Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(53,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.l (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: | \(3.11416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 2 x^{18} - 12 x^{17} + 6 x^{16} - 24 x^{15} + 72 x^{14} - 112 x^{13} + 189 x^{12} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 287.3 | ||
Root | \(-0.807075 - 1.53252i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.287 |
Dual form | 390.2.l.c.53.3 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||
\(3\) | −0.807075 | − | 1.53252i | −0.465965 | − | 0.884803i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −2.02552 | − | 0.947239i | −0.905841 | − | 0.423618i | ||||
\(6\) | 1.65435 | + | 0.512970i | 0.675384 | + | 0.209419i | ||||
\(7\) | −1.59729 | − | 1.59729i | −0.603720 | − | 0.603720i | 0.337578 | − | 0.941298i | \(-0.390392\pi\) |
−0.941298 | + | 0.337578i | \(0.890392\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | −1.69726 | + | 2.47372i | −0.565754 | + | 0.824574i | ||||
\(10\) | 2.10206 | − | 0.762461i | 0.664730 | − | 0.241111i | ||||
\(11\) | 2.58997i | 0.780905i | 0.920623 | + | 0.390453i | \(0.127681\pi\) | ||||
−0.920623 | + | 0.390453i | \(0.872319\pi\) | |||||||
\(12\) | −1.53252 | + | 0.807075i | −0.442402 | + | 0.232982i | ||||
\(13\) | 0.707107 | − | 0.707107i | 0.196116 | − | 0.196116i | ||||
\(14\) | 2.25891 | 0.603720 | ||||||||
\(15\) | 0.183080 | + | 3.86865i | 0.0472710 | + | 0.998882i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.155426 | + | 0.155426i | −0.0376964 | + | 0.0376964i | −0.725704 | − | 0.688007i | \(-0.758486\pi\) |
0.688007 | + | 0.725704i | \(0.258486\pi\) | |||||||
\(18\) | −0.549041 | − | 2.94933i | −0.129410 | − | 0.695164i | ||||
\(19\) | 6.77461i | 1.55420i | 0.629376 | + | 0.777101i | \(0.283311\pi\) | ||||
−0.629376 | + | 0.777101i | \(0.716689\pi\) | |||||||
\(20\) | −0.947239 | + | 2.02552i | −0.211809 | + | 0.452920i | ||||
\(21\) | −1.15876 | + | 3.73703i | −0.252861 | + | 0.815486i | ||||
\(22\) | −1.83139 | − | 1.83139i | −0.390453 | − | 0.390453i | ||||
\(23\) | 1.81338 | + | 1.81338i | 0.378116 | + | 0.378116i | 0.870422 | − | 0.492306i | \(-0.163846\pi\) |
−0.492306 | + | 0.870422i | \(0.663846\pi\) | |||||||
\(24\) | 0.512970 | − | 1.65435i | 0.104710 | − | 0.337692i | ||||
\(25\) | 3.20547 | + | 3.83731i | 0.641095 | + | 0.767462i | ||||
\(26\) | 1.00000i | 0.196116i | ||||||||
\(27\) | 5.16086 | + | 0.604615i | 0.993207 | + | 0.116358i | ||||
\(28\) | −1.59729 | + | 1.59729i | −0.301860 | + | 0.301860i | ||||
\(29\) | −0.890831 | −0.165423 | −0.0827115 | − | 0.996574i | \(-0.526358\pi\) | ||||
−0.0827115 | + | 0.996574i | \(0.526358\pi\) | |||||||
\(30\) | −2.86501 | − | 2.60609i | −0.523077 | − | 0.475806i | ||||
\(31\) | −9.39662 | −1.68768 | −0.843841 | − | 0.536593i | \(-0.819711\pi\) | ||||
−0.843841 | + | 0.536593i | \(0.819711\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 3.96919 | − | 2.09030i | 0.690947 | − | 0.363874i | ||||
\(34\) | − | 0.219806i | − | 0.0376964i | ||||||
\(35\) | 1.72233 | + | 4.74837i | 0.291127 | + | 0.802621i | ||||
\(36\) | 2.47372 | + | 1.69726i | 0.412287 | + | 0.282877i | ||||
\(37\) | −2.88699 | − | 2.88699i | −0.474618 | − | 0.474618i | 0.428788 | − | 0.903405i | \(-0.358941\pi\) |
−0.903405 | + | 0.428788i | \(0.858941\pi\) | |||||||
\(38\) | −4.79037 | − | 4.79037i | −0.777101 | − | 0.777101i | ||||
\(39\) | −1.65435 | − | 0.512970i | −0.264907 | − | 0.0821410i | ||||
\(40\) | −0.762461 | − | 2.10206i | −0.120556 | − | 0.332365i | ||||
\(41\) | 2.11082i | 0.329654i | 0.986322 | + | 0.164827i | \(0.0527067\pi\) | ||||
−0.986322 | + | 0.164827i | \(0.947293\pi\) | |||||||
\(42\) | −1.82311 | − | 3.46184i | −0.281312 | − | 0.534174i | ||||
\(43\) | −4.38869 | + | 4.38869i | −0.669269 | + | 0.669269i | −0.957547 | − | 0.288278i | \(-0.906917\pi\) |
0.288278 | + | 0.957547i | \(0.406917\pi\) | |||||||
\(44\) | 2.58997 | 0.390453 | ||||||||
\(45\) | 5.78105 | − | 3.40287i | 0.861788 | − | 0.507269i | ||||
\(46\) | −2.56451 | −0.378116 | ||||||||
\(47\) | −3.71800 | + | 3.71800i | −0.542326 | + | 0.542326i | −0.924210 | − | 0.381884i | \(-0.875275\pi\) |
0.381884 | + | 0.924210i | \(0.375275\pi\) | |||||||
\(48\) | 0.807075 | + | 1.53252i | 0.116491 | + | 0.221201i | ||||
\(49\) | − | 1.89731i | − | 0.271044i | ||||||
\(50\) | −4.98000 | − | 0.446773i | −0.704278 | − | 0.0631833i | ||||
\(51\) | 0.363635 | + | 0.112754i | 0.0509191 | + | 0.0157887i | ||||
\(52\) | −0.707107 | − | 0.707107i | −0.0980581 | − | 0.0980581i | ||||
\(53\) | −2.24202 | − | 2.24202i | −0.307965 | − | 0.307965i | 0.536155 | − | 0.844120i | \(-0.319876\pi\) |
−0.844120 | + | 0.536155i | \(0.819876\pi\) | |||||||
\(54\) | −4.07680 | + | 3.22175i | −0.554783 | + | 0.438425i | ||||
\(55\) | 2.45332 | − | 5.24604i | 0.330806 | − | 0.707376i | ||||
\(56\) | − | 2.25891i | − | 0.301860i | ||||||
\(57\) | 10.3823 | − | 5.46761i | 1.37516 | − | 0.724203i | ||||
\(58\) | 0.629912 | − | 0.629912i | 0.0827115 | − | 0.0827115i | ||||
\(59\) | 2.75114 | 0.358169 | 0.179084 | − | 0.983834i | \(-0.442687\pi\) | ||||
0.179084 | + | 0.983834i | \(0.442687\pi\) | |||||||
\(60\) | 3.86865 | − | 0.183080i | 0.499441 | − | 0.0236355i | ||||
\(61\) | −2.28989 | −0.293191 | −0.146595 | − | 0.989197i | \(-0.546831\pi\) | ||||
−0.146595 | + | 0.989197i | \(0.546831\pi\) | |||||||
\(62\) | 6.64441 | − | 6.64441i | 0.843841 | − | 0.843841i | ||||
\(63\) | 6.66228 | − | 1.24024i | 0.839369 | − | 0.156255i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −2.10206 | + | 0.762461i | −0.260728 | + | 0.0945716i | ||||
\(66\) | −1.32858 | + | 4.28471i | −0.163537 | + | 0.527411i | ||||
\(67\) | −10.9926 | − | 10.9926i | −1.34295 | − | 1.34295i | −0.893104 | − | 0.449850i | \(-0.851477\pi\) |
−0.449850 | − | 0.893104i | \(-0.648523\pi\) | |||||||
\(68\) | 0.155426 | + | 0.155426i | 0.0188482 | + | 0.0188482i | ||||
\(69\) | 1.31552 | − | 4.24259i | 0.158370 | − | 0.510747i | ||||
\(70\) | −4.57548 | − | 2.13973i | −0.546874 | − | 0.255747i | ||||
\(71\) | 9.60806i | 1.14027i | 0.821552 | + | 0.570134i | \(0.193109\pi\) | ||||
−0.821552 | + | 0.570134i | \(0.806891\pi\) | |||||||
\(72\) | −2.94933 | + | 0.549041i | −0.347582 | + | 0.0647052i | ||||
\(73\) | −1.65186 | + | 1.65186i | −0.193336 | + | 0.193336i | −0.797136 | − | 0.603800i | \(-0.793653\pi\) |
0.603800 | + | 0.797136i | \(0.293653\pi\) | |||||||
\(74\) | 4.08282 | 0.474618 | ||||||||
\(75\) | 3.29371 | − | 8.00946i | 0.380325 | − | 0.924853i | ||||
\(76\) | 6.77461 | 0.777101 | ||||||||
\(77\) | 4.13694 | − | 4.13694i | 0.471448 | − | 0.471448i | ||||
\(78\) | 1.53252 | − | 0.807075i | 0.173524 | − | 0.0913832i | ||||
\(79\) | 12.1165i | 1.36321i | 0.731721 | + | 0.681605i | \(0.238718\pi\) | ||||
−0.731721 | + | 0.681605i | \(0.761282\pi\) | |||||||
\(80\) | 2.02552 | + | 0.947239i | 0.226460 | + | 0.105905i | ||||
\(81\) | −3.23861 | − | 8.39711i | −0.359846 | − | 0.933012i | ||||
\(82\) | −1.49257 | − | 1.49257i | −0.164827 | − | 0.164827i | ||||
\(83\) | −5.93928 | − | 5.93928i | −0.651921 | − | 0.651921i | 0.301534 | − | 0.953455i | \(-0.402501\pi\) |
−0.953455 | + | 0.301534i | \(0.902501\pi\) | |||||||
\(84\) | 3.73703 | + | 1.15876i | 0.407743 | + | 0.126431i | ||||
\(85\) | 0.462045 | − | 0.167593i | 0.0501158 | − | 0.0181780i | ||||
\(86\) | − | 6.20654i | − | 0.669269i | ||||||
\(87\) | 0.718967 | + | 1.36522i | 0.0770813 | + | 0.146367i | ||||
\(88\) | −1.83139 | + | 1.83139i | −0.195226 | + | 0.195226i | ||||
\(89\) | 6.43585 | 0.682199 | 0.341099 | − | 0.940027i | \(-0.389201\pi\) | ||||
0.341099 | + | 0.940027i | \(0.389201\pi\) | |||||||
\(90\) | −1.68163 | + | 6.49401i | −0.177259 | + | 0.684528i | ||||
\(91\) | −2.25891 | −0.236798 | ||||||||
\(92\) | 1.81338 | − | 1.81338i | 0.189058 | − | 0.189058i | ||||
\(93\) | 7.58377 | + | 14.4005i | 0.786400 | + | 1.49327i | ||||
\(94\) | − | 5.25805i | − | 0.542326i | ||||||
\(95\) | 6.41718 | − | 13.7221i | 0.658388 | − | 1.40786i | ||||
\(96\) | −1.65435 | − | 0.512970i | −0.168846 | − | 0.0523548i | ||||
\(97\) | 8.84860 | + | 8.84860i | 0.898439 | + | 0.898439i | 0.995298 | − | 0.0968592i | \(-0.0308796\pi\) |
−0.0968592 | + | 0.995298i | \(0.530880\pi\) | |||||||
\(98\) | 1.34160 | + | 1.34160i | 0.135522 | + | 0.135522i | ||||
\(99\) | −6.40687 | − | 4.39585i | −0.643914 | − | 0.441800i | ||||
\(100\) | 3.83731 | − | 3.20547i | 0.383731 | − | 0.320547i | ||||
\(101\) | − | 16.1955i | − | 1.61151i | −0.592246 | − | 0.805757i | \(-0.701759\pi\) | ||
0.592246 | − | 0.805757i | \(-0.298241\pi\) | |||||||
\(102\) | −0.336858 | + | 0.177400i | −0.0333539 | + | 0.0175652i | ||||
\(103\) | 11.4202 | − | 11.4202i | 1.12526 | − | 1.12526i | 0.134326 | − | 0.990937i | \(-0.457113\pi\) |
0.990937 | − | 0.134326i | \(-0.0428869\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 5.88694 | − | 6.47181i | 0.574507 | − | 0.631584i | ||||
\(106\) | 3.17070 | 0.307965 | ||||||||
\(107\) | −10.0756 | + | 10.0756i | −0.974043 | + | 0.974043i | −0.999672 | − | 0.0256290i | \(-0.991841\pi\) |
0.0256290 | + | 0.999672i | \(0.491841\pi\) | |||||||
\(108\) | 0.604615 | − | 5.16086i | 0.0581791 | − | 0.496604i | ||||
\(109\) | 9.17905i | 0.879194i | 0.898195 | + | 0.439597i | \(0.144879\pi\) | ||||
−0.898195 | + | 0.439597i | \(0.855121\pi\) | |||||||
\(110\) | 1.97475 | + | 5.44427i | 0.188285 | + | 0.519091i | ||||
\(111\) | −2.09436 | + | 6.75439i | −0.198788 | + | 0.641098i | ||||
\(112\) | 1.59729 | + | 1.59729i | 0.150930 | + | 0.150930i | ||||
\(113\) | 7.84170 | + | 7.84170i | 0.737685 | + | 0.737685i | 0.972130 | − | 0.234444i | \(-0.0753271\pi\) |
−0.234444 | + | 0.972130i | \(0.575327\pi\) | |||||||
\(114\) | −3.47517 | + | 11.2075i | −0.325480 | + | 1.04968i | ||||
