Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(316,507)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.316");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.j (of order \(6\), 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: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.17213603549184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 316.1 | ||
Root | \(1.56052 - 0.900969i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.316 |
Dual form | 507.2.j.i.361.1 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.33136 | − | 1.34601i | −1.64852 | − | 0.951773i | −0.977661 | − | 0.210188i | \(-0.932592\pi\) |
−0.670859 | − | 0.741585i | \(-0.734074\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 2.62349 | + | 4.54402i | 1.31174 | + | 2.27201i | ||||
\(5\) | − | 1.04892i | − | 0.469090i | −0.972105 | − | 0.234545i | \(-0.924640\pi\) | ||
0.972105 | − | 0.234545i | \(-0.0753600\pi\) | |||||||
\(6\) | −2.33136 | + | 1.34601i | −0.951773 | + | 0.549507i | ||||
\(7\) | −0.480608 | + | 0.277479i | −0.181653 | + | 0.104877i | −0.588069 | − | 0.808811i | \(-0.700112\pi\) |
0.406416 | + | 0.913688i | \(0.366778\pi\) | |||||||
\(8\) | − | 8.74094i | − | 3.09039i | ||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −1.41185 | + | 2.44540i | −0.446467 | + | 0.773304i | ||||
\(11\) | 2.52174 | + | 1.45593i | 0.760333 | + | 0.438979i | 0.829415 | − | 0.558632i | \(-0.188674\pi\) |
−0.0690822 | + | 0.997611i | \(0.522007\pi\) | |||||||
\(12\) | 5.24698 | 1.51467 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.49396 | 0.399277 | ||||||||
\(15\) | −0.908389 | − | 0.524459i | −0.234545 | − | 0.135415i | ||||
\(16\) | −6.51842 | + | 11.2902i | −1.62960 | + | 2.82256i | ||||
\(17\) | −2.42543 | − | 4.20096i | −0.588253 | − | 1.01888i | −0.994461 | − | 0.105103i | \(-0.966483\pi\) |
0.406209 | − | 0.913780i | \(-0.366851\pi\) | |||||||
\(18\) | 2.69202i | 0.634516i | ||||||||
\(19\) | −0.652135 | + | 0.376510i | −0.149610 | + | 0.0863774i | −0.572936 | − | 0.819600i | \(-0.694196\pi\) |
0.423326 | + | 0.905977i | \(0.360862\pi\) | |||||||
\(20\) | 4.76630 | − | 2.75182i | 1.06578 | − | 0.615327i | ||||
\(21\) | 0.554958i | 0.121102i | ||||||||
\(22\) | −3.91939 | − | 6.78858i | −0.835616 | − | 1.44733i | ||||
\(23\) | 2.88135 | − | 4.99065i | 0.600804 | − | 1.04062i | −0.391896 | − | 0.920010i | \(-0.628181\pi\) |
0.992700 | − | 0.120613i | \(-0.0384861\pi\) | |||||||
\(24\) | −7.56988 | − | 4.37047i | −1.54519 | − | 0.892118i | ||||
\(25\) | 3.89977 | 0.779954 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.52174 | − | 1.45593i | −0.476564 | − | 0.275144i | ||||
\(29\) | 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 | ||||
\(31\) | − | 9.51573i | − | 1.70908i | −0.519389 | − | 0.854538i | \(-0.673841\pi\) | ||
0.519389 | − | 0.854538i | \(-0.326159\pi\) | |||||||
\(32\) | 15.2538 | − | 8.80678i | 2.69652 | − | 1.55683i | ||||
\(33\) | 2.52174 | − | 1.45593i | 0.438979 | − | 0.253444i | ||||
\(34\) | 13.0586i | 2.23953i | ||||||||
\(35\) | 0.291053 | + | 0.504118i | 0.0491969 | + | 0.0852115i | ||||
\(36\) | 2.62349 | − | 4.54402i | 0.437248 | − | 0.757336i | ||||
\(37\) | 4.98226 | + | 2.87651i | 0.819079 | + | 0.472895i | 0.850099 | − | 0.526623i | \(-0.176542\pi\) |
−0.0310199 | + | 0.999519i | \(0.509876\pi\) | |||||||
\(38\) | 2.02715 | 0.328847 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.16852 | −1.44967 | ||||||||
\(41\) | −4.25379 | − | 2.45593i | −0.664330 | − | 0.383551i | 0.129595 | − | 0.991567i | \(-0.458632\pi\) |
−0.793925 | + | 0.608016i | \(0.791966\pi\) | |||||||
\(42\) | 0.746980 | − | 1.29381i | 0.115261 | − | 0.199639i | ||||
\(43\) | −5.54892 | − | 9.61101i | −0.846202 | − | 1.46566i | −0.884573 | − | 0.466401i | \(-0.845550\pi\) |
0.0383713 | − | 0.999264i | \(-0.487783\pi\) | |||||||
\(44\) | 15.2784i | 2.30331i | ||||||||
\(45\) | −0.908389 | + | 0.524459i | −0.135415 | + | 0.0781817i | ||||
\(46\) | −13.4349 | + | 7.75667i | −1.98087 | + | 1.14366i | ||||
\(47\) | − | 0.753020i | − | 0.109839i | −0.998491 | − | 0.0549197i | \(-0.982510\pi\) | ||
0.998491 | − | 0.0549197i | \(-0.0174903\pi\) | |||||||
\(48\) | 6.51842 | + | 11.2902i | 0.940853 | + | 1.62960i | ||||
\(49\) | −3.34601 | + | 5.79546i | −0.478002 | + | 0.827923i | ||||
\(50\) | −9.09177 | − | 5.24914i | −1.28577 | − | 0.742340i | ||||
\(51\) | −4.85086 | −0.679256 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.58211 | −1.04148 | −0.520741 | − | 0.853715i | \(-0.674344\pi\) | ||||
−0.520741 | + | 0.853715i | \(0.674344\pi\) | |||||||
\(54\) | 2.33136 | + | 1.34601i | 0.317258 | + | 0.183169i | ||||
\(55\) | 1.52715 | − | 2.64510i | 0.205920 | − | 0.356665i | ||||
\(56\) | 2.42543 | + | 4.20096i | 0.324111 | + | 0.561377i | ||||
\(57\) | 0.753020i | 0.0997400i | ||||||||
\(58\) | −4.45722 | + | 2.57338i | −0.585261 | + | 0.337901i | ||||
\(59\) | −3.54883 | + | 2.04892i | −0.462018 | + | 0.266746i | −0.712892 | − | 0.701273i | \(-0.752615\pi\) |
0.250874 | + | 0.968020i | \(0.419282\pi\) | |||||||
\(60\) | − | 5.50365i | − | 0.710518i | ||||||
\(61\) | 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 | ||||
\(63\) | 0.480608 | + | 0.277479i | 0.0605509 | + | 0.0349591i | ||||
\(64\) | −21.3424 | −2.66780 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.83877 | −0.964886 | ||||||||
\(67\) | 1.62174 | + | 0.936313i | 0.198127 | + | 0.114389i | 0.595782 | − | 0.803146i | \(-0.296842\pi\) |
−0.397654 | + | 0.917535i | \(0.630176\pi\) | |||||||
\(68\) | 12.7262 | − | 22.0424i | 1.54327 | − | 2.67303i | ||||
\(69\) | −2.88135 | − | 4.99065i | −0.346874 | − | 0.600804i | ||||
\(70\) | − | 1.56704i | − | 0.187297i | ||||||
\(71\) | −9.09643 | + | 5.25182i | −1.07955 | + | 0.623277i | −0.930774 | − | 0.365595i | \(-0.880866\pi\) |
−0.148773 | + | 0.988871i | \(0.547532\pi\) | |||||||
\(72\) | −7.56988 | + | 4.37047i | −0.892118 | + | 0.515065i | ||||
\(73\) | − | 10.4765i | − | 1.22618i | −0.790012 | − | 0.613091i | \(-0.789926\pi\) | ||
0.790012 | − | 0.613091i | \(-0.210074\pi\) | |||||||
\(74\) | −7.74363 | − | 13.4124i | −0.900178 | − | 1.55915i | ||||
\(75\) | 1.94989 | − | 3.37730i | 0.225153 | − | 0.389977i | ||||
\(76\) | −3.42174 | − | 1.97554i | −0.392500 | − | 0.226610i | ||||
\(77\) | −1.61596 | −0.184155 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.33513 | 0.150213 | 0.0751067 | − | 0.997176i | \(-0.476070\pi\) | ||||
0.0751067 | + | 0.997176i | \(0.476070\pi\) | |||||||
\(80\) | 11.8425 | + | 6.83728i | 1.32403 | + | 0.764431i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 6.61141 | + | 11.4513i | 0.730108 | + | 1.26458i | ||||
\(83\) | 2.64310i | 0.290118i | 0.989423 | + | 0.145059i | \(0.0463373\pi\) | ||||
−0.989423 | + | 0.145059i | \(0.953663\pi\) | |||||||
\(84\) | −2.52174 | + | 1.45593i | −0.275144 | + | 0.158855i | ||||
\(85\) | −4.40646 | + | 2.54407i | −0.477948 | + | 0.275943i | ||||
\(86\) | 29.8756i | 3.22157i | ||||||||
\(87\) | −0.955927 | − | 1.65571i | −0.102486 | − | 0.177511i | ||||
\(88\) | 12.7262 | − | 22.0424i | 1.35661 | − | 2.34972i | ||||
\(89\) | 8.59696 | + | 4.96346i | 0.911276 | + | 0.526126i | 0.880842 | − | 0.473411i | \(-0.156977\pi\) |
0.0304348 | + | 0.999537i | \(0.490311\pi\) | |||||||
\(90\) | 2.82371 | 0.297645 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 30.2368 | 3.15241 | ||||||||
\(93\) | −8.24086 | − | 4.75786i | −0.854538 | − | 0.493368i | ||||
\(94\) | −1.01357 | + | 1.75556i | −0.104542 | + | 0.181072i | ||||
\(95\) | 0.394928 | + | 0.684035i | 0.0405188 | + | 0.0701806i | ||||
\(96\) | − | 17.6136i | − | 1.79768i | ||||||
\(97\) | 14.7862 | − | 8.53684i | 1.50131 | − | 0.866784i | 0.501316 | − | 0.865264i | \(-0.332850\pi\) |
0.999999 | − | 0.00151988i | \(-0.000483794\pi\) | |||||||
\(98\) | 15.6015 | − | 9.00753i | 1.57599 | − | 0.909898i | ||||
\(99\) | − | 2.91185i | − | 0.292652i | ||||||
\(100\) | 10.2310 | + | 17.7206i | 1.02310 | + | 1.77206i | ||||
\(101\) | 3.66152 | − | 6.34194i | 0.364335 | − | 0.631047i | −0.624334 | − | 0.781157i | \(-0.714630\pi\) |
0.988669 | + | 0.150111i | \(0.0479630\pi\) | |||||||
\(102\) | 11.3091 | + | 6.52930i | 1.11977 | + | 0.646497i | ||||
\(103\) | 4.21983 | 0.415792 | 0.207896 | − | 0.978151i | \(-0.433338\pi\) | ||||
0.207896 | + | 0.978151i | \(0.433338\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.582105 | 0.0568077 | ||||||||
\(106\) | 17.6766 | + | 10.2056i | 1.71690 | + | 0.991255i | ||||
\(107\) | −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 | ||||
\(109\) | − | 3.46011i | − | 0.331418i | −0.986175 | − | 0.165709i | \(-0.947009\pi\) | ||
0.986175 | − | 0.165709i | \(-0.0529913\pi\) | |||||||
\(110\) | −7.12066 | + | 4.11111i | −0.678928 | + | 0.391979i | ||||
\(111\) | 4.98226 | − | 2.87651i | 0.472895 | − | 0.273026i | ||||
\(112\) | − | 7.23490i | − | 0.683634i | ||||||
\(113\) | −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 | ||||
