Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(109,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.h (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 378) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 541.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.541 |
Dual form | 1134.2.h.g.109.1 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 3.00000 | 1.34164 | 0.670820 | − | 0.741620i | \(-0.265942\pi\) | ||||
0.670820 | + | 0.741620i | \(0.265942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | − | 0.866025i | 0.944911 | − | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.50000 | − | 2.59808i | −0.474342 | − | 0.821584i | ||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | + | 3.46410i | 0.554700 | + | 0.960769i | 0.997927 | + | 0.0643593i | \(0.0205004\pi\) |
−0.443227 | + | 0.896410i | \(0.646166\pi\) | |||||||
\(14\) | −2.00000 | − | 1.73205i | −0.534522 | − | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.00000 | − | 5.19615i | −0.727607 | − | 1.26025i | −0.957892 | − | 0.287129i | \(-0.907299\pi\) |
0.230285 | − | 0.973123i | \(-0.426034\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | − | 3.46410i | 0.458831 | − | 0.794719i | −0.540068 | − | 0.841621i | \(-0.681602\pi\) |
0.998899 | + | 0.0469020i | \(0.0149348\pi\) | |||||||
\(20\) | −1.50000 | + | 2.59808i | −0.335410 | + | 0.580948i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.00000 | 1.25109 | 0.625543 | − | 0.780189i | \(-0.284877\pi\) | ||||
0.625543 | + | 0.780189i | \(0.284877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 2.00000 | − | 3.46410i | 0.392232 | − | 0.679366i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.500000 | + | 2.59808i | −0.0944911 | + | 0.490990i | ||||
\(29\) | 1.50000 | − | 2.59808i | 0.278543 | − | 0.482451i | −0.692480 | − | 0.721437i | \(-0.743482\pi\) |
0.971023 | + | 0.238987i | \(0.0768152\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | + | 6.92820i | −0.718421 | + | 1.24434i | 0.243204 | + | 0.969975i | \(0.421802\pi\) |
−0.961625 | + | 0.274367i | \(0.911532\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.00000 | + | 5.19615i | −0.514496 | + | 0.891133i | ||||
\(35\) | 7.50000 | − | 2.59808i | 1.26773 | − | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | + | 6.92820i | −0.657596 | + | 1.13899i | 0.323640 | + | 0.946180i | \(0.395093\pi\) |
−0.981236 | + | 0.192809i | \(0.938240\pi\) | |||||||
\(38\) | −4.00000 | −0.648886 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.00000 | 0.474342 | ||||||||
\(41\) | 3.00000 | + | 5.19615i | 0.468521 | + | 0.811503i | 0.999353 | − | 0.0359748i | \(-0.0114536\pi\) |
−0.530831 | + | 0.847477i | \(0.678120\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | + | 6.92820i | −0.609994 | + | 1.05654i | 0.381246 | + | 0.924473i | \(0.375495\pi\) |
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | − | 5.19615i | −0.442326 | − | 0.766131i | ||||
\(47\) | −3.00000 | − | 5.19615i | −0.437595 | − | 0.757937i | 0.559908 | − | 0.828554i | \(-0.310836\pi\) |
−0.997503 | + | 0.0706177i | \(0.977503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | −2.00000 | − | 3.46410i | −0.282843 | − | 0.489898i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.00000 | −0.554700 | ||||||||
\(53\) | −4.50000 | − | 7.79423i | −0.618123 | − | 1.07062i | −0.989828 | − | 0.142269i | \(-0.954560\pi\) |
0.371706 | − | 0.928351i | \(-0.378773\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.50000 | − | 0.866025i | 0.334077 | − | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.00000 | −0.393919 | ||||||||
\(59\) | 1.50000 | − | 2.59808i | 0.195283 | − | 0.338241i | −0.751710 | − | 0.659494i | \(-0.770771\pi\) |
0.946993 | + | 0.321253i | \(0.104104\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | + | 8.66025i | 0.640184 | + | 1.10883i | 0.985391 | + | 0.170305i | \(0.0544754\pi\) |
−0.345207 | + | 0.938527i | \(0.612191\pi\) | |||||||
\(62\) | 8.00000 | 1.01600 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.00000 | + | 10.3923i | 0.744208 | + | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.00000 | − | 8.66025i | 0.610847 | − | 1.05802i | −0.380251 | − | 0.924883i | \(-0.624162\pi\) |
0.991098 | − | 0.133135i | \(-0.0425044\pi\) | |||||||
\(68\) | 6.00000 | 0.727607 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.00000 | − | 5.19615i | −0.717137 | − | 0.621059i | ||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.50000 | + | 6.06218i | 0.409644 | + | 0.709524i | 0.994850 | − | 0.101361i | \(-0.0323196\pi\) |
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | 8.00000 | 0.929981 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | + | 3.46410i | 0.229416 | + | 0.397360i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.50000 | − | 14.7224i | −0.956325 | − | 1.65640i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
−0.225018 | − | 0.974355i | \(-0.572244\pi\) | |||||||
\(80\) | −1.50000 | − | 2.59808i | −0.167705 | − | 0.290474i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.00000 | − | 5.19615i | 0.331295 | − | 0.573819i | ||||
\(83\) | 6.00000 | − | 10.3923i | 0.658586 | − | 1.14070i | −0.322396 | − | 0.946605i | \(-0.604488\pi\) |
0.980982 | − | 0.194099i | \(-0.0621783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.00000 | − | 15.5885i | −0.976187 | − | 1.69081i | ||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | + | 5.19615i | −0.317999 | + | 0.550791i | −0.980071 | − | 0.198650i | \(-0.936344\pi\) |
0.662071 | + | 0.749441i | \(0.269678\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.00000 | + | 6.92820i | 0.838628 | + | 0.726273i | ||||
\(92\) | −3.00000 | + | 5.19615i | −0.312772 | + | 0.541736i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.00000 | + | 5.19615i | −0.309426 | + | 0.535942i | ||||
\(95\) | 6.00000 | − | 10.3923i | 0.615587 | − | 1.06623i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.00000 | − | 8.66025i | 0.507673 | − | 0.879316i | −0.492287 | − | 0.870433i | \(-0.663839\pi\) |
0.999961 | − | 0.00888289i | \(-0.00282755\pi\) | |||||||
\(98\) | −6.50000 | − | 2.59808i | −0.656599 | − | 0.262445i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | + | 3.46410i | −0.200000 | + | 0.346410i | ||||
\(101\) | −15.0000 | −1.49256 | −0.746278 | − | 0.665635i | \(-0.768161\pi\) | ||||
−0.746278 | + | 0.665635i | \(0.768161\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 2.00000 | + | 3.46410i | 0.196116 | + | 0.339683i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.50000 | + | 7.79423i | −0.437079 | + | 0.757042i | ||||
\(107\) | 1.50000 | − | 2.59808i | 0.145010 | − | 0.251166i | −0.784366 | − | 0.620298i | \(-0.787012\pi\) |
0.929377 | + | 0.369132i | \(0.120345\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | + | 3.46410i | 0.191565 | + | 0.331801i | 0.945769 | − | 0.324840i | \(-0.105310\pi\) |
−0.754204 | + | 0.656640i | \(0.771977\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.00000 | − | 1.73205i | −0.188982 | − | 0.163663i | ||||
\(113\) | 3.00000 | + | 5.19615i | 0.282216 | + | 0.488813i | 0.971930 | − | 0.235269i | \(-0.0755971\pi\) |
−0.689714 | + | 0.724082i | \(0.742264\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.0000 | 1.67851 | ||||||||
\(116\) | 1.50000 | + | 2.59808i | 0.139272 | + | 0.241225i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.00000 | −0.276172 | ||||||||
