Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(295,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.295");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.f (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 295.3 | ||
Root | \(-0.437442 - 0.757672i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.295 |
Dual form | 637.2.f.j.393.3 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.134063 | − | 0.232203i | 0.0947966 | − | 0.164193i | −0.814727 | − | 0.579845i | \(-0.803113\pi\) |
0.909524 | + | 0.415652i | \(0.136447\pi\) | |||||||
\(3\) | −0.571504 | + | 0.989875i | −0.329958 | + | 0.571504i | −0.982503 | − | 0.186246i | \(-0.940368\pi\) |
0.652545 | + | 0.757750i | \(0.273701\pi\) | |||||||
\(4\) | 0.964054 | + | 1.66979i | 0.482027 | + | 0.834896i | ||||
\(5\) | 2.56175 | 1.14565 | 0.572826 | − | 0.819677i | \(-0.305847\pi\) | ||||
0.572826 | + | 0.819677i | \(0.305847\pi\) | |||||||
\(6\) | 0.153235 | + | 0.265410i | 0.0625578 | + | 0.108353i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.05323 | 0.372371 | ||||||||
\(9\) | 0.846765 | + | 1.46664i | 0.282255 | + | 0.488880i | ||||
\(10\) | 0.343436 | − | 0.594848i | 0.108604 | − | 0.188107i | ||||
\(11\) | −1.97300 | + | 3.41734i | −0.594882 | + | 1.03037i | 0.398681 | + | 0.917090i | \(0.369468\pi\) |
−0.993563 | + | 0.113277i | \(0.963865\pi\) | |||||||
\(12\) | −2.20385 | −0.636195 | ||||||||
\(13\) | 3.15374 | − | 1.74755i | 0.874690 | − | 0.484682i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.46405 | + | 2.53582i | −0.378017 | + | 0.654745i | ||||
\(16\) | −1.78691 | + | 3.09502i | −0.446728 | + | 0.773755i | ||||
\(17\) | 0.392550 | + | 0.679916i | 0.0952073 | + | 0.164904i | 0.909695 | − | 0.415277i | \(-0.136315\pi\) |
−0.814488 | + | 0.580181i | \(0.802982\pi\) | |||||||
\(18\) | 0.454078 | 0.107027 | ||||||||
\(19\) | −3.74764 | − | 6.49110i | −0.859767 | − | 1.48916i | −0.872151 | − | 0.489236i | \(-0.837276\pi\) |
0.0123849 | − | 0.999923i | \(-0.496058\pi\) | |||||||
\(20\) | 2.46967 | + | 4.27760i | 0.552235 | + | 0.956500i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.529011 | + | 0.916274i | 0.112786 | + | 0.195350i | ||||
\(23\) | 3.97759 | − | 6.88938i | 0.829384 | − | 1.43654i | −0.0691375 | − | 0.997607i | \(-0.522025\pi\) |
0.898522 | − | 0.438929i | \(-0.144642\pi\) | |||||||
\(24\) | −0.601923 | + | 1.04256i | −0.122867 | + | 0.212812i | ||||
\(25\) | 1.56259 | 0.312518 | ||||||||
\(26\) | 0.0170128 | − | 0.966590i | 0.00333648 | − | 0.189564i | ||||
\(27\) | −5.36475 | −1.03245 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.17586 | + | 2.03666i | −0.218353 | + | 0.378198i | −0.954304 | − | 0.298836i | \(-0.903402\pi\) |
0.735952 | + | 0.677034i | \(0.236735\pi\) | |||||||
\(30\) | 0.392550 | + | 0.679916i | 0.0716695 | + | 0.124135i | ||||
\(31\) | 2.55437 | 0.458778 | 0.229389 | − | 0.973335i | \(-0.426327\pi\) | ||||
0.229389 | + | 0.973335i | \(0.426327\pi\) | |||||||
\(32\) | 1.53234 | + | 2.65409i | 0.270882 | + | 0.469182i | ||||
\(33\) | −2.25516 | − | 3.90605i | −0.392573 | − | 0.679956i | ||||
\(34\) | 0.210505 | 0.0361013 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.63266 | + | 2.82784i | −0.272109 | + | 0.471307i | ||||
\(37\) | −3.37858 | + | 5.85187i | −0.555435 | + | 0.962041i | 0.442435 | + | 0.896801i | \(0.354115\pi\) |
−0.997870 | + | 0.0652406i | \(0.979219\pi\) | |||||||
\(38\) | −2.00967 | −0.326012 | ||||||||
\(39\) | −0.0725249 | + | 4.12054i | −0.0116133 | + | 0.659814i | ||||
\(40\) | 2.69810 | 0.426608 | ||||||||
\(41\) | −1.21874 | + | 2.11091i | −0.190335 | + | 0.329669i | −0.945361 | − | 0.326025i | \(-0.894291\pi\) |
0.755027 | + | 0.655694i | \(0.227624\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.12473 | + | 1.94809i | 0.171520 | + | 0.297081i | 0.938951 | − | 0.344050i | \(-0.111799\pi\) |
−0.767432 | + | 0.641131i | \(0.778466\pi\) | |||||||
\(44\) | −7.60832 | −1.14700 | ||||||||
\(45\) | 2.16920 | + | 3.75717i | 0.323366 | + | 0.560086i | ||||
\(46\) | −1.06649 | − | 1.84722i | −0.157246 | − | 0.272357i | ||||
\(47\) | −1.31655 | −0.192039 | −0.0960195 | − | 0.995379i | \(-0.530611\pi\) | ||||
−0.0960195 | + | 0.995379i | \(0.530611\pi\) | |||||||
\(48\) | −2.04246 | − | 3.53764i | −0.294803 | − | 0.510614i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.209485 | − | 0.362838i | 0.0296256 | − | 0.0513130i | ||||
\(51\) | −0.897376 | −0.125658 | ||||||||
\(52\) | 5.95842 | + | 3.58136i | 0.826284 | + | 0.496645i | ||||
\(53\) | 9.27954 | 1.27464 | 0.637321 | − | 0.770598i | \(-0.280042\pi\) | ||||
0.637321 | + | 0.770598i | \(0.280042\pi\) | |||||||
\(54\) | −0.719212 | + | 1.24571i | −0.0978724 | + | 0.169520i | ||||
\(55\) | −5.05434 | + | 8.75438i | −0.681528 | + | 1.18044i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.56716 | 1.13475 | ||||||||
\(58\) | 0.315279 | + | 0.546079i | 0.0413981 | + | 0.0717037i | ||||
\(59\) | −4.48335 | − | 7.76540i | −0.583683 | − | 1.01097i | −0.995038 | − | 0.0994935i | \(-0.968278\pi\) |
0.411355 | − | 0.911475i | \(-0.365056\pi\) | |||||||
\(60\) | −5.64571 | −0.728858 | ||||||||
\(61\) | 4.72273 | + | 8.18002i | 0.604684 | + | 1.04734i | 0.992101 | + | 0.125439i | \(0.0400340\pi\) |
−0.387417 | + | 0.921905i | \(0.626633\pi\) | |||||||
\(62\) | 0.342445 | − | 0.593132i | 0.0434906 | − | 0.0753279i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.32592 | −0.790741 | ||||||||
\(65\) | 8.07911 | − | 4.47679i | 1.00209 | − | 0.555277i | ||||
\(66\) | −1.20933 | −0.148858 | ||||||||
\(67\) | 0.676281 | − | 1.17135i | 0.0826209 | − | 0.143104i | −0.821754 | − | 0.569842i | \(-0.807004\pi\) |
0.904375 | + | 0.426739i | \(0.140338\pi\) | |||||||
\(68\) | −0.756879 | + | 1.31095i | −0.0917851 | + | 0.158976i | ||||
\(69\) | 4.54642 | + | 7.87463i | 0.547324 | + | 0.947994i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.15808 | − | 10.6661i | −0.730829 | − | 1.26583i | −0.956529 | − | 0.291637i | \(-0.905800\pi\) |
0.225700 | − | 0.974197i | \(-0.427533\pi\) | |||||||
\(72\) | 0.891834 | + | 1.54470i | 0.105104 | + | 0.182045i | ||||
\(73\) | −0.768590 | −0.0899567 | −0.0449783 | − | 0.998988i | \(-0.514322\pi\) | ||||
−0.0449783 | + | 0.998988i | \(0.514322\pi\) | |||||||
\(74\) | 0.905882 | + | 1.56903i | 0.105307 | + | 0.182396i | ||||
\(75\) | −0.893026 | + | 1.54677i | −0.103118 | + | 0.178605i | ||||
\(76\) | 7.22585 | − | 12.5155i | 0.828862 | − | 1.43563i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.947080 | + | 0.569251i | 0.107236 | + | 0.0644550i | ||||
\(79\) | 6.19284 | 0.696749 | 0.348375 | − | 0.937355i | \(-0.386734\pi\) | ||||
0.348375 | + | 0.937355i | \(0.386734\pi\) | |||||||
\(80\) | −4.57763 | + | 7.92868i | −0.511794 | + | 0.886454i | ||||
\(81\) | 0.525682 | − | 0.910507i | 0.0584091 | − | 0.101167i | ||||
\(82\) | 0.326774 | + | 0.565989i | 0.0360861 | + | 0.0625030i | ||||
\(83\) | 1.07292 | 0.117768 | 0.0588841 | − | 0.998265i | \(-0.481246\pi\) | ||||
0.0588841 | + | 0.998265i | \(0.481246\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00562 | + | 1.74178i | 0.109074 | + | 0.188922i | ||||
\(86\) | 0.603137 | 0.0650379 | ||||||||
\(87\) | −1.34402 | − | 2.32792i | −0.144094 | − | 0.249579i | ||||
\(88\) | −2.07801 | + | 3.59923i | −0.221517 | + | 0.383679i | ||||
\(89\) | 3.83149 | − | 6.63634i | 0.406138 | − | 0.703451i | −0.588316 | − | 0.808631i | \(-0.700209\pi\) |
0.994453 | + | 0.105180i | \(0.0335420\pi\) | |||||||
\(90\) | 1.16324 | 0.122616 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 15.3384 | 1.59914 | ||||||||
\(93\) | −1.45983 | + | 2.52850i | −0.151378 | + | 0.262194i | ||||
\(94\) | −0.176501 | + | 0.305708i | −0.0182046 | + | 0.0315314i | ||||
\(95\) | −9.60052 | − | 16.6286i | −0.984993 | − | 1.70606i | ||||
\(96\) | −3.50296 | −0.357519 | ||||||||
\(97\) | −1.18601 | − | 2.05423i | −0.120421 | − | 0.208575i | 0.799513 | − | 0.600649i | \(-0.205091\pi\) |
−0.919934 | + | 0.392074i | \(0.871758\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.68267 | −0.671634 | ||||||||
\(100\) | 1.50642 | + | 2.60920i | 0.150642 | + | 0.260920i | ||||
\(101\) | −0.398665 | + | 0.690508i | −0.0396686 | + | 0.0687081i | −0.885178 | − | 0.465252i | \(-0.845964\pi\) |
0.845509 | + | 0.533961i | \(0.179297\pi\) | |||||||
\(102\) | −0.120305 | + | 0.208374i | −0.0119119 | + | 0.0206321i | ||||
\(103\) | −2.16618 | −0.213440 | −0.106720 | − | 0.994289i | \(-0.534035\pi\) | ||||
−0.106720 | + | 0.994289i | \(0.534035\pi\) | |||||||
\(104\) | 3.32160 | − | 1.84056i | 0.325710 | − | 0.180482i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.24404 | − | 2.15474i | 0.120832 | − | 0.209287i | ||||
\(107\) | 5.76311 | − | 9.98201i | 0.557141 | − | 0.964997i | −0.440592 | − | 0.897707i | \(-0.645232\pi\) |
0.997733 | − | 0.0672896i | \(-0.0214351\pi\) | |||||||
\(108\) | −5.17191 | − | 8.95801i | −0.497667 | − | 0.861985i | ||||
\(109\) | 8.07823 | 0.773754 | 0.386877 | − | 0.922131i | \(-0.373554\pi\) | ||||
0.386877 | + | 0.922131i | \(0.373554\pi\) | |||||||
\(110\) | 1.35520 | + | 2.34727i | 0.129213 | + | 0.223803i | ||||
\(111\) | −3.86174 | − | 6.68874i | −0.366541 | − | 0.634867i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.02067 | − | 6.96401i | −0.378233 | − | 0.655119i | 0.612572 | − | 0.790415i | \(-0.290135\pi\) |
−0.990805 | + | 0.135296i | \(0.956802\pi\) | |||||||
