Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(5,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5, 15]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.ck (of order \(18\), degree \(6\), 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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 605.5 | ||
Character | \(\chi\) | \(=\) | 756.605 |
Dual form | 756.2.ck.a.5.5 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.61581 | + | 0.623825i | −0.932888 | + | 0.360166i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.221654 | − | 1.25706i | −0.0991267 | − | 0.562176i | −0.993404 | − | 0.114663i | \(-0.963421\pi\) |
0.894278 | − | 0.447512i | \(-0.147690\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.55927 | + | 0.670941i | 0.967311 | + | 0.253592i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.22168 | − | 2.01597i | 0.740561 | − | 0.671989i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.67482 | − | 1.00062i | −1.71102 | − | 0.301699i | −0.769499 | − | 0.638648i | \(-0.779494\pi\) |
−0.941523 | + | 0.336949i | \(0.890605\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.02767 | + | 3.60823i | 0.839724 | + | 1.00074i | 0.999907 | + | 0.0136566i | \(0.00434715\pi\) |
−0.160183 | + | 0.987087i | \(0.551208\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.14234 | + | 1.89290i | 0.294950 | + | 0.488745i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.342095 | 0.0829702 | 0.0414851 | − | 0.999139i | \(-0.486791\pi\) | ||||
0.0414851 | + | 0.999139i | \(0.486791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 8.19307i | − | 1.87962i | −0.341697 | − | 0.939810i | \(-0.611002\pi\) | ||
0.341697 | − | 0.939810i | \(-0.388998\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.55384 | + | 0.512420i | −0.993729 | + | 0.111819i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.332785 | + | 0.396598i | 0.0693905 | + | 0.0826964i | 0.799623 | − | 0.600502i | \(-0.205033\pi\) |
−0.730232 | + | 0.683199i | \(0.760588\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.16739 | − | 1.15283i | 0.633477 | − | 0.230567i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.33221 | + | 4.64336i | −0.448834 | + | 0.893615i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.622374 | − | 0.741717i | 0.115572 | − | 0.137733i | −0.705157 | − | 0.709052i | \(-0.749123\pi\) |
0.820729 | + | 0.571318i | \(0.193568\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.45520 | − | 3.99812i | 0.261361 | − | 0.718083i | −0.737716 | − | 0.675112i | \(-0.764095\pi\) |
0.999076 | − | 0.0429711i | \(-0.0136823\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.79364 | − | 1.92328i | 1.70485 | − | 0.334799i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.276144 | − | 3.36587i | 0.0466768 | − | 0.568936i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.18931 | + | 2.05995i | −0.195522 | + | 0.338653i | −0.947071 | − | 0.321023i | \(-0.895973\pi\) |
0.751550 | + | 0.659676i | \(0.229307\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.14304 | − | 3.94148i | −1.14380 | − | 0.631143i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.78109 | − | 6.52911i | 1.21520 | − | 1.01968i | 0.216140 | − | 0.976362i | \(-0.430653\pi\) |
0.999062 | − | 0.0433131i | \(-0.0137913\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.17869 | − | 1.52092i | 0.637245 | − | 0.231938i | −0.00313689 | − | 0.999995i | \(-0.500999\pi\) |
0.640381 | + | 0.768057i | \(0.278776\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.02664 | − | 2.34595i | −0.451185 | − | 0.349713i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.92248 | − | 1.06369i | 0.426287 | − | 0.155156i | −0.119962 | − | 0.992778i | \(-0.538277\pi\) |
0.546249 | + | 0.837623i | \(0.316055\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.09968 | + | 3.43423i | 0.871382 | + | 0.490605i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.552760 | + | 0.213407i | −0.0774019 | + | 0.0298830i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.32288 | + | 3.07317i | 0.731154 | + | 0.422132i | 0.818844 | − | 0.574016i | \(-0.194615\pi\) |
−0.0876903 | + | 0.996148i | \(0.527949\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.35539i | 0.991801i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.11105 | + | 13.2385i | 0.676975 | + | 1.75348i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.66502 | − | 8.10991i | 1.25828 | − | 1.05582i | 0.262415 | − | 0.964955i | \(-0.415481\pi\) |
0.995863 | − | 0.0908657i | \(-0.0289634\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.33107 | − | 6.40456i | −0.298463 | − | 0.820020i | −0.994757 | − | 0.102264i | \(-0.967391\pi\) |
0.696294 | − | 0.717756i | \(-0.254831\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.03847 | − | 3.66877i | 0.886764 | − | 0.462222i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.86468 | − | 4.60575i | 0.479355 | − | 0.571273i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.683823 | − | 3.87815i | −0.0835423 | − | 0.473792i | −0.997662 | − | 0.0683466i | \(-0.978228\pi\) |
0.914119 | − | 0.405445i | \(-0.132883\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.785125 | − | 0.433227i | −0.0945180 | − | 0.0521544i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.19597 | + | 1.26784i | −0.260614 | + | 0.150465i | −0.624614 | − | 0.780933i | \(-0.714744\pi\) |
0.364001 | + | 0.931399i | \(0.381411\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.4470 | − | 6.03160i | 1.22273 | − | 0.705945i | 0.257233 | − | 0.966349i | \(-0.417189\pi\) |
0.965500 | + | 0.260404i | \(0.0838559\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.39873 | + | 3.83866i | −0.507921 | + | 0.443250i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.8520 | − | 6.36833i | −1.57858 | − | 0.725738i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.898458 | + | 5.09541i | −0.101084 | + | 0.573278i | 0.891628 | + | 0.452769i | \(0.149564\pi\) |
−0.992712 | + | 0.120509i | \(0.961547\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.871763 | − | 8.95768i | 0.0968626 | − | 0.995298i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.555623 | − | 0.466223i | −0.0609875 | − | 0.0511746i | 0.611784 | − | 0.791025i | \(-0.290452\pi\) |
−0.672772 | + | 0.739850i | \(0.734896\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0758267 | − | 0.430035i | −0.00822456 | − | 0.0466438i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.542937 | + | 1.58673i | −0.0582090 | + | 0.170115i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.2413 | −1.08558 | −0.542790 | − | 0.839868i | \(-0.682632\pi\) | ||||
−0.542790 | + | 0.839868i | \(0.682632\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.32769 | + | 11.2658i | 0.558494 | + | 1.18098i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.142806 | + | 7.36798i | 0.0148083 | + | 0.764024i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.2992 | + | 1.81603i | −1.05668 | + | 0.186321i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.14019 | − | 8.62759i | −0.318838 | − | 0.875999i | −0.990790 | − | 0.135405i | \(-0.956766\pi\) |
0.671953 | − | 0.740594i | \(-0.265456\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14.6249 | + | 9.21717i | −1.46985 | + | 0.926360i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.23150 | + | 1.03335i | 0.122539 | + | 0.102822i | 0.701998 | − | 0.712179i | \(-0.252292\pi\) |
−0.579459 | + | 0.815001i | \(0.696736\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.07793 | + | 0.542722i | −0.303277 | + | 0.0534759i | −0.323216 | − | 0.946325i | \(-0.604764\pi\) |
0.0199387 | + | 0.999801i | \(0.493653\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.65352 | + | 5.61088i | 0.161367 | + | 0.547566i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.1503 | + | 8.74701i | −1.46463 | + | 0.845605i | −0.999220 | − | 0.0394897i | \(-0.987427\pi\) |
−0.465411 | + | 0.885095i | \(0.654093\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.26215 | + | 14.3105i | −0.791371 | + | 1.37069i | 0.133748 | + | 0.991015i | \(0.457299\pi\) |
