Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(99,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.u (of order \(18\), degree \(6\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{18})\) |
Coefficient field: | \(\Q(\zeta_{36})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{6} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 549.2 | ||
Root | \(0.342020 + 0.939693i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.549 |
Dual form | 950.2.u.a.199.2 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.984808 | + | 0.173648i | 0.696364 | + | 0.122788i | ||||
\(3\) | −0.984808 | + | 1.17365i | −0.568579 | + | 0.677606i | −0.971339 | − | 0.237700i | \(-0.923607\pi\) |
0.402760 | + | 0.915306i | \(0.368051\pi\) | |||||||
\(4\) | 0.939693 | + | 0.342020i | 0.469846 | + | 0.171010i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.17365 | + | 0.984808i | −0.479140 | + | 0.402046i | ||||
\(7\) | −1.62760 | + | 0.939693i | −0.615173 | + | 0.355170i | −0.774987 | − | 0.631977i | \(-0.782244\pi\) |
0.159814 | + | 0.987147i | \(0.448910\pi\) | |||||||
\(8\) | 0.866025 | + | 0.500000i | 0.306186 | + | 0.176777i | ||||
\(9\) | 0.113341 | + | 0.642788i | 0.0377803 | + | 0.214263i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0812519 | − | 0.140732i | 0.0244984 | − | 0.0424324i | −0.853516 | − | 0.521066i | \(-0.825534\pi\) |
0.878015 | + | 0.478634i | \(0.158868\pi\) | |||||||
\(12\) | −1.32683 | + | 0.766044i | −0.383022 | + | 0.221138i | ||||
\(13\) | 3.03195 | + | 3.61334i | 0.840912 | + | 1.00216i | 0.999889 | + | 0.0148781i | \(0.00473603\pi\) |
−0.158977 | + | 0.987282i | \(0.550820\pi\) | |||||||
\(14\) | −1.76604 | + | 0.642788i | −0.471995 | + | 0.171792i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.766044 | + | 0.642788i | 0.191511 | + | 0.160697i | ||||
\(17\) | −4.28125 | − | 0.754900i | −1.03836 | − | 0.183090i | −0.371621 | − | 0.928385i | \(-0.621198\pi\) |
−0.666735 | + | 0.745295i | \(0.732309\pi\) | |||||||
\(18\) | 0.652704i | 0.153844i | ||||||||
\(19\) | −2.77719 | − | 3.35965i | −0.637131 | − | 0.770756i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.500000 | − | 2.83564i | 0.109109 | − | 0.618788i | ||||
\(22\) | 0.104455 | − | 0.124485i | 0.0222700 | − | 0.0265403i | ||||
\(23\) | −2.08840 | + | 5.73783i | −0.435461 | + | 1.19642i | 0.506954 | + | 0.861973i | \(0.330771\pi\) |
−0.942415 | + | 0.334446i | \(0.891451\pi\) | |||||||
\(24\) | −1.43969 | + | 0.524005i | −0.293876 | + | 0.106962i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.35844 | + | 4.08494i | 0.462528 | + | 0.801122i | ||||
\(27\) | −4.84651 | − | 2.79813i | −0.932711 | − | 0.538501i | ||||
\(28\) | −1.85083 | + | 0.326352i | −0.349775 | + | 0.0616747i | ||||
\(29\) | −0.414878 | − | 2.35289i | −0.0770409 | − | 0.436920i | −0.998792 | − | 0.0491384i | \(-0.984352\pi\) |
0.921751 | − | 0.387782i | \(-0.126759\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.81908 | + | 3.15074i | 0.326716 | + | 0.565889i | 0.981858 | − | 0.189617i | \(-0.0607246\pi\) |
−0.655142 | + | 0.755506i | \(0.727391\pi\) | |||||||
\(32\) | 0.642788 | + | 0.766044i | 0.113630 | + | 0.135419i | ||||
\(33\) | 0.0851529 | + | 0.233956i | 0.0148232 | + | 0.0407264i | ||||
\(34\) | −4.08512 | − | 1.48686i | −0.700593 | − | 0.254995i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.113341 | + | 0.642788i | −0.0188901 | + | 0.107131i | ||||
\(37\) | 7.36959i | 1.21155i | 0.795635 | + | 0.605776i | \(0.207137\pi\) | ||||
−0.795635 | + | 0.605776i | \(0.792863\pi\) | |||||||
\(38\) | −2.15160 | − | 3.79086i | −0.349036 | − | 0.614959i | ||||
\(39\) | −7.22668 | −1.15720 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.81521 | + | 1.52314i | 0.283488 | + | 0.237874i | 0.773432 | − | 0.633879i | \(-0.218538\pi\) |
−0.489944 | + | 0.871754i | \(0.662983\pi\) | |||||||
\(42\) | 0.984808 | − | 2.70574i | 0.151959 | − | 0.417504i | ||||
\(43\) | 0.223238 | + | 0.613341i | 0.0340434 | + | 0.0935336i | 0.955550 | − | 0.294830i | \(-0.0952629\pi\) |
−0.921506 | + | 0.388363i | \(0.873041\pi\) | |||||||
\(44\) | 0.124485 | − | 0.104455i | 0.0187668 | − | 0.0157473i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.05303 | + | 5.28801i | −0.450145 | + | 0.779674i | ||||
\(47\) | −6.77487 | + | 1.19459i | −0.988217 | + | 0.174249i | −0.644318 | − | 0.764758i | \(-0.722859\pi\) |
−0.343899 | + | 0.939007i | \(0.611748\pi\) | |||||||
\(48\) | −1.50881 | + | 0.266044i | −0.217778 | + | 0.0384002i | ||||
\(49\) | −1.73396 | + | 3.00330i | −0.247708 | + | 0.429043i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.10220 | − | 4.28125i | 0.714450 | − | 0.599495i | ||||
\(52\) | 1.61327 | + | 4.43242i | 0.223720 | + | 0.614666i | ||||
\(53\) | −2.03282 | + | 5.58512i | −0.279229 | + | 0.767176i | 0.718221 | + | 0.695815i | \(0.244956\pi\) |
−0.997451 | + | 0.0713610i | \(0.977266\pi\) | |||||||
\(54\) | −4.28699 | − | 3.59721i | −0.583385 | − | 0.489518i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.87939 | −0.251143 | ||||||||
\(57\) | 6.67804 | + | 0.0491630i | 0.884528 | + | 0.00651180i | ||||
\(58\) | − | 2.38919i | − | 0.313715i | ||||||
\(59\) | 0.708263 | − | 4.01676i | 0.0922080 | − | 0.522938i | −0.903359 | − | 0.428885i | \(-0.858907\pi\) |
0.995567 | − | 0.0940529i | \(-0.0299823\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.21301 | − | 0.805470i | −0.283347 | − | 0.103130i | 0.196437 | − | 0.980516i | \(-0.437063\pi\) |
−0.479784 | + | 0.877387i | \(0.659285\pi\) | |||||||
\(62\) | 1.24432 | + | 3.41875i | 0.158029 | + | 0.434181i | ||||
\(63\) | −0.788496 | − | 0.939693i | −0.0993411 | − | 0.118390i | ||||
\(64\) | 0.500000 | + | 0.866025i | 0.0625000 | + | 0.108253i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.0432332 | + | 0.245188i | 0.00532164 | + | 0.0301805i | ||||
\(67\) | −1.61327 | + | 0.284463i | −0.197092 | + | 0.0347527i | −0.271323 | − | 0.962488i | \(-0.587461\pi\) |
0.0742305 | + | 0.997241i | \(0.476350\pi\) | |||||||
\(68\) | −3.76487 | − | 2.17365i | −0.456557 | − | 0.263594i | ||||
\(69\) | −4.67752 | − | 8.10170i | −0.563107 | − | 0.975330i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.39780 | − | 0.872729i | 0.284567 | − | 0.103574i | −0.195793 | − | 0.980645i | \(-0.562728\pi\) |
0.480360 | + | 0.877071i | \(0.340506\pi\) | |||||||
\(72\) | −0.223238 | + | 0.613341i | −0.0263088 | + | 0.0722829i | ||||
\(73\) | 10.0933 | − | 12.0287i | 1.18133 | − | 1.40785i | 0.288483 | − | 0.957485i | \(-0.406849\pi\) |
0.892844 | − | 0.450366i | \(-0.148707\pi\) | |||||||
\(74\) | −1.27972 | + | 7.25762i | −0.148764 | + | 0.843682i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.46064 | − | 4.10689i | −0.167547 | − | 0.471093i | ||||
\(77\) | 0.305407i | 0.0348044i | ||||||||
\(78\) | −7.11689 | − | 1.25490i | −0.805829 | − | 0.142089i | ||||
\(79\) | 0.766044 | + | 0.642788i | 0.0861867 | + | 0.0723193i | 0.684863 | − | 0.728672i | \(-0.259862\pi\) |
−0.598676 | + | 0.800991i | \(0.704306\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.21688 | − | 2.26276i | 0.690765 | − | 0.251418i | ||||
\(82\) | 1.52314 | + | 1.81521i | 0.168203 | + | 0.200456i | ||||
\(83\) | 0.885328 | − | 0.511144i | 0.0971774 | − | 0.0561054i | −0.450624 | − | 0.892714i | \(-0.648798\pi\) |
0.547801 | + | 0.836609i | \(0.315465\pi\) | |||||||
\(84\) | 1.43969 | − | 2.49362i | 0.157083 | − | 0.272076i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.113341 | + | 0.642788i | 0.0122219 | + | 0.0693136i | ||||
\(87\) | 3.17004 | + | 1.83022i | 0.339864 | + | 0.196220i | ||||
\(88\) | 0.140732 | − | 0.0812519i | 0.0150021 | − | 0.00866148i | ||||
\(89\) | 2.57011 | − | 2.15658i | 0.272431 | − | 0.228597i | −0.496328 | − | 0.868135i | \(-0.665319\pi\) |
0.768759 | + | 0.639538i | \(0.220874\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.33022 | − | 3.03195i | −0.873245 | − | 0.317835i | ||||
\(92\) | −3.92490 | + | 4.67752i | −0.409200 | + | 0.487665i | ||||
\(93\) | −5.48930 | − | 0.967911i | −0.569214 | − | 0.100368i | ||||
\(94\) | −6.87939 | −0.709554 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.53209 | −0.156368 | ||||||||
\(97\) | 17.6011 | + | 3.10354i | 1.78712 | + | 0.315117i | 0.966558 | − | 0.256447i | \(-0.0825518\pi\) |
0.820558 | + | 0.571563i | \(0.193663\pi\) | |||||||
\(98\) | −2.22913 | + | 2.65657i | −0.225176 | + | 0.268355i | ||||
\(99\) | 0.0996702 | + | 0.0362770i | 0.0100172 | + | 0.00364598i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.82295 | − | 5.72513i | 0.678909 | − | 0.569672i | −0.236779 | − | 0.971564i | \(-0.576092\pi\) |
0.915687 | + | 0.401892i | \(0.131647\pi\) | |||||||
\(102\) | 5.76811 | − | 3.33022i | 0.571128 | − | 0.329741i | ||||
\(103\) | 7.14382 | + | 4.12449i | 0.703901 | + | 0.406398i | 0.808799 | − | 0.588085i | \(-0.200118\pi\) |
−0.104898 | + | 0.994483i | \(0.533451\pi\) | |||||||
\(104\) | 0.819078 | + | 4.64522i | 0.0803172 | + | 0.455501i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.97178 | + | 5.14728i | −0.288645 | + | 0.499948i | ||||
\(107\) | 3.17004 | − | 1.83022i | 0.306459 | − | 0.176934i | −0.338882 | − | 0.940829i | \(-0.610049\pi\) |
0.645341 | + | 0.763895i | \(0.276715\pi\) | |||||||
\(108\) | −3.59721 | − | 4.28699i | −0.346142 | − | 0.412516i | ||||
\(109\) | 3.03936 | − | 1.10624i | 0.291118 | − | 0.105958i | −0.192333 | − | 0.981330i | \(-0.561605\pi\) |
0.483451 | + | 0.875371i | \(0.339383\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.64930 | − | 7.25762i | −0.820955 | − | 0.688863i | ||||
