Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(13,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.m (of order \(4\), 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: | \(1.67685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.4 | ||
Root | \(-0.692297i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.13 |
Dual form | 210.2.m.b.97.4 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 1.19663 | + | 1.88893i | 0.535151 | + | 0.844756i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 0.510472 | + | 2.59604i | 0.192940 | + | 0.981211i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 2.18183 | + | 0.489528i | 0.689954 | + | 0.154802i | ||||
\(11\) | 4.79881 | 1.44690 | 0.723448 | − | 0.690379i | \(-0.242556\pi\) | ||||
0.723448 | + | 0.690379i | \(0.242556\pi\) | |||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | 0.585786 | − | 0.585786i | 0.162468 | − | 0.162468i | −0.621191 | − | 0.783659i | \(-0.713351\pi\) |
0.783659 | + | 0.621191i | \(0.213351\pi\) | |||||||
\(14\) | 2.19663 | + | 1.47472i | 0.587075 | + | 0.394135i | ||||
\(15\) | −2.18183 | − | 0.489528i | −0.563345 | − | 0.126396i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.10651 | − | 4.10651i | −0.995975 | − | 0.995975i | 0.00401675 | − | 0.999992i | \(-0.498721\pi\) |
−0.999992 | + | 0.00401675i | \(0.998721\pi\) | |||||||
\(18\) | −0.707107 | − | 0.707107i | −0.166667 | − | 0.166667i | ||||
\(19\) | −2.36365 | −0.542259 | −0.271129 | − | 0.962543i | \(-0.587397\pi\) | ||||
−0.271129 | + | 0.962543i | \(0.587397\pi\) | |||||||
\(20\) | 1.88893 | − | 1.19663i | 0.422378 | − | 0.267576i | ||||
\(21\) | −2.19663 | − | 1.47472i | −0.479345 | − | 0.321810i | ||||
\(22\) | 3.39327 | − | 3.39327i | 0.723448 | − | 0.723448i | ||||
\(23\) | 2.97906 | + | 2.97906i | 0.621176 | + | 0.621176i | 0.945832 | − | 0.324656i | \(-0.105249\pi\) |
−0.324656 | + | 0.945832i | \(0.605249\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −2.13613 | + | 4.52072i | −0.427226 | + | 0.904145i | ||||
\(26\) | − | 0.828427i | − | 0.162468i | ||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 2.59604 | − | 0.510472i | 0.490605 | − | 0.0964701i | ||||
\(29\) | − | 9.94900i | − | 1.84748i | −0.383017 | − | 0.923741i | \(-0.625115\pi\) | ||
0.383017 | − | 0.923741i | \(-0.374885\pi\) | |||||||
\(30\) | −1.88893 | + | 1.19663i | −0.344870 | + | 0.218475i | ||||
\(31\) | 3.02094i | 0.542578i | 0.962498 | + | 0.271289i | \(0.0874498\pi\) | ||||
−0.962498 | + | 0.271289i | \(0.912550\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −3.39327 | + | 3.39327i | −0.590692 | + | 0.590692i | ||||
\(34\) | −5.80748 | −0.995975 | ||||||||
\(35\) | −4.29289 | + | 4.07076i | −0.725631 | + | 0.688084i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −6.10651 | + | 6.10651i | −1.00390 | + | 1.00390i | −0.00391185 | + | 0.999992i | \(0.501245\pi\) |
−0.999992 | + | 0.00391185i | \(0.998755\pi\) | |||||||
\(38\) | −1.67135 | + | 1.67135i | −0.271129 | + | 0.271129i | ||||
\(39\) | 0.828427i | 0.132655i | ||||||||
\(40\) | 0.489528 | − | 2.18183i | 0.0774012 | − | 0.344977i | ||||
\(41\) | − | 10.9996i | − | 1.71784i | −0.512107 | − | 0.858921i | \(-0.671135\pi\) | ||
0.512107 | − | 0.858921i | \(-0.328865\pi\) | |||||||
\(42\) | −2.59604 | + | 0.510472i | −0.400578 | + | 0.0787675i | ||||
\(43\) | −5.74825 | − | 5.74825i | −0.876599 | − | 0.876599i | 0.116582 | − | 0.993181i | \(-0.462806\pi\) |
−0.993181 | + | 0.116582i | \(0.962806\pi\) | |||||||
\(44\) | − | 4.79881i | − | 0.723448i | ||||||
\(45\) | 1.88893 | − | 1.19663i | 0.281585 | − | 0.178384i | ||||
\(46\) | 4.21302 | 0.621176 | ||||||||
\(47\) | 0.363651 | + | 0.363651i | 0.0530439 | + | 0.0530439i | 0.733131 | − | 0.680087i | \(-0.238058\pi\) |
−0.680087 | + | 0.733131i | \(0.738058\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | −6.47884 | + | 2.65041i | −0.925548 | + | 0.378630i | ||||
\(50\) | 1.68616 | + | 4.70711i | 0.238459 | + | 0.665685i | ||||
\(51\) | 5.80748 | 0.813210 | ||||||||
\(52\) | −0.585786 | − | 0.585786i | −0.0812340 | − | 0.0812340i | ||||
\(53\) | 2.36365 | + | 2.36365i | 0.324672 | + | 0.324672i | 0.850556 | − | 0.525884i | \(-0.176265\pi\) |
−0.525884 | + | 0.850556i | \(0.676265\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 5.74242 | + | 9.06462i | 0.774308 | + | 1.22227i | ||||
\(56\) | 1.47472 | − | 2.19663i | 0.197068 | − | 0.293538i | ||||
\(57\) | 1.67135 | − | 1.67135i | 0.221376 | − | 0.221376i | ||||
\(58\) | −7.03500 | − | 7.03500i | −0.923741 | − | 0.923741i | ||||
\(59\) | −2.07912 | −0.270679 | −0.135339 | − | 0.990799i | \(-0.543212\pi\) | ||||
−0.135339 | + | 0.990799i | \(0.543212\pi\) | |||||||
\(60\) | −0.489528 | + | 2.18183i | −0.0631978 | + | 0.281672i | ||||
\(61\) | − | 5.55573i | − | 0.711338i | −0.934612 | − | 0.355669i | \(-0.884253\pi\) | ||
0.934612 | − | 0.355669i | \(-0.115747\pi\) | |||||||
\(62\) | 2.13613 | + | 2.13613i | 0.271289 | + | 0.271289i | ||||
\(63\) | 2.59604 | − | 0.510472i | 0.327070 | − | 0.0643134i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 1.80748 | + | 0.405538i | 0.224191 | + | 0.0503008i | ||||
\(66\) | 4.79881i | 0.590692i | ||||||||
\(67\) | −0.979056 | + | 0.979056i | −0.119611 | + | 0.119611i | −0.764379 | − | 0.644768i | \(-0.776954\pi\) |
0.644768 | + | 0.764379i | \(0.276954\pi\) | |||||||
\(68\) | −4.10651 | + | 4.10651i | −0.497988 | + | 0.497988i | ||||
\(69\) | −4.21302 | −0.507188 | ||||||||
\(70\) | −0.157074 | + | 5.91399i | −0.0187739 | + | 0.706858i | ||||
\(71\) | 5.25132 | 0.623217 | 0.311608 | − | 0.950211i | \(-0.399132\pi\) | ||||
0.311608 | + | 0.950211i | \(0.399132\pi\) | |||||||
\(72\) | −0.707107 | + | 0.707107i | −0.0833333 | + | 0.0833333i | ||||
\(73\) | 6.11519 | − | 6.11519i | 0.715728 | − | 0.715728i | −0.251999 | − | 0.967727i | \(-0.581088\pi\) |
0.967727 | + | 0.251999i | \(0.0810880\pi\) | |||||||
\(74\) | 8.63591i | 1.00390i | ||||||||
\(75\) | −1.68616 | − | 4.70711i | −0.194701 | − | 0.543530i | ||||
\(76\) | 2.36365i | 0.271129i | ||||||||
\(77\) | 2.44966 | + | 12.4579i | 0.279164 | + | 1.41971i | ||||
\(78\) | 0.585786 | + | 0.585786i | 0.0663273 | + | 0.0663273i | ||||
\(79\) | − | 5.10069i | − | 0.573872i | −0.957950 | − | 0.286936i | \(-0.907363\pi\) | ||
0.957950 | − | 0.286936i | \(-0.0926367\pi\) | |||||||
\(80\) | −1.19663 | − | 1.88893i | −0.133788 | − | 0.211189i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −7.77786 | − | 7.77786i | −0.858921 | − | 0.858921i | ||||
\(83\) | −3.22170 | + | 3.22170i | −0.353627 | + | 0.353627i | −0.861457 | − | 0.507830i | \(-0.830448\pi\) |
0.507830 | + | 0.861457i | \(0.330448\pi\) | |||||||
\(84\) | −1.47472 | + | 2.19663i | −0.160905 | + | 0.239673i | ||||
\(85\) | 2.84293 | − | 12.6709i | 0.308359 | − | 1.37435i | ||||
\(86\) | −8.12925 | −0.876599 | ||||||||
\(87\) | 7.03500 | + | 7.03500i | 0.754232 | + | 0.754232i | ||||
\(88\) | −3.39327 | − | 3.39327i | −0.361724 | − | 0.361724i | ||||
\(89\) | 11.8989 | 1.26128 | 0.630639 | − | 0.776076i | \(-0.282793\pi\) | ||||
0.630639 | + | 0.776076i | \(0.282793\pi\) | |||||||
\(90\) | 0.489528 | − | 2.18183i | 0.0516008 | − | 0.229985i | ||||
\(91\) | 1.81975 | + | 1.22170i | 0.190762 | + | 0.128069i | ||||
\(92\) | 2.97906 | − | 2.97906i | 0.310588 | − | 0.310588i | ||||
\(93\) | −2.13613 | − | 2.13613i | −0.221506 | − | 0.221506i | ||||
\(94\) | 0.514280 | 0.0530439 | ||||||||
\(95\) | −2.82843 | − | 4.46478i | −0.290191 | − | 0.458076i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 8.05595 | + | 8.05595i | 0.817958 | + | 0.817958i | 0.985812 | − | 0.167854i | \(-0.0536838\pi\) |
−0.167854 | + | 0.985812i | \(0.553684\pi\) | |||||||
\(98\) | −2.70711 | + | 6.45535i | −0.273459 | + | 0.652089i | ||||
\(99\) | − | 4.79881i | − | 0.482298i | ||||||
\(100\) | 4.52072 | + | 2.13613i | 0.452072 | + | 0.213613i | ||||
\(101\) | − | 4.89020i | − | 0.486593i | −0.969952 | − | 0.243297i | \(-0.921771\pi\) | ||
0.969952 | − | 0.243297i | \(-0.0782288\pi\) | |||||||
\(102\) | 4.10651 | − | 4.10651i | 0.406605 | − | 0.406605i | ||||
\(103\) | 1.06462 | − | 1.06462i | 0.104900 | − | 0.104900i | −0.652709 | − | 0.757609i | \(-0.726367\pi\) |
0.757609 | + | 0.652709i | \(0.226367\pi\) | |||||||
\(104\) | −0.828427 | −0.0812340 | ||||||||
\(105\) | 0.157074 | − | 5.91399i | 0.0153288 | − | 0.577147i | ||||
\(106\) | 3.34271 | 0.324672 | ||||||||
\(107\) | 2.15063 | − | 2.15063i | 0.207909 | − | 0.207909i | −0.595469 | − | 0.803378i | \(-0.703034\pi\) |
0.803378 | + | 0.595469i | \(0.203034\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | 12.8984i | 1.23545i | 0.786396 | + | 0.617723i | \(0.211945\pi\) | ||||
−0.786396 | + | 0.617723i | \(0.788055\pi\) | |||||||
\(110\) | 10.4702 | + | 2.34915i | 0.998291 | + | 0.223983i | ||||
\(111\) | − | 8.63591i | − | 0.819684i | ||||||
\(112\) | −0.510472 | − | 2.59604i | −0.0482351 | − | 0.245303i | ||||
\(113\) | −11.5853 | − | 11.5853i | −1.08986 | − | 1.08986i | −0.995542 | − | 0.0943155i | \(-0.969934\pi\) |
−0.0943155 | − | 0.995542i | \(-0.530066\pi\) | |||||||
\(114\) | − | 2.36365i | − | 0.221376i | ||||||
\(115\) | −2.06239 | + | 9.19208i | −0.192319 | + | 0.857166i | ||||
\(116\) | −9.94900 | −0.923741 | ||||||||
\(117\) | −0.585786 | − | 0.585786i | −0.0541560 | − | 0.0541560i | ||||
\(118\) | −1.47016 | + | 1.47016i | −0.135339 | + | 0.135339i | ||||
\(119\) | 8.56440 | − | 12.7569i | 0.785098 | − | 1.16943i | ||||
\(120\) | 1.19663 | + | 1.88893i | 0.109237 | + | 0.172435i | ||||
\(121\) | 12.0286 | 1.09351 | ||||||||
\(122\) | −3.92849 | − | 3.92849i | −0.355669 | − | 0.355669i | ||||