−0.925118 | + | 0.379679i | \(0.876034\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.636654 | − | 4.07041i | 0.0604286 | − | 0.386346i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.603550 | + | 1.65824i | −0.0567772 | + | 0.155994i | −0.964839 | − | 0.262843i | \(-0.915340\pi\) |
0.908061 | + | 0.418837i | \(0.137562\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.424785 | − | 0.506239i | 0.0396114 | − | 0.0472070i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.0006 | + | 1.91268i | 1.29436 | + | 0.176827i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.875511 | + | 0.229526i | 0.0802580 | + | 0.0210406i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.8657 | + | 7.59448i | 1.89688 | + | 0.690408i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.49974 | + | 15.4038i | −0.766396 | + | 1.38892i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.34239 | − | 9.25329i | −0.477838 | − | 0.827639i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.47580 | + | 12.9485i | −0.663370 | + | 1.14899i | 0.316355 | + | 0.948641i | \(0.397541\pi\) |
−0.979725 | + | 0.200349i | \(0.935792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.80318 | + | 5.06429i | −0.510942 | + | 0.445886i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.41368 | + | 7.89901i | −0.822477 | + | 0.690140i | −0.953551 | − | 0.301232i | \(-0.902602\pi\) |
0.131074 | + | 0.991373i | \(0.458158\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.49707 | − | 20.9683i | 0.476657 | − | 1.81818i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.35394 | + | 1.90251i | 0.546860 | + | 0.163742i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.439344 | − | 1.20709i | −0.0375357 | − | 0.103128i | 0.919509 | − | 0.393069i | \(-0.128587\pi\) |
−0.957045 | + | 0.289941i | \(0.906364\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.844510 | + | 0.148910i | −0.0716304 | + | 0.0126304i | −0.209349 | − | 0.977841i | \(-0.567134\pi\) |
0.137718 | + | 0.990471i | \(0.456023\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.05861 | + | 3.54184i | −0.341796 | + | 0.298277i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.5710 | − | 23.5056i | −1.13486 | − | 1.96564i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.07034 | − | 0.617959i | −0.0888866 | − | 0.0513187i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.9983 | − | 1.74394i | −0.989601 | − | 0.143838i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.43770 | − | 17.6874i | 0.527397 | − | 1.44901i | −0.334728 | − | 0.942315i | \(-0.608644\pi\) |
0.862125 | − | 0.506696i | \(-0.169133\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.178851 | + | 1.01431i | −0.0145547 | + | 0.0825435i | −0.991220 | − | 0.132224i | \(-0.957788\pi\) |
0.976665 | + | 0.214767i | \(0.0688993\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.760027 | − | 0.689651i | 0.0614445 | − | 0.0557550i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.34843 | − | 0.943073i | −0.429596 | − | 0.0757494i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.27157 | − | 5.09066i | −0.340909 | − | 0.406279i | 0.568165 | − | 0.822915i | \(-0.307654\pi\) |
−0.909074 | + | 0.416636i | \(0.863209\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.5179 | − | 1.64511i | −0.834122 | − | 0.130465i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.585591 | + | 1.23828i | 0.0461511 | + | 0.0975900i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.59932 | + | 2.77011i | 0.125269 | + | 0.216972i | 0.921838 | − | 0.387576i | \(-0.126687\pi\) |
−0.796569 | + | 0.604547i | \(0.793354\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.58848 | − | 11.8849i | −0.357213 | − | 0.925239i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.3814 | + | 7.05424i | 1.49977 | + | 0.545873i | 0.956002 | − | 0.293359i | \(-0.0947732\pi\) |
0.543773 | + | 0.839233i | \(0.316995\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.59515 | + | 9.04656i | −0.122704 | + | 0.695889i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.5170 | − | 18.2024i | −1.26308 | − | 1.39197i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.1747 | + | 13.5722i | 1.22974 | + | 1.03187i | 0.998256 | + | 0.0590352i | \(0.0188024\pi\) |
0.231484 | + | 0.972839i | \(0.425642\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.87967 | − | 0.825279i | 0.671240 | − | 0.0623852i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.5577 | + | 19.1334i | −0.793563 | + | 1.43815i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 11.6254i | − | 0.868924i | −0.900690 | − | 0.434462i | \(-0.856939\pi\) | ||
0.900690 | − | 0.434462i | \(-0.143061\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.09964 | − | 4.09898i | −0.527712 | − | 0.304675i | 0.212372 | − | 0.977189i | \(-0.431881\pi\) |
−0.740084 | + | 0.672514i | \(0.765214\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.76189 | + | 8.89437i | 0.573776 | + | 0.657491i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.85310 | + | 1.03844i | 0.209764 | + | 0.0763479i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.94133 | − | 0.342308i | −0.141964 | − | 0.0250320i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.08417 | + | 10.3188i | −0.660776 | + | 0.750583i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.3214 | − | 3.23055i | −1.32569 | − | 0.233754i | −0.534417 | − | 0.845221i | \(-0.679469\pi\) |
−0.791270 | + | 0.611467i | \(0.790580\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.1705 | − | 5.88558i | −1.16398 | − | 0.423654i | −0.313461 | − | 0.949601i | \(-0.601489\pi\) |
−0.850517 | + | 0.525947i | \(0.823711\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.37141 | + | 9.85290i | −0.241432 | + | 0.705581i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.64136 | + | 4.98909i | 0.615671 | + | 0.355458i | 0.775182 | − | 0.631738i | \(-0.217658\pi\) |
−0.159510 | + | 0.987196i | \(0.550992\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.1342i | 1.21461i | 0.794467 | + | 0.607307i | \(0.207750\pi\) | ||||
−0.794467 | + | 0.607307i | \(0.792250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.52422 | + | 5.83977i | 0.248579 | + | 0.411906i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.09047 | − | 1.48067i | 0.146722 | − | 0.103923i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.93221 | − | 8.33411i | −0.693696 | − | 0.582080i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.53887 | + | 0.210232i | 0.106959 | + | 0.0146121i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.19818 | + | 46.4942i | −0.567080 | + | 3.21607i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.9938 | + | 6.91319i | 1.30759 | + | 0.475923i | 0.899461 | − | 0.437001i | \(-0.143960\pi\) |
0.408128 | + | 0.912925i | \(0.366182\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.75736 | − | 3.41849i | 0.188931 | − | 0.234231i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.83812 | − | 4.91576i | −0.193558 | − | 0.335252i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.40673 | − | 9.25589i | 0.434917 | − | 0.628331i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.1178 | + | 16.2630i | −0.886416 | + | 1.09895i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.03575 | + | 1.23436i | 0.0696720 | + | 0.0830319i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.90013 | + | 1.21668i | 0.462067 | + | 0.0814749i | 0.399836 | − | 0.916587i | \(-0.369067\pi\) |
0.0622313 | + | 0.998062i | \(0.480178\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.71286 | − | 8.94658i | 0.314191 | − | 0.596439i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.38774 | − | 13.5416i | 0.158480 | − | 0.898784i | −0.797055 | − | 0.603907i | \(-0.793610\pi\) |
0.955535 | − | 0.294878i | \(-0.0952789\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.05870 | + | 19.3936i | −0.466452 | + | 1.28157i | 0.454101 | + | 0.890950i | \(0.349960\pi\) |
−0.920553 | + | 0.390617i | \(0.872262\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 26.3549 | + | 1.64878i | 1.73403 | + | 0.108482i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.1468 | − | 13.9412i | −1.58191 | − | 0.913317i | −0.994580 | − | 0.103970i | \(-0.966846\pi\) |