\(112\) | −1.85083 | − | 0.326352i | −0.174887 | − | 0.0308373i | ||||
\(113\) | 15.1753i | 1.42757i | 0.700364 | + | 0.713786i | \(0.253021\pi\) | ||||
−0.700364 | + | 0.713786i | \(0.746979\pi\) | |||||||
\(114\) | 6.56805 | + | 1.20805i | 0.615154 | + | 0.113144i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.414878 | − | 2.35289i | 0.0385204 | − | 0.218460i | ||||
\(117\) | −1.97897 | + | 2.35844i | −0.182956 | + | 0.218038i | ||||
\(118\) | 1.39501 | − | 3.83275i | 0.128421 | − | 0.352833i | ||||
\(119\) | 7.67752 | − | 2.79439i | 0.703797 | − | 0.256161i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.48680 | + | 9.50341i | 0.498800 | + | 0.863946i | ||||
\(122\) | −2.03952 | − | 1.17752i | −0.184650 | − | 0.106608i | ||||
\(123\) | −3.57526 | + | 0.630415i | −0.322370 | + | 0.0568426i | ||||
\(124\) | 0.631759 | + | 3.58288i | 0.0567336 | + | 0.321752i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.613341 | − | 1.06234i | −0.0546407 | − | 0.0946405i | ||||
\(127\) | −12.8227 | − | 15.2815i | −1.13783 | − | 1.35602i | −0.925468 | − | 0.378826i | \(-0.876328\pi\) |
−0.212365 | − | 0.977191i | \(-0.568116\pi\) | |||||||
\(128\) | 0.342020 | + | 0.939693i | 0.0302306 | + | 0.0830579i | ||||
\(129\) | −0.939693 | − | 0.342020i | −0.0827353 | − | 0.0301132i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.93376 | + | 16.6382i | −0.256324 | + | 1.45369i | 0.536327 | + | 0.844010i | \(0.319811\pi\) |
−0.792651 | + | 0.609676i | \(0.791300\pi\) | |||||||
\(132\) | 0.248970i | 0.0216701i | ||||||||
\(133\) | 7.67717 | + | 2.85844i | 0.665695 | + | 0.247858i | ||||
\(134\) | −1.63816 | −0.141515 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.33022 | − | 2.79439i | −0.285564 | − | 0.239617i | ||||
\(137\) | −1.70248 | + | 4.67752i | −0.145452 | + | 0.399627i | −0.990929 | − | 0.134385i | \(-0.957094\pi\) |
0.845477 | + | 0.534012i | \(0.179316\pi\) | |||||||
\(138\) | −3.19961 | − | 8.79086i | −0.272369 | − | 0.748328i | ||||
\(139\) | 14.3439 | − | 12.0360i | 1.21663 | − | 1.02088i | 0.217639 | − | 0.976029i | \(-0.430164\pi\) |
0.998994 | − | 0.0448471i | \(-0.0142801\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.26991 | − | 9.12776i | 0.443807 | − | 0.768696i | ||||
\(142\) | 2.51292 | − | 0.443096i | 0.210880 | − | 0.0371838i | ||||
\(143\) | 0.754866 | − | 0.133103i | 0.0631251 | − | 0.0111307i | ||||
\(144\) | −0.326352 | + | 0.565258i | −0.0271960 | + | 0.0471048i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.0287 | − | 10.0933i | 0.995501 | − | 0.835325i | ||||
\(147\) | −1.81720 | − | 4.99273i | −0.149880 | − | 0.411793i | ||||
\(148\) | −2.52055 | + | 6.92514i | −0.207188 | + | 0.569243i | ||||
\(149\) | 10.2476 | + | 8.59878i | 0.839518 | + | 0.704439i | 0.957455 | − | 0.288582i | \(-0.0931837\pi\) |
−0.117937 | + | 0.993021i | \(0.537628\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.8648 | −1.20968 | −0.604842 | − | 0.796346i | \(-0.706764\pi\) | ||||
−0.604842 | + | 0.796346i | \(0.706764\pi\) | |||||||
\(152\) | −0.725293 | − | 4.29813i | −0.0588290 | − | 0.348625i | ||||
\(153\) | − | 2.83750i | − | 0.229398i | ||||||
\(154\) | −0.0530334 | + | 0.300767i | −0.00427355 | + | 0.0242365i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.79086 | − | 2.47167i | −0.543704 | − | 0.197892i | ||||
\(157\) | 2.54747 | + | 6.99912i | 0.203310 | + | 0.558591i | 0.998882 | − | 0.0472685i | \(-0.0150516\pi\) |
−0.795572 | + | 0.605859i | \(0.792829\pi\) | |||||||
\(158\) | 0.642788 | + | 0.766044i | 0.0511374 | + | 0.0609432i | ||||
\(159\) | −4.55303 | − | 7.88609i | −0.361079 | − | 0.625407i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.99273 | − | 11.3013i | −0.157049 | − | 0.890668i | ||||
\(162\) | 6.51536 | − | 1.14883i | 0.511895 | − | 0.0902609i | ||||
\(163\) | 5.84737 | + | 3.37598i | 0.458002 | + | 0.264427i | 0.711204 | − | 0.702986i | \(-0.248150\pi\) |
−0.253202 | + | 0.967413i | \(0.581484\pi\) | |||||||
\(164\) | 1.18479 | + | 2.05212i | 0.0925168 | + | 0.160244i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.960637 | − | 0.349643i | 0.0745599 | − | 0.0271376i | ||||
\(167\) | 5.55920 | − | 15.2738i | 0.430184 | − | 1.18192i | −0.515516 | − | 0.856880i | \(-0.672400\pi\) |
0.945700 | − | 0.325041i | \(-0.105378\pi\) | |||||||
\(168\) | 1.85083 | − | 2.20574i | 0.142795 | − | 0.170176i | ||||
\(169\) | −1.60607 | + | 9.10846i | −0.123544 | + | 0.700651i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.84477 | − | 2.16593i | 0.141073 | − | 0.165633i | ||||
\(172\) | 0.652704i | 0.0497682i | ||||||||
\(173\) | 5.55250 | + | 0.979055i | 0.422149 | + | 0.0744362i | 0.380687 | − | 0.924704i | \(-0.375687\pi\) |
0.0414616 | + | 0.999140i | \(0.486799\pi\) | |||||||
\(174\) | 2.80406 | + | 2.35289i | 0.212575 | + | 0.178372i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.152704 | − | 0.0555796i | 0.0115105 | − | 0.00418947i | ||||
\(177\) | 4.01676 | + | 4.78699i | 0.301918 | + | 0.359812i | ||||
\(178\) | 2.90555 | − | 1.67752i | 0.217780 | − | 0.125735i | ||||
\(179\) | 5.74763 | − | 9.95518i | 0.429598 | − | 0.744085i | −0.567240 | − | 0.823553i | \(-0.691989\pi\) |
0.996837 | + | 0.0794676i | \(0.0253220\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.61200 | + | 14.8134i | 0.194148 | + | 1.10107i | 0.913627 | + | 0.406554i | \(0.133270\pi\) |
−0.719478 | + | 0.694515i | \(0.755619\pi\) | |||||||
\(182\) | −7.67717 | − | 4.43242i | −0.569070 | − | 0.328553i | ||||
\(183\) | 3.12473 | − | 1.80406i | 0.230987 | − | 0.133360i | ||||
\(184\) | −4.67752 | + | 3.92490i | −0.344831 | + | 0.289348i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.23783 | − | 1.90641i | −0.384056 | − | 0.139785i | ||||
\(187\) | −0.454099 | + | 0.541174i | −0.0332070 | + | 0.0395746i | ||||
\(188\) | −6.77487 | − | 1.19459i | −0.494108 | − | 0.0871246i | ||||
\(189\) | 10.5175 | 0.765039 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.2131 | 1.46257 | 0.731283 | − | 0.682074i | \(-0.238922\pi\) | ||||
0.731283 | + | 0.682074i | \(0.238922\pi\) | |||||||
\(192\) | −1.50881 | − | 0.266044i | −0.108889 | − | 0.0192001i | ||||
\(193\) | 6.47735 | − | 7.71941i | 0.466250 | − | 0.555655i | −0.480763 | − | 0.876851i | \(-0.659640\pi\) |
0.947013 | + | 0.321196i | \(0.104085\pi\) | |||||||
\(194\) | 16.7947 | + | 6.11278i | 1.20579 | + | 0.438872i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.65657 | + | 2.22913i | −0.189755 | + | 0.159224i | ||||
\(197\) | 11.3435 | − | 6.54916i | 0.808190 | − | 0.466609i | −0.0381371 | − | 0.999273i | \(-0.512142\pi\) |
0.846327 | + | 0.532664i | \(0.178809\pi\) | |||||||
\(198\) | 0.0918566 | + | 0.0530334i | 0.00652796 | + | 0.00376892i | ||||
\(199\) | 3.05257 | + | 17.3120i | 0.216391 | + | 1.22721i | 0.878477 | + | 0.477785i | \(0.158560\pi\) |
−0.662086 | + | 0.749428i | \(0.730329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.25490 | − | 2.17355i | 0.0885138 | − | 0.153310i | ||||
\(202\) | 7.71345 | − | 4.45336i | 0.542717 | − | 0.313338i | ||||
\(203\) | 2.88624 | + | 3.43969i | 0.202575 | + | 0.241419i | ||||
\(204\) | 6.25877 | − | 2.27801i | 0.438202 | − | 0.159492i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.31908 | + | 5.30234i | 0.440271 | + | 0.369431i | ||||
\(207\) | −3.92490 | − | 0.692066i | −0.272800 | − | 0.0481019i | ||||
\(208\) | 4.71688i | 0.327057i | ||||||||
\(209\) | −0.698463 | + | 0.117863i | −0.0483137 | + | 0.00815275i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.29561 | + | 24.3616i | −0.295722 | + | 1.67712i | 0.368532 | + | 0.929615i | \(0.379860\pi\) |
−0.664254 | + | 0.747507i | \(0.731251\pi\) | |||||||
\(212\) | −3.82045 | + | 4.55303i | −0.262389 | + | 0.312704i | ||||
\(213\) | −1.33710 | + | 3.67365i | −0.0916165 | + | 0.251714i | ||||
\(214\) | 3.43969 | − | 1.25195i | 0.235133 | − | 0.0855812i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.79813 | − | 4.84651i | −0.190389 | − | 0.329763i | ||||
\(217\) | −5.92145 | − | 3.41875i | −0.401974 | − | 0.232080i | ||||
\(218\) | 3.18528 | − | 0.561652i | 0.215735 | − | 0.0380398i | ||||
\(219\) | 4.17752 | + | 23.6919i | 0.282291 | + | 1.60095i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.2528 | − | 17.7584i | −0.689681 | − | 1.19456i | ||||
\(222\) | −7.25762 | − | 8.64930i | −0.487100 | − | 0.580503i | ||||
\(223\) | −5.19880 | − | 14.2836i | −0.348137 | − | 0.956500i | −0.982956 | − | 0.183839i | \(-0.941148\pi\) |
0.634819 | − | 0.772661i | \(-0.281075\pi\) | |||||||
\(224\) | −1.76604 | − | 0.642788i | −0.117999 | − | 0.0429481i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.63516 | + | 14.9448i | −0.175288 | + | 0.994110i | ||||
\(227\) | − | 18.6973i | − | 1.24098i | −0.784214 | − | 0.620491i | \(-0.786933\pi\) | ||
0.784214 | − | 0.620491i | \(-0.213067\pi\) | |||||||
\(228\) | 6.25849 | + | 2.33022i | 0.414479 | + | 0.154323i | ||||
\(229\) | 19.9094 | 1.31565 | 0.657826 | − | 0.753170i | \(-0.271476\pi\) | ||||
0.657826 | + | 0.753170i | \(0.271476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.358441 | − | 0.300767i | −0.0235837 | − | 0.0197890i | ||||
\(232\) | 0.817150 | − | 2.24510i | 0.0536485 | − | 0.147398i | ||||
\(233\) | −9.56926 | − | 26.2913i | −0.626903 | − | 1.72240i | −0.689424 | − | 0.724358i | \(-0.742136\pi\) |
0.0625206 | − | 0.998044i | \(-0.480086\pi\) | |||||||
\(234\) | −2.35844 | + | 1.97897i | −0.154176 | + | 0.129369i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.03936 | − | 3.53228i | 0.132751 | − | 0.229932i | ||||
\(237\) | −1.50881 | + | 0.266044i | −0.0980079 | + | 0.0172814i | ||||
