Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(229,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.229");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.k (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 229.4 | ||
Character | \(\chi\) | \(=\) | 966.229 |
Dual form | 966.2.k.b.367.4 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.139134 | + | 0.240988i | −0.0622228 | + | 0.107773i | −0.895459 | − | 0.445145i | \(-0.853152\pi\) |
0.833236 | + | 0.552918i | \(0.186486\pi\) | |||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 2.42763 | + | 1.05197i | 0.917556 | + | 0.397606i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0.139134 | + | 0.240988i | 0.0439982 | + | 0.0762071i | ||||
\(11\) | 1.25854 | − | 0.726620i | 0.379465 | − | 0.219084i | −0.298120 | − | 0.954528i | \(-0.596360\pi\) |
0.677585 | + | 0.735444i | \(0.263026\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | 5.02248i | 1.39298i | 0.717564 | + | 0.696492i | \(0.245257\pi\) | ||||
−0.717564 | + | 0.696492i | \(0.754743\pi\) | |||||||
\(14\) | 2.12484 | − | 1.57640i | 0.567888 | − | 0.421311i | ||||
\(15\) | − | 0.278269i | − | 0.0718487i | ||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.48923 | − | 4.31148i | −0.603728 | − | 1.04569i | −0.992251 | − | 0.124249i | \(-0.960348\pi\) |
0.388523 | − | 0.921439i | \(-0.372985\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | −1.02940 | + | 1.78298i | −0.236161 | + | 0.409043i | −0.959610 | − | 0.281335i | \(-0.909223\pi\) |
0.723448 | + | 0.690379i | \(0.242556\pi\) | |||||||
\(20\) | 0.278269 | 0.0622228 | ||||||||
\(21\) | −2.62837 | + | 0.302783i | −0.573557 | + | 0.0660726i | ||||
\(22\) | − | 1.45324i | − | 0.309832i | ||||||
\(23\) | 2.68233 | + | 3.97556i | 0.559305 | + | 0.828962i | ||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 2.46128 | + | 4.26307i | 0.492257 | + | 0.852614i | ||||
\(26\) | 4.34959 | + | 2.51124i | 0.853025 | + | 0.492494i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −0.302783 | − | 2.62837i | −0.0572206 | − | 0.496715i | ||||
\(29\) | 5.24874 | 0.974666 | 0.487333 | − | 0.873216i | \(-0.337970\pi\) | ||||
0.487333 | + | 0.873216i | \(0.337970\pi\) | |||||||
\(30\) | −0.240988 | − | 0.139134i | −0.0439982 | − | 0.0254024i | ||||
\(31\) | 0.516456 | − | 0.298176i | 0.0927582 | − | 0.0535540i | −0.452903 | − | 0.891560i | \(-0.649612\pi\) |
0.545662 | + | 0.838006i | \(0.316278\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −0.726620 | + | 1.25854i | −0.126488 | + | 0.219084i | ||||
\(34\) | −4.97847 | −0.853800 | ||||||||
\(35\) | −0.591278 | + | 0.438664i | −0.0999442 | + | 0.0741477i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 2.31382 | + | 1.33588i | 0.380389 | + | 0.219618i | 0.677988 | − | 0.735073i | \(-0.262852\pi\) |
−0.297598 | + | 0.954691i | \(0.596186\pi\) | |||||||
\(38\) | 1.02940 | + | 1.78298i | 0.166991 | + | 0.289237i | ||||
\(39\) | −2.51124 | − | 4.34959i | −0.402120 | − | 0.696492i | ||||
\(40\) | 0.139134 | − | 0.240988i | 0.0219991 | − | 0.0381035i | ||||
\(41\) | 3.01009i | 0.470098i | 0.971984 | + | 0.235049i | \(0.0755250\pi\) | ||||
−0.971984 | + | 0.235049i | \(0.924475\pi\) | |||||||
\(42\) | −1.05197 | + | 2.42763i | −0.162322 | + | 0.374591i | ||||
\(43\) | − | 6.84595i | − | 1.04400i | −0.852946 | − | 0.521999i | \(-0.825186\pi\) | ||
0.852946 | − | 0.521999i | \(-0.174814\pi\) | |||||||
\(44\) | −1.25854 | − | 0.726620i | −0.189732 | − | 0.109542i | ||||
\(45\) | 0.139134 | + | 0.240988i | 0.0207409 | + | 0.0359244i | ||||
\(46\) | 4.78410 | − | 0.335188i | 0.705378 | − | 0.0494207i | ||||
\(47\) | 8.05896 | + | 4.65284i | 1.17552 | + | 0.678687i | 0.954974 | − | 0.296690i | \(-0.0958827\pi\) |
0.220546 | + | 0.975377i | \(0.429216\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 4.78673 | + | 5.10756i | 0.683819 | + | 0.729652i | ||||
\(50\) | 4.92257 | 0.696156 | ||||||||
\(51\) | 4.31148 | + | 2.48923i | 0.603728 | + | 0.348563i | ||||
\(52\) | 4.34959 | − | 2.51124i | 0.603180 | − | 0.348246i | ||||
\(53\) | 8.65735 | − | 4.99832i | 1.18918 | − | 0.686573i | 0.231059 | − | 0.972940i | \(-0.425781\pi\) |
0.958120 | + | 0.286367i | \(0.0924477\pi\) | |||||||
\(54\) | 0.866025 | + | 0.500000i | 0.117851 | + | 0.0680414i | ||||
\(55\) | 0.404392i | 0.0545281i | ||||||||
\(56\) | −2.42763 | − | 1.05197i | −0.324405 | − | 0.140575i | ||||
\(57\) | − | 2.05881i | − | 0.272695i | ||||||
\(58\) | 2.62437 | − | 4.54554i | 0.344596 | − | 0.596858i | ||||
\(59\) | 2.40462 | − | 1.38831i | 0.313055 | − | 0.180742i | −0.335238 | − | 0.942134i | \(-0.608817\pi\) |
0.648293 | + | 0.761391i | \(0.275483\pi\) | |||||||
\(60\) | −0.240988 | + | 0.139134i | −0.0311114 | + | 0.0179622i | ||||
\(61\) | 0.995536 | − | 1.72432i | 0.127465 | − | 0.220776i | −0.795229 | − | 0.606310i | \(-0.792649\pi\) |
0.922694 | + | 0.385533i | \(0.125983\pi\) | |||||||
\(62\) | − | 0.596352i | − | 0.0757367i | ||||||
\(63\) | 2.12484 | − | 1.57640i | 0.267705 | − | 0.198608i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.21036 | − | 0.698800i | −0.150126 | − | 0.0866754i | ||||
\(66\) | 0.726620 | + | 1.25854i | 0.0894408 | + | 0.154916i | ||||
\(67\) | 5.81351 | − | 3.35643i | 0.710233 | − | 0.410053i | −0.100914 | − | 0.994895i | \(-0.532177\pi\) |
0.811147 | + | 0.584842i | \(0.198843\pi\) | |||||||
\(68\) | −2.48923 | + | 4.31148i | −0.301864 | + | 0.522844i | ||||
\(69\) | −4.31075 | − | 2.10177i | −0.518953 | − | 0.253023i | ||||
\(70\) | 0.0842550 | + | 0.731393i | 0.0100704 | + | 0.0874182i | ||||
\(71\) | −0.995488 | −0.118143 | −0.0590713 | − | 0.998254i | \(-0.518814\pi\) | ||||
−0.0590713 | + | 0.998254i | \(0.518814\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −13.8151 | + | 7.97614i | −1.61693 | + | 0.933537i | −0.629226 | + | 0.777222i | \(0.716628\pi\) |
−0.987707 | + | 0.156315i | \(0.950039\pi\) | |||||||
\(74\) | 2.31382 | − | 1.33588i | 0.268976 | − | 0.155293i | ||||
\(75\) | −4.26307 | − | 2.46128i | −0.492257 | − | 0.284205i | ||||
\(76\) | 2.05881 | 0.236161 | ||||||||
\(77\) | 3.81965 | − | 0.440016i | 0.435290 | − | 0.0501445i | ||||
\(78\) | −5.02248 | −0.568684 | ||||||||
\(79\) | 2.24875 | + | 1.29832i | 0.253005 | + | 0.146072i | 0.621139 | − | 0.783700i | \(-0.286670\pi\) |
−0.368135 | + | 0.929772i | \(0.620003\pi\) | |||||||
\(80\) | −0.139134 | − | 0.240988i | −0.0155557 | − | 0.0269433i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 2.60682 | + | 1.50505i | 0.287875 | + | 0.166205i | ||||
\(83\) | −8.53132 | −0.936434 | −0.468217 | − | 0.883614i | \(-0.655103\pi\) | ||||
−0.468217 | + | 0.883614i | \(0.655103\pi\) | |||||||
\(84\) | 1.57640 | + | 2.12484i | 0.172000 | + | 0.231839i | ||||
\(85\) | 1.38535 | 0.150263 | ||||||||
\(86\) | −5.92877 | − | 3.42298i | −0.639316 | − | 0.369109i | ||||
\(87\) | −4.54554 | + | 2.62437i | −0.487333 | + | 0.281362i | ||||
\(88\) | −1.25854 | + | 0.726620i | −0.134161 | + | 0.0774580i | ||||
\(89\) | 3.83696 | − | 6.64582i | 0.406717 | − | 0.704455i | −0.587802 | − | 0.809005i | \(-0.700007\pi\) |
0.994520 | + | 0.104549i | \(0.0333400\pi\) | |||||||
\(90\) | 0.278269 | 0.0293321 | ||||||||
\(91\) | −5.28348 | + | 12.1927i | −0.553859 | + | 1.27814i | ||||
\(92\) | 2.10177 | − | 4.31075i | 0.219125 | − | 0.449427i | ||||
\(93\) | −0.298176 | + | 0.516456i | −0.0309194 | + | 0.0535540i | ||||
\(94\) | 8.05896 | − | 4.65284i | 0.831218 | − | 0.479904i | ||||
\(95\) | −0.286451 | − | 0.496147i | −0.0293892 | − | 0.0509036i | ||||
\(96\) | −0.866025 | − | 0.500000i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | 4.93232 | 0.500802 | 0.250401 | − | 0.968142i | \(-0.419438\pi\) | ||||
0.250401 | + | 0.968142i | \(0.419438\pi\) | |||||||
\(98\) | 6.81665 | − | 1.59165i | 0.688585 | − | 0.160781i | ||||
\(99\) | − | 1.45324i | − | 0.146056i | ||||||
\(100\) | 2.46128 | − | 4.26307i | 0.246128 | − | 0.426307i | ||||
\(101\) | 10.4065 | − | 6.00820i | 1.03549 | − | 0.597838i | 0.116935 | − | 0.993140i | \(-0.462693\pi\) |
0.918552 | + | 0.395301i | \(0.129360\pi\) | |||||||
\(102\) | 4.31148 | − | 2.48923i | 0.426900 | − | 0.246471i | ||||
\(103\) | −9.18802 | + | 15.9141i | −0.905322 | + | 1.56806i | −0.0848386 | + | 0.996395i | \(0.527037\pi\) |
−0.820484 | + | 0.571670i | \(0.806296\pi\) | |||||||
\(104\) | − | 5.02248i | − | 0.492494i | ||||||
\(105\) | 0.292730 | − | 0.675533i | 0.0285675 | − | 0.0659252i | ||||
\(106\) | − | 9.99665i | − | 0.970960i | ||||||
\(107\) | −12.9046 | − | 7.45046i | −1.24753 | − | 0.720264i | −0.276916 | − | 0.960894i | \(-0.589312\pi\) |
−0.970617 | + | 0.240631i | \(0.922646\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 11.0866 | − | 6.40085i | 1.06190 | − | 0.613090i | 0.135945 | − | 0.990716i | \(-0.456593\pi\) |
0.925958 | + | 0.377627i | \(0.123260\pi\) | |||||||
\(110\) | 0.350213 | + | 0.202196i | 0.0333915 | + | 0.0192786i | ||||
\(111\) | −2.67177 | −0.253593 | ||||||||
\(112\) | −2.12484 | + | 1.57640i | −0.200779 | + | 0.148956i | ||||
\(113\) | 16.8220i | 1.58248i | 0.611507 | + | 0.791239i | \(0.290563\pi\) | ||||
−0.611507 | + | 0.791239i | \(0.709437\pi\) | |||||||
\(114\) | −1.78298 | − | 1.02940i | −0.166991 | − | 0.0964124i | ||||
\(115\) | −1.33127 | + | 0.0932723i | −0.124141 | + | 0.00869768i | ||||
\(116\) | −2.62437 | − | 4.54554i | −0.243666 | − | 0.422043i | ||||
\(117\) | 4.34959 | + | 2.51124i | 0.402120 | + | 0.232164i | ||||
\(118\) | − | 2.77662i | − | 0.255608i | ||||||
\(119\) | −1.50739 | − | 13.0853i | −0.138183 | − | 1.19952i | ||||
\(120\) | 0.278269i | 0.0254024i | ||||||||
\(121\) | −4.44405 | + | 7.69731i | −0.404004 | + | 0.699756i | ||||
\(122\) | −0.995536 | − | 1.72432i | −0.0901316 | − | 0.156113i | ||||
