Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,2,Mod(305,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.cn (of order \(12\), degree \(4\), 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: | \(4.98266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 312) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 305.6 | ||
Character | \(\chi\) | \(=\) | 624.305 |
Dual form | 624.2.cn.f.401.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.315401 | + | 1.70309i | −0.182097 | + | 0.983281i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.72616 | − | 1.72616i | −0.771963 | − | 0.771963i | 0.206486 | − | 0.978449i | \(-0.433797\pi\) |
−0.978449 | + | 0.206486i | \(0.933797\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.574711 | − | 2.14485i | 0.217220 | − | 0.810677i | −0.768153 | − | 0.640266i | \(-0.778824\pi\) |
0.985373 | − | 0.170411i | \(-0.0545094\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.80104 | − | 1.07431i | −0.933682 | − | 0.358104i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.47004 | + | 5.48627i | 0.443234 | + | 1.65417i | 0.720557 | + | 0.693396i | \(0.243886\pi\) |
−0.277323 | + | 0.960777i | \(0.589447\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.76028 | − | 2.31967i | 0.765564 | − | 0.643360i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.48425 | − | 2.39538i | 0.899628 | − | 0.618484i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.40933 | + | 2.44104i | 0.341813 | + | 0.592038i | 0.984770 | − | 0.173865i | \(-0.0556256\pi\) |
−0.642956 | + | 0.765903i | \(0.722292\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.85833 | + | 2.10563i | 1.80282 | + | 0.483065i | 0.994414 | − | 0.105553i | \(-0.0336613\pi\) |
0.808411 | + | 0.588618i | \(0.200328\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.47161 | + | 1.65527i | 0.757568 | + | 0.361210i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.84516 | − | 3.19592i | 0.384743 | − | 0.666395i | −0.606990 | − | 0.794709i | \(-0.707623\pi\) |
0.991734 | + | 0.128314i | \(0.0409566\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.959270i | 0.191854i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.71311 | − | 4.43160i | 0.522137 | − | 0.852861i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.95737 | + | 1.13009i | 0.363475 | + | 0.209853i | 0.670604 | − | 0.741815i | \(-0.266035\pi\) |
−0.307129 | + | 0.951668i | \(0.599368\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.13483 | + | 3.13483i | −0.563031 | + | 0.563031i | −0.930167 | − | 0.367136i | \(-0.880338\pi\) |
0.367136 | + | 0.930167i | \(0.380338\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.80727 | + | 0.773242i | −1.70723 | + | 0.134604i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.69440 | + | 2.71031i | −0.793499 | + | 0.458127i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.36333 | − | 1.97300i | 1.21052 | − | 0.324359i | 0.403557 | − | 0.914955i | \(-0.367774\pi\) |
0.806968 | + | 0.590596i | \(0.201107\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.08001 | + | 5.43263i | 0.493197 | + | 0.869918i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.02869 | − | 1.88333i | 1.09770 | − | 0.294127i | 0.335870 | − | 0.941908i | \(-0.390970\pi\) |
0.761826 | + | 0.647781i | \(0.224303\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.416760 | − | 0.240616i | 0.0635553 | − | 0.0366937i | −0.467886 | − | 0.883789i | \(-0.654984\pi\) |
0.531441 | + | 0.847095i | \(0.321651\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.98062 | + | 6.68949i | 0.444324 | + | 0.997211i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.57953 | + | 9.57953i | −1.39732 | + | 1.39732i | −0.589685 | + | 0.807633i | \(0.700748\pi\) |
−0.807633 | + | 0.589685i | \(0.799252\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.79209 | + | 1.03466i | 0.256013 | + | 0.147809i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.60181 | + | 1.63032i | −0.644383 | + | 0.228290i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 0.617097i | − | 0.0847648i | −0.999101 | − | 0.0423824i | \(-0.986505\pi\) | ||
0.999101 | − | 0.0423824i | \(-0.0134948\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.93266 | − | 12.0077i | 0.934800 | − | 1.61912i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.06461 | + | 12.7193i | −0.803277 | + | 1.68472i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.94720 | − | 0.521752i | −0.253504 | − | 0.0679263i | 0.129829 | − | 0.991536i | \(-0.458557\pi\) |
−0.383333 | + | 0.923610i | \(0.625224\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.667748 | + | 1.15657i | 0.0854964 | + | 0.148084i | 0.905603 | − | 0.424127i | \(-0.139419\pi\) |
−0.820106 | + | 0.572211i | \(0.806086\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.91403 | + | 5.39040i | −0.493121 | + | 0.679127i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.76881 | − | 0.760564i | −1.08764 | − | 0.0943364i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.667631 | + | 2.49163i | 0.0815641 | + | 0.304401i | 0.994641 | − | 0.103385i | \(-0.0329674\pi\) |
−0.913077 | + | 0.407787i | \(0.866301\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.86098 | + | 4.15048i | 0.585193 | + | 0.499659i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.81372 | − | 6.76890i | 0.215249 | − | 0.803320i | −0.770830 | − | 0.637041i | \(-0.780158\pi\) |
0.986079 | − | 0.166279i | \(-0.0531752\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.75039 | − | 6.75039i | −0.790073 | − | 0.790073i | 0.191432 | − | 0.981506i | \(-0.438687\pi\) |
−0.981506 | + | 0.191432i | \(0.938687\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.63372 | − | 0.302554i | −0.188646 | − | 0.0349360i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.6121 | 1.43728 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.372617 | 0.0419226 | 0.0209613 | − | 0.999780i | \(-0.493327\pi\) | ||||
0.0209613 | + | 0.999780i | \(0.493327\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.69170 | + | 6.01840i | 0.743523 | + | 0.668711i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.99123 | − | 4.99123i | −0.547858 | − | 0.547858i | 0.377963 | − | 0.925821i | \(-0.376625\pi\) |
−0.925821 | + | 0.377963i | \(0.876625\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.78089 | − | 6.64636i | 0.193164 | − | 0.720899i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.54201 | + | 2.97716i | −0.272532 | + | 0.319185i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.17011 | − | 8.09895i | −0.230031 | − | 0.858487i | −0.980326 | − | 0.197384i | \(-0.936755\pi\) |
0.750295 | − | 0.661103i | \(-0.229911\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.38898 | − | 7.25352i | −0.355261 | − | 0.760376i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.35017 | − | 6.32762i | −0.451092 | − | 0.656144i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.93009 | − | 17.1994i | −1.01881 | − | 1.76462i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.03688 | + | 0.813729i | 0.308348 | + | 0.0826217i | 0.409675 | − | 0.912232i | \(-0.365642\pi\) |
−0.101327 | + | 0.994853i | \(0.532309\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.77632 | − | 16.9466i | 0.178527 | − | 1.70319i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.672751 | + | 1.16524i | −0.0669412 | + | 0.115946i | −0.897553 | − | 0.440906i | \(-0.854657\pi\) |
0.830612 | + | 0.556851i | \(0.187991\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.0519i | − | 0.990446i | −0.868766 | − | 0.495223i | \(-0.835086\pi\) | ||
0.868766 | − | 0.495223i | \(-0.164914\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.13530 | − | 8.84983i | −0.305974 | − | 0.863655i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.9381 | + | 7.46982i | 1.25077 | + | 0.722135i | 0.971263 | − | 0.238008i | \(-0.0764943\pi\) |
0.279511 | + | 0.960143i | \(0.409828\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.96629 | + | 5.96629i | −0.571467 | + | 0.571467i | −0.932538 | − | 0.361071i | \(-0.882411\pi\) |