\(114\) | 1.14854 | − | 1.98932i | 0.107570 | − | 0.186317i | ||||
\(115\) | 10.1896 | − | 17.6489i | 0.950186 | − | 1.64577i | ||||
\(116\) | −4.53439 | −0.421007 | ||||||||
\(117\) | 5.23350 | + | 3.14564i | 0.483837 | + | 0.290815i | ||||
\(118\) | −2.40420 | −0.221325 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.54198 | + | 2.67079i | −0.140763 | + | 0.243808i | ||||
\(121\) | −2.28546 | − | 3.95854i | −0.207769 | − | 0.359867i | ||||
\(122\) | 2.53257 | 0.229288 | ||||||||
\(123\) | −1.39303 | − | 2.41279i | −0.125605 | − | 0.217554i | ||||
\(124\) | 2.46255 | + | 4.26526i | 0.221143 | + | 0.383032i | ||||
\(125\) | −8.80581 | −0.787615 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.894023 | + | 1.54849i | −0.0793317 | + | 0.137406i | −0.902962 | − | 0.429721i | \(-0.858612\pi\) |
0.823630 | + | 0.567127i | \(0.191945\pi\) | |||||||
\(128\) | −3.91275 | + | 6.77709i | −0.345842 | + | 0.599015i | ||||
\(129\) | −2.57115 | −0.226377 | ||||||||
\(130\) | 0.0435826 | − | 2.47617i | 0.00382245 | − | 0.217174i | ||||
\(131\) | 6.39091 | 0.558376 | 0.279188 | − | 0.960236i | \(-0.409935\pi\) | ||||
0.279188 | + | 0.960236i | \(0.409935\pi\) | |||||||
\(132\) | 4.34819 | − | 7.53129i | 0.378461 | − | 0.655514i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.181328 | − | 0.314069i | −0.0156644 | − | 0.0271315i | ||||
\(135\) | −13.7432 | −1.18282 | ||||||||
\(136\) | 0.413443 | + | 0.716105i | 0.0354525 | + | 0.0614055i | ||||
\(137\) | −5.01827 | − | 8.69190i | −0.428740 | − | 0.742599i | 0.568022 | − | 0.823014i | \(-0.307709\pi\) |
−0.996762 | + | 0.0804144i | \(0.974376\pi\) | |||||||
\(138\) | 2.43802 | 0.207538 | ||||||||
\(139\) | −2.77278 | − | 4.80260i | −0.235184 | − | 0.407351i | 0.724142 | − | 0.689651i | \(-0.242236\pi\) |
−0.959326 | + | 0.282300i | \(0.908903\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.752416 | − | 1.30322i | 0.0633648 | − | 0.109751i | ||||
\(142\) | −3.30227 | −0.277121 | ||||||||
\(143\) | −0.250377 | + | 14.2253i | −0.0209376 | + | 1.18958i | ||||
\(144\) | −6.05238 | −0.504365 | ||||||||
\(145\) | −3.01228 | + | 5.21742i | −0.250156 | + | 0.433283i | ||||
\(146\) | −0.103039 | + | 0.178469i | −0.00852759 | + | 0.0147702i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −13.0285 | −1.07094 | ||||||||
\(149\) | −9.23254 | − | 15.9912i | −0.756359 | − | 1.31005i | −0.944696 | − | 0.327947i | \(-0.893643\pi\) |
0.188337 | − | 0.982104i | \(-0.439690\pi\) | |||||||
\(150\) | 0.239443 | + | 0.414727i | 0.0195504 | + | 0.0338623i | ||||
\(151\) | 1.60736 | 0.130805 | 0.0654024 | − | 0.997859i | \(-0.479167\pi\) | ||||
0.0654024 | + | 0.997859i | \(0.479167\pi\) | |||||||
\(152\) | −3.94710 | − | 6.83658i | −0.320152 | − | 0.554520i | ||||
\(153\) | −0.664795 | + | 1.15146i | −0.0537455 | + | 0.0930900i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.54366 | 0.525600 | ||||||||
\(156\) | −6.95036 | + | 3.85132i | −0.556474 | + | 0.308353i | ||||
\(157\) | 1.64593 | 0.131360 | 0.0656799 | − | 0.997841i | \(-0.479078\pi\) | ||||
0.0656799 | + | 0.997841i | \(0.479078\pi\) | |||||||
\(158\) | 0.830229 | − | 1.43800i | 0.0660494 | − | 0.114401i | ||||
\(159\) | −5.30330 | + | 9.18558i | −0.420579 | + | 0.728464i | ||||
\(160\) | 3.92548 | + | 6.79913i | 0.310337 | + | 0.537519i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.140949 | − | 0.244130i | −0.0110740 | − | 0.0191807i | ||||
\(163\) | 3.27409 | + | 5.67090i | 0.256447 | + | 0.444179i | 0.965287 | − | 0.261190i | \(-0.0841148\pi\) |
−0.708841 | + | 0.705369i | \(0.750782\pi\) | |||||||
\(164\) | −4.69971 | −0.366986 | ||||||||
\(165\) | −5.77716 | − | 10.0063i | −0.449751 | − | 0.778992i | ||||
\(166\) | 0.143838 | − | 0.249135i | 0.0111640 | − | 0.0193367i | ||||
\(167\) | 4.77440 | − | 8.26950i | 0.369454 | − | 0.639913i | −0.620026 | − | 0.784581i | \(-0.712878\pi\) |
0.989480 | + | 0.144668i | \(0.0462114\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.89216 | − | 11.0226i | 0.530166 | − | 0.847894i | ||||
\(170\) | 0.539262 | 0.0413595 | ||||||||
\(171\) | 6.34673 | − | 10.9929i | 0.485347 | − | 0.840646i | ||||
\(172\) | −2.16860 | + | 3.75613i | −0.165354 | + | 0.286402i | ||||
\(173\) | 5.56582 | + | 9.64028i | 0.423161 | + | 0.732937i | 0.996247 | − | 0.0865588i | \(-0.0275870\pi\) |
−0.573085 | + | 0.819496i | \(0.694254\pi\) | |||||||
\(174\) | −0.720733 | −0.0546386 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.05115 | − | 12.2130i | −0.531501 | − | 0.920586i | ||||
\(177\) | 10.2490 | 0.770364 | ||||||||
\(178\) | −1.02732 | − | 1.77937i | −0.0770009 | − | 0.133369i | ||||
\(179\) | 6.32173 | − | 10.9496i | 0.472508 | − | 0.818409i | −0.526997 | − | 0.849867i | \(-0.676682\pi\) |
0.999505 | + | 0.0314588i | \(0.0100153\pi\) | |||||||
\(180\) | −4.18246 | + | 7.24424i | −0.311742 | + | 0.539954i | ||||
\(181\) | −14.9158 | −1.10868 | −0.554341 | − | 0.832289i | \(-0.687030\pi\) | ||||
−0.554341 | + | 0.832289i | \(0.687030\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.7963 | −0.798082 | ||||||||
\(184\) | 4.18930 | − | 7.25607i | 0.308839 | − | 0.534925i | ||||
\(185\) | −8.65509 | + | 14.9911i | −0.636335 | + | 1.10216i | ||||
\(186\) | 0.391418 | + | 0.677956i | 0.0287001 | + | 0.0497101i | ||||
\(187\) | −3.09801 | −0.226549 | ||||||||
\(188\) | −1.26923 | − | 2.19837i | −0.0925680 | − | 0.160332i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.14829 | −0.373496 | ||||||||
\(191\) | 7.06528 | + | 12.2374i | 0.511226 | + | 0.885469i | 0.999915 | + | 0.0130110i | \(0.00414165\pi\) |
−0.488690 | + | 0.872458i | \(0.662525\pi\) | |||||||
\(192\) | 3.61529 | − | 6.26187i | 0.260911 | − | 0.451912i | ||||
\(193\) | −1.94727 | + | 3.37277i | −0.140167 | + | 0.242777i | −0.927560 | − | 0.373675i | \(-0.878097\pi\) |
0.787392 | + | 0.616452i | \(0.211431\pi\) | |||||||
\(194\) | −0.635998 | −0.0456620 | ||||||||
\(195\) | −0.185791 | + | 10.5558i | −0.0133048 | + | 0.755917i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.85445 | − | 10.1402i | 0.417112 | − | 0.722459i | −0.578536 | − | 0.815657i | \(-0.696376\pi\) |
0.995648 | + | 0.0931979i | \(0.0297089\pi\) | |||||||
\(198\) | −0.895897 | + | 1.55174i | −0.0636686 | + | 0.110277i | ||||
\(199\) | 1.74842 | + | 3.02835i | 0.123942 | + | 0.214674i | 0.921319 | − | 0.388808i | \(-0.127113\pi\) |
−0.797377 | + | 0.603482i | \(0.793780\pi\) | |||||||
\(200\) | 1.64576 | 0.116373 | ||||||||
\(201\) | 0.772995 | + | 1.33887i | 0.0545229 | + | 0.0944364i | ||||
\(202\) | 0.106892 | + | 0.185143i | 0.00752090 | + | 0.0130266i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.865120 | − | 1.49843i | −0.0605705 | − | 0.104911i | ||||
\(205\) | −3.12210 | + | 5.40764i | −0.218057 | + | 0.377686i | ||||
\(206\) | −0.290403 | + | 0.502994i | −0.0202334 | + | 0.0350452i | ||||
\(207\) | 13.4723 | 0.936392 | ||||||||
\(208\) | −0.226762 | + | 12.8836i | −0.0157231 | + | 0.893317i | ||||
\(209\) | 29.5764 | 2.04584 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.50258 | + | 16.4589i | −0.654184 | + | 1.13308i | 0.327913 | + | 0.944708i | \(0.393655\pi\) |
−0.982098 | + | 0.188373i | \(0.939679\pi\) | |||||||
\(212\) | 8.94598 | + | 15.4949i | 0.614412 | + | 1.06419i | ||||
\(213\) | 14.0775 | 0.964573 | ||||||||
\(214\) | −1.54524 | − | 2.67643i | −0.105630 | − | 0.182957i | ||||
\(215\) | 2.88128 | + | 4.99053i | 0.196502 | + | 0.340351i | ||||
\(216\) | −5.65029 | −0.384453 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.08299 | − | 1.87579i | 0.0733492 | − | 0.127045i | ||||
\(219\) | 0.439253 | − | 0.760808i | 0.0296820 | − | 0.0514106i | ||||
\(220\) | −19.4907 | −1.31406 | ||||||||
\(221\) | 2.42619 | + | 1.45828i | 0.163203 | + | 0.0980946i | ||||
\(222\) | −2.07086 | −0.138987 | ||||||||
\(223\) | −5.98311 | + | 10.3630i | −0.400658 | + | 0.693961i | −0.993805 | − | 0.111133i | \(-0.964552\pi\) |
0.593147 | + | 0.805094i | \(0.297885\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.32315 | + | 2.29175i | 0.0882097 | + | 0.152784i | ||||
\(226\) | −2.15609 | −0.143421 | ||||||||
\(227\) | 7.69209 | + | 13.3231i | 0.510542 | + | 0.884284i | 0.999925 | + | 0.0122157i | \(0.00388847\pi\) |
−0.489384 | + | 0.872069i | \(0.662778\pi\) | |||||||
\(228\) | 8.25921 | + | 14.3054i | 0.546980 | + | 0.947396i | ||||
\(229\) | −8.66168 | −0.572380 | −0.286190 | − | 0.958173i | \(-0.592389\pi\) | ||||
−0.286190 | + | 0.958173i | \(0.592389\pi\) | |||||||
\(230\) | −2.73209 | − | 4.73212i | −0.180149 | − | 0.312027i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.23845 | + | 2.14506i | −0.0813082 | + | 0.140830i | ||||
\(233\) | 20.2507 | 1.32667 | 0.663333 | − | 0.748325i | \(-0.269141\pi\) | ||||
0.663333 | + | 0.748325i | \(0.269141\pi\) | |||||||
\(234\) | 1.43205 | − | 0.793523i | 0.0936157 | − | 0.0518742i | ||||
\(235\) | −3.37269 | −0.220010 | ||||||||
\(236\) | 8.64440 | − | 14.9725i | 0.562702 | − | 0.974629i | ||||
\(237\) | −3.53924 | + | 6.13014i | −0.229898 | + | 0.398195i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.5526 | 1.07070 | 0.535350 | − | 0.844630i | \(-0.320180\pi\) | ||||
0.535350 | + | 0.844630i | \(0.320180\pi\) | |||||||
\(240\) | −5.23227 | − | 9.06256i | −0.337742 | − | 0.584985i | ||||
\(241\) | −8.20038 | − | 14.2035i | −0.528233 | − | 0.914926i | −0.999458 | − | 0.0329132i | \(-0.989522\pi\) |
