Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(79,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 235.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.235 |
Dual form | 546.2.i.i.79.2 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.70711 | + | 2.95680i | 0.763441 | + | 1.32232i | 0.941067 | + | 0.338221i | \(0.109825\pi\) |
−0.177625 | + | 0.984098i | \(0.556842\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.62132 | + | 0.358719i | −0.990766 | + | 0.135583i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1.70711 | − | 2.95680i | 0.539835 | − | 0.935021i | ||||
\(11\) | −1.20711 | + | 2.09077i | −0.363956 | + | 0.630391i | −0.988608 | − | 0.150513i | \(-0.951908\pi\) |
0.624652 | + | 0.780903i | \(0.285241\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 1.62132 | + | 2.09077i | 0.433316 | + | 0.558782i | ||||
\(15\) | 3.41421 | 0.881546 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −0.207107 | + | 0.358719i | −0.0502308 | + | 0.0870023i | −0.890048 | − | 0.455868i | \(-0.849329\pi\) |
0.839817 | + | 0.542870i | \(0.182662\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 3.91421 | + | 6.77962i | 0.897982 | + | 1.55535i | 0.830070 | + | 0.557659i | \(0.188300\pi\) |
0.0679123 | + | 0.997691i | \(0.478366\pi\) | |||||||
\(20\) | −3.41421 | −0.763441 | ||||||||
\(21\) | −1.00000 | + | 2.44949i | −0.218218 | + | 0.534522i | ||||
\(22\) | 2.41421 | 0.514712 | ||||||||
\(23\) | 0.707107 | + | 1.22474i | 0.147442 | + | 0.255377i | 0.930281 | − | 0.366847i | \(-0.119563\pi\) |
−0.782839 | + | 0.622224i | \(0.786229\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −3.32843 | + | 5.76500i | −0.665685 | + | 1.15300i | ||||
\(26\) | −0.500000 | − | 0.866025i | −0.0980581 | − | 0.169842i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | − | 2.44949i | 0.188982 | − | 0.462910i | ||||
\(29\) | 3.82843 | 0.710921 | 0.355461 | − | 0.934691i | \(-0.384324\pi\) | ||||
0.355461 | + | 0.934691i | \(0.384324\pi\) | |||||||
\(30\) | −1.70711 | − | 2.95680i | −0.311674 | − | 0.539835i | ||||
\(31\) | −4.24264 | + | 7.34847i | −0.762001 | + | 1.31982i | 0.179817 | + | 0.983700i | \(0.442449\pi\) |
−0.941818 | + | 0.336124i | \(0.890884\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 1.20711 | + | 2.09077i | 0.210130 | + | 0.363956i | ||||
\(34\) | 0.414214 | 0.0710370 | ||||||||
\(35\) | −5.53553 | − | 7.13834i | −0.935676 | − | 1.20660i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.707107 | + | 1.22474i | 0.116248 | + | 0.201347i | 0.918278 | − | 0.395937i | \(-0.129580\pi\) |
−0.802030 | + | 0.597284i | \(0.796247\pi\) | |||||||
\(38\) | 3.91421 | − | 6.77962i | 0.634969 | − | 1.09980i | ||||
\(39\) | 0.500000 | − | 0.866025i | 0.0800641 | − | 0.138675i | ||||
\(40\) | 1.70711 | + | 2.95680i | 0.269917 | + | 0.467510i | ||||
\(41\) | 9.89949 | 1.54604 | 0.773021 | − | 0.634381i | \(-0.218745\pi\) | ||||
0.773021 | + | 0.634381i | \(0.218745\pi\) | |||||||
\(42\) | 2.62132 | − | 0.358719i | 0.404479 | − | 0.0553516i | ||||
\(43\) | −10.4853 | −1.59899 | −0.799495 | − | 0.600672i | \(-0.794900\pi\) | ||||
−0.799495 | + | 0.600672i | \(0.794900\pi\) | |||||||
\(44\) | −1.20711 | − | 2.09077i | −0.181978 | − | 0.315195i | ||||
\(45\) | 1.70711 | − | 2.95680i | 0.254480 | − | 0.440773i | ||||
\(46\) | 0.707107 | − | 1.22474i | 0.104257 | − | 0.180579i | ||||
\(47\) | −0.500000 | − | 0.866025i | −0.0729325 | − | 0.126323i | 0.827253 | − | 0.561830i | \(-0.189902\pi\) |
−0.900185 | + | 0.435507i | \(0.856569\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 6.74264 | − | 1.88064i | 0.963234 | − | 0.268662i | ||||
\(50\) | 6.65685 | 0.941421 | ||||||||
\(51\) | 0.207107 | + | 0.358719i | 0.0290008 | + | 0.0502308i | ||||
\(52\) | −0.500000 | + | 0.866025i | −0.0693375 | + | 0.120096i | ||||
\(53\) | 3.74264 | − | 6.48244i | 0.514091 | − | 0.890432i | −0.485775 | − | 0.874084i | \(-0.661463\pi\) |
0.999866 | − | 0.0163483i | \(-0.00520406\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | −8.24264 | −1.11144 | ||||||||
\(56\) | −2.62132 | + | 0.358719i | −0.350289 | + | 0.0479359i | ||||
\(57\) | 7.82843 | 1.03690 | ||||||||
\(58\) | −1.91421 | − | 3.31552i | −0.251349 | − | 0.435348i | ||||
\(59\) | 6.03553 | − | 10.4539i | 0.785760 | − | 1.36098i | −0.142785 | − | 0.989754i | \(-0.545606\pi\) |
0.928544 | − | 0.371222i | \(-0.121061\pi\) | |||||||
\(60\) | −1.70711 | + | 2.95680i | −0.220387 | + | 0.381721i | ||||
\(61\) | 0.792893 | + | 1.37333i | 0.101520 | + | 0.175837i | 0.912311 | − | 0.409498i | \(-0.134296\pi\) |
−0.810791 | + | 0.585335i | \(0.800963\pi\) | |||||||
\(62\) | 8.48528 | 1.07763 | ||||||||
\(63\) | 1.62132 | + | 2.09077i | 0.204267 | + | 0.263412i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.70711 | + | 2.95680i | 0.211741 | + | 0.366745i | ||||
\(66\) | 1.20711 | − | 2.09077i | 0.148585 | − | 0.257356i | ||||
\(67\) | 1.91421 | − | 3.31552i | 0.233858 | − | 0.405055i | −0.725082 | − | 0.688663i | \(-0.758198\pi\) |
0.958940 | + | 0.283608i | \(0.0915314\pi\) | |||||||
\(68\) | −0.207107 | − | 0.358719i | −0.0251154 | − | 0.0435011i | ||||
\(69\) | 1.41421 | 0.170251 | ||||||||
\(70\) | −3.41421 | + | 8.36308i | −0.408077 | + | 0.999579i | ||||
\(71\) | −5.00000 | −0.593391 | −0.296695 | − | 0.954972i | \(-0.595885\pi\) | ||||
−0.296695 | + | 0.954972i | \(0.595885\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 0.707107 | − | 1.22474i | 0.0827606 | − | 0.143346i | −0.821674 | − | 0.569958i | \(-0.806960\pi\) |
0.904435 | + | 0.426612i | \(0.140293\pi\) | |||||||
\(74\) | 0.707107 | − | 1.22474i | 0.0821995 | − | 0.142374i | ||||
\(75\) | 3.32843 | + | 5.76500i | 0.384334 | + | 0.665685i | ||||
\(76\) | −7.82843 | −0.897982 | ||||||||
\(77\) | 2.41421 | − | 5.91359i | 0.275125 | − | 0.673916i | ||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | 0.171573 | + | 0.297173i | 0.0193035 | + | 0.0334346i | 0.875516 | − | 0.483190i | \(-0.160522\pi\) |
−0.856212 | + | 0.516624i | \(0.827188\pi\) | |||||||
\(80\) | 1.70711 | − | 2.95680i | 0.190860 | − | 0.330580i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −4.94975 | − | 8.57321i | −0.546608 | − | 0.946753i | ||||
\(83\) | −3.65685 | −0.401392 | −0.200696 | − | 0.979654i | \(-0.564320\pi\) | ||||
−0.200696 | + | 0.979654i | \(0.564320\pi\) | |||||||
\(84\) | −1.62132 | − | 2.09077i | −0.176901 | − | 0.228122i | ||||
\(85\) | −1.41421 | −0.153393 | ||||||||
\(86\) | 5.24264 | + | 9.08052i | 0.565328 | + | 0.979178i | ||||
\(87\) | 1.91421 | − | 3.31552i | 0.205225 | − | 0.355461i | ||||
\(88\) | −1.20711 | + | 2.09077i | −0.128678 | + | 0.222877i | ||||
\(89\) | −2.70711 | − | 4.68885i | −0.286953 | − | 0.497017i | 0.686128 | − | 0.727481i | \(-0.259309\pi\) |
−0.973081 | + | 0.230464i | \(0.925976\pi\) | |||||||
\(90\) | −3.41421 | −0.359890 | ||||||||
\(91\) | −2.62132 | + | 0.358719i | −0.274789 | + | 0.0376040i | ||||
\(92\) | −1.41421 | −0.147442 | ||||||||
\(93\) | 4.24264 | + | 7.34847i | 0.439941 | + | 0.762001i | ||||
\(94\) | −0.500000 | + | 0.866025i | −0.0515711 | + | 0.0893237i | ||||
\(95\) | −13.3640 | + | 23.1471i | −1.37111 | + | 2.37484i | ||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | −15.0711 | −1.53024 | −0.765118 | − | 0.643891i | \(-0.777319\pi\) | ||||
−0.765118 | + | 0.643891i | \(0.777319\pi\) | |||||||
\(98\) | −5.00000 | − | 4.89898i | −0.505076 | − | 0.494872i | ||||
\(99\) | 2.41421 | 0.242638 | ||||||||
\(100\) | −3.32843 | − | 5.76500i | −0.332843 | − | 0.576500i | ||||
\(101\) | 4.58579 | − | 7.94282i | 0.456303 | − | 0.790340i | −0.542459 | − | 0.840082i | \(-0.682507\pi\) |
0.998762 | + | 0.0497425i | \(0.0158401\pi\) | |||||||
\(102\) | 0.207107 | − | 0.358719i | 0.0205066 | − | 0.0355185i | ||||
\(103\) | 5.58579 | + | 9.67487i | 0.550384 | + | 0.953293i | 0.998247 | + | 0.0591906i | \(0.0188520\pi\) |
−0.447863 | + | 0.894102i | \(0.647815\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −8.94975 | + | 1.22474i | −0.873406 | + | 0.119523i | ||||
\(106\) | −7.48528 | −0.727035 | ||||||||
\(107\) | −1.65685 | − | 2.86976i | −0.160174 | − | 0.277430i | 0.774757 | − | 0.632259i | \(-0.217872\pi\) |
−0.934931 | + | 0.354830i | \(0.884539\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | −0.828427 | + | 1.43488i | −0.0793489 | + | 0.137436i | −0.902969 | − | 0.429705i | \(-0.858617\pi\) |
0.823620 | + | 0.567142i | \(0.191951\pi\) | |||||||
\(110\) | 4.12132 | + | 7.13834i | 0.392952 | + | 0.680614i | ||||
\(111\) | 1.41421 | 0.134231 | ||||||||
\(112\) | 1.62132 | + | 2.09077i | 0.153200 | + | 0.197559i | ||||
\(113\) | −14.8995 | −1.40163 | −0.700813 | − | 0.713345i | \(-0.747179\pi\) | ||||
−0.700813 | + | 0.713345i | \(0.747179\pi\) | |||||||
\(114\) | −3.91421 | − | 6.77962i | −0.366600 | − | 0.634969i | ||||
\(115\) | −2.41421 | + | 4.18154i | −0.225127 | + | 0.389931i | ||||
\(116\) | −1.91421 | + | 3.31552i | −0.177730 | + | 0.307838i | ||||
\(117\) | −0.500000 | − | 0.866025i | −0.0462250 | − | 0.0800641i | ||||
\(118\) | −12.0711 | −1.11123 | ||||||||
\(119\) | 0.414214 | − | 1.01461i | 0.0379709 | − | 0.0930093i | ||||
\(120\) | 3.41421 | 0.311674 | ||||||||
\(121\) | 2.58579 | + | 4.47871i | 0.235071 | + | 0.407156i | ||||
\(122\) | 0.792893 | − | 1.37333i | 0.0717852 | − | 0.124336i | ||||
\(123\) | 4.94975 | − | 8.57321i | 0.446304 | − | 0.773021i | ||||
\(124\) | −4.24264 | − | 7.34847i | −0.381000 | − | 0.659912i | ||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 1.00000 | − | 2.44949i | 0.0890871 | − | 0.218218i | ||||