\(238\) | 8.04612 | − | 1.41875i | 0.521553 | − | 0.0919638i | ||||
\(239\) | −13.1814 | + | 22.8308i | −0.852633 | + | 1.47680i | 0.0261903 | + | 0.999657i | \(0.491662\pi\) |
−0.878823 | + | 0.477147i | \(0.841671\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.1570 | − | 11.0401i | 0.847520 | − | 0.711153i | −0.111722 | − | 0.993739i | \(-0.535637\pi\) |
0.959242 | + | 0.282586i | \(0.0911923\pi\) | |||||||
\(242\) | 3.75319 | + | 10.3118i | 0.241264 | + | 0.662868i | ||||
\(243\) | 2.27536 | − | 6.25150i | 0.145964 | − | 0.401034i | ||||
\(244\) | −1.80406 | − | 1.51379i | −0.115493 | − | 0.0969104i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.63041 | −0.231467 | ||||||||
\(247\) | 3.71924 | − | 20.2212i | 0.236650 | − | 1.28665i | ||||
\(248\) | 3.63816i | 0.231023i | ||||||||
\(249\) | −0.271974 | + | 1.54244i | −0.0172357 | + | 0.0977483i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.1211 | − | 5.50362i | −0.954434 | − | 0.347386i | −0.182584 | − | 0.983190i | \(-0.558446\pi\) |
−0.771850 | + | 0.635805i | \(0.780668\pi\) | |||||||
\(252\) | −0.419550 | − | 1.15270i | −0.0264292 | − | 0.0726135i | ||||
\(253\) | 0.637812 | + | 0.760115i | 0.0400989 | + | 0.0477880i | ||||
\(254\) | −9.97431 | − | 17.2760i | −0.625844 | − | 1.08399i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.173648 | + | 0.984808i | 0.0108530 | + | 0.0615505i | ||||
\(257\) | −13.9290 | + | 2.45605i | −0.868865 | + | 0.153204i | −0.590271 | − | 0.807205i | \(-0.700979\pi\) |
−0.278593 | + | 0.960409i | \(0.589868\pi\) | |||||||
\(258\) | −0.866025 | − | 0.500000i | −0.0539164 | − | 0.0311286i | ||||
\(259\) | −6.92514 | − | 11.9947i | −0.430308 | − | 0.745315i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.46538 | − | 0.533356i | 0.0907050 | − | 0.0330139i | ||||
\(262\) | −5.77838 | + | 15.8760i | −0.356990 | + | 0.980821i | ||||
\(263\) | 8.43437 | − | 10.0517i | 0.520085 | − | 0.619814i | −0.440515 | − | 0.897745i | \(-0.645204\pi\) |
0.960601 | + | 0.277931i | \(0.0896488\pi\) | |||||||
\(264\) | −0.0432332 | + | 0.245188i | −0.00266082 | + | 0.0150903i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.06418 | + | 4.14814i | 0.433133 | + | 0.254339i | ||||
\(267\) | 5.14022i | 0.314576i | ||||||||
\(268\) | −1.61327 | − | 0.284463i | −0.0985461 | − | 0.0173763i | ||||
\(269\) | 17.2003 | + | 14.4327i | 1.04872 | + | 0.879980i | 0.992958 | − | 0.118464i | \(-0.0377971\pi\) |
0.0557609 | + | 0.998444i | \(0.482242\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.41787 | − | 1.97194i | 0.329112 | − | 0.119787i | −0.172179 | − | 0.985066i | \(-0.555081\pi\) |
0.501291 | + | 0.865279i | \(0.332859\pi\) | |||||||
\(272\) | −2.79439 | − | 3.33022i | −0.169435 | − | 0.201924i | ||||
\(273\) | 11.7621 | − | 6.79086i | 0.711875 | − | 0.411002i | ||||
\(274\) | −2.48886 | + | 4.31082i | −0.150357 | + | 0.260426i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.62449 | − | 9.21291i | −0.0977825 | − | 0.554552i | ||||
\(277\) | 17.1242 | + | 9.88666i | 1.02889 | + | 0.594032i | 0.916667 | − | 0.399651i | \(-0.130869\pi\) |
0.112226 | + | 0.993683i | \(0.464202\pi\) | |||||||
\(278\) | 16.2160 | − | 9.36231i | 0.972571 | − | 0.561514i | ||||
\(279\) | −1.81908 | + | 1.52639i | −0.108905 | + | 0.0913824i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.7904 | − | 10.8428i | −1.77715 | − | 0.646829i | −0.999843 | − | 0.0177066i | \(-0.994364\pi\) |
−0.777306 | − | 0.629123i | \(-0.783414\pi\) | |||||||
\(282\) | 6.77487 | − | 8.07398i | 0.403438 | − | 0.480798i | ||||
\(283\) | 2.89620 | + | 0.510678i | 0.172161 | + | 0.0303566i | 0.259064 | − | 0.965860i | \(-0.416586\pi\) |
−0.0869031 | + | 0.996217i | \(0.527697\pi\) | |||||||
\(284\) | 2.55169 | 0.151415 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.766511 | 0.0453248 | ||||||||
\(287\) | −4.38571 | − | 0.773318i | −0.258880 | − | 0.0456475i | ||||
\(288\) | −0.419550 | + | 0.500000i | −0.0247222 | + | 0.0294628i | ||||
\(289\) | 1.78446 | + | 0.649491i | 0.104968 | + | 0.0382054i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.9761 | + | 17.6011i | −1.22964 | + | 1.03179i | ||||
\(292\) | 13.5986 | − | 7.85117i | 0.795799 | − | 0.459455i | ||||
\(293\) | −14.1142 | − | 8.14883i | −0.824560 | − | 0.476060i | 0.0274264 | − | 0.999624i | \(-0.491269\pi\) |
−0.851986 | + | 0.523564i | \(0.824602\pi\) | |||||||
\(294\) | −0.922618 | − | 5.23243i | −0.0538082 | − | 0.305161i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.68479 | + | 6.38225i | −0.214174 | + | 0.370961i | ||||
\(297\) | −0.787576 | + | 0.454707i | −0.0456998 | + | 0.0263848i | ||||
\(298\) | 8.59878 | + | 10.2476i | 0.498114 | + | 0.593629i | ||||
\(299\) | −27.0646 | + | 9.85073i | −1.56519 | + | 0.569682i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.939693 | − | 0.788496i | −0.0541630 | − | 0.0454481i | ||||
\(302\) | −14.6390 | − | 2.58125i | −0.842380 | − | 0.148534i | ||||
\(303\) | 13.6459i | 0.783936i | ||||||||
\(304\) | 0.0320889 | − | 4.35878i | 0.00184042 | − | 0.249993i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.492726 | − | 2.79439i | 0.0281673 | − | 0.159745i | ||||
\(307\) | −14.2590 | + | 16.9932i | −0.813803 | + | 0.969853i | −0.999920 | − | 0.0126749i | \(-0.995965\pi\) |
0.186117 | + | 0.982528i | \(0.440410\pi\) | |||||||
\(308\) | −0.104455 | + | 0.286989i | −0.00595190 | + | 0.0163527i | ||||
\(309\) | −11.8760 | + | 4.32250i | −0.675601 | + | 0.245899i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.46198 | + | 7.72838i | 0.253016 | + | 0.438236i | 0.964355 | − | 0.264613i | \(-0.0852442\pi\) |
−0.711339 | + | 0.702849i | \(0.751911\pi\) | |||||||
\(312\) | −6.25849 | − | 3.61334i | −0.354317 | − | 0.204565i | ||||
\(313\) | −18.0475 | + | 3.18227i | −1.02011 | + | 0.179872i | −0.658597 | − | 0.752496i | \(-0.728850\pi\) |
−0.361510 | + | 0.932368i | \(0.617739\pi\) | |||||||
\(314\) | 1.29339 | + | 7.33515i | 0.0729900 | + | 0.413947i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.500000 | + | 0.866025i | 0.0281272 | + | 0.0487177i | ||||
\(317\) | −15.5952 | − | 18.5856i | −0.875912 | − | 1.04387i | −0.998676 | − | 0.0514349i | \(-0.983621\pi\) |
0.122765 | − | 0.992436i | \(-0.460824\pi\) | |||||||
\(318\) | −3.11446 | − | 8.55690i | −0.174650 | − | 0.479847i | ||||
\(319\) | −0.364837 | − | 0.132790i | −0.0204270 | − | 0.00743481i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.973841 | + | 5.52293i | −0.0543545 | + | 0.308260i | ||||
\(322\) | − | 11.4757i | − | 0.639513i | ||||||
\(323\) | 9.35365 | + | 16.4800i | 0.520451 | + | 0.916971i | ||||
\(324\) | 6.61587 | 0.367548 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.17230 | + | 4.34008i | 0.286467 | + | 0.240375i | ||||
\(327\) | −1.69485 | + | 4.65657i | −0.0937257 | + | 0.257509i | ||||
\(328\) | 0.810446 | + | 2.22668i | 0.0447494 | + | 0.122948i | ||||
\(329\) | 9.90420 | − | 8.31061i | 0.546036 | − | 0.458179i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.8974 | + | 29.2671i | −0.928765 | + | 1.60867i | −0.143373 | + | 0.989669i | \(0.545795\pi\) |
−0.785392 | + | 0.618999i | \(0.787539\pi\) | |||||||
\(332\) | 1.00676 | − | 0.177519i | 0.0552530 | − | 0.00974260i | ||||
\(333\) | −4.73708 | + | 0.835275i | −0.259590 | + | 0.0457728i | ||||
\(334\) | 8.12701 | − | 14.0764i | 0.444690 | − | 0.770226i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.20574 | − | 1.85083i | 0.120333 | − | 0.100971i | ||||
\(337\) | 10.1825 | + | 27.9761i | 0.554675 | + | 1.52396i | 0.827257 | + | 0.561824i | \(0.189900\pi\) |
−0.272582 | + | 0.962132i | \(0.587878\pi\) | |||||||
\(338\) | −3.16333 | + | 8.69119i | −0.172063 | + | 0.472738i | ||||
\(339\) | −17.8105 | − | 14.9448i | −0.967331 | − | 0.811687i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.591214 | 0.0320160 | ||||||||
\(342\) | 2.19285 | − | 1.81268i | 0.118576 | − | 0.0980186i | ||||
\(343\) | − | 19.6732i | − | 1.06225i | ||||||
\(344\) | −0.113341 | + | 0.642788i | −0.00611093 | + | 0.0346568i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.29813 | + | 1.92836i | 0.284829 | + | 0.103669i | ||||
\(347\) | −1.06904 | − | 2.93717i | −0.0573891 | − | 0.157675i | 0.907685 | − | 0.419652i | \(-0.137848\pi\) |
−0.965074 | + | 0.261977i | \(0.915626\pi\) | |||||||
\(348\) | 2.35289 | + | 2.80406i | 0.126128 | + | 0.150314i | ||||
\(349\) | −3.88666 | − | 6.73189i | −0.208048 | − | 0.360350i | 0.743052 | − | 0.669234i | \(-0.233378\pi\) |
−0.951100 | + | 0.308884i | \(0.900044\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.58378 | − | 25.9959i | −0.244664 | − | 1.38756i | ||||
\(352\) | 0.160035 | − | 0.0282185i | 0.00852990 | − | 0.00150405i | ||||
\(353\) | −25.3162 | − | 14.6163i | −1.34745 | − | 0.777949i | −0.359560 | − | 0.933122i | \(-0.617073\pi\) |
−0.987887 | + | 0.155173i | \(0.950406\pi\) | |||||||
\(354\) | 3.12449 | + | 5.41177i | 0.166065 | + | 0.287632i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.15270 | − | 1.14749i | 0.167093 | − | 0.0608169i | ||||
\(357\) | −4.28125 | + | 11.7626i | −0.226588 | + | 0.622545i | ||||
\(358\) | 7.38901 | − | 8.80587i | 0.390521 | − | 0.465405i | ||||
\(359\) | −3.13310 | + | 17.7687i | −0.165359 | + | 0.937797i | 0.783335 | + | 0.621600i | \(0.213517\pi\) |
−0.948694 | + | 0.316197i | \(0.897594\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.57444 | + | 18.6607i | −0.188129 | + | 0.982144i | ||||
\(362\) | 15.0419i | 0.790584i | ||||||||
\(363\) | −16.5571 | − | 2.91946i | −0.869022 | − | 0.153232i | ||||
