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 | 97.4 | ||
Root | \(-1.69230i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.97 |
Dual form | 210.2.m.a.13.4 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(5\) | 0.489528 | − | 2.18183i | 0.218924 | − | 0.975742i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 1.47472 | + | 2.19663i | 0.557391 | + | 0.830250i | ||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 1.88893 | − | 1.19663i | 0.597333 | − | 0.378409i | ||||
\(11\) | 0.0296189 | 0.00893045 | 0.00446522 | − | 0.999990i | \(-0.498579\pi\) | ||||
0.00446522 | + | 0.999990i | \(0.498579\pi\) | |||||||
\(12\) | −0.707107 | + | 0.707107i | −0.204124 | + | 0.204124i | ||||
\(13\) | −0.585786 | − | 0.585786i | −0.162468 | − | 0.162468i | 0.621191 | − | 0.783659i | \(-0.286649\pi\) |
−0.783659 | + | 0.621191i | \(0.786649\pi\) | |||||||
\(14\) | −0.510472 | + | 2.59604i | −0.136429 | + | 0.693821i | ||||
\(15\) | 1.88893 | − | 1.19663i | 0.487720 | − | 0.308970i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 1.72192 | − | 1.72192i | 0.417626 | − | 0.417626i | −0.466759 | − | 0.884385i | \(-0.654578\pi\) |
0.884385 | + | 0.466759i | \(0.154578\pi\) | |||||||
\(18\) | −0.707107 | + | 0.707107i | −0.166667 | + | 0.166667i | ||||
\(19\) | −5.77786 | −1.32553 | −0.662767 | − | 0.748826i | \(-0.730618\pi\) | ||||
−0.662767 | + | 0.748826i | \(0.730618\pi\) | |||||||
\(20\) | 2.18183 | + | 0.489528i | 0.487871 | + | 0.109462i | ||||
\(21\) | −0.510472 | + | 2.59604i | −0.111394 | + | 0.566502i | ||||
\(22\) | 0.0209438 | + | 0.0209438i | 0.00446522 | + | 0.00446522i | ||||
\(23\) | −0.393270 | + | 0.393270i | −0.0820024 | + | 0.0820024i | −0.746918 | − | 0.664916i | \(-0.768467\pi\) |
0.664916 | + | 0.746918i | \(0.268467\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.52072 | − | 2.13613i | −0.904145 | − | 0.427226i | ||||
\(26\) | − | 0.828427i | − | 0.162468i | ||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | −2.19663 | + | 1.47472i | −0.415125 | + | 0.278696i | ||||
\(29\) | − | 9.70636i | − | 1.80243i | −0.433377 | − | 0.901213i | \(-0.642678\pi\) | ||
0.433377 | − | 0.901213i | \(-0.357322\pi\) | |||||||
\(30\) | 2.18183 | + | 0.489528i | 0.398345 | + | 0.0893752i | ||||
\(31\) | 6.39327i | 1.14827i | 0.818762 | + | 0.574133i | \(0.194661\pi\) | ||||
−0.818762 | + | 0.574133i | \(0.805339\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0.0209438 | + | 0.0209438i | 0.00364584 | + | 0.00364584i | ||||
\(34\) | 2.43516 | 0.417626 | ||||||||
\(35\) | 5.51459 | − | 2.14226i | 0.932136 | − | 0.362109i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −3.72192 | − | 3.72192i | −0.611879 | − | 0.611879i | 0.331556 | − | 0.943435i | \(-0.392426\pi\) |
−0.943435 | + | 0.331556i | \(0.892426\pi\) | |||||||
\(38\) | −4.08557 | − | 4.08557i | −0.662767 | − | 0.662767i | ||||
\(39\) | − | 0.828427i | − | 0.132655i | ||||||
\(40\) | 1.19663 | + | 1.88893i | 0.189205 | + | 0.298666i | ||||
\(41\) | 0.514280i | 0.0803170i | 0.999193 | + | 0.0401585i | \(0.0127863\pi\) | ||||
−0.999193 | + | 0.0401585i | \(0.987214\pi\) | |||||||
\(42\) | −2.19663 | + | 1.47472i | −0.338948 | + | 0.227554i | ||||
\(43\) | 7.16246 | − | 7.16246i | 1.09226 | − | 1.09226i | 0.0969783 | − | 0.995286i | \(-0.469082\pi\) |
0.995286 | − | 0.0969783i | \(-0.0309177\pi\) | |||||||
\(44\) | 0.0296189i | 0.00446522i | ||||||||
\(45\) | 2.18183 | + | 0.489528i | 0.325247 | + | 0.0729745i | ||||
\(46\) | −0.556167 | −0.0820024 | ||||||||
\(47\) | 7.77786 | − | 7.77786i | 1.13452 | − | 1.13452i | 0.145101 | − | 0.989417i | \(-0.453649\pi\) |
0.989417 | − | 0.145101i | \(-0.0463508\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | −2.65041 | + | 6.47884i | −0.378630 | + | 0.925548i | ||||
\(50\) | −1.68616 | − | 4.70711i | −0.238459 | − | 0.665685i | ||||
\(51\) | 2.43516 | 0.340990 | ||||||||
\(52\) | 0.585786 | − | 0.585786i | 0.0812340 | − | 0.0812340i | ||||
\(53\) | −5.77786 | + | 5.77786i | −0.793651 | + | 0.793651i | −0.982086 | − | 0.188435i | \(-0.939659\pi\) |
0.188435 | + | 0.982086i | \(0.439659\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0.0144993 | − | 0.0646234i | 0.00195509 | − | 0.00871381i | ||||
\(56\) | −2.59604 | − | 0.510472i | −0.346910 | − | 0.0682147i | ||||
\(57\) | −4.08557 | − | 4.08557i | −0.541147 | − | 0.541147i | ||||
\(58\) | 6.86343 | − | 6.86343i | 0.901213 | − | 0.901213i | ||||
\(59\) | −12.8070 | −1.66734 | −0.833668 | − | 0.552267i | \(-0.813763\pi\) | ||||
−0.833668 | + | 0.552267i | \(0.813763\pi\) | |||||||
\(60\) | 1.19663 | + | 1.88893i | 0.154485 | + | 0.243860i | ||||
\(61\) | 10.7273i | 1.37349i | 0.726898 | + | 0.686745i | \(0.240961\pi\) | ||||
−0.726898 | + | 0.686745i | \(0.759039\pi\) | |||||||
\(62\) | −4.52072 | + | 4.52072i | −0.574133 | + | 0.574133i | ||||
\(63\) | −2.19663 | + | 1.47472i | −0.276750 | + | 0.185797i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −1.56484 | + | 0.991325i | −0.194095 | + | 0.122959i | ||||
\(66\) | 0.0296189i | 0.00364584i | ||||||||
\(67\) | 2.39327 | + | 2.39327i | 0.292384 | + | 0.292384i | 0.838022 | − | 0.545637i | \(-0.183712\pi\) |
−0.545637 | + | 0.838022i | \(0.683712\pi\) | |||||||
\(68\) | 1.72192 | + | 1.72192i | 0.208813 | + | 0.208813i | ||||
\(69\) | −0.556167 | −0.0669547 | ||||||||
\(70\) | 5.41421 | + | 2.38459i | 0.647122 | + | 0.285014i | ||||
\(71\) | 6.64818 | 0.788994 | 0.394497 | − | 0.918897i | \(-0.370919\pi\) | ||||
0.394497 | + | 0.918897i | \(0.370919\pi\) | |||||||
\(72\) | −0.707107 | − | 0.707107i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | −5.12745 | − | 5.12745i | −0.600123 | − | 0.600123i | 0.340222 | − | 0.940345i | \(-0.389498\pi\) |
−0.940345 | + | 0.340222i | \(0.889498\pi\) | |||||||
\(74\) | − | 5.26358i | − | 0.611879i | ||||||
\(75\) | −1.68616 | − | 4.70711i | −0.194701 | − | 0.543530i | ||||
\(76\) | − | 5.77786i | − | 0.662767i | ||||||
\(77\) | 0.0436796 | + | 0.0650620i | 0.00497775 | + | 0.00741450i | ||||
\(78\) | 0.585786 | − | 0.585786i | 0.0663273 | − | 0.0663273i | ||||
\(79\) | 9.86988i | 1.11045i | 0.831701 | + | 0.555224i | \(0.187367\pi\) | ||||
−0.831701 | + | 0.555224i | \(0.812633\pi\) | |||||||
\(80\) | −0.489528 | + | 2.18183i | −0.0547309 | + | 0.243935i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −0.363651 | + | 0.363651i | −0.0401585 | + | 0.0401585i | ||||
\(83\) | −0.150629 | − | 0.150629i | −0.0165337 | − | 0.0165337i | 0.698792 | − | 0.715325i | \(-0.253721\pi\) |
−0.715325 | + | 0.698792i | \(0.753721\pi\) | |||||||
\(84\) | −2.59604 | − | 0.510472i | −0.283251 | − | 0.0556970i | ||||
\(85\) | −2.91399 | − | 4.59985i | −0.316067 | − | 0.498923i | ||||
\(86\) | 10.1292 | 1.09226 | ||||||||
\(87\) | 6.86343 | − | 6.86343i | 0.735837 | − | 0.735837i | ||||
\(88\) | −0.0209438 | + | 0.0209438i | −0.00223261 | + | 0.00223261i | ||||
\(89\) | 4.38416 | 0.464720 | 0.232360 | − | 0.972630i | \(-0.425355\pi\) | ||||
0.232360 | + | 0.972630i | \(0.425355\pi\) | |||||||
\(90\) | 1.19663 | + | 1.88893i | 0.126136 | + | 0.199111i | ||||
\(91\) | 0.422889 | − | 2.15063i | 0.0443308 | − | 0.225447i | ||||
\(92\) | −0.393270 | − | 0.393270i | −0.0410012 | − | 0.0410012i | ||||
\(93\) | −4.52072 | + | 4.52072i | −0.468777 | + | 0.468777i | ||||
\(94\) | 10.9996 | 1.13452 | ||||||||
\(95\) | −2.82843 | + | 12.6063i | −0.290191 | + | 1.29338i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 2.47016 | − | 2.47016i | 0.250807 | − | 0.250807i | −0.570494 | − | 0.821301i | \(-0.693248\pi\) |
0.821301 | + | 0.570494i | \(0.193248\pi\) | |||||||
\(98\) | −6.45535 | + | 2.70711i | −0.652089 | + | 0.273459i | ||||
\(99\) | 0.0296189i | 0.00297682i | ||||||||
\(100\) | 2.13613 | − | 4.52072i | 0.213613 | − | 0.452072i | ||||
\(101\) | 12.7897i | 1.27262i | 0.771433 | + | 0.636311i | \(0.219541\pi\) | ||||
−0.771433 | + | 0.636311i | \(0.780459\pi\) | |||||||
\(102\) | 1.72192 | + | 1.72192i | 0.170495 | + | 0.170495i | ||||
\(103\) | 8.06462 | + | 8.06462i | 0.794631 | + | 0.794631i | 0.982243 | − | 0.187612i | \(-0.0600748\pi\) |
−0.187612 | + | 0.982243i | \(0.560075\pi\) | |||||||
\(104\) | 0.828427 | 0.0812340 | ||||||||
\(105\) | 5.41421 | + | 2.38459i | 0.528373 | + | 0.232713i | ||||
\(106\) | −8.17113 | −0.793651 | ||||||||
\(107\) | −1.22170 | − | 1.22170i | −0.118106 | − | 0.118106i | 0.645584 | − | 0.763690i | \(-0.276614\pi\) |
−0.763690 | + | 0.645584i | \(0.776614\pi\) | |||||||
\(108\) | −0.707107 | − | 0.707107i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | 14.8984i | 1.42701i | 0.700649 | + | 0.713506i | \(0.252894\pi\) | ||||
−0.700649 | + | 0.713506i | \(0.747106\pi\) | |||||||
\(110\) | 0.0559482 | − | 0.0354431i | 0.00533445 | − | 0.00337936i | ||||
\(111\) | − | 5.26358i | − | 0.499597i | ||||||
\(112\) | −1.47472 | − | 2.19663i | −0.139348 | − | 0.207562i | ||||
\(113\) | −0.0715065 | + | 0.0715065i | −0.00672676 | + | 0.00672676i | −0.710462 | − | 0.703735i | \(-0.751514\pi\) |
0.703735 | + | 0.710462i | \(0.251514\pi\) | |||||||
\(114\) | − | 5.77786i | − | 0.541147i | ||||||
\(115\) | 0.665529 | + | 1.05056i | 0.0620609 | + | 0.0979655i | ||||
\(116\) | 9.70636 | 0.901213 | ||||||||
\(117\) | 0.585786 | − | 0.585786i | 0.0541560 | − | 0.0541560i | ||||
\(118\) | −9.05595 | − | 9.05595i | −0.833668 | − | 0.833668i | ||||
\(119\) | 6.32176 | + | 1.24308i | 0.579515 | + | 0.113953i | ||||
\(120\) | −0.489528 | + | 2.18183i | −0.0446876 | + | 0.199173i | ||||
\(121\) | −10.9991 | −0.999920 | ||||||||
\(122\) | −7.58535 | + | 7.58535i | −0.686745 | + | 0.686745i | ||||
\(123\) | −0.363651 | + | 0.363651i | −0.0327893 | + | 0.0327893i | ||||
