Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(146,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("735.146");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.856615824.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 146.7 | ||
Root | \(-2.06288i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 735.146 |
Dual form | 735.2.b.d.146.2 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.06288i | 1.45868i | 0.684153 | + | 0.729338i | \(0.260172\pi\) | ||||
−0.684153 | + | 0.729338i | \(0.739828\pi\) | |||||||
\(3\) | 1.71189 | − | 0.263509i | 0.988359 | − | 0.152137i | ||||
\(4\) | −2.25548 | −1.12774 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.543588 | + | 3.53142i | 0.221919 | + | 1.44170i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 0.527019i | − | 0.186329i | ||||||
\(9\) | 2.86113 | − | 0.902197i | 0.953709 | − | 0.300732i | ||||
\(10\) | − | 2.06288i | − | 0.652340i | ||||||
\(11\) | 4.69211i | 1.41472i | 0.706852 | + | 0.707362i | \(0.250115\pi\) | ||||
−0.706852 | + | 0.707362i | \(0.749885\pi\) | |||||||
\(12\) | −3.86113 | + | 0.594339i | −1.11461 | + | 0.171571i | ||||
\(13\) | 0.638688i | 0.177140i | 0.996070 | + | 0.0885701i | \(0.0282297\pi\) | ||||
−0.996070 | + | 0.0885701i | \(0.971770\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.71189 | + | 0.263509i | −0.442008 | + | 0.0680378i | ||||
\(16\) | −3.42378 | −0.855944 | ||||||||
\(17\) | 4.14924 | 1.00634 | 0.503169 | − | 0.864188i | \(-0.332167\pi\) | ||||
0.503169 | + | 0.864188i | \(0.332167\pi\) | |||||||
\(18\) | 1.86113 | + | 5.90216i | 0.438672 | + | 1.39115i | ||||
\(19\) | − | 0.897174i | − | 0.205826i | −0.994690 | − | 0.102913i | \(-0.967184\pi\) | ||
0.994690 | − | 0.102913i | \(-0.0328163\pi\) | |||||||
\(20\) | 2.25548 | 0.504340 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.67925 | −2.06362 | ||||||||
\(23\) | 6.80436i | 1.41881i | 0.704803 | + | 0.709403i | \(0.251036\pi\) | ||||
−0.704803 | + | 0.709403i | \(0.748964\pi\) | |||||||
\(24\) | −0.138874 | − | 0.902197i | −0.0283476 | − | 0.184160i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.31754 | −0.258390 | ||||||||
\(27\) | 4.66019 | − | 2.29839i | 0.896854 | − | 0.442326i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.14740i | − | 0.398762i | −0.979922 | − | 0.199381i | \(-0.936107\pi\) | ||
0.979922 | − | 0.199381i | \(-0.0638932\pi\) | |||||||
\(30\) | −0.543588 | − | 3.53142i | −0.0992452 | − | 0.644747i | ||||
\(31\) | 2.33772i | 0.419867i | 0.977716 | + | 0.209933i | \(0.0673247\pi\) | ||||
−0.977716 | + | 0.209933i | \(0.932675\pi\) | |||||||
\(32\) | − | 8.11688i | − | 1.43488i | ||||||
\(33\) | 1.23641 | + | 8.03236i | 0.215232 | + | 1.39825i | ||||
\(34\) | 8.55938i | 1.46792i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.45320 | + | 2.03489i | −1.07553 | + | 0.339148i | ||||
\(37\) | −11.3824 | −1.87126 | −0.935631 | − | 0.352980i | \(-0.885168\pi\) | ||||
−0.935631 | + | 0.352980i | \(0.885168\pi\) | |||||||
\(38\) | 1.85076 | 0.300233 | ||||||||
\(39\) | 0.168300 | + | 1.09336i | 0.0269496 | + | 0.175078i | ||||
\(40\) | 0.527019i | 0.0833290i | ||||||||
\(41\) | −4.10624 | −0.641287 | −0.320643 | − | 0.947200i | \(-0.603899\pi\) | ||||
−0.320643 | + | 0.947200i | \(0.603899\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.14924 | 0.480254 | 0.240127 | − | 0.970741i | \(-0.422811\pi\) | ||||
0.240127 | + | 0.970741i | \(0.422811\pi\) | |||||||
\(44\) | − | 10.5829i | − | 1.59544i | ||||||
\(45\) | −2.86113 | + | 0.902197i | −0.426511 | + | 0.134492i | ||||
\(46\) | −14.0366 | −2.06958 | ||||||||
\(47\) | 6.80943 | 0.993257 | 0.496629 | − | 0.867963i | \(-0.334571\pi\) | ||||
0.496629 | + | 0.867963i | \(0.334571\pi\) | |||||||
\(48\) | −5.86113 | + | 0.902197i | −0.845981 | + | 0.130221i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.06288i | 0.291735i | ||||||||
\(51\) | 7.10303 | − | 1.09336i | 0.994623 | − | 0.153101i | ||||
\(52\) | − | 1.44055i | − | 0.199768i | ||||||
\(53\) | − | 2.26538i | − | 0.311173i | −0.987822 | − | 0.155587i | \(-0.950273\pi\) | ||
0.987822 | − | 0.155587i | \(-0.0497268\pi\) | |||||||
\(54\) | 4.74131 | + | 9.61342i | 0.645211 | + | 1.30822i | ||||
\(55\) | − | 4.69211i | − | 0.632683i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.236414 | − | 1.53586i | −0.0313138 | − | 0.203430i | ||||
\(58\) | 4.42983 | 0.581665 | ||||||||
\(59\) | 0.508109 | 0.0661502 | 0.0330751 | − | 0.999453i | \(-0.489470\pi\) | ||||
0.0330751 | + | 0.999453i | \(0.489470\pi\) | |||||||
\(60\) | 3.86113 | − | 0.594339i | 0.498469 | − | 0.0767289i | ||||
\(61\) | 5.18398i | 0.663740i | 0.943325 | + | 0.331870i | \(0.107680\pi\) | ||||
−0.943325 | + | 0.331870i | \(0.892320\pi\) | |||||||
\(62\) | −4.82244 | −0.612450 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 9.89660 | 1.23708 | ||||||||
\(65\) | − | 0.638688i | − | 0.0792195i | ||||||
\(66\) | −16.5698 | + | 2.55057i | −2.03960 | + | 0.313954i | ||||
\(67\) | 4.82849 | 0.589894 | 0.294947 | − | 0.955514i | \(-0.404698\pi\) | ||||
0.294947 | + | 0.955514i | \(0.404698\pi\) | |||||||
\(68\) | −9.35851 | −1.13489 | ||||||||
\(69\) | 1.79301 | + | 11.6483i | 0.215853 | + | 1.40229i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.22800i | 0.145737i | 0.997342 | + | 0.0728686i | \(0.0232154\pi\) | ||||
−0.997342 | + | 0.0728686i | \(0.976785\pi\) | |||||||
\(72\) | −0.475475 | − | 1.50787i | −0.0560353 | − | 0.177704i | ||||
\(73\) | − | 14.4565i | − | 1.69201i | −0.533177 | − | 0.846004i | \(-0.679002\pi\) | ||
0.533177 | − | 0.846004i | \(-0.320998\pi\) | |||||||