\(123\) | −1.50505 | − | 2.60682i | −0.135706 | − | 0.235049i | ||||
\(124\) | −0.516456 | − | 0.298176i | −0.0463791 | − | 0.0267770i | ||||
\(125\) | −2.76114 | −0.246964 | ||||||||
\(126\) | −0.302783 | − | 2.62837i | −0.0269740 | − | 0.234154i | ||||
\(127\) | −16.6311 | −1.47577 | −0.737886 | − | 0.674926i | \(-0.764176\pi\) | ||||
−0.737886 | + | 0.674926i | \(0.764176\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 3.42298 | + | 5.92877i | 0.301376 | + | 0.521999i | ||||
\(130\) | −1.21036 | + | 0.698800i | −0.106155 | + | 0.0612888i | ||||
\(131\) | −7.13164 | − | 4.11746i | −0.623094 | − | 0.359744i | 0.154978 | − | 0.987918i | \(-0.450469\pi\) |
−0.778073 | + | 0.628174i | \(0.783803\pi\) | |||||||
\(132\) | 1.45324 | 0.126488 | ||||||||
\(133\) | −4.37464 | + | 3.24551i | −0.379329 | + | 0.281421i | ||||
\(134\) | − | 6.71286i | − | 0.579903i | ||||||
\(135\) | −0.240988 | − | 0.139134i | −0.0207409 | − | 0.0119748i | ||||
\(136\) | 2.48923 | + | 4.31148i | 0.213450 | + | 0.369706i | ||||
\(137\) | 2.87537 | − | 1.66010i | 0.245659 | − | 0.141832i | −0.372116 | − | 0.928186i | \(-0.621368\pi\) |
0.617775 | + | 0.786355i | \(0.288034\pi\) | |||||||
\(138\) | −3.97556 | + | 2.68233i | −0.338422 | + | 0.228335i | ||||
\(139\) | − | 3.39108i | − | 0.287628i | −0.989605 | − | 0.143814i | \(-0.954063\pi\) | ||
0.989605 | − | 0.143814i | \(-0.0459366\pi\) | |||||||
\(140\) | 0.675533 | + | 0.292730i | 0.0570929 | + | 0.0247402i | ||||
\(141\) | −9.30569 | −0.783680 | ||||||||
\(142\) | −0.497744 | + | 0.862118i | −0.0417697 | + | 0.0723473i | ||||
\(143\) | 3.64943 | + | 6.32100i | 0.305181 | + | 0.528589i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −0.730280 | + | 1.26488i | −0.0606464 | + | 0.105043i | ||||
\(146\) | 15.9523i | 1.32022i | ||||||||
\(147\) | −6.69921 | − | 2.02991i | −0.552542 | − | 0.167424i | ||||
\(148\) | − | 2.67177i | − | 0.219618i | ||||||
\(149\) | −15.5768 | − | 8.99329i | −1.27610 | − | 0.736759i | −0.299974 | − | 0.953947i | \(-0.596978\pi\) |
−0.976130 | + | 0.217188i | \(0.930311\pi\) | |||||||
\(150\) | −4.26307 | + | 2.46128i | −0.348078 | + | 0.200963i | ||||
\(151\) | −6.22898 | − | 10.7889i | −0.506907 | − | 0.877988i | −0.999968 | − | 0.00799384i | \(-0.997455\pi\) |
0.493061 | − | 0.869995i | \(-0.335878\pi\) | |||||||
\(152\) | 1.02940 | − | 1.78298i | 0.0834956 | − | 0.144619i | ||||
\(153\) | −4.97847 | −0.402485 | ||||||||
\(154\) | 1.52876 | − | 3.52792i | 0.123191 | − | 0.284288i | ||||
\(155\) | 0.165946i | 0.0133291i | ||||||||
\(156\) | −2.51124 | + | 4.34959i | −0.201060 | + | 0.348246i | ||||
\(157\) | 1.75657 | + | 3.04247i | 0.140189 | + | 0.242815i | 0.927568 | − | 0.373655i | \(-0.121896\pi\) |
−0.787378 | + | 0.616470i | \(0.788562\pi\) | |||||||
\(158\) | 2.24875 | − | 1.29832i | 0.178901 | − | 0.103289i | ||||
\(159\) | −4.99832 | + | 8.65735i | −0.396393 | + | 0.686573i | ||||
\(160\) | −0.278269 | −0.0219991 | ||||||||
\(161\) | 2.32954 | + | 12.4729i | 0.183593 | + | 0.983002i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −8.13414 | + | 14.0887i | −0.637115 | + | 1.10352i | 0.348948 | + | 0.937142i | \(0.386539\pi\) |
−0.986063 | + | 0.166373i | \(0.946794\pi\) | |||||||
\(164\) | 2.60682 | − | 1.50505i | 0.203558 | − | 0.117524i | ||||
\(165\) | −0.202196 | − | 0.350213i | −0.0157409 | − | 0.0272641i | ||||
\(166\) | −4.26566 | + | 7.38834i | −0.331079 | + | 0.573446i | ||||
\(167\) | − | 1.88937i | − | 0.146204i | −0.997324 | − | 0.0731019i | \(-0.976710\pi\) | ||
0.997324 | − | 0.0731019i | \(-0.0232898\pi\) | |||||||
\(168\) | 2.62837 | − | 0.302783i | 0.202783 | − | 0.0233602i | ||||
\(169\) | −12.2253 | −0.940406 | ||||||||
\(170\) | 0.692677 | − | 1.19975i | 0.0531259 | − | 0.0920167i | ||||
\(171\) | 1.02940 | + | 1.78298i | 0.0787204 | + | 0.136348i | ||||
\(172\) | −5.92877 | + | 3.42298i | −0.452064 | + | 0.260999i | ||||
\(173\) | −2.63472 | − | 1.52116i | −0.200314 | − | 0.115652i | 0.396488 | − | 0.918040i | \(-0.370229\pi\) |
−0.596802 | + | 0.802388i | \(0.703562\pi\) | |||||||
\(174\) | 5.24874i | 0.397906i | ||||||||
\(175\) | 1.49047 | + | 12.9383i | 0.112669 | + | 0.978045i | ||||
\(176\) | 1.45324i | 0.109542i | ||||||||
\(177\) | −1.38831 | + | 2.40462i | −0.104352 | + | 0.180742i | ||||
\(178\) | −3.83696 | − | 6.64582i | −0.287593 | − | 0.498125i | ||||
\(179\) | −9.89020 | − | 17.1303i | −0.739228 | − | 1.28038i | −0.952843 | − | 0.303463i | \(-0.901857\pi\) |
0.213615 | − | 0.976918i | \(-0.431476\pi\) | |||||||
\(180\) | 0.139134 | − | 0.240988i | 0.0103705 | − | 0.0179622i | ||||
\(181\) | 12.9611 | 0.963390 | 0.481695 | − | 0.876339i | \(-0.340021\pi\) | ||||
0.481695 | + | 0.876339i | \(0.340021\pi\) | |||||||
\(182\) | 7.91744 | + | 10.6720i | 0.586880 | + | 0.791059i | ||||
\(183\) | 1.99107i | 0.147184i | ||||||||
\(184\) | −2.68233 | − | 3.97556i | −0.197744 | − | 0.293082i | ||||
\(185\) | −0.643863 | + | 0.371735i | −0.0473378 | + | 0.0273305i | ||||
\(186\) | 0.298176 | + | 0.516456i | 0.0218633 | + | 0.0378684i | ||||
\(187\) | −6.26562 | − | 3.61746i | −0.458187 | − | 0.264535i | ||||
\(188\) | − | 9.30569i | − | 0.678687i | ||||||
\(189\) | −1.05197 | + | 2.42763i | −0.0765193 | + | 0.176584i | ||||
\(190\) | −0.572902 | −0.0415626 | ||||||||
\(191\) | 6.47964 | + | 3.74102i | 0.468850 | + | 0.270691i | 0.715758 | − | 0.698348i | \(-0.246081\pi\) |
−0.246908 | + | 0.969039i | \(0.579415\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −6.83388 | − | 11.8366i | −0.491914 | − | 0.852019i | 0.508043 | − | 0.861332i | \(-0.330369\pi\) |
−0.999957 | + | 0.00931234i | \(0.997036\pi\) | |||||||
\(194\) | 2.46616 | − | 4.27152i | 0.177060 | − | 0.306677i | ||||
\(195\) | 1.39760 | 0.100084 | ||||||||
\(196\) | 2.02991 | − | 6.69921i | 0.144994 | − | 0.478515i | ||||
\(197\) | 22.4667 | 1.60069 | 0.800344 | − | 0.599540i | \(-0.204650\pi\) | ||||
0.800344 | + | 0.599540i | \(0.204650\pi\) | |||||||
\(198\) | −1.25854 | − | 0.726620i | −0.0894408 | − | 0.0516386i | ||||
\(199\) | −11.2769 | − | 19.5322i | −0.799400 | − | 1.38460i | −0.920008 | − | 0.391901i | \(-0.871818\pi\) |
0.120608 | − | 0.992700i | \(-0.461516\pi\) | |||||||
\(200\) | −2.46128 | − | 4.26307i | −0.174039 | − | 0.301444i | ||||
\(201\) | −3.35643 | + | 5.81351i | −0.236744 | + | 0.410053i | ||||
\(202\) | − | 12.0164i | − | 0.845471i | ||||||
\(203\) | 12.7420 | + | 5.52150i | 0.894311 | + | 0.387533i | ||||
\(204\) | − | 4.97847i | − | 0.348563i | ||||||
\(205\) | −0.725396 | − | 0.418808i | −0.0506639 | − | 0.0292508i | ||||
\(206\) | 9.18802 | + | 15.9141i | 0.640160 | + | 1.10879i | ||||
\(207\) | 4.78410 | − | 0.335188i | 0.332518 | − | 0.0232971i | ||||
\(208\) | −4.34959 | − | 2.51124i | −0.301590 | − | 0.174123i | ||||
\(209\) | 2.99194i | 0.206957i | ||||||||
\(210\) | −0.438664 | − | 0.591278i | −0.0302707 | − | 0.0408020i | ||||
\(211\) | −9.48946 | −0.653281 | −0.326641 | − | 0.945149i | \(-0.605917\pi\) | ||||
−0.326641 | + | 0.945149i | \(0.605917\pi\) | |||||||
\(212\) | −8.65735 | − | 4.99832i | −0.594589 | − | 0.343286i | ||||
\(213\) | 0.862118 | − | 0.497744i | 0.0590713 | − | 0.0341048i | ||||
\(214\) | −12.9046 | + | 7.45046i | −0.882139 | + | 0.509303i | ||||
\(215\) | 1.64979 | + | 0.952508i | 0.112515 | + | 0.0649605i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 1.56743 | − | 0.180565i | 0.106404 | − | 0.0122575i | ||||
\(218\) | − | 12.8017i | − | 0.867040i | ||||||
\(219\) | 7.97614 | − | 13.8151i | 0.538978 | − | 0.933537i | ||||
\(220\) | 0.350213 | − | 0.202196i | 0.0236114 | − | 0.0136320i | ||||
\(221\) | 21.6543 | − | 12.5021i | 1.45663 | − | 0.840984i | ||||
\(222\) | −1.33588 | + | 2.31382i | −0.0896586 | + | 0.155293i | ||||
\(223\) | 3.96221i | 0.265329i | 0.991161 | + | 0.132664i | \(0.0423533\pi\) | ||||
−0.991161 | + | 0.132664i | \(0.957647\pi\) | |||||||
\(224\) | 0.302783 | + | 2.62837i | 0.0202305 | + | 0.175615i | ||||
\(225\) | 4.92257 | 0.328171 | ||||||||
\(226\) | 14.5683 | + | 8.41098i | 0.969066 | + | 0.559490i | ||||
\(227\) | −9.70885 | − | 16.8162i | −0.644399 | − | 1.11613i | −0.984440 | − | 0.175721i | \(-0.943774\pi\) |
0.340041 | − | 0.940411i | \(-0.389559\pi\) | |||||||
\(228\) | −1.78298 | + | 1.02940i | −0.118081 | + | 0.0681739i | ||||
\(229\) | −10.7428 | + | 18.6070i | −0.709902 | + | 1.22959i | 0.254992 | + | 0.966943i | \(0.417927\pi\) |
−0.964893 | + | 0.262642i | \(0.915406\pi\) | |||||||
\(230\) | −0.584858 | + | 1.19955i | −0.0385644 | + | 0.0790958i | ||||
\(231\) | −3.08791 | + | 2.29089i | −0.203169 | + | 0.150730i | ||||
\(232\) | −5.24874 | −0.344596 | ||||||||
\(233\) | 2.13431 | − | 3.69673i | 0.139823 | − | 0.242181i | −0.787606 | − | 0.616179i | \(-0.788680\pi\) |
0.927430 | + | 0.373998i | \(0.122013\pi\) | |||||||
\(234\) | 4.34959 | − | 2.51124i | 0.284342 | − | 0.164165i | ||||
\(235\) | −2.24256 | + | 1.29474i | −0.146288 | + | 0.0844596i | ||||
\(236\) | −2.40462 | − | 1.38831i | −0.156528 | − | 0.0903712i | ||||
\(237\) | −2.59664 | −0.168670 | ||||||||
\(238\) | −12.0859 | − | 5.23718i | −0.783410 | − | 0.339476i | ||||
\(239\) | −16.3611 | −1.05831 | −0.529155 | − | 0.848525i | \(-0.677491\pi\) | ||||
−0.529155 | + | 0.848525i | \(0.677491\pi\) | |||||||
\(240\) | 0.240988 | + | 0.139134i | 0.0155557 | + | 0.00898109i | ||||
\(241\) | 4.89018 | + | 8.47005i | 0.315004 | + | 0.545604i | 0.979438 | − | 0.201743i | \(-0.0646607\pi\) |
−0.664434 | + | 0.747347i | \(0.731327\pi\) | |||||||
\(242\) | 4.44405 | + | 7.69731i | 0.285674 | + | 0.494802i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | −1.99107 | −0.127465 | ||||||||
\(245\) | −1.89686 | + | 0.442906i | −0.121186 | + | 0.0282963i | ||||
