) | |||||||
\(224\) | 16.0000 | + | 16.0000i | 1.06904 | + | 1.06904i | ||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 6.00000 | + | 6.00000i | 0.399114 | + | 0.399114i | ||||
\(227\) | −7.79423 | + | 4.50000i | −0.517321 | + | 0.298675i | −0.735838 | − | 0.677158i | \(-0.763211\pi\) |
0.218517 | + | 0.975833i | \(0.429878\pi\) | |||||||
\(228\) | −24.2487 | −1.60591 | ||||||||
\(229\) | −3.46410 | − | 2.00000i | −0.228914 | − | 0.132164i | 0.381157 | − | 0.924510i | \(-0.375526\pi\) |
−0.610071 | + | 0.792347i | \(0.708859\pi\) | |||||||
\(230\) | −0.732051 | − | 2.73205i | −0.0482700 | − | 0.180146i | ||||
\(231\) | 34.6410i | 2.27921i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −27.0000 | −1.76883 | −0.884414 | − | 0.466702i | \(-0.845442\pi\) | ||||
−0.884414 | + | 0.466702i | \(0.845442\pi\) | |||||||
\(234\) | 6.58846 | + | 24.5885i | 0.430701 | + | 1.60740i | ||||
\(235\) | 2.00000i | 0.130466i | ||||||||
\(236\) | 7.00000 | + | 12.1244i | 0.455661 | + | 0.789228i | ||||
\(237\) | 8.66025 | − | 15.0000i | 0.562544 | − | 0.974355i | ||||
\(238\) | −16.3923 | + | 4.39230i | −1.06256 | + | 0.284711i | ||||
\(239\) | 7.00000 | − | 12.1244i | 0.452792 | − | 0.784259i | −0.545766 | − | 0.837938i | \(-0.683761\pi\) |
0.998558 | + | 0.0536783i | \(0.0170946\pi\) | |||||||
\(240\) | 6.00000 | − | 3.46410i | 0.387298 | − | 0.223607i | ||||
\(241\) | 7.50000 | + | 12.9904i | 0.483117 | + | 0.836784i | 0.999812 | − | 0.0193858i | \(-0.00617107\pi\) |
−0.516695 | + | 0.856170i | \(0.672838\pi\) | |||||||
\(242\) | −14.0000 | − | 14.0000i | −0.899954 | − | 0.899954i | ||||
\(243\) | 7.79423 | − | 13.5000i | 0.500000 | − | 0.866025i | ||||
\(244\) | 8.00000 | 0.512148 | ||||||||
\(245\) | 7.79423 | − | 4.50000i | 0.497955 | − | 0.287494i | ||||
\(246\) | 3.16987 | − | 11.8301i | 0.202104 | − | 0.754261i | ||||
\(247\) | 21.0000 | − | 36.3731i | 1.33620 | − | 2.31436i | ||||
\(248\) | −2.92820 | − | 10.9282i | −0.185941 | − | 0.693942i | ||||
\(249\) | 18.0000 | + | 10.3923i | 1.14070 | + | 0.658586i | ||||
\(250\) | −1.36603 | − | 0.366025i | −0.0863950 | − | 0.0231495i | ||||
\(251\) | 9.00000i | 0.568075i | 0.958813 | + | 0.284037i | \(0.0916740\pi\) | ||||
−0.958813 | + | 0.284037i | \(0.908326\pi\) | |||||||
\(252\) | 20.7846 | + | 12.0000i | 1.30931 | + | 0.755929i | ||||
\(253\) | 10.0000i | 0.628695i | ||||||||
\(254\) | −6.58846 | + | 24.5885i | −0.413397 | + | 1.54282i | ||||
\(255\) | 5.19615i | 0.325396i | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −3.50000 | + | 6.06218i | −0.218324 | + | 0.378148i | −0.954296 | − | 0.298864i | \(-0.903392\pi\) |
0.735972 | + | 0.677012i | \(0.236726\pi\) | |||||||
\(258\) | −8.66025 | + | 8.66025i | −0.539164 | + | 0.539164i | ||||
\(259\) | −6.92820 | + | 4.00000i | −0.430498 | + | 0.248548i | ||||
\(260\) | 12.0000i | 0.744208i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.0000 | + | 12.0000i | −0.741362 | + | 0.741362i | ||||
\(263\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | −23.6603 | + | 6.33975i | −1.45619 | + | 0.390184i | ||||
\(265\) | −4.00000 | + | 6.92820i | −0.245718 | + | 0.425596i | ||||
\(266\) | −10.2487 | − | 38.2487i | −0.628389 | − | 2.34518i | ||||
\(267\) | 1.73205 | + | 3.00000i | 0.106000 | + | 0.183597i | ||||
\(268\) | 3.00000 | + | 5.19615i | 0.183254 | + | 0.317406i | ||||
\(269\) | 20.0000i | 1.21942i | 0.792624 | + | 0.609711i | \(0.208714\pi\) | ||||
−0.792624 | + | 0.609711i | \(0.791286\pi\) | |||||||
\(270\) | 5.19615 | − | 5.19615i | 0.316228 | − | 0.316228i | ||||
\(271\) | 28.0000 | 1.70088 | 0.850439 | − | 0.526073i | \(-0.176336\pi\) | ||||
0.850439 | + | 0.526073i | \(0.176336\pi\) | |||||||
\(272\) | −6.00000 | − | 10.3923i | −0.363803 | − | 0.630126i | ||||
\(273\) | −36.0000 | + | 20.7846i | −2.17882 | + | 1.25794i | ||||
\(274\) | 23.2224 | − | 6.22243i | 1.40292 | − | 0.375911i | ||||
\(275\) | 4.33013 | + | 2.50000i | 0.261116 | + | 0.150756i | ||||
\(276\) | 6.00000 | + | 3.46410i | 0.361158 | + | 0.208514i | ||||
\(277\) | −1.73205 | + | 1.00000i | −0.104069 | + | 0.0600842i | −0.551131 | − | 0.834419i | \(-0.685804\pi\) |
0.447062 | + | 0.894503i | \(0.352470\pi\) | |||||||
\(278\) | 11.0000 | − | 11.0000i | 0.659736 | − | 0.659736i | ||||
\(279\) | −6.00000 | − | 10.3923i | −0.359211 | − | 0.622171i | ||||
\(280\) | 8.00000 | + | 8.00000i | 0.478091 | + | 0.478091i | ||||
\(281\) | 11.0000 | + | 19.0526i | 0.656205 | + | 1.13658i | 0.981590 | + | 0.190999i | \(0.0611727\pi\) |
−0.325385 | + | 0.945582i | \(0.605494\pi\) | |||||||
\(282\) | −3.46410 | − | 3.46410i | −0.206284 | − | 0.206284i | ||||
\(283\) | −3.46410 | − | 2.00000i | −0.205919 | − | 0.118888i | 0.393494 | − | 0.919327i | \(-0.371266\pi\) |
−0.599414 | + | 0.800439i | \(0.704600\pi\) | |||||||
\(284\) | −3.46410 | − | 2.00000i | −0.205557 | − | 0.118678i | ||||
\(285\) | −12.1244 | −0.718185 | ||||||||
\(286\) | 10.9808 | − | 40.9808i | 0.649306 | − | 2.42324i | ||||
\(287\) | 20.0000 | 1.18056 | ||||||||
\(288\) | −4.39230 | + | 16.3923i | −0.258819 | + | 0.965926i | ||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.06218 | + | 10.5000i | −0.355371 | + | 0.615521i | ||||
\(292\) | −1.73205 | − | 1.00000i | −0.101361 | − | 0.0585206i | ||||
\(293\) | 3.46410 | + | 2.00000i | 0.202375 | + | 0.116841i | 0.597763 | − | 0.801673i | \(-0.296056\pi\) |
−0.395388 | + | 0.918514i | \(0.629390\pi\) | |||||||
\(294\) | −5.70577 | + | 21.2942i | −0.332767 | + | 1.24190i | ||||
\(295\) | 3.50000 | + | 6.06218i | 0.203778 | + | 0.352954i | ||||
\(296\) | −4.00000 | − | 4.00000i | −0.232495 | − | 0.232495i | ||||
\(297\) | −22.5000 | + | 12.9904i | −1.30558 | + | 0.753778i | ||||
\(298\) | 6.00000 | − | 6.00000i | 0.347571 | − | 0.347571i | ||||
\(299\) | −10.3923 | + | 6.00000i | −0.601003 | + | 0.346989i | ||||
\(300\) | 3.00000 | − | 1.73205i | 0.173205 | − | 0.100000i | ||||
\(301\) | −17.3205 | − | 10.0000i | −0.998337 | − | 0.576390i | ||||
\(302\) | −13.6603 | + | 3.66025i | −0.786059 | + | 0.210624i | ||||
\(303\) | −21.0000 | − | 12.1244i | −1.20642 | − | 0.696526i | ||||
\(304\) | 24.2487 | − | 14.0000i | 1.39076 | − | 0.802955i | ||||
\(305\) | 4.00000 | 0.229039 | ||||||||
\(306\) | −9.00000 | − | 9.00000i | −0.514496 | − | 0.514496i | ||||
\(307\) | 23.0000i | 1.31268i | 0.754466 | + | 0.656340i | \(0.227896\pi\) | ||||
−0.754466 | + | 0.656340i | \(0.772104\pi\) | |||||||
\(308\) | −20.0000 | − | 34.6410i | −1.13961 | − | 1.97386i | ||||
\(309\) | 24.2487 | 1.37946 | ||||||||
\(310\) | −1.46410 | − | 5.46410i | −0.0831554 | − | 0.310340i | ||||
\(311\) | −10.0000 | + | 17.3205i | −0.567048 | + | 0.982156i | 0.429808 | + | 0.902920i | \(0.358581\pi\) |
−0.996856 | + | 0.0792356i | \(0.974752\pi\) | |||||||
\(312\) | −20.7846 | − | 20.7846i | −1.17670 | − | 1.17670i | ||||
\(313\) | 4.50000 | + | 7.79423i | 0.254355 | + | 0.440556i | 0.964720 | − | 0.263278i | \(-0.0848035\pi\) |
−0.710365 | + | 0.703833i | \(0.751470\pi\) | |||||||
\(314\) | 20.0000 | − | 20.0000i | 1.12867 | − | 1.12867i | ||||
\(315\) | 10.3923 | + | 6.00000i | 0.585540 | + | 0.338062i | ||||
\(316\) | 20.0000i | 1.12509i | ||||||||
\(317\) | −15.5885 | + | 9.00000i | −0.875535 | + | 0.505490i | −0.869184 | − | 0.494489i | \(-0.835355\pi\) |
−0.00635137 | + | 0.999980i | \(0.502022\pi\) | |||||||
\(318\) | −5.07180 | − | 18.9282i | −0.284412 | − | 1.06144i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −4.00000 | + | 6.92820i | −0.223607 | + | 0.387298i | ||||