\(127\) | 11.8995 | 1.05591 | 0.527955 | − | 0.849273i | \(-0.322959\pi\) | ||||
0.527955 | + | 0.849273i | \(0.322959\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −5.24264 | + | 9.08052i | −0.461589 | + | 0.799495i | ||||
\(130\) | 1.70711 | − | 2.95680i | 0.149723 | − | 0.259328i | ||||
\(131\) | −10.7782 | − | 18.6683i | −0.941693 | − | 1.63106i | −0.762240 | − | 0.647295i | \(-0.775900\pi\) |
−0.179453 | − | 0.983766i | \(-0.557433\pi\) | |||||||
\(132\) | −2.41421 | −0.210130 | ||||||||
\(133\) | −12.6924 | − | 16.3674i | −1.10057 | − | 1.41924i | ||||
\(134\) | −3.82843 | −0.330726 | ||||||||
\(135\) | −1.70711 | − | 2.95680i | −0.146924 | − | 0.254480i | ||||
\(136\) | −0.207107 | + | 0.358719i | −0.0177593 | + | 0.0307599i | ||||
\(137\) | 1.53553 | − | 2.65962i | 0.131190 | − | 0.227227i | −0.792946 | − | 0.609292i | \(-0.791454\pi\) |
0.924135 | + | 0.382065i | \(0.124787\pi\) | |||||||
\(138\) | −0.707107 | − | 1.22474i | −0.0601929 | − | 0.104257i | ||||
\(139\) | 1.07107 | 0.0908468 | 0.0454234 | − | 0.998968i | \(-0.485536\pi\) | ||||
0.0454234 | + | 0.998968i | \(0.485536\pi\) | |||||||
\(140\) | 8.94975 | − | 1.22474i | 0.756392 | − | 0.103510i | ||||
\(141\) | −1.00000 | −0.0842152 | ||||||||
\(142\) | 2.50000 | + | 4.33013i | 0.209795 | + | 0.363376i | ||||
\(143\) | −1.20711 | + | 2.09077i | −0.100943 | + | 0.174839i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 6.53553 | + | 11.3199i | 0.542747 | + | 0.940065i | ||||
\(146\) | −1.41421 | −0.117041 | ||||||||
\(147\) | 1.74264 | − | 6.77962i | 0.143731 | − | 0.559173i | ||||
\(148\) | −1.41421 | −0.116248 | ||||||||
\(149\) | 9.53553 | + | 16.5160i | 0.781181 | + | 1.35305i | 0.931254 | + | 0.364371i | \(0.118716\pi\) |
−0.150073 | + | 0.988675i | \(0.547951\pi\) | |||||||
\(150\) | 3.32843 | − | 5.76500i | 0.271765 | − | 0.470711i | ||||
\(151\) | 5.03553 | − | 8.72180i | 0.409786 | − | 0.709770i | −0.585080 | − | 0.810976i | \(-0.698937\pi\) |
0.994866 | + | 0.101206i | \(0.0322701\pi\) | |||||||
\(152\) | 3.91421 | + | 6.77962i | 0.317485 | + | 0.549900i | ||||
\(153\) | 0.414214 | 0.0334872 | ||||||||
\(154\) | −6.32843 | + | 0.866025i | −0.509959 | + | 0.0697863i | ||||
\(155\) | −28.9706 | −2.32697 | ||||||||
\(156\) | 0.500000 | + | 0.866025i | 0.0400320 | + | 0.0693375i | ||||
\(157\) | 7.86396 | − | 13.6208i | 0.627612 | − | 1.08706i | −0.360417 | − | 0.932791i | \(-0.617366\pi\) |
0.988029 | − | 0.154265i | \(-0.0493011\pi\) | |||||||
\(158\) | 0.171573 | − | 0.297173i | 0.0136496 | − | 0.0236418i | ||||
\(159\) | −3.74264 | − | 6.48244i | −0.296811 | − | 0.514091i | ||||
\(160\) | −3.41421 | −0.269917 | ||||||||
\(161\) | −2.29289 | − | 2.95680i | −0.180705 | − | 0.233028i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 3.67157 | + | 6.35935i | 0.287580 | + | 0.498103i | 0.973232 | − | 0.229827i | \(-0.0738160\pi\) |
−0.685652 | + | 0.727930i | \(0.740483\pi\) | |||||||
\(164\) | −4.94975 | + | 8.57321i | −0.386510 | + | 0.669456i | ||||
\(165\) | −4.12132 | + | 7.13834i | −0.320844 | + | 0.555719i | ||||
\(166\) | 1.82843 | + | 3.16693i | 0.141913 | + | 0.245801i | ||||
\(167\) | 10.6569 | 0.824652 | 0.412326 | − | 0.911036i | \(-0.364716\pi\) | ||||
0.412326 | + | 0.911036i | \(0.364716\pi\) | |||||||
\(168\) | −1.00000 | + | 2.44949i | −0.0771517 | + | 0.188982i | ||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.707107 | + | 1.22474i | 0.0542326 | + | 0.0939336i | ||||
\(171\) | 3.91421 | − | 6.77962i | 0.299327 | − | 0.518450i | ||||
\(172\) | 5.24264 | − | 9.08052i | 0.399748 | − | 0.692383i | ||||
\(173\) | 5.74264 | + | 9.94655i | 0.436605 | + | 0.756222i | 0.997425 | − | 0.0717158i | \(-0.0228474\pi\) |
−0.560820 | + | 0.827938i | \(0.689514\pi\) | |||||||
\(174\) | −3.82843 | −0.290232 | ||||||||
\(175\) | 6.65685 | − | 16.3059i | 0.503211 | − | 1.23261i | ||||
\(176\) | 2.41421 | 0.181978 | ||||||||
\(177\) | −6.03553 | − | 10.4539i | −0.453659 | − | 0.785760i | ||||
\(178\) | −2.70711 | + | 4.68885i | −0.202906 | + | 0.351444i | ||||
\(179\) | −4.17157 | + | 7.22538i | −0.311798 | + | 0.540050i | −0.978752 | − | 0.205049i | \(-0.934265\pi\) |
0.666954 | + | 0.745099i | \(0.267598\pi\) | |||||||
\(180\) | 1.70711 | + | 2.95680i | 0.127240 | + | 0.220387i | ||||
\(181\) | −16.8995 | −1.25613 | −0.628065 | − | 0.778161i | \(-0.716153\pi\) | ||||
−0.628065 | + | 0.778161i | \(0.716153\pi\) | |||||||
\(182\) | 1.62132 | + | 2.09077i | 0.120180 | + | 0.154978i | ||||
\(183\) | 1.58579 | 0.117225 | ||||||||
\(184\) | 0.707107 | + | 1.22474i | 0.0521286 | + | 0.0902894i | ||||
\(185\) | −2.41421 | + | 4.18154i | −0.177497 | + | 0.307433i | ||||
\(186\) | 4.24264 | − | 7.34847i | 0.311086 | − | 0.538816i | ||||
\(187\) | −0.500000 | − | 0.866025i | −0.0365636 | − | 0.0633300i | ||||
\(188\) | 1.00000 | 0.0729325 | ||||||||
\(189\) | 2.62132 | − | 0.358719i | 0.190673 | − | 0.0260930i | ||||
\(190\) | 26.7279 | 1.93905 | ||||||||
\(191\) | 10.8284 | + | 18.7554i | 0.783517 | + | 1.35709i | 0.929881 | + | 0.367861i | \(0.119910\pi\) |
−0.146363 | + | 0.989231i | \(0.546757\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 8.53553 | − | 14.7840i | 0.614401 | − | 1.06417i | −0.376088 | − | 0.926584i | \(-0.622731\pi\) |
0.990489 | − | 0.137590i | \(-0.0439357\pi\) | |||||||
\(194\) | 7.53553 | + | 13.0519i | 0.541020 | + | 0.937074i | ||||
\(195\) | 3.41421 | 0.244497 | ||||||||
\(196\) | −1.74264 | + | 6.77962i | −0.124474 | + | 0.484258i | ||||
\(197\) | 15.5563 | 1.10834 | 0.554172 | − | 0.832402i | \(-0.313035\pi\) | ||||
0.554172 | + | 0.832402i | \(0.313035\pi\) | |||||||
\(198\) | −1.20711 | − | 2.09077i | −0.0857853 | − | 0.148585i | ||||
\(199\) | 11.3640 | − | 19.6830i | 0.805570 | − | 1.39529i | −0.110336 | − | 0.993894i | \(-0.535193\pi\) |
0.915906 | − | 0.401394i | \(-0.131474\pi\) | |||||||
\(200\) | −3.32843 | + | 5.76500i | −0.235355 | + | 0.407647i | ||||
\(201\) | −1.91421 | − | 3.31552i | −0.135018 | − | 0.233858i | ||||
\(202\) | −9.17157 | −0.645310 | ||||||||
\(203\) | −10.0355 | + | 1.37333i | −0.704356 | + | 0.0963890i | ||||
\(204\) | −0.414214 | −0.0290008 | ||||||||
\(205\) | 16.8995 | + | 29.2708i | 1.18031 | + | 2.04436i | ||||
\(206\) | 5.58579 | − | 9.67487i | 0.389180 | − | 0.674080i | ||||
\(207\) | 0.707107 | − | 1.22474i | 0.0491473 | − | 0.0851257i | ||||
\(208\) | −0.500000 | − | 0.866025i | −0.0346688 | − | 0.0600481i | ||||
\(209\) | −18.8995 | −1.30731 | ||||||||
\(210\) | 5.53553 | + | 7.13834i | 0.381988 | + | 0.492592i | ||||
\(211\) | −27.0711 | −1.86365 | −0.931825 | − | 0.362909i | \(-0.881784\pi\) | ||||
−0.931825 | + | 0.362909i | \(0.881784\pi\) | |||||||
\(212\) | 3.74264 | + | 6.48244i | 0.257046 | + | 0.445216i | ||||
\(213\) | −2.50000 | + | 4.33013i | −0.171297 | + | 0.296695i | ||||
\(214\) | −1.65685 | + | 2.86976i | −0.113260 | + | 0.196172i | ||||
\(215\) | −17.8995 | − | 31.0028i | −1.22074 | − | 2.11438i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 8.48528 | − | 20.7846i | 0.576018 | − | 1.41095i | ||||
\(218\) | 1.65685 | 0.112216 | ||||||||
\(219\) | −0.707107 | − | 1.22474i | −0.0477818 | − | 0.0827606i | ||||
\(220\) | 4.12132 | − | 7.13834i | 0.277859 | − | 0.481267i | ||||
\(221\) | −0.207107 | + | 0.358719i | −0.0139315 | + | 0.0241301i | ||||
\(222\) | −0.707107 | − | 1.22474i | −0.0474579 | − | 0.0821995i | ||||
\(223\) | −22.0711 | −1.47799 | −0.738994 | − | 0.673712i | \(-0.764699\pi\) | ||||
−0.738994 | + | 0.673712i | \(0.764699\pi\) | |||||||
\(224\) | 1.00000 | − | 2.44949i | 0.0668153 | − | 0.163663i | ||||
\(225\) | 6.65685 | 0.443790 | ||||||||
\(226\) | 7.44975 | + | 12.9033i | 0.495550 | + | 0.858317i | ||||
\(227\) | 13.4142 | − | 23.2341i | 0.890333 | − | 1.54210i | 0.0508557 | − | 0.998706i | \(-0.483805\pi\) |
0.839477 | − | 0.543395i | \(-0.182862\pi\) | |||||||
\(228\) | −3.91421 | + | 6.77962i | −0.259225 | + | 0.448991i | ||||
\(229\) | −4.75736 | − | 8.23999i | −0.314375 | − | 0.544514i | 0.664929 | − | 0.746906i | \(-0.268462\pi\) |
−0.979304 | + | 0.202393i | \(0.935128\pi\) | |||||||
\(230\) | 4.82843 | 0.318377 | ||||||||
\(231\) | −3.91421 | − | 5.04757i | −0.257536 | − | 0.332105i | ||||
\(232\) | 3.82843 | 0.251349 | ||||||||
\(233\) | −3.86396 | − | 6.69258i | −0.253137 | − | 0.438445i | 0.711251 | − | 0.702938i | \(-0.248129\pi\) |
−0.964388 | + | 0.264493i | \(0.914796\pi\) | |||||||
\(234\) | −0.500000 | + | 0.866025i | −0.0326860 | + | 0.0566139i | ||||
\(235\) | 1.70711 | − | 2.95680i | 0.111359 | − | 0.192880i | ||||
\(236\) | 6.03553 | + | 10.4539i | 0.392880 | + | 0.680488i | ||||
\(237\) | 0.343146 | 0.0222897 | ||||||||
\(238\) | −1.08579 | + | 0.148586i | −0.0703811 | + | 0.00963143i | ||||
\(239\) | 21.4853 | 1.38977 | 0.694884 | − | 0.719122i | \(-0.255456\pi\) | ||||
0.694884 | + | 0.719122i | \(0.255456\pi\) | |||||||
\(240\) | −1.70711 | − | 2.95680i | −0.110193 | − | 0.190860i | ||||
\(241\) | −13.0711 | + | 22.6398i | −0.841981 | + | 1.45835i | 0.0462355 | + | 0.998931i | \(0.485278\pi\) |
−0.888217 | + | 0.459424i | \(0.848056\pi\) | |||||||
\(242\) | 2.58579 | − | 4.47871i | 0.166221 | − | 0.287903i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −1.58579 | −0.101520 | ||||||||
\(245\) | 17.0711 | + | 16.7262i | 1.09063 | + | 1.06860i | ||||
\(246\) | −9.89949 | −0.631169 | ||||||||
\(247\) | 3.91421 | + | 6.77962i | 0.249055 | + | 0.431377i | ||||
\(248\) | −4.24264 | + | 7.34847i | −0.269408 | + | 0.466628i | ||||
