Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(271,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.271");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.bf (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: | \(6.03669039281\) |
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 | 271.14 | ||
Character | \(\chi\) | \(=\) | 756.271 |
Dual form | 756.2.bf.b.703.14 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.29094 | − | 0.577482i | 0.912829 | − | 0.408341i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.33303 | − | 1.49098i | 0.666515 | − | 0.745492i | ||||
\(5\) | −3.03704 | − | 1.75344i | −1.35821 | − | 0.784161i | −0.368825 | − | 0.929499i | \(-0.620240\pi\) |
−0.989382 | + | 0.145338i | \(0.953573\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.151085 | − | 2.64143i | −0.0571049 | − | 0.998368i | ||||
\(8\) | 0.859840 | − | 2.69456i | 0.303999 | − | 0.952672i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.93321 | − | 0.509738i | −1.56002 | − | 0.161193i | ||||
\(11\) | −2.81992 | + | 1.62808i | −0.850238 | + | 0.490885i | −0.860731 | − | 0.509060i | \(-0.829993\pi\) |
0.0104932 | + | 0.999945i | \(0.496660\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.17573i | 0.603440i | 0.953397 | + | 0.301720i | \(0.0975607\pi\) | ||||
−0.953397 | + | 0.301720i | \(0.902439\pi\) | |||||||
\(14\) | −1.72042 | − | 3.32267i | −0.459802 | − | 0.888022i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.446063 | − | 3.97505i | −0.111516 | − | 0.993763i | ||||
\(17\) | −4.04232 | + | 2.33383i | −0.980406 | + | 0.566038i | −0.902393 | − | 0.430915i | \(-0.858191\pi\) |
−0.0780131 | + | 0.996952i | \(0.524858\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0375730 | + | 0.0650784i | −0.00861984 | + | 0.0149300i | −0.870303 | − | 0.492516i | \(-0.836077\pi\) |
0.861683 | + | 0.507446i | \(0.169410\pi\) | |||||||
\(20\) | −6.66282 | + | 2.19080i | −1.48985 | + | 0.489877i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.70015 | + | 3.73020i | −0.575674 | + | 0.795281i | ||||
\(23\) | −2.40399 | − | 1.38795i | −0.501267 | − | 0.289407i | 0.227970 | − | 0.973668i | \(-0.426791\pi\) |
−0.729237 | + | 0.684262i | \(0.760125\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.64909 | + | 6.32041i | 0.729818 | + | 1.26408i | ||||
\(26\) | 1.25645 | + | 2.80873i | 0.246409 | + | 0.550837i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.13974 | − | 3.29584i | −0.782336 | − | 0.622856i | ||||
\(29\) | 8.09040 | 1.50235 | 0.751175 | − | 0.660104i | \(-0.229488\pi\) | ||||
0.751175 | + | 0.660104i | \(0.229488\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.66393 | − | 6.34611i | −0.658060 | − | 1.13979i | −0.981117 | − | 0.193415i | \(-0.938044\pi\) |
0.323057 | − | 0.946380i | \(-0.395290\pi\) | |||||||
\(32\) | −2.87136 | − | 4.87394i | −0.507589 | − | 0.861599i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.87063 | + | 5.34719i | −0.663807 | + | 0.917036i | ||||
\(35\) | −4.17274 | + | 8.28707i | −0.705321 | + | 1.40077i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.08610 | − | 8.80938i | 0.836150 | − | 1.44825i | −0.0569410 | − | 0.998378i | \(-0.518135\pi\) |
0.893091 | − | 0.449876i | \(-0.148532\pi\) | |||||||
\(38\) | −0.0109228 | + | 0.105710i | −0.00177191 | + | 0.0171484i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.33612 | + | 6.67583i | −1.15994 | + | 1.05554i | ||||
\(41\) | − | 7.20413i | − | 1.12510i | −0.826765 | − | 0.562548i | \(-0.809821\pi\) | ||
0.826765 | − | 0.562548i | \(-0.190179\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.49705i | − | 0.228299i | −0.993464 | − | 0.114149i | \(-0.963586\pi\) | ||
0.993464 | − | 0.114149i | \(-0.0364142\pi\) | |||||||
\(44\) | −1.33159 | + | 6.37474i | −0.200745 | + | 0.961028i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.90491 | − | 0.403487i | −0.575748 | − | 0.0594909i | ||||
\(47\) | −0.225780 | + | 0.391063i | −0.0329334 | + | 0.0570424i | −0.882022 | − | 0.471208i | \(-0.843818\pi\) |
0.849089 | + | 0.528250i | \(0.177152\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.95435 | + | 0.798164i | −0.993478 | + | 0.114023i | ||||
\(50\) | 8.36066 | + | 6.05196i | 1.18238 | + | 0.855876i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.24398 | + | 2.90032i | 0.449859 | + | 0.402201i | ||||
\(53\) | 1.69463 | + | 2.93518i | 0.232775 | + | 0.403178i | 0.958624 | − | 0.284677i | \(-0.0918862\pi\) |
−0.725849 | + | 0.687854i | \(0.758553\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.4190 | 1.53973 | ||||||||
\(56\) | −7.24742 | − | 1.86410i | −0.968477 | − | 0.249101i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.4442 | − | 4.67206i | 1.37139 | − | 0.613471i | ||||
\(59\) | −6.23214 | − | 10.7944i | −0.811356 | − | 1.40531i | −0.911915 | − | 0.410378i | \(-0.865397\pi\) |
0.100560 | − | 0.994931i | \(-0.467937\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.7098 | + | 7.33802i | 1.62733 | + | 0.939537i | 0.984886 | + | 0.173202i | \(0.0554112\pi\) |
0.642440 | + | 0.766336i | \(0.277922\pi\) | |||||||
\(62\) | −8.39465 | − | 6.07656i | −1.06612 | − | 0.771724i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.52135 | − | 4.63379i | −0.815169 | − | 0.579224i | ||||
\(65\) | 3.81501 | − | 6.60779i | 0.473194 | − | 0.819596i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.05831 | − | 4.65247i | 0.984479 | − | 0.568389i | 0.0808598 | − | 0.996725i | \(-0.474233\pi\) |
0.903619 | + | 0.428336i | \(0.140900\pi\) | |||||||
\(68\) | −1.90882 | + | 9.13810i | −0.231479 | + | 1.10816i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.601105 | + | 13.1078i | −0.0718458 | + | 1.56668i | ||||
\(71\) | − | 11.8379i | − | 1.40490i | −0.711731 | − | 0.702452i | \(-0.752089\pi\) | ||
0.711731 | − | 0.702452i | \(-0.247911\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.852826 | + | 0.492379i | −0.0998157 | + | 0.0576286i | −0.549077 | − | 0.835772i | \(-0.685021\pi\) |
0.449261 | + | 0.893400i | \(0.351687\pi\) | |||||||
\(74\) | 1.47857 | − | 14.3095i | 0.171880 | − | 1.66344i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.0469448 | + | 0.142772i | 0.00538494 | + | 0.0163771i | ||||
\(77\) | 4.72652 | + | 7.20265i | 0.538637 | + | 0.820819i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.09707 | − | 1.78809i | −0.348447 | − | 0.201176i | 0.315554 | − | 0.948908i | \(-0.397810\pi\) |
−0.664001 | + | 0.747731i | \(0.731143\pi\) | |||||||
\(80\) | −5.61529 | + | 12.8545i | −0.627809 | + | 1.43718i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.16025 | − | 9.30006i | −0.459423 | − | 1.02702i | ||||
\(83\) | 0.350331 | 0.0384538 | 0.0192269 | − | 0.999815i | \(-0.493880\pi\) | ||||
0.0192269 | + | 0.999815i | \(0.493880\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.3689 | 1.77546 | ||||||||
\(86\) | −0.864522 | − | 1.93260i | −0.0932238 | − | 0.208398i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.96229 | + | 8.99834i | 0.209181 | + | 0.959227i | ||||
\(89\) | 3.06210 | + | 1.76790i | 0.324582 | + | 0.187397i | 0.653433 | − | 0.756984i | \(-0.273328\pi\) |
−0.328851 | + | 0.944382i | \(0.606661\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.74705 | − | 0.328721i | 0.602455 | − | 0.0344594i | ||||
\(92\) | −5.27400 | + | 1.73414i | −0.549852 | + | 0.180797i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.0656362 | + | 0.635221i | −0.00676985 | + | 0.0655181i | ||||
\(95\) | 0.228222 | − | 0.131764i | 0.0234151 | − | 0.0135187i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.05525i | 0.107145i | 0.998564 | + | 0.0535723i | \(0.0170607\pi\) | ||||
−0.998564 | + | 0.0535723i | \(0.982939\pi\) | |||||||
\(98\) | −8.51669 | + | 5.04639i | −0.860315 | + | 0.509762i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 14.2880 | + | 2.98456i | 1.42880 | + | 0.298456i | ||||
\(101\) | −10.8723 | + | 6.27713i | −1.08183 | + | 0.624597i | −0.931391 | − | 0.364021i | \(-0.881404\pi\) |
−0.150444 | + | 0.988619i | \(0.548070\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.80411 | + | 4.85686i | −0.276297 | + | 0.478561i | −0.970462 | − | 0.241256i | \(-0.922441\pi\) |
0.694164 | + | 0.719817i | \(0.255774\pi\) | |||||||
\(104\) | 5.86265 | + | 1.87078i | 0.574880 | + | 0.183445i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.88266 | + | 2.81051i | 0.377118 | + | 0.272981i | ||||
\(107\) | 15.8399 | + | 9.14518i | 1.53130 | + | 0.884098i | 0.999302 | + | 0.0373531i | \(0.0118926\pi\) |
0.532000 | + | 0.846744i | \(0.321441\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.43893 | + | 12.8846i | 0.712520 | + | 1.23412i | 0.963908 | + | 0.266234i | \(0.0857795\pi\) |
−0.251388 | + | 0.967886i | \(0.580887\pi\) | |||||||
\(110\) | 14.7411 | − | 6.59424i | 1.40551 | − | 0.628736i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.4324 | + | 1.77882i | −0.985773 | + | 0.168083i | ||||
