Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.324000000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) |
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 | 366.2 | ||
Root | \(-0.535233 - 1.64728i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.366 |
Dual form | 605.2.g.h.81.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.40126 | − | 1.01807i | 0.990839 | − | 0.719887i | 0.0307347 | − | 0.999528i | \(-0.490215\pi\) |
0.960105 | + | 0.279641i | \(0.0902153\pi\) | |||||||
\(3\) | 0.618034 | + | 1.90211i | 0.356822 | + | 1.09819i | 0.954945 | + | 0.296781i | \(0.0959133\pi\) |
−0.598123 | + | 0.801404i | \(0.704087\pi\) | |||||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | −0.809017 | − | 0.587785i | −0.361803 | − | 0.262866i | ||||
\(6\) | 2.80252 | + | 2.03615i | 1.14412 | + | 0.831254i | ||||
\(7\) | −1.07047 | + | 3.29456i | −0.404598 | + | 1.24523i | 0.516632 | + | 0.856208i | \(0.327186\pi\) |
−0.921230 | + | 0.389018i | \(0.872814\pi\) | |||||||
\(8\) | 0.535233 | + | 1.64728i | 0.189233 | + | 0.582401i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | −1.73205 | −0.547723 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.00000 | 0.577350 | ||||||||
\(13\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(14\) | 1.85410 | + | 5.70634i | 0.495530 | + | 1.52508i | ||||
\(15\) | 0.618034 | − | 1.90211i | 0.159576 | − | 0.491123i | ||||
\(16\) | 4.04508 | + | 2.93893i | 1.01127 | + | 0.734732i | ||||
\(17\) | −5.60503 | − | 4.07230i | −1.35942 | − | 0.987677i | −0.998482 | − | 0.0550873i | \(-0.982456\pi\) |
−0.360939 | − | 0.932589i | \(-0.617544\pi\) | |||||||
\(18\) | −0.535233 | + | 1.64728i | −0.126156 | + | 0.388267i | ||||
\(19\) | 2.14093 | + | 6.58911i | 0.491164 | + | 1.51165i | 0.822851 | + | 0.568257i | \(0.192382\pi\) |
−0.331688 | + | 0.943389i | \(0.607618\pi\) | |||||||
\(20\) | −0.809017 | + | 0.587785i | −0.180902 | + | 0.131433i | ||||
\(21\) | −6.92820 | −1.51186 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.00000 | 1.25109 | 0.625543 | − | 0.780189i | \(-0.284877\pi\) | ||||
0.625543 | + | 0.780189i | \(0.284877\pi\) | |||||||
\(24\) | −2.80252 | + | 2.03615i | −0.572061 | + | 0.415627i | ||||
\(25\) | 0.309017 | + | 0.951057i | 0.0618034 | + | 0.190211i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.23607 | + | 2.35114i | 0.622782 | + | 0.452477i | ||||
\(28\) | 2.80252 | + | 2.03615i | 0.529626 | + | 0.384796i | ||||
\(29\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(30\) | −1.07047 | − | 3.29456i | −0.195440 | − | 0.601501i | ||||
\(31\) | −3.23607 | + | 2.35114i | −0.581215 | + | 0.422277i | −0.839162 | − | 0.543882i | \(-0.816954\pi\) |
0.257947 | + | 0.966159i | \(0.416954\pi\) | |||||||
\(32\) | 5.19615 | 0.918559 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12.0000 | −2.05798 | ||||||||
\(35\) | 2.80252 | − | 2.03615i | 0.473712 | − | 0.344172i | ||||
\(36\) | 0.309017 | + | 0.951057i | 0.0515028 | + | 0.158509i | ||||
\(37\) | 3.09017 | − | 9.51057i | 0.508021 | − | 1.56353i | −0.287611 | − | 0.957747i | \(-0.592861\pi\) |
0.795632 | − | 0.605780i | \(-0.207139\pi\) | |||||||
\(38\) | 9.70820 | + | 7.05342i | 1.57488 | + | 1.14422i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.535233 | − | 1.64728i | 0.0846278 | − | 0.260458i | ||||
\(41\) | −2.14093 | − | 6.58911i | −0.334357 | − | 1.02905i | −0.967038 | − | 0.254633i | \(-0.918045\pi\) |
0.632680 | − | 0.774413i | \(-0.281955\pi\) | |||||||
\(42\) | −9.70820 | + | 7.05342i | −1.49801 | + | 1.08837i | ||||
\(43\) | 3.46410 | 0.528271 | 0.264135 | − | 0.964486i | \(-0.414913\pi\) | ||||
0.264135 | + | 0.964486i | \(0.414913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 8.40755 | − | 6.10844i | 1.23963 | − | 0.900641i | ||||
\(47\) | −1.85410 | − | 5.70634i | −0.270449 | − | 0.832355i | −0.990388 | − | 0.138318i | \(-0.955830\pi\) |
0.719939 | − | 0.694037i | \(-0.244170\pi\) | |||||||
\(48\) | −3.09017 | + | 9.51057i | −0.446028 | + | 1.37273i | ||||
\(49\) | −4.04508 | − | 2.93893i | −0.577869 | − | 0.419847i | ||||
\(50\) | 1.40126 | + | 1.01807i | 0.198168 | + | 0.143977i | ||||
\(51\) | 4.28187 | − | 13.1782i | 0.599581 | − | 1.84532i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.85410 | − | 3.52671i | 0.666762 | − | 0.484431i | −0.202178 | − | 0.979349i | \(-0.564802\pi\) |
0.868940 | + | 0.494918i | \(0.164802\pi\) | |||||||
\(54\) | 6.92820 | 0.942809 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.00000 | −0.801784 | ||||||||
\(57\) | −11.2101 | + | 8.14459i | −1.48481 | + | 1.07878i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(60\) | −1.61803 | − | 1.17557i | −0.208887 | − | 0.151765i | ||||
\(61\) | 5.60503 | + | 4.07230i | 0.717651 | + | 0.521404i | 0.885633 | − | 0.464386i | \(-0.153725\pi\) |
−0.167982 | + | 0.985790i | \(0.553725\pi\) | |||||||
\(62\) | −2.14093 | + | 6.58911i | −0.271899 | + | 0.836818i | ||||
\(63\) | −1.07047 | − | 3.29456i | −0.134866 | − | 0.415075i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0000 | 1.22169 | 0.610847 | − | 0.791748i | \(-0.290829\pi\) | ||||
0.610847 | + | 0.791748i | \(0.290829\pi\) | |||||||
\(68\) | −5.60503 | + | 4.07230i | −0.679710 | + | 0.493838i | ||||
\(69\) | 3.70820 | + | 11.4127i | 0.446415 | + | 1.37393i | ||||
\(70\) | 1.85410 | − | 5.70634i | 0.221608 | − | 0.682038i | ||||
\(71\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(72\) | −1.40126 | − | 1.01807i | −0.165140 | − | 0.119981i | ||||
\(73\) | 2.14093 | − | 6.58911i | 0.250577 | − | 0.771197i | −0.744092 | − | 0.668077i | \(-0.767117\pi\) |
0.994669 | − | 0.103120i | \(-0.0328825\pi\) | |||||||
\(74\) | −5.35233 | − | 16.4728i | −0.622196 | − | 1.91492i | ||||
\(75\) | −1.61803 | + | 1.17557i | −0.186834 | + | 0.135743i | ||||
\(76\) | 6.92820 | 0.794719 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.60503 | + | 4.07230i | −0.630616 | + | 0.458169i | −0.856613 | − | 0.515959i | \(-0.827436\pi\) |
0.225998 | + | 0.974128i | \(0.427436\pi\) | |||||||
\(80\) | −1.54508 | − | 4.75528i | −0.172746 | − | 0.531657i | ||||
\(81\) | −3.39919 | + | 10.4616i | −0.377687 | + | 1.16240i | ||||
\(82\) | −9.70820 | − | 7.05342i | −1.07209 | − | 0.778920i | ||||
\(83\) | −14.0126 | − | 10.1807i | −1.53808 | − | 1.11748i | −0.951524 | − | 0.307573i | \(-0.900483\pi\) |
−0.586557 | − | 0.809908i | \(-0.699517\pi\) | |||||||
\(84\) | −2.14093 | + | 6.58911i | −0.233595 | + | 0.718931i | ||||
\(85\) | 2.14093 | + | 6.58911i | 0.232217 | + | 0.714690i | ||||
\(86\) | 4.85410 | − | 3.52671i | 0.523431 | − | 0.380295i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 1.40126 | − | 1.01807i | 0.147706 | − | 0.107314i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.85410 | − | 5.70634i | 0.193303 | − | 0.594927i | ||||
\(93\) | −6.47214 | − | 4.70228i | −0.671129 | − | 0.487604i | ||||
\(94\) | −8.40755 | − | 6.10844i | −0.867173 | − | 0.630038i | ||||
\(95\) | 2.14093 | − | 6.58911i | 0.219655 | − | 0.676029i | ||||
\(96\) | 3.21140 | + | 9.88367i | 0.327762 | + | 1.00875i | ||||
\(97\) | 8.09017 | − | 5.87785i | 0.821432 | − | 0.596806i | −0.0956901 | − | 0.995411i | \(-0.530506\pi\) |
0.917122 | + | 0.398606i | \(0.130506\pi\) | |||||||
\(98\) | −8.66025 | −0.874818 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 11.2101 | − | 8.14459i | 1.11544 | − | 0.810417i | 0.131931 | − | 0.991259i | \(-0.457882\pi\) |
0.983512 | + | 0.180842i | \(0.0578822\pi\) | |||||||
\(102\) | −7.41641 | − | 22.8254i | −0.734334 | − | 2.26005i | ||||
\(103\) | 0.618034 | − | 1.90211i | 0.0608967 | − | 0.187421i | −0.915980 | − | 0.401224i | \(-0.868585\pi\) |
0.976877 | + | 0.213803i | \(0.0685850\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.60503 | + | 4.07230i | 0.546995 | + | 0.397415i | ||||
\(106\) | 3.21140 | − | 9.88367i | 0.311919 | − | 0.959987i | ||||
\(107\) | 1.07047 | + | 3.29456i | 0.103486 | + | 0.318497i | 0.989372 | − | 0.145406i | \(-0.0464488\pi\) |
−0.885886 | + | 0.463903i | \(0.846449\pi\) | |||||||
\(108\) | 3.23607 | − | 2.35114i | 0.311391 | − | 0.226239i | ||||
\(109\) | −6.92820 | −0.663602 | −0.331801 | − | 0.943349i | \(-0.607656\pi\) | ||||
−0.331801 | + | 0.943349i | \(0.607656\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 20.0000 | 1.89832 | ||||||||
\(112\) | −14.0126 | + | 10.1807i | −1.32406 | + | 0.961989i | ||||
\(113\) | 1.85410 | + | 5.70634i | 0.174419 | + | 0.536807i | 0.999606 | − | 0.0280521i | \(-0.00893043\pi\) |
−0.825187 | + | 0.564859i | \(0.808930\pi\) | |||||||
\(114\) | −7.41641 | + | 22.8254i | −0.694610 | + | 2.13779i | ||||
\(115\) | −4.85410 | − | 3.52671i | −0.452647 | − | 0.328868i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.4164 | − | 14.1068i | 1.77990 | − | 1.29317i | ||||
