Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [93,2,Mod(92,93)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(93, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("93.92");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 93 = 3 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 93.c (of order \(2\), degree \(1\), 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: | \(0.742608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.16845963264.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 6x^{6} + 15x^{4} + 8x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 92.5 | ||
Root | \(1.95007 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 93.92 |
Dual form | 93.2.c.a.92.3 |
$q$-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 \(\left(\mathbb{Z}/93\mathbb{Z}\right)^\times\).
\(n\) | \(32\) | \(34\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.835000i | 0.590434i | 0.955430 | + | 0.295217i | \(0.0953919\pi\) | ||||
−0.955430 | + | 0.295217i | \(0.904608\pi\) | |||||||
\(3\) | −0.590434 | − | 1.62831i | −0.340887 | − | 0.940104i | ||||
\(4\) | 1.30278 | 0.651388 | ||||||||
\(5\) | − | 2.75782i | − | 1.23333i | −0.787225 | − | 0.616666i | \(-0.788483\pi\) | ||
0.787225 | − | 0.616666i | \(-0.211517\pi\) | |||||||
\(6\) | 1.35964 | − | 0.493012i | 0.555069 | − | 0.201271i | ||||
\(7\) | −1.00000 | −0.377964 | −0.188982 | − | 0.981981i | \(-0.560519\pi\) | ||||
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 2.75782i | 0.975035i | ||||||||
\(9\) | −2.30278 | + | 1.92282i | −0.767592 | + | 0.640939i | ||||
\(10\) | 2.30278 | 0.728202 | ||||||||
\(11\) | 5.08101 | 1.53198 | 0.765991 | − | 0.642851i | \(-0.222249\pi\) | ||||
0.765991 | + | 0.642851i | \(0.222249\pi\) | |||||||
\(12\) | −0.769203 | − | 2.12132i | −0.222050 | − | 0.612372i | ||||
\(13\) | 4.24264i | 1.17670i | 0.808608 | + | 0.588348i | \(0.200222\pi\) | ||||
−0.808608 | + | 0.588348i | \(0.799778\pi\) | |||||||
\(14\) | − | 0.835000i | − | 0.223163i | ||||||
\(15\) | −4.49058 | + | 1.62831i | −1.15946 | + | 0.420427i | ||||
\(16\) | 0.302776 | 0.0756939 | ||||||||
\(17\) | −6.61941 | −1.60544 | −0.802722 | − | 0.596353i | \(-0.796616\pi\) | ||||
−0.802722 | + | 0.596353i | \(0.796616\pi\) | |||||||
\(18\) | −1.60555 | − | 1.92282i | −0.378432 | − | 0.453212i | ||||
\(19\) | −3.60555 | −0.827170 | −0.413585 | − | 0.910465i | \(-0.635724\pi\) | ||||
−0.413585 | + | 0.910465i | \(0.635724\pi\) | |||||||
\(20\) | − | 3.59282i | − | 0.803378i | ||||||
\(21\) | 0.590434 | + | 1.62831i | 0.128843 | + | 0.355326i | ||||
\(22\) | 4.24264i | 0.904534i | ||||||||
\(23\) | 1.53841 | 0.320780 | 0.160390 | − | 0.987054i | \(-0.448725\pi\) | ||||
0.160390 | + | 0.987054i | \(0.448725\pi\) | |||||||
\(24\) | 4.49058 | − | 1.62831i | 0.916635 | − | 0.332377i | ||||
\(25\) | −2.60555 | −0.521110 | ||||||||
\(26\) | −3.54260 | −0.694762 | ||||||||
\(27\) | 4.49058 | + | 2.61433i | 0.864212 | + | 0.503129i | ||||
\(28\) | −1.30278 | −0.246201 | ||||||||
\(29\) | −1.53841 | −0.285675 | −0.142837 | − | 0.989746i | \(-0.545623\pi\) | ||||
−0.142837 | + | 0.989746i | \(0.545623\pi\) | |||||||
\(30\) | −1.35964 | − | 3.74963i | −0.248235 | − | 0.684585i | ||||
\(31\) | 3.60555 | − | 4.24264i | 0.647576 | − | 0.762001i | ||||
\(32\) | 5.76845i | 1.01973i | ||||||||
\(33\) | −3.00000 | − | 8.27345i | −0.522233 | − | 1.44022i | ||||
\(34\) | − | 5.52721i | − | 0.947909i | ||||||
\(35\) | 2.75782i | 0.466156i | ||||||||
\(36\) | −3.00000 | + | 2.50500i | −0.500000 | + | 0.417500i | ||||
\(37\) | 5.52721i | 0.908668i | 0.890832 | + | 0.454334i | \(0.150123\pi\) | ||||
−0.890832 | + | 0.454334i | \(0.849877\pi\) | |||||||
\(38\) | − | 3.01063i | − | 0.488389i | ||||||
\(39\) | 6.90833 | − | 2.50500i | 1.10622 | − | 0.401121i | ||||
\(40\) | 7.60555 | 1.20254 | ||||||||
\(41\) | 6.60345i | 1.03129i | 0.856804 | + | 0.515643i | \(0.172447\pi\) | ||||
−0.856804 | + | 0.515643i | \(0.827553\pi\) | |||||||
\(42\) | −1.35964 | + | 0.493012i | −0.209797 | + | 0.0760734i | ||||
\(43\) | − | 4.24264i | − | 0.646997i | −0.946229 | − | 0.323498i | \(-0.895141\pi\) | ||
0.946229 | − | 0.323498i | \(-0.104859\pi\) | |||||||
\(44\) | 6.61941 | 0.997914 | ||||||||
\(45\) | 5.30278 | + | 6.35063i | 0.790491 | + | 0.946696i | ||||
\(46\) | 1.28457i | 0.189399i | ||||||||
\(47\) | − | 3.84563i | − | 0.560943i | −0.959862 | − | 0.280472i | \(-0.909509\pi\) | ||
0.959862 | − | 0.280472i | \(-0.0904909\pi\) | |||||||
\(48\) | −0.178769 | − | 0.493012i | −0.0258031 | − | 0.0711602i | ||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | − | 2.17563i | − | 0.307681i | ||||||
\(51\) | 3.90833 | + | 10.7784i | 0.547275 | + | 1.50928i | ||||
\(52\) | 5.52721i | 0.766486i | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | −2.18297 | + | 3.74963i | −0.297064 | + | 0.510260i | ||||
\(55\) | − | 14.0125i | − | 1.88944i | ||||||
\(56\) | − | 2.75782i | − | 0.368529i | ||||||
\(57\) | 2.12884 | + | 5.87095i | 0.281972 | + | 0.777626i | ||||
\(58\) | − | 1.28457i | − | 0.168672i | ||||||
\(59\) | − | 2.75782i | − | 0.359037i | −0.983755 | − | 0.179519i | \(-0.942546\pi\) | ||
0.983755 | − | 0.179519i | \(-0.0574540\pi\) | |||||||
\(60\) | −5.85021 | + | 2.12132i | −0.755259 | + | 0.273861i | ||||
\(61\) | − | 9.76985i | − | 1.25090i | −0.780264 | − | 0.625451i | \(-0.784915\pi\) | ||
0.780264 | − | 0.625451i | \(-0.215085\pi\) | |||||||
\(62\) | 3.54260 | + | 3.01063i | 0.449911 | + | 0.382351i | ||||
\(63\) | 2.30278 | − | 1.92282i | 0.290122 | − | 0.242252i | ||||
\(64\) | −4.21110 | −0.526388 | ||||||||
\(65\) | 11.7004 | 1.45126 | ||||||||
\(66\) | 6.90833 | − | 2.50500i | 0.850356 | − | 0.308344i | ||||
\(67\) | −0.605551 | −0.0739799 | −0.0369899 | − | 0.999316i | \(-0.511777\pi\) | ||||
−0.0369899 | + | 0.999316i | \(0.511777\pi\) | |||||||
\(68\) | −8.62361 | −1.04577 | ||||||||
\(69\) | −0.908327 | − | 2.50500i | −0.109350 | − | 0.301566i | ||||
\(70\) | −2.30278 | −0.275234 | ||||||||
\(71\) | − | 4.93345i | − | 0.585493i | −0.956190 | − | 0.292746i | \(-0.905431\pi\) | ||
0.956190 | − | 0.292746i | \(-0.0945692\pi\) | |||||||
\(72\) | −5.30278 | − | 6.35063i | −0.624938 | − | 0.748429i | ||||
\(73\) | − | 5.52721i | − | 0.646911i | −0.946243 | − | 0.323455i | \(-0.895155\pi\) | ||
0.946243 | − | 0.323455i | \(-0.104845\pi\) | |||||||
\(74\) | −4.61522 | −0.536508 | ||||||||
\(75\) | 1.53841 | + | 4.24264i | 0.177640 | + | 0.489898i | ||||
\(76\) | −4.69722 | −0.538809 | ||||||||
\(77\) | −5.08101 | −0.579035 | ||||||||
\(78\) | 2.09167 | + | 5.76845i | 0.236835 | + | 0.653148i | ||||
\(79\) | 1.28457i | 0.144525i | 0.997386 | + | 0.0722626i | \(0.0230220\pi\) | ||||
−0.997386 | + | 0.0722626i | \(0.976978\pi\) | |||||||
\(80\) | − | 0.835000i | − | 0.0933558i | ||||||
\(81\) | 1.60555 | − | 8.85563i | 0.178395 | − | 0.983959i | ||||
\(82\) | −5.51388 | −0.608906 | ||||||||
\(83\) | −10.1620 | −1.11543 | −0.557713 | − | 0.830034i | \(-0.688321\pi\) | ||||
−0.557713 | + | 0.830034i | \(0.688321\pi\) | |||||||
\(84\) | 0.769203 | + | 2.12132i | 0.0839269 | + | 0.231455i | ||||
\(85\) | 18.2551i | 1.98005i | ||||||||
\(86\) | 3.54260 | 0.382009 | ||||||||
\(87\) | 0.908327 | + | 2.50500i | 0.0973829 | + | 0.268564i | ||||
\(88\) | 14.0125i | 1.49374i | ||||||||
\(89\) | 6.61941 | 0.701657 | 0.350828 | − | 0.936440i | \(-0.385900\pi\) | ||||
0.350828 | + | 0.936440i | \(0.385900\pi\) | |||||||
\(90\) | −5.30278 | + | 4.42782i | −0.558962 | + | 0.466733i | ||||
\(91\) | − | 4.24264i | − | 0.444750i | ||||||
\(92\) | 2.00420 | 0.208952 | ||||||||
\(93\) | −9.03717 | − | 3.36595i | −0.937111 | − | 0.349033i | ||||
\(94\) | 3.21110 | 0.331200 | ||||||||
\(95\) | 9.94345i | 1.02018i | ||||||||
\(96\) | 9.39282 | − | 3.40589i | 0.958650 | − | 0.347612i | ||||
\(97\) | −8.81665 | −0.895196 | −0.447598 | − | 0.894235i | \(-0.647720\pi\) | ||||
−0.447598 | + | 0.894235i | \(0.647720\pi\) | |||||||
\(98\) | − | 5.01000i | − | 0.506086i | ||||||
\(99\) | −11.7004 | + | 9.76985i | −1.17594 | + | 0.981907i | ||||
\(100\) | −3.39445 | −0.339445 | ||||||||
\(101\) | 11.6134i | 1.15558i | 0.816185 | + | 0.577791i | \(0.196085\pi\) | ||||
−0.816185 | + | 0.577791i | \(0.803915\pi\) | |||||||
\(102\) | −9.00000 | + | 3.26345i | −0.891133 | + | 0.323130i | ||||
\(103\) | 16.2111 | 1.59733 | 0.798664 | − | 0.601778i | \(-0.205541\pi\) | ||||
0.798664 | + | 0.601778i | \(0.205541\pi\) | |||||||
\(104\) | −11.7004 | −1.14732 | ||||||||
\(105\) | 4.49058 | − | 1.62831i | 0.438235 | − | 0.158907i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 7.76781i | − | 0.750943i | −0.926834 | − | 0.375471i | \(-0.877481\pi\) | ||