\(119\) | −12.0000 | − | 10.3923i | −1.10004 | − | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 5.00000 | − | 8.66025i | 0.452679 | − | 0.784063i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.00000 | − | 6.92820i | −0.359211 | − | 0.622171i | ||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.00000 | 0.443678 | 0.221839 | − | 0.975083i | \(-0.428794\pi\) | ||||
0.221839 | + | 0.975083i | \(0.428794\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.00000 | − | 10.3923i | 0.526235 | − | 0.911465i | ||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000 | − | 10.3923i | 0.173422 | − | 0.901127i | ||||
\(134\) | −10.0000 | −0.863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | − | 5.19615i | −0.257248 | − | 0.445566i | ||||
\(137\) | 12.0000 | 1.02523 | 0.512615 | − | 0.858619i | \(-0.328677\pi\) | ||||
0.512615 | + | 0.858619i | \(0.328677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.00000 | − | 1.73205i | −0.0848189 | − | 0.146911i | 0.820495 | − | 0.571654i | \(-0.193698\pi\) |
−0.905314 | + | 0.424743i | \(0.860365\pi\) | |||||||
\(140\) | −1.50000 | + | 7.79423i | −0.126773 | + | 0.658733i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.00000 | − | 5.19615i | −0.251754 | − | 0.436051i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.50000 | − | 7.79423i | 0.373705 | − | 0.647275i | ||||
\(146\) | 3.50000 | − | 6.06218i | 0.289662 | − | 0.501709i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.00000 | − | 6.92820i | −0.328798 | − | 0.569495i | ||||
\(149\) | −21.0000 | −1.72039 | −0.860194 | − | 0.509968i | \(-0.829657\pi\) | ||||
−0.860194 | + | 0.509968i | \(0.829657\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 2.00000 | − | 3.46410i | 0.162221 | − | 0.280976i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0000 | + | 20.7846i | −0.963863 | + | 1.66946i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.00000 | + | 12.1244i | −0.558661 | + | 0.967629i | 0.438948 | + | 0.898513i | \(0.355351\pi\) |
−0.997609 | + | 0.0691164i | \(0.977982\pi\) | |||||||
\(158\) | −8.50000 | + | 14.7224i | −0.676224 | + | 1.17125i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.50000 | + | 2.59808i | −0.118585 | + | 0.205396i | ||||
\(161\) | 15.0000 | − | 5.19615i | 1.18217 | − | 0.409514i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.00000 | + | 1.73205i | −0.0783260 | + | 0.135665i | −0.902528 | − | 0.430632i | \(-0.858291\pi\) |
0.824202 | + | 0.566296i | \(0.191624\pi\) | |||||||
\(164\) | −6.00000 | −0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.0000 | −0.931381 | ||||||||
\(167\) | −3.00000 | − | 5.19615i | −0.232147 | − | 0.402090i | 0.726293 | − | 0.687386i | \(-0.241242\pi\) |
−0.958440 | + | 0.285295i | \(0.907908\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | + | 2.59808i | −0.115385 | + | 0.199852i | ||||
\(170\) | −9.00000 | + | 15.5885i | −0.690268 | + | 1.19558i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.00000 | − | 6.92820i | −0.304997 | − | 0.528271i | ||||
\(173\) | 4.50000 | + | 7.79423i | 0.342129 | + | 0.592584i | 0.984828 | − | 0.173534i | \(-0.0555188\pi\) |
−0.642699 | + | 0.766119i | \(0.722185\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.0000 | − | 3.46410i | 0.755929 | − | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.00000 | 0.449719 | ||||||||
\(179\) | 7.50000 | + | 12.9904i | 0.560576 | + | 0.970947i | 0.997446 | + | 0.0714220i | \(0.0227537\pi\) |
−0.436870 | + | 0.899525i | \(0.643913\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 2.00000 | − | 10.3923i | 0.148250 | − | 0.770329i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.00000 | 0.442326 | ||||||||
\(185\) | −12.0000 | + | 20.7846i | −0.882258 | + | 1.52811i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.00000 | 0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.0000 | −0.870572 | ||||||||
\(191\) | 9.00000 | + | 15.5885i | 0.651217 | + | 1.12794i | 0.982828 | + | 0.184525i | \(0.0590746\pi\) |
−0.331611 | + | 0.943416i | \(0.607592\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.0000 | + | 22.5167i | −0.935760 | + | 1.62078i | −0.162488 | + | 0.986710i | \(0.551952\pi\) |
−0.773272 | + | 0.634074i | \(0.781381\pi\) | |||||||
\(194\) | −10.0000 | −0.717958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | + | 6.92820i | 0.0714286 | + | 0.494872i | ||||
\(197\) | −15.0000 | −1.06871 | −0.534353 | − | 0.845262i | \(-0.679445\pi\) | ||||
−0.534353 | + | 0.845262i | \(0.679445\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.50000 | − | 9.52628i | −0.389885 | − | 0.675300i | 0.602549 | − | 0.798082i | \(-0.294152\pi\) |
−0.992434 | + | 0.122782i | \(0.960818\pi\) | |||||||
\(200\) | 4.00000 | 0.282843 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.50000 | + | 12.9904i | 0.527698 | + | 0.914000i | ||||
\(203\) | 1.50000 | − | 7.79423i | 0.105279 | − | 0.547048i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.00000 | + | 15.5885i | 0.628587 | + | 1.08875i | ||||
\(206\) | −4.00000 | − | 6.92820i | −0.278693 | − | 0.482711i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000 | − | 3.46410i | 0.138675 | − | 0.240192i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | + | 3.46410i | 0.137686 | + | 0.238479i | 0.926620 | − | 0.375999i | \(-0.122700\pi\) |
−0.788935 | + | 0.614477i | \(0.789367\pi\) | |||||||
\(212\) | 9.00000 | 0.618123 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.00000 | −0.205076 | ||||||||
\(215\) | −12.0000 | + | 20.7846i | −0.818393 | + | 1.41750i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | + | 20.7846i | −0.271538 | + | 1.41095i | ||||
\(218\) | 2.00000 | − | 3.46410i | 0.135457 | − | 0.234619i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | − | 20.7846i | 0.807207 | − | 1.39812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.500000 | − | 0.866025i | 0.0334825 | − | 0.0579934i | −0.848799 | − | 0.528716i | \(-0.822674\pi\) |
0.882281 | + | 0.470723i | \(0.156007\pi\) | |||||||
\(224\) | −0.500000 | + | 2.59808i | −0.0334077 | + | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.00000 | − | 5.19615i | 0.199557 | − | 0.345643i | ||||
\(227\) | 3.00000 | 0.199117 | 0.0995585 | − | 0.995032i | \(-0.468257\pi\) | ||||
0.0995585 | + | 0.995032i | \(0.468257\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000 | 0.925146 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(230\) | −9.00000 | − | 15.5885i | −0.593442 | − | 1.02787i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.50000 | − | 2.59808i | 0.0984798 | − | 0.170572i | ||||
\(233\) | −9.00000 | + | 15.5885i | −0.589610 | + | 1.02123i | 0.404674 | + | 0.914461i | \(0.367385\pi\) |
−0.994283 | + | 0.106773i | \(0.965948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.00000 | − | 15.5885i | −0.587095 | − | 1.01688i | ||||
\(236\) | 1.50000 | + | 2.59808i | 0.0976417 | + | 0.169120i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.00000 | + | 15.5885i | −0.194461 | + | 1.01045i | ||||
\(239\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | −0.0322078 | − | 0.999481i | \(-0.510254\pi\) | ||||
−0.0322078 | + | 0.999481i | \(0.510254\pi\) | |||||||
\(242\) | 5.50000 | + | 9.52628i | 0.353553 | + | 0.612372i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | 16.5000 | − | 12.9904i | 1.05415 | − | 0.829925i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.0000 | 1.01806 | ||||||||
\(248\) | −4.00000 | + | 6.92820i | −0.254000 | + | 0.439941i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.50000 | + | 2.59808i | 0.0948683 | + | 0.164317i | ||||
\(251\) | 9.00000 | 0.568075 | 0.284037 | − | 0.958813i | \(-0.408326\pi\) | ||||
