Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} - 1175 x^{7} + 2135 x^{6} - 2300 x^{5} + 1850 x^{4} - 925 x^{3} + 700 x^{2} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 729.1 | ||
Root | \(0.751051 - 2.31150i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.729 |
Dual form | 847.2.f.v.323.1 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.96628 | + | 1.42858i | −1.39037 | + | 1.01016i | −0.394543 | + | 0.918877i | \(0.629097\pi\) |
−0.995825 | + | 0.0912842i | \(0.970903\pi\) | |||||||
\(3\) | 0.443194 | + | 1.36401i | 0.255878 | + | 0.787512i | 0.993655 | + | 0.112468i | \(0.0358755\pi\) |
−0.737777 | + | 0.675044i | \(0.764124\pi\) | |||||||
\(4\) | 1.20736 | − | 3.71587i | 0.603680 | − | 1.85794i | ||||
\(5\) | −1.01825 | − | 0.739805i | −0.455377 | − | 0.330851i | 0.336338 | − | 0.941741i | \(-0.390812\pi\) |
−0.791715 | + | 0.610891i | \(0.790812\pi\) | |||||||
\(6\) | −2.82005 | − | 2.04888i | −1.15128 | − | 0.836454i | ||||
\(7\) | −0.309017 | + | 0.951057i | −0.116797 | + | 0.359466i | ||||
\(8\) | 1.43233 | + | 4.40826i | 0.506405 | + | 1.55855i | ||||
\(9\) | 0.762946 | − | 0.554312i | 0.254315 | − | 0.184771i | ||||
\(10\) | 3.05904 | 0.967354 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 5.60359 | 1.61762 | ||||||||
\(13\) | −2.57131 | + | 1.86816i | −0.713152 | + | 0.518135i | −0.884189 | − | 0.467129i | \(-0.845288\pi\) |
0.171037 | + | 0.985265i | \(0.445288\pi\) | |||||||
\(14\) | −0.751051 | − | 2.31150i | −0.200727 | − | 0.617774i | ||||
\(15\) | 0.557818 | − | 1.71679i | 0.144028 | − | 0.443272i | ||||
\(16\) | −2.79210 | − | 2.02858i | −0.698026 | − | 0.507145i | ||||
\(17\) | 4.79276 | + | 3.48215i | 1.16242 | + | 0.844544i | 0.990082 | − | 0.140494i | \(-0.0448691\pi\) |
0.172334 | + | 0.985039i | \(0.444869\pi\) | |||||||
\(18\) | −0.708281 | + | 2.17986i | −0.166943 | + | 0.513799i | ||||
\(19\) | −0.884474 | − | 2.72213i | −0.202912 | − | 0.624500i | −0.999793 | − | 0.0203626i | \(-0.993518\pi\) |
0.796880 | − | 0.604137i | \(-0.206482\pi\) | |||||||
\(20\) | −3.97842 | + | 2.89049i | −0.889602 | + | 0.646333i | ||||
\(21\) | −1.43421 | −0.312969 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.76343 | 1.41027 | 0.705136 | − | 0.709072i | \(-0.250886\pi\) | ||||
0.705136 | + | 0.709072i | \(0.250886\pi\) | |||||||
\(24\) | −5.37811 | + | 3.90743i | −1.09780 | + | 0.797600i | ||||
\(25\) | −1.05555 | − | 3.24866i | −0.211111 | − | 0.649733i | ||||
\(26\) | 2.38707 | − | 7.34665i | 0.468144 | − | 1.44080i | ||||
\(27\) | 4.57511 | + | 3.32401i | 0.880481 | + | 0.639707i | ||||
\(28\) | 3.16091 | + | 2.29654i | 0.597356 | + | 0.434004i | ||||
\(29\) | −1.38918 | + | 4.27547i | −0.257965 | + | 0.793934i | 0.735266 | + | 0.677779i | \(0.237057\pi\) |
−0.993231 | + | 0.116156i | \(0.962943\pi\) | |||||||
\(30\) | 1.35575 | + | 4.17257i | 0.247525 | + | 0.761803i | ||||
\(31\) | −7.86972 | + | 5.71769i | −1.41344 | + | 1.02693i | −0.420634 | + | 0.907231i | \(0.638192\pi\) |
−0.992811 | + | 0.119697i | \(0.961808\pi\) | |||||||
\(32\) | −0.882184 | −0.155950 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −14.3984 | −2.46931 | ||||||||
\(35\) | 1.01825 | − | 0.739805i | 0.172116 | − | 0.125050i | ||||
\(36\) | −1.13860 | − | 3.50426i | −0.189767 | − | 0.584044i | ||||
\(37\) | −1.68567 | + | 5.18797i | −0.277123 | + | 0.852897i | 0.711527 | + | 0.702659i | \(0.248004\pi\) |
−0.988650 | + | 0.150238i | \(0.951996\pi\) | |||||||
\(38\) | 5.62791 | + | 4.08892i | 0.912968 | + | 0.663310i | ||||
\(39\) | −3.68778 | − | 2.67933i | −0.590518 | − | 0.429036i | ||||
\(40\) | 1.80277 | − | 5.54837i | 0.285044 | − | 0.877274i | ||||
\(41\) | 0.0971810 | + | 0.299092i | 0.0151771 | + | 0.0467104i | 0.958358 | − | 0.285569i | \(-0.0921824\pi\) |
−0.943181 | + | 0.332279i | \(0.892182\pi\) | |||||||
\(42\) | 2.82005 | − | 2.04888i | 0.435143 | − | 0.316150i | ||||
\(43\) | 0.132562 | 0.0202155 | 0.0101078 | − | 0.999949i | \(-0.496783\pi\) | ||||
0.0101078 | + | 0.999949i | \(0.496783\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.18696 | −0.176941 | ||||||||
\(46\) | −13.2988 | + | 9.66213i | −1.96080 | + | 1.42460i | ||||
\(47\) | 2.89705 | + | 8.91620i | 0.422578 | + | 1.30056i | 0.905294 | + | 0.424785i | \(0.139650\pi\) |
−0.482716 | + | 0.875777i | \(0.660350\pi\) | |||||||
\(48\) | 1.52956 | − | 4.70751i | 0.220774 | − | 0.679471i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | 6.71650 | + | 4.87983i | 0.949857 | + | 0.690112i | ||||
\(51\) | −2.62556 | + | 8.08065i | −0.367652 | + | 1.13152i | ||||
\(52\) | 3.83736 | + | 11.8102i | 0.532147 | + | 1.63778i | ||||
\(53\) | −3.52078 | + | 2.55800i | −0.483616 | + | 0.351368i | −0.802724 | − | 0.596351i | \(-0.796617\pi\) |
0.319108 | + | 0.947718i | \(0.396617\pi\) | |||||||
\(54\) | −13.7446 | −1.87040 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.63512 | −0.619393 | ||||||||
\(57\) | 3.32102 | − | 2.41286i | 0.439880 | − | 0.319592i | ||||
\(58\) | −3.37635 | − | 10.3913i | −0.443336 | − | 1.36445i | ||||
\(59\) | −2.14670 | + | 6.60685i | −0.279476 | + | 0.860139i | 0.708524 | + | 0.705686i | \(0.249361\pi\) |
−0.988000 | + | 0.154452i | \(0.950639\pi\) | |||||||
\(60\) | −5.70587 | − | 4.14556i | −0.736625 | − | 0.535190i | ||||
\(61\) | −1.98383 | − | 1.44134i | −0.254004 | − | 0.184545i | 0.453495 | − | 0.891259i | \(-0.350177\pi\) |
−0.707499 | + | 0.706714i | \(0.750177\pi\) | |||||||
\(62\) | 7.30586 | − | 22.4851i | 0.927845 | − | 2.85561i | ||||
\(63\) | 0.291419 | + | 0.896896i | 0.0367154 | + | 0.112998i | ||||
\(64\) | 7.31882 | − | 5.31744i | 0.914853 | − | 0.664679i | ||||
\(65\) | 4.00032 | 0.496179 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.41987 | −1.15082 | −0.575410 | − | 0.817865i | \(-0.695158\pi\) | ||||
−0.575410 | + | 0.817865i | \(0.695158\pi\) | |||||||
\(68\) | 18.7258 | − | 13.6051i | 2.27084 | − | 1.64986i | ||||
\(69\) | 2.99751 | + | 9.22539i | 0.360858 | + | 1.11061i | ||||
\(70\) | −0.945296 | + | 2.90932i | −0.112985 | + | 0.347731i | ||||
\(71\) | 0.0943396 | + | 0.0685417i | 0.0111961 | + | 0.00813441i | 0.593369 | − | 0.804930i | \(-0.297797\pi\) |
−0.582173 | + | 0.813065i | \(0.697797\pi\) | |||||||
\(72\) | 3.53634 | + | 2.56930i | 0.416762 | + | 0.302795i | ||||
\(73\) | −0.190055 | + | 0.584930i | −0.0222443 | + | 0.0684608i | −0.961562 | − | 0.274586i | \(-0.911459\pi\) |
0.939318 | + | 0.343047i | \(0.111459\pi\) | |||||||
\(74\) | −4.09695 | − | 12.6091i | −0.476261 | − | 1.46578i | ||||
\(75\) | 3.96340 | − | 2.87958i | 0.457654 | − | 0.332505i | ||||
\(76\) | −11.1830 | −1.28277 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 11.0789 | 1.25443 | ||||||||
\(79\) | 6.90033 | − | 5.01339i | 0.776348 | − | 0.564050i | −0.127533 | − | 0.991834i | \(-0.540706\pi\) |
0.903881 | + | 0.427784i | \(0.140706\pi\) | |||||||
\(80\) | 1.34232 | + | 4.13122i | 0.150075 | + | 0.461885i | ||||
\(81\) | −1.63207 | + | 5.02300i | −0.181341 | + | 0.558111i | ||||
\(82\) | −0.618364 | − | 0.449267i | −0.0682868 | − | 0.0496133i | ||||
\(83\) | 0.768997 | + | 0.558709i | 0.0844083 | + | 0.0613262i | 0.629189 | − | 0.777252i | \(-0.283387\pi\) |
−0.544781 | + | 0.838579i | \(0.683387\pi\) | |||||||
\(84\) | −1.73160 | + | 5.32933i | −0.188933 | + | 0.581477i | ||||
\(85\) | −2.30414 | − | 7.09142i | −0.249919 | − | 0.769172i | ||||
\(86\) | −0.260654 | + | 0.189376i | −0.0281070 | + | 0.0204209i | ||||
\(87\) | −6.44746 | −0.691241 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0552 | 1.06585 | 0.532923 | − | 0.846164i | \(-0.321094\pi\) | ||||
0.532923 | + | 0.846164i | \(0.321094\pi\) | |||||||
\(90\) | 2.33388 | − | 1.69567i | 0.246013 | − | 0.178739i | ||||
\(91\) | −0.982152 | − | 3.02275i | −0.102957 | − | 0.316870i | ||||
\(92\) | 8.16590 | − | 25.1320i | 0.851353 | − | 2.62020i | ||||
\(93\) | −11.2868 | − | 8.20034i | −1.17039 | − | 0.850336i | ||||
\(94\) | −18.4339 | − | 13.3930i | −1.90132 | − | 1.38139i | ||||
\(95\) | −1.11323 | + | 3.42616i | −0.114215 | + | 0.351516i | ||||
\(96\) | −0.390979 | − | 1.20331i | −0.0399041 | − | 0.122812i | ||||
\(97\) | −14.2201 | + | 10.3315i | −1.44383 | + | 1.04901i | −0.456608 | + | 0.889668i | \(0.650936\pi\) |
−0.987224 | + | 0.159337i | \(0.949064\pi\) | |||||||
\(98\) | 2.43045 | 0.245513 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.3461 | −1.33461 | ||||||||
\(101\) | −10.0934 | + | 7.33330i | −1.00433 | + | 0.729690i | −0.963013 | − | 0.269456i | \(-0.913156\pi\) |
−0.0413196 | + | 0.999146i | \(0.513156\pi\) | |||||||
\(102\) | −6.38130 | − | 19.6396i | −0.631843 | − | 1.94461i | ||||
\(103\) | 2.53951 | − | 7.81581i | 0.250225 | − | 0.770114i | −0.744508 | − | 0.667614i | \(-0.767316\pi\) |
0.994733 | − | 0.102500i | \(-0.0326843\pi\) | |||||||
\(104\) | −11.9183 | − | 8.65915i | −1.16869 | − | 0.849100i | ||||
\(105\) | 1.46039 | + | 1.06103i | 0.142519 | + | 0.103546i | ||||
\(106\) | 3.26852 | − | 10.0595i | 0.317466 | − | 0.977061i | ||||
\(107\) | −3.76646 | − | 11.5920i | −0.364117 | − | 1.12064i | −0.950532 | − | 0.310627i | \(-0.899461\pi\) |
0.586414 | − | 0.810011i | \(-0.300539\pi\) | |||||||
\(108\) | 17.8754 | − | 12.9873i | 1.72006 | − | 1.24970i | ||||
\(109\) | −0.886088 | −0.0848718 | −0.0424359 | − | 0.999099i | \(-0.513512\pi\) | ||||
−0.0424359 | + | 0.999099i | \(0.513512\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.82353 | −0.742577 | ||||||||
\(112\) | 2.79210 | − | 2.02858i | 0.263829 | − | 0.191683i | ||||
\(113\) | 1.40449 | + | 4.32257i | 0.132123 | + | 0.406633i | 0.995131 | − | 0.0985566i | \(-0.0314225\pi\) |
−0.863008 | + | 0.505190i | \(0.831423\pi\) | |||||||
\(114\) | −3.08307 | + | 9.48872i | −0.288756 | + | 0.888700i | ||||
\(115\) | −6.88689 | − | 5.00362i | −0.642206 | − | 0.466590i | ||||
\(116\) | 14.2098 | + | 10.3241i | 1.31935 | + | 0.958565i | ||||
