Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 729.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.729 |
Dual form | 847.2.f.j.323.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | + | 0.224514i | −0.218508 | + | 0.158755i | −0.691655 | − | 0.722228i | \(-0.743118\pi\) |
0.473147 | + | 0.880984i | \(0.343118\pi\) | |||||||
\(3\) | −0.500000 | − | 1.53884i | −0.288675 | − | 0.888451i | −0.985273 | − | 0.170989i | \(-0.945304\pi\) |
0.696598 | − | 0.717462i | \(-0.254696\pi\) | |||||||
\(4\) | −0.572949 | + | 1.76336i | −0.286475 | + | 0.881678i | ||||
\(5\) | −0.809017 | − | 0.587785i | −0.361803 | − | 0.262866i | 0.392000 | − | 0.919965i | \(-0.371783\pi\) |
−0.753804 | + | 0.657099i | \(0.771783\pi\) | |||||||
\(6\) | 0.500000 | + | 0.363271i | 0.204124 | + | 0.148305i | ||||
\(7\) | −0.309017 | + | 0.951057i | −0.116797 | + | 0.359466i | ||||
\(8\) | −0.454915 | − | 1.40008i | −0.160837 | − | 0.495005i | ||||
\(9\) | 0.309017 | − | 0.224514i | 0.103006 | − | 0.0748380i | ||||
\(10\) | 0.381966 | 0.120788 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.00000 | 0.866025 | ||||||||
\(13\) | −1.00000 | + | 0.726543i | −0.277350 | + | 0.201507i | −0.717761 | − | 0.696290i | \(-0.754833\pi\) |
0.440411 | + | 0.897796i | \(0.354833\pi\) | |||||||
\(14\) | −0.118034 | − | 0.363271i | −0.0315459 | − | 0.0970883i | ||||
\(15\) | −0.500000 | + | 1.53884i | −0.129099 | + | 0.397327i | ||||
\(16\) | −2.54508 | − | 1.84911i | −0.636271 | − | 0.462278i | ||||
\(17\) | 2.50000 | + | 1.81636i | 0.606339 | + | 0.440531i | 0.848123 | − | 0.529799i | \(-0.177733\pi\) |
−0.241784 | + | 0.970330i | \(0.577733\pi\) | |||||||
\(18\) | −0.0450850 | + | 0.138757i | −0.0106266 | + | 0.0327054i | ||||
\(19\) | 0.545085 | + | 1.67760i | 0.125051 | + | 0.384868i | 0.993910 | − | 0.110191i | \(-0.0351464\pi\) |
−0.868859 | + | 0.495059i | \(0.835146\pi\) | |||||||
\(20\) | 1.50000 | − | 1.08981i | 0.335410 | − | 0.243690i | ||||
\(21\) | 1.61803 | 0.353084 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.09017 | 1.06137 | 0.530687 | − | 0.847568i | \(-0.321934\pi\) | ||||
0.530687 | + | 0.847568i | \(0.321934\pi\) | |||||||
\(24\) | −1.92705 | + | 1.40008i | −0.393358 | + | 0.285791i | ||||
\(25\) | −1.23607 | − | 3.80423i | −0.247214 | − | 0.760845i | ||||
\(26\) | 0.145898 | − | 0.449028i | 0.0286130 | − | 0.0880616i | ||||
\(27\) | −4.42705 | − | 3.21644i | −0.851986 | − | 0.619004i | ||||
\(28\) | −1.50000 | − | 1.08981i | −0.283473 | − | 0.205955i | ||||
\(29\) | 1.42705 | − | 4.39201i | 0.264997 | − | 0.815576i | −0.726697 | − | 0.686958i | \(-0.758946\pi\) |
0.991694 | − | 0.128618i | \(-0.0410542\pi\) | |||||||
\(30\) | −0.190983 | − | 0.587785i | −0.0348686 | − | 0.107314i | ||||
\(31\) | 3.42705 | − | 2.48990i | 0.615517 | − | 0.447199i | −0.235836 | − | 0.971793i | \(-0.575783\pi\) |
0.851353 | + | 0.524594i | \(0.175783\pi\) | |||||||
\(32\) | 4.14590 | 0.732898 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.18034 | −0.202427 | ||||||||
\(35\) | 0.809017 | − | 0.587785i | 0.136749 | − | 0.0993538i | ||||
\(36\) | 0.218847 | + | 0.673542i | 0.0364745 | + | 0.112257i | ||||
\(37\) | 2.00000 | − | 6.15537i | 0.328798 | − | 1.01194i | −0.640899 | − | 0.767625i | \(-0.721438\pi\) |
0.969697 | − | 0.244311i | \(-0.0785617\pi\) | |||||||
\(38\) | −0.545085 | − | 0.396027i | −0.0884245 | − | 0.0642441i | ||||
\(39\) | 1.61803 | + | 1.17557i | 0.259093 | + | 0.188242i | ||||
\(40\) | −0.454915 | + | 1.40008i | −0.0719284 | + | 0.221373i | ||||
\(41\) | 3.45492 | + | 10.6331i | 0.539567 | + | 1.66062i | 0.733569 | + | 0.679615i | \(0.237853\pi\) |
−0.194001 | + | 0.981001i | \(0.562147\pi\) | |||||||
\(42\) | −0.500000 | + | 0.363271i | −0.0771517 | + | 0.0560540i | ||||
\(43\) | 12.5623 | 1.91573 | 0.957867 | − | 0.287213i | \(-0.0927286\pi\) | ||||
0.957867 | + | 0.287213i | \(0.0927286\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.381966 | −0.0569401 | ||||||||
\(46\) | −1.57295 | + | 1.14281i | −0.231919 | + | 0.168499i | ||||
\(47\) | −2.04508 | − | 6.29412i | −0.298306 | − | 0.918092i | −0.982091 | − | 0.188408i | \(-0.939667\pi\) |
0.683784 | − | 0.729684i | \(-0.260333\pi\) | |||||||
\(48\) | −1.57295 | + | 4.84104i | −0.227036 | + | 0.698744i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | 1.23607 | + | 0.898056i | 0.174806 | + | 0.127004i | ||||
\(51\) | 1.54508 | − | 4.75528i | 0.216355 | − | 0.665873i | ||||
\(52\) | −0.708204 | − | 2.17963i | −0.0982102 | − | 0.302260i | ||||
\(53\) | 1.92705 | − | 1.40008i | 0.264701 | − | 0.192316i | −0.447516 | − | 0.894276i | \(-0.647691\pi\) |
0.712217 | + | 0.701960i | \(0.247691\pi\) | |||||||
\(54\) | 2.09017 | 0.284436 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.47214 | 0.196722 | ||||||||
\(57\) | 2.30902 | − | 1.67760i | 0.305837 | − | 0.222203i | ||||
\(58\) | 0.545085 | + | 1.67760i | 0.0715732 | + | 0.220280i | ||||
\(59\) | 3.42705 | − | 10.5474i | 0.446164 | − | 1.37315i | −0.435038 | − | 0.900412i | \(-0.643265\pi\) |
0.881202 | − | 0.472740i | \(-0.156735\pi\) | |||||||
\(60\) | −2.42705 | − | 1.76336i | −0.313331 | − | 0.227648i | ||||
\(61\) | −6.16312 | − | 4.47777i | −0.789107 | − | 0.573319i | 0.118592 | − | 0.992943i | \(-0.462162\pi\) |
−0.907698 | + | 0.419624i | \(0.862162\pi\) | |||||||
\(62\) | −0.500000 | + | 1.53884i | −0.0635001 | + | 0.195433i | ||||
\(63\) | 0.118034 | + | 0.363271i | 0.0148709 | + | 0.0457679i | ||||
\(64\) | 3.80902 | − | 2.76741i | 0.476127 | − | 0.345927i | ||||
\(65\) | 1.23607 | 0.153315 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.32624 | −1.01721 | −0.508606 | − | 0.860999i | \(-0.669839\pi\) | ||||
−0.508606 | + | 0.860999i | \(0.669839\pi\) | |||||||
\(68\) | −4.63525 | + | 3.36771i | −0.562107 | + | 0.408395i | ||||
\(69\) | −2.54508 | − | 7.83297i | −0.306392 | − | 0.942978i | ||||
\(70\) | −0.118034 | + | 0.363271i | −0.0141078 | + | 0.0434192i | ||||
\(71\) | 13.0172 | + | 9.45756i | 1.54486 | + | 1.12241i | 0.947194 | + | 0.320661i | \(0.103905\pi\) |
0.597666 | + | 0.801745i | \(0.296095\pi\) | |||||||
\(72\) | −0.454915 | − | 0.330515i | −0.0536123 | − | 0.0389516i | ||||
\(73\) | 4.39919 | − | 13.5393i | 0.514886 | − | 1.58466i | −0.268604 | − | 0.963251i | \(-0.586562\pi\) |
0.783490 | − | 0.621405i | \(-0.213438\pi\) | |||||||
\(74\) | 0.763932 | + | 2.35114i | 0.0888053 | + | 0.273315i | ||||
\(75\) | −5.23607 | + | 3.80423i | −0.604609 | + | 0.439274i | ||||
\(76\) | −3.27051 | −0.375153 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.763932 | −0.0864983 | ||||||||
\(79\) | 5.16312 | − | 3.75123i | 0.580896 | − | 0.422046i | −0.258151 | − | 0.966105i | \(-0.583113\pi\) |
0.839047 | + | 0.544059i | \(0.183113\pi\) | |||||||
\(80\) | 0.972136 | + | 2.99193i | 0.108688 | + | 0.334508i | ||||
\(81\) | −2.38197 | + | 7.33094i | −0.264663 | + | 0.814549i | ||||
\(82\) | −3.45492 | − | 2.51014i | −0.381532 | − | 0.277199i | ||||
\(83\) | 2.19098 | + | 1.59184i | 0.240492 | + | 0.174727i | 0.701502 | − | 0.712667i | \(-0.252513\pi\) |
−0.461011 | + | 0.887395i | \(0.652513\pi\) | |||||||
\(84\) | −0.927051 | + | 2.85317i | −0.101150 | + | 0.311306i | ||||
\(85\) | −0.954915 | − | 2.93893i | −0.103575 | − | 0.318771i | ||||
\(86\) | −3.88197 | + | 2.82041i | −0.418603 | + | 0.304133i | ||||
\(87\) | −7.47214 | −0.801097 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.85410 | 0.726533 | 0.363267 | − | 0.931685i | \(-0.381661\pi\) | ||||
0.363267 | + | 0.931685i | \(0.381661\pi\) | |||||||
\(90\) | 0.118034 | − | 0.0857567i | 0.0124419 | − | 0.00903955i | ||||
\(91\) | −0.381966 | − | 1.17557i | −0.0400409 | − | 0.123233i | ||||
\(92\) | −2.91641 | + | 8.97578i | −0.304057 | + | 0.935790i | ||||
\(93\) | −5.54508 | − | 4.02874i | −0.574999 | − | 0.417761i | ||||
\(94\) | 2.04508 | + | 1.48584i | 0.210934 | + | 0.153253i | ||||
\(95\) | 0.545085 | − | 1.67760i | 0.0559245 | − | 0.172118i | ||||
\(96\) | −2.07295 | − | 6.37988i | −0.211569 | − | 0.651144i | ||||
\(97\) | −5.66312 | + | 4.11450i | −0.575003 | + | 0.417764i | −0.836919 | − | 0.547327i | \(-0.815646\pi\) |
0.261916 | + | 0.965091i | \(0.415646\pi\) | |||||||
\(98\) | 0.381966 | 0.0385844 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.41641 | 0.741641 | ||||||||
\(101\) | −11.9721 | + | 8.69827i | −1.19127 | + | 0.865510i | −0.993398 | − | 0.114718i | \(-0.963404\pi\) |
−0.197874 | + | 0.980227i | \(0.563404\pi\) | |||||||
\(102\) | 0.590170 | + | 1.81636i | 0.0584355 | + | 0.179846i | ||||
\(103\) | 2.73607 | − | 8.42075i | 0.269593 | − | 0.829721i | −0.721007 | − | 0.692928i | \(-0.756320\pi\) |
0.990600 | − | 0.136793i | \(-0.0436796\pi\) | |||||||
\(104\) | 1.47214 | + | 1.06957i | 0.144355 | + | 0.104880i | ||||
\(105\) | −1.30902 | − | 0.951057i | −0.127747 | − | 0.0928136i | ||||
\(106\) | −0.281153 | + | 0.865300i | −0.0273080 | + | 0.0840453i | ||||
\(107\) | −0.836881 | − | 2.57565i | −0.0809043 | − | 0.248998i | 0.902420 | − | 0.430857i | \(-0.141789\pi\) |
−0.983325 | + | 0.181859i | \(0.941789\pi\) | |||||||
\(108\) | 8.20820 | − | 5.96361i | 0.789835 | − | 0.573849i | ||||
\(109\) | 1.52786 | 0.146343 | 0.0731714 | − | 0.997319i | \(-0.476688\pi\) | ||||
0.0731714 | + | 0.997319i | \(0.476688\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.4721 | −0.993971 | ||||||||
\(112\) | 2.54508 | − | 1.84911i | 0.240488 | − | 0.174725i | ||||
\(113\) | 0.0450850 | + | 0.138757i | 0.00424124 | + | 0.0130532i | 0.953155 | − | 0.302483i | \(-0.0978156\pi\) |
−0.948914 | + | 0.315536i | \(0.897816\pi\) | |||||||
\(114\) | −0.336881 | + | 1.03681i | −0.0315518 | + | 0.0971065i | ||||
\(115\) | −4.11803 | − | 2.99193i | −0.384009 | − | 0.278999i | ||||