\(364\) | −6.79086 | − | 5.69821i | −0.355938 | − | 0.298667i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.39053 | − | 1.23405i | 0.177226 | − | 0.0645049i | ||||
\(367\) | 10.7252 | + | 12.7818i | 0.559850 | + | 0.667203i | 0.969515 | − | 0.245033i | \(-0.0787988\pi\) |
−0.409665 | + | 0.912236i | \(0.634354\pi\) | |||||||
\(368\) | −5.28801 | + | 3.05303i | −0.275657 | + | 0.159150i | ||||
\(369\) | −0.773318 | + | 1.33943i | −0.0402573 | + | 0.0697278i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.93969 | − | 11.0005i | −0.100704 | − | 0.571120i | ||||
\(372\) | −4.82721 | − | 2.78699i | −0.250279 | − | 0.144499i | ||||
\(373\) | −6.75352 | + | 3.89915i | −0.349684 | + | 0.201890i | −0.664546 | − | 0.747247i | \(-0.731375\pi\) |
0.314862 | + | 0.949137i | \(0.398042\pi\) | |||||||
\(374\) | −0.541174 | + | 0.454099i | −0.0279834 | + | 0.0234809i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.46451 | − | 2.35289i | −0.333382 | − | 0.121341i | ||||
\(377\) | 7.24390 | − | 8.63294i | 0.373080 | − | 0.444619i | ||||
\(378\) | 10.3578 | + | 1.82635i | 0.532745 | + | 0.0939374i | ||||
\(379\) | −1.31996 | −0.0678015 | −0.0339008 | − | 0.999425i | \(-0.510793\pi\) | ||||
−0.0339008 | + | 0.999425i | \(0.510793\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 30.5631 | 1.56579 | ||||||||
\(382\) | 19.9060 | + | 3.50996i | 1.01848 | + | 0.179585i | ||||
\(383\) | −21.3425 | + | 25.4349i | −1.09055 | + | 1.29966i | −0.139637 | + | 0.990203i | \(0.544593\pi\) |
−0.950912 | + | 0.309462i | \(0.899851\pi\) | |||||||
\(384\) | −1.43969 | − | 0.524005i | −0.0734690 | − | 0.0267405i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.71941 | − | 6.47735i | 0.392908 | − | 0.329689i | ||||
\(387\) | −0.368946 | + | 0.213011i | −0.0187546 | + | 0.0108280i | ||||
\(388\) | 15.4781 | + | 8.93629i | 0.785782 | + | 0.453671i | ||||
\(389\) | −2.57991 | − | 14.6314i | −0.130807 | − | 0.741841i | −0.977689 | − | 0.210060i | \(-0.932634\pi\) |
0.846882 | − | 0.531781i | \(-0.178477\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.2724 | − | 22.9885i | 0.671216 | − | 1.16258i | ||||
\(392\) | −3.00330 | + | 1.73396i | −0.151690 | + | 0.0875780i | ||||
\(393\) | −16.6382 | − | 19.8286i | −0.839286 | − | 1.00022i | ||||
\(394\) | 12.3084 | − | 4.47989i | 0.620088 | − | 0.225694i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.0812519 | + | 0.0681784i | 0.00408306 | + | 0.00342610i | ||||
\(397\) | 8.48233 | + | 1.49566i | 0.425716 | + | 0.0750652i | 0.382401 | − | 0.923996i | \(-0.375097\pi\) |
0.0433144 | + | 0.999061i | \(0.486208\pi\) | |||||||
\(398\) | 17.5790i | 0.881157i | ||||||||
\(399\) | −10.9153 | + | 6.19529i | −0.546451 | + | 0.310152i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.886821 | + | 5.02941i | −0.0442857 | + | 0.251157i | −0.998911 | − | 0.0466521i | \(-0.985145\pi\) |
0.954625 | + | 0.297809i | \(0.0962559\pi\) | |||||||
\(402\) | 1.61327 | − | 1.92262i | 0.0804625 | − | 0.0958915i | ||||
\(403\) | −5.86932 | + | 16.1258i | −0.292372 | + | 0.803285i | ||||
\(404\) | 8.36959 | − | 3.04628i | 0.416402 | − | 0.151558i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.24510 | + | 3.88863i | 0.111422 | + | 0.192989i | ||||
\(407\) | 1.03714 | + | 0.598793i | 0.0514091 | + | 0.0296811i | ||||
\(408\) | 6.55926 | − | 1.15657i | 0.324732 | − | 0.0572589i | ||||
\(409\) | −5.00640 | − | 28.3927i | −0.247550 | − | 1.40393i | −0.814494 | − | 0.580172i | \(-0.802985\pi\) |
0.566944 | − | 0.823756i | \(-0.308126\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.81315 | − | 6.60457i | −0.188089 | − | 0.325779i | ||||
\(412\) | 5.30234 | + | 6.31908i | 0.261227 | + | 0.311319i | ||||
\(413\) | 2.62175 | + | 7.20321i | 0.129008 | + | 0.354447i | ||||
\(414\) | −3.74510 | − | 1.36310i | −0.184062 | − | 0.0669930i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.819078 | + | 4.64522i | −0.0401586 | + | 0.227751i | ||||
\(417\) | 28.6878i | 1.40485i | ||||||||
\(418\) | −0.708319 | − | 0.00521457i | −0.0346450 | − | 0.000255053i | ||||
\(419\) | 7.66313 | 0.374369 | 0.187184 | − | 0.982325i | \(-0.440064\pi\) | ||||
0.187184 | + | 0.982325i | \(0.440064\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.14930 | + | 4.32078i | 0.250962 | + | 0.210582i | 0.759586 | − | 0.650407i | \(-0.225401\pi\) |
−0.508625 | + | 0.860988i | \(0.669846\pi\) | |||||||
\(422\) | −8.46069 | + | 23.2456i | −0.411860 | + | 1.13158i | ||||
\(423\) | −1.53574 | − | 4.21941i | −0.0746702 | − | 0.205155i | ||||
\(424\) | −4.55303 | + | 3.82045i | −0.221115 | + | 0.185537i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.95471 | + | 3.38565i | −0.0947059 | + | 0.164035i | ||||
\(427\) | 4.35878 | − | 0.768571i | 0.210936 | − | 0.0371937i | ||||
\(428\) | 3.60483 | − | 0.635630i | 0.174246 | − | 0.0307243i | ||||
\(429\) | −0.587182 | + | 1.01703i | −0.0283494 | + | 0.0491026i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.5307 | − | 10.5145i | 0.603585 | − | 0.506468i | −0.289011 | − | 0.957326i | \(-0.593326\pi\) |
0.892596 | + | 0.450858i | \(0.148882\pi\) | |||||||
\(432\) | −1.91404 | − | 5.25877i | −0.0920891 | − | 0.253013i | ||||
\(433\) | −3.49103 | + | 9.59152i | −0.167768 | + | 0.460939i | −0.994876 | − | 0.101104i | \(-0.967762\pi\) |
0.827108 | + | 0.562043i | \(0.189985\pi\) | |||||||
\(434\) | −5.23783 | − | 4.39506i | −0.251424 | − | 0.210970i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.23442 | 0.154901 | ||||||||
\(437\) | 25.0769 | − | 8.91875i | 1.19959 | − | 0.426642i | ||||
\(438\) | 24.0574i | 1.14951i | ||||||||
\(439\) | 1.65523 | − | 9.38728i | 0.0789998 | − | 0.448030i | −0.919491 | − | 0.393111i | \(-0.871399\pi\) |
0.998491 | − | 0.0549191i | \(-0.0174901\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.12701 | − | 0.774169i | −0.101286 | − | 0.0368652i | ||||
\(442\) | −7.01336 | − | 19.2690i | −0.333591 | − | 0.916535i | ||||
\(443\) | 3.84565 | + | 4.58306i | 0.182712 | + | 0.217748i | 0.849624 | − | 0.527389i | \(-0.176829\pi\) |
−0.666912 | + | 0.745136i | \(0.732384\pi\) | |||||||
\(444\) | −5.64543 | − | 9.77817i | −0.267920 | − | 0.464051i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.63950 | − | 14.9693i | −0.124984 | − | 0.708819i | ||||
\(447\) | −20.1839 | + | 3.55896i | −0.954665 | + | 0.168333i | ||||
\(448\) | −1.62760 | − | 0.939693i | −0.0768967 | − | 0.0443963i | ||||
\(449\) | −7.67752 | − | 13.2979i | −0.362325 | − | 0.627564i | 0.626018 | − | 0.779808i | \(-0.284683\pi\) |
−0.988343 | + | 0.152244i | \(0.951350\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.361844 | − | 0.131701i | 0.0170386 | − | 0.00620154i | ||||
\(452\) | −5.19026 | + | 14.2601i | −0.244129 | + | 0.670739i | ||||
\(453\) | 14.6390 | − | 17.4461i | 0.687801 | − | 0.819689i | ||||
\(454\) | 3.24675 | − | 18.4132i | 0.152377 | − | 0.864176i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.75877 | + | 3.38160i | 0.269679 | + | 0.158358i | ||||
\(457\) | 11.3987i | 0.533208i | 0.963806 | + | 0.266604i | \(0.0859015\pi\) | ||||
−0.963806 | + | 0.266604i | \(0.914098\pi\) | |||||||
\(458\) | 19.6069 | + | 3.45723i | 0.916172 | + | 0.161546i | ||||
\(459\) | 18.6368 | + | 15.6381i | 0.869892 | + | 0.729926i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.9847 | − | 13.8253i | 1.76913 | − | 0.643909i | 0.769137 | − | 0.639084i | \(-0.220686\pi\) |
0.999988 | − | 0.00482537i | \(-0.00153597\pi\) | |||||||
\(462\) | −0.300767 | − | 0.358441i | −0.0139930 | − | 0.0166762i | ||||
\(463\) | 8.62246 | − | 4.97818i | 0.400720 | − | 0.231356i | −0.286075 | − | 0.958207i | \(-0.592351\pi\) |
0.686794 | + | 0.726852i | \(0.259017\pi\) | |||||||
\(464\) | 1.19459 | − | 2.06910i | 0.0554576 | − | 0.0960553i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.85844 | − | 27.5536i | −0.225063 | − | 1.27640i | ||||
\(467\) | −4.85678 | − | 2.80406i | −0.224745 | − | 0.129757i | 0.383400 | − | 0.923582i | \(-0.374753\pi\) |
−0.608145 | + | 0.793826i | \(0.708086\pi\) | |||||||
\(468\) | −2.66625 | + | 1.53936i | −0.123248 | + | 0.0711571i | ||||
\(469\) | 2.35844 | − | 1.97897i | 0.108903 | − | 0.0913802i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.7233 | − | 3.90295i | −0.494103 | − | 0.179839i | ||||
\(472\) | 2.62175 | − | 3.12449i | 0.120676 | − | 0.143816i | ||||
\(473\) | 0.104455 | + | 0.0184183i | 0.00480287 | + | 0.000846875i | ||||
\(474\) | −1.53209 | −0.0703712 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.17024 | 0.374483 | ||||||||
\(477\) | −3.82045 | − | 0.673648i | −0.174926 | − | 0.0308442i | ||||
\(478\) | −16.9457 | + | 20.1951i | −0.775077 | + | 0.923701i | ||||
\(479\) | −23.2383 | − | 8.45805i | −1.06178 | − | 0.386458i | −0.248686 | − | 0.968584i | \(-0.579999\pi\) |
−0.813099 | + | 0.582126i | \(0.802221\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.6288 | + | 22.3442i | −1.21417 | + | 1.01881i | ||||
\(482\) | 14.8742 | − | 8.58765i | 0.677503 | − | 0.391157i | ||||
\(483\) | 15.2262 | + | 8.79086i | 0.692817 | + | 0.399998i | ||||
\(484\) | 1.90554 | + | 10.8069i | 0.0866157 | + | 0.491222i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.32635 | − | 5.76141i | 0.150886 | − | 0.261343i | ||||
\(487\) | 11.2501 | − | 6.49525i | 0.509791 | − | 0.294328i | −0.222957 | − | 0.974828i | \(-0.571571\pi\) |
0.732748 | + | 0.680500i | \(0.238238\pi\) | |||||||
\(488\) | −1.51379 | − | 1.80406i | −0.0685260 | − | 0.0816661i | ||||
\(489\) | −9.72075 | + | 3.53806i | −0.439588 | + | 0.159997i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.2947 | + | 11.9947i | 0.645112 | + | 0.541313i | 0.905583 | − | 0.424168i | \(-0.139433\pi\) |