\(117\) | −0.926221 | + | 2.85061i | −0.0856291 | + | 0.263539i | ||||
\(118\) | −5.21744 | − | 16.0576i | −0.480304 | − | 1.47823i | ||||
\(119\) | −4.79276 | + | 3.48215i | −0.439352 | + | 0.319208i | ||||
\(120\) | 8.36702 | 0.763801 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 5.95984 | 0.539579 | ||||||||
\(123\) | −0.364895 | + | 0.265112i | −0.0329015 | + | 0.0239043i | ||||
\(124\) | 11.7446 | + | 36.1462i | 1.05470 | + | 3.24602i | ||||
\(125\) | −3.27325 | + | 10.0740i | −0.292768 | + | 0.901047i | ||||
\(126\) | −1.85430 | − | 1.34723i | −0.165194 | − | 0.120021i | ||||
\(127\) | −6.49462 | − | 4.71861i | −0.576304 | − | 0.418709i | 0.261086 | − | 0.965316i | \(-0.415919\pi\) |
−0.837390 | + | 0.546606i | \(0.815919\pi\) | |||||||
\(128\) | −6.24921 | + | 19.2331i | −0.552357 | + | 1.69998i | ||||
\(129\) | 0.0587507 | + | 0.180816i | 0.00517271 | + | 0.0159200i | ||||
\(130\) | −7.86574 | + | 5.71479i | −0.689871 | + | 0.501220i | ||||
\(131\) | −0.101461 | −0.00886466 | −0.00443233 | − | 0.999990i | \(-0.501411\pi\) | ||||
−0.00443233 | + | 0.999990i | \(0.501411\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.86222 | 0.248186 | ||||||||
\(134\) | 18.5221 | − | 13.4571i | 1.60006 | − | 1.16251i | ||||
\(135\) | −2.19951 | − | 6.76938i | −0.189303 | − | 0.582616i | ||||
\(136\) | −8.48538 | + | 26.1153i | −0.727615 | + | 2.23937i | ||||
\(137\) | 3.69243 | + | 2.68271i | 0.315465 | + | 0.229199i | 0.734238 | − | 0.678892i | \(-0.237540\pi\) |
−0.418773 | + | 0.908091i | \(0.637540\pi\) | |||||||
\(138\) | −19.0732 | − | 13.8575i | −1.62362 | − | 1.17963i | ||||
\(139\) | 1.18209 | − | 3.63810i | 0.100264 | − | 0.308580i | −0.888326 | − | 0.459213i | \(-0.848131\pi\) |
0.988590 | + | 0.150634i | \(0.0481314\pi\) | |||||||
\(140\) | −1.51962 | − | 4.67691i | −0.128431 | − | 0.395271i | ||||
\(141\) | −10.8778 | + | 7.90322i | −0.916080 | + | 0.665571i | ||||
\(142\) | −0.283415 | −0.0237837 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.25469 | −0.271224 | ||||||||
\(145\) | 4.57755 | − | 3.32579i | 0.380145 | − | 0.276192i | ||||
\(146\) | −0.461920 | − | 1.42164i | −0.0382288 | − | 0.117656i | ||||
\(147\) | 0.443194 | − | 1.36401i | 0.0365540 | − | 0.112502i | ||||
\(148\) | 17.2426 | + | 12.5275i | 1.41733 | + | 1.02975i | ||||
\(149\) | −3.94172 | − | 2.86383i | −0.322918 | − | 0.234614i | 0.414501 | − | 0.910049i | \(-0.363956\pi\) |
−0.737420 | + | 0.675435i | \(0.763956\pi\) | |||||||
\(150\) | −3.67942 | + | 11.3241i | −0.300424 | + | 0.924609i | ||||
\(151\) | 5.24521 | + | 16.1431i | 0.426849 | + | 1.31371i | 0.901212 | + | 0.433378i | \(0.142678\pi\) |
−0.474363 | + | 0.880329i | \(0.657322\pi\) | |||||||
\(152\) | 10.7330 | − | 7.79798i | 0.870561 | − | 0.632499i | ||||
\(153\) | 5.58681 | 0.451667 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.2434 | 0.983410 | ||||||||
\(156\) | −14.4085 | + | 10.4684i | −1.15361 | + | 0.838144i | ||||
\(157\) | 0.693691 | + | 2.13496i | 0.0553625 | + | 0.170388i | 0.974914 | − | 0.222580i | \(-0.0714480\pi\) |
−0.919552 | + | 0.392969i | \(0.871448\pi\) | |||||||
\(158\) | −6.40593 | + | 19.7154i | −0.509628 | + | 1.56847i | ||||
\(159\) | −5.04952 | − | 3.66869i | −0.400453 | − | 0.290946i | ||||
\(160\) | 0.898287 | + | 0.652644i | 0.0710158 | + | 0.0515960i | ||||
\(161\) | −2.09001 | + | 6.43240i | −0.164716 | + | 0.506944i | ||||
\(162\) | −3.96667 | − | 12.2082i | −0.311651 | − | 0.959164i | ||||
\(163\) | 12.8126 | − | 9.30890i | 1.00356 | − | 0.729129i | 0.0407118 | − | 0.999171i | \(-0.487037\pi\) |
0.962849 | + | 0.270042i | \(0.0870374\pi\) | |||||||
\(164\) | 1.22872 | 0.0959470 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.31022 | −0.179308 | ||||||||
\(167\) | 16.7803 | − | 12.1916i | 1.29850 | − | 0.943413i | 0.298557 | − | 0.954392i | \(-0.403495\pi\) |
0.999940 | + | 0.0109787i | \(0.00349470\pi\) | |||||||
\(168\) | −2.05426 | − | 6.32235i | −0.158489 | − | 0.487780i | ||||
\(169\) | −0.895639 | + | 2.75649i | −0.0688953 | + | 0.212038i | ||||
\(170\) | 14.6613 | + | 10.6520i | 1.12447 | + | 0.816974i | ||||
\(171\) | −2.18372 | − | 1.58656i | −0.166993 | − | 0.121327i | ||||
\(172\) | 0.160050 | − | 0.492583i | 0.0122037 | − | 0.0375591i | ||||
\(173\) | 6.66099 | + | 20.5004i | 0.506426 | + | 1.55862i | 0.798361 | + | 0.602180i | \(0.205701\pi\) |
−0.291935 | + | 0.956438i | \(0.594299\pi\) | |||||||
\(174\) | 12.6775 | − | 9.21075i | 0.961079 | − | 0.698265i | ||||
\(175\) | 3.41585 | 0.258214 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.96322 | −0.748881 | ||||||||
\(178\) | −19.7712 | + | 14.3647i | −1.48192 | + | 1.07668i | ||||
\(179\) | 1.47760 | + | 4.54758i | 0.110441 | + | 0.339902i | 0.990969 | − | 0.134092i | \(-0.0428118\pi\) |
−0.880528 | + | 0.473994i | \(0.842812\pi\) | |||||||
\(180\) | −1.43308 | + | 4.41057i | −0.106816 | + | 0.328745i | ||||
\(181\) | 6.35309 | + | 4.61579i | 0.472221 | + | 0.343089i | 0.798306 | − | 0.602252i | \(-0.205730\pi\) |
−0.326085 | + | 0.945340i | \(0.605730\pi\) | |||||||
\(182\) | 6.24944 | + | 4.54048i | 0.463239 | + | 0.336563i | ||||
\(183\) | 1.08678 | − | 3.34477i | 0.0803371 | − | 0.247252i | ||||
\(184\) | 9.68746 | + | 29.8149i | 0.714169 | + | 2.19799i | ||||
\(185\) | 5.55453 | − | 4.03560i | 0.408377 | − | 0.296703i | ||||
\(186\) | 33.9079 | 2.48625 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 36.6293 | 2.67146 | ||||||||
\(189\) | −4.57511 | + | 3.32401i | −0.332790 | + | 0.241786i | ||||
\(190\) | −2.70564 | − | 8.32712i | −0.196288 | − | 0.604112i | ||||
\(191\) | −2.72871 | + | 8.39810i | −0.197442 | + | 0.607665i | 0.802497 | + | 0.596656i | \(0.203504\pi\) |
−0.999939 | + | 0.0110091i | \(0.996496\pi\) | |||||||
\(192\) | 10.4967 | + | 7.62630i | 0.757534 | + | 0.550381i | ||||
\(193\) | 20.7127 | + | 15.0486i | 1.49093 | + | 1.08322i | 0.973824 | + | 0.227303i | \(0.0729908\pi\) |
0.517106 | + | 0.855921i | \(0.327009\pi\) | |||||||
\(194\) | 13.2012 | − | 40.6292i | 0.947793 | − | 2.91701i | ||||
\(195\) | 1.77292 | + | 5.45648i | 0.126961 | + | 0.390747i | ||||
\(196\) | −3.16091 | + | 2.29654i | −0.225779 | + | 0.164038i | ||||
\(197\) | 11.1977 | 0.797802 | 0.398901 | − | 0.916994i | \(-0.369392\pi\) | ||||
0.398901 | + | 0.916994i | \(0.369392\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.2503 | −0.868400 | −0.434200 | − | 0.900817i | \(-0.642969\pi\) | ||||
−0.434200 | + | 0.900817i | \(0.642969\pi\) | |||||||
\(200\) | 12.8090 | − | 9.30631i | 0.905736 | − | 0.658056i | ||||
\(201\) | −4.17483 | − | 12.8488i | −0.294470 | − | 0.906285i | ||||
\(202\) | 9.37022 | − | 28.8386i | 0.659287 | − | 2.02908i | ||||
\(203\) | −3.63693 | − | 2.64238i | −0.255262 | − | 0.185459i | ||||
\(204\) | 26.8567 | + | 19.5125i | 1.88034 | + | 1.36615i | ||||
\(205\) | 0.122315 | − | 0.376447i | 0.00854285 | − | 0.0262922i | ||||
\(206\) | 6.17216 | + | 18.9959i | 0.430035 | + | 1.32351i | ||||
\(207\) | 5.16013 | − | 3.74905i | 0.358654 | − | 0.260577i | ||||
\(208\) | 10.9691 | 0.760568 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −4.38730 | −0.302752 | ||||||||
\(211\) | −11.5395 | + | 8.38393i | −0.794411 | + | 0.577174i | −0.909269 | − | 0.416208i | \(-0.863359\pi\) |
0.114858 | + | 0.993382i | \(0.463359\pi\) | |||||||
\(212\) | 5.25434 | + | 16.1712i | 0.360869 | + | 1.11064i | ||||
\(213\) | −0.0516809 | + | 0.159058i | −0.00354112 | + | 0.0108984i | ||||
\(214\) | 23.9660 | + | 17.4123i | 1.63828 | + | 1.19028i | ||||
\(215\) | −0.134982 | − | 0.0980700i | −0.00920568 | − | 0.00668832i | ||||
\(216\) | −8.10004 | + | 24.9294i | −0.551138 | + | 1.69623i | ||||
\(217\) | −3.00597 | − | 9.25141i | −0.204058 | − | 0.628027i | ||||
\(218\) | 1.74229 | − | 1.26585i | 0.118003 | − | 0.0857343i | ||||
\(219\) | −0.882082 | −0.0596056 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.8289 | −1.26657 | ||||||||
\(222\) | 15.3832 | − | 11.1766i | 1.03245 | − | 0.750122i | ||||
\(223\) | −0.915926 | − | 2.81893i | −0.0613350 | − | 0.188770i | 0.915694 | − | 0.401876i | \(-0.131642\pi\) |
−0.977029 | + | 0.213107i | \(0.931642\pi\) | |||||||
\(224\) | 0.272610 | − | 0.839006i | 0.0182145 | − | 0.0560585i | ||||
\(225\) | −2.60611 | − | 1.89345i | −0.173740 | − | 0.126230i | ||||
\(226\) | −8.93677 | − | 6.49294i | −0.594465 | − | 0.431904i | ||||
\(227\) | −2.55126 | + | 7.85197i | −0.169333 | + | 0.521154i | −0.999329 | − | 0.0366150i | \(-0.988342\pi\) |
0.829996 | + | 0.557769i | \(0.188342\pi\) | |||||||
\(228\) | −4.95623 | − | 15.2537i | −0.328234 | − | 1.01020i | ||||
\(229\) | −10.6047 | + | 7.70475i | −0.700777 | + | 0.509145i | −0.880185 | − | 0.474630i | \(-0.842582\pi\) |
0.179408 | + | 0.983775i | \(0.442582\pi\) | |||||||
\(230\) | 20.6896 | 1.36423 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −20.8371 | −1.36802 | ||||||||
\(233\) | −10.3778 | + | 7.53992i | −0.679873 | + | 0.493957i | −0.873316 | − | 0.487155i | \(-0.838035\pi\) |
0.193443 | + | 0.981112i | \(0.438035\pi\) | |||||||
\(234\) | −2.25114 | − | 6.92828i | −0.147161 | − | 0.452916i | ||||
\(235\) | 3.64632 | − | 11.2222i | 0.237860 | − | 0.732056i | ||||
\(236\) | 21.9584 | + | 15.9537i | 1.42937 | + | 1.03850i | ||||
\(237\) | 9.89650 | + | 7.19023i | 0.642847 | + | 0.467056i | ||||
\(238\) | 4.44936 | − | 13.6937i | 0.288409 | − | 0.887633i | ||||
\(239\) | 1.53924 | + | 4.73730i | 0.0995653 | + | 0.306430i | 0.988417 | − | 0.151765i | \(-0.0484958\pi\) |
−0.888851 | + | 0.458196i | \(0.848496\pi\) | |||||||
\(240\) | −5.04013 | + | 3.66187i | −0.325339 | + | 0.236372i | ||||
\(241\) | 2.62686 | 0.169211 | 0.0846053 | − | 0.996415i | \(-0.473037\pi\) | ||||
0.0846053 | + | 0.996415i | \(0.473037\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.39070 | 0.602414 | ||||||||