0.284037 | + | 0.958813i | \(0.408326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.50000 | − | 4.33013i | −0.156864 | − | 0.271696i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | + | 20.7846i | −0.248548 | + | 1.29149i | ||||
\(260\) | −12.0000 | −0.744208 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.00000 | + | 10.3923i | 0.370681 | + | 0.642039i | ||||
\(263\) | −18.0000 | −1.10993 | −0.554964 | − | 0.831875i | \(-0.687268\pi\) | ||||
−0.554964 | + | 0.831875i | \(0.687268\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.5000 | − | 23.3827i | −0.829298 | − | 1.43639i | ||||
\(266\) | −10.0000 | + | 3.46410i | −0.613139 | + | 0.212398i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.00000 | + | 8.66025i | 0.305424 | + | 0.529009i | ||||
\(269\) | −10.5000 | − | 18.1865i | −0.640196 | − | 1.10885i | −0.985389 | − | 0.170321i | \(-0.945520\pi\) |
0.345192 | − | 0.938532i | \(-0.387814\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.5000 | − | 21.6506i | 0.759321 | − | 1.31518i | −0.183876 | − | 0.982949i | \(-0.558865\pi\) |
0.943197 | − | 0.332233i | \(-0.107802\pi\) | |||||||
\(272\) | −3.00000 | + | 5.19615i | −0.181902 | + | 0.315063i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.00000 | − | 10.3923i | −0.362473 | − | 0.627822i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.0000 | −1.68236 | −0.841178 | − | 0.540758i | \(-0.818138\pi\) | ||||
−0.841178 | + | 0.540758i | \(0.818138\pi\) | |||||||
\(278\) | −1.00000 | + | 1.73205i | −0.0599760 | + | 0.103882i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.50000 | − | 2.59808i | 0.448211 | − | 0.155265i | ||||
\(281\) | 9.00000 | − | 15.5885i | 0.536895 | − | 0.929929i | −0.462174 | − | 0.886789i | \(-0.652930\pi\) |
0.999069 | − | 0.0431402i | \(-0.0137362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.00000 | − | 3.46410i | 0.118888 | − | 0.205919i | −0.800439 | − | 0.599414i | \(-0.795400\pi\) |
0.919327 | + | 0.393494i | \(0.128734\pi\) | |||||||
\(284\) | −3.00000 | + | 5.19615i | −0.178017 | + | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.0000 | + | 10.3923i | 0.708338 | + | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | −9.00000 | −0.528498 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.00000 | −0.409644 | ||||||||
\(293\) | 1.50000 | + | 2.59808i | 0.0876309 | + | 0.151781i | 0.906509 | − | 0.422186i | \(-0.138737\pi\) |
−0.818878 | + | 0.573967i | \(0.805404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.50000 | − | 7.79423i | 0.262000 | − | 0.453798i | ||||
\(296\) | −4.00000 | + | 6.92820i | −0.232495 | + | 0.402694i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.5000 | + | 18.1865i | 0.608249 | + | 1.05352i | ||||
\(299\) | 12.0000 | + | 20.7846i | 0.693978 | + | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00000 | + | 20.7846i | −0.230556 | + | 1.19800i | ||||
\(302\) | −4.00000 | − | 6.92820i | −0.230174 | − | 0.398673i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.00000 | −0.229416 | ||||||||
\(305\) | 15.0000 | + | 25.9808i | 0.858898 | + | 1.48765i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.00000 | 0.456584 | 0.228292 | − | 0.973593i | \(-0.426686\pi\) | ||||
0.228292 | + | 0.973593i | \(0.426686\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 24.0000 | 1.36311 | ||||||||
\(311\) | −6.00000 | + | 10.3923i | −0.340229 | + | 0.589294i | −0.984475 | − | 0.175525i | \(-0.943838\pi\) |
0.644246 | + | 0.764818i | \(0.277171\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.50000 | − | 4.33013i | −0.141308 | − | 0.244753i | 0.786681 | − | 0.617359i | \(-0.211798\pi\) |
−0.927990 | + | 0.372606i | \(0.878464\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.0000 | 0.956325 | ||||||||
\(317\) | 9.00000 | + | 15.5885i | 0.505490 | + | 0.875535i | 0.999980 | + | 0.00635137i | \(0.00202172\pi\) |
−0.494489 | + | 0.869184i | \(0.664645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.00000 | 0.167705 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.0000 | − | 10.3923i | −0.668734 | − | 0.579141i | ||||
\(323\) | −24.0000 | −1.33540 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.00000 | + | 13.8564i | 0.443760 | + | 0.768615i | ||||
\(326\) | 2.00000 | 0.110770 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.00000 | + | 5.19615i | 0.165647 | + | 0.286910i | ||||
\(329\) | −12.0000 | − | 10.3923i | −0.661581 | − | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.00000 | − | 1.73205i | −0.0549650 | − | 0.0952021i | 0.837234 | − | 0.546845i | \(-0.184171\pi\) |
−0.892199 | + | 0.451643i | \(0.850838\pi\) | |||||||
\(332\) | 6.00000 | + | 10.3923i | 0.329293 | + | 0.570352i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.00000 | + | 5.19615i | −0.164153 | + | 0.284321i | ||||
\(335\) | 15.0000 | − | 25.9808i | 0.819538 | − | 1.41948i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.50000 | + | 6.06218i | 0.190657 | + | 0.330228i | 0.945468 | − | 0.325714i | \(-0.105605\pi\) |
−0.754811 | + | 0.655942i | \(0.772271\pi\) | |||||||
\(338\) | 3.00000 | 0.163178 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 18.0000 | 0.976187 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | −4.00000 | + | 6.92820i | −0.215666 | + | 0.373544i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.50000 | − | 7.79423i | 0.241921 | − | 0.419020i | ||||
\(347\) | −16.5000 | + | 28.5788i | −0.885766 | + | 1.53419i | −0.0409337 | + | 0.999162i | \(0.513033\pi\) |
−0.844833 | + | 0.535031i | \(0.820300\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.00000 | − | 8.66025i | 0.267644 | − | 0.463573i | −0.700609 | − | 0.713545i | \(-0.747088\pi\) |
0.968253 | + | 0.249973i | \(0.0804216\pi\) | |||||||
\(350\) | −8.00000 | − | 6.92820i | −0.427618 | − | 0.370328i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.0000 | −1.59674 | −0.798369 | − | 0.602168i | \(-0.794304\pi\) | ||||
−0.798369 | + | 0.602168i | \(0.794304\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.0000 | 0.955341 | ||||||||
\(356\) | −3.00000 | − | 5.19615i | −0.159000 | − | 0.275396i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.50000 | − | 12.9904i | 0.396387 | − | 0.686563i | ||||
\(359\) | −18.0000 | + | 31.1769i | −0.950004 | + | 1.64545i | −0.204595 | + | 0.978847i | \(0.565588\pi\) |
−0.745409 | + | 0.666608i | \(0.767746\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | + | 2.59808i | 0.0789474 | + | 0.136741i | ||||
\(362\) | 5.00000 | + | 8.66025i | 0.262794 | + | 0.455173i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.0000 | + | 3.46410i | −0.524142 | + | 0.181568i | ||||
\(365\) | 10.5000 | + | 18.1865i | 0.549595 | + | 0.951927i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.0000 | −0.991792 | −0.495896 | − | 0.868382i | \(-0.665160\pi\) | ||||
−0.495896 | + | 0.868382i | \(0.665160\pi\) | |||||||
\(368\) | −3.00000 | − | 5.19615i | −0.156386 | − | 0.270868i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 24.0000 | 1.24770 | ||||||||
\(371\) | −18.0000 | − | 15.5885i | −0.934513 | − | 0.809312i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | − | 5.19615i | −0.154713 | − | 0.267971i | ||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.0000 | −0.513665 | −0.256833 | − | 0.966456i | \(-0.582679\pi\) | ||||
−0.256833 | + | 0.966456i | \(0.582679\pi\) | |||||||
\(380\) | 6.00000 | + | 10.3923i | 0.307794 | + | 0.533114i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.00000 | − | 15.5885i | 0.460480 | − | 0.797575i | ||||
\(383\) | 6.00000 | 0.306586 | 0.153293 | − | 0.988181i | \(-0.451012\pi\) | ||||
