Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(22,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.e (of order \(3\), degree \(2\), 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: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.64827.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 22.1 | ||
Root | \(-0.623490 + 1.07992i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.22 |
Dual form | 507.2.e.i.484.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.34601 | + | 2.33136i | −0.951773 | + | 1.64852i | −0.210188 | + | 0.977661i | \(0.567408\pi\) |
−0.741585 | + | 0.670859i | \(0.765926\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −2.62349 | − | 4.54402i | −1.31174 | − | 2.27201i | ||||
\(5\) | −1.04892 | −0.469090 | −0.234545 | − | 0.972105i | \(-0.575360\pi\) | ||||
−0.234545 | + | 0.972105i | \(0.575360\pi\) | |||||||
\(6\) | 1.34601 | + | 2.33136i | 0.549507 | + | 0.951773i | ||||
\(7\) | −0.277479 | − | 0.480608i | −0.104877 | − | 0.181653i | 0.808811 | − | 0.588069i | \(-0.200112\pi\) |
−0.913688 | + | 0.406416i | \(0.866778\pi\) | |||||||
\(8\) | 8.74094 | 3.09039 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1.41185 | − | 2.44540i | 0.446467 | − | 0.773304i | ||||
\(11\) | −1.45593 | + | 2.52174i | −0.438979 | + | 0.760333i | −0.997611 | − | 0.0690822i | \(-0.977993\pi\) |
0.558632 | + | 0.829415i | \(0.311326\pi\) | |||||||
\(12\) | −5.24698 | −1.51467 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.49396 | 0.399277 | ||||||||
\(15\) | −0.524459 | + | 0.908389i | −0.135415 | + | 0.234545i | ||||
\(16\) | −6.51842 | + | 11.2902i | −1.62960 | + | 2.82256i | ||||
\(17\) | 2.42543 | + | 4.20096i | 0.588253 | + | 1.01888i | 0.994461 | + | 0.105103i | \(0.0335172\pi\) |
−0.406209 | + | 0.913780i | \(0.633149\pi\) | |||||||
\(18\) | 2.69202 | 0.634516 | ||||||||
\(19\) | 0.376510 | + | 0.652135i | 0.0863774 | + | 0.149610i | 0.905977 | − | 0.423326i | \(-0.139138\pi\) |
−0.819600 | + | 0.572936i | \(0.805804\pi\) | |||||||
\(20\) | 2.75182 | + | 4.76630i | 0.615327 | + | 1.06578i | ||||
\(21\) | −0.554958 | −0.121102 | ||||||||
\(22\) | −3.91939 | − | 6.78858i | −0.835616 | − | 1.44733i | ||||
\(23\) | −2.88135 | + | 4.99065i | −0.600804 | + | 1.04062i | 0.391896 | + | 0.920010i | \(0.371819\pi\) |
−0.992700 | + | 0.120613i | \(0.961514\pi\) | |||||||
\(24\) | 4.37047 | − | 7.56988i | 0.892118 | − | 1.54519i | ||||
\(25\) | −3.89977 | −0.779954 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.45593 | + | 2.52174i | −0.275144 | + | 0.476564i | ||||
\(29\) | 0.955927 | − | 1.65571i | 0.177511 | − | 0.307458i | −0.763516 | − | 0.645789i | \(-0.776529\pi\) |
0.941027 | + | 0.338330i | \(0.109862\pi\) | |||||||
\(30\) | −1.41185 | − | 2.44540i | −0.257768 | − | 0.446467i | ||||
\(31\) | −9.51573 | −1.70908 | −0.854538 | − | 0.519389i | \(-0.826159\pi\) | ||||
−0.854538 | + | 0.519389i | \(0.826159\pi\) | |||||||
\(32\) | −8.80678 | − | 15.2538i | −1.55683 | − | 2.69652i | ||||
\(33\) | 1.45593 | + | 2.52174i | 0.253444 | + | 0.438979i | ||||
\(34\) | −13.0586 | −2.23953 | ||||||||
\(35\) | 0.291053 | + | 0.504118i | 0.0491969 | + | 0.0852115i | ||||
\(36\) | −2.62349 | + | 4.54402i | −0.437248 | + | 0.757336i | ||||
\(37\) | −2.87651 | + | 4.98226i | −0.472895 | + | 0.819079i | −0.999519 | − | 0.0310199i | \(-0.990124\pi\) |
0.526623 | + | 0.850099i | \(0.323458\pi\) | |||||||
\(38\) | −2.02715 | −0.328847 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.16852 | −1.44967 | ||||||||
\(41\) | −2.45593 | + | 4.25379i | −0.383551 | + | 0.664330i | −0.991567 | − | 0.129595i | \(-0.958632\pi\) |
0.608016 | + | 0.793925i | \(0.291966\pi\) | |||||||
\(42\) | 0.746980 | − | 1.29381i | 0.115261 | − | 0.199639i | ||||
\(43\) | 5.54892 | + | 9.61101i | 0.846202 | + | 1.46566i | 0.884573 | + | 0.466401i | \(0.154450\pi\) |
−0.0383713 | + | 0.999264i | \(0.512217\pi\) | |||||||
\(44\) | 15.2784 | 2.30331 | ||||||||
\(45\) | 0.524459 | + | 0.908389i | 0.0781817 | + | 0.135415i | ||||
\(46\) | −7.75667 | − | 13.4349i | −1.14366 | − | 1.98087i | ||||
\(47\) | 0.753020 | 0.109839 | 0.0549197 | − | 0.998491i | \(-0.482510\pi\) | ||||
0.0549197 | + | 0.998491i | \(0.482510\pi\) | |||||||
\(48\) | 6.51842 | + | 11.2902i | 0.940853 | + | 1.62960i | ||||
\(49\) | 3.34601 | − | 5.79546i | 0.478002 | − | 0.827923i | ||||
\(50\) | 5.24914 | − | 9.09177i | 0.742340 | − | 1.28577i | ||||
\(51\) | 4.85086 | 0.679256 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.58211 | −1.04148 | −0.520741 | − | 0.853715i | \(-0.674344\pi\) | ||||
−0.520741 | + | 0.853715i | \(0.674344\pi\) | |||||||
\(54\) | 1.34601 | − | 2.33136i | 0.183169 | − | 0.317258i | ||||
\(55\) | 1.52715 | − | 2.64510i | 0.205920 | − | 0.356665i | ||||
\(56\) | −2.42543 | − | 4.20096i | −0.324111 | − | 0.561377i | ||||
\(57\) | 0.753020 | 0.0997400 | ||||||||
\(58\) | 2.57338 | + | 4.45722i | 0.337901 | + | 0.585261i | ||||
\(59\) | −2.04892 | − | 3.54883i | −0.266746 | − | 0.462018i | 0.701273 | − | 0.712892i | \(-0.252615\pi\) |
−0.968020 | + | 0.250874i | \(0.919282\pi\) | |||||||
\(60\) | 5.50365 | 0.710518 | ||||||||
\(61\) | 1.71164 | + | 2.96464i | 0.219153 | + | 0.379583i | 0.954549 | − | 0.298054i | \(-0.0963374\pi\) |
−0.735397 | + | 0.677637i | \(0.763004\pi\) | |||||||
\(62\) | 12.8083 | − | 22.1846i | 1.62665 | − | 2.81744i | ||||
\(63\) | −0.277479 | + | 0.480608i | −0.0349591 | + | 0.0605509i | ||||
\(64\) | 21.3424 | 2.66780 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.83877 | −0.964886 | ||||||||
\(67\) | 0.936313 | − | 1.62174i | 0.114389 | − | 0.198127i | −0.803146 | − | 0.595782i | \(-0.796842\pi\) |
0.917535 | + | 0.397654i | \(0.130176\pi\) | |||||||
\(68\) | 12.7262 | − | 22.0424i | 1.54327 | − | 2.67303i | ||||
\(69\) | 2.88135 | + | 4.99065i | 0.346874 | + | 0.600804i | ||||
\(70\) | −1.56704 | −0.187297 | ||||||||
\(71\) | 5.25182 | + | 9.09643i | 0.623277 | + | 1.07955i | 0.988871 | + | 0.148773i | \(0.0475324\pi\) |
−0.365595 | + | 0.930774i | \(0.619134\pi\) | |||||||
\(72\) | −4.37047 | − | 7.56988i | −0.515065 | − | 0.892118i | ||||
\(73\) | 10.4765 | 1.22618 | 0.613091 | − | 0.790012i | \(-0.289926\pi\) | ||||
0.613091 | + | 0.790012i | \(0.289926\pi\) | |||||||
\(74\) | −7.74363 | − | 13.4124i | −0.900178 | − | 1.55915i | ||||
\(75\) | −1.94989 | + | 3.37730i | −0.225153 | + | 0.389977i | ||||
\(76\) | 1.97554 | − | 3.42174i | 0.226610 | − | 0.392500i | ||||
\(77\) | 1.61596 | 0.184155 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.33513 | 0.150213 | 0.0751067 | − | 0.997176i | \(-0.476070\pi\) | ||||
0.0751067 | + | 0.997176i | \(0.476070\pi\) | |||||||
\(80\) | 6.83728 | − | 11.8425i | 0.764431 | − | 1.32403i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −6.61141 | − | 11.4513i | −0.730108 | − | 1.26458i | ||||
\(83\) | 2.64310 | 0.290118 | 0.145059 | − | 0.989423i | \(-0.453663\pi\) | ||||
0.145059 | + | 0.989423i | \(0.453663\pi\) | |||||||
\(84\) | 1.45593 | + | 2.52174i | 0.158855 | + | 0.275144i | ||||
\(85\) | −2.54407 | − | 4.40646i | −0.275943 | − | 0.477948i | ||||
\(86\) | −29.8756 | −3.22157 | ||||||||
\(87\) | −0.955927 | − | 1.65571i | −0.102486 | − | 0.177511i | ||||
\(88\) | −12.7262 | + | 22.0424i | −1.35661 | + | 2.34972i | ||||
\(89\) | −4.96346 | + | 8.59696i | −0.526126 | + | 0.911276i | 0.473411 | + | 0.880842i | \(0.343023\pi\) |
−0.999537 | + | 0.0304348i | \(0.990311\pi\) | |||||||
\(90\) | −2.82371 | −0.297645 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 30.2368 | 3.15241 | ||||||||
\(93\) | −4.75786 | + | 8.24086i | −0.493368 | + | 0.854538i | ||||
\(94\) | −1.01357 | + | 1.75556i | −0.104542 | + | 0.181072i | ||||
\(95\) | −0.394928 | − | 0.684035i | −0.0405188 | − | 0.0701806i | ||||
\(96\) | −17.6136 | −1.79768 | ||||||||
\(97\) | −8.53684 | − | 14.7862i | −0.866784 | − | 1.50131i | −0.865264 | − | 0.501316i | \(-0.832850\pi\) |
−0.00151988 | − | 0.999999i | \(-0.500484\pi\) | |||||||
\(98\) | 9.00753 | + | 15.6015i | 0.909898 | + | 1.57599i | ||||
\(99\) | 2.91185 | 0.292652 | ||||||||
\(100\) | 10.2310 | + | 17.7206i | 1.02310 | + | 1.77206i | ||||
\(101\) | −3.66152 | + | 6.34194i | −0.364335 | + | 0.631047i | −0.988669 | − | 0.150111i | \(-0.952037\pi\) |
0.624334 | + | 0.781157i | \(0.285370\pi\) | |||||||
\(102\) | −6.52930 | + | 11.3091i | −0.646497 | + | 1.11977i | ||||
\(103\) | −4.21983 | −0.415792 | −0.207896 | − | 0.978151i | \(-0.566662\pi\) | ||||
−0.207896 | + | 0.978151i | \(0.566662\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.582105 | 0.0568077 | ||||||||
\(106\) | 10.2056 | − | 17.6766i | 0.991255 | − | 1.71690i | ||||
\(107\) | −3.19687 | + | 5.53713i | −0.309053 | + | 0.535295i | −0.978155 | − | 0.207875i | \(-0.933345\pi\) |
0.669103 | + | 0.743170i | \(0.266679\pi\) | |||||||
\(108\) | 2.62349 | + | 4.54402i | 0.252445 | + | 0.437248i | ||||
\(109\) | −3.46011 | −0.331418 | −0.165709 | − | 0.986175i | \(-0.552991\pi\) | ||||
−0.165709 | + | 0.986175i | \(0.552991\pi\) | |||||||
\(110\) | 4.11111 | + | 7.12066i | 0.391979 | + | 0.678928i | ||||
\(111\) | 2.87651 | + | 4.98226i | 0.273026 | + | 0.472895i | ||||
\(112\) | 7.23490 | 0.683634 | ||||||||
\(113\) | −4.67845 | − | 8.10331i | −0.440111 | − | 0.762295i | 0.557586 | − | 0.830119i | \(-0.311728\pi\) |
−0.997697 | + | 0.0678240i | \(0.978394\pi\) | |||||||