\(124\) | −6.39327 | −0.574133 | ||||||||
\(125\) | −6.87368 | + | 8.81774i | −0.614801 | + | 0.788682i | ||||
\(126\) | −2.59604 | − | 0.510472i | −0.231274 | − | 0.0454764i | ||||
\(127\) | 6.15663 | + | 6.15663i | 0.546313 | + | 0.546313i | 0.925372 | − | 0.379059i | \(-0.123752\pi\) |
−0.379059 | + | 0.925372i | \(0.623752\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 10.1292 | 0.891830 | ||||||||
\(130\) | −1.80748 | − | 0.405538i | −0.158527 | − | 0.0355681i | ||||
\(131\) | 4.52401i | 0.395265i | 0.980276 | + | 0.197632i | \(0.0633253\pi\) | ||||
−0.980276 | + | 0.197632i | \(0.936675\pi\) | |||||||
\(132\) | −0.0209438 | + | 0.0209438i | −0.00182292 | + | 0.00182292i | ||||
\(133\) | −8.52072 | − | 12.6919i | −0.738841 | − | 1.10052i | ||||
\(134\) | 3.38459i | 0.292384i | ||||||||
\(135\) | 1.19663 | + | 1.88893i | 0.102990 | + | 0.162573i | ||||
\(136\) | 2.43516i | 0.208813i | ||||||||
\(137\) | 5.58535 | + | 5.58535i | 0.477188 | + | 0.477188i | 0.904231 | − | 0.427043i | \(-0.140445\pi\) |
−0.427043 | + | 0.904231i | \(0.640445\pi\) | |||||||
\(138\) | −0.393270 | − | 0.393270i | −0.0334773 | − | 0.0334773i | ||||
\(139\) | 16.6063 | 1.40853 | 0.704264 | − | 0.709939i | \(-0.251277\pi\) | ||||
0.704264 | + | 0.709939i | \(0.251277\pi\) | |||||||
\(140\) | 2.14226 | + | 5.51459i | 0.181054 | + | 0.466068i | ||||
\(141\) | 10.9996 | 0.926330 | ||||||||
\(142\) | 4.70097 | + | 4.70097i | 0.394497 | + | 0.394497i | ||||
\(143\) | −0.0173504 | − | 0.0173504i | −0.00145091 | − | 0.00145091i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | −21.1776 | − | 4.75154i | −1.75870 | − | 0.394594i | ||||
\(146\) | − | 7.25132i | − | 0.600123i | ||||||
\(147\) | −6.45535 | + | 2.70711i | −0.532428 | + | 0.223278i | ||||
\(148\) | 3.72192 | − | 3.72192i | 0.305940 | − | 0.305940i | ||||
\(149\) | − | 7.80748i | − | 0.639614i | −0.947483 | − | 0.319807i | \(-0.896382\pi\) | ||
0.947483 | − | 0.319807i | \(-0.103618\pi\) | |||||||
\(150\) | 2.13613 | − | 4.52072i | 0.174414 | − | 0.369116i | ||||
\(151\) | 0.870315 | 0.0708252 | 0.0354126 | − | 0.999373i | \(-0.488725\pi\) | ||||
0.0354126 | + | 0.999373i | \(0.488725\pi\) | |||||||
\(152\) | 4.08557 | − | 4.08557i | 0.331383 | − | 0.331383i | ||||
\(153\) | 1.72192 | + | 1.72192i | 0.139209 | + | 0.139209i | ||||
\(154\) | −0.0151196 | + | 0.0768919i | −0.00121838 | + | 0.00619613i | ||||
\(155\) | 13.9490 | + | 3.12969i | 1.12041 | + | 0.251382i | ||||
\(156\) | 0.828427 | 0.0663273 | ||||||||
\(157\) | 15.8403 | − | 15.8403i | 1.26419 | − | 1.26419i | 0.315147 | − | 0.949043i | \(-0.397946\pi\) |
0.949043 | − | 0.315147i | \(-0.102054\pi\) | |||||||
\(158\) | −6.97906 | + | 6.97906i | −0.555224 | + | 0.555224i | ||||
\(159\) | −8.17113 | −0.648013 | ||||||||
\(160\) | −1.88893 | + | 1.19663i | −0.149333 | + | 0.0946023i | ||||
\(161\) | −1.44383 | − | 0.283908i | −0.113790 | − | 0.0223751i | ||||
\(162\) | −0.707107 | − | 0.707107i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 2.70742 | − | 2.70742i | 0.212061 | − | 0.212061i | −0.593081 | − | 0.805143i | \(-0.702089\pi\) |
0.805143 | + | 0.593081i | \(0.202089\pi\) | |||||||
\(164\) | −0.514280 | −0.0401585 | ||||||||
\(165\) | 0.0559482 | − | 0.0354431i | 0.00435556 | − | 0.00275924i | ||||
\(166\) | − | 0.213022i | − | 0.0165337i | ||||||
\(167\) | −13.7779 | + | 13.7779i | −1.06616 | + | 1.06616i | −0.0685129 | + | 0.997650i | \(0.521825\pi\) |
−0.997650 | + | 0.0685129i | \(0.978175\pi\) | |||||||
\(168\) | −1.47472 | − | 2.19663i | −0.113777 | − | 0.169474i | ||||
\(169\) | − | 12.3137i | − | 0.947208i | ||||||
\(170\) | 1.19208 | − | 5.31309i | 0.0914282 | − | 0.407495i | ||||
\(171\) | − | 5.77786i | − | 0.441844i | ||||||
\(172\) | 7.16246 | + | 7.16246i | 0.546132 | + | 0.546132i | ||||
\(173\) | 10.3077 | + | 10.3077i | 0.783680 | + | 0.783680i | 0.980450 | − | 0.196770i | \(-0.0630451\pi\) |
−0.196770 | + | 0.980450i | \(0.563045\pi\) | |||||||
\(174\) | 9.70636 | 0.735837 | ||||||||
\(175\) | −1.97450 | − | 13.0806i | −0.149258 | − | 0.988798i | ||||
\(176\) | −0.0296189 | −0.00223261 | ||||||||
\(177\) | −9.05595 | − | 9.05595i | −0.680687 | − | 0.680687i | ||||
\(178\) | 3.10007 | + | 3.10007i | 0.232360 | + | 0.232360i | ||||
\(179\) | − | 17.2422i | − | 1.28874i | −0.764713 | − | 0.644371i | \(-0.777119\pi\) | ||
0.764713 | − | 0.644371i | \(-0.222881\pi\) | |||||||
\(180\) | −0.489528 | + | 2.18183i | −0.0364873 | + | 0.162624i | ||||
\(181\) | − | 22.4015i | − | 1.66509i | −0.553957 | − | 0.832545i | \(-0.686883\pi\) | ||
0.553957 | − | 0.832545i | \(-0.313117\pi\) | |||||||
\(182\) | 1.81975 | − | 1.22170i | 0.134889 | − | 0.0905582i | ||||
\(183\) | −7.58535 | + | 7.58535i | −0.560725 | + | 0.560725i | ||||
\(184\) | − | 0.556167i | − | 0.0410012i | ||||||
\(185\) | −9.94255 | + | 6.29859i | −0.730991 | + | 0.463081i | ||||
\(186\) | −6.39327 | −0.468777 | ||||||||
\(187\) | 0.0510013 | − | 0.0510013i | 0.00372959 | − | 0.00372959i | ||||
\(188\) | 7.77786 | + | 7.77786i | 0.567259 | + | 0.567259i | ||||
\(189\) | −2.59604 | − | 0.510472i | −0.188834 | − | 0.0371314i | ||||
\(190\) | −10.9140 | + | 6.91399i | −0.791784 | + | 0.501594i | ||||
\(191\) | −22.5644 | −1.63270 | −0.816351 | − | 0.577555i | \(-0.804007\pi\) | ||||
−0.816351 | + | 0.577555i | \(0.804007\pi\) | |||||||
\(192\) | 0.707107 | − | 0.707107i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | 4.94076 | − | 4.94076i | 0.355644 | − | 0.355644i | −0.506561 | − | 0.862204i | \(-0.669083\pi\) |
0.862204 | + | 0.506561i | \(0.169083\pi\) | |||||||
\(194\) | 3.49334 | 0.250807 | ||||||||
\(195\) | −1.80748 | − | 0.405538i | −0.129437 | − | 0.0290412i | ||||
\(196\) | −6.47884 | − | 2.65041i | −0.462774 | − | 0.189315i | ||||
\(197\) | −6.64818 | − | 6.64818i | −0.473663 | − | 0.473663i | 0.429435 | − | 0.903098i | \(-0.358713\pi\) |
−0.903098 | + | 0.429435i | \(0.858713\pi\) | |||||||
\(198\) | −0.0209438 | + | 0.0209438i | −0.00148841 | + | 0.00148841i | ||||
\(199\) | −12.2631 | −0.869311 | −0.434656 | − | 0.900597i | \(-0.643130\pi\) | ||||
−0.434656 | + | 0.900597i | \(0.643130\pi\) | |||||||
\(200\) | 4.70711 | − | 1.68616i | 0.332843 | − | 0.119230i | ||||
\(201\) | 3.38459i | 0.238731i | ||||||||
\(202\) | −9.04368 | + | 9.04368i | −0.636311 | + | 0.636311i | ||||
\(203\) | 21.3213 | − | 14.3141i | 1.49646 | − | 1.00466i | ||||
\(204\) | 2.43516i | 0.170495i | ||||||||
\(205\) | 1.12207 | + | 0.251755i | 0.0783687 | + | 0.0175833i | ||||
\(206\) | 11.4051i | 0.794631i | ||||||||
\(207\) | −0.393270 | − | 0.393270i | −0.0273341 | − | 0.0273341i | ||||
\(208\) | 0.585786 | + | 0.585786i | 0.0406170 | + | 0.0406170i | ||||
\(209\) | −0.171134 | −0.0118376 | ||||||||
\(210\) | 2.14226 | + | 5.51459i | 0.147830 | + | 0.380543i | ||||
\(211\) | −4.62829 | −0.318625 | −0.159312 | − | 0.987228i | \(-0.550928\pi\) | ||||
−0.159312 | + | 0.987228i | \(0.550928\pi\) | |||||||
\(212\) | −5.77786 | − | 5.77786i | −0.396825 | − | 0.396825i | ||||
\(213\) | 4.70097 | + | 4.70097i | 0.322105 | + | 0.322105i | ||||
\(214\) | − | 1.72774i | − | 0.118106i | ||||||
\(215\) | −12.1210 | − | 19.1335i | −0.826646 | − | 1.30489i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −14.0437 | + | 9.42827i | −0.953347 | + | 0.640033i | ||||
\(218\) | −10.5348 | + | 10.5348i | −0.713506 | + | 0.713506i | ||||
\(219\) | − | 7.25132i | − | 0.489999i | ||||||
\(220\) | 0.0646234 | + | 0.0144993i | 0.00435691 | + | 0.000977543i | ||||
\(221\) | −2.01735 | −0.135702 | ||||||||
\(222\) | 3.72192 | − | 3.72192i | 0.249799 | − | 0.249799i | ||||
\(223\) | 18.2266 | + | 18.2266i | 1.22055 | + | 1.22055i | 0.967438 | + | 0.253108i | \(0.0814529\pi\) |
0.253108 | + | 0.967438i | \(0.418547\pi\) | |||||||
\(224\) | 0.510472 | − | 2.59604i | 0.0341073 | − | 0.173455i | ||||
\(225\) | 2.13613 | − | 4.52072i | 0.142409 | − | 0.301382i | ||||
\(226\) | −0.101125 | −0.00672676 | ||||||||
\(227\) | −8.89844 | + | 8.89844i | −0.590610 | + | 0.590610i | −0.937796 | − | 0.347186i | \(-0.887137\pi\) |
0.347186 | + | 0.937796i | \(0.387137\pi\) | |||||||
\(228\) | 4.08557 | − | 4.08557i | 0.270573 | − | 0.270573i | ||||
\(229\) | 13.3137 | 0.879795 | 0.439897 | − | 0.898048i | \(-0.355015\pi\) | ||||
0.439897 | + | 0.898048i | \(0.355015\pi\) | |||||||
\(230\) | −0.272260 | + | 1.21346i | −0.0179523 | + | 0.0800132i | ||||
\(231\) | −0.0151196 | + | 0.0768919i | −0.000994799 | + | 0.00505912i | ||||
\(232\) | 6.86343 | + | 6.86343i | 0.450606 | + | 0.450606i | ||||
\(233\) | −2.18340 | + | 2.18340i | −0.143039 | + | 0.143039i | −0.775000 | − | 0.631961i | \(-0.782250\pi\) |
0.631961 | + | 0.775000i | \(0.282250\pi\) | |||||||
\(234\) | 0.828427 | 0.0541560 | ||||||||
\(235\) | −13.1625 | − | 20.7774i | −0.858624 | − | 1.35537i | ||||
\(236\) | − | 12.8070i | − | 0.833668i | ||||||
\(237\) | −6.97906 | + | 6.97906i | −0.453338 | + | 0.453338i | ||||
\(238\) | 3.59117 | + | 5.34915i | 0.232781 | + | 0.346734i | ||||
\(239\) | 18.1201i | 1.17209i | 0.810277 | + | 0.586047i | \(0.199317\pi\) | ||||
−0.810277 | + | 0.586047i | \(0.800683\pi\) | |||||||
\(240\) | −1.88893 | + | 1.19663i | −0.121930 | + | 0.0772425i | ||||
\(241\) | − | 19.6257i | − | 1.26420i | −0.774885 | − | 0.632102i | \(-0.782192\pi\) | ||
0.774885 | − | 0.632102i | \(-0.217808\pi\) | |||||||
\(242\) | −7.77755 | − | 7.77755i | −0.499960 | − | 0.499960i | ||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | −10.7273 | −0.686745 | ||||||||
\(245\) | 12.8382 | + | 8.95430i | 0.820205 | + | 0.572070i | ||||
\(246\) | −0.514280 | −0.0327893 | ||||||||
\(247\) | 3.38459 | + | 3.38459i | 0.215357 | + | 0.215357i | ||||