\(123\) | 7.77786 | + | 7.77786i | 0.701306 | + | 0.701306i | ||||
\(124\) | 3.02094 | 0.271289 | ||||||||
\(125\) | −11.0955 | + | 1.37465i | −0.992413 | + | 0.122953i | ||||
\(126\) | 1.47472 | − | 2.19663i | 0.131378 | − | 0.195692i | ||||
\(127\) | 0.399714 | − | 0.399714i | 0.0354689 | − | 0.0354689i | −0.689150 | − | 0.724619i | \(-0.742016\pi\) |
0.724619 | + | 0.689150i | \(0.242016\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 8.12925 | 0.715740 | ||||||||
\(130\) | 1.56484 | − | 0.991325i | 0.137246 | − | 0.0869449i | ||||
\(131\) | 22.2039i | 1.93996i | 0.243176 | + | 0.969982i | \(0.421811\pi\) | ||||
−0.243176 | + | 0.969982i | \(0.578189\pi\) | |||||||
\(132\) | 3.39327 | + | 3.39327i | 0.295346 | + | 0.295346i | ||||
\(133\) | −1.20658 | − | 6.13613i | −0.104624 | − | 0.532070i | ||||
\(134\) | 1.38459i | 0.119611i | ||||||||
\(135\) | −0.489528 | + | 2.18183i | −0.0421319 | + | 0.187782i | ||||
\(136\) | 5.80748i | 0.497988i | ||||||||
\(137\) | −5.92849 | + | 5.92849i | −0.506505 | + | 0.506505i | −0.913452 | − | 0.406947i | \(-0.866594\pi\) |
0.406947 | + | 0.913452i | \(0.366594\pi\) | |||||||
\(138\) | −2.97906 | + | 2.97906i | −0.253594 | + | 0.253594i | ||||
\(139\) | −8.46478 | −0.717973 | −0.358986 | − | 0.933343i | \(-0.616878\pi\) | ||||
−0.358986 | + | 0.933343i | \(0.616878\pi\) | |||||||
\(140\) | 4.07076 | + | 4.29289i | 0.344042 | + | 0.362816i | ||||
\(141\) | −0.514280 | −0.0433102 | ||||||||
\(142\) | 3.71324 | − | 3.71324i | 0.311608 | − | 0.311608i | ||||
\(143\) | 2.81108 | − | 2.81108i | 0.235074 | − | 0.235074i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | 18.7930 | − | 11.9053i | 1.56067 | − | 0.988683i | ||||
\(146\) | − | 8.64818i | − | 0.715728i | ||||||
\(147\) | 2.70711 | − | 6.45535i | 0.223278 | − | 0.532428i | ||||
\(148\) | 6.10651 | + | 6.10651i | 0.501952 | + | 0.501952i | ||||
\(149\) | 4.43516i | 0.363342i | 0.983359 | + | 0.181671i | \(0.0581506\pi\) | ||||
−0.983359 | + | 0.181671i | \(0.941849\pi\) | |||||||
\(150\) | −4.52072 | − | 2.13613i | −0.369116 | − | 0.174414i | ||||
\(151\) | 7.61497 | 0.619697 | 0.309849 | − | 0.950786i | \(-0.399722\pi\) | ||||
0.309849 | + | 0.950786i | \(0.399722\pi\) | |||||||
\(152\) | 1.67135 | + | 1.67135i | 0.135565 | + | 0.135565i | ||||
\(153\) | −4.10651 | + | 4.10651i | −0.331992 | + | 0.331992i | ||||
\(154\) | 10.5412 | + | 7.07689i | 0.849436 | + | 0.570272i | ||||
\(155\) | −5.70636 | + | 3.61497i | −0.458346 | + | 0.290361i | ||||
\(156\) | 0.828427 | 0.0663273 | ||||||||
\(157\) | −6.30188 | − | 6.30188i | −0.502945 | − | 0.502945i | 0.409407 | − | 0.912352i | \(-0.365736\pi\) |
−0.912352 | + | 0.409407i | \(0.865736\pi\) | |||||||
\(158\) | −3.60673 | − | 3.60673i | −0.286936 | − | 0.286936i | ||||
\(159\) | −3.34271 | −0.265094 | ||||||||
\(160\) | −2.18183 | − | 0.489528i | −0.172488 | − | 0.0387006i | ||||
\(161\) | −6.21302 | + | 9.25447i | −0.489655 | + | 0.729354i | ||||
\(162\) | −0.707107 | + | 0.707107i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | 10.8489 | + | 10.8489i | 0.849754 | + | 0.849754i | 0.990102 | − | 0.140348i | \(-0.0448222\pi\) |
−0.140348 | + | 0.990102i | \(0.544822\pi\) | |||||||
\(164\) | −10.9996 | −0.858921 | ||||||||
\(165\) | −10.4702 | − | 2.34915i | −0.815101 | − | 0.182881i | ||||
\(166\) | 4.55617i | 0.353627i | ||||||||
\(167\) | 5.63635 | + | 5.63635i | 0.436154 | + | 0.436154i | 0.890715 | − | 0.454562i | \(-0.150204\pi\) |
−0.454562 | + | 0.890715i | \(0.650204\pi\) | |||||||
\(168\) | 0.510472 | + | 2.59604i | 0.0393838 | + | 0.200289i | ||||
\(169\) | 12.3137i | 0.947208i | ||||||||
\(170\) | −6.94944 | − | 10.9699i | −0.532998 | − | 0.841356i | ||||
\(171\) | 2.36365i | 0.180753i | ||||||||
\(172\) | −5.74825 | + | 5.74825i | −0.438300 | + | 0.438300i | ||||
\(173\) | −12.6923 | + | 12.6923i | −0.964977 | + | 0.964977i | −0.999407 | − | 0.0344296i | \(-0.989039\pi\) |
0.0344296 | + | 0.999407i | \(0.489039\pi\) | |||||||
\(174\) | 9.94900 | 0.754232 | ||||||||
\(175\) | −12.8264 | − | 3.23777i | −0.969586 | − | 0.244753i | ||||
\(176\) | −4.79881 | −0.361724 | ||||||||
\(177\) | 1.47016 | − | 1.47016i | 0.110504 | − | 0.110504i | ||||
\(178\) | 8.41377 | − | 8.41377i | 0.630639 | − | 0.630639i | ||||
\(179\) | 5.72836i | 0.428158i | 0.976816 | + | 0.214079i | \(0.0686750\pi\) | ||||
−0.976816 | + | 0.214079i | \(0.931325\pi\) | |||||||
\(180\) | −1.19663 | − | 1.88893i | −0.0891919 | − | 0.140793i | ||||
\(181\) | − | 8.91220i | − | 0.662439i | −0.943554 | − | 0.331219i | \(-0.892540\pi\) | ||
0.943554 | − | 0.331219i | \(-0.107460\pi\) | |||||||
\(182\) | 2.15063 | − | 0.422889i | 0.159415 | − | 0.0313466i | ||||
\(183\) | 3.92849 | + | 3.92849i | 0.290403 | + | 0.290403i | ||||
\(184\) | − | 4.21302i | − | 0.310588i | ||||||
\(185\) | −18.8420 | − | 4.22752i | −1.38530 | − | 0.310814i | ||||
\(186\) | −3.02094 | −0.221506 | ||||||||
\(187\) | −19.7064 | − | 19.7064i | −1.44107 | − | 1.44107i | ||||
\(188\) | 0.363651 | − | 0.363651i | 0.0265220 | − | 0.0265220i | ||||
\(189\) | −1.47472 | + | 2.19663i | −0.107270 | + | 0.159782i | ||||
\(190\) | −5.15707 | − | 1.15707i | −0.374133 | − | 0.0839429i | ||||
\(191\) | −7.67824 | −0.555578 | −0.277789 | − | 0.960642i | \(-0.589602\pi\) | ||||
−0.277789 | + | 0.960642i | \(0.589602\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | −4.59762 | − | 4.59762i | −0.330944 | − | 0.330944i | 0.522001 | − | 0.852945i | \(-0.325186\pi\) |
−0.852945 | + | 0.522001i | \(0.825186\pi\) | |||||||
\(194\) | 11.3928 | 0.817958 | ||||||||
\(195\) | −1.56484 | + | 0.991325i | −0.112061 | + | 0.0709902i | ||||
\(196\) | 2.65041 | + | 6.47884i | 0.189315 | + | 0.462774i | ||||
\(197\) | −5.25132 | + | 5.25132i | −0.374141 | + | 0.374141i | −0.868983 | − | 0.494842i | \(-0.835226\pi\) |
0.494842 | + | 0.868983i | \(0.335226\pi\) | |||||||
\(198\) | −3.39327 | − | 3.39327i | −0.241149 | − | 0.241149i | ||||
\(199\) | 4.12163 | 0.292175 | 0.146087 | − | 0.989272i | \(-0.453332\pi\) | ||||
0.146087 | + | 0.989272i | \(0.453332\pi\) | |||||||
\(200\) | 4.70711 | − | 1.68616i | 0.332843 | − | 0.119230i | ||||
\(201\) | − | 1.38459i | − | 0.0976618i | ||||||
\(202\) | −3.45789 | − | 3.45789i | −0.243297 | − | 0.243297i | ||||
\(203\) | 25.8280 | − | 5.07868i | 1.81277 | − | 0.356454i | ||||
\(204\) | − | 5.80748i | − | 0.406605i | ||||||
\(205\) | 20.7774 | − | 13.1625i | 1.45116 | − | 0.919306i | ||||
\(206\) | − | 1.50560i | − | 0.104900i | ||||||
\(207\) | 2.97906 | − | 2.97906i | 0.207059 | − | 0.207059i | ||||
\(208\) | −0.585786 | + | 0.585786i | −0.0406170 | + | 0.0406170i | ||||
\(209\) | −11.3427 | −0.784591 | ||||||||
\(210\) | −4.07076 | − | 4.29289i | −0.280909 | − | 0.296238i | ||||
\(211\) | −27.6560 | −1.90392 | −0.951958 | − | 0.306229i | \(-0.900933\pi\) | ||||
−0.951958 | + | 0.306229i | \(0.900933\pi\) | |||||||
\(212\) | 2.36365 | − | 2.36365i | 0.162336 | − | 0.162336i | ||||
\(213\) | −3.71324 | + | 3.71324i | −0.254427 | + | 0.254427i | ||||
\(214\) | − | 3.04145i | − | 0.207909i | ||||||
\(215\) | 3.97949 | − | 17.7366i | 0.271399 | − | 1.20963i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −7.84249 | + | 1.54211i | −0.532383 | + | 0.104685i | ||||
\(218\) | 9.12057 | + | 9.12057i | 0.617723 | + | 0.617723i | ||||
\(219\) | 8.64818i | 0.584390i | ||||||||
\(220\) | 9.06462 | − | 5.74242i | 0.611137 | − | 0.387154i | ||||
\(221\) | −4.81108 | −0.323628 | ||||||||
\(222\) | −6.10651 | − | 6.10651i | −0.409842 | − | 0.409842i | ||||
\(223\) | 15.3271 | − | 15.3271i | 1.02638 | − | 1.02638i | 0.0267394 | − | 0.999642i | \(-0.491488\pi\) |
0.999642 | − | 0.0267394i | \(-0.00851242\pi\) | |||||||
\(224\) | −2.19663 | − | 1.47472i | −0.146769 | − | 0.0985338i | ||||
\(225\) | 4.52072 | + | 2.13613i | 0.301382 | + | 0.142409i | ||||
\(226\) | −16.3842 | −1.08986 | ||||||||
\(227\) | −18.8984 | − | 18.8984i | −1.25433 | − | 1.25433i | −0.953758 | − | 0.300575i | \(-0.902821\pi\) |
−0.300575 | − | 0.953758i | \(-0.597179\pi\) | |||||||
\(228\) | −1.67135 | − | 1.67135i | −0.110688 | − | 0.110688i | ||||
\(229\) | −13.3137 | −0.879795 | −0.439897 | − | 0.898048i | \(-0.644985\pi\) | ||||
−0.439897 | + | 0.898048i | \(0.644985\pi\) | |||||||
\(230\) | 5.04145 | + | 7.95811i | 0.332423 | + | 0.524742i | ||||
\(231\) | −10.5412 | − | 7.07689i | −0.693562 | − | 0.465625i | ||||
\(232\) | −7.03500 | + | 7.03500i | −0.461871 | + | 0.461871i | ||||
\(233\) | 7.35498 | + | 7.35498i | 0.481840 | + | 0.481840i | 0.905719 | − | 0.423879i | \(-0.139332\pi\) |
−0.423879 | + | 0.905719i | \(0.639332\pi\) | |||||||
\(234\) | −0.828427 | −0.0541560 | ||||||||
\(235\) | −0.251755 | + | 1.12207i | −0.0164227 | + | 0.0731957i | ||||
\(236\) | 2.07912i | 0.135339i | ||||||||
\(237\) | 3.60673 | + | 3.60673i | 0.234282 | + | 0.234282i | ||||
\(238\) | −2.96456 | − | 15.0765i | −0.192164 | − | 0.977261i | ||||
\(239\) | 13.0491i | 0.844074i | 0.906579 | + | 0.422037i | \(0.138685\pi\) | ||||
−0.906579 | + | 0.422037i | \(0.861315\pi\) | |||||||
\(240\) | 2.18183 | + | 0.489528i | 0.140836 | + | 0.0315989i | ||||
\(241\) | 24.4542i | 1.57523i | 0.616167 | + | 0.787616i | \(0.288685\pi\) | ||||
−0.616167 | + | 0.787616i | \(0.711315\pi\) | |||||||
\(242\) | 8.50548 | − | 8.50548i | 0.546753 | − | 0.546753i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −5.55573 | −0.355669 | ||||||||
\(245\) | −12.7592 | − | 9.06651i | −0.815158 | − | 0.579238i | ||||
\(246\) | 10.9996 | 0.701306 | ||||||||
\(247\) | −1.38459 | + | 1.38459i | −0.0880996 | + | 0.0880996i | ||||