\(321\) | 19.5000 | − | 11.2583i | 1.08838 | − | 0.628379i | ||||
\(322\) | −2.92820 | + | 10.9282i | −0.163182 | + | 0.609005i | ||||
\(323\) | 21.0000i | 1.16847i | ||||||||
\(324\) | 18.0000i | 1.00000i | ||||||||
\(325\) | 6.00000i | 0.332820i | ||||||||
\(326\) | −27.3205 | − | 7.32051i | −1.51314 | − | 0.405445i | ||||
\(327\) | 6.00000 | − | 3.46410i | 0.331801 | − | 0.191565i | ||||
\(328\) | 3.66025 | + | 13.6603i | 0.202104 | + | 0.754261i | ||||
\(329\) | 4.00000 | − | 6.92820i | 0.220527 | − | 0.381964i | ||||
\(330\) | −11.8301 | + | 3.16987i | −0.651227 | + | 0.174496i | ||||
\(331\) | 17.3205 | − | 10.0000i | 0.952021 | − | 0.549650i | 0.0583130 | − | 0.998298i | \(-0.481428\pi\) |
0.893708 | + | 0.448649i | \(0.148095\pi\) | |||||||
\(332\) | −24.0000 | −1.31717 | ||||||||
\(333\) | −5.19615 | − | 3.00000i | −0.284747 | − | 0.164399i | ||||
\(334\) | 6.00000 | + | 6.00000i | 0.328305 | + | 0.328305i | ||||
\(335\) | 1.50000 | + | 2.59808i | 0.0819538 | + | 0.141948i | ||||
\(336\) | −27.7128 | −1.51186 | ||||||||
\(337\) | −7.50000 | + | 12.9904i | −0.408551 | + | 0.707631i | −0.994728 | − | 0.102552i | \(-0.967299\pi\) |
0.586177 | + | 0.810183i | \(0.300632\pi\) | |||||||
\(338\) | 31.4186 | − | 8.41858i | 1.70895 | − | 0.457911i | ||||
\(339\) | −10.3923 | −0.564433 | ||||||||
\(340\) | −3.00000 | − | 5.19615i | −0.162698 | − | 0.281801i | ||||
\(341\) | 20.0000i | 1.08306i | ||||||||
\(342\) | 21.0000 | − | 21.0000i | 1.13555 | − | 1.13555i | ||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 3.66025 | − | 13.6603i | 0.197348 | − | 0.736512i | ||||
\(345\) | 3.00000 | + | 1.73205i | 0.161515 | + | 0.0932505i | ||||
\(346\) | 2.92820 | + | 10.9282i | 0.157421 | + | 0.587504i | ||||
\(347\) | 16.4545 | + | 9.50000i | 0.883323 | + | 0.509987i | 0.871753 | − | 0.489946i | \(-0.162984\pi\) |
0.0115703 | + | 0.999933i | \(0.496317\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.8564 | − | 8.00000i | 0.741716 | − | 0.428230i | −0.0809766 | − | 0.996716i | \(-0.525804\pi\) |
0.822693 | + | 0.568486i | \(0.192471\pi\) | |||||||
\(350\) | 4.00000 | + | 4.00000i | 0.213809 | + | 0.213809i | ||||
\(351\) | −27.0000 | − | 15.5885i | −1.44115 | − | 0.832050i | ||||
\(352\) | 20.0000 | − | 20.0000i | 1.06600 | − | 1.06600i | ||||
\(353\) | 4.50000 | + | 7.79423i | 0.239511 | + | 0.414845i | 0.960574 | − | 0.278024i | \(-0.0896796\pi\) |
−0.721063 | + | 0.692869i | \(0.756346\pi\) | |||||||
\(354\) | −16.5622 | − | 4.43782i | −0.880270 | − | 0.235868i | ||||
\(355\) | −1.73205 | − | 1.00000i | −0.0919277 | − | 0.0530745i | ||||
\(356\) | −3.46410 | − | 2.00000i | −0.183597 | − | 0.106000i | ||||
\(357\) | 10.3923 | − | 18.0000i | 0.550019 | − | 0.952661i | ||||
\(358\) | −16.3923 | − | 4.39230i | −0.866360 | − | 0.232141i | ||||
\(359\) | −12.0000 | −0.633336 | −0.316668 | − | 0.948536i | \(-0.602564\pi\) | ||||
−0.316668 | + | 0.948536i | \(0.602564\pi\) | |||||||
\(360\) | −2.19615 | + | 8.19615i | −0.115747 | + | 0.431975i | ||||
\(361\) | −30.0000 | −1.57895 | ||||||||
\(362\) | 2.73205 | + | 0.732051i | 0.143593 | + | 0.0384757i | ||||
\(363\) | 24.2487 | 1.27273 | ||||||||
\(364\) | 24.0000 | − | 41.5692i | 1.25794 | − | 2.17882i | ||||
\(365\) | −0.866025 | − | 0.500000i | −0.0453298 | − | 0.0261712i | ||||
\(366\) | −6.92820 | + | 6.92820i | −0.362143 | + | 0.362143i | ||||
\(367\) | −9.00000 | − | 15.5885i | −0.469796 | − | 0.813711i | 0.529607 | − | 0.848243i | \(-0.322339\pi\) |
−0.999404 | + | 0.0345320i | \(0.989006\pi\) | |||||||
\(368\) | −8.00000 | −0.417029 | ||||||||
\(369\) | 7.50000 | + | 12.9904i | 0.390434 | + | 0.676252i | ||||
\(370\) | −2.00000 | − | 2.00000i | −0.103975 | − | 0.103975i | ||||
\(371\) | 27.7128 | − | 16.0000i | 1.43878 | − | 0.830679i | ||||
\(372\) | 12.0000 | + | 6.92820i | 0.622171 | + | 0.359211i | ||||
\(373\) | −19.0526 | − | 11.0000i | −0.986504 | − | 0.569558i | −0.0822766 | − | 0.996610i | \(-0.526219\pi\) |
−0.904227 | + | 0.427051i | \(0.859552\pi\) | |||||||
\(374\) | 5.49038 | + | 20.4904i | 0.283901 | + | 1.05953i | ||||
\(375\) | 1.50000 | − | 0.866025i | 0.0774597 | − | 0.0447214i | ||||
\(376\) | 5.46410 | + | 1.46410i | 0.281790 | + | 0.0755053i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −28.3923 | + | 7.60770i | −1.46034 | + | 0.391298i | ||||
\(379\) | 3.00000i | 0.154100i | 0.997027 | + | 0.0770498i | \(0.0245501\pi\) | ||||
−0.997027 | + | 0.0770498i | \(0.975450\pi\) | |||||||
\(380\) | 12.1244 | − | 7.00000i | 0.621966 | − | 0.359092i | ||||
\(381\) | −15.5885 | − | 27.0000i | −0.798621 | − | 1.38325i | ||||
\(382\) | 10.9282 | − | 2.92820i | 0.559136 | − | 0.149820i | ||||
\(383\) | −9.00000 | + | 15.5885i | −0.459879 | + | 0.796533i | −0.998954 | − | 0.0457244i | \(-0.985440\pi\) |
0.539076 | + | 0.842257i | \(0.318774\pi\) | |||||||
\(384\) | −5.07180 | − | 18.9282i | −0.258819 | − | 0.965926i | ||||
\(385\) | −10.0000 | − | 17.3205i | −0.509647 | − | 0.882735i | ||||
\(386\) | −23.0000 | − | 23.0000i | −1.17067 | − | 1.17067i | ||||
\(387\) | − | 15.0000i | − | 0.762493i | ||||||
\(388\) | − | 14.0000i | − | 0.710742i | ||||||
\(389\) | −13.8564 | + | 8.00000i | −0.702548 | + | 0.405616i | −0.808296 | − | 0.588777i | \(-0.799610\pi\) |
0.105748 | + | 0.994393i | \(0.466276\pi\) | |||||||
\(390\) | −10.3923 | − | 10.3923i | −0.526235 | − | 0.526235i | ||||
\(391\) | 3.00000 | − | 5.19615i | 0.151717 | − | 0.262781i | ||||
\(392\) | −6.58846 | − | 24.5885i | −0.332767 | − | 1.24190i | ||||
\(393\) | − | 20.7846i | − | 1.04844i | ||||||
\(394\) | −10.9282 | − | 2.92820i | −0.550555 | − | 0.147521i | ||||
\(395\) | 10.0000i | 0.503155i | ||||||||
\(396\) | 15.0000 | − | 25.9808i | 0.753778 | − | 1.30558i | ||||
\(397\) | − | 26.0000i | − | 1.30490i | −0.757831 | − | 0.652451i | \(-0.773741\pi\) | ||
0.757831 | − | 0.652451i | \(-0.226259\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 42.0000 | + | 24.2487i | 2.10263 | + | 1.21395i | ||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | 7.50000 | − | 12.9904i | 0.374532 | − | 0.648709i | −0.615725 | − | 0.787961i | \(-0.711137\pi\) |
0.990257 | + | 0.139253i | \(0.0444700\pi\) | |||||||
\(402\) | −7.09808 | − | 1.90192i | −0.354020 | − | 0.0948593i | ||||
\(403\) | −20.7846 | + | 12.0000i | −1.03536 | + | 0.597763i | ||||
\(404\) | 28.0000 | 1.39305 | ||||||||
\(405\) | 9.00000i | 0.447214i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.00000 | + | 8.66025i | 0.247841 | + | 0.429273i | ||||
\(408\) | 14.1962 | + | 3.80385i | 0.702814 | + | 0.188319i | ||||
\(409\) | −7.50000 | + | 12.9904i | −0.370851 | + | 0.642333i | −0.989697 | − | 0.143180i | \(-0.954267\pi\) |
0.618846 | + | 0.785513i | \(0.287601\pi\) | |||||||
\(410\) | 1.83013 | + | 6.83013i | 0.0903835 | + | 0.337316i | ||||
\(411\) | −14.7224 | + | 25.5000i | −0.726204 | + | 1.25782i | ||||
\(412\) | −24.2487 | + | 14.0000i | −1.19465 | + | 0.689730i | ||||
\(413\) | − | 28.0000i | − | 1.37779i | ||||||
\(414\) | −8.19615 | + | 2.19615i | −0.402819 | + | 0.107935i | ||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | 32.7846 | + | 8.78461i | 1.60740 | + | 0.430701i | ||||
\(417\) | 19.0526i | 0.933008i | ||||||||
\(418\) | −47.8109 | + | 12.8109i | −2.33851 | + | 0.626601i | ||||
\(419\) | −3.46410 | − | 2.00000i | −0.169232 | − | 0.0977064i | 0.412991 | − | 0.910735i | \(-0.364484\pi\) |
−0.582224 | + | 0.813029i | \(0.697817\pi\) | |||||||
\(420\) | −13.8564 | −0.676123 | ||||||||