\(115\) | −1.95534 | − | 5.39075i | −0.182336 | − | 0.502690i | ||||
\(116\) | 0.890831i | 0.0827115i | ||||||||
\(117\) | 0.549041 | + | 2.94933i | 0.0507589 | + | 0.272666i | ||||
\(118\) | −1.94535 | + | 1.94535i | −0.179084 | + | 0.179084i | ||||
\(119\) | 0.496523 | 0.0455161 | ||||||||
\(120\) | −2.60609 | + | 2.86501i | −0.237903 | + | 0.261538i | ||||
\(121\) | 4.29206 | 0.390187 | ||||||||
\(122\) | 1.61920 | − | 1.61920i | 0.146595 | − | 0.146595i | ||||
\(123\) | 3.23488 | − | 1.70359i | 0.291679 | − | 0.153607i | ||||
\(124\) | 9.39662i | 0.843841i | ||||||||
\(125\) | −2.85791 | − | 10.8089i | −0.255619 | − | 0.966778i | ||||
\(126\) | −3.83397 | + | 5.58793i | −0.341557 | + | 0.497812i | ||||
\(127\) | −8.05797 | − | 8.05797i | −0.715029 | − | 0.715029i | 0.252554 | − | 0.967583i | \(-0.418729\pi\) |
−0.967583 | + | 0.252554i | \(0.918729\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 10.2678 | + | 3.18377i | 0.904027 | + | 0.280315i | ||||
\(130\) | 0.947239 | − | 2.02552i | 0.0830784 | − | 0.177650i | ||||
\(131\) | − | 14.2078i | − | 1.24134i | −0.784071 | − | 0.620671i | \(-0.786860\pi\) | ||
0.784071 | − | 0.620671i | \(-0.213140\pi\) | |||||||
\(132\) | −2.09030 | − | 3.96919i | −0.181937 | − | 0.345474i | ||||
\(133\) | 10.8210 | − | 10.8210i | 0.938303 | − | 0.938303i | ||||
\(134\) | 15.5458 | 1.34295 | ||||||||
\(135\) | −9.88071 | − | 6.11323i | −0.850396 | − | 0.526143i | ||||
\(136\) | −0.219806 | −0.0188482 | ||||||||
\(137\) | −10.9549 | + | 10.9549i | −0.935939 | + | 0.935939i | −0.998068 | − | 0.0621288i | \(-0.980211\pi\) |
0.0621288 | + | 0.998068i | \(0.480211\pi\) | |||||||
\(138\) | 2.06975 | + | 3.93017i | 0.176189 | + | 0.334558i | ||||
\(139\) | 15.0559i | 1.27703i | 0.769611 | + | 0.638513i | \(0.220450\pi\) | ||||
−0.769611 | + | 0.638513i | \(0.779550\pi\) | |||||||
\(140\) | 4.74837 | − | 1.72233i | 0.401311 | − | 0.145564i | ||||
\(141\) | 8.69863 | + | 2.69722i | 0.732557 | + | 0.227147i | ||||
\(142\) | −6.79393 | − | 6.79393i | −0.570134 | − | 0.570134i | ||||
\(143\) | 1.83139 | + | 1.83139i | 0.153148 | + | 0.153148i | ||||
\(144\) | 1.69726 | − | 2.47372i | 0.141438 | − | 0.206144i | ||||
\(145\) | 1.80440 | + | 0.843830i | 0.149847 | + | 0.0700763i | ||||
\(146\) | − | 2.33609i | − | 0.193336i | ||||||
\(147\) | −2.90767 | + | 1.53127i | −0.239821 | + | 0.126297i | ||||
\(148\) | −2.88699 | + | 2.88699i | −0.237309 | + | 0.237309i | ||||
\(149\) | −15.7204 | −1.28787 | −0.643934 | − | 0.765081i | \(-0.722699\pi\) | ||||
−0.643934 | + | 0.765081i | \(0.722699\pi\) | |||||||
\(150\) | 3.33454 | + | 7.99255i | 0.272264 | + | 0.652589i | ||||
\(151\) | −14.3294 | −1.16611 | −0.583056 | − | 0.812432i | \(-0.698143\pi\) | ||||
−0.583056 | + | 0.812432i | \(0.698143\pi\) | |||||||
\(152\) | −4.79037 | + | 4.79037i | −0.388550 | + | 0.388550i | ||||
\(153\) | −0.120683 | − | 0.648280i | −0.00975661 | − | 0.0524104i | ||||
\(154\) | 5.85052i | 0.471448i | ||||||||
\(155\) | 19.0330 | + | 8.90085i | 1.52877 | + | 0.714933i | ||||
\(156\) | −0.512970 | + | 1.65435i | −0.0410705 | + | 0.132454i | ||||
\(157\) | −9.89671 | − | 9.89671i | −0.789843 | − | 0.789843i | 0.191625 | − | 0.981468i | \(-0.438624\pi\) |
−0.981468 | + | 0.191625i | \(0.938624\pi\) | |||||||
\(158\) | −8.56764 | − | 8.56764i | −0.681605 | − | 0.681605i | ||||
\(159\) | −1.62647 | + | 5.24543i | −0.128988 | + | 0.415990i | ||||
\(160\) | −2.10206 | + | 0.762461i | −0.166182 | + | 0.0602778i | ||||
\(161\) | − | 5.79300i | − | 0.456553i | ||||||
\(162\) | 8.22769 | + | 3.64761i | 0.646429 | + | 0.286583i | ||||
\(163\) | −9.12788 | + | 9.12788i | −0.714951 | + | 0.714951i | −0.967567 | − | 0.252616i | \(-0.918709\pi\) |
0.252616 | + | 0.967567i | \(0.418709\pi\) | |||||||
\(164\) | 2.11082 | 0.164827 | ||||||||
\(165\) | −10.0197 | + | 0.474171i | −0.780032 | + | 0.0369141i | ||||
\(166\) | 8.39941 | 0.651921 | ||||||||
\(167\) | −13.1748 | + | 13.1748i | −1.01950 | + | 1.01950i | −0.0196916 | + | 0.999806i | \(0.506268\pi\) |
−0.999806 | + | 0.0196916i | \(0.993732\pi\) | |||||||
\(168\) | −3.46184 | + | 1.82311i | −0.267087 | + | 0.140656i | ||||
\(169\) | − | 1.00000i | − | 0.0769231i | ||||||
\(170\) | −0.208209 | + | 0.445222i | −0.0159689 | + | 0.0341469i | ||||
\(171\) | −16.7585 | − | 11.4983i | −1.28155 | − | 0.879295i | ||||
\(172\) | 4.38869 | + | 4.38869i | 0.334634 | + | 0.334634i | ||||
\(173\) | −11.0567 | − | 11.0567i | −0.840628 | − | 0.840628i | 0.148312 | − | 0.988941i | \(-0.452616\pi\) |
−0.988941 | + | 0.148312i | \(0.952616\pi\) | |||||||
\(174\) | −1.47374 | − | 0.456970i | −0.111724 | − | 0.0346428i | ||||
\(175\) | 1.00922 | − | 11.2494i | 0.0762900 | − | 0.850374i | ||||
\(176\) | − | 2.58997i | − | 0.195226i | ||||||
\(177\) | −2.22038 | − | 4.21620i | −0.166894 | − | 0.316909i | ||||
\(178\) | −4.55083 | + | 4.55083i | −0.341099 | + | 0.341099i | ||||
\(179\) | −11.4964 | −0.859281 | −0.429641 | − | 0.903000i | \(-0.641360\pi\) | ||||
−0.429641 | + | 0.903000i | \(0.641360\pi\) | |||||||
\(180\) | −3.40287 | − | 5.78105i | −0.253635 | − | 0.430894i | ||||
\(181\) | 17.6773 | 1.31394 | 0.656970 | − | 0.753917i | \(-0.271838\pi\) | ||||
0.656970 | + | 0.753917i | \(0.271838\pi\) | |||||||
\(182\) | 1.59729 | − | 1.59729i | 0.118399 | − | 0.118399i | ||||
\(183\) | 1.84811 | + | 3.50931i | 0.136616 | + | 0.259416i | ||||
\(184\) | 2.56451i | 0.189058i | ||||||||
\(185\) | 3.11299 | + | 8.58232i | 0.228871 | + | 0.630985i | ||||
\(186\) | −15.5453 | − | 4.82019i | −1.13983 | − | 0.353433i | ||||
\(187\) | −0.402549 | − | 0.402549i | −0.0294373 | − | 0.0294373i | ||||
\(188\) | 3.71800 | + | 3.71800i | 0.271163 | + | 0.271163i | ||||
\(189\) | −7.27765 | − | 9.20915i | −0.529371 | − | 0.669867i | ||||
\(190\) | 5.16537 | + | 14.2406i | 0.374735 | + | 1.03312i | ||||
\(191\) | 18.0153i | 1.30354i | 0.758416 | + | 0.651771i | \(0.225974\pi\) | ||||
−0.758416 | + | 0.651771i | \(0.774026\pi\) | |||||||
\(192\) | 1.53252 | − | 0.807075i | 0.110600 | − | 0.0582456i | ||||
\(193\) | 3.58559 | − | 3.58559i | 0.258097 | − | 0.258097i | −0.566183 | − | 0.824280i | \(-0.691580\pi\) |
0.824280 | + | 0.566183i | \(0.191580\pi\) | |||||||
\(194\) | −12.5138 | −0.898439 | ||||||||
\(195\) | 2.86501 | + | 2.60609i | 0.205167 | + | 0.186626i | ||||
\(196\) | −1.89731 | −0.135522 | ||||||||
\(197\) | −11.8377 | + | 11.8377i | −0.843398 | + | 0.843398i | −0.989299 | − | 0.145901i | \(-0.953392\pi\) |
0.145901 | + | 0.989299i | \(0.453392\pi\) | |||||||
\(198\) | 7.63868 | − | 1.42200i | 0.542857 | − | 0.101057i | ||||
\(199\) | − | 6.88147i | − | 0.487814i | −0.969799 | − | 0.243907i | \(-0.921571\pi\) | ||
0.969799 | − | 0.243907i | \(-0.0784292\pi\) | |||||||
\(200\) | −0.446773 | + | 4.98000i | −0.0315916 | + | 0.352139i | ||||
\(201\) | −7.97454 | + | 25.7182i | −0.562481 | + | 1.81402i | ||||
\(202\) | 11.4520 | + | 11.4520i | 0.805757 | + | 0.805757i | ||||
\(203\) | 1.42292 | + | 1.42292i | 0.0998692 | + | 0.0998692i | ||||
\(204\) | 0.112754 | − | 0.363635i | 0.00789435 | − | 0.0254595i | ||||
\(205\) | 1.99945 | − | 4.27551i | 0.139648 | − | 0.298614i | ||||
\(206\) | 16.1506i | 1.12526i | ||||||||
\(207\) | −7.56358 | + | 1.40802i | −0.525705 | + | 0.0978643i | ||||
\(208\) | −0.707107 | + | 0.707107i | −0.0490290 | + | 0.0490290i | ||||
\(209\) | −17.5460 | −1.21368 | ||||||||
\(210\) | 0.413561 | + | 8.73895i | 0.0285384 | + | 0.603045i | ||||
\(211\) | −7.30339 | −0.502786 | −0.251393 | − | 0.967885i | \(-0.580889\pi\) | ||||
−0.251393 | + | 0.967885i | \(0.580889\pi\) | |||||||
\(212\) | −2.24202 | + | 2.24202i | −0.153983 | + | 0.153983i | ||||
\(213\) | 14.7246 | − | 7.75442i | 1.00891 | − | 0.531324i | ||||
\(214\) | − | 14.2490i | − | 0.974043i | ||||||
\(215\) | 13.0465 | − | 4.73224i | 0.889765 | − | 0.322736i | ||||
\(216\) | 3.22175 | + | 4.07680i | 0.219212 | + | 0.277391i | ||||
\(217\) | 15.0092 | + | 15.0092i | 1.01889 | + | 1.01889i | ||||
\(218\) | −6.49057 | − | 6.49057i | −0.439597 | − | 0.439597i | ||||
\(219\) | 3.86470 | + | 1.19834i | 0.261152 | + | 0.0809765i | ||||
\(220\) | −5.24604 | − | 2.45332i | −0.353688 | − | 0.165403i | ||||
\(221\) | 0.219806i | 0.0147857i | ||||||||
\(222\) | −3.29514 | − | 6.25701i | −0.221155 | − | 0.419943i | ||||
\(223\) | 16.1979 | − | 16.1979i | 1.08469 | − | 1.08469i | 0.0886232 | − | 0.996065i | \(-0.471753\pi\) |
0.996065 | − | 0.0886232i | \(-0.0282467\pi\) | |||||||
\(224\) | −2.25891 | −0.150930 | ||||||||
\(225\) | −14.9330 | + | 1.41654i | −0.995531 | + | 0.0944362i | ||||
\(226\) | −11.0898 | −0.737685 | ||||||||
\(227\) | −17.2226 | + | 17.2226i | −1.14310 | + | 1.14310i | −0.155223 | + | 0.987879i | \(0.549610\pi\) |
−0.987879 | + | 0.155223i | \(0.950390\pi\) | |||||||
\(228\) | −5.46761 | − | 10.3823i | −0.362102 | − | 0.687581i | ||||
\(229\) | − | 23.5974i | − | 1.55936i | −0.626177 | − | 0.779681i | \(-0.715381\pi\) | ||
0.626177 | − | 0.779681i | \(-0.284619\pi\) | |||||||
\(230\) | 5.19447 | + | 2.42920i | 0.342513 | + | 0.160177i | ||||
\(231\) | −9.67878 | − | 3.00114i | −0.636817 | − | 0.197461i | ||||
\(232\) | −0.629912 | − | 0.629912i | −0.0413558 | − | 0.0413558i | ||||
\(233\) | −7.44530 | − | 7.44530i | −0.487758 | − | 0.487758i | 0.419840 | − | 0.907598i | \(-0.362086\pi\) |
−0.907598 | + | 0.419840i | \(0.862086\pi\) | |||||||
\(234\) | −2.47372 | − | 1.69726i | −0.161712 | − | 0.110953i | ||||
\(235\) | 11.0527 | − | 4.00905i | 0.721000 | − | 0.261522i | ||||
\(236\) | − | 2.75114i | − | 0.179084i | ||||||
\(237\) | 18.5688 | − | 9.77889i | 1.20617 | − | 0.635207i | ||||
\(238\) | −0.351094 | + | 0.351094i | −0.0227581 | + | 0.0227581i | ||||
\(239\) | 19.2221 | 1.24337 | 0.621687 | − | 0.783266i | \(-0.286448\pi\) | ||||