\(113\) | −6.67916 | −0.628323 | −0.314161 | − | 0.949370i | \(-0.601723\pi\) | ||||
−0.314161 | + | 0.949370i | \(0.601723\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.86735 | + | 8.43050i | 0.453883 | + | 0.786149i | ||||
\(116\) | 10.7847 | − | 12.0626i | 1.00134 | − | 1.11999i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −14.2789 | − | 10.3359i | −1.31448 | − | 0.951498i | ||||
\(119\) | 6.77540 | + | 10.3249i | 0.621100 | + | 0.946482i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.198701 | + | 0.344159i | −0.0180637 | + | 0.0312872i | ||||
\(122\) | 20.6451 | + | 2.13322i | 1.86912 | + | 0.193133i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −14.3461 | − | 2.99670i | −1.28831 | − | 0.269111i | ||||
\(125\) | − | 8.05942i | − | 0.720856i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.237718i | − | 0.0210941i | −0.999944 | − | 0.0105470i | \(-0.996643\pi\) | ||
0.999944 | − | 0.0105470i | \(-0.00335729\pi\) | |||||||
\(128\) | −11.0946 | − | 2.21596i | −0.980631 | − | 0.195865i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.10905 | − | 10.7333i | 0.0972705 | − | 0.941376i | ||||
\(131\) | 4.92994 | − | 8.53891i | 0.430731 | − | 0.746048i | −0.566206 | − | 0.824264i | \(-0.691589\pi\) |
0.996936 | + | 0.0782164i | \(0.0249225\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.177577 | + | 0.0894143i | 0.0153979 | + | 0.00775320i | ||||
\(134\) | 7.71604 | − | 10.6596i | 0.666565 | − | 0.920846i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.81292 | + | 12.8990i | 0.241205 | + | 1.10608i | ||||
\(137\) | −3.27562 | − | 5.67353i | −0.279855 | − | 0.484723i | 0.691494 | − | 0.722382i | \(-0.256953\pi\) |
−0.971348 | + | 0.237660i | \(0.923620\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.30200 | −0.449710 | −0.224855 | − | 0.974392i | \(-0.572191\pi\) | ||||
−0.224855 | + | 0.974392i | \(0.572191\pi\) | |||||||
\(140\) | 6.79350 | + | 17.2684i | 0.574155 | + | 1.45945i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.83619 | − | 15.2820i | −0.573680 | − | 1.28244i | ||||
\(143\) | −3.54227 | − | 6.13539i | −0.296219 | − | 0.513067i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −24.5709 | − | 14.1860i | −2.04050 | − | 1.17808i | ||||
\(146\) | −0.816603 | + | 1.12812i | −0.0675826 | + | 0.0933640i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.35472 | − | 19.3265i | −0.522355 | − | 1.58863i | ||||
\(149\) | 0.192950 | − | 0.334200i | 0.0158071 | − | 0.0273787i | −0.858014 | − | 0.513627i | \(-0.828302\pi\) |
0.873821 | + | 0.486248i | \(0.161635\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.9039 | + | 8.60478i | −1.21286 | + | 0.700247i | −0.963382 | − | 0.268132i | \(-0.913594\pi\) |
−0.249482 | + | 0.968380i | \(0.580260\pi\) | |||||||
\(152\) | 0.143051 | + | 0.157200i | 0.0116030 | + | 0.0127506i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.2610 | + | 6.56868i | 0.826858 | + | 0.529320i | ||||
\(155\) | 25.6979i | 2.06410i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.83943 | − | 3.94874i | 0.545846 | − | 0.315144i | −0.201599 | − | 0.979468i | \(-0.564614\pi\) |
0.747445 | + | 0.664324i | \(0.231280\pi\) | |||||||
\(158\) | −5.03071 | − | 0.519813i | −0.400222 | − | 0.0413541i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.174285 | + | 19.8371i | 0.0137784 | + | 1.56826i | ||||
\(161\) | −3.30296 | + | 6.55969i | −0.260310 | + | 0.516976i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.1449 | − | 12.2080i | −1.65620 | − | 0.956207i | −0.974445 | − | 0.224625i | \(-0.927884\pi\) |
−0.681753 | − | 0.731582i | \(-0.738782\pi\) | |||||||
\(164\) | −10.7412 | − | 9.60331i | −0.838749 | − | 0.749893i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.452254 | − | 0.202310i | 0.0351017 | − | 0.0157023i | ||||
\(167\) | 18.5223 | 1.43330 | 0.716648 | − | 0.697435i | \(-0.245675\pi\) | ||||
0.716648 | + | 0.697435i | \(0.245675\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.26619 | 0.635861 | ||||||||
\(170\) | 21.1312 | − | 9.45275i | 1.62069 | − | 0.724993i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.23208 | − | 1.99562i | −0.170195 | − | 0.152164i | ||||
\(173\) | 13.0506 | + | 7.53479i | 0.992222 | + | 0.572860i | 0.905938 | − | 0.423411i | \(-0.139167\pi\) |
0.0862842 | + | 0.996271i | \(0.472501\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.1436 | − | 10.5937i | 1.22034 | − | 0.800812i | ||||
\(176\) | 7.72957 | + | 10.4831i | 0.582638 | + | 0.790193i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.97390 | + | 0.513944i | 0.372810 | + | 0.0385217i | ||||
\(179\) | −5.38111 | + | 3.10679i | −0.402203 | + | 0.232212i | −0.687434 | − | 0.726247i | \(-0.741263\pi\) |
0.285231 | + | 0.958459i | \(0.407930\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 12.1266i | − | 0.901366i | −0.892684 | − | 0.450683i | \(-0.851180\pi\) | ||
0.892684 | − | 0.450683i | \(-0.148820\pi\) | |||||||
\(182\) | 7.22924 | − | 3.74318i | 0.535867 | − | 0.277463i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.80696 | + | 5.28430i | −0.428095 | + | 0.389564i | ||||
\(185\) | −30.8934 | + | 17.8363i | −2.27133 | + | 1.31135i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.59934 | − | 13.1624i | 0.555719 | − | 0.962533i | ||||
\(188\) | 0.282097 | + | 0.857933i | 0.0205740 | + | 0.0625712i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.218528 | − | 0.301893i | 0.0158537 | − | 0.0219016i | ||||
\(191\) | 7.71716 | + | 4.45550i | 0.558394 | + | 0.322389i | 0.752501 | − | 0.658591i | \(-0.228847\pi\) |
−0.194107 | + | 0.980980i | \(0.562181\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.51542 | + | 2.62478i | 0.109082 | + | 0.188936i | 0.915399 | − | 0.402548i | \(-0.131875\pi\) |
−0.806316 | + | 0.591484i | \(0.798542\pi\) | |||||||
\(194\) | 0.609388 | + | 1.36226i | 0.0437515 | + | 0.0978047i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.08030 | + | 11.4328i | −0.577164 | + | 0.816628i | ||||
\(197\) | 17.5070 | 1.24733 | 0.623663 | − | 0.781694i | \(-0.285644\pi\) | ||||
0.623663 | + | 0.781694i | \(0.285644\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.12491 | − | 15.8048i | −0.646848 | − | 1.12037i | −0.983871 | − | 0.178877i | \(-0.942753\pi\) |
0.337023 | − | 0.941496i | \(-0.390580\pi\) | |||||||
\(200\) | 20.1684 | − | 4.39816i | 1.42612 | − | 0.310997i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.4105 | + | 14.3819i | −0.732481 | + | 1.01191i | ||||
\(203\) | −1.22234 | − | 21.3703i | −0.0857915 | − | 1.49990i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.6320 | + | 21.8792i | −0.882256 | + | 1.52811i | ||||
\(206\) | −0.815177 | + | 7.88922i | −0.0567961 | + | 0.549668i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8.64865 | − | 0.970514i | 0.599676 | − | 0.0672930i | ||||
\(209\) | − | 0.244688i | − | 0.0169254i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.8486i | 1.43528i | 0.696414 | + | 0.717640i | \(0.254778\pi\) | ||||
−0.696414 | + | 0.717640i | \(0.745222\pi\) | |||||||
\(212\) | 6.63529 | + | 1.38602i | 0.455713 | + | 0.0951923i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 25.7295 | + | 2.65858i | 1.75883 | + | 0.181737i | ||||
\(215\) | −2.62499 | + | 4.54662i | −0.179023 | + | 0.310077i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.2093 | + | 10.6368i | −1.10036 | + | 0.722074i | ||||
\(218\) | 17.0438 | + | 12.3373i | 1.15435 | + | 0.835590i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 15.2218 | − | 17.0255i | 1.02625 | − | 1.14786i | ||||
\(221\) | −5.07779 | − | 8.79500i | −0.341569 | − | 0.591616i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.6765 | 1.58550 | 0.792748 | − | 0.609550i | \(-0.208650\pi\) | ||||
0.792748 | + | 0.609550i | \(0.208650\pi\) | |||||||
\(224\) | −12.4404 | + | 8.32088i | −0.831207 | + | 0.555962i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.62237 | + | 3.85710i | −0.573552 | + | 0.256570i | ||||
\(227\) | −0.833064 | − | 1.44291i | −0.0552924 | − | 0.0957692i | 0.837054 | − | 0.547120i | \(-0.184276\pi\) |
−0.892347 | + | 0.451350i | \(0.850942\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.6839 | − | 11.3645i | −1.30075 | − | 0.750989i | −0.320218 | − | 0.947344i | \(-0.603756\pi\) |
−0.980533 | + | 0.196355i | \(0.937089\pi\) | |||||||
\(230\) | 11.1519 | + | 8.07243i | 0.735335 | + | 0.532280i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.95645 | − | 21.8001i | 0.456713 | − | 1.43125i | ||||
\(233\) | 0.739972 | − | 1.28167i | 0.0484772 | − | 0.0839649i | −0.840769 | − | 0.541395i | \(-0.817897\pi\) |
0.889246 | + | 0.457430i | \(0.151230\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.37141 | − | 0.791784i | 0.0894609 | − | 0.0516503i | ||||
\(236\) | −24.4019 | − | 5.09722i | −1.58843 | − | 0.331801i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 14.7090 | + | 9.41612i | 0.953446 | + | 0.610356i | ||||
