Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [196,2,Mod(19,196)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(196, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("196.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.f (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.56506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 4x^{14} + 6x^{12} + 8x^{10} + 20x^{8} + 32x^{6} + 96x^{4} + 256x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.6 | ||
Root | \(1.33546 - 0.465333i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 196.31 |
Dual form | 196.2.f.d.19.6 |
$q$-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 \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).
\(n\) | \(99\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.10799 | − | 0.878843i | 0.783465 | − | 0.621436i | ||||
\(3\) | 1.07072 | − | 1.85455i | 0.618182 | − | 1.07072i | −0.371635 | − | 0.928379i | \(-0.621203\pi\) |
0.989817 | − | 0.142344i | \(-0.0454638\pi\) | |||||||
\(4\) | 0.455270 | − | 1.94749i | 0.227635 | − | 0.973746i | ||||
\(5\) | −2.26303 | + | 1.30656i | −1.01206 | + | 0.584313i | −0.911794 | − | 0.410648i | \(-0.865303\pi\) |
−0.100265 | + | 0.994961i | \(0.531969\pi\) | |||||||
\(6\) | −0.443508 | − | 2.99581i | −0.181061 | − | 1.22303i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.20711 | − | 2.55791i | −0.426777 | − | 0.904357i | ||||
\(9\) | −0.792893 | − | 1.37333i | −0.264298 | − | 0.457777i | ||||
\(10\) | −1.35915 | + | 3.43651i | −0.429800 | + | 1.08672i | ||||
\(11\) | 3.42675 | + | 1.97844i | 1.03321 | + | 0.596521i | 0.917901 | − | 0.396809i | \(-0.129882\pi\) |
0.115304 | + | 0.993330i | \(0.463216\pi\) | |||||||
\(12\) | −3.12425 | − | 2.92954i | −0.901892 | − | 0.845687i | ||||
\(13\) | − | 1.08239i | − | 0.300202i | −0.988671 | − | 0.150101i | \(-0.952040\pi\) | ||
0.988671 | − | 0.150101i | \(-0.0479598\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.59587i | 1.44485i | ||||||||
\(16\) | −3.58546 | − | 1.77327i | −0.896364 | − | 0.443318i | ||||
\(17\) | 0.274552 | + | 0.158513i | 0.0665886 | + | 0.0384450i | 0.532925 | − | 0.846163i | \(-0.321093\pi\) |
−0.466336 | + | 0.884608i | \(0.654426\pi\) | |||||||
\(18\) | −2.08546 | − | 0.824805i | −0.491547 | − | 0.194408i | ||||
\(19\) | 2.58495 | + | 4.47727i | 0.593029 | + | 1.02716i | 0.993822 | + | 0.110987i | \(0.0354013\pi\) |
−0.400793 | + | 0.916169i | \(0.631265\pi\) | |||||||
\(20\) | 1.51423 | + | 5.00208i | 0.338592 | + | 1.11850i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.53553 | − | 0.819496i | 1.18018 | − | 0.174717i | ||||
\(23\) | −2.00735 | + | 1.15894i | −0.418561 | + | 0.241656i | −0.694461 | − | 0.719530i | \(-0.744357\pi\) |
0.275901 | + | 0.961186i | \(0.411024\pi\) | |||||||
\(24\) | −6.03623 | − | 0.500175i | −1.23214 | − | 0.102098i | ||||
\(25\) | 0.914214 | − | 1.58346i | 0.182843 | − | 0.316693i | ||||
\(26\) | −0.951253 | − | 1.19928i | −0.186556 | − | 0.235197i | ||||
\(27\) | 3.02846 | 0.582827 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.82843 | −1.26801 | −0.634004 | − | 0.773330i | \(-0.718590\pi\) | ||||
−0.634004 | + | 0.773330i | \(0.718590\pi\) | |||||||
\(30\) | 4.91789 | + | 6.20015i | 0.897879 | + | 1.13199i | ||||
\(31\) | 3.02846 | − | 5.24545i | 0.543928 | − | 0.942110i | −0.454746 | − | 0.890621i | \(-0.650270\pi\) |
0.998674 | − | 0.0514890i | \(-0.0163967\pi\) | |||||||
\(32\) | −5.53107 | + | 1.18629i | −0.977764 | + | 0.209709i | ||||
\(33\) | 7.33820 | − | 4.23671i | 1.27742 | − | 0.737517i | ||||
\(34\) | 0.443508 | − | 0.0656581i | 0.0760610 | − | 0.0112603i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.03553 | + | 0.918917i | −0.505922 | + | 0.153153i | ||||
\(37\) | 2.00000 | + | 3.46410i | 0.328798 | + | 0.569495i | 0.982274 | − | 0.187453i | \(-0.0600231\pi\) |
−0.653476 | + | 0.756948i | \(0.726690\pi\) | |||||||
\(38\) | 6.79891 | + | 2.68899i | 1.10293 | + | 0.436212i | ||||
\(39\) | −2.00735 | − | 1.15894i | −0.321433 | − | 0.185579i | ||||
\(40\) | 6.07379 | + | 4.21147i | 0.960351 | + | 0.665892i | ||||
\(41\) | 2.29610i | 0.358591i | 0.983795 | + | 0.179295i | \(0.0573818\pi\) | ||||
−0.983795 | + | 0.179295i | \(0.942618\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.23486i | − | 1.10331i | −0.834074 | − | 0.551653i | \(-0.813997\pi\) | ||
0.834074 | − | 0.551653i | \(-0.186003\pi\) | |||||||
\(44\) | 5.41309 | − | 5.77286i | 0.816054 | − | 0.870291i | ||||
\(45\) | 3.58869 | + | 2.07193i | 0.534970 | + | 0.308865i | ||||
\(46\) | −1.20559 | + | 3.04823i | −0.177754 | + | 0.449438i | ||||
\(47\) | −2.14144 | − | 3.70909i | −0.312362 | − | 0.541027i | 0.666511 | − | 0.745495i | \(-0.267787\pi\) |
−0.978873 | + | 0.204468i | \(0.934453\pi\) | |||||||
\(48\) | −7.12764 | + | 4.75071i | −1.02879 | + | 0.685706i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.378680 | − | 2.55791i | −0.0535534 | − | 0.361743i | ||||
\(51\) | 0.587938 | − | 0.339446i | 0.0823278 | − | 0.0475320i | ||||
\(52\) | −2.10795 | − | 0.492781i | −0.292320 | − | 0.0683364i | ||||
\(53\) | −5.24264 | + | 9.08052i | −0.720132 | + | 1.24731i | 0.240814 | + | 0.970571i | \(0.422585\pi\) |
−0.960947 | + | 0.276734i | \(0.910748\pi\) | |||||||
\(54\) | 3.35549 | − | 2.66154i | 0.456625 | − | 0.362190i | ||||
\(55\) | −10.3398 | −1.39422 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.0711 | 1.46640 | ||||||||
\(58\) | −7.56581 | + | 6.00111i | −0.993439 | + | 0.787985i | ||||
\(59\) | −5.61341 | + | 9.72272i | −0.730804 | + | 1.26579i | 0.225736 | + | 0.974189i | \(0.427521\pi\) |
−0.956540 | + | 0.291601i | \(0.905812\pi\) | |||||||
\(60\) | 10.8979 | + | 2.54763i | 1.40691 | + | 0.328898i | ||||
\(61\) | −4.68690 | + | 2.70598i | −0.600096 | + | 0.346465i | −0.769079 | − | 0.639154i | \(-0.779285\pi\) |
0.168984 | + | 0.985619i | \(0.445951\pi\) | |||||||
\(62\) | −1.25443 | − | 8.47343i | −0.159313 | − | 1.07613i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.08579 | + | 6.17534i | −0.635723 | + | 0.771917i | ||||
\(65\) | 1.41421 | + | 2.44949i | 0.175412 | + | 0.303822i | ||||
\(66\) | 4.40723 | − | 11.1434i | 0.542492 | − | 1.37165i | ||||
\(67\) | −2.83882 | − | 1.63899i | −0.346817 | − | 0.200235i | 0.316466 | − | 0.948604i | \(-0.397504\pi\) |
−0.663282 | + | 0.748369i | \(0.730837\pi\) | |||||||
\(68\) | 0.433698 | − | 0.462522i | 0.0525936 | − | 0.0560890i | ||||
\(69\) | 4.96362i | 0.597550i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | −2.55575 | + | 3.68591i | −0.301198 | + | 0.434388i | ||||
\(73\) | −12.1388 | − | 7.00835i | −1.42074 | − | 0.820266i | −0.424380 | − | 0.905484i | \(-0.639508\pi\) |
−0.996362 | + | 0.0852188i | \(0.972841\pi\) | |||||||
\(74\) | 5.26038 | + | 2.08049i | 0.611506 | + | 0.241852i | ||||
\(75\) | −1.95774 | − | 3.39090i | −0.226060 | − | 0.391548i | ||||
\(76\) | 9.89630 | − | 2.99581i | 1.13518 | − | 0.343643i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.24264 | + | 0.480049i | −0.367157 | + | 0.0543549i | ||||
\(79\) | 6.85351 | − | 3.95687i | 0.771080 | − | 0.445183i | −0.0621799 | − | 0.998065i | \(-0.519805\pi\) |
0.833260 | + | 0.552882i | \(0.186472\pi\) | |||||||
\(80\) | 10.4309 | − | 0.671654i | 1.16621 | − | 0.0750932i | ||||
\(81\) | 5.62132 | − | 9.73641i | 0.624591 | − | 1.08182i | ||||
\(82\) | 2.01791 | + | 2.54405i | 0.222841 | + | 0.280943i | ||||
\(83\) | 9.45280 | 1.03758 | 0.518790 | − | 0.854902i | \(-0.326383\pi\) | ||||
0.518790 | + | 0.854902i | \(0.326383\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.828427 | −0.0898555 | ||||||||
\(86\) | −6.35830 | − | 8.01613i | −0.685633 | − | 0.864401i | ||||
\(87\) | −7.31135 | + | 12.6636i | −0.783859 | + | 1.35768i | ||||
\(88\) | 0.924203 | − | 11.1535i | 0.0985203 | − | 1.18897i | ||||
\(89\) | −5.18889 | + | 2.99581i | −0.550022 | + | 0.317555i | −0.749131 | − | 0.662422i | \(-0.769529\pi\) |
0.199109 | + | 0.979977i | \(0.436195\pi\) | |||||||
\(90\) | 5.79712 | − | 0.858221i | 0.611070 | − | 0.0904645i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.34315 | + | 4.43692i | 0.140033 | + | 0.462581i | ||||
\(93\) | −6.48528 | − | 11.2328i | −0.672492 | − | 1.16479i | ||||
\(94\) | −5.63240 | − | 2.22763i | −0.580938 | − | 0.229763i | ||||
\(95\) | −11.6997 | − | 6.75481i | −1.20036 | − | 0.693029i | ||||
\(96\) | −3.72221 | + | 11.5278i | −0.379896 | + | 1.17655i | ||||
\(97\) | − | 9.23880i | − | 0.938058i | −0.883183 | − | 0.469029i | \(-0.844604\pi\) | ||
0.883183 | − | 0.469029i | \(-0.155396\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 6.27476i | − | 0.630637i | ||||||
\(100\) | −2.66757 | − | 2.50133i | −0.266757 | − | 0.250133i | ||||
\(101\) | 13.1899 | + | 7.61521i | 1.31245 | + | 0.757741i | 0.982501 | − | 0.186258i | \(-0.0596362\pi\) |
0.329946 | + | 0.944000i | \(0.392970\pi\) | |||||||
\(102\) | 0.353108 | − | 0.892807i | 0.0349629 | − | 0.0884011i | ||||
\(103\) | −6.05692 | − | 10.4909i | −0.596806 | − | 1.03370i | −0.993289 | − | 0.115657i | \(-0.963103\pi\) |
0.396483 | − | 0.918042i | \(-0.370231\pi\) | |||||||
\(104\) | −2.76866 | + | 1.30656i | −0.271489 | + | 0.128119i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.17157 | + | 14.6686i | 0.210922 | + | 1.42474i | ||||
\(107\) | −2.00735 | + | 1.15894i | −0.194057 | + | 0.112039i | −0.593881 | − | 0.804553i | \(-0.702405\pi\) |
0.399823 | + | 0.916592i | \(0.369072\pi\) | |||||||
\(108\) | 1.37877 | − | 5.89791i | 0.132672 | − | 0.567526i | ||||
\(109\) | 2.82843 | − | 4.89898i | 0.270914 | − | 0.469237i | −0.698182 | − | 0.715920i | \(-0.746007\pi\) |
0.969096 | + | 0.246683i | \(0.0793407\pi\) | |||||||
