Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(47,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.i (of order \(4\), 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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.11 | ||
Character | \(\chi\) | \(=\) | 690.47 |
Dual form | 690.2.i.f.323.11 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | −0.838057 | + | 1.51580i | −0.483853 | + | 0.875150i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 2.23509 | + | 0.0661068i | 0.999563 | + | 0.0295639i | ||||
\(6\) | 0.479239 | + | 1.66443i | 0.195649 | + | 0.679501i | ||||
\(7\) | 2.39575 | + | 2.39575i | 0.905508 | + | 0.905508i | 0.995906 | − | 0.0903979i | \(-0.0288139\pi\) |
−0.0903979 | + | 0.995906i | \(0.528814\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −1.59532 | − | 2.54066i | −0.531773 | − | 0.846887i | ||||
\(10\) | 1.62719 | − | 1.53370i | 0.514563 | − | 0.485000i | ||||
\(11\) | − | 3.77229i | − | 1.13739i | −0.822549 | − | 0.568694i | \(-0.807449\pi\) | ||
0.822549 | − | 0.568694i | \(-0.192551\pi\) | |||||||
\(12\) | 1.51580 | + | 0.838057i | 0.437575 | + | 0.241926i | ||||
\(13\) | 3.87255 | − | 3.87255i | 1.07405 | − | 1.07405i | 0.0770227 | − | 0.997029i | \(-0.475459\pi\) |
0.997029 | − | 0.0770227i | \(-0.0245414\pi\) | |||||||
\(14\) | 3.38810 | 0.905508 | ||||||||
\(15\) | −1.97334 | + | 3.33256i | −0.509514 | + | 0.860462i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −2.58226 | + | 2.58226i | −0.626291 | + | 0.626291i | −0.947133 | − | 0.320842i | \(-0.896034\pi\) |
0.320842 | + | 0.947133i | \(0.396034\pi\) | |||||||
\(18\) | −2.92458 | − | 0.668456i | −0.689330 | − | 0.157557i | ||||
\(19\) | 6.80541i | 1.56127i | 0.624988 | + | 0.780634i | \(0.285104\pi\) | ||||
−0.624988 | + | 0.780634i | \(0.714896\pi\) | |||||||
\(20\) | 0.0661068 | − | 2.23509i | 0.0147819 | − | 0.499781i | ||||
\(21\) | −5.63926 | + | 1.62371i | −1.23059 | + | 0.354323i | ||||
\(22\) | −2.66741 | − | 2.66741i | −0.568694 | − | 0.568694i | ||||
\(23\) | 0.707107 | + | 0.707107i | 0.147442 | + | 0.147442i | ||||
\(24\) | 1.66443 | − | 0.479239i | 0.339751 | − | 0.0978243i | ||||
\(25\) | 4.99126 | + | 0.295509i | 0.998252 | + | 0.0591019i | ||||
\(26\) | − | 5.47661i | − | 1.07405i | ||||||
\(27\) | 5.18811 | − | 0.288974i | 0.998452 | − | 0.0556131i | ||||
\(28\) | 2.39575 | − | 2.39575i | 0.452754 | − | 0.452754i | ||||
\(29\) | 6.48520 | 1.20427 | 0.602136 | − | 0.798394i | \(-0.294317\pi\) | ||||
0.602136 | + | 0.798394i | \(0.294317\pi\) | |||||||
\(30\) | 0.961112 | + | 3.75183i | 0.175474 | + | 0.684988i | ||||
\(31\) | −7.09492 | −1.27428 | −0.637142 | − | 0.770746i | \(-0.719884\pi\) | ||||
−0.637142 | + | 0.770746i | \(0.719884\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 5.71805 | + | 3.16139i | 0.995384 | + | 0.550328i | ||||
\(34\) | 3.65187i | 0.626291i | ||||||||
\(35\) | 5.19634 | + | 5.51309i | 0.878342 | + | 0.931882i | ||||
\(36\) | −2.54066 | + | 1.59532i | −0.423443 | + | 0.265887i | ||||
\(37\) | 4.68887 | + | 4.68887i | 0.770846 | + | 0.770846i | 0.978254 | − | 0.207409i | \(-0.0665030\pi\) |
−0.207409 | + | 0.978254i | \(0.566503\pi\) | |||||||
\(38\) | 4.81215 | + | 4.81215i | 0.780634 | + | 0.780634i | ||||
\(39\) | 2.62461 | + | 9.11544i | 0.420273 | + | 1.45964i | ||||
\(40\) | −1.53370 | − | 1.62719i | −0.242500 | − | 0.257282i | ||||
\(41\) | − | 8.03681i | − | 1.25514i | −0.778561 | − | 0.627569i | \(-0.784050\pi\) | ||
0.778561 | − | 0.627569i | \(-0.215950\pi\) | |||||||
\(42\) | −2.83942 | + | 5.13569i | −0.438132 | + | 0.792455i | ||||
\(43\) | −2.86760 | + | 2.86760i | −0.437304 | + | 0.437304i | −0.891104 | − | 0.453799i | \(-0.850068\pi\) |
0.453799 | + | 0.891104i | \(0.350068\pi\) | |||||||
\(44\) | −3.77229 | −0.568694 | ||||||||
\(45\) | −3.39773 | − | 5.78407i | −0.506504 | − | 0.862238i | ||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 3.40424 | − | 3.40424i | 0.496559 | − | 0.496559i | −0.413806 | − | 0.910365i | \(-0.635801\pi\) |
0.910365 | + | 0.413806i | \(0.135801\pi\) | |||||||
\(48\) | 0.838057 | − | 1.51580i | 0.120963 | − | 0.218787i | ||||
\(49\) | 4.47922i | 0.639889i | ||||||||
\(50\) | 3.73831 | − | 3.32040i | 0.528677 | − | 0.469575i | ||||
\(51\) | −1.75012 | − | 6.07829i | −0.245066 | − | 0.851131i | ||||
\(52\) | −3.87255 | − | 3.87255i | −0.537026 | − | 0.537026i | ||||
\(53\) | −1.15188 | − | 1.15188i | −0.158223 | − | 0.158223i | 0.623556 | − | 0.781779i | \(-0.285687\pi\) |
−0.781779 | + | 0.623556i | \(0.785687\pi\) | |||||||
\(54\) | 3.46421 | − | 3.87288i | 0.471420 | − | 0.527033i | ||||
\(55\) | 0.249374 | − | 8.43140i | 0.0336256 | − | 1.13689i | ||||
\(56\) | − | 3.38810i | − | 0.452754i | ||||||
\(57\) | −10.3157 | − | 5.70332i | −1.36634 | − | 0.755424i | ||||
\(58\) | 4.58573 | − | 4.58573i | 0.602136 | − | 0.602136i | ||||
\(59\) | 0.993207 | 0.129304 | 0.0646522 | − | 0.997908i | \(-0.479406\pi\) | ||||
0.0646522 | + | 0.997908i | \(0.479406\pi\) | |||||||
\(60\) | 3.33256 | + | 1.97334i | 0.430231 | + | 0.254757i | ||||
\(61\) | −11.6640 | −1.49343 | −0.746713 | − | 0.665146i | \(-0.768369\pi\) | ||||
−0.746713 | + | 0.665146i | \(0.768369\pi\) | |||||||
\(62\) | −5.01686 | + | 5.01686i | −0.637142 | + | 0.637142i | ||||
\(63\) | 2.26480 | − | 9.90877i | 0.285337 | − | 1.24839i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 8.91150 | − | 8.39950i | 1.10534 | − | 1.04183i | ||||
\(66\) | 6.27871 | − | 1.80783i | 0.772856 | − | 0.222528i | ||||
\(67\) | 1.09345 | + | 1.09345i | 0.133587 | + | 0.133587i | 0.770738 | − | 0.637152i | \(-0.219888\pi\) |
−0.637152 | + | 0.770738i | \(0.719888\pi\) | |||||||
\(68\) | 2.58226 | + | 2.58226i | 0.313145 | + | 0.313145i | ||||
\(69\) | −1.66443 | + | 0.479239i | −0.200374 | + | 0.0576936i | ||||
\(70\) | 7.57271 | + | 0.223976i | 0.905112 | + | 0.0267703i | ||||
\(71\) | 9.26157i | 1.09915i | 0.835446 | + | 0.549573i | \(0.185210\pi\) | ||||
−0.835446 | + | 0.549573i | \(0.814790\pi\) | |||||||
\(72\) | −0.668456 | + | 2.92458i | −0.0787783 | + | 0.344665i | ||||
\(73\) | 2.14788 | − | 2.14788i | 0.251390 | − | 0.251390i | −0.570150 | − | 0.821540i | \(-0.693115\pi\) |
0.821540 | + | 0.570150i | \(0.193115\pi\) | |||||||
\(74\) | 6.63106 | 0.770846 | ||||||||
\(75\) | −4.63090 | + | 7.31812i | −0.534730 | + | 0.845023i | ||||
\(76\) | 6.80541 | 0.780634 | ||||||||
\(77\) | 9.03745 | − | 9.03745i | 1.02991 | − | 1.02991i | ||||
\(78\) | 8.30147 | + | 4.58971i | 0.939956 | + | 0.519683i | ||||
\(79\) | 4.59709i | 0.517213i | 0.965983 | + | 0.258607i | \(0.0832633\pi\) | ||||
−0.965983 | + | 0.258607i | \(0.916737\pi\) | |||||||
\(80\) | −2.23509 | − | 0.0661068i | −0.249891 | − | 0.00739096i | ||||
\(81\) | −3.90991 | + | 8.10633i | −0.434434 | + | 0.900704i | ||||
\(82\) | −5.68288 | − | 5.68288i | −0.627569 | − | 0.627569i | ||||
\(83\) | −5.20343 | − | 5.20343i | −0.571151 | − | 0.571151i | 0.361299 | − | 0.932450i | \(-0.382333\pi\) |
−0.932450 | + | 0.361299i | \(0.882333\pi\) | |||||||
\(84\) | 1.62371 | + | 5.63926i | 0.177161 | + | 0.615293i | ||||
\(85\) | −5.94230 | + | 5.60089i | −0.644533 | + | 0.607502i | ||||
\(86\) | 4.05539i | 0.437304i | ||||||||
\(87\) | −5.43497 | + | 9.83029i | −0.582690 | + | 1.05392i | ||||
\(88\) | −2.66741 | + | 2.66741i | −0.284347 | + | 0.284347i | ||||
\(89\) | −9.56617 | −1.01401 | −0.507006 | − | 0.861943i | \(-0.669248\pi\) | ||||
−0.507006 | + | 0.861943i | \(0.669248\pi\) | |||||||
\(90\) | −6.49251 | − | 1.68739i | −0.684371 | − | 0.177867i | ||||
\(91\) | 18.5553 | 1.94512 | ||||||||
\(92\) | 0.707107 | − | 0.707107i | 0.0737210 | − | 0.0737210i | ||||
\(93\) | 5.94594 | − | 10.7545i | 0.616566 | − | 1.11519i | ||||
\(94\) | − | 4.81432i | − | 0.496559i | ||||||
\(95\) | −0.449884 | + | 15.2107i | −0.0461571 | + | 1.56059i | ||||
\(96\) | −0.479239 | − | 1.66443i | −0.0489121 | − | 0.169875i | ||||
\(97\) | −10.5684 | − | 10.5684i | −1.07306 | − | 1.07306i | −0.997111 | − | 0.0759519i | \(-0.975800\pi\) |
−0.0759519 | − | 0.997111i | \(-0.524200\pi\) | |||||||
\(98\) | 3.16729 | + | 3.16729i | 0.319944 | + | 0.319944i | ||||
\(99\) | −9.58410 | + | 6.01801i | −0.963238 | + | 0.604833i | ||||
\(100\) | 0.295509 | − | 4.99126i | 0.0295509 | − | 0.499126i | ||||
\(101\) | 3.09956i | 0.308418i | 0.988038 | + | 0.154209i | \(0.0492829\pi\) | ||||
−0.988038 | + | 0.154209i | \(0.950717\pi\) | |||||||
\(102\) | −5.53552 | − | 3.06048i | −0.548098 | − | 0.303032i | ||||
\(103\) | −4.89445 | + | 4.89445i | −0.482264 | + | 0.482264i | −0.905854 | − | 0.423590i | \(-0.860770\pi\) |
0.423590 | + | 0.905854i | \(0.360770\pi\) | |||||||
\(104\) | −5.47661 | −0.537026 | ||||||||
\(105\) | −12.7116 | + | 3.25635i | −1.24052 | + | 0.317787i | ||||
\(106\) | −1.62900 | −0.158223 | ||||||||
\(107\) | 7.11744 | − | 7.11744i | 0.688069 | − | 0.688069i | −0.273736 | − | 0.961805i | \(-0.588259\pi\) |
0.961805 | + | 0.273736i | \(0.0882594\pi\) | |||||||
\(108\) | −0.288974 | − | 5.18811i | −0.0278065 | − | 0.499226i | ||||
\(109\) | 18.1228i | 1.73584i | 0.496700 | + | 0.867922i | \(0.334545\pi\) | ||||
−0.496700 | + | 0.867922i | \(0.665455\pi\) | |||||||
\(110\) | −5.78557 | − | 6.13824i | −0.551632 | − | 0.585258i | ||||
\(111\) | −11.0369 | + | 3.17786i | −1.04758 | + | 0.301630i | ||||
\(112\) | −2.39575 | − | 2.39575i | −0.226377 | − | 0.226377i | ||||
\(113\) | −14.5951 | − | 14.5951i | −1.37299 | − | 1.37299i | −0.855978 | − | 0.517012i | \(-0.827044\pi\) |
−0.517012 | − | 0.855978i | \(-0.672956\pi\) | |||||||
\(114\) | −11.3271 | + | 3.26142i | −1.06088 | + | 0.305460i | ||||
\(115\) | 1.53370 | + | 1.62719i | 0.143019 | + | 0.151736i | ||||
\(116\) | − | 6.48520i | − | 0.602136i | ||||||