\(249\) | −1.82843 | + | 3.16693i | −0.115872 | + | 0.200696i | ||||
\(250\) | 2.82843 | + | 4.89898i | 0.178885 | + | 0.309839i | ||||
\(251\) | 19.1716 | 1.21010 | 0.605049 | − | 0.796188i | \(-0.293153\pi\) | ||||
0.605049 | + | 0.796188i | \(0.293153\pi\) | |||||||
\(252\) | −2.62132 | + | 0.358719i | −0.165128 | + | 0.0225972i | ||||
\(253\) | −3.41421 | −0.214650 | ||||||||
\(254\) | −5.94975 | − | 10.3053i | −0.373320 | − | 0.646610i | ||||
\(255\) | −0.707107 | + | 1.22474i | −0.0442807 | + | 0.0766965i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −4.75736 | − | 8.23999i | −0.296756 | − | 0.513996i | 0.678636 | − | 0.734475i | \(-0.262571\pi\) |
−0.975392 | + | 0.220479i | \(0.929238\pi\) | |||||||
\(258\) | 10.4853 | 0.652785 | ||||||||
\(259\) | −2.29289 | − | 2.95680i | −0.142473 | − | 0.183726i | ||||
\(260\) | −3.41421 | −0.211741 | ||||||||
\(261\) | −1.91421 | − | 3.31552i | −0.118487 | − | 0.205225i | ||||
\(262\) | −10.7782 | + | 18.6683i | −0.665878 | + | 1.15333i | ||||
\(263\) | −11.7071 | + | 20.2773i | −0.721891 | + | 1.25035i | 0.238350 | + | 0.971179i | \(0.423394\pi\) |
−0.960241 | + | 0.279173i | \(0.909940\pi\) | |||||||
\(264\) | 1.20711 | + | 2.09077i | 0.0742923 | + | 0.128678i | ||||
\(265\) | 25.5563 | 1.56991 | ||||||||
\(266\) | −7.82843 | + | 19.1757i | −0.479992 | + | 1.17573i | ||||
\(267\) | −5.41421 | −0.331344 | ||||||||
\(268\) | 1.91421 | + | 3.31552i | 0.116929 | + | 0.202527i | ||||
\(269\) | −9.57107 | + | 16.5776i | −0.583558 | + | 1.01075i | 0.411495 | + | 0.911412i | \(0.365007\pi\) |
−0.995053 | + | 0.0993407i | \(0.968327\pi\) | |||||||
\(270\) | −1.70711 | + | 2.95680i | −0.103891 | + | 0.179945i | ||||
\(271\) | 8.10660 | + | 14.0410i | 0.492441 | + | 0.852933i | 0.999962 | − | 0.00870652i | \(-0.00277141\pi\) |
−0.507521 | + | 0.861639i | \(0.669438\pi\) | |||||||
\(272\) | 0.414214 | 0.0251154 | ||||||||
\(273\) | −1.00000 | + | 2.44949i | −0.0605228 | + | 0.148250i | ||||
\(274\) | −3.07107 | −0.185530 | ||||||||
\(275\) | −8.03553 | − | 13.9180i | −0.484561 | − | 0.839284i | ||||
\(276\) | −0.707107 | + | 1.22474i | −0.0425628 | + | 0.0737210i | ||||
\(277\) | −1.96447 | + | 3.40256i | −0.118033 | + | 0.204440i | −0.918988 | − | 0.394285i | \(-0.870992\pi\) |
0.800955 | + | 0.598725i | \(0.204326\pi\) | |||||||
\(278\) | −0.535534 | − | 0.927572i | −0.0321192 | − | 0.0556321i | ||||
\(279\) | 8.48528 | 0.508001 | ||||||||
\(280\) | −5.53553 | − | 7.13834i | −0.330811 | − | 0.426597i | ||||
\(281\) | 23.3137 | 1.39078 | 0.695390 | − | 0.718633i | \(-0.255232\pi\) | ||||
0.695390 | + | 0.718633i | \(0.255232\pi\) | |||||||
\(282\) | 0.500000 | + | 0.866025i | 0.0297746 | + | 0.0515711i | ||||
\(283\) | 12.1213 | − | 20.9947i | 0.720538 | − | 1.24801i | −0.240247 | − | 0.970712i | \(-0.577228\pi\) |
0.960785 | − | 0.277296i | \(-0.0894383\pi\) | |||||||
\(284\) | 2.50000 | − | 4.33013i | 0.148348 | − | 0.256946i | ||||
\(285\) | 13.3640 | + | 23.1471i | 0.791613 | + | 1.37111i | ||||
\(286\) | 2.41421 | 0.142755 | ||||||||
\(287\) | −25.9497 | + | 3.55114i | −1.53177 | + | 0.209617i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 8.41421 | + | 14.5738i | 0.494954 | + | 0.857285i | ||||
\(290\) | 6.53553 | − | 11.3199i | 0.383780 | − | 0.664726i | ||||
\(291\) | −7.53553 | + | 13.0519i | −0.441741 | + | 0.765118i | ||||
\(292\) | 0.707107 | + | 1.22474i | 0.0413803 | + | 0.0716728i | ||||
\(293\) | 9.89949 | 0.578335 | 0.289167 | − | 0.957279i | \(-0.406622\pi\) | ||||
0.289167 | + | 0.957279i | \(0.406622\pi\) | |||||||
\(294\) | −6.74264 | + | 1.88064i | −0.393239 | + | 0.109681i | ||||
\(295\) | 41.2132 | 2.39953 | ||||||||
\(296\) | 0.707107 | + | 1.22474i | 0.0410997 | + | 0.0711868i | ||||
\(297\) | 1.20711 | − | 2.09077i | 0.0700434 | − | 0.121319i | ||||
\(298\) | 9.53553 | − | 16.5160i | 0.552379 | − | 0.956748i | ||||
\(299\) | 0.707107 | + | 1.22474i | 0.0408930 | + | 0.0708288i | ||||
\(300\) | −6.65685 | −0.384334 | ||||||||
\(301\) | 27.4853 | − | 3.76127i | 1.58423 | − | 0.216796i | ||||
\(302\) | −10.0711 | −0.579525 | ||||||||
\(303\) | −4.58579 | − | 7.94282i | −0.263447 | − | 0.456303i | ||||
\(304\) | 3.91421 | − | 6.77962i | 0.224496 | − | 0.388838i | ||||
\(305\) | −2.70711 | + | 4.68885i | −0.155008 | + | 0.268483i | ||||
\(306\) | −0.207107 | − | 0.358719i | −0.0118395 | − | 0.0205066i | ||||
\(307\) | 34.1127 | 1.94691 | 0.973457 | − | 0.228869i | \(-0.0735027\pi\) | ||||
0.973457 | + | 0.228869i | \(0.0735027\pi\) | |||||||
\(308\) | 3.91421 | + | 5.04757i | 0.223033 | + | 0.287612i | ||||
\(309\) | 11.1716 | 0.635529 | ||||||||
\(310\) | 14.4853 | + | 25.0892i | 0.822709 | + | 1.42497i | ||||
\(311\) | 13.9497 | − | 24.1617i | 0.791018 | − | 1.37008i | −0.134320 | − | 0.990938i | \(-0.542885\pi\) |
0.925337 | − | 0.379145i | \(-0.123782\pi\) | |||||||
\(312\) | 0.500000 | − | 0.866025i | 0.0283069 | − | 0.0490290i | ||||
\(313\) | −10.2426 | − | 17.7408i | −0.578948 | − | 1.00277i | −0.995600 | − | 0.0937018i | \(-0.970130\pi\) |
0.416652 | − | 0.909066i | \(-0.363203\pi\) | |||||||
\(314\) | −15.7279 | −0.887578 | ||||||||
\(315\) | −3.41421 | + | 8.36308i | −0.192369 | + | 0.471206i | ||||
\(316\) | −0.343146 | −0.0193035 | ||||||||
\(317\) | 4.89949 | + | 8.48617i | 0.275183 | + | 0.476631i | 0.970181 | − | 0.242380i | \(-0.0779282\pi\) |
−0.694998 | + | 0.719011i | \(0.744595\pi\) | |||||||
\(318\) | −3.74264 | + | 6.48244i | −0.209877 | + | 0.363517i | ||||
\(319\) | −4.62132 | + | 8.00436i | −0.258744 | + | 0.448158i | ||||
\(320\) | 1.70711 | + | 2.95680i | 0.0954302 | + | 0.165290i | ||||
\(321\) | −3.31371 | −0.184953 | ||||||||
\(322\) | −1.41421 | + | 3.46410i | −0.0788110 | + | 0.193047i | ||||
\(323\) | −3.24264 | −0.180425 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −3.32843 | + | 5.76500i | −0.184628 | + | 0.319785i | ||||
\(326\) | 3.67157 | − | 6.35935i | 0.203350 | − | 0.352212i | ||||
\(327\) | 0.828427 | + | 1.43488i | 0.0458121 | + | 0.0793489i | ||||
\(328\) | 9.89949 | 0.546608 | ||||||||
\(329\) | 1.62132 | + | 2.09077i | 0.0893863 | + | 0.115268i | ||||
\(330\) | 8.24264 | 0.453742 | ||||||||
\(331\) | 2.75736 | + | 4.77589i | 0.151558 | + | 0.262506i | 0.931800 | − | 0.362971i | \(-0.118238\pi\) |
−0.780242 | + | 0.625477i | \(0.784904\pi\) | |||||||
\(332\) | 1.82843 | − | 3.16693i | 0.100348 | − | 0.173808i | ||||
\(333\) | 0.707107 | − | 1.22474i | 0.0387492 | − | 0.0671156i | ||||
\(334\) | −5.32843 | − | 9.22911i | −0.291559 | − | 0.504994i | ||||
\(335\) | 13.0711 | 0.714149 | ||||||||
\(336\) | 2.62132 | − | 0.358719i | 0.143005 | − | 0.0195698i | ||||
\(337\) | 2.31371 | 0.126036 | 0.0630179 | − | 0.998012i | \(-0.479927\pi\) | ||||
0.0630179 | + | 0.998012i | \(0.479927\pi\) | |||||||
\(338\) | −0.500000 | − | 0.866025i | −0.0271964 | − | 0.0471056i | ||||
\(339\) | −7.44975 | + | 12.9033i | −0.404615 | + | 0.700813i | ||||
\(340\) | 0.707107 | − | 1.22474i | 0.0383482 | − | 0.0664211i | ||||
\(341\) | −10.2426 | − | 17.7408i | −0.554670 | − | 0.960717i | ||||
\(342\) | −7.82843 | −0.423313 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | −10.4853 | −0.565328 | ||||||||
\(345\) | 2.41421 | + | 4.18154i | 0.129977 | + | 0.225127i | ||||
\(346\) | 5.74264 | − | 9.94655i | 0.308726 | − | 0.534730i | ||||
\(347\) | −8.36396 | + | 14.4868i | −0.449001 | + | 0.777692i | −0.998321 | − | 0.0579194i | \(-0.981553\pi\) |
0.549320 | + | 0.835612i | \(0.314887\pi\) | |||||||
\(348\) | 1.91421 | + | 3.31552i | 0.102613 | + | 0.177730i | ||||
\(349\) | 18.7279 | 1.00248 | 0.501241 | − | 0.865308i | \(-0.332877\pi\) | ||||
0.501241 | + | 0.865308i | \(0.332877\pi\) | |||||||
\(350\) | −17.4497 | + | 2.38794i | −0.932728 | + | 0.127641i | ||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −1.20711 | − | 2.09077i | −0.0643390 | − | 0.111438i | ||||
\(353\) | 16.3137 | − | 28.2562i | 0.868291 | − | 1.50392i | 0.00454930 | − | 0.999990i | \(-0.498552\pi\) |
0.863742 | − | 0.503935i | \(-0.168115\pi\) | |||||||
\(354\) | −6.03553 | + | 10.4539i | −0.320785 | + | 0.555616i | ||||
\(355\) | −8.53553 | − | 14.7840i | −0.453019 | − | 0.784652i | ||||
\(356\) | 5.41421 | 0.286953 | ||||||||
\(357\) | −0.671573 | − | 0.866025i | −0.0355434 | − | 0.0458349i | ||||
\(358\) | 8.34315 | 0.440949 | ||||||||
\(359\) | −2.41421 | − | 4.18154i | −0.127417 | − | 0.220693i | 0.795258 | − | 0.606271i | \(-0.207335\pi\) |
−0.922675 | + | 0.385578i | \(0.874002\pi\) | |||||||
\(360\) | 1.70711 | − | 2.95680i | 0.0899724 | − | 0.155837i | ||||
\(361\) | −21.1421 | + | 36.6193i | −1.11274 | + | 1.92733i | ||||
\(362\) | 8.44975 | + | 14.6354i | 0.444109 | + | 0.769219i | ||||
\(363\) | 5.17157 | 0.271437 | ||||||||
\(364\) | 1.00000 | − | 2.44949i | 0.0524142 | − | 0.128388i | ||||
\(365\) | 4.82843 | 0.252731 | ||||||||
\(366\) | −0.792893 | − | 1.37333i | −0.0414452 | − | 0.0717852i | ||||
\(367\) | 16.3137 | − | 28.2562i | 0.851569 | − | 1.47496i | −0.0282235 | − | 0.999602i | \(-0.508985\pi\) |
0.879792 | − | 0.475359i | \(-0.157682\pi\) | |||||||
\(368\) | 0.707107 | − | 1.22474i | 0.0368605 | − | 0.0638442i | ||||
\(369\) | −4.94975 | − | 8.57321i | −0.257674 | − | 0.446304i | ||||
\(370\) | 4.82843 | 0.251018 | ||||||||
\(371\) | −7.48528 | + | 18.3351i | −0.388616 | + | 0.951912i | ||||
\(372\) | −8.48528 | −0.439941 | ||||||||
\(373\) | 4.20711 | + | 7.28692i | 0.217836 | + | 0.377303i | 0.954146 | − | 0.299341i | \(-0.0967670\pi\) |
−0.736310 | + | 0.676644i | \(0.763434\pi\) | |||||||