\(248\) | −4.52072 | − | 4.52072i | −0.287066 | − | 0.287066i | ||||
\(249\) | − | 0.213022i | − | 0.0134997i | ||||||
\(250\) | −11.0955 | + | 1.37465i | −0.701742 | + | 0.0869406i | ||||
\(251\) | − | 28.7478i | − | 1.81455i | −0.420543 | − | 0.907273i | \(-0.638160\pi\) | ||
0.420543 | − | 0.907273i | \(-0.361840\pi\) | |||||||
\(252\) | −1.47472 | − | 2.19663i | −0.0928985 | − | 0.138375i | ||||
\(253\) | −0.0116482 | + | 0.0116482i | −0.000732318 | + | 0.000732318i | ||||
\(254\) | 8.70680i | 0.546313i | ||||||||
\(255\) | 1.19208 | − | 5.31309i | 0.0746508 | − | 0.332718i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.5789 | − | 15.5789i | 0.971785 | − | 0.971785i | −0.0278275 | − | 0.999613i | \(-0.508859\pi\) |
0.999613 | + | 0.0278275i | \(0.00885890\pi\) | |||||||
\(258\) | 7.16246 | + | 7.16246i | 0.445915 | + | 0.445915i | ||||
\(259\) | 2.68691 | − | 13.6645i | 0.166957 | − | 0.849069i | ||||
\(260\) | −0.991325 | − | 1.56484i | −0.0614794 | − | 0.0970474i | ||||
\(261\) | 9.70636 | 0.600808 | ||||||||
\(262\) | −3.19896 | + | 3.19896i | −0.197632 | + | 0.197632i | ||||
\(263\) | 7.34271 | − | 7.34271i | 0.452771 | − | 0.452771i | −0.443502 | − | 0.896273i | \(-0.646264\pi\) |
0.896273 | + | 0.443502i | \(0.146264\pi\) | |||||||
\(264\) | −0.0296189 | −0.00182292 | ||||||||
\(265\) | 9.77786 | + | 15.4347i | 0.600649 | + | 0.948147i | ||||
\(266\) | 2.94944 | − | 14.9996i | 0.180842 | − | 0.919682i | ||||
\(267\) | 3.10007 | + | 3.10007i | 0.189721 | + | 0.189721i | ||||
\(268\) | −2.39327 | + | 2.39327i | −0.146192 | + | 0.146192i | ||||
\(269\) | −16.6069 | −1.01254 | −0.506271 | − | 0.862375i | \(-0.668976\pi\) | ||||
−0.506271 | + | 0.862375i | \(0.668976\pi\) | |||||||
\(270\) | −0.489528 | + | 2.18183i | −0.0297917 | + | 0.132782i | ||||
\(271\) | 9.90353i | 0.601596i | 0.953688 | + | 0.300798i | \(0.0972531\pi\) | ||||
−0.953688 | + | 0.300798i | \(0.902747\pi\) | |||||||
\(272\) | −1.72192 | + | 1.72192i | −0.104407 | + | 0.104407i | ||||
\(273\) | 1.81975 | − | 1.22170i | 0.110136 | − | 0.0739405i | ||||
\(274\) | 7.89887i | 0.477188i | ||||||||
\(275\) | −0.133899 | − | 0.0632699i | −0.00807442 | − | 0.00381532i | ||||
\(276\) | − | 0.556167i | − | 0.0334773i | ||||||
\(277\) | 2.93538 | + | 2.93538i | 0.176370 | + | 0.176370i | 0.789771 | − | 0.613402i | \(-0.210199\pi\) |
−0.613402 | + | 0.789771i | \(0.710199\pi\) | |||||||
\(278\) | 11.7424 | + | 11.7424i | 0.704264 | + | 0.704264i | ||||
\(279\) | −6.39327 | −0.382755 | ||||||||
\(280\) | −2.38459 | + | 5.41421i | −0.142507 | + | 0.323561i | ||||
\(281\) | −4.70995 | −0.280972 | −0.140486 | − | 0.990083i | \(-0.544867\pi\) | ||||
−0.140486 | + | 0.990083i | \(0.544867\pi\) | |||||||
\(282\) | 7.77786 | + | 7.77786i | 0.463165 | + | 0.463165i | ||||
\(283\) | 13.0588 | + | 13.0588i | 0.776265 | + | 0.776265i | 0.979194 | − | 0.202929i | \(-0.0650459\pi\) |
−0.202929 | + | 0.979194i | \(0.565046\pi\) | |||||||
\(284\) | 6.64818i | 0.394497i | ||||||||
\(285\) | −10.9140 | + | 6.91399i | −0.646489 | + | 0.409550i | ||||
\(286\) | − | 0.0245371i | − | 0.00145091i | ||||||
\(287\) | −1.12969 | + | 0.758418i | −0.0666832 | + | 0.0447680i | ||||
\(288\) | 0.707107 | − | 0.707107i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | 11.0700i | 0.651177i | ||||||||
\(290\) | −11.6150 | − | 18.3347i | −0.682054 | − | 1.07665i | ||||
\(291\) | 3.49334 | 0.204783 | ||||||||
\(292\) | 5.12745 | − | 5.12745i | 0.300062 | − | 0.300062i | ||||
\(293\) | −16.8844 | − | 16.8844i | −0.986396 | − | 0.986396i | 0.0135130 | − | 0.999909i | \(-0.495699\pi\) |
−0.999909 | + | 0.0135130i | \(0.995699\pi\) | |||||||
\(294\) | −6.47884 | − | 2.65041i | −0.377853 | − | 0.154575i | ||||
\(295\) | −6.26941 | + | 27.9427i | −0.365019 | + | 1.62689i | ||||
\(296\) | 5.26358 | 0.305940 | ||||||||
\(297\) | −0.0209438 | + | 0.0209438i | −0.00121528 | + | 0.00121528i | ||||
\(298\) | 5.52072 | − | 5.52072i | 0.319807 | − | 0.319807i | ||||
\(299\) | 0.460744 | 0.0266455 | ||||||||
\(300\) | 4.70711 | − | 1.68616i | 0.271765 | − | 0.0973507i | ||||
\(301\) | 26.2959 | + | 5.17070i | 1.51567 | + | 0.298034i | ||||
\(302\) | 0.615405 | + | 0.615405i | 0.0354126 | + | 0.0354126i | ||||
\(303\) | −9.04368 | + | 9.04368i | −0.519546 | + | 0.519546i | ||||
\(304\) | 5.77786 | 0.331383 | ||||||||
\(305\) | 23.4051 | + | 5.25132i | 1.34017 | + | 0.300689i | ||||
\(306\) | 2.43516i | 0.139209i | ||||||||
\(307\) | −11.5185 | + | 11.5185i | −0.657395 | + | 0.657395i | −0.954763 | − | 0.297368i | \(-0.903891\pi\) |
0.297368 | + | 0.954763i | \(0.403891\pi\) | |||||||
\(308\) | −0.0650620 | + | 0.0436796i | −0.00370725 | + | 0.00248888i | ||||
\(309\) | 11.4051i | 0.648813i | ||||||||
\(310\) | 7.65041 | + | 12.0765i | 0.434514 | + | 0.685896i | ||||
\(311\) | − | 9.59762i | − | 0.544231i | −0.962265 | − | 0.272115i | \(-0.912277\pi\) | ||
0.962265 | − | 0.272115i | \(-0.0877233\pi\) | |||||||
\(312\) | 0.585786 | + | 0.585786i | 0.0331636 | + | 0.0331636i | ||||
\(313\) | −0.529400 | − | 0.529400i | −0.0299234 | − | 0.0299234i | 0.691987 | − | 0.721910i | \(-0.256736\pi\) |
−0.721910 | + | 0.691987i | \(0.756736\pi\) | |||||||
\(314\) | 22.4015 | 1.26419 | ||||||||
\(315\) | 2.14226 | + | 5.51459i | 0.120703 | + | 0.310712i | ||||
\(316\) | −9.86988 | −0.555224 | ||||||||
\(317\) | 19.8576 | + | 19.8576i | 1.11531 | + | 1.11531i | 0.992420 | + | 0.122895i | \(0.0392177\pi\) |
0.122895 | + | 0.992420i | \(0.460782\pi\) | |||||||
\(318\) | −5.77786 | − | 5.77786i | −0.324007 | − | 0.324007i | ||||
\(319\) | − | 0.287492i | − | 0.0160965i | ||||||
\(320\) | −2.18183 | − | 0.489528i | −0.121968 | − | 0.0273655i | ||||
\(321\) | − | 1.72774i | − | 0.0964331i | ||||||
\(322\) | −0.820191 | − | 1.22170i | −0.0457074 | − | 0.0680825i | ||||
\(323\) | −9.94900 | + | 9.94900i | −0.553577 | + | 0.553577i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | 1.39686 | + | 3.89949i | 0.0774840 | + | 0.216305i | ||||
\(326\) | 3.82887 | 0.212061 | ||||||||
\(327\) | −10.5348 | + | 10.5348i | −0.582575 | + | 0.582575i | ||||
\(328\) | −0.363651 | − | 0.363651i | −0.0200793 | − | 0.0200793i | ||||
\(329\) | 28.5553 | + | 5.61497i | 1.57430 | + | 0.309563i | ||||
\(330\) | 0.0646234 | + | 0.0144993i | 0.00355740 | + | 0.000798160i | ||||
\(331\) | 4.64353 | 0.255231 | 0.127616 | − | 0.991824i | \(-0.459268\pi\) | ||||
0.127616 | + | 0.991824i | \(0.459268\pi\) | |||||||
\(332\) | 0.150629 | − | 0.150629i | 0.00826685 | − | 0.00826685i | ||||
\(333\) | 3.72192 | − | 3.72192i | 0.203960 | − | 0.203960i | ||||
\(334\) | −19.4848 | −1.06616 | ||||||||
\(335\) | 6.39327 | − | 4.05012i | 0.349302 | − | 0.221282i | ||||
\(336\) | 0.510472 | − | 2.59604i | 0.0278485 | − | 0.141626i | ||||
\(337\) | 7.05924 | + | 7.05924i | 0.384541 | + | 0.384541i | 0.872735 | − | 0.488194i | \(-0.162344\pi\) |
−0.488194 | + | 0.872735i | \(0.662344\pi\) | |||||||
\(338\) | 8.70711 | − | 8.70711i | 0.473604 | − | 0.473604i | ||||
\(339\) | −0.101125 | −0.00549238 | ||||||||
\(340\) | 4.59985 | − | 2.91399i | 0.249462 | − | 0.158034i | ||||
\(341\) | 0.189362i | 0.0102545i | ||||||||
\(342\) | 4.08557 | − | 4.08557i | 0.220922 | − | 0.220922i | ||||
\(343\) | −18.1402 | + | 3.73248i | −0.979481 | + | 0.201535i | ||||
\(344\) | 10.1292i | 0.546132i | ||||||||
\(345\) | −0.272260 | + | 1.21346i | −0.0146580 | + | 0.0653305i | ||||
\(346\) | 14.5773i | 0.783680i | ||||||||
\(347\) | −23.4925 | − | 23.4925i | −1.26114 | − | 1.26114i | −0.950540 | − | 0.310601i | \(-0.899470\pi\) |
−0.310601 | − | 0.950540i | \(-0.600530\pi\) | |||||||
\(348\) | 6.86343 | + | 6.86343i | 0.367919 | + | 0.367919i | ||||
\(349\) | 20.1819 | 1.08031 | 0.540156 | − | 0.841565i | \(-0.318365\pi\) | ||||
0.540156 | + | 0.841565i | \(0.318365\pi\) | |||||||
\(350\) | 7.85318 | − | 10.6455i | 0.419770 | − | 0.569028i | ||||
\(351\) | 0.828427 | 0.0442182 | ||||||||
\(352\) | −0.0209438 | − | 0.0209438i | −0.00111631 | − | 0.00111631i | ||||
\(353\) | 7.44966 | + | 7.44966i | 0.396505 | + | 0.396505i | 0.876998 | − | 0.480493i | \(-0.159542\pi\) |
−0.480493 | + | 0.876998i | \(0.659542\pi\) | |||||||
\(354\) | − | 12.8070i | − | 0.680687i | ||||||
\(355\) | 3.25447 | − | 14.5052i | 0.172729 | − | 0.769854i | ||||
\(356\) | 4.38416i | 0.232360i | ||||||||
\(357\) | 3.59117 | + | 5.34915i | 0.190065 | + | 0.283107i | ||||
\(358\) | 12.1921 | − | 12.1921i | 0.644371 | − | 0.644371i | ||||
\(359\) | 16.6063i | 0.876447i | 0.898866 | + | 0.438223i | \(0.144392\pi\) | ||||
−0.898866 | + | 0.438223i | \(0.855608\pi\) | |||||||
\(360\) | −1.88893 | + | 1.19663i | −0.0995555 | + | 0.0630682i | ||||
\(361\) | 14.3837 | 0.757038 | ||||||||
\(362\) | 15.8403 | − | 15.8403i | 0.832545 | − | 0.832545i | ||||
\(363\) | −7.77755 | − | 7.77755i | −0.408216 | − | 0.408216i | ||||
\(364\) | 2.15063 | + | 0.422889i | 0.112724 | + | 0.0221654i | ||||
\(365\) | −13.6972 | + | 8.67718i | −0.716947 | + | 0.454184i | ||||
\(366\) | −10.7273 | −0.560725 | ||||||||
\(367\) | 2.87317 | − | 2.87317i | 0.149978 | − | 0.149978i | −0.628130 | − | 0.778108i | \(-0.716179\pi\) |
0.778108 | + | 0.628130i | \(0.216179\pi\) | |||||||
\(368\) | 0.393270 | − | 0.393270i | 0.0205006 | − | 0.0205006i | ||||
\(369\) | −0.514280 | −0.0267723 | ||||||||
\(370\) | −11.4842 | − | 2.57667i | −0.597036 | − | 0.133955i | ||||
\(371\) | −21.2126 | − | 4.17113i | −1.10130 | − | 0.216554i | ||||
\(372\) | −4.52072 | − | 4.52072i | −0.234389 | − | 0.234389i | ||||
\(373\) | −1.55078 | + | 1.55078i | −0.0802964 | + | 0.0802964i | −0.746114 | − | 0.665818i | \(-0.768083\pi\) |
0.665818 | + | 0.746114i | \(0.268083\pi\) | |||||||