\(110\) | −11.4564 | + | 9.08707i | −1.09232 | + | 0.866418i | ||||
\(111\) | 8.56578 | 0.813028 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.24264 | −0.399114 | −0.199557 | − | 0.979886i | \(-0.563950\pi\) | ||||
−0.199557 | + | 0.979886i | \(0.563950\pi\) | |||||||
\(114\) | 12.2666 | − | 9.72973i | 1.14887 | − | 0.911273i | ||||
\(115\) | 3.02846 | − | 5.24545i | 0.282405 | − | 0.489140i | ||||
\(116\) | −3.10878 | + | 13.2983i | −0.288643 | + | 1.23472i | ||||
\(117\) | −1.48648 | + | 0.858221i | −0.137425 | + | 0.0793426i | ||||
\(118\) | 2.32515 | + | 15.7060i | 0.214048 | + | 1.44585i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 14.3137 | − | 6.75481i | 1.30666 | − | 0.616627i | ||||
\(121\) | 2.32843 | + | 4.03295i | 0.211675 | + | 0.366632i | ||||
\(122\) | −2.81489 | + | 7.11724i | −0.254848 | + | 0.644364i | ||||
\(123\) | 4.25822 | + | 2.45849i | 0.383951 | + | 0.221674i | ||||
\(124\) | −8.83670 | − | 8.28600i | −0.793559 | − | 0.744105i | ||||
\(125\) | − | 8.28772i | − | 0.741276i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.2316i | − | 0.907911i | −0.891024 | − | 0.453955i | \(-0.850013\pi\) | ||
0.891024 | − | 0.453955i | \(-0.149987\pi\) | |||||||
\(128\) | −0.207835 | + | 11.3118i | −0.0183702 | + | 0.999831i | ||||
\(129\) | −13.4174 | − | 7.74652i | −1.18133 | − | 0.682043i | ||||
\(130\) | 3.71965 | + | 1.47113i | 0.326235 | + | 0.129027i | ||||
\(131\) | −0.183707 | − | 0.318190i | −0.0160505 | − | 0.0278004i | 0.857889 | − | 0.513836i | \(-0.171776\pi\) |
−0.873939 | + | 0.486035i | \(0.838443\pi\) | |||||||
\(132\) | −4.91010 | − | 16.2200i | −0.427370 | − | 1.41177i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.58579 | + | 0.678892i | −0.396152 | + | 0.0586474i | ||||
\(135\) | −6.85351 | + | 3.95687i | −0.589856 | + | 0.340554i | ||||
\(136\) | 0.0740472 | − | 0.893620i | 0.00634950 | − | 0.0766273i | ||||
\(137\) | 4.12132 | − | 7.13834i | 0.352108 | − | 0.609869i | −0.634510 | − | 0.772914i | \(-0.718798\pi\) |
0.986619 | + | 0.163045i | \(0.0521316\pi\) | |||||||
\(138\) | 4.36224 | + | 5.49963i | 0.371339 | + | 0.468159i | ||||
\(139\) | −22.8211 | −1.93566 | −0.967829 | − | 0.251610i | \(-0.919040\pi\) | ||||
−0.967829 | + | 0.251610i | \(0.919040\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.17157 | −0.772386 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.14144 | − | 3.70909i | 0.179077 | − | 0.310170i | ||||
\(144\) | 0.407596 | + | 6.33004i | 0.0339663 | + | 0.527503i | ||||
\(145\) | 15.4530 | − | 8.92177i | 1.28330 | − | 0.740913i | ||||
\(146\) | −19.6089 | + | 2.90295i | −1.62284 | + | 0.240250i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.65685 | − | 2.31788i | 0.629390 | − | 0.190529i | ||||
\(149\) | −2.41421 | − | 4.18154i | −0.197780 | − | 0.342565i | 0.750028 | − | 0.661406i | \(-0.230040\pi\) |
−0.947808 | + | 0.318841i | \(0.896707\pi\) | |||||||
\(150\) | −5.14922 | − | 2.03653i | −0.420432 | − | 0.166282i | ||||
\(151\) | 18.5532 | + | 10.7117i | 1.50984 | + | 0.871704i | 0.999934 | + | 0.0114717i | \(0.00365163\pi\) |
0.509902 | + | 0.860233i | \(0.329682\pi\) | |||||||
\(152\) | 8.33213 | − | 12.0166i | 0.675825 | − | 0.974676i | ||||
\(153\) | − | 0.502734i | − | 0.0406437i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.8275i | 1.27130i | ||||||||
\(156\) | −3.17092 | + | 3.38166i | −0.253876 | + | 0.270749i | ||||
\(157\) | 16.6178 | + | 9.59428i | 1.32624 | + | 0.765707i | 0.984717 | − | 0.174165i | \(-0.0557226\pi\) |
0.341527 | + | 0.939872i | \(0.389056\pi\) | |||||||
\(158\) | 4.11613 | − | 10.4073i | 0.327461 | − | 0.827962i | ||||
\(159\) | 11.2268 | + | 19.4454i | 0.890345 | + | 1.54212i | ||||
\(160\) | 10.9670 | − | 9.91131i | 0.867019 | − | 0.783558i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.32843 | − | 15.7281i | −0.182939 | − | 1.23571i | ||||
\(163\) | 13.1191 | − | 7.57430i | 1.02757 | − | 0.593265i | 0.111279 | − | 0.993789i | \(-0.464505\pi\) |
0.916286 | + | 0.400524i | \(0.131172\pi\) | |||||||
\(164\) | 4.47164 | + | 1.04535i | 0.349176 | + | 0.0816278i | ||||
\(165\) | −11.0711 | + | 19.1757i | −0.861881 | + | 1.49282i | ||||
\(166\) | 10.4736 | − | 8.30752i | 0.812907 | − | 0.644789i | ||||
\(167\) | 7.83095 | 0.605977 | 0.302989 | − | 0.952994i | \(-0.402016\pi\) | ||||
0.302989 | + | 0.952994i | \(0.402016\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8284 | 0.909879 | ||||||||
\(170\) | −0.917886 | + | 0.728057i | −0.0703987 | + | 0.0558394i | ||||
\(171\) | 4.09918 | − | 7.09999i | 0.313472 | − | 0.542950i | ||||
\(172\) | −14.0898 | − | 3.29382i | −1.07434 | − | 0.251151i | ||||
\(173\) | −5.69089 | + | 3.28564i | −0.432671 | + | 0.249802i | −0.700484 | − | 0.713668i | \(-0.747032\pi\) |
0.267813 | + | 0.963471i | \(0.413699\pi\) | |||||||
\(174\) | 3.02846 | + | 20.4567i | 0.229587 | + | 1.55082i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.77817 | − | 13.1702i | −0.661680 | − | 0.992739i | ||||
\(177\) | 12.0208 | + | 20.8207i | 0.903540 | + | 1.56498i | ||||
\(178\) | −3.11638 | + | 7.87954i | −0.233583 | + | 0.590597i | ||||
\(179\) | −11.6997 | − | 6.75481i | −0.874474 | − | 0.504878i | −0.00564179 | − | 0.999984i | \(-0.501796\pi\) |
−0.868833 | + | 0.495106i | \(0.835129\pi\) | |||||||
\(180\) | 5.66889 | − | 6.04566i | 0.422534 | − | 0.450617i | ||||
\(181\) | 21.9874i | 1.63431i | 0.576418 | + | 0.817155i | \(0.304450\pi\) | ||||
−0.576418 | + | 0.817155i | \(0.695550\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.5894i | 0.856714i | ||||||||
\(184\) | 5.38755 | + | 3.73564i | 0.397175 | + | 0.275395i | ||||
\(185\) | −9.05213 | − | 5.22625i | −0.665526 | − | 0.384242i | ||||
\(186\) | −17.0575 | − | 6.74629i | −1.25072 | − | 0.494662i | ||||
\(187\) | 0.627215 | + | 1.08637i | 0.0458665 | + | 0.0794431i | ||||
\(188\) | −8.19837 | + | 2.48181i | −0.597927 | + | 0.181005i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.8995 | + | 2.79793i | −1.37111 | + | 0.202983i | ||||
\(191\) | −5.67763 | + | 3.27798i | −0.410819 | + | 0.237186i | −0.691142 | − | 0.722719i | \(-0.742892\pi\) |
0.280323 | + | 0.959906i | \(0.409559\pi\) | |||||||
\(192\) | 6.00698 | + | 16.0439i | 0.433516 | + | 1.15787i | ||||
\(193\) | −7.29289 | + | 12.6317i | −0.524954 | + | 0.909247i | 0.474624 | + | 0.880189i | \(0.342584\pi\) |
−0.999578 | + | 0.0290581i | \(0.990749\pi\) | |||||||
\(194\) | −8.11945 | − | 10.2365i | −0.582943 | − | 0.734935i | ||||
\(195\) | 6.05692 | 0.433745 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | −5.51453 | − | 6.95235i | −0.391900 | − | 0.494082i | ||||
\(199\) | 8.56578 | − | 14.8364i | 0.607212 | − | 1.05172i | −0.384486 | − | 0.923131i | \(-0.625621\pi\) |
0.991698 | − | 0.128591i | \(-0.0410455\pi\) | |||||||
\(200\) | −5.15391 | − | 0.427064i | −0.364436 | − | 0.0301980i | ||||
\(201\) | −6.07917 | + | 3.50981i | −0.428791 | + | 0.247563i | ||||
\(202\) | 21.3068 | − | 3.15432i | 1.49914 | − | 0.221937i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.393398 | − | 1.29954i | −0.0275434 | − | 0.0909863i | ||||
\(205\) | −3.00000 | − | 5.19615i | −0.209529 | − | 0.362915i | ||||
\(206\) | −15.9308 | − | 6.30069i | −1.10995 | − | 0.438990i | ||||
\(207\) | 3.18322 | + | 1.83783i | 0.221249 | + | 0.127738i | ||||
\(208\) | −1.91938 | + | 3.88087i | −0.133085 | + | 0.269090i | ||||
\(209\) | 20.4567i | 1.41502i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.4697i | 0.996136i | 0.867138 | + | 0.498068i | \(0.165957\pi\) | ||||
−0.867138 | + | 0.498068i | \(0.834043\pi\) | |||||||
\(212\) | 15.2974 | + | 14.3441i | 1.05063 | + | 0.985157i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.20559 | + | 3.04823i | −0.0824121 | + | 0.208373i | ||||
\(215\) | 9.45280 | + | 16.3727i | 0.644675 | + | 1.11661i | ||||
\(216\) | −3.65568 | − | 7.74652i | −0.248737 | − | 0.527084i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.17157 | − | 7.91375i | −0.0793489 | − | 0.535987i | ||||
\(219\) | −25.9946 | + | 15.0080i | −1.75655 | + | 1.01415i | ||||
\(220\) | −4.70741 | + | 20.1367i | −0.317373 | + | 1.35762i | ||||
\(221\) | 0.171573 | − | 0.297173i | 0.0115412 | − | 0.0199900i | ||||
\(222\) | 9.49077 | − | 7.52797i | 0.636979 | − | 0.505245i | ||||
\(223\) | 7.83095 | 0.524399 | 0.262200 | − | 0.965014i | \(-0.415552\pi\) | ||||
0.262200 | + | 0.965014i | \(0.415552\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.89949 | −0.193300 | ||||||||
\(226\) | −4.70079 | + | 3.72861i | −0.312692 | + | 0.248024i | ||||
\(227\) | 4.98620 | − | 8.63635i | 0.330946 | − | 0.573215i | −0.651752 | − | 0.758432i | \(-0.725966\pi\) |
0.982698 | + | 0.185218i | \(0.0592990\pi\) | |||||||
\(228\) | 5.04033 | − | 21.5608i | 0.333804 | − | 1.42790i | ||||
\(229\) | 1.16483 | − | 0.672512i | 0.0769738 | − | 0.0444409i | −0.461019 | − | 0.887390i | \(-0.652516\pi\) |
0.537993 | + | 0.842949i | \(0.319183\pi\) | |||||||
\(230\) | −1.25443 | − | 8.47343i | −0.0827146 | − | 0.558721i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.24264 | + | 17.4665i | 0.541156 | + | 1.14673i | ||||
\(233\) | −8.12132 | − | 14.0665i | −0.532045 | − | 0.921530i | −0.999300 | − | 0.0374069i | \(-0.988090\pi\) |
0.467255 | − | 0.884123i | \(-0.345243\pi\) | |||||||
\(234\) | −0.892762 | + | 2.25728i | −0.0583617 | + | 0.147563i | ||||
\(235\) | 9.69232 | + | 5.59587i | 0.632257 | + | 0.365034i | ||||
\(236\) | 16.3793 | + | 15.3585i | 1.06620 | + | 0.999756i | ||||
\(237\) | − | 16.9469i | − | 1.10082i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.2316i | − | 0.661829i | −0.943661 | − | 0.330915i | \(-0.892643\pi\) | ||
0.943661 | − | 0.330915i | \(-0.107357\pi\) | |||||||