\(374\) | −0.500000 | + | 0.866025i | −0.0258544 | + | 0.0447811i | ||||
\(375\) | −2.82843 | + | 4.89898i | −0.146059 | + | 0.252982i | ||||
\(376\) | −0.500000 | − | 0.866025i | −0.0257855 | − | 0.0446619i | ||||
\(377\) | 3.82843 | 0.197174 | ||||||||
\(378\) | −1.62132 | − | 2.09077i | −0.0833917 | − | 0.107538i | ||||
\(379\) | −26.6274 | −1.36776 | −0.683879 | − | 0.729595i | \(-0.739709\pi\) | ||||
−0.683879 | + | 0.729595i | \(0.739709\pi\) | |||||||
\(380\) | −13.3640 | − | 23.1471i | −0.685557 | − | 1.18742i | ||||
\(381\) | 5.94975 | − | 10.3053i | 0.304815 | − | 0.527955i | ||||
\(382\) | 10.8284 | − | 18.7554i | 0.554031 | − | 0.959609i | ||||
\(383\) | −8.41421 | − | 14.5738i | −0.429946 | − | 0.744689i | 0.566922 | − | 0.823772i | \(-0.308134\pi\) |
−0.996868 | + | 0.0790829i | \(0.974801\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 21.6066 | − | 2.95680i | 1.10117 | − | 0.150692i | ||||
\(386\) | −17.0711 | −0.868894 | ||||||||
\(387\) | 5.24264 | + | 9.08052i | 0.266498 | + | 0.461589i | ||||
\(388\) | 7.53553 | − | 13.0519i | 0.382559 | − | 0.662611i | ||||
\(389\) | 10.7426 | − | 18.6068i | 0.544674 | − | 0.943402i | −0.453954 | − | 0.891025i | \(-0.649987\pi\) |
0.998627 | − | 0.0523770i | \(-0.0166797\pi\) | |||||||
\(390\) | −1.70711 | − | 2.95680i | −0.0864427 | − | 0.149723i | ||||
\(391\) | −0.585786 | −0.0296245 | ||||||||
\(392\) | 6.74264 | − | 1.88064i | 0.340555 | − | 0.0949865i | ||||
\(393\) | −21.5563 | −1.08737 | ||||||||
\(394\) | −7.77817 | − | 13.4722i | −0.391859 | − | 0.678719i | ||||
\(395\) | −0.585786 | + | 1.01461i | −0.0294741 | + | 0.0510507i | ||||
\(396\) | −1.20711 | + | 2.09077i | −0.0606594 | + | 0.105065i | ||||
\(397\) | −10.7782 | − | 18.6683i | −0.540941 | − | 0.936937i | −0.998850 | − | 0.0479385i | \(-0.984735\pi\) |
0.457909 | − | 0.888999i | \(-0.348598\pi\) | |||||||
\(398\) | −22.7279 | −1.13925 | ||||||||
\(399\) | −20.5208 | + | 2.80821i | −1.02733 | + | 0.140586i | ||||
\(400\) | 6.65685 | 0.332843 | ||||||||
\(401\) | −0.0502525 | − | 0.0870399i | −0.00250949 | − | 0.00434657i | 0.864768 | − | 0.502172i | \(-0.167465\pi\) |
−0.867277 | + | 0.497825i | \(0.834132\pi\) | |||||||
\(402\) | −1.91421 | + | 3.31552i | −0.0954723 | + | 0.165363i | ||||
\(403\) | −4.24264 | + | 7.34847i | −0.211341 | + | 0.366053i | ||||
\(404\) | 4.58579 | + | 7.94282i | 0.228151 | + | 0.395170i | ||||
\(405\) | −3.41421 | −0.169654 | ||||||||
\(406\) | 6.20711 | + | 8.00436i | 0.308054 | + | 0.397250i | ||||
\(407\) | −3.41421 | −0.169236 | ||||||||
\(408\) | 0.207107 | + | 0.358719i | 0.0102533 | + | 0.0177593i | ||||
\(409\) | −17.7071 | + | 30.6696i | −0.875560 | + | 1.51651i | −0.0193952 | + | 0.999812i | \(0.506174\pi\) |
−0.856165 | + | 0.516703i | \(0.827159\pi\) | |||||||
\(410\) | 16.8995 | − | 29.2708i | 0.834607 | − | 1.44558i | ||||
\(411\) | −1.53553 | − | 2.65962i | −0.0757423 | − | 0.131190i | ||||
\(412\) | −11.1716 | −0.550384 | ||||||||
\(413\) | −12.0711 | + | 29.5680i | −0.593978 | + | 1.45494i | ||||
\(414\) | −1.41421 | −0.0695048 | ||||||||
\(415\) | −6.24264 | − | 10.8126i | −0.306439 | − | 0.530768i | ||||
\(416\) | −0.500000 | + | 0.866025i | −0.0245145 | + | 0.0424604i | ||||
\(417\) | 0.535534 | − | 0.927572i | 0.0262252 | − | 0.0454234i | ||||
\(418\) | 9.44975 | + | 16.3674i | 0.462202 | + | 0.800558i | ||||
\(419\) | −23.4558 | −1.14589 | −0.572946 | − | 0.819593i | \(-0.694200\pi\) | ||||
−0.572946 | + | 0.819593i | \(0.694200\pi\) | |||||||
\(420\) | 3.41421 | − | 8.36308i | 0.166597 | − | 0.408077i | ||||
\(421\) | −13.0711 | −0.637045 | −0.318522 | − | 0.947915i | \(-0.603187\pi\) | ||||
−0.318522 | + | 0.947915i | \(0.603187\pi\) | |||||||
\(422\) | 13.5355 | + | 23.4442i | 0.658899 | + | 1.14125i | ||||
\(423\) | −0.500000 | + | 0.866025i | −0.0243108 | + | 0.0421076i | ||||
\(424\) | 3.74264 | − | 6.48244i | 0.181759 | − | 0.314815i | ||||
\(425\) | −1.37868 | − | 2.38794i | −0.0668758 | − | 0.115832i | ||||
\(426\) | 5.00000 | 0.242251 | ||||||||
\(427\) | −2.57107 | − | 3.31552i | −0.124423 | − | 0.160449i | ||||
\(428\) | 3.31371 | 0.160174 | ||||||||
\(429\) | 1.20711 | + | 2.09077i | 0.0582797 | + | 0.100943i | ||||
\(430\) | −17.8995 | + | 31.0028i | −0.863190 | + | 1.49509i | ||||
\(431\) | −6.75736 | + | 11.7041i | −0.325491 | + | 0.563766i | −0.981612 | − | 0.190890i | \(-0.938863\pi\) |
0.656121 | + | 0.754656i | \(0.272196\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −3.97056 | −0.190813 | −0.0954065 | − | 0.995438i | \(-0.530415\pi\) | ||||
−0.0954065 | + | 0.995438i | \(0.530415\pi\) | |||||||
\(434\) | −22.2426 | + | 3.04384i | −1.06768 | + | 0.146109i | ||||
\(435\) | 13.0711 | 0.626710 | ||||||||
\(436\) | −0.828427 | − | 1.43488i | −0.0396745 | − | 0.0687182i | ||||
\(437\) | −5.53553 | + | 9.58783i | −0.264800 | + | 0.458648i | ||||
\(438\) | −0.707107 | + | 1.22474i | −0.0337869 | + | 0.0585206i | ||||
\(439\) | −9.70711 | − | 16.8132i | −0.463295 | − | 0.802450i | 0.535828 | − | 0.844327i | \(-0.320000\pi\) |
−0.999123 | + | 0.0418769i | \(0.986666\pi\) | |||||||
\(440\) | −8.24264 | −0.392952 | ||||||||
\(441\) | −5.00000 | − | 4.89898i | −0.238095 | − | 0.233285i | ||||
\(442\) | 0.414214 | 0.0197021 | ||||||||
\(443\) | −12.8492 | − | 22.2555i | −0.610486 | − | 1.05739i | −0.991159 | − | 0.132683i | \(-0.957641\pi\) |
0.380673 | − | 0.924710i | \(-0.375692\pi\) | |||||||
\(444\) | −0.707107 | + | 1.22474i | −0.0335578 | + | 0.0581238i | ||||
\(445\) | 9.24264 | − | 16.0087i | 0.438143 | − | 0.758886i | ||||
\(446\) | 11.0355 | + | 19.1141i | 0.522548 | + | 0.905079i | ||||
\(447\) | 19.0711 | 0.902031 | ||||||||
\(448\) | −2.62132 | + | 0.358719i | −0.123846 | + | 0.0169479i | ||||
\(449\) | −8.97056 | −0.423347 | −0.211674 | − | 0.977340i | \(-0.567891\pi\) | ||||
−0.211674 | + | 0.977340i | \(0.567891\pi\) | |||||||
\(450\) | −3.32843 | − | 5.76500i | −0.156904 | − | 0.271765i | ||||
\(451\) | −11.9497 | + | 20.6976i | −0.562692 | + | 0.974610i | ||||
\(452\) | 7.44975 | − | 12.9033i | 0.350407 | − | 0.606922i | ||||
\(453\) | −5.03553 | − | 8.72180i | −0.236590 | − | 0.409786i | ||||
\(454\) | −26.8284 | −1.25912 | ||||||||
\(455\) | −5.53553 | − | 7.13834i | −0.259510 | − | 0.334650i | ||||
\(456\) | 7.82843 | 0.366600 | ||||||||
\(457\) | −5.53553 | − | 9.58783i | −0.258941 | − | 0.448500i | 0.707017 | − | 0.707196i | \(-0.250040\pi\) |
−0.965959 | + | 0.258697i | \(0.916707\pi\) | |||||||
\(458\) | −4.75736 | + | 8.23999i | −0.222297 | + | 0.385029i | ||||
\(459\) | 0.207107 | − | 0.358719i | 0.00966692 | − | 0.0167436i | ||||
\(460\) | −2.41421 | − | 4.18154i | −0.112563 | − | 0.194965i | ||||
\(461\) | 12.4853 | 0.581498 | 0.290749 | − | 0.956799i | \(-0.406096\pi\) | ||||
0.290749 | + | 0.956799i | \(0.406096\pi\) | |||||||
\(462\) | −2.41421 | + | 5.91359i | −0.112319 | + | 0.275125i | ||||
\(463\) | 12.9706 | 0.602793 | 0.301397 | − | 0.953499i | \(-0.402547\pi\) | ||||
0.301397 | + | 0.953499i | \(0.402547\pi\) | |||||||
\(464\) | −1.91421 | − | 3.31552i | −0.0888651 | − | 0.153919i | ||||
\(465\) | −14.4853 | + | 25.0892i | −0.671739 | + | 1.16349i | ||||
\(466\) | −3.86396 | + | 6.69258i | −0.178995 | + | 0.310028i | ||||
\(467\) | 4.29289 | + | 7.43551i | 0.198651 | + | 0.344074i | 0.948091 | − | 0.317998i | \(-0.103011\pi\) |
−0.749440 | + | 0.662072i | \(0.769677\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −3.82843 | + | 9.37769i | −0.176780 | + | 0.433022i | ||||
\(470\) | −3.41421 | −0.157486 | ||||||||
\(471\) | −7.86396 | − | 13.6208i | −0.362352 | − | 0.627612i | ||||
\(472\) | 6.03553 | − | 10.4539i | 0.277808 | − | 0.481178i | ||||
\(473\) | 12.6569 | − | 21.9223i | 0.581963 | − | 1.00799i | ||||
\(474\) | −0.171573 | − | 0.297173i | −0.00788060 | − | 0.0136496i | ||||
\(475\) | −52.1127 | −2.39109 | ||||||||
\(476\) | 0.671573 | + | 0.866025i | 0.0307815 | + | 0.0396942i | ||||
\(477\) | −7.48528 | −0.342727 | ||||||||
\(478\) | −10.7426 | − | 18.6068i | −0.491357 | − | 0.851055i | ||||
\(479\) | −15.0563 | + | 26.0784i | −0.687942 | + | 1.19155i | 0.284560 | + | 0.958658i | \(0.408152\pi\) |
−0.972502 | + | 0.232893i | \(0.925181\pi\) | |||||||
\(480\) | −1.70711 | + | 2.95680i | −0.0779184 | + | 0.134959i | ||||
\(481\) | 0.707107 | + | 1.22474i | 0.0322413 | + | 0.0558436i | ||||
\(482\) | 26.1421 | 1.19074 | ||||||||
\(483\) | −3.70711 | + | 0.507306i | −0.168679 | + | 0.0230832i | ||||
\(484\) | −5.17157 | −0.235071 | ||||||||
\(485\) | −25.7279 | − | 44.5621i | −1.16824 | − | 2.02346i | ||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | 13.1066 | − | 22.7013i | 0.593917 | − | 1.02869i | −0.399782 | − | 0.916610i | \(-0.630914\pi\) |
0.993699 | − | 0.112084i | \(-0.0357525\pi\) | |||||||
\(488\) | 0.792893 | + | 1.37333i | 0.0358926 | + | 0.0621678i | ||||
\(489\) | 7.34315 | 0.332069 | ||||||||
\(490\) | 5.94975 | − | 23.1471i | 0.268782 | − | 1.04568i | ||||
\(491\) | 12.3431 | 0.557038 | 0.278519 | − | 0.960431i | \(-0.410156\pi\) | ||||
0.278519 | + | 0.960431i | \(0.410156\pi\) | |||||||
\(492\) | 4.94975 | + | 8.57321i | 0.223152 | + | 0.386510i | ||||
\(493\) | −0.792893 | + | 1.37333i | −0.0357101 | + | 0.0618517i | ||||
\(494\) | 3.91421 | − | 6.77962i | 0.176109 | − | 0.305029i | ||||
\(495\) | 4.12132 | + | 7.13834i | 0.185240 | + | 0.320844i | ||||
\(496\) | 8.48528 | 0.381000 | ||||||||
\(497\) | 13.1066 | − | 1.79360i | 0.587911 | − | 0.0804538i | ||||
\(498\) | 3.65685 | 0.163868 | ||||||||