\(374\) | 0.0721268 | 0.00372959 | ||||||||
\(375\) | −11.0955 | + | 1.37465i | −0.572970 | + | 0.0709867i | ||||
\(376\) | 10.9996i | 0.567259i | ||||||||
\(377\) | −5.68585 | + | 5.68585i | −0.292836 | + | 0.292836i | ||||
\(378\) | −1.47472 | − | 2.19663i | −0.0758513 | − | 0.112983i | ||||
\(379\) | 6.92743i | 0.355838i | 0.984045 | + | 0.177919i | \(0.0569366\pi\) | ||||
−0.984045 | + | 0.177919i | \(0.943063\pi\) | |||||||
\(380\) | −12.6063 | − | 2.82843i | −0.646689 | − | 0.145095i | ||||
\(381\) | 8.70680i | 0.446063i | ||||||||
\(382\) | −15.9554 | − | 15.9554i | −0.816351 | − | 0.816351i | ||||
\(383\) | 3.46372 | + | 3.46372i | 0.176988 | + | 0.176988i | 0.790041 | − | 0.613054i | \(-0.210059\pi\) |
−0.613054 | + | 0.790041i | \(0.710059\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0.163336 | − | 0.0634516i | 0.00832439 | − | 0.00323379i | ||||
\(386\) | 6.98729 | 0.355644 | ||||||||
\(387\) | 7.16246 | + | 7.16246i | 0.364088 | + | 0.364088i | ||||
\(388\) | 2.47016 | + | 2.47016i | 0.125403 | + | 0.125403i | ||||
\(389\) | − | 24.9198i | − | 1.26348i | −0.775178 | − | 0.631742i | \(-0.782340\pi\) | ||
0.775178 | − | 0.631742i | \(-0.217660\pi\) | |||||||
\(390\) | −0.991325 | − | 1.56484i | −0.0501977 | − | 0.0792389i | ||||
\(391\) | 1.35436i | 0.0684927i | ||||||||
\(392\) | −2.70711 | − | 6.45535i | −0.136730 | − | 0.326045i | ||||
\(393\) | −3.19896 | + | 3.19896i | −0.161366 | + | 0.161366i | ||||
\(394\) | − | 9.40194i | − | 0.473663i | ||||||
\(395\) | 21.5343 | + | 4.83158i | 1.08351 | + | 0.243103i | ||||
\(396\) | −0.0296189 | −0.00148841 | ||||||||
\(397\) | 13.6562 | − | 13.6562i | 0.685387 | − | 0.685387i | −0.275822 | − | 0.961209i | \(-0.588950\pi\) |
0.961209 | + | 0.275822i | \(0.0889500\pi\) | |||||||
\(398\) | −8.67135 | − | 8.67135i | −0.434656 | − | 0.434656i | ||||
\(399\) | 2.94944 | − | 14.9996i | 0.147657 | − | 0.750917i | ||||
\(400\) | 4.52072 | + | 2.13613i | 0.226036 | + | 0.106806i | ||||
\(401\) | 13.0125 | 0.649811 | 0.324905 | − | 0.945747i | \(-0.394668\pi\) | ||||
0.324905 | + | 0.945747i | \(0.394668\pi\) | |||||||
\(402\) | −2.39327 | + | 2.39327i | −0.119365 | + | 0.119365i | ||||
\(403\) | 3.74509 | − | 3.74509i | 0.186556 | − | 0.186556i | ||||
\(404\) | −12.7897 | −0.636311 | ||||||||
\(405\) | −0.489528 | + | 2.18183i | −0.0243248 | + | 0.108416i | ||||
\(406\) | 25.1981 | + | 4.95482i | 1.25056 | + | 0.245904i | ||||
\(407\) | −0.110239 | − | 0.110239i | −0.00546436 | − | 0.00546436i | ||||
\(408\) | −1.72192 | + | 1.72192i | −0.0852476 | + | 0.0852476i | ||||
\(409\) | −10.6154 | −0.524898 | −0.262449 | − | 0.964946i | \(-0.584530\pi\) | ||||
−0.262449 | + | 0.964946i | \(0.584530\pi\) | |||||||
\(410\) | 0.615405 | + | 0.971440i | 0.0303927 | + | 0.0479760i | ||||
\(411\) | 7.89887i | 0.389623i | ||||||||
\(412\) | −8.06462 | + | 8.06462i | −0.397315 | + | 0.397315i | ||||
\(413\) | −18.8868 | − | 28.1324i | −0.929358 | − | 1.38430i | ||||
\(414\) | − | 0.556167i | − | 0.0273341i | ||||||
\(415\) | −0.402384 | + | 0.254909i | −0.0197522 | + | 0.0125130i | ||||
\(416\) | 0.828427i | 0.0406170i | ||||||||
\(417\) | 11.7424 | + | 11.7424i | 0.575029 | + | 0.575029i | ||||
\(418\) | −0.121010 | − | 0.121010i | −0.00591880 | − | 0.00591880i | ||||
\(419\) | −9.83560 | −0.480501 | −0.240250 | − | 0.970711i | \(-0.577230\pi\) | ||||
−0.240250 | + | 0.970711i | \(0.577230\pi\) | |||||||
\(420\) | −2.38459 | + | 5.41421i | −0.116356 | + | 0.264187i | ||||
\(421\) | −32.5963 | −1.58865 | −0.794323 | − | 0.607495i | \(-0.792174\pi\) | ||||
−0.794323 | + | 0.607495i | \(0.792174\pi\) | |||||||
\(422\) | −3.27270 | − | 3.27270i | −0.159312 | − | 0.159312i | ||||
\(423\) | 7.77786 | + | 7.77786i | 0.378173 | + | 0.378173i | ||||
\(424\) | − | 8.17113i | − | 0.396825i | ||||||
\(425\) | −11.4625 | + | 4.10607i | −0.556015 | + | 0.199174i | ||||
\(426\) | 6.64818i | 0.322105i | ||||||||
\(427\) | −23.5640 | + | 15.8198i | −1.14034 | + | 0.765571i | ||||
\(428\) | 1.22170 | − | 1.22170i | 0.0590530 | − | 0.0590530i | ||||
\(429\) | − | 0.0245371i | − | 0.00118466i | ||||||
\(430\) | 4.95855 | − | 22.1002i | 0.239123 | − | 1.06577i | ||||
\(431\) | −29.3746 | −1.41492 | −0.707462 | − | 0.706751i | \(-0.750160\pi\) | ||||
−0.707462 | + | 0.706751i | \(0.750160\pi\) | |||||||
\(432\) | 0.707107 | − | 0.707107i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | −17.1266 | − | 17.1266i | −0.823051 | − | 0.823051i | 0.163494 | − | 0.986544i | \(-0.447724\pi\) |
−0.986544 | + | 0.163494i | \(0.947724\pi\) | |||||||
\(434\) | −16.5972 | − | 3.26358i | −0.796690 | − | 0.156657i | ||||
\(435\) | −11.6150 | − | 18.3347i | −0.556895 | − | 0.879079i | ||||
\(436\) | −14.8984 | −0.713506 | ||||||||
\(437\) | 2.27226 | − | 2.27226i | 0.108697 | − | 0.108697i | ||||
\(438\) | 5.12745 | − | 5.12745i | 0.244999 | − | 0.244999i | ||||
\(439\) | −2.29872 | −0.109712 | −0.0548561 | − | 0.998494i | \(-0.517470\pi\) | ||||
−0.0548561 | + | 0.998494i | \(0.517470\pi\) | |||||||
\(440\) | 0.0354431 | + | 0.0559482i | 0.00168968 | + | 0.00266722i | ||||
\(441\) | −6.47884 | − | 2.65041i | −0.308516 | − | 0.126210i | ||||
\(442\) | −1.42648 | − | 1.42648i | −0.0678508 | − | 0.0678508i | ||||
\(443\) | −1.39433 | + | 1.39433i | −0.0662466 | + | 0.0662466i | −0.739454 | − | 0.673207i | \(-0.764916\pi\) |
0.673207 | + | 0.739454i | \(0.264916\pi\) | |||||||
\(444\) | 5.26358 | 0.249799 | ||||||||
\(445\) | 2.14617 | − | 9.56546i | 0.101738 | − | 0.453446i | ||||
\(446\) | 25.7764i | 1.22055i | ||||||||
\(447\) | 5.52072 | − | 5.52072i | 0.261121 | − | 0.261121i | ||||
\(448\) | 2.19663 | − | 1.47472i | 0.103781 | − | 0.0696739i | ||||
\(449\) | − | 6.72730i | − | 0.317481i | −0.987320 | − | 0.158740i | \(-0.949257\pi\) | ||
0.987320 | − | 0.158740i | \(-0.0507433\pi\) | |||||||
\(450\) | 4.70711 | − | 1.68616i | 0.221895 | − | 0.0794865i | ||||
\(451\) | 0.0152324i | 0.000717267i | ||||||||
\(452\) | −0.0715065 | − | 0.0715065i | −0.00336338 | − | 0.00336338i | ||||
\(453\) | 0.615405 | + | 0.615405i | 0.0289143 | + | 0.0289143i | ||||
\(454\) | −12.5843 | −0.590610 | ||||||||
\(455\) | −4.48528 | − | 1.97546i | −0.210273 | − | 0.0926111i | ||||
\(456\) | 5.77786 | 0.270573 | ||||||||
\(457\) | −16.6569 | − | 16.6569i | −0.779175 | − | 0.779175i | 0.200516 | − | 0.979690i | \(-0.435738\pi\) |
−0.979690 | + | 0.200516i | \(0.935738\pi\) | |||||||
\(458\) | 9.41421 | + | 9.41421i | 0.439897 | + | 0.439897i | ||||
\(459\) | 2.43516i | 0.113663i | ||||||||
\(460\) | −1.05056 | + | 0.665529i | −0.0489827 | + | 0.0310305i | ||||
\(461\) | 11.5655i | 0.538657i | 0.963048 | + | 0.269329i | \(0.0868018\pi\) | ||||
−0.963048 | + | 0.269329i | \(0.913198\pi\) | |||||||
\(462\) | −0.0650620 | + | 0.0436796i | −0.00302696 | + | 0.00203216i | ||||
\(463\) | −12.4160 | + | 12.4160i | −0.577021 | + | 0.577021i | −0.934081 | − | 0.357061i | \(-0.883779\pi\) |
0.357061 | + | 0.934081i | \(0.383779\pi\) | |||||||
\(464\) | 9.70636i | 0.450606i | ||||||||
\(465\) | 7.65041 | + | 12.0765i | 0.354779 | + | 0.560032i | ||||
\(466\) | −3.08780 | −0.143039 | ||||||||
\(467\) | −6.14975 | + | 6.14975i | −0.284577 | + | 0.284577i | −0.834931 | − | 0.550355i | \(-0.814493\pi\) |
0.550355 | + | 0.834931i | \(0.314493\pi\) | |||||||
\(468\) | 0.585786 | + | 0.585786i | 0.0270780 | + | 0.0270780i | ||||
\(469\) | −1.72774 | + | 8.78654i | −0.0797796 | + | 0.405725i | ||||
\(470\) | 5.38459 | − | 23.9991i | 0.248373 | − | 1.10700i | ||||
\(471\) | 22.4015 | 1.03221 | ||||||||
\(472\) | 9.05595 | − | 9.05595i | 0.416834 | − | 0.416834i | ||||
\(473\) | 0.212144 | − | 0.212144i | 0.00975441 | − | 0.00975441i | ||||
\(474\) | −9.86988 | −0.453338 | ||||||||
\(475\) | 26.1201 | + | 12.3423i | 1.19847 | + | 0.566302i | ||||
\(476\) | −1.24308 | + | 6.32176i | −0.0569764 | + | 0.289758i | ||||
\(477\) | −5.77786 | − | 5.77786i | −0.264550 | − | 0.264550i | ||||
\(478\) | −12.8129 | + | 12.8129i | −0.586047 | + | 0.586047i | ||||
\(479\) | −6.82843 | −0.311999 | −0.155999 | − | 0.987757i | \(-0.549860\pi\) | ||||
−0.155999 | + | 0.987757i | \(0.549860\pi\) | |||||||
\(480\) | −2.18183 | − | 0.489528i | −0.0995863 | − | 0.0223438i | ||||
\(481\) | 4.36050i | 0.198822i | ||||||||
\(482\) | 13.8775 | − | 13.8775i | 0.632102 | − | 0.632102i | ||||
\(483\) | −0.820191 | − | 1.22170i | −0.0373200 | − | 0.0555891i | ||||
\(484\) | − | 10.9991i | − | 0.499960i | ||||||
\(485\) | −4.18025 | − | 6.59868i | −0.189815 | − | 0.299630i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −21.7124 | − | 21.7124i | −0.983881 | − | 0.983881i | 0.0159910 | − | 0.999872i | \(-0.494910\pi\) |
−0.999872 | + | 0.0159910i | \(0.994910\pi\) | |||||||
\(488\) | −7.58535 | − | 7.58535i | −0.343373 | − | 0.343373i | ||||
\(489\) | 3.82887 | 0.173147 | ||||||||
\(490\) | 2.74636 | + | 15.4097i | 0.124068 | + | 0.696137i | ||||
\(491\) | 14.8991 | 0.672385 | 0.336192 | − | 0.941793i | \(-0.390861\pi\) | ||||
0.336192 | + | 0.941793i | \(0.390861\pi\) | |||||||
\(492\) | −0.363651 | − | 0.363651i | −0.0163946 | − | 0.0163946i | ||||
\(493\) | −16.7135 | − | 16.7135i | −0.752740 | − | 0.752740i | ||||
\(494\) | 4.78654i | 0.215357i | ||||||||
\(495\) | 0.0646234 | + | 0.0144993i | 0.00290460 | + | 0.000651695i | ||||
\(496\) | − | 6.39327i | − | 0.287066i | ||||||
\(497\) | 9.80419 | + | 14.6036i | 0.439778 | + | 0.655062i | ||||
\(498\) | 0.150629 | − | 0.150629i | 0.00674985 | − | 0.00674985i | ||||
\(499\) | − | 32.7928i | − | 1.46801i | −0.679144 | − | 0.734005i | \(-0.737649\pi\) | ||
0.679144 | − | 0.734005i | \(-0.262351\pi\) | |||||||
\(500\) | −8.81774 | − | 6.87368i | −0.394341 | − | 0.307400i | ||||