\(120\) | 3.46410 | 0.316228 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 12.0000 | 1.08643 | ||||||||
\(123\) | 11.2101 | − | 8.14459i | 1.01078 | − | 0.734373i | ||||
\(124\) | 1.23607 | + | 3.80423i | 0.111002 | + | 0.341630i | ||||
\(125\) | 0.309017 | − | 0.951057i | 0.0276393 | − | 0.0850651i | ||||
\(126\) | −4.85410 | − | 3.52671i | −0.432438 | − | 0.314184i | ||||
\(127\) | 8.40755 | + | 6.10844i | 0.746050 | + | 0.542037i | 0.894600 | − | 0.446868i | \(-0.147461\pi\) |
−0.148550 | + | 0.988905i | \(0.547461\pi\) | |||||||
\(128\) | −3.74663 | + | 11.5309i | −0.331159 | + | 1.01920i | ||||
\(129\) | 2.14093 | + | 6.58911i | 0.188499 | + | 0.580139i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.92820 | −0.605320 | −0.302660 | − | 0.953099i | \(-0.597875\pi\) | ||||
−0.302660 | + | 0.953099i | \(0.597875\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.0000 | −2.08106 | ||||||||
\(134\) | 14.0126 | − | 10.1807i | 1.21050 | − | 0.879482i | ||||
\(135\) | −1.23607 | − | 3.80423i | −0.106384 | − | 0.327416i | ||||
\(136\) | 3.70820 | − | 11.4127i | 0.317976 | − | 0.978629i | ||||
\(137\) | −4.85410 | − | 3.52671i | −0.414714 | − | 0.301307i | 0.360794 | − | 0.932646i | \(-0.382506\pi\) |
−0.775507 | + | 0.631338i | \(0.782506\pi\) | |||||||
\(138\) | 16.8151 | + | 12.2169i | 1.43140 | + | 1.03997i | ||||
\(139\) | −4.28187 | + | 13.1782i | −0.363183 | + | 1.11776i | 0.587928 | + | 0.808913i | \(0.299944\pi\) |
−0.951111 | + | 0.308849i | \(0.900056\pi\) | |||||||
\(140\) | −1.07047 | − | 3.29456i | −0.0904709 | − | 0.278441i | ||||
\(141\) | 9.70820 | − | 7.05342i | 0.817578 | − | 0.594005i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −5.00000 | −0.416667 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.70820 | − | 11.4127i | −0.306893 | − | 0.944520i | ||||
\(147\) | 3.09017 | − | 9.51057i | 0.254873 | − | 0.784418i | ||||
\(148\) | −8.09017 | − | 5.87785i | −0.665008 | − | 0.483157i | ||||
\(149\) | 5.60503 | + | 4.07230i | 0.459182 | + | 0.333615i | 0.793210 | − | 0.608948i | \(-0.208408\pi\) |
−0.334028 | + | 0.942563i | \(0.608408\pi\) | |||||||
\(150\) | −1.07047 | + | 3.29456i | −0.0874032 | + | 0.268999i | ||||
\(151\) | −2.14093 | − | 6.58911i | −0.174227 | − | 0.536214i | 0.825371 | − | 0.564591i | \(-0.190966\pi\) |
−0.999597 | + | 0.0283768i | \(0.990966\pi\) | |||||||
\(152\) | −9.70820 | + | 7.05342i | −0.787439 | + | 0.572108i | ||||
\(153\) | 6.92820 | 0.560112 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.618034 | − | 1.90211i | −0.0493245 | − | 0.151805i | 0.923361 | − | 0.383934i | \(-0.125431\pi\) |
−0.972685 | + | 0.232129i | \(0.925431\pi\) | |||||||
\(158\) | −3.70820 | + | 11.4127i | −0.295009 | + | 0.907944i | ||||
\(159\) | 9.70820 | + | 7.05342i | 0.769911 | + | 0.559373i | ||||
\(160\) | −4.20378 | − | 3.05422i | −0.332338 | − | 0.241457i | ||||
\(161\) | −6.42280 | + | 19.7673i | −0.506187 | + | 1.55788i | ||||
\(162\) | 5.88756 | + | 18.1201i | 0.462571 | + | 1.42365i | ||||
\(163\) | −1.61803 | + | 1.17557i | −0.126734 | + | 0.0920778i | −0.649347 | − | 0.760493i | \(-0.724958\pi\) |
0.522612 | + | 0.852570i | \(0.324958\pi\) | |||||||
\(164\) | −6.92820 | −0.541002 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −30.0000 | −2.32845 | ||||||||
\(167\) | 8.40755 | − | 6.10844i | 0.650596 | − | 0.472686i | −0.212878 | − | 0.977079i | \(-0.568284\pi\) |
0.863474 | + | 0.504393i | \(0.168284\pi\) | |||||||
\(168\) | −3.70820 | − | 11.4127i | −0.286094 | − | 0.880507i | ||||
\(169\) | −4.01722 | + | 12.3637i | −0.309017 | + | 0.951057i | ||||
\(170\) | 9.70820 | + | 7.05342i | 0.744585 | + | 0.540973i | ||||
\(171\) | −5.60503 | − | 4.07230i | −0.428628 | − | 0.311416i | ||||
\(172\) | 1.07047 | − | 3.29456i | 0.0816223 | − | 0.251208i | ||||
\(173\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.46410 | −0.261861 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.40755 | + | 6.10844i | −0.630173 | + | 0.457847i | ||||
\(179\) | −3.70820 | − | 11.4127i | −0.277164 | − | 0.853024i | −0.988639 | − | 0.150312i | \(-0.951972\pi\) |
0.711474 | − | 0.702712i | \(-0.248028\pi\) | |||||||
\(180\) | 0.309017 | − | 0.951057i | 0.0230328 | − | 0.0708876i | ||||
\(181\) | −11.3262 | − | 8.22899i | −0.841873 | − | 0.611656i | 0.0810205 | − | 0.996712i | \(-0.474182\pi\) |
−0.922893 | + | 0.385056i | \(0.874182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.28187 | + | 13.1782i | −0.316525 | + | 0.974162i | ||||
\(184\) | 3.21140 | + | 9.88367i | 0.236747 | + | 0.728634i | ||||
\(185\) | −8.09017 | + | 5.87785i | −0.594801 | + | 0.432148i | ||||
\(186\) | −13.8564 | −1.01600 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | −11.2101 | + | 8.14459i | −0.815412 | + | 0.592432i | ||||
\(190\) | −3.70820 | − | 11.4127i | −0.269021 | − | 0.827963i | ||||
\(191\) | −3.70820 | + | 11.4127i | −0.268316 | + | 0.825792i | 0.722595 | + | 0.691272i | \(0.242949\pi\) |
−0.990911 | + | 0.134520i | \(0.957051\pi\) | |||||||
\(192\) | −1.61803 | − | 1.17557i | −0.116772 | − | 0.0848395i | ||||
\(193\) | −5.60503 | − | 4.07230i | −0.403459 | − | 0.293130i | 0.367489 | − | 0.930028i | \(-0.380217\pi\) |
−0.770949 | + | 0.636897i | \(0.780217\pi\) | |||||||
\(194\) | 5.35233 | − | 16.4728i | 0.384275 | − | 1.18268i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.04508 | + | 2.93893i | −0.288935 | + | 0.209923i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.00000 | 0.283552 | 0.141776 | − | 0.989899i | \(-0.454719\pi\) | ||||
0.141776 | + | 0.989899i | \(0.454719\pi\) | |||||||
\(200\) | −1.40126 | + | 1.01807i | −0.0990839 | + | 0.0719887i | ||||
\(201\) | 6.18034 | + | 19.0211i | 0.435928 | + | 1.34165i | ||||
\(202\) | 7.41641 | − | 22.8254i | 0.521817 | − | 1.60599i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −11.2101 | − | 8.14459i | −0.784862 | − | 0.570235i | ||||
\(205\) | −2.14093 | + | 6.58911i | −0.149529 | + | 0.460204i | ||||
\(206\) | −1.07047 | − | 3.29456i | −0.0745829 | − | 0.229543i | ||||
\(207\) | −4.85410 | + | 3.52671i | −0.337383 | + | 0.245123i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 12.0000 | 0.828079 | ||||||||
\(211\) | −16.8151 | + | 12.2169i | −1.15760 | + | 0.841045i | −0.989473 | − | 0.144720i | \(-0.953772\pi\) |
−0.168127 | + | 0.985765i | \(0.553772\pi\) | |||||||
\(212\) | −1.85410 | − | 5.70634i | −0.127340 | − | 0.391913i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.85410 | + | 3.52671i | 0.331820 | + | 0.241081i | ||||
\(215\) | −2.80252 | − | 2.03615i | −0.191130 | − | 0.138864i | ||||
\(216\) | −2.14093 | + | 6.58911i | −0.145672 | + | 0.448332i | ||||
\(217\) | −4.28187 | − | 13.1782i | −0.290672 | − | 0.894596i | ||||
\(218\) | −9.70820 | + | 7.05342i | −0.657523 | + | 0.477718i | ||||
\(219\) | 13.8564 | 0.936329 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 28.0252 | − | 20.3615i | 1.88093 | − | 1.36657i | ||||
\(223\) | 4.32624 | + | 13.3148i | 0.289706 | + | 0.891624i | 0.984948 | + | 0.172849i | \(0.0552972\pi\) |
−0.695242 | + | 0.718776i | \(0.744703\pi\) | |||||||
\(224\) | −5.56231 | + | 17.1190i | −0.371647 | + | 1.14381i | ||||
\(225\) | −0.809017 | − | 0.587785i | −0.0539345 | − | 0.0391857i | ||||
\(226\) | 8.40755 | + | 6.10844i | 0.559262 | + | 0.406328i | ||||
\(227\) | −1.07047 | + | 3.29456i | −0.0710493 | + | 0.218667i | −0.980276 | − | 0.197635i | \(-0.936674\pi\) |
0.909226 | + | 0.416302i | \(0.136674\pi\) | |||||||
\(228\) | 4.28187 | + | 13.1782i | 0.283573 | + | 0.872749i | ||||
\(229\) | 1.61803 | − | 1.17557i | 0.106923 | − | 0.0776839i | −0.533039 | − | 0.846091i | \(-0.678950\pi\) |
0.639962 | + | 0.768407i | \(0.278950\pi\) | |||||||
\(230\) | −10.3923 | −0.685248 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.60503 | − | 4.07230i | 0.367198 | − | 0.266785i | −0.388850 | − | 0.921301i | \(-0.627128\pi\) |
0.756048 | + | 0.654516i | \(0.227128\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.85410 | + | 5.70634i | −0.120948 | + | 0.372241i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.2101 | − | 8.14459i | −0.728172 | − | 0.529048i | ||||
\(238\) | 12.8456 | − | 39.5347i | 0.832656 | − | 2.56265i | ||||
\(239\) | 2.14093 | + | 6.58911i | 0.138485 | + | 0.426214i | 0.996116 | − | 0.0880522i | \(-0.0280642\pi\) |
−0.857630 | + | 0.514266i | \(0.828064\pi\) | |||||||
\(240\) | 8.09017 | − | 5.87785i | 0.522218 | − | 0.379414i | ||||
\(241\) | 20.7846 | 1.33885 | 0.669427 | − | 0.742878i | \(-0.266540\pi\) | ||||
0.669427 | + | 0.742878i | \(0.266540\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.0000 | −0.641500 | ||||||||
\(244\) | 5.60503 | − | 4.07230i | 0.358826 | − | 0.260702i | ||||
\(245\) | 1.54508 | + | 4.75528i | 0.0987119 | + | 0.303804i | ||||