0.471225 | − | 0.882013i | \(-0.343812\pi\) | |||||||
\(242\) | −1.22558 | −0.0787834 | ||||||||
\(243\) | −7.44626 | − | 12.8973i | −0.477678 | − | 0.827362i | ||||
\(244\) | −9.10595 | + | 15.7720i | −0.582949 | + | 1.00970i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.747011 | −0.0476277 | ||||||||
\(247\) | −23.1626 | − | 13.9221i | −1.47380 | − | 0.885840i | ||||
\(248\) | 2.69032 | 0.170836 | ||||||||
\(249\) | −0.613178 | + | 1.06206i | −0.0388586 | + | 0.0673051i | ||||
\(250\) | −1.18053 | + | 2.04474i | −0.0746632 | + | 0.129321i | ||||
\(251\) | −10.2154 | − | 17.6935i | −0.644788 | − | 1.11681i | −0.984350 | − | 0.176222i | \(-0.943612\pi\) |
0.339563 | − | 0.940583i | \(-0.389721\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.6956 | + | 27.1855i | 0.986772 | + | 1.70914i | ||||
\(254\) | 0.239710 | + | 0.415190i | 0.0150407 | + | 0.0260513i | ||||
\(255\) | −2.29886 | −0.143960 | ||||||||
\(256\) | −5.27682 | − | 9.13972i | −0.329801 | − | 0.571232i | ||||
\(257\) | 6.88895 | − | 11.9320i | 0.429721 | − | 0.744299i | −0.567127 | − | 0.823630i | \(-0.691945\pi\) |
0.996848 | + | 0.0793315i | \(0.0252786\pi\) | |||||||
\(258\) | −0.344695 | + | 0.597030i | −0.0214598 | + | 0.0371695i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 15.2640 | + | 9.17456i | 0.946633 | + | 0.568982i | ||||
\(261\) | −3.98272 | −0.246524 | ||||||||
\(262\) | 0.856782 | − | 1.48399i | 0.0529321 | − | 0.0916812i | ||||
\(263\) | −12.9587 | + | 22.4451i | −0.799065 | + | 1.38402i | 0.121160 | + | 0.992633i | \(0.461338\pi\) |
−0.920225 | + | 0.391389i | \(0.871995\pi\) | |||||||
\(264\) | −2.37519 | − | 4.11395i | −0.146183 | − | 0.253196i | ||||
\(265\) | 23.7719 | 1.46030 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.37943 | + | 7.58540i | 0.268017 | + | 0.464219i | ||||
\(268\) | 2.60789 | 0.159302 | ||||||||
\(269\) | −15.0333 | − | 26.0384i | −0.916596 | − | 1.58759i | −0.804547 | − | 0.593889i | \(-0.797592\pi\) |
−0.112050 | − | 0.993703i | \(-0.535742\pi\) | |||||||
\(270\) | −1.84245 | + | 3.19121i | −0.112128 | + | 0.194211i | ||||
\(271\) | 7.22527 | − | 12.5145i | 0.438904 | − | 0.760204i | −0.558701 | − | 0.829369i | \(-0.688700\pi\) |
0.997605 | + | 0.0691651i | \(0.0220335\pi\) | |||||||
\(272\) | −2.80581 | −0.170127 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.69105 | −0.162572 | ||||||||
\(275\) | −3.08299 | + | 5.33989i | −0.185911 | + | 0.322008i | ||||
\(276\) | −8.76599 | + | 15.1831i | −0.527651 | + | 0.913918i | ||||
\(277\) | 7.66274 | + | 13.2723i | 0.460409 | + | 0.797452i | 0.998981 | − | 0.0451272i | \(-0.0143693\pi\) |
−0.538572 | + | 0.842580i | \(0.681036\pi\) | |||||||
\(278\) | −1.48691 | −0.0891787 | ||||||||
\(279\) | 2.16295 | + | 3.74634i | 0.129492 | + | 0.224287i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.29279 | 0.315741 | 0.157871 | − | 0.987460i | \(-0.449537\pi\) | ||||
0.157871 | + | 0.987460i | \(0.449537\pi\) | |||||||
\(282\) | −0.201742 | − | 0.349427i | −0.0120135 | − | 0.0208081i | ||||
\(283\) | −15.3923 | + | 26.6602i | −0.914975 | + | 1.58478i | −0.108036 | + | 0.994147i | \(0.534456\pi\) |
−0.806938 | + | 0.590636i | \(0.798877\pi\) | |||||||
\(284\) | 11.8734 | − | 20.5654i | 0.704559 | − | 1.22033i | ||||
\(285\) | 21.9470 | 1.30003 | ||||||||
\(286\) | 3.26960 | + | 1.96522i | 0.193335 | + | 0.116206i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.59507 | + | 4.49479i | −0.152916 | + | 0.264858i | ||||
\(289\) | 8.19181 | − | 14.1886i | 0.481871 | − | 0.834625i | ||||
\(290\) | 0.807667 | + | 1.39892i | 0.0474279 | + | 0.0821474i | ||||
\(291\) | 2.71124 | 0.158935 | ||||||||
\(292\) | −0.740963 | − | 1.28339i | −0.0433616 | − | 0.0751044i | ||||
\(293\) | −8.75864 | − | 15.1704i | −0.511685 | − | 0.886265i | −0.999908 | − | 0.0135461i | \(-0.995688\pi\) |
0.488223 | − | 0.872719i | \(-0.337645\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.4853 | − | 19.8930i | −0.668697 | − | 1.15822i | ||||
\(296\) | −3.55840 | + | 6.16333i | −0.206828 | + | 0.358237i | ||||
\(297\) | 10.5847 | − | 18.3332i | 0.614184 | − | 1.06380i | ||||
\(298\) | −4.95095 | −0.286801 | ||||||||
\(299\) | 0.504763 | − | 28.6784i | 0.0291912 | − | 1.65851i | ||||
\(300\) | −3.44370 | −0.198822 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.215486 | − | 0.373233i | 0.0123998 | − | 0.0214772i | ||||
\(303\) | −0.455678 | − | 0.789257i | −0.0261780 | − | 0.0453416i | ||||
\(304\) | 26.7868 | 1.53633 | ||||||||
\(305\) | 12.0985 | + | 20.9552i | 0.692757 | + | 1.19989i | ||||
\(306\) | 0.178248 | + | 0.308735i | 0.0101898 | + | 0.0176492i | ||||
\(307\) | 8.63573 | 0.492867 | 0.246434 | − | 0.969160i | \(-0.420741\pi\) | ||||
0.246434 | + | 0.969160i | \(0.420741\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.23798 | − | 2.14425i | 0.0704262 | − | 0.121982i | ||||
\(310\) | 0.877260 | − | 1.51946i | 0.0498250 | − | 0.0862995i | ||||
\(311\) | 16.4226 | 0.931240 | 0.465620 | − | 0.884985i | \(-0.345831\pi\) | ||||
0.465620 | + | 0.884985i | \(0.345831\pi\) | |||||||
\(312\) | −0.0763851 | + | 4.33986i | −0.00432445 | + | 0.245696i | ||||
\(313\) | −10.0462 | −0.567843 | −0.283921 | − | 0.958848i | \(-0.591636\pi\) | ||||
−0.283921 | + | 0.958848i | \(0.591636\pi\) | |||||||
\(314\) | 0.220658 | − | 0.382191i | 0.0124525 | − | 0.0215683i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.97024 | + | 10.3408i | 0.335852 | + | 0.581713i | ||||
\(317\) | 10.1450 | 0.569799 | 0.284899 | − | 0.958557i | \(-0.408040\pi\) | ||||
0.284899 | + | 0.958557i | \(0.408040\pi\) | |||||||
\(318\) | 1.42195 | + | 2.46289i | 0.0797389 | + | 0.138112i | ||||
\(319\) | −4.63996 | − | 8.03665i | −0.259788 | − | 0.449966i | ||||
\(320\) | −16.2055 | −0.905913 | ||||||||
\(321\) | 6.58729 | + | 11.4095i | 0.367667 | + | 0.636817i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.94227 | − | 5.09616i | 0.163712 | − | 0.283558i | ||||
\(324\) | 2.02714 | 0.112619 | ||||||||
\(325\) | 4.92800 | − | 2.73070i | 0.273356 | − | 0.151472i | ||||
\(326\) | 1.75573 | 0.0972411 | ||||||||
\(327\) | −4.61674 | + | 7.99644i | −0.255307 | + | 0.442204i | ||||
\(328\) | −1.28360 | + | 2.22327i | −0.0708751 | + | 0.122759i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.09801 | −0.170540 | ||||||||
\(331\) | −1.15958 | − | 2.00845i | −0.0637363 | − | 0.110395i | 0.832396 | − | 0.554181i | \(-0.186968\pi\) |
−0.896133 | + | 0.443786i | \(0.853635\pi\) | |||||||
\(332\) | 1.03435 | + | 1.79155i | 0.0567675 | + | 0.0983242i | ||||
\(333\) | −11.4434 | −0.627097 | ||||||||
\(334\) | −1.28014 | − | 2.21726i | −0.0700460 | − | 0.121323i | ||||
\(335\) | 1.73247 | − | 3.00072i | 0.0946547 | − | 0.163947i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.9998 | −0.871565 | −0.435783 | − | 0.900052i | \(-0.643528\pi\) | ||||
−0.435783 | + | 0.900052i | \(0.643528\pi\) | |||||||
\(338\) | −1.63551 | − | 3.07810i | −0.0889598 | − | 0.167427i | ||||
\(339\) | 9.19133 | 0.499205 | ||||||||
\(340\) | −1.93894 | + | 3.35834i | −0.105154 | + | 0.182132i | ||||
\(341\) | −5.03977 | + | 8.72913i | −0.272919 | + | 0.472709i | ||||
\(342\) | −1.70172 | − | 2.94747i | −0.0920185 | − | 0.159381i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.18459 | + | 2.05178i | 0.0638690 | + | 0.110624i | ||||
\(345\) | 11.6468 | + | 20.1729i | 0.627043 | + | 1.08607i | ||||
\(346\) | 2.98467 | 0.160457 | ||||||||
\(347\) | 11.4104 | + | 19.7634i | 0.612543 | + | 1.06096i | 0.990810 | + | 0.135259i | \(0.0431867\pi\) |
−0.378267 | + | 0.925696i | \(0.623480\pi\) | |||||||
\(348\) | 2.59142 | − | 4.48848i | 0.138915 | − | 0.240608i | ||||
\(349\) | −11.3511 | + | 19.6607i | −0.607612 | + | 1.05241i | 0.384021 | + | 0.923324i | \(0.374539\pi\) |
−0.991633 | + | 0.129090i | \(0.958794\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.9190 | + | 9.37515i | −0.903071 | + | 0.500408i | ||||
\(352\) | −12.0932 | −0.644572 | ||||||||
\(353\) | −13.6322 | + | 23.6116i | −0.725568 | + | 1.25672i | 0.233171 | + | 0.972436i | \(0.425090\pi\) |
−0.958740 | + | 0.284286i | \(0.908244\pi\) | |||||||
\(354\) | 1.37401 | − | 2.37986i | 0.0730279 | − | 0.126488i | ||||
\(355\) | −15.7755 | − | 27.3239i | −0.837276 | − | 1.45020i | ||||
\(356\) | 14.7751 | 0.783077 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.69502 | − | 2.93585i | −0.0895844 | − | 0.155165i | ||||
\(359\) | −14.4262 | −0.761385 | −0.380692 | − | 0.924702i | \(-0.624314\pi\) | ||||
−0.380692 | + | 0.924702i | \(0.624314\pi\) | |||||||
\(360\) | 2.28466 | + | 3.95715i | 0.120412 | + | 0.208560i | ||||
\(361\) | −18.5895 | + | 32.1980i | −0.978397 | + | 1.69463i | ||||
\(362\) | −1.99965 | + | 3.46350i | −0.105099 | + | 0.182037i | ||||
\(363\) | 5.22461 | 0.274221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.96894 | −0.103059 | ||||||||
\(366\) | −1.44737 | + | 2.50693i | −0.0756555 | + | 0.131039i | ||||
\(367\) | −5.69586 | + | 9.86553i | −0.297322 | + | 0.514976i | −0.975522 | − | 0.219901i | \(-0.929427\pi\) |
0.678201 | + | 0.734877i | \(0.262760\pi\) | |||||||
\(368\) | 14.2152 | + | 24.6214i | 0.741018 | + | 1.28348i | ||||
\(369\) | −4.12793 | −0.214892 | ||||||||
\(370\) | 2.32065 | + | 4.01948i | 0.120645 | + | 0.208963i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.62943 | −0.291872 | ||||||||