0.621687 | + | 0.783266i | \(0.286448\pi\) | |||||||
\(240\) | −0.183080 | − | 3.86865i | −0.0118177 | − | 0.249721i | ||||
\(241\) | 16.0808 | 1.03586 | 0.517928 | − | 0.855424i | \(-0.326704\pi\) | ||||
0.517928 | + | 0.855424i | \(0.326704\pi\) | |||||||
\(242\) | −3.03494 | + | 3.03494i | −0.195094 | + | 0.195094i | ||||
\(243\) | −10.2550 | + | 11.7403i | −0.657857 | + | 0.753143i | ||||
\(244\) | 2.28989i | 0.146595i | ||||||||
\(245\) | −1.79721 | + | 3.84304i | −0.114819 | + | 0.245523i | ||||
\(246\) | −1.08279 | + | 3.49202i | −0.0690360 | + | 0.222643i | ||||
\(247\) | 4.79037 | + | 4.79037i | 0.304804 | + | 0.304804i | ||||
\(248\) | −6.64441 | − | 6.64441i | −0.421921 | − | 0.421921i | ||||
\(249\) | −4.30865 | + | 13.8955i | −0.273050 | + | 0.880594i | ||||
\(250\) | 9.66389 | + | 5.62220i | 0.611198 | + | 0.355579i | ||||
\(251\) | − | 25.4480i | − | 1.60626i | −0.595801 | − | 0.803132i | \(-0.703165\pi\) | ||
0.595801 | − | 0.803132i | \(-0.296835\pi\) | |||||||
\(252\) | −1.24024 | − | 6.66228i | −0.0781276 | − | 0.419684i | ||||
\(253\) | −4.69660 | + | 4.69660i | −0.295273 | + | 0.295273i | ||||
\(254\) | 11.3957 | 0.715029 | ||||||||
\(255\) | −0.629746 | − | 0.572835i | −0.0394362 | − | 0.0358723i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.1316 | − | 12.1316i | 0.756749 | − | 0.756749i | −0.218980 | − | 0.975729i | \(-0.570273\pi\) |
0.975729 | + | 0.218980i | \(0.0702731\pi\) | |||||||
\(258\) | −9.51167 | + | 5.00914i | −0.592171 | + | 0.311856i | ||||
\(259\) | 9.22273i | 0.573073i | ||||||||
\(260\) | 0.762461 | + | 2.10206i | 0.0472858 | + | 0.130364i | ||||
\(261\) | 1.51197 | − | 2.20367i | 0.0935887 | − | 0.136404i | ||||
\(262\) | 10.0464 | + | 10.0464i | 0.620671 | + | 0.620671i | ||||
\(263\) | 3.81582 | + | 3.81582i | 0.235294 | + | 0.235294i | 0.814898 | − | 0.579604i | \(-0.196793\pi\) |
−0.579604 | + | 0.814898i | \(0.696793\pi\) | |||||||
\(264\) | 4.28471 | + | 1.32858i | 0.263705 | + | 0.0817683i | ||||
\(265\) | 2.41753 | + | 6.66499i | 0.148508 | + | 0.409427i | ||||
\(266\) | 15.3033i | 0.938303i | ||||||||
\(267\) | −5.19421 | − | 9.86310i | −0.317881 | − | 0.603612i | ||||
\(268\) | −10.9926 | + | 10.9926i | −0.671477 | + | 0.671477i | ||||
\(269\) | −2.98732 | −0.182140 | −0.0910701 | − | 0.995844i | \(-0.529029\pi\) | ||||
−0.0910701 | + | 0.995844i | \(0.529029\pi\) | |||||||
\(270\) | 11.3094 | − | 2.66401i | 0.688270 | − | 0.162127i | ||||
\(271\) | 17.9161 | 1.08832 | 0.544162 | − | 0.838980i | \(-0.316848\pi\) | ||||
0.544162 | + | 0.838980i | \(0.316848\pi\) | |||||||
\(272\) | 0.155426 | − | 0.155426i | 0.00942410 | − | 0.00942410i | ||||
\(273\) | 1.82311 | + | 3.46184i | 0.110340 | + | 0.209520i | ||||
\(274\) | − | 15.4926i | − | 0.935939i | ||||||
\(275\) | −9.93851 | + | 8.30208i | −0.599315 | + | 0.500634i | ||||
\(276\) | −4.24259 | − | 1.31552i | −0.255374 | − | 0.0791848i | ||||
\(277\) | 11.8188 | + | 11.8188i | 0.710120 | + | 0.710120i | 0.966560 | − | 0.256440i | \(-0.0825496\pi\) |
−0.256440 | + | 0.966560i | \(0.582550\pi\) | |||||||
\(278\) | −10.6461 | − | 10.6461i | −0.638513 | − | 0.638513i | ||||
\(279\) | 15.9485 | − | 23.2446i | 0.954812 | − | 1.39162i | ||||
\(280\) | −2.13973 | + | 4.57548i | −0.127873 | + | 0.273437i | ||||
\(281\) | − | 0.763857i | − | 0.0455679i | −0.999740 | − | 0.0227839i | \(-0.992747\pi\) | ||
0.999740 | − | 0.0227839i | \(-0.00725298\pi\) | |||||||
\(282\) | −8.05808 | + | 4.24364i | −0.479852 | + | 0.252705i | ||||
\(283\) | −3.73216 | + | 3.73216i | −0.221854 | + | 0.221854i | −0.809279 | − | 0.587425i | \(-0.800142\pi\) |
0.587425 | + | 0.809279i | \(0.300142\pi\) | |||||||
\(284\) | 9.60806 | 0.570134 | ||||||||
\(285\) | −26.2086 | + | 1.24029i | −1.55246 | + | 0.0734686i | ||||
\(286\) | −2.58997 | −0.153148 | ||||||||
\(287\) | 3.37160 | − | 3.37160i | 0.199019 | − | 0.199019i | ||||
\(288\) | 0.549041 | + | 2.94933i | 0.0323526 | + | 0.173791i | ||||
\(289\) | 16.9517i | 0.997158i | ||||||||
\(290\) | −1.87258 | + | 0.679223i | −0.109962 | + | 0.0398854i | ||||
\(291\) | 6.41921 | − | 20.7022i | 0.376301 | − | 1.21358i | ||||
\(292\) | 1.65186 | + | 1.65186i | 0.0966680 | + | 0.0966680i | ||||
\(293\) | 22.4543 | + | 22.4543i | 1.31180 | + | 1.31180i | 0.920091 | + | 0.391704i | \(0.128114\pi\) |
0.391704 | + | 0.920091i | \(0.371886\pi\) | |||||||
\(294\) | 0.973263 | − | 3.13881i | 0.0567619 | − | 0.183059i | ||||
\(295\) | −5.57250 | − | 2.60599i | −0.324444 | − | 0.151727i | ||||
\(296\) | − | 4.08282i | − | 0.237309i | ||||||
\(297\) | −1.56593 | + | 13.3665i | −0.0908647 | + | 0.775601i | ||||
\(298\) | 11.1160 | − | 11.1160i | 0.643934 | − | 0.643934i | ||||
\(299\) | 2.56451 | 0.148309 | ||||||||
\(300\) | −8.00946 | − | 3.29371i | −0.462426 | − | 0.190162i | ||||
\(301\) | 14.0200 | 0.808102 | ||||||||
\(302\) | 10.1324 | − | 10.1324i | 0.583056 | − | 0.583056i | ||||
\(303\) | −24.8200 | + | 13.0710i | −1.42587 | + | 0.750909i | ||||
\(304\) | − | 6.77461i | − | 0.388550i | ||||||
\(305\) | 4.63822 | + | 2.16908i | 0.265584 | + | 0.124201i | ||||
\(306\) | 0.543739 | + | 0.373068i | 0.0310835 | + | 0.0213269i | ||||
\(307\) | 4.92117 | + | 4.92117i | 0.280866 | + | 0.280866i | 0.833454 | − | 0.552588i | \(-0.186360\pi\) |
−0.552588 | + | 0.833454i | \(0.686360\pi\) | |||||||
\(308\) | −4.13694 | − | 4.13694i | −0.235724 | − | 0.235724i | ||||
\(309\) | −26.7186 | − | 8.28476i | −1.51997 | − | 0.471304i | ||||
\(310\) | −19.7522 | + | 7.16455i | −1.12185 | + | 0.406919i | ||||
\(311\) | 2.99483i | 0.169821i | 0.996389 | + | 0.0849107i | \(0.0270605\pi\) | ||||
−0.996389 | + | 0.0849107i | \(0.972940\pi\) | |||||||
\(312\) | −0.807075 | − | 1.53252i | −0.0456916 | − | 0.0867621i | ||||
\(313\) | −22.8829 | + | 22.8829i | −1.29342 | + | 1.29342i | −0.360759 | + | 0.932659i | \(0.617482\pi\) |
−0.932659 | + | 0.360759i | \(0.882518\pi\) | |||||||
\(314\) | 13.9961 | 0.789843 | ||||||||
\(315\) | −14.6694 | − | 3.79865i | −0.826527 | − | 0.214030i | ||||
\(316\) | 12.1165 | 0.681605 | ||||||||
\(317\) | 14.7717 | − | 14.7717i | 0.829659 | − | 0.829659i | −0.157810 | − | 0.987469i | \(-0.550444\pi\) |
0.987469 | + | 0.157810i | \(0.0504435\pi\) | |||||||
\(318\) | −2.55899 | − | 4.85917i | −0.143501 | − | 0.272489i | ||||
\(319\) | − | 2.30722i | − | 0.129180i | ||||||
\(320\) | 0.947239 | − | 2.02552i | 0.0529523 | − | 0.113230i | ||||
\(321\) | 23.5728 | + | 7.30932i | 1.31571 | + | 0.407967i | ||||
\(322\) | 4.09627 | + | 4.09627i | 0.228276 | + | 0.228276i | ||||
\(323\) | −1.05295 | − | 1.05295i | −0.0585878 | − | 0.0585878i | ||||
\(324\) | −8.39711 | + | 3.23861i | −0.466506 | + | 0.179923i | ||||
\(325\) | 4.98000 | + | 0.446773i | 0.276241 | + | 0.0247825i | ||||
\(326\) | − | 12.9088i | − | 0.714951i | ||||||
\(327\) | 14.0671 | − | 7.40818i | 0.777914 | − | 0.409673i | ||||
\(328\) | −1.49257 | + | 1.49257i | −0.0824136 | + | 0.0824136i | ||||
\(329\) | 11.8775 | 0.654826 | ||||||||
\(330\) | 6.74971 | − | 7.42028i | 0.371559 | − | 0.408473i | ||||
\(331\) | −0.111775 | −0.00614372 | −0.00307186 | − | 0.999995i | \(-0.500978\pi\) | ||||
−0.00307186 | + | 0.999995i | \(0.500978\pi\) | |||||||
\(332\) | −5.93928 | + | 5.93928i | −0.325960 | + | 0.325960i | ||||
\(333\) | 12.0416 | − | 2.24164i | 0.659874 | − | 0.122841i | ||||
\(334\) | − | 18.6320i | − | 1.01950i | ||||||
\(335\) | 11.8531 | + | 32.6782i | 0.647603 | + | 1.78540i | ||||
\(336\) | 1.15876 | − | 3.73703i | 0.0632153 | − | 0.203871i | ||||
\(337\) | −8.54851 | − | 8.54851i | −0.465667 | − | 0.465667i | 0.434840 | − | 0.900508i | \(-0.356805\pi\) |
−0.900508 | + | 0.434840i | \(0.856805\pi\) | |||||||
\(338\) | 0.707107 | + | 0.707107i | 0.0384615 | + | 0.0384615i | ||||
\(339\) | 5.68876 | − | 18.3464i | 0.308971 | − | 0.996442i | ||||
\(340\) | −0.167593 | − | 0.462045i | −0.00908902 | − | 0.0250579i | ||||
\(341\) | − | 24.3370i | − | 1.31792i | ||||||
\(342\) | 19.9806 | − | 3.71954i | 1.08043 | − | 0.201130i | ||||
\(343\) | −14.2116 | + | 14.2116i | −0.767355 | + | 0.767355i | ||||
\(344\) | −6.20654 | −0.334634 | ||||||||
\(345\) | −6.68335 | + | 7.34734i | −0.359820 | + | 0.395567i | ||||
\(346\) | 15.6366 | 0.840628 | ||||||||
\(347\) | 6.09851 | − | 6.09851i | 0.327385 | − | 0.327385i | −0.524206 | − | 0.851591i | \(-0.675638\pi\) |
0.851591 | + | 0.524206i | \(0.175638\pi\) | |||||||
\(348\) | 1.36522 | − | 0.718967i | 0.0731834 | − | 0.0385407i | ||||
\(349\) | − | 4.89335i | − | 0.261935i | −0.991387 | − | 0.130967i | \(-0.958192\pi\) | ||
0.991387 | − | 0.130967i | \(-0.0418083\pi\) | |||||||
\(350\) | 7.24089 | + | 8.66815i | 0.387042 | + | 0.463332i | ||||
\(351\) | 4.07680 | − | 3.22175i | 0.217604 | − | 0.171964i | ||||
\(352\) | 1.83139 | + | 1.83139i | 0.0976132 | + | 0.0976132i | ||||
\(353\) | 8.68950 | + | 8.68950i | 0.462495 | + | 0.462495i | 0.899473 | − | 0.436977i | \(-0.143951\pi\) |
−0.436977 | + | 0.899473i | \(0.643951\pi\) | |||||||
\(354\) | 4.55135 | + | 1.41126i | 0.241901 | + | 0.0750074i | ||||
\(355\) | 9.10114 | − | 19.4613i | 0.483038 | − | 1.03290i | ||||
\(356\) | − | 6.43585i | − | 0.341099i | ||||||
\(357\) | −0.400731 | − | 0.760933i | −0.0212089 | − | 0.0402728i | ||||
\(358\) | 8.12918 | − | 8.12918i | 0.429641 | − | 0.429641i | ||||
\(359\) | 31.8464 | 1.68079 | 0.840394 | − | 0.541975i | \(-0.182323\pi\) | ||||
0.840394 | + | 0.541975i | \(0.182323\pi\) | |||||||
\(360\) | 6.49401 | + | 1.68163i | 0.342264 | + | 0.0886296i | ||||
\(361\) | −26.8953 | −1.41554 | ||||||||
\(362\) | −12.4997 | + | 12.4997i | −0.656970 | + | 0.656970i | ||||
\(363\) | −3.46401 | − | 6.57768i | −0.181813 | − | 0.345239i | ||||
\(364\) | 2.25891i | 0.118399i | ||||||||
\(365\) | 4.91059 | − | 1.78117i | 0.257032 | − | 0.0932309i | ||||
