Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(245,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 8]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.245");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.h (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 16.0.343361479062744140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + 3 x^{14} - 8 x^{13} + 8 x^{12} + 7 x^{11} + 6 x^{10} + 56 x^{9} - 137 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 269.2 | ||
Root | \(-0.144291 + 1.72603i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.269 |
Dual form | 363.3.h.m.251.2 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.753510 | + | 0.244830i | −0.376755 | + | 0.122415i | −0.491272 | − | 0.871006i | \(-0.663468\pi\) |
0.114517 | + | 0.993421i | \(0.463468\pi\) | |||||||
\(3\) | −1.91055 | + | 2.31296i | −0.636850 | + | 0.770988i | ||||
\(4\) | −2.72823 | + | 1.98218i | −0.682058 | + | 0.495544i | ||||
\(5\) | 2.40079 | + | 0.780063i | 0.480158 | + | 0.156013i | 0.539088 | − | 0.842249i | \(-0.318769\pi\) |
−0.0589304 | + | 0.998262i | \(0.518769\pi\) | |||||||
\(6\) | 0.873334 | − | 2.21060i | 0.145556 | − | 0.368433i | ||||
\(7\) | 3.83843 | − | 2.78878i | 0.548347 | − | 0.398398i | −0.278828 | − | 0.960341i | \(-0.589946\pi\) |
0.827176 | + | 0.561943i | \(0.189946\pi\) | |||||||
\(8\) | 3.43323 | − | 4.72544i | 0.429154 | − | 0.590680i | ||||
\(9\) | −1.69960 | − | 8.83806i | −0.188845 | − | 0.982007i | ||||
\(10\) | −2.00000 | −0.200000 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.627719 | − | 10.0974i | 0.0523099 | − | 0.841446i | ||||
\(13\) | −4.16837 | − | 12.8289i | −0.320644 | − | 0.986840i | −0.973369 | − | 0.229245i | \(-0.926374\pi\) |
0.652725 | − | 0.757595i | \(-0.273626\pi\) | |||||||
\(14\) | −2.20952 | + | 3.04114i | −0.157823 | + | 0.217224i | ||||
\(15\) | −6.39108 | + | 4.06259i | −0.426072 | + | 0.270839i | ||||
\(16\) | 2.73833 | − | 8.42770i | 0.171145 | − | 0.526731i | ||||
\(17\) | 21.5549 | + | 7.00360i | 1.26793 | + | 0.411977i | 0.864315 | − | 0.502951i | \(-0.167752\pi\) |
0.403619 | + | 0.914927i | \(0.367752\pi\) | |||||||
\(18\) | 3.44449 | + | 6.24345i | 0.191361 | + | 0.346858i | ||||
\(19\) | −6.66119 | − | 4.83964i | −0.350589 | − | 0.254718i | 0.398527 | − | 0.917157i | \(-0.369522\pi\) |
−0.749116 | + | 0.662439i | \(0.769522\pi\) | |||||||
\(20\) | −8.09613 | + | 2.63059i | −0.404807 | + | 0.131530i | ||||
\(21\) | −0.883156 | + | 14.2063i | −0.0420550 | + | 0.676489i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 30.2372i | − | 1.31466i | −0.753603 | − | 0.657329i | \(-0.771686\pi\) | ||
0.753603 | − | 0.657329i | \(-0.228314\pi\) | |||||||
\(24\) | 4.37041 | + | 16.9691i | 0.182100 | + | 0.707047i | ||||
\(25\) | −15.0701 | − | 10.9491i | −0.602806 | − | 0.437964i | ||||
\(26\) | 6.28181 | + | 8.64617i | 0.241608 | + | 0.332545i | ||||
\(27\) | 23.6893 | + | 12.9544i | 0.877381 | + | 0.479794i | ||||
\(28\) | −4.94427 | + | 15.2169i | −0.176581 | + | 0.543461i | ||||
\(29\) | 31.5381 | + | 43.4085i | 1.08752 | + | 1.49685i | 0.850960 | + | 0.525230i | \(0.176021\pi\) |
0.236562 | + | 0.971616i | \(0.423979\pi\) | |||||||
\(30\) | 3.82110 | − | 4.62593i | 0.127370 | − | 0.154198i | ||||
\(31\) | 7.99161 | + | 24.5957i | 0.257794 | + | 0.793408i | 0.993266 | + | 0.115854i | \(0.0369603\pi\) |
−0.735472 | + | 0.677555i | \(0.763040\pi\) | |||||||
\(32\) | 30.3846i | 0.949520i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −17.9565 | −0.528132 | ||||||||
\(35\) | 11.3907 | − | 3.70106i | 0.325448 | − | 0.105745i | ||||
\(36\) | 22.1555 | + | 20.7434i | 0.615431 | + | 0.576205i | ||||
\(37\) | 34.4690 | − | 25.0432i | 0.931593 | − | 0.676842i | −0.0147891 | − | 0.999891i | \(-0.504708\pi\) |
0.946382 | + | 0.323048i | \(0.104708\pi\) | |||||||
\(38\) | 6.20416 | + | 2.01586i | 0.163267 | + | 0.0530488i | ||||
\(39\) | 37.6367 | + | 14.8690i | 0.965044 | + | 0.381256i | ||||
\(40\) | 11.9286 | − | 8.66664i | 0.298215 | − | 0.216666i | ||||
\(41\) | 18.1520 | − | 24.9840i | 0.442731 | − | 0.609367i | −0.528085 | − | 0.849191i | \(-0.677090\pi\) |
0.970816 | + | 0.239825i | \(0.0770899\pi\) | |||||||
\(42\) | −2.81265 | − | 10.9208i | −0.0669680 | − | 0.260019i | ||||
\(43\) | 35.4891 | 0.825328 | 0.412664 | − | 0.910883i | \(-0.364598\pi\) | ||||
0.412664 | + | 0.910883i | \(0.364598\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.81386 | − | 22.5441i | 0.0625302 | − | 0.500980i | ||||
\(46\) | 7.40297 | + | 22.7840i | 0.160934 | + | 0.495304i | ||||
\(47\) | −18.3899 | + | 25.3115i | −0.391274 | + | 0.538542i | −0.958527 | − | 0.285001i | \(-0.908006\pi\) |
0.567253 | + | 0.823543i | \(0.308006\pi\) | |||||||
\(48\) | 14.2613 | + | 22.4352i | 0.297110 | + | 0.467400i | ||||
\(49\) | −8.18559 | + | 25.1927i | −0.167053 | + | 0.514136i | ||||
\(50\) | 14.0362 | + | 4.56063i | 0.280723 | + | 0.0912125i | ||||
\(51\) | −57.3807 | + | 36.4749i | −1.12511 | + | 0.715195i | ||||
\(52\) | 36.8015 | + | 26.7378i | 0.707721 | + | 0.514189i | ||||
\(53\) | −9.42707 | + | 3.06304i | −0.177869 | + | 0.0577932i | −0.396598 | − | 0.917993i | \(-0.629809\pi\) |
0.218728 | + | 0.975786i | \(0.429809\pi\) | |||||||
\(54\) | −21.0217 | − | 3.96143i | −0.389292 | − | 0.0733599i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 27.7128i | − | 0.494872i | ||||||
\(57\) | 23.9205 | − | 6.16073i | 0.419657 | − | 0.108083i | ||||
\(58\) | −34.3920 | − | 24.9873i | −0.592966 | − | 0.430815i | ||||
\(59\) | −36.1628 | − | 49.7739i | −0.612929 | − | 0.843625i | 0.383885 | − | 0.923381i | \(-0.374586\pi\) |
−0.996814 | + | 0.0797561i | \(0.974586\pi\) | |||||||
\(60\) | 9.38359 | − | 23.7519i | 0.156393 | − | 0.395866i | ||||
\(61\) | 15.8976 | − | 48.9277i | 0.260616 | − | 0.802093i | −0.732055 | − | 0.681245i | \(-0.761439\pi\) |
0.992671 | − | 0.120848i | \(-0.0385614\pi\) | |||||||
\(62\) | −12.0435 | − | 16.5765i | −0.194250 | − | 0.267363i | ||||
\(63\) | −31.1713 | − | 29.1845i | −0.494782 | − | 0.463246i | ||||
\(64\) | 3.51423 | + | 10.8157i | 0.0549098 | + | 0.168995i | ||||
\(65\) | − | 34.0511i | − | 0.523863i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 34.3288 | 0.512370 | 0.256185 | − | 0.966628i | \(-0.417534\pi\) | ||||
0.256185 | + | 0.966628i | \(0.417534\pi\) | |||||||
\(68\) | −72.6891 | + | 23.6181i | −1.06896 | + | 0.347325i | ||||
\(69\) | 69.9374 | + | 57.7696i | 1.01359 | + | 0.837240i | ||||
\(70\) | −7.67686 | + | 5.57757i | −0.109669 | + | 0.0796795i | ||||
\(71\) | 13.7915 | + | 4.48112i | 0.194246 | + | 0.0631144i | 0.404525 | − | 0.914527i | \(-0.367437\pi\) |
−0.210278 | + | 0.977642i | \(0.567437\pi\) | |||||||
\(72\) | −47.5988 | − | 22.3117i | −0.661095 | − | 0.309885i | ||||
\(73\) | 71.3826 | − | 51.8625i | 0.977843 | − | 0.710445i | 0.0206176 | − | 0.999787i | \(-0.493437\pi\) |
0.957226 | + | 0.289343i | \(0.0934367\pi\) | |||||||
\(74\) | −19.8414 | + | 27.3093i | −0.268127 | + | 0.369045i | ||||
\(75\) | 54.1171 | − | 13.9379i | 0.721562 | − | 0.185839i | ||||
\(76\) | 27.7663 | 0.365346 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −32.0000 | − | 1.98933i | −0.410256 | − | 0.0255043i | ||||
\(79\) | −28.9485 | − | 89.0943i | −0.366437 | − | 1.12778i | −0.949076 | − | 0.315046i | \(-0.897980\pi\) |
0.582640 | − | 0.812731i | \(-0.302020\pi\) | |||||||
\(80\) | 13.1483 | − | 18.0970i | 0.164353 | − | 0.226213i | ||||
\(81\) | −75.2227 | + | 30.0424i | −0.928675 | + | 0.370894i | ||||
\(82\) | −7.56083 | + | 23.2699i | −0.0922053 | + | 0.283779i | ||||
\(83\) | −32.4890 | − | 10.5563i | −0.391433 | − | 0.127184i | 0.106686 | − | 0.994293i | \(-0.465976\pi\) |
−0.498120 | + | 0.867108i | \(0.665976\pi\) | |||||||
\(84\) | −25.7499 | − | 40.5086i | −0.306546 | − | 0.482245i | ||||
\(85\) | 46.2854 | + | 33.6283i | 0.544534 | + | 0.395627i | ||||
\(86\) | −26.7414 | + | 8.68881i | −0.310947 | + | 0.101033i | ||||
\(87\) | −160.658 | − | 9.98755i | −1.84664 | − | 0.114799i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 143.482i | 1.61216i | 0.591805 | + | 0.806081i | \(0.298416\pi\) | ||||
−0.591805 | + | 0.806081i | \(0.701584\pi\) | |||||||
\(90\) | 3.39921 | + | 17.6761i | 0.0377690 | + | 0.196401i | ||||
\(91\) | −51.7771 | − | 37.6183i | −0.568979 | − | 0.413387i | ||||
\(92\) | 59.9354 | + | 82.4940i | 0.651472 | + | 0.896674i | ||||
\(93\) | −72.1572 | − | 28.5069i | −0.775884 | − | 0.306526i | ||||
\(94\) | 7.65993 | − | 23.5748i | 0.0814886 | − | 0.250796i | ||||
\(95\) | −12.2169 | − | 16.8151i | −0.128599 | − | 0.177001i | ||||
\(96\) | −70.2785 | − | 58.0513i | −0.732068 | − | 0.604701i | ||||
\(97\) | −12.4488 | − | 38.3136i | −0.128339 | − | 0.394985i | 0.866156 | − | 0.499774i | \(-0.166583\pi\) |
−0.994495 | + | 0.104788i | \(0.966583\pi\) | |||||||
\(98\) | − | 20.9870i | − | 0.214153i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 62.8179 | 0.628179 | ||||||||
\(101\) | 88.2159 | − | 28.6631i | 0.873425 | − | 0.283793i | 0.162200 | − | 0.986758i | \(-0.448141\pi\) |
0.711224 | + | 0.702965i | \(0.248141\pi\) | |||||||
\(102\) | 34.3068 | − | 41.5327i | 0.336341 | − | 0.407184i | ||||
\(103\) | 15.8374 | − | 11.5066i | 0.153761 | − | 0.111714i | −0.508245 | − | 0.861213i | \(-0.669705\pi\) |
0.662006 | + | 0.749499i | \(0.269705\pi\) | |||||||
\(104\) | −74.9332 | − | 24.3473i | −0.720512 | − | 0.234109i | ||||
\(105\) | −13.2021 | + | 33.4173i | −0.125734 | + | 0.318260i | ||||
\(106\) | 6.35346 | − | 4.61606i | 0.0599383 | − | 0.0435477i | ||||
\(107\) | −49.6256 | + | 68.3037i | −0.463790 | + | 0.638353i | −0.975289 | − | 0.220931i | \(-0.929090\pi\) |
0.511499 | + | 0.859284i | \(0.329090\pi\) | |||||||
\(108\) | −90.3079 | + | 11.6137i | −0.836184 | + | 0.107534i | ||||
\(109\) | 167.723 | 1.53874 | 0.769371 | − | 0.638803i | \(-0.220570\pi\) | ||||
0.769371 | + | 0.638803i | \(0.220570\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.93070 | + | 127.572i | −0.0714478 | + | 1.14929i | ||||
\(112\) | −12.9922 | − | 39.9857i | −0.116001 | − | 0.357016i | ||||
