Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(298,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.298");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 23x^{12} + 201x^{10} + 835x^{8} + 1695x^{6} + 1565x^{4} + 511x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 298.11 | ||
Root | \(1.42819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.298 |
Dual form | 429.2.b.b.298.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.42819i | 1.00989i | 0.863153 | + | 0.504943i | \(0.168486\pi\) | ||||
−0.863153 | + | 0.504943i | \(0.831514\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.0397381 | −0.0198691 | ||||||||
\(5\) | 0.0606573i | 0.0271268i | 0.999908 | + | 0.0135634i | \(0.00431749\pi\) | ||||
−0.999908 | + | 0.0135634i | \(0.995683\pi\) | |||||||
\(6\) | 1.42819i | 0.583058i | ||||||||
\(7\) | 1.70646i | 0.644980i | 0.946573 | + | 0.322490i | \(0.104520\pi\) | ||||
−0.946573 | + | 0.322490i | \(0.895480\pi\) | |||||||
\(8\) | 2.79963i | 0.989820i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.0866304 | −0.0273949 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | −0.0397381 | −0.0114714 | ||||||||
\(13\) | 3.52912 | − | 0.738445i | 0.978802 | − | 0.204808i | ||||
\(14\) | −2.43715 | −0.651356 | ||||||||
\(15\) | 0.0606573i | 0.0156616i | ||||||||
\(16\) | −4.07790 | −1.01947 | ||||||||
\(17\) | −3.75599 | −0.910962 | −0.455481 | − | 0.890246i | \(-0.650533\pi\) | ||||
−0.455481 | + | 0.890246i | \(0.650533\pi\) | |||||||
\(18\) | 1.42819i | 0.336629i | ||||||||
\(19\) | 2.02597i | 0.464790i | 0.972621 | + | 0.232395i | \(0.0746562\pi\) | ||||
−0.972621 | + | 0.232395i | \(0.925344\pi\) | |||||||
\(20\) | − | 0.00241041i | − | 0.000538983i | ||||||
\(21\) | 1.70646i | 0.372379i | ||||||||
\(22\) | 1.42819 | 0.304492 | ||||||||
\(23\) | −0.704722 | −0.146945 | −0.0734723 | − | 0.997297i | \(-0.523408\pi\) | ||||
−0.0734723 | + | 0.997297i | \(0.523408\pi\) | |||||||
\(24\) | 2.79963i | 0.571473i | ||||||||
\(25\) | 4.99632 | 0.999264 | ||||||||
\(26\) | 1.05464 | + | 5.04027i | 0.206832 | + | 0.988478i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | − | 0.0678114i | − | 0.0128151i | ||||||
\(29\) | −0.0346842 | −0.00644069 | −0.00322035 | − | 0.999995i | \(-0.501025\pi\) | ||||
−0.00322035 | + | 0.999995i | \(0.501025\pi\) | |||||||
\(30\) | −0.0866304 | −0.0158165 | ||||||||
\(31\) | 1.85987i | 0.334042i | 0.985953 | + | 0.167021i | \(0.0534148\pi\) | ||||
−0.985953 | + | 0.167021i | \(0.946585\pi\) | |||||||
\(32\) | − | 0.224760i | − | 0.0397323i | ||||||
\(33\) | − | 1.00000i | − | 0.174078i | ||||||
\(34\) | − | 5.36429i | − | 0.919967i | ||||||
\(35\) | −0.103509 | −0.0174962 | ||||||||
\(36\) | −0.0397381 | −0.00662302 | ||||||||
\(37\) | − | 8.82674i | − | 1.45111i | −0.688166 | − | 0.725553i | \(-0.741584\pi\) | ||
0.688166 | − | 0.725553i | \(-0.258416\pi\) | |||||||
\(38\) | −2.89348 | −0.469385 | ||||||||
\(39\) | 3.52912 | − | 0.738445i | 0.565112 | − | 0.118246i | ||||
\(40\) | −0.169818 | −0.0268506 | ||||||||
\(41\) | 3.32960i | 0.519996i | 0.965609 | + | 0.259998i | \(0.0837220\pi\) | ||||
−0.965609 | + | 0.259998i | \(0.916278\pi\) | |||||||
\(42\) | −2.43715 | −0.376061 | ||||||||
\(43\) | −5.29022 | −0.806751 | −0.403376 | − | 0.915035i | \(-0.632163\pi\) | ||||
−0.403376 | + | 0.915035i | \(0.632163\pi\) | |||||||
\(44\) | 0.0397381i | 0.00599075i | ||||||||
\(45\) | 0.0606573i | 0.00904225i | ||||||||
\(46\) | − | 1.00648i | − | 0.148397i | ||||||
\(47\) | − | 6.04622i | − | 0.881931i | −0.897524 | − | 0.440966i | \(-0.854636\pi\) | ||
0.897524 | − | 0.440966i | \(-0.145364\pi\) | |||||||
\(48\) | −4.07790 | −0.588594 | ||||||||
\(49\) | 4.08800 | 0.584001 | ||||||||
\(50\) | 7.13572i | 1.00914i | ||||||||
\(51\) | −3.75599 | −0.525944 | ||||||||
\(52\) | −0.140241 | + | 0.0293444i | −0.0194479 | + | 0.00406934i | ||||
\(53\) | −10.6694 | −1.46555 | −0.732775 | − | 0.680471i | \(-0.761775\pi\) | ||||
−0.732775 | + | 0.680471i | \(0.761775\pi\) | |||||||
\(54\) | 1.42819i | 0.194353i | ||||||||
\(55\) | 0.0606573 | 0.00817903 | ||||||||
\(56\) | −4.77746 | −0.638414 | ||||||||
\(57\) | 2.02597i | 0.268347i | ||||||||
\(58\) | − | 0.0495358i | − | 0.00650436i | ||||||
\(59\) | − | 3.34547i | − | 0.435543i | −0.976000 | − | 0.217771i | \(-0.930121\pi\) | ||
0.976000 | − | 0.217771i | \(-0.0698787\pi\) | |||||||
\(60\) | − | 0.00241041i | − | 0.000311182i | ||||||
\(61\) | 3.26757 | 0.418369 | 0.209185 | − | 0.977876i | \(-0.432919\pi\) | ||||
0.209185 | + | 0.977876i | \(0.432919\pi\) | |||||||
\(62\) | −2.65625 | −0.337344 | ||||||||
\(63\) | 1.70646i | 0.214993i | ||||||||
\(64\) | −7.83479 | −0.979349 | ||||||||
\(65\) | 0.0447920 | + | 0.214067i | 0.00555577 | + | 0.0265517i | ||||
\(66\) | 1.42819 | 0.175799 | ||||||||
\(67\) | − | 10.9701i | − | 1.34021i | −0.742268 | − | 0.670103i | \(-0.766250\pi\) | ||
0.742268 | − | 0.670103i | \(-0.233750\pi\) | |||||||
\(68\) | 0.149256 | 0.0181000 | ||||||||
\(69\) | −0.704722 | −0.0848385 | ||||||||
\(70\) | − | 0.147831i | − | 0.0176692i | ||||||
\(71\) | 1.96928i | 0.233711i | 0.993149 | + | 0.116855i | \(0.0372814\pi\) | ||||
−0.993149 | + | 0.116855i | \(0.962719\pi\) | |||||||
\(72\) | 2.79963i | 0.329940i | ||||||||
\(73\) | − | 15.3057i | − | 1.79140i | −0.444659 | − | 0.895700i | \(-0.646675\pi\) | ||
0.444659 | − | 0.895700i | \(-0.353325\pi\) | |||||||
\(74\) | 12.6063 | 1.46545 | ||||||||
\(75\) | 4.99632 | 0.576925 | ||||||||
\(76\) | − | 0.0805084i | − | 0.00923494i | ||||||
\(77\) | 1.70646 | 0.194469 | ||||||||
\(78\) | 1.05464 | + | 5.04027i | 0.119415 | + | 0.570698i | ||||
\(79\) | 10.5938 | 1.19190 | 0.595951 | − | 0.803021i | \(-0.296775\pi\) | ||||
0.595951 | + | 0.803021i | \(0.296775\pi\) | |||||||
\(80\) | − | 0.247354i | − | 0.0276550i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.75532 | −0.525137 | ||||||||
\(83\) | 4.19820i | 0.460812i | 0.973095 | + | 0.230406i | \(0.0740055\pi\) | ||||
−0.973095 | + | 0.230406i | \(0.925994\pi\) | |||||||
\(84\) | − | 0.0678114i | − | 0.00739883i | ||||||
\(85\) | − | 0.227828i | − | 0.0247114i | ||||||
\(86\) | − | 7.55546i | − | 0.814726i | ||||||
\(87\) | −0.0346842 | −0.00371854 | ||||||||
\(88\) | 2.79963 | 0.298442 | ||||||||
\(89\) | − | 14.3643i | − | 1.52261i | −0.648393 | − | 0.761305i | \(-0.724559\pi\) | ||
0.648393 | − | 0.761305i | \(-0.275441\pi\) | |||||||
\(90\) | −0.0866304 | −0.00913164 | ||||||||
\(91\) | 1.26012 | + | 6.02229i | 0.132097 | + | 0.631308i | ||||
\(92\) | 0.0280043 | 0.00291965 | ||||||||
\(93\) | 1.85987i | 0.192859i | ||||||||
\(94\) | 8.63517 | 0.890650 | ||||||||
\(95\) | −0.122890 | −0.0126082 | ||||||||
\(96\) | − | 0.224760i | − | 0.0229394i | ||||||
\(97\) | 5.86228i | 0.595224i | 0.954687 | + | 0.297612i | \(0.0961902\pi\) | ||||
−0.954687 | + | 0.297612i | \(0.903810\pi\) | |||||||
\(98\) | 5.83846i | 0.589774i | ||||||||
\(99\) | − | 1.00000i | − | 0.100504i | ||||||
\(100\) | −0.198544 | −0.0198544 | ||||||||
\(101\) | 12.3706 | 1.23092 | 0.615460 | − | 0.788168i | \(-0.288970\pi\) | ||||
0.615460 | + | 0.788168i | \(0.288970\pi\) | |||||||
\(102\) | − | 5.36429i | − | 0.531143i | ||||||
\(103\) | −10.0788 | −0.993094 | −0.496547 | − | 0.868010i | \(-0.665399\pi\) | ||||
−0.496547 | + | 0.868010i | \(0.665399\pi\) | |||||||
\(104\) | 2.06738 | + | 9.88025i | 0.202723 | + | 0.968838i | ||||
\(105\) | −0.103509 | −0.0101014 | ||||||||
\(106\) | − | 15.2379i | − | 1.48004i | ||||||
\(107\) | 6.17793 | 0.597243 | 0.298622 | − | 0.954372i | \(-0.403473\pi\) | ||||
0.298622 | + | 0.954372i | \(0.403473\pi\) | |||||||
\(108\) | −0.0397381 | −0.00382380 | ||||||||
\(109\) | 4.64928i | 0.445320i | 0.974896 | + | 0.222660i | \(0.0714740\pi\) | ||||
−0.974896 | + | 0.222660i | \(0.928526\pi\) | |||||||
\(110\) | 0.0866304i | 0.00825988i | ||||||||