\(244\) | −7.75104 | + | 5.63146i | −0.496209 | + | 0.360517i | ||||
\(245\) | 0.388938 | + | 1.19703i | 0.0248484 | + | 0.0764754i | ||||
\(246\) | 0.338751 | − | 1.04257i | 0.0215980 | − | 0.0664717i | ||||
\(247\) | 7.35964 | + | 5.34709i | 0.468283 | + | 0.340227i | ||||
\(248\) | −36.4771 | − | 26.5021i | −2.31630 | − | 1.68289i | ||||
\(249\) | −0.421270 | + | 1.29654i | −0.0266969 | + | 0.0821646i | ||||
\(250\) | −7.95547 | − | 24.4844i | −0.503148 | − | 1.54853i | ||||
\(251\) | 21.2148 | − | 15.4134i | 1.33906 | − | 0.972888i | 0.339587 | − | 0.940575i | \(-0.389713\pi\) |
0.999478 | − | 0.0323129i | \(-0.0102873\pi\) | |||||||
\(252\) | 3.68460 | 0.232108 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 19.5112 | 1.22424 | ||||||||
\(255\) | 8.65159 | − | 6.28575i | 0.541784 | − | 0.393629i | ||||
\(256\) | −9.59733 | − | 29.5375i | −0.599833 | − | 1.84610i | ||||
\(257\) | 9.25561 | − | 28.4858i | 0.577349 | − | 1.77690i | −0.0506881 | − | 0.998715i | \(-0.516141\pi\) |
0.628037 | − | 0.778183i | \(-0.283859\pi\) | |||||||
\(258\) | −0.373831 | − | 0.271604i | −0.0232737 | − | 0.0169093i | ||||
\(259\) | −4.41315 | − | 3.20634i | −0.274220 | − | 0.199232i | ||||
\(260\) | 4.82983 | − | 14.8647i | 0.299533 | − | 0.921868i | ||||
\(261\) | 1.31007 | + | 4.03199i | 0.0810915 | + | 0.249574i | ||||
\(262\) | 0.199500 | − | 0.144945i | 0.0123251 | − | 0.00895474i | ||||
\(263\) | −3.33709 | −0.205774 | −0.102887 | − | 0.994693i | \(-0.532808\pi\) | ||||
−0.102887 | + | 0.994693i | \(0.532808\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.47747 | 0.336478 | ||||||||
\(266\) | −5.62791 | + | 4.08892i | −0.345070 | + | 0.250708i | ||||
\(267\) | 4.45639 | + | 13.7154i | 0.272727 | + | 0.839366i | ||||
\(268\) | −11.3732 | + | 35.0030i | −0.694727 | + | 2.13815i | ||||
\(269\) | 1.40430 | + | 1.02028i | 0.0856218 | + | 0.0622079i | 0.629773 | − | 0.776780i | \(-0.283148\pi\) |
−0.544151 | + | 0.838987i | \(0.683148\pi\) | |||||||
\(270\) | 13.9955 | + | 10.1683i | 0.851737 | + | 0.618823i | ||||
\(271\) | 0.765113 | − | 2.35478i | 0.0464773 | − | 0.143042i | −0.925125 | − | 0.379663i | \(-0.876040\pi\) |
0.971602 | + | 0.236621i | \(0.0760399\pi\) | |||||||
\(272\) | −6.31807 | − | 19.4450i | −0.383089 | − | 1.17903i | ||||
\(273\) | 3.68778 | − | 2.67933i | 0.223195 | − | 0.162161i | ||||
\(274\) | −11.0928 | −0.670141 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 37.8995 | 2.28128 | ||||||||
\(277\) | 4.17105 | − | 3.03045i | 0.250614 | − | 0.182082i | −0.455385 | − | 0.890295i | \(-0.650498\pi\) |
0.705999 | + | 0.708213i | \(0.250498\pi\) | |||||||
\(278\) | 2.87302 | + | 8.84223i | 0.172312 | + | 0.530322i | ||||
\(279\) | −2.83478 | + | 8.72457i | −0.169714 | + | 0.522326i | ||||
\(280\) | 4.71972 | + | 3.42908i | 0.282057 | + | 0.204927i | ||||
\(281\) | −18.2599 | − | 13.2666i | −1.08930 | − | 0.791419i | −0.110015 | − | 0.993930i | \(-0.535090\pi\) |
−0.979280 | + | 0.202510i | \(0.935090\pi\) | |||||||
\(282\) | 10.0984 | − | 31.0798i | 0.601354 | − | 1.85078i | ||||
\(283\) | 2.62280 | + | 8.07216i | 0.155909 | + | 0.479840i | 0.998252 | − | 0.0591027i | \(-0.0188239\pi\) |
−0.842342 | + | 0.538943i | \(0.818824\pi\) | |||||||
\(284\) | 0.368594 | − | 0.267799i | 0.0218720 | − | 0.0158910i | ||||
\(285\) | −5.16669 | −0.306049 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.314484 | −0.0185634 | ||||||||
\(288\) | −0.673058 | + | 0.489005i | −0.0396603 | + | 0.0288149i | ||||
\(289\) | 5.59195 | + | 17.2102i | 0.328938 | + | 1.01237i | ||||
\(290\) | −4.24957 | + | 13.0788i | −0.249544 | + | 0.768016i | ||||
\(291\) | −20.3945 | − | 14.8175i | −1.19555 | − | 0.868618i | ||||
\(292\) | 1.94406 | + | 1.41244i | 0.113767 | + | 0.0826569i | ||||
\(293\) | −7.60988 | + | 23.4208i | −0.444574 | + | 1.36826i | 0.438376 | + | 0.898792i | \(0.355554\pi\) |
−0.882950 | + | 0.469467i | \(0.844446\pi\) | |||||||
\(294\) | 1.07716 | + | 3.31516i | 0.0628214 | + | 0.193344i | ||||
\(295\) | 7.07366 | − | 5.13932i | 0.411844 | − | 0.299223i | ||||
\(296\) | −25.2843 | −1.46962 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.8417 | 0.685973 | ||||||||
\(299\) | −17.3908 | + | 12.6352i | −1.00574 | + | 0.730712i | ||||
\(300\) | −5.91489 | − | 18.2042i | −0.341497 | − | 1.05102i | ||||
\(301\) | −0.0409639 | + | 0.126074i | −0.00236112 | + | 0.00726678i | ||||
\(302\) | −33.3753 | − | 24.2486i | −1.92053 | − | 1.39535i | ||||
\(303\) | −14.4760 | − | 10.5175i | −0.831627 | − | 0.604212i | ||||
\(304\) | −3.05252 | + | 9.39470i | −0.175074 | + | 0.538823i | ||||
\(305\) | 0.953737 | + | 2.93530i | 0.0546108 | + | 0.168075i | ||||
\(306\) | −10.9852 | + | 7.98123i | −0.627984 | + | 0.456257i | ||||
\(307\) | −4.59391 | −0.262188 | −0.131094 | − | 0.991370i | \(-0.541849\pi\) | ||||
−0.131094 | + | 0.991370i | \(0.541849\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.7863 | 0.670502 | ||||||||
\(310\) | −24.0738 | + | 17.4907i | −1.36730 | + | 0.993403i | ||||
\(311\) | −0.683154 | − | 2.10253i | −0.0387381 | − | 0.119224i | 0.929817 | − | 0.368021i | \(-0.119965\pi\) |
−0.968556 | + | 0.248798i | \(0.919965\pi\) | |||||||
\(312\) | 6.52906 | − | 20.0944i | 0.369635 | − | 1.13762i | ||||
\(313\) | 7.84688 | + | 5.70110i | 0.443532 | + | 0.322245i | 0.787037 | − | 0.616906i | \(-0.211614\pi\) |
−0.343505 | + | 0.939151i | \(0.611614\pi\) | |||||||
\(314\) | −4.41396 | − | 3.20693i | −0.249094 | − | 0.180977i | ||||
\(315\) | 0.366789 | − | 1.12886i | 0.0206662 | − | 0.0636041i | ||||
\(316\) | −10.2979 | − | 31.6937i | −0.579303 | − | 1.78291i | ||||
\(317\) | −5.22252 | + | 3.79439i | −0.293326 | + | 0.213114i | −0.724709 | − | 0.689055i | \(-0.758026\pi\) |
0.431383 | + | 0.902169i | \(0.358026\pi\) | |||||||
\(318\) | 15.1698 | 0.850680 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −11.3863 | −0.636513 | ||||||||
\(321\) | 14.1423 | − | 10.2750i | 0.789347 | − | 0.573494i | ||||
\(322\) | −5.07968 | − | 15.6337i | −0.283080 | − | 0.871229i | ||||
\(323\) | 5.23978 | − | 16.1264i | 0.291549 | − | 0.897297i | ||||
\(324\) | 16.6943 | + | 12.1291i | 0.927463 | + | 0.673841i | ||||
\(325\) | 8.78319 | + | 6.38136i | 0.487204 | + | 0.353974i | ||||
\(326\) | −11.8946 | + | 36.6078i | −0.658780 | + | 2.02752i | ||||
\(327\) | −0.392709 | − | 1.20863i | −0.0217169 | − | 0.0668376i | ||||
\(328\) | −1.17928 | + | 0.856798i | −0.0651149 | + | 0.0473087i | ||||
\(329\) | −9.37505 | −0.516863 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.62076 | 0.199015 | 0.0995075 | − | 0.995037i | \(-0.468273\pi\) | ||||
0.0995075 | + | 0.995037i | \(0.468273\pi\) | |||||||
\(332\) | 3.00455 | − | 2.18293i | 0.164896 | − | 0.119804i | ||||
\(333\) | 1.58968 | + | 4.89253i | 0.0871139 | + | 0.268109i | ||||
\(334\) | −15.5780 | + | 47.9441i | −0.852389 | + | 2.62338i | ||||
\(335\) | 9.59182 | + | 6.96886i | 0.524057 | + | 0.380750i | ||||
\(336\) | 4.00445 | + | 2.90940i | 0.218461 | + | 0.158721i | ||||
\(337\) | 1.97928 | − | 6.09161i | 0.107818 | − | 0.331831i | −0.882563 | − | 0.470194i | \(-0.844184\pi\) |
0.990382 | + | 0.138363i | \(0.0441840\pi\) | |||||||
\(338\) | −2.17681 | − | 6.69953i | −0.118403 | − | 0.364406i | ||||
\(339\) | −5.27357 | + | 3.83147i | −0.286421 | + | 0.208097i | ||||
\(340\) | −29.1327 | −1.57994 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 6.56033 | 0.354742 | ||||||||
\(343\) | 0.809017 | − | 0.587785i | 0.0436828 | − | 0.0317374i | ||||
\(344\) | 0.189872 | + | 0.584367i | 0.0102372 | + | 0.0315070i | ||||
\(345\) | 3.77276 | − | 11.6114i | 0.203119 | − | 0.625135i | ||||
\(346\) | −42.3839 | − | 30.7937i | −2.27857 | − | 1.65548i | ||||
\(347\) | −14.1254 | − | 10.2627i | −0.758293 | − | 0.550932i | 0.140093 | − | 0.990138i | \(-0.455260\pi\) |
−0.898386 | + | 0.439206i | \(0.855260\pi\) | |||||||
\(348\) | −7.78441 | + | 23.9580i | −0.417288 | + | 1.28428i | ||||
\(349\) | 6.68246 | + | 20.5665i | 0.357704 | + | 1.10090i | 0.954425 | + | 0.298451i | \(0.0964699\pi\) |
−0.596721 | + | 0.802449i | \(0.703530\pi\) | |||||||
\(350\) | −6.71650 | + | 4.87983i | −0.359012 | + | 0.260838i | ||||
\(351\) | −17.9738 | −0.959371 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.40150 | 0.234268 | 0.117134 | − | 0.993116i | \(-0.462629\pi\) | ||||
0.117134 | + | 0.993116i | \(0.462629\pi\) | |||||||
\(354\) | 19.5905 | − | 14.2333i | 1.04122 | − | 0.756491i | ||||
\(355\) | −0.0453542 | − | 0.139586i | −0.00240715 | − | 0.00740844i | ||||
\(356\) | 12.1402 | − | 37.3637i | 0.643430 | − | 1.98027i | ||||
\(357\) | −6.87381 | − | 4.99412i | −0.363801 | − | 0.264317i | ||||
\(358\) | −9.40197 | − | 6.83093i | −0.496909 | − | 0.361026i | ||||
\(359\) | 3.30084 | − | 10.1589i | 0.174212 | − | 0.536168i | −0.825385 | − | 0.564570i | \(-0.809042\pi\) |
0.999597 | + | 0.0284023i | \(0.00904194\pi\) | |||||||
\(360\) | −1.70011 | − | 5.23240i | −0.0896037 | − | 0.275772i | ||||
\(361\) | 8.74362 | − | 6.35261i | 0.460191 | − | 0.334348i | ||||
\(362\) | −19.0860 | −1.00314 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.4180 | −0.650879 | ||||||||
\(365\) | 0.626258 | − | 0.455003i | 0.0327799 | − | 0.0238160i | ||||
\(366\) | 2.64137 | + | 8.12929i | 0.138067 | + | 0.424925i | ||||
\(367\) | 3.15715 | − | 9.71670i | 0.164802 | − | 0.507207i | −0.834220 | − | 0.551432i | \(-0.814082\pi\) |
0.999022 | + | 0.0442244i | \(0.0140817\pi\) | |||||||
\(368\) | −18.8842 | − | 13.7202i | −0.984406 | − | 0.715213i | ||||
\(369\) | 0.239934 | + | 0.174323i | 0.0124905 | + | 0.00907487i | ||||
\(370\) | −5.15655 | + | 15.8702i | −0.268076 | + | 0.825054i | ||||
\(371\) | −1.34482 | − | 4.13893i | −0.0698195 | − | 0.214882i | ||||
\(372\) | −44.0987 | + | 32.0396i | −2.28641 | + | 1.66117i | ||||
\(373\) | 27.8851 | 1.44383 | 0.721917 | − | 0.691980i | \(-0.243261\pi\) | ||||
