Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(235,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.235");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.j (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 352.3 | ||
Root | \(-0.132804 + 0.230024i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.352 |
Dual form | 819.2.j.h.235.3 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.632804 | − | 1.09605i | 0.447460 | − | 0.775024i | −0.550760 | − | 0.834664i | \(-0.685662\pi\) |
0.998220 | + | 0.0596401i | \(0.0189953\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.199118 | + | 0.344882i | 0.0995588 | + | 0.172441i | ||||
\(5\) | −1.45130 | + | 2.51373i | −0.649041 | + | 1.12417i | 0.334311 | + | 0.942463i | \(0.391496\pi\) |
−0.983352 | + | 0.181709i | \(0.941837\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.29536 | − | 2.30696i | −0.489599 | − | 0.871948i | ||||
\(8\) | 3.03523 | 1.07311 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.83678 | + | 3.18139i | 0.580840 | + | 1.00604i | ||||
\(11\) | 1.01828 | + | 1.76372i | 0.307024 | + | 0.531780i | 0.977710 | − | 0.209961i | \(-0.0673336\pi\) |
−0.670686 | + | 0.741741i | \(0.734000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −3.34825 | − | 0.0400756i | −0.894856 | − | 0.0107107i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.52247 | − | 2.63699i | 0.380617 | − | 0.659249i | ||||
\(17\) | 1.99933 | + | 3.46294i | 0.484909 | + | 0.839887i | 0.999850 | − | 0.0173386i | \(-0.00551934\pi\) |
−0.514941 | + | 0.857226i | \(0.672186\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.48105 | + | 6.02935i | −0.798608 | + | 1.38323i | 0.121915 | + | 0.992540i | \(0.461096\pi\) |
−0.920523 | + | 0.390688i | \(0.872237\pi\) | |||||||
\(20\) | −1.15592 | −0.258471 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.57749 | 0.549523 | ||||||||
\(23\) | −0.313640 | + | 0.543240i | −0.0653985 | + | 0.113273i | −0.896871 | − | 0.442293i | \(-0.854165\pi\) |
0.831472 | + | 0.555566i | \(0.187499\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.71254 | − | 2.96621i | −0.342509 | − | 0.593243i | ||||
\(26\) | 0.632804 | − | 1.09605i | 0.124103 | − | 0.214953i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.537699 | − | 0.906101i | 0.101615 | − | 0.171237i | ||||
\(29\) | −1.09606 | −0.203534 | −0.101767 | − | 0.994808i | \(-0.532450\pi\) | ||||
−0.101767 | + | 0.994808i | \(0.532450\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.21624 | + | 9.03479i | 0.936864 | + | 1.62270i | 0.771275 | + | 0.636502i | \(0.219619\pi\) |
0.165589 | + | 0.986195i | \(0.447047\pi\) | |||||||
\(32\) | 1.10838 | + | 1.91977i | 0.195935 | + | 0.339370i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.06074 | 0.867910 | ||||||||
\(35\) | 7.67901 | + | 0.0919110i | 1.29799 | + | 0.0155358i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.54268 | − | 2.67201i | 0.253616 | − | 0.439275i | −0.710903 | − | 0.703290i | \(-0.751713\pi\) |
0.964519 | + | 0.264015i | \(0.0850468\pi\) | |||||||
\(38\) | 4.40565 | + | 7.63080i | 0.714690 | + | 1.23788i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.40502 | + | 7.62973i | −0.696496 | + | 1.20637i | ||||
\(41\) | 0.521150 | 0.0813900 | 0.0406950 | − | 0.999172i | \(-0.487043\pi\) | ||||
0.0406950 | + | 0.999172i | \(0.487043\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.329024 | 0.0501757 | 0.0250879 | − | 0.999685i | \(-0.492013\pi\) | ||||
0.0250879 | + | 0.999685i | \(0.492013\pi\) | |||||||
\(44\) | −0.405516 | + | 0.702374i | −0.0611338 | + | 0.105887i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.396945 | + | 0.687530i | 0.0585264 | + | 0.101371i | ||||
\(47\) | 5.27284 | − | 9.13283i | 0.769123 | − | 1.33216i | −0.168916 | − | 0.985630i | \(-0.554027\pi\) |
0.938039 | − | 0.346530i | \(-0.112640\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.64409 | + | 5.97667i | −0.520585 | + | 0.853810i | ||||
\(50\) | −4.33482 | −0.613036 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.199118 | + | 0.344882i | 0.0276126 | + | 0.0478265i | ||||
\(53\) | 3.55950 | + | 6.16523i | 0.488935 | + | 0.846860i | 0.999919 | − | 0.0127302i | \(-0.00405225\pi\) |
−0.510984 | + | 0.859590i | \(0.670719\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.91133 | −0.797084 | ||||||||
\(56\) | −3.93171 | − | 7.00214i | −0.525396 | − | 0.935700i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.693593 | + | 1.20134i | −0.0910733 | + | 0.157744i | ||||
\(59\) | 1.01828 | + | 1.76372i | 0.132569 | + | 0.229616i | 0.924666 | − | 0.380779i | \(-0.124344\pi\) |
−0.792097 | + | 0.610395i | \(0.791011\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.20041 | + | 2.07917i | −0.153696 | + | 0.266210i | −0.932584 | − | 0.360954i | \(-0.882451\pi\) |
0.778887 | + | 0.627164i | \(0.215784\pi\) | |||||||
\(62\) | 13.2034 | 1.67684 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.89542 | 1.11193 | ||||||||
\(65\) | −1.45130 | + | 2.51373i | −0.180012 | + | 0.311789i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.34709 | − | 12.7255i | −0.897589 | − | 1.55467i | −0.830567 | − | 0.556919i | \(-0.811983\pi\) |
−0.0670226 | − | 0.997751i | \(-0.521350\pi\) | |||||||
\(68\) | −0.796204 | + | 1.37907i | −0.0965539 | + | 0.167236i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.96005 | − | 8.35841i | 0.592839 | − | 0.999021i | ||||
\(71\) | −3.60141 | −0.427409 | −0.213704 | − | 0.976898i | \(-0.568553\pi\) | ||||
−0.213704 | + | 0.976898i | \(0.568553\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.48786 | − | 2.57706i | −0.174141 | − | 0.301622i | 0.765722 | − | 0.643171i | \(-0.222382\pi\) |
−0.939864 | + | 0.341550i | \(0.889048\pi\) | |||||||
\(74\) | −1.95243 | − | 3.38172i | −0.226966 | − | 0.393117i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.77255 | −0.318034 | ||||||||
\(77\) | 2.74978 | − | 4.63378i | 0.313366 | − | 0.528068i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.38075 | − | 7.58769i | 0.492873 | − | 0.853681i | −0.507093 | − | 0.861891i | \(-0.669280\pi\) |
0.999966 | + | 0.00820995i | \(0.00261334\pi\) | |||||||
\(80\) | 4.41912 | + | 7.65414i | 0.494073 | + | 0.855759i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.329786 | − | 0.571206i | 0.0364188 | − | 0.0630792i | ||||
\(83\) | −12.8039 | −1.40541 | −0.702703 | − | 0.711483i | \(-0.748024\pi\) | ||||
−0.702703 | + | 0.711483i | \(0.748024\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.6065 | −1.25890 | ||||||||
\(86\) | 0.208208 | − | 0.360627i | 0.0224516 | − | 0.0388874i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.09072 | + | 5.35328i | 0.329471 | + | 0.570661i | ||||
\(89\) | −1.34049 | + | 2.32180i | −0.142092 | + | 0.246110i | −0.928284 | − | 0.371872i | \(-0.878716\pi\) |
0.786192 | + | 0.617982i | \(0.212050\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.29536 | − | 2.30696i | −0.135790 | − | 0.241835i | ||||
\(92\) | −0.249805 | −0.0260440 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.67335 | − | 11.5586i | −0.688304 | − | 1.19218i | ||||
\(95\) | −10.1041 | − | 17.5008i | −1.03666 | − | 1.79554i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.32902 | −0.236477 | −0.118238 | − | 0.992985i | \(-0.537725\pi\) | ||||
−0.118238 | + | 0.992985i | \(0.537725\pi\) | |||||||
\(98\) | 4.24472 | + | 7.77617i | 0.428782 | + | 0.785512i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.681995 | − | 1.18125i | 0.0681995 | − | 0.118125i | ||||
\(101\) | 0.726620 | + | 1.25854i | 0.0723014 | + | 0.125230i | 0.899910 | − | 0.436077i | \(-0.143632\pi\) |
−0.827608 | + | 0.561306i | \(0.810299\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.81765 | − | 10.0765i | 0.573230 | − | 0.992864i | −0.423001 | − | 0.906129i | \(-0.639023\pi\) |
0.996231 | − | 0.0867346i | \(-0.0276432\pi\) | |||||||
\(104\) | 3.03523 | 0.297628 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.00987 | 0.875115 | ||||||||
\(107\) | 9.81297 | − | 16.9966i | 0.948656 | − | 1.64312i | 0.200395 | − | 0.979715i | \(-0.435777\pi\) |
0.748261 | − | 0.663405i | \(-0.230889\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.553378 | + | 0.958479i | 0.0530040 | + | 0.0918057i | 0.891310 | − | 0.453394i | \(-0.149787\pi\) |
−0.838306 | + | 0.545200i | \(0.816454\pi\) | |||||||
\(110\) | −3.74071 | + | 6.47911i | −0.356663 | + | 0.617759i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.05557 | − | 0.0964182i | −0.761180 | − | 0.00911066i | ||||
\(113\) | 1.09606 | 0.103109 | 0.0515545 | − | 0.998670i | \(-0.483582\pi\) | ||||