0.926834 | − | 0.375471i | \(-0.122519\pi\) | |||||||
\(108\) | 5.85021 | + | 3.40589i | 0.562937 | + | 0.327732i | ||||
\(109\) | −7.00000 | −0.670478 | −0.335239 | − | 0.942133i | \(-0.608817\pi\) | ||||
−0.335239 | + | 0.942133i | \(0.608817\pi\) | |||||||
\(110\) | 11.7004 | 1.11559 | ||||||||
\(111\) | 9.00000 | − | 3.26345i | 0.854242 | − | 0.309753i | ||||
\(112\) | −0.302776 | −0.0286096 | ||||||||
\(113\) | − | 14.9534i | − | 1.40670i | −0.710843 | − | 0.703351i | \(-0.751686\pi\) | ||
0.710843 | − | 0.703351i | \(-0.248314\pi\) | |||||||
\(114\) | −4.90224 | + | 1.77758i | −0.459137 | + | 0.166486i | ||||
\(115\) | − | 4.24264i | − | 0.395628i | ||||||
\(116\) | −2.00420 | −0.186085 | ||||||||
\(117\) | −8.15782 | − | 9.76985i | −0.754191 | − | 0.903223i | ||||
\(118\) | 2.30278 | 0.211988 | ||||||||
\(119\) | 6.61941 | 0.606801 | ||||||||
\(120\) | −4.49058 | − | 12.3842i | −0.409932 | − | 1.13052i | ||||
\(121\) | 14.8167 | 1.34697 | ||||||||
\(122\) | 8.15782 | 0.738574 | ||||||||
\(123\) | 10.7525 | − | 3.89890i | 0.969516 | − | 0.351552i | ||||
\(124\) | 4.69722 | − | 5.52721i | 0.421823 | − | 0.496358i | ||||
\(125\) | − | 6.60345i | − | 0.590631i | ||||||
\(126\) | 1.60555 | + | 1.92282i | 0.143034 | + | 0.171298i | ||||
\(127\) | − | 5.52721i | − | 0.490460i | −0.969465 | − | 0.245230i | \(-0.921136\pi\) | ||
0.969465 | − | 0.245230i | \(-0.0788636\pi\) | |||||||
\(128\) | 8.02063i | 0.708930i | ||||||||
\(129\) | −6.90833 | + | 2.50500i | −0.608244 | + | 0.220553i | ||||
\(130\) | 9.76985i | 0.856872i | ||||||||
\(131\) | 12.7013i | 1.10971i | 0.831946 | + | 0.554857i | \(0.187227\pi\) | ||||
−0.831946 | + | 0.554857i | \(0.812773\pi\) | |||||||
\(132\) | −3.90833 | − | 10.7784i | −0.340176 | − | 0.938143i | ||||
\(133\) | 3.60555 | 0.312641 | ||||||||
\(134\) | − | 0.505635i | − | 0.0436802i | ||||||
\(135\) | 7.20985 | − | 12.3842i | 0.620525 | − | 1.06586i | ||||
\(136\) | − | 18.2551i | − | 1.56536i | ||||||
\(137\) | −18.7856 | −1.60496 | −0.802482 | − | 0.596676i | \(-0.796488\pi\) | ||||
−0.802482 | + | 0.596676i | \(0.796488\pi\) | |||||||
\(138\) | 2.09167 | − | 0.758453i | 0.178055 | − | 0.0645638i | ||||
\(139\) | 22.4978i | 1.90824i | 0.299431 | + | 0.954118i | \(0.403203\pi\) | ||||
−0.299431 | + | 0.954118i | \(0.596797\pi\) | |||||||
\(140\) | 3.59282i | 0.303648i | ||||||||
\(141\) | −6.26188 | + | 2.27059i | −0.527345 | + | 0.191218i | ||||
\(142\) | 4.11943 | 0.345695 | ||||||||
\(143\) | 21.5569i | 1.80268i | ||||||||
\(144\) | −0.697224 | + | 0.582182i | −0.0581020 | + | 0.0485152i | ||||
\(145\) | 4.24264i | 0.352332i | ||||||||
\(146\) | 4.61522 | 0.381958 | ||||||||
\(147\) | 3.54260 | + | 9.76985i | 0.292189 | + | 0.805804i | ||||
\(148\) | 7.20071i | 0.591895i | ||||||||
\(149\) | − | 8.85563i | − | 0.725482i | −0.931890 | − | 0.362741i | \(-0.881841\pi\) | ||
0.931890 | − | 0.362741i | \(-0.118159\pi\) | |||||||
\(150\) | −3.54260 | + | 1.28457i | −0.289252 | + | 0.104885i | ||||
\(151\) | − | 4.24264i | − | 0.345261i | −0.984987 | − | 0.172631i | \(-0.944773\pi\) | ||
0.984987 | − | 0.172631i | \(-0.0552267\pi\) | |||||||
\(152\) | − | 9.94345i | − | 0.806520i | ||||||
\(153\) | 15.2430 | − | 12.7279i | 1.23233 | − | 1.02899i | ||||
\(154\) | − | 4.24264i | − | 0.341882i | ||||||
\(155\) | −11.7004 | − | 9.94345i | −0.939801 | − | 0.798677i | ||||
\(156\) | 9.00000 | − | 3.26345i | 0.720577 | − | 0.261285i | ||||
\(157\) | 16.2111 | 1.29379 | 0.646893 | − | 0.762580i | \(-0.276068\pi\) | ||||
0.646893 | + | 0.762580i | \(0.276068\pi\) | |||||||
\(158\) | −1.07261 | −0.0853326 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 15.9083 | 1.25766 | ||||||||
\(161\) | −1.53841 | −0.121243 | ||||||||
\(162\) | 7.39445 | + | 1.34063i | 0.580963 | + | 0.105330i | ||||
\(163\) | −7.00000 | −0.548282 | −0.274141 | − | 0.961689i | \(-0.588394\pi\) | ||||
−0.274141 | + | 0.961689i | \(0.588394\pi\) | |||||||
\(164\) | 8.60281i | 0.671767i | ||||||||
\(165\) | −22.8167 | + | 8.27345i | −1.77627 | + | 0.644087i | ||||
\(166\) | − | 8.48528i | − | 0.658586i | ||||||
\(167\) | 8.15782 | 0.631271 | 0.315636 | − | 0.948880i | \(-0.397782\pi\) | ||||
0.315636 | + | 0.948880i | \(0.397782\pi\) | |||||||
\(168\) | −4.49058 | + | 1.62831i | −0.346455 | + | 0.125627i | ||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | −15.2430 | −1.16909 | ||||||||
\(171\) | 8.30278 | − | 6.93281i | 0.634929 | − | 0.530166i | ||||
\(172\) | − | 5.52721i | − | 0.421446i | ||||||
\(173\) | 2.68127i | 0.203853i | 0.994792 | + | 0.101927i | \(0.0325007\pi\) | ||||
−0.994792 | + | 0.101927i | \(0.967499\pi\) | |||||||
\(174\) | −2.09167 | + | 0.758453i | −0.158569 | + | 0.0574981i | ||||
\(175\) | 2.60555 | 0.196961 | ||||||||
\(176\) | 1.53841 | 0.115962 | ||||||||
\(177\) | −4.49058 | + | 1.62831i | −0.337532 | + | 0.122391i | ||||
\(178\) | 5.52721i | 0.414282i | ||||||||
\(179\) | 10.6278 | 0.794360 | 0.397180 | − | 0.917741i | \(-0.369989\pi\) | ||||
0.397180 | + | 0.917741i | \(0.369989\pi\) | |||||||
\(180\) | 6.90833 | + | 8.27345i | 0.514916 | + | 0.616666i | ||||
\(181\) | 18.2551i | 1.35689i | 0.734650 | + | 0.678447i | \(0.237347\pi\) | ||||
−0.734650 | + | 0.678447i | \(0.762653\pi\) | |||||||
\(182\) | 3.54260 | 0.262595 | ||||||||
\(183\) | −15.9083 | + | 5.76845i | −1.17598 | + | 0.426416i | ||||
\(184\) | 4.24264i | 0.312772i | ||||||||
\(185\) | 15.2430 | 1.12069 | ||||||||
\(186\) | 2.81057 | − | 7.54603i | 0.206081 | − | 0.553302i | ||||
\(187\) | −33.6333 | −2.45951 | ||||||||
\(188\) | − | 5.01000i | − | 0.365392i | ||||||
\(189\) | −4.49058 | − | 2.61433i | −0.326641 | − | 0.190165i | ||||
\(190\) | −8.30278 | −0.602347 | ||||||||
\(191\) | 8.77908i | 0.635232i | 0.948219 | + | 0.317616i | \(0.102882\pi\) | ||||
−0.948219 | + | 0.317616i | \(0.897118\pi\) | |||||||
\(192\) | 2.48638 | + | 6.85697i | 0.179439 | + | 0.494859i | ||||
\(193\) | −1.78890 | −0.128768 | −0.0643838 | − | 0.997925i | \(-0.520508\pi\) | ||||
−0.0643838 | + | 0.997925i | \(0.520508\pi\) | |||||||
\(194\) | − | 7.36190i | − | 0.528554i | ||||||
\(195\) | −6.90833 | − | 19.0519i | −0.494716 | − | 1.36433i | ||||
\(196\) | −7.81665 | −0.558332 | ||||||||
\(197\) | 15.2430 | 1.08602 | 0.543010 | − | 0.839726i | \(-0.317284\pi\) | ||||
0.543010 | + | 0.839726i | \(0.317284\pi\) | |||||||
\(198\) | −8.15782 | − | 9.76985i | −0.579751 | − | 0.694313i | ||||
\(199\) | 5.52721i | 0.391813i | 0.980623 | + | 0.195907i | \(0.0627650\pi\) | ||||
−0.980623 | + | 0.195907i | \(0.937235\pi\) | |||||||
\(200\) | − | 7.18563i | − | 0.508101i | ||||||
\(201\) | 0.357538 | + | 0.986024i | 0.0252188 | + | 0.0695488i | ||||
\(202\) | −9.69722 | −0.682294 | ||||||||
\(203\) | 1.53841 | 0.107975 | ||||||||
\(204\) | 5.09167 | + | 14.0419i | 0.356488 | + | 0.983130i | ||||
\(205\) | 18.2111 | 1.27192 | ||||||||
\(206\) | 13.5363i | 0.943116i | ||||||||
\(207\) | −3.54260 | + | 2.95807i | −0.246228 | + | 0.205600i | ||||
\(208\) | 1.28457i | 0.0890688i | ||||||||
\(209\) | −18.3198 | −1.26721 | ||||||||
\(210\) | 1.35964 | + | 3.74963i | 0.0938239 | + | 0.258749i | ||||
\(211\) | −2.81665 | −0.193906 | −0.0969532 | − | 0.995289i | \(-0.530910\pi\) | ||||
−0.0969532 | + | 0.995289i | \(0.530910\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.03318 | + | 2.91288i | −0.550424 | + | 0.199587i | ||||
\(214\) | 6.48612 | 0.443382 | ||||||||
\(215\) | −11.7004 | −0.797962 | ||||||||
\(216\) | −7.20985 | + | 12.3842i | −0.490568 | + | 0.842637i | ||||
\(217\) | −3.60555 | + | 4.24264i | −0.244761 | + | 0.288009i | ||||
\(218\) | − | 5.84500i | − | 0.395873i | ||||||
\(219\) | −9.00000 | + | 3.26345i | −0.608164 | + | 0.220524i | ||||
\(220\) | − | 18.2551i | − | 1.23076i | ||||||
\(221\) | − | 28.0838i | − | 1.88912i | ||||||
\(222\) | 2.72498 | + | 7.51500i | 0.182889 | + | 0.504374i | ||||
\(223\) | 14.0125i | 0.938346i | 0.883106 | + | 0.469173i | \(0.155448\pi\) | ||||
−0.883106 | + | 0.469173i | \(0.844552\pi\) | |||||||
\(224\) | − | 5.76845i | − | 0.385421i | ||||||
\(225\) | 6.00000 | − | 5.01000i | 0.400000 | − | 0.334000i | ||||
\(226\) | 12.4861 | 0.830564 | ||||||||
\(227\) | − | 25.4025i | − | 1.68603i | −0.537894 | − | 0.843013i | \(-0.680780\pi\) | ||
0.537894 | − | 0.843013i | \(-0.319220\pi\) | |||||||
\(228\) | 2.77340 | + | 7.64853i | 0.183673 | + | 0.506536i | ||||
\(229\) | 11.4434i | 0.756198i | 0.925765 | + | 0.378099i | \(0.123422\pi\) | ||||
−0.925765 | + | 0.378099i | \(0.876578\pi\) | |||||||
\(230\) | 3.54260 | 0.233592 | ||||||||
\(231\) | 3.00000 | + | 8.27345i | 0.197386 | + | 0.544353i | ||||
\(232\) | − | 4.24264i | − | 0.278543i | ||||||