0.721917 | + | 0.691980i | \(0.243261\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15.1918 | −0.784499 | ||||||||
\(376\) | −35.1554 | + | 25.5419i | −1.81300 | + | 1.31722i | ||||
\(377\) | −4.41526 | − | 13.5888i | −0.227397 | − | 0.699857i | ||||
\(378\) | 4.24731 | − | 13.0719i | 0.218458 | − | 0.672344i | ||||
\(379\) | −0.928776 | − | 0.674795i | −0.0477080 | − | 0.0346619i | 0.563676 | − | 0.825996i | \(-0.309387\pi\) |
−0.611384 | + | 0.791334i | \(0.709387\pi\) | |||||||
\(380\) | 11.3871 | + | 8.27322i | 0.584146 | + | 0.424407i | ||||
\(381\) | 3.55787 | − | 10.9500i | 0.182275 | − | 0.560985i | ||||
\(382\) | −6.63200 | − | 20.4112i | −0.339322 | − | 1.04433i | ||||
\(383\) | 16.1412 | − | 11.7273i | 0.824777 | − | 0.599235i | −0.0933000 | − | 0.995638i | \(-0.529742\pi\) |
0.918077 | + | 0.396403i | \(0.129742\pi\) | |||||||
\(384\) | −29.0038 | −1.48009 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −62.2251 | −3.16717 | ||||||||
\(387\) | 0.101138 | − | 0.0734808i | 0.00514111 | − | 0.00373524i | ||||
\(388\) | 21.2218 | + | 65.3139i | 1.07737 | + | 3.31581i | ||||
\(389\) | 0.803445 | − | 2.47275i | 0.0407363 | − | 0.125373i | −0.928620 | − | 0.371032i | \(-0.879004\pi\) |
0.969356 | + | 0.245658i | \(0.0790041\pi\) | |||||||
\(390\) | −11.2811 | − | 8.19619i | −0.571240 | − | 0.415030i | ||||
\(391\) | 32.4155 | + | 23.5512i | 1.63932 | + | 1.19104i | ||||
\(392\) | 1.43233 | − | 4.40826i | 0.0723436 | − | 0.222651i | ||||
\(393\) | −0.0449668 | − | 0.138393i | −0.00226827 | − | 0.00698103i | ||||
\(394\) | −22.0178 | + | 15.9968i | −1.10924 | + | 0.805909i | ||||
\(395\) | −10.7352 | −0.540148 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.77237 | 0.440272 | 0.220136 | − | 0.975469i | \(-0.429350\pi\) | ||||
0.220136 | + | 0.975469i | \(0.429350\pi\) | |||||||
\(398\) | 24.0875 | − | 17.5006i | 1.20740 | − | 0.877224i | ||||
\(399\) | 1.26852 | + | 3.90410i | 0.0635053 | + | 0.195449i | ||||
\(400\) | −3.64296 | + | 11.2119i | −0.182148 | + | 0.560594i | ||||
\(401\) | −22.9385 | − | 16.6658i | −1.14549 | − | 0.832249i | −0.157617 | − | 0.987500i | \(-0.550381\pi\) |
−0.987875 | + | 0.155252i | \(0.950381\pi\) | |||||||
\(402\) | 26.5645 | + | 19.3002i | 1.32492 | + | 0.962607i | ||||
\(403\) | 9.55389 | − | 29.4039i | 0.475913 | − | 1.46471i | ||||
\(404\) | 15.0632 | + | 46.3598i | 0.749422 | + | 2.30648i | ||||
\(405\) | 5.37790 | − | 3.90727i | 0.267230 | − | 0.194154i | ||||
\(406\) | 10.9261 | 0.542252 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −39.3822 | −1.94971 | ||||||||
\(409\) | 16.1039 | − | 11.7002i | 0.796286 | − | 0.578536i | −0.113536 | − | 0.993534i | \(-0.536218\pi\) |
0.909822 | + | 0.414998i | \(0.136218\pi\) | |||||||
\(410\) | 0.297281 | + | 0.914937i | 0.0146817 | + | 0.0451855i | ||||
\(411\) | −2.02278 | + | 6.22547i | −0.0997763 | + | 0.307080i | ||||
\(412\) | −25.9764 | − | 18.8730i | −1.27977 | − | 0.929805i | ||||
\(413\) | −5.62012 | − | 4.08326i | −0.276548 | − | 0.200924i | ||||
\(414\) | −4.79041 | + | 14.7434i | −0.235436 | + | 0.724596i | ||||
\(415\) | −0.369698 | − | 1.13781i | −0.0181478 | − | 0.0558531i | ||||
\(416\) | 2.26836 | − | 1.64806i | 0.111216 | − | 0.0808029i | ||||
\(417\) | 5.48631 | 0.268666 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.8957 | −1.50935 | −0.754676 | − | 0.656097i | \(-0.772206\pi\) | ||||
−0.754676 | + | 0.656097i | \(0.772206\pi\) | |||||||
\(420\) | 5.70587 | − | 4.14556i | 0.278418 | − | 0.202283i | ||||
\(421\) | −7.47609 | − | 23.0090i | −0.364362 | − | 1.12139i | −0.950379 | − | 0.311093i | \(-0.899305\pi\) |
0.586017 | − | 0.810299i | \(-0.300695\pi\) | |||||||
\(422\) | 10.7127 | − | 32.9703i | 0.521486 | − | 1.60497i | ||||
\(423\) | 7.15265 | + | 5.19671i | 0.347774 | + | 0.252673i | ||||
\(424\) | −16.3192 | − | 11.8566i | −0.792531 | − | 0.575808i | ||||
\(425\) | 6.25330 | − | 19.2457i | 0.303330 | − | 0.933552i | ||||
\(426\) | −0.125608 | − | 0.386582i | −0.00608573 | − | 0.0187300i | ||||
\(427\) | 1.98383 | − | 1.44134i | 0.0960045 | − | 0.0697513i | ||||
\(428\) | −47.6218 | −2.30188 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.405513 | 0.0195556 | ||||||||
\(431\) | 15.6950 | − | 11.4031i | 0.756000 | − | 0.549266i | −0.141681 | − | 0.989912i | \(-0.545251\pi\) |
0.897681 | + | 0.440646i | \(0.145251\pi\) | |||||||
\(432\) | −6.03115 | − | 18.5620i | −0.290174 | − | 0.893063i | ||||
\(433\) | −6.60917 | + | 20.3409i | −0.317616 | + | 0.977522i | 0.657048 | + | 0.753849i | \(0.271805\pi\) |
−0.974664 | + | 0.223674i | \(0.928195\pi\) | |||||||
\(434\) | 19.1270 | + | 13.8966i | 0.918125 | + | 0.667057i | ||||
\(435\) | 6.56516 | + | 4.76987i | 0.314775 | + | 0.228698i | ||||
\(436\) | −1.06983 | + | 3.29259i | −0.0512354 | + | 0.157686i | ||||
\(437\) | −5.98208 | − | 18.4109i | −0.286162 | − | 0.880715i | ||||
\(438\) | 1.73442 | − | 1.26013i | 0.0828737 | − | 0.0602113i | ||||
\(439\) | 31.7315 | 1.51446 | 0.757232 | − | 0.653146i | \(-0.226551\pi\) | ||||
0.757232 | + | 0.653146i | \(0.226551\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.943053 | −0.0449073 | ||||||||
\(442\) | 37.0228 | − | 26.8986i | 1.76100 | − | 1.27944i | ||||
\(443\) | −0.514855 | − | 1.58456i | −0.0244615 | − | 0.0752847i | 0.938081 | − | 0.346417i | \(-0.112602\pi\) |
−0.962542 | + | 0.271133i | \(0.912602\pi\) | |||||||
\(444\) | −9.44582 | + | 29.0712i | −0.448279 | + | 1.37966i | ||||
\(445\) | −10.2387 | − | 7.43886i | −0.485362 | − | 0.352636i | ||||
\(446\) | 5.82805 | + | 4.23432i | 0.275966 | + | 0.200501i | ||||
\(447\) | 2.15935 | − | 6.64578i | 0.102134 | − | 0.314335i | ||||
\(448\) | 2.79554 | + | 8.60379i | 0.132077 | + | 0.406491i | ||||
\(449\) | 13.9036 | − | 10.1016i | 0.656151 | − | 0.476722i | −0.209210 | − | 0.977871i | \(-0.567089\pi\) |
0.865361 | + | 0.501149i | \(0.167089\pi\) | |||||||
\(450\) | 7.82927 | 0.369076 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 17.7578 | 0.835258 | ||||||||
\(453\) | −19.6947 | + | 14.3091i | −0.925339 | + | 0.672298i | ||||
\(454\) | −6.20072 | − | 19.0839i | −0.291014 | − | 0.895650i | ||||
\(455\) | −1.23617 | + | 3.80453i | −0.0579524 | + | 0.178359i | ||||
\(456\) | 15.3933 | + | 11.1839i | 0.720858 | + | 0.523734i | ||||
\(457\) | 8.26867 | + | 6.00754i | 0.386792 | + | 0.281021i | 0.764140 | − | 0.645051i | \(-0.223164\pi\) |
−0.377348 | + | 0.926072i | \(0.623164\pi\) | |||||||
\(458\) | 9.84486 | − | 30.2994i | 0.460020 | − | 1.41580i | ||||
\(459\) | 10.3527 | + | 31.8624i | 0.483224 | + | 1.48721i | ||||
\(460\) | −26.9078 | + | 19.5496i | −1.25458 | + | 0.911506i | ||||
\(461\) | 22.1160 | 1.03004 | 0.515022 | − | 0.857177i | \(-0.327784\pi\) | ||||
0.515022 | + | 0.857177i | \(0.327784\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.3717 | −1.41149 | −0.705747 | − | 0.708464i | \(-0.749389\pi\) | ||||
−0.705747 | + | 0.708464i | \(0.749389\pi\) | |||||||
\(464\) | 12.5519 | − | 9.11947i | 0.582706 | − | 0.423361i | ||||
\(465\) | 5.42618 | + | 16.7001i | 0.251633 | + | 0.774447i | ||||
\(466\) | 9.63424 | − | 29.6512i | 0.446298 | − | 1.37356i | ||||
\(467\) | −20.3799 | − | 14.8068i | −0.943067 | − | 0.685178i | 0.00608981 | − | 0.999981i | \(-0.498062\pi\) |
−0.949157 | + | 0.314803i | \(0.898062\pi\) | |||||||
\(468\) | 9.47424 | + | 6.88344i | 0.437947 | + | 0.318187i | ||||
\(469\) | 2.91090 | − | 8.95883i | 0.134413 | − | 0.413680i | ||||
\(470\) | 8.86220 | + | 27.2751i | 0.408783 | + | 1.25810i | ||||
\(471\) | −2.60467 | + | 1.89240i | −0.120017 | + | 0.0871973i | ||||
\(472\) | −32.1995 | −1.48210 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −29.7311 | −1.36560 | ||||||||
\(475\) | −7.90968 | + | 5.74672i | −0.362921 | + | 0.263677i | ||||
\(476\) | 7.15262 | + | 22.0135i | 0.327840 | + | 1.00899i | ||||
\(477\) | −1.26823 | + | 3.90322i | −0.0580685 | + | 0.178716i | ||||
\(478\) | −9.79421 | − | 7.11591i | −0.447977 | − | 0.325474i | ||||
\(479\) | −17.1544 | − | 12.4634i | −0.783804 | − | 0.569467i | 0.122314 | − | 0.992491i | \(-0.460968\pi\) |
−0.906118 | + | 0.423025i | \(0.860968\pi\) | |||||||
\(480\) | −0.492098 | + | 1.51452i | −0.0224611 | + | 0.0691281i | ||||
\(481\) | −5.35759 | − | 16.4890i | −0.244285 | − | 0.751832i | ||||
\(482\) | −5.16513 | + | 3.75268i | −0.235265 | + | 0.170930i | ||||
\(483\) | −9.70015 | −0.441372 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.1230 | 1.00455 | ||||||||
\(486\) | −18.4647 | + | 13.4154i | −0.837577 | + | 0.608535i | ||||
\(487\) | −5.19759 | − | 15.9965i | −0.235525 | − | 0.724873i | −0.997051 | − | 0.0767381i | \(-0.975549\pi\) |
0.761526 | − | 0.648134i | \(-0.224451\pi\) | |||||||
\(488\) | 3.51229 | − | 10.8097i | 0.158994 | − | 0.489333i | ||||
\(489\) | 18.3759 | + | 13.3509i | 0.830988 | + | 0.603748i | ||||
\(490\) | −2.47482 | − | 1.79806i | −0.111801 | − | 0.0812281i | ||||
\(491\) | −1.49504 | + | 4.60125i | −0.0674701 | + | 0.207652i | −0.979107 | − | 0.203344i | \(-0.934819\pi\) |
0.911637 | + | 0.410996i | \(0.134819\pi\) | |||||||
\(492\) | 0.544562 | + | 1.67599i | 0.0245508 | + | 0.0755595i | ||||
\(493\) | −21.5458 | + | 15.6540i | −0.970376 | + | 0.705019i | ||||
\(494\) | −22.1099 | −0.994770 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 33.5719 | 1.50742 | ||||||||
\(497\) | −0.0943396 | + | 0.0685417i | −0.00423171 | + | 0.00307452i | ||||
\(498\) | −1.02388 | − | 3.15117i | −0.0458810 | − | 0.141207i | ||||
\(499\) | 9.45084 | − | 29.0867i | 0.423078 | − | 1.30210i | −0.481745 | − | 0.876311i | \(-0.659997\pi\) |
0.904823 | − | 0.425788i | \(-0.140003\pi\) | |||||||
\(500\) | 33.4818 | + | 24.3259i | 1.49735 | + | 1.08789i | ||||
\(501\) | 24.0664 | + | 17.4852i | 1.07521 | + | 0.781183i | ||||
\(502\) | −19.6947 | + | 60.6142i | −0.879019 | + | 2.70534i | ||||