\(117\) | −16.0168 | − | 3.66087i | −1.48075 | − | 0.338448i | ||||
\(118\) | 0.702303 | − | 0.702303i | 0.0646522 | − | 0.0646522i | ||||
\(119\) | −12.3729 | −1.13422 | ||||||||
\(120\) | 3.75183 | − | 0.961112i | 0.342494 | − | 0.0877372i | ||||
\(121\) | −3.23015 | −0.293650 | ||||||||
\(122\) | −8.24772 | + | 8.24772i | −0.746713 | + | 0.746713i | ||||
\(123\) | 12.1822 | + | 6.73531i | 1.09843 | + | 0.607302i | ||||
\(124\) | 7.09492i | 0.637142i | ||||||||
\(125\) | 11.1364 | + | 0.990446i | 0.996068 | + | 0.0885882i | ||||
\(126\) | −5.40511 | − | 8.60801i | −0.481525 | − | 0.766862i | ||||
\(127\) | 4.72572 | + | 4.72572i | 0.419339 | + | 0.419339i | 0.884976 | − | 0.465637i | \(-0.154175\pi\) |
−0.465637 | + | 0.884976i | \(0.654175\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −1.94350 | − | 6.74992i | −0.171116 | − | 0.594298i | ||||
\(130\) | 0.362041 | − | 12.2407i | 0.0317531 | − | 1.07358i | ||||
\(131\) | − | 9.59773i | − | 0.838558i | −0.907858 | − | 0.419279i | \(-0.862283\pi\) | ||
0.907858 | − | 0.419279i | \(-0.137717\pi\) | |||||||
\(132\) | 3.16139 | − | 5.71805i | 0.275164 | − | 0.497692i | ||||
\(133\) | −16.3041 | + | 16.3041i | −1.41374 | + | 1.41374i | ||||
\(134\) | 1.54638 | 0.133587 | ||||||||
\(135\) | 11.6150 | − | 0.302914i | 0.999660 | − | 0.0260707i | ||||
\(136\) | 3.65187 | 0.313145 | ||||||||
\(137\) | 5.29519 | − | 5.29519i | 0.452399 | − | 0.452399i | −0.443751 | − | 0.896150i | \(-0.646353\pi\) |
0.896150 | + | 0.443751i | \(0.146353\pi\) | |||||||
\(138\) | −0.838057 | + | 1.51580i | −0.0713402 | + | 0.129034i | ||||
\(139\) | − | 12.6513i | − | 1.07307i | −0.843879 | − | 0.536533i | \(-0.819734\pi\) | ||
0.843879 | − | 0.536533i | \(-0.180266\pi\) | |||||||
\(140\) | 5.51309 | − | 5.19634i | 0.465941 | − | 0.439171i | ||||
\(141\) | 2.30721 | + | 8.01310i | 0.194302 | + | 0.674825i | ||||
\(142\) | 6.54892 | + | 6.54892i | 0.549573 | + | 0.549573i | ||||
\(143\) | −14.6084 | − | 14.6084i | −1.22161 | − | 1.22161i | ||||
\(144\) | 1.59532 | + | 2.54066i | 0.132943 | + | 0.211722i | ||||
\(145\) | 14.4950 | + | 0.428716i | 1.20375 | + | 0.0356029i | ||||
\(146\) | − | 3.03756i | − | 0.251390i | ||||||
\(147\) | −6.78962 | − | 3.75384i | −0.559998 | − | 0.309612i | ||||
\(148\) | 4.68887 | − | 4.68887i | 0.385423 | − | 0.385423i | ||||
\(149\) | −13.7580 | −1.12710 | −0.563551 | − | 0.826081i | \(-0.690565\pi\) | ||||
−0.563551 | + | 0.826081i | \(0.690565\pi\) | |||||||
\(150\) | 1.90015 | + | 8.44923i | 0.155147 | + | 0.689876i | ||||
\(151\) | −1.62442 | −0.132194 | −0.0660969 | − | 0.997813i | \(-0.521055\pi\) | ||||
−0.0660969 | + | 0.997813i | \(0.521055\pi\) | |||||||
\(152\) | 4.81215 | − | 4.81215i | 0.390317 | − | 0.390317i | ||||
\(153\) | 10.6802 | + | 2.44112i | 0.863442 | + | 0.197353i | ||||
\(154\) | − | 12.7809i | − | 1.02991i | ||||||
\(155\) | −15.8578 | − | 0.469022i | −1.27373 | − | 0.0376728i | ||||
\(156\) | 9.11544 | − | 2.62461i | 0.729819 | − | 0.210137i | ||||
\(157\) | −12.9821 | − | 12.9821i | −1.03608 | − | 1.03608i | −0.999324 | − | 0.0367599i | \(-0.988296\pi\) |
−0.0367599 | − | 0.999324i | \(-0.511704\pi\) | |||||||
\(158\) | 3.25064 | + | 3.25064i | 0.258607 | + | 0.258607i | ||||
\(159\) | 2.71137 | − | 0.780682i | 0.215025 | − | 0.0619121i | ||||
\(160\) | −1.62719 | + | 1.53370i | −0.128641 | + | 0.121250i | ||||
\(161\) | 3.38810i | 0.267020i | ||||||||
\(162\) | 2.96732 | + | 8.49676i | 0.233135 | + | 0.667569i | ||||
\(163\) | −5.71990 | + | 5.71990i | −0.448017 | + | 0.448017i | −0.894695 | − | 0.446678i | \(-0.852607\pi\) |
0.446678 | + | 0.894695i | \(0.352607\pi\) | |||||||
\(164\) | −8.03681 | −0.627569 | ||||||||
\(165\) | 12.5714 | + | 7.44400i | 0.978679 | + | 0.579515i | ||||
\(166\) | −7.35876 | −0.571151 | ||||||||
\(167\) | −9.01194 | + | 9.01194i | −0.697365 | + | 0.697365i | −0.963841 | − | 0.266476i | \(-0.914141\pi\) |
0.266476 | + | 0.963841i | \(0.414141\pi\) | |||||||
\(168\) | 5.13569 | + | 2.83942i | 0.396227 | + | 0.219066i | ||||
\(169\) | − | 16.9933i | − | 1.30718i | ||||||
\(170\) | −0.241414 | + | 8.16227i | −0.0185156 | + | 0.626017i | ||||
\(171\) | 17.2902 | − | 10.8568i | 1.32222 | − | 0.830241i | ||||
\(172\) | 2.86760 | + | 2.86760i | 0.218652 | + | 0.218652i | ||||
\(173\) | −14.7185 | − | 14.7185i | −1.11903 | − | 1.11903i | −0.991884 | − | 0.127145i | \(-0.959419\pi\) |
−0.127145 | − | 0.991884i | \(-0.540581\pi\) | |||||||
\(174\) | 3.10796 | + | 10.7942i | 0.235614 | + | 0.818304i | ||||
\(175\) | 11.2498 | + | 12.6658i | 0.850408 | + | 0.957442i | ||||
\(176\) | 3.77229i | 0.284347i | ||||||||
\(177\) | −0.832364 | + | 1.50551i | −0.0625643 | + | 0.113161i | ||||
\(178\) | −6.76430 | + | 6.76430i | −0.507006 | + | 0.507006i | ||||
\(179\) | −6.08838 | −0.455067 | −0.227533 | − | 0.973770i | \(-0.573066\pi\) | ||||
−0.227533 | + | 0.973770i | \(0.573066\pi\) | |||||||
\(180\) | −5.78407 | + | 3.39773i | −0.431119 | + | 0.253252i | ||||
\(181\) | −11.1245 | −0.826878 | −0.413439 | − | 0.910532i | \(-0.635673\pi\) | ||||
−0.413439 | + | 0.910532i | \(0.635673\pi\) | |||||||
\(182\) | 13.1206 | − | 13.1206i | 0.972562 | − | 0.972562i | ||||
\(183\) | 9.77513 | − | 17.6804i | 0.722598 | − | 1.30697i | ||||
\(184\) | − | 1.00000i | − | 0.0737210i | ||||||
\(185\) | 10.1701 | + | 10.7900i | 0.747719 | + | 0.793298i | ||||
\(186\) | −3.40016 | − | 11.8090i | −0.249312 | − | 0.865878i | ||||
\(187\) | 9.74104 | + | 9.74104i | 0.712335 | + | 0.712335i | ||||
\(188\) | −3.40424 | − | 3.40424i | −0.248280 | − | 0.248280i | ||||
\(189\) | 13.1217 | + | 11.7371i | 0.954465 | + | 0.853748i | ||||
\(190\) | 10.4375 | + | 11.0737i | 0.757214 | + | 0.803371i | ||||
\(191\) | − | 5.61428i | − | 0.406235i | −0.979154 | − | 0.203118i | \(-0.934893\pi\) | ||
0.979154 | − | 0.203118i | \(-0.0651074\pi\) | |||||||
\(192\) | −1.51580 | − | 0.838057i | −0.109394 | − | 0.0604816i | ||||
\(193\) | 9.77402 | − | 9.77402i | 0.703549 | − | 0.703549i | −0.261621 | − | 0.965171i | \(-0.584257\pi\) |
0.965171 | + | 0.261621i | \(0.0842572\pi\) | |||||||
\(194\) | −14.9460 | −1.07306 | ||||||||
\(195\) | 5.26364 | + | 20.5473i | 0.376937 | + | 1.47143i | ||||
\(196\) | 4.47922 | 0.319944 | ||||||||
\(197\) | −1.13050 | + | 1.13050i | −0.0805446 | + | 0.0805446i | −0.746231 | − | 0.665687i | \(-0.768139\pi\) |
0.665687 | + | 0.746231i | \(0.268139\pi\) | |||||||
\(198\) | −2.52161 | + | 11.0324i | −0.179203 | + | 0.784035i | ||||
\(199\) | 4.63646i | 0.328670i | 0.986405 | + | 0.164335i | \(0.0525478\pi\) | ||||
−0.986405 | + | 0.164335i | \(0.947452\pi\) | |||||||
\(200\) | −3.32040 | − | 3.73831i | −0.234788 | − | 0.264338i | ||||
\(201\) | −2.57384 | + | 0.741085i | −0.181545 | + | 0.0522721i | ||||
\(202\) | 2.19172 | + | 2.19172i | 0.154209 | + | 0.154209i | ||||
\(203\) | 15.5369 | + | 15.5369i | 1.09048 | + | 1.09048i | ||||
\(204\) | −6.07829 | + | 1.75012i | −0.425565 | + | 0.122533i | ||||
\(205\) | 0.531288 | − | 17.9630i | 0.0371068 | − | 1.25459i | ||||
\(206\) | 6.92180i | 0.482264i | ||||||||
\(207\) | 0.668456 | − | 2.92458i | 0.0464609 | − | 0.203272i | ||||
\(208\) | −3.87255 | + | 3.87255i | −0.268513 | + | 0.268513i | ||||
\(209\) | 25.6720 | 1.77577 | ||||||||
\(210\) | −6.68587 | + | 11.2910i | −0.461369 | + | 0.779155i | ||||
\(211\) | −8.96557 | −0.617215 | −0.308608 | − | 0.951189i | \(-0.599863\pi\) | ||||
−0.308608 | + | 0.951189i | \(0.599863\pi\) | |||||||
\(212\) | −1.15188 | + | 1.15188i | −0.0791114 | + | 0.0791114i | ||||
\(213\) | −14.0387 | − | 7.76173i | −0.961918 | − | 0.531825i | ||||
\(214\) | − | 10.0656i | − | 0.688069i | ||||||
\(215\) | −6.59891 | + | 6.21977i | −0.450042 | + | 0.424185i | ||||
\(216\) | −3.87288 | − | 3.46421i | −0.263516 | − | 0.235710i | ||||
\(217\) | −16.9976 | − | 16.9976i | −1.15387 | − | 1.15387i | ||||
\(218\) | 12.8147 | + | 12.8147i | 0.867922 | + | 0.867922i | ||||
\(219\) | 1.45572 | + | 5.05580i | 0.0983681 | + | 0.341639i | ||||
\(220\) | −8.43140 | − | 0.249374i | −0.568445 | − | 0.0168128i | ||||
\(221\) | 19.9999i | 1.34534i | ||||||||
\(222\) | −5.55721 | + | 10.0514i | −0.372976 | + | 0.674605i | ||||
\(223\) | 15.5814 | − | 15.5814i | 1.04341 | − | 1.04341i | 0.0443938 | − | 0.999014i | \(-0.485864\pi\) |
0.999014 | − | 0.0443938i | \(-0.0141356\pi\) | |||||||
\(224\) | −3.38810 | −0.226377 | ||||||||
\(225\) | −7.21187 | − | 13.1525i | −0.480791 | − | 0.876835i | ||||
\(226\) | −20.6406 | −1.37299 | ||||||||
\(227\) | −17.4824 | + | 17.4824i | −1.16035 | + | 1.16035i | −0.175945 | + | 0.984400i | \(0.556298\pi\) |
−0.984400 | + | 0.175945i | \(0.943702\pi\) | |||||||
\(228\) | −5.70332 | + | 10.3157i | −0.377712 | + | 0.683172i | ||||
\(229\) | 9.74724i | 0.644116i | 0.946720 | + | 0.322058i | \(0.104375\pi\) | ||||
−0.946720 | + | 0.322058i | \(0.895625\pi\) | |||||||
\(230\) | 2.23509 | + | 0.0661068i | 0.147378 | + | 0.00435895i | ||||
\(231\) | 6.12510 | + | 21.2729i | 0.403002 | + | 1.39965i | ||||
\(232\) | −4.58573 | − | 4.58573i | −0.301068 | − | 0.301068i | ||||
\(233\) | 6.27349 | + | 6.27349i | 0.410990 | + | 0.410990i | 0.882083 | − | 0.471093i | \(-0.156140\pi\) |
−0.471093 | + | 0.882083i | \(0.656140\pi\) | |||||||
\(234\) | −13.9142 | + | 8.73695i | −0.909600 | + | 0.571152i | ||||
\(235\) | 7.83382 | − | 7.38374i | 0.511022 | − | 0.481662i | ||||
\(236\) | − | 0.993207i | − | 0.0646522i | ||||||
\(237\) | −6.96829 | − | 3.85263i | −0.452639 | − | 0.250255i | ||||
\(238\) | −8.74897 | + | 8.74897i | −0.567111 | + | 0.567111i | ||||
\(239\) | 23.7283 | 1.53486 | 0.767428 | − | 0.641135i | \(-0.221536\pi\) | ||||
0.767428 | + | 0.641135i | \(0.221536\pi\) | |||||||
\(240\) | 1.97334 | − | 3.33256i | 0.127378 | − | 0.215116i | ||||