0.0515545 | + | 0.998670i | \(0.483582\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.910371 | − | 1.57681i | −0.0848926 | − | 0.147038i | ||||
\(116\) | −0.218245 | − | 0.378012i | −0.0202636 | − | 0.0350975i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.57749 | 0.237277 | ||||||||
\(119\) | 5.39901 | − | 9.09812i | 0.494926 | − | 0.834024i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.42620 | − | 5.93436i | 0.311473 | − | 0.539487i | ||||
\(122\) | 1.51925 | + | 2.63141i | 0.137546 | + | 0.238237i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.07729 | + | 3.59797i | −0.186546 | + | 0.323107i | ||||
\(125\) | −4.57134 | −0.408873 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.18143 | 0.459778 | 0.229889 | − | 0.973217i | \(-0.426164\pi\) | ||||
0.229889 | + | 0.973217i | \(0.426164\pi\) | |||||||
\(128\) | 3.41231 | − | 5.91029i | 0.301608 | − | 0.522400i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.83678 | + | 3.18139i | 0.161096 | + | 0.279027i | ||||
\(131\) | 5.28335 | − | 9.15103i | 0.461609 | − | 0.799530i | −0.537433 | − | 0.843307i | \(-0.680606\pi\) |
0.999041 | + | 0.0437770i | \(0.0139391\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.4187 | + | 0.220455i | 1.59710 | + | 0.0191159i | ||||
\(134\) | −18.5971 | −1.60654 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.06842 | + | 10.5108i | 0.520363 | + | 0.901295i | ||||
\(137\) | −2.93589 | − | 5.08510i | −0.250830 | − | 0.434450i | 0.712925 | − | 0.701241i | \(-0.247370\pi\) |
−0.963754 | + | 0.266791i | \(0.914037\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 1.49733 | + | 2.66665i | 0.126547 | + | 0.225373i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.27899 | + | 3.94732i | −0.191248 | + | 0.331252i | ||||
\(143\) | 1.01828 | + | 1.76372i | 0.0851530 | + | 0.147489i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.59072 | − | 2.75520i | 0.132102 | − | 0.228807i | ||||
\(146\) | −3.76611 | −0.311685 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.22870 | 0.100999 | ||||||||
\(149\) | −5.05271 | + | 8.75155i | −0.413934 | + | 0.716955i | −0.995316 | − | 0.0966760i | \(-0.969179\pi\) |
0.581382 | + | 0.813631i | \(0.302512\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.0938631 | + | 0.162576i | 0.00763847 | + | 0.0132302i | 0.869819 | − | 0.493370i | \(-0.164235\pi\) |
−0.862181 | + | 0.506601i | \(0.830902\pi\) | |||||||
\(152\) | −10.5658 | + | 18.3005i | −0.856998 | + | 1.48436i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.33878 | − | 5.94616i | −0.269046 | − | 0.479155i | ||||
\(155\) | −30.2813 | −2.43225 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.03590 | + | 10.4545i | 0.481717 | + | 0.834358i | 0.999780 | − | 0.0209844i | \(-0.00668003\pi\) |
−0.518063 | + | 0.855343i | \(0.673347\pi\) | |||||||
\(158\) | −5.54432 | − | 9.60304i | −0.441082 | − | 0.763977i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.43435 | −0.508680 | ||||||||
\(161\) | 1.65951 | + | 0.0198629i | 0.130788 | + | 0.00156541i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.45678 | + | 12.9155i | −0.584060 | + | 1.01162i | 0.410932 | + | 0.911666i | \(0.365203\pi\) |
−0.994992 | + | 0.0999554i | \(0.968130\pi\) | |||||||
\(164\) | 0.103770 | + | 0.179735i | 0.00810309 | + | 0.0140350i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.10234 | + | 14.0337i | −0.628863 | + | 1.08922i | ||||
\(167\) | −5.05664 | −0.391294 | −0.195647 | − | 0.980674i | \(-0.562681\pi\) | ||||
−0.195647 | + | 0.980674i | \(0.562681\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −7.34465 | + | 12.7213i | −0.563309 | + | 0.975680i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.0655145 | + | 0.113474i | 0.00499543 | + | 0.00865235i | ||||
\(173\) | −0.297807 | + | 0.515817i | −0.0226419 | + | 0.0392169i | −0.877124 | − | 0.480263i | \(-0.840541\pi\) |
0.854482 | + | 0.519480i | \(0.173874\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.62457 | + | 7.79307i | −0.349584 | + | 0.589101i | ||||
\(176\) | 6.20121 | 0.467434 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.69654 | + | 2.93849i | 0.127161 | + | 0.220249i | ||||
\(179\) | 4.03832 | + | 6.99458i | 0.301838 | + | 0.522799i | 0.976552 | − | 0.215280i | \(-0.0690664\pi\) |
−0.674714 | + | 0.738079i | \(0.735733\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.89324 | 0.140724 | 0.0703618 | − | 0.997522i | \(-0.477585\pi\) | ||||
0.0703618 | + | 0.997522i | \(0.477585\pi\) | |||||||
\(182\) | −3.34825 | − | 0.0400756i | −0.248188 | − | 0.00297060i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.951968 | + | 1.64886i | −0.0701800 | + | 0.121555i | ||||
\(185\) | 4.47780 | + | 7.75577i | 0.329214 | + | 0.570216i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.07177 | + | 7.05251i | −0.297757 | + | 0.515730i | ||||
\(188\) | 4.19966 | 0.306292 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −25.5757 | −1.85545 | ||||||||
\(191\) | 1.85087 | − | 3.20580i | 0.133924 | − | 0.231964i | −0.791262 | − | 0.611478i | \(-0.790575\pi\) |
0.925186 | + | 0.379514i | \(0.123909\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.79373 | − | 11.7671i | −0.489024 | − | 0.847014i | 0.510897 | − | 0.859642i | \(-0.329313\pi\) |
−0.999920 | + | 0.0126285i | \(0.995980\pi\) | |||||||
\(194\) | −1.47382 | + | 2.55272i | −0.105814 | + | 0.183275i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.78685 | − | 0.0667218i | −0.199061 | − | 0.00476585i | ||||
\(197\) | 9.70258 | 0.691280 | 0.345640 | − | 0.938367i | \(-0.387662\pi\) | ||||
0.345640 | + | 0.938367i | \(0.387662\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.1360 | − | 22.7522i | −0.931185 | − | 1.61286i | −0.781299 | − | 0.624156i | \(-0.785443\pi\) |
−0.149885 | − | 0.988703i | \(-0.547891\pi\) | |||||||
\(200\) | −5.19796 | − | 9.00313i | −0.367551 | − | 0.636617i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.83923 | 0.129408 | ||||||||
\(203\) | 1.41979 | + | 2.52857i | 0.0996500 | + | 0.177471i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.756345 | + | 1.31003i | −0.0528255 | + | 0.0914964i | ||||
\(206\) | −7.36287 | − | 12.7529i | −0.512995 | − | 0.888534i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.52247 | − | 2.63699i | 0.105564 | − | 0.182843i | ||||
\(209\) | −14.1788 | −0.980765 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0338 | 0.690758 | 0.345379 | − | 0.938463i | \(-0.387750\pi\) | ||||
0.345379 | + | 0.938463i | \(0.387750\pi\) | |||||||
\(212\) | −1.41752 | + | 2.45521i | −0.0973555 | + | 0.168625i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.4194 | − | 21.5110i | −0.848971 | − | 1.47046i | ||||
\(215\) | −0.477513 | + | 0.827077i | −0.0325661 | + | 0.0564062i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.0860 | − | 23.7369i | 0.956218 | − | 1.61137i | ||||
\(218\) | 1.40072 | 0.0948688 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.17705 | − | 2.03871i | −0.0793567 | − | 0.137450i | ||||
\(221\) | 1.99933 | + | 3.46294i | 0.134490 | + | 0.232943i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.4961 | 1.17163 | 0.585813 | − | 0.810446i | \(-0.300775\pi\) | ||||
0.585813 | + | 0.810446i | \(0.300775\pi\) | |||||||
\(224\) | 2.99307 | − | 5.04376i | 0.199983 | − | 0.337000i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.693593 | − | 1.20134i | 0.0461371 | − | 0.0799119i | ||||
\(227\) | −4.75815 | − | 8.24136i | −0.315810 | − | 0.546998i | 0.663800 | − | 0.747910i | \(-0.268943\pi\) |
−0.979609 | + | 0.200912i | \(0.935609\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.5585 | + | 18.2878i | −0.697725 | + | 1.20849i | 0.271529 | + | 0.962430i | \(0.412471\pi\) |
−0.969254 | + | 0.246064i | \(0.920863\pi\) | |||||||
\(230\) | −2.30435 | −0.151944 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.32680 | −0.218415 | ||||||||
\(233\) | 7.08938 | − | 12.2792i | 0.464441 | − | 0.804435i | −0.534735 | − | 0.845020i | \(-0.679589\pi\) |
0.999176 | + | 0.0405847i | \(0.0129221\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.3050 | + | 26.5090i | 0.998385 | + | 1.72925i | ||||
\(236\) | −0.405516 | + | 0.702374i | −0.0263968 | + | 0.0457206i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.55547 | − | 11.6749i | −0.424928 | − | 0.756772i | ||||
\(239\) | 16.5275 | 1.06907 | 0.534536 | − | 0.845145i | \(-0.320486\pi\) | ||||
0.534536 | + | 0.845145i | \(0.320486\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.84450 | + | 11.8550i | 0.440893 | + | 0.763649i | 0.997756 | − | 0.0669552i | \(-0.0213284\pi\) |