\(503\) | 8.72684 | + | 26.8585i | 0.389111 | + | 1.19756i | 0.933454 | + | 0.358697i | \(0.116779\pi\) |
−0.544343 | + | 0.838863i | \(0.683221\pi\) | |||||||
\(504\) | −3.53634 | + | 2.56930i | −0.157521 | + | 0.114446i | ||||
\(505\) | 15.7029 | 0.698768 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.15683 | −0.184611 | ||||||||
\(508\) | −25.3751 | + | 18.4361i | −1.12584 | + | 0.817970i | ||||
\(509\) | −1.29807 | − | 3.99505i | −0.0575360 | − | 0.177078i | 0.918158 | − | 0.396214i | \(-0.129676\pi\) |
−0.975694 | + | 0.219136i | \(0.929676\pi\) | |||||||
\(510\) | −8.03171 | + | 24.7191i | −0.355650 | + | 1.09458i | ||||
\(511\) | −0.497571 | − | 0.361506i | −0.0220112 | − | 0.0159921i | ||||
\(512\) | 28.3466 | + | 20.5950i | 1.25275 | + | 0.910179i | ||||
\(513\) | 5.00183 | − | 15.3941i | 0.220836 | − | 0.679664i | ||||
\(514\) | 22.4953 | + | 69.2335i | 0.992226 | + | 3.05376i | ||||
\(515\) | −8.36804 | + | 6.07973i | −0.368740 | + | 0.267905i | ||||
\(516\) | 0.742823 | 0.0327009 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 13.2580 | 0.582523 | ||||||||
\(519\) | −25.0107 | + | 18.1713i | −1.09785 | + | 0.797633i | ||||
\(520\) | 5.72977 | + | 17.6344i | 0.251267 | + | 0.773321i | ||||
\(521\) | −6.38026 | + | 19.6364i | −0.279524 | + | 0.860287i | 0.708462 | + | 0.705749i | \(0.249389\pi\) |
−0.987987 | + | 0.154539i | \(0.950611\pi\) | |||||||
\(522\) | −8.33601 | − | 6.05646i | −0.364857 | − | 0.265084i | ||||
\(523\) | −18.3113 | − | 13.3040i | −0.800699 | − | 0.581742i | 0.110420 | − | 0.993885i | \(-0.464780\pi\) |
−0.911119 | + | 0.412143i | \(0.864780\pi\) | |||||||
\(524\) | −0.122500 | + | 0.377015i | −0.00535142 | + | 0.0164700i | ||||
\(525\) | 1.51388 | + | 4.65925i | 0.0660713 | + | 0.203347i | ||||
\(526\) | 6.56164 | − | 4.76731i | 0.286101 | − | 0.207865i | ||||
\(527\) | −57.6275 | −2.51030 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.7440 | 0.988869 | ||||||||
\(530\) | −10.7702 | + | 7.82502i | −0.467828 | + | 0.339897i | ||||
\(531\) | 2.02445 | + | 6.23061i | 0.0878535 | + | 0.270385i | ||||
\(532\) | 3.45573 | − | 10.6356i | 0.149825 | − | 0.461113i | ||||
\(533\) | −0.808636 | − | 0.587508i | −0.0350259 | − | 0.0254478i | ||||
\(534\) | −28.3560 | − | 20.6019i | −1.22709 | − | 0.891530i | ||||
\(535\) | −4.74058 | + | 14.5900i | −0.204953 | + | 0.630781i | ||||
\(536\) | −13.4924 | − | 41.5252i | −0.582781 | − | 1.79362i | ||||
\(537\) | −5.54808 | + | 4.03092i | −0.239418 | + | 0.173947i | ||||
\(538\) | −4.21881 | −0.181886 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −27.8098 | −1.19674 | ||||||||
\(541\) | 34.5582 | − | 25.1080i | 1.48577 | − | 1.07948i | 0.510134 | − | 0.860095i | \(-0.329596\pi\) |
0.975639 | − | 0.219383i | \(-0.0704043\pi\) | |||||||
\(542\) | 1.85957 | + | 5.72317i | 0.0798754 | + | 0.245831i | ||||
\(543\) | −3.48033 | + | 10.7114i | −0.149355 | + | 0.459669i | ||||
\(544\) | −4.22810 | − | 3.07189i | −0.181278 | − | 0.131706i | ||||
\(545\) | 0.902263 | + | 0.655532i | 0.0386487 | + | 0.0280799i | ||||
\(546\) | −3.42355 | + | 10.5366i | −0.146515 | + | 0.450926i | ||||
\(547\) | −13.7459 | − | 42.3056i | −0.587733 | − | 1.80886i | −0.588007 | − | 0.808856i | \(-0.700087\pi\) |
0.000274240 | − | 1.00000i | \(-0.499913\pi\) | |||||||
\(548\) | 14.4267 | − | 10.4816i | 0.616277 | − | 0.447752i | ||||
\(549\) | −2.31251 | −0.0986955 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.8671 | 0.548156 | ||||||||
\(552\) | −36.3745 | + | 26.4276i | −1.54820 | + | 1.12483i | ||||
\(553\) | 2.63569 | + | 8.11183i | 0.112081 | + | 0.344950i | ||||
\(554\) | −3.87220 | + | 11.9174i | −0.164514 | + | 0.506322i | ||||
\(555\) | 7.96634 | + | 5.78788i | 0.338152 | + | 0.245682i | ||||
\(556\) | −12.0915 | − | 8.78500i | −0.512794 | − | 0.372567i | ||||
\(557\) | 7.72268 | − | 23.7680i | 0.327220 | − | 1.00708i | −0.643208 | − | 0.765691i | \(-0.722397\pi\) |
0.970428 | − | 0.241389i | \(-0.0776030\pi\) | |||||||
\(558\) | −6.88981 | − | 21.2047i | −0.291669 | − | 0.897665i | ||||
\(559\) | −0.340857 | + | 0.247647i | −0.0144167 | + | 0.0104744i | ||||
\(560\) | −4.34382 | −0.183560 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 54.8565 | 2.31398 | ||||||||
\(563\) | 7.28929 | − | 5.29598i | 0.307207 | − | 0.223199i | −0.423490 | − | 0.905901i | \(-0.639195\pi\) |
0.730697 | + | 0.682702i | \(0.239195\pi\) | |||||||
\(564\) | 16.2339 | + | 49.9627i | 0.683569 | + | 2.10381i | ||||
\(565\) | 1.76773 | − | 5.44052i | 0.0743690 | − | 0.228884i | ||||
\(566\) | −16.6889 | − | 12.1252i | −0.701487 | − | 0.509660i | ||||
\(567\) | −4.27282 | − | 3.10438i | −0.179442 | − | 0.130372i | ||||
\(568\) | −0.167024 | + | 0.514048i | −0.00700818 | + | 0.0215690i | ||||
\(569\) | −9.01521 | − | 27.7460i | −0.377937 | − | 1.16317i | −0.941475 | − | 0.337082i | \(-0.890560\pi\) |
0.563538 | − | 0.826090i | \(-0.309440\pi\) | |||||||
\(570\) | 10.1592 | − | 7.38106i | 0.425520 | − | 0.309158i | ||||
\(571\) | −1.78994 | −0.0749067 | −0.0374533 | − | 0.999298i | \(-0.511925\pi\) | ||||
−0.0374533 | + | 0.999298i | \(0.511925\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.6645 | −0.529065 | ||||||||
\(574\) | 0.618364 | − | 0.449267i | 0.0258100 | − | 0.0187521i | ||||
\(575\) | −7.13917 | − | 21.9721i | −0.297724 | − | 0.916300i | ||||
\(576\) | 2.63634 | − | 8.11383i | 0.109848 | − | 0.338076i | ||||
\(577\) | 17.4626 | + | 12.6873i | 0.726978 | + | 0.528180i | 0.888606 | − | 0.458671i | \(-0.151675\pi\) |
−0.161628 | + | 0.986852i | \(0.551675\pi\) | |||||||
\(578\) | −35.5816 | − | 25.8515i | −1.48000 | − | 1.07528i | ||||
\(579\) | −11.3468 | + | 34.9218i | −0.471556 | + | 1.45130i | ||||
\(580\) | −6.83145 | − | 21.0250i | −0.283660 | − | 0.873017i | ||||
\(581\) | −0.768997 | + | 0.558709i | −0.0319034 | + | 0.0231791i | ||||
\(582\) | 61.2694 | 2.53970 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.85074 | −0.117965 | ||||||||
\(585\) | 3.05203 | − | 2.21743i | 0.126186 | − | 0.0916793i | ||||
\(586\) | −18.4955 | − | 56.9232i | −0.764040 | − | 2.35147i | ||||
\(587\) | 1.70687 | − | 5.25321i | 0.0704501 | − | 0.216823i | −0.909632 | − | 0.415414i | \(-0.863637\pi\) |
0.980082 | + | 0.198591i | \(0.0636366\pi\) | |||||||
\(588\) | −4.53340 | − | 3.29371i | −0.186954 | − | 0.135830i | ||||
\(589\) | 22.5249 | + | 16.3653i | 0.928121 | + | 0.674319i | ||||
\(590\) | −6.56684 | + | 20.2106i | −0.270352 | + | 0.832059i | ||||
\(591\) | 4.96275 | + | 15.2738i | 0.204140 | + | 0.628279i | ||||
\(592\) | 15.2308 | − | 11.0658i | 0.625982 | − | 0.454802i | ||||
\(593\) | 40.7867 | 1.67491 | 0.837454 | − | 0.546508i | \(-0.184043\pi\) | ||||
0.837454 | + | 0.546508i | \(0.184043\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.45636 | 0.305681 | ||||||||
\(596\) | −15.4007 | + | 11.1893i | −0.630837 | + | 0.458330i | ||||
\(597\) | −5.42925 | − | 16.7095i | −0.222205 | − | 0.683875i | ||||
\(598\) | 16.1448 | − | 49.6886i | 0.660210 | − | 2.03192i | ||||
\(599\) | 21.4510 | + | 15.5851i | 0.876465 | + | 0.636789i | 0.932314 | − | 0.361650i | \(-0.117787\pi\) |
−0.0558491 | + | 0.998439i | \(0.517787\pi\) | |||||||
\(600\) | 18.3708 | + | 13.3472i | 0.749985 | + | 0.544896i | ||||
\(601\) | 11.6715 | − | 35.9213i | 0.476092 | − | 1.46526i | −0.368387 | − | 0.929673i | \(-0.620090\pi\) |
0.844479 | − | 0.535589i | \(-0.179910\pi\) | |||||||
\(602\) | −0.0995608 | − | 0.306417i | −0.00405780 | − | 0.0124886i | ||||
\(603\) | −7.18685 | + | 5.22155i | −0.292671 | + | 0.212638i | ||||
\(604\) | 66.3186 | 2.69847 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 43.4890 | 1.76662 | ||||||||
\(607\) | −22.4295 | + | 16.2960i | −0.910385 | + | 0.661433i | −0.941112 | − | 0.338095i | \(-0.890218\pi\) |
0.0307275 | + | 0.999528i | \(0.490218\pi\) | |||||||
\(608\) | 0.780268 | + | 2.40142i | 0.0316441 | + | 0.0973904i | ||||
\(609\) | 1.99238 | − | 6.13190i | 0.0807351 | − | 0.248477i | ||||
\(610\) | −6.06864 | − | 4.40912i | −0.245712 | − | 0.178520i | ||||
\(611\) | −24.1061 | − | 17.5141i | −0.975229 | − | 0.708546i | ||||
\(612\) | 6.74530 | − | 20.7599i | 0.272662 | − | 0.839169i | ||||
\(613\) | −11.1946 | − | 34.4534i | −0.452145 | − | 1.39156i | −0.874454 | − | 0.485108i | \(-0.838780\pi\) |
0.422309 | − | 0.906452i | \(-0.361220\pi\) | |||||||
\(614\) | 9.03289 | − | 6.56278i | 0.364538 | − | 0.264852i | ||||
\(615\) | 0.567687 | 0.0228914 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.1920 | 1.65833 | 0.829163 | − | 0.559007i | \(-0.188817\pi\) | ||||
0.829163 | + | 0.559007i | \(0.188817\pi\) | |||||||
\(618\) | −23.1752 | + | 16.8378i | −0.932244 | + | 0.677315i | ||||
\(619\) | −11.0441 | − | 33.9903i | −0.443901 | − | 1.36619i | −0.883685 | − | 0.468082i | \(-0.844945\pi\) |
0.439784 | − | 0.898104i | \(-0.355055\pi\) | |||||||
\(620\) | 14.7821 | − | 45.4947i | 0.593665 | − | 1.82711i | ||||
\(621\) | 30.9435 | + | 22.4817i | 1.24172 | + | 0.902161i | ||||
\(622\) | 4.34691 | + | 3.15822i | 0.174295 | + | 0.126633i | ||||
\(623\) | −3.10722 | + | 9.56303i | −0.124488 | + | 0.383135i | ||||
\(624\) | 4.86143 | + | 14.9619i | 0.194613 | + | 0.598957i | ||||
\(625\) | −3.03159 | + | 2.20258i | −0.121264 | + | 0.0881032i | ||||
\(626\) | −23.5736 | −0.942192 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.77077 | 0.349992 | ||||||||
\(629\) | −26.1443 | + | 18.9949i | −1.04244 | + | 0.757378i | ||||
\(630\) | 0.891464 | + | 2.74364i | 0.0355168 | + | 0.109309i | ||||
\(631\) | 0.854456 | − | 2.62975i | 0.0340154 | − | 0.104689i | −0.932607 | − | 0.360893i | \(-0.882472\pi\) |
0.966623 | + | 0.256204i | \(0.0824720\pi\) | |||||||
\(632\) | 31.9838 | + | 23.2376i | 1.27225 | + | 0.924343i | ||||
\(633\) | −16.5500 | − | 12.0243i | −0.657804 | − | 0.477922i | ||||
\(634\) | 4.84833 | − | 14.9216i | 0.192552 | − | 0.592614i | ||||