\(114\) | −1.01357 | + | 1.75556i | −0.0949299 | + | 0.164423i | ||||
\(115\) | 3.02230 | − | 5.23478i | 0.281831 | − | 0.488146i | ||||
\(116\) | −10.0315 | −0.931398 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.0315 | 1.01553 | ||||||||
\(119\) | 1.34601 | − | 2.33136i | 0.123389 | − | 0.213715i | ||||
\(120\) | −4.58426 | + | 7.94017i | −0.418484 | + | 0.724835i | ||||
\(121\) | 1.26055 | + | 2.18334i | 0.114596 | + | 0.198486i | ||||
\(122\) | −9.21552 | −0.834334 | ||||||||
\(123\) | 2.45593 | + | 4.25379i | 0.221443 | + | 0.383551i | ||||
\(124\) | 24.9644 | + | 43.2396i | 2.24187 | + | 3.88303i | ||||
\(125\) | 9.33513 | 0.834959 | ||||||||
\(126\) | −0.746980 | − | 1.29381i | −0.0665462 | − | 0.115261i | ||||
\(127\) | 2.24094 | − | 3.88142i | 0.198851 | − | 0.344420i | −0.749305 | − | 0.662225i | \(-0.769612\pi\) |
0.948156 | + | 0.317805i | \(0.102946\pi\) | |||||||
\(128\) | −11.1136 | + | 19.2493i | −0.982310 | + | 1.70141i | ||||
\(129\) | 11.0978 | 0.977110 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.21744 | −0.805331 | −0.402666 | − | 0.915347i | \(-0.631916\pi\) | ||||
−0.402666 | + | 0.915347i | \(0.631916\pi\) | |||||||
\(132\) | 7.63922 | − | 13.2315i | 0.664909 | − | 1.15166i | ||||
\(133\) | 0.208947 | − | 0.361908i | 0.0181180 | − | 0.0313814i | ||||
\(134\) | 2.52057 | + | 4.36576i | 0.217744 | + | 0.377144i | ||||
\(135\) | 1.04892 | 0.0902764 | ||||||||
\(136\) | 21.2005 | + | 36.7204i | 1.81793 | + | 3.14875i | ||||
\(137\) | 3.73490 | + | 6.46903i | 0.319094 | + | 0.552687i | 0.980299 | − | 0.197518i | \(-0.0632881\pi\) |
−0.661205 | + | 0.750205i | \(0.729955\pi\) | |||||||
\(138\) | −15.5133 | −1.32058 | ||||||||
\(139\) | 8.99880 | + | 15.5864i | 0.763269 | + | 1.32202i | 0.941157 | + | 0.337969i | \(0.109740\pi\) |
−0.177889 | + | 0.984051i | \(0.556927\pi\) | |||||||
\(140\) | 1.52715 | − | 2.64510i | 0.129067 | − | 0.223551i | ||||
\(141\) | 0.376510 | − | 0.652135i | 0.0317079 | − | 0.0549197i | ||||
\(142\) | −28.2760 | −2.37287 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 13.0368 | 1.08640 | ||||||||
\(145\) | −1.00269 | + | 1.73671i | −0.0832687 | + | 0.144226i | ||||
\(146\) | −14.1015 | + | 24.4245i | −1.16705 | + | 2.02138i | ||||
\(147\) | −3.34601 | − | 5.79546i | −0.275974 | − | 0.478002i | ||||
\(148\) | 30.1860 | 2.48127 | ||||||||
\(149\) | −7.66756 | − | 13.2806i | −0.628151 | − | 1.08799i | −0.987922 | − | 0.154949i | \(-0.950479\pi\) |
0.359771 | − | 0.933041i | \(-0.382855\pi\) | |||||||
\(150\) | −5.24914 | − | 9.09177i | −0.428590 | − | 0.742340i | ||||
\(151\) | 2.53079 | 0.205953 | 0.102977 | − | 0.994684i | \(-0.467163\pi\) | ||||
0.102977 | + | 0.994684i | \(0.467163\pi\) | |||||||
\(152\) | 3.29105 | + | 5.70027i | 0.266940 | + | 0.462353i | ||||
\(153\) | 2.42543 | − | 4.20096i | 0.196084 | − | 0.339628i | ||||
\(154\) | −2.17510 | + | 3.76738i | −0.175274 | + | 0.303584i | ||||
\(155\) | 9.98121 | 0.801710 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.2392 | 1.37584 | 0.687919 | − | 0.725787i | \(-0.258524\pi\) | ||||
0.687919 | + | 0.725787i | \(0.258524\pi\) | |||||||
\(158\) | −1.79709 | + | 3.11266i | −0.142969 | + | 0.247630i | ||||
\(159\) | −3.79105 | + | 6.56630i | −0.300650 | + | 0.520741i | ||||
\(160\) | 9.23759 | + | 16.0000i | 0.730295 | + | 1.26491i | ||||
\(161\) | 3.19806 | 0.252043 | ||||||||
\(162\) | −1.34601 | − | 2.33136i | −0.105753 | − | 0.183169i | ||||
\(163\) | −7.85354 | − | 13.6027i | −0.615137 | − | 1.06545i | −0.990360 | − | 0.138514i | \(-0.955767\pi\) |
0.375223 | − | 0.926934i | \(-0.377566\pi\) | |||||||
\(164\) | 25.7724 | 2.01249 | ||||||||
\(165\) | −1.52715 | − | 2.64510i | −0.118888 | − | 0.205920i | ||||
\(166\) | −3.55765 | + | 6.16202i | −0.276127 | + | 0.478266i | ||||
\(167\) | −2.69806 | + | 4.67318i | −0.208782 | + | 0.361622i | −0.951331 | − | 0.308170i | \(-0.900283\pi\) |
0.742549 | + | 0.669792i | \(0.233617\pi\) | |||||||
\(168\) | −4.85086 | −0.374252 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 13.6974 | 1.05054 | ||||||||
\(171\) | 0.376510 | − | 0.652135i | 0.0287925 | − | 0.0498700i | ||||
\(172\) | 29.1151 | − | 50.4288i | 2.22000 | − | 3.84516i | ||||
\(173\) | −11.9710 | − | 20.7344i | −0.910138 | − | 1.57640i | −0.813868 | − | 0.581049i | \(-0.802642\pi\) |
−0.0962694 | − | 0.995355i | \(-0.530691\pi\) | |||||||
\(174\) | 5.14675 | 0.390174 | ||||||||
\(175\) | 1.08211 | + | 1.87426i | 0.0817995 | + | 0.141681i | ||||
\(176\) | −18.9807 | − | 32.8755i | −1.43072 | − | 2.47808i | ||||
\(177\) | −4.09783 | −0.308012 | ||||||||
\(178\) | −13.3617 | − | 23.1432i | −1.00150 | − | 1.73466i | ||||
\(179\) | −9.20440 | + | 15.9425i | −0.687969 | + | 1.19160i | 0.284525 | + | 0.958669i | \(0.408164\pi\) |
−0.972494 | + | 0.232929i | \(0.925169\pi\) | |||||||
\(180\) | 2.75182 | − | 4.76630i | 0.205109 | − | 0.355259i | ||||
\(181\) | −3.63342 | −0.270070 | −0.135035 | − | 0.990841i | \(-0.543115\pi\) | ||||
−0.135035 | + | 0.990841i | \(0.543115\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.42327 | 0.253056 | ||||||||
\(184\) | −25.1857 | + | 43.6230i | −1.85672 | + | 3.21593i | ||||
\(185\) | 3.01722 | − | 5.22598i | 0.221831 | − | 0.384222i | ||||
\(186\) | −12.8083 | − | 22.1846i | −0.939148 | − | 1.62665i | ||||
\(187\) | −14.1250 | −1.03292 | ||||||||
\(188\) | −1.97554 | − | 3.42174i | −0.144081 | − | 0.249556i | ||||
\(189\) | 0.277479 | + | 0.480608i | 0.0201836 | + | 0.0349591i | ||||
\(190\) | 2.12631 | 0.154259 | ||||||||
\(191\) | 10.5891 | + | 18.3409i | 0.766201 | + | 1.32710i | 0.939609 | + | 0.342249i | \(0.111189\pi\) |
−0.173409 | + | 0.984850i | \(0.555478\pi\) | |||||||
\(192\) | 10.6712 | − | 18.4831i | 0.770128 | − | 1.33390i | ||||
\(193\) | 8.80559 | − | 15.2517i | 0.633840 | − | 1.09784i | −0.352920 | − | 0.935654i | \(-0.614811\pi\) |
0.986760 | − | 0.162189i | \(-0.0518555\pi\) | |||||||
\(194\) | 45.9627 | 3.29993 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −35.1129 | −2.50806 | ||||||||
\(197\) | 2.33124 | − | 4.03783i | 0.166094 | − | 0.287683i | −0.770949 | − | 0.636897i | \(-0.780218\pi\) |
0.937043 | + | 0.349213i | \(0.113551\pi\) | |||||||
\(198\) | −3.91939 | + | 6.78858i | −0.278539 | + | 0.482443i | ||||
\(199\) | −7.51842 | − | 13.0223i | −0.532967 | − | 0.923125i | −0.999259 | − | 0.0384944i | \(-0.987744\pi\) |
0.466292 | − | 0.884631i | \(-0.345590\pi\) | |||||||
\(200\) | −34.0877 | −2.41036 | ||||||||
\(201\) | −0.936313 | − | 1.62174i | −0.0660424 | − | 0.114389i | ||||
\(202\) | −9.85690 | − | 17.0726i | −0.693529 | − | 1.20123i | ||||
\(203\) | −1.06100 | −0.0744675 | ||||||||
\(204\) | −12.7262 | − | 22.0424i | −0.891010 | − | 1.54327i | ||||
\(205\) | 2.57606 | − | 4.46187i | 0.179920 | − | 0.311631i | ||||
\(206\) | 5.67994 | − | 9.83794i | 0.395740 | − | 0.685442i | ||||
\(207\) | 5.76271 | 0.400536 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.19269 | −0.151671 | ||||||||
\(210\) | −0.783520 | + | 1.35710i | −0.0540680 | + | 0.0936485i | ||||
\(211\) | 0.230054 | − | 0.398465i | 0.0158375 | − | 0.0274314i | −0.857998 | − | 0.513653i | \(-0.828292\pi\) |
0.873836 | + | 0.486222i | \(0.161625\pi\) | |||||||
\(212\) | 19.8916 | + | 34.4532i | 1.36616 | + | 2.36626i | ||||
\(213\) | 10.5036 | 0.719698 | ||||||||
\(214\) | −8.60603 | − | 14.9061i | −0.588296 | − | 1.01896i | ||||
\(215\) | −5.82036 | − | 10.0812i | −0.396945 | − | 0.687529i | ||||
\(216\) | −8.74094 | −0.594746 | ||||||||
\(217\) | 2.64042 | + | 4.57333i | 0.179243 | + | 0.310458i | ||||
\(218\) | 4.65734 | − | 8.06675i | 0.315435 | − | 0.546349i | ||||
\(219\) | 5.23825 | − | 9.07292i | 0.353968 | − | 0.613091i | ||||
\(220\) | −16.0258 | −1.08046 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −15.4873 | −1.03944 | ||||||||
\(223\) | 8.17510 | − | 14.1597i | 0.547445 | − | 0.948202i | −0.451004 | − | 0.892522i | \(-0.648934\pi\) |
0.998449 | − | 0.0556803i | \(-0.0177328\pi\) | |||||||
\(224\) | −4.88740 | + | 8.46522i | −0.326553 | + | 0.565606i | ||||
\(225\) | 1.94989 | + | 3.37730i | 0.129992 | + | 0.225153i | ||||
\(226\) | 25.1890 | 1.67555 | ||||||||
\(227\) | −3.28017 | − | 5.68142i | −0.217712 | − | 0.377089i | 0.736396 | − | 0.676551i | \(-0.236526\pi\) |
−0.954108 | + | 0.299462i | \(0.903193\pi\) | |||||||
\(228\) | −1.97554 | − | 3.42174i | −0.130833 | − | 0.226610i | ||||
\(229\) | −3.95539 | −0.261380 | −0.130690 | − | 0.991423i | \(-0.541719\pi\) | ||||
−0.130690 | + | 0.991423i | \(0.541719\pi\) | |||||||
\(230\) | 8.13610 | + | 14.0921i | 0.536479 | + | 0.929209i | ||||
\(231\) | 0.807979 | − | 1.39946i | 0.0531611 | − | 0.0920777i | ||||
\(232\) | 8.35570 | − | 14.4725i | 0.548579 | − | 0.950166i | ||||
\(233\) | 8.35690 | 0.547478 | 0.273739 | − | 0.961804i | \(-0.411739\pi\) | ||||
0.273739 | + | 0.961804i | \(0.411739\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.789856 | −0.0515245 | ||||||||
\(236\) | −10.7506 | + | 18.6206i | −0.699806 | + | 1.21210i | ||||
\(237\) | 0.667563 | − | 1.15625i | 0.0433629 | − | 0.0751067i | ||||
\(238\) | 3.62349 | + | 6.27607i | 0.234876 | + | 0.406817i | ||||
\(239\) | 20.1008 | 1.30021 | 0.650107 | − | 0.759843i | \(-0.274724\pi\) | ||||
0.650107 | + | 0.759843i | \(0.274724\pi\) | |||||||
\(240\) | −6.83728 | − | 11.8425i | −0.441345 | − | 0.764431i | ||||