\(366\) | −3.78827 | − | 1.17465i | −0.198016 | − | 0.0613997i | ||||
\(367\) | 14.9797 | + | 14.9797i | 0.781935 | + | 0.781935i | 0.980157 | − | 0.198222i | \(-0.0635167\pi\) |
−0.198222 | + | 0.980157i | \(0.563517\pi\) | |||||||
\(368\) | −1.81338 | − | 1.81338i | −0.0945290 | − | 0.0945290i | ||||
\(369\) | −5.22158 | − | 3.58261i | −0.271825 | − | 0.186503i | ||||
\(370\) | −8.26983 | − | 3.86740i | −0.429928 | − | 0.201057i | ||||
\(371\) | 7.16233i | 0.371850i | ||||||||
\(372\) | 14.4005 | − | 7.58377i | 0.746633 | − | 0.393200i | ||||
\(373\) | 16.2983 | − | 16.2983i | 0.843893 | − | 0.843893i | −0.145470 | − | 0.989363i | \(-0.546469\pi\) |
0.989363 | + | 0.145470i | \(0.0464693\pi\) | |||||||
\(374\) | 0.569291 | 0.0294373 | ||||||||
\(375\) | −14.2584 | + | 13.1034i | −0.736298 | + | 0.676657i | ||||
\(376\) | −5.25805 | −0.271163 | ||||||||
\(377\) | −0.629912 | + | 0.629912i | −0.0324421 | + | 0.0324421i | ||||
\(378\) | 11.6579 | + | 1.36577i | 0.599619 | + | 0.0702478i | ||||
\(379\) | − | 6.82263i | − | 0.350455i | −0.984528 | − | 0.175228i | \(-0.943934\pi\) | ||
0.984528 | − | 0.175228i | \(-0.0560661\pi\) | |||||||
\(380\) | −13.7221 | − | 6.41718i | −0.703930 | − | 0.329194i | ||||
\(381\) | −5.84565 | + | 18.8524i | −0.299482 | + | 0.965838i | ||||
\(382\) | −12.7388 | − | 12.7388i | −0.651771 | − | 0.651771i | ||||
\(383\) | −15.1912 | − | 15.1912i | −0.776235 | − | 0.776235i | 0.202953 | − | 0.979188i | \(-0.434946\pi\) |
−0.979188 | + | 0.202953i | \(0.934946\pi\) | |||||||
\(384\) | −0.512970 | + | 1.65435i | −0.0261774 | + | 0.0844230i | ||||
\(385\) | −12.2981 | + | 4.46079i | −0.626771 | + | 0.227343i | ||||
\(386\) | 5.07079i | 0.258097i | ||||||||
\(387\) | −3.40765 | − | 18.3051i | −0.173220 | − | 0.930503i | ||||
\(388\) | 8.84860 | − | 8.84860i | 0.449219 | − | 0.449219i | ||||
\(389\) | −2.88396 | −0.146222 | −0.0731112 | − | 0.997324i | \(-0.523293\pi\) | ||||
−0.0731112 | + | 0.997324i | \(0.523293\pi\) | |||||||
\(390\) | −3.86865 | + | 0.183080i | −0.195897 | + | 0.00927060i | ||||
\(391\) | −0.563694 | −0.0285072 | ||||||||
\(392\) | 1.34160 | − | 1.34160i | 0.0677610 | − | 0.0677610i | ||||
\(393\) | −21.7738 | + | 11.4668i | −1.09834 | + | 0.578422i | ||||
\(394\) | − | 16.7410i | − | 0.843398i | ||||||
\(395\) | 11.4772 | − | 24.5422i | 0.577480 | − | 1.23485i | ||||
\(396\) | −4.39585 | + | 6.40687i | −0.220900 | + | 0.321957i | ||||
\(397\) | −26.9155 | − | 26.9155i | −1.35085 | − | 1.35085i | −0.884712 | − | 0.466137i | \(-0.845645\pi\) |
−0.466137 | − | 0.884712i | \(-0.654355\pi\) | |||||||
\(398\) | 4.86593 | + | 4.86593i | 0.243907 | + | 0.243907i | ||||
\(399\) | −25.3169 | − | 7.85012i | −1.26743 | − | 0.392997i | ||||
\(400\) | −3.20547 | − | 3.83731i | −0.160274 | − | 0.191865i | ||||
\(401\) | − | 29.6662i | − | 1.48146i | −0.671803 | − | 0.740729i | \(-0.734480\pi\) | ||
0.671803 | − | 0.740729i | \(-0.265520\pi\) | |||||||
\(402\) | −12.5466 | − | 23.8243i | −0.625769 | − | 1.18825i | ||||
\(403\) | −6.64441 | + | 6.64441i | −0.330982 | + | 0.330982i | ||||
\(404\) | −16.1955 | −0.805757 | ||||||||
\(405\) | −1.39420 | + | 20.0763i | −0.0692782 | + | 0.997597i | ||||
\(406\) | −2.01231 | −0.0998692 | ||||||||
\(407\) | 7.47721 | − | 7.47721i | 0.370631 | − | 0.370631i | ||||
\(408\) | 0.177400 | + | 0.336858i | 0.00878260 | + | 0.0166769i | ||||
\(409\) | − | 3.05276i | − | 0.150949i | −0.997148 | − | 0.0754747i | \(-0.975953\pi\) | ||
0.997148 | − | 0.0754747i | \(-0.0240472\pi\) | |||||||
\(410\) | 1.60942 | + | 4.43707i | 0.0794834 | + | 0.219131i | ||||
\(411\) | 25.6300 | + | 7.94722i | 1.26424 | + | 0.392007i | ||||
\(412\) | −11.4202 | − | 11.4202i | −0.562632 | − | 0.562632i | ||||
\(413\) | −4.39438 | − | 4.39438i | −0.216234 | − | 0.216234i | ||||
\(414\) | 4.35264 | − | 6.34388i | 0.213921 | − | 0.311785i | ||||
\(415\) | 6.40422 | + | 17.6561i | 0.314371 | + | 0.866702i | ||||
\(416\) | − | 1.00000i | − | 0.0490290i | ||||||
\(417\) | 23.0736 | − | 12.1513i | 1.12992 | − | 0.595049i | ||||
\(418\) | 12.4069 | − | 12.4069i | 0.606842 | − | 0.606842i | ||||
\(419\) | 6.17929 | 0.301878 | 0.150939 | − | 0.988543i | \(-0.451770\pi\) | ||||
0.150939 | + | 0.988543i | \(0.451770\pi\) | |||||||
\(420\) | −6.47181 | − | 5.88694i | −0.315792 | − | 0.287253i | ||||
\(421\) | 2.65347 | 0.129322 | 0.0646610 | − | 0.997907i | \(-0.479403\pi\) | ||||
0.0646610 | + | 0.997907i | \(0.479403\pi\) | |||||||
\(422\) | 5.16428 | − | 5.16428i | 0.251393 | − | 0.251393i | ||||
\(423\) | −2.88688 | − | 15.5077i | −0.140365 | − | 0.754011i | ||||
\(424\) | − | 3.17070i | − | 0.153983i | ||||||
\(425\) | −1.09463 | − | 0.0982034i | −0.0530975 | − | 0.00476357i | ||||
\(426\) | −4.92865 | + | 15.8951i | −0.238794 | + | 0.770118i | ||||
\(427\) | 3.65763 | + | 3.65763i | 0.177005 | + | 0.177005i | ||||
\(428\) | 10.0756 | + | 10.0756i | 0.487021 | + | 0.487021i | ||||
\(429\) | 1.32858 | − | 4.28471i | 0.0641443 | − | 0.206868i | ||||
\(430\) | −5.87908 | + | 12.5715i | −0.283514 | + | 0.606251i | ||||
\(431\) | − | 35.9248i | − | 1.73043i | −0.501397 | − | 0.865217i | \(-0.667180\pi\) | ||
0.501397 | − | 0.865217i | \(-0.332820\pi\) | |||||||
\(432\) | −5.16086 | − | 0.604615i | −0.248302 | − | 0.0290895i | ||||
\(433\) | −8.25075 | + | 8.25075i | −0.396506 | + | 0.396506i | −0.876999 | − | 0.480493i | \(-0.840458\pi\) |
0.480493 | + | 0.876999i | \(0.340458\pi\) | |||||||
\(434\) | −21.2261 | −1.01889 | ||||||||
\(435\) | −0.163093 | − | 3.44632i | −0.00781971 | − | 0.165238i | ||||
\(436\) | 9.17905 | 0.439597 | ||||||||
\(437\) | −12.2849 | + | 12.2849i | −0.587669 | + | 0.587669i | ||||
\(438\) | −3.58011 | + | 1.88540i | −0.171064 | + | 0.0900877i | ||||
\(439\) | − | 5.36829i | − | 0.256215i | −0.991760 | − | 0.128107i | \(-0.959110\pi\) | ||
0.991760 | − | 0.128107i | \(-0.0408902\pi\) | |||||||
\(440\) | 5.44427 | − | 1.97475i | 0.259545 | − | 0.0941425i | ||||
\(441\) | 4.69342 | + | 3.22023i | 0.223496 | + | 0.153344i | ||||
\(442\) | −0.155426 | − | 0.155426i | −0.00739287 | − | 0.00739287i | ||||
\(443\) | 11.3450 | + | 11.3450i | 0.539018 | + | 0.539018i | 0.923241 | − | 0.384223i | \(-0.125530\pi\) |
−0.384223 | + | 0.923241i | \(0.625530\pi\) | |||||||
\(444\) | 6.75439 | + | 2.09436i | 0.320549 | + | 0.0993941i | ||||
\(445\) | −13.0360 | − | 6.09629i | −0.617964 | − | 0.288992i | ||||
\(446\) | 22.9072i | 1.08469i | ||||||||
\(447\) | 12.6876 | + | 24.0920i | 0.600102 | + | 1.13951i | ||||
\(448\) | 1.59729 | − | 1.59729i | 0.0754650 | − | 0.0754650i | ||||
\(449\) | −16.0281 | −0.756412 | −0.378206 | − | 0.925721i | \(-0.623459\pi\) | ||||
−0.378206 | + | 0.925721i | \(0.623459\pi\) | |||||||
\(450\) | 9.55755 | − | 11.5608i | 0.450547 | − | 0.544984i | ||||
\(451\) | −5.46696 | −0.257429 | ||||||||
\(452\) | 7.84170 | − | 7.84170i | 0.368843 | − | 0.368843i | ||||
\(453\) | 11.5649 | + | 21.9602i | 0.543367 | + | 1.03178i | ||||
\(454\) | − | 24.3564i | − | 1.14310i | ||||||
\(455\) | 4.57548 | + | 2.13973i | 0.214502 | + | 0.100312i | ||||
\(456\) | 11.2075 | + | 3.47517i | 0.524842 | + | 0.162740i | ||||
\(457\) | 0.963319 | + | 0.963319i | 0.0450621 | + | 0.0450621i | 0.729279 | − | 0.684217i | \(-0.239856\pi\) |
−0.684217 | + | 0.729279i | \(0.739856\pi\) | |||||||
\(458\) | 16.6859 | + | 16.6859i | 0.779681 | + | 0.779681i | ||||
\(459\) | −0.896106 | + | 0.708160i | −0.0418266 | + | 0.0330541i | ||||
\(460\) | −5.39075 | + | 1.95534i | −0.251345 | + | 0.0911680i | ||||
\(461\) | 17.4655i | 0.813447i | 0.913551 | + | 0.406724i | \(0.133329\pi\) | ||||
−0.913551 | + | 0.406724i | \(0.866671\pi\) | |||||||
\(462\) | 8.96606 | − | 4.72180i | 0.417139 | − | 0.219678i | ||||
\(463\) | −0.256369 | + | 0.256369i | −0.0119145 | + | 0.0119145i | −0.713039 | − | 0.701124i | \(-0.752682\pi\) |
0.701124 | + | 0.713039i | \(0.252682\pi\) | |||||||
\(464\) | 0.890831 | 0.0413558 | ||||||||
\(465\) | −1.72033 | − | 36.3523i | −0.0797784 | − | 1.68580i | ||||
\(466\) | 10.5292 | 0.487758 | ||||||||
\(467\) | −17.7653 | + | 17.7653i | −0.822079 | + | 0.822079i | −0.986406 | − | 0.164327i | \(-0.947455\pi\) |
0.164327 | + | 0.986406i | \(0.447455\pi\) | |||||||
\(468\) | 2.94933 | − | 0.549041i | 0.136333 | − | 0.0253794i | ||||
\(469\) | 35.1167i | 1.62154i | ||||||||
\(470\) | −4.98063 | + | 10.6503i | −0.229739 | + | 0.491261i | ||||
\(471\) | −7.17956 | + | 23.1543i | −0.330817 | + | 1.06690i | ||||
\(472\) | 1.94535 | + | 1.94535i | 0.0895421 | + | 0.0895421i | ||||
\(473\) | −11.3666 | − | 11.3666i | −0.522635 | − | 0.522635i | ||||
\(474\) | −6.21539 | + | 20.0448i | −0.285482 | + | 0.920690i | ||||
\(475\) | −25.9963 | + | 21.7158i | −1.19279 | + | 0.996391i | ||||
\(476\) | − | 0.496523i | − | 0.0227581i | ||||||
\(477\) | 9.35144 | − | 1.74084i | 0.428173 | − | 0.0797078i | ||||
\(478\) | −13.5921 | + | 13.5921i | −0.621687 | + | 0.621687i | ||||
\(479\) | 21.2442 | 0.970671 | 0.485336 | − | 0.874328i | \(-0.338697\pi\) | ||||
0.485336 | + | 0.874328i | \(0.338697\pi\) | |||||||
\(480\) | 2.86501 | + | 2.60609i | 0.130769 | + | 0.118951i | ||||
\(481\) | −4.08282 | −0.186160 | ||||||||
\(482\) | −11.3708 | + | 11.3708i | −0.517928 | + | 0.517928i | ||||
\(483\) | −8.87792 | + | 4.67539i | −0.403959 | + | 0.212737i | ||||
\(484\) | − | 4.29206i | − | 0.195094i | ||||||
\(485\) | −9.54128 | − | 26.3048i | −0.433247 | − | 1.19444i | ||||
\(486\) | −1.05032 | − | 15.5530i | −0.0476433 | − | 0.705500i | ||||
\(487\) | 10.4620 | + | 10.4620i | 0.474077 | + | 0.474077i | 0.903231 | − | 0.429154i | \(-0.141188\pi\) |
−0.429154 | + | 0.903231i | \(0.641188\pi\) | |||||||
\(488\) | −1.61920 | − | 1.61920i | −0.0732976 | − | 0.0732976i | ||||
\(489\) | 21.3556 | + | 6.62182i | 0.965733 | + | 0.299449i | ||||
\(490\) | −1.44662 | − | 3.98826i | −0.0653518 | − | 0.180171i | ||||