\(246\) | 7.41641 | − | 22.8254i | 0.472853 | − | 1.45529i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5.60503 | − | 4.07230i | −0.355920 | − | 0.258591i | ||||
\(249\) | 10.7047 | − | 32.9456i | 0.678380 | − | 2.08784i | ||||
\(250\) | −0.535233 | − | 1.64728i | −0.0338511 | − | 0.104183i | ||||
\(251\) | −9.70820 | + | 7.05342i | −0.612776 | + | 0.445208i | −0.850391 | − | 0.526151i | \(-0.823635\pi\) |
0.237614 | + | 0.971360i | \(0.423635\pi\) | |||||||
\(252\) | −3.46410 | −0.218218 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 18.0000 | 1.12942 | ||||||||
\(255\) | −11.2101 | + | 8.14459i | −0.702002 | + | 0.510034i | ||||
\(256\) | 5.87132 | + | 18.0701i | 0.366958 | + | 1.12938i | ||||
\(257\) | −1.85410 | + | 5.70634i | −0.115656 | + | 0.355952i | −0.992083 | − | 0.125582i | \(-0.959920\pi\) |
0.876428 | + | 0.481534i | \(0.159920\pi\) | |||||||
\(258\) | 9.70820 | + | 7.05342i | 0.604406 | + | 0.439127i | ||||
\(259\) | 28.0252 | + | 20.3615i | 1.74140 | + | 1.26520i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.70820 | + | 7.05342i | −0.599775 | + | 0.435762i | ||||
\(263\) | −3.46410 | −0.213606 | −0.106803 | − | 0.994280i | \(-0.534061\pi\) | ||||
−0.106803 | + | 0.994280i | \(0.534061\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | −33.6302 | + | 24.4338i | −2.06200 | + | 1.49813i | ||||
\(267\) | −3.70820 | − | 11.4127i | −0.226938 | − | 0.698445i | ||||
\(268\) | 3.09017 | − | 9.51057i | 0.188762 | − | 0.580950i | ||||
\(269\) | 24.2705 | + | 17.6336i | 1.47980 | + | 1.07514i | 0.977621 | + | 0.210373i | \(0.0674677\pi\) |
0.502178 | + | 0.864764i | \(0.332532\pi\) | |||||||
\(270\) | −5.60503 | − | 4.07230i | −0.341112 | − | 0.247832i | ||||
\(271\) | −2.14093 | + | 6.58911i | −0.130052 | + | 0.400260i | −0.994788 | − | 0.101968i | \(-0.967486\pi\) |
0.864735 | + | 0.502228i | \(0.167486\pi\) | |||||||
\(272\) | −10.7047 | − | 32.9456i | −0.649066 | − | 1.99762i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.3923 | −0.627822 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 12.0000 | 0.722315 | ||||||||
\(277\) | 22.4201 | − | 16.2892i | 1.34710 | − | 0.978722i | 0.347945 | − | 0.937515i | \(-0.386880\pi\) |
0.999151 | − | 0.0412071i | \(-0.0131203\pi\) | |||||||
\(278\) | 7.41641 | + | 22.8254i | 0.444807 | + | 1.36897i | ||||
\(279\) | 1.23607 | − | 3.80423i | 0.0740015 | − | 0.227753i | ||||
\(280\) | 4.85410 | + | 3.52671i | 0.290088 | + | 0.210761i | ||||
\(281\) | −5.60503 | − | 4.07230i | −0.334368 | − | 0.242933i | 0.407914 | − | 0.913021i | \(-0.366256\pi\) |
−0.742282 | + | 0.670088i | \(0.766256\pi\) | |||||||
\(282\) | 6.42280 | − | 19.7673i | 0.382472 | − | 1.17713i | ||||
\(283\) | −7.49326 | − | 23.0619i | −0.445428 | − | 1.37089i | −0.882013 | − | 0.471224i | \(-0.843812\pi\) |
0.436585 | − | 0.899663i | \(-0.356188\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.8564 | 0.820783 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.0000 | 1.41668 | ||||||||
\(288\) | −4.20378 | + | 3.05422i | −0.247710 | + | 0.179972i | ||||
\(289\) | 9.57953 | + | 29.4828i | 0.563502 | + | 1.73428i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.1803 | + | 11.7557i | 0.948508 | + | 0.689132i | ||||
\(292\) | −5.60503 | − | 4.07230i | −0.328010 | − | 0.238313i | ||||
\(293\) | −4.28187 | + | 13.1782i | −0.250149 | + | 0.769880i | 0.744598 | + | 0.667514i | \(0.232641\pi\) |
−0.994747 | + | 0.102366i | \(0.967359\pi\) | |||||||
\(294\) | −5.35233 | − | 16.4728i | −0.312154 | − | 0.960712i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 17.3205 | 1.00673 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.0000 | 0.695141 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.618034 | + | 1.90211i | 0.0356822 | + | 0.109819i | ||||
\(301\) | −3.70820 | + | 11.4127i | −0.213737 | + | 0.657816i | ||||
\(302\) | −9.70820 | − | 7.05342i | −0.558644 | − | 0.405879i | ||||
\(303\) | 22.4201 | + | 16.2892i | 1.28800 | + | 0.935789i | ||||
\(304\) | −10.7047 | + | 32.9456i | −0.613955 | + | 1.88956i | ||||
\(305\) | −2.14093 | − | 6.58911i | −0.122589 | − | 0.377292i | ||||
\(306\) | 9.70820 | − | 7.05342i | 0.554981 | − | 0.403217i | ||||
\(307\) | 3.46410 | 0.197707 | 0.0988534 | − | 0.995102i | \(-0.468483\pi\) | ||||
0.0988534 | + | 0.995102i | \(0.468483\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.00000 | 0.227552 | ||||||||
\(310\) | 5.60503 | − | 4.07230i | 0.318345 | − | 0.231291i | ||||
\(311\) | −7.41641 | − | 22.8254i | −0.420546 | − | 1.29431i | −0.907195 | − | 0.420710i | \(-0.861781\pi\) |
0.486649 | − | 0.873597i | \(-0.338219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.5066 | − | 19.9847i | −1.55476 | − | 1.12960i | −0.940144 | − | 0.340779i | \(-0.889309\pi\) |
−0.614620 | − | 0.788823i | \(-0.710691\pi\) | |||||||
\(314\) | −2.80252 | − | 2.03615i | −0.158155 | − | 0.114906i | ||||
\(315\) | −1.07047 | + | 3.29456i | −0.0603139 | + | 0.185627i | ||||
\(316\) | 2.14093 | + | 6.58911i | 0.120437 | + | 0.370667i | ||||
\(317\) | 14.5623 | − | 10.5801i | 0.817901 | − | 0.594240i | −0.0982098 | − | 0.995166i | \(-0.531312\pi\) |
0.916110 | + | 0.400926i | \(0.131312\pi\) | |||||||
\(318\) | 20.7846 | 1.16554 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −5.60503 | + | 4.07230i | −0.312842 | + | 0.227293i | ||||
\(322\) | 11.1246 | + | 34.2380i | 0.619950 | + | 1.90801i | ||||
\(323\) | 14.8328 | − | 45.6507i | 0.825320 | − | 2.54007i | ||||
\(324\) | 8.89919 | + | 6.46564i | 0.494399 | + | 0.359202i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.07047 | + | 3.29456i | −0.0592876 | + | 0.182469i | ||||
\(327\) | −4.28187 | − | 13.1782i | −0.236788 | − | 0.728758i | ||||
\(328\) | 9.70820 | − | 7.05342i | 0.536046 | − | 0.389460i | ||||
\(329\) | 20.7846 | 1.14589 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | −14.0126 | + | 10.1807i | −0.769041 | + | 0.558741i | ||||
\(333\) | 3.09017 | + | 9.51057i | 0.169340 | + | 0.521176i | ||||
\(334\) | 5.56231 | − | 17.1190i | 0.304356 | − | 0.936711i | ||||
\(335\) | −8.09017 | − | 5.87785i | −0.442013 | − | 0.321141i | ||||
\(336\) | −28.0252 | − | 20.3615i | −1.52890 | − | 1.11081i | ||||
\(337\) | 6.42280 | − | 19.7673i | 0.349872 | − | 1.07680i | −0.609051 | − | 0.793131i | \(-0.708450\pi\) |
0.958924 | − | 0.283665i | \(-0.0915503\pi\) | |||||||
\(338\) | 6.95803 | + | 21.4146i | 0.378467 | + | 1.16480i | ||||
\(339\) | −9.70820 | + | 7.05342i | −0.527277 | + | 0.383089i | ||||
\(340\) | 6.92820 | 0.375735 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −12.0000 | −0.648886 | ||||||||
\(343\) | −5.60503 | + | 4.07230i | −0.302643 | + | 0.219883i | ||||
\(344\) | 1.85410 | + | 5.70634i | 0.0999665 | + | 0.307665i | ||||
\(345\) | 3.70820 | − | 11.4127i | 0.199643 | − | 0.614438i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.6176 | + | 14.2530i | 1.05313 | + | 0.765143i | 0.972805 | − | 0.231626i | \(-0.0744045\pi\) |
0.0803240 | + | 0.996769i | \(0.474404\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.28187 | + | 13.1782i | 0.229203 | + | 0.705414i | 0.997838 | + | 0.0657263i | \(0.0209364\pi\) |
−0.768635 | + | 0.639688i | \(0.779064\pi\) | |||||||
\(350\) | −4.85410 | + | 3.52671i | −0.259463 | + | 0.188511i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.85410 | + | 5.70634i | −0.0982672 | + | 0.302435i | ||||
\(357\) | 38.8328 | + | 28.2137i | 2.05525 | + | 1.49323i | ||||
\(358\) | −16.8151 | − | 12.2169i | −0.888706 | − | 0.645683i | ||||
\(359\) | 10.7047 | − | 32.9456i | 0.564970 | − | 1.73880i | −0.103069 | − | 0.994674i | \(-0.532866\pi\) |
0.668039 | − | 0.744126i | \(-0.267134\pi\) | |||||||
\(360\) | 0.535233 | + | 1.64728i | 0.0282093 | + | 0.0868192i | ||||
\(361\) | −23.4615 | + | 17.0458i | −1.23482 | + | 0.897146i | ||||
\(362\) | −24.2487 | −1.27448 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.60503 | + | 4.07230i | −0.293381 | + | 0.213154i | ||||
\(366\) | 7.41641 | + | 22.8254i | 0.387662 | + | 1.19310i | ||||
\(367\) | 0.618034 | − | 1.90211i | 0.0322611 | − | 0.0992895i | −0.933629 | − | 0.358240i | \(-0.883377\pi\) |
0.965890 | + | 0.258951i | \(0.0833768\pi\) | |||||||
\(368\) | 24.2705 | + | 17.6336i | 1.26519 | + | 0.919213i | ||||
\(369\) | 5.60503 | + | 4.07230i | 0.291786 | + | 0.211995i | ||||
\(370\) | −5.35233 | + | 16.4728i | −0.278254 | + | 0.856379i | ||||
\(371\) | 6.42280 | + | 19.7673i | 0.333455 | + | 1.02627i | ||||
\(372\) | −6.47214 | + | 4.70228i | −0.335565 | + | 0.243802i | ||||
\(373\) | −27.7128 | −1.43492 | −0.717458 | − | 0.696602i | \(-0.754694\pi\) | ||||
−0.717458 | + | 0.696602i | \(0.754694\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.00000 | 0.103280 | ||||||||
