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 | 298.4 | ||
Root | \(-1.42819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.298 |
Dual form | 429.2.b.b.298.11 |
$q$-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 | \(-0.831514\pi\) | ||
0.863153 | − | 0.504943i | \(-0.168486\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.0397381 | −0.0198691 | ||||||||
\(5\) | − | 0.0606573i | − | 0.0271268i | −0.999908 | − | 0.0135634i | \(-0.995683\pi\) | ||
0.999908 | − | 0.0135634i | \(-0.00431749\pi\) | |||||||
\(6\) | − | 1.42819i | − | 0.583058i | ||||||
\(7\) | − | 1.70646i | − | 0.644980i | −0.946573 | − | 0.322490i | \(-0.895480\pi\) | ||
0.946573 | − | 0.322490i | \(-0.104520\pi\) | |||||||
\(8\) | − | 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 | \(-0.925344\pi\) | ||
0.972621 | − | 0.232395i | \(-0.0746562\pi\) | |||||||
\(20\) | 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 | \(-0.946585\pi\) | ||
0.985953 | − | 0.167021i | \(-0.0534148\pi\) | |||||||
\(32\) | 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 | \(0.258416\pi\) | ||||
−0.688166 | + | 0.725553i | \(0.741584\pi\) | |||||||
\(38\) | −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 | \(-0.916278\pi\) | ||
0.965609 | − | 0.259998i | \(-0.0837220\pi\) | |||||||
\(42\) | −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 | \(0.145364\pi\) | ||||
−0.897524 | + | 0.440966i | \(0.854636\pi\) | |||||||
\(48\) | −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 | \(0.0698787\pi\) | ||||
−0.976000 | + | 0.217771i | \(0.930121\pi\) | |||||||
\(60\) | 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 | \(0.233750\pi\) | ||||
−0.742268 | + | 0.670103i | \(0.766250\pi\) | |||||||
\(68\) | 0.149256 | 0.0181000 | ||||||||
\(69\) | −0.704722 | −0.0848385 | ||||||||
\(70\) | 0.147831i | 0.0176692i | ||||||||
\(71\) | − | 1.96928i | − | 0.233711i | −0.993149 | − | 0.116855i | \(-0.962719\pi\) | ||
0.993149 | − | 0.116855i | \(-0.0372814\pi\) | |||||||
\(72\) | − | 2.79963i | − | 0.329940i | ||||||
\(73\) | 15.3057i | 1.79140i | 0.444659 | + | 0.895700i | \(0.353325\pi\) | ||||
−0.444659 | + | 0.895700i | \(0.646675\pi\) | |||||||
\(74\) | 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 | \(-0.925994\pi\) | ||
0.973095 | − | 0.230406i | \(-0.0740055\pi\) | |||||||
\(84\) | 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 | \(0.275441\pi\) | ||||
−0.648393 | + | 0.761305i | \(0.724559\pi\) | |||||||
\(90\) | −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 | \(-0.903810\pi\) | ||
0.954687 | − | 0.297612i | \(-0.0961902\pi\) | |||||||
\(98\) | − | 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 | \(-0.928526\pi\) | ||
0.974896 | − | 0.222660i | \(-0.0714740\pi\) | |||||||
\(110\) | − | 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 | \(0.0421144\pi\) | ||||
−0.991260 | + | 0.131921i | \(0.957886\pi\) | |||||||
\(138\) | 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 | \(-0.879090\pi\) | ||
0.928720 | − | 0.370781i | \(-0.120910\pi\) | |||||||
\(150\) | − | 7.13572i | − | 0.582629i | ||||||
\(151\) | 2.44462i | 0.198940i | 0.995041 | + | 0.0994702i | \(0.0317148\pi\) | ||||
−0.995041 | + | 0.0994702i | \(0.968285\pi\) | |||||||
\(152\) | −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 | \(-0.761408\pi\) | ||
0.731990 | − | 0.681316i | \(-0.238592\pi\) | |||||||
\(164\) | 0.132312i | 0.0103318i | ||||||||
\(165\) | 0.0606573 | 0.00472216 | ||||||||
\(166\) | −5.99585 | −0.465368 | ||||||||
\(167\) | 1.05104i | 0.0813320i | 0.999173 | + | 0.0406660i | \(0.0129480\pi\) | ||||
−0.999173 | + | 0.0406660i | \(0.987052\pi\) | |||||||