\(248\) | 2.13613 | − | 2.13613i | 0.135644 | − | 0.135644i | ||||
\(249\) | − | 4.55617i | − | 0.288735i | ||||||
\(250\) | −6.87368 | + | 8.81774i | −0.434730 | + | 0.557683i | ||||
\(251\) | − | 4.32326i | − | 0.272882i | −0.990648 | − | 0.136441i | \(-0.956434\pi\) | ||
0.990648 | − | 0.136441i | \(-0.0435664\pi\) | |||||||
\(252\) | −0.510472 | − | 2.59604i | −0.0321567 | − | 0.163535i | ||||
\(253\) | 14.2959 | + | 14.2959i | 0.898777 | + | 0.898777i | ||||
\(254\) | − | 0.565281i | − | 0.0354689i | ||||||
\(255\) | 6.94944 | + | 10.9699i | 0.435191 | + | 0.686964i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.06418 | + | 5.06418i | 0.315895 | + | 0.315895i | 0.847188 | − | 0.531293i | \(-0.178294\pi\) |
−0.531293 | + | 0.847188i | \(0.678294\pi\) | |||||||
\(258\) | 5.74825 | − | 5.74825i | 0.357870 | − | 0.357870i | ||||
\(259\) | −18.9699 | − | 12.7355i | −1.17873 | − | 0.791348i | ||||
\(260\) | 0.405538 | − | 1.80748i | 0.0251504 | − | 0.112095i | ||||
\(261\) | −9.94900 | −0.615828 | ||||||||
\(262\) | 15.7005 | + | 15.7005i | 0.969982 | + | 0.969982i | ||||
\(263\) | −4.17113 | − | 4.17113i | −0.257203 | − | 0.257203i | 0.566712 | − | 0.823916i | \(-0.308215\pi\) |
−0.823916 | + | 0.566712i | \(0.808215\pi\) | |||||||
\(264\) | 4.79881 | 0.295346 | ||||||||
\(265\) | −1.63635 | + | 7.29320i | −0.100520 | + | 0.448018i | ||||
\(266\) | −5.19208 | − | 3.48572i | −0.318347 | − | 0.213723i | ||||
\(267\) | −8.41377 | + | 8.41377i | −0.514915 | + | 0.514915i | ||||
\(268\) | 0.979056 | + | 0.979056i | 0.0598054 | + | 0.0598054i | ||||
\(269\) | 24.7484 | 1.50894 | 0.754469 | − | 0.656336i | \(-0.227894\pi\) | ||||
0.754469 | + | 0.656336i | \(0.227894\pi\) | |||||||
\(270\) | 1.19663 | + | 1.88893i | 0.0728249 | + | 0.114957i | ||||
\(271\) | 21.9960i | 1.33616i | 0.744089 | + | 0.668080i | \(0.232884\pi\) | ||||
−0.744089 | + | 0.668080i | \(0.767116\pi\) | |||||||
\(272\) | 4.10651 | + | 4.10651i | 0.248994 | + | 0.248994i | ||||
\(273\) | −2.15063 | + | 0.422889i | −0.130162 | + | 0.0255944i | ||||
\(274\) | 8.38416i | 0.506505i | ||||||||
\(275\) | −10.2509 | + | 21.6941i | −0.618151 | + | 1.30820i | ||||
\(276\) | 4.21302i | 0.253594i | ||||||||
\(277\) | 12.0646 | − | 12.0646i | 0.724893 | − | 0.724893i | −0.244705 | − | 0.969598i | \(-0.578691\pi\) |
0.969598 | + | 0.244705i | \(0.0786910\pi\) | |||||||
\(278\) | −5.98550 | + | 5.98550i | −0.358986 | + | 0.358986i | ||||
\(279\) | 3.02094 | 0.180859 | ||||||||
\(280\) | 5.91399 | + | 0.157074i | 0.353429 | + | 0.00938694i | ||||
\(281\) | 14.3668 | 0.857052 | 0.428526 | − | 0.903530i | \(-0.359033\pi\) | ||||
0.428526 | + | 0.903530i | \(0.359033\pi\) | |||||||
\(282\) | −0.363651 | + | 0.363651i | −0.0216551 | + | 0.0216551i | ||||
\(283\) | −11.0833 | + | 11.0833i | −0.658836 | + | 0.658836i | −0.955105 | − | 0.296269i | \(-0.904258\pi\) |
0.296269 | + | 0.955105i | \(0.404258\pi\) | |||||||
\(284\) | − | 5.25132i | − | 0.311608i | ||||||
\(285\) | 5.15707 | + | 1.15707i | 0.305479 | + | 0.0685391i | ||||
\(286\) | − | 3.97546i | − | 0.235074i | ||||||
\(287\) | 28.5553 | − | 5.61497i | 1.68557 | − | 0.331441i | ||||
\(288\) | 0.707107 | + | 0.707107i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | 16.7269i | 0.983933i | ||||||||
\(290\) | 4.87031 | − | 21.7070i | 0.285995 | − | 1.27468i | ||||
\(291\) | −11.3928 | −0.667860 | ||||||||
\(292\) | −6.11519 | − | 6.11519i | −0.357864 | − | 0.357864i | ||||
\(293\) | 6.35827 | − | 6.35827i | 0.371454 | − | 0.371454i | −0.496553 | − | 0.868007i | \(-0.665401\pi\) |
0.868007 | + | 0.496553i | \(0.165401\pi\) | |||||||
\(294\) | −2.65041 | − | 6.47884i | −0.154575 | − | 0.377853i | ||||
\(295\) | −2.48795 | − | 3.92732i | −0.144854 | − | 0.228658i | ||||
\(296\) | 8.63591 | 0.501952 | ||||||||
\(297\) | 3.39327 | + | 3.39327i | 0.196897 | + | 0.196897i | ||||
\(298\) | 3.13613 | + | 3.13613i | 0.181671 | + | 0.181671i | ||||
\(299\) | 3.49018 | 0.201842 | ||||||||
\(300\) | −4.70711 | + | 1.68616i | −0.271765 | + | 0.0973507i | ||||
\(301\) | 11.9884 | − | 17.8570i | 0.690997 | − | 1.02926i | ||||
\(302\) | 5.38459 | − | 5.38459i | 0.309849 | − | 0.309849i | ||||
\(303\) | 3.45789 | + | 3.45789i | 0.198651 | + | 0.198651i | ||||
\(304\) | 2.36365 | 0.135565 | ||||||||
\(305\) | 10.4944 | − | 6.64818i | 0.600907 | − | 0.380674i | ||||
\(306\) | 5.80748i | 0.331992i | ||||||||
\(307\) | 16.8663 | + | 16.8663i | 0.962610 | + | 0.962610i | 0.999326 | − | 0.0367161i | \(-0.0116897\pi\) |
−0.0367161 | + | 0.999326i | \(0.511690\pi\) | |||||||
\(308\) | 12.4579 | − | 2.44966i | 0.709854 | − | 0.139582i | ||||
\(309\) | 1.50560i | 0.0856509i | ||||||||
\(310\) | −1.47884 | + | 6.59117i | −0.0839923 | + | 0.374353i | ||||
\(311\) | − | 0.0592379i | − | 0.00335907i | −0.999999 | − | 0.00167954i | \(-0.999465\pi\) | ||
0.999999 | − | 0.00167954i | \(-0.000534613\pi\) | |||||||
\(312\) | 0.585786 | − | 0.585786i | 0.0331636 | − | 0.0331636i | ||||
\(313\) | −0.458332 | + | 0.458332i | −0.0259064 | + | 0.0259064i | −0.719941 | − | 0.694035i | \(-0.755831\pi\) |
0.694035 | + | 0.719941i | \(0.255831\pi\) | |||||||
\(314\) | −8.91220 | −0.502945 | ||||||||
\(315\) | 4.07076 | + | 4.29289i | 0.229361 | + | 0.241877i | ||||
\(316\) | −5.10069 | −0.286936 | ||||||||
\(317\) | 13.1130 | − | 13.1130i | 0.736497 | − | 0.736497i | −0.235401 | − | 0.971898i | \(-0.575640\pi\) |
0.971898 | + | 0.235401i | \(0.0756404\pi\) | |||||||
\(318\) | −2.36365 | + | 2.36365i | −0.132547 | + | 0.132547i | ||||
\(319\) | − | 47.7433i | − | 2.67311i | ||||||
\(320\) | −1.88893 | + | 1.19663i | −0.105595 | + | 0.0668939i | ||||
\(321\) | 3.04145i | 0.169757i | ||||||||
\(322\) | 2.15063 | + | 10.9372i | 0.119850 | + | 0.609505i | ||||
\(323\) | 9.70636 | + | 9.70636i | 0.540076 | + | 0.540076i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | 1.39686 | + | 3.89949i | 0.0774840 | + | 0.216305i | ||||
\(326\) | 15.3427 | 0.849754 | ||||||||
\(327\) | −9.12057 | − | 9.12057i | −0.504369 | − | 0.504369i | ||||
\(328\) | −7.77786 | + | 7.77786i | −0.429461 | + | 0.429461i | ||||
\(329\) | −0.758418 | + | 1.12969i | −0.0418130 | + | 0.0622816i | ||||
\(330\) | −9.06462 | + | 5.74242i | −0.498991 | + | 0.316110i | ||||
\(331\) | −25.1288 | −1.38120 | −0.690602 | − | 0.723235i | \(-0.742654\pi\) | ||||
−0.690602 | + | 0.723235i | \(0.742654\pi\) | |||||||
\(332\) | 3.22170 | + | 3.22170i | 0.176814 | + | 0.176814i | ||||
\(333\) | 6.10651 | + | 6.10651i | 0.334635 | + | 0.334635i | ||||
\(334\) | 7.97100 | 0.436154 | ||||||||
\(335\) | −3.02094 | − | 0.677798i | −0.165052 | − | 0.0370321i | ||||
\(336\) | 2.19663 | + | 1.47472i | 0.119836 | + | 0.0804525i | ||||
\(337\) | 16.5976 | − | 16.5976i | 0.904130 | − | 0.904130i | −0.0916605 | − | 0.995790i | \(-0.529217\pi\) |
0.995790 | + | 0.0916605i | \(0.0292175\pi\) | |||||||
\(338\) | 8.70711 | + | 8.70711i | 0.473604 | + | 0.473604i | ||||
\(339\) | 16.3842 | 0.889865 | ||||||||
\(340\) | −12.6709 | − | 2.84293i | −0.687177 | − | 0.154179i | ||||
\(341\) | 14.4969i | 0.785053i | ||||||||
\(342\) | 1.67135 | + | 1.67135i | 0.0903764 | + | 0.0903764i | ||||
\(343\) | −10.1878 | − | 15.4664i | −0.550091 | − | 0.835105i | ||||
\(344\) | 8.12925i | 0.438300i | ||||||||
\(345\) | −5.04145 | − | 7.95811i | −0.271422 | − | 0.428450i | ||||
\(346\) | 17.9496i | 0.964977i | ||||||||
\(347\) | 14.4214 | − | 14.4214i | 0.774181 | − | 0.774181i | −0.204654 | − | 0.978834i | \(-0.565607\pi\) |
0.978834 | + | 0.204654i | \(0.0656068\pi\) | |||||||
\(348\) | 7.03500 | − | 7.03500i | 0.377116 | − | 0.377116i | ||||
\(349\) | 28.6672 | 1.53452 | 0.767260 | − | 0.641337i | \(-0.221620\pi\) | ||||
0.767260 | + | 0.641337i | \(0.221620\pi\) | |||||||
\(350\) | −11.3591 | + | 6.78019i | −0.607169 | + | 0.362416i | ||||
\(351\) | 0.828427 | 0.0442182 | ||||||||
\(352\) | −3.39327 | + | 3.39327i | −0.180862 | + | 0.180862i | ||||
\(353\) | −5.06506 | + | 5.06506i | −0.269586 | + | 0.269586i | −0.828933 | − | 0.559347i | \(-0.811052\pi\) |
0.559347 | + | 0.828933i | \(0.311052\pi\) | |||||||
\(354\) | − | 2.07912i | − | 0.110504i | ||||||
\(355\) | 6.28391 | + | 9.91938i | 0.333515 | + | 0.526466i | ||||
\(356\) | − | 11.8989i | − | 0.630639i | ||||||
\(357\) | 2.96456 | + | 15.0765i | 0.156901 | + | 0.797931i | ||||
\(358\) | 4.05056 | + | 4.05056i | 0.214079 | + | 0.214079i | ||||
\(359\) | − | 8.46478i | − | 0.446754i | −0.974732 | − | 0.223377i | \(-0.928292\pi\) | ||
0.974732 | − | 0.223377i | \(-0.0717081\pi\) | |||||||
\(360\) | −2.18183 | − | 0.489528i | −0.114992 | − | 0.0258004i | ||||
\(361\) | −13.4132 | −0.705956 | ||||||||
\(362\) | −6.30188 | − | 6.30188i | −0.331219 | − | 0.331219i | ||||
\(363\) | −8.50548 | + | 8.50548i | −0.446422 | + | 0.446422i | ||||
\(364\) | 1.22170 | − | 1.81975i | 0.0640343 | − | 0.0953809i | ||||
\(365\) | 18.8688 | + | 4.23353i | 0.987639 | + | 0.221593i | ||||
\(366\) | 5.55573 | 0.290403 | ||||||||
\(367\) | −18.1685 | − | 18.1685i | −0.948386 | − | 0.948386i | 0.0503457 | − | 0.998732i | \(-0.483968\pi\) |
−0.998732 | + | 0.0503457i | \(0.983968\pi\) | |||||||
\(368\) | −2.97906 | − | 2.97906i | −0.155294 | − | 0.155294i | ||||
\(369\) | −10.9996 | −0.572614 | ||||||||
\(370\) | −16.3126 | + | 10.3340i | −0.848054 | + | 0.537241i | ||||
\(371\) | −4.92955 | + | 7.34271i | −0.255930 | + | 0.381214i | ||||
\(372\) | −2.13613 | + | 2.13613i | −0.110753 | + | 0.110753i | ||||
\(373\) | −15.4492 | − | 15.4492i | −0.799930 | − | 0.799930i | 0.183154 | − | 0.983084i | \(-0.441369\pi\) |
−0.983084 | + | 0.183154i | \(0.941369\pi\) | |||||||