\(115\) | −5.23478 | − | 3.02230i | −0.488146 | − | 0.281831i | ||||
\(116\) | 10.0315 | 0.931398 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.0315 | 1.01553 | ||||||||
\(119\) | 2.33136 | + | 1.34601i | 0.213715 | + | 0.123389i | ||||
\(120\) | −4.58426 | + | 7.94017i | −0.418484 | + | 0.724835i | ||||
\(121\) | −1.26055 | − | 2.18334i | −0.114596 | − | 0.198486i | ||||
\(122\) | − | 9.21552i | − | 0.834334i | ||||||
\(123\) | −4.25379 | + | 2.45593i | −0.383551 | + | 0.221443i | ||||
\(124\) | 43.2396 | − | 24.9644i | 3.88303 | − | 2.24187i | ||||
\(125\) | − | 9.33513i | − | 0.834959i | ||||||
\(126\) | −0.746980 | − | 1.29381i | −0.0665462 | − | 0.115261i | ||||
\(127\) | −2.24094 | + | 3.88142i | −0.198851 | + | 0.344420i | −0.948156 | − | 0.317805i | \(-0.897054\pi\) |
0.749305 | + | 0.662225i | \(0.230388\pi\) | |||||||
\(128\) | 19.2493 | + | 11.1136i | 1.70141 | + | 0.982310i | ||||
\(129\) | −11.0978 | −0.977110 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.21744 | −0.805331 | −0.402666 | − | 0.915347i | \(-0.631916\pi\) | ||||
−0.402666 | + | 0.915347i | \(0.631916\pi\) | |||||||
\(132\) | 13.2315 | + | 7.63922i | 1.15166 | + | 0.664909i | ||||
\(133\) | 0.208947 | − | 0.361908i | 0.0181180 | − | 0.0313814i | ||||
\(134\) | −2.52057 | − | 4.36576i | −0.217744 | − | 0.377144i | ||||
\(135\) | 1.04892i | 0.0902764i | ||||||||
\(136\) | −36.7204 | + | 21.2005i | −3.14875 | + | 1.81793i | ||||
\(137\) | 6.46903 | − | 3.73490i | 0.552687 | − | 0.319094i | −0.197518 | − | 0.980299i | \(-0.563288\pi\) |
0.750205 | + | 0.661205i | \(0.229955\pi\) | |||||||
\(138\) | 15.5133i | 1.32058i | ||||||||
\(139\) | 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 | ||||
\(141\) | −0.652135 | − | 0.376510i | −0.0549197 | − | 0.0317079i | ||||
\(142\) | 28.2760 | 2.37287 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 13.0368 | 1.08640 | ||||||||
\(145\) | −1.73671 | − | 1.00269i | −0.144226 | − | 0.0832687i | ||||
\(146\) | −14.1015 | + | 24.4245i | −1.16705 | + | 2.02138i | ||||
\(147\) | 3.34601 | + | 5.79546i | 0.275974 | + | 0.478002i | ||||
\(148\) | 30.1860i | 2.48127i | ||||||||
\(149\) | 13.2806 | − | 7.66756i | 1.08799 | − | 0.628151i | 0.154949 | − | 0.987922i | \(-0.450479\pi\) |
0.933041 | + | 0.359771i | \(0.117145\pi\) | |||||||
\(150\) | −9.09177 | + | 5.24914i | −0.742340 | + | 0.428590i | ||||
\(151\) | − | 2.53079i | − | 0.205953i | −0.994684 | − | 0.102977i | \(-0.967163\pi\) | ||
0.994684 | − | 0.102977i | \(-0.0328367\pi\) | |||||||
\(152\) | 3.29105 | + | 5.70027i | 0.266940 | + | 0.462353i | ||||
\(153\) | −2.42543 | + | 4.20096i | −0.196084 | + | 0.339628i | ||||
\(154\) | 3.76738 | + | 2.17510i | 0.303584 | + | 0.175274i | ||||
\(155\) | −9.98121 | −0.801710 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.2392 | 1.37584 | 0.687919 | − | 0.725787i | \(-0.258524\pi\) | ||||
0.687919 | + | 0.725787i | \(0.258524\pi\) | |||||||
\(158\) | −3.11266 | − | 1.79709i | −0.247630 | − | 0.142969i | ||||
\(159\) | −3.79105 | + | 6.56630i | −0.300650 | + | 0.520741i | ||||
\(160\) | −9.23759 | − | 16.0000i | −0.730295 | − | 1.26491i | ||||
\(161\) | 3.19806i | 0.252043i | ||||||||
\(162\) | 2.33136 | − | 1.34601i | 0.183169 | − | 0.105753i | ||||
\(163\) | −13.6027 | + | 7.85354i | −1.06545 | + | 0.615137i | −0.926934 | − | 0.375223i | \(-0.877566\pi\) |
−0.138514 | + | 0.990360i | \(0.544233\pi\) | |||||||
\(164\) | − | 25.7724i | − | 2.01249i | ||||||
\(165\) | −1.52715 | − | 2.64510i | −0.118888 | − | 0.205920i | ||||
\(166\) | 3.55765 | − | 6.16202i | 0.276127 | − | 0.478266i | ||||
\(167\) | 4.67318 | + | 2.69806i | 0.361622 | + | 0.208782i | 0.669792 | − | 0.742549i | \(-0.266383\pi\) |
−0.308170 | + | 0.951331i | \(0.599717\pi\) | |||||||
\(168\) | 4.85086 | 0.374252 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 13.6974 | 1.05054 | ||||||||
\(171\) | 0.652135 | + | 0.376510i | 0.0498700 | + | 0.0287925i | ||||
\(172\) | 29.1151 | − | 50.4288i | 2.22000 | − | 3.84516i | ||||
\(173\) | 11.9710 | + | 20.7344i | 0.910138 | + | 1.57640i | 0.813868 | + | 0.581049i | \(0.197358\pi\) |
0.0962694 | + | 0.995355i | \(0.469309\pi\) | |||||||
\(174\) | 5.14675i | 0.390174i | ||||||||
\(175\) | −1.87426 | + | 1.08211i | −0.141681 | + | 0.0817995i | ||||
\(176\) | −32.8755 | + | 18.9807i | −2.47808 | + | 1.43072i | ||||
\(177\) | 4.09783i | 0.308012i | ||||||||
\(178\) | −13.3617 | − | 23.1432i | −1.00150 | − | 1.73466i | ||||
\(179\) | 9.20440 | − | 15.9425i | 0.687969 | − | 1.19160i | −0.284525 | − | 0.958669i | \(-0.591836\pi\) |
0.972494 | − | 0.232929i | \(-0.0748309\pi\) | |||||||
\(180\) | −4.76630 | − | 2.75182i | −0.355259 | − | 0.205109i | ||||
\(181\) | 3.63342 | 0.270070 | 0.135035 | − | 0.990841i | \(-0.456885\pi\) | ||||
0.135035 | + | 0.990841i | \(0.456885\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.42327 | 0.253056 | ||||||||
\(184\) | −43.6230 | − | 25.1857i | −3.21593 | − | 1.85672i | ||||
\(185\) | 3.01722 | − | 5.22598i | 0.221831 | − | 0.384222i | ||||
\(186\) | 12.8083 | + | 22.1846i | 0.939148 | + | 1.62665i | ||||
\(187\) | − | 14.1250i | − | 1.03292i | ||||||
\(188\) | 3.42174 | − | 1.97554i | 0.249556 | − | 0.144081i | ||||
\(189\) | 0.480608 | − | 0.277479i | 0.0349591 | − | 0.0201836i | ||||
\(190\) | − | 2.12631i | − | 0.154259i | ||||||
\(191\) | 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 | ||||
\(193\) | −15.2517 | − | 8.80559i | −1.09784 | − | 0.633840i | −0.162189 | − | 0.986760i | \(-0.551856\pi\) |
−0.935654 | + | 0.352920i | \(0.885189\pi\) | |||||||
\(194\) | −45.9627 | −3.29993 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −35.1129 | −2.50806 | ||||||||
\(197\) | 4.03783 | + | 2.33124i | 0.287683 | + | 0.166094i | 0.636897 | − | 0.770949i | \(-0.280218\pi\) |
−0.349213 | + | 0.937043i | \(0.613551\pi\) | |||||||
\(198\) | −3.91939 | + | 6.78858i | −0.278539 | + | 0.482443i | ||||
\(199\) | 7.51842 | + | 13.0223i | 0.532967 | + | 0.923125i | 0.999259 | + | 0.0384944i | \(0.0122562\pi\) |
−0.466292 | + | 0.884631i | \(0.654410\pi\) | |||||||
\(200\) | − | 34.0877i | − | 2.41036i | ||||||
\(201\) | 1.62174 | − | 0.936313i | 0.114389 | − | 0.0660424i | ||||
\(202\) | −17.0726 | + | 9.85690i | −1.20123 | + | 0.693529i | ||||
\(203\) | 1.06100i | 0.0744675i | ||||||||
\(204\) | −12.7262 | − | 22.0424i | −0.891010 | − | 1.54327i | ||||
\(205\) | −2.57606 | + | 4.46187i | −0.179920 | + | 0.311631i | ||||
\(206\) | −9.83794 | − | 5.67994i | −0.685442 | − | 0.395740i | ||||
\(207\) | −5.76271 | −0.400536 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.19269 | −0.151671 | ||||||||
\(210\) | −1.35710 | − | 0.783520i | −0.0936485 | − | 0.0540680i | ||||
\(211\) | 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 | ||||
\(213\) | 10.5036i | 0.719698i | ||||||||
\(214\) | 14.9061 | − | 8.60603i | 1.01896 | − | 0.588296i | ||||
\(215\) | −10.0812 | + | 5.82036i | −0.687529 | + | 0.396945i | ||||
\(216\) | 8.74094i | 0.594746i | ||||||||
\(217\) | 2.64042 | + | 4.57333i | 0.179243 | + | 0.310458i | ||||
\(218\) | −4.65734 | + | 8.06675i | −0.315435 | + | 0.546349i | ||||
\(219\) | −9.07292 | − | 5.23825i | −0.613091 | − | 0.353968i | ||||
\(220\) | 16.0258 | 1.08046 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −15.4873 | −1.03944 | ||||||||
\(223\) | 14.1597 | + | 8.17510i | 0.948202 | + | 0.547445i | 0.892522 | − | 0.451004i | \(-0.148934\pi\) |
0.0556803 | + | 0.998449i | \(0.482267\pi\) | |||||||
\(224\) | −4.88740 | + | 8.46522i | −0.326553 | + | 0.565606i | ||||
\(225\) | −1.94989 | − | 3.37730i | −0.129992 | − | 0.225153i | ||||
\(226\) | 25.1890i | 1.67555i | ||||||||
\(227\) | 5.68142 | − | 3.28017i | 0.377089 | − | 0.217712i | −0.299462 | − | 0.954108i | \(-0.596807\pi\) |
0.676551 | + | 0.736396i | \(0.263474\pi\) | |||||||
\(228\) | −3.42174 | + | 1.97554i | −0.226610 | + | 0.130833i | ||||
\(229\) | 3.95539i | 0.261380i | 0.991423 | + | 0.130690i | \(0.0417192\pi\) | ||||
−0.991423 | + | 0.130690i | \(0.958281\pi\) | |||||||
\(230\) | 8.13610 | + | 14.0921i | 0.536479 | + | 0.929209i | ||||
\(231\) | −0.807979 | + | 1.39946i | −0.0531611 | + | 0.0920777i | ||||
\(232\) | −14.4725 | − | 8.35570i | −0.950166 | − | 0.548579i | ||||
\(233\) | −8.35690 | −0.547478 | −0.273739 | − | 0.961804i | \(-0.588261\pi\) | ||||
−0.273739 | + | 0.961804i | \(0.588261\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.789856 | −0.0515245 | ||||||||
\(236\) | −18.6206 | − | 10.7506i | −1.21210 | − | 0.699806i | ||||
\(237\) | 0.667563 | − | 1.15625i | 0.0433629 | − | 0.0751067i | ||||
\(238\) | −3.62349 | − | 6.27607i | −0.234876 | − | 0.406817i | ||||
\(239\) | 20.1008i | 1.30021i | 0.759843 | + | 0.650107i | \(0.225276\pi\) | ||||
−0.759843 | + | 0.650107i | \(0.774724\pi\) | |||||||
\(240\) | 11.8425 | − | 6.83728i | 0.764431 | − | 0.441345i | ||||