\(241\) | 9.50634 | + | 16.4655i | 0.612357 | + | 1.06063i | 0.990842 | + | 0.135026i | \(0.0431118\pi\) |
−0.378485 | + | 0.925607i | \(0.623555\pi\) | |||||||
\(242\) | −6.78687 | −0.436277 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 8.98092 | − | 15.5554i | 0.574944 | − | 0.995833i | ||||
\(245\) | −3.50969 | + | 6.07896i | −0.224226 | + | 0.388370i | ||||
\(246\) | −13.2228 | −0.843056 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −83.1764 | −5.28171 | ||||||||
\(249\) | 1.32155 | − | 2.28900i | 0.0837500 | − | 0.145059i | ||||
\(250\) | −12.5652 | + | 21.7635i | −0.794692 | + | 1.37645i | ||||
\(251\) | 0.381887 | + | 0.661448i | 0.0241045 | + | 0.0417502i | 0.877826 | − | 0.478980i | \(-0.158993\pi\) |
−0.853722 | + | 0.520730i | \(0.825660\pi\) | |||||||
\(252\) | 2.91185 | 0.183430 | ||||||||
\(253\) | −8.39008 | − | 14.5321i | −0.527480 | − | 0.913622i | ||||
\(254\) | 6.03266 | + | 10.4489i | 0.378522 | + | 0.655620i | ||||
\(255\) | −5.08815 | −0.318632 | ||||||||
\(256\) | −8.57553 | − | 14.8533i | −0.535971 | − | 0.928329i | ||||
\(257\) | 6.54556 | − | 11.3373i | 0.408301 | − | 0.707198i | −0.586398 | − | 0.810023i | \(-0.699455\pi\) |
0.994700 | + | 0.102825i | \(0.0327880\pi\) | |||||||
\(258\) | −14.9378 | + | 25.8730i | −0.929987 | + | 1.61078i | ||||
\(259\) | 3.19269 | 0.198384 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.91185 | −0.118341 | ||||||||
\(262\) | 12.4068 | − | 21.4892i | 0.766493 | − | 1.32760i | ||||
\(263\) | −9.18867 | + | 15.9152i | −0.566598 | + | 0.981376i | 0.430301 | + | 0.902685i | \(0.358407\pi\) |
−0.996899 | + | 0.0786906i | \(0.974926\pi\) | |||||||
\(264\) | 12.7262 | + | 22.0424i | 0.783242 | + | 1.35661i | ||||
\(265\) | 7.95300 | 0.488549 | ||||||||
\(266\) | 0.562491 | + | 0.974263i | 0.0344885 | + | 0.0597359i | ||||
\(267\) | 4.96346 | + | 8.59696i | 0.303759 | + | 0.526126i | ||||
\(268\) | −9.82563 | −0.600196 | ||||||||
\(269\) | −11.8312 | − | 20.4923i | −0.721363 | − | 1.24944i | −0.960453 | − | 0.278441i | \(-0.910182\pi\) |
0.239090 | − | 0.970997i | \(-0.423151\pi\) | |||||||
\(270\) | −1.41185 | + | 2.44540i | −0.0859227 | + | 0.148822i | ||||
\(271\) | 9.87651 | − | 17.1066i | 0.599955 | − | 1.03915i | −0.392872 | − | 0.919593i | \(-0.628518\pi\) |
0.992827 | − | 0.119560i | \(-0.0381483\pi\) | |||||||
\(272\) | −63.2398 | −3.83448 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.1089 | −1.21482 | ||||||||
\(275\) | 5.67778 | − | 9.83421i | 0.342383 | − | 0.593025i | ||||
\(276\) | 15.1184 | − | 26.1859i | 0.910021 | − | 1.57620i | ||||
\(277\) | −0.888887 | − | 1.53960i | −0.0534081 | − | 0.0925055i | 0.838085 | − | 0.545539i | \(-0.183675\pi\) |
−0.891493 | + | 0.453034i | \(0.850342\pi\) | |||||||
\(278\) | −48.4499 | −2.90583 | ||||||||
\(279\) | 4.75786 | + | 8.24086i | 0.284846 | + | 0.493368i | ||||
\(280\) | 2.54407 | + | 4.40646i | 0.152037 | + | 0.263337i | ||||
\(281\) | 1.62133 | 0.0967207 | 0.0483603 | − | 0.998830i | \(-0.484600\pi\) | ||||
0.0483603 | + | 0.998830i | \(0.484600\pi\) | |||||||
\(282\) | 1.01357 | + | 1.75556i | 0.0603574 | + | 0.104542i | ||||
\(283\) | −2.49180 | + | 4.31593i | −0.148122 | + | 0.256555i | −0.930533 | − | 0.366207i | \(-0.880656\pi\) |
0.782411 | + | 0.622762i | \(0.213990\pi\) | |||||||
\(284\) | 27.5562 | − | 47.7288i | 1.63516 | − | 2.83218i | ||||
\(285\) | −0.789856 | −0.0467870 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.72587 | 0.160903 | ||||||||
\(288\) | −8.80678 | + | 15.2538i | −0.518945 | + | 0.898838i | ||||
\(289\) | −3.26540 | + | 5.65583i | −0.192082 | + | 0.332696i | ||||
\(290\) | −2.69926 | − | 4.67525i | −0.158506 | − | 0.274540i | ||||
\(291\) | −17.0737 | −1.00088 | ||||||||
\(292\) | −27.4850 | − | 47.6054i | −1.60844 | − | 2.78590i | ||||
\(293\) | 0.0358763 | + | 0.0621395i | 0.00209591 | + | 0.00363023i | 0.867071 | − | 0.498184i | \(-0.166000\pi\) |
−0.864976 | + | 0.501814i | \(0.832666\pi\) | |||||||
\(294\) | 18.0151 | 1.05066 | ||||||||
\(295\) | 2.14914 | + | 3.72243i | 0.125128 | + | 0.216728i | ||||
\(296\) | −25.1434 | + | 43.5496i | −1.46143 | + | 2.53127i | ||||
\(297\) | 1.45593 | − | 2.52174i | 0.0844815 | − | 0.146326i | ||||
\(298\) | 41.2825 | 2.39143 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 20.4620 | 1.18138 | ||||||||
\(301\) | 3.07942 | − | 5.33371i | 0.177495 | − | 0.307430i | ||||
\(302\) | −3.40648 | + | 5.90019i | −0.196021 | + | 0.339518i | ||||
\(303\) | 3.66152 | + | 6.34194i | 0.210349 | + | 0.364335i | ||||
\(304\) | −9.81700 | −0.563044 | ||||||||
\(305\) | −1.79536 | − | 3.10966i | −0.102802 | − | 0.178059i | ||||
\(306\) | 6.52930 | + | 11.3091i | 0.373255 | + | 0.646497i | ||||
\(307\) | −5.19806 | −0.296669 | −0.148335 | − | 0.988937i | \(-0.547391\pi\) | ||||
−0.148335 | + | 0.988937i | \(0.547391\pi\) | |||||||
\(308\) | −4.23945 | − | 7.34294i | −0.241565 | − | 0.418403i | ||||
\(309\) | −2.10992 | + | 3.65448i | −0.120029 | + | 0.207896i | ||||
\(310\) | −13.4348 | + | 23.2698i | −0.763047 | + | 1.32164i | ||||
\(311\) | −22.5429 | −1.27829 | −0.639145 | − | 0.769087i | \(-0.720711\pi\) | ||||
−0.639145 | + | 0.769087i | \(0.720711\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.6612 | 1.28088 | 0.640442 | − | 0.768006i | \(-0.278751\pi\) | ||||
0.640442 | + | 0.768006i | \(0.278751\pi\) | |||||||
\(314\) | −23.2042 | + | 40.1908i | −1.30949 | + | 2.26810i | ||||
\(315\) | 0.291053 | − | 0.504118i | 0.0163990 | − | 0.0284038i | ||||
\(316\) | −3.50269 | − | 6.06683i | −0.197042 | − | 0.341286i | ||||
\(317\) | 26.3424 | 1.47954 | 0.739769 | − | 0.672861i | \(-0.234935\pi\) | ||||
0.739769 | + | 0.672861i | \(0.234935\pi\) | |||||||
\(318\) | −10.2056 | − | 17.6766i | −0.572301 | − | 0.991255i | ||||
\(319\) | 2.78352 | + | 4.82120i | 0.155847 | + | 0.269935i | ||||
\(320\) | −22.3864 | −1.25144 | ||||||||
\(321\) | 3.19687 | + | 5.53713i | 0.178432 | + | 0.309053i | ||||
\(322\) | −4.30463 | + | 7.45583i | −0.239887 | + | 0.415497i | ||||
\(323\) | −1.82640 | + | 3.16341i | −0.101623 | + | 0.176017i | ||||
\(324\) | 5.24698 | 0.291499 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 42.2838 | 2.34188 | ||||||||
\(327\) | −1.73005 | + | 2.99654i | −0.0956722 | + | 0.165709i | ||||
\(328\) | −21.4671 | + | 37.1821i | −1.18532 | + | 2.05304i | ||||
\(329\) | −0.208947 | − | 0.361908i | −0.0115196 | − | 0.0199526i | ||||
\(330\) | 8.22223 | 0.452619 | ||||||||
\(331\) | 5.61476 | + | 9.72505i | 0.308615 | + | 0.534537i | 0.978060 | − | 0.208325i | \(-0.0668011\pi\) |
−0.669445 | + | 0.742862i | \(0.733468\pi\) | |||||||
\(332\) | −6.93416 | − | 12.0103i | −0.380561 | − | 0.659151i | ||||
\(333\) | 5.75302 | 0.315264 | ||||||||
\(334\) | −7.26324 | − | 12.5803i | −0.397427 | − | 0.688364i | ||||
\(335\) | −0.982115 | + | 1.70107i | −0.0536587 | + | 0.0929395i | ||||
\(336\) | 3.61745 | − | 6.26561i | 0.197348 | − | 0.341817i | ||||
\(337\) | 2.30798 | 0.125724 | 0.0628618 | − | 0.998022i | \(-0.479977\pi\) | ||||
0.0628618 | + | 0.998022i | \(0.479977\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.35690 | −0.508197 | ||||||||
\(340\) | −13.3487 | + | 23.1206i | −0.723935 | + | 1.25389i | ||||
\(341\) | 13.8542 | − | 23.9962i | 0.750247 | − | 1.29947i | ||||
\(342\) | 1.01357 | + | 1.75556i | 0.0548078 | + | 0.0949299i | ||||
\(343\) | −7.59850 | −0.410280 | ||||||||
\(344\) | 48.5027 | + | 84.0092i | 2.61509 | + | 4.52947i | ||||
\(345\) | −3.02230 | − | 5.23478i | −0.162715 | − | 0.281831i | ||||
\(346\) | 64.4523 | 3.46498 | ||||||||
\(347\) | 4.56853 | + | 7.91293i | 0.245252 | + | 0.424788i | 0.962202 | − | 0.272336i | \(-0.0877961\pi\) |
−0.716951 | + | 0.697124i | \(0.754463\pi\) | |||||||
\(348\) | −5.01573 | + | 8.68750i | −0.268871 | + | 0.465699i | ||||
\(349\) | −11.9879 | + | 20.7637i | −0.641699 | + | 1.11145i | 0.343355 | + | 0.939206i | \(0.388437\pi\) |
−0.985053 | + | 0.172249i | \(0.944897\pi\) | |||||||
\(350\) | −5.82610 | −0.311418 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 51.2881 | 2.73367 | ||||||||
\(353\) | 13.5620 | − | 23.4900i | 0.721830 | − | 1.25025i | −0.238435 | − | 0.971158i | \(-0.576634\pi\) |
0.960265 | − | 0.279088i | \(-0.0900322\pi\) | |||||||
\(354\) | 5.51573 | − | 9.55352i | 0.293158 | − | 0.507764i | ||||
\(355\) | −5.50873 | − | 9.54140i | −0.292373 | − | 0.506405i | ||||
\(356\) | 52.0863 | 2.76057 | ||||||||
\(357\) | −1.34601 | − | 2.33136i | −0.0712384 | − | 0.123389i | ||||
\(358\) | −24.7784 | − | 42.9175i | −1.30958 | − | 2.26826i | ||||
\(359\) | −26.0790 | −1.37640 | −0.688200 | − | 0.725521i | \(-0.741599\pi\) | ||||
−0.688200 | + | 0.725521i | \(0.741599\pi\) | |||||||
\(360\) | 4.58426 | + | 7.94017i | 0.241612 | + | 0.418484i | ||||
\(361\) | 9.21648 | − | 15.9634i | 0.485078 | − | 0.840180i | ||||
\(362\) | 4.89062 | − | 8.47080i | 0.257045 | − | 0.445215i | ||||
\(363\) | 2.52111 | 0.132324 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.9890 | −0.575190 | ||||||||
\(366\) | −4.60776 | + | 7.98088i | −0.240851 | + | 0.417167i | ||||
\(367\) | −4.78717 | + | 8.29162i | −0.249888 | + | 0.432819i | −0.963495 | − | 0.267728i | \(-0.913727\pi\) |
0.713606 | + | 0.700547i | \(0.247061\pi\) | |||||||
\(368\) | −37.5637 | − | 65.0623i | −1.95815 | − | 3.39161i | ||||
\(369\) | 4.91185 | 0.255701 | ||||||||
