Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [250,2,Mod(49,250)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(250, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("250.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 250 = 2 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 250.e (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.99626005053\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | no (minimal twist has level 50) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 99.4 | ||
Root | \(-0.644389 - 0.983224i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 250.99 |
Dual form | 250.2.e.c.149.4 |
$q$-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 \(\left(\mathbb{Z}/250\mathbb{Z}\right)^\times\).
\(n\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{9}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.951057 | − | 0.309017i | 0.672499 | − | 0.218508i | ||||
\(3\) | 0.792578 | + | 1.09089i | 0.457595 | + | 0.629826i | 0.974008 | − | 0.226514i | \(-0.0727330\pi\) |
−0.516413 | + | 0.856340i | \(0.672733\pi\) | |||||||
\(4\) | 0.809017 | − | 0.587785i | 0.404508 | − | 0.293893i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.09089 | + | 0.792578i | 0.445354 | + | 0.323569i | ||||
\(7\) | 0.833366i | 0.314983i | 0.987520 | + | 0.157491i | \(0.0503406\pi\) | ||||
−0.987520 | + | 0.157491i | \(0.949659\pi\) | |||||||
\(8\) | 0.587785 | − | 0.809017i | 0.207813 | − | 0.286031i | ||||
\(9\) | 0.365190 | − | 1.12394i | 0.121730 | − | 0.374646i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.257524 | + | 0.792578i | 0.0776465 | + | 0.238971i | 0.982344 | − | 0.187083i | \(-0.0599033\pi\) |
−0.904698 | + | 0.426054i | \(0.859903\pi\) | |||||||
\(12\) | 1.28242 | + | 0.416683i | 0.370202 | + | 0.120286i | ||||
\(13\) | 4.34038 | + | 1.41027i | 1.20380 | + | 0.391140i | 0.841159 | − | 0.540787i | \(-0.181874\pi\) |
0.362645 | + | 0.931927i | \(0.381874\pi\) | |||||||
\(14\) | 0.257524 | + | 0.792578i | 0.0688262 | + | 0.211825i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | −3.20425 | + | 4.41027i | −0.777145 | + | 1.06965i | 0.218446 | + | 0.975849i | \(0.429901\pi\) |
−0.995591 | + | 0.0937997i | \(0.970099\pi\) | |||||||
\(18\) | − | 1.18178i | − | 0.278548i | ||||||
\(19\) | −7.00116 | − | 5.08664i | −1.60618 | − | 1.16696i | −0.874116 | − | 0.485718i | \(-0.838558\pi\) |
−0.732062 | − | 0.681238i | \(-0.761442\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.909110 | + | 0.660507i | −0.198384 | + | 0.144134i | ||||
\(22\) | 0.489840 | + | 0.674207i | 0.104434 | + | 0.143741i | ||||
\(23\) | −3.35741 | + | 1.09089i | −0.700069 | + | 0.227466i | −0.637361 | − | 0.770566i | \(-0.719974\pi\) |
−0.0627085 | + | 0.998032i | \(0.519974\pi\) | |||||||
\(24\) | 1.34841 | 0.275244 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.56375 | 0.895024 | ||||||||
\(27\) | 5.36279 | − | 1.74248i | 1.03207 | − | 0.335340i | ||||
\(28\) | 0.489840 | + | 0.674207i | 0.0925711 | + | 0.127413i | ||||
\(29\) | 2.64518 | − | 1.92183i | 0.491197 | − | 0.356876i | −0.314447 | − | 0.949275i | \(-0.601819\pi\) |
0.805645 | + | 0.592399i | \(0.201819\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.85599 | − | 3.52808i | −0.872161 | − | 0.633662i | 0.0590050 | − | 0.998258i | \(-0.481207\pi\) |
−0.931166 | + | 0.364596i | \(0.881207\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −0.660507 | + | 0.909110i | −0.114980 | + | 0.158256i | ||||
\(34\) | −1.68458 | + | 5.18459i | −0.288902 | + | 0.889150i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.365190 | − | 1.12394i | −0.0608650 | − | 0.187323i | ||||
\(37\) | −6.95685 | − | 2.26042i | −1.14370 | − | 0.371610i | −0.324932 | − | 0.945737i | \(-0.605342\pi\) |
−0.818766 | + | 0.574127i | \(0.805342\pi\) | |||||||
\(38\) | −8.23036 | − | 2.67421i | −1.33514 | − | 0.433814i | ||||
\(39\) | 1.90163 | + | 5.85263i | 0.304505 | + | 0.937171i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.576909 | − | 1.77554i | 0.0900981 | − | 0.277293i | −0.895847 | − | 0.444362i | \(-0.853430\pi\) |
0.985945 | + | 0.167069i | \(0.0534303\pi\) | |||||||
\(42\) | −0.660507 | + | 0.909110i | −0.101918 | + | 0.140279i | ||||
\(43\) | − | 1.63877i | − | 0.249910i | −0.992162 | − | 0.124955i | \(-0.960121\pi\) | ||
0.992162 | − | 0.124955i | \(-0.0398787\pi\) | |||||||
\(44\) | 0.674207 | + | 0.489840i | 0.101641 | + | 0.0738462i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.85599 | + | 2.07500i | −0.421092 | + | 0.305941i | ||||
\(47\) | −0.489840 | − | 0.674207i | −0.0714505 | − | 0.0983432i | 0.771796 | − | 0.635870i | \(-0.219359\pi\) |
−0.843247 | + | 0.537527i | \(0.819359\pi\) | |||||||
\(48\) | 1.28242 | − | 0.416683i | 0.185101 | − | 0.0601430i | ||||
\(49\) | 6.30550 | 0.900786 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.35074 | −1.02931 | ||||||||
\(52\) | 4.34038 | − | 1.41027i | 0.601902 | − | 0.195570i | ||||
\(53\) | −3.77782 | − | 5.19972i | −0.518923 | − | 0.714237i | 0.466469 | − | 0.884538i | \(-0.345526\pi\) |
−0.985392 | + | 0.170301i | \(0.945526\pi\) | |||||||
\(54\) | 4.56186 | − | 3.31439i | 0.620791 | − | 0.451031i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.674207 | + | 0.489840i | 0.0900947 | + | 0.0654576i | ||||
\(57\) | − | 11.6691i | − | 1.54560i | ||||||
\(58\) | 1.92183 | − | 2.64518i | 0.252349 | − | 0.347329i | ||||
\(59\) | −4.18178 | + | 12.8702i | −0.544421 | + | 1.67556i | 0.177940 | + | 0.984041i | \(0.443057\pi\) |
−0.722362 | + | 0.691515i | \(0.756943\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.81832 | + | 5.59621i | 0.232812 | + | 0.716521i | 0.997404 | + | 0.0720066i | \(0.0229403\pi\) |
−0.764592 | + | 0.644514i | \(0.777060\pi\) | |||||||
\(62\) | −5.70855 | − | 1.85482i | −0.724987 | − | 0.235563i | ||||
\(63\) | 0.936652 | + | 0.304337i | 0.118007 | + | 0.0383428i | ||||
\(64\) | −0.309017 | − | 0.951057i | −0.0386271 | − | 0.118882i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.347249 | + | 1.06872i | −0.0427434 | + | 0.131551i | ||||
\(67\) | −0.881621 | + | 1.21345i | −0.107707 | + | 0.148246i | −0.859468 | − | 0.511190i | \(-0.829205\pi\) |
0.751761 | + | 0.659436i | \(0.229205\pi\) | |||||||
\(68\) | 5.45140i | 0.661079i | ||||||||
\(69\) | −3.85105 | − | 2.79795i | −0.463612 | − | 0.336834i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.91027 | − | 1.38790i | 0.226708 | − | 0.164713i | −0.468633 | − | 0.883393i | \(-0.655253\pi\) |
0.695341 | + | 0.718680i | \(0.255253\pi\) | |||||||
\(72\) | −0.694633 | − | 0.956080i | −0.0818632 | − | 0.112675i | ||||
\(73\) | 3.16703 | − | 1.02903i | 0.370672 | − | 0.120439i | −0.117756 | − | 0.993043i | \(-0.537570\pi\) |
0.488429 | + | 0.872604i | \(0.337570\pi\) | |||||||
\(74\) | −7.31486 | −0.850335 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.65392 | −0.992672 | ||||||||
\(77\) | −0.660507 | + | 0.214612i | −0.0752718 | + | 0.0244573i | ||||
\(78\) | 3.61712 | + | 4.97854i | 0.409559 | + | 0.563709i | ||||
\(79\) | 4.18178 | − | 3.03824i | 0.470487 | − | 0.341829i | −0.327144 | − | 0.944974i | \(-0.606086\pi\) |
0.797631 | + | 0.603146i | \(0.206086\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.28304 | + | 2.38527i | 0.364782 | + | 0.265030i | ||||
\(82\) | − | 1.86692i | − | 0.206167i | ||||||
\(83\) | −7.25068 | + | 9.97971i | −0.795866 | + | 1.09542i | 0.197487 | + | 0.980306i | \(0.436722\pi\) |
−0.993353 | + | 0.115110i | \(0.963278\pi\) | |||||||
\(84\) | −0.347249 | + | 1.06872i | −0.0378880 | + | 0.116607i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.506408 | − | 1.55856i | −0.0546074 | − | 0.168064i | ||||
\(87\) | 4.19302 | + | 1.36239i | 0.449539 | + | 0.146064i | ||||
\(88\) | 0.792578 | + | 0.257524i | 0.0844891 | + | 0.0274522i | ||||
\(89\) | 2.16491 | + | 6.66290i | 0.229480 | + | 0.706266i | 0.997806 | + | 0.0662073i | \(0.0210899\pi\) |
−0.768326 | + | 0.640058i | \(0.778910\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.17527 | + | 3.61712i | −0.123202 | + | 0.379178i | ||||
\(92\) | −2.07500 | + | 2.85599i | −0.216333 | + | 0.297757i | ||||
\(93\) | − | 8.09363i | − | 0.839270i | ||||||
\(94\) | −0.674207 | − | 0.489840i | −0.0695391 | − | 0.0505231i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.09089 | − | 0.792578i | 0.111338 | − | 0.0808921i | ||||
\(97\) | 6.51864 | + | 8.97214i | 0.661867 | + | 0.910982i | 0.999541 | − | 0.0302807i | \(-0.00964013\pi\) |
−0.337674 | + | 0.941263i | \(0.609640\pi\) | |||||||
\(98\) | 5.99689 | − | 1.94851i | 0.605777 | − | 0.196829i | ||||
\(99\) | 0.984855 | 0.0989816 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.7085 | 1.26454 | 0.632272 | − | 0.774746i | \(-0.282122\pi\) | ||||
0.632272 | + | 0.774746i | \(0.282122\pi\) | |||||||
\(102\) | −6.99097 | + | 2.27150i | −0.692209 | + | 0.224912i | ||||
\(103\) | −4.12340 | − | 5.67537i | −0.406291 | − | 0.559211i | 0.556018 | − | 0.831170i | \(-0.312328\pi\) |
−0.962309 | + | 0.271959i | \(0.912328\pi\) | |||||||
\(104\) | 3.69215 | − | 2.68250i | 0.362045 | − | 0.263041i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.19972 | − | 3.77782i | −0.505042 | − | 0.366934i | ||||
\(107\) | 10.7700i | 1.04118i | 0.853807 | + | 0.520589i | \(0.174288\pi\) | ||||
−0.853807 | + | 0.520589i | \(0.825712\pi\) | |||||||
\(108\) | 3.31439 | − | 4.56186i | 0.318927 | − | 0.438965i | ||||
\(109\) | 3.28655 | − | 10.1150i | 0.314795 | − | 0.968838i | −0.661044 | − | 0.750347i | \(-0.729886\pi\) |