\(233\) | 7.26218i | 0.475761i | 0.971294 | + | 0.237881i | \(0.0764527\pi\) | ||||
−0.971294 | + | 0.237881i | \(0.923547\pi\) | |||||||
\(234\) | 8.15782 | − | 6.81178i | 0.533293 | − | 0.445300i | ||||
\(235\) | −10.6056 | −0.691830 | ||||||||
\(236\) | − | 3.59282i | − | 0.233872i | ||||||
\(237\) | 2.09167 | − | 0.758453i | 0.135869 | − | 0.0492668i | ||||
\(238\) | 5.52721i | 0.358276i | ||||||||
\(239\) | −9.69623 | −0.627197 | −0.313598 | − | 0.949556i | \(-0.601535\pi\) | ||||
−0.313598 | + | 0.949556i | \(0.601535\pi\) | |||||||
\(240\) | −1.35964 | + | 0.493012i | −0.0877642 | + | 0.0318238i | ||||
\(241\) | − | 22.4978i | − | 1.44921i | −0.689165 | − | 0.724604i | \(-0.742022\pi\) | ||
0.689165 | − | 0.724604i | \(-0.257978\pi\) | |||||||
\(242\) | 12.3719i | 0.795296i | ||||||||
\(243\) | −15.3677 | + | 2.61433i | −0.985836 | + | 0.167710i | ||||
\(244\) | − | 12.7279i | − | 0.814822i | ||||||
\(245\) | 16.5469i | 1.05714i | ||||||||
\(246\) | 3.25558 | + | 8.97829i | 0.207568 | + | 0.572435i | ||||
\(247\) | − | 15.2971i | − | 0.973329i | ||||||
\(248\) | 11.7004 | + | 9.94345i | 0.742978 | + | 0.631410i | ||||
\(249\) | 6.00000 | + | 16.5469i | 0.380235 | + | 1.04862i | ||||
\(250\) | 5.51388 | 0.348728 | ||||||||
\(251\) | −21.8624 | −1.37995 | −0.689973 | − | 0.723836i | \(-0.742377\pi\) | ||||
−0.689973 | + | 0.723836i | \(0.742377\pi\) | |||||||
\(252\) | 3.00000 | − | 2.50500i | 0.188982 | − | 0.157800i | ||||
\(253\) | 7.81665 | 0.491429 | ||||||||
\(254\) | 4.61522 | 0.289584 | ||||||||
\(255\) | 29.7250 | − | 10.7784i | 1.86145 | − | 0.674973i | ||||
\(256\) | −15.1194 | −0.944964 | ||||||||
\(257\) | 18.7991i | 1.17265i | 0.810074 | + | 0.586327i | \(0.199427\pi\) | ||||
−0.810074 | + | 0.586327i | \(0.800573\pi\) | |||||||
\(258\) | −2.09167 | − | 5.76845i | −0.130222 | − | 0.359128i | ||||
\(259\) | − | 5.52721i | − | 0.343444i | ||||||
\(260\) | 15.2430 | 0.945332 | ||||||||
\(261\) | 3.54260 | − | 2.95807i | 0.219282 | − | 0.183100i | ||||
\(262\) | −10.6056 | −0.655213 | ||||||||
\(263\) | 22.9351 | 1.41424 | 0.707118 | − | 0.707095i | \(-0.249995\pi\) | ||||
0.707118 | + | 0.707095i | \(0.249995\pi\) | |||||||
\(264\) | 22.8167 | − | 8.27345i | 1.40427 | − | 0.509196i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.01063i | 0.184594i | ||||||||
\(267\) | −3.90833 | − | 10.7784i | −0.239186 | − | 0.659630i | ||||
\(268\) | −0.788897 | −0.0481896 | ||||||||
\(269\) | 28.4819 | 1.73657 | 0.868285 | − | 0.496066i | \(-0.165223\pi\) | ||||
0.868285 | + | 0.496066i | \(0.165223\pi\) | |||||||
\(270\) | 10.3408 | + | 6.02022i | 0.629320 | + | 0.366379i | ||||
\(271\) | − | 7.20071i | − | 0.437412i | −0.975791 | − | 0.218706i | \(-0.929816\pi\) | ||
0.975791 | − | 0.218706i | \(-0.0701836\pi\) | |||||||
\(272\) | −2.00420 | −0.121522 | ||||||||
\(273\) | −6.90833 | + | 2.50500i | −0.418111 | + | 0.151609i | ||||
\(274\) | − | 15.6860i | − | 0.947626i | ||||||
\(275\) | −13.2388 | −0.798331 | ||||||||
\(276\) | −1.18335 | − | 3.26345i | −0.0712291 | − | 0.196437i | ||||
\(277\) | − | 9.76985i | − | 0.587013i | −0.955957 | − | 0.293507i | \(-0.905178\pi\) | ||
0.955957 | − | 0.293507i | \(-0.0948223\pi\) | |||||||
\(278\) | −18.7856 | −1.12669 | ||||||||
\(279\) | −0.144955 | + | 16.7027i | −0.00867823 | + | 0.999962i | ||||
\(280\) | −7.60555 | −0.454519 | ||||||||
\(281\) | 2.25218i | 0.134354i | 0.997741 | + | 0.0671769i | \(0.0213992\pi\) | ||||
−0.997741 | + | 0.0671769i | \(0.978601\pi\) | |||||||
\(282\) | −1.89594 | − | 5.22866i | −0.112902 | − | 0.311362i | ||||
\(283\) | 3.81665 | 0.226877 | 0.113438 | − | 0.993545i | \(-0.463814\pi\) | ||||
0.113438 | + | 0.993545i | \(0.463814\pi\) | |||||||
\(284\) | − | 6.42718i | − | 0.381383i | ||||||
\(285\) | 16.1910 | − | 5.87095i | 0.959072 | − | 0.347765i | ||||
\(286\) | −18.0000 | −1.06436 | ||||||||
\(287\) | − | 6.60345i | − | 0.389789i | ||||||
\(288\) | −11.0917 | − | 13.2834i | −0.653583 | − | 0.782735i | ||||
\(289\) | 26.8167 | 1.57745 | ||||||||
\(290\) | −3.54260 | −0.208029 | ||||||||
\(291\) | 5.20565 | + | 14.3562i | 0.305161 | + | 0.841577i | ||||
\(292\) | − | 7.20071i | − | 0.421390i | ||||||
\(293\) | 12.7013i | 0.742016i | 0.928630 | + | 0.371008i | \(0.120988\pi\) | ||||
−0.928630 | + | 0.371008i | \(0.879012\pi\) | |||||||
\(294\) | −8.15782 | + | 2.95807i | −0.475774 | + | 0.172518i | ||||
\(295\) | −7.60555 | −0.442812 | ||||||||
\(296\) | −15.2430 | −0.885983 | ||||||||
\(297\) | 22.8167 | + | 13.2834i | 1.32396 | + | 0.770784i | ||||
\(298\) | 7.39445 | 0.428349 | ||||||||
\(299\) | 6.52690i | 0.377461i | ||||||||
\(300\) | 2.00420 | + | 5.52721i | 0.115712 | + | 0.319114i | ||||
\(301\) | 4.24264i | 0.244542i | ||||||||
\(302\) | 3.54260 | 0.203854 | ||||||||
\(303\) | 18.9103 | − | 6.85697i | 1.08637 | − | 0.393923i | ||||
\(304\) | −1.09167 | −0.0626117 | ||||||||
\(305\) | −26.9435 | −1.54278 | ||||||||
\(306\) | 10.6278 | + | 12.7279i | 0.607551 | + | 0.727607i | ||||
\(307\) | 14.3944 | 0.821535 | 0.410767 | − | 0.911740i | \(-0.365261\pi\) | ||||
0.410767 | + | 0.911740i | \(0.365261\pi\) | |||||||
\(308\) | −6.61941 | −0.377176 | ||||||||
\(309\) | −9.57158 | − | 26.3967i | −0.544508 | − | 1.50165i | ||||
\(310\) | 8.30278 | − | 9.76985i | 0.471566 | − | 0.554890i | ||||
\(311\) | − | 21.4803i | − | 1.21804i | −0.793155 | − | 0.609019i | \(-0.791563\pi\) | ||
0.793155 | − | 0.609019i | \(-0.208437\pi\) | |||||||
\(312\) | 6.90833 | + | 19.0519i | 0.391107 | + | 1.07860i | ||||
\(313\) | 12.3390i | 0.697441i | 0.937227 | + | 0.348720i | \(0.113384\pi\) | ||||
−0.937227 | + | 0.348720i | \(0.886616\pi\) | |||||||
\(314\) | 13.5363i | 0.763896i | ||||||||
\(315\) | −5.30278 | − | 6.35063i | −0.298778 | − | 0.357818i | ||||
\(316\) | 1.67350i | 0.0941420i | ||||||||
\(317\) | 11.6134i | 0.652276i | 0.945322 | + | 0.326138i | \(0.105747\pi\) | ||||
−0.945322 | + | 0.326138i | \(0.894253\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.81665 | −0.437649 | ||||||||
\(320\) | 11.6134i | 0.649211i | ||||||||
\(321\) | −12.6484 | + | 4.58638i | −0.705965 | + | 0.255987i | ||||
\(322\) | − | 1.28457i | − | 0.0715862i | ||||||
\(323\) | 23.8666 | 1.32798 | ||||||||
\(324\) | 2.09167 | − | 11.5369i | 0.116204 | − | 0.640939i | ||||
\(325\) | − | 11.0544i | − | 0.613189i | ||||||
\(326\) | − | 5.84500i | − | 0.323724i | ||||||
\(327\) | 4.13304 | + | 11.3982i | 0.228557 | + | 0.630320i | ||||
\(328\) | −18.2111 | −1.00554 | ||||||||
\(329\) | 3.84563i | 0.212017i | ||||||||
\(330\) | −6.90833 | − | 19.0519i | −0.380291 | − | 1.04877i | ||||
\(331\) | − | 2.56914i | − | 0.141213i | −0.997504 | − | 0.0706063i | \(-0.977507\pi\) | ||
0.997504 | − | 0.0706063i | \(-0.0224934\pi\) | |||||||
\(332\) | −13.2388 | −0.726575 | ||||||||
\(333\) | −10.6278 | − | 12.7279i | −0.582400 | − | 0.697486i | ||||
\(334\) | 6.81178i | 0.372724i | ||||||||
\(335\) | 1.67000i | 0.0912418i | ||||||||
\(336\) | 0.178769 | + | 0.493012i | 0.00975265 | + | 0.0268960i | ||||
\(337\) | 20.8243i | 1.13437i | 0.823590 | + | 0.567185i | \(0.191968\pi\) | ||||
−0.823590 | + | 0.567185i | \(0.808032\pi\) | |||||||
\(338\) | − | 4.17500i | − | 0.227090i | ||||||
\(339\) | −24.3488 | + | 8.82902i | −1.32245 | + | 0.479527i | ||||
\(340\) | 23.7823i | 1.28978i | ||||||||
\(341\) | 18.3198 | − | 21.5569i | 0.992075 | − | 1.16737i | ||||
\(342\) | 5.78890 | + | 6.93281i | 0.313028 | + | 0.374884i | ||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 11.7004 | 0.630845 | ||||||||
\(345\) | −6.90833 | + | 2.50500i | −0.371932 | + | 0.134865i | ||||
\(346\) | −2.23886 | −0.120362 | ||||||||
\(347\) | 1.53841 | 0.0825859 | 0.0412930 | − | 0.999147i | \(-0.486852\pi\) | ||||
0.0412930 | + | 0.999147i | \(0.486852\pi\) | |||||||
\(348\) | 1.18335 | + | 3.26345i | 0.0634340 | + | 0.174939i | ||||
\(349\) | 1.21110 | 0.0648288 | 0.0324144 | − | 0.999475i | \(-0.489680\pi\) | ||||
0.0324144 | + | 0.999475i | \(0.489680\pi\) | |||||||
\(350\) | 2.17563i | 0.116293i | ||||||||
\(351\) | −11.0917 | + | 19.0519i | −0.592030 | + | 1.01692i | ||||
\(352\) | 29.3095i | 1.56220i | ||||||||
\(353\) | 1.07261 | 0.0570895 | 0.0285447 | − | 0.999593i | \(-0.490913\pi\) | ||||
0.0285447 | + | 0.999593i | \(0.490913\pi\) | |||||||
\(354\) | −1.35964 | − | 3.74963i | −0.0722639 | − | 0.199291i | ||||
\(355\) | −13.6056 | −0.722108 | ||||||||
\(356\) | 8.62361 | 0.457051 | ||||||||
\(357\) | −3.90833 | − | 10.7784i | −0.206851 | − | 0.570456i | ||||
\(358\) | 8.87422i | 0.469017i | ||||||||
\(359\) | − | 26.4903i | − | 1.39811i | −0.715069 | − | 0.699054i | \(-0.753605\pi\) | ||
0.715069 | − | 0.699054i | \(-0.246395\pi\) | |||||||