−0.260471 | + | 0.965482i | \(0.583878\pi\) | |||||||
\(492\) | −3.57526 | − | 0.630415i | −0.161185 | − | 0.0284213i | ||||
\(493\) | 10.3865i | 0.467784i | ||||||||
\(494\) | 7.17412 | − | 19.2682i | 0.322779 | − | 0.866916i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.631759 | + | 3.58288i | −0.0283668 | + | 0.160876i | ||||
\(497\) | −3.08256 | + | 3.67365i | −0.138272 | + | 0.164786i | ||||
\(498\) | −0.535685 | + | 1.47178i | −0.0240046 | + | 0.0659521i | ||||
\(499\) | −16.2353 | + | 5.90917i | −0.726792 | + | 0.264531i | −0.678806 | − | 0.734317i | \(-0.737502\pi\) |
−0.0479856 | + | 0.998848i | \(0.515280\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.4513 | + | 21.5663i | 0.556283 | + | 0.963511i | ||||
\(502\) | −13.9357 | − | 8.04576i | −0.621979 | − | 0.359100i | ||||
\(503\) | −36.7562 | + | 6.48111i | −1.63888 | + | 0.288979i | −0.915754 | − | 0.401739i | \(-0.868406\pi\) |
−0.723125 | + | 0.690717i | \(0.757295\pi\) | |||||||
\(504\) | −0.213011 | − | 1.20805i | −0.00948827 | − | 0.0538106i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.496130 | + | 0.859322i | 0.0220557 | + | 0.0382015i | ||||
\(507\) | −9.10846 | − | 10.8550i | −0.404521 | − | 0.482089i | ||||
\(508\) | −6.82283 | − | 18.7456i | −0.302714 | − | 0.831700i | ||||
\(509\) | −17.9522 | − | 6.53406i | −0.795716 | − | 0.289617i | −0.0880062 | − | 0.996120i | \(-0.528050\pi\) |
−0.707710 | + | 0.706503i | \(0.750272\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.12449 | + | 29.0624i | −0.226694 | + | 1.28564i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 4.05893 | + | 24.0535i | 0.179206 | + | 1.06199i | ||||
\(514\) | −14.1438 | −0.623858 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.766044 | − | 0.642788i | −0.0337232 | − | 0.0282971i | ||||
\(517\) | −0.382353 | + | 1.05051i | −0.0168159 | + | 0.0462013i | ||||
\(518\) | −4.73708 | − | 13.0150i | −0.208135 | − | 0.571847i | ||||
\(519\) | −6.61721 | + | 5.55250i | −0.290463 | + | 0.243728i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.5287 | − | 30.3606i | 0.767946 | − | 1.33012i | −0.170729 | − | 0.985318i | \(-0.554612\pi\) |
0.938675 | − | 0.344803i | \(-0.112054\pi\) | |||||||
\(522\) | 1.53574 | − | 0.270792i | 0.0672175 | − | 0.0118523i | ||||
\(523\) | 23.8367 | − | 4.20305i | 1.04230 | − | 0.183786i | 0.373812 | − | 0.927505i | \(-0.378051\pi\) |
0.668493 | + | 0.743718i | \(0.266940\pi\) | |||||||
\(524\) | −8.44743 | + | 14.6314i | −0.369028 | + | 0.639175i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.0517 | − | 8.43437i | 0.438274 | − | 0.367756i | ||||
\(527\) | −5.40944 | − | 14.8623i | −0.235639 | − | 0.647412i | ||||
\(528\) | −0.0851529 | + | 0.233956i | −0.00370580 | + | 0.0101816i | ||||
\(529\) | −10.9422 | − | 9.18161i | −0.475749 | − | 0.399201i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.66220 | 0.115530 | ||||||||
\(532\) | 6.23654 | + | 5.31180i | 0.270388 | + | 0.230296i | ||||
\(533\) | 11.1771i | 0.484132i | ||||||||
\(534\) | −0.892589 | + | 5.06212i | −0.0386261 | + | 0.219060i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.53936 | − | 0.560282i | −0.0664903 | − | 0.0242005i | ||||
\(537\) | 6.02357 | + | 16.5496i | 0.259936 | + | 0.714169i | ||||
\(538\) | 14.4327 | + | 17.2003i | 0.622240 | + | 0.741556i | ||||
\(539\) | 0.281774 | + | 0.488048i | 0.0121369 | + | 0.0210217i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.37955 | + | 36.1802i | 0.274278 | + | 1.55551i | 0.741245 | + | 0.671234i | \(0.234235\pi\) |
−0.466967 | + | 0.884275i | \(0.654653\pi\) | |||||||
\(542\) | 5.67799 | − | 1.00118i | 0.243890 | − | 0.0430045i | ||||
\(543\) | −19.9580 | − | 11.5228i | −0.856480 | − | 0.494489i | ||||
\(544\) | −2.17365 | − | 3.76487i | −0.0931944 | − | 0.161417i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 12.7626 | − | 4.64522i | 0.546191 | − | 0.198797i | ||||
\(547\) | 6.59289 | − | 18.1138i | 0.281891 | − | 0.774490i | −0.715245 | − | 0.698873i | \(-0.753685\pi\) |
0.997137 | − | 0.0756171i | \(-0.0240927\pi\) | |||||||
\(548\) | −3.19961 | + | 3.81315i | −0.136681 | + | 0.162890i | ||||
\(549\) | 0.266922 | − | 1.51379i | 0.0113919 | − | 0.0646069i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.75268 | + | 7.92826i | −0.287674 | + | 0.337755i | ||||
\(552\) | − | 9.35504i | − | 0.398177i | ||||||
\(553\) | −1.85083 | − | 0.326352i | −0.0787054 | − | 0.0138779i | ||||
\(554\) | 15.1472 | + | 12.7100i | 0.643545 | + | 0.539998i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.5954 | − | 6.40420i | 0.746211 | − | 0.271598i | ||||
\(557\) | 27.4216 | + | 32.6798i | 1.16189 | + | 1.38469i | 0.908793 | + | 0.417247i | \(0.137005\pi\) |
0.253097 | + | 0.967441i | \(0.418551\pi\) | |||||||
\(558\) | −2.05650 | + | 1.18732i | −0.0870584 | + | 0.0502632i | ||||
\(559\) | −1.53936 | + | 2.66625i | −0.0651081 | + | 0.112771i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.187948 | − | 1.06590i | −0.00793516 | − | 0.0450025i | ||||
\(562\) | −27.4550 | − | 15.8512i | −1.15812 | − | 0.668641i | ||||
\(563\) | −10.2176 | + | 5.89915i | −0.430621 | + | 0.248619i | −0.699611 | − | 0.714524i | \(-0.746644\pi\) |
0.268990 | + | 0.963143i | \(0.413310\pi\) | |||||||
\(564\) | 8.07398 | − | 6.77487i | 0.339976 | − | 0.285274i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.76352 | + | 1.00584i | 0.116159 | + | 0.0422785i | ||||
\(567\) | −7.99227 | + | 9.52481i | −0.335644 | + | 0.400005i | ||||
\(568\) | 2.51292 | + | 0.443096i | 0.105440 | + | 0.0185919i | ||||
\(569\) | 1.87164 | 0.0784634 | 0.0392317 | − | 0.999230i | \(-0.487509\pi\) | ||||
0.0392317 | + | 0.999230i | \(0.487509\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.14197 | −0.340731 | −0.170365 | − | 0.985381i | \(-0.554495\pi\) | ||||
−0.170365 | + | 0.985381i | \(0.554495\pi\) | |||||||
\(572\) | 0.754866 | + | 0.133103i | 0.0315625 | + | 0.00556533i | ||||
\(573\) | −19.9060 | + | 23.7230i | −0.831584 | + | 0.991044i | ||||
\(574\) | −4.18479 | − | 1.52314i | −0.174670 | − | 0.0635746i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.419550i | −0.0208333 | + | 0.0174812i | ||||
\(577\) | −7.82380 | + | 4.51707i | −0.325709 | + | 0.188048i | −0.653934 | − | 0.756551i | \(-0.726883\pi\) |
0.328225 | + | 0.944599i | \(0.393549\pi\) | |||||||
\(578\) | 1.64457 | + | 0.949493i | 0.0684051 | + | 0.0394937i | ||||
\(579\) | 2.68092 | + | 15.2043i | 0.111415 | + | 0.631868i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.960637 | + | 1.66387i | −0.0398539 | + | 0.0690291i | ||||
\(582\) | −23.7138 | + | 13.6912i | −0.982970 | + | 0.567518i | ||||
\(583\) | 0.620838 | + | 0.739885i | 0.0257125 | + | 0.0306429i | ||||
\(584\) | 14.7554 | − | 5.37051i | 0.610581 | − | 0.222233i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.4847 | − | 10.4759i | −0.515740 | − | 0.432757i | ||||
\(587\) | 38.8935 | + | 6.85797i | 1.60531 | + | 0.283059i | 0.903267 | − | 0.429079i | \(-0.141162\pi\) |
0.702040 | + | 0.712138i | \(0.252273\pi\) | |||||||
\(588\) | − | 5.31315i | − | 0.219111i | ||||||
\(589\) | 5.53343 | − | 14.8616i | 0.228001 | − | 0.612363i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.48474 | + | 19.7629i | −0.143343 | + | 0.812938i | ||||
\(592\) | −4.73708 | + | 5.64543i | −0.194693 | + | 0.232026i | ||||
\(593\) | 9.88852 | − | 27.1685i | 0.406073 | − | 1.11568i | −0.553164 | − | 0.833072i | \(-0.686580\pi\) |
0.959237 | − | 0.282604i | \(-0.0911981\pi\) | |||||||
\(594\) | −0.854570 | + | 0.311038i | −0.0350634 | + | 0.0127621i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.68866 | + | 11.5851i | 0.273978 | + | 0.474544i | ||||
\(597\) | −23.3243 | − | 13.4663i | −0.954602 | − | 0.551140i | ||||
\(598\) | −28.3640 | + | 5.00134i | −1.15989 | + | 0.204520i | ||||
\(599\) | −3.16931 | − | 17.9741i | −0.129495 | − | 0.734400i | −0.978536 | − | 0.206074i | \(-0.933931\pi\) |
0.849042 | − | 0.528326i | \(-0.177180\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.18433 | − | 7.24746i | −0.170682 | − | 0.295630i | 0.767976 | − | 0.640478i | \(-0.221264\pi\) |
−0.938659 | + | 0.344848i | \(0.887930\pi\) | |||||||
\(602\) | −0.788496 | − | 0.939693i | −0.0321367 | − | 0.0382990i | ||||
\(603\) | −0.365698 | − | 1.00475i | −0.0148924 | − | 0.0409165i | ||||
\(604\) | −13.9684 | − | 5.08407i | −0.568365 | − | 0.206868i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.36959 | + | 13.4386i | −0.0962578 | + | 0.545905i | ||||
\(607\) | 28.1138i | 1.14110i | 0.821261 | + | 0.570552i | \(0.193271\pi\) | ||||
−0.821261 | + | 0.570552i | \(0.806729\pi\) | |||||||
\(608\) | 0.788496 | − | 4.28699i | 0.0319777 | − | 0.173860i | ||||
\(609\) | −6.87939 | −0.278767 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.8576 | − | 20.8580i | −1.00563 | − | 0.843823i | ||||
\(612\) | 0.970481 | − | 2.66637i | 0.0392294 | − | 0.107782i | ||||
\(613\) | 7.28861 | + | 20.0253i | 0.294384 | + | 0.808814i | 0.995412 | + | 0.0956799i | \(0.0305025\pi\) |
−0.701028 | + | 0.713134i | \(0.747275\pi\) | |||||||
\(614\) | −16.9932 | + | 14.2590i | −0.685789 | + | 0.575446i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.152704 | + | 0.264490i | −0.00615261 | + | 0.0106566i | ||||
\(617\) | −15.6255 | + | 2.75520i | −0.629061 | + | 0.110920i | −0.479084 | − | 0.877769i | \(-0.659031\pi\) |
−0.149977 | + | 0.988690i | \(0.547920\pi\) | |||||||
\(618\) | −12.4462 | + | 2.19459i | −0.500658 | + | 0.0882795i | ||||
\(619\) | −1.20527 | + | 2.08759i | −0.0484439 | + | 0.0839073i | −0.889231 | − | 0.457459i | \(-0.848760\pi\) |