\(421\) | −1.73205 | + | 1.00000i | −0.0844150 | + | 0.0487370i | −0.541613 | − | 0.840628i | \(-0.682186\pi\) |
0.457198 | + | 0.889365i | \(0.348853\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.00000 | 0.291730 | ||||||||
\(424\) | 16.0000 | + | 16.0000i | 0.777029 | + | 0.777029i | ||||
\(425\) | −1.50000 | − | 2.59808i | −0.0727607 | − | 0.126025i | ||||
\(426\) | 4.73205 | − | 1.26795i | 0.229269 | − | 0.0614323i | ||||
\(427\) | −13.8564 | − | 8.00000i | −0.670559 | − | 0.387147i | ||||
\(428\) | −13.0000 | + | 22.5167i | −0.628379 | + | 1.08838i | ||||
\(429\) | 25.9808 | + | 45.0000i | 1.25436 | + | 2.17262i | ||||
\(430\) | 1.83013 | − | 6.83013i | 0.0882566 | − | 0.329378i | ||||
\(431\) | −12.0000 | −0.578020 | −0.289010 | − | 0.957326i | \(-0.593326\pi\) | ||||
−0.289010 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(432\) | −10.3923 | − | 18.0000i | −0.500000 | − | 0.866025i | ||||
\(433\) | 29.0000 | 1.39365 | 0.696826 | − | 0.717241i | \(-0.254595\pi\) | ||||
0.696826 | + | 0.717241i | \(0.254595\pi\) | |||||||
\(434\) | −5.85641 | + | 21.8564i | −0.281117 | + | 1.04914i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.00000 | + | 6.92820i | −0.191565 | + | 0.331801i | ||||
\(437\) | 12.1244 | + | 7.00000i | 0.579987 | + | 0.334855i | ||||
\(438\) | 2.36603 | − | 0.633975i | 0.113053 | − | 0.0302925i | ||||
\(439\) | 20.0000 | + | 34.6410i | 0.954548 | + | 1.65333i | 0.735399 | + | 0.677634i | \(0.236995\pi\) |
0.219149 | + | 0.975691i | \(0.429672\pi\) | |||||||
\(440\) | 10.0000 | − | 10.0000i | 0.476731 | − | 0.476731i | ||||
\(441\) | −13.5000 | − | 23.3827i | −0.642857 | − | 1.11346i | ||||
\(442\) | −18.0000 | + | 18.0000i | −0.856173 | + | 0.856173i | ||||
\(443\) | −21.6506 | + | 12.5000i | −1.02865 | + | 0.593893i | −0.916598 | − | 0.399809i | \(-0.869076\pi\) |
−0.112054 | + | 0.993702i | \(0.535743\pi\) | |||||||
\(444\) | 6.92820 | 0.328798 | ||||||||
\(445\) | −1.73205 | − | 1.00000i | −0.0821071 | − | 0.0474045i | ||||
\(446\) | 19.1244 | − | 5.12436i | 0.905564 | − | 0.242645i | ||||
\(447\) | 10.3923i | 0.491539i | ||||||||
\(448\) | 27.7128 | − | 16.0000i | 1.30931 | − | 0.755929i | ||||
\(449\) | −27.0000 | −1.27421 | −0.637104 | − | 0.770778i | \(-0.719868\pi\) | ||||
−0.637104 | + | 0.770778i | \(0.719868\pi\) | |||||||
\(450\) | −1.09808 | + | 4.09808i | −0.0517638 | + | 0.193185i | ||||
\(451\) | − | 25.0000i | − | 1.17720i | ||||||
\(452\) | 10.3923 | − | 6.00000i | 0.488813 | − | 0.282216i | ||||
\(453\) | 8.66025 | − | 15.0000i | 0.406894 | − | 0.704761i | ||||
\(454\) | 3.29423 | + | 12.2942i | 0.154606 | + | 0.576997i | ||||
\(455\) | 12.0000 | − | 20.7846i | 0.562569 | − | 0.974398i | ||||
\(456\) | −8.87564 | + | 33.1244i | −0.415640 | + | 1.55119i | ||||
\(457\) | −1.50000 | − | 2.59808i | −0.0701670 | − | 0.121533i | 0.828807 | − | 0.559534i | \(-0.189020\pi\) |
−0.898974 | + | 0.438001i | \(0.855687\pi\) | |||||||
\(458\) | −4.00000 | + | 4.00000i | −0.186908 | + | 0.186908i | ||||
\(459\) | 15.5885 | 0.727607 | ||||||||
\(460\) | −4.00000 | −0.186501 | ||||||||
\(461\) | −12.1244 | + | 7.00000i | −0.564688 | + | 0.326023i | −0.755025 | − | 0.655696i | \(-0.772375\pi\) |
0.190337 | + | 0.981719i | \(0.439042\pi\) | |||||||
\(462\) | 47.3205 | + | 12.6795i | 2.20155 | + | 0.589903i | ||||
\(463\) | −13.0000 | + | 22.5167i | −0.604161 | + | 1.04644i | 0.388022 | + | 0.921650i | \(0.373158\pi\) |
−0.992183 | + | 0.124788i | \(0.960175\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.00000 | + | 3.46410i | 0.278243 | + | 0.160644i | ||||
\(466\) | −9.88269 | + | 36.8827i | −0.457807 | + | 1.70856i | ||||
\(467\) | − | 13.0000i | − | 0.601568i | −0.953692 | − | 0.300784i | \(-0.902752\pi\) | ||
0.953692 | − | 0.300784i | \(-0.0972484\pi\) | |||||||
\(468\) | 36.0000 | 1.66410 | ||||||||
\(469\) | − | 12.0000i | − | 0.554109i | ||||||
\(470\) | 2.73205 | + | 0.732051i | 0.126020 | + | 0.0337670i | ||||
\(471\) | 34.6410i | 1.59617i | ||||||||
\(472\) | 19.1244 | − | 5.12436i | 0.880270 | − | 0.235868i | ||||
\(473\) | −12.5000 | + | 21.6506i | −0.574751 | + | 0.995497i | ||||
\(474\) | −17.3205 | − | 17.3205i | −0.795557 | − | 0.795557i | ||||
\(475\) | 6.06218 | − | 3.50000i | 0.278152 | − | 0.160591i | ||||
\(476\) | 24.0000i | 1.10004i | ||||||||
\(477\) | 20.7846 | + | 12.0000i | 0.951662 | + | 0.549442i | ||||
\(478\) | −14.0000 | − | 14.0000i | −0.640345 | − | 0.640345i | ||||
\(479\) | −8.00000 | − | 13.8564i | −0.365529 | − | 0.633115i | 0.623332 | − | 0.781958i | \(-0.285779\pi\) |
−0.988861 | + | 0.148842i | \(0.952445\pi\) | |||||||
\(480\) | −2.53590 | − | 9.46410i | −0.115747 | − | 0.431975i | ||||
\(481\) | −6.00000 | + | 10.3923i | −0.273576 | + | 0.473848i | ||||
\(482\) | 20.4904 | − | 5.49038i | 0.933311 | − | 0.250080i | ||||
\(483\) | −6.92820 | − | 12.0000i | −0.315244 | − | 0.546019i | ||||
\(484\) | −24.2487 | + | 14.0000i | −1.10221 | + | 0.636364i | ||||
\(485\) | − | 7.00000i | − | 0.317854i | ||||||
\(486\) | −15.5885 | − | 15.5885i | −0.707107 | − | 0.707107i | ||||
\(487\) | −12.0000 | −0.543772 | −0.271886 | − | 0.962329i | \(-0.587647\pi\) | ||||
−0.271886 | + | 0.962329i | \(0.587647\pi\) | |||||||
\(488\) | 2.92820 | − | 10.9282i | 0.132554 | − | 0.494697i | ||||
\(489\) | 30.0000 | − | 17.3205i | 1.35665 | − | 0.783260i | ||||
\(490\) | −3.29423 | − | 12.2942i | −0.148818 | − | 0.555397i | ||||
\(491\) | 9.52628 | + | 5.50000i | 0.429915 | + | 0.248212i | 0.699310 | − | 0.714818i | \(-0.253491\pi\) |
−0.269395 | + | 0.963030i | \(0.586824\pi\) | |||||||
\(492\) | −15.0000 | − | 8.66025i | −0.676252 | − | 0.390434i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −42.0000 | − | 42.0000i | −1.88967 | − | 1.88967i | ||||
\(495\) | 7.50000 | − | 12.9904i | 0.337100 | − | 0.583874i | ||||
\(496\) | −16.0000 | −0.718421 | ||||||||
\(497\) | 4.00000 | + | 6.92820i | 0.179425 | + | 0.310772i | ||||
\(498\) | 20.7846 | − | 20.7846i | 0.931381 | − | 0.931381i | ||||
\(499\) | −35.5070 | − | 20.5000i | −1.58951 | − | 0.917706i | −0.993387 | − | 0.114816i | \(-0.963372\pi\) |
−0.596127 | − | 0.802890i | \(-0.703294\pi\) | |||||||
\(500\) | −1.00000 | + | 1.73205i | −0.0447214 | + | 0.0774597i | ||||
\(501\) | −10.3923 | −0.464294 | ||||||||
\(502\) | 12.2942 | + | 3.29423i | 0.548718 | + | 0.147029i | ||||
\(503\) | 12.0000 | 0.535054 | 0.267527 | − | 0.963550i | \(-0.413794\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413794\pi\) | |||||||
\(504\) | 24.0000 | − | 24.0000i | 1.06904 | − | 1.06904i | ||||
\(505\) | 14.0000 | 0.622992 | ||||||||
\(506\) | 13.6603 | + | 3.66025i | 0.607272 | + | 0.162718i | ||||
\(507\) | −19.9186 | + | 34.5000i | −0.884615 | + | 1.53220i | ||||
\(508\) | 31.1769 | + | 18.0000i | 1.38325 | + | 0.798621i | ||||
\(509\) | −10.3923 | − | 6.00000i | −0.460631 | − | 0.265945i | 0.251679 | − | 0.967811i | \(-0.419017\pi\) |
−0.712309 | + | 0.701866i | \(0.752351\pi\) | |||||||
\(510\) | 7.09808 | + | 1.90192i | 0.314308 | + | 0.0842186i | ||||
\(511\) | 2.00000 | + | 3.46410i | 0.0884748 | + | 0.153243i | ||||
\(512\) | 16.0000 | + | 16.0000i | 0.707107 | + | 0.707107i | ||||
\(513\) | 36.3731i | 1.60591i | ||||||||
\(514\) | 7.00000 | + | 7.00000i | 0.308757 | + | 0.308757i | ||||
\(515\) | −12.1244 | + | 7.00000i | −0.534263 | + | 0.308457i | ||||
\(516\) | 8.66025 | + | 15.0000i | 0.381246 | + | 0.660338i | ||||
\(517\) | −8.66025 | − | 5.00000i | −0.380878 | − | 0.219900i | ||||
\(518\) | 2.92820 | + | 10.9282i | 0.128658 | + | 0.480158i | ||||