\(113\) | 72.5958 | − | 99.9196i | 0.642441 | − | 0.884244i | −0.356302 | − | 0.934371i | \(-0.615963\pi\) |
0.998743 | + | 0.0501267i | \(0.0159625\pi\) | |||||||
\(114\) | −16.5160 | + | 10.4986i | −0.144877 | + | 0.0920931i | ||||
\(115\) | 23.5869 | − | 72.5930i | 0.205103 | − | 0.631243i | ||||
\(116\) | −172.087 | − | 55.9144i | −1.48351 | − | 0.482021i | ||||
\(117\) | −106.298 | + | 58.6444i | −0.908532 | + | 0.501234i | ||||
\(118\) | 39.4352 | + | 28.6513i | 0.334196 | + | 0.242808i | ||||
\(119\) | 102.268 | − | 33.2290i | 0.859399 | − | 0.279236i | ||||
\(120\) | −2.74456 | + | 44.1485i | −0.0228714 | + | 0.367904i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 40.7597i | 0.334096i | ||||||||
\(123\) | 23.1069 | + | 89.7181i | 0.187861 | + | 0.729415i | ||||
\(124\) | −70.5559 | − | 51.2619i | −0.569000 | − | 0.413402i | ||||
\(125\) | −64.7334 | − | 89.0979i | −0.517867 | − | 0.712783i | ||||
\(126\) | 30.6331 | + | 14.3591i | 0.243120 | + | 0.113961i | ||||
\(127\) | −39.8161 | + | 122.541i | −0.313513 | + | 0.964894i | 0.662849 | + | 0.748753i | \(0.269347\pi\) |
−0.976362 | + | 0.216141i | \(0.930653\pi\) | |||||||
\(128\) | −76.7346 | − | 105.616i | −0.599489 | − | 0.825125i | ||||
\(129\) | −67.8037 | + | 82.0851i | −0.525610 | + | 0.636318i | ||||
\(130\) | 8.33674 | + | 25.6578i | 0.0641288 | + | 0.197368i | ||||
\(131\) | − | 125.997i | − | 0.961811i | −0.876772 | − | 0.480906i | \(-0.840308\pi\) | ||
0.876772 | − | 0.480906i | \(-0.159692\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −39.0652 | −0.293724 | ||||||||
\(134\) | −25.8671 | + | 8.40472i | −0.193038 | + | 0.0627218i | ||||
\(135\) | 46.7677 | + | 49.5800i | 0.346427 | + | 0.367259i | ||||
\(136\) | 107.098 | − | 77.8112i | 0.787485 | − | 0.572141i | ||||
\(137\) | −56.4118 | − | 18.3293i | −0.411765 | − | 0.133791i | 0.0958068 | − | 0.995400i | \(-0.469457\pi\) |
−0.507572 | + | 0.861609i | \(0.669457\pi\) | |||||||
\(138\) | −66.8423 | − | 26.4071i | −0.484364 | − | 0.191356i | ||||
\(139\) | 105.928 | − | 76.9615i | 0.762075 | − | 0.553680i | −0.137471 | − | 0.990506i | \(-0.543897\pi\) |
0.899546 | + | 0.436826i | \(0.143897\pi\) | |||||||
\(140\) | −23.7403 | + | 32.6757i | −0.169574 | + | 0.233398i | ||||
\(141\) | −23.4098 | − | 90.8940i | −0.166027 | − | 0.644638i | ||||
\(142\) | −11.4891 | −0.0809093 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −79.1386 | − | 9.87774i | −0.549574 | − | 0.0685954i | ||||
\(145\) | 41.8550 | + | 128.816i | 0.288655 | + | 0.888389i | ||||
\(146\) | −41.0900 | + | 56.5555i | −0.281438 | + | 0.387366i | ||||
\(147\) | −42.6307 | − | 67.0648i | −0.290005 | − | 0.456223i | ||||
\(148\) | −44.3993 | + | 136.647i | −0.299996 | + | 0.923292i | ||||
\(149\) | 70.6927 | + | 22.9695i | 0.474448 | + | 0.154157i | 0.536474 | − | 0.843917i | \(-0.319756\pi\) |
−0.0620259 | + | 0.998075i | \(0.519756\pi\) | |||||||
\(150\) | −37.3654 | + | 23.7518i | −0.249102 | + | 0.158346i | ||||
\(151\) | 5.04316 | + | 3.66407i | 0.0333984 | + | 0.0242654i | 0.604359 | − | 0.796712i | \(-0.293429\pi\) |
−0.570961 | + | 0.820977i | \(0.693429\pi\) | |||||||
\(152\) | −45.7388 | + | 14.8615i | −0.300913 | + | 0.0977727i | ||||
\(153\) | 25.2635 | − | 202.407i | 0.165121 | − | 1.32292i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 65.2829i | 0.421180i | ||||||||
\(156\) | −132.155 | + | 34.0365i | −0.847145 | + | 0.218183i | ||||
\(157\) | −79.9278 | − | 58.0709i | −0.509094 | − | 0.369879i | 0.303386 | − | 0.952868i | \(-0.401883\pi\) |
−0.812480 | + | 0.582989i | \(0.801883\pi\) | |||||||
\(158\) | 43.6260 | + | 60.0460i | 0.276114 | + | 0.380038i | ||||
\(159\) | 10.9262 | − | 27.6565i | 0.0687181 | − | 0.173941i | ||||
\(160\) | −23.7019 | + | 72.9470i | −0.148137 | + | 0.455919i | ||||
\(161\) | −84.3249 | − | 116.063i | −0.523757 | − | 0.720890i | ||||
\(162\) | 49.3257 | − | 41.0540i | 0.304480 | − | 0.253420i | ||||
\(163\) | 64.2352 | + | 197.696i | 0.394081 | + | 1.21286i | 0.929675 | + | 0.368381i | \(0.120088\pi\) |
−0.535594 | + | 0.844476i | \(0.679912\pi\) | |||||||
\(164\) | 104.143i | 0.635016i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 27.0652 | 0.163044 | ||||||||
\(167\) | 60.0719 | − | 19.5185i | 0.359712 | − | 0.116878i | −0.123585 | − | 0.992334i | \(-0.539439\pi\) |
0.483297 | + | 0.875456i | \(0.339439\pi\) | |||||||
\(168\) | 64.0987 | + | 52.9467i | 0.381540 | + | 0.315159i | ||||
\(169\) | −10.4820 | + | 7.61564i | −0.0620238 | + | 0.0450630i | ||||
\(170\) | −43.1098 | − | 14.0072i | −0.253587 | − | 0.0823953i | ||||
\(171\) | −31.4517 | + | 67.0975i | −0.183928 | + | 0.392383i | ||||
\(172\) | −96.8226 | + | 70.3457i | −0.562922 | + | 0.408987i | ||||
\(173\) | 113.654 | − | 156.431i | 0.656957 | − | 0.904223i | −0.342419 | − | 0.939547i | \(-0.611246\pi\) |
0.999376 | + | 0.0353239i | \(0.0112463\pi\) | |||||||
\(174\) | 123.502 | − | 31.8081i | 0.709783 | − | 0.182805i | ||||
\(175\) | −88.3804 | −0.505031 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 184.216 | + | 11.4521i | 1.04077 | + | 0.0647011i | ||||
\(178\) | −35.1288 | − | 108.115i | −0.197353 | − | 0.607390i | ||||
\(179\) | −18.2285 | + | 25.0894i | −0.101835 | + | 0.140164i | −0.856893 | − | 0.515494i | \(-0.827609\pi\) |
0.755058 | + | 0.655658i | \(0.227609\pi\) | |||||||
\(180\) | 37.0096 | + | 67.0832i | 0.205609 | + | 0.372684i | ||||
\(181\) | 31.5626 | − | 97.1396i | 0.174379 | − | 0.536683i | −0.825226 | − | 0.564803i | \(-0.808952\pi\) |
0.999605 | + | 0.0281203i | \(0.00895215\pi\) | |||||||
\(182\) | 48.2246 | + | 15.6691i | 0.264970 | + | 0.0860941i | ||||
\(183\) | 82.7949 | + | 130.249i | 0.452431 | + | 0.711745i | ||||
\(184\) | −142.884 | − | 103.811i | −0.776542 | − | 0.564191i | ||||
\(185\) | 102.288 | − | 33.2354i | 0.552908 | − | 0.179651i | ||||
\(186\) | 61.3505 | + | 3.81396i | 0.329842 | + | 0.0205052i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 105.508i | − | 0.561211i | ||||||
\(189\) | 127.057 | − | 16.3396i | 0.672258 | − | 0.0864531i | ||||
\(190\) | 13.3224 | + | 9.67928i | 0.0701178 | + | 0.0509436i | ||||
\(191\) | −40.8438 | − | 56.2167i | −0.213842 | − | 0.294328i | 0.688599 | − | 0.725143i | \(-0.258226\pi\) |
−0.902440 | + | 0.430815i | \(0.858226\pi\) | |||||||
\(192\) | −31.7304 | − | 12.5356i | −0.165262 | − | 0.0652896i | ||||
\(193\) | 83.8998 | − | 258.217i | 0.434714 | − | 1.33791i | −0.458666 | − | 0.888609i | \(-0.651673\pi\) |
0.893380 | − | 0.449303i | \(-0.148327\pi\) | |||||||
\(194\) | 18.7606 | + | 25.8218i | 0.0967043 | + | 0.133102i | ||||
\(195\) | 78.7590 | + | 65.0563i | 0.403892 | + | 0.333622i | ||||
\(196\) | −27.6041 | − | 84.9567i | −0.140837 | − | 0.433453i | ||||
\(197\) | 106.612i | 0.541178i | 0.962695 | + | 0.270589i | \(0.0872185\pi\) | ||||
−0.962695 | + | 0.270589i | \(0.912782\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −289.272 | −1.45363 | −0.726813 | − | 0.686835i | \(-0.758999\pi\) | ||||
−0.726813 | + | 0.686835i | \(0.758999\pi\) | |||||||
\(200\) | −103.479 | + | 33.6222i | −0.517393 | + | 0.168111i | ||||
\(201\) | −65.5868 | + | 79.4012i | −0.326303 | + | 0.395031i | ||||
\(202\) | −59.4540 | + | 43.1958i | −0.294326 | + | 0.213841i | ||||
\(203\) | 242.114 | + | 78.6676i | 1.19268 | + | 0.387525i | ||||
\(204\) | 84.2482 | − | 213.251i | 0.412982 | − | 1.04535i | ||||
\(205\) | 63.0681 | − | 45.8217i | 0.307649 | − | 0.223520i | ||||
\(206\) | −9.11649 | + | 12.5478i | −0.0442548 | + | 0.0609115i | ||||
\(207\) | −267.238 | + | 51.3912i | −1.29100 | + | 0.248267i | ||||
\(208\) | −119.533 | −0.574676 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.76631 | − | 28.4125i | 0.00841101 | − | 0.135298i | ||||
\(211\) | −57.8517 | − | 178.049i | −0.274179 | − | 0.843835i | −0.989436 | − | 0.144973i | \(-0.953690\pi\) |
0.715257 | − | 0.698861i | \(-0.246310\pi\) | |||||||
\(212\) | 19.6477 | − | 27.0428i | 0.0926780 | − | 0.127560i | ||||
\(213\) | −36.7140 | + | 23.3378i | −0.172366 | + | 0.109567i | ||||
\(214\) | 20.6705 | − | 63.6174i | 0.0965913 | − | 0.297277i | ||||
\(215\) | 85.2019 | + | 27.6838i | 0.396288 | + | 0.128762i | ||||
\(216\) | 142.546 | − | 67.4667i | 0.659936 | − | 0.312346i | ||||
\(217\) | 99.2672 | + | 72.1219i | 0.457453 | + | 0.332359i | ||||
\(218\) | −126.381 | + | 41.0636i | −0.579728 | + | 0.188365i | ||||
\(219\) | −16.4239 | + | 264.191i | −0.0749949 | + | 1.20635i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 305.719i | − | 1.38335i | ||||||
\(222\) | −25.2575 | − | 98.0681i | −0.113773 | − | 0.441748i | ||||
\(223\) | 184.238 | + | 133.857i | 0.826180 | + | 0.600255i | 0.918476 | − | 0.395477i | \(-0.129421\pi\) |
−0.0922959 | + | 0.995732i | \(0.529421\pi\) | |||||||
\(224\) | 84.7362 | + | 116.629i | 0.378286 | + | 0.520667i | ||||
\(225\) | −71.1555 | + | 151.800i | −0.316247 | + | 0.674667i | ||||
\(226\) | −30.2383 | + | 93.0640i | −0.133798 | + | 0.411788i | ||||
\(227\) | 250.596 | + | 344.915i | 1.10395 | + | 1.51945i | 0.830049 | + | 0.557691i | \(0.188312\pi\) |
0.273896 | + | 0.961759i | \(0.411688\pi\) | |||||||
\(228\) | −53.0489 | + | 64.2225i | −0.232671 | + | 0.281678i | ||||
\(229\) | −31.3913 | − | 96.6123i | −0.137080 | − | 0.421888i | 0.858828 | − | 0.512264i | \(-0.171193\pi\) |
−0.995908 | + | 0.0903761i | \(0.971193\pi\) | |||||||
\(230\) | 60.4743i | 0.262932i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 313.402 | 1.35087 | ||||||||
\(233\) | 164.728 | − | 53.5233i | 0.706986 | − | 0.229714i | 0.0666145 | − | 0.997779i | \(-0.478780\pi\) |
0.640372 | + | 0.768065i | \(0.278780\pi\) | |||||||
\(234\) | 65.7388 | − | 70.2141i | 0.280935 | − | 0.300060i | ||||
\(235\) | −63.8947 | + | 46.4223i | −0.271893 | + | 0.197541i | ||||
\(236\) | 197.321 | + | 64.1135i | 0.836107 | + | 0.271668i | ||||
\(237\) | 261.379 | + | 103.262i | 1.10287 | + | 0.435706i | ||||
\(238\) | −68.9248 | + | 50.0768i | −0.289600 | + | 0.210407i | ||||
\(239\) | −94.8081 | + | 130.492i | −0.396687 | + | 0.545992i | −0.959909 | − | 0.280313i | \(-0.909562\pi\) |
0.563222 | + | 0.826306i | \(0.309562\pi\) | |||||||