\(239\) | − | 7.69359i | − | 0.497657i | −0.968548 | − | 0.248829i | \(-0.919954\pi\) | ||
0.968548 | − | 0.248829i | \(-0.0800456\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.47981 | + | 0.854368i | −0.0953229 | + | 0.0550347i | −0.546904 | − | 0.837196i | \(-0.684194\pi\) |
0.451581 | + | 0.892230i | \(0.350860\pi\) | |||||||
\(242\) | −0.0577639 | + | 0.559034i | −0.00371320 | + | 0.0359360i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 27.8834 | − | 9.16834i | 1.78505 | − | 0.586943i | ||||
\(245\) | 22.5202 | + | 9.76995i | 1.43876 | + | 0.624180i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.141593 | − | 0.0817488i | −0.00900936 | − | 0.00520155i | ||||
\(248\) | −20.2504 | + | 4.41605i | −1.28590 | + | 0.280419i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.65417 | − | 10.4042i | −0.294355 | − | 0.658019i | ||||
\(251\) | 15.5203 | 0.979630 | 0.489815 | − | 0.871826i | \(-0.337064\pi\) | ||||
0.489815 | + | 0.871826i | \(0.337064\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.03876 | 0.568262 | ||||||||
\(254\) | −0.137278 | − | 0.306879i | −0.00861358 | − | 0.0192553i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.6021 | + | 3.54625i | −0.975128 | + | 0.221640i | ||||
\(257\) | −11.3136 | − | 6.53193i | −0.705726 | − | 0.407451i | 0.103751 | − | 0.994603i | \(-0.466916\pi\) |
−0.809476 | + | 0.587152i | \(0.800249\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.0378 | − | 12.1036i | −1.49364 | − | 0.752083i | ||||
\(260\) | −4.76659 | − | 14.4965i | −0.295611 | − | 0.899035i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.43317 | − | 13.8701i | 0.0885417 | − | 0.856899i | ||||
\(263\) | 6.59070 | − | 3.80514i | 0.406400 | − | 0.234635i | −0.282842 | − | 0.959167i | \(-0.591277\pi\) |
0.689242 | + | 0.724531i | \(0.257944\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 11.8857i | − | 0.730132i | ||||||
\(266\) | 0.280876 | + | 0.0128806i | 0.0172216 | + | 0.000789761i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.80522 | − | 18.2167i | 0.232441 | − | 1.11276i | ||||
\(269\) | 14.2226 | − | 8.21140i | 0.867165 | − | 0.500658i | 0.000759905 | − | 1.00000i | \(-0.499758\pi\) |
0.866405 | + | 0.499342i | \(0.166425\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.95296 | + | 13.7749i | −0.483108 | + | 0.836767i | −0.999812 | − | 0.0193968i | \(-0.993825\pi\) |
0.516704 | + | 0.856164i | \(0.327159\pi\) | |||||||
\(272\) | 11.0802 | + | 15.0274i | 0.671838 | + | 0.911169i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.50497 | − | 5.43256i | −0.453392 | − | 0.328193i | ||||
\(275\) | −20.5803 | − | 11.8820i | −1.24104 | − | 0.716513i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.9147 | − | 25.8330i | −0.896136 | − | 1.55215i | −0.832392 | − | 0.554187i | \(-0.813029\pi\) |
−0.0637443 | − | 0.997966i | \(-0.520304\pi\) | |||||||
\(278\) | −6.84454 | + | 3.06181i | −0.410508 | + | 0.183635i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 18.7421 | + | 18.3693i | 1.12006 | + | 1.09777i | ||||
\(281\) | 12.6113 | 0.752324 | 0.376162 | − | 0.926554i | \(-0.377244\pi\) | ||||
0.376162 | + | 0.926554i | \(0.377244\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00631 | + | 6.93912i | 0.238150 | + | 0.412488i | 0.960183 | − | 0.279370i | \(-0.0901256\pi\) |
−0.722033 | + | 0.691858i | \(0.756792\pi\) | |||||||
\(284\) | −17.6502 | − | 15.7803i | −1.04734 | − | 0.936389i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.11592 | − | 5.87480i | −0.479904 | − | 0.347384i | ||||
\(287\) | −19.0292 | + | 1.08844i | −1.12326 | + | 0.0642485i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.39355 | − | 4.14575i | 0.140797 | − | 0.243868i | ||||
\(290\) | −39.9116 | − | 4.12399i | −2.34369 | − | 0.242169i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.402713 | + | 1.92791i | −0.0235670 | + | 0.112822i | ||||
\(293\) | 16.8878i | 0.986596i | 0.869861 | + | 0.493298i | \(0.164209\pi\) | ||||
−0.869861 | + | 0.493298i | \(0.835791\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 43.7107i | 2.54493i | ||||||||
\(296\) | −19.3642 | − | 21.2795i | −1.12552 | − | 1.23685i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.0560922 | − | 0.542855i | 0.00324933 | − | 0.0314468i | ||||
\(299\) | 3.01980 | − | 5.23044i | 0.174639 | − | 0.302484i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.95437 | + | 0.226183i | −0.227926 | + | 0.0130370i | ||||
\(302\) | −14.2709 | + | 19.7150i | −0.821198 | + | 1.13447i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.275450 | + | 0.120326i | 0.0157981 | + | 0.00690115i | ||||
\(305\) | −25.7335 | − | 44.5718i | −1.47350 | − | 2.55217i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.3886 | 0.992420 | 0.496210 | − | 0.868202i | \(-0.334725\pi\) | ||||
0.496210 | + | 0.868202i | \(0.334725\pi\) | |||||||
\(308\) | 17.0396 | + | 2.55419i | 0.970923 | + | 0.145539i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.8400 | + | 33.1743i | 0.842858 | + | 1.88417i | ||||
\(311\) | 4.32502 | + | 7.49115i | 0.245249 | + | 0.424784i | 0.962202 | − | 0.272338i | \(-0.0877968\pi\) |
−0.716952 | + | 0.697122i | \(0.754463\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.49650 | + | 4.32810i | 0.423727 | + | 0.244639i | 0.696671 | − | 0.717391i | \(-0.254664\pi\) |
−0.272944 | + | 0.962030i | \(0.587997\pi\) | |||||||
\(314\) | 6.54893 | − | 9.04722i | 0.369578 | − | 0.510564i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.79450 | + | 2.23410i | −0.382221 | + | 0.125678i | ||||
\(317\) | 3.65839 | − | 6.33651i | 0.205475 | − | 0.355894i | −0.744809 | − | 0.667278i | \(-0.767459\pi\) |
0.950284 | + | 0.311384i | \(0.100793\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.8143 | + | 13.1718i | −1.27735 | + | 0.737481i | ||||
\(320\) | 11.6806 | + | 25.5078i | 0.652963 | + | 1.42593i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.475809 | + | 10.3755i | −0.0265158 | + | 0.578206i | ||||
\(323\) | − | 0.350757i | − | 0.0195166i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.7515 | + | 7.93944i | −0.762797 | + | 0.440401i | ||||
\(326\) | −34.3467 | − | 3.54897i | −1.90229 | − | 0.196559i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −19.4120 | − | 6.19440i | −1.07185 | − | 0.342028i | ||||
\(329\) | 1.06708 | + | 0.537300i | 0.0588300 | + | 0.0296223i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.1557 | − | 7.59544i | −0.723102 | − | 0.417483i | 0.0927914 | − | 0.995686i | \(-0.470421\pi\) |
−0.815893 | + | 0.578203i | \(0.803754\pi\) | |||||||
\(332\) | 0.467001 | − | 0.522337i | 0.0256300 | − | 0.0286670i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 23.9111 | − | 10.6963i | 1.30836 | − | 0.585274i | ||||
\(335\) | −32.6312 | −1.78284 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.46246 | −0.460980 | −0.230490 | − | 0.973075i | \(-0.574033\pi\) | ||||
−0.230490 | + | 0.973075i | \(0.574033\pi\) | |||||||
\(338\) | 10.6711 | − | 4.77357i | 0.580432 | − | 0.259648i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 21.8203 | − | 24.4058i | 1.18337 | − | 1.32359i | ||||
\(341\) | 20.6640 | + | 11.9303i | 1.11902 | + | 0.646064i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.15900 | + | 18.2489i | 0.170570 | + | 0.985346i | ||||
\(344\) | −4.03391 | − | 1.28723i | −0.217494 | − | 0.0694027i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.1987 | + | 2.19042i | 1.13965 | + | 0.117758i | ||||
\(347\) | 18.7881 | − | 10.8473i | 1.00860 | − | 0.582313i | 0.0978156 | − | 0.995205i | \(-0.468814\pi\) |
0.910780 | + | 0.412892i | \(0.135481\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 34.5359i | − | 1.84867i | −0.381586 | − | 0.924333i | \(-0.624622\pi\) | ||
0.381586 | − | 0.924333i | \(-0.375378\pi\) | |||||||
\(350\) | 14.7227 | − | 22.9985i | 0.786960 | − | 1.22932i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.0322 | + | 9.06932i | 0.854518 | + | 0.483396i | ||||
\(353\) | 7.93449 | − | 4.58098i | 0.422311 | − | 0.243821i | −0.273755 | − | 0.961799i | \(-0.588266\pi\) |
0.696065 | + | 0.717978i | \(0.254932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.7571 | + | 35.9523i | −1.10167 | + | 1.90815i | ||||
\(356\) | 6.71778 | − | 2.20887i | 0.356042 | − | 0.117070i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.15256 | + | 7.11815i | −0.272321 | + | 0.376206i | ||||
\(359\) | −13.6912 | − | 7.90464i | −0.722596 | − | 0.417191i | 0.0931113 | − | 0.995656i | \(-0.470319\pi\) |
−0.815707 | + | 0.578465i | \(0.803652\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.49718 | + | 16.4496i | 0.499851 | + | 0.865768i | ||||
\(362\) | −7.00291 | − | 15.6547i | −0.368065 | − | 0.822793i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.17087 | − | 9.00696i | 0.375856 | − | 0.472093i | ||||