\(635\) | 3.12231 | + | 9.60950i | 0.123905 | + | 0.381341i | ||||
\(636\) | −19.7290 | + | 14.3340i | −0.782306 | + | 0.568378i | ||||
\(637\) | 3.17831 | 0.125929 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.109970 | 0.00435033 | ||||||||
\(640\) | 20.5920 | − | 14.9610i | 0.813971 | − | 0.591385i | ||||
\(641\) | 11.8930 | + | 36.6028i | 0.469744 | + | 1.44572i | 0.852917 | + | 0.522046i | \(0.174831\pi\) |
−0.383173 | + | 0.923676i | \(0.625169\pi\) | |||||||
\(642\) | −13.1290 | + | 40.4070i | −0.518161 | + | 1.59474i | ||||
\(643\) | 21.3404 | + | 15.5047i | 0.841582 | + | 0.611445i | 0.922812 | − | 0.385250i | \(-0.125885\pi\) |
−0.0812301 | + | 0.996695i | \(0.525885\pi\) | |||||||
\(644\) | 21.3786 | + | 15.5325i | 0.842435 | + | 0.612065i | ||||
\(645\) | 0.0739455 | − | 0.227581i | 0.00291160 | − | 0.00896098i | ||||
\(646\) | 12.7350 | + | 39.1944i | 0.501054 | + | 1.54208i | ||||
\(647\) | 22.1032 | − | 16.0589i | 0.868968 | − | 0.631342i | −0.0613422 | − | 0.998117i | \(-0.519538\pi\) |
0.930310 | + | 0.366775i | \(0.119538\pi\) | |||||||
\(648\) | −24.4803 | −0.961678 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −26.3865 | −1.03496 | ||||||||
\(651\) | 11.2868 | − | 8.20034i | 0.442365 | − | 0.321397i | ||||
\(652\) | −19.1213 | − | 58.8492i | −0.748846 | − | 2.30471i | ||||
\(653\) | −2.61479 | + | 8.04751i | −0.102325 | + | 0.314923i | −0.989093 | − | 0.147290i | \(-0.952945\pi\) |
0.886768 | + | 0.462214i | \(0.152945\pi\) | |||||||
\(654\) | 2.49881 | + | 1.81549i | 0.0977112 | + | 0.0709913i | ||||
\(655\) | 0.103313 | + | 0.0750611i | 0.00403676 | + | 0.00293288i | ||||
\(656\) | 0.335394 | − | 1.03224i | 0.0130949 | − | 0.0403021i | ||||
\(657\) | 0.179232 | + | 0.551619i | 0.00699251 | + | 0.0215207i | ||||
\(658\) | 18.4339 | − | 13.3930i | 0.718630 | − | 0.522115i | ||||
\(659\) | 5.29247 | 0.206165 | 0.103083 | − | 0.994673i | \(-0.467129\pi\) | ||||
0.103083 | + | 0.994673i | \(0.467129\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.2700 | −0.749517 | −0.374759 | − | 0.927122i | \(-0.622274\pi\) | ||||
−0.374759 | + | 0.927122i | \(0.622274\pi\) | |||||||
\(662\) | −7.11942 | + | 5.17256i | −0.276704 | + | 0.201037i | ||||
\(663\) | −8.34485 | − | 25.6828i | −0.324087 | − | 0.997437i | ||||
\(664\) | −1.36147 | + | 4.19019i | −0.0528355 | + | 0.162611i | ||||
\(665\) | −2.91446 | − | 2.11748i | −0.113018 | − | 0.0821124i | ||||
\(666\) | −10.1151 | − | 7.34908i | −0.391954 | − | 0.284771i | ||||
\(667\) | −9.39565 | + | 28.9168i | −0.363801 | + | 1.11966i | ||||
\(668\) | −25.0425 | − | 77.0730i | −0.968925 | − | 2.98204i | ||||
\(669\) | 3.43912 | − | 2.49867i | 0.132964 | − | 0.0966041i | ||||
\(670\) | −28.8158 | −1.11325 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.26523 | 0.0488074 | ||||||||
\(673\) | −15.3650 | + | 11.1633i | −0.592278 | + | 0.430315i | −0.843130 | − | 0.537710i | \(-0.819289\pi\) |
0.250851 | + | 0.968026i | \(0.419289\pi\) | |||||||
\(674\) | 4.81055 | + | 14.8054i | 0.185296 | + | 0.570281i | ||||
\(675\) | 5.96932 | − | 18.3717i | 0.229759 | − | 0.707126i | ||||
\(676\) | 9.16142 | + | 6.65616i | 0.352362 | + | 0.256006i | ||||
\(677\) | 26.2299 | + | 19.0571i | 1.00810 | + | 0.732424i | 0.963809 | − | 0.266595i | \(-0.0858986\pi\) |
0.0442864 | + | 0.999019i | \(0.485899\pi\) | |||||||
\(678\) | 4.89572 | − | 15.0675i | 0.188019 | − | 0.578663i | ||||
\(679\) | −5.43159 | − | 16.7167i | −0.208445 | − | 0.641529i | ||||
\(680\) | 27.9605 | − | 20.3145i | 1.07224 | − | 0.779025i | ||||
\(681\) | −11.8409 | −0.453744 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.1260 | 0.578779 | 0.289389 | − | 0.957211i | \(-0.406548\pi\) | ||||
0.289389 | + | 0.957211i | \(0.406548\pi\) | |||||||
\(684\) | −8.53200 | + | 6.19886i | −0.326229 | + | 0.237019i | ||||
\(685\) | −1.77515 | − | 5.46335i | −0.0678250 | − | 0.208744i | ||||
\(686\) | −0.751051 | + | 2.31150i | −0.0286753 | + | 0.0882534i | ||||
\(687\) | −15.2093 | − | 11.0502i | −0.580271 | − | 0.421592i | ||||
\(688\) | −0.370127 | − | 0.268913i | −0.0141109 | − | 0.0102522i | ||||
\(689\) | 4.27425 | − | 13.1548i | 0.162836 | − | 0.501157i | ||||
\(690\) | 9.16952 | + | 28.2209i | 0.349078 | + | 1.07435i | ||||
\(691\) | 25.4119 | − | 18.4628i | 0.966712 | − | 0.702358i | 0.0120125 | − | 0.999928i | \(-0.496176\pi\) |
0.954700 | + | 0.297570i | \(0.0961762\pi\) | |||||||
\(692\) | 84.2192 | 3.20153 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 42.4357 | 1.61084 | ||||||||
\(695\) | −3.89515 | + | 2.83000i | −0.147752 | + | 0.107348i | ||||
\(696\) | −9.23489 | − | 28.4221i | −0.350048 | − | 1.07734i | ||||
\(697\) | −0.575718 | + | 1.77188i | −0.0218069 | + | 0.0671146i | ||||
\(698\) | −42.5205 | − | 30.8930i | −1.60943 | − | 1.16932i | ||||
\(699\) | −14.8839 | − | 10.8138i | −0.562962 | − | 0.409016i | ||||
\(700\) | 4.12416 | − | 12.6929i | 0.155879 | − | 0.479745i | ||||
\(701\) | 4.96426 | + | 15.2784i | 0.187498 | + | 0.577058i | 0.999982 | − | 0.00592402i | \(-0.00188568\pi\) |
−0.812485 | + | 0.582982i | \(0.801886\pi\) | |||||||
\(702\) | 35.3415 | − | 25.6771i | 1.33388 | − | 0.969120i | ||||
\(703\) | 15.6133 | 0.588865 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.9232 | 0.637366 | ||||||||
\(706\) | −8.65457 | + | 6.28791i | −0.325719 | + | 0.236649i | ||||
\(707\) | −3.85534 | − | 11.8655i | −0.144995 | − | 0.446249i | ||||
\(708\) | −12.0292 | + | 37.0221i | −0.452085 | + | 1.39137i | ||||
\(709\) | −32.1162 | − | 23.3338i | −1.20615 | − | 0.876318i | −0.211273 | − | 0.977427i | \(-0.567761\pi\) |
−0.994875 | + | 0.101109i | \(0.967761\pi\) | |||||||
\(710\) | 0.288589 | + | 0.209672i | 0.0108306 | + | 0.00786886i | ||||
\(711\) | 2.48560 | − | 7.64988i | 0.0932172 | − | 0.286893i | ||||
\(712\) | 14.4023 | + | 44.3258i | 0.539749 | + | 1.66118i | ||||
\(713\) | −53.2263 | + | 38.6712i | −1.99334 | + | 1.44825i | ||||
\(714\) | 20.6503 | 0.772819 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.6822 | 0.698187 | ||||||||
\(717\) | −5.77954 | + | 4.19909i | −0.215841 | + | 0.156818i | ||||
\(718\) | 8.02253 | + | 24.6908i | 0.299398 | + | 0.921453i | ||||
\(719\) | −3.04765 | + | 9.37971i | −0.113658 | + | 0.349804i | −0.991665 | − | 0.128845i | \(-0.958873\pi\) |
0.878007 | + | 0.478649i | \(0.158873\pi\) | |||||||
\(720\) | 3.31410 | + | 2.40784i | 0.123509 | + | 0.0897347i | ||||
\(721\) | 6.64852 | + | 4.83043i | 0.247604 | + | 0.179895i | ||||
\(722\) | −8.11714 | + | 24.9820i | −0.302089 | + | 0.929734i | ||||
\(723\) | 1.16421 | + | 3.58306i | 0.0432973 | + | 0.133255i | ||||
\(724\) | 24.8221 | − | 18.0343i | 0.922507 | − | 0.670241i | ||||
\(725\) | 15.3559 | 0.570305 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.5764 | −1.17111 | −0.585553 | − | 0.810634i | \(-0.699122\pi\) | ||||
−0.585553 | + | 0.810634i | \(0.699122\pi\) | |||||||
\(728\) | 11.9183 | − | 8.65915i | 0.441722 | − | 0.320930i | ||||
\(729\) | 9.05812 | + | 27.8780i | 0.335486 | + | 1.03252i | ||||
\(730\) | −0.581387 | + | 1.78933i | −0.0215181 | + | 0.0662259i | ||||
\(731\) | 0.635338 | + | 0.461600i | 0.0234988 | + | 0.0170729i | ||||
\(732\) | −11.1166 | − | 8.07667i | −0.410881 | − | 0.298522i | ||||
\(733\) | −12.7601 | + | 39.2716i | −0.471305 | + | 1.45053i | 0.379571 | + | 0.925163i | \(0.376072\pi\) |
−0.850876 | + | 0.525366i | \(0.823928\pi\) | |||||||
\(734\) | 7.67329 | + | 23.6160i | 0.283226 | + | 0.871681i | ||||
\(735\) | −1.46039 | + | 1.06103i | −0.0538672 | + | 0.0391368i | ||||
\(736\) | −5.96659 | −0.219931 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.720812 | −0.0265335 | ||||||||
\(739\) | 28.6469 | − | 20.8132i | 1.05379 | − | 0.765626i | 0.0808639 | − | 0.996725i | \(-0.474232\pi\) |
0.972930 | + | 0.231099i | \(0.0742321\pi\) | |||||||
\(740\) | −8.28946 | − | 25.5123i | −0.304727 | − | 0.937853i | ||||
\(741\) | −4.03174 | + | 12.4084i | −0.148110 | + | 0.455835i | ||||
\(742\) | 8.55709 | + | 6.21709i | 0.314141 | + | 0.228237i | ||||
\(743\) | −3.25555 | − | 2.36530i | −0.119435 | − | 0.0867743i | 0.526464 | − | 0.850197i | \(-0.323517\pi\) |
−0.645899 | + | 0.763423i | \(0.723517\pi\) | |||||||
\(744\) | 19.9828 | − | 61.5007i | 0.732605 | − | 2.25473i | ||||
\(745\) | 1.89500 | + | 5.83221i | 0.0694274 | + | 0.213676i | ||||
\(746\) | −54.8298 | + | 39.8361i | −2.00746 | + | 1.45850i | ||||
\(747\) | 0.896402 | 0.0327976 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.1885 | 0.445359 | ||||||||
\(750\) | 29.8712 | − | 21.7027i | 1.09074 | − | 0.792471i | ||||
\(751\) | 7.54588 | + | 23.2238i | 0.275353 | + | 0.847450i | 0.989126 | + | 0.147072i | \(0.0469850\pi\) |
−0.713773 | + | 0.700378i | \(0.753015\pi\) | |||||||
\(752\) | 9.99838 | − | 30.7719i | 0.364603 | − | 1.12213i | ||||
\(753\) | 30.4264 | + | 22.1060i | 1.10880 | + | 0.805589i | ||||
\(754\) | 28.0943 | + | 20.4117i | 1.02313 | + | 0.743351i | ||||
\(755\) | 6.60179 | − | 20.3182i | 0.240264 | − | 0.739456i | ||||
\(756\) | 6.82780 | + | 21.0138i | 0.248325 | + | 0.764265i | ||||
\(757\) | 1.06566 | − | 0.774247i | 0.0387321 | − | 0.0281405i | −0.568251 | − | 0.822855i | \(-0.692380\pi\) |
0.606983 | + | 0.794715i | \(0.292380\pi\) | |||||||
\(758\) | 2.79023 | 0.101346 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16.6979 | −0.605696 | ||||||||
\(761\) | −5.86055 | + | 4.25794i | −0.212445 | + | 0.154350i | −0.688919 | − | 0.724838i | \(-0.741915\pi\) |
0.476474 | + | 0.879188i | \(0.341915\pi\) | |||||||
\(762\) | 8.64723 | + | 26.6134i | 0.313256 | + | 0.964103i | ||||
\(763\) | 0.273816 | − | 0.842720i | 0.00991281 | − | 0.0305085i | ||||
\(764\) | 27.9117 | + | 20.2791i | 1.00981 | + | 0.733671i | ||||
\(765\) | −5.68880 | − | 4.13315i | −0.205679 | − | 0.149434i | ||||
\(766\) | −14.9847 | + | 46.1181i | −0.541419 | + | 1.66632i | ||||
