Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(64,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.726638658394\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 64.6 | ||
Root | \(0.403032 - 0.403032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.64 |
Dual form | 91.2.c.a.64.1 |
$q$-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 \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.48119i | 1.75447i | 0.480062 | + | 0.877235i | \(0.340614\pi\) | ||||
−0.480062 | + | 0.877235i | \(0.659386\pi\) | |||||||
\(3\) | 1.67513 | 0.967137 | 0.483569 | − | 0.875306i | \(-0.339340\pi\) | ||||
0.483569 | + | 0.875306i | \(0.339340\pi\) | |||||||
\(4\) | −4.15633 | −2.07816 | ||||||||
\(5\) | − | 0.675131i | − | 0.301928i | −0.988539 | − | 0.150964i | \(-0.951762\pi\) | ||
0.988539 | − | 0.150964i | \(-0.0482377\pi\) | |||||||
\(6\) | 4.15633i | 1.69681i | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | − | 5.35026i | − | 1.89160i | ||||||
\(9\) | −0.193937 | −0.0646455 | ||||||||
\(10\) | 1.67513 | 0.529723 | ||||||||
\(11\) | − | 4.48119i | − | 1.35113i | −0.737300 | − | 0.675565i | \(-0.763900\pi\) | ||
0.737300 | − | 0.675565i | \(-0.236100\pi\) | |||||||
\(12\) | −6.96239 | −2.00987 | ||||||||
\(13\) | 3.28726 | − | 1.48119i | 0.911721 | − | 0.410809i | ||||
\(14\) | −2.48119 | −0.663127 | ||||||||
\(15\) | − | 1.13093i | − | 0.292006i | ||||||
\(16\) | 4.96239 | 1.24060 | ||||||||
\(17\) | −3.28726 | −0.797277 | −0.398639 | − | 0.917108i | \(-0.630517\pi\) | ||||
−0.398639 | + | 0.917108i | \(0.630517\pi\) | |||||||
\(18\) | − | 0.481194i | − | 0.113419i | ||||||
\(19\) | 5.21933i | 1.19740i | 0.800975 | + | 0.598698i | \(0.204315\pi\) | ||||
−0.800975 | + | 0.598698i | \(0.795685\pi\) | |||||||
\(20\) | 2.80606i | 0.627455i | ||||||||
\(21\) | 1.67513i | 0.365544i | ||||||||
\(22\) | 11.1187 | 2.37052 | ||||||||
\(23\) | 4.76845 | 0.994291 | 0.497145 | − | 0.867667i | \(-0.334382\pi\) | ||||
0.497145 | + | 0.867667i | \(0.334382\pi\) | |||||||
\(24\) | − | 8.96239i | − | 1.82944i | ||||||
\(25\) | 4.54420 | 0.908840 | ||||||||
\(26\) | 3.67513 | + | 8.15633i | 0.720752 | + | 1.59959i | ||||
\(27\) | −5.35026 | −1.02966 | ||||||||
\(28\) | − | 4.15633i | − | 0.785472i | ||||||
\(29\) | −9.31265 | −1.72932 | −0.864658 | − | 0.502361i | \(-0.832465\pi\) | ||||
−0.864658 | + | 0.502361i | \(0.832465\pi\) | |||||||
\(30\) | 2.80606 | 0.512315 | ||||||||
\(31\) | − | 1.63752i | − | 0.294107i | −0.989129 | − | 0.147054i | \(-0.953021\pi\) | ||
0.989129 | − | 0.147054i | \(-0.0469790\pi\) | |||||||
\(32\) | 1.61213i | 0.284986i | ||||||||
\(33\) | − | 7.50659i | − | 1.30673i | ||||||
\(34\) | − | 8.15633i | − | 1.39880i | ||||||
\(35\) | 0.675131 | 0.114118 | ||||||||
\(36\) | 0.806063 | 0.134344 | ||||||||
\(37\) | 1.44358i | 0.237324i | 0.992935 | + | 0.118662i | \(0.0378604\pi\) | ||||
−0.992935 | + | 0.118662i | \(0.962140\pi\) | |||||||
\(38\) | −12.9502 | −2.10079 | ||||||||
\(39\) | 5.50659 | − | 2.48119i | 0.881760 | − | 0.397309i | ||||
\(40\) | −3.61213 | −0.571127 | ||||||||
\(41\) | 7.92478i | 1.23764i | 0.785532 | + | 0.618821i | \(0.212389\pi\) | ||||
−0.785532 | + | 0.618821i | \(0.787611\pi\) | |||||||
\(42\) | −4.15633 | −0.641335 | ||||||||
\(43\) | −4.61213 | −0.703343 | −0.351671 | − | 0.936124i | \(-0.614387\pi\) | ||||
−0.351671 | + | 0.936124i | \(0.614387\pi\) | |||||||
\(44\) | 18.6253i | 2.80787i | ||||||||
\(45\) | 0.130933i | 0.0195183i | ||||||||
\(46\) | 11.8315i | 1.74445i | ||||||||
\(47\) | − | 7.86907i | − | 1.14782i | −0.818918 | − | 0.573911i | \(-0.805426\pi\) | ||
0.818918 | − | 0.573911i | \(-0.194574\pi\) | |||||||
\(48\) | 8.31265 | 1.19983 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 11.2750i | 1.59453i | ||||||||
\(51\) | −5.50659 | −0.771076 | ||||||||
\(52\) | −13.6629 | + | 6.15633i | −1.89471 | + | 0.853729i | ||||
\(53\) | −3.15633 | −0.433555 | −0.216777 | − | 0.976221i | \(-0.569555\pi\) | ||||
−0.216777 | + | 0.976221i | \(0.569555\pi\) | |||||||
\(54\) | − | 13.2750i | − | 1.80650i | ||||||
\(55\) | −3.02539 | −0.407944 | ||||||||
\(56\) | 5.35026 | 0.714959 | ||||||||
\(57\) | 8.74306i | 1.15805i | ||||||||
\(58\) | − | 23.1065i | − | 3.03403i | ||||||
\(59\) | 2.54420i | 0.331226i | 0.986191 | + | 0.165613i | \(0.0529603\pi\) | ||||
−0.986191 | + | 0.165613i | \(0.947040\pi\) | |||||||
\(60\) | 4.70052i | 0.606835i | ||||||||
\(61\) | −2.31265 | −0.296105 | −0.148052 | − | 0.988980i | \(-0.547300\pi\) | ||||
−0.148052 | + | 0.988980i | \(0.547300\pi\) | |||||||
\(62\) | 4.06300 | 0.516002 | ||||||||
\(63\) | − | 0.193937i | − | 0.0244337i | ||||||
\(64\) | 5.92478 | 0.740597 | ||||||||
\(65\) | −1.00000 | − | 2.21933i | −0.124035 | − | 0.275274i | ||||
\(66\) | 18.6253 | 2.29262 | ||||||||
\(67\) | − | 7.35026i | − | 0.897977i | −0.893537 | − | 0.448989i | \(-0.851784\pi\) | ||
0.893537 | − | 0.448989i | \(-0.148216\pi\) | |||||||
\(68\) | 13.6629 | 1.65687 | ||||||||
\(69\) | 7.98778 | 0.961616 | ||||||||
\(70\) | 1.67513i | 0.200216i | ||||||||
\(71\) | − | 7.75623i | − | 0.920496i | −0.887791 | − | 0.460248i | \(-0.847761\pi\) | ||
0.887791 | − | 0.460248i | \(-0.152239\pi\) | |||||||
\(72\) | 1.03761i | 0.122284i | ||||||||
\(73\) | 15.1441i | 1.77248i | 0.463223 | + | 0.886242i | \(0.346693\pi\) | ||||
−0.463223 | + | 0.886242i | \(0.653307\pi\) | |||||||
\(74\) | −3.58181 | −0.416377 | ||||||||
\(75\) | 7.61213 | 0.878973 | ||||||||
\(76\) | − | 21.6932i | − | 2.48838i | ||||||
\(77\) | 4.48119 | 0.510679 | ||||||||
\(78\) | 6.15633 | + | 13.6629i | 0.697067 | + | 1.54702i | ||||
\(79\) | 14.6629 | 1.64971 | 0.824853 | − | 0.565347i | \(-0.191258\pi\) | ||||
0.824853 | + | 0.565347i | \(0.191258\pi\) | |||||||
\(80\) | − | 3.35026i | − | 0.374571i | ||||||
\(81\) | −8.38058 | −0.931175 | ||||||||
\(82\) | −19.6629 | −2.17141 | ||||||||
\(83\) | 1.45088i | 0.159254i | 0.996825 | + | 0.0796272i | \(0.0253730\pi\) | ||||
−0.996825 | + | 0.0796272i | \(0.974627\pi\) | |||||||
\(84\) | − | 6.96239i | − | 0.759659i | ||||||
\(85\) | 2.21933i | 0.240720i | ||||||||
\(86\) | − | 11.4436i | − | 1.23399i | ||||||
\(87\) | −15.5999 | −1.67249 | ||||||||
\(88\) | −23.9756 | −2.55580 | ||||||||
\(89\) | 7.79384i | 0.826146i | 0.910698 | + | 0.413073i | \(0.135545\pi\) | ||||
−0.910698 | + | 0.413073i | \(0.864455\pi\) | |||||||
\(90\) | −0.324869 | −0.0342442 | ||||||||
\(91\) | 1.48119 | + | 3.28726i | 0.155271 | + | 0.344598i | ||||
\(92\) | −19.8192 | −2.06630 | ||||||||
\(93\) | − | 2.74306i | − | 0.284442i | ||||||
\(94\) | 19.5247 | 2.01382 | ||||||||
\(95\) | 3.52373 | 0.361527 | ||||||||
\(96\) | 2.70052i | 0.275621i | ||||||||
\(97\) | 17.9805i | 1.82564i | 0.408360 | + | 0.912821i | \(0.366101\pi\) | ||||
−0.408360 | + | 0.912821i | \(0.633899\pi\) | |||||||
\(98\) | − | 2.48119i | − | 0.250638i | ||||||
\(99\) | 0.869067i | 0.0873446i | ||||||||
\(100\) | −18.8872 | −1.88872 | ||||||||
\(101\) | 9.33804 | 0.929170 | 0.464585 | − | 0.885529i | \(-0.346204\pi\) | ||||
0.464585 | + | 0.885529i | \(0.346204\pi\) | |||||||
\(102\) | − | 13.6629i | − | 1.35283i | ||||||
\(103\) | 6.23743 | 0.614592 | 0.307296 | − | 0.951614i | \(-0.400576\pi\) | ||||
0.307296 | + | 0.951614i | \(0.400576\pi\) | |||||||
\(104\) | −7.92478 | − | 17.5877i | −0.777088 | − | 1.72461i | ||||
\(105\) | 1.13093 | 0.110368 | ||||||||
\(106\) | − | 7.83146i | − | 0.760658i | ||||||
\(107\) | 7.24472 | 0.700374 | 0.350187 | − | 0.936680i | \(-0.386118\pi\) | ||||
0.350187 | + | 0.936680i | \(0.386118\pi\) | |||||||
\(108\) | 22.2374 | 2.13980 | ||||||||
\(109\) | − | 4.79384i | − | 0.459167i | −0.973289 | − | 0.229584i | \(-0.926264\pi\) | ||
0.973289 | − | 0.229584i | \(-0.0737364\pi\) | |||||||
\(110\) | − | 7.50659i | − | 0.715725i | ||||||
\(111\) | 2.41819i | 0.229524i | ||||||||
\(112\) | 4.96239i | 0.468902i | ||||||||