−0.556863 | + | 0.830604i | \(0.687995\pi\) | |||||||
\(242\) | −4.33623 | − | 7.51058i | −0.278744 | − | 0.482798i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.956089 | −0.0612073 | ||||||||
\(245\) | −9.73503 | − | 17.8342i | −0.621948 | − | 1.13938i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.48105 | + | 6.02935i | −0.221494 | + | 0.383639i | ||||
\(248\) | 15.8325 | + | 27.4226i | 1.00536 | + | 1.74134i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.89276 | + | 5.01042i | −0.182954 | + | 0.316886i | ||||
\(251\) | 14.6603 | 0.925349 | 0.462674 | − | 0.886528i | \(-0.346890\pi\) | ||||
0.462674 | + | 0.886528i | \(0.346890\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.27750 | −0.0803155 | ||||||||
\(254\) | 3.27883 | − | 5.67910i | 0.205732 | − | 0.356339i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.57678 | + | 7.92721i | 0.286049 | + | 0.495451i | ||||
\(257\) | −0.876387 | + | 1.51795i | −0.0546675 | + | 0.0946869i | −0.892064 | − | 0.451909i | \(-0.850743\pi\) |
0.837397 | + | 0.546596i | \(0.184077\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.16254 | − | 0.0976985i | −0.507195 | − | 0.00607069i | ||||
\(260\) | −1.15592 | −0.0716870 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.68666 | − | 11.5816i | −0.413103 | − | 0.715515i | ||||
\(263\) | 13.4708 | + | 23.3321i | 0.830645 | + | 1.43872i | 0.897527 | + | 0.440959i | \(0.145361\pi\) |
−0.0668823 | + | 0.997761i | \(0.521305\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.6636 | −1.26936 | ||||||||
\(266\) | 11.8970 | − | 20.0483i | 0.729454 | − | 1.22924i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.92587 | − | 5.06775i | 0.178726 | − | 0.309562i | ||||
\(269\) | −11.0346 | − | 19.1124i | −0.672789 | − | 1.16530i | −0.977110 | − | 0.212735i | \(-0.931763\pi\) |
0.304321 | − | 0.952570i | \(-0.401570\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.48105 | − | 7.76141i | 0.272204 | − | 0.471472i | −0.697222 | − | 0.716856i | \(-0.745581\pi\) |
0.969426 | + | 0.245384i | \(0.0789140\pi\) | |||||||
\(272\) | 12.1757 | 0.738259 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.43137 | −0.448945 | ||||||||
\(275\) | 3.48770 | − | 6.04088i | 0.210316 | − | 0.364279i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.76463 | + | 6.52052i | 0.226194 | + | 0.391780i | 0.956677 | − | 0.291151i | \(-0.0940382\pi\) |
−0.730483 | + | 0.682931i | \(0.760705\pi\) | |||||||
\(278\) | −2.53122 | + | 4.38420i | −0.151812 | + | 0.262947i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 23.3075 | + | 0.278971i | 1.39289 | + | 0.0166717i | ||||
\(281\) | −29.7762 | −1.77630 | −0.888151 | − | 0.459553i | \(-0.848010\pi\) | ||||
−0.888151 | + | 0.459553i | \(0.848010\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.150726 | − | 0.261064i | −0.00895970 | − | 0.0155187i | 0.861511 | − | 0.507739i | \(-0.169519\pi\) |
−0.870470 | + | 0.492221i | \(0.836185\pi\) | |||||||
\(284\) | −0.717104 | − | 1.24206i | −0.0425523 | − | 0.0737027i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.57749 | 0.152410 | ||||||||
\(287\) | −0.675076 | − | 1.20227i | −0.0398485 | − | 0.0709678i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.505347 | − | 0.875286i | 0.0297263 | − | 0.0514874i | ||||
\(290\) | −2.01322 | − | 3.48701i | −0.118221 | − | 0.204764i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.592520 | − | 1.02627i | 0.0346746 | − | 0.0600582i | ||||
\(293\) | 19.2471 | 1.12443 | 0.562214 | − | 0.826992i | \(-0.309950\pi\) | ||||
0.562214 | + | 0.826992i | \(0.309950\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.91133 | −0.344171 | ||||||||
\(296\) | 4.68240 | − | 8.11015i | 0.272159 | − | 0.471393i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.39475 | + | 11.0760i | 0.370438 | + | 0.641618i | ||||
\(299\) | −0.313640 | + | 0.543240i | −0.0181383 | + | 0.0314164i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.426204 | − | 0.759044i | −0.0245660 | − | 0.0437506i | ||||
\(302\) | 0.237588 | 0.0136716 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.5996 | + | 18.3590i | 0.607928 | + | 1.05296i | ||||
\(305\) | −3.48430 | − | 6.03499i | −0.199511 | − | 0.345562i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.57779 | −0.204195 | −0.102098 | − | 0.994774i | \(-0.532555\pi\) | ||||
−0.102098 | + | 0.994774i | \(0.532555\pi\) | |||||||
\(308\) | 2.14563 | + | 0.0256814i | 0.122259 | + | 0.00146333i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −19.1621 | + | 33.1898i | −1.08834 | + | 1.88505i | ||||
\(311\) | −11.9153 | − | 20.6379i | −0.675655 | − | 1.17027i | −0.976277 | − | 0.216526i | \(-0.930527\pi\) |
0.300622 | − | 0.953743i | \(-0.402806\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.04068 | − | 15.6589i | 0.511009 | − | 0.885094i | −0.488909 | − | 0.872335i | \(-0.662605\pi\) |
0.999919 | − | 0.0127596i | \(-0.00406161\pi\) | |||||||
\(314\) | 15.2782 | 0.862196 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.48914 | 0.196279 | ||||||||
\(317\) | −13.7741 | + | 23.8574i | −0.773630 | + | 1.33997i | 0.161931 | + | 0.986802i | \(0.448228\pi\) |
−0.935561 | + | 0.353164i | \(0.885106\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.11610 | − | 1.93314i | −0.0624897 | − | 0.108235i | ||||
\(320\) | −12.9099 | + | 22.3606i | −0.721687 | + | 1.25000i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.07191 | − | 1.80633i | 0.0597355 | − | 0.100663i | ||||
\(323\) | −27.8391 | −1.54901 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.71254 | − | 2.96621i | −0.0949948 | − | 0.164536i | ||||
\(326\) | 9.43736 | + | 16.3460i | 0.522687 | + | 0.905321i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.58181 | 0.0873408 | ||||||||
\(329\) | −27.8993 | − | 0.333930i | −1.53814 | − | 0.0184101i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.09069 | − | 15.7455i | 0.499669 | − | 0.865453i | −0.500331 | − | 0.865834i | \(-0.666788\pi\) |
1.00000 | 0.000381757i | \(0.000121517\pi\) | ||||||||
\(332\) | −2.54947 | − | 4.41582i | −0.139921 | − | 0.242350i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.19986 | + | 5.54232i | −0.175089 | + | 0.303262i | ||||
\(335\) | 42.6513 | 2.33029 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.1381 | −0.933572 | −0.466786 | − | 0.884370i | \(-0.654588\pi\) | ||||
−0.466786 | + | 0.884370i | \(0.654588\pi\) | |||||||
\(338\) | 0.632804 | − | 1.09605i | 0.0344200 | − | 0.0596172i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.31106 | − | 4.00288i | −0.125335 | − | 0.217086i | ||||
\(341\) | −10.6232 | + | 18.3999i | −0.575279 | + | 0.996412i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5083 | + | 0.664840i | 0.999355 | + | 0.0358980i | ||||
\(344\) | 0.998663 | 0.0538443 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.376907 | + | 0.652823i | 0.0202627 | + | 0.0350960i | ||||
\(347\) | 11.1344 | + | 19.2853i | 0.597725 | + | 1.03529i | 0.993156 | + | 0.116794i | \(0.0372619\pi\) |
−0.395431 | + | 0.918496i | \(0.629405\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.9368 | 1.06719 | 0.533595 | − | 0.845740i | \(-0.320841\pi\) | ||||
0.533595 | + | 0.845740i | \(0.320841\pi\) | |||||||
\(350\) | 5.61514 | + | 10.0002i | 0.300142 | + | 0.534535i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.25728 | + | 3.90972i | −0.120313 | + | 0.208389i | ||||
\(353\) | 11.4576 | + | 19.8451i | 0.609825 | + | 1.05625i | 0.991269 | + | 0.131856i | \(0.0420937\pi\) |
−0.381444 | + | 0.924392i | \(0.624573\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.22673 | − | 9.05296i | 0.277406 | − | 0.480481i | ||||
\(356\) | −1.06766 | −0.0565860 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.2219 | 0.540242 | ||||||||
\(359\) | 13.6157 | − | 23.5831i | 0.718610 | − | 1.24467i | −0.242940 | − | 0.970041i | \(-0.578112\pi\) |
0.961551 | − | 0.274628i | \(-0.0885547\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.7354 | − | 25.5225i | −0.775548 | − | 1.34329i | ||||
\(362\) | 1.19805 | − | 2.07509i | 0.0629682 | − | 0.109064i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.537699 | − | 0.906101i | 0.0281831 | − | 0.0474926i | ||||
\(365\) | 8.63735 | 0.452099 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.42822 | + | 9.40195i | 0.283351 | + | 0.490778i | 0.972208 | − | 0.234119i | \(-0.0752206\pi\) |
−0.688857 | + | 0.724897i | \(0.741887\pi\) | |||||||
\(368\) | 0.955014 | + | 1.65413i | 0.0497836 | + | 0.0862277i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11.3343 | 0.589241 | ||||||||