\(74\) | − | 23.4806i | − | 2.72957i | ||||||
\(75\) | 1.71189 | − | 0.263509i | 0.197672 | − | 0.0304274i | ||||
\(76\) | 2.02356i | 0.232118i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.25548 | + | 0.347183i | −0.255382 | + | 0.0393108i | ||||
\(79\) | 9.08112 | 1.02171 | 0.510853 | − | 0.859668i | \(-0.329330\pi\) | ||||
0.510853 | + | 0.859668i | \(0.329330\pi\) | |||||||
\(80\) | 3.42378 | 0.382790 | ||||||||
\(81\) | 7.37208 | − | 5.16260i | 0.819120 | − | 0.573622i | ||||
\(82\) | − | 8.47068i | − | 0.935431i | ||||||
\(83\) | 2.76359 | 0.303343 | 0.151671 | − | 0.988431i | \(-0.451534\pi\) | ||||
0.151671 | + | 0.988431i | \(0.451534\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.14924 | −0.450048 | ||||||||
\(86\) | 6.49650i | 0.700536i | ||||||||
\(87\) | −0.565860 | − | 3.67611i | −0.0606666 | − | 0.394120i | ||||
\(88\) | 2.47283 | 0.263604 | ||||||||
\(89\) | 13.8013 | 1.46294 | 0.731470 | − | 0.681874i | \(-0.238835\pi\) | ||||
0.731470 | + | 0.681874i | \(0.238835\pi\) | |||||||
\(90\) | −1.86113 | − | 5.90216i | −0.196180 | − | 0.622142i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 15.3471i | − | 1.60004i | ||||||
\(93\) | 0.616011 | + | 4.00192i | 0.0638774 | + | 0.414979i | ||||
\(94\) | 14.0470i | 1.44884i | ||||||||
\(95\) | 0.897174i | 0.0920481i | ||||||||
\(96\) | −2.13887 | − | 13.8952i | −0.218298 | − | 1.41817i | ||||
\(97\) | − | 12.9085i | − | 1.31066i | −0.755344 | − | 0.655329i | \(-0.772530\pi\) | ||
0.755344 | − | 0.655329i | \(-0.227470\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.23321 | + | 13.4247i | 0.425453 | + | 1.34923i | ||||
\(100\) | −2.25548 | −0.225548 | ||||||||
\(101\) | 9.03979 | 0.899493 | 0.449746 | − | 0.893156i | \(-0.351514\pi\) | ||||
0.449746 | + | 0.893156i | \(0.351514\pi\) | |||||||
\(102\) | 2.25548 | + | 14.6527i | 0.223326 | + | 1.45083i | ||||
\(103\) | − | 15.5206i | − | 1.52929i | −0.644451 | − | 0.764645i | \(-0.722914\pi\) | ||
0.644451 | − | 0.764645i | \(-0.277086\pi\) | |||||||
\(104\) | 0.336601 | 0.0330064 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.67320 | 0.453901 | ||||||||
\(107\) | − | 5.35794i | − | 0.517972i | −0.965881 | − | 0.258986i | \(-0.916612\pi\) | ||
0.965881 | − | 0.258986i | \(-0.0833883\pi\) | |||||||
\(108\) | −10.5110 | + | 5.18398i | −1.01142 | + | 0.498828i | ||||
\(109\) | 1.35887 | 0.130156 | 0.0650782 | − | 0.997880i | \(-0.479270\pi\) | ||||
0.0650782 | + | 0.997880i | \(0.479270\pi\) | |||||||
\(110\) | 9.67925 | 0.922881 | ||||||||
\(111\) | −19.4855 | + | 2.99938i | −1.84948 | + | 0.284689i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 11.9390i | − | 1.12312i | −0.827435 | − | 0.561562i | \(-0.810201\pi\) | ||
0.827435 | − | 0.561562i | \(-0.189799\pi\) | |||||||
\(114\) | 3.16830 | − | 0.487693i | 0.296739 | − | 0.0456767i | ||||
\(115\) | − | 6.80436i | − | 0.634510i | ||||||
\(116\) | 4.84341i | 0.449700i | ||||||||
\(117\) | 0.576223 | + | 1.82737i | 0.0532718 | + | 0.168940i | ||||
\(118\) | 1.04817i | 0.0964917i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.138874 | + | 0.902197i | 0.0126774 | + | 0.0823590i | ||||
\(121\) | −11.0159 | −1.00144 | ||||||||
\(122\) | −10.6939 | −0.968183 | ||||||||
\(123\) | −7.02943 | + | 1.08203i | −0.633822 | + | 0.0975636i | ||||
\(124\) | − | 5.27267i | − | 0.473500i | ||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.8492 | −1.49513 | −0.747563 | − | 0.664191i | \(-0.768776\pi\) | ||||
−0.747563 | + | 0.664191i | \(0.768776\pi\) | |||||||
\(128\) | 4.18175i | 0.369618i | ||||||||
\(129\) | 5.39114 | − | 0.829853i | 0.474664 | − | 0.0730645i | ||||
\(130\) | 1.31754 | 0.115556 | ||||||||
\(131\) | −13.8695 | −1.21178 | −0.605890 | − | 0.795548i | \(-0.707183\pi\) | ||||
−0.605890 | + | 0.795548i | \(0.707183\pi\) | |||||||
\(132\) | −2.78870 | − | 18.1168i | −0.242725 | − | 1.57687i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 9.96060i | 0.860465i | ||||||||
\(135\) | −4.66019 | + | 2.29839i | −0.401085 | + | 0.197814i | ||||
\(136\) | − | 2.18673i | − | 0.187510i | ||||||
\(137\) | 4.33830i | 0.370646i | 0.982678 | + | 0.185323i | \(0.0593332\pi\) | ||||
−0.982678 | + | 0.185323i | \(0.940667\pi\) | |||||||
\(138\) | −24.0291 | + | 3.69877i | −2.04549 | + | 0.314860i | ||||
\(139\) | − | 10.9631i | − | 0.929881i | −0.885342 | − | 0.464941i | \(-0.846076\pi\) | ||
0.885342 | − | 0.464941i | \(-0.153924\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.6570 | − | 1.79435i | 0.981695 | − | 0.151111i | ||||
\(142\) | −2.53323 | −0.212584 | ||||||||
\(143\) | −2.99679 | −0.250604 | ||||||||
\(144\) | −9.79586 | + | 3.08892i | −0.816321 | + | 0.257410i | ||||
\(145\) | 2.14740i | 0.178332i | ||||||||
\(146\) | 29.8221 | 2.46809 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 25.6728 | 2.11029 | ||||||||
\(149\) | 8.66656i | 0.709992i | 0.934868 | + | 0.354996i | \(0.115518\pi\) | ||||
−0.934868 | + | 0.354996i | \(0.884482\pi\) | |||||||
\(150\) | 0.543588 | + | 3.53142i | 0.0443838 | + | 0.288339i | ||||
\(151\) | 13.4604 | 1.09539 | 0.547694 | − | 0.836679i | \(-0.315506\pi\) | ||||
0.547694 | + | 0.836679i | \(0.315506\pi\) | |||||||
\(152\) | −0.472828 | −0.0383514 | ||||||||
\(153\) | 11.8715 | − | 3.74343i | 0.959753 | − | 0.302638i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.33772i | − | 0.187770i | ||||||
\(156\) | −0.379597 | − | 2.46605i | −0.0303921 | − | 0.197442i | ||||
\(157\) | 7.81320i | 0.623561i | 0.950154 | + | 0.311781i | \(0.100925\pi\) | ||||
−0.950154 | + | 0.311781i | \(0.899075\pi\) | |||||||