0.975839 | − | 0.218491i | \(-0.0701136\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.04798 | − | 9.38071i | −0.289301 | − | 0.890378i | ||||
\(112\) | 0.792578 | + | 0.257524i | 0.0748916 | + | 0.0243337i | ||||
\(113\) | 1.65651 | + | 0.538232i | 0.155831 | + | 0.0506326i | 0.385894 | − | 0.922543i | \(-0.373893\pi\) |
−0.230063 | + | 0.973176i | \(0.573893\pi\) | |||||||
\(114\) | −3.60594 | − | 11.0979i | −0.337727 | − | 1.03942i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.01037 | − | 3.10959i | 0.0938103 | − | 0.288718i | ||||
\(117\) | 3.17013 | − | 4.36331i | 0.293078 | − | 0.403388i | ||||
\(118\) | 13.5325i | 1.24577i | ||||||||
\(119\) | −3.67537 | − | 2.67031i | −0.336921 | − | 0.244787i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.33733 | − | 6.05742i | 0.757939 | − | 0.550675i | ||||
\(122\) | 3.45865 | + | 4.76042i | 0.313131 | + | 0.430988i | ||||
\(123\) | 2.39417 | − | 0.777913i | 0.215875 | − | 0.0701420i | ||||
\(124\) | −6.00233 | −0.539025 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.984855 | 0.0877378 | ||||||||
\(127\) | 5.38938 | − | 1.75112i | 0.478230 | − | 0.155386i | −0.0599756 | − | 0.998200i | \(-0.519102\pi\) |
0.538206 | + | 0.842813i | \(0.319102\pi\) | |||||||
\(128\) | −0.587785 | − | 0.809017i | −0.0519534 | − | 0.0715077i | ||||
\(129\) | 1.78772 | − | 1.29885i | 0.157400 | − | 0.114358i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.3281 | + | 9.68345i | 1.16448 | + | 0.846047i | 0.990338 | − | 0.138673i | \(-0.0442838\pi\) |
0.174145 | + | 0.984720i | \(0.444284\pi\) | |||||||
\(132\) | 1.12372i | 0.0978074i | ||||||||
\(133\) | 4.23903 | − | 5.83453i | 0.367571 | − | 0.505918i | ||||
\(134\) | −0.463496 | + | 1.42649i | −0.0400399 | + | 0.123230i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.68458 | + | 5.18459i | 0.144451 | + | 0.444575i | ||||
\(137\) | 2.75164 | + | 0.894062i | 0.235088 | + | 0.0763849i | 0.424192 | − | 0.905572i | \(-0.360558\pi\) |
−0.189104 | + | 0.981957i | \(0.560558\pi\) | |||||||
\(138\) | −4.52718 | − | 1.47097i | −0.385379 | − | 0.125217i | ||||
\(139\) | −1.54184 | − | 4.74531i | −0.130778 | − | 0.402492i | 0.864132 | − | 0.503266i | \(-0.167868\pi\) |
−0.994909 | + | 0.100774i | \(0.967868\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.347249 | − | 1.06872i | 0.0292437 | − | 0.0900027i | ||||
\(142\) | 1.38790 | − | 1.91027i | 0.116470 | − | 0.160307i | ||||
\(143\) | 3.80327i | 0.318045i | ||||||||
\(144\) | −0.956080 | − | 0.694633i | −0.0796733 | − | 0.0578861i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.69403 | − | 1.95733i | 0.222960 | − | 0.161990i | ||||
\(147\) | 4.99760 | + | 6.87861i | 0.412195 | + | 0.567338i | ||||
\(148\) | −6.95685 | + | 2.26042i | −0.571849 | + | 0.185805i | ||||
\(149\) | −2.00579 | −0.164320 | −0.0821602 | − | 0.996619i | \(-0.526182\pi\) | ||||
−0.0821602 | + | 0.996619i | \(0.526182\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.96971 | −0.160293 | −0.0801463 | − | 0.996783i | \(-0.525539\pi\) | ||||
−0.0801463 | + | 0.996783i | \(0.525539\pi\) | |||||||
\(152\) | −8.23036 | + | 2.67421i | −0.667571 | + | 0.216907i | ||||
\(153\) | 3.78672 | + | 5.21197i | 0.306138 | + | 0.421363i | ||||
\(154\) | −0.561861 | + | 0.408216i | −0.0452760 | + | 0.0328950i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.97854 | + | 3.61712i | 0.398603 | + | 0.289602i | ||||
\(157\) | − | 7.78467i | − | 0.621284i | −0.950527 | − | 0.310642i | \(-0.899456\pi\) | ||
0.950527 | − | 0.310642i | \(-0.100544\pi\) | |||||||
\(158\) | 3.03824 | − | 4.18178i | 0.241709 | − | 0.332685i | ||||
\(159\) | 2.67811 | − | 8.24237i | 0.212388 | − | 0.653662i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.909110 | − | 2.79795i | −0.0716479 | − | 0.220510i | ||||
\(162\) | 3.85944 | + | 1.25401i | 0.303226 | + | 0.0985242i | ||||
\(163\) | 13.4060 | + | 4.35589i | 1.05004 | + | 0.341180i | 0.782685 | − | 0.622418i | \(-0.213849\pi\) |
0.267358 | + | 0.963597i | \(0.413849\pi\) | |||||||
\(164\) | −0.576909 | − | 1.77554i | −0.0450490 | − | 0.138647i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.81191 | + | 11.7319i | −0.295862 | + | 0.910568i | ||||
\(167\) | 4.79406 | − | 6.59846i | 0.370976 | − | 0.510604i | −0.582190 | − | 0.813053i | \(-0.697804\pi\) |
0.953166 | + | 0.302448i | \(0.0978040\pi\) | |||||||
\(168\) | 1.12372i | 0.0866970i | ||||||||
\(169\) | 6.33280 | + | 4.60105i | 0.487139 | + | 0.353927i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.27383 | + | 6.01129i | −0.632716 | + | 0.459695i | ||||
\(172\) | −0.963245 | − | 1.32579i | −0.0734467 | − | 0.101091i | ||||
\(173\) | 2.38084 | − | 0.773580i | 0.181012 | − | 0.0588142i | −0.217109 | − | 0.976147i | \(-0.569663\pi\) |
0.398120 | + | 0.917333i | \(0.369663\pi\) | |||||||
\(174\) | 4.40880 | 0.334230 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.833366 | 0.0628173 | ||||||||
\(177\) | −17.3544 | + | 5.63877i | −1.30443 | + | 0.423836i | ||||
\(178\) | 4.11790 | + | 5.66780i | 0.308649 | + | 0.424820i | ||||
\(179\) | −16.2067 | + | 11.7749i | −1.21135 | + | 0.880096i | −0.995352 | − | 0.0962986i | \(-0.969300\pi\) |
−0.215995 | + | 0.976394i | \(0.569300\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.37367 | − | 4.63074i | −0.473751 | − | 0.344201i | 0.325150 | − | 0.945662i | \(-0.394585\pi\) |
−0.798902 | + | 0.601462i | \(0.794585\pi\) | |||||||
\(182\) | 3.80327i | 0.281917i | ||||||||
\(183\) | −4.66369 | + | 6.41901i | −0.344750 | + | 0.474507i | ||||
\(184\) | −1.09089 | + | 3.35741i | −0.0804215 | + | 0.247512i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.50107 | − | 7.69750i | −0.183387 | − | 0.564408i | ||||
\(187\) | −4.32066 | − | 1.40387i | −0.315958 | − | 0.102661i | ||||
\(188\) | −0.792578 | − | 0.257524i | −0.0578047 | − | 0.0187819i | ||||
\(189\) | 1.45212 | + | 4.46916i | 0.105626 | + | 0.325084i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.63013 | + | 5.01702i | −0.117952 | + | 0.363019i | −0.992551 | − | 0.121827i | \(-0.961125\pi\) |
0.874599 | + | 0.484847i | \(0.161125\pi\) | |||||||
\(192\) | 0.792578 | − | 1.09089i | 0.0571994 | − | 0.0787282i | ||||
\(193\) | − | 13.4461i | − | 0.967873i | −0.875103 | − | 0.483937i | \(-0.839207\pi\) | ||
0.875103 | − | 0.483937i | \(-0.160793\pi\) | |||||||
\(194\) | 8.97214 | + | 6.51864i | 0.644162 | + | 0.468011i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.10126 | − | 3.70628i | 0.364376 | − | 0.264734i | ||||
\(197\) | −3.19672 | − | 4.39991i | −0.227757 | − | 0.313480i | 0.679810 | − | 0.733388i | \(-0.262062\pi\) |
−0.907567 | + | 0.419908i | \(0.862062\pi\) | |||||||
\(198\) | 0.936652 | − | 0.304337i | 0.0665650 | − | 0.0216283i | ||||
\(199\) | 17.4090 | 1.23409 | 0.617045 | − | 0.786927i | \(-0.288329\pi\) | ||||
0.617045 | + | 0.786927i | \(0.288329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.02249 | −0.142655 | ||||||||
\(202\) | 12.0865 | − | 3.92715i | 0.850404 | − | 0.276313i | ||||
\(203\) | 1.60159 | + | 2.20440i | 0.112410 | + | 0.154719i | ||||
\(204\) | −5.94688 | + | 4.32066i | −0.416365 | + | 0.302507i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.67537 | − | 4.12340i | −0.395422 | − | 0.287291i | ||||
\(207\) | 4.17191i | 0.289968i | ||||||||
\(208\) | 2.68250 | − | 3.69215i | 0.185998 | − | 0.256004i | ||||
\(209\) | 2.22859 | − | 6.85890i | 0.154155 | − | 0.474440i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.0834142 | − | 0.256723i | −0.00574247 | − | 0.0176735i | 0.948144 | − | 0.317840i | \(-0.102958\pi\) |
−0.953887 | + | 0.300167i | \(0.902958\pi\) | |||||||
\(212\) | −6.11264 | − | 1.98612i | −0.419818 | − | 0.136407i | ||||
\(213\) | 3.02808 | + | 0.983884i | 0.207481 | + | 0.0674146i | ||||
\(214\) | 3.32812 | + | 10.2429i | 0.227506 | + | 0.700191i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.74248 | − | 5.36279i | 0.118560 | − | 0.364892i | ||||
\(217\) | 2.94018 | − | 4.04681i | 0.199593 | − | 0.274716i | ||||
\(218\) | − | 10.6355i | − | 0.720328i | ||||||
\(219\) | 3.63267 | + | 2.63929i | 0.245473 | + | 0.178347i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.1274 | + | 14.6234i | −1.35391 | + | 0.983676i | ||||
\(222\) | −5.79760 | − | 7.97971i | −0.389109 | − | 0.535563i | ||||
\(223\) | −22.0372 | + | 7.16032i | −1.47572 | + | 0.479491i | −0.932831 | − | 0.360313i | \(-0.882670\pi\) |
−0.542889 | + | 0.839804i | \(0.682670\pi\) | |||||||
\(224\) | 0.833366 | 0.0556816 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.74176 | 0.115860 | ||||||||
\(227\) | −0.240287 | + | 0.0780741i | −0.0159484 | + | 0.00518196i | −0.316980 | − | 0.948432i | \(-0.602669\pi\) |
0.301032 | + | 0.953614i | \(0.402669\pi\) | |||||||
\(228\) | −6.85890 | − | 9.44047i | −0.454242 | − | 0.625210i | ||||
\(229\) | −17.0625 | + | 12.3966i | −1.12752 | + | 0.819191i | −0.985332 | − | 0.170649i | \(-0.945414\pi\) |
−0.142187 | + | 0.989840i | \(0.545414\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.757621 | − | 0.550444i | −0.0498478 | − | 0.0362166i | ||||
\(232\) | − | 3.26962i | − | 0.214661i | ||||||
\(233\) | −8.58610 | + | 11.8178i | −0.562494 | + | 0.774207i | −0.991641 | − | 0.129028i | \(-0.958814\pi\) |
0.429147 | + | 0.903235i | \(0.358814\pi\) | |||||||
\(234\) | 1.66663 | − | 5.12937i | 0.108951 | − | 0.335318i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.18178 | + | 12.8702i | 0.272211 | + | 0.837778i | ||||