\(240\) | 16.7374 | + | 64.9868i | 0.0697391 | + | 0.270778i | ||||
\(241\) | −56.7011 | −0.235274 | −0.117637 | − | 0.993057i | \(-0.537532\pi\) | ||||
−0.117637 | + | 0.993057i | \(0.537532\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 74.2296 | − | 231.385i | 0.305472 | − | 0.952201i | ||||
\(244\) | 53.6111 | + | 164.998i | 0.219718 | + | 0.676221i | ||||
\(245\) | −39.3037 | + | 54.0969i | −0.160423 | + | 0.220804i | ||||
\(246\) | −39.3770 | − | 61.9461i | −0.160069 | − | 0.251814i | ||||
\(247\) | −34.3210 | + | 105.629i | −0.138952 | + | 0.427649i | ||||
\(248\) | 143.662 | + | 46.6787i | 0.579284 | + | 0.188221i | ||||
\(249\) | 86.4881 | − | 54.9775i | 0.347342 | − | 0.220793i | ||||
\(250\) | 70.5911 | + | 51.2875i | 0.282365 | + | 0.205150i | ||||
\(251\) | 64.1886 | − | 20.8561i | 0.255731 | − | 0.0830922i | −0.178346 | − | 0.983968i | \(-0.557075\pi\) |
0.434077 | + | 0.900876i | \(0.357075\pi\) | |||||||
\(252\) | 142.891 | + | 17.8351i | 0.567029 | + | 0.0707741i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 102.084i | − | 0.401907i | ||||||
\(255\) | −166.212 | + | 42.8079i | −0.651811 | + | 0.167874i | ||||
\(256\) | 46.8767 | + | 34.0580i | 0.183112 | + | 0.133039i | ||||
\(257\) | 86.2117 | + | 118.660i | 0.335454 | + | 0.461713i | 0.943107 | − | 0.332490i | \(-0.107889\pi\) |
−0.607653 | + | 0.794203i | \(0.707889\pi\) | |||||||
\(258\) | 30.9939 | − | 78.4523i | 0.120131 | − | 0.304079i | ||||
\(259\) | 62.4668 | − | 192.253i | 0.241184 | − | 0.742289i | ||||
\(260\) | 67.4953 | + | 92.8994i | 0.259597 | + | 0.357305i | ||||
\(261\) | 330.045 | − | 352.513i | 1.26454 | − | 1.35063i | ||||
\(262\) | 30.8479 | + | 94.9402i | 0.117740 | + | 0.362367i | ||||
\(263\) | 146.192i | 0.555863i | 0.960601 | + | 0.277932i | \(0.0896488\pi\) | ||||
−0.960601 | + | 0.277932i | \(0.910351\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.0217 | −0.0944217 | ||||||||
\(266\) | 29.4360 | − | 9.56435i | 0.110662 | − | 0.0359562i | ||||
\(267\) | −331.870 | − | 274.130i | −1.24296 | − | 1.02671i | ||||
\(268\) | −93.6569 | + | 68.0457i | −0.349466 | + | 0.253902i | ||||
\(269\) | −54.2199 | − | 17.6171i | −0.201561 | − | 0.0654912i | 0.206497 | − | 0.978447i | \(-0.433794\pi\) |
−0.408058 | + | 0.912956i | \(0.633794\pi\) | |||||||
\(270\) | −47.3786 | − | 25.9089i | −0.175476 | − | 0.0959587i | ||||
\(271\) | −103.862 | + | 75.4601i | −0.383254 | + | 0.278451i | −0.762686 | − | 0.646769i | \(-0.776120\pi\) |
0.379431 | + | 0.925220i | \(0.376120\pi\) | |||||||
\(272\) | 118.049 | − | 162.480i | 0.434002 | − | 0.597352i | ||||
\(273\) | 185.932 | − | 47.8870i | 0.681071 | − | 0.175410i | ||||
\(274\) | 46.9944 | 0.171513 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −305.315 | − | 18.9804i | −1.10621 | − | 0.0687697i | ||||
\(277\) | 73.0137 | + | 224.713i | 0.263587 | + | 0.811238i | 0.992015 | + | 0.126116i | \(0.0402512\pi\) |
−0.728428 | + | 0.685122i | \(0.759749\pi\) | |||||||
\(278\) | −60.9756 | + | 83.9257i | −0.219337 | + | 0.301891i | ||||
\(279\) | 203.795 | − | 112.433i | 0.730449 | − | 0.402987i | ||||
\(280\) | 21.6177 | − | 66.5326i | 0.0772062 | − | 0.237616i | ||||
\(281\) | 193.994 | + | 63.0324i | 0.690370 | + | 0.224315i | 0.633130 | − | 0.774046i | \(-0.281770\pi\) |
0.0572400 | + | 0.998360i | \(0.481770\pi\) | |||||||
\(282\) | 39.8931 | + | 62.7581i | 0.141465 | + | 0.222546i | ||||
\(283\) | −387.691 | − | 281.674i | −1.36993 | − | 0.995313i | −0.997742 | − | 0.0671565i | \(-0.978607\pi\) |
−0.372189 | − | 0.928157i | \(-0.621393\pi\) | |||||||
\(284\) | −46.5087 | + | 15.1116i | −0.163763 | + | 0.0532099i | ||||
\(285\) | 62.2337 | + | 3.86886i | 0.218364 | + | 0.0135750i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 146.521i | − | 0.510528i | ||||||
\(288\) | 268.541 | − | 51.6418i | 0.932435 | − | 0.179312i | ||||
\(289\) | 181.756 | + | 132.054i | 0.628914 | + | 0.456933i | ||||
\(290\) | −63.0763 | − | 86.8171i | −0.217504 | − | 0.299369i | ||||
\(291\) | 112.402 | + | 44.4063i | 0.386261 | + | 0.152599i | ||||
\(292\) | −91.9476 | + | 282.986i | −0.314889 | + | 0.969129i | ||||
\(293\) | 5.49977 | + | 7.56978i | 0.0187705 | + | 0.0258354i | 0.818299 | − | 0.574793i | \(-0.194917\pi\) |
−0.799529 | + | 0.600628i | \(0.794917\pi\) | |||||||
\(294\) | 48.5421 | + | 40.0967i | 0.165109 | + | 0.136383i | ||||
\(295\) | −47.9925 | − | 147.706i | −0.162686 | − | 0.500698i | ||||
\(296\) | − | 248.860i | − | 0.840743i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −58.8913 | −0.197622 | ||||||||
\(299\) | −387.910 | + | 126.040i | −1.29736 | + | 0.421537i | ||||
\(300\) | −120.017 | + | 145.296i | −0.400056 | + | 0.484319i | ||||
\(301\) | 136.223 | − | 98.9715i | 0.452567 | − | 0.328809i | ||||
\(302\) | −4.69714 | − | 1.52619i | −0.0155535 | − | 0.00505362i | ||||
\(303\) | −102.244 | + | 258.802i | −0.337439 | + | 0.854133i | ||||
\(304\) | −59.0275 | + | 42.8860i | −0.194170 | + | 0.141072i | ||||
\(305\) | 76.3334 | − | 105.064i | 0.250273 | − | 0.344472i | ||||
\(306\) | 30.5189 | + | 158.701i | 0.0997351 | + | 0.518630i | ||||
\(307\) | 72.5271 | 0.236245 | 0.118122 | − | 0.992999i | \(-0.462313\pi\) | ||||
0.118122 | + | 0.992999i | \(0.462313\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.64391 | + | 58.6152i | −0.0117926 | + | 0.189693i | ||||
\(310\) | −15.9832 | − | 49.1913i | −0.0515588 | − | 0.158682i | ||||
\(311\) | −223.738 | + | 307.949i | −0.719416 | + | 0.990191i | 0.280127 | + | 0.959963i | \(0.409623\pi\) |
−0.999543 | + | 0.0302281i | \(0.990377\pi\) | |||||||
\(312\) | 199.478 | − | 126.801i | 0.639353 | − | 0.406414i | ||||
\(313\) | 16.4090 | − | 50.5017i | 0.0524249 | − | 0.161347i | −0.921416 | − | 0.388577i | \(-0.872967\pi\) |
0.973841 | + | 0.227230i | \(0.0729668\pi\) | |||||||
\(314\) | 74.4439 | + | 24.1883i | 0.237082 | + | 0.0770327i | ||||
\(315\) | −52.0699 | − | 94.3813i | −0.165301 | − | 0.299623i | ||||
\(316\) | 255.579 | + | 185.689i | 0.808794 | + | 0.587623i | ||||
\(317\) | −69.6617 | + | 22.6345i | −0.219753 | + | 0.0714021i | −0.416824 | − | 0.908987i | \(-0.636857\pi\) |
0.197071 | + | 0.980389i | \(0.436857\pi\) | |||||||
\(318\) | −1.46182 | + | 23.5145i | −0.00459692 | + | 0.0739451i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 28.7075i | 0.0897109i | ||||||||
\(321\) | −63.1720 | − | 245.280i | −0.196797 | − | 0.764111i | ||||
\(322\) | 91.9554 | + | 66.8095i | 0.285576 | + | 0.207483i | ||||
\(323\) | −109.686 | − | 150.970i | −0.339586 | − | 0.467400i | ||||
\(324\) | 145.676 | − | 231.067i | 0.449616 | − | 0.713171i | ||||
\(325\) | −77.6472 | + | 238.974i | −0.238914 | + | 0.735303i | ||||
\(326\) | −96.8037 | − | 133.239i | −0.296944 | − | 0.408708i | ||||
\(327\) | −320.443 | + | 387.937i | −0.979947 | + | 1.18635i | ||||
\(328\) | −55.7406 | − | 171.552i | −0.169941 | − | 0.523024i | ||||
\(329\) | 148.442i | 0.451191i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −167.351 | −0.505591 | −0.252795 | − | 0.967520i | \(-0.581350\pi\) | ||||
−0.252795 | + | 0.967520i | \(0.581350\pi\) | |||||||
\(332\) | 109.562 | − | 35.5988i | 0.330006 | − | 0.107225i | ||||
\(333\) | −279.917 | − | 262.075i | −0.840590 | − | 0.787013i | ||||
\(334\) | −40.4860 | + | 29.4148i | −0.121216 | + | 0.0880684i | ||||
\(335\) | 82.4161 | + | 26.7786i | 0.246018 | + | 0.0799362i | ||||
\(336\) | 117.308 | + | 46.3443i | 0.349130 | + | 0.137930i | ||||
\(337\) | −347.288 | + | 252.320i | −1.03053 | + | 0.748723i | −0.968414 | − | 0.249346i | \(-0.919784\pi\) |
−0.0621140 | + | 0.998069i | \(0.519784\pi\) | |||||||
\(338\) | 6.03377 | − | 8.30478i | 0.0178514 | − | 0.0245703i | ||||
\(339\) | 92.4125 | + | 358.813i | 0.272603 | + | 1.05844i | ||||
\(340\) | −192.935 | −0.567455 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 7.27163 | − | 58.2589i | 0.0212621 | − | 0.170348i | ||||
\(343\) | 110.678 | + | 340.633i | 0.322678 | + | 0.993100i | ||||
\(344\) | 121.842 | − | 167.702i | 0.354193 | − | 0.487505i | ||||
\(345\) | 122.841 | + | 193.248i | 0.356061 | + | 0.560139i | ||||
\(346\) | −47.3401 | + | 145.698i | −0.136821 | + | 0.421092i | ||||
\(347\) | −490.113 | − | 159.247i | −1.41243 | − | 0.458926i | −0.499241 | − | 0.866463i | \(-0.666388\pi\) |
−0.913189 | + | 0.407537i | \(0.866388\pi\) | |||||||
\(348\) | 458.108 | − | 291.203i | 1.31640 | − | 0.836791i | ||||
\(349\) | −226.538 | − | 164.589i | −0.649106 | − | 0.471603i | 0.213861 | − | 0.976864i | \(-0.431396\pi\) |
−0.862966 | + | 0.505261i | \(0.831396\pi\) | |||||||
\(350\) | 66.5955 | − | 21.6382i | 0.190273 | − | 0.0618234i | ||||
\(351\) | 67.4456 | − | 357.907i | 0.192153 | − | 1.01968i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 373.911i | 1.05924i | 0.848236 | + | 0.529619i | \(0.177665\pi\) | ||||
−0.848236 | + | 0.529619i | \(0.822335\pi\) | |||||||
\(354\) | −141.612 | + | 36.4724i | −0.400035 | + | 0.103029i | ||||
\(355\) | 29.6149 | + | 21.5164i | 0.0834221 | + | 0.0606097i | ||||
\(356\) | −284.408 | − | 391.454i | −0.798898 | − | 1.09959i | ||||
\(357\) | −118.531 | + | 300.029i | −0.332021 | + | 0.840417i | ||||
\(358\) | 7.59272 | − | 23.3680i | 0.0212087 | − | 0.0652737i | ||||
\(359\) | −63.9874 | − | 88.0711i | −0.178238 | − | 0.245324i | 0.710545 | − | 0.703652i | \(-0.248448\pi\) |
−0.888783 | + | 0.458328i | \(0.848448\pi\) | |||||||
\(360\) | −96.8702 | − | 90.6959i | −0.269084 | − | 0.251933i | ||||
\(361\) | −90.6058 | − | 278.856i | −0.250985 | − | 0.772454i | ||||
\(362\) | 80.9231i | 0.223544i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 215.826 | 0.592929 | ||||||||
\(365\) | 211.830 | − | 68.8279i | 0.580357 | − | 0.188569i | ||||
\(366\) | −94.2757 | − | 77.8734i | −0.257584 | − | 0.212769i | ||||
\(367\) | −386.681 | + | 280.941i | −1.05363 | + | 0.765506i | −0.972899 | − | 0.231231i | \(-0.925725\pi\) |
−0.0807290 | + | 0.996736i | \(0.525725\pi\) | |||||||
\(368\) | −254.830 | − | 82.7992i | −0.692472 | − | 0.224998i | ||||
\(369\) | −251.662 | − | 117.965i | −0.682010 | − | 0.319689i | ||||
\(370\) | −68.9379 | + | 50.0863i | −0.186319 | + | 0.135368i | ||||