\(241\) | 16.4655 | − | 9.50634i | 1.06063 | − | 0.612357i | 0.135026 | − | 0.990842i | \(-0.456888\pi\) |
0.925607 | + | 0.378485i | \(0.123555\pi\) | |||||||
\(242\) | 6.78687i | 0.436277i | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −8.98092 | + | 15.5554i | −0.574944 | + | 0.995833i | ||||
\(245\) | 6.07896 | + | 3.50969i | 0.388370 | + | 0.224226i | ||||
\(246\) | 13.2228 | 0.843056 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −83.1764 | −5.28171 | ||||||||
\(249\) | 2.28900 | + | 1.32155i | 0.145059 | + | 0.0837500i | ||||
\(250\) | −12.5652 | + | 21.7635i | −0.794692 | + | 1.37645i | ||||
\(251\) | −0.381887 | − | 0.661448i | −0.0241045 | − | 0.0417502i | 0.853722 | − | 0.520730i | \(-0.174340\pi\) |
−0.877826 | + | 0.478980i | \(0.841007\pi\) | |||||||
\(252\) | 2.91185i | 0.183430i | ||||||||
\(253\) | 14.5321 | − | 8.39008i | 0.913622 | − | 0.527480i | ||||
\(254\) | 10.4489 | − | 6.03266i | 0.655620 | − | 0.378522i | ||||
\(255\) | 5.08815i | 0.318632i | ||||||||
\(256\) | −8.57553 | − | 14.8533i | −0.535971 | − | 0.928329i | ||||
\(257\) | −6.54556 | + | 11.3373i | −0.408301 | + | 0.707198i | −0.994700 | − | 0.102825i | \(-0.967212\pi\) |
0.586398 | + | 0.810023i | \(0.300545\pi\) | |||||||
\(258\) | 25.8730 | + | 14.9378i | 1.61078 | + | 0.929987i | ||||
\(259\) | −3.19269 | −0.198384 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.91185 | −0.118341 | ||||||||
\(262\) | 21.4892 | + | 12.4068i | 1.32760 | + | 0.766493i | ||||
\(263\) | −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 | ||||
\(265\) | 7.95300i | 0.488549i | ||||||||
\(266\) | −0.974263 | + | 0.562491i | −0.0597359 | + | 0.0344885i | ||||
\(267\) | 8.59696 | − | 4.96346i | 0.526126 | − | 0.303759i | ||||
\(268\) | 9.82563i | 0.600196i | ||||||||
\(269\) | −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 | ||||
\(271\) | −17.1066 | − | 9.87651i | −1.03915 | − | 0.599955i | −0.119560 | − | 0.992827i | \(-0.538148\pi\) |
−0.919593 | + | 0.392872i | \(0.871482\pi\) | |||||||
\(272\) | 63.2398 | 3.83448 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.1089 | −1.21482 | ||||||||
\(275\) | 9.83421 | + | 5.67778i | 0.593025 | + | 0.342383i | ||||
\(276\) | 15.1184 | − | 26.1859i | 0.910021 | − | 1.57620i | ||||
\(277\) | 0.888887 | + | 1.53960i | 0.0534081 | + | 0.0925055i | 0.891493 | − | 0.453034i | \(-0.149658\pi\) |
−0.838085 | + | 0.545539i | \(0.816325\pi\) | |||||||
\(278\) | − | 48.4499i | − | 2.90583i | ||||||
\(279\) | −8.24086 | + | 4.75786i | −0.493368 | + | 0.284846i | ||||
\(280\) | 4.40646 | − | 2.54407i | 0.263337 | − | 0.152037i | ||||
\(281\) | − | 1.62133i | − | 0.0967207i | −0.998830 | − | 0.0483603i | \(-0.984600\pi\) | ||
0.998830 | − | 0.0483603i | \(-0.0153996\pi\) | |||||||
\(282\) | 1.01357 | + | 1.75556i | 0.0603574 | + | 0.104542i | ||||
\(283\) | 2.49180 | − | 4.31593i | 0.148122 | − | 0.256555i | −0.782411 | − | 0.622762i | \(-0.786010\pi\) |
0.930533 | + | 0.366207i | \(0.119344\pi\) | |||||||
\(284\) | −47.7288 | − | 27.5562i | −2.83218 | − | 1.63516i | ||||
\(285\) | 0.789856 | 0.0467870 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.72587 | 0.160903 | ||||||||
\(288\) | −15.2538 | − | 8.80678i | −0.898838 | − | 0.518945i | ||||
\(289\) | −3.26540 | + | 5.65583i | −0.192082 | + | 0.332696i | ||||
\(290\) | 2.69926 | + | 4.67525i | 0.158506 | + | 0.274540i | ||||
\(291\) | − | 17.0737i | − | 1.00088i | ||||||
\(292\) | 47.6054 | − | 27.4850i | 2.78590 | − | 1.60844i | ||||
\(293\) | 0.0621395 | − | 0.0358763i | 0.00363023 | − | 0.00209591i | −0.498184 | − | 0.867071i | \(-0.666000\pi\) |
0.501814 | + | 0.864976i | \(0.332666\pi\) | |||||||
\(294\) | − | 18.0151i | − | 1.05066i | ||||||
\(295\) | 2.14914 | + | 3.72243i | 0.125128 | + | 0.216728i | ||||
\(296\) | 25.1434 | − | 43.5496i | 1.46143 | − | 2.53127i | ||||
\(297\) | −2.52174 | − | 1.45593i | −0.146326 | − | 0.0844815i | ||||
\(298\) | −41.2825 | −2.39143 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 20.4620 | 1.18138 | ||||||||
\(301\) | 5.33371 | + | 3.07942i | 0.307430 | + | 0.177495i | ||||
\(302\) | −3.40648 | + | 5.90019i | −0.196021 | + | 0.339518i | ||||
\(303\) | −3.66152 | − | 6.34194i | −0.210349 | − | 0.364335i | ||||
\(304\) | − | 9.81700i | − | 0.563044i | ||||||
\(305\) | 3.10966 | − | 1.79536i | 0.178059 | − | 0.102802i | ||||
\(306\) | 11.3091 | − | 6.52930i | 0.646497 | − | 0.373255i | ||||
\(307\) | 5.19806i | 0.296669i | 0.988937 | + | 0.148335i | \(0.0473912\pi\) | ||||
−0.988937 | + | 0.148335i | \(0.952609\pi\) | |||||||
\(308\) | −4.23945 | − | 7.34294i | −0.241565 | − | 0.418403i | ||||
\(309\) | 2.10992 | − | 3.65448i | 0.120029 | − | 0.207896i | ||||
\(310\) | 23.2698 | + | 13.4348i | 1.32164 | + | 0.763047i | ||||
\(311\) | 22.5429 | 1.27829 | 0.639145 | − | 0.769087i | \(-0.279289\pi\) | ||||
0.639145 | + | 0.769087i | \(0.279289\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.6612 | 1.28088 | 0.640442 | − | 0.768006i | \(-0.278751\pi\) | ||||
0.640442 | + | 0.768006i | \(0.278751\pi\) | |||||||
\(314\) | −40.1908 | − | 23.2042i | −2.26810 | − | 1.30949i | ||||
\(315\) | 0.291053 | − | 0.504118i | 0.0163990 | − | 0.0284038i | ||||
\(316\) | 3.50269 | + | 6.06683i | 0.197042 | + | 0.341286i | ||||
\(317\) | 26.3424i | 1.47954i | 0.672861 | + | 0.739769i | \(0.265065\pi\) | ||||
−0.672861 | + | 0.739769i | \(0.734935\pi\) | |||||||
\(318\) | 17.6766 | − | 10.2056i | 0.991255 | − | 0.572301i | ||||
\(319\) | 4.82120 | − | 2.78352i | 0.269935 | − | 0.155847i | ||||
\(320\) | 22.3864i | 1.25144i | ||||||||
\(321\) | 3.19687 | + | 5.53713i | 0.178432 | + | 0.309053i | ||||
\(322\) | 4.30463 | − | 7.45583i | 0.239887 | − | 0.415497i | ||||
\(323\) | 3.16341 | + | 1.82640i | 0.176017 | + | 0.101623i | ||||
\(324\) | −5.24698 | −0.291499 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 42.2838 | 2.34188 | ||||||||
\(327\) | −2.99654 | − | 1.73005i | −0.165709 | − | 0.0956722i | ||||
\(328\) | −21.4671 | + | 37.1821i | −1.18532 | + | 2.05304i | ||||
\(329\) | 0.208947 | + | 0.361908i | 0.0115196 | + | 0.0199526i | ||||
\(330\) | 8.22223i | 0.452619i | ||||||||
\(331\) | −9.72505 | + | 5.61476i | −0.534537 | + | 0.308615i | −0.742862 | − | 0.669445i | \(-0.766532\pi\) |
0.208325 | + | 0.978060i | \(0.433199\pi\) | |||||||
\(332\) | −12.0103 | + | 6.93416i | −0.659151 | + | 0.380561i | ||||
\(333\) | − | 5.75302i | − | 0.315264i | ||||||
\(334\) | −7.26324 | − | 12.5803i | −0.397427 | − | 0.688364i | ||||
\(335\) | 0.982115 | − | 1.70107i | 0.0536587 | − | 0.0929395i | ||||
\(336\) | −6.26561 | − | 3.61745i | −0.341817 | − | 0.197348i | ||||
\(337\) | −2.30798 | −0.125724 | −0.0628618 | − | 0.998022i | \(-0.520023\pi\) | ||||
−0.0628618 | + | 0.998022i | \(0.520023\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.35690 | −0.508197 | ||||||||
\(340\) | −23.1206 | − | 13.3487i | −1.25389 | − | 0.723935i | ||||
\(341\) | 13.8542 | − | 23.9962i | 0.750247 | − | 1.29947i | ||||
\(342\) | −1.01357 | − | 1.75556i | −0.0548078 | − | 0.0949299i | ||||
\(343\) | − | 7.59850i | − | 0.410280i | ||||||
\(344\) | −84.0092 | + | 48.5027i | −4.52947 | + | 2.61509i | ||||
\(345\) | −5.23478 | + | 3.02230i | −0.281831 | + | 0.162715i | ||||
\(346\) | − | 64.4523i | − | 3.46498i | ||||||
\(347\) | 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 | ||||
\(349\) | 20.7637 | + | 11.9879i | 1.11145 | + | 0.641699i | 0.939206 | − | 0.343355i | \(-0.111563\pi\) |
0.172249 | + | 0.985053i | \(0.444897\pi\) | |||||||
\(350\) | 5.82610 | 0.311418 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 51.2881 | 2.73367 | ||||||||
\(353\) | 23.4900 | + | 13.5620i | 1.25025 | + | 0.721830i | 0.971158 | − | 0.238435i | \(-0.0766345\pi\) |
0.279088 | + | 0.960265i | \(0.409968\pi\) | |||||||
\(354\) | 5.51573 | − | 9.55352i | 0.293158 | − | 0.507764i | ||||
\(355\) | 5.50873 | + | 9.54140i | 0.292373 | + | 0.506405i | ||||
\(356\) | 52.0863i | 2.76057i | ||||||||
\(357\) | 2.33136 | − | 1.34601i | 0.123389 | − | 0.0712384i | ||||
\(358\) | −42.9175 | + | 24.7784i | −2.26826 | + | 1.30958i | ||||
\(359\) | 26.0790i | 1.37640i | 0.725521 | + | 0.688200i | \(0.241599\pi\) | ||||
−0.725521 | + | 0.688200i | \(0.758401\pi\) | |||||||
\(360\) | 4.58426 | + | 7.94017i | 0.241612 | + | 0.418484i | ||||
\(361\) | −9.21648 | + | 15.9634i | −0.485078 | + | 0.840180i | ||||
\(362\) | −8.47080 | − | 4.89062i | −0.445215 | − | 0.257045i | ||||
\(363\) | −2.52111 | −0.132324 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.9890 | −0.575190 | ||||||||
\(366\) | −7.98088 | − | 4.60776i | −0.417167 | − | 0.240851i | ||||
\(367\) | −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 | ||||
\(369\) | 4.91185i | 0.255701i | ||||||||
\(370\) | −14.0685 | + | 8.12242i | −0.731384 | + | 0.422265i | ||||
\(371\) | 3.64402 | − | 2.10388i | 0.189188 | − | 0.109228i | ||||
\(372\) | − | 49.9288i | − | 2.58869i | ||||||