\(240\) | 9.92299 | − | 20.0637i | 0.640526 | − | 1.29511i | ||||
\(241\) | 4.41234 | + | 2.54747i | 0.284224 | + | 0.164097i | 0.635334 | − | 0.772237i | \(-0.280862\pi\) |
−0.351110 | + | 0.936334i | \(0.614196\pi\) | |||||||
\(242\) | 6.12420 | + | 2.42214i | 0.393678 | + | 0.155701i | ||||
\(243\) | −7.49506 | − | 12.9818i | −0.480808 | − | 0.832784i | ||||
\(244\) | 3.13607 | + | 10.3596i | 0.200767 | + | 0.663209i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.87868 | − | 1.01834i | 0.438569 | − | 0.0649269i | ||||
\(247\) | 4.84616 | − | 2.79793i | 0.308354 | − | 0.178028i | ||||
\(248\) | −17.0730 | − | 1.41471i | −1.08414 | − | 0.0898341i | ||||
\(249\) | 10.1213 | − | 17.5306i | 0.641413 | − | 1.11096i | ||||
\(250\) | −7.28360 | − | 9.18269i | −0.460656 | − | 0.580764i | ||||
\(251\) | −3.91548 | −0.247143 | −0.123571 | − | 0.992336i | \(-0.539435\pi\) | ||||
−0.123571 | + | 0.992336i | \(0.539435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.17157 | −0.576612 | ||||||||
\(254\) | −8.99200 | − | 11.3365i | −0.564208 | − | 0.711316i | ||||
\(255\) | −0.887016 | + | 1.53636i | −0.0555471 | + | 0.0962103i | ||||
\(256\) | 9.71102 | + | 12.7160i | 0.606939 | + | 0.794749i | ||||
\(257\) | 16.5041 | − | 9.52862i | 1.02950 | − | 0.594379i | 0.112655 | − | 0.993634i | \(-0.464064\pi\) |
0.916840 | + | 0.399255i | \(0.130731\pi\) | |||||||
\(258\) | −21.6743 | + | 3.20871i | −1.34938 | + | 0.199766i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.41421 | − | 1.63899i | 0.335775 | − | 0.101646i | ||||
\(261\) | 5.41421 | + | 9.37769i | 0.335131 | + | 0.580465i | ||||
\(262\) | −0.483184 | − | 0.191101i | −0.0298512 | − | 0.0118062i | ||||
\(263\) | 22.2235 | + | 12.8307i | 1.37036 | + | 0.791176i | 0.990973 | − | 0.134063i | \(-0.0428024\pi\) |
0.379385 | + | 0.925239i | \(0.376136\pi\) | |||||||
\(264\) | −19.6951 | − | 13.6563i | −1.21215 | − | 0.840486i | ||||
\(265\) | − | 27.3994i | − | 1.68313i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.8307i | 0.785227i | ||||||||
\(268\) | −4.48435 | + | 4.78239i | −0.273925 | + | 0.292131i | ||||
\(269\) | −4.36524 | − | 2.52027i | −0.266153 | − | 0.153664i | 0.360985 | − | 0.932572i | \(-0.382441\pi\) |
−0.627138 | + | 0.778908i | \(0.715774\pi\) | |||||||
\(270\) | −4.11613 | + | 10.4073i | −0.250499 | + | 0.633369i | ||||
\(271\) | −2.14144 | − | 3.70909i | −0.130084 | − | 0.225311i | 0.793625 | − | 0.608407i | \(-0.208191\pi\) |
−0.923709 | + | 0.383096i | \(0.874858\pi\) | |||||||
\(272\) | −0.703309 | − | 1.05520i | −0.0426443 | − | 0.0639806i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.70711 | − | 11.5312i | −0.103130 | − | 0.696624i | ||||
\(275\) | 6.26557 | − | 3.61743i | 0.377828 | − | 0.218139i | ||||
\(276\) | 9.66661 | + | 2.25979i | 0.581862 | + | 0.136023i | ||||
\(277\) | 2.07107 | − | 3.58719i | 0.124438 | − | 0.215534i | −0.797075 | − | 0.603880i | \(-0.793620\pi\) |
0.921513 | + | 0.388347i | \(0.126954\pi\) | |||||||
\(278\) | −25.2854 | + | 20.0561i | −1.51652 | + | 1.20289i | ||||
\(279\) | −9.60498 | −0.575035 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3848 | 0.619504 | 0.309752 | − | 0.950817i | \(-0.399754\pi\) | ||||
0.309752 | + | 0.950817i | \(0.399754\pi\) | |||||||
\(282\) | −10.1620 | + | 8.06037i | −0.605137 | + | 0.479988i | ||||
\(283\) | −1.69794 | + | 2.94091i | −0.100932 | + | 0.174819i | −0.912069 | − | 0.410037i | \(-0.865516\pi\) |
0.811137 | + | 0.584856i | \(0.198849\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −25.0542 | + | 14.4650i | −1.48408 | + | 0.856835i | ||||
\(286\) | −0.887016 | − | 5.99162i | −0.0524503 | − | 0.354292i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.01472 | + | 6.65539i | 0.354421 | + | 0.392172i | ||||
\(289\) | −8.44975 | − | 14.6354i | −0.497044 | − | 0.860905i | ||||
\(290\) | 9.28084 | − | 23.4659i | 0.544990 | − | 1.37797i | ||||
\(291\) | −17.1338 | − | 9.89219i | −1.00440 | − | 0.579890i | ||||
\(292\) | −19.1752 | + | 20.4496i | −1.12214 | + | 1.19672i | ||||
\(293\) | − | 11.7975i | − | 0.689219i | −0.938746 | − | 0.344609i | \(-0.888011\pi\) | ||
0.938746 | − | 0.344609i | \(-0.111989\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 29.3371i | − | 1.70807i | ||||||
\(296\) | 6.44664 | − | 9.29736i | 0.374703 | − | 0.540398i | ||||
\(297\) | 10.3778 | + | 5.99162i | 0.602180 | + | 0.347669i | ||||
\(298\) | −6.34983 | − | 2.51138i | −0.367836 | − | 0.145480i | ||||
\(299\) | 1.25443 | + | 2.17274i | 0.0725455 | + | 0.125653i | ||||
\(300\) | −7.49506 | + | 2.26890i | −0.432727 | + | 0.130995i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 29.9706 | − | 4.43692i | 1.72461 | − | 0.255316i | ||||
\(303\) | 28.2455 | − | 16.3075i | 1.62266 | − | 0.936844i | ||||
\(304\) | −1.32882 | − | 20.6369i | −0.0762133 | − | 1.18361i | ||||
\(305\) | 7.07107 | − | 12.2474i | 0.404888 | − | 0.701287i | ||||
\(306\) | −0.441825 | − | 0.557023i | −0.0252574 | − | 0.0318429i | ||||
\(307\) | −3.91548 | −0.223468 | −0.111734 | − | 0.993738i | \(-0.535640\pi\) | ||||
−0.111734 | + | 0.993738i | \(0.535640\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.9411 | −1.47574 | ||||||||
\(310\) | 13.9099 | + | 17.5367i | 0.790028 | + | 0.996015i | ||||
\(311\) | −10.3398 | + | 17.9091i | −0.586317 | + | 1.01553i | 0.408393 | + | 0.912806i | \(0.366089\pi\) |
−0.994710 | + | 0.102724i | \(0.967244\pi\) | |||||||
\(312\) | −0.541385 | + | 6.53357i | −0.0306499 | + | 0.369891i | ||||
\(313\) | −11.0406 | + | 6.37430i | −0.624052 | + | 0.360297i | −0.778445 | − | 0.627713i | \(-0.783991\pi\) |
0.154393 | + | 0.988010i | \(0.450658\pi\) | |||||||
\(314\) | 26.8442 | − | 3.97408i | 1.51490 | − | 0.224270i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.58579 | − | 15.1486i | −0.257971 | − | 0.852176i | ||||
\(317\) | 2.75736 | + | 4.77589i | 0.154869 | + | 0.268241i | 0.933011 | − | 0.359847i | \(-0.117171\pi\) |
−0.778142 | + | 0.628088i | \(0.783838\pi\) | |||||||
\(318\) | 29.5287 | + | 11.6787i | 1.65588 | + | 0.654907i | ||||
\(319\) | −23.3993 | − | 13.5096i | −1.31011 | − | 0.756393i | ||||
\(320\) | 3.44084 | − | 20.6199i | 0.192349 | − | 1.15269i | ||||
\(321\) | 4.96362i | 0.277042i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.63899i | 0.0911959i | ||||||||
\(324\) | −16.4024 | − | 15.3802i | −0.911243 | − | 0.854455i | ||||
\(325\) | −1.71393 | − | 0.989538i | −0.0950717 | − | 0.0548897i | ||||
\(326\) | 7.87914 | − | 19.9218i | 0.436385 | − | 1.10337i | ||||
\(327\) | −6.05692 | − | 10.4909i | −0.334948 | − | 0.580148i | ||||
\(328\) | 5.87321 | − | 2.77164i | 0.324294 | − | 0.153038i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.58579 | + | 30.9761i | 0.252439 | + | 1.70518i | ||||
\(331\) | 13.1191 | − | 7.57430i | 0.721090 | − | 0.416321i | −0.0940639 | − | 0.995566i | \(-0.529986\pi\) |
0.815154 | + | 0.579245i | \(0.196652\pi\) | |||||||
\(332\) | 4.30358 | − | 18.4093i | 0.236189 | − | 1.01034i | ||||
\(333\) | 3.17157 | − | 5.49333i | 0.173801 | − | 0.301032i | ||||
\(334\) | 8.67659 | − | 6.88218i | 0.474762 | − | 0.376576i | ||||
\(335\) | 8.56578 | 0.467999 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.8284 | 0.589862 | 0.294931 | − | 0.955519i | \(-0.404703\pi\) | ||||
0.294931 | + | 0.955519i | \(0.404703\pi\) | |||||||
\(338\) | 13.1057 | − | 10.3953i | 0.712858 | − | 0.565431i | ||||
\(339\) | −4.54269 | + | 7.86817i | −0.246725 | + | 0.427340i | ||||
\(340\) | −0.377158 | + | 1.61336i | −0.0204543 | + | 0.0874965i | ||||
\(341\) | 20.7556 | − | 11.9832i | 1.12398 | − | 0.648929i | ||||
\(342\) | −1.69794 | − | 11.4692i | −0.0918139 | − | 0.620185i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −18.5061 | + | 8.73324i | −0.997782 | + | 0.470865i | ||||
\(345\) | −6.48528 | − | 11.2328i | −0.349156 | − | 0.604756i | ||||
\(346\) | −3.41787 | + | 8.64184i | −0.183746 | + | 0.464588i | ||||
\(347\) | 3.42675 | + | 1.97844i | 0.183958 | + | 0.106208i | 0.589151 | − | 0.808023i | \(-0.299462\pi\) |
−0.405193 | + | 0.914231i | \(0.632796\pi\) | |||||||
\(348\) | 21.3337 | + | 20.0042i | 1.14361 | + | 1.07234i | ||||
\(349\) | 8.47343i | 0.453572i | 0.973945 | + | 0.226786i | \(0.0728218\pi\) | ||||
−0.973945 | + | 0.226786i | \(0.927178\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 3.27798i | − | 0.174966i | ||||||
\(352\) | −21.3006 | − | 6.87774i | −1.13533 | − | 0.366585i | ||||
\(353\) | −8.71096 | − | 5.02928i | −0.463638 | − | 0.267681i | 0.249935 | − | 0.968263i | \(-0.419591\pi\) |
−0.713573 | + | 0.700581i | \(0.752924\pi\) | |||||||
\(354\) | 31.6170 | + | 12.5046i | 1.68042 | + | 0.664613i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.47197 | + | 11.4692i | 0.184014 | + | 0.607868i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.8995 | + | 2.79793i | −0.998869 | + | 0.147875i | ||||
\(359\) | −27.0696 | + | 15.6287i | −1.42868 | + | 0.824849i | −0.997017 | − | 0.0771860i | \(-0.975406\pi\) |
−0.431663 | + | 0.902035i | \(0.642073\pi\) | |||||||
\(360\) | 0.967877 | − | 11.6806i | 0.0510116 | − | 0.615620i | ||||
\(361\) | −3.86396 | + | 6.69258i | −0.203366 | + | 0.352241i | ||||
\(362\) | 19.3235 | + | 24.3618i | 1.01562 | + | 1.28043i | ||||
\(363\) | 9.97240 | 0.523415 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.6274 | 1.91717 | ||||||||
\(366\) | 10.1853 | + | 12.8409i | 0.532393 | + | 0.671206i | ||||
\(367\) | −6.42433 | + | 11.1273i | −0.335348 | + | 0.580839i | −0.983552 | − | 0.180628i | \(-0.942187\pi\) |
0.648204 | + | 0.761467i | \(0.275520\pi\) | |||||||
\(368\) | 9.25237 | − | 0.595767i | 0.482313 | − | 0.0310565i | ||||
\(369\) | 3.15331 | − | 1.82056i | 0.164155 | − | 0.0947747i | ||||