\(491\) | 16.1195i | 0.727462i | 0.931504 | + | 0.363731i | \(0.118497\pi\) | ||||
−0.931504 | + | 0.363731i | \(0.881503\pi\) | |||||||
\(492\) | −1.70359 | − | 3.23488i | −0.0768037 | − | 0.145840i | ||||
\(493\) | 0.138458 | − | 0.138458i | 0.00623586 | − | 0.00623586i | ||||
\(494\) | −6.77461 | −0.304804 | ||||||||
\(495\) | 8.81332 | + | 14.9727i | 0.396129 | + | 0.672974i | ||||
\(496\) | 9.39662 | 0.421921 | ||||||||
\(497\) | 15.3469 | − | 15.3469i | 0.688402 | − | 0.688402i | ||||
\(498\) | −6.77895 | − | 12.8723i | −0.303772 | − | 0.576822i | ||||
\(499\) | − | 0.297723i | − | 0.0133279i | −0.999978 | − | 0.00666395i | \(-0.997879\pi\) | ||
0.999978 | − | 0.00666395i | \(-0.00212122\pi\) | |||||||
\(500\) | −10.8089 | + | 2.85791i | −0.483389 | + | 0.127810i | ||||
\(501\) | 30.8238 | + | 9.55766i | 1.37710 | + | 0.427005i | ||||
\(502\) | 17.9945 | + | 17.9945i | 0.803132 | + | 0.803132i | ||||
\(503\) | −7.46751 | − | 7.46751i | −0.332960 | − | 0.332960i | 0.520750 | − | 0.853709i | \(-0.325653\pi\) |
−0.853709 | + | 0.520750i | \(0.825653\pi\) | |||||||
\(504\) | 5.58793 | + | 3.83397i | 0.248906 | + | 0.170778i | ||||
\(505\) | −15.3410 | + | 32.8044i | −0.682667 | + | 1.45978i | ||||
\(506\) | − | 6.64200i | − | 0.295273i | ||||||
\(507\) | −1.53252 | + | 0.807075i | −0.0680618 | + | 0.0358434i | ||||
\(508\) | −8.05797 | + | 8.05797i | −0.357514 | + | 0.357514i | ||||
\(509\) | −9.67667 | −0.428911 | −0.214456 | − | 0.976734i | \(-0.568798\pi\) | ||||
−0.214456 | + | 0.976734i | \(0.568798\pi\) | |||||||
\(510\) | 0.850353 | − | 0.0402420i | 0.0376543 | − | 0.00178195i | ||||
\(511\) | 5.27702 | 0.233442 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −4.09603 | + | 34.9628i | −0.180844 | + | 1.54364i | ||||
\(514\) | 17.1567i | 0.756749i | ||||||||
\(515\) | −33.9494 | + | 12.3142i | −1.49599 | + | 0.542627i | ||||
\(516\) | 3.18377 | − | 10.2678i | 0.140158 | − | 0.452013i | ||||
\(517\) | −9.62951 | − | 9.62951i | −0.423505 | − | 0.423505i | ||||
\(518\) | −6.52145 | − | 6.52145i | −0.286536 | − | 0.286536i | ||||
\(519\) | −8.02111 | + | 25.8683i | −0.352088 | + | 1.13549i | ||||
\(520\) | −2.02552 | − | 0.947239i | −0.0888250 | − | 0.0415392i | ||||
\(521\) | 24.0972i | 1.05572i | 0.849332 | + | 0.527860i | \(0.177005\pi\) | ||||
−0.849332 | + | 0.527860i | \(0.822995\pi\) | |||||||
\(522\) | 0.489103 | + | 2.62735i | 0.0214075 | + | 0.114996i | ||||
\(523\) | 2.67631 | − | 2.67631i | 0.117027 | − | 0.117027i | −0.646168 | − | 0.763195i | \(-0.723630\pi\) |
0.763195 | + | 0.646168i | \(0.223630\pi\) | |||||||
\(524\) | −14.2078 | −0.620671 | ||||||||
\(525\) | −18.0545 | + | 7.53244i | −0.787962 | + | 0.328743i | ||||
\(526\) | −5.39638 | −0.235294 | ||||||||
\(527\) | 1.46048 | − | 1.46048i | 0.0636195 | − | 0.0636195i | ||||
\(528\) | −3.96919 | + | 2.09030i | −0.172737 | + | 0.0909686i | ||||
\(529\) | − | 16.4233i | − | 0.714056i | ||||||
\(530\) | −6.42232 | − | 3.00341i | −0.278968 | − | 0.130460i | ||||
\(531\) | −4.66941 | + | 6.80557i | −0.202635 | + | 0.295337i | ||||
\(532\) | −10.8210 | − | 10.8210i | −0.469151 | − | 0.469151i | ||||
\(533\) | 1.49257 | + | 1.49257i | 0.0646506 | + | 0.0646506i | ||||
\(534\) | 10.6471 | + | 3.30140i | 0.460746 | + | 0.142866i | ||||
\(535\) | 29.9523 | − | 10.8643i | 1.29495 | − | 0.469705i | ||||
\(536\) | − | 15.5458i | − | 0.671477i | ||||||
\(537\) | 9.27845 | + | 17.6185i | 0.400395 | + | 0.760295i | ||||
\(538\) | 2.11235 | − | 2.11235i | 0.0910701 | − | 0.0910701i | ||||
\(539\) | 4.91397 | 0.211660 | ||||||||
\(540\) | −6.11323 | + | 9.88071i | −0.263071 | + | 0.425198i | ||||
\(541\) | −31.9887 | −1.37530 | −0.687650 | − | 0.726042i | \(-0.741358\pi\) | ||||
−0.687650 | + | 0.726042i | \(0.741358\pi\) | |||||||
\(542\) | −12.6686 | + | 12.6686i | −0.544162 | + | 0.544162i | ||||
\(543\) | −14.2669 | − | 27.0908i | −0.612250 | − | 1.16258i | ||||
\(544\) | 0.219806i | 0.00942410i | ||||||||
\(545\) | 8.69476 | − | 18.5924i | 0.372443 | − | 0.796410i | ||||
\(546\) | −3.73703 | − | 1.15876i | −0.159930 | − | 0.0495902i | ||||
\(547\) | 6.13891 | + | 6.13891i | 0.262481 | + | 0.262481i | 0.826061 | − | 0.563580i | \(-0.190576\pi\) |
−0.563580 | + | 0.826061i | \(0.690576\pi\) | |||||||
\(548\) | 10.9549 | + | 10.9549i | 0.467970 | + | 0.467970i | ||||
\(549\) | 3.88654 | − | 5.66456i | 0.165874 | − | 0.241757i | ||||
\(550\) | 1.15713 | − | 12.8980i | 0.0493402 | − | 0.549975i | ||||
\(551\) | − | 6.03503i | − | 0.257101i | ||||||
\(552\) | 3.93017 | − | 2.06975i | 0.167279 | − | 0.0880944i | ||||
\(553\) | 19.3536 | − | 19.3536i | 0.822997 | − | 0.822997i | ||||
\(554\) | −16.7142 | −0.710120 | ||||||||
\(555\) | 10.6402 | − | 11.6973i | 0.451652 | − | 0.496523i | ||||
\(556\) | 15.0559 | 0.638513 | ||||||||
\(557\) | 6.14058 | − | 6.14058i | 0.260185 | − | 0.260185i | −0.564944 | − | 0.825129i | \(-0.691102\pi\) |
0.825129 | + | 0.564944i | \(0.191102\pi\) | |||||||
\(558\) | 5.15913 | + | 27.7137i | 0.218403 | + | 1.17322i | ||||
\(559\) | 6.20654i | 0.262509i | ||||||||
\(560\) | −1.72233 | − | 4.74837i | −0.0727818 | − | 0.200655i | ||||
\(561\) | −0.292029 | + | 0.941804i | −0.0123295 | + | 0.0397630i | ||||
\(562\) | 0.540129 | + | 0.540129i | 0.0227839 | + | 0.0227839i | ||||
\(563\) | 24.9348 | + | 24.9348i | 1.05088 | + | 1.05088i | 0.998634 | + | 0.0522422i | \(0.0166368\pi\) |
0.0522422 | + | 0.998634i | \(0.483363\pi\) | |||||||
\(564\) | 2.69722 | − | 8.69863i | 0.113574 | − | 0.366278i | ||||
\(565\) | −8.45557 | − | 23.3115i | −0.355728 | − | 0.980722i | ||||
\(566\) | − | 5.27807i | − | 0.221854i | ||||||
\(567\) | −8.23963 | + | 18.5857i | −0.346032 | + | 0.780524i | ||||
\(568\) | −6.79393 | + | 6.79393i | −0.285067 | + | 0.285067i | ||||
\(569\) | −5.56111 | −0.233134 | −0.116567 | − | 0.993183i | \(-0.537189\pi\) | ||||
−0.116567 | + | 0.993183i | \(0.537189\pi\) | |||||||
\(570\) | 17.6553 | − | 19.4093i | 0.739498 | − | 0.812966i | ||||
\(571\) | 33.8131 | 1.41503 | 0.707517 | − | 0.706697i | \(-0.249815\pi\) | ||||
0.707517 | + | 0.706697i | \(0.249815\pi\) | |||||||
\(572\) | 1.83139 | − | 1.83139i | 0.0765741 | − | 0.0765741i | ||||
\(573\) | 27.6089 | − | 14.5397i | 1.15338 | − | 0.607405i | ||||
\(574\) | 4.76816i | 0.199019i | ||||||||
\(575\) | −1.14575 | + | 12.7713i | −0.0477812 | + | 0.532598i | ||||
\(576\) | −2.47372 | − | 1.69726i | −0.103072 | − | 0.0707192i | ||||
\(577\) | 0.174550 | + | 0.174550i | 0.00726661 | + | 0.00726661i | 0.710731 | − | 0.703464i | \(-0.248364\pi\) |
−0.703464 | + | 0.710731i | \(0.748364\pi\) | |||||||
\(578\) | −11.9867 | − | 11.9867i | −0.498579 | − | 0.498579i | ||||
\(579\) | −8.38885 | − | 2.60117i | −0.348629 | − | 0.108101i | ||||
\(580\) | 0.843830 | − | 1.80440i | 0.0350381 | − | 0.0749235i | ||||
\(581\) | 18.9736i | 0.787156i | ||||||||
\(582\) | 10.0996 | + | 19.1777i | 0.418641 | + | 0.794942i | ||||
\(583\) | 5.80677 | − | 5.80677i | 0.240492 | − | 0.240492i | ||||
\(584\) | −2.33609 | −0.0966680 | ||||||||
\(585\) | 1.68163 | − | 6.49401i | 0.0695267 | − | 0.268494i | ||||
\(586\) | −31.7552 | −1.31180 | ||||||||
\(587\) | 6.55064 | − | 6.55064i | 0.270374 | − | 0.270374i | −0.558877 | − | 0.829251i | \(-0.688768\pi\) |
0.829251 | + | 0.558877i | \(0.188768\pi\) | |||||||
\(588\) | 1.53127 | + | 2.90767i | 0.0631485 | + | 0.119910i | ||||
\(589\) | − | 63.6584i | − | 2.62300i | ||||||
\(590\) | 5.78307 | − | 2.09764i | 0.238085 | − | 0.0863584i | ||||
\(591\) | 27.6954 | + | 8.58762i | 1.13924 | + | 0.353248i | ||||
\(592\) | 2.88699 | + | 2.88699i | 0.118654 | + | 0.118654i | ||||
\(593\) | −17.9410 | − | 17.9410i | −0.736747 | − | 0.736747i | 0.235200 | − | 0.971947i | \(-0.424425\pi\) |
−0.971947 | + | 0.235200i | \(0.924425\pi\) | |||||||
\(594\) | −8.34423 | − | 10.5588i | −0.342368 | − | 0.433233i | ||||
\(595\) | −1.00572 | − | 0.470326i | −0.0412304 | − | 0.0192815i | ||||
\(596\) | 15.7204i | 0.643934i | ||||||||
\(597\) | −10.5460 | + | 5.55386i | −0.431620 | + | 0.227304i | ||||
\(598\) | −1.81338 | + | 1.81338i | −0.0741547 | + | 0.0741547i | ||||
\(599\) | −41.6634 | −1.70232 | −0.851161 | − | 0.524905i | \(-0.824101\pi\) | ||||
−0.851161 | + | 0.524905i | \(0.824101\pi\) | |||||||
\(600\) | 7.99255 | − | 3.33454i | 0.326294 | − | 0.136132i | ||||
\(601\) | −22.6630 | −0.924444 | −0.462222 | − | 0.886764i | \(-0.652948\pi\) | ||||
−0.462222 | + | 0.886764i | \(0.652948\pi\) | |||||||
\(602\) | −9.91367 | + | 9.91367i | −0.404051 | + | 0.404051i | ||||
\(603\) | 45.8498 | − | 8.53530i | 1.86715 | − | 0.347584i | ||||
\(604\) | 14.3294i | 0.583056i | ||||||||
\(605\) | −8.69365 | − | 4.06561i | −0.353447 | − | 0.165290i | ||||
\(606\) | 8.30782 | − | 26.7930i | 0.337482 | − | 1.08839i | ||||
\(607\) | 11.2274 | + | 11.2274i | 0.455706 | + | 0.455706i | 0.897243 | − | 0.441537i | \(-0.145567\pi\) |
−0.441537 | + | 0.897243i | \(0.645567\pi\) | |||||||
\(608\) | 4.79037 | + | 4.79037i | 0.194275 | + | 0.194275i | ||||
\(609\) | 1.03226 | − | 3.32906i | 0.0418291 | − | 0.134900i | ||||
\(610\) | −4.81349 | + | 1.74595i | −0.194892 | + | 0.0706915i | ||||
\(611\) | 5.25805i | 0.212718i | ||||||||
\(612\) | −0.648280 | + | 0.120683i | −0.0262052 | + | 0.00487830i | ||||
\(613\) | 6.53782 | − | 6.53782i | 0.264060 | − | 0.264060i | −0.562641 | − | 0.826701i | \(-0.690215\pi\) |
0.826701 | + | 0.562641i | \(0.190215\pi\) | |||||||
\(614\) | −6.95958 | −0.280866 | ||||||||
\(615\) | −8.16603 | + | 0.386448i | −0.329286 | + | 0.0155831i | ||||
\(616\) | 5.85052 | 0.235724 | ||||||||
\(617\) | 22.7714 | − | 22.7714i | 0.916744 | − | 0.916744i | −0.0800471 | − | 0.996791i | \(-0.525507\pi\) |
0.996791 | + | 0.0800471i | \(0.0255071\pi\) | |||||||
\(618\) | 24.7511 | − | 13.0347i | 0.995636 | − | 0.524333i | ||||