\(237\) | 6.62877 | + | 2.15382i | 0.430585 | + | 0.139906i | ||||
\(238\) | −4.32066 | − | 1.40387i | −0.280067 | − | 0.0909992i | ||||
\(239\) | −1.79793 | − | 5.53346i | −0.116298 | − | 0.357930i | 0.875917 | − | 0.482461i | \(-0.160257\pi\) |
−0.992216 | + | 0.124532i | \(0.960257\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.24254 | − | 13.0572i | 0.273286 | − | 0.841087i | −0.716382 | − | 0.697708i | \(-0.754203\pi\) |
0.989668 | − | 0.143379i | \(-0.0457968\pi\) | |||||||
\(242\) | 6.05742 | − | 8.33733i | 0.389386 | − | 0.535944i | ||||
\(243\) | − | 11.4444i | − | 0.734157i | ||||||
\(244\) | 4.76042 | + | 3.45865i | 0.304754 | + | 0.221417i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.03660 | − | 1.47968i | 0.129849 | − | 0.0943408i | ||||
\(247\) | −23.2141 | − | 31.9515i | −1.47708 | − | 2.03303i | ||||
\(248\) | −5.70855 | + | 1.85482i | −0.362494 | + | 0.117781i | ||||
\(249\) | −16.6335 | −1.05410 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.8938 | −1.00320 | −0.501602 | − | 0.865098i | \(-0.667256\pi\) | ||||
−0.501602 | + | 0.865098i | \(0.667256\pi\) | |||||||
\(252\) | 0.936652 | − | 0.304337i | 0.0590036 | − | 0.0191714i | ||||
\(253\) | −1.72923 | − | 2.38008i | −0.108716 | − | 0.149634i | ||||
\(254\) | 4.58448 | − | 3.33082i | 0.287656 | − | 0.208994i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 2.31253i | 0.144252i | 0.997396 | + | 0.0721259i | \(0.0229783\pi\) | ||||
−0.997396 | + | 0.0721259i | \(0.977022\pi\) | |||||||
\(258\) | 1.29885 | − | 1.78772i | 0.0808631 | − | 0.111298i | ||||
\(259\) | 1.88375 | − | 5.79760i | 0.117051 | − | 0.360245i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.19403 | − | 3.67485i | −0.0739088 | − | 0.227468i | ||||
\(262\) | 15.6681 | + | 5.09089i | 0.967981 | + | 0.314516i | ||||
\(263\) | −20.4090 | − | 6.63129i | −1.25847 | − | 0.408903i | −0.397524 | − | 0.917592i | \(-0.630130\pi\) |
−0.860951 | + | 0.508689i | \(0.830130\pi\) | |||||||
\(264\) | 0.347249 | + | 1.06872i | 0.0213717 | + | 0.0657754i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.22859 | − | 6.85890i | 0.136644 | − | 0.420546i | ||||
\(267\) | −5.55263 | + | 7.64254i | −0.339815 | + | 0.467716i | ||||
\(268\) | 1.49990i | 0.0916212i | ||||||||
\(269\) | 17.3020 | + | 12.5706i | 1.05492 | + | 0.766445i | 0.973142 | − | 0.230206i | \(-0.0739399\pi\) |
0.0817787 | + | 0.996651i | \(0.473940\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.1400 | − | 15.3591i | 1.28417 | − | 0.933001i | 0.284495 | − | 0.958677i | \(-0.408174\pi\) |
0.999670 | + | 0.0256766i | \(0.00817402\pi\) | |||||||
\(272\) | 3.20425 | + | 4.41027i | 0.194286 | + | 0.267412i | ||||
\(273\) | −4.87738 | + | 1.58476i | −0.295192 | + | 0.0959139i | ||||
\(274\) | 2.89324 | 0.174787 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.76016 | −0.286528 | ||||||||
\(277\) | −17.7342 | + | 5.76220i | −1.06555 | + | 0.346217i | −0.788752 | − | 0.614712i | \(-0.789272\pi\) |
−0.276795 | + | 0.960929i | \(0.589272\pi\) | |||||||
\(278\) | −2.93276 | − | 4.03660i | −0.175895 | − | 0.242099i | ||||
\(279\) | −5.73871 | + | 4.16941i | −0.343567 | + | 0.249616i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.9886 | − | 8.71023i | −0.715180 | − | 0.519609i | 0.169661 | − | 0.985503i | \(-0.445733\pi\) |
−0.884841 | + | 0.465894i | \(0.845733\pi\) | |||||||
\(282\) | − | 1.12372i | − | 0.0669167i | ||||||
\(283\) | 9.27523 | − | 12.7663i | 0.551355 | − | 0.758875i | −0.438840 | − | 0.898565i | \(-0.644611\pi\) |
0.990195 | + | 0.139690i | \(0.0446105\pi\) | |||||||
\(284\) | 0.729660 | − | 2.24566i | 0.0432974 | − | 0.133256i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.17527 | + | 3.61712i | 0.0694955 | + | 0.213885i | ||||
\(287\) | 1.47968 | + | 0.480776i | 0.0873426 | + | 0.0283793i | ||||
\(288\) | −1.12394 | − | 0.365190i | −0.0662288 | − | 0.0215190i | ||||
\(289\) | −3.93000 | − | 12.0953i | −0.231177 | − | 0.711489i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.62108 | + | 14.2222i | −0.270893 | + | 0.833722i | ||||
\(292\) | 1.95733 | − | 2.69403i | 0.114544 | − | 0.157656i | ||||
\(293\) | 18.4003i | 1.07496i | 0.843277 | + | 0.537479i | \(0.180623\pi\) | ||||
−0.843277 | + | 0.537479i | \(0.819377\pi\) | |||||||
\(294\) | 6.87861 | + | 4.99760i | 0.401169 | + | 0.291466i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.91785 | + | 4.29957i | −0.343968 | + | 0.249907i | ||||
\(297\) | 2.76210 | + | 3.80170i | 0.160273 | + | 0.220597i | ||||
\(298\) | −1.90761 | + | 0.619822i | −0.110505 | + | 0.0359053i | ||||
\(299\) | −16.1109 | −0.931718 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.36569 | 0.0787173 | ||||||||
\(302\) | −1.87330 | + | 0.608674i | −0.107797 | + | 0.0350252i | ||||
\(303\) | 10.0725 | + | 13.8636i | 0.578649 | + | 0.796443i | ||||
\(304\) | −7.00116 | + | 5.08664i | −0.401544 | + | 0.291739i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.21197 | + | 3.78672i | 0.297949 | + | 0.216472i | ||||
\(307\) | 34.1179i | 1.94721i | 0.228237 | + | 0.973606i | \(0.426704\pi\) | ||||
−0.228237 | + | 0.973606i | \(0.573296\pi\) | |||||||
\(308\) | −0.408216 | + | 0.561861i | −0.0232603 | + | 0.0320150i | ||||
\(309\) | 2.92309 | − | 8.99635i | 0.166289 | − | 0.511784i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.02893 | − | 12.3998i | −0.228460 | − | 0.703127i | −0.997922 | − | 0.0644345i | \(-0.979476\pi\) |
0.769462 | − | 0.638692i | \(-0.220524\pi\) | |||||||
\(312\) | 5.85263 | + | 1.90163i | 0.331340 | + | 0.107659i | ||||
\(313\) | 3.31217 | + | 1.07619i | 0.187215 | + | 0.0608298i | 0.401124 | − | 0.916024i | \(-0.368620\pi\) |
−0.213909 | + | 0.976854i | \(0.568620\pi\) | |||||||
\(314\) | −2.40559 | − | 7.40366i | −0.135756 | − | 0.417813i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.59730 | − | 4.91598i | 0.0898550 | − | 0.276545i | ||||
\(317\) | −2.83333 | + | 3.89975i | −0.159136 | + | 0.219032i | −0.881138 | − | 0.472859i | \(-0.843222\pi\) |
0.722002 | + | 0.691891i | \(0.243222\pi\) | |||||||
\(318\) | − | 8.66654i | − | 0.485995i | ||||||
\(319\) | 2.20440 | + | 1.60159i | 0.123423 | + | 0.0896719i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.7489 | + | 8.53609i | −0.655761 | + | 0.476438i | ||||
\(322\) | −1.72923 | − | 2.38008i | −0.0963662 | − | 0.132637i | ||||
\(323\) | 44.8670 | − | 14.5782i | 2.49647 | − | 0.811151i | ||||
\(324\) | 4.05806 | 0.225448 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.0960 | 0.780703 | ||||||||
\(327\) | 13.6392 | − | 4.43163i | 0.754248 | − | 0.245070i | ||||
\(328\) | −1.09735 | − | 1.51037i | −0.0605908 | − | 0.0833961i | ||||
\(329\) | 0.561861 | − | 0.408216i | 0.0309764 | − | 0.0225057i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.92796 | − | 5.03346i | −0.380795 | − | 0.276664i | 0.380878 | − | 0.924625i | \(-0.375622\pi\) |
−0.761673 | + | 0.647961i | \(0.775622\pi\) | |||||||
\(332\) | 12.3356i | 0.677004i | ||||||||
\(333\) | −5.08114 | + | 6.99359i | −0.278445 | + | 0.383246i | ||||
\(334\) | 2.52039 | − | 7.75696i | 0.137910 | − | 0.424442i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.347249 | + | 1.06872i | 0.0189440 | + | 0.0583036i | ||||
\(337\) | 13.9531 | + | 4.53365i | 0.760076 | + | 0.246964i | 0.663311 | − | 0.748344i | \(-0.269151\pi\) |
0.0967646 | + | 0.995307i | \(0.469151\pi\) | |||||||
\(338\) | 7.44466 | + | 2.41892i | 0.404936 | + | 0.131572i | ||||
\(339\) | 0.725760 | + | 2.23366i | 0.0394179 | + | 0.121316i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.54574 | − | 4.75731i | 0.0837068 | − | 0.257623i | ||||
\(342\) | −6.01129 | + | 8.27383i | −0.325053 | + | 0.447398i | ||||
\(343\) | 11.0883i | 0.598715i | ||||||||
\(344\) | −1.32579 | − | 0.963245i | −0.0714820 | − | 0.0519347i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.02526 | − | 1.47144i | 0.108879 | − | 0.0791049i | ||||
\(347\) | −13.5115 | − | 18.5970i | −0.725337 | − | 0.998340i | −0.999330 | − | 0.0366088i | \(-0.988344\pi\) |
0.273993 | − | 0.961732i | \(-0.411656\pi\) | |||||||
\(348\) | 4.19302 | − | 1.36239i | 0.224769 | − | 0.0730320i | ||||
\(349\) | −3.55023 | −0.190040 | −0.0950198 | − | 0.995475i | \(-0.530291\pi\) | ||||
−0.0950198 | + | 0.995475i | \(0.530291\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.7339 | 1.37357 | ||||||||
\(352\) | 0.792578 | − | 0.257524i | 0.0422445 | − | 0.0137261i | ||||
\(353\) | 3.31576 | + | 4.56375i | 0.176480 | + | 0.242904i | 0.888089 | − | 0.459672i | \(-0.152033\pi\) |
−0.711609 | + | 0.702576i | \(0.752033\pi\) | |||||||
\(354\) | −14.7625 | + | 10.7256i | −0.784618 | + | 0.570058i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.66780 | + | 4.11790i | 0.300393 | + | 0.218248i | ||||
\(357\) | − | 6.12586i | − | 0.324215i | ||||||
\(358\) | −11.7749 | + | 16.2067i | −0.622322 | + | 0.856552i | ||||
\(359\) | 5.22442 | − | 16.0791i | 0.275734 | − | 0.848623i | −0.713290 | − | 0.700869i | \(-0.752796\pi\) |
0.989024 | − | 0.147754i | \(-0.0472043\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.2710 | + | 53.1548i | 0.909002 | + | 2.79762i | ||||
\(362\) | −7.49270 | − | 2.43453i | −0.393808 | − | 0.127956i | ||||
\(363\) | 13.2160 | + | 4.29413i | 0.693658 | + | 0.225383i | ||||
\(364\) | 1.17527 | + | 3.61712i | 0.0616011 | + | 0.189589i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.45184 | + | 7.54600i | −0.128160 | + | 0.394436i | ||||