\(376\) | 8.40755 | − | 6.10844i | 0.433586 | − | 0.315019i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −7.41641 | + | 22.8254i | −0.381459 | + | 1.17401i | ||||
\(379\) | −25.8885 | − | 18.8091i | −1.32981 | − | 0.966160i | −0.999754 | − | 0.0221971i | \(-0.992934\pi\) |
−0.330052 | − | 0.943963i | \(-0.607066\pi\) | |||||||
\(380\) | −5.60503 | − | 4.07230i | −0.287532 | − | 0.208904i | ||||
\(381\) | −6.42280 | + | 19.7673i | −0.329050 | + | 1.01271i | ||||
\(382\) | 6.42280 | + | 19.7673i | 0.328619 | + | 1.01139i | ||||
\(383\) | −14.5623 | + | 10.5801i | −0.744099 | + | 0.540620i | −0.893992 | − | 0.448083i | \(-0.852107\pi\) |
0.149893 | + | 0.988702i | \(0.452107\pi\) | |||||||
\(384\) | −24.2487 | −1.23744 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.0000 | −0.610784 | ||||||||
\(387\) | −2.80252 | + | 2.03615i | −0.142460 | + | 0.103503i | ||||
\(388\) | −3.09017 | − | 9.51057i | −0.156880 | − | 0.482826i | ||||
\(389\) | 1.85410 | − | 5.70634i | 0.0940067 | − | 0.289323i | −0.892987 | − | 0.450083i | \(-0.851394\pi\) |
0.986994 | + | 0.160760i | \(0.0513945\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −33.6302 | − | 24.4338i | −1.70075 | − | 1.23567i | ||||
\(392\) | 2.67617 | − | 8.23639i | 0.135167 | − | 0.416001i | ||||
\(393\) | −4.28187 | − | 13.1782i | −0.215992 | − | 0.664754i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.92820 | 0.348596 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.0000 | −1.70641 | −0.853206 | − | 0.521575i | \(-0.825345\pi\) | ||||
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | 5.60503 | − | 4.07230i | 0.280955 | − | 0.204126i | ||||
\(399\) | −14.8328 | − | 45.6507i | −0.742570 | − | 2.28539i | ||||
\(400\) | −1.54508 | + | 4.75528i | −0.0772542 | + | 0.237764i | ||||
\(401\) | 14.5623 | + | 10.5801i | 0.727207 | + | 0.528347i | 0.888679 | − | 0.458531i | \(-0.151624\pi\) |
−0.161472 | + | 0.986877i | \(0.551624\pi\) | |||||||
\(402\) | 28.0252 | + | 20.3615i | 1.39777 | + | 1.01554i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −4.28187 | − | 13.1782i | −0.213031 | − | 0.655641i | ||||
\(405\) | 8.89919 | − | 6.46564i | 0.442204 | − | 0.321280i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 24.0000 | 1.18818 | ||||||||
\(409\) | 16.8151 | − | 12.2169i | 0.831453 | − | 0.604086i | −0.0885168 | − | 0.996075i | \(-0.528213\pi\) |
0.919970 | + | 0.391988i | \(0.128213\pi\) | |||||||
\(410\) | 3.70820 | + | 11.4127i | 0.183135 | + | 0.563632i | ||||
\(411\) | 3.70820 | − | 11.4127i | 0.182912 | − | 0.562946i | ||||
\(412\) | −1.61803 | − | 1.17557i | −0.0797148 | − | 0.0579162i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.21140 | + | 9.88367i | −0.157832 | + | 0.485756i | ||||
\(415\) | 5.35233 | + | 16.4728i | 0.262736 | + | 0.808617i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −27.7128 | −1.35710 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 5.60503 | − | 4.07230i | 0.273498 | − | 0.198708i | ||||
\(421\) | −8.03444 | − | 24.7275i | −0.391575 | − | 1.20514i | −0.931597 | − | 0.363492i | \(-0.881584\pi\) |
0.540022 | − | 0.841651i | \(-0.318416\pi\) | |||||||
\(422\) | −11.1246 | + | 34.2380i | −0.541538 | + | 1.66668i | ||||
\(423\) | 4.85410 | + | 3.52671i | 0.236015 | + | 0.171475i | ||||
\(424\) | 8.40755 | + | 6.10844i | 0.408307 | + | 0.296652i | ||||
\(425\) | 2.14093 | − | 6.58911i | 0.103850 | − | 0.319619i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.4164 | + | 14.1068i | −0.939626 | + | 0.682678i | ||||
\(428\) | 3.46410 | 0.167444 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.00000 | −0.289346 | ||||||||
\(431\) | 22.4201 | − | 16.2892i | 1.07994 | − | 0.784622i | 0.102268 | − | 0.994757i | \(-0.467390\pi\) |
0.977672 | + | 0.210135i | \(0.0673902\pi\) | |||||||
\(432\) | 6.18034 | + | 19.0211i | 0.297352 | + | 0.915155i | ||||
\(433\) | −10.5066 | + | 32.3359i | −0.504914 | + | 1.55397i | 0.296001 | + | 0.955188i | \(0.404347\pi\) |
−0.800915 | + | 0.598778i | \(0.795653\pi\) | |||||||
\(434\) | −19.4164 | − | 14.1068i | −0.932017 | − | 0.677150i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.14093 | + | 6.58911i | −0.102532 | + | 0.315561i | ||||
\(437\) | 12.8456 | + | 39.5347i | 0.614488 | + | 1.89120i | ||||
\(438\) | 19.4164 | − | 14.1068i | 0.927752 | − | 0.674051i | ||||
\(439\) | −13.8564 | −0.661330 | −0.330665 | − | 0.943748i | \(-0.607273\pi\) | ||||
−0.330665 | + | 0.943748i | \(0.607273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.00000 | 0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.85410 | − | 5.70634i | −0.0880910 | − | 0.271116i | 0.897301 | − | 0.441420i | \(-0.145525\pi\) |
−0.985392 | + | 0.170304i | \(0.945525\pi\) | |||||||
\(444\) | 6.18034 | − | 19.0211i | 0.293306 | − | 0.902703i | ||||
\(445\) | 4.85410 | + | 3.52671i | 0.230107 | + | 0.167182i | ||||
\(446\) | 19.6176 | + | 14.2530i | 0.928921 | + | 0.674901i | ||||
\(447\) | −4.28187 | + | 13.1782i | −0.202525 | + | 0.623309i | ||||
\(448\) | −1.07047 | − | 3.29456i | −0.0505748 | − | 0.155653i | ||||
\(449\) | −24.2705 | + | 17.6336i | −1.14540 | + | 0.832179i | −0.987862 | − | 0.155334i | \(-0.950354\pi\) |
−0.157534 | + | 0.987514i | \(0.550354\pi\) | |||||||
\(450\) | −1.73205 | −0.0816497 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | 11.2101 | − | 8.14459i | 0.526695 | − | 0.382666i | ||||
\(454\) | 1.85410 | + | 5.70634i | 0.0870173 | + | 0.267812i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −19.4164 | − | 14.1068i | −0.909257 | − | 0.660614i | ||||
\(457\) | 16.8151 | + | 12.2169i | 0.786577 | + | 0.571482i | 0.906946 | − | 0.421247i | \(-0.138408\pi\) |
−0.120368 | + | 0.992729i | \(0.538408\pi\) | |||||||
\(458\) | 1.07047 | − | 3.29456i | 0.0500196 | − | 0.153945i | ||||
\(459\) | −8.56373 | − | 26.3565i | −0.399721 | − | 1.23021i | ||||
\(460\) | −4.85410 | + | 3.52671i | −0.226324 | + | 0.164434i | ||||
\(461\) | 27.7128 | 1.29071 | 0.645357 | − | 0.763881i | \(-0.276709\pi\) | ||||
0.645357 | + | 0.763881i | \(0.276709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0000 | 0.650635 | 0.325318 | − | 0.945605i | \(-0.394529\pi\) | ||||
0.325318 | + | 0.945605i | \(0.394529\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.47214 | + | 7.60845i | 0.114643 | + | 0.352834i | ||||
\(466\) | 3.70820 | − | 11.4127i | 0.171779 | − | 0.528682i | ||||
\(467\) | −14.5623 | − | 10.5801i | −0.673863 | − | 0.489590i | 0.197453 | − | 0.980312i | \(-0.436733\pi\) |
−0.871316 | + | 0.490722i | \(0.836733\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.7047 | + | 32.9456i | −0.494295 | + | 1.52128i | ||||
\(470\) | 3.21140 | + | 9.88367i | 0.148131 | + | 0.455900i | ||||
\(471\) | 3.23607 | − | 2.35114i | 0.149110 | − | 0.108335i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −24.0000 | −1.10236 | ||||||||
\(475\) | −5.60503 | + | 4.07230i | −0.257177 | + | 0.186850i | ||||
\(476\) | −7.41641 | − | 22.8254i | −0.339930 | − | 1.04620i | ||||
\(477\) | −1.85410 | + | 5.70634i | −0.0848935 | + | 0.261275i | ||||
\(478\) | 9.70820 | + | 7.05342i | 0.444043 | + | 0.322616i | ||||
\(479\) | −16.8151 | − | 12.2169i | −0.768302 | − | 0.558204i | 0.133144 | − | 0.991097i | \(-0.457493\pi\) |
−0.901445 | + | 0.432893i | \(0.857493\pi\) | |||||||
\(480\) | 3.21140 | − | 9.88367i | 0.146580 | − | 0.451126i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 29.1246 | − | 21.1603i | 1.32659 | − | 0.963824i | ||||
\(483\) | −41.5692 | −1.89146 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.0000 | −0.454077 | ||||||||
\(486\) | −14.0126 | + | 10.1807i | −0.635624 | + | 0.461808i | ||||
\(487\) | −4.32624 | − | 13.3148i | −0.196041 | − | 0.603351i | −0.999963 | − | 0.00861648i | \(-0.997257\pi\) |
0.803922 | − | 0.594734i | \(-0.202743\pi\) | |||||||
\(488\) | −3.70820 | + | 11.4127i | −0.167863 | + | 0.516628i | ||||
\(489\) | −3.23607 | − | 2.35114i | −0.146340 | − | 0.106322i | ||||
\(490\) | 7.00629 | + | 5.09037i | 0.316512 | + | 0.229959i | ||||
\(491\) | −4.28187 | + | 13.1782i | −0.193238 | + | 0.594725i | 0.806755 | + | 0.590886i | \(0.201222\pi\) |
−0.999993 | + | 0.00383859i | \(0.998778\pi\) | |||||||
\(492\) | −4.28187 | − | 13.1782i | −0.193041 | − | 0.594120i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −20.0000 | −0.898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −18.5410 | − | 57.0634i | −0.830843 | − | 2.55707i | ||||
\(499\) | 4.94427 | − | 15.2169i | 0.221336 | − | 0.681202i | −0.777307 | − | 0.629122i | \(-0.783415\pi\) |
0.998643 | − | 0.0520806i | \(-0.0165853\pi\) | |||||||
\(500\) | −0.809017 | − | 0.587785i | −0.0361803 | − | 0.0262866i | ||||
\(501\) | 16.8151 | + | 12.2169i | 0.751243 | + | 0.545810i | ||||
\(502\) | −6.42280 | + | 19.7673i | −0.286663 | + | 0.882259i | ||||