0.361071 | + | 0.932538i | \(0.382411\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.03780 | + | 13.1627i | 0.0985034 | + | 1.24935i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.1400 | − | 8.74110i | 1.42425 | − | 0.822294i | 0.427596 | − | 0.903970i | \(-0.359361\pi\) |
0.996659 | + | 0.0816760i | \(0.0260273\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.70173 | + | 2.33162i | −0.811440 | + | 0.217425i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.2237 | + | 3.53209i | −0.945183 | + | 0.326542i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.04561 | − | 1.61992i | 0.554200 | − | 0.148498i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −18.4119 | + | 10.6301i | −1.67380 | + | 0.966372i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.990633 | + | 12.5645i | 0.0893224 | + | 1.13290i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.97495 | + | 6.97495i | −0.623859 | + | 0.623859i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.06716 | + | 0.616127i | 0.0946954 | + | 0.0546724i | 0.546600 | − | 0.837394i | \(-0.315922\pi\) |
−0.451904 | + | 0.892066i | \(0.649255\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.278346 | + | 0.785671i | 0.0245070 | + | 0.0691745i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 7.17983i | − | 0.627305i | −0.949538 | − | 0.313652i | \(-0.898447\pi\) | ||
0.949538 | − | 0.313652i | \(-0.101553\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.03253 | − | 15.6448i | 0.783220 | − | 1.35658i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.3329 | + | 2.96640i | −1.06145 | + | 0.255307i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.6202 | − | 3.11363i | −0.992783 | − | 0.266015i | −0.274364 | − | 0.961626i | \(-0.588467\pi\) |
−0.718419 | + | 0.695611i | \(0.755134\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.16445 | − | 2.01689i | −0.0987677 | − | 0.171071i | 0.812407 | − | 0.583091i | \(-0.198157\pi\) |
−0.911175 | + | 0.412020i | \(0.864823\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.2934 | − | 19.3362i | −1.11951 | − | 1.62840i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.7841 | + | 11.7336i | 1.40355 | + | 0.981215i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.42803 | − | 5.32947i | −0.118591 | − | 0.442588i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.32735 | + | 2.72576i | −0.191957 | + | 0.224817i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.04901 | + | 18.8432i | −0.413631 | + | 1.54369i | 0.373930 | + | 0.927457i | \(0.378010\pi\) |
−0.787562 | + | 0.616236i | \(0.788657\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.712411 | − | 0.712411i | −0.0579752 | − | 0.0579752i | 0.677525 | − | 0.735500i | \(-0.263053\pi\) |
−0.735500 | + | 0.677525i | \(0.763053\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.32517 | − | 8.35151i | −0.107133 | − | 0.675180i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.8224 | 0.869279 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.0306 | 1.35919 | 0.679594 | − | 0.733588i | \(-0.262156\pi\) | ||||
0.679594 | + | 0.733588i | \(0.262156\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.05097 | + | 0.194633i | 0.0833476 | + | 0.0154354i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.79433 | − | 5.79433i | −0.456657 | − | 0.456657i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.57138 | + | 9.59651i | −0.201406 | + | 0.751657i | 0.789109 | + | 0.614253i | \(0.210542\pi\) |
−0.990515 | + | 0.137404i | \(0.956124\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 18.2637 | + | 15.5942i | 1.42183 | + | 1.21401i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.68928 | + | 10.0365i | 0.208102 | + | 0.776649i | 0.988481 | + | 0.151342i | \(0.0483595\pi\) |
−0.780379 | + | 0.625307i | \(0.784974\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.23828 | − | 12.8059i | 0.172175 | − | 0.985066i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −19.7494 | − | 14.3403i | −1.51028 | − | 1.09663i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.65624 | − | 11.5289i | −0.506064 | − | 0.876529i | −0.999975 | − | 0.00701675i | \(-0.997766\pi\) |
0.493911 | − | 0.869512i | \(-0.335567\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.05749 | + | 0.551303i | 0.155532 | + | 0.0416746i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.50274 | − | 3.15171i | 0.112953 | − | 0.236897i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.225490 | − | 0.390560i | 0.0168539 | − | 0.0291918i | −0.857475 | − | 0.514525i | \(-0.827968\pi\) |
0.874329 | + | 0.485333i | \(0.161302\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.572791i | − | 0.0425752i | −0.999773 | − | 0.0212876i | \(-0.993223\pi\) | ||
0.999773 | − | 0.0212876i | \(-0.00677657\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.18036 | + | 0.772452i | −0.161177 | + | 0.0571013i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.1160 | − | 9.30459i | −1.18487 | − | 0.684087i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.3204 | + | 11.3204i | −0.827830 | + | 0.827830i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.94586 | − | 8.36609i | −0.577976 | − | 0.608544i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.87896 | + | 4.54892i | −0.570102 | + | 0.329148i | −0.757190 | − | 0.653195i | \(-0.773428\pi\) |
0.187088 | + | 0.982343i | \(0.440095\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.9688 | + | 3.74292i | −1.00549 | + | 0.269421i | −0.723745 | − | 0.690067i | \(-0.757581\pi\) |
−0.281748 | + | 0.959488i | \(0.590914\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.06100 | − | 14.6942i | 0.290814 | − | 1.05227i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.22190 | + | 1.66715i | −0.443292 | + | 0.118780i | −0.473559 | − | 0.880762i | \(-0.657031\pi\) |
0.0302668 | + | 0.999542i | \(0.490364\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.683303 | − | 0.394505i | 0.0484381 | − | 0.0279657i | −0.475585 | − | 0.879670i | \(-0.657764\pi\) |
0.524023 | + | 0.851704i | \(0.324430\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.45405 | + | 0.351174i | −0.314164 | + | 0.0247699i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.54880 | − | 3.54880i | 0.249077 | − | 0.249077i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.3836 | − | 8.88172i | −1.07444 | − | 0.620326i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.60181 | + | 6.96963i | −0.597867 | + | 0.484423i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 46.2083i | 3.19629i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.5246 | + | 19.9611i | −0.793383 | + | 1.37418i | 0.130478 | + | 0.991451i | \(0.458349\pi\) |
−0.923861 | + | 0.382729i | \(0.874984\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.9560 | + | 5.22385i | 0.750693 | + | 0.357932i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.13474 | − | 0.304052i | −0.0773885 | − | 0.0207362i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.92211 | + | 8.52535i | 0.334135 | + | 0.578738i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.6256 | − | 9.36746i | 0.920734 | − | 0.632994i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.55254 | + | 3.46875i | 0.642574 | + | 0.233334i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.35292 | − | 12.5133i | −0.224528 | − | 0.837950i | −0.982593 | − | 0.185771i | \(-0.940522\pi\) |
0.758065 | − | 0.652179i | \(-0.226145\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.03056 | − | 2.68696i | 0.0687037 | − | 0.179130i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.62037 | − | 9.77935i | 0.173920 | − | 0.649079i | −0.822813 | − | 0.568312i | \(-0.807597\pi\) |
0.996733 | − | 0.0807663i | \(-0.0257368\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.04210 | + | 6.04210i | 0.399273 | + | 0.399273i | 0.877977 | − | 0.478703i | \(-0.158893\pi\) |
−0.478703 | + | 0.877977i | \(0.658893\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.97786 | + | 21.4795i | −0.261724 | + | 1.41325i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.52224 | −0.623823 | −0.311911 | − | 0.950111i | \(-0.600969\pi\) | ||||
−0.311911 | + | 0.950111i | \(0.600969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.0716 | 2.15736 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.117524 | + | 0.634600i | −0.00763398 | + | 0.0412217i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.346997 | + | 0.346997i | 0.0224454 | + | 0.0224454i | 0.718240 | − | 0.695795i | \(-0.244948\pi\) |