\(365\) | 3.45343 | 0.180761 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.321922 | − | 0.557586i | −0.0168042 | − | 0.0291057i | 0.857501 | − | 0.514482i | \(-0.172016\pi\) |
−0.874305 | + | 0.485377i | \(0.838683\pi\) | |||||||
\(368\) | −4.44482 | + | 10.1751i | −0.231702 | + | 0.530414i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −29.5813 | + | 40.8659i | −1.53786 | + | 2.12452i | ||||
\(371\) | 7.49704 | − | 4.91970i | 0.389227 | − | 0.255418i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.4675 | + | 25.0584i | −0.749098 | + | 1.29748i | 0.199158 | + | 0.979967i | \(0.436179\pi\) |
−0.948256 | + | 0.317508i | \(0.897154\pi\) | |||||||
\(374\) | 2.20919 | − | 21.3803i | 0.114234 | − | 1.10555i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.859609 | + | 0.944631i | 0.0443310 | + | 0.0487156i | ||||
\(377\) | 17.6025i | 0.906577i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.6164i | 1.05899i | 0.848312 | + | 0.529496i | \(0.177619\pi\) | ||||
−0.848312 | + | 0.529496i | \(0.822381\pi\) | |||||||
\(380\) | 0.107769 | − | 0.515920i | 0.00552842 | − | 0.0264661i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.5353 | + | 1.29525i | 0.641363 | + | 0.0662708i | ||||
\(383\) | −11.1672 | + | 19.3421i | −0.570616 | + | 0.988336i | 0.425886 | + | 0.904777i | \(0.359962\pi\) |
−0.996503 | + | 0.0835599i | \(0.973371\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.72524 | − | 30.1624i | −0.0879263 | − | 1.53722i | ||||
\(386\) | 3.47207 | + | 2.51330i | 0.176724 | + | 0.127924i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.57336 | + | 1.40668i | 0.0798753 | + | 0.0714134i | ||||
\(389\) | 0.312454 | + | 0.541186i | 0.0158420 | + | 0.0274392i | 0.873838 | − | 0.486218i | \(-0.161624\pi\) |
−0.857996 | + | 0.513657i | \(0.828290\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.9569 | 0.655260 | ||||||||
\(392\) | −3.82892 | + | 19.4252i | −0.193390 | + | 0.981122i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 22.6005 | − | 10.1100i | 1.13860 | − | 0.509334i | ||||
\(395\) | 6.27062 | + | 10.8610i | 0.315509 | + | 0.546478i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.4487 | + | 8.34197i | 0.725160 | + | 0.418671i | 0.816649 | − | 0.577135i | \(-0.195829\pi\) |
−0.0914889 | + | 0.995806i | \(0.529163\pi\) | |||||||
\(398\) | −20.9067 | − | 15.1335i | −1.04796 | − | 0.758575i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 23.4962 | − | 17.3246i | 1.17481 | − | 0.866231i | ||||
\(401\) | 3.39351 | − | 5.87773i | 0.169464 | − | 0.293520i | −0.768768 | − | 0.639528i | \(-0.779130\pi\) |
0.938231 | + | 0.346008i | \(0.112463\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.8074 | − | 7.97172i | 0.687797 | − | 0.397100i | ||||
\(404\) | −5.13401 | + | 24.5780i | −0.255427 | + | 1.22280i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.9189 | − | 26.8817i | −0.690783 | − | 1.33412i | ||||
\(407\) | 33.1223i | 1.64181i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.576150 | + | 0.332640i | −0.0284888 | + | 0.0164480i | −0.514177 | − | 0.857684i | \(-0.671902\pi\) |
0.485688 | + | 0.874132i | \(0.338569\pi\) | |||||||
\(410\) | −3.67222 | + | 35.5394i | −0.181358 | + | 1.75517i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.50354 | + | 10.6552i | 0.172607 | + | 0.524945i | ||||
\(413\) | −27.5711 | + | 18.0927i | −1.35668 | + | 0.890282i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.06397 | − | 0.614283i | −0.0522282 | − | 0.0301540i | ||||
\(416\) | 10.6044 | − | 6.24731i | 0.519923 | − | 0.306299i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.141303 | − | 0.315876i | −0.00691134 | − | 0.0154500i | ||||
\(419\) | −34.3592 | −1.67856 | −0.839278 | − | 0.543702i | \(-0.817022\pi\) | ||||
−0.839278 | + | 0.543702i | \(0.817022\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.1909 | −1.52015 | −0.760076 | − | 0.649835i | \(-0.774838\pi\) | ||||
−0.760076 | + | 0.649835i | \(0.774838\pi\) | |||||||
\(422\) | 12.0397 | + | 26.9143i | 0.586084 | + | 1.31017i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.36613 | − | 2.04249i | 0.454859 | − | 0.0991922i | ||||
\(425\) | −29.5015 | − | 17.0327i | −1.43103 | − | 0.826208i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.4626 | − | 34.6808i | 0.845076 | − | 1.67832i | ||||
\(428\) | 34.7504 | − | 11.4263i | 1.67972 | − | 0.552309i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.763106 | + | 7.38528i | −0.0368003 | + | 0.356150i | ||||
\(431\) | −5.25944 | + | 3.03654i | −0.253339 | + | 0.146265i | −0.621292 | − | 0.783579i | \(-0.713392\pi\) |
0.367953 | + | 0.929844i | \(0.380059\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.56176i | − | 0.459509i | −0.973249 | − | 0.229754i | \(-0.926208\pi\) | ||
0.973249 | − | 0.229754i | \(-0.0737923\pi\) | |||||||
\(434\) | −14.7825 | + | 23.0920i | −0.709584 | + | 1.10845i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 29.1270 | + | 6.08424i | 1.39493 | + | 0.291382i | ||||
\(437\) | 0.180651 | − | 0.104299i | 0.00864169 | − | 0.00498928i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.6732 | − | 23.6827i | 0.652586 | − | 1.13031i | −0.329907 | − | 0.944013i | \(-0.607017\pi\) |
0.982493 | − | 0.186299i | \(-0.0596493\pi\) | |||||||
\(440\) | 9.81848 | − | 30.7691i | 0.468078 | − | 1.46686i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.6341 | − | 8.42144i | −0.553376 | − | 0.400567i | ||||
\(443\) | −20.2373 | − | 11.6840i | −0.961502 | − | 0.555123i | −0.0648670 | − | 0.997894i | \(-0.520662\pi\) |
−0.896635 | + | 0.442770i | \(0.853996\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.19982 | − | 10.7384i | −0.293900 | − | 0.509049i | ||||
\(446\) | 30.5648 | − | 13.6727i | 1.44729 | − | 0.647423i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −11.2546 | + | 17.9258i | −0.531728 | + | 0.846915i | ||||
\(449\) | −18.8468 | −0.889436 | −0.444718 | − | 0.895671i | \(-0.646696\pi\) | ||||
−0.444718 | + | 0.895671i | \(0.646696\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.7289 | + | 20.3151i | 0.552293 | + | 0.956599i | ||||
\(452\) | −8.90353 | + | 9.95852i | −0.418787 | + | 0.468410i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.90869 | − | 1.38162i | −0.0895790 | − | 0.0648428i | ||||
\(455\) | −18.0304 | − | 9.07876i | −0.845280 | − | 0.425619i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.63991 | + | 6.30451i | −0.170268 | + | 0.294913i | −0.938513 | − | 0.345243i | \(-0.887797\pi\) |
0.768246 | + | 0.640155i | \(0.221130\pi\) | |||||||
\(458\) | −31.9735 | − | 3.30376i | −1.49402 | − | 0.154374i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 19.0581 | + | 3.98097i | 0.888587 | + | 0.185614i | ||||
\(461\) | − | 3.58604i | − | 0.167019i | −0.996507 | − | 0.0835093i | \(-0.973387\pi\) | ||
0.996507 | − | 0.0835093i | \(-0.0266128\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 28.4541i | − | 1.32237i | −0.750221 | − | 0.661187i | \(-0.770053\pi\) | ||
0.750221 | − | 0.661187i | \(-0.229947\pi\) | |||||||
\(464\) | −3.60883 | − | 32.1597i | −0.167536 | − | 1.49298i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.215116 | − | 2.08187i | 0.00996504 | − | 0.0964409i | ||||
\(467\) | −12.4728 | + | 21.6035i | −0.577173 | + | 0.999692i | 0.418629 | + | 0.908157i | \(0.362511\pi\) |
−0.995802 | + | 0.0915351i | \(0.970823\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.5067 | − | 20.5826i | −0.623680 | − | 0.950415i | ||||
\(470\) | 1.31316 | − | 1.81411i | 0.0605716 | − | 0.0836784i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −34.4448 | + | 7.51146i | −1.58545 | + | 0.345743i | ||||
\(473\) | 2.43733 | + | 4.22157i | 0.112068 | + | 0.194108i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.548429 | −0.0251637 | ||||||||
\(476\) | 24.4261 | + | 3.66140i | 1.11957 | + | 0.167820i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.44291 | − | 9.93193i | −0.203214 | − | 0.454276i | ||||
\(479\) | 1.73949 | + | 3.01289i | 0.0794795 | + | 0.137662i | 0.903025 | − | 0.429587i | \(-0.141341\pi\) |
−0.823546 | + | 0.567249i | \(0.808008\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.1669 | + | 11.0660i | 0.873934 | + | 0.504566i | ||||
\(482\) | −1.41696 | + | 1.95750i | −0.0645406 | + | 0.0891615i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.248262 | + | 0.755034i | 0.0112846 | + | 0.0343197i | ||||
\(485\) | 1.85032 | − | 3.20484i | 0.0840186 | − | 0.145524i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.5540 | + | 7.82541i | −0.614191 | + | 0.354603i | −0.774604 | − | 0.632447i | \(-0.782051\pi\) |
0.160413 | + | 0.987050i | \(0.448717\pi\) | |||||||
\(488\) | 30.7012 | − | 27.9379i | 1.38978 | − | 1.26469i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 34.7141 | − | 0.392610i | 1.56822 | − | 0.0177363i | ||||
\(491\) | 2.07316i | 0.0935606i | 0.998905 | + | 0.0467803i | \(0.0148961\pi\) | ||||