\(370\) | −14.6227 | + | 2.16478i | −0.760198 | + | 0.112542i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −24.8284 | + | 7.51606i | −1.28729 | + | 0.389690i | ||||
\(373\) | 10.0711 | + | 17.4436i | 0.521460 | + | 0.903195i | 0.999688 | + | 0.0249599i | \(0.00794580\pi\) |
−0.478228 | + | 0.878236i | \(0.658721\pi\) | |||||||
\(374\) | 1.64969 | + | 0.652458i | 0.0853036 | + | 0.0337378i | ||||
\(375\) | −15.3700 | − | 8.87385i | −0.793701 | − | 0.458244i | ||||
\(376\) | −6.90256 | + | 9.95489i | −0.355972 | + | 0.513384i | ||||
\(377\) | 7.39104i | 0.380658i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 21.7046i | − | 1.11489i | −0.830214 | − | 0.557444i | \(-0.811782\pi\) | ||
0.830214 | − | 0.557444i | \(-0.188218\pi\) | |||||||
\(380\) | −18.4815 | + | 19.7098i | −0.948078 | + | 1.01109i | ||||
\(381\) | −18.9750 | − | 10.9552i | −0.972120 | − | 0.561254i | ||||
\(382\) | −3.40991 | + | 8.62171i | −0.174466 | + | 0.441125i | ||||
\(383\) | −15.5097 | − | 26.8636i | −0.792509 | − | 1.37267i | −0.924409 | − | 0.381404i | \(-0.875441\pi\) |
0.131899 | − | 0.991263i | \(-0.457892\pi\) | |||||||
\(384\) | 20.7557 | + | 12.4972i | 1.05919 | + | 0.637747i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.02082 | + | 20.4050i | 0.153755 | + | 1.03859i | ||||
\(387\) | −9.93585 | + | 5.73647i | −0.505068 | + | 0.291601i | ||||
\(388\) | −17.9925 | − | 4.20615i | −0.913430 | − | 0.213535i | ||||
\(389\) | −7.07107 | + | 12.2474i | −0.358517 | + | 0.620970i | −0.987713 | − | 0.156276i | \(-0.950051\pi\) |
0.629196 | + | 0.777247i | \(0.283384\pi\) | |||||||
\(390\) | 6.71099 | − | 5.32308i | 0.339824 | − | 0.269545i | ||||
\(391\) | −0.734828 | −0.0371618 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.786797 | −0.0396886 | ||||||||
\(394\) | 2.21597 | − | 1.75769i | 0.111639 | − | 0.0885509i | ||||
\(395\) | −10.3398 | + | 17.9091i | −0.520252 | + | 0.901103i | ||||
\(396\) | −12.2200 | − | 2.85671i | −0.614080 | − | 0.143555i | ||||
\(397\) | −13.9665 | + | 8.06355i | −0.700957 | + | 0.404698i | −0.807704 | − | 0.589588i | \(-0.799290\pi\) |
0.106747 | + | 0.994286i | \(0.465957\pi\) | |||||||
\(398\) | −3.54806 | − | 23.9665i | −0.177848 | − | 1.20133i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.08579 | + | 4.05630i | −0.304289 | + | 0.202815i | ||||
\(401\) | 6.41421 | + | 11.1097i | 0.320311 | + | 0.554794i | 0.980552 | − | 0.196259i | \(-0.0628794\pi\) |
−0.660242 | + | 0.751053i | \(0.729546\pi\) | |||||||
\(402\) | −3.65107 | + | 9.23146i | −0.182099 | + | 0.460423i | ||||
\(403\) | −5.67763 | − | 3.27798i | −0.282823 | − | 0.163288i | ||||
\(404\) | 20.8355 | − | 22.2203i | 1.03661 | − | 1.10550i | ||||
\(405\) | 29.3784i | 1.45983i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.8275i | 0.784540i | ||||||||
\(408\) | −1.57798 | − | 1.09414i | −0.0781214 | − | 0.0541682i | ||||
\(409\) | 11.9780 | + | 6.91550i | 0.592274 | + | 0.341949i | 0.765996 | − | 0.642845i | \(-0.222246\pi\) |
−0.173722 | + | 0.984795i | \(0.555580\pi\) | |||||||
\(410\) | −7.89056 | − | 3.12074i | −0.389687 | − | 0.154122i | ||||
\(411\) | −8.82558 | − | 15.2864i | −0.435334 | − | 0.754020i | ||||
\(412\) | −23.1885 | + | 7.01962i | −1.14241 | + | 0.345832i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.14214 | − | 0.761256i | 0.252722 | − | 0.0374137i | ||||
\(415\) | −21.3920 | + | 12.3507i | −1.05009 | + | 0.606271i | ||||
\(416\) | 1.28403 | + | 5.98678i | 0.0629549 | + | 0.293526i | ||||
\(417\) | −24.4350 | + | 42.3227i | −1.19659 | + | 2.07255i | ||||
\(418\) | 17.9782 | + | 22.6657i | 0.879342 | + | 1.10862i | ||||
\(419\) | −17.2837 | −0.844366 | −0.422183 | − | 0.906511i | \(-0.638736\pi\) | ||||
−0.422183 | + | 0.906511i | \(0.638736\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.4853 | −0.511021 | −0.255511 | − | 0.966806i | \(-0.582244\pi\) | ||||
−0.255511 | + | 0.966806i | \(0.582244\pi\) | |||||||
\(422\) | 12.7166 | + | 16.0323i | 0.619035 | + | 0.780438i | ||||
\(423\) | −3.39587 | + | 5.88183i | −0.165113 | + | 0.285984i | ||||
\(424\) | 29.5556 | + | 2.44904i | 1.43534 | + | 0.118936i | ||||
\(425\) | 0.501998 | − | 0.289829i | 0.0243505 | − | 0.0140588i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.34315 | + | 4.43692i | 0.0649234 | + | 0.214467i | ||||
\(429\) | −4.58579 | − | 7.94282i | −0.221404 | − | 0.383483i | ||||
\(430\) | 24.8626 | + | 9.83324i | 1.19898 | + | 0.474201i | ||||
\(431\) | 0.831470 | + | 0.480049i | 0.0400505 | + | 0.0231232i | 0.519892 | − | 0.854232i | \(-0.325972\pi\) |
−0.479841 | + | 0.877355i | \(0.659306\pi\) | |||||||
\(432\) | −10.8584 | − | 5.37028i | −0.522426 | − | 0.258378i | ||||
\(433\) | 26.1857i | 1.25840i | 0.777243 | + | 0.629201i | \(0.216618\pi\) | ||||
−0.777243 | + | 0.629201i | \(0.783382\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 38.2110i | − | 1.83208i | ||||||
\(436\) | −8.25303 | − | 7.73870i | −0.395248 | − | 0.370617i | ||||
\(437\) | −10.3778 | − | 5.99162i | −0.496437 | − | 0.286618i | ||||
\(438\) | −15.6120 | + | 39.4739i | −0.745971 | + | 1.88613i | ||||
\(439\) | 11.2268 | + | 19.4454i | 0.535827 | + | 0.928080i | 0.999123 | + | 0.0418761i | \(0.0133335\pi\) |
−0.463296 | + | 0.886204i | \(0.653333\pi\) | |||||||
\(440\) | 12.4813 | + | 26.4483i | 0.595021 | + | 1.26087i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.0710678 | − | 0.480049i | −0.00338035 | − | 0.0228336i | ||||
\(443\) | 24.5752 | − | 14.1885i | 1.16760 | − | 0.674116i | 0.214489 | − | 0.976726i | \(-0.431191\pi\) |
0.953114 | + | 0.302610i | \(0.0978580\pi\) | |||||||
\(444\) | 3.89975 | − | 16.6818i | 0.185074 | − | 0.791683i | ||||
\(445\) | 7.82843 | − | 13.5592i | 0.371103 | − | 0.642769i | ||||
\(446\) | 8.67659 | − | 6.88218i | 0.410849 | − | 0.325881i | ||||
\(447\) | −10.3398 | −0.489056 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.2843 | −0.768502 | −0.384251 | − | 0.923229i | \(-0.625540\pi\) | ||||
−0.384251 | + | 0.923229i | \(0.625540\pi\) | |||||||
\(450\) | −3.21260 | + | 2.54820i | −0.151444 | + | 0.120123i | ||||
\(451\) | −4.54269 | + | 7.86817i | −0.213907 | + | 0.370498i | ||||
\(452\) | −1.93155 | + | 8.26251i | −0.0908524 | + | 0.388636i | ||||
\(453\) | 39.7306 | − | 22.9385i | 1.86671 | − | 1.07774i | ||||
\(454\) | −2.06535 | − | 13.9510i | −0.0969317 | − | 0.654755i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.3640 | − | 28.3188i | −0.625825 | − | 1.32615i | ||||
\(457\) | −0.363961 | − | 0.630399i | −0.0170254 | − | 0.0294888i | 0.857387 | − | 0.514672i | \(-0.172086\pi\) |
−0.874413 | + | 0.485183i | \(0.838753\pi\) | |||||||
\(458\) | 0.699579 | − | 1.76883i | 0.0326892 | − | 0.0826522i | ||||
\(459\) | 0.831470 | + | 0.480049i | 0.0388097 | + | 0.0224068i | ||||
\(460\) | −8.83670 | − | 8.28600i | −0.412013 | − | 0.386337i | ||||
\(461\) | − | 29.7499i | − | 1.38559i | −0.721135 | − | 0.692794i | \(-0.756379\pi\) | ||
0.721135 | − | 0.692794i | \(-0.243621\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.9330i | 1.62347i | 0.584024 | + | 0.811737i | \(0.301477\pi\) | ||||
−0.584024 | + | 0.811737i | \(0.698523\pi\) | |||||||
\(464\) | 24.4830 | + | 12.1087i | 1.13660 | + | 0.562130i | ||||
\(465\) | 29.3528 | + | 16.9469i | 1.36120 | + | 0.785892i | ||||
\(466\) | −21.3606 | − | 8.44818i | −0.989510 | − | 0.391354i | ||||
\(467\) | 12.0377 | + | 20.8500i | 0.557041 | + | 0.964823i | 0.997742 | + | 0.0671686i | \(0.0213965\pi\) |
−0.440701 | + | 0.897654i | \(0.645270\pi\) | |||||||
\(468\) | 0.994629 | + | 3.28564i | 0.0459767 | + | 0.151879i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 15.6569 | − | 2.31788i | 0.722197 | − | 0.106916i | ||||
\(471\) | 35.5861 | − | 20.5456i | 1.63972 | − | 0.946693i | ||||
\(472\) | 31.6458 | + | 2.62224i | 1.45662 | + | 0.120698i | ||||
\(473\) | 14.3137 | − | 24.7921i | 0.658145 | − | 1.13994i | ||||
\(474\) | −14.8936 | − | 18.7769i | −0.684087 | − | 0.862451i | ||||
\(475\) | 9.45280 | 0.433724 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.6274 | 0.761317 | ||||||||
\(478\) | −8.99200 | − | 11.3365i | −0.411284 | − | 0.518520i | ||||
\(479\) | 16.3967 | − | 28.4000i | 0.749186 | − | 1.29763i | −0.199028 | − | 0.979994i | \(-0.563778\pi\) |
0.948213 | − | 0.317634i | \(-0.102888\pi\) | |||||||
\(480\) | −6.63833 | − | 30.9511i | −0.302997 | − | 1.41272i | ||||
\(481\) | 3.74952 | − | 2.16478i | 0.170963 | − | 0.0987057i | ||||
\(482\) | 7.12764 | − | 1.05520i | 0.324655 | − | 0.0480628i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.91421 | − | 2.69851i | 0.405192 | − | 0.122660i | ||||
\(485\) | 12.0711 | + | 20.9077i | 0.548119 | + | 0.949370i | ||||
\(486\) | −19.7134 | − | 7.79671i | −0.894218 | − | 0.353666i | ||||
\(487\) | −16.8902 | − | 9.75158i | −0.765370 | − | 0.441886i | 0.0658507 | − | 0.997829i | \(-0.479024\pi\) |
−0.831220 | + | 0.555943i | \(0.812357\pi\) | |||||||
\(488\) | 12.5792 | + | 8.72224i | 0.569435 | + | 0.394837i | ||||
\(489\) | − | 32.4399i | − | 1.46698i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.4697i | − | 0.653009i | −0.945196 | − | 0.326504i | \(-0.894129\pi\) | ||
0.945196 | − | 0.326504i | \(-0.105871\pi\) | |||||||
\(492\) | 6.72653 | − | 7.17358i | 0.303255 | − | 0.323410i | ||||
\(493\) | −1.87476 | − | 1.08239i | −0.0844349 | − | 0.0487485i | ||||
\(494\) | 2.91054 | − | 7.35909i | 0.130951 | − | 0.331101i | ||||
\(495\) | 8.19837 | + | 14.2000i | 0.368489 | + | 0.638242i | ||||
\(496\) | −20.1600 | + | 13.4370i | −0.905212 | + | 0.603341i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.19239 | − | 28.3188i | −0.187865 | − | 1.26899i | ||||