\(373\) | 15.4815 | + | 26.8147i | 0.801599 | + | 1.38841i | 0.918563 | + | 0.395274i | \(0.129351\pi\) |
−0.116964 | + | 0.993136i | \(0.537316\pi\) | |||||||
\(374\) | −0.415327 | + | 0.719367i | −0.0214760 | + | 0.0371976i | ||||
\(375\) | 5.03256 | − | 8.71665i | 0.259880 | − | 0.450126i | ||||
\(376\) | −1.38663 | −0.0715098 | ||||||||
\(377\) | −0.149219 | + | 8.47796i | −0.00768518 | + | 0.436637i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.29330 | + | 9.16826i | −0.271898 | + | 0.470942i | −0.969348 | − | 0.245692i | \(-0.920985\pi\) |
0.697450 | + | 0.716634i | \(0.254318\pi\) | |||||||
\(380\) | 18.5109 | − | 32.0617i | 0.949587 | − | 1.64473i | ||||
\(381\) | −1.02188 | − | 1.76994i | −0.0523523 | − | 0.0906768i | ||||
\(382\) | 3.78876 | 0.193850 | ||||||||
\(383\) | 15.3758 | + | 26.6317i | 0.785668 | + | 1.36082i | 0.928599 | + | 0.371084i | \(0.121014\pi\) |
−0.142931 | + | 0.989733i | \(0.545653\pi\) | |||||||
\(384\) | −4.47231 | − | 7.74627i | −0.228227 | − | 0.395300i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.522112 | + | 0.904324i | 0.0265748 | + | 0.0460289i | ||||
\(387\) | −1.90476 | + | 3.29915i | −0.0968246 | + | 0.167705i | ||||
\(388\) | 2.28675 | − | 3.96077i | 0.116092 | − | 0.201078i | ||||
\(389\) | −16.3796 | −0.830477 | −0.415239 | − | 0.909713i | \(-0.636302\pi\) | ||||
−0.415239 | + | 0.909713i | \(0.636302\pi\) | |||||||
\(390\) | 2.42619 | + | 1.45828i | 0.122855 | + | 0.0738429i | ||||
\(391\) | 6.24561 | 0.315854 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.65243 | + | 6.32620i | −0.184241 | + | 0.319114i | ||||
\(394\) | −1.56972 | − | 2.71884i | −0.0790816 | − | 0.136973i | ||||
\(395\) | 15.8645 | 0.798232 | ||||||||
\(396\) | −6.44246 | − | 11.1587i | −0.323746 | − | 0.560744i | ||||
\(397\) | −7.94133 | − | 13.7548i | −0.398564 | − | 0.690333i | 0.594985 | − | 0.803737i | \(-0.297158\pi\) |
−0.993549 | + | 0.113404i | \(0.963825\pi\) | |||||||
\(398\) | 0.937591 | 0.0469972 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.79221 | + | 4.83624i | −0.139610 | + | 0.241812i | ||||
\(401\) | −3.31787 | + | 5.74671i | −0.165686 | + | 0.286977i | −0.936899 | − | 0.349601i | \(-0.886317\pi\) |
0.771212 | + | 0.636578i | \(0.219651\pi\) | |||||||
\(402\) | 0.414519 | 0.0206743 | ||||||||
\(403\) | 8.05581 | − | 4.46387i | 0.401289 | − | 0.222361i | ||||
\(404\) | −1.53734 | −0.0764855 | ||||||||
\(405\) | 1.34667 | − | 2.33250i | 0.0669164 | − | 0.115903i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.3319 | − | 23.0915i | −0.660836 | − | 1.14460i | ||||
\(408\) | −0.945139 | −0.0467914 | ||||||||
\(409\) | 2.93617 | + | 5.08560i | 0.145184 | + | 0.251467i | 0.929442 | − | 0.368969i | \(-0.120289\pi\) |
−0.784257 | + | 0.620436i | \(0.786956\pi\) | |||||||
\(410\) | 0.837115 | + | 1.44992i | 0.0413421 | + | 0.0716067i | ||||
\(411\) | 11.4719 | 0.565865 | ||||||||
\(412\) | −2.08831 | − | 3.61707i | −0.102884 | − | 0.178200i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.80614 | − | 3.12832i | 0.0887667 | − | 0.153749i | ||||
\(415\) | 2.74856 | 0.134921 | ||||||||
\(416\) | 9.47076 | + | 5.69248i | 0.464342 | + | 0.279097i | ||||
\(417\) | 6.33863 | 0.310404 | ||||||||
\(418\) | 3.96508 | − | 6.86773i | 0.193939 | − | 0.335911i | ||||
\(419\) | −15.0712 | + | 26.1040i | −0.736274 | + | 1.27526i | 0.217888 | + | 0.975974i | \(0.430083\pi\) |
−0.954162 | + | 0.299290i | \(0.903250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 40.0580 | 1.95231 | 0.976153 | − | 0.217083i | \(-0.0696543\pi\) | ||||
0.976153 | + | 0.217083i | \(0.0696543\pi\) | |||||||
\(422\) | 2.54788 | + | 4.41306i | 0.124029 | + | 0.214824i | ||||
\(423\) | −1.11481 | − | 1.93091i | −0.0542040 | − | 0.0938840i | ||||
\(424\) | 9.77344 | 0.474640 | ||||||||
\(425\) | 0.613394 | + | 1.06243i | 0.0297540 | + | 0.0515354i | ||||
\(426\) | 1.88726 | − | 3.26884i | 0.0914382 | − | 0.158376i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 22.2238 | 1.07423 | ||||||||
\(429\) | −13.9382 | − | 8.37767i | −0.672942 | − | 0.404478i | ||||
\(430\) | 1.54509 | 0.0745108 | ||||||||
\(431\) | 1.95793 | − | 3.39124i | 0.0943104 | − | 0.163350i | −0.815010 | − | 0.579447i | \(-0.803269\pi\) |
0.909321 | + | 0.416096i | \(0.136602\pi\) | |||||||
\(432\) | 9.58632 | − | 16.6040i | 0.461222 | − | 0.798860i | ||||
\(433\) | −20.3963 | − | 35.3274i | −0.980182 | − | 1.69772i | −0.661650 | − | 0.749813i | \(-0.730144\pi\) |
−0.318532 | − | 0.947912i | \(-0.603190\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.44306 | − | 5.96355i | −0.165082 | − | 0.285930i | ||||
\(436\) | 7.78785 | + | 13.4890i | 0.372971 | + | 0.646004i | ||||
\(437\) | −59.6262 | −2.85231 | ||||||||
\(438\) | −0.117775 | − | 0.203992i | −0.00562750 | − | 0.00974711i | ||||
\(439\) | −12.7811 | + | 22.1376i | −0.610010 | + | 1.05657i | 0.381228 | + | 0.924481i | \(0.375501\pi\) |
−0.991238 | + | 0.132087i | \(0.957832\pi\) | |||||||
\(440\) | −5.32336 | + | 9.22033i | −0.253781 | + | 0.439562i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.663878 | − | 0.367867i | 0.0315775 | − | 0.0174977i | ||||
\(443\) | −27.4564 | −1.30449 | −0.652247 | − | 0.758007i | \(-0.726173\pi\) | ||||
−0.652247 | + | 0.758007i | \(0.726173\pi\) | |||||||
\(444\) | 7.44586 | − | 12.8966i | 0.353365 | − | 0.612046i | ||||
\(445\) | 9.81535 | − | 17.0007i | 0.465292 | − | 0.805910i | ||||
\(446\) | 1.60422 | + | 2.77859i | 0.0759621 | + | 0.131570i | ||||
\(447\) | 21.1057 | 0.998267 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.40181 | + | 12.8203i | 0.349313 | + | 0.605028i | 0.986128 | − | 0.165989i | \(-0.0530816\pi\) |
−0.636815 | + | 0.771017i | \(0.719748\pi\) | |||||||
\(450\) | 0.709537 | 0.0334479 | ||||||||
\(451\) | −4.80913 | − | 8.32966i | −0.226453 | − | 0.392229i | ||||
\(452\) | 7.75230 | − | 13.4274i | 0.364637 | − | 0.631571i | ||||
\(453\) | −0.918611 | + | 1.59108i | −0.0431601 | + | 0.0747555i | ||||
\(454\) | 4.12489 | 0.193590 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.02315 | 0.422548 | ||||||||
\(457\) | 0.325975 | − | 0.564606i | 0.0152485 | − | 0.0264112i | −0.858300 | − | 0.513147i | \(-0.828479\pi\) |
0.873549 | + | 0.486736i | \(0.161813\pi\) | |||||||
\(458\) | −1.16121 | + | 2.01127i | −0.0542596 | + | 0.0939805i | ||||
\(459\) | −2.10593 | − | 3.64758i | −0.0982965 | − | 0.170254i | ||||
\(460\) | 39.2933 | 1.83206 | ||||||||
\(461\) | 6.24774 | + | 10.8214i | 0.290986 | + | 0.504003i | 0.974043 | − | 0.226362i | \(-0.0726833\pi\) |
−0.683057 | + | 0.730365i | \(0.739350\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.309503 | −0.0143838 | −0.00719190 | − | 0.999974i | \(-0.502289\pi\) | ||||
−0.00719190 | + | 0.999974i | \(0.502289\pi\) | |||||||
\(464\) | −4.20233 | − | 7.27865i | −0.195088 | − | 0.337903i | ||||
\(465\) | −3.73973 | + | 6.47741i | −0.173426 | + | 0.300382i | ||||
\(466\) | 2.71486 | − | 4.70227i | 0.125763 | − | 0.217829i | ||||
\(467\) | −24.4773 | −1.13268 | −0.566338 | − | 0.824173i | \(-0.691640\pi\) | ||||
−0.566338 | + | 0.824173i | \(0.691640\pi\) | |||||||
\(468\) | −0.207187 | + | 11.7714i | −0.00957722 | + | 0.544134i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.452151 | + | 0.783149i | −0.0208562 | + | 0.0361240i | ||||
\(471\) | −0.940659 | + | 1.62927i | −0.0433433 | + | 0.0750727i | ||||
\(472\) | −4.72198 | − | 8.17871i | −0.217347 | − | 0.376456i | ||||
\(473\) | −8.87637 | −0.408136 | ||||||||
\(474\) | 0.948959 | + | 1.64364i | 0.0435871 | + | 0.0754951i | ||||
\(475\) | −5.85601 | − | 10.1429i | −0.268692 | − | 0.465389i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.85759 | + | 13.6097i | 0.359774 | + | 0.623147i | ||||
\(478\) | 2.21909 | − | 3.84357i | 0.101499 | − | 0.175801i | ||||
\(479\) | 4.06925 | − | 7.04815i | 0.185929 | − | 0.322038i | −0.757960 | − | 0.652301i | \(-0.773804\pi\) |
0.943889 | + | 0.330262i | \(0.107137\pi\) | |||||||
\(480\) | −8.97372 | −0.409593 | ||||||||
\(481\) | −0.428748 | + | 24.3595i | −0.0195492 | + | 1.11070i | ||||
\(482\) | −4.39746 | −0.200299 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.40662 | − | 7.63250i | 0.200301 | − | 0.346932i | ||||
\(485\) | −3.03826 | − | 5.26243i | −0.137960 | − | 0.238954i | ||||
\(486\) | −3.99306 | −0.181129 | ||||||||
\(487\) | −2.30480 | − | 3.99203i | −0.104440 | − | 0.180896i | 0.809069 | − | 0.587714i | \(-0.199972\pi\) |
−0.913509 | + | 0.406817i | \(0.866638\pi\) | |||||||
\(488\) | 4.97410 | + | 8.61540i | 0.225167 | + | 0.390001i | ||||
\(489\) | −7.48464 | −0.338467 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.50947 | + | 11.2747i | −0.293768 | + | 0.508822i | −0.974698 | − | 0.223527i | \(-0.928243\pi\) |
0.680929 | + | 0.732349i | \(0.261576\pi\) | |||||||
\(492\) | 2.68591 | − | 4.65213i | 0.121090 | − | 0.209734i | ||||
\(493\) | −1.84634 | −0.0831551 | ||||||||
\(494\) | −6.33798 | + | 3.51199i | −0.285159 | + | 0.158012i | ||||
\(495\) | −17.1194 | −0.769459 | ||||||||
\(496\) | −4.56443 | + | 7.90582i | −0.204949 | + | 0.354982i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.164409 | + | 0.284764i | 0.00736733 | + | 0.0127606i | ||||
\(499\) | −32.3207 | −1.44687 | −0.723436 | − | 0.690391i | \(-0.757438\pi\) | ||||
−0.723436 | + | 0.690391i | \(0.757438\pi\) | |||||||
\(500\) | −8.48928 | − | 14.7039i | −0.379652 | − | 0.657577i | ||||