\(113\) | −9.34297 | −0.878912 | −0.439456 | − | 0.898264i | \(-0.644829\pi\) | ||||
−0.439456 | + | 0.898264i | \(0.644829\pi\) | |||||||
\(114\) | −21.6932 | −2.03176 | ||||||||
\(115\) | − | 3.21933i | − | 0.300204i | ||||||
\(116\) | 38.7064 | 3.59380 | ||||||||
\(117\) | −0.637519 | + | 0.287258i | −0.0589387 | + | 0.0265570i | ||||
\(118\) | −6.31265 | −0.581127 | ||||||||
\(119\) | − | 3.28726i | − | 0.301342i | ||||||
\(120\) | −6.05079 | −0.552359 | ||||||||
\(121\) | −9.08110 | −0.825555 | ||||||||
\(122\) | − | 5.73813i | − | 0.519506i | ||||||
\(123\) | 13.2750i | 1.19697i | ||||||||
\(124\) | 6.80606i | 0.611203i | ||||||||
\(125\) | − | 6.44358i | − | 0.576332i | ||||||
\(126\) | 0.481194 | 0.0428682 | ||||||||
\(127\) | −1.38058 | −0.122507 | −0.0612533 | − | 0.998122i | \(-0.519510\pi\) | ||||
−0.0612533 | + | 0.998122i | \(0.519510\pi\) | |||||||
\(128\) | 17.9248i | 1.58434i | ||||||||
\(129\) | −7.72592 | −0.680229 | ||||||||
\(130\) | 5.50659 | − | 2.48119i | 0.482960 | − | 0.217615i | ||||
\(131\) | 12.4993 | 1.09207 | 0.546034 | − | 0.837763i | \(-0.316137\pi\) | ||||
0.546034 | + | 0.837763i | \(0.316137\pi\) | |||||||
\(132\) | 31.1998i | 2.71560i | ||||||||
\(133\) | −5.21933 | −0.452573 | ||||||||
\(134\) | 18.2374 | 1.57547 | ||||||||
\(135\) | 3.61213i | 0.310882i | ||||||||
\(136\) | 17.5877i | 1.50813i | ||||||||
\(137\) | − | 3.20616i | − | 0.273920i | −0.990577 | − | 0.136960i | \(-0.956267\pi\) | ||
0.990577 | − | 0.136960i | \(-0.0437332\pi\) | |||||||
\(138\) | 19.8192i | 1.68713i | ||||||||
\(139\) | −0.249646 | −0.0211747 | −0.0105874 | − | 0.999944i | \(-0.503370\pi\) | ||||
−0.0105874 | + | 0.999944i | \(0.503370\pi\) | |||||||
\(140\) | −2.80606 | −0.237156 | ||||||||
\(141\) | − | 13.1817i | − | 1.11010i | ||||||
\(142\) | 19.2447 | 1.61498 | ||||||||
\(143\) | −6.63752 | − | 14.7308i | −0.555057 | − | 1.23185i | ||||
\(144\) | −0.962389 | −0.0801991 | ||||||||
\(145\) | 6.28726i | 0.522128i | ||||||||
\(146\) | −37.5755 | −3.10977 | ||||||||
\(147\) | −1.67513 | −0.138162 | ||||||||
\(148\) | − | 6.00000i | − | 0.493197i | ||||||
\(149\) | 4.03269i | 0.330371i | 0.986263 | + | 0.165185i | \(0.0528222\pi\) | ||||
−0.986263 | + | 0.165185i | \(0.947178\pi\) | |||||||
\(150\) | 18.8872i | 1.54213i | ||||||||
\(151\) | − | 1.56959i | − | 0.127731i | −0.997958 | − | 0.0638657i | \(-0.979657\pi\) | ||
0.997958 | − | 0.0638657i | \(-0.0203429\pi\) | |||||||
\(152\) | 27.9248 | 2.26500 | ||||||||
\(153\) | 0.637519 | 0.0515404 | ||||||||
\(154\) | 11.1187i | 0.895971i | ||||||||
\(155\) | −1.10554 | −0.0887991 | ||||||||
\(156\) | −22.8872 | + | 10.3127i | −1.83244 | + | 0.825673i | ||||
\(157\) | 2.89938 | 0.231396 | 0.115698 | − | 0.993284i | \(-0.463090\pi\) | ||||
0.115698 | + | 0.993284i | \(0.463090\pi\) | |||||||
\(158\) | 36.3815i | 2.89436i | ||||||||
\(159\) | −5.28726 | −0.419307 | ||||||||
\(160\) | 1.08840 | 0.0860453 | ||||||||
\(161\) | 4.76845i | 0.375807i | ||||||||
\(162\) | − | 20.7938i | − | 1.63372i | ||||||
\(163\) | − | 17.2750i | − | 1.35309i | −0.736403 | − | 0.676543i | \(-0.763477\pi\) | ||
0.736403 | − | 0.676543i | \(-0.236523\pi\) | |||||||
\(164\) | − | 32.9380i | − | 2.57202i | ||||||
\(165\) | −5.06793 | −0.394538 | ||||||||
\(166\) | −3.59991 | −0.279407 | ||||||||
\(167\) | − | 16.2931i | − | 1.26080i | −0.776270 | − | 0.630400i | \(-0.782891\pi\) | ||
0.776270 | − | 0.630400i | \(-0.217109\pi\) | |||||||
\(168\) | 8.96239 | 0.691463 | ||||||||
\(169\) | 8.61213 | − | 9.73813i | 0.662471 | − | 0.749087i | ||||
\(170\) | −5.50659 | −0.422336 | ||||||||
\(171\) | − | 1.01222i | − | 0.0774063i | ||||||
\(172\) | 19.1695 | 1.46166 | ||||||||
\(173\) | 2.17442 | 0.165318 | 0.0826592 | − | 0.996578i | \(-0.473659\pi\) | ||||
0.0826592 | + | 0.996578i | \(0.473659\pi\) | |||||||
\(174\) | − | 38.7064i | − | 2.93432i | ||||||
\(175\) | 4.54420i | 0.343509i | ||||||||
\(176\) | − | 22.2374i | − | 1.67621i | ||||||
\(177\) | 4.26187i | 0.320341i | ||||||||
\(178\) | −19.3380 | −1.44945 | ||||||||
\(179\) | −0.551493 | −0.0412205 | −0.0206102 | − | 0.999788i | \(-0.506561\pi\) | ||||
−0.0206102 | + | 0.999788i | \(0.506561\pi\) | |||||||
\(180\) | − | 0.544198i | − | 0.0405621i | ||||||
\(181\) | 0.511511 | 0.0380203 | 0.0190102 | − | 0.999819i | \(-0.493949\pi\) | ||||
0.0190102 | + | 0.999819i | \(0.493949\pi\) | |||||||
\(182\) | −8.15633 | + | 3.67513i | −0.604587 | + | 0.272419i | ||||
\(183\) | −3.87399 | −0.286374 | ||||||||
\(184\) | − | 25.5125i | − | 1.88080i | ||||||
\(185\) | 0.974607 | 0.0716546 | ||||||||
\(186\) | 6.80606 | 0.499045 | ||||||||
\(187\) | 14.7308i | 1.07723i | ||||||||
\(188\) | 32.7064i | 2.38536i | ||||||||
\(189\) | − | 5.35026i | − | 0.389174i | ||||||
\(190\) | 8.74306i | 0.634288i | ||||||||
\(191\) | −16.5442 | −1.19710 | −0.598548 | − | 0.801087i | \(-0.704255\pi\) | ||||
−0.598548 | + | 0.801087i | \(0.704255\pi\) | |||||||
\(192\) | 9.92478 | 0.716259 | ||||||||
\(193\) | − | 7.41090i | − | 0.533448i | −0.963773 | − | 0.266724i | \(-0.914059\pi\) | ||
0.963773 | − | 0.266724i | \(-0.0859412\pi\) | |||||||
\(194\) | −44.6131 | −3.20303 | ||||||||
\(195\) | −1.67513 | − | 3.71767i | −0.119959 | − | 0.266228i | ||||
\(196\) | 4.15633 | 0.296880 | ||||||||
\(197\) | − | 7.14903i | − | 0.509347i | −0.967027 | − | 0.254674i | \(-0.918032\pi\) | ||
0.967027 | − | 0.254674i | \(-0.0819681\pi\) | |||||||
\(198\) | −2.15633 | −0.153243 | ||||||||
\(199\) | 5.10062 | 0.361573 | 0.180787 | − | 0.983522i | \(-0.442136\pi\) | ||||
0.180787 | + | 0.983522i | \(0.442136\pi\) | |||||||
\(200\) | − | 24.3127i | − | 1.71916i | ||||||
\(201\) | − | 12.3127i | − | 0.868467i | ||||||
\(202\) | 23.1695i | 1.63020i | ||||||||
\(203\) | − | 9.31265i | − | 0.653620i | ||||||
\(204\) | 22.8872 | 1.60242 | ||||||||
\(205\) | 5.35026 | 0.373678 | ||||||||
\(206\) | 15.4763i | 1.07828i | ||||||||
\(207\) | −0.924777 | −0.0642765 | ||||||||
\(208\) | 16.3127 | − | 7.35026i | 1.13108 | − | 0.509649i | ||||
\(209\) | 23.3888 | 1.61784 | ||||||||
\(210\) | 2.80606i | 0.193637i | ||||||||
\(211\) | 0.193937 | 0.0133511 | 0.00667557 | − | 0.999978i | \(-0.497875\pi\) | ||||
0.00667557 | + | 0.999978i | \(0.497875\pi\) | |||||||
\(212\) | 13.1187 | 0.900997 | ||||||||
\(213\) | − | 12.9927i | − | 0.890246i | ||||||
\(214\) | 17.9756i | 1.22878i | ||||||||
\(215\) | 3.11379i | 0.212359i | ||||||||
\(216\) | 28.6253i | 1.94771i | ||||||||
\(217\) | 1.63752 | 0.111162 | ||||||||
\(218\) | 11.8945 | 0.805594 | ||||||||
\(219\) | 25.3684i | 1.71423i | ||||||||
\(220\) | 12.5745 | 0.847774 | ||||||||
\(221\) | −10.8061 | + | 4.86907i | −0.726894 | + | 0.327529i | ||||
\(222\) | −6.00000 | −0.402694 | ||||||||
\(223\) | − | 5.83875i | − | 0.390992i | −0.980705 | − | 0.195496i | \(-0.937368\pi\) | ||
0.980705 | − | 0.195496i | \(-0.0626316\pi\) | |||||||
\(224\) | −1.61213 | −0.107715 | ||||||||
\(225\) | −0.881286 | −0.0587524 | ||||||||
\(226\) | − | 23.1817i | − | 1.54202i | ||||||
\(227\) | 3.68735i | 0.244738i | 0.992485 | + | 0.122369i | \(0.0390491\pi\) | ||||
−0.992485 | + | 0.122369i | \(0.960951\pi\) | |||||||
\(228\) | − | 36.3390i | − | 2.40661i | ||||||
\(229\) | 5.65703i | 0.373827i | 0.982376 | + | 0.186914i | \(0.0598484\pi\) | ||||
−0.982376 | + | 0.186914i | \(0.940152\pi\) | |||||||
\(230\) | 7.98778 | 0.526699 | ||||||||
\(231\) | 7.50659 | 0.493897 | ||||||||
\(232\) | 49.8251i | 3.27118i | ||||||||
\(233\) | −10.3258 | −0.676467 | −0.338234 | − | 0.941062i | \(-0.609829\pi\) | ||||
−0.338234 | + | 0.941062i | \(0.609829\pi\) | |||||||
\(234\) | −0.712742 | − | 1.58181i | −0.0465934 | − | 0.103406i | ||||
\(235\) | −5.31265 | −0.346559 | ||||||||
\(236\) | − | 10.5745i | − | 0.688342i | ||||||
\(237\) | 24.5623 | 1.59549 | ||||||||
\(238\) | 8.15633 | 0.528696 | ||||||||
\(239\) | 22.2882i | 1.44170i | 0.693089 | + | 0.720852i | \(0.256249\pi\) | ||||