\(370\) | 8.12242 | + | 14.0685i | 0.422265 | + | 0.731384i | ||||
\(371\) | 2.10388 | + | 3.64402i | 0.109228 | + | 0.189188i | ||||
\(372\) | 49.9288 | 2.58869 | ||||||||
\(373\) | −14.0749 | − | 24.3784i | −0.728769 | − | 1.26227i | −0.957404 | − | 0.288753i | \(-0.906759\pi\) |
0.228635 | − | 0.973512i | \(-0.426574\pi\) | |||||||
\(374\) | 19.0124 | − | 32.9304i | 0.983107 | − | 1.70279i | ||||
\(375\) | 4.66756 | − | 8.08446i | 0.241032 | − | 0.417480i | ||||
\(376\) | 6.58211 | 0.339446 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.49396 | −0.0768410 | ||||||||
\(379\) | −8.02326 | + | 13.8967i | −0.412127 | + | 0.713825i | −0.995122 | − | 0.0986504i | \(-0.968547\pi\) |
0.582995 | + | 0.812476i | \(0.301881\pi\) | |||||||
\(380\) | −2.07218 | + | 3.58912i | −0.106301 | + | 0.184118i | ||||
\(381\) | −2.24094 | − | 3.88142i | −0.114807 | − | 0.198851i | ||||
\(382\) | −57.0122 | −2.91700 | ||||||||
\(383\) | 12.3083 | + | 21.3186i | 0.628923 | + | 1.08933i | 0.987768 | + | 0.155930i | \(0.0498374\pi\) |
−0.358845 | + | 0.933397i | \(0.616829\pi\) | |||||||
\(384\) | 11.1136 | + | 19.2493i | 0.567137 | + | 0.982310i | ||||
\(385\) | −1.69501 | −0.0863855 | ||||||||
\(386\) | 23.7048 | + | 41.0580i | 1.20654 | + | 2.08980i | ||||
\(387\) | 5.54892 | − | 9.61101i | 0.282067 | − | 0.488555i | ||||
\(388\) | −44.7926 | + | 77.5831i | −2.27400 | + | 3.93868i | ||||
\(389\) | −17.2198 | −0.873080 | −0.436540 | − | 0.899685i | \(-0.643796\pi\) | ||||
−0.436540 | + | 0.899685i | \(0.643796\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.9541 | −1.41370 | ||||||||
\(392\) | 29.2473 | − | 50.6578i | 1.47721 | − | 2.55860i | ||||
\(393\) | −4.60872 | + | 7.98254i | −0.232479 | + | 0.402666i | ||||
\(394\) | 6.27575 | + | 10.8699i | 0.316168 | + | 0.547619i | ||||
\(395\) | −1.40044 | −0.0704636 | ||||||||
\(396\) | −7.63922 | − | 13.2315i | −0.383885 | − | 0.664909i | ||||
\(397\) | 1.01961 | + | 1.76602i | 0.0511730 | + | 0.0886342i | 0.890477 | − | 0.455028i | \(-0.150371\pi\) |
−0.839304 | + | 0.543662i | \(0.817037\pi\) | |||||||
\(398\) | 40.4795 | 2.02905 | ||||||||
\(399\) | −0.208947 | − | 0.361908i | −0.0104605 | − | 0.0181180i | ||||
\(400\) | 25.4203 | − | 44.0293i | 1.27102 | − | 2.20147i | ||||
\(401\) | 0.730718 | − | 1.26564i | 0.0364903 | − | 0.0632031i | −0.847203 | − | 0.531269i | \(-0.821716\pi\) |
0.883694 | + | 0.468065i | \(0.155049\pi\) | |||||||
\(402\) | 5.04115 | 0.251430 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 38.4239 | 1.91166 | ||||||||
\(405\) | 0.524459 | − | 0.908389i | 0.0260606 | − | 0.0451382i | ||||
\(406\) | 1.42812 | − | 2.47357i | 0.0708762 | − | 0.122761i | ||||
\(407\) | −8.37598 | − | 14.5076i | −0.415182 | − | 0.719116i | ||||
\(408\) | 42.4010 | 2.09916 | ||||||||
\(409\) | 14.9695 | + | 25.9279i | 0.740194 | + | 1.28205i | 0.952407 | + | 0.304830i | \(0.0985998\pi\) |
−0.212213 | + | 0.977224i | \(0.568067\pi\) | |||||||
\(410\) | 6.93482 | + | 12.0115i | 0.342486 | + | 0.593204i | ||||
\(411\) | 7.46980 | 0.368458 | ||||||||
\(412\) | 11.0707 | + | 19.1750i | 0.545414 | + | 0.944684i | ||||
\(413\) | −1.13706 | + | 1.96945i | −0.0559512 | + | 0.0969104i | ||||
\(414\) | −7.75667 | + | 13.4349i | −0.381219 | + | 0.660291i | ||||
\(415\) | −2.77240 | −0.136092 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.9976 | 0.881347 | ||||||||
\(418\) | 2.95138 | − | 5.11194i | 0.144357 | − | 0.250033i | ||||
\(419\) | −3.32371 | + | 5.75683i | −0.162374 | + | 0.281240i | −0.935720 | − | 0.352745i | \(-0.885248\pi\) |
0.773346 | + | 0.633984i | \(0.218582\pi\) | |||||||
\(420\) | −1.52715 | − | 2.64510i | −0.0745171 | − | 0.129067i | ||||
\(421\) | 13.5646 | 0.661100 | 0.330550 | − | 0.943788i | \(-0.392766\pi\) | ||||
0.330550 | + | 0.943788i | \(0.392766\pi\) | |||||||
\(422\) | 0.619309 | + | 1.07268i | 0.0301475 | + | 0.0522170i | ||||
\(423\) | −0.376510 | − | 0.652135i | −0.0183066 | − | 0.0317079i | ||||
\(424\) | −66.2747 | −3.21858 | ||||||||
\(425\) | −9.45862 | − | 16.3828i | −0.458810 | − | 0.794683i | ||||
\(426\) | −14.1380 | + | 24.4878i | −0.684989 | + | 1.18644i | ||||
\(427\) | 0.949886 | − | 1.64525i | 0.0459682 | − | 0.0796193i | ||||
\(428\) | 33.5478 | 1.62159 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 31.3370 | 1.51121 | ||||||||
\(431\) | −17.9731 | + | 31.1304i | −0.865736 | + | 1.49950i | 0.000578325 | 1.00000i | \(0.499816\pi\) | |
−0.866314 | + | 0.499499i | \(0.833517\pi\) | |||||||
\(432\) | 6.51842 | − | 11.2902i | 0.313618 | − | 0.543201i | ||||
\(433\) | 16.2371 | + | 28.1234i | 0.780303 | + | 1.35152i | 0.931765 | + | 0.363061i | \(0.118268\pi\) |
−0.151462 | + | 0.988463i | \(0.548398\pi\) | |||||||
\(434\) | −14.2161 | −0.682395 | ||||||||
\(435\) | 1.00269 | + | 1.73671i | 0.0480752 | + | 0.0832687i | ||||
\(436\) | 9.07756 | + | 15.7228i | 0.434736 | + | 0.752985i | ||||
\(437\) | −4.33944 | −0.207583 | ||||||||
\(438\) | 14.1015 | + | 24.4245i | 0.673795 | + | 1.16705i | ||||
\(439\) | −6.41603 | + | 11.1129i | −0.306221 | + | 0.530390i | −0.977532 | − | 0.210785i | \(-0.932398\pi\) |
0.671312 | + | 0.741175i | \(0.265731\pi\) | |||||||
\(440\) | 13.3487 | − | 23.1206i | 0.636374 | − | 1.10223i | ||||
\(441\) | −6.69202 | −0.318668 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.9608 | 0.568273 | 0.284137 | − | 0.958784i | \(-0.408293\pi\) | ||||
0.284137 | + | 0.958784i | \(0.408293\pi\) | |||||||
\(444\) | 15.0930 | − | 26.1418i | 0.716282 | − | 1.24064i | ||||
\(445\) | 5.20626 | − | 9.01751i | 0.246800 | − | 0.427471i | ||||
\(446\) | 22.0075 | + | 38.1182i | 1.04209 | + | 1.80495i | ||||
\(447\) | −15.3351 | −0.725327 | ||||||||
\(448\) | −5.92208 | − | 10.2573i | −0.279792 | − | 0.484614i | ||||
\(449\) | 6.23945 | + | 10.8070i | 0.294458 | + | 0.510016i | 0.974859 | − | 0.222824i | \(-0.0715277\pi\) |
−0.680401 | + | 0.732840i | \(0.738194\pi\) | |||||||
\(450\) | −10.4983 | −0.494893 | ||||||||
\(451\) | −7.15130 | − | 12.3864i | −0.336742 | − | 0.583254i | ||||
\(452\) | −24.5477 | + | 42.5179i | −1.15463 | + | 1.99987i | ||||
\(453\) | 1.26540 | − | 2.19173i | 0.0594536 | − | 0.102977i | ||||
\(454\) | 17.6606 | 0.828851 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.58211 | 0.308235 | ||||||||
\(457\) | −16.2262 | + | 28.1045i | −0.759028 | + | 1.31468i | 0.184319 | + | 0.982867i | \(0.440992\pi\) |
−0.943347 | + | 0.331809i | \(0.892341\pi\) | |||||||
\(458\) | 5.32400 | − | 9.22144i | 0.248774 | − | 0.430890i | ||||
\(459\) | −2.42543 | − | 4.20096i | −0.113209 | − | 0.196084i | ||||
\(460\) | −31.7159 | −1.47876 | ||||||||
\(461\) | −12.2017 | − | 21.1340i | −0.568290 | − | 0.984308i | −0.996735 | − | 0.0807398i | \(-0.974272\pi\) |
0.428445 | − | 0.903568i | \(-0.359062\pi\) | |||||||
\(462\) | 2.17510 | + | 3.76738i | 0.101195 | + | 0.175274i | ||||
\(463\) | −33.1836 | −1.54217 | −0.771086 | − | 0.636731i | \(-0.780286\pi\) | ||||
−0.771086 | + | 0.636731i | \(0.780286\pi\) | |||||||
\(464\) | 12.4623 | + | 21.5853i | 0.578546 | + | 1.00207i | ||||
\(465\) | 4.99061 | − | 8.64398i | 0.231434 | − | 0.400855i | ||||
\(466\) | −11.2485 | + | 19.4829i | −0.521075 | + | 0.902529i | ||||
\(467\) | −38.5206 | −1.78252 | −0.891261 | − | 0.453490i | \(-0.850179\pi\) | ||||
−0.891261 | + | 0.453490i | \(0.850179\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.03923 | −0.0479871 | ||||||||
\(470\) | 1.06315 | − | 1.84144i | 0.0490397 | − | 0.0849392i | ||||
\(471\) | 8.61960 | − | 14.9296i | 0.397170 | − | 0.687919i | ||||
\(472\) | −17.9095 | − | 31.0201i | −0.824350 | − | 1.42782i | ||||
\(473\) | −32.3153 | −1.48586 | ||||||||
\(474\) | 1.79709 | + | 3.11266i | 0.0825432 | + | 0.142969i | ||||
\(475\) | −1.46830 | − | 2.54318i | −0.0673704 | − | 0.116689i | ||||
\(476\) | −14.1250 | −0.647417 | ||||||||
\(477\) | 3.79105 | + | 6.56630i | 0.173580 | + | 0.300650i | ||||
\(478\) | −27.0559 | + | 46.8622i | −1.23751 | + | 2.14343i | ||||
\(479\) | 4.17241 | − | 7.22682i | 0.190642 | − | 0.330202i | −0.754821 | − | 0.655931i | \(-0.772276\pi\) |
0.945463 | + | 0.325729i | \(0.105610\pi\) | |||||||
\(480\) | 18.4752 | 0.843272 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −51.1825 | −2.33130 | ||||||||
\(483\) | 1.59903 | − | 2.76960i | 0.0727584 | − | 0.126021i | ||||
\(484\) | 6.61410 | − | 11.4560i | 0.300641 | − | 0.520725i | ||||
\(485\) | 8.95444 | + | 15.5095i | 0.406600 | + | 0.704252i | ||||
\(486\) | −2.69202 | −0.122113 | ||||||||
\(487\) | 7.42931 | + | 12.8679i | 0.336654 | + | 0.583102i | 0.983801 | − | 0.179263i | \(-0.0573713\pi\) |
−0.647147 | + | 0.762365i | \(0.724038\pi\) | |||||||
\(488\) | 14.9613 | + | 25.9137i | 0.677266 | + | 1.17306i | ||||
\(489\) | −15.7071 | −0.710299 | ||||||||
\(490\) | −9.44816 | − | 16.3647i | −0.426824 | − | 0.739281i | ||||
\(491\) | −2.49947 | + | 4.32920i | −0.112799 | + | 0.195374i | −0.916898 | − | 0.399122i | \(-0.869315\pi\) |
0.804099 | + | 0.594496i | \(0.202648\pi\) | |||||||
\(492\) | 12.8862 | − | 22.3196i | 0.580955 | − | 1.00624i | ||||
\(493\) | 9.27413 | 0.417686 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.05429 | −0.137280 | ||||||||
\(496\) | 62.0275 | − | 107.435i | 2.78512 | − | 4.82396i | ||||
\(497\) | 2.91454 | − | 5.04814i | 0.130735 | − | 0.226440i | ||||
\(498\) | 3.55765 | + | 6.16202i | 0.159422 | + | 0.276127i | ||||