\(499\) | 3.82843 | + | 6.63103i | 0.171384 | + | 0.296846i | 0.938904 | − | 0.344179i | \(-0.111843\pi\) |
−0.767520 | + | 0.641025i | \(0.778509\pi\) | |||||||
\(500\) | 2.82843 | − | 4.89898i | 0.126491 | − | 0.219089i | ||||
\(501\) | 5.32843 | − | 9.22911i | 0.238057 | − | 0.412326i | ||||
\(502\) | −9.58579 | − | 16.6031i | −0.427835 | − | 0.741031i | ||||
\(503\) | −2.14214 | −0.0955131 | −0.0477566 | − | 0.998859i | \(-0.515207\pi\) | ||||
−0.0477566 | + | 0.998859i | \(0.515207\pi\) | |||||||
\(504\) | 1.62132 | + | 2.09077i | 0.0722193 | + | 0.0931303i | ||||
\(505\) | 31.3137 | 1.39344 | ||||||||
\(506\) | 1.70711 | + | 2.95680i | 0.0758902 | + | 0.131446i | ||||
\(507\) | 0.500000 | − | 0.866025i | 0.0222058 | − | 0.0384615i | ||||
\(508\) | −5.94975 | + | 10.3053i | −0.263977 | + | 0.457222i | ||||
\(509\) | 17.3137 | + | 29.9882i | 0.767417 | + | 1.32920i | 0.938959 | + | 0.344028i | \(0.111791\pi\) |
−0.171543 | + | 0.985177i | \(0.554875\pi\) | |||||||
\(510\) | 1.41421 | 0.0626224 | ||||||||
\(511\) | −1.41421 | + | 3.46410i | −0.0625611 | + | 0.153243i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.91421 | − | 6.77962i | −0.172817 | − | 0.299327i | ||||
\(514\) | −4.75736 | + | 8.23999i | −0.209838 | + | 0.363450i | ||||
\(515\) | −19.0711 | + | 33.0321i | −0.840372 | + | 1.45557i | ||||
\(516\) | −5.24264 | − | 9.08052i | −0.230794 | − | 0.399748i | ||||
\(517\) | 2.41421 | 0.106177 | ||||||||
\(518\) | −1.41421 | + | 3.46410i | −0.0621370 | + | 0.152204i | ||||
\(519\) | 11.4853 | 0.504148 | ||||||||
\(520\) | 1.70711 | + | 2.95680i | 0.0748616 | + | 0.129664i | ||||
\(521\) | 2.31371 | − | 4.00746i | 0.101365 | − | 0.175570i | −0.810882 | − | 0.585210i | \(-0.801012\pi\) |
0.912247 | + | 0.409640i | \(0.134346\pi\) | |||||||
\(522\) | −1.91421 | + | 3.31552i | −0.0837829 | + | 0.145116i | ||||
\(523\) | 5.58579 | + | 9.67487i | 0.244249 | + | 0.423052i | 0.961920 | − | 0.273330i | \(-0.0881251\pi\) |
−0.717671 | + | 0.696382i | \(0.754792\pi\) | |||||||
\(524\) | 21.5563 | 0.941693 | ||||||||
\(525\) | −10.7929 | − | 13.9180i | −0.471040 | − | 0.607429i | ||||
\(526\) | 23.4142 | 1.02091 | ||||||||
\(527\) | −1.75736 | − | 3.04384i | −0.0765518 | − | 0.132592i | ||||
\(528\) | 1.20711 | − | 2.09077i | 0.0525326 | − | 0.0909891i | ||||
\(529\) | 10.5000 | − | 18.1865i | 0.456522 | − | 0.790719i | ||||
\(530\) | −12.7782 | − | 22.1324i | −0.555048 | − | 0.961372i | ||||
\(531\) | −12.0711 | −0.523840 | ||||||||
\(532\) | 20.5208 | − | 2.80821i | 0.889690 | − | 0.121751i | ||||
\(533\) | 9.89949 | 0.428795 | ||||||||
\(534\) | 2.70711 | + | 4.68885i | 0.117148 | + | 0.202906i | ||||
\(535\) | 5.65685 | − | 9.79796i | 0.244567 | − | 0.423603i | ||||
\(536\) | 1.91421 | − | 3.31552i | 0.0826814 | − | 0.143208i | ||||
\(537\) | 4.17157 | + | 7.22538i | 0.180017 | + | 0.311798i | ||||
\(538\) | 19.1421 | 0.825276 | ||||||||
\(539\) | −4.20711 | + | 16.3674i | −0.181213 | + | 0.704996i | ||||
\(540\) | 3.41421 | 0.146924 | ||||||||
\(541\) | −4.46447 | − | 7.73268i | −0.191942 | − | 0.332454i | 0.753952 | − | 0.656930i | \(-0.228145\pi\) |
−0.945894 | + | 0.324476i | \(0.894812\pi\) | |||||||
\(542\) | 8.10660 | − | 14.0410i | 0.348208 | − | 0.603115i | ||||
\(543\) | −8.44975 | + | 14.6354i | −0.362613 | + | 0.628065i | ||||
\(544\) | −0.207107 | − | 0.358719i | −0.00887963 | − | 0.0153800i | ||||
\(545\) | −5.65685 | −0.242313 | ||||||||
\(546\) | 2.62132 | − | 0.358719i | 0.112182 | − | 0.0153518i | ||||
\(547\) | 22.8701 | 0.977853 | 0.488927 | − | 0.872325i | \(-0.337389\pi\) | ||||
0.488927 | + | 0.872325i | \(0.337389\pi\) | |||||||
\(548\) | 1.53553 | + | 2.65962i | 0.0655948 | + | 0.113613i | ||||
\(549\) | 0.792893 | − | 1.37333i | 0.0338399 | − | 0.0586124i | ||||
\(550\) | −8.03553 | + | 13.9180i | −0.342636 | + | 0.593464i | ||||
\(551\) | 14.9853 | + | 25.9553i | 0.638394 | + | 1.10573i | ||||
\(552\) | 1.41421 | 0.0601929 | ||||||||
\(553\) | −0.556349 | − | 0.717439i | −0.0236584 | − | 0.0305086i | ||||
\(554\) | 3.92893 | 0.166924 | ||||||||
\(555\) | 2.41421 | + | 4.18154i | 0.102478 | + | 0.177497i | ||||
\(556\) | −0.535534 | + | 0.927572i | −0.0227117 | + | 0.0393378i | ||||
\(557\) | −6.31371 | + | 10.9357i | −0.267520 | + | 0.463359i | −0.968221 | − | 0.250097i | \(-0.919538\pi\) |
0.700700 | + | 0.713456i | \(0.252871\pi\) | |||||||
\(558\) | −4.24264 | − | 7.34847i | −0.179605 | − | 0.311086i | ||||
\(559\) | −10.4853 | −0.443480 | ||||||||
\(560\) | −3.41421 | + | 8.36308i | −0.144277 | + | 0.353405i | ||||
\(561\) | −1.00000 | −0.0422200 | ||||||||
\(562\) | −11.6569 | − | 20.1903i | −0.491715 | − | 0.851675i | ||||
\(563\) | −20.3848 | + | 35.3075i | −0.859116 | + | 1.48803i | 0.0136575 | + | 0.999907i | \(0.495653\pi\) |
−0.872773 | + | 0.488126i | \(0.837681\pi\) | |||||||
\(564\) | 0.500000 | − | 0.866025i | 0.0210538 | − | 0.0364662i | ||||
\(565\) | −25.4350 | − | 44.0548i | −1.07006 | − | 1.85340i | ||||
\(566\) | −24.2426 | −1.01899 | ||||||||
\(567\) | 1.00000 | − | 2.44949i | 0.0419961 | − | 0.102869i | ||||
\(568\) | −5.00000 | −0.209795 | ||||||||
\(569\) | 0.863961 | + | 1.49642i | 0.0362191 | + | 0.0627334i | 0.883567 | − | 0.468305i | \(-0.155135\pi\) |
−0.847348 | + | 0.531039i | \(0.821802\pi\) | |||||||
\(570\) | 13.3640 | − | 23.1471i | 0.559755 | − | 0.969524i | ||||
\(571\) | 4.34315 | − | 7.52255i | 0.181755 | − | 0.314809i | −0.760723 | − | 0.649076i | \(-0.775156\pi\) |
0.942478 | + | 0.334267i | \(0.108489\pi\) | |||||||
\(572\) | −1.20711 | − | 2.09077i | −0.0504717 | − | 0.0874195i | ||||
\(573\) | 21.6569 | 0.904728 | ||||||||
\(574\) | 16.0503 | + | 20.6976i | 0.669925 | + | 0.863900i | ||||
\(575\) | −9.41421 | −0.392600 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −13.8284 | + | 23.9515i | −0.575685 | + | 0.997116i | 0.420282 | + | 0.907394i | \(0.361931\pi\) |
−0.995967 | + | 0.0897220i | \(0.971402\pi\) | |||||||
\(578\) | 8.41421 | − | 14.5738i | 0.349985 | − | 0.606192i | ||||
\(579\) | −8.53553 | − | 14.7840i | −0.354725 | − | 0.614401i | ||||
\(580\) | −13.0711 | −0.542747 | ||||||||
\(581\) | 9.58579 | − | 1.31178i | 0.397685 | − | 0.0544220i | ||||
\(582\) | 15.0711 | 0.624716 | ||||||||
\(583\) | 9.03553 | + | 15.6500i | 0.374214 | + | 0.648157i | ||||
\(584\) | 0.707107 | − | 1.22474i | 0.0292603 | − | 0.0506803i | ||||
\(585\) | 1.70711 | − | 2.95680i | 0.0705802 | − | 0.122248i | ||||
\(586\) | −4.94975 | − | 8.57321i | −0.204472 | − | 0.354156i | ||||
\(587\) | −4.41421 | −0.182194 | −0.0910970 | − | 0.995842i | \(-0.529037\pi\) | ||||
−0.0910970 | + | 0.995842i | \(0.529037\pi\) | |||||||
\(588\) | 5.00000 | + | 4.89898i | 0.206197 | + | 0.202031i | ||||
\(589\) | −66.4264 | −2.73705 | ||||||||
\(590\) | −20.6066 | − | 35.6917i | −0.848360 | − | 1.46940i | ||||
\(591\) | 7.77817 | − | 13.4722i | 0.319951 | − | 0.554172i | ||||
\(592\) | 0.707107 | − | 1.22474i | 0.0290619 | − | 0.0503367i | ||||
\(593\) | −1.19239 | − | 2.06528i | −0.0489655 | − | 0.0848108i | 0.840504 | − | 0.541806i | \(-0.182259\pi\) |
−0.889469 | + | 0.456995i | \(0.848926\pi\) | |||||||
\(594\) | −2.41421 | −0.0990564 | ||||||||
\(595\) | 3.70711 | − | 0.507306i | 0.151977 | − | 0.0207975i | ||||
\(596\) | −19.0711 | −0.781181 | ||||||||
\(597\) | −11.3640 | − | 19.6830i | −0.465096 | − | 0.805570i | ||||
\(598\) | 0.707107 | − | 1.22474i | 0.0289157 | − | 0.0500835i | ||||
\(599\) | 14.7782 | − | 25.5965i | 0.603820 | − | 1.04585i | −0.388417 | − | 0.921484i | \(-0.626978\pi\) |
0.992237 | − | 0.124363i | \(-0.0396887\pi\) | |||||||
\(600\) | 3.32843 | + | 5.76500i | 0.135882 | + | 0.235355i | ||||
\(601\) | 40.7990 | 1.66423 | 0.832113 | − | 0.554606i | \(-0.187131\pi\) | ||||
0.832113 | + | 0.554606i | \(0.187131\pi\) | |||||||
\(602\) | −17.0000 | − | 21.9223i | −0.692868 | − | 0.893487i | ||||
\(603\) | −3.82843 | −0.155906 | ||||||||
\(604\) | 5.03553 | + | 8.72180i | 0.204893 | + | 0.354885i | ||||
\(605\) | −8.82843 | + | 15.2913i | −0.358927 | + | 0.621679i | ||||
\(606\) | −4.58579 | + | 7.94282i | −0.186285 | + | 0.322655i | ||||
\(607\) | 15.2635 | + | 26.4371i | 0.619525 | + | 1.07305i | 0.989573 | + | 0.144035i | \(0.0460079\pi\) |
−0.370048 | + | 0.929013i | \(0.620659\pi\) | |||||||
\(608\) | −7.82843 | −0.317485 | ||||||||
\(609\) | −3.82843 | + | 9.37769i | −0.155136 | + | 0.380003i | ||||
\(610\) | 5.41421 | 0.219215 | ||||||||
\(611\) | −0.500000 | − | 0.866025i | −0.0202278 | − | 0.0350356i | ||||
\(612\) | −0.207107 | + | 0.358719i | −0.00837180 | + | 0.0145004i | ||||
\(613\) | −15.8995 | + | 27.5387i | −0.642175 | + | 1.11228i | 0.342772 | + | 0.939419i | \(0.388634\pi\) |
−0.984946 | + | 0.172860i | \(0.944699\pi\) | |||||||
\(614\) | −17.0563 | − | 29.5425i | −0.688338 | − | 1.19224i | ||||
\(615\) | 33.7990 | 1.36291 | ||||||||
\(616\) | 2.41421 | − | 5.91359i | 0.0972714 | − | 0.238265i | ||||
\(617\) | 4.14214 | 0.166756 | 0.0833781 | − | 0.996518i | \(-0.473429\pi\) | ||||
0.0833781 | + | 0.996518i | \(0.473429\pi\) | |||||||
\(618\) | −5.58579 | − | 9.67487i | −0.224693 | − | 0.389180i | ||||
\(619\) | −7.58579 | + | 13.1390i | −0.304898 | + | 0.528100i | −0.977239 | − | 0.212143i | \(-0.931956\pi\) |
0.672340 | + | 0.740242i | \(0.265289\pi\) | |||||||
\(620\) | 14.4853 | − | 25.0892i | 0.581743 | − | 1.00761i | ||||
\(621\) | −0.707107 | − | 1.22474i | −0.0283752 | − | 0.0491473i | ||||
\(622\) | −27.8995 | −1.11867 | ||||||||
\(623\) | 8.77817 | + | 11.3199i | 0.351690 | + | 0.453521i | ||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 6.98528 | + | 12.0989i | 0.279411 | + | 0.483954i | ||||