\(503\) | 5.35233 | + | 16.4728i | 0.238649 | + | 0.734485i | 0.996616 | + | 0.0821930i | \(0.0261924\pi\) |
−0.757968 | + | 0.652292i | \(0.773808\pi\) | |||||||
\(504\) | 4.85410 | − | 3.52671i | 0.216219 | − | 0.157092i | ||||
\(505\) | −13.8564 | −0.616602 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −26.0000 | −1.15470 | ||||||||
\(508\) | 8.40755 | − | 6.10844i | 0.373025 | − | 0.271018i | ||||
\(509\) | 1.85410 | + | 5.70634i | 0.0821816 | + | 0.252929i | 0.983702 | − | 0.179808i | \(-0.0575477\pi\) |
−0.901520 | + | 0.432737i | \(0.857548\pi\) | |||||||
\(510\) | −7.41641 | + | 22.8254i | −0.328404 | + | 1.01072i | ||||
\(511\) | 19.4164 | + | 14.1068i | 0.858931 | + | 0.624050i | ||||
\(512\) | 7.00629 | + | 5.09037i | 0.309637 | + | 0.224965i | ||||
\(513\) | −8.56373 | + | 26.3565i | −0.378098 | + | 1.16367i | ||||
\(514\) | 3.21140 | + | 9.88367i | 0.141649 | + | 0.435950i | ||||
\(515\) | −1.61803 | + | 1.17557i | −0.0712991 | + | 0.0518018i | ||||
\(516\) | 6.92820 | 0.304997 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 60.0000 | 2.63625 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.9787 | + | 39.9444i | −0.568608 | + | 1.74999i | 0.0883730 | + | 0.996087i | \(0.471833\pi\) |
−0.656981 | + | 0.753907i | \(0.728167\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.6176 | − | 14.2530i | −0.857819 | − | 0.623242i | 0.0694720 | − | 0.997584i | \(-0.477869\pi\) |
−0.927291 | + | 0.374342i | \(0.877869\pi\) | |||||||
\(524\) | −2.14093 | + | 6.58911i | −0.0935271 | + | 0.287847i | ||||
\(525\) | −2.14093 | − | 6.58911i | −0.0934380 | − | 0.287572i | ||||
\(526\) | −4.85410 | + | 3.52671i | −0.211649 | + | 0.153772i | ||||
\(527\) | 27.7128 | 1.20719 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | −8.40755 | + | 6.10844i | −0.365201 | + | 0.265334i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.41641 | + | 22.8254i | −0.321542 | + | 0.989605i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −16.8151 | − | 12.2169i | −0.727661 | − | 0.528676i | ||||
\(535\) | 1.07047 | − | 3.29456i | 0.0462803 | − | 0.142436i | ||||
\(536\) | 5.35233 | + | 16.4728i | 0.231186 | + | 0.711516i | ||||
\(537\) | 19.4164 | − | 14.1068i | 0.837880 | − | 0.608755i | ||||
\(538\) | 51.9615 | 2.24022 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.00000 | −0.172133 | ||||||||
\(541\) | −11.2101 | + | 8.14459i | −0.481958 | + | 0.350163i | −0.802083 | − | 0.597212i | \(-0.796275\pi\) |
0.320125 | + | 0.947375i | \(0.396275\pi\) | |||||||
\(542\) | 3.70820 | + | 11.4127i | 0.159281 | + | 0.490217i | ||||
\(543\) | 8.65248 | − | 26.6296i | 0.371313 | − | 1.14278i | ||||
\(544\) | −29.1246 | − | 21.1603i | −1.24871 | − | 0.907239i | ||||
\(545\) | 5.60503 | + | 4.07230i | 0.240093 | + | 0.174438i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.35233 | − | 16.4728i | −0.228849 | − | 0.704325i | −0.997878 | − | 0.0651112i | \(-0.979260\pi\) |
0.769029 | − | 0.639214i | \(-0.220740\pi\) | |||||||
\(548\) | −4.85410 | + | 3.52671i | −0.207357 | + | 0.150654i | ||||
\(549\) | −6.92820 | −0.295689 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −16.8151 | + | 12.2169i | −0.715698 | + | 0.519985i | ||||
\(553\) | −7.41641 | − | 22.8254i | −0.315378 | − | 0.970633i | ||||
\(554\) | 14.8328 | − | 45.6507i | 0.630186 | − | 1.93951i | ||||
\(555\) | −16.1803 | − | 11.7557i | −0.686817 | − | 0.499002i | ||||
\(556\) | 11.2101 | + | 8.14459i | 0.475413 | + | 0.345408i | ||||
\(557\) | 8.56373 | − | 26.3565i | 0.362857 | − | 1.11676i | −0.588455 | − | 0.808530i | \(-0.700264\pi\) |
0.951312 | − | 0.308229i | \(-0.0997363\pi\) | |||||||
\(558\) | −2.14093 | − | 6.58911i | −0.0906329 | − | 0.278939i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 17.3205 | 0.731925 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.0000 | −0.506189 | ||||||||
\(563\) | −8.40755 | + | 6.10844i | −0.354336 | + | 0.257440i | −0.750686 | − | 0.660659i | \(-0.770277\pi\) |
0.396350 | + | 0.918100i | \(0.370277\pi\) | |||||||
\(564\) | −3.70820 | − | 11.4127i | −0.156144 | − | 0.480560i | ||||
\(565\) | 1.85410 | − | 5.70634i | 0.0780027 | − | 0.240067i | ||||
\(566\) | −33.9787 | − | 24.6870i | −1.42823 | − | 1.03767i | ||||
\(567\) | −30.8277 | − | 22.3976i | −1.29464 | − | 0.940612i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.14093 | + | 6.58911i | 0.0897526 | + | 0.276230i | 0.985851 | − | 0.167626i | \(-0.0536101\pi\) |
−0.896098 | + | 0.443856i | \(0.853610\pi\) | |||||||
\(570\) | 19.4164 | − | 14.1068i | 0.813264 | − | 0.590871i | ||||
\(571\) | −27.7128 | −1.15975 | −0.579873 | − | 0.814707i | \(-0.696898\pi\) | ||||
−0.579873 | + | 0.814707i | \(0.696898\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.0000 | −1.00261 | ||||||||
\(574\) | 33.6302 | − | 24.4338i | 1.40370 | − | 1.01985i | ||||
\(575\) | 1.85410 | + | 5.70634i | 0.0773214 | + | 0.237971i | ||||
\(576\) | 0.309017 | − | 0.951057i | 0.0128757 | − | 0.0396274i | ||||
\(577\) | 1.61803 | + | 1.17557i | 0.0673596 | + | 0.0489396i | 0.620956 | − | 0.783846i | \(-0.286745\pi\) |
−0.553596 | + | 0.832785i | \(0.686745\pi\) | |||||||
\(578\) | 43.4390 | + | 31.5603i | 1.80682 | + | 1.31274i | ||||
\(579\) | 4.28187 | − | 13.1782i | 0.177948 | − | 0.547668i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 48.5410 | − | 35.2671i | 2.01382 | − | 1.46313i | ||||
\(582\) | 34.6410 | 1.43592 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 12.0000 | 0.496564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.41641 | + | 22.8254i | 0.306369 | + | 0.942907i | ||||
\(587\) | −9.27051 | + | 28.5317i | −0.382635 | + | 1.17763i | 0.555547 | + | 0.831485i | \(0.312509\pi\) |
−0.938182 | + | 0.346144i | \(0.887491\pi\) | |||||||
\(588\) | −8.09017 | − | 5.87785i | −0.333633 | − | 0.242399i | ||||
\(589\) | −22.4201 | − | 16.2892i | −0.923806 | − | 0.671184i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 40.4508 | − | 29.3893i | 1.66252 | − | 1.20789i | ||||
\(593\) | 6.92820 | 0.284507 | 0.142254 | − | 0.989830i | \(-0.454565\pi\) | ||||
0.142254 | + | 0.989830i | \(0.454565\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.0000 | −0.983904 | ||||||||
\(596\) | 5.60503 | − | 4.07230i | 0.229591 | − | 0.166808i | ||||
\(597\) | 2.47214 | + | 7.60845i | 0.101178 | + | 0.311393i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.4164 | − | 14.1068i | −0.793333 | − | 0.576390i | 0.115618 | − | 0.993294i | \(-0.463115\pi\) |
−0.908951 | + | 0.416904i | \(0.863115\pi\) | |||||||
\(600\) | −2.80252 | − | 2.03615i | −0.114412 | − | 0.0831254i | ||||
\(601\) | 14.9865 | − | 46.1238i | 0.611313 | − | 1.88143i | 0.165781 | − | 0.986163i | \(-0.446985\pi\) |
0.445532 | − | 0.895266i | \(-0.353015\pi\) | |||||||
\(602\) | 6.42280 | + | 19.7673i | 0.261774 | + | 0.805657i | ||||
\(603\) | −8.09017 | + | 5.87785i | −0.329457 | + | 0.239365i | ||||
\(604\) | −6.92820 | −0.281905 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 48.0000 | 1.94987 | ||||||||
\(607\) | −2.80252 | + | 2.03615i | −0.113751 | + | 0.0826447i | −0.643206 | − | 0.765693i | \(-0.722396\pi\) |
0.529456 | + | 0.848338i | \(0.322396\pi\) | |||||||
\(608\) | 11.1246 | + | 34.2380i | 0.451163 | + | 1.38854i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.70820 | − | 7.05342i | −0.393074 | − | 0.285585i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.14093 | − | 6.58911i | 0.0865421 | − | 0.266349i | ||||
\(613\) | −8.56373 | − | 26.3565i | −0.345886 | − | 1.06453i | −0.961108 | − | 0.276173i | \(-0.910934\pi\) |
0.615222 | − | 0.788354i | \(-0.289066\pi\) | |||||||
\(614\) | 4.85410 | − | 3.52671i | 0.195896 | − | 0.142326i | ||||
\(615\) | −13.8564 | −0.558744 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | 5.60503 | − | 4.07230i | 0.225468 | − | 0.163812i | ||||
\(619\) | −8.65248 | − | 26.6296i | −0.347772 | − | 1.07033i | −0.960083 | − | 0.279716i | \(-0.909760\pi\) |
0.612310 | − | 0.790617i | \(-0.290240\pi\) | |||||||
\(620\) | 1.23607 | − | 3.80423i | 0.0496417 | − | 0.152781i | ||||
\(621\) | 19.4164 | + | 14.1068i | 0.779154 | + | 0.566088i | ||||
\(622\) | −33.6302 | − | 24.4338i | −1.34845 | − | 0.979705i | ||||
\(623\) | 6.42280 | − | 19.7673i | 0.257324 | − | 0.791962i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.809017 | + | 0.587785i | −0.0323607 | + | 0.0235114i | ||||
\(626\) | −58.8897 | −2.35371 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.00000 | −0.0798087 | ||||||||
\(629\) | −56.0503 | + | 40.7230i | −2.23487 | + | 1.62373i | ||||
\(630\) | 1.85410 | + | 5.70634i | 0.0738692 | + | 0.227346i | ||||
\(631\) | 4.94427 | − | 15.2169i | 0.196828 | − | 0.605775i | −0.803122 | − | 0.595815i | \(-0.796829\pi\) |
0.999950 | − | 0.00996082i | \(-0.00317068\pi\) | |||||||