−0.998905 | + | 0.0467803i | \(0.985104\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.7039 | + | 18.8816i | −1.47291 | + | 0.850386i | ||||
\(494\) | −0.229996 | − | 0.0237650i | −0.0103480 | − | 0.00106924i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −23.5917 | + | 17.3951i | −1.05930 | + | 0.781061i | ||||
\(497\) | −31.2691 | + | 1.78854i | −1.40261 | + | 0.0802269i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.85785 | + | 2.80468i | 0.217467 | + | 0.125555i | 0.604777 | − | 0.796395i | \(-0.293262\pi\) |
−0.387310 | + | 0.921950i | \(0.626596\pi\) | |||||||
\(500\) | −12.0165 | − | 10.7434i | −0.537393 | − | 0.480462i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.0357 | − | 8.96267i | 0.894235 | − | 0.400023i | ||||
\(503\) | 16.2015 | 0.722390 | 0.361195 | − | 0.932490i | \(-0.382369\pi\) | ||||
0.361195 | + | 0.932490i | \(0.382369\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 44.0262 | 1.95914 | ||||||||
\(506\) | 11.6685 | − | 5.21972i | 0.518726 | − | 0.232045i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.354434 | − | 0.316885i | −0.0157255 | − | 0.0140595i | ||||
\(509\) | 21.5238 | + | 12.4268i | 0.954026 | + | 0.550807i | 0.894329 | − | 0.447409i | \(-0.147653\pi\) |
0.0596966 | + | 0.998217i | \(0.480987\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.42944 | + | 2.17829i | 0.0632346 | + | 0.0963620i | ||||
\(512\) | −18.0934 | + | 13.5879i | −0.799621 | + | 0.600505i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.3773 | − | 1.89889i | −0.810586 | − | 0.0837563i | ||||
\(515\) | 17.0324 | − | 9.83367i | 0.750538 | − | 0.433323i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.47036i | − | 0.0646662i | ||||||
\(518\) | −38.0209 | − | 1.74359i | −1.67054 | − | 0.0766091i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −14.5248 | − | 15.9614i | −0.636956 | − | 0.699955i | ||||
\(521\) | 13.3491 | − | 7.70713i | 0.584837 | − | 0.337656i | −0.178217 | − | 0.983991i | \(-0.557033\pi\) |
0.763053 | + | 0.646336i | \(0.223699\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.33526 | + | 12.7050i | −0.320748 | + | 0.555553i | −0.980643 | − | 0.195806i | \(-0.937268\pi\) |
0.659894 | + | 0.751358i | \(0.270601\pi\) | |||||||
\(524\) | −6.15961 | − | 18.7331i | −0.269084 | − | 0.818358i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.31077 | − | 8.71820i | 0.275163 | − | 0.380132i | ||||
\(527\) | 29.6215 | + | 17.1020i | 1.29033 | + | 0.744974i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.64721 | − | 13.2454i | −0.332487 | − | 0.575885i | ||||
\(530\) | −6.86376 | − | 15.3436i | −0.298143 | − | 0.666485i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.370031 | − | 0.145572i | 0.0160429 | − | 0.00631137i | ||||
\(533\) | 15.6742 | 0.678927 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.0710 | − | 55.5486i | −1.38655 | − | 2.40158i | ||||
\(536\) | −5.60751 | − | 25.7140i | −0.242208 | − | 1.11068i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.6185 | − | 18.8137i | 0.587134 | − | 0.811114i | ||||
\(539\) | 18.3112 | − | 13.5730i | 0.788720 | − | 0.584631i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.68184 | + | 16.7694i | −0.416255 | + | 0.720975i | −0.995559 | − | 0.0941366i | \(-0.969991\pi\) |
0.579304 | + | 0.815111i | \(0.303324\pi\) | |||||||
\(542\) | −2.31199 | + | 22.3752i | −0.0993084 | + | 0.961099i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 22.9819 | + | 13.0007i | 0.985341 | + | 0.557402i | ||||
\(545\) | − | 52.1748i | − | 2.23492i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.2986i | 0.654120i | 0.945004 | + | 0.327060i | \(0.106058\pi\) | ||||
−0.945004 | + | 0.327060i | \(0.893942\pi\) | |||||||
\(548\) | −12.8256 | − | 2.67910i | −0.547884 | − | 0.114445i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −33.4295 | − | 3.45420i | −1.42544 | − | 0.147288i | ||||
\(551\) | −0.303981 | + | 0.526510i | −0.0129500 | + | 0.0224301i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.25521 | + | 8.45086i | −0.180950 | + | 0.359367i | ||||
\(554\) | −34.1720 | − | 24.7358i | −1.45183 | − | 1.05092i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.06773 | + | 7.90520i | −0.299738 | + | 0.335255i | ||||
\(557\) | 3.01197 | + | 5.21688i | 0.127621 | + | 0.221046i | 0.922754 | − | 0.385388i | \(-0.125933\pi\) |
−0.795133 | + | 0.606435i | \(0.792599\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.25719 | 0.137764 | ||||||||
\(560\) | 34.8028 | + | 12.8903i | 1.47069 | + | 0.544714i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.2803 | − | 7.28277i | 0.686744 | − | 0.307205i | ||||
\(563\) | 7.04736 | + | 12.2064i | 0.297011 | + | 0.514438i | 0.975451 | − | 0.220218i | \(-0.0706769\pi\) |
−0.678440 | + | 0.734656i | \(0.737344\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.2849 | + | 11.7115i | 0.853393 | + | 0.492706i | ||||
\(566\) | 9.17910 | + | 6.64439i | 0.385826 | + | 0.279285i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −31.8981 | − | 10.1787i | −1.33841 | − | 0.427090i | ||||
\(569\) | −8.82158 | + | 15.2794i | −0.369820 | + | 0.640547i | −0.989537 | − | 0.144278i | \(-0.953914\pi\) |
0.619717 | + | 0.784825i | \(0.287247\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.3514 | + | 12.9046i | −0.935378 | + | 0.540041i | −0.888508 | − | 0.458860i | \(-0.848258\pi\) |
−0.0468695 | + | 0.998901i | \(0.514924\pi\) | |||||||
\(572\) | −13.8697 | − | 2.89719i | −0.579922 | − | 0.121138i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −23.9369 | + | 12.3941i | −0.999109 | + | 0.517321i | ||||
\(575\) | − | 20.2589i | − | 0.844857i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.08344 | − | 2.93493i | 0.211626 | − | 0.122183i | −0.390441 | − | 0.920628i | \(-0.627677\pi\) |
0.602067 | + | 0.798446i | \(0.294344\pi\) | |||||||
\(578\) | 0.695824 | − | 6.73412i | 0.0289425 | − | 0.280103i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −53.9048 | + | 17.7244i | −2.23828 | + | 0.735966i | ||||
\(581\) | −0.0529298 | − | 0.925375i | −0.00219590 | − | 0.0383910i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.55742 | − | 5.51798i | −0.395828 | − | 0.228531i | ||||
\(584\) | 0.593454 | + | 2.72136i | 0.0245573 | + | 0.112611i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.75239 | + | 21.8011i | 0.402868 | + | 0.900593i | ||||
\(587\) | 1.21088 | 0.0499786 | 0.0249893 | − | 0.999688i | \(-0.492045\pi\) | ||||
0.0249893 | + | 0.999688i | \(0.492045\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.550659 | 0.0226895 | ||||||||
\(590\) | 25.2421 | + | 56.4277i | 1.03920 | + | 2.32309i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −37.2865 | − | 16.2880i | −1.53246 | − | 0.669431i | ||||
\(593\) | 5.75014 | + | 3.31984i | 0.236130 | + | 0.136330i | 0.613397 | − | 0.789775i | \(-0.289803\pi\) |
−0.377267 | + | 0.926105i | \(0.623136\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.47310 | − | 43.2374i | −0.101387 | − | 1.77256i | ||||
\(596\) | −0.241078 | − | 0.733183i | −0.00987492 | − | 0.0300324i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.877880 | − | 8.49605i | 0.0358992 | − | 0.347429i | ||||
\(599\) | 36.2905 | − | 20.9523i | 1.48279 | − | 0.856089i | 0.482980 | − | 0.875631i | \(-0.339554\pi\) |
0.999809 | + | 0.0195424i | \(0.00622094\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.27647i | − | 0.133650i | −0.997765 | − | 0.0668250i | \(-0.978713\pi\) | ||
0.997765 | − | 0.0668250i | \(-0.0212869\pi\) | |||||||
\(602\) | −4.97422 | + | 2.57556i | −0.202734 | + | 0.104972i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.03778 | + | 33.6919i | −0.286363 | + | 1.37090i | ||||
\(605\) | 1.20692 | − | 0.696818i | 0.0490685 | − | 0.0283297i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.148269 | − | 0.256810i | 0.00601806 | − | 0.0104236i | −0.863001 | − | 0.505203i | \(-0.831418\pi\) |
0.869019 | + | 0.494779i | \(0.164751\pi\) | |||||||
\(608\) | 0.425074 | − | 0.00373461i | 0.0172390 | − | 0.000151459i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −58.9597 | − | 42.6787i | −2.38721 | − | 1.72801i | ||||
\(611\) | −0.850848 | − | 0.491238i | −0.0344216 | − | 0.0198733i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.32452 | + | 5.75823i | 0.134276 | + | 0.232573i | 0.925321 | − | 0.379186i | \(-0.123796\pi\) |
−0.791045 | + | 0.611758i | \(0.790462\pi\) | |||||||
\(614\) | 22.4476 | − | 10.0416i | 0.905910 | − | 0.405246i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 23.4721 | − | 6.54278i | 0.945716 | − | 0.263616i | ||||
\(617\) | −0.955148 | −0.0384528 | −0.0192264 | − | 0.999815i | \(-0.506120\pi\) | ||||
−0.0192264 | + | 0.999815i | \(0.506120\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.38442 | + | 11.0581i | 0.256611 | + | 0.444464i | 0.965332 | − | 0.261025i | \(-0.0840606\pi\) |
−0.708721 | + | 0.705489i | \(0.750727\pi\) | |||||||