\(246\) | −3.01009 | −0.191917 | ||||||||
\(247\) | −8.95497 | − | 5.17015i | −0.569791 | − | 0.328969i | ||||
\(248\) | −0.516456 | + | 0.298176i | −0.0327950 | + | 0.0189342i | ||||
\(249\) | 7.38834 | − | 4.26566i | 0.468217 | − | 0.270325i | ||||
\(250\) | −1.38057 | + | 2.39122i | −0.0873150 | + | 0.151234i | ||||
\(251\) | −13.4746 | −0.850510 | −0.425255 | − | 0.905074i | \(-0.639816\pi\) | ||||
−0.425255 | + | 0.905074i | \(0.639816\pi\) | |||||||
\(252\) | −2.42763 | − | 1.05197i | −0.152926 | − | 0.0662677i | ||||
\(253\) | 6.26455 | + | 3.05438i | 0.393849 | + | 0.192027i | ||||
\(254\) | −8.31555 | + | 14.4030i | −0.521764 | + | 0.903722i | ||||
\(255\) | −1.19975 | + | 0.692677i | −0.0751313 | + | 0.0433771i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 17.9057 | + | 10.3379i | 1.11693 | + | 0.644858i | 0.940614 | − | 0.339477i | \(-0.110250\pi\) |
0.176312 | + | 0.984334i | \(0.443583\pi\) | |||||||
\(258\) | 6.84595 | 0.426210 | ||||||||
\(259\) | 4.21178 | + | 5.67708i | 0.261707 | + | 0.352757i | ||||
\(260\) | 1.39760i | 0.0866754i | ||||||||
\(261\) | 2.62437 | − | 4.54554i | 0.162444 | − | 0.281362i | ||||
\(262\) | −7.13164 | + | 4.11746i | −0.440594 | + | 0.254377i | ||||
\(263\) | 21.9199 | − | 12.6554i | 1.35164 | − | 0.780368i | 0.363158 | − | 0.931728i | \(-0.381698\pi\) |
0.988479 | + | 0.151360i | \(0.0483651\pi\) | |||||||
\(264\) | 0.726620 | − | 1.25854i | 0.0447204 | − | 0.0774580i | ||||
\(265\) | 2.78176i | 0.170882i | ||||||||
\(266\) | 0.623371 | + | 5.41130i | 0.0382213 | + | 0.331788i | ||||
\(267\) | 7.67393i | 0.469637i | ||||||||
\(268\) | −5.81351 | − | 3.35643i | −0.355117 | − | 0.205027i | ||||
\(269\) | 1.65705 | − | 0.956701i | 0.101032 | − | 0.0583311i | −0.448632 | − | 0.893716i | \(-0.648089\pi\) |
0.549665 | + | 0.835385i | \(0.314755\pi\) | |||||||
\(270\) | −0.240988 | + | 0.139134i | −0.0146661 | + | 0.00846745i | ||||
\(271\) | 16.2938 | + | 9.40723i | 0.989778 | + | 0.571448i | 0.905208 | − | 0.424969i | \(-0.139715\pi\) |
0.0845698 | + | 0.996418i | \(0.473048\pi\) | |||||||
\(272\) | 4.97847 | 0.301864 | ||||||||
\(273\) | −1.52072 | − | 13.2009i | −0.0920381 | − | 0.798956i | ||||
\(274\) | − | 3.32019i | − | 0.200580i | ||||||
\(275\) | 6.19526 | + | 3.57684i | 0.373588 | + | 0.215691i | ||||
\(276\) | 0.335188 | + | 4.78410i | 0.0201759 | + | 0.287969i | ||||
\(277\) | −2.82129 | − | 4.88662i | −0.169515 | − | 0.293609i | 0.768734 | − | 0.639568i | \(-0.220887\pi\) |
−0.938249 | + | 0.345959i | \(0.887553\pi\) | |||||||
\(278\) | −2.93676 | − | 1.69554i | −0.176135 | − | 0.101692i | ||||
\(279\) | − | 0.596352i | − | 0.0357026i | ||||||
\(280\) | 0.591278 | − | 0.438664i | 0.0353356 | − | 0.0262152i | ||||
\(281\) | − | 9.86793i | − | 0.588671i | −0.955702 | − | 0.294336i | \(-0.904902\pi\) | ||
0.955702 | − | 0.294336i | \(-0.0950983\pi\) | |||||||
\(282\) | −4.65284 | + | 8.05896i | −0.277073 | + | 0.479904i | ||||
\(283\) | 0.299057 | + | 0.517982i | 0.0177771 | + | 0.0307908i | 0.874777 | − | 0.484526i | \(-0.161008\pi\) |
−0.857000 | + | 0.515316i | \(0.827674\pi\) | |||||||
\(284\) | 0.497744 | + | 0.862118i | 0.0295357 | + | 0.0511573i | ||||
\(285\) | 0.496147 | + | 0.286451i | 0.0293892 | + | 0.0169679i | ||||
\(286\) | 7.29887 | 0.431591 | ||||||||
\(287\) | −3.16652 | + | 7.30738i | −0.186914 | + | 0.431341i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −3.89258 | + | 6.74214i | −0.228975 | + | 0.396596i | ||||
\(290\) | 0.730280 | + | 1.26488i | 0.0428835 | + | 0.0742764i | ||||
\(291\) | −4.27152 | + | 2.46616i | −0.250401 | + | 0.144569i | ||||
\(292\) | 13.8151 | + | 7.97614i | 0.808467 | + | 0.466769i | ||||
\(293\) | −23.6190 | −1.37984 | −0.689918 | − | 0.723887i | \(-0.742354\pi\) | ||||
−0.689918 | + | 0.723887i | \(0.742354\pi\) | |||||||
\(294\) | −5.10756 | + | 4.78673i | −0.297879 | + | 0.279168i | ||||
\(295\) | 0.772647i | 0.0449852i | ||||||||
\(296\) | −2.31382 | − | 1.33588i | −0.134488 | − | 0.0776466i | ||||
\(297\) | 0.726620 | + | 1.25854i | 0.0421628 | + | 0.0730281i | ||||
\(298\) | −15.5768 | + | 8.99329i | −0.902342 | + | 0.520967i | ||||
\(299\) | −19.9672 | + | 13.4720i | −1.15473 | + | 0.779103i | ||||
\(300\) | 4.92257i | 0.284205i | ||||||||
\(301\) | 7.20171 | − | 16.6194i | 0.415100 | − | 0.957927i | ||||
\(302\) | −12.4580 | −0.716875 | ||||||||
\(303\) | −6.00820 | + | 10.4065i | −0.345162 | + | 0.597838i | ||||
\(304\) | −1.02940 | − | 1.78298i | −0.0590403 | − | 0.102261i | ||||
\(305\) | 0.277027 | + | 0.479824i | 0.0158625 | + | 0.0274747i | ||||
\(306\) | −2.48923 | + | 4.31148i | −0.142300 | + | 0.246471i | ||||
\(307\) | 13.2254i | 0.754812i | 0.926048 | + | 0.377406i | \(0.123184\pi\) | ||||
−0.926048 | + | 0.377406i | \(0.876816\pi\) | |||||||
\(308\) | −2.29089 | − | 3.08791i | −0.130536 | − | 0.175950i | ||||
\(309\) | − | 18.3760i | − | 1.04538i | ||||||
\(310\) | 0.143714 | + | 0.0829731i | 0.00816238 | + | 0.00471255i | ||||
\(311\) | −20.3311 | + | 11.7382i | −1.15287 | + | 0.665610i | −0.949585 | − | 0.313510i | \(-0.898495\pi\) |
−0.203285 | + | 0.979120i | \(0.565162\pi\) | |||||||
\(312\) | 2.51124 | + | 4.34959i | 0.142171 | + | 0.246247i | ||||
\(313\) | 8.95215 | − | 15.5056i | 0.506006 | − | 0.876427i | −0.493970 | − | 0.869479i | \(-0.664455\pi\) |
0.999976 | − | 0.00694863i | \(-0.00221184\pi\) | |||||||
\(314\) | 3.51314 | 0.198258 | ||||||||
\(315\) | 0.0842550 | + | 0.731393i | 0.00474723 | + | 0.0412093i | ||||
\(316\) | − | 2.59664i | − | 0.146072i | ||||||
\(317\) | 4.20294 | − | 7.27971i | 0.236061 | − | 0.408869i | −0.723520 | − | 0.690304i | \(-0.757477\pi\) |
0.959580 | + | 0.281435i | \(0.0908103\pi\) | |||||||
\(318\) | 4.99832 | + | 8.65735i | 0.280292 | + | 0.485480i | ||||
\(319\) | 6.60576 | − | 3.81384i | 0.369852 | − | 0.213534i | ||||
\(320\) | −0.139134 | + | 0.240988i | −0.00777785 | + | 0.0134716i | ||||
\(321\) | 14.9009 | 0.831689 | ||||||||
\(322\) | 11.9666 | + | 4.21901i | 0.666874 | + | 0.235116i | ||||
\(323\) | 10.2497 | 0.570309 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −21.4112 | + | 12.3617i | −1.18768 | + | 0.685706i | ||||
\(326\) | 8.13414 | + | 14.0887i | 0.450508 | + | 0.780303i | ||||
\(327\) | −6.40085 | + | 11.0866i | −0.353968 | + | 0.613090i | ||||
\(328\) | − | 3.01009i | − | 0.166205i | ||||||
\(329\) | 14.6695 | + | 19.7731i | 0.808756 | + | 1.09013i | ||||
\(330\) | −0.404392 | −0.0222610 | ||||||||
\(331\) | −0.0738206 | + | 0.127861i | −0.00405755 | + | 0.00702787i | −0.868047 | − | 0.496482i | \(-0.834625\pi\) |
0.863990 | + | 0.503510i | \(0.167958\pi\) | |||||||
\(332\) | 4.26566 | + | 7.38834i | 0.234108 | + | 0.405488i | ||||
\(333\) | 2.31382 | − | 1.33588i | 0.126796 | − | 0.0732059i | ||||
\(334\) | −1.63624 | − | 0.944685i | −0.0895312 | − | 0.0516909i | ||||
\(335\) | 1.86798i | 0.102059i | ||||||||
\(336\) | 1.05197 | − | 2.42763i | 0.0573895 | − | 0.132438i | ||||
\(337\) | − | 26.5506i | − | 1.44630i | −0.690689 | − | 0.723152i | \(-0.742693\pi\) | ||
0.690689 | − | 0.723152i | \(-0.257307\pi\) | |||||||
\(338\) | −6.11264 | + | 10.5874i | −0.332484 | + | 0.575879i | ||||
\(339\) | −8.41098 | − | 14.5683i | −0.456822 | − | 0.791239i | ||||
\(340\) | −0.692677 | − | 1.19975i | −0.0375657 | − | 0.0650656i | ||||
\(341\) | 0.433321 | − | 0.750534i | 0.0234657 | − | 0.0406437i | ||||
\(342\) | 2.05881 | 0.111327 | ||||||||
\(343\) | 6.24740 | + | 17.4347i | 0.337328 | + | 0.941387i | ||||
\(344\) | 6.84595i | 0.369109i | ||||||||
\(345\) | 1.10628 | − | 0.746410i | 0.0595599 | − | 0.0401854i | ||||
\(346\) | −2.63472 | + | 1.52116i | −0.141644 | + | 0.0817780i | ||||
\(347\) | −3.99997 | − | 6.92816i | −0.214730 | − | 0.371923i | 0.738459 | − | 0.674298i | \(-0.235554\pi\) |
−0.953189 | + | 0.302375i | \(0.902220\pi\) | |||||||
\(348\) | 4.54554 | + | 2.62437i | 0.243666 | + | 0.140681i | ||||
\(349\) | − | 33.9485i | − | 1.81722i | −0.417642 | − | 0.908612i | \(-0.637143\pi\) | ||
0.417642 | − | 0.908612i | \(-0.362857\pi\) | |||||||
\(350\) | 11.9501 | + | 5.17838i | 0.638762 | + | 0.276796i | ||||
\(351\) | −5.02248 | −0.268080 | ||||||||
\(352\) | 1.25854 | + | 0.726620i | 0.0670806 | + | 0.0387290i | ||||
\(353\) | 16.5387 | − | 9.54860i | 0.880264 | − | 0.508221i | 0.00951850 | − | 0.999955i | \(-0.496970\pi\) |
0.870745 | + | 0.491734i | \(0.163637\pi\) | |||||||
\(354\) | 1.38831 | + | 2.40462i | 0.0737878 | + | 0.127804i | ||||
\(355\) | 0.138507 | − | 0.239901i | 0.00735117 | − | 0.0127326i | ||||
\(356\) | −7.67393 | −0.406717 | ||||||||
\(357\) | 7.84807 | + | 10.5785i | 0.415364 | + | 0.559872i | ||||
\(358\) | −19.7804 | −1.04543 | ||||||||
\(359\) | −15.3719 | − | 8.87498i | −0.811298 | − | 0.468403i | 0.0361083 | − | 0.999348i | \(-0.488504\pi\) |
−0.847407 | + | 0.530945i | \(0.821837\pi\) | |||||||
\(360\) | −0.139134 | − | 0.240988i | −0.00733303 | − | 0.0127012i | ||||
\(361\) | 7.38066 | + | 12.7837i | 0.388456 | + | 0.672825i | ||||
\(362\) | 6.48055 | − | 11.2246i | 0.340610 | − | 0.589954i | ||||
\(363\) | − | 8.88809i | − | 0.466504i | ||||||
\(364\) | 13.2009 | − | 1.52072i | 0.691916 | − | 0.0797073i | ||||
\(365\) | − | 4.43903i | − | 0.232349i | ||||||
\(366\) | 1.72432 | + | 0.995536i | 0.0901316 | + | 0.0520375i | ||||
\(367\) | −0.753044 | − | 1.30431i | −0.0393086 | − | 0.0680845i | 0.845702 | − | 0.533656i | \(-0.179182\pi\) |
−0.885010 | + | 0.465571i | \(0.845849\pi\) | |||||||
\(368\) | −4.78410 | + | 0.335188i | −0.249389 | + | 0.0174729i | ||||
\(369\) | 2.60682 | + | 1.50505i | 0.135706 | + | 0.0783496i | ||||
\(370\) | 0.743469i | 0.0386511i | ||||||||
\(371\) | 26.2749 | − | 3.02681i | 1.36412 | − | 0.157144i | ||||