\(371\) | −27.6430 | + | 38.0473i | −0.0745094 | + | 0.102553i | ||||
\(372\) | 253.367 | − | 65.2550i | 0.681095 | − | 0.175417i | ||||
\(373\) | −207.081 | −0.555178 | −0.277589 | − | 0.960700i | \(-0.589535\pi\) | ||||
−0.277589 | + | 0.960700i | \(0.589535\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 329.757 | + | 20.4999i | 0.879351 | + | 0.0546663i | ||||
\(376\) | 56.4712 | + | 173.800i | 0.150189 | + | 0.462235i | ||||
\(377\) | 425.422 | − | 585.543i | 1.12844 | − | 1.55317i | ||||
\(378\) | −91.7381 | + | 43.4194i | −0.242693 | + | 0.114866i | ||||
\(379\) | 95.9825 | − | 295.404i | 0.253252 | − | 0.779430i | −0.740917 | − | 0.671597i | \(-0.765609\pi\) |
0.994169 | − | 0.107833i | \(-0.0343912\pi\) | |||||||
\(380\) | 66.6610 | + | 21.6595i | 0.175424 | + | 0.0569986i | ||||
\(381\) | −207.363 | − | 326.215i | −0.544261 | − | 0.856207i | ||||
\(382\) | 44.5397 | + | 32.3600i | 0.116596 | + | 0.0847121i | ||||
\(383\) | −342.256 | + | 111.206i | −0.893619 | + | 0.290354i | −0.719601 | − | 0.694388i | \(-0.755675\pi\) |
−0.174018 | + | 0.984742i | \(0.555675\pi\) | |||||||
\(384\) | 390.891 | + | 24.3004i | 1.01795 | + | 0.0632823i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 215.110i | 0.557280i | ||||||||
\(387\) | −60.3175 | − | 313.655i | −0.155859 | − | 0.810478i | ||||
\(388\) | 109.908 | + | 79.8526i | 0.283267 | + | 0.205806i | ||||
\(389\) | 367.096 | + | 505.264i | 0.943691 | + | 1.29888i | 0.954273 | + | 0.298935i | \(0.0966314\pi\) |
−0.0105826 | + | 0.999944i | \(0.503369\pi\) | |||||||
\(390\) | −75.2734 | − | 29.7380i | −0.193009 | − | 0.0762513i | ||||
\(391\) | 211.769 | − | 651.758i | 0.541609 | − | 1.66690i | ||||
\(392\) | 90.9433 | + | 125.173i | 0.231998 | + | 0.319318i | ||||
\(393\) | 291.427 | + | 240.724i | 0.741545 | + | 0.612529i | ||||
\(394\) | −26.1019 | − | 80.3332i | −0.0662484 | − | 0.203891i | ||||
\(395\) | − | 236.478i | − | 0.598679i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −78.7284 | −0.198308 | −0.0991541 | − | 0.995072i | \(-0.531614\pi\) | ||||
−0.0991541 | + | 0.995072i | \(0.531614\pi\) | |||||||
\(398\) | 217.969 | − | 70.8224i | 0.547661 | − | 0.177946i | ||||
\(399\) | 74.6361 | − | 90.3565i | 0.187058 | − | 0.226457i | ||||
\(400\) | −133.543 | + | 97.0244i | −0.333857 | + | 0.242561i | ||||
\(401\) | −751.433 | − | 244.155i | −1.87390 | − | 0.608867i | −0.989977 | − | 0.141232i | \(-0.954894\pi\) |
−0.883922 | − | 0.467635i | \(-0.845106\pi\) | |||||||
\(402\) | 29.9805 | − | 75.8872i | 0.0745783 | − | 0.188774i | ||||
\(403\) | 282.224 | − | 205.048i | 0.700307 | − | 0.508803i | ||||
\(404\) | −183.858 | + | 253.059i | −0.455095 | + | 0.626384i | ||||
\(405\) | −204.029 | + | 13.4470i | −0.503775 | + | 0.0332025i | ||||
\(406\) | −201.696 | −0.496787 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −24.6414 | + | 396.376i | −0.0603955 | + | 0.971510i | ||||
\(409\) | −156.887 | − | 482.847i | −0.383586 | − | 1.18056i | −0.937501 | − | 0.347982i | \(-0.886867\pi\) |
0.553915 | − | 0.832573i | \(-0.313133\pi\) | |||||||
\(410\) | −36.3039 | + | 49.9681i | −0.0885462 | + | 0.121873i | ||||
\(411\) | 150.173 | − | 95.4595i | 0.365384 | − | 0.232262i | ||||
\(412\) | −20.4001 | + | 62.7851i | −0.0495149 | + | 0.152391i | ||||
\(413\) | −277.617 | − | 90.2033i | −0.672196 | − | 0.218410i | ||||
\(414\) | 188.784 | − | 104.152i | 0.456000 | − | 0.251574i | ||||
\(415\) | −69.7645 | − | 50.6869i | −0.168107 | − | 0.122137i | ||||
\(416\) | 389.802 | − | 126.654i | 0.937024 | − | 0.304458i | ||||
\(417\) | −24.3723 | + | 392.047i | −0.0584467 | + | 0.940162i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 334.392i | 0.798073i | 0.916935 | + | 0.399036i | \(0.130655\pi\) | ||||
−0.916935 | + | 0.399036i | \(0.869345\pi\) | |||||||
\(420\) | −30.2207 | − | 117.339i | −0.0719542 | − | 0.279379i | ||||
\(421\) | 358.649 | + | 260.574i | 0.851899 | + | 0.618941i | 0.925669 | − | 0.378334i | \(-0.123503\pi\) |
−0.0737700 | + | 0.997275i | \(0.523503\pi\) | |||||||
\(422\) | 87.1836 | + | 119.998i | 0.206596 | + | 0.284355i | ||||
\(423\) | 254.960 | + | 119.511i | 0.602742 | + | 0.282533i | ||||
\(424\) | −17.8911 | + | 55.0631i | −0.0421960 | + | 0.129866i | ||||
\(425\) | −248.152 | − | 341.552i | −0.583887 | − | 0.803651i | ||||
\(426\) | 21.9505 | − | 26.5739i | 0.0515271 | − | 0.0623801i | ||||
\(427\) | −75.4270 | − | 232.141i | −0.176644 | − | 0.543655i | ||||
\(428\) | − | 284.715i | − | 0.665222i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −70.9783 | −0.165066 | ||||||||
\(431\) | −756.378 | + | 245.762i | −1.75494 | + | 0.570214i | −0.996656 | − | 0.0817130i | \(-0.973961\pi\) |
−0.758282 | + | 0.651927i | \(0.773961\pi\) | |||||||
\(432\) | 174.045 | − | 164.173i | 0.402882 | − | 0.380030i | ||||
\(433\) | 15.0656 | − | 10.9458i | 0.0347936 | − | 0.0252791i | −0.570253 | − | 0.821469i | \(-0.693155\pi\) |
0.605046 | + | 0.796190i | \(0.293155\pi\) | |||||||
\(434\) | −92.4564 | − | 30.0409i | −0.213033 | − | 0.0692187i | ||||
\(435\) | −377.914 | − | 149.301i | −0.868767 | − | 0.343221i | ||||
\(436\) | −457.587 | + | 332.456i | −1.04951 | + | 0.762515i | ||||
\(437\) | −146.337 | + | 201.416i | −0.334867 | + | 0.460905i | ||||
\(438\) | −52.3064 | − | 203.092i | −0.119421 | − | 0.463679i | ||||
\(439\) | −254.891 | −0.580618 | −0.290309 | − | 0.956933i | \(-0.593758\pi\) | ||||
−0.290309 | + | 0.956933i | \(0.593758\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 236.567 | + | 29.5272i | 0.536432 | + | 0.0669551i | ||||
\(442\) | 74.8493 | + | 230.363i | 0.169342 | + | 0.521182i | ||||
\(443\) | −36.1793 | + | 49.7965i | −0.0816689 | + | 0.112408i | −0.847897 | − | 0.530161i | \(-0.822131\pi\) |
0.766228 | + | 0.642569i | \(0.222131\pi\) | |||||||
\(444\) | −231.233 | − | 363.765i | −0.520795 | − | 0.819291i | ||||
\(445\) | −111.925 | + | 344.471i | −0.251518 | + | 0.774092i | ||||
\(446\) | −171.597 | − | 55.7554i | −0.384748 | − | 0.125012i | ||||
\(447\) | −188.189 | + | 119.625i | −0.421005 | + | 0.267618i | ||||
\(448\) | 43.6517 | + | 31.7148i | 0.0974369 | + | 0.0707920i | ||||
\(449\) | −130.706 | + | 42.4691i | −0.291105 | + | 0.0945859i | −0.450929 | − | 0.892560i | \(-0.648907\pi\) |
0.159824 | + | 0.987146i | \(0.448907\pi\) | |||||||
\(450\) | 16.4512 | − | 131.804i | 0.0365582 | − | 0.292897i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 416.502i | 0.921464i | ||||||||
\(453\) | −18.1101 | + | 4.66426i | −0.0399781 | + | 0.0102964i | ||||
\(454\) | −273.272 | − | 198.544i | −0.601920 | − | 0.437321i | ||||
\(455\) | −94.9612 | − | 130.703i | −0.208706 | − | 0.287259i | ||||
\(456\) | 53.0123 | − | 134.186i | 0.116255 | − | 0.294267i | ||||
\(457\) | −95.0513 | + | 292.538i | −0.207990 | + | 0.640126i | 0.791588 | + | 0.611056i | \(0.209255\pi\) |
−0.999577 | + | 0.0290707i | \(0.990745\pi\) | |||||||
\(458\) | 47.3072 | + | 65.1128i | 0.103291 | + | 0.142168i | ||||
\(459\) | 419.892 | + | 445.142i | 0.914798 | + | 0.969807i | ||||
\(460\) | 79.5416 | + | 244.804i | 0.172917 | + | 0.532183i | ||||
\(461\) | − | 528.162i | − | 1.14569i | −0.819664 | − | 0.572844i | \(-0.805840\pi\) | ||
0.819664 | − | 0.572844i | \(-0.194160\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −45.9484 | −0.0992406 | −0.0496203 | − | 0.998768i | \(-0.515801\pi\) | ||||
−0.0496203 | + | 0.998768i | \(0.515801\pi\) | |||||||
\(464\) | 452.196 | − | 146.927i | 0.974560 | − | 0.316654i | ||||
\(465\) | −150.997 | − | 124.726i | −0.324725 | − | 0.268228i | ||||
\(466\) | −111.020 | + | 80.6607i | −0.238240 | + | 0.173092i | ||||
\(467\) | 341.492 | + | 110.958i | 0.731247 | + | 0.237597i | 0.650893 | − | 0.759170i | \(-0.274395\pi\) |
0.0803544 | + | 0.996766i | \(0.474395\pi\) | |||||||
\(468\) | 173.763 | − | 370.697i | 0.371288 | − | 0.792089i | ||||
\(469\) | 131.769 | − | 95.7356i | 0.280957 | − | 0.204127i | ||||
\(470\) | 36.7797 | − | 50.6230i | 0.0782548 | − | 0.107708i | ||||
\(471\) | 287.022 | − | 73.9227i | 0.609388 | − | 0.156948i | ||||
\(472\) | −359.359 | −0.761353 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −222.234 | − | 13.8155i | −0.468847 | − | 0.0291467i | ||||
\(475\) | 47.3954 | + | 145.868i | 0.0997798 | + | 0.307091i | ||||
\(476\) | −213.146 | + | 293.371i | −0.447786 | + | 0.616325i | ||||
\(477\) | 43.0936 | + | 78.1110i | 0.0903430 | + | 0.163755i | ||||
\(478\) | 39.4904 | − | 121.539i | 0.0826159 | − | 0.254266i | ||||
\(479\) | −549.141 | − | 178.427i | −1.14643 | − | 0.372498i | −0.326633 | − | 0.945151i | \(-0.605914\pi\) |
−0.819798 | + | 0.572653i | \(0.805914\pi\) | |||||||
\(480\) | −123.440 | − | 194.191i | −0.257167 | − | 0.404564i | ||||
\(481\) | −464.956 | − | 337.810i | −0.966645 | − | 0.702308i | ||||
\(482\) | 42.7248 | − | 13.8821i | 0.0886407 | − | 0.0288011i | ||||
\(483\) | 429.557 | + | 26.7041i | 0.889352 | + | 0.0552880i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 101.694i | − | 0.209678i | ||||||
\(486\) | 0.717239 | + | 192.524i | 0.00147580 | + | 0.396141i | ||||
\(487\) | 490.992 | + | 356.726i | 1.00820 | + | 0.732498i | 0.963830 | − | 0.266517i | \(-0.0858730\pi\) |
0.0443668 | + | 0.999015i | \(0.485873\pi\) | |||||||
\(488\) | −176.625 | − | 243.103i | −0.361936 | − | 0.498162i | ||||
\(489\) | −579.987 | − | 229.134i | −1.18607 | − | 0.468576i | ||||
\(490\) | 16.3712 | − | 50.3853i | 0.0334106 | − | 0.102827i | ||||
\(491\) | −451.929 | − | 622.027i | −0.920425 | − | 1.26686i | −0.963479 | − | 0.267784i | \(-0.913709\pi\) |
0.0430540 | − | 0.999073i | \(-0.486291\pi\) | |||||||
\(492\) | −240.878 | − | 198.970i | −0.489590 | − | 0.404410i | ||||
\(493\) | 375.785 | + | 1156.55i | 0.762241 | + | 2.34594i | ||||
\(494\) | − | 87.9956i | − | 0.178129i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 229.168 | 0.462033 | ||||||||
\(497\) | 65.4345 | − | 21.2610i | 0.131659 | − | 0.0427786i | ||||
\(498\) | −51.7095 | + | 62.6009i | −0.103834 | + | 0.125705i | ||||
\(499\) | 402.917 | − | 292.736i | 0.807448 | − | 0.586645i | −0.105641 | − | 0.994404i | \(-0.533690\pi\) |