0.153293 | + | 0.988181i | \(0.451012\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.0000 | 1.32337 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.00000 | + | 8.66025i | 0.253837 | + | 0.439658i | ||||
\(389\) | −9.00000 | −0.456318 | −0.228159 | − | 0.973624i | \(-0.573271\pi\) | ||||
−0.228159 | + | 0.973624i | \(0.573271\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | − | 31.1769i | −0.910299 | − | 1.57668i | ||||
\(392\) | 5.50000 | − | 4.33013i | 0.277792 | − | 0.218704i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.50000 | + | 12.9904i | 0.377845 | + | 0.654446i | ||||
\(395\) | −25.5000 | − | 44.1673i | −1.28304 | − | 2.22230i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.0000 | + | 27.7128i | −0.803017 | + | 1.39087i | 0.114605 | + | 0.993411i | \(0.463440\pi\) |
−0.917622 | + | 0.397455i | \(0.869893\pi\) | |||||||
\(398\) | −5.50000 | + | 9.52628i | −0.275690 | + | 0.477509i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | −18.0000 | −0.898877 | −0.449439 | − | 0.893311i | \(-0.648376\pi\) | ||||
−0.449439 | + | 0.893311i | \(0.648376\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.0000 | −1.59403 | ||||||||
\(404\) | 7.50000 | − | 12.9904i | 0.373139 | − | 0.646296i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.50000 | + | 2.59808i | −0.372219 | + | 0.128940i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.5000 | − | 21.6506i | 0.618085 | − | 1.07056i | −0.371750 | − | 0.928333i | \(-0.621242\pi\) |
0.989835 | − | 0.142222i | \(-0.0454247\pi\) | |||||||
\(410\) | 9.00000 | − | 15.5885i | 0.444478 | − | 0.769859i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.00000 | + | 6.92820i | −0.197066 | + | 0.341328i | ||||
\(413\) | 1.50000 | − | 7.79423i | 0.0738102 | − | 0.383529i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.0000 | − | 31.1769i | 0.883585 | − | 1.53041i | ||||
\(416\) | −4.00000 | −0.196116 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.00000 | − | 10.3923i | −0.293119 | − | 0.507697i | 0.681426 | − | 0.731887i | \(-0.261360\pi\) |
−0.974546 | + | 0.224189i | \(0.928027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0000 | + | 27.7128i | −0.779792 | + | 1.35064i | 0.152269 | + | 0.988339i | \(0.451342\pi\) |
−0.932061 | + | 0.362301i | \(0.881991\pi\) | |||||||
\(422\) | 2.00000 | − | 3.46410i | 0.0973585 | − | 0.168630i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.50000 | − | 7.79423i | −0.218539 | − | 0.378521i | ||||
\(425\) | −12.0000 | − | 20.7846i | −0.582086 | − | 1.00820i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.0000 | + | 17.3205i | 0.967868 | + | 0.838198i | ||||
\(428\) | 1.50000 | + | 2.59808i | 0.0725052 | + | 0.125583i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 24.0000 | 1.15738 | ||||||||
\(431\) | −6.00000 | − | 10.3923i | −0.289010 | − | 0.500580i | 0.684564 | − | 0.728953i | \(-0.259993\pi\) |
−0.973574 | + | 0.228373i | \(0.926659\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.00000 | −0.336399 | −0.168199 | − | 0.985753i | \(-0.553795\pi\) | ||||
−0.168199 | + | 0.985753i | \(0.553795\pi\) | |||||||
\(434\) | 20.0000 | − | 6.92820i | 0.960031 | − | 0.332564i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.00000 | −0.191565 | ||||||||
\(437\) | 12.0000 | − | 20.7846i | 0.574038 | − | 0.994263i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.00000 | − | 6.92820i | −0.190910 | − | 0.330665i | 0.754642 | − | 0.656136i | \(-0.227810\pi\) |
−0.945552 | + | 0.325471i | \(0.894477\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.0000 | −1.14156 | ||||||||
\(443\) | 19.5000 | + | 33.7750i | 0.926473 | + | 1.60470i | 0.789175 | + | 0.614168i | \(0.210508\pi\) |
0.137298 | + | 0.990530i | \(0.456158\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.00000 | + | 15.5885i | −0.426641 | + | 0.738964i | ||||
\(446\) | −1.00000 | −0.0473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.50000 | − | 0.866025i | 0.118114 | − | 0.0409159i | ||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6.00000 | −0.282216 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.50000 | − | 2.59808i | −0.0703985 | − | 0.121934i | ||||
\(455\) | 24.0000 | + | 20.7846i | 1.12514 | + | 0.974398i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.500000 | + | 0.866025i | 0.0233890 | + | 0.0405110i | 0.877483 | − | 0.479608i | \(-0.159221\pi\) |
−0.854094 | + | 0.520119i | \(0.825888\pi\) | |||||||
\(458\) | −7.00000 | − | 12.1244i | −0.327089 | − | 0.566534i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.00000 | + | 15.5885i | −0.419627 | + | 0.726816i | ||||
\(461\) | 16.5000 | − | 28.5788i | 0.768482 | − | 1.33105i | −0.169904 | − | 0.985461i | \(-0.554346\pi\) |
0.938386 | − | 0.345589i | \(-0.112321\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.50000 | + | 16.4545i | 0.441502 | + | 0.764705i | 0.997801 | − | 0.0662777i | \(-0.0211123\pi\) |
−0.556299 | + | 0.830982i | \(0.687779\pi\) | |||||||
\(464\) | −3.00000 | −0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.0000 | 0.833834 | ||||||||
\(467\) | 16.5000 | − | 28.5788i | 0.763529 | − | 1.32247i | −0.177492 | − | 0.984122i | \(-0.556798\pi\) |
0.941021 | − | 0.338349i | \(-0.109868\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.00000 | − | 25.9808i | 0.230879 | − | 1.19968i | ||||
\(470\) | −9.00000 | + | 15.5885i | −0.415139 | + | 0.719042i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.50000 | − | 2.59808i | 0.0690431 | − | 0.119586i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.00000 | − | 13.8564i | 0.367065 | − | 0.635776i | ||||
\(476\) | 15.0000 | − | 5.19615i | 0.687524 | − | 0.238165i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.0000 | −1.09659 | −0.548294 | − | 0.836286i | \(-0.684723\pi\) | ||||
−0.548294 | + | 0.836286i | \(0.684723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.0000 | −1.45907 | ||||||||
\(482\) | 0.500000 | + | 0.866025i | 0.0227744 | + | 0.0394464i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.50000 | − | 9.52628i | 0.250000 | − | 0.433013i | ||||
\(485\) | 15.0000 | − | 25.9808i | 0.681115 | − | 1.17973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.50000 | + | 11.2583i | 0.294543 | + | 0.510164i | 0.974879 | − | 0.222737i | \(-0.0714992\pi\) |
−0.680335 | + | 0.732901i | \(0.738166\pi\) | |||||||
\(488\) | 5.00000 | + | 8.66025i | 0.226339 | + | 0.392031i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −19.5000 | − | 7.79423i | −0.880920 | − | 0.352107i | ||||
\(491\) | −13.5000 | − | 23.3827i | −0.609246 | − | 1.05525i | −0.991365 | − | 0.131132i | \(-0.958139\pi\) |
0.382118 | − | 0.924113i | \(-0.375195\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.0000 | −0.810679 | ||||||||
\(494\) | −8.00000 | − | 13.8564i | −0.359937 | − | 0.623429i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 15.0000 | − | 5.19615i | 0.672842 | − | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.00000 | 0.0895323 | 0.0447661 | − | 0.998997i | \(-0.485746\pi\) | ||||
0.0447661 | + | 0.998997i | \(0.485746\pi\) | |||||||
\(500\) | 1.50000 | − | 2.59808i | 0.0670820 | − | 0.116190i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.50000 | − | 7.79423i | −0.200845 | − | 0.347873i | ||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −45.0000 | −2.00247 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.50000 | + | 4.33013i | −0.110920 | + | 0.192118i | ||||
\(509\) | 18.0000 | 0.797836 | 0.398918 | − | 0.916987i | \(-0.369386\pi\) | ||||