\(501\) | 5.45718 | + | 9.45211i | 0.243809 | + | 0.422289i | ||||
\(502\) | −5.47799 | −0.244495 | ||||||||
\(503\) | −15.9126 | − | 27.5615i | −0.709509 | − | 1.22891i | −0.965039 | − | 0.262105i | \(-0.915583\pi\) |
0.255531 | − | 0.966801i | \(-0.417750\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.02128 | + | 1.76891i | −0.0454465 | + | 0.0787156i | ||||
\(506\) | 8.41676 | 0.374170 | ||||||||
\(507\) | 6.97211 | + | 13.1219i | 0.309642 | + | 0.582762i | ||||
\(508\) | −3.44755 | −0.152960 | ||||||||
\(509\) | 1.12788 | − | 1.95354i | 0.0499922 | − | 0.0865891i | −0.839946 | − | 0.542669i | \(-0.817414\pi\) |
0.889939 | + | 0.456080i | \(0.150747\pi\) | |||||||
\(510\) | −0.308191 | + | 0.533802i | −0.0136469 | + | 0.0236372i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −18.4807 | −0.816739 | ||||||||
\(513\) | 20.1051 | + | 34.8231i | 0.887663 | + | 1.53748i | ||||
\(514\) | −1.84710 | − | 3.19927i | −0.0814722 | − | 0.141114i | ||||
\(515\) | −5.54922 | −0.244528 | ||||||||
\(516\) | −2.47873 | − | 4.29329i | −0.109120 | − | 0.189001i | ||||
\(517\) | 2.59756 | − | 4.49911i | 0.114241 | − | 0.197870i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.7236 | −0.558502 | ||||||||
\(520\) | 8.50912 | − | 4.71506i | 0.373150 | − | 0.206769i | ||||
\(521\) | −10.7712 | −0.471897 | −0.235948 | − | 0.971766i | \(-0.575820\pi\) | ||||
−0.235948 | + | 0.971766i | \(0.575820\pi\) | |||||||
\(522\) | −0.533934 | + | 0.924801i | −0.0233697 | + | 0.0404775i | ||||
\(523\) | 3.70397 | − | 6.41546i | 0.161963 | − | 0.280528i | −0.773610 | − | 0.633663i | \(-0.781551\pi\) |
0.935573 | + | 0.353134i | \(0.114884\pi\) | |||||||
\(524\) | 6.16118 | + | 10.6715i | 0.269152 | + | 0.466186i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.47454 | + | 6.01809i | 0.151497 | + | 0.262401i | ||||
\(527\) | 1.00272 | + | 1.73676i | 0.0436790 | + | 0.0756543i | ||||
\(528\) | 16.1191 | 0.701492 | ||||||||
\(529\) | −20.1424 | − | 34.8877i | −0.875757 | − | 1.51686i | ||||
\(530\) | 3.18692 | − | 5.51991i | 0.138431 | − | 0.239770i | ||||
\(531\) | 7.59270 | − | 13.1509i | 0.329495 | − | 0.570702i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.154660 | + | 8.78707i | −0.00669906 | + | 0.380610i | ||||
\(534\) | 2.34847 | 0.101628 | ||||||||
\(535\) | 14.7637 | − | 25.5715i | 0.638290 | − | 1.10555i | ||||
\(536\) | 0.712276 | − | 1.23370i | 0.0307656 | − | 0.0532876i | ||||
\(537\) | 7.22580 | + | 12.5154i | 0.311816 | + | 0.540081i | ||||
\(538\) | −8.06161 | −0.347561 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −13.2492 | − | 22.9482i | −0.570153 | − | 0.987534i | ||||
\(541\) | 32.5481 | 1.39935 | 0.699676 | − | 0.714460i | \(-0.253327\pi\) | ||||
0.699676 | + | 0.714460i | \(0.253327\pi\) | |||||||
\(542\) | −1.93728 | − | 3.35546i | −0.0832132 | − | 0.144129i | ||||
\(543\) | 8.52445 | − | 14.7648i | 0.365819 | − | 0.633617i | ||||
\(544\) | −1.20304 | + | 2.08373i | −0.0515799 | + | 0.0893391i | ||||
\(545\) | 20.6944 | 0.886453 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.4997 | −0.577206 | −0.288603 | − | 0.957449i | \(-0.593191\pi\) | ||||
−0.288603 | + | 0.957449i | \(0.593191\pi\) | |||||||
\(548\) | 9.67577 | − | 16.7589i | 0.413329 | − | 0.715906i | ||||
\(549\) | −7.99810 | + | 13.8531i | −0.341350 | + | 0.591236i | ||||
\(550\) | 0.826627 | + | 1.43176i | 0.0352475 | + | 0.0610504i | ||||
\(551\) | 17.6268 | 0.750929 | ||||||||
\(552\) | 4.78840 | + | 8.29376i | 0.203808 | + | 0.353006i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.10915 | 0.174581 | ||||||||
\(555\) | −9.89284 | − | 17.1349i | −0.419928 | − | 0.727336i | ||||
\(556\) | 5.34623 | − | 9.25994i | 0.226731 | − | 0.392709i | ||||
\(557\) | 14.8851 | − | 25.7818i | 0.630703 | − | 1.09241i | −0.356705 | − | 0.934217i | \(-0.616100\pi\) |
0.987408 | − | 0.158193i | \(-0.0505668\pi\) | |||||||
\(558\) | 1.15988 | 0.0491017 | ||||||||
\(559\) | 6.95148 | + | 4.17825i | 0.294016 | + | 0.176721i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.77052 | − | 3.06664i | 0.0747516 | − | 0.129474i | ||||
\(562\) | 0.709566 | − | 1.22900i | 0.0299312 | − | 0.0518424i | ||||
\(563\) | 7.06629 | + | 12.2392i | 0.297809 | + | 0.515819i | 0.975634 | − | 0.219403i | \(-0.0704110\pi\) |
−0.677826 | + | 0.735223i | \(0.737078\pi\) | |||||||
\(564\) | 2.90148 | 0.122174 | ||||||||
\(565\) | −10.3000 | − | 17.8401i | −0.433324 | − | 0.750538i | ||||
\(566\) | 4.12705 | + | 7.14826i | 0.173473 | + | 0.300464i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.48584 | − | 11.2338i | −0.272140 | − | 0.471360i | ||||
\(569\) | 12.1270 | − | 21.0046i | 0.508391 | − | 0.880558i | −0.491562 | − | 0.870842i | \(-0.663574\pi\) |
0.999953 | − | 0.00971585i | \(-0.00309270\pi\) | |||||||
\(570\) | 2.94227 | − | 5.09616i | 0.123238 | − | 0.213455i | ||||
\(571\) | 1.20832 | 0.0505665 | 0.0252832 | − | 0.999680i | \(-0.491951\pi\) | ||||
0.0252832 | + | 0.999680i | \(0.491951\pi\) | |||||||
\(572\) | −23.9947 | + | 13.2959i | −1.00327 | + | 0.555929i | ||||
\(573\) | −16.1514 | −0.674732 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.21533 | − | 10.7653i | 0.259197 | − | 0.448943i | ||||
\(576\) | −5.35657 | − | 9.27786i | −0.223191 | − | 0.386577i | ||||
\(577\) | 14.6104 | 0.608237 | 0.304119 | − | 0.952634i | \(-0.401638\pi\) | ||||
0.304119 | + | 0.952634i | \(0.401638\pi\) | |||||||
\(578\) | −2.19643 | − | 3.80433i | −0.0913595 | − | 0.158239i | ||||
\(579\) | −2.22575 | − | 3.85510i | −0.0924988 | − | 0.160213i | ||||
\(580\) | −11.6160 | −0.482328 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.363475 | − | 0.629558i | 0.0150665 | − | 0.0260960i | ||||
\(583\) | −18.3085 | + | 31.7113i | −0.758262 | + | 1.31335i | ||||
\(584\) | −0.809498 | −0.0334973 | ||||||||
\(585\) | 13.4069 | + | 8.05836i | 0.554309 | + | 0.333172i | ||||
\(586\) | −4.69683 | −0.194024 | ||||||||
\(587\) | 10.7548 | − | 18.6278i | 0.443897 | − | 0.768852i | −0.554078 | − | 0.832465i | \(-0.686929\pi\) |
0.997975 | + | 0.0636132i | \(0.0202624\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.57284 | − | 16.5806i | −0.394442 | − | 0.683193i | ||||
\(590\) | −6.15897 | −0.253561 | ||||||||
\(591\) | 6.69168 | + | 11.5903i | 0.275259 | + | 0.476763i | ||||
\(592\) | −12.0744 | − | 20.9135i | −0.496256 | − | 0.859541i | ||||
\(593\) | 2.64857 | 0.108764 | 0.0543820 | − | 0.998520i | \(-0.482681\pi\) | ||||
0.0543820 | + | 0.998520i | \(0.482681\pi\) | |||||||
\(594\) | −2.83801 | − | 4.91558i | −0.116445 | − | 0.201689i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.8013 | − | 30.8328i | 0.729171 | − | 1.26296i | ||||
\(597\) | −3.99692 | −0.163583 | ||||||||
\(598\) | −6.59154 | − | 3.96190i | −0.269548 | − | 0.162014i | ||||
\(599\) | −40.2501 | −1.64457 | −0.822287 | − | 0.569074i | \(-0.807302\pi\) | ||||
−0.822287 | + | 0.569074i | \(0.807302\pi\) | |||||||
\(600\) | −0.940558 | + | 1.62909i | −0.0383981 | + | 0.0665075i | ||||
\(601\) | 19.1725 | − | 33.2077i | 0.782061 | − | 1.35457i | −0.148679 | − | 0.988886i | \(-0.547502\pi\) |
0.930739 | − | 0.365683i | \(-0.119165\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.29060 | 0.0932806 | ||||||||
\(604\) | 1.54958 | + | 2.68395i | 0.0630515 | + | 0.109208i | ||||
\(605\) | −5.85480 | − | 10.1408i | −0.238031 | − | 0.412283i | ||||
\(606\) | −0.244357 | −0.00992634 | ||||||||
\(607\) | 21.2773 | + | 36.8534i | 0.863620 | + | 1.49583i | 0.868411 | + | 0.495845i | \(0.165142\pi\) |
−0.00479063 | + | 0.999989i | \(0.501525\pi\) | |||||||
\(608\) | 11.4853 | − | 19.8931i | 0.465791 | − | 0.806773i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.48782 | 0.262684 | ||||||||
\(611\) | −4.15207 | + | 2.30074i | −0.167975 | + | 0.0930779i | ||||
\(612\) | −2.56360 | −0.103627 | ||||||||
\(613\) | −7.63261 | + | 13.2201i | −0.308278 | + | 0.533953i | −0.977986 | − | 0.208672i | \(-0.933086\pi\) |
0.669708 | + | 0.742625i | \(0.266419\pi\) | |||||||
\(614\) | 1.15773 | − | 2.00524i | 0.0467221 | − | 0.0809251i | ||||
\(615\) | −3.56859 | − | 6.18098i | −0.143899 | − | 0.249241i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.99061 | − | 12.1081i | −0.281431 | − | 0.487453i | 0.690306 | − | 0.723517i | \(-0.257476\pi\) |
−0.971737 | + | 0.236064i | \(0.924142\pi\) | |||||||
\(618\) | −0.331934 | − | 0.574926i | −0.0133523 | − | 0.0231269i | ||||
\(619\) | 8.51585 | 0.342281 | 0.171140 | − | 0.985247i | \(-0.445255\pi\) | ||||
0.171140 | + | 0.985247i | \(0.445255\pi\) | |||||||
\(620\) | 6.30845 | + | 10.9265i | 0.253353 | + | 0.438821i | ||||
\(621\) | −21.3388 | + | 36.9598i | −0.856295 | + | 1.48315i | ||||
\(622\) | 2.20166 | − | 3.81338i | 0.0882784 | − | 0.152903i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −12.6236 | − | 7.58750i | −0.505347 | − | 0.303743i | ||||
\(625\) | −30.3713 | −1.21485 | ||||||||
\(626\) | −1.34682 | + | 2.33275i | −0.0538296 | + | 0.0932356i | ||||
\(627\) | −16.9030 | + | 29.2769i | −0.675042 | + | 1.16921i | ||||
\(628\) | 1.58677 | + | 2.74837i | 0.0633190 | + | 0.109672i | ||||
\(629\) | −5.30504 | −0.211526 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.4146 | − | 31.8950i | −0.733074 | − | 1.26972i | −0.955563 | − | 0.294786i | \(-0.904752\pi\) |
0.222490 | − | 0.974935i | \(-0.428582\pi\) | |||||||
\(632\) | 6.52246 | 0.259449 | ||||||||
\(633\) | −10.8615 | − | 18.8127i | −0.431707 | − | 0.747739i | ||||