\(168\) | −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 | \(-0.900946\pi\) | ||
0.951971 | − | 0.306189i | \(-0.0990539\pi\) | |||||||
\(194\) | −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 | \(0.171825\pi\) | ||||
−0.857810 | + | 0.513968i | \(0.828175\pi\) | |||||||
\(198\) | 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 | \(-0.538409\pi\) | ||
0.120372 | − | 0.992729i | \(-0.461591\pi\) | |||||||
\(224\) | 0.383543 | 0.0256265 | ||||||||
\(225\) | 4.99632 | 0.333088 | ||||||||
\(226\) | − | 12.8416i | − | 0.854208i | ||||||
\(227\) | 2.17847i | 0.144590i | 0.997383 | + | 0.0722951i | \(0.0230323\pi\) | ||||
−0.997383 | + | 0.0722951i | \(0.976968\pi\) | |||||||
\(228\) | 0.0805084i | 0.00533180i | ||||||||
\(229\) | − | 2.89071i | − | 0.191024i | −0.995428 | − | 0.0955118i | \(-0.969551\pi\) | ||
0.995428 | − | 0.0955118i | \(-0.0304488\pi\) | |||||||
\(230\) | 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 | \(-0.626913\pi\) | ||
0.388229 | − | 0.921563i | \(-0.373087\pi\) | |||||||
\(240\) | 0.247354i | 0.0159666i | ||||||||
\(241\) | − | 15.6266i | − | 1.00660i | −0.864112 | − | 0.503299i | \(-0.832119\pi\) | ||
0.864112 | − | 0.503299i | \(-0.167881\pi\) | |||||||
\(242\) | 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 | \(-0.868348\pi\) | ||
0.915681 | − | 0.401905i | \(-0.131652\pi\) | |||||||
\(272\) | 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 | \(0.279930\pi\) | ||||
−0.637593 | + | 0.770373i | \(0.720070\pi\) | |||||||
\(282\) | 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 | \(-0.920193\pi\) | ||
0.968734 | − | 0.248102i | \(-0.0798070\pi\) | |||||||
\(294\) | − | 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 | \(-0.901996\pi\) | ||
0.952976 | − | 0.303047i | \(-0.0980040\pi\) | |||||||
\(308\) | −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 | \(0.0949837\pi\) | ||||
−0.955808 | + | 0.293991i | \(0.905016\pi\) | |||||||
\(318\) | 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 | \(-0.802529\pi\) | ||
0.813661 | − | 0.581339i | \(-0.197471\pi\) | |||||||
\(332\) | 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 | \(0.226243\pi\) | ||||
−0.757864 | + | 0.652412i | \(0.773757\pi\) | |||||||
\(350\) | −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 | \(0.193446\pi\) | ||||
−0.820947 | + | 0.571004i | \(0.806554\pi\) | |||||||
\(354\) | 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 | \(-0.658616\pi\) | ||
0.477939 | − | 0.878393i | \(-0.341384\pi\) | |||||||
\(360\) | −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 | \(0.182188\pi\) | ||||
−0.840624 | + | 0.541619i | \(0.817812\pi\) | |||||||
\(380\) | 0.00488342 | 0.000250514 | ||||||||
\(381\) | −1.74493 | −0.0893955 | ||||||||
\(382\) | − | 3.95764i | − | 0.202490i | ||||||
\(383\) | − | 6.90976i | − | 0.353072i | −0.984294 | − | 0.176536i | \(-0.943511\pi\) | ||
0.984294 | − | 0.176536i | \(-0.0564892\pi\) | |||||||
\(384\) | 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 | \(-0.918420\pi\) | ||
0.967337 | − | 0.253494i | \(-0.0815797\pi\) | |||||||
\(398\) | 22.7585i | 1.14078i | ||||||||
\(399\) | −3.45724 | −0.173078 | ||||||||
\(400\) | −20.3745 | −1.01872 | ||||||||
\(401\) | 18.3377i | 0.915739i | 0.889019 | + | 0.457870i | \(0.151387\pi\) | ||||
−0.889019 | + | 0.457870i | \(0.848613\pi\) | |||||||
\(402\) | 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 | \(0.0442349\pi\) | ||||
−0.990359 | + | 0.138521i | \(0.955765\pi\) | |||||||
\(410\) | 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 | \(-0.787553\pi\) | ||
0.785419 | − | 0.618964i | \(-0.212447\pi\) | |||||||