\(499\) | −10.8682 | + | 6.27476i | −0.486527 | + | 0.280897i | −0.723133 | − | 0.690709i | \(-0.757299\pi\) |
0.236605 | + | 0.971606i | \(0.423965\pi\) | |||||||
\(500\) | −16.1403 | − | 3.77315i | −0.721815 | − | 0.168741i | ||||
\(501\) | 8.38478 | − | 14.5229i | 0.374604 | − | 0.648833i | ||||
\(502\) | −4.33830 | + | 3.44109i | −0.193628 | + | 0.153583i | ||||
\(503\) | −7.83095 | −0.349165 | −0.174582 | − | 0.984643i | \(-0.555858\pi\) | ||||
−0.174582 | + | 0.984643i | \(0.555858\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39.7990 | −1.77103 | ||||||||
\(506\) | −10.1620 | + | 8.06037i | −0.451755 | + | 0.358327i | ||||
\(507\) | 12.6650 | − | 21.9364i | 0.562471 | − | 0.974228i | ||||
\(508\) | −19.9260 | − | 4.65816i | −0.884075 | − | 0.206672i | ||||
\(509\) | −5.69089 | + | 3.28564i | −0.252244 | + | 0.145633i | −0.620791 | − | 0.783976i | \(-0.713189\pi\) |
0.368547 | + | 0.929609i | \(0.379855\pi\) | |||||||
\(510\) | 0.367414 | + | 2.48181i | 0.0162694 | + | 0.109896i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 21.9350 | + | 5.55468i | 0.969400 | + | 0.245485i | ||||
\(513\) | 7.82843 | + | 13.5592i | 0.345634 | + | 0.598655i | ||||
\(514\) | 9.91212 | − | 25.0621i | 0.437205 | − | 1.10544i | ||||
\(515\) | 27.4140 | + | 15.8275i | 1.20801 | + | 0.697443i | ||||
\(516\) | −21.1948 | + | 22.6035i | −0.933050 | + | 0.995063i | ||||
\(517\) | − | 16.9469i | − | 0.745322i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.0720i | 0.617693i | ||||||||
\(520\) | 4.55846 | − | 6.57422i | 0.199902 | − | 0.288299i | ||||
\(521\) | −10.4249 | − | 6.01882i | −0.456723 | − | 0.263689i | 0.253942 | − | 0.967219i | \(-0.418273\pi\) |
−0.710665 | + | 0.703530i | \(0.751606\pi\) | |||||||
\(522\) | 14.2404 | + | 5.63212i | 0.623285 | + | 0.246511i | ||||
\(523\) | 3.73177 | + | 6.46361i | 0.163179 | + | 0.282634i | 0.936007 | − | 0.351981i | \(-0.114492\pi\) |
−0.772828 | + | 0.634615i | \(0.781159\pi\) | |||||||
\(524\) | −0.703309 | + | 0.212906i | −0.0307242 | + | 0.00930083i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 35.8995 | − | 5.31466i | 1.56529 | − | 0.231730i | ||||
\(527\) | 1.66294 | − | 0.960099i | 0.0724388 | − | 0.0418226i | ||||
\(528\) | −33.8237 | + | 2.17793i | −1.47199 | + | 0.0947823i | ||||
\(529\) | −8.81371 | + | 15.2658i | −0.383205 | + | 0.663730i | ||||
\(530\) | −24.0797 | − | 30.3581i | −1.04596 | − | 1.31867i | ||||
\(531\) | 17.8033 | 0.772600 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.48528 | 0.107649 | ||||||||
\(534\) | 11.2762 | + | 14.2163i | 0.487968 | + | 0.615198i | ||||
\(535\) | 3.02846 | − | 5.24545i | 0.130932 | − | 0.226780i | ||||
\(536\) | −0.765634 | + | 9.23987i | −0.0330704 | + | 0.399101i | ||||
\(537\) | −25.0542 | + | 14.4650i | −1.08117 | + | 0.624213i | ||||
\(538\) | −7.05155 | + | 1.04393i | −0.304014 | + | 0.0450070i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.58579 | + | 15.1486i | 0.197341 | + | 0.651892i | ||||
\(541\) | −22.6569 | − | 39.2428i | −0.974094 | − | 1.68718i | −0.682892 | − | 0.730519i | \(-0.739278\pi\) |
−0.291202 | − | 0.956662i | \(-0.594055\pi\) | |||||||
\(542\) | −5.63240 | − | 2.22763i | −0.241932 | − | 0.0956850i | ||||
\(543\) | 40.7766 | + | 23.5424i | 1.74989 | + | 1.01030i | ||||
\(544\) | −1.70661 | − | 0.551045i | −0.0731702 | − | 0.0236259i | ||||
\(545\) | 14.7821i | 0.633194i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.6981i | 1.18429i | 0.805833 | + | 0.592143i | \(0.201718\pi\) | ||||
−0.805833 | + | 0.592143i | \(0.798282\pi\) | |||||||
\(548\) | −12.0255 | − | 11.2761i | −0.513706 | − | 0.481692i | ||||
\(549\) | 7.43242 | + | 4.29111i | 0.317208 | + | 0.183140i | ||||
\(550\) | 3.76302 | − | 9.51451i | 0.160456 | − | 0.405700i | ||||
\(551\) | −17.6512 | − | 30.5727i | −0.751965 | − | 1.30244i | ||||
\(552\) | 12.6965 | − | 5.99162i | 0.540398 | − | 0.255020i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.857864 | − | 5.79471i | −0.0364472 | − | 0.246194i | ||||
\(555\) | −19.3846 | + | 11.1917i | −0.822832 | + | 0.475063i | ||||
\(556\) | −10.3898 | + | 44.4439i | −0.440624 | + | 1.88484i | ||||
\(557\) | 9.82843 | − | 17.0233i | 0.416444 | − | 0.721302i | −0.579135 | − | 0.815232i | \(-0.696610\pi\) |
0.995579 | + | 0.0939298i | \(0.0299429\pi\) | |||||||
\(558\) | −10.6422 | + | 8.44127i | −0.450520 | + | 0.357348i | ||||
\(559\) | −7.83095 | −0.331214 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.68629 | 0.113415 | ||||||||
\(562\) | 11.5062 | − | 9.12659i | 0.485360 | − | 0.384982i | ||||
\(563\) | 10.5235 | − | 18.2273i | 0.443513 | − | 0.768188i | −0.554434 | − | 0.832228i | \(-0.687065\pi\) |
0.997947 | + | 0.0640400i | \(0.0203985\pi\) | |||||||
\(564\) | −4.17554 | + | 17.8616i | −0.175822 | + | 0.752108i | ||||
\(565\) | 9.60124 | − | 5.54328i | 0.403927 | − | 0.233207i | ||||
\(566\) | 0.703309 | + | 4.75071i | 0.0295623 | + | 0.199687i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.41421 | − | 16.3059i | −0.394664 | − | 0.683579i | 0.598394 | − | 0.801202i | \(-0.295806\pi\) |
−0.993058 | + | 0.117623i | \(0.962472\pi\) | |||||||
\(570\) | −15.0472 | + | 38.0458i | −0.630259 | + | 1.59356i | ||||
\(571\) | 8.61732 | + | 4.97521i | 0.360624 | + | 0.208206i | 0.669354 | − | 0.742943i | \(-0.266571\pi\) |
−0.308731 | + | 0.951150i | \(0.599904\pi\) | |||||||
\(572\) | −6.24849 | − | 5.85909i | −0.261263 | − | 0.244981i | ||||
\(573\) | 14.0392i | 0.586497i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.23808i | 0.176740i | ||||||||
\(576\) | 12.5133 | + | 2.08809i | 0.521386 | + | 0.0870037i | ||||
\(577\) | −0.729445 | − | 0.421145i | −0.0303672 | − | 0.0175325i | 0.484740 | − | 0.874659i | \(-0.338914\pi\) |
−0.515107 | + | 0.857126i | \(0.672248\pi\) | |||||||
\(578\) | −22.2244 | − | 8.78982i | −0.924414 | − | 0.365608i | ||||
\(579\) | 15.6173 | + | 27.0500i | 0.649034 | + | 1.12416i | ||||
\(580\) | −10.3398 | − | 34.1563i | −0.429337 | − | 1.41827i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −27.6777 | + | 4.09748i | −1.14728 | + | 0.169846i | ||||
\(583\) | −35.9305 | + | 20.7445i | −1.48809 | + | 0.859148i | ||||
\(584\) | −3.27387 | + | 39.5098i | −0.135474 | + | 1.63493i | ||||
\(585\) | 2.24264 | − | 3.88437i | 0.0927218 | − | 0.160599i | ||||
\(586\) | −10.3682 | − | 13.0715i | −0.428305 | − | 0.539979i | ||||
\(587\) | 22.8211 | 0.941926 | 0.470963 | − | 0.882153i | \(-0.343906\pi\) | ||||
0.470963 | + | 0.882153i | \(0.343906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.3137 | 1.29026 | ||||||||
\(590\) | −25.7827 | − | 32.5051i | −1.06146 | − | 1.33822i | ||||
\(591\) | 2.14144 | − | 3.70909i | 0.0880873 | − | 0.152572i | ||||
\(592\) | −1.02812 | − | 15.9669i | −0.0422556 | − | 0.656237i | ||||
\(593\) | −32.4395 | + | 18.7290i | −1.33213 | + | 0.769106i | −0.985626 | − | 0.168942i | \(-0.945965\pi\) |
−0.346505 | + | 0.938048i | \(0.612632\pi\) | |||||||
\(594\) | 16.7641 | − | 2.48181i | 0.687841 | − | 0.101830i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.24264 | + | 2.79793i | −0.378593 | + | 0.114608i | ||||
\(597\) | −18.3431 | − | 31.7713i | −0.750735 | − | 1.30031i | ||||
\(598\) | 3.29938 | + | 1.30492i | 0.134922 | + | 0.0533620i | ||||
\(599\) | −27.9011 | − | 16.1087i | −1.14001 | − | 0.658184i | −0.193575 | − | 0.981085i | \(-0.562008\pi\) |
−0.946433 | + | 0.322902i | \(0.895342\pi\) | |||||||
\(600\) | −6.31042 | + | 9.10089i | −0.257622 | + | 0.371542i | ||||
\(601\) | − | 25.5516i | − | 1.04227i | −0.853474 | − | 0.521136i | \(-0.825509\pi\) | ||
0.853474 | − | 0.521136i | \(-0.174491\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.19818i | 0.211686i | ||||||||
\(604\) | 29.3076 | − | 31.2555i | 1.19251 | − | 1.27177i | ||||
\(605\) | −10.5386 | − | 6.08447i | −0.428456 | − | 0.247369i | ||||
\(606\) | 16.9639 | − | 42.8919i | 0.689110 | − | 1.74236i | ||||
\(607\) | −6.05692 | − | 10.4909i | −0.245843 | − | 0.425812i | 0.716525 | − | 0.697561i | \(-0.245731\pi\) |
−0.962368 | + | 0.271749i | \(0.912398\pi\) | |||||||
\(608\) | −19.6089 | − | 21.6976i | −0.795246 | − | 0.879953i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.92893 | − | 19.7844i | −0.118589 | − | 0.801046i | ||||
\(611\) | −4.01469 | + | 2.31788i | −0.162417 | + | 0.0937715i | ||||
\(612\) | −0.979072 | − | 0.228880i | −0.0395766 | − | 0.00925193i | ||||
\(613\) | 4.34315 | − | 7.52255i | 0.175418 | − | 0.303833i | −0.764888 | − | 0.644163i | \(-0.777206\pi\) |
0.940306 | + | 0.340331i | \(0.110539\pi\) | |||||||
\(614\) | −4.33830 | + | 3.44109i | −0.175079 | + | 0.138871i | ||||
\(615\) | −12.8487 | −0.518108 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.4558 | −1.42740 | −0.713699 | − | 0.700452i | \(-0.752982\pi\) | ||||
−0.713699 | + | 0.700452i | \(0.752982\pi\) | |||||||
\(618\) | −28.7424 | + | 22.7982i | −1.15619 | + | 0.917077i | ||||
\(619\) | −6.76023 | + | 11.7091i | −0.271717 | + | 0.470627i | −0.969301 | − | 0.245875i | \(-0.920925\pi\) |
0.697585 | + | 0.716502i | \(0.254258\pi\) | |||||||
\(620\) | 30.8239 | + | 7.20579i | 1.23792 | + | 0.289391i | ||||
\(621\) | −6.07917 | + | 3.50981i | −0.243949 | + | 0.140844i | ||||
\(622\) | 4.28289 | + | 28.9301i | 0.171728 | + | 1.15999i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.14214 | + | 7.71491i | 0.205850 | + | 0.308843i | ||||
\(625\) | 15.3995 | + | 26.6727i | 0.615980 | + | 1.06691i | ||||
\(626\) | −6.63085 | + | 16.7656i | −0.265022 | + | 0.670089i | ||||
\(627\) | 37.9378 | + | 21.9034i | 1.51509 | + | 0.874738i | ||||
\(628\) | 26.2504 | − | 27.9950i | 1.04750 | − | 1.11712i | ||||