\(499\) | −0.385371 | −0.0172516 | −0.00862579 | − | 0.999963i | \(-0.502746\pi\) | ||||
−0.00862579 | + | 0.999963i | \(0.502746\pi\) | |||||||
\(500\) | −24.4906 | − | 42.4190i | −1.09525 | − | 1.89703i | ||||
\(501\) | 2.69806 | + | 4.67318i | 0.120541 | + | 0.208782i | ||||
\(502\) | −2.05610 | −0.0917681 | ||||||||
\(503\) | −11.3089 | − | 19.5877i | −0.504241 | − | 0.873370i | −0.999988 | − | 0.00490359i | \(-0.998439\pi\) |
0.495747 | − | 0.868467i | \(-0.334894\pi\) | |||||||
\(504\) | −2.42543 | + | 4.20096i | −0.108037 | + | 0.187126i | ||||
\(505\) | 3.84063 | − | 6.65217i | 0.170906 | − | 0.296018i | ||||
\(506\) | 45.1726 | 2.00817 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −23.5163 | −1.04337 | ||||||||
\(509\) | 5.80194 | − | 10.0493i | 0.257166 | − | 0.445425i | −0.708315 | − | 0.705896i | \(-0.750544\pi\) |
0.965482 | + | 0.260471i | \(0.0838778\pi\) | |||||||
\(510\) | 6.84870 | − | 11.8623i | 0.303265 | − | 0.525271i | ||||
\(511\) | −2.90701 | − | 5.03509i | −0.128599 | − | 0.222739i | ||||
\(512\) | 1.71678 | 0.0758715 | ||||||||
\(513\) | −0.376510 | − | 0.652135i | −0.0166233 | − | 0.0287925i | ||||
\(514\) | 17.6208 | + | 30.5201i | 0.777220 | + | 1.34618i | ||||
\(515\) | 4.42626 | 0.195044 | ||||||||
\(516\) | −29.1151 | − | 50.4288i | −1.28172 | − | 2.22000i | ||||
\(517\) | −1.09634 | + | 1.89892i | −0.0482171 | + | 0.0835145i | ||||
\(518\) | −4.29739 | + | 7.44330i | −0.188816 | + | 0.327040i | ||||
\(519\) | −23.9420 | −1.05094 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.62671 | −0.0712675 | −0.0356337 | − | 0.999365i | \(-0.511345\pi\) | ||||
−0.0356337 | + | 0.999365i | \(0.511345\pi\) | |||||||
\(522\) | 2.57338 | − | 4.45722i | 0.112634 | − | 0.195087i | ||||
\(523\) | −5.03588 | + | 8.72239i | −0.220203 | + | 0.381404i | −0.954870 | − | 0.297025i | \(-0.904005\pi\) |
0.734666 | + | 0.678429i | \(0.237339\pi\) | |||||||
\(524\) | 24.1819 | + | 41.8842i | 1.05639 | + | 1.82972i | ||||
\(525\) | 2.16421 | 0.0944539 | ||||||||
\(526\) | −24.7361 | − | 42.8442i | −1.07854 | − | 1.86809i | ||||
\(527\) | −23.0797 | − | 39.9752i | −1.00537 | − | 1.74135i | ||||
\(528\) | −37.9614 | −1.65206 | ||||||||
\(529\) | −5.10441 | − | 8.84109i | −0.221931 | − | 0.384395i | ||||
\(530\) | −10.7048 | + | 18.5413i | −0.464988 | + | 0.805383i | ||||
\(531\) | −2.04892 | + | 3.54883i | −0.0889154 | + | 0.154006i | ||||
\(532\) | −2.19269 | −0.0950650 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −26.7235 | −1.15644 | ||||||||
\(535\) | 3.35325 | − | 5.80800i | 0.144974 | − | 0.251102i | ||||
\(536\) | 8.18425 | − | 14.1755i | 0.353506 | − | 0.612290i | ||||
\(537\) | 9.20440 | + | 15.9425i | 0.397199 | + | 0.687969i | ||||
\(538\) | 63.6999 | 2.74630 | ||||||||
\(539\) | 9.74309 | + | 16.8755i | 0.419665 | + | 0.726881i | ||||
\(540\) | −2.75182 | − | 4.76630i | −0.118420 | − | 0.205109i | ||||
\(541\) | −20.4674 | −0.879962 | −0.439981 | − | 0.898007i | \(-0.645015\pi\) | ||||
−0.439981 | + | 0.898007i | \(0.645015\pi\) | |||||||
\(542\) | 26.5878 | + | 46.0514i | 1.14204 | + | 1.97808i | ||||
\(543\) | −1.81671 | + | 3.14663i | −0.0779624 | + | 0.135035i | ||||
\(544\) | 42.7204 | − | 73.9939i | 1.83162 | − | 3.17246i | ||||
\(545\) | 3.62937 | 0.155465 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.5478 | −1.17786 | −0.588929 | − | 0.808185i | \(-0.700450\pi\) | ||||
−0.588929 | + | 0.808185i | \(0.700450\pi\) | |||||||
\(548\) | 19.5969 | − | 33.9429i | 0.837140 | − | 1.44997i | ||||
\(549\) | 1.71164 | − | 2.96464i | 0.0730508 | − | 0.126528i | ||||
\(550\) | 15.2847 | + | 26.4739i | 0.651742 | + | 1.12885i | ||||
\(551\) | 1.43967 | 0.0613318 | ||||||||
\(552\) | 25.1857 | + | 43.6230i | 1.07198 | + | 1.85672i | ||||
\(553\) | −0.370469 | − | 0.641672i | −0.0157540 | − | 0.0272867i | ||||
\(554\) | 4.78581 | 0.203329 | ||||||||
\(555\) | −3.01722 | − | 5.22598i | −0.128074 | − | 0.221831i | ||||
\(556\) | 47.2165 | − | 81.7814i | 2.00243 | − | 3.46831i | ||||
\(557\) | −18.9928 | + | 32.8964i | −0.804749 | + | 1.39387i | 0.111711 | + | 0.993741i | \(0.464367\pi\) |
−0.916460 | + | 0.400126i | \(0.868966\pi\) | |||||||
\(558\) | −25.6165 | −1.08443 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −7.58881 | −0.320686 | ||||||||
\(561\) | −7.06249 | + | 12.2326i | −0.298179 | + | 0.516460i | ||||
\(562\) | −2.18233 | + | 3.77991i | −0.0920562 | + | 0.159446i | ||||
\(563\) | 14.8862 | + | 25.7837i | 0.627378 | + | 1.08665i | 0.988076 | + | 0.153968i | \(0.0492054\pi\) |
−0.360697 | + | 0.932683i | \(0.617461\pi\) | |||||||
\(564\) | −3.95108 | −0.166371 | ||||||||
\(565\) | 4.90731 | + | 8.49970i | 0.206452 | + | 0.357585i | ||||
\(566\) | −6.70799 | − | 11.6186i | −0.281958 | − | 0.488365i | ||||
\(567\) | 0.554958 | 0.0233061 | ||||||||
\(568\) | 45.9059 | + | 79.5113i | 1.92617 | + | 3.33622i | ||||
\(569\) | 10.9770 | − | 19.0128i | 0.460181 | − | 0.797057i | −0.538788 | − | 0.842441i | \(-0.681118\pi\) |
0.998970 | + | 0.0453839i | \(0.0144511\pi\) | |||||||
\(570\) | 1.06315 | − | 1.84144i | 0.0445307 | − | 0.0771294i | ||||
\(571\) | 2.46575 | 0.103188 | 0.0515942 | − | 0.998668i | \(-0.483570\pi\) | ||||
0.0515942 | + | 0.998668i | \(0.483570\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.1782 | 0.884732 | ||||||||
\(574\) | −3.66905 | + | 6.35499i | −0.153143 | + | 0.265252i | ||||
\(575\) | 11.2366 | − | 19.4624i | 0.468600 | − | 0.811639i | ||||
\(576\) | −10.6712 | − | 18.4831i | −0.444634 | − | 0.770128i | ||||
\(577\) | 17.4547 | 0.726650 | 0.363325 | − | 0.931662i | \(-0.381641\pi\) | ||||
0.363325 | + | 0.931662i | \(0.381641\pi\) | |||||||
\(578\) | −8.79052 | − | 15.2256i | −0.365637 | − | 0.633303i | ||||
\(579\) | −8.80559 | − | 15.2517i | −0.365948 | − | 0.633840i | ||||
\(580\) | 10.5222 | 0.436909 | ||||||||
\(581\) | −0.733406 | − | 1.27030i | −0.0304268 | − | 0.0527008i | ||||
\(582\) | 22.9813 | − | 39.8049i | 0.952607 | − | 1.64996i | ||||
\(583\) | 11.0390 | − | 19.1201i | 0.457188 | − | 0.791873i | ||||
\(584\) | 91.5745 | 3.78938 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.193159 | −0.00797934 | ||||||||
\(587\) | −3.13169 | + | 5.42424i | −0.129259 | + | 0.223882i | −0.923390 | − | 0.383864i | \(-0.874593\pi\) |
0.794131 | + | 0.607747i | \(0.207926\pi\) | |||||||
\(588\) | −17.5565 | + | 30.4087i | −0.724016 | + | 1.25403i | ||||
\(589\) | −3.58277 | − | 6.20554i | −0.147625 | − | 0.255695i | ||||
\(590\) | −11.5711 | −0.476374 | ||||||||
\(591\) | −2.33124 | − | 4.03783i | −0.0958944 | − | 0.166094i | ||||
\(592\) | −37.5006 | − | 64.9529i | −1.54126 | − | 2.66955i | ||||
\(593\) | 22.8745 | 0.939345 | 0.469672 | − | 0.882841i | \(-0.344372\pi\) | ||||
0.469672 | + | 0.882841i | \(0.344372\pi\) | |||||||
\(594\) | 3.91939 | + | 6.78858i | 0.160814 | + | 0.278539i | ||||
\(595\) | −1.41185 | + | 2.44540i | −0.0578804 | + | 0.100252i | ||||
\(596\) | −40.2315 | + | 69.6831i | −1.64795 | + | 2.85433i | ||||
\(597\) | −15.0368 | −0.615417 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.05621 | −0.0431557 | −0.0215778 | − | 0.999767i | \(-0.506869\pi\) | ||||
−0.0215778 | + | 0.999767i | \(0.506869\pi\) | |||||||
\(600\) | −17.0438 | + | 29.5208i | −0.695812 | + | 1.20518i | ||||
\(601\) | 16.6618 | − | 28.8591i | 0.679650 | − | 1.17719i | −0.295437 | − | 0.955362i | \(-0.595465\pi\) |
0.975086 | − | 0.221826i | \(-0.0712015\pi\) | |||||||
\(602\) | 8.28986 | + | 14.3585i | 0.337869 | + | 0.585207i | ||||
\(603\) | −1.87263 | −0.0762592 | ||||||||
\(604\) | −6.63951 | − | 11.5000i | −0.270158 | − | 0.467927i | ||||
\(605\) | −1.32222 | − | 2.29015i | −0.0537557 | − | 0.0931076i | ||||
\(606\) | −19.7138 | −0.800818 | ||||||||
\(607\) | −8.12014 | − | 14.0645i | −0.329586 | − | 0.570860i | 0.652844 | − | 0.757493i | \(-0.273576\pi\) |
−0.982430 | + | 0.186633i | \(0.940243\pi\) | |||||||
\(608\) | 6.63169 | − | 11.4864i | 0.268950 | − | 0.465836i | ||||
\(609\) | −0.530499 | + | 0.918852i | −0.0214969 | + | 0.0372338i | ||||
\(610\) | 9.66632 | 0.391378 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −25.4523 | −1.02885 | ||||||||
\(613\) | −5.52393 | + | 9.56772i | −0.223109 | + | 0.386437i | −0.955751 | − | 0.294178i | \(-0.904954\pi\) |
0.732641 | + | 0.680615i | \(0.238287\pi\) | |||||||
\(614\) | 6.99665 | − | 12.1185i | 0.282362 | − | 0.489065i | ||||
\(615\) | −2.57606 | − | 4.46187i | −0.103877 | − | 0.179920i | ||||
\(616\) | 14.1250 | 0.569112 | ||||||||
\(617\) | 2.32975 | + | 4.03524i | 0.0937922 | + | 0.162453i | 0.909104 | − | 0.416570i | \(-0.136768\pi\) |
−0.815312 | + | 0.579022i | \(0.803434\pi\) | |||||||
\(618\) | −5.67994 | − | 9.83794i | −0.228481 | − | 0.395740i | ||||
\(619\) | 31.9259 | 1.28321 | 0.641604 | − | 0.767036i | \(-0.278269\pi\) | ||||
0.641604 | + | 0.767036i | \(0.278269\pi\) | |||||||
\(620\) | −26.1856 | − | 45.3548i | −1.05164 | − | 1.82149i | ||||
\(621\) | 2.88135 | − | 4.99065i | 0.115625 | − | 0.200268i | ||||
\(622\) | 30.3430 | − | 52.5555i | 1.21664 | − | 2.10729i | ||||
\(623\) | 5.50902 | 0.220714 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.70709 | 0.388283 | ||||||||
\(626\) | −30.5022 | + | 52.8313i | −1.21911 | + | 2.11156i | ||||
\(627\) | −1.09634 | + | 1.89892i | −0.0437837 | + | 0.0758356i | ||||
\(628\) | −45.2269 | − | 78.3353i | −1.80475 | − | 3.12592i | ||||