\(626\) | −10.2426 | + | 17.7408i | −0.409378 | + | 0.709064i | ||||
\(627\) | −9.44975 | + | 16.3674i | −0.377387 | + | 0.653653i | ||||
\(628\) | 7.86396 | + | 13.6208i | 0.313806 | + | 0.543528i | ||||
\(629\) | −0.585786 | −0.0233568 | ||||||||
\(630\) | 8.94975 | − | 1.22474i | 0.356566 | − | 0.0487950i | ||||
\(631\) | −12.6274 | −0.502690 | −0.251345 | − | 0.967898i | \(-0.580873\pi\) | ||||
−0.251345 | + | 0.967898i | \(0.580873\pi\) | |||||||
\(632\) | 0.171573 | + | 0.297173i | 0.00682480 | + | 0.0118209i | ||||
\(633\) | −13.5355 | + | 23.4442i | −0.537989 | + | 0.931825i | ||||
\(634\) | 4.89949 | − | 8.48617i | 0.194584 | − | 0.337029i | ||||
\(635\) | 20.3137 | + | 35.1844i | 0.806125 | + | 1.39625i | ||||
\(636\) | 7.48528 | 0.296811 | ||||||||
\(637\) | 6.74264 | − | 1.88064i | 0.267153 | − | 0.0745136i | ||||
\(638\) | 9.24264 | 0.365920 | ||||||||
\(639\) | 2.50000 | + | 4.33013i | 0.0988985 | + | 0.171297i | ||||
\(640\) | 1.70711 | − | 2.95680i | 0.0674793 | − | 0.116878i | ||||
\(641\) | 3.89949 | − | 6.75412i | 0.154021 | − | 0.266772i | −0.778681 | − | 0.627420i | \(-0.784111\pi\) |
0.932702 | + | 0.360648i | \(0.117444\pi\) | |||||||
\(642\) | 1.65685 | + | 2.86976i | 0.0653908 | + | 0.113260i | ||||
\(643\) | −19.4853 | −0.768424 | −0.384212 | − | 0.923245i | \(-0.625527\pi\) | ||||
−0.384212 | + | 0.923245i | \(0.625527\pi\) | |||||||
\(644\) | 3.70711 | − | 0.507306i | 0.146080 | − | 0.0199907i | ||||
\(645\) | −35.7990 | −1.40958 | ||||||||
\(646\) | 1.62132 | + | 2.80821i | 0.0637900 | + | 0.110488i | ||||
\(647\) | 21.4853 | − | 37.2136i | 0.844674 | − | 1.46302i | −0.0412308 | − | 0.999150i | \(-0.513128\pi\) |
0.885904 | − | 0.463868i | \(-0.153539\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 14.5711 | + | 25.2378i | 0.571964 | + | 0.990671i | ||||
\(650\) | 6.65685 | 0.261103 | ||||||||
\(651\) | −13.7574 | − | 17.7408i | −0.539193 | − | 0.695316i | ||||
\(652\) | −7.34315 | −0.287580 | ||||||||
\(653\) | 3.07107 | + | 5.31925i | 0.120180 | + | 0.208158i | 0.919839 | − | 0.392297i | \(-0.128319\pi\) |
−0.799658 | + | 0.600455i | \(0.794986\pi\) | |||||||
\(654\) | 0.828427 | − | 1.43488i | 0.0323941 | − | 0.0561082i | ||||
\(655\) | 36.7990 | − | 63.7377i | 1.43786 | − | 2.49044i | ||||
\(656\) | −4.94975 | − | 8.57321i | −0.193255 | − | 0.334728i | ||||
\(657\) | −1.41421 | −0.0551737 | ||||||||
\(658\) | 1.00000 | − | 2.44949i | 0.0389841 | − | 0.0954911i | ||||
\(659\) | 13.4142 | 0.522544 | 0.261272 | − | 0.965265i | \(-0.415858\pi\) | ||||
0.261272 | + | 0.965265i | \(0.415858\pi\) | |||||||
\(660\) | −4.12132 | − | 7.13834i | −0.160422 | − | 0.277859i | ||||
\(661\) | −15.8787 | + | 27.5027i | −0.617609 | + | 1.06973i | 0.372312 | + | 0.928108i | \(0.378565\pi\) |
−0.989921 | + | 0.141623i | \(0.954768\pi\) | |||||||
\(662\) | 2.75736 | − | 4.77589i | 0.107168 | − | 0.185620i | ||||
\(663\) | 0.207107 | + | 0.358719i | 0.00804336 | + | 0.0139315i | ||||
\(664\) | −3.65685 | −0.141913 | ||||||||
\(665\) | 26.7279 | − | 65.4698i | 1.03646 | − | 2.53881i | ||||
\(666\) | −1.41421 | −0.0547997 | ||||||||
\(667\) | 2.70711 | + | 4.68885i | 0.104820 | + | 0.181553i | ||||
\(668\) | −5.32843 | + | 9.22911i | −0.206163 | + | 0.357085i | ||||
\(669\) | −11.0355 | + | 19.1141i | −0.426658 | + | 0.738994i | ||||
\(670\) | −6.53553 | − | 11.3199i | −0.252490 | − | 0.437325i | ||||
\(671\) | −3.82843 | −0.147795 | ||||||||
\(672\) | −1.62132 | − | 2.09077i | −0.0625438 | − | 0.0806532i | ||||
\(673\) | 13.8579 | 0.534181 | 0.267091 | − | 0.963671i | \(-0.413938\pi\) | ||||
0.267091 | + | 0.963671i | \(0.413938\pi\) | |||||||
\(674\) | −1.15685 | − | 2.00373i | −0.0445604 | − | 0.0771808i | ||||
\(675\) | 3.32843 | − | 5.76500i | 0.128111 | − | 0.221895i | ||||
\(676\) | −0.500000 | + | 0.866025i | −0.0192308 | + | 0.0333087i | ||||
\(677\) | −7.50000 | − | 12.9904i | −0.288248 | − | 0.499261i | 0.685143 | − | 0.728408i | \(-0.259740\pi\) |
−0.973392 | + | 0.229147i | \(0.926406\pi\) | |||||||
\(678\) | 14.8995 | 0.572212 | ||||||||
\(679\) | 39.5061 | − | 5.40629i | 1.51610 | − | 0.207474i | ||||
\(680\) | −1.41421 | −0.0542326 | ||||||||
\(681\) | −13.4142 | − | 23.2341i | −0.514034 | − | 0.890333i | ||||
\(682\) | −10.2426 | + | 17.7408i | −0.392211 | + | 0.679329i | ||||
\(683\) | −7.07107 | + | 12.2474i | −0.270567 | + | 0.468636i | −0.969007 | − | 0.247033i | \(-0.920544\pi\) |
0.698440 | + | 0.715668i | \(0.253878\pi\) | |||||||
\(684\) | 3.91421 | + | 6.77962i | 0.149664 | + | 0.259225i | ||||
\(685\) | 10.4853 | 0.400622 | ||||||||
\(686\) | 14.8640 | + | 11.0482i | 0.567509 | + | 0.421822i | ||||
\(687\) | −9.51472 | −0.363009 | ||||||||
\(688\) | 5.24264 | + | 9.08052i | 0.199874 | + | 0.346192i | ||||
\(689\) | 3.74264 | − | 6.48244i | 0.142583 | − | 0.246961i | ||||
\(690\) | 2.41421 | − | 4.18154i | 0.0919075 | − | 0.159189i | ||||
\(691\) | 4.67157 | + | 8.09140i | 0.177715 | + | 0.307811i | 0.941098 | − | 0.338135i | \(-0.109796\pi\) |
−0.763383 | + | 0.645947i | \(0.776463\pi\) | |||||||
\(692\) | −11.4853 | −0.436605 | ||||||||
\(693\) | −6.32843 | + | 0.866025i | −0.240397 | + | 0.0328976i | ||||
\(694\) | 16.7279 | 0.634983 | ||||||||
\(695\) | 1.82843 | + | 3.16693i | 0.0693562 | + | 0.120128i | ||||
\(696\) | 1.91421 | − | 3.31552i | 0.0725581 | − | 0.125674i | ||||
\(697\) | −2.05025 | + | 3.55114i | −0.0776589 | + | 0.134509i | ||||
\(698\) | −9.36396 | − | 16.2189i | −0.354431 | − | 0.613893i | ||||
\(699\) | −7.72792 | −0.292297 | ||||||||
\(700\) | 10.7929 | + | 13.9180i | 0.407933 | + | 0.526049i | ||||
\(701\) | −34.8284 | −1.31545 | −0.657726 | − | 0.753257i | \(-0.728481\pi\) | ||||
−0.657726 | + | 0.753257i | \(0.728481\pi\) | |||||||
\(702\) | 0.500000 | + | 0.866025i | 0.0188713 | + | 0.0326860i | ||||
\(703\) | −5.53553 | + | 9.58783i | −0.208777 | + | 0.361612i | ||||
\(704\) | −1.20711 | + | 2.09077i | −0.0454945 | + | 0.0787989i | ||||
\(705\) | −1.70711 | − | 2.95680i | −0.0642934 | − | 0.111359i | ||||
\(706\) | −32.6274 | −1.22795 | ||||||||
\(707\) | −9.17157 | + | 22.4657i | −0.344932 | + | 0.844909i | ||||
\(708\) | 12.0711 | 0.453659 | ||||||||
\(709\) | −8.43503 | − | 14.6099i | −0.316784 | − | 0.548686i | 0.663031 | − | 0.748592i | \(-0.269270\pi\) |
−0.979815 | + | 0.199906i | \(0.935936\pi\) | |||||||
\(710\) | −8.53553 | + | 14.7840i | −0.320333 | + | 0.554833i | ||||
\(711\) | 0.171573 | − | 0.297173i | 0.00643449 | − | 0.0111449i | ||||
\(712\) | −2.70711 | − | 4.68885i | −0.101453 | − | 0.175722i | ||||
\(713\) | −12.0000 | −0.449404 | ||||||||
\(714\) | −0.414214 | + | 1.01461i | −0.0155016 | + | 0.0379709i | ||||
\(715\) | −8.24264 | −0.308257 | ||||||||
\(716\) | −4.17157 | − | 7.22538i | −0.155899 | − | 0.270025i | ||||
\(717\) | 10.7426 | − | 18.6068i | 0.401191 | − | 0.694884i | ||||
\(718\) | −2.41421 | + | 4.18154i | −0.0900976 | + | 0.156054i | ||||
\(719\) | 6.65685 | + | 11.5300i | 0.248259 | + | 0.429997i | 0.963043 | − | 0.269348i | \(-0.0868083\pi\) |
−0.714784 | + | 0.699345i | \(0.753475\pi\) | |||||||
\(720\) | −3.41421 | −0.127240 | ||||||||
\(721\) | −18.1127 | − | 23.3572i | −0.674552 | − | 0.869867i | ||||
\(722\) | 42.2843 | 1.57366 | ||||||||
\(723\) | 13.0711 | + | 22.6398i | 0.486118 | + | 0.841981i | ||||
\(724\) | 8.44975 | − | 14.6354i | 0.314032 | − | 0.543920i | ||||
\(725\) | −12.7426 | + | 22.0709i | −0.473250 | + | 0.819693i | ||||
\(726\) | −2.58579 | − | 4.47871i | −0.0959675 | − | 0.166221i | ||||
\(727\) | 34.4264 | 1.27680 | 0.638402 | − | 0.769703i | \(-0.279596\pi\) | ||||
0.638402 | + | 0.769703i | \(0.279596\pi\) | |||||||
\(728\) | −2.62132 | + | 0.358719i | −0.0971526 | + | 0.0132950i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.41421 | − | 4.18154i | −0.0893541 | − | 0.154766i | ||||
\(731\) | 2.17157 | − | 3.76127i | 0.0803185 | − | 0.139116i | ||||
\(732\) | −0.792893 | + | 1.37333i | −0.0293062 | + | 0.0507598i | ||||
\(733\) | 15.7071 | + | 27.2055i | 0.580155 | + | 1.00486i | 0.995460 | + | 0.0951762i | \(0.0303415\pi\) |
−0.415305 | + | 0.909682i | \(0.636325\pi\) | |||||||
\(734\) | −32.6274 | −1.20430 | ||||||||
\(735\) | 23.0208 | − | 6.42090i | 0.849136 | − | 0.236838i | ||||
\(736\) | −1.41421 | −0.0521286 | ||||||||
\(737\) | 4.62132 | + | 8.00436i | 0.170229 | + | 0.294844i | ||||
\(738\) | −4.94975 | + | 8.57321i | −0.182203 | + | 0.315584i | ||||
\(739\) | 15.0000 | − | 25.9808i | 0.551784 | − | 0.955718i | −0.446362 | − | 0.894852i | \(-0.647281\pi\) |
0.998146 | − | 0.0608653i | \(-0.0193860\pi\) | |||||||
\(740\) | −2.41421 | − | 4.18154i | −0.0887483 | − | 0.153716i | ||||
\(741\) | 7.82843 | 0.287584 | ||||||||
\(742\) | 19.6213 | − | 2.68512i | 0.720321 | − | 0.0985737i | ||||
\(743\) | 17.8284 | 0.654062 | 0.327031 | − | 0.945014i | \(-0.393952\pi\) | ||||
0.327031 | + | 0.945014i | \(0.393952\pi\) | |||||||
\(744\) | 4.24264 | + | 7.34847i | 0.155543 | + | 0.269408i | ||||
\(745\) | −32.5563 | + | 56.3893i | −1.19277 | + | 2.06594i | ||||
\(746\) | 4.20711 | − | 7.28692i | 0.154033 | − | 0.266793i | ||||
\(747\) | 1.82843 | + | 3.16693i | 0.0668987 | + | 0.115872i | ||||
\(748\) | 1.00000 | 0.0365636 | ||||||||
\(749\) | 5.37258 | + | 6.92820i | 0.196310 | + | 0.253151i | ||||
\(750\) | 5.65685 | 0.206559 | ||||||||
\(751\) | −1.65685 | − | 2.86976i | −0.0604595 | − | 0.104719i | 0.834211 | − | 0.551445i | \(-0.185923\pi\) |
−0.894671 | + | 0.446726i | \(0.852590\pi\) | |||||||