\(519\) | −12.0000 | − | 6.92820i | −0.526742 | − | 0.304114i | ||||
\(520\) | 16.3923 | + | 4.39230i | 0.718850 | + | 0.192615i | ||||
\(521\) | 15.0000 | 0.657162 | 0.328581 | − | 0.944476i | \(-0.393430\pi\) | ||||
0.328581 | + | 0.944476i | \(0.393430\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 4.00000i | − | 0.174908i | −0.996169 | − | 0.0874539i | \(-0.972127\pi\) | ||
0.996169 | − | 0.0874539i | \(-0.0278730\pi\) | |||||||
\(524\) | 12.0000 | + | 20.7846i | 0.524222 | + | 0.907980i | ||||
\(525\) | −6.92820 | −0.302372 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.00000 | − | 10.3923i | 0.261364 | − | 0.452696i | ||||
\(528\) | 34.6410i | 1.50756i | ||||||||
\(529\) | 9.50000 | + | 16.4545i | 0.413043 | + | 0.715412i | ||||
\(530\) | 8.00000 | + | 8.00000i | 0.347498 | + | 0.347498i | ||||
\(531\) | 18.1865 | − | 10.5000i | 0.789228 | − | 0.455661i | ||||
\(532\) | −56.0000 | −2.42791 | ||||||||
\(533\) | 25.9808 | − | 15.0000i | 1.12535 | − | 0.649722i | ||||
\(534\) | 4.73205 | − | 1.26795i | 0.204776 | − | 0.0548695i | ||||
\(535\) | −6.50000 | + | 11.2583i | −0.281020 | + | 0.486740i | ||||
\(536\) | 8.19615 | − | 2.19615i | 0.354020 | − | 0.0948593i | ||||
\(537\) | 18.0000 | − | 10.3923i | 0.776757 | − | 0.448461i | ||||
\(538\) | 27.3205 | + | 7.32051i | 1.17787 | + | 0.315610i | ||||
\(539\) | 45.0000i | 1.93829i | ||||||||
\(540\) | −5.19615 | − | 9.00000i | −0.223607 | − | 0.387298i | ||||
\(541\) | − | 22.0000i | − | 0.945854i | −0.881102 | − | 0.472927i | \(-0.843197\pi\) | ||
0.881102 | − | 0.472927i | \(-0.156803\pi\) | |||||||
\(542\) | 10.2487 | − | 38.2487i | 0.440220 | − | 1.64292i | ||||
\(543\) | −3.00000 | + | 1.73205i | −0.128742 | + | 0.0743294i | ||||
\(544\) | −16.3923 | + | 4.39230i | −0.702814 | + | 0.188319i | ||||
\(545\) | −2.00000 | + | 3.46410i | −0.0856706 | + | 0.148386i | ||||
\(546\) | 15.2154 | + | 56.7846i | 0.651159 | + | 2.43016i | ||||
\(547\) | 11.2583 | − | 6.50000i | 0.481371 | − | 0.277920i | −0.239616 | − | 0.970868i | \(-0.577022\pi\) |
0.720988 | + | 0.692948i | \(0.243688\pi\) | |||||||
\(548\) | − | 34.0000i | − | 1.45241i | ||||||
\(549\) | − | 12.0000i | − | 0.512148i | ||||||
\(550\) | 5.00000 | − | 5.00000i | 0.213201 | − | 0.213201i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 6.92820 | − | 6.92820i | 0.294884 | − | 0.294884i | ||||
\(553\) | 20.0000 | − | 34.6410i | 0.850487 | − | 1.47309i | ||||
\(554\) | 0.732051 | + | 2.73205i | 0.0311019 | + | 0.116074i | ||||
\(555\) | 3.46410 | 0.147043 | ||||||||
\(556\) | −11.0000 | − | 19.0526i | −0.466504 | − | 0.808008i | ||||
\(557\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(558\) | −16.3923 | + | 4.39230i | −0.693942 | + | 0.185941i | ||||
\(559\) | −30.0000 | −1.26886 | ||||||||
\(560\) | 13.8564 | − | 8.00000i | 0.585540 | − | 0.338062i | ||||
\(561\) | −22.5000 | − | 12.9904i | −0.949951 | − | 0.548454i | ||||
\(562\) | 30.0526 | − | 8.05256i | 1.26769 | − | 0.339677i | ||||
\(563\) | −33.7750 | − | 19.5000i | −1.42345 | − | 0.821827i | −0.426855 | − | 0.904320i | \(-0.640378\pi\) |
−0.996592 | + | 0.0824933i | \(0.973712\pi\) | |||||||
\(564\) | −6.00000 | + | 3.46410i | −0.252646 | + | 0.145865i | ||||
\(565\) | 5.19615 | − | 3.00000i | 0.218604 | − | 0.126211i | ||||
\(566\) | −4.00000 | + | 4.00000i | −0.168133 | + | 0.168133i | ||||
\(567\) | 18.0000 | − | 31.1769i | 0.755929 | − | 1.30931i | ||||
\(568\) | −4.00000 | + | 4.00000i | −0.167836 | + | 0.167836i | ||||
\(569\) | 12.5000 | + | 21.6506i | 0.524027 | + | 0.907642i | 0.999609 | + | 0.0279702i | \(0.00890434\pi\) |
−0.475581 | + | 0.879672i | \(0.657762\pi\) | |||||||
\(570\) | −4.43782 | + | 16.5622i | −0.185880 | + | 0.693713i | ||||
\(571\) | 11.2583 | + | 6.50000i | 0.471146 | + | 0.272017i | 0.716720 | − | 0.697362i | \(-0.245643\pi\) |
−0.245573 | + | 0.969378i | \(0.578976\pi\) | |||||||
\(572\) | −51.9615 | − | 30.0000i | −2.17262 | − | 1.25436i | ||||
\(573\) | −6.92820 | + | 12.0000i | −0.289430 | + | 0.501307i | ||||
\(574\) | 7.32051 | − | 27.3205i | 0.305552 | − | 1.14034i | ||||
\(575\) | −2.00000 | −0.0834058 | ||||||||
\(576\) | 20.7846 | + | 12.0000i | 0.866025 | + | 0.500000i | ||||
\(577\) | 7.00000 | 0.291414 | 0.145707 | − | 0.989328i | \(-0.453454\pi\) | ||||
0.145707 | + | 0.989328i | \(0.453454\pi\) | |||||||
\(578\) | −2.92820 | + | 10.9282i | −0.121797 | + | 0.454553i | ||||
\(579\) | 39.8372 | 1.65558 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 41.5692 | + | 24.0000i | 1.72458 | + | 0.995688i | ||||
\(582\) | 12.1244 | + | 12.1244i | 0.502571 | + | 0.502571i | ||||
\(583\) | −20.0000 | − | 34.6410i | −0.828315 | − | 1.43468i | ||||
\(584\) | −2.00000 | + | 2.00000i | −0.0827606 | + | 0.0827606i | ||||
\(585\) | 18.0000 | 0.744208 | ||||||||
\(586\) | 4.00000 | − | 4.00000i | 0.165238 | − | 0.165238i | ||||
\(587\) | 23.3827 | − | 13.5000i | 0.965107 | − | 0.557205i | 0.0673658 | − | 0.997728i | \(-0.478541\pi\) |
0.897741 | + | 0.440524i | \(0.145207\pi\) | |||||||
\(588\) | 27.0000 | + | 15.5885i | 1.11346 | + | 0.642857i | ||||
\(589\) | 24.2487 | + | 14.0000i | 0.999151 | + | 0.576860i | ||||
\(590\) | 9.56218 | − | 2.56218i | 0.393669 | − | 0.105483i | ||||
\(591\) | 12.0000 | − | 6.92820i | 0.493614 | − | 0.284988i | ||||
\(592\) | −6.92820 | + | 4.00000i | −0.284747 | + | 0.164399i | ||||
\(593\) | 34.0000 | 1.39621 | 0.698106 | − | 0.715994i | \(-0.254026\pi\) | ||||
0.698106 | + | 0.715994i | \(0.254026\pi\) | |||||||
\(594\) | 9.50962 | + | 35.4904i | 0.390184 | + | 1.45619i | ||||
\(595\) | 12.0000i | 0.491952i | ||||||||
\(596\) | −6.00000 | − | 10.3923i | −0.245770 | − | 0.425685i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.39230 | + | 16.3923i | 0.179615 | + | 0.670331i | ||||
\(599\) | 21.0000 | − | 36.3731i | 0.858037 | − | 1.48616i | −0.0157622 | − | 0.999876i | \(-0.505017\pi\) |
0.873799 | − | 0.486287i | \(-0.161649\pi\) | |||||||
\(600\) | −1.26795 | − | 4.73205i | −0.0517638 | − | 0.193185i | ||||
\(601\) | −18.5000 | − | 32.0429i | −0.754631 | − | 1.30706i | −0.945558 | − | 0.325455i | \(-0.894483\pi\) |
0.190927 | − | 0.981604i | \(-0.438851\pi\) | |||||||
\(602\) | −20.0000 | + | 20.0000i | −0.815139 | + | 0.815139i | ||||
\(603\) | 7.79423 | − | 4.50000i | 0.317406 | − | 0.183254i | ||||
\(604\) | 20.0000i | 0.813788i | ||||||||
\(605\) | −12.1244 | + | 7.00000i | −0.492925 | + | 0.284590i | ||||
\(606\) | −24.2487 | + | 24.2487i | −0.985037 | + | 0.985037i | ||||
\(607\) | 2.00000 | − | 3.46410i | 0.0811775 | − | 0.140604i | −0.822578 | − | 0.568652i | \(-0.807465\pi\) |
0.903756 | + | 0.428048i | \(0.140799\pi\) | |||||||
\(608\) | −10.2487 | − | 38.2487i | −0.415640 | − | 1.55119i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.46410 | − | 5.46410i | 0.0592797 | − | 0.221235i | ||||
\(611\) | − | 12.0000i | − | 0.485468i | ||||||
\(612\) | −15.5885 | + | 9.00000i | −0.630126 | + | 0.363803i | ||||
\(613\) | 26.0000i | 1.05013i | 0.851062 | + | 0.525065i | \(0.175959\pi\) | ||||
−0.851062 | + | 0.525065i | \(0.824041\pi\) | |||||||
\(614\) | 31.4186 | + | 8.41858i | 1.26795 | + | 0.339746i | ||||
\(615\) | −7.50000 | − | 4.33013i | −0.302429 | − | 0.174608i | ||||
\(616\) | −54.6410 | + | 14.6410i | −2.20155 | + | 0.589903i | ||||
\(617\) | 1.50000 | − | 2.59808i | 0.0603877 | − | 0.104595i | −0.834251 | − | 0.551385i | \(-0.814100\pi\) |
0.894639 | + | 0.446790i | \(0.147433\pi\) | |||||||
\(618\) | 8.87564 | − | 33.1244i | 0.357031 | − | 1.33246i | ||||