−0.695795 | + | 0.718240i | \(0.744948\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.84098 | + | 25.5309i | −0.440667 | + | 1.64459i | 0.286464 | + | 0.958091i | \(0.407520\pi\) |
−0.727131 | + | 0.686499i | \(0.759147\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.3605 | + | 9.49838i | −0.792923 | + | 0.609321i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.30744 | − | 4.87943i | −0.0835293 | − | 0.311736i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.5756 | − | 12.4166i | 1.69096 | − | 0.790049i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.0748 | − | 6.92628i | 0.638462 | − | 0.438935i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.74616 | − | 11.6847i | −0.425814 | − | 0.737531i | 0.570682 | − | 0.821171i | \(-0.306679\pi\) |
−0.996496 | + | 0.0836399i | \(0.973345\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.2461 | + | 5.42494i | 1.27286 | + | 0.341063i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.7577 | + | 5.12928i | 0.673671 | + | 0.321208i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.24981 | − | 2.16473i | 0.0779610 | − | 0.135032i | −0.824409 | − | 0.565994i | \(-0.808492\pi\) |
0.902370 | + | 0.430962i | \(0.141826\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 16.9271i | − | 1.05180i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.26862 | − | 5.26827i | −0.264221 | − | 0.326098i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.32134 | + | 4.80433i | 0.513116 | + | 0.296248i | 0.734114 | − | 0.679027i | \(-0.237598\pi\) |
−0.220998 | + | 0.975274i | \(0.570931\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.06521 | + | 1.06521i | −0.0654353 | + | 0.0654353i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.4777 | − | 1.14148i | 0.886021 | − | 0.0698572i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.4109 | − | 8.32012i | 0.878646 | − | 0.507286i | 0.00843422 | − | 0.999964i | \(-0.497315\pi\) |
0.870212 | + | 0.492678i | \(0.163982\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.2838 | + | 8.11452i | −1.83961 | + | 0.492922i | −0.998826 | − | 0.0484469i | \(-0.984573\pi\) |
−0.840785 | + | 0.541369i | \(0.817906\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.4223 | − | 3.48398i | 0.812355 | − | 0.210860i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.26281 | + | 1.41017i | −0.317360 | + | 0.0850362i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.36855 | + | 3.67688i | −0.382649 | + | 0.220923i | −0.678970 | − | 0.734166i | \(-0.737573\pi\) |
0.296321 | + | 0.955088i | \(0.404240\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.1486 | − | 5.41300i | 0.727316 | − | 0.324068i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.52193 | − | 5.52193i | 0.329411 | − | 0.329411i | −0.522952 | − | 0.852362i | \(-0.675169\pi\) |
0.852362 | + | 0.522952i | \(0.175169\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.91761 | − | 5.14859i | −0.530097 | − | 0.306052i | 0.210959 | − | 0.977495i | \(-0.432341\pi\) |
−0.741056 | + | 0.671443i | \(0.765675\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 32.4241 | − | 11.4871i | 1.92064 | − | 0.680440i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 16.1578i | − | 0.953768i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.52756 | − | 7.84197i | 0.266327 | − | 0.461292i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.34369 | + | 4.91543i | −0.137390 | + | 0.288148i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.2842 | + | 7.31077i | 1.59396 | + | 0.427100i | 0.943211 | − | 0.332194i | \(-0.107789\pi\) |
0.650748 | + | 0.759294i | \(0.274456\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.46056 | + | 4.26182i | 0.143259 | + | 0.248133i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 28.3013 | + | 8.37020i | 1.64221 | + | 0.485688i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.32030 | − | 13.1018i | −0.134187 | − | 0.757696i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.276570 | − | 1.03217i | −0.0159412 | − | 0.0594934i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.77232 | − | 1.51327i | −0.101817 | − | 0.0869353i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.843792 | − | 3.14907i | 0.0483154 | − | 0.180315i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.0722051 | + | 0.0722051i | 0.00412096 | + | 0.00412096i | 0.709164 | − | 0.705043i | \(-0.249072\pi\) |
−0.705043 | + | 0.709164i | \(0.749072\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.1194 | + | 3.17039i | 0.973886 | + | 0.180357i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.0161 | −1.13501 | −0.567504 | − | 0.823370i | \(-0.692091\pi\) | ||||
−0.567504 | + | 0.823370i | \(0.692091\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.626697 | 0.0354230 | 0.0177115 | − | 0.999843i | \(-0.494362\pi\) | ||||
0.0177115 | + | 0.999843i | \(0.494362\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 16.0610 | − | 2.54845i | 0.904932 | − | 0.143589i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.4492 | − | 14.4492i | −0.811546 | − | 0.811546i | 0.173320 | − | 0.984866i | \(-0.444551\pi\) |
−0.984866 | + | 0.173320i | \(0.944551\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.32256 | + | 12.4000i | −0.186028 | + | 0.694265i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.8025 | + | 19.6788i | −0.937823 | + | 1.09836i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.93508 | + | 22.1500i | 0.330236 | + | 1.23246i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.22519 | + | 2.64785i | 0.123431 | + | 0.146876i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.27938 | − | 12.0429i | −0.457850 | − | 0.665975i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.0412 | + | 26.0521i | 0.829248 | + | 1.43630i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.05445 | + | 2.42613i | 0.497678 | + | 0.133352i | 0.498922 | − | 0.866647i | \(-0.333729\pi\) |
−0.00124426 | + | 0.999999i | \(0.500396\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −22.7446 | − | 2.38407i | −1.24640 | − | 0.130646i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.14852 | − | 5.45340i | 0.172022 | − | 0.297951i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 20.6022i | − | 1.12227i | −0.827724 | − | 0.561136i | \(-0.810365\pi\) | ||
0.827724 | − | 0.561136i | \(-0.189635\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.1117 | + | 28.5418i | 0.549194 | + | 1.55018i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.8068 | − | 12.5902i | −1.18091 | − | 0.681796i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.2401 | − | 14.2401i | 0.768893 | − | 0.768893i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.22643 | − | 15.5552i | −0.0660289 | − | 0.837466i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.7808 | + | 11.9978i | −1.11557 | + | 0.644076i | −0.940267 | − | 0.340437i | \(-0.889425\pi\) |
−0.175306 | + | 0.984514i | \(0.556091\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.5949 | + | 7.92992i | −1.58418 | + | 0.424479i | −0.940216 | − | 0.340579i | \(-0.889377\pi\) |
−0.643961 | + | 0.765058i | \(0.722710\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.79091 | − | 18.5259i | −0.148968 | − | 0.988842i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.6149 | − | 7.66733i | 1.52302 | − | 0.408091i | 0.602282 | − | 0.798283i | \(-0.294258\pi\) |
0.920733 | + | 0.390193i | \(0.127592\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.8150 | + | 8.55343i | −0.786298 | + | 0.453969i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.852077 | + | 10.8072i | 0.0450967 | + | 0.571976i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.69605 | − | 9.69605i | 0.511738 | − | 0.511738i | −0.403321 | − | 0.915059i | \(-0.632144\pi\) |
0.915059 | + | 0.403321i | \(0.132144\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40.8652 | + | 23.5935i | 2.15080 | + | 1.24176i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.2969 | − | 34.7098i | −0.645420 | − | 1.82179i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.3045i | 1.21981i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.92261 | − | 10.2583i | 0.309158 | − | 0.535477i | −0.669020 | − | 0.743244i | \(-0.733286\pi\) |