\(634\) | 1.36006 | − | 2.35570i | 0.0540150 | − | 0.0935567i | ||||
\(635\) | −2.29027 | + | 3.96686i | −0.0908865 | + | 0.157420i | ||||
\(636\) | −20.4507 | −0.810922 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.48818 | −0.0985081 | ||||||||
\(639\) | 10.4289 | − | 18.0634i | 0.412561 | − | 0.714576i | ||||
\(640\) | −10.0235 | + | 17.3612i | −0.396214 | + | 0.686263i | ||||
\(641\) | −12.9374 | − | 22.4082i | −0.510996 | − | 0.885070i | −0.999919 | − | 0.0127435i | \(-0.995944\pi\) |
0.488923 | − | 0.872327i | \(-0.337390\pi\) | |||||||
\(642\) | 3.53244 | 0.139414 | ||||||||
\(643\) | 20.2626 | + | 35.0958i | 0.799078 | + | 1.38404i | 0.920217 | + | 0.391408i | \(0.128012\pi\) |
−0.121139 | + | 0.992636i | \(0.538655\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.58666 | −0.259350 | ||||||||
\(646\) | −0.788896 | − | 1.36641i | −0.0310387 | − | 0.0537606i | ||||
\(647\) | 0.892002 | − | 1.54499i | 0.0350682 | − | 0.0607399i | −0.847959 | − | 0.530062i | \(-0.822168\pi\) |
0.883027 | + | 0.469322i | \(0.155502\pi\) | |||||||
\(648\) | 0.553661 | − | 0.958969i | 0.0217499 | − | 0.0376719i | ||||
\(649\) | 35.3826 | 1.38889 | ||||||||
\(650\) | 0.0265840 | − | 1.51038i | 0.00104271 | − | 0.0592420i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.31281 | + | 10.9341i | −0.247229 | + | 0.428213i | ||||
\(653\) | −6.20210 | + | 10.7424i | −0.242707 | + | 0.420381i | −0.961484 | − | 0.274860i | \(-0.911369\pi\) |
0.718778 | + | 0.695240i | \(0.244702\pi\) | |||||||
\(654\) | 1.23787 | + | 2.14405i | 0.0484044 | + | 0.0838389i | ||||
\(655\) | 16.3719 | 0.639704 | ||||||||
\(656\) | −4.35554 | − | 7.54402i | −0.170055 | − | 0.294545i | ||||
\(657\) | −0.650815 | − | 1.12725i | −0.0253907 | − | 0.0439780i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.564336 | + | 0.977458i | 0.0219834 | + | 0.0380764i | 0.876808 | − | 0.480841i | \(-0.159669\pi\) |
−0.854824 | + | 0.518917i | \(0.826335\pi\) | |||||||
\(660\) | 11.1390 | − | 19.2933i | 0.433585 | − | 0.750991i | ||||
\(661\) | −14.4627 | + | 25.0502i | −0.562534 | + | 0.974338i | 0.434740 | + | 0.900556i | \(0.356840\pi\) |
−0.997274 | + | 0.0737821i | \(0.976493\pi\) | |||||||
\(662\) | −0.621826 | −0.0241680 | ||||||||
\(663\) | −2.83009 | + | 1.56821i | −0.109912 | + | 0.0609041i | ||||
\(664\) | 1.13003 | 0.0438535 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.53414 | + | 2.65721i | −0.0594467 | + | 0.102965i | ||||
\(667\) | 9.35421 | + | 16.2020i | 0.362196 | + | 0.627342i | ||||
\(668\) | 18.4111 | 0.712348 | ||||||||
\(669\) | −6.83874 | − | 11.8451i | −0.264401 | − | 0.457956i | ||||
\(670\) | −0.464518 | − | 0.804568i | −0.0179459 | − | 0.0310832i | ||||
\(671\) | −37.2718 | −1.43886 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.54980 | − | 6.14843i | 0.136835 | − | 0.237005i | −0.789462 | − | 0.613799i | \(-0.789640\pi\) |
0.926297 | + | 0.376795i | \(0.122974\pi\) | |||||||
\(674\) | −2.14498 | + | 3.71521i | −0.0826214 | + | 0.143104i | ||||
\(675\) | −8.38289 | −0.322658 | ||||||||
\(676\) | 25.0499 | + | 0.882071i | 0.963457 | + | 0.0339258i | ||||
\(677\) | 50.4020 | 1.93710 | 0.968552 | − | 0.248811i | \(-0.0800397\pi\) | ||||
0.968552 | + | 0.248811i | \(0.0800397\pi\) | |||||||
\(678\) | 1.23221 | − | 2.13426i | 0.0473229 | − | 0.0819657i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.05914 | + | 1.83449i | 0.0406162 | + | 0.0703493i | ||||
\(681\) | −17.5843 | −0.673830 | ||||||||
\(682\) | 1.35129 | + | 2.34050i | 0.0517435 | + | 0.0896224i | ||||
\(683\) | −13.7641 | − | 23.8401i | −0.526669 | − | 0.912217i | −0.999517 | − | 0.0310735i | \(-0.990107\pi\) |
0.472848 | − | 0.881144i | \(-0.343226\pi\) | |||||||
\(684\) | 24.4744 | 0.935802 | ||||||||
\(685\) | −12.8556 | − | 22.2665i | −0.491186 | − | 0.850760i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.95019 | − | 8.57398i | 0.188861 | − | 0.327118i | ||||
\(688\) | −8.03917 | −0.306490 | ||||||||
\(689\) | 29.2653 | − | 16.2164i | 1.11492 | − | 0.617796i | ||||
\(690\) | 6.24561 | 0.237766 | ||||||||
\(691\) | −12.1669 | + | 21.0737i | −0.462851 | + | 0.801682i | −0.999102 | − | 0.0423772i | \(-0.986507\pi\) |
0.536251 | + | 0.844059i | \(0.319840\pi\) | |||||||
\(692\) | −10.7315 | + | 18.5875i | −0.407950 | + | 0.706591i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.11884 | 0.232268 | ||||||||
\(695\) | −7.10319 | − | 12.3031i | −0.269439 | − | 0.466683i | ||||
\(696\) | −1.41556 | − | 2.45182i | −0.0536566 | − | 0.0929360i | ||||
\(697\) | −1.91366 | −0.0724850 | ||||||||
\(698\) | 3.04352 | + | 5.27153i | 0.115199 | + | 0.199531i | ||||
\(699\) | −11.5733 | + | 20.0456i | −0.437744 | + | 0.758195i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.5588 | −0.776495 | −0.388248 | − | 0.921555i | \(-0.626919\pi\) | ||||
−0.388248 | + | 0.921555i | \(0.626919\pi\) | |||||||
\(702\) | −0.0912693 | + | 5.18551i | −0.00344474 | + | 0.195714i | ||||
\(703\) | 50.6467 | 1.91018 | ||||||||
\(704\) | 12.4811 | − | 21.6178i | 0.470397 | − | 0.814752i | ||||
\(705\) | 1.92751 | − | 3.33854i | 0.0725940 | − | 0.125737i | ||||
\(706\) | 3.65513 | + | 6.33088i | 0.137563 | + | 0.238266i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 9.88062 | + | 17.1137i | 0.371336 | + | 0.643174i | ||||
\(709\) | −20.4544 | − | 35.4281i | −0.768183 | − | 1.33053i | −0.938547 | − | 0.345151i | \(-0.887828\pi\) |
0.170364 | − | 0.985381i | \(-0.445506\pi\) | |||||||
\(710\) | −8.45961 | −0.317484 | ||||||||
\(711\) | 5.24388 | + | 9.08267i | 0.196661 | + | 0.340627i | ||||
\(712\) | 4.03543 | − | 6.98956i | 0.151234 | − | 0.261945i | ||||
\(713\) | 10.1602 | − | 17.5980i | 0.380503 | − | 0.659051i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.641405 | + | 36.4418i | −0.0239872 | + | 1.36284i | ||||
\(716\) | 24.3780 | 0.911048 | ||||||||
\(717\) | −9.45989 | + | 16.3850i | −0.353286 | + | 0.611910i | ||||
\(718\) | −1.93401 | + | 3.34981i | −0.0721767 | + | 0.125014i | ||||
\(719\) | −0.599734 | − | 1.03877i | −0.0223663 | − | 0.0387396i | 0.854626 | − | 0.519245i | \(-0.173787\pi\) |
−0.876992 | + | 0.480505i | \(0.840453\pi\) | |||||||
\(720\) | −15.5047 | −0.577826 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 4.98433 | + | 8.63311i | 0.185497 | + | 0.321291i | ||||
\(723\) | 18.7462 | 0.697179 | ||||||||
\(724\) | −14.3796 | − | 24.9063i | −0.534415 | − | 0.925634i | ||||
\(725\) | −1.83739 | + | 3.18246i | −0.0682390 | + | 0.118193i | ||||
\(726\) | 0.700425 | − | 1.21317i | 0.0259952 | − | 0.0450250i | ||||
\(727\) | 2.06230 | 0.0764865 | 0.0382433 | − | 0.999268i | \(-0.487824\pi\) | ||||
0.0382433 | + | 0.999268i | \(0.487824\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.1764 | 0.747273 | ||||||||
\(730\) | −0.263961 | + | 0.457194i | −0.00976964 | + | 0.0169215i | ||||
\(731\) | −0.883025 | + | 1.52944i | −0.0326599 | + | 0.0565685i | ||||
\(732\) | −10.4082 | − | 18.0275i | −0.384697 | − | 0.666315i | ||||
\(733\) | −30.0621 | −1.11037 | −0.555184 | − | 0.831728i | \(-0.687352\pi\) | ||||
−0.555184 | + | 0.831728i | \(0.687352\pi\) | |||||||
\(734\) | 1.52720 | + | 2.64520i | 0.0563702 | + | 0.0976360i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24.3801 | 0.898662 | ||||||||
\(737\) | 2.66861 | + | 4.62216i | 0.0982993 | + | 0.170259i | ||||
\(738\) | −0.553401 | + | 0.958519i | −0.0203710 | + | 0.0352836i | ||||
\(739\) | −22.1274 | + | 38.3257i | −0.813969 | + | 1.40984i | 0.0960970 | + | 0.995372i | \(0.469364\pi\) |
−0.910066 | + | 0.414464i | \(0.863969\pi\) | |||||||
\(740\) | −33.3759 | −1.22692 | ||||||||
\(741\) | 27.0186 | − | 14.9715i | 0.992553 | − | 0.549992i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.31326 | − | 7.47078i | 0.158238 | − | 0.274076i | −0.775995 | − | 0.630739i | \(-0.782752\pi\) |
0.934233 | + | 0.356662i | \(0.116085\pi\) | |||||||
\(744\) | −1.53753 | + | 2.66308i | −0.0563686 | + | 0.0976334i | ||||
\(745\) | −23.6515 | − | 40.9656i | −0.866524 | − | 1.50086i | ||||
\(746\) | 8.30194 | 0.303955 | ||||||||
\(747\) | 0.908511 | + | 1.57359i | 0.0332407 | + | 0.0575746i | ||||
\(748\) | −2.98665 | − | 5.17302i | −0.109203 | − | 0.189144i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.34936 | − | 2.33715i | −0.0492715 | − | 0.0853408i | ||||
\(751\) | −2.86105 | + | 4.95549i | −0.104401 | + | 0.180828i | −0.913493 | − | 0.406853i | \(-0.866626\pi\) |
0.809092 | + | 0.587682i | \(0.199959\pi\) | |||||||
\(752\) | 2.35256 | − | 4.07476i | 0.0857891 | − | 0.148591i | ||||
\(753\) | 23.3525 | 0.851012 | ||||||||
\(754\) | 1.94861 | + | 1.17123i | 0.0709641 | + | 0.0426536i | ||||
\(755\) | 4.11765 | 0.149857 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.3611 | − | 30.0703i | 0.631000 | − | 1.09292i | −0.356347 | − | 0.934354i | \(-0.615978\pi\) |
0.987348 | − | 0.158571i | \(-0.0506887\pi\) | |||||||
\(758\) | 1.41927 | + | 2.45824i | 0.0515501 | + | 0.0892873i | ||||
\(759\) | −35.8803 | −1.30237 | ||||||||
\(760\) | −10.1115 | − | 17.5137i | −0.366783 | − | 0.635287i | ||||
\(761\) | −26.5867 | − | 46.0496i | −0.963768 | − | 1.66930i | −0.712888 | − | 0.701278i | \(-0.752613\pi\) |
−0.250880 | − | 0.968018i | \(-0.580720\pi\) | |||||||
\(762\) | −0.547981 | −0.0198513 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −13.6226 | + | 23.5951i | −0.492849 | + | 0.853640i | ||||