\(372\) | 0.596352 | 0.0309194 | ||||||||
\(373\) | −15.6481 | − | 9.03445i | −0.810230 | − | 0.467786i | 0.0368060 | − | 0.999322i | \(-0.488282\pi\) |
−0.847036 | + | 0.531536i | \(0.821615\pi\) | |||||||
\(374\) | −6.26562 | + | 3.61746i | −0.323987 | + | 0.187054i | ||||
\(375\) | 2.39122 | − | 1.38057i | 0.123482 | − | 0.0712924i | ||||
\(376\) | −8.05896 | − | 4.65284i | −0.415609 | − | 0.239952i | ||||
\(377\) | 26.3617i | 1.35769i | ||||||||
\(378\) | 1.57640 | + | 2.12484i | 0.0810814 | + | 0.109290i | ||||
\(379\) | − | 4.50478i | − | 0.231395i | −0.993284 | − | 0.115697i | \(-0.963090\pi\) | ||
0.993284 | − | 0.115697i | \(-0.0369103\pi\) | |||||||
\(380\) | −0.286451 | + | 0.496147i | −0.0146946 | + | 0.0254518i | ||||
\(381\) | 14.4030 | − | 8.31555i | 0.737886 | − | 0.426019i | ||||
\(382\) | 6.47964 | − | 3.74102i | 0.331527 | − | 0.191407i | ||||
\(383\) | −0.360283 | + | 0.624029i | −0.0184096 | + | 0.0318864i | −0.875083 | − | 0.483972i | \(-0.839194\pi\) |
0.856674 | + | 0.515858i | \(0.172527\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | −0.425407 | + | 0.981711i | −0.0216807 | + | 0.0500326i | ||||
\(386\) | −13.6678 | −0.695671 | ||||||||
\(387\) | −5.92877 | − | 3.42298i | −0.301376 | − | 0.174000i | ||||
\(388\) | −2.46616 | − | 4.27152i | −0.125200 | − | 0.216853i | ||||
\(389\) | −13.8804 | + | 8.01386i | −0.703764 | + | 0.406319i | −0.808748 | − | 0.588155i | \(-0.799854\pi\) |
0.104984 | + | 0.994474i | \(0.466521\pi\) | |||||||
\(390\) | 0.698800 | − | 1.21036i | 0.0353851 | − | 0.0612888i | ||||
\(391\) | 10.4636 | − | 21.4609i | 0.529167 | − | 1.08533i | ||||
\(392\) | −4.78673 | − | 5.10756i | −0.241766 | − | 0.257971i | ||||
\(393\) | 8.23491 | 0.415396 | ||||||||
\(394\) | 11.2334 | − | 19.4568i | 0.565929 | − | 0.980218i | ||||
\(395\) | −0.625758 | + | 0.361282i | −0.0314853 | + | 0.0181781i | ||||
\(396\) | −1.25854 | + | 0.726620i | −0.0632442 | + | 0.0365140i | ||||
\(397\) | 14.0889 | + | 8.13423i | 0.707101 | + | 0.408245i | 0.809987 | − | 0.586448i | \(-0.199474\pi\) |
−0.102886 | + | 0.994693i | \(0.532808\pi\) | |||||||
\(398\) | −22.5538 | −1.13052 | ||||||||
\(399\) | 2.16580 | − | 4.99801i | 0.108425 | − | 0.250213i | ||||
\(400\) | −4.92257 | −0.246128 | ||||||||
\(401\) | 5.37637 | + | 3.10405i | 0.268483 | + | 0.155009i | 0.628198 | − | 0.778053i | \(-0.283793\pi\) |
−0.359715 | + | 0.933062i | \(0.617126\pi\) | |||||||
\(402\) | 3.35643 | + | 5.81351i | 0.167404 | + | 0.289951i | ||||
\(403\) | 1.49758 | + | 2.59389i | 0.0745998 | + | 0.129211i | ||||
\(404\) | −10.4065 | − | 6.00820i | −0.517743 | − | 0.298919i | ||||
\(405\) | 0.278269 | 0.0138273 | ||||||||
\(406\) | 11.1527 | − | 8.27412i | 0.553501 | − | 0.410638i | ||||
\(407\) | 3.88272 | 0.192459 | ||||||||
\(408\) | −4.31148 | − | 2.48923i | −0.213450 | − | 0.123235i | ||||
\(409\) | 17.5282 | − | 10.1199i | 0.866712 | − | 0.500396i | 0.000457799 | − | 1.00000i | \(-0.499854\pi\) |
0.866254 | + | 0.499603i | \(0.166521\pi\) | |||||||
\(410\) | −0.725396 | + | 0.418808i | −0.0358248 | + | 0.0206834i | ||||
\(411\) | −1.66010 | + | 2.87537i | −0.0818865 | + | 0.141832i | ||||
\(412\) | 18.3760 | 0.905322 | ||||||||
\(413\) | 7.29798 | − | 0.840712i | 0.359110 | − | 0.0413687i | ||||
\(414\) | 2.10177 | − | 4.31075i | 0.103296 | − | 0.211862i | ||||
\(415\) | 1.18700 | − | 2.05594i | 0.0582675 | − | 0.100922i | ||||
\(416\) | −4.34959 | + | 2.51124i | −0.213256 | + | 0.123124i | ||||
\(417\) | 1.69554 | + | 2.93676i | 0.0830309 | + | 0.143814i | ||||
\(418\) | 2.59110 | + | 1.49597i | 0.126735 | + | 0.0731703i | ||||
\(419\) | −8.90997 | −0.435281 | −0.217640 | − | 0.976029i | \(-0.569836\pi\) | ||||
−0.217640 | + | 0.976029i | \(0.569836\pi\) | |||||||
\(420\) | −0.731393 | + | 0.0842550i | −0.0356883 | + | 0.00411122i | ||||
\(421\) | 36.2767i | 1.76802i | 0.467469 | + | 0.884009i | \(0.345166\pi\) | ||||
−0.467469 | + | 0.884009i | \(0.654834\pi\) | |||||||
\(422\) | −4.74473 | + | 8.21811i | −0.230970 | + | 0.400051i | ||||
\(423\) | 8.05896 | − | 4.65284i | 0.391840 | − | 0.226229i | ||||
\(424\) | −8.65735 | + | 4.99832i | −0.420438 | + | 0.242740i | ||||
\(425\) | 12.2534 | − | 21.2235i | 0.594378 | − | 1.02949i | ||||
\(426\) | − | 0.995488i | − | 0.0482315i | ||||||
\(427\) | 4.23072 | − | 3.13873i | 0.204739 | − | 0.151894i | ||||
\(428\) | 14.9009i | 0.720264i | ||||||||
\(429\) | −6.32100 | − | 3.64943i | −0.305181 | − | 0.176196i | ||||
\(430\) | 1.64979 | − | 0.952508i | 0.0795600 | − | 0.0459340i | ||||
\(431\) | −1.00463 | + | 0.580021i | −0.0483911 | + | 0.0279386i | −0.524000 | − | 0.851718i | \(-0.675561\pi\) |
0.475609 | + | 0.879657i | \(0.342228\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | 17.5484 | 0.843325 | 0.421662 | − | 0.906753i | \(-0.361447\pi\) | ||||
0.421662 | + | 0.906753i | \(0.361447\pi\) | |||||||
\(434\) | 0.627342 | − | 1.44772i | 0.0301134 | − | 0.0694927i | ||||
\(435\) | − | 1.46056i | − | 0.0700285i | ||||||
\(436\) | −11.0866 | − | 6.40085i | −0.530951 | − | 0.306545i | ||||
\(437\) | −9.84954 | + | 0.690086i | −0.471167 | + | 0.0330113i | ||||
\(438\) | −7.97614 | − | 13.8151i | −0.381115 | − | 0.660110i | ||||
\(439\) | −16.9006 | − | 9.75755i | −0.806620 | − | 0.465702i | 0.0391606 | − | 0.999233i | \(-0.487532\pi\) |
−0.845781 | + | 0.533531i | \(0.820865\pi\) | |||||||
\(440\) | − | 0.404392i | − | 0.0192786i | ||||||
\(441\) | 6.81665 | − | 1.59165i | 0.324602 | − | 0.0757928i | ||||
\(442\) | − | 25.0042i | − | 1.18933i | ||||||
\(443\) | −0.389410 | + | 0.674478i | −0.0185014 | + | 0.0320454i | −0.875128 | − | 0.483892i | \(-0.839223\pi\) |
0.856626 | + | 0.515937i | \(0.172556\pi\) | |||||||
\(444\) | 1.33588 | + | 2.31382i | 0.0633982 | + | 0.109809i | ||||
\(445\) | 1.06771 | + | 1.84932i | 0.0506142 | + | 0.0876664i | ||||
\(446\) | 3.43137 | + | 1.98110i | 0.162480 | + | 0.0938079i | ||||
\(447\) | 17.9866 | 0.850736 | ||||||||
\(448\) | 2.42763 | + | 1.05197i | 0.114695 | + | 0.0497008i | ||||
\(449\) | 25.0675 | 1.18301 | 0.591504 | − | 0.806302i | \(-0.298534\pi\) | ||||
0.591504 | + | 0.806302i | \(0.298534\pi\) | |||||||
\(450\) | 2.46128 | − | 4.26307i | 0.116026 | − | 0.200963i | ||||
\(451\) | 2.18720 | + | 3.78833i | 0.102991 | + | 0.178386i | ||||
\(452\) | 14.5683 | − | 8.41098i | 0.685233 | − | 0.395619i | ||||
\(453\) | 10.7889 | + | 6.22898i | 0.506907 | + | 0.292663i | ||||
\(454\) | −19.4177 | −0.911318 | ||||||||
\(455\) | −2.20318 | − | 2.96968i | −0.103287 | − | 0.139221i | ||||
\(456\) | 2.05881i | 0.0964124i | ||||||||
\(457\) | −13.3581 | − | 7.71230i | −0.624866 | − | 0.360766i | 0.153895 | − | 0.988087i | \(-0.450818\pi\) |
−0.778761 | + | 0.627321i | \(0.784151\pi\) | |||||||
\(458\) | 10.7428 | + | 18.6070i | 0.501976 | + | 0.869448i | ||||
\(459\) | 4.31148 | − | 2.48923i | 0.201243 | − | 0.116188i | ||||
\(460\) | 0.746410 | + | 1.10628i | 0.0348015 | + | 0.0515803i | ||||
\(461\) | 8.17952i | 0.380958i | 0.981691 | + | 0.190479i | \(0.0610042\pi\) | ||||
−0.981691 | + | 0.190479i | \(0.938996\pi\) | |||||||
\(462\) | 0.440016 | + | 3.81965i | 0.0204714 | + | 0.177706i | ||||
\(463\) | 23.6105 | 1.09727 | 0.548637 | − | 0.836061i | \(-0.315147\pi\) | ||||
0.548637 | + | 0.836061i | \(0.315147\pi\) | |||||||
\(464\) | −2.62437 | + | 4.54554i | −0.121833 | + | 0.211021i | ||||
\(465\) | −0.0829731 | − | 0.143714i | −0.00384778 | − | 0.00666456i | ||||
\(466\) | −2.13431 | − | 3.69673i | −0.0988700 | − | 0.171248i | ||||
\(467\) | −4.19554 | + | 7.26688i | −0.194146 | + | 0.336271i | −0.946620 | − | 0.322351i | \(-0.895527\pi\) |
0.752474 | + | 0.658622i | \(0.228860\pi\) | |||||||
\(468\) | − | 5.02248i | − | 0.232164i | ||||||
\(469\) | 17.6439 | − | 2.03254i | 0.814718 | − | 0.0938539i | ||||
\(470\) | 2.58948i | 0.119444i | ||||||||
\(471\) | −3.04247 | − | 1.75657i | −0.140189 | − | 0.0809384i | ||||
\(472\) | −2.40462 | + | 1.38831i | −0.110682 | + | 0.0639021i | ||||
\(473\) | −4.97441 | − | 8.61592i | −0.228723 | − | 0.396161i | ||||
\(474\) | −1.29832 | + | 2.24875i | −0.0596338 | + | 0.103289i | ||||
\(475\) | −10.1346 | −0.465008 | ||||||||
\(476\) | −10.5785 | + | 7.84807i | −0.484863 | + | 0.359716i | ||||
\(477\) | − | 9.99665i | − | 0.457715i | ||||||
\(478\) | −8.18054 | + | 14.1691i | −0.374169 | + | 0.648080i | ||||
\(479\) | 0.233245 | + | 0.403992i | 0.0106572 | + | 0.0184589i | 0.871305 | − | 0.490742i | \(-0.163274\pi\) |
−0.860648 | + | 0.509201i | \(0.829941\pi\) | |||||||
\(480\) | 0.240988 | − | 0.139134i | 0.0109995 | − | 0.00635059i | ||||
\(481\) | −6.70944 | + | 11.6211i | −0.305924 | + | 0.529876i | ||||
\(482\) | 9.78037 | 0.445483 | ||||||||
\(483\) | −8.25389 | − | 9.63708i | −0.375565 | − | 0.438502i | ||||
\(484\) | 8.88809 | 0.404004 | ||||||||
\(485\) | −0.686256 | + | 1.18863i | −0.0311613 | + | 0.0539729i | ||||
\(486\) | 0.866025 | − | 0.500000i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | 12.5261 | + | 21.6958i | 0.567610 | + | 0.983129i | 0.996802 | + | 0.0799156i | \(0.0254651\pi\) |
−0.429192 | + | 0.903213i | \(0.641202\pi\) | |||||||
\(488\) | −0.995536 | + | 1.72432i | −0.0450658 | + | 0.0780563i | ||||
\(489\) | − | 16.2683i | − | 0.735677i | ||||||
\(490\) | −0.564862 | + | 1.86418i | −0.0255179 | + | 0.0842152i | ||||
\(491\) | 2.14815 | 0.0969448 | 0.0484724 | − | 0.998825i | \(-0.484565\pi\) | ||||
0.0484724 | + | 0.998825i | \(0.484565\pi\) | |||||||
\(492\) | −1.50505 | + | 2.60682i | −0.0678528 | + | 0.117524i | ||||
\(493\) | −13.0653 | − | 22.6298i | −0.588433 | − | 1.01920i | ||||
\(494\) | −8.95497 | + | 5.17015i | −0.402903 | + | 0.232616i | ||||
\(495\) | 0.350213 | + | 0.202196i | 0.0157409 | + | 0.00908802i | ||||