\(360\) | −17.5139 | + | 14.6241i | −0.923062 | + | 0.770757i | ||||
\(361\) | −6.00000 | −0.315789 | ||||||||
\(362\) | −15.2430 | −0.801156 | ||||||||
\(363\) | −8.74825 | − | 24.1261i | −0.459164 | − | 1.26629i | ||||
\(364\) | − | 5.52721i | − | 0.289704i | ||||||
\(365\) | −15.2430 | −0.797857 | ||||||||
\(366\) | −4.81665 | − | 13.2834i | −0.251771 | − | 0.694337i | ||||
\(367\) | − | 28.0250i | − | 1.46289i | −0.681899 | − | 0.731446i | \(-0.738846\pi\) | ||
0.681899 | − | 0.731446i | \(-0.261154\pi\) | |||||||
\(368\) | 0.465792 | 0.0242811 | ||||||||
\(369\) | −12.6972 | − | 15.2063i | −0.660991 | − | 0.791606i | ||||
\(370\) | 12.7279i | 0.661693i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −11.7734 | − | 4.38508i | −0.610422 | − | 0.227356i | ||||
\(373\) | 20.6333 | 1.06835 | 0.534176 | − | 0.845373i | \(-0.320622\pi\) | ||||
0.534176 | + | 0.845373i | \(0.320622\pi\) | |||||||
\(374\) | − | 28.0838i | − | 1.45218i | ||||||
\(375\) | −10.7525 | + | 3.89890i | −0.555254 | + | 0.201338i | ||||
\(376\) | 10.6056 | 0.546940 | ||||||||
\(377\) | − | 6.52690i | − | 0.336153i | ||||||
\(378\) | 2.18297 | − | 3.74963i | 0.112280 | − | 0.192860i | ||||
\(379\) | −31.6333 | −1.62489 | −0.812447 | − | 0.583035i | \(-0.801865\pi\) | ||||
−0.812447 | + | 0.583035i | \(0.801865\pi\) | |||||||
\(380\) | 12.9541i | 0.664530i | ||||||||
\(381\) | −9.00000 | + | 3.26345i | −0.461084 | + | 0.167192i | ||||
\(382\) | −7.33053 | −0.375063 | ||||||||
\(383\) | −3.07681 | −0.157218 | −0.0786089 | − | 0.996906i | \(-0.525048\pi\) | ||||
−0.0786089 | + | 0.996906i | \(0.525048\pi\) | |||||||
\(384\) | 13.0601 | − | 4.73565i | 0.666468 | − | 0.241665i | ||||
\(385\) | 14.0125i | 0.714143i | ||||||||
\(386\) | − | 1.49373i | − | 0.0760288i | ||||||
\(387\) | 8.15782 | + | 9.76985i | 0.414685 | + | 0.496629i | ||||
\(388\) | −11.4861 | −0.583119 | ||||||||
\(389\) | 5.08101 | 0.257617 | 0.128809 | − | 0.991669i | \(-0.458885\pi\) | ||||
0.128809 | + | 0.991669i | \(0.458885\pi\) | |||||||
\(390\) | 15.9083 | − | 5.76845i | 0.805549 | − | 0.292097i | ||||
\(391\) | −10.1833 | −0.514994 | ||||||||
\(392\) | − | 16.5469i | − | 0.835745i | ||||||
\(393\) | 20.6816 | − | 7.49926i | 1.04325 | − | 0.378287i | ||||
\(394\) | 12.7279i | 0.641223i | ||||||||
\(395\) | 3.54260 | 0.178248 | ||||||||
\(396\) | −15.2430 | + | 12.7279i | −0.765991 | + | 0.639602i | ||||
\(397\) | 34.4500 | 1.72899 | 0.864497 | − | 0.502638i | \(-0.167637\pi\) | ||||
0.864497 | + | 0.502638i | \(0.167637\pi\) | |||||||
\(398\) | −4.61522 | −0.231340 | ||||||||
\(399\) | −2.12884 | − | 5.87095i | −0.106575 | − | 0.293915i | ||||
\(400\) | −0.788897 | −0.0394449 | ||||||||
\(401\) | 18.7856 | 0.938110 | 0.469055 | − | 0.883169i | \(-0.344595\pi\) | ||||
0.469055 | + | 0.883169i | \(0.344595\pi\) | |||||||
\(402\) | −0.823330 | + | 0.298544i | −0.0410640 | + | 0.0148900i | ||||
\(403\) | 18.0000 | + | 15.2971i | 0.896644 | + | 0.762001i | ||||
\(404\) | 15.1297i | 0.752732i | ||||||||
\(405\) | −24.4222 | − | 4.42782i | −1.21355 | − | 0.220020i | ||||
\(406\) | 1.28457i | 0.0637521i | ||||||||
\(407\) | 28.0838i | 1.39206i | ||||||||
\(408\) | −29.7250 | + | 10.7784i | −1.47161 | + | 0.533613i | ||||
\(409\) | − | 32.2676i | − | 1.59553i | −0.602968 | − | 0.797766i | \(-0.706015\pi\) | ||
0.602968 | − | 0.797766i | \(-0.293985\pi\) | |||||||
\(410\) | 15.2063i | 0.750984i | ||||||||
\(411\) | 11.0917 | + | 30.5888i | 0.547112 | + | 1.50883i | ||||
\(412\) | 21.1194 | 1.04048 | ||||||||
\(413\) | 2.75782i | 0.135703i | ||||||||
\(414\) | −2.46999 | − | 2.95807i | −0.121393 | − | 0.145381i | ||||
\(415\) | 28.0250i | 1.37569i | ||||||||
\(416\) | −24.4735 | −1.19991 | ||||||||
\(417\) | 36.6333 | − | 13.2834i | 1.79394 | − | 0.650493i | ||||
\(418\) | − | 15.2971i | − | 0.748204i | ||||||
\(419\) | 34.6872i | 1.69458i | 0.531128 | + | 0.847292i | \(0.321768\pi\) | ||||
−0.531128 | + | 0.847292i | \(0.678232\pi\) | |||||||
\(420\) | 5.85021 | − | 2.12132i | 0.285461 | − | 0.103510i | ||||
\(421\) | −23.4222 | −1.14153 | −0.570764 | − | 0.821114i | \(-0.693353\pi\) | ||||
−0.570764 | + | 0.821114i | \(0.693353\pi\) | |||||||
\(422\) | − | 2.35190i | − | 0.114489i | ||||||
\(423\) | 7.39445 | + | 8.85563i | 0.359530 | + | 0.430576i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.2472 | 0.836613 | ||||||||
\(426\) | −2.43225 | − | 6.70770i | −0.117843 | − | 0.324989i | ||||
\(427\) | 9.76985i | 0.472796i | ||||||||
\(428\) | − | 10.1197i | − | 0.489155i | ||||||
\(429\) | 35.1013 | − | 12.7279i | 1.69471 | − | 0.614510i | ||||
\(430\) | − | 9.76985i | − | 0.471144i | ||||||
\(431\) | 1.16436i | 0.0560854i | 0.999607 | + | 0.0280427i | \(0.00892745\pi\) | ||||
−0.999607 | + | 0.0280427i | \(0.991073\pi\) | |||||||
\(432\) | 1.35964 | + | 0.791556i | 0.0654156 | + | 0.0380838i | ||||
\(433\) | 7.20071i | 0.346044i | 0.984918 | + | 0.173022i | \(0.0553532\pi\) | ||||
−0.984918 | + | 0.173022i | \(0.944647\pi\) | |||||||
\(434\) | −3.54260 | − | 3.01063i | −0.170050 | − | 0.144515i | ||||
\(435\) | 6.90833 | − | 2.50500i | 0.331229 | − | 0.120106i | ||||
\(436\) | −9.11943 | −0.436741 | ||||||||
\(437\) | −5.54680 | −0.265339 | ||||||||
\(438\) | −2.72498 | − | 7.51500i | −0.130205 | − | 0.359080i | ||||
\(439\) | 18.0278 | 0.860418 | 0.430209 | − | 0.902729i | \(-0.358440\pi\) | ||||
0.430209 | + | 0.902729i | \(0.358440\pi\) | |||||||
\(440\) | 38.6439 | 1.84227 | ||||||||
\(441\) | 13.8167 | − | 11.5369i | 0.657936 | − | 0.549376i | ||||
\(442\) | 23.4500 | 1.11540 | ||||||||
\(443\) | 2.25218i | 0.107004i | 0.998568 | + | 0.0535022i | \(0.0170384\pi\) | ||||
−0.998568 | + | 0.0535022i | \(0.982962\pi\) | |||||||
\(444\) | 11.7250 | − | 4.25155i | 0.556443 | − | 0.201769i | ||||
\(445\) | − | 18.2551i | − | 0.865376i | ||||||
\(446\) | −11.7004 | −0.554031 | ||||||||
\(447\) | −14.4197 | + | 5.22866i | −0.682028 | + | 0.247307i | ||||
\(448\) | 4.21110 | 0.198956 | ||||||||
\(449\) | 2.00420 | 0.0945839 | 0.0472920 | − | 0.998881i | \(-0.484941\pi\) | ||||
0.0472920 | + | 0.998881i | \(0.484941\pi\) | |||||||
\(450\) | 4.18335 | + | 5.01000i | 0.197205 | + | 0.236174i | ||||
\(451\) | 33.5522i | 1.57991i | ||||||||
\(452\) | − | 19.4810i | − | 0.916308i | ||||||
\(453\) | −6.90833 | + | 2.50500i | −0.324582 | + | 0.117695i | ||||
\(454\) | 21.2111 | 0.995486 | ||||||||
\(455\) | −11.7004 | −0.548524 | ||||||||
\(456\) | −16.1910 | + | 5.87095i | −0.758213 | + | 0.274932i | ||||
\(457\) | − | 22.4978i | − | 1.05240i | −0.850360 | − | 0.526201i | \(-0.823616\pi\) | ||
0.850360 | − | 0.526201i | \(-0.176384\pi\) | |||||||
\(458\) | −9.55520 | −0.446485 | ||||||||
\(459\) | −29.7250 | − | 17.3054i | −1.38744 | − | 0.807745i | ||||
\(460\) | − | 5.52721i | − | 0.257707i | ||||||
\(461\) | −27.4092 | −1.27658 | −0.638288 | − | 0.769798i | \(-0.720357\pi\) | ||||
−0.638288 | + | 0.769798i | \(0.720357\pi\) | |||||||
\(462\) | −6.90833 | + | 2.50500i | −0.321404 | + | 0.116543i | ||||
\(463\) | − | 8.48528i | − | 0.394344i | −0.980369 | − | 0.197172i | \(-0.936824\pi\) | ||
0.980369 | − | 0.197172i | \(-0.0631758\pi\) | |||||||
\(464\) | −0.465792 | −0.0216238 | ||||||||
\(465\) | −9.28267 | + | 24.9228i | −0.430474 | + | 1.15577i | ||||
\(466\) | −6.06392 | −0.280906 | ||||||||
\(467\) | 1.59345i | 0.0737362i | 0.999320 | + | 0.0368681i | \(0.0117381\pi\) | ||||
−0.999320 | + | 0.0368681i | \(0.988262\pi\) | |||||||
\(468\) | −10.6278 | − | 12.7279i | −0.491271 | − | 0.588348i | ||||
\(469\) | 0.605551 | 0.0279618 | ||||||||
\(470\) | − | 8.85563i | − | 0.408480i | ||||||
\(471\) | −9.57158 | − | 26.3967i | −0.441035 | − | 1.21629i | ||||
\(472\) | 7.60555 | 0.350074 | ||||||||
\(473\) | − | 21.5569i | − | 0.991187i | ||||||
\(474\) | 0.633308 | + | 1.74655i | 0.0290888 | + | 0.0802215i | ||||
\(475\) | 9.39445 | 0.431047 | ||||||||
\(476\) | 8.62361 | 0.395263 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 8.09635i | − | 0.370318i | ||||||
\(479\) | − | 4.27472i | − | 0.195317i | −0.995220 | − | 0.0976585i | \(-0.968865\pi\) | ||
0.995220 | − | 0.0976585i | \(-0.0311353\pi\) | |||||||
\(480\) | −9.39282 | − | 25.9037i | −0.428721 | − | 1.18233i | ||||
\(481\) | −23.4500 | −1.06923 | ||||||||
\(482\) | 18.7856 | 0.855662 | ||||||||
\(483\) | 0.908327 | + | 2.50500i | 0.0413303 | + | 0.113981i | ||||
\(484\) | 19.3028 | 0.877399 | ||||||||
\(485\) | 24.3147i | 1.10407i | ||||||||
\(486\) | −2.18297 | − | 12.8320i | −0.0990214 | − | 0.582071i | ||||
\(487\) | − | 23.7823i | − | 1.07768i | −0.842408 | − | 0.538840i | \(-0.818863\pi\) | ||
0.842408 | − | 0.538840i | \(-0.181137\pi\) | |||||||