−0.587331 | − | 0.809347i | \(-0.699821\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.98491 | − | 3.43796i | −0.129481 | − | 0.224268i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.72691 | − | 8.79369i | −0.112175 | − | 0.571212i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.7274 | − | 4.18378i | 1.53480 | − | 0.270626i | 0.658569 | − | 0.752520i | \(-0.271162\pi\) |
0.876229 | + | 0.481894i | \(0.160051\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.589073 | + | 1.61847i | 0.0379455 | + | 0.104255i | 0.957218 | − | 0.289366i | \(-0.0934445\pi\) |
−0.919273 | + | 0.393621i | \(0.871222\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.17942 | + | 15.0177i | 0.268110 | + | 0.963388i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.96503 | − | 8.42889i | 0.189429 | − | 0.538502i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.5625 | − | 24.8059i | 1.88102 | − | 1.57836i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.18862 | + | 0.406716i | 0.0753259 | + | 0.0257746i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.34720 | − | 2.33342i | 0.0850344 | − | 0.147284i | −0.820371 | − | 0.571831i | \(-0.806233\pi\) |
0.905406 | + | 0.424547i | \(0.139567\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.49165 | − | 2.58361i | −0.0937792 | − | 0.162430i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.390788 | + | 0.647552i | 0.0244721 | + | 0.0405513i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.8813 | + | 6.50824i | 1.11540 | + | 0.405973i | 0.832972 | − | 0.553315i | \(-0.186637\pi\) |
0.282430 | + | 0.959288i | \(0.408860\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.42587 | + | 4.47400i | −0.275010 | + | 0.278001i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.112557 | − | 2.90255i | −0.00696707 | − | 0.179663i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.5166 | + | 22.0672i | −1.14178 | + | 1.36072i | −0.218853 | + | 0.975758i | \(0.570231\pi\) |
−0.922931 | + | 0.384966i | \(0.874213\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.68332 | − | 7.37237i | 0.164835 | − | 0.452881i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.5481 | − | 6.38881i | 1.01272 | − | 0.390989i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.04832 | + | 13.9401i | −0.490715 | + | 0.849943i | −0.999943 | − | 0.0106885i | \(-0.996598\pi\) |
0.509228 | + | 0.860632i | \(0.329931\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.2246 | − | 9.36726i | 0.985572 | − | 0.569020i | 0.0816245 | − | 0.996663i | \(-0.473989\pi\) |
0.903948 | + | 0.427643i | \(0.140656\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −15.6364 | − | 14.8799i | −0.946360 | − | 0.900571i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −19.1279 | + | 3.37276i | −1.15346 | + | 0.203385i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.44806 | − | 7.92786i | −0.567679 | − | 0.476339i | 0.313196 | − | 0.949689i | \(-0.398600\pi\) |
−0.880875 | + | 0.473349i | \(0.843045\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.82708 | − | 11.8162i | −0.288990 | − | 0.707416i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.46150 | + | 9.51038i | 0.206496 | + | 0.567342i | 0.999101 | − | 0.0423930i | \(-0.0134982\pi\) |
−0.792606 | + | 0.609735i | \(0.791276\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.58146 | − | 1.68947i | 0.569559 | − | 0.100429i | 0.118550 | − | 0.992948i | \(-0.462175\pi\) |
0.451009 | + | 0.892520i | \(0.351064\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.5087 | − | 9.35926i | 0.918655 | − | 0.554395i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.2945 | − | 11.4891i | 1.43406 | − | 0.678178i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8830 | −0.993116 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.4561 | + | 11.9816i | 0.612945 | + | 0.702375i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.111390 | − | 0.631726i | −0.00650749 | − | 0.0369058i | 0.981381 | − | 0.192071i | \(-0.0615203\pi\) |
−0.987889 | + | 0.155165i | \(0.950409\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.3370 | − | 10.3519i | −0.718286 | − | 0.602713i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.8811 | − | 24.0166i | 1.03757 | − | 1.39358i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.423455 | + | 2.40153i | −0.0244890 | + | 0.138884i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.7148 | − | 1.08878i | 0.675231 | − | 0.0627562i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.63450 | − | 0.901457i | −0.151348 | − | 0.0517874i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.53424 | + | 4.34990i | −0.431410 | + | 0.249074i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.14240 | + | 4.12367i | −0.407638 | + | 0.235350i | −0.689774 | − | 0.724024i | \(-0.742290\pi\) |
0.282136 | + | 0.959374i | \(0.408957\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.63478 | − | 2.79702i | 0.263664 | − | 0.159117i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.05631 | − | 17.3332i | −0.173308 | − | 0.982876i | −0.940079 | − | 0.340956i | \(-0.889249\pi\) |
0.766772 | − | 0.641920i | \(-0.221862\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.9360 | + | 15.4166i | −0.731188 | + | 0.871396i | −0.995667 | − | 0.0929954i | \(-0.970356\pi\) |
0.264478 | + | 0.964392i | \(0.414800\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.17198 | − | 8.03460i | −0.347752 | − | 0.452699i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.39446 | + | 14.8212i | 0.302983 | + | 0.832440i | 0.993978 | + | 0.109580i | \(0.0349505\pi\) |
−0.690995 | + | 0.722860i | \(0.742827\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.27404 | + | 3.58634i | −0.239300 | + | 0.200797i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.0233 | − | 23.5846i | 1.06178 | − | 1.31636i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.80281i | − | 0.155952i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.7495 | + | 7.93827i | 0.762685 | + | 0.440336i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.42284 | − | 28.2771i | 0.244584 | − | 1.56373i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.19306 | − | 0.761466i | 0.451698 | − | 0.0419810i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.42503 | + | 1.61058i | −0.243222 | + | 0.0885255i | −0.460755 | − | 0.887527i | \(-0.652421\pi\) |
0.217533 | + | 0.976053i | \(0.430199\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.51051 | + | 6.97417i | 0.0827755 | + | 0.382182i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.72351 | + | 1.71922i | −0.258073 | + | 0.0939308i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.80872 | − | 2.35680i | 0.153001 | − | 0.128383i | −0.563074 | − | 0.826407i | \(-0.690381\pi\) |
0.716075 | + | 0.698024i | \(0.245937\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.0592296 | − | 3.05591i | −0.00321691 | − | 0.165974i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.2586 | + | 21.2325i | −0.663839 | + | 1.14980i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.3065 | + | 12.8816i | 0.718484 | + | 0.695543i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.370567 | + | 1.08298i | −0.0199507 | + | 0.0583056i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.3261 | − | 28.3708i | 0.554335 | − | 1.52302i | −0.273399 | − | 0.961901i | \(-0.588148\pi\) |
0.827734 | − | 0.561121i | \(-0.189630\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.5777 | + | 22.1400i | −0.994441 | + | 1.18513i | −0.0117402 | + | 0.999931i | \(0.503737\pi\) |
−0.982701 | + | 0.185198i | \(0.940707\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −23.8155 | + | 5.64339i | −1.27118 | + | 0.301222i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.7762 | − | 7.19796i | 1.05258 | − | 0.383109i | 0.242946 | − | 0.970040i | \(-0.421886\pi\) |
0.809637 | + | 0.586931i | \(0.199664\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.08050 | + | 2.47945i | 0.110422 | + | 0.131595i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.55784 | + | 0.175296i | −0.0824498 | + | 0.00927766i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.7571i | 0.673296i | 0.941631 | + | 0.336648i | \(0.109293\pi\) | ||||