0.913090 | + | 0.407759i | \(0.133690\pi\) | |||||||
\(500\) | 353.216 | + | 114.767i | 0.706432 | + | 0.229534i | ||||
\(501\) | −69.6246 | + | 176.235i | −0.138971 | + | 0.351767i | ||||
\(502\) | −43.2605 | + | 31.4306i | −0.0861763 | + | 0.0626108i | ||||
\(503\) | −100.227 | + | 137.950i | −0.199258 | + | 0.274255i | −0.896940 | − | 0.442153i | \(-0.854215\pi\) |
0.697682 | + | 0.716408i | \(0.254215\pi\) | |||||||
\(504\) | −244.928 | + | 47.1008i | −0.485967 | + | 0.0934540i | ||||
\(505\) | 234.147 | 0.463657 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.41173 | − | 38.7946i | 0.00475687 | − | 0.0765180i | ||||
\(508\) | −134.271 | − | 413.244i | −0.264313 | − | 0.813473i | ||||
\(509\) | 242.636 | − | 333.960i | 0.476692 | − | 0.656110i | −0.501173 | − | 0.865347i | \(-0.667098\pi\) |
0.977865 | + | 0.209237i | \(0.0670979\pi\) | |||||||
\(510\) | 114.761 | − | 72.9498i | 0.225022 | − | 0.143039i | ||||
\(511\) | 129.364 | − | 398.141i | 0.253158 | − | 0.779141i | ||||
\(512\) | 452.976 | + | 147.181i | 0.884719 | + | 0.287463i | ||||
\(513\) | −95.1042 | − | 200.940i | −0.185388 | − | 0.391695i | ||||
\(514\) | −94.0129 | − | 68.3044i | −0.182905 | − | 0.132888i | ||||
\(515\) | 46.9981 | − | 15.2706i | 0.0912585 | − | 0.0296517i | ||||
\(516\) | 22.2772 | − | 358.346i | 0.0431728 | − | 0.694469i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 160.158i | 0.309186i | ||||||||
\(519\) | 144.678 | + | 561.745i | 0.278763 | + | 1.08236i | ||||
\(520\) | −160.906 | − | 116.905i | −0.309435 | − | 0.224818i | ||||
\(521\) | −65.4029 | − | 90.0193i | −0.125533 | − | 0.172782i | 0.741624 | − | 0.670815i | \(-0.234056\pi\) |
−0.867158 | + | 0.498033i | \(0.834056\pi\) | |||||||
\(522\) | −162.386 | + | 346.427i | −0.311085 | + | 0.663654i | ||||
\(523\) | −94.5104 | + | 290.873i | −0.180708 | + | 0.556163i | −0.999848 | − | 0.0174310i | \(-0.994451\pi\) |
0.819140 | + | 0.573594i | \(0.194451\pi\) | |||||||
\(524\) | 249.749 | + | 343.750i | 0.476620 | + | 0.656011i | ||||
\(525\) | 168.855 | − | 204.421i | 0.321629 | − | 0.389373i | ||||
\(526\) | −35.7922 | − | 110.157i | −0.0680460 | − | 0.209424i | ||||
\(527\) | 586.126i | 1.11219i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −385.285 | −0.728328 | ||||||||
\(530\) | 18.8541 | − | 6.12608i | 0.0355738 | − | 0.0115586i | ||||
\(531\) | −378.442 | + | 404.205i | −0.712697 | + | 0.761215i | ||||
\(532\) | 106.579 | − | 77.4342i | 0.200337 | − | 0.145553i | ||||
\(533\) | −396.182 | − | 128.727i | −0.743306 | − | 0.241515i | ||||
\(534\) | 317.183 | + | 125.308i | 0.593975 | + | 0.234659i | ||||
\(535\) | −172.422 | + | 125.272i | −0.322284 | + | 0.234153i | ||||
\(536\) | 117.859 | − | 162.219i | 0.219886 | − | 0.302647i | ||||
\(537\) | −23.2044 | − | 90.0964i | −0.0432112 | − | 0.167777i | ||||
\(538\) | 45.1684 | 0.0839562 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −225.870 | − | 42.5639i | −0.418277 | − | 0.0788220i | ||||
\(541\) | 96.3495 | + | 296.533i | 0.178095 | + | 0.548121i | 0.999761 | − | 0.0218484i | \(-0.00695512\pi\) |
−0.821666 | + | 0.569969i | \(0.806955\pi\) | |||||||
\(542\) | 59.7861 | − | 82.2884i | 0.110306 | − | 0.151824i | ||||
\(543\) | 164.379 | + | 258.593i | 0.302723 | + | 0.476230i | ||||
\(544\) | −212.802 | + | 654.937i | −0.391180 | + | 1.20393i | ||||
\(545\) | 402.667 | + | 130.834i | 0.738838 | + | 0.240063i | ||||
\(546\) | −128.378 | + | 81.6052i | −0.235124 | + | 0.149460i | ||||
\(547\) | 714.349 | + | 519.005i | 1.30594 | + | 0.948820i | 0.999995 | − | 0.00322943i | \(-0.00102796\pi\) |
0.305944 | + | 0.952050i | \(0.401028\pi\) | |||||||
\(548\) | 190.237 | − | 61.8116i | 0.347147 | − | 0.112795i | ||||
\(549\) | −459.446 | − | 57.3460i | −0.836877 | − | 0.104455i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 441.786i | − | 0.801789i | ||||||
\(552\) | 513.098 | − | 132.149i | 0.929525 | − | 0.239400i | ||||
\(553\) | −359.582 | − | 261.251i | −0.650238 | − | 0.472426i | ||||
\(554\) | −110.033 | − | 151.447i | −0.198616 | − | 0.273371i | ||||
\(555\) | −118.554 | + | 300.086i | −0.213611 | + | 0.540695i | ||||
\(556\) | −136.446 | + | 419.938i | −0.245407 | + | 0.755284i | ||||
\(557\) | 190.382 | + | 262.038i | 0.341798 | + | 0.470445i | 0.944966 | − | 0.327170i | \(-0.106095\pi\) |
−0.603167 | + | 0.797615i | \(0.706095\pi\) | |||||||
\(558\) | −126.035 | + | 134.615i | −0.225869 | + | 0.241245i | ||||
\(559\) | −147.932 | − | 455.287i | −0.264636 | − | 0.814467i | ||||
\(560\) | − | 106.132i | − | 0.189521i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −161.609 | −0.287560 | ||||||||
\(563\) | −470.984 | + | 153.032i | −0.836562 | + | 0.271815i | −0.695807 | − | 0.718229i | \(-0.744953\pi\) |
−0.140755 | + | 0.990044i | \(0.544953\pi\) | |||||||
\(564\) | 244.035 | + | 201.577i | 0.432687 | + | 0.357407i | ||||
\(565\) | 252.231 | − | 183.256i | 0.446426 | − | 0.324348i | ||||
\(566\) | 361.091 | + | 117.326i | 0.637970 | + | 0.207289i | ||||
\(567\) | −204.955 | + | 325.096i | −0.361473 | + | 0.573361i | ||||
\(568\) | 68.5246 | − | 49.7860i | 0.120642 | − | 0.0876515i | ||||
\(569\) | 320.018 | − | 440.467i | 0.562422 | − | 0.774108i | −0.429210 | − | 0.903205i | \(-0.641208\pi\) |
0.991632 | + | 0.129097i | \(0.0412079\pi\) | |||||||
\(570\) | −47.8409 | + | 12.3215i | −0.0839314 | + | 0.0216166i | ||||
\(571\) | 779.886 | 1.36582 | 0.682912 | − | 0.730500i | \(-0.260713\pi\) | ||||
0.682912 | + | 0.730500i | \(0.260713\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 208.061 | + | 12.9345i | 0.363109 | + | 0.0225732i | ||||
\(574\) | 35.8729 | + | 110.405i | 0.0624963 | + | 0.192344i | ||||
\(575\) | −331.070 | + | 455.678i | −0.575773 | + | 0.792484i | ||||
\(576\) | 89.6169 | − | 49.4413i | 0.155585 | − | 0.0858357i | ||||
\(577\) | 350.826 | − | 1079.73i | 0.608017 | − | 1.87128i | 0.133471 | − | 0.991053i | \(-0.457388\pi\) |
0.474546 | − | 0.880231i | \(-0.342612\pi\) | |||||||
\(578\) | −169.286 | − | 55.0043i | −0.292882 | − | 0.0951632i | ||||
\(579\) | 436.952 | + | 687.393i | 0.754666 | + | 1.18721i | ||||
\(580\) | −369.527 | − | 268.477i | −0.637116 | − | 0.462892i | ||||
\(581\) | −154.146 | + | 50.0850i | −0.265311 | + | 0.0862049i | ||||
\(582\) | −95.5680 | − | 5.94115i | −0.164206 | − | 0.0102082i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 515.370i | − | 0.882482i | ||||||
\(585\) | −300.946 | + | 57.8734i | −0.514437 | + | 0.0989289i | ||||
\(586\) | −5.99744 | − | 4.35739i | −0.0102345 | − | 0.00743582i | ||||
\(587\) | 368.838 | + | 507.662i | 0.628344 | + | 0.864841i | 0.997927 | − | 0.0643568i | \(-0.0204996\pi\) |
−0.369583 | + | 0.929198i | \(0.620500\pi\) | |||||||
\(588\) | 249.241 | + | 98.4667i | 0.423879 | + | 0.167460i | ||||
\(589\) | 65.8005 | − | 202.513i | 0.111716 | − | 0.343825i | ||||
\(590\) | 72.3256 | + | 99.5477i | 0.122586 | + | 0.168725i | ||||
\(591\) | −246.590 | − | 203.688i | −0.417242 | − | 0.344649i | ||||
\(592\) | −116.669 | − | 359.070i | −0.197076 | − | 0.606538i | ||||
\(593\) | 961.677i | 1.62171i | 0.585244 | + | 0.810857i | \(0.300999\pi\) | ||||
−0.585244 | + | 0.810857i | \(0.699001\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 271.446 | 0.456211 | ||||||||
\(596\) | −238.396 | + | 77.4595i | −0.399993 | + | 0.129966i | ||||
\(597\) | 552.668 | − | 669.075i | 0.925741 | − | 1.12073i | ||||
\(598\) | 261.436 | − | 189.944i | 0.437183 | − | 0.317632i | ||||
\(599\) | 934.344 | + | 303.587i | 1.55984 | + | 0.506822i | 0.956765 | − | 0.290863i | \(-0.0939422\pi\) |
0.603074 | + | 0.797685i | \(0.293942\pi\) | |||||||
\(600\) | 119.934 | − | 303.579i | 0.199890 | − | 0.505965i | ||||
\(601\) | 259.888 | − | 188.820i | 0.432426 | − | 0.314176i | −0.350192 | − | 0.936678i | \(-0.613884\pi\) |
0.782618 | + | 0.622502i | \(0.213884\pi\) | |||||||
\(602\) | −78.4138 | + | 107.927i | −0.130256 | + | 0.179281i | ||||
\(603\) | −58.3453 | − | 303.400i | −0.0967584 | − | 0.503151i | ||||
\(604\) | −21.0217 | −0.0348042 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.6793 | − | 220.043i | 0.0225731 | − | 0.363107i | ||||
\(607\) | −154.991 | − | 477.012i | −0.255339 | − | 0.785851i | −0.993763 | − | 0.111515i | \(-0.964430\pi\) |
0.738424 | − | 0.674337i | \(-0.235570\pi\) | |||||||
\(608\) | 147.051 | − | 202.398i | 0.241860 | − | 0.332891i | ||||
\(609\) | −644.526 | + | 409.703i | −1.05834 | + | 0.672747i | ||||
\(610\) | −31.7951 | + | 97.8554i | −0.0521232 | + | 0.160419i | ||||
\(611\) | 401.375 | + | 130.415i | 0.656915 | + | 0.213445i | ||||
\(612\) | 332.281 | + | 602.289i | 0.542943 | + | 0.984133i | ||||
\(613\) | 299.134 | + | 217.334i | 0.487984 | + | 0.354541i | 0.804408 | − | 0.594077i | \(-0.202482\pi\) |
−0.316425 | + | 0.948618i | \(0.602482\pi\) | |||||||
\(614\) | −54.6499 | + | 17.7568i | −0.0890063 | + | 0.0289199i | ||||
\(615\) | −14.5109 | + | 233.419i | −0.0235949 | + | 0.379543i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 560.582i | − | 0.908560i | −0.890859 | − | 0.454280i | \(-0.849897\pi\) | ||
0.890859 | − | 0.454280i | \(-0.150103\pi\) | |||||||
\(618\) | −11.6050 | − | 45.0593i | −0.0187784 | − | 0.0729114i | ||||
\(619\) | −334.456 | − | 242.996i | −0.540316 | − | 0.392563i | 0.283886 | − | 0.958858i | \(-0.408376\pi\) |
−0.824203 | + | 0.566295i | \(0.808376\pi\) | |||||||
\(620\) | −129.402 | − | 178.107i | −0.208713 | − | 0.287269i | ||||
\(621\) | 391.705 | − | 716.297i | 0.630765 | − | 1.15346i | ||||
\(622\) | 93.1937 | − | 286.821i | 0.149829 | − | 0.461127i | ||||
\(623\) | 400.142 | + | 550.748i | 0.642282 | + | 0.884025i | ||||
\(624\) | 228.373 | − | 276.475i | 0.365982 | − | 0.443068i | ||||
\(625\) | 57.9978 | + | 178.499i | 0.0927965 | + | 0.285598i | ||||
\(626\) | 42.0710i | 0.0672060i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 333.168 | 0.530523 | ||||||||
\(629\) | 918.366 | − | 298.395i | 1.46004 | − | 0.474396i | ||||
\(630\) | 62.3425 | + | 58.3689i | 0.0989564 | + | 0.0926491i | ||||
\(631\) | −886.280 | + | 643.920i | −1.40456 | + | 1.02048i | −0.410479 | + | 0.911870i | \(0.634639\pi\) |