\(620\) | 38.3151 | + | 34.2560i | 1.53877 | + | 1.37575i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9.90933 | + | 7.17298i | 0.397328 | + | 0.287610i | ||||
\(623\) | 4.20716 | − | 8.35543i | 0.168556 | − | 0.334753i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.11375 | − | 7.12522i | 0.164550 | − | 0.285009i | ||||
\(626\) | 12.1769 | + | 1.25821i | 0.486687 | + | 0.0502884i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.22965 | − | 15.4613i | 0.128877 | − | 0.616972i | ||||
\(629\) | 47.4804i | 1.89317i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.9142i | 0.474298i | 0.971473 | + | 0.237149i | \(0.0762129\pi\) | ||||
−0.971473 | + | 0.237149i | \(0.923787\pi\) | |||||||
\(632\) | −7.48111 | + | 6.80777i | −0.297583 | + | 0.270799i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.06352 | − | 10.2927i | 0.0422379 | − | 0.408774i | ||||
\(635\) | −0.416824 | + | 0.721961i | −0.0165412 | + | 0.0286501i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.73659 | − | 15.1308i | −0.0688063 | − | 0.599504i | ||||
\(638\) | −21.8453 | + | 30.1788i | −0.864863 | + | 1.19479i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 29.8091 | + | 26.1836i | 1.17831 | + | 1.03500i | ||||
\(641\) | −0.801420 | − | 1.38810i | −0.0316542 | − | 0.0548266i | 0.849764 | − | 0.527163i | \(-0.176744\pi\) |
−0.881419 | + | 0.472336i | \(0.843411\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.7304 | 0.817525 | 0.408763 | − | 0.912641i | \(-0.365960\pi\) | ||||
0.408763 | + | 0.912641i | \(0.365960\pi\) | |||||||
\(644\) | 5.37744 | + | 13.6689i | 0.211901 | + | 0.538631i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.202556 | − | 0.452804i | −0.00796944 | − | 0.0178153i | ||||
\(647\) | −7.97304 | − | 13.8097i | −0.313452 | − | 0.542916i | 0.665655 | − | 0.746260i | \(-0.268152\pi\) |
−0.979107 | + | 0.203344i | \(0.934819\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.1483 | + | 20.2929i | 1.37969 | + | 0.796565i | ||||
\(650\) | −13.1674 | + | 18.1906i | −0.516469 | + | 0.713492i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −46.3888 | + | 15.2531i | −1.81673 | + | 0.597356i | ||||
\(653\) | 16.5069 | − | 28.5908i | 0.645966 | − | 1.11885i | −0.338112 | − | 0.941106i | \(-0.609788\pi\) |
0.984078 | − | 0.177740i | \(-0.0568785\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −29.9449 | + | 17.2887i | −1.17004 | + | 0.675525i | ||||
\(656\) | −28.6368 | + | 3.21349i | −1.11808 | + | 0.125466i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.68781 | + | 0.0774009i | 0.0657977 | + | 0.00301740i | ||||
\(659\) | − | 34.3288i | − | 1.33726i | −0.743595 | − | 0.668630i | \(-0.766881\pi\) | ||
0.743595 | − | 0.668630i | \(-0.233119\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.72551 | + | 0.996223i | −0.0671145 | + | 0.0387486i | −0.533182 | − | 0.846001i | \(-0.679004\pi\) |
0.466067 | + | 0.884749i | \(0.345670\pi\) | |||||||
\(662\) | −21.3694 | − | 2.20805i | −0.830544 | − | 0.0858185i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.301228 | − | 0.943988i | 0.0116899 | − | 0.0366339i | ||||
\(665\) | −0.382527 | − | 0.582925i | −0.0148338 | − | 0.0226049i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.4493 | − | 11.2290i | −0.753078 | − | 0.434790i | ||||
\(668\) | 24.6907 | − | 27.6164i | 0.955313 | − | 1.06851i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −42.1248 | + | 18.8439i | −1.62742 | + | 0.728005i | ||||
\(671\) | −47.7876 | −1.84482 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.6634 | 0.835063 | 0.417531 | − | 0.908663i | \(-0.362895\pi\) | ||||
0.417531 | + | 0.908663i | \(0.362895\pi\) | |||||||
\(674\) | −10.9245 | + | 4.88692i | −0.420796 | + | 0.188237i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.0191 | − | 12.3248i | 0.423811 | − | 0.474029i | ||||
\(677\) | 18.4674 | + | 10.6622i | 0.709760 | + | 0.409780i | 0.810972 | − | 0.585085i | \(-0.198939\pi\) |
−0.101212 | + | 0.994865i | \(0.532272\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.78738 | − | 0.159433i | 0.106970 | − | 0.00611848i | ||||
\(680\) | 14.0747 | − | 44.1071i | 0.539738 | − | 1.69143i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 33.5654 | + | 3.46825i | 1.28529 | + | 0.132806i | ||||
\(683\) | −24.6393 | + | 14.2255i | −0.942798 | + | 0.544325i | −0.890836 | − | 0.454324i | \(-0.849881\pi\) |
−0.0519619 | + | 0.998649i | \(0.516547\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.9744i | 0.877805i | ||||||||
\(686\) | 14.6164 | + | 21.7338i | 0.558058 | + | 0.829802i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.95087 | + | 0.667781i | −0.226875 | + | 0.0254589i | ||||
\(689\) | −6.38616 | + | 3.68705i | −0.243293 | + | 0.140465i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.4507 | − | 37.1536i | 0.816022 | − | 1.41339i | −0.0925703 | − | 0.995706i | \(-0.529508\pi\) |
0.908592 | − | 0.417685i | \(-0.137158\pi\) | |||||||
\(692\) | 28.6311 | − | 9.41419i | 1.08839 | − | 0.357874i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.9901 | − | 24.8529i | 0.682893 | − | 0.943404i | ||||
\(695\) | 16.1024 | + | 9.29673i | 0.610799 | + | 0.352645i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.8132 | + | 29.1214i | 0.636846 | + | 1.10305i | ||||
\(698\) | −19.9439 | − | 44.5837i | −0.754887 | − | 1.68752i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.72482 | − | 38.1916i | 0.216378 | − | 1.44351i | ||||
\(701\) | 29.6874 | 1.12128 | 0.560639 | − | 0.828061i | \(-0.310556\pi\) | ||||
0.560639 | + | 0.828061i | \(0.310556\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.382200 | + | 0.661991i | 0.0144150 | + | 0.0249674i | ||||
\(704\) | 25.9339 | + | 2.44962i | 0.977420 | + | 0.0923236i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.59749 | − | 10.4958i | 0.285935 | − | 0.395014i | ||||
\(707\) | 18.2233 | + | 27.7701i | 0.685356 | + | 1.04440i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.3262 | − | 17.8854i | 0.387807 | − | 0.671702i | −0.604347 | − | 0.796721i | \(-0.706566\pi\) |
0.992154 | + | 0.125019i | \(0.0398993\pi\) | |||||||
\(710\) | −6.03425 | + | 58.3990i | −0.226461 | + | 2.19167i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.39664 | − | 6.73091i | 0.277201 | − | 0.252251i | ||||
\(713\) | 20.3413i | 0.761789i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.8446i | 0.929135i | ||||||||
\(716\) | −2.54101 | + | 12.1646i | −0.0949622 | + | 0.454612i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.2393 | − | 2.29794i | −0.829963 | − | 0.0857585i | ||||
\(719\) | 20.9300 | − | 36.2519i | 0.780559 | − | 1.35197i | −0.151058 | − | 0.988525i | \(-0.548268\pi\) |
0.931617 | − | 0.363443i | \(-0.118399\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.2527 | + | 6.67307i | 0.493558 | + | 0.248518i | ||||
\(722\) | 21.7596 | + | 15.7509i | 0.809808 | + | 0.586189i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18.0806 | − | 16.1652i | −0.671961 | − | 0.600774i | ||||
\(725\) | 29.5226 | + | 51.1346i | 1.09644 | + | 1.89909i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.7901 | 1.21612 | 0.608059 | − | 0.793892i | \(-0.291949\pi\) | ||||
0.608059 | + | 0.793892i | \(0.291949\pi\) | |||||||
\(728\) | 4.05579 | − | 15.7684i | 0.150317 | − | 0.584418i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.45815 | − | 1.99429i | 0.165004 | − | 0.0738120i | ||||
\(731\) | 3.49388 | + | 6.05157i | 0.129226 | + | 0.223825i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.1489 | + | 15.6744i | 1.00277 | + | 0.578948i | 0.909066 | − | 0.416652i | \(-0.136797\pi\) |
0.0937014 | + | 0.995600i | \(0.470130\pi\) | |||||||
\(734\) | −0.737576 | − | 0.533903i | −0.0272244 | − | 0.0197067i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.137956 | + | 15.7022i | 0.00508514 | + | 0.578791i | ||||
\(737\) | −15.1492 | + | 26.2392i | −0.558028 | + | 0.966532i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.6466 | − | 15.3844i | 0.980211 | − | 0.565925i | 0.0778770 | − | 0.996963i | \(-0.475186\pi\) |
0.902334 | + | 0.431038i | \(0.141853\pi\) | |||||||
\(740\) | −14.5882 | + | 69.8379i | −0.536272 | + | 2.56729i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.83716 | − | 10.6804i | 0.251000 | − | 0.392091i | ||||
\(743\) | − | 24.1452i | − | 0.885801i | −0.896571 | − | 0.442901i | \(-0.853949\pi\) | ||
0.896571 | − | 0.442901i | \(-0.146051\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.17200 | + | 0.676652i | −0.0429386 | + | 0.0247906i | ||||
\(746\) | −4.20581 | + | 40.7035i | −0.153986 | + | 1.49026i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.49484 | − | 28.8764i | −0.347166 | − | 1.05583i | ||||
\(749\) | 21.7632 | − | 43.2218i | 0.795210 | − | 1.57929i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.7871 | + | 18.9297i | 1.19642 | + | 0.690753i | 0.959755 | − | 0.280838i | \(-0.0906124\pi\) |