\(373\) | −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 | ||||
\(375\) | −8.08446 | − | 4.66756i | −0.417480 | − | 0.241032i | ||||
\(376\) | −6.58211 | −0.339446 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.49396 | −0.0768410 | ||||||||
\(379\) | −13.8967 | − | 8.02326i | −0.713825 | − | 0.412127i | 0.0986504 | − | 0.995122i | \(-0.468547\pi\) |
−0.812476 | + | 0.582995i | \(0.801881\pi\) | |||||||
\(380\) | −2.07218 | + | 3.58912i | −0.106301 | + | 0.184118i | ||||
\(381\) | 2.24094 | + | 3.88142i | 0.114807 | + | 0.198851i | ||||
\(382\) | − | 57.0122i | − | 2.91700i | ||||||
\(383\) | −21.3186 | + | 12.3083i | −1.08933 | + | 0.628923i | −0.933397 | − | 0.358845i | \(-0.883171\pi\) |
−0.155930 | + | 0.987768i | \(0.549837\pi\) | |||||||
\(384\) | 19.2493 | − | 11.1136i | 0.982310 | − | 0.567137i | ||||
\(385\) | 1.69501i | 0.0863855i | ||||||||
\(386\) | 23.7048 | + | 41.0580i | 1.20654 | + | 2.08980i | ||||
\(387\) | −5.54892 | + | 9.61101i | −0.282067 | + | 0.488555i | ||||
\(388\) | 77.5831 | + | 44.7926i | 3.93868 | + | 2.27400i | ||||
\(389\) | 17.2198 | 0.873080 | 0.436540 | − | 0.899685i | \(-0.356204\pi\) | ||||
0.436540 | + | 0.899685i | \(0.356204\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.9541 | −1.41370 | ||||||||
\(392\) | 50.6578 | + | 29.2473i | 2.55860 | + | 1.47721i | ||||
\(393\) | −4.60872 | + | 7.98254i | −0.232479 | + | 0.402666i | ||||
\(394\) | −6.27575 | − | 10.8699i | −0.316168 | − | 0.547619i | ||||
\(395\) | − | 1.40044i | − | 0.0704636i | ||||||
\(396\) | 13.2315 | − | 7.63922i | 0.664909 | − | 0.383885i | ||||
\(397\) | 1.76602 | − | 1.01961i | 0.0886342 | − | 0.0511730i | −0.455028 | − | 0.890477i | \(-0.650371\pi\) |
0.543662 | + | 0.839304i | \(0.317037\pi\) | |||||||
\(398\) | − | 40.4795i | − | 2.02905i | ||||||
\(399\) | −0.208947 | − | 0.361908i | −0.0104605 | − | 0.0181180i | ||||
\(400\) | −25.4203 | + | 44.0293i | −1.27102 | + | 2.20147i | ||||
\(401\) | −1.26564 | − | 0.730718i | −0.0632031 | − | 0.0364903i | 0.468065 | − | 0.883694i | \(-0.344951\pi\) |
−0.531269 | + | 0.847203i | \(0.678284\pi\) | |||||||
\(402\) | −5.04115 | −0.251430 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 38.4239 | 1.91166 | ||||||||
\(405\) | 0.908389 | + | 0.524459i | 0.0451382 | + | 0.0260606i | ||||
\(406\) | 1.42812 | − | 2.47357i | 0.0708762 | − | 0.122761i | ||||
\(407\) | 8.37598 | + | 14.5076i | 0.415182 | + | 0.719116i | ||||
\(408\) | 42.4010i | 2.09916i | ||||||||
\(409\) | −25.9279 | + | 14.9695i | −1.28205 | + | 0.740194i | −0.977224 | − | 0.212213i | \(-0.931933\pi\) |
−0.304830 | + | 0.952407i | \(0.598600\pi\) | |||||||
\(410\) | 12.0115 | − | 6.93482i | 0.593204 | − | 0.342486i | ||||
\(411\) | − | 7.46980i | − | 0.368458i | ||||||
\(412\) | 11.0707 | + | 19.1750i | 0.545414 | + | 0.944684i | ||||
\(413\) | 1.13706 | − | 1.96945i | 0.0559512 | − | 0.0969104i | ||||
\(414\) | 13.4349 | + | 7.75667i | 0.660291 | + | 0.381219i | ||||
\(415\) | 2.77240 | 0.136092 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.9976 | 0.881347 | ||||||||
\(418\) | 5.11194 | + | 2.95138i | 0.250033 | + | 0.144357i | ||||
\(419\) | −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 | ||||
\(421\) | 13.5646i | 0.661100i | 0.943788 | + | 0.330550i | \(0.107234\pi\) | ||||
−0.943788 | + | 0.330550i | \(0.892766\pi\) | |||||||
\(422\) | −1.07268 | + | 0.619309i | −0.0522170 | + | 0.0301475i | ||||
\(423\) | −0.652135 | + | 0.376510i | −0.0317079 | + | 0.0183066i | ||||
\(424\) | 66.2747i | 3.21858i | ||||||||
\(425\) | −9.45862 | − | 16.3828i | −0.458810 | − | 0.794683i | ||||
\(426\) | 14.1380 | − | 24.4878i | 0.684989 | − | 1.18644i | ||||
\(427\) | −1.64525 | − | 0.949886i | −0.0796193 | − | 0.0459682i | ||||
\(428\) | −33.5478 | −1.62159 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 31.3370 | 1.51121 | ||||||||
\(431\) | −31.1304 | − | 17.9731i | −1.49950 | − | 0.865736i | −0.499499 | − | 0.866314i | \(-0.666483\pi\) |
−1.00000 | 0.000578325i | \(0.999816\pi\) | ||||||||
\(432\) | 6.51842 | − | 11.2902i | 0.313618 | − | 0.543201i | ||||
\(433\) | −16.2371 | − | 28.1234i | −0.780303 | − | 1.35152i | −0.931765 | − | 0.363061i | \(-0.881732\pi\) |
0.151462 | − | 0.988463i | \(-0.451602\pi\) | |||||||
\(434\) | − | 14.2161i | − | 0.682395i | ||||||
\(435\) | −1.73671 | + | 1.00269i | −0.0832687 | + | 0.0480752i | ||||
\(436\) | 15.7228 | − | 9.07756i | 0.752985 | − | 0.434736i | ||||
\(437\) | 4.33944i | 0.207583i | ||||||||
\(438\) | 14.1015 | + | 24.4245i | 0.673795 | + | 1.16705i | ||||
\(439\) | 6.41603 | − | 11.1129i | 0.306221 | − | 0.530390i | −0.671312 | − | 0.741175i | \(-0.734269\pi\) |
0.977532 | + | 0.210785i | \(0.0676021\pi\) | |||||||
\(440\) | −23.1206 | − | 13.3487i | −1.10223 | − | 0.636374i | ||||
\(441\) | 6.69202 | 0.318668 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.9608 | 0.568273 | 0.284137 | − | 0.958784i | \(-0.408293\pi\) | ||||
0.284137 | + | 0.958784i | \(0.408293\pi\) | |||||||
\(444\) | 26.1418 | + | 15.0930i | 1.24064 | + | 0.716282i | ||||
\(445\) | 5.20626 | − | 9.01751i | 0.246800 | − | 0.427471i | ||||
\(446\) | −22.0075 | − | 38.1182i | −1.04209 | − | 1.80495i | ||||
\(447\) | − | 15.3351i | − | 0.725327i | ||||||
\(448\) | 10.2573 | − | 5.92208i | 0.484614 | − | 0.279792i | ||||
\(449\) | 10.8070 | − | 6.23945i | 0.510016 | − | 0.294458i | −0.222824 | − | 0.974859i | \(-0.571528\pi\) |
0.732840 | + | 0.680401i | \(0.238194\pi\) | |||||||
\(450\) | 10.4983i | 0.494893i | ||||||||
\(451\) | −7.15130 | − | 12.3864i | −0.336742 | − | 0.583254i | ||||
\(452\) | 24.5477 | − | 42.5179i | 1.15463 | − | 1.99987i | ||||
\(453\) | −2.19173 | − | 1.26540i | −0.102977 | − | 0.0594536i | ||||
\(454\) | −17.6606 | −0.828851 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.58211 | 0.308235 | ||||||||
\(457\) | −28.1045 | − | 16.2262i | −1.31468 | − | 0.759028i | −0.331809 | − | 0.943347i | \(-0.607659\pi\) |
−0.982867 | + | 0.184319i | \(0.940992\pi\) | |||||||
\(458\) | 5.32400 | − | 9.22144i | 0.248774 | − | 0.430890i | ||||
\(459\) | 2.42543 | + | 4.20096i | 0.113209 | + | 0.196084i | ||||
\(460\) | − | 31.7159i | − | 1.47876i | ||||||
\(461\) | 21.1340 | − | 12.2017i | 0.984308 | − | 0.568290i | 0.0807398 | − | 0.996735i | \(-0.474272\pi\) |
0.903568 | + | 0.428445i | \(0.140938\pi\) | |||||||
\(462\) | 3.76738 | − | 2.17510i | 0.175274 | − | 0.101195i | ||||
\(463\) | 33.1836i | 1.54217i | 0.636731 | + | 0.771086i | \(0.280286\pi\) | ||||
−0.636731 | + | 0.771086i | \(0.719714\pi\) | |||||||
\(464\) | 12.4623 | + | 21.5853i | 0.578546 | + | 1.00207i | ||||
\(465\) | −4.99061 | + | 8.64398i | −0.231434 | + | 0.400855i | ||||
\(466\) | 19.4829 | + | 11.2485i | 0.902529 | + | 0.521075i | ||||
\(467\) | 38.5206 | 1.78252 | 0.891261 | − | 0.453490i | \(-0.149821\pi\) | ||||
0.891261 | + | 0.453490i | \(0.149821\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.03923 | −0.0479871 | ||||||||
\(470\) | 1.84144 | + | 1.06315i | 0.0849392 | + | 0.0490397i | ||||
\(471\) | 8.61960 | − | 14.9296i | 0.397170 | − | 0.687919i | ||||
\(472\) | 17.9095 | + | 31.0201i | 0.824350 | + | 1.42782i | ||||
\(473\) | − | 32.3153i | − | 1.48586i | ||||||
\(474\) | −3.11266 | + | 1.79709i | −0.142969 | + | 0.0825432i | ||||
\(475\) | −2.54318 | + | 1.46830i | −0.116689 | + | 0.0673704i | ||||
\(476\) | 14.1250i | 0.647417i | ||||||||
\(477\) | 3.79105 | + | 6.56630i | 0.173580 | + | 0.300650i | ||||
\(478\) | 27.0559 | − | 46.8622i | 1.23751 | − | 2.14343i | ||||
\(479\) | −7.22682 | − | 4.17241i | −0.330202 | − | 0.190642i | 0.325729 | − | 0.945463i | \(-0.394390\pi\) |
−0.655931 | + | 0.754821i | \(0.727724\pi\) | |||||||
\(480\) | −18.4752 | −0.843272 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −51.1825 | −2.33130 | ||||||||
\(483\) | 2.76960 | + | 1.59903i | 0.126021 | + | 0.0727584i | ||||
\(484\) | 6.61410 | − | 11.4560i | 0.300641 | − | 0.520725i | ||||
\(485\) | −8.95444 | − | 15.5095i | −0.406600 | − | 0.704252i | ||||
\(486\) | − | 2.69202i | − | 0.122113i | ||||||
\(487\) | −12.8679 | + | 7.42931i | −0.583102 | + | 0.336654i | −0.762365 | − | 0.647147i | \(-0.775962\pi\) |
0.179263 | + | 0.983801i | \(0.442629\pi\) | |||||||
\(488\) | 25.9137 | − | 14.9613i | 1.17306 | − | 0.677266i | ||||
\(489\) | 15.7071i | 0.710299i | ||||||||
\(490\) | −9.44816 | − | 16.3647i | −0.426824 | − | 0.739281i | ||||
\(491\) | 2.49947 | − | 4.32920i | 0.112799 | − | 0.195374i | −0.804099 | − | 0.594496i | \(-0.797352\pi\) |
0.916898 | + | 0.399122i | \(0.130685\pi\) | |||||||
\(492\) | −22.3196 | − | 12.8862i | −1.00624 | − | 0.580955i | ||||
\(493\) | −9.27413 | −0.417686 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.05429 | −0.137280 | ||||||||
\(496\) | 107.435 | + | 62.0275i | 4.82396 | + | 2.78512i | ||||
\(497\) | 2.91454 | − | 5.04814i | 0.130735 | − | 0.226440i | ||||
\(498\) | −3.55765 | − | 6.16202i | −0.159422 | − | 0.276127i | ||||