0.978178 | + | 0.207767i | \(0.0666195\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −21.7110 | − | 2.27572i | −1.13023 | − | 0.118469i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.32358 | − | 0.354652i | −0.0687169 | − | 0.0184126i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5599 | + | 21.7543i | 0.650325 | + | 1.12640i | 0.983044 | + | 0.183369i | \(0.0587004\pi\) |
−0.332719 | + | 0.943026i | \(0.607966\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.67908 | − | 14.0789i | −0.499826 | − | 0.727031i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.02434 | − | 1.42109i | 0.413274 | − | 0.0731901i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.78147 | + | 29.0409i | 0.399707 | + | 1.49173i | 0.813612 | + | 0.581408i | \(0.197498\pi\) |
−0.413904 | + | 0.910320i | \(0.635835\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.38590 | + | 1.62315i | −0.0710020 | + | 0.0831565i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.42225 | + | 12.7720i | −0.174869 | + | 0.652620i | 0.821705 | + | 0.569913i | \(0.193023\pi\) |
−0.996574 | + | 0.0827069i | \(0.973643\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.7705 | − | 21.7705i | −1.10953 | − | 1.10953i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.42586 | + | 0.226247i | −0.0724806 | + | 0.0115008i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.5709 | −1.80352 | −0.901759 | − | 0.432239i | \(-0.857724\pi\) | ||||
−0.901759 | + | 0.432239i | \(0.857724\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.4018 | 0.526042 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.2279 | + | 2.26452i | 0.616817 | + | 0.114230i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.643197 | − | 0.643197i | −0.0323627 | − | 0.0323627i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.0698912 | − | 0.260837i | 0.00350774 | − | 0.0130911i | −0.964150 | − | 0.265359i | \(-0.914510\pi\) |
0.967658 | + | 0.252268i | \(0.0811763\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 23.7957 | + | 20.3176i | 1.19127 | + | 1.01715i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.32674 | − | 12.4156i | −0.166130 | − | 0.620004i | −0.997893 | − | 0.0648745i | \(-0.979335\pi\) |
0.831764 | − | 0.555130i | \(-0.187331\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.38124 | + | 15.9248i | −0.0688043 | + | 0.793268i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.16223 | − | 21.9397i | −0.0577519 | − | 1.09019i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.6488 | + | 37.4968i | 1.07309 | + | 1.85865i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.0337 | − | 3.76033i | −0.693924 | − | 0.185936i | −0.105417 | − | 0.994428i | \(-0.533618\pi\) |
−0.588508 | + | 0.808492i | \(0.700284\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.96782 | − | 18.8083i | 0.442350 | − | 0.927743i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.23816 | + | 3.87660i | −0.110133 | + | 0.190755i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.2313i | 0.845853i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.80223 | − | 1.34704i | 0.186196 | − | 0.0659650i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.4856 | − | 16.4462i | −1.39161 | − | 0.803448i | −0.398118 | − | 0.917334i | \(-0.630337\pi\) |
−0.993494 | + | 0.113887i | \(0.963670\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.6319 | + | 12.6319i | −0.615641 | + | 0.615641i | −0.944410 | − | 0.328769i | \(-0.893366\pi\) |
0.328769 | + | 0.944410i | \(0.393366\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 37.1241 | − | 16.5413i | 1.80504 | − | 0.804265i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.34161 | + | 1.35193i | −0.113585 | + | 0.0655782i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.86444 | − | 0.767524i | 0.138620 | − | 0.0371431i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −25.2771 | + | 24.8840i | −1.22039 | + | 1.20141i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.3199 | − | 5.71266i | 1.02694 | − | 0.275169i | 0.294252 | − | 0.955728i | \(-0.404930\pi\) |
0.732693 | + | 0.680559i | \(0.238263\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.4780 | − | 18.7512i | 1.56079 | − | 0.901125i | 0.563618 | − | 0.826035i | \(-0.309409\pi\) |
0.997177 | − | 0.0750900i | \(-0.0239244\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.52697 | − | 0.751142i | 0.456783 | − | 0.0360145i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.2293 | − | 21.2293i | 1.01554 | − | 1.01554i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.7404 | − | 10.8198i | −0.894431 | − | 0.516400i | −0.0190419 | − | 0.999819i | \(-0.506062\pi\) |
−0.875389 | + | 0.483419i | \(0.839395\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.90817 | − | 4.82340i | −0.186103 | − | 0.229686i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.66009i | 0.363942i | 0.983304 | + | 0.181971i | \(0.0582477\pi\) | ||||
−0.983304 | + | 0.181971i | \(0.941752\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.2341 | + | 17.7260i | −0.485145 | + | 0.840295i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −30.4992 | − | 14.5421i | −1.44256 | − | 0.687817i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.38164 | − | 2.24585i | −0.395554 | − | 0.105988i | 0.0555585 | − | 0.998455i | \(-0.482306\pi\) |
−0.451113 | + | 0.892467i | \(0.648973\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.6649 | + | 35.7927i | 0.973073 | + | 1.68541i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.43800 | − | 0.988606i | 0.0675629 | − | 0.0464488i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.67083 | + | 18.3707i | −0.312733 | + | 0.861231i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.2516 | + | 38.2595i | 0.479550 | + | 1.78970i | 0.603439 | + | 0.797409i | \(0.293796\pi\) |
−0.123890 | + | 0.992296i | \(0.539537\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.6414 | + | 0.377192i | 0.683400 | + | 0.0176058i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.25094 | − | 8.40062i | 0.104837 | − | 0.391256i | −0.893490 | − | 0.449083i | \(-0.851751\pi\) |
0.998327 | + | 0.0578275i | \(0.0184173\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.9840 | − | 13.9840i | −0.649893 | − | 0.649893i | 0.303074 | − | 0.952967i | \(-0.401987\pi\) |
−0.952967 | + | 0.303074i | \(0.901987\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.41340 | + | 18.4316i | −0.158293 | + | 0.854745i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.4617 | 1.36333 | 0.681663 | − | 0.731666i | \(-0.261257\pi\) | ||||
0.681663 | + | 0.731666i | \(0.261257\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.72787 | 0.264489 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.37146 | + | 29.0047i | −0.247504 | + | 1.33646i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.93274 | + | 1.93274i | 0.0888675 | + | 0.0888675i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.01987 | + | 7.53826i | −0.0926780 | + | 0.345879i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.662956 | + | 1.72852i | −0.0303547 | + | 0.0791434i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.50742 | − | 31.7501i | −0.388714 | − | 1.45070i | −0.832228 | − | 0.554433i | \(-0.812935\pi\) |
0.443514 | − | 0.896267i | \(-0.353732\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.7481 | − | 22.5265i | 0.718054 | − | 1.02712i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.6958 | − | 8.04074i | 0.532178 | − | 0.365866i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.83752 | − | 6.64677i | −0.174253 | − | 0.301814i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0631 | − | 2.96434i | −0.501316 | − | 0.134327i | −0.000705427 | − | 1.00000i | \(-0.500225\pi\) |
−0.500611 | + | 0.865672i | \(0.666891\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.5327 | − | 7.40604i | −0.702414 | − | 0.334913i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.607370 | − | 1.05200i | 0.0274102 | − | 0.0474759i | −0.851995 | − | 0.523550i | \(-0.824607\pi\) |