\(116\) | 6.92705 | + | 5.03280i | 0.643161 | + | 0.467283i | ||||
\(117\) | −0.145898 | + | 0.449028i | −0.0134883 | + | 0.0415127i | ||||
\(118\) | 1.30902 | + | 4.02874i | 0.120505 | + | 0.370876i | ||||
\(119\) | −2.50000 | + | 1.81636i | −0.229175 | + | 0.166505i | ||||
\(120\) | 2.38197 | 0.217443 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 2.90983 | 0.263444 | ||||||||
\(123\) | 14.6353 | − | 10.6331i | 1.31962 | − | 0.958758i | ||||
\(124\) | 2.42705 | + | 7.46969i | 0.217956 | + | 0.670798i | ||||
\(125\) | −2.78115 | + | 8.55951i | −0.248754 | + | 0.765586i | ||||
\(126\) | −0.118034 | − | 0.0857567i | −0.0105153 | − | 0.00763982i | ||||
\(127\) | 2.38197 | + | 1.73060i | 0.211365 | + | 0.153566i | 0.688431 | − | 0.725302i | \(-0.258300\pi\) |
−0.477066 | + | 0.878868i | \(0.658300\pi\) | |||||||
\(128\) | −3.11803 | + | 9.59632i | −0.275598 | + | 0.848203i | ||||
\(129\) | −6.28115 | − | 19.3314i | −0.553025 | − | 1.70203i | ||||
\(130\) | −0.381966 | + | 0.277515i | −0.0335006 | + | 0.0243396i | ||||
\(131\) | −18.9443 | −1.65517 | −0.827584 | − | 0.561341i | \(-0.810285\pi\) | ||||
−0.827584 | + | 0.561341i | \(0.810285\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.76393 | −0.152952 | ||||||||
\(134\) | 2.57295 | − | 1.86936i | 0.222269 | − | 0.161488i | ||||
\(135\) | 1.69098 | + | 5.20431i | 0.145537 | + | 0.447916i | ||||
\(136\) | 1.40576 | − | 4.32650i | 0.120543 | − | 0.370994i | ||||
\(137\) | 12.3992 | + | 9.00854i | 1.05933 | + | 0.769651i | 0.973965 | − | 0.226698i | \(-0.0727931\pi\) |
0.0853690 | + | 0.996349i | \(0.472793\pi\) | |||||||
\(138\) | 2.54508 | + | 1.84911i | 0.216652 | + | 0.157407i | ||||
\(139\) | −3.69098 | + | 11.3597i | −0.313065 | + | 0.963515i | 0.663478 | + | 0.748195i | \(0.269079\pi\) |
−0.976544 | + | 0.215320i | \(0.930921\pi\) | |||||||
\(140\) | 0.572949 | + | 1.76336i | 0.0484230 | + | 0.149031i | ||||
\(141\) | −8.66312 | + | 6.29412i | −0.729566 | + | 0.530061i | ||||
\(142\) | −6.14590 | −0.515752 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.20163 | −0.100136 | ||||||||
\(145\) | −3.73607 | + | 2.71441i | −0.310264 | + | 0.225420i | ||||
\(146\) | 1.68034 | + | 5.17155i | 0.139066 | + | 0.428001i | ||||
\(147\) | −0.500000 | + | 1.53884i | −0.0412393 | + | 0.126922i | ||||
\(148\) | 9.70820 | + | 7.05342i | 0.798009 | + | 0.579788i | ||||
\(149\) | −7.16312 | − | 5.20431i | −0.586826 | − | 0.426354i | 0.254353 | − | 0.967112i | \(-0.418138\pi\) |
−0.841178 | + | 0.540758i | \(0.818138\pi\) | |||||||
\(150\) | 0.763932 | − | 2.35114i | 0.0623748 | − | 0.191970i | ||||
\(151\) | −0.0172209 | − | 0.0530006i | −0.00140142 | − | 0.00431312i | 0.950353 | − | 0.311173i | \(-0.100722\pi\) |
−0.951755 | + | 0.306860i | \(0.900722\pi\) | |||||||
\(152\) | 2.10081 | − | 1.52633i | 0.170398 | − | 0.123802i | ||||
\(153\) | 1.18034 | 0.0954248 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.23607 | −0.340249 | ||||||||
\(156\) | −3.00000 | + | 2.17963i | −0.240192 | + | 0.174510i | ||||
\(157\) | 6.14590 | + | 18.9151i | 0.490496 | + | 1.50959i | 0.823860 | + | 0.566793i | \(0.191816\pi\) |
−0.333364 | + | 0.942798i | \(0.608184\pi\) | |||||||
\(158\) | −0.753289 | + | 2.31838i | −0.0599284 | + | 0.184441i | ||||
\(159\) | −3.11803 | − | 2.26538i | −0.247276 | − | 0.179657i | ||||
\(160\) | −3.35410 | − | 2.43690i | −0.265165 | − | 0.192654i | ||||
\(161\) | −1.57295 | + | 4.84104i | −0.123966 | + | 0.381527i | ||||
\(162\) | −0.909830 | − | 2.80017i | −0.0714830 | − | 0.220002i | ||||
\(163\) | 7.04508 | − | 5.11855i | 0.551814 | − | 0.400916i | −0.276640 | − | 0.960974i | \(-0.589221\pi\) |
0.828454 | + | 0.560058i | \(0.189221\pi\) | |||||||
\(164\) | −20.7295 | −1.61870 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.03444 | −0.0802883 | ||||||||
\(167\) | 5.23607 | − | 3.80423i | 0.405179 | − | 0.294380i | −0.366468 | − | 0.930431i | \(-0.619433\pi\) |
0.771647 | + | 0.636051i | \(0.219433\pi\) | |||||||
\(168\) | −0.736068 | − | 2.26538i | −0.0567889 | − | 0.174778i | ||||
\(169\) | −3.54508 | + | 10.9106i | −0.272699 | + | 0.839281i | ||||
\(170\) | 0.954915 | + | 0.693786i | 0.0732386 | + | 0.0532110i | ||||
\(171\) | 0.545085 | + | 0.396027i | 0.0416837 | + | 0.0302850i | ||||
\(172\) | −7.19756 | + | 22.1518i | −0.548809 | + | 1.68906i | ||||
\(173\) | 4.75329 | + | 14.6291i | 0.361386 | + | 1.11223i | 0.952213 | + | 0.305433i | \(0.0988014\pi\) |
−0.590828 | + | 0.806798i | \(0.701199\pi\) | |||||||
\(174\) | 2.30902 | − | 1.67760i | 0.175046 | − | 0.127178i | ||||
\(175\) | 4.00000 | 0.302372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.9443 | −1.34877 | ||||||||
\(178\) | −2.11803 | + | 1.53884i | −0.158753 | + | 0.115341i | ||||
\(179\) | −1.16312 | − | 3.57971i | −0.0869356 | − | 0.267560i | 0.898133 | − | 0.439725i | \(-0.144924\pi\) |
−0.985068 | + | 0.172164i | \(0.944924\pi\) | |||||||
\(180\) | 0.218847 | − | 0.673542i | 0.0163119 | − | 0.0502029i | ||||
\(181\) | 6.00000 | + | 4.35926i | 0.445976 | + | 0.324021i | 0.788005 | − | 0.615669i | \(-0.211114\pi\) |
−0.342029 | + | 0.939690i | \(0.611114\pi\) | |||||||
\(182\) | 0.381966 | + | 0.277515i | 0.0283132 | + | 0.0205707i | ||||
\(183\) | −3.80902 | + | 11.7229i | −0.281571 | + | 0.866585i | ||||
\(184\) | −2.31559 | − | 7.12667i | −0.170708 | − | 0.525385i | ||||
\(185\) | −5.23607 | + | 3.80423i | −0.384963 | + | 0.279692i | ||||
\(186\) | 2.61803 | 0.191964 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.2705 | 0.894919 | ||||||||
\(189\) | 4.42705 | − | 3.21644i | 0.322021 | − | 0.233962i | ||||
\(190\) | 0.208204 | + | 0.640786i | 0.0151047 | + | 0.0464875i | ||||
\(191\) | 4.87132 | − | 14.9924i | 0.352477 | − | 1.08481i | −0.604982 | − | 0.796239i | \(-0.706820\pi\) |
0.957458 | − | 0.288572i | \(-0.0931804\pi\) | |||||||
\(192\) | −6.16312 | − | 4.47777i | −0.444785 | − | 0.323155i | ||||
\(193\) | −12.3992 | − | 9.00854i | −0.892513 | − | 0.648449i | 0.0440190 | − | 0.999031i | \(-0.485984\pi\) |
−0.936532 | + | 0.350582i | \(0.885984\pi\) | |||||||
\(194\) | 0.826238 | − | 2.54290i | 0.0593204 | − | 0.182569i | ||||
\(195\) | −0.618034 | − | 1.90211i | −0.0442583 | − | 0.136213i | ||||
\(196\) | 1.50000 | − | 1.08981i | 0.107143 | − | 0.0778438i | ||||
\(197\) | 4.29180 | 0.305778 | 0.152889 | − | 0.988243i | \(-0.451142\pi\) | ||||
0.152889 | + | 0.988243i | \(0.451142\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.23607 | −0.583839 | −0.291920 | − | 0.956443i | \(-0.594294\pi\) | ||||
−0.291920 | + | 0.956443i | \(0.594294\pi\) | |||||||
\(200\) | −4.76393 | + | 3.46120i | −0.336861 | + | 0.244744i | ||||
\(201\) | 4.16312 | + | 12.8128i | 0.293644 | + | 0.903743i | ||||
\(202\) | 1.74671 | − | 5.37582i | 0.122898 | − | 0.378242i | ||||
\(203\) | 3.73607 | + | 2.71441i | 0.262221 | + | 0.190514i | ||||
\(204\) | 7.50000 | + | 5.44907i | 0.525105 | + | 0.381511i | ||||
\(205\) | 3.45492 | − | 10.6331i | 0.241302 | − | 0.742650i | ||||
\(206\) | 1.04508 | + | 3.21644i | 0.0728145 | + | 0.224100i | ||||
\(207\) | 1.57295 | − | 1.14281i | 0.109328 | − | 0.0794311i | ||||
\(208\) | 3.88854 | 0.269622 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.618034 | 0.0426484 | ||||||||
\(211\) | 12.6353 | − | 9.18005i | 0.869847 | − | 0.631981i | −0.0606990 | − | 0.998156i | \(-0.519333\pi\) |
0.930546 | + | 0.366175i | \(0.119333\pi\) | |||||||
\(212\) | 1.36475 | + | 4.20025i | 0.0937311 | + | 0.288475i | ||||
\(213\) | 8.04508 | − | 24.7602i | 0.551240 | − | 1.69654i | ||||
\(214\) | 0.836881 | + | 0.608030i | 0.0572080 | + | 0.0415641i | ||||
\(215\) | −10.1631 | − | 7.38394i | −0.693119 | − | 0.503580i | ||||
\(216\) | −2.48936 | + | 7.66145i | −0.169379 | + | 0.521296i | ||||
\(217\) | 1.30902 | + | 4.02874i | 0.0888619 | + | 0.273489i | ||||
\(218\) | −0.472136 | + | 0.343027i | −0.0319771 | + | 0.0232327i | ||||
\(219\) | −23.0344 | −1.55652 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.81966 | −0.256938 | ||||||||
\(222\) | 3.23607 | − | 2.35114i | 0.217191 | − | 0.157798i | ||||
\(223\) | 0.628677 | + | 1.93487i | 0.0420993 | + | 0.129568i | 0.969897 | − | 0.243515i | \(-0.0783005\pi\) |
−0.927798 | + | 0.373083i | \(0.878301\pi\) | |||||||
\(224\) | −1.28115 | + | 3.94298i | −0.0856006 | + | 0.263452i | ||||
\(225\) | −1.23607 | − | 0.898056i | −0.0824045 | − | 0.0598704i | ||||
\(226\) | −0.0450850 | − | 0.0327561i | −0.00299901 | − | 0.00217891i | ||||
\(227\) | 4.95492 | − | 15.2497i | 0.328869 | − | 1.01216i | −0.640794 | − | 0.767713i | \(-0.721395\pi\) |
0.969664 | − | 0.244443i | \(-0.0786051\pi\) | |||||||
\(228\) | 1.63525 | + | 5.03280i | 0.108297 | + | 0.333305i | ||||
\(229\) | −5.47214 | + | 3.97574i | −0.361609 | + | 0.262724i | −0.753723 | − | 0.657192i | \(-0.771744\pi\) |
0.392114 | + | 0.919917i | \(0.371744\pi\) | |||||||
\(230\) | 1.94427 | 0.128201 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.79837 | −0.446335 | ||||||||
\(233\) | −23.7984 | + | 17.2905i | −1.55908 | + | 1.13274i | −0.622327 | + | 0.782757i | \(0.713813\pi\) |
−0.936756 | + | 0.349983i | \(0.886187\pi\) | |||||||
\(234\) | −0.0557281 | − | 0.171513i | −0.00364306 | − | 0.0112122i | ||||
\(235\) | −2.04508 | + | 6.29412i | −0.133407 | + | 0.410583i | ||||
\(236\) | 16.6353 | + | 12.0862i | 1.08286 | + | 0.786746i | ||||
\(237\) | −8.35410 | − | 6.06961i | −0.542657 | − | 0.394264i | ||||
\(238\) | 0.364745 | − | 1.12257i | 0.0236429 | − | 0.0727654i | ||||
\(239\) | 5.28115 | + | 16.2537i | 0.341609 | + | 1.05137i | 0.963374 | + | 0.268161i | \(0.0864161\pi\) |
−0.621765 | + | 0.783204i | \(0.713584\pi\) | |||||||
\(240\) | 4.11803 | − | 2.99193i | 0.265818 | − | 0.193128i | ||||
\(241\) | −16.2705 | −1.04808 | −0.524038 | − | 0.851695i | \(-0.675575\pi\) | ||||