0.840787 | + | 0.541367i | \(0.182093\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.1766 | − | 21.9648i | 1.05043 | − | 0.881417i | ||||
\(622\) | 3.05217 | + | 8.38578i | 0.122381 | + | 0.336239i | ||||
\(623\) | −2.15658 | + | 5.92514i | −0.0864014 | + | 0.237386i | ||||
\(624\) | −5.53596 | − | 4.64522i | −0.221616 | − | 0.185958i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −18.3259 | −0.732452 | ||||||||
\(627\) | 0.549522 | − | 0.935822i | 0.0219458 | − | 0.0373731i | ||||
\(628\) | 7.44831i | 0.297220i | ||||||||
\(629\) | 5.56330 | − | 31.5510i | 0.221823 | − | 1.25802i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.26769 | + | 0.461403i | 0.0504661 | + | 0.0183681i | 0.367130 | − | 0.930170i | \(-0.380340\pi\) |
−0.316664 | + | 0.948538i | \(0.602563\pi\) | |||||||
\(632\) | 0.342020 | + | 0.939693i | 0.0136048 | + | 0.0373790i | ||||
\(633\) | −24.3616 | − | 29.0330i | −0.968287 | − | 1.15396i | ||||
\(634\) | −12.1309 | − | 21.0113i | −0.481779 | − | 0.834465i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.58125 | − | 8.96773i | −0.0627007 | − | 0.355593i | ||||
\(637\) | −16.1092 | + | 2.84049i | −0.638270 | + | 0.112544i | ||||
\(638\) | −0.336236 | − | 0.194126i | −0.0133117 | − | 0.00768552i | ||||
\(639\) | 0.832748 | + | 1.44236i | 0.0329430 | + | 0.0570590i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.3910 | + | 11.7894i | −1.27937 | + | 0.465652i | −0.890223 | − | 0.455525i | \(-0.849452\pi\) |
−0.389144 | + | 0.921177i | \(0.627229\pi\) | |||||||
\(642\) | −1.91809 | + | 5.26991i | −0.0757011 | + | 0.207987i | ||||
\(643\) | 13.0729 | − | 15.5797i | 0.515544 | − | 0.614402i | −0.443977 | − | 0.896038i | \(-0.646433\pi\) |
0.959521 | + | 0.281636i | \(0.0908772\pi\) | |||||||
\(644\) | 1.99273 | − | 11.3013i | 0.0785244 | − | 0.445334i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.34982 | + | 17.8539i | 0.249830 | + | 0.702451i | ||||
\(647\) | − | 41.9427i | − | 1.64894i | −0.565906 | − | 0.824470i | \(-0.691474\pi\) | ||
0.565906 | − | 0.824470i | \(-0.308526\pi\) | |||||||
\(648\) | 6.51536 | + | 1.14883i | 0.255947 | + | 0.0451304i | ||||
\(649\) | −0.507741 | − | 0.426045i | −0.0199306 | − | 0.0167237i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.84389 | − | 3.58288i | 0.385813 | − | 0.140424i | ||||
\(652\) | 4.34008 | + | 5.17230i | 0.169971 | + | 0.202563i | ||||
\(653\) | 26.0497 | − | 15.0398i | 1.01941 | − | 0.588554i | 0.105474 | − | 0.994422i | \(-0.466364\pi\) |
0.913932 | + | 0.405868i | \(0.133031\pi\) | |||||||
\(654\) | −2.47771 | + | 4.29152i | −0.0968862 | + | 0.167812i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.411474 | + | 2.33359i | 0.0160654 | + | 0.0911112i | ||||
\(657\) | 8.87587 | + | 5.12449i | 0.346281 | + | 0.199925i | ||||
\(658\) | 11.1969 | − | 6.46451i | 0.436499 | − | 0.252013i | ||||
\(659\) | −37.7001 | + | 31.6342i | −1.46859 | + | 1.23229i | −0.551154 | + | 0.834404i | \(0.685812\pi\) |
−0.917434 | + | 0.397888i | \(0.869743\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.5330 | − | 16.2087i | −1.73213 | − | 0.630445i | −0.733355 | − | 0.679846i | \(-0.762047\pi\) |
−0.998779 | + | 0.0494010i | \(0.984269\pi\) | |||||||
\(662\) | −21.7229 | + | 25.8883i | −0.844283 | + | 1.00618i | ||||
\(663\) | 30.9392 | + | 5.45542i | 1.20158 | + | 0.211871i | ||||
\(664\) | 1.02229 | 0.0396725 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.81016 | −0.186390 | ||||||||
\(667\) | 14.3669 | + | 2.53327i | 0.556288 | + | 0.0980886i | ||||
\(668\) | 10.4479 | − | 12.4513i | 0.404241 | − | 0.481755i | ||||
\(669\) | 21.8837 | + | 7.96502i | 0.846074 | + | 0.307946i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.293167 | + | 0.245996i | −0.0113176 | + | 0.00949659i | ||||
\(672\) | 2.49362 | − | 1.43969i | 0.0961935 | − | 0.0555373i | ||||
\(673\) | 1.33586 | + | 0.771259i | 0.0514936 | + | 0.0297299i | 0.525526 | − | 0.850778i | \(-0.323869\pi\) |
−0.474032 | + | 0.880508i | \(0.657202\pi\) | |||||||
\(674\) | 5.16978 | + | 29.3193i | 0.199132 | + | 1.12934i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.62449 | + | 8.00984i | −0.177865 | + | 0.308071i | ||||
\(677\) | −15.6595 | + | 9.04101i | −0.601843 | + | 0.347474i | −0.769766 | − | 0.638326i | \(-0.779627\pi\) |
0.167923 | + | 0.985800i | \(0.446294\pi\) | |||||||
\(678\) | −14.9448 | − | 17.8105i | −0.573950 | − | 0.684007i | ||||
\(679\) | −31.5638 | + | 11.4883i | −1.21131 | + | 0.440879i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.9440 | + | 18.4132i | 0.840897 | + | 0.705596i | ||||
\(682\) | 0.582232 | + | 0.102663i | 0.0222948 | + | 0.00393118i | ||||
\(683\) | − | 22.1976i | − | 0.849367i | −0.905342 | − | 0.424684i | \(-0.860385\pi\) | ||
0.905342 | − | 0.424684i | \(-0.139615\pi\) | |||||||
\(684\) | 2.47431 | − | 1.40436i | 0.0946075 | − | 0.0536970i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.41622 | − | 19.3744i | 0.130432 | − | 0.739716i | ||||
\(687\) | −19.6069 | + | 23.3666i | −0.748052 | + | 0.891493i | ||||
\(688\) | −0.223238 | + | 0.613341i | −0.00851086 | + | 0.0233834i | ||||
\(689\) | −26.3444 | + | 9.58856i | −1.00364 | + | 0.365295i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.9449 | + | 38.0097i | 0.834824 | + | 1.44596i | 0.894174 | + | 0.447720i | \(0.147764\pi\) |
−0.0593503 | + | 0.998237i | \(0.518903\pi\) | |||||||
\(692\) | 4.88279 | + | 2.81908i | 0.185616 | + | 0.107165i | ||||
\(693\) | −0.196312 | + | 0.0346151i | −0.00745728 | + | 0.00131492i | ||||
\(694\) | −0.542766 | − | 3.07818i | −0.0206031 | − | 0.116846i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.83022 | + | 3.17004i | 0.0693744 | + | 0.120160i | ||||
\(697\) | −6.62154 | − | 7.89124i | −0.250809 | − | 0.298902i | ||||
\(698\) | −2.65863 | − | 7.30453i | −0.100631 | − | 0.276481i | ||||
\(699\) | 40.2806 | + | 14.6610i | 1.52355 | + | 0.554528i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.955423 | + | 5.41847i | −0.0360858 | + | 0.204653i | −0.997520 | − | 0.0703819i | \(-0.977578\pi\) |
0.961434 | + | 0.275035i | \(0.0886893\pi\) | |||||||
\(702\) | − | 26.3969i | − | 0.996288i | ||||||
\(703\) | 24.7592 | − | 20.4667i | 0.933811 | − | 0.771917i | ||||
\(704\) | 0.162504 | 0.00612459 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.3935 | − | 18.7904i | −0.842791 | − | 0.707186i | ||||
\(707\) | −5.72513 | + | 15.7297i | −0.215316 | + | 0.591575i | ||||
\(708\) | 2.13727 | + | 5.87211i | 0.0803237 | + | 0.220687i | ||||
\(709\) | 35.7105 | − | 29.9647i | 1.34114 | − | 1.12535i | 0.359805 | − | 0.933027i | \(-0.382843\pi\) |
0.981332 | − | 0.192321i | \(-0.0616014\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.326352 | + | 0.565258i | −0.0122391 | + | 0.0211988i | ||||
\(712\) | 3.30407 | − | 0.582596i | 0.123825 | − | 0.0218337i | ||||
\(713\) | −21.8773 | + | 3.85756i | −0.819312 | + | 0.144467i | ||||
\(714\) | −6.25877 | + | 10.8405i | −0.234229 | + | 0.405696i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.80587 | − | 7.38901i | 0.329091 | − | 0.276140i | ||||
\(717\) | −13.8142 | − | 37.9543i | −0.515902 | − | 1.41743i | ||||
\(718\) | −6.17101 | + | 16.9547i | −0.230300 | + | 0.632744i | ||||
\(719\) | 9.20052 | + | 7.72016i | 0.343122 | + | 0.287913i | 0.798021 | − | 0.602630i | \(-0.205880\pi\) |
−0.454899 | + | 0.890543i | \(0.650325\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.5030 | −0.577362 | ||||||||
\(722\) | −6.76055 | + | 17.7565i | −0.251601 | + | 0.660830i | ||||
\(723\) | 26.3141i | 0.978631i | ||||||||
\(724\) | −2.61200 | + | 14.8134i | −0.0970741 | + | 0.550535i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −15.7986 | − | 5.75022i | −0.586341 | − | 0.213411i | ||||
\(727\) | −10.5994 | − | 29.1215i | −0.393109 | − | 1.08006i | −0.965574 | − | 0.260129i | \(-0.916235\pi\) |
0.572465 | − | 0.819929i | \(-0.305987\pi\) | |||||||
\(728\) | −5.69821 | − | 6.79086i | −0.211190 | − | 0.251686i | ||||
\(729\) | 15.0201 | + | 26.0155i | 0.556299 | + | 0.963538i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.492726 | − | 2.79439i | −0.0182241 | − | 0.103354i | ||||
\(732\) | 3.55331 | − | 0.626545i | 0.131334 | − | 0.0231578i | ||||
\(733\) | 1.03947 | + | 0.600137i | 0.0383936 | + | 0.0221666i | 0.519074 | − | 0.854729i | \(-0.326277\pi\) |
−0.480680 | + | 0.876896i | \(0.659610\pi\) | |||||||
\(734\) | 8.34271 | + | 14.4500i | 0.307935 | + | 0.533359i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.73783 | + | 2.08840i | −0.211499 | + | 0.0769794i | ||||
\(737\) | −0.0910480 | + | 0.250152i | −0.00335380 | + | 0.00921448i | ||||
\(738\) | −0.994159 | + | 1.18479i | −0.0365955 | + | 0.0436128i | ||||
\(739\) | 2.15880 | − | 12.2431i | 0.0794126 | − | 0.450371i | −0.919010 | − | 0.394233i | \(-0.871010\pi\) |
0.998423 | − | 0.0561379i | \(-0.0178787\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.0699 | + | 24.2791i | 0.737285 | + | 0.891915i | ||||
\(742\) | − | 11.1702i | − | 0.410073i | ||||||
\(743\) | 2.76838 | + | 0.488140i | 0.101562 | + | 0.0179081i | 0.224198 | − | 0.974544i | \(-0.428024\pi\) |
−0.122636 | + | 0.992452i | \(0.539135\pi\) | |||||||
\(744\) | −4.26991 | − | 3.58288i | −0.156543 | − | 0.131355i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.32800 | + | 2.66717i | −0.268297 | + | 0.0976522i | ||||
\(747\) | 0.428901 | + | 0.511144i | 0.0156927 | + | 0.0187018i | ||||
\(748\) | −0.611806 | + | 0.353226i | −0.0223698 | + | 0.0129152i | ||||
\(749\) | −3.43969 | + | 5.95772i | −0.125684 | + | 0.217690i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.38326 | − | 7.84483i | −0.0504757 | − | 0.286262i | 0.949113 | − | 0.314935i | \(-0.101983\pi\) |