\(499\) | − | 0.385371i | − | 0.0172516i | −0.999963 | − | 0.00862579i | \(-0.997254\pi\) | ||
0.999963 | − | 0.00862579i | \(-0.00274571\pi\) | |||||||
\(500\) | 42.4190 | − | 24.4906i | 1.89703 | − | 1.09525i | ||||
\(501\) | 4.67318 | − | 2.69806i | 0.208782 | − | 0.120541i | ||||
\(502\) | 2.05610i | 0.0917681i | ||||||||
\(503\) | −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 | ||||
\(505\) | −6.65217 | − | 3.84063i | −0.296018 | − | 0.170906i | ||||
\(506\) | −45.1726 | −2.00817 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −23.5163 | −1.04337 | ||||||||
\(509\) | 10.0493 | + | 5.80194i | 0.445425 | + | 0.257166i | 0.705896 | − | 0.708315i | \(-0.250544\pi\) |
−0.260471 | + | 0.965482i | \(0.583878\pi\) | |||||||
\(510\) | 6.84870 | − | 11.8623i | 0.303265 | − | 0.525271i | ||||
\(511\) | 2.90701 | + | 5.03509i | 0.128599 | + | 0.222739i | ||||
\(512\) | 1.71678i | 0.0758715i | ||||||||
\(513\) | 0.652135 | − | 0.376510i | 0.0287925 | − | 0.0166233i | ||||
\(514\) | 30.5201 | − | 17.6208i | 1.34618 | − | 0.777220i | ||||
\(515\) | − | 4.42626i | − | 0.195044i | ||||||
\(516\) | −29.1151 | − | 50.4288i | −1.28172 | − | 2.22000i | ||||
\(517\) | 1.09634 | − | 1.89892i | 0.0482171 | − | 0.0835145i | ||||
\(518\) | 7.44330 | + | 4.29739i | 0.327040 | + | 0.188816i | ||||
\(519\) | 23.9420 | 1.05094 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.62671 | −0.0712675 | −0.0356337 | − | 0.999365i | \(-0.511345\pi\) | ||||
−0.0356337 | + | 0.999365i | \(0.511345\pi\) | |||||||
\(522\) | 4.45722 | + | 2.57338i | 0.195087 | + | 0.112634i | ||||
\(523\) | −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 | ||||
\(525\) | 2.16421i | 0.0944539i | ||||||||
\(526\) | 42.8442 | − | 24.7361i | 1.86809 | − | 1.07854i | ||||
\(527\) | −39.9752 | + | 23.0797i | −1.74135 | + | 1.00537i | ||||
\(528\) | 37.9614i | 1.65206i | ||||||||
\(529\) | −5.10441 | − | 8.84109i | −0.221931 | − | 0.384395i | ||||
\(530\) | 10.7048 | − | 18.5413i | 0.464988 | − | 0.805383i | ||||
\(531\) | 3.54883 | + | 2.04892i | 0.154006 | + | 0.0889154i | ||||
\(532\) | 2.19269 | 0.0950650 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −26.7235 | −1.15644 | ||||||||
\(535\) | 5.80800 | + | 3.35325i | 0.251102 | + | 0.144974i | ||||
\(536\) | 8.18425 | − | 14.1755i | 0.353506 | − | 0.612290i | ||||
\(537\) | −9.20440 | − | 15.9425i | −0.397199 | − | 0.687969i | ||||
\(538\) | 63.6999i | 2.74630i | ||||||||
\(539\) | −16.8755 | + | 9.74309i | −0.726881 | + | 0.419665i | ||||
\(540\) | −4.76630 | + | 2.75182i | −0.205109 | + | 0.118420i | ||||
\(541\) | 20.4674i | 0.879962i | 0.898007 | + | 0.439981i | \(0.145015\pi\) | ||||
−0.898007 | + | 0.439981i | \(0.854985\pi\) | |||||||
\(542\) | 26.5878 | + | 46.0514i | 1.14204 | + | 1.97808i | ||||
\(543\) | 1.81671 | − | 3.14663i | 0.0779624 | − | 0.135035i | ||||
\(544\) | −73.9939 | − | 42.7204i | −3.17246 | − | 1.83162i | ||||
\(545\) | −3.62937 | −0.155465 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.5478 | −1.17786 | −0.588929 | − | 0.808185i | \(-0.700450\pi\) | ||||
−0.588929 | + | 0.808185i | \(0.700450\pi\) | |||||||
\(548\) | 33.9429 | + | 19.5969i | 1.44997 | + | 0.837140i | ||||
\(549\) | 1.71164 | − | 2.96464i | 0.0730508 | − | 0.126528i | ||||
\(550\) | −15.2847 | − | 26.4739i | −0.651742 | − | 1.12885i | ||||
\(551\) | 1.43967i | 0.0613318i | ||||||||
\(552\) | −43.6230 | + | 25.1857i | −1.85672 | + | 1.07198i | ||||
\(553\) | −0.641672 | + | 0.370469i | −0.0272867 | + | 0.0157540i | ||||
\(554\) | − | 4.78581i | − | 0.203329i | ||||||
\(555\) | −3.01722 | − | 5.22598i | −0.128074 | − | 0.221831i | ||||
\(556\) | −47.2165 | + | 81.7814i | −2.00243 | + | 3.46831i | ||||
\(557\) | 32.8964 | + | 18.9928i | 1.39387 | + | 0.804749i | 0.993741 | − | 0.111711i | \(-0.0356331\pi\) |
0.400126 | + | 0.916460i | \(0.368966\pi\) | |||||||
\(558\) | 25.6165 | 1.08443 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −7.58881 | −0.320686 | ||||||||
\(561\) | −12.2326 | − | 7.06249i | −0.516460 | − | 0.298179i | ||||
\(562\) | −2.18233 | + | 3.77991i | −0.0920562 | + | 0.159446i | ||||
\(563\) | −14.8862 | − | 25.7837i | −0.627378 | − | 1.08665i | −0.988076 | − | 0.153968i | \(-0.950795\pi\) |
0.360697 | − | 0.932683i | \(-0.382539\pi\) | |||||||
\(564\) | − | 3.95108i | − | 0.166371i | ||||||
\(565\) | −8.49970 | + | 4.90731i | −0.357585 | + | 0.206452i | ||||
\(566\) | −11.6186 | + | 6.70799i | −0.488365 | + | 0.281958i | ||||
\(567\) | − | 0.554958i | − | 0.0233061i | ||||||
\(568\) | 45.9059 | + | 79.5113i | 1.92617 | + | 3.33622i | ||||
\(569\) | −10.9770 | + | 19.0128i | −0.460181 | + | 0.797057i | −0.998970 | − | 0.0453839i | \(-0.985549\pi\) |
0.538788 | + | 0.842441i | \(0.318882\pi\) | |||||||
\(570\) | −1.84144 | − | 1.06315i | −0.0771294 | − | 0.0445307i | ||||
\(571\) | −2.46575 | −0.103188 | −0.0515942 | − | 0.998668i | \(-0.516430\pi\) | ||||
−0.0515942 | + | 0.998668i | \(0.516430\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.1782 | 0.884732 | ||||||||
\(574\) | −6.35499 | − | 3.66905i | −0.265252 | − | 0.153143i | ||||
\(575\) | 11.2366 | − | 19.4624i | 0.468600 | − | 0.811639i | ||||
\(576\) | 10.6712 | + | 18.4831i | 0.444634 | + | 0.770128i | ||||
\(577\) | 17.4547i | 0.726650i | 0.931662 | + | 0.363325i | \(0.118359\pi\) | ||||
−0.931662 | + | 0.363325i | \(0.881641\pi\) | |||||||
\(578\) | 15.2256 | − | 8.79052i | 0.633303 | − | 0.365637i | ||||
\(579\) | −15.2517 | + | 8.80559i | −0.633840 | + | 0.365948i | ||||
\(580\) | − | 10.5222i | − | 0.436909i | ||||||
\(581\) | −0.733406 | − | 1.27030i | −0.0304268 | − | 0.0527008i | ||||
\(582\) | −22.9813 | + | 39.8049i | −0.952607 | + | 1.64996i | ||||
\(583\) | −19.1201 | − | 11.0390i | −0.791873 | − | 0.457188i | ||||
\(584\) | −91.5745 | −3.78938 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.193159 | −0.00797934 | ||||||||
\(587\) | −5.42424 | − | 3.13169i | −0.223882 | − | 0.129259i | 0.383864 | − | 0.923390i | \(-0.374593\pi\) |
−0.607747 | + | 0.794131i | \(0.707926\pi\) | |||||||
\(588\) | −17.5565 | + | 30.4087i | −0.724016 | + | 1.25403i | ||||
\(589\) | 3.58277 | + | 6.20554i | 0.147625 | + | 0.255695i | ||||
\(590\) | − | 11.5711i | − | 0.476374i | ||||||
\(591\) | 4.03783 | − | 2.33124i | 0.166094 | − | 0.0958944i | ||||
\(592\) | −64.9529 | + | 37.5006i | −2.66955 | + | 1.54126i | ||||
\(593\) | − | 22.8745i | − | 0.939345i | −0.882841 | − | 0.469672i | \(-0.844372\pi\) | ||
0.882841 | − | 0.469672i | \(-0.155628\pi\) | |||||||
\(594\) | 3.91939 | + | 6.78858i | 0.160814 | + | 0.278539i | ||||
\(595\) | 1.41185 | − | 2.44540i | 0.0578804 | − | 0.100252i | ||||
\(596\) | 69.6831 | + | 40.2315i | 2.85433 | + | 1.64795i | ||||
\(597\) | 15.0368 | 0.615417 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.05621 | −0.0431557 | −0.0215778 | − | 0.999767i | \(-0.506869\pi\) | ||||
−0.0215778 | + | 0.999767i | \(0.506869\pi\) | |||||||
\(600\) | −29.5208 | − | 17.0438i | −1.20518 | − | 0.695812i | ||||
\(601\) | 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 | ||||
\(603\) | − | 1.87263i | − | 0.0762592i | ||||||
\(604\) | 11.5000 | − | 6.63951i | 0.467927 | − | 0.270158i | ||||
\(605\) | −2.29015 | + | 1.32222i | −0.0931076 | + | 0.0537557i | ||||
\(606\) | 19.7138i | 0.800818i | ||||||||
\(607\) | −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 | ||||
\(609\) | 0.918852 | + | 0.530499i | 0.0372338 | + | 0.0214969i | ||||
\(610\) | −9.66632 | −0.391378 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −25.4523 | −1.02885 | ||||||||
\(613\) | −9.56772 | − | 5.52393i | −0.386437 | − | 0.223109i | 0.294178 | − | 0.955751i | \(-0.404954\pi\) |
−0.680615 | + | 0.732641i | \(0.738287\pi\) | |||||||
\(614\) | 6.99665 | − | 12.1185i | 0.282362 | − | 0.489065i | ||||
\(615\) | 2.57606 | + | 4.46187i | 0.103877 | + | 0.179920i | ||||
\(616\) | 14.1250i | 0.569112i | ||||||||
\(617\) | −4.03524 | + | 2.32975i | −0.162453 | + | 0.0937922i | −0.579022 | − | 0.815312i | \(-0.696566\pi\) |
0.416570 | + | 0.909104i | \(0.363232\pi\) | |||||||
\(618\) | −9.83794 | + | 5.67994i | −0.395740 | + | 0.228481i | ||||
\(619\) | − | 31.9259i | − | 1.28321i | −0.767036 | − | 0.641604i | \(-0.778269\pi\) | ||
0.767036 | − | 0.641604i | \(-0.221731\pi\) | |||||||
\(620\) | −26.1856 | − | 45.3548i | −1.05164 | − | 1.82149i | ||||
\(621\) | −2.88135 | + | 4.99065i | −0.115625 | + | 0.200268i | ||||
\(622\) | −52.5555 | − | 30.3430i | −2.10729 | − | 1.21664i | ||||
\(623\) | −5.50902 | −0.220714 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.70709 | 0.388283 | ||||||||
\(626\) | −52.8313 | − | 30.5022i | −2.11156 | − | 1.21911i | ||||
\(627\) | −1.09634 | + | 1.89892i | −0.0437837 | + | 0.0758356i | ||||
\(628\) | 45.2269 | + | 78.3353i | 1.80475 | + | 3.12592i | ||||
\(629\) | − | 27.9071i | − | 1.11273i | ||||||
\(630\) | −1.35710 | + | 0.783520i | −0.0540680 | + | 0.0312162i | ||||