−0.994085 | + | 0.108606i | \(0.965361\pi\) | |||||||
\(632\) | −520.397 | − | 169.087i | −0.823412 | − | 0.267543i | ||||
\(633\) | 522.350 | + | 206.363i | 0.825197 | + | 0.326008i | ||||
\(634\) | 46.9492 | − | 34.1106i | 0.0740523 | − | 0.0538022i | ||||
\(635\) | −191.180 | + | 263.137i | −0.301071 | + | 0.414389i | ||||
\(636\) | 25.0110 | + | 97.1111i | 0.0393255 | + | 0.152690i | ||||
\(637\) | 357.315 | 0.560934 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.1644 | − | 129.506i | 0.0252964 | − | 0.202670i | ||||
\(640\) | −101.836 | − | 313.420i | −0.159119 | − | 0.489718i | ||||
\(641\) | −580.698 | + | 799.262i | −0.905925 | + | 1.24690i | 0.0626148 | + | 0.998038i | \(0.480056\pi\) |
−0.968539 | + | 0.248860i | \(0.919944\pi\) | |||||||
\(642\) | 107.653 | + | 169.354i | 0.167683 | + | 0.263792i | ||||
\(643\) | −316.955 | + | 975.487i | −0.492931 | + | 1.51709i | 0.327225 | + | 0.944947i | \(0.393887\pi\) |
−0.820156 | + | 0.572140i | \(0.806113\pi\) | |||||||
\(644\) | 460.116 | + | 149.501i | 0.714466 | + | 0.232144i | ||||
\(645\) | −226.814 | + | 144.178i | −0.351649 | + | 0.223531i | ||||
\(646\) | 119.612 | + | 86.9030i | 0.185157 | + | 0.134525i | ||||
\(647\) | −457.467 | + | 148.640i | −0.707059 | + | 0.229737i | −0.640404 | − | 0.768039i | \(-0.721233\pi\) |
−0.0666556 | + | 0.997776i | \(0.521233\pi\) | |||||||
\(648\) | −116.293 | + | 458.603i | −0.179465 | + | 0.707720i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 199.079i | − | 0.306276i | ||||||
\(651\) | −356.470 | + | 91.8092i | −0.547573 | + | 0.141028i | ||||
\(652\) | −567.116 | − | 412.034i | −0.869810 | − | 0.631954i | ||||
\(653\) | 456.234 | + | 627.953i | 0.698674 | + | 0.961643i | 0.999967 | + | 0.00811121i | \(0.00258191\pi\) |
−0.301293 | + | 0.953532i | \(0.597418\pi\) | |||||||
\(654\) | 146.478 | − | 370.768i | 0.223973 | − | 0.566924i | ||||
\(655\) | 98.2859 | − | 302.493i | 0.150055 | − | 0.461821i | ||||
\(656\) | −160.852 | − | 221.394i | −0.245201 | − | 0.337490i | ||||
\(657\) | −579.686 | − | 542.738i | −0.882322 | − | 0.826085i | ||||
\(658\) | −36.3430 | − | 111.852i | −0.0552326 | − | 0.169988i | ||||
\(659\) | 52.5987i | 0.0798160i | 0.999203 | + | 0.0399080i | \(0.0127065\pi\) | ||||
−0.999203 | + | 0.0399080i | \(0.987294\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −233.530 | −0.353297 | −0.176649 | − | 0.984274i | \(-0.556526\pi\) | ||||
−0.176649 | + | 0.984274i | \(0.556526\pi\) | |||||||
\(662\) | 126.100 | − | 40.9725i | 0.190484 | − | 0.0618919i | ||||
\(663\) | 707.118 | + | 584.092i | 1.06654 | + | 0.880983i | ||||
\(664\) | −161.425 | + | 117.282i | −0.243110 | + | 0.176630i | ||||
\(665\) | −93.7874 | − | 30.4734i | −0.141034 | − | 0.0458246i | ||||
\(666\) | 275.084 | + | 128.944i | 0.413039 | + | 0.193610i | ||||
\(667\) | 1312.55 | − | 953.624i | 1.96784 | − | 1.42972i | ||||
\(668\) | −125.201 | + | 172.324i | −0.187427 | + | 0.257971i | ||||
\(669\) | −661.602 | + | 170.396i | −0.988942 | + | 0.254703i | ||||
\(670\) | −68.6576 | −0.102474 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −431.652 | − | 26.8344i | −0.642339 | − | 0.0399321i | ||||
\(673\) | 73.0859 | + | 224.935i | 0.108597 | + | 0.334228i | 0.990558 | − | 0.137095i | \(-0.0437766\pi\) |
−0.881961 | + | 0.471323i | \(0.843777\pi\) | |||||||
\(674\) | 199.909 | − | 275.152i | 0.296602 | − | 0.408237i | ||||
\(675\) | −215.162 | − | 454.602i | −0.318758 | − | 0.673484i | ||||
\(676\) | 13.5019 | − | 41.5545i | 0.0199732 | − | 0.0614711i | ||||
\(677\) | 281.192 | + | 91.3649i | 0.415350 | + | 0.134955i | 0.509235 | − | 0.860628i | \(-0.329928\pi\) |
−0.0938846 | + | 0.995583i | \(0.529928\pi\) | |||||||
\(678\) | −157.482 | − | 247.744i | −0.232274 | − | 0.365404i | ||||
\(679\) | −154.632 | − | 112.347i | −0.227735 | − | 0.165459i | ||||
\(680\) | 317.817 | − | 103.265i | 0.467378 | − | 0.151860i | ||||
\(681\) | −1276.55 | − | 79.3589i | −1.87452 | − | 0.116533i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 905.661i | − | 1.32600i | −0.748617 | − | 0.663002i | \(-0.769282\pi\) | ||
0.748617 | − | 0.663002i | \(-0.230718\pi\) | |||||||
\(684\) | −47.1917 | − | 245.400i | −0.0689938 | − | 0.358773i | ||||
\(685\) | −121.135 | − | 88.0096i | −0.176839 | − | 0.128481i | ||||
\(686\) | −166.795 | − | 229.573i | −0.243141 | − | 0.334654i | ||||
\(687\) | 283.435 | + | 111.976i | 0.412570 | + | 0.162992i | ||||
\(688\) | 97.1808 | − | 299.092i | 0.141251 | − | 0.434726i | ||||
\(689\) | 78.5910 | + | 108.171i | 0.114065 | + | 0.156997i | ||||
\(690\) | −139.875 | − | 115.539i | −0.202717 | − | 0.167448i | ||||
\(691\) | −108.781 | − | 334.795i | −0.157426 | − | 0.484508i | 0.840972 | − | 0.541078i | \(-0.181984\pi\) |
−0.998399 | + | 0.0565700i | \(0.981984\pi\) | |||||||
\(692\) | 652.061i | 0.942284i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 408.293 | 0.588319 | ||||||||
\(695\) | 314.347 | − | 102.137i | 0.452297 | − | 0.146960i | ||||
\(696\) | −598.770 | + | 724.888i | −0.860302 | + | 1.04151i | ||||
\(697\) | 566.242 | − | 411.399i | 0.812398 | − | 0.590242i | ||||
\(698\) | 210.995 | + | 68.5564i | 0.302285 | + | 0.0982183i | ||||
\(699\) | −190.923 | + | 483.268i | −0.273137 | + | 0.691371i | ||||
\(700\) | 241.122 | − | 175.186i | 0.344460 | − | 0.250265i | ||||
\(701\) | 734.941 | − | 1011.56i | 1.04842 | − | 1.44302i | 0.158244 | − | 0.987400i | \(-0.449417\pi\) |
0.890173 | − | 0.455623i | \(-0.150583\pi\) | |||||||
\(702\) | 36.8055 | + | 286.199i | 0.0524294 | + | 0.407691i | ||||
\(703\) | −350.804 | −0.499010 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.7011 | − | 236.478i | 0.0208526 | − | 0.335430i | ||||
\(706\) | −91.5447 | − | 281.746i | −0.129667 | − | 0.399073i | ||||
\(707\) | 258.676 | − | 356.036i | 0.365878 | − | 0.503588i | ||||
\(708\) | −525.284 | + | 333.905i | −0.741927 | + | 0.471617i | ||||
\(709\) | −41.6962 | + | 128.328i | −0.0588099 | + | 0.180998i | −0.976146 | − | 0.217116i | \(-0.930335\pi\) |
0.917336 | + | 0.398114i | \(0.130335\pi\) | |||||||
\(710\) | −27.5830 | − | 8.96224i | −0.0388492 | − | 0.0126229i | ||||
\(711\) | −738.220 | + | 407.274i | −1.03828 | + | 0.572818i | ||||
\(712\) | 678.018 | + | 492.609i | 0.952272 | + | 0.691866i | ||||
\(713\) | 743.703 | − | 241.644i | 1.04306 | − | 0.338911i | ||||
\(714\) | 15.8584 | − | 255.095i | 0.0222106 | − | 0.357276i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 104.582i | − | 0.146064i | ||||||
\(717\) | −120.688 | − | 468.599i | −0.168324 | − | 0.653555i | ||||
\(718\) | 69.7776 | + | 50.6964i | 0.0971833 | + | 0.0706078i | ||||
\(719\) | −65.9951 | − | 90.8344i | −0.0917873 | − | 0.126334i | 0.760654 | − | 0.649158i | \(-0.224879\pi\) |
−0.852441 | + | 0.522824i | \(0.824879\pi\) | |||||||
\(720\) | −182.290 | − | 85.4475i | −0.253180 | − | 0.118677i | ||||
\(721\) | 28.7015 | − | 88.3343i | 0.0398080 | − | 0.122516i | ||||
\(722\) | 136.545 | + | 187.938i | 0.189120 | + | 0.260301i | ||||
\(723\) | 108.330 | − | 131.148i | 0.149834 | − | 0.181394i | ||||
\(724\) | 106.438 | + | 327.582i | 0.147014 | + | 0.452461i | ||||
\(725\) | − | 999.487i | − | 1.37860i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 160.372 | 0.220595 | 0.110297 | − | 0.993899i | \(-0.464820\pi\) | ||||
0.110297 | + | 0.993899i | \(0.464820\pi\) | |||||||
\(728\) | −355.525 | + | 115.517i | −0.488359 | + | 0.158678i | ||||
\(729\) | 393.365 | + | 613.763i | 0.539596 | + | 0.841924i | ||||
\(730\) | −142.765 | + | 103.725i | −0.195569 | + | 0.142089i | ||||
\(731\) | 764.964 | + | 248.552i | 1.04646 | + | 0.340016i | ||||
\(732\) | −484.061 | − | 191.236i | −0.661285 | − | 0.261252i | ||||
\(733\) | −397.210 | + | 288.590i | −0.541896 | + | 0.393710i | −0.824789 | − | 0.565441i | \(-0.808706\pi\) |
0.282893 | + | 0.959152i | \(0.408706\pi\) | |||||||
\(734\) | 222.586 | − | 306.363i | 0.303250 | − | 0.417388i | ||||
\(735\) | −50.0326 | − | 194.263i | −0.0680715 | − | 0.264303i | ||||
\(736\) | 918.745 | 1.24829 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 218.511 | + | 27.2736i | 0.296085 | + | 0.0369561i | ||||
\(739\) | −73.3479 | − | 225.741i | −0.0992528 | − | 0.305469i | 0.889086 | − | 0.457741i | \(-0.151341\pi\) |
−0.988339 | + | 0.152272i | \(0.951341\pi\) | |||||||
\(740\) | −213.187 | + | 293.427i | −0.288090 | + | 0.396522i | ||||
\(741\) | −178.745 | − | 281.193i | −0.241221 | − | 0.379478i | ||||
\(742\) | 11.5141 | − | 35.4369i | 0.0155177 | − | 0.0477586i | ||||
\(743\) | 233.203 | + | 75.7723i | 0.313867 | + | 0.101982i | 0.461714 | − | 0.887029i | \(-0.347235\pi\) |
−0.147848 | + | 0.989010i | \(0.547235\pi\) | |||||||
\(744\) | −382.440 | + | 243.104i | −0.514032 | + | 0.326752i | ||||
\(745\) | 151.801 | + | 110.290i | 0.203759 | + | 0.148040i | ||||
\(746\) | 156.038 | − | 50.6998i | 0.209166 | − | 0.0679622i | ||||
\(747\) | −38.0789 | + | 305.081i | −0.0509758 | + | 0.408408i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 400.574i | 0.534812i | ||||||||
\(750\) | −253.494 | + | 65.2875i | −0.337992 | + | 0.0870500i | ||||
\(751\) | −599.185 | − | 435.333i | −0.797849 | − | 0.579672i | 0.112433 | − | 0.993659i | \(-0.464136\pi\) |
−0.910282 | + | 0.413988i | \(0.864136\pi\) | |||||||
\(752\) | 162.960 | + | 224.295i | 0.216702 | + | 0.298265i | ||||
\(753\) | −74.3960 | + | 188.313i | −0.0987994 | + | 0.250083i | ||||
\(754\) | −177.201 | + | 545.369i | −0.235015 | + | 0.723301i | ||||
\(755\) | 9.24935 | + | 12.7306i | 0.0122508 | + | 0.0168618i | ||||
\(756\) | −314.253 | + | 296.428i | −0.415678 | + | 0.392100i | ||||
\(757\) | 100.343 | + | 308.824i | 0.132554 | + | 0.407958i | 0.995201 | − | 0.0978467i | \(-0.0311955\pi\) |
−0.862648 | + | 0.505805i | \(0.831195\pi\) | |||||||
\(758\) | 246.089i | 0.324656i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −121.402 | −0.159740 | ||||||||
\(761\) | −644.390 | + | 209.375i | −0.846767 | + | 0.275131i | −0.700091 | − | 0.714053i | \(-0.746857\pi\) |
−0.146676 | + | 0.989185i | \(0.546857\pi\) | |||||||