\(371\) | 9.61210 | − | 16.1978i | 0.499035 | − | 0.840948i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.18572 | − | 2.05373i | 0.0613943 | − | 0.106338i | −0.833695 | − | 0.552226i | \(-0.813779\pi\) |
0.895089 | + | 0.445888i | \(0.147112\pi\) | |||||||
\(374\) | 5.15326 | + | 8.92571i | 0.266469 | + | 0.461538i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.0043 | − | 27.7202i | 0.825357 | − | 1.42956i | ||||
\(377\) | −1.09606 | −0.0564501 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.2197 | −1.50092 | −0.750458 | − | 0.660918i | \(-0.770167\pi\) | ||||
−0.750458 | + | 0.660918i | \(0.770167\pi\) | |||||||
\(380\) | 4.02381 | − | 6.96944i | 0.206417 | − | 0.357525i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.34248 | − | 4.05729i | −0.119852 | − | 0.207589i | ||||
\(383\) | −1.53297 | + | 2.65519i | −0.0783313 | + | 0.135674i | −0.902530 | − | 0.430627i | \(-0.858293\pi\) |
0.824199 | + | 0.566301i | \(0.191626\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.65729 | + | 13.6372i | 0.390252 | + | 0.695015i | ||||
\(386\) | −17.1964 | −0.875274 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.463750 | − | 0.803238i | −0.0235433 | − | 0.0407782i | ||||
\(389\) | 13.8705 | + | 24.0244i | 0.703261 | + | 1.21808i | 0.967315 | + | 0.253576i | \(0.0816069\pi\) |
−0.264054 | + | 0.964508i | \(0.585060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.50828 | −0.126849 | ||||||||
\(392\) | −11.0607 | + | 18.1405i | −0.558647 | + | 0.916236i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.13984 | − | 10.6345i | 0.309320 | − | 0.535759i | ||||
\(395\) | 12.7156 | + | 22.0240i | 0.639790 | + | 1.10815i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.61559 | + | 14.9226i | −0.432404 | + | 0.748946i | −0.997080 | − | 0.0763669i | \(-0.975668\pi\) |
0.564676 | + | 0.825313i | \(0.309001\pi\) | |||||||
\(398\) | −33.2500 | −1.66667 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.4292 | −0.521459 | ||||||||
\(401\) | 8.32201 | − | 14.4142i | 0.415582 | − | 0.719808i | −0.579908 | − | 0.814682i | \(-0.696911\pi\) |
0.995489 | + | 0.0948737i | \(0.0302447\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.21624 | + | 9.03479i | 0.259839 | + | 0.450055i | ||||
\(404\) | −0.289366 | + | 0.501196i | −0.0143965 | + | 0.0249354i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.66989 | + | 0.0439254i | 0.182133 | + | 0.00217998i | ||||
\(407\) | 6.28355 | 0.311464 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.81689 | + | 11.8072i | 0.337073 | + | 0.583828i | 0.983881 | − | 0.178825i | \(-0.0572296\pi\) |
−0.646807 | + | 0.762653i | \(0.723896\pi\) | |||||||
\(410\) | 0.957237 | + | 1.65798i | 0.0472746 | + | 0.0818820i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.63359 | 0.228280 | ||||||||
\(413\) | 2.74978 | − | 4.63378i | 0.135308 | − | 0.228013i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.5822 | − | 32.1854i | 0.912167 | − | 1.57992i | ||||
\(416\) | 1.10838 | + | 1.91977i | 0.0543426 | + | 0.0941242i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.97238 | + | 15.5406i | −0.438853 | + | 0.760116i | ||||
\(419\) | 10.8502 | 0.530066 | 0.265033 | − | 0.964239i | \(-0.414617\pi\) | ||||
0.265033 | + | 0.964239i | \(0.414617\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 6.34946 | − | 10.9976i | 0.309087 | − | 0.535354i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.8039 | + | 18.7129i | 0.524683 | + | 0.908778i | ||||
\(425\) | 6.84788 | − | 11.8609i | 0.332171 | − | 0.575337i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.35150 | + | 0.0760220i | 0.307371 | + | 0.00367896i | ||||
\(428\) | 7.81574 | 0.377788 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.604344 | + | 1.04676i | 0.0291441 | + | 0.0504790i | ||||
\(431\) | 0.604764 | + | 1.04748i | 0.0291304 | + | 0.0504554i | 0.880223 | − | 0.474560i | \(-0.157393\pi\) |
−0.851093 | + | 0.525016i | \(0.824060\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.56422 | −0.267399 | −0.133700 | − | 0.991022i | \(-0.542686\pi\) | ||||
−0.133700 | + | 0.991022i | \(0.542686\pi\) | |||||||
\(434\) | −17.1032 | − | 30.4597i | −0.820979 | − | 1.46211i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.220375 | + | 0.381700i | −0.0105540 | + | 0.0182801i | ||||
\(437\) | −2.18359 | − | 3.78209i | −0.104455 | − | 0.180922i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.85960 | − | 17.0773i | 0.470573 | − | 0.815057i | −0.528860 | − | 0.848709i | \(-0.677381\pi\) |
0.999434 | + | 0.0336522i | \(0.0107139\pi\) | |||||||
\(440\) | −17.9422 | −0.855362 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.06074 | 0.240715 | ||||||||
\(443\) | 11.1155 | − | 19.2526i | 0.528113 | − | 0.914719i | −0.471350 | − | 0.881946i | \(-0.656233\pi\) |
0.999463 | − | 0.0327726i | \(-0.0104337\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.89091 | − | 6.73926i | −0.184447 | − | 0.319471i | ||||
\(446\) | 11.0716 | − | 19.1766i | 0.524256 | − | 0.908039i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −11.5228 | − | 20.5213i | −0.544399 | − | 0.969542i | ||||
\(449\) | −18.4579 | −0.871082 | −0.435541 | − | 0.900169i | \(-0.643443\pi\) | ||||
−0.435541 | + | 0.900169i | \(0.643443\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.530678 | + | 0.919161i | 0.0249886 | + | 0.0432816i | ||||
\(452\) | 0.218245 | + | 0.378012i | 0.0102654 | + | 0.0177802i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.0439 | −0.565249 | ||||||||
\(455\) | 7.67901 | + | 0.0919110i | 0.359997 | + | 0.00430886i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.9910 | − | 25.9651i | 0.701248 | − | 1.21460i | −0.266781 | − | 0.963757i | \(-0.585960\pi\) |
0.968029 | − | 0.250840i | \(-0.0807067\pi\) | |||||||
\(458\) | 13.3629 | + | 23.1452i | 0.624408 | + | 1.08151i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.362542 | − | 0.627941i | 0.0169036 | − | 0.0292779i | ||||
\(461\) | −29.1498 | −1.35764 | −0.678821 | − | 0.734304i | \(-0.737509\pi\) | ||||
−0.678821 | + | 0.734304i | \(0.737509\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.55900 | 0.0724530 | 0.0362265 | − | 0.999344i | \(-0.488466\pi\) | ||||
0.0362265 | + | 0.999344i | \(0.488466\pi\) | |||||||
\(464\) | −1.66872 | + | 2.89031i | −0.0774685 | + | 0.134179i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.97238 | − | 15.5406i | −0.415637 | − | 0.719905i | ||||
\(467\) | 6.21156 | − | 10.7587i | 0.287437 | − | 0.497855i | −0.685760 | − | 0.727827i | \(-0.740530\pi\) |
0.973197 | + | 0.229972i | \(0.0738635\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.8401 | + | 33.4335i | −0.916132 | + | 1.54382i | ||||
\(470\) | 38.7402 | 1.78695 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.09072 | + | 5.35328i | 0.142262 | + | 0.246405i | ||||
\(473\) | 0.335039 | + | 0.580305i | 0.0154051 | + | 0.0266825i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.8458 | 1.09412 | ||||||||
\(476\) | 4.21281 | + | 0.0504237i | 0.193094 | + | 0.00231117i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.4587 | − | 18.1149i | 0.478368 | − | 0.828557i | ||||
\(479\) | 18.0279 | + | 31.2252i | 0.823716 | + | 1.42672i | 0.902897 | + | 0.429857i | \(0.141436\pi\) |
−0.0791811 | + | 0.996860i | \(0.525231\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.54268 | − | 2.67201i | 0.0703404 | − | 0.121833i | ||||
\(482\) | 17.3249 | 0.789128 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.72887 | 0.124040 | ||||||||
\(485\) | 3.38011 | − | 5.85453i | 0.153483 | − | 0.265840i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.65002 | − | 6.32202i | −0.165398 | − | 0.286478i | 0.771398 | − | 0.636352i | \(-0.219558\pi\) |
−0.936797 | + | 0.349874i | \(0.886224\pi\) | |||||||
\(488\) | −3.64351 | + | 6.31074i | −0.164934 | + | 0.285674i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −25.7075 | − | 0.615481i | −1.16135 | − | 0.0278046i | ||||
\(491\) | −4.49178 | −0.202711 | −0.101356 | − | 0.994850i | \(-0.532318\pi\) | ||||
−0.101356 | + | 0.994850i | \(0.532318\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.19139 | − | 3.79560i | −0.0986954 | − | 0.170945i | ||||
\(494\) | 4.40565 | + | 7.63080i | 0.198219 | + | 0.343326i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 31.7663 | 1.42635 | ||||||||
\(497\) | 4.66512 | + | 8.30829i | 0.209259 | + | 0.372678i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.68369 | + | 9.84443i | −0.254437 | + | 0.440697i | −0.964742 | − | 0.263196i | \(-0.915223\pi\) |