−0.524038 | + | 0.851695i | \(0.675575\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | 11.4271 | − | 8.30224i | 0.731542 | − | 0.531496i | ||||
\(245\) | 0.309017 | + | 0.951057i | 0.0197424 | + | 0.0607608i | ||||
\(246\) | −2.13525 | + | 6.57164i | −0.136139 | + | 0.418992i | ||||
\(247\) | −1.76393 | − | 1.28157i | −0.112236 | − | 0.0815445i | ||||
\(248\) | −5.04508 | − | 3.66547i | −0.320363 | − | 0.232758i | ||||
\(249\) | 1.35410 | − | 4.16750i | 0.0858127 | − | 0.264104i | ||||
\(250\) | −1.06231 | − | 3.26944i | −0.0671861 | − | 0.206778i | ||||
\(251\) | −18.6074 | + | 13.5191i | −1.17449 | + | 0.853316i | −0.991539 | − | 0.129807i | \(-0.958564\pi\) |
−0.182949 | + | 0.983122i | \(0.558564\pi\) | |||||||
\(252\) | −0.708204 | −0.0446127 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.12461 | −0.0705644 | ||||||||
\(255\) | −4.04508 | + | 2.93893i | −0.253313 | + | 0.184043i | ||||
\(256\) | 1.71885 | + | 5.29007i | 0.107428 | + | 0.330629i | ||||
\(257\) | −2.64590 | + | 8.14324i | −0.165047 | + | 0.507961i | −0.999040 | − | 0.0438137i | \(-0.986049\pi\) |
0.833993 | + | 0.551775i | \(0.186049\pi\) | |||||||
\(258\) | 6.28115 | + | 4.56352i | 0.391048 | + | 0.284113i | ||||
\(259\) | 5.23607 | + | 3.80423i | 0.325353 | + | 0.236383i | ||||
\(260\) | −0.708204 | + | 2.17963i | −0.0439209 | + | 0.135175i | ||||
\(261\) | −0.545085 | − | 1.67760i | −0.0337399 | − | 0.103841i | ||||
\(262\) | 5.85410 | − | 4.25325i | 0.361668 | − | 0.262767i | ||||
\(263\) | 17.1246 | 1.05595 | 0.527974 | − | 0.849260i | \(-0.322952\pi\) | ||||
0.527974 | + | 0.849260i | \(0.322952\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.38197 | −0.146323 | ||||||||
\(266\) | 0.545085 | − | 0.396027i | 0.0334213 | − | 0.0242820i | ||||
\(267\) | −3.42705 | − | 10.5474i | −0.209732 | − | 0.645489i | ||||
\(268\) | 4.77051 | − | 14.6821i | 0.291405 | − | 0.896853i | ||||
\(269\) | −13.6353 | − | 9.90659i | −0.831356 | − | 0.604016i | 0.0885865 | − | 0.996068i | \(-0.471765\pi\) |
−0.919943 | + | 0.392053i | \(0.871765\pi\) | |||||||
\(270\) | −1.69098 | − | 1.22857i | −0.102910 | − | 0.0747685i | ||||
\(271\) | 1.48278 | − | 4.56352i | 0.0900724 | − | 0.277214i | −0.895866 | − | 0.444325i | \(-0.853444\pi\) |
0.985938 | + | 0.167110i | \(0.0534436\pi\) | |||||||
\(272\) | −3.00407 | − | 9.24556i | −0.182148 | − | 0.560595i | ||||
\(273\) | −1.61803 | + | 1.17557i | −0.0979279 | + | 0.0711488i | ||||
\(274\) | −5.85410 | −0.353659 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 15.2705 | 0.919177 | ||||||||
\(277\) | 18.6353 | − | 13.5393i | 1.11968 | − | 0.813498i | 0.135523 | − | 0.990774i | \(-0.456729\pi\) |
0.984161 | + | 0.177276i | \(0.0567286\pi\) | |||||||
\(278\) | −1.40983 | − | 4.33901i | −0.0845560 | − | 0.260237i | ||||
\(279\) | 0.500000 | − | 1.53884i | 0.0299342 | − | 0.0921280i | ||||
\(280\) | −1.19098 | − | 0.865300i | −0.0711748 | − | 0.0517116i | ||||
\(281\) | −20.3713 | − | 14.8006i | −1.21525 | − | 0.882932i | −0.219554 | − | 0.975600i | \(-0.570460\pi\) |
−0.995697 | + | 0.0926686i | \(0.970460\pi\) | |||||||
\(282\) | 1.26393 | − | 3.88998i | 0.0752661 | − | 0.231645i | ||||
\(283\) | −3.69098 | − | 11.3597i | −0.219406 | − | 0.675263i | −0.998811 | − | 0.0487426i | \(-0.984479\pi\) |
0.779405 | − | 0.626520i | \(-0.215521\pi\) | |||||||
\(284\) | −24.1353 | + | 17.5353i | −1.43216 | + | 1.04053i | ||||
\(285\) | −2.85410 | −0.169062 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.1803 | −0.659955 | ||||||||
\(288\) | 1.28115 | − | 0.930812i | 0.0754927 | − | 0.0548486i | ||||
\(289\) | −2.30244 | − | 7.08618i | −0.135438 | − | 0.416834i | ||||
\(290\) | 0.545085 | − | 1.67760i | 0.0320085 | − | 0.0985120i | ||||
\(291\) | 9.16312 | + | 6.65740i | 0.537152 | + | 0.390263i | ||||
\(292\) | 21.3541 | + | 15.5147i | 1.24965 | + | 0.907927i | ||||
\(293\) | 3.39919 | − | 10.4616i | 0.198583 | − | 0.611174i | −0.801333 | − | 0.598218i | \(-0.795876\pi\) |
0.999916 | − | 0.0129565i | \(-0.00412430\pi\) | |||||||
\(294\) | −0.190983 | − | 0.587785i | −0.0111384 | − | 0.0342803i | ||||
\(295\) | −8.97214 | + | 6.51864i | −0.522378 | + | 0.379530i | ||||
\(296\) | −9.52786 | −0.553796 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.38197 | 0.195912 | ||||||||
\(299\) | −5.09017 | + | 3.69822i | −0.294372 | + | 0.213874i | ||||
\(300\) | −3.70820 | − | 11.4127i | −0.214093 | − | 0.658911i | ||||
\(301\) | −3.88197 | + | 11.9475i | −0.223753 | + | 0.688640i | ||||
\(302\) | 0.0172209 | + | 0.0125117i | 0.000990953 | + | 0.000719969i | ||||
\(303\) | 19.3713 | + | 14.0741i | 1.11285 | + | 0.808535i | ||||
\(304\) | 1.71478 | − | 5.27756i | 0.0983495 | − | 0.302689i | ||||
\(305\) | 2.35410 | + | 7.24518i | 0.134795 | + | 0.414858i | ||||
\(306\) | −0.364745 | + | 0.265003i | −0.0208511 | + | 0.0151492i | ||||
\(307\) | 23.1803 | 1.32297 | 0.661486 | − | 0.749958i | \(-0.269926\pi\) | ||||
0.661486 | + | 0.749958i | \(0.269926\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.3262 | −0.814991 | ||||||||
\(310\) | 1.30902 | − | 0.951057i | 0.0743472 | − | 0.0540164i | ||||
\(311\) | 2.78115 | + | 8.55951i | 0.157705 | + | 0.485365i | 0.998425 | − | 0.0561046i | \(-0.0178680\pi\) |
−0.840720 | + | 0.541470i | \(0.817868\pi\) | |||||||
\(312\) | 0.909830 | − | 2.80017i | 0.0515090 | − | 0.158528i | ||||
\(313\) | −14.8262 | − | 10.7719i | −0.838029 | − | 0.608863i | 0.0837907 | − | 0.996483i | \(-0.473297\pi\) |
−0.921819 | + | 0.387620i | \(0.873297\pi\) | |||||||
\(314\) | −6.14590 | − | 4.46526i | −0.346833 | − | 0.251989i | ||||
\(315\) | 0.118034 | − | 0.363271i | 0.00665046 | − | 0.0204680i | ||||
\(316\) | 3.65654 | + | 11.2537i | 0.205697 | + | 0.633069i | ||||
\(317\) | 3.59017 | − | 2.60841i | 0.201644 | − | 0.146503i | −0.482381 | − | 0.875962i | \(-0.660228\pi\) |
0.684025 | + | 0.729459i | \(0.260228\pi\) | |||||||
\(318\) | 1.47214 | 0.0825533 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −4.70820 | −0.263197 | ||||||||
\(321\) | −3.54508 | + | 2.57565i | −0.197867 | + | 0.143759i | ||||
\(322\) | −0.600813 | − | 1.84911i | −0.0334820 | − | 0.103047i | ||||
\(323\) | −1.68441 | + | 5.18407i | −0.0937228 | + | 0.288449i | ||||
\(324\) | −11.5623 | − | 8.40051i | −0.642350 | − | 0.466695i | ||||
\(325\) | 4.00000 | + | 2.90617i | 0.221880 | + | 0.161205i | ||||
\(326\) | −1.02786 | + | 3.16344i | −0.0569281 | + | 0.175207i | ||||
\(327\) | −0.763932 | − | 2.35114i | −0.0422455 | − | 0.130018i | ||||
\(328\) | 13.3156 | − | 9.67435i | 0.735231 | − | 0.534176i | ||||
\(329\) | 6.61803 | 0.364864 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.18034 | 0.339702 | 0.169851 | − | 0.985470i | \(-0.445671\pi\) | ||||
0.169851 | + | 0.985470i | \(0.445671\pi\) | |||||||
\(332\) | −4.06231 | + | 2.95144i | −0.222948 | + | 0.161981i | ||||
\(333\) | −0.763932 | − | 2.35114i | −0.0418632 | − | 0.128842i | ||||
\(334\) | −0.763932 | + | 2.35114i | −0.0418005 | + | 0.128649i | ||||
\(335\) | 6.73607 | + | 4.89404i | 0.368031 | + | 0.267390i | ||||
\(336\) | −4.11803 | − | 2.99193i | −0.224657 | − | 0.163223i | ||||
\(337\) | −8.01722 | + | 24.6745i | −0.436726 | + | 1.34410i | 0.454582 | + | 0.890705i | \(0.349789\pi\) |
−0.891308 | + | 0.453399i | \(0.850211\pi\) | |||||||
\(338\) | −1.35410 | − | 4.16750i | −0.0736534 | − | 0.226682i | ||||
\(339\) | 0.190983 | − | 0.138757i | 0.0103728 | − | 0.00753626i | ||||
\(340\) | 5.72949 | 0.310725 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.257354 | −0.0139161 | ||||||||
\(343\) | 0.809017 | − | 0.587785i | 0.0436828 | − | 0.0317374i | ||||
\(344\) | −5.71478 | − | 17.5883i | −0.308120 | − | 0.948297i | ||||
\(345\) | −2.54508 | + | 7.83297i | −0.137023 | + | 0.421713i | ||||
\(346\) | −4.75329 | − | 3.45347i | −0.255538 | − | 0.185660i | ||||
\(347\) | 1.89919 | + | 1.37984i | 0.101954 | + | 0.0740737i | 0.637594 | − | 0.770373i | \(-0.279930\pi\) |
−0.535640 | + | 0.844446i | \(0.679930\pi\) | |||||||
\(348\) | 4.28115 | − | 13.1760i | 0.229494 | − | 0.706310i | ||||
\(349\) | −10.1353 | − | 31.1931i | −0.542528 | − | 1.66973i | −0.726797 | − | 0.686853i | \(-0.758992\pi\) |
0.184269 | − | 0.982876i | \(-0.441008\pi\) | |||||||
\(350\) | −1.23607 | + | 0.898056i | −0.0660706 | + | 0.0480031i | ||||
\(351\) | 6.76393 | 0.361032 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.0902 | 1.28219 | 0.641095 | − | 0.767461i | \(-0.278480\pi\) | ||||
0.641095 | + | 0.767461i | \(0.278480\pi\) | |||||||
\(354\) | 5.54508 | − | 4.02874i | 0.294718 | − | 0.214125i | ||||
\(355\) | −4.97214 | − | 15.3027i | −0.263894 | − | 0.812181i | ||||
\(356\) | −3.92705 | + | 12.0862i | −0.208133 | + | 0.640568i | ||||
\(357\) | 4.04508 | + | 2.93893i | 0.214089 | + | 0.155544i | ||||
\(358\) | 1.16312 | + | 0.845055i | 0.0614727 | + | 0.0446626i | ||||
\(359\) | 4.82624 | − | 14.8536i | 0.254719 | − | 0.783945i | −0.739166 | − | 0.673524i | \(-0.764780\pi\) |
0.993885 | − | 0.110421i | \(-0.0352200\pi\) | |||||||
\(360\) | 0.173762 | + | 0.534785i | 0.00915807 | + | 0.0281856i | ||||
\(361\) | 12.8541 | − | 9.33905i | 0.676532 | − | 0.491529i | ||||
\(362\) | −2.83282 | −0.148889 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.29180 | 0.120123 | ||||||||
\(365\) | −11.5172 | + | 8.36775i | −0.602839 | + | 0.437988i | ||||
\(366\) | −1.45492 | − | 4.47777i | −0.0760496 | − | 0.234057i | ||||
\(367\) | 10.1459 | − | 31.2259i | 0.529612 | − | 1.62998i | −0.225401 | − | 0.974266i | \(-0.572369\pi\) |
0.755012 | − | 0.655711i | \(-0.227631\pi\) | |||||||
\(368\) | −12.9549 | − | 9.41230i | −0.675322 | − | 0.490650i | ||||
\(369\) | 3.45492 | + | 2.51014i | 0.179856 | + | 0.130673i | ||||