\(374\) | −27.8690 | −1.44107 | ||||||||
\(375\) | 6.87368 | − | 8.81774i | 0.354956 | − | 0.455346i | ||||
\(376\) | − | 0.514280i | − | 0.0265220i | ||||||
\(377\) | −5.82799 | − | 5.82799i | −0.300157 | − | 0.300157i | ||||
\(378\) | 0.510472 | + | 2.59604i | 0.0262558 | + | 0.133526i | ||||
\(379\) | 32.3833i | 1.66342i | 0.555212 | + | 0.831709i | \(0.312637\pi\) | ||||
−0.555212 | + | 0.831709i | \(0.687363\pi\) | |||||||
\(380\) | −4.46478 | + | 2.82843i | −0.229038 | + | 0.145095i | ||||
\(381\) | 0.565281i | 0.0289602i | ||||||||
\(382\) | −5.42933 | + | 5.42933i | −0.277789 | + | 0.277789i | ||||
\(383\) | 16.1916 | − | 16.1916i | 0.827354 | − | 0.827354i | −0.159796 | − | 0.987150i | \(-0.551084\pi\) |
0.987150 | + | 0.159796i | \(0.0510836\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −20.6008 | + | 19.5348i | −1.04991 | + | 0.995585i | ||||
\(386\) | −6.50201 | −0.330944 | ||||||||
\(387\) | −5.74825 | + | 5.74825i | −0.292200 | + | 0.292200i | ||||
\(388\) | 8.05595 | − | 8.05595i | 0.408979 | − | 0.408979i | ||||
\(389\) | 12.0091i | 0.608886i | 0.952531 | + | 0.304443i | \(0.0984704\pi\) | ||||
−0.952531 | + | 0.304443i | \(0.901530\pi\) | |||||||
\(390\) | −0.405538 | + | 1.80748i | −0.0205352 | + | 0.0915255i | ||||
\(391\) | − | 24.4671i | − | 1.23735i | ||||||
\(392\) | 6.45535 | + | 2.70711i | 0.326045 | + | 0.136730i | ||||
\(393\) | −15.7005 | − | 15.7005i | −0.791987 | − | 0.791987i | ||||
\(394\) | 7.42648i | 0.374141i | ||||||||
\(395\) | 9.63485 | − | 6.10366i | 0.484782 | − | 0.307108i | ||||
\(396\) | −4.79881 | −0.241149 | ||||||||
\(397\) | 2.62680 | + | 2.62680i | 0.131835 | + | 0.131835i | 0.769945 | − | 0.638110i | \(-0.220284\pi\) |
−0.638110 | + | 0.769945i | \(0.720284\pi\) | |||||||
\(398\) | 2.91443 | − | 2.91443i | 0.146087 | − | 0.146087i | ||||
\(399\) | 5.19208 | + | 3.48572i | 0.259929 | + | 0.174504i | ||||
\(400\) | 2.13613 | − | 4.52072i | 0.106806 | − | 0.226036i | ||||
\(401\) | 19.7571 | 0.986623 | 0.493311 | − | 0.869853i | \(-0.335786\pi\) | ||||
0.493311 | + | 0.869853i | \(0.335786\pi\) | |||||||
\(402\) | −0.979056 | − | 0.979056i | −0.0488309 | − | 0.0488309i | ||||
\(403\) | 1.76963 | + | 1.76963i | 0.0881514 | + | 0.0881514i | ||||
\(404\) | −4.89020 | −0.243297 | ||||||||
\(405\) | −1.19663 | − | 1.88893i | −0.0594613 | − | 0.0938618i | ||||
\(406\) | 14.6720 | − | 21.8543i | 0.728158 | − | 1.08461i | ||||
\(407\) | −29.3040 | + | 29.3040i | −1.45254 | + | 1.45254i | ||||
\(408\) | −4.10651 | − | 4.10651i | −0.203303 | − | 0.203303i | ||||
\(409\) | 15.3846 | 0.760719 | 0.380360 | − | 0.924839i | \(-0.375800\pi\) | ||||
0.380360 | + | 0.924839i | \(0.375800\pi\) | |||||||
\(410\) | 5.38459 | − | 23.9991i | 0.265926 | − | 1.18523i | ||||
\(411\) | − | 8.38416i | − | 0.413560i | ||||||
\(412\) | −1.06462 | − | 1.06462i | −0.0524502 | − | 0.0524502i | ||||
\(413\) | −1.06133 | − | 5.39748i | −0.0522248 | − | 0.265593i | ||||
\(414\) | − | 4.21302i | − | 0.207059i | ||||||
\(415\) | −9.94076 | − | 2.23037i | −0.487973 | − | 0.109485i | ||||
\(416\) | 0.828427i | 0.0406170i | ||||||||
\(417\) | 5.98550 | − | 5.98550i | 0.293111 | − | 0.293111i | ||||
\(418\) | −8.02051 | + | 8.02051i | −0.392296 | + | 0.392296i | ||||
\(419\) | −28.0782 | −1.37171 | −0.685856 | − | 0.727737i | \(-0.740572\pi\) | ||||
−0.685856 | + | 0.727737i | \(0.740572\pi\) | |||||||
\(420\) | −5.91399 | − | 0.157074i | −0.288573 | − | 0.00766441i | ||||
\(421\) | 11.4836 | 0.559677 | 0.279838 | − | 0.960047i | \(-0.409719\pi\) | ||||
0.279838 | + | 0.960047i | \(0.409719\pi\) | |||||||
\(422\) | −19.5557 | + | 19.5557i | −0.951958 | + | 0.951958i | ||||
\(423\) | 0.363651 | − | 0.363651i | 0.0176813 | − | 0.0176813i | ||||
\(424\) | − | 3.34271i | − | 0.162336i | ||||||
\(425\) | 27.3364 | − | 9.79236i | 1.32601 | − | 0.474999i | ||||
\(426\) | 5.25132i | 0.254427i | ||||||||
\(427\) | 14.4229 | − | 2.83604i | 0.697973 | − | 0.137246i | ||||
\(428\) | −2.15063 | − | 2.15063i | −0.103955 | − | 0.103955i | ||||
\(429\) | 3.97546i | 0.191937i | ||||||||
\(430\) | −9.72774 | − | 15.3556i | −0.469113 | − | 0.740513i | ||||
\(431\) | 11.3330 | 0.545890 | 0.272945 | − | 0.962030i | \(-0.412002\pi\) | ||||
0.272945 | + | 0.962030i | \(0.412002\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | −4.91337 | + | 4.91337i | −0.236122 | + | 0.236122i | −0.815242 | − | 0.579120i | \(-0.803396\pi\) |
0.579120 | + | 0.815242i | \(0.303396\pi\) | |||||||
\(434\) | −4.45504 | + | 6.63591i | −0.213849 | + | 0.318534i | ||||
\(435\) | −4.87031 | + | 21.7070i | −0.233514 | + | 1.04077i | ||||
\(436\) | 12.8984 | 0.617723 | ||||||||
\(437\) | −7.04145 | − | 7.04145i | −0.336838 | − | 0.336838i | ||||
\(438\) | 6.11519 | + | 6.11519i | 0.292195 | + | 0.292195i | ||||
\(439\) | 22.7723 | 1.08686 | 0.543432 | − | 0.839453i | \(-0.317124\pi\) | ||||
0.543432 | + | 0.839453i | \(0.317124\pi\) | |||||||
\(440\) | 2.34915 | − | 10.4702i | 0.111991 | − | 0.499145i | ||||
\(441\) | 2.65041 | + | 6.47884i | 0.126210 | + | 0.308516i | ||||
\(442\) | −3.40194 | + | 3.40194i | −0.161814 | + | 0.161814i | ||||
\(443\) | −25.8189 | − | 25.8189i | −1.22669 | − | 1.22669i | −0.965208 | − | 0.261484i | \(-0.915788\pi\) |
−0.261484 | − | 0.965208i | \(-0.584212\pi\) | |||||||
\(444\) | −8.63591 | −0.409842 | ||||||||
\(445\) | 14.2386 | + | 22.4762i | 0.674975 | + | 1.06547i | ||||
\(446\) | − | 21.6759i | − | 1.02638i | ||||||
\(447\) | −3.13613 | − | 3.13613i | −0.148334 | − | 0.148334i | ||||
\(448\) | −2.59604 | + | 0.510472i | −0.122651 | + | 0.0241175i | ||||
\(449\) | − | 9.55573i | − | 0.450963i | −0.974247 | − | 0.225481i | \(-0.927605\pi\) | ||
0.974247 | − | 0.225481i | \(-0.0723955\pi\) | |||||||
\(450\) | 4.70711 | − | 1.68616i | 0.221895 | − | 0.0794865i | ||||
\(451\) | − | 52.7848i | − | 2.48554i | ||||||
\(452\) | −11.5853 | + | 11.5853i | −0.544929 | + | 0.544929i | ||||
\(453\) | −5.38459 | + | 5.38459i | −0.252990 | + | 0.252990i | ||||
\(454\) | −26.7264 | −1.25433 | ||||||||
\(455\) | −0.130124 | + | 4.89931i | −0.00610031 | + | 0.229683i | ||||
\(456\) | −2.36365 | −0.110688 | ||||||||
\(457\) | −16.6569 | + | 16.6569i | −0.779175 | + | 0.779175i | −0.979690 | − | 0.200516i | \(-0.935738\pi\) |
0.200516 | + | 0.979690i | \(0.435738\pi\) | |||||||
\(458\) | −9.41421 | + | 9.41421i | −0.439897 | + | 0.439897i | ||||
\(459\) | − | 5.80748i | − | 0.271070i | ||||||
\(460\) | 9.19208 | + | 2.06239i | 0.428583 | + | 0.0961596i | ||||
\(461\) | 24.4762i | 1.13997i | 0.821656 | + | 0.569984i | \(0.193051\pi\) | ||||
−0.821656 | + | 0.569984i | \(0.806949\pi\) | |||||||
\(462\) | −12.4579 | + | 2.44966i | −0.579594 | + | 0.113968i | ||||
\(463\) | 6.83022 | + | 6.83022i | 0.317427 | + | 0.317427i | 0.847778 | − | 0.530351i | \(-0.177940\pi\) |
−0.530351 | + | 0.847778i | \(0.677940\pi\) | |||||||
\(464\) | 9.94900i | 0.461871i | ||||||||
\(465\) | 1.47884 | − | 6.59117i | 0.0685794 | − | 0.305658i | ||||
\(466\) | 10.4015 | 0.481840 | ||||||||
\(467\) | −20.2503 | − | 20.2503i | −0.937070 | − | 0.937070i | 0.0610637 | − | 0.998134i | \(-0.480551\pi\) |
−0.998134 | + | 0.0610637i | \(0.980551\pi\) | |||||||
\(468\) | −0.585786 | + | 0.585786i | −0.0270780 | + | 0.0270780i | ||||
\(469\) | −3.04145 | − | 2.04189i | −0.140441 | − | 0.0942856i | ||||
\(470\) | 0.615405 | + | 0.971440i | 0.0283865 | + | 0.0448092i | ||||
\(471\) | 8.91220 | 0.410653 | ||||||||
\(472\) | 1.47016 | + | 1.47016i | 0.0676697 | + | 0.0676697i | ||||
\(473\) | −27.5847 | − | 27.5847i | −1.26835 | − | 1.26835i | ||||
\(474\) | 5.10069 | 0.234282 | ||||||||
\(475\) | 5.04907 | − | 10.6854i | 0.231667 | − | 0.490280i | ||||
\(476\) | −12.7569 | − | 8.56440i | −0.584713 | − | 0.392549i | ||||
\(477\) | 2.36365 | − | 2.36365i | 0.108224 | − | 0.108224i | ||||
\(478\) | 9.22708 | + | 9.22708i | 0.422037 | + | 0.422037i | ||||
\(479\) | 6.82843 | 0.311999 | 0.155999 | − | 0.987757i | \(-0.450140\pi\) | ||||
0.155999 | + | 0.987757i | \(0.450140\pi\) | |||||||
\(480\) | 1.88893 | − | 1.19663i | 0.0862176 | − | 0.0546187i | ||||
\(481\) | 7.15422i | 0.326204i | ||||||||
\(482\) | 17.2917 | + | 17.2917i | 0.787616 | + | 0.787616i | ||||
\(483\) | −2.15063 | − | 10.9372i | −0.0978570 | − | 0.497658i | ||||
\(484\) | − | 12.0286i | − | 0.546753i | ||||||
\(485\) | −5.57711 | + | 24.8572i | −0.253244 | + | 1.12871i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 0.327587 | − | 0.327587i | 0.0148444 | − | 0.0148444i | −0.699646 | − | 0.714490i | \(-0.746659\pi\) |
0.714490 | + | 0.699646i | \(0.246659\pi\) | |||||||
\(488\) | −3.92849 | + | 3.92849i | −0.177835 | + | 0.177835i | ||||
\(489\) | −15.3427 | −0.693821 | ||||||||
\(490\) | −15.4331 | + | 2.61116i | −0.697198 | + | 0.117960i | ||||
\(491\) | 3.38521 | 0.152773 | 0.0763863 | − | 0.997078i | \(-0.475662\pi\) | ||||
0.0763863 | + | 0.997078i | \(0.475662\pi\) | |||||||
\(492\) | 7.77786 | − | 7.77786i | 0.350653 | − | 0.350653i | ||||
\(493\) | −40.8557 | + | 40.8557i | −1.84005 | + | 1.84005i | ||||
\(494\) | 1.95811i | 0.0880996i | ||||||||
\(495\) | 9.06462 | − | 5.74242i | 0.407425 | − | 0.258103i | ||||
\(496\) | − | 3.02094i | − | 0.135644i | ||||||
\(497\) | 2.68065 | + | 13.6326i | 0.120244 | + | 0.611507i | ||||
\(498\) | −3.22170 | − | 3.22170i | −0.144368 | − | 0.144368i | ||||
\(499\) | 4.17771i | 0.187020i | 0.995618 | + | 0.0935101i | \(0.0298087\pi\) | ||||
−0.995618 | + | 0.0935101i | \(0.970191\pi\) | |||||||
\(500\) | 1.37465 | + | 11.0955i | 0.0614763 | + | 0.496206i | ||||
\(501\) | −7.97100 | −0.356118 | ||||||||