\(767\) | −6.82286 | − | 20.9986i | −0.246359 | − | 0.758216i | ||||
\(768\) | 36.0361 | − | 26.1817i | 1.30034 | − | 0.944752i | ||||
\(769\) | −44.3139 | −1.59800 | −0.798999 | − | 0.601332i | \(-0.794637\pi\) | ||||
−0.798999 | + | 0.601332i | \(0.794637\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 42.9570 | 1.54706 | ||||||||
\(772\) | 80.9265 | − | 58.7965i | 2.91261 | − | 2.11613i | ||||
\(773\) | 5.88861 | + | 18.1233i | 0.211799 | + | 0.651849i | 0.999365 | + | 0.0356198i | \(0.0113405\pi\) |
−0.787567 | + | 0.616229i | \(0.788659\pi\) | |||||||
\(774\) | −0.0938911 | + | 0.288967i | −0.00337485 | + | 0.0103867i | ||||
\(775\) | 26.8818 | + | 19.5308i | 0.965622 | + | 0.701565i | ||||
\(776\) | −65.9118 | − | 47.8877i | −2.36610 | − | 1.71907i | ||||
\(777\) | 2.41760 | − | 7.44062i | 0.0867310 | − | 0.266931i | ||||
\(778\) | 1.95273 | + | 6.00990i | 0.0700089 | + | 0.215465i | ||||
\(779\) | 0.728215 | − | 0.529079i | 0.0260910 | − | 0.0189562i | ||||
\(780\) | 22.4161 | 0.802626 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −97.3828 | −3.48240 | ||||||||
\(783\) | −20.5674 | + | 14.9431i | −0.735018 | + | 0.534022i | ||||
\(784\) | 1.06649 | + | 3.28231i | 0.0380889 | + | 0.117225i | ||||
\(785\) | 0.873101 | − | 2.68713i | 0.0311623 | − | 0.0959077i | ||||
\(786\) | 0.286124 | + | 0.207881i | 0.0102057 | + | 0.00741488i | ||||
\(787\) | 25.4517 | + | 18.4917i | 0.907255 | + | 0.659159i | 0.940319 | − | 0.340294i | \(-0.110527\pi\) |
−0.0330644 | + | 0.999453i | \(0.510527\pi\) | |||||||
\(788\) | 13.5196 | − | 41.6092i | 0.481617 | − | 1.48227i | ||||
\(789\) | −1.47898 | − | 4.55182i | −0.0526530 | − | 0.162049i | ||||
\(790\) | 21.1084 | − | 15.3362i | 0.751004 | − | 0.545636i | ||||
\(791\) | −4.54502 | −0.161602 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.79370 | 0.276763 | ||||||||
\(794\) | −17.2489 | + | 12.5321i | −0.612141 | + | 0.444746i | ||||
\(795\) | 2.42758 | + | 7.47133i | 0.0860974 | + | 0.264981i | ||||
\(796\) | −14.7905 | + | 45.5205i | −0.524236 | + | 1.61343i | ||||
\(797\) | 10.1493 | + | 7.37392i | 0.359508 | + | 0.261198i | 0.752847 | − | 0.658196i | \(-0.228680\pi\) |
−0.393339 | + | 0.919394i | \(0.628680\pi\) | |||||||
\(798\) | −8.07159 | − | 5.86435i | −0.285731 | − | 0.207596i | ||||
\(799\) | −17.1626 | + | 52.8212i | −0.607171 | + | 1.86868i | ||||
\(800\) | 0.931193 | + | 2.86592i | 0.0329227 | + | 0.101326i | ||||
\(801\) | 7.67154 | − | 5.57370i | 0.271061 | − | 0.196937i | ||||
\(802\) | 68.9118 | 2.43336 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −52.7850 | −1.86159 | ||||||||
\(805\) | 6.88689 | − | 5.00362i | 0.242731 | − | 0.176354i | ||||
\(806\) | 23.2203 | + | 71.4647i | 0.817900 | + | 2.51724i | ||||
\(807\) | −0.769302 | + | 2.36767i | −0.0270807 | + | 0.0833458i | ||||
\(808\) | −46.7841 | − | 33.9907i | −1.64586 | − | 1.19579i | ||||
\(809\) | −4.35271 | − | 3.16243i | −0.153033 | − | 0.111185i | 0.508634 | − | 0.860983i | \(-0.330151\pi\) |
−0.661667 | + | 0.749798i | \(0.730151\pi\) | |||||||
\(810\) | −4.99258 | + | 15.3656i | −0.175421 | + | 0.539891i | ||||
\(811\) | −4.23351 | − | 13.0294i | −0.148659 | − | 0.457524i | 0.848805 | − | 0.528707i | \(-0.177323\pi\) |
−0.997463 | + | 0.0711822i | \(0.977323\pi\) | |||||||
\(812\) | −14.2098 | + | 10.3241i | −0.498668 | + | 0.362303i | ||||
\(813\) | 3.55103 | 0.124540 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.9333 | −0.698231 | ||||||||
\(816\) | 23.7231 | − | 17.2358i | 0.830474 | − | 0.603375i | ||||
\(817\) | −0.117248 | − | 0.360851i | −0.00410198 | − | 0.0126246i | ||||
\(818\) | −14.9501 | + | 46.0115i | −0.522716 | + | 1.60876i | ||||
\(819\) | −2.42488 | − | 1.76178i | −0.0847321 | − | 0.0615614i | ||||
\(820\) | −1.25115 | − | 0.909014i | −0.0436921 | − | 0.0317442i | ||||
\(821\) | 2.85258 | − | 8.77935i | 0.0995559 | − | 0.306401i | −0.888858 | − | 0.458182i | \(-0.848501\pi\) |
0.988414 | + | 0.151781i | \(0.0485007\pi\) | |||||||
\(822\) | −4.91627 | − | 15.1307i | −0.171474 | − | 0.527744i | ||||
\(823\) | 10.0663 | − | 7.31362i | 0.350890 | − | 0.254937i | −0.398352 | − | 0.917233i | \(-0.630418\pi\) |
0.749242 | + | 0.662296i | \(0.230418\pi\) | |||||||
\(824\) | 38.0915 | 1.32698 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.8840 | 0.587469 | ||||||||
\(827\) | −3.62752 | + | 2.63555i | −0.126141 | + | 0.0916471i | −0.649067 | − | 0.760731i | \(-0.724841\pi\) |
0.522926 | + | 0.852378i | \(0.324841\pi\) | |||||||
\(828\) | −7.70087 | − | 23.7008i | −0.267624 | − | 0.823661i | ||||
\(829\) | −11.3958 | + | 35.0726i | −0.395792 | + | 1.21812i | 0.532551 | + | 0.846398i | \(0.321234\pi\) |
−0.928343 | + | 0.371725i | \(0.878766\pi\) | |||||||
\(830\) | 2.35239 | + | 1.70911i | 0.0816528 | + | 0.0593242i | ||||
\(831\) | 5.98215 | + | 4.34629i | 0.207519 | + | 0.150771i | ||||
\(832\) | −8.88510 | + | 27.3455i | −0.308035 | + | 0.948035i | ||||
\(833\) | −1.83067 | − | 5.63423i | −0.0634290 | − | 0.195215i | ||||
\(834\) | −10.7876 | + | 7.83765i | −0.373544 | + | 0.271396i | ||||
\(835\) | −26.1060 | −0.903435 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −55.0105 | −1.90144 | ||||||||
\(838\) | 60.7495 | − | 44.1371i | 2.09856 | − | 1.52469i | ||||
\(839\) | 2.83185 | + | 8.71555i | 0.0977665 | + | 0.300894i | 0.987965 | − | 0.154679i | \(-0.0494343\pi\) |
−0.890198 | + | 0.455573i | \(0.849434\pi\) | |||||||
\(840\) | −2.58555 | + | 7.95751i | −0.0892100 | + | 0.274560i | ||||
\(841\) | 7.11170 | + | 5.16695i | 0.245231 | + | 0.178171i | ||||
\(842\) | 47.5704 | + | 34.5619i | 1.63938 | + | 1.19108i | ||||
\(843\) | 10.0031 | − | 30.7864i | 0.344526 | − | 1.06034i | ||||
\(844\) | 17.2213 | + | 53.0017i | 0.592782 | + | 1.82439i | ||||
\(845\) | 2.95126 | − | 2.14421i | 0.101526 | − | 0.0737632i | ||||
\(846\) | −21.4880 | −0.738774 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 15.0195 | 0.515771 | ||||||||
\(849\) | −9.84810 | + | 7.15507i | −0.337986 | + | 0.245561i | ||||
\(850\) | 15.1983 | + | 46.7757i | 0.521299 | + | 1.60439i | ||||
\(851\) | −11.4009 | + | 35.0885i | −0.390819 | + | 1.20282i | ||||
\(852\) | 0.528640 | + | 0.384080i | 0.0181109 | + | 0.0131583i | ||||
\(853\) | 5.27519 | + | 3.83265i | 0.180619 | + | 0.131227i | 0.674421 | − | 0.738347i | \(-0.264393\pi\) |
−0.493802 | + | 0.869574i | \(0.664393\pi\) | |||||||
\(854\) | −1.84169 | + | 5.66815i | −0.0630214 | + | 0.193960i | ||||
\(855\) | 1.04983 | + | 3.23105i | 0.0359035 | + | 0.110500i | ||||
\(856\) | 45.7056 | − | 33.2070i | 1.56218 | − | 1.13499i | ||||
\(857\) | −48.0736 | −1.64216 | −0.821082 | − | 0.570810i | \(-0.806629\pi\) | ||||
−0.821082 | + | 0.570810i | \(0.806629\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.316298 | −0.0107920 | −0.00539598 | − | 0.999985i | \(-0.501718\pi\) | ||||
−0.00539598 | + | 0.999985i | \(0.501718\pi\) | |||||||
\(860\) | −0.527387 | + | 0.383169i | −0.0179838 | + | 0.0130660i | ||||
\(861\) | −0.139378 | − | 0.428960i | −0.00474998 | − | 0.0146189i | ||||
\(862\) | −14.5704 | + | 44.8432i | −0.496271 | + | 1.52736i | ||||
\(863\) | −2.93425 | − | 2.13186i | −0.0998830 | − | 0.0725692i | 0.536723 | − | 0.843759i | \(-0.319662\pi\) |
−0.636606 | + | 0.771189i | \(0.719662\pi\) | |||||||
\(864\) | −4.03609 | − | 2.93239i | −0.137311 | − | 0.0997620i | ||||
\(865\) | 8.38373 | − | 25.8025i | 0.285055 | − | 0.877310i | ||||
\(866\) | −16.0633 | − | 49.4377i | −0.545852 | − | 1.67996i | ||||
\(867\) | −20.9966 | + | 15.2550i | −0.713083 | + | 0.518085i | ||||
\(868\) | −38.0064 | −1.29002 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −19.7231 | −0.668675 | ||||||||
\(871\) | 24.2214 | − | 17.5979i | 0.820710 | − | 0.596280i | ||||
\(872\) | −1.26917 | − | 3.90610i | −0.0429795 | − | 0.132277i | ||||
\(873\) | −5.12228 | + | 15.7648i | −0.173363 | + | 0.533556i | ||||
\(874\) | 38.0640 | + | 27.6551i | 1.28753 | + | 0.935448i | ||||
\(875\) | −8.56947 | − | 6.22608i | −0.289701 | − | 0.210480i | ||||
\(876\) | −1.06499 | + | 3.27770i | −0.0359827 | + | 0.110743i | ||||
\(877\) | −8.25311 | − | 25.4004i | −0.278688 | − | 0.857712i | −0.988220 | − | 0.153039i | \(-0.951094\pi\) |
0.709533 | − | 0.704673i | \(-0.248906\pi\) | |||||||
\(878\) | −62.3930 | + | 45.3312i | −2.10566 | + | 1.52985i | ||||
\(879\) | −35.3189 | −1.19128 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.91937 | 0.0983560 | 0.0491780 | − | 0.998790i | \(-0.484340\pi\) | ||||
0.0491780 | + | 0.998790i | \(0.484340\pi\) | |||||||
\(882\) | 1.85430 | − | 1.34723i | 0.0624376 | − | 0.0453636i | ||||
\(883\) | −13.9544 | − | 42.9472i | −0.469603 | − | 1.44529i | −0.853100 | − | 0.521748i | \(-0.825280\pi\) |
0.383497 | − | 0.923542i | \(-0.374720\pi\) | |||||||
\(884\) | −22.7332 | + | 69.9657i | −0.764602 | + | 2.35320i | ||||
\(885\) | 10.1451 | + | 7.37084i | 0.341023 | + | 0.247768i | ||||
\(886\) | 3.27602 | + | 2.38017i | 0.110060 | + | 0.0799634i | ||||
\(887\) | 7.42409 | − | 22.8490i | 0.249277 | − | 0.767194i | −0.745627 | − | 0.666363i | \(-0.767850\pi\) |
0.994904 | − | 0.100831i | \(-0.0321501\pi\) | |||||||
\(888\) | −11.2059 | − | 34.4881i | −0.376044 | − | 1.15735i | ||||
\(889\) | 6.49462 | − | 4.71861i | 0.217822 | − | 0.158257i | ||||
\(890\) | 30.7592 | 1.03105 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.5806 | −0.387749 | ||||||||
\(893\) | 21.7087 | − | 15.7723i | 0.726454 | − | 0.527800i | ||||
\(894\) | 5.24819 | + | 16.1523i | 0.175526 | + | 0.540212i | ||||
\(895\) | 1.85975 | − | 5.72372i | 0.0621646 | − | 0.191323i | ||||
\(896\) | −16.3606 | − | 11.8867i | −0.546571 | − | 0.397107i | ||||
\(897\) | −24.9421 | − | 18.1215i | −0.832791 | − | 0.605058i | ||||
\(898\) | −12.9074 | + | 39.7249i | −0.430726 | + | 1.32564i | ||||
\(899\) | −13.5133 | − | 41.5897i | −0.450694 | − | 1.38709i | ||||