0.398918 | + | 0.916987i | \(0.369386\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.0000 | + | 12.1244i | 0.619324 | + | 0.536350i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.0000 | 1.05757 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 20.0000 | − | 6.92820i | 0.878750 | − | 0.304408i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.00000 | + | 10.3923i | 0.263117 | + | 0.455733i | ||||
\(521\) | 15.0000 | + | 25.9808i | 0.657162 | + | 1.13824i | 0.981347 | + | 0.192244i | \(0.0615766\pi\) |
−0.324185 | + | 0.945994i | \(0.605090\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.00000 | − | 3.46410i | 0.0874539 | − | 0.151475i | −0.818980 | − | 0.573822i | \(-0.805460\pi\) |
0.906434 | + | 0.422347i | \(0.138794\pi\) | |||||||
\(524\) | 6.00000 | − | 10.3923i | 0.262111 | − | 0.453990i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.00000 | + | 15.5885i | 0.392419 | + | 0.679689i | ||||
\(527\) | 48.0000 | 2.09091 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | −13.5000 | + | 23.3827i | −0.586403 | + | 1.01568i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.00000 | + | 6.92820i | 0.346844 | + | 0.300376i | ||||
\(533\) | −12.0000 | + | 20.7846i | −0.519778 | + | 0.900281i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.50000 | − | 7.79423i | 0.194552 | − | 0.336974i | ||||
\(536\) | 5.00000 | − | 8.66025i | 0.215967 | − | 0.374066i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.5000 | + | 18.1865i | −0.452687 | + | 0.784077i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | − | 8.66025i | 0.214967 | − | 0.372333i | −0.738296 | − | 0.674477i | \(-0.764369\pi\) |
0.953262 | + | 0.302144i | \(0.0977023\pi\) | |||||||
\(542\) | −25.0000 | −1.07384 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.00000 | 0.257248 | ||||||||
\(545\) | 6.00000 | + | 10.3923i | 0.257012 | + | 0.445157i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0000 | − | 24.2487i | 0.598597 | − | 1.03680i | −0.394432 | − | 0.918925i | \(-0.629059\pi\) |
0.993028 | − | 0.117875i | \(-0.0376081\pi\) | |||||||
\(548\) | −6.00000 | + | 10.3923i | −0.256307 | + | 0.443937i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.00000 | − | 10.3923i | −0.255609 | − | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −34.0000 | − | 29.4449i | −1.44583 | − | 1.25212i | ||||
\(554\) | 14.0000 | + | 24.2487i | 0.594803 | + | 1.03023i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | 0.0848189 | ||||||||
\(557\) | 3.00000 | + | 5.19615i | 0.127114 | + | 0.220168i | 0.922557 | − | 0.385860i | \(-0.126095\pi\) |
−0.795443 | + | 0.606028i | \(0.792762\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.0000 | −1.35346 | ||||||||
\(560\) | −6.00000 | − | 5.19615i | −0.253546 | − | 0.219578i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.0000 | −0.759284 | ||||||||
\(563\) | −7.50000 | + | 12.9904i | −0.316087 | + | 0.547479i | −0.979668 | − | 0.200625i | \(-0.935703\pi\) |
0.663581 | + | 0.748105i | \(0.269036\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.00000 | + | 15.5885i | 0.378633 | + | 0.655811i | ||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.00000 | 0.251754 | ||||||||
\(569\) | −9.00000 | − | 15.5885i | −0.377300 | − | 0.653502i | 0.613369 | − | 0.789797i | \(-0.289814\pi\) |
−0.990668 | + | 0.136295i | \(0.956481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.00000 | − | 15.5885i | 0.125218 | − | 0.650650i | ||||
\(575\) | 24.0000 | 1.00087 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.5000 | − | 19.9186i | −0.478751 | − | 0.829222i | 0.520952 | − | 0.853586i | \(-0.325577\pi\) |
−0.999703 | + | 0.0243645i | \(0.992244\pi\) | |||||||
\(578\) | 19.0000 | 0.790296 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.50000 | + | 7.79423i | 0.186852 | + | 0.323638i | ||||
\(581\) | 6.00000 | − | 31.1769i | 0.248922 | − | 1.29344i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.50000 | + | 6.06218i | 0.144831 | + | 0.250855i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.50000 | − | 2.59808i | 0.0619644 | − | 0.107326i | ||||
\(587\) | 7.50000 | − | 12.9904i | 0.309558 | − | 0.536170i | −0.668708 | − | 0.743525i | \(-0.733152\pi\) |
0.978266 | + | 0.207355i | \(0.0664855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | + | 27.7128i | 0.659269 | + | 1.14189i | ||||
\(590\) | −9.00000 | −0.370524 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.00000 | 0.328798 | ||||||||
\(593\) | −3.00000 | + | 5.19615i | −0.123195 | + | 0.213380i | −0.921026 | − | 0.389501i | \(-0.872647\pi\) |
0.797831 | + | 0.602881i | \(0.205981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.0000 | − | 31.1769i | −1.47586 | − | 1.27813i | ||||
\(596\) | 10.5000 | − | 18.1865i | 0.430097 | − | 0.744949i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.0000 | − | 20.7846i | 0.490716 | − | 0.849946i | ||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.5000 | − | 21.6506i | 0.509886 | − | 0.883148i | −0.490049 | − | 0.871695i | \(-0.663021\pi\) |
0.999934 | − | 0.0114528i | \(-0.00364562\pi\) | |||||||
\(602\) | 20.0000 | − | 6.92820i | 0.815139 | − | 0.282372i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.00000 | + | 6.92820i | −0.162758 | + | 0.281905i | ||||
\(605\) | −33.0000 | −1.34164 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.0000 | 0.446476 | 0.223238 | − | 0.974764i | \(-0.428337\pi\) | ||||
0.223238 | + | 0.974764i | \(0.428337\pi\) | |||||||
\(608\) | 2.00000 | + | 3.46410i | 0.0811107 | + | 0.140488i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.0000 | − | 25.9808i | 0.607332 | − | 1.05193i | ||||
\(611\) | 12.0000 | − | 20.7846i | 0.485468 | − | 0.840855i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.00000 | + | 13.8564i | 0.323117 | + | 0.559655i | 0.981129 | − | 0.193352i | \(-0.0619359\pi\) |
−0.658012 | + | 0.753007i | \(0.728603\pi\) | |||||||
\(614\) | −4.00000 | − | 6.92820i | −0.161427 | − | 0.279600i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.00000 | + | 15.5885i | 0.362326 | + | 0.627568i | 0.988343 | − | 0.152242i | \(-0.0486493\pi\) |
−0.626017 | + | 0.779809i | \(0.715316\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.0000 | −0.643094 | −0.321547 | − | 0.946894i | \(-0.604203\pi\) | ||||
−0.321547 | + | 0.946894i | \(0.604203\pi\) | |||||||
\(620\) | −12.0000 | − | 20.7846i | −0.481932 | − | 0.834730i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.0000 | 0.481156 | ||||||||
\(623\) | −3.00000 | + | 15.5885i | −0.120192 | + | 0.624538i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | −2.50000 | + | 4.33013i | −0.0999201 | + | 0.173067i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.00000 | − | 12.1244i | −0.279330 | − | 0.483814i | ||||
\(629\) | 48.0000 | 1.91389 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | −8.50000 | − | 14.7224i | −0.338112 | − | 0.585627i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.00000 | − | 15.5885i | 0.357436 | − | 0.619097i | ||||
\(635\) | 15.0000 | 0.595257 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.0000 | + | 10.3923i | 1.03016 | + | 0.411758i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.50000 | − | 2.59808i | −0.0592927 | − | 0.102698i | ||||
\(641\) | 24.0000 | 0.947943 | 0.473972 | − | 0.880540i | \(-0.342820\pi\) | ||||
0.473972 | + | 0.880540i | \(0.342820\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.00000 | + | 13.8564i | 0.315489 | + | 0.546443i | 0.979541 | − | 0.201243i | \(-0.0644981\pi\) |
−0.664052 | + | 0.747686i | \(0.731165\pi\) | |||||||