\(111\) | − | 8.82674i | − | 0.837797i | ||||||
\(112\) | − | 6.95876i | − | 0.657541i | ||||||
\(113\) | 8.99146 | 0.845846 | 0.422923 | − | 0.906166i | \(-0.361004\pi\) | ||||
0.422923 | + | 0.906166i | \(0.361004\pi\) | |||||||
\(114\) | −2.89348 | −0.270999 | ||||||||
\(115\) | − | 0.0427465i | − | 0.00398613i | ||||||
\(116\) | 0.00137828 | 0.000127971 | ||||||||
\(117\) | 3.52912 | − | 0.738445i | 0.326267 | − | 0.0682692i | ||||
\(118\) | 4.77798 | 0.439848 | ||||||||
\(119\) | − | 6.40944i | − | 0.587552i | ||||||
\(120\) | −0.169818 | −0.0155022 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 4.66672i | 0.422505i | ||||||||
\(123\) | 3.32960i | 0.300220i | ||||||||
\(124\) | − | 0.0739076i | − | 0.00663710i | ||||||
\(125\) | 0.606350i | 0.0542336i | ||||||||
\(126\) | −2.43715 | −0.217119 | ||||||||
\(127\) | −1.74493 | −0.154837 | −0.0774187 | − | 0.996999i | \(-0.524668\pi\) | ||||
−0.0774187 | + | 0.996999i | \(0.524668\pi\) | |||||||
\(128\) | − | 11.6391i | − | 1.02876i | ||||||
\(129\) | −5.29022 | −0.465778 | ||||||||
\(130\) | −0.305729 | + | 0.0639717i | −0.0268142 | + | 0.00561069i | ||||
\(131\) | −13.8961 | −1.21411 | −0.607054 | − | 0.794661i | \(-0.707649\pi\) | ||||
−0.607054 | + | 0.794661i | \(0.707649\pi\) | |||||||
\(132\) | 0.0397381i | 0.00345876i | ||||||||
\(133\) | −3.45724 | −0.299780 | ||||||||
\(134\) | 15.6674 | 1.35345 | ||||||||
\(135\) | 0.0606573i | 0.00522055i | ||||||||
\(136\) | − | 10.5154i | − | 0.901689i | ||||||
\(137\) | − | 3.08818i | − | 0.263841i | −0.991260 | − | 0.131921i | \(-0.957886\pi\) | ||
0.991260 | − | 0.131921i | \(-0.0421144\pi\) | |||||||
\(138\) | − | 1.00648i | − | 0.0856772i | ||||||
\(139\) | 1.92887 | 0.163605 | 0.0818023 | − | 0.996649i | \(-0.473932\pi\) | ||||
0.0818023 | + | 0.996649i | \(0.473932\pi\) | |||||||
\(140\) | 0.00411325 | 0.000347633 | ||||||||
\(141\) | − | 6.04622i | − | 0.509183i | ||||||
\(142\) | −2.81252 | −0.236021 | ||||||||
\(143\) | −0.738445 | − | 3.52912i | −0.0617519 | − | 0.295120i | ||||
\(144\) | −4.07790 | −0.339825 | ||||||||
\(145\) | − | 0.00210385i | − | 0.000174715i | ||||||
\(146\) | 21.8595 | 1.80911 | ||||||||
\(147\) | 4.08800 | 0.337173 | ||||||||
\(148\) | 0.350758i | 0.0288321i | ||||||||
\(149\) | 9.05192i | 0.741563i | 0.928720 | + | 0.370781i | \(0.120910\pi\) | ||||
−0.928720 | + | 0.370781i | \(0.879090\pi\) | |||||||
\(150\) | 7.13572i | 0.582629i | ||||||||
\(151\) | − | 2.44462i | − | 0.198940i | −0.995041 | − | 0.0994702i | \(-0.968285\pi\) | ||
0.995041 | − | 0.0994702i | \(-0.0317148\pi\) | |||||||
\(152\) | −5.67198 | −0.460059 | ||||||||
\(153\) | −3.75599 | −0.303654 | ||||||||
\(154\) | 2.43715i | 0.196391i | ||||||||
\(155\) | −0.112814 | −0.00906147 | ||||||||
\(156\) | −0.140241 | + | 0.0293444i | −0.0112282 | + | 0.00234943i | ||||
\(157\) | −8.42793 | −0.672622 | −0.336311 | − | 0.941751i | \(-0.609179\pi\) | ||||
−0.336311 | + | 0.941751i | \(0.609179\pi\) | |||||||
\(158\) | 15.1301i | 1.20368i | ||||||||
\(159\) | −10.6694 | −0.846135 | ||||||||
\(160\) | 0.0136333 | 0.00107781 | ||||||||
\(161\) | − | 1.20258i | − | 0.0947763i | ||||||
\(162\) | 1.42819i | 0.112210i | ||||||||
\(163\) | 17.3969i | 1.36263i | 0.731990 | + | 0.681316i | \(0.238592\pi\) | ||||
−0.731990 | + | 0.681316i | \(0.761408\pi\) | |||||||
\(164\) | − | 0.132312i | − | 0.0103318i | ||||||
\(165\) | 0.0606573 | 0.00472216 | ||||||||
\(166\) | −5.99585 | −0.465368 | ||||||||
\(167\) | − | 1.05104i | − | 0.0813320i | −0.999173 | − | 0.0406660i | \(-0.987052\pi\) | ||
0.999173 | − | 0.0406660i | \(-0.0129480\pi\) | |||||||
\(168\) | −4.77746 | −0.368589 | ||||||||
\(169\) | 11.9094 | − | 5.21212i | 0.916108 | − | 0.400933i | ||||
\(170\) | 0.325383 | 0.0249557 | ||||||||
\(171\) | 2.02597i | 0.154930i | ||||||||
\(172\) | 0.210223 | 0.0160294 | ||||||||
\(173\) | −18.6654 | −1.41910 | −0.709552 | − | 0.704653i | \(-0.751103\pi\) | ||||
−0.709552 | + | 0.704653i | \(0.751103\pi\) | |||||||
\(174\) | − | 0.0495358i | − | 0.00375530i | ||||||
\(175\) | 8.52601i | 0.644505i | ||||||||
\(176\) | 4.07790i | 0.307383i | ||||||||
\(177\) | − | 3.34547i | − | 0.251461i | ||||||
\(178\) | 20.5150 | 1.53766 | ||||||||
\(179\) | 24.2443 | 1.81210 | 0.906051 | − | 0.423168i | \(-0.139082\pi\) | ||||
0.906051 | + | 0.423168i | \(0.139082\pi\) | |||||||
\(180\) | − | 0.00241041i | − | 0.000179661i | ||||||
\(181\) | −20.9251 | −1.55535 | −0.777675 | − | 0.628666i | \(-0.783601\pi\) | ||||
−0.777675 | + | 0.628666i | \(0.783601\pi\) | |||||||
\(182\) | −8.60100 | + | 1.79970i | −0.637549 | + | 0.133403i | ||||
\(183\) | 3.26757 | 0.241545 | ||||||||
\(184\) | − | 1.97296i | − | 0.145449i | ||||||
\(185\) | 0.535406 | 0.0393638 | ||||||||
\(186\) | −2.65625 | −0.194766 | ||||||||
\(187\) | 3.75599i | 0.274665i | ||||||||
\(188\) | 0.240265i | 0.0175231i | ||||||||
\(189\) | 1.70646i | 0.124126i | ||||||||
\(190\) | − | 0.175511i | − | 0.0127329i | ||||||
\(191\) | 2.77108 | 0.200508 | 0.100254 | − | 0.994962i | \(-0.468034\pi\) | ||||
0.100254 | + | 0.994962i | \(0.468034\pi\) | |||||||
\(192\) | −7.83479 | −0.565428 | ||||||||
\(193\) | 8.50742i | 0.612378i | 0.951971 | + | 0.306189i | \(0.0990539\pi\) | ||||
−0.951971 | + | 0.306189i | \(0.900946\pi\) | |||||||
\(194\) | −8.37247 | −0.601108 | ||||||||
\(195\) | 0.0447920 | + | 0.214067i | 0.00320763 | + | 0.0153296i | ||||
\(196\) | −0.162450 | −0.0116035 | ||||||||
\(197\) | − | 14.4278i | − | 1.02794i | −0.857810 | − | 0.513968i | \(-0.828175\pi\) | ||
0.857810 | − | 0.513968i | \(-0.171825\pi\) | |||||||
\(198\) | 1.42819 | 0.101497 | ||||||||
\(199\) | −15.9351 | −1.12961 | −0.564806 | − | 0.825224i | \(-0.691049\pi\) | ||||
−0.564806 | + | 0.825224i | \(0.691049\pi\) | |||||||
\(200\) | 13.9879i | 0.989092i | ||||||||
\(201\) | − | 10.9701i | − | 0.773768i | ||||||
\(202\) | 17.6676i | 1.24309i | ||||||||
\(203\) | − | 0.0591871i | − | 0.00415412i | ||||||
\(204\) | 0.149256 | 0.0104500 | ||||||||
\(205\) | −0.201965 | −0.0141058 | ||||||||
\(206\) | − | 14.3945i | − | 1.00291i | ||||||
\(207\) | −0.704722 | −0.0489815 | ||||||||
\(208\) | −14.3914 | + | 3.01130i | −0.997864 | + | 0.208796i | ||||
\(209\) | 2.02597 | 0.140139 | ||||||||
\(210\) | − | 0.147831i | − | 0.0102013i | ||||||
\(211\) | −16.6404 | −1.14557 | −0.572786 | − | 0.819705i | \(-0.694138\pi\) | ||||
−0.572786 | + | 0.819705i | \(0.694138\pi\) | |||||||
\(212\) | 0.423980 | 0.0291191 | ||||||||
\(213\) | 1.96928i | 0.134933i | ||||||||
\(214\) | 8.82329i | 0.603147i | ||||||||
\(215\) | − | 0.320890i | − | 0.0218845i | ||||||
\(216\) | 2.79963i | 0.190491i | ||||||||
\(217\) | −3.17378 | −0.215450 | ||||||||
\(218\) | −6.64007 | −0.449722 | ||||||||
\(219\) | − | 15.3057i | − | 1.03427i | ||||||
\(220\) | −0.00241041 | −0.000162510 | ||||||||
\(221\) | −13.2554 | + | 2.77359i | −0.891652 | + | 0.186572i | ||||
\(222\) | 12.6063 | 0.846079 | ||||||||
\(223\) | 29.6492i | 1.98546i | 0.120372 | + | 0.992729i | \(0.461591\pi\) | ||||
−0.120372 | + | 0.992729i | \(0.538409\pi\) | |||||||
\(224\) | 0.383543 | 0.0256265 | ||||||||
\(225\) | 4.99632 | 0.333088 | ||||||||
\(226\) | 12.8416i | 0.854208i | ||||||||
\(227\) | − | 2.17847i | − | 0.144590i | −0.997383 | − | 0.0722951i | \(-0.976968\pi\) | ||
0.997383 | − | 0.0722951i | \(-0.0230323\pi\) | |||||||
\(228\) | − | 0.0805084i | − | 0.00533180i | ||||||
\(229\) | 2.89071i | 0.191024i | 0.995428 | + | 0.0955118i | \(0.0304488\pi\) | ||||
−0.995428 | + | 0.0955118i | \(0.969551\pi\) | |||||||
\(230\) | 0.0610503 | 0.00402554 | ||||||||
\(231\) | 1.70646 | 0.112277 | ||||||||
\(232\) | − | 0.0971031i | − | 0.00637513i | ||||||
\(233\) | −8.88961 | −0.582377 | −0.291189 | − | 0.956666i | \(-0.594051\pi\) | ||||
−0.291189 | + | 0.956666i | \(0.594051\pi\) | |||||||
\(234\) | 1.05464 | + | 5.04027i | 0.0689441 | + | 0.329493i | ||||