0.710306 | + | 0.703893i | \(0.248557\pi\) | |||||||
\(500\) | −0.910235 | − | 1.57657i | −0.0407069 | − | 0.0705065i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.27709 | − | 16.0684i | 0.414057 | − | 0.717167i | ||||
\(503\) | −17.1080 | −0.762806 | −0.381403 | − | 0.924409i | \(-0.624559\pi\) | ||||
−0.381403 | + | 0.924409i | \(0.624559\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.21818 | −0.187706 | ||||||||
\(506\) | −0.808405 | + | 1.40020i | −0.0359380 | + | 0.0622464i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.03171 | + | 1.78698i | 0.0457749 | + | 0.0792845i | ||||
\(509\) | 1.64142 | − | 2.84303i | 0.0727547 | − | 0.126015i | −0.827353 | − | 0.561682i | \(-0.810154\pi\) |
0.900108 | + | 0.435667i | \(0.143488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.01784 | + | 6.77065i | −0.177739 | + | 0.299516i | ||||
\(512\) | 25.2340 | 1.11520 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.10916 | + | 1.92113i | 0.0489231 | + | 0.0847373i | ||||
\(515\) | 16.8863 | + | 29.2479i | 0.744100 | + | 1.28882i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.4770 | 0.944555 | ||||||||
\(518\) | −5.27237 | + | 8.88472i | −0.231655 | + | 0.390372i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.40502 | + | 7.62973i | −0.193173 | + | 0.334586i | ||||
\(521\) | −2.38530 | − | 4.13147i | −0.104502 | − | 0.181003i | 0.809033 | − | 0.587764i | \(-0.199992\pi\) |
−0.913535 | + | 0.406761i | \(0.866658\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.7562 | + | 22.0944i | −0.557789 | + | 0.966119i | 0.439892 | + | 0.898051i | \(0.355017\pi\) |
−0.997681 | + | 0.0680682i | \(0.978316\pi\) | |||||||
\(524\) | 4.20803 | 0.183829 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 34.0975 | 1.48672 | ||||||||
\(527\) | −20.8580 | + | 36.1271i | −0.908588 | + | 1.57372i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.3033 | + | 19.5778i | 0.491446 | + | 0.851210i | ||||
\(530\) | −13.0760 | + | 22.6483i | −0.567986 | + | 0.983780i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.59145 | + | 6.39616i | 0.155709 | + | 0.277309i | ||||
\(533\) | 0.521150 | 0.0225735 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.4831 | + | 49.3342i | 1.23143 | + | 2.13290i | ||||
\(536\) | −22.3001 | − | 38.6249i | −0.963216 | − | 1.66834i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −27.9309 | −1.20418 | ||||||||
\(539\) | −14.2519 | − | 0.341214i | −0.613871 | − | 0.0146971i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.25784 | − | 14.3030i | 0.355032 | − | 0.614934i | −0.632091 | − | 0.774894i | \(-0.717803\pi\) |
0.987123 | + | 0.159960i | \(0.0511366\pi\) | |||||||
\(542\) | −5.67125 | − | 9.82290i | −0.243601 | − | 0.421930i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.43203 | + | 7.67649i | −0.190022 | + | 0.329127i | ||||
\(545\) | −3.21247 | −0.137607 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.3317 | 0.997591 | 0.498796 | − | 0.866720i | \(-0.333776\pi\) | ||||
0.498796 | + | 0.866720i | \(0.333776\pi\) | |||||||
\(548\) | 1.16917 | − | 2.02507i | 0.0499446 | − | 0.0865066i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.41407 | − | 7.64539i | −0.188216 | − | 0.326001i | ||||
\(551\) | 3.81545 | − | 6.60855i | 0.162544 | − | 0.281534i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.1791 | − | 0.277434i | −0.985676 | − | 0.0117977i | ||||
\(554\) | 9.52909 | 0.404852 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.796470 | − | 1.37953i | −0.0337779 | − | 0.0585050i | ||||
\(557\) | −10.0235 | − | 17.3613i | −0.424711 | − | 0.735621i | 0.571682 | − | 0.820475i | \(-0.306291\pi\) |
−0.996393 | + | 0.0848540i | \(0.972958\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.329024 | 0.0139162 | ||||||||
\(560\) | 11.9334 | − | 20.1096i | 0.504279 | − | 0.849784i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.8425 | + | 32.6362i | −0.794824 | + | 1.37668i | ||||
\(563\) | −20.2642 | − | 35.0986i | −0.854034 | − | 1.47923i | −0.877539 | − | 0.479506i | \(-0.840816\pi\) |
0.0235047 | − | 0.999724i | \(-0.492518\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.59072 | + | 2.75520i | −0.0669219 | + | 0.115912i | ||||
\(566\) | −0.381519 | −0.0160364 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.9311 | −0.458659 | ||||||||
\(569\) | −10.7252 | + | 18.5766i | −0.449623 | + | 0.778770i | −0.998361 | − | 0.0572245i | \(-0.981775\pi\) |
0.548739 | + | 0.835994i | \(0.315108\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.47793 | + | 9.48806i | 0.229244 | + | 0.397063i | 0.957584 | − | 0.288153i | \(-0.0930412\pi\) |
−0.728340 | + | 0.685216i | \(0.759708\pi\) | |||||||
\(572\) | −0.405516 | + | 0.702374i | −0.0169555 | + | 0.0293677i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.74494 | − | 0.0208854i | −0.0728323 | − | 0.000871740i | ||||
\(575\) | 2.14849 | 0.0895982 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.3708 | − | 30.0870i | −0.723154 | − | 1.25254i | −0.959729 | − | 0.280927i | \(-0.909358\pi\) |
0.236575 | − | 0.971613i | \(-0.423975\pi\) | |||||||
\(578\) | −0.639571 | − | 1.10777i | −0.0266027 | − | 0.0460771i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.26696 | 0.0526076 | ||||||||
\(581\) | 16.5856 | + | 29.5380i | 0.688086 | + | 1.22544i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.24915 | + | 12.5559i | −0.300229 | + | 0.520012i | ||||
\(584\) | −4.51600 | − | 7.82195i | −0.186874 | − | 0.323675i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.1796 | − | 21.0958i | 0.503136 | − | 0.871458i | ||||
\(587\) | 22.8463 | 0.942967 | 0.471483 | − | 0.881875i | \(-0.343719\pi\) | ||||
0.471483 | + | 0.881875i | \(0.343719\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −72.6320 | −2.99275 | ||||||||
\(590\) | −3.74071 | + | 6.47911i | −0.154003 | + | 0.266741i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.69738 | − | 8.13610i | −0.193061 | − | 0.334392i | ||||
\(593\) | 8.79676 | − | 15.2364i | 0.361240 | − | 0.625686i | −0.626925 | − | 0.779079i | \(-0.715687\pi\) |
0.988165 | + | 0.153394i | \(0.0490202\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.0346 | + | 26.7757i | 0.616359 | + | 1.09770i | ||||
\(596\) | −4.02433 | −0.164843 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.396945 | + | 0.687530i | 0.0162323 | + | 0.0281152i | ||||
\(599\) | 15.5036 | + | 26.8531i | 0.633461 | + | 1.09719i | 0.986839 | + | 0.161706i | \(0.0516997\pi\) |
−0.353378 | + | 0.935481i | \(0.614967\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.43754 | −0.0586385 | −0.0293193 | − | 0.999570i | \(-0.509334\pi\) | ||||
−0.0293193 | + | 0.999570i | \(0.509334\pi\) | |||||||
\(602\) | −1.10165 | − | 0.0131858i | −0.0449001 | − | 0.000537415i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.0373796 | + | 0.0647433i | −0.00152095 | + | 0.00263437i | ||||
\(605\) | 9.94490 | + | 17.2251i | 0.404318 | + | 0.700299i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.5085 | − | 28.5936i | 0.670061 | − | 1.16058i | −0.307826 | − | 0.951443i | \(-0.599601\pi\) |
0.977887 | − | 0.209136i | \(-0.0670652\pi\) | |||||||
\(608\) | −15.4333 | −0.625901 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.81953 | −0.357092 | ||||||||
\(611\) | 5.27284 | − | 9.13283i | 0.213316 | − | 0.369475i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.5829 | + | 37.3826i | 0.871723 | + | 1.50987i | 0.860213 | + | 0.509935i | \(0.170331\pi\) |
0.0115102 | + | 0.999934i | \(0.496336\pi\) | |||||||
\(614\) | −2.26404 | + | 3.92143i | −0.0913692 | + | 0.158256i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.34619 | − | 14.0646i | 0.336278 | − | 0.566677i | ||||
\(617\) | −2.45772 | −0.0989441 | −0.0494721 | − | 0.998776i | \(-0.515754\pi\) | ||||
−0.0494721 | + | 0.998776i | \(0.515754\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.8894 | − | 32.7175i | −0.759231 | − | 1.31503i | −0.943243 | − | 0.332102i | \(-0.892242\pi\) |
0.184013 | − | 0.982924i | \(-0.441091\pi\) | |||||||
\(620\) | −6.02954 | − | 10.4435i | −0.242152 | − | 0.419420i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −30.1602 | −1.20932 | ||||||||
\(623\) | 7.09271 | + | 0.0848936i | 0.284163 | + | 0.00340119i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.1971 | − | 26.3222i | 0.607884 | − | 1.05289i | ||||
\(626\) | −11.4420 | − | 19.8181i | −0.457313 | − | 0.792089i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.40371 | + | 4.16334i | −0.0959183 | + | 0.166135i | ||||