\(501\) | −19.4848 | −0.870519 | ||||||||
\(502\) | 20.3278 | − | 20.3278i | 0.907273 | − | 0.907273i | ||||
\(503\) | 4.33403 | + | 4.33403i | 0.193245 | + | 0.193245i | 0.797097 | − | 0.603852i | \(-0.206368\pi\) |
−0.603852 | + | 0.797097i | \(0.706368\pi\) | |||||||
\(504\) | 0.510472 | − | 2.59604i | 0.0227382 | − | 0.115637i | ||||
\(505\) | 27.9049 | + | 6.26092i | 1.24175 | + | 0.278607i | ||||
\(506\) | −0.0164731 | −0.000732318 | ||||||||
\(507\) | 8.70711 | − | 8.70711i | 0.386696 | − | 0.386696i | ||||
\(508\) | −6.15663 | + | 6.15663i | −0.273157 | + | 0.273157i | ||||
\(509\) | 12.2581 | 0.543329 | 0.271665 | − | 0.962392i | \(-0.412426\pi\) | ||||
0.271665 | + | 0.962392i | \(0.412426\pi\) | |||||||
\(510\) | 4.59985 | − | 2.91399i | 0.203685 | − | 0.129034i | ||||
\(511\) | 3.70159 | − | 18.8247i | 0.163749 | − | 0.832756i | ||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 4.08557 | − | 4.08557i | 0.180382 | − | 0.180382i | ||||
\(514\) | 22.0319 | 0.971785 | ||||||||
\(515\) | 21.5435 | − | 13.6477i | 0.949318 | − | 0.601391i | ||||
\(516\) | 10.1292i | 0.445915i | ||||||||
\(517\) | 0.230372 | − | 0.230372i | 0.0101318 | − | 0.0101318i | ||||
\(518\) | 11.5622 | − | 7.76231i | 0.508013 | − | 0.341056i | ||||
\(519\) | 14.5773i | 0.639872i | ||||||||
\(520\) | 0.405538 | − | 1.80748i | 0.0177840 | − | 0.0792634i | ||||
\(521\) | 10.1828i | 0.446116i | 0.974805 | + | 0.223058i | \(0.0716039\pi\) | ||||
−0.974805 | + | 0.223058i | \(0.928396\pi\) | |||||||
\(522\) | 6.86343 | + | 6.86343i | 0.300404 | + | 0.300404i | ||||
\(523\) | −7.86522 | − | 7.86522i | −0.343922 | − | 0.343922i | 0.513917 | − | 0.857840i | \(-0.328194\pi\) |
−0.857840 | + | 0.513917i | \(0.828194\pi\) | |||||||
\(524\) | −4.52401 | −0.197632 | ||||||||
\(525\) | 7.85318 | − | 10.6455i | 0.342741 | − | 0.464610i | ||||
\(526\) | 10.3842 | 0.452771 | ||||||||
\(527\) | 11.0087 | + | 11.0087i | 0.479545 | + | 0.479545i | ||||
\(528\) | −0.0209438 | − | 0.0209438i | −0.000911460 | − | 0.000911460i | ||||
\(529\) | 22.6907i | 0.986551i | ||||||||
\(530\) | −4.00000 | + | 17.8280i | −0.173749 | + | 0.774398i | ||||
\(531\) | − | 12.8070i | − | 0.555778i | ||||||
\(532\) | 12.6919 | − | 8.52072i | 0.550262 | − | 0.369420i | ||||
\(533\) | 0.301258 | − | 0.301258i | 0.0130489 | − | 0.0130489i | ||||
\(534\) | 4.38416i | 0.189721i | ||||||||
\(535\) | −3.26358 | + | 2.06747i | −0.141097 | + | 0.0893847i | ||||
\(536\) | −3.38459 | −0.146192 | ||||||||
\(537\) | 12.1921 | − | 12.1921i | 0.526127 | − | 0.526127i | ||||
\(538\) | −11.7429 | − | 11.7429i | −0.506271 | − | 0.506271i | ||||
\(539\) | −0.0785023 | + | 0.191896i | −0.00338133 | + | 0.00826556i | ||||
\(540\) | −1.88893 | + | 1.19663i | −0.0812867 | + | 0.0514950i | ||||
\(541\) | 17.5312 | 0.753725 | 0.376862 | − | 0.926269i | \(-0.377003\pi\) | ||||
0.376862 | + | 0.926269i | \(0.377003\pi\) | |||||||
\(542\) | −7.00285 | + | 7.00285i | −0.300798 | + | 0.300798i | ||||
\(543\) | 15.8403 | − | 15.8403i | 0.679770 | − | 0.679770i | ||||
\(544\) | −2.43516 | −0.104407 | ||||||||
\(545\) | 32.5058 | + | 7.29320i | 1.39239 | + | 0.312407i | ||||
\(546\) | 2.15063 | + | 0.422889i | 0.0920384 | + | 0.0180980i | ||||
\(547\) | 12.5889 | + | 12.5889i | 0.538264 | + | 0.538264i | 0.923019 | − | 0.384755i | \(-0.125714\pi\) |
−0.384755 | + | 0.923019i | \(0.625714\pi\) | |||||||
\(548\) | −5.58535 | + | 5.58535i | −0.238594 | + | 0.238594i | ||||
\(549\) | −10.7273 | −0.457830 | ||||||||
\(550\) | −0.0499424 | − | 0.139420i | −0.00212955 | − | 0.00594487i | ||||
\(551\) | 56.0820i | 2.38917i | ||||||||
\(552\) | 0.393270 | − | 0.393270i | 0.0167387 | − | 0.0167387i | ||||
\(553\) | −21.6805 | + | 14.5553i | −0.921949 | + | 0.618954i | ||||
\(554\) | 4.15125i | 0.176370i | ||||||||
\(555\) | −11.4842 | − | 2.57667i | −0.487478 | − | 0.109374i | ||||
\(556\) | 16.6063i | 0.704264i | ||||||||
\(557\) | 24.5752 | + | 24.5752i | 1.04128 | + | 1.04128i | 0.999110 | + | 0.0421733i | \(0.0134282\pi\) |
0.0421733 | + | 0.999110i | \(0.486572\pi\) | |||||||
\(558\) | −4.52072 | − | 4.52072i | −0.191378 | − | 0.191378i | ||||
\(559\) | −8.39134 | −0.354916 | ||||||||
\(560\) | −5.51459 | + | 2.14226i | −0.233034 | + | 0.0905272i | ||||
\(561\) | 0.0721268 | 0.00304520 | ||||||||
\(562\) | −3.33044 | − | 3.33044i | −0.140486 | − | 0.140486i | ||||
\(563\) | −6.28391 | − | 6.28391i | −0.264835 | − | 0.264835i | 0.562180 | − | 0.827015i | \(-0.309963\pi\) |
−0.827015 | + | 0.562180i | \(0.809963\pi\) | |||||||
\(564\) | 10.9996i | 0.463165i | ||||||||
\(565\) | 0.121010 | + | 0.191019i | 0.00509094 | + | 0.00803623i | ||||
\(566\) | 18.4679i | 0.776265i | ||||||||
\(567\) | −1.47472 | − | 2.19663i | −0.0619324 | − | 0.0922500i | ||||
\(568\) | −4.70097 | + | 4.70097i | −0.197248 | + | 0.197248i | ||||
\(569\) | − | 15.0696i | − | 0.631749i | −0.948801 | − | 0.315875i | \(-0.897702\pi\) | ||
0.948801 | − | 0.315875i | \(-0.102298\pi\) | |||||||
\(570\) | −12.6063 | − | 2.82843i | −0.528019 | − | 0.118470i | ||||
\(571\) | 28.0757 | 1.17493 | 0.587466 | − | 0.809249i | \(-0.300126\pi\) | ||||
0.587466 | + | 0.809249i | \(0.300126\pi\) | |||||||
\(572\) | 0.0173504 | − | 0.0173504i | 0.000725456 | − | 0.000725456i | ||||
\(573\) | −15.9554 | − | 15.9554i | −0.666548 | − | 0.666548i | ||||
\(574\) | −1.33509 | − | 0.262525i | −0.0557256 | − | 0.0109576i | ||||
\(575\) | 2.61794 | − | 0.937789i | 0.109176 | − | 0.0391085i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −14.2455 | + | 14.2455i | −0.593048 | + | 0.593048i | −0.938453 | − | 0.345406i | \(-0.887741\pi\) |
0.345406 | + | 0.938453i | \(0.387741\pi\) | |||||||
\(578\) | −7.82768 | + | 7.82768i | −0.325588 | + | 0.325588i | ||||
\(579\) | 6.98729 | 0.290382 | ||||||||
\(580\) | 4.75154 | − | 21.1776i | 0.197297 | − | 0.879351i | ||||
\(581\) | 0.108742 | − | 0.553013i | 0.00451136 | − | 0.0229428i | ||||
\(582\) | 2.47016 | + | 2.47016i | 0.102391 | + | 0.102391i | ||||
\(583\) | −0.171134 | + | 0.171134i | −0.00708766 | + | 0.00708766i | ||||
\(584\) | 7.25132 | 0.300062 | ||||||||
\(585\) | −0.991325 | − | 1.56484i | −0.0409862 | − | 0.0646983i | ||||
\(586\) | − | 23.8781i | − | 0.986396i | ||||||
\(587\) | −6.03786 | + | 6.03786i | −0.249209 | + | 0.249209i | −0.820646 | − | 0.571437i | \(-0.806386\pi\) |
0.571437 | + | 0.820646i | \(0.306386\pi\) | |||||||
\(588\) | −2.70711 | − | 6.45535i | −0.111639 | − | 0.266214i | ||||
\(589\) | − | 36.9394i | − | 1.52206i | ||||||
\(590\) | −24.1916 | + | 15.3254i | −0.995954 | + | 0.630935i | ||||
\(591\) | − | 9.40194i | − | 0.386744i | ||||||
\(592\) | 3.72192 | + | 3.72192i | 0.152970 | + | 0.152970i | ||||
\(593\) | −18.9043 | − | 18.9043i | −0.776305 | − | 0.776305i | 0.202895 | − | 0.979200i | \(-0.434965\pi\) |
−0.979200 | + | 0.202895i | \(0.934965\pi\) | |||||||
\(594\) | −0.0296189 | −0.00121528 | ||||||||
\(595\) | 5.80686 | − | 13.1845i | 0.238058 | − | 0.540510i | ||||
\(596\) | 7.80748 | 0.319807 | ||||||||
\(597\) | −8.67135 | − | 8.67135i | −0.354895 | − | 0.354895i | ||||
\(598\) | 0.325795 | + | 0.325795i | 0.0133228 | + | 0.0133228i | ||||
\(599\) | 24.1620i | 0.987233i | 0.869680 | + | 0.493617i | \(0.164325\pi\) | ||||
−0.869680 | + | 0.493617i | \(0.835675\pi\) | |||||||
\(600\) | 4.52072 | + | 2.13613i | 0.184558 | + | 0.0872071i | ||||
\(601\) | 46.4416i | 1.89439i | 0.320652 | + | 0.947197i | \(0.396098\pi\) | ||||
−0.320652 | + | 0.947197i | \(0.603902\pi\) | |||||||
\(602\) | 14.9378 | + | 22.2503i | 0.608819 | + | 0.906853i | ||||
\(603\) | −2.39327 | + | 2.39327i | −0.0974615 | + | 0.0974615i | ||||
\(604\) | 0.870315i | 0.0354126i | ||||||||
\(605\) | −5.38438 | + | 23.9982i | −0.218906 | + | 0.975664i | ||||
\(606\) | −12.7897 | −0.519546 | ||||||||
\(607\) | 24.4860 | − | 24.4860i | 0.993857 | − | 0.993857i | −0.00612457 | − | 0.999981i | \(-0.501950\pi\) |
0.999981 | + | 0.00612457i | \(0.00194952\pi\) | |||||||
\(608\) | 4.08557 | + | 4.08557i | 0.165692 | + | 0.165692i | ||||
\(609\) | 25.1981 | + | 4.95482i | 1.02108 | + | 0.200780i | ||||
\(610\) | 12.8367 | + | 20.2631i | 0.519741 | + | 0.820431i | ||||
\(611\) | −9.11233 | −0.368646 | ||||||||
\(612\) | −1.72192 | + | 1.72192i | −0.0696043 | + | 0.0696043i | ||||
\(613\) | −29.5909 | + | 29.5909i | −1.19517 | + | 1.19517i | −0.219569 | + | 0.975597i | \(0.570465\pi\) |
−0.975597 | + | 0.219569i | \(0.929535\pi\) | |||||||
\(614\) | −16.2896 | −0.657395 | ||||||||
\(615\) | 0.615405 | + | 0.971440i | 0.0248155 | + | 0.0391722i | ||||
\(616\) | −0.0768919 | − | 0.0151196i | −0.00309806 | − | 0.000609188i | ||||
\(617\) | −30.3710 | − | 30.3710i | −1.22269 | − | 1.22269i | −0.966672 | − | 0.256019i | \(-0.917589\pi\) |
−0.256019 | − | 0.966672i | \(-0.582411\pi\) | |||||||
\(618\) | −8.06462 | + | 8.06462i | −0.324407 | + | 0.324407i | ||||
\(619\) | −41.0141 | −1.64850 | −0.824248 | − | 0.566229i | \(-0.808402\pi\) | ||||
−0.824248 | + | 0.566229i | \(0.808402\pi\) | |||||||
\(620\) | −3.12969 | + | 13.9490i | −0.125691 | + | 0.560205i | ||||
\(621\) | − | 0.556167i | − | 0.0223182i | ||||||
\(622\) | 6.78654 | − | 6.78654i | 0.272115 | − | 0.272115i | ||||
\(623\) | 6.46540 | + | 9.63039i | 0.259031 | + | 0.385833i | ||||
\(624\) | 0.828427i | 0.0331636i | ||||||||
\(625\) | 15.8739 | + | 19.3137i | 0.634956 | + | 0.772548i | ||||
\(626\) | − | 0.748684i | − | 0.0299234i | ||||||
\(627\) | −0.121010 | − | 0.121010i | −0.00483268 | − | 0.00483268i | ||||
\(628\) | 15.8403 | + | 15.8403i | 0.632095 | + | 0.632095i | ||||
\(629\) | −12.8177 | −0.511073 | ||||||||
\(630\) | −2.38459 | + | 5.41421i | −0.0950045 | + | 0.215707i | ||||