−0.693089 | + | 0.720852i | \(0.743751\pi\) | |||||||
\(240\) | − | 5.61213i | − | 0.362261i | ||||||
\(241\) | − | 29.4264i | − | 1.89552i | −0.318979 | − | 0.947762i | \(-0.603340\pi\) | ||
0.318979 | − | 0.947762i | \(-0.396660\pi\) | |||||||
\(242\) | − | 22.5320i | − | 1.44841i | ||||||
\(243\) | 2.01222 | 0.129084 | ||||||||
\(244\) | 9.61213 | 0.615353 | ||||||||
\(245\) | 0.675131i | 0.0431325i | ||||||||
\(246\) | −32.9380 | −2.10005 | ||||||||
\(247\) | 7.73084 | + | 17.1573i | 0.491902 | + | 1.09169i | ||||
\(248\) | −8.76116 | −0.556334 | ||||||||
\(249\) | 2.43041i | 0.154021i | ||||||||
\(250\) | 15.9878 | 1.01116 | ||||||||
\(251\) | −21.5247 | −1.35863 | −0.679313 | − | 0.733849i | \(-0.737722\pi\) | ||||
−0.679313 | + | 0.733849i | \(0.737722\pi\) | |||||||
\(252\) | 0.806063i | 0.0507772i | ||||||||
\(253\) | − | 21.3684i | − | 1.34342i | ||||||
\(254\) | − | 3.42548i | − | 0.214934i | ||||||
\(255\) | 3.71767i | 0.232809i | ||||||||
\(256\) | −32.6253 | −2.03908 | ||||||||
\(257\) | 0.661957 | 0.0412917 | 0.0206459 | − | 0.999787i | \(-0.493428\pi\) | ||||
0.0206459 | + | 0.999787i | \(0.493428\pi\) | |||||||
\(258\) | − | 19.1695i | − | 1.19344i | ||||||
\(259\) | −1.44358 | −0.0896999 | ||||||||
\(260\) | 4.15633 | + | 9.22425i | 0.257764 | + | 0.572064i | ||||
\(261\) | 1.80606 | 0.111793 | ||||||||
\(262\) | 31.0132i | 1.91600i | ||||||||
\(263\) | 5.18664 | 0.319822 | 0.159911 | − | 0.987131i | \(-0.448879\pi\) | ||||
0.159911 | + | 0.987131i | \(0.448879\pi\) | |||||||
\(264\) | −40.1622 | −2.47181 | ||||||||
\(265\) | 2.13093i | 0.130902i | ||||||||
\(266\) | − | 12.9502i | − | 0.794026i | ||||||
\(267\) | 13.0557i | 0.798996i | ||||||||
\(268\) | 30.5501i | 1.86614i | ||||||||
\(269\) | 27.2506 | 1.66150 | 0.830749 | − | 0.556647i | \(-0.187912\pi\) | ||||
0.830749 | + | 0.556647i | \(0.187912\pi\) | |||||||
\(270\) | −8.96239 | −0.545434 | ||||||||
\(271\) | 18.7612i | 1.13966i | 0.821763 | + | 0.569830i | \(0.192991\pi\) | ||||
−0.821763 | + | 0.569830i | \(0.807009\pi\) | |||||||
\(272\) | −16.3127 | −0.989100 | ||||||||
\(273\) | 2.48119 | + | 5.50659i | 0.150169 | + | 0.333274i | ||||
\(274\) | 7.95509 | 0.480585 | ||||||||
\(275\) | − | 20.3634i | − | 1.22796i | ||||||
\(276\) | −33.1998 | −1.99839 | ||||||||
\(277\) | −15.4241 | −0.926743 | −0.463371 | − | 0.886164i | \(-0.653360\pi\) | ||||
−0.463371 | + | 0.886164i | \(0.653360\pi\) | |||||||
\(278\) | − | 0.619421i | − | 0.0371504i | ||||||
\(279\) | 0.317575i | 0.0190127i | ||||||||
\(280\) | − | 3.61213i | − | 0.215866i | ||||||
\(281\) | 24.8446i | 1.48211i | 0.671446 | + | 0.741053i | \(0.265673\pi\) | ||||
−0.671446 | + | 0.741053i | \(0.734327\pi\) | |||||||
\(282\) | 32.7064 | 1.94764 | ||||||||
\(283\) | −22.8872 | −1.36050 | −0.680250 | − | 0.732980i | \(-0.738129\pi\) | ||||
−0.680250 | + | 0.732980i | \(0.738129\pi\) | |||||||
\(284\) | 32.2374i | 1.91294i | ||||||||
\(285\) | 5.90271 | 0.349646 | ||||||||
\(286\) | 36.5501 | − | 16.4690i | 2.16125 | − | 0.973831i | ||||
\(287\) | −7.92478 | −0.467785 | ||||||||
\(288\) | − | 0.312650i | − | 0.0184231i | ||||||
\(289\) | −6.19394 | −0.364349 | ||||||||
\(290\) | −15.5999 | −0.916058 | ||||||||
\(291\) | 30.1197i | 1.76565i | ||||||||
\(292\) | − | 62.9438i | − | 3.68351i | ||||||
\(293\) | − | 25.2193i | − | 1.47333i | −0.676258 | − | 0.736664i | \(-0.736400\pi\) | ||
0.676258 | − | 0.736664i | \(-0.263600\pi\) | |||||||
\(294\) | − | 4.15633i | − | 0.242402i | ||||||
\(295\) | 1.71767 | 0.100006 | ||||||||
\(296\) | 7.72355 | 0.448922 | ||||||||
\(297\) | 23.9756i | 1.39120i | ||||||||
\(298\) | −10.0059 | −0.579625 | ||||||||
\(299\) | 15.6751 | − | 7.06300i | 0.906516 | − | 0.408464i | ||||
\(300\) | −31.6385 | −1.82665 | ||||||||
\(301\) | − | 4.61213i | − | 0.265839i | ||||||
\(302\) | 3.89446 | 0.224101 | ||||||||
\(303\) | 15.6424 | 0.898635 | ||||||||
\(304\) | 25.9003i | 1.48549i | ||||||||
\(305\) | 1.56134i | 0.0894022i | ||||||||
\(306\) | 1.58181i | 0.0904260i | ||||||||
\(307\) | − | 7.24965i | − | 0.413759i | −0.978366 | − | 0.206880i | \(-0.933669\pi\) | ||
0.978366 | − | 0.206880i | \(-0.0663308\pi\) | |||||||
\(308\) | −18.6253 | −1.06128 | ||||||||
\(309\) | 10.4485 | 0.594395 | ||||||||
\(310\) | − | 2.74306i | − | 0.155795i | ||||||
\(311\) | 20.2398 | 1.14769 | 0.573847 | − | 0.818963i | \(-0.305450\pi\) | ||||
0.573847 | + | 0.818963i | \(0.305450\pi\) | |||||||
\(312\) | −13.2750 | − | 29.4617i | −0.751551 | − | 1.66794i | ||||
\(313\) | −33.1368 | −1.87300 | −0.936502 | − | 0.350663i | \(-0.885956\pi\) | ||||
−0.936502 | + | 0.350663i | \(0.885956\pi\) | |||||||
\(314\) | 7.19394i | 0.405977i | ||||||||
\(315\) | −0.130933 | −0.00737721 | ||||||||
\(316\) | −60.9438 | −3.42836 | ||||||||
\(317\) | − | 17.0132i | − | 0.955555i | −0.878481 | − | 0.477778i | \(-0.841443\pi\) | ||
0.878481 | − | 0.477778i | \(-0.158557\pi\) | |||||||
\(318\) | − | 13.1187i | − | 0.735661i | ||||||
\(319\) | 41.7318i | 2.33653i | ||||||||
\(320\) | − | 4.00000i | − | 0.223607i | ||||||
\(321\) | 12.1359 | 0.677357 | ||||||||
\(322\) | −11.8315 | −0.659341 | ||||||||
\(323\) | − | 17.1573i | − | 0.954657i | ||||||
\(324\) | 34.8324 | 1.93513 | ||||||||
\(325\) | 14.9380 | − | 6.73084i | 0.828608 | − | 0.373360i | ||||
\(326\) | 42.8627 | 2.37395 | ||||||||
\(327\) | − | 8.03032i | − | 0.444078i | ||||||
\(328\) | 42.3996 | 2.34113 | ||||||||
\(329\) | 7.86907 | 0.433836 | ||||||||
\(330\) | − | 12.5745i | − | 0.692204i | ||||||
\(331\) | 10.8364i | 0.595621i | 0.954625 | + | 0.297811i | \(0.0962564\pi\) | ||||
−0.954625 | + | 0.297811i | \(0.903744\pi\) | |||||||
\(332\) | − | 6.03032i | − | 0.330957i | ||||||
\(333\) | − | 0.279964i | − | 0.0153419i | ||||||
\(334\) | 40.4264 | 2.21204 | ||||||||
\(335\) | −4.96239 | −0.271124 | ||||||||
\(336\) | 8.31265i | 0.453492i | ||||||||
\(337\) | −2.96968 | −0.161769 | −0.0808845 | − | 0.996723i | \(-0.525774\pi\) | ||||
−0.0808845 | + | 0.996723i | \(0.525774\pi\) | |||||||
\(338\) | 24.1622 | + | 21.3684i | 1.31425 | + | 1.16229i | ||||
\(339\) | −15.6507 | −0.850029 | ||||||||
\(340\) | − | 9.22425i | − | 0.500255i | ||||||
\(341\) | −7.33804 | −0.397377 | ||||||||
\(342\) | 2.51151 | 0.135807 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 24.6761i | 1.33045i | ||||||||
\(345\) | − | 5.39280i | − | 0.290338i | ||||||
\(346\) | 5.39517i | 0.290046i | ||||||||
\(347\) | 30.7367 | 1.65003 | 0.825017 | − | 0.565108i | \(-0.191166\pi\) | ||||
0.825017 | + | 0.565108i | \(0.191166\pi\) | |||||||
\(348\) | 64.8383 | 3.47570 | ||||||||
\(349\) | − | 2.00492i | − | 0.107321i | −0.998559 | − | 0.0536606i | \(-0.982911\pi\) | ||
0.998559 | − | 0.0536606i | \(-0.0170889\pi\) | |||||||
\(350\) | −11.2750 | −0.602676 | ||||||||
\(351\) | −17.5877 | + | 7.92478i | −0.938761 | + | 0.422993i | ||||
\(352\) | 7.22425 | 0.385054 | ||||||||
\(353\) | 17.2546i | 0.918368i | 0.888341 | + | 0.459184i | \(0.151858\pi\) | ||||
−0.888341 | + | 0.459184i | \(0.848142\pi\) | |||||||
\(354\) | −10.5745 | −0.562029 | ||||||||
\(355\) | −5.23647 | −0.277923 | ||||||||
\(356\) | − | 32.3938i | − | 1.71687i | ||||||
\(357\) | − | 5.50659i | − | 0.291439i | ||||||
\(358\) | − | 1.36836i | − | 0.0723201i | ||||||
\(359\) | 7.10650i | 0.375066i | 0.982258 | + | 0.187533i | \(0.0600492\pi\) | ||||
−0.982258 | + | 0.187533i | \(0.939951\pi\) | |||||||
\(360\) | 0.700523 | 0.0369208 | ||||||||
\(361\) | −8.24140 | −0.433758 | ||||||||
\(362\) | 1.26916i | 0.0667055i | ||||||||
\(363\) | −15.2120 | −0.798425 | ||||||||
\(364\) | −6.15633 | − | 13.6629i | −0.322679 | − | 0.716131i | ||||
\(365\) | 10.2243 | 0.535162 | ||||||||
\(366\) | − | 9.61213i | − | 0.502434i | ||||||
\(367\) | −27.2628 | −1.42311 | −0.711554 | − | 0.702632i | \(-0.752008\pi\) | ||||
−0.711554 | + | 0.702632i | \(0.752008\pi\) | |||||||
\(368\) | 23.6629 | 1.23351 | ||||||||