\(629\) | 1.26810i | 0.0505625i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.4633i | 0.814630i | 0.913288 | + | 0.407315i | \(0.133535\pi\) | ||||
−0.913288 | + | 0.407315i | \(0.866465\pi\) | |||||||
\(632\) | −18.3942 | − | 12.7543i | −0.731683 | − | 0.507338i | ||||
\(633\) | 26.8347 | + | 15.4930i | 1.06659 | + | 0.615793i | ||||
\(634\) | 7.25237 | + | 2.86833i | 0.288028 | + | 0.113916i | ||||
\(635\) | 13.3683 | + | 23.1545i | 0.530504 | + | 0.918859i | ||||
\(636\) | 42.9811 | − | 13.0112i | 1.70431 | − | 0.515929i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −37.7990 | + | 5.59587i | −1.49648 | + | 0.221542i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −14.3092 | − | 25.8705i | −0.565622 | − | 1.02262i | ||||
\(641\) | −24.7279 | + | 42.8300i | −0.976694 | + | 1.69168i | −0.302467 | + | 0.953160i | \(0.597810\pi\) |
−0.674227 | + | 0.738524i | \(0.735523\pi\) | |||||||
\(642\) | 4.36224 | + | 5.49963i | 0.172164 | + | 0.217053i | ||||
\(643\) | 41.7267 | 1.64554 | 0.822769 | − | 0.568375i | \(-0.192428\pi\) | ||||
0.822769 | + | 0.568375i | \(0.192428\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 40.4853 | 1.59411 | ||||||||
\(646\) | 1.44042 | + | 1.81598i | 0.0566724 | + | 0.0714488i | ||||
\(647\) | 21.9341 | − | 37.9909i | 0.862317 | − | 1.49358i | −0.00737070 | − | 0.999973i | \(-0.502346\pi\) |
0.869687 | − | 0.493603i | \(-0.164320\pi\) | |||||||
\(648\) | −31.6904 | − | 2.62593i | −1.24492 | − | 0.103156i | ||||
\(649\) | −38.4716 | + | 22.2116i | −1.51014 | + | 0.871880i | ||||
\(650\) | −2.76866 | + | 0.409880i | −0.108596 | + | 0.0160768i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.77817 | − | 28.9977i | −0.343780 | − | 1.13564i | ||||
\(653\) | 11.8995 | + | 20.6105i | 0.465663 | + | 0.806552i | 0.999231 | − | 0.0392048i | \(-0.0124825\pi\) |
−0.533568 | + | 0.845757i | \(0.679149\pi\) | |||||||
\(654\) | −15.9308 | − | 6.30069i | −0.622945 | − | 0.246377i | ||||
\(655\) | 0.831470 | + | 0.480049i | 0.0324882 | + | 0.0187571i | ||||
\(656\) | 4.07161 | − | 8.23257i | 0.158970 | − | 0.321428i | ||||
\(657\) | 22.2275i | 0.867177i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.2284i | 0.515306i | 0.966238 | + | 0.257653i | \(0.0829491\pi\) | ||||
−0.966238 | + | 0.257653i | \(0.917051\pi\) | |||||||
\(660\) | 32.3041 | + | 30.2909i | 1.25744 | + | 1.17907i | ||||
\(661\) | −32.6198 | − | 18.8331i | −1.26877 | − | 0.732522i | −0.294011 | − | 0.955802i | \(-0.594990\pi\) |
−0.974754 | + | 0.223280i | \(0.928323\pi\) | |||||||
\(662\) | 7.87914 | − | 19.9218i | 0.306232 | − | 0.774284i | ||||
\(663\) | −0.367414 | − | 0.636379i | −0.0142692 | − | 0.0247149i | ||||
\(664\) | −11.4105 | − | 24.1794i | −0.442815 | − | 0.938342i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.31371 | − | 8.87385i | −0.0509052 | − | 0.343855i | ||||
\(667\) | 13.7070 | − | 7.91375i | 0.530738 | − | 0.306422i | ||||
\(668\) | 3.56520 | − | 15.2507i | 0.137942 | − | 0.590068i | ||||
\(669\) | 8.38478 | − | 14.5229i | 0.324174 | − | 0.561486i | ||||
\(670\) | 9.49077 | − | 7.52797i | 0.366661 | − | 0.290831i | ||||
\(671\) | −21.4144 | −0.826696 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.3848 | 0.400304 | 0.200152 | − | 0.979765i | \(-0.435856\pi\) | ||||
0.200152 | + | 0.979765i | \(0.435856\pi\) | |||||||
\(674\) | 11.9978 | − | 9.51649i | 0.462136 | − | 0.366561i | ||||
\(675\) | 2.76866 | − | 4.79546i | 0.106566 | − | 0.184577i | ||||
\(676\) | 5.38513 | − | 23.0358i | 0.207120 | − | 0.885991i | ||||
\(677\) | 24.9876 | − | 14.4266i | 0.960351 | − | 0.554459i | 0.0640697 | − | 0.997945i | \(-0.479592\pi\) |
0.896281 | + | 0.443487i | \(0.146259\pi\) | |||||||
\(678\) | 1.88164 | + | 12.7101i | 0.0722641 | + | 0.488130i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.00000 | + | 2.11904i | 0.0383482 | + | 0.0812615i | ||||
\(681\) | −10.6777 | − | 18.4943i | −0.409169 | − | 0.708702i | ||||
\(682\) | 12.4655 | − | 31.5182i | 0.477330 | − | 1.20689i | ||||
\(683\) | −27.9011 | − | 16.1087i | −1.06761 | − | 0.616382i | −0.140079 | − | 0.990140i | \(-0.544736\pi\) |
−0.927526 | + | 0.373758i | \(0.878069\pi\) | |||||||
\(684\) | −11.9610 | − | 11.2155i | −0.457338 | − | 0.428837i | ||||
\(685\) | 21.5391i | 0.822965i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 2.88030i | − | 0.109890i | ||||||
\(688\) | −12.8294 | + | 25.9403i | −0.489115 | + | 0.988964i | ||||
\(689\) | 9.82868 | + | 5.67459i | 0.374443 | + | 0.216185i | ||||
\(690\) | −17.0575 | − | 6.74629i | −0.649368 | − | 0.256827i | ||||
\(691\) | −4.09918 | − | 7.09999i | −0.155940 | − | 0.270096i | 0.777461 | − | 0.628931i | \(-0.216507\pi\) |
−0.933401 | + | 0.358835i | \(0.883174\pi\) | |||||||
\(692\) | 3.80786 | + | 12.5788i | 0.144753 | + | 0.478175i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.53553 | − | 0.819496i | 0.210126 | − | 0.0311076i | ||||
\(695\) | 51.6448 | − | 29.8172i | 1.95900 | − | 1.13103i | ||||
\(696\) | 41.2180 | + | 3.41541i | 1.56236 | + | 0.129461i | ||||
\(697\) | −0.363961 | + | 0.630399i | −0.0137860 | + | 0.0238781i | ||||
\(698\) | 7.44681 | + | 9.38845i | 0.281866 | + | 0.355358i | ||||
\(699\) | −34.7827 | −1.31560 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.0000 | 0.604312 | 0.302156 | − | 0.953259i | \(-0.402294\pi\) | ||||
0.302156 | + | 0.953259i | \(0.402294\pi\) | |||||||
\(702\) | −2.88083 | − | 3.63196i | −0.108730 | − | 0.137080i | ||||
\(703\) | −10.3398 | + | 17.9091i | −0.389973 | + | 0.675454i | ||||
\(704\) | −29.6453 | + | 11.0994i | −1.11730 | + | 0.418326i | ||||
\(705\) | 20.7556 | − | 11.9832i | 0.781700 | − | 0.451315i | ||||
\(706\) | −14.0716 | + | 2.08319i | −0.529591 | + | 0.0784021i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 46.0208 | − | 13.9314i | 1.72957 | − | 0.523575i | ||||
\(709\) | 23.3137 | + | 40.3805i | 0.875565 | + | 1.51652i | 0.856160 | + | 0.516711i | \(0.172844\pi\) |
0.0194047 | + | 0.999812i | \(0.493823\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.8682 | − | 6.27476i | −0.407589 | − | 0.235322i | ||||
\(712\) | 13.9266 | + | 9.65645i | 0.521920 | + | 0.361891i | ||||
\(713\) | 14.0392i | 0.525774i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.1917i | 0.418547i | ||||||||
\(716\) | −18.4815 | + | 19.7098i | −0.690684 | + | 0.736588i | ||||
\(717\) | −18.9750 | − | 10.9552i | −0.708635 | − | 0.409131i | ||||
\(718\) | −16.2577 | + | 41.1063i | −0.606730 | + | 1.53407i | ||||
\(719\) | 16.7641 | + | 29.0364i | 0.625197 | + | 1.08287i | 0.988503 | + | 0.151203i | \(0.0483148\pi\) |
−0.363306 | + | 0.931670i | \(0.618352\pi\) | |||||||
\(720\) | −9.19299 | − | 13.7925i | −0.342603 | − | 0.514017i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.60051 | + | 10.8111i | 0.0595646 | + | 0.402348i | ||||
\(723\) | 9.44879 | − | 5.45526i | 0.351404 | − | 0.202883i | ||||
\(724\) | 42.8203 | + | 10.0102i | 1.59140 | + | 0.372027i | ||||
\(725\) | −6.24264 | + | 10.8126i | −0.231846 | + | 0.401569i | ||||
\(726\) | 11.0493 | − | 8.76417i | 0.410077 | − | 0.325269i | ||||
\(727\) | 29.9802 | 1.11191 | 0.555953 | − | 0.831214i | \(-0.312354\pi\) | ||||
0.555953 | + | 0.831214i | \(0.312354\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.62742 | 0.0602747 | ||||||||
\(730\) | 40.5827 | − | 32.1897i | 1.50203 | − | 1.19140i | ||||
\(731\) | 1.14682 | − | 1.98634i | 0.0424165 | − | 0.0734676i | ||||
\(732\) | 22.5703 | + | 5.27632i | 0.834223 | + | 0.195018i | ||||
\(733\) | 17.7160 | − | 10.2283i | 0.654355 | − | 0.377792i | −0.135768 | − | 0.990741i | \(-0.543350\pi\) |
0.790123 | + | 0.612949i | \(0.210017\pi\) | |||||||
\(734\) | 2.66105 | + | 17.9749i | 0.0982210 | + | 0.663464i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.72792 | − | 8.79148i | 0.358576 | − | 0.324058i | ||||
\(737\) | −6.48528 | − | 11.2328i | −0.238888 | − | 0.413767i | ||||
\(738\) | 1.89383 | − | 4.78842i | 0.0697130 | − | 0.176264i | ||||
\(739\) | 10.7673 | + | 6.21652i | 0.396082 | + | 0.228678i | 0.684792 | − | 0.728738i | \(-0.259893\pi\) |
−0.288710 | + | 0.957417i | \(0.593226\pi\) | |||||||
\(740\) | −14.2993 | + | 15.2496i | −0.525651 | + | 0.560587i | ||||
\(741\) | − | 11.9832i | − | 0.440215i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 45.1646i | − | 1.65693i | −0.560042 | − | 0.828464i | \(-0.689215\pi\) | ||
0.560042 | − | 0.828464i | \(-0.310785\pi\) | |||||||
\(744\) | −20.9041 | + | 30.1480i | −0.766383 | + | 1.10528i | ||||
\(745\) | 10.9269 | + | 6.30864i | 0.400330 | + | 0.231131i | ||||
\(746\) | 26.4888 | + | 10.4764i | 0.969824 | + | 0.383568i | ||||
\(747\) | −7.49506 | − | 12.9818i | −0.274230 | − | 0.474980i | ||||
\(748\) | 2.40125 | − | 0.726905i | 0.0877982 | − | 0.0265783i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −24.8284 | + | 3.67567i | −0.906606 | + | 0.134216i | ||||
\(751\) | −32.2602 | + | 18.6254i | −1.17719 | + | 0.679652i | −0.955363 | − | 0.295434i | \(-0.904536\pi\) |
−0.221828 | + | 0.975086i | \(0.571202\pi\) | |||||||
\(752\) | 1.10083 | + | 17.0962i | 0.0401433 | + | 0.623433i | ||||
\(753\) | −4.19239 | + | 7.26143i | −0.152779 | + | 0.264621i | ||||
\(754\) | 6.49556 | + | 8.18917i | 0.236554 | + | 0.298232i | ||||
\(755\) | −55.9819 | −2.03739 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.2843 | −1.60954 | −0.804770 | − | 0.593587i | \(-0.797711\pi\) | ||||
−0.804770 | + | 0.593587i | \(0.797711\pi\) | |||||||
\(758\) | −19.0749 | − | 24.0484i | −0.692832 | − | 0.873476i | ||||
\(759\) | −9.82021 | + | 17.0091i | −0.356451 | + | 0.617391i | ||||
\(760\) | −3.15542 | + | 38.0804i | −0.114459 | + | 1.38132i | ||||
\(761\) | −0.0471057 | + | 0.0271965i | −0.00170758 | + | 0.000985871i | −0.500854 | − | 0.865532i | \(-0.666980\pi\) |