\(496\) | 0.596352i | 0.0267770i | ||||||||
\(497\) | −2.41667 | − | 1.04722i | −0.108403 | − | 0.0469742i | ||||
\(498\) | − | 8.53132i | − | 0.382297i | ||||||
\(499\) | 17.7523 | − | 30.7479i | 0.794702 | − | 1.37646i | −0.128327 | − | 0.991732i | \(-0.540961\pi\) |
0.923029 | − | 0.384732i | \(-0.125706\pi\) | |||||||
\(500\) | 1.38057 | + | 2.39122i | 0.0617410 | + | 0.106939i | ||||
\(501\) | 0.944685 | + | 1.63624i | 0.0422054 | + | 0.0731019i | ||||
\(502\) | −6.73730 | + | 11.6694i | −0.300701 | + | 0.520829i | ||||
\(503\) | 28.2838 | 1.26111 | 0.630556 | − | 0.776144i | \(-0.282827\pi\) | ||||
0.630556 | + | 0.776144i | \(0.282827\pi\) | |||||||
\(504\) | −2.12484 | + | 1.57640i | −0.0946480 | + | 0.0702185i | ||||
\(505\) | 3.34379i | 0.148797i | ||||||||
\(506\) | 5.77745 | − | 3.89807i | 0.256839 | − | 0.173291i | ||||
\(507\) | 10.5874 | − | 6.11264i | 0.470203 | − | 0.271472i | ||||
\(508\) | 8.31555 | + | 14.4030i | 0.368943 | + | 0.639028i | ||||
\(509\) | −21.4524 | − | 12.3855i | −0.950859 | − | 0.548979i | −0.0575113 | − | 0.998345i | \(-0.518317\pi\) |
−0.893348 | + | 0.449366i | \(0.851650\pi\) | |||||||
\(510\) | 1.38535i | 0.0613445i | ||||||||
\(511\) | −41.9285 | + | 4.83008i | −1.85481 | + | 0.213670i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.78298 | − | 1.02940i | −0.0787204 | − | 0.0454492i | ||||
\(514\) | 17.9057 | − | 10.3379i | 0.789786 | − | 0.455983i | ||||
\(515\) | −2.55674 | − | 4.42840i | −0.112663 | − | 0.195139i | ||||
\(516\) | 3.42298 | − | 5.92877i | 0.150688 | − | 0.260999i | ||||
\(517\) | 13.5234 | 0.594758 | ||||||||
\(518\) | 7.02238 | − | 0.808964i | 0.308546 | − | 0.0355439i | ||||
\(519\) | 3.04232 | 0.133543 | ||||||||
\(520\) | 1.21036 | + | 0.698800i | 0.0530776 | + | 0.0306444i | ||||
\(521\) | −20.7362 | − | 35.9161i | −0.908467 | − | 1.57351i | −0.816194 | − | 0.577778i | \(-0.803920\pi\) |
−0.0922736 | − | 0.995734i | \(-0.529413\pi\) | |||||||
\(522\) | −2.62437 | − | 4.54554i | −0.114865 | − | 0.198953i | ||||
\(523\) | 13.2843 | − | 23.0090i | 0.580880 | − | 1.00611i | −0.414495 | − | 0.910051i | \(-0.636042\pi\) |
0.995375 | − | 0.0960622i | \(-0.0306248\pi\) | |||||||
\(524\) | 8.23491i | 0.359744i | ||||||||
\(525\) | −7.75994 | − | 10.4597i | −0.338672 | − | 0.456498i | ||||
\(526\) | − | 25.3109i | − | 1.10361i | ||||||
\(527\) | −2.57116 | − | 1.48446i | −0.112001 | − | 0.0646640i | ||||
\(528\) | −0.726620 | − | 1.25854i | −0.0316221 | − | 0.0547711i | ||||
\(529\) | −8.61018 | + | 21.3276i | −0.374356 | + | 0.927285i | ||||
\(530\) | 2.40907 | + | 1.39088i | 0.104643 | + | 0.0604159i | ||||
\(531\) | − | 2.77662i | − | 0.120495i | ||||||
\(532\) | 4.99801 | + | 2.16580i | 0.216691 | + | 0.0938991i | ||||
\(533\) | −15.1181 | −0.654839 | ||||||||
\(534\) | 6.64582 | + | 3.83696i | 0.287593 | + | 0.166042i | ||||
\(535\) | 3.59094 | − | 2.07323i | 0.155250 | − | 0.0896337i | ||||
\(536\) | −5.81351 | + | 3.35643i | −0.251105 | + | 0.144976i | ||||
\(537\) | 17.1303 | + | 9.89020i | 0.739228 | + | 0.426794i | ||||
\(538\) | − | 1.91340i | − | 0.0824926i | ||||||
\(539\) | 9.73557 | + | 2.94995i | 0.419340 | + | 0.127063i | ||||
\(540\) | 0.278269i | 0.0119748i | ||||||||
\(541\) | −3.35014 | + | 5.80261i | −0.144034 | + | 0.249474i | −0.929012 | − | 0.370050i | \(-0.879341\pi\) |
0.784978 | + | 0.619523i | \(0.212674\pi\) | |||||||
\(542\) | 16.2938 | − | 9.40723i | 0.699879 | − | 0.404075i | ||||
\(543\) | −11.2246 | + | 6.48055i | −0.481695 | + | 0.278107i | ||||
\(544\) | 2.48923 | − | 4.31148i | 0.106725 | − | 0.184853i | ||||
\(545\) | 3.56231i | 0.152593i | ||||||||
\(546\) | −12.1927 | − | 5.28348i | −0.521799 | − | 0.226112i | ||||
\(547\) | 13.8116 | 0.590543 | 0.295271 | − | 0.955413i | \(-0.404590\pi\) | ||||
0.295271 | + | 0.955413i | \(0.404590\pi\) | |||||||
\(548\) | −2.87537 | − | 1.66010i | −0.122830 | − | 0.0709158i | ||||
\(549\) | −0.995536 | − | 1.72432i | −0.0424885 | − | 0.0735922i | ||||
\(550\) | 6.19526 | − | 3.57684i | 0.264167 | − | 0.152517i | ||||
\(551\) | −5.40306 | + | 9.35838i | −0.230178 | + | 0.398680i | ||||
\(552\) | 4.31075 | + | 2.10177i | 0.183478 | + | 0.0894573i | ||||
\(553\) | 4.09335 | + | 5.51745i | 0.174067 | + | 0.234626i | ||||
\(554\) | −5.64259 | −0.239731 | ||||||||
\(555\) | 0.371735 | − | 0.643863i | 0.0157793 | − | 0.0273305i | ||||
\(556\) | −2.93676 | + | 1.69554i | −0.124546 | + | 0.0719069i | ||||
\(557\) | 13.0235 | − | 7.51910i | 0.551822 | − | 0.318595i | −0.198034 | − | 0.980195i | \(-0.563456\pi\) |
0.749857 | + | 0.661600i | \(0.230122\pi\) | |||||||
\(558\) | −0.516456 | − | 0.298176i | −0.0218633 | − | 0.0126228i | ||||
\(559\) | 34.3836 | 1.45427 | ||||||||
\(560\) | −0.0842550 | − | 0.731393i | −0.00356042 | − | 0.0309070i | ||||
\(561\) | 7.23491 | 0.305458 | ||||||||
\(562\) | −8.54587 | − | 4.93396i | −0.360486 | − | 0.208127i | ||||
\(563\) | −15.0948 | − | 26.1449i | −0.636169 | − | 1.10188i | −0.986266 | − | 0.165163i | \(-0.947185\pi\) |
0.350098 | − | 0.936713i | \(-0.386148\pi\) | |||||||
\(564\) | 4.65284 | + | 8.05896i | 0.195920 | + | 0.339343i | ||||
\(565\) | −4.05389 | − | 2.34052i | −0.170548 | − | 0.0984662i | ||||
\(566\) | 0.598114 | 0.0251406 | ||||||||
\(567\) | −0.302783 | − | 2.62837i | −0.0127157 | − | 0.110381i | ||||
\(568\) | 0.995488 | 0.0417697 | ||||||||
\(569\) | −5.12949 | − | 2.96151i | −0.215039 | − | 0.124153i | 0.388612 | − | 0.921402i | \(-0.372955\pi\) |
−0.603651 | + | 0.797249i | \(0.706288\pi\) | |||||||
\(570\) | 0.496147 | − | 0.286451i | 0.0207813 | − | 0.0119981i | ||||
\(571\) | 9.92289 | − | 5.72898i | 0.415260 | − | 0.239750i | −0.277787 | − | 0.960643i | \(-0.589601\pi\) |
0.693047 | + | 0.720892i | \(0.256268\pi\) | |||||||
\(572\) | 3.64943 | − | 6.32100i | 0.152590 | − | 0.264294i | ||||
\(573\) | −7.48204 | −0.312567 | ||||||||
\(574\) | 4.74512 | + | 6.39598i | 0.198057 | + | 0.266963i | ||||
\(575\) | −10.3461 | + | 21.2199i | −0.431463 | + | 0.884933i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −4.01217 | + | 2.31643i | −0.167029 | + | 0.0964342i | −0.581184 | − | 0.813772i | \(-0.697410\pi\) |
0.414155 | + | 0.910206i | \(0.364077\pi\) | |||||||
\(578\) | 3.89258 | + | 6.74214i | 0.161910 | + | 0.280436i | ||||
\(579\) | 11.8366 | + | 6.83388i | 0.491914 | + | 0.284006i | ||||
\(580\) | 1.46056 | 0.0606464 | ||||||||
\(581\) | −20.7108 | − | 8.97466i | −0.859231 | − | 0.372332i | ||||
\(582\) | 4.93232i | 0.204451i | ||||||||
\(583\) | 7.26377 | − | 12.5812i | 0.300834 | − | 0.521061i | ||||
\(584\) | 13.8151 | − | 7.97614i | 0.571672 | − | 0.330055i | ||||
\(585\) | −1.21036 | + | 0.698800i | −0.0500421 | + | 0.0288918i | ||||
\(586\) | −11.8095 | + | 20.4547i | −0.487846 | + | 0.844974i | ||||
\(587\) | − | 26.8682i | − | 1.10897i | −0.832194 | − | 0.554485i | \(-0.812915\pi\) | ||
0.832194 | − | 0.554485i | \(-0.187085\pi\) | |||||||
\(588\) | 1.59165 | + | 6.81665i | 0.0656385 | + | 0.281114i | ||||
\(589\) | 1.22777i | 0.0505895i | ||||||||
\(590\) | 0.669132 | + | 0.386323i | 0.0275477 | + | 0.0159047i | ||||
\(591\) | −19.4568 | + | 11.2334i | −0.800344 | + | 0.462079i | ||||
\(592\) | −2.31382 | + | 1.33588i | −0.0950973 | + | 0.0549044i | ||||
\(593\) | 21.6059 | + | 12.4742i | 0.887250 | + | 0.512254i | 0.873042 | − | 0.487645i | \(-0.162144\pi\) |
0.0142078 | + | 0.999899i | \(0.495477\pi\) | |||||||
\(594\) | 1.45324 | 0.0596272 | ||||||||
\(595\) | 3.36312 | + | 1.45735i | 0.137874 | + | 0.0597453i | ||||
\(596\) | 17.9866i | 0.736759i | ||||||||
\(597\) | 19.5322 | + | 11.2769i | 0.799400 | + | 0.461534i | ||||
\(598\) | 1.68347 | + | 24.0281i | 0.0688423 | + | 0.982580i | ||||
\(599\) | −12.9076 | − | 22.3566i | −0.527390 | − | 0.913466i | −0.999490 | − | 0.0319215i | \(-0.989837\pi\) |
0.472100 | − | 0.881545i | \(-0.343496\pi\) | |||||||
\(600\) | 4.26307 | + | 2.46128i | 0.174039 | + | 0.100481i | ||||
\(601\) | 8.13523i | 0.331843i | 0.986139 | + | 0.165921i | \(0.0530598\pi\) | ||||
−0.986139 | + | 0.165921i | \(0.946940\pi\) | |||||||
\(602\) | −10.7920 | − | 14.5466i | −0.439848 | − | 0.592874i | ||||
\(603\) | − | 6.71286i | − | 0.273369i | ||||||
\(604\) | −6.22898 | + | 10.7889i | −0.253453 | + | 0.438994i | ||||
\(605\) | −1.23664 | − | 2.14192i | −0.0502766 | − | 0.0870816i | ||||
\(606\) | 6.00820 | + | 10.4065i | 0.244066 | + | 0.422736i | ||||
\(607\) | 32.7070 | + | 18.8834i | 1.32753 | + | 0.766452i | 0.984918 | − | 0.173023i | \(-0.0553534\pi\) |
0.342617 | + | 0.939475i | \(0.388687\pi\) | |||||||
\(608\) | −2.05881 | −0.0834956 | ||||||||
\(609\) | −13.7956 | + | 1.58923i | −0.559026 | + | 0.0643987i | ||||
\(610\) | 0.554054 | 0.0224330 | ||||||||
\(611\) | −23.3688 | + | 40.4759i | −0.945400 | + | 1.63748i | ||||
\(612\) | 2.48923 | + | 4.31148i | 0.100621 | + | 0.174281i | ||||
\(613\) | −18.8185 | + | 10.8648i | −0.760070 | + | 0.438827i | −0.829321 | − | 0.558772i | \(-0.811273\pi\) |
0.0692507 | + | 0.997599i | \(0.477939\pi\) | |||||||
\(614\) | 11.4535 | + | 6.61269i | 0.462226 | + | 0.266866i | ||||
\(615\) | 0.837616 | 0.0337759 | ||||||||
\(616\) | −3.81965 | + | 0.440016i | −0.153898 | + | 0.0177288i | ||||
\(617\) | 31.4466i | 1.26599i | 0.774155 | + | 0.632996i | \(0.218175\pi\) | ||||
−0.774155 | + | 0.632996i | \(0.781825\pi\) | |||||||
\(618\) | −15.9141 | − | 9.18802i | −0.640160 | − | 0.369596i | ||||
\(619\) | −7.06979 | − | 12.2452i | −0.284159 | − | 0.492177i | 0.688246 | − | 0.725477i | \(-0.258381\pi\) |
−0.972405 | + | 0.233300i | \(0.925048\pi\) | |||||||
\(620\) | 0.143714 | − | 0.0829731i | 0.00577168 | − | 0.00333228i | ||||
\(621\) | −3.97556 | + | 2.68233i | −0.159534 | + | 0.107638i | ||||