\(752\) | −0.500000 | + | 0.866025i | −0.0182331 | + | 0.0315807i | ||||
\(753\) | 9.58579 | − | 16.6031i | 0.349325 | − | 0.605049i | ||||
\(754\) | −1.91421 | − | 3.31552i | −0.0697115 | − | 0.120744i | ||||
\(755\) | 34.3848 | 1.25139 | ||||||||
\(756\) | −1.00000 | + | 2.44949i | −0.0363696 | + | 0.0890871i | ||||
\(757\) | −39.2426 | −1.42630 | −0.713149 | − | 0.701012i | \(-0.752732\pi\) | ||||
−0.713149 | + | 0.701012i | \(0.752732\pi\) | |||||||
\(758\) | 13.3137 | + | 23.0600i | 0.483576 | + | 0.837578i | ||||
\(759\) | −1.70711 | + | 2.95680i | −0.0619641 | + | 0.107325i | ||||
\(760\) | −13.3640 | + | 23.1471i | −0.484762 | + | 0.839632i | ||||
\(761\) | 9.55635 | + | 16.5521i | 0.346417 | + | 0.600013i | 0.985610 | − | 0.169034i | \(-0.0540648\pi\) |
−0.639193 | + | 0.769046i | \(0.720731\pi\) | |||||||
\(762\) | −11.8995 | −0.431073 | ||||||||
\(763\) | 1.65685 | − | 4.05845i | 0.0599822 | − | 0.146926i | ||||
\(764\) | −21.6569 | −0.783517 | ||||||||
\(765\) | 0.707107 | + | 1.22474i | 0.0255655 | + | 0.0442807i | ||||
\(766\) | −8.41421 | + | 14.5738i | −0.304018 | + | 0.526574i | ||||
\(767\) | 6.03553 | − | 10.4539i | 0.217930 | − | 0.377467i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −9.89949 | −0.356985 | −0.178492 | − | 0.983941i | \(-0.557122\pi\) | ||||
−0.178492 | + | 0.983941i | \(0.557122\pi\) | |||||||
\(770\) | −13.3640 | − | 17.2335i | −0.481604 | − | 0.621051i | ||||
\(771\) | −9.51472 | −0.342664 | ||||||||
\(772\) | 8.53553 | + | 14.7840i | 0.307201 | + | 0.532087i | ||||
\(773\) | 7.48528 | − | 12.9649i | 0.269227 | − | 0.466315i | −0.699436 | − | 0.714696i | \(-0.746565\pi\) |
0.968662 | + | 0.248381i | \(0.0798985\pi\) | |||||||
\(774\) | 5.24264 | − | 9.08052i | 0.188443 | − | 0.326393i | ||||
\(775\) | −28.2426 | − | 48.9177i | −1.01451 | − | 1.75718i | ||||
\(776\) | −15.0711 | −0.541020 | ||||||||
\(777\) | −3.70711 | + | 0.507306i | −0.132992 | + | 0.0181995i | ||||
\(778\) | −21.4853 | −0.770285 | ||||||||
\(779\) | 38.7487 | + | 67.1148i | 1.38832 | + | 2.40464i | ||||
\(780\) | −1.70711 | + | 2.95680i | −0.0611242 | + | 0.105870i | ||||
\(781\) | 6.03553 | − | 10.4539i | 0.215968 | − | 0.374068i | ||||
\(782\) | 0.292893 | + | 0.507306i | 0.0104738 | + | 0.0181412i | ||||
\(783\) | −3.82843 | −0.136817 | ||||||||
\(784\) | −5.00000 | − | 4.89898i | −0.178571 | − | 0.174964i | ||||
\(785\) | 53.6985 | 1.91658 | ||||||||
\(786\) | 10.7782 | + | 18.6683i | 0.384445 | + | 0.665878i | ||||
\(787\) | 1.84315 | − | 3.19242i | 0.0657011 | − | 0.113798i | −0.831304 | − | 0.555818i | \(-0.812405\pi\) |
0.897005 | + | 0.442021i | \(0.145738\pi\) | |||||||
\(788\) | −7.77817 | + | 13.4722i | −0.277086 | + | 0.479927i | ||||
\(789\) | 11.7071 | + | 20.2773i | 0.416784 | + | 0.721891i | ||||
\(790\) | 1.17157 | 0.0416827 | ||||||||
\(791\) | 39.0563 | − | 5.34474i | 1.38868 | − | 0.190037i | ||||
\(792\) | 2.41421 | 0.0857853 | ||||||||
\(793\) | 0.792893 | + | 1.37333i | 0.0281565 | + | 0.0487684i | ||||
\(794\) | −10.7782 | + | 18.6683i | −0.382503 | + | 0.662515i | ||||
\(795\) | 12.7782 | − | 22.1324i | 0.453195 | − | 0.784957i | ||||
\(796\) | 11.3640 | + | 19.6830i | 0.402785 | + | 0.697644i | ||||
\(797\) | 45.6569 | 1.61725 | 0.808624 | − | 0.588325i | \(-0.200213\pi\) | ||||
0.808624 | + | 0.588325i | \(0.200213\pi\) | |||||||
\(798\) | 12.6924 | + | 16.3674i | 0.449306 | + | 0.579401i | ||||
\(799\) | 0.414214 | 0.0146538 | ||||||||
\(800\) | −3.32843 | − | 5.76500i | −0.117678 | − | 0.203824i | ||||
\(801\) | −2.70711 | + | 4.68885i | −0.0956509 | + | 0.165672i | ||||
\(802\) | −0.0502525 | + | 0.0870399i | −0.00177448 | + | 0.00307349i | ||||
\(803\) | 1.70711 | + | 2.95680i | 0.0602425 | + | 0.104343i | ||||
\(804\) | 3.82843 | 0.135018 | ||||||||
\(805\) | 4.82843 | − | 11.8272i | 0.170180 | − | 0.416853i | ||||
\(806\) | 8.48528 | 0.298881 | ||||||||
\(807\) | 9.57107 | + | 16.5776i | 0.336918 | + | 0.583558i | ||||
\(808\) | 4.58579 | − | 7.94282i | 0.161327 | − | 0.279427i | ||||
\(809\) | 10.2071 | − | 17.6792i | 0.358863 | − | 0.621569i | −0.628908 | − | 0.777479i | \(-0.716498\pi\) |
0.987771 | + | 0.155911i | \(0.0498313\pi\) | |||||||
\(810\) | 1.70711 | + | 2.95680i | 0.0599816 | + | 0.103891i | ||||
\(811\) | 4.54416 | 0.159567 | 0.0797834 | − | 0.996812i | \(-0.474577\pi\) | ||||
0.0797834 | + | 0.996812i | \(0.474577\pi\) | |||||||
\(812\) | 3.82843 | − | 9.37769i | 0.134351 | − | 0.329093i | ||||
\(813\) | 16.2132 | 0.568622 | ||||||||
\(814\) | 1.70711 | + | 2.95680i | 0.0598341 | + | 0.103636i | ||||
\(815\) | −12.5355 | + | 21.7122i | −0.439101 | + | 0.760545i | ||||
\(816\) | 0.207107 | − | 0.358719i | 0.00725019 | − | 0.0125577i | ||||
\(817\) | −41.0416 | − | 71.0862i | −1.43586 | − | 2.48699i | ||||
\(818\) | 35.4142 | 1.23823 | ||||||||
\(819\) | 1.62132 | + | 2.09077i | 0.0566535 | + | 0.0730574i | ||||
\(820\) | −33.7990 | −1.18031 | ||||||||
\(821\) | −14.0503 | − | 24.3358i | −0.490357 | − | 0.849324i | 0.509581 | − | 0.860423i | \(-0.329800\pi\) |
−0.999938 | + | 0.0110990i | \(0.996467\pi\) | |||||||
\(822\) | −1.53553 | + | 2.65962i | −0.0535579 | + | 0.0927650i | ||||
\(823\) | −21.9203 | + | 37.9671i | −0.764094 | + | 1.32345i | 0.176630 | + | 0.984277i | \(0.443480\pi\) |
−0.940724 | + | 0.339172i | \(0.889853\pi\) | |||||||
\(824\) | 5.58579 | + | 9.67487i | 0.194590 | + | 0.337040i | ||||
\(825\) | −16.0711 | −0.559523 | ||||||||
\(826\) | 31.6421 | − | 4.33013i | 1.10097 | − | 0.150664i | ||||
\(827\) | −24.3553 | −0.846918 | −0.423459 | − | 0.905915i | \(-0.639184\pi\) | ||||
−0.423459 | + | 0.905915i | \(0.639184\pi\) | |||||||
\(828\) | 0.707107 | + | 1.22474i | 0.0245737 | + | 0.0425628i | ||||
\(829\) | −16.3492 | + | 28.3177i | −0.567833 | + | 0.983515i | 0.428947 | + | 0.903330i | \(0.358885\pi\) |
−0.996780 | + | 0.0801855i | \(0.974449\pi\) | |||||||
\(830\) | −6.24264 | + | 10.8126i | −0.216685 | + | 0.375310i | ||||
\(831\) | 1.96447 | + | 3.40256i | 0.0681466 | + | 0.118033i | ||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −0.721825 | + | 2.80821i | −0.0250098 | + | 0.0972987i | ||||
\(834\) | −1.07107 | −0.0370880 | ||||||||
\(835\) | 18.1924 | + | 31.5101i | 0.629574 | + | 1.09045i | ||||
\(836\) | 9.44975 | − | 16.3674i | 0.326826 | − | 0.566080i | ||||
\(837\) | 4.24264 | − | 7.34847i | 0.146647 | − | 0.254000i | ||||
\(838\) | 11.7279 | + | 20.3134i | 0.405134 | + | 0.701713i | ||||
\(839\) | −26.1716 | −0.903543 | −0.451772 | − | 0.892134i | \(-0.649208\pi\) | ||||
−0.451772 | + | 0.892134i | \(0.649208\pi\) | |||||||
\(840\) | −8.94975 | + | 1.22474i | −0.308796 | + | 0.0422577i | ||||
\(841\) | −14.3431 | −0.494591 | ||||||||
\(842\) | 6.53553 | + | 11.3199i | 0.225229 | + | 0.390109i | ||||
\(843\) | 11.6569 | − | 20.1903i | 0.401483 | − | 0.695390i | ||||
\(844\) | 13.5355 | − | 23.4442i | 0.465912 | − | 0.806984i | ||||
\(845\) | 1.70711 | + | 2.95680i | 0.0587263 | + | 0.101717i | ||||
\(846\) | 1.00000 | 0.0343807 | ||||||||
\(847\) | −8.38478 | − | 10.8126i | −0.288104 | − | 0.371524i | ||||
\(848\) | −7.48528 | −0.257046 | ||||||||
\(849\) | −12.1213 | − | 20.9947i | −0.416003 | − | 0.720538i | ||||
\(850\) | −1.37868 | + | 2.38794i | −0.0472883 | + | 0.0819058i | ||||
\(851\) | −1.00000 | + | 1.73205i | −0.0342796 | + | 0.0593739i | ||||
\(852\) | −2.50000 | − | 4.33013i | −0.0856486 | − | 0.148348i | ||||
\(853\) | −18.7279 | −0.641232 | −0.320616 | − | 0.947209i | \(-0.603890\pi\) | ||||
−0.320616 | + | 0.947209i | \(0.603890\pi\) | |||||||
\(854\) | −1.58579 | + | 3.88437i | −0.0542645 | + | 0.132920i | ||||
\(855\) | 26.7279 | 0.914076 | ||||||||
\(856\) | −1.65685 | − | 2.86976i | −0.0566301 | − | 0.0980862i | ||||
\(857\) | 5.27817 | − | 9.14207i | 0.180299 | − | 0.312287i | −0.761683 | − | 0.647949i | \(-0.775627\pi\) |
0.941982 | + | 0.335662i | \(0.108960\pi\) | |||||||
\(858\) | 1.20711 | − | 2.09077i | 0.0412099 | − | 0.0713777i | ||||
\(859\) | −13.8995 | − | 24.0746i | −0.474245 | − | 0.821416i | 0.525320 | − | 0.850904i | \(-0.323945\pi\) |
−0.999565 | + | 0.0294886i | \(0.990612\pi\) | |||||||
\(860\) | 35.7990 | 1.22074 | ||||||||
\(861\) | −9.89949 | + | 24.2487i | −0.337374 | + | 0.826394i | ||||
\(862\) | 13.5147 | 0.460313 | ||||||||
\(863\) | −8.34315 | − | 14.4508i | −0.284004 | − | 0.491909i | 0.688363 | − | 0.725366i | \(-0.258330\pi\) |
−0.972367 | + | 0.233457i | \(0.924996\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | −19.6066 | + | 33.9596i | −0.666644 | + | 1.15466i | ||||
\(866\) | 1.98528 | + | 3.43861i | 0.0674626 | + | 0.116849i | ||||
\(867\) | 16.8284 | 0.571523 | ||||||||
\(868\) | 13.7574 | + | 17.7408i | 0.466955 | + | 0.602161i | ||||
\(869\) | −0.828427 | −0.0281025 | ||||||||
\(870\) | −6.53553 | − | 11.3199i | −0.221575 | − | 0.383780i | ||||
\(871\) | 1.91421 | − | 3.31552i | 0.0648607 | − | 0.112342i | ||||
\(872\) | −0.828427 | + | 1.43488i | −0.0280541 | + | 0.0485911i | ||||
\(873\) | 7.53553 | + | 13.0519i | 0.255039 | + | 0.441741i | ||||
\(874\) | 11.0711 | 0.374484 | ||||||||
\(875\) | 14.8284 | − | 2.02922i | 0.501292 | − | 0.0686003i | ||||
\(876\) | 1.41421 | 0.0477818 | ||||||||
\(877\) | −4.02082 | − | 6.96426i | −0.135773 | − | 0.235166i | 0.790119 | − | 0.612953i | \(-0.210019\pi\) |
−0.925893 | + | 0.377787i | \(0.876685\pi\) | |||||||
\(878\) | −9.70711 | + | 16.8132i | −0.327599 | + | 0.567418i | ||||
\(879\) | 4.94975 | − | 8.57321i | 0.166951 | − | 0.289167i | ||||
\(880\) | 4.12132 | + | 7.13834i | 0.138930 | + | 0.240633i | ||||