\(241\) | 6.12180 | 0.394340 | 0.197170 | − | 0.980369i | \(-0.436825\pi\) | ||||
0.197170 | + | 0.980369i | \(0.436825\pi\) | |||||||
\(242\) | −2.28406 | + | 2.28406i | −0.146825 | + | 0.146825i | ||||
\(243\) | −9.01088 | − | 12.7202i | −0.578048 | − | 0.816002i | ||||
\(244\) | 11.6640i | 0.746713i | ||||||||
\(245\) | −0.296107 | + | 10.0115i | −0.0189176 | + | 0.639609i | ||||
\(246\) | 13.3767 | − | 3.85155i | 0.852868 | − | 0.245566i | ||||
\(247\) | 26.3543 | + | 26.3543i | 1.67688 | + | 1.67688i | ||||
\(248\) | 5.01686 | + | 5.01686i | 0.318571 | + | 0.318571i | ||||
\(249\) | 12.2481 | − | 3.52661i | 0.776195 | − | 0.223490i | ||||
\(250\) | 8.57496 | − | 7.17426i | 0.542328 | − | 0.453740i | ||||
\(251\) | − | 14.4578i | − | 0.912566i | −0.889835 | − | 0.456283i | \(-0.849180\pi\) | ||
0.889835 | − | 0.456283i | \(-0.150820\pi\) | |||||||
\(252\) | −9.90877 | − | 2.26480i | −0.624194 | − | 0.142669i | ||||
\(253\) | 2.66741 | − | 2.66741i | 0.167699 | − | 0.167699i | ||||
\(254\) | 6.68317 | 0.419339 | ||||||||
\(255\) | −3.50986 | − | 13.7012i | −0.219796 | − | 0.858004i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.8018 | − | 18.8018i | 1.17282 | − | 1.17282i | 0.191288 | − | 0.981534i | \(-0.438733\pi\) |
0.981534 | − | 0.191288i | \(-0.0612665\pi\) | |||||||
\(258\) | −6.14718 | − | 3.39865i | −0.382707 | − | 0.211591i | ||||
\(259\) | 22.4667i | 1.39601i | ||||||||
\(260\) | −8.39950 | − | 8.91150i | −0.520915 | − | 0.552668i | ||||
\(261\) | −10.3460 | − | 16.4767i | −0.640400 | − | 1.01988i | ||||
\(262\) | −6.78662 | − | 6.78662i | −0.419279 | − | 0.419279i | ||||
\(263\) | 9.69602 | + | 9.69602i | 0.597882 | + | 0.597882i | 0.939749 | − | 0.341866i | \(-0.111059\pi\) |
−0.341866 | + | 0.939749i | \(0.611059\pi\) | |||||||
\(264\) | −1.80783 | − | 6.27871i | −0.111264 | − | 0.386428i | ||||
\(265\) | −2.49841 | − | 2.65070i | −0.153476 | − | 0.162831i | ||||
\(266\) | 23.0574i | 1.41374i | ||||||||
\(267\) | 8.01700 | − | 14.5004i | 0.490632 | − | 0.887412i | ||||
\(268\) | 1.09345 | − | 1.09345i | 0.0667934 | − | 0.0667934i | ||||
\(269\) | 4.30558 | 0.262516 | 0.131258 | − | 0.991348i | \(-0.458098\pi\) | ||||
0.131258 | + | 0.991348i | \(0.458098\pi\) | |||||||
\(270\) | 7.99885 | − | 8.42724i | 0.486795 | − | 0.512865i | ||||
\(271\) | −8.66444 | −0.526327 | −0.263164 | − | 0.964751i | \(-0.584766\pi\) | ||||
−0.263164 | + | 0.964751i | \(0.584766\pi\) | |||||||
\(272\) | 2.58226 | − | 2.58226i | 0.156573 | − | 0.156573i | ||||
\(273\) | −15.5504 | + | 28.1262i | −0.941154 | + | 1.70228i | ||||
\(274\) | − | 7.48853i | − | 0.452399i | ||||||
\(275\) | 1.11475 | − | 18.8285i | 0.0672217 | − | 1.13540i | ||||
\(276\) | 0.479239 | + | 1.66443i | 0.0288468 | + | 0.100187i | ||||
\(277\) | 20.8795 | + | 20.8795i | 1.25453 | + | 1.25453i | 0.953668 | + | 0.300862i | \(0.0972743\pi\) |
0.300862 | + | 0.953668i | \(0.402726\pi\) | |||||||
\(278\) | −8.94580 | − | 8.94580i | −0.536533 | − | 0.536533i | ||||
\(279\) | 11.3187 | + | 18.0258i | 0.677631 | + | 1.07917i | ||||
\(280\) | 0.223976 | − | 7.57271i | 0.0133852 | − | 0.452556i | ||||
\(281\) | 21.9320i | 1.30835i | 0.756341 | + | 0.654177i | \(0.226985\pi\) | ||||
−0.756341 | + | 0.654177i | \(0.773015\pi\) | |||||||
\(282\) | 7.29756 | + | 4.03467i | 0.434564 | + | 0.240261i | ||||
\(283\) | −1.56401 | + | 1.56401i | −0.0929709 | + | 0.0929709i | −0.752063 | − | 0.659092i | \(-0.770941\pi\) |
0.659092 | + | 0.752063i | \(0.270941\pi\) | |||||||
\(284\) | 9.26157 | 0.549573 | ||||||||
\(285\) | −22.6794 | − | 13.4294i | −1.34341 | − | 0.795488i | ||||
\(286\) | −20.6594 | −1.22161 | ||||||||
\(287\) | 19.2542 | − | 19.2542i | 1.13654 | − | 1.13654i | ||||
\(288\) | 2.92458 | + | 0.668456i | 0.172333 | + | 0.0393891i | ||||
\(289\) | 3.66383i | 0.215519i | ||||||||
\(290\) | 10.5527 | − | 9.94637i | 0.619674 | − | 0.584071i | ||||
\(291\) | 24.8767 | − | 7.16273i | 1.45830 | − | 0.419887i | ||||
\(292\) | −2.14788 | − | 2.14788i | −0.125695 | − | 0.125695i | ||||
\(293\) | 6.39663 | + | 6.39663i | 0.373695 | + | 0.373695i | 0.868821 | − | 0.495126i | \(-0.164878\pi\) |
−0.495126 | + | 0.868821i | \(0.664878\pi\) | |||||||
\(294\) | −7.45535 | + | 2.14662i | −0.434805 | + | 0.125193i | ||||
\(295\) | 2.21991 | + | 0.0656577i | 0.129248 | + | 0.00382274i | ||||
\(296\) | − | 6.63106i | − | 0.385423i | ||||||
\(297\) | −1.09009 | − | 19.5710i | −0.0632536 | − | 1.13563i | ||||
\(298\) | −9.72840 | + | 9.72840i | −0.563551 | + | 0.563551i | ||||
\(299\) | 5.47661 | 0.316721 | ||||||||
\(300\) | 7.31812 | + | 4.63090i | 0.422512 | + | 0.267365i | ||||
\(301\) | −13.7401 | −0.791965 | ||||||||
\(302\) | −1.14864 | + | 1.14864i | −0.0660969 | + | 0.0660969i | ||||
\(303\) | −4.69832 | − | 2.59761i | −0.269912 | − | 0.149229i | ||||
\(304\) | − | 6.80541i | − | 0.390317i | ||||||
\(305\) | −26.0702 | − | 0.771072i | −1.49277 | − | 0.0441514i | ||||
\(306\) | 9.27817 | − | 5.82591i | 0.530397 | − | 0.333045i | ||||
\(307\) | −17.5324 | − | 17.5324i | −1.00063 | − | 1.00063i | −1.00000 | 0.000625972i | \(-0.999801\pi\) | |
−0.000625972 | − | 1.00000i | \(-0.500199\pi\) | |||||||
\(308\) | −9.03745 | − | 9.03745i | −0.514957 | − | 0.514957i | ||||
\(309\) | −3.31719 | − | 11.5208i | −0.188709 | − | 0.655398i | ||||
\(310\) | −11.5448 | + | 10.8815i | −0.655700 | + | 0.618027i | ||||
\(311\) | 1.02922i | 0.0583619i | 0.999574 | + | 0.0291810i | \(0.00928991\pi\) | ||||
−0.999574 | + | 0.0291810i | \(0.990710\pi\) | |||||||
\(312\) | 4.58971 | − | 8.30147i | 0.259841 | − | 0.469978i | ||||
\(313\) | −5.15305 | + | 5.15305i | −0.291268 | + | 0.291268i | −0.837581 | − | 0.546313i | \(-0.816031\pi\) |
0.546313 | + | 0.837581i | \(0.316031\pi\) | |||||||
\(314\) | −18.3595 | −1.03608 | ||||||||
\(315\) | 5.71706 | − | 21.9973i | 0.322120 | − | 1.23941i | ||||
\(316\) | 4.59709 | 0.258607 | ||||||||
\(317\) | 2.15191 | − | 2.15191i | 0.120863 | − | 0.120863i | −0.644088 | − | 0.764951i | \(-0.722763\pi\) |
0.764951 | + | 0.644088i | \(0.222763\pi\) | |||||||
\(318\) | 1.36520 | − | 2.46925i | 0.0765565 | − | 0.138469i | ||||
\(319\) | − | 24.4640i | − | 1.36972i | ||||||
\(320\) | −0.0661068 | + | 2.23509i | −0.00369548 | + | 0.124945i | ||||
\(321\) | 4.82382 | + | 16.7535i | 0.269239 | + | 0.935087i | ||||
\(322\) | 2.39575 | + | 2.39575i | 0.133510 | + | 0.133510i | ||||
\(323\) | −17.5734 | − | 17.5734i | −0.977808 | − | 0.977808i | ||||
\(324\) | 8.10633 | + | 3.90991i | 0.450352 | + | 0.217217i | ||||
\(325\) | 20.4733 | − | 18.1845i | 1.13565 | − | 1.00870i | ||||
\(326\) | 8.08915i | 0.448017i | ||||||||
\(327\) | −27.4705 | − | 15.1879i | −1.51912 | − | 0.839893i | ||||
\(328\) | −5.68288 | + | 5.68288i | −0.313785 | + | 0.313785i | ||||
\(329\) | 16.3114 | 0.899276 | ||||||||
\(330\) | 14.1530 | − | 3.62559i | 0.779097 | − | 0.199582i | ||||
\(331\) | −10.0289 | −0.551239 | −0.275619 | − | 0.961267i | \(-0.588883\pi\) | ||||
−0.275619 | + | 0.961267i | \(0.588883\pi\) | |||||||
\(332\) | −5.20343 | + | 5.20343i | −0.285575 | + | 0.285575i | ||||
\(333\) | 4.43257 | − | 19.3931i | 0.242904 | − | 1.06273i | ||||
\(334\) | 12.7448i | 0.697365i | ||||||||
\(335\) | 2.37169 | + | 2.51626i | 0.129579 | + | 0.137478i | ||||
\(336\) | 5.63926 | − | 1.62371i | 0.307647 | − | 0.0885806i | ||||
\(337\) | 17.9924 | + | 17.9924i | 0.980107 | + | 0.980107i | 0.999806 | − | 0.0196990i | \(-0.00627080\pi\) |
−0.0196990 | + | 0.999806i | \(0.506271\pi\) | |||||||
\(338\) | −12.0161 | − | 12.0161i | −0.653588 | − | 0.653588i | ||||
\(339\) | 34.3548 | − | 9.89176i | 1.86590 | − | 0.537247i | ||||
\(340\) | 5.60089 | + | 5.94230i | 0.303751 | + | 0.322266i | ||||
\(341\) | 26.7641i | 1.44936i | ||||||||
\(342\) | 4.54912 | − | 19.9030i | 0.245988 | − | 1.07623i | ||||
\(343\) | 6.03915 | − | 6.03915i | 0.326084 | − | 0.326084i | ||||
\(344\) | 4.05539 | 0.218652 | ||||||||
\(345\) | −3.75183 | + | 0.961112i | −0.201992 | + | 0.0517446i | ||||
\(346\) | −20.8151 | −1.11903 | ||||||||
\(347\) | −16.7568 | + | 16.7568i | −0.899551 | + | 0.899551i | −0.995396 | − | 0.0958454i | \(-0.969445\pi\) |
0.0958454 | + | 0.995396i | \(0.469445\pi\) | |||||||
\(348\) | 9.83029 | + | 5.43497i | 0.526959 | + | 0.291345i | ||||
\(349\) | − | 13.6323i | − | 0.729723i | −0.931062 | − | 0.364861i | \(-0.881116\pi\) | ||
0.931062 | − | 0.364861i | \(-0.118884\pi\) | |||||||
\(350\) | 16.9109 | + | 1.00122i | 0.903925 | + | 0.0535172i | ||||
\(351\) | 18.9722 | − | 21.2103i | 1.01266 | − | 1.13212i | ||||
\(352\) | 2.66741 | + | 2.66741i | 0.142173 | + | 0.142173i | ||||
\(353\) | 4.64603 | + | 4.64603i | 0.247283 | + | 0.247283i | 0.819855 | − | 0.572571i | \(-0.194054\pi\) |
−0.572571 | + | 0.819855i | \(0.694054\pi\) | |||||||
\(354\) | 0.475983 | + | 1.65312i | 0.0252982 | + | 0.0878625i | ||||
\(355\) | −0.612253 | + | 20.7005i | −0.0324950 | + | 1.09867i | ||||
\(356\) | 9.56617i | 0.507006i | ||||||||
\(357\) | 10.3692 | − | 18.7549i | 0.548796 | − | 0.992614i | ||||
\(358\) | −4.30513 | + | 4.30513i | −0.227533 | + | 0.227533i | ||||
\(359\) | −34.5145 | −1.82160 | −0.910802 | − | 0.412845i | \(-0.864535\pi\) | ||||
−0.910802 | + | 0.412845i | \(0.864535\pi\) | |||||||
\(360\) | −1.68739 | + | 6.49251i | −0.0889335 | + | 0.342185i | ||||
\(361\) | −27.3136 | −1.43756 | ||||||||
\(362\) | −7.86622 | + | 7.86622i | −0.413439 | + | 0.413439i | ||||
\(363\) | 2.70705 | − | 4.89628i | 0.142083 | − | 0.256988i | ||||
\(364\) | − | 18.5553i | − | 0.972562i | ||||||
\(365\) | 4.94269 | − | 4.65871i | 0.258712 | − | 0.243848i | ||||
\(366\) | −5.58986 | − | 19.4140i | −0.292187 | − | 1.01478i | ||||
\(367\) | 8.38016 | + | 8.38016i | 0.437441 | + | 0.437441i | 0.891150 | − | 0.453709i | \(-0.149899\pi\) |