\(619\) | −4.33013 | + | 2.50000i | −0.174042 | + | 0.100483i | −0.584491 | − | 0.811400i | \(-0.698706\pi\) |
0.410448 | + | 0.911884i | \(0.365372\pi\) | |||||||
\(620\) | −8.00000 | −0.321288 | ||||||||
\(621\) | 5.19615 | − | 9.00000i | 0.208514 | − | 0.361158i | ||||
\(622\) | 20.0000 | + | 20.0000i | 0.801927 | + | 0.801927i | ||||
\(623\) | 4.00000 | + | 6.92820i | 0.160257 | + | 0.277573i | ||||
\(624\) | −36.0000 | + | 20.7846i | −1.44115 | + | 0.832050i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 12.2942 | − | 3.29423i | 0.491376 | − | 0.131664i | ||||
\(627\) | 30.3109 | − | 52.5000i | 1.21050 | − | 2.09665i | ||||
\(628\) | −20.0000 | − | 34.6410i | −0.798087 | − | 1.38233i | ||||
\(629\) | − | 6.00000i | − | 0.239236i | ||||||
\(630\) | 12.0000 | − | 12.0000i | 0.478091 | − | 0.478091i | ||||
\(631\) | −6.00000 | −0.238856 | −0.119428 | − | 0.992843i | \(-0.538106\pi\) | ||||
−0.119428 | + | 0.992843i | \(0.538106\pi\) | |||||||
\(632\) | 27.3205 | + | 7.32051i | 1.08675 | + | 0.291194i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.58846 | + | 24.5885i | 0.261661 | + | 0.976532i | ||||
\(635\) | 15.5885 | + | 9.00000i | 0.618609 | + | 0.357154i | ||||
\(636\) | −27.7128 | −1.09888 | ||||||||
\(637\) | −46.7654 | + | 27.0000i | −1.85291 | + | 1.06978i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.00000 | + | 5.19615i | −0.118678 | + | 0.205557i | ||||
\(640\) | 8.00000 | + | 8.00000i | 0.316228 | + | 0.316228i | ||||
\(641\) | −8.50000 | − | 14.7224i | −0.335730 | − | 0.581501i | 0.647895 | − | 0.761730i | \(-0.275650\pi\) |
−0.983625 | + | 0.180229i | \(0.942316\pi\) | |||||||
\(642\) | −8.24167 | − | 30.7583i | −0.325273 | − | 1.21393i | ||||
\(643\) | −18.1865 | − | 10.5000i | −0.717207 | − | 0.414080i | 0.0965169 | − | 0.995331i | \(-0.469230\pi\) |
−0.813724 | + | 0.581252i | \(0.802563\pi\) | |||||||
\(644\) | 13.8564 | + | 8.00000i | 0.546019 | + | 0.315244i | ||||
\(645\) | 4.33013 | + | 7.50000i | 0.170499 | + | 0.295312i | ||||
\(646\) | 28.6865 | + | 7.68653i | 1.12866 | + | 0.302423i | ||||
\(647\) | −24.0000 | −0.943537 | −0.471769 | − | 0.881722i | \(-0.656384\pi\) | ||||
−0.471769 | + | 0.881722i | \(0.656384\pi\) | |||||||
\(648\) | 24.5885 | + | 6.58846i | 0.965926 | + | 0.258819i | ||||
\(649\) | −35.0000 | −1.37387 | ||||||||
\(650\) | 8.19615 | + | 2.19615i | 0.321480 | + | 0.0861402i | ||||
\(651\) | −13.8564 | − | 24.0000i | −0.543075 | − | 0.940634i | ||||
\(652\) | −20.0000 | + | 34.6410i | −0.783260 | + | 1.35665i | ||||
\(653\) | 10.3923 | + | 6.00000i | 0.406682 | + | 0.234798i | 0.689363 | − | 0.724416i | \(-0.257890\pi\) |
−0.282681 | + | 0.959214i | \(0.591224\pi\) | |||||||
\(654\) | −2.53590 | − | 9.46410i | −0.0991615 | − | 0.370076i | ||||
\(655\) | 6.00000 | + | 10.3923i | 0.234439 | + | 0.406061i | ||||
\(656\) | 20.0000 | 0.780869 | ||||||||
\(657\) | −1.50000 | + | 2.59808i | −0.0585206 | + | 0.101361i | ||||
\(658\) | −8.00000 | − | 8.00000i | −0.311872 | − | 0.311872i | ||||
\(659\) | 31.1769 | − | 18.0000i | 1.21448 | − | 0.701180i | 0.250748 | − | 0.968052i | \(-0.419323\pi\) |
0.963732 | + | 0.266872i | \(0.0859901\pi\) | |||||||
\(660\) | 17.3205i | 0.674200i | ||||||||
\(661\) | −39.8372 | − | 23.0000i | −1.54949 | − | 0.894596i | −0.998181 | − | 0.0602929i | \(-0.980797\pi\) |
−0.551306 | − | 0.834303i | \(-0.685870\pi\) | |||||||
\(662\) | −7.32051 | − | 27.3205i | −0.284520 | − | 1.06184i | ||||
\(663\) | − | 31.1769i | − | 1.21081i | ||||||
\(664\) | −8.78461 | + | 32.7846i | −0.340909 | + | 1.27229i | ||||
\(665\) | −28.0000 | −1.08579 | ||||||||
\(666\) | −6.00000 | + | 6.00000i | −0.232495 | + | 0.232495i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 10.3923 | − | 6.00000i | 0.402090 | − | 0.232147i | ||||
\(669\) | −12.1244 | + | 21.0000i | −0.468755 | + | 0.811907i | ||||
\(670\) | 4.09808 | − | 1.09808i | 0.158322 | − | 0.0424224i | ||||
\(671\) | −10.0000 | + | 17.3205i | −0.386046 | + | 0.668651i | ||||
\(672\) | −10.1436 | + | 37.8564i | −0.391298 | + | 1.46034i | ||||
\(673\) | −5.00000 | − | 8.66025i | −0.192736 | − | 0.333828i | 0.753420 | − | 0.657539i | \(-0.228403\pi\) |
−0.946156 | + | 0.323711i | \(0.895069\pi\) | |||||||
\(674\) | 15.0000 | + | 15.0000i | 0.577778 | + | 0.577778i | ||||
\(675\) | −2.59808 | − | 4.50000i | −0.100000 | − | 0.173205i | ||||
\(676\) | − | 46.0000i | − | 1.76923i | ||||||
\(677\) | −13.8564 | + | 8.00000i | −0.532545 | + | 0.307465i | −0.742052 | − | 0.670342i | \(-0.766147\pi\) |
0.209507 | + | 0.977807i | \(0.432814\pi\) | |||||||
\(678\) | −3.80385 | + | 14.1962i | −0.146086 | + | 0.545200i | ||||
\(679\) | −14.0000 | + | 24.2487i | −0.537271 | + | 0.930580i | ||||
\(680\) | −8.19615 | + | 2.19615i | −0.314308 | + | 0.0842186i | ||||
\(681\) | −13.5000 | − | 7.79423i | −0.517321 | − | 0.298675i | ||||
\(682\) | 27.3205 | + | 7.32051i | 1.04616 | + | 0.280317i | ||||
\(683\) | 51.0000i | 1.95146i | 0.218975 | + | 0.975730i | \(0.429729\pi\) | ||||
−0.218975 | + | 0.975730i | \(0.570271\pi\) | |||||||
\(684\) | −21.0000 | − | 36.3731i | −0.802955 | − | 1.39076i | ||||
\(685\) | − | 17.0000i | − | 0.649537i | ||||||
\(686\) | −2.92820 | + | 10.9282i | −0.111799 | + | 0.417241i | ||||
\(687\) | − | 6.92820i | − | 0.264327i | ||||||
\(688\) | −17.3205 | − | 10.0000i | −0.660338 | − | 0.381246i | ||||
\(689\) | 24.0000 | − | 41.5692i | 0.914327 | − | 1.58366i | ||||
\(690\) | 3.46410 | − | 3.46410i | 0.131876 | − | 0.131876i | ||||
\(691\) | 10.3923 | − | 6.00000i | 0.395342 | − | 0.228251i | −0.289130 | − | 0.957290i | \(-0.593366\pi\) |
0.684472 | + | 0.729039i | \(0.260033\pi\) | |||||||
\(692\) | 16.0000 | 0.608229 | ||||||||
\(693\) | −51.9615 | + | 30.0000i | −1.97386 | + | 1.13961i | ||||
\(694\) | 19.0000 | − | 19.0000i | 0.721230 | − | 0.721230i | ||||
\(695\) | −5.50000 | − | 9.52628i | −0.208627 | − | 0.361352i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.50000 | + | 12.9904i | −0.284083 | + | 0.492046i | ||||
\(698\) | −5.85641 | − | 21.8564i | −0.221668 | − | 0.827277i | ||||
\(699\) | −23.3827 | − | 40.5000i | −0.884414 | − | 1.53185i | ||||
\(700\) | 6.92820 | − | 4.00000i | 0.261861 | − | 0.151186i | ||||
\(701\) | 10.0000i | 0.377695i | 0.982006 | + | 0.188847i | \(0.0604752\pi\) | ||||
−0.982006 | + | 0.188847i | \(0.939525\pi\) | |||||||
\(702\) | −31.1769 | + | 31.1769i | −1.17670 | + | 1.17670i | ||||
\(703\) | 14.0000 | 0.528020 | ||||||||
\(704\) | −20.0000 | − | 34.6410i | −0.753778 | − | 1.30558i | ||||
\(705\) | −3.00000 | + | 1.73205i | −0.112987 | + | 0.0652328i | ||||
\(706\) | 12.2942 | − | 3.29423i | 0.462699 | − | 0.123980i | ||||
\(707\) | −48.4974 | − | 28.0000i | −1.82393 | − | 1.05305i | ||||
\(708\) | −12.1244 | + | 21.0000i | −0.455661 | + | 0.789228i | ||||
\(709\) | −27.7128 | + | 16.0000i | −1.04078 | + | 0.600893i | −0.920053 | − | 0.391794i | \(-0.871855\pi\) |
−0.120723 | + | 0.992686i | \(0.538521\pi\) | |||||||
\(710\) | −2.00000 | + | 2.00000i | −0.0750587 | + | 0.0750587i | ||||
\(711\) | 30.0000 | 1.12509 | ||||||||
\(712\) | −4.00000 | + | 4.00000i | −0.149906 | + | 0.149906i | ||||
\(713\) | −4.00000 | − | 6.92820i | −0.149801 | − | 0.259463i | ||||
\(714\) | −20.7846 | − | 20.7846i | −0.777844 | − | 0.777844i | ||||
\(715\) | −25.9808 | − | 15.0000i | −0.971625 | − | 0.560968i | ||||
\(716\) | −12.0000 | + | 20.7846i | −0.448461 | + | 0.776757i | ||||
\(717\) | 24.2487 | 0.905585 | ||||||||
\(718\) | −4.39230 | + | 16.3923i | −0.163919 | + | 0.611755i | ||||