\(488\) | 26.9435 | 1.21967 | ||||||||
\(489\) | 4.13304 | + | 11.3982i | 0.186902 | + | 0.515443i | ||||
\(490\) | −13.8167 | −0.624173 | ||||||||
\(491\) | 25.4050 | 1.14651 | 0.573257 | − | 0.819376i | \(-0.305680\pi\) | ||||
0.573257 | + | 0.819376i | \(0.305680\pi\) | |||||||
\(492\) | 14.0080 | − | 5.07939i | 0.631531 | − | 0.228997i | ||||
\(493\) | 10.1833 | 0.458635 | ||||||||
\(494\) | 12.7730 | 0.574686 | ||||||||
\(495\) | 26.9435 | + | 32.2676i | 1.21102 | + | 1.45032i | ||||
\(496\) | 1.09167 | − | 1.28457i | 0.0490176 | − | 0.0576788i | ||||
\(497\) | 4.93345i | 0.221296i | ||||||||
\(498\) | −13.8167 | + | 5.01000i | −0.619139 | + | 0.224503i | ||||
\(499\) | 28.0250i | 1.25457i | 0.778790 | + | 0.627285i | \(0.215834\pi\) | ||||
−0.778790 | + | 0.627285i | \(0.784166\pi\) | |||||||
\(500\) | − | 8.60281i | − | 0.384730i | ||||||
\(501\) | −4.81665 | − | 13.2834i | −0.215192 | − | 0.593461i | ||||
\(502\) | − | 18.2551i | − | 0.814766i | ||||||
\(503\) | − | 29.3247i | − | 1.30752i | −0.756700 | − | 0.653762i | \(-0.773190\pi\) | ||
0.756700 | − | 0.653762i | \(-0.226810\pi\) | |||||||
\(504\) | 5.30278 | + | 6.35063i | 0.236204 | + | 0.282880i | ||||
\(505\) | 32.0278 | 1.42522 | ||||||||
\(506\) | 6.52690i | 0.290156i | ||||||||
\(507\) | 2.95217 | + | 8.14154i | 0.131110 | + | 0.361579i | ||||
\(508\) | − | 7.20071i | − | 0.319480i | ||||||
\(509\) | −15.7088 | −0.696281 | −0.348141 | − | 0.937442i | \(-0.613187\pi\) | ||||
−0.348141 | + | 0.937442i | \(0.613187\pi\) | |||||||
\(510\) | 9.00000 | + | 24.8203i | 0.398527 | + | 1.09906i | ||||
\(511\) | 5.52721i | 0.244509i | ||||||||
\(512\) | 3.41655i | 0.150991i | ||||||||
\(513\) | −16.1910 | − | 9.42611i | −0.714850 | − | 0.416173i | ||||
\(514\) | −15.6972 | −0.692375 | ||||||||
\(515\) | − | 44.7072i | − | 1.97004i | ||||||
\(516\) | −9.00000 | + | 3.26345i | −0.396203 | + | 0.143665i | ||||
\(517\) | − | 19.5397i | − | 0.859355i | ||||||
\(518\) | 4.61522 | 0.202781 | ||||||||
\(519\) | 4.36593 | − | 1.58311i | 0.191643 | − | 0.0694909i | ||||
\(520\) | 32.2676i | 1.41503i | ||||||||
\(521\) | 14.2182i | 0.622909i | 0.950261 | + | 0.311455i | \(0.100816\pi\) | ||||
−0.950261 | + | 0.311455i | \(0.899184\pi\) | |||||||
\(522\) | 2.46999 | + | 2.95807i | 0.108108 | + | 0.129471i | ||||
\(523\) | 12.7279i | 0.556553i | 0.960501 | + | 0.278277i | \(0.0897632\pi\) | ||||
−0.960501 | + | 0.278277i | \(0.910237\pi\) | |||||||
\(524\) | 16.5469i | 0.722855i | ||||||||
\(525\) | −1.53841 | − | 4.24264i | −0.0671415 | − | 0.185164i | ||||
\(526\) | 19.1508i | 0.835013i | ||||||||
\(527\) | −23.8666 | + | 28.0838i | −1.03965 | + | 1.22335i | ||||
\(528\) | −0.908327 | − | 2.50500i | −0.0395299 | − | 0.109016i | ||||
\(529\) | −20.6333 | −0.897100 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.30278 | + | 6.35063i | 0.230121 | + | 0.275594i | ||||
\(532\) | 4.69722 | 0.203651 | ||||||||
\(533\) | −28.0161 | −1.21351 | ||||||||
\(534\) | 9.00000 | − | 3.26345i | 0.389468 | − | 0.141223i | ||||
\(535\) | −21.4222 | −0.926163 | ||||||||
\(536\) | − | 1.67000i | − | 0.0721330i | ||||||
\(537\) | −6.27502 | − | 17.3054i | −0.270787 | − | 0.746781i | ||||
\(538\) | 23.7823i | 1.02533i | ||||||||
\(539\) | −30.4861 | −1.31313 | ||||||||
\(540\) | 9.39282 | − | 16.1338i | 0.404202 | − | 0.694289i | ||||
\(541\) | −21.6056 | −0.928895 | −0.464448 | − | 0.885601i | \(-0.653747\pi\) | ||||
−0.464448 | + | 0.885601i | \(0.653747\pi\) | |||||||
\(542\) | 6.01259 | 0.258263 | ||||||||
\(543\) | 29.7250 | − | 10.7784i | 1.27562 | − | 0.462547i | ||||
\(544\) | − | 38.1838i | − | 1.63712i | ||||||
\(545\) | 19.3047i | 0.826923i | ||||||||
\(546\) | −2.09167 | − | 5.76845i | −0.0895153 | − | 0.246867i | ||||
\(547\) | −15.6056 | −0.667245 | −0.333623 | − | 0.942707i | \(-0.608271\pi\) | ||||
−0.333623 | + | 0.942707i | \(0.608271\pi\) | |||||||
\(548\) | −24.4735 | −1.04545 | ||||||||
\(549\) | 18.7856 | + | 22.4978i | 0.801751 | + | 0.960181i | ||||
\(550\) | − | 11.0544i | − | 0.471362i | ||||||
\(551\) | 5.54680 | 0.236302 | ||||||||
\(552\) | 6.90833 | − | 2.50500i | 0.294038 | − | 0.106620i | ||||
\(553\) | − | 1.28457i | − | 0.0546254i | ||||||
\(554\) | 8.15782 | 0.346593 | ||||||||
\(555\) | −9.00000 | − | 24.8203i | −0.382029 | − | 1.05357i | ||||
\(556\) | 29.3095i | 1.24300i | ||||||||
\(557\) | 2.00420 | 0.0849206 | 0.0424603 | − | 0.999098i | \(-0.486480\pi\) | ||||
0.0424603 | + | 0.999098i | \(0.486480\pi\) | |||||||
\(558\) | −13.9467 | − | 0.121037i | −0.590412 | − | 0.00512392i | ||||
\(559\) | 18.0000 | 0.761319 | ||||||||
\(560\) | 0.835000i | 0.0352852i | ||||||||
\(561\) | 19.8582 | + | 54.7654i | 0.838416 | + | 2.31220i | ||||
\(562\) | −1.88057 | −0.0793271 | ||||||||
\(563\) | 0.0765470i | 0.00322607i | 0.999999 | + | 0.00161304i | \(0.000513445\pi\) | ||||
−0.999999 | + | 0.00161304i | \(0.999487\pi\) | |||||||
\(564\) | −8.15782 | + | 2.95807i | −0.343506 | + | 0.124557i | ||||
\(565\) | −41.2389 | −1.73493 | ||||||||
\(566\) | 3.18690i | 0.133956i | ||||||||
\(567\) | −1.60555 | + | 8.85563i | −0.0674268 | + | 0.371902i | ||||
\(568\) | 13.6056 | 0.570876 | ||||||||
\(569\) | −27.4092 | −1.14906 | −0.574528 | − | 0.818485i | \(-0.694814\pi\) | ||||
−0.574528 | + | 0.818485i | \(0.694814\pi\) | |||||||
\(570\) | 4.90224 | + | 13.5195i | 0.205332 | + | 0.566269i | ||||
\(571\) | − | 32.2676i | − | 1.35036i | −0.737654 | − | 0.675179i | \(-0.764066\pi\) | ||
0.737654 | − | 0.675179i | \(-0.235934\pi\) | |||||||
\(572\) | 28.0838i | 1.17424i | ||||||||
\(573\) | 14.2951 | − | 5.18347i | 0.597185 | − | 0.216543i | ||||
\(574\) | 5.51388 | 0.230145 | ||||||||
\(575\) | −4.00840 | −0.167162 | ||||||||
\(576\) | 9.69722 | − | 8.09718i | 0.404051 | − | 0.337382i | ||||
\(577\) | −20.4222 | −0.850188 | −0.425094 | − | 0.905149i | \(-0.639759\pi\) | ||||
−0.425094 | + | 0.905149i | \(0.639759\pi\) | |||||||
\(578\) | 22.3919i | 0.931380i | ||||||||
\(579\) | 1.05623 | + | 2.91288i | 0.0438952 | + | 0.121055i | ||||
\(580\) | 5.52721i | 0.229505i | ||||||||
\(581\) | 10.1620 | 0.421592 | ||||||||
\(582\) | −11.9874 | + | 4.34672i | −0.496896 | + | 0.180177i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 15.2430 | 0.630761 | ||||||||
\(585\) | −26.9435 | + | 22.4978i | −1.11397 | + | 0.930168i | ||||
\(586\) | −10.6056 | −0.438111 | ||||||||
\(587\) | 20.3240 | 0.838863 | 0.419431 | − | 0.907787i | \(-0.362229\pi\) | ||||
0.419431 | + | 0.907787i | \(0.362229\pi\) | |||||||
\(588\) | 4.61522 | + | 12.7279i | 0.190328 | + | 0.524891i | ||||
\(589\) | −13.0000 | + | 15.2971i | −0.535656 | + | 0.630304i | ||||
\(590\) | − | 6.35063i | − | 0.261451i | ||||||
\(591\) | −9.00000 | − | 24.8203i | −0.370211 | − | 1.02097i | ||||
\(592\) | 1.67350i | 0.0687806i | ||||||||
\(593\) | − | 7.76781i | − | 0.318986i | −0.987199 | − | 0.159493i | \(-0.949014\pi\) | ||
0.987199 | − | 0.159493i | \(-0.0509859\pi\) | |||||||
\(594\) | −11.0917 | + | 19.0519i | −0.455097 | + | 0.781709i | ||||
\(595\) | − | 18.2551i | − | 0.748387i | ||||||
\(596\) | − | 11.5369i | − | 0.472570i | ||||||
\(597\) | 9.00000 | − | 3.26345i | 0.368345 | − | 0.133564i | ||||
\(598\) | −5.44996 | −0.222865 | ||||||||
\(599\) | 25.3260i | 1.03479i | 0.855746 | + | 0.517396i | \(0.173098\pi\) | ||||
−0.855746 | + | 0.517396i | \(0.826902\pi\) | |||||||
\(600\) | −11.7004 | + | 4.24264i | −0.477668 | + | 0.173205i | ||||
\(601\) | 6.81178i | 0.277858i | 0.990302 | + | 0.138929i | \(0.0443660\pi\) | ||||
−0.990302 | + | 0.138929i | \(0.955634\pi\) | |||||||
\(602\) | −3.54260 | −0.144386 | ||||||||
\(603\) | 1.39445 | − | 1.16436i | 0.0567863 | − | 0.0474166i | ||||
\(604\) | − | 5.52721i | − | 0.224899i | ||||||
\(605\) | − | 40.8616i | − | 1.66126i | ||||||
\(606\) | 5.72557 | + | 15.7901i | 0.232585 | + | 0.641428i | ||||
\(607\) | −34.2389 | −1.38971 | −0.694856 | − | 0.719149i | \(-0.744532\pi\) | ||||
−0.694856 | + | 0.719149i | \(0.744532\pi\) | |||||||
\(608\) | − | 20.7984i | − | 0.843488i | ||||||
\(609\) | −0.908327 | − | 2.50500i | −0.0368073 | − | 0.101508i | ||||
\(610\) | − | 22.4978i | − | 0.910908i | ||||||
\(611\) | 16.3156 | 0.660060 | ||||||||
\(612\) | 19.8582 | − | 16.5816i | 0.802722 | − | 0.670273i | ||||
\(613\) | 25.4558i | 1.02815i | 0.857745 | + | 0.514076i | \(0.171865\pi\) | ||||
−0.857745 | + | 0.514076i | \(0.828135\pi\) | |||||||
\(614\) | 12.0194i | 0.485062i | ||||||||
\(615\) | −10.7525 | − | 29.6533i | −0.433581 | − | 1.19574i | ||||
\(616\) | − | 14.0125i | − | 0.564579i | ||||||
\(617\) | 12.7013i | 0.511334i | 0.966765 | + | 0.255667i | \(0.0822950\pi\) | ||||