\(765\) | −1.70304 | + | 2.94976i | −0.0615736 | + | 0.106649i | ||||
\(766\) | 8.24529 | 0.297915 | ||||||||
\(767\) | −27.7097 | − | 16.6552i | −1.00054 | − | 0.601384i | ||||
\(768\) | 12.0629 | 0.435282 | ||||||||
\(769\) | 2.45578 | − | 4.25354i | 0.0885578 | − | 0.153387i | −0.818344 | − | 0.574729i | \(-0.805108\pi\) |
0.906902 | + | 0.421342i | \(0.138441\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.87414 | + | 13.6384i | 0.283580 | + | 0.491175i | ||||
\(772\) | −7.50909 | −0.270258 | ||||||||
\(773\) | −11.4903 | − | 19.9018i | −0.413279 | − | 0.715819i | 0.581967 | − | 0.813212i | \(-0.302283\pi\) |
−0.995246 | + | 0.0973926i | \(0.968950\pi\) | |||||||
\(774\) | 0.510715 | + | 0.884585i | 0.0183573 | + | 0.0317957i | ||||
\(775\) | 3.99142 | 0.143376 | ||||||||
\(776\) | −1.24913 | − | 2.16356i | −0.0448413 | − | 0.0776674i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.19589 | + | 3.80339i | −0.0787264 | + | 0.136358i | ||||
\(779\) | 18.2695 | 0.654573 | ||||||||
\(780\) | −17.8051 | + | 9.86614i | −0.637525 | + | 0.353265i | ||||
\(781\) | 48.5996 | 1.73903 | ||||||||
\(782\) | 0.837302 | − | 1.45025i | 0.0299419 | − | 0.0518608i | ||||
\(783\) | 6.30821 | − | 10.9261i | 0.225437 | − | 0.390469i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.21648 | 0.150493 | ||||||||
\(786\) | 0.979309 | + | 1.69621i | 0.0349308 | + | 0.0605019i | ||||
\(787\) | −1.59387 | − | 2.76067i | −0.0568154 | − | 0.0984071i | 0.836219 | − | 0.548396i | \(-0.184761\pi\) |
−0.893034 | + | 0.449989i | \(0.851428\pi\) | |||||||
\(788\) | 22.5760 | 0.804237 | ||||||||
\(789\) | −14.8119 | − | 25.6549i | −0.527316 | − | 0.913339i | ||||
\(790\) | 2.12684 | − | 3.68380i | 0.0756696 | − | 0.131064i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −7.03836 | −0.250097 | ||||||||
\(793\) | 29.1892 | + | 17.5445i | 1.03654 | + | 0.623022i | ||||
\(794\) | −4.25854 | −0.151130 | ||||||||
\(795\) | −13.5857 | + | 23.5312i | −0.481837 | + | 0.834566i | ||||
\(796\) | −3.37114 | + | 5.83899i | −0.119487 | + | 0.206958i | ||||
\(797\) | 27.3255 | + | 47.3291i | 0.967918 | + | 1.67648i | 0.701562 | + | 0.712608i | \(0.252486\pi\) |
0.266355 | + | 0.963875i | \(0.414180\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.516813 | − | 0.895146i | −0.0182835 | − | 0.0316680i | ||||
\(800\) | 2.39442 | + | 4.14725i | 0.0846554 | + | 0.146628i | ||||
\(801\) | 12.9775 | 0.458538 | ||||||||
\(802\) | 0.889604 | + | 1.54084i | 0.0314130 | + | 0.0544089i | ||||
\(803\) | 1.51643 | − | 2.62653i | 0.0535136 | − | 0.0926883i | ||||
\(804\) | −1.49042 | + | 2.58148i | −0.0525630 | + | 0.0910418i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.0434569 | − | 2.46902i | 0.00153070 | − | 0.0869677i | ||||
\(807\) | 34.3664 | 1.20975 | ||||||||
\(808\) | −0.419884 | + | 0.727260i | −0.0147715 | + | 0.0255849i | ||||
\(809\) | 10.1498 | − | 17.5799i | 0.356847 | − | 0.618077i | −0.630585 | − | 0.776120i | \(-0.717185\pi\) |
0.987432 | + | 0.158043i | \(0.0505185\pi\) | |||||||
\(810\) | −0.361076 | − | 0.625401i | −0.0126869 | − | 0.0219744i | ||||
\(811\) | −2.43587 | −0.0855350 | −0.0427675 | − | 0.999085i | \(-0.513617\pi\) | ||||
−0.0427675 | + | 0.999085i | \(0.513617\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.25855 | + | 14.3042i | 0.289640 | + | 0.501671i | ||||
\(814\) | −7.14922 | −0.250580 | ||||||||
\(815\) | 8.38742 | + | 14.5274i | 0.293799 | + | 0.508874i | ||||
\(816\) | 1.60353 | − | 2.77740i | 0.0561348 | − | 0.0972284i | ||||
\(817\) | 8.43015 | − | 14.6015i | 0.294934 | − | 0.510840i | ||||
\(818\) | 1.57452 | 0.0550519 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.0395 | −0.420438 | ||||||||
\(821\) | −22.6762 | + | 39.2763i | −0.791405 | + | 1.37075i | 0.133692 | + | 0.991023i | \(0.457317\pi\) |
−0.925097 | + | 0.379731i | \(0.876017\pi\) | |||||||
\(822\) | 1.53795 | − | 2.66380i | 0.0536421 | − | 0.0929108i | ||||
\(823\) | 1.37871 | + | 2.38800i | 0.0480588 | + | 0.0832403i | 0.889054 | − | 0.457802i | \(-0.151363\pi\) |
−0.840995 | + | 0.541042i | \(0.818030\pi\) | |||||||
\(824\) | −2.28147 | −0.0794789 | ||||||||
\(825\) | −3.52388 | − | 6.10354i | −0.122686 | − | 0.212498i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.64504 | −0.300618 | −0.150309 | − | 0.988639i | \(-0.548027\pi\) | ||||
−0.150309 | + | 0.988639i | \(0.548027\pi\) | |||||||
\(828\) | 12.9881 | + | 22.4960i | 0.451366 | + | 0.781789i | ||||
\(829\) | −14.7871 | + | 25.6119i | −0.513576 | + | 0.889540i | 0.486300 | + | 0.873792i | \(0.338346\pi\) |
−0.999876 | + | 0.0157478i | \(0.994987\pi\) | |||||||
\(830\) | 0.368479 | − | 0.638224i | 0.0127901 | − | 0.0221531i | ||||
\(831\) | −17.5172 | −0.607663 | ||||||||
\(832\) | −19.9503 | + | 11.0548i | −0.691653 | + | 0.383258i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.849774 | − | 1.47185i | 0.0294253 | − | 0.0509660i | ||||
\(835\) | 12.2308 | − | 21.1844i | 0.423266 | − | 0.733117i | ||||
\(836\) | 28.5132 | + | 49.3863i | 0.986150 | + | 1.70806i | ||||
\(837\) | −13.7035 | −0.473663 | ||||||||
\(838\) | 4.04096 | + | 6.99914i | 0.139593 | + | 0.241781i | ||||
\(839\) | 12.6236 | + | 21.8648i | 0.435817 | + | 0.754857i | 0.997362 | − | 0.0725895i | \(-0.0231263\pi\) |
−0.561545 | + | 0.827446i | \(0.689793\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.7347 | + | 20.3251i | 0.404644 | + | 0.700865i | ||||
\(842\) | 5.37028 | − | 9.30159i | 0.185072 | − | 0.320554i | ||||
\(843\) | −3.02485 | + | 5.23920i | −0.104182 | + | 0.180448i | ||||
\(844\) | −36.6440 | −1.26134 | ||||||||
\(845\) | 17.6560 | − | 28.2372i | 0.607386 | − | 0.971391i | ||||
\(846\) | −0.597818 | −0.0205534 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −16.5817 | + | 28.7204i | −0.569418 | + | 0.986261i | ||||
\(849\) | −17.5935 | − | 30.4728i | −0.603807 | − | 1.04582i | ||||
\(850\) | 0.328933 | 0.0112823 | ||||||||
\(851\) | 26.8772 | + | 46.5526i | 0.921338 | + | 1.59580i | ||||
\(852\) | 13.5715 | + | 23.5064i | 0.464950 | + | 0.805318i | ||||
\(853\) | 35.1368 | 1.20306 | 0.601531 | − | 0.798850i | \(-0.294558\pi\) | ||||
0.601531 | + | 0.798850i | \(0.294558\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.2588 | − | 28.1610i | 0.556039 | − | 0.963087i | ||||
\(856\) | 6.06986 | − | 10.5133i | 0.207463 | − | 0.359337i | ||||
\(857\) | 1.34269 | 0.0458654 | 0.0229327 | − | 0.999737i | \(-0.492700\pi\) | ||||
0.0229327 | + | 0.999737i | \(0.492700\pi\) | |||||||
\(858\) | −3.81391 | + | 2.11336i | −0.130205 | + | 0.0721489i | ||||
\(859\) | −4.76772 | −0.162673 | −0.0813363 | − | 0.996687i | \(-0.525919\pi\) | ||||
−0.0813363 | + | 0.996687i | \(0.525919\pi\) | |||||||
\(860\) | −5.55542 | + | 9.62228i | −0.189438 | + | 0.328117i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.524972 | − | 0.909278i | −0.0178806 | − | 0.0309701i | ||||
\(863\) | −26.6105 | −0.905830 | −0.452915 | − | 0.891554i | \(-0.649616\pi\) | ||||
−0.452915 | + | 0.891554i | \(0.649616\pi\) | |||||||
\(864\) | −8.22062 | − | 14.2385i | −0.279671 | − | 0.484405i | ||||
\(865\) | 14.2583 | + | 24.6960i | 0.484795 | + | 0.839690i | ||||
\(866\) | −10.9375 | −0.371672 | ||||||||
\(867\) | 9.36331 | + | 16.2177i | 0.317995 | + | 0.550783i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.2185 | + | 21.1630i | −0.414484 | + | 0.717907i | ||||
\(870\) | −1.84634 | −0.0625968 | ||||||||
\(871\) | 0.0858212 | − | 4.87598i | 0.00290794 | − | 0.165216i | ||||
\(872\) | 8.50819 | 0.288124 | ||||||||
\(873\) | 2.00854 | − | 3.47890i | 0.0679788 | − | 0.117743i | ||||
\(874\) | −7.99364 | + | 13.8454i | −0.270389 | + | 0.468328i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.69385 | 0.0572300 | ||||||||
\(877\) | −4.01848 | − | 6.96022i | −0.135695 | − | 0.235030i | 0.790168 | − | 0.612890i | \(-0.209993\pi\) |
−0.925863 | + | 0.377860i | \(0.876660\pi\) | |||||||
\(878\) | 3.42694 | + | 5.93564i | 0.115654 | + | 0.200318i | ||||
\(879\) | 20.0224 | 0.675339 | ||||||||
\(880\) | −18.0633 | − | 31.2866i | −0.608915 | − | 1.05467i | ||||
\(881\) | −27.3349 | + | 47.3454i | −0.920935 | + | 1.59511i | −0.122964 | + | 0.992411i | \(0.539240\pi\) |
−0.797971 | + | 0.602695i | \(0.794093\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.45085 | −0.284394 | −0.142197 | − | 0.989838i | \(-0.545417\pi\) | ||||
−0.142197 | + | 0.989838i | \(0.545417\pi\) | |||||||
\(884\) | −0.0960493 | + | 5.45709i | −0.00323049 | + | 0.183542i | ||||
\(885\) | 26.2555 | 0.882569 | ||||||||
\(886\) | −3.68088 | + | 6.37547i | −0.123662 | + | 0.214188i | ||||
\(887\) | −5.17784 | + | 8.96829i | −0.173855 | + | 0.301126i | −0.939764 | − | 0.341823i | \(-0.888956\pi\) |
0.765909 | + | 0.642948i | \(0.222289\pi\) | |||||||
\(888\) | −4.06729 | − | 7.04475i | −0.136489 | − | 0.236406i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.63174 | − | 4.55831i | −0.0882162 | − | 0.152795i | ||||
\(891\) | 2.07434 | + | 3.59286i | 0.0694930 | + | 0.120365i | ||||
\(892\) | −23.0722 | −0.772513 | ||||||||
\(893\) | 4.93396 | + | 8.54587i | 0.165109 | + | 0.285977i | ||||
\(894\) | 2.82949 | − | 4.90082i | 0.0946323 | − | 0.163908i | ||||
\(895\) | 16.1947 | − | 28.0501i | 0.541330 | − | 0.937611i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.0995 | + | 16.8895i | 0.938215 | + | 0.563923i | ||||
\(898\) | 3.96922 | 0.132455 | ||||||||