0.236665 | + | 0.971591i | \(0.423946\pi\) | |||||||
\(752\) | 1.65521 | + | 0.723050i | 0.0603592 | + | 0.0263669i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.1651 | + | 22.7237i | 0.370193 | + | 0.827550i | ||||
\(755\) | 60.3518 | 2.19643 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.5471 | −0.819489 | −0.409744 | − | 0.912200i | \(-0.634382\pi\) | ||||
−0.409744 | + | 0.912200i | \(0.634382\pi\) | |||||||
\(758\) | 11.9056 | + | 26.6144i | 0.432430 | + | 0.966679i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.158812 | − | 0.728254i | −0.00576072 | − | 0.0264166i | ||||
\(761\) | −12.8446 | − | 7.41584i | −0.465617 | − | 0.268824i | 0.248786 | − | 0.968558i | \(-0.419968\pi\) |
−0.714403 | + | 0.699734i | \(0.753302\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.9099 | − | 21.5961i | 1.19142 | − | 0.781832i | ||||
\(764\) | 16.9303 | − | 5.56684i | 0.612516 | − | 0.201401i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.24639 | + | 31.4183i | −0.117297 | + | 1.13519i | ||||
\(767\) | 23.4857 | − | 13.5595i | 0.848019 | − | 0.489604i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 41.7367i | − | 1.50506i | −0.658556 | − | 0.752532i | \(-0.728833\pi\) | ||
0.658556 | − | 0.752532i | \(-0.271167\pi\) | |||||||
\(770\) | −19.6454 | − | 37.9415i | −0.707972 | − | 1.36732i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.93361 | + | 1.23945i | 0.213555 | + | 0.0446088i | ||||
\(773\) | 17.7798 | − | 10.2652i | 0.639497 | − | 0.369214i | −0.144924 | − | 0.989443i | \(-0.546294\pi\) |
0.784421 | + | 0.620229i | \(0.212960\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.7400 | − | 46.3150i | 0.960528 | − | 1.66368i | ||||
\(776\) | 2.84344 | + | 0.907347i | 0.102074 | + | 0.0325719i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.715882 | + | 0.518199i | 0.0256656 | + | 0.0185784i | ||||
\(779\) | 0.468833 | + | 0.270681i | 0.0167977 | + | 0.00969815i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.2731 | + | 33.3820i | 0.689646 | + | 1.19450i | ||||
\(782\) | 16.7266 | − | 7.48239i | 0.598141 | − | 0.267570i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.27482 | + | 27.2878i | 0.224101 | + | 0.974566i | ||||
\(785\) | −27.6955 | −0.988495 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.37470 | + | 7.57720i | 0.155941 | + | 0.270098i | 0.933401 | − | 0.358834i | \(-0.116826\pi\) |
−0.777460 | + | 0.628932i | \(0.783492\pi\) | |||||||
\(788\) | 23.3374 | − | 26.1027i | 0.831361 | − | 0.929871i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 14.3670 | + | 10.3997i | 0.511155 | + | 0.370006i | ||||
\(791\) | 1.00912 | + | 17.6426i | 0.0358803 | + | 0.627298i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.9656 | + | 27.6532i | −0.566954 | + | 0.981993i | ||||
\(794\) | 23.4697 | + | 2.42508i | 0.832908 | + | 0.0860628i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −35.7285 | − | 7.46319i | −1.26636 | − | 0.264526i | ||||
\(797\) | − | 11.5319i | − | 0.408480i | −0.978921 | − | 0.204240i | \(-0.934528\pi\) | ||
0.978921 | − | 0.204240i | \(-0.0654722\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.10773i | − | 0.0745663i | ||||||
\(800\) | 20.3275 | − | 35.9336i | 0.718684 | − | 1.27044i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.986520 | − | 9.54746i | 0.0348352 | − | 0.337132i | ||||
\(803\) | 1.60327 | − | 2.77694i | 0.0565781 | − | 0.0979961i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.5332 | − | 14.1305i | 0.758947 | − | 0.498035i | ||||
\(806\) | 13.2210 | − | 18.2645i | 0.465689 | − | 0.643340i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.56568 | + | 34.6934i | 0.266160 | + | 1.22051i | ||||
\(809\) | −17.0250 | − | 29.4882i | −0.598567 | − | 1.03675i | −0.993033 | − | 0.117838i | \(-0.962404\pi\) |
0.394465 | − | 0.918911i | \(-0.370930\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.87280 | −0.346681 | −0.173340 | − | 0.984862i | \(-0.555456\pi\) | ||||
−0.173340 | + | 0.984862i | \(0.555456\pi\) | |||||||
\(812\) | −33.4921 | − | 26.6647i | −1.17534 | − | 0.935747i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 19.1275 | + | 42.7588i | 0.670420 | + | 1.49870i | ||||
\(815\) | 42.8120 | + | 74.1526i | 1.49964 | + | 2.59745i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.0974259 | + | 0.0562489i | 0.00340850 | + | 0.00196790i | ||||
\(818\) | −0.551679 | + | 0.762133i | −0.0192890 | + | 0.0266474i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.7828 | + | 47.9998i | 0.551158 | + | 1.67622i | ||||
\(821\) | −22.1782 | + | 38.4138i | −0.774024 | + | 1.34065i | 0.161317 | + | 0.986903i | \(0.448426\pi\) |
−0.935341 | + | 0.353747i | \(0.884908\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.6005 | − | 13.6257i | 0.822660 | − | 0.474963i | −0.0286727 | − | 0.999589i | \(-0.509128\pi\) |
0.851333 | + | 0.524626i | \(0.175795\pi\) | |||||||
\(824\) | 10.6760 | + | 11.7320i | 0.371917 | + | 0.408703i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −25.1443 | + | 39.2783i | −0.874882 | + | 1.36667i | ||||
\(827\) | 31.6550i | 1.10075i | 0.834917 | + | 0.550376i | \(0.185515\pi\) | ||||
−0.834917 | + | 0.550376i | \(0.814485\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.5060 | − | 14.1485i | 0.851128 | − | 0.491399i | −0.00990312 | − | 0.999951i | \(-0.503152\pi\) |
0.861031 | + | 0.508552i | \(0.169819\pi\) | |||||||
\(830\) | −1.72825 | − | 0.178577i | −0.0599886 | − | 0.00619850i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 10.0819 | − | 14.1887i | 0.349526 | − | 0.491905i | ||||
\(833\) | 26.2489 | − | 19.4567i | 0.909470 | − | 0.674135i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −56.2529 | − | 32.4777i | −1.94671 | − | 1.12394i | ||||
\(836\) | −0.364825 | − | 0.326176i | −0.0126178 | − | 0.0112810i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −44.3555 | + | 19.8418i | −1.53224 | + | 0.685424i | ||||
\(839\) | −20.6201 | −0.711884 | −0.355942 | − | 0.934508i | \(-0.615840\pi\) | ||||
−0.355942 | + | 0.934508i | \(0.615840\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.4545 | 1.25705 | ||||||||
\(842\) | −40.2654 | + | 18.0122i | −1.38764 | + | 0.620740i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 31.0850 | + | 27.7919i | 1.06999 | + | 0.956635i | ||||
\(845\) | −25.1048 | − | 14.4942i | −0.863631 | − | 0.498617i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.939095 | + | 0.472857i | 0.0322677 | + | 0.0162476i | ||||
\(848\) | 10.9116 | − | 8.04550i | 0.374705 | − | 0.276283i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −47.9207 | − | 4.95155i | −1.64367 | − | 0.169837i | ||||
\(851\) | −24.4539 | + | 14.1185i | −0.838269 | + | 0.483975i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.1322i | 0.518116i | 0.965862 | + | 0.259058i | \(0.0834121\pi\) | ||||
−0.965862 | + | 0.259058i | \(0.916588\pi\) | |||||||
\(854\) | 2.51559 | − | 54.8551i | 0.0860816 | − | 1.87710i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 38.2621 | − | 34.8183i | 1.30777 | − | 1.19006i | ||||
\(857\) | −16.9075 | + | 9.76153i | −0.577548 | + | 0.333447i | −0.760158 | − | 0.649738i | \(-0.774879\pi\) |
0.182610 | + | 0.983185i | \(0.441545\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.4937 | + | 49.3526i | −0.972193 | + | 1.68389i | −0.283290 | + | 0.959034i | \(0.591426\pi\) |
−0.688903 | + | 0.724854i | \(0.741907\pi\) | |||||||
\(860\) | 3.27974 | + | 9.97460i | 0.111838 | + | 0.340131i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.03606 | + | 6.95721i | −0.171529 | + | 0.236964i | ||||
\(863\) | 27.0749 | + | 15.6317i | 0.921640 | + | 0.532109i | 0.884158 | − | 0.467188i | \(-0.154733\pi\) |
0.0374820 | + | 0.999297i | \(0.488066\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.4236 | − | 45.7670i | −0.898429 | − | 1.55612i | ||||
\(866\) | −5.52174 | − | 12.3436i | −0.187636 | − | 0.419453i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.74809 | + | 38.3469i | −0.195103 | + | 1.30158i | ||||
\(869\) | 11.6446 | 0.395018 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.1225 | + | 17.5327i | 0.342989 | + | 0.594074i | ||||
\(872\) | 41.1147 | − | 8.96597i | 1.39232 | − | 0.303626i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.172978 | − | 0.238965i | 0.00585106 | − | 0.00808312i | ||||
\(875\) | −21.2884 | + | 1.21766i | −0.719680 | + | 0.0411644i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.9419 | + | 31.0762i | −0.605853 | + | 1.04937i | 0.386063 | + | 0.922473i | \(0.373835\pi\) |
−0.991916 | + | 0.126896i | \(0.959498\pi\) | |||||||
\(878\) | 3.97491 | − | 38.4688i | 0.134147 | − | 1.29826i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.09358 | − | 45.3909i | −0.171704 | − | 1.53013i | ||||
\(881\) | − | 10.6024i | − | 0.357203i | −0.983921 | − | 0.178601i | \(-0.942843\pi\) | ||