−0.999589 | + | 0.0286734i | \(0.990872\pi\) | |||||||
\(752\) | −5.95772 | − | 3.43969i | −0.217256 | − | 0.125433i | ||||
\(753\) | 21.3507 | − | 12.3268i | 0.778062 | − | 0.449214i | ||||
\(754\) | 8.63294 | − | 7.24390i | 0.314393 | − | 0.263807i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 9.88326 | + | 3.59721i | 0.359451 | + | 0.130829i | ||||
\(757\) | 8.96448 | − | 10.6834i | 0.325819 | − | 0.388297i | −0.578124 | − | 0.815949i | \(-0.696215\pi\) |
0.903943 | + | 0.427653i | \(0.140659\pi\) | |||||||
\(758\) | −1.29990 | − | 0.229208i | −0.0472146 | − | 0.00832520i | ||||
\(759\) | −1.52023 | −0.0551808 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −47.8043 | −1.73290 | −0.866452 | − | 0.499261i | \(-0.833605\pi\) | ||||
−0.866452 | + | 0.499261i | \(0.833605\pi\) | |||||||
\(762\) | 30.0987 | + | 5.30722i | 1.09036 | + | 0.192260i | ||||
\(763\) | −3.90733 | + | 4.65657i | −0.141455 | + | 0.168579i | ||||
\(764\) | 18.9941 | + | 6.91328i | 0.687181 | + | 0.250114i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.4349 | + | 21.3425i | −0.919002 | + | 0.771134i | ||||
\(767\) | 16.6613 | − | 9.61943i | 0.601606 | − | 0.347338i | ||||
\(768\) | −1.32683 | − | 0.766044i | −0.0478778 | − | 0.0276422i | ||||
\(769\) | 2.86080 | + | 16.2244i | 0.103163 | + | 0.585068i | 0.991938 | + | 0.126724i | \(0.0404462\pi\) |
−0.888775 | + | 0.458344i | \(0.848443\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.8348 | − | 18.7664i | 0.390206 | − | 0.675857i | ||||
\(772\) | 8.72691 | − | 5.03849i | 0.314088 | − | 0.181339i | ||||
\(773\) | −6.48233 | − | 7.72534i | −0.233153 | − | 0.277861i | 0.636764 | − | 0.771059i | \(-0.280272\pi\) |
−0.869917 | + | 0.493197i | \(0.835828\pi\) | |||||||
\(774\) | −0.400330 | + | 0.145708i | −0.0143896 | + | 0.00523737i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 13.6912 | + | 11.4883i | 0.491485 | + | 0.412405i | ||||
\(777\) | 20.8975 | + | 3.68479i | 0.749694 | + | 0.132191i | ||||
\(778\) | − | 14.8571i | − | 0.532653i | ||||||
\(779\) | 0.0760373 | − | 10.3285i | 0.00272432 | − | 0.370057i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0720048 | − | 0.408360i | 0.00257654 | − | 0.0146123i | ||||
\(782\) | 17.0627 | − | 20.3346i | 0.610162 | − | 0.727162i | ||||
\(783\) | −4.57299 | + | 12.5642i | −0.163425 | + | 0.449007i | ||||
\(784\) | −3.25877 | + | 1.18610i | −0.116385 | + | 0.0423606i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −12.9422 | − | 22.4166i | −0.461634 | − | 0.799573i | ||||
\(787\) | 31.2148 | + | 18.0219i | 1.11269 | + | 0.642411i | 0.939524 | − | 0.342483i | \(-0.111268\pi\) |
0.173164 | + | 0.984893i | \(0.444601\pi\) | |||||||
\(788\) | 12.8993 | − | 2.27450i | 0.459520 | − | 0.0810257i | ||||
\(789\) | 3.49092 | + | 19.7980i | 0.124280 | + | 0.704826i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.2601 | − | 24.6992i | −0.507031 | − | 0.878204i | ||||
\(792\) | 0.0681784 | + | 0.0812519i | 0.00242262 | + | 0.00288716i | ||||
\(793\) | −3.79931 | − | 10.4385i | −0.134917 | − | 0.370682i | ||||
\(794\) | 8.09374 | + | 2.94588i | 0.287236 | + | 0.104545i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.05257 | + | 17.3120i | −0.108195 | + | 0.613606i | ||||
\(797\) | − | 3.42190i | − | 0.121210i | −0.998162 | − | 0.0606050i | \(-0.980697\pi\) | ||
0.998162 | − | 0.0606050i | \(-0.0193030\pi\) | |||||||
\(798\) | −11.8253 | + | 4.20574i | −0.418612 | + | 0.148881i | ||||
\(799\) | 29.9067 | 1.05802 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.67752 | + | 1.40761i | 0.0592722 | + | 0.0497353i | ||||
\(802\) | −1.74670 | + | 4.79901i | −0.0616780 | + | 0.169459i | ||||
\(803\) | −0.872729 | − | 2.39780i | −0.0307979 | − | 0.0846166i | ||||
\(804\) | 1.92262 | − | 1.61327i | 0.0678055 | − | 0.0568956i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.58037 | + | 14.8616i | −0.302231 | + | 0.523479i | ||||
\(807\) | −33.8779 | + | 5.97359i | −1.19256 | + | 0.210280i | ||||
\(808\) | 8.77141 | − | 1.54664i | 0.308577 | − | 0.0544105i | ||||
\(809\) | 3.73870 | − | 6.47562i | 0.131446 | − | 0.227671i | −0.792788 | − | 0.609497i | \(-0.791371\pi\) |
0.924234 | + | 0.381826i | \(0.124705\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.6810 | − | 31.6181i | 1.32316 | − | 1.11026i | 0.337533 | − | 0.941314i | \(-0.390408\pi\) |
0.985625 | − | 0.168948i | \(-0.0540369\pi\) | |||||||
\(812\) | 1.53574 | + | 4.21941i | 0.0538939 | + | 0.148072i | ||||
\(813\) | −3.02119 | + | 8.30066i | −0.105958 | + | 0.291117i | ||||
\(814\) | 0.917404 | + | 0.769793i | 0.0321550 | + | 0.0269812i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.66044 | 0.233162 | ||||||||
\(817\) | 1.44063 | − | 2.45336i | 0.0504014 | − | 0.0858323i | ||||
\(818\) | − | 28.8307i | − | 1.00804i | ||||||
\(819\) | 1.00475 | − | 5.69821i | 0.0351087 | − | 0.199111i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.84611 | − | 3.21972i | −0.308732 | − | 0.112369i | 0.183008 | − | 0.983111i | \(-0.441417\pi\) |
−0.491740 | + | 0.870742i | \(0.663639\pi\) | |||||||
\(822\) | −2.60835 | − | 7.16637i | −0.0909765 | − | 0.249956i | ||||
\(823\) | 27.2007 | + | 32.4165i | 0.948157 | + | 1.12997i | 0.991395 | + | 0.130904i | \(0.0417881\pi\) |
−0.0432384 | + | 0.999065i | \(0.513767\pi\) | |||||||
\(824\) | 4.12449 | + | 7.14382i | 0.143683 | + | 0.248867i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.33110 | + | 7.54904i | 0.0463149 | + | 0.262665i | ||||
\(827\) | −26.3119 | + | 4.63950i | −0.914955 | + | 0.161331i | −0.611252 | − | 0.791436i | \(-0.709334\pi\) |
−0.303702 | + | 0.952767i | \(0.598223\pi\) | |||||||
\(828\) | −3.45150 | − | 1.99273i | −0.119948 | − | 0.0692520i | ||||
\(829\) | 7.24257 | + | 12.5445i | 0.251545 | + | 0.435689i | 0.963951 | − | 0.266078i | \(-0.0857280\pi\) |
−0.712406 | + | 0.701767i | \(0.752395\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.4675 | + | 10.3613i | −0.987527 | + | 0.359430i | ||||
\(832\) | −1.61327 | + | 4.43242i | −0.0559300 | + | 0.153666i | ||||
\(833\) | 9.69069 | − | 11.5489i | 0.335763 | − | 0.400146i | ||||
\(834\) | −4.98158 | + | 28.2520i | −0.172498 | + | 0.978285i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.696652 | − | 0.128134i | −0.0240942 | − | 0.00443159i | ||||
\(837\) | − | 20.3601i | − | 0.703748i | ||||||
\(838\) | 7.54671 | + | 1.33069i | 0.260697 | + | 0.0459679i | ||||
\(839\) | −0.409663 | − | 0.343748i | −0.0141431 | − | 0.0118675i | 0.635689 | − | 0.771946i | \(-0.280716\pi\) |
−0.649832 | + | 0.760078i | \(0.725161\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.8871 | − | 7.96626i | 0.754728 | − | 0.274699i | ||||
\(842\) | 4.32078 | + | 5.14930i | 0.148904 | + | 0.177457i | ||||
\(843\) | 42.0635 | − | 24.2854i | 1.44875 | − | 0.836433i | ||||
\(844\) | −12.3687 | + | 21.4232i | −0.425748 | + | 0.737418i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.779715 | − | 4.42198i | −0.0268072 | − | 0.152031i | ||||
\(847\) | −17.8606 | − | 10.3118i | −0.613696 | − | 0.354318i | ||||
\(848\) | −5.14728 | + | 2.97178i | −0.176758 | + | 0.102051i | ||||
\(849\) | −3.45155 | + | 2.89620i | −0.118457 | + | 0.0993972i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −42.2854 | − | 15.3906i | −1.44952 | − | 0.527584i | ||||
\(852\) | −2.51292 | + | 2.99479i | −0.0860913 | + | 0.102600i | ||||
\(853\) | 6.14906 | + | 1.08424i | 0.210540 | + | 0.0371238i | 0.277923 | − | 0.960603i | \(-0.410354\pi\) |
−0.0673834 | + | 0.997727i | \(0.521465\pi\) | |||||||
\(854\) | 4.42602 | 0.151455 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.66044 | 0.125111 | ||||||||
\(857\) | −13.1571 | − | 2.31996i | −0.449439 | − | 0.0792482i | −0.0556524 | − | 0.998450i | \(-0.517724\pi\) |
−0.393786 | + | 0.919202i | \(0.628835\pi\) | |||||||
\(858\) | −0.754866 | + | 0.899615i | −0.0257707 | + | 0.0307123i | ||||
\(859\) | −6.98070 | − | 2.54077i | −0.238179 | − | 0.0866899i | 0.220173 | − | 0.975461i | \(-0.429338\pi\) |
−0.458352 | + | 0.888771i | \(0.651560\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.22668 | − | 4.38571i | 0.178125 | − | 0.149464i | ||||
\(862\) | 14.1662 | − | 8.17886i | 0.482503 | − | 0.278573i | ||||
\(863\) | −15.9916 | − | 9.23277i | −0.544362 | − | 0.314287i | 0.202483 | − | 0.979286i | \(-0.435099\pi\) |
−0.746845 | + | 0.664998i | \(0.768432\pi\) | |||||||
\(864\) | −0.971782 | − | 5.51125i | −0.0330607 | − | 0.187496i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.10354 | + | 8.83959i | −0.173425 | + | 0.300382i | ||||
\(867\) | −2.51963 | + | 1.45471i | −0.0855710 | + | 0.0494045i | ||||
\(868\) | −4.39506 | − | 5.23783i | −0.149178 | − | 0.177783i | ||||
\(869\) | 0.152704 | − | 0.0555796i | 0.00518012 | − | 0.00188541i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.91921 | − | 4.96681i | −0.200565 | − | 0.168294i | ||||
\(872\) | 3.18528 | + | 0.561652i | 0.107867 | + | 0.0190199i | ||||
\(873\) | 11.6655i | 0.394817i | ||||||||
\(874\) | 26.2447 | − | 4.42869i | 0.887740 | − | 0.149803i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.17752 | + | 23.6919i | −0.141145 | + | 0.800475i | ||||
\(877\) | 9.59506 | − | 11.4349i | 0.324002 | − | 0.386131i | −0.579315 | − | 0.815104i | \(-0.696680\pi\) |
0.903317 | + | 0.428973i | \(0.141124\pi\) | |||||||
\(878\) | 3.26017 | − | 8.95723i | 0.110025 | − | 0.302292i | ||||
\(879\) | 23.4636 | − | 8.54006i | 0.791409 | − | 0.288049i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.8491 | + | 20.5233i | 0.399207 | + | 0.691446i | 0.993628 | − | 0.112707i | \(-0.0359523\pi\) |