\(900\) | −10.1823 | + | 7.39788i | −0.339411 | + | 0.246596i | ||||
\(901\) | −25.7816 | −0.858909 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.190121 | −0.00632684 | ||||||||
\(904\) | −17.0433 | + | 12.3827i | −0.566852 | + | 0.411842i | ||||
\(905\) | −3.05427 | − | 9.40009i | −0.101527 | − | 0.312469i | ||||
\(906\) | 18.2836 | − | 56.2712i | 0.607432 | − | 1.86948i | ||||
\(907\) | 12.9661 | + | 9.42041i | 0.430532 | + | 0.312800i | 0.781861 | − | 0.623452i | \(-0.214270\pi\) |
−0.351330 | + | 0.936252i | \(0.614270\pi\) | |||||||
\(908\) | 26.0966 | + | 18.9603i | 0.866048 | + | 0.629220i | ||||
\(909\) | −3.63579 | + | 11.1898i | −0.120592 | + | 0.371143i | ||||
\(910\) | −3.00444 | − | 9.24673i | −0.0995964 | − | 0.306526i | ||||
\(911\) | 13.2714 | − | 9.64223i | 0.439701 | − | 0.319461i | −0.345815 | − | 0.938303i | \(-0.612398\pi\) |
0.785516 | + | 0.618841i | \(0.212398\pi\) | |||||||
\(912\) | −14.1673 | −0.469127 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −24.8408 | −0.821660 | ||||||||
\(915\) | −3.58109 | + | 2.60182i | −0.118387 | + | 0.0860134i | ||||
\(916\) | 15.8262 | + | 48.7081i | 0.522913 | + | 1.60936i | ||||
\(917\) | 0.0313531 | − | 0.0964948i | 0.00103537 | − | 0.00318654i | ||||
\(918\) | −65.8745 | − | 47.8606i | −2.17418 | − | 1.57964i | ||||
\(919\) | 26.1475 | + | 18.9973i | 0.862527 | + | 0.626663i | 0.928571 | − | 0.371154i | \(-0.121038\pi\) |
−0.0660439 | + | 0.997817i | \(0.521038\pi\) | |||||||
\(920\) | 12.1929 | − | 37.5260i | 0.401989 | − | 1.23720i | ||||
\(921\) | −2.03599 | − | 6.26614i | −0.0670882 | − | 0.206476i | ||||
\(922\) | −43.4861 | + | 31.5945i | −1.43214 | + | 1.04051i | ||||
\(923\) | −0.370623 | −0.0121992 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.6333 | 0.612659 | ||||||||
\(926\) | 59.7193 | − | 43.3886i | 1.96250 | − | 1.42584i | ||||
\(927\) | −2.39489 | − | 7.37072i | −0.0786585 | − | 0.242086i | ||||
\(928\) | 1.22552 | − | 3.77175i | 0.0402295 | − | 0.123814i | ||||
\(929\) | 6.63015 | + | 4.81708i | 0.217528 | + | 0.158043i | 0.691213 | − | 0.722651i | \(-0.257077\pi\) |
−0.473685 | + | 0.880694i | \(0.657077\pi\) | |||||||
\(930\) | −34.5268 | − | 25.0852i | −1.13218 | − | 0.822576i | ||||
\(931\) | −0.884474 | + | 2.72213i | −0.0289875 | + | 0.0892142i | ||||
\(932\) | 15.4876 | + | 47.6660i | 0.507314 | + | 1.56135i | ||||
\(933\) | 2.56511 | − | 1.86366i | 0.0839778 | − | 0.0610135i | ||||
\(934\) | 61.2253 | 2.00335 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −13.8929 | −0.454103 | ||||||||
\(937\) | 27.6178 | − | 20.0655i | 0.902233 | − | 0.655510i | −0.0368058 | − | 0.999322i | \(-0.511718\pi\) |
0.939038 | + | 0.343812i | \(0.111718\pi\) | |||||||
\(938\) | 7.07480 | + | 21.7740i | 0.231000 | + | 0.710946i | ||||
\(939\) | −4.29866 | + | 13.2299i | −0.140282 | + | 0.431742i | ||||
\(940\) | −37.2979 | − | 27.0985i | −1.21652 | − | 0.883856i | ||||
\(941\) | 0.792327 | + | 0.575660i | 0.0258291 | + | 0.0187660i | 0.600625 | − | 0.799531i | \(-0.294919\pi\) |
−0.574796 | + | 0.818297i | \(0.694919\pi\) | |||||||
\(942\) | 2.41805 | − | 7.44198i | 0.0787842 | − | 0.242473i | ||||
\(943\) | 0.657277 | + | 2.02289i | 0.0214039 | + | 0.0658744i | ||||
\(944\) | 19.3963 | − | 14.0923i | 0.631297 | − | 0.458664i | ||||
\(945\) | 7.11775 | 0.231540 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.935599 | 0.0304029 | 0.0152014 | − | 0.999884i | \(-0.495161\pi\) | ||||
0.0152014 | + | 0.999884i | \(0.495161\pi\) | |||||||
\(948\) | 38.6666 | − | 28.0929i | 1.25583 | − | 0.912416i | ||||
\(949\) | −0.604054 | − | 1.85909i | −0.0196084 | − | 0.0603485i | ||||
\(950\) | 7.34295 | − | 22.5993i | 0.238237 | − | 0.733217i | ||||
\(951\) | −7.49017 | − | 5.44193i | −0.242886 | − | 0.176467i | ||||
\(952\) | −22.2150 | − | 16.1401i | −0.719993 | − | 0.523105i | ||||
\(953\) | −5.17049 | + | 15.9131i | −0.167489 | + | 0.515477i | −0.999211 | − | 0.0397147i | \(-0.987355\pi\) |
0.831722 | + | 0.555192i | \(0.187355\pi\) | |||||||
\(954\) | −3.08238 | − | 9.48660i | −0.0997958 | − | 0.307140i | ||||
\(955\) | 8.99147 | − | 6.53269i | 0.290957 | − | 0.211393i | ||||
\(956\) | 19.4616 | 0.629434 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 51.5353 | 1.66503 | ||||||||
\(959\) | −3.69243 | + | 2.68271i | −0.119235 | + | 0.0866291i | ||||
\(960\) | −5.04633 | − | 15.5310i | −0.162870 | − | 0.501262i | ||||
\(961\) | 19.6611 | − | 60.5105i | 0.634228 | − | 1.95195i | ||||
\(962\) | 34.0904 | + | 24.7681i | 1.09912 | + | 0.798556i | ||||
\(963\) | −9.29918 | − | 6.75625i | −0.299662 | − | 0.217717i | ||||
\(964\) | 3.17156 | − | 9.76106i | 0.102149 | − | 0.314383i | ||||
\(965\) | −9.95770 | − | 30.6467i | −0.320550 | − | 0.986551i | ||||
\(966\) | 19.0732 | − | 13.8575i | 0.613670 | − | 0.445857i | ||||
\(967\) | −36.4439 | −1.17196 | −0.585978 | − | 0.810327i | \(-0.699290\pi\) | ||||
−0.585978 | + | 0.810327i | \(0.699290\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 24.3188 | 0.781233 | ||||||||
\(970\) | −43.4999 | + | 31.6045i | −1.39670 | + | 1.01476i | ||||
\(971\) | −10.2723 | − | 31.6148i | −0.329653 | − | 1.01457i | −0.969296 | − | 0.245895i | \(-0.920918\pi\) |
0.639644 | − | 0.768671i | \(-0.279082\pi\) | |||||||
\(972\) | 11.3380 | − | 34.8946i | 0.363665 | − | 1.11925i | ||||
\(973\) | 3.09475 | + | 2.24847i | 0.0992133 | + | 0.0720827i | ||||
\(974\) | 33.0723 | + | 24.0284i | 1.05971 | + | 0.769921i | ||||
\(975\) | −4.81159 | + | 14.8086i | −0.154094 | + | 0.474253i | ||||
\(976\) | 2.61519 | + | 8.04874i | 0.0837103 | + | 0.257634i | ||||
\(977\) | −18.2568 | + | 13.2643i | −0.584086 | + | 0.424363i | −0.840195 | − | 0.542285i | \(-0.817559\pi\) |
0.256109 | + | 0.966648i | \(0.417559\pi\) | |||||||
\(978\) | −55.2050 | −1.76526 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 4.91760 | 0.157087 | ||||||||
\(981\) | −0.676037 | + | 0.491170i | −0.0215842 | + | 0.0156818i | ||||
\(982\) | −3.63362 | − | 11.1831i | −0.115953 | − | 0.356868i | ||||
\(983\) | −4.66763 | + | 14.3655i | −0.148874 | + | 0.458188i | −0.997489 | − | 0.0708236i | \(-0.977437\pi\) |
0.848615 | + | 0.529012i | \(0.177437\pi\) | |||||||
\(984\) | −1.69133 | − | 1.22882i | −0.0539177 | − | 0.0391735i | ||||
\(985\) | −11.4021 | − | 8.28410i | −0.363301 | − | 0.263953i | ||||
\(986\) | 20.0021 | − | 61.5601i | 0.636996 | − | 1.96047i | ||||
\(987\) | −4.15497 | − | 12.7877i | −0.132254 | − | 0.407036i | ||||
\(988\) | 28.7548 | − | 20.8916i | 0.914813 | − | 0.664651i | ||||
\(989\) | 0.896574 | 0.0285094 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.1534 | −1.75201 | −0.876003 | − | 0.482305i | \(-0.839800\pi\) | ||||
−0.876003 | + | 0.482305i | \(0.839800\pi\) | |||||||
\(992\) | 6.94254 | − | 5.04405i | 0.220426 | − | 0.160149i | ||||
\(993\) | 1.60470 | + | 4.93876i | 0.0509236 | + | 0.156727i | ||||
\(994\) | 0.0875802 | − | 0.269544i | 0.00277788 | − | 0.00854942i | ||||
\(995\) | 12.4739 | + | 9.06282i | 0.395449 | + | 0.287311i | ||||
\(996\) | 4.30914 | + | 3.13077i | 0.136540 | + | 0.0992023i | ||||
\(997\) | −15.3596 | + | 47.2721i | −0.486444 | + | 1.49712i | 0.343434 | + | 0.939177i | \(0.388410\pi\) |
−0.829878 | + | 0.557944i | \(0.811590\pi\) | |||||||
\(998\) | 22.9698 | + | 70.6938i | 0.727097 | + | 2.23777i | ||||
\(999\) | −24.9570 | + | 18.1323i | −0.789606 | + | 0.573682i |
(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 | 847.2.f.v.729.1 | 16 | ||
11.2 | odd | 10 | 847.2.a.p.1.1 | 8 | |||
11.3 | even | 5 | 847.2.f.x.148.4 | 16 | |||
11.4 | even | 5 | inner | 847.2.f.v.323.1 | 16 | ||
11.5 | even | 5 | 847.2.f.x.372.4 | 16 | |||
11.6 | odd | 10 | 77.2.f.b.64.1 | ✓ | 16 | ||
11.7 | odd | 10 | 847.2.f.w.323.4 | 16 | |||
11.8 | odd | 10 | 77.2.f.b.71.1 | yes | 16 | ||
11.9 | even | 5 | 847.2.a.o.1.8 | 8 | |||
11.10 | odd | 2 | 847.2.f.w.729.4 | 16 | |||
33.2 | even | 10 | 7623.2.a.ct.1.8 | 8 | |||
33.8 | even | 10 | 693.2.m.i.379.4 | 16 | |||
33.17 | even | 10 | 693.2.m.i.64.4 | 16 | |||
33.20 | odd | 10 | 7623.2.a.cw.1.1 | 8 | |||
77.6 | even | 10 | 539.2.f.e.295.1 | 16 | |||
77.13 | even | 10 | 5929.2.a.bt.1.1 | 8 | |||
77.17 | even | 30 | 539.2.q.f.471.1 | 32 | |||
77.19 | even | 30 | 539.2.q.f.214.1 | 32 | |||
77.20 | odd | 10 | 5929.2.a.bs.1.8 | 8 | |||
77.30 | odd | 30 | 539.2.q.g.214.1 | 32 | |||
77.39 | odd | 30 | 539.2.q.g.471.1 | 32 | |||
77.41 | even | 10 | 539.2.f.e.148.1 | 16 | |||
77.52 | even | 30 | 539.2.q.f.324.4 | 32 | |||
77.61 | even | 30 | 539.2.q.f.361.4 | 32 | |||
77.72 | odd | 30 | 539.2.q.g.361.4 | 32 | |||
77.74 | odd | 30 | 539.2.q.g.324.4 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.64.1 | ✓ | 16 | 11.6 | odd | 10 | ||
77.2.f.b.71.1 | yes | 16 | 11.8 | odd | 10 | ||
539.2.f.e.148.1 | 16 | 77.41 | even | 10 | |||
539.2.f.e.295.1 | 16 | 77.6 | even | 10 | |||
539.2.q.f.214.1 | 32 | 77.19 | even | 30 | |||
539.2.q.f.324.4 | 32 | 77.52 | even | 30 | |||
539.2.q.f.361.4 | 32 | 77.61 | even | 30 | |||
539.2.q.f.471.1 | 32 | 77.17 | even | 30 | |||
539.2.q.g.214.1 | 32 | 77.30 | odd | 30 | |||
539.2.q.g.324.4 | 32 | 77.74 | odd | 30 | |||
539.2.q.g.361.4 | 32 | 77.72 | odd | 30 | |||
539.2.q.g.471.1 | 32 | 77.39 | odd | 30 | |||
693.2.m.i.64.4 | 16 | 33.17 | even | 10 | |||
693.2.m.i.379.4 | 16 | 33.8 | even | 10 | |||
847.2.a.o.1.8 | 8 | 11.9 | even | 5 | |||
847.2.a.p.1.1 | 8 | 11.2 | odd | 10 | |||
847.2.f.v.323.1 | 16 | 11.4 | even | 5 | inner | ||
847.2.f.v.729.1 | 16 | 1.1 | even | 1 | trivial | ||
847.2.f.w.323.4 | 16 | 11.7 | odd | 10 | |||
847.2.f.w.729.4 | 16 | 11.10 | odd | 2 | |||
847.2.f.x.148.4 | 16 | 11.3 | even | 5 | |||
847.2.f.x.372.4 | 16 | 11.5 | even | 5 | |||
5929.2.a.bs.1.8 | 8 | 77.20 | odd | 10 | |||
5929.2.a.bt.1.1 | 8 | 77.13 | even | 10 | |||
7623.2.a.ct.1.8 | 8 | 33.2 | even | 10 | |||
7623.2.a.cw.1.1 | 8 | 33.20 | odd | 10 |