\(719\) | −18.0000 | −0.671287 | −0.335643 | − | 0.941989i | \(-0.608954\pi\) | ||||
−0.335643 | + | 0.941989i | \(0.608954\pi\) | |||||||
\(720\) | 10.3923 | + | 6.00000i | 0.387298 | + | 0.223607i | ||||
\(721\) | 56.0000 | 2.08555 | ||||||||
\(722\) | −10.9808 | + | 40.9808i | −0.408662 | + | 1.52515i | ||||
\(723\) | −12.9904 | + | 22.5000i | −0.483117 | + | 0.836784i | ||||
\(724\) | 2.00000 | − | 3.46410i | 0.0743294 | − | 0.128742i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.87564 | − | 33.1244i | 0.329406 | − | 1.22936i | ||||
\(727\) | 25.0000 | + | 43.3013i | 0.927199 | + | 1.60596i | 0.787986 | + | 0.615693i | \(0.211124\pi\) |
0.139212 | + | 0.990263i | \(0.455543\pi\) | |||||||
\(728\) | −48.0000 | − | 48.0000i | −1.77900 | − | 1.77900i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −1.00000 | + | 1.00000i | −0.0370117 | + | 0.0370117i | ||||
\(731\) | 12.9904 | − | 7.50000i | 0.480467 | − | 0.277398i | ||||
\(732\) | 6.92820 | + | 12.0000i | 0.256074 | + | 0.443533i | ||||
\(733\) | 31.1769 | + | 18.0000i | 1.15155 | + | 0.664845i | 0.949263 | − | 0.314482i | \(-0.101831\pi\) |
0.202282 | + | 0.979327i | \(0.435164\pi\) | |||||||
\(734\) | −24.5885 | + | 6.58846i | −0.907577 | + | 0.243184i | ||||
\(735\) | 13.5000 | + | 7.79423i | 0.497955 | + | 0.287494i | ||||
\(736\) | −2.92820 | + | 10.9282i | −0.107935 | + | 0.402819i | ||||
\(737\) | −15.0000 | −0.552532 | ||||||||
\(738\) | 20.4904 | − | 5.49038i | 0.754261 | − | 0.202104i | ||||
\(739\) | − | 15.0000i | − | 0.551784i | −0.961189 | − | 0.275892i | \(-0.911027\pi\) | ||
0.961189 | − | 0.275892i | \(-0.0889732\pi\) | |||||||
\(740\) | −3.46410 | + | 2.00000i | −0.127343 | + | 0.0735215i | ||||
\(741\) | 72.7461 | 2.67240 | ||||||||
\(742\) | −11.7128 | − | 43.7128i | −0.429991 | − | 1.60475i | ||||
\(743\) | −18.0000 | + | 31.1769i | −0.660356 | + | 1.14377i | 0.320166 | + | 0.947361i | \(0.396261\pi\) |
−0.980522 | + | 0.196409i | \(0.937072\pi\) | |||||||
\(744\) | 13.8564 | − | 13.8564i | 0.508001 | − | 0.508001i | ||||
\(745\) | −3.00000 | − | 5.19615i | −0.109911 | − | 0.190372i | ||||
\(746\) | −22.0000 | + | 22.0000i | −0.805477 | + | 0.805477i | ||||
\(747\) | 36.0000i | 1.31717i | ||||||||
\(748\) | 30.0000 | 1.09691 | ||||||||
\(749\) | 45.0333 | − | 26.0000i | 1.64548 | − | 0.950019i | ||||
\(750\) | −0.633975 | − | 2.36603i | −0.0231495 | − | 0.0863950i | ||||
\(751\) | 23.0000 | − | 39.8372i | 0.839282 | − | 1.45368i | −0.0512140 | − | 0.998688i | \(-0.516309\pi\) |
0.890496 | − | 0.454991i | \(-0.150358\pi\) | |||||||
\(752\) | 4.00000 | − | 6.92820i | 0.145865 | − | 0.252646i | ||||
\(753\) | −13.5000 | + | 7.79423i | −0.491967 | + | 0.284037i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.0000i | 0.363937i | ||||||||
\(756\) | 41.5692i | 1.51186i | ||||||||
\(757\) | − | 4.00000i | − | 0.145382i | −0.997354 | − | 0.0726912i | \(-0.976841\pi\) | ||
0.997354 | − | 0.0726912i | \(-0.0231588\pi\) | |||||||
\(758\) | 4.09808 | + | 1.09808i | 0.148849 | + | 0.0398839i | ||||
\(759\) | −15.0000 | + | 8.66025i | −0.544466 | + | 0.314347i | ||||
\(760\) | −5.12436 | − | 19.1244i | −0.185880 | − | 0.693713i | ||||
\(761\) | 25.0000 | − | 43.3013i | 0.906249 | − | 1.56967i | 0.0870179 | − | 0.996207i | \(-0.472266\pi\) |
0.819231 | − | 0.573463i | \(-0.194400\pi\) | |||||||
\(762\) | −42.5885 | + | 11.4115i | −1.54282 | + | 0.413397i | ||||
\(763\) | 13.8564 | − | 8.00000i | 0.501636 | − | 0.289619i | ||||
\(764\) | − | 16.0000i | − | 0.578860i | ||||||
\(765\) | −7.79423 | + | 4.50000i | −0.281801 | + | 0.162698i | ||||
\(766\) | 18.0000 | + | 18.0000i | 0.650366 | + | 0.650366i | ||||
\(767\) | −21.0000 | − | 36.3731i | −0.758266 | − | 1.31336i | ||||
\(768\) | −27.7128 | −1.00000 | ||||||||
\(769\) | 15.0000 | − | 25.9808i | 0.540914 | − | 0.936890i | −0.457938 | − | 0.888984i | \(-0.651412\pi\) |
0.998852 | − | 0.0479061i | \(-0.0152548\pi\) | |||||||
\(770\) | −27.3205 | + | 7.32051i | −0.984563 | + | 0.263813i | ||||
\(771\) | −12.1244 | −0.436648 | ||||||||
\(772\) | −39.8372 | + | 23.0000i | −1.43377 | + | 0.827788i | ||||
\(773\) | 42.0000i | 1.51064i | 0.655359 | + | 0.755318i | \(0.272517\pi\) | ||||
−0.655359 | + | 0.755318i | \(0.727483\pi\) | |||||||
\(774\) | −20.4904 | − | 5.49038i | −0.736512 | − | 0.197348i | ||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | −19.1244 | − | 5.12436i | −0.686524 | − | 0.183954i | ||||
\(777\) | −12.0000 | − | 6.92820i | −0.430498 | − | 0.248548i | ||||
\(778\) | 5.85641 | + | 21.8564i | 0.209962 | + | 0.783590i | ||||
\(779\) | −30.3109 | − | 17.5000i | −1.08600 | − | 0.627003i | ||||
\(780\) | −18.0000 | + | 10.3923i | −0.644503 | + | 0.372104i | ||||
\(781\) | 8.66025 | − | 5.00000i | 0.309888 | − | 0.178914i | ||||
\(782\) | −6.00000 | − | 6.00000i | −0.214560 | − | 0.214560i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −36.0000 | −1.28571 | ||||||||
\(785\) | −10.0000 | − | 17.3205i | −0.356915 | − | 0.618195i | ||||
\(786\) | −28.3923 | − | 7.60770i | −1.01272 | − | 0.271357i | ||||
\(787\) | 45.0333 | + | 26.0000i | 1.60526 | + | 0.926800i | 0.990410 | + | 0.138159i | \(0.0441186\pi\) |
0.614855 | + | 0.788641i | \(0.289215\pi\) | |||||||
\(788\) | −8.00000 | + | 13.8564i | −0.284988 | + | 0.493614i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13.6603 | + | 3.66025i | 0.486010 | + | 0.130226i | ||||
\(791\) | −24.0000 | −0.853342 | ||||||||
\(792\) | −30.0000 | − | 30.0000i | −1.06600 | − | 1.06600i | ||||
\(793\) | −24.0000 | −0.852265 | ||||||||
\(794\) | −35.5167 | − | 9.51666i | −1.26044 | − | 0.337734i | ||||
\(795\) | −13.8564 | −0.491436 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.19615 | + | 3.00000i | 0.184057 | + | 0.106265i | 0.589197 | − | 0.807989i | \(-0.299444\pi\) |
−0.405140 | + | 0.914255i | \(0.632777\pi\) | |||||||
\(798\) | 48.4974 | − | 48.4974i | 1.71679 | − | 1.71679i | ||||
\(799\) | 3.00000 | + | 5.19615i | 0.106132 | + | 0.183827i | ||||
\(800\) | 4.00000 | + | 4.00000i | 0.141421 | + | 0.141421i | ||||
\(801\) | −3.00000 | + | 5.19615i | −0.106000 | + | 0.183597i | ||||
\(802\) | −15.0000 | − | 15.0000i | −0.529668 | − | 0.529668i | ||||
\(803\) | 4.33013 | − | 2.50000i | 0.152807 | − | 0.0882231i | ||||
\(804\) | −5.19615 | + | 9.00000i | −0.183254 | + | 0.317406i | ||||
\(805\) | 6.92820 | + | 4.00000i | 0.244187 | + | 0.140981i | ||||
\(806\) | 8.78461 | + | 32.7846i | 0.309425 | + | 1.15479i | ||||
\(807\) | −30.0000 | + | 17.3205i | −1.05605 | + | 0.609711i | ||||
\(808\) | 10.2487 | − | 38.2487i | 0.360548 | − | 1.34558i | ||||
\(809\) | 7.00000 | 0.246107 | 0.123053 | − | 0.992400i | \(-0.460731\pi\) | ||||
0.123053 | + | 0.992400i | \(0.460731\pi\) | |||||||
\(810\) | 12.2942 | + | 3.29423i | 0.431975 | + | 0.115747i | ||||
\(811\) | 1.00000i | 0.0351147i | 0.999846 | + | 0.0175574i | \(0.00558897\pi\) | ||||
−0.999846 | + | 0.0175574i | \(0.994411\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.2487 | + | 42.0000i | 0.850439 | + | 1.47300i | ||||
\(814\) | 13.6603 | − | 3.66025i | 0.478792 | − | 0.128292i | ||||
\(815\) | −10.0000 | + | 17.3205i | −0.350285 | + | 0.606711i | ||||
\(816\) | 10.3923 | − | 18.0000i | 0.363803 | − | 0.630126i | ||||
\(817\) | 17.5000 | + | 30.3109i | 0.612247 | + | 1.06044i | ||||
\(818\) | 15.0000 | + | 15.0000i | 0.524463 | + | 0.524463i | ||||
\(819\) | −62.3538 | − | 36.0000i | −2.17882 | − | 1.25794i | ||||
\(820\) | 10.0000 | 0.349215 | ||||||||