\(370\) | 0.763932 | − | 2.35114i | 0.0397149 | − | 0.122230i | ||||
\(371\) | 0.736068 | + | 2.26538i | 0.0382147 | + | 0.117613i | ||||
\(372\) | 10.2812 | − | 7.46969i | 0.533053 | − | 0.387286i | ||||
\(373\) | 15.4377 | 0.799334 | 0.399667 | − | 0.916661i | \(-0.369126\pi\) | ||||
0.399667 | + | 0.916661i | \(0.369126\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.5623 | 0.751994 | ||||||||
\(376\) | −7.88197 | + | 5.72658i | −0.406481 | + | 0.295326i | ||||
\(377\) | 1.76393 | + | 5.42882i | 0.0908471 | + | 0.279599i | ||||
\(378\) | −0.645898 | + | 1.98787i | −0.0332214 | + | 0.102245i | ||||
\(379\) | −25.9443 | − | 18.8496i | −1.33267 | − | 0.968240i | −0.999680 | − | 0.0253087i | \(-0.991943\pi\) |
−0.332988 | − | 0.942931i | \(-0.608057\pi\) | |||||||
\(380\) | 2.64590 | + | 1.92236i | 0.135732 | + | 0.0986149i | ||||
\(381\) | 1.47214 | − | 4.53077i | 0.0754198 | − | 0.232118i | ||||
\(382\) | 1.86068 | + | 5.72658i | 0.0952007 | + | 0.292998i | ||||
\(383\) | 27.9894 | − | 20.3355i | 1.43019 | − | 1.03909i | 0.440208 | − | 0.897896i | \(-0.354905\pi\) |
0.989981 | − | 0.141197i | \(-0.0450953\pi\) | |||||||
\(384\) | 16.3262 | 0.833145 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.85410 | 0.297966 | ||||||||
\(387\) | 3.88197 | − | 2.82041i | 0.197331 | − | 0.143370i | ||||
\(388\) | −4.01064 | − | 12.3435i | −0.203610 | − | 0.626646i | ||||
\(389\) | −10.5623 | + | 32.5074i | −0.535530 | + | 1.64819i | 0.206971 | + | 0.978347i | \(0.433640\pi\) |
−0.742501 | + | 0.669845i | \(0.766360\pi\) | |||||||
\(390\) | 0.618034 | + | 0.449028i | 0.0312954 | + | 0.0227374i | ||||
\(391\) | 12.7254 | + | 9.24556i | 0.643552 | + | 0.467568i | ||||
\(392\) | −0.454915 | + | 1.40008i | −0.0229767 | + | 0.0707149i | ||||
\(393\) | 9.47214 | + | 29.1522i | 0.477806 | + | 1.47054i | ||||
\(394\) | −1.32624 | + | 0.963568i | −0.0668149 | + | 0.0485439i | ||||
\(395\) | −6.38197 | −0.321112 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.819660 | −0.0411376 | −0.0205688 | − | 0.999788i | \(-0.506548\pi\) | ||||
−0.0205688 | + | 0.999788i | \(0.506548\pi\) | |||||||
\(398\) | 2.54508 | − | 1.84911i | 0.127574 | − | 0.0926876i | ||||
\(399\) | 0.881966 | + | 2.71441i | 0.0441535 | + | 0.135891i | ||||
\(400\) | −3.88854 | + | 11.9677i | −0.194427 | + | 0.598385i | ||||
\(401\) | 14.1803 | + | 10.3026i | 0.708132 | + | 0.514488i | 0.882571 | − | 0.470180i | \(-0.155811\pi\) |
−0.174438 | + | 0.984668i | \(0.555811\pi\) | |||||||
\(402\) | −4.16312 | − | 3.02468i | −0.207638 | − | 0.150857i | ||||
\(403\) | −1.61803 | + | 4.97980i | −0.0806000 | + | 0.248061i | ||||
\(404\) | −8.47871 | − | 26.0948i | −0.421832 | − | 1.29826i | ||||
\(405\) | 6.23607 | − | 4.53077i | 0.309873 | − | 0.225136i | ||||
\(406\) | −1.76393 | −0.0875425 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −7.36068 | −0.364408 | ||||||||
\(409\) | −14.3262 | + | 10.4086i | −0.708387 | + | 0.514673i | −0.882653 | − | 0.470025i | \(-0.844245\pi\) |
0.174266 | + | 0.984699i | \(0.444245\pi\) | |||||||
\(410\) | 1.31966 | + | 4.06150i | 0.0651734 | + | 0.200583i | ||||
\(411\) | 7.66312 | − | 23.5847i | 0.377994 | − | 1.16335i | ||||
\(412\) | 13.2812 | + | 9.64932i | 0.654315 | + | 0.475388i | ||||
\(413\) | 8.97214 | + | 6.51864i | 0.441490 | + | 0.320761i | ||||
\(414\) | −0.229490 | + | 0.706298i | −0.0112788 | + | 0.0347127i | ||||
\(415\) | −0.836881 | − | 2.57565i | −0.0410809 | − | 0.126434i | ||||
\(416\) | −4.14590 | + | 3.01217i | −0.203269 | + | 0.147684i | ||||
\(417\) | 19.3262 | 0.946410 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.8885 | 1.46015 | 0.730075 | − | 0.683367i | \(-0.239485\pi\) | ||||
0.730075 | + | 0.683367i | \(0.239485\pi\) | |||||||
\(420\) | 2.42705 | − | 1.76336i | 0.118428 | − | 0.0860430i | ||||
\(421\) | 0.236068 | + | 0.726543i | 0.0115052 | + | 0.0354095i | 0.956644 | − | 0.291259i | \(-0.0940740\pi\) |
−0.945139 | + | 0.326668i | \(0.894074\pi\) | |||||||
\(422\) | −1.84346 | + | 5.67358i | −0.0897382 | + | 0.276186i | ||||
\(423\) | −2.04508 | − | 1.48584i | −0.0994354 | − | 0.0722441i | ||||
\(424\) | −2.83688 | − | 2.06111i | −0.137771 | − | 0.100097i | ||||
\(425\) | 3.81966 | − | 11.7557i | 0.185281 | − | 0.570235i | ||||
\(426\) | 3.07295 | + | 9.45756i | 0.148885 | + | 0.458221i | ||||
\(427\) | 6.16312 | − | 4.47777i | 0.298254 | − | 0.216694i | ||||
\(428\) | 5.02129 | 0.242713 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.79837 | 0.231398 | ||||||||
\(431\) | −11.2082 | + | 8.14324i | −0.539880 | + | 0.392246i | −0.824041 | − | 0.566531i | \(-0.808285\pi\) |
0.284160 | + | 0.958777i | \(0.408285\pi\) | |||||||
\(432\) | 5.31966 | + | 16.3722i | 0.255942 | + | 0.787709i | ||||
\(433\) | −2.77051 | + | 8.52675i | −0.133142 | + | 0.409770i | −0.995296 | − | 0.0968764i | \(-0.969115\pi\) |
0.862154 | + | 0.506646i | \(0.169115\pi\) | |||||||
\(434\) | −1.30902 | − | 0.951057i | −0.0628348 | − | 0.0456522i | ||||
\(435\) | 6.04508 | + | 4.39201i | 0.289840 | + | 0.210581i | ||||
\(436\) | −0.875388 | + | 2.69417i | −0.0419235 | + | 0.129027i | ||||
\(437\) | 2.77458 | + | 8.53926i | 0.132726 | + | 0.408488i | ||||
\(438\) | 7.11803 | − | 5.17155i | 0.340113 | − | 0.247106i | ||||
\(439\) | −3.38197 | −0.161412 | −0.0807062 | − | 0.996738i | \(-0.525718\pi\) | ||||
−0.0807062 | + | 0.996738i | \(0.525718\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.381966 | −0.0181889 | ||||||||
\(442\) | 1.18034 | − | 0.857567i | 0.0561430 | − | 0.0407903i | ||||
\(443\) | 0.954915 | + | 2.93893i | 0.0453694 | + | 0.139633i | 0.971175 | − | 0.238367i | \(-0.0766121\pi\) |
−0.925806 | + | 0.378000i | \(0.876612\pi\) | |||||||
\(444\) | 6.00000 | − | 18.4661i | 0.284747 | − | 0.876362i | ||||
\(445\) | −5.54508 | − | 4.02874i | −0.262862 | − | 0.190981i | ||||
\(446\) | −0.628677 | − | 0.456761i | −0.0297687 | − | 0.0216282i | ||||
\(447\) | −4.42705 | + | 13.6251i | −0.209392 | + | 0.644443i | ||||
\(448\) | 1.45492 | + | 4.47777i | 0.0687383 | + | 0.211555i | ||||
\(449\) | −9.97214 | + | 7.24518i | −0.470614 | + | 0.341921i | −0.797681 | − | 0.603080i | \(-0.793940\pi\) |
0.327066 | + | 0.945001i | \(0.393940\pi\) | |||||||
\(450\) | 0.583592 | 0.0275108 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.270510 | −0.0127237 | ||||||||
\(453\) | −0.0729490 | + | 0.0530006i | −0.00342744 | + | 0.00249018i | ||||
\(454\) | 1.89261 | + | 5.82485i | 0.0888245 | + | 0.273374i | ||||
\(455\) | −0.381966 | + | 1.17557i | −0.0179068 | + | 0.0551116i | ||||
\(456\) | −3.39919 | − | 2.46965i | −0.159182 | − | 0.115652i | ||||
\(457\) | −0.118034 | − | 0.0857567i | −0.00552140 | − | 0.00401153i | 0.585021 | − | 0.811018i | \(-0.301086\pi\) |
−0.590543 | + | 0.807007i | \(0.701086\pi\) | |||||||
\(458\) | 0.798374 | − | 2.45714i | 0.0373056 | − | 0.114815i | ||||
\(459\) | −5.22542 | − | 16.0822i | −0.243902 | − | 0.750653i | ||||
\(460\) | 7.63525 | − | 5.54734i | 0.355996 | − | 0.258646i | ||||
\(461\) | 18.5066 | 0.861937 | 0.430969 | − | 0.902367i | \(-0.358172\pi\) | ||||
0.430969 | + | 0.902367i | \(0.358172\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.2361 | 1.03340 | 0.516699 | − | 0.856167i | \(-0.327161\pi\) | ||||
0.516699 | + | 0.856167i | \(0.327161\pi\) | |||||||
\(464\) | −11.7533 | + | 8.53926i | −0.545633 | + | 0.396425i | ||||
\(465\) | 2.11803 | + | 6.51864i | 0.0982215 | + | 0.302295i | ||||
\(466\) | 3.47214 | − | 10.6861i | 0.160844 | − | 0.495026i | ||||
\(467\) | 3.64590 | + | 2.64890i | 0.168712 | + | 0.122576i | 0.668937 | − | 0.743319i | \(-0.266749\pi\) |
−0.500225 | + | 0.865895i | \(0.666749\pi\) | |||||||
\(468\) | −0.708204 | − | 0.514540i | −0.0327367 | − | 0.0237846i | ||||
\(469\) | 2.57295 | − | 7.91872i | 0.118808 | − | 0.365653i | ||||
\(470\) | −0.781153 | − | 2.40414i | −0.0360319 | − | 0.110895i | ||||
\(471\) | 26.0344 | − | 18.9151i | 1.19960 | − | 0.871563i | ||||
\(472\) | −16.3262 | −0.751476 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.94427 | 0.181166 | ||||||||
\(475\) | 5.70820 | − | 4.14725i | 0.261910 | − | 0.190289i | ||||
\(476\) | −1.77051 | − | 5.44907i | −0.0811512 | − | 0.249758i | ||||
\(477\) | 0.281153 | − | 0.865300i | 0.0128731 | − | 0.0396194i | ||||
\(478\) | −5.28115 | − | 3.83698i | −0.241554 | − | 0.175499i | ||||
\(479\) | 17.6074 | + | 12.7925i | 0.804502 | + | 0.584505i | 0.912231 | − | 0.409675i | \(-0.134358\pi\) |
−0.107729 | + | 0.994180i | \(0.534358\pi\) | |||||||
\(480\) | −2.07295 | + | 6.37988i | −0.0946167 | + | 0.291200i | ||||
\(481\) | 2.47214 | + | 7.60845i | 0.112720 | + | 0.346916i | ||||
\(482\) | 5.02786 | − | 3.65296i | 0.229013 | − | 0.166388i | ||||
\(483\) | 8.23607 | 0.374754 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.00000 | 0.317854 | ||||||||
\(486\) | 1.21885 | − | 0.885544i | 0.0552880 | − | 0.0401691i | ||||
\(487\) | −10.0729 | − | 31.0013i | −0.456449 | − | 1.40481i | −0.869426 | − | 0.494064i | \(-0.835511\pi\) |
0.412977 | − | 0.910742i | \(-0.364489\pi\) | |||||||
\(488\) | −3.46556 | + | 10.6659i | −0.156878 | + | 0.482822i | ||||
\(489\) | −11.3992 | − | 8.28199i | −0.515489 | − | 0.374525i | ||||
\(490\) | −0.309017 | − | 0.224514i | −0.0139600 | − | 0.0101425i | ||||
\(491\) | −6.84346 | + | 21.0620i | −0.308841 | + | 0.950515i | 0.669375 | + | 0.742925i | \(0.266562\pi\) |
−0.978216 | + | 0.207590i | \(0.933438\pi\) | |||||||
\(492\) | 10.3647 | + | 31.8994i | 0.467279 | + | 1.43814i | ||||
\(493\) | 11.5451 | − | 8.38800i | 0.519964 | − | 0.377776i | ||||
\(494\) | 0.832816 | 0.0374702 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.3262 | −0.598366 | ||||||||
\(497\) | −13.0172 | + | 9.45756i | −0.583902 | + | 0.424230i | ||||