\(369\) | − | 1.53690i | − | 0.0800080i | ||||||
\(370\) | 2.41819i | 0.125716i | ||||||||
\(371\) | − | 3.15633i | − | 0.163868i | ||||||
\(372\) | 11.4010i | 0.591117i | ||||||||
\(373\) | −5.91890 | −0.306469 | −0.153234 | − | 0.988190i | \(-0.548969\pi\) | ||||
−0.153234 | + | 0.988190i | \(0.548969\pi\) | |||||||
\(374\) | −36.5501 | −1.88996 | ||||||||
\(375\) | − | 10.7938i | − | 0.557392i | ||||||
\(376\) | −42.1016 | −2.17122 | ||||||||
\(377\) | −30.6131 | + | 13.7938i | −1.57665 | + | 0.710419i | ||||
\(378\) | 13.2750 | 0.682794 | ||||||||
\(379\) | − | 28.9706i | − | 1.48812i | −0.668112 | − | 0.744061i | \(-0.732897\pi\) | ||
0.668112 | − | 0.744061i | \(-0.267103\pi\) | |||||||
\(380\) | −14.6458 | −0.751312 | ||||||||
\(381\) | −2.31265 | −0.118481 | ||||||||
\(382\) | − | 41.0494i | − | 2.10027i | ||||||
\(383\) | 23.2243i | 1.18670i | 0.804943 | + | 0.593352i | \(0.202196\pi\) | ||||
−0.804943 | + | 0.593352i | \(0.797804\pi\) | |||||||
\(384\) | 30.0263i | 1.53228i | ||||||||
\(385\) | − | 3.02539i | − | 0.154188i | ||||||
\(386\) | 18.3879 | 0.935918 | ||||||||
\(387\) | 0.894460 | 0.0454680 | ||||||||
\(388\) | − | 74.7328i | − | 3.79398i | ||||||
\(389\) | −16.1319 | −0.817919 | −0.408960 | − | 0.912552i | \(-0.634108\pi\) | ||||
−0.408960 | + | 0.912552i | \(0.634108\pi\) | |||||||
\(390\) | 9.22425 | − | 4.15633i | 0.467088 | − | 0.210464i | ||||
\(391\) | −15.6751 | −0.792725 | ||||||||
\(392\) | 5.35026i | 0.270229i | ||||||||
\(393\) | 20.9380 | 1.05618 | ||||||||
\(394\) | 17.7381 | 0.893634 | ||||||||
\(395\) | − | 9.89938i | − | 0.498092i | ||||||
\(396\) | − | 3.61213i | − | 0.181516i | ||||||
\(397\) | − | 24.0557i | − | 1.20732i | −0.797241 | − | 0.603661i | \(-0.793708\pi\) | ||
0.797241 | − | 0.603661i | \(-0.206292\pi\) | |||||||
\(398\) | 12.6556i | 0.634369i | ||||||||
\(399\) | −8.74306 | −0.437700 | ||||||||
\(400\) | 22.5501 | 1.12750 | ||||||||
\(401\) | − | 2.77575i | − | 0.138614i | −0.997595 | − | 0.0693071i | \(-0.977921\pi\) | ||
0.997595 | − | 0.0693071i | \(-0.0220788\pi\) | |||||||
\(402\) | 30.5501 | 1.52370 | ||||||||
\(403\) | −2.42548 | − | 5.38295i | −0.120822 | − | 0.268144i | ||||
\(404\) | −38.8119 | −1.93097 | ||||||||
\(405\) | 5.65799i | 0.281148i | ||||||||
\(406\) | 23.1065 | 1.14676 | ||||||||
\(407\) | 6.46898 | 0.320655 | ||||||||
\(408\) | 29.4617i | 1.45857i | ||||||||
\(409\) | − | 20.1309i | − | 0.995411i | −0.867346 | − | 0.497705i | \(-0.834176\pi\) | ||
0.867346 | − | 0.497705i | \(-0.165824\pi\) | |||||||
\(410\) | 13.2750i | 0.655607i | ||||||||
\(411\) | − | 5.37073i | − | 0.264919i | ||||||
\(412\) | −25.9248 | −1.27722 | ||||||||
\(413\) | −2.54420 | −0.125192 | ||||||||
\(414\) | − | 2.29455i | − | 0.112771i | ||||||
\(415\) | 0.979532 | 0.0480833 | ||||||||
\(416\) | 2.38787 | + | 5.29948i | 0.117075 | + | 0.259828i | ||||
\(417\) | −0.418190 | −0.0204789 | ||||||||
\(418\) | 58.0322i | 2.83845i | ||||||||
\(419\) | −0.385503 | −0.0188331 | −0.00941654 | − | 0.999956i | \(-0.502997\pi\) | ||||
−0.00941654 | + | 0.999956i | \(0.502997\pi\) | |||||||
\(420\) | −4.70052 | −0.229362 | ||||||||
\(421\) | 15.6810i | 0.764246i | 0.924112 | + | 0.382123i | \(0.124807\pi\) | ||||
−0.924112 | + | 0.382123i | \(0.875193\pi\) | |||||||
\(422\) | 0.481194i | 0.0234242i | ||||||||
\(423\) | 1.52610i | 0.0742015i | ||||||||
\(424\) | 16.8872i | 0.820113i | ||||||||
\(425\) | −14.9380 | −0.724597 | ||||||||
\(426\) | 32.2374 | 1.56191 | ||||||||
\(427\) | − | 2.31265i | − | 0.111917i | ||||||
\(428\) | −30.1114 | −1.45549 | ||||||||
\(429\) | −11.1187 | − | 24.6761i | −0.536817 | − | 1.19137i | ||||
\(430\) | −7.72592 | −0.372577 | ||||||||
\(431\) | 1.53690i | 0.0740301i | 0.999315 | + | 0.0370150i | \(0.0117849\pi\) | ||||
−0.999315 | + | 0.0370150i | \(0.988215\pi\) | |||||||
\(432\) | −26.5501 | −1.27739 | ||||||||
\(433\) | 26.0362 | 1.25122 | 0.625610 | − | 0.780136i | \(-0.284850\pi\) | ||||
0.625610 | + | 0.780136i | \(0.284850\pi\) | |||||||
\(434\) | 4.06300i | 0.195030i | ||||||||
\(435\) | 10.5320i | 0.504970i | ||||||||
\(436\) | 19.9248i | 0.954224i | ||||||||
\(437\) | 24.8881i | 1.19056i | ||||||||
\(438\) | −62.9438 | −3.00757 | ||||||||
\(439\) | −19.1246 | −0.912767 | −0.456384 | − | 0.889783i | \(-0.650855\pi\) | ||||
−0.456384 | + | 0.889783i | \(0.650855\pi\) | |||||||
\(440\) | 16.1866i | 0.771668i | ||||||||
\(441\) | 0.193937 | 0.00923507 | ||||||||
\(442\) | −12.0811 | − | 26.8119i | −0.574639 | − | 1.27531i | ||||
\(443\) | −12.6180 | −0.599500 | −0.299750 | − | 0.954018i | \(-0.596903\pi\) | ||||
−0.299750 | + | 0.954018i | \(0.596903\pi\) | |||||||
\(444\) | − | 10.0508i | − | 0.476989i | ||||||
\(445\) | 5.26187 | 0.249436 | ||||||||
\(446\) | 14.4871 | 0.685983 | ||||||||
\(447\) | 6.75528i | 0.319514i | ||||||||
\(448\) | 5.92478i | 0.279919i | ||||||||
\(449\) | 1.02302i | 0.0482794i | 0.999709 | + | 0.0241397i | \(0.00768466\pi\) | ||||
−0.999709 | + | 0.0241397i | \(0.992315\pi\) | |||||||
\(450\) | − | 2.18664i | − | 0.103079i | ||||||
\(451\) | 35.5125 | 1.67222 | ||||||||
\(452\) | 38.8324 | 1.82652 | ||||||||
\(453\) | − | 2.62927i | − | 0.123534i | ||||||
\(454\) | −9.14903 | −0.429385 | ||||||||
\(455\) | 2.21933 | − | 1.00000i | 0.104044 | − | 0.0468807i | ||||
\(456\) | 46.7777 | 2.19056 | ||||||||
\(457\) | 28.5320i | 1.33467i | 0.744758 | + | 0.667335i | \(0.232565\pi\) | ||||
−0.744758 | + | 0.667335i | \(0.767435\pi\) | |||||||
\(458\) | −14.0362 | −0.655868 | ||||||||
\(459\) | 17.5877 | 0.820923 | ||||||||
\(460\) | 13.3806i | 0.623873i | ||||||||
\(461\) | 25.3503i | 1.18068i | 0.807155 | + | 0.590340i | \(0.201006\pi\) | ||||
−0.807155 | + | 0.590340i | \(0.798994\pi\) | |||||||
\(462\) | 18.6253i | 0.866527i | ||||||||
\(463\) | − | 39.6810i | − | 1.84413i | −0.387032 | − | 0.922066i | \(-0.626500\pi\) | ||
0.387032 | − | 0.922066i | \(-0.373500\pi\) | |||||||
\(464\) | −46.2130 | −2.14538 | ||||||||
\(465\) | −1.85192 | −0.0858809 | ||||||||
\(466\) | − | 25.6204i | − | 1.18684i | ||||||
\(467\) | −1.95158 | −0.0903086 | −0.0451543 | − | 0.998980i | \(-0.514378\pi\) | ||||
−0.0451543 | + | 0.998980i | \(0.514378\pi\) | |||||||
\(468\) | 2.64974 | − | 1.19394i | 0.122484 | − | 0.0551897i | ||||
\(469\) | 7.35026 | 0.339404 | ||||||||
\(470\) | − | 13.1817i | − | 0.608027i | ||||||
\(471\) | 4.85685 | 0.223792 | ||||||||
\(472\) | 13.6121 | 0.626549 | ||||||||
\(473\) | 20.6678i | 0.950308i | ||||||||
\(474\) | 60.9438i | 2.79924i | ||||||||
\(475\) | 23.7177i | 1.08824i | ||||||||
\(476\) | 13.6629i | 0.626239i | ||||||||
\(477\) | 0.612127 | 0.0280274 | ||||||||
\(478\) | −55.3014 | −2.52943 | ||||||||
\(479\) | 26.1368i | 1.19422i | 0.802159 | + | 0.597111i | \(0.203685\pi\) | ||||
−0.802159 | + | 0.597111i | \(0.796315\pi\) | |||||||
\(480\) | 1.82321 | 0.0832176 | ||||||||
\(481\) | 2.13823 | + | 4.74543i | 0.0974947 | + | 0.216373i | ||||
\(482\) | 73.0127 | 3.32564 | ||||||||
\(483\) | 7.98778i | 0.363457i | ||||||||
\(484\) | 37.7440 | 1.71564 | ||||||||
\(485\) | 12.1392 | 0.551212 | ||||||||
\(486\) | 4.99271i | 0.226474i | ||||||||
\(487\) | − | 20.9624i | − | 0.949896i | −0.880014 | − | 0.474948i | \(-0.842467\pi\) | ||
0.880014 | − | 0.474948i | \(-0.157533\pi\) | |||||||
\(488\) | 12.3733i | 0.560112i | ||||||||
\(489\) | − | 28.9380i | − | 1.30862i | ||||||
\(490\) | −1.67513 | −0.0756747 | ||||||||
\(491\) | 2.95651 | 0.133425 | 0.0667127 | − | 0.997772i | \(-0.478749\pi\) | ||||
0.0667127 | + | 0.997772i | \(0.478749\pi\) | |||||||
\(492\) | − | 55.1754i | − | 2.48750i | ||||||
\(493\) | 30.6131 | 1.37874 | ||||||||
\(494\) | −42.5705 | + | 19.1817i | −1.91534 | + | 0.863026i | ||||
\(495\) | 0.586734 | 0.0263717 | ||||||||
\(496\) | − | 8.12601i | − | 0.364869i | ||||||
\(497\) | 7.75623 | 0.347915 | ||||||||
\(498\) | −6.03032 | −0.270225 | ||||||||