\(821\) | 3.46410 | − | 2.00000i | 0.120898 | − | 0.0698005i | −0.438331 | − | 0.898813i | \(-0.644430\pi\) |
0.559229 | + | 0.829013i | \(0.311097\pi\) | |||||||
\(822\) | 29.4449 | + | 29.4449i | 1.02701 | + | 1.02701i | ||||
\(823\) | 3.00000 | − | 5.19615i | 0.104573 | − | 0.181126i | −0.808990 | − | 0.587822i | \(-0.799986\pi\) |
0.913564 | + | 0.406695i | \(0.133319\pi\) | |||||||
\(824\) | 10.2487 | + | 38.2487i | 0.357031 | + | 1.33246i | ||||
\(825\) | 8.66025i | 0.301511i | ||||||||
\(826\) | −38.2487 | − | 10.2487i | −1.33084 | − | 0.356598i | ||||
\(827\) | 16.0000i | 0.556375i | 0.960527 | + | 0.278187i | \(0.0897336\pi\) | ||||
−0.960527 | + | 0.278187i | \(0.910266\pi\) | |||||||
\(828\) | 12.0000i | 0.417029i | ||||||||
\(829\) | 8.00000i | 0.277851i | 0.990303 | + | 0.138926i | \(0.0443649\pi\) | ||||
−0.990303 | + | 0.138926i | \(0.955635\pi\) | |||||||
\(830\) | −4.39230 | + | 16.3923i | −0.152459 | + | 0.568985i | ||||
\(831\) | −3.00000 | − | 1.73205i | −0.104069 | − | 0.0600842i | ||||
\(832\) | 24.0000 | − | 41.5692i | 0.832050 | − | 1.44115i | ||||
\(833\) | 13.5000 | − | 23.3827i | 0.467747 | − | 0.810162i | ||||
\(834\) | 26.0263 | + | 6.97372i | 0.901216 | + | 0.241480i | ||||
\(835\) | 5.19615 | − | 3.00000i | 0.179820 | − | 0.103819i | ||||
\(836\) | 70.0000i | 2.42100i | ||||||||
\(837\) | 10.3923 | − | 18.0000i | 0.359211 | − | 0.622171i | ||||
\(838\) | −4.00000 | + | 4.00000i | −0.138178 | + | 0.138178i | ||||
\(839\) | −14.0000 | − | 24.2487i | −0.483334 | − | 0.837158i | 0.516483 | − | 0.856297i | \(-0.327241\pi\) |
−0.999817 | + | 0.0191389i | \(0.993908\pi\) | |||||||
\(840\) | −5.07180 | + | 18.9282i | −0.174994 | + | 0.653085i | ||||
\(841\) | −14.5000 | + | 25.1147i | −0.500000 | + | 0.866025i | ||||
\(842\) | 0.732051 | + | 2.73205i | 0.0252281 | + | 0.0941527i | ||||
\(843\) | −19.0526 | + | 33.0000i | −0.656205 | + | 1.13658i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 23.0000i | − | 0.791224i | ||||||
\(846\) | 2.19615 | − | 8.19615i | 0.0755053 | − | 0.281790i | ||||
\(847\) | 56.0000 | 1.92418 | ||||||||
\(848\) | 27.7128 | − | 16.0000i | 0.951662 | − | 0.549442i | ||||
\(849\) | − | 6.92820i | − | 0.237775i | ||||||
\(850\) | −4.09808 | + | 1.09808i | −0.140563 | + | 0.0376637i | ||||
\(851\) | −3.46410 | − | 2.00000i | −0.118748 | − | 0.0685591i | ||||
\(852\) | − | 6.92820i | − | 0.237356i | ||||||
\(853\) | −39.8372 | + | 23.0000i | −1.36400 | + | 0.787505i | −0.990153 | − | 0.139986i | \(-0.955294\pi\) |
−0.373845 | + | 0.927491i | \(0.621961\pi\) | |||||||
\(854\) | −16.0000 | + | 16.0000i | −0.547509 | + | 0.547509i | ||||
\(855\) | −10.5000 | − | 18.1865i | −0.359092 | − | 0.621966i | ||||
\(856\) | 26.0000 | + | 26.0000i | 0.888662 | + | 0.888662i | ||||
\(857\) | 21.0000 | + | 36.3731i | 0.717346 | + | 1.24248i | 0.962048 | + | 0.272882i | \(0.0879768\pi\) |
−0.244701 | + | 0.969599i | \(0.578690\pi\) | |||||||
\(858\) | 70.9808 | − | 19.0192i | 2.42324 | − | 0.649306i | ||||
\(859\) | 32.0429 | + | 18.5000i | 1.09329 | + | 0.631212i | 0.934451 | − | 0.356092i | \(-0.115891\pi\) |
0.158840 | + | 0.987304i | \(0.449225\pi\) | |||||||
\(860\) | −8.66025 | − | 5.00000i | −0.295312 | − | 0.170499i | ||||
\(861\) | 17.3205 | + | 30.0000i | 0.590281 | + | 1.02240i | ||||
\(862\) | −4.39230 | + | 16.3923i | −0.149602 | + | 0.558324i | ||||
\(863\) | 30.0000 | 1.02121 | 0.510606 | − | 0.859815i | \(-0.329421\pi\) | ||||
0.510606 | + | 0.859815i | \(0.329421\pi\) | |||||||
\(864\) | −28.3923 | + | 7.60770i | −0.965926 | + | 0.258819i | ||||
\(865\) | 8.00000 | 0.272008 | ||||||||
\(866\) | 10.6147 | − | 39.6147i | 0.360703 | − | 1.34616i | ||||
\(867\) | −6.92820 | − | 12.0000i | −0.235294 | − | 0.407541i | ||||
\(868\) | 27.7128 | + | 16.0000i | 0.940634 | + | 0.543075i | ||||
\(869\) | −43.3013 | − | 25.0000i | −1.46889 | − | 0.848067i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.00000 | − | 15.5885i | −0.304953 | − | 0.528195i | ||||
\(872\) | 8.00000 | + | 8.00000i | 0.270914 | + | 0.270914i | ||||
\(873\) | −21.0000 | −0.710742 | ||||||||
\(874\) | 14.0000 | − | 14.0000i | 0.473557 | − | 0.473557i | ||||
\(875\) | 3.46410 | − | 2.00000i | 0.117108 | − | 0.0676123i | ||||
\(876\) | − | 3.46410i | − | 0.117041i | ||||||
\(877\) | 27.7128 | + | 16.0000i | 0.935795 | + | 0.540282i | 0.888640 | − | 0.458606i | \(-0.151651\pi\) |
0.0471555 | + | 0.998888i | \(0.484984\pi\) | |||||||
\(878\) | 54.6410 | − | 14.6410i | 1.84404 | − | 0.494110i | ||||
\(879\) | 6.92820i | 0.233682i | ||||||||
\(880\) | −10.0000 | − | 17.3205i | −0.337100 | − | 0.583874i | ||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | −36.8827 | + | 9.88269i | −1.24190 | + | 0.332767i | ||||
\(883\) | − | 41.0000i | − | 1.37976i | −0.723924 | − | 0.689880i | \(-0.757663\pi\) | ||
0.723924 | − | 0.689880i | \(-0.242337\pi\) | |||||||
\(884\) | 18.0000 | + | 31.1769i | 0.605406 | + | 1.04859i | ||||
\(885\) | −6.06218 | + | 10.5000i | −0.203778 | + | 0.352954i | ||||
\(886\) | 9.15064 | + | 34.1506i | 0.307422 | + | 1.14731i | ||||
\(887\) | −11.0000 | + | 19.0526i | −0.369344 | + | 0.639722i | −0.989463 | − | 0.144785i | \(-0.953751\pi\) |
0.620119 | + | 0.784508i | \(0.287084\pi\) | |||||||
\(888\) | 2.53590 | − | 9.46410i | 0.0850992 | − | 0.317594i | ||||
\(889\) | −36.0000 | − | 62.3538i | −1.20740 | − | 2.09128i | ||||
\(890\) | −2.00000 | + | 2.00000i | −0.0670402 | + | 0.0670402i | ||||
\(891\) | −38.9711 | − | 22.5000i | −1.30558 | − | 0.753778i | ||||
\(892\) | − | 28.0000i | − | 0.937509i | ||||||
\(893\) | −12.1244 | + | 7.00000i | −0.405726 | + | 0.234246i | ||||
\(894\) | 14.1962 | + | 3.80385i | 0.474790 | + | 0.127220i | ||||
\(895\) | −6.00000 | + | 10.3923i | −0.200558 | + | 0.347376i | ||||
\(896\) | −11.7128 | − | 43.7128i | −0.391298 | − | 1.46034i | ||||
\(897\) | −18.0000 | − | 10.3923i | −0.601003 | − | 0.346989i | ||||
\(898\) | −9.88269 | + | 36.8827i | −0.329789 | + | 1.23079i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 5.19615 | + | 3.00000i | 0.173205 | + | 0.100000i | ||||
\(901\) | 24.0000i | 0.799556i | ||||||||
\(902\) | −34.1506 | − | 9.15064i | −1.13709 | − | 0.304683i | ||||
\(903\) | − | 34.6410i | − | 1.15278i | ||||||
\(904\) | −4.39230 | − | 16.3923i | −0.146086 | − | 0.545200i | ||||
\(905\) | 1.00000 | − | 1.73205i | 0.0332411 | − | 0.0575753i | ||||
\(906\) | −17.3205 | − | 17.3205i | −0.575435 | − | 0.575435i | ||||
\(907\) | 21.6506 | − | 12.5000i | 0.718898 | − | 0.415056i | −0.0954492 | − | 0.995434i | \(-0.530429\pi\) |
0.814347 | + | 0.580379i | \(0.197095\pi\) | |||||||
\(908\) | 18.0000 | 0.597351 | ||||||||
\(909\) | − | 42.0000i | − | 1.39305i | ||||||
\(910\) | −24.0000 | − | 24.0000i | −0.795592 | − | 0.795592i | ||||
\(911\) | −18.0000 | − | 31.1769i | −0.596367 | − | 1.03294i | −0.993352 | − | 0.115113i | \(-0.963277\pi\) |
0.396986 | − | 0.917825i | \(-0.370056\pi\) | |||||||
\(912\) | 42.0000 | + | 24.2487i | 1.39076 | + | 0.802955i | ||||
\(913\) | 30.0000 | − | 51.9615i | 0.992855 | − | 1.71968i | ||||
\(914\) | −4.09808 | + | 1.09808i | −0.135552 | + | 0.0363211i | ||||
\(915\) | 3.46410 | + | 6.00000i | 0.114520 | + | 0.198354i | ||||
\(916\) | 4.00000 | + | 6.92820i | 0.132164 | + | 0.228914i | ||||
\(917\) | − | 48.0000i | − | 1.58510i | ||||||
\(918\) | 5.70577 | − | 21.2942i | 0.188319 | − | 0.702814i | ||||
\(919\) | −26.0000 | −0.857661 | −0.428830 | − | 0.903385i | \(-0.641074\pi\) | ||||
−0.428830 | + | 0.903385i | \(0.641074\pi\) | |||||||
\(920\) | −1.46410 | + | 5.46410i | −0.0482700 | + | 0.180146i | ||||