\(631\) | −4.08948 | −0.162800 | −0.0813998 | − | 0.996682i | \(-0.525939\pi\) | ||||
−0.0813998 | + | 0.996682i | \(0.525939\pi\) | |||||||
\(632\) | −6.97906 | − | 6.97906i | −0.277612 | − | 0.277612i | ||||
\(633\) | −3.27270 | − | 3.27270i | −0.130078 | − | 0.130078i | ||||
\(634\) | 28.0829i | 1.11531i | ||||||||
\(635\) | 16.4465 | − | 10.4189i | 0.652661 | − | 0.413460i | ||||
\(636\) | − | 8.17113i | − | 0.324007i | ||||||
\(637\) | 5.34779 | − | 2.24264i | 0.211887 | − | 0.0888567i | ||||
\(638\) | 0.203288 | − | 0.203288i | 0.00804823 | − | 0.00804823i | ||||
\(639\) | 6.64818i | 0.262998i | ||||||||
\(640\) | −1.19663 | − | 1.88893i | −0.0473011 | − | 0.0746666i | ||||
\(641\) | 11.8151 | 0.466668 | 0.233334 | − | 0.972397i | \(-0.425036\pi\) | ||||
0.233334 | + | 0.972397i | \(0.425036\pi\) | |||||||
\(642\) | 1.22170 | − | 1.22170i | 0.0482165 | − | 0.0482165i | ||||
\(643\) | −6.35138 | − | 6.35138i | −0.250474 | − | 0.250474i | 0.570691 | − | 0.821165i | \(-0.306675\pi\) |
−0.821165 | + | 0.570691i | \(0.806675\pi\) | |||||||
\(644\) | 0.283908 | − | 1.44383i | 0.0111875 | − | 0.0568950i | ||||
\(645\) | 4.95855 | − | 22.1002i | 0.195243 | − | 0.870196i | ||||
\(646\) | −14.0700 | −0.553577 | ||||||||
\(647\) | 34.1901 | − | 34.1901i | 1.34415 | − | 1.34415i | 0.452274 | − | 0.891879i | \(-0.350613\pi\) |
0.891879 | − | 0.452274i | \(-0.149387\pi\) | |||||||
\(648\) | 0.707107 | − | 0.707107i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | −0.379331 | −0.0148900 | ||||||||
\(650\) | −1.76963 | + | 3.74509i | −0.0694105 | + | 0.146895i | ||||
\(651\) | −16.5972 | − | 3.26358i | −0.650495 | − | 0.127910i | ||||
\(652\) | 2.70742 | + | 2.70742i | 0.106031 | + | 0.106031i | ||||
\(653\) | 30.0988 | − | 30.0988i | 1.17786 | − | 1.17786i | 0.197565 | − | 0.980290i | \(-0.436697\pi\) |
0.980290 | − | 0.197565i | \(-0.0633035\pi\) | |||||||
\(654\) | −14.8984 | −0.582575 | ||||||||
\(655\) | 9.87061 | + | 2.21463i | 0.385677 | + | 0.0865328i | ||||
\(656\) | − | 0.514280i | − | 0.0200793i | ||||||
\(657\) | 5.12745 | − | 5.12745i | 0.200041 | − | 0.200041i | ||||
\(658\) | 16.2213 | + | 24.1620i | 0.632370 | + | 0.941934i | ||||
\(659\) | 27.3843i | 1.06674i | 0.845881 | + | 0.533371i | \(0.179075\pi\) | ||||
−0.845881 | + | 0.533371i | \(0.820925\pi\) | |||||||
\(660\) | 0.0354431 | + | 0.0559482i | 0.00137962 | + | 0.00217778i | ||||
\(661\) | − | 22.5855i | − | 0.878475i | −0.898371 | − | 0.439238i | \(-0.855249\pi\) | ||
0.898371 | − | 0.439238i | \(-0.144751\pi\) | |||||||
\(662\) | 3.28347 | + | 3.28347i | 0.127616 | + | 0.127616i | ||||
\(663\) | −1.42648 | − | 1.42648i | −0.0554000 | − | 0.0554000i | ||||
\(664\) | 0.213022 | 0.00826685 | ||||||||
\(665\) | −31.8626 | + | 12.3777i | −1.23558 | + | 0.479987i | ||||
\(666\) | 5.26358 | 0.203960 | ||||||||
\(667\) | 3.81722 | + | 3.81722i | 0.147803 | + | 0.147803i | ||||
\(668\) | −13.7779 | − | 13.7779i | −0.533082 | − | 0.533082i | ||||
\(669\) | 25.7764i | 0.996572i | ||||||||
\(670\) | 7.38459 | + | 1.65685i | 0.285292 | + | 0.0640099i | ||||
\(671\) | 0.317731i | 0.0122659i | ||||||||
\(672\) | 2.19663 | − | 1.47472i | 0.0847370 | − | 0.0568885i | ||||
\(673\) | 17.7447 | − | 17.7447i | 0.684006 | − | 0.684006i | −0.276894 | − | 0.960900i | \(-0.589305\pi\) |
0.960900 | + | 0.276894i | \(0.0893052\pi\) | |||||||
\(674\) | 9.98327i | 0.384541i | ||||||||
\(675\) | 4.70711 | − | 1.68616i | 0.181177 | − | 0.0649004i | ||||
\(676\) | 12.3137 | 0.473604 | ||||||||
\(677\) | −18.4477 | + | 18.4477i | −0.709003 | + | 0.709003i | −0.966326 | − | 0.257322i | \(-0.917160\pi\) |
0.257322 | + | 0.966326i | \(0.417160\pi\) | |||||||
\(678\) | −0.0715065 | − | 0.0715065i | −0.00274619 | − | 0.00274619i | ||||
\(679\) | 9.06884 | + | 1.78325i | 0.348030 | + | 0.0684349i | ||||
\(680\) | 5.31309 | + | 1.19208i | 0.203748 | + | 0.0457141i | ||||
\(681\) | −12.5843 | −0.482231 | ||||||||
\(682\) | −0.133899 | + | 0.133899i | −0.00512726 | + | 0.00512726i | ||||
\(683\) | 1.35560 | − | 1.35560i | 0.0518704 | − | 0.0518704i | −0.680696 | − | 0.732566i | \(-0.738322\pi\) |
0.732566 | + | 0.680696i | \(0.238322\pi\) | |||||||
\(684\) | 5.77786 | 0.220922 | ||||||||
\(685\) | 14.9204 | − | 9.45207i | 0.570081 | − | 0.361145i | ||||
\(686\) | −15.4664 | − | 10.1878i | −0.590508 | − | 0.388973i | ||||
\(687\) | 9.41421 | + | 9.41421i | 0.359175 | + | 0.359175i | ||||
\(688\) | −7.16246 | + | 7.16246i | −0.273066 | + | 0.273066i | ||||
\(689\) | 6.76919 | 0.257886 | ||||||||
\(690\) | −1.05056 | + | 0.665529i | −0.0399942 | + | 0.0253363i | ||||
\(691\) | − | 4.24455i | − | 0.161470i | −0.996736 | − | 0.0807352i | \(-0.974273\pi\) | ||
0.996736 | − | 0.0807352i | \(-0.0257268\pi\) | |||||||
\(692\) | −10.3077 | + | 10.3077i | −0.391840 | + | 0.391840i | ||||
\(693\) | −0.0650620 | + | 0.0436796i | −0.00247150 | + | 0.00165925i | ||||
\(694\) | − | 33.2234i | − | 1.26114i | ||||||
\(695\) | 8.12925 | − | 36.2320i | 0.308360 | − | 1.37436i | ||||
\(696\) | 9.70636i | 0.367919i | ||||||||
\(697\) | 0.885547 | + | 0.885547i | 0.0335425 | + | 0.0335425i | ||||
\(698\) | 14.2708 | + | 14.2708i | 0.540156 | + | 0.540156i | ||||
\(699\) | −3.08780 | −0.116791 | ||||||||
\(700\) | 13.0806 | − | 1.97450i | 0.494399 | − | 0.0746291i | ||||
\(701\) | 11.1047 | 0.419419 | 0.209710 | − | 0.977764i | \(-0.432748\pi\) | ||||
0.209710 | + | 0.977764i | \(0.432748\pi\) | |||||||
\(702\) | 0.585786 | + | 0.585786i | 0.0221091 | + | 0.0221091i | ||||
\(703\) | 21.5047 | + | 21.5047i | 0.811066 | + | 0.811066i | ||||
\(704\) | − | 0.0296189i | − | 0.00111631i | ||||||
\(705\) | 5.38459 | − | 23.9991i | 0.202796 | − | 0.903859i | ||||
\(706\) | 10.5354i | 0.396505i | ||||||||
\(707\) | −28.0943 | + | 18.8612i | −1.05659 | + | 0.709348i | ||||
\(708\) | 9.05595 | − | 9.05595i | 0.340343 | − | 0.340343i | ||||
\(709\) | − | 34.1694i | − | 1.28326i | −0.767015 | − | 0.641629i | \(-0.778259\pi\) | ||
0.767015 | − | 0.641629i | \(-0.221741\pi\) | |||||||
\(710\) | 12.5580 | − | 7.95544i | 0.471292 | − | 0.298562i | ||||
\(711\) | −9.86988 | −0.370149 | ||||||||
\(712\) | −3.10007 | + | 3.10007i | −0.116180 | + | 0.116180i | ||||
\(713\) | −2.51428 | − | 2.51428i | −0.0941605 | − | 0.0941605i | ||||
\(714\) | −1.24308 | + | 6.32176i | −0.0465211 | + | 0.236586i | ||||
\(715\) | −0.0463490 | + | 0.0293620i | −0.00173335 | + | 0.00109808i | ||||
\(716\) | 17.2422 | 0.644371 | ||||||||
\(717\) | −12.8129 | + | 12.8129i | −0.478505 | + | 0.478505i | ||||
\(718\) | −11.7424 | + | 11.7424i | −0.438223 | + | 0.438223i | ||||
\(719\) | −27.7960 | −1.03662 | −0.518308 | − | 0.855194i | \(-0.673438\pi\) | ||||
−0.518308 | + | 0.855194i | \(0.673438\pi\) | |||||||
\(720\) | −2.18183 | − | 0.489528i | −0.0813118 | − | 0.0182436i | ||||
\(721\) | −5.82198 | + | 29.6081i | −0.216822 | + | 1.10266i | ||||
\(722\) | 10.1708 | + | 10.1708i | 0.378519 | + | 0.378519i | ||||
\(723\) | 13.8775 | − | 13.8775i | 0.516109 | − | 0.516109i | ||||
\(724\) | 22.4015 | 0.832545 | ||||||||
\(725\) | −20.7340 | + | 43.8798i | −0.770043 | + | 1.62965i | ||||
\(726\) | − | 10.9991i | − | 0.408216i | ||||||
\(727\) | −9.37456 | + | 9.37456i | −0.347683 | + | 0.347683i | −0.859246 | − | 0.511563i | \(-0.829067\pi\) |
0.511563 | + | 0.859246i | \(0.329067\pi\) | |||||||
\(728\) | 1.22170 | + | 1.81975i | 0.0452791 | + | 0.0674445i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −15.8211 | − | 3.54972i | −0.585565 | − | 0.131381i | ||||
\(731\) | − | 24.6663i | − | 0.912316i | ||||||
\(732\) | −7.58535 | − | 7.58535i | −0.280363 | − | 0.280363i | ||||
\(733\) | 8.54390 | + | 8.54390i | 0.315576 | + | 0.315576i | 0.847065 | − | 0.531489i | \(-0.178367\pi\) |
−0.531489 | + | 0.847065i | \(0.678367\pi\) | |||||||
\(734\) | 4.06327 | 0.149978 | ||||||||
\(735\) | 2.74636 | + | 15.4097i | 0.101301 | + | 0.568394i | ||||
\(736\) | 0.556167 | 0.0205006 | ||||||||
\(737\) | 0.0708861 | + | 0.0708861i | 0.00261112 | + | 0.00261112i | ||||
\(738\) | −0.363651 | − | 0.363651i | −0.0133862 | − | 0.0133862i | ||||
\(739\) | 24.4015i | 0.897624i | 0.893626 | + | 0.448812i | \(0.148153\pi\) | ||||
−0.893626 | + | 0.448812i | \(0.851847\pi\) | |||||||
\(740\) | −6.29859 | − | 9.94255i | −0.231541 | − | 0.365496i | ||||
\(741\) | 4.78654i | 0.175838i | ||||||||
\(742\) | −12.0501 | − | 17.9490i | −0.442374 | − | 0.658928i | ||||
\(743\) | 16.3076 | − | 16.3076i | 0.598267 | − | 0.598267i | −0.341584 | − | 0.939851i | \(-0.610964\pi\) |
0.939851 | + | 0.341584i | \(0.110964\pi\) | |||||||
\(744\) | − | 6.39327i | − | 0.234389i | ||||||
\(745\) | −17.0346 | − | 3.82198i | −0.624098 | − | 0.140027i | ||||
\(746\) | −2.19314 | −0.0802964 | ||||||||
\(747\) | 0.150629 | − | 0.150629i | 0.00551123 | − | 0.00551123i | ||||
\(748\) | 0.0510013 | + | 0.0510013i | 0.00186479 | + | 0.00186479i | ||||
\(749\) | 0.881963 | − | 4.48528i | 0.0322262 | − | 0.163889i | ||||
\(750\) | −8.81774 | − | 6.87368i | −0.321978 | − | 0.250991i | ||||
\(751\) | 27.6503 | 1.00897 | 0.504486 | − | 0.863420i | \(-0.331682\pi\) | ||||
0.504486 | + | 0.863420i | \(0.331682\pi\) | |||||||
\(752\) | −7.77786 | + | 7.77786i | −0.283630 | + | 0.283630i | ||||
\(753\) | 20.3278 | − | 20.3278i | 0.740785 | − | 0.740785i | ||||
\(754\) | −8.04101 | −0.292836 | ||||||||
\(755\) | 0.426043 | − | 1.89887i | 0.0155053 | − | 0.0691071i | ||||
\(756\) | 0.510472 | − | 2.59604i | 0.0185657 | − | 0.0944170i | ||||
\(757\) | −20.2224 | − | 20.2224i | −0.734997 | − | 0.734997i | 0.236608 | − | 0.971605i | \(-0.423964\pi\) |
−0.971605 | + | 0.236608i | \(0.923964\pi\) | |||||||
\(758\) | −4.89844 | + | 4.89844i | −0.177919 | + | 0.177919i | ||||