\(499\) | − | 2.85448i | − | 0.127784i | −0.997957 | − | 0.0638920i | \(-0.979649\pi\) | ||
0.997957 | − | 0.0638920i | \(-0.0203513\pi\) | |||||||
\(500\) | 26.7816i | 1.19771i | ||||||||
\(501\) | − | 27.2931i | − | 1.21937i | ||||||
\(502\) | − | 53.4069i | − | 2.38367i | ||||||
\(503\) | 23.8641 | 1.06405 | 0.532025 | − | 0.846729i | \(-0.321431\pi\) | ||||
0.532025 | + | 0.846729i | \(0.321431\pi\) | |||||||
\(504\) | −1.03761 | −0.0462189 | ||||||||
\(505\) | − | 6.30440i | − | 0.280542i | ||||||
\(506\) | 53.0191 | 2.35698 | ||||||||
\(507\) | 14.4264 | − | 16.3127i | 0.640701 | − | 0.724470i | ||||
\(508\) | 5.73813 | 0.254589 | ||||||||
\(509\) | − | 11.1949i | − | 0.496205i | −0.968734 | − | 0.248102i | \(-0.920193\pi\) | ||
0.968734 | − | 0.248102i | \(-0.0798070\pi\) | |||||||
\(510\) | −9.22425 | −0.408457 | ||||||||
\(511\) | −15.1441 | −0.669936 | ||||||||
\(512\) | − | 45.1002i | − | 1.99316i | ||||||
\(513\) | − | 27.9248i | − | 1.23291i | ||||||
\(514\) | 1.64244i | 0.0724451i | ||||||||
\(515\) | − | 4.21108i | − | 0.185562i | ||||||
\(516\) | 32.1114 | 1.41363 | ||||||||
\(517\) | −35.2628 | −1.55086 | ||||||||
\(518\) | − | 3.58181i | − | 0.157376i | ||||||
\(519\) | 3.64244 | 0.159886 | ||||||||
\(520\) | −11.8740 | + | 5.35026i | −0.520709 | + | 0.234624i | ||||
\(521\) | −26.4894 | −1.16052 | −0.580262 | − | 0.814430i | \(-0.697050\pi\) | ||||
−0.580262 | + | 0.814430i | \(0.697050\pi\) | |||||||
\(522\) | 4.48119i | 0.196137i | ||||||||
\(523\) | −12.9525 | −0.566375 | −0.283188 | − | 0.959065i | \(-0.591392\pi\) | ||||
−0.283188 | + | 0.959065i | \(0.591392\pi\) | |||||||
\(524\) | −51.9511 | −2.26950 | ||||||||
\(525\) | 7.61213i | 0.332220i | ||||||||
\(526\) | 12.8691i | 0.561118i | ||||||||
\(527\) | 5.38295i | 0.234485i | ||||||||
\(528\) | − | 37.2506i | − | 1.62112i | ||||||
\(529\) | −0.261865 | −0.0113854 | ||||||||
\(530\) | −5.28726 | −0.229664 | ||||||||
\(531\) | − | 0.493413i | − | 0.0214123i | ||||||
\(532\) | 21.6932 | 0.940521 | ||||||||
\(533\) | 11.7381 | + | 26.0508i | 0.508435 | + | 1.12838i | ||||
\(534\) | −32.3938 | −1.40181 | ||||||||
\(535\) | − | 4.89114i | − | 0.211462i | ||||||
\(536\) | −39.3258 | −1.69862 | ||||||||
\(537\) | −0.923822 | −0.0398659 | ||||||||
\(538\) | 67.6140i | 2.91505i | ||||||||
\(539\) | 4.48119i | 0.193019i | ||||||||
\(540\) | − | 15.0132i | − | 0.646064i | ||||||
\(541\) | 28.0933i | 1.20783i | 0.797050 | + | 0.603913i | \(0.206393\pi\) | ||||
−0.797050 | + | 0.603913i | \(0.793607\pi\) | |||||||
\(542\) | −46.5501 | −1.99950 | ||||||||
\(543\) | 0.856849 | 0.0367709 | ||||||||
\(544\) | − | 5.29948i | − | 0.227213i | ||||||
\(545\) | −3.23647 | −0.138635 | ||||||||
\(546\) | −13.6629 | + | 6.15633i | −0.584719 | + | 0.263466i | ||||
\(547\) | 14.8192 | 0.633625 | 0.316812 | − | 0.948488i | \(-0.397387\pi\) | ||||
0.316812 | + | 0.948488i | \(0.397387\pi\) | |||||||
\(548\) | 13.3258i | 0.569251i | ||||||||
\(549\) | 0.448507 | 0.0191418 | ||||||||
\(550\) | 50.5256 | 2.15442 | ||||||||
\(551\) | − | 48.6058i | − | 2.07068i | ||||||
\(552\) | − | 42.7367i | − | 1.81900i | ||||||
\(553\) | 14.6629i | 0.623530i | ||||||||
\(554\) | − | 38.2701i | − | 1.62594i | ||||||
\(555\) | 1.63259 | 0.0692998 | ||||||||
\(556\) | 1.03761 | 0.0440045 | ||||||||
\(557\) | − | 18.3879i | − | 0.779119i | −0.921001 | − | 0.389560i | \(-0.872627\pi\) | ||
0.921001 | − | 0.389560i | \(-0.127373\pi\) | |||||||
\(558\) | −0.787965 | −0.0333572 | ||||||||
\(559\) | −15.1612 | + | 6.83146i | −0.641253 | + | 0.288940i | ||||
\(560\) | 3.35026 | 0.141574 | ||||||||
\(561\) | 24.6761i | 1.04183i | ||||||||
\(562\) | −61.6444 | −2.60031 | ||||||||
\(563\) | 15.3357 | 0.646322 | 0.323161 | − | 0.946344i | \(-0.395255\pi\) | ||||
0.323161 | + | 0.946344i | \(0.395255\pi\) | |||||||
\(564\) | 54.7875i | 2.30697i | ||||||||
\(565\) | 6.30773i | 0.265368i | ||||||||
\(566\) | − | 56.7875i | − | 2.38696i | ||||||
\(567\) | − | 8.38058i | − | 0.351951i | ||||||
\(568\) | −41.4979 | −1.74121 | ||||||||
\(569\) | −1.32250 | −0.0554421 | −0.0277210 | − | 0.999616i | \(-0.508825\pi\) | ||||
−0.0277210 | + | 0.999616i | \(0.508825\pi\) | |||||||
\(570\) | 14.6458i | 0.613444i | ||||||||
\(571\) | 37.9175 | 1.58680 | 0.793399 | − | 0.608702i | \(-0.208310\pi\) | ||||
0.793399 | + | 0.608702i | \(0.208310\pi\) | |||||||
\(572\) | 27.5877 | + | 61.2262i | 1.15350 | + | 2.55999i | ||||
\(573\) | −27.7137 | −1.15776 | ||||||||
\(574\) | − | 19.6629i | − | 0.820714i | ||||||
\(575\) | 21.6688 | 0.903651 | ||||||||
\(576\) | −1.14903 | −0.0478763 | ||||||||
\(577\) | − | 12.8627i | − | 0.535482i | −0.963491 | − | 0.267741i | \(-0.913723\pi\) | ||
0.963491 | − | 0.267741i | \(-0.0862772\pi\) | |||||||
\(578\) | − | 15.3684i | − | 0.639240i | ||||||
\(579\) | − | 12.4142i | − | 0.515917i | ||||||
\(580\) | − | 26.1319i | − | 1.08507i | ||||||
\(581\) | −1.45088 | −0.0601925 | ||||||||
\(582\) | −74.7328 | −3.09777 | ||||||||
\(583\) | 14.1441i | 0.585789i | ||||||||
\(584\) | 81.0249 | 3.35284 | ||||||||
\(585\) | 0.193937 | + | 0.430409i | 0.00801829 | + | 0.0177952i | ||||
\(586\) | 62.5741 | 2.58491 | ||||||||
\(587\) | − | 31.0240i | − | 1.28050i | −0.768168 | − | 0.640248i | \(-0.778831\pi\) | ||
0.768168 | − | 0.640248i | \(-0.221169\pi\) | |||||||
\(588\) | 6.96239 | 0.287124 | ||||||||
\(589\) | 8.54675 | 0.352163 | ||||||||
\(590\) | 4.26187i | 0.175458i | ||||||||
\(591\) | − | 11.9756i | − | 0.492609i | ||||||
\(592\) | 7.16362i | 0.294423i | ||||||||
\(593\) | 11.4119i | 0.468629i | 0.972161 | + | 0.234314i | \(0.0752845\pi\) | ||||
−0.972161 | + | 0.234314i | \(0.924716\pi\) | |||||||
\(594\) | −59.4880 | −2.44082 | ||||||||
\(595\) | −2.21933 | −0.0909836 | ||||||||
\(596\) | − | 16.7612i | − | 0.686564i | ||||||
\(597\) | 8.54420 | 0.349691 | ||||||||
\(598\) | 17.5247 | + | 38.8930i | 0.716638 | + | 1.59045i | ||||
\(599\) | 7.37328 | 0.301264 | 0.150632 | − | 0.988590i | \(-0.451869\pi\) | ||||
0.150632 | + | 0.988590i | \(0.451869\pi\) | |||||||
\(600\) | − | 40.7269i | − | 1.66267i | ||||||
\(601\) | 17.2144 | 0.702190 | 0.351095 | − | 0.936340i | \(-0.385809\pi\) | ||||
0.351095 | + | 0.936340i | \(0.385809\pi\) | |||||||
\(602\) | 11.4436 | 0.466406 | ||||||||
\(603\) | 1.42548i | 0.0580502i | ||||||||
\(604\) | 6.52373i | 0.265447i | ||||||||
\(605\) | 6.13093i | 0.249258i | ||||||||
\(606\) | 38.8119i | 1.57663i | ||||||||
\(607\) | 32.4264 | 1.31615 | 0.658074 | − | 0.752953i | \(-0.271371\pi\) | ||||
0.658074 | + | 0.752953i | \(0.271371\pi\) | |||||||
\(608\) | −8.41422 | −0.341242 | ||||||||
\(609\) | − | 15.5999i | − | 0.632140i | ||||||
\(610\) | −3.87399 | −0.156853 | ||||||||
\(611\) | −11.6556 | − | 25.8677i | −0.471536 | − | 1.04649i | ||||
\(612\) | −2.64974 | −0.107109 | ||||||||
\(613\) | − | 35.6991i | − | 1.44187i | −0.693001 | − | 0.720937i | \(-0.743712\pi\) | ||
0.693001 | − | 0.720937i | \(-0.256288\pi\) | |||||||
\(614\) | 17.9878 | 0.725928 | ||||||||
\(615\) | 8.96239 | 0.361398 | ||||||||
\(616\) | − | 23.9756i | − | 0.966003i | ||||||
\(617\) | 20.3733i | 0.820198i | 0.912041 | + | 0.410099i | \(0.134506\pi\) | ||||
−0.912041 | + | 0.410099i | \(0.865494\pi\) | |||||||
\(618\) | 25.9248i | 1.04285i | ||||||||
\(619\) | 40.0118i | 1.60821i | 0.594488 | + | 0.804104i | \(0.297355\pi\) | ||||
−0.594488 | + | 0.804104i | \(0.702645\pi\) | |||||||
\(620\) | 4.59498 | 0.184539 | ||||||||
\(621\) | −25.5125 | −1.02378 | ||||||||
\(622\) | 50.2189i | 2.01359i | ||||||||
\(623\) | −7.79384 | −0.312254 | ||||||||
\(624\) | 27.3258 | − | 12.3127i | 1.09391 | − | 0.492900i | ||||
\(625\) | 18.3707 | 0.734829 | ||||||||
\(626\) | − | 82.2189i | − | 3.28613i | ||||||
\(627\) | 39.1793 | 1.56467 | ||||||||
\(628\) | −12.0508 | −0.480879 | ||||||||
\(629\) | − | 4.74543i | − | 0.189213i | ||||||
\(630\) | − | 0.324869i | − | 0.0129431i | ||||||