−0.941631 | + | 0.336648i | \(0.890707\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −48.1265 | −2.53297 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −38.4526 | + | 0.745288i | −2.01824 | + | 0.0391175i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.89772 | − | 11.7956i | −0.518070 | − | 0.617412i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.3571 | − | 5.52911i | −1.63683 | − | 0.288617i | −0.721829 | − | 0.692071i | \(-0.756698\pi\) |
−0.915000 | + | 0.403454i | \(0.867809\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.12466 | − | 30.1920i | 0.214721 | − | 1.57173i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.5607 | + | 11.4364i | 0.600204 | + | 0.593748i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.05676 | − | 5.99316i | −0.0547167 | − | 0.310314i | 0.945150 | − | 0.326636i | \(-0.105915\pi\) |
−0.999867 | + | 0.0163225i | \(0.994804\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.4047 | + | 11.6188i | 0.743856 | + | 0.599994i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.56063 | 0.234884 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.73209 | −0.140338 | −0.0701690 | − | 0.997535i | \(-0.522354\pi\) | ||||
−0.0701690 | + | 0.997535i | \(0.522354\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.00189 | − | 25.5858i | 0.205023 | − | 1.31080i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.927013 | + | 5.25735i | 0.0473681 | + | 0.268638i | 0.999289 | − | 0.0377064i | \(-0.0120052\pi\) |
−0.951921 | + | 0.306344i | \(0.900894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.93504 | + | 18.8244i | −0.251513 | + | 0.959380i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.21761 | − | 11.8031i | 0.316059 | − | 0.599985i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.3024 | + | 4.28518i | 1.23218 | + | 0.217267i | 0.751563 | − | 0.659662i | \(-0.229300\pi\) |
0.480620 | + | 0.876929i | \(0.340412\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.113844 | + | 0.135674i | 0.00575734 | + | 0.00686133i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.2831 | − | 18.6358i | 0.518714 | − | 0.940052i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.60439 | 0.332303 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 9.61693i | − | 0.482660i | −0.970443 | − | 0.241330i | \(-0.922416\pi\) | ||
0.970443 | − | 0.241330i | \(-0.0775836\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.19830 | + | 37.3099i | 0.210178 | + | 1.86783i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.9612 | + | 24.9806i | 1.04675 | + | 1.24747i | 0.968099 | + | 0.250567i | \(0.0806172\pi\) |
0.0786520 | + | 0.996902i | \(0.474938\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.8320 | − | 6.85428i | 0.938088 | − | 0.341436i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.4536 | + | 0.889645i | −0.569134 | + | 0.0442068i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.81036 | − | 10.4998i | 0.436713 | − | 0.520455i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.279129 | + | 0.766899i | −0.0138020 | + | 0.0379207i | −0.946402 | − | 0.322990i | \(-0.895312\pi\) |
0.932600 | + | 0.360911i | \(0.117534\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.46291 | + | 1.67635i | 0.0721600 | + | 0.0826883i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 30.1766 | − | 14.2708i | 1.48489 | − | 0.702218i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.462915 | + | 0.801793i | −0.0227236 | + | 0.0393585i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.27167 | − | 0.767437i | 0.0622741 | − | 0.0375815i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.632382 | − | 0.530632i | 0.0308939 | − | 0.0259231i | −0.627210 | − | 0.778850i | \(-0.715803\pi\) |
0.658104 | + | 0.752927i | \(0.271359\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.9353 | − | 11.9875i | 1.60517 | − | 0.584233i | 0.624690 | − | 0.780873i | \(-0.285225\pi\) |
0.980476 | + | 0.196640i | \(0.0630030\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.34845 | − | 8.25480i | 0.211429 | − | 0.401362i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.08355 | − | 0.394379i | 0.0525597 | − | 0.0191302i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.66874 | − | 17.9550i | −0.0807560 | − | 0.868902i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 36.5915 | + | 29.5147i | 1.76665 | + | 1.42498i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.84508 | − | 1.06526i | −0.0888745 | − | 0.0513117i | 0.454904 | − | 0.890540i | \(-0.349674\pi\) |
−0.543779 | + | 0.839229i | \(0.683007\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 24.2310i | − | 1.16447i | −0.813022 | − | 0.582233i | \(-0.802179\pi\) | ||
0.813022 | − | 0.582233i | \(-0.197821\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.11496 | + | 0.330802i | 0.101404 | + | 0.0158607i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.24936 | − | 2.72653i | 0.155438 | − | 0.130428i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.0841 | − | 27.7057i | −0.481286 | − | 1.32232i | −0.908392 | − | 0.418120i | \(-0.862689\pi\) |
0.427106 | − | 0.904202i | \(-0.359533\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.4749 | − | 4.66696i | 0.974993 | − | 0.222236i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.29303 | + | 6.30799i | −0.251480 | + | 0.299702i | −0.876985 | − | 0.480518i | \(-0.840449\pi\) |
0.625505 | + | 0.780220i | \(0.284893\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.27003 | + | 12.8740i | 0.107610 | + | 0.610286i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.631766 | + | 32.5955i | 0.0298815 | + | 1.54172i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.8671 | + | 18.3985i | −1.50390 | + | 0.868278i | −0.503911 | + | 0.863755i | \(0.668106\pi\) |
−0.999990 | + | 0.00452223i | \(0.998561\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −50.6894 | + | 29.2656i | −2.38687 | + | 1.37806i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.343765 | − | 1.75051i | −0.0161515 | − | 0.0822460i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.9809 | − | 9.19435i | 0.608555 | − | 0.431038i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.68848 | − | 32.2609i | 0.266096 | − | 1.50910i | −0.499801 | − | 0.866140i | \(-0.666594\pi\) |
0.765897 | − | 0.642963i | \(-0.222295\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.797837 | + | 1.58847i | −0.0372398 | + | 0.0741434i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.7198 | − | 24.0988i | −1.33762 | − | 1.12239i | −0.982231 | − | 0.187674i | \(-0.939905\pi\) |
−0.355385 | − | 0.934720i | \(-0.615650\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.27116 | + | 24.2230i | 0.198498 | + | 1.12574i | 0.907349 | + | 0.420379i | \(0.138103\pi\) |
−0.708851 | + | 0.705358i | \(0.750786\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.23036 | − | 1.81266i | 0.428048 | − | 0.0840601i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.7729 | 0.961257 | 0.480628 | − | 0.876924i | \(-0.340409\pi\) | ||||
0.480628 | + | 0.876924i | \(0.340409\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.851928 | − | 10.3840i | 0.0393384 | − | 0.479490i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.0777 | + | 5.56083i | 0.464358 | + | 0.256230i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −25.2352 | + | 4.44964i | −1.16031 | + | 0.204595i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.44526 | − | 25.9506i | −0.433378 | − | 1.19070i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.0212 | − | 3.90314i | 0.825132 | − | 0.178712i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.0139 | + | 25.1847i | 1.37137 | + | 1.15072i | 0.972283 | + | 0.233805i | \(0.0751178\pi\) |
0.399088 | + | 0.916912i | \(0.369327\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.0336 | + | 1.94552i | −0.503090 | + | 0.0887083i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.71867 | − | 1.63552i | −0.0782024 | − | 0.0744185i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.1494 | + | 5.85975i | −0.460860 | + | 0.266078i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.541148 | − | 0.937296i | 0.0245218 | − | 0.0424729i | −0.853504 | − | 0.521086i | \(-0.825527\pi\) |