0.879405 | + | 0.476074i | \(0.157941\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.37070i | 0.286922i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −32.3187 | + | 26.1863i | −1.45262 | + | 1.17699i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.4759 | − | 7.78031i | −0.604477 | − | 0.348995i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.3336 | + | 21.3336i | −0.955024 | + | 0.955024i | −0.999031 | − | 0.0440068i | \(-0.985988\pi\) |
0.0440068 | + | 0.999031i | \(0.485988\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.9413 | + | 1.41456i | −0.801559 | + | 0.0631979i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.6423 | + | 11.3405i | −0.875808 | + | 0.505648i | −0.869274 | − | 0.494331i | \(-0.835413\pi\) |
−0.00653389 | + | 0.999979i | \(0.502080\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.17267 | − | 0.850114i | 0.141182 | − | 0.0378296i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.1036 | + | 7.85097i | 0.937244 | + | 0.348674i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.3215 | + | 5.17719i | −0.856412 | + | 0.229475i | −0.660203 | − | 0.751087i | \(-0.729530\pi\) |
−0.196209 | + | 0.980562i | \(0.562863\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.3581 | + | 10.5991i | −0.812114 | + | 0.468874i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 30.6518 | − | 29.1122i | 1.35331 | − | 1.28533i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.3513 | + | 17.3513i | −0.764588 | + | 0.764588i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −66.6382 | − | 38.4736i | −2.93075 | − | 1.69207i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.7342 | − | 7.69995i | 0.954027 | − | 0.337990i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 19.4238i | − | 0.850973i | −0.904965 | − | 0.425486i | \(-0.860103\pi\) | ||
0.904965 | − | 0.425486i | \(-0.139897\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.1755 | − | 17.6244i | 0.444942 | − | 0.770663i | −0.553106 | − | 0.833111i | \(-0.686557\pi\) |
0.998048 | + | 0.0624482i | \(0.0198908\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.58785 | + | 3.33021i | −0.0692996 | + | 0.145342i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.0702 | − | 3.23421i | −0.525788 | − | 0.140884i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.69074 | + | 8.12459i | 0.203945 | + | 0.353243i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.89368 | + | 3.55336i | 0.212368 | + | 0.154203i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.0324 | − | 21.5027i | 0.651127 | − | 0.931387i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.43915 | − | 35.2274i | −0.408090 | − | 1.52301i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.594040 | + | 0.507213i | 0.0256347 | + | 0.0218879i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.04200 | + | 11.3529i | −0.131028 | + | 0.489003i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.28291 | + | 5.28291i | 0.227130 | + | 0.227130i | 0.811493 | − | 0.584363i | \(-0.198655\pi\) |
−0.584363 | + | 0.811493i | \(0.698655\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.975516 | + | 0.180659i | 0.0418634 | + | 0.00775281i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.5976 | 0.882303 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.2518 | −0.652122 | −0.326061 | − | 0.945349i | \(-0.605721\pi\) | ||||
−0.326061 | + | 0.945349i | \(0.605721\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.627870 | − | 3.95698i | −0.0267968 | − | 0.168880i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.0021 | + | 13.0021i | 0.553910 | + | 0.553910i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.214147 | − | 0.799207i | 0.00910645 | − | 0.0339857i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 20.9296 | − | 24.5124i | 0.888411 | − | 1.04049i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.77202 | + | 6.61326i | 0.0750828 | + | 0.280213i | 0.993252 | − | 0.115975i | \(-0.0369994\pi\) |
−0.918169 | + | 0.396188i | \(0.870333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.592223 | − | 1.63091i | 0.0250484 | − | 0.0689803i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.7092 | − | 22.8502i | −0.663244 | − | 0.964734i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.52928 | − | 16.5052i | −0.401611 | − | 0.695611i | 0.592309 | − | 0.805711i | \(-0.298216\pi\) |
−0.993921 | + | 0.110099i | \(0.964883\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −41.2227 | − | 11.0456i | −1.73425 | − | 0.464692i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.7544 | − | 10.8939i | 0.703617 | − | 0.457499i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.18974 | − | 5.52479i | 0.133721 | − | 0.231611i | −0.791387 | − | 0.611315i | \(-0.790641\pi\) |
0.925108 | + | 0.379704i | \(0.123974\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.64342i | 0.194321i | 0.995269 | + | 0.0971605i | \(0.0309760\pi\) | ||||
−0.995269 | + | 0.0971605i | \(0.969024\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.26220 | − | 14.8533i | −0.219832 | − | 0.620507i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.06575 | + | 1.77001i | 0.127851 | + | 0.0738145i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.3269 | + | 16.3269i | −0.679699 | + | 0.679699i | −0.959932 | − | 0.280233i | \(-0.909588\pi\) |
0.280233 | + | 0.959932i | \(0.409588\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.96878 | − | 24.9706i | −0.0818195 | − | 1.03774i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.5739 | + | 7.83692i | −0.563142 | + | 0.325130i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.38556 | − | 0.907159i | 0.140216 | − | 0.0375707i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 23.7447 | + | 11.5508i | 0.981724 | + | 0.477568i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.6852 | − | 4.73874i | 0.729948 | − | 0.195589i | 0.125342 | − | 0.992114i | \(-0.459997\pi\) |
0.604606 | + | 0.796525i | \(0.293331\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.2353 | + | 18.0337i | −1.28703 | + | 0.743066i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.876924 | − | 11.1223i | −0.0360718 | − | 0.457510i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.8285 | − | 11.8285i | 0.485739 | − | 0.485739i | −0.421220 | − | 0.906959i | \(-0.638398\pi\) |
0.906959 | + | 0.421220i | \(0.138398\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.2319 | − | 7.63947i | −0.542457 | − | 0.313188i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.456364 | + | 1.28816i | 0.0186777 | + | 0.0527207i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 36.6793i | − | 1.49867i | −0.662188 | − | 0.749337i | \(-0.730372\pi\) | ||
0.662188 | − | 0.749337i | \(-0.269628\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.04984 | + | 3.55043i | −0.0836147 | + | 0.144825i | −0.904800 | − | 0.425837i | \(-0.859980\pi\) |
0.821185 | + | 0.570662i | \(0.193313\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.806729 | − | 7.69642i | 0.0328525 | − | 0.313422i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 50.1311 | + | 13.4326i | 2.03812 | + | 0.546112i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.15357 | − | 7.19419i | −0.168588 | − | 0.292003i | 0.769336 | − | 0.638845i | \(-0.220587\pi\) |
−0.937924 | + | 0.346842i | \(0.887254\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.92464 | + | 7.16323i | 0.199556 | + | 0.290269i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.22084 | + | 48.6635i | −0.170757 | + | 1.96872i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.42881 | − | 5.33239i | −0.0577091 | − | 0.215373i | 0.931050 | − | 0.364892i | \(-0.118894\pi\) |
−0.988759 | + | 0.149519i | \(0.952227\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19.9784 | − | 23.3984i | 0.805606 | − | 0.943513i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.17063 | + | 23.0291i | −0.248420 | + | 0.927117i | 0.723213 | + | 0.690625i | \(0.242664\pi\) |
−0.971633 | + | 0.236492i | \(0.924002\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.4317 | − | 19.4317i | −0.781028 | − | 0.781028i | 0.198976 | − | 0.980004i | \(-0.436238\pi\) |