\(422\) | 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 | \(-0.699555\pi\) | ||
0.586653 | − | 0.809838i | \(-0.300445\pi\) | |||||||
\(432\) | −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 | \(-0.932205\pi\) | ||
0.977404 | − | 0.211378i | \(-0.0677950\pi\) | |||||||
\(450\) | − | 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 | \(0.344971\pi\) | ||||
−0.468011 | + | 0.883722i | \(0.655029\pi\) | |||||||
\(458\) | −4.12850 | −0.192912 | ||||||||
\(459\) | −3.75599 | −0.175315 | ||||||||
\(460\) | − | 0.00169867i | − | 7.92007e-5i | ||||||
\(461\) | 6.10348i | 0.284268i | 0.989847 | + | 0.142134i | \(0.0453963\pi\) | ||||
−0.989847 | + | 0.142134i | \(0.954604\pi\) | |||||||
\(462\) | − | 2.43715i | − | 0.113387i | ||||||
\(463\) | − | 37.1501i | − | 1.72651i | −0.504768 | − | 0.863255i | \(-0.668422\pi\) | ||
0.504768 | − | 0.863255i | \(-0.331578\pi\) | |||||||
\(464\) | 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 | \(0.154354\pi\) | ||||
−0.884713 | + | 0.466136i | \(0.845646\pi\) | |||||||
\(480\) | 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 | \(-0.864893\pi\) | ||
0.911264 | − | 0.411822i | \(-0.135107\pi\) | |||||||
\(488\) | − | 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 | \(0.0462196\pi\) | ||||
−0.989477 | + | 0.144693i | \(0.953780\pi\) | |||||||
\(500\) | 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 | \(-0.772591\pi\) | ||
0.755470 | − | 0.655183i | \(-0.227409\pi\) | |||||||
\(510\) | 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 | \(0.114789\pi\) | ||||
−0.935678 | + | 0.352856i | \(0.885211\pi\) | |||||||
\(542\) | −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 | \(-0.937683\pi\) | ||
0.980897 | − | 0.194527i | \(-0.0623171\pi\) | |||||||
\(558\) | −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 | \(0.169431\pi\) | ||||
−0.861650 | + | 0.507502i | \(0.830569\pi\) | |||||||
\(578\) | 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 | \(-0.956429\pi\) | ||
0.990646 | − | 0.136455i | \(-0.0435709\pi\) | |||||||
\(588\) | −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 | \(-0.817545\pi\) | ||
0.840170 | − | 0.542322i | \(-0.182455\pi\) | |||||||
\(594\) | 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 | \(0.172488\pi\) | ||||
−0.856736 | + | 0.515755i | \(0.827512\pi\) | |||||||
\(614\) | −15.1669 | −0.612086 | ||||||||
\(615\) | −0.201965 | −0.00814400 | ||||||||
\(616\) | − | 4.77746i | − | 0.192489i | ||||||
\(617\) | − | 33.4193i | − | 1.34541i | −0.739910 | − | 0.672706i | \(-0.765132\pi\) | ||
0.739910 | − | 0.672706i | \(-0.234868\pi\) | |||||||
\(618\) | 14.3945i | 0.579031i | ||||||||
\(619\) | 34.5887i | 1.39024i | 0.718895 | + | 0.695119i | \(0.244648\pi\) | ||||
−0.718895 | + | 0.695119i | \(0.755352\pi\) | |||||||
\(620\) | 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 | \(-0.918638\pi\) | ||
0.967510 | − | 0.252831i | \(-0.0813617\pi\) | |||||||
\(632\) | − | 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 | \(-0.775428\pi\) | ||
0.761278 | − | 0.648425i | \(-0.224572\pi\) | |||||||
\(644\) | − | 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 | \(-0.984866\pi\) | ||
0.998870 | − | 0.0475276i | \(-0.0151342\pi\) | |||||||
\(662\) | −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 | \(0.0791704\pi\) | ||||
−0.969228 | + | 0.246165i | \(0.920830\pi\) | |||||||
\(684\) | 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 | \(0.223623\pi\) | ||||
−0.763208 | + | 0.646152i | \(0.776377\pi\) | |||||||
\(692\) | 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 | \(0.219516\pi\) | ||||
−0.771482 | + | 0.636251i | \(0.780484\pi\) | |||||||