\(235\) | 0.366747 | 0.0239239 | ||||||||
\(236\) | 0.132943i | 0.00865382i | ||||||||
\(237\) | 10.5938 | 0.688144 | ||||||||
\(238\) | 9.15392 | 0.593361 | ||||||||
\(239\) | 28.4940i | 1.84313i | 0.388229 | + | 0.921563i | \(0.373087\pi\) | ||||
−0.388229 | + | 0.921563i | \(0.626913\pi\) | |||||||
\(240\) | − | 0.247354i | − | 0.0159666i | ||||||
\(241\) | 15.6266i | 1.00660i | 0.864112 | + | 0.503299i | \(0.167881\pi\) | ||||
−0.864112 | + | 0.503299i | \(0.832119\pi\) | |||||||
\(242\) | − | 1.42819i | − | 0.0918078i | ||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.129847 | −0.00831260 | ||||||||
\(245\) | 0.247967i | 0.0158420i | ||||||||
\(246\) | −4.75532 | −0.303188 | ||||||||
\(247\) | 1.49607 | + | 7.14991i | 0.0951926 | + | 0.454938i | ||||
\(248\) | −5.20695 | −0.330641 | ||||||||
\(249\) | 4.19820i | 0.266050i | ||||||||
\(250\) | −0.865985 | −0.0547697 | ||||||||
\(251\) | −20.7286 | −1.30838 | −0.654189 | − | 0.756331i | \(-0.726990\pi\) | ||||
−0.654189 | + | 0.756331i | \(0.726990\pi\) | |||||||
\(252\) | − | 0.0678114i | − | 0.00427172i | ||||||
\(253\) | 0.704722i | 0.0443055i | ||||||||
\(254\) | − | 2.49210i | − | 0.156368i | ||||||
\(255\) | − | 0.227828i | − | 0.0142672i | ||||||
\(256\) | 0.953341 | 0.0595838 | ||||||||
\(257\) | 1.38511 | 0.0864008 | 0.0432004 | − | 0.999066i | \(-0.486245\pi\) | ||||
0.0432004 | + | 0.999066i | \(0.486245\pi\) | |||||||
\(258\) | − | 7.55546i | − | 0.470383i | ||||||
\(259\) | 15.0624 | 0.935935 | ||||||||
\(260\) | −0.00177995 | − | 0.00850662i | −0.000110388 | − | 0.000527558i | ||||
\(261\) | −0.0346842 | −0.00214690 | ||||||||
\(262\) | − | 19.8463i | − | 1.22611i | ||||||
\(263\) | −17.4668 | −1.07705 | −0.538524 | − | 0.842610i | \(-0.681018\pi\) | ||||
−0.538524 | + | 0.842610i | \(0.681018\pi\) | |||||||
\(264\) | 2.79963 | 0.172306 | ||||||||
\(265\) | − | 0.647174i | − | 0.0397556i | ||||||
\(266\) | − | 4.93760i | − | 0.302744i | ||||||
\(267\) | − | 14.3643i | − | 0.879080i | ||||||
\(268\) | 0.435929i | 0.0266286i | ||||||||
\(269\) | 0.559556 | 0.0341167 | 0.0170584 | − | 0.999854i | \(-0.494570\pi\) | ||||
0.0170584 | + | 0.999854i | \(0.494570\pi\) | |||||||
\(270\) | −0.0866304 | −0.00527216 | ||||||||
\(271\) | 13.2324i | 0.803810i | 0.915681 | + | 0.401905i | \(0.131652\pi\) | ||||
−0.915681 | + | 0.401905i | \(0.868348\pi\) | |||||||
\(272\) | 15.3166 | 0.928702 | ||||||||
\(273\) | 1.26012 | + | 6.02229i | 0.0762662 | + | 0.364486i | ||||
\(274\) | 4.41053 | 0.266450 | ||||||||
\(275\) | − | 4.99632i | − | 0.301289i | ||||||
\(276\) | 0.0280043 | 0.00168566 | ||||||||
\(277\) | 18.4921 | 1.11108 | 0.555541 | − | 0.831489i | \(-0.312511\pi\) | ||||
0.555541 | + | 0.831489i | \(0.312511\pi\) | |||||||
\(278\) | 2.75480i | 0.165222i | ||||||||
\(279\) | 1.85987i | 0.111347i | ||||||||
\(280\) | − | 0.289787i | − | 0.0173181i | ||||||
\(281\) | − | 25.8276i | − | 1.54075i | −0.637593 | − | 0.770373i | \(-0.720070\pi\) | ||
0.637593 | − | 0.770373i | \(-0.279930\pi\) | |||||||
\(282\) | 8.63517 | 0.514217 | ||||||||
\(283\) | −6.19965 | −0.368531 | −0.184265 | − | 0.982877i | \(-0.558991\pi\) | ||||
−0.184265 | + | 0.982877i | \(0.558991\pi\) | |||||||
\(284\) | − | 0.0782556i | − | 0.00464362i | ||||||
\(285\) | −0.122890 | −0.00727938 | ||||||||
\(286\) | 5.04027 | − | 1.05464i | 0.298037 | − | 0.0623623i | ||||
\(287\) | −5.68182 | −0.335387 | ||||||||
\(288\) | − | 0.224760i | − | 0.0132441i | ||||||
\(289\) | −2.89252 | −0.170148 | ||||||||
\(290\) | 0.00300470 | 0.000176442 | ||||||||
\(291\) | 5.86228i | 0.343653i | ||||||||
\(292\) | 0.608221i | 0.0355934i | ||||||||
\(293\) | 8.49366i | 0.496205i | 0.968734 | + | 0.248102i | \(0.0798070\pi\) | ||||
−0.968734 | + | 0.248102i | \(0.920193\pi\) | |||||||
\(294\) | 5.83846i | 0.340506i | ||||||||
\(295\) | 0.202927 | 0.0118149 | ||||||||
\(296\) | 24.7116 | 1.43633 | ||||||||
\(297\) | − | 1.00000i | − | 0.0580259i | ||||||
\(298\) | −12.9279 | −0.748893 | ||||||||
\(299\) | −2.48705 | + | 0.520398i | −0.143830 | + | 0.0300954i | ||||
\(300\) | −0.198544 | −0.0114630 | ||||||||
\(301\) | − | 9.02753i | − | 0.520338i | ||||||
\(302\) | 3.49139 | 0.200907 | ||||||||
\(303\) | 12.3706 | 0.710672 | ||||||||
\(304\) | − | 8.26171i | − | 0.473842i | ||||||
\(305\) | 0.198202i | 0.0113490i | ||||||||
\(306\) | − | 5.36429i | − | 0.306656i | ||||||
\(307\) | 10.6196i | 0.606095i | 0.952976 | + | 0.303047i | \(0.0980040\pi\) | ||||
−0.952976 | + | 0.303047i | \(0.901996\pi\) | |||||||
\(308\) | −0.0678114 | −0.00386391 | ||||||||
\(309\) | −10.0788 | −0.573363 | ||||||||
\(310\) | − | 0.161121i | − | 0.00915105i | ||||||
\(311\) | 27.5052 | 1.55968 | 0.779838 | − | 0.625981i | \(-0.215301\pi\) | ||||
0.779838 | + | 0.625981i | \(0.215301\pi\) | |||||||
\(312\) | 2.06738 | + | 9.88025i | 0.117042 | + | 0.559359i | ||||
\(313\) | 0.791246 | 0.0447239 | 0.0223619 | − | 0.999750i | \(-0.492881\pi\) | ||||
0.0223619 | + | 0.999750i | \(0.492881\pi\) | |||||||
\(314\) | − | 12.0367i | − | 0.679271i | ||||||
\(315\) | −0.103509 | −0.00583207 | ||||||||
\(316\) | −0.420980 | −0.0236820 | ||||||||
\(317\) | − | 10.4687i | − | 0.587983i | −0.955808 | − | 0.293991i | \(-0.905016\pi\) | ||
0.955808 | − | 0.293991i | \(-0.0949837\pi\) | |||||||
\(318\) | − | 15.2379i | − | 0.854500i | ||||||
\(319\) | 0.0346842i | 0.00194194i | ||||||||
\(320\) | − | 0.475237i | − | 0.0265666i | ||||||
\(321\) | 6.17793 | 0.344819 | ||||||||
\(322\) | 1.71751 | 0.0957133 | ||||||||
\(323\) | − | 7.60954i | − | 0.423406i | ||||||
\(324\) | −0.0397381 | −0.00220767 | ||||||||
\(325\) | 17.6326 | − | 3.68951i | 0.978082 | − | 0.204657i | ||||
\(326\) | −24.8462 | −1.37610 | ||||||||
\(327\) | 4.64928i | 0.257106i | ||||||||
\(328\) | −9.32167 | −0.514703 | ||||||||
\(329\) | 10.3176 | 0.568828 | ||||||||
\(330\) | 0.0866304i | 0.00476884i | ||||||||
\(331\) | 21.1531i | 1.16268i | 0.813661 | + | 0.581339i | \(0.197471\pi\) | ||||
−0.813661 | + | 0.581339i | \(0.802529\pi\) | |||||||
\(332\) | − | 0.166829i | − | 0.00915591i | ||||||
\(333\) | − | 8.82674i | − | 0.483702i | ||||||
\(334\) | 1.50109 | 0.0821361 | ||||||||
\(335\) | 0.665414 | 0.0363554 | ||||||||
\(336\) | − | 6.95876i | − | 0.379631i | ||||||
\(337\) | 4.33688 | 0.236245 | 0.118123 | − | 0.992999i | \(-0.462312\pi\) | ||||
0.118123 | + | 0.992999i | \(0.462312\pi\) | |||||||
\(338\) | 7.44392 | + | 17.0089i | 0.404896 | + | 0.925164i | ||||
\(339\) | 8.99146 | 0.488349 | ||||||||
\(340\) | 0.00905347i | 0.000490993i | ||||||||
\(341\) | 1.85987 | 0.100717 | ||||||||
\(342\) | −2.89348 | −0.156462 | ||||||||
\(343\) | 18.9212i | 1.02165i | ||||||||
\(344\) | − | 14.8107i | − | 0.798539i | ||||||
\(345\) | − | 0.0427465i | − | 0.00230139i | ||||||
\(346\) | − | 26.6578i | − | 1.43313i | ||||||
\(347\) | −10.5906 | −0.568532 | −0.284266 | − | 0.958745i | \(-0.591750\pi\) | ||||
−0.284266 | + | 0.958745i | \(0.591750\pi\) | |||||||
\(348\) | 0.00137828 | 7.38838e−5 | ||||||||
\(349\) | − | 24.3761i | − | 1.30482i | −0.757864 | − | 0.652412i | \(-0.773757\pi\) | ||
0.757864 | − | 0.652412i | \(-0.226243\pi\) | |||||||
\(350\) | −12.1768 | −0.650877 | ||||||||
\(351\) | 3.52912 | − | 0.738445i | 0.188371 | − | 0.0394153i | ||||
\(352\) | −0.224760 | −0.0119797 | ||||||||
\(353\) | − | 21.4564i | − | 1.14201i | −0.820947 | − | 0.571004i | \(-0.806554\pi\) | ||
0.820947 | − | 0.571004i | \(-0.193446\pi\) | |||||||
\(354\) | 4.77798 | 0.253947 | ||||||||
\(355\) | −0.119451 | −0.00633982 | ||||||||
\(356\) | 0.570810i | 0.0302528i | ||||||||
\(357\) | − | 6.40944i | − | 0.339224i | ||||||
\(358\) | 34.6255i | 1.83002i | ||||||||
\(359\) | 33.2863i | 1.75679i | 0.477939 | + | 0.878393i | \(0.341384\pi\) | ||||
−0.477939 | + | 0.878393i | \(0.658616\pi\) | |||||||
\(360\) | −0.169818 | −0.00895020 | ||||||||
\(361\) | 14.8954 | 0.783970 | ||||||||