\(629\) | −27.9071 | −1.11273 | ||||||||
\(630\) | 0.783520 | + | 1.35710i | 0.0312162 | + | 0.0540680i | ||||
\(631\) | 19.7207 | + | 34.1572i | 0.785067 | + | 1.35978i | 0.928959 | + | 0.370183i | \(0.120705\pi\) |
−0.143892 | + | 0.989593i | \(0.545962\pi\) | |||||||
\(632\) | 11.6703 | 0.464218 | ||||||||
\(633\) | −0.230054 | − | 0.398465i | −0.00914381 | − | 0.0158375i | ||||
\(634\) | −35.4572 | + | 61.4136i | −1.40818 | + | 2.43905i | ||||
\(635\) | −2.35056 | + | 4.07129i | −0.0932791 | + | 0.161564i | ||||
\(636\) | 39.7832 | 1.57750 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.9866 | −0.593325 | ||||||||
\(639\) | 5.25182 | − | 9.09643i | 0.207759 | − | 0.359849i | ||||
\(640\) | 11.6572 | − | 20.1909i | 0.460792 | − | 0.798115i | ||||
\(641\) | −22.7255 | − | 39.3617i | −0.897603 | − | 1.55469i | −0.830549 | − | 0.556946i | \(-0.811973\pi\) |
−0.0670544 | − | 0.997749i | \(-0.521360\pi\) | |||||||
\(642\) | −17.2121 | −0.679306 | ||||||||
\(643\) | 14.8735 | + | 25.7616i | 0.586552 | + | 1.01594i | 0.994680 | + | 0.103013i | \(0.0328483\pi\) |
−0.408128 | + | 0.912925i | \(0.633818\pi\) | |||||||
\(644\) | −8.39008 | − | 14.5321i | −0.330616 | − | 0.572643i | ||||
\(645\) | −11.6407 | −0.458353 | ||||||||
\(646\) | −4.91670 | − | 8.51597i | −0.193445 | − | 0.335056i | ||||
\(647\) | 8.46562 | − | 14.6629i | 0.332818 | − | 0.576457i | −0.650245 | − | 0.759724i | \(-0.725334\pi\) |
0.983063 | + | 0.183267i | \(0.0586673\pi\) | |||||||
\(648\) | −4.37047 | + | 7.56988i | −0.171688 | + | 0.297373i | ||||
\(649\) | 11.9323 | 0.468384 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.28083 | 0.206972 | ||||||||
\(652\) | −41.2074 | + | 71.3733i | −1.61381 | + | 2.79519i | ||||
\(653\) | 16.5988 | − | 28.7500i | 0.649561 | − | 1.12507i | −0.333667 | − | 0.942691i | \(-0.608286\pi\) |
0.983228 | − | 0.182382i | \(-0.0583806\pi\) | |||||||
\(654\) | −4.65734 | − | 8.06675i | −0.182116 | − | 0.315435i | ||||
\(655\) | 9.66833 | 0.377773 | ||||||||
\(656\) | −32.0175 | − | 55.4560i | −1.25007 | − | 2.16519i | ||||
\(657\) | −5.23825 | − | 9.07292i | −0.204364 | − | 0.353968i | ||||
\(658\) | 1.12498 | 0.0438564 | ||||||||
\(659\) | 21.3286 | + | 36.9421i | 0.830842 | + | 1.43906i | 0.897371 | + | 0.441277i | \(0.145474\pi\) |
−0.0665286 | + | 0.997785i | \(0.521192\pi\) | |||||||
\(660\) | −8.01291 | + | 13.8788i | −0.311902 | + | 0.540230i | ||||
\(661\) | −19.3451 | + | 33.5067i | −0.752438 | + | 1.30326i | 0.194201 | + | 0.980962i | \(0.437789\pi\) |
−0.946638 | + | 0.322298i | \(0.895545\pi\) | |||||||
\(662\) | −30.2301 | −1.17493 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 23.1032 | 0.896578 | ||||||||
\(665\) | −0.219169 | + | 0.379611i | −0.00849899 | + | 0.0147207i | ||||
\(666\) | −7.74363 | + | 13.4124i | −0.300059 | + | 0.519718i | ||||
\(667\) | 5.50873 | + | 9.54140i | 0.213299 | + | 0.369444i | ||||
\(668\) | 28.3134 | 1.09548 | ||||||||
\(669\) | −8.17510 | − | 14.1597i | −0.316067 | − | 0.547445i | ||||
\(670\) | −2.64387 | − | 4.57932i | −0.102142 | − | 0.176915i | ||||
\(671\) | −9.96807 | −0.384813 | ||||||||
\(672\) | 4.88740 | + | 8.46522i | 0.188535 | + | 0.326553i | ||||
\(673\) | 1.29709 | − | 2.24663i | 0.0499993 | − | 0.0866013i | −0.839943 | − | 0.542675i | \(-0.817411\pi\) |
0.889942 | + | 0.456074i | \(0.150745\pi\) | |||||||
\(674\) | −3.10656 | + | 5.38073i | −0.119660 | + | 0.207258i | ||||
\(675\) | 3.89977 | 0.150102 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.75302 | 0.0673740 | 0.0336870 | − | 0.999432i | \(-0.489275\pi\) | ||||
0.0336870 | + | 0.999432i | \(0.489275\pi\) | |||||||
\(678\) | 12.5945 | − | 21.8143i | 0.483688 | − | 0.837773i | ||||
\(679\) | −4.73759 | + | 8.20574i | −0.181812 | + | 0.314907i | ||||
\(680\) | −22.2376 | − | 38.5166i | −0.852773 | − | 1.47705i | ||||
\(681\) | −6.56033 | −0.251393 | ||||||||
\(682\) | 37.2958 | + | 64.5983i | 1.42813 | + | 2.47360i | ||||
\(683\) | −8.16756 | − | 14.1466i | −0.312523 | − | 0.541306i | 0.666385 | − | 0.745608i | \(-0.267841\pi\) |
−0.978908 | + | 0.204302i | \(0.934508\pi\) | |||||||
\(684\) | −3.95108 | −0.151073 | ||||||||
\(685\) | −3.91760 | − | 6.78548i | −0.149684 | − | 0.259260i | ||||
\(686\) | 10.2277 | − | 17.7148i | 0.390494 | − | 0.676355i | ||||
\(687\) | −1.97770 | + | 3.42547i | −0.0754539 | + | 0.130690i | ||||
\(688\) | −144.681 | −5.51590 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 16.2722 | 0.619472 | ||||||||
\(691\) | −7.95526 | + | 13.7789i | −0.302632 | + | 0.524175i | −0.976731 | − | 0.214466i | \(-0.931199\pi\) |
0.674099 | + | 0.738641i | \(0.264532\pi\) | |||||||
\(692\) | −62.8116 | + | 108.793i | −2.38774 | + | 4.13568i | ||||
\(693\) | −0.807979 | − | 1.39946i | −0.0306926 | − | 0.0531611i | ||||
\(694\) | −24.5972 | −0.933696 | ||||||||
\(695\) | −9.43900 | − | 16.3488i | −0.358042 | − | 0.620146i | ||||
\(696\) | −8.35570 | − | 14.4725i | −0.316722 | − | 0.548579i | ||||
\(697\) | −23.8267 | −0.902500 | ||||||||
\(698\) | −32.2717 | − | 55.8963i | −1.22150 | − | 2.11571i | ||||
\(699\) | 4.17845 | − | 7.23728i | 0.158043 | − | 0.273739i | ||||
\(700\) | 5.67778 | − | 9.83421i | 0.214600 | − | 0.371698i | ||||
\(701\) | −20.8635 | −0.788005 | −0.394002 | − | 0.919109i | \(-0.628910\pi\) | ||||
−0.394002 | + | 0.919109i | \(0.628910\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.33214 | −0.163390 | ||||||||
\(704\) | −31.0730 | + | 53.8200i | −1.17111 | + | 2.02842i | ||||
\(705\) | −0.394928 | + | 0.684035i | −0.0148739 | + | 0.0257623i | ||||
\(706\) | 36.5091 | + | 63.2356i | 1.37404 | + | 2.37990i | ||||
\(707\) | 4.06398 | 0.152842 | ||||||||
\(708\) | 10.7506 | + | 18.6206i | 0.404033 | + | 0.699806i | ||||
\(709\) | −7.82424 | − | 13.5520i | −0.293846 | − | 0.508955i | 0.680870 | − | 0.732404i | \(-0.261602\pi\) |
−0.974716 | + | 0.223449i | \(0.928268\pi\) | |||||||
\(710\) | 29.6592 | 1.11309 | ||||||||
\(711\) | −0.667563 | − | 1.15625i | −0.0250356 | − | 0.0433629i | ||||
\(712\) | −43.3853 | + | 75.1455i | −1.62593 | + | 2.81620i | ||||
\(713\) | 27.4182 | − | 47.4897i | 1.02682 | − | 1.77850i | ||||
\(714\) | 7.24698 | 0.271211 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 96.5906 | 3.60976 | ||||||||
\(717\) | 10.0504 | − | 17.4078i | 0.375339 | − | 0.650107i | ||||
\(718\) | 35.1027 | − | 60.7996i | 1.31002 | − | 2.26902i | ||||
\(719\) | 13.5797 | + | 23.5208i | 0.506438 | + | 0.877176i | 0.999972 | + | 0.00744977i | \(0.00237136\pi\) |
−0.493534 | + | 0.869726i | \(0.664295\pi\) | |||||||
\(720\) | −13.6746 | −0.509621 | ||||||||
\(721\) | 1.17092 | + | 2.02808i | 0.0436072 | + | 0.0755298i | ||||
\(722\) | 24.8110 | + | 42.9738i | 0.923368 | + | 1.59932i | ||||
\(723\) | 19.0127 | 0.707089 | ||||||||
\(724\) | 9.53223 | + | 16.5103i | 0.354262 | + | 0.613601i | ||||
\(725\) | −3.72790 | + | 6.45691i | −0.138451 | + | 0.239804i | ||||
\(726\) | −3.39344 | + | 5.87760i | −0.125942 | + | 0.218138i | ||||
\(727\) | 31.7784 | 1.17859 | 0.589297 | − | 0.807916i | \(-0.299405\pi\) | ||||
0.589297 | + | 0.807916i | \(0.299405\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.7913 | − | 25.6193i | 0.547450 | − | 0.948212i | ||||
\(731\) | −26.9170 | + | 46.6216i | −0.995561 | + | 1.72436i | ||||
\(732\) | −8.98092 | − | 15.5554i | −0.331944 | − | 0.574944i | ||||
\(733\) | 46.8907 | 1.73195 | 0.865973 | − | 0.500090i | \(-0.166700\pi\) | ||||
0.865973 | + | 0.500090i | \(0.166700\pi\) | |||||||
\(734\) | −12.8872 | − | 22.3212i | −0.475674 | − | 0.823891i | ||||
\(735\) | 3.50969 | + | 6.07896i | 0.129457 | + | 0.224226i | ||||
\(736\) | 101.502 | 3.74141 | ||||||||
\(737\) | 2.72641 | + | 4.72227i | 0.100428 | + | 0.173947i | ||||
\(738\) | −6.61141 | + | 11.4513i | −0.243369 | + | 0.421528i | ||||
\(739\) | −8.52393 | + | 14.7639i | −0.313558 | + | 0.543098i | −0.979130 | − | 0.203236i | \(-0.934854\pi\) |
0.665572 | + | 0.746334i | \(0.268188\pi\) | |||||||
\(740\) | −31.6626 | −1.16394 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.3274 | −0.415840 | ||||||||
\(743\) | 5.81618 | − | 10.0739i | 0.213375 | − | 0.369576i | −0.739394 | − | 0.673273i | \(-0.764888\pi\) |
0.952769 | + | 0.303697i | \(0.0982211\pi\) | |||||||
\(744\) | −41.5882 | + | 72.0329i | −1.52470 | + | 2.64085i | ||||
\(745\) | 8.04264 | + | 13.9303i | 0.294660 | + | 0.510365i | ||||
\(746\) | 75.7797 | 2.77449 | ||||||||
\(747\) | −1.32155 | − | 2.28900i | −0.0483531 | − | 0.0837500i | ||||
\(748\) | 37.0567 | + | 64.1842i | 1.35493 | + | 2.34681i | ||||
\(749\) | 3.54825 | 0.129650 | ||||||||
\(750\) | 12.5652 | + | 21.7635i | 0.458815 | + | 0.794692i | ||||
\(751\) | 6.51477 | − | 11.2839i | 0.237727 | − | 0.411756i | −0.722334 | − | 0.691544i | \(-0.756931\pi\) |
0.960062 | + | 0.279788i | \(0.0902642\pi\) | |||||||
\(752\) | −4.90850 | + | 8.50177i | −0.178995 | + | 0.310028i | ||||
\(753\) | 0.763774 | 0.0278335 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.65459 | −0.0966106 | ||||||||
\(756\) | 1.45593 | − | 2.52174i | 0.0529516 | − | 0.0917148i | ||||
\(757\) | −11.3949 | + | 19.7366i | −0.414156 | + | 0.717339i | −0.995339 | − | 0.0964337i | \(-0.969256\pi\) |
0.581184 | + | 0.813772i | \(0.302590\pi\) | |||||||
\(758\) | −21.5988 | − | 37.4102i | −0.784504 | − | 1.35880i | ||||
\(759\) | −16.7802 | −0.609081 | ||||||||