\(710\) | 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 | \(0.0260121\pi\) | ||||
−0.996663 | + | 0.0816285i | \(0.973988\pi\) | |||||||
\(734\) | − | 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 | \(-0.918531\pi\) | ||
0.967425 | − | 0.253159i | \(-0.0814695\pi\) | |||||||
\(740\) | −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 | \(-0.593595\pi\) | ||
0.289819 | − | 0.957081i | \(-0.406405\pi\) | |||||||
\(744\) | −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 | \(0.147077\pi\) | ||||
−0.895139 | + | 0.445788i | \(0.852923\pi\) | |||||||
\(762\) | 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 | \(0.333091\pi\) | ||||
−0.500660 | + | 0.865644i | \(0.666909\pi\) | |||||||
\(770\) | −0.147831 | −0.00532746 | ||||||||
\(771\) | 1.38511 | 0.0498835 | ||||||||
\(772\) | 0.338069i | 0.0121674i | ||||||||
\(773\) | 20.9744i | 0.754398i | 0.926132 | + | 0.377199i | \(0.123113\pi\) | ||||
−0.926132 | + | 0.377199i | \(0.876887\pi\) | |||||||
\(774\) | 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 | \(0.270293\pi\) | ||||
−0.660622 | + | 0.750719i | \(0.729707\pi\) | |||||||
\(788\) | − | 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 | \(0.0773294\pi\) | ||||
−0.970636 | + | 0.240555i | \(0.922671\pi\) | |||||||
\(812\) | − | 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 | \(0.212732\pi\) | ||||
−0.784866 | + | 0.619666i | \(0.787268\pi\) | |||||||
\(822\) | 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 | \(0.200565\pi\) | ||||
−0.807972 | + | 0.589221i | \(0.799435\pi\) | |||||||
\(828\) | 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 | \(0.381190\pi\) | ||||
−0.364646 | + | 0.931146i | \(0.618810\pi\) | |||||||
\(840\) | 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 | \(0.113928\pi\) | ||||
−0.936629 | + | 0.350324i | \(0.886072\pi\) | |||||||
\(854\) | −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 | \(0.0422980\pi\) | ||||
−0.991184 | + | 0.132492i | \(0.957702\pi\) | |||||||
\(864\) | 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 | \(-0.849351\pi\) | ||
0.890079 | − | 0.455807i | \(-0.150649\pi\) | |||||||
\(878\) | 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 | \(-0.957783\pi\) | ||
0.991218 | − | 0.132240i | \(-0.0422169\pi\) | |||||||
\(930\) | 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 | \(-0.910293\pi\) | ||
0.960550 | − | 0.278107i | \(-0.0897071\pi\) | |||||||
\(942\) | 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 | \(0.379127\pi\) | ||||
−0.370673 | + | 0.928763i | \(0.620873\pi\) | |||||||
\(948\) | −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 | \(0.256043\pi\) | ||||
−0.693557 | + | 0.720402i | \(0.743957\pi\) | |||||||
\(968\) | 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 | \(-0.958521\pi\) | ||
0.991522 | − | 0.129941i | \(-0.0414787\pi\) | |||||||
\(978\) | −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 | \(0.0838908\pi\) | ||||
−0.965471 | + | 0.260510i | \(0.916109\pi\) | |||||||
\(984\) | −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.298.4 | ✓ | 14 | |
3.2 | odd | 2 | 1287.2.b.c.298.11 | 14 | |||
13.5 | odd | 4 | 5577.2.a.x.1.3 | 7 | |||
13.8 | odd | 4 | 5577.2.a.y.1.5 | 7 | |||
13.12 | even | 2 | inner | 429.2.b.b.298.11 | yes | 14 | |
39.38 | odd | 2 | 1287.2.b.c.298.4 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.b.b.298.4 | ✓ | 14 | 1.1 | even | 1 | trivial | |
429.2.b.b.298.11 | yes | 14 | 13.12 | even | 2 | inner | |
1287.2.b.c.298.4 | 14 | 39.38 | odd | 2 | |||
1287.2.b.c.298.11 | 14 | 3.2 | odd | 2 | |||
5577.2.a.x.1.3 | 7 | 13.5 | odd | 4 | |||
5577.2.a.y.1.5 | 7 | 13.8 | odd | 4 |