\(158\) | 18.7333i | 1.49034i | ||||||||
\(159\) | −0.596948 | − | 3.87807i | −0.0473410 | − | 0.307551i | ||||
\(160\) | 8.11688i | 0.641696i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 10.6498 | + | 15.2077i | 0.836730 | + | 1.19483i | ||||
\(163\) | 16.6789 | 1.30639 | 0.653196 | − | 0.757189i | \(-0.273428\pi\) | ||||
0.653196 | + | 0.757189i | \(0.273428\pi\) | |||||||
\(164\) | 9.26153 | 0.723204 | ||||||||
\(165\) | −1.23641 | − | 8.03236i | −0.0962547 | − | 0.625319i | ||||
\(166\) | 5.70095i | 0.442479i | ||||||||
\(167\) | 0.465112 | 0.0359915 | 0.0179957 | − | 0.999838i | \(-0.494271\pi\) | ||||
0.0179957 | + | 0.999838i | \(0.494271\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5921 | 0.968621 | ||||||||
\(170\) | − | 8.55938i | − | 0.656475i | ||||||
\(171\) | −0.809428 | − | 2.56693i | −0.0618985 | − | 0.196298i | ||||
\(172\) | −7.10303 | −0.541601 | ||||||||
\(173\) | −11.1842 | −0.850316 | −0.425158 | − | 0.905119i | \(-0.639781\pi\) | ||||
−0.425158 | + | 0.905119i | \(0.639781\pi\) | |||||||
\(174\) | 7.58338 | − | 1.16730i | 0.574894 | − | 0.0884929i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 16.0647i | − | 1.21092i | ||||||
\(177\) | 0.869826 | − | 0.133892i | 0.0653802 | − | 0.0100639i | ||||
\(178\) | 28.4705i | 2.13396i | ||||||||
\(179\) | 0.247690i | 0.0185132i | 0.999957 | + | 0.00925660i | \(0.00294651\pi\) | ||||
−0.999957 | + | 0.00925660i | \(0.997053\pi\) | |||||||
\(180\) | 6.45320 | − | 2.03489i | 0.480993 | − | 0.151671i | ||||
\(181\) | − | 14.3385i | − | 1.06578i | −0.846186 | − | 0.532888i | \(-0.821107\pi\) | ||
0.846186 | − | 0.532888i | \(-0.178893\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.36603 | + | 8.87439i | 0.100980 | + | 0.656014i | ||||
\(184\) | 3.58602 | 0.264365 | ||||||||
\(185\) | 11.3824 | 0.836854 | ||||||||
\(186\) | −8.25548 | + | 1.27076i | −0.605321 | + | 0.0931765i | ||||
\(187\) | 19.4687i | 1.42369i | ||||||||
\(188\) | −15.3585 | −1.12013 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.85076 | −0.134268 | ||||||||
\(191\) | 17.0401i | 1.23298i | 0.787363 | + | 0.616490i | \(0.211446\pi\) | ||||
−0.787363 | + | 0.616490i | \(0.788554\pi\) | |||||||
\(192\) | 16.9419 | − | 2.60785i | 1.22268 | − | 0.188205i | ||||
\(193\) | 2.82362 | 0.203249 | 0.101624 | − | 0.994823i | \(-0.467596\pi\) | ||||
0.101624 | + | 0.994823i | \(0.467596\pi\) | |||||||
\(194\) | 26.6287 | 1.91183 | ||||||||
\(195\) | −0.168300 | − | 1.09336i | −0.0120522 | − | 0.0782973i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.59675i | 0.683740i | 0.939747 | + | 0.341870i | \(0.111060\pi\) | ||||
−0.939747 | + | 0.341870i | \(0.888940\pi\) | |||||||
\(198\) | −27.6936 | + | 8.73260i | −1.96810 | + | 0.620599i | ||||
\(199\) | − | 12.2141i | − | 0.865836i | −0.901433 | − | 0.432918i | \(-0.857484\pi\) | ||
0.901433 | − | 0.432918i | \(-0.142516\pi\) | |||||||
\(200\) | − | 0.527019i | − | 0.0372659i | ||||||
\(201\) | 8.26584 | − | 1.27235i | 0.583027 | − | 0.0897448i | ||||
\(202\) | 18.6480i | 1.31207i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −16.0207 | + | 2.46605i | −1.12168 | + | 0.172658i | ||||
\(205\) | 4.10624 | 0.286792 | ||||||||
\(206\) | 32.0172 | 2.23074 | ||||||||
\(207\) | 6.13887 | + | 19.4681i | 0.426681 | + | 1.35313i | ||||
\(208\) | − | 2.18673i | − | 0.151622i | ||||||
\(209\) | 4.20964 | 0.291187 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.64113 | 0.388351 | 0.194176 | − | 0.980967i | \(-0.437797\pi\) | ||||
0.194176 | + | 0.980967i | \(0.437797\pi\) | |||||||
\(212\) | 5.10950i | 0.350922i | ||||||||
\(213\) | 0.323591 | + | 2.10221i | 0.0221721 | + | 0.144041i | ||||
\(214\) | 11.0528 | 0.755554 | ||||||||
\(215\) | −3.14924 | −0.214776 | ||||||||
\(216\) | −1.21130 | − | 2.45601i | −0.0824183 | − | 0.167110i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.80319i | 0.189856i | ||||||||
\(219\) | −3.80943 | − | 24.7480i | −0.257417 | − | 1.67231i | ||||
\(220\) | 10.5829i | 0.713501i | ||||||||
\(221\) | 2.65007i | 0.178263i | ||||||||
\(222\) | −6.18736 | − | 40.1962i | −0.415269 | − | 2.69779i | ||||
\(223\) | − | 0.392378i | − | 0.0262755i | −0.999914 | − | 0.0131378i | \(-0.995818\pi\) | ||
0.999914 | − | 0.0131378i | \(-0.00418200\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.86113 | − | 0.902197i | 0.190742 | − | 0.0601465i | ||||
\(226\) | 24.6287 | 1.63827 | ||||||||
\(227\) | −23.4251 | −1.55478 | −0.777388 | − | 0.629021i | \(-0.783456\pi\) | ||||
−0.777388 | + | 0.629021i | \(0.783456\pi\) | |||||||
\(228\) | 0.533226 | + | 3.46410i | 0.0353137 | + | 0.229416i | ||||
\(229\) | 7.72824i | 0.510697i | 0.966849 | + | 0.255348i | \(0.0821902\pi\) | ||||
−0.966849 | + | 0.255348i | \(0.917810\pi\) | |||||||
\(230\) | 14.0366 | 0.925545 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.13172 | −0.0743011 | ||||||||
\(233\) | 4.07982i | 0.267278i | 0.991030 | + | 0.133639i | \(0.0426662\pi\) | ||||
−0.991030 | + | 0.133639i | \(0.957334\pi\) | |||||||
\(234\) | −3.76964 | + | 1.18868i | −0.246429 | + | 0.0777064i | ||||
\(235\) | −6.80943 | −0.444198 | ||||||||
\(236\) | −1.14603 | −0.0746001 | ||||||||
\(237\) | 15.5459 | − | 2.39296i | 1.00981 | − | 0.155440i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.76281i | 0.372765i | 0.982477 | + | 0.186383i | \(0.0596764\pi\) | ||||
−0.982477 | + | 0.186383i | \(0.940324\pi\) | |||||||
\(240\) | 5.86113 | − | 0.902197i | 0.378334 | − | 0.0582366i | ||||
\(241\) | 20.4197i | 1.31535i | 0.753303 | + | 0.657674i | \(0.228460\pi\) | ||||