\(631\) | 16.3879i | 0.652391i | 0.945302 | + | 0.326195i | \(0.105767\pi\) | ||||
−0.945302 | + | 0.326195i | \(0.894233\pi\) | |||||||
\(632\) | − | 78.4504i | − | 3.12059i | ||||||
\(633\) | 0.324869 | 0.0129124 | ||||||||
\(634\) | 42.2130 | 1.67649 | ||||||||
\(635\) | 0.932071i | 0.0369881i | ||||||||
\(636\) | 21.9756 | 0.871388 | ||||||||
\(637\) | −3.28726 | + | 1.48119i | −0.130246 | + | 0.0586871i | ||||
\(638\) | −103.545 | −4.09937 | ||||||||
\(639\) | 1.50422i | 0.0595059i | ||||||||
\(640\) | 12.1016 | 0.478357 | ||||||||
\(641\) | 8.23884 | 0.325415 | 0.162707 | − | 0.986674i | \(-0.447977\pi\) | ||||
0.162707 | + | 0.986674i | \(0.447977\pi\) | |||||||
\(642\) | 30.1114i | 1.18840i | ||||||||
\(643\) | − | 30.4847i | − | 1.20220i | −0.799174 | − | 0.601100i | \(-0.794729\pi\) | ||
0.799174 | − | 0.601100i | \(-0.205271\pi\) | |||||||
\(644\) | − | 19.8192i | − | 0.780987i | ||||||
\(645\) | 5.21600i | 0.205380i | ||||||||
\(646\) | 42.5705 | 1.67492 | ||||||||
\(647\) | −28.8388 | −1.13377 | −0.566884 | − | 0.823798i | \(-0.691851\pi\) | ||||
−0.566884 | + | 0.823798i | \(0.691851\pi\) | |||||||
\(648\) | 44.8383i | 1.76141i | ||||||||
\(649\) | 11.4010 | 0.447530 | ||||||||
\(650\) | 16.7005 | + | 37.0640i | 0.655048 | + | 1.45377i | ||||
\(651\) | 2.74306 | 0.107509 | ||||||||
\(652\) | 71.8007i | 2.81193i | ||||||||
\(653\) | 21.4518 | 0.839475 | 0.419738 | − | 0.907646i | \(-0.362122\pi\) | ||||
0.419738 | + | 0.907646i | \(0.362122\pi\) | |||||||
\(654\) | 19.9248 | 0.779120 | ||||||||
\(655\) | − | 8.43866i | − | 0.329726i | ||||||
\(656\) | 39.3258i | 1.53542i | ||||||||
\(657\) | − | 2.93700i | − | 0.114583i | ||||||
\(658\) | 19.5247i | 0.761151i | ||||||||
\(659\) | −50.6589 | −1.97339 | −0.986696 | − | 0.162575i | \(-0.948020\pi\) | ||||
−0.986696 | + | 0.162575i | \(0.948020\pi\) | |||||||
\(660\) | 21.0640 | 0.819913 | ||||||||
\(661\) | 15.5477i | 0.604736i | 0.953191 | + | 0.302368i | \(0.0977771\pi\) | ||||
−0.953191 | + | 0.302368i | \(0.902223\pi\) | |||||||
\(662\) | −26.8872 | −1.04500 | ||||||||
\(663\) | −18.1016 | + | 8.15633i | −0.703007 | + | 0.316765i | ||||
\(664\) | 7.76257 | 0.301246 | ||||||||
\(665\) | 3.52373i | 0.136644i | ||||||||
\(666\) | 0.694644 | 0.0269169 | ||||||||
\(667\) | −44.4069 | −1.71944 | ||||||||
\(668\) | 67.7196i | 2.62015i | ||||||||
\(669\) | − | 9.78067i | − | 0.378143i | ||||||
\(670\) | − | 12.3127i | − | 0.475679i | ||||||
\(671\) | 10.3634i | 0.400076i | ||||||||
\(672\) | −2.70052 | −0.104175 | ||||||||
\(673\) | 26.8700 | 1.03576 | 0.517882 | − | 0.855452i | \(-0.326721\pi\) | ||||
0.517882 | + | 0.855452i | \(0.326721\pi\) | |||||||
\(674\) | − | 7.36836i | − | 0.283819i | ||||||
\(675\) | −24.3127 | −0.935794 | ||||||||
\(676\) | −35.7948 | + | 40.4749i | −1.37672 | + | 1.55673i | ||||
\(677\) | 16.3757 | 0.629368 | 0.314684 | − | 0.949197i | \(-0.398102\pi\) | ||||
0.314684 | + | 0.949197i | \(0.398102\pi\) | |||||||
\(678\) | − | 38.8324i | − | 1.49135i | ||||||
\(679\) | −17.9805 | −0.690028 | ||||||||
\(680\) | 11.8740 | 0.455347 | ||||||||
\(681\) | 6.17679i | 0.236695i | ||||||||
\(682\) | − | 18.2071i | − | 0.697186i | ||||||
\(683\) | 15.7988i | 0.604523i | 0.953225 | + | 0.302262i | \(0.0977416\pi\) | ||||
−0.953225 | + | 0.302262i | \(0.902258\pi\) | |||||||
\(684\) | 4.20711i | 0.160863i | ||||||||
\(685\) | −2.16457 | −0.0827041 | ||||||||
\(686\) | 2.48119 | 0.0947324 | ||||||||
\(687\) | 9.47627i | 0.361542i | ||||||||
\(688\) | −22.8872 | −0.872565 | ||||||||
\(689\) | −10.3757 | + | 4.67513i | −0.395281 | + | 0.178108i | ||||
\(690\) | 13.3806 | 0.509390 | ||||||||
\(691\) | 7.56818i | 0.287907i | 0.989584 | + | 0.143953i | \(0.0459816\pi\) | ||||
−0.989584 | + | 0.143953i | \(0.954018\pi\) | |||||||
\(692\) | −9.03761 | −0.343558 | ||||||||
\(693\) | −0.869067 | −0.0330131 | ||||||||
\(694\) | 76.2638i | 2.89493i | ||||||||
\(695\) | 0.168544i | 0.00639324i | ||||||||
\(696\) | 83.4636i | 3.16368i | ||||||||
\(697\) | − | 26.0508i | − | 0.986744i | ||||||
\(698\) | 4.97461 | 0.188292 | ||||||||
\(699\) | −17.2971 | −0.654237 | ||||||||
\(700\) | − | 18.8872i | − | 0.713868i | ||||||
\(701\) | −32.6629 | −1.23366 | −0.616831 | − | 0.787096i | \(-0.711584\pi\) | ||||
−0.616831 | + | 0.787096i | \(0.711584\pi\) | |||||||
\(702\) | −19.6629 | − | 43.6385i | −0.742129 | − | 1.64703i | ||||
\(703\) | −7.53453 | −0.284170 | ||||||||
\(704\) | − | 26.5501i | − | 1.00064i | ||||||
\(705\) | −8.89938 | −0.335170 | ||||||||
\(706\) | −42.8119 | −1.61125 | ||||||||
\(707\) | 9.33804i | 0.351193i | ||||||||
\(708\) | − | 17.7137i | − | 0.665722i | ||||||
\(709\) | − | 25.0214i | − | 0.939699i | −0.882746 | − | 0.469850i | \(-0.844308\pi\) | ||
0.882746 | − | 0.469850i | \(-0.155692\pi\) | |||||||
\(710\) | − | 12.9927i | − | 0.487608i | ||||||
\(711\) | −2.84367 | −0.106646 | ||||||||
\(712\) | 41.6991 | 1.56274 | ||||||||
\(713\) | − | 7.80843i | − | 0.292428i | ||||||
\(714\) | 13.6629 | 0.511322 | ||||||||
\(715\) | −9.94525 | + | 4.48119i | −0.371931 | + | 0.167587i | ||||
\(716\) | 2.29218 | 0.0856629 | ||||||||
\(717\) | 37.3357i | 1.39433i | ||||||||
\(718\) | −17.6326 | −0.658043 | ||||||||
\(719\) | 1.85192 | 0.0690651 | 0.0345326 | − | 0.999404i | \(-0.489006\pi\) | ||||
0.0345326 | + | 0.999404i | \(0.489006\pi\) | |||||||
\(720\) | 0.649738i | 0.0242143i | ||||||||
\(721\) | 6.23743i | 0.232294i | ||||||||
\(722\) | − | 20.4485i | − | 0.761015i | ||||||
\(723\) | − | 49.2931i | − | 1.83323i | ||||||
\(724\) | −2.12601 | −0.0790125 | ||||||||
\(725\) | −42.3185 | −1.57167 | ||||||||
\(726\) | − | 37.7440i | − | 1.40081i | ||||||
\(727\) | −10.8265 | −0.401534 | −0.200767 | − | 0.979639i | \(-0.564343\pi\) | ||||
−0.200767 | + | 0.979639i | \(0.564343\pi\) | |||||||
\(728\) | 17.5877 | − | 7.92478i | 0.651843 | − | 0.293712i | ||||
\(729\) | 28.5125 | 1.05602 | ||||||||
\(730\) | 25.3684i | 0.938925i | ||||||||
\(731\) | 15.1612 | 0.560759 | ||||||||
\(732\) | 16.1016 | 0.595131 | ||||||||
\(733\) | − | 23.4264i | − | 0.865275i | −0.901568 | − | 0.432638i | \(-0.857583\pi\) | ||
0.901568 | − | 0.432638i | \(-0.142417\pi\) | |||||||
\(734\) | − | 67.6444i | − | 2.49680i | ||||||
\(735\) | 1.13093i | 0.0417151i | ||||||||
\(736\) | 7.68735i | 0.283359i | ||||||||
\(737\) | −32.9380 | −1.21329 | ||||||||
\(738\) | 3.81336 | 0.140372 | ||||||||
\(739\) | − | 0.481194i | − | 0.0177010i | −0.999961 | − | 0.00885051i | \(-0.997183\pi\) | ||
0.999961 | − | 0.00885051i | \(-0.00281724\pi\) | |||||||
\(740\) | −4.05079 | −0.148910 | ||||||||
\(741\) | 12.9502 | + | 28.7407i | 0.475736 | + | 1.05582i | ||||
\(742\) | 7.83146 | 0.287502 | ||||||||
\(743\) | 13.7889i | 0.505866i | 0.967484 | + | 0.252933i | \(0.0813953\pi\) | ||||
−0.967484 | + | 0.252933i | \(0.918605\pi\) | |||||||
\(744\) | −14.6761 | −0.538051 | ||||||||
\(745\) | 2.72259 | 0.0997480 | ||||||||
\(746\) | − | 14.6859i | − | 0.537690i | ||||||
\(747\) | − | 0.281378i | − | 0.0102951i | ||||||
\(748\) | − | 61.2262i | − | 2.23865i | ||||||
\(749\) | 7.24472i | 0.264716i | ||||||||
\(750\) | 26.7816 | 0.977927 | ||||||||
\(751\) | 26.4617 | 0.965600 | 0.482800 | − | 0.875731i | \(-0.339620\pi\) | ||||
0.482800 | + | 0.875731i | \(0.339620\pi\) | |||||||
\(752\) | − | 39.0494i | − | 1.42398i | ||||||
\(753\) | −36.0567 | −1.31398 | ||||||||
\(754\) | −34.2252 | − | 75.9570i | −1.24641 | − | 2.76619i | ||||
\(755\) | −1.05968 | −0.0385657 | ||||||||
\(756\) | 22.2374i | 0.808767i | ||||||||
\(757\) | −21.1114 | −0.767308 | −0.383654 | − | 0.923477i | \(-0.625334\pi\) | ||||
−0.383654 | + | 0.923477i | \(0.625334\pi\) | |||||||
\(758\) | 71.8818 | 2.61086 | ||||||||
\(759\) | − | 35.7948i | − | 1.29927i | ||||||
\(760\) | − | 18.8529i | − | 0.683866i | ||||||
\(761\) | 28.5247i | 1.03402i | 0.855980 | + | 0.517010i | \(0.172955\pi\) | ||||
−0.855980 | + | 0.517010i | \(0.827045\pi\) | |||||||