\(622\) | 23.4763i | 0.941314i | ||||||||
\(623\) | 16.3059 | − | 12.0972i | 0.653282 | − | 0.484664i | ||||
\(624\) | 5.02248 | 0.201060 | ||||||||
\(625\) | −11.9222 | + | 20.6499i | −0.476890 | + | 0.825997i | ||||
\(626\) | −8.95215 | − | 15.5056i | −0.357800 | − | 0.619728i | ||||
\(627\) | −1.49597 | − | 2.59110i | −0.0597433 | − | 0.103478i | ||||
\(628\) | 1.75657 | − | 3.04247i | 0.0700947 | − | 0.121408i | ||||
\(629\) | − | 13.3013i | − | 0.530358i | ||||||
\(630\) | 0.675533 | + | 0.292730i | 0.0269139 | + | 0.0116626i | ||||
\(631\) | − | 41.5475i | − | 1.65398i | −0.562216 | − | 0.826991i | \(-0.690051\pi\) | ||
0.562216 | − | 0.826991i | \(-0.309949\pi\) | |||||||
\(632\) | −2.24875 | − | 1.29832i | −0.0894506 | − | 0.0516444i | ||||
\(633\) | 8.21811 | − | 4.74473i | 0.326641 | − | 0.188586i | ||||
\(634\) | −4.20294 | − | 7.27971i | −0.166920 | − | 0.289114i | ||||
\(635\) | 2.31396 | − | 4.00790i | 0.0918267 | − | 0.159048i | ||||
\(636\) | 9.99665 | 0.396393 | ||||||||
\(637\) | −25.6526 | + | 24.0412i | −1.01639 | + | 0.952549i | ||||
\(638\) | − | 7.62767i | − | 0.301982i | ||||||
\(639\) | −0.497744 | + | 0.862118i | −0.0196904 | + | 0.0341048i | ||||
\(640\) | 0.139134 | + | 0.240988i | 0.00549977 | + | 0.00952588i | ||||
\(641\) | 21.7291 | − | 12.5453i | 0.858249 | − | 0.495510i | −0.00517640 | − | 0.999987i | \(-0.501648\pi\) |
0.863426 | + | 0.504476i | \(0.168314\pi\) | |||||||
\(642\) | 7.45046 | − | 12.9046i | 0.294046 | − | 0.509303i | ||||
\(643\) | 35.3614 | 1.39452 | 0.697259 | − | 0.716819i | \(-0.254403\pi\) | ||||
0.697259 | + | 0.716819i | \(0.254403\pi\) | |||||||
\(644\) | 9.63708 | − | 8.25389i | 0.379754 | − | 0.325249i | ||||
\(645\) | −1.90502 | −0.0750099 | ||||||||
\(646\) | 5.12485 | − | 8.87650i | 0.201635 | − | 0.349241i | ||||
\(647\) | −34.5265 | + | 19.9339i | −1.35738 | + | 0.783682i | −0.989270 | − | 0.146101i | \(-0.953327\pi\) |
−0.368107 | + | 0.929783i | \(0.619994\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 2.01755 | − | 3.49449i | 0.0791957 | − | 0.137171i | ||||
\(650\) | 24.7235i | 0.969735i | ||||||||
\(651\) | −1.26715 | + | 0.940090i | −0.0496637 | + | 0.0368450i | ||||
\(652\) | 16.2683 | 0.637115 | ||||||||
\(653\) | 4.50651 | − | 7.80550i | 0.176353 | − | 0.305453i | −0.764275 | − | 0.644890i | \(-0.776903\pi\) |
0.940629 | + | 0.339437i | \(0.110237\pi\) | |||||||
\(654\) | 6.40085 | + | 11.0866i | 0.250293 | + | 0.433520i | ||||
\(655\) | 1.98451 | − | 1.14576i | 0.0775414 | − | 0.0447685i | ||||
\(656\) | −2.60682 | − | 1.50505i | −0.101779 | − | 0.0587622i | ||||
\(657\) | 15.9523i | 0.622358i | ||||||||
\(658\) | 24.4588 | − | 2.81760i | 0.953502 | − | 0.109842i | ||||
\(659\) | 26.1914i | 1.02027i | 0.860094 | + | 0.510136i | \(0.170405\pi\) | ||||
−0.860094 | + | 0.510136i | \(0.829595\pi\) | |||||||
\(660\) | −0.202196 | + | 0.350213i | −0.00787046 | + | 0.0136320i | ||||
\(661\) | −13.8305 | − | 23.9551i | −0.537944 | − | 0.931746i | −0.999015 | − | 0.0443825i | \(-0.985868\pi\) |
0.461071 | − | 0.887363i | \(-0.347465\pi\) | |||||||
\(662\) | 0.0738206 | + | 0.127861i | 0.00286912 | + | 0.00496946i | ||||
\(663\) | −12.5021 | + | 21.6543i | −0.485542 | + | 0.840984i | ||||
\(664\) | 8.53132 | 0.331079 | ||||||||
\(665\) | −0.173465 | − | 1.50580i | −0.00672667 | − | 0.0583923i | ||||
\(666\) | − | 2.67177i | − | 0.103529i | ||||||
\(667\) | 14.0789 | + | 20.8667i | 0.545135 | + | 0.807961i | ||||
\(668\) | −1.63624 | + | 0.944685i | −0.0633081 | + | 0.0365510i | ||||
\(669\) | −1.98110 | − | 3.43137i | −0.0765939 | − | 0.132664i | ||||
\(670\) | 1.61772 | + | 0.933990i | 0.0624979 | + | 0.0360832i | ||||
\(671\) | − | 2.89351i | − | 0.111703i | ||||||
\(672\) | −1.57640 | − | 2.12484i | −0.0608110 | − | 0.0819676i | ||||
\(673\) | 26.5244 | 1.02244 | 0.511221 | − | 0.859449i | \(-0.329193\pi\) | ||||
0.511221 | + | 0.859449i | \(0.329193\pi\) | |||||||
\(674\) | −22.9935 | − | 13.2753i | −0.885677 | − | 0.511346i | ||||
\(675\) | −4.26307 | + | 2.46128i | −0.164086 | + | 0.0947348i | ||||
\(676\) | 6.11264 | + | 10.5874i | 0.235101 | + | 0.407208i | ||||
\(677\) | −7.79131 | + | 13.4950i | −0.299445 | + | 0.518653i | −0.976009 | − | 0.217730i | \(-0.930135\pi\) |
0.676564 | + | 0.736383i | \(0.263468\pi\) | |||||||
\(678\) | −16.8220 | −0.646044 | ||||||||
\(679\) | 11.9738 | + | 5.18864i | 0.459514 | + | 0.199122i | ||||
\(680\) | −1.38535 | −0.0531259 | ||||||||
\(681\) | 16.8162 | + | 9.70885i | 0.644399 | + | 0.372044i | ||||
\(682\) | −0.433321 | − | 0.750534i | −0.0165927 | − | 0.0287394i | ||||
\(683\) | −13.7433 | − | 23.8040i | −0.525872 | − | 0.910836i | −0.999546 | − | 0.0301361i | \(-0.990406\pi\) |
0.473674 | − | 0.880700i | \(-0.342927\pi\) | |||||||
\(684\) | 1.02940 | − | 1.78298i | 0.0393602 | − | 0.0681739i | ||||
\(685\) | 0.923906i | 0.0353006i | ||||||||
\(686\) | 18.2226 | + | 3.30696i | 0.695743 | + | 0.126260i | ||||
\(687\) | − | 21.4855i | − | 0.819724i | ||||||
\(688\) | 5.92877 | + | 3.42298i | 0.226032 | + | 0.130500i | ||||
\(689\) | 25.1040 | + | 43.4814i | 0.956385 | + | 1.65651i | ||||
\(690\) | −0.0932723 | − | 1.33127i | −0.00355081 | − | 0.0506805i | ||||
\(691\) | 2.01095 | + | 1.16102i | 0.0765002 | + | 0.0441674i | 0.537762 | − | 0.843097i | \(-0.319270\pi\) |
−0.461262 | + | 0.887264i | \(0.652603\pi\) | |||||||
\(692\) | 3.04232i | 0.115652i | ||||||||
\(693\) | 1.52876 | − | 3.52792i | 0.0580728 | − | 0.134015i | ||||
\(694\) | −7.99995 | −0.303674 | ||||||||
\(695\) | 0.817209 | + | 0.471816i | 0.0309985 | + | 0.0178970i | ||||
\(696\) | 4.54554 | − | 2.62437i | 0.172298 | − | 0.0994764i | ||||
\(697\) | 12.9780 | − | 7.49283i | 0.491575 | − | 0.283811i | ||||
\(698\) | −29.4003 | − | 16.9743i | −1.11282 | − | 0.642486i | ||||
\(699\) | 4.26862i | 0.161454i | ||||||||
\(700\) | 10.4597 | − | 7.75994i | 0.395339 | − | 0.293298i | ||||
\(701\) | − | 8.60233i | − | 0.324906i | −0.986716 | − | 0.162453i | \(-0.948059\pi\) | ||
0.986716 | − | 0.162453i | \(-0.0519405\pi\) | |||||||
\(702\) | −2.51124 | + | 4.34959i | −0.0947806 | + | 0.164165i | ||||
\(703\) | −4.76370 | + | 2.75032i | −0.179666 | + | 0.103730i | ||||
\(704\) | 1.25854 | − | 0.726620i | 0.0474331 | − | 0.0273855i | ||||
\(705\) | 1.29474 | − | 2.24256i | 0.0487628 | − | 0.0844596i | ||||
\(706\) | − | 19.0972i | − | 0.718732i | ||||||
\(707\) | 31.5835 | − | 3.63836i | 1.18782 | − | 0.136835i | ||||
\(708\) | 2.77662 | 0.104352 | ||||||||
\(709\) | 39.5163 | + | 22.8148i | 1.48407 | + | 0.856827i | 0.999836 | − | 0.0181134i | \(-0.00576598\pi\) |
0.484231 | + | 0.874940i | \(0.339099\pi\) | |||||||
\(710\) | −0.138507 | − | 0.239901i | −0.00519806 | − | 0.00900331i | ||||
\(711\) | 2.24875 | − | 1.29832i | 0.0843349 | − | 0.0486908i | ||||
\(712\) | −3.83696 | + | 6.64582i | −0.143796 | + | 0.249063i | ||||
\(713\) | 2.57072 | + | 1.25339i | 0.0962743 | + | 0.0469400i | ||||
\(714\) | 13.0853 | − | 1.50739i | 0.489703 | − | 0.0564128i | ||||
\(715\) | −2.03105 | −0.0759569 | ||||||||
\(716\) | −9.89020 | + | 17.1303i | −0.369614 | + | 0.640190i | ||||
\(717\) | 14.1691 | − | 8.18054i | 0.529155 | − | 0.305508i | ||||
\(718\) | −15.3719 | + | 8.87498i | −0.573675 | + | 0.331211i | ||||
\(719\) | −4.58681 | − | 2.64820i | −0.171059 | − | 0.0987611i | 0.412026 | − | 0.911172i | \(-0.364821\pi\) |
−0.583085 | + | 0.812411i | \(0.698155\pi\) | |||||||
\(720\) | −0.278269 | −0.0103705 | ||||||||
\(721\) | −39.0462 | + | 28.9680i | −1.45416 | + | 1.07883i | ||||
\(722\) | 14.7613 | 0.549359 | ||||||||
\(723\) | −8.47005 | − | 4.89018i | −0.315004 | − | 0.181868i | ||||
\(724\) | −6.48055 | − | 11.2246i | −0.240848 | − | 0.417160i | ||||
\(725\) | 12.9186 | + | 22.3757i | 0.479786 | + | 0.831013i | ||||
\(726\) | −7.69731 | − | 4.44405i | −0.285674 | − | 0.164934i | ||||
\(727\) | 42.7188 | 1.58435 | 0.792177 | − | 0.610292i | \(-0.208948\pi\) | ||||
0.792177 | + | 0.610292i | \(0.208948\pi\) | |||||||
\(728\) | 5.28348 | − | 12.1927i | 0.195819 | − | 0.451891i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −3.84431 | − | 2.21951i | −0.142284 | − | 0.0821479i | ||||
\(731\) | −29.5162 | + | 17.0412i | −1.09170 | + | 0.630291i | ||||
\(732\) | 1.72432 | − | 0.995536i | 0.0637327 | − | 0.0367961i | ||||
\(733\) | 5.60709 | − | 9.71177i | 0.207103 | − | 0.358712i | −0.743698 | − | 0.668516i | \(-0.766930\pi\) |
0.950801 | + | 0.309803i | \(0.100263\pi\) | |||||||
\(734\) | −1.50609 | −0.0555907 | ||||||||
\(735\) | 1.42128 | − | 1.33200i | 0.0524246 | − | 0.0491315i | ||||
\(736\) | −2.10177 | + | 4.31075i | −0.0774723 | + | 0.158896i | ||||
\(737\) | 4.87770 | − | 8.44842i | 0.179672 | − | 0.311202i | ||||
\(738\) | 2.60682 | − | 1.50505i | 0.0959583 | − | 0.0554016i | ||||
\(739\) | 16.5349 | + | 28.6394i | 0.608247 | + | 1.05352i | 0.991529 | + | 0.129884i | \(0.0414605\pi\) |
−0.383282 | + | 0.923631i | \(0.625206\pi\) | |||||||
\(740\) | 0.643863 | + | 0.371735i | 0.0236689 | + | 0.0136652i | ||||
\(741\) | 10.3403 | 0.379861 | ||||||||
\(742\) | 10.5161 | − | 24.2681i | 0.386060 | − | 0.890911i | ||||
\(743\) | 48.1965i | 1.76816i | 0.467337 | + | 0.884079i | \(0.345214\pi\) | ||||
−0.467337 | + | 0.884079i | \(0.654786\pi\) | |||||||
\(744\) | 0.298176 | − | 0.516456i | 0.0109317 | − | 0.0189342i | ||||
\(745\) | 4.33455 | − | 2.50255i | 0.158806 | − | 0.0916865i | ||||
\(746\) | −15.6481 | + | 9.03445i | −0.572919 | + | 0.330775i | ||||
\(747\) | −4.26566 | + | 7.38834i | −0.156072 | + | 0.270325i | ||||
\(748\) | 7.23491i | 0.264535i | ||||||||
\(749\) | −23.4899 | − | 31.6621i | −0.858300 | − | 1.15691i | ||||
\(750\) | − | 2.76114i | − | 0.100823i | ||||||