\(631\) | 34.1572 | − | 19.7207i | 1.35978 | − | 0.785067i | 0.370183 | − | 0.928959i | \(-0.379295\pi\) |
0.989593 | + | 0.143892i | \(0.0459618\pi\) | |||||||
\(632\) | − | 11.6703i | − | 0.464218i | ||||||
\(633\) | −0.230054 | − | 0.398465i | −0.00914381 | − | 0.0158375i | ||||
\(634\) | 35.4572 | − | 61.4136i | 1.40818 | − | 2.43905i | ||||
\(635\) | 4.07129 | + | 2.35056i | 0.161564 | + | 0.0932791i | ||||
\(636\) | −39.7832 | −1.57750 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.9866 | −0.593325 | ||||||||
\(639\) | 9.09643 | + | 5.25182i | 0.359849 | + | 0.207759i | ||||
\(640\) | 11.6572 | − | 20.1909i | 0.460792 | − | 0.798115i | ||||
\(641\) | 22.7255 | + | 39.3617i | 0.897603 | + | 1.55469i | 0.830549 | + | 0.556946i | \(0.188027\pi\) |
0.0670544 | + | 0.997749i | \(0.478640\pi\) | |||||||
\(642\) | − | 17.2121i | − | 0.679306i | ||||||
\(643\) | −25.7616 | + | 14.8735i | −1.01594 | + | 0.586552i | −0.912925 | − | 0.408128i | \(-0.866182\pi\) |
−0.103013 | + | 0.994680i | \(0.532848\pi\) | |||||||
\(644\) | −14.5321 | + | 8.39008i | −0.572643 | + | 0.330616i | ||||
\(645\) | 11.6407i | 0.458353i | ||||||||
\(646\) | −4.91670 | − | 8.51597i | −0.193445 | − | 0.335056i | ||||
\(647\) | −8.46562 | + | 14.6629i | −0.332818 | + | 0.576457i | −0.983063 | − | 0.183267i | \(-0.941333\pi\) |
0.650245 | + | 0.759724i | \(0.274666\pi\) | |||||||
\(648\) | 7.56988 | + | 4.37047i | 0.297373 | + | 0.171688i | ||||
\(649\) | −11.9323 | −0.468384 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.28083 | 0.206972 | ||||||||
\(652\) | −71.3733 | − | 41.2074i | −2.79519 | − | 1.61381i | ||||
\(653\) | 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 | ||||
\(655\) | 9.66833i | 0.377773i | ||||||||
\(656\) | 55.4560 | − | 32.0175i | 2.16519 | − | 1.25007i | ||||
\(657\) | −9.07292 | + | 5.23825i | −0.353968 | + | 0.204364i | ||||
\(658\) | − | 1.12498i | − | 0.0438564i | ||||||
\(659\) | 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 | ||||
\(661\) | 33.5067 | + | 19.3451i | 1.30326 | + | 0.752438i | 0.980962 | − | 0.194201i | \(-0.0622113\pi\) |
0.322298 | + | 0.946638i | \(0.395545\pi\) | |||||||
\(662\) | 30.2301 | 1.17493 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 23.1032 | 0.896578 | ||||||||
\(665\) | −0.379611 | − | 0.219169i | −0.0147207 | − | 0.00849899i | ||||
\(666\) | −7.74363 | + | 13.4124i | −0.300059 | + | 0.519718i | ||||
\(667\) | −5.50873 | − | 9.54140i | −0.213299 | − | 0.369444i | ||||
\(668\) | 28.3134i | 1.09548i | ||||||||
\(669\) | 14.1597 | − | 8.17510i | 0.547445 | − | 0.316067i | ||||
\(670\) | −4.57932 | + | 2.64387i | −0.176915 | + | 0.102142i | ||||
\(671\) | 9.96807i | 0.384813i | ||||||||
\(672\) | 4.88740 | + | 8.46522i | 0.188535 | + | 0.326553i | ||||
\(673\) | −1.29709 | + | 2.24663i | −0.0499993 | + | 0.0866013i | −0.889942 | − | 0.456074i | \(-0.849255\pi\) |
0.839943 | + | 0.542675i | \(0.182589\pi\) | |||||||
\(674\) | 5.38073 | + | 3.10656i | 0.207258 | + | 0.119660i | ||||
\(675\) | −3.89977 | −0.150102 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.75302 | 0.0673740 | 0.0336870 | − | 0.999432i | \(-0.489275\pi\) | ||||
0.0336870 | + | 0.999432i | \(0.489275\pi\) | |||||||
\(678\) | 21.8143 | + | 12.5945i | 0.837773 | + | 0.483688i | ||||
\(679\) | −4.73759 | + | 8.20574i | −0.181812 | + | 0.314907i | ||||
\(680\) | 22.2376 | + | 38.5166i | 0.852773 | + | 1.47705i | ||||
\(681\) | − | 6.56033i | − | 0.251393i | ||||||
\(682\) | −64.5983 | + | 37.2958i | −2.47360 | + | 1.42813i | ||||
\(683\) | −14.1466 | + | 8.16756i | −0.541306 | + | 0.312523i | −0.745608 | − | 0.666385i | \(-0.767841\pi\) |
0.204302 | + | 0.978908i | \(0.434508\pi\) | |||||||
\(684\) | 3.95108i | 0.151073i | ||||||||
\(685\) | −3.91760 | − | 6.78548i | −0.149684 | − | 0.259260i | ||||
\(686\) | −10.2277 | + | 17.7148i | −0.390494 | + | 0.676355i | ||||
\(687\) | 3.42547 | + | 1.97770i | 0.130690 | + | 0.0754539i | ||||
\(688\) | 144.681 | 5.51590 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 16.2722 | 0.619472 | ||||||||
\(691\) | −13.7789 | − | 7.95526i | −0.524175 | − | 0.302632i | 0.214466 | − | 0.976731i | \(-0.431199\pi\) |
−0.738641 | + | 0.674099i | \(0.764532\pi\) | |||||||
\(692\) | −62.8116 | + | 108.793i | −2.38774 | + | 4.13568i | ||||
\(693\) | 0.807979 | + | 1.39946i | 0.0306926 | + | 0.0531611i | ||||
\(694\) | − | 24.5972i | − | 0.933696i | ||||||
\(695\) | 16.3488 | − | 9.43900i | 0.620146 | − | 0.358042i | ||||
\(696\) | −14.4725 | + | 8.35570i | −0.548579 | + | 0.316722i | ||||
\(697\) | 23.8267i | 0.902500i | ||||||||
\(698\) | −32.2717 | − | 55.8963i | −1.22150 | − | 2.11571i | ||||
\(699\) | −4.17845 | + | 7.23728i | −0.158043 | + | 0.273739i | ||||
\(700\) | −9.83421 | − | 5.67778i | −0.371698 | − | 0.214600i | ||||
\(701\) | 20.8635 | 0.788005 | 0.394002 | − | 0.919109i | \(-0.371090\pi\) | ||||
0.394002 | + | 0.919109i | \(0.371090\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.33214 | −0.163390 | ||||||||
\(704\) | −53.8200 | − | 31.0730i | −2.02842 | − | 1.17111i | ||||
\(705\) | −0.394928 | + | 0.684035i | −0.0148739 | + | 0.0257623i | ||||
\(706\) | −36.5091 | − | 63.2356i | −1.37404 | − | 2.37990i | ||||
\(707\) | 4.06398i | 0.152842i | ||||||||
\(708\) | −18.6206 | + | 10.7506i | −0.699806 | + | 0.404033i | ||||
\(709\) | −13.5520 | + | 7.82424i | −0.508955 | + | 0.293846i | −0.732404 | − | 0.680870i | \(-0.761602\pi\) |
0.223449 | + | 0.974716i | \(0.428268\pi\) | |||||||
\(710\) | − | 29.6592i | − | 1.11309i | ||||||
\(711\) | −0.667563 | − | 1.15625i | −0.0250356 | − | 0.0433629i | ||||
\(712\) | 43.3853 | − | 75.1455i | 1.62593 | − | 2.81620i | ||||
\(713\) | −47.4897 | − | 27.4182i | −1.77850 | − | 1.02682i | ||||
\(714\) | −7.24698 | −0.271211 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 96.5906 | 3.60976 | ||||||||
\(717\) | 17.4078 | + | 10.0504i | 0.650107 | + | 0.375339i | ||||
\(718\) | 35.1027 | − | 60.7996i | 1.31002 | − | 2.26902i | ||||
\(719\) | −13.5797 | − | 23.5208i | −0.506438 | − | 0.877176i | −0.999972 | − | 0.00744977i | \(-0.997629\pi\) |
0.493534 | − | 0.869726i | \(-0.335705\pi\) | |||||||
\(720\) | − | 13.6746i | − | 0.509621i | ||||||
\(721\) | −2.02808 | + | 1.17092i | −0.0755298 | + | 0.0436072i | ||||
\(722\) | 42.9738 | − | 24.8110i | 1.59932 | − | 0.923368i | ||||
\(723\) | − | 19.0127i | − | 0.707089i | ||||||
\(724\) | 9.53223 | + | 16.5103i | 0.354262 | + | 0.613601i | ||||
\(725\) | 3.72790 | − | 6.45691i | 0.138451 | − | 0.239804i | ||||
\(726\) | 5.87760 | + | 3.39344i | 0.218138 | + | 0.125942i | ||||
\(727\) | −31.7784 | −1.17859 | −0.589297 | − | 0.807916i | \(-0.700595\pi\) | ||||
−0.589297 | + | 0.807916i | \(0.700595\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 25.6193 | + | 14.7913i | 0.948212 | + | 0.547450i | ||||
\(731\) | −26.9170 | + | 46.6216i | −0.995561 | + | 1.72436i | ||||
\(732\) | 8.98092 | + | 15.5554i | 0.331944 | + | 0.574944i | ||||
\(733\) | 46.8907i | 1.73195i | 0.500090 | + | 0.865973i | \(0.333300\pi\) | ||||
−0.500090 | + | 0.865973i | \(0.666700\pi\) | |||||||
\(734\) | 22.3212 | − | 12.8872i | 0.823891 | − | 0.475674i | ||||
\(735\) | 6.07896 | − | 3.50969i | 0.224226 | − | 0.129457i | ||||
\(736\) | − | 101.502i | − | 3.74141i | ||||||
\(737\) | 2.72641 | + | 4.72227i | 0.100428 | + | 0.173947i | ||||
\(738\) | 6.61141 | − | 11.4513i | 0.243369 | − | 0.421528i | ||||
\(739\) | 14.7639 | + | 8.52393i | 0.543098 | + | 0.313558i | 0.746334 | − | 0.665572i | \(-0.231812\pi\) |
−0.203236 | + | 0.979130i | \(0.565146\pi\) | |||||||
\(740\) | 31.6626 | 1.16394 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.3274 | −0.415840 | ||||||||
\(743\) | 10.0739 | + | 5.81618i | 0.369576 | + | 0.213375i | 0.673273 | − | 0.739394i | \(-0.264888\pi\) |
−0.303697 | + | 0.952769i | \(0.598221\pi\) | |||||||
\(744\) | −41.5882 | + | 72.0329i | −1.52470 | + | 2.64085i | ||||
\(745\) | −8.04264 | − | 13.9303i | −0.294660 | − | 0.510365i | ||||
\(746\) | 75.7797i | 2.77449i | ||||||||
\(747\) | 2.28900 | − | 1.32155i | 0.0837500 | − | 0.0483531i | ||||
\(748\) | 64.1842 | − | 37.0567i | 2.34681 | − | 1.35493i | ||||
\(749\) | − | 3.54825i | − | 0.129650i | ||||||
\(750\) | 12.5652 | + | 21.7635i | 0.458815 | + | 0.794692i | ||||
\(751\) | −6.51477 | + | 11.2839i | −0.237727 | + | 0.411756i | −0.960062 | − | 0.279788i | \(-0.909736\pi\) |
0.722334 | + | 0.691544i | \(0.243069\pi\) | |||||||
\(752\) | 8.50177 | + | 4.90850i | 0.310028 | + | 0.178995i | ||||
\(753\) | −0.763774 | −0.0278335 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.65459 | −0.0966106 | ||||||||
\(756\) | 2.52174 | + | 1.45593i | 0.0917148 | + | 0.0529516i | ||||
\(757\) | −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 | ||||
\(759\) | − | 16.7802i | − | 0.609081i | ||||||
\(760\) | 5.97911 | − | 3.45204i | 0.216885 | − | 0.125219i | ||||