\(762\) | − | 5.73813i | − | 0.207871i | ||||||
\(763\) | 4.79384 | 0.173549 | ||||||||
\(764\) | 68.7631 | 2.48776 | ||||||||
\(765\) | − | 0.430409i | − | 0.0155615i | ||||||
\(766\) | −57.6239 | −2.08204 | ||||||||
\(767\) | 3.76845 | + | 8.36344i | 0.136071 | + | 0.301986i | ||||
\(768\) | −54.6516 | −1.97207 | ||||||||
\(769\) | 25.8388i | 0.931769i | 0.884845 | + | 0.465885i | \(0.154264\pi\) | ||||
−0.884845 | + | 0.465885i | \(0.845736\pi\) | |||||||
\(770\) | 7.50659 | 0.270519 | ||||||||
\(771\) | 1.10886 | 0.0399348 | ||||||||
\(772\) | 30.8021i | 1.10859i | ||||||||
\(773\) | 27.4010i | 0.985547i | 0.870158 | + | 0.492774i | \(0.164017\pi\) | ||||
−0.870158 | + | 0.492774i | \(0.835983\pi\) | |||||||
\(774\) | 2.21933i | 0.0797721i | ||||||||
\(775\) | − | 7.44121i | − | 0.267296i | ||||||
\(776\) | 96.2003 | 3.45339 | ||||||||
\(777\) | −2.41819 | −0.0867521 | ||||||||
\(778\) | − | 40.0263i | − | 1.43501i | ||||||
\(779\) | −41.3620 | −1.48195 | ||||||||
\(780\) | 6.96239 | + | 15.4518i | 0.249294 | + | 0.553264i | ||||
\(781\) | −34.7572 | −1.24371 | ||||||||
\(782\) | − | 38.8930i | − | 1.39081i | ||||||
\(783\) | 49.8251 | 1.78060 | ||||||||
\(784\) | −4.96239 | −0.177228 | ||||||||
\(785\) | − | 1.95746i | − | 0.0698649i | ||||||
\(786\) | 51.9511i | 1.85304i | ||||||||
\(787\) | − | 31.0240i | − | 1.10589i | −0.833219 | − | 0.552943i | \(-0.813505\pi\) | ||
0.833219 | − | 0.552943i | \(-0.186495\pi\) | |||||||
\(788\) | 29.7137i | 1.05851i | ||||||||
\(789\) | 8.68830 | 0.309312 | ||||||||
\(790\) | 24.5623 | 0.873887 | ||||||||
\(791\) | − | 9.34297i | − | 0.332198i | ||||||
\(792\) | 4.64974 | 0.165221 | ||||||||
\(793\) | −7.60228 | + | 3.42548i | −0.269965 | + | 0.121643i | ||||
\(794\) | 59.6869 | 2.11821 | ||||||||
\(795\) | 3.56959i | 0.126600i | ||||||||
\(796\) | −21.1998 | −0.751408 | ||||||||
\(797\) | −16.1378 | −0.571629 | −0.285815 | − | 0.958285i | \(-0.592264\pi\) | ||||
−0.285815 | + | 0.958285i | \(0.592264\pi\) | |||||||
\(798\) | − | 21.6932i | − | 0.767932i | ||||||
\(799\) | 25.8677i | 0.915132i | ||||||||
\(800\) | 7.32582i | 0.259007i | ||||||||
\(801\) | − | 1.51151i | − | 0.0534066i | ||||||
\(802\) | 6.88717 | 0.243194 | ||||||||
\(803\) | 67.8637 | 2.39486 | ||||||||
\(804\) | 51.1754i | 1.80482i | ||||||||
\(805\) | 3.21933 | 0.113466 | ||||||||
\(806\) | 13.3561 | − | 6.01810i | 0.470450 | − | 0.211978i | ||||
\(807\) | 45.6483 | 1.60690 | ||||||||
\(808\) | − | 49.9610i | − | 1.75762i | ||||||
\(809\) | −10.3503 | −0.363896 | −0.181948 | − | 0.983308i | \(-0.558240\pi\) | ||||
−0.181948 | + | 0.983308i | \(0.558240\pi\) | |||||||
\(810\) | −14.0386 | −0.493265 | ||||||||
\(811\) | 46.3752i | 1.62845i | 0.580547 | + | 0.814227i | \(0.302839\pi\) | ||||
−0.580547 | + | 0.814227i | \(0.697161\pi\) | |||||||
\(812\) | 38.7064i | 1.35833i | ||||||||
\(813\) | 31.4274i | 1.10221i | ||||||||
\(814\) | 16.0508i | 0.562580i | ||||||||
\(815\) | −11.6629 | −0.408534 | ||||||||
\(816\) | −27.3258 | −0.956595 | ||||||||
\(817\) | − | 24.0722i | − | 0.842180i | ||||||
\(818\) | 49.9488 | 1.74642 | ||||||||
\(819\) | −0.287258 | − | 0.637519i | −0.0100376 | − | 0.0222767i | ||||
\(820\) | −22.2374 | −0.776565 | ||||||||
\(821\) | 55.5388i | 1.93832i | 0.246436 | + | 0.969159i | \(0.420740\pi\) | ||||
−0.246436 | + | 0.969159i | \(0.579260\pi\) | |||||||
\(822\) | 13.3258 | 0.464791 | ||||||||
\(823\) | 20.8324 | 0.726172 | 0.363086 | − | 0.931756i | \(-0.381723\pi\) | ||||
0.363086 | + | 0.931756i | \(0.381723\pi\) | |||||||
\(824\) | − | 33.3719i | − | 1.16256i | ||||||
\(825\) | − | 34.1114i | − | 1.18761i | ||||||
\(826\) | − | 6.31265i | − | 0.219645i | ||||||
\(827\) | − | 2.47295i | − | 0.0859927i | −0.999075 | − | 0.0429964i | \(-0.986310\pi\) | ||
0.999075 | − | 0.0429964i | \(-0.0136904\pi\) | |||||||
\(828\) | 3.84367 | 0.133577 | ||||||||
\(829\) | 34.5623 | 1.20040 | 0.600199 | − | 0.799851i | \(-0.295088\pi\) | ||||
0.600199 | + | 0.799851i | \(0.295088\pi\) | |||||||
\(830\) | 2.43041i | 0.0843607i | ||||||||
\(831\) | −25.8373 | −0.896287 | ||||||||
\(832\) | 19.4763 | − | 8.77575i | 0.675218 | − | 0.304244i | ||||
\(833\) | 3.28726 | 0.113897 | ||||||||
\(834\) | − | 1.03761i | − | 0.0359295i | ||||||
\(835\) | −11.0000 | −0.380671 | ||||||||
\(836\) | −97.2116 | −3.36213 | ||||||||
\(837\) | 8.76116i | 0.302830i | ||||||||
\(838\) | − | 0.956509i | − | 0.0330421i | ||||||
\(839\) | 39.9149i | 1.37802i | 0.724754 | + | 0.689008i | \(0.241954\pi\) | ||||
−0.724754 | + | 0.689008i | \(0.758046\pi\) | |||||||
\(840\) | − | 6.05079i | − | 0.208772i | ||||||
\(841\) | 57.7255 | 1.99053 | ||||||||
\(842\) | −38.9076 | −1.34085 | ||||||||
\(843\) | 41.6180i | 1.43340i | ||||||||
\(844\) | −0.806063 | −0.0277458 | ||||||||
\(845\) | −6.57452 | − | 5.81431i | −0.226170 | − | 0.200018i | ||||
\(846\) | −3.78655 | −0.130184 | ||||||||
\(847\) | − | 9.08110i | − | 0.312030i | ||||||
\(848\) | −15.6629 | −0.537867 | ||||||||
\(849\) | −38.3390 | −1.31579 | ||||||||
\(850\) | − | 37.0640i | − | 1.27128i | ||||||
\(851\) | 6.88366i | 0.235969i | ||||||||
\(852\) | 54.0019i | 1.85007i | ||||||||
\(853\) | 32.6507i | 1.11794i | 0.829188 | + | 0.558969i | \(0.188803\pi\) | ||||
−0.829188 | + | 0.558969i | \(0.811197\pi\) | |||||||
\(854\) | 5.73813 | 0.196355 | ||||||||
\(855\) | −0.683380 | −0.0233711 | ||||||||
\(856\) | − | 38.7612i | − | 1.32483i | ||||||
\(857\) | 7.63656 | 0.260860 | 0.130430 | − | 0.991458i | \(-0.458364\pi\) | ||||
0.130430 | + | 0.991458i | \(0.458364\pi\) | |||||||
\(858\) | 61.2262 | − | 27.5877i | 2.09023 | − | 0.941828i | ||||
\(859\) | −8.96239 | −0.305793 | −0.152896 | − | 0.988242i | \(-0.548860\pi\) | ||||
−0.152896 | + | 0.988242i | \(0.548860\pi\) | |||||||
\(860\) | − | 12.9419i | − | 0.441316i | ||||||
\(861\) | −13.2750 | −0.452412 | ||||||||
\(862\) | −3.81336 | −0.129883 | ||||||||
\(863\) | − | 46.8021i | − | 1.59316i | −0.604532 | − | 0.796581i | \(-0.706640\pi\) | ||
0.604532 | − | 0.796581i | \(-0.293360\pi\) | |||||||
\(864\) | − | 8.62530i | − | 0.293439i | ||||||
\(865\) | − | 1.46802i | − | 0.0499142i | ||||||
\(866\) | 64.6009i | 2.19523i | ||||||||
\(867\) | −10.3757 | −0.352376 | ||||||||
\(868\) | −6.80606 | −0.231013 | ||||||||
\(869\) | − | 65.7074i | − | 2.22897i | ||||||
\(870\) | −26.1319 | −0.885954 | ||||||||
\(871\) | −10.8872 | − | 24.1622i | −0.368898 | − | 0.818705i | ||||
\(872\) | −25.6483 | −0.868562 | ||||||||
\(873\) | − | 3.48707i | − | 0.118020i | ||||||
\(874\) | −61.7523 | −2.08880 | ||||||||
\(875\) | 6.44358 | 0.217833 | ||||||||
\(876\) | − | 105.439i | − | 3.56246i | ||||||
\(877\) | 10.3406i | 0.349177i | 0.984641 | + | 0.174589i | \(0.0558595\pi\) | ||||
−0.984641 | + | 0.174589i | \(0.944140\pi\) | |||||||
\(878\) | − | 47.4518i | − | 1.60142i | ||||||
\(879\) | − | 42.2457i | − | 1.42491i | ||||||
\(880\) | −15.0132 | −0.506094 | ||||||||
\(881\) | −15.1538 | −0.510543 | −0.255272 | − | 0.966869i | \(-0.582165\pi\) | ||||
−0.255272 | + | 0.966869i | \(0.582165\pi\) | |||||||
\(882\) | 0.481194i | 0.0162027i | ||||||||
\(883\) | 51.5983 | 1.73642 | 0.868211 | − | 0.496196i | \(-0.165270\pi\) | ||||
0.868211 | + | 0.496196i | \(0.165270\pi\) | |||||||
\(884\) | 44.9135 | − | 20.2374i | 1.51060 | − | 0.680658i | ||||
\(885\) | 2.87732 | 0.0967199 | ||||||||
\(886\) | − | 31.3077i | − | 1.05180i | ||||||
\(887\) | 4.18664 | 0.140574 | 0.0702868 | − | 0.997527i | \(-0.477609\pi\) | ||||
0.0702868 | + | 0.997527i | \(0.477609\pi\) | |||||||
\(888\) | 12.9380 | 0.434169 | ||||||||
\(889\) | − | 1.38058i | − | 0.0463031i | ||||||
\(890\) | 13.0557i | 0.437628i | ||||||||
\(891\) | 37.5550i | 1.25814i | ||||||||
\(892\) | 24.2677i | 0.812544i | ||||||||
\(893\) | 41.0713 | 1.37440 | ||||||||
\(894\) | −16.7612 | −0.560577 | ||||||||
\(895\) | 0.372330i | 0.0124456i | ||||||||