\(502\) | −3.05701 | − | 3.05701i | −0.136441 | − | 0.136441i | ||||
\(503\) | 8.57667 | − | 8.57667i | 0.382415 | − | 0.382415i | −0.489557 | − | 0.871972i | \(-0.662841\pi\) |
0.871972 | + | 0.489557i | \(0.162841\pi\) | |||||||
\(504\) | −2.19663 | − | 1.47472i | −0.0978459 | − | 0.0656892i | ||||
\(505\) | 9.23726 | − | 5.85178i | 0.411052 | − | 0.260401i | ||||
\(506\) | 20.2175 | 0.898777 | ||||||||
\(507\) | −8.70711 | − | 8.70711i | −0.386696 | − | 0.386696i | ||||
\(508\) | −0.399714 | − | 0.399714i | −0.0177345 | − | 0.0177345i | ||||
\(509\) | −3.29829 | −0.146194 | −0.0730970 | − | 0.997325i | \(-0.523288\pi\) | ||||
−0.0730970 | + | 0.997325i | \(0.523288\pi\) | |||||||
\(510\) | 12.6709 | + | 2.84293i | 0.561078 | + | 0.125887i | ||||
\(511\) | 18.9969 | + | 12.7536i | 0.840373 | + | 0.564187i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −1.67135 | − | 1.67135i | −0.0737921 | − | 0.0737921i | ||||
\(514\) | 7.16184 | 0.315895 | ||||||||
\(515\) | 3.28497 | + | 0.737036i | 0.144753 | + | 0.0324777i | ||||
\(516\) | − | 8.12925i | − | 0.357870i | ||||||
\(517\) | 1.74509 | + | 1.74509i | 0.0767490 | + | 0.0767490i | ||||
\(518\) | −22.4192 | + | 4.40839i | −0.985041 | + | 0.193694i | ||||
\(519\) | − | 17.9496i | − | 0.787901i | ||||||
\(520\) | −0.991325 | − | 1.56484i | −0.0434725 | − | 0.0686229i | ||||
\(521\) | − | 15.6386i | − | 0.685141i | −0.939492 | − | 0.342570i | \(-0.888702\pi\) | ||
0.939492 | − | 0.342570i | \(-0.111298\pi\) | |||||||
\(522\) | −7.03500 | + | 7.03500i | −0.307914 | + | 0.307914i | ||||
\(523\) | −25.2794 | + | 25.2794i | −1.10539 | + | 1.10539i | −0.111644 | + | 0.993748i | \(0.535612\pi\) |
−0.993748 | + | 0.111644i | \(0.964388\pi\) | |||||||
\(524\) | 22.2039 | 0.969982 | ||||||||
\(525\) | 11.3591 | − | 6.78019i | 0.495752 | − | 0.295912i | ||||
\(526\) | −5.89887 | −0.257203 | ||||||||
\(527\) | 12.4055 | − | 12.4055i | 0.540394 | − | 0.540394i | ||||
\(528\) | 3.39327 | − | 3.39327i | 0.147673 | − | 0.147673i | ||||
\(529\) | − | 5.25045i | − | 0.228280i | ||||||
\(530\) | 4.00000 | + | 6.31415i | 0.173749 | + | 0.274269i | ||||
\(531\) | 2.07912i | 0.0902262i | ||||||||
\(532\) | −6.13613 | + | 1.20658i | −0.266035 | + | 0.0523118i | ||||
\(533\) | −6.44339 | − | 6.44339i | −0.279094 | − | 0.279094i | ||||
\(534\) | 11.8989i | 0.514915i | ||||||||
\(535\) | 6.63591 | + | 1.48887i | 0.286895 | + | 0.0643697i | ||||
\(536\) | 1.38459 | 0.0598054 | ||||||||
\(537\) | −4.05056 | − | 4.05056i | −0.174795 | − | 0.174795i | ||||
\(538\) | 17.4998 | − | 17.4998i | 0.754469 | − | 0.754469i | ||||
\(539\) | −31.0907 | + | 12.7188i | −1.33917 | + | 0.547838i | ||||
\(540\) | 2.18183 | + | 0.489528i | 0.0938908 | + | 0.0210659i | ||||
\(541\) | −2.70276 | −0.116201 | −0.0581005 | − | 0.998311i | \(-0.518504\pi\) | ||||
−0.0581005 | + | 0.998311i | \(0.518504\pi\) | |||||||
\(542\) | 15.5535 | + | 15.5535i | 0.668080 | + | 0.668080i | ||||
\(543\) | 6.30188 | + | 6.30188i | 0.270439 | + | 0.270439i | ||||
\(544\) | 5.80748 | 0.248994 | ||||||||
\(545\) | −24.3643 | + | 15.4347i | −1.04365 | + | 0.661151i | ||||
\(546\) | −1.22170 | + | 1.81975i | −0.0522838 | + | 0.0778782i | ||||
\(547\) | 1.65370 | − | 1.65370i | 0.0707071 | − | 0.0707071i | −0.670869 | − | 0.741576i | \(-0.734079\pi\) |
0.741576 | + | 0.670869i | \(0.234079\pi\) | |||||||
\(548\) | 5.92849 | + | 5.92849i | 0.253253 | + | 0.253253i | ||||
\(549\) | −5.55573 | −0.237113 | ||||||||
\(550\) | 8.09157 | + | 22.5885i | 0.345026 | + | 0.963177i | ||||
\(551\) | 23.5160i | 1.00181i | ||||||||
\(552\) | 2.97906 | + | 2.97906i | 0.126797 | + | 0.126797i | ||||
\(553\) | 13.2416 | − | 2.60376i | 0.563089 | − | 0.110723i | ||||
\(554\) | − | 17.0620i | − | 0.724893i | ||||||
\(555\) | 16.3126 | − | 10.3340i | 0.692433 | − | 0.438655i | ||||
\(556\) | 8.46478i | 0.358986i | ||||||||
\(557\) | −27.6462 | + | 27.6462i | −1.17141 | + | 1.17141i | −0.189535 | + | 0.981874i | \(0.560698\pi\) |
−0.981874 | + | 0.189535i | \(0.939302\pi\) | |||||||
\(558\) | 2.13613 | − | 2.13613i | 0.0904296 | − | 0.0904296i | ||||
\(559\) | −6.73449 | −0.284839 | ||||||||
\(560\) | 4.29289 | − | 4.07076i | 0.181408 | − | 0.172021i | ||||
\(561\) | 27.8690 | 1.17663 | ||||||||
\(562\) | 10.1589 | − | 10.1589i | 0.428526 | − | 0.428526i | ||||
\(563\) | −3.25447 | + | 3.25447i | −0.137160 | + | 0.137160i | −0.772353 | − | 0.635193i | \(-0.780920\pi\) |
0.635193 | + | 0.772353i | \(0.280920\pi\) | |||||||
\(564\) | 0.514280i | 0.0216551i | ||||||||
\(565\) | 8.02051 | − | 35.7474i | 0.337425 | − | 1.50390i | ||||
\(566\) | 15.6742i | 0.658836i | ||||||||
\(567\) | −0.510472 | − | 2.59604i | −0.0214378 | − | 0.109023i | ||||
\(568\) | −3.71324 | − | 3.71324i | −0.155804 | − | 0.155804i | ||||
\(569\) | − | 24.2411i | − | 1.01624i | −0.861286 | − | 0.508121i | \(-0.830340\pi\) | ||
0.861286 | − | 0.508121i | \(-0.169660\pi\) | |||||||
\(570\) | 4.46478 | − | 2.82843i | 0.187009 | − | 0.118470i | ||||
\(571\) | 17.3801 | 0.727336 | 0.363668 | − | 0.931529i | \(-0.381524\pi\) | ||||
0.363668 | + | 0.931529i | \(0.381524\pi\) | |||||||
\(572\) | −2.81108 | − | 2.81108i | −0.117537 | − | 0.117537i | ||||
\(573\) | 5.42933 | − | 5.42933i | 0.226814 | − | 0.226814i | ||||
\(574\) | 16.2213 | − | 24.1620i | 0.677062 | − | 1.00850i | ||||
\(575\) | −19.8311 | + | 7.10384i | −0.827016 | + | 0.296251i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 22.7961 | + | 22.7961i | 0.949016 | + | 0.949016i | 0.998762 | − | 0.0497462i | \(-0.0158413\pi\) |
−0.0497462 | + | 0.998762i | \(0.515841\pi\) | |||||||
\(578\) | 11.8277 | + | 11.8277i | 0.491967 | + | 0.491967i | ||||
\(579\) | 6.50201 | 0.270214 | ||||||||
\(580\) | −11.9053 | − | 18.7930i | −0.494341 | − | 0.780336i | ||||
\(581\) | −10.0082 | − | 6.71907i | −0.415212 | − | 0.278754i | ||||
\(582\) | −8.05595 | + | 8.05595i | −0.333930 | + | 0.333930i | ||||
\(583\) | 11.3427 | + | 11.3427i | 0.469767 | + | 0.469767i | ||||
\(584\) | −8.64818 | −0.357864 | ||||||||
\(585\) | 0.405538 | − | 1.80748i | 0.0167669 | − | 0.0747302i | ||||
\(586\) | − | 8.99195i | − | 0.371454i | ||||||
\(587\) | 0.690067 | + | 0.690067i | 0.0284821 | + | 0.0284821i | 0.721204 | − | 0.692722i | \(-0.243589\pi\) |
−0.692722 | + | 0.721204i | \(0.743589\pi\) | |||||||
\(588\) | −6.45535 | − | 2.70711i | −0.266214 | − | 0.111639i | ||||
\(589\) | − | 7.14046i | − | 0.294217i | ||||||
\(590\) | −4.53628 | − | 1.01779i | −0.186756 | − | 0.0419017i | ||||
\(591\) | − | 7.42648i | − | 0.305485i | ||||||
\(592\) | 6.10651 | − | 6.10651i | 0.250976 | − | 0.250976i | ||||
\(593\) | −16.0464 | + | 16.0464i | −0.658946 | + | 0.658946i | −0.955131 | − | 0.296184i | \(-0.904286\pi\) |
0.296184 | + | 0.955131i | \(0.404286\pi\) | |||||||
\(594\) | 4.79881 | 0.196897 | ||||||||
\(595\) | 34.3454 | + | 0.912202i | 1.40803 | + | 0.0373966i | ||||
\(596\) | 4.43516 | 0.181671 | ||||||||
\(597\) | −2.91443 | + | 2.91443i | −0.119280 | + | 0.119280i | ||||
\(598\) | 2.46793 | − | 2.46793i | 0.100921 | − | 0.100921i | ||||
\(599\) | 0.262525i | 0.0107265i | 0.999986 | + | 0.00536325i | \(0.00170718\pi\) | ||||
−0.999986 | + | 0.00536325i | \(0.998293\pi\) | |||||||
\(600\) | −2.13613 | + | 4.52072i | −0.0872071 | + | 0.184558i | ||||
\(601\) | − | 6.35838i | − | 0.259364i | −0.991556 | − | 0.129682i | \(-0.958604\pi\) | ||
0.991556 | − | 0.129682i | \(-0.0413956\pi\) | |||||||
\(602\) | −4.14975 | − | 21.1038i | −0.169131 | − | 0.860128i | ||||
\(603\) | 0.979056 | + | 0.979056i | 0.0398703 | + | 0.0398703i | ||||
\(604\) | − | 7.61497i | − | 0.309849i | ||||||
\(605\) | 14.3938 | + | 22.7211i | 0.585191 | + | 0.923745i | ||||
\(606\) | 4.89020 | 0.198651 | ||||||||
\(607\) | 22.5571 | + | 22.5571i | 0.915564 | + | 0.915564i | 0.996703 | − | 0.0811391i | \(-0.0258558\pi\) |
−0.0811391 | + | 0.996703i | \(0.525856\pi\) | |||||||
\(608\) | 1.67135 | − | 1.67135i | 0.0677823 | − | 0.0677823i | ||||
\(609\) | −14.6720 | + | 21.8543i | −0.594538 | + | 0.885582i | ||||
\(610\) | 2.71969 | − | 12.1216i | 0.110117 | − | 0.490790i | ||||
\(611\) | 0.426043 | 0.0172359 | ||||||||
\(612\) | 4.10651 | + | 4.10651i | 0.165996 | + | 0.165996i | ||||
\(613\) | −4.17864 | − | 4.17864i | −0.168774 | − | 0.168774i | 0.617667 | − | 0.786440i | \(-0.288078\pi\) |
−0.786440 | + | 0.617667i | \(0.788078\pi\) | |||||||
\(614\) | 23.8525 | 0.962610 | ||||||||
\(615\) | −5.38459 | + | 23.9991i | −0.217128 | + | 0.967738i | ||||
\(616\) | 7.07689 | − | 10.5412i | 0.285136 | − | 0.424718i | ||||
\(617\) | 10.9152 | − | 10.9152i | 0.439428 | − | 0.439428i | −0.452391 | − | 0.891819i | \(-0.649429\pi\) |
0.891819 | + | 0.452391i | \(0.149429\pi\) | |||||||
\(618\) | 1.06462 | + | 1.06462i | 0.0428254 | + | 0.0428254i | ||||
\(619\) | −2.48720 | −0.0999688 | −0.0499844 | − | 0.998750i | \(-0.515917\pi\) | ||||
−0.0499844 | + | 0.998750i | \(0.515917\pi\) | |||||||
\(620\) | 3.61497 | + | 5.70636i | 0.145181 | + | 0.229173i | ||||
\(621\) | 4.21302i | 0.169063i | ||||||||
\(622\) | −0.0418875 | − | 0.0418875i | −0.00167954 | − | 0.00167954i | ||||
\(623\) | 6.07404 | + | 30.8899i | 0.243351 | + | 1.23758i | ||||
\(624\) | − | 0.828427i | − | 0.0331636i | ||||||
\(625\) | −15.8739 | − | 19.3137i | −0.634956 | − | 0.772548i | ||||
\(626\) | 0.648179i | 0.0259064i | ||||||||
\(627\) | 8.02051 | − | 8.02051i | 0.320308 | − | 0.320308i | ||||
\(628\) | −6.30188 | + | 6.30188i | −0.251472 | + | 0.251472i | ||||
\(629\) | 50.1529 | 1.99973 | ||||||||
\(630\) | 5.91399 | + | 0.157074i | 0.235619 | + | 0.00625796i | ||||