\(761\) | 33.2055 | − | 19.1712i | 1.20370 | − | 0.694956i | 0.242323 | − | 0.970196i | \(-0.422091\pi\) |
0.961376 | + | 0.275240i | \(0.0887572\pi\) | |||||||
\(762\) | − | 12.0653i | − | 0.437080i | ||||||
\(763\) | 0.960107 | + | 1.66295i | 0.0347582 | + | 0.0602030i | ||||
\(764\) | −55.5608 | + | 96.2342i | −2.01012 | + | 3.48163i | ||||
\(765\) | 4.40646 | + | 2.54407i | 0.159316 | + | 0.0919812i | ||||
\(766\) | 66.2683 | 2.39437 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −17.1511 | −0.618886 | ||||||||
\(769\) | 3.15129 | + | 1.81940i | 0.113638 | + | 0.0656091i | 0.555742 | − | 0.831355i | \(-0.312434\pi\) |
−0.442104 | + | 0.896964i | \(0.645768\pi\) | |||||||
\(770\) | 2.28150 | − | 3.95167i | 0.0822194 | − | 0.142408i | ||||
\(771\) | 6.54556 | + | 11.3373i | 0.235733 | + | 0.408301i | ||||
\(772\) | − | 92.4055i | − | 3.32575i | ||||||
\(773\) | −34.0715 | + | 19.6712i | −1.22547 | + | 0.707524i | −0.966079 | − | 0.258249i | \(-0.916855\pi\) |
−0.259389 | + | 0.965773i | \(0.583521\pi\) | |||||||
\(774\) | 25.8730 | − | 14.9378i | 0.929987 | − | 0.536928i | ||||
\(775\) | − | 37.1092i | − | 1.33300i | ||||||
\(776\) | −74.6200 | − | 129.246i | −2.67870 | − | 4.63965i | ||||
\(777\) | −1.59634 | + | 2.76495i | −0.0572685 | + | 0.0991919i | ||||
\(778\) | −40.1456 | − | 23.1781i | −1.43929 | − | 0.830974i | ||||
\(779\) | 3.69873 | 0.132521 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.5851 | −1.09442 | ||||||||
\(782\) | 65.1710 | + | 37.6265i | 2.33051 | + | 1.34552i | ||||
\(783\) | −0.955927 | + | 1.65571i | −0.0341620 | + | 0.0591704i | ||||
\(784\) | −43.6214 | − | 75.5545i | −1.55791 | − | 2.69837i | ||||
\(785\) | − | 18.0825i | − | 0.645392i | ||||||
\(786\) | 21.4892 | − | 12.4068i | 0.766493 | − | 0.442535i | ||||
\(787\) | 22.0189 | − | 12.7126i | 0.784888 | − | 0.453155i | −0.0532720 | − | 0.998580i | \(-0.516965\pi\) |
0.838160 | + | 0.545425i | \(0.183632\pi\) | |||||||
\(788\) | 24.4639i | 0.871492i | ||||||||
\(789\) | 9.18867 | + | 15.9152i | 0.327125 | + | 0.566598i | ||||
\(790\) | −1.88500 | + | 3.26492i | −0.0670654 | + | 0.116161i | ||||
\(791\) | 4.49700 | + | 2.59634i | 0.159895 | + | 0.0923153i | ||||
\(792\) | −25.4523 | −0.904409 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −5.48965 | −0.194820 | ||||||||
\(795\) | 6.88750 | + | 3.97650i | 0.244275 | + | 0.141032i | ||||
\(796\) | −39.4490 | + | 68.3276i | −1.39823 | + | 2.42181i | ||||
\(797\) | 10.3569 | + | 17.9387i | 0.366860 | + | 0.635420i | 0.989073 | − | 0.147428i | \(-0.0470994\pi\) |
−0.622213 | + | 0.782848i | \(0.713766\pi\) | |||||||
\(798\) | 1.12498i | 0.0398239i | ||||||||
\(799\) | −3.16341 | + | 1.82640i | −0.111913 | + | 0.0646133i | ||||
\(800\) | 59.4863 | − | 34.3444i | 2.10316 | − | 1.21426i | ||||
\(801\) | − | 9.92692i | − | 0.350750i | ||||||
\(802\) | 1.96711 | + | 3.40713i | 0.0694610 | + | 0.120310i | ||||
\(803\) | 15.2530 | − | 26.4190i | 0.538267 | − | 0.932306i | ||||
\(804\) | 8.50924 | + | 4.91281i | 0.300098 | + | 0.173262i | ||||
\(805\) | 3.35450 | 0.118231 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.6625 | −0.832959 | ||||||||
\(808\) | −55.4345 | − | 32.0051i | −1.95018 | − | 1.12594i | ||||
\(809\) | −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 | ||||
\(811\) | − | 4.84223i | − | 0.170034i | −0.996380 | − | 0.0850169i | \(-0.972906\pi\) | ||
0.996380 | − | 0.0850169i | \(-0.0270944\pi\) | |||||||
\(812\) | −4.82120 | + | 2.78352i | −0.169191 | + | 0.0976824i | ||||
\(813\) | −17.1066 | + | 9.87651i | −0.599955 | + | 0.346384i | ||||
\(814\) | − | 45.0966i | − | 1.58064i | ||||||
\(815\) | 8.23772 | + | 14.2681i | 0.288555 | + | 0.499791i | ||||
\(816\) | 31.6199 | − | 54.7673i | 1.10692 | − | 1.91724i | ||||
\(817\) | 7.23728 | + | 4.17845i | 0.253201 | + | 0.146185i | ||||
\(818\) | 80.5964 | 2.81799 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −27.0331 | −0.944037 | ||||||||
\(821\) | 37.8783 | + | 21.8690i | 1.32196 | + | 0.763235i | 0.984041 | − | 0.177940i | \(-0.0569434\pi\) |
0.337920 | + | 0.941175i | \(0.390277\pi\) | |||||||
\(822\) | −10.0544 | + | 17.4148i | −0.350688 | + | 0.607410i | ||||
\(823\) | 6.04988 | + | 10.4787i | 0.210885 | + | 0.365264i | 0.951992 | − | 0.306123i | \(-0.0990320\pi\) |
−0.741106 | + | 0.671388i | \(0.765699\pi\) | |||||||
\(824\) | − | 36.8853i | − | 1.28496i | ||||||
\(825\) | 9.83421 | − | 5.67778i | 0.342383 | − | 0.197675i | ||||
\(826\) | −5.30181 | + | 3.06100i | −0.184473 | + | 0.106506i | ||||
\(827\) | 35.3212i | 1.22824i | 0.789213 | + | 0.614120i | \(0.210489\pi\) | ||||
−0.789213 | + | 0.614120i | \(0.789511\pi\) | |||||||
\(828\) | −15.1184 | − | 26.1859i | −0.525401 | − | 0.910021i | ||||
\(829\) | 26.7473 | − | 46.3276i | 0.928971 | − | 1.60903i | 0.143925 | − | 0.989589i | \(-0.454028\pi\) |
0.785047 | − | 0.619437i | \(-0.212639\pi\) | |||||||
\(830\) | −6.46345 | − | 3.73168i | −0.224350 | − | 0.129528i | ||||
\(831\) | 1.77777 | 0.0616703 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 32.4620 | 1.12474 | ||||||||
\(834\) | −41.9589 | − | 24.2250i | −1.45292 | − | 0.838842i | ||||
\(835\) | 2.83004 | − | 4.90178i | 0.0979377 | − | 0.169633i | ||||
\(836\) | −5.75249 | − | 9.96360i | −0.198954 | − | 0.344598i | ||||
\(837\) | 9.51573i | 0.328912i | ||||||||
\(838\) | 15.4975 | − | 8.94749i | 0.535353 | − | 0.309086i | ||||
\(839\) | −20.0503 | + | 11.5761i | −0.692214 | + | 0.399650i | −0.804441 | − | 0.594033i | \(-0.797535\pi\) |
0.112227 | + | 0.993683i | \(0.464202\pi\) | |||||||
\(840\) | − | 5.08815i | − | 0.175558i | ||||||
\(841\) | 12.6724 | + | 21.9493i | 0.436980 | + | 0.756871i | ||||
\(842\) | 18.2582 | − | 31.6241i | 0.629218 | − | 1.08984i | ||||
\(843\) | −1.40412 | − | 0.810667i | −0.0483603 | − | 0.0279209i | ||||
\(844\) | 2.41417 | 0.0830993 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.02715 | 0.0696948 | ||||||||
\(847\) | 1.21166 | + | 0.699554i | 0.0416332 | + | 0.0240370i | ||||
\(848\) | 49.4233 | − | 85.6037i | 1.69720 | − | 2.93964i | ||||
\(849\) | −2.49180 | − | 4.31593i | −0.0855185 | − | 0.148122i | ||||
\(850\) | 50.9256i | 1.74673i | ||||||||
\(851\) | 28.7113 | − | 16.5765i | 0.984212 | − | 0.568235i | ||||
\(852\) | −47.7288 | + | 27.5562i | −1.63516 | + | 0.944060i | ||||
\(853\) | − | 26.7265i | − | 0.915097i | −0.889185 | − | 0.457548i | \(-0.848728\pi\) | ||
0.889185 | − | 0.457548i | \(-0.151272\pi\) | |||||||
\(854\) | 2.55711 | + | 4.42905i | 0.0875026 | + | 0.151559i | ||||
\(855\) | 0.394928 | − | 0.684035i | 0.0135063 | − | 0.0233935i | ||||
\(856\) | 48.3997 | + | 27.9436i | 1.65427 | + | 0.955093i | ||||
\(857\) | −42.6064 | −1.45541 | −0.727703 | − | 0.685892i | \(-0.759412\pi\) | ||||
−0.727703 | + | 0.685892i | \(0.759412\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.6079 | 1.14669 | 0.573344 | − | 0.819315i | \(-0.305646\pi\) | ||||
0.573344 | + | 0.819315i | \(0.305646\pi\) | |||||||
\(860\) | −52.8956 | − | 30.5393i | −1.80372 | − | 1.04138i | ||||
\(861\) | 1.36294 | − | 2.36068i | 0.0464488 | − | 0.0804516i | ||||
\(862\) | 48.3841 | + | 83.8037i | 1.64797 | + | 2.85437i | ||||
\(863\) | 18.7047i | 0.636715i | 0.947971 | + | 0.318358i | \(0.103131\pi\) | ||||
−0.947971 | + | 0.318358i | \(0.896869\pi\) | |||||||
\(864\) | −15.2538 | + | 8.80678i | −0.518945 | + | 0.299613i | ||||
\(865\) | 21.7486 | − | 12.5566i | 0.739476 | − | 0.426937i | ||||
\(866\) | 87.4210i | 2.97069i | ||||||||
\(867\) | 3.26540 | + | 5.65583i | 0.110899 | + | 0.192082i | ||||
\(868\) | −13.8542 | + | 23.9962i | −0.470242 | + | 0.814484i | ||||
\(869\) | 3.36684 | + | 1.94385i | 0.114212 | + | 0.0659404i | ||||
\(870\) | 5.39852 | 0.183027 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −30.2446 | −1.02421 | ||||||||
\(873\) | −14.7862 | − | 8.53684i | −0.500438 | − | 0.288928i | ||||
\(874\) | 5.84093 | − | 10.1168i | 0.197572 | − | 0.342205i | ||||
\(875\) | 2.59030 | + | 4.48653i | 0.0875682 | + | 0.151673i | ||||
\(876\) | − | 54.9700i | − | 1.85726i | ||||||
\(877\) | 31.8903 | − | 18.4119i | 1.07686 | − | 0.621724i | 0.146811 | − | 0.989165i | \(-0.453099\pi\) |
0.930047 | + | 0.367440i | \(0.119766\pi\) | |||||||
\(878\) | −29.9162 | + | 17.2721i | −1.00962 | + | 0.582905i | ||||
\(879\) | − | 0.0717525i | − | 0.00242015i | ||||||
\(880\) | 19.9092 | + | 34.4837i | 0.671138 | + | 1.16244i | ||||
\(881\) | −20.5625 | + | 35.6153i | −0.692768 | + | 1.19991i | 0.278159 | + | 0.960535i | \(0.410276\pi\) |
−0.970927 | + | 0.239374i | \(0.923058\pi\) | |||||||
\(882\) | −15.6015 | − | 9.00753i | −0.525330 | − | 0.303299i | ||||
\(883\) | −30.7482 | −1.03476 | −0.517380 | − | 0.855756i | \(-0.673093\pi\) | ||||
−0.517380 | + | 0.855756i | \(0.673093\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.29829 | 0.144485 | ||||||||
\(886\) | −27.8849 | − | 16.0993i | −0.936810 | − | 0.540867i | ||||