\(619\) | 5.97955i | 0.240338i | 0.992753 | + | 0.120169i | \(0.0383437\pi\) | ||||
−0.992753 | + | 0.120169i | \(0.961656\pi\) | |||||||
\(620\) | 8.90085 | − | 19.0330i | 0.357467 | − | 0.764386i | ||||
\(621\) | 8.26220 | + | 10.4550i | 0.331551 | + | 0.419545i | ||||
\(622\) | −2.11767 | − | 2.11767i | −0.0849107 | − | 0.0849107i | ||||
\(623\) | −10.2799 | − | 10.2799i | −0.411857 | − | 0.411857i | ||||
\(624\) | 1.65435 | + | 0.512970i | 0.0662269 | + | 0.0205352i | ||||
\(625\) | −4.44986 | + | 24.6008i | −0.177994 | + | 0.984031i | ||||
\(626\) | − | 32.3613i | − | 1.29342i | ||||||
\(627\) | 14.1610 | + | 26.8897i | 0.565534 | + | 1.07387i | ||||
\(628\) | −9.89671 | + | 9.89671i | −0.394922 | + | 0.394922i | ||||
\(629\) | 0.897427 | 0.0357828 | ||||||||
\(630\) | 13.0589 | − | 7.68678i | 0.520278 | − | 0.306249i | ||||
\(631\) | −13.0508 | −0.519544 | −0.259772 | − | 0.965670i | \(-0.583647\pi\) | ||||
−0.259772 | + | 0.965670i | \(0.583647\pi\) | |||||||
\(632\) | −8.56764 | + | 8.56764i | −0.340802 | + | 0.340802i | ||||
\(633\) | 5.89438 | + | 11.1926i | 0.234281 | + | 0.444867i | ||||
\(634\) | 20.8903i | 0.829659i | ||||||||
\(635\) | 8.68876 | + | 23.9544i | 0.344803 | + | 0.950602i | ||||
\(636\) | 5.24543 | + | 1.62647i | 0.207995 | + | 0.0644939i | ||||
\(637\) | −1.34160 | − | 1.34160i | −0.0531561 | − | 0.0531561i | ||||
\(638\) | 1.63145 | + | 1.63145i | 0.0645899 | + | 0.0645899i | ||||
\(639\) | −23.7677 | − | 16.3074i | −0.940235 | − | 0.645111i | ||||
\(640\) | 0.762461 | + | 2.10206i | 0.0301389 | + | 0.0830912i | ||||
\(641\) | 24.2560i | 0.958055i | 0.877800 | + | 0.479027i | \(0.159011\pi\) | ||||
−0.877800 | + | 0.479027i | \(0.840989\pi\) | |||||||
\(642\) | −21.8370 | + | 11.5000i | −0.861836 | + | 0.453870i | ||||
\(643\) | −13.2221 | + | 13.2221i | −0.521429 | + | 0.521429i | −0.918003 | − | 0.396574i | \(-0.870199\pi\) |
0.396574 | + | 0.918003i | \(0.370199\pi\) | |||||||
\(644\) | −5.79300 | −0.228276 | ||||||||
\(645\) | −17.7818 | − | 16.1748i | −0.700157 | − | 0.636883i | ||||
\(646\) | 1.48910 | 0.0585878 | ||||||||
\(647\) | −8.17921 | + | 8.17921i | −0.321558 | + | 0.321558i | −0.849365 | − | 0.527807i | \(-0.823015\pi\) |
0.527807 | + | 0.849365i | \(0.323015\pi\) | |||||||
\(648\) | 3.64761 | − | 8.22769i | 0.143292 | − | 0.323214i | ||||
\(649\) | 7.12538i | 0.279696i | ||||||||
\(650\) | −3.83731 | + | 3.20547i | −0.150512 | + | 0.125729i | ||||
\(651\) | 10.8884 | − | 35.1154i | 0.426749 | − | 1.37628i | ||||
\(652\) | 9.12788 | + | 9.12788i | 0.357476 | + | 0.357476i | ||||
\(653\) | 12.1320 | + | 12.1320i | 0.474763 | + | 0.474763i | 0.903452 | − | 0.428689i | \(-0.141024\pi\) |
−0.428689 | + | 0.903452i | \(0.641024\pi\) | |||||||
\(654\) | −4.70858 | + | 15.1853i | −0.184120 | + | 0.593793i | ||||
\(655\) | −13.4582 | + | 28.7782i | −0.525855 | + | 1.12446i | ||||
\(656\) | − | 2.11082i | − | 0.0824136i | ||||||
\(657\) | −1.28261 | − | 6.88989i | −0.0500393 | − | 0.268800i | ||||
\(658\) | −8.39864 | + | 8.39864i | −0.327413 | + | 0.327413i | ||||
\(659\) | 13.1366 | 0.511731 | 0.255865 | − | 0.966712i | \(-0.417640\pi\) | ||||
0.255865 | + | 0.966712i | \(0.417640\pi\) | |||||||
\(660\) | 0.474171 | + | 10.0197i | 0.0184571 | + | 0.390016i | ||||
\(661\) | −34.2832 | −1.33346 | −0.666731 | − | 0.745298i | \(-0.732307\pi\) | ||||
−0.666731 | + | 0.745298i | \(0.732307\pi\) | |||||||
\(662\) | 0.0790370 | − | 0.0790370i | 0.00307186 | − | 0.00307186i | ||||
\(663\) | 0.336858 | − | 0.177400i | 0.0130825 | − | 0.00688964i | ||||
\(664\) | − | 8.39941i | − | 0.325960i | ||||||
\(665\) | −32.1684 | + | 11.6681i | −1.24744 | + | 0.452471i | ||||
\(666\) | −6.92960 | + | 10.0998i | −0.268517 | + | 0.391358i | ||||
\(667\) | −1.61542 | − | 1.61542i | −0.0625491 | − | 0.0625491i | ||||
\(668\) | 13.1748 | + | 13.1748i | 0.509749 | + | 0.509749i | ||||
\(669\) | −37.8965 | − | 11.7507i | −1.46516 | − | 0.454309i | ||||
\(670\) | −31.4884 | − | 14.7256i | −1.21650 | − | 0.568900i | ||||
\(671\) | − | 5.93075i | − | 0.228954i | ||||||
\(672\) | 1.82311 | + | 3.46184i | 0.0703281 | + | 0.133543i | ||||
\(673\) | 0.645929 | − | 0.645929i | 0.0248987 | − | 0.0248987i | −0.694548 | − | 0.719447i | \(-0.744396\pi\) |
0.719447 | + | 0.694548i | \(0.244396\pi\) | |||||||
\(674\) | 12.0894 | 0.465667 | ||||||||
\(675\) | 14.2229 | + | 21.7419i | 0.547440 | + | 0.836845i | ||||
\(676\) | −1.00000 | −0.0384615 | ||||||||
\(677\) | 10.5020 | − | 10.5020i | 0.403624 | − | 0.403624i | −0.475884 | − | 0.879508i | \(-0.657872\pi\) |
0.879508 | + | 0.475884i | \(0.157872\pi\) | |||||||
\(678\) | 8.95033 | + | 16.9954i | 0.343735 | + | 0.652706i | ||||
\(679\) | − | 28.2676i | − | 1.08481i | ||||||
\(680\) | 0.445222 | + | 0.208209i | 0.0170735 | + | 0.00798444i | ||||
\(681\) | 40.2939 | + | 12.4941i | 1.54407 | + | 0.478775i | ||||
\(682\) | 17.2088 | + | 17.2088i | 0.658960 | + | 0.658960i | ||||
\(683\) | −19.5328 | − | 19.5328i | −0.747401 | − | 0.747401i | 0.226590 | − | 0.973990i | \(-0.427242\pi\) |
−0.973990 | + | 0.226590i | \(0.927242\pi\) | |||||||
\(684\) | −11.4983 | + | 16.7585i | −0.439648 | + | 0.640777i | ||||
\(685\) | 32.5663 | − | 11.8125i | 1.24429 | − | 0.451331i | ||||
\(686\) | − | 20.0983i | − | 0.767355i | ||||||
\(687\) | −36.1636 | + | 19.0449i | −1.37973 | + | 0.726608i | ||||
\(688\) | 4.38869 | − | 4.38869i | 0.167317 | − | 0.167317i | ||||
\(689\) | −3.17070 | −0.120794 | ||||||||
\(690\) | −0.469509 | − | 9.92120i | −0.0178739 | − | 0.377693i | ||||
\(691\) | 7.28568 | 0.277160 | 0.138580 | − | 0.990351i | \(-0.455746\pi\) | ||||
0.138580 | + | 0.990351i | \(0.455746\pi\) | |||||||
\(692\) | −11.0567 | + | 11.0567i | −0.420314 | + | 0.420314i | ||||
\(693\) | 3.21218 | + | 17.2551i | 0.122021 | + | 0.655468i | ||||
\(694\) | 8.62460i | 0.327385i | ||||||||
\(695\) | 14.2616 | − | 30.4961i | 0.540972 | − | 1.15678i | ||||
\(696\) | −0.456970 | + | 1.47374i | −0.0173214 | + | 0.0558621i | ||||
\(697\) | −0.328077 | − | 0.328077i | −0.0124268 | − | 0.0124268i | ||||
\(698\) | 3.46012 | + | 3.46012i | 0.130967 | + | 0.130967i | ||||
\(699\) | −5.40119 | + | 17.4190i | −0.204292 | + | 0.658848i | ||||
\(700\) | −11.2494 | − | 1.00922i | −0.425187 | − | 0.0381450i | ||||
\(701\) | 16.4241i | 0.620330i | 0.950683 | + | 0.310165i | \(0.100384\pi\) | ||||
−0.950683 | + | 0.310165i | \(0.899616\pi\) | |||||||
\(702\) | −0.604615 | + | 5.16086i | −0.0228197 | + | 0.194784i | ||||
\(703\) | 19.5582 | − | 19.5582i | 0.737652 | − | 0.737652i | ||||
\(704\) | −2.58997 | −0.0976132 | ||||||||
\(705\) | −15.0643 | − | 13.7030i | −0.567356 | − | 0.516083i | ||||
\(706\) | −12.2888 | −0.462495 | ||||||||
\(707\) | −25.8690 | + | 25.8690i | −0.972903 | + | 0.972903i | ||||
\(708\) | −4.21620 | + | 2.22038i | −0.158454 | + | 0.0834470i | ||||
\(709\) | 25.9013i | 0.972742i | 0.873752 | + | 0.486371i | \(0.161680\pi\) | ||||
−0.873752 | + | 0.486371i | \(0.838320\pi\) | |||||||
\(710\) | 7.32577 | + | 20.1967i | 0.274931 | + | 0.757969i | ||||
\(711\) | −29.9728 | − | 20.5648i | −1.12407 | − | 0.771241i | ||||
\(712\) | 4.55083 | + | 4.55083i | 0.170550 | + | 0.170550i | ||||
\(713\) | −17.0396 | − | 17.0396i | −0.638140 | − | 0.638140i | ||||
\(714\) | 0.821420 | + | 0.254701i | 0.0307409 | + | 0.00953196i | ||||
\(715\) | −1.97475 | − | 5.44427i | −0.0738515 | − | 0.203604i | ||||
\(716\) | 11.4964i | 0.429641i | ||||||||
\(717\) | −15.5137 | − | 29.4583i | −0.579368 | − | 1.10014i | ||||
\(718\) | −22.5188 | + | 22.5188i | −0.840394 | + | 0.840394i | ||||
\(719\) | 7.92976 | 0.295730 | 0.147865 | − | 0.989008i | \(-0.452760\pi\) | ||||
0.147865 | + | 0.989008i | \(0.452760\pi\) | |||||||
\(720\) | −5.78105 | + | 3.40287i | −0.215447 | + | 0.126817i | ||||
\(721\) | −36.4827 | −1.35869 | ||||||||
\(722\) | 19.0179 | − | 19.0179i | 0.707772 | − | 0.707772i | ||||
\(723\) | −12.9784 | − | 24.6442i | −0.482672 | − | 0.916529i | ||||
\(724\) | − | 17.6773i | − | 0.656970i | ||||||
\(725\) | −2.85554 | − | 3.41839i | −0.106052 | − | 0.126956i | ||||
\(726\) | 7.10055 | + | 2.20170i | 0.263526 | + | 0.0817127i | ||||
\(727\) | −13.1739 | − | 13.1739i | −0.488594 | − | 0.488594i | 0.419268 | − | 0.907862i | \(-0.362287\pi\) |
−0.907862 | + | 0.419268i | \(0.862287\pi\) | |||||||
\(728\) | −1.59729 | − | 1.59729i | −0.0591996 | − | 0.0591996i | ||||
\(729\) | 26.2689 | + | 6.24066i | 0.972922 | + | 0.231136i | ||||
\(730\) | −2.21283 | + | 4.73180i | −0.0819007 | + | 0.175132i | ||||
\(731\) | − | 1.36423i | − | 0.0504580i | ||||||
\(732\) | 3.50931 | − | 1.84811i | 0.129708 | − | 0.0683082i | ||||
\(733\) | −4.39131 | + | 4.39131i | −0.162197 | + | 0.162197i | −0.783539 | − | 0.621342i | \(-0.786588\pi\) |
0.621342 | + | 0.783539i | \(0.286588\pi\) | |||||||
\(734\) | −21.1845 | −0.781935 | ||||||||
\(735\) | 7.34003 | − | 0.347359i | 0.270741 | − | 0.0128125i | ||||
\(736\) | 2.56451 | 0.0945290 | ||||||||
\(737\) | 28.4704 | − | 28.4704i | 1.04872 | − | 1.04872i | ||||
\(738\) | 6.22550 | − | 1.15893i | 0.229164 | − | 0.0426607i | ||||
\(739\) | 13.4115i | 0.493350i | 0.969098 | + | 0.246675i | \(0.0793380\pi\) | ||||
−0.969098 | + | 0.246675i | \(0.920662\pi\) | |||||||
\(740\) | 8.58232 | − | 3.11299i | 0.315492 | − | 0.114436i | ||||
\(741\) | 3.47517 | − | 11.2075i | 0.127664 | − | 0.411720i | ||||
\(742\) | −5.06453 | − | 5.06453i | −0.185925 | − | 0.185925i | ||||
\(743\) | 6.99293 | + | 6.99293i | 0.256546 | + | 0.256546i | 0.823648 | − | 0.567102i | \(-0.191935\pi\) |
−0.567102 | + | 0.823648i | \(0.691935\pi\) | |||||||
\(744\) | −4.82019 | + | 15.5453i | −0.176717 | + | 0.569917i | ||||
\(745\) | 31.8421 | + | 14.8910i | 1.16660 | + | 0.545565i | ||||
\(746\) | 23.0492i | 0.843893i | ||||||||