\(631\) | −34.6801 | −1.38059 | −0.690296 | − | 0.723527i | \(-0.742520\pi\) | ||||
−0.690296 | + | 0.723527i | \(0.742520\pi\) | |||||||
\(632\) | −3.60673 | + | 3.60673i | −0.143468 | + | 0.143468i | ||||
\(633\) | 19.5557 | − | 19.5557i | 0.777270 | − | 0.777270i | ||||
\(634\) | − | 18.5445i | − | 0.736497i | ||||||
\(635\) | 1.23335 | + | 0.276721i | 0.0489438 | + | 0.0109813i | ||||
\(636\) | 3.34271i | 0.132547i | ||||||||
\(637\) | −2.24264 | + | 5.34779i | −0.0888567 | + | 0.211887i | ||||
\(638\) | −33.7596 | − | 33.7596i | −1.33656 | − | 1.33656i | ||||
\(639\) | − | 5.25132i | − | 0.207739i | ||||||
\(640\) | −0.489528 | + | 2.18183i | −0.0193503 | + | 0.0862442i | ||||
\(641\) | −17.9572 | −0.709268 | −0.354634 | − | 0.935005i | \(-0.615395\pi\) | ||||
−0.354634 | + | 0.935005i | \(0.615395\pi\) | |||||||
\(642\) | 2.15063 | + | 2.15063i | 0.0848786 | + | 0.0848786i | ||||
\(643\) | −3.76560 | + | 3.76560i | −0.148501 | + | 0.148501i | −0.777448 | − | 0.628947i | \(-0.783486\pi\) |
0.628947 | + | 0.777448i | \(0.283486\pi\) | |||||||
\(644\) | 9.25447 | + | 6.21302i | 0.364677 | + | 0.244827i | ||||
\(645\) | 9.72774 | + | 15.3556i | 0.383029 | + | 0.604626i | ||||
\(646\) | 13.7269 | 0.540076 | ||||||||
\(647\) | 24.7759 | + | 24.7759i | 0.974042 | + | 0.974042i | 0.999672 | − | 0.0256293i | \(-0.00815894\pi\) |
−0.0256293 | + | 0.999672i | \(0.508159\pi\) | |||||||
\(648\) | 0.707107 | + | 0.707107i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | −9.97731 | −0.391644 | ||||||||
\(650\) | 3.74509 | + | 1.76963i | 0.146895 | + | 0.0694105i | ||||
\(651\) | 4.45504 | − | 6.63591i | 0.174607 | − | 0.260082i | ||||
\(652\) | 10.8489 | − | 10.8489i | 0.424877 | − | 0.424877i | ||||
\(653\) | −15.9566 | − | 15.9566i | −0.624431 | − | 0.624431i | 0.322231 | − | 0.946661i | \(-0.395567\pi\) |
−0.946661 | + | 0.322231i | \(0.895567\pi\) | |||||||
\(654\) | −12.8984 | −0.504369 | ||||||||
\(655\) | −41.9417 | + | 26.5700i | −1.63880 | + | 1.03817i | ||||
\(656\) | 10.9996i | 0.429461i | ||||||||
\(657\) | −6.11519 | − | 6.11519i | −0.238576 | − | 0.238576i | ||||
\(658\) | 0.262525 | + | 1.33509i | 0.0102343 | + | 0.0520473i | ||||
\(659\) | − | 15.8705i | − | 0.618227i | −0.951025 | − | 0.309113i | \(-0.899968\pi\) | ||
0.951025 | − | 0.309113i | \(-0.100032\pi\) | |||||||
\(660\) | −2.34915 | + | 10.4702i | −0.0914406 | + | 0.407550i | ||||
\(661\) | − | 15.8409i | − | 0.616139i | −0.951364 | − | 0.308069i | \(-0.900317\pi\) | ||
0.951364 | − | 0.308069i | \(-0.0996829\pi\) | |||||||
\(662\) | −17.7688 | + | 17.7688i | −0.690602 | + | 0.690602i | ||||
\(663\) | 3.40194 | − | 3.40194i | 0.132121 | − | 0.132121i | ||||
\(664\) | 4.55617 | 0.176814 | ||||||||
\(665\) | 10.1469 | − | 9.62185i | 0.393480 | − | 0.373119i | ||||
\(666\) | 8.63591 | 0.334635 | ||||||||
\(667\) | 29.6386 | − | 29.6386i | 1.14761 | − | 1.14761i | ||||
\(668\) | 5.63635 | − | 5.63635i | 0.218077 | − | 0.218077i | ||||
\(669\) | 21.6759i | 0.838037i | ||||||||
\(670\) | −2.61541 | + | 1.65685i | −0.101042 | + | 0.0640099i | ||||
\(671\) | − | 26.6609i | − | 1.02923i | ||||||
\(672\) | 2.59604 | − | 0.510472i | 0.100144 | − | 0.0196919i | ||||
\(673\) | 4.25535 | + | 4.25535i | 0.164032 | + | 0.164032i | 0.784350 | − | 0.620318i | \(-0.212997\pi\) |
−0.620318 | + | 0.784350i | \(0.712997\pi\) | |||||||
\(674\) | − | 23.4726i | − | 0.904130i | ||||||
\(675\) | −4.70711 | + | 1.68616i | −0.181177 | + | 0.0649004i | ||||
\(676\) | 12.3137 | 0.473604 | ||||||||
\(677\) | −34.7614 | − | 34.7614i | −1.33599 | − | 1.33599i | −0.899906 | − | 0.436085i | \(-0.856365\pi\) |
−0.436085 | − | 0.899906i | \(-0.643635\pi\) | |||||||
\(678\) | 11.5853 | − | 11.5853i | 0.444933 | − | 0.444933i | ||||
\(679\) | −16.8012 | + | 25.0259i | −0.644772 | + | 0.960406i | ||||
\(680\) | −10.9699 | + | 6.94944i | −0.420678 | + | 0.266499i | ||||
\(681\) | 26.7264 | 1.02416 | ||||||||
\(682\) | 10.2509 | + | 10.2509i | 0.392526 | + | 0.392526i | ||||
\(683\) | 8.10025 | + | 8.10025i | 0.309947 | + | 0.309947i | 0.844889 | − | 0.534942i | \(-0.179666\pi\) |
−0.534942 | + | 0.844889i | \(0.679666\pi\) | |||||||
\(684\) | 2.36365 | 0.0903764 | ||||||||
\(685\) | −18.2928 | − | 4.10428i | −0.698931 | − | 0.156816i | ||||
\(686\) | −18.1402 | − | 3.73248i | −0.692598 | − | 0.142507i | ||||
\(687\) | 9.41421 | − | 9.41421i | 0.359175 | − | 0.359175i | ||||
\(688\) | 5.74825 | + | 5.74825i | 0.219150 | + | 0.219150i | ||||
\(689\) | 2.76919 | 0.105498 | ||||||||
\(690\) | −9.19208 | − | 2.06239i | −0.349936 | − | 0.0785139i | ||||
\(691\) | 39.2567i | 1.49340i | 0.665163 | + | 0.746699i | \(0.268362\pi\) | ||||
−0.665163 | + | 0.746699i | \(0.731638\pi\) | |||||||
\(692\) | 12.6923 | + | 12.6923i | 0.482489 | + | 0.482489i | ||||
\(693\) | 12.4579 | − | 2.44966i | 0.473236 | − | 0.0930548i | ||||
\(694\) | − | 20.3949i | − | 0.774181i | ||||||
\(695\) | −10.1292 | − | 15.9894i | −0.384224 | − | 0.606512i | ||||
\(696\) | − | 9.94900i | − | 0.377116i | ||||||
\(697\) | −45.1698 | + | 45.1698i | −1.71093 | + | 1.71093i | ||||
\(698\) | 20.2708 | − | 20.2708i | 0.767260 | − | 0.767260i | ||||
\(699\) | −10.4015 | −0.393421 | ||||||||
\(700\) | −3.23777 | + | 12.8264i | −0.122376 | + | 0.484793i | ||||
\(701\) | 27.9663 | 1.05627 | 0.528137 | − | 0.849159i | \(-0.322891\pi\) | ||||
0.528137 | + | 0.849159i | \(0.322891\pi\) | |||||||
\(702\) | 0.585786 | − | 0.585786i | 0.0221091 | − | 0.0221091i | ||||
\(703\) | 14.4337 | − | 14.4337i | 0.544376 | − | 0.544376i | ||||
\(704\) | 4.79881i | 0.180862i | ||||||||
\(705\) | −0.615405 | − | 0.971440i | −0.0231775 | − | 0.0365865i | ||||
\(706\) | 7.16308i | 0.269586i | ||||||||
\(707\) | 12.6951 | − | 2.49631i | 0.477450 | − | 0.0938834i | ||||
\(708\) | −1.47016 | − | 1.47016i | −0.0552521 | − | 0.0552521i | ||||
\(709\) | − | 23.3998i | − | 0.878799i | −0.898292 | − | 0.439399i | \(-0.855191\pi\) | ||
0.898292 | − | 0.439399i | \(-0.144809\pi\) | |||||||
\(710\) | 11.4575 | + | 2.57067i | 0.429991 | + | 0.0964754i | ||||
\(711\) | −5.10069 | −0.191291 | ||||||||
\(712\) | −8.41377 | − | 8.41377i | −0.315320 | − | 0.315320i | ||||
\(713\) | −8.99956 | + | 8.99956i | −0.337036 | + | 0.337036i | ||||
\(714\) | 12.7569 | + | 8.56440i | 0.477416 | + | 0.320515i | ||||
\(715\) | 8.67377 | + | 1.94610i | 0.324380 | + | 0.0727800i | ||||
\(716\) | 5.72836 | 0.214079 | ||||||||
\(717\) | −9.22708 | − | 9.22708i | −0.344592 | − | 0.344592i | ||||
\(718\) | −5.98550 | − | 5.98550i | −0.223377 | − | 0.223377i | ||||
\(719\) | −50.8254 | −1.89547 | −0.947734 | − | 0.319060i | \(-0.896633\pi\) | ||||
−0.947734 | + | 0.319060i | \(0.896633\pi\) | |||||||
\(720\) | −1.88893 | + | 1.19663i | −0.0703963 | + | 0.0445959i | ||||
\(721\) | 3.30726 | + | 2.22034i | 0.123169 | + | 0.0826899i | ||||
\(722\) | −9.48453 | + | 9.48453i | −0.352978 | + | 0.352978i | ||||
\(723\) | −17.2917 | − | 17.2917i | −0.643085 | − | 0.643085i | ||||
\(724\) | −8.91220 | −0.331219 | ||||||||
\(725\) | 44.9767 | + | 21.2524i | 1.67039 | + | 0.789293i | ||||
\(726\) | 12.0286i | 0.446422i | ||||||||
\(727\) | −5.10248 | − | 5.10248i | −0.189240 | − | 0.189240i | 0.606127 | − | 0.795368i | \(-0.292722\pi\) |
−0.795368 | + | 0.606127i | \(0.792722\pi\) | |||||||
\(728\) | −0.422889 | − | 2.15063i | −0.0156733 | − | 0.0797076i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 16.3358 | − | 10.3487i | 0.604616 | − | 0.383023i | ||||
\(731\) | 47.2105i | 1.74614i | ||||||||
\(732\) | 3.92849 | − | 3.92849i | 0.145201 | − | 0.145201i | ||||
\(733\) | −1.79925 | + | 1.79925i | −0.0664567 | + | 0.0664567i | −0.739554 | − | 0.673097i | \(-0.764964\pi\) |
0.673097 | + | 0.739554i | \(0.264964\pi\) | |||||||
\(734\) | −25.6941 | −0.948386 | ||||||||
\(735\) | 15.4331 | − | 2.61116i | 0.569260 | − | 0.0963140i | ||||
\(736\) | −4.21302 | −0.155294 | ||||||||
\(737\) | −4.69830 | + | 4.69830i | −0.173064 | + | 0.173064i | ||||
\(738\) | −7.77786 | + | 7.77786i | −0.286307 | + | 0.286307i | ||||
\(739\) | − | 10.9122i | − | 0.401412i | −0.979652 | − | 0.200706i | \(-0.935676\pi\) | ||
0.979652 | − | 0.200706i | \(-0.0643236\pi\) | |||||||
\(740\) | −4.22752 | + | 18.8420i | −0.155407 | + | 0.692648i | ||||
\(741\) | − | 1.95811i | − | 0.0719331i | ||||||
\(742\) | 1.70636 | + | 8.67780i | 0.0626424 | + | 0.318572i | ||||
\(743\) | −12.3076 | − | 12.3076i | −0.451521 | − | 0.451521i | 0.444338 | − | 0.895859i | \(-0.353439\pi\) |
−0.895859 | + | 0.444338i | \(0.853439\pi\) | |||||||
\(744\) | 3.02094i | 0.110753i | ||||||||
\(745\) | −8.37771 | + | 5.30726i | −0.306936 | + | 0.194443i | ||||
\(746\) | −21.8485 | −0.799930 | ||||||||
\(747\) | 3.22170 | + | 3.22170i | 0.117876 | + | 0.117876i | ||||
\(748\) | −19.7064 | + | 19.7064i | −0.720536 | + | 0.720536i | ||||
\(749\) | 6.68095 | + | 4.48528i | 0.244117 | + | 0.163889i | ||||
\(750\) | −1.37465 | − | 11.0955i | −0.0501952 | − | 0.405151i | ||||
\(751\) | −12.4787 | −0.455354 | −0.227677 | − | 0.973737i | \(-0.573113\pi\) | ||||
−0.227677 | + | 0.973737i | \(0.573113\pi\) | |||||||
\(752\) | −0.363651 | − | 0.363651i | −0.0132610 | − | 0.0132610i | ||||
\(753\) | 3.05701 | + | 3.05701i | 0.111404 | + | 0.111404i | ||||
\(754\) | −8.24202 | −0.300157 | ||||||||
\(755\) | 9.11233 | + | 14.3842i | 0.331632 | + | 0.523493i | ||||
\(756\) | 2.19663 | + | 1.47472i | 0.0798908 | + | 0.0536350i | ||||
\(757\) | 30.1930 | − | 30.1930i | 1.09738 | − | 1.09738i | 0.102667 | − | 0.994716i | \(-0.467262\pi\) |
0.994716 | − | 0.102667i | \(-0.0327377\pi\) | |||||||
\(758\) | 22.8984 | + | 22.8984i | 0.831709 | + | 0.831709i | ||||