\(760\) | −3.45204 | − | 5.97911i | −0.125219 | − | 0.216885i | ||||
\(761\) | 19.1712 | + | 33.2055i | 0.694956 | + | 1.20370i | 0.970196 | + | 0.242323i | \(0.0779094\pi\) |
−0.275240 | + | 0.961376i | \(0.588757\pi\) | |||||||
\(762\) | 12.0653 | 0.437080 | ||||||||
\(763\) | 0.960107 | + | 1.66295i | 0.0347582 | + | 0.0602030i | ||||
\(764\) | 55.5608 | − | 96.2342i | 2.01012 | − | 3.48163i | ||||
\(765\) | −2.54407 | + | 4.40646i | −0.0919812 | + | 0.159316i | ||||
\(766\) | −66.2683 | −2.39437 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −17.1511 | −0.618886 | ||||||||
\(769\) | 1.81940 | − | 3.15129i | 0.0656091 | − | 0.113638i | −0.831355 | − | 0.555742i | \(-0.812434\pi\) |
0.896964 | + | 0.442104i | \(0.145768\pi\) | |||||||
\(770\) | 2.28150 | − | 3.95167i | 0.0822194 | − | 0.142408i | ||||
\(771\) | −6.54556 | − | 11.3373i | −0.235733 | − | 0.408301i | ||||
\(772\) | −92.4055 | −3.32575 | ||||||||
\(773\) | 19.6712 | + | 34.0715i | 0.707524 | + | 1.22547i | 0.965773 | + | 0.259389i | \(0.0835213\pi\) |
−0.258249 | + | 0.966079i | \(0.583145\pi\) | |||||||
\(774\) | 14.9378 | + | 25.8730i | 0.536928 | + | 0.929987i | ||||
\(775\) | 37.1092 | 1.33300 | ||||||||
\(776\) | −74.6200 | − | 129.246i | −2.67870 | − | 4.63965i | ||||
\(777\) | 1.59634 | − | 2.76495i | 0.0572685 | − | 0.0991919i | ||||
\(778\) | 23.1781 | − | 40.1456i | 0.830974 | − | 1.43929i | ||||
\(779\) | −3.69873 | −0.132521 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.5851 | −1.09442 | ||||||||
\(782\) | 37.6265 | − | 65.1710i | 1.34552 | − | 2.33051i | ||||
\(783\) | −0.955927 | + | 1.65571i | −0.0341620 | + | 0.0591704i | ||||
\(784\) | 43.6214 | + | 75.5545i | 1.55791 | + | 2.69837i | ||||
\(785\) | −18.0825 | −0.645392 | ||||||||
\(786\) | −12.4068 | − | 21.4892i | −0.442535 | − | 0.766493i | ||||
\(787\) | 12.7126 | + | 22.0189i | 0.453155 | + | 0.784888i | 0.998580 | − | 0.0532720i | \(-0.0169650\pi\) |
−0.545425 | + | 0.838160i | \(0.683632\pi\) | |||||||
\(788\) | −24.4639 | −0.871492 | ||||||||
\(789\) | 9.18867 | + | 15.9152i | 0.327125 | + | 0.566598i | ||||
\(790\) | 1.88500 | − | 3.26492i | 0.0670654 | − | 0.116161i | ||||
\(791\) | −2.59634 | + | 4.49700i | −0.0923153 | + | 0.159895i | ||||
\(792\) | 25.4523 | 0.904409 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −5.48965 | −0.194820 | ||||||||
\(795\) | 3.97650 | − | 6.88750i | 0.141032 | − | 0.244275i | ||||
\(796\) | −39.4490 | + | 68.3276i | −1.39823 | + | 2.42181i | ||||
\(797\) | −10.3569 | − | 17.9387i | −0.366860 | − | 0.635420i | 0.622213 | − | 0.782848i | \(-0.286234\pi\) |
−0.989073 | + | 0.147428i | \(0.952901\pi\) | |||||||
\(798\) | 1.12498 | 0.0398239 | ||||||||
\(799\) | 1.82640 | + | 3.16341i | 0.0646133 | + | 0.111913i | ||||
\(800\) | 34.3444 | + | 59.4863i | 1.21426 | + | 2.10316i | ||||
\(801\) | 9.92692 | 0.350750 | ||||||||
\(802\) | 1.96711 | + | 3.40713i | 0.0694610 | + | 0.120310i | ||||
\(803\) | −15.2530 | + | 26.4190i | −0.538267 | + | 0.932306i | ||||
\(804\) | −4.91281 | + | 8.50924i | −0.173262 | + | 0.300098i | ||||
\(805\) | −3.35450 | −0.118231 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.6625 | −0.832959 | ||||||||
\(808\) | −32.0051 | + | 55.4345i | −1.12594 | + | 1.95018i | ||||
\(809\) | −5.54892 | + | 9.61101i | −0.195090 | + | 0.337905i | −0.946930 | − | 0.321440i | \(-0.895833\pi\) |
0.751840 | + | 0.659345i | \(0.229166\pi\) | |||||||
\(810\) | 1.41185 | + | 2.44540i | 0.0496075 | + | 0.0859227i | ||||
\(811\) | −4.84223 | −0.170034 | −0.0850169 | − | 0.996380i | \(-0.527094\pi\) | ||||
−0.0850169 | + | 0.996380i | \(0.527094\pi\) | |||||||
\(812\) | 2.78352 | + | 4.82120i | 0.0976824 | + | 0.169191i | ||||
\(813\) | −9.87651 | − | 17.1066i | −0.346384 | − | 0.599955i | ||||
\(814\) | 45.0966 | 1.58064 | ||||||||
\(815\) | 8.23772 | + | 14.2681i | 0.288555 | + | 0.499791i | ||||
\(816\) | −31.6199 | + | 54.7673i | −1.10692 | + | 1.91724i | ||||
\(817\) | −4.17845 | + | 7.23728i | −0.146185 | + | 0.253201i | ||||
\(818\) | −80.5964 | −2.81799 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −27.0331 | −0.944037 | ||||||||
\(821\) | 21.8690 | − | 37.8783i | 0.763235 | − | 1.32196i | −0.177940 | − | 0.984041i | \(-0.556943\pi\) |
0.941175 | − | 0.337920i | \(-0.109723\pi\) | |||||||
\(822\) | −10.0544 | + | 17.4148i | −0.350688 | + | 0.607410i | ||||
\(823\) | −6.04988 | − | 10.4787i | −0.210885 | − | 0.365264i | 0.741106 | − | 0.671388i | \(-0.234301\pi\) |
−0.951992 | + | 0.306123i | \(0.900968\pi\) | |||||||
\(824\) | −36.8853 | −1.28496 | ||||||||
\(825\) | −5.67778 | − | 9.83421i | −0.197675 | − | 0.342383i | ||||
\(826\) | −3.06100 | − | 5.30181i | −0.106506 | − | 0.184473i | ||||
\(827\) | −35.3212 | −1.22824 | −0.614120 | − | 0.789213i | \(-0.710489\pi\) | ||||
−0.614120 | + | 0.789213i | \(0.710489\pi\) | |||||||
\(828\) | −15.1184 | − | 26.1859i | −0.525401 | − | 0.910021i | ||||
\(829\) | −26.7473 | + | 46.3276i | −0.928971 | + | 1.60903i | −0.143925 | + | 0.989589i | \(0.545972\pi\) |
−0.785047 | + | 0.619437i | \(0.787361\pi\) | |||||||
\(830\) | 3.73168 | − | 6.46345i | 0.129528 | − | 0.224350i | ||||
\(831\) | −1.77777 | −0.0616703 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 32.4620 | 1.12474 | ||||||||
\(834\) | −24.2250 | + | 41.9589i | −0.838842 | + | 1.45292i | ||||
\(835\) | 2.83004 | − | 4.90178i | 0.0979377 | − | 0.169633i | ||||
\(836\) | 5.75249 | + | 9.96360i | 0.198954 | + | 0.344598i | ||||
\(837\) | 9.51573 | 0.328912 | ||||||||
\(838\) | −8.94749 | − | 15.4975i | −0.309086 | − | 0.535353i | ||||
\(839\) | −11.5761 | − | 20.0503i | −0.399650 | − | 0.692214i | 0.594033 | − | 0.804441i | \(-0.297535\pi\) |
−0.993683 | + | 0.112227i | \(0.964202\pi\) | |||||||
\(840\) | 5.08815 | 0.175558 | ||||||||
\(841\) | 12.6724 | + | 21.9493i | 0.436980 | + | 0.756871i | ||||
\(842\) | −18.2582 | + | 31.6241i | −0.629218 | + | 1.08984i | ||||
\(843\) | 0.810667 | − | 1.40412i | 0.0279209 | − | 0.0483603i | ||||
\(844\) | −2.41417 | −0.0830993 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.02715 | 0.0696948 | ||||||||
\(847\) | 0.699554 | − | 1.21166i | 0.0240370 | − | 0.0416332i | ||||
\(848\) | 49.4233 | − | 85.6037i | 1.69720 | − | 2.93964i | ||||
\(849\) | 2.49180 | + | 4.31593i | 0.0855185 | + | 0.148122i | ||||
\(850\) | 50.9256 | 1.74673 | ||||||||
\(851\) | −16.5765 | − | 28.7113i | −0.568235 | − | 0.984212i | ||||
\(852\) | −27.5562 | − | 47.7288i | −0.944060 | − | 1.63516i | ||||
\(853\) | 26.7265 | 0.915097 | 0.457548 | − | 0.889185i | \(-0.348728\pi\) | ||||
0.457548 | + | 0.889185i | \(0.348728\pi\) | |||||||
\(854\) | 2.55711 | + | 4.42905i | 0.0875026 | + | 0.151559i | ||||
\(855\) | −0.394928 | + | 0.684035i | −0.0135063 | + | 0.0233935i | ||||
\(856\) | −27.9436 | + | 48.3997i | −0.955093 | + | 1.65427i | ||||
\(857\) | 42.6064 | 1.45541 | 0.727703 | − | 0.685892i | \(-0.240588\pi\) | ||||
0.727703 | + | 0.685892i | \(0.240588\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.6079 | 1.14669 | 0.573344 | − | 0.819315i | \(-0.305646\pi\) | ||||
0.573344 | + | 0.819315i | \(0.305646\pi\) | |||||||
\(860\) | −30.5393 | + | 52.8956i | −1.04138 | + | 1.80372i | ||||
\(861\) | 1.36294 | − | 2.36068i | 0.0464488 | − | 0.0804516i | ||||
\(862\) | −48.3841 | − | 83.8037i | −1.64797 | − | 2.85437i | ||||
\(863\) | 18.7047 | 0.636715 | 0.318358 | − | 0.947971i | \(-0.396869\pi\) | ||||
0.318358 | + | 0.947971i | \(0.396869\pi\) | |||||||
\(864\) | 8.80678 | + | 15.2538i | 0.299613 | + | 0.518945i | ||||
\(865\) | 12.5566 | + | 21.7486i | 0.426937 | + | 0.739476i | ||||
\(866\) | −87.4210 | −2.97069 | ||||||||
\(867\) | 3.26540 | + | 5.65583i | 0.110899 | + | 0.192082i | ||||
\(868\) | 13.8542 | − | 23.9962i | 0.470242 | − | 0.814484i | ||||
\(869\) | −1.94385 | + | 3.36684i | −0.0659404 | + | 0.114212i | ||||
\(870\) | −5.39852 | −0.183027 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −30.2446 | −1.02421 | ||||||||
\(873\) | −8.53684 | + | 14.7862i | −0.288928 | + | 0.500438i | ||||
\(874\) | 5.84093 | − | 10.1168i | 0.197572 | − | 0.342205i | ||||
\(875\) | −2.59030 | − | 4.48653i | −0.0875682 | − | 0.151673i | ||||
\(876\) | −54.9700 | −1.85726 | ||||||||
\(877\) | −18.4119 | − | 31.8903i | −0.621724 | − | 1.07686i | −0.989165 | − | 0.146811i | \(-0.953099\pi\) |
0.367440 | − | 0.930047i | \(-0.380234\pi\) | |||||||
\(878\) | −17.2721 | − | 29.9162i | −0.582905 | − | 1.00962i | ||||
\(879\) | 0.0717525 | 0.00242015 | ||||||||
\(880\) | 19.9092 | + | 34.4837i | 0.671138 | + | 1.16244i | ||||
\(881\) | 20.5625 | − | 35.6153i | 0.692768 | − | 1.19991i | −0.278159 | − | 0.960535i | \(-0.589724\pi\) |
0.970927 | − | 0.239374i | \(-0.0769423\pi\) | |||||||
\(882\) | 9.00753 | − | 15.6015i | 0.303299 | − | 0.525330i | ||||
\(883\) | 30.7482 | 1.03476 | 0.517380 | − | 0.855756i | \(-0.326907\pi\) | ||||
0.517380 | + | 0.855756i | \(0.326907\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.29829 | 0.144485 | ||||||||
\(886\) | −16.0993 | + | 27.8849i | −0.540867 | + | 0.936810i | ||||
\(887\) | −3.79470 | + | 6.57261i | −0.127414 | + | 0.220687i | −0.922674 | − | 0.385581i | \(-0.874001\pi\) |
0.795260 | + | 0.606268i | \(0.207334\pi\) | |||||||
\(888\) | 25.1434 | + | 43.5496i | 0.843757 | + | 1.46143i | ||||
\(889\) | −2.48725 | −0.0834198 | ||||||||