−0.966765 | + | 0.255667i | \(0.917705\pi\) | |||||||
\(618\) | 22.0412 | − | 7.99227i | 0.886628 | − | 0.321496i | ||||
\(619\) | 1.28457i | 0.0516312i | 0.999667 | + | 0.0258156i | \(0.00821827\pi\) | ||||
−0.999667 | + | 0.0258156i | \(0.991782\pi\) | |||||||
\(620\) | −15.2430 | − | 12.9541i | −0.612175 | − | 0.520248i | ||||
\(621\) | 6.90833 | + | 4.02190i | 0.277222 | + | 0.161393i | ||||
\(622\) | 17.9361 | 0.719171 | ||||||||
\(623\) | −6.61941 | −0.265201 | ||||||||
\(624\) | 2.09167 | − | 0.758453i | 0.0837339 | − | 0.0303624i | ||||
\(625\) | −31.2389 | −1.24955 | ||||||||
\(626\) | −10.3030 | −0.411793 | ||||||||
\(627\) | 10.8167 | + | 29.8303i | 0.431976 | + | 1.19131i | ||||
\(628\) | 21.1194 | 0.842757 | ||||||||
\(629\) | − | 36.5869i | − | 1.45881i | ||||||
\(630\) | 5.30278 | − | 4.42782i | 0.211268 | − | 0.176408i | ||||
\(631\) | − | 11.0544i | − | 0.440069i | −0.975492 | − | 0.220035i | \(-0.929383\pi\) | ||
0.975492 | − | 0.220035i | \(-0.0706171\pi\) | |||||||
\(632\) | −3.54260 | −0.140917 | ||||||||
\(633\) | 1.66305 | + | 4.58638i | 0.0661002 | + | 0.182292i | ||||
\(634\) | −9.69722 | −0.385126 | ||||||||
\(635\) | −15.2430 | −0.604901 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 25.4558i | − | 1.00860i | ||||||
\(638\) | − | 6.52690i | − | 0.258403i | ||||||
\(639\) | 9.48612 | + | 11.3606i | 0.375265 | + | 0.449420i | ||||
\(640\) | 22.1194 | 0.874347 | ||||||||
\(641\) | 37.5713 | 1.48398 | 0.741988 | − | 0.670413i | \(-0.233883\pi\) | ||||
0.741988 | + | 0.670413i | \(0.233883\pi\) | |||||||
\(642\) | −3.82963 | − | 10.5614i | −0.151143 | − | 0.416825i | ||||
\(643\) | − | 30.5941i | − | 1.20651i | −0.797547 | − | 0.603257i | \(-0.793869\pi\) | ||
0.797547 | − | 0.603257i | \(-0.206131\pi\) | |||||||
\(644\) | −2.00420 | −0.0789764 | ||||||||
\(645\) | 6.90833 | + | 19.0519i | 0.272015 | + | 0.750168i | ||||
\(646\) | 19.9286i | 0.784082i | ||||||||
\(647\) | 11.2346 | 0.441679 | 0.220839 | − | 0.975310i | \(-0.429120\pi\) | ||||
0.220839 | + | 0.975310i | \(0.429120\pi\) | |||||||
\(648\) | 24.4222 | + | 4.42782i | 0.959395 | + | 0.173941i | ||||
\(649\) | − | 14.0125i | − | 0.550038i | ||||||
\(650\) | 9.23043 | 0.362047 | ||||||||
\(651\) | 9.03717 | + | 3.36595i | 0.354194 | + | 0.131922i | ||||
\(652\) | −9.11943 | −0.357144 | ||||||||
\(653\) | 6.17436i | 0.241621i | 0.992676 | + | 0.120811i | \(0.0385494\pi\) | ||||
−0.992676 | + | 0.120811i | \(0.961451\pi\) | |||||||
\(654\) | −9.51746 | + | 3.45108i | −0.372162 | + | 0.134948i | ||||
\(655\) | 35.0278 | 1.36865 | ||||||||
\(656\) | 1.99936i | 0.0780620i | ||||||||
\(657\) | 10.6278 | + | 12.7279i | 0.414630 | + | 0.496564i | ||||
\(658\) | −3.21110 | −0.125182 | ||||||||
\(659\) | 2.25218i | 0.0877325i | 0.999037 | + | 0.0438663i | \(0.0139675\pi\) | ||||
−0.999037 | + | 0.0438663i | \(0.986032\pi\) | |||||||
\(660\) | −29.7250 | + | 10.7784i | −1.15704 | + | 0.419551i | ||||
\(661\) | 15.1833 | 0.590564 | 0.295282 | − | 0.955410i | \(-0.404586\pi\) | ||||
0.295282 | + | 0.955410i | \(0.404586\pi\) | |||||||
\(662\) | 2.14523 | 0.0833767 | ||||||||
\(663\) | −45.7291 | + | 16.5816i | −1.77597 | + | 0.643977i | ||||
\(664\) | − | 28.0250i | − | 1.08758i | ||||||
\(665\) | − | 9.94345i | − | 0.385590i | ||||||
\(666\) | 10.6278 | − | 8.87422i | 0.411819 | − | 0.343869i | ||||
\(667\) | −2.36669 | −0.0916387 | ||||||||
\(668\) | 10.6278 | 0.411202 | ||||||||
\(669\) | 22.8167 | − | 8.27345i | 0.882143 | − | 0.319870i | ||||
\(670\) | −1.39445 | −0.0538723 | ||||||||
\(671\) | − | 49.6407i | − | 1.91636i | ||||||
\(672\) | −9.39282 | + | 3.40589i | −0.362336 | + | 0.131385i | ||||
\(673\) | − | 29.6985i | − | 1.14479i | −0.819977 | − | 0.572396i | \(-0.806014\pi\) | ||
0.819977 | − | 0.572396i | \(-0.193986\pi\) | |||||||
\(674\) | −17.3883 | −0.669771 | ||||||||
\(675\) | −11.7004 | − | 6.81178i | −0.450350 | − | 0.262185i | ||||
\(676\) | −6.51388 | −0.250534 | ||||||||
\(677\) | 35.5671 | 1.36695 | 0.683477 | − | 0.729972i | \(-0.260467\pi\) | ||||
0.683477 | + | 0.729972i | \(0.260467\pi\) | |||||||
\(678\) | −7.37223 | − | 20.3313i | −0.283129 | − | 0.780817i | ||||
\(679\) | 8.81665 | 0.338352 | ||||||||
\(680\) | −50.3443 | −1.93062 | ||||||||
\(681\) | −41.3631 | + | 14.9985i | −1.58504 | + | 0.574744i | ||||
\(682\) | 18.0000 | + | 15.2971i | 0.689256 | + | 0.585755i | ||||
\(683\) | 50.3760i | 1.92758i | 0.266657 | + | 0.963791i | \(0.414081\pi\) | ||||
−0.266657 | + | 0.963791i | \(0.585919\pi\) | |||||||
\(684\) | 10.8167 | − | 9.03190i | 0.413585 | − | 0.345343i | ||||
\(685\) | 51.8073i | 1.97946i | ||||||||
\(686\) | 10.8550i | 0.414446i | ||||||||
\(687\) | 18.6333 | − | 6.75654i | 0.710905 | − | 0.257778i | ||||
\(688\) | − | 1.28457i | − | 0.0489737i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −2.09167 | − | 5.76845i | −0.0796286 | − | 0.219601i | ||||
\(691\) | −19.0000 | −0.722794 | −0.361397 | − | 0.932412i | \(-0.617700\pi\) | ||||
−0.361397 | + | 0.932412i | \(0.617700\pi\) | |||||||
\(692\) | 3.49309i | 0.132787i | ||||||||
\(693\) | 11.7004 | − | 9.76985i | 0.444462 | − | 0.371126i | ||||
\(694\) | 1.28457i | 0.0487615i | ||||||||
\(695\) | 62.0447 | 2.35349 | ||||||||
\(696\) | −6.90833 | + | 2.50500i | −0.261859 | + | 0.0949517i | ||||
\(697\) | − | 43.7110i | − | 1.65567i | ||||||
\(698\) | 1.01127i | 0.0382771i | ||||||||
\(699\) | 11.8251 | − | 4.28784i | 0.447265 | − | 0.162181i | ||||
\(700\) | 3.39445 | 0.128298 | ||||||||
\(701\) | 44.7072i | 1.68857i | 0.535895 | + | 0.844285i | \(0.319974\pi\) | ||||
−0.535895 | + | 0.844285i | \(0.680026\pi\) | |||||||
\(702\) | −15.9083 | − | 9.26154i | −0.600421 | − | 0.349554i | ||||
\(703\) | − | 19.9286i | − | 0.751623i | ||||||
\(704\) | −21.3967 | −0.806417 | ||||||||
\(705\) | 6.26188 | + | 17.2691i | 0.235836 | + | 0.650392i | ||||
\(706\) | 0.895632i | 0.0337076i | ||||||||
\(707\) | − | 11.6134i | − | 0.436769i | ||||||
\(708\) | −5.85021 | + | 2.12132i | −0.219864 | + | 0.0797241i | ||||
\(709\) | 44.9955i | 1.68984i | 0.534890 | + | 0.844922i | \(0.320353\pi\) | ||||
−0.534890 | + | 0.844922i | \(0.679647\pi\) | |||||||
\(710\) | − | 11.3606i | − | 0.426357i | ||||||
\(711\) | −2.46999 | − | 2.95807i | −0.0926318 | − | 0.110936i | ||||
\(712\) | 18.2551i | 0.684140i | ||||||||
\(713\) | 5.54680 | − | 6.52690i | 0.207729 | − | 0.244434i | ||||
\(714\) | 9.00000 | − | 3.26345i | 0.336817 | − | 0.122132i | ||||
\(715\) | 59.4500 | 2.22330 | ||||||||
\(716\) | 13.8457 | 0.517436 | ||||||||
\(717\) | 5.72498 | + | 15.7884i | 0.213803 | + | 0.589630i | ||||
\(718\) | 22.1194 | 0.825490 | ||||||||
\(719\) | −6.61941 | −0.246863 | −0.123431 | − | 0.992353i | \(-0.539390\pi\) | ||||
−0.123431 | + | 0.992353i | \(0.539390\pi\) | |||||||
\(720\) | 1.60555 | + | 1.92282i | 0.0598354 | + | 0.0716592i | ||||
\(721\) | −16.2111 | −0.603733 | ||||||||
\(722\) | − | 5.01000i | − | 0.186453i | ||||||
\(723\) | −36.6333 | + | 13.2834i | −1.36241 | + | 0.494017i | ||||
\(724\) | 23.7823i | 0.883864i | ||||||||
\(725\) | 4.00840 | 0.148868 | ||||||||
\(726\) | 20.1453 | − | 7.30479i | 0.747661 | − | 0.271106i | ||||
\(727\) | 17.0000 | 0.630495 | 0.315248 | − | 0.949009i | \(-0.397912\pi\) | ||||
0.315248 | + | 0.949009i | \(0.397912\pi\) | |||||||
\(728\) | 11.7004 | 0.433647 | ||||||||
\(729\) | 13.3305 | + | 23.4797i | 0.493723 | + | 0.869619i | ||||
\(730\) | − | 12.7279i | − | 0.471082i | ||||||
\(731\) | 28.0838i | 1.03872i | ||||||||
\(732\) | −20.7250 | + | 7.51500i | −0.766017 | + | 0.277762i | ||||
\(733\) | −1.78890 | −0.0660744 | −0.0330372 | − | 0.999454i | \(-0.510518\pi\) | ||||
−0.0330372 | + | 0.999454i | \(0.510518\pi\) | |||||||
\(734\) | 23.4008 | 0.863741 | ||||||||
\(735\) | 26.9435 | − | 9.76985i | 0.993824 | − | 0.360366i | ||||
\(736\) | 8.87422i | 0.327108i | ||||||||
\(737\) | −3.07681 | −0.113336 | ||||||||
\(738\) | 12.6972 | − | 10.6022i | 0.467391 | − | 0.390272i | ||||
\(739\) | − | 34.8368i | − | 1.28149i | −0.767753 | − | 0.640745i | \(-0.778625\pi\) | ||
0.767753 | − | 0.640745i | \(-0.221375\pi\) | |||||||
\(740\) | 19.8582 | 0.730004 | ||||||||
\(741\) | −24.9083 | + | 9.03190i | −0.915030 | + | 0.331795i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.9393 | −0.914932 | −0.457466 | − | 0.889227i | \(-0.651243\pi\) | ||||
−0.457466 | + | 0.889227i | \(0.651243\pi\) | |||||||
\(744\) | 9.28267 | − | 24.9228i | 0.340319 | − | 0.913716i | ||||
\(745\) | −24.4222 | −0.894760 | ||||||||
\(746\) | 17.2288i | 0.630791i | ||||||||
\(747\) | 23.4008 | − | 19.5397i | 0.856192 | − | 0.714920i | ||||
\(748\) | −43.8167 | −1.60210 | ||||||||
\(749\) | 7.76781i | 0.283830i | ||||||||