\(629\) | 12.3374 | 0.491922 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.4828 | −1.13388 | −0.566942 | − | 0.823758i | \(-0.691874\pi\) | ||||
−0.566942 | + | 0.823758i | \(0.691874\pi\) | |||||||
\(632\) | 13.2966 | − | 23.0303i | 0.528909 | − | 0.916098i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17.4326 | + | 30.1942i | 0.692337 | + | 1.19916i | ||||
\(635\) | −7.51981 | + | 13.0247i | −0.298415 | + | 0.516869i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.64409 | + | 5.97667i | −0.144384 | + | 0.236804i | ||||
\(638\) | −2.82509 | −0.111847 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.90456 | + | 17.1552i | 0.391512 | + | 0.678119i | ||||
\(641\) | −13.5961 | − | 23.5492i | −0.537014 | − | 0.930136i | −0.999063 | − | 0.0432812i | \(-0.986219\pi\) |
0.462049 | − | 0.886854i | \(-0.347114\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.1664 | −1.46570 | −0.732849 | − | 0.680391i | \(-0.761810\pi\) | ||||
−0.732849 | + | 0.680391i | \(0.761810\pi\) | |||||||
\(644\) | 0.323587 | + | 0.576289i | 0.0127511 | + | 0.0227090i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.6167 | + | 30.5130i | −0.693120 | + | 1.20052i | ||||
\(647\) | 9.41593 | + | 16.3089i | 0.370178 | + | 0.641168i | 0.989593 | − | 0.143896i | \(-0.0459632\pi\) |
−0.619414 | + | 0.785064i | \(0.712630\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.07380 | + | 3.59192i | −0.0814036 | + | 0.140995i | ||||
\(650\) | −4.33482 | −0.170026 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.93910 | −0.232593 | ||||||||
\(653\) | −13.0092 | + | 22.5326i | −0.509090 | + | 0.881770i | 0.490854 | + | 0.871242i | \(0.336685\pi\) |
−0.999945 | + | 0.0105286i | \(0.996649\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.3355 | + | 26.5618i | 0.599206 | + | 1.03786i | ||||
\(656\) | 0.793435 | − | 1.37427i | 0.0309784 | − | 0.0536562i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18.0208 | + | 30.3676i | −0.702523 | + | 1.18385i | ||||
\(659\) | 33.3339 | 1.29851 | 0.649253 | − | 0.760573i | \(-0.275082\pi\) | ||||
0.649253 | + | 0.760573i | \(0.275082\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.14920 | − | 5.45458i | −0.122490 | − | 0.212159i | 0.798259 | − | 0.602314i | \(-0.205755\pi\) |
−0.920749 | + | 0.390156i | \(0.872421\pi\) | |||||||
\(662\) | −11.5053 | − | 19.9277i | −0.447164 | − | 0.774511i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −38.8626 | −1.50816 | ||||||||
\(665\) | −27.2852 | + | 45.9795i | −1.05807 | + | 1.78301i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.343769 | − | 0.595426i | 0.0133108 | − | 0.0230550i | ||||
\(668\) | −1.00687 | − | 1.74394i | −0.0389568 | − | 0.0674752i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 26.9899 | − | 46.7479i | 1.04271 | − | 1.80603i | ||||
\(671\) | −4.88941 | −0.188754 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.3188 | 0.706137 | 0.353068 | − | 0.935598i | \(-0.385138\pi\) | ||||
0.353068 | + | 0.935598i | \(0.385138\pi\) | |||||||
\(674\) | −10.8451 | + | 18.7842i | −0.417736 | + | 0.723541i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.199118 | + | 0.344882i | 0.00765837 | + | 0.0132647i | ||||
\(677\) | 12.1696 | − | 21.0783i | 0.467715 | − | 0.810106i | −0.531604 | − | 0.846993i | \(-0.678411\pi\) |
0.999319 | + | 0.0368866i | \(0.0117440\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.01692 | + | 5.37296i | 0.115779 | + | 0.206195i | ||||
\(680\) | −35.2284 | −1.35095 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 13.4448 | + | 23.2871i | 0.514829 | + | 0.891709i | ||||
\(683\) | 5.88409 | + | 10.1916i | 0.225149 | + | 0.389969i | 0.956364 | − | 0.292178i | \(-0.0943799\pi\) |
−0.731215 | + | 0.682147i | \(0.761047\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.0434 | 0.651195 | ||||||||
\(686\) | 12.4408 | − | 19.8653i | 0.474994 | − | 0.758461i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.500929 | − | 0.867635i | 0.0190977 | − | 0.0330783i | ||||
\(689\) | 3.55950 | + | 6.16523i | 0.135606 | + | 0.234877i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.588923 | + | 1.02004i | −0.0224037 | + | 0.0388043i | −0.877010 | − | 0.480472i | \(-0.840465\pi\) |
0.854606 | + | 0.519277i | \(0.173799\pi\) | |||||||
\(692\) | −0.237195 | −0.00901679 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.1835 | 1.06983 | ||||||||
\(695\) | 5.80520 | − | 10.0549i | 0.220204 | − | 0.381404i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.04195 | + | 1.80471i | 0.0394668 | + | 0.0683584i | ||||
\(698\) | 12.6161 | − | 21.8517i | 0.477525 | − | 0.827097i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.60852 | − | 0.0431908i | −0.136389 | − | 0.00163246i | ||||
\(701\) | 31.2867 | 1.18168 | 0.590841 | − | 0.806788i | \(-0.298796\pi\) | ||||
0.590841 | + | 0.806788i | \(0.298796\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.7403 | + | 18.6028i | 0.405079 | + | 0.701617i | ||||
\(704\) | 9.05804 | + | 15.6890i | 0.341388 | + | 0.591301i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 29.0016 | 1.09149 | ||||||||
\(707\) | 1.96217 | − | 3.30654i | 0.0737950 | − | 0.124355i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.68738 | + | 13.3149i | −0.288706 | + | 0.500053i | −0.973501 | − | 0.228682i | \(-0.926558\pi\) |
0.684795 | + | 0.728735i | \(0.259892\pi\) | |||||||
\(710\) | −6.61499 | − | 11.4575i | −0.248256 | − | 0.429992i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.06870 | + | 7.04719i | −0.152481 | + | 0.264105i | ||||
\(713\) | −6.54409 | −0.245078 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.91133 | −0.221071 | ||||||||
\(716\) | −1.60820 | + | 2.78549i | −0.0601013 | + | 0.104098i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −17.2322 | − | 29.8470i | −0.643099 | − | 1.11388i | ||||
\(719\) | −5.57087 | + | 9.64904i | −0.207759 | + | 0.359848i | −0.951008 | − | 0.309166i | \(-0.899950\pi\) |
0.743250 | + | 0.669014i | \(0.233283\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.7819 | − | 0.368433i | −1.14638 | − | 0.0137211i | ||||
\(722\) | −37.2985 | −1.38811 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.376978 | + | 0.652945i | 0.0140103 | + | 0.0242665i | ||||
\(725\) | 1.87706 | + | 3.25116i | 0.0697121 | + | 0.120745i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.24735 | −0.231702 | −0.115851 | − | 0.993267i | \(-0.536959\pi\) | ||||
−0.115851 | + | 0.993267i | \(0.536959\pi\) | |||||||
\(728\) | −3.93171 | − | 7.00214i | −0.145719 | − | 0.259516i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.46575 | − | 9.46696i | 0.202296 | − | 0.350388i | ||||
\(731\) | 0.657828 | + | 1.13939i | 0.0243307 | + | 0.0421419i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.4834 | + | 26.8181i | −0.571894 | + | 0.990550i | 0.424477 | + | 0.905439i | \(0.360458\pi\) |
−0.996371 | + | 0.0851111i | \(0.972875\pi\) | |||||||
\(734\) | 13.7400 | 0.507153 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.39053 | −0.0512554 | ||||||||
\(737\) | 14.9628 | − | 25.9163i | 0.551162 | − | 0.954641i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.16872 | − | 2.02429i | −0.0429921 | − | 0.0744646i | 0.843729 | − | 0.536770i | \(-0.180356\pi\) |
−0.886721 | + | 0.462305i | \(0.847022\pi\) | |||||||
\(740\) | −1.78322 | + | 3.08862i | −0.0655523 | + | 0.113540i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.6710 | − | 20.7854i | −0.428456 | − | 0.763055i | ||||
\(743\) | −24.3612 | −0.893726 | −0.446863 | − | 0.894603i | \(-0.647459\pi\) | ||||
−0.446863 | + | 0.894603i | \(0.647459\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.6660 | − | 25.4022i | −0.537321 | − | 0.930666i | ||||
\(746\) | −1.50066 | − | 2.59922i | −0.0549430 | − | 0.0951641i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.24304 | −0.118577 | ||||||||
\(749\) | −51.9216 | − | 0.621457i | −1.89718 | − | 0.0227075i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.01266 | − | 10.4142i | 0.219405 | − | 0.380021i | −0.735221 | − | 0.677827i | \(-0.762922\pi\) |
0.954626 | + | 0.297806i | \(0.0962550\pi\) | |||||||
\(752\) | −16.0555 | − | 27.8089i | −0.585483 | − | 1.01409i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.693593 | + | 1.20134i | −0.0252592 | + | 0.0437502i | ||||
\(755\) | −0.544894 | −0.0198307 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.9905 | 0.944641 | 0.472321 | − | 0.881427i | \(-0.343416\pi\) | ||||
0.472321 | + | 0.881427i | \(0.343416\pi\) | |||||||