0.878026 | + | 0.478613i | \(0.158860\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.31227 | − | 3.47827i | −0.195007 | − | 0.157293i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.76500 | − | 26.8291i | 0.440688 | − | 1.21078i | −0.498353 | − | 0.866974i | \(-0.666061\pi\) |
0.939041 | − | 0.343806i | \(-0.111716\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.212911 | − | 0.253737i | 0.00958903 | − | 0.0114278i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.8282 | + | 16.3414i | 0.666479 | + | 0.734489i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.47071 | + | 1.77138i | −0.290251 | + | 0.0794573i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.15959 | + | 0.786028i | 0.0966767 | + | 0.0351874i | 0.389906 | − | 0.920855i | \(-0.372508\pi\) |
−0.293229 | + | 0.956042i | \(0.594730\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −35.7172 | + | 0.692271i | −1.59573 | + | 0.0309284i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.80677 | − | 13.5217i | −0.348087 | − | 0.602904i | 0.637823 | − | 0.770183i | \(-0.279835\pi\) |
−0.985910 | + | 0.167279i | \(0.946502\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.02602 | − | 1.77712i | 0.0456572 | − | 0.0790807i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.06601 | − | 15.6126i | −0.136166 | − | 0.693381i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.9005 | + | 27.6068i | −1.45829 | + | 1.22365i | −0.532049 | + | 0.846714i | \(0.678578\pi\) |
−0.926240 | + | 0.376935i | \(0.876978\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.7836 | − | 8.42711i | 1.36178 | − | 0.372793i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 38.0434 | + | 19.1080i | 1.67966 | + | 0.843637i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.36447 | + | 3.74885i | 0.0601257 | + | 0.165194i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.6489 | + | 3.11197i | −0.776196 | + | 0.136864i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −34.6019 | − | 11.8399i | −1.51886 | − | 0.519713i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.7637 | + | 23.8394i | 0.602997 | + | 1.04442i | 0.992365 | + | 0.123339i | \(0.0393604\pi\) |
−0.389367 | + | 0.921083i | \(0.627306\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.10797 | − | 4.68114i | −0.354537 | − | 0.204692i | 0.312145 | − | 0.950035i | \(-0.398953\pi\) |
−0.666682 | + | 0.745343i | \(0.732286\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −13.8330 | + | 6.87285i | −0.603723 | + | 0.299956i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.497815 | − | 1.36773i | 0.0216851 | − | 0.0595795i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.94736 | − | 22.3866i | 0.171625 | − | 0.973331i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.12331 | − | 37.5020i | 0.222333 | − | 1.62745i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 47.1171 | + | 8.30802i | 2.04087 | + | 0.359860i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.3537 | + | 17.1060i | 0.620562 | + | 0.739558i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.25222 | + | 18.7844i | 0.312956 | + | 0.810609i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −31.1782 | − | 25.5921i | −1.34294 | − | 1.10233i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.19661 | + | 10.7328i | 0.266413 | + | 0.461441i | 0.967933 | − | 0.251209i | \(-0.0808281\pi\) |
−0.701520 | + | 0.712650i | \(0.747495\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.0287 | + | 2.19424i | 0.602030 | + | 0.0941638i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.8205 | + | 7.21407i | 0.849017 | + | 0.309017i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.56791 | + | 25.9059i | −0.195310 | + | 1.10766i | 0.716667 | + | 0.697415i | \(0.245667\pi\) |
−0.911977 | + | 0.410241i | \(0.865444\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.0903 | − | 9.52956i | −0.772074 | − | 0.406712i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.07694 | − | 5.09916i | −0.258886 | − | 0.217231i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.71811 | + | 12.4377i | −0.243159 | + | 0.528904i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.25788 | + | 0.101908i | −0.223184 | + | 0.00432576i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 8.39463i | − | 0.355692i | −0.984058 | − | 0.177846i | \(-0.943087\pi\) | ||
0.984058 | − | 0.177846i | \(-0.0569129\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.1395 | + | 10.4729i | 0.767220 | + | 0.442955i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.35035 | − | 0.657943i | 0.141452 | − | 0.0277784i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.96933 | + | 1.80869i | 0.209432 | + | 0.0762271i | 0.444606 | − | 0.895726i | \(-0.353344\pi\) |
−0.235174 | + | 0.971953i | \(0.575566\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.21829 | + | 0.391144i | 0.0933241 | + | 0.0164556i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.24115 | − | 22.3402i | 0.346096 | − | 0.938199i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.1074 | − | 2.31119i | −0.549492 | − | 0.0968902i | −0.107992 | − | 0.994152i | \(-0.534442\pi\) |
−0.441500 | + | 0.897261i | \(0.645553\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.0745 | + | 6.94253i | 0.798241 | + | 0.290536i | 0.708757 | − | 0.705452i | \(-0.249256\pi\) |
0.0894837 | + | 0.995988i | \(0.471478\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 31.6191 | − | 6.20937i | 1.32091 | − | 0.259400i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.51127 | + | 0.872533i | 0.0630244 | + | 0.0363871i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.4169i | 0.433663i | 0.976209 | + | 0.216832i | \(0.0695723\pi\) | ||||
−0.976209 | + | 0.216832i | \(0.930428\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29.8000 | − | 0.577584i | 1.23845 | − | 0.0240036i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.10918 | − | 1.56598i | −0.0460165 | − | 0.0649677i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.1313 | − | 22.7658i | −1.12366 | − | 0.942865i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.698928 | − | 18.0236i | −0.0288971 | − | 0.745183i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.0514158 | + | 0.291593i | −0.00212216 | + | 0.0120354i | −0.985850 | − | 0.167627i | \(-0.946389\pi\) |
0.983728 | + | 0.179663i | \(0.0575006\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.7569 | − | 11.9225i | −1.34972 | − | 0.491259i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.0751 | − | 2.67073i | −0.702376 | − | 0.109859i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.3529 | + | 26.5920i | 0.630467 | + | 1.09200i | 0.987456 | + | 0.157893i | \(0.0504701\pi\) |
−0.356989 | + | 0.934109i | \(0.616197\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0944673 | − | 1.15145i | 0.00387278 | − | 0.0472048i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.6888 | − | 27.6857i | −0.437462 | − | 1.13310i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.2095 | + | 22.8930i | 0.784879 | + | 0.935382i | 0.999143 | − | 0.0413935i | \(-0.0131797\pi\) |
−0.214264 | + | 0.976776i | \(0.568735\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.31717 | + | 1.29022i | 0.298474 | + | 0.0526290i | 0.320880 | − | 0.947120i | \(-0.396021\pi\) |
−0.0224059 | + | 0.999749i | \(0.507133\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.33746 | − | 7.23747i | −0.380251 | − | 0.294732i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.92178 | − | 27.9128i | 0.200099 | − | 1.13482i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.1959 | − | 33.5078i | 0.495014 | − | 1.36004i | −0.401025 | − | 0.916067i | \(-0.631346\pi\) |
0.896040 | − | 0.443974i | \(-0.146432\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.45412 | + | 3.69657i | −0.0994460 | + | 0.149793i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.6863 | + | 7.32446i | 0.513234 | + | 0.296316i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.49646 | + | 12.9843i | 0.302779 | + | 0.524429i | 0.976764 | − | 0.214316i | \(-0.0687522\pi\) |
−0.673985 | + | 0.738745i | \(0.735419\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 21.2476 | + | 7.27038i | 0.856786 | + | 0.293170i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.8177 | + | 2.61276i | −0.596537 | + | 0.105186i | −0.463761 | − | 0.885960i | \(-0.653500\pi\) |