−0.980004 | + | 0.198976i | \(0.936238\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.15690 | − | 16.8479i | −0.367454 | − | 0.676083i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.6182 | −0.745923 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 28.8762 | 1.15505 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −78.6970 | − | 14.5741i | −3.14285 | − | 0.582035i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.1935 | + | 15.1935i | 0.605806 | + | 0.605806i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.00162 | − | 11.2022i | 0.119493 | − | 0.445953i | −0.880091 | − | 0.474805i | \(-0.842519\pi\) |
0.999584 | + | 0.0288524i | \(0.00918527\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −30.3608 | − | 25.9231i | −1.20673 | − | 1.03035i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.778561 | − | 2.90563i | −0.0308963 | − | 0.115306i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.34674 | − | 1.30109i | 0.291089 | − | 0.0515512i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.3522 | + | 17.0115i | −0.488646 | + | 0.672964i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.29977 | + | 16.1077i | 0.367319 | + | 0.636215i | 0.989145 | − | 0.146940i | \(-0.0469424\pi\) |
−0.621826 | + | 0.783155i | \(0.713609\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.9091 | − | 7.74616i | −1.14006 | − | 0.305479i | −0.361086 | − | 0.932532i | \(-0.617594\pi\) |
−0.778976 | + | 0.627054i | \(0.784261\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.875726 | − | 1.83667i | 0.0344817 | − | 0.0723186i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.6735 | − | 18.4871i | 0.419619 | − | 0.726802i | −0.576282 | − | 0.817251i | \(-0.695497\pi\) |
0.995901 | + | 0.0904492i | \(0.0288303\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 11.4499i | − | 0.449447i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.0719 | + | 5.69391i | −0.629907 | + | 0.223162i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.3357 | + | 10.5861i | 0.717533 | + | 0.414268i | 0.813844 | − | 0.581084i | \(-0.197371\pi\) |
−0.0963112 | + | 0.995351i | \(0.530704\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.3936 | + | 12.3936i | −0.484256 | + | 0.484256i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.6561 | + | 26.1602i | 0.454748 | + | 1.02061i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.9228 | − | 17.8533i | 1.20458 | − | 0.695464i | 0.243010 | − | 0.970024i | \(-0.421865\pi\) |
0.961570 | + | 0.274559i | \(0.0885320\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.7357 | + | 4.75228i | −0.689840 | + | 0.184842i | −0.586675 | − | 0.809822i | \(-0.699564\pi\) |
−0.103165 | + | 0.994664i | \(0.532897\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.92049 | + | 15.1748i | −0.346443 | + | 0.589341i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −42.5971 | + | 11.4139i | −1.65184 | + | 0.442610i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.22336 | − | 4.17041i | 0.279690 | − | 0.161479i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22.3688 | − | 1.76364i | 0.864826 | − | 0.0681861i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.36366 | + | 5.36366i | −0.207062 | + | 0.207062i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.8577 | − | 14.9289i | −0.996740 | − | 0.575468i | −0.0894579 | − | 0.995991i | \(-0.528513\pi\) |
−0.907282 | + | 0.420522i | \(0.861847\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.25110 | + | 2.60260i | 0.163625 | + | 0.100174i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 21.5956i | − | 0.829988i | −0.909824 | − | 0.414994i | \(-0.863784\pi\) | ||
0.909824 | − | 0.414994i | \(-0.136216\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.49065 | − | 6.04599i | 0.133959 | − | 0.232024i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.8287 | + | 7.54715i | 0.606556 | + | 0.289207i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.6457 | − | 9.01534i | −1.28742 | − | 0.344962i | −0.450738 | − | 0.892656i | \(-0.648839\pi\) |
−0.836679 | + | 0.547694i | \(0.815506\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.6838 | + | 25.4330i | 0.561038 | + | 0.971746i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.1959 | + | 8.38457i | −0.465304 | + | 0.319891i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.43146 | − | 1.70336i | −0.0545343 | − | 0.0648929i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.05147 | + | 26.3164i | 0.268250 | + | 1.00112i | 0.960231 | + | 0.279208i | \(0.0900718\pi\) |
−0.691980 | + | 0.721916i | \(0.743262\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −35.3270 | − | 13.5493i | −1.34196 | − | 0.514696i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.47145 | + | 5.49152i | −0.0558152 | + | 0.208305i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.5030 | + | 14.5030i | 0.549342 | + | 0.549342i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.00332 | − | 16.2172i | 0.113596 | − | 0.613393i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.80915 | −0.294948 | −0.147474 | − | 0.989066i | \(-0.547114\pi\) | ||||
−0.147474 | + | 0.989066i | \(0.547114\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 62.0179 | 2.33905 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.4308 | + | 56.3241i | −0.392848 | + | 2.12129i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.11262 | + | 2.11262i | 0.0794534 | + | 0.0794534i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.07769 | − | 30.1463i | 0.303364 | − | 1.13217i | −0.630981 | − | 0.775799i | \(-0.717347\pi\) |
0.934345 | − | 0.356371i | \(-0.115986\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.04372 | − | 0.400307i | −0.0391424 | − | 0.0150127i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.23438 | + | 15.8029i | 0.158579 | + | 0.591824i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.71785 | − | 49.2261i | −0.326029 | − | 1.84095i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.700411 | + | 0.481525i | −0.0261573 | + | 0.0179829i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.01546 | − | 3.49089i | −0.0751641 | − | 0.130188i | 0.825993 | − | 0.563680i | \(-0.190615\pi\) |
−0.901158 | + | 0.433492i | \(0.857281\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.5599 | − | 5.77695i | −0.802932 | − | 0.215145i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −41.3238 | − | 19.7033i | −1.53685 | − | 0.732773i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.08406 | + | 1.87765i | −0.0402611 | + | 0.0697342i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.5507i | 0.984711i | 0.870394 | + | 0.492356i | \(0.163864\pi\) | ||||
−0.870394 | + | 0.492356i | \(0.836136\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.2781 | − | 24.0468i | −0.454745 | − | 0.890622i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.17471 | + | 0.678217i | 0.0434481 | + | 0.0250848i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.7035 | − | 15.7035i | 0.580021 | − | 0.580021i | −0.354888 | − | 0.934909i | \(-0.615481\pi\) |
0.934909 | + | 0.354888i | \(0.115481\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.72249 | − | 0.687714i | 0.321734 | − | 0.0253667i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.6883 | + | 7.32561i | −0.467380 | + | 0.269842i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.55841 | − | 1.75732i | 0.241255 | − | 0.0646441i | −0.136165 | − | 0.990686i | \(-0.543478\pi\) |
0.377420 | + | 0.926042i | \(0.376811\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.7646 | + | 49.1768i | 0.468921 | + | 1.80656i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.6931 | + | 10.9037i | −1.49288 | + | 0.400017i | −0.910709 | − | 0.413047i | \(-0.864464\pi\) |
−0.582174 | + | 0.813064i | \(0.697798\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 41.2418 | − | 23.8110i | 1.51098 | − | 0.872366i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.61851 | + | 19.3428i | 0.315335 | + | 0.707716i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.4573 | − | 23.4573i | 0.857112 | − | 0.857112i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.3813 | + | 18.1180i | 1.14512 | + | 0.661135i | 0.947693 | − | 0.319183i | \(-0.103408\pi\) |