\(498\) | 0.517221 | + | 1.59184i | 0.0231772 | + | 0.0713322i | ||||
\(499\) | −3.11803 | + | 9.59632i | −0.139582 | + | 0.429590i | −0.996275 | − | 0.0862375i | \(-0.972516\pi\) |
0.856692 | + | 0.515828i | \(0.172516\pi\) | |||||||
\(500\) | −13.5000 | − | 9.80832i | −0.603738 | − | 0.438642i | ||||
\(501\) | −8.47214 | − | 6.15537i | −0.378507 | − | 0.275002i | ||||
\(502\) | 2.71478 | − | 8.35524i | 0.121167 | − | 0.372913i | ||||
\(503\) | 10.7639 | + | 33.1280i | 0.479940 | + | 1.47710i | 0.839178 | + | 0.543857i | \(0.183037\pi\) |
−0.359238 | + | 0.933246i | \(0.616963\pi\) | |||||||
\(504\) | 0.454915 | − | 0.330515i | 0.0202635 | − | 0.0147223i | ||||
\(505\) | 14.7984 | 0.658519 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.5623 | 0.824381 | ||||||||
\(508\) | −4.41641 | + | 3.20871i | −0.195946 | + | 0.142363i | ||||
\(509\) | −3.31966 | − | 10.2169i | −0.147141 | − | 0.452855i | 0.850139 | − | 0.526559i | \(-0.176518\pi\) |
−0.997280 | + | 0.0737042i | \(0.976518\pi\) | |||||||
\(510\) | 0.590170 | − | 1.81636i | 0.0261332 | − | 0.0804296i | ||||
\(511\) | 11.5172 | + | 8.36775i | 0.509492 | + | 0.370168i | ||||
\(512\) | −18.0451 | − | 13.1105i | −0.797488 | − | 0.579409i | ||||
\(513\) | 2.98278 | − | 9.18005i | 0.131693 | − | 0.405309i | ||||
\(514\) | −1.01064 | − | 3.11044i | −0.0445776 | − | 0.137196i | ||||
\(515\) | −7.16312 | + | 5.20431i | −0.315645 | + | 0.229329i | ||||
\(516\) | 37.6869 | 1.65907 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.47214 | −0.108619 | ||||||||
\(519\) | 20.1353 | − | 14.6291i | 0.883840 | − | 0.642147i | ||||
\(520\) | −0.562306 | − | 1.73060i | −0.0246587 | − | 0.0758918i | ||||
\(521\) | −3.78115 | + | 11.6372i | −0.165655 | + | 0.509835i | −0.999084 | − | 0.0427924i | \(-0.986375\pi\) |
0.833429 | + | 0.552627i | \(0.186375\pi\) | |||||||
\(522\) | 0.545085 | + | 0.396027i | 0.0238577 | + | 0.0173336i | ||||
\(523\) | 13.3992 | + | 9.73508i | 0.585906 | + | 0.425685i | 0.840848 | − | 0.541271i | \(-0.182057\pi\) |
−0.254943 | + | 0.966956i | \(0.582057\pi\) | |||||||
\(524\) | 10.8541 | − | 33.4055i | 0.474164 | − | 1.45933i | ||||
\(525\) | −2.00000 | − | 6.15537i | −0.0872872 | − | 0.268642i | ||||
\(526\) | −5.29180 | + | 3.84471i | −0.230733 | + | 0.167638i | ||||
\(527\) | 13.0902 | 0.570217 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.90983 | 0.126514 | ||||||||
\(530\) | 0.736068 | − | 0.534785i | 0.0319727 | − | 0.0232296i | ||||
\(531\) | −1.30902 | − | 4.02874i | −0.0568065 | − | 0.174832i | ||||
\(532\) | 1.01064 | − | 3.11044i | 0.0438169 | − | 0.134855i | ||||
\(533\) | −11.1803 | − | 8.12299i | −0.484274 | − | 0.351846i | ||||
\(534\) | 3.42705 | + | 2.48990i | 0.148303 | + | 0.107748i | ||||
\(535\) | −0.836881 | + | 2.57565i | −0.0361815 | + | 0.111355i | ||||
\(536\) | 3.78773 | + | 11.6574i | 0.163605 | + | 0.503525i | ||||
\(537\) | −4.92705 | + | 3.57971i | −0.212618 | + | 0.154476i | ||||
\(538\) | 6.43769 | 0.277549 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −10.1459 | −0.436610 | ||||||||
\(541\) | 0.572949 | − | 0.416272i | 0.0246330 | − | 0.0178969i | −0.575401 | − | 0.817872i | \(-0.695154\pi\) |
0.600034 | + | 0.799975i | \(0.295154\pi\) | |||||||
\(542\) | 0.566371 | + | 1.74311i | 0.0243277 | + | 0.0748730i | ||||
\(543\) | 3.70820 | − | 11.4127i | 0.159134 | − | 0.489765i | ||||
\(544\) | 10.3647 | + | 7.53043i | 0.444385 | + | 0.322864i | ||||
\(545\) | −1.23607 | − | 0.898056i | −0.0529473 | − | 0.0384685i | ||||
\(546\) | 0.236068 | − | 0.726543i | 0.0101028 | − | 0.0310931i | ||||
\(547\) | 0.534442 | + | 1.64484i | 0.0228511 | + | 0.0703284i | 0.961832 | − | 0.273641i | \(-0.0882282\pi\) |
−0.938981 | + | 0.343970i | \(0.888228\pi\) | |||||||
\(548\) | −22.9894 | + | 16.7027i | −0.982057 | + | 0.713506i | ||||
\(549\) | −2.90983 | −0.124189 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.14590 | 0.347027 | ||||||||
\(552\) | −9.80902 | + | 7.12667i | −0.417499 | + | 0.303331i | ||||
\(553\) | 1.97214 | + | 6.06961i | 0.0838638 | + | 0.258106i | ||||
\(554\) | −2.71885 | + | 8.36775i | −0.115513 | + | 0.355512i | ||||
\(555\) | 8.47214 | + | 6.15537i | 0.359622 | + | 0.261281i | ||||
\(556\) | −17.9164 | − | 13.0170i | −0.759825 | − | 0.552045i | ||||
\(557\) | 3.01722 | − | 9.28605i | 0.127844 | − | 0.393463i | −0.866565 | − | 0.499065i | \(-0.833677\pi\) |
0.994408 | + | 0.105602i | \(0.0336770\pi\) | |||||||
\(558\) | 0.190983 | + | 0.587785i | 0.00808496 | + | 0.0248829i | ||||
\(559\) | −12.5623 | + | 9.12705i | −0.531329 | + | 0.386033i | ||||
\(560\) | −3.14590 | −0.132938 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.61803 | 0.405712 | ||||||||
\(563\) | −25.8713 | + | 18.7966i | −1.09035 | + | 0.792183i | −0.979458 | − | 0.201650i | \(-0.935370\pi\) |
−0.110889 | + | 0.993833i | \(0.535370\pi\) | |||||||
\(564\) | −6.13525 | − | 18.8824i | −0.258341 | − | 0.795091i | ||||
\(565\) | 0.0450850 | − | 0.138757i | 0.00189674 | − | 0.00583756i | ||||
\(566\) | 3.69098 | + | 2.68166i | 0.155144 | + | 0.112718i | ||||
\(567\) | −6.23607 | − | 4.53077i | −0.261890 | − | 0.190274i | ||||
\(568\) | 7.31966 | − | 22.5276i | 0.307126 | − | 0.945237i | ||||
\(569\) | −11.5279 | − | 35.4791i | −0.483273 | − | 1.48736i | −0.834466 | − | 0.551059i | \(-0.814224\pi\) |
0.351193 | − | 0.936303i | \(-0.385776\pi\) | |||||||
\(570\) | 0.881966 | − | 0.640786i | 0.0369415 | − | 0.0268396i | ||||
\(571\) | −34.3050 | −1.43562 | −0.717809 | − | 0.696240i | \(-0.754855\pi\) | ||||
−0.717809 | + | 0.696240i | \(0.754855\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.5066 | −1.06555 | ||||||||
\(574\) | 3.45492 | − | 2.51014i | 0.144205 | − | 0.104771i | ||||
\(575\) | −6.29180 | − | 19.3642i | −0.262386 | − | 0.807541i | ||||
\(576\) | 0.555728 | − | 1.71036i | 0.0231553 | − | 0.0712648i | ||||
\(577\) | −7.80902 | − | 5.67358i | −0.325094 | − | 0.236194i | 0.413252 | − | 0.910617i | \(-0.364393\pi\) |
−0.738346 | + | 0.674422i | \(0.764393\pi\) | |||||||
\(578\) | 2.30244 | + | 1.67282i | 0.0957688 | + | 0.0695801i | ||||
\(579\) | −7.66312 | + | 23.5847i | −0.318468 | + | 0.980145i | ||||
\(580\) | −2.64590 | − | 8.14324i | −0.109865 | − | 0.338130i | ||||
\(581\) | −2.19098 | + | 1.59184i | −0.0908973 | + | 0.0660407i | ||||
\(582\) | −4.32624 | −0.179328 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −20.9574 | −0.867225 | ||||||||
\(585\) | 0.381966 | − | 0.277515i | 0.0157924 | − | 0.0114738i | ||||
\(586\) | 1.29837 | + | 3.99598i | 0.0536353 | + | 0.165073i | ||||
\(587\) | 0.309017 | − | 0.951057i | 0.0127545 | − | 0.0392543i | −0.944477 | − | 0.328578i | \(-0.893431\pi\) |
0.957231 | + | 0.289324i | \(0.0934305\pi\) | |||||||
\(588\) | −2.42705 | − | 1.76336i | −0.100090 | − | 0.0727196i | ||||
\(589\) | 6.04508 | + | 4.39201i | 0.249083 | + | 0.180970i | ||||
\(590\) | 1.30902 | − | 4.02874i | 0.0538914 | − | 0.165861i | ||||
\(591\) | −2.14590 | − | 6.60440i | −0.0882705 | − | 0.271669i | ||||
\(592\) | −16.4721 | + | 11.9677i | −0.677001 | + | 0.491870i | ||||
\(593\) | −11.1246 | −0.456833 | −0.228417 | − | 0.973564i | \(-0.573355\pi\) | ||||
−0.228417 | + | 0.973564i | \(0.573355\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.09017 | 0.126685 | ||||||||
\(596\) | 13.2812 | − | 9.64932i | 0.544017 | − | 0.395252i | ||||
\(597\) | 4.11803 | + | 12.6740i | 0.168540 | + | 0.518713i | ||||
\(598\) | 0.742646 | − | 2.28563i | 0.0303690 | − | 0.0934663i | ||||
\(599\) | 12.9443 | + | 9.40456i | 0.528889 | + | 0.384260i | 0.819942 | − | 0.572447i | \(-0.194006\pi\) |
−0.291053 | + | 0.956707i | \(0.594006\pi\) | |||||||
\(600\) | 7.70820 | + | 5.60034i | 0.314686 | + | 0.228633i | ||||
\(601\) | −4.23607 | + | 13.0373i | −0.172793 | + | 0.531802i | −0.999526 | − | 0.0307929i | \(-0.990197\pi\) |
0.826733 | + | 0.562595i | \(0.190197\pi\) | |||||||
\(602\) | −1.48278 | − | 4.56352i | −0.0604336 | − | 0.185995i | ||||
\(603\) | −2.57295 | + | 1.86936i | −0.104779 | + | 0.0761261i | ||||
\(604\) | 0.103326 | 0.00420426 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.14590 | −0.371527 | ||||||||
\(607\) | 16.3435 | − | 11.8742i | 0.663361 | − | 0.481960i | −0.204436 | − | 0.978880i | \(-0.565536\pi\) |
0.867796 | + | 0.496920i | \(0.165536\pi\) | |||||||
\(608\) | 2.25987 | + | 6.95515i | 0.0916497 | + | 0.282069i | ||||
\(609\) | 2.30902 | − | 7.10642i | 0.0935661 | − | 0.287967i | ||||
\(610\) | −2.35410 | − | 1.71036i | −0.0953148 | − | 0.0692503i | ||||
\(611\) | 6.61803 | + | 4.80828i | 0.267737 | + | 0.194522i | ||||
\(612\) | −0.676275 | + | 2.08136i | −0.0273368 | + | 0.0841340i | ||||
\(613\) | 0.274575 | + | 0.845055i | 0.0110900 | + | 0.0341315i | 0.956448 | − | 0.291902i | \(-0.0942879\pi\) |
−0.945358 | + | 0.326033i | \(0.894288\pi\) | |||||||
\(614\) | −7.16312 | + | 5.20431i | −0.289080 | + | 0.210029i | ||||
\(615\) | −18.0902 | −0.729466 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.41641 | 0.379090 | 0.189545 | − | 0.981872i | \(-0.439299\pi\) | ||||
0.189545 | + | 0.981872i | \(0.439299\pi\) | |||||||
\(618\) | 4.42705 | − | 3.21644i | 0.178082 | − | 0.129384i | ||||
\(619\) | −12.2705 | − | 37.7647i | −0.493193 | − | 1.51789i | −0.819753 | − | 0.572717i | \(-0.805889\pi\) |
0.326560 | − | 0.945177i | \(-0.394111\pi\) | |||||||
\(620\) | 2.42705 | − | 7.46969i | 0.0974727 | − | 0.299990i | ||||
\(621\) | −22.5344 | − | 16.3722i | −0.904276 | − | 0.656995i | ||||
\(622\) | −2.78115 | − | 2.02063i | −0.111514 | − | 0.0810197i | ||||
\(623\) | −2.11803 | + | 6.51864i | −0.0848572 | + | 0.261164i | ||||
\(624\) | −1.94427 | − | 5.98385i | −0.0778332 | − | 0.239546i | ||||
\(625\) | −8.89919 | + | 6.46564i | −0.355967 | + | 0.258626i | ||||