−0.753303 | + | 0.657674i | \(0.771540\pi\) | |||||||
\(242\) | − | 22.7244i | − | 1.46078i | ||||||
\(243\) | 11.2598 | − | 10.7804i | 0.722316 | − | 0.691564i | ||||
\(244\) | − | 11.6923i | − | 0.748525i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.23210 | − | 14.5009i | −0.142314 | − | 0.924542i | ||||
\(247\) | 0.573014 | 0.0364600 | ||||||||
\(248\) | 1.23202 | 0.0782335 | ||||||||
\(249\) | 4.73095 | − | 0.728231i | 0.299812 | − | 0.0461498i | ||||
\(250\) | − | 2.06288i | − | 0.130468i | ||||||
\(251\) | 4.42544 | 0.279331 | 0.139666 | − | 0.990199i | \(-0.455397\pi\) | ||||
0.139666 | + | 0.990199i | \(0.455397\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −31.9268 | −2.00722 | ||||||||
\(254\) | − | 34.7579i | − | 2.18091i | ||||||
\(255\) | −7.10303 | + | 1.09336i | −0.444809 | + | 0.0684690i | ||||
\(256\) | 11.1668 | 0.697922 | ||||||||
\(257\) | −25.5077 | −1.59113 | −0.795565 | − | 0.605869i | \(-0.792826\pi\) | ||||
−0.795565 | + | 0.605869i | \(0.792826\pi\) | |||||||
\(258\) | 1.71189 | + | 11.1213i | 0.106578 | + | 0.692381i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.44055i | 0.0893389i | ||||||||
\(261\) | −1.93738 | − | 6.14398i | −0.119921 | − | 0.380303i | ||||
\(262\) | − | 28.6110i | − | 1.76760i | ||||||
\(263\) | − | 0.357980i | − | 0.0220740i | −0.999939 | − | 0.0110370i | \(-0.996487\pi\) | ||
0.999939 | − | 0.0110370i | \(-0.00351325\pi\) | |||||||
\(264\) | 4.23321 | − | 0.651613i | 0.260536 | − | 0.0401040i | ||||
\(265\) | 2.26538i | 0.139161i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23.6264 | − | 3.63678i | 1.44591 | − | 0.222568i | ||||
\(268\) | −10.8906 | −0.665246 | ||||||||
\(269\) | −8.53810 | −0.520577 | −0.260288 | − | 0.965531i | \(-0.583818\pi\) | ||||
−0.260288 | + | 0.965531i | \(0.583818\pi\) | |||||||
\(270\) | −4.74131 | − | 9.61342i | −0.288547 | − | 0.585054i | ||||
\(271\) | − | 8.43479i | − | 0.512377i | −0.966627 | − | 0.256188i | \(-0.917533\pi\) | ||
0.966627 | − | 0.256188i | \(-0.0824667\pi\) | |||||||
\(272\) | −14.2061 | −0.861369 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.94940 | −0.540653 | ||||||||
\(275\) | 4.69211i | 0.282945i | ||||||||
\(276\) | −4.04410 | − | 26.2725i | −0.243426 | − | 1.58142i | ||||
\(277\) | 10.1059 | 0.607203 | 0.303602 | − | 0.952799i | \(-0.401811\pi\) | ||||
0.303602 | + | 0.952799i | \(0.401811\pi\) | |||||||
\(278\) | 22.6156 | 1.35640 | ||||||||
\(279\) | 2.10909 | + | 6.68851i | 0.126268 | + | 0.400431i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.1554i | 0.904094i | 0.891994 | + | 0.452047i | \(0.149306\pi\) | ||||
−0.891994 | + | 0.452047i | \(0.850694\pi\) | |||||||
\(282\) | 3.70153 | + | 24.0470i | 0.220423 | + | 1.43198i | ||||
\(283\) | − | 23.9395i | − | 1.42305i | −0.702659 | − | 0.711527i | \(-0.748004\pi\) | ||
0.702659 | − | 0.711527i | \(-0.251996\pi\) | |||||||
\(284\) | − | 2.76973i | − | 0.164354i | ||||||
\(285\) | 0.236414 | + | 1.53586i | 0.0140039 | + | 0.0909766i | ||||
\(286\) | − | 6.18202i | − | 0.365551i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −7.32303 | − | 23.2234i | −0.431514 | − | 1.36845i | ||||
\(289\) | 0.216167 | 0.0127157 | ||||||||
\(290\) | −4.42983 | −0.260129 | ||||||||
\(291\) | −3.40151 | − | 22.0979i | −0.199400 | − | 1.29540i | ||||
\(292\) | 32.6063i | 1.90814i | ||||||||
\(293\) | −21.2223 | −1.23982 | −0.619909 | − | 0.784673i | \(-0.712831\pi\) | ||||
−0.619909 | + | 0.784673i | \(0.712831\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.508109 | −0.0295833 | ||||||||
\(296\) | 5.99876i | 0.348671i | ||||||||
\(297\) | 10.7843 | + | 21.8661i | 0.625769 | + | 1.26880i | ||||
\(298\) | −17.8781 | −1.03565 | ||||||||
\(299\) | −4.34586 | −0.251328 | ||||||||
\(300\) | −3.86113 | + | 0.594339i | −0.222922 | + | 0.0343142i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 27.7671i | 1.59782i | ||||||||
\(303\) | 15.4751 | − | 2.38207i | 0.889022 | − | 0.136846i | ||||
\(304\) | 3.07172i | 0.176175i | ||||||||
\(305\) | − | 5.18398i | − | 0.296834i | ||||||
\(306\) | 7.72225 | + | 24.4895i | 0.441452 | + | 1.39997i | ||||
\(307\) | 24.2817i | 1.38583i | 0.721019 | + | 0.692916i | \(0.243674\pi\) | ||||
−0.721019 | + | 0.692916i | \(0.756326\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.08982 | − | 26.5695i | −0.232662 | − | 1.51149i | ||||
\(310\) | 4.82244 | 0.273896 | ||||||||
\(311\) | −7.11716 | −0.403577 | −0.201789 | − | 0.979429i | \(-0.564675\pi\) | ||||
−0.201789 | + | 0.979429i | \(0.564675\pi\) | |||||||
\(312\) | 0.576223 | − | 0.0886974i | 0.0326222 | − | 0.00502150i | ||||
\(313\) | 3.54724i | 0.200502i | 0.994962 | + | 0.100251i | \(0.0319646\pi\) | ||||
−0.994962 | + | 0.100251i | \(0.968035\pi\) | |||||||
\(314\) | −16.1177 | −0.909575 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.4823 | −1.15222 | ||||||||
\(317\) | − | 21.0764i | − | 1.18377i | −0.806022 | − | 0.591885i | \(-0.798384\pi\) | ||
0.806022 | − | 0.591885i | \(-0.201616\pi\) | |||||||
\(318\) | 8.00000 | − | 1.23143i | 0.448618 | − | 0.0690553i | ||||
\(319\) | 10.0758 | 0.564138 | ||||||||
\(320\) | −9.89660 | −0.553237 | ||||||||
\(321\) | −1.41187 | − | 9.17220i | −0.0788028 | − | 0.511942i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.72259i | − | 0.207130i | ||||||
\(324\) | −16.6276 | + | 11.6441i | −0.923753 | + | 0.646896i | ||||
\(325\) | 0.638688i | 0.0354280i | ||||||||
\(326\) | 34.4066i | 1.90560i | ||||||||
\(327\) | 2.32624 | − | 0.358076i | 0.128641 | − | 0.0198016i | ||||