−0.132776 | + | 0.991146i | \(0.542389\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.13530 | − | 19.6041i | −0.286792 | − | 0.787954i | −0.996510 | − | 0.0834686i | \(-0.973400\pi\) |
0.709719 | − | 0.704485i | \(-0.248822\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.61767 | + | 0.620292i | −0.105044 | + | 0.0248915i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −26.2103 | − | 6.87134i | −1.05009 | − | 0.275294i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.46259 | − | 2.06636i | 0.0985036 | − | 0.0826544i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.7575 | − | 80.2400i | −0.629296 | − | 3.20448i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.406857 | + | 0.704698i | −0.0162225 | + | 0.0280981i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.15238 | + | 10.6562i | 0.244923 | + | 0.424218i | 0.962110 | − | 0.272662i | \(-0.0879041\pi\) |
−0.717187 | + | 0.696880i | \(0.754571\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −35.0030 | + | 0.678428i | −1.39125 | + | 0.0269651i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.9341 | + | 6.52747i | 0.711692 | + | 0.259035i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.07627 | + | 32.4068i | 0.240751 | + | 1.28400i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.32282 | + | 7.24374i | −0.0918894 | + | 0.286558i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.33066 | + | 3.96933i | −0.131553 | + | 0.156779i | −0.827800 | − | 0.561024i | \(-0.810408\pi\) |
0.696246 | + | 0.717803i | \(0.254852\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.2007 | + | 41.7635i | −0.599457 | + | 1.64699i | 0.152903 | + | 0.988241i | \(0.451138\pi\) |
−0.752360 | + | 0.658752i | \(0.771085\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.65243 | + | 6.17245i | 0.301314 | + | 0.243040i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.558967 | + | 0.968159i | −0.0219753 | + | 0.0380623i | −0.876804 | − | 0.480848i | \(-0.840329\pi\) |
0.854829 | + | 0.518910i | \(0.173662\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −62.9622 | + | 36.3512i | −2.47148 | + | 1.42691i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.57801 | + | 18.9524i | −0.179426 | + | 0.742805i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30.4355 | + | 5.36660i | −1.19103 | + | 0.210011i | −0.733819 | − | 0.679345i | \(-0.762264\pi\) |
−0.457215 | + | 0.889356i | \(0.651153\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.0161 | + | 10.0827i | 0.469509 | + | 0.393965i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.0505 | − | 34.4612i | 0.431122 | − | 1.34446i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.4980 | + | 34.3381i | 0.486855 | + | 1.33762i | 0.903514 | + | 0.428559i | \(0.140979\pi\) |
−0.416659 | + | 0.909063i | \(0.636799\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.1321 | + | 4.25514i | −0.938631 | + | 0.165506i | −0.621977 | − | 0.783035i | \(-0.713670\pi\) |
−0.316654 | + | 0.948541i | \(0.602559\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.44360 | − | 1.34836i | −0.0949015 | − | 0.0523660i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −27.5769 | − | 2.26247i | −1.06938 | − | 0.0877347i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.501280 | 0.0194096 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.9083 | + | 2.33855i | −0.460401 | + | 0.0904136i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.81984 | + | 38.6772i | 0.263277 | + | 1.49312i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.11606 | + | 3.45379i | 0.158663 | + | 0.133134i | 0.718663 | − | 0.695359i | \(-0.244755\pi\) |
−0.560000 | + | 0.828492i | \(0.689199\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.03398 | + | 17.3960i | −0.0782881 | + | 0.669571i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.21240 | + | 12.5472i | −0.0850295 | + | 0.482226i | 0.912321 | + | 0.409476i | \(0.134289\pi\) |
−0.997350 | + | 0.0727498i | \(0.976823\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.24796 | − | 24.1872i | −0.0862689 | − | 0.928219i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.58942 | + | 23.3701i | 0.175867 | + | 0.895545i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.9994 | + | 17.8975i | −1.18616 | + | 0.684830i | −0.957432 | − | 0.288660i | \(-0.906790\pi\) |
−0.228729 | + | 0.973490i | \(0.573457\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.42000 | + | 0.819839i | −0.0542555 | + | 0.0313244i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.692709 | − | 35.7398i | −0.0264285 | − | 1.36356i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.02721 | + | 28.5107i | 0.191521 | + | 1.08617i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.636884 | − | 0.759009i | 0.0242282 | − | 0.0288740i | −0.753794 | − | 0.657110i | \(-0.771778\pi\) |
0.778022 | + | 0.628236i | \(0.216223\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −43.6131 | + | 13.7767i | −1.65672 | + | 0.523335i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.374378 | + | 1.02860i | 0.0142010 | + | 0.0390169i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.66187 | − | 2.23357i | 0.100826 | − | 0.0846027i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 47.7135 | + | 7.46290i | 1.80469 | + | 0.282273i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.7180i | − | 0.820277i | −0.912023 | − | 0.410139i | \(-0.865480\pi\) | ||
0.912023 | − | 0.410139i | \(-0.134520\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.8773 | + | 9.74412i | 0.636540 | + | 0.367506i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.35192 | + | 4.31686i | 0.201565 | + | 0.162582i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.45841 | + | 3.47088i | 0.0924582 | + | 0.130536i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.7552 | − | 4.64252i | 0.479032 | − | 0.174354i | −0.0912072 | − | 0.995832i | \(-0.529073\pi\) |
0.570240 | + | 0.821478i | \(0.306850\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.27608 | + | 13.1316i | 0.310377 | + | 0.492475i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.06991 | − | 0.753386i | 0.0775188 | − | 0.0282145i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26.5400 | + | 22.2697i | −0.992539 | + | 0.832839i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −35.7290 | + | 21.5620i | −1.33433 | + | 0.805246i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.02285 | + | 10.4319i | −0.224614 | + | 0.389044i | −0.956204 | − | 0.292702i | \(-0.905446\pi\) |
0.731589 | + | 0.681746i | \(0.238779\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.24137 | − | 0.676140i | −0.306924 | − | 0.0251808i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.96147 | − | 2.24765i | −0.0729479 | − | 0.0835912i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.11622 | − | 3.06680i | 0.0414555 | − | 0.113898i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.9518 | + | 35.6951i | −1.11085 | + | 1.32386i | −0.169842 | + | 0.985471i | \(0.554326\pi\) |
−0.941007 | + | 0.338387i | \(0.890119\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.1216 | − | 21.6586i | −0.597096 | − | 0.802170i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.42951 | − | 0.520299i | 0.0528723 | − | 0.0192439i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.7050 | − | 25.8670i | −0.801691 | − | 0.955418i | 0.198002 | − | 0.980202i | \(-0.436555\pi\) |
−0.999693 | + | 0.0247835i | \(0.992110\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.467228 | + | 15.4691i | 0.0172340 | + | 0.570588i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.6920i | 0.835872i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.3481 | 0.417448 | 0.208724 | − | 0.977975i | \(-0.433069\pi\) | ||||
0.208724 | + | 0.977975i | \(0.433069\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −32.2929 | + | 58.5235i | −1.18631 | + | 2.14991i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.8314 | + | 23.6342i | 0.727544 | + | 0.867053i | 0.995341 | − | 0.0964222i | \(-0.0307399\pi\) |