\(362\) | − | 29.8851i | − | 1.57073i | ||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −0.0500750 | − | 0.239315i | −0.00262464 | − | 0.0125435i | ||||
\(365\) | 0.928404 | 0.0485949 | ||||||||
\(366\) | 4.66672i | 0.243933i | ||||||||
\(367\) | 15.3463 | 0.801073 | 0.400536 | − | 0.916281i | \(-0.368824\pi\) | ||||
0.400536 | + | 0.916281i | \(0.368824\pi\) | |||||||
\(368\) | 2.87378 | 0.149806 | ||||||||
\(369\) | 3.32960i | 0.173332i | ||||||||
\(370\) | 0.764663i | 0.0397529i | ||||||||
\(371\) | − | 18.2068i | − | 0.945250i | ||||||
\(372\) | − | 0.0739076i | − | 0.00383193i | ||||||
\(373\) | −22.1576 | −1.14728 | −0.573638 | − | 0.819109i | \(-0.694469\pi\) | ||||
−0.573638 | + | 0.819109i | \(0.694469\pi\) | |||||||
\(374\) | −5.36429 | −0.277381 | ||||||||
\(375\) | 0.606350i | 0.0313118i | ||||||||
\(376\) | 16.9272 | 0.872954 | ||||||||
\(377\) | −0.122405 | + | 0.0256124i | −0.00630416 | + | 0.00131910i | ||||
\(378\) | −2.43715 | −0.125354 | ||||||||
\(379\) | − | 21.0884i | − | 1.08324i | −0.840624 | − | 0.541619i | \(-0.817812\pi\) | ||
0.840624 | − | 0.541619i | \(-0.182188\pi\) | |||||||
\(380\) | 0.00488342 | 0.000250514 | ||||||||
\(381\) | −1.74493 | −0.0893955 | ||||||||
\(382\) | 3.95764i | 0.202490i | ||||||||
\(383\) | 6.90976i | 0.353072i | 0.984294 | + | 0.176536i | \(0.0564892\pi\) | ||||
−0.984294 | + | 0.176536i | \(0.943511\pi\) | |||||||
\(384\) | − | 11.6391i | − | 0.593957i | ||||||
\(385\) | 0.103509i | 0.00527531i | ||||||||
\(386\) | −12.1502 | −0.618431 | ||||||||
\(387\) | −5.29022 | −0.268917 | ||||||||
\(388\) | − | 0.232956i | − | 0.0118265i | ||||||
\(389\) | 32.7232 | 1.65913 | 0.829565 | − | 0.558410i | \(-0.188588\pi\) | ||||
0.829565 | + | 0.558410i | \(0.188588\pi\) | |||||||
\(390\) | −0.305729 | + | 0.0639717i | −0.0154812 | + | 0.00323933i | ||||
\(391\) | 2.64693 | 0.133861 | ||||||||
\(392\) | 11.4449i | 0.578056i | ||||||||
\(393\) | −13.8961 | −0.700966 | ||||||||
\(394\) | 20.6056 | 1.03810 | ||||||||
\(395\) | 0.642594i | 0.0323324i | ||||||||
\(396\) | 0.0397381i | 0.00199692i | ||||||||
\(397\) | 10.1016i | 0.506987i | 0.967337 | + | 0.253494i | \(0.0815797\pi\) | ||||
−0.967337 | + | 0.253494i | \(0.918420\pi\) | |||||||
\(398\) | − | 22.7585i | − | 1.14078i | ||||||
\(399\) | −3.45724 | −0.173078 | ||||||||
\(400\) | −20.3745 | −1.01872 | ||||||||
\(401\) | − | 18.3377i | − | 0.915739i | −0.889019 | − | 0.457870i | \(-0.848613\pi\) | ||
0.889019 | − | 0.457870i | \(-0.151387\pi\) | |||||||
\(402\) | 15.6674 | 0.781417 | ||||||||
\(403\) | 1.37341 | + | 6.56369i | 0.0684144 | + | 0.326961i | ||||
\(404\) | −0.491584 | −0.0244572 | ||||||||
\(405\) | 0.0606573i | 0.00301408i | ||||||||
\(406\) | 0.0845306 | 0.00419518 | ||||||||
\(407\) | −8.82674 | −0.437525 | ||||||||
\(408\) | − | 10.5154i | − | 0.520590i | ||||||
\(409\) | − | 5.60283i | − | 0.277042i | −0.990359 | − | 0.138521i | \(-0.955765\pi\) | ||
0.990359 | − | 0.138521i | \(-0.0442349\pi\) | |||||||
\(410\) | − | 0.288445i | − | 0.0142453i | ||||||
\(411\) | − | 3.08818i | − | 0.152329i | ||||||
\(412\) | 0.400513 | 0.0197318 | ||||||||
\(413\) | 5.70890 | 0.280916 | ||||||||
\(414\) | − | 1.00648i | − | 0.0494657i | ||||||
\(415\) | −0.254651 | −0.0125003 | ||||||||
\(416\) | −0.165973 | − | 0.793204i | −0.00813748 | − | 0.0388900i | ||||
\(417\) | 1.92887 | 0.0944572 | ||||||||
\(418\) | 2.89348i | 0.141525i | ||||||||
\(419\) | −24.6413 | −1.20380 | −0.601902 | − | 0.798570i | \(-0.705590\pi\) | ||||
−0.601902 | + | 0.798570i | \(0.705590\pi\) | |||||||
\(420\) | 0.00411325 | 0.000200706 | ||||||||
\(421\) | 25.4002i | 1.23793i | 0.785419 | + | 0.618964i | \(0.212447\pi\) | ||||
−0.785419 | + | 0.618964i | \(0.787553\pi\) | |||||||
\(422\) | − | 23.7657i | − | 1.15690i | ||||||
\(423\) | − | 6.04622i | − | 0.293977i | ||||||
\(424\) | − | 29.8703i | − | 1.45063i | ||||||
\(425\) | −18.7661 | −0.910292 | ||||||||
\(426\) | −2.81252 | −0.136267 | ||||||||
\(427\) | 5.57596i | 0.269840i | ||||||||
\(428\) | −0.245499 | −0.0118667 | ||||||||
\(429\) | −0.738445 | − | 3.52912i | −0.0356525 | − | 0.170388i | ||||
\(430\) | 0.458294 | 0.0221009 | ||||||||
\(431\) | 33.6254i | 1.61968i | 0.586653 | + | 0.809838i | \(0.300445\pi\) | ||||
−0.586653 | + | 0.809838i | \(0.699555\pi\) | |||||||
\(432\) | −4.07790 | −0.196198 | ||||||||
\(433\) | −9.72637 | −0.467420 | −0.233710 | − | 0.972306i | \(-0.575087\pi\) | ||||
−0.233710 | + | 0.972306i | \(0.575087\pi\) | |||||||
\(434\) | − | 4.53278i | − | 0.217580i | ||||||
\(435\) | − | 0.00210385i | − | 0.000100872i | ||||||
\(436\) | − | 0.184754i | − | 0.00884809i | ||||||
\(437\) | − | 1.42775i | − | 0.0682984i | ||||||
\(438\) | 21.8595 | 1.04449 | ||||||||
\(439\) | −17.0758 | −0.814986 | −0.407493 | − | 0.913208i | \(-0.633597\pi\) | ||||
−0.407493 | + | 0.913208i | \(0.633597\pi\) | |||||||
\(440\) | 0.169818i | 0.00809576i | ||||||||
\(441\) | 4.08800 | 0.194667 | ||||||||
\(442\) | −3.96123 | − | 18.9312i | −0.188416 | − | 0.900466i | ||||
\(443\) | 21.8637 | 1.03878 | 0.519389 | − | 0.854538i | \(-0.326160\pi\) | ||||
0.519389 | + | 0.854538i | \(0.326160\pi\) | |||||||
\(444\) | 0.350758i | 0.0166462i | ||||||||
\(445\) | 0.871298 | 0.0413035 | ||||||||
\(446\) | −42.3448 | −2.00509 | ||||||||
\(447\) | 9.05192i | 0.428141i | ||||||||
\(448\) | − | 13.3697i | − | 0.631661i | ||||||
\(449\) | 8.95803i | 0.422755i | 0.977404 | + | 0.211378i | \(0.0677950\pi\) | ||||
−0.977404 | + | 0.211378i | \(0.932205\pi\) | |||||||
\(450\) | 7.13572i | 0.336381i | ||||||||
\(451\) | 3.32960 | 0.156785 | ||||||||
\(452\) | −0.357304 | −0.0168062 | ||||||||
\(453\) | − | 2.44462i | − | 0.114858i | ||||||
\(454\) | 3.11128 | 0.146020 | ||||||||
\(455\) | −0.365296 | + | 0.0764357i | −0.0171253 | + | 0.00358336i | ||||
\(456\) | −5.67198 | −0.265615 | ||||||||
\(457\) | − | 37.7837i | − | 1.76744i | −0.468011 | − | 0.883722i | \(-0.655029\pi\) | ||
0.468011 | − | 0.883722i | \(-0.344971\pi\) | |||||||
\(458\) | −4.12850 | −0.192912 | ||||||||
\(459\) | −3.75599 | −0.175315 | ||||||||
\(460\) | 0.00169867i | 7.92007e-5i | ||||||||
\(461\) | − | 6.10348i | − | 0.284268i | −0.989847 | − | 0.142134i | \(-0.954604\pi\) | ||
0.989847 | − | 0.142134i | \(-0.0453963\pi\) | |||||||
\(462\) | 2.43715i | 0.113387i | ||||||||
\(463\) | 37.1501i | 1.72651i | 0.504768 | + | 0.863255i | \(0.331578\pi\) | ||||
−0.504768 | + | 0.863255i | \(0.668422\pi\) | |||||||
\(464\) | 0.141439 | 0.00656612 | ||||||||
\(465\) | −0.112814 | −0.00523164 | ||||||||
\(466\) | − | 12.6961i | − | 0.588135i | ||||||
\(467\) | 10.3642 | 0.479598 | 0.239799 | − | 0.970823i | \(-0.422919\pi\) | ||||
0.239799 | + | 0.970823i | \(0.422919\pi\) | |||||||
\(468\) | −0.140241 | + | 0.0293444i | −0.00648263 | + | 0.00135645i | ||||
\(469\) | 18.7199 | 0.864406 | ||||||||
\(470\) | 0.523786i | 0.0241604i | ||||||||
\(471\) | −8.42793 | −0.388338 | ||||||||
\(472\) | 9.36608 | 0.431109 | ||||||||
\(473\) | 5.29022i | 0.243245i | ||||||||
\(474\) | 15.1301i | 0.694947i | ||||||||
\(475\) | 10.1224i | 0.464448i | ||||||||
\(476\) | 0.254699i | 0.0116741i | ||||||||
\(477\) | −10.6694 | −0.488516 | ||||||||
\(478\) | −40.6950 | −1.86135 | ||||||||
\(479\) | − | 20.4038i | − | 0.932273i | −0.884713 | − | 0.466136i | \(-0.845646\pi\) | ||
0.884713 | − | 0.466136i | \(-0.154354\pi\) | |||||||
\(480\) | 0.0136333 | 0.000622273 | ||||||||
\(481\) | −6.51806 | − | 31.1506i | −0.297198 | − | 1.42035i | ||||
\(482\) | −22.3178 | −1.01655 | ||||||||
\(483\) | − | 1.20258i | − | 0.0547191i | ||||||
\(484\) | 0.0397381 | 0.00180628 | ||||||||
\(485\) | −0.355590 | −0.0161465 | ||||||||
\(486\) | 1.42819i | 0.0647842i | ||||||||
\(487\) | 18.1762i | 0.823644i | 0.911264 | + | 0.411822i | \(0.135107\pi\) | ||||
−0.911264 | + | 0.411822i | \(0.864893\pi\) | |||||||
\(488\) | 9.14799i | 0.414110i | ||||||||