\(328\) | 2.16407i | 0.119491i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 16.5698 | − | 2.55057i | 0.912138 | − | 0.140404i | ||||
\(331\) | −14.8082 | −0.813935 | −0.406967 | − | 0.913443i | \(-0.633414\pi\) | ||||
−0.406967 | + | 0.913443i | \(0.633414\pi\) | |||||||
\(332\) | −6.23321 | −0.342092 | ||||||||
\(333\) | −32.5666 | + | 10.2692i | −1.78464 | + | 0.562749i | ||||
\(334\) | 0.959471i | 0.0524999i | ||||||||
\(335\) | −4.82849 | −0.263809 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.5062 | 1.11704 | 0.558522 | − | 0.829490i | \(-0.311369\pi\) | ||||
0.558522 | + | 0.829490i | \(0.311369\pi\) | |||||||
\(338\) | 25.9760i | 1.41291i | ||||||||
\(339\) | −3.14603 | − | 20.4382i | −0.170869 | − | 1.11005i | ||||
\(340\) | 9.35851 | 0.507536 | ||||||||
\(341\) | −10.9688 | −0.593995 | ||||||||
\(342\) | 5.29527 | − | 1.66975i | 0.286335 | − | 0.0902899i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 1.65971i | − | 0.0894854i | ||||||
\(345\) | −1.79301 | − | 11.6483i | −0.0965325 | − | 0.627124i | ||||
\(346\) | − | 23.0716i | − | 1.24034i | ||||||
\(347\) | − | 15.8313i | − | 0.849871i | −0.905224 | − | 0.424935i | \(-0.860297\pi\) | ||
0.905224 | − | 0.424935i | \(-0.139703\pi\) | |||||||
\(348\) | 1.27628 | + | 8.29138i | 0.0684160 | + | 0.444465i | ||||
\(349\) | − | 8.96019i | − | 0.479628i | −0.970819 | − | 0.239814i | \(-0.922914\pi\) | ||
0.970819 | − | 0.239814i | \(-0.0770865\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.46796 | + | 2.97641i | 0.0783538 | + | 0.158869i | ||||
\(352\) | 38.0853 | 2.02995 | ||||||||
\(353\) | −13.4575 | −0.716271 | −0.358136 | − | 0.933670i | \(-0.616587\pi\) | ||||
−0.358136 | + | 0.933670i | \(0.616587\pi\) | |||||||
\(354\) | 0.276202 | + | 1.79435i | 0.0146800 | + | 0.0953685i | ||||
\(355\) | − | 1.22800i | − | 0.0651757i | ||||||
\(356\) | −31.1286 | −1.64981 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.510954 | −0.0270048 | ||||||||
\(359\) | − | 5.60981i | − | 0.296074i | −0.988982 | − | 0.148037i | \(-0.952704\pi\) | ||
0.988982 | − | 0.148037i | \(-0.0472956\pi\) | |||||||
\(360\) | 0.475475 | + | 1.50787i | 0.0250597 | + | 0.0794716i | ||||
\(361\) | 18.1951 | 0.957636 | ||||||||
\(362\) | 29.5787 | 1.55462 | ||||||||
\(363\) | −18.8579 | + | 2.90278i | −0.989784 | + | 0.152356i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.4565i | 0.756689i | ||||||||
\(366\) | −18.3068 | + | 2.81795i | −0.956912 | + | 0.147297i | ||||
\(367\) | 1.97631i | 0.103163i | 0.998669 | + | 0.0515813i | \(0.0164261\pi\) | ||||
−0.998669 | + | 0.0515813i | \(0.983574\pi\) | |||||||
\(368\) | − | 23.2966i | − | 1.21442i | ||||||
\(369\) | −11.7485 | + | 3.70464i | −0.611601 | + | 0.192856i | ||||
\(370\) | 23.4806i | 1.22070i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.38940 | − | 9.02623i | −0.0720370 | − | 0.467988i | ||||
\(373\) | −23.0934 | −1.19573 | −0.597866 | − | 0.801596i | \(-0.703984\pi\) | ||||
−0.597866 | + | 0.801596i | \(0.703984\pi\) | |||||||
\(374\) | −40.1615 | −2.07670 | ||||||||
\(375\) | −1.71189 | + | 0.263509i | −0.0884016 | + | 0.0136076i | ||||
\(376\) | − | 3.58870i | − | 0.185073i | ||||||
\(377\) | 1.37152 | 0.0706368 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.0645 | −0.876547 | −0.438273 | − | 0.898842i | \(-0.644410\pi\) | ||||
−0.438273 | + | 0.898842i | \(0.644410\pi\) | |||||||
\(380\) | − | 2.02356i | − | 0.103806i | ||||||
\(381\) | −28.8440 | + | 4.43993i | −1.47772 | + | 0.227464i | ||||
\(382\) | −35.1517 | −1.79852 | ||||||||
\(383\) | −26.6113 | −1.35977 | −0.679886 | − | 0.733318i | \(-0.737971\pi\) | ||||
−0.679886 | + | 0.733318i | \(0.737971\pi\) | |||||||
\(384\) | 1.10193 | + | 7.15869i | 0.0562327 | + | 0.365316i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.82479i | 0.296474i | ||||||||
\(387\) | 9.01036 | − | 2.84123i | 0.458022 | − | 0.144428i | ||||
\(388\) | 29.1148i | 1.47808i | ||||||||
\(389\) | − | 9.47953i | − | 0.480631i | −0.970695 | − | 0.240316i | \(-0.922749\pi\) | ||
0.970695 | − | 0.240316i | \(-0.0772509\pi\) | |||||||
\(390\) | 2.25548 | − | 0.347183i | 0.114211 | − | 0.0175803i | ||||
\(391\) | 28.2329i | 1.42780i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23.7430 | + | 3.65473i | −1.19767 | + | 0.184357i | ||||
\(394\) | −19.7970 | −0.997356 | ||||||||
\(395\) | −9.08112 | −0.456921 | ||||||||
\(396\) | −9.54790 | − | 30.2791i | −0.479800 | − | 1.52158i | ||||
\(397\) | 12.3602i | 0.620340i | 0.950681 | + | 0.310170i | \(0.100386\pi\) | ||||
−0.950681 | + | 0.310170i | \(0.899614\pi\) | |||||||
\(398\) | 25.1963 | 1.26297 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.42378 | −0.171189 | ||||||||
\(401\) | 8.21563i | 0.410269i | 0.978734 | + | 0.205134i | \(0.0657631\pi\) | ||||
−0.978734 | + | 0.205134i | \(0.934237\pi\) | |||||||
\(402\) | 2.62471 | + | 17.0514i | 0.130909 | + | 0.850449i | ||||
\(403\) | −1.49307 | −0.0743753 | ||||||||
\(404\) | −20.3890 | −1.01439 | ||||||||
\(405\) | −7.37208 | + | 5.16260i | −0.366322 | + | 0.256532i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 53.4076i | − | 2.64732i | ||||||
\(408\) | −0.576223 | − | 3.74343i | −0.0285273 | − | 0.185327i | ||||
\(409\) | 20.7355i | 1.02531i | 0.858596 | + | 0.512653i | \(0.171337\pi\) | ||||
−0.858596 | + | 0.512653i | \(0.828663\pi\) | |||||||
\(410\) | 8.47068i | 0.418337i | ||||||||
\(411\) | 1.14318 | + | 7.42669i | 0.0563891 | + | 0.366332i | ||||
\(412\) | 35.0064i | 1.72464i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −40.1604 | + | 12.6638i | −1.97378 | + | 0.622390i | ||||
\(415\) | −2.76359 | −0.135659 | ||||||||