0.197426 | + | 0.980318i | \(0.436742\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.0278 | − | 7.80397i | 0.802739 | − | 0.284392i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.45947i | 0.0895093i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.17824 | + | 5.50487i | −0.115515 | + | 0.200078i | −0.917986 | − | 0.396614i | \(-0.870185\pi\) |
0.802470 | + | 0.596692i | \(0.203519\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.6248 | + | 32.7700i | −0.567145 | + | 1.18948i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0411 | + | 5.63796i | 0.762741 | + | 0.204376i | 0.619162 | − | 0.785263i | \(-0.287472\pi\) |
0.143579 | + | 0.989639i | \(0.454139\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.36791 | + | 16.2257i | 0.339141 | + | 0.587410i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.1286 | + | 16.7035i | −0.438511 | + | 0.603917i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.58512 | + | 3.07669i | −0.237775 | + | 0.111093i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.69721 | − | 13.7982i | −0.133325 | − | 0.497575i | 0.866674 | − | 0.498874i | \(-0.166253\pi\) |
−0.999999 | + | 0.00129915i | \(0.999586\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.29255 | + | 2.81130i | 0.118578 | + | 0.101246i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.17937 | − | 8.13353i | 0.0783866 | − | 0.292543i | −0.915593 | − | 0.402106i | \(-0.868278\pi\) |
0.993980 | + | 0.109563i | \(0.0349451\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.00714 | − | 3.00714i | −0.108020 | − | 0.108020i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 28.8285 | + | 5.33883i | 1.03422 | + | 0.191530i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 59.1994 | 2.12104 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.8022 | 1.42424 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.3187 | − | 5.60824i | 0.368759 | − | 0.200422i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −29.3975 | − | 29.3975i | −1.04924 | − | 1.04924i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.57267 | + | 31.9936i | −0.305583 | + | 1.14045i | 0.626860 | + | 0.779132i | \(0.284340\pi\) |
−0.932443 | + | 0.361318i | \(0.882327\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.8068 | + | 12.6567i | −0.384731 | + | 0.450591i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.0472 | − | 37.4967i | −0.357238 | − | 1.33323i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.52604 | + | 1.64351i | 0.160724 | + | 0.0583628i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.47818 | − | 2.15012i | −0.0524257 | − | 0.0762568i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.4840 | − | 47.6037i | −0.973534 | − | 1.68621i | −0.684691 | − | 0.728834i | \(-0.740063\pi\) |
−0.288843 | − | 0.957376i | \(-0.593271\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.8847 | − | 9.88323i | −1.30489 | − | 0.349644i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.62224 | + | 25.0169i | −0.0926523 | + | 0.883928i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.1111 | − | 46.9578i | 0.956730 | − | 1.65711i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.0039i | 0.705045i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.62473 | + | 27.1672i | 0.338806 | + | 0.956331i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.7137 | + | 16.0005i | 0.974361 | + | 0.562547i | 0.900563 | − | 0.434726i | \(-0.143155\pi\) |
0.0737978 | + | 0.997273i | \(0.476488\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.5566 | − | 34.5566i | 1.21344 | − | 1.21344i | 0.243559 | − | 0.969886i | \(-0.421685\pi\) |
0.969886 | − | 0.243559i | \(-0.0783148\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.26824 | − | 54.1355i | −0.149694 | − | 1.89861i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.0037 | − | 12.1265i | 0.735729 | − | 0.424773i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.78169 | − | 1.01330i | 0.132304 | − | 0.0354509i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.70013 | + | 23.9583i | 0.0594073 | + | 0.837169i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.31469 | − | 1.69202i | 0.220384 | − | 0.0590518i | −0.146937 | − | 0.989146i | \(-0.546942\pi\) |
0.367321 | + | 0.930094i | \(0.380275\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.88316 | − | 5.70605i | 0.344505 | − | 0.198900i | −0.317757 | − | 0.948172i | \(-0.602930\pi\) |
0.662263 | + | 0.749272i | \(0.269596\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.741748 | − | 9.40782i | −0.0258243 | − | 0.327538i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.1511 | + | 16.1511i | −0.561628 | + | 0.561628i | −0.929770 | − | 0.368142i | \(-0.879994\pi\) |
0.368142 | + | 0.929770i | \(0.379994\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.4973 | + | 6.06059i | 0.364585 | + | 0.210493i | 0.671090 | − | 0.741376i | \(-0.265826\pi\) |
−0.306505 | + | 0.951869i | \(0.599160\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.25343 | − | 12.0059i | −0.147550 | − | 0.416481i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.83274i | 0.202092i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.6825 | − | 21.9668i | 0.438897 | − | 0.760192i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.38717 | + | 22.3974i | 0.186208 | + | 0.774168i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.4519 | − | 8.69547i | −1.12036 | − | 0.300201i | −0.349334 | − | 0.936998i | \(-0.613592\pi\) |
−0.771031 | + | 0.636798i | \(0.780259\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.9458 | − | 20.6907i | −0.411924 | − | 0.713473i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.66274 | + | 11.1460i | 0.263919 | + | 0.383888i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.9686 | + | 18.2414i | −0.893348 | + | 0.627522i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.2185 | + | 45.5999i | 0.419831 | + | 1.56683i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.5811 | − | 13.5636i | 0.397464 | − | 0.465503i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.28102 | − | 27.1731i | 0.249590 | − | 0.931483i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.0421 | + | 14.0421i | 0.480792 | + | 0.480792i | 0.905385 | − | 0.424592i | \(-0.139583\pi\) |
−0.424592 | + | 0.905385i | \(0.639583\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.33706 | + | 58.8444i | 0.319321 | + | 2.01243i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.0059 | −0.990824 | −0.495412 | − | 0.868658i | \(-0.664983\pi\) | ||||
−0.495412 | + | 0.868658i | \(0.664983\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0160 | 0.375859 | 0.187930 | − | 0.982182i | \(-0.439822\pi\) | ||||
0.187930 | + | 0.982182i | \(0.439822\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.5183 | + | 5.09620i | 0.937821 | + | 0.173678i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.8394 | + | 21.8394i | 0.743422 | + | 0.743422i | 0.973235 | − | 0.229813i | \(-0.0738115\pi\) |
−0.229813 | + | 0.973235i | \(0.573811\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.41108 | + | 31.3906i | −0.285985 | + | 1.06731i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.9276 | + | 10.1842i | 0.405082 | + | 0.345874i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.547762 | + | 2.04428i | 0.0185816 | + | 0.0693473i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.62261 | + | 5.32892i | 0.258282 | + | 0.180563i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.63223 | − | 5.54185i | −0.258312 | − | 0.187563i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.9516 | + | 18.9688i | 0.370233 | + | 0.641263i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 51.5387 | + | 13.8098i | 1.74034 | + | 0.466322i | 0.982522 | − | 0.186146i | \(-0.0595996\pi\) |
0.757816 | + | 0.652468i | \(0.226266\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.0564 | + | 44.1616i | −0.710214 | + | 1.48954i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.5586 | + | 40.8048i | −0.793711 | + | 1.37475i | 0.129943 | + | 0.991521i | \(0.458520\pi\) |