\(632\) | −9.70820 | − | 7.05342i | −0.386172 | − | 0.280570i | ||||
\(633\) | −33.6302 | − | 24.4338i | −1.33668 | − | 0.971155i | ||||
\(634\) | 9.63420 | − | 29.6510i | 0.382623 | − | 1.17759i | ||||
\(635\) | −3.21140 | − | 9.88367i | −0.127440 | − | 0.392221i | ||||
\(636\) | 9.70820 | − | 7.05342i | 0.384955 | − | 0.279686i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.80881 | − | 7.12652i | 0.387727 | − | 0.281700i | ||||
\(641\) | −12.9787 | − | 39.9444i | −0.512628 | − | 1.57771i | −0.787556 | − | 0.616243i | \(-0.788654\pi\) |
0.274928 | − | 0.961465i | \(-0.411346\pi\) | |||||||
\(642\) | −3.70820 | + | 11.4127i | −0.146351 | + | 0.450422i | ||||
\(643\) | −21.0344 | − | 15.2824i | −0.829517 | − | 0.602680i | 0.0899053 | − | 0.995950i | \(-0.471344\pi\) |
−0.919423 | + | 0.393271i | \(0.871344\pi\) | |||||||
\(644\) | 16.8151 | + | 12.2169i | 0.662608 | + | 0.481413i | ||||
\(645\) | 2.14093 | − | 6.58911i | 0.0842991 | − | 0.259446i | ||||
\(646\) | −25.6912 | − | 79.0694i | −1.01081 | − | 3.11094i | ||||
\(647\) | −4.85410 | + | 3.52671i | −0.190834 | + | 0.138649i | −0.679100 | − | 0.734046i | \(-0.737630\pi\) |
0.488266 | + | 0.872695i | \(0.337630\pi\) | |||||||
\(648\) | −19.0526 | −0.748455 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.4201 | − | 16.2892i | 0.878714 | − | 0.638423i | ||||
\(652\) | 0.618034 | + | 1.90211i | 0.0242041 | + | 0.0744925i | ||||
\(653\) | −1.85410 | + | 5.70634i | −0.0725566 | + | 0.223306i | −0.980758 | − | 0.195227i | \(-0.937456\pi\) |
0.908201 | + | 0.418533i | \(0.137456\pi\) | |||||||
\(654\) | −19.4164 | − | 14.1068i | −0.759242 | − | 0.551621i | ||||
\(655\) | 5.60503 | + | 4.07230i | 0.219007 | + | 0.159118i | ||||
\(656\) | 10.7047 | − | 32.9456i | 0.417947 | − | 1.28631i | ||||
\(657\) | 2.14093 | + | 6.58911i | 0.0835257 | + | 0.257066i | ||||
\(658\) | 29.1246 | − | 21.1603i | 1.13540 | − | 0.824913i | ||||
\(659\) | 27.7128 | 1.07954 | 0.539769 | − | 0.841813i | \(-0.318512\pi\) | ||||
0.539769 | + | 0.841813i | \(0.318512\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | 11.2101 | − | 8.14459i | 0.435692 | − | 0.316549i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.27051 | − | 28.5317i | 0.359766 | − | 1.10724i | ||||
\(665\) | 19.4164 | + | 14.1068i | 0.752936 | + | 0.547040i | ||||
\(666\) | 14.0126 | + | 10.1807i | 0.542977 | + | 0.394496i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −3.21140 | − | 9.88367i | −0.124253 | − | 0.382411i | ||||
\(669\) | −22.6525 | + | 16.4580i | −0.875795 | + | 0.636303i | ||||
\(670\) | −17.3205 | −0.669150 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −36.0000 | −1.38873 | ||||||||
\(673\) | −28.0252 | + | 20.3615i | −1.08029 | + | 0.784877i | −0.977734 | − | 0.209850i | \(-0.932703\pi\) |
−0.102557 | + | 0.994727i | \(0.532703\pi\) | |||||||
\(674\) | −11.1246 | − | 34.2380i | −0.428504 | − | 1.31880i | ||||
\(675\) | −1.23607 | + | 3.80423i | −0.0475763 | + | 0.146425i | ||||
\(676\) | 10.5172 | + | 7.64121i | 0.404508 | + | 0.293893i | ||||
\(677\) | −11.2101 | − | 8.14459i | −0.430838 | − | 0.313022i | 0.351146 | − | 0.936321i | \(-0.385792\pi\) |
−0.781984 | + | 0.623299i | \(0.785792\pi\) | |||||||
\(678\) | −6.42280 | + | 19.7673i | −0.246666 | + | 0.759160i | ||||
\(679\) | 10.7047 | + | 32.9456i | 0.410807 | + | 1.26433i | ||||
\(680\) | −9.70820 | + | 7.05342i | −0.372293 | + | 0.270486i | ||||
\(681\) | −6.92820 | −0.265489 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −42.0000 | −1.60709 | −0.803543 | − | 0.595247i | \(-0.797054\pi\) | ||||
−0.803543 | + | 0.595247i | \(0.797054\pi\) | |||||||
\(684\) | −5.60503 | + | 4.07230i | −0.214314 | + | 0.155708i | ||||
\(685\) | 1.85410 | + | 5.70634i | 0.0708416 | + | 0.218028i | ||||
\(686\) | −3.70820 | + | 11.4127i | −0.141580 | + | 0.435738i | ||||
\(687\) | 3.23607 | + | 2.35114i | 0.123464 | + | 0.0897016i | ||||
\(688\) | 14.0126 | + | 10.1807i | 0.534225 | + | 0.388137i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −6.42280 | − | 19.7673i | −0.244512 | − | 0.752530i | ||||
\(691\) | −16.1803 | + | 11.7557i | −0.615529 | + | 0.447208i | −0.851357 | − | 0.524587i | \(-0.824220\pi\) |
0.235828 | + | 0.971795i | \(0.424220\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 42.0000 | 1.59430 | ||||||||
\(695\) | 11.2101 | − | 8.14459i | 0.425222 | − | 0.308942i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.8328 | + | 45.6507i | −0.561833 | + | 1.72914i | ||||
\(698\) | 19.4164 | + | 14.1068i | 0.734922 | + | 0.533952i | ||||
\(699\) | 11.2101 | + | 8.14459i | 0.424004 | + | 0.308057i | ||||
\(700\) | −1.07047 | + | 3.29456i | −0.0404598 | + | 0.124523i | ||||
\(701\) | −6.42280 | − | 19.7673i | −0.242586 | − | 0.746602i | −0.996024 | − | 0.0890836i | \(-0.971606\pi\) |
0.753438 | − | 0.657518i | \(-0.228394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 69.2820 | 2.61302 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.0000 | −0.451946 | ||||||||
\(706\) | −8.40755 | + | 6.10844i | −0.316422 | + | 0.229894i | ||||
\(707\) | 14.8328 | + | 45.6507i | 0.557845 | + | 1.71687i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.0344 | + | 15.2824i | 0.789965 | + | 0.573943i | 0.907953 | − | 0.419072i | \(-0.137644\pi\) |
−0.117988 | + | 0.993015i | \(0.537644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.14093 | − | 6.58911i | 0.0802912 | − | 0.247111i | ||||
\(712\) | −3.21140 | − | 9.88367i | −0.120352 | − | 0.370406i | ||||
\(713\) | −19.4164 | + | 14.1068i | −0.727150 | + | 0.528306i | ||||
\(714\) | 83.1384 | 3.11138 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | −11.2101 | + | 8.14459i | −0.418648 | + | 0.304165i | ||||
\(718\) | −18.5410 | − | 57.0634i | −0.691945 | − | 2.12959i | ||||
\(719\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(720\) | 4.04508 | + | 2.93893i | 0.150751 | + | 0.109527i | ||||
\(721\) | 5.60503 | + | 4.07230i | 0.208742 | + | 0.151660i | ||||
\(722\) | −15.5218 | + | 47.7711i | −0.577660 | + | 1.77786i | ||||
\(723\) | 12.8456 | + | 39.5347i | 0.477733 | + | 1.47031i | ||||
\(724\) | −11.3262 | + | 8.22899i | −0.420936 | + | 0.305828i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.0000 | 1.70605 | 0.853023 | − | 0.521874i | \(-0.174767\pi\) | ||||
0.853023 | + | 0.521874i | \(0.174767\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.01722 | + | 12.3637i | 0.148786 | + | 0.457916i | ||||
\(730\) | −3.70820 | + | 11.4127i | −0.137247 | + | 0.422402i | ||||
\(731\) | −19.4164 | − | 14.1068i | −0.718142 | − | 0.521761i | ||||
\(732\) | 11.2101 | + | 8.14459i | 0.414336 | + | 0.301033i | ||||
\(733\) | 12.8456 | − | 39.5347i | 0.474463 | − | 1.46025i | −0.372218 | − | 0.928145i | \(-0.621403\pi\) |
0.846681 | − | 0.532101i | \(-0.178597\pi\) | |||||||
\(734\) | −1.07047 | − | 3.29456i | −0.0395116 | − | 0.121604i | ||||
\(735\) | −8.09017 | + | 5.87785i | −0.298410 | + | 0.216808i | ||||
\(736\) | 31.1769 | 1.14920 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 12.0000 | 0.441726 | ||||||||
\(739\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(740\) | 3.09017 | + | 9.51057i | 0.113597 | + | 0.349615i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 29.1246 | + | 21.1603i | 1.06920 | + | 0.776818i | ||||
\(743\) | 25.2227 | + | 18.3253i | 0.925329 | + | 0.672291i | 0.944845 | − | 0.327518i | \(-0.106212\pi\) |
−0.0195154 | + | 0.999810i | \(0.506212\pi\) | |||||||
\(744\) | 4.28187 | − | 13.1782i | 0.156981 | − | 0.483137i | ||||
\(745\) | −2.14093 | − | 6.58911i | −0.0784377 | − | 0.241406i | ||||
\(746\) | −38.8328 | + | 28.2137i | −1.42177 | + | 1.03298i | ||||
\(747\) | 17.3205 | 0.633724 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0000 | −0.438470 | ||||||||
\(750\) | 2.80252 | − | 2.03615i | 0.102333 | − | 0.0743496i | ||||
\(751\) | 4.94427 | + | 15.2169i | 0.180419 | + | 0.555273i | 0.999839 | − | 0.0179203i | \(-0.00570452\pi\) |
−0.819420 | + | 0.573193i | \(0.805705\pi\) | |||||||
\(752\) | 9.27051 | − | 28.5317i | 0.338061 | − | 1.04044i | ||||
\(753\) | −19.4164 | − | 14.1068i | −0.707573 | − | 0.514082i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.14093 | + | 6.58911i | −0.0779165 | + | 0.239802i | ||||
\(756\) | 4.28187 | + | 13.1782i | 0.155730 | + | 0.479287i | ||||
\(757\) | 1.61803 | − | 1.17557i | 0.0588084 | − | 0.0427268i | −0.557993 | − | 0.829846i | \(-0.688428\pi\) |
0.616801 | + | 0.787119i | \(0.288428\pi\) | |||||||
\(758\) | −55.4256 | −2.01315 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.0000 | 0.435286 | ||||||||
\(761\) | 11.2101 | − | 8.14459i | 0.406365 | − | 0.295241i | −0.365764 | − | 0.930708i | \(-0.619192\pi\) |
0.772128 | + | 0.635467i | \(0.219192\pi\) | |||||||
\(762\) | 11.1246 | + | 34.2380i | 0.403002 | + | 1.24031i | ||||