\(626\) | 7.00000 | 0.279776 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −36.8754 | −1.47149 | ||||||||
\(629\) | 16.1803 | − | 11.7557i | 0.645152 | − | 0.468731i | ||||
\(630\) | 0.0450850 | + | 0.138757i | 0.00179623 | + | 0.00552822i | ||||
\(631\) | 5.51064 | − | 16.9600i | 0.219375 | − | 0.675168i | −0.779439 | − | 0.626478i | \(-0.784496\pi\) |
0.998814 | − | 0.0486891i | \(-0.0155044\pi\) | |||||||
\(632\) | −7.60081 | − | 5.52231i | −0.302344 | − | 0.219666i | ||||
\(633\) | −20.4443 | − | 14.8536i | −0.812587 | − | 0.590379i | ||||
\(634\) | −0.523799 | + | 1.61209i | −0.0208027 | + | 0.0640241i | ||||
\(635\) | −0.909830 | − | 2.80017i | −0.0361055 | − | 0.111121i | ||||
\(636\) | 5.78115 | − | 4.20025i | 0.229238 | − | 0.166551i | ||||
\(637\) | 1.23607 | 0.0489748 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.14590 | 0.243128 | ||||||||
\(640\) | 8.16312 | − | 5.93085i | 0.322676 | − | 0.234438i | ||||
\(641\) | 9.78115 | + | 30.1033i | 0.386332 | + | 1.18901i | 0.935509 | + | 0.353302i | \(0.114941\pi\) |
−0.549177 | + | 0.835706i | \(0.685059\pi\) | |||||||
\(642\) | 0.517221 | − | 1.59184i | 0.0204131 | − | 0.0628250i | ||||
\(643\) | −1.28115 | − | 0.930812i | −0.0505237 | − | 0.0367076i | 0.562237 | − | 0.826976i | \(-0.309941\pi\) |
−0.612760 | + | 0.790269i | \(0.709941\pi\) | |||||||
\(644\) | −7.63525 | − | 5.54734i | −0.300871 | − | 0.218596i | ||||
\(645\) | −6.28115 | + | 19.3314i | −0.247320 | + | 0.761173i | ||||
\(646\) | −0.643386 | − | 1.98014i | −0.0253137 | − | 0.0779075i | ||||
\(647\) | −5.00000 | + | 3.63271i | −0.196570 | + | 0.142817i | −0.681717 | − | 0.731616i | \(-0.738766\pi\) |
0.485146 | + | 0.874433i | \(0.338766\pi\) | |||||||
\(648\) | 11.3475 | 0.445773 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.88854 | −0.0740748 | ||||||||
\(651\) | 5.54508 | − | 4.02874i | 0.217329 | − | 0.157899i | ||||
\(652\) | 4.98936 | + | 15.3557i | 0.195398 | + | 0.601374i | ||||
\(653\) | 5.63525 | − | 17.3435i | 0.220525 | − | 0.678705i | −0.778191 | − | 0.628028i | \(-0.783862\pi\) |
0.998715 | − | 0.0506766i | \(-0.0161378\pi\) | |||||||
\(654\) | 0.763932 | + | 0.555029i | 0.0298721 | + | 0.0217034i | ||||
\(655\) | 15.3262 | + | 11.1352i | 0.598846 | + | 0.435087i | ||||
\(656\) | 10.8688 | − | 33.4508i | 0.424356 | − | 1.30603i | ||||
\(657\) | −1.68034 | − | 5.17155i | −0.0655563 | − | 0.201762i | ||||
\(658\) | −2.04508 | + | 1.48584i | −0.0797257 | + | 0.0579241i | ||||
\(659\) | −31.4721 | −1.22598 | −0.612990 | − | 0.790091i | \(-0.710033\pi\) | ||||
−0.612990 | + | 0.790091i | \(0.710033\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.5623 | −1.34432 | −0.672159 | − | 0.740407i | \(-0.734633\pi\) | ||||
−0.672159 | + | 0.740407i | \(0.734633\pi\) | |||||||
\(662\) | −1.90983 | + | 1.38757i | −0.0742277 | + | 0.0539295i | ||||
\(663\) | 1.90983 | + | 5.87785i | 0.0741717 | + | 0.228277i | ||||
\(664\) | 1.23200 | − | 3.79171i | 0.0478110 | − | 0.147147i | ||||
\(665\) | 1.42705 | + | 1.03681i | 0.0553387 | + | 0.0402059i | ||||
\(666\) | 0.763932 | + | 0.555029i | 0.0296018 | + | 0.0215069i | ||||
\(667\) | 7.26393 | − | 22.3561i | 0.281261 | − | 0.865631i | ||||
\(668\) | 3.70820 | + | 11.4127i | 0.143475 | + | 0.441570i | ||||
\(669\) | 2.66312 | − | 1.93487i | 0.102962 | − | 0.0748064i | ||||
\(670\) | −3.18034 | −0.122867 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 6.70820 | 0.258775 | ||||||||
\(673\) | −5.32624 | + | 3.86974i | −0.205311 | + | 0.149167i | −0.685690 | − | 0.727894i | \(-0.740499\pi\) |
0.480378 | + | 0.877061i | \(0.340499\pi\) | |||||||
\(674\) | −3.06231 | − | 9.42481i | −0.117956 | − | 0.363030i | ||||
\(675\) | −6.76393 | + | 20.8172i | −0.260344 | + | 0.801256i | ||||
\(676\) | −17.2082 | − | 12.5025i | −0.661854 | − | 0.480865i | ||||
\(677\) | −29.3435 | − | 21.3193i | −1.12776 | − | 0.819366i | −0.142393 | − | 0.989810i | \(-0.545480\pi\) |
−0.985367 | + | 0.170444i | \(0.945480\pi\) | |||||||
\(678\) | −0.0278640 | + | 0.0857567i | −0.00107011 | + | 0.00329347i | ||||
\(679\) | −2.16312 | − | 6.65740i | −0.0830129 | − | 0.255487i | ||||
\(680\) | −3.68034 | + | 2.67392i | −0.141135 | + | 0.102540i | ||||
\(681\) | −25.9443 | −0.994187 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.493422 | 0.0188803 | 0.00944014 | − | 0.999955i | \(-0.496995\pi\) | ||||
0.00944014 | + | 0.999955i | \(0.496995\pi\) | |||||||
\(684\) | −1.01064 | + | 0.734275i | −0.0386429 | + | 0.0280757i | ||||
\(685\) | −4.73607 | − | 14.5761i | −0.180956 | − | 0.556925i | ||||
\(686\) | −0.118034 | + | 0.363271i | −0.00450656 | + | 0.0138698i | ||||
\(687\) | 8.85410 | + | 6.43288i | 0.337805 | + | 0.245430i | ||||
\(688\) | −31.9721 | − | 23.2291i | −1.21893 | − | 0.885602i | ||||
\(689\) | −0.909830 | + | 2.80017i | −0.0346618 | + | 0.106678i | ||||
\(690\) | −0.972136 | − | 2.99193i | −0.0370086 | − | 0.113901i | ||||
\(691\) | −15.0000 | + | 10.8981i | −0.570627 | + | 0.414585i | −0.835333 | − | 0.549744i | \(-0.814725\pi\) |
0.264706 | + | 0.964329i | \(0.414725\pi\) | |||||||
\(692\) | −28.5197 | −1.08416 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.896674 | −0.0340373 | ||||||||
\(695\) | 9.66312 | − | 7.02067i | 0.366543 | − | 0.266309i | ||||
\(696\) | 3.39919 | + | 10.4616i | 0.128846 | + | 0.396547i | ||||
\(697\) | −10.6763 | + | 32.8582i | −0.404393 | + | 1.24459i | ||||
\(698\) | 10.1353 | + | 7.36369i | 0.383625 | + | 0.278720i | ||||
\(699\) | 38.5066 | + | 27.9767i | 1.45645 | + | 1.05817i | ||||
\(700\) | −2.29180 | + | 7.05342i | −0.0866217 | + | 0.266594i | ||||
\(701\) | −5.71885 | − | 17.6008i | −0.215998 | − | 0.664773i | −0.999081 | − | 0.0428564i | \(-0.986354\pi\) |
0.783083 | − | 0.621917i | \(-0.213646\pi\) | |||||||
\(702\) | −2.09017 | + | 1.51860i | −0.0788884 | + | 0.0573158i | ||||
\(703\) | 11.4164 | 0.430578 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.7082 | 0.403294 | ||||||||
\(706\) | −7.44427 | + | 5.40858i | −0.280169 | + | 0.203555i | ||||
\(707\) | −4.57295 | − | 14.0741i | −0.171983 | − | 0.529311i | ||||
\(708\) | 10.2812 | − | 31.6421i | 0.386389 | − | 1.18918i | ||||
\(709\) | 5.69098 | + | 4.13474i | 0.213729 | + | 0.155283i | 0.689499 | − | 0.724286i | \(-0.257831\pi\) |
−0.475770 | + | 0.879570i | \(0.657831\pi\) | |||||||
\(710\) | 4.97214 | + | 3.61247i | 0.186601 | + | 0.135574i | ||||
\(711\) | 0.753289 | − | 2.31838i | 0.0282505 | − | 0.0869462i | ||||
\(712\) | −3.11803 | − | 9.59632i | −0.116853 | − | 0.359637i | ||||
\(713\) | 17.4443 | − | 12.6740i | 0.653293 | − | 0.474645i | ||||
\(714\) | −1.90983 | −0.0714736 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.97871 | 0.260807 | ||||||||
\(717\) | 22.3713 | − | 16.2537i | 0.835472 | − | 0.607006i | ||||
\(718\) | 1.84346 | + | 5.67358i | 0.0687973 | + | 0.211736i | ||||
\(719\) | −0.892609 | + | 2.74717i | −0.0332887 | + | 0.102452i | −0.966320 | − | 0.257342i | \(-0.917153\pi\) |
0.933032 | + | 0.359794i | \(0.117153\pi\) | |||||||
\(720\) | 0.972136 | + | 0.706298i | 0.0362294 | + | 0.0263222i | ||||
\(721\) | 7.16312 | + | 5.20431i | 0.266768 | + | 0.193819i | ||||
\(722\) | −1.87539 | + | 5.77185i | −0.0697947 | + | 0.214806i | ||||
\(723\) | 8.13525 | + | 25.0377i | 0.302553 | + | 0.931164i | ||||
\(724\) | −11.1246 | + | 8.08250i | −0.413443 | + | 0.300384i | ||||
\(725\) | −18.4721 | −0.686038 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.4508 | −0.461776 | −0.230888 | − | 0.972980i | \(-0.574163\pi\) | ||||
−0.230888 | + | 0.972980i | \(0.574163\pi\) | |||||||
\(728\) | −1.47214 | + | 1.06957i | −0.0545610 | + | 0.0396409i | ||||
\(729\) | 9.11803 | + | 28.0624i | 0.337705 | + | 1.03935i | ||||
\(730\) | 1.68034 | − | 5.17155i | 0.0621922 | − | 0.191408i | ||||
\(731\) | 31.4058 | + | 22.8176i | 1.16158 | + | 0.843940i | ||||
\(732\) | −18.4894 | − | 13.4333i | −0.683386 | − | 0.496509i | ||||
\(733\) | −16.3607 | + | 50.3530i | −0.604295 | + | 1.85983i | −0.102733 | + | 0.994709i | \(0.532759\pi\) |
−0.501563 | + | 0.865121i | \(0.667241\pi\) | |||||||
\(734\) | 3.87539 | + | 11.9272i | 0.143043 | + | 0.440242i | ||||
\(735\) | 1.30902 | − | 0.951057i | 0.0482838 | − | 0.0350802i | ||||
\(736\) | 21.1033 | 0.777879 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −1.63119 | −0.0600449 | ||||||||
\(739\) | −9.20820 | + | 6.69015i | −0.338729 | + | 0.246101i | −0.744125 | − | 0.668040i | \(-0.767134\pi\) |
0.405396 | + | 0.914141i | \(0.367134\pi\) | |||||||
\(740\) | −3.70820 | − | 11.4127i | −0.136316 | − | 0.419538i | ||||
\(741\) | −1.09017 | + | 3.35520i | −0.0400484 | + | 0.123256i | ||||
\(742\) | −0.736068 | − | 0.534785i | −0.0270219 | − | 0.0196326i | ||||
\(743\) | −12.0623 | − | 8.76378i | −0.442523 | − | 0.321512i | 0.344114 | − | 0.938928i | \(-0.388179\pi\) |
−0.786637 | + | 0.617416i | \(0.788179\pi\) | |||||||
\(744\) | −3.11803 | + | 9.59632i | −0.114313 | + | 0.351818i | ||||
\(745\) | 2.73607 | + | 8.42075i | 0.100242 | + | 0.308512i | ||||
\(746\) | −4.77051 | + | 3.46598i | −0.174661 | + | 0.126898i | ||||
\(747\) | 1.03444 | 0.0378482 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.70820 | 0.0989556 | ||||||||
\(750\) | −4.50000 | + | 3.26944i | −0.164317 | + | 0.119383i | ||||
\(751\) | 12.7639 | + | 39.2833i | 0.465762 | + | 1.43347i | 0.858021 | + | 0.513615i | \(0.171694\pi\) |
−0.392259 | + | 0.919855i | \(0.628306\pi\) | |||||||
\(752\) | −6.43363 | + | 19.8007i | −0.234610 | + | 0.722056i | ||||
\(753\) | 30.1074 | + | 21.8743i | 1.09717 | + | 0.797144i | ||||
\(754\) | −1.76393 | − | 1.28157i | −0.0642386 | − | 0.0466721i | ||||
\(755\) | −0.0172209 | + | 0.0530006i | −0.000626734 | + | 0.00192889i | ||||