\(759\) | −20.2175 | −0.733848 | ||||||||
\(760\) | −1.15707 | + | 5.15707i | −0.0419715 | + | 0.187067i | ||||
\(761\) | − | 33.4920i | − | 1.21409i | −0.794669 | − | 0.607043i | \(-0.792356\pi\) | ||
0.794669 | − | 0.607043i | \(-0.207644\pi\) | |||||||
\(762\) | 0.399714 | + | 0.399714i | 0.0144801 | + | 0.0144801i | ||||
\(763\) | −33.4848 | + | 6.58429i | −1.21223 | + | 0.238367i | ||||
\(764\) | 7.67824i | 0.277789i | ||||||||
\(765\) | −12.6709 | − | 2.84293i | −0.458118 | − | 0.102786i | ||||
\(766\) | − | 22.8984i | − | 0.827354i | ||||||
\(767\) | −1.21792 | + | 1.21792i | −0.0439766 | + | 0.0439766i | ||||
\(768\) | −0.707107 | + | 0.707107i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | 31.8992 | 1.15032 | 0.575158 | − | 0.818042i | \(-0.304941\pi\) | ||||
0.575158 | + | 0.818042i | \(0.304941\pi\) | |||||||
\(770\) | −0.753766 | + | 28.3801i | −0.0271638 | + | 1.02275i | ||||
\(771\) | −7.16184 | −0.257927 | ||||||||
\(772\) | −4.59762 | + | 4.59762i | −0.165472 | + | 0.165472i | ||||
\(773\) | 11.0809 | − | 11.0809i | 0.398553 | − | 0.398553i | −0.479170 | − | 0.877722i | \(-0.659062\pi\) |
0.877722 | + | 0.479170i | \(0.159062\pi\) | |||||||
\(774\) | 8.12925i | 0.292200i | ||||||||
\(775\) | −13.6569 | − | 6.45313i | −0.490569 | − | 0.231803i | ||||
\(776\) | − | 11.3928i | − | 0.408979i | ||||||
\(777\) | 22.4192 | − | 4.40839i | 0.804283 | − | 0.158150i | ||||
\(778\) | 8.49173 | + | 8.49173i | 0.304443 | + | 0.304443i | ||||
\(779\) | 25.9991i | 0.931515i | ||||||||
\(780\) | 0.991325 | + | 1.56484i | 0.0354951 | + | 0.0560304i | ||||
\(781\) | 25.2001 | 0.901729 | ||||||||
\(782\) | −17.3008 | − | 17.3008i | −0.618676 | − | 0.618676i | ||||
\(783\) | 7.03500 | − | 7.03500i | 0.251411 | − | 0.251411i | ||||
\(784\) | 6.47884 | − | 2.65041i | 0.231387 | − | 0.0946575i | ||||
\(785\) | 4.36277 | − | 19.4449i | 0.155714 | − | 0.694017i | ||||
\(786\) | −22.2039 | −0.791987 | ||||||||
\(787\) | −27.9894 | − | 27.9894i | −0.997714 | − | 0.997714i | 0.00228344 | − | 0.999997i | \(-0.499273\pi\) |
−0.999997 | + | 0.00228344i | \(0.999273\pi\) | |||||||
\(788\) | 5.25132 | + | 5.25132i | 0.187070 | + | 0.187070i | ||||
\(789\) | 5.89887 | 0.210005 | ||||||||
\(790\) | 2.49693 | − | 11.1288i | 0.0888368 | − | 0.395945i | ||||
\(791\) | 24.1620 | − | 35.9900i | 0.859103 | − | 1.27966i | ||||
\(792\) | −3.39327 | + | 3.39327i | −0.120575 | + | 0.120575i | ||||
\(793\) | −3.25447 | − | 3.25447i | −0.115570 | − | 0.115570i | ||||
\(794\) | 3.71485 | 0.131835 | ||||||||
\(795\) | −4.00000 | − | 6.31415i | −0.141865 | − | 0.223940i | ||||
\(796\) | − | 4.12163i | − | 0.146087i | ||||||
\(797\) | −6.43293 | − | 6.43293i | −0.227866 | − | 0.227866i | 0.583935 | − | 0.811801i | \(-0.301512\pi\) |
−0.811801 | + | 0.583935i | \(0.801512\pi\) | |||||||
\(798\) | 6.13613 | − | 1.20658i | 0.217217 | − | 0.0427124i | ||||
\(799\) | − | 2.98667i | − | 0.105661i | ||||||
\(800\) | −1.68616 | − | 4.70711i | −0.0596149 | − | 0.166421i | ||||
\(801\) | − | 11.8989i | − | 0.420426i | ||||||
\(802\) | 13.9704 | − | 13.9704i | 0.493311 | − | 0.493311i | ||||
\(803\) | 29.3456 | − | 29.3456i | 1.03558 | − | 1.03558i | ||||
\(804\) | −1.38459 | −0.0488309 | ||||||||
\(805\) | −24.9158 | − | 0.661754i | −0.878166 | − | 0.0233238i | ||||
\(806\) | 2.50263 | 0.0881514 | ||||||||
\(807\) | −17.4998 | + | 17.4998i | −0.616021 | + | 0.616021i | ||||
\(808\) | −3.45789 | + | 3.45789i | −0.121648 | + | 0.121648i | ||||
\(809\) | 36.3842i | 1.27920i | 0.768708 | + | 0.639599i | \(0.220900\pi\) | ||||
−0.768708 | + | 0.639599i | \(0.779100\pi\) | |||||||
\(810\) | −2.18183 | − | 0.489528i | −0.0766615 | − | 0.0172003i | ||||
\(811\) | 26.5629i | 0.932750i | 0.884587 | + | 0.466375i | \(0.154440\pi\) | ||||
−0.884587 | + | 0.466375i | \(0.845560\pi\) | |||||||
\(812\) | −5.07868 | − | 25.8280i | −0.178227 | − | 0.906385i | ||||
\(813\) | −15.5535 | − | 15.5535i | −0.545485 | − | 0.545485i | ||||
\(814\) | 41.4421i | 1.45254i | ||||||||
\(815\) | −7.51069 | + | 33.4751i | −0.263088 | + | 1.17258i | ||||
\(816\) | −5.80748 | −0.203303 | ||||||||
\(817\) | 13.5868 | + | 13.5868i | 0.475344 | + | 0.475344i | ||||
\(818\) | 10.8786 | − | 10.8786i | 0.380360 | − | 0.380360i | ||||
\(819\) | 1.22170 | − | 1.81975i | 0.0426895 | − | 0.0635873i | ||||
\(820\) | −13.1625 | − | 20.7774i | −0.459653 | − | 0.725579i | ||||
\(821\) | −45.9655 | −1.60421 | −0.802103 | − | 0.597186i | \(-0.796286\pi\) | ||||
−0.802103 | + | 0.597186i | \(0.796286\pi\) | |||||||
\(822\) | −5.92849 | − | 5.92849i | −0.206780 | − | 0.206780i | ||||
\(823\) | 36.5397 | + | 36.5397i | 1.27369 | + | 1.27369i | 0.944134 | + | 0.329561i | \(0.106901\pi\) |
0.329561 | + | 0.944134i | \(0.393099\pi\) | |||||||
\(824\) | −1.50560 | −0.0524502 | ||||||||
\(825\) | −8.09157 | − | 22.5885i | −0.281712 | − | 0.786431i | ||||
\(826\) | −4.56707 | − | 3.06612i | −0.158909 | − | 0.106684i | ||||
\(827\) | 15.7275 | − | 15.7275i | 0.546898 | − | 0.546898i | −0.378644 | − | 0.925542i | \(-0.623610\pi\) |
0.925542 | + | 0.378644i | \(0.123610\pi\) | |||||||
\(828\) | −2.97906 | − | 2.97906i | −0.103529 | − | 0.103529i | ||||
\(829\) | −29.2892 | −1.01725 | −0.508627 | − | 0.860987i | \(-0.669847\pi\) | ||||
−0.508627 | + | 0.860987i | \(0.669847\pi\) | |||||||
\(830\) | −8.60629 | + | 5.45207i | −0.298729 | + | 0.189244i | ||||
\(831\) | 17.0620i | 0.591873i | ||||||||
\(832\) | 0.585786 | + | 0.585786i | 0.0203085 | + | 0.0203085i | ||||
\(833\) | 37.4894 | + | 15.7215i | 1.29893 | + | 0.544717i | ||||
\(834\) | − | 8.46478i | − | 0.293111i | ||||||
\(835\) | −3.90203 | + | 17.3913i | −0.135035 | + | 0.601852i | ||||
\(836\) | 11.3427i | 0.392296i | ||||||||
\(837\) | −2.13613 | + | 2.13613i | −0.0738354 | + | 0.0738354i | ||||
\(838\) | −19.8543 | + | 19.8543i | −0.685856 | + | 0.685856i | ||||
\(839\) | 2.41886 | 0.0835082 | 0.0417541 | − | 0.999128i | \(-0.486705\pi\) | ||||
0.0417541 | + | 0.999128i | \(0.486705\pi\) | |||||||
\(840\) | −4.29289 | + | 4.07076i | −0.148119 | + | 0.140454i | ||||
\(841\) | −69.9826 | −2.41319 | ||||||||
\(842\) | 8.12013 | − | 8.12013i | 0.279838 | − | 0.279838i | ||||
\(843\) | −10.1589 | + | 10.1589i | −0.349890 | + | 0.349890i | ||||
\(844\) | 27.6560i | 0.951958i | ||||||||
\(845\) | −23.2598 | + | 14.7350i | −0.800160 | + | 0.506900i | ||||
\(846\) | − | 0.514280i | − | 0.0176813i | ||||||
\(847\) | 6.14024 | + | 31.2266i | 0.210981 | + | 1.07296i | ||||
\(848\) | −2.36365 | − | 2.36365i | −0.0811681 | − | 0.0811681i | ||||
\(849\) | − | 15.6742i | − | 0.537937i | ||||||
\(850\) | 12.4055 | − | 26.2540i | 0.425506 | − | 0.900506i | ||||
\(851\) | −36.3833 | −1.24720 | ||||||||
\(852\) | 3.71324 | + | 3.71324i | 0.127214 | + | 0.127214i | ||||
\(853\) | 28.0222 | − | 28.0222i | 0.959461 | − | 0.959461i | −0.0397491 | − | 0.999210i | \(-0.512656\pi\) |
0.999210 | + | 0.0397491i | \(0.0126559\pi\) | |||||||
\(854\) | 8.19314 | − | 12.2039i | 0.280363 | − | 0.417609i | ||||
\(855\) | −4.46478 | + | 2.82843i | −0.152692 | + | 0.0967302i | ||||
\(856\) | −3.04145 | −0.103955 | ||||||||
\(857\) | −19.1782 | − | 19.1782i | −0.655115 | − | 0.655115i | 0.299105 | − | 0.954220i | \(-0.403312\pi\) |
−0.954220 | + | 0.299105i | \(0.903312\pi\) | |||||||
\(858\) | 2.81108 | + | 2.81108i | 0.0959686 | + | 0.0959686i | ||||
\(859\) | 45.5754 | 1.55501 | 0.777506 | − | 0.628876i | \(-0.216485\pi\) | ||||
0.777506 | + | 0.628876i | \(0.216485\pi\) | |||||||
\(860\) | −17.7366 | − | 3.97949i | −0.604813 | − | 0.135700i | ||||
\(861\) | −16.2213 | + | 24.1620i | −0.552819 | + | 0.823439i | ||||
\(862\) | 8.01362 | − | 8.01362i | 0.272945 | − | 0.272945i | ||||
\(863\) | 4.69515 | + | 4.69515i | 0.159825 | + | 0.159825i | 0.782489 | − | 0.622664i | \(-0.213950\pi\) |
−0.622664 | + | 0.782489i | \(0.713950\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −39.1629 | − | 8.78684i | −1.33158 | − | 0.298762i | ||||
\(866\) | 6.94856i | 0.236122i | ||||||||
\(867\) | −11.8277 | − | 11.8277i | −0.401689 | − | 0.401689i | ||||
\(868\) | 1.54211 | + | 7.84249i | 0.0523425 | + | 0.266191i | ||||
\(869\) | − | 24.4772i | − | 0.830333i | ||||||
\(870\) | 11.9053 | + | 18.7930i | 0.403628 | + | 0.637142i | ||||
\(871\) | 1.14704i | 0.0388658i | ||||||||
\(872\) | 9.12057 | − | 9.12057i | 0.308862 | − | 0.308862i | ||||
\(873\) | 8.05595 | − | 8.05595i | 0.272653 | − | 0.272653i | ||||
\(874\) | −9.95811 | −0.336838 | ||||||||
\(875\) | −9.23260 | − | 28.1027i | −0.312119 | − | 0.950043i | ||||
\(876\) | 8.64818 | 0.292195 | ||||||||
\(877\) | 17.5321 | − | 17.5321i | 0.592017 | − | 0.592017i | −0.346159 | − | 0.938176i | \(-0.612514\pi\) |
0.938176 | + | 0.346159i | \(0.112514\pi\) | |||||||
\(878\) | 16.1025 | − | 16.1025i | 0.543432 | − | 0.543432i | ||||
\(879\) | 8.99195i | 0.303291i | ||||||||
\(880\) | −5.74242 | − | 9.06462i | −0.193577 | − | 0.305568i | ||||
\(881\) | 3.93358i | 0.132526i | 0.997802 | + | 0.0662628i | \(0.0211076\pi\) | ||||
−0.997802 | + | 0.0662628i | \(0.978892\pi\) | |||||||
\(882\) | 6.45535 | + | 2.70711i | 0.217363 | + | 0.0911530i | ||||
\(883\) | 34.7362 | + | 34.7362i | 1.16896 | + | 1.16896i | 0.982453 | + | 0.186512i | \(0.0597184\pi\) |
0.186512 | + | 0.982453i | \(0.440282\pi\) | |||||||
\(884\) | 4.81108i | 0.161814i | ||||||||
\(885\) | 4.53628 | + | 1.01779i | 0.152485 | + | 0.0342126i | ||||
\(886\) | −36.5134 | −1.22669 | ||||||||
\(887\) | 33.3213 | + | 33.3213i | 1.11882 | + | 1.11882i | 0.991915 | + | 0.126906i | \(0.0405046\pi\) |
0.126906 | + | 0.991915i | \(0.459495\pi\) | |||||||