\(367\) | 7.41393 | − | 10.2044i | 0.387004 | − | 0.532665i | −0.570419 | − | 0.821354i | \(-0.693219\pi\) |
0.957423 | + | 0.288688i | \(0.0932192\pi\) | |||||||
\(368\) | 3.53019i | 0.184024i | ||||||||
\(369\) | −1.78492 | − | 1.29682i | −0.0929193 | − | 0.0675099i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.33327 | − | 3.14830i | 0.224972 | − | 0.163452i | ||||
\(372\) | −4.75731 | − | 6.54788i | −0.246655 | − | 0.339492i | ||||
\(373\) | −12.6011 | + | 4.09435i | −0.652460 | + | 0.211997i | −0.616499 | − | 0.787356i | \(-0.711449\pi\) |
−0.0359616 | + | 0.999353i | \(0.511449\pi\) | |||||||
\(374\) | −4.54301 | −0.234913 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.833366 | −0.0429776 | ||||||||
\(377\) | 14.1914 | − | 4.61106i | 0.730894 | − | 0.237482i | ||||
\(378\) | 2.76210 | + | 3.80170i | 0.142067 | + | 0.195538i | ||||
\(379\) | 18.0702 | − | 13.1288i | 0.928203 | − | 0.674379i | −0.0173488 | − | 0.999849i | \(-0.505523\pi\) |
0.945552 | + | 0.325470i | \(0.105523\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.18178 | + | 4.49133i | 0.316702 | + | 0.230098i | ||||
\(382\) | 5.27521i | 0.269903i | ||||||||
\(383\) | 14.3143 | − | 19.7019i | 0.731425 | − | 1.00672i | −0.267642 | − | 0.963519i | \(-0.586244\pi\) |
0.999066 | − | 0.0432012i | \(-0.0137557\pi\) | |||||||
\(384\) | 0.416683 | − | 1.28242i | 0.0212638 | − | 0.0654431i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.15508 | − | 12.7880i | −0.211488 | − | 0.650893i | ||||
\(387\) | −1.84188 | − | 0.598463i | −0.0936279 | − | 0.0304216i | ||||
\(388\) | 10.5474 | + | 3.42705i | 0.535462 | + | 0.173982i | ||||
\(389\) | −9.30500 | − | 28.6378i | −0.471782 | − | 1.45200i | −0.850249 | − | 0.526381i | \(-0.823548\pi\) |
0.378467 | − | 0.925615i | \(-0.376452\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.94688 | − | 18.3026i | 0.300746 | − | 0.925602i | ||||
\(392\) | 3.70628 | − | 5.10126i | 0.187195 | − | 0.257652i | ||||
\(393\) | 22.2144i | 1.12057i | ||||||||
\(394\) | −4.39991 | − | 3.19672i | −0.221664 | − | 0.161048i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.796764 | − | 0.578883i | 0.0400389 | − | 0.0290900i | ||||
\(397\) | 20.7902 | + | 28.6152i | 1.04343 | + | 1.43616i | 0.894370 | + | 0.447328i | \(0.147624\pi\) |
0.149059 | + | 0.988828i | \(0.452376\pi\) | |||||||
\(398\) | 16.5569 | − | 5.37968i | 0.829924 | − | 0.269659i | ||||
\(399\) | 9.72459 | 0.486839 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.66794 | −0.283043 | −0.141522 | − | 0.989935i | \(-0.545199\pi\) | ||||
−0.141522 | + | 0.989935i | \(0.545199\pi\) | |||||||
\(402\) | −1.92350 | + | 0.624984i | −0.0959356 | + | 0.0311714i | ||||
\(403\) | −16.1013 | − | 22.1615i | −0.802061 | − | 1.10394i | ||||
\(404\) | 10.2814 | − | 7.46988i | 0.511519 | − | 0.371640i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.20440 | + | 1.60159i | 0.109403 | + | 0.0794856i | ||||
\(407\) | − | 6.09595i | − | 0.302165i | ||||||
\(408\) | −4.32066 | + | 5.94688i | −0.213904 | + | 0.294414i | ||||
\(409\) | −5.98493 | + | 18.4197i | −0.295936 | + | 0.910797i | 0.686970 | + | 0.726686i | \(0.258940\pi\) |
−0.982906 | + | 0.184111i | \(0.941060\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.20557 | + | 3.71035i | 0.0594662 | + | 0.183018i | ||||
\(412\) | −6.67180 | − | 2.16780i | −0.328696 | − | 0.106800i | ||||
\(413\) | −10.7256 | − | 3.48495i | −0.527771 | − | 0.171483i | ||||
\(414\) | 1.28919 | + | 3.96772i | 0.0633603 | + | 0.195003i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.41027 | − | 4.34038i | 0.0691444 | − | 0.212805i | ||||
\(417\) | 3.95458 | − | 5.44301i | 0.193657 | − | 0.266545i | ||||
\(418\) | − | 7.21188i | − | 0.352744i | ||||||
\(419\) | 18.5906 | + | 13.5068i | 0.908209 | + | 0.659853i | 0.940561 | − | 0.339624i | \(-0.110300\pi\) |
−0.0323520 | + | 0.999477i | \(0.510300\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.19306 | − | 5.95261i | 0.399305 | − | 0.290112i | −0.369953 | − | 0.929051i | \(-0.620626\pi\) |
0.769258 | + | 0.638938i | \(0.220626\pi\) | |||||||
\(422\) | −0.158663 | − | 0.218381i | −0.00772361 | − | 0.0106306i | ||||
\(423\) | −0.936652 | + | 0.304337i | −0.0455416 | + | 0.0147974i | ||||
\(424\) | −6.42721 | −0.312133 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.18392 | 0.154261 | ||||||||
\(427\) | −4.66369 | + | 1.51532i | −0.225692 | + | 0.0733316i | ||||
\(428\) | 6.33047 | + | 8.71314i | 0.305995 | + | 0.421165i | ||||
\(429\) | −4.14895 | + | 3.01439i | −0.200313 | + | 0.145536i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.0589 | + | 16.7533i | 1.11071 | + | 0.806978i | 0.982775 | − | 0.184804i | \(-0.0591651\pi\) |
0.127935 | + | 0.991783i | \(0.459165\pi\) | |||||||
\(432\) | − | 5.63877i | − | 0.271295i | ||||||
\(433\) | 9.33971 | − | 12.8550i | 0.448838 | − | 0.617772i | −0.523309 | − | 0.852143i | \(-0.675303\pi\) |
0.972147 | + | 0.234370i | \(0.0753028\pi\) | |||||||
\(434\) | 1.54574 | − | 4.75731i | 0.0741981 | − | 0.228358i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.28655 | − | 10.1150i | −0.157397 | − | 0.484419i | ||||
\(437\) | 29.0548 | + | 9.44047i | 1.38988 | + | 0.451599i | ||||
\(438\) | 4.27046 | + | 1.38756i | 0.204051 | + | 0.0663000i | ||||
\(439\) | −0.910550 | − | 2.80238i | −0.0434582 | − | 0.133751i | 0.926973 | − | 0.375127i | \(-0.122401\pi\) |
−0.970431 | + | 0.241377i | \(0.922401\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.30271 | − | 7.08700i | 0.109653 | − | 0.337476i | ||||
\(442\) | −14.6234 | + | 20.1274i | −0.695564 | + | 0.957362i | ||||
\(443\) | − | 5.27327i | − | 0.250541i | −0.992123 | − | 0.125270i | \(-0.960020\pi\) | ||
0.992123 | − | 0.125270i | \(-0.0399798\pi\) | |||||||
\(444\) | −7.97971 | − | 5.79760i | −0.378700 | − | 0.275142i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −18.7460 | + | 13.6197i | −0.887647 | + | 0.644914i | ||||
\(447\) | −1.58974 | − | 2.18809i | −0.0751922 | − | 0.103493i | ||||
\(448\) | 0.792578 | − | 0.257524i | 0.0374458 | − | 0.0121669i | ||||
\(449\) | 6.81659 | 0.321695 | 0.160847 | − | 0.986979i | \(-0.448577\pi\) | ||||
0.160847 | + | 0.986979i | \(0.448577\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.55583 | 0.0732609 | ||||||||
\(452\) | 1.65651 | − | 0.538232i | 0.0779156 | − | 0.0253163i | ||||
\(453\) | −1.56115 | − | 2.14874i | −0.0733491 | − | 0.100956i | ||||
\(454\) | −0.204401 | + | 0.148506i | −0.00959300 | + | 0.00696972i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.44047 | − | 6.85890i | −0.442090 | − | 0.321198i | ||||
\(457\) | − | 4.17712i | − | 0.195397i | −0.995216 | − | 0.0976987i | \(-0.968852\pi\) | ||
0.995216 | − | 0.0976987i | \(-0.0311482\pi\) | |||||||
\(458\) | −12.3966 | + | 17.0625i | −0.579255 | + | 0.797277i | ||||
\(459\) | −9.49893 | + | 29.2347i | −0.443372 | + | 1.36456i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.5678 | − | 35.6020i | −0.538766 | − | 1.65815i | −0.735367 | − | 0.677669i | \(-0.762990\pi\) |
0.196601 | − | 0.980484i | \(-0.437010\pi\) | |||||||
\(462\) | −0.890637 | − | 0.289386i | −0.0414362 | − | 0.0134634i | ||||
\(463\) | −13.1995 | − | 4.28879i | −0.613434 | − | 0.199317i | −0.0142111 | − | 0.999899i | \(-0.504524\pi\) |
−0.599223 | + | 0.800582i | \(0.704524\pi\) | |||||||
\(464\) | −1.01037 | − | 3.10959i | −0.0469052 | − | 0.144359i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.51398 | + | 13.8926i | −0.209106 | + | 0.643562i | ||||
\(467\) | −8.14705 | + | 11.2134i | −0.377000 | + | 0.518896i | −0.954787 | − | 0.297292i | \(-0.903917\pi\) |
0.577786 | + | 0.816188i | \(0.303917\pi\) | |||||||
\(468\) | − | 5.39334i | − | 0.249307i | ||||||
\(469\) | −1.01125 | − | 0.734713i | −0.0466950 | − | 0.0339259i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.49222 | − | 6.16996i | 0.391301 | − | 0.284297i | ||||
\(472\) | 7.95422 | + | 10.9480i | 0.366123 | + | 0.503924i | ||||
\(473\) | 1.29885 | − | 0.422023i | 0.0597213 | − | 0.0194046i | ||||
\(474\) | 6.96990 | 0.320138 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.54301 | −0.208228 | ||||||||
\(477\) | −7.22379 | + | 2.34715i | −0.330755 | + | 0.107469i | ||||
\(478\) | −3.41986 | − | 4.70704i | −0.156421 | − | 0.215295i | ||||
\(479\) | 23.2976 | − | 16.9267i | 1.06450 | − | 0.773401i | 0.0895806 | − | 0.995980i | \(-0.471447\pi\) |
0.974915 | + | 0.222578i | \(0.0714473\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.0076 | − | 19.6221i | −1.23144 | − | 0.894692i | ||||
\(482\) | − | 13.7291i | − | 0.625345i | ||||||
\(483\) | 2.33172 | − | 3.20933i | 0.106097 | − | 0.146030i | ||||
\(484\) | 3.18458 | − | 9.80111i | 0.144753 | − | 0.445505i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.53650 | − | 10.8842i | −0.160419 | − | 0.493719i | ||||
\(487\) | −37.0449 | − | 12.0366i | −1.67866 | − | 0.545430i | −0.694011 | − | 0.719964i | \(-0.744158\pi\) |
−0.984651 | + | 0.174534i | \(0.944158\pi\) | |||||||
\(488\) | 5.59621 | + | 1.81832i | 0.253328 | + | 0.0823114i | ||||
\(489\) | 5.87354 | + | 18.0769i | 0.265611 | + | 0.817466i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.26403 | + | 22.3564i | −0.327821 | + | 1.00893i | 0.642330 | + | 0.766428i | \(0.277968\pi\) |
−0.970151 | + | 0.242501i | \(0.922032\pi\) | |||||||
\(492\) | 1.47968 | − | 2.03660i | 0.0667090 | − | 0.0918171i | ||||
\(493\) | 17.8240i | 0.802753i | ||||||||