\(644\) | −3.00000 | + | 15.5885i | −0.118217 | + | 0.614271i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | + | 20.7846i | 0.472134 | + | 0.817760i | ||||
\(647\) | −21.0000 | − | 36.3731i | −0.825595 | − | 1.42997i | −0.901464 | − | 0.432855i | \(-0.857506\pi\) |
0.0758684 | − | 0.997118i | \(-0.475827\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 8.00000 | − | 13.8564i | 0.313786 | − | 0.543493i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.00000 | − | 1.73205i | −0.0391630 | − | 0.0678323i | ||||
\(653\) | 3.00000 | 0.117399 | 0.0586995 | − | 0.998276i | \(-0.481305\pi\) | ||||
0.0586995 | + | 0.998276i | \(0.481305\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.0000 | −1.40664 | ||||||||
\(656\) | 3.00000 | − | 5.19615i | 0.117130 | − | 0.202876i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.00000 | + | 15.5885i | −0.116952 | + | 0.607701i | ||||
\(659\) | −10.5000 | + | 18.1865i | −0.409022 | + | 0.708447i | −0.994780 | − | 0.102039i | \(-0.967463\pi\) |
0.585758 | + | 0.810486i | \(0.300797\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0000 | + | 27.7128i | −0.622328 | + | 1.07790i | 0.366723 | + | 0.930330i | \(0.380480\pi\) |
−0.989051 | + | 0.147573i | \(0.952854\pi\) | |||||||
\(662\) | −1.00000 | + | 1.73205i | −0.0388661 | + | 0.0673181i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | − | 10.3923i | 0.232845 | − | 0.403300i | ||||
\(665\) | 6.00000 | − | 31.1769i | 0.232670 | − | 1.20899i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.00000 | − | 15.5885i | 0.348481 | − | 0.603587i | ||||
\(668\) | 6.00000 | 0.232147 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −30.0000 | −1.15900 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.5000 | − | 37.2391i | 0.828764 | − | 1.43546i | −0.0702442 | − | 0.997530i | \(-0.522378\pi\) |
0.899008 | − | 0.437932i | \(-0.144289\pi\) | |||||||
\(674\) | 3.50000 | − | 6.06218i | 0.134815 | − | 0.233506i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.50000 | − | 2.59808i | −0.0576923 | − | 0.0999260i | ||||
\(677\) | 10.5000 | + | 18.1865i | 0.403548 | + | 0.698965i | 0.994151 | − | 0.107997i | \(-0.0344436\pi\) |
−0.590603 | + | 0.806962i | \(0.701110\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.00000 | − | 25.9808i | 0.191882 | − | 0.997050i | ||||
\(680\) | −9.00000 | − | 15.5885i | −0.345134 | − | 0.597790i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.50000 | + | 7.79423i | 0.172188 | + | 0.298238i | 0.939184 | − | 0.343413i | \(-0.111583\pi\) |
−0.766997 | + | 0.641651i | \(0.778250\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.0000 | 1.37549 | ||||||||
\(686\) | −18.5000 | − | 0.866025i | −0.706333 | − | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.00000 | 0.304997 | ||||||||
\(689\) | 18.0000 | − | 31.1769i | 0.685745 | − | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | − | 6.92820i | −0.152167 | − | 0.263561i | 0.779857 | − | 0.625958i | \(-0.215292\pi\) |
−0.932024 | + | 0.362397i | \(0.881959\pi\) | |||||||
\(692\) | −9.00000 | −0.342129 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 33.0000 | 1.25266 | ||||||||
\(695\) | −3.00000 | − | 5.19615i | −0.113796 | − | 0.197101i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | − | 31.1769i | 0.681799 | − | 1.18091i | ||||
\(698\) | −10.0000 | −0.378506 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.00000 | + | 10.3923i | −0.0755929 | + | 0.392792i | ||||
\(701\) | −39.0000 | −1.47301 | −0.736505 | − | 0.676432i | \(-0.763525\pi\) | ||||
−0.736505 | + | 0.676432i | \(0.763525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.0000 | + | 27.7128i | 0.603451 | + | 1.04521i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.0000 | + | 25.9808i | 0.564532 | + | 0.977799i | ||||
\(707\) | −37.5000 | + | 12.9904i | −1.41033 | + | 0.488554i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.00000 | − | 6.92820i | −0.150223 | − | 0.260194i | 0.781086 | − | 0.624423i | \(-0.214666\pi\) |
−0.931309 | + | 0.364229i | \(0.881333\pi\) | |||||||
\(710\) | −9.00000 | − | 15.5885i | −0.337764 | − | 0.585024i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.00000 | + | 5.19615i | −0.112430 | + | 0.194734i | ||||
\(713\) | −24.0000 | + | 41.5692i | −0.898807 | + | 1.55678i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.0000 | −0.560576 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 36.0000 | 1.34351 | ||||||||
\(719\) | 12.0000 | − | 20.7846i | 0.447524 | − | 0.775135i | −0.550700 | − | 0.834703i | \(-0.685639\pi\) |
0.998224 | + | 0.0595683i | \(0.0189724\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.0000 | − | 6.92820i | 0.744839 | − | 0.258020i | ||||
\(722\) | 1.50000 | − | 2.59808i | 0.0558242 | − | 0.0966904i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.00000 | − | 8.66025i | 0.185824 | − | 0.321856i | ||||
\(725\) | 6.00000 | − | 10.3923i | 0.222834 | − | 0.385961i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.5000 | + | 19.9186i | −0.426511 | + | 0.738739i | −0.996560 | − | 0.0828714i | \(-0.973591\pi\) |
0.570049 | + | 0.821611i | \(0.306924\pi\) | |||||||
\(728\) | 8.00000 | + | 6.92820i | 0.296500 | + | 0.256776i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.5000 | − | 18.1865i | 0.388622 | − | 0.673114i | ||||
\(731\) | 48.0000 | 1.77534 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.0000 | 1.62518 | 0.812589 | − | 0.582838i | \(-0.198058\pi\) | ||||
0.812589 | + | 0.582838i | \(0.198058\pi\) | |||||||
\(734\) | 9.50000 | + | 16.4545i | 0.350651 | + | 0.607346i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.00000 | + | 5.19615i | −0.110581 | + | 0.191533i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.00000 | − | 12.1244i | −0.257499 | − | 0.446002i | 0.708072 | − | 0.706140i | \(-0.249565\pi\) |
−0.965571 | + | 0.260138i | \(0.916232\pi\) | |||||||
\(740\) | −12.0000 | − | 20.7846i | −0.441129 | − | 0.764057i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.50000 | + | 23.3827i | −0.165200 | + | 0.858405i | ||||
\(743\) | −12.0000 | − | 20.7846i | −0.440237 | − | 0.762513i | 0.557470 | − | 0.830197i | \(-0.311772\pi\) |
−0.997707 | + | 0.0676840i | \(0.978439\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −63.0000 | −2.30814 | ||||||||
\(746\) | 5.00000 | + | 8.66025i | 0.183063 | + | 0.317074i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.50000 | − | 7.79423i | 0.0548088 | − | 0.284795i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.0000 | −1.56909 | −0.784546 | − | 0.620070i | \(-0.787104\pi\) | ||||
−0.784546 | + | 0.620070i | \(0.787104\pi\) | |||||||
\(752\) | −3.00000 | + | 5.19615i | −0.109399 | + | 0.189484i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.00000 | − | 10.3923i | −0.218507 | − | 0.378465i | ||||
\(755\) | 24.0000 | 0.873449 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | 5.00000 | + | 8.66025i | 0.181608 | + | 0.314555i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.00000 | − | 10.3923i | 0.217643 | − | 0.376969i | ||||
\(761\) | 48.0000 | 1.74000 | 0.869999 | − | 0.493053i | \(-0.164119\pi\) | ||||
0.869999 | + | 0.493053i | \(0.164119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.00000 | + | 6.92820i | 0.289619 | + | 0.250818i | ||||
\(764\) | −18.0000 | −0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.00000 | − | 5.19615i | −0.108394 | − | 0.187745i | ||||
\(767\) | 12.0000 | 0.433295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.0000 | − | 22.5167i | −0.468792 | − | 0.811972i | 0.530572 | − | 0.847640i | \(-0.321977\pi\) |