−0.453709 | + | 0.891150i | \(0.649899\pi\) | |||||||
\(368\) | −0.707107 | − | 0.707107i | −0.0368605 | − | 0.0368605i | ||||
\(369\) | −20.4188 | + | 12.8213i | −1.06296 | + | 0.667450i | ||||
\(370\) | 14.8210 | + | 0.438358i | 0.770509 | + | 0.0227892i | ||||
\(371\) | − | 5.51923i | − | 0.286544i | ||||||
\(372\) | −10.7545 | − | 5.94594i | −0.557595 | − | 0.308283i | ||||
\(373\) | 7.63967 | − | 7.63967i | 0.395567 | − | 0.395567i | −0.481099 | − | 0.876666i | \(-0.659762\pi\) |
0.876666 | + | 0.481099i | \(0.159762\pi\) | |||||||
\(374\) | 13.7759 | 0.712335 | ||||||||
\(375\) | −10.8342 | + | 16.0505i | −0.559478 | + | 0.828845i | ||||
\(376\) | −4.81432 | −0.248280 | ||||||||
\(377\) | 25.1143 | − | 25.1143i | 1.29345 | − | 1.29345i | ||||
\(378\) | 17.5778 | − | 0.979073i | 0.904106 | − | 0.0503581i | ||||
\(379\) | 1.05138i | 0.0540060i | 0.999635 | + | 0.0270030i | \(0.00859636\pi\) | ||||
−0.999635 | + | 0.0270030i | \(0.991404\pi\) | |||||||
\(380\) | 15.2107 | + | 0.449884i | 0.780293 | + | 0.0230786i | ||||
\(381\) | −11.1237 | + | 3.20284i | −0.569883 | + | 0.164086i | ||||
\(382\) | −3.96990 | − | 3.96990i | −0.203118 | − | 0.203118i | ||||
\(383\) | 16.4304 | + | 16.4304i | 0.839554 | + | 0.839554i | 0.988800 | − | 0.149246i | \(-0.0476845\pi\) |
−0.149246 | + | 0.988800i | \(0.547685\pi\) | |||||||
\(384\) | −1.66443 | + | 0.479239i | −0.0849376 | + | 0.0244561i | ||||
\(385\) | 20.7970 | − | 19.6021i | 1.05991 | − | 0.999015i | ||||
\(386\) | − | 13.8225i | − | 0.703549i | ||||||
\(387\) | 11.8603 | + | 2.71085i | 0.602894 | + | 0.137800i | ||||
\(388\) | −10.5684 | + | 10.5684i | −0.536532 | + | 0.536532i | ||||
\(389\) | −4.44285 | −0.225261 | −0.112631 | − | 0.993637i | \(-0.535928\pi\) | ||||
−0.112631 | + | 0.993637i | \(0.535928\pi\) | |||||||
\(390\) | 18.2511 | + | 10.8072i | 0.924181 | + | 0.547244i | ||||
\(391\) | −3.65187 | −0.184683 | ||||||||
\(392\) | 3.16729 | − | 3.16729i | 0.159972 | − | 0.159972i | ||||
\(393\) | 14.5483 | + | 8.04345i | 0.733863 | + | 0.405738i | ||||
\(394\) | 1.59876i | 0.0805446i | ||||||||
\(395\) | −0.303899 | + | 10.2749i | −0.0152908 | + | 0.516987i | ||||
\(396\) | 6.01801 | + | 9.58410i | 0.302416 | + | 0.481619i | ||||
\(397\) | 2.78289 | + | 2.78289i | 0.139669 | + | 0.139669i | 0.773485 | − | 0.633815i | \(-0.218512\pi\) |
−0.633815 | + | 0.773485i | \(0.718512\pi\) | |||||||
\(398\) | 3.27847 | + | 3.27847i | 0.164335 | + | 0.164335i | ||||
\(399\) | −11.0500 | − | 38.3775i | −0.553192 | − | 1.92128i | ||||
\(400\) | −4.99126 | − | 0.295509i | −0.249563 | − | 0.0147755i | ||||
\(401\) | − | 1.11565i | − | 0.0557131i | −0.999612 | − | 0.0278565i | \(-0.991132\pi\) | ||
0.999612 | − | 0.0278565i | \(-0.00886816\pi\) | |||||||
\(402\) | −1.29595 | + | 2.34401i | −0.0646363 | + | 0.116908i | ||||
\(403\) | −27.4754 | + | 27.4754i | −1.36865 | + | 1.36865i | ||||
\(404\) | 3.09956 | 0.154209 | ||||||||
\(405\) | −9.27488 | + | 17.8599i | −0.460872 | + | 0.887466i | ||||
\(406\) | 21.9725 | 1.09048 | ||||||||
\(407\) | 17.6878 | − | 17.6878i | 0.876750 | − | 0.876750i | ||||
\(408\) | −3.06048 | + | 5.53552i | −0.151516 | + | 0.274049i | ||||
\(409\) | 15.3832i | 0.760653i | 0.924852 | + | 0.380326i | \(0.124188\pi\) | ||||
−0.924852 | + | 0.380326i | \(0.875812\pi\) | |||||||
\(410\) | −12.3261 | − | 13.0774i | −0.608742 | − | 0.645849i | ||||
\(411\) | 3.58880 | + | 12.4641i | 0.177022 | + | 0.614811i | ||||
\(412\) | 4.89445 | + | 4.89445i | 0.241132 | + | 0.241132i | ||||
\(413\) | 2.37947 | + | 2.37947i | 0.117086 | + | 0.117086i | ||||
\(414\) | −1.59532 | − | 2.54066i | −0.0784057 | − | 0.124867i | ||||
\(415\) | −11.2862 | − | 11.9741i | −0.554016 | − | 0.587786i | ||||
\(416\) | 5.47661i | 0.268513i | ||||||||
\(417\) | 19.1768 | + | 10.6025i | 0.939094 | + | 0.519206i | ||||
\(418\) | 18.1528 | − | 18.1528i | 0.887883 | − | 0.887883i | ||||
\(419\) | 3.29476 | 0.160960 | 0.0804798 | − | 0.996756i | \(-0.474355\pi\) | ||||
0.0804798 | + | 0.996756i | \(0.474355\pi\) | |||||||
\(420\) | 3.25635 | + | 12.7116i | 0.158893 | + | 0.620262i | ||||
\(421\) | 26.2854 | 1.28107 | 0.640537 | − | 0.767927i | \(-0.278712\pi\) | ||||
0.640537 | + | 0.767927i | \(0.278712\pi\) | |||||||
\(422\) | −6.33962 | + | 6.33962i | −0.308608 | + | 0.308608i | ||||
\(423\) | −14.0799 | − | 3.21816i | −0.684586 | − | 0.156472i | ||||
\(424\) | 1.62900i | 0.0791114i | ||||||||
\(425\) | −13.6518 | + | 12.1257i | −0.662211 | + | 0.588181i | ||||
\(426\) | −15.4152 | + | 4.43851i | −0.746871 | + | 0.215046i | ||||
\(427\) | −27.9441 | − | 27.9441i | −1.35231 | − | 1.35231i | ||||
\(428\) | −7.11744 | − | 7.11744i | −0.344035 | − | 0.344035i | ||||
\(429\) | 34.3861 | − | 9.90077i | 1.66018 | − | 0.478014i | ||||
\(430\) | −0.268089 | + | 9.06417i | −0.0129284 | + | 0.437113i | ||||
\(431\) | 12.3440i | 0.594591i | 0.954786 | + | 0.297296i | \(0.0960847\pi\) | ||||
−0.954786 | + | 0.297296i | \(0.903915\pi\) | |||||||
\(432\) | −5.18811 | + | 0.288974i | −0.249613 | + | 0.0139033i | ||||
\(433\) | 4.20594 | − | 4.20594i | 0.202124 | − | 0.202124i | −0.598785 | − | 0.800910i | \(-0.704350\pi\) |
0.800910 | + | 0.598785i | \(0.204350\pi\) | |||||||
\(434\) | −24.0383 | −1.15387 | ||||||||
\(435\) | −12.7975 | + | 21.6123i | −0.613593 | + | 1.03623i | ||||
\(436\) | 18.1228 | 0.867922 | ||||||||
\(437\) | −4.81215 | + | 4.81215i | −0.230196 | + | 0.230196i | ||||
\(438\) | 4.60434 | + | 2.54565i | 0.220004 | + | 0.121636i | ||||
\(439\) | − | 23.3960i | − | 1.11663i | −0.829629 | − | 0.558315i | \(-0.811448\pi\) | ||
0.829629 | − | 0.558315i | \(-0.188552\pi\) | |||||||
\(440\) | −6.13824 | + | 5.78557i | −0.292629 | + | 0.275816i | ||||
\(441\) | 11.3802 | − | 7.14579i | 0.541913 | − | 0.340276i | ||||
\(442\) | 14.1421 | + | 14.1421i | 0.672669 | + | 0.672669i | ||||
\(443\) | 1.58931 | + | 1.58931i | 0.0755103 | + | 0.0755103i | 0.743853 | − | 0.668343i | \(-0.232996\pi\) |
−0.668343 | + | 0.743853i | \(0.732996\pi\) | |||||||
\(444\) | 3.17786 | + | 11.0369i | 0.150815 | + | 0.523790i | ||||
\(445\) | −21.3813 | − | 0.632389i | −1.01357 | − | 0.0299781i | ||||
\(446\) | − | 22.0354i | − | 1.04341i | ||||||
\(447\) | 11.5300 | − | 20.8545i | 0.545351 | − | 0.986383i | ||||
\(448\) | −2.39575 | + | 2.39575i | −0.113188 | + | 0.113188i | ||||
\(449\) | −22.0511 | −1.04066 | −0.520328 | − | 0.853966i | \(-0.674190\pi\) | ||||
−0.520328 | + | 0.853966i | \(0.674190\pi\) | |||||||
\(450\) | −14.3998 | − | 4.20068i | −0.678813 | − | 0.198022i | ||||
\(451\) | −30.3172 | −1.42758 | ||||||||
\(452\) | −14.5951 | + | 14.5951i | −0.686495 | + | 0.686495i | ||||
\(453\) | 1.36136 | − | 2.46231i | 0.0639623 | − | 0.115689i | ||||
\(454\) | 24.7238i | 1.16035i | ||||||||
\(455\) | 41.4728 | + | 1.22663i | 1.94427 | + | 0.0575054i | ||||
\(456\) | 3.26142 | + | 11.3271i | 0.152730 | + | 0.530442i | ||||
\(457\) | 26.3823 | + | 26.3823i | 1.23411 | + | 1.23411i | 0.962370 | + | 0.271741i | \(0.0875993\pi\) |
0.271741 | + | 0.962370i | \(0.412401\pi\) | |||||||
\(458\) | 6.89234 | + | 6.89234i | 0.322058 | + | 0.322058i | ||||
\(459\) | −12.6509 | + | 14.1433i | −0.590492 | + | 0.660152i | ||||
\(460\) | 1.62719 | − | 1.53370i | 0.0758682 | − | 0.0715093i | ||||
\(461\) | − | 12.2104i | − | 0.568695i | −0.958721 | − | 0.284348i | \(-0.908223\pi\) | ||
0.958721 | − | 0.284348i | \(-0.0917770\pi\) | |||||||
\(462\) | 19.3733 | + | 10.7111i | 0.901328 | + | 0.498326i | ||||
\(463\) | 12.7159 | − | 12.7159i | 0.590959 | − | 0.590959i | −0.346931 | − | 0.937891i | \(-0.612776\pi\) |
0.937891 | + | 0.346931i | \(0.112776\pi\) | |||||||
\(464\) | −6.48520 | −0.301068 | ||||||||
\(465\) | 14.0007 | − | 23.6442i | 0.649266 | − | 1.09647i | ||||
\(466\) | 8.87206 | 0.410990 | ||||||||
\(467\) | −13.8067 | + | 13.8067i | −0.638896 | + | 0.638896i | −0.950283 | − | 0.311387i | \(-0.899207\pi\) |
0.311387 | + | 0.950283i | \(0.399207\pi\) | |||||||
\(468\) | −3.66087 | + | 16.0168i | −0.169224 | + | 0.740376i | ||||
\(469\) | 5.23929i | 0.241928i | ||||||||
\(470\) | 0.318259 | − | 10.7604i | 0.0146802 | − | 0.496342i | ||||
\(471\) | 30.5580 | − | 8.79857i | 1.40804 | − | 0.405417i | ||||
\(472\) | −0.702303 | − | 0.702303i | −0.0323261 | − | 0.0323261i | ||||
\(473\) | 10.8174 | + | 10.8174i | 0.497385 | + | 0.497385i | ||||
\(474\) | −7.65154 | + | 2.20311i | −0.351447 | + | 0.101192i | ||||
\(475\) | −2.01106 | + | 33.9676i | −0.0922739 | + | 1.55854i | ||||
\(476\) | 12.3729i | 0.567111i | ||||||||
\(477\) | −1.08892 | + | 4.76415i | −0.0498581 | + | 0.218136i | ||||
\(478\) | 16.7784 | − | 16.7784i | 0.767428 | − | 0.767428i | ||||
\(479\) | −12.4597 | −0.569300 | −0.284650 | − | 0.958632i | \(-0.591877\pi\) | ||||
−0.284650 | + | 0.958632i | \(0.591877\pi\) | |||||||
\(480\) | −0.961112 | − | 3.75183i | −0.0438686 | − | 0.171247i | ||||
\(481\) | 36.3158 | 1.65586 | ||||||||
\(482\) | 4.32877 | − | 4.32877i | 0.197170 | − | 0.197170i | ||||
\(483\) | −5.13569 | − | 2.83942i | −0.233682 | − | 0.129198i | ||||
\(484\) | 3.23015i | 0.146825i | ||||||||
\(485\) | −22.9228 | − | 24.3201i | −1.04087 | − | 1.10432i | ||||
\(486\) | −15.3662 | − | 2.62290i | −0.697025 | − | 0.118977i | ||||
\(487\) | −1.80667 | − | 1.80667i | −0.0818682 | − | 0.0818682i | 0.664987 | − | 0.746855i | \(-0.268437\pi\) |
−0.746855 | + | 0.664987i | \(0.768437\pi\) | |||||||
\(488\) | 8.24772 | + | 8.24772i | 0.373357 | + | 0.373357i | ||||
\(489\) | −3.87664 | − | 13.4638i | −0.175308 | − | 0.608856i | ||||
\(490\) | 6.86980 | + | 7.28855i | 0.310346 | + | 0.329263i | ||||
\(491\) | − | 28.0135i | − | 1.26423i | −0.774874 | − | 0.632116i | \(-0.782187\pi\) | ||
0.774874 | − | 0.632116i | \(-0.217813\pi\) | |||||||