\(888\) | −6.10651 | + | 6.10651i | −0.204921 | + | 0.204921i | ||||
\(889\) | 1.24172 | + | 0.833631i | 0.0416458 | + | 0.0279591i | ||||
\(890\) | 25.9613 | + | 5.82483i | 0.870224 | + | 0.195249i | ||||
\(891\) | −4.79881 | −0.160766 | ||||||||
\(892\) | −15.3271 | − | 15.3271i | −0.513191 | − | 0.513191i | ||||
\(893\) | −0.859544 | − | 0.859544i | −0.0287635 | − | 0.0287635i | ||||
\(894\) | −4.43516 | −0.148334 | ||||||||
\(895\) | −10.8205 | + | 6.85476i | −0.361689 | + | 0.229129i | ||||
\(896\) | −1.47472 | + | 2.19663i | −0.0492669 | + | 0.0733844i | ||||
\(897\) | −2.46793 | + | 2.46793i | −0.0824018 | + | 0.0824018i | ||||
\(898\) | −6.75692 | − | 6.75692i | −0.225481 | − | 0.225481i | ||||
\(899\) | 30.0554 | 1.00240 | ||||||||
\(900\) | 2.13613 | − | 4.52072i | 0.0712043 | − | 0.150691i | ||||
\(901\) | − | 19.4127i | − | 0.646731i | ||||||
\(902\) | −37.3245 | − | 37.3245i | −1.24277 | − | 1.24277i | ||||
\(903\) | 4.14975 | + | 21.1038i | 0.138095 | + | 0.702292i | ||||
\(904\) | 16.3842i | 0.544929i | ||||||||
\(905\) | 16.8345 | − | 10.6647i | 0.559599 | − | 0.354505i | ||||
\(906\) | 7.61497i | 0.252990i | ||||||||
\(907\) | −0.932707 | + | 0.932707i | −0.0309700 | + | 0.0309700i | −0.722422 | − | 0.691452i | \(-0.756971\pi\) |
0.691452 | + | 0.722422i | \(0.256971\pi\) | |||||||
\(908\) | −18.8984 | + | 18.8984i | −0.627167 | + | 0.627167i | ||||
\(909\) | −4.89020 | −0.162198 | ||||||||
\(910\) | 3.37233 | + | 3.55635i | 0.111792 | + | 0.117892i | ||||
\(911\) | 45.5690 | 1.50977 | 0.754885 | − | 0.655857i | \(-0.227693\pi\) | ||||
0.754885 | + | 0.655857i | \(0.227693\pi\) | |||||||
\(912\) | −1.67135 | + | 1.67135i | −0.0553440 | + | 0.0553440i | ||||
\(913\) | −15.4603 | + | 15.4603i | −0.511661 | + | 0.511661i | ||||
\(914\) | 23.5563i | 0.779175i | ||||||||
\(915\) | −2.71969 | + | 12.1216i | −0.0899100 | + | 0.400729i | ||||
\(916\) | 13.3137i | 0.439897i | ||||||||
\(917\) | −57.6422 | + | 11.3345i | −1.90351 | + | 0.374297i | ||||
\(918\) | −4.10651 | − | 4.10651i | −0.135535 | − | 0.135535i | ||||
\(919\) | − | 20.8574i | − | 0.688023i | −0.938965 | − | 0.344011i | \(-0.888214\pi\) | ||
0.938965 | − | 0.344011i | \(-0.111786\pi\) | |||||||
\(920\) | 7.95811 | − | 5.04145i | 0.262371 | − | 0.166212i | ||||
\(921\) | −23.8525 | −0.785967 | ||||||||
\(922\) | 17.3073 | + | 17.3073i | 0.569984 | + | 0.569984i | ||||
\(923\) | 3.07615 | − | 3.07615i | 0.101253 | − | 0.101253i | ||||
\(924\) | −7.07689 | + | 10.5412i | −0.232813 | + | 0.346781i | ||||
\(925\) | −14.5616 | − | 40.6502i | −0.478781 | − | 1.33657i | ||||
\(926\) | 9.65939 | 0.317427 | ||||||||
\(927\) | −1.06462 | − | 1.06462i | −0.0349668 | − | 0.0349668i | ||||
\(928\) | 7.03500 | + | 7.03500i | 0.230935 | + | 0.230935i | ||||
\(929\) | −9.10069 | −0.298584 | −0.149292 | − | 0.988793i | \(-0.547699\pi\) | ||||
−0.149292 | + | 0.988793i | \(0.547699\pi\) | |||||||
\(930\) | −3.61497 | − | 5.70636i | −0.118539 | − | 0.187119i | ||||
\(931\) | 15.3137 | − | 6.26464i | 0.501887 | − | 0.205315i | ||||
\(932\) | 7.35498 | − | 7.35498i | 0.240920 | − | 0.240920i | ||||
\(933\) | 0.0418875 | + | 0.0418875i | 0.00137134 | + | 0.00137134i | ||||
\(934\) | −28.6382 | −0.937070 | ||||||||
\(935\) | 13.6427 | − | 60.8053i | 0.446163 | − | 1.98855i | ||||
\(936\) | 0.828427i | 0.0270780i | ||||||||
\(937\) | −3.34154 | − | 3.34154i | −0.109163 | − | 0.109163i | 0.650415 | − | 0.759579i | \(-0.274595\pi\) |
−0.759579 | + | 0.650415i | \(0.774595\pi\) | |||||||
\(938\) | −3.59446 | + | 0.706797i | −0.117363 | + | 0.0230777i | ||||
\(939\) | − | 0.648179i | − | 0.0211525i | ||||||
\(940\) | 1.12207 | + | 0.251755i | 0.0365979 | + | 0.00821133i | ||||
\(941\) | − | 42.2862i | − | 1.37849i | −0.724528 | − | 0.689245i | \(-0.757942\pi\) | ||
0.724528 | − | 0.689245i | \(-0.242058\pi\) | |||||||
\(942\) | 6.30188 | − | 6.30188i | 0.205326 | − | 0.205326i | ||||
\(943\) | 32.7683 | − | 32.7683i | 1.06708 | − | 1.06708i | ||||
\(944\) | 2.07912 | 0.0676697 | ||||||||
\(945\) | −5.91399 | − | 0.157074i | −0.192382 | − | 0.00510960i | ||||
\(946\) | −39.0107 | −1.26835 | ||||||||
\(947\) | −0.00253441 | + | 0.00253441i | −8.23572e−5 | + | 8.23572e-5i | −0.707148 | − | 0.707066i | \(-0.750019\pi\) |
0.707066 | + | 0.707148i | \(0.250019\pi\) | |||||||
\(948\) | 3.60673 | − | 3.60673i | 0.117141 | − | 0.117141i | ||||
\(949\) | − | 7.16439i | − | 0.232566i | ||||||
\(950\) | −3.98550 | − | 11.1260i | −0.129307 | − | 0.360974i | ||||
\(951\) | 18.5445i | 0.601347i | ||||||||
\(952\) | −15.0765 | + | 2.96456i | −0.488631 | + | 0.0960818i | ||||
\(953\) | 14.4673 | + | 14.4673i | 0.468642 | + | 0.468642i | 0.901474 | − | 0.432832i | \(-0.142486\pi\) |
−0.432832 | + | 0.901474i | \(0.642486\pi\) | |||||||
\(954\) | − | 3.34271i | − | 0.108224i | ||||||
\(955\) | −9.18805 | − | 14.5037i | −0.297318 | − | 0.469328i | ||||
\(956\) | 13.0491 | 0.422037 | ||||||||
\(957\) | 33.7596 | + | 33.7596i | 1.09129 | + | 1.09129i | ||||
\(958\) | 4.82843 | − | 4.82843i | 0.155999 | − | 0.155999i | ||||
\(959\) | −18.4169 | − | 12.3643i | −0.594714 | − | 0.399263i | ||||
\(960\) | 0.489528 | − | 2.18183i | 0.0157995 | − | 0.0704181i | ||||
\(961\) | 21.8739 | 0.705610 | ||||||||
\(962\) | 5.05880 | + | 5.05880i | 0.163102 | + | 0.163102i | ||||
\(963\) | −2.15063 | − | 2.15063i | −0.0693031 | − | 0.0693031i | ||||
\(964\) | 24.4542 | 0.787616 | ||||||||
\(965\) | 3.18292 | − | 14.1863i | 0.102462 | − | 0.456672i | ||||
\(966\) | −9.25447 | − | 6.21302i | −0.297758 | − | 0.199901i | ||||
\(967\) | −4.38595 | + | 4.38595i | −0.141043 | + | 0.141043i | −0.774103 | − | 0.633060i | \(-0.781799\pi\) |
0.633060 | + | 0.774103i | \(0.281799\pi\) | |||||||
\(968\) | −8.50548 | − | 8.50548i | −0.273376 | − | 0.273376i | ||||
\(969\) | −13.7269 | −0.440970 | ||||||||
\(970\) | 13.6331 | + | 21.5203i | 0.437731 | + | 0.690975i | ||||
\(971\) | − | 24.3630i | − | 0.781847i | −0.920423 | − | 0.390923i | \(-0.872156\pi\) | ||
0.920423 | − | 0.390923i | \(-0.127844\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | −4.32103 | − | 21.9749i | −0.138526 | − | 0.704483i | ||||
\(974\) | − | 0.463279i | − | 0.0148444i | ||||||
\(975\) | −3.74509 | − | 1.76963i | −0.119939 | − | 0.0566734i | ||||
\(976\) | 5.55573i | 0.177835i | ||||||||
\(977\) | 38.9763 | − | 38.9763i | 1.24696 | − | 1.24696i | 0.289905 | − | 0.957055i | \(-0.406376\pi\) |
0.957055 | − | 0.289905i | \(-0.0936239\pi\) | |||||||
\(978\) | −10.8489 | + | 10.8489i | −0.346911 | + | 0.346911i | ||||
\(979\) | 57.1004 | 1.82494 | ||||||||
\(980\) | −9.06651 | + | 12.7592i | −0.289619 | + | 0.407579i | ||||
\(981\) | 12.8984 | 0.411815 | ||||||||
\(982\) | 2.39371 | − | 2.39371i | 0.0763863 | − | 0.0763863i | ||||
\(983\) | −14.5896 | + | 14.5896i | −0.465335 | + | 0.465335i | −0.900399 | − | 0.435065i | \(-0.856726\pi\) |
0.435065 | + | 0.900399i | \(0.356726\pi\) | |||||||
\(984\) | − | 10.9996i | − | 0.350653i | ||||||
\(985\) | −16.2033 | − | 3.63547i | −0.516280 | − | 0.115836i | ||||
\(986\) | 57.7786i | 1.84005i | ||||||||
\(987\) | −0.262525 | − | 1.33509i | −0.00835628 | − | 0.0424964i | ||||
\(988\) | 1.38459 | + | 1.38459i | 0.0440498 | + | 0.0440498i | ||||
\(989\) | − | 34.2487i | − | 1.08905i | ||||||
\(990\) | 2.34915 | − | 10.4702i | 0.0746609 | − | 0.332764i | ||||
\(991\) | 47.6560 | 1.51384 | 0.756921 | − | 0.653506i | \(-0.226703\pi\) | ||||
0.756921 | + | 0.653506i | \(0.226703\pi\) | |||||||
\(992\) | −2.13613 | − | 2.13613i | −0.0678222 | − | 0.0678222i | ||||
\(993\) | 17.7688 | − | 17.7688i | 0.563874 | − | 0.563874i | ||||
\(994\) | 11.5352 | + | 7.74421i | 0.365875 | + | 0.245632i | ||||
\(995\) | 4.93209 | + | 7.78548i | 0.156358 | + | 0.246816i | ||||
\(996\) | −4.55617 | −0.144368 | ||||||||
\(997\) | 0.631258 | + | 0.631258i | 0.0199921 | + | 0.0199921i | 0.717032 | − | 0.697040i | \(-0.245500\pi\) |
−0.697040 | + | 0.717032i | \(0.745500\pi\) | |||||||
\(998\) | 2.95409 | + | 2.95409i | 0.0935101 | + | 0.0935101i | ||||
\(999\) | −8.63591 | −0.273228 |
(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 | 210.2.m.b.13.4 | yes | 8 | |
3.2 | odd | 2 | 630.2.p.c.433.1 | 8 | |||
4.3 | odd | 2 | 1680.2.cz.a.433.4 | 8 | |||
5.2 | odd | 4 | 210.2.m.a.97.3 | yes | 8 | ||
5.3 | odd | 4 | 1050.2.m.b.307.2 | 8 | |||
5.4 | even | 2 | 1050.2.m.a.643.2 | 8 | |||
7.6 | odd | 2 | 210.2.m.a.13.3 | ✓ | 8 | ||
15.2 | even | 4 | 630.2.p.b.307.2 | 8 | |||
20.7 | even | 4 | 1680.2.cz.b.97.1 | 8 | |||
21.20 | even | 2 | 630.2.p.b.433.2 | 8 | |||
28.27 | even | 2 | 1680.2.cz.b.433.1 | 8 | |||
35.13 | even | 4 | 1050.2.m.a.307.2 | 8 | |||
35.27 | even | 4 | inner | 210.2.m.b.97.4 | yes | 8 | |
35.34 | odd | 2 | 1050.2.m.b.643.2 | 8 | |||
105.62 | odd | 4 | 630.2.p.c.307.1 | 8 | |||
140.27 | odd | 4 | 1680.2.cz.a.97.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.m.a.13.3 | ✓ | 8 | 7.6 | odd | 2 | ||
210.2.m.a.97.3 | yes | 8 | 5.2 | odd | 4 | ||
210.2.m.b.13.4 | yes | 8 | 1.1 | even | 1 | trivial | |
210.2.m.b.97.4 | yes | 8 | 35.27 | even | 4 | inner | |
630.2.p.b.307.2 | 8 | 15.2 | even | 4 | |||
630.2.p.b.433.2 | 8 | 21.20 | even | 2 | |||
630.2.p.c.307.1 | 8 | 105.62 | odd | 4 | |||
630.2.p.c.433.1 | 8 | 3.2 | odd | 2 | |||
1050.2.m.a.307.2 | 8 | 35.13 | even | 4 | |||
1050.2.m.a.643.2 | 8 | 5.4 | even | 2 | |||
1050.2.m.b.307.2 | 8 | 5.3 | odd | 4 | |||
1050.2.m.b.643.2 | 8 | 35.34 | odd | 2 | |||
1680.2.cz.a.97.4 | 8 | 140.27 | odd | 4 | |||
1680.2.cz.a.433.4 | 8 | 4.3 | odd | 2 | |||
1680.2.cz.b.97.1 | 8 | 20.7 | even | 4 | |||
1680.2.cz.b.433.1 | 8 | 28.27 | even | 2 |