\(896\) | −17.9248 | −0.598825 | ||||||||
\(897\) | 26.2579 | − | 11.8315i | 0.876726 | − | 0.395041i | ||||
\(898\) | −2.53832 | −0.0847048 | ||||||||
\(899\) | 15.2496i | 0.508604i | ||||||||
\(900\) | 3.66291 | 0.122097 | ||||||||
\(901\) | 10.3757 | 0.345663 | ||||||||
\(902\) | 88.1133i | 2.93385i | ||||||||
\(903\) | − | 7.72592i | − | 0.257102i | ||||||
\(904\) | 49.9873i | 1.66255i | ||||||||
\(905\) | − | 0.345337i | − | 0.0114794i | ||||||
\(906\) | 6.52373 | 0.216736 | ||||||||
\(907\) | 9.60483 | 0.318923 | 0.159462 | − | 0.987204i | \(-0.449024\pi\) | ||||
0.159462 | + | 0.987204i | \(0.449024\pi\) | |||||||
\(908\) | − | 15.3258i | − | 0.508605i | ||||||
\(909\) | −1.81099 | −0.0600667 | ||||||||
\(910\) | 2.48119 | + | 5.50659i | 0.0822508 | + | 0.182542i | ||||
\(911\) | −1.82653 | −0.0605157 | −0.0302578 | − | 0.999542i | \(-0.509633\pi\) | ||||
−0.0302578 | + | 0.999542i | \(0.509633\pi\) | |||||||
\(912\) | 43.3865i | 1.43667i | ||||||||
\(913\) | 6.50166 | 0.215174 | ||||||||
\(914\) | −70.7934 | −2.34164 | ||||||||
\(915\) | 2.61545i | 0.0864642i | ||||||||
\(916\) | − | 23.5125i | − | 0.776874i | ||||||
\(917\) | 12.4993i | 0.412763i | ||||||||
\(918\) | 43.6385i | 1.44028i | ||||||||
\(919\) | 15.7842 | 0.520672 | 0.260336 | − | 0.965518i | \(-0.416167\pi\) | ||||
0.260336 | + | 0.965518i | \(0.416167\pi\) | |||||||
\(920\) | −17.2243 | −0.567867 | ||||||||
\(921\) | − | 12.1441i | − | 0.400162i | ||||||
\(922\) | −62.8989 | −2.07147 | ||||||||
\(923\) | −11.4885 | − | 25.4967i | −0.378148 | − | 0.839235i | ||||
\(924\) | −31.1998 | −1.02640 | ||||||||
\(925\) | 6.55993i | 0.215689i | ||||||||
\(926\) | 98.4563 | 3.23547 | ||||||||
\(927\) | −1.20967 | −0.0397306 | ||||||||
\(928\) | − | 15.0132i | − | 0.492832i | ||||||
\(929\) | − | 16.8011i | − | 0.551227i | −0.961268 | − | 0.275614i | \(-0.911119\pi\) | ||
0.961268 | − | 0.275614i | \(-0.0888811\pi\) | |||||||
\(930\) | − | 4.59498i | − | 0.150675i | ||||||
\(931\) | − | 5.21933i | − | 0.171057i | ||||||
\(932\) | 42.9175 | 1.40581 | ||||||||
\(933\) | 33.9043 | 1.10998 | ||||||||
\(934\) | − | 4.84226i | − | 0.158444i | ||||||
\(935\) | 9.94525 | 0.325244 | ||||||||
\(936\) | 1.53690 | + | 3.41090i | 0.0502353 | + | 0.111489i | ||||
\(937\) | −38.3004 | −1.25122 | −0.625610 | − | 0.780136i | \(-0.715150\pi\) | ||||
−0.625610 | + | 0.780136i | \(0.715150\pi\) | |||||||
\(938\) | 18.2374i | 0.595473i | ||||||||
\(939\) | −55.5085 | −1.81145 | ||||||||
\(940\) | 22.0811 | 0.720206 | ||||||||
\(941\) | − | 45.2496i | − | 1.47510i | −0.675295 | − | 0.737548i | \(-0.735983\pi\) | ||
0.675295 | − | 0.737548i | \(-0.264017\pi\) | |||||||
\(942\) | 12.0508i | 0.392636i | ||||||||
\(943\) | 37.7889i | 1.23058i | ||||||||
\(944\) | 12.6253i | 0.410919i | ||||||||
\(945\) | −3.61213 | −0.117502 | ||||||||
\(946\) | −51.2809 | −1.66729 | ||||||||
\(947\) | − | 4.73672i | − | 0.153923i | −0.997034 | − | 0.0769614i | \(-0.975478\pi\) | ||
0.997034 | − | 0.0769614i | \(-0.0245218\pi\) | |||||||
\(948\) | −102.089 | −3.31569 | ||||||||
\(949\) | 22.4314 | + | 49.7826i | 0.728153 | + | 1.61601i | ||||
\(950\) | −58.8481 | −1.90929 | ||||||||
\(951\) | − | 28.4993i | − | 0.924153i | ||||||
\(952\) | −17.5877 | −0.570020 | ||||||||
\(953\) | −44.8007 | −1.45124 | −0.725618 | − | 0.688098i | \(-0.758446\pi\) | ||||
−0.725618 | + | 0.688098i | \(0.758446\pi\) | |||||||
\(954\) | 1.51881i | 0.0491732i | ||||||||
\(955\) | 11.1695i | 0.361436i | ||||||||
\(956\) | − | 92.6371i | − | 2.99610i | ||||||
\(957\) | 69.9062i | 2.25975i | ||||||||
\(958\) | −64.8505 | −2.09522 | ||||||||
\(959\) | 3.20616 | 0.103532 | ||||||||
\(960\) | − | 6.70052i | − | 0.216258i | ||||||
\(961\) | 28.3185 | 0.913501 | ||||||||
\(962\) | −11.7743 | + | 5.30536i | −0.379620 | + | 0.171052i | ||||
\(963\) | −1.40502 | −0.0452760 | ||||||||
\(964\) | 122.306i | 3.93921i | ||||||||
\(965\) | −5.00332 | −0.161063 | ||||||||
\(966\) | −19.8192 | −0.637674 | ||||||||
\(967\) | − | 40.6843i | − | 1.30832i | −0.756356 | − | 0.654160i | \(-0.773022\pi\) | ||
0.756356 | − | 0.654160i | \(-0.226978\pi\) | |||||||
\(968\) | 48.5863i | 1.56162i | ||||||||
\(969\) | − | 28.7407i | − | 0.923284i | ||||||
\(970\) | 30.1197i | 0.967084i | ||||||||
\(971\) | −41.4109 | −1.32894 | −0.664469 | − | 0.747315i | \(-0.731342\pi\) | ||||
−0.664469 | + | 0.747315i | \(0.731342\pi\) | |||||||
\(972\) | −8.36344 | −0.268257 | ||||||||
\(973\) | − | 0.249646i | − | 0.00800329i | ||||||
\(974\) | 52.0118 | 1.66656 | ||||||||
\(975\) | 25.0230 | − | 11.2750i | 0.801378 | − | 0.361090i | ||||
\(976\) | −11.4763 | −0.367346 | ||||||||
\(977\) | 50.6072i | 1.61907i | 0.587073 | + | 0.809534i | \(0.300280\pi\) | ||||
−0.587073 | + | 0.809534i | \(0.699720\pi\) | |||||||
\(978\) | 71.8007 | 2.29593 | ||||||||
\(979\) | 34.9257 | 1.11623 | ||||||||
\(980\) | − | 2.80606i | − | 0.0896364i | ||||||
\(981\) | 0.929702i | 0.0296831i | ||||||||
\(982\) | 7.33567i | 0.234091i | ||||||||
\(983\) | − | 24.5452i | − | 0.782869i | −0.920206 | − | 0.391434i | \(-0.871979\pi\) | ||
0.920206 | − | 0.391434i | \(-0.128021\pi\) | |||||||
\(984\) | 71.0249 | 2.26419 | ||||||||
\(985\) | −4.82653 | −0.153786 | ||||||||
\(986\) | 75.9570i | 2.41896i | ||||||||
\(987\) | 13.1817 | 0.419579 | ||||||||
\(988\) | −32.1319 | − | 71.3112i | −1.02225 | − | 2.26871i | ||||
\(989\) | −21.9927 | −0.699327 | ||||||||
\(990\) | 1.45580i | 0.0462684i | ||||||||
\(991\) | −31.6542 | −1.00553 | −0.502764 | − | 0.864423i | \(-0.667684\pi\) | ||||
−0.502764 | + | 0.864423i | \(0.667684\pi\) | |||||||
\(992\) | 2.63989 | 0.0838166 | ||||||||
\(993\) | 18.1524i | 0.576048i | ||||||||
\(994\) | 19.2447i | 0.610406i | ||||||||
\(995\) | − | 3.44358i | − | 0.109169i | ||||||
\(996\) | − | 10.1016i | − | 0.320081i | ||||||
\(997\) | −29.1852 | −0.924305 | −0.462153 | − | 0.886800i | \(-0.652923\pi\) | ||||
−0.462153 | + | 0.886800i | \(0.652923\pi\) | |||||||
\(998\) | 7.08252 | 0.224193 | ||||||||
\(999\) | − | 7.72355i | − | 0.244362i |
(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 | 91.2.c.a.64.6 | yes | 6 | |
3.2 | odd | 2 | 819.2.c.b.64.1 | 6 | |||
4.3 | odd | 2 | 1456.2.k.c.337.1 | 6 | |||
7.2 | even | 3 | 637.2.r.e.116.6 | 12 | |||
7.3 | odd | 6 | 637.2.r.d.324.1 | 12 | |||
7.4 | even | 3 | 637.2.r.e.324.1 | 12 | |||
7.5 | odd | 6 | 637.2.r.d.116.6 | 12 | |||
7.6 | odd | 2 | 637.2.c.d.246.6 | 6 | |||
13.5 | odd | 4 | 1183.2.a.j.1.3 | 3 | |||
13.8 | odd | 4 | 1183.2.a.h.1.1 | 3 | |||
13.12 | even | 2 | inner | 91.2.c.a.64.1 | ✓ | 6 | |
39.38 | odd | 2 | 819.2.c.b.64.6 | 6 | |||
52.51 | odd | 2 | 1456.2.k.c.337.2 | 6 | |||
91.12 | odd | 6 | 637.2.r.d.116.1 | 12 | |||
91.25 | even | 6 | 637.2.r.e.324.6 | 12 | |||
91.34 | even | 4 | 8281.2.a.be.1.1 | 3 | |||
91.38 | odd | 6 | 637.2.r.d.324.6 | 12 | |||
91.51 | even | 6 | 637.2.r.e.116.1 | 12 | |||
91.83 | even | 4 | 8281.2.a.bi.1.3 | 3 | |||
91.90 | odd | 2 | 637.2.c.d.246.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.c.a.64.1 | ✓ | 6 | 13.12 | even | 2 | inner | |
91.2.c.a.64.6 | yes | 6 | 1.1 | even | 1 | trivial | |
637.2.c.d.246.1 | 6 | 91.90 | odd | 2 | |||
637.2.c.d.246.6 | 6 | 7.6 | odd | 2 | |||
637.2.r.d.116.1 | 12 | 91.12 | odd | 6 | |||
637.2.r.d.116.6 | 12 | 7.5 | odd | 6 | |||
637.2.r.d.324.1 | 12 | 7.3 | odd | 6 | |||
637.2.r.d.324.6 | 12 | 91.38 | odd | 6 | |||
637.2.r.e.116.1 | 12 | 91.51 | even | 6 | |||
637.2.r.e.116.6 | 12 | 7.2 | even | 3 | |||
637.2.r.e.324.1 | 12 | 7.4 | even | 3 | |||
637.2.r.e.324.6 | 12 | 91.25 | even | 6 | |||
819.2.c.b.64.1 | 6 | 3.2 | odd | 2 | |||
819.2.c.b.64.6 | 6 | 39.38 | odd | 2 | |||
1183.2.a.h.1.1 | 3 | 13.8 | odd | 4 | |||
1183.2.a.j.1.3 | 3 | 13.5 | odd | 4 | |||
1456.2.k.c.337.1 | 6 | 4.3 | odd | 2 | |||
1456.2.k.c.337.2 | 6 | 52.51 | odd | 2 | |||
8281.2.a.be.1.1 | 3 | 91.34 | even | 4 | |||
8281.2.a.bi.1.3 | 3 | 91.83 | even | 4 |