\(763\) | 7.41641 | − | 22.8254i | 0.268492 | − | 0.826333i | ||||
\(764\) | 9.70820 | + | 7.05342i | 0.351230 | + | 0.255184i | ||||
\(765\) | −5.60503 | − | 4.07230i | −0.202650 | − | 0.147234i | ||||
\(766\) | −9.63420 | + | 29.6510i | −0.348098 | + | 1.07133i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −30.7426 | + | 22.3358i | −1.10933 | + | 0.805975i | ||||
\(769\) | −41.5692 | −1.49902 | −0.749512 | − | 0.661991i | \(-0.769712\pi\) | ||||
−0.749512 | + | 0.661991i | \(0.769712\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0000 | −0.432169 | ||||||||
\(772\) | −5.60503 | + | 4.07230i | −0.201730 | + | 0.146565i | ||||
\(773\) | −1.85410 | − | 5.70634i | −0.0666874 | − | 0.205243i | 0.912160 | − | 0.409834i | \(-0.134413\pi\) |
−0.978847 | + | 0.204591i | \(0.934413\pi\) | |||||||
\(774\) | −1.85410 | + | 5.70634i | −0.0666443 | + | 0.205110i | ||||
\(775\) | −3.23607 | − | 2.35114i | −0.116243 | − | 0.0844555i | ||||
\(776\) | 14.0126 | + | 10.1807i | 0.503023 | + | 0.365467i | ||||
\(777\) | −21.4093 | + | 65.8911i | −0.768055 | + | 2.36383i | ||||
\(778\) | −3.21140 | − | 9.88367i | −0.115134 | − | 0.354347i | ||||
\(779\) | 38.8328 | − | 28.2137i | 1.39133 | − | 1.01086i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −72.0000 | −2.57471 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.72542 | − | 23.7764i | −0.275908 | − | 0.849158i | ||||
\(785\) | −0.618034 | + | 1.90211i | −0.0220586 | + | 0.0678893i | ||||
\(786\) | −19.4164 | − | 14.1068i | −0.692560 | − | 0.503175i | ||||
\(787\) | −36.4327 | − | 26.4699i | −1.29869 | − | 0.943551i | −0.298744 | − | 0.954333i | \(-0.596568\pi\) |
−0.999942 | + | 0.0107823i | \(0.996568\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.14093 | − | 6.58911i | −0.0762192 | − | 0.234579i | ||||
\(790\) | 9.70820 | − | 7.05342i | 0.345402 | − | 0.250950i | ||||
\(791\) | −20.7846 | −0.739016 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −47.6428 | + | 34.6145i | −1.69078 | + | 1.22842i | ||||
\(795\) | −3.70820 | − | 11.4127i | −0.131516 | − | 0.404766i | ||||
\(796\) | 1.23607 | − | 3.80423i | 0.0438113 | − | 0.134837i | ||||
\(797\) | 14.5623 | + | 10.5801i | 0.515823 | + | 0.374768i | 0.815028 | − | 0.579421i | \(-0.196721\pi\) |
−0.299205 | + | 0.954189i | \(0.596721\pi\) | |||||||
\(798\) | −67.2604 | − | 48.8675i | −2.38099 | − | 1.72989i | ||||
\(799\) | −12.8456 | + | 39.5347i | −0.454444 | + | 1.39864i | ||||
\(800\) | 1.60570 | + | 4.94183i | 0.0567700 | + | 0.174720i | ||||
\(801\) | 4.85410 | − | 3.52671i | 0.171511 | − | 0.124610i | ||||
\(802\) | 31.1769 | 1.10090 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 20.0000 | 0.705346 | ||||||||
\(805\) | 16.8151 | − | 12.2169i | 0.592654 | − | 0.430589i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.5410 | + | 57.0634i | −0.652675 | + | 2.00873i | ||||
\(808\) | 19.4164 | + | 14.1068i | 0.683067 | + | 0.496277i | ||||
\(809\) | 11.2101 | + | 8.14459i | 0.394125 | + | 0.286349i | 0.767144 | − | 0.641475i | \(-0.221677\pi\) |
−0.373019 | + | 0.927824i | \(0.621677\pi\) | |||||||
\(810\) | 5.88756 | − | 18.1201i | 0.206868 | − | 0.636674i | ||||
\(811\) | 4.28187 | + | 13.1782i | 0.150357 | + | 0.462750i | 0.997661 | − | 0.0683577i | \(-0.0217759\pi\) |
−0.847304 | + | 0.531108i | \(0.821776\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.8564 | −0.485965 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.00000 | 0.0700569 | ||||||||
\(816\) | 56.0503 | − | 40.7230i | 1.96215 | − | 1.42559i | ||||
\(817\) | 7.41641 | + | 22.8254i | 0.259467 | + | 0.798558i | ||||
\(818\) | 11.1246 | − | 34.2380i | 0.388963 | − | 1.19710i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.60503 | + | 4.07230i | 0.195736 | + | 0.142211i | ||||
\(821\) | 14.9865 | − | 46.1238i | 0.523033 | − | 1.60973i | −0.245139 | − | 0.969488i | \(-0.578834\pi\) |
0.768172 | − | 0.640243i | \(-0.221166\pi\) | |||||||
\(822\) | −6.42280 | − | 19.7673i | −0.224021 | − | 0.689465i | ||||
\(823\) | −21.0344 | + | 15.2824i | −0.733215 | + | 0.532712i | −0.890579 | − | 0.454829i | \(-0.849700\pi\) |
0.157364 | + | 0.987541i | \(0.449700\pi\) | |||||||
\(824\) | 3.46410 | 0.120678 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.0126 | + | 10.1807i | −0.487265 | + | 0.354019i | −0.804132 | − | 0.594451i | \(-0.797369\pi\) |
0.316866 | + | 0.948470i | \(0.397369\pi\) | |||||||
\(828\) | 1.85410 | + | 5.70634i | 0.0644345 | + | 0.198309i | ||||
\(829\) | −10.5066 | + | 32.3359i | −0.364909 | + | 1.12307i | 0.585130 | + | 0.810940i | \(0.301044\pi\) |
−0.950038 | + | 0.312133i | \(0.898956\pi\) | |||||||
\(830\) | 24.2705 | + | 17.6336i | 0.842442 | + | 0.612070i | ||||
\(831\) | 44.8403 | + | 32.5784i | 1.55549 | + | 1.13013i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.7047 | + | 32.9456i | 0.370895 | + | 1.14150i | ||||
\(834\) | −38.8328 | + | 28.2137i | −1.34467 | + | 0.976960i | ||||
\(835\) | −10.3923 | −0.359641 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.0000 | −0.553041 | ||||||||
\(838\) | −16.8151 | + | 12.2169i | −0.580868 | + | 0.422025i | ||||
\(839\) | −3.70820 | − | 11.4127i | −0.128021 | − | 0.394009i | 0.866418 | − | 0.499319i | \(-0.166417\pi\) |
−0.994439 | + | 0.105310i | \(0.966417\pi\) | |||||||
\(840\) | −3.70820 | + | 11.4127i | −0.127945 | + | 0.393775i | ||||
\(841\) | 23.4615 | + | 17.0458i | 0.809017 | + | 0.587785i | ||||
\(842\) | −36.4327 | − | 26.4699i | −1.25555 | − | 0.912214i | ||||
\(843\) | 4.28187 | − | 13.1782i | 0.147475 | − | 0.453882i | ||||
\(844\) | 6.42280 | + | 19.7673i | 0.221082 | + | 0.680420i | ||||
\(845\) | 10.5172 | − | 7.64121i | 0.361803 | − | 0.262866i | ||||
\(846\) | 10.3923 | 0.357295 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 30.0000 | 1.03020 | ||||||||
\(849\) | 39.2352 | − | 28.5061i | 1.34655 | − | 0.978326i | ||||
\(850\) | −3.70820 | − | 11.4127i | −0.127190 | − | 0.391452i | ||||
\(851\) | 18.5410 | − | 57.0634i | 0.635578 | − | 1.95611i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.6302 | + | 24.4338i | 1.15148 | + | 0.836596i | 0.988676 | − | 0.150063i | \(-0.0479475\pi\) |
0.162800 | + | 0.986659i | \(0.447948\pi\) | |||||||
\(854\) | −12.8456 | + | 39.5347i | −0.439567 | + | 1.35285i | ||||
\(855\) | 2.14093 | + | 6.58911i | 0.0732183 | + | 0.225343i | ||||
\(856\) | −4.85410 | + | 3.52671i | −0.165910 | + | 0.120541i | ||||
\(857\) | −20.7846 | −0.709989 | −0.354994 | − | 0.934868i | \(-0.615517\pi\) | ||||
−0.354994 | + | 0.934868i | \(0.615517\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00000 | −0.136478 | −0.0682391 | − | 0.997669i | \(-0.521738\pi\) | ||||
−0.0682391 | + | 0.997669i | \(0.521738\pi\) | |||||||
\(860\) | −2.80252 | + | 2.03615i | −0.0955650 | + | 0.0694321i | ||||
\(861\) | 14.8328 | + | 45.6507i | 0.505501 | + | 1.55577i | ||||
\(862\) | 14.8328 | − | 45.6507i | 0.505208 | − | 1.55487i | ||||
\(863\) | 43.6869 | + | 31.7404i | 1.48712 | + | 1.08046i | 0.975174 | + | 0.221438i | \(0.0710750\pi\) |
0.511946 | + | 0.859018i | \(0.328925\pi\) | |||||||
\(864\) | 16.8151 | + | 12.2169i | 0.572061 | + | 0.415627i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 18.1979 | + | 56.0075i | 0.618391 | + | 1.90321i | ||||
\(867\) | −50.1591 | + | 36.4427i | −1.70349 | + | 1.23766i | ||||
\(868\) | −13.8564 | −0.470317 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −3.70820 | − | 11.4127i | −0.125576 | − | 0.386482i | ||||
\(873\) | −3.09017 | + | 9.51057i | −0.104586 | + | 0.321884i | ||||
\(874\) | 58.2492 | + | 42.3205i | 1.97031 | + | 1.43151i | ||||
\(875\) | 2.80252 | + | 2.03615i | 0.0947424 | + | 0.0688344i | ||||
\(876\) | 4.28187 | − | 13.1782i | 0.144671 | − | 0.445251i | ||||
\(877\) | −8.56373 | − | 26.3565i | −0.289177 | − | 0.889994i | −0.985116 | − | 0.171893i | \(-0.945012\pi\) |
0.695939 | − | 0.718101i | \(-0.254988\pi\) | |||||||
\(878\) | −19.4164 | + | 14.1068i | −0.655272 | + | 0.476083i | ||||
\(879\) | −27.7128 | −0.934730 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | 7.00629 | − | 5.09037i | 0.235914 | − | 0.171402i | ||||
\(883\) | 10.5066 | + | 32.3359i | 0.353574 | + | 1.08819i | 0.956831 | + | 0.290643i | \(0.0938694\pi\) |
−0.603257 | + | 0.797547i | \(0.706131\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.40755 | − | 6.10844i | −0.282457 | − | 0.205217i | ||||
\(887\) | 5.35233 | − | 16.4728i | 0.179714 | − | 0.553102i | −0.820104 | − | 0.572215i | \(-0.806084\pi\) |
0.999817 | + | 0.0191131i | \(0.00608427\pi\) | |||||||
\(888\) | 10.7047 | + | 32.9456i | 0.359225 | + | 1.10558i | ||||
\(889\) | −29.1246 | + | 21.1603i | −0.976808 | + | 0.709693i | ||||
\(890\) | 10.3923 | 0.348351 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.0000 | 0.468755 | ||||||||