\(492\) | 6.73531 | − | 12.1822i | 0.303651 | − | 0.549217i | ||||
\(493\) | −16.7465 | + | 16.7465i | −0.754224 | + | 0.754224i | ||||
\(494\) | 37.2706 | 1.67688 | ||||||||
\(495\) | −21.8192 | + | 12.8172i | −0.980698 | + | 0.576091i | ||||
\(496\) | 7.09492 | 0.318571 | ||||||||
\(497\) | −22.1884 | + | 22.1884i | −0.995286 | + | 0.995286i | ||||
\(498\) | 6.16706 | − | 11.1544i | 0.276353 | − | 0.499842i | ||||
\(499\) | 26.7176i | 1.19605i | 0.801479 | + | 0.598023i | \(0.204047\pi\) | ||||
−0.801479 | + | 0.598023i | \(0.795953\pi\) | |||||||
\(500\) | 0.990446 | − | 11.1364i | 0.0442941 | − | 0.498034i | ||||
\(501\) | −6.10781 | − | 21.2129i | −0.272877 | − | 0.947720i | ||||
\(502\) | −10.2232 | − | 10.2232i | −0.456283 | − | 0.456283i | ||||
\(503\) | 26.3520 | + | 26.3520i | 1.17498 | + | 1.17498i | 0.981007 | + | 0.193973i | \(0.0621374\pi\) |
0.193973 | + | 0.981007i | \(0.437863\pi\) | |||||||
\(504\) | −8.60801 | + | 5.40511i | −0.383431 | + | 0.240763i | ||||
\(505\) | −0.204902 | + | 6.92780i | −0.00911802 | + | 0.308283i | ||||
\(506\) | − | 3.77229i | − | 0.167699i | ||||||
\(507\) | 25.7585 | + | 14.2413i | 1.14397 | + | 0.632480i | ||||
\(508\) | 4.72572 | − | 4.72572i | 0.209670 | − | 0.209670i | ||||
\(509\) | −9.42990 | −0.417973 | −0.208986 | − | 0.977919i | \(-0.567016\pi\) | ||||
−0.208986 | + | 0.977919i | \(0.567016\pi\) | |||||||
\(510\) | −12.1701 | − | 7.20638i | −0.538900 | − | 0.319104i | ||||
\(511\) | 10.2915 | 0.455271 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 1.96659 | + | 35.3072i | 0.0868270 | + | 1.55885i | ||||
\(514\) | − | 26.5897i | − | 1.17282i | ||||||
\(515\) | −11.2631 | + | 10.6160i | −0.496311 | + | 0.467796i | ||||
\(516\) | −6.74992 | + | 1.94350i | −0.297149 | + | 0.0855580i | ||||
\(517\) | −12.8418 | − | 12.8418i | −0.564780 | − | 0.564780i | ||||
\(518\) | 15.8864 | + | 15.8864i | 0.698007 | + | 0.698007i | ||||
\(519\) | 34.6454 | − | 9.97543i | 1.52076 | − | 0.437873i | ||||
\(520\) | −12.2407 | − | 0.362041i | −0.536791 | − | 0.0158766i | ||||
\(521\) | 13.8604i | 0.607237i | 0.952794 | + | 0.303618i | \(0.0981948\pi\) | ||||
−0.952794 | + | 0.303618i | \(0.901805\pi\) | |||||||
\(522\) | −18.9665 | − | 4.33507i | −0.830141 | − | 0.189741i | ||||
\(523\) | 14.8570 | − | 14.8570i | 0.649650 | − | 0.649650i | −0.303259 | − | 0.952908i | \(-0.598075\pi\) |
0.952908 | + | 0.303259i | \(0.0980746\pi\) | |||||||
\(524\) | −9.59773 | −0.419279 | ||||||||
\(525\) | −28.6268 | + | 6.43790i | −1.24938 | + | 0.280973i | ||||
\(526\) | 13.7122 | 0.597882 | ||||||||
\(527\) | 18.3209 | − | 18.3209i | 0.798073 | − | 0.798073i | ||||
\(528\) | −5.71805 | − | 3.16139i | −0.248846 | − | 0.137582i | ||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | −3.64097 | − | 0.107688i | −0.158154 | − | 0.00467768i | ||||
\(531\) | −1.58448 | − | 2.52340i | −0.0687607 | − | 0.109506i | ||||
\(532\) | 16.3041 | + | 16.3041i | 0.706870 | + | 0.706870i | ||||
\(533\) | −31.1229 | − | 31.1229i | −1.34808 | − | 1.34808i | ||||
\(534\) | −4.58448 | − | 15.9222i | −0.198390 | − | 0.689022i | ||||
\(535\) | 16.3786 | − | 15.4376i | 0.708110 | − | 0.667426i | ||||
\(536\) | − | 1.54638i | − | 0.0667934i | ||||||
\(537\) | 5.10241 | − | 9.22879i | 0.220185 | − | 0.398251i | ||||
\(538\) | 3.04451 | − | 3.04451i | 0.131258 | − | 0.131258i | ||||
\(539\) | 16.8969 | 0.727801 | ||||||||
\(540\) | −0.302914 | − | 11.6150i | −0.0130353 | − | 0.499830i | ||||
\(541\) | −19.6739 | −0.845846 | −0.422923 | − | 0.906166i | \(-0.638996\pi\) | ||||
−0.422923 | + | 0.906166i | \(0.638996\pi\) | |||||||
\(542\) | −6.12669 | + | 6.12669i | −0.263164 | + | 0.263164i | ||||
\(543\) | 9.32297 | − | 16.8626i | 0.400087 | − | 0.723642i | ||||
\(544\) | − | 3.65187i | − | 0.156573i | ||||||
\(545\) | −1.19804 | + | 40.5060i | −0.0513183 | + | 1.73509i | ||||
\(546\) | 8.89243 | + | 30.8840i | 0.380561 | + | 1.32171i | ||||
\(547\) | 20.3990 | + | 20.3990i | 0.872198 | + | 0.872198i | 0.992712 | − | 0.120514i | \(-0.0384543\pi\) |
−0.120514 | + | 0.992712i | \(0.538454\pi\) | |||||||
\(548\) | −5.29519 | − | 5.29519i | −0.226199 | − | 0.226199i | ||||
\(549\) | 18.6079 | + | 29.6343i | 0.794165 | + | 1.26476i | ||||
\(550\) | −12.5255 | − | 14.1020i | −0.534089 | − | 0.601311i | ||||
\(551\) | 44.1345i | 1.88019i | ||||||||
\(552\) | 1.51580 | + | 0.838057i | 0.0645169 | + | 0.0356701i | ||||
\(553\) | −11.0135 | + | 11.0135i | −0.468341 | + | 0.468341i | ||||
\(554\) | 29.5281 | 1.25453 | ||||||||
\(555\) | −24.8787 | + | 6.37320i | −1.05604 | + | 0.270527i | ||||
\(556\) | −12.6513 | −0.536533 | ||||||||
\(557\) | −3.65261 | + | 3.65261i | −0.154766 | + | 0.154766i | −0.780243 | − | 0.625477i | \(-0.784904\pi\) |
0.625477 | + | 0.780243i | \(0.284904\pi\) | |||||||
\(558\) | 20.7496 | + | 4.74264i | 0.878403 | + | 0.200772i | ||||
\(559\) | 22.2098i | 0.939375i | ||||||||
\(560\) | −5.19634 | − | 5.51309i | −0.219585 | − | 0.232971i | ||||
\(561\) | −22.9291 | + | 6.60195i | −0.968065 | + | 0.278735i | ||||
\(562\) | 15.5083 | + | 15.5083i | 0.654177 | + | 0.654177i | ||||
\(563\) | 26.8125 | + | 26.8125i | 1.13001 | + | 1.13001i | 0.990175 | + | 0.139836i | \(0.0446576\pi\) |
0.139836 | + | 0.990175i | \(0.455342\pi\) | |||||||
\(564\) | 8.01310 | − | 2.30721i | 0.337412 | − | 0.0971511i | ||||
\(565\) | −31.6565 | − | 33.5862i | −1.33180 | − | 1.41298i | ||||
\(566\) | 2.21185i | 0.0929709i | ||||||||
\(567\) | −28.7879 | + | 10.0536i | −1.20898 | + | 0.422211i | ||||
\(568\) | 6.54892 | − | 6.54892i | 0.274787 | − | 0.274787i | ||||
\(569\) | −35.3739 | −1.48295 | −0.741475 | − | 0.670980i | \(-0.765874\pi\) | ||||
−0.741475 | + | 0.670980i | \(0.765874\pi\) | |||||||
\(570\) | −25.5328 | + | 6.54076i | −1.06945 | + | 0.273962i | ||||
\(571\) | −33.8705 | −1.41744 | −0.708718 | − | 0.705492i | \(-0.750726\pi\) | ||||
−0.708718 | + | 0.705492i | \(0.750726\pi\) | |||||||
\(572\) | −14.6084 | + | 14.6084i | −0.610807 | + | 0.610807i | ||||
\(573\) | 8.51015 | + | 4.70509i | 0.355516 | + | 0.196558i | ||||
\(574\) | − | 27.2295i | − | 1.13654i | ||||||
\(575\) | 3.32040 | + | 3.73831i | 0.138470 | + | 0.155898i | ||||
\(576\) | 2.54066 | − | 1.59532i | 0.105861 | − | 0.0664717i | ||||
\(577\) | 25.3921 | + | 25.3921i | 1.05709 | + | 1.05709i | 0.998269 | + | 0.0588185i | \(0.0187333\pi\) |
0.0588185 | + | 0.998269i | \(0.481267\pi\) | |||||||
\(578\) | 2.59072 | + | 2.59072i | 0.107760 | + | 0.107760i | ||||
\(579\) | 6.62430 | + | 23.0067i | 0.275297 | + | 0.956125i | ||||
\(580\) | 0.428716 | − | 14.4950i | 0.0178015 | − | 0.601873i | ||||
\(581\) | − | 24.9322i | − | 1.03436i | ||||||
\(582\) | 12.5256 | − | 22.6553i | 0.519204 | − | 0.939091i | ||||
\(583\) | −4.34522 | + | 4.34522i | −0.179961 | + | 0.179961i | ||||
\(584\) | −3.03756 | −0.125695 | ||||||||
\(585\) | −35.5570 | − | 9.24120i | −1.47010 | − | 0.382077i | ||||
\(586\) | 9.04621 | 0.373695 | ||||||||
\(587\) | −31.7362 | + | 31.7362i | −1.30989 | + | 1.30989i | −0.388402 | + | 0.921490i | \(0.626973\pi\) |
−0.921490 | + | 0.388402i | \(0.873027\pi\) | |||||||
\(588\) | −3.75384 | + | 6.78962i | −0.154806 | + | 0.279999i | ||||
\(589\) | − | 48.2838i | − | 1.98950i | ||||||
\(590\) | 1.61614 | − | 1.52328i | 0.0665354 | − | 0.0627126i | ||||
\(591\) | −0.766190 | − | 2.66103i | −0.0315169 | − | 0.109460i | ||||
\(592\) | −4.68887 | − | 4.68887i | −0.192711 | − | 0.192711i | ||||
\(593\) | −21.4857 | − | 21.4857i | −0.882314 | − | 0.882314i | 0.111456 | − | 0.993769i | \(-0.464449\pi\) |
−0.993769 | + | 0.111456i | \(0.964449\pi\) | |||||||
\(594\) | −14.6096 | − | 13.0680i | −0.599440 | − | 0.536187i | ||||
\(595\) | −27.6546 | − | 0.817933i | −1.13373 | − | 0.0335320i | ||||
\(596\) | 13.7580i | 0.563551i | ||||||||
\(597\) | −7.02796 | − | 3.88562i | −0.287635 | − | 0.159028i | ||||
\(598\) | 3.87255 | − | 3.87255i | 0.158360 | − | 0.158360i | ||||
\(599\) | −28.3661 | −1.15901 | −0.579504 | − | 0.814969i | \(-0.696754\pi\) | ||||
−0.579504 | + | 0.814969i | \(0.696754\pi\) | |||||||
\(600\) | 8.44923 | − | 1.90015i | 0.344938 | − | 0.0775734i | ||||
\(601\) | 40.0727 | 1.63460 | 0.817300 | − | 0.576213i | \(-0.195470\pi\) | ||||
0.817300 | + | 0.576213i | \(0.195470\pi\) | |||||||
\(602\) | −9.71571 | + | 9.71571i | −0.395983 | + | 0.395983i | ||||
\(603\) | 1.03369 | − | 4.52251i | 0.0420950 | − | 0.184171i | ||||
\(604\) | 1.62442i | 0.0660969i | ||||||||
\(605\) | −7.21969 | − | 0.213535i | −0.293522 | − | 0.00868144i | ||||
\(606\) | −5.15900 | + | 1.48543i | −0.209570 | + | 0.0603415i | ||||
\(607\) | −1.59716 | − | 1.59716i | −0.0648268 | − | 0.0648268i | 0.673950 | − | 0.738777i | \(-0.264596\pi\) |
−0.738777 | + | 0.673950i | \(0.764596\pi\) | |||||||
\(608\) | −4.81215 | − | 4.81215i | −0.195159 | − | 0.195159i | ||||
\(609\) | −36.5717 | + | 10.5301i | −1.48196 | + | 0.426701i | ||||
\(610\) | −18.9796 | + | 17.8892i | −0.768463 | + | 0.724311i | ||||
\(611\) | − | 26.3662i | − | 1.06666i | ||||||
\(612\) | 2.44112 | − | 10.6802i | 0.0986763 | − | 0.431721i | ||||
\(613\) | 12.0113 | − | 12.0113i | 0.485130 | − | 0.485130i | −0.421636 | − | 0.906765i | \(-0.638544\pi\) |
0.906765 | + | 0.421636i | \(0.138544\pi\) | |||||||
\(614\) | −24.7945 | −1.00063 | ||||||||
\(615\) | 26.7831 | + | 15.8593i | 1.08000 | + | 0.639511i | ||||
\(616\) | −12.7809 | −0.514957 | ||||||||
\(617\) | 20.3489 | − | 20.3489i | 0.819214 | − | 0.819214i | −0.166780 | − | 0.985994i | \(-0.553337\pi\) |
0.985994 | + | 0.166780i | \(0.0533370\pi\) | |||||||
\(618\) | −10.4921 | − | 5.80086i | −0.422053 | − | 0.233345i | ||||
\(619\) | − | 11.4711i | − | 0.461063i | −0.973065 | − | 0.230531i | \(-0.925954\pi\) | ||