0.983921 | − | 0.178601i | \(-0.0571573\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.32656i | 0.246558i | 0.992372 | + | 0.123279i | \(0.0393410\pi\) | ||||
−0.992372 | + | 0.123279i | \(0.960659\pi\) | |||||||
\(884\) | −19.8820 | − | 4.15309i | −0.668706 | − | 0.139683i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.8723 | − | 3.39663i | −1.10437 | − | 0.114112i | ||||
\(887\) | 1.07737 | − | 1.86607i | 0.0361747 | − | 0.0626564i | −0.847371 | − | 0.531001i | \(-0.821816\pi\) |
0.883546 | + | 0.468345i | \(0.155149\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.627917 | + | 0.0359157i | −0.0210597 | + | 0.00120458i | ||||
\(890\) | −14.2048 | − | 10.2823i | −0.476146 | − | 0.344663i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 31.5615 | − | 35.3013i | 1.05676 | − | 1.18197i | ||||
\(893\) | −0.0169665 | − | 0.0293868i | −0.000567762 | − | 0.000983393i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.7902 | 0.728367 | ||||||||
\(896\) | −4.17709 | + | 29.6404i | −0.139547 | + | 0.990215i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −24.3300 | + | 10.8837i | −0.811904 | + | 0.363193i | ||||
\(899\) | −29.6426 | − | 51.3425i | −0.988637 | − | 1.71237i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.7004 | − | 7.90994i | −0.456427 | − | 0.263518i | ||||
\(902\) | 26.8728 | + | 19.4522i | 0.894768 | + | 0.647688i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.74301 | + | 17.9974i | −0.191010 | + | 0.598586i | ||||
\(905\) | −21.2633 | + | 36.8291i | −0.706816 | + | 1.22424i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.8453 | − | 19.5406i | 1.12381 | − | 0.648834i | 0.181441 | − | 0.983402i | \(-0.441924\pi\) |
0.942372 | + | 0.334568i | \(0.108590\pi\) | |||||||
\(908\) | −3.26185 | − | 0.681356i | −0.108248 | − | 0.0226116i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −28.5190 | − | 1.30784i | −0.945394 | − | 0.0433546i | ||||
\(911\) | − | 46.5980i | − | 1.54386i | −0.635708 | − | 0.771930i | \(-0.719292\pi\) | ||
0.635708 | − | 0.771930i | \(-0.280708\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.987905 | + | 0.570367i | −0.0326949 | + | 0.0188764i | ||||
\(914\) | −1.05815 | + | 10.2407i | −0.0350005 | + | 0.338732i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −43.1836 | + | 14.1992i | −1.42683 | + | 0.469154i | ||||
\(917\) | −23.2998 | − | 11.7320i | −0.769427 | − | 0.387425i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.4307 | − | 12.3730i | −0.706932 | − | 0.408148i | 0.102992 | − | 0.994682i | \(-0.467158\pi\) |
−0.809924 | + | 0.586535i | \(0.800492\pi\) | |||||||
\(920\) | 26.9017 | − | 5.86651i | 0.886922 | − | 0.193413i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.07087 | − | 4.62935i | −0.0682006 | − | 0.152459i | ||||
\(923\) | 25.7562 | 0.847775 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 74.2385 | 2.44095 | ||||||||
\(926\) | −16.4317 | − | 36.7324i | −0.539980 | − | 1.20710i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −23.2304 | − | 39.4321i | −0.762576 | − | 1.29442i | ||||
\(929\) | −28.3285 | − | 16.3555i | −0.929429 | − | 0.536606i | −0.0427979 | − | 0.999084i | \(-0.513627\pi\) |
−0.886631 | + | 0.462478i | \(0.846960\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.209353 | − | 0.482567i | 0.00686125 | − | 0.0158155i | ||||
\(932\) | −0.924542 | − | 2.81179i | −0.0302844 | − | 0.0921032i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.62595 | + | 35.0916i | −0.118645 | + | 1.14823i | ||||
\(935\) | −46.1590 | + | 26.6499i | −1.50956 | + | 0.871546i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.6897i | 0.447223i | 0.974678 | + | 0.223611i | \(0.0717846\pi\) | ||||
−0.974678 | + | 0.223611i | \(0.928215\pi\) | |||||||
\(938\) | −29.3223 | − | 18.7709i | −0.957407 | − | 0.612892i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.647593 | − | 3.10022i | 0.0211222 | − | 0.101118i | ||||
\(941\) | 4.94838 | − | 2.85695i | 0.161313 | − | 0.0931338i | −0.417171 | − | 0.908828i | \(-0.636978\pi\) |
0.578483 | + | 0.815694i | \(0.303645\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.99894 | + | 17.3187i | −0.325610 | + | 0.563973i | ||||
\(944\) | −40.1283 | + | 29.5881i | −1.30607 | + | 0.963009i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.58432 | + | 4.04227i | 0.181562 | + | 0.131426i | ||||
\(947\) | −2.09868 | − | 1.21167i | −0.0681980 | − | 0.0393741i | 0.465513 | − | 0.885041i | \(-0.345870\pi\) |
−0.533711 | + | 0.845667i | \(0.679203\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.07129 | − | 1.85552i | −0.0347754 | − | 0.0602328i | ||||
\(950\) | −0.707987 | + | 0.316708i | −0.0229701 | + | 0.0102754i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 33.6469 | − | 9.37898i | 1.09050 | − | 0.303975i | ||||
\(953\) | −56.4286 | −1.82790 | −0.913950 | − | 0.405827i | \(-0.866984\pi\) | ||||
−0.913950 | + | 0.405827i | \(0.866984\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.6249 | − | 27.0631i | −0.505610 | − | 0.875742i | ||||
\(956\) | −11.4710 | − | 10.2558i | −0.370999 | − | 0.331696i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.98546 | + | 2.88492i | 0.128764 | + | 0.0932076i | ||||
\(959\) | −14.4914 | + | 9.50951i | −0.467951 | + | 0.307078i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.3487 | + | 19.6565i | −0.366087 | + | 0.634082i | ||||
\(962\) | 31.1336 | + | 3.21697i | 1.00379 | + | 0.103719i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.698781 | + | 3.34527i | −0.0225062 | + | 0.107744i | ||||
\(965\) | − | 10.6288i | − | 0.342152i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 10.0918i | − | 0.324531i | −0.986747 | − | 0.162265i | \(-0.948120\pi\) | ||
0.986747 | − | 0.162265i | \(-0.0518801\pi\) | |||||||
\(968\) | 0.756509 | + | 0.831333i | 0.0243151 | + | 0.0267201i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.537902 | − | 5.20577i | 0.0172710 | − | 0.167147i | ||||
\(971\) | −0.0300724 | + | 0.0520869i | −0.000965069 | + | 0.00167155i | −0.866508 | − | 0.499164i | \(-0.833641\pi\) |
0.865542 | + | 0.500836i | \(0.166974\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.801055 | + | 14.0049i | 0.0256806 | + | 0.448976i | ||||
\(974\) | −12.9783 | + | 17.9293i | −0.415852 | + | 0.574492i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 23.4996 | − | 53.7954i | 0.752205 | − | 1.72195i | ||||
\(977\) | 26.7586 | + | 46.3473i | 0.856084 | + | 1.48278i | 0.875636 | + | 0.482971i | \(0.160443\pi\) |
−0.0195525 | + | 0.999809i | \(0.506224\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.5132 | −0.367962 | ||||||||
\(980\) | 44.5869 | − | 20.5536i | 1.42428 | − | 0.656560i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.19721 | + | 2.67632i | 0.0382046 | + | 0.0854048i | ||||
\(983\) | −22.7855 | − | 39.4657i | −0.726745 | − | 1.25876i | −0.958252 | − | 0.285926i | \(-0.907699\pi\) |
0.231507 | − | 0.972833i | \(-0.425634\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −53.1697 | − | 30.6975i | −1.69413 | − | 0.978104i | ||||
\(986\) | −31.3149 | + | 43.2609i | −0.997269 | + | 1.37771i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.310634 | + | 0.102139i | −0.00988259 | + | 0.00324949i | ||||
\(989\) | −2.07783 | + | 3.59891i | −0.0660712 | + | 0.114439i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.2624 | + | 15.7399i | −0.866018 | + | 0.499996i | −0.866023 | − | 0.500004i | \(-0.833332\pi\) |
4.71668e−6 | 1.00000i | \(0.499998\pi\) | ||||||||
\(992\) | −20.4101 | + | 36.0797i | −0.648021 | + | 1.14553i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −39.3336 | + | 20.3662i | −1.24758 | + | 0.645978i | ||||
\(995\) | 63.9999i | 2.02893i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.7278 | − | 24.0916i | 1.32153 | − | 0.762988i | 0.337561 | − | 0.941304i | \(-0.390398\pi\) |
0.983973 | + | 0.178316i | \(0.0570649\pi\) | |||||||
\(998\) | 7.89082 | + | 0.815343i | 0.249779 | + | 0.0258092i | ||||
\(999\) | 0 | 0 |
(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 | 756.2.bf.b.271.14 | yes | 32 | |
3.2 | odd | 2 | 756.2.bf.c.271.3 | yes | 32 | ||
4.3 | odd | 2 | 756.2.bf.c.271.8 | yes | 32 | ||
7.3 | odd | 6 | 756.2.bf.c.703.8 | yes | 32 | ||
12.11 | even | 2 | inner | 756.2.bf.b.271.9 | ✓ | 32 | |
21.17 | even | 6 | inner | 756.2.bf.b.703.9 | yes | 32 | |
28.3 | even | 6 | inner | 756.2.bf.b.703.14 | yes | 32 | |
84.59 | odd | 6 | 756.2.bf.c.703.3 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.bf.b.271.9 | ✓ | 32 | 12.11 | even | 2 | inner | |
756.2.bf.b.271.14 | yes | 32 | 1.1 | even | 1 | trivial | |
756.2.bf.b.703.9 | yes | 32 | 21.17 | even | 6 | inner | |
756.2.bf.b.703.14 | yes | 32 | 28.3 | even | 6 | inner | |
756.2.bf.c.271.3 | yes | 32 | 3.2 | odd | 2 | ||
756.2.bf.c.271.8 | yes | 32 | 4.3 | odd | 2 | ||
756.2.bf.c.703.3 | yes | 32 | 84.59 | odd | 6 | ||
756.2.bf.c.703.8 | yes | 32 | 7.3 | odd | 6 |