\(893\) | 33.6302 | − | 24.4338i | 1.12539 | − | 0.817645i | ||||
\(894\) | 7.41641 | + | 22.8254i | 0.248042 | + | 0.763394i | ||||
\(895\) | −3.70820 | + | 11.4127i | −0.123952 | + | 0.381484i | ||||
\(896\) | −33.9787 | − | 24.6870i | −1.13515 | − | 0.824734i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16.0570 | + | 49.4183i | −0.535829 | + | 1.64911i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.809017 | + | 0.587785i | −0.0269672 | + | 0.0195928i | ||||
\(901\) | −41.5692 | −1.38487 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.0000 | −0.798670 | ||||||||
\(904\) | −8.40755 | + | 6.10844i | −0.279631 | + | 0.203164i | ||||
\(905\) | 4.32624 | + | 13.3148i | 0.143809 | + | 0.442599i | ||||
\(906\) | 7.41641 | − | 22.8254i | 0.246394 | − | 0.758322i | ||||
\(907\) | −21.0344 | − | 15.2824i | −0.698437 | − | 0.507444i | 0.180986 | − | 0.983486i | \(-0.442071\pi\) |
−0.879423 | + | 0.476041i | \(0.842071\pi\) | |||||||
\(908\) | 2.80252 | + | 2.03615i | 0.0930048 | + | 0.0675719i | ||||
\(909\) | −4.28187 | + | 13.1782i | −0.142020 | + | 0.437094i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.1246 | − | 21.1603i | 0.964941 | − | 0.701071i | 0.0106483 | − | 0.999943i | \(-0.496610\pi\) |
0.954293 | + | 0.298872i | \(0.0966105\pi\) | |||||||
\(912\) | −69.2820 | −2.29416 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 36.0000 | 1.19077 | ||||||||
\(915\) | 11.2101 | − | 8.14459i | 0.370593 | − | 0.269252i | ||||
\(916\) | −0.618034 | − | 1.90211i | −0.0204204 | − | 0.0628476i | ||||
\(917\) | 7.41641 | − | 22.8254i | 0.244911 | − | 0.753760i | ||||
\(918\) | −38.8328 | − | 28.2137i | −1.28167 | − | 0.931191i | ||||
\(919\) | −11.2101 | − | 8.14459i | −0.369786 | − | 0.268665i | 0.387336 | − | 0.921939i | \(-0.373395\pi\) |
−0.757122 | + | 0.653273i | \(0.773395\pi\) | |||||||
\(920\) | 3.21140 | − | 9.88367i | 0.105877 | − | 0.325855i | ||||
\(921\) | 2.14093 | + | 6.58911i | 0.0705461 | + | 0.217119i | ||||
\(922\) | 38.8328 | − | 28.2137i | 1.27889 | − | 0.929168i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0000 | 0.328798 | ||||||||
\(926\) | 19.6176 | − | 14.2530i | 0.644675 | − | 0.468384i | ||||
\(927\) | 0.618034 | + | 1.90211i | 0.0202989 | + | 0.0624736i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.85410 | + | 3.52671i | 0.159258 | + | 0.115708i | 0.664560 | − | 0.747235i | \(-0.268619\pi\) |
−0.505302 | + | 0.862942i | \(0.668619\pi\) | |||||||
\(930\) | 11.2101 | + | 8.14459i | 0.367593 | + | 0.267072i | ||||
\(931\) | 10.7047 | − | 32.9456i | 0.350831 | − | 1.07975i | ||||
\(932\) | −2.14093 | − | 6.58911i | −0.0701286 | − | 0.215834i | ||||
\(933\) | 38.8328 | − | 28.2137i | 1.27133 | − | 0.923675i | ||||
\(934\) | −31.1769 | −1.02014 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.0252 | + | 20.3615i | −0.915542 | + | 0.665181i | −0.942410 | − | 0.334458i | \(-0.891447\pi\) |
0.0268681 | + | 0.999639i | \(0.491447\pi\) | |||||||
\(938\) | 18.5410 | + | 57.0634i | 0.605386 | + | 1.86319i | ||||
\(939\) | 21.0132 | − | 64.6718i | 0.685738 | − | 2.11049i | ||||
\(940\) | 4.85410 | + | 3.52671i | 0.158323 | + | 0.115029i | ||||
\(941\) | −11.2101 | − | 8.14459i | −0.365438 | − | 0.265506i | 0.389879 | − | 0.920866i | \(-0.372517\pi\) |
−0.755317 | + | 0.655360i | \(0.772517\pi\) | |||||||
\(942\) | 2.14093 | − | 6.58911i | 0.0697554 | − | 0.214685i | ||||
\(943\) | −12.8456 | − | 39.5347i | −0.418310 | − | 1.28743i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.8564 | 0.450749 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.00000 | −0.194974 | −0.0974869 | − | 0.995237i | \(-0.531080\pi\) | ||||
−0.0974869 | + | 0.995237i | \(0.531080\pi\) | |||||||
\(948\) | −11.2101 | + | 8.14459i | −0.364086 | + | 0.264524i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −3.70820 | + | 11.4127i | −0.120310 | + | 0.370276i | ||||
\(951\) | 29.1246 | + | 21.1603i | 0.944430 | + | 0.686169i | ||||
\(952\) | 33.6302 | + | 24.4338i | 1.08996 | + | 0.791903i | ||||
\(953\) | −10.7047 | + | 32.9456i | −0.346758 | + | 1.06721i | 0.613878 | + | 0.789401i | \(0.289609\pi\) |
−0.960636 | + | 0.277810i | \(0.910391\pi\) | |||||||
\(954\) | 3.21140 | + | 9.88367i | 0.103973 | + | 0.319996i | ||||
\(955\) | 9.70820 | − | 7.05342i | 0.314150 | − | 0.228243i | ||||
\(956\) | 6.92820 | 0.224074 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −36.0000 | −1.16311 | ||||||||
\(959\) | 16.8151 | − | 12.2169i | 0.542988 | − | 0.394504i | ||||
\(960\) | 0.618034 | + | 1.90211i | 0.0199470 | + | 0.0613904i | ||||
\(961\) | −4.63525 | + | 14.2658i | −0.149524 | + | 0.460189i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.80252 | − | 2.03615i | −0.0903099 | − | 0.0656139i | ||||
\(964\) | 6.42280 | − | 19.7673i | 0.206864 | − | 0.636663i | ||||
\(965\) | 2.14093 | + | 6.58911i | 0.0689191 | + | 0.212111i | ||||
\(966\) | −58.2492 | + | 42.3205i | −1.87414 | + | 1.36164i | ||||
\(967\) | −24.2487 | −0.779786 | −0.389893 | − | 0.920860i | \(-0.627488\pi\) | ||||
−0.389893 | + | 0.920860i | \(0.627488\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 96.0000 | 3.08396 | ||||||||
\(970\) | −14.0126 | + | 10.1807i | −0.449917 | + | 0.326884i | ||||
\(971\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(972\) | −3.09017 | + | 9.51057i | −0.0991172 | + | 0.305052i | ||||
\(973\) | −38.8328 | − | 28.2137i | −1.24492 | − | 0.904489i | ||||
\(974\) | −19.6176 | − | 14.2530i | −0.628589 | − | 0.456697i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.7047 | + | 32.9456i | 0.342648 | + | 1.05456i | ||||
\(977\) | 33.9787 | − | 24.6870i | 1.08708 | − | 0.789806i | 0.108172 | − | 0.994132i | \(-0.465500\pi\) |
0.978903 | + | 0.204326i | \(0.0655002\pi\) | |||||||
\(978\) | −6.92820 | −0.221540 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 5.00000 | 0.159719 | ||||||||
\(981\) | 5.60503 | − | 4.07230i | 0.178955 | − | 0.130018i | ||||
\(982\) | 7.41641 | + | 22.8254i | 0.236667 | + | 0.728386i | ||||
\(983\) | 12.9787 | − | 39.9444i | 0.413957 | − | 1.27403i | −0.499224 | − | 0.866473i | \(-0.666382\pi\) |
0.913181 | − | 0.407555i | \(-0.133618\pi\) | |||||||
\(984\) | 19.4164 | + | 14.1068i | 0.618972 | + | 0.449710i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.8456 | + | 39.5347i | 0.408880 | + | 1.25840i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.7846 | 0.660912 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.0000 | 0.889449 | 0.444725 | − | 0.895667i | \(-0.353302\pi\) | ||||
0.444725 | + | 0.895667i | \(0.353302\pi\) | |||||||
\(992\) | −16.8151 | + | 12.2169i | −0.533880 | + | 0.387887i | ||||
\(993\) | 4.94427 | + | 15.2169i | 0.156902 | + | 0.482894i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.23607 | − | 2.35114i | −0.102590 | − | 0.0745362i | ||||
\(996\) | −28.0252 | − | 20.3615i | −0.888012 | − | 0.645178i | ||||
\(997\) | −12.8456 | + | 39.5347i | −0.406824 | + | 1.25208i | 0.512538 | + | 0.858664i | \(0.328705\pi\) |
−0.919362 | + | 0.393411i | \(0.871295\pi\) | |||||||
\(998\) | −8.56373 | − | 26.3565i | −0.271080 | − | 0.834299i | ||||
\(999\) | 32.3607 | − | 23.5114i | 1.02385 | − | 0.743868i |
(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 | 605.2.g.h.366.2 | 8 | ||
11.2 | odd | 10 | 605.2.a.f.1.2 | yes | 2 | ||
11.3 | even | 5 | inner | 605.2.g.h.511.1 | 8 | ||
11.4 | even | 5 | inner | 605.2.g.h.81.2 | 8 | ||
11.5 | even | 5 | inner | 605.2.g.h.251.1 | 8 | ||
11.6 | odd | 10 | inner | 605.2.g.h.251.2 | 8 | ||
11.7 | odd | 10 | inner | 605.2.g.h.81.1 | 8 | ||
11.8 | odd | 10 | inner | 605.2.g.h.511.2 | 8 | ||
11.9 | even | 5 | 605.2.a.f.1.1 | ✓ | 2 | ||
11.10 | odd | 2 | inner | 605.2.g.h.366.1 | 8 | ||
33.2 | even | 10 | 5445.2.a.r.1.1 | 2 | |||
33.20 | odd | 10 | 5445.2.a.r.1.2 | 2 | |||
44.31 | odd | 10 | 9680.2.a.bg.1.2 | 2 | |||
44.35 | even | 10 | 9680.2.a.bg.1.1 | 2 | |||
55.9 | even | 10 | 3025.2.a.j.1.2 | 2 | |||
55.24 | odd | 10 | 3025.2.a.j.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.a.f.1.1 | ✓ | 2 | 11.9 | even | 5 | ||
605.2.a.f.1.2 | yes | 2 | 11.2 | odd | 10 | ||
605.2.g.h.81.1 | 8 | 11.7 | odd | 10 | inner | ||
605.2.g.h.81.2 | 8 | 11.4 | even | 5 | inner | ||
605.2.g.h.251.1 | 8 | 11.5 | even | 5 | inner | ||
605.2.g.h.251.2 | 8 | 11.6 | odd | 10 | inner | ||
605.2.g.h.366.1 | 8 | 11.10 | odd | 2 | inner | ||
605.2.g.h.366.2 | 8 | 1.1 | even | 1 | trivial | ||
605.2.g.h.511.1 | 8 | 11.3 | even | 5 | inner | ||
605.2.g.h.511.2 | 8 | 11.8 | odd | 10 | inner | ||
3025.2.a.j.1.1 | 2 | 55.24 | odd | 10 | |||
3025.2.a.j.1.2 | 2 | 55.9 | even | 10 | |||
5445.2.a.r.1.1 | 2 | 33.2 | even | 10 | |||
5445.2.a.r.1.2 | 2 | 33.20 | odd | 10 | |||
9680.2.a.bg.1.1 | 2 | 44.35 | even | 10 | |||
9680.2.a.bg.1.2 | 2 | 44.31 | odd | 10 |