\(899\) | −3.00359 | + | 5.20237i | −0.100175 | + | 0.173509i | ||||
\(900\) | −2.55117 | + | 4.41875i | −0.0850389 | + | 0.147292i | ||||
\(901\) | 3.64268 | + | 6.30931i | 0.121355 | + | 0.210194i | ||||
\(902\) | −2.57890 | −0.0858680 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.23468 | − | 7.33467i | −0.140843 | − | 0.243948i | ||||
\(905\) | −38.2106 | −1.27016 | ||||||||
\(906\) | 0.246303 | + | 0.426609i | 0.00818287 | + | 0.0141731i | ||||
\(907\) | −9.24019 | + | 16.0045i | −0.306815 | + | 0.531420i | −0.977664 | − | 0.210175i | \(-0.932597\pi\) |
0.670849 | + | 0.741594i | \(0.265930\pi\) | |||||||
\(908\) | −14.8312 | + | 25.6884i | −0.492190 | + | 0.852498i | ||||
\(909\) | −1.35030 | −0.0447867 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.6282 | −0.882230 | −0.441115 | − | 0.897451i | \(-0.645417\pi\) | ||||
−0.441115 | + | 0.897451i | \(0.645417\pi\) | |||||||
\(912\) | −15.3088 | + | 26.5155i | −0.506924 | + | 0.878017i | ||||
\(913\) | −2.11687 | + | 3.66653i | −0.0700582 | + | 0.121344i | ||||
\(914\) | −0.0874022 | − | 0.151385i | −0.00289101 | − | 0.00500737i | ||||
\(915\) | −27.6574 | −0.914324 | ||||||||
\(916\) | −8.35033 | − | 14.4632i | −0.275903 | − | 0.477877i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.12931 | −0.0372727 | ||||||||
\(919\) | 5.57467 | + | 9.65561i | 0.183891 | + | 0.318509i | 0.943202 | − | 0.332219i | \(-0.107797\pi\) |
−0.759311 | + | 0.650728i | \(0.774464\pi\) | |||||||
\(920\) | 10.7319 | − | 18.5883i | 0.353822 | − | 0.612837i | ||||
\(921\) | −4.93536 | + | 8.54829i | −0.162626 | + | 0.281676i | ||||
\(922\) | 3.35035 | 0.110338 | ||||||||
\(923\) | −38.0605 | − | 22.8766i | −1.25278 | − | 0.752993i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.27933 | + | 9.14406i | −0.173583 | + | 0.300655i | ||||
\(926\) | −0.0414927 | + | 0.0718675i | −0.00136354 | + | 0.00236171i | ||||
\(927\) | −1.83424 | − | 3.17700i | −0.0602445 | − | 0.104347i | ||||
\(928\) | −7.20730 | −0.236591 | ||||||||
\(929\) | 3.87255 | + | 6.70745i | 0.127054 | + | 0.220064i | 0.922534 | − | 0.385916i | \(-0.126114\pi\) |
−0.795480 | + | 0.605980i | \(0.792781\pi\) | |||||||
\(930\) | 1.00272 | + | 1.73676i | 0.0328804 | + | 0.0569505i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 19.5227 | + | 33.8144i | 0.639489 | + | 1.10763i | ||||
\(933\) | −9.38559 | + | 16.2563i | −0.307270 | + | 0.532208i | ||||
\(934\) | −3.28149 | + | 5.68371i | −0.107374 | + | 0.185977i | ||||
\(935\) | −7.93633 | −0.259546 | ||||||||
\(936\) | 5.51205 | + | 3.31307i | 0.180167 | + | 0.108291i | ||||
\(937\) | −36.4239 | −1.18992 | −0.594959 | − | 0.803756i | \(-0.702832\pi\) | ||||
−0.594959 | + | 0.803756i | \(0.702832\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.74143 | − | 9.94445i | 0.187364 | − | 0.324525i | ||||
\(940\) | −3.25145 | − | 5.63168i | −0.106051 | − | 0.183685i | ||||
\(941\) | 19.7893 | 0.645114 | 0.322557 | − | 0.946550i | \(-0.395458\pi\) | ||||
0.322557 | + | 0.946550i | \(0.395458\pi\) | |||||||
\(942\) | 0.252214 | + | 0.436848i | 0.00821759 | + | 0.0142333i | ||||
\(943\) | 9.69526 | + | 16.7927i | 0.315721 | + | 0.546845i | ||||
\(944\) | 32.0454 | 1.04299 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.18999 | + | 2.06112i | −0.0386899 | + | 0.0670129i | ||||
\(947\) | −4.97398 | + | 8.61519i | −0.161633 | + | 0.279956i | −0.935454 | − | 0.353448i | \(-0.885009\pi\) |
0.773822 | + | 0.633403i | \(0.218343\pi\) | |||||||
\(948\) | −13.6481 | −0.443269 | ||||||||
\(949\) | −2.42393 | + | 1.34315i | −0.0786842 | + | 0.0436004i | ||||
\(950\) | −3.14029 | −0.101884 | ||||||||
\(951\) | −5.79790 | + | 10.0423i | −0.188010 | + | 0.325643i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.0105567 | − | 0.0182847i | −0.000341965 | − | 0.000592300i | 0.865854 | − | 0.500296i | \(-0.166776\pi\) |
−0.866196 | + | 0.499704i | \(0.833442\pi\) | |||||||
\(954\) | 4.21364 | 0.136422 | ||||||||
\(955\) | 18.0995 | + | 31.3493i | 0.585686 | + | 1.01444i | ||||
\(956\) | 15.9576 | + | 27.6394i | 0.516106 | + | 0.893922i | ||||
\(957\) | 10.6070 | 0.342877 | ||||||||
\(958\) | −1.09107 | − | 1.88979i | −0.0352508 | − | 0.0610562i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 9.26150 | − | 16.0414i | 0.298914 | − | 0.517733i | ||||
\(961\) | −24.4752 | −0.789523 | ||||||||
\(962\) | 5.59888 | + | 3.36525i | 0.180515 | + | 0.108500i | ||||
\(963\) | 19.5200 | 0.629024 | ||||||||
\(964\) | 15.8112 | − | 27.3858i | 0.509245 | − | 0.882039i | ||||
\(965\) | −4.98842 | + | 8.64020i | −0.160583 | + | 0.278138i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.8102 | −0.637053 | −0.318526 | − | 0.947914i | \(-0.603188\pi\) | ||||
−0.318526 | + | 0.947914i | \(0.603188\pi\) | |||||||
\(968\) | −2.40711 | − | 4.16923i | −0.0773674 | − | 0.134004i | ||||
\(969\) | 3.36304 | + | 5.82495i | 0.108036 | + | 0.187124i | ||||
\(970\) | −1.62927 | −0.0523127 | ||||||||
\(971\) | −1.80887 | − | 3.13305i | −0.0580493 | − | 0.100544i | 0.835540 | − | 0.549429i | \(-0.185155\pi\) |
−0.893590 | + | 0.448885i | \(0.851821\pi\) | |||||||
\(972\) | 14.3572 | − | 24.8674i | 0.460508 | − | 0.797622i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.23595 | −0.0396024 | ||||||||
\(975\) | −0.113327 | + | 6.43871i | −0.00362936 | + | 0.206204i | ||||
\(976\) | −33.7564 | −1.08052 | ||||||||
\(977\) | −1.08085 | + | 1.87208i | −0.0345793 | + | 0.0598931i | −0.882797 | − | 0.469754i | \(-0.844342\pi\) |
0.848218 | + | 0.529648i | \(0.177676\pi\) | |||||||
\(978\) | −1.00341 | + | 1.73796i | −0.0320855 | + | 0.0555737i | ||||
\(979\) | 15.1191 | + | 26.1870i | 0.483208 | + | 0.836941i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.84036 | + | 11.8479i | 0.218396 | + | 0.378273i | ||||
\(982\) | 1.74535 | + | 3.02304i | 0.0556965 | + | 0.0964692i | ||||
\(983\) | 30.1091 | 0.960331 | 0.480165 | − | 0.877178i | \(-0.340577\pi\) | ||||
0.480165 | + | 0.877178i | \(0.340577\pi\) | |||||||
\(984\) | −1.46717 | − | 2.54121i | −0.0467717 | − | 0.0810109i | ||||
\(985\) | 14.9977 | − | 25.9767i | 0.477865 | − | 0.827687i | ||||
\(986\) | −0.247525 | + | 0.428727i | −0.00788281 | + | 0.0136534i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.916973 | − | 52.0983i | 0.0291728 | − | 1.65747i | ||||
\(989\) | 17.8948 | 0.569023 | ||||||||
\(990\) | −2.29507 | + | 3.97517i | −0.0729420 | + | 0.126339i | ||||
\(991\) | 13.5730 | − | 23.5092i | 0.431161 | − | 0.746793i | −0.565812 | − | 0.824534i | \(-0.691437\pi\) |
0.996974 | + | 0.0777408i | \(0.0247706\pi\) | |||||||
\(992\) | 3.91416 | + | 6.77953i | 0.124275 | + | 0.215250i | ||||
\(993\) | 2.65082 | 0.0841213 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.47902 | + | 7.75790i | 0.141995 | + | 0.245942i | ||||
\(996\) | −2.36455 | −0.0749236 | ||||||||
\(997\) | 25.4005 | + | 43.9949i | 0.804441 | + | 1.39333i | 0.916668 | + | 0.399650i | \(0.130868\pi\) |
−0.112227 | + | 0.993683i | \(0.535798\pi\) | |||||||
\(998\) | −4.33300 | + | 7.50497i | −0.137159 | + | 0.237566i | ||||
\(999\) | 18.1252 | − | 31.3938i | 0.573456 | − | 0.993256i |
(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 | 637.2.f.j.295.3 | 12 | ||
7.2 | even | 3 | 637.2.h.l.165.4 | 12 | |||
7.3 | odd | 6 | 91.2.g.b.9.3 | ✓ | 12 | ||
7.4 | even | 3 | 637.2.g.l.373.3 | 12 | |||
7.5 | odd | 6 | 91.2.h.b.74.4 | yes | 12 | ||
7.6 | odd | 2 | 637.2.f.k.295.3 | 12 | |||
13.3 | even | 3 | inner | 637.2.f.j.393.3 | 12 | ||
13.4 | even | 6 | 8281.2.a.cf.1.3 | 6 | |||
13.9 | even | 3 | 8281.2.a.ca.1.4 | 6 | |||
21.5 | even | 6 | 819.2.s.d.802.3 | 12 | |||
21.17 | even | 6 | 819.2.n.d.100.4 | 12 | |||
91.3 | odd | 6 | 91.2.h.b.16.4 | yes | 12 | ||
91.16 | even | 3 | 637.2.g.l.263.3 | 12 | |||
91.17 | odd | 6 | 1183.2.e.g.170.4 | 12 | |||
91.48 | odd | 6 | 8281.2.a.bz.1.4 | 6 | |||
91.55 | odd | 6 | 637.2.f.k.393.3 | 12 | |||
91.61 | odd | 6 | 1183.2.e.h.508.3 | 12 | |||
91.68 | odd | 6 | 91.2.g.b.81.3 | yes | 12 | ||
91.69 | odd | 6 | 8281.2.a.ce.1.3 | 6 | |||
91.81 | even | 3 | 637.2.h.l.471.4 | 12 | |||
91.82 | odd | 6 | 1183.2.e.g.508.4 | 12 | |||
91.87 | odd | 6 | 1183.2.e.h.170.3 | 12 | |||
273.68 | even | 6 | 819.2.n.d.172.4 | 12 | |||
273.185 | even | 6 | 819.2.s.d.289.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.b.9.3 | ✓ | 12 | 7.3 | odd | 6 | ||
91.2.g.b.81.3 | yes | 12 | 91.68 | odd | 6 | ||
91.2.h.b.16.4 | yes | 12 | 91.3 | odd | 6 | ||
91.2.h.b.74.4 | yes | 12 | 7.5 | odd | 6 | ||
637.2.f.j.295.3 | 12 | 1.1 | even | 1 | trivial | ||
637.2.f.j.393.3 | 12 | 13.3 | even | 3 | inner | ||
637.2.f.k.295.3 | 12 | 7.6 | odd | 2 | |||
637.2.f.k.393.3 | 12 | 91.55 | odd | 6 | |||
637.2.g.l.263.3 | 12 | 91.16 | even | 3 | |||
637.2.g.l.373.3 | 12 | 7.4 | even | 3 | |||
637.2.h.l.165.4 | 12 | 7.2 | even | 3 | |||
637.2.h.l.471.4 | 12 | 91.81 | even | 3 | |||
819.2.n.d.100.4 | 12 | 21.17 | even | 6 | |||
819.2.n.d.172.4 | 12 | 273.68 | even | 6 | |||
819.2.s.d.289.3 | 12 | 273.185 | even | 6 | |||
819.2.s.d.802.3 | 12 | 21.5 | even | 6 | |||
1183.2.e.g.170.4 | 12 | 91.17 | odd | 6 | |||
1183.2.e.g.508.4 | 12 | 91.82 | odd | 6 | |||
1183.2.e.h.170.3 | 12 | 91.87 | odd | 6 | |||
1183.2.e.h.508.3 | 12 | 91.61 | odd | 6 | |||
8281.2.a.bz.1.4 | 6 | 91.48 | odd | 6 | |||
8281.2.a.ca.1.4 | 6 | 13.9 | even | 3 | |||
8281.2.a.ce.1.3 | 6 | 91.69 | odd | 6 | |||
8281.2.a.cf.1.3 | 6 | 13.4 | even | 6 |