−0.267796 | + | 0.963476i | \(0.586295\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.6612 | − | 4.17210i | −0.866878 | − | 0.152854i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.17431 | + | 0.0843165i | −0.0795538 | + | 0.00308498i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −44.6423 | + | 12.2210i | −1.63119 | + | 0.446545i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.22235 | − | 23.9461i | −0.154076 | − | 0.873807i | −0.959626 | − | 0.281279i | \(-0.909241\pi\) |
0.805550 | − | 0.592528i | \(-0.201870\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.721173 | + | 4.61077i | −0.0262810 | + | 0.168026i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.31470 | 0.0478467 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.10213 | −0.221786 | −0.110893 | − | 0.993832i | \(-0.535371\pi\) | ||||
−0.110893 | + | 0.993832i | \(0.535371\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.02194 | + | 3.24410i | 0.145987 | + | 0.117753i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.51770 | − | 14.2786i | −0.0912667 | − | 0.517599i | −0.995828 | − | 0.0912546i | \(-0.970912\pi\) |
0.904561 | − | 0.426344i | \(-0.140199\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.7465 | + | 31.0809i | −1.11310 | + | 1.12520i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.03540 | − | 0.802537i | −0.0374349 | − | 0.0290158i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 58.5249 | + | 10.3195i | 2.11321 | + | 0.372616i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.5194 | − | 26.8375i | −0.812069 | − | 0.967786i | 0.187827 | − | 0.982202i | \(-0.439856\pi\) |
−0.999896 | + | 0.0144157i | \(0.995411\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −32.9527 | + | 0.638689i | −1.18676 | + | 0.0230018i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.8404 | 1.39699 | 0.698496 | − | 0.715614i | \(-0.253853\pi\) | ||||
0.698496 | + | 0.715614i | \(0.253853\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 14.3412i | − | 0.515150i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.36037 | − | 9.99010i | 0.156427 | − | 0.358393i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −53.4935 | − | 63.7510i | −1.91660 | − | 2.28412i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.7304 | − | 4.99744i | 0.491311 | − | 0.178822i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.99255 | + | 4.61975i | 0.0712080 | + | 0.165096i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.45247 | + | 6.49800i | −0.194607 | + | 0.231924i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.35885 | + | 11.9758i | −0.155376 | + | 0.426892i | −0.992818 | − | 0.119634i | \(-0.961828\pi\) |
0.837442 | + | 0.546526i | \(0.184050\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.1532 | − | 47.2076i | 0.575070 | − | 1.68063i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.65722 | + | 3.83893i | −0.0944800 | + | 0.136496i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.0514 | − | 27.8019i | 0.570004 | − | 0.987275i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.263329 | + | 13.5863i | 0.00933932 | + | 0.481856i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.9959 | − | 22.6523i | 0.956245 | − | 0.802385i | −0.0240929 | − | 0.999710i | \(-0.507670\pi\) |
0.980338 | + | 0.197325i | \(0.0632253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.999764 | − | 0.363884i | 0.0353691 | − | 0.0128733i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.7530 | + | 20.6462i | −0.803939 | + | 0.729497i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −65.3203 | + | 23.7747i | −2.30510 | + | 0.838989i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.42679 | − | 1.01059i | 0.0502879 | − | 0.0356188i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.30837 | − | 27.5453i | 0.151662 | − | 0.969641i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.66941 | + | 0.963835i | 0.0586934 | + | 0.0338866i | 0.529060 | − | 0.848585i | \(-0.322545\pi\) |
−0.470366 | + | 0.882471i | \(0.655878\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 28.0560i | − | 0.985179i | −0.870262 | − | 0.492589i | \(-0.836050\pi\) | ||
0.870262 | − | 0.492589i | \(-0.163950\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.3723 | + | 25.2570i | −0.714487 | + | 0.885802i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.12770 | − | 2.62445i | 0.109559 | − | 0.0919306i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.4610 | − | 34.2363i | −0.435955 | − | 1.19778i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 34.5479 | + | 14.2886i | 1.20720 | + | 0.499285i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.4620 | − | 23.1940i | 0.679230 | − | 0.809475i | −0.310778 | − | 0.950482i | \(-0.600590\pi\) |
0.990009 | + | 0.141007i | \(0.0450342\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.579831 | + | 3.28839i | 0.0202116 | + | 0.114626i | 0.993244 | − | 0.116041i | \(-0.0370204\pi\) |
−0.973033 | + | 0.230667i | \(0.925909\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 28.8030 | − | 17.3822i | 1.00279 | − | 0.605171i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.2554 | + | 10.5397i | −0.634801 | + | 0.366503i | −0.782609 | − | 0.622513i | \(-0.786112\pi\) |
0.147808 | + | 0.989016i | \(0.452778\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.6887 | − | 14.8314i | 0.892206 | − | 0.515115i | 0.0175426 | − | 0.999846i | \(-0.494416\pi\) |
0.874663 | + | 0.484731i | \(0.161082\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.2119 | + | 6.91598i | 0.701142 | + | 0.239913i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.08667 | + | 1.17483i | 0.0722987 | + | 0.0407056i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.57166 | − | 25.9272i | 0.158209 | − | 0.897247i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.1709 | + | 16.0814i | 0.524382 | + | 0.555856i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.0322 | − | 10.9353i | −0.449921 | − | 0.377529i | 0.389485 | − | 0.921033i | \(-0.372653\pi\) |
−0.839407 | + | 0.543504i | \(0.817097\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.87300 | + | 27.6362i | 0.168035 | + | 0.952972i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.5259 | − | 13.2076i | −0.396974 | − | 0.454894i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.7257 | 0.403375 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.3053 | + | 33.4359i | 1.65979 | + | 1.14887i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.4279 | + | 8.70702i | −0.495164 | + | 0.298824i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.21276 | + | 0.213842i | −0.0415728 | + | 0.00733040i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.4221 | + | 45.1192i | 0.562281 | + | 1.54485i | 0.816285 | + | 0.577650i | \(0.196030\pi\) |
−0.254004 | + | 0.967203i | \(0.581748\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.2205 | + | 24.7975i | −0.657329 | + | 0.848056i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.21447 | + | 6.05366i | 0.246442 | + | 0.206789i | 0.757638 | − | 0.652675i | \(-0.226353\pi\) |
−0.511197 | + | 0.859464i | \(0.670798\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.1411 | − | 1.96448i | 0.380131 | − | 0.0670273i | 0.0196820 | − | 0.999806i | \(-0.493735\pi\) |
0.360449 | + | 0.932779i | \(0.382624\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −32.0882 | + | 33.7197i | −1.09356 | + | 1.14916i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.3985 | − | 26.2109i | 1.54538 | − | 0.892228i | 0.546899 | − | 0.837198i | \(-0.315808\pi\) |
0.998485 | − | 0.0550294i | \(-0.0175253\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.4759 | − | 23.3409i | 0.458194 | − | 0.793616i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 27.2797 | − | 10.5320i | 0.926466 | − | 0.357686i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.1972 | − | 28.0165i | 0.345915 | − | 0.950394i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.9229 | − | 14.2091i | 0.403992 | − | 0.481459i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −24.3694 | − | 12.8373i | −0.824780 | − | 0.434476i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.46417 | − | 27.2660i | −0.252335 | − | 0.921760i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.87567 | + | 0.682688i | 0.0633369 | + | 0.0230527i | 0.373494 | − | 0.927632i | \(-0.378160\pi\) |