\(494\) | −31.9515 | − | 23.2141i | −1.43757 | − | 1.04445i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.85599 | + | 3.52808i | −0.218040 | + | 0.158416i | ||||
\(497\) | 1.15662 | + | 1.59196i | 0.0518817 | + | 0.0714091i | ||||
\(498\) | −15.8194 | + | 5.14003i | −0.708884 | + | 0.230330i | ||||
\(499\) | −28.2651 | −1.26532 | −0.632660 | − | 0.774430i | \(-0.718037\pi\) | ||||
−0.632660 | + | 0.774430i | \(0.718037\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.9979 | 0.491348 | ||||||||
\(502\) | −15.1159 | + | 4.91144i | −0.674654 | + | 0.219208i | ||||
\(503\) | −4.05821 | − | 5.58565i | −0.180947 | − | 0.249052i | 0.708903 | − | 0.705306i | \(-0.249191\pi\) |
−0.889849 | + | 0.456255i | \(0.849191\pi\) | |||||||
\(504\) | 0.796764 | − | 0.578883i | 0.0354907 | − | 0.0257855i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.38008 | − | 1.72923i | −0.105808 | − | 0.0768737i | ||||
\(507\) | 10.5551i | 0.468768i | ||||||||
\(508\) | 3.33082 | − | 4.58448i | 0.147781 | − | 0.203403i | ||||
\(509\) | −10.3641 | + | 31.8975i | −0.459382 | + | 1.41383i | 0.406531 | + | 0.913637i | \(0.366738\pi\) |
−0.865913 | + | 0.500195i | \(0.833262\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.857557 | + | 2.63929i | 0.0379361 | + | 0.116755i | ||||
\(512\) | −0.951057 | − | 0.309017i | −0.0420312 | − | 0.0136568i | ||||
\(513\) | −46.4091 | − | 15.0792i | −2.04901 | − | 0.665765i | ||||
\(514\) | 0.714612 | + | 2.19935i | 0.0315202 | + | 0.0970091i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.682847 | − | 2.10159i | 0.0300607 | − | 0.0925173i | ||||
\(517\) | 0.408216 | − | 0.561861i | 0.0179533 | − | 0.0247106i | ||||
\(518\) | − | 6.09595i | − | 0.267841i | ||||||
\(519\) | 2.73089 | + | 1.98411i | 0.119873 | + | 0.0870926i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.997861 | + | 0.724989i | −0.0437171 | + | 0.0317623i | −0.609429 | − | 0.792840i | \(-0.708601\pi\) |
0.565712 | + | 0.824603i | \(0.308601\pi\) | |||||||
\(522\) | −2.27118 | − | 3.12602i | −0.0994071 | − | 0.136822i | ||||
\(523\) | −21.9033 | + | 7.11681i | −0.957764 | + | 0.311196i | −0.745867 | − | 0.666095i | \(-0.767964\pi\) |
−0.211898 | + | 0.977292i | \(0.567964\pi\) | |||||||
\(524\) | 16.4745 | 0.719690 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.4593 | −0.935671 | ||||||||
\(527\) | 31.1196 | − | 10.1114i | 1.35559 | − | 0.440458i | ||||
\(528\) | 0.660507 | + | 0.909110i | 0.0287449 | + | 0.0395639i | ||||
\(529\) | −8.52520 | + | 6.19392i | −0.370661 | + | 0.269301i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.9382 | + | 9.40013i | 0.561469 | + | 0.407931i | ||||
\(532\) | − | 7.21188i | − | 0.312674i | ||||||
\(533\) | 5.00801 | − | 6.89294i | 0.216921 | − | 0.298566i | ||||
\(534\) | −2.91919 | + | 8.98434i | −0.126326 | + | 0.388791i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.463496 | + | 1.42649i | 0.0200200 | + | 0.0616151i | ||||
\(537\) | −25.6902 | − | 8.34725i | −1.10861 | − | 0.360210i | ||||
\(538\) | 20.3397 | + | 6.60877i | 0.876907 | + | 0.284924i | ||||
\(539\) | 1.62382 | + | 4.99760i | 0.0699428 | + | 0.215262i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.27238 | + | 25.4598i | −0.355657 | + | 1.09460i | 0.599970 | + | 0.800023i | \(0.295179\pi\) |
−0.955627 | + | 0.294578i | \(0.904821\pi\) | |||||||
\(542\) | 15.3591 | − | 21.1400i | 0.659731 | − | 0.908042i | ||||
\(543\) | − | 10.6232i | − | 0.455885i | ||||||
\(544\) | 4.41027 | + | 3.20425i | 0.189089 | + | 0.137381i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.14895 | + | 3.01439i | −0.177559 | + | 0.129004i | ||||
\(547\) | 3.77763 | + | 5.19947i | 0.161520 | + | 0.222313i | 0.882104 | − | 0.471054i | \(-0.156126\pi\) |
−0.720584 | + | 0.693367i | \(0.756126\pi\) | |||||||
\(548\) | 2.75164 | − | 0.894062i | 0.117544 | − | 0.0381924i | ||||
\(549\) | 6.95383 | 0.296782 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.2950 | −1.20541 | ||||||||
\(552\) | −4.52718 | + | 1.47097i | −0.192690 | + | 0.0626087i | ||||
\(553\) | 2.53197 | + | 3.48495i | 0.107670 | + | 0.148195i | ||||
\(554\) | −15.0856 | + | 10.9604i | −0.640928 | + | 0.465661i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.03660 | − | 2.93276i | −0.171190 | − | 0.124377i | ||||
\(557\) | − | 44.0843i | − | 1.86791i | −0.357386 | − | 0.933957i | \(-0.616332\pi\) | ||
0.357386 | − | 0.933957i | \(-0.383668\pi\) | |||||||
\(558\) | −4.16941 | + | 5.73871i | −0.176505 | + | 0.242939i | ||||
\(559\) | 2.31112 | − | 7.11289i | 0.0977498 | − | 0.300843i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.89299 | − | 5.82604i | −0.0799223 | − | 0.245975i | ||||
\(562\) | −14.0934 | − | 4.57924i | −0.594496 | − | 0.193164i | ||||
\(563\) | 19.0952 | + | 6.20440i | 0.804766 | + | 0.261484i | 0.682379 | − | 0.730998i | \(-0.260945\pi\) |
0.122387 | + | 0.992483i | \(0.460945\pi\) | |||||||
\(564\) | −0.347249 | − | 1.06872i | −0.0146218 | − | 0.0450014i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.87628 | − | 15.0076i | 0.204965 | − | 0.630818i | ||||
\(567\) | −1.98780 | + | 2.73597i | −0.0834797 | + | 0.114900i | ||||
\(568\) | − | 2.36123i | − | 0.0990750i | ||||||
\(569\) | −24.2170 | − | 17.5947i | −1.01523 | − | 0.737609i | −0.0499312 | − | 0.998753i | \(-0.515900\pi\) |
−0.965300 | + | 0.261144i | \(0.915900\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.5201 | − | 8.36985i | 0.482102 | − | 0.350267i | −0.320037 | − | 0.947405i | \(-0.603695\pi\) |
0.802139 | + | 0.597138i | \(0.203695\pi\) | |||||||
\(572\) | 2.23551 | + | 3.07691i | 0.0934712 | + | 0.128652i | ||||
\(573\) | −6.76503 | + | 2.19809i | −0.282613 | + | 0.0918265i | ||||
\(574\) | 1.55583 | 0.0649389 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.18178 | −0.0492408 | ||||||||
\(577\) | −17.3177 | + | 5.62687i | −0.720946 | + | 0.234250i | −0.646433 | − | 0.762970i | \(-0.723740\pi\) |
−0.0745128 | + | 0.997220i | \(0.523740\pi\) | |||||||
\(578\) | −7.47531 | − | 10.2889i | −0.310932 | − | 0.427961i | ||||
\(579\) | 14.6682 | − | 10.6571i | 0.609591 | − | 0.442894i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.31675 | − | 6.04247i | −0.345037 | − | 0.250684i | ||||
\(582\) | 14.9541i | 0.619869i | ||||||||
\(583\) | 3.14830 | − | 4.33327i | 0.130389 | − | 0.179466i | ||||
\(584\) | 1.02903 | − | 3.16703i | 0.0425815 | − | 0.131052i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.68601 | + | 17.4998i | 0.234887 | + | 0.722908i | ||||
\(587\) | −4.91155 | − | 1.59586i | −0.202721 | − | 0.0658681i | 0.205896 | − | 0.978574i | \(-0.433989\pi\) |
−0.408618 | + | 0.912706i | \(0.633989\pi\) | |||||||
\(588\) | 8.08629 | + | 2.62739i | 0.333473 | + | 0.108352i | ||||
\(589\) | 16.0515 | + | 49.4014i | 0.661389 | + | 2.03555i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.26616 | − | 6.97454i | 0.0932176 | − | 0.286894i | ||||
\(592\) | −4.29957 | + | 5.91785i | −0.176711 | + | 0.243222i | ||||
\(593\) | − | 35.6286i | − | 1.46309i | −0.681793 | − | 0.731546i | \(-0.738799\pi\) | ||
0.681793 | − | 0.731546i | \(-0.261201\pi\) | |||||||
\(594\) | 3.80170 | + | 2.76210i | 0.155986 | + | 0.113330i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.62271 | + | 1.17897i | −0.0664690 | + | 0.0482925i | ||||
\(597\) | 13.7980 | + | 18.9913i | 0.564714 | + | 0.777262i | ||||
\(598\) | −15.3224 | + | 4.97854i | −0.626579 | + | 0.203588i | ||||
\(599\) | 31.8284 | 1.30047 | 0.650236 | − | 0.759733i | \(-0.274670\pi\) | ||||
0.650236 | + | 0.759733i | \(0.274670\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.6378 | −0.515508 | −0.257754 | − | 0.966211i | \(-0.582982\pi\) | ||||
−0.257754 | + | 0.966211i | \(0.582982\pi\) | |||||||
\(602\) | 1.29885 | − | 0.422023i | 0.0529373 | − | 0.0172004i | ||||
\(603\) | 1.04188 | + | 1.43403i | 0.0424287 | + | 0.0583981i | ||||
\(604\) | −1.59353 | + | 1.15777i | −0.0648397 | + | 0.0471088i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.8636 | + | 10.0725i | 0.563170 | + | 0.409167i | ||||
\(607\) | − | 34.9481i | − | 1.41850i | −0.704957 | − | 0.709250i | \(-0.749034\pi\) | ||
0.704957 | − | 0.709250i | \(-0.250966\pi\) | |||||||
\(608\) | −5.08664 | + | 7.00116i | −0.206291 | + | 0.283935i | ||||
\(609\) | −1.13537 | + | 3.49432i | −0.0460076 | + | 0.141597i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.17527 | − | 3.61712i | −0.0475465 | − | 0.146333i | ||||
\(612\) | 6.12704 | + | 1.99080i | 0.247671 | + | 0.0804732i | ||||
\(613\) | 6.77418 | + | 2.20106i | 0.273606 | + | 0.0889001i | 0.442607 | − | 0.896716i | \(-0.354054\pi\) |
−0.169000 | + | 0.985616i | \(0.554054\pi\) | |||||||
\(614\) | 10.5430 | + | 32.4480i | 0.425481 | + | 1.30950i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.214612 | + | 0.660507i | −0.00864696 | + | 0.0266126i | ||||
\(617\) | 9.45572 | − | 13.0147i | 0.380673 | − | 0.523951i | −0.575090 | − | 0.818090i | \(-0.695033\pi\) |
0.955763 | + | 0.294139i | \(0.0950329\pi\) | |||||||
\(618\) | − | 9.45932i | − | 0.380510i | ||||||
\(619\) | −0.607103 | − | 0.441086i | −0.0244015 | − | 0.0177287i | 0.575518 | − | 0.817789i | \(-0.304801\pi\) |
−0.599919 | + | 0.800061i | \(0.704801\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.1043 | + | 11.7004i | −0.646241 | + | 0.469522i | ||||
\(622\) | −7.66348 | − | 10.5479i | −0.307278 | − | 0.422931i | ||||
\(623\) | −5.55263 | + | 1.80416i | −0.222461 | + | 0.0722821i | ||||
\(624\) | 6.15382 | 0.246350 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.48262 | 0.139194 | ||||||||