\(762\) | 236.118 | + | 195.037i | 0.309866 | + | 0.255954i | ||||
\(763\) | 643.793 | − | 467.743i | 0.843765 | − | 0.613031i | ||||
\(764\) | 222.863 | + | 72.4125i | 0.291705 | + | 0.0947808i | ||||
\(765\) | 218.542 | − | 466.228i | 0.285676 | − | 0.609449i | ||||
\(766\) | 230.667 | − | 167.589i | 0.301132 | − | 0.218785i | ||||
\(767\) | −487.805 | + | 671.406i | −0.635991 | + | 0.875366i | ||||
\(768\) | −168.335 | + | 43.3548i | −0.219186 | + | 0.0564516i | ||||
\(769\) | 632.440 | 0.822419 | 0.411209 | − | 0.911541i | \(-0.365106\pi\) | ||||
0.411209 | + | 0.911541i | \(0.365106\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −439.168 | − | 27.3016i | −0.569609 | − | 0.0354107i | ||||
\(772\) | 282.934 | + | 870.780i | 0.366494 | + | 1.12795i | ||||
\(773\) | −108.795 | + | 149.744i | −0.140744 | + | 0.193718i | −0.873570 | − | 0.486698i | \(-0.838201\pi\) |
0.732826 | + | 0.680416i | \(0.238201\pi\) | |||||||
\(774\) | 122.242 | + | 221.575i | 0.157935 | + | 0.286272i | ||||
\(775\) | 148.866 | − | 458.161i | 0.192085 | − | 0.591176i | ||||
\(776\) | −223.788 | − | 72.7132i | −0.288387 | − | 0.0937026i | ||||
\(777\) | 325.328 | + | 511.792i | 0.418698 | + | 0.658677i | ||||
\(778\) | −400.314 | − | 290.845i | −0.514542 | − | 0.373837i | ||||
\(779\) | −241.827 | + | 78.5745i | −0.310433 | + | 0.100866i | ||||
\(780\) | −343.826 | − | 21.3745i | −0.440803 | − | 0.0274032i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 542.953i | 0.694314i | ||||||||
\(783\) | 184.784 | + | 1436.88i | 0.235994 | + | 1.83509i | ||||
\(784\) | 189.901 | + | 137.971i | 0.242221 | + | 0.175984i | ||||
\(785\) | −146.591 | − | 201.765i | −0.186740 | − | 0.257025i | ||||
\(786\) | −278.530 | − | 110.038i | −0.354363 | − | 0.139997i | ||||
\(787\) | 287.300 | − | 884.219i | 0.365057 | − | 1.12353i | −0.584888 | − | 0.811114i | \(-0.698861\pi\) |
0.949945 | − | 0.312417i | \(-0.101139\pi\) | |||||||
\(788\) | −211.324 | − | 290.863i | −0.268178 | − | 0.369115i | ||||
\(789\) | −338.137 | − | 279.307i | −0.428564 | − | 0.354001i | ||||
\(790\) | 57.8970 | + | 178.189i | 0.0732873 | + | 0.225555i | ||||
\(791\) | − | 585.989i | − | 0.740820i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −693.957 | −0.875103 | ||||||||
\(794\) | 59.3226 | − | 19.2751i | 0.0747136 | − | 0.0242759i | ||||
\(795\) | 47.8053 | − | 57.8744i | 0.0601324 | − | 0.0727980i | ||||
\(796\) | 789.200 | − | 573.388i | 0.991458 | − | 0.720336i | ||||
\(797\) | −858.556 | − | 278.962i | −1.07723 | − | 0.350015i | −0.283933 | − | 0.958844i | \(-0.591639\pi\) |
−0.793301 | + | 0.608830i | \(0.791639\pi\) | |||||||
\(798\) | −34.1170 | + | 86.3577i | −0.0427531 | + | 0.108218i | ||||
\(799\) | −573.663 | + | 416.791i | −0.717976 | + | 0.521640i | ||||
\(800\) | 332.684 | − | 457.901i | 0.415855 | − | 0.572376i | ||||
\(801\) | 1268.11 | − | 243.863i | 1.58316 | − | 0.304449i | ||||
\(802\) | 625.989 | 0.780535 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 21.5488 | − | 346.630i | 0.0268020 | − | 0.431132i | ||||
\(805\) | −111.909 | − | 344.422i | −0.139018 | − | 0.427853i | ||||
\(806\) | −162.457 | + | 223.602i | −0.201559 | + | 0.277422i | ||||
\(807\) | 144.338 | − | 91.7503i | 0.178857 | − | 0.113693i | ||||
\(808\) | 167.420 | − | 515.266i | 0.207203 | − | 0.637705i | ||||
\(809\) | 291.657 | + | 94.7652i | 0.360516 | + | 0.117139i | 0.483674 | − | 0.875248i | \(-0.339302\pi\) |
−0.123158 | + | 0.992387i | \(0.539302\pi\) | |||||||
\(810\) | 150.445 | − | 60.0848i | 0.185735 | − | 0.0741788i | ||||
\(811\) | 1054.85 | + | 766.395i | 1.30068 | + | 0.945000i | 0.999962 | − | 0.00871236i | \(-0.00277327\pi\) |
0.300719 | + | 0.953713i | \(0.402773\pi\) | |||||||
\(812\) | −816.477 | + | 265.289i | −1.00551 | + | 0.326711i | ||||
\(813\) | 23.8968 | − | 384.399i | 0.0293934 | − | 0.472816i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 524.733i | 0.643844i | ||||||||
\(816\) | 150.273 | + | 583.468i | 0.184158 | + | 0.715034i | ||||
\(817\) | −236.400 | − | 171.755i | −0.289351 | − | 0.210226i | ||||
\(818\) | 236.431 | + | 325.419i | 0.289036 | + | 0.397823i | ||||
\(819\) | −244.472 | + | 521.545i | −0.298501 | + | 0.636807i | ||||
\(820\) | −81.2379 | + | 250.024i | −0.0990706 | + | 0.304908i | ||||
\(821\) | −801.178 | − | 1102.73i | −0.975856 | − | 1.34315i | −0.939032 | − | 0.343829i | \(-0.888276\pi\) |
−0.0368241 | − | 0.999322i | \(-0.511724\pi\) | |||||||
\(822\) | −89.7852 | + | 108.696i | −0.109228 | + | 0.132234i | ||||
\(823\) | 82.9097 | + | 255.170i | 0.100741 | + | 0.310048i | 0.988707 | − | 0.149860i | \(-0.0478823\pi\) |
−0.887966 | + | 0.459908i | \(0.847882\pi\) | |||||||
\(824\) | − | 114.343i | − | 0.138766i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 231.272 | 0.279990 | ||||||||
\(827\) | 605.846 | − | 196.851i | 0.732583 | − | 0.238031i | 0.0811129 | − | 0.996705i | \(-0.474153\pi\) |
0.651470 | + | 0.758674i | \(0.274153\pi\) | |||||||
\(828\) | 627.221 | − | 669.920i | 0.757513 | − | 0.809082i | ||||
\(829\) | −21.9994 | + | 15.9835i | −0.0265373 | + | 0.0192804i | −0.600975 | − | 0.799268i | \(-0.705221\pi\) |
0.574438 | + | 0.818548i | \(0.305221\pi\) | |||||||
\(830\) | 64.9779 | + | 21.1126i | 0.0782867 | + | 0.0254369i | ||||
\(831\) | −659.249 | − | 260.447i | −0.793320 | − | 0.313414i | ||||
\(832\) | 124.105 | − | 90.1675i | 0.149165 | − | 0.108374i | ||||
\(833\) | −352.879 | + | 485.696i | −0.423624 | + | 0.583068i | ||||
\(834\) | −77.6203 | − | 301.379i | −0.0930699 | − | 0.361365i | ||||
\(835\) | 159.446 | 0.190953 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −129.307 | + | 686.181i | −0.154489 | + | 0.819810i | ||||
\(838\) | −81.8693 | − | 251.968i | −0.0976961 | − | 0.300678i | ||||
\(839\) | 595.967 | − | 820.278i | 0.710330 | − | 0.977685i | −0.289460 | − | 0.957190i | \(-0.593476\pi\) |
0.999790 | − | 0.0204952i | \(-0.00652429\pi\) | |||||||
\(840\) | 112.586 | + | 177.115i | 0.134031 | + | 0.210851i | ||||
\(841\) | −629.763 | + | 1938.21i | −0.748826 | + | 2.30465i | ||||
\(842\) | −334.042 | − | 108.537i | −0.396725 | − | 0.128904i | ||||
\(843\) | −516.427 | + | 328.274i | −0.612606 | + | 0.389412i | ||||
\(844\) | 510.758 | + | 371.087i | 0.605163 | + | 0.439677i | ||||
\(845\) | −31.1058 | + | 10.1069i | −0.0368116 | + | 0.0119608i | ||||
\(846\) | −221.375 | − | 27.6311i | −0.261672 | − | 0.0326608i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 87.8361i | 0.103580i | ||||||||
\(849\) | 1392.20 | − | 358.563i | 1.63982 | − | 0.422336i | ||||
\(850\) | 270.607 | + | 196.607i | 0.318361 | + | 0.231303i | ||||
\(851\) | −757.234 | − | 1042.24i | −0.889816 | − | 1.22473i | ||||
\(852\) | 53.9046 | − | 136.444i | 0.0632683 | − | 0.160146i | ||||
\(853\) | −398.741 | + | 1227.20i | −0.467457 | + | 1.43869i | 0.388408 | + | 0.921487i | \(0.373025\pi\) |
−0.855866 | + | 0.517198i | \(0.826975\pi\) | |||||||
\(854\) | 113.670 | + | 156.453i | 0.133103 | + | 0.183201i | ||||
\(855\) | −127.849 | + | 136.553i | −0.149531 | + | 0.159711i | ||||
\(856\) | 152.389 | + | 469.005i | 0.178025 | + | 0.547903i | ||||
\(857\) | 618.449i | 0.721644i | 0.932635 | + | 0.360822i | \(0.117504\pi\) | ||||
−0.932635 | + | 0.360822i | \(0.882496\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1207.23 | 1.40538 | 0.702692 | − | 0.711494i | \(-0.251981\pi\) | ||||
0.702692 | + | 0.711494i | \(0.251981\pi\) | |||||||
\(860\) | −287.325 | + | 93.3574i | −0.334098 | + | 0.108555i | ||||
\(861\) | 338.899 | + | 279.936i | 0.393611 | + | 0.325129i | ||||
\(862\) | 509.768 | − | 370.368i | 0.591379 | − | 0.429662i | ||||
\(863\) | −1051.19 | − | 341.551i | −1.21806 | − | 0.395772i | −0.371686 | − | 0.928359i | \(-0.621220\pi\) |
−0.846376 | + | 0.532587i | \(0.821220\pi\) | |||||||
\(864\) | −393.616 | + | 719.790i | −0.455574 | + | 0.833091i | ||||
\(865\) | 394.884 | − | 286.900i | 0.456513 | − | 0.331676i | ||||
\(866\) | −8.67224 | + | 11.9363i | −0.0100141 | + | 0.0137833i | ||||
\(867\) | −652.690 | + | 168.101i | −0.752814 | + | 0.193888i | ||||
\(868\) | −413.783 | −0.476708 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 321.315 | + | 19.9751i | 0.369328 | + | 0.0229599i | ||||
\(871\) | −143.095 | − | 440.401i | −0.164288 | − | 0.505627i | ||||
\(872\) | 575.831 | − | 792.564i | 0.660357 | − | 0.908903i | ||||
\(873\) | −317.460 | + | 175.142i | −0.363642 | + | 0.200620i | ||||
\(874\) | 60.9537 | − | 187.596i | 0.0697411 | − | 0.214641i | ||||
\(875\) | −496.950 | − | 161.469i | −0.567943 | − | 0.184536i | ||||
\(876\) | −478.865 | − | 753.330i | −0.546650 | − | 0.859965i | ||||
\(877\) | −1077.90 | − | 783.140i | −1.22908 | − | 0.892977i | −0.232256 | − | 0.972655i | \(-0.574611\pi\) |
−0.996821 | + | 0.0796781i | \(0.974611\pi\) | |||||||
\(878\) | 192.063 | − | 62.4051i | 0.218751 | − | 0.0710764i | ||||
\(879\) | −28.0162 | − | 1.74167i | −0.0318728 | − | 0.00198143i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1171.98i | 1.33029i | 0.746715 | + | 0.665145i | \(0.231630\pi\) | ||||
−0.746715 | + | 0.665145i | \(0.768370\pi\) | |||||||
\(882\) | −185.484 | + | 35.6696i | −0.210300 | + | 0.0404417i | ||||
\(883\) | −589.122 | − | 428.022i | −0.667183 | − | 0.484737i | 0.201898 | − | 0.979407i | \(-0.435289\pi\) |
−0.869081 | + | 0.494670i | \(0.835289\pi\) | |||||||
\(884\) | 605.990 | + | 834.074i | 0.685509 | + | 0.943522i | ||||
\(885\) | 433.330 | + | 171.194i | 0.489639 | + | 0.193440i | ||||
\(886\) | 15.0698 | − | 46.3800i | 0.0170088 | − | 0.0523476i | ||||
\(887\) | 575.896 | + | 792.653i | 0.649262 | + | 0.893633i | 0.999067 | − | 0.0431896i | \(-0.0137520\pi\) |
−0.349804 | + | 0.936823i | \(0.613752\pi\) | |||||||
\(888\) | 575.604 | + | 475.459i | 0.648203 | + | 0.535427i | ||||
\(889\) | 188.910 | + | 581.406i | 0.212497 | + | 0.654000i | ||||
\(890\) | − | 286.965i | − | 0.322433i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −767.973 | −0.860956 | ||||||||
\(893\) | 244.997 | − | 79.6044i | 0.274353 | − | 0.0891426i | ||||
\(894\) | 112.515 | − | 136.213i | 0.125855 | − | 0.152364i | ||||