\(881\) | 1.51472 | 0.0510322 | 0.0255161 | − | 0.999674i | \(-0.491877\pi\) | ||||
0.0255161 | + | 0.999674i | \(0.491877\pi\) | |||||||
\(882\) | −1.74264 | + | 6.77962i | −0.0586778 | + | 0.228282i | ||||
\(883\) | −18.2426 | −0.613914 | −0.306957 | − | 0.951723i | \(-0.599311\pi\) | ||||
−0.306957 | + | 0.951723i | \(0.599311\pi\) | |||||||
\(884\) | −0.207107 | − | 0.358719i | −0.00696575 | − | 0.0120650i | ||||
\(885\) | 20.6066 | − | 35.6917i | 0.692683 | − | 1.19976i | ||||
\(886\) | −12.8492 | + | 22.2555i | −0.431679 | + | 0.747690i | ||||
\(887\) | 26.4558 | + | 45.8229i | 0.888300 | + | 1.53858i | 0.841884 | + | 0.539659i | \(0.181447\pi\) |
0.0464167 | + | 0.998922i | \(0.485220\pi\) | |||||||
\(888\) | 1.41421 | 0.0474579 | ||||||||
\(889\) | −31.1924 | + | 4.26858i | −1.04616 | + | 0.143164i | ||||
\(890\) | −18.4853 | −0.619628 | ||||||||
\(891\) | −1.20711 | − | 2.09077i | −0.0404396 | − | 0.0700434i | ||||
\(892\) | 11.0355 | − | 19.1141i | 0.369497 | − | 0.639988i | ||||
\(893\) | 3.91421 | − | 6.77962i | 0.130984 | − | 0.226871i | ||||
\(894\) | −9.53553 | − | 16.5160i | −0.318916 | − | 0.552379i | ||||
\(895\) | −28.4853 | −0.952158 | ||||||||
\(896\) | 1.62132 | + | 2.09077i | 0.0541645 | + | 0.0698477i | ||||
\(897\) | 1.41421 | 0.0472192 | ||||||||
\(898\) | 4.48528 | + | 7.76874i | 0.149676 | + | 0.259246i | ||||
\(899\) | −16.2426 | + | 28.1331i | −0.541722 | + | 0.938291i | ||||
\(900\) | −3.32843 | + | 5.76500i | −0.110948 | + | 0.192167i | ||||
\(901\) | 1.55025 | + | 2.68512i | 0.0516464 | + | 0.0894542i | ||||
\(902\) | 23.8995 | 0.795766 | ||||||||
\(903\) | 10.4853 | − | 25.6836i | 0.348928 | − | 0.854696i | ||||
\(904\) | −14.8995 | −0.495550 | ||||||||
\(905\) | −28.8492 | − | 49.9684i | −0.958981 | − | 1.66100i | ||||
\(906\) | −5.03553 | + | 8.72180i | −0.167294 | + | 0.289762i | ||||
\(907\) | −8.80761 | + | 15.2552i | −0.292452 | + | 0.506542i | −0.974389 | − | 0.224869i | \(-0.927804\pi\) |
0.681937 | + | 0.731411i | \(0.261138\pi\) | |||||||
\(908\) | 13.4142 | + | 23.2341i | 0.445166 | + | 0.771051i | ||||
\(909\) | −9.17157 | −0.304202 | ||||||||
\(910\) | −3.41421 | + | 8.36308i | −0.113180 | + | 0.277233i | ||||
\(911\) | −15.6569 | −0.518735 | −0.259367 | − | 0.965779i | \(-0.583514\pi\) | ||||
−0.259367 | + | 0.965779i | \(0.583514\pi\) | |||||||
\(912\) | −3.91421 | − | 6.77962i | −0.129613 | − | 0.224496i | ||||
\(913\) | 4.41421 | − | 7.64564i | 0.146089 | − | 0.253034i | ||||
\(914\) | −5.53553 | + | 9.58783i | −0.183099 | + | 0.317137i | ||||
\(915\) | 2.70711 | + | 4.68885i | 0.0894942 | + | 0.155008i | ||||
\(916\) | 9.51472 | 0.314375 | ||||||||
\(917\) | 34.9497 | + | 45.0694i | 1.15414 | + | 1.48832i | ||||
\(918\) | −0.414214 | −0.0136711 | ||||||||
\(919\) | 18.8995 | + | 32.7349i | 0.623437 | + | 1.07982i | 0.988841 | + | 0.148975i | \(0.0475975\pi\) |
−0.365404 | + | 0.930849i | \(0.619069\pi\) | |||||||
\(920\) | −2.41421 | + | 4.18154i | −0.0795943 | + | 0.137861i | ||||
\(921\) | 17.0563 | − | 29.5425i | 0.562026 | − | 0.973457i | ||||
\(922\) | −6.24264 | − | 10.8126i | −0.205590 | − | 0.356093i | ||||
\(923\) | −5.00000 | −0.164577 | ||||||||
\(924\) | 6.32843 | − | 0.866025i | 0.208190 | − | 0.0284901i | ||||
\(925\) | −9.41421 | −0.309537 | ||||||||
\(926\) | −6.48528 | − | 11.2328i | −0.213120 | − | 0.369134i | ||||
\(927\) | 5.58579 | − | 9.67487i | 0.183461 | − | 0.317764i | ||||
\(928\) | −1.91421 | + | 3.31552i | −0.0628371 | + | 0.108837i | ||||
\(929\) | −28.6569 | − | 49.6351i | −0.940201 | − | 1.62848i | −0.765086 | − | 0.643928i | \(-0.777304\pi\) |
−0.175114 | − | 0.984548i | \(-0.556030\pi\) | |||||||
\(930\) | 28.9706 | 0.949982 | ||||||||
\(931\) | 39.1421 | + | 38.3513i | 1.28283 | + | 1.25691i | ||||
\(932\) | 7.72792 | 0.253137 | ||||||||
\(933\) | −13.9497 | − | 24.1617i | −0.456694 | − | 0.791018i | ||||
\(934\) | 4.29289 | − | 7.43551i | 0.140468 | − | 0.243297i | ||||
\(935\) | 1.70711 | − | 2.95680i | 0.0558284 | − | 0.0966976i | ||||
\(936\) | −0.500000 | − | 0.866025i | −0.0163430 | − | 0.0283069i | ||||
\(937\) | 31.3431 | 1.02394 | 0.511968 | − | 0.859005i | \(-0.328917\pi\) | ||||
0.511968 | + | 0.859005i | \(0.328917\pi\) | |||||||
\(938\) | 10.0355 | − | 1.37333i | 0.327672 | − | 0.0448409i | ||||
\(939\) | −20.4853 | −0.668512 | ||||||||
\(940\) | 1.70711 | + | 2.95680i | 0.0556797 | + | 0.0964400i | ||||
\(941\) | −10.4853 | + | 18.1610i | −0.341810 | + | 0.592033i | −0.984769 | − | 0.173868i | \(-0.944373\pi\) |
0.642959 | + | 0.765901i | \(0.277707\pi\) | |||||||
\(942\) | −7.86396 | + | 13.6208i | −0.256222 | + | 0.443789i | ||||
\(943\) | 7.00000 | + | 12.1244i | 0.227951 | + | 0.394823i | ||||
\(944\) | −12.0711 | −0.392880 | ||||||||
\(945\) | 5.53553 | + | 7.13834i | 0.180071 | + | 0.232210i | ||||
\(946\) | −25.3137 | −0.823020 | ||||||||
\(947\) | −2.79289 | − | 4.83743i | −0.0907568 | − | 0.157195i | 0.817073 | − | 0.576534i | \(-0.195595\pi\) |
−0.907830 | + | 0.419339i | \(0.862262\pi\) | |||||||
\(948\) | −0.171573 | + | 0.297173i | −0.00557243 | + | 0.00965173i | ||||
\(949\) | 0.707107 | − | 1.22474i | 0.0229537 | − | 0.0397569i | ||||
\(950\) | 26.0563 | + | 45.1309i | 0.845380 | + | 1.46424i | ||||
\(951\) | 9.79899 | 0.317754 | ||||||||
\(952\) | 0.414214 | − | 1.01461i | 0.0134247 | − | 0.0328838i | ||||
\(953\) | −44.4142 | −1.43872 | −0.719359 | − | 0.694639i | \(-0.755564\pi\) | ||||
−0.719359 | + | 0.694639i | \(0.755564\pi\) | |||||||
\(954\) | 3.74264 | + | 6.48244i | 0.121172 | + | 0.209877i | ||||
\(955\) | −36.9706 | + | 64.0349i | −1.19634 | + | 2.07212i | ||||
\(956\) | −10.7426 | + | 18.6068i | −0.347442 | + | 0.601787i | ||||
\(957\) | 4.62132 | + | 8.00436i | 0.149386 | + | 0.258744i | ||||
\(958\) | 30.1127 | 0.972897 | ||||||||
\(959\) | −3.07107 | + | 7.52255i | −0.0991700 | + | 0.242916i | ||||
\(960\) | 3.41421 | 0.110193 | ||||||||
\(961\) | −20.5000 | − | 35.5070i | −0.661290 | − | 1.14539i | ||||
\(962\) | 0.707107 | − | 1.22474i | 0.0227980 | − | 0.0394874i | ||||
\(963\) | −1.65685 | + | 2.86976i | −0.0533914 | + | 0.0924766i | ||||
\(964\) | −13.0711 | − | 22.6398i | −0.420991 | − | 0.729177i | ||||
\(965\) | 58.2843 | 1.87624 | ||||||||
\(966\) | 2.29289 | + | 2.95680i | 0.0737726 | + | 0.0951333i | ||||
\(967\) | −16.4142 | −0.527846 | −0.263923 | − | 0.964544i | \(-0.585016\pi\) | ||||
−0.263923 | + | 0.964544i | \(0.585016\pi\) | |||||||
\(968\) | 2.58579 | + | 4.47871i | 0.0831103 | + | 0.143951i | ||||
\(969\) | −1.62132 | + | 2.80821i | −0.0520843 | + | 0.0902127i | ||||
\(970\) | −25.7279 | + | 44.5621i | −0.826074 | + | 1.43080i | ||||
\(971\) | −16.2635 | − | 28.1691i | −0.521919 | − | 0.903990i | −0.999675 | − | 0.0254978i | \(-0.991883\pi\) |
0.477756 | − | 0.878493i | \(-0.341450\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −2.80761 | + | 0.384213i | −0.0900079 | + | 0.0123173i | ||||
\(974\) | −26.2132 | −0.839925 | ||||||||
\(975\) | 3.32843 | + | 5.76500i | 0.106595 | + | 0.184628i | ||||
\(976\) | 0.792893 | − | 1.37333i | 0.0253799 | − | 0.0439593i | ||||
\(977\) | −24.4142 | + | 42.2867i | −0.781080 | + | 1.35287i | 0.150233 | + | 0.988651i | \(0.451998\pi\) |
−0.931313 | + | 0.364219i | \(0.881336\pi\) | |||||||
\(978\) | −3.67157 | − | 6.35935i | −0.117404 | − | 0.203350i | ||||
\(979\) | 13.0711 | 0.417753 | ||||||||
\(980\) | −23.0208 | + | 6.42090i | −0.735373 | + | 0.205108i | ||||
\(981\) | 1.65685 | 0.0528993 | ||||||||
\(982\) | −6.17157 | − | 10.6895i | −0.196943 | − | 0.341115i | ||||
\(983\) | 6.25736 | − | 10.8381i | 0.199579 | − | 0.345681i | −0.748813 | − | 0.662781i | \(-0.769376\pi\) |
0.948392 | + | 0.317101i | \(0.102709\pi\) | |||||||
\(984\) | 4.94975 | − | 8.57321i | 0.157792 | − | 0.273304i | ||||
\(985\) | 26.5563 | + | 45.9969i | 0.846156 | + | 1.46558i | ||||
\(986\) | 1.58579 | 0.0505017 | ||||||||
\(987\) | 2.62132 | − | 0.358719i | 0.0834375 | − | 0.0114182i | ||||
\(988\) | −7.82843 | −0.249055 | ||||||||
\(989\) | −7.41421 | − | 12.8418i | −0.235758 | − | 0.408345i | ||||
\(990\) | 4.12132 | − | 7.13834i | 0.130984 | − | 0.226871i | ||||
\(991\) | 11.6569 | − | 20.1903i | 0.370292 | − | 0.641365i | −0.619318 | − | 0.785140i | \(-0.712591\pi\) |
0.989610 | + | 0.143775i | \(0.0459242\pi\) | |||||||
\(992\) | −4.24264 | − | 7.34847i | −0.134704 | − | 0.233314i | ||||
\(993\) | 5.51472 | 0.175004 | ||||||||
\(994\) | −8.10660 | − | 10.4539i | −0.257126 | − | 0.331576i | ||||
\(995\) | 77.5980 | 2.46002 | ||||||||
\(996\) | −1.82843 | − | 3.16693i | −0.0579359 | − | 0.100348i | ||||
\(997\) | 23.2487 | − | 40.2680i | 0.736295 | − | 1.27530i | −0.217858 | − | 0.975980i | \(-0.569907\pi\) |
0.954153 | − | 0.299320i | \(-0.0967597\pi\) | |||||||
\(998\) | 3.82843 | − | 6.63103i | 0.121187 | − | 0.209902i | ||||
\(999\) | −0.707107 | − | 1.22474i | −0.0223719 | − | 0.0387492i |
(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 | 546.2.i.i.235.2 | yes | 4 | |
3.2 | odd | 2 | 1638.2.j.m.235.1 | 4 | |||
7.2 | even | 3 | inner | 546.2.i.i.79.2 | ✓ | 4 | |
7.3 | odd | 6 | 3822.2.a.bu.1.2 | 2 | |||
7.4 | even | 3 | 3822.2.a.bn.1.1 | 2 | |||
21.2 | odd | 6 | 1638.2.j.m.1171.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.i.i.79.2 | ✓ | 4 | 7.2 | even | 3 | inner | |
546.2.i.i.235.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1638.2.j.m.235.1 | 4 | 3.2 | odd | 2 | |||
1638.2.j.m.1171.1 | 4 | 21.2 | odd | 6 | |||
3822.2.a.bn.1.1 | 2 | 7.4 | even | 3 | |||
3822.2.a.bu.1.2 | 2 | 7.3 | odd | 6 |