−0.594422 | + | 0.804154i | \(0.702619\pi\) | |||||||
\(882\) | −1.96026 | − | 1.13176i | −0.0660055 | − | 0.0381083i | ||||
\(883\) | −13.2633 | + | 2.33868i | −0.446346 | + | 0.0787028i | −0.392303 | − | 0.919836i | \(-0.628322\pi\) |
−0.0540423 | + | 0.998539i | \(0.517211\pi\) | |||||||
\(884\) | −3.56077 | − | 20.1942i | −0.119762 | − | 0.679203i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.99138 | + | 5.18123i | 0.100497 | + | 0.174067i | ||||
\(887\) | −17.7903 | − | 21.2017i | −0.597341 | − | 0.711884i | 0.379658 | − | 0.925127i | \(-0.376042\pi\) |
−0.976999 | + | 0.213243i | \(0.931597\pi\) | |||||||
\(888\) | −3.86170 | − | 10.6099i | −0.129590 | − | 0.356046i | ||||
\(889\) | 35.2301 | + | 12.8227i | 1.18158 | + | 0.430060i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.186690 | − | 1.05877i | 0.00625434 | − | 0.0354701i | ||||
\(892\) | − | 15.2003i | − | 0.508943i | ||||||
\(893\) | 22.8285 | + | 19.4436i | 0.763927 | + | 0.650654i | ||||
\(894\) | −20.4953 | −0.685464 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.43969 | − | 1.20805i | −0.0480968 | − | 0.0403580i | ||||
\(897\) | 15.0922 | − | 41.4654i | 0.503913 | − | 1.38449i | ||||
\(898\) | −5.25173 | − | 14.4290i | −0.175253 | − | 0.481502i | ||||
\(899\) | 6.65863 | − | 5.58726i | 0.222078 | − | 0.186345i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.9192 | − | 22.3767i | 0.430401 | − | 0.745477i | ||||
\(902\) | 0.379217 | − | 0.0668661i | 0.0126265 | − | 0.00222640i | ||||
\(903\) | 1.85083 | − | 0.326352i | 0.0615919 | − | 0.0108603i | ||||
\(904\) | −7.58765 | + | 13.1422i | −0.252361 | + | 0.437103i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 17.4461 | − | 14.6390i | 0.579607 | − | 0.486348i | ||||
\(907\) | −0.155059 | − | 0.426022i | −0.00514866 | − | 0.0141458i | 0.937092 | − | 0.349083i | \(-0.113507\pi\) |
−0.942240 | + | 0.334938i | \(0.891285\pi\) | |||||||
\(908\) | 6.39485 | − | 17.5697i | 0.212220 | − | 0.583071i | ||||
\(909\) | 4.45336 | + | 3.73682i | 0.147709 | + | 0.123942i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.6492 | 1.61182 | 0.805910 | − | 0.592038i | \(-0.201677\pi\) | ||||
0.805910 | + | 0.592038i | \(0.201677\pi\) | |||||||
\(912\) | 5.08407 | + | 4.33022i | 0.168351 | + | 0.143388i | ||||
\(913\) | − | 0.166126i | − | 0.00549796i | ||||||
\(914\) | −1.97936 | + | 11.2255i | −0.0654714 | + | 0.371307i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.7087 | + | 6.80942i | 0.618154 | + | 0.224990i | ||||
\(917\) | −10.8598 | − | 29.8371i | −0.358623 | − | 0.985307i | ||||
\(918\) | 15.6381 | + | 18.6368i | 0.516136 | + | 0.615106i | ||||
\(919\) | 16.7733 | + | 29.0522i | 0.553301 | + | 0.958345i | 0.998034 | + | 0.0626817i | \(0.0199653\pi\) |
−0.444733 | + | 0.895663i | \(0.646701\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.90167 | − | 33.4701i | −0.194467 | − | 1.10288i | ||||
\(922\) | 39.8084 | − | 7.01930i | 1.31102 | − | 0.231168i | ||||
\(923\) | 10.4235 | + | 6.01801i | 0.343094 | + | 0.198085i | ||||
\(924\) | −0.233956 | − | 0.405223i | −0.00769657 | − | 0.0133309i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.35591 | − | 3.40527i | 0.307454 | − | 0.111904i | ||||
\(927\) | −1.84148 | + | 5.05943i | −0.0604822 | + | 0.166173i | ||||
\(928\) | 1.53574 | − | 1.83022i | 0.0504131 | − | 0.0600800i | ||||
\(929\) | 6.50016 | − | 36.8643i | 0.213263 | − | 1.20948i | −0.670631 | − | 0.741791i | \(-0.733977\pi\) |
0.883895 | − | 0.467686i | \(-0.154912\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.9055 | − | 2.51525i | 0.488509 | − | 0.0824340i | ||||
\(932\) | − | 27.9786i | − | 0.916471i | ||||||
\(933\) | −13.4646 | − | 2.37417i | −0.440811 | − | 0.0777269i | ||||
\(934\) | −4.29607 | − | 3.60483i | −0.140572 | − | 0.117954i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.89306 | + | 1.05299i | −0.0945625 | + | 0.0344179i | ||||
\(937\) | 2.32039 | + | 2.76533i | 0.0758037 | + | 0.0903394i | 0.802613 | − | 0.596500i | \(-0.203442\pi\) |
−0.726810 | + | 0.686839i | \(0.758998\pi\) | |||||||
\(938\) | 2.66625 | − | 1.53936i | 0.0870563 | − | 0.0502620i | ||||
\(939\) | 14.0385 | − | 24.3154i | 0.458129 | − | 0.793502i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.28540 | − | 35.6463i | −0.204898 | − | 1.16203i | −0.897600 | − | 0.440811i | \(-0.854691\pi\) |
0.692702 | − | 0.721224i | \(-0.256420\pi\) | |||||||
\(942\) | −9.88263 | − | 5.70574i | −0.321993 | − | 0.185903i | ||||
\(943\) | −12.5304 | + | 7.23442i | −0.408046 | + | 0.235585i | ||||
\(944\) | 3.12449 | − | 2.62175i | 0.101693 | − | 0.0853308i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.0996702 | + | 0.0362770i | 0.00324056 | + | 0.00117947i | ||||
\(947\) | 19.0801 | − | 22.7388i | 0.620019 | − | 0.738910i | −0.361054 | − | 0.932545i | \(-0.617583\pi\) |
0.981074 | + | 0.193634i | \(0.0620276\pi\) | |||||||
\(948\) | −1.50881 | − | 0.266044i | −0.0490040 | − | 0.00864072i | ||||
\(949\) | 74.0660 | 2.40429 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 37.1712 | 1.20536 | ||||||||
\(952\) | 8.04612 | + | 1.41875i | 0.260776 | + | 0.0459819i | ||||
\(953\) | 9.50698 | − | 11.3300i | 0.307961 | − | 0.367014i | −0.589759 | − | 0.807579i | \(-0.700777\pi\) |
0.897721 | + | 0.440565i | \(0.145222\pi\) | |||||||
\(954\) | −3.64543 | − | 1.32683i | −0.118025 | − | 0.0429576i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −20.1951 | + | 16.9457i | −0.653155 | + | 0.548062i | ||||
\(957\) | 0.515143 | − | 0.297418i | 0.0166522 | − | 0.00961416i | ||||
\(958\) | −21.4165 | − | 12.3648i | −0.691937 | − | 0.399490i | ||||
\(959\) | −1.62449 | − | 9.21291i | −0.0524574 | − | 0.297500i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.88191 | − | 15.3839i | 0.286513 | − | 0.496256i | ||||
\(962\) | −30.1043 | + | 17.3807i | −0.970602 | + | 0.560377i | ||||
\(963\) | 1.53574 | + | 1.83022i | 0.0494885 | + | 0.0589781i | ||||
\(964\) | 16.1395 | − | 5.87430i | 0.519818 | − | 0.189198i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 13.4684 | + | 11.3013i | 0.433338 | + | 0.363614i | ||||
\(967\) | 44.2523 | + | 7.80288i | 1.42306 | + | 0.250924i | 0.831584 | − | 0.555399i | \(-0.187435\pi\) |
0.591475 | + | 0.806323i | \(0.298546\pi\) | |||||||
\(968\) | 10.9736i | 0.352705i | ||||||||
\(969\) | −28.5533 | − | 5.25173i | −0.917263 | − | 0.168710i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.95946 | + | 39.4690i | −0.223340 | + | 1.26662i | 0.642495 | + | 0.766290i | \(0.277900\pi\) |
−0.865834 | + | 0.500331i | \(0.833212\pi\) | |||||||
\(972\) | 4.27628 | − | 5.09627i | 0.137162 | − | 0.163463i | ||||
\(973\) | −12.0360 | + | 33.0685i | −0.385855 | + | 1.06013i | ||||
\(974\) | 12.2071 | − | 4.44301i | 0.391140 | − | 0.142363i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.17752 | − | 2.03952i | −0.0376915 | − | 0.0652835i | ||||
\(977\) | 44.3593 | + | 25.6109i | 1.41918 | + | 0.819364i | 0.996227 | − | 0.0867869i | \(-0.0276599\pi\) |
0.422954 | + | 0.906151i | \(0.360993\pi\) | |||||||
\(978\) | −10.1875 | + | 1.79632i | −0.325759 | + | 0.0574401i | ||||
\(979\) | −0.0946741 | − | 0.536923i | −0.00302580 | − | 0.0171601i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.05556 | + | 1.82828i | 0.0337014 | + | 0.0583726i | ||||
\(982\) | 11.9947 | + | 14.2947i | 0.382766 | + | 0.456163i | ||||
\(983\) | 3.12939 | + | 8.59792i | 0.0998119 | + | 0.274231i | 0.979541 | − | 0.201244i | \(-0.0644984\pi\) |
−0.879729 | + | 0.475475i | \(0.842276\pi\) | |||||||
\(984\) | −3.41147 | − | 1.24168i | −0.108754 | − | 0.0395832i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.80360 | + | 10.2287i | −0.0574382 | + | 0.325748i | ||||
\(987\) | 19.8084i | 0.630508i | ||||||||
\(988\) | 10.4110 | − | 17.7297i | 0.331218 | − | 0.564056i | ||||
\(989\) | −3.98545 | −0.126730 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.2153 | − | 17.8017i | −0.673926 | − | 0.565491i | 0.240299 | − | 0.970699i | \(-0.422755\pi\) |
−0.914224 | + | 0.405208i | \(0.867199\pi\) | |||||||
\(992\) | −1.24432 | + | 3.41875i | −0.0395073 | + | 0.108545i | ||||
\(993\) | −17.7086 | − | 48.6541i | −0.561967 | − | 1.54399i | ||||
\(994\) | −3.67365 | + | 3.08256i | −0.116521 | + | 0.0977728i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.783119 | + | 1.35640i | −0.0248141 | + | 0.0429792i | ||||
\(997\) | −35.6343 | + | 6.28328i | −1.12855 | + | 0.198993i | −0.706591 | − | 0.707622i | \(-0.749768\pi\) |
−0.421957 | + | 0.906616i | \(0.638657\pi\) | |||||||
\(998\) | −17.0148 | + | 3.00016i | −0.538593 | + | 0.0949685i | ||||
\(999\) | 20.6211 | − | 35.7168i | 0.652422 | − | 1.13003i |
(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 | 950.2.u.a.549.2 | 12 | ||
5.2 | odd | 4 | 950.2.l.f.701.1 | yes | 6 | ||
5.3 | odd | 4 | 950.2.l.a.701.1 | yes | 6 | ||
5.4 | even | 2 | inner | 950.2.u.a.549.1 | 12 | ||
19.9 | even | 9 | inner | 950.2.u.a.199.1 | 12 | ||
95.9 | even | 18 | inner | 950.2.u.a.199.2 | 12 | ||
95.28 | odd | 36 | 950.2.l.a.351.1 | ✓ | 6 | ||
95.47 | odd | 36 | 950.2.l.f.351.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.l.a.351.1 | ✓ | 6 | 95.28 | odd | 36 | ||
950.2.l.a.701.1 | yes | 6 | 5.3 | odd | 4 | ||
950.2.l.f.351.1 | yes | 6 | 95.47 | odd | 36 | ||
950.2.l.f.701.1 | yes | 6 | 5.2 | odd | 4 | ||
950.2.u.a.199.1 | 12 | 19.9 | even | 9 | inner | ||
950.2.u.a.199.2 | 12 | 95.9 | even | 18 | inner | ||
950.2.u.a.549.1 | 12 | 5.4 | even | 2 | inner | ||
950.2.u.a.549.2 | 12 | 1.1 | even | 1 | trivial |