−0.923654 | + | 0.383226i | \(0.874813\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 21.4475i | − | 0.721765i | −0.932611 | − | 0.360882i | \(-0.882476\pi\) | ||
0.932611 | − | 0.360882i | \(-0.117524\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.03433 | + | 2.84638i | −0.270071 | + | 0.0956801i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.6954 | + | 12.5259i | 0.728461 | + | 0.420577i | 0.817859 | − | 0.575419i | \(-0.195161\pi\) |
−0.0893977 | + | 0.995996i | \(0.528494\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.93481 | − | 1.93481i | 0.0648914 | − | 0.0648914i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.1815 | + | 45.5598i | −0.776609 | + | 1.52631i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −95.4501 | + | 55.1082i | −3.19412 | + | 1.84412i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.06340 | + | 0.284938i | −0.0355456 | + | 0.00952442i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.0454 | + | 0.180626i | 0.769463 | + | 0.00603092i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.67867 | + | 2.59339i | −0.322802 | + | 0.0864944i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.50636 | − | 0.869695i | 0.0501840 | − | 0.0289738i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.84511 | − | 0.145476i | 0.0614016 | − | 0.00484113i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.988730 | + | 0.988730i | −0.0328665 | + | 0.0328665i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.8693 | − | 14.3583i | −0.825772 | − | 0.476760i | 0.0266307 | − | 0.999645i | \(-0.491522\pi\) |
−0.852403 | + | 0.522886i | \(0.824856\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.13624 | − | 2.54114i | 0.104022 | − | 0.0842843i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.6397i | 1.01514i | 0.861611 | + | 0.507569i | \(0.169456\pi\) | ||||
−0.861611 | + | 0.507569i | \(0.830544\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.0459 | − | 34.7205i | 0.663423 | − | 1.14908i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.09703 | + | 2.43028i | 0.168503 | + | 0.0803424i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.3997 | − | 4.12633i | −0.508542 | − | 0.136263i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.08612 | + | 8.80943i | 0.167776 | + | 0.290596i | 0.937638 | − | 0.347615i | \(-0.113008\pi\) |
−0.769862 | + | 0.638211i | \(0.779675\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.145745 | + | 0.100198i | −0.00480248 | + | 0.00330165i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.6952 | − | 22.8913i | −0.352037 | − | 0.753475i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.89264 | + | 7.06342i | 0.0622296 | + | 0.232244i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.7989 | + | 28.1559i | −0.354683 | + | 0.924761i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.27665 | − | 23.4248i | 0.205930 | − | 0.768542i | −0.783234 | − | 0.621727i | \(-0.786431\pi\) |
0.989164 | − | 0.146815i | \(-0.0469022\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.9042 | + | 11.9042i | 0.390145 | + | 0.390145i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.31309 | − | 34.0892i | 0.206681 | − | 1.11603i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 39.0817 | 1.27811 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.1432 | 0.527376 | 0.263688 | − | 0.964608i | \(-0.415061\pi\) | ||||
0.263688 | + | 0.964608i | \(0.415061\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.197661 | + | 1.06732i | −0.00645042 | + | 0.0348308i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.888058 | − | 0.888058i | −0.0289499 | − | 0.0289499i | 0.692484 | − | 0.721434i | \(-0.256516\pi\) |
−0.721434 | + | 0.692484i | \(0.756516\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.95011 | − | 25.9382i | 0.226327 | − | 0.844663i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.725386 | + | 28.1571i | −0.0235968 | + | 0.915949i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.622237 | − | 2.32222i | −0.0202200 | − | 0.0754620i | 0.955079 | − | 0.296352i | \(-0.0957703\pi\) |
−0.975299 | + | 0.220891i | \(0.929104\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34.2916 | − | 2.97429i | −1.11315 | − | 0.0965496i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.1655 | − | 20.0510i | 0.945757 | − | 0.650198i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.06072 | − | 10.4975i | −0.196326 | − | 0.340046i | 0.751008 | − | 0.660293i | \(-0.229568\pi\) |
−0.947334 | + | 0.320246i | \(0.896234\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.4525 | + | 5.74819i | 0.694188 | + | 0.186007i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.0703 | − | 9.56959i | −0.648782 | − | 0.309341i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.3565 | + | 23.1342i | −0.431305 | + | 0.747042i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.3457i | 0.365991i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −28.2153 | − | 34.8229i | −0.909225 | − | 1.12215i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 30.5732 | + | 17.6515i | 0.984187 | + | 0.568220i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.7092 | − | 10.7092i | 0.344386 | − | 0.344386i | −0.513628 | − | 0.858013i | \(-0.671699\pi\) |
0.858013 | + | 0.513628i | \(0.171699\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −39.5954 | + | 3.12185i | −1.27199 | + | 0.100288i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.1662 | + | 5.86945i | −0.326248 | + | 0.188360i | −0.654174 | − | 0.756344i | \(-0.726984\pi\) |
0.327926 | + | 0.944703i | \(0.393650\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.99516 | + | 1.33845i | −0.160137 | + | 0.0429087i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.21136 | + | 2.95456i | −0.166897 | + | 0.0946218i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.0380 | + | 4.29736i | −0.513100 | + | 0.137485i | −0.506073 | − | 0.862491i | \(-0.668903\pi\) |
−0.00702677 | + | 0.999975i | \(0.502237\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 41.2429 | − | 23.8116i | 1.31813 | − | 0.761021i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.1215 | − | 10.3022i | 0.738214 | − | 0.328924i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.9952 | − | 25.9952i | 0.829118 | − | 0.829118i | −0.158277 | − | 0.987395i | \(-0.550594\pi\) |
0.987395 | + | 0.158277i | \(0.0505938\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.6178 | + | 7.86223i | 0.433899 | + | 0.250512i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −49.1132 | + | 17.3997i | −1.56329 | + | 0.553838i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.77591i | − | 0.0564706i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.1294 | − | 21.0088i | 0.385304 | − | 0.667366i | −0.606508 | − | 0.795078i | \(-0.707430\pi\) |
0.991811 | + | 0.127712i | \(0.0407634\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.98771 | + | 14.6554i | −0.221748 | + | 0.465074i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.86047 | − | 0.498512i | −0.0589809 | − | 0.0158039i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.5907 | − | 47.7884i | −0.873805 | − | 1.51347i | −0.858030 | − | 0.513599i | \(-0.828312\pi\) |
−0.0157748 | − | 0.999876i | \(-0.505021\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.2340 | − | 37.9843i | 0.355427 | − | 1.20177i |
(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 | 624.2.cn.f.305.6 | 56 | ||
3.2 | odd | 2 | inner | 624.2.cn.f.305.4 | 56 | ||
4.3 | odd | 2 | 312.2.bp.a.305.9 | yes | 56 | ||
12.11 | even | 2 | 312.2.bp.a.305.11 | yes | 56 | ||
13.11 | odd | 12 | inner | 624.2.cn.f.401.4 | 56 | ||
39.11 | even | 12 | inner | 624.2.cn.f.401.6 | 56 | ||
52.11 | even | 12 | 312.2.bp.a.89.11 | yes | 56 | ||
156.11 | odd | 12 | 312.2.bp.a.89.9 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.2.bp.a.89.9 | ✓ | 56 | 156.11 | odd | 12 | ||
312.2.bp.a.89.11 | yes | 56 | 52.11 | even | 12 | ||
312.2.bp.a.305.9 | yes | 56 | 4.3 | odd | 2 | ||
312.2.bp.a.305.11 | yes | 56 | 12.11 | even | 2 | ||
624.2.cn.f.305.4 | 56 | 3.2 | odd | 2 | inner | ||
624.2.cn.f.305.6 | 56 | 1.1 | even | 1 | trivial | ||
624.2.cn.f.401.4 | 56 | 13.11 | odd | 12 | inner | ||
624.2.cn.f.401.6 | 56 | 39.11 | even | 12 | inner |