\(895\) | −63.3341 | + | 46.0149i | −0.0707644 | + | 0.0514133i | ||||
\(896\) | −589.081 | − | 191.404i | −0.657456 | − | 0.213620i | ||||
\(897\) | 449.596 | − | 1138.03i | 0.501222 | − | 1.26870i | ||||
\(898\) | 88.0908 | − | 64.0017i | 0.0980966 | − | 0.0712714i | ||||
\(899\) | −815.621 | + | 1122.61i | −0.907253 | + | 1.24873i | ||||
\(900\) | −106.766 | − | 555.189i | −0.118628 | − | 0.616876i | ||||
\(901\) | −224.652 | −0.249336 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −31.3424 | + | 504.168i | −0.0347092 | + | 0.558325i | ||||
\(904\) | −222.926 | − | 686.094i | −0.246599 | − | 0.758954i | ||||
\(905\) | 151.550 | − | 208.591i | 0.167459 | − | 0.230487i | ||||
\(906\) | 12.5042 | − | 7.94846i | 0.0138015 | − | 0.00877313i | ||||
\(907\) | 340.755 | − | 1048.74i | 0.375695 | − | 1.15627i | −0.567314 | − | 0.823501i | \(-0.692018\pi\) |
0.943009 | − | 0.332768i | \(-0.107982\pi\) | |||||||
\(908\) | −1367.37 | − | 444.284i | −1.50591 | − | 0.489300i | ||||
\(909\) | −403.258 | − | 730.942i | −0.443628 | − | 0.804116i | ||||
\(910\) | 103.554 | + | 75.2365i | 0.113796 | + | 0.0826775i | ||||
\(911\) | 440.602 | − | 143.160i | 0.483647 | − | 0.157146i | −0.0570373 | − | 0.998372i | \(-0.518165\pi\) |
0.540684 | + | 0.841226i | \(0.318165\pi\) | |||||||
\(912\) | 13.5812 | − | 218.464i | 0.0148917 | − | 0.239544i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 243.701i | − | 0.266632i | ||||||
\(915\) | 97.1703 | + | 377.286i | 0.106197 | + | 0.412335i | ||||
\(916\) | 277.145 | + | 201.358i | 0.302560 | + | 0.219823i | ||||
\(917\) | −351.379 | − | 483.632i | −0.383183 | − | 0.527407i | ||||
\(918\) | −425.377 | − | 232.616i | −0.463373 | − | 0.253395i | ||||
\(919\) | 60.5455 | − | 186.340i | 0.0658819 | − | 0.202764i | −0.912697 | − | 0.408638i | \(-0.866004\pi\) |
0.978578 | + | 0.205874i | \(0.0660039\pi\) | |||||||
\(920\) | −262.054 | − | 360.687i | −0.284842 | − | 0.392051i | ||||
\(921\) | −138.567 | + | 167.752i | −0.150452 | + | 0.182142i | ||||
\(922\) | 129.310 | + | 397.976i | 0.140250 | + | 0.431644i | ||||
\(923\) | − | 195.609i | − | 0.211927i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −793.652 | −0.858002 | ||||||||
\(926\) | 34.6226 | − | 11.2496i | 0.0373894 | − | 0.0121485i | ||||
\(927\) | −128.613 | − | 120.415i | −0.138741 | − | 0.129898i | ||||
\(928\) | −1318.95 | + | 958.275i | −1.42128 | + | 1.03262i | ||||
\(929\) | 115.578 | + | 37.5535i | 0.124411 | + | 0.0404236i | 0.370561 | − | 0.928808i | \(-0.379166\pi\) |
−0.246150 | + | 0.969232i | \(0.579166\pi\) | |||||||
\(930\) | 144.314 | + | 57.0138i | 0.155177 | + | 0.0613052i | ||||
\(931\) | 176.449 | − | 128.198i | 0.189527 | − | 0.137699i | ||||
\(932\) | −343.323 | + | 472.544i | −0.368372 | + | 0.507021i | ||||
\(933\) | −284.813 | − | 1105.85i | −0.305266 | − | 1.18526i | ||||
\(934\) | −284.484 | −0.304586 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −87.8260 | + | 703.645i | −0.0938312 | + | 0.751758i | ||||
\(937\) | 102.105 | + | 314.247i | 0.108970 | + | 0.335376i | 0.990642 | − | 0.136488i | \(-0.0435815\pi\) |
−0.881672 | + | 0.471864i | \(0.843581\pi\) | |||||||
\(938\) | −75.8500 | + | 104.399i | −0.0808636 | + | 0.111299i | ||||
\(939\) | 85.4584 | + | 134.439i | 0.0910101 | + | 0.143173i | ||||
\(940\) | 82.3026 | − | 253.301i | 0.0875560 | − | 0.269470i | ||||
\(941\) | −851.275 | − | 276.596i | −0.904650 | − | 0.293939i | −0.180495 | − | 0.983576i | \(-0.557770\pi\) |
−0.724155 | + | 0.689637i | \(0.757770\pi\) | |||||||
\(942\) | −198.175 | + | 125.973i | −0.210377 | + | 0.133729i | ||||
\(943\) | −755.446 | − | 548.864i | −0.801109 | − | 0.582040i | ||||
\(944\) | −518.505 | + | 168.472i | −0.549263 | + | 0.178466i | ||||
\(945\) | 317.783 | + | 59.8844i | 0.336278 | + | 0.0633697i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1308.11i | 1.38132i | 0.723181 | + | 0.690659i | \(0.242679\pi\) | ||||
−0.723181 | + | 0.690659i | \(0.757321\pi\) | |||||||
\(948\) | −917.788 | + | 236.377i | −0.968131 | + | 0.249343i | ||||
\(949\) | −962.888 | − | 699.579i | −1.01463 | − | 0.737175i | ||||
\(950\) | −71.4258 | − | 98.3092i | −0.0751851 | − | 0.103483i | ||||
\(951\) | 80.7394 | − | 204.369i | 0.0848995 | − | 0.214899i | ||||
\(952\) | 194.090 | − | 597.346i | 0.203876 | − | 0.627465i | ||||
\(953\) | −1.19333 | − | 1.64248i | −0.00125218 | − | 0.00172348i | 0.808390 | − | 0.588647i | \(-0.200339\pi\) |
−0.809643 | + | 0.586923i | \(0.800339\pi\) | |||||||
\(954\) | −51.5954 | − | 48.3068i | −0.0540832 | − | 0.0506361i | ||||
\(955\) | −54.2047 | − | 166.825i | −0.0567589 | − | 0.174686i | ||||
\(956\) | − | 543.939i | − | 0.568974i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 457.467 | 0.477523 | ||||||||
\(959\) | −267.650 | + | 86.9646i | −0.279092 | + | 0.0906826i | ||||
\(960\) | −66.3994 | − | 54.8471i | −0.0691660 | − | 0.0571323i | ||||
\(961\) | 236.385 | − | 171.744i | 0.245978 | − | 0.178713i | ||||
\(962\) | 433.055 | + | 140.708i | 0.450161 | + | 0.146266i | ||||
\(963\) | 688.016 | + | 322.505i | 0.714451 | + | 0.334896i | ||||
\(964\) | 154.694 | − | 112.392i | 0.160471 | − | 0.116589i | ||||
\(965\) | 402.851 | − | 554.477i | 0.417462 | − | 0.574587i | ||||
\(966\) | −330.213 | + | 85.0467i | −0.341836 | + | 0.0880400i | ||||
\(967\) | −520.674 | −0.538442 | −0.269221 | − | 0.963078i | \(-0.586766\pi\) | ||||
−0.269221 | + | 0.963078i | \(0.586766\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 558.750 | + | 34.7356i | 0.576625 | + | 0.0358469i | ||||
\(970\) | 24.8977 | + | 76.6272i | 0.0256677 | + | 0.0789971i | ||||
\(971\) | −1065.10 | + | 1465.98i | −1.09691 | + | 1.50977i | −0.257492 | + | 0.966280i | \(0.582896\pi\) |
−0.839418 | + | 0.543487i | \(0.817104\pi\) | |||||||
\(972\) | 256.130 | + | 778.408i | 0.263508 | + | 0.800831i | ||||
\(973\) | 191.970 | − | 590.823i | 0.197297 | − | 0.607218i | ||||
\(974\) | −457.305 | − | 148.587i | −0.469512 | − | 0.152554i | ||||
\(975\) | −404.388 | − | 636.166i | −0.414757 | − | 0.652478i | ||||
\(976\) | −368.815 | − | 267.960i | −0.377884 | − | 0.274549i | ||||
\(977\) | 406.470 | − | 132.070i | 0.416039 | − | 0.135179i | −0.0935151 | − | 0.995618i | \(-0.529810\pi\) |
0.509554 | + | 0.860439i | \(0.329810\pi\) | |||||||
\(978\) | 493.125 | + | 30.6559i | 0.504218 | + | 0.0313455i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 225.496i | − | 0.230098i | ||||||
\(981\) | −285.062 | − | 1482.34i | −0.290583 | − | 1.51105i | ||||
\(982\) | 492.824 | + | 358.057i | 0.501857 | + | 0.364620i | ||||
\(983\) | −589.855 | − | 811.865i | −0.600056 | − | 0.825906i | 0.395658 | − | 0.918398i | \(-0.370517\pi\) |
−0.995713 | + | 0.0924923i | \(0.970517\pi\) | |||||||
\(984\) | 503.289 | + | 198.832i | 0.511472 | + | 0.202065i | ||||
\(985\) | −83.1642 | + | 255.953i | −0.0844306 | + | 0.259851i | ||||
\(986\) | −566.315 | − | 779.465i | −0.574356 | − | 0.790533i | ||||
\(987\) | −343.341 | − | 283.605i | −0.347863 | − | 0.287341i | ||||
\(988\) | −115.740 | − | 356.212i | −0.117146 | − | 0.360538i | ||||
\(989\) | − | 1073.09i | − | 1.08503i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 862.380 | 0.870212 | 0.435106 | − | 0.900379i | \(-0.356711\pi\) | ||||
0.435106 | + | 0.900379i | \(0.356711\pi\) | |||||||
\(992\) | −747.330 | + | 242.822i | −0.753357 | + | 0.244780i | ||||
\(993\) | 319.731 | − | 387.076i | 0.321985 | − | 0.389804i | ||||
\(994\) | −44.1002 | + | 32.0407i | −0.0443664 | + | 0.0322341i | ||||
\(995\) | −694.480 | − | 225.650i | −0.697970 | − | 0.226784i | ||||
\(996\) | −126.985 | + | 321.426i | −0.127495 | + | 0.322717i | ||||
\(997\) | 230.794 | − | 167.681i | 0.231488 | − | 0.168186i | −0.465995 | − | 0.884788i | \(-0.654303\pi\) |
0.697483 | + | 0.716602i | \(0.254303\pi\) | |||||||
\(998\) | −231.931 | + | 319.226i | −0.232396 | + | 0.319865i | ||||
\(999\) | 1140.97 | − | 146.729i | 1.14211 | − | 0.146876i |
(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 | 363.3.h.m.269.2 | 16 | ||
3.2 | odd | 2 | inner | 363.3.h.m.269.3 | 16 | ||
11.2 | odd | 10 | 363.3.h.l.251.2 | 16 | |||
11.3 | even | 5 | 33.3.b.b.23.3 | yes | 4 | ||
11.4 | even | 5 | inner | 363.3.h.m.245.2 | 16 | ||
11.5 | even | 5 | inner | 363.3.h.m.323.3 | 16 | ||
11.6 | odd | 10 | 363.3.h.l.323.2 | 16 | |||
11.7 | odd | 10 | 363.3.h.l.245.3 | 16 | |||
11.8 | odd | 10 | 363.3.b.h.122.2 | 4 | |||
11.9 | even | 5 | inner | 363.3.h.m.251.3 | 16 | ||
11.10 | odd | 2 | 363.3.h.l.269.3 | 16 | |||
33.2 | even | 10 | 363.3.h.l.251.3 | 16 | |||
33.5 | odd | 10 | inner | 363.3.h.m.323.2 | 16 | ||
33.8 | even | 10 | 363.3.b.h.122.3 | 4 | |||
33.14 | odd | 10 | 33.3.b.b.23.2 | ✓ | 4 | ||
33.17 | even | 10 | 363.3.h.l.323.3 | 16 | |||
33.20 | odd | 10 | inner | 363.3.h.m.251.2 | 16 | ||
33.26 | odd | 10 | inner | 363.3.h.m.245.3 | 16 | ||
33.29 | even | 10 | 363.3.h.l.245.2 | 16 | |||
33.32 | even | 2 | 363.3.h.l.269.2 | 16 | |||
44.3 | odd | 10 | 528.3.i.d.353.2 | 4 | |||
132.47 | even | 10 | 528.3.i.d.353.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.b.b.23.2 | ✓ | 4 | 33.14 | odd | 10 | ||
33.3.b.b.23.3 | yes | 4 | 11.3 | even | 5 | ||
363.3.b.h.122.2 | 4 | 11.8 | odd | 10 | |||
363.3.b.h.122.3 | 4 | 33.8 | even | 10 | |||
363.3.h.l.245.2 | 16 | 33.29 | even | 10 | |||
363.3.h.l.245.3 | 16 | 11.7 | odd | 10 | |||
363.3.h.l.251.2 | 16 | 11.2 | odd | 10 | |||
363.3.h.l.251.3 | 16 | 33.2 | even | 10 | |||
363.3.h.l.269.2 | 16 | 33.32 | even | 2 | |||
363.3.h.l.269.3 | 16 | 11.10 | odd | 2 | |||
363.3.h.l.323.2 | 16 | 11.6 | odd | 10 | |||
363.3.h.l.323.3 | 16 | 33.17 | even | 10 | |||
363.3.h.m.245.2 | 16 | 11.4 | even | 5 | inner | ||
363.3.h.m.245.3 | 16 | 33.26 | odd | 10 | inner | ||
363.3.h.m.251.2 | 16 | 33.20 | odd | 10 | inner | ||
363.3.h.m.251.3 | 16 | 11.9 | even | 5 | inner | ||
363.3.h.m.269.2 | 16 | 1.1 | even | 1 | trivial | ||
363.3.h.m.269.3 | 16 | 3.2 | odd | 2 | inner | ||
363.3.h.m.323.2 | 16 | 33.5 | odd | 10 | inner | ||
363.3.h.m.323.3 | 16 | 11.5 | even | 5 | inner | ||
528.3.i.d.353.1 | 4 | 132.47 | even | 10 | |||
528.3.i.d.353.2 | 4 | 44.3 | odd | 10 |