\(416\) | 5.18416 | 0.254174 | ||||||||
\(417\) | −2.88889 | − | 18.7677i | −0.141470 | − | 0.919057i | ||||
\(418\) | 8.68398i | 0.424747i | ||||||||
\(419\) | 6.93924 | 0.339004 | 0.169502 | − | 0.985530i | \(-0.445784\pi\) | ||||
0.169502 | + | 0.985530i | \(0.445784\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.2162 | −0.741594 | −0.370797 | − | 0.928714i | \(-0.620915\pi\) | ||||
−0.370797 | + | 0.928714i | \(0.620915\pi\) | |||||||
\(422\) | 11.6370i | 0.566479i | ||||||||
\(423\) | 19.4826 | − | 6.14345i | 0.947278 | − | 0.298705i | ||||
\(424\) | −1.19390 | −0.0579807 | ||||||||
\(425\) | 4.14924 | 0.201268 | ||||||||
\(426\) | −4.33660 | + | 0.667529i | −0.210109 | + | 0.0323419i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.0847i | 0.584137i | ||||||||
\(429\) | −5.13017 | + | 0.789683i | −0.247687 | + | 0.0381262i | ||||
\(430\) | − | 6.49650i | − | 0.313289i | ||||||
\(431\) | 31.0664i | 1.49642i | 0.663463 | + | 0.748209i | \(0.269086\pi\) | ||||
−0.663463 | + | 0.748209i | \(0.730914\pi\) | |||||||
\(432\) | −15.9555 | + | 7.86919i | −0.767657 | + | 0.378607i | ||||
\(433\) | − | 22.3083i | − | 1.07207i | −0.844196 | − | 0.536034i | \(-0.819922\pi\) | ||
0.844196 | − | 0.536034i | \(-0.180078\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.565860 | + | 3.67611i | 0.0271309 | + | 0.176256i | ||||
\(436\) | −3.06491 | −0.146782 | ||||||||
\(437\) | 6.10469 | 0.292027 | ||||||||
\(438\) | 51.0521 | − | 7.85840i | 2.43936 | − | 0.375489i | ||||
\(439\) | − | 25.8799i | − | 1.23518i | −0.786500 | − | 0.617590i | \(-0.788109\pi\) | ||
0.786500 | − | 0.617590i | \(-0.211891\pi\) | |||||||
\(440\) | −2.47283 | −0.117887 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.46677 | −0.260028 | ||||||||
\(443\) | − | 30.9651i | − | 1.47120i | −0.677418 | − | 0.735599i | \(-0.736901\pi\) | ||
0.677418 | − | 0.735599i | \(-0.263099\pi\) | |||||||
\(444\) | 43.9490 | − | 6.76503i | 2.08573 | − | 0.321054i | ||||
\(445\) | −13.8013 | −0.654247 | ||||||||
\(446\) | 0.809428 | 0.0383275 | ||||||||
\(447\) | 2.28372 | + | 14.8362i | 0.108016 | + | 0.701728i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 24.2032i | − | 1.14222i | −0.820874 | − | 0.571110i | \(-0.806513\pi\) | ||
0.820874 | − | 0.571110i | \(-0.193487\pi\) | |||||||
\(450\) | 1.86113 | + | 5.90216i | 0.0877343 | + | 0.278231i | ||||
\(451\) | − | 19.2669i | − | 0.907243i | ||||||
\(452\) | 26.9281i | 1.26659i | ||||||||
\(453\) | 23.0426 | − | 3.54693i | 1.08264 | − | 0.166649i | ||||
\(454\) | − | 48.3231i | − | 2.26792i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.809428 | + | 0.124594i | −0.0379049 | + | 0.00583467i | ||||
\(457\) | −2.41452 | −0.112946 | −0.0564731 | − | 0.998404i | \(-0.517986\pi\) | ||||
−0.0564731 | + | 0.998404i | \(0.517986\pi\) | |||||||
\(458\) | −15.9424 | −0.744942 | ||||||||
\(459\) | 19.3362 | − | 9.53658i | 0.902538 | − | 0.445130i | ||||
\(460\) | 15.3471i | 0.715561i | ||||||||
\(461\) | 7.45376 | 0.347156 | 0.173578 | − | 0.984820i | \(-0.444467\pi\) | ||||
0.173578 | + | 0.984820i | \(0.444467\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.8862 | 0.645345 | 0.322672 | − | 0.946511i | \(-0.395419\pi\) | ||||
0.322672 | + | 0.946511i | \(0.395419\pi\) | |||||||
\(464\) | 7.35222i | 0.341318i | ||||||||
\(465\) | −0.616011 | − | 4.00192i | −0.0285668 | − | 0.185584i | ||||
\(466\) | −8.41618 | −0.389872 | ||||||||
\(467\) | 20.1384 | 0.931895 | 0.465948 | − | 0.884812i | \(-0.345713\pi\) | ||||
0.465948 | + | 0.884812i | \(0.345713\pi\) | |||||||
\(468\) | −1.29966 | − | 4.12158i | −0.0600767 | − | 0.190520i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 14.0470i | − | 0.647942i | ||||||
\(471\) | 2.05885 | + | 13.3753i | 0.0948669 | + | 0.616303i | ||||
\(472\) | − | 0.267783i | − | 0.0123257i | ||||||
\(473\) | 14.7766i | 0.679427i | ||||||||
\(474\) | 4.93639 | + | 32.0693i | 0.226736 | + | 1.47299i | ||||
\(475\) | − | 0.897174i | − | 0.0411652i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.04382 | − | 6.48153i | −0.0935799 | − | 0.296769i | ||||
\(478\) | −11.8880 | −0.543744 | ||||||||
\(479\) | 33.2377 | 1.51867 | 0.759335 | − | 0.650700i | \(-0.225524\pi\) | ||||
0.759335 | + | 0.650700i | \(0.225524\pi\) | |||||||
\(480\) | 2.13887 | + | 13.8952i | 0.0976258 | + | 0.634226i | ||||
\(481\) | − | 7.26983i | − | 0.331476i | ||||||
\(482\) | −42.1234 | −1.91867 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 24.8460 | 1.12936 | ||||||||
\(485\) | 12.9085i | 0.586144i | ||||||||
\(486\) | 22.2387 | + | 23.2276i | 1.00877 | + | 1.05363i | ||||
\(487\) | −32.2077 | −1.45947 | −0.729736 | − | 0.683729i | \(-0.760357\pi\) | ||||
−0.729736 | + | 0.683729i | \(0.760357\pi\) | |||||||
\(488\) | 2.73205 | 0.123674 | ||||||||
\(489\) | 28.5524 | − | 4.39504i | 1.29118 | − | 0.198751i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.5003i | 1.01542i | 0.861527 | + | 0.507712i | \(0.169509\pi\) | ||||
−0.861527 | + | 0.507712i | \(0.830491\pi\) | |||||||
\(492\) | 15.8547 | − | 2.44050i | 0.714785 | − | 0.110026i | ||||
\(493\) | − | 8.91007i | − | 0.401289i | ||||||
\(494\) | 1.18206i | 0.0531834i | ||||||||
\(495\) | −4.23321 | − | 13.4247i | −0.190268 | − | 0.603396i | ||||
\(496\) | − | 8.00383i | − | 0.359383i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.50225 | + | 9.75939i | 0.0673176 | + | 0.437329i | ||||
\(499\) | 6.41404 | 0.287132 | 0.143566 | − | 0.989641i | \(-0.454143\pi\) | ||||
0.143566 | + | 0.989641i | \(0.454143\pi\) | |||||||
\(500\) | 2.25548 | 0.100868 | ||||||||