\(489\) | 17.3969i | 0.786716i | ||||||||
\(490\) | −0.354145 | −0.0159987 | ||||||||
\(491\) | 19.2029 | 0.866613 | 0.433307 | − | 0.901247i | \(-0.357347\pi\) | ||||
0.433307 | + | 0.901247i | \(0.357347\pi\) | |||||||
\(492\) | − | 0.132312i | − | 0.00596509i | ||||||
\(493\) | 0.130274 | 0.00586723 | ||||||||
\(494\) | −10.2115 | + | 2.13668i | −0.459435 | + | 0.0961337i | ||||
\(495\) | 0.0606573 | 0.00272634 | ||||||||
\(496\) | − | 7.58434i | − | 0.340547i | ||||||
\(497\) | −3.36050 | −0.150739 | ||||||||
\(498\) | −5.99585 | −0.268680 | ||||||||
\(499\) | − | 6.46441i | − | 0.289387i | −0.989477 | − | 0.144693i | \(-0.953780\pi\) | ||
0.989477 | − | 0.144693i | \(-0.0462196\pi\) | |||||||
\(500\) | − | 0.0240952i | − | 0.00107757i | ||||||
\(501\) | − | 1.05104i | − | 0.0469571i | ||||||
\(502\) | − | 29.6045i | − | 1.32131i | ||||||
\(503\) | −23.6756 | −1.05564 | −0.527821 | − | 0.849355i | \(-0.676991\pi\) | ||||
−0.527821 | + | 0.849355i | \(0.676991\pi\) | |||||||
\(504\) | −4.77746 | −0.212805 | ||||||||
\(505\) | 0.750367i | 0.0333909i | ||||||||
\(506\) | −1.00648 | −0.0447435 | ||||||||
\(507\) | 11.9094 | − | 5.21212i | 0.528915 | − | 0.231479i | ||||
\(508\) | 0.0693402 | 0.00307648 | ||||||||
\(509\) | 29.5632i | 1.31037i | 0.755470 | + | 0.655183i | \(0.227409\pi\) | ||||
−0.755470 | + | 0.655183i | \(0.772591\pi\) | |||||||
\(510\) | 0.325383 | 0.0144082 | ||||||||
\(511\) | 26.1186 | 1.15542 | ||||||||
\(512\) | − | 21.9167i | − | 0.968590i | ||||||
\(513\) | 2.02597i | 0.0894489i | ||||||||
\(514\) | 1.97821i | 0.0872550i | ||||||||
\(515\) | − | 0.611353i | − | 0.0269394i | ||||||
\(516\) | 0.210223 | 0.00925457 | ||||||||
\(517\) | −6.04622 | −0.265912 | ||||||||
\(518\) | 21.5121i | 0.945187i | ||||||||
\(519\) | −18.6654 | −0.819320 | ||||||||
\(520\) | −0.599309 | + | 0.125401i | −0.0262814 | + | 0.00549921i | ||||
\(521\) | 35.0790 | 1.53684 | 0.768420 | − | 0.639946i | \(-0.221043\pi\) | ||||
0.768420 | + | 0.639946i | \(0.221043\pi\) | |||||||
\(522\) | − | 0.0495358i | − | 0.00216812i | ||||||
\(523\) | 12.7792 | 0.558797 | 0.279399 | − | 0.960175i | \(-0.409865\pi\) | ||||
0.279399 | + | 0.960175i | \(0.409865\pi\) | |||||||
\(524\) | 0.552205 | 0.0241232 | ||||||||
\(525\) | 8.52601i | 0.372105i | ||||||||
\(526\) | − | 24.9459i | − | 1.08769i | ||||||
\(527\) | − | 6.98564i | − | 0.304299i | ||||||
\(528\) | 4.07790i | 0.177468i | ||||||||
\(529\) | −22.5034 | −0.978407 | ||||||||
\(530\) | 0.924290 | 0.0401486 | ||||||||
\(531\) | − | 3.34547i | − | 0.145181i | ||||||
\(532\) | 0.137384 | 0.00595635 | ||||||||
\(533\) | 2.45873 | + | 11.7506i | 0.106499 | + | 0.508974i | ||||
\(534\) | 20.5150 | 0.887770 | ||||||||
\(535\) | 0.374737i | 0.0162013i | ||||||||
\(536\) | 30.7121 | 1.32656 | ||||||||
\(537\) | 24.2443 | 1.04622 | ||||||||
\(538\) | 0.799155i | 0.0344540i | ||||||||
\(539\) | − | 4.08800i | − | 0.176083i | ||||||
\(540\) | − | 0.00241041i | − | 0.000103727i | ||||||
\(541\) | − | 16.4144i | − | 0.705711i | −0.935678 | − | 0.352856i | \(-0.885211\pi\) | ||
0.935678 | − | 0.352856i | \(-0.114789\pi\) | |||||||
\(542\) | −18.8984 | −0.811756 | ||||||||
\(543\) | −20.9251 | −0.897982 | ||||||||
\(544\) | 0.844196i | 0.0361946i | ||||||||
\(545\) | −0.282013 | −0.0120801 | ||||||||
\(546\) | −8.60100 | + | 1.79970i | −0.368089 | + | 0.0770201i | ||||
\(547\) | −30.0865 | −1.28640 | −0.643202 | − | 0.765696i | \(-0.722395\pi\) | ||||
−0.643202 | + | 0.765696i | \(0.722395\pi\) | |||||||
\(548\) | 0.122719i | 0.00524228i | ||||||||
\(549\) | 3.26757 | 0.139456 | ||||||||
\(550\) | 7.13572 | 0.304268 | ||||||||
\(551\) | − | 0.0702692i | − | 0.00299357i | ||||||
\(552\) | − | 1.97296i | − | 0.0839749i | ||||||
\(553\) | 18.0779i | 0.768753i | ||||||||
\(554\) | 26.4103i | 1.12207i | ||||||||
\(555\) | 0.535406 | 0.0227267 | ||||||||
\(556\) | −0.0766497 | −0.00325067 | ||||||||
\(557\) | 9.18200i | 0.389054i | 0.980897 | + | 0.194527i | \(0.0623171\pi\) | ||||
−0.980897 | + | 0.194527i | \(0.937683\pi\) | |||||||
\(558\) | −2.65625 | −0.112448 | ||||||||
\(559\) | −18.6698 | + | 3.90654i | −0.789650 | + | 0.165229i | ||||
\(560\) | 0.422099 | 0.0178369 | ||||||||
\(561\) | 3.75599i | 0.158578i | ||||||||
\(562\) | 36.8868 | 1.55598 | ||||||||
\(563\) | 15.8217 | 0.666804 | 0.333402 | − | 0.942785i | \(-0.391803\pi\) | ||||
0.333402 | + | 0.942785i | \(0.391803\pi\) | |||||||
\(564\) | 0.240265i | 0.0101170i | ||||||||
\(565\) | 0.545398i | 0.0229451i | ||||||||
\(566\) | − | 8.85430i | − | 0.372174i | ||||||
\(567\) | 1.70646i | 0.0716645i | ||||||||
\(568\) | −5.51327 | −0.231332 | ||||||||
\(569\) | 35.8645 | 1.50352 | 0.751760 | − | 0.659437i | \(-0.229205\pi\) | ||||
0.751760 | + | 0.659437i | \(0.229205\pi\) | |||||||
\(570\) | − | 0.175511i | − | 0.00735134i | ||||||
\(571\) | −0.130007 | −0.00544063 | −0.00272032 | − | 0.999996i | \(-0.500866\pi\) | ||||
−0.00272032 | + | 0.999996i | \(0.500866\pi\) | |||||||
\(572\) | 0.0293444 | + | 0.140241i | 0.00122695 | + | 0.00586376i | ||||
\(573\) | 2.77108 | 0.115763 | ||||||||
\(574\) | − | 8.11474i | − | 0.338703i | ||||||
\(575\) | −3.52101 | −0.146836 | ||||||||
\(576\) | −7.83479 | −0.326450 | ||||||||
\(577\) | − | 24.3812i | − | 1.01500i | −0.861650 | − | 0.507502i | \(-0.830569\pi\) | ||
0.861650 | − | 0.507502i | \(-0.169431\pi\) | |||||||
\(578\) | − | 4.13108i | − | 0.171830i | ||||||
\(579\) | 8.50742i | 0.353556i | ||||||||
\(580\) | 0 | 8.36030e-5i | 0 | 3.47143e-6i | ||||||
\(581\) | −7.16405 | −0.297215 | ||||||||
\(582\) | −8.37247 | −0.347050 | ||||||||
\(583\) | 10.6694i | 0.441880i | ||||||||
\(584\) | 42.8504 | 1.77316 | ||||||||
\(585\) | 0.0447920 | + | 0.214067i | 0.00185192 | + | 0.00885058i | ||||
\(586\) | −12.1306 | −0.501110 | ||||||||
\(587\) | 6.61208i | 0.272910i | 0.990646 | + | 0.136455i | \(0.0435709\pi\) | ||||
−0.990646 | + | 0.136455i | \(0.956429\pi\) | |||||||
\(588\) | −0.162450 | −0.00669931 | ||||||||
\(589\) | −3.76804 | −0.155259 | ||||||||
\(590\) | 0.289819i | 0.0119317i | ||||||||
\(591\) | − | 14.4278i | − | 0.593479i | ||||||
\(592\) | 35.9945i | 1.47937i | ||||||||
\(593\) | 26.4128i | 1.08464i | 0.840170 | + | 0.542322i | \(0.182455\pi\) | ||||
−0.840170 | + | 0.542322i | \(0.817545\pi\) | |||||||
\(594\) | 1.42819 | 0.0585995 | ||||||||
\(595\) | 0.388779 | 0.0159384 | ||||||||
\(596\) | − | 0.359706i | − | 0.0147342i | ||||||
\(597\) | −15.9351 | −0.652182 | ||||||||
\(598\) | −0.743229 | − | 3.55199i | −0.0303929 | − | 0.145252i | ||||
\(599\) | 21.4702 | 0.877248 | 0.438624 | − | 0.898671i | \(-0.355466\pi\) | ||||
0.438624 | + | 0.898671i | \(0.355466\pi\) | |||||||
\(600\) | 13.9879i | 0.571052i | ||||||||
\(601\) | −9.57861 | −0.390720 | −0.195360 | − | 0.980732i | \(-0.562587\pi\) | ||||
−0.195360 | + | 0.980732i | \(0.562587\pi\) | |||||||
\(602\) | 12.8931 | 0.525482 | ||||||||
\(603\) | − | 10.9701i | − | 0.446735i | ||||||
\(604\) | 0.0971446i | 0.00395276i | ||||||||
\(605\) | − | 0.0606573i | − | 0.00246607i | ||||||
\(606\) | 17.6676i | 0.717698i | ||||||||
\(607\) | −28.5549 | −1.15901 | −0.579504 | − | 0.814969i | \(-0.696754\pi\) | ||||
−0.579504 | + | 0.814969i | \(0.696754\pi\) | |||||||
\(608\) | 0.455357 | 0.0184672 | ||||||||
\(609\) | − | 0.0591871i | − | 0.00239838i | ||||||
\(610\) | −0.283070 | −0.0114612 | ||||||||
\(611\) | −4.46480 | − | 21.3378i | −0.180626 | − | 0.863236i | ||||
\(612\) | 0.149256 | 0.00603332 | ||||||||
\(613\) | − | 25.5390i | − | 1.03151i | −0.856736 | − | 0.515755i | \(-0.827512\pi\) | ||
0.856736 | − | 0.515755i | \(-0.172488\pi\) | |||||||
\(614\) | −15.1669 | −0.612086 | ||||||||
\(615\) | −0.201965 | −0.00814400 | ||||||||
\(616\) | 4.77746i | 0.192489i | ||||||||
\(617\) | 33.4193i | 1.34541i | 0.739910 | + | 0.672706i | \(0.234868\pi\) | ||||
−0.739910 | + | 0.672706i | \(0.765132\pi\) | |||||||