\(890\) | 14.0154 | + | 24.2753i | 0.469796 | + | 0.813710i | ||||
\(891\) | −1.45593 | − | 2.52174i | −0.0487754 | − | 0.0844815i | ||||
\(892\) | −85.7891 | −2.87243 | ||||||||
\(893\) | 0.283520 | + | 0.491071i | 0.00948763 | + | 0.0164331i | ||||
\(894\) | 20.6412 | − | 35.7517i | 0.690346 | − | 1.19572i | ||||
\(895\) | 9.65465 | − | 16.7223i | 0.322719 | − | 0.558967i | ||||
\(896\) | 12.3351 | 0.412088 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.5934 | −1.12103 | ||||||||
\(899\) | −9.09634 | + | 15.7553i | −0.303380 | + | 0.525470i | ||||
\(900\) | 10.2310 | − | 17.7206i | 0.341034 | − | 0.590688i | ||||
\(901\) | −18.3898 | − | 31.8521i | −0.612655 | − | 1.06115i | ||||
\(902\) | 38.5029 | 1.28201 | ||||||||
\(903\) | −3.07942 | − | 5.33371i | −0.102477 | − | 0.177495i | ||||
\(904\) | −40.8940 | − | 70.8305i | −1.36012 | − | 2.35579i | ||||
\(905\) | 3.81115 | 0.126687 | ||||||||
\(906\) | 3.40648 | + | 5.90019i | 0.113173 | + | 0.196021i | ||||
\(907\) | −9.66666 | + | 16.7431i | −0.320976 | + | 0.555947i | −0.980690 | − | 0.195570i | \(-0.937344\pi\) |
0.659713 | + | 0.751517i | \(0.270678\pi\) | |||||||
\(908\) | −17.2110 | + | 29.8103i | −0.571166 | + | 0.989289i | ||||
\(909\) | 7.32304 | 0.242890 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.7149 | 0.752577 | 0.376288 | − | 0.926503i | \(-0.377200\pi\) | ||||
0.376288 | + | 0.926503i | \(0.377200\pi\) | |||||||
\(912\) | −4.90850 | + | 8.50177i | −0.162537 | + | 0.281522i | ||||
\(913\) | −3.84817 | + | 6.66522i | −0.127356 | + | 0.220587i | ||||
\(914\) | −43.6812 | − | 75.6580i | −1.44485 | − | 2.50255i | ||||
\(915\) | −3.59073 | −0.118706 | ||||||||
\(916\) | 10.3769 | + | 17.9734i | 0.342864 | + | 0.593857i | ||||
\(917\) | 2.55765 | + | 4.42997i | 0.0844609 | + | 0.146291i | ||||
\(918\) | 13.0586 | 0.430998 | ||||||||
\(919\) | −7.14556 | − | 12.3765i | −0.235710 | − | 0.408262i | 0.723769 | − | 0.690043i | \(-0.242408\pi\) |
−0.959479 | + | 0.281781i | \(0.909075\pi\) | |||||||
\(920\) | 26.4178 | − | 45.7569i | 0.870968 | − | 1.50856i | ||||
\(921\) | −2.59903 | + | 4.50165i | −0.0856410 | + | 0.148335i | ||||
\(922\) | 65.6945 | 2.16353 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −8.47889 | −0.278935 | ||||||||
\(925\) | 11.2177 | − | 19.4297i | 0.368837 | − | 0.638844i | ||||
\(926\) | 44.6655 | − | 77.3629i | 1.46780 | − | 2.54230i | ||||
\(927\) | 2.10992 | + | 3.65448i | 0.0692987 | + | 0.120029i | ||||
\(928\) | −33.6746 | −1.10542 | ||||||||
\(929\) | −16.3605 | − | 28.3373i | −0.536772 | − | 0.929716i | −0.999075 | − | 0.0429946i | \(-0.986310\pi\) |
0.462303 | − | 0.886722i | \(-0.347023\pi\) | |||||||
\(930\) | 13.4348 | + | 23.2698i | 0.440545 | + | 0.763047i | ||||
\(931\) | 5.03923 | 0.165154 | ||||||||
\(932\) | −21.9242 | − | 37.9739i | −0.718152 | − | 1.24388i | ||||
\(933\) | −11.2714 | + | 19.5227i | −0.369010 | + | 0.639145i | ||||
\(934\) | 51.8492 | − | 89.8054i | 1.69656 | − | 2.93852i | ||||
\(935\) | 14.8159 | 0.484533 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.01400 | −0.131132 | −0.0655658 | − | 0.997848i | \(-0.520885\pi\) | ||||
−0.0655658 | + | 0.997848i | \(0.520885\pi\) | |||||||
\(938\) | 1.39881 | − | 2.42282i | 0.0456729 | − | 0.0791077i | ||||
\(939\) | 11.3306 | − | 19.6251i | 0.369759 | − | 0.640442i | ||||
\(940\) | 2.07218 | + | 3.58912i | 0.0675870 | + | 0.117064i | ||||
\(941\) | −28.2669 | −0.921476 | −0.460738 | − | 0.887536i | \(-0.652415\pi\) | ||||
−0.460738 | + | 0.887536i | \(0.652415\pi\) | |||||||
\(942\) | 23.2042 | + | 40.1908i | 0.756032 | + | 1.30949i | ||||
\(943\) | −14.1528 | − | 24.5134i | −0.460878 | − | 0.798265i | ||||
\(944\) | 53.4228 | 1.73876 | ||||||||
\(945\) | −0.291053 | − | 0.504118i | −0.00946794 | − | 0.0163990i | ||||
\(946\) | 43.4967 | − | 75.3385i | 1.41420 | − | 2.44947i | ||||
\(947\) | 18.9227 | − | 32.7751i | 0.614906 | − | 1.06505i | −0.375495 | − | 0.926825i | \(-0.622527\pi\) |
0.990401 | − | 0.138225i | \(-0.0441396\pi\) | |||||||
\(948\) | −7.00538 | −0.227524 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 7.90541 | 0.256485 | ||||||||
\(951\) | 13.1712 | − | 22.8132i | 0.427106 | − | 0.739769i | ||||
\(952\) | 11.7654 | − | 20.3783i | 0.381319 | − | 0.660463i | ||||
\(953\) | 20.4128 | + | 35.3560i | 0.661236 | + | 1.14529i | 0.980291 | + | 0.197558i | \(0.0633011\pi\) |
−0.319055 | + | 0.947736i | \(0.603366\pi\) | |||||||
\(954\) | −20.4112 | −0.660837 | ||||||||
\(955\) | −11.1071 | − | 19.2381i | −0.359417 | − | 0.622529i | ||||
\(956\) | −52.7343 | − | 91.3385i | −1.70555 | − | 2.95410i | ||||
\(957\) | 5.56704 | 0.179957 | ||||||||
\(958\) | 11.2322 | + | 19.4548i | 0.362896 | + | 0.628555i | ||||
\(959\) | 2.07271 | − | 3.59004i | 0.0669314 | − | 0.115929i | ||||
\(960\) | −11.1932 | + | 19.3872i | −0.361260 | + | 0.625720i | ||||
\(961\) | 59.5491 | 1.92094 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.39373 | 0.206035 | ||||||||
\(964\) | 49.8796 | − | 86.3939i | 1.60651 | − | 2.78256i | ||||
\(965\) | −9.23633 | + | 15.9978i | −0.297328 | + | 0.514987i | ||||
\(966\) | 4.30463 | + | 7.45583i | 0.138499 | + | 0.239887i | ||||
\(967\) | 10.2798 | 0.330575 | 0.165288 | − | 0.986245i | \(-0.447145\pi\) | ||||
0.165288 | + | 0.986245i | \(0.447145\pi\) | |||||||
\(968\) | 11.0184 | + | 19.0845i | 0.354145 | + | 0.613398i | ||||
\(969\) | 1.82640 | + | 3.16341i | 0.0586723 | + | 0.101623i | ||||
\(970\) | −48.2111 | −1.54796 | ||||||||
\(971\) | 9.74027 | + | 16.8707i | 0.312580 | + | 0.541405i | 0.978920 | − | 0.204243i | \(-0.0654733\pi\) |
−0.666340 | + | 0.745648i | \(0.732140\pi\) | |||||||
\(972\) | 2.62349 | − | 4.54402i | 0.0841485 | − | 0.145749i | ||||
\(973\) | 4.99396 | − | 8.64979i | 0.160099 | − | 0.277300i | ||||
\(974\) | −39.9997 | −1.28167 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −44.6286 | −1.42853 | ||||||||
\(977\) | −23.5269 | + | 40.7498i | −0.752693 | + | 1.30370i | 0.193821 | + | 0.981037i | \(0.437912\pi\) |
−0.946513 | + | 0.322665i | \(0.895421\pi\) | |||||||
\(978\) | 21.1419 | − | 36.6189i | 0.676044 | − | 1.17094i | ||||
\(979\) | −14.4529 | − | 25.0331i | −0.461916 | − | 0.800062i | ||||
\(980\) | 36.8305 | 1.17651 | ||||||||
\(981\) | 1.73005 | + | 2.99654i | 0.0552364 | + | 0.0956722i | ||||
\(982\) | −6.72862 | − | 11.6543i | −0.214719 | − | 0.371904i | ||||
\(983\) | 34.4295 | 1.09813 | 0.549065 | − | 0.835779i | \(-0.314984\pi\) | ||||
0.549065 | + | 0.835779i | \(0.314984\pi\) | |||||||
\(984\) | 21.4671 | + | 37.1821i | 0.684346 | + | 1.18532i | ||||
\(985\) | −2.44528 | + | 4.23535i | −0.0779131 | + | 0.134949i | ||||
\(986\) | −12.4831 | + | 21.6213i | −0.397542 | + | 0.688563i | ||||
\(987\) | −0.417895 | −0.0133017 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −63.9536 | −2.03361 | ||||||||
\(990\) | 4.11111 | − | 7.12066i | 0.130660 | − | 0.226309i | ||||
\(991\) | −3.65399 | + | 6.32890i | −0.116073 | + | 0.201044i | −0.918208 | − | 0.396098i | \(-0.870364\pi\) |
0.802135 | + | 0.597142i | \(0.203697\pi\) | |||||||
\(992\) | 83.8030 | + | 145.151i | 2.66075 | + | 4.60855i | ||||
\(993\) | 11.2295 | 0.356358 | ||||||||
\(994\) | 7.84601 | + | 13.5897i | 0.248860 | + | 0.431039i | ||||
\(995\) | 7.88620 | + | 13.6593i | 0.250009 | + | 0.433029i | ||||
\(996\) | −13.8683 | −0.439434 | ||||||||
\(997\) | 17.8458 | + | 30.9098i | 0.565181 | + | 0.978923i | 0.997033 | + | 0.0769780i | \(0.0245271\pi\) |
−0.431851 | + | 0.901945i | \(0.642140\pi\) | |||||||
\(998\) | 0.518713 | − | 0.898438i | 0.0164196 | − | 0.0284396i | ||||
\(999\) | 2.87651 | − | 4.98226i | 0.0910088 | − | 0.157632i |
(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 | 507.2.e.i.22.1 | 6 | ||
13.2 | odd | 12 | 507.2.j.i.361.1 | 12 | |||
13.3 | even | 3 | inner | 507.2.e.i.484.1 | 6 | ||
13.4 | even | 6 | 507.2.a.i.1.1 | ✓ | 3 | ||
13.5 | odd | 4 | 507.2.j.i.316.6 | 12 | |||
13.6 | odd | 12 | 507.2.b.f.337.1 | 6 | |||
13.7 | odd | 12 | 507.2.b.f.337.6 | 6 | |||
13.8 | odd | 4 | 507.2.j.i.316.1 | 12 | |||
13.9 | even | 3 | 507.2.a.l.1.3 | yes | 3 | ||
13.10 | even | 6 | 507.2.e.l.484.3 | 6 | |||
13.11 | odd | 12 | 507.2.j.i.361.6 | 12 | |||
13.12 | even | 2 | 507.2.e.l.22.3 | 6 | |||
39.17 | odd | 6 | 1521.2.a.s.1.3 | 3 | |||
39.20 | even | 12 | 1521.2.b.k.1351.1 | 6 | |||
39.32 | even | 12 | 1521.2.b.k.1351.6 | 6 | |||
39.35 | odd | 6 | 1521.2.a.n.1.1 | 3 | |||
52.35 | odd | 6 | 8112.2.a.cp.1.1 | 3 | |||
52.43 | odd | 6 | 8112.2.a.cg.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.a.i.1.1 | ✓ | 3 | 13.4 | even | 6 | ||
507.2.a.l.1.3 | yes | 3 | 13.9 | even | 3 | ||
507.2.b.f.337.1 | 6 | 13.6 | odd | 12 | |||
507.2.b.f.337.6 | 6 | 13.7 | odd | 12 | |||
507.2.e.i.22.1 | 6 | 1.1 | even | 1 | trivial | ||
507.2.e.i.484.1 | 6 | 13.3 | even | 3 | inner | ||
507.2.e.l.22.3 | 6 | 13.12 | even | 2 | |||
507.2.e.l.484.3 | 6 | 13.10 | even | 6 | |||
507.2.j.i.316.1 | 12 | 13.8 | odd | 4 | |||
507.2.j.i.316.6 | 12 | 13.5 | odd | 4 | |||
507.2.j.i.361.1 | 12 | 13.2 | odd | 12 | |||
507.2.j.i.361.6 | 12 | 13.11 | odd | 12 | |||
1521.2.a.n.1.1 | 3 | 39.35 | odd | 6 | |||
1521.2.a.s.1.3 | 3 | 39.17 | odd | 6 | |||
1521.2.b.k.1351.1 | 6 | 39.20 | even | 12 | |||
1521.2.b.k.1351.6 | 6 | 39.32 | even | 12 | |||
8112.2.a.cg.1.3 | 3 | 52.43 | odd | 6 | |||
8112.2.a.cp.1.1 | 3 | 52.35 | odd | 6 |