\(921\) | −34.5000 | + | 19.9186i | −1.13681 | + | 0.656340i | ||||
\(922\) | 5.12436 | + | 19.1244i | 0.168762 | + | 0.629827i | ||||
\(923\) | 10.3923 | + | 6.00000i | 0.342067 | + | 0.197492i | ||||
\(924\) | 34.6410 | − | 60.0000i | 1.13961 | − | 1.97386i | ||||
\(925\) | −1.73205 | + | 1.00000i | −0.0569495 | + | 0.0328798i | ||||
\(926\) | 26.0000 | + | 26.0000i | 0.854413 | + | 0.854413i | ||||
\(927\) | 21.0000 | + | 36.3731i | 0.689730 | + | 1.19465i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.0000 | + | 43.3013i | 0.820223 | + | 1.42067i | 0.905516 | + | 0.424313i | \(0.139484\pi\) |
−0.0852924 | + | 0.996356i | \(0.527182\pi\) | |||||||
\(930\) | 6.92820 | − | 6.92820i | 0.227185 | − | 0.227185i | ||||
\(931\) | 54.5596 | + | 31.5000i | 1.78812 | + | 1.03237i | ||||
\(932\) | 46.7654 | + | 27.0000i | 1.53185 | + | 0.884414i | ||||
\(933\) | −34.6410 | −1.13410 | ||||||||
\(934\) | −17.7583 | − | 4.75833i | −0.581070 | − | 0.155697i | ||||
\(935\) | 15.0000 | 0.490552 | ||||||||
\(936\) | 13.1769 | − | 49.1769i | 0.430701 | − | 1.60740i | ||||
\(937\) | −14.0000 | −0.457360 | −0.228680 | − | 0.973502i | \(-0.573441\pi\) | ||||
−0.228680 | + | 0.973502i | \(0.573441\pi\) | |||||||
\(938\) | −16.3923 | − | 4.39230i | −0.535228 | − | 0.143414i | ||||
\(939\) | −7.79423 | + | 13.5000i | −0.254355 | + | 0.440556i | ||||
\(940\) | 2.00000 | − | 3.46410i | 0.0652328 | − | 0.112987i | ||||
\(941\) | −6.92820 | − | 4.00000i | −0.225853 | − | 0.130396i | 0.382804 | − | 0.923829i | \(-0.374958\pi\) |
−0.608657 | + | 0.793433i | \(0.708292\pi\) | |||||||
\(942\) | 47.3205 | + | 12.6795i | 1.54179 | + | 0.413120i | ||||
\(943\) | 5.00000 | + | 8.66025i | 0.162822 | + | 0.282017i | ||||
\(944\) | − | 28.0000i | − | 0.911322i | ||||||
\(945\) | 20.7846i | 0.676123i | ||||||||
\(946\) | 25.0000 | + | 25.0000i | 0.812820 | + | 0.812820i | ||||
\(947\) | −44.1673 | + | 25.5000i | −1.43524 | + | 0.828639i | −0.997514 | − | 0.0704677i | \(-0.977551\pi\) |
−0.437730 | + | 0.899106i | \(0.644217\pi\) | |||||||
\(948\) | −30.0000 | + | 17.3205i | −0.974355 | + | 0.562544i | ||||
\(949\) | 5.19615 | + | 3.00000i | 0.168674 | + | 0.0973841i | ||||
\(950\) | −2.56218 | − | 9.56218i | −0.0831280 | − | 0.310238i | ||||
\(951\) | −27.0000 | − | 15.5885i | −0.875535 | − | 0.505490i | ||||
\(952\) | 32.7846 | + | 8.78461i | 1.06256 | + | 0.284711i | ||||
\(953\) | −29.0000 | −0.939402 | −0.469701 | − | 0.882826i | \(-0.655638\pi\) | ||||
−0.469701 | + | 0.882826i | \(0.655638\pi\) | |||||||
\(954\) | 24.0000 | − | 24.0000i | 0.777029 | − | 0.777029i | ||||
\(955\) | − | 8.00000i | − | 0.258874i | ||||||
\(956\) | −24.2487 | + | 14.0000i | −0.784259 | + | 0.452792i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.8564 | + | 5.85641i | −0.706148 | + | 0.189212i | ||||
\(959\) | −34.0000 | + | 58.8897i | −1.09792 | + | 1.90165i | ||||
\(960\) | −13.8564 | −0.447214 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 12.0000 | + | 12.0000i | 0.386896 | + | 0.386896i | ||||
\(963\) | 33.7750 | + | 19.5000i | 1.08838 | + | 0.628379i | ||||
\(964\) | − | 30.0000i | − | 0.966235i | ||||||
\(965\) | −19.9186 | + | 11.5000i | −0.641202 | + | 0.370198i | ||||
\(966\) | −18.9282 | + | 5.07180i | −0.609005 | + | 0.163182i | ||||
\(967\) | −14.0000 | + | 24.2487i | −0.450210 | + | 0.779786i | −0.998399 | − | 0.0565684i | \(-0.981984\pi\) |
0.548189 | + | 0.836354i | \(0.315317\pi\) | |||||||
\(968\) | 10.2487 | + | 38.2487i | 0.329406 | + | 1.22936i | ||||
\(969\) | −31.5000 | + | 18.1865i | −1.01193 | + | 0.584236i | ||||
\(970\) | −9.56218 | − | 2.56218i | −0.307023 | − | 0.0822666i | ||||
\(971\) | − | 36.0000i | − | 1.15529i | −0.816286 | − | 0.577647i | \(-0.803971\pi\) | ||
0.816286 | − | 0.577647i | \(-0.196029\pi\) | |||||||
\(972\) | −27.0000 | + | 15.5885i | −0.866025 | + | 0.500000i | ||||
\(973\) | 44.0000i | 1.41058i | ||||||||
\(974\) | −4.39230 | + | 16.3923i | −0.140739 | + | 0.525243i | ||||
\(975\) | −9.00000 | + | 5.19615i | −0.288231 | + | 0.166410i | ||||
\(976\) | −13.8564 | − | 8.00000i | −0.443533 | − | 0.256074i | ||||
\(977\) | 27.5000 | − | 47.6314i | 0.879803 | − | 1.52386i | 0.0282462 | − | 0.999601i | \(-0.491008\pi\) |
0.851557 | − | 0.524262i | \(-0.175659\pi\) | |||||||
\(978\) | −12.6795 | − | 47.3205i | −0.405445 | − | 1.51314i | ||||
\(979\) | 8.66025 | − | 5.00000i | 0.276783 | − | 0.159801i | ||||
\(980\) | −18.0000 | −0.574989 | ||||||||
\(981\) | 10.3923 | + | 6.00000i | 0.331801 | + | 0.191565i | ||||
\(982\) | 11.0000 | − | 11.0000i | 0.351024 | − | 0.351024i | ||||
\(983\) | 25.0000 | + | 43.3013i | 0.797376 | + | 1.38110i | 0.921319 | + | 0.388807i | \(0.127113\pi\) |
−0.123943 | + | 0.992289i | \(0.539554\pi\) | |||||||
\(984\) | −17.3205 | + | 17.3205i | −0.552158 | + | 0.552158i | ||||
\(985\) | −4.00000 | + | 6.92820i | −0.127451 | + | 0.220751i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.8564 | 0.441054 | ||||||||
\(988\) | −72.7461 | + | 42.0000i | −2.31436 | + | 1.33620i | ||||
\(989\) | − | 10.0000i | − | 0.317982i | ||||||
\(990\) | −15.0000 | − | 15.0000i | −0.476731 | − | 0.476731i | ||||
\(991\) | 8.00000 | 0.254128 | 0.127064 | − | 0.991894i | \(-0.459445\pi\) | ||||
0.127064 | + | 0.991894i | \(0.459445\pi\) | |||||||
\(992\) | −5.85641 | + | 21.8564i | −0.185941 | + | 0.693942i | ||||
\(993\) | 30.0000 | + | 17.3205i | 0.952021 | + | 0.549650i | ||||
\(994\) | 10.9282 | − | 2.92820i | 0.346622 | − | 0.0928770i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −20.7846 | − | 36.0000i | −0.658586 | − | 1.14070i | ||||
\(997\) | 24.2487 | − | 14.0000i | 0.767964 | − | 0.443384i | −0.0641836 | − | 0.997938i | \(-0.520444\pi\) |
0.832148 | + | 0.554554i | \(0.187111\pi\) | |||||||
\(998\) | −41.0000 | + | 41.0000i | −1.29783 | + | 1.29783i | ||||
\(999\) | − | 10.3923i | − | 0.328798i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 360.2.bf.a.301.2 | yes | 4 | |
3.2 | odd | 2 | 1080.2.bf.a.901.1 | 4 | |||
4.3 | odd | 2 | 1440.2.bv.a.1201.1 | 4 | |||
8.3 | odd | 2 | 1440.2.bv.a.1201.2 | 4 | |||
8.5 | even | 2 | inner | 360.2.bf.a.301.1 | yes | 4 | |
9.2 | odd | 6 | 1080.2.bf.a.181.2 | 4 | |||
9.7 | even | 3 | inner | 360.2.bf.a.61.1 | ✓ | 4 | |
12.11 | even | 2 | 4320.2.bv.a.3601.2 | 4 | |||
24.5 | odd | 2 | 1080.2.bf.a.901.2 | 4 | |||
24.11 | even | 2 | 4320.2.bv.a.3601.1 | 4 | |||
36.7 | odd | 6 | 1440.2.bv.a.241.2 | 4 | |||
36.11 | even | 6 | 4320.2.bv.a.721.1 | 4 | |||
72.11 | even | 6 | 4320.2.bv.a.721.2 | 4 | |||
72.29 | odd | 6 | 1080.2.bf.a.181.1 | 4 | |||
72.43 | odd | 6 | 1440.2.bv.a.241.1 | 4 | |||
72.61 | even | 6 | inner | 360.2.bf.a.61.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.bf.a.61.1 | ✓ | 4 | 9.7 | even | 3 | inner | |
360.2.bf.a.61.2 | yes | 4 | 72.61 | even | 6 | inner | |
360.2.bf.a.301.1 | yes | 4 | 8.5 | even | 2 | inner | |
360.2.bf.a.301.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1080.2.bf.a.181.1 | 4 | 72.29 | odd | 6 | |||
1080.2.bf.a.181.2 | 4 | 9.2 | odd | 6 | |||
1080.2.bf.a.901.1 | 4 | 3.2 | odd | 2 | |||
1080.2.bf.a.901.2 | 4 | 24.5 | odd | 2 | |||
1440.2.bv.a.241.1 | 4 | 72.43 | odd | 6 | |||
1440.2.bv.a.241.2 | 4 | 36.7 | odd | 6 | |||
1440.2.bv.a.1201.1 | 4 | 4.3 | odd | 2 | |||
1440.2.bv.a.1201.2 | 4 | 8.3 | odd | 2 | |||
4320.2.bv.a.721.1 | 4 | 36.11 | even | 6 | |||
4320.2.bv.a.721.2 | 4 | 72.11 | even | 6 | |||
4320.2.bv.a.3601.1 | 4 | 24.11 | even | 2 | |||
4320.2.bv.a.3601.2 | 4 | 12.11 | even | 2 |