\(618\) | − | 14.3945i | − | 0.579031i | ||||||
\(619\) | − | 34.5887i | − | 1.39024i | −0.718895 | − | 0.695119i | \(-0.755352\pi\) | ||
0.718895 | − | 0.695119i | \(-0.244648\pi\) | |||||||
\(620\) | 0.00448303 | 0.000180043 | ||||||||
\(621\) | −0.704722 | −0.0282795 | ||||||||
\(622\) | 39.2827i | 1.57509i | ||||||||
\(623\) | 24.5120 | 0.982054 | ||||||||
\(624\) | −14.3914 | + | 3.01130i | −0.576117 | + | 0.120549i | ||||
\(625\) | 24.9448 | 0.997793 | ||||||||
\(626\) | 1.13005i | 0.0451660i | ||||||||
\(627\) | 2.02597 | 0.0809096 | ||||||||
\(628\) | 0.334910 | 0.0133644 | ||||||||
\(629\) | 33.1532i | 1.32190i | ||||||||
\(630\) | − | 0.147831i | − | 0.00588973i | ||||||
\(631\) | 12.7021i | 0.505662i | 0.967510 | + | 0.252831i | \(0.0813617\pi\) | ||||
−0.967510 | + | 0.252831i | \(0.918638\pi\) | |||||||
\(632\) | 29.6589i | 1.17977i | ||||||||
\(633\) | −16.6404 | −0.661397 | ||||||||
\(634\) | 14.9514 | 0.593796 | ||||||||
\(635\) | − | 0.105843i | − | 0.00420024i | ||||||
\(636\) | 0.423980 | 0.0168119 | ||||||||
\(637\) | 14.4271 | − | 3.01877i | 0.571621 | − | 0.119608i | ||||
\(638\) | −0.0495358 | −0.00196114 | ||||||||
\(639\) | 1.96928i | 0.0779036i | ||||||||
\(640\) | 0.705998 | 0.0279070 | ||||||||
\(641\) | 25.9825 | 1.02625 | 0.513124 | − | 0.858314i | \(-0.328488\pi\) | ||||
0.513124 | + | 0.858314i | \(0.328488\pi\) | |||||||
\(642\) | 8.82329i | 0.348227i | ||||||||
\(643\) | 32.8848i | 1.29685i | 0.761278 | + | 0.648425i | \(0.224572\pi\) | ||||
−0.761278 | + | 0.648425i | \(0.775428\pi\) | |||||||
\(644\) | 0.0477881i | 0.00188312i | ||||||||
\(645\) | − | 0.320890i | − | 0.0126350i | ||||||
\(646\) | 10.8679 | 0.427592 | ||||||||
\(647\) | −2.75086 | −0.108148 | −0.0540738 | − | 0.998537i | \(-0.517221\pi\) | ||||
−0.0540738 | + | 0.998537i | \(0.517221\pi\) | |||||||
\(648\) | 2.79963i | 0.109980i | ||||||||
\(649\) | −3.34547 | −0.131321 | ||||||||
\(650\) | 5.26933 | + | 25.1828i | 0.206680 | + | 0.987751i | ||||
\(651\) | −3.17378 | −0.124390 | ||||||||
\(652\) | − | 0.691321i | − | 0.0270742i | ||||||
\(653\) | 27.4851 | 1.07557 | 0.537787 | − | 0.843081i | \(-0.319260\pi\) | ||||
0.537787 | + | 0.843081i | \(0.319260\pi\) | |||||||
\(654\) | −6.64007 | −0.259647 | ||||||||
\(655\) | − | 0.842900i | − | 0.0329348i | ||||||
\(656\) | − | 13.5778i | − | 0.530123i | ||||||
\(657\) | − | 15.3057i | − | 0.597133i | ||||||
\(658\) | 14.7355i | 0.574451i | ||||||||
\(659\) | 17.2631 | 0.672474 | 0.336237 | − | 0.941777i | \(-0.390846\pi\) | ||||
0.336237 | + | 0.941777i | \(0.390846\pi\) | |||||||
\(660\) | −0.00241041 | −9.38249e−5 | ||||||||
\(661\) | 2.44386i | 0.0950551i | 0.998870 | + | 0.0475276i | \(0.0151342\pi\) | ||||
−0.998870 | + | 0.0475276i | \(0.984866\pi\) | |||||||
\(662\) | −30.2107 | −1.17417 | ||||||||
\(663\) | −13.2554 | + | 2.77359i | −0.514795 | + | 0.107717i | ||||
\(664\) | −11.7534 | −0.456122 | ||||||||
\(665\) | − | 0.209706i | − | 0.00813207i | ||||||
\(666\) | 12.6063 | 0.488484 | ||||||||
\(667\) | 0.0244427 | 0.000946425 | ||||||||
\(668\) | 0.0417664i | 0.00161599i | ||||||||
\(669\) | 29.6492i | 1.14630i | ||||||||
\(670\) | 0.950340i | 0.0367148i | ||||||||
\(671\) | − | 3.26757i | − | 0.126143i | ||||||
\(672\) | 0.383543 | 0.0147955 | ||||||||
\(673\) | −26.7842 | −1.03246 | −0.516228 | − | 0.856451i | \(-0.672664\pi\) | ||||
−0.516228 | + | 0.856451i | \(0.672664\pi\) | |||||||
\(674\) | 6.19391i | 0.238581i | ||||||||
\(675\) | 4.99632 | 0.192308 | ||||||||
\(676\) | −0.473257 | + | 0.207120i | −0.0182022 | + | 0.00796615i | ||||
\(677\) | −25.7769 | −0.990687 | −0.495343 | − | 0.868697i | \(-0.664958\pi\) | ||||
−0.495343 | + | 0.868697i | \(0.664958\pi\) | |||||||
\(678\) | 12.8416i | 0.493177i | ||||||||
\(679\) | −10.0037 | −0.383908 | ||||||||
\(680\) | 0.637836 | 0.0244599 | ||||||||
\(681\) | − | 2.17847i | − | 0.0834792i | ||||||
\(682\) | 2.65625i | 0.101713i | ||||||||
\(683\) | − | 12.8667i | − | 0.492329i | −0.969228 | − | 0.246165i | \(-0.920830\pi\) | ||
0.969228 | − | 0.246165i | \(-0.0791704\pi\) | |||||||
\(684\) | − | 0.0805084i | − | 0.00307831i | ||||||
\(685\) | 0.187321 | 0.00715716 | ||||||||
\(686\) | −27.0231 | −1.03175 | ||||||||
\(687\) | 2.89071i | 0.110288i | ||||||||
\(688\) | 21.5730 | 0.822462 | ||||||||
\(689\) | −37.6535 | + | 7.87873i | −1.43448 | + | 0.300156i | ||||
\(690\) | 0.0610503 | 0.00232414 | ||||||||
\(691\) | − | 33.9707i | − | 1.29230i | −0.763208 | − | 0.646152i | \(-0.776377\pi\) | ||
0.763208 | − | 0.646152i | \(-0.223623\pi\) | |||||||
\(692\) | 0.741728 | 0.0281963 | ||||||||
\(693\) | 1.70646 | 0.0648229 | ||||||||
\(694\) | − | 15.1254i | − | 0.574152i | ||||||
\(695\) | 0.117000i | 0.00443806i | ||||||||
\(696\) | − | 0.0971031i | − | 0.00368068i | ||||||
\(697\) | − | 12.5060i | − | 0.473697i | ||||||
\(698\) | 34.8138 | 1.31772 | ||||||||
\(699\) | −8.88961 | −0.336236 | ||||||||
\(700\) | − | 0.338807i | − | 0.0128057i | ||||||
\(701\) | 18.4719 | 0.697675 | 0.348837 | − | 0.937183i | \(-0.386577\pi\) | ||||
0.348837 | + | 0.937183i | \(0.386577\pi\) | |||||||
\(702\) | 1.05464 | + | 5.04027i | 0.0398049 | + | 0.190233i | ||||
\(703\) | 17.8827 | 0.674460 | ||||||||
\(704\) | 7.83479i | 0.295285i | ||||||||
\(705\) | 0.366747 | 0.0138125 | ||||||||
\(706\) | 30.6439 | 1.15330 | ||||||||
\(707\) | 21.1099i | 0.793919i | ||||||||
\(708\) | 0.132943i | 0.00499629i | ||||||||
\(709\) | − | 33.8830i | − | 1.27250i | −0.771482 | − | 0.636251i | \(-0.780484\pi\) | ||
0.771482 | − | 0.636251i | \(-0.219516\pi\) | |||||||
\(710\) | − | 0.170600i | − | 0.00640249i | ||||||
\(711\) | 10.5938 | 0.397300 | ||||||||
\(712\) | 40.2147 | 1.50711 | ||||||||
\(713\) | − | 1.31069i | − | 0.0490856i | ||||||
\(714\) | 9.15392 | 0.342577 | ||||||||
\(715\) | 0.214067 | − | 0.0447920i | 0.00800565 | − | 0.00167513i | ||||
\(716\) | −0.963422 | −0.0360048 | ||||||||
\(717\) | 28.4940i | 1.06413i | ||||||||
\(718\) | −47.5393 | −1.77415 | ||||||||
\(719\) | −31.1501 | −1.16170 | −0.580851 | − | 0.814010i | \(-0.697280\pi\) | ||||
−0.580851 | + | 0.814010i | \(0.697280\pi\) | |||||||
\(720\) | − | 0.247354i | − | 0.00921834i | ||||||
\(721\) | − | 17.1990i | − | 0.640526i | ||||||
\(722\) | 21.2736i | 0.791720i | ||||||||
\(723\) | 15.6266i | 0.581160i | ||||||||
\(724\) | 0.831524 | 0.0309034 | ||||||||
\(725\) | −0.173293 | −0.00643595 | ||||||||
\(726\) | − | 1.42819i | − | 0.0530053i | ||||||
\(727\) | −1.50815 | −0.0559341 | −0.0279671 | − | 0.999609i | \(-0.508903\pi\) | ||||
−0.0279671 | + | 0.999609i | \(0.508903\pi\) | |||||||
\(728\) | −16.8602 | + | 3.52789i | −0.624881 | + | 0.130752i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.32594i | 0.0490753i | ||||||||
\(731\) | 19.8700 | 0.734920 | ||||||||
\(732\) | −0.129847 | −0.00479928 | ||||||||
\(733\) | − | 4.42002i | − | 0.163257i | −0.996663 | − | 0.0816285i | \(-0.973988\pi\) | ||
0.996663 | − | 0.0816285i | \(-0.0260121\pi\) | |||||||
\(734\) | 21.9176i | 0.808992i | ||||||||
\(735\) | 0.247967i | 0.00914641i | ||||||||
\(736\) | 0.158393i | 0.00583844i | ||||||||
\(737\) | −10.9701 | −0.404087 | ||||||||
\(738\) | −4.75532 | −0.175046 | ||||||||
\(739\) | 13.7640i | 0.506317i | 0.967425 | + | 0.253159i | \(0.0814695\pi\) | ||||
−0.967425 | + | 0.253159i | \(0.918531\pi\) | |||||||
\(740\) | −0.0212760 | −0.000782122 | ||||||||
\(741\) | 1.49607 | + | 7.14991i | 0.0549595 | + | 0.262658i | ||||
\(742\) | 26.0028 | 0.954594 | ||||||||
\(743\) | 52.1763i | 1.91416i | 0.289819 | + | 0.957081i | \(0.406405\pi\) | ||||
−0.289819 | + | 0.957081i | \(0.593595\pi\) | |||||||
\(744\) | −5.20695 | −0.190896 | ||||||||
\(745\) | −0.549065 | −0.0201162 | ||||||||
\(746\) | − | 31.6453i | − | 1.15862i | ||||||
\(747\) | 4.19820i | 0.153604i | ||||||||
\(748\) | − | 0.149256i | − | 0.00545734i | ||||||