\(887\) | −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 | ||||
\(889\) | − | 2.48725i | − | 0.0834198i | ||||||
\(890\) | −24.2753 | + | 14.0154i | −0.813710 | + | 0.469796i | ||||
\(891\) | −2.52174 | + | 1.45593i | −0.0844815 | + | 0.0487754i | ||||
\(892\) | 85.7891i | 2.87243i | ||||||||
\(893\) | 0.283520 | + | 0.491071i | 0.00948763 | + | 0.0164331i | ||||
\(894\) | −20.6412 | + | 35.7517i | −0.690346 | + | 1.19572i | ||||
\(895\) | −16.7223 | − | 9.65465i | −0.558967 | − | 0.322719i | ||||
\(896\) | −12.3351 | −0.412088 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.5934 | −1.12103 | ||||||||
\(899\) | −15.7553 | − | 9.09634i | −0.525470 | − | 0.303380i | ||||
\(900\) | 10.2310 | − | 17.7206i | 0.341034 | − | 0.590688i | ||||
\(901\) | 18.3898 | + | 31.8521i | 0.612655 | + | 1.06115i | ||||
\(902\) | 38.5029i | 1.28201i | ||||||||
\(903\) | 5.33371 | − | 3.07942i | 0.177495 | − | 0.102477i | ||||
\(904\) | −70.8305 | + | 40.8940i | −2.35579 | + | 1.36012i | ||||
\(905\) | − | 3.81115i | − | 0.126687i | ||||||
\(906\) | 3.40648 | + | 5.90019i | 0.113173 | + | 0.196021i | ||||
\(907\) | 9.66666 | − | 16.7431i | 0.320976 | − | 0.555947i | −0.659713 | − | 0.751517i | \(-0.729322\pi\) |
0.980690 | + | 0.195570i | \(0.0626557\pi\) | |||||||
\(908\) | 29.8103 | + | 17.2110i | 0.989289 | + | 0.571166i | ||||
\(909\) | −7.32304 | −0.242890 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.7149 | 0.752577 | 0.376288 | − | 0.926503i | \(-0.377200\pi\) | ||||
0.376288 | + | 0.926503i | \(0.377200\pi\) | |||||||
\(912\) | −8.50177 | − | 4.90850i | −0.281522 | − | 0.162537i | ||||
\(913\) | −3.84817 | + | 6.66522i | −0.127356 | + | 0.220587i | ||||
\(914\) | 43.6812 | + | 75.6580i | 1.44485 | + | 2.50255i | ||||
\(915\) | − | 3.59073i | − | 0.118706i | ||||||
\(916\) | −17.9734 | + | 10.3769i | −0.593857 | + | 0.342864i | ||||
\(917\) | 4.42997 | − | 2.55765i | 0.146291 | − | 0.0844609i | ||||
\(918\) | − | 13.0586i | − | 0.430998i | ||||||
\(919\) | −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 | ||||
\(921\) | 4.50165 | + | 2.59903i | 0.148335 | + | 0.0856410i | ||||
\(922\) | −65.6945 | −2.16353 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −8.47889 | −0.278935 | ||||||||
\(925\) | 19.4297 | + | 11.2177i | 0.638844 | + | 0.368837i | ||||
\(926\) | 44.6655 | − | 77.3629i | 1.46780 | − | 2.54230i | ||||
\(927\) | −2.10992 | − | 3.65448i | −0.0692987 | − | 0.120029i | ||||
\(928\) | − | 33.6746i | − | 1.10542i | ||||||
\(929\) | 28.3373 | − | 16.3605i | 0.929716 | − | 0.536772i | 0.0429946 | − | 0.999075i | \(-0.486310\pi\) |
0.886722 | + | 0.462303i | \(0.152977\pi\) | |||||||
\(930\) | 23.2698 | − | 13.4348i | 0.763047 | − | 0.440545i | ||||
\(931\) | − | 5.03923i | − | 0.165154i | ||||||
\(932\) | −21.9242 | − | 37.9739i | −0.718152 | − | 1.24388i | ||||
\(933\) | 11.2714 | − | 19.5227i | 0.369010 | − | 0.639145i | ||||
\(934\) | −89.8054 | − | 51.8492i | −2.93852 | − | 1.69656i | ||||
\(935\) | −14.8159 | −0.484533 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.01400 | −0.131132 | −0.0655658 | − | 0.997848i | \(-0.520885\pi\) | ||||
−0.0655658 | + | 0.997848i | \(0.520885\pi\) | |||||||
\(938\) | 2.42282 | + | 1.39881i | 0.0791077 | + | 0.0456729i | ||||
\(939\) | 11.3306 | − | 19.6251i | 0.369759 | − | 0.640442i | ||||
\(940\) | −2.07218 | − | 3.58912i | −0.0675870 | − | 0.117064i | ||||
\(941\) | − | 28.2669i | − | 0.921476i | −0.887536 | − | 0.460738i | \(-0.847585\pi\) | ||
0.887536 | − | 0.460738i | \(-0.152415\pi\) | |||||||
\(942\) | −40.1908 | + | 23.2042i | −1.30949 | + | 0.756032i | ||||
\(943\) | −24.5134 | + | 14.1528i | −0.798265 | + | 0.460878i | ||||
\(944\) | − | 53.4228i | − | 1.73876i | ||||||
\(945\) | −0.291053 | − | 0.504118i | −0.00946794 | − | 0.0163990i | ||||
\(946\) | −43.4967 | + | 75.3385i | −1.41420 | + | 2.44947i | ||||
\(947\) | −32.7751 | − | 18.9227i | −1.06505 | − | 0.614906i | −0.138225 | − | 0.990401i | \(-0.544140\pi\) |
−0.926825 | + | 0.375495i | \(0.877473\pi\) | |||||||
\(948\) | 7.00538 | 0.227524 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 7.90541 | 0.256485 | ||||||||
\(951\) | 22.8132 | + | 13.1712i | 0.739769 | + | 0.427106i | ||||
\(952\) | 11.7654 | − | 20.3783i | 0.381319 | − | 0.660463i | ||||
\(953\) | −20.4128 | − | 35.3560i | −0.661236 | − | 1.14529i | −0.980291 | − | 0.197558i | \(-0.936699\pi\) |
0.319055 | − | 0.947736i | \(-0.396634\pi\) | |||||||
\(954\) | − | 20.4112i | − | 0.660837i | ||||||
\(955\) | 19.2381 | − | 11.1071i | 0.622529 | − | 0.359417i | ||||
\(956\) | −91.3385 | + | 52.7343i | −2.95410 | + | 1.70555i | ||||
\(957\) | − | 5.56704i | − | 0.179957i | ||||||
\(958\) | 11.2322 | + | 19.4548i | 0.362896 | + | 0.628555i | ||||
\(959\) | −2.07271 | + | 3.59004i | −0.0669314 | + | 0.115929i | ||||
\(960\) | 19.3872 | + | 11.1932i | 0.625720 | + | 0.361260i | ||||
\(961\) | −59.5491 | −1.92094 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.39373 | 0.206035 | ||||||||
\(964\) | 86.3939 | + | 49.8796i | 2.78256 | + | 1.60651i | ||||
\(965\) | −9.23633 | + | 15.9978i | −0.297328 | + | 0.514987i | ||||
\(966\) | −4.30463 | − | 7.45583i | −0.138499 | − | 0.239887i | ||||
\(967\) | 10.2798i | 0.330575i | 0.986245 | + | 0.165288i | \(0.0528552\pi\) | ||||
−0.986245 | + | 0.165288i | \(0.947145\pi\) | |||||||
\(968\) | −19.0845 | + | 11.0184i | −0.613398 | + | 0.354145i | ||||
\(969\) | 3.16341 | − | 1.82640i | 0.101623 | − | 0.0586723i | ||||
\(970\) | 48.2111i | 1.54796i | ||||||||
\(971\) | 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 | ||||
\(973\) | −8.64979 | − | 4.99396i | −0.277300 | − | 0.160099i | ||||
\(974\) | 39.9997 | 1.28167 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −44.6286 | −1.42853 | ||||||||
\(977\) | −40.7498 | − | 23.5269i | −1.30370 | − | 0.752693i | −0.322665 | − | 0.946513i | \(-0.604579\pi\) |
−0.981037 | + | 0.193821i | \(0.937912\pi\) | |||||||
\(978\) | 21.1419 | − | 36.6189i | 0.676044 | − | 1.17094i | ||||
\(979\) | 14.4529 | + | 25.0331i | 0.461916 | + | 0.800062i | ||||
\(980\) | 36.8305i | 1.17651i | ||||||||
\(981\) | −2.99654 | + | 1.73005i | −0.0956722 | + | 0.0552364i | ||||
\(982\) | −11.6543 | + | 6.72862i | −0.371904 | + | 0.214719i | ||||
\(983\) | − | 34.4295i | − | 1.09813i | −0.835779 | − | 0.549065i | \(-0.814984\pi\) | ||
0.835779 | − | 0.549065i | \(-0.185016\pi\) | |||||||
\(984\) | 21.4671 | + | 37.1821i | 0.684346 | + | 1.18532i | ||||
\(985\) | 2.44528 | − | 4.23535i | 0.0779131 | − | 0.134949i | ||||
\(986\) | 21.6213 | + | 12.4831i | 0.688563 | + | 0.397542i | ||||
\(987\) | 0.417895 | 0.0133017 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −63.9536 | −2.03361 | ||||||||
\(990\) | 7.12066 | + | 4.11111i | 0.226309 | + | 0.130660i | ||||
\(991\) | −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 | ||||
\(993\) | 11.2295i | 0.356358i | ||||||||
\(994\) | −13.5897 | + | 7.84601i | −0.431039 | + | 0.248860i | ||||
\(995\) | 13.6593 | − | 7.88620i | 0.433029 | − | 0.250009i | ||||
\(996\) | 13.8683i | 0.439434i | ||||||||
\(997\) | 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 | ||||
\(999\) | −4.98226 | − | 2.87651i | −0.157632 | − | 0.0910088i |
(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.j.i.316.1 | 12 | ||
13.2 | odd | 12 | 507.2.e.i.484.1 | 6 | |||
13.3 | even | 3 | inner | 507.2.j.i.361.6 | 12 | ||
13.4 | even | 6 | 507.2.b.f.337.1 | 6 | |||
13.5 | odd | 4 | 507.2.e.i.22.1 | 6 | |||
13.6 | odd | 12 | 507.2.a.l.1.3 | yes | 3 | ||
13.7 | odd | 12 | 507.2.a.i.1.1 | ✓ | 3 | ||
13.8 | odd | 4 | 507.2.e.l.22.3 | 6 | |||
13.9 | even | 3 | 507.2.b.f.337.6 | 6 | |||
13.10 | even | 6 | inner | 507.2.j.i.361.1 | 12 | ||
13.11 | odd | 12 | 507.2.e.l.484.3 | 6 | |||
13.12 | even | 2 | inner | 507.2.j.i.316.6 | 12 | ||
39.17 | odd | 6 | 1521.2.b.k.1351.6 | 6 | |||
39.20 | even | 12 | 1521.2.a.s.1.3 | 3 | |||
39.32 | even | 12 | 1521.2.a.n.1.1 | 3 | |||
39.35 | odd | 6 | 1521.2.b.k.1351.1 | 6 | |||
52.7 | even | 12 | 8112.2.a.cg.1.3 | 3 | |||
52.19 | even | 12 | 8112.2.a.cp.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.a.i.1.1 | ✓ | 3 | 13.7 | odd | 12 | ||
507.2.a.l.1.3 | yes | 3 | 13.6 | odd | 12 | ||
507.2.b.f.337.1 | 6 | 13.4 | even | 6 | |||
507.2.b.f.337.6 | 6 | 13.9 | even | 3 | |||
507.2.e.i.22.1 | 6 | 13.5 | odd | 4 | |||
507.2.e.i.484.1 | 6 | 13.2 | odd | 12 | |||
507.2.e.l.22.3 | 6 | 13.8 | odd | 4 | |||
507.2.e.l.484.3 | 6 | 13.11 | odd | 12 | |||
507.2.j.i.316.1 | 12 | 1.1 | even | 1 | trivial | ||
507.2.j.i.316.6 | 12 | 13.12 | even | 2 | inner | ||
507.2.j.i.361.1 | 12 | 13.10 | even | 6 | inner | ||
507.2.j.i.361.6 | 12 | 13.3 | even | 3 | inner | ||
1521.2.a.n.1.1 | 3 | 39.32 | even | 12 | |||
1521.2.a.s.1.3 | 3 | 39.20 | even | 12 | |||
1521.2.b.k.1351.1 | 6 | 39.35 | odd | 6 | |||
1521.2.b.k.1351.6 | 6 | 39.17 | odd | 6 | |||
8112.2.a.cg.1.3 | 3 | 52.7 | even | 12 | |||
8112.2.a.cp.1.1 | 3 | 52.19 | even | 12 |