\(501\) | 0.796221 | − | 0.122561i | 0.0355725 | − | 0.00547564i | ||||
\(502\) | 9.12915i | 0.407454i | ||||||||
\(503\) | 38.0103 | 1.69479 | 0.847397 | − | 0.530960i | \(-0.178169\pi\) | ||||
0.847397 | + | 0.530960i | \(0.178169\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.03979 | −0.402265 | ||||||||
\(506\) | − | 65.8611i | − | 2.92788i | ||||||
\(507\) | 21.5562 | − | 3.31813i | 0.957346 | − | 0.147363i | ||||
\(508\) | 38.0030 | 1.68611 | ||||||||
\(509\) | 12.6996 | 0.562901 | 0.281450 | − | 0.959576i | \(-0.409185\pi\) | ||||
0.281450 | + | 0.959576i | \(0.409185\pi\) | |||||||
\(510\) | −2.25548 | − | 14.6527i | −0.0998742 | − | 0.648833i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 31.3992i | 1.38766i | ||||||||
\(513\) | −2.06206 | − | 4.18100i | −0.0910422 | − | 0.184596i | ||||
\(514\) | − | 52.6194i | − | 2.32094i | ||||||
\(515\) | 15.5206i | 0.683919i | ||||||||
\(516\) | −12.1596 | + | 1.87172i | −0.535297 | + | 0.0823977i | ||||
\(517\) | 31.9506i | 1.40518i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.1460 | + | 2.94713i | −0.840417 | + | 0.129365i | ||||
\(520\) | −0.336601 | −0.0147609 | ||||||||
\(521\) | −36.1940 | −1.58569 | −0.792843 | − | 0.609426i | \(-0.791400\pi\) | ||||
−0.792843 | + | 0.609426i | \(0.791400\pi\) | |||||||
\(522\) | 12.6743 | − | 3.99658i | 0.554739 | − | 0.174926i | ||||
\(523\) | − | 4.93499i | − | 0.215792i | −0.994162 | − | 0.107896i | \(-0.965589\pi\) | ||
0.994162 | − | 0.107896i | \(-0.0344113\pi\) | |||||||
\(524\) | 31.2823 | 1.36657 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.738470 | 0.0321988 | ||||||||
\(527\) | 9.69976i | 0.422528i | ||||||||
\(528\) | −4.23321 | − | 27.5010i | −0.184227 | − | 1.19683i | ||||
\(529\) | −23.2993 | −1.01301 | ||||||||
\(530\) | −4.67320 | −0.202991 | ||||||||
\(531\) | 1.45376 | − | 0.458415i | 0.0630880 | − | 0.0198935i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.62261i | − | 0.113598i | ||||||
\(534\) | 7.50225 | + | 48.7384i | 0.324654 | + | 2.10912i | ||||
\(535\) | 5.35794i | 0.231644i | ||||||||
\(536\) | − | 2.54471i | − | 0.109915i | ||||||
\(537\) | 0.0652685 | + | 0.424017i | 0.00281655 | + | 0.0182977i | ||||
\(538\) | − | 17.6131i | − | 0.759354i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 10.5110 | − | 5.18398i | 0.452319 | − | 0.223083i | ||||
\(541\) | 16.6570 | 0.716140 | 0.358070 | − | 0.933695i | \(-0.383435\pi\) | ||||
0.358070 | + | 0.933695i | \(0.383435\pi\) | |||||||
\(542\) | 17.4000 | 0.747392 | ||||||||
\(543\) | −3.77834 | − | 24.5460i | −0.162144 | − | 1.05337i | ||||
\(544\) | − | 33.6789i | − | 1.44397i | ||||||
\(545\) | −1.35887 | −0.0582077 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.2868 | 0.910159 | 0.455079 | − | 0.890451i | \(-0.349611\pi\) | ||||
0.455079 | + | 0.890451i | \(0.349611\pi\) | |||||||
\(548\) | − | 9.78494i | − | 0.417992i | ||||||
\(549\) | 4.67697 | + | 14.8320i | 0.199608 | + | 0.633015i | ||||
\(550\) | −9.67925 | −0.412725 | ||||||||
\(551\) | −1.92659 | −0.0820756 | ||||||||
\(552\) | 6.13887 | − | 0.944951i | 0.261288 | − | 0.0402198i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 20.8472i | 0.885713i | ||||||||
\(555\) | 19.4855 | − | 2.99938i | 0.827112 | − | 0.127317i | ||||
\(556\) | 24.7271i | 1.04866i | ||||||||
\(557\) | 19.1608i | 0.811869i | 0.913902 | + | 0.405935i | \(0.133054\pi\) | ||||
−0.913902 | + | 0.405935i | \(0.866946\pi\) | |||||||
\(558\) | −13.7976 | + | 4.35079i | −0.584099 | + | 0.184184i | ||||
\(559\) | 2.01138i | 0.0850723i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.13017 | + | 33.3282i | 0.216596 | + | 1.40712i | ||||
\(562\) | −31.2637 | −1.31878 | ||||||||
\(563\) | 27.2487 | 1.14840 | 0.574198 | − | 0.818717i | \(-0.305314\pi\) | ||||
0.574198 | + | 0.818717i | \(0.305314\pi\) | |||||||
\(564\) | −26.2921 | + | 4.04711i | −1.10710 | + | 0.170414i | ||||
\(565\) | 11.9390i | 0.502276i | ||||||||
\(566\) | 49.3843 | 2.07578 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.647181 | 0.0271551 | ||||||||
\(569\) | 26.2260i | 1.09945i | 0.835345 | + | 0.549726i | \(0.185268\pi\) | ||||
−0.835345 | + | 0.549726i | \(0.814732\pi\) | |||||||
\(570\) | −3.16830 | + | 0.487693i | −0.132705 | + | 0.0204272i | ||||
\(571\) | −26.8777 | −1.12479 | −0.562397 | − | 0.826867i | \(-0.690121\pi\) | ||||
−0.562397 | + | 0.826867i | \(0.690121\pi\) | |||||||
\(572\) | 6.75919 | 0.282616 | ||||||||
\(573\) | 4.49023 | + | 29.1708i | 0.187582 | + | 1.21863i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.80436i | 0.283761i | ||||||||
\(576\) | 28.3154 | − | 8.92869i | 1.17981 | − | 0.372029i | ||||
\(577\) | 10.3123i | 0.429306i | 0.976690 | + | 0.214653i | \(0.0688620\pi\) | ||||
−0.976690 | + | 0.214653i | \(0.931138\pi\) | |||||||
\(578\) | 0.445928i | 0.0185481i | ||||||||
\(579\) | 4.83373 | − | 0.744051i | 0.200883 | − | 0.0309217i | ||||
\(580\) | − | 4.84341i | − | 0.201112i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 45.5853 | − | 7.01690i | 1.88957 | − | 0.290860i | ||||
\(583\) | 10.6294 | 0.440224 | ||||||||
\(584\) | −7.61886 | −0.315271 | ||||||||
\(585\) | −0.576223 | − | 1.82737i | −0.0238239 | − | 0.0755523i | ||||
\(586\) | − | 43.7790i | − | 1.80850i | ||||||
\(587\) | 22.1492 | 0.914197 | 0.457098 | − | 0.889416i | \(-0.348889\pi\) | ||||
0.457098 | + | 0.889416i | \(0.348889\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.09734 | 0.0864195 | ||||||||
\(590\) | − | 1.04817i | − | 0.0431524i | ||||||
\(591\) | 2.52883 | + | 16.4286i | 0.104022 | + | 0.675781i | ||||