0.499146 | + | 0.866518i | \(0.333647\pi\) | |||||||
\(762\) | −30.6520 | + | 4.53781i | −1.11041 | + | 0.164387i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.79899 | + | 12.5495i | 0.137443 | + | 0.454026i | ||||
\(765\) | 0.656854 | + | 1.13770i | 0.0237486 | + | 0.0411338i | ||||
\(766\) | −40.7935 | − | 16.1339i | −1.47393 | − | 0.582943i | ||||
\(767\) | 10.5238 | + | 6.07591i | 0.379992 | + | 0.219389i | ||||
\(768\) | 33.9802 | − | 4.39424i | 1.22615 | − | 0.158563i | ||||
\(769\) | − | 19.1342i | − | 0.689996i | −0.938603 | − | 0.344998i | \(-0.887880\pi\) | ||
0.938603 | − | 0.344998i | \(-0.112120\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 40.8100i | − | 1.46974i | ||||||
\(772\) | 21.2798 | + | 19.9537i | 0.765878 | + | 0.718149i | ||||
\(773\) | 42.8644 | + | 24.7478i | 1.54173 | + | 0.890116i | 0.998730 | + | 0.0503797i | \(0.0160432\pi\) |
0.542995 | + | 0.839736i | \(0.317290\pi\) | |||||||
\(774\) | −5.96734 | + | 15.0880i | −0.214492 | + | 0.542327i | ||||
\(775\) | −5.53732 | − | 9.59092i | −0.198906 | − | 0.344516i | ||||
\(776\) | −23.6320 | + | 11.1522i | −0.848339 | + | 0.400341i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.92893 | + | 19.7844i | 0.105007 | + | 0.709304i | ||||
\(779\) | −10.2803 | + | 5.93531i | −0.368329 | + | 0.212655i | ||||
\(780\) | 2.75754 | − | 11.7958i | 0.0987356 | − | 0.422358i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −0.814180 | + | 0.645798i | −0.0291150 | + | 0.0230937i | ||||
\(783\) | −20.6796 | −0.739029 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −50.1421 | −1.78965 | ||||||||
\(786\) | −0.871760 | + | 0.691471i | −0.0310947 | + | 0.0246639i | ||||
\(787\) | −20.6035 | + | 35.6864i | −0.734436 | + | 1.27208i | 0.220534 | + | 0.975379i | \(0.429220\pi\) |
−0.954970 | + | 0.296702i | \(0.904113\pi\) | |||||||
\(788\) | 0.910541 | − | 3.89499i | 0.0324367 | − | 0.138753i | ||||
\(789\) | 47.5903 | − | 27.4763i | 1.69426 | − | 0.978182i | ||||
\(790\) | 4.28289 | + | 28.9301i | 0.152378 | + | 1.02929i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −16.0503 | + | 7.57430i | −0.570321 | + | 0.269141i | ||||
\(793\) | 2.92893 | + | 5.07306i | 0.104009 | + | 0.180150i | ||||
\(794\) | −8.38808 | + | 21.2086i | −0.297682 | + | 0.752667i | ||||
\(795\) | −50.8134 | − | 29.3371i | −1.80216 | − | 1.04048i | ||||
\(796\) | −24.9940 | − | 23.4364i | −0.885888 | − | 0.830680i | ||||
\(797\) | − | 20.1940i | − | 0.715309i | −0.933854 | − | 0.357655i | \(-0.883576\pi\) | ||
0.933854 | − | 0.357655i | \(-0.116424\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.35778i | − | 0.0480350i | ||||||
\(800\) | −3.17813 | + | 9.84277i | −0.112364 | + | 0.347995i | ||||
\(801\) | 8.22848 | + | 4.75071i | 0.290739 | + | 0.167858i | ||||
\(802\) | 16.8706 | + | 6.67237i | 0.595721 | + | 0.235609i | ||||
\(803\) | −27.7312 | − | 48.0318i | −0.978612 | − | 1.69501i | ||||
\(804\) | 4.06766 | + | 13.4370i | 0.143455 | + | 0.473888i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.17157 | + | 1.35778i | −0.323055 | + | 0.0478259i | ||||
\(807\) | −9.34792 | + | 5.39702i | −0.329062 | + | 0.189984i | ||||
\(808\) | 3.55735 | − | 42.9310i | 0.125147 | − | 1.51031i | ||||
\(809\) | 0.0208153 | − | 0.0360531i | 0.000731826 | − | 0.00126756i | −0.865659 | − | 0.500634i | \(-0.833100\pi\) |
0.866391 | + | 0.499366i | \(0.166434\pi\) | |||||||
\(810\) | 25.8190 | + | 32.5509i | 0.907188 | + | 1.14372i | ||||
\(811\) | 39.4330 | 1.38468 | 0.692340 | − | 0.721571i | \(-0.256580\pi\) | ||||
0.692340 | + | 0.721571i | \(0.256580\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.17157 | −0.321661 | ||||||||
\(814\) | 13.9099 | + | 17.5367i | 0.487541 | + | 0.614660i | ||||
\(815\) | −19.7926 | + | 34.2818i | −0.693305 | + | 1.20084i | ||||
\(816\) | −2.70996 | + | 0.174496i | −0.0948675 | + | 0.00610859i | ||||
\(817\) | 32.3924 | − | 18.7018i | 1.13327 | − | 0.654292i | ||||
\(818\) | 19.3491 | − | 2.86449i | 0.676525 | − | 0.100155i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.4853 | + | 3.47682i | −0.401083 | + | 0.121416i | ||||
\(821\) | 9.00000 | + | 15.5885i | 0.314102 | + | 0.544041i | 0.979246 | − | 0.202674i | \(-0.0649632\pi\) |
−0.665144 | + | 0.746715i | \(0.731630\pi\) | |||||||
\(822\) | −23.2129 | − | 9.18078i | −0.809644 | − | 0.320217i | ||||
\(823\) | 14.8829 | + | 8.59264i | 0.518785 | + | 0.299521i | 0.736437 | − | 0.676506i | \(-0.236507\pi\) |
−0.217652 | + | 0.976026i | \(0.569840\pi\) | |||||||
\(824\) | −19.5234 | + | 28.1567i | −0.680130 | + | 0.980884i | ||||
\(825\) | − | 15.4930i | − | 0.539399i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 45.1646i | − | 1.57053i | −0.619162 | − | 0.785264i | \(-0.712527\pi\) | ||
0.619162 | − | 0.785264i | \(-0.287473\pi\) | |||||||
\(828\) | 5.02840 | − | 5.36259i | 0.174749 | − | 0.186363i | ||||
\(829\) | −40.8954 | − | 23.6110i | −1.42036 | − | 0.820044i | −0.424028 | − | 0.905649i | \(-0.639384\pi\) |
−0.996329 | + | 0.0856056i | \(0.972717\pi\) | |||||||
\(830\) | −12.8477 | + | 32.4846i | −0.445952 | + | 1.12756i | ||||
\(831\) | −4.43508 | − | 7.68178i | −0.153851 | − | 0.266478i | ||||
\(832\) | 6.68414 | + | 5.50482i | 0.231731 | + | 0.190845i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.1213 | + | 68.3676i | 0.350473 | + | 2.36738i | ||||
\(835\) | −17.7217 | + | 10.2316i | −0.613285 | + | 0.354080i | ||||
\(836\) | 39.8392 | + | 9.31331i | 1.37787 | + | 0.322108i | ||||
\(837\) | 9.17157 | − | 15.8856i | 0.317016 | − | 0.549088i | ||||
\(838\) | −19.1502 | + | 15.1897i | −0.661532 | + | 0.524719i | ||||
\(839\) | 42.3984 | 1.46376 | 0.731878 | − | 0.681435i | \(-0.238644\pi\) | ||||
0.731878 | + | 0.681435i | \(0.238644\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.6274 | 0.607842 | ||||||||
\(842\) | −11.6176 | + | 9.21492i | −0.400367 | + | 0.317567i | ||||
\(843\) | 11.1192 | − | 19.2590i | 0.382966 | − | 0.663317i | ||||
\(844\) | 28.1797 | + | 6.58763i | 0.969984 | + | 0.226756i | ||||
\(845\) | −26.7681 | + | 15.4546i | −0.920852 | + | 0.531654i | ||||
\(846\) | 1.40662 | + | 9.50143i | 0.0483605 | + | 0.326666i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 34.8995 | − | 23.2612i | 1.19845 | − | 0.798793i | ||||
\(849\) | 3.63604 | + | 6.29780i | 0.124789 | + | 0.216140i | ||||
\(850\) | 0.301494 | − | 0.762304i | 0.0103411 | − | 0.0261468i | ||||
\(851\) | −8.02938 | − | 4.63577i | −0.275244 | − | 0.158912i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.3002i | 1.31137i | 0.755033 | + | 0.655687i | \(0.227621\pi\) | ||||
−0.755033 | + | 0.655687i | \(0.772379\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.4234i | 0.732664i | ||||||||
\(856\) | 5.38755 | + | 3.73564i | 0.184143 | + | 0.127682i | ||||
\(857\) | 2.99248 | + | 1.72771i | 0.102221 | + | 0.0590174i | 0.550239 | − | 0.835007i | \(-0.314537\pi\) |
−0.448018 | + | 0.894025i | \(0.647870\pi\) | |||||||
\(858\) | −12.0615 | − | 4.77035i | −0.411772 | − | 0.162857i | ||||
\(859\) | −1.33052 | − | 2.30453i | −0.0453969 | − | 0.0786297i | 0.842434 | − | 0.538799i | \(-0.181122\pi\) |
−0.887831 | + | 0.460170i | \(0.847789\pi\) | |||||||
\(860\) | 36.1893 | − | 10.9552i | 1.23405 | − | 0.373571i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.34315 | − | 0.198843i | 0.0457477 | − | 0.00677262i | ||||
\(863\) | −10.8682 | + | 6.27476i | −0.369958 | + | 0.213595i | −0.673440 | − | 0.739242i | \(-0.735184\pi\) |
0.303482 | + | 0.952837i | \(0.401851\pi\) | |||||||
\(864\) | −16.7506 | + | 3.59264i | −0.569868 | + | 0.122224i | ||||
\(865\) | 8.58579 | − | 14.8710i | 0.291925 | − | 0.505630i | ||||
\(866\) | 23.0131 | + | 29.0134i | 0.782016 | + | 0.985914i | ||||
\(867\) | −36.1893 | −1.22905 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.3137 | 1.06224 | ||||||||
\(870\) | −33.5814 | − | 42.3372i | −1.13852 | − | 1.43537i | ||||
\(871\) | −1.77403 | + | 3.07271i | −0.0601107 | + | 0.104115i | ||||
\(872\) | −15.9454 | − | 1.32126i | −0.539978 | − | 0.0447437i | ||||
\(873\) | −12.6879 | + | 7.32538i | −0.429421 | + | 0.247926i | ||||
\(874\) | −16.7641 | + | 2.48181i | −0.567056 | + | 0.0839485i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 17.3934 | + | 57.4570i | 0.587668 | + | 1.94129i | ||||
\(877\) | −15.2132 | − | 26.3500i | −0.513713 | − | 0.889778i | −0.999873 | − | 0.0159079i | \(-0.994936\pi\) |
0.486160 | − | 0.873870i | \(-0.338397\pi\) | |||||||
\(878\) | 29.5287 | + | 11.6787i | 0.996544 | + | 0.394136i | ||||
\(879\) | −21.8791 | − | 12.6319i | −0.737962 | − | 0.426063i | ||||
\(880\) | 37.0730 | + | 18.3353i | 1.24973 | + | 0.618083i | ||||
\(881\) | 26.1857i | 0.882217i | 0.897454 | + | 0.441109i | \(0.145415\pi\) | ||||
−0.897454 | + | 0.441109i | \(0.854585\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.7013i | 0.831266i | 0.909532 | + | 0.415633i | \(0.136440\pi\) | ||||
−0.909532 | + | 0.415633i | \(0.863560\pi\) | |||||||
\(884\) | −0.500630 | − | 0.469431i | −0.0168380 | − | 0.0157887i | ||||
\(885\) | −54.4070 | − | 31.4119i | −1.82887 | − | 1.05590i | ||||
\(886\) | 14.7595 | − | 37.3184i | 0.495857 | − | 1.25374i | ||||
\(887\) | 11.2268 | + | 19.4454i | 0.376960 | + | 0.652914i | 0.990618 | − | 0.136658i | \(-0.0436361\pi\) |
−0.613658 | + | 0.789572i | \(0.710303\pi\) | |||||||
\(888\) | −10.3398 | − | 21.9105i | −0.346981 | − | 0.735267i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.24264 | − | 21.9034i | −0.108694 | − | 0.734204i | ||||
\(891\) | 38.5258 | − | 22.2429i | 1.29066 | − | 0.745164i | ||||
\(892\) | 3.56520 | − | 15.2507i | 0.119372 | − | 0.510632i | ||||