\(758\) | −18.4904 | + | 32.0263i | −0.671600 | + | 1.16325i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −30.6682 | − | 53.1189i | −1.11245 | − | 1.92683i | ||||
\(761\) | 6.66350 | − | 11.5415i | 0.241552 | − | 0.418380i | −0.719605 | − | 0.694384i | \(-0.755677\pi\) |
0.961156 | + | 0.276004i | \(0.0890103\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.49435 | − | 2.51819i | 0.0540990 | − | 0.0911647i | ||||
\(764\) | 1.47416 | 0.0533334 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.94014 | + | 3.36043i | 0.0701002 | + | 0.121417i | ||||
\(767\) | 1.01828 | + | 1.76372i | 0.0367680 | + | 0.0636841i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.24486 | 0.333378 | 0.166689 | − | 0.986010i | \(-0.446692\pi\) | ||||
0.166689 | + | 0.986010i | \(0.446692\pi\) | |||||||
\(770\) | 19.7926 | + | 0.236900i | 0.713275 | + | 0.00853728i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.70550 | − | 4.68607i | 0.0973732 | − | 0.168655i | ||||
\(773\) | −5.07097 | − | 8.78317i | −0.182390 | − | 0.315909i | 0.760304 | − | 0.649568i | \(-0.225050\pi\) |
−0.942694 | + | 0.333659i | \(0.891717\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.8661 | − | 30.9450i | 0.641768 | − | 1.11158i | ||||
\(776\) | −7.06912 | −0.253766 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 35.1092 | 1.25873 | ||||||||
\(779\) | −1.81415 | + | 3.14220i | −0.0649987 | + | 0.112581i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.66725 | − | 6.35186i | −0.131225 | − | 0.227288i | ||||
\(782\) | −1.58725 | + | 2.74920i | −0.0567600 | + | 0.0983112i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.2124 | + | 18.7088i | 0.364729 | + | 0.668170i | ||||
\(785\) | −35.0396 | −1.25062 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.6411 | − | 39.2156i | −0.807070 | − | 1.39789i | −0.914885 | − | 0.403715i | \(-0.867719\pi\) |
0.107815 | − | 0.994171i | \(-0.465614\pi\) | |||||||
\(788\) | 1.93195 | + | 3.34624i | 0.0688230 | + | 0.119205i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 32.1859 | 1.14512 | ||||||||
\(791\) | −1.41979 | − | 2.52857i | −0.0504821 | − | 0.0899056i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.20041 | + | 2.07917i | −0.0426277 | + | 0.0738334i | ||||
\(794\) | 10.9040 | + | 18.8862i | 0.386967 | + | 0.670247i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.23121 | − | 9.06072i | 0.185415 | − | 0.321149i | ||||
\(797\) | −27.0784 | −0.959165 | −0.479583 | − | 0.877497i | \(-0.659212\pi\) | ||||
−0.479583 | + | 0.877497i | \(0.659212\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.1686 | 1.49182 | ||||||||
\(800\) | 3.79629 | − | 6.57536i | 0.134219 | − | 0.232474i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.5324 | − | 18.2427i | −0.371912 | − | 0.644171i | ||||
\(803\) | 3.03013 | − | 5.24834i | 0.106931 | − | 0.185210i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.45837 | + | 4.14272i | −0.0866463 | + | 0.146012i | ||||
\(806\) | 13.2034 | 0.465071 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.20546 | + | 3.81996i | 0.0775877 | + | 0.134386i | ||||
\(809\) | −12.8899 | − | 22.3260i | −0.453185 | − | 0.784939i | 0.545397 | − | 0.838178i | \(-0.316379\pi\) |
−0.998582 | + | 0.0532388i | \(0.983046\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.7829 | −0.905362 | −0.452681 | − | 0.891673i | \(-0.649532\pi\) | ||||
−0.452681 | + | 0.891673i | \(0.649532\pi\) | |||||||
\(812\) | −0.589352 | + | 0.993144i | −0.0206822 | + | 0.0348525i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.97626 | − | 6.88708i | 0.139368 | − | 0.241392i | ||||
\(815\) | −21.6440 | − | 37.4886i | −0.758158 | − | 1.31317i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.14535 | + | 1.98380i | −0.0400707 | + | 0.0694045i | ||||
\(818\) | 17.2550 | 0.603308 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.602407 | −0.0210370 | ||||||||
\(821\) | −0.855366 | + | 1.48154i | −0.0298525 | + | 0.0517060i | −0.880566 | − | 0.473924i | \(-0.842837\pi\) |
0.850713 | + | 0.525630i | \(0.176170\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.1887 | + | 34.9678i | 0.703733 | + | 1.21890i | 0.967147 | + | 0.254218i | \(0.0818181\pi\) |
−0.263414 | + | 0.964683i | \(0.584849\pi\) | |||||||
\(824\) | 17.6579 | − | 30.5844i | 0.615142 | − | 1.06546i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.33878 | − | 5.94616i | −0.116171 | − | 0.206893i | ||||
\(827\) | −19.5698 | −0.680509 | −0.340254 | − | 0.940333i | \(-0.610513\pi\) | ||||
−0.340254 | + | 0.940333i | \(0.610513\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.7871 | − | 36.0043i | −0.721966 | − | 1.25048i | −0.960211 | − | 0.279277i | \(-0.909905\pi\) |
0.238244 | − | 0.971205i | \(-0.423428\pi\) | |||||||
\(830\) | −23.5178 | − | 40.7341i | −0.816316 | − | 1.41390i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.89542 | 0.308393 | ||||||||
\(833\) | −27.9826 | − | 0.669951i | −0.969540 | − | 0.0232124i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.33870 | − | 12.7110i | 0.253966 | − | 0.439882i | ||||
\(836\) | −2.82324 | − | 4.89000i | −0.0976438 | − | 0.169124i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.86604 | − | 11.8923i | 0.237183 | − | 0.410814i | ||||
\(839\) | −45.8480 | −1.58285 | −0.791425 | − | 0.611266i | \(-0.790660\pi\) | ||||
−0.791425 | + | 0.611266i | \(0.790660\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7986 | −0.958574 | ||||||||
\(842\) | −6.32804 | + | 10.9605i | −0.218079 | + | 0.377723i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.99791 | + | 3.46049i | 0.0687710 | + | 0.119115i | ||||
\(845\) | −1.45130 | + | 2.51373i | −0.0499262 | + | 0.0864748i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.1285 | − | 0.216982i | −0.622902 | − | 0.00745559i | ||||
\(848\) | 21.6769 | 0.744388 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.66674 | − | 15.0112i | −0.297267 | − | 0.514881i | ||||
\(851\) | 0.967695 | + | 1.67610i | 0.0331722 | + | 0.0574559i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.0236 | 1.37038 | 0.685191 | − | 0.728364i | \(-0.259719\pi\) | ||||
0.685191 | + | 0.728364i | \(0.259719\pi\) | |||||||
\(854\) | 4.10258 | − | 6.91345i | 0.140387 | − | 0.236573i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.7846 | − | 51.5884i | 1.01802 | − | 1.76326i | ||||
\(857\) | 16.4351 | + | 28.4664i | 0.561412 | + | 0.972395i | 0.997374 | + | 0.0724294i | \(0.0230752\pi\) |
−0.435961 | + | 0.899966i | \(0.643591\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.0252 | − | 29.4885i | 0.580891 | − | 1.00613i | −0.414483 | − | 0.910057i | \(-0.636037\pi\) |
0.995374 | − | 0.0960762i | \(-0.0306292\pi\) | |||||||
\(860\) | −0.380325 | −0.0129690 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.53079 | 0.0521388 | ||||||||
\(863\) | −7.03208 | + | 12.1799i | −0.239375 | + | 0.414609i | −0.960535 | − | 0.278159i | \(-0.910276\pi\) |
0.721160 | + | 0.692768i | \(0.243609\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.864415 | − | 1.49721i | −0.0293910 | − | 0.0509067i | ||||
\(866\) | −3.52106 | + | 6.09866i | −0.119651 | + | 0.207241i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10.9912 | + | 0.131555i | 0.373066 | + | 0.00446527i | ||||
\(869\) | 17.8434 | 0.605295 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.34709 | − | 12.7255i | −0.248947 | − | 0.431188i | ||||
\(872\) | 1.67963 | + | 2.90920i | 0.0568794 | + | 0.0985180i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.52715 | −0.186959 | ||||||||
\(875\) | 5.92153 | + | 10.5459i | 0.200184 | + | 0.356516i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.5335 | + | 44.2252i | −0.862204 | + | 1.49338i | 0.00759373 | + | 0.999971i | \(0.497583\pi\) |
−0.869797 | + | 0.493409i | \(0.835751\pi\) | |||||||
\(878\) | −12.4784 | − | 21.6132i | −0.421125 | − | 0.729411i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.99982 | + | 15.5881i | −0.303384 | + | 0.525476i | ||||
\(881\) | 18.4203 | 0.620597 | 0.310298 | − | 0.950639i | \(-0.399571\pi\) | ||||
0.310298 | + | 0.950639i | \(0.399571\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.126678 | 0.00426305 | 0.00213153 | − | 0.999998i | \(-0.499322\pi\) | ||||
0.00213153 | + | 0.999998i | \(0.499322\pi\) | |||||||
\(884\) | −0.796204 | + | 1.37907i | −0.0267792 | + | 0.0463830i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.0679 | − | 24.3663i | −0.472619 | − | 0.818601i | ||||
\(887\) | 1.93735 | − | 3.35559i | 0.0650498 | − | 0.112670i | −0.831666 | − | 0.555276i | \(-0.812613\pi\) |