0.973065 | − | 0.230531i | \(-0.0740464\pi\) | |||||||
\(620\) | −0.469022 | + | 15.8578i | −0.0188364 | + | 0.636864i | ||||
\(621\) | 3.87288 | + | 3.46421i | 0.155413 | + | 0.139014i | ||||
\(622\) | 0.727771 | + | 0.727771i | 0.0291810 | + | 0.0291810i | ||||
\(623\) | −22.9181 | − | 22.9181i | −0.918196 | − | 0.918196i | ||||
\(624\) | −2.62461 | − | 9.11544i | −0.105068 | − | 0.364910i | ||||
\(625\) | 24.8253 | + | 2.94993i | 0.993014 | + | 0.117997i | ||||
\(626\) | 7.28751i | 0.291268i | ||||||||
\(627\) | −21.5146 | + | 38.9137i | −0.859209 | + | 1.55406i | ||||
\(628\) | −12.9821 | + | 12.9821i | −0.518042 | + | 0.518042i | ||||
\(629\) | −24.2158 | −0.965547 | ||||||||
\(630\) | −11.5119 | − | 19.5970i | −0.458643 | − | 0.780763i | ||||
\(631\) | 1.12832 | 0.0449177 | 0.0224588 | − | 0.999748i | \(-0.492851\pi\) | ||||
0.0224588 | + | 0.999748i | \(0.492851\pi\) | |||||||
\(632\) | 3.25064 | − | 3.25064i | 0.129303 | − | 0.129303i | ||||
\(633\) | 7.51366 | − | 13.5900i | 0.298641 | − | 0.540156i | ||||
\(634\) | − | 3.04326i | − | 0.120863i | ||||||
\(635\) | 10.2500 | + | 10.8748i | 0.406759 | + | 0.431553i | ||||
\(636\) | −0.780682 | − | 2.71137i | −0.0309561 | − | 0.107513i | ||||
\(637\) | 17.3460 | + | 17.3460i | 0.687274 | + | 0.687274i | ||||
\(638\) | −17.2987 | − | 17.2987i | −0.684862 | − | 0.684862i | ||||
\(639\) | 23.5305 | − | 14.7752i | 0.930852 | − | 0.584497i | ||||
\(640\) | 1.53370 | + | 1.62719i | 0.0606249 | + | 0.0643204i | ||||
\(641\) | − | 31.3115i | − | 1.23673i | −0.785892 | − | 0.618364i | \(-0.787796\pi\) | ||
0.785892 | − | 0.618364i | \(-0.212204\pi\) | |||||||
\(642\) | 15.2574 | + | 8.43553i | 0.602163 | + | 0.332924i | ||||
\(643\) | 5.97111 | − | 5.97111i | 0.235478 | − | 0.235478i | −0.579497 | − | 0.814974i | \(-0.696751\pi\) |
0.814974 | + | 0.579497i | \(0.196751\pi\) | |||||||
\(644\) | 3.38810 | 0.133510 | ||||||||
\(645\) | −3.89769 | − | 15.2152i | −0.153471 | − | 0.599097i | ||||
\(646\) | −24.8525 | −0.977808 | ||||||||
\(647\) | 10.0814 | − | 10.0814i | 0.396340 | − | 0.396340i | −0.480600 | − | 0.876940i | \(-0.659581\pi\) |
0.876940 | + | 0.480600i | \(0.159581\pi\) | |||||||
\(648\) | 8.49676 | − | 2.96732i | 0.333784 | − | 0.116567i | ||||
\(649\) | − | 3.74666i | − | 0.147069i | ||||||
\(650\) | 1.61839 | − | 27.3352i | 0.0634785 | − | 1.07217i | ||||
\(651\) | 40.0101 | − | 11.5201i | 1.56812 | − | 0.451508i | ||||
\(652\) | 5.71990 | + | 5.71990i | 0.224008 | + | 0.224008i | ||||
\(653\) | 14.5180 | + | 14.5180i | 0.568134 | + | 0.568134i | 0.931605 | − | 0.363472i | \(-0.118409\pi\) |
−0.363472 | + | 0.931605i | \(0.618409\pi\) | |||||||
\(654\) | −30.1641 | + | 8.68513i | −1.17951 | + | 0.339615i | ||||
\(655\) | 0.634475 | − | 21.4518i | 0.0247910 | − | 0.838191i | ||||
\(656\) | 8.03681i | 0.313785i | ||||||||
\(657\) | −8.88357 | − | 2.03047i | −0.346581 | − | 0.0792163i | ||||
\(658\) | 11.5339 | − | 11.5339i | 0.449638 | − | 0.449638i | ||||
\(659\) | −20.3327 | −0.792048 | −0.396024 | − | 0.918240i | \(-0.629610\pi\) | ||||
−0.396024 | + | 0.918240i | \(0.629610\pi\) | |||||||
\(660\) | 7.44400 | − | 12.5714i | 0.289757 | − | 0.489340i | ||||
\(661\) | −31.1622 | −1.21207 | −0.606035 | − | 0.795438i | \(-0.707241\pi\) | ||||
−0.606035 | + | 0.795438i | \(0.707241\pi\) | |||||||
\(662\) | −7.09151 | + | 7.09151i | −0.275619 | + | 0.275619i | ||||
\(663\) | −30.3159 | − | 16.7610i | −1.17737 | − | 0.650945i | ||||
\(664\) | 7.35876i | 0.285575i | ||||||||
\(665\) | −37.5188 | + | 35.3632i | −1.45492 | + | 1.37133i | ||||
\(666\) | −10.5787 | − | 16.8473i | −0.409915 | − | 0.652819i | ||||
\(667\) | 4.58573 | + | 4.58573i | 0.177560 | + | 0.177560i | ||||
\(668\) | 9.01194 | + | 9.01194i | 0.348682 | + | 0.348682i | ||||
\(669\) | 10.5602 | + | 36.6764i | 0.408282 | + | 1.41799i | ||||
\(670\) | 3.45630 | + | 0.102226i | 0.133528 | + | 0.00394934i | ||||
\(671\) | 44.0001i | 1.69860i | ||||||||
\(672\) | 2.83942 | − | 5.13569i | 0.109533 | − | 0.198114i | ||||
\(673\) | 32.7647 | − | 32.7647i | 1.26299 | − | 1.26299i | 0.313348 | − | 0.949638i | \(-0.398549\pi\) |
0.949638 | − | 0.313348i | \(-0.101451\pi\) | |||||||
\(674\) | 25.4451 | 0.980107 | ||||||||
\(675\) | 25.9806 | + | 0.0907905i | 0.999994 | + | 0.00349453i | ||||
\(676\) | −16.9933 | −0.653588 | ||||||||
\(677\) | −10.4956 | + | 10.4956i | −0.403380 | + | 0.403380i | −0.879422 | − | 0.476043i | \(-0.842071\pi\) |
0.476043 | + | 0.879422i | \(0.342071\pi\) | |||||||
\(678\) | 17.2980 | − | 31.2870i | 0.664325 | − | 1.20157i | ||||
\(679\) | − | 50.6387i | − | 1.94333i | ||||||
\(680\) | 8.16227 | + | 0.241414i | 0.313009 | + | 0.00925779i | ||||
\(681\) | −11.8486 | − | 41.1510i | −0.454040 | − | 1.57691i | ||||
\(682\) | 18.9250 | + | 18.9250i | 0.724678 | + | 0.724678i | ||||
\(683\) | 2.34519 | + | 2.34519i | 0.0897362 | + | 0.0897362i | 0.750550 | − | 0.660814i | \(-0.229789\pi\) |
−0.660814 | + | 0.750550i | \(0.729789\pi\) | |||||||
\(684\) | −10.8568 | − | 17.2902i | −0.415121 | − | 0.661109i | ||||
\(685\) | 12.1853 | − | 11.4852i | 0.465575 | − | 0.438826i | ||||
\(686\) | − | 8.54065i | − | 0.326084i | ||||||
\(687\) | −14.7749 | − | 8.16874i | −0.563698 | − | 0.311657i | ||||
\(688\) | 2.86760 | − | 2.86760i | 0.109326 | − | 0.109326i | ||||
\(689\) | −8.92143 | −0.339879 | ||||||||
\(690\) | −1.97334 | + | 3.33256i | −0.0751237 | + | 0.126868i | ||||
\(691\) | 49.5125 | 1.88355 | 0.941773 | − | 0.336250i | \(-0.109159\pi\) | ||||
0.941773 | + | 0.336250i | \(0.109159\pi\) | |||||||
\(692\) | −14.7185 | + | 14.7185i | −0.559515 | + | 0.559515i | ||||
\(693\) | −37.3787 | − | 8.54346i | −1.41990 | − | 0.324539i | ||||
\(694\) | 23.6977i | 0.899551i | ||||||||
\(695\) | 0.836335 | − | 28.2767i | 0.0317240 | − | 1.07260i | ||||
\(696\) | 10.7942 | − | 3.10796i | 0.409152 | − | 0.117807i | ||||
\(697\) | 20.7532 | + | 20.7532i | 0.786082 | + | 0.786082i | ||||
\(698\) | −9.63952 | − | 9.63952i | −0.364861 | − | 0.364861i | ||||
\(699\) | −14.7669 | + | 4.25184i | −0.558536 | + | 0.160819i | ||||
\(700\) | 12.6658 | − | 11.2498i | 0.478721 | − | 0.425204i | ||||
\(701\) | 43.6716i | 1.64945i | 0.565532 | + | 0.824726i | \(0.308671\pi\) | ||||
−0.565532 | + | 0.824726i | \(0.691329\pi\) | |||||||
\(702\) | −1.58260 | − | 28.4133i | −0.0597314 | − | 1.07239i | ||||
\(703\) | −31.9097 | + | 31.9097i | −1.20350 | + | 1.20350i | ||||
\(704\) | 3.77229 | 0.142173 | ||||||||
\(705\) | 4.62710 | + | 18.0625i | 0.174267 | + | 0.680274i | ||||
\(706\) | 6.57049 | 0.247283 | ||||||||
\(707\) | −7.42577 | + | 7.42577i | −0.279275 | + | 0.279275i | ||||
\(708\) | 1.50551 | + | 0.832364i | 0.0565804 | + | 0.0312822i | ||||
\(709\) | − | 17.3686i | − | 0.652292i | −0.945319 | − | 0.326146i | \(-0.894250\pi\) | ||
0.945319 | − | 0.326146i | \(-0.105750\pi\) | |||||||
\(710\) | 14.2045 | + | 15.0704i | 0.533085 | + | 0.565581i | ||||
\(711\) | 11.6796 | − | 7.33384i | 0.438021 | − | 0.275040i | ||||
\(712\) | 6.76430 | + | 6.76430i | 0.253503 | + | 0.253503i | ||||
\(713\) | −5.01686 | − | 5.01686i | −0.187883 | − | 0.187883i | ||||
\(714\) | −5.92958 | − | 20.5938i | −0.221909 | − | 0.770705i | ||||
\(715\) | −31.6853 | − | 33.6167i | −1.18496 | − | 1.25719i | ||||
\(716\) | 6.08838i | 0.227533i | ||||||||
\(717\) | −19.8857 | + | 35.9674i | −0.742644 | + | 1.34323i | ||||
\(718\) | −24.4054 | + | 24.4054i | −0.910802 | + | 0.910802i | ||||
\(719\) | 13.0073 | 0.485089 | 0.242545 | − | 0.970140i | \(-0.422018\pi\) | ||||
0.242545 | + | 0.970140i | \(0.422018\pi\) | |||||||
\(720\) | 3.39773 | + | 5.78407i | 0.126626 | + | 0.215559i | ||||
\(721\) | −23.4517 | −0.873388 | ||||||||
\(722\) | −19.3136 | + | 19.3136i | −0.718779 | + | 0.718779i | ||||
\(723\) | −5.13042 | + | 9.27945i | −0.190802 | + | 0.345106i | ||||
\(724\) | 11.1245i | 0.413439i | ||||||||
\(725\) | 32.3693 | + | 1.91644i | 1.20217 | + | 0.0711747i | ||||
\(726\) | −1.54802 | − | 5.37637i | −0.0574523 | − | 0.199536i | ||||
\(727\) | 3.34014 | + | 3.34014i | 0.123879 | + | 0.123879i | 0.766328 | − | 0.642449i | \(-0.222082\pi\) |
−0.642449 | + | 0.766328i | \(0.722082\pi\) | |||||||
\(728\) | −13.1206 | − | 13.1206i | −0.486281 | − | 0.486281i | ||||
\(729\) | 26.8330 | − | 2.99846i | 0.993814 | − | 0.111054i | ||||
\(730\) | 0.200803 | − | 6.78921i | 0.00743206 | − | 0.251280i | ||||
\(731\) | − | 14.8098i | − | 0.547760i | ||||||
\(732\) | −17.6804 | − | 9.77513i | −0.653486 | − | 0.361299i | ||||
\(733\) | 21.3827 | − | 21.3827i | 0.789788 | − | 0.789788i | −0.191671 | − | 0.981459i | \(-0.561391\pi\) |
0.981459 | + | 0.191671i | \(0.0613906\pi\) | |||||||
\(734\) | 11.8513 | 0.437441 | ||||||||
\(735\) | −14.9273 | − | 8.83902i | −0.550600 | − | 0.326032i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 4.12483 | − | 4.12483i | 0.151940 | − | 0.151940i | ||||
\(738\) | −5.37225 | + | 23.5043i | −0.197755 | + | 0.865205i | ||||
\(739\) | − | 27.3440i | − | 1.00587i | −0.864326 | − | 0.502933i | \(-0.832254\pi\) | ||
0.864326 | − | 0.502933i | \(-0.167746\pi\) | |||||||
\(740\) | 10.7900 | − | 10.1701i | 0.396649 | − | 0.373860i | ||||
\(741\) | −62.0343 | + | 17.8615i | −2.27889 | + | 0.656159i | ||||
\(742\) | −3.90268 | − | 3.90268i | −0.143272 | − | 0.143272i | ||||
\(743\) | −24.1777 | − | 24.1777i | −0.886995 | − | 0.886995i | 0.107238 | − | 0.994233i | \(-0.465799\pi\) |
−0.994233 | + | 0.107238i | \(0.965799\pi\) | |||||||
\(744\) | −11.8090 | + | 3.40016i | −0.432939 | + | 0.124656i | ||||
\(745\) | −30.7505 | − | 0.909500i | −1.12661 | − | 0.0333215i | ||||
\(746\) | − | 10.8041i | − | 0.395567i | ||||||
\(747\) | −4.91901 | + | 21.5213i | −0.179977 | + | 0.787423i | ||||