\(747\) | 24.7727 | − | 4.61163i | 0.906384 | − | 0.168731i | ||||
\(748\) | −0.402549 | + | 0.402549i | −0.0147187 | + | 0.0147187i | ||||
\(749\) | 32.1873 | 1.17610 | ||||||||
\(750\) | 0.816675 | − | 19.3477i | 0.0298207 | − | 0.706478i | ||||
\(751\) | −11.5511 | −0.421507 | −0.210754 | − | 0.977539i | \(-0.567592\pi\) | ||||
−0.210754 | + | 0.977539i | \(0.567592\pi\) | |||||||
\(752\) | 3.71800 | − | 3.71800i | 0.135581 | − | 0.135581i | ||||
\(753\) | −38.9997 | + | 20.5384i | −1.42123 | + | 0.748462i | ||||
\(754\) | − | 0.890831i | − | 0.0324421i | ||||||
\(755\) | 29.0245 | + | 13.5734i | 1.05631 | + | 0.493986i | ||||
\(756\) | −9.20915 | + | 7.27765i | −0.334933 | + | 0.264686i | ||||
\(757\) | −5.58355 | − | 5.58355i | −0.202938 | − | 0.202938i | 0.598320 | − | 0.801257i | \(-0.295835\pi\) |
−0.801257 | + | 0.598320i | \(0.795835\pi\) | |||||||
\(758\) | 4.82433 | + | 4.82433i | 0.175228 | + | 0.175228i | ||||
\(759\) | 10.9882 | + | 3.40715i | 0.398845 | + | 0.123672i | ||||
\(760\) | 14.2406 | − | 5.16537i | 0.516562 | − | 0.187368i | ||||
\(761\) | − | 37.4923i | − | 1.35909i | −0.733632 | − | 0.679547i | \(-0.762176\pi\) | ||
0.733632 | − | 0.679547i | \(-0.237824\pi\) | |||||||
\(762\) | −9.19717 | − | 17.4642i | −0.333178 | − | 0.632660i | ||||
\(763\) | 14.6616 | − | 14.6616i | 0.530787 | − | 0.530787i | ||||
\(764\) | 18.0153 | 0.651771 | ||||||||
\(765\) | −0.369632 | + | 1.42742i | −0.0133641 | + | 0.0516085i | ||||
\(766\) | 21.4836 | 0.776235 | ||||||||
\(767\) | 1.94535 | − | 1.94535i | 0.0702426 | − | 0.0702426i | ||||
\(768\) | −0.807075 | − | 1.53252i | −0.0291228 | − | 0.0553002i | ||||
\(769\) | − | 25.0653i | − | 0.903880i | −0.892048 | − | 0.451940i | \(-0.850732\pi\) | ||
0.892048 | − | 0.451940i | \(-0.149268\pi\) | |||||||
\(770\) | 5.54184 | − | 11.8503i | 0.199714 | − | 0.427057i | ||||
\(771\) | −28.3831 | − | 8.80087i | −1.02219 | − | 0.316956i | ||||
\(772\) | −3.58559 | − | 3.58559i | −0.129048 | − | 0.129048i | ||||
\(773\) | 2.54918 | + | 2.54918i | 0.0916877 | + | 0.0916877i | 0.751463 | − | 0.659775i | \(-0.229349\pi\) |
−0.659775 | + | 0.751463i | \(0.729349\pi\) | |||||||
\(774\) | 15.3533 | + | 10.5341i | 0.551862 | + | 0.378641i | ||||
\(775\) | −30.1206 | − | 36.0577i | −1.08196 | − | 1.29523i | ||||
\(776\) | 12.5138i | 0.449219i | ||||||||
\(777\) | 14.1341 | − | 7.44343i | 0.507056 | − | 0.267032i | ||||
\(778\) | 2.03926 | − | 2.03926i | 0.0731112 | − | 0.0731112i | ||||
\(779\) | −14.3000 | −0.512350 | ||||||||
\(780\) | 2.60609 | − | 2.86501i | 0.0933131 | − | 0.102584i | ||||
\(781\) | −24.8846 | −0.890441 | ||||||||
\(782\) | 0.398592 | − | 0.398592i | 0.0142536 | − | 0.0142536i | ||||
\(783\) | −4.59745 | − | 0.538609i | −0.164299 | − | 0.0192483i | ||||
\(784\) | 1.89731i | 0.0677610i | ||||||||
\(785\) | 10.6714 | + | 29.4205i | 0.380880 | + | 1.05006i | ||||
\(786\) | 7.28818 | − | 23.5046i | 0.259961 | − | 0.838382i | ||||
\(787\) | −32.8392 | − | 32.8392i | −1.17059 | − | 1.17059i | −0.982069 | − | 0.188522i | \(-0.939630\pi\) |
−0.188522 | − | 0.982069i | \(-0.560370\pi\) | |||||||
\(788\) | 11.8377 | + | 11.8377i | 0.421699 | + | 0.421699i | ||||
\(789\) | 2.76819 | − | 8.92749i | 0.0985500 | − | 0.317827i | ||||
\(790\) | 9.23833 | + | 25.4695i | 0.328685 | + | 0.906165i | ||||
\(791\) | − | 25.0510i | − | 0.890711i | ||||||
\(792\) | −1.42200 | − | 7.63868i | −0.0505286 | − | 0.271429i | ||||
\(793\) | −1.61920 | + | 1.61920i | −0.0574994 | + | 0.0574994i | ||||
\(794\) | 38.0643 | 1.35085 | ||||||||
\(795\) | 8.26314 | − | 9.08407i | 0.293063 | − | 0.322179i | ||||
\(796\) | −6.88147 | −0.243907 | ||||||||
\(797\) | 5.07364 | − | 5.07364i | 0.179717 | − | 0.179717i | −0.611515 | − | 0.791233i | \(-0.709440\pi\) |
0.791233 | + | 0.611515i | \(0.209440\pi\) | |||||||
\(798\) | 23.4526 | − | 12.3509i | 0.830213 | − | 0.437216i | ||||
\(799\) | − | 1.15575i | − | 0.0408875i | ||||||
\(800\) | 4.98000 | + | 0.446773i | 0.176070 | + | 0.0157958i | ||||
\(801\) | −10.9233 | + | 15.9205i | −0.385957 | + | 0.562524i | ||||
\(802\) | 20.9772 | + | 20.9772i | 0.740729 | + | 0.740729i | ||||
\(803\) | −4.27828 | − | 4.27828i | −0.150977 | − | 0.150977i | ||||
\(804\) | 25.7182 | + | 7.97454i | 0.907010 | + | 0.281240i | ||||
\(805\) | −5.48736 | + | 11.7339i | −0.193404 | + | 0.413564i | ||||
\(806\) | − | 9.39662i | − | 0.330982i | ||||||
\(807\) | 2.41099 | + | 4.57814i | 0.0848709 | + | 0.161158i | ||||
\(808\) | 11.4520 | − | 11.4520i | 0.402879 | − | 0.402879i | ||||
\(809\) | −15.3637 | −0.540159 | −0.270079 | − | 0.962838i | \(-0.587050\pi\) | ||||
−0.270079 | + | 0.962838i | \(0.587050\pi\) | |||||||
\(810\) | −13.2102 | − | 15.1819i | −0.464160 | − | 0.533438i | ||||
\(811\) | 34.1631 | 1.19963 | 0.599815 | − | 0.800139i | \(-0.295241\pi\) | ||||
0.599815 | + | 0.800139i | \(0.295241\pi\) | |||||||
\(812\) | 1.42292 | − | 1.42292i | 0.0499346 | − | 0.0499346i | ||||
\(813\) | −14.4596 | − | 27.4568i | −0.507120 | − | 0.962952i | ||||
\(814\) | 10.5744i | 0.370631i | ||||||||
\(815\) | 27.1350 | − | 9.84243i | 0.950498 | − | 0.344765i | ||||
\(816\) | −0.363635 | − | 0.112754i | −0.0127298 | − | 0.00394718i | ||||
\(817\) | −29.7316 | − | 29.7316i | −1.04018 | − | 1.04018i | ||||
\(818\) | 2.15863 | + | 2.15863i | 0.0754747 | + | 0.0754747i | ||||
\(819\) | 3.83397 | − | 5.58793i | 0.133970 | − | 0.195258i | ||||
\(820\) | −4.27551 | − | 1.99945i | −0.149307 | − | 0.0698238i | ||||
\(821\) | 30.8200i | 1.07563i | 0.843064 | + | 0.537813i | \(0.180749\pi\) | ||||
−0.843064 | + | 0.537813i | \(0.819251\pi\) | |||||||
\(822\) | −23.7427 | + | 12.5036i | −0.828122 | + | 0.436115i | ||||
\(823\) | −7.53031 | + | 7.53031i | −0.262490 | + | 0.262490i | −0.826065 | − | 0.563575i | \(-0.809426\pi\) |
0.563575 | + | 0.826065i | \(0.309426\pi\) | |||||||
\(824\) | 16.1506 | 0.562632 | ||||||||
\(825\) | 20.7443 | + | 8.53061i | 0.722223 | + | 0.296998i | ||||
\(826\) | 6.21460 | 0.216234 | ||||||||
\(827\) | 4.04738 | − | 4.04738i | 0.140741 | − | 0.140741i | −0.633226 | − | 0.773967i | \(-0.718270\pi\) |
0.773967 | + | 0.633226i | \(0.218270\pi\) | |||||||
\(828\) | 1.40802 | + | 7.56358i | 0.0489321 | + | 0.262853i | ||||
\(829\) | 6.31884i | 0.219462i | 0.993961 | + | 0.109731i | \(0.0349990\pi\) | ||||
−0.993961 | + | 0.109731i | \(0.965001\pi\) | |||||||
\(830\) | −17.0132 | − | 7.95626i | −0.590537 | − | 0.276166i | ||||
\(831\) | 8.57391 | − | 27.6511i | 0.297426 | − | 0.959208i | ||||
\(832\) | 0.707107 | + | 0.707107i | 0.0245145 | + | 0.0245145i | ||||
\(833\) | 0.294892 | + | 0.294892i | 0.0102174 | + | 0.0102174i | ||||
\(834\) | −7.72324 | + | 24.9077i | −0.267434 | + | 0.862483i | ||||
\(835\) | 39.1656 | − | 14.2062i | 1.35538 | − | 0.491625i | ||||
\(836\) | 17.5460i | 0.606842i | ||||||||
\(837\) | −48.4946 | − | 5.68133i | −1.67622 | − | 0.196376i | ||||
\(838\) | −4.36942 | + | 4.36942i | −0.150939 | + | 0.150939i | ||||
\(839\) | 35.0294 | 1.20935 | 0.604675 | − | 0.796472i | \(-0.293303\pi\) | ||||
0.604675 | + | 0.796472i | \(0.293303\pi\) | |||||||
\(840\) | 8.73895 | − | 0.413561i | 0.301523 | − | 0.0142692i | ||||
\(841\) | −28.2064 | −0.972635 | ||||||||
\(842\) | −1.87628 | + | 1.87628i | −0.0646610 | + | 0.0646610i | ||||
\(843\) | −1.17063 | + | 0.616490i | −0.0403186 | + | 0.0212330i | ||||
\(844\) | 7.30339i | 0.251393i | ||||||||
\(845\) | −0.947239 | + | 2.02552i | −0.0325860 | + | 0.0696801i | ||||
\(846\) | 13.0069 | + | 8.92428i | 0.447188 | + | 0.306823i | ||||
\(847\) | −6.85567 | − | 6.85567i | −0.235564 | − | 0.235564i | ||||
\(848\) | 2.24202 | + | 2.24202i | 0.0769913 | + | 0.0769913i | ||||
\(849\) | 8.73175 | + | 2.70749i | 0.299673 | + | 0.0929209i | ||||
\(850\) | 0.843463 | − | 0.704582i | 0.0289305 | − | 0.0241670i | ||||
\(851\) | − | 10.4704i | − | 0.358921i | ||||||
\(852\) | −7.75442 | − | 14.7246i | −0.265662 | − | 0.504456i | ||||
\(853\) | 10.5775 | − | 10.5775i | 0.362167 | − | 0.362167i | −0.502443 | − | 0.864610i | \(-0.667565\pi\) |
0.864610 | + | 0.502443i | \(0.167565\pi\) | |||||||
\(854\) | −5.17267 | −0.177005 | ||||||||
\(855\) | 23.0531 | + | 39.1643i | 0.788399 | + | 1.33939i | ||||
\(856\) | −14.2490 | −0.487021 | ||||||||
\(857\) | 16.4306 | − | 16.4306i | 0.561257 | − | 0.561257i | −0.368407 | − | 0.929665i | \(-0.620097\pi\) |
0.929665 | + | 0.368407i | \(0.120097\pi\) | |||||||
\(858\) | 2.09030 | + | 3.96919i | 0.0713616 | + | 0.135506i | ||||
\(859\) | − | 26.0435i | − | 0.888591i | −0.895880 | − | 0.444296i | \(-0.853454\pi\) | ||
0.895880 | − | 0.444296i | \(-0.146546\pi\) | |||||||
\(860\) | −4.73224 | − | 13.0465i | −0.161368 | − | 0.444883i | ||||
\(861\) | −7.88818 | − | 2.44592i | −0.268829 | − | 0.0833568i | ||||
\(862\) | 25.4026 | + | 25.4026i | 0.865217 | + | 0.865217i | ||||
\(863\) | −18.9471 | − | 18.9471i | −0.644966 | − | 0.644966i | 0.306806 | − | 0.951772i | \(-0.400740\pi\) |
−0.951772 | + | 0.306806i | \(0.900740\pi\) | |||||||
\(864\) | 4.07680 | − | 3.22175i | 0.138696 | − | 0.109606i | ||||
\(865\) | 11.9223 | + | 32.8690i | 0.405370 | + | 1.11758i | ||||
\(866\) | − | 11.6683i | − | 0.396506i | ||||||
\(867\) | 25.9789 | − | 13.6813i | 0.882289 | − | 0.464640i | ||||
\(868\) | 15.0092 | − | 15.0092i | 0.509444 | − | 0.509444i | ||||
\(869\) | −31.3813 | −1.06454 | ||||||||
\(870\) | 2.55224 | + | 2.32159i | 0.0865289 | + | 0.0787092i | ||||
\(871\) | −15.5458 | −0.526750 | ||||||||
\(872\) | −6.49057 | + | 6.49057i | −0.219798 | + | 0.219798i | ||||
\(873\) | −36.9074 | + | 6.87060i | −1.24912 | + | 0.232535i | ||||
\(874\) | − | 17.3735i | − | 0.587669i | ||||||
\(875\) | −12.7001 | + | 21.8299i | −0.429341 | + | 0.737985i | ||||
\(876\) | 1.19834 | − | 3.86470i | 0.0404883 | − | 0.130576i | ||||