\(750\) | −3.25558 | − | 8.97829i | −0.118877 | − | 0.327841i | ||||
\(751\) | 39.6611 | 1.44725 | 0.723626 | − | 0.690192i | \(-0.242474\pi\) | ||||
0.723626 | + | 0.690192i | \(0.242474\pi\) | |||||||
\(752\) | − | 1.16436i | − | 0.0424600i | ||||||
\(753\) | 12.9083 | + | 35.5988i | 0.470406 | + | 1.29729i | ||||
\(754\) | 5.44996 | 0.198476 | ||||||||
\(755\) | −11.7004 | −0.425822 | ||||||||
\(756\) | −5.85021 | − | 3.40589i | −0.212770 | − | 0.123871i | ||||
\(757\) | 23.7823i | 0.864384i | 0.901782 | + | 0.432192i | \(0.142260\pi\) | ||||
−0.901782 | + | 0.432192i | \(0.857740\pi\) | |||||||
\(758\) | − | 26.4138i | − | 0.959392i | ||||||
\(759\) | −4.61522 | − | 12.7279i | −0.167522 | − | 0.461994i | ||||
\(760\) | −27.4222 | −0.994708 | ||||||||
\(761\) | −31.5587 | −1.14400 | −0.572000 | − | 0.820253i | \(-0.693832\pi\) | ||||
−0.572000 | + | 0.820253i | \(0.693832\pi\) | |||||||
\(762\) | −2.72498 | − | 7.51500i | −0.0987156 | − | 0.272240i | ||||
\(763\) | 7.00000 | 0.253417 | ||||||||
\(764\) | 11.4372i | 0.413783i | ||||||||
\(765\) | −35.1013 | − | 42.0375i | −1.26909 | − | 1.51987i | ||||
\(766\) | − | 2.56914i | − | 0.0928267i | ||||||
\(767\) | 11.7004 | 0.422478 | ||||||||
\(768\) | 8.92702 | + | 24.6191i | 0.322126 | + | 0.888365i | ||||
\(769\) | 0.577795 | 0.0208358 | 0.0104179 | − | 0.999946i | \(-0.496684\pi\) | ||||
0.0104179 | + | 0.999946i | \(0.496684\pi\) | |||||||
\(770\) | −11.7004 | −0.421654 | ||||||||
\(771\) | 30.6107 | − | 11.0996i | 1.10242 | − | 0.399743i | ||||
\(772\) | −2.33053 | −0.0838777 | ||||||||
\(773\) | −35.1013 | −1.26251 | −0.631253 | − | 0.775577i | \(-0.717459\pi\) | ||||
−0.631253 | + | 0.775577i | \(0.717459\pi\) | |||||||
\(774\) | −8.15782 | + | 6.81178i | −0.293227 | + | 0.244844i | ||||
\(775\) | −9.39445 | + | 11.0544i | −0.337459 | + | 0.397086i | ||||
\(776\) | − | 24.3147i | − | 0.872847i | ||||||
\(777\) | −9.00000 | + | 3.26345i | −0.322873 | + | 0.117076i | ||||
\(778\) | 4.24264i | 0.152106i | ||||||||
\(779\) | − | 23.8091i | − | 0.853049i | ||||||
\(780\) | −9.00000 | − | 24.8203i | −0.322252 | − | 0.888711i | ||||
\(781\) | − | 25.0669i | − | 0.896964i | ||||||
\(782\) | − | 8.50309i | − | 0.304070i | ||||||
\(783\) | −6.90833 | − | 4.02190i | −0.246883 | − | 0.143731i | ||||
\(784\) | −1.81665 | −0.0648805 | ||||||||
\(785\) | − | 44.7072i | − | 1.59567i | ||||||
\(786\) | 6.26188 | + | 17.2691i | 0.223354 | + | 0.615969i | ||||
\(787\) | 31.8787i | 1.13635i | 0.822907 | + | 0.568176i | \(0.192351\pi\) | ||||
−0.822907 | + | 0.568176i | \(0.807649\pi\) | |||||||
\(788\) | 19.8582 | 0.707421 | ||||||||
\(789\) | −13.5416 | − | 37.3453i | −0.482095 | − | 1.32953i | ||||
\(790\) | 2.95807i | 0.105243i | ||||||||
\(791\) | 14.9534i | 0.531683i | ||||||||
\(792\) | −26.9435 | − | 32.2676i | −0.957394 | − | 1.14658i | ||||
\(793\) | 41.4500 | 1.47193 | ||||||||
\(794\) | 28.7657i | 1.02086i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.20071i | 0.255223i | ||||||||
\(797\) | 6.15362 | 0.217973 | 0.108986 | − | 0.994043i | \(-0.465240\pi\) | ||||
0.108986 | + | 0.994043i | \(0.465240\pi\) | |||||||
\(798\) | 4.90224 | − | 1.77758i | 0.173537 | − | 0.0629257i | ||||
\(799\) | 25.4558i | 0.900563i | ||||||||
\(800\) | − | 15.0300i | − | 0.531391i | ||||||
\(801\) | −15.2430 | + | 12.7279i | −0.538586 | + | 0.449719i | ||||
\(802\) | 15.6860i | 0.553892i | ||||||||
\(803\) | − | 28.0838i | − | 0.991056i | ||||||
\(804\) | 0.465792 | + | 1.28457i | 0.0164272 | + | 0.0453032i | ||||
\(805\) | 4.24264i | 0.149533i | ||||||||
\(806\) | −12.7730 | + | 15.0300i | −0.449911 | + | 0.529409i | ||||
\(807\) | −16.8167 | − | 46.3772i | −0.591974 | − | 1.63256i | ||||
\(808\) | −32.0278 | −1.12673 | ||||||||
\(809\) | −6.01259 | −0.211392 | −0.105696 | − | 0.994399i | \(-0.533707\pi\) | ||||
−0.105696 | + | 0.994399i | \(0.533707\pi\) | |||||||
\(810\) | 3.69722 | − | 20.3925i | 0.129907 | − | 0.716521i | ||||
\(811\) | 21.0278 | 0.738384 | 0.369192 | − | 0.929353i | \(-0.379634\pi\) | ||||
0.369192 | + | 0.929353i | \(0.379634\pi\) | |||||||
\(812\) | 2.00420 | 0.0703335 | ||||||||
\(813\) | −11.7250 | + | 4.25155i | −0.411213 | + | 0.149108i | ||||
\(814\) | −23.4500 | −0.821921 | ||||||||
\(815\) | 19.3047i | 0.676215i | ||||||||
\(816\) | 1.18335 | + | 3.26345i | 0.0414254 | + | 0.114244i | ||||
\(817\) | 15.2971i | 0.535176i | ||||||||
\(818\) | 26.9435 | 0.942056 | ||||||||
\(819\) | 8.15782 | + | 9.76985i | 0.285057 | + | 0.341386i | ||||
\(820\) | 23.7250 | 0.828512 | ||||||||
\(821\) | −43.2591 | −1.50975 | −0.754876 | − | 0.655867i | \(-0.772303\pi\) | ||||
−0.754876 | + | 0.655867i | \(0.772303\pi\) | |||||||
\(822\) | −25.5416 | + | 9.26154i | −0.890867 | + | 0.323033i | ||||
\(823\) | 35.2257i | 1.22789i | 0.789349 | + | 0.613945i | \(0.210418\pi\) | ||||
−0.789349 | + | 0.613945i | \(0.789582\pi\) | |||||||
\(824\) | 44.7072i | 1.55745i | ||||||||
\(825\) | 7.81665 | + | 21.5569i | 0.272141 | + | 0.750515i | ||||
\(826\) | −2.30278 | −0.0801238 | ||||||||
\(827\) | 4.61522 | 0.160487 | 0.0802434 | − | 0.996775i | \(-0.474430\pi\) | ||||
0.0802434 | + | 0.996775i | \(0.474430\pi\) | |||||||
\(828\) | −4.61522 | + | 3.85370i | −0.160390 | + | 0.133925i | ||||
\(829\) | 25.4558i | 0.884118i | 0.896986 | + | 0.442059i | \(0.145752\pi\) | ||||
−0.896986 | + | 0.442059i | \(0.854248\pi\) | |||||||
\(830\) | −23.4008 | −0.812255 | ||||||||
\(831\) | −15.9083 | + | 5.76845i | −0.551854 | + | 0.200105i | ||||
\(832\) | − | 17.8662i | − | 0.619399i | ||||||
\(833\) | 39.7165 | 1.37609 | ||||||||
\(834\) | 11.0917 | + | 30.5888i | 0.384073 | + | 1.05920i | ||||
\(835\) | − | 22.4978i | − | 0.778567i | ||||||
\(836\) | −23.8666 | −0.825445 | ||||||||
\(837\) | 27.2827 | − | 9.62579i | 0.943027 | − | 0.332716i | ||||
\(838\) | −28.9638 | −1.00054 | ||||||||
\(839\) | 17.7113i | 0.611461i | 0.952118 | + | 0.305730i | \(0.0989006\pi\) | ||||
−0.952118 | + | 0.305730i | \(0.901099\pi\) | |||||||
\(840\) | 4.49058 | + | 12.3842i | 0.154940 | + | 0.427295i | ||||
\(841\) | −26.6333 | −0.918390 | ||||||||
\(842\) | − | 19.5575i | − | 0.673997i | ||||||
\(843\) | 3.66725 | − | 1.32976i | 0.126307 | − | 0.0457995i | ||||
\(844\) | −3.66947 | −0.126308 | ||||||||
\(845\) | 13.7891i | 0.474359i | ||||||||
\(846\) | −7.39445 | + | 6.17436i | −0.254226 | + | 0.212279i | ||||
\(847\) | −14.8167 | −0.509106 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.25348 | − | 6.21469i | −0.0773393 | − | 0.213288i | ||||
\(850\) | 14.4014i | 0.493965i | ||||||||
\(851\) | 8.50309i | 0.291482i | ||||||||
\(852\) | −10.4654 | + | 3.79482i | −0.358540 | + | 0.130009i | ||||
\(853\) | 19.2111 | 0.657776 | 0.328888 | − | 0.944369i | \(-0.393326\pi\) | ||||
0.328888 | + | 0.944369i | \(0.393326\pi\) | |||||||
\(854\) | −8.15782 | −0.279155 | ||||||||
\(855\) | −19.1194 | − | 22.8975i | −0.653871 | − | 0.783079i | ||||
\(856\) | 21.4222 | 0.732196 | ||||||||
\(857\) | − | 3.84563i | − | 0.131364i | −0.997841 | − | 0.0656822i | \(-0.979078\pi\) | ||
0.997841 | − | 0.0656822i | \(-0.0209223\pi\) | |||||||
\(858\) | 10.6278 | + | 29.3095i | 0.362827 | + | 1.00061i | ||||
\(859\) | 0.388936i | 0.0132703i | 0.999978 | + | 0.00663516i | \(0.00211205\pi\) | ||||
−0.999978 | + | 0.00663516i | \(0.997888\pi\) | |||||||
\(860\) | −15.2430 | −0.519783 | ||||||||
\(861\) | −10.7525 | + | 3.89890i | −0.366443 | + | 0.132874i | ||||
\(862\) | −0.972244 | −0.0331147 | ||||||||
\(863\) | −2.61102 | −0.0888801 | −0.0444401 | − | 0.999012i | \(-0.514150\pi\) | ||||
−0.0444401 | + | 0.999012i | \(0.514150\pi\) | |||||||
\(864\) | −15.0806 | + | 25.9037i | −0.513054 | + | 0.881260i | ||||
\(865\) | 7.39445 | 0.251419 | ||||||||
\(866\) | −6.01259 | −0.204316 | ||||||||
\(867\) | −15.8335 | − | 43.6658i | −0.537733 | − | 1.48297i | ||||
\(868\) | −4.69722 | + | 5.52721i | −0.159434 | + | 0.187606i | ||||
\(869\) | 6.52690i | 0.221410i | ||||||||
\(870\) | 2.09167 | + | 5.76845i | 0.0709144 | + | 0.195569i | ||||
\(871\) | − | 2.56914i | − | 0.0870519i | ||||||
\(872\) | − | 19.3047i | − | 0.653740i | ||||||
\(873\) | 20.3028 | − | 16.9528i | 0.687145 | − | 0.573766i | ||||
\(874\) | − | 4.63158i | − | 0.156665i | ||||||
\(875\) | 6.60345i | 0.223237i | ||||||||
\(876\) | −11.7250 | + | 4.25155i | −0.396150 | + | 0.143646i | ||||
\(877\) | 24.0278 | 0.811360 | 0.405680 | − | 0.914015i | \(-0.367035\pi\) | ||||
0.405680 | + | 0.914015i | \(0.367035\pi\) | |||||||
\(878\) | 15.0532i | 0.508020i | ||||||||
\(879\) | 20.6816 | − | 7.49926i | 0.697572 | − | 0.252944i | ||||
\(880\) | − | 4.24264i | − | 0.143019i | ||||||