\(751\) | −42.6259 | − | 24.6101i | −1.55544 | − | 0.898034i | −0.997683 | − | 0.0680307i | \(-0.978328\pi\) |
−0.557758 | − | 0.830004i | \(-0.688338\pi\) | |||||||
\(752\) | −8.05896 | + | 4.65284i | −0.293880 | + | 0.169672i | ||||
\(753\) | 11.6694 | − | 6.73730i | 0.425255 | − | 0.245521i | ||||
\(754\) | 22.8299 | + | 13.1808i | 0.831414 | + | 0.480017i | ||||
\(755\) | 3.46666 | 0.126165 | ||||||||
\(756\) | 2.62837 | − | 0.302783i | 0.0955928 | − | 0.0110121i | ||||
\(757\) | 50.3061i | 1.82841i | 0.405255 | + | 0.914204i | \(0.367183\pi\) | ||||
−0.405255 | + | 0.914204i | \(0.632817\pi\) | |||||||
\(758\) | −3.90125 | − | 2.25239i | −0.141700 | − | 0.0818105i | ||||
\(759\) | −6.95245 | + | 0.487108i | −0.252358 | + | 0.0176809i | ||||
\(760\) | 0.286451 | + | 0.496147i | 0.0103907 | + | 0.0179972i | ||||
\(761\) | −1.60034 | − | 0.923955i | −0.0580122 | − | 0.0334934i | 0.470713 | − | 0.882286i | \(-0.343997\pi\) |
−0.528726 | + | 0.848793i | \(0.677330\pi\) | |||||||
\(762\) | − | 16.6311i | − | 0.602481i | ||||||
\(763\) | 33.6476 | − | 3.87613i | 1.21812 | − | 0.140325i | ||||
\(764\) | − | 7.48204i | − | 0.270691i | ||||||
\(765\) | 0.692677 | − | 1.19975i | 0.0250438 | − | 0.0433771i | ||||
\(766\) | 0.360283 | + | 0.624029i | 0.0130176 | + | 0.0225471i | ||||
\(767\) | 6.97275 | + | 12.0772i | 0.251771 | + | 0.436081i | ||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | −41.7478 | −1.50546 | −0.752732 | − | 0.658327i | \(-0.771264\pi\) | ||||
−0.752732 | + | 0.658327i | \(0.771264\pi\) | |||||||
\(770\) | 0.637484 | + | 0.859268i | 0.0229733 | + | 0.0309659i | ||||
\(771\) | −20.6757 | −0.744617 | ||||||||
\(772\) | −6.83388 | + | 11.8366i | −0.245957 | + | 0.426010i | ||||
\(773\) | −12.9260 | − | 22.3886i | −0.464917 | − | 0.805260i | 0.534281 | − | 0.845307i | \(-0.320583\pi\) |
−0.999198 | + | 0.0400470i | \(0.987249\pi\) | |||||||
\(774\) | −5.92877 | + | 3.42298i | −0.213105 | + | 0.123036i | ||||
\(775\) | 2.54229 | + | 1.46779i | 0.0913217 | + | 0.0527246i | ||||
\(776\) | −4.93232 | −0.177060 | ||||||||
\(777\) | −6.48605 | − | 2.81061i | −0.232686 | − | 0.100830i | ||||
\(778\) | 16.0277i | 0.574621i | ||||||||
\(779\) | −5.36693 | − | 3.09860i | −0.192290 | − | 0.111019i | ||||
\(780\) | −0.698800 | − | 1.21036i | −0.0250210 | − | 0.0433377i | ||||
\(781\) | −1.25286 | + | 0.723341i | −0.0448310 | + | 0.0258832i | ||||
\(782\) | −13.3539 | − | 19.7922i | −0.477535 | − | 0.707768i | ||||
\(783\) | 5.24874i | 0.187575i | ||||||||
\(784\) | −6.81665 | + | 1.59165i | −0.243452 | + | 0.0568446i | ||||
\(785\) | −0.977597 | −0.0348919 | ||||||||
\(786\) | 4.11746 | − | 7.13164i | 0.146865 | − | 0.254377i | ||||
\(787\) | −13.8316 | − | 23.9571i | −0.493044 | − | 0.853977i | 0.506924 | − | 0.861991i | \(-0.330783\pi\) |
−0.999968 | + | 0.00801348i | \(0.997449\pi\) | |||||||
\(788\) | −11.2334 | − | 19.4568i | −0.400172 | − | 0.693119i | ||||
\(789\) | −12.6554 | + | 21.9199i | −0.450546 | + | 0.780368i | ||||
\(790\) | 0.722564i | 0.0257077i | ||||||||
\(791\) | −17.6962 | + | 40.8374i | −0.629203 | + | 1.45201i | ||||
\(792\) | 1.45324i | 0.0516386i | ||||||||
\(793\) | 8.66035 | + | 5.00006i | 0.307538 | + | 0.177557i | ||||
\(794\) | 14.0889 | − | 8.13423i | 0.499996 | − | 0.288673i | ||||
\(795\) | −1.39088 | − | 2.40907i | −0.0493294 | − | 0.0854410i | ||||
\(796\) | −11.2769 | + | 19.5322i | −0.399700 | + | 0.692300i | ||||
\(797\) | −43.0699 | −1.52561 | −0.762807 | − | 0.646626i | \(-0.776179\pi\) | ||||
−0.762807 | + | 0.646626i | \(0.776179\pi\) | |||||||
\(798\) | −3.24551 | − | 4.37464i | −0.114890 | − | 0.154861i | ||||
\(799\) | − | 46.3281i | − | 1.63897i | ||||||
\(800\) | −2.46128 | + | 4.26307i | −0.0870195 | + | 0.150722i | ||||
\(801\) | −3.83696 | − | 6.64582i | −0.135572 | − | 0.234818i | ||||
\(802\) | 5.37637 | − | 3.10405i | 0.189846 | − | 0.109608i | ||||
\(803\) | −11.5913 | + | 20.0766i | −0.409046 | + | 0.708489i | ||||
\(804\) | 6.71286 | 0.236744 | ||||||||
\(805\) | −3.32994 | − | 1.17402i | −0.117365 | − | 0.0413787i | ||||
\(806\) | 2.99516 | 0.105500 | ||||||||
\(807\) | −0.956701 | + | 1.65705i | −0.0336775 | + | 0.0583311i | ||||
\(808\) | −10.4065 | + | 6.00820i | −0.366100 | + | 0.211368i | ||||
\(809\) | −3.62789 | − | 6.28369i | −0.127550 | − | 0.220923i | 0.795177 | − | 0.606378i | \(-0.207378\pi\) |
−0.922727 | + | 0.385455i | \(0.874045\pi\) | |||||||
\(810\) | 0.139134 | − | 0.240988i | 0.00488869 | − | 0.00846745i | ||||
\(811\) | − | 19.3552i | − | 0.679652i | −0.940488 | − | 0.339826i | \(-0.889632\pi\) | ||
0.940488 | − | 0.339826i | \(-0.110368\pi\) | |||||||
\(812\) | −1.58923 | − | 13.7956i | −0.0557709 | − | 0.484131i | ||||
\(813\) | −18.8145 | −0.659852 | ||||||||
\(814\) | 1.94136 | − | 3.36253i | 0.0680446 | − | 0.117857i | ||||
\(815\) | −2.26348 | − | 3.92046i | −0.0792862 | − | 0.137328i | ||||
\(816\) | −4.31148 | + | 2.48923i | −0.150932 | + | 0.0871406i | ||||
\(817\) | 12.2062 | + | 7.04724i | 0.427040 | + | 0.246552i | ||||
\(818\) | − | 20.2398i | − | 0.707667i | ||||||
\(819\) | 7.91744 | + | 10.6720i | 0.276658 | + | 0.372909i | ||||
\(820\) | 0.837616i | 0.0292508i | ||||||||
\(821\) | 6.20841 | − | 10.7533i | 0.216675 | − | 0.375292i | −0.737114 | − | 0.675768i | \(-0.763812\pi\) |
0.953789 | + | 0.300476i | \(0.0971455\pi\) | |||||||
\(822\) | 1.66010 | + | 2.87537i | 0.0579025 | + | 0.100290i | ||||
\(823\) | −1.89373 | − | 3.28004i | −0.0660113 | − | 0.114335i | 0.831131 | − | 0.556077i | \(-0.187694\pi\) |
−0.897142 | + | 0.441742i | \(0.854361\pi\) | |||||||
\(824\) | 9.18802 | − | 15.9141i | 0.320080 | − | 0.554394i | ||||
\(825\) | −7.15367 | −0.249059 | ||||||||
\(826\) | 2.92091 | − | 6.74059i | 0.101631 | − | 0.234535i | ||||
\(827\) | 54.9015i | 1.90911i | 0.298034 | + | 0.954555i | \(0.403669\pi\) | ||||
−0.298034 | + | 0.954555i | \(0.596331\pi\) | |||||||
\(828\) | −2.68233 | − | 3.97556i | −0.0932175 | − | 0.138160i | ||||
\(829\) | −4.52448 | + | 2.61221i | −0.157142 | + | 0.0907258i | −0.576509 | − | 0.817091i | \(-0.695585\pi\) |
0.419367 | + | 0.907817i | \(0.362252\pi\) | |||||||
\(830\) | −1.18700 | − | 2.05594i | −0.0412014 | − | 0.0713629i | ||||
\(831\) | 4.88662 | + | 2.82129i | 0.169515 | + | 0.0978696i | ||||
\(832\) | 5.02248i | 0.174123i | ||||||||
\(833\) | 10.1059 | − | 33.3518i | 0.350147 | − | 1.15557i | ||||
\(834\) | 3.39108 | 0.117423 | ||||||||
\(835\) | 0.455315 | + | 0.262876i | 0.0157568 | + | 0.00909721i | ||||
\(836\) | 2.59110 | − | 1.49597i | 0.0896149 | − | 0.0517392i | ||||
\(837\) | 0.298176 | + | 0.516456i | 0.0103065 | + | 0.0178513i | ||||
\(838\) | −4.45499 | + | 7.71626i | −0.153895 | + | 0.266554i | ||||
\(839\) | −43.9656 | −1.51786 | −0.758930 | − | 0.651172i | \(-0.774278\pi\) | ||||
−0.758930 | + | 0.651172i | \(0.774278\pi\) | |||||||
\(840\) | −0.292730 | + | 0.675533i | −0.0101001 | + | 0.0233081i | ||||
\(841\) | −1.45078 | −0.0500268 | ||||||||
\(842\) | 31.4166 | + | 18.1384i | 1.08269 | + | 0.625089i | ||||
\(843\) | 4.93396 | + | 8.54587i | 0.169935 | + | 0.294336i | ||||
\(844\) | 4.74473 | + | 8.21811i | 0.163320 | + | 0.282879i | ||||
\(845\) | 1.70096 | − | 2.94614i | 0.0585147 | − | 0.101350i | ||||
\(846\) | − | 9.30569i | − | 0.319936i | ||||||
\(847\) | −18.8858 | + | 14.0112i | −0.648924 | + | 0.481431i | ||||
\(848\) | 9.99665i | 0.343286i | ||||||||
\(849\) | −0.517982 | − | 0.299057i | −0.0177771 | − | 0.0102636i | ||||
\(850\) | −12.2534 | − | 21.2235i | −0.420289 | − | 0.727962i | ||||
\(851\) | 0.895542 | + | 12.7820i | 0.0306988 | + | 0.438161i | ||||
\(852\) | −0.862118 | − | 0.497744i | −0.0295357 | − | 0.0170524i | ||||
\(853\) | 4.98034i | 0.170524i | 0.996359 | + | 0.0852618i | \(0.0271727\pi\) | ||||
−0.996359 | + | 0.0852618i | \(0.972827\pi\) | |||||||
\(854\) | −0.602862 | − | 5.23327i | −0.0206295 | − | 0.179079i | ||||
\(855\) | −0.572902 | −0.0195928 | ||||||||
\(856\) | 12.9046 | + | 7.45046i | 0.441070 | + | 0.254652i | ||||
\(857\) | −37.7406 | + | 21.7896i | −1.28920 | + | 0.744318i | −0.978511 | − | 0.206195i | \(-0.933892\pi\) |
−0.310685 | + | 0.950513i | \(0.600558\pi\) | |||||||
\(858\) | −6.32100 | + | 3.64943i | −0.215795 | + | 0.124590i | ||||
\(859\) | −16.9065 | − | 9.76097i | −0.576842 | − | 0.333040i | 0.183035 | − | 0.983106i | \(-0.441408\pi\) |
−0.759877 | + | 0.650066i | \(0.774741\pi\) | |||||||
\(860\) | − | 1.90502i | − | 0.0649605i | ||||||
\(861\) | −0.911405 | − | 7.91164i | −0.0310606 | − | 0.269628i | ||||
\(862\) | 1.16004i | 0.0395112i | ||||||||
\(863\) | −4.74463 | + | 8.21794i | −0.161509 | + | 0.279742i | −0.935410 | − | 0.353565i | \(-0.884969\pi\) |
0.773901 | + | 0.633307i | \(0.218303\pi\) | |||||||
\(864\) | −0.866025 | + | 0.500000i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 0.733161 | − | 0.423291i | 0.0249282 | − | 0.0143923i | ||||
\(866\) | 8.77422 | − | 15.1974i | 0.298160 | − | 0.516429i | ||||
\(867\) | − | 7.78515i | − | 0.264398i | ||||||
\(868\) | −0.940090 | − | 1.26715i | −0.0319087 | − | 0.0430100i | ||||
\(869\) | 3.77354 | 0.128009 | ||||||||
\(870\) | −1.26488 | − | 0.730280i | −0.0428835 | − | 0.0247588i | ||||
\(871\) | 16.8576 | + | 29.1982i | 0.571198 | + | 0.989344i | ||||
\(872\) | −11.0866 | + | 6.40085i | −0.375439 | + | 0.216760i | ||||
\(873\) | 2.46616 | − | 4.27152i | 0.0834669 | − | 0.144569i | ||||
\(874\) | −4.32714 | + | 8.87499i | −0.146368 | + | 0.300201i | ||||
\(875\) | −6.70302 | − | 2.90463i | −0.226603 | − | 0.0981944i | ||||
\(876\) | −15.9523 | −0.538978 | ||||||||
\(877\) | 23.2436 | − | 40.2592i | 0.784882 | − | 1.35946i | −0.144187 | − | 0.989550i | \(-0.546057\pi\) |
0.929069 | − | 0.369905i | \(-0.120610\pi\) | |||||||