\(756\) | 3.13525 | + | 9.64932i | 0.114028 | + | 0.350942i | ||||
\(757\) | 11.9443 | − | 8.67802i | 0.434122 | − | 0.315408i | −0.349173 | − | 0.937058i | \(-0.613537\pi\) |
0.783295 | + | 0.621650i | \(0.213537\pi\) | |||||||
\(758\) | 12.2492 | 0.444912 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.59675 | −0.0941939 | ||||||||
\(761\) | 12.3820 | − | 8.99602i | 0.448846 | − | 0.326106i | −0.340294 | − | 0.940319i | \(-0.610527\pi\) |
0.789140 | + | 0.614213i | \(0.210527\pi\) | |||||||
\(762\) | 0.562306 | + | 1.73060i | 0.0203702 | + | 0.0626930i | ||||
\(763\) | −0.472136 | + | 1.45309i | −0.0170925 | + | 0.0526052i | ||||
\(764\) | 23.6459 | + | 17.1798i | 0.855479 | + | 0.621542i | ||||
\(765\) | −0.954915 | − | 0.693786i | −0.0345250 | − | 0.0250839i | ||||
\(766\) | −4.08359 | + | 12.5680i | −0.147546 | + | 0.454100i | ||||
\(767\) | 4.23607 | + | 13.0373i | 0.152956 | + | 0.470749i | ||||
\(768\) | 7.28115 | − | 5.29007i | 0.262736 | − | 0.190889i | ||||
\(769\) | −48.5623 | −1.75120 | −0.875601 | − | 0.483035i | \(-0.839534\pi\) | ||||
−0.875601 | + | 0.483035i | \(0.839534\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.8541 | 0.498943 | ||||||||
\(772\) | 22.9894 | − | 16.7027i | 0.827405 | − | 0.601145i | ||||
\(773\) | 12.4336 | + | 38.2668i | 0.447207 | + | 1.37636i | 0.880046 | + | 0.474889i | \(0.157512\pi\) |
−0.432839 | + | 0.901471i | \(0.642488\pi\) | |||||||
\(774\) | −0.566371 | + | 1.74311i | −0.0203578 | + | 0.0626548i | ||||
\(775\) | −13.7082 | − | 9.95959i | −0.492413 | − | 0.357759i | ||||
\(776\) | 8.33688 | + | 6.05710i | 0.299277 | + | 0.217437i | ||||
\(777\) | 3.23607 | − | 9.95959i | 0.116093 | − | 0.357298i | ||||
\(778\) | −4.03444 | − | 12.4167i | −0.144642 | − | 0.445162i | ||||
\(779\) | −15.9549 | + | 11.5919i | −0.571644 | + | 0.415324i | ||||
\(780\) | 3.70820 | 0.132775 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −6.00813 | −0.214850 | ||||||||
\(783\) | −20.4443 | + | 14.8536i | −0.730619 | + | 0.530826i | ||||
\(784\) | 0.972136 | + | 2.99193i | 0.0347191 | + | 0.106855i | ||||
\(785\) | 6.14590 | − | 18.9151i | 0.219357 | − | 0.675110i | ||||
\(786\) | −9.47214 | − | 6.88191i | −0.337860 | − | 0.245470i | ||||
\(787\) | 16.6353 | + | 12.0862i | 0.592983 | + | 0.430827i | 0.843381 | − | 0.537316i | \(-0.180562\pi\) |
−0.250398 | + | 0.968143i | \(0.580562\pi\) | |||||||
\(788\) | −2.45898 | + | 7.56796i | −0.0875975 | + | 0.269598i | ||||
\(789\) | −8.56231 | − | 26.3521i | −0.304826 | − | 0.938158i | ||||
\(790\) | 1.97214 | − | 1.43284i | 0.0701654 | − | 0.0509782i | ||||
\(791\) | −0.145898 | −0.00518754 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.41641 | 0.334386 | ||||||||
\(794\) | 0.253289 | − | 0.184025i | 0.00898889 | − | 0.00653081i | ||||
\(795\) | 1.19098 | + | 3.66547i | 0.0422398 | + | 0.130001i | ||||
\(796\) | 4.71885 | − | 14.5231i | 0.167255 | − | 0.514758i | ||||
\(797\) | −26.0795 | − | 18.9479i | −0.923784 | − | 0.671169i | 0.0206788 | − | 0.999786i | \(-0.493417\pi\) |
−0.944463 | + | 0.328618i | \(0.893417\pi\) | |||||||
\(798\) | −0.881966 | − | 0.640786i | −0.0312213 | − | 0.0226836i | ||||
\(799\) | 6.31966 | − | 19.4499i | 0.223574 | − | 0.688088i | ||||
\(800\) | −5.12461 | − | 15.7719i | −0.181182 | − | 0.557622i | ||||
\(801\) | 2.11803 | − | 1.53884i | 0.0748371 | − | 0.0543723i | ||||
\(802\) | −6.69505 | −0.236410 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −24.9787 | −0.880931 | ||||||||
\(805\) | 4.11803 | − | 2.99193i | 0.145142 | − | 0.105452i | ||||
\(806\) | −0.618034 | − | 1.90211i | −0.0217693 | − | 0.0669991i | ||||
\(807\) | −8.42705 | + | 25.9358i | −0.296646 | + | 0.912983i | ||||
\(808\) | 17.6246 | + | 12.8050i | 0.620032 | + | 0.450479i | ||||
\(809\) | 26.2984 | + | 19.1069i | 0.924602 | + | 0.671762i | 0.944665 | − | 0.328036i | \(-0.106387\pi\) |
−0.0200635 | + | 0.999799i | \(0.506387\pi\) | |||||||
\(810\) | −0.909830 | + | 2.80017i | −0.0319682 | + | 0.0983879i | ||||
\(811\) | −0.360680 | − | 1.11006i | −0.0126652 | − | 0.0389794i | 0.944524 | − | 0.328442i | \(-0.106523\pi\) |
−0.957189 | + | 0.289462i | \(0.906523\pi\) | |||||||
\(812\) | −6.92705 | + | 5.03280i | −0.243092 | + | 0.176617i | ||||
\(813\) | −7.76393 | −0.272293 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.70820 | −0.305035 | ||||||||
\(816\) | −12.7254 | + | 9.24556i | −0.445479 | + | 0.323659i | ||||
\(817\) | 6.84752 | + | 21.0745i | 0.239565 | + | 0.737304i | ||||
\(818\) | 2.09017 | − | 6.43288i | 0.0730811 | − | 0.224920i | ||||
\(819\) | −0.381966 | − | 0.277515i | −0.0133470 | − | 0.00969714i | ||||
\(820\) | 16.7705 | + | 12.1845i | 0.585652 | + | 0.425501i | ||||
\(821\) | −17.5106 | + | 53.8922i | −0.611126 | + | 1.88085i | −0.163760 | + | 0.986500i | \(0.552362\pi\) |
−0.447366 | + | 0.894351i | \(0.647638\pi\) | |||||||
\(822\) | 2.92705 | + | 9.00854i | 0.102093 | + | 0.314209i | ||||
\(823\) | 25.7984 | − | 18.7436i | 0.899275 | − | 0.653361i | −0.0390048 | − | 0.999239i | \(-0.512419\pi\) |
0.938280 | + | 0.345878i | \(0.112419\pi\) | |||||||
\(824\) | −13.0344 | −0.454076 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.23607 | −0.147392 | ||||||||
\(827\) | −15.8541 | + | 11.5187i | −0.551301 | + | 0.400544i | −0.828265 | − | 0.560337i | \(-0.810672\pi\) |
0.276964 | + | 0.960880i | \(0.410672\pi\) | |||||||
\(828\) | 1.11397 | + | 3.42844i | 0.0387131 | + | 0.119147i | ||||
\(829\) | −14.8262 | + | 45.6305i | −0.514937 | + | 1.58481i | 0.268461 | + | 0.963291i | \(0.413485\pi\) |
−0.783397 | + | 0.621521i | \(0.786515\pi\) | |||||||
\(830\) | 0.836881 | + | 0.608030i | 0.0290486 | + | 0.0211050i | ||||
\(831\) | −30.1525 | − | 21.9071i | −1.04598 | − | 0.759947i | ||||
\(832\) | −1.79837 | + | 5.53483i | −0.0623474 | + | 0.191886i | ||||
\(833\) | −0.954915 | − | 2.93893i | −0.0330858 | − | 0.101828i | ||||
\(834\) | −5.97214 | + | 4.33901i | −0.206798 | + | 0.150248i | ||||
\(835\) | −6.47214 | −0.223978 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.1803 | −0.801230 | ||||||||
\(838\) | −9.23607 | + | 6.71040i | −0.319055 | + | 0.231807i | ||||
\(839\) | 9.45492 | + | 29.0992i | 0.326420 | + | 1.00462i | 0.970796 | + | 0.239908i | \(0.0771173\pi\) |
−0.644376 | + | 0.764709i | \(0.722883\pi\) | |||||||
\(840\) | −0.736068 | + | 2.26538i | −0.0253968 | + | 0.0781632i | ||||
\(841\) | 6.20820 | + | 4.51052i | 0.214076 | + | 0.155535i | ||||
\(842\) | −0.236068 | − | 0.171513i | −0.00813544 | − | 0.00591074i | ||||
\(843\) | −12.5902 | + | 38.7486i | −0.433628 | + | 1.33457i | ||||
\(844\) | 8.94834 | + | 27.5402i | 0.308014 | + | 0.947971i | ||||
\(845\) | 9.28115 | − | 6.74315i | 0.319281 | − | 0.231971i | ||||
\(846\) | 0.965558 | 0.0331966 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.49342 | −0.257325 | ||||||||
\(849\) | −15.6353 | + | 11.3597i | −0.536601 | + | 0.389863i | ||||
\(850\) | 1.45898 | + | 4.49028i | 0.0500426 | + | 0.154015i | ||||
\(851\) | 10.1803 | − | 31.3319i | 0.348978 | − | 1.07404i | ||||
\(852\) | 39.0517 | + | 28.3727i | 1.33789 | + | 0.972032i | ||||
\(853\) | −28.2426 | − | 20.5195i | −0.967010 | − | 0.702574i | −0.0122416 | − | 0.999925i | \(-0.503897\pi\) |
−0.954768 | + | 0.297351i | \(0.903897\pi\) | |||||||
\(854\) | −0.899187 | + | 2.76741i | −0.0307695 | + | 0.0946989i | ||||
\(855\) | −0.208204 | − | 0.640786i | −0.00712042 | − | 0.0219144i | ||||
\(856\) | −3.22542 | + | 2.34341i | −0.110243 | + | 0.0800960i | ||||
\(857\) | 15.0902 | 0.515470 | 0.257735 | − | 0.966216i | \(-0.417024\pi\) | ||||
0.257735 | + | 0.966216i | \(0.417024\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.5623 | 0.735696 | 0.367848 | − | 0.929886i | \(-0.380095\pi\) | ||||
0.367848 | + | 0.929886i | \(0.380095\pi\) | |||||||
\(860\) | 18.8435 | − | 13.6906i | 0.642557 | − | 0.466845i | ||||
\(861\) | 5.59017 | + | 17.2048i | 0.190512 | + | 0.586337i | ||||
\(862\) | 1.63525 | − | 5.03280i | 0.0556970 | − | 0.171418i | ||||
\(863\) | 38.7877 | + | 28.1809i | 1.32035 | + | 0.959290i | 0.999928 | + | 0.0120153i | \(0.00382467\pi\) |
0.320422 | + | 0.947275i | \(0.396175\pi\) | |||||||
\(864\) | −18.3541 | − | 13.3350i | −0.624419 | − | 0.453667i | ||||
\(865\) | 4.75329 | − | 14.6291i | 0.161617 | − | 0.497405i | ||||
\(866\) | −1.05824 | − | 3.25693i | −0.0359605 | − | 0.110675i | ||||
\(867\) | −9.75329 | + | 7.08618i | −0.331239 | + | 0.240659i | ||||
\(868\) | −7.85410 | −0.266586 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2.85410 | −0.0967631 | ||||||||
\(871\) | 8.32624 | − | 6.04937i | 0.282124 | − | 0.204975i | ||||
\(872\) | −0.695048 | − | 2.13914i | −0.0235373 | − | 0.0724404i | ||||
\(873\) | −0.826238 | + | 2.54290i | −0.0279639 | + | 0.0860641i | ||||
\(874\) | −2.77458 | − | 2.01585i | −0.0938514 | − | 0.0681870i | ||||
\(875\) | −7.28115 | − | 5.29007i | −0.246148 | − | 0.178837i | ||||
\(876\) | 13.1976 | − | 40.6179i | 0.445904 | − | 1.37235i | ||||
\(877\) | −4.01722 | − | 12.3637i | −0.135652 | − | 0.417494i | 0.860039 | − | 0.510228i | \(-0.170439\pi\) |
−0.995691 | + | 0.0927348i | \(0.970439\pi\) | |||||||
\(878\) | 1.04508 | − | 0.759299i | 0.0352699 | − | 0.0256251i | ||||
\(879\) | −17.7984 | −0.600324 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.1459 | 0.476587 | 0.238294 | − | 0.971193i | \(-0.423412\pi\) | ||||
0.238294 | + | 0.971193i | \(0.423412\pi\) | |||||||
\(882\) | 0.118034 | − | 0.0857567i | 0.00397441 | − | 0.00288758i | ||||
\(883\) | 9.77458 | + | 30.0830i | 0.328941 | + | 1.01238i | 0.969630 | + | 0.244575i | \(0.0786485\pi\) |
−0.640690 | + | 0.767800i | \(0.721351\pi\) | |||||||
\(884\) | 2.18847 | − | 6.73542i | 0.0736062 | − | 0.226537i | ||||
\(885\) | 14.5172 | + | 10.5474i | 0.487991 | + | 0.354546i | ||||