\(877\) | 20.9293 | + | 20.9293i | 0.706733 | + | 0.706733i | 0.965847 | − | 0.259114i | \(-0.0834305\pi\) |
−0.259114 | + | 0.965847i | \(0.583431\pi\) | |||||||
\(878\) | 3.79596 | + | 3.79596i | 0.128107 | + | 0.128107i | ||||
\(879\) | 16.2895 | − | 52.5341i | 0.549430 | − | 1.77193i | ||||
\(880\) | −2.45332 | + | 5.24604i | −0.0827014 | + | 0.176844i | ||||
\(881\) | 50.6327i | 1.70586i | 0.522027 | + | 0.852929i | \(0.325176\pi\) | ||||
−0.522027 | + | 0.852929i | \(0.674824\pi\) | |||||||
\(882\) | −5.59579 | + | 1.04170i | −0.188420 | + | 0.0350759i | ||||
\(883\) | 12.6846 | − | 12.6846i | 0.426870 | − | 0.426870i | −0.460690 | − | 0.887561i | \(-0.652398\pi\) |
0.887561 | + | 0.460690i | \(0.152398\pi\) | |||||||
\(884\) | 0.219806 | 0.00739287 | ||||||||
\(885\) | 0.503679 | + | 10.6432i | 0.0169310 | + | 0.357768i | ||||
\(886\) | −16.0443 | −0.539018 | ||||||||
\(887\) | 1.82891 | − | 1.82891i | 0.0614087 | − | 0.0614087i | −0.675735 | − | 0.737144i | \(-0.736174\pi\) |
0.737144 | + | 0.675735i | \(0.236174\pi\) | |||||||
\(888\) | −6.25701 | + | 3.29514i | −0.209972 | + | 0.110578i | ||||
\(889\) | 25.7419i | 0.863355i | ||||||||
\(890\) | 13.5285 | − | 4.90708i | 0.453478 | − | 0.164486i | ||||
\(891\) | 21.7483 | − | 8.38790i | 0.728594 | − | 0.281005i | ||||
\(892\) | −16.1979 | − | 16.1979i | −0.542344 | − | 0.542344i | ||||
\(893\) | −25.1880 | − | 25.1880i | −0.842884 | − | 0.842884i | ||||
\(894\) | −26.0071 | − | 8.06412i | −0.869806 | − | 0.269705i | ||||
\(895\) | 23.2862 | + | 10.8898i | 0.778372 | + | 0.364007i | ||||
\(896\) | 2.25891i | 0.0754650i | ||||||||
\(897\) | −2.06975 | − | 3.93017i | −0.0691069 | − | 0.131225i | ||||
\(898\) | 11.3336 | − | 11.3336i | 0.378206 | − | 0.378206i | ||||
\(899\) | 8.37079 | 0.279182 | ||||||||
\(900\) | 1.41654 | + | 14.9330i | 0.0472181 | + | 0.497765i | ||||
\(901\) | 0.696938 | 0.0232184 | ||||||||
\(902\) | 3.86572 | − | 3.86572i | 0.128714 | − | 0.128714i | ||||
\(903\) | −11.3152 | − | 21.4861i | −0.376547 | − | 0.715011i | ||||
\(904\) | 11.0898i | 0.368843i | ||||||||
\(905\) | −35.8057 | − | 16.7446i | −1.19022 | − | 0.556609i | ||||
\(906\) | −23.7058 | − | 7.35057i | −0.787573 | − | 0.244206i | ||||
\(907\) | 17.4232 | + | 17.4232i | 0.578527 | + | 0.578527i | 0.934497 | − | 0.355970i | \(-0.115850\pi\) |
−0.355970 | + | 0.934497i | \(0.615850\pi\) | |||||||
\(908\) | 17.2226 | + | 17.2226i | 0.571551 | + | 0.571551i | ||||
\(909\) | 40.0632 | + | 27.4880i | 1.32881 | + | 0.911720i | ||||
\(910\) | −4.74837 | + | 1.72233i | −0.157407 | + | 0.0570948i | ||||
\(911\) | 14.2063i | 0.470675i | 0.971914 | + | 0.235337i | \(0.0756195\pi\) | ||||
−0.971914 | + | 0.235337i | \(0.924380\pi\) | |||||||
\(912\) | −10.3823 | + | 5.46761i | −0.343791 | + | 0.181051i | ||||
\(913\) | 15.3826 | − | 15.3826i | 0.509088 | − | 0.509088i | ||||
\(914\) | −1.36234 | −0.0450621 | ||||||||
\(915\) | −0.419232 | − | 8.85880i | −0.0138594 | − | 0.292863i | ||||
\(916\) | −23.5974 | −0.779681 | ||||||||
\(917\) | −22.6940 | + | 22.6940i | −0.749423 | + | 0.749423i | ||||
\(918\) | 0.132898 | − | 1.13439i | 0.00438628 | − | 0.0374403i | ||||
\(919\) | 43.6851i | 1.44104i | 0.693435 | + | 0.720519i | \(0.256096\pi\) | ||||
−0.693435 | + | 0.720519i | \(0.743904\pi\) | |||||||
\(920\) | 2.42920 | − | 5.19447i | 0.0800885 | − | 0.171257i | ||||
\(921\) | 3.57006 | − | 11.5136i | 0.117637 | − | 0.379384i | ||||
\(922\) | −12.3499 | − | 12.3499i | −0.406724 | − | 0.406724i | ||||
\(923\) | 6.79393 | + | 6.79393i | 0.223625 | + | 0.223625i | ||||
\(924\) | −3.00114 | + | 9.67878i | −0.0987303 | + | 0.318409i | ||||
\(925\) | 1.82409 | − | 20.3324i | 0.0599758 | − | 0.668526i | ||||
\(926\) | − | 0.362561i | − | 0.0119145i | ||||||
\(927\) | 8.86733 | + | 47.6334i | 0.291241 | + | 1.56448i | ||||
\(928\) | −0.629912 | + | 0.629912i | −0.0206779 | + | 0.0206779i | ||||
\(929\) | 56.7945 | 1.86337 | 0.931683 | − | 0.363271i | \(-0.118340\pi\) | ||||
0.931683 | + | 0.363271i | \(0.118340\pi\) | |||||||
\(930\) | 26.9214 | + | 24.4885i | 0.882787 | + | 0.803009i | ||||
\(931\) | 12.8535 | 0.421257 | ||||||||
\(932\) | −7.44530 | + | 7.44530i | −0.243879 | + | 0.243879i | ||||
\(933\) | 4.58965 | − | 2.41705i | 0.150259 | − | 0.0791308i | ||||
\(934\) | − | 25.1239i | − | 0.822079i | ||||||
\(935\) | 0.434062 | + | 1.19668i | 0.0141953 | + | 0.0391357i | ||||
\(936\) | −1.69726 | + | 2.47372i | −0.0554767 | + | 0.0808562i | ||||
\(937\) | −26.3475 | − | 26.3475i | −0.860735 | − | 0.860735i | 0.130689 | − | 0.991423i | \(-0.458281\pi\) |
−0.991423 | + | 0.130689i | \(0.958281\pi\) | |||||||
\(938\) | −24.8312 | − | 24.8312i | −0.810768 | − | 0.810768i | ||||
\(939\) | 53.5368 | + | 16.6004i | 1.74711 | + | 0.541733i | ||||
\(940\) | −4.00905 | − | 11.0527i | −0.130761 | − | 0.360500i | ||||
\(941\) | 52.6644i | 1.71681i | 0.512973 | + | 0.858405i | \(0.328544\pi\) | ||||
−0.512973 | + | 0.858405i | \(0.671456\pi\) | |||||||
\(942\) | −11.2959 | − | 21.4493i | −0.368039 | − | 0.698856i | ||||
\(943\) | −3.82772 | + | 3.82772i | −0.124648 | + | 0.124648i | ||||
\(944\) | −2.75114 | −0.0895421 | ||||||||
\(945\) | 6.01778 | + | 25.5470i | 0.195758 | + | 0.831044i | ||||
\(946\) | 16.0748 | 0.522635 | ||||||||
\(947\) | 42.2920 | − | 42.2920i | 1.37431 | − | 1.37431i | 0.520356 | − | 0.853950i | \(-0.325799\pi\) |
0.853950 | − | 0.520356i | \(-0.174201\pi\) | |||||||
\(948\) | −9.77889 | − | 18.5688i | −0.317604 | − | 0.603086i | ||||
\(949\) | 2.33609i | 0.0758326i | ||||||||
\(950\) | 3.02671 | − | 33.7375i | 0.0981996 | − | 1.09459i | ||||
\(951\) | −34.5598 | − | 10.7161i | −1.12068 | − | 0.347493i | ||||
\(952\) | 0.351094 | + | 0.351094i | 0.0113790 | + | 0.0113790i | ||||
\(953\) | 4.65373 | + | 4.65373i | 0.150749 | + | 0.150749i | 0.778452 | − | 0.627704i | \(-0.216005\pi\) |
−0.627704 | + | 0.778452i | \(0.716005\pi\) | |||||||
\(954\) | −5.38150 | + | 7.84343i | −0.174233 | + | 0.253940i | ||||
\(955\) | 17.0648 | − | 36.4904i | 0.552205 | − | 1.18080i | ||||
\(956\) | − | 19.2221i | − | 0.621687i | ||||||
\(957\) | −3.53588 | + | 1.86210i | −0.114299 | + | 0.0601932i | ||||
\(958\) | −15.0219 | + | 15.0219i | −0.485336 | + | 0.485336i | ||||
\(959\) | 34.9963 | 1.13009 | ||||||||
\(960\) | −3.86865 | + | 0.183080i | −0.124860 | + | 0.00590887i | ||||
\(961\) | 57.2964 | 1.84827 | ||||||||
\(962\) | 2.88699 | − | 2.88699i | 0.0930802 | − | 0.0930802i | ||||
\(963\) | −7.82330 | − | 42.0251i | −0.252102 | − | 1.35424i | ||||
\(964\) | − | 16.0808i | − | 0.517928i | ||||||
\(965\) | −10.6591 | + | 3.86628i | −0.343129 | + | 0.124460i | ||||
\(966\) | 2.97164 | − | 9.58363i | 0.0956109 | − | 0.308348i | ||||
\(967\) | −21.6611 | − | 21.6611i | −0.696575 | − | 0.696575i | 0.267095 | − | 0.963670i | \(-0.413936\pi\) |
−0.963670 | + | 0.267095i | \(0.913936\pi\) | |||||||
\(968\) | 3.03494 | + | 3.03494i | 0.0975468 | + | 0.0975468i | ||||
\(969\) | −0.763864 | + | 2.46349i | −0.0245388 | + | 0.0791385i | ||||
\(970\) | 25.3470 | + | 11.8536i | 0.813843 | + | 0.380595i | ||||
\(971\) | − | 34.7889i | − | 1.11643i | −0.829697 | − | 0.558215i | \(-0.811487\pi\) | ||
0.829697 | − | 0.558215i | \(-0.188513\pi\) | |||||||
\(972\) | 11.7403 | + | 10.2550i | 0.376572 | + | 0.328928i | ||||
\(973\) | 24.0487 | − | 24.0487i | 0.770967 | − | 0.770967i | ||||
\(974\) | −14.7955 | −0.474077 | ||||||||
\(975\) | −3.33454 | − | 7.99255i | −0.106791 | − | 0.255966i | ||||
\(976\) | 2.28989 | 0.0732976 | ||||||||
\(977\) | −23.2379 | + | 23.2379i | −0.743445 | + | 0.743445i | −0.973239 | − | 0.229794i | \(-0.926195\pi\) |
0.229794 | + | 0.973239i | \(0.426195\pi\) | |||||||
\(978\) | −19.7830 | + | 10.4183i | −0.632591 | + | 0.333142i | ||||
\(979\) | 16.6687i | 0.532733i | ||||||||
\(980\) | 3.84304 | + | 1.79721i | 0.122761 | + | 0.0574096i | ||||
\(981\) | −22.7064 | − | 15.5792i | −0.724961 | − | 0.497407i | ||||
\(982\) | −11.3982 | − | 11.3982i | −0.363731 | − | 0.363731i | ||||
\(983\) | −6.01349 | − | 6.01349i | −0.191801 | − | 0.191801i | 0.604673 | − | 0.796474i | \(-0.293304\pi\) |
−0.796474 | + | 0.604673i | \(0.793304\pi\) | |||||||
\(984\) | 3.49202 | + | 1.08279i | 0.111322 | + | 0.0345180i | ||||
\(985\) | 35.1905 | − | 12.7643i | 1.12126 | − | 0.406705i | ||||
\(986\) | 0.195810i | 0.00623586i | ||||||||
\(987\) | −9.58601 | − | 18.2025i | −0.305126 | − | 0.579392i | ||||
\(988\) | 4.79037 | − | 4.79037i | 0.152402 | − | 0.152402i | ||||
\(989\) | −15.9167 | −0.506122 | ||||||||
\(990\) | −16.8193 | − | 4.35536i | −0.534552 | − | 0.138423i | ||||
\(991\) | −23.6719 | −0.751961 | −0.375981 | − | 0.926628i | \(-0.622694\pi\) | ||||
−0.375981 | + | 0.926628i | \(0.622694\pi\) | |||||||
\(992\) | −6.64441 | + | 6.64441i | −0.210960 | + | 0.210960i | ||||
\(993\) | 0.0902109 | + | 0.171298i | 0.00286276 | + | 0.00543598i | ||||
\(994\) | 21.7038i | 0.688402i | ||||||||
\(995\) | −6.51840 | + | 13.9386i | −0.206647 | + | 0.441882i | ||||
\(996\) | 13.8955 | + | 4.30865i | 0.440297 | + | 0.136525i | ||||
\(997\) | 17.4439 | + | 17.4439i | 0.552453 | + | 0.552453i | 0.927148 | − | 0.374695i | \(-0.122253\pi\) |
−0.374695 | + | 0.927148i | \(0.622253\pi\) | |||||||
\(998\) | 0.210522 | + | 0.210522i | 0.00666395 | + | 0.00666395i | ||||
\(999\) | −13.1538 | − | 16.6448i | −0.416168 | − | 0.526619i |
(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 | 390.2.l.c.287.3 | yes | 20 | |
3.2 | odd | 2 | 390.2.l.d.287.9 | yes | 20 | ||
5.3 | odd | 4 | 390.2.l.d.53.9 | yes | 20 | ||
15.8 | even | 4 | inner | 390.2.l.c.53.3 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.l.c.53.3 | ✓ | 20 | 15.8 | even | 4 | inner | |
390.2.l.c.287.3 | yes | 20 | 1.1 | even | 1 | trivial | |
390.2.l.d.53.9 | yes | 20 | 5.3 | odd | 4 | ||
390.2.l.d.287.9 | yes | 20 | 3.2 | odd | 2 |