\(627\) | 9.24864 | − | 3.00507i | 0.369355 | − | 0.120011i | ||||
\(628\) | −4.57571 | − | 6.29793i | −0.182591 | − | 0.251315i | ||||
\(629\) | 32.2606 | − | 23.4387i | 1.28631 | − | 0.934561i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.4391 | + | 9.03753i | 0.495192 | + | 0.359778i | 0.807178 | − | 0.590309i | \(-0.200994\pi\) |
−0.311985 | + | 0.950087i | \(0.600994\pi\) | |||||||
\(632\) | − | 5.16896i | − | 0.205610i | ||||||
\(633\) | 0.213944 | − | 0.294468i | 0.00850350 | − | 0.0117041i | ||||
\(634\) | −1.48957 | + | 4.58443i | −0.0591585 | + | 0.182071i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.67811 | − | 8.24237i | −0.106194 | − | 0.326831i | ||||
\(637\) | 27.3683 | + | 8.89249i | 1.08437 | + | 0.352333i | ||||
\(638\) | 2.59143 | + | 0.842006i | 0.102596 | + | 0.0333353i | ||||
\(639\) | −0.862297 | − | 2.65388i | −0.0341120 | − | 0.104986i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.92140 | − | 8.99114i | 0.115388 | − | 0.355129i | −0.876639 | − | 0.481148i | \(-0.840220\pi\) |
0.992028 | + | 0.126019i | \(0.0402200\pi\) | |||||||
\(642\) | −8.53609 | + | 11.7489i | −0.336893 | + | 0.463693i | ||||
\(643\) | 32.8334i | 1.29482i | 0.762141 | + | 0.647411i | \(0.224148\pi\) | ||||
−0.762141 | + | 0.647411i | \(0.775852\pi\) | |||||||
\(644\) | −2.38008 | − | 1.72923i | −0.0937883 | − | 0.0681412i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 38.1661 | − | 27.7293i | 1.50163 | − | 1.09100i | ||||
\(647\) | 10.5026 | + | 14.4556i | 0.412901 | + | 0.568309i | 0.963923 | − | 0.266182i | \(-0.0857621\pi\) |
−0.551022 | + | 0.834490i | \(0.685762\pi\) | |||||||
\(648\) | 3.85944 | − | 1.25401i | 0.151613 | − | 0.0492621i | ||||
\(649\) | −11.2775 | −0.442682 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.74495 | 0.264355 | ||||||||
\(652\) | 13.4060 | − | 4.35589i | 0.525021 | − | 0.170590i | ||||
\(653\) | 18.7881 | + | 25.8596i | 0.735235 | + | 1.01196i | 0.998879 | + | 0.0473435i | \(0.0150755\pi\) |
−0.263644 | + | 0.964620i | \(0.584924\pi\) | |||||||
\(654\) | 11.6022 | − | 8.42947i | 0.453681 | − | 0.329618i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.51037 | − | 1.09735i | −0.0589700 | − | 0.0428442i | ||||
\(657\) | − | 3.93534i | − | 0.153532i | ||||||
\(658\) | 0.408216 | − | 0.561861i | 0.0159139 | − | 0.0219036i | ||||
\(659\) | 3.52244 | − | 10.8410i | 0.137215 | − | 0.422304i | −0.858713 | − | 0.512457i | \(-0.828736\pi\) |
0.995928 | + | 0.0901527i | \(0.0287355\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.26642 | + | 6.97531i | 0.0881533 | + | 0.271308i | 0.985409 | − | 0.170203i | \(-0.0544425\pi\) |
−0.897256 | + | 0.441511i | \(0.854442\pi\) | |||||||
\(662\) | −8.14431 | − | 2.64625i | −0.316537 | − | 0.102849i | ||||
\(663\) | −31.9050 | − | 10.3666i | −1.23909 | − | 0.402604i | ||||
\(664\) | 3.81191 | + | 11.7319i | 0.147931 | + | 0.455284i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.67131 | + | 8.22146i | −0.103511 | + | 0.318575i | ||||
\(667\) | −6.78445 | + | 9.33799i | −0.262695 | + | 0.361568i | ||||
\(668\) | − | 8.15615i | − | 0.315571i | ||||||
\(669\) | −25.2773 | − | 18.3651i | −0.977278 | − | 0.710034i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.96717 | + | 2.88232i | −0.153151 | + | 0.111271i | ||||
\(672\) | 0.660507 | + | 0.909110i | 0.0254796 | + | 0.0350697i | ||||
\(673\) | 31.1595 | − | 10.1243i | 1.20111 | − | 0.390264i | 0.360940 | − | 0.932589i | \(-0.382456\pi\) |
0.840169 | + | 0.542325i | \(0.182456\pi\) | |||||||
\(674\) | 14.6712 | 0.565113 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.82777 | 0.301068 | ||||||||
\(677\) | −30.9879 | + | 10.0686i | −1.19096 | + | 0.386967i | −0.836428 | − | 0.548076i | \(-0.815360\pi\) |
−0.354534 | + | 0.935043i | \(0.615360\pi\) | |||||||
\(678\) | 1.38048 | + | 1.90006i | 0.0530169 | + | 0.0729715i | ||||
\(679\) | −7.47707 | + | 5.43241i | −0.286944 | + | 0.208477i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.275617 | − | 0.200247i | −0.0105617 | − | 0.00767349i | ||||
\(682\) | − | 5.00214i | − | 0.191542i | ||||||
\(683\) | −2.55652 | + | 3.51875i | −0.0978227 | + | 0.134641i | −0.855123 | − | 0.518426i | \(-0.826518\pi\) |
0.757300 | + | 0.653067i | \(0.226518\pi\) | |||||||
\(684\) | −3.16032 | + | 9.72648i | −0.120838 | + | 0.371901i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.42649 | + | 10.5456i | 0.130824 | + | 0.402635i | ||||
\(687\) | −27.0467 | − | 8.78799i | −1.03189 | − | 0.335283i | ||||
\(688\) | −1.55856 | − | 0.506408i | −0.0594197 | − | 0.0193066i | ||||
\(689\) | −9.06413 | − | 27.8965i | −0.345316 | − | 1.06277i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.26053 | + | 19.2679i | −0.238162 | + | 0.732987i | 0.758524 | + | 0.651645i | \(0.225921\pi\) |
−0.996686 | + | 0.0813423i | \(0.974079\pi\) | |||||||
\(692\) | 1.47144 | − | 2.02526i | 0.0559356 | − | 0.0769888i | ||||
\(693\) | 0.820744i | 0.0311775i | ||||||||
\(694\) | −18.5970 | − | 13.5115i | −0.705933 | − | 0.512891i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.56680 | − | 2.59143i | 0.135199 | − | 0.0982278i | ||||
\(697\) | 5.98208 | + | 8.23362i | 0.226587 | + | 0.311871i | ||||
\(698\) | −3.37647 | + | 1.09708i | −0.127801 | + | 0.0415252i | ||||
\(699\) | −19.6970 | −0.745010 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.5964 | 0.475758 | 0.237879 | − | 0.971295i | \(-0.423548\pi\) | ||||
0.237879 | + | 0.971295i | \(0.423548\pi\) | |||||||
\(702\) | 24.4744 | − | 7.95222i | 0.923727 | − | 0.300137i | ||||
\(703\) | 37.2081 | + | 51.2126i | 1.40333 | + | 1.93152i | ||||
\(704\) | 0.674207 | − | 0.489840i | 0.0254101 | − | 0.0184615i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.56375 | + | 3.31576i | 0.171759 | + | 0.124790i | ||||
\(707\) | 10.5908i | 0.398310i | ||||||||
\(708\) | −10.7256 | + | 14.7625i | −0.403092 | + | 0.554808i | ||||
\(709\) | −9.10924 | + | 28.0354i | −0.342105 | + | 1.05289i | 0.621011 | + | 0.783802i | \(0.286722\pi\) |
−0.963116 | + | 0.269088i | \(0.913278\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.88765 | − | 5.80960i | −0.0707926 | − | 0.217877i | ||||
\(712\) | 6.66290 | + | 2.16491i | 0.249703 | + | 0.0811333i | ||||
\(713\) | 20.1523 | + | 6.54788i | 0.754710 | + | 0.245220i | ||||
\(714\) | −1.89299 | − | 5.82604i | −0.0708435 | − | 0.218034i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.19042 | + | 19.0522i | −0.231347 | + | 0.712012i | ||||
\(717\) | 4.61139 | − | 6.34704i | 0.172216 | − | 0.237034i | ||||
\(718\) | − | 16.9066i | − | 0.630948i | ||||||
\(719\) | −24.3987 | − | 17.7267i | −0.909919 | − | 0.661095i | 0.0310756 | − | 0.999517i | \(-0.490107\pi\) |
−0.940994 | + | 0.338422i | \(0.890107\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.72966 | − | 3.43630i | 0.176142 | − | 0.127974i | ||||
\(722\) | 32.8515 | + | 45.2162i | 1.22261 | + | 1.68277i | ||||
\(723\) | 17.6065 | − | 5.72069i | 0.654792 | − | 0.212755i | ||||
\(724\) | −7.87829 | −0.292794 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13.8961 | 0.515732 | ||||||||
\(727\) | 5.65626 | − | 1.83783i | 0.209779 | − | 0.0681614i | −0.202242 | − | 0.979336i | \(-0.564823\pi\) |
0.412021 | + | 0.911174i | \(0.364823\pi\) | |||||||
\(728\) | 2.23551 | + | 3.07691i | 0.0828533 | + | 0.114038i | ||||
\(729\) | 22.3337 | − | 16.2264i | 0.827173 | − | 0.600976i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.22743 | + | 5.25103i | 0.267316 | + | 0.194216i | ||||
\(732\) | 7.93434i | 0.293261i | ||||||||
\(733\) | 5.98148 | − | 8.23281i | 0.220931 | − | 0.304086i | −0.684136 | − | 0.729355i | \(-0.739820\pi\) |
0.905067 | + | 0.425269i | \(0.139820\pi\) | |||||||
\(734\) | 3.89773 | − | 11.9960i | 0.143868 | − | 0.442780i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.09089 | + | 3.35741i | 0.0402107 | + | 0.123756i | ||||
\(737\) | −1.18879 | − | 0.386261i | −0.0437896 | − | 0.0142281i | ||||
\(738\) | −2.09830 | − | 0.681780i | −0.0772396 | − | 0.0250967i | ||||
\(739\) | −11.2234 | − | 34.5422i | −0.412861 | − | 1.27066i | −0.914150 | − | 0.405376i | \(-0.867141\pi\) |
0.501289 | − | 0.865280i | \(-0.332859\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.4566 | − | 50.6482i | 0.604548 | − | 1.86061i | ||||
\(742\) | 3.14830 | − | 4.33327i | 0.115578 | − | 0.159079i | ||||
\(743\) | 2.84832i | 0.104495i | 0.998634 | + | 0.0522473i | \(0.0166384\pi\) | ||||
−0.998634 | + | 0.0522473i | \(0.983362\pi\) | |||||||
\(744\) | −6.54788 | − | 4.75731i | −0.240057 | − | 0.174412i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10.7191 | + | 7.78791i | −0.392455 | + | 0.285136i | ||||
\(747\) | 8.56871 | + | 11.7938i | 0.313513 | + | 0.431513i | ||||
\(748\) | −4.32066 | + | 1.40387i | −0.157979 | + | 0.0513305i | ||||
\(749\) | −8.97537 | −0.327953 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.5502 | −1.15128 | −0.575641 | − | 0.817702i | \(-0.695248\pi\) | ||||
−0.575641 | + | 0.817702i | \(0.695248\pi\) | |||||||
\(752\) | −0.792578 | + | 0.257524i | −0.0289023 | + | 0.00939094i | ||||
\(753\) | −12.5970 | − | 17.3383i | −0.459062 | − | 0.631844i | ||||
\(754\) | 12.0719 | − | 8.77076i | 0.439633 | − | 0.319412i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.80170 | + | 2.76210i | 0.138266 | + | 0.100456i | ||||
\(757\) | 45.6446i | 1.65898i | 0.558520 | + | 0.829491i | \(0.311369\pi\) | ||||
−0.558520 | + | 0.829491i | \(0.688631\pi\) | |||||||