\(749\) | 10.5424i | 0.385210i | ||||||||
\(750\) | −0.865985 | −0.0316213 | ||||||||
\(751\) | −13.4236 | −0.489836 | −0.244918 | − | 0.969544i | \(-0.578761\pi\) | ||||
−0.244918 | + | 0.969544i | \(0.578761\pi\) | |||||||
\(752\) | 24.6559i | 0.899106i | ||||||||
\(753\) | −20.7286 | −0.755393 | ||||||||
\(754\) | −0.0365794 | − | 0.174818i | −0.00133214 | − | 0.00636649i | ||||
\(755\) | 0.148284 | 0.00539661 | ||||||||
\(756\) | − | 0.0678114i | − | 0.00246628i | ||||||
\(757\) | 12.9431 | 0.470426 | 0.235213 | − | 0.971944i | \(-0.424421\pi\) | ||||
0.235213 | + | 0.971944i | \(0.424421\pi\) | |||||||
\(758\) | 30.1183 | 1.09395 | ||||||||
\(759\) | 0.704722i | 0.0255798i | ||||||||
\(760\) | − | 0.344047i | − | 0.0124799i | ||||||
\(761\) | − | 24.5952i | − | 0.891576i | −0.895139 | − | 0.445788i | \(-0.852923\pi\) | ||
0.895139 | − | 0.445788i | \(-0.147077\pi\) | |||||||
\(762\) | − | 2.49210i | − | 0.0902792i | ||||||
\(763\) | −7.93379 | −0.287223 | ||||||||
\(764\) | −0.110117 | −0.00398391 | ||||||||
\(765\) | − | 0.227828i | − | 0.00823715i | ||||||
\(766\) | −9.86847 | −0.356562 | ||||||||
\(767\) | −2.47044 | − | 11.8066i | −0.0892025 | − | 0.426310i | ||||
\(768\) | 0.953341 | 0.0344007 | ||||||||
\(769\) | − | 48.0101i | − | 1.73129i | −0.500660 | − | 0.865644i | \(-0.666909\pi\) | ||
0.500660 | − | 0.865644i | \(-0.333091\pi\) | |||||||
\(770\) | −0.147831 | −0.00532746 | ||||||||
\(771\) | 1.38511 | 0.0498835 | ||||||||
\(772\) | − | 0.338069i | − | 0.0121674i | ||||||
\(773\) | − | 20.9744i | − | 0.754398i | −0.926132 | − | 0.377199i | \(-0.876887\pi\) | ||
0.926132 | − | 0.377199i | \(-0.123113\pi\) | |||||||
\(774\) | − | 7.55546i | − | 0.271575i | ||||||
\(775\) | 9.29249i | 0.333796i | ||||||||
\(776\) | −16.4122 | −0.589165 | ||||||||
\(777\) | 15.0624 | 0.540362 | ||||||||
\(778\) | 46.7350i | 1.67553i | ||||||||
\(779\) | −6.74568 | −0.241689 | ||||||||
\(780\) | −0.00177995 | − | 0.00850662i | −6.37325e−5 | − | 0.000304586i | ||||
\(781\) | 1.96928 | 0.0704665 | ||||||||
\(782\) | 3.78033i | 0.135184i | ||||||||
\(783\) | −0.0346842 | −0.00123951 | ||||||||
\(784\) | −16.6705 | −0.595374 | ||||||||
\(785\) | − | 0.511215i | − | 0.0182460i | ||||||
\(786\) | − | 19.8463i | − | 0.707895i | ||||||
\(787\) | − | 42.1206i | − | 1.50144i | −0.660622 | − | 0.750719i | \(-0.729707\pi\) | ||
0.660622 | − | 0.750719i | \(-0.270293\pi\) | |||||||
\(788\) | 0.573332i | 0.0204241i | ||||||||
\(789\) | −17.4668 | −0.621834 | ||||||||
\(790\) | −0.917749 | −0.0326520 | ||||||||
\(791\) | 15.3435i | 0.545554i | ||||||||
\(792\) | 2.79963 | 0.0994807 | ||||||||
\(793\) | 11.5316 | − | 2.41292i | 0.409501 | − | 0.0856852i | ||||
\(794\) | −14.4271 | −0.511999 | ||||||||
\(795\) | − | 0.647174i | − | 0.0229529i | ||||||
\(796\) | 0.633232 | 0.0224443 | ||||||||
\(797\) | −24.5853 | −0.870855 | −0.435428 | − | 0.900224i | \(-0.643403\pi\) | ||||
−0.435428 | + | 0.900224i | \(0.643403\pi\) | |||||||
\(798\) | − | 4.93760i | − | 0.174789i | ||||||
\(799\) | 22.7095i | 0.803406i | ||||||||
\(800\) | − | 1.12297i | − | 0.0397030i | ||||||
\(801\) | − | 14.3643i | − | 0.507537i | ||||||
\(802\) | 26.1897 | 0.924792 | ||||||||
\(803\) | −15.3057 | −0.540127 | ||||||||
\(804\) | 0.435929i | 0.0153740i | ||||||||
\(805\) | 0.0729450 | 0.00257097 | ||||||||
\(806\) | −9.37423 | + | 1.96149i | −0.330193 | + | 0.0690907i | ||||
\(807\) | 0.559556 | 0.0196973 | ||||||||
\(808\) | 34.6332i | 1.21839i | ||||||||
\(809\) | −23.9067 | −0.840516 | −0.420258 | − | 0.907405i | \(-0.638060\pi\) | ||||
−0.420258 | + | 0.907405i | \(0.638060\pi\) | |||||||
\(810\) | −0.0866304 | −0.00304388 | ||||||||
\(811\) | − | 13.7011i | − | 0.481110i | −0.970636 | − | 0.240555i | \(-0.922671\pi\) | ||
0.970636 | − | 0.240555i | \(-0.0773294\pi\) | |||||||
\(812\) | 0.00235198i | 8.25384e-5i | ||||||||
\(813\) | 13.2324i | 0.464080i | ||||||||
\(814\) | − | 12.6063i | − | 0.441850i | ||||||
\(815\) | −1.05525 | −0.0369638 | ||||||||
\(816\) | 15.3166 | 0.536187 | ||||||||
\(817\) | − | 10.7178i | − | 0.374970i | ||||||
\(818\) | 8.00193 | 0.279781 | ||||||||
\(819\) | 1.26012 | + | 6.02229i | 0.0440323 | + | 0.210436i | ||||
\(820\) | 0.00802569 | 0.000280269 | ||||||||
\(821\) | − | 35.5107i | − | 1.23933i | −0.784866 | − | 0.619666i | \(-0.787268\pi\) | ||
0.784866 | − | 0.619666i | \(-0.212732\pi\) | |||||||
\(822\) | 4.41053 | 0.153835 | ||||||||
\(823\) | 33.6096 | 1.17156 | 0.585778 | − | 0.810471i | \(-0.300789\pi\) | ||||
0.585778 | + | 0.810471i | \(0.300789\pi\) | |||||||
\(824\) | − | 28.2170i | − | 0.982984i | ||||||
\(825\) | − | 4.99632i | − | 0.173950i | ||||||
\(826\) | 8.15341i | 0.283693i | ||||||||
\(827\) | − | 33.8892i | − | 1.17844i | −0.807972 | − | 0.589221i | \(-0.799435\pi\) | ||
0.807972 | − | 0.589221i | \(-0.200565\pi\) | |||||||
\(828\) | 0.0280043 | 0.000973217 | ||||||||
\(829\) | −1.03923 | −0.0360941 | −0.0180470 | − | 0.999837i | \(-0.505745\pi\) | ||||
−0.0180470 | + | 0.999837i | \(0.505745\pi\) | |||||||
\(830\) | − | 0.363692i | − | 0.0126239i | ||||||
\(831\) | 18.4921 | 0.641484 | ||||||||
\(832\) | −27.6499 | + | 5.78556i | −0.958589 | + | 0.200578i | ||||
\(833\) | −15.3545 | −0.532002 | ||||||||
\(834\) | 2.75480i | 0.0953909i | ||||||||
\(835\) | 0.0637533 | 0.00220627 | ||||||||
\(836\) | −0.0805084 | −0.00278444 | ||||||||
\(837\) | 1.85987i | 0.0642864i | ||||||||
\(838\) | − | 35.1925i | − | 1.21570i | ||||||
\(839\) | − | 53.9422i | − | 1.86229i | −0.364646 | − | 0.931146i | \(-0.618810\pi\) | ||
0.364646 | − | 0.931146i | \(-0.381190\pi\) | |||||||
\(840\) | − | 0.289787i | − | 0.00999862i | ||||||
\(841\) | −28.9988 | −0.999959 | ||||||||
\(842\) | −36.2764 | −1.25017 | ||||||||
\(843\) | − | 25.8276i | − | 0.889550i | ||||||
\(844\) | 0.661258 | 0.0227615 | ||||||||
\(845\) | 0.316153 | + | 0.722392i | 0.0108760 | + | 0.0248510i | ||||
\(846\) | 8.63517 | 0.296883 | ||||||||
\(847\) | − | 1.70646i | − | 0.0586346i | ||||||
\(848\) | 43.5085 | 1.49409 | ||||||||
\(849\) | −6.19965 | −0.212771 | ||||||||
\(850\) | − | 26.8017i | − | 0.919291i | ||||||
\(851\) | 6.22039i | 0.213232i | ||||||||
\(852\) | − | 0.0782556i | − | 0.00268099i | ||||||
\(853\) | − | 20.4632i | − | 0.700647i | −0.936629 | − | 0.350324i | \(-0.886072\pi\) | ||
0.936629 | − | 0.350324i | \(-0.113928\pi\) | |||||||
\(854\) | −7.96355 | −0.272507 | ||||||||
\(855\) | −0.122890 | −0.00420275 | ||||||||
\(856\) | 17.2959i | 0.591163i | ||||||||
\(857\) | −24.3582 | −0.832059 | −0.416029 | − | 0.909351i | \(-0.636579\pi\) | ||||
−0.416029 | + | 0.909351i | \(0.636579\pi\) | |||||||
\(858\) | 5.04027 | − | 1.05464i | 0.172072 | − | 0.0360049i | ||||
\(859\) | 14.8900 | 0.508042 | 0.254021 | − | 0.967199i | \(-0.418247\pi\) | ||||
0.254021 | + | 0.967199i | \(0.418247\pi\) | |||||||
\(860\) | 0.0127516i | 0.000434825i | ||||||||
\(861\) | −5.68182 | −0.193636 | ||||||||
\(862\) | −48.0235 | −1.63569 | ||||||||
\(863\) | − | 7.78442i | − | 0.264985i | −0.991184 | − | 0.132492i | \(-0.957702\pi\) | ||
0.991184 | − | 0.132492i | \(-0.0422980\pi\) | |||||||
\(864\) | − | 0.224760i | − | 0.00764648i | ||||||
\(865\) | − | 1.13219i | − | 0.0384957i | ||||||
\(866\) | − | 13.8911i | − | 0.472040i | ||||||
\(867\) | −2.89252 | −0.0982351 | ||||||||
\(868\) | 0.126120 | 0.00428080 | ||||||||
\(869\) | − | 10.5938i | − | 0.359372i | ||||||
\(870\) | 0.00300470 | 0.000101869 | ||||||||
\(871\) | −8.10078 | − | 38.7147i | −0.274484 | − | 1.31180i | ||||
\(872\) | −13.0163 | −0.440787 | ||||||||
\(873\) | 5.86228i | 0.198408i | ||||||||
\(874\) | 2.03910 | 0.0689736 | ||||||||
\(875\) | −1.03471 | −0.0349796 | ||||||||
\(876\) | 0.608221i | 0.0205499i | ||||||||
\(877\) | 26.9967i | 0.911614i | 0.890079 | + | 0.455807i | \(0.150649\pi\) | ||||
−0.890079 | + | 0.455807i | \(0.849351\pi\) | |||||||
\(878\) | − | 24.3876i | − | 0.823042i | ||||||