\(759\) | −0.0164731 | −0.000597935 | ||||||||
\(760\) | −6.91399 | − | 10.9140i | −0.250797 | − | 0.395892i | ||||
\(761\) | − | 23.1354i | − | 0.838657i | −0.907835 | − | 0.419329i | \(-0.862266\pi\) | ||
0.907835 | − | 0.419329i | \(-0.137734\pi\) | |||||||
\(762\) | −6.15663 | + | 6.15663i | −0.223031 | + | 0.223031i | ||||
\(763\) | −32.7264 | + | 21.9710i | −1.18478 | + | 0.795404i | ||||
\(764\) | − | 22.5644i | − | 0.816351i | ||||||
\(765\) | 4.59985 | − | 2.91399i | 0.166308 | − | 0.105356i | ||||
\(766\) | 4.89844i | 0.176988i | ||||||||
\(767\) | 7.50219 | + | 7.50219i | 0.270888 | + | 0.270888i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | −25.1546 | −0.907098 | −0.453549 | − | 0.891231i | \(-0.649842\pi\) | ||||
−0.453549 | + | 0.891231i | \(0.649842\pi\) | |||||||
\(770\) | 0.160363 | + | 0.0706292i | 0.00577909 | + | 0.00254530i | ||||
\(771\) | 22.0319 | 0.793459 | ||||||||
\(772\) | 4.94076 | + | 4.94076i | 0.177822 | + | 0.177822i | ||||
\(773\) | 23.0515 | + | 23.0515i | 0.829104 | + | 0.829104i | 0.987393 | − | 0.158289i | \(-0.0505977\pi\) |
−0.158289 | + | 0.987393i | \(0.550598\pi\) | |||||||
\(774\) | 10.1292i | 0.364088i | ||||||||
\(775\) | 13.6569 | − | 28.9022i | 0.490569 | − | 1.03820i | ||||
\(776\) | 3.49334i | 0.125403i | ||||||||
\(777\) | 11.5622 | − | 7.76231i | 0.414791 | − | 0.278471i | ||||
\(778\) | 17.6210 | − | 17.6210i | 0.631742 | − | 0.631742i | ||||
\(779\) | − | 2.97144i | − | 0.106463i | ||||||
\(780\) | 0.405538 | − | 1.80748i | 0.0145206 | − | 0.0647183i | ||||
\(781\) | 0.196912 | 0.00704607 | ||||||||
\(782\) | −0.957674 | + | 0.957674i | −0.0342463 | + | 0.0342463i | ||||
\(783\) | 6.86343 | + | 6.86343i | 0.245279 | + | 0.245279i | ||||
\(784\) | 2.65041 | − | 6.47884i | 0.0946575 | − | 0.231387i | ||||
\(785\) | −26.8064 | − | 42.3149i | −0.956762 | − | 1.51028i | ||||
\(786\) | −4.52401 | −0.161366 | ||||||||
\(787\) | −24.2320 | + | 24.2320i | −0.863779 | + | 0.863779i | −0.991775 | − | 0.127996i | \(-0.959145\pi\) |
0.127996 | + | 0.991775i | \(0.459145\pi\) | |||||||
\(788\) | 6.64818 | − | 6.64818i | 0.236832 | − | 0.236832i | ||||
\(789\) | 10.3842 | 0.369686 | ||||||||
\(790\) | 11.8106 | + | 18.6435i | 0.420204 | + | 0.663307i | ||||
\(791\) | −0.262525 | − | 0.0516217i | −0.00933433 | − | 0.00183546i | ||||
\(792\) | −0.0209438 | − | 0.0209438i | −0.000744204 | − | 0.000744204i | ||||
\(793\) | 6.28391 | − | 6.28391i | 0.223148 | − | 0.223148i | ||||
\(794\) | 19.3128 | 0.685387 | ||||||||
\(795\) | −4.00000 | + | 17.8280i | −0.141865 | + | 0.632294i | ||||
\(796\) | − | 12.2631i | − | 0.434656i | ||||||
\(797\) | 17.5376 | − | 17.5376i | 0.621215 | − | 0.621215i | −0.324627 | − | 0.945842i | \(-0.605239\pi\) |
0.945842 | + | 0.324627i | \(0.105239\pi\) | |||||||
\(798\) | 12.6919 | − | 8.52072i | 0.449287 | − | 0.301630i | ||||
\(799\) | − | 26.7857i | − | 0.947609i | ||||||
\(800\) | 1.68616 | + | 4.70711i | 0.0596149 | + | 0.166421i | ||||
\(801\) | 4.38416i | 0.154907i | ||||||||
\(802\) | 9.20119 | + | 9.20119i | 0.324905 | + | 0.324905i | ||||
\(803\) | −0.151870 | − | 0.151870i | −0.00535937 | − | 0.00535937i | ||||
\(804\) | −3.38459 | −0.119365 | ||||||||
\(805\) | −1.32623 | + | 3.01121i | −0.0467436 | + | 0.106131i | ||||
\(806\) | 5.29636 | 0.186556 | ||||||||
\(807\) | −11.7429 | − | 11.7429i | −0.413368 | − | 0.413368i | ||||
\(808\) | −9.04368 | − | 9.04368i | −0.318156 | − | 0.318156i | ||||
\(809\) | − | 20.1011i | − | 0.706718i | −0.935488 | − | 0.353359i | \(-0.885039\pi\) | ||
0.935488 | − | 0.353359i | \(-0.114961\pi\) | |||||||
\(810\) | −1.88893 | + | 1.19663i | −0.0663703 | + | 0.0420455i | ||||
\(811\) | − | 27.6340i | − | 0.970360i | −0.874414 | − | 0.485180i | \(-0.838754\pi\) | ||
0.874414 | − | 0.485180i | \(-0.161246\pi\) | |||||||
\(812\) | 14.3141 | + | 21.3213i | 0.502328 | + | 0.748232i | ||||
\(813\) | −7.00285 | + | 7.00285i | −0.245601 | + | 0.245601i | ||||
\(814\) | − | 0.155902i | − | 0.00546436i | ||||||
\(815\) | −4.58175 | − | 7.23247i | −0.160492 | − | 0.253342i | ||||
\(816\) | −2.43516 | −0.0852476 | ||||||||
\(817\) | −41.3837 | + | 41.3837i | −1.44783 | + | 1.44783i | ||||
\(818\) | −7.50623 | − | 7.50623i | −0.262449 | − | 0.262449i | ||||
\(819\) | 2.15063 | + | 0.422889i | 0.0751491 | + | 0.0147769i | ||||
\(820\) | −0.251755 | + | 1.12207i | −0.00879165 | + | 0.0391844i | ||||
\(821\) | −6.07616 | −0.212059 | −0.106030 | − | 0.994363i | \(-0.533814\pi\) | ||||
−0.106030 | + | 0.994363i | \(0.533814\pi\) | |||||||
\(822\) | −5.58535 | + | 5.58535i | −0.194811 | + | 0.194811i | ||||
\(823\) | −13.2971 | + | 13.2971i | −0.463507 | + | 0.463507i | −0.899803 | − | 0.436296i | \(-0.856290\pi\) |
0.436296 | + | 0.899803i | \(0.356290\pi\) | |||||||
\(824\) | −11.4051 | −0.397315 | ||||||||
\(825\) | −0.0499424 | − | 0.139420i | −0.00173877 | − | 0.00485396i | ||||
\(826\) | 6.53764 | − | 33.2476i | 0.227473 | − | 1.15683i | ||||
\(827\) | 4.21364 | + | 4.21364i | 0.146523 | + | 0.146523i | 0.776563 | − | 0.630040i | \(-0.216962\pi\) |
−0.630040 | + | 0.776563i | \(0.716962\pi\) | |||||||
\(828\) | 0.393270 | − | 0.393270i | 0.0136671 | − | 0.0136671i | ||||
\(829\) | 25.3382 | 0.880034 | 0.440017 | − | 0.897990i | \(-0.354972\pi\) | ||||
0.440017 | + | 0.897990i | \(0.354972\pi\) | |||||||
\(830\) | −0.464776 | − | 0.104280i | −0.0161326 | − | 0.00361962i | ||||
\(831\) | 4.15125i | 0.144005i | ||||||||
\(832\) | −0.585786 | + | 0.585786i | −0.0203085 | + | 0.0203085i | ||||
\(833\) | 6.59223 | + | 15.7198i | 0.228407 | + | 0.544659i | ||||
\(834\) | 16.6063i | 0.575029i | ||||||||
\(835\) | 23.3162 | + | 36.8055i | 0.806892 | + | 1.27371i | ||||
\(836\) | − | 0.171134i | − | 0.00591880i | ||||||
\(837\) | −4.52072 | − | 4.52072i | −0.156259 | − | 0.156259i | ||||
\(838\) | −6.95482 | − | 6.95482i | −0.240250 | − | 0.240250i | ||||
\(839\) | 8.27672 | 0.285744 | 0.142872 | − | 0.989741i | \(-0.454366\pi\) | ||||
0.142872 | + | 0.989741i | \(0.454366\pi\) | |||||||
\(840\) | −5.51459 | + | 2.14226i | −0.190271 | + | 0.0739151i | ||||
\(841\) | −65.2134 | −2.24874 | ||||||||
\(842\) | −23.0491 | − | 23.0491i | −0.794323 | − | 0.794323i | ||||
\(843\) | −3.33044 | − | 3.33044i | −0.114706 | − | 0.114706i | ||||
\(844\) | − | 4.62829i | − | 0.159312i | ||||||
\(845\) | −26.8664 | − | 6.02791i | −0.924231 | − | 0.207366i | ||||
\(846\) | 10.9996i | 0.378173i | ||||||||
\(847\) | −16.2206 | − | 24.1611i | −0.557347 | − | 0.830184i | ||||
\(848\) | 5.77786 | − | 5.77786i | 0.198413 | − | 0.198413i | ||||
\(849\) | 18.4679i | 0.633818i | ||||||||
\(850\) | −11.0087 | − | 5.20181i | −0.377594 | − | 0.178421i | ||||
\(851\) | 2.92743 | 0.100351 | ||||||||
\(852\) | −4.70097 | + | 4.70097i | −0.161053 | + | 0.161053i | ||||
\(853\) | 30.3653 | + | 30.3653i | 1.03969 | + | 1.03969i | 0.999179 | + | 0.0405092i | \(0.0128980\pi\) |
0.0405092 | + | 0.999179i | \(0.487102\pi\) | |||||||
\(854\) | −27.8485 | − | 5.47599i | −0.952956 | − | 0.187384i | ||||
\(855\) | −12.6063 | − | 2.82843i | −0.431126 | − | 0.0967302i | ||||
\(856\) | 1.72774 | 0.0590530 | ||||||||
\(857\) | 33.0766 | − | 33.0766i | 1.12988 | − | 1.12988i | 0.139680 | − | 0.990197i | \(-0.455393\pi\) |
0.990197 | − | 0.139680i | \(-0.0446072\pi\) | |||||||
\(858\) | 0.0173504 | − | 0.0173504i | 0.000592332 | − | 0.000592332i | ||||
\(859\) | 1.87687 | 0.0640380 | 0.0320190 | − | 0.999487i | \(-0.489806\pi\) | ||||
0.0320190 | + | 0.999487i | \(0.489806\pi\) | |||||||
\(860\) | 19.1335 | − | 12.1210i | 0.652446 | − | 0.413323i | ||||
\(861\) | −1.33509 | − | 0.262525i | −0.0454998 | − | 0.00894684i | ||||
\(862\) | −20.7710 | − | 20.7710i | −0.707462 | − | 0.707462i | ||||
\(863\) | 10.8612 | − | 10.8612i | 0.369720 | − | 0.369720i | −0.497655 | − | 0.867375i | \(-0.665806\pi\) |
0.867375 | + | 0.497655i | \(0.165806\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 27.5355 | − | 17.4437i | 0.936236 | − | 0.593104i | ||||
\(866\) | − | 24.2206i | − | 0.823051i | ||||||
\(867\) | −7.82768 | + | 7.82768i | −0.265842 | + | 0.265842i | ||||
\(868\) | −9.42827 | − | 14.0437i | −0.320016 | − | 0.476674i | ||||
\(869\) | 0.292335i | 0.00991680i | ||||||||
\(870\) | 4.75154 | − | 21.1776i | 0.161092 | − | 0.717987i | ||||
\(871\) | − | 2.80389i | − | 0.0950062i | ||||||
\(872\) | −10.5348 | − | 10.5348i | −0.356753 | − | 0.356753i | ||||
\(873\) | 2.47016 | + | 2.47016i | 0.0836023 | + | 0.0836023i | ||||
\(874\) | 3.21346 | 0.108697 | ||||||||
\(875\) | −29.5061 | − | 2.09529i | −0.997488 | − | 0.0708339i | ||||
\(876\) | 7.25132 | 0.244999 | ||||||||
\(877\) | −5.90470 | − | 5.90470i | −0.199388 | − | 0.199388i | 0.600350 | − | 0.799737i | \(-0.295028\pi\) |
−0.799737 | + | 0.600350i | \(0.795028\pi\) | |||||||
\(878\) | −1.62544 | − | 1.62544i | −0.0548561 | − | 0.0548561i | ||||
\(879\) | − | 23.8781i | − | 0.805389i | ||||||
\(880\) | −0.0144993 | + | 0.0646234i | −0.000488771 | + | 0.00217845i | ||||
\(881\) | − | 6.76200i | − | 0.227818i | −0.993491 | − | 0.113909i | \(-0.963663\pi\) | ||
0.993491 | − | 0.113909i | \(-0.0363372\pi\) | |||||||
\(882\) | −2.70711 | − | 6.45535i | −0.0911530 | − | 0.217363i | ||||
\(883\) | 24.6192 | − | 24.6192i | 0.828501 | − | 0.828501i | −0.158808 | − | 0.987309i | \(-0.550765\pi\) |
0.987309 | + | 0.158808i | \(0.0507651\pi\) | |||||||
\(884\) | − | 2.01735i | − | 0.0678508i | ||||||
\(885\) | −24.1916 | + | 15.3254i | −0.813193 | + | 0.515156i | ||||
\(886\) | −1.97188 | −0.0662466 | ||||||||
\(887\) | −6.92132 | + | 6.92132i | −0.232395 | + | 0.232395i | −0.813692 | − | 0.581297i | \(-0.802546\pi\) |
0.581297 | + | 0.813692i | \(0.302546\pi\) | |||||||