\(748\) | 9.74104 | − | 9.74104i | 0.356168 | − | 0.356168i | ||||
\(749\) | 34.1032 | 1.24610 | ||||||||
\(750\) | 3.68846 | + | 19.0104i | 0.134684 | + | 0.694162i | ||||
\(751\) | 34.8097 | 1.27022 | 0.635112 | − | 0.772420i | \(-0.280954\pi\) | ||||
0.635112 | + | 0.772420i | \(0.280954\pi\) | |||||||
\(752\) | −3.40424 | + | 3.40424i | −0.124140 | + | 0.124140i | ||||
\(753\) | 21.9151 | + | 12.1164i | 0.798632 | + | 0.441548i | ||||
\(754\) | − | 35.5169i | − | 1.29345i | ||||||
\(755\) | −3.63074 | − | 0.107385i | −0.132136 | − | 0.00390816i | ||||
\(756\) | 11.7371 | − | 13.1217i | 0.426874 | − | 0.477232i | ||||
\(757\) | −18.4573 | − | 18.4573i | −0.670841 | − | 0.670841i | 0.287069 | − | 0.957910i | \(-0.407319\pi\) |
−0.957910 | + | 0.287069i | \(0.907319\pi\) | |||||||
\(758\) | 0.743441 | + | 0.743441i | 0.0270030 | + | 0.0270030i | ||||
\(759\) | 1.80783 | + | 6.27871i | 0.0656200 | + | 0.227903i | ||||
\(760\) | 11.0737 | − | 10.4375i | 0.401686 | − | 0.378607i | ||||
\(761\) | 4.20612i | 0.152472i | 0.997090 | + | 0.0762358i | \(0.0242902\pi\) | ||||
−0.997090 | + | 0.0762358i | \(0.975710\pi\) | |||||||
\(762\) | −5.60088 | + | 10.1304i | −0.202898 | + | 0.366985i | ||||
\(763\) | −43.4176 | + | 43.4176i | −1.57182 | + | 1.57182i | ||||
\(764\) | −5.61428 | −0.203118 | ||||||||
\(765\) | 23.7098 | + | 6.16215i | 0.857230 | + | 0.222793i | ||||
\(766\) | 23.2361 | 0.839554 | ||||||||
\(767\) | 3.84624 | − | 3.84624i | 0.138880 | − | 0.138880i | ||||
\(768\) | −0.838057 | + | 1.51580i | −0.0302408 | + | 0.0546968i | ||||
\(769\) | − | 32.2378i | − | 1.16253i | −0.813716 | − | 0.581263i | \(-0.802559\pi\) | ||
0.813716 | − | 0.581263i | \(-0.197441\pi\) | |||||||
\(770\) | 0.844904 | − | 28.5664i | 0.0304482 | − | 1.02946i | ||||
\(771\) | 12.7428 | + | 44.2567i | 0.458922 | + | 1.59387i | ||||
\(772\) | −9.77402 | − | 9.77402i | −0.351775 | − | 0.351775i | ||||
\(773\) | −0.232058 | − | 0.232058i | −0.00834653 | − | 0.00834653i | 0.702921 | − | 0.711268i | \(-0.251879\pi\) |
−0.711268 | + | 0.702921i | \(0.751879\pi\) | |||||||
\(774\) | 10.3034 | − | 6.46965i | 0.370347 | − | 0.232547i | ||||
\(775\) | −35.4126 | − | 2.09661i | −1.27206 | − | 0.0753126i | ||||
\(776\) | 14.9460i | 0.536532i | ||||||||
\(777\) | −34.0551 | − | 18.8284i | −1.22172 | − | 0.675465i | ||||
\(778\) | −3.14157 | + | 3.14157i | −0.112631 | + | 0.112631i | ||||
\(779\) | 54.6938 | 1.95961 | ||||||||
\(780\) | 20.5473 | − | 5.26364i | 0.735713 | − | 0.188469i | ||||
\(781\) | 34.9373 | 1.25016 | ||||||||
\(782\) | −2.58226 | + | 2.58226i | −0.0923416 | + | 0.0923416i | ||||
\(783\) | 33.6459 | − | 1.87406i | 1.20241 | − | 0.0669733i | ||||
\(784\) | − | 4.47922i | − | 0.159972i | ||||||
\(785\) | −28.1580 | − | 29.8744i | −1.00500 | − | 1.06626i | ||||
\(786\) | 15.9748 | − | 4.59961i | 0.569801 | − | 0.164063i | ||||
\(787\) | 0.613938 | + | 0.613938i | 0.0218845 | + | 0.0218845i | 0.717964 | − | 0.696080i | \(-0.245074\pi\) |
−0.696080 | + | 0.717964i | \(0.745074\pi\) | |||||||
\(788\) | 1.13050 | + | 1.13050i | 0.0402723 | + | 0.0402723i | ||||
\(789\) | −22.8231 | + | 6.57144i | −0.812523 | + | 0.233949i | ||||
\(790\) | 7.05058 | + | 7.48035i | 0.250848 | + | 0.266139i | ||||
\(791\) | − | 69.9323i | − | 2.48651i | ||||||
\(792\) | 11.0324 | + | 2.52161i | 0.392018 | + | 0.0896014i | ||||
\(793\) | −45.1695 | + | 45.1695i | −1.60402 | + | 1.60402i | ||||
\(794\) | 3.93560 | 0.139669 | ||||||||
\(795\) | 6.11175 | − | 1.56566i | 0.216762 | − | 0.0555281i | ||||
\(796\) | 4.63646 | 0.164335 | ||||||||
\(797\) | 2.57948 | − | 2.57948i | 0.0913700 | − | 0.0913700i | −0.659944 | − | 0.751314i | \(-0.729420\pi\) |
0.751314 | + | 0.659944i | \(0.229420\pi\) | |||||||
\(798\) | −34.9505 | − | 19.3234i | −1.23723 | − | 0.684042i | ||||
\(799\) | 17.5813i | 0.621981i | ||||||||
\(800\) | −3.73831 | + | 3.32040i | −0.132169 | + | 0.117394i | ||||
\(801\) | 15.2611 | + | 24.3044i | 0.539225 | + | 0.858753i | ||||
\(802\) | −0.788886 | − | 0.788886i | −0.0278565 | − | 0.0278565i | ||||
\(803\) | −8.10241 | − | 8.10241i | −0.285928 | − | 0.285928i | ||||
\(804\) | 0.741085 | + | 2.57384i | 0.0261361 | + | 0.0907724i | ||||
\(805\) | −0.223976 | + | 7.57271i | −0.00789413 | + | 0.266903i | ||||
\(806\) | 38.8561i | 1.36865i | ||||||||
\(807\) | −3.60833 | + | 6.52642i | −0.127019 | + | 0.229741i | ||||
\(808\) | 2.19172 | − | 2.19172i | 0.0771044 | − | 0.0771044i | ||||
\(809\) | 54.2052 | 1.90575 | 0.952876 | − | 0.303359i | \(-0.0981083\pi\) | ||||
0.952876 | + | 0.303359i | \(0.0981083\pi\) | |||||||
\(810\) | 6.07054 | + | 19.1872i | 0.213297 | + | 0.674169i | ||||
\(811\) | −24.4217 | −0.857561 | −0.428781 | − | 0.903409i | \(-0.641057\pi\) | ||||
−0.428781 | + | 0.903409i | \(0.641057\pi\) | |||||||
\(812\) | 15.5369 | − | 15.5369i | 0.545239 | − | 0.545239i | ||||
\(813\) | 7.26130 | − | 13.1336i | 0.254665 | − | 0.460615i | ||||
\(814\) | − | 25.0143i | − | 0.876750i | ||||||
\(815\) | −13.1626 | + | 12.4064i | −0.461066 | + | 0.434576i | ||||
\(816\) | 1.75012 | + | 6.07829i | 0.0612664 | + | 0.212783i | ||||
\(817\) | −19.5152 | − | 19.5152i | −0.682750 | − | 0.682750i | ||||
\(818\) | 10.8776 | + | 10.8776i | 0.380326 | + | 0.380326i | ||||
\(819\) | −29.6017 | − | 47.1427i | −1.03437 | − | 1.64730i | ||||
\(820\) | −17.9630 | − | 0.531288i | −0.627295 | − | 0.0185534i | ||||
\(821\) | − | 23.6788i | − | 0.826396i | −0.910641 | − | 0.413198i | \(-0.864412\pi\) | ||
0.910641 | − | 0.413198i | \(-0.135588\pi\) | |||||||
\(822\) | 11.3511 | + | 6.27581i | 0.395916 | + | 0.218894i | ||||
\(823\) | −21.7706 | + | 21.7706i | −0.758875 | + | 0.758875i | −0.976118 | − | 0.217243i | \(-0.930294\pi\) |
0.217243 | + | 0.976118i | \(0.430294\pi\) | |||||||
\(824\) | 6.92180 | 0.241132 | ||||||||
\(825\) | 27.6060 | + | 17.4691i | 0.961119 | + | 0.608195i | ||||
\(826\) | 3.36508 | 0.117086 | ||||||||
\(827\) | 10.4409 | − | 10.4409i | 0.363065 | − | 0.363065i | −0.501875 | − | 0.864940i | \(-0.667356\pi\) |
0.864940 | + | 0.501875i | \(0.167356\pi\) | |||||||
\(828\) | −2.92458 | − | 0.668456i | −0.101636 | − | 0.0232304i | ||||
\(829\) | 17.3634i | 0.603056i | 0.953457 | + | 0.301528i | \(0.0974967\pi\) | ||||
−0.953457 | + | 0.301528i | \(0.902503\pi\) | |||||||
\(830\) | −16.4475 | − | 0.486464i | −0.570901 | − | 0.0168854i | ||||
\(831\) | −49.1475 | + | 14.1510i | −1.70491 | + | 0.490894i | ||||
\(832\) | 3.87255 | + | 3.87255i | 0.134257 | + | 0.134257i | ||||
\(833\) | −11.5665 | − | 11.5665i | −0.400756 | − | 0.400756i | ||||
\(834\) | 21.0572 | − | 6.06298i | 0.729150 | − | 0.209944i | ||||
\(835\) | −20.7383 | + | 19.5468i | −0.717677 | + | 0.676443i | ||||
\(836\) | − | 25.6720i | − | 0.887883i | ||||||
\(837\) | −36.8092 | + | 2.05025i | −1.27231 | + | 0.0708669i | ||||
\(838\) | 2.32975 | − | 2.32975i | 0.0804798 | − | 0.0804798i | ||||
\(839\) | −7.86161 | −0.271413 | −0.135706 | − | 0.990749i | \(-0.543330\pi\) | ||||
−0.135706 | + | 0.990749i | \(0.543330\pi\) | |||||||
\(840\) | 11.2910 | + | 6.68587i | 0.389578 | + | 0.230684i | ||||
\(841\) | 13.0578 | 0.450270 | ||||||||
\(842\) | 18.5866 | − | 18.5866i | 0.640537 | − | 0.640537i | ||||
\(843\) | −33.2446 | − | 18.3803i | −1.14501 | − | 0.633051i | ||||
\(844\) | 8.96557i | 0.308608i | ||||||||
\(845\) | 1.12337 | − | 37.9815i | 0.0386451 | − | 1.30660i | ||||
\(846\) | −12.2315 | + | 7.68038i | −0.420529 | + | 0.264057i | ||||
\(847\) | −7.73864 | − | 7.73864i | −0.265903 | − | 0.265903i | ||||
\(848\) | 1.15188 | + | 1.15188i | 0.0395557 | + | 0.0395557i | ||||
\(849\) | −1.06000 | − | 3.68147i | −0.0363792 | − | 0.126348i | ||||
\(850\) | −1.07916 | + | 18.2274i | −0.0370150 | + | 0.625196i | ||||
\(851\) | 6.63106i | 0.227310i | ||||||||
\(852\) | −7.76173 | + | 14.0387i | −0.265912 | + | 0.480959i | ||||
\(853\) | −22.8283 | + | 22.8283i | −0.781627 | + | 0.781627i | −0.980105 | − | 0.198478i | \(-0.936400\pi\) |
0.198478 | + | 0.980105i | \(0.436400\pi\) | |||||||
\(854\) | −39.5189 | −1.35231 | ||||||||
\(855\) | 39.3629 | − | 23.1230i | 1.34618 | − | 0.790788i | ||||
\(856\) | −10.0656 | −0.344035 | ||||||||
\(857\) | −32.4516 | + | 32.4516i | −1.10852 | + | 1.10852i | −0.115180 | + | 0.993345i | \(0.536744\pi\) |
−0.993345 | + | 0.115180i | \(0.963256\pi\) | |||||||
\(858\) | 17.3137 | − | 31.3155i | 0.591081 | − | 1.06909i | ||||
\(859\) | 35.0172i | 1.19477i | 0.801954 | + | 0.597386i | \(0.203794\pi\) | ||||
−0.801954 | + | 0.597386i | \(0.796206\pi\) | |||||||
\(860\) | 6.21977 | + | 6.59891i | 0.212092 | + | 0.225021i | ||||
\(861\) | 13.0494 | + | 45.3216i | 0.444724 | + | 1.54456i | ||||
\(862\) | 8.72855 | + | 8.72855i | 0.297296 | + | 0.297296i | ||||
\(863\) | −10.3748 | − | 10.3748i | −0.353162 | − | 0.353162i | 0.508123 | − | 0.861285i | \(-0.330340\pi\) |
−0.861285 | + | 0.508123i | \(0.830340\pi\) | |||||||
\(864\) | −3.46421 | + | 3.87288i | −0.117855 | + | 0.131758i | ||||
\(865\) | −31.9243 | − | 33.8702i | −1.08546 | − | 1.15162i | ||||
\(866\) | − | 5.94809i | − | 0.202124i | ||||||
\(867\) | −5.55365 | − | 3.07050i | −0.188612 | − | 0.104280i | ||||
\(868\) | −16.9976 | + | 16.9976i | −0.576937 | + | 0.576937i | ||||
\(869\) | 17.3416 | 0.588272 | ||||||||
\(870\) | 6.23301 | + | 24.3314i | 0.211319 | + | 0.824912i | ||||
\(871\) | 8.46892 | 0.286958 | ||||||||
\(872\) | 12.8147 | − | 12.8147i | 0.433961 | − | 0.433961i | ||||
\(873\) | −9.99077 | + | 43.7109i | −0.338136 | + | 1.47939i | ||||
\(874\) | 6.80541i | 0.230196i | ||||||||
\(875\) | 24.3071 | + | 29.0528i | 0.821730 | + | 0.982165i | ||||
\(876\) | 5.05580 | − | 1.45572i | 0.170820 | − | 0.0491841i | ||||
\(877\) | 39.1429 | + | 39.1429i | 1.32176 | + | 1.32176i | 0.912349 | + | 0.409413i | \(0.134267\pi\) |