−0.999364 | + | 0.0356685i | \(0.988644\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.0000 | − | 22.5167i | −0.467880 | − | 0.810392i | ||||
\(773\) | 9.00000 | + | 15.5885i | 0.323708 | + | 0.560678i | 0.981250 | − | 0.192740i | \(-0.0617373\pi\) |
−0.657542 | + | 0.753418i | \(0.728404\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.0000 | + | 27.7128i | −0.574737 | + | 0.995474i | ||||
\(776\) | 5.00000 | − | 8.66025i | 0.179490 | − | 0.310885i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.50000 | + | 7.79423i | 0.161333 | + | 0.279437i | ||||
\(779\) | 24.0000 | 0.859889 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −18.0000 | + | 31.1769i | −0.643679 | + | 1.11488i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.50000 | − | 2.59808i | −0.232143 | − | 0.0927884i | ||||
\(785\) | −21.0000 | + | 36.3731i | −0.749522 | + | 1.29821i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.0000 | − | 19.0526i | 0.392108 | − | 0.679150i | −0.600620 | − | 0.799535i | \(-0.705079\pi\) |
0.992727 | + | 0.120384i | \(0.0384127\pi\) | |||||||
\(788\) | 7.50000 | − | 12.9904i | 0.267176 | − | 0.462763i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −25.5000 | + | 44.1673i | −0.907249 | + | 1.57140i | ||||
\(791\) | 12.0000 | + | 10.3923i | 0.426671 | + | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.0000 | + | 34.6410i | −0.710221 | + | 1.23014i | ||||
\(794\) | 32.0000 | 1.13564 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.0000 | 0.389885 | ||||||||
\(797\) | −9.00000 | − | 15.5885i | −0.318796 | − | 0.552171i | 0.661441 | − | 0.749997i | \(-0.269945\pi\) |
−0.980237 | + | 0.197826i | \(0.936612\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.0000 | + | 31.1769i | −0.636794 | + | 1.10296i | ||||
\(800\) | −2.00000 | + | 3.46410i | −0.0707107 | + | 0.122474i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.00000 | + | 15.5885i | 0.317801 | + | 0.550448i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 45.0000 | − | 15.5885i | 1.58604 | − | 0.549421i | ||||
\(806\) | 16.0000 | + | 27.7128i | 0.563576 | + | 0.976142i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.0000 | −0.527698 | ||||||||
\(809\) | −12.0000 | − | 20.7846i | −0.421898 | − | 0.730748i | 0.574228 | − | 0.818696i | \(-0.305302\pi\) |
−0.996125 | + | 0.0879478i | \(0.971969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | 6.00000 | + | 5.19615i | 0.210559 | + | 0.182349i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.00000 | + | 5.19615i | −0.105085 | + | 0.182013i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.0000 | + | 27.7128i | 0.559769 | + | 0.969549i | ||||
\(818\) | −25.0000 | −0.874105 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −18.0000 | −0.628587 | ||||||||
\(821\) | −10.5000 | − | 18.1865i | −0.366453 | − | 0.634714i | 0.622556 | − | 0.782576i | \(-0.286094\pi\) |
−0.989008 | + | 0.147861i | \(0.952761\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.5000 | + | 19.9186i | −0.400865 | + | 0.694318i | −0.993831 | − | 0.110910i | \(-0.964624\pi\) |
0.592966 | + | 0.805228i | \(0.297957\pi\) | |||||||
\(824\) | 8.00000 | 0.278693 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.50000 | + | 2.59808i | −0.260958 | + | 0.0903986i | ||||
\(827\) | 21.0000 | 0.730242 | 0.365121 | − | 0.930960i | \(-0.381028\pi\) | ||||
0.365121 | + | 0.930960i | \(0.381028\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.0000 | − | 27.7128i | −0.555703 | − | 0.962506i | −0.997848 | − | 0.0655624i | \(-0.979116\pi\) |
0.442145 | − | 0.896943i | \(-0.354217\pi\) | |||||||
\(830\) | −36.0000 | −1.24958 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.00000 | + | 3.46410i | 0.0693375 | + | 0.120096i | ||||
\(833\) | −39.0000 | − | 15.5885i | −1.35127 | − | 0.540108i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.00000 | − | 15.5885i | −0.311458 | − | 0.539461i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.00000 | + | 10.3923i | −0.207267 | + | 0.358996i | ||||
\(839\) | 12.0000 | − | 20.7846i | 0.414286 | − | 0.717564i | −0.581067 | − | 0.813856i | \(-0.697365\pi\) |
0.995353 | + | 0.0962912i | \(0.0306980\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 32.0000 | 1.10279 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.00000 | −0.137686 | ||||||||
\(845\) | −4.50000 | + | 7.79423i | −0.154805 | + | 0.268130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.5000 | + | 9.52628i | −0.944911 | + | 0.327327i | ||||
\(848\) | −4.50000 | + | 7.79423i | −0.154531 | + | 0.267655i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.0000 | + | 20.7846i | −0.411597 | + | 0.712906i | ||||
\(851\) | −24.0000 | + | 41.5692i | −0.822709 | + | 1.42497i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.0000 | + | 38.1051i | −0.753266 | + | 1.30469i | 0.192966 | + | 0.981205i | \(0.438189\pi\) |
−0.946232 | + | 0.323489i | \(0.895144\pi\) | |||||||
\(854\) | 5.00000 | − | 25.9808i | 0.171096 | − | 0.889043i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.50000 | − | 2.59808i | 0.0512689 | − | 0.0888004i | ||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.0000 | 0.477674 | 0.238837 | − | 0.971060i | \(-0.423234\pi\) | ||||
0.238837 | + | 0.971060i | \(0.423234\pi\) | |||||||
\(860\) | −12.0000 | − | 20.7846i | −0.409197 | − | 0.708749i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.00000 | + | 10.3923i | −0.204361 | + | 0.353963i | ||||
\(863\) | −21.0000 | + | 36.3731i | −0.714848 | + | 1.23815i | 0.248170 | + | 0.968717i | \(0.420171\pi\) |
−0.963018 | + | 0.269437i | \(0.913162\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.5000 | + | 23.3827i | 0.459014 | + | 0.795035i | ||||
\(866\) | 3.50000 | + | 6.06218i | 0.118935 | + | 0.206001i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −16.0000 | − | 13.8564i | −0.543075 | − | 0.470317i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.0000 | 1.35535 | ||||||||
\(872\) | 2.00000 | + | 3.46410i | 0.0677285 | + | 0.117309i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24.0000 | −0.811812 | ||||||||
\(875\) | −7.50000 | + | 2.59808i | −0.253546 | + | 0.0878310i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.0000 | 0.472746 | 0.236373 | − | 0.971662i | \(-0.424041\pi\) | ||||
0.236373 | + | 0.971662i | \(0.424041\pi\) | |||||||
\(878\) | −4.00000 | + | 6.92820i | −0.134993 | + | 0.233816i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.00000 | 0.202145 | 0.101073 | − | 0.994879i | \(-0.467773\pi\) | ||||
0.101073 | + | 0.994879i | \(0.467773\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.0000 | 1.07689 | 0.538443 | − | 0.842662i | \(-0.319013\pi\) | ||||
0.538443 | + | 0.842662i | \(0.319013\pi\) | |||||||
\(884\) | 12.0000 | + | 20.7846i | 0.403604 | + | 0.699062i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19.5000 | − | 33.7750i | 0.655115 | − | 1.13469i | ||||
\(887\) | −42.0000 | −1.41022 | −0.705111 | − | 0.709097i | \(-0.749103\pi\) | ||||
−0.705111 | + | 0.709097i | \(0.749103\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.5000 | − | 4.33013i | 0.419237 | − | 0.145228i | ||||
\(890\) | 18.0000 | 0.603361 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.500000 | + | 0.866025i | 0.0167412 | + | 0.0289967i | ||||
\(893\) | −24.0000 | −0.803129 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.5000 | + | 38.9711i | 0.752092 | + | 1.30266i | ||||
\(896\) | −2.00000 | − | 1.73205i | −0.0668153 | − | 0.0578638i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.00000 | − | 5.19615i | −0.100111 | − | 0.173398i | ||||