\(888\) | 3.72192 | + | 3.72192i | 0.124899 | + | 0.124899i | ||||
\(889\) | −4.44457 | + | 22.6032i | −0.149066 | + | 0.758086i | ||||
\(890\) | 8.28137 | − | 5.24623i | 0.277592 | − | 0.175854i | ||||
\(891\) | −0.0296189 | −0.000992272 | ||||||||
\(892\) | −18.2266 | + | 18.2266i | −0.610273 | + | 0.610273i | ||||
\(893\) | −44.9394 | + | 44.9394i | −1.50384 | + | 1.50384i | ||||
\(894\) | 7.80748 | 0.261121 | ||||||||
\(895\) | −37.6195 | − | 8.44054i | −1.25748 | − | 0.282136i | ||||
\(896\) | 2.59604 | + | 0.510472i | 0.0867276 | + | 0.0170537i | ||||
\(897\) | 0.325795 | + | 0.325795i | 0.0108780 | + | 0.0108780i | ||||
\(898\) | 4.75692 | − | 4.75692i | 0.158740 | − | 0.158740i | ||||
\(899\) | 62.0554 | 2.06966 | ||||||||
\(900\) | 4.52072 | + | 2.13613i | 0.150691 | + | 0.0712043i | ||||
\(901\) | 19.8980i | 0.662898i | ||||||||
\(902\) | −0.0107710 | + | 0.0107710i | −0.000358634 | + | 0.000358634i | ||||
\(903\) | 14.9378 | + | 22.2503i | 0.497098 | + | 0.740442i | ||||
\(904\) | − | 0.101125i | − | 0.00336338i | ||||||
\(905\) | −48.8762 | − | 10.9662i | −1.62470 | − | 0.364528i | ||||
\(906\) | 0.870315i | 0.0289143i | ||||||||
\(907\) | −6.28050 | − | 6.28050i | −0.208540 | − | 0.208540i | 0.595106 | − | 0.803647i | \(-0.297110\pi\) |
−0.803647 | + | 0.595106i | \(0.797110\pi\) | |||||||
\(908\) | −8.89844 | − | 8.89844i | −0.295305 | − | 0.295305i | ||||
\(909\) | −12.7897 | −0.424207 | ||||||||
\(910\) | −1.77471 | − | 4.56844i | −0.0588311 | − | 0.151442i | ||||
\(911\) | 19.9873 | 0.662209 | 0.331104 | − | 0.943594i | \(-0.392579\pi\) | ||||
0.331104 | + | 0.943594i | \(0.392579\pi\) | |||||||
\(912\) | 4.08557 | + | 4.08557i | 0.135287 | + | 0.135287i | ||||
\(913\) | −0.00446148 | − | 0.00446148i | −0.000147653 | − | 0.000147653i | ||||
\(914\) | − | 23.5563i | − | 0.779175i | ||||||
\(915\) | 12.8367 | + | 20.2631i | 0.424367 | + | 0.669879i | ||||
\(916\) | 13.3137i | 0.439897i | ||||||||
\(917\) | −9.93761 | + | 6.67165i | −0.328169 | + | 0.220317i | ||||
\(918\) | −1.72192 | + | 1.72192i | −0.0568317 | + | 0.0568317i | ||||
\(919\) | 9.34358i | 0.308216i | 0.988054 | + | 0.154108i | \(0.0492504\pi\) | ||||
−0.988054 | + | 0.154108i | \(0.950750\pi\) | |||||||
\(920\) | −1.21346 | − | 0.272260i | −0.0400066 | − | 0.00897613i | ||||
\(921\) | −16.2896 | −0.536761 | ||||||||
\(922\) | −8.17802 | + | 8.17802i | −0.269329 | + | 0.269329i | ||||
\(923\) | −3.89441 | − | 3.89441i | −0.128186 | − | 0.128186i | ||||
\(924\) | −0.0768919 | − | 0.0151196i | −0.00252956 | − | 0.000497400i | ||||
\(925\) | 8.87526 | + | 24.7763i | 0.291817 | + | 0.814638i | ||||
\(926\) | −17.5589 | −0.577021 | ||||||||
\(927\) | −8.06462 | + | 8.06462i | −0.264877 | + | 0.264877i | ||||
\(928\) | −6.86343 | + | 6.86343i | −0.225303 | + | 0.225303i | ||||
\(929\) | 13.8699 | 0.455056 | 0.227528 | − | 0.973772i | \(-0.426936\pi\) | ||||
0.227528 | + | 0.973772i | \(0.426936\pi\) | |||||||
\(930\) | −3.12969 | + | 13.9490i | −0.102626 | + | 0.457406i | ||||
\(931\) | 15.3137 | − | 37.4338i | 0.501887 | − | 1.22684i | ||||
\(932\) | −2.18340 | − | 2.18340i | −0.0715197 | − | 0.0715197i | ||||
\(933\) | 6.78654 | − | 6.78654i | 0.222181 | − | 0.222181i | ||||
\(934\) | −8.69706 | −0.284577 | ||||||||
\(935\) | −0.0863094 | − | 0.136243i | −0.00282262 | − | 0.00445561i | ||||
\(936\) | 0.828427i | 0.0270780i | ||||||||
\(937\) | 27.3569 | − | 27.3569i | 0.893713 | − | 0.893713i | −0.101158 | − | 0.994870i | \(-0.532255\pi\) |
0.994870 | + | 0.101158i | \(0.0322547\pi\) | |||||||
\(938\) | −7.43472 | + | 4.99132i | −0.242752 | + | 0.162973i | ||||
\(939\) | − | 0.748684i | − | 0.0244324i | ||||||
\(940\) | 20.7774 | − | 13.1625i | 0.677685 | − | 0.429312i | ||||
\(941\) | − | 54.0397i | − | 1.76164i | −0.473448 | − | 0.880822i | \(-0.656991\pi\) | ||
0.473448 | − | 0.880822i | \(-0.343009\pi\) | |||||||
\(942\) | 15.8403 | + | 15.8403i | 0.516103 | + | 0.516103i | ||||
\(943\) | −0.202251 | − | 0.202251i | −0.00658619 | − | 0.00658619i | ||||
\(944\) | 12.8070 | 0.416834 | ||||||||
\(945\) | −2.38459 | + | 5.41421i | −0.0775709 | + | 0.176124i | ||||
\(946\) | 0.300018 | 0.00975441 | ||||||||
\(947\) | 27.2157 | + | 27.2157i | 0.884393 | + | 0.884393i | 0.993977 | − | 0.109585i | \(-0.0349521\pi\) |
−0.109585 | + | 0.993977i | \(0.534952\pi\) | |||||||
\(948\) | −6.97906 | − | 6.97906i | −0.226669 | − | 0.226669i | ||||
\(949\) | 6.00719i | 0.195002i | ||||||||
\(950\) | 9.74242 | + | 27.1970i | 0.316086 | + | 0.882388i | ||||
\(951\) | 28.0829i | 0.910650i | ||||||||
\(952\) | −5.34915 | + | 3.59117i | −0.173367 | + | 0.116391i | ||||
\(953\) | −4.60945 | + | 4.60945i | −0.149315 | + | 0.149315i | −0.777812 | − | 0.628497i | \(-0.783670\pi\) |
0.628497 | + | 0.777812i | \(0.283670\pi\) | |||||||
\(954\) | − | 8.17113i | − | 0.264550i | ||||||
\(955\) | −11.0459 | + | 49.2316i | −0.357437 | + | 1.59310i | ||||
\(956\) | −18.1201 | −0.586047 | ||||||||
\(957\) | 0.203288 | − | 0.203288i | 0.00657135 | − | 0.00657135i | ||||
\(958\) | −4.82843 | − | 4.82843i | −0.155999 | − | 0.155999i | ||||
\(959\) | −4.03215 | + | 20.5058i | −0.130205 | + | 0.662166i | ||||
\(960\) | −1.19663 | − | 1.88893i | −0.0386212 | − | 0.0609650i | ||||
\(961\) | −9.87390 | −0.318513 | ||||||||
\(962\) | −3.08334 | + | 3.08334i | −0.0994108 | + | 0.0994108i | ||||
\(963\) | 1.22170 | − | 1.22170i | 0.0393686 | − | 0.0393686i | ||||
\(964\) | 19.6257 | 0.632102 | ||||||||
\(965\) | −8.36124 | − | 13.1985i | −0.269158 | − | 0.424875i | ||||
\(966\) | 0.283908 | − | 1.44383i | 0.00913459 | − | 0.0464545i | ||||
\(967\) | 31.1433 | + | 31.1433i | 1.00150 | + | 1.00150i | 0.999999 | + | 0.00150238i | \(0.000478222\pi\) |
0.00150238 | + | 0.999999i | \(0.499522\pi\) | |||||||
\(968\) | 7.77755 | − | 7.77755i | 0.249980 | − | 0.249980i | ||||
\(969\) | −14.0700 | −0.451994 | ||||||||
\(970\) | 1.71009 | − | 7.62185i | 0.0549076 | − | 0.244723i | ||||
\(971\) | 0.0615153i | 0.00197412i | 1.00000 | 0.000987061i | \(0.000314191\pi\) | |||||
−1.00000 | 0.000987061i | \(0.999686\pi\) | ||||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | 24.4896 | + | 36.4780i | 0.785101 | + | 1.16943i | ||||
\(974\) | − | 30.7059i | − | 0.983881i | ||||||
\(975\) | −1.76963 | + | 3.74509i | −0.0566734 | + | 0.119939i | ||||
\(976\) | − | 10.7273i | − | 0.343373i | ||||||
\(977\) | 0.822738 | + | 0.822738i | 0.0263217 | + | 0.0263217i | 0.720145 | − | 0.693823i | \(-0.244075\pi\) |
−0.693823 | + | 0.720145i | \(0.744075\pi\) | |||||||
\(978\) | 2.70742 | + | 2.70742i | 0.0865736 | + | 0.0865736i | ||||
\(979\) | 0.129854 | 0.00415015 | ||||||||
\(980\) | −8.95430 | + | 12.8382i | −0.286035 | + | 0.410103i | ||||
\(981\) | −14.8984 | −0.475670 | ||||||||
\(982\) | 10.5352 | + | 10.5352i | 0.336192 | + | 0.336192i | ||||
\(983\) | 19.9374 | + | 19.9374i | 0.635903 | + | 0.635903i | 0.949542 | − | 0.313639i | \(-0.101548\pi\) |
−0.313639 | + | 0.949542i | \(0.601548\pi\) | |||||||
\(984\) | − | 0.514280i | − | 0.0163946i | ||||||
\(985\) | −17.7596 | + | 11.2507i | −0.565869 | + | 0.358477i | ||||
\(986\) | − | 23.6365i | − | 0.752740i | ||||||
\(987\) | 16.2213 | + | 24.1620i | 0.516328 | + | 0.769086i | ||||
\(988\) | −3.38459 | + | 3.38459i | −0.107678 | + | 0.107678i | ||||
\(989\) | 5.63356i | 0.179137i | ||||||||
\(990\) | 0.0354431 | + | 0.0559482i | 0.00112645 | + | 0.00177815i | ||||
\(991\) | 24.6283 | 0.782344 | 0.391172 | − | 0.920318i | \(-0.372070\pi\) | ||||
0.391172 | + | 0.920318i | \(0.372070\pi\) | |||||||
\(992\) | 4.52072 | − | 4.52072i | 0.143533 | − | 0.143533i | ||||
\(993\) | 3.28347 | + | 3.28347i | 0.104198 | + | 0.104198i | ||||
\(994\) | −3.39371 | + | 17.2589i | −0.107642 | + | 0.547420i | ||||
\(995\) | −6.00315 | + | 26.7560i | −0.190313 | + | 0.848224i | ||||
\(996\) | 0.213022 | 0.00674985 | ||||||||
\(997\) | 31.1165 | − | 31.1165i | 0.985471 | − | 0.985471i | −0.0144253 | − | 0.999896i | \(-0.504592\pi\) |
0.999896 | + | 0.0144253i | \(0.00459186\pi\) | |||||||
\(998\) | 23.1880 | − | 23.1880i | 0.734005 | − | 0.734005i | ||||
\(999\) | 5.26358 | 0.166532 |
(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.a.97.4 | yes | 8 | |
3.2 | odd | 2 | 630.2.p.b.307.1 | 8 | |||
4.3 | odd | 2 | 1680.2.cz.b.97.2 | 8 | |||
5.2 | odd | 4 | 1050.2.m.a.643.1 | 8 | |||
5.3 | odd | 4 | 210.2.m.b.13.3 | yes | 8 | ||
5.4 | even | 2 | 1050.2.m.b.307.1 | 8 | |||
7.6 | odd | 2 | 210.2.m.b.97.3 | yes | 8 | ||
15.8 | even | 4 | 630.2.p.c.433.2 | 8 | |||
20.3 | even | 4 | 1680.2.cz.a.433.3 | 8 | |||
21.20 | even | 2 | 630.2.p.c.307.2 | 8 | |||
28.27 | even | 2 | 1680.2.cz.a.97.3 | 8 | |||
35.13 | even | 4 | inner | 210.2.m.a.13.4 | ✓ | 8 | |
35.27 | even | 4 | 1050.2.m.b.643.1 | 8 | |||
35.34 | odd | 2 | 1050.2.m.a.307.1 | 8 | |||
105.83 | odd | 4 | 630.2.p.b.433.1 | 8 | |||
140.83 | odd | 4 | 1680.2.cz.b.433.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.m.a.13.4 | ✓ | 8 | 35.13 | even | 4 | inner | |
210.2.m.a.97.4 | yes | 8 | 1.1 | even | 1 | trivial | |
210.2.m.b.13.3 | yes | 8 | 5.3 | odd | 4 | ||
210.2.m.b.97.3 | yes | 8 | 7.6 | odd | 2 | ||
630.2.p.b.307.1 | 8 | 3.2 | odd | 2 | |||
630.2.p.b.433.1 | 8 | 105.83 | odd | 4 | |||
630.2.p.c.307.2 | 8 | 21.20 | even | 2 | |||
630.2.p.c.433.2 | 8 | 15.8 | even | 4 | |||
1050.2.m.a.307.1 | 8 | 35.34 | odd | 2 | |||
1050.2.m.a.643.1 | 8 | 5.2 | odd | 4 | |||
1050.2.m.b.307.1 | 8 | 5.4 | even | 2 | |||
1050.2.m.b.643.1 | 8 | 35.27 | even | 4 | |||
1680.2.cz.a.97.3 | 8 | 28.27 | even | 2 | |||
1680.2.cz.a.433.3 | 8 | 20.3 | even | 4 | |||
1680.2.cz.b.97.2 | 8 | 4.3 | odd | 2 | |||
1680.2.cz.b.433.2 | 8 | 140.83 | odd | 4 |