\(878\) | −16.9006 | + | 9.75755i | −0.570367 | + | 0.329301i | ||||
\(879\) | 20.4547 | − | 11.8095i | 0.689918 | − | 0.398325i | ||||
\(880\) | −0.350213 | − | 0.202196i | −0.0118057 | − | 0.00681602i | ||||
\(881\) | 16.8333 | 0.567127 | 0.283564 | − | 0.958953i | \(-0.408483\pi\) | ||||
0.283564 | + | 0.958953i | \(0.408483\pi\) | |||||||
\(882\) | 2.02991 | − | 6.69921i | 0.0683508 | − | 0.225574i | ||||
\(883\) | −18.3341 | −0.616993 | −0.308497 | − | 0.951225i | \(-0.599826\pi\) | ||||
−0.308497 | + | 0.951225i | \(0.599826\pi\) | |||||||
\(884\) | −21.6543 | − | 12.5021i | −0.728313 | − | 0.420492i | ||||
\(885\) | −0.386323 | − | 0.669132i | −0.0129861 | − | 0.0224926i | ||||
\(886\) | 0.389410 | + | 0.674478i | 0.0130825 | + | 0.0226595i | ||||
\(887\) | −29.8410 | − | 17.2287i | −1.00196 | − | 0.578483i | −0.0931333 | − | 0.995654i | \(-0.529688\pi\) |
−0.908828 | + | 0.417171i | \(0.863022\pi\) | |||||||
\(888\) | 2.67177 | 0.0896586 | ||||||||
\(889\) | −40.3741 | − | 17.4954i | −1.35410 | − | 0.586776i | ||||
\(890\) | 2.13542 | 0.0715793 | ||||||||
\(891\) | −1.25854 | − | 0.726620i | −0.0421628 | − | 0.0243427i | ||||
\(892\) | 3.43137 | − | 1.98110i | 0.114891 | − | 0.0663322i | ||||
\(893\) | −16.5918 | + | 9.57930i | −0.555225 | + | 0.320559i | ||||
\(894\) | 8.99329 | − | 15.5768i | 0.300781 | − | 0.520967i | ||||
\(895\) | 5.50427 | 0.183987 | ||||||||
\(896\) | 2.12484 | − | 1.57640i | 0.0709860 | − | 0.0526639i | ||||
\(897\) | 10.5561 | − | 21.6506i | 0.352458 | − | 0.722894i | ||||
\(898\) | 12.5338 | − | 21.7091i | 0.418257 | − | 0.724442i | ||||
\(899\) | 2.71074 | − | 1.56505i | 0.0904082 | − | 0.0521972i | ||||
\(900\) | −2.46128 | − | 4.26307i | −0.0820428 | − | 0.142102i | ||||
\(901\) | −43.1004 | − | 24.8840i | −1.43588 | − | 0.829006i | ||||
\(902\) | 4.37439 | 0.145651 | ||||||||
\(903\) | 2.07284 | + | 17.9937i | 0.0689797 | + | 0.598792i | ||||
\(904\) | − | 16.8220i | − | 0.559490i | ||||||
\(905\) | −1.80333 | + | 3.12347i | −0.0599449 | + | 0.103828i | ||||
\(906\) | 10.7889 | − | 6.22898i | 0.358437 | − | 0.206944i | ||||
\(907\) | −16.6813 | + | 9.63096i | −0.553894 | + | 0.319791i | −0.750691 | − | 0.660653i | \(-0.770279\pi\) |
0.196797 | + | 0.980444i | \(0.436946\pi\) | |||||||
\(908\) | −9.70885 | + | 16.8162i | −0.322200 | + | 0.558066i | ||||
\(909\) | − | 12.0164i | − | 0.398559i | ||||||
\(910\) | −3.67341 | + | 0.423169i | −0.121772 | + | 0.0140279i | ||||
\(911\) | 20.0169i | 0.663191i | 0.943422 | + | 0.331595i | \(0.107587\pi\) | ||||
−0.943422 | + | 0.331595i | \(0.892413\pi\) | |||||||
\(912\) | 1.78298 | + | 1.02940i | 0.0590403 | + | 0.0340869i | ||||
\(913\) | −10.7370 | + | 6.19903i | −0.355344 | + | 0.205158i | ||||
\(914\) | −13.3581 | + | 7.71230i | −0.441847 | + | 0.255100i | ||||
\(915\) | −0.479824 | − | 0.277027i | −0.0158625 | − | 0.00915822i | ||||
\(916\) | 21.4855 | 0.709902 | ||||||||
\(917\) | −12.9815 | − | 17.4979i | −0.428688 | − | 0.577831i | ||||
\(918\) | − | 4.97847i | − | 0.164314i | ||||||
\(919\) | 15.7091 | + | 9.06966i | 0.518196 | + | 0.299181i | 0.736196 | − | 0.676768i | \(-0.236620\pi\) |
−0.218000 | + | 0.975949i | \(0.569953\pi\) | |||||||
\(920\) | 1.33127 | − | 0.0932723i | 0.0438906 | − | 0.00307510i | ||||
\(921\) | −6.61269 | − | 11.4535i | −0.217895 | − | 0.377406i | ||||
\(922\) | 7.08367 | + | 4.08976i | 0.233288 | + | 0.134689i | ||||
\(923\) | − | 4.99981i | − | 0.164571i | ||||||
\(924\) | 3.52792 | + | 1.52876i | 0.116060 | + | 0.0502925i | ||||
\(925\) | 13.1519i | 0.432433i | ||||||||
\(926\) | 11.8053 | − | 20.4473i | 0.387945 | − | 0.671940i | ||||
\(927\) | 9.18802 | + | 15.9141i | 0.301774 | + | 0.522688i | ||||
\(928\) | 2.62437 | + | 4.54554i | 0.0861491 | + | 0.149215i | ||||
\(929\) | −29.2612 | − | 16.8939i | −0.960028 | − | 0.554272i | −0.0638460 | − | 0.997960i | \(-0.520337\pi\) |
−0.896182 | + | 0.443688i | \(0.853670\pi\) | |||||||
\(930\) | −0.165946 | −0.00544159 | ||||||||
\(931\) | −14.0341 | + | 3.27690i | −0.459951 | + | 0.107396i | ||||
\(932\) | −4.26862 | −0.139823 | ||||||||
\(933\) | 11.7382 | − | 20.3311i | 0.384290 | − | 0.665610i | ||||
\(934\) | 4.19554 | + | 7.26688i | 0.137282 | + | 0.237780i | ||||
\(935\) | 1.74353 | − | 1.00663i | 0.0570194 | − | 0.0329202i | ||||
\(936\) | −4.34959 | − | 2.51124i | −0.142171 | − | 0.0820824i | ||||
\(937\) | 37.0047 | 1.20889 | 0.604446 | − | 0.796646i | \(-0.293395\pi\) | ||||
0.604446 | + | 0.796646i | \(0.293395\pi\) | |||||||
\(938\) | 7.06171 | − | 16.2963i | 0.230573 | − | 0.532094i | ||||
\(939\) | 17.9043i | 0.584285i | ||||||||
\(940\) | 2.24256 | + | 1.29474i | 0.0731442 | + | 0.0422298i | ||||
\(941\) | 16.5258 | + | 28.6235i | 0.538726 | + | 0.933101i | 0.998973 | + | 0.0453099i | \(0.0144275\pi\) |
−0.460247 | + | 0.887791i | \(0.652239\pi\) | |||||||
\(942\) | −3.04247 | + | 1.75657i | −0.0991289 | + | 0.0572321i | ||||
\(943\) | −11.9668 | + | 8.07407i | −0.389693 | + | 0.262928i | ||||
\(944\) | 2.77662i | 0.0903712i | ||||||||
\(945\) | −0.438664 | − | 0.591278i | −0.0142697 | − | 0.0192343i | ||||
\(946\) | −9.94881 | −0.323464 | ||||||||
\(947\) | −15.7760 | + | 27.3249i | −0.512652 | + | 0.887940i | 0.487240 | + | 0.873268i | \(0.338004\pi\) |
−0.999892 | + | 0.0146716i | \(0.995330\pi\) | |||||||
\(948\) | 1.29832 | + | 2.24875i | 0.0421674 | + | 0.0730361i | ||||
\(949\) | −40.0600 | − | 69.3860i | −1.30040 | − | 2.25236i | ||||
\(950\) | −5.06730 | + | 8.77683i | −0.164405 | + | 0.284758i | ||||
\(951\) | 8.40588i | 0.272579i | ||||||||
\(952\) | 1.50739 | + | 13.0853i | 0.0488549 | + | 0.424095i | ||||
\(953\) | 44.6275i | 1.44563i | 0.691043 | + | 0.722813i | \(0.257151\pi\) | ||||
−0.691043 | + | 0.722813i | \(0.742849\pi\) | |||||||
\(954\) | −8.65735 | − | 4.99832i | −0.280292 | − | 0.161827i | ||||
\(955\) | −1.80308 | + | 1.04101i | −0.0583464 | + | 0.0336863i | ||||
\(956\) | 8.18054 | + | 14.1691i | 0.264578 | + | 0.458262i | ||||
\(957\) | −3.81384 | + | 6.60576i | −0.123284 | + | 0.213534i | ||||
\(958\) | 0.466489 | 0.0150716 | ||||||||
\(959\) | 8.72669 | − | 1.00530i | 0.281799 | − | 0.0324627i | ||||
\(960\) | − | 0.278269i | − | 0.00898109i | ||||||
\(961\) | −15.3222 | + | 26.5388i | −0.494264 | + | 0.856090i | ||||
\(962\) | 6.70944 | + | 11.6211i | 0.216321 | + | 0.374679i | ||||
\(963\) | −12.9046 | + | 7.45046i | −0.415844 | + | 0.240088i | ||||
\(964\) | 4.89018 | − | 8.47005i | 0.157502 | − | 0.272802i | ||||
\(965\) | 3.80331 | 0.122433 | ||||||||
\(966\) | −12.4729 | + | 2.32954i | −0.401309 | + | 0.0749517i | ||||
\(967\) | −43.5435 | −1.40027 | −0.700133 | − | 0.714013i | \(-0.746876\pi\) | ||||
−0.700133 | + | 0.714013i | \(0.746876\pi\) | |||||||
\(968\) | 4.44405 | − | 7.69731i | 0.142837 | − | 0.247401i | ||||
\(969\) | −8.87650 | + | 5.12485i | −0.285154 | + | 0.164634i | ||||
\(970\) | 0.686256 | + | 1.18863i | 0.0220344 | + | 0.0381646i | ||||
\(971\) | 10.1990 | − | 17.6651i | 0.327300 | − | 0.566901i | −0.654675 | − | 0.755911i | \(-0.727194\pi\) |
0.981975 | + | 0.189010i | \(0.0605278\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 3.56730 | − | 8.23227i | 0.114363 | − | 0.263915i | ||||
\(974\) | 25.0521 | 0.802721 | ||||||||
\(975\) | 12.3617 | − | 21.4112i | 0.395892 | − | 0.685706i | ||||
\(976\) | 0.995536 | + | 1.72432i | 0.0318663 | + | 0.0551941i | ||||
\(977\) | 12.5614 | − | 7.25231i | 0.401874 | − | 0.232022i | −0.285418 | − | 0.958403i | \(-0.592133\pi\) |
0.687292 | + | 0.726381i | \(0.258799\pi\) | |||||||
\(978\) | −14.0887 | − | 8.13414i | −0.450508 | − | 0.260101i | ||||
\(979\) | − | 11.1521i | − | 0.356421i | ||||||
\(980\) | 1.33200 | + | 1.42128i | 0.0425491 | + | 0.0454010i | ||||
\(981\) | − | 12.8017i | − | 0.408727i | ||||||
\(982\) | 1.07408 | − | 1.86036i | 0.0342752 | − | 0.0593663i | ||||
\(983\) | −12.9159 | − | 22.3710i | −0.411954 | − | 0.713524i | 0.583150 | − | 0.812365i | \(-0.301820\pi\) |
−0.995103 | + | 0.0988402i | \(0.968487\pi\) | |||||||
\(984\) | 1.50505 | + | 2.60682i | 0.0479792 | + | 0.0831023i | ||||
\(985\) | −3.12590 | + | 5.41421i | −0.0995994 | + | 0.172511i | ||||
\(986\) | −26.1307 | −0.832170 | ||||||||
\(987\) | −22.5907 | − | 9.78927i | −0.719071 | − | 0.311596i | ||||
\(988\) | 10.3403i | 0.328969i | ||||||||
\(989\) | 27.2165 | − | 18.3631i | 0.865434 | − | 0.583913i | ||||
\(990\) | 0.350213 | − | 0.202196i | 0.0111305 | − | 0.00642620i | ||||
\(991\) | −24.3217 | − | 42.1264i | −0.772605 | − | 1.33819i | −0.936131 | − | 0.351652i | \(-0.885620\pi\) |
0.163526 | − | 0.986539i | \(-0.447713\pi\) | |||||||
\(992\) | 0.516456 | + | 0.298176i | 0.0163975 | + | 0.00946709i | ||||
\(993\) | − | 0.147641i | − | 0.00468525i | ||||||
\(994\) | −2.11525 | + | 1.56929i | −0.0670918 | + | 0.0497748i | ||||
\(995\) | 6.27603 | 0.198964 | ||||||||
\(996\) | −7.38834 | − | 4.26566i | −0.234108 | − | 0.135163i | ||||
\(997\) | 32.1334 | − | 18.5522i | 1.01767 | − | 0.587554i | 0.104245 | − | 0.994552i | \(-0.466757\pi\) |
0.913429 | + | 0.406997i | \(0.133424\pi\) | |||||||
\(998\) | −17.7523 | − | 30.7479i | −0.561939 | − | 0.973307i | ||||
\(999\) | −1.33588 | + | 2.31382i | −0.0422655 | + | 0.0732059i |
(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 | 966.2.k.b.229.4 | ✓ | 32 | |
7.3 | odd | 6 | inner | 966.2.k.b.367.5 | yes | 32 | |
23.22 | odd | 2 | inner | 966.2.k.b.229.5 | yes | 32 | |
161.45 | even | 6 | inner | 966.2.k.b.367.4 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.k.b.229.4 | ✓ | 32 | 1.1 | even | 1 | trivial | |
966.2.k.b.229.5 | yes | 32 | 23.22 | odd | 2 | inner | |
966.2.k.b.367.4 | yes | 32 | 161.45 | even | 6 | inner | |
966.2.k.b.367.5 | yes | 32 | 7.3 | odd | 6 | inner |