−0.310157 | + | 0.950685i | \(0.600382\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.574072 | + | 0.951261i | 0.0193630 | + | 0.0320852i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.50503 | + | 16.4632i | 0.320233 | + | 0.554659i | 0.980536 | − | 0.196340i | \(-0.0629056\pi\) |
−0.660303 | + | 0.750999i | \(0.729572\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.4288 | − | 26.7235i | 0.519221 | − | 0.899317i | −0.480529 | − | 0.876979i | \(-0.659555\pi\) |
0.999750 | − | 0.0223387i | \(-0.00711123\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 26.3920 | + | 9.03066i | 0.887157 | + | 0.303562i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.9246 | − | 26.7879i | 1.07192 | − | 0.899450i | 0.0766978 | − | 0.997054i | \(-0.475562\pi\) |
0.995225 | + | 0.0976041i | \(0.0311179\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.8202 | + | 28.1227i | −0.933060 | + | 0.943206i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.9104 | + | 49.9609i | −0.466014 | + | 1.67375i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.71492 | − | 23.9441i | −0.291634 | − | 0.801257i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.6139 | + | 2.57682i | −0.488488 | + | 0.0861335i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.813914 | − | 4.14458i | −0.0271758 | − | 0.138384i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.05979 | − | 3.56767i | −0.0686980 | − | 0.118988i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.82093 | + | 1.05131i | 0.0606640 | + | 0.0350244i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.2497 | + | 9.06726i | −0.607313 | + | 0.301740i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.57901 | + | 9.83325i | −0.118970 | + | 0.326868i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.59665 | + | 26.0689i | −0.152629 | + | 0.865604i | 0.808292 | + | 0.588782i | \(0.200392\pi\) |
−0.960921 | + | 0.276822i | \(0.910719\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.81920 | − | 0.186882i | 0.159843 | − | 0.00619847i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.8822 | − | 2.97679i | −0.559333 | − | 0.0986255i | −0.113167 | − | 0.993576i | \(-0.536100\pi\) |
−0.446166 | + | 0.894950i | \(0.647211\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.68654 | + | 3.20170i | 0.0889116 | + | 0.105961i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.46033 | − | 11.7287i | 0.312749 | − | 0.387738i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29.3919 | + | 13.8996i | −0.970605 | + | 0.459007i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.8096 | + | 20.4549i | 0.389564 | + | 0.674745i | 0.992391 | − | 0.123127i | \(-0.0392924\pi\) |
−0.602827 | + | 0.797872i | \(0.705959\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.96832 | − | 11.1187i | 0.295516 | − | 0.366373i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.2233 | − | 4.08496i | −0.369421 | − | 0.134458i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.39223 | + | 7.89573i | −0.0457763 | + | 0.259610i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.74407 | + | 7.41075i | −0.188660 | + | 0.243401i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.66871 | + | 4.75661i | 0.185984 | + | 0.156059i | 0.731026 | − | 0.682350i | \(-0.239042\pi\) |
−0.545042 | + | 0.838409i | \(0.683486\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.1369 | − | 49.9751i | 0.922151 | − | 1.63787i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.7513 | + | 26.1006i | 0.515675 | + | 0.854494i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.51624i | 0.0822899i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.6771 | − | 21.1756i | −1.19819 | − | 0.691775i | −0.238039 | − | 0.971256i | \(-0.576504\pi\) |
−0.960151 | + | 0.279480i | \(0.909838\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.2849 | − | 32.9801i | 0.368270 | − | 1.07626i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.6740 | − | 4.61296i | −0.413161 | − | 0.150378i | 0.127073 | − | 0.991893i | \(-0.459442\pi\) |
−0.540233 | + | 0.841515i | \(0.681664\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.17886 | + | 0.913173i | 0.168647 | + | 0.0297370i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.9849 | + | 9.13216i | 0.487460 | + | 0.297069i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44.9493 | − | 7.92578i | −1.46066 | − | 0.257553i | −0.613837 | − | 0.789433i | \(-0.710375\pi\) |
−0.846820 | + | 0.531879i | \(0.821486\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 53.3935 | + | 19.4337i | 1.73323 | + | 0.630843i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.9622 | − | 20.5830i | −0.582466 | − | 0.667449i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.3815 | − | 22.7369i | −1.27569 | − | 0.736522i | −0.299640 | − | 0.954052i | \(-0.596867\pi\) |
−0.976054 | + | 0.217530i | \(0.930200\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.7472i | 0.768440i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.66878 | − | 8.46110i | 0.150920 | − | 0.273509i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.314513 | − | 3.38403i | −0.0101561 | − | 0.109276i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.88004 | + | 8.29034i | 0.318711 | + | 0.267430i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.0254 | + | 49.9755i | −0.516412 | + | 1.61044i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.81429 | + | 21.6319i | −0.122786 | + | 0.696356i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.8633 | + | 7.59361i | 0.670918 | + | 0.244194i | 0.654943 | − | 0.755678i | \(-0.272693\pi\) |
0.0159747 | + | 0.999872i | \(0.494915\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.74846 | + | 4.52881i | 0.0561687 | + | 0.145486i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.22659 | − | 10.7848i | −0.199821 | − | 0.346100i | 0.748649 | − | 0.662966i | \(-0.230703\pi\) |
−0.948470 | + | 0.316866i | \(0.897369\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.26123 | − | 0.185517i | −0.0724919 | − | 0.00594739i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −27.1687 | − | 4.24946i | −0.870093 | − | 0.136092i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.16163 | + | 8.53489i | 0.229121 | + | 0.273055i | 0.868340 | − | 0.495969i | \(-0.165187\pi\) |
−0.639220 | + | 0.769024i | \(0.720743\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58.1177 | + | 10.2477i | 1.85745 | + | 0.327519i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.4935 | + | 48.4496i | 0.335032 | + | 1.54688i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.53848 | − | 20.0677i | 0.112860 | − | 0.640060i | −0.874928 | − | 0.484254i | \(-0.839091\pi\) |
0.987788 | − | 0.155807i | \(-0.0497977\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.35621 | − | 11.9686i | 0.138800 | − | 0.381351i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.7634 | + | 6.34142i | −0.406264 | + | 0.201850i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.99380 | + | 1.15112i | 0.0633991 | + | 0.0366035i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.54592 | − | 6.14172i | −0.112640 | − | 0.195098i | 0.804194 | − | 0.594367i | \(-0.202597\pi\) |
−0.916834 | + | 0.399269i | \(0.869264\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.14529 | − | 5.36284i | 0.195015 | − | 0.170185i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.5388 | − | 3.79787i | 0.682826 | − | 0.120401i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.2664 | + | 50.1865i | 0.578503 | + | 1.58942i | 0.790705 | + | 0.612197i | \(0.209714\pi\) |
−0.212203 | + | 0.977226i | \(0.568064\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.79136 | − | 10.3266i | −0.214869 | − | 0.326720i |
(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 | 756.2.ck.a.605.5 | yes | 144 | |
7.5 | odd | 6 | 756.2.ca.a.173.12 | ✓ | 144 | ||
27.5 | odd | 18 | 756.2.ca.a.437.12 | yes | 144 | ||
189.5 | even | 18 | inner | 756.2.ck.a.5.5 | yes | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.ca.a.173.12 | ✓ | 144 | 7.5 | odd | 6 | ||
756.2.ca.a.437.12 | yes | 144 | 27.5 | odd | 18 | ||
756.2.ck.a.5.5 | yes | 144 | 189.5 | even | 18 | inner | |
756.2.ck.a.605.5 | yes | 144 | 1.1 | even | 1 | trivial |