\(886\) | −0.954915 | − | 0.693786i | −0.0320810 | − | 0.0233082i | ||||
\(887\) | −17.6803 | + | 54.4145i | −0.593648 | + | 1.82706i | −0.0323024 | + | 0.999478i | \(0.510284\pi\) |
−0.561345 | + | 0.827582i | \(0.689716\pi\) | |||||||
\(888\) | 4.76393 | + | 14.6619i | 0.159867 | + | 0.492020i | ||||
\(889\) | −2.38197 | + | 1.73060i | −0.0798886 | + | 0.0580424i | ||||
\(890\) | 2.61803 | 0.0877567 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.77206 | −0.126298 | ||||||||
\(893\) | 9.44427 | − | 6.86167i | 0.316041 | − | 0.229617i | ||||
\(894\) | −1.69098 | − | 5.20431i | −0.0565549 | − | 0.174058i | ||||
\(895\) | −1.16312 | + | 3.57971i | −0.0388788 | + | 0.119657i | ||||
\(896\) | −8.16312 | − | 5.93085i | −0.272711 | − | 0.198136i | ||||
\(897\) | 8.23607 | + | 5.98385i | 0.274994 | + | 0.199795i | ||||
\(898\) | 1.45492 | − | 4.47777i | 0.0485511 | − | 0.149425i | ||||
\(899\) | −6.04508 | − | 18.6049i | −0.201615 | − | 0.620507i | ||||
\(900\) | 2.29180 | − | 1.66509i | 0.0763932 | − | 0.0555029i | ||||
\(901\) | 7.36068 | 0.245220 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.3262 | 0.676415 | ||||||||
\(904\) | 0.173762 | − | 0.126246i | 0.00577924 | − | 0.00419886i | ||||
\(905\) | −2.29180 | − | 7.05342i | −0.0761819 | − | 0.234464i | ||||
\(906\) | 0.0106431 | − | 0.0327561i | 0.000353594 | − | 0.00108825i | ||||
\(907\) | 12.7533 | + | 9.26581i | 0.423466 | + | 0.307666i | 0.779031 | − | 0.626986i | \(-0.215711\pi\) |
−0.355565 | + | 0.934652i | \(0.615711\pi\) | |||||||
\(908\) | 24.0517 | + | 17.4746i | 0.798182 | + | 0.579914i | ||||
\(909\) | −1.74671 | + | 5.37582i | −0.0579348 | + | 0.178305i | ||||
\(910\) | −0.145898 | − | 0.449028i | −0.00483647 | − | 0.0148851i | ||||
\(911\) | 36.5517 | − | 26.5563i | 1.21101 | − | 0.879851i | 0.215688 | − | 0.976462i | \(-0.430800\pi\) |
0.995322 | + | 0.0966115i | \(0.0308004\pi\) | |||||||
\(912\) | −8.97871 | −0.297315 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.0557281 | 0.00184332 | ||||||||
\(915\) | 9.97214 | − | 7.24518i | 0.329669 | − | 0.239518i | ||||
\(916\) | −3.87539 | − | 11.9272i | −0.128046 | − | 0.394086i | ||||
\(917\) | 5.85410 | − | 18.0171i | 0.193319 | − | 0.594976i | ||||
\(918\) | 5.22542 | + | 3.79649i | 0.172465 | + | 0.125303i | ||||
\(919\) | −12.0451 | − | 8.75127i | −0.397331 | − | 0.288678i | 0.371122 | − | 0.928584i | \(-0.378973\pi\) |
−0.768453 | + | 0.639906i | \(0.778973\pi\) | |||||||
\(920\) | −2.31559 | + | 7.12667i | −0.0763429 | + | 0.234959i | ||||
\(921\) | −11.5902 | − | 35.6709i | −0.381909 | − | 1.17540i | ||||
\(922\) | −5.71885 | + | 4.15499i | −0.188340 | + | 0.136837i | ||||
\(923\) | −19.8885 | −0.654639 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.8885 | −0.851210 | ||||||||
\(926\) | −6.87132 | + | 4.99231i | −0.225806 | + | 0.164057i | ||||
\(927\) | −1.04508 | − | 3.21644i | −0.0343251 | − | 0.105642i | ||||
\(928\) | 5.91641 | − | 18.2088i | 0.194216 | − | 0.597734i | ||||
\(929\) | −19.4164 | − | 14.1068i | −0.637032 | − | 0.462831i | 0.221797 | − | 0.975093i | \(-0.428808\pi\) |
−0.858829 | + | 0.512262i | \(0.828808\pi\) | |||||||
\(930\) | −2.11803 | − | 1.53884i | −0.0694531 | − | 0.0504606i | ||||
\(931\) | 0.545085 | − | 1.67760i | 0.0178644 | − | 0.0549811i | ||||
\(932\) | −16.8541 | − | 51.8716i | −0.552074 | − | 1.69911i | ||||
\(933\) | 11.7812 | − | 8.55951i | 0.385698 | − | 0.280226i | ||||
\(934\) | −1.72136 | −0.0563246 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.695048 | 0.0227184 | ||||||||
\(937\) | −41.8435 | + | 30.4011i | −1.36697 | + | 0.993159i | −0.368999 | + | 0.929430i | \(0.620299\pi\) |
−0.997967 | + | 0.0637293i | \(0.979701\pi\) | |||||||
\(938\) | 0.982779 | + | 3.02468i | 0.0320889 | + | 0.0987594i | ||||
\(939\) | −9.16312 | + | 28.2012i | −0.299027 | + | 0.920311i | ||||
\(940\) | −9.92705 | − | 7.21242i | −0.323785 | − | 0.235243i | ||||
\(941\) | 21.8992 | + | 15.9107i | 0.713893 | + | 0.518674i | 0.884427 | − | 0.466678i | \(-0.154549\pi\) |
−0.170534 | + | 0.985352i | \(0.554549\pi\) | |||||||
\(942\) | −3.79837 | + | 11.6902i | −0.123758 | + | 0.380887i | ||||
\(943\) | 17.5861 | + | 54.1245i | 0.572682 | + | 1.76254i | ||||
\(944\) | −28.2254 | + | 20.5070i | −0.918659 | + | 0.667445i | ||||
\(945\) | −5.47214 | −0.178009 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.29180 | 0.204456 | 0.102228 | − | 0.994761i | \(-0.467403\pi\) | ||||
0.102228 | + | 0.994761i | \(0.467403\pi\) | |||||||
\(948\) | 15.4894 | − | 11.2537i | 0.503071 | − | 0.365502i | ||||
\(949\) | 5.43769 | + | 16.7355i | 0.176515 | + | 0.543257i | ||||
\(950\) | −0.832816 | + | 2.56314i | −0.0270201 | + | 0.0831593i | ||||
\(951\) | −5.80902 | − | 4.22050i | −0.188370 | − | 0.136859i | ||||
\(952\) | 3.68034 | + | 2.67392i | 0.119281 | + | 0.0866624i | ||||
\(953\) | 1.92705 | − | 5.93085i | 0.0624233 | − | 0.192119i | −0.914981 | − | 0.403496i | \(-0.867795\pi\) |
0.977405 | + | 0.211377i | \(0.0677948\pi\) | |||||||
\(954\) | 0.107391 | + | 0.330515i | 0.00347691 | + | 0.0107008i | ||||
\(955\) | −12.7533 | + | 9.26581i | −0.412687 | + | 0.299834i | ||||
\(956\) | −31.6869 | −1.02483 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.31308 | −0.268583 | ||||||||
\(959\) | −12.3992 | + | 9.00854i | −0.400391 | + | 0.290901i | ||||
\(960\) | 2.35410 | + | 7.24518i | 0.0759783 | + | 0.233837i | ||||
\(961\) | −4.03444 | + | 12.4167i | −0.130143 | + | 0.400540i | ||||
\(962\) | −2.47214 | − | 1.79611i | −0.0797049 | − | 0.0579090i | ||||
\(963\) | −0.836881 | − | 0.608030i | −0.0269681 | − | 0.0195935i | ||||
\(964\) | 9.32217 | − | 28.6907i | 0.300247 | − | 0.924065i | ||||
\(965\) | 4.73607 | + | 14.5761i | 0.152459 | + | 0.469222i | ||||
\(966\) | −2.54508 | + | 1.84911i | −0.0818868 | + | 0.0594942i | ||||
\(967\) | −27.4508 | −0.882760 | −0.441380 | − | 0.897320i | \(-0.645511\pi\) | ||||
−0.441380 | + | 0.897320i | \(0.645511\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.81966 | 0.283328 | ||||||||
\(970\) | −2.16312 | + | 1.57160i | −0.0694536 | + | 0.0504610i | ||||
\(971\) | −8.72949 | − | 26.8666i | −0.280143 | − | 0.862190i | −0.987813 | − | 0.155647i | \(-0.950254\pi\) |
0.707670 | − | 0.706543i | \(-0.249746\pi\) | |||||||
\(972\) | 2.25987 | − | 6.95515i | 0.0724853 | − | 0.223087i | ||||
\(973\) | −9.66312 | − | 7.02067i | −0.309785 | − | 0.225072i | ||||
\(974\) | 10.0729 | + | 7.31843i | 0.322758 | + | 0.234497i | ||||
\(975\) | 2.47214 | − | 7.60845i | 0.0791717 | − | 0.243665i | ||||
\(976\) | 7.40576 | + | 22.7926i | 0.237053 | + | 0.729573i | ||||
\(977\) | 8.75329 | − | 6.35964i | 0.280043 | − | 0.203463i | −0.438893 | − | 0.898539i | \(-0.644629\pi\) |
0.718936 | + | 0.695076i | \(0.244629\pi\) | |||||||
\(978\) | 5.38197 | 0.172096 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.85410 | −0.0592271 | ||||||||
\(981\) | 0.472136 | − | 0.343027i | 0.0150741 | − | 0.0109520i | ||||
\(982\) | −2.61397 | − | 8.04497i | −0.0834151 | − | 0.256725i | ||||
\(983\) | −3.82624 | + | 11.7759i | −0.122038 | + | 0.375594i | −0.993350 | − | 0.115135i | \(-0.963270\pi\) |
0.871312 | + | 0.490730i | \(0.163270\pi\) | |||||||
\(984\) | −21.5451 | − | 15.6534i | −0.686832 | − | 0.499013i | ||||
\(985\) | −3.47214 | − | 2.52265i | −0.110631 | − | 0.0803785i | ||||
\(986\) | −1.68441 | + | 5.18407i | −0.0536424 | + | 0.165094i | ||||
\(987\) | −3.30902 | − | 10.1841i | −0.105327 | − | 0.324164i | ||||
\(988\) | 3.27051 | − | 2.37616i | 0.104049 | − | 0.0755959i | ||||
\(989\) | 63.9443 | 2.03331 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.729490 | −0.0231730 | −0.0115865 | − | 0.999933i | \(-0.503688\pi\) | ||||
−0.0115865 | + | 0.999933i | \(0.503688\pi\) | |||||||
\(992\) | 14.2082 | − | 10.3229i | 0.451111 | − | 0.327751i | ||||
\(993\) | −3.09017 | − | 9.51057i | −0.0980636 | − | 0.301809i | ||||
\(994\) | 1.89919 | − | 5.84510i | 0.0602386 | − | 0.185395i | ||||
\(995\) | 6.66312 | + | 4.84104i | 0.211235 | + | 0.153471i | ||||
\(996\) | 6.57295 | + | 4.77553i | 0.208272 | + | 0.151318i | ||||
\(997\) | 17.2639 | − | 53.1329i | 0.546754 | − | 1.68274i | −0.170028 | − | 0.985439i | \(-0.554386\pi\) |
0.716782 | − | 0.697297i | \(-0.245614\pi\) | |||||||
\(998\) | −1.19098 | − | 3.66547i | −0.0376999 | − | 0.116028i | ||||
\(999\) | −28.6525 | + | 20.8172i | −0.906524 | + | 0.658628i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 847.2.f.j.729.1 | 4 | ||
11.2 | odd | 10 | 847.2.a.d.1.2 | ✓ | 2 | ||
11.3 | even | 5 | 847.2.f.c.148.1 | 4 | |||
11.4 | even | 5 | inner | 847.2.f.j.323.1 | 4 | ||
11.5 | even | 5 | 847.2.f.c.372.1 | 4 | |||
11.6 | odd | 10 | 847.2.f.l.372.1 | 4 | |||
11.7 | odd | 10 | 847.2.f.d.323.1 | 4 | |||
11.8 | odd | 10 | 847.2.f.l.148.1 | 4 | |||
11.9 | even | 5 | 847.2.a.h.1.1 | yes | 2 | ||
11.10 | odd | 2 | 847.2.f.d.729.1 | 4 | |||
33.2 | even | 10 | 7623.2.a.bx.1.1 | 2 | |||
33.20 | odd | 10 | 7623.2.a.t.1.2 | 2 | |||
77.13 | even | 10 | 5929.2.a.i.1.2 | 2 | |||
77.20 | odd | 10 | 5929.2.a.s.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.d.1.2 | ✓ | 2 | 11.2 | odd | 10 | ||
847.2.a.h.1.1 | yes | 2 | 11.9 | even | 5 | ||
847.2.f.c.148.1 | 4 | 11.3 | even | 5 | |||
847.2.f.c.372.1 | 4 | 11.5 | even | 5 | |||
847.2.f.d.323.1 | 4 | 11.7 | odd | 10 | |||
847.2.f.d.729.1 | 4 | 11.10 | odd | 2 | |||
847.2.f.j.323.1 | 4 | 11.4 | even | 5 | inner | ||
847.2.f.j.729.1 | 4 | 1.1 | even | 1 | trivial | ||
847.2.f.l.148.1 | 4 | 11.8 | odd | 10 | |||
847.2.f.l.372.1 | 4 | 11.6 | odd | 10 | |||
5929.2.a.i.1.2 | 2 | 77.13 | even | 10 | |||
5929.2.a.s.1.1 | 2 | 77.20 | odd | 10 | |||
7623.2.a.t.1.2 | 2 | 33.20 | odd | 10 | |||
7623.2.a.bx.1.1 | 2 | 33.2 | even | 10 |