\(592\) | 38.9709 | 1.60170 | ||||||||
\(593\) | −2.91721 | −0.119796 | −0.0598978 | − | 0.998205i | \(-0.519077\pi\) | ||||
−0.0598978 | + | 0.998205i | \(0.519077\pi\) | |||||||
\(594\) | −45.1072 | + | 22.2467i | −1.85077 | + | 0.912795i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 19.5472i | − | 0.800686i | ||||||
\(597\) | −3.21853 | − | 20.9092i | −0.131726 | − | 0.855757i | ||||
\(598\) | − | 8.96500i | − | 0.366606i | ||||||
\(599\) | 36.3212i | 1.48405i | 0.670374 | + | 0.742023i | \(0.266133\pi\) | ||||
−0.670374 | + | 0.742023i | \(0.733867\pi\) | |||||||
\(600\) | −0.138874 | − | 0.902197i | −0.00566952 | − | 0.0368321i | ||||
\(601\) | 7.15198i | 0.291735i | 0.989304 | + | 0.145868i | \(0.0465974\pi\) | ||||
−0.989304 | + | 0.145868i | \(0.953403\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.8149 | − | 4.35625i | 0.562587 | − | 0.177400i | ||||
\(604\) | −30.3595 | −1.23531 | ||||||||
\(605\) | 11.0159 | 0.447858 | ||||||||
\(606\) | 4.91392 | + | 31.9233i | 0.199615 | + | 1.29680i | ||||
\(607\) | − | 43.6763i | − | 1.77277i | −0.462951 | − | 0.886384i | \(-0.653209\pi\) | ||
0.462951 | − | 0.886384i | \(-0.346791\pi\) | |||||||
\(608\) | −7.28226 | −0.295334 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.6939 | 0.432984 | ||||||||
\(611\) | 4.34910i | 0.175946i | ||||||||
\(612\) | −26.7759 | + | 8.44322i | −1.08235 | + | 0.341297i | ||||
\(613\) | −14.5585 | −0.588013 | −0.294007 | − | 0.955803i | \(-0.594989\pi\) | ||||
−0.294007 | + | 0.955803i | \(0.594989\pi\) | |||||||
\(614\) | −50.0903 | −2.02148 | ||||||||
\(615\) | 7.02943 | − | 1.08203i | 0.283454 | − | 0.0436318i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 4.68442i | − | 0.188588i | −0.995544 | − | 0.0942938i | \(-0.969941\pi\) | ||
0.995544 | − | 0.0942938i | \(-0.0300593\pi\) | |||||||
\(618\) | 54.8098 | − | 8.43682i | 2.20477 | − | 0.339379i | ||||
\(619\) | 38.1546i | 1.53356i | 0.641908 | + | 0.766782i | \(0.278143\pi\) | ||||
−0.641908 | + | 0.766782i | \(0.721857\pi\) | |||||||
\(620\) | 5.27267i | 0.211756i | ||||||||
\(621\) | 15.6391 | + | 31.7096i | 0.627576 | + | 1.27246i | ||||
\(622\) | − | 14.6819i | − | 0.588689i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.576223 | − | 3.74343i | −0.0230674 | − | 0.149857i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −7.31754 | −0.292468 | ||||||||
\(627\) | 7.20643 | − | 1.10928i | 0.287797 | − | 0.0443003i | ||||
\(628\) | − | 17.6225i | − | 0.703214i | ||||||
\(629\) | −47.2285 | −1.88312 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.9959 | 0.955264 | 0.477632 | − | 0.878560i | \(-0.341495\pi\) | ||||
0.477632 | + | 0.878560i | \(0.341495\pi\) | |||||||
\(632\) | − | 4.78592i | − | 0.190374i | ||||||
\(633\) | 9.65698 | − | 1.48649i | 0.383831 | − | 0.0590827i | ||||
\(634\) | 43.4782 | 1.72674 | ||||||||
\(635\) | 16.8492 | 0.668641 | ||||||||
\(636\) | 1.34640 | + | 8.74690i | 0.0533883 | + | 0.346837i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 20.7852i | 0.822895i | ||||||||
\(639\) | 1.10790 | + | 3.51347i | 0.0438279 | + | 0.138991i | ||||
\(640\) | − | 4.18175i | − | 0.165298i | ||||||
\(641\) | − | 23.0983i | − | 0.912328i | −0.889896 | − | 0.456164i | \(-0.849223\pi\) | ||
0.889896 | − | 0.456164i | \(-0.150777\pi\) | |||||||
\(642\) | 18.9212 | − | 2.91252i | 0.746759 | − | 0.114948i | ||||
\(643\) | − | 22.7592i | − | 0.897536i | −0.893648 | − | 0.448768i | \(-0.851863\pi\) | ||
0.893648 | − | 0.448768i | \(-0.148137\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.39114 | + | 0.829853i | −0.212276 | + | 0.0326754i | ||||
\(646\) | 7.67925 | 0.302136 | ||||||||
\(647\) | −2.42699 | −0.0954147 | −0.0477073 | − | 0.998861i | \(-0.515191\pi\) | ||||
−0.0477073 | + | 0.998861i | \(0.515191\pi\) | |||||||
\(648\) | −2.72079 | − | 3.88522i | −0.106883 | − | 0.152626i | ||||
\(649\) | 2.38410i | 0.0935842i | ||||||||
\(650\) | −1.31754 | −0.0516781 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −37.6189 | −1.47327 | ||||||||
\(653\) | − | 40.1558i | − | 1.57142i | −0.618596 | − | 0.785709i | \(-0.712298\pi\) | ||
0.618596 | − | 0.785709i | \(-0.287702\pi\) | |||||||
\(654\) | 0.738667 | + | 4.79875i | 0.0288842 | + | 0.187646i | ||||
\(655\) | 13.8695 | 0.541925 | ||||||||
\(656\) | 14.0589 | 0.548906 | ||||||||
\(657\) | −13.0426 | − | 41.3619i | −0.508842 | − | 1.61368i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 0.627454i | − | 0.0244421i | −0.999925 | − | 0.0122211i | \(-0.996110\pi\) | ||
0.999925 | − | 0.0122211i | \(-0.00389018\pi\) | |||||||
\(660\) | 2.78870 | + | 18.1168i | 0.108550 | + | 0.705196i | ||||
\(661\) | 32.9950i | 1.28336i | 0.766974 | + | 0.641678i | \(0.221761\pi\) | ||||
−0.766974 | + | 0.641678i | \(0.778239\pi\) | |||||||
\(662\) | − | 30.5476i | − | 1.18727i | ||||||
\(663\) | 0.698318 | + | 4.53662i | 0.0271204 | + | 0.176188i | ||||
\(664\) | − | 1.45646i | − | 0.0565217i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −21.1842 | − | 67.1810i | −0.820869 | − | 2.60321i | ||||
\(667\) | 14.6117 | 0.565767 | ||||||||
\(668\) | −1.04905 | −0.0405890 | ||||||||
\(669\) | −0.103395 | − | 0.671707i | −0.00399749 | − | 0.0259697i | ||||
\(670\) | − | 9.96060i | − | 0.384812i | ||||||
\(671\) | −24.3238 | −0.939009 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.14437 | 0.0441121 | 0.0220560 | − | 0.999757i | \(-0.492979\pi\) | ||||
0.0220560 | + | 0.999757i | \(0.492979\pi\) | |||||||
\(674\) | 42.3018i | 1.62941i | ||||||||
\(675\) | 4.66019 | − | 2.29839i | 0.179371 | − | 0.0884653i | ||||
\(676\) | −28.4011 | