Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(369,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{11} + 39 x^{10} - 10 x^{9} + 2 x^{8} - 26 x^{7} + 297 x^{6} - 116 x^{5} + 24 x^{4} + \cdots + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 920) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.4 | ||
Root | \(-1.71470 - 1.71470i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.369 |
Dual form | 1840.2.e.g.369.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.58319i | − | 0.914057i | −0.889452 | − | 0.457029i | \(-0.848914\pi\) | ||
0.889452 | − | 0.457029i | \(-0.151086\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.09277 | + | 0.787606i | −0.935914 | + | 0.352228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.84620i | 1.07576i | 0.843020 | + | 0.537881i | \(0.180775\pi\) | ||||
−0.843020 | + | 0.537881i | \(0.819225\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.493499 | 0.164500 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.98637 | −0.598913 | −0.299457 | − | 0.954110i | \(-0.596805\pi\) | ||||
−0.299457 | + | 0.954110i | \(0.596805\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.69204i | − | 1.30134i | −0.759362 | − | 0.650668i | \(-0.774489\pi\) | ||
0.759362 | − | 0.650668i | \(-0.225511\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.24693 | + | 3.31326i | 0.321957 | + | 0.855479i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.16675i | 0.768050i | 0.923323 | + | 0.384025i | \(0.125462\pi\) | ||||
−0.923323 | + | 0.384025i | \(0.874538\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.16110 | −1.41345 | −0.706727 | − | 0.707486i | \(-0.749829\pi\) | ||||
−0.706727 | + | 0.707486i | \(0.749829\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.50609 | 0.983309 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.75935 | − | 3.29655i | 0.751871 | − | 0.659311i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.53088i | − | 1.06442i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.61816 | 1.22896 | 0.614481 | − | 0.788932i | \(-0.289365\pi\) | ||||
0.614481 | + | 0.788932i | \(0.289365\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.29732 | 1.49024 | 0.745121 | − | 0.666929i | \(-0.232392\pi\) | ||||
0.745121 | + | 0.666929i | \(0.232392\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.14481i | 0.547441i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.24169 | − | 5.95644i | −0.378914 | − | 1.00682i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.71181i | − | 0.281420i | −0.990051 | − | 0.140710i | \(-0.955061\pi\) | ||
0.990051 | − | 0.140710i | \(-0.0449386\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.42840 | −1.18950 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.72440 | 1.05018 | 0.525088 | − | 0.851048i | \(-0.324033\pi\) | ||||
0.525088 | + | 0.851048i | \(0.324033\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.177968i | − | 0.0271399i | −0.999908 | − | 0.0135700i | \(-0.995680\pi\) | ||
0.999908 | − | 0.0135700i | \(-0.00431958\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.03278 | + | 0.388683i | −0.153958 | + | 0.0579414i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 11.4749i | − | 1.67378i | −0.547369 | − | 0.836891i | \(-0.684371\pi\) | ||
0.547369 | − | 0.836891i | \(-0.315629\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.10086 | −0.157266 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.01358 | 0.702042 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.18762i | − | 0.849934i | −0.905209 | − | 0.424967i | \(-0.860286\pi\) | ||
0.905209 | − | 0.424967i | \(-0.139714\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.15701 | − | 1.56448i | 0.560531 | − | 0.210954i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.75422i | 1.29198i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.61559 | −0.991465 | −0.495733 | − | 0.868475i | \(-0.665100\pi\) | ||||
−0.495733 | + | 0.868475i | \(0.665100\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.8577 | 1.51822 | 0.759109 | − | 0.650964i | \(-0.225635\pi\) | ||||
0.759109 | + | 0.650964i | \(0.225635\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.40460i | 0.176963i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.69548 | + | 9.81934i | 0.458367 | + | 1.21794i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.07554i | − | 0.375737i | −0.982194 | − | 0.187868i | \(-0.939842\pi\) | ||
0.982194 | − | 0.187868i | \(-0.0601579\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.58319 | 0.190594 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.96195 | 0.232840 | 0.116420 | − | 0.993200i | \(-0.462858\pi\) | ||||
0.116420 | + | 0.993200i | \(0.462858\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.94732i | − | 0.579041i | −0.957172 | − | 0.289520i | \(-0.906504\pi\) | ||
0.957172 | − | 0.289520i | \(-0.0934958\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.21908 | − | 5.95178i | −0.602647 | − | 0.687253i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 5.65361i | − | 0.644289i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.53182 | 0.959905 | 0.479952 | − | 0.877295i | \(-0.340654\pi\) | ||||
0.479952 | + | 0.877295i | \(0.340654\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.27596 | −0.808440 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.49429i | 0.383548i | 0.981439 | + | 0.191774i | \(0.0614241\pi\) | ||||
−0.981439 | + | 0.191774i | \(0.938576\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.49415 | − | 6.62728i | −0.270529 | − | 0.718829i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 10.4778i | − | 1.12334i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.07506 | −0.749954 | −0.374977 | − | 0.927034i | \(-0.622349\pi\) | ||||
−0.374977 | + | 0.927034i | \(0.622349\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.3545 | 1.39993 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 13.1363i | − | 1.36217i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.8938 | − | 4.85252i | 1.32287 | − | 0.497858i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 7.00705i | − | 0.711458i | −0.934589 | − | 0.355729i | \(-0.884233\pi\) | ||
0.934589 | − | 0.355729i | \(-0.115767\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.980272 | −0.0985210 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.22362 | 0.718777 | 0.359389 | − | 0.933188i | \(-0.382985\pi\) | ||||
0.359389 | + | 0.933188i | \(0.382985\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.8178i | − | 1.26297i | −0.775386 | − | 0.631487i | \(-0.782445\pi\) | ||
0.775386 | − | 0.631487i | \(-0.217555\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.43019 | + | 3.54902i | −0.920293 | + | 0.346349i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.6841i | 1.12954i | 0.825247 | + | 0.564772i | \(0.191036\pi\) | ||||
−0.825247 | + | 0.564772i | \(0.808964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.6019 | 1.30283 | 0.651413 | − | 0.758723i | \(-0.274176\pi\) | ||||
0.651413 | + | 0.758723i | \(0.274176\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.71013 | −0.257234 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.44526i | − | 0.135959i | −0.997687 | − | 0.0679795i | \(-0.978345\pi\) | ||
0.997687 | − | 0.0679795i | \(-0.0216553\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.787606 | − | 2.09277i | −0.0734446 | − | 0.195152i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 2.31552i | − | 0.214069i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.01322 | −0.826240 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.05433 | −0.641303 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 10.6460i | − | 0.959920i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.27107 | + | 9.85981i | −0.471459 | + | 0.881888i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.12328i | 0.809561i | 0.914414 | + | 0.404780i | \(0.132652\pi\) | ||||
−0.914414 | + | 0.404780i | \(0.867348\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.281758 | −0.0248074 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.33180 | −0.815323 | −0.407661 | − | 0.913133i | \(-0.633656\pi\) | ||||
−0.407661 | + | 0.913133i | \(0.633656\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 17.5357i | − | 1.52054i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.35616 | + | 11.5749i | 0.374918 | + | 0.996205i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 21.0013i | − | 1.79426i | −0.441768 | − | 0.897129i | \(-0.645649\pi\) | ||
0.441768 | − | 0.897129i | \(-0.354351\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.1299 | −1.36812 | −0.684061 | − | 0.729425i | \(-0.739788\pi\) | ||||
−0.684061 | + | 0.729425i | \(0.739788\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.1669 | −1.52993 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.32012i | 0.779388i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.8503 | + | 5.21251i | −1.15020 | + | 0.432875i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.74288i | 0.143750i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.57227 | 0.784191 | 0.392096 | − | 0.919925i | \(-0.371750\pi\) | ||||
0.392096 | + | 0.919925i | \(0.371750\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.04120 | −0.247489 | −0.123745 | − | 0.992314i | \(-0.539490\pi\) | ||||
−0.123745 | + | 0.992314i | \(0.539490\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.56279i | 0.126344i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.3644 | + | 6.53502i | −1.39474 | + | 0.524905i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.4786i | − | 0.995900i | −0.867206 | − | 0.497950i | \(-0.834086\pi\) | ||
0.867206 | − | 0.497950i | \(-0.165914\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.79619 | −0.776889 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.84620 | −0.224312 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 16.3939i | − | 1.28407i | −0.766676 | − | 0.642034i | \(-0.778091\pi\) | ||
0.766676 | − | 0.642034i | \(-0.221909\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.47687 | − | 6.58135i | −0.192824 | − | 0.512358i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.13265i | 0.629323i | 0.949204 | + | 0.314662i | \(0.101891\pi\) | ||||
−0.949204 | + | 0.314662i | \(0.898109\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.01521 | −0.693477 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.04050 | −0.232513 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5256i | 0.800250i | 0.916461 | + | 0.400125i | \(0.131033\pi\) | ||||
−0.916461 | + | 0.400125i | \(0.868967\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.38265 | + | 10.6999i | 0.709262 | + | 0.808835i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.0570i | 0.906256i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.5421 | 1.53539 | 0.767695 | − | 0.640816i | \(-0.221404\pi\) | ||||
0.767695 | + | 0.640816i | \(0.221404\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0754 | −1.64085 | −0.820424 | − | 0.571756i | \(-0.806263\pi\) | ||||
−0.820424 | + | 0.571756i | \(0.806263\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 18.7730i | − | 1.38774i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.34823 | + | 3.58243i | 0.0991242 | + | 0.263385i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.29034i | − | 0.459995i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 15.7420 | 1.14506 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.50910 | 0.326267 | 0.163133 | − | 0.986604i | \(-0.447840\pi\) | ||||
0.163133 | + | 0.986604i | \(0.447840\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 21.1534i | − | 1.52266i | −0.648366 | − | 0.761329i | \(-0.724547\pi\) | ||
0.648366 | − | 0.761329i | \(-0.275453\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 15.5459 | − | 5.85065i | 1.11327 | − | 0.418974i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.1475i | 0.722980i | 0.932376 | + | 0.361490i | \(0.117732\pi\) | ||||
−0.932376 | + | 0.361490i | \(0.882268\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.57598 | 0.466159 | 0.233079 | − | 0.972458i | \(-0.425120\pi\) | ||||
0.233079 | + | 0.972458i | \(0.425120\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.86917 | −0.343445 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.8366i | 1.32207i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.0726 | + | 5.29618i | −0.982874 | + | 0.369901i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.493499i | 0.0343005i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.2382 | 0.846536 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.5357 | 1.82680 | 0.913398 | − | 0.407069i | \(-0.133449\pi\) | ||||
0.913398 | + | 0.407069i | \(0.133449\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 3.10614i | − | 0.212829i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.140169 | + | 0.372446i | 0.00955944 | + | 0.0254006i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.6158i | 1.60315i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.83257 | −0.529276 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.8585 | 0.999492 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 20.9231i | − | 1.40111i | −0.713597 | − | 0.700557i | \(-0.752935\pi\) | ||
0.713597 | − | 0.700557i | \(-0.247065\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.85524 | − | 1.62685i | 0.123682 | − | 0.108456i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.32581i | 0.618975i | 0.950903 | + | 0.309488i | \(0.100158\pi\) | ||||
−0.950903 | + | 0.309488i | \(0.899842\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −29.5189 | −1.95066 | −0.975332 | − | 0.220742i | \(-0.929152\pi\) | ||||
−0.975332 | + | 0.220742i | \(0.929152\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.95076 | −0.588917 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.9849i | 1.89886i | 0.313974 | + | 0.949431i | \(0.398339\pi\) | ||||
−0.313974 | + | 0.949431i | \(0.601661\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.03768 | + | 24.0142i | 0.589553 | + | 1.56652i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 13.5075i | − | 0.877408i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.62209 | −0.622401 | −0.311201 | − | 0.950344i | \(-0.600731\pi\) | ||||
−0.311201 | + | 0.950344i | \(0.600731\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.5745 | 1.00324 | 0.501621 | − | 0.865088i | \(-0.332737\pi\) | ||||
0.501621 | + | 0.865088i | \(0.332737\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 5.07340i | − | 0.325459i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.30385 | − | 0.867045i | 0.147187 | − | 0.0553935i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28.9081i | 1.83938i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.53214 | 0.350585 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.8066 | 1.43954 | 0.719770 | − | 0.694213i | \(-0.244247\pi\) | ||||
0.719770 | + | 0.694213i | \(0.244247\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.98637i | − | 0.124882i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.4923 | + | 3.94873i | −0.657051 | + | 0.247279i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.5591i | 0.721038i | 0.932752 | + | 0.360519i | \(0.117400\pi\) | ||||
−0.932752 | + | 0.360519i | \(0.882600\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.87216 | 0.302742 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.26606 | 0.202164 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.57534i | 0.405453i | 0.979235 | + | 0.202726i | \(0.0649802\pi\) | ||||
−0.979235 | + | 0.202726i | \(0.935020\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.87340 | + | 12.9492i | 0.299371 | + | 0.795466i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.2012i | 0.685501i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.6536 | 1.01539 | 0.507694 | − | 0.861537i | \(-0.330498\pi\) | ||||
0.507694 | + | 0.861537i | \(0.330498\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.8675 | 1.44985 | 0.724925 | − | 0.688828i | \(-0.241874\pi\) | ||||
0.724925 | + | 0.688828i | \(0.241874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 21.1427i | − | 1.27962i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.46747 | + | 6.54817i | −0.450305 | + | 0.394870i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.65369i | 0.339697i | 0.985470 | + | 0.169849i | \(0.0543279\pi\) | ||||
−0.985470 | + | 0.169849i | \(0.945672\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.09472 | 0.245144 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.7408 | −1.89350 | −0.946750 | − | 0.321971i | \(-0.895655\pi\) | ||||
−0.946750 | + | 0.321971i | \(0.895655\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 0.998092i | − | 0.0593304i | −0.999560 | − | 0.0296652i | \(-0.990556\pi\) | ||
0.999560 | − | 0.0296652i | \(-0.00944412\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.68248 | − | 20.4133i | −0.455071 | − | 1.20918i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 19.1390i | 1.12974i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.97168 | 0.410099 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.0935 | −0.650314 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 13.8947i | − | 0.811739i | −0.913931 | − | 0.405869i | \(-0.866969\pi\) | ||
0.913931 | − | 0.405869i | \(-0.133031\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.9377 | − | 5.99808i | 0.927927 | − | 0.349222i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.9864i | 0.637495i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.69204 | 0.271347 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.506534 | 0.0291961 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 11.4364i | − | 0.657003i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −24.8153 | + | 9.33916i | −1.42092 | + | 0.534759i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.66633i | − | 0.209249i | −0.994512 | − | 0.104624i | \(-0.966636\pi\) | ||
0.994512 | − | 0.104624i | \(-0.0333640\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.2930 | −1.15443 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.4210 | 0.817741 | 0.408870 | − | 0.912593i | \(-0.365923\pi\) | ||||
0.408870 | + | 0.912593i | \(0.365923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.5046i | 0.593754i | 0.954916 | + | 0.296877i | \(0.0959451\pi\) | ||||
−0.954916 | + | 0.296877i | \(0.904055\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.10627 | − | 2.93950i | −0.0623312 | − | 0.165622i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.0818i | 1.80189i | 0.433931 | + | 0.900946i | \(0.357126\pi\) | ||||
−0.433931 | + | 0.900946i | \(0.642874\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.1461 | −0.736042 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.4982 | 1.03247 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 19.5107i | − | 1.08560i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.4675 | − | 17.6390i | −0.857985 | − | 0.978437i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 21.5344i | − | 1.19086i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 32.6598 | 1.80059 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.71307 | −0.533879 | −0.266939 | − | 0.963713i | \(-0.586012\pi\) | ||||
−0.266939 | + | 0.963713i | \(0.586012\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 0.844778i | − | 0.0462935i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.42231 | + | 6.43639i | 0.132345 | + | 0.351657i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.131832i | 0.00718136i | 0.999994 | + | 0.00359068i | \(0.00114295\pi\) | ||||
−0.999994 | + | 0.00359068i | \(0.998857\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.28813 | −0.124274 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.4815 | −0.892526 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.7901i | 0.906582i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.31326 | + | 1.24693i | −0.178380 | + | 0.0671326i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 13.1981i | − | 0.708512i | −0.935148 | − | 0.354256i | \(-0.884734\pi\) | ||
0.935148 | − | 0.354256i | \(-0.115266\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.0451 | 1.82239 | 0.911197 | − | 0.411971i | \(-0.135159\pi\) | ||||
0.911197 | + | 0.411971i | \(0.135159\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.9511 | −1.38517 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.8593i | 0.577984i | 0.957331 | + | 0.288992i | \(0.0933201\pi\) | ||||
−0.957331 | + | 0.288992i | \(0.906680\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.10590 | + | 1.54524i | −0.217919 | + | 0.0820129i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.2697i | 0.755231i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.3091 | −1.07188 | −0.535938 | − | 0.844257i | \(-0.680042\pi\) | ||||
−0.535938 | + | 0.844257i | \(0.680042\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9592 | 0.997853 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.1684i | 0.586188i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.89654 | + | 10.3536i | 0.203954 | + | 0.541932i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 18.6731i | − | 0.974727i | −0.873199 | − | 0.487364i | \(-0.837959\pi\) | ||
0.873199 | − | 0.487364i | \(-0.162041\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.31848 | 0.172753 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.6112 | 0.914328 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.51979i | 0.492916i | 0.969153 | + | 0.246458i | \(0.0792667\pi\) | ||||
−0.969153 | + | 0.246458i | \(0.920733\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.6100 | + | 8.34512i | 0.806096 | + | 0.430940i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 31.0527i | − | 1.59929i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.8304 | 0.967251 | 0.483625 | − | 0.875275i | \(-0.339320\pi\) | ||||
0.483625 | + | 0.875275i | \(0.339320\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.4439 | 0.739985 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.9401i | 0.559015i | 0.960144 | + | 0.279507i | \(0.0901712\pi\) | ||||
−0.960144 | + | 0.279507i | \(0.909829\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.45282 | + | 11.8317i | 0.226937 | + | 0.602999i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 0.0878272i | − | 0.00446451i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.2830 | −1.12979 | −0.564896 | − | 0.825162i | \(-0.691084\pi\) | ||||
−0.564896 | + | 0.825162i | \(0.691084\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.16675 | −0.160150 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.7740i | 0.745252i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.8551 | + | 6.71971i | −0.898389 | + | 0.338105i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.8388i | 0.543983i | 0.962300 | + | 0.271991i | \(0.0876822\pi\) | ||||
−0.962300 | + | 0.271991i | \(0.912318\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −27.7625 | −1.38986 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.71329 | −0.135495 | −0.0677476 | − | 0.997702i | \(-0.521581\pi\) | ||||
−0.0677476 | + | 0.997702i | \(0.521581\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 38.9313i | − | 1.93931i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.2269 | − | 5.73059i | 0.756631 | − | 0.284755i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.40029i | 0.168546i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.6271 | −1.06939 | −0.534696 | − | 0.845044i | \(-0.679574\pi\) | ||||
−0.534696 | + | 0.845044i | \(0.679574\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −33.2490 | −1.64005 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 21.6755i | − | 1.06658i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.75212 | − | 7.31274i | −0.135097 | − | 0.358968i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25.5368i | 1.25054i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.00587 | 0.195700 | 0.0978498 | − | 0.995201i | \(-0.468804\pi\) | ||||
0.0978498 | + | 0.995201i | \(0.468804\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.4251 | 1.23914 | 0.619572 | − | 0.784940i | \(-0.287306\pi\) | ||||
0.619572 | + | 0.784940i | \(0.287306\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 5.66284i | − | 0.275337i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.4394 | + | 11.9049i | 0.506384 | + | 0.577475i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 33.7493i | 1.63324i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.7556 | 0.712405 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.07679 | −0.0518673 | −0.0259336 | − | 0.999664i | \(-0.508256\pi\) | ||||
−0.0259336 | + | 0.999664i | \(0.508256\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.93871i | − | 0.189283i | −0.995511 | − | 0.0946413i | \(-0.969830\pi\) | ||
0.995511 | − | 0.0946413i | \(-0.0301704\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.25240 | + | 21.9277i | 0.395672 | + | 1.05135i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 6.16110i | − | 0.294726i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.1539 | 0.627802 | 0.313901 | − | 0.949456i | \(-0.398364\pi\) | ||||
0.313901 | + | 0.949456i | \(0.398364\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.543274 | −0.0258702 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.95394i | 0.425415i | 0.977116 | + | 0.212707i | \(0.0682281\pi\) | ||||
−0.977116 | + | 0.212707i | \(0.931772\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.8064 | − | 5.57236i | 0.701893 | − | 0.264155i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 15.1548i | − | 0.716795i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.23267 | −0.388524 | −0.194262 | − | 0.980950i | \(-0.562231\pi\) | ||||
−0.194262 | + | 0.980950i | \(0.562231\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.3571 | −0.628964 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.81480i | 0.226219i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −27.9478 | + | 10.5181i | −1.31021 | + | 0.493095i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 36.3473i | − | 1.70026i | −0.526576 | − | 0.850128i | \(-0.676524\pi\) | ||
0.526576 | − | 0.850128i | \(-0.323476\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.5149 | 0.817527 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.2421 | −0.709894 | −0.354947 | − | 0.934886i | \(-0.615501\pi\) | ||||
−0.354947 | + | 0.934886i | \(0.615501\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.57424i | 0.259057i | 0.991576 | + | 0.129528i | \(0.0413463\pi\) | ||||
−0.991576 | + | 0.129528i | \(0.958654\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.3462 | + | 27.4911i | 0.479793 | + | 1.27487i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 6.21488i | − | 0.287590i | −0.989607 | − | 0.143795i | \(-0.954069\pi\) | ||
0.989607 | − | 0.143795i | \(-0.0459306\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.75360 | 0.404204 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.7560 | −0.910309 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.353511i | 0.0162545i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.1618 | + | 20.3104i | −1.06273 | + | 0.931905i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 3.05358i | − | 0.139814i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.4168 | −1.57254 | −0.786272 | − | 0.617880i | \(-0.787992\pi\) | ||||
−0.786272 | + | 0.617880i | \(0.787992\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.03189 | −0.366223 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.50609i | 0.205034i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.51880 | + | 14.6641i | 0.250596 | + | 0.665864i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.7752i | 1.03204i | 0.856576 | + | 0.516021i | \(0.172587\pi\) | ||||
−0.856576 | + | 0.516021i | \(0.827413\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −25.9547 | −1.17371 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.16911 | −0.143020 | −0.0715099 | − | 0.997440i | \(-0.522782\pi\) | ||||
−0.0715099 | + | 0.997440i | \(0.522782\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.9581i | 0.943905i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.05148 | − | 0.772068i | 0.0922072 | − | 0.0347019i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.58410i | 0.250481i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0809 | −0.630346 | −0.315173 | − | 0.949034i | \(-0.602063\pi\) | ||||
−0.315173 | + | 0.949034i | \(0.602063\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.8756 | 0.575237 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 21.4946i | − | 0.958399i | −0.877706 | − | 0.479199i | \(-0.840927\pi\) | ||
0.877706 | − | 0.479199i | \(-0.159073\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.1174 | + | 5.68937i | −0.672714 | + | 0.253173i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.2728i | 0.633878i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.0952 | 1.51124 | 0.755622 | − | 0.655008i | \(-0.227335\pi\) | ||||
0.755622 | + | 0.655008i | \(0.227335\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.0811 | 0.622910 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 34.0764i | 1.50451i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.0954 | + | 26.8247i | 0.444855 | + | 1.18204i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.7933i | 1.00245i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.6641 | 0.731474 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.1367 | −0.619339 | −0.309669 | − | 0.950844i | \(-0.600218\pi\) | ||||
−0.309669 | + | 0.950844i | \(0.600218\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.2020i | 0.489828i | 0.969545 | + | 0.244914i | \(0.0787598\pi\) | ||||
−0.969545 | + | 0.244914i | \(0.921240\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.9400 | − | 14.8546i | 0.739321 | − | 0.648306i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.2756i | 1.14458i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.75829 | −0.163096 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 31.5511i | − | 1.36663i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.20247 | − | 24.4521i | −0.397857 | − | 1.05716i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 32.5221i | − | 1.40343i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.18672 | 0.0941887 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.6704 | −1.44760 | −0.723802 | − | 0.690008i | \(-0.757607\pi\) | ||||
−0.723802 | + | 0.690008i | \(0.757607\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 34.9496i | 1.49983i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −28.4656 | + | 10.7129i | −1.21933 | + | 0.458892i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.1062i | 0.987949i | 0.869476 | + | 0.493975i | \(0.164456\pi\) | ||||
−0.869476 | + | 0.493975i | \(0.835544\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.85174 | 0.249746 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −40.7752 | −1.73708 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.2833i | 1.03263i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.67167 | − | 2.13452i | 0.240749 | − | 0.0906051i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.48937i | 0.147849i | 0.997264 | + | 0.0739246i | \(0.0235524\pi\) | ||||
−0.997264 | + | 0.0739246i | \(0.976448\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.835034 | −0.0353182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.95883 | −0.420462 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 38.8593i | − | 1.63772i | −0.573991 | − | 0.818862i | \(-0.694606\pi\) | ||
0.573991 | − | 0.818862i | \(-0.305394\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.13830 | + | 3.02460i | 0.0478886 | + | 0.127246i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 20.7089i | − | 0.869690i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.2055 | 0.972823 | 0.486412 | − | 0.873730i | \(-0.338306\pi\) | ||||
0.486412 | + | 0.873730i | \(0.338306\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.39836 | 0.225914 | 0.112957 | − | 0.993600i | \(-0.463968\pi\) | ||||
0.112957 | + | 0.993600i | \(0.463968\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 7.13877i | − | 0.298226i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.29655 | + | 3.75935i | 0.137476 | + | 0.156776i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 13.1082i | − | 0.545701i | −0.962056 | − | 0.272850i | \(-0.912034\pi\) | ||
0.962056 | − | 0.272850i | \(-0.0879664\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −33.4900 | −1.39180 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.94546 | −0.412607 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.2909i | 0.509037i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.82371 | + | 4.84584i | 0.0754013 | + | 0.200351i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 12.9646i | − | 0.535108i | −0.963543 | − | 0.267554i | \(-0.913785\pi\) | ||
0.963543 | − | 0.267554i | \(-0.0862154\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −51.1206 | −2.10639 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.0655 | 0.660845 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.0225i | 0.699030i | 0.936931 | + | 0.349515i | \(0.113654\pi\) | ||||
−0.936931 | + | 0.349515i | \(0.886346\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.8626 | − | 7.09886i | 0.773290 | − | 0.291025i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 10.4110i | − | 0.426096i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.98111 | −0.244381 | −0.122191 | − | 0.992507i | \(-0.538992\pi\) | ||||
−0.122191 | + | 0.992507i | \(0.538992\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.3680 | −0.871617 | −0.435809 | − | 0.900039i | \(-0.643538\pi\) | ||||
−0.435809 | + | 0.900039i | \(0.643538\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.51778i | − | 0.0618086i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.7631 | − | 5.55604i | 0.600205 | − | 0.225885i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 17.5464i | − | 0.712186i | −0.934450 | − | 0.356093i | \(-0.884109\pi\) | ||
0.934450 | − | 0.356093i | \(-0.115891\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29.8220 | 1.20845 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −53.8405 | −2.17815 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 45.4601i | − | 1.83612i | −0.396444 | − | 0.918059i | \(-0.629756\pi\) | ||
0.396444 | − | 0.918059i | \(-0.370244\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.38487 | + | 22.2797i | 0.338111 | + | 0.898403i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.8720i | 1.04157i | 0.853688 | + | 0.520785i | \(0.174360\pi\) | ||||
−0.853688 | + | 0.520785i | \(0.825640\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.20381 | −0.128772 | −0.0643859 | − | 0.997925i | \(-0.520509\pi\) | ||||
−0.0643859 | + | 0.997925i | \(0.520509\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.53088 | 0.221947 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 20.1370i | − | 0.806773i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.26548 | − | 24.7858i | 0.130619 | − | 0.991433i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 19.3755i | − | 0.773783i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.42089 | 0.216145 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.0248650 | −0.000989858 | −0.000494929 | − | 1.00000i | \(-0.500158\pi\) | ||||
−0.000494929 | 1.00000i | \(0.500158\pi\) | ||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 42.0112i | − | 1.66980i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.18555 | − | 19.0929i | −0.285150 | − | 0.757679i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.16528i | 0.204656i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.968219 | 0.0383022 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.77145 | −0.385949 | −0.192975 | − | 0.981204i | \(-0.561813\pi\) | ||||
−0.192975 | + | 0.981204i | \(0.561813\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 36.8211i | − | 1.45208i | −0.687651 | − | 0.726041i | \(-0.741358\pi\) | ||
0.687651 | − | 0.726041i | \(-0.258642\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.589655 | − | 0.221914i | 0.0232176 | − | 0.00873787i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 46.5570i | − | 1.83034i | −0.403064 | − | 0.915172i | \(-0.632055\pi\) | ||
0.403064 | − | 0.915172i | \(-0.367945\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.1274 | 0.593802 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 37.3884 | 1.46537 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 2.76029i | − | 0.108018i | −0.998540 | − | 0.0540092i | \(-0.982800\pi\) | ||
0.998540 | − | 0.0540092i | \(-0.0172000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.5293 | − | 7.34978i | 0.763072 | − | 0.287180i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 2.44150i | − | 0.0952520i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.3922 | 1.53450 | 0.767252 | − | 0.641346i | \(-0.221624\pi\) | ||||
0.767252 | + | 0.641346i | \(0.221624\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.7641 | −0.690943 | −0.345472 | − | 0.938429i | \(-0.612281\pi\) | ||||
−0.345472 | + | 0.938429i | \(0.612281\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 23.5239i | − | 0.913593i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.8113 | + | 36.6982i | 0.535578 | + | 1.42310i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.61816i | 0.256256i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −33.1253 | −1.28070 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.5537 | −0.909280 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.7072i | 0.913847i | 0.889506 | + | 0.456923i | \(0.151049\pi\) | ||||
−0.889506 | + | 0.456923i | \(0.848951\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.2329 | − | 20.7925i | −0.701783 | − | 0.800306i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 49.3507i | 1.89670i | 0.317221 | + | 0.948352i | \(0.397250\pi\) | ||||
−0.317221 | + | 0.948352i | \(0.602750\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.9435 | 0.765361 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.7646 | 0.565779 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.6461i | 0.598682i | 0.954146 | + | 0.299341i | \(0.0967669\pi\) | ||||
−0.954146 | + | 0.299341i | \(0.903233\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.5407 | + | 43.9507i | 0.631988 | + | 1.67927i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 46.7341i | 1.78302i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −29.0325 | −1.10605 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.79498 | −0.144368 | −0.0721839 | − | 0.997391i | \(-0.522997\pi\) | ||||
−0.0721839 | + | 0.997391i | \(0.522997\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 2.79005i | − | 0.105985i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.7562 | − | 12.7040i | 1.28044 | − | 0.481891i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.2945i | 0.806587i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 45.8887 | 1.73567 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.751725 | 0.0283923 | 0.0141961 | − | 0.999899i | \(-0.495481\pi\) | ||||
0.0141961 | + | 0.999899i | \(0.495481\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.5467i | 0.397775i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 38.0192 | − | 14.3084i | 1.43189 | − | 0.538885i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.5599i | 0.773234i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.52035 | −0.169765 | −0.0848827 | − | 0.996391i | \(-0.527052\pi\) | ||||
−0.0848827 | + | 0.996391i | \(0.527052\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.21044 | 0.157904 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.29732i | 0.310737i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.34058 | − | 19.5048i | −0.274522 | − | 0.729440i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.2336i | 0.568910i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.6742 | −1.36772 | −0.683859 | − | 0.729614i | \(-0.739700\pi\) | ||||
−0.683859 | + | 0.729614i | \(0.739700\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.4820 | 1.35866 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 24.6574i | − | 0.917020i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.8800 | − | 21.8171i | 0.924021 | − | 0.810268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.6449i | 1.24782i | 0.781496 | + | 0.623910i | \(0.214457\pi\) | ||||
−0.781496 | + | 0.623910i | \(0.785543\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.8601 | −1.10593 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.563582 | 0.0208448 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 47.5745i | − | 1.75720i | −0.477555 | − | 0.878602i | \(-0.658477\pi\) | ||
0.477555 | − | 0.878602i | \(-0.341523\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.37270 | − | 3.64744i | −0.0506328 | − | 0.134538i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.10916i | 0.225034i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.8914 | 1.06279 | 0.531395 | − | 0.847124i | \(-0.321668\pi\) | ||||
0.531395 | + | 0.847124i | \(0.321668\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 45.7672 | 1.68130 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.61970i | 0.132794i | 0.997793 | + | 0.0663969i | \(0.0211504\pi\) | ||||
−0.997793 | + | 0.0663969i | \(0.978850\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.0325 | + | 7.53918i | −0.733936 | + | 0.276214i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.72443i | 0.0630936i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −33.2553 | −1.21512 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.2050 | −0.700801 | −0.350401 | − | 0.936600i | \(-0.613955\pi\) | ||||
−0.350401 | + | 0.936600i | \(0.613955\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 36.1073i | − | 1.31582i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.36452 | − | 2.39527i | 0.231629 | − | 0.0871726i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 12.6638i | − | 0.460275i | −0.973158 | − | 0.230137i | \(-0.926082\pi\) | ||
0.973158 | − | 0.230137i | \(-0.0739176\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.14481 | −0.114149 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.9053 | −1.41032 | −0.705159 | − | 0.709050i | \(-0.749124\pi\) | ||||
−0.705159 | + | 0.709050i | \(0.749124\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38.7138i | 1.40153i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.23086 | − | 3.27055i | −0.0445019 | − | 0.118247i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35.7326i | 1.29023i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.16816 | −0.150308 | −0.0751539 | − | 0.997172i | \(-0.523945\pi\) | ||||
−0.0751539 | + | 0.997172i | \(0.523945\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.3003 | 0.659070 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 26.6030i | − | 0.956842i | −0.878131 | − | 0.478421i | \(-0.841209\pi\) | ||
0.878131 | − | 0.478421i | \(-0.158791\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.1926 | − | 27.3525i | 1.12047 | − | 0.982533i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 7.71358i | − | 0.276723i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −41.4297 | −1.48437 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.89716 | −0.139451 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 36.6043i | − | 1.30813i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.82821 | + | 26.1148i | 0.350784 | + | 0.932077i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 21.7538i | − | 0.775440i | −0.921777 | − | 0.387720i | \(-0.873263\pi\) | ||
0.921777 | − | 0.387720i | \(-0.126737\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.4100 | 0.370607 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.11351 | 0.146260 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 55.6366i | − | 1.97571i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20.5012 | − | 7.71554i | 0.727101 | − | 0.273642i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.2490i | 0.363039i | 0.983387 | + | 0.181519i | \(0.0581015\pi\) | ||||
−0.983387 | + | 0.181519i | \(0.941898\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.3381 | 1.28555 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.49153 | −0.123367 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.82722i | 0.346795i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.95644 | − | 2.24169i | 0.209937 | − | 0.0790090i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 26.3659i | − | 0.928123i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.0993 | −1.30434 | −0.652170 | − | 0.758072i | \(-0.726141\pi\) | ||||
−0.652170 | + | 0.758072i | \(0.726141\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.8084 | −1.25740 | −0.628701 | − | 0.777647i | \(-0.716413\pi\) | ||||
−0.628701 | + | 0.777647i | \(0.716413\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 37.7869i | − | 1.32525i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.9119 | + | 34.3086i | 0.452285 | + | 1.20178i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.09648i | 0.0383610i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.59042 | 0.230288 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.5343 | −0.751551 | −0.375775 | − | 0.926711i | \(-0.622624\pi\) | ||||
−0.375775 | + | 0.926711i | \(0.622624\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 41.1466i | − | 1.43428i | −0.696929 | − | 0.717140i | \(-0.745451\pi\) | ||
0.696929 | − | 0.717140i | \(-0.254549\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.3670 | + | 11.8224i | 0.360933 | + | 0.411605i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.48319i | 0.329763i | 0.986313 | + | 0.164881i | \(0.0527241\pi\) | ||||
−0.986313 | + | 0.164881i | \(0.947276\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.0091 | −0.833872 | −0.416936 | − | 0.908936i | \(-0.636896\pi\) | ||||
−0.416936 | + | 0.908936i | \(0.636896\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.95088 | 0.310503 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 3.48616i | − | 0.120788i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.40532 | − | 17.0197i | −0.221665 | − | 0.588992i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 45.8915i | − | 1.58624i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.89039 | 0.341454 | 0.170727 | − | 0.985318i | \(-0.445388\pi\) | ||||
0.170727 | + | 0.985318i | \(0.445388\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.8001 | 0.510348 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 50.2519i | 1.73077i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.8667 | − | 7.10043i | 0.649035 | − | 0.244262i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 20.0781i | − | 0.689890i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.58017 | −0.0542314 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.71181 | 0.0586802 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 5.02358i | − | 0.172004i | −0.996295 | − | 0.0860021i | \(-0.972591\pi\) | ||
0.996295 | − | 0.0860021i | \(-0.0274092\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.36306 | − | 2.39471i | 0.217612 | − | 0.0818975i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 26.8011i | − | 0.915509i | −0.889079 | − | 0.457754i | \(-0.848654\pi\) | ||
0.889079 | − | 0.457754i | \(-0.151346\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.3018 | 0.931525 | 0.465763 | − | 0.884910i | \(-0.345780\pi\) | ||||
0.465763 | + | 0.884910i | \(0.345780\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 30.3007 | 1.03265 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.22910i | 0.0758796i | 0.999280 | + | 0.0379398i | \(0.0120795\pi\) | ||||
−0.999280 | + | 0.0379398i | \(0.987920\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.29006 | − | 22.0277i | −0.281871 | − | 0.748965i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 11.0375i | − | 0.374854i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.9474 | −0.574900 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.4305 | −0.488960 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 3.45797i | − | 0.117035i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −28.0630 | − | 15.0025i | −0.948703 | − | 0.507178i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 46.4517i | − | 1.56856i | −0.620407 | − | 0.784280i | \(-0.713032\pi\) | ||
0.620407 | − | 0.784280i | \(-0.286968\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.9980 | −0.741975 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.6878 | −0.865444 | −0.432722 | − | 0.901527i | \(-0.642447\pi\) | ||||
−0.432722 | + | 0.901527i | \(0.642447\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.8481i | 1.64387i | 0.569582 | + | 0.821934i | \(0.307105\pi\) | ||||
−0.569582 | + | 0.821934i | \(0.692895\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.49613 | − | 25.2324i | −0.319209 | − | 0.848178i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 45.1121i | − | 1.51472i | −0.653000 | − | 0.757358i | \(-0.726490\pi\) | ||
0.653000 | − | 0.757358i | \(-0.273510\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.9667 | −0.870895 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.4528 | 0.484185 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 70.6979i | 2.36581i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −42.9899 | + | 16.1791i | −1.43699 | + | 0.540807i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 7.42840i | − | 0.248027i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 54.9130 | 1.83145 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.5947 | 0.652792 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 0.801941i | − | 0.0266869i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 46.1986 | − | 17.3867i | 1.53569 | − | 0.577953i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 15.5516i | − | 0.516382i | −0.966094 | − | 0.258191i | \(-0.916874\pi\) | ||
0.966094 | − | 0.258191i | \(-0.0831264\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.56485 | 0.118239 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.1283 | 0.998195 | 0.499097 | − | 0.866546i | \(-0.333665\pi\) | ||||
0.499097 | + | 0.866546i | \(0.333665\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 6.94096i | − | 0.229712i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.7857 | + | 39.2874i | 0.488800 | + | 1.29880i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 26.5602i | − | 0.877094i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.2483 | 1.12975 | 0.564874 | − | 0.825177i | \(-0.308925\pi\) | ||||
0.564874 | + | 0.825177i | \(0.308925\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.80452 | −0.191265 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 9.20553i | − | 0.303004i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.64308 | − | 6.43531i | −0.185543 | − | 0.211592i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 6.32556i | − | 0.207759i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 54.6989 | 1.79461 | 0.897307 | − | 0.441408i | \(-0.145521\pi\) | ||||
0.897307 | + | 0.441408i | \(0.145521\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.78252 | 0.222288 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 22.8312i | − | 0.747462i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.95431 | + | 13.1642i | 0.162023 | + | 0.430516i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 12.1635i | − | 0.397364i | −0.980064 | − | 0.198682i | \(-0.936334\pi\) | ||
0.980064 | − | 0.198682i | \(-0.0636661\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.6308 | 0.542725 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.9048 | −0.909672 | −0.454836 | − | 0.890575i | \(-0.650302\pi\) | ||||
−0.454836 | + | 0.890575i | \(0.650302\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.72440i | 0.218977i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −32.9444 | + | 12.3985i | −1.07168 | + | 0.403323i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.5104i | 0.341541i | 0.985311 | + | 0.170770i | \(0.0546256\pi\) | ||||
−0.985311 | + | 0.170770i | \(0.945374\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.2130 | −0.753527 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 50.7916 | 1.64703 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 11.7005i | − | 0.379017i | −0.981879 | − | 0.189508i | \(-0.939311\pi\) | ||
0.981879 | − | 0.189508i | \(-0.0606894\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.43649 | + | 3.55139i | −0.305358 | + | 0.114920i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.8129i | 0.672784i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 59.7738 | 1.93020 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.8455 | 1.22082 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.76609i | 0.185810i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.6606 | + | 44.2692i | 0.536323 | + | 1.42508i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.7133i | 0.376673i | 0.982105 | + | 0.188337i | \(0.0603096\pi\) | ||||
−0.982105 | + | 0.188337i | \(0.939690\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −30.8892 | −0.992304 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.8963 | 1.21615 | 0.608075 | − | 0.793879i | \(-0.291942\pi\) | ||||
0.608075 | + | 0.793879i | \(0.291942\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 45.9090i | − | 1.47178i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −27.9260 | + | 24.4881i | −0.894347 | + | 0.784247i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.83500i | 0.0906997i | 0.998971 | + | 0.0453499i | \(0.0144403\pi\) | ||||
−0.998971 | + | 0.0453499i | \(0.985560\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.0537 | 0.449158 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.71253 | 0.214314 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.47696i | 0.142793i | 0.997448 | + | 0.0713964i | \(0.0227455\pi\) | ||||
−0.997448 | + | 0.0713964i | \(0.977254\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.99224 | − | 21.2364i | −0.254654 | − | 0.676647i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 51.7068i | − | 1.64584i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.177968 | 0.00565906 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.2466 | 1.02435 | 0.512173 | − | 0.858882i | \(-0.328841\pi\) | ||||
0.512173 | + | 0.858882i | \(0.328841\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.3777i | 0.487996i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.7620 | + | 5.17928i | −0.436285 | + | 0.164194i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.5708i | 0.873177i | 0.899661 | + | 0.436589i | \(0.143813\pi\) | ||||
−0.899661 | + | 0.436589i | \(0.856187\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.46784 | −0.299549 |
(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 | 1840.2.e.g.369.4 | 14 | ||
4.3 | odd | 2 | 920.2.e.b.369.11 | yes | 14 | ||
5.2 | odd | 4 | 9200.2.a.cz.1.3 | 7 | |||
5.3 | odd | 4 | 9200.2.a.dc.1.5 | 7 | |||
5.4 | even | 2 | inner | 1840.2.e.g.369.11 | 14 | ||
20.3 | even | 4 | 4600.2.a.bh.1.3 | 7 | |||
20.7 | even | 4 | 4600.2.a.bi.1.5 | 7 | |||
20.19 | odd | 2 | 920.2.e.b.369.4 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.b.369.4 | ✓ | 14 | 20.19 | odd | 2 | ||
920.2.e.b.369.11 | yes | 14 | 4.3 | odd | 2 | ||
1840.2.e.g.369.4 | 14 | 1.1 | even | 1 | trivial | ||
1840.2.e.g.369.11 | 14 | 5.4 | even | 2 | inner | ||
4600.2.a.bh.1.3 | 7 | 20.3 | even | 4 | |||
4600.2.a.bi.1.5 | 7 | 20.7 | even | 4 | |||
9200.2.a.cz.1.3 | 7 | 5.2 | odd | 4 | |||
9200.2.a.dc.1.5 | 7 | 5.3 | odd | 4 |