0.409413 | + | 0.912349i | \(0.365733\pi\) | |||||||
\(878\) | −16.5435 | − | 16.5435i | −0.558315 | − | 0.558315i | ||||
\(879\) | −15.0568 | + | 4.33529i | −0.507853 | + | 0.146226i | ||||
\(880\) | −0.249374 | + | 8.43140i | −0.00840639 | + | 0.284223i | ||||
\(881\) | 16.8954i | 0.569221i | 0.958643 | + | 0.284611i | \(0.0918643\pi\) | ||||
−0.958643 | + | 0.284611i | \(0.908136\pi\) | |||||||
\(882\) | 2.99416 | − | 13.0998i | 0.100819 | − | 0.441095i | ||||
\(883\) | 3.79807 | − | 3.79807i | 0.127815 | − | 0.127815i | −0.640305 | − | 0.768121i | \(-0.721192\pi\) |
0.768121 | + | 0.640305i | \(0.221192\pi\) | |||||||
\(884\) | 19.9999 | 0.672669 | ||||||||
\(885\) | −1.95993 | + | 3.30992i | −0.0658824 | + | 0.111262i | ||||
\(886\) | 2.24762 | 0.0755103 | ||||||||
\(887\) | −1.76712 | + | 1.76712i | −0.0593341 | + | 0.0593341i | −0.736151 | − | 0.676817i | \(-0.763359\pi\) |
0.676817 | + | 0.736151i | \(0.263359\pi\) | |||||||
\(888\) | 10.0514 | + | 5.55721i | 0.337303 | + | 0.186488i | ||||
\(889\) | 22.6432i | 0.759430i | ||||||||
\(890\) | −15.5660 | + | 14.6717i | −0.521773 | + | 0.491795i | ||||
\(891\) | 30.5794 | + | 14.7493i | 1.02445 | + | 0.494120i | ||||
\(892\) | −15.5814 | − | 15.5814i | −0.521704 | − | 0.521704i | ||||
\(893\) | 23.1672 | + | 23.1672i | 0.775262 | + | 0.775262i | ||||
\(894\) | −6.59339 | − | 22.8993i | −0.220516 | − | 0.765867i | ||||
\(895\) | −13.6081 | − | 0.402483i | −0.454868 | − | 0.0134535i | ||||
\(896\) | 3.38810i | 0.113188i | ||||||||
\(897\) | −4.58971 | + | 8.30147i | −0.153246 | + | 0.277178i | ||||
\(898\) | −15.5925 | + | 15.5925i | −0.520328 | + | 0.520328i | ||||
\(899\) | −46.0119 | −1.53458 | ||||||||
\(900\) | −13.1525 | + | 7.21187i | −0.438418 | + | 0.240396i | ||||
\(901\) | 5.94892 | 0.198187 | ||||||||
\(902\) | −21.4375 | + | 21.4375i | −0.713790 | + | 0.713790i | ||||
\(903\) | 11.5150 | − | 20.8273i | 0.383194 | − | 0.693088i | ||||
\(904\) | 20.6406i | 0.686495i | ||||||||
\(905\) | −24.8643 | − | 0.735406i | −0.826517 | − | 0.0244457i | ||||
\(906\) | −0.778487 | − | 2.70374i | −0.0258635 | − | 0.0898258i | ||||
\(907\) | 1.92387 | + | 1.92387i | 0.0638810 | + | 0.0638810i | 0.738326 | − | 0.674445i | \(-0.235617\pi\) |
−0.674445 | + | 0.738326i | \(0.735617\pi\) | |||||||
\(908\) | 17.4824 | + | 17.4824i | 0.580173 | + | 0.580173i | ||||
\(909\) | 7.87493 | − | 4.94479i | 0.261195 | − | 0.164008i | ||||
\(910\) | 30.1931 | − | 28.4583i | 1.00089 | − | 0.943385i | ||||
\(911\) | − | 15.9216i | − | 0.527508i | −0.964590 | − | 0.263754i | \(-0.915039\pi\) | ||
0.964590 | − | 0.263754i | \(-0.0849607\pi\) | |||||||
\(912\) | 10.3157 | + | 5.70332i | 0.341586 | + | 0.188856i | ||||
\(913\) | −19.6288 | + | 19.6288i | −0.649620 | + | 0.649620i | ||||
\(914\) | 37.3102 | 1.23411 | ||||||||
\(915\) | 23.0171 | − | 38.8711i | 0.760921 | − | 1.28504i | ||||
\(916\) | 9.74724 | 0.322058 | ||||||||
\(917\) | 22.9938 | − | 22.9938i | 0.759321 | − | 0.759321i | ||||
\(918\) | 1.05530 | + | 18.9463i | 0.0348300 | + | 0.625322i | ||||
\(919\) | 16.0962i | 0.530965i | 0.964116 | + | 0.265483i | \(0.0855313\pi\) | ||||
−0.964116 | + | 0.265483i | \(0.914469\pi\) | |||||||
\(920\) | 0.0661068 | − | 2.23509i | 0.00217948 | − | 0.0736888i | ||||
\(921\) | 41.2688 | − | 11.8825i | 1.35985 | − | 0.391542i | ||||
\(922\) | −8.63406 | − | 8.63406i | −0.284348 | − | 0.284348i | ||||
\(923\) | 35.8659 | + | 35.8659i | 1.18054 | + | 1.18054i | ||||
\(924\) | 21.2729 | − | 6.12510i | 0.699827 | − | 0.201501i | ||||
\(925\) | 22.0178 | + | 24.7890i | 0.723940 | + | 0.815056i | ||||
\(926\) | − | 17.9830i | − | 0.590959i | ||||||
\(927\) | 20.2433 | + | 4.62692i | 0.664879 | + | 0.151968i | ||||
\(928\) | −4.58573 | + | 4.58573i | −0.150534 | + | 0.150534i | ||||
\(929\) | 30.0036 | 0.984388 | 0.492194 | − | 0.870486i | \(-0.336195\pi\) | ||||
0.492194 | + | 0.870486i | \(0.336195\pi\) | |||||||
\(930\) | −6.81901 | − | 26.6189i | −0.223604 | − | 0.872870i | ||||
\(931\) | −30.4829 | −0.999038 | ||||||||
\(932\) | 6.27349 | − | 6.27349i | 0.205495 | − | 0.205495i | ||||
\(933\) | −1.56010 | − | 0.862548i | −0.0510754 | − | 0.0282386i | ||||
\(934\) | 19.5256i | 0.638896i | ||||||||
\(935\) | 21.1282 | + | 22.4161i | 0.690965 | + | 0.733083i | ||||
\(936\) | 8.73695 | + | 13.9142i | 0.285576 | + | 0.454800i | ||||
\(937\) | 6.00639 | + | 6.00639i | 0.196220 | + | 0.196220i | 0.798378 | − | 0.602157i | \(-0.205692\pi\) |
−0.602157 | + | 0.798378i | \(0.705692\pi\) | |||||||
\(938\) | 3.70473 | + | 3.70473i | 0.120964 | + | 0.120964i | ||||
\(939\) | −3.49246 | − | 12.1296i | −0.113972 | − | 0.395833i | ||||
\(940\) | −7.38374 | − | 7.83382i | −0.240831 | − | 0.255511i | ||||
\(941\) | 53.2449i | 1.73573i | 0.496796 | + | 0.867867i | \(0.334510\pi\) | ||||
−0.496796 | + | 0.867867i | \(0.665490\pi\) | |||||||
\(942\) | 15.3863 | − | 27.8293i | 0.501312 | − | 0.906728i | ||||
\(943\) | 5.68288 | − | 5.68288i | 0.185060 | − | 0.185060i | ||||
\(944\) | −0.993207 | −0.0323261 | ||||||||
\(945\) | 28.5523 | + | 27.1009i | 0.928807 | + | 0.881593i | ||||
\(946\) | 15.2981 | 0.497385 | ||||||||
\(947\) | 13.3329 | − | 13.3329i | 0.433261 | − | 0.433261i | −0.456475 | − | 0.889736i | \(-0.650888\pi\) |
0.889736 | + | 0.456475i | \(0.150888\pi\) | |||||||
\(948\) | −3.85263 | + | 6.96829i | −0.125127 | + | 0.226320i | ||||
\(949\) | − | 16.6355i | − | 0.540012i | ||||||
\(950\) | 22.5967 | + | 25.4407i | 0.733133 | + | 0.825406i | ||||
\(951\) | 1.45845 | + | 5.06530i | 0.0472935 | + | 0.164254i | ||||
\(952\) | 8.74897 | + | 8.74897i | 0.283556 | + | 0.283556i | ||||
\(953\) | −7.38618 | − | 7.38618i | −0.239262 | − | 0.239262i | 0.577283 | − | 0.816544i | \(-0.304113\pi\) |
−0.816544 | + | 0.577283i | \(0.804113\pi\) | |||||||
\(954\) | 2.59878 | + | 4.13875i | 0.0841387 | + | 0.133997i | ||||
\(955\) | 0.371142 | − | 12.5484i | 0.0120099 | − | 0.406057i | ||||
\(956\) | − | 23.7283i | − | 0.767428i | ||||||
\(957\) | 37.0827 | + | 20.5023i | 1.19871 | + | 0.662744i | ||||
\(958\) | −8.81037 | + | 8.81037i | −0.284650 | + | 0.284650i | ||||
\(959\) | 25.3719 | 0.819301 | ||||||||
\(960\) | −3.33256 | − | 1.97334i | −0.107558 | − | 0.0636892i | ||||
\(961\) | 19.3378 | 0.623801 | ||||||||
\(962\) | 25.6791 | − | 25.6791i | 0.827928 | − | 0.827928i | ||||
\(963\) | −29.4376 | − | 6.72840i | −0.948614 | − | 0.216820i | ||||
\(964\) | − | 6.12180i | − | 0.197170i | ||||||
\(965\) | 22.4919 | − | 21.1997i | 0.724041 | − | 0.682442i | ||||
\(966\) | −5.63926 | + | 1.62371i | −0.181440 | + | 0.0522420i | ||||
\(967\) | 1.76939 | + | 1.76939i | 0.0568999 | + | 0.0568999i | 0.734984 | − | 0.678084i | \(-0.237190\pi\) |
−0.678084 | + | 0.734984i | \(0.737190\pi\) | |||||||
\(968\) | 2.28406 | + | 2.28406i | 0.0734126 | + | 0.0734126i | ||||
\(969\) | 41.3652 | − | 11.9103i | 1.32884 | − | 0.382613i | ||||
\(970\) | −33.4058 | − | 0.988035i | −1.07259 | − | 0.0317239i | ||||
\(971\) | − | 53.9969i | − | 1.73284i | −0.499314 | − | 0.866421i | \(-0.666414\pi\) | ||
0.499314 | − | 0.866421i | \(-0.333586\pi\) | |||||||
\(972\) | −12.7202 | + | 9.01088i | −0.408001 | + | 0.289024i | ||||
\(973\) | 30.3093 | − | 30.3093i | 0.971670 | − | 0.971670i | ||||
\(974\) | −2.55502 | −0.0818682 | ||||||||
\(975\) | 10.4064 | + | 46.2731i | 0.333271 | + | 1.48193i | ||||
\(976\) | 11.6640 | 0.373357 | ||||||||
\(977\) | 6.00002 | − | 6.00002i | 0.191958 | − | 0.191958i | −0.604584 | − | 0.796541i | \(-0.706661\pi\) |
0.796541 | + | 0.604584i | \(0.206661\pi\) | |||||||
\(978\) | −12.2616 | − | 6.77917i | −0.392082 | − | 0.216774i | ||||
\(979\) | 36.0863i | 1.15332i | ||||||||
\(980\) | 10.0115 | + | 0.296107i | 0.319805 | + | 0.00945879i | ||||
\(981\) | 46.0437 | − | 28.9116i | 1.47006 | − | 0.923076i | ||||
\(982\) | −19.8085 | − | 19.8085i | −0.632116 | − | 0.632116i | ||||
\(983\) | −11.3165 | − | 11.3165i | −0.360940 | − | 0.360940i | 0.503219 | − | 0.864159i | \(-0.332149\pi\) |
−0.864159 | + | 0.503219i | \(0.832149\pi\) | |||||||
\(984\) | −3.85155 | − | 13.3767i | −0.122783 | − | 0.426434i | ||||
\(985\) | −2.60150 | + | 2.45203i | −0.0828906 | + | 0.0781282i | ||||
\(986\) | 23.6831i | 0.754224i | ||||||||
\(987\) | −13.6699 | + | 24.7249i | −0.435117 | + | 0.787001i | ||||
\(988\) | 26.3543 | − | 26.3543i | 0.838442 | − | 0.838442i | ||||
\(989\) | −4.05539 | −0.128954 | ||||||||
\(990\) | −6.36534 | + | 24.4916i | −0.202304 | + | 0.778395i | ||||
\(991\) | −28.3161 | −0.899490 | −0.449745 | − | 0.893157i | \(-0.648485\pi\) | ||||
−0.449745 | + | 0.893157i | \(0.648485\pi\) | |||||||
\(992\) | 5.01686 | − | 5.01686i | 0.159286 | − | 0.159286i | ||||
\(993\) | 8.40480 | − | 15.2019i | 0.266718 | − | 0.482416i | ||||
\(994\) | 31.3791i | 0.995286i | ||||||||
\(995\) | −0.306501 | + | 10.3629i | −0.00971675 | + | 0.328526i | ||||
\(996\) | −3.52661 | − | 12.2481i | −0.111745 | − | 0.388097i | ||||
\(997\) | −25.6038 | − | 25.6038i | −0.810882 | − | 0.810882i | 0.173884 | − | 0.984766i | \(-0.444368\pi\) |
−0.984766 | + | 0.173884i | \(0.944368\pi\) | |||||||
\(998\) | 18.8922 | + | 18.8922i | 0.598023 | + | 0.598023i | ||||
\(999\) | 25.6813 | + | 22.9714i | 0.812522 | + | 0.726783i |
(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 | 690.2.i.f.47.11 | yes | 32 | |
3.2 | odd | 2 | inner | 690.2.i.f.47.2 | ✓ | 32 | |
5.3 | odd | 4 | inner | 690.2.i.f.323.2 | yes | 32 | |
15.8 | even | 4 | inner | 690.2.i.f.323.11 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.i.f.47.2 | ✓ | 32 | 3.2 | odd | 2 | inner | |
690.2.i.f.47.11 | yes | 32 | 1.1 | even | 1 | trivial | |
690.2.i.f.323.2 | yes | 32 | 5.3 | odd | 4 | inner | |
690.2.i.f.323.11 | yes | 32 | 15.8 | even | 4 | inner |