\(893\) | 11.0711 | − | 19.1757i | 0.370479 | − | 0.641689i | ||||
\(894\) | −11.4564 | + | 9.08707i | −0.383159 | + | 0.303917i | ||||
\(895\) | 35.3023 | 1.18003 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.37258 | 0.179385 | ||||||||
\(898\) | −18.0428 | + | 14.3113i | −0.602095 | + | 0.477575i | ||||
\(899\) | −20.6796 | + | 35.8182i | −0.689704 | + | 1.19460i | ||||
\(900\) | −1.32005 | + | 5.64675i | −0.0440018 | + | 0.188225i | ||||
\(901\) | −2.87875 | + | 1.66205i | −0.0959052 | + | 0.0553709i | ||||
\(902\) | 1.88164 | + | 12.7101i | 0.0626519 | + | 0.423201i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.12132 | + | 10.8523i | 0.170333 | + | 0.360942i | ||||
\(905\) | −28.7279 | − | 49.7582i | −0.954948 | − | 1.65402i | ||||
\(906\) | 23.8617 | − | 60.3325i | 0.792751 | − | 2.00441i | ||||
\(907\) | −29.4214 | − | 16.9864i | −0.976921 | − | 0.564025i | −0.0755817 | − | 0.997140i | \(-0.524081\pi\) |
−0.901339 | + | 0.433114i | \(0.857415\pi\) | |||||||
\(908\) | −14.5492 | − | 13.6425i | −0.482831 | − | 0.452741i | ||||
\(909\) | − | 24.1522i | − | 0.801077i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 18.7078i | − | 0.619817i | −0.950766 | − | 0.309908i | \(-0.899702\pi\) | ||
0.950766 | − | 0.309908i | \(-0.100298\pi\) | |||||||
\(912\) | −39.6948 | − | 19.6320i | −1.31443 | − | 0.650081i | ||||
\(913\) | 32.3924 | + | 18.7018i | 1.07203 | + | 0.618938i | ||||
\(914\) | −0.957286 | − | 0.378609i | −0.0316642 | − | 0.0125233i | ||||
\(915\) | −15.1423 | − | 26.2272i | −0.500589 | − | 0.867046i | ||||
\(916\) | −0.779403 | − | 2.57466i | −0.0257522 | − | 0.0850693i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.34315 | − | 0.198843i | 0.0443304 | − | 0.00656280i | ||||
\(919\) | 42.2969 | − | 24.4201i | 1.39525 | − | 0.805546i | 0.401357 | − | 0.915922i | \(-0.368539\pi\) |
0.993890 | + | 0.110376i | \(0.0352054\pi\) | |||||||
\(920\) | −17.0730 | − | 1.41471i | −0.562882 | − | 0.0466415i | ||||
\(921\) | −4.19239 | + | 7.26143i | −0.138144 | + | 0.239272i | ||||
\(922\) | −26.1454 | − | 32.9625i | −0.861054 | − | 1.08556i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.31371 | 0.240473 | ||||||||
\(926\) | 30.7006 | + | 38.7053i | 1.00888 | + | 1.27193i | ||||
\(927\) | −9.60498 | + | 16.6363i | −0.315469 | + | 0.546408i | ||||
\(928\) | 37.7685 | − | 8.10051i | 1.23981 | − | 0.265912i | ||||
\(929\) | −25.8779 | + | 14.9406i | −0.849025 | + | 0.490185i | −0.860322 | − | 0.509751i | \(-0.829737\pi\) |
0.0112969 | + | 0.999936i | \(0.496404\pi\) | |||||||
\(930\) | 47.4162 | − | 7.01962i | 1.55484 | − | 0.230182i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −31.0919 | + | 9.41214i | −1.01845 | + | 0.308305i | ||||
\(933\) | 22.1421 | + | 38.3513i | 0.724901 | + | 1.25557i | ||||
\(934\) | 31.6615 | + | 12.5222i | 1.03600 | + | 0.409740i | ||||
\(935\) | −2.83882 | − | 1.63899i | −0.0928392 | − | 0.0536007i | ||||
\(936\) | 3.98960 | + | 2.76632i | 0.130404 | + | 0.0904201i | ||||
\(937\) | 29.8042i | 0.973662i | 0.873496 | + | 0.486831i | \(0.161847\pi\) | ||||
−0.873496 | + | 0.486831i | \(0.838153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.3004i | 0.890916i | ||||||||
\(940\) | 15.3105 | − | 16.3281i | 0.499375 | − | 0.532564i | ||||
\(941\) | 21.4655 | + | 12.3931i | 0.699756 | + | 0.404004i | 0.807256 | − | 0.590201i | \(-0.200951\pi\) |
−0.107501 | + | 0.994205i | \(0.534285\pi\) | |||||||
\(942\) | 21.3725 | − | 54.0389i | 0.696354 | − | 1.76068i | ||||
\(943\) | −2.66105 | − | 4.60907i | −0.0866556 | − | 0.150092i | ||||
\(944\) | 37.3677 | − | 24.9063i | 1.21621 | − | 0.810631i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.92893 | − | 40.0488i | −0.192766 | − | 1.30210i | ||||
\(947\) | 7.92851 | − | 4.57753i | 0.257642 | − | 0.148750i | −0.365616 | − | 0.930766i | \(-0.619142\pi\) |
0.623258 | + | 0.782016i | \(0.285808\pi\) | |||||||
\(948\) | −33.0039 | − | 7.71540i | −1.07192 | − | 0.250585i | ||||
\(949\) | −7.58579 | + | 13.1390i | −0.246245 | + | 0.426509i | ||||
\(950\) | 10.4736 | − | 8.30752i | 0.339808 | − | 0.269532i | ||||
\(951\) | 11.8095 | 0.382948 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.3431 | 0.853338 | 0.426669 | − | 0.904408i | \(-0.359687\pi\) | ||||
0.426669 | + | 0.904408i | \(0.359687\pi\) | |||||||
\(954\) | 18.4230 | − | 14.6129i | 0.596465 | − | 0.473110i | ||||
\(955\) | 8.56578 | − | 14.8364i | 0.277182 | − | 0.480094i | ||||
\(956\) | −19.9260 | − | 4.65816i | −0.644454 | − | 0.150656i | ||||
\(957\) | −50.1084 | + | 28.9301i | −1.61977 | + | 0.935177i | ||||
\(958\) | −6.79175 | − | 45.8770i | −0.219431 | − | 1.48222i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −34.5563 | − | 28.4594i | −1.11530 | − | 0.918522i | ||||
\(961\) | −2.84315 | − | 4.92447i | −0.0917144 | − | 0.158854i | ||||
\(962\) | 2.25191 | − | 5.69379i | 0.0726045 | − | 0.183575i | ||||
\(963\) | 3.18322 | + | 1.83783i | 0.102578 | + | 0.0592234i | ||||
\(964\) | 6.96998 | − | 7.43322i | 0.224488 | − | 0.239408i | ||||
\(965\) | − | 38.1145i | − | 1.22695i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 45.1646i | − | 1.45240i | −0.687486 | − | 0.726198i | \(-0.741286\pi\) | ||
0.687486 | − | 0.726198i | \(-0.258714\pi\) | |||||||
\(968\) | 7.50527 | − | 10.8241i | 0.241228 | − | 0.347900i | ||||
\(969\) | 3.03958 | + | 1.75490i | 0.0976455 | + | 0.0563757i | ||||
\(970\) | 31.7492 | + | 12.5569i | 1.01940 | + | 0.403177i | ||||
\(971\) | 6.50043 | + | 11.2591i | 0.208609 | + | 0.361321i | 0.951276 | − | 0.308339i | \(-0.0997732\pi\) |
−0.742668 | + | 0.669660i | \(0.766440\pi\) | |||||||
\(972\) | −28.6943 | + | 8.68633i | −0.920369 | + | 0.278614i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −27.2843 | + | 4.03924i | −0.874244 | + | 0.129426i | ||||
\(975\) | −3.67029 | + | 2.11904i | −0.117543 | + | 0.0678636i | ||||
\(976\) | 21.6031 | − | 1.39104i | 0.691499 | − | 0.0445261i | ||||
\(977\) | −8.80761 | + | 15.2552i | −0.281780 | + | 0.488058i | −0.971823 | − | 0.235710i | \(-0.924258\pi\) |
0.690043 | + | 0.723768i | \(0.257592\pi\) | |||||||
\(978\) | −28.5096 | − | 35.9430i | −0.911636 | − | 1.14933i | ||||
\(979\) | −23.7081 | −0.757714 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.97056 | −0.286408 | ||||||||
\(982\) | −12.7166 | − | 16.0323i | −0.405803 | − | 0.511610i | ||||
\(983\) | −4.80249 | + | 8.31816i | −0.153176 | + | 0.265308i | −0.932393 | − | 0.361445i | \(-0.882283\pi\) |
0.779218 | + | 0.626754i | \(0.215617\pi\) | |||||||
\(984\) | 1.14845 | − | 13.8598i | 0.0366113 | − | 0.441834i | ||||
\(985\) | −4.52607 | + | 2.61313i | −0.144212 | + | 0.0832611i | ||||
\(986\) | −3.02846 | + | 0.448342i | −0.0964458 | + | 0.0142781i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.24264 | − | 10.7117i | −0.103162 | − | 0.340784i | ||||
\(989\) | 8.38478 | + | 14.5229i | 0.266620 | + | 0.461800i | ||||
\(990\) | 21.5632 | + | 8.52832i | 0.685325 | + | 0.271048i | ||||
\(991\) | 22.2235 | + | 12.8307i | 0.705952 | + | 0.407581i | 0.809560 | − | 0.587037i | \(-0.199706\pi\) |
−0.103609 | + | 0.994618i | \(0.533039\pi\) | |||||||
\(992\) | −10.5280 | + | 32.6056i | −0.334264 | + | 1.03523i | ||||
\(993\) | − | 32.4399i | − | 1.02945i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 44.7669i | 1.41921i | ||||||||
\(996\) | −29.5329 | − | 27.6924i | −0.935785 | − | 0.877467i | ||||
\(997\) | −26.7681 | − | 15.4546i | −0.847755 | − | 0.489452i | 0.0121377 | − | 0.999926i | \(-0.496136\pi\) |
−0.859893 | + | 0.510475i | \(0.829470\pi\) | |||||||
\(998\) | −6.52730 | + | 16.5038i | −0.206618 | + | 0.522418i | ||||
\(999\) | 6.05692 | + | 10.4909i | 0.191632 | + | 0.331917i |
(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 | 196.2.f.d.31.6 | 16 | ||
4.3 | odd | 2 | inner | 196.2.f.d.31.1 | 16 | ||
7.2 | even | 3 | inner | 196.2.f.d.19.2 | 16 | ||
7.3 | odd | 6 | 196.2.d.c.195.8 | yes | 8 | ||
7.4 | even | 3 | 196.2.d.c.195.7 | yes | 8 | ||
7.5 | odd | 6 | inner | 196.2.f.d.19.1 | 16 | ||
7.6 | odd | 2 | inner | 196.2.f.d.31.5 | 16 | ||
21.11 | odd | 6 | 1764.2.b.k.1567.2 | 8 | |||
21.17 | even | 6 | 1764.2.b.k.1567.1 | 8 | |||
28.3 | even | 6 | 196.2.d.c.195.5 | ✓ | 8 | ||
28.11 | odd | 6 | 196.2.d.c.195.6 | yes | 8 | ||
28.19 | even | 6 | inner | 196.2.f.d.19.6 | 16 | ||
28.23 | odd | 6 | inner | 196.2.f.d.19.5 | 16 | ||
28.27 | even | 2 | inner | 196.2.f.d.31.2 | 16 | ||
56.3 | even | 6 | 3136.2.f.i.3135.5 | 8 | |||
56.11 | odd | 6 | 3136.2.f.i.3135.4 | 8 | |||
56.45 | odd | 6 | 3136.2.f.i.3135.3 | 8 | |||
56.53 | even | 6 | 3136.2.f.i.3135.6 | 8 | |||
84.11 | even | 6 | 1764.2.b.k.1567.4 | 8 | |||
84.59 | odd | 6 | 1764.2.b.k.1567.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
196.2.d.c.195.5 | ✓ | 8 | 28.3 | even | 6 | ||
196.2.d.c.195.6 | yes | 8 | 28.11 | odd | 6 | ||
196.2.d.c.195.7 | yes | 8 | 7.4 | even | 3 | ||
196.2.d.c.195.8 | yes | 8 | 7.3 | odd | 6 | ||
196.2.f.d.19.1 | 16 | 7.5 | odd | 6 | inner | ||
196.2.f.d.19.2 | 16 | 7.2 | even | 3 | inner | ||
196.2.f.d.19.5 | 16 | 28.23 | odd | 6 | inner | ||
196.2.f.d.19.6 | 16 | 28.19 | even | 6 | inner | ||
196.2.f.d.31.1 | 16 | 4.3 | odd | 2 | inner | ||
196.2.f.d.31.2 | 16 | 28.27 | even | 2 | inner | ||
196.2.f.d.31.5 | 16 | 7.6 | odd | 2 | inner | ||
196.2.f.d.31.6 | 16 | 1.1 | even | 1 | trivial | ||
1764.2.b.k.1567.1 | 8 | 21.17 | even | 6 | |||
1764.2.b.k.1567.2 | 8 | 21.11 | odd | 6 | |||
1764.2.b.k.1567.3 | 8 | 84.59 | odd | 6 | |||
1764.2.b.k.1567.4 | 8 | 84.11 | even | 6 | |||
3136.2.f.i.3135.3 | 8 | 56.45 | odd | 6 | |||
3136.2.f.i.3135.4 | 8 | 56.11 | odd | 6 | |||
3136.2.f.i.3135.5 | 8 | 56.3 | even | 6 | |||
3136.2.f.i.3135.6 | 8 | 56.53 | even | 6 |