\(881\) | −26.4777 | −0.892055 | −0.446028 | − | 0.895019i | \(-0.647162\pi\) | ||||
−0.446028 | + | 0.895019i | \(0.647162\pi\) | |||||||
\(882\) | 9.63331 | + | 11.5369i | 0.324370 | + | 0.388468i | ||||
\(883\) | 11.0544i | 0.372011i | 0.982549 | + | 0.186005i | \(0.0595542\pi\) | ||||
−0.982549 | + | 0.186005i | \(0.940446\pi\) | |||||||
\(884\) | − | 36.5869i | − | 1.23055i | ||||||
\(885\) | 4.49058 | + | 12.3842i | 0.150949 | + | 0.416290i | ||||
\(886\) | −1.88057 | −0.0631790 | ||||||||
\(887\) | − | 36.5103i | − | 1.22590i | −0.790123 | − | 0.612949i | \(-0.789983\pi\) | ||
0.790123 | − | 0.612949i | \(-0.210017\pi\) | |||||||
\(888\) | 9.00000 | + | 24.8203i | 0.302020 | + | 0.832916i | ||||
\(889\) | 5.52721i | 0.185377i | ||||||||
\(890\) | 15.2430 | 0.510947 | ||||||||
\(891\) | 8.15782 | − | 44.9955i | 0.273297 | − | 1.50741i | ||||
\(892\) | 18.2551i | 0.611227i | ||||||||
\(893\) | 13.8656i | 0.463996i | ||||||||
\(894\) | −4.36593 | − | 12.0404i | −0.146019 | − | 0.402693i | ||||
\(895\) | − | 29.3095i | − | 0.979710i | ||||||
\(896\) | − | 8.02063i | − | 0.267950i | ||||||
\(897\) | 10.6278 | − | 3.85370i | 0.354852 | − | 0.128671i | ||||
\(898\) | 1.67350i | 0.0558456i | ||||||||
\(899\) | −5.54680 | + | 6.52690i | −0.184996 | + | 0.217684i | ||||
\(900\) | 7.81665 | − | 6.52690i | 0.260555 | − | 0.217563i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −28.0161 | −0.932833 | ||||||||
\(903\) | 6.90833 | − | 2.50500i | 0.229895 | − | 0.0833611i | ||||
\(904\) | 41.2389 | 1.37158 | ||||||||
\(905\) | 50.3443 | 1.67350 | ||||||||
\(906\) | −2.09167 | − | 5.76845i | −0.0694912 | − | 0.191644i | ||||
\(907\) | 0.0277564 | 0.000921635 | 0.000460818 | − | 1.00000i | \(-0.499853\pi\) | ||||
0.000460818 | 1.00000i | \(0.499853\pi\) | ||||||||
\(908\) | − | 33.0938i | − | 1.09826i | ||||||
\(909\) | −22.3305 | − | 26.7432i | −0.740657 | − | 0.887015i | ||||
\(910\) | − | 9.76985i | − | 0.323867i | ||||||
\(911\) | −5.54680 | −0.183774 | −0.0918869 | − | 0.995769i | \(-0.529290\pi\) | ||||
−0.0918869 | + | 0.995769i | \(0.529290\pi\) | |||||||
\(912\) | 0.644561 | + | 1.77758i | 0.0213435 | + | 0.0588616i | ||||
\(913\) | −51.6333 | −1.70881 | ||||||||
\(914\) | 18.7856 | 0.621373 | ||||||||
\(915\) | 15.9083 | + | 43.8722i | 0.525913 | + | 1.45037i | ||||
\(916\) | 14.9081i | 0.492578i | ||||||||
\(917\) | − | 12.7013i | − | 0.419433i | ||||||
\(918\) | 14.4500 | − | 24.8203i | 0.476920 | − | 0.819194i | ||||
\(919\) | −2.42221 | −0.0799012 | −0.0399506 | − | 0.999202i | \(-0.512720\pi\) | ||||
−0.0399506 | + | 0.999202i | \(0.512720\pi\) | |||||||
\(920\) | 11.7004 | 0.385752 | ||||||||
\(921\) | −8.49897 | − | 23.4386i | −0.280051 | − | 0.772328i | ||||
\(922\) | − | 22.8867i | − | 0.753734i | ||||||
\(923\) | 20.9309 | 0.688948 | ||||||||
\(924\) | 3.90833 | + | 10.7784i | 0.128575 | + | 0.354585i | ||||
\(925\) | − | 14.4014i | − | 0.473516i | ||||||
\(926\) | 7.08521 | 0.232834 | ||||||||
\(927\) | −37.3305 | + | 31.1710i | −1.22610 | + | 1.02379i | ||||
\(928\) | − | 8.87422i | − | 0.291310i | ||||||
\(929\) | 5.08101 | 0.166703 | 0.0833513 | − | 0.996520i | \(-0.473438\pi\) | ||||
0.0833513 | + | 0.996520i | \(0.473438\pi\) | |||||||
\(930\) | −20.8106 | − | 7.75103i | −0.682405 | − | 0.254166i | ||||
\(931\) | 21.6333 | 0.709003 | ||||||||
\(932\) | 9.46099i | 0.309905i | ||||||||
\(933\) | −34.9766 | + | 12.6827i | −1.14508 | + | 0.415214i | ||||
\(934\) | −1.33053 | −0.0435363 | ||||||||
\(935\) | 92.7545i | 3.03340i | ||||||||
\(936\) | 26.9435 | − | 22.4978i | 0.880674 | − | 0.735363i | ||||
\(937\) | 15.5778 | 0.508904 | 0.254452 | − | 0.967085i | \(-0.418105\pi\) | ||||
0.254452 | + | 0.967085i | \(0.418105\pi\) | |||||||
\(938\) | 0.505635i | 0.0165096i | ||||||||
\(939\) | 20.0917 | − | 7.28536i | 0.655667 | − | 0.237749i | ||||
\(940\) | −13.8167 | −0.450650 | ||||||||
\(941\) | 44.6565 | 1.45576 | 0.727880 | − | 0.685705i | \(-0.240506\pi\) | ||||
0.727880 | + | 0.685705i | \(0.240506\pi\) | |||||||
\(942\) | 22.0412 | − | 7.99227i | 0.718141 | − | 0.260402i | ||||
\(943\) | 10.1588i | 0.330816i | ||||||||
\(944\) | − | 0.835000i | − | 0.0271769i | ||||||
\(945\) | −7.20985 | + | 12.3842i | −0.234536 | + | 0.402857i | ||||
\(946\) | 18.0000 | 0.585230 | ||||||||
\(947\) | −38.6439 | −1.25576 | −0.627879 | − | 0.778311i | \(-0.716077\pi\) | ||||
−0.627879 | + | 0.778311i | \(0.716077\pi\) | |||||||
\(948\) | 2.72498 | − | 0.988094i | 0.0885033 | − | 0.0320918i | ||||
\(949\) | 23.4500 | 0.761218 | ||||||||
\(950\) | 7.84436i | 0.254505i | ||||||||
\(951\) | 18.9103 | − | 6.85697i | 0.613208 | − | 0.222353i | ||||
\(952\) | 18.2551i | 0.591652i | ||||||||
\(953\) | 29.0887 | 0.942275 | 0.471137 | − | 0.882060i | \(-0.343844\pi\) | ||||
0.471137 | + | 0.882060i | \(0.343844\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.2111 | 0.783453 | ||||||||
\(956\) | −12.6320 | −0.408548 | ||||||||
\(957\) | 4.61522 | + | 12.7279i | 0.149189 | + | 0.411435i | ||||
\(958\) | 3.56939 | 0.115322 | ||||||||
\(959\) | 18.7856 | 0.606620 | ||||||||
\(960\) | 18.9103 | − | 6.85697i | 0.610326 | − | 0.221308i | ||||
\(961\) | −5.00000 | − | 30.5941i | −0.161290 | − | 0.986907i | ||||
\(962\) | − | 19.5807i | − | 0.631307i | ||||||
\(963\) | 14.9361 | + | 17.8875i | 0.481309 | + | 0.576418i | ||||
\(964\) | − | 29.3095i | − | 0.943997i | ||||||
\(965\) | 4.93345i | 0.158813i | ||||||||
\(966\) | −2.09167 | + | 0.758453i | −0.0672985 | + | 0.0244028i | ||||
\(967\) | 33.5522i | 1.07897i | 0.841997 | + | 0.539483i | \(0.181380\pi\) | ||||
−0.841997 | + | 0.539483i | \(0.818620\pi\) | |||||||
\(968\) | 40.8616i | 1.31334i | ||||||||
\(969\) | −14.0917 | − | 38.8622i | −0.452690 | − | 1.24844i | ||||
\(970\) | −20.3028 | −0.651883 | ||||||||
\(971\) | − | 26.9194i | − | 0.863886i | −0.901901 | − | 0.431943i | \(-0.857828\pi\) | ||
0.901901 | − | 0.431943i | \(-0.142172\pi\) | |||||||
\(972\) | −20.0206 | + | 3.40589i | −0.642162 | + | 0.109244i | ||||
\(973\) | − | 22.4978i | − | 0.721245i | ||||||
\(974\) | 19.8582 | 0.636299 | ||||||||
\(975\) | −18.0000 | + | 6.52690i | −0.576461 | + | 0.209028i | ||||
\(976\) | − | 2.95807i | − | 0.0946856i | ||||||
\(977\) | − | 43.0372i | − | 1.37688i | −0.725292 | − | 0.688442i | \(-0.758295\pi\) | ||
0.725292 | − | 0.688442i | \(-0.241705\pi\) | |||||||
\(978\) | −9.51746 | + | 3.45108i | −0.304335 | + | 0.110354i | ||||
\(979\) | 33.6333 | 1.07493 | ||||||||
\(980\) | 21.5569i | 0.688610i | ||||||||
\(981\) | 16.1194 | − | 13.4597i | 0.514654 | − | 0.429736i | ||||
\(982\) | 21.2132i | 0.676941i | ||||||||
\(983\) | −34.6355 | −1.10470 | −0.552350 | − | 0.833612i | \(-0.686269\pi\) | ||||
−0.552350 | + | 0.833612i | \(0.686269\pi\) | |||||||
\(984\) | 10.7525 | + | 29.6533i | 0.342776 | + | 0.945312i | ||||
\(985\) | − | 42.0375i | − | 1.33943i | ||||||
\(986\) | 8.50309i | 0.270794i | ||||||||
\(987\) | 6.26188 | − | 2.27059i | 0.199318 | − | 0.0722738i | ||||
\(988\) | − | 19.9286i | − | 0.634014i | ||||||
\(989\) | − | 6.52690i | − | 0.207543i | ||||||
\(990\) | −26.9435 | + | 22.4978i | −0.856319 | + | 0.715026i | ||||
\(991\) | 3.85370i | 0.122417i | 0.998125 | + | 0.0612085i | \(0.0194955\pi\) | ||||
−0.998125 | + | 0.0612085i | \(0.980505\pi\) | |||||||
\(992\) | 24.4735 | + | 20.7984i | 0.777033 | + | 0.660351i | ||||
\(993\) | −4.18335 | + | 1.51691i | −0.132754 | + | 0.0481375i | ||||
\(994\) | −4.11943 | −0.130660 | ||||||||
\(995\) | 15.2430 | 0.483236 | ||||||||
\(996\) | 7.81665 | + | 21.5569i | 0.247680 | + | 0.683056i | ||||
\(997\) | −60.4500 | −1.91447 | −0.957235 | − | 0.289312i | \(-0.906573\pi\) | ||||
−0.957235 | + | 0.289312i | \(0.906573\pi\) | |||||||
\(998\) | −23.4008 | −0.740741 | ||||||||
\(999\) | −14.4500 | + | 24.8203i | −0.457177 | + | 0.785281i |
(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 | 93.2.c.a.92.5 | yes | 8 | |
3.2 | odd | 2 | inner | 93.2.c.a.92.4 | yes | 8 | |
4.3 | odd | 2 | 1488.2.h.e.929.6 | 8 | |||
12.11 | even | 2 | 1488.2.h.e.929.4 | 8 | |||
31.30 | odd | 2 | inner | 93.2.c.a.92.6 | yes | 8 | |
93.92 | even | 2 | inner | 93.2.c.a.92.3 | ✓ | 8 | |
124.123 | even | 2 | 1488.2.h.e.929.3 | 8 | |||
372.371 | odd | 2 | 1488.2.h.e.929.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
93.2.c.a.92.3 | ✓ | 8 | 93.92 | even | 2 | inner | |
93.2.c.a.92.4 | yes | 8 | 3.2 | odd | 2 | inner | |
93.2.c.a.92.5 | yes | 8 | 1.1 | even | 1 | trivial | |
93.2.c.a.92.6 | yes | 8 | 31.30 | odd | 2 | inner | |
1488.2.h.e.929.3 | 8 | 124.123 | even | 2 | |||
1488.2.h.e.929.4 | 8 | 12.11 | even | 2 | |||
1488.2.h.e.929.5 | 8 | 372.371 | odd | 2 | |||
1488.2.h.e.929.6 | 8 | 4.3 | odd | 2 |