\(899\) | 12.0000 | + | 20.7846i | 0.400222 | + | 0.693206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.0000 | + | 46.7654i | −0.899500 | + | 1.55798i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.00000 | + | 5.19615i | 0.0997785 | + | 0.172821i | ||||
\(905\) | −30.0000 | −0.997234 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.00000 | 0.265636 | 0.132818 | − | 0.991140i | \(-0.457597\pi\) | ||||
0.132818 | + | 0.991140i | \(0.457597\pi\) | |||||||
\(908\) | −1.50000 | + | 2.59808i | −0.0497792 | + | 0.0862202i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.00000 | − | 31.1769i | 0.198898 | − | 1.03350i | ||||
\(911\) | 27.0000 | − | 46.7654i | 0.894550 | − | 1.54941i | 0.0601892 | − | 0.998187i | \(-0.480830\pi\) |
0.834361 | − | 0.551219i | \(-0.185837\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.500000 | − | 0.866025i | 0.0165385 | − | 0.0286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.00000 | + | 12.1244i | −0.231287 | + | 0.400600i | ||||
\(917\) | −30.0000 | + | 10.3923i | −0.990687 | + | 0.343184i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.5000 | − | 32.0429i | 0.610259 | − | 1.05700i | −0.380938 | − | 0.924601i | \(-0.624399\pi\) |
0.991197 | − | 0.132398i | \(-0.0422678\pi\) | |||||||
\(920\) | 18.0000 | 0.593442 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −33.0000 | −1.08680 | ||||||||
\(923\) | 12.0000 | + | 20.7846i | 0.394985 | + | 0.684134i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.0000 | + | 27.7128i | −0.526077 | + | 0.911192i | ||||
\(926\) | 9.50000 | − | 16.4545i | 0.312189 | − | 0.540728i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.50000 | + | 2.59808i | 0.0492399 | + | 0.0852860i | ||||
\(929\) | −3.00000 | − | 5.19615i | −0.0984268 | − | 0.170480i | 0.812607 | − | 0.582812i | \(-0.198048\pi\) |
−0.911034 | + | 0.412332i | \(0.864714\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.00000 | − | 27.7128i | −0.131095 | − | 0.908251i | ||||
\(932\) | −9.00000 | − | 15.5885i | −0.294805 | − | 0.510617i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −33.0000 | −1.07979 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.00000 | −0.0326686 | −0.0163343 | − | 0.999867i | \(-0.505200\pi\) | ||||
−0.0163343 | + | 0.999867i | \(0.505200\pi\) | |||||||
\(938\) | −25.0000 | + | 8.66025i | −0.816279 | + | 0.282767i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 18.0000 | 0.587095 | ||||||||
\(941\) | −9.00000 | + | 15.5885i | −0.293392 | + | 0.508169i | −0.974609 | − | 0.223912i | \(-0.928117\pi\) |
0.681218 | + | 0.732081i | \(0.261451\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.0000 | + | 31.1769i | 0.586161 | + | 1.01526i | ||||
\(944\) | −3.00000 | −0.0976417 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.5000 | − | 38.9711i | −0.731152 | − | 1.26639i | −0.956391 | − | 0.292089i | \(-0.905650\pi\) |
0.225240 | − | 0.974303i | \(-0.427684\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.0000 | + | 24.2487i | −0.454459 | + | 0.787146i | ||||
\(950\) | −16.0000 | −0.519109 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.0000 | − | 10.3923i | −0.388922 | − | 0.336817i | ||||
\(953\) | −48.0000 | −1.55487 | −0.777436 | − | 0.628962i | \(-0.783480\pi\) | ||||
−0.777436 | + | 0.628962i | \(0.783480\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.0000 | + | 46.7654i | 0.873699 | + | 1.51329i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.0000 | + | 20.7846i | 0.387702 | + | 0.671520i | ||||
\(959\) | 30.0000 | − | 10.3923i | 0.968751 | − | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | 16.0000 | + | 27.7128i | 0.515861 | + | 0.893497i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.500000 | − | 0.866025i | 0.0161039 | − | 0.0278928i | ||||
\(965\) | −39.0000 | + | 67.5500i | −1.25545 | + | 2.17451i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.5000 | + | 32.0429i | 0.594920 | + | 1.03043i | 0.993558 | + | 0.113323i | \(0.0361496\pi\) |
−0.398638 | + | 0.917108i | \(0.630517\pi\) | |||||||
\(968\) | −11.0000 | −0.353553 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −30.0000 | −0.963242 | ||||||||
\(971\) | 1.50000 | − | 2.59808i | 0.0481373 | − | 0.0833762i | −0.840953 | − | 0.541108i | \(-0.818005\pi\) |
0.889090 | + | 0.457732i | \(0.151338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.00000 | − | 3.46410i | −0.128234 | − | 0.111054i | ||||
\(974\) | 6.50000 | − | 11.2583i | 0.208273 | − | 0.360740i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.00000 | − | 8.66025i | 0.160046 | − | 0.277208i | ||||
\(977\) | −6.00000 | + | 10.3923i | −0.191957 | + | 0.332479i | −0.945899 | − | 0.324462i | \(-0.894817\pi\) |
0.753942 | + | 0.656941i | \(0.228150\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 3.00000 | + | 20.7846i | 0.0958315 | + | 0.663940i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.5000 | + | 23.3827i | −0.430802 | + | 0.746171i | ||||
\(983\) | −24.0000 | −0.765481 | −0.382741 | − | 0.923856i | \(-0.625020\pi\) | ||||
−0.382741 | + | 0.923856i | \(0.625020\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −45.0000 | −1.43382 | ||||||||
\(986\) | 9.00000 | + | 15.5885i | 0.286618 | + | 0.496438i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.00000 | + | 13.8564i | −0.254514 | + | 0.440831i | ||||
\(989\) | −24.0000 | + | 41.5692i | −0.763156 | + | 1.32182i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.5000 | − | 19.9186i | −0.365310 | − | 0.632735i | 0.623516 | − | 0.781810i | \(-0.285704\pi\) |
−0.988826 | + | 0.149076i | \(0.952370\pi\) | |||||||
\(992\) | −4.00000 | − | 6.92820i | −0.127000 | − | 0.219971i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.0000 | − | 10.3923i | −0.380617 | − | 0.329624i | ||||
\(995\) | −16.5000 | − | 28.5788i | −0.523085 | − | 0.906010i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.0000 | 1.01345 | 0.506725 | − | 0.862108i | \(-0.330856\pi\) | ||||
0.506725 | + | 0.862108i | \(0.330856\pi\) | |||||||
\(998\) | −1.00000 | − | 1.73205i | −0.0316544 | − | 0.0548271i | ||||
\(999\) | 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 | 1134.2.h.g.541.1 | 2 | ||
3.2 | odd | 2 | 1134.2.h.k.541.1 | 2 | |||
7.4 | even | 3 | 1134.2.e.j.865.1 | 2 | |||
9.2 | odd | 6 | 378.2.g.f.163.1 | yes | 2 | ||
9.4 | even | 3 | 1134.2.e.j.919.1 | 2 | |||
9.5 | odd | 6 | 1134.2.e.f.919.1 | 2 | |||
9.7 | even | 3 | 378.2.g.a.163.1 | yes | 2 | ||
21.11 | odd | 6 | 1134.2.e.f.865.1 | 2 | |||
63.2 | odd | 6 | 2646.2.a.b.1.1 | 1 | |||
63.4 | even | 3 | inner | 1134.2.h.g.109.1 | 2 | ||
63.11 | odd | 6 | 378.2.g.f.109.1 | yes | 2 | ||
63.16 | even | 3 | 2646.2.a.bc.1.1 | 1 | |||
63.25 | even | 3 | 378.2.g.a.109.1 | ✓ | 2 | ||
63.32 | odd | 6 | 1134.2.h.k.109.1 | 2 | |||
63.47 | even | 6 | 2646.2.a.m.1.1 | 1 | |||
63.61 | odd | 6 | 2646.2.a.r.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.g.a.109.1 | ✓ | 2 | 63.25 | even | 3 | ||
378.2.g.a.163.1 | yes | 2 | 9.7 | even | 3 | ||
378.2.g.f.109.1 | yes | 2 | 63.11 | odd | 6 | ||
378.2.g.f.163.1 | yes | 2 | 9.2 | odd | 6 | ||
1134.2.e.f.865.1 | 2 | 21.11 | odd | 6 | |||
1134.2.e.f.919.1 | 2 | 9.5 | odd | 6 | |||
1134.2.e.j.865.1 | 2 | 7.4 | even | 3 | |||
1134.2.e.j.919.1 | 2 | 9.4 | even | 3 | |||
1134.2.h.g.109.1 | 2 | 63.4 | even | 3 | inner | ||
1134.2.h.g.541.1 | 2 | 1.1 | even | 1 | trivial | ||
1134.2.h.k.109.1 | 2 | 63.32 | odd | 6 | |||
1134.2.h.k.541.1 | 2 | 3.2 | odd | 2 | |||
2646.2.a.b.1.1 | 1 | 63.2 | odd | 6 | |||
2646.2.a.m.1.1 | 1 | 63.47 | even | 6 | |||
2646.2.a.r.1.1 | 1 | 63.61 | odd | 6 | |||
2646.2.a.bc.1.1 | 1 | 63.16 | even | 3 |