0.896716 | + | 0.442606i | \(0.145946\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.71181 | − | 11.9533i | −0.225107 | − | 0.400902i | ||||
\(890\) | −9.84874 | −0.330131 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.48378 | + | 6.03409i | 0.116646 | + | 0.202036i | ||||
\(893\) | 36.7100 | + | 63.5837i | 1.22845 | + | 2.12775i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.4433 | −0.783622 | ||||||||
\(896\) | −18.0549 | − | 0.216102i | −0.603173 | − | 0.00721945i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.6802 | + | 20.2308i | −0.389775 | + | 0.675109i | ||||
\(899\) | −5.71733 | − | 9.90270i | −0.190684 | − | 0.330274i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.2332 | + | 24.6527i | −0.474178 | + | 0.821300i | ||||
\(902\) | 1.34326 | 0.0447257 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.32680 | 0.110648 | ||||||||
\(905\) | −2.74766 | + | 4.75909i | −0.0913355 | + | 0.158198i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.3871 | + | 40.5076i | 0.776555 | + | 1.34503i | 0.933916 | + | 0.357491i | \(0.116368\pi\) |
−0.157362 | + | 0.987541i | \(0.550299\pi\) | |||||||
\(908\) | 1.89486 | − | 3.28200i | 0.0628832 | − | 0.108917i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.96005 | − | 8.35841i | 0.164424 | − | 0.277079i | ||||
\(911\) | −5.93675 | −0.196693 | −0.0983467 | − | 0.995152i | \(-0.531355\pi\) | ||||
−0.0983467 | + | 0.995152i | \(0.531355\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.0379 | − | 22.5824i | −0.431493 | − | 0.747368i | ||||
\(914\) | −18.9727 | − | 32.8617i | −0.627561 | − | 1.08697i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.40952 | −0.277858 | ||||||||
\(917\) | −27.9549 | − | 0.334595i | −0.923151 | − | 0.0110493i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.29351 | − | 7.43657i | 0.141630 | − | 0.245310i | −0.786481 | − | 0.617615i | \(-0.788099\pi\) |
0.928110 | + | 0.372305i | \(0.121432\pi\) | |||||||
\(920\) | −2.76318 | − | 4.78597i | −0.0910995 | − | 0.157789i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.4461 | + | 31.9496i | −0.607490 | + | 1.05220i | ||||
\(923\) | −3.60141 | −0.118542 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.5677 | −0.347463 | ||||||||
\(926\) | 0.986543 | − | 1.70874i | 0.0324198 | − | 0.0561528i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.21485 | − | 2.10418i | −0.0398794 | − | 0.0690732i | ||||
\(929\) | −4.22972 | + | 7.32610i | −0.138773 | + | 0.240361i | −0.927032 | − | 0.374981i | \(-0.877649\pi\) |
0.788260 | + | 0.615343i | \(0.210982\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.3502 | − | 42.7766i | −0.765271 | − | 1.40195i | ||||
\(932\) | 5.64648 | 0.184957 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.86141 | − | 13.6164i | −0.257233 | − | 0.445541i | ||||
\(935\) | −11.8187 | − | 20.4706i | −0.386513 | − | 0.669460i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.3596 | −1.08981 | −0.544905 | − | 0.838498i | \(-0.683434\pi\) | ||||
−0.544905 | + | 0.838498i | \(0.683434\pi\) | |||||||
\(938\) | 24.0899 | + | 42.9026i | 0.786562 | + | 1.40082i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.09497 | + | 10.5568i | −0.198796 | + | 0.344325i | ||||
\(941\) | −6.70187 | − | 11.6080i | −0.218475 | − | 0.378409i | 0.735867 | − | 0.677126i | \(-0.236775\pi\) |
−0.954342 | + | 0.298717i | \(0.903441\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.163454 | + | 0.283110i | −0.00532278 | + | 0.00921933i | ||||
\(944\) | 6.20121 | 0.201832 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.848057 | 0.0275727 | ||||||||
\(947\) | 21.5397 | − | 37.3078i | 0.699946 | − | 1.21234i | −0.268539 | − | 0.963269i | \(-0.586541\pi\) |
0.968485 | − | 0.249073i | \(-0.0801259\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.48786 | − | 2.57706i | −0.0482981 | − | 0.0836548i | ||||
\(950\) | 15.0897 | − | 26.1362i | 0.489575 | − | 0.847969i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 16.3872 | − | 27.6149i | 0.531113 | − | 0.895003i | ||||
\(953\) | −16.7332 | −0.542040 | −0.271020 | − | 0.962574i | \(-0.587361\pi\) | ||||
−0.271020 | + | 0.962574i | \(0.587361\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.37234 | + | 9.30517i | 0.173845 | + | 0.301108i | ||||
\(956\) | 3.29091 | + | 5.70002i | 0.106436 | + | 0.184352i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 45.6325 | 1.47432 | ||||||||
\(959\) | −7.92809 | + | 13.3600i | −0.256011 | + | 0.431417i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −38.9183 | + | 67.4085i | −1.25543 | + | 2.17447i | ||||
\(962\) | −1.95243 | − | 3.38172i | −0.0629490 | − | 0.109031i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.72572 | + | 4.72109i | −0.0877896 | + | 0.152056i | ||||
\(965\) | 39.4390 | 1.26959 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.7594 | 1.43937 | 0.719683 | − | 0.694303i | \(-0.244287\pi\) | ||||
0.719683 | + | 0.694303i | \(0.244287\pi\) | |||||||
\(968\) | 10.3993 | − | 18.0121i | 0.334246 | − | 0.578932i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.27790 | − | 7.40954i | −0.137355 | − | 0.237906i | ||||
\(971\) | −2.10129 | + | 3.63955i | −0.0674337 | + | 0.116799i | −0.897771 | − | 0.440463i | \(-0.854814\pi\) |
0.830337 | + | 0.557261i | \(0.188148\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.18143 | + | 9.22783i | 0.166109 | + | 0.295830i | ||||
\(974\) | −9.23899 | −0.296036 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.65517 | + | 6.33093i | 0.116999 | + | 0.202648i | ||||
\(977\) | −12.8449 | − | 22.2481i | −0.410946 | − | 0.711779i | 0.584048 | − | 0.811719i | \(-0.301468\pi\) |
−0.994993 | + | 0.0999403i | \(0.968135\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.45999 | −0.174502 | ||||||||
\(980\) | 4.21227 | − | 6.90854i | 0.134556 | − | 0.220685i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.84242 | + | 4.92321i | −0.0907051 | + | 0.157106i | ||||
\(983\) | −15.9122 | − | 27.5607i | −0.507520 | − | 0.879051i | −0.999962 | − | 0.00870538i | \(-0.997229\pi\) |
0.492442 | − | 0.870345i | \(-0.336104\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.0814 | + | 24.3896i | −0.448669 | + | 0.777118i | ||||
\(986\) | −5.54689 | −0.176649 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.77255 | −0.0882067 | ||||||||
\(989\) | −0.103195 | + | 0.178739i | −0.00328141 | + | 0.00568358i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.73739 | − | 8.20540i | −0.150488 | − | 0.260653i | 0.780919 | − | 0.624632i | \(-0.214751\pi\) |
−0.931407 | + | 0.363979i | \(0.881418\pi\) | |||||||
\(992\) | −11.5631 | + | 20.0279i | −0.367129 | + | 0.635887i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.0584 | + | 0.144329i | 0.382469 | + | 0.00457783i | ||||
\(995\) | 76.2570 | 2.41751 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.9755 | − | 19.0102i | −0.347599 | − | 0.602059i | 0.638224 | − | 0.769851i | \(-0.279670\pi\) |
−0.985822 | + | 0.167792i | \(0.946336\pi\) | |||||||
\(998\) | 7.19332 | + | 12.4592i | 0.227701 | + | 0.394389i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 819.2.j.h.352.3 | 10 | ||
3.2 | odd | 2 | 91.2.e.c.79.3 | yes | 10 | ||
7.2 | even | 3 | 5733.2.a.bl.1.3 | 5 | |||
7.4 | even | 3 | inner | 819.2.j.h.235.3 | 10 | ||
7.5 | odd | 6 | 5733.2.a.bm.1.3 | 5 | |||
12.11 | even | 2 | 1456.2.r.p.625.1 | 10 | |||
21.2 | odd | 6 | 637.2.a.l.1.3 | 5 | |||
21.5 | even | 6 | 637.2.a.k.1.3 | 5 | |||
21.11 | odd | 6 | 91.2.e.c.53.3 | ✓ | 10 | ||
21.17 | even | 6 | 637.2.e.m.508.3 | 10 | |||
21.20 | even | 2 | 637.2.e.m.79.3 | 10 | |||
39.38 | odd | 2 | 1183.2.e.f.170.3 | 10 | |||
84.11 | even | 6 | 1456.2.r.p.417.1 | 10 | |||
273.116 | odd | 6 | 1183.2.e.f.508.3 | 10 | |||
273.194 | even | 6 | 8281.2.a.bx.1.3 | 5 | |||
273.233 | odd | 6 | 8281.2.a.bw.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.e.c.53.3 | ✓ | 10 | 21.11 | odd | 6 | ||
91.2.e.c.79.3 | yes | 10 | 3.2 | odd | 2 | ||
637.2.a.k.1.3 | 5 | 21.5 | even | 6 | |||
637.2.a.l.1.3 | 5 | 21.2 | odd | 6 | |||
637.2.e.m.79.3 | 10 | 21.20 | even | 2 | |||
637.2.e.m.508.3 | 10 | 21.17 | even | 6 | |||
819.2.j.h.235.3 | 10 | 7.4 | even | 3 | inner | ||
819.2.j.h.352.3 | 10 | 1.1 | even | 1 | trivial | ||
1183.2.e.f.170.3 | 10 | 39.38 | odd | 2 | |||
1183.2.e.f.508.3 | 10 | 273.116 | odd | 6 | |||
1456.2.r.p.417.1 | 10 | 84.11 | even | 6 | |||
1456.2.r.p.625.1 | 10 | 12.11 | even | 2 | |||
5733.2.a.bl.1.3 | 5 | 7.2 | even | 3 | |||
5733.2.a.bm.1.3 | 5 | 7.5 | odd | 6 | |||
8281.2.a.bw.1.3 | 5 | 273.233 | odd | 6 | |||
8281.2.a.bx.1.3 | 5 | 273.194 | even | 6 |