\(758\) | 13.1288 | − | 18.0702i | 0.476858 | − | 0.656339i | ||||
\(759\) | 1.22586 | − | 3.77280i | 0.0444958 | − | 0.136944i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.80550 | + | 8.63445i | 0.101699 | + | 0.312998i | 0.988942 | − | 0.148305i | \(-0.0473818\pi\) |
−0.887242 | + | 0.461304i | \(0.847382\pi\) | |||||||
\(762\) | 7.26712 | + | 2.36123i | 0.263260 | + | 0.0855383i | ||||
\(763\) | 8.42947 | + | 2.73890i | 0.305167 | + | 0.0991549i | ||||
\(764\) | 1.63013 | + | 5.01702i | 0.0589760 | + | 0.181510i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.52545 | − | 23.1610i | 0.271906 | − | 0.836840i | ||||
\(767\) | −36.3010 | + | 49.9641i | −1.31075 | + | 1.80410i | ||||
\(768\) | − | 1.34841i | − | 0.0486567i | ||||||
\(769\) | −20.5964 | − | 14.9641i | −0.742724 | − | 0.539621i | 0.150839 | − | 0.988558i | \(-0.451802\pi\) |
−0.893563 | + | 0.448938i | \(0.851802\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.52272 | + | 1.83286i | −0.0908535 | + | 0.0660089i | ||||
\(772\) | −7.90343 | − | 10.8781i | −0.284451 | − | 0.391513i | ||||
\(773\) | −16.3128 | + | 5.30034i | −0.586729 | + | 0.190640i | −0.587313 | − | 0.809360i | \(-0.699814\pi\) |
0.000583568 | 1.00000i | \(0.499814\pi\) | ||||||||
\(774\) | −1.93667 | −0.0696120 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.0902 | 0.398114 | ||||||||
\(777\) | 7.81756 | − | 2.54008i | 0.280453 | − | 0.0911249i | ||||
\(778\) | −17.6992 | − | 24.3608i | −0.634546 | − | 0.873377i | ||||
\(779\) | −13.0706 | + | 9.49635i | −0.468303 | + | 0.340242i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.59196 | + | 1.15662i | 0.0569647 | + | 0.0413873i | ||||
\(782\) | − | 19.2445i | − | 0.688182i | ||||||
\(783\) | 10.8368 | − | 14.9156i | 0.387275 | − | 0.533038i | ||||
\(784\) | 1.94851 | − | 5.99689i | 0.0695895 | − | 0.214175i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.86463 | + | 21.1271i | 0.244853 | + | 0.753580i | ||||
\(787\) | −10.7211 | − | 3.48351i | −0.382168 | − | 0.124174i | 0.111632 | − | 0.993750i | \(-0.464392\pi\) |
−0.493799 | + | 0.869576i | \(0.664392\pi\) | |||||||
\(788\) | −5.17240 | − | 1.68061i | −0.184259 | − | 0.0598694i | ||||
\(789\) | −8.94173 | − | 27.5198i | −0.318334 | − | 0.979731i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.448544 | + | 1.38048i | −0.0159484 | + | 0.0490841i | ||||
\(792\) | 0.578883 | − | 0.796764i | 0.0205697 | − | 0.0283118i | ||||
\(793\) | 26.8540i | 0.953613i | ||||||||
\(794\) | 28.6152 | + | 20.7902i | 1.01552 | + | 0.737816i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.0842 | − | 10.2328i | 0.499200 | − | 0.362690i | ||||
\(797\) | −15.6770 | − | 21.5775i | −0.555307 | − | 0.764315i | 0.435413 | − | 0.900231i | \(-0.356602\pi\) |
−0.990720 | + | 0.135916i | \(0.956602\pi\) | |||||||
\(798\) | 9.24864 | − | 3.00507i | 0.327398 | − | 0.106378i | ||||
\(799\) | 4.54301 | 0.160720 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.27929 | 0.292534 | ||||||||
\(802\) | −5.39053 | + | 1.75149i | −0.190346 | + | 0.0618472i | ||||
\(803\) | 1.63117 | + | 2.24511i | 0.0575628 | + | 0.0792284i | ||||
\(804\) | −1.63623 | + | 1.18879i | −0.0577053 | + | 0.0419254i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −22.1615 | − | 16.1013i | −0.780605 | − | 0.567143i | ||||
\(807\) | 28.8378i | 1.01514i | ||||||||
\(808\) | 7.46988 | − | 10.2814i | 0.262789 | − | 0.361699i | ||||
\(809\) | −3.39121 | + | 10.4371i | −0.119229 | + | 0.366948i | −0.992805 | − | 0.119738i | \(-0.961794\pi\) |
0.873577 | + | 0.486686i | \(0.161794\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.04882 | − | 9.38329i | −0.107058 | − | 0.329492i | 0.883150 | − | 0.469091i | \(-0.155419\pi\) |
−0.990208 | + | 0.139599i | \(0.955419\pi\) | |||||||
\(812\) | 2.59143 | + | 0.842006i | 0.0909413 | + | 0.0295486i | ||||
\(813\) | 33.5102 | + | 10.8881i | 1.17526 | + | 0.381864i | ||||
\(814\) | −1.88375 | − | 5.79760i | −0.0660255 | − | 0.203206i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.27150 | + | 6.99097i | −0.0795186 | + | 0.244733i | ||||
\(817\) | −8.33584 | + | 11.4733i | −0.291634 | + | 0.401400i | ||||
\(818\) | 19.3676i | 0.677174i | ||||||||
\(819\) | 3.63623 | + | 2.64187i | 0.127060 | + | 0.0923146i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.85904 | − | 1.35067i | 0.0648808 | − | 0.0471387i | −0.554872 | − | 0.831936i | \(-0.687233\pi\) |
0.619753 | + | 0.784797i | \(0.287233\pi\) | |||||||
\(822\) | 2.29312 | + | 3.15621i | 0.0799818 | + | 0.110086i | ||||
\(823\) | −0.765985 | + | 0.248884i | −0.0267006 | + | 0.00867554i | −0.322337 | − | 0.946625i | \(-0.604468\pi\) |
0.295636 | + | 0.955301i | \(0.404468\pi\) | |||||||
\(824\) | −7.01515 | −0.244384 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.2775 | −0.392396 | ||||||||
\(827\) | 34.6701 | − | 11.2650i | 1.20560 | − | 0.391722i | 0.363780 | − | 0.931485i | \(-0.381486\pi\) |
0.841817 | + | 0.539762i | \(0.181486\pi\) | |||||||
\(828\) | 2.45219 | + | 3.37515i | 0.0852194 | + | 0.117294i | ||||
\(829\) | 23.9231 | − | 17.3811i | 0.830883 | − | 0.603672i | −0.0889263 | − | 0.996038i | \(-0.528344\pi\) |
0.919809 | + | 0.392367i | \(0.128344\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.3417 | − | 14.7791i | −0.705646 | − | 0.512682i | ||||
\(832\) | − | 4.56375i | − | 0.158219i | ||||||
\(833\) | −20.2044 | + | 27.8090i | −0.700042 | + | 0.963525i | ||||
\(834\) | 2.07904 | − | 6.39864i | 0.0719914 | − | 0.221567i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.22859 | − | 6.85890i | −0.0770775 | − | 0.237220i | ||||
\(837\) | −32.1892 | − | 10.4589i | −1.11262 | − | 0.361513i | ||||
\(838\) | 21.8545 | + | 7.10097i | 0.754953 | + | 0.245299i | ||||
\(839\) | 13.4507 | + | 41.3969i | 0.464369 | + | 1.42918i | 0.859774 | + | 0.510674i | \(0.170604\pi\) |
−0.395405 | + | 0.918507i | \(0.629396\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.65797 | + | 17.4135i | −0.195103 | + | 0.600464i | ||||
\(842\) | 5.95261 | − | 8.19306i | 0.205140 | − | 0.282351i | ||||
\(843\) | − | 19.9818i | − | 0.688209i | ||||||
\(844\) | −0.218381 | − | 0.158663i | −0.00751699 | − | 0.00546141i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.796764 | + | 0.578883i | −0.0273933 | + | 0.0199024i | ||||
\(847\) | 5.04805 | + | 6.94804i | 0.173453 | + | 0.238738i | ||||
\(848\) | −6.11264 | + | 1.98612i | −0.209909 | + | 0.0682035i | ||||
\(849\) | 21.2779 | 0.730257 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.8229 | 0.885197 | ||||||||
\(852\) | 3.02808 | − | 0.983884i | 0.103740 | − | 0.0337073i | ||||
\(853\) | −29.7458 | − | 40.9415i | −1.01848 | − | 1.40181i | −0.913267 | − | 0.407361i | \(-0.866449\pi\) |
−0.105208 | − | 0.994450i | \(-0.533551\pi\) | |||||||
\(854\) | −3.96717 | + | 2.88232i | −0.135754 | + | 0.0986308i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.71314 | + | 6.33047i | 0.297809 | + | 0.216371i | ||||
\(857\) | − | 34.1589i | − | 1.16684i | −0.812169 | − | 0.583422i | \(-0.801713\pi\) | ||
0.812169 | − | 0.583422i | \(-0.198287\pi\) | |||||||
\(858\) | −3.01439 | + | 4.14895i | −0.102909 | + | 0.141643i | ||||
\(859\) | −3.39523 | + | 10.4494i | −0.115844 | + | 0.356530i | −0.992122 | − | 0.125275i | \(-0.960019\pi\) |
0.876278 | + | 0.481805i | \(0.160019\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.648286 | + | 1.99522i | 0.0220935 | + | 0.0679968i | ||||
\(862\) | 27.1074 | + | 8.80773i | 0.923282 | + | 0.299993i | ||||
\(863\) | −44.0415 | − | 14.3100i | −1.49919 | − | 0.487117i | −0.559410 | − | 0.828891i | \(-0.688972\pi\) |
−0.939782 | + | 0.341774i | \(0.888972\pi\) | |||||||
\(864\) | −1.74248 | − | 5.36279i | −0.0592802 | − | 0.182446i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.91018 | − | 15.1120i | 0.166855 | − | 0.513526i | ||||
\(867\) | 10.0798 | − | 13.8737i | 0.342328 | − | 0.471175i | ||||
\(868\) | − | 5.00214i | − | 0.169784i | ||||||
\(869\) | 3.48495 | + | 2.53197i | 0.118219 | + | 0.0858911i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.53786 | + | 4.02349i | −0.187643 | + | 0.136331i | ||||
\(872\) | −6.25140 | − | 8.60431i | −0.211699 | − | 0.291379i | ||||
\(873\) | 12.4647 | − | 4.05002i | 0.421865 | − | 0.137072i | ||||
\(874\) | 30.5500 | 1.03337 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.49023 | 0.151711 | ||||||||
\(877\) | 19.9505 | − | 6.48231i | 0.673681 | − | 0.218892i | 0.0478541 | − | 0.998854i | \(-0.484762\pi\) |
0.625827 | + | 0.779962i | \(0.284762\pi\) | |||||||
\(878\) | −1.73197 | − | 2.38385i | −0.0584511 | − | 0.0804511i | ||||
\(879\) | −20.0727 | + | 14.5837i | −0.677037 | + | 0.491896i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.1491 | + | 29.8966i | 1.38635 | + | 1.00724i | 0.996255 | + | 0.0864666i | \(0.0275576\pi\) |
0.390094 | + | 0.920775i | \(0.372442\pi\) | |||||||
\(882\) | − | 7.45171i | − | 0.250912i | ||||||
\(883\) | −28.8540 | + | 39.7141i | −0.971014 | + | 1.33649i | −0.0294804 | + | 0.999565i | \(0.509385\pi\) |
−0.941533 | + | 0.336920i | \(0.890615\pi\) | |||||||
\(884\) | −7.68797 | + | 23.6611i | −0.258574 | + | 0.795810i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.62953 | − | 5.01518i | −0.0547451 | − | 0.168488i | ||||
\(887\) | 35.1599 | + | 11.4242i | 1.18056 | + | 0.383586i | 0.832573 | − | 0.553915i | \(-0.186867\pi\) |
0.347982 | + | 0.937501i | \(0.386867\pi\) | |||||||
\(888\) | −9.38071 | − | 3.04798i | −0.314796 | − | 0.102283i | ||||