\(879\) | 8.49366i | 0.286484i | ||||||||
\(880\) | −0.247354 | −0.00833831 | ||||||||
\(881\) | −18.7865 | −0.632934 | −0.316467 | − | 0.948603i | \(-0.602497\pi\) | ||||
−0.316467 | + | 0.948603i | \(0.602497\pi\) | |||||||
\(882\) | 5.83846i | 0.196591i | ||||||||
\(883\) | −34.5728 | −1.16347 | −0.581734 | − | 0.813379i | \(-0.697625\pi\) | ||||
−0.581734 | + | 0.813379i | \(0.697625\pi\) | |||||||
\(884\) | 0.526743 | − | 0.110217i | 0.0177163 | − | 0.00370701i | ||||
\(885\) | 0.202927 | 0.00682131 | ||||||||
\(886\) | 31.2257i | 1.04905i | ||||||||
\(887\) | −32.8755 | −1.10385 | −0.551926 | − | 0.833893i | \(-0.686107\pi\) | ||||
−0.551926 | + | 0.833893i | \(0.686107\pi\) | |||||||
\(888\) | 24.7116 | 0.829268 | ||||||||
\(889\) | − | 2.97765i | − | 0.0998671i | ||||||
\(890\) | 1.24438i | 0.0417118i | ||||||||
\(891\) | − | 1.00000i | − | 0.0335013i | ||||||
\(892\) | − | 1.17820i | − | 0.0394492i | ||||||
\(893\) | 12.2495 | 0.409913 | ||||||||
\(894\) | −12.9279 | −0.432374 | ||||||||
\(895\) | 1.47059i | 0.0491565i | ||||||||
\(896\) | 19.8617 | 0.663532 | ||||||||
\(897\) | −2.48705 | + | 0.520398i | −0.0830401 | + | 0.0173756i | ||||
\(898\) | −12.7938 | −0.426935 | ||||||||
\(899\) | − | 0.0645080i | − | 0.00215146i | ||||||
\(900\) | −0.198544 | −0.00661815 | ||||||||
\(901\) | 40.0740 | 1.33506 | ||||||||
\(902\) | 4.75532i | 0.158335i | ||||||||
\(903\) | − | 9.02753i | − | 0.300418i | ||||||
\(904\) | 25.1728i | 0.837235i | ||||||||
\(905\) | − | 1.26926i | − | 0.0421916i | ||||||
\(906\) | 3.49139 | 0.115994 | ||||||||
\(907\) | 5.02982 | 0.167013 | 0.0835063 | − | 0.996507i | \(-0.473388\pi\) | ||||
0.0835063 | + | 0.996507i | \(0.473388\pi\) | |||||||
\(908\) | 0.0865684i | 0.00287287i | ||||||||
\(909\) | 12.3706 | 0.410307 | ||||||||
\(910\) | −0.109165 | − | 0.521713i | −0.00361878 | − | 0.0172946i | ||||
\(911\) | 22.8563 | 0.757263 | 0.378632 | − | 0.925547i | \(-0.376395\pi\) | ||||
0.378632 | + | 0.925547i | \(0.376395\pi\) | |||||||
\(912\) | − | 8.26171i | − | 0.273573i | ||||||
\(913\) | 4.19820 | 0.138940 | ||||||||
\(914\) | 53.9624 | 1.78492 | ||||||||
\(915\) | 0.198202i | 0.00655235i | ||||||||
\(916\) | − | 0.114871i | − | 0.00379546i | ||||||
\(917\) | − | 23.7131i | − | 0.783075i | ||||||
\(918\) | − | 5.36429i | − | 0.177048i | ||||||
\(919\) | 2.37935 | 0.0784875 | 0.0392437 | − | 0.999230i | \(-0.487505\pi\) | ||||
0.0392437 | + | 0.999230i | \(0.487505\pi\) | |||||||
\(920\) | 0.119675 | 0.00394555 | ||||||||
\(921\) | 10.6196i | 0.349929i | ||||||||
\(922\) | 8.71696 | 0.287078 | ||||||||
\(923\) | 1.45421 | + | 6.94984i | 0.0478658 | + | 0.228757i | ||||
\(924\) | −0.0678114 | −0.00223083 | ||||||||
\(925\) | − | 44.1012i | − | 1.45004i | ||||||
\(926\) | −53.0575 | −1.74358 | ||||||||
\(927\) | −10.0788 | −0.331031 | ||||||||
\(928\) | 0.00779561i | 0.000255903i | ||||||||
\(929\) | 8.06120i | 0.264480i | 0.991218 | + | 0.132240i | \(0.0422169\pi\) | ||||
−0.991218 | + | 0.132240i | \(0.957783\pi\) | |||||||
\(930\) | − | 0.161121i | − | 0.00528336i | ||||||
\(931\) | 8.28219i | 0.271438i | ||||||||
\(932\) | 0.353256 | 0.0115713 | ||||||||
\(933\) | 27.5052 | 0.900479 | ||||||||
\(934\) | 14.8021i | 0.484339i | ||||||||
\(935\) | −0.227828 | −0.00745078 | ||||||||
\(936\) | 2.06738 | + | 9.88025i | 0.0675743 | + | 0.322946i | ||||
\(937\) | −24.3236 | −0.794618 | −0.397309 | − | 0.917685i | \(-0.630056\pi\) | ||||
−0.397309 | + | 0.917685i | \(0.630056\pi\) | |||||||
\(938\) | 26.7357i | 0.872951i | ||||||||
\(939\) | 0.791246 | 0.0258213 | ||||||||
\(940\) | −0.0145738 | −0.000475346 | ||||||||
\(941\) | 17.0623i | 0.556215i | 0.960550 | + | 0.278107i | \(0.0897071\pi\) | ||||
−0.960550 | + | 0.278107i | \(0.910293\pi\) | |||||||
\(942\) | − | 12.0367i | − | 0.392177i | ||||||
\(943\) | − | 2.34644i | − | 0.0764107i | ||||||
\(944\) | 13.6425i | 0.444025i | ||||||||
\(945\) | −0.103509 | −0.00336715 | ||||||||
\(946\) | −7.55546 | −0.245649 | ||||||||
\(947\) | − | 57.1623i | − | 1.85753i | −0.370673 | − | 0.928763i | \(-0.620873\pi\) | ||
0.370673 | − | 0.928763i | \(-0.379127\pi\) | |||||||
\(948\) | −0.420980 | −0.0136728 | ||||||||
\(949\) | −11.3024 | − | 54.0158i | −0.366893 | − | 1.75343i | ||||
\(950\) | −14.4568 | −0.469039 | ||||||||
\(951\) | − | 10.4687i | − | 0.339472i | ||||||
\(952\) | 17.9441 | 0.581571 | ||||||||
\(953\) | 2.88446 | 0.0934370 | 0.0467185 | − | 0.998908i | \(-0.485124\pi\) | ||||
0.0467185 | + | 0.998908i | \(0.485124\pi\) | |||||||
\(954\) | − | 15.2379i | − | 0.493346i | ||||||
\(955\) | 0.168086i | 0.00543914i | ||||||||
\(956\) | − | 1.13230i | − | 0.0366212i | ||||||
\(957\) | 0.0346842i | 0.00112118i | ||||||||
\(958\) | 29.1406 | 0.941489 | ||||||||
\(959\) | 5.26985 | 0.170172 | ||||||||
\(960\) | − | 0.475237i | − | 0.0153382i | ||||||
\(961\) | 27.5409 | 0.888416 | ||||||||
\(962\) | 44.4891 | − | 9.30905i | 1.43439 | − | 0.300136i | ||||
\(963\) | 6.17793 | 0.199081 | ||||||||
\(964\) | − | 0.620972i | − | 0.0200002i | ||||||
\(965\) | −0.516037 | −0.0166118 | ||||||||
\(966\) | 1.71751 | 0.0552601 | ||||||||
\(967\) | − | 44.8041i | − | 1.44080i | −0.693557 | − | 0.720402i | \(-0.743957\pi\) | ||
0.693557 | − | 0.720402i | \(-0.256043\pi\) | |||||||
\(968\) | − | 2.79963i | − | 0.0899837i | ||||||
\(969\) | − | 7.60954i | − | 0.244454i | ||||||
\(970\) | − | 0.507851i | − | 0.0163061i | ||||||
\(971\) | 36.2237 | 1.16247 | 0.581237 | − | 0.813735i | \(-0.302569\pi\) | ||||
0.581237 | + | 0.813735i | \(0.302569\pi\) | |||||||
\(972\) | −0.0397381 | −0.00127460 | ||||||||
\(973\) | 3.29153i | 0.105522i | ||||||||
\(974\) | −25.9592 | −0.831786 | ||||||||
\(975\) | 17.6326 | − | 3.68951i | 0.564696 | − | 0.118159i | ||||
\(976\) | −13.3248 | −0.426516 | ||||||||
\(977\) | 8.12311i | 0.259881i | 0.991522 | + | 0.129941i | \(0.0414787\pi\) | ||||
−0.991522 | + | 0.129941i | \(0.958521\pi\) | |||||||
\(978\) | −24.8462 | −0.794493 | ||||||||
\(979\) | −14.3643 | −0.459084 | ||||||||
\(980\) | − | 0.00985375i | − | 0.000314767i | ||||||
\(981\) | 4.64928i | 0.148440i | ||||||||
\(982\) | 27.4254i | 0.875180i | ||||||||
\(983\) | − | 16.3355i | − | 0.521020i | −0.965471 | − | 0.260510i | \(-0.916109\pi\) | ||
0.965471 | − | 0.260510i | \(-0.0838908\pi\) | |||||||
\(984\) | −9.32167 | −0.297164 | ||||||||
\(985\) | 0.875149 | 0.0278846 | ||||||||
\(986\) | 0.186056i | 0.00592523i | ||||||||
\(987\) | 10.3176 | 0.328413 | ||||||||
\(988\) | −0.0594510 | − | 0.284124i | −0.00189139 | − | 0.00903918i | ||||
\(989\) | 3.72813 | 0.118548 | ||||||||
\(990\) | 0.0866304i | 0.00275329i | ||||||||
\(991\) | 19.8188 | 0.629565 | 0.314783 | − | 0.949164i | \(-0.398068\pi\) | ||||
0.314783 | + | 0.949164i | \(0.398068\pi\) | |||||||
\(992\) | 0.418023 | 0.0132722 | ||||||||
\(993\) | 21.1531i | 0.671273i | ||||||||
\(994\) | − | 4.79944i | − | 0.152229i | ||||||
\(995\) | − | 0.966582i | − | 0.0306427i | ||||||
\(996\) | − | 0.166829i | − | 0.00528617i | ||||||
\(997\) | 37.6595 | 1.19269 | 0.596344 | − | 0.802729i | \(-0.296619\pi\) | ||||
0.596344 | + | 0.802729i | \(0.296619\pi\) | |||||||
\(998\) | 9.23243 | 0.292248 | ||||||||
\(999\) | − | 8.82674i | − | 0.279266i |
(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 | 429.2.b.b.298.11 | yes | 14 | |
3.2 | odd | 2 | 1287.2.b.c.298.4 | 14 | |||
13.5 | odd | 4 | 5577.2.a.y.1.5 | 7 | |||
13.8 | odd | 4 | 5577.2.a.x.1.3 | 7 | |||
13.12 | even | 2 | inner | 429.2.b.b.298.4 | ✓ | 14 | |
39.38 | odd | 2 | 1287.2.b.c.298.11 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.b.b.298.4 | ✓ | 14 | 13.12 | even | 2 | inner | |
429.2.b.b.298.11 | yes | 14 | 1.1 | even | 1 | trivial | |
1287.2.b.c.298.4 | 14 | 3.2 | odd | 2 | |||
1287.2.b.c.298.11 | 14 | 39.38 | odd | 2 | |||
5577.2.a.x.1.3 | 7 | 13.8 | odd | 4 | |||
5577.2.a.y.1.5 | 7 | 13.5 | odd | 4 |