\(889\) | 1.45932 | + | 4.49133i | 0.0489440 | + | 0.150634i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.04505 | + | 3.21633i | −0.0350104 | + | 0.107751i | ||||
\(892\) | −13.6197 | + | 18.7460i | −0.456023 | + | 0.627662i | ||||
\(893\) | 7.21188i | 0.241336i | ||||||||
\(894\) | −2.18809 | − | 1.58974i | −0.0731807 | − | 0.0531689i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.674207 | − | 0.489840i | 0.0225237 | − | 0.0163644i | ||||
\(897\) | −12.7691 | − | 17.5752i | −0.426349 | − | 0.586820i | ||||
\(898\) | 6.48297 | − | 2.10644i | 0.216339 | − | 0.0702929i | ||||
\(899\) | −19.6253 | −0.654542 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35.0373 | 1.16726 | ||||||||
\(902\) | 1.47968 | − | 0.480776i | 0.0492679 | − | 0.0160081i | ||||
\(903\) | 1.08242 | + | 1.48982i | 0.0360207 | + | 0.0495782i | ||||
\(904\) | 1.40911 | − | 1.02378i | 0.0468663 | − | 0.0340504i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.14874 | − | 1.56115i | −0.0713870 | − | 0.0518657i | ||||
\(907\) | − | 44.9718i | − | 1.49326i | −0.665237 | − | 0.746632i | \(-0.731670\pi\) | ||
0.665237 | − | 0.746632i | \(-0.268330\pi\) | |||||||
\(908\) | −0.148506 | + | 0.204401i | −0.00492834 | + | 0.00678327i | ||||
\(909\) | 4.64102 | − | 14.2836i | 0.153933 | − | 0.473757i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.32785 | − | 25.6305i | −0.275914 | − | 0.849176i | −0.988976 | − | 0.148075i | \(-0.952692\pi\) |
0.713062 | − | 0.701101i | \(-0.247308\pi\) | |||||||
\(912\) | −11.0979 | − | 3.60594i | −0.367489 | − | 0.119405i | ||||
\(913\) | −9.77692 | − | 3.17671i | −0.323569 | − | 0.105134i | ||||
\(914\) | −1.29080 | − | 3.97268i | −0.0426959 | − | 0.131404i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.51728 | + | 20.0581i | −0.215337 | + | 0.662739i | ||||
\(917\) | −8.06985 | + | 11.1072i | −0.266490 | + | 0.366792i | ||||
\(918\) | 30.7392i | 1.01454i | ||||||||
\(919\) | 25.8087 | + | 18.7511i | 0.851350 | + | 0.618542i | 0.925518 | − | 0.378704i | \(-0.123630\pi\) |
−0.0741679 | + | 0.997246i | \(0.523630\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −37.2189 | + | 27.0411i | −1.22640 | + | 0.891034i | ||||
\(922\) | −22.0033 | − | 30.2849i | −0.724639 | − | 0.997380i | ||||
\(923\) | 10.2486 | − | 3.32998i | 0.337338 | − | 0.109608i | ||||
\(924\) | −0.936471 | −0.0308076 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −13.8788 | −0.456086 | ||||||||
\(927\) | −7.88460 | + | 2.56186i | −0.258964 | + | 0.0841426i | ||||
\(928\) | −1.92183 | − | 2.64518i | −0.0630873 | − | 0.0868322i | ||||
\(929\) | −5.06070 | + | 3.67681i | −0.166036 | + | 0.120632i | −0.667700 | − | 0.744430i | \(-0.732721\pi\) |
0.501664 | + | 0.865062i | \(0.332721\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −44.1459 | − | 32.0738i | −1.44682 | − | 1.05118i | ||||
\(932\) | 14.6075i | 0.478486i | ||||||||
\(933\) | 10.3335 | − | 14.2229i | 0.338305 | − | 0.465637i | ||||
\(934\) | −4.28316 | + | 13.1822i | −0.140149 | + | 0.431335i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.66663 | − | 5.12937i | −0.0544756 | − | 0.167659i | ||||
\(937\) | 29.4062 | + | 9.55466i | 0.960660 | + | 0.312137i | 0.747040 | − | 0.664780i | \(-0.231475\pi\) |
0.213620 | + | 0.976917i | \(0.431475\pi\) | |||||||
\(938\) | −1.18879 | − | 0.386261i | −0.0388154 | − | 0.0126119i | ||||
\(939\) | 1.45115 | + | 4.46618i | 0.0473565 | + | 0.145748i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.92136 | + | 24.3794i | −0.258229 | + | 0.794747i | 0.734947 | + | 0.678124i | \(0.237207\pi\) |
−0.993176 | + | 0.116623i | \(0.962793\pi\) | |||||||
\(942\) | 6.16996 | − | 8.49222i | 0.201028 | − | 0.276691i | ||||
\(943\) | 6.59058i | 0.214619i | ||||||||
\(944\) | 10.9480 | + | 7.95422i | 0.356328 | + | 0.258888i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.10487 | − | 0.802735i | 0.0359224 | − | 0.0260992i | ||||
\(947\) | −26.5751 | − | 36.5775i | −0.863575 | − | 1.18861i | −0.980705 | − | 0.195492i | \(-0.937370\pi\) |
0.117130 | − | 0.993117i | \(-0.462630\pi\) | |||||||
\(948\) | 6.62877 | − | 2.15382i | 0.215293 | − | 0.0699528i | ||||
\(949\) | 15.1973 | 0.493325 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.49984 | −0.210772 | ||||||||
\(952\) | −4.32066 | + | 1.40387i | −0.140033 | + | 0.0454996i | ||||
\(953\) | 12.1107 | + | 16.6690i | 0.392304 | + | 0.539961i | 0.958792 | − | 0.284110i | \(-0.0916980\pi\) |
−0.566487 | + | 0.824070i | \(0.691698\pi\) | |||||||
\(954\) | −6.14492 | + | 4.46455i | −0.198949 | + | 0.144545i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.70704 | − | 3.41986i | −0.152237 | − | 0.110606i | ||||
\(957\) | 3.67414i | 0.118768i | ||||||||
\(958\) | 16.9267 | − | 23.2976i | 0.546877 | − | 0.752712i | ||||
\(959\) | −0.745080 | + | 2.29312i | −0.0240599 | + | 0.0740488i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.55373 | + | 4.78188i | 0.0501202 | + | 0.154254i | ||||
\(962\) | −31.7493 | − | 10.3160i | −1.02364 | − | 0.332600i | ||||
\(963\) | 12.1049 | + | 3.93311i | 0.390074 | + | 0.126743i | ||||
\(964\) | −4.24254 | − | 13.0572i | −0.136643 | − | 0.420544i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.22586 | − | 3.77280i | 0.0394413 | − | 0.121388i | ||||
\(967\) | 30.0333 | − | 41.3373i | 0.965806 | − | 1.32932i | 0.0216692 | − | 0.999765i | \(-0.493102\pi\) |
0.944137 | − | 0.329553i | \(-0.106898\pi\) | |||||||
\(968\) | − | 10.3055i | − | 0.331231i | ||||||
\(969\) | 51.4638 | + | 37.3906i | 1.65325 | + | 1.20116i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.8229 | + | 8.58982i | −0.379414 | + | 0.275661i | −0.761104 | − | 0.648630i | \(-0.775342\pi\) |
0.381690 | + | 0.924291i | \(0.375342\pi\) | |||||||
\(972\) | −6.72683 | − | 9.25869i | −0.215763 | − | 0.296973i | ||||
\(973\) | 3.95458 | − | 1.28492i | 0.126778 | − | 0.0411927i | ||||
\(974\) | −38.9513 | −1.24808 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.88420 | 0.188349 | ||||||||
\(977\) | −49.6981 | + | 16.1479i | −1.58998 | + | 0.516616i | −0.964603 | − | 0.263705i | \(-0.915055\pi\) |
−0.625379 | + | 0.780322i | \(0.715055\pi\) | |||||||
\(978\) | 11.1721 | + | 15.3771i | 0.357246 | + | 0.491707i | ||||
\(979\) | −4.72335 | + | 3.43171i | −0.150959 | + | 0.109678i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.1684 | − | 7.38777i | −0.324652 | − | 0.235873i | ||||
\(982\) | 23.5069i | 0.750135i | ||||||||
\(983\) | 17.4037 | − | 23.9541i | 0.555090 | − | 0.764016i | −0.435602 | − | 0.900140i | \(-0.643464\pi\) |
0.990692 | + | 0.136123i | \(0.0434643\pi\) | |||||||
\(984\) | 0.777913 | − | 2.39417i | 0.0247989 | − | 0.0763233i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.50792 | + | 16.9516i | 0.175408 | + | 0.539850i | ||||
\(987\) | 0.890637 | + | 0.289386i | 0.0283493 | + | 0.00921124i | ||||
\(988\) | −37.5613 | − | 12.2044i | −1.19498 | − | 0.388274i | ||||
\(989\) | 1.78772 | + | 5.50203i | 0.0568461 | + | 0.174954i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.59673 | − | 14.1473i | 0.146020 | − | 0.449403i | −0.851121 | − | 0.524970i | \(-0.824077\pi\) |
0.997141 | + | 0.0755666i | \(0.0240765\pi\) | |||||||
\(992\) | −3.52808 | + | 4.85599i | −0.112017 | + | 0.154178i | ||||
\(993\) | − | 11.5471i | − | 0.366435i | ||||||
\(994\) | 1.59196 | + | 1.15662i | 0.0504938 | + | 0.0366859i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13.4568 | + | 9.77692i | −0.426394 | + | 0.309794i | ||||
\(997\) | −18.0888 | − | 24.8971i | −0.572879 | − | 0.788500i | 0.420013 | − | 0.907518i | \(-0.362026\pi\) |
−0.992892 | + | 0.119018i | \(0.962026\pi\) | |||||||
\(998\) | −26.8817 | + | 8.73440i | −0.850926 | + | 0.276483i | ||||
\(999\) | −41.2468 | −1.30499 |
(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 | 250.2.e.c.99.4 | 16 | ||
5.2 | odd | 4 | 50.2.d.b.31.2 | yes | 8 | ||
5.3 | odd | 4 | 250.2.d.d.151.1 | 8 | |||
5.4 | even | 2 | inner | 250.2.e.c.99.1 | 16 | ||
15.2 | even | 4 | 450.2.h.e.181.2 | 8 | |||
20.7 | even | 4 | 400.2.u.d.81.1 | 8 | |||
25.2 | odd | 20 | 1250.2.a.l.1.2 | 4 | |||
25.3 | odd | 20 | 250.2.d.d.101.1 | 8 | |||
25.4 | even | 10 | inner | 250.2.e.c.149.4 | 16 | ||
25.11 | even | 5 | 1250.2.b.e.1249.2 | 8 | |||
25.14 | even | 10 | 1250.2.b.e.1249.7 | 8 | |||
25.21 | even | 5 | inner | 250.2.e.c.149.1 | 16 | ||
25.22 | odd | 20 | 50.2.d.b.21.2 | ✓ | 8 | ||
25.23 | odd | 20 | 1250.2.a.f.1.3 | 4 | |||
75.47 | even | 20 | 450.2.h.e.271.2 | 8 | |||
100.23 | even | 20 | 10000.2.a.x.1.2 | 4 | |||
100.27 | even | 20 | 10000.2.a.t.1.3 | 4 | |||
100.47 | even | 20 | 400.2.u.d.321.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.2.d.b.21.2 | ✓ | 8 | 25.22 | odd | 20 | ||
50.2.d.b.31.2 | yes | 8 | 5.2 | odd | 4 | ||
250.2.d.d.101.1 | 8 | 25.3 | odd | 20 | |||
250.2.d.d.151.1 | 8 | 5.3 | odd | 4 | |||
250.2.e.c.99.1 | 16 | 5.4 | even | 2 | inner | ||
250.2.e.c.99.4 | 16 | 1.1 | even | 1 | trivial | ||
250.2.e.c.149.1 | 16 | 25.21 | even | 5 | inner | ||
250.2.e.c.149.4 | 16 | 25.4 | even | 10 | inner | ||
400.2.u.d.81.1 | 8 | 20.7 | even | 4 | |||
400.2.u.d.321.1 | 8 | 100.47 | even | 20 | |||
450.2.h.e.181.2 | 8 | 15.2 | even | 4 | |||
450.2.h.e.271.2 | 8 | 75.47 | even | 20 | |||
1250.2.a.f.1.3 | 4 | 25.23 | odd | 20 | |||
1250.2.a.l.1.2 | 4 | 25.2 | odd | 20 | |||
1250.2.b.e.1249.2 | 8 | 25.11 | even | 5 | |||
1250.2.b.e.1249.7 | 8 | 25.14 | even | 10 | |||
10000.2.a.t.1.3 | 4 | 100.27 | even | 20 | |||
10000.2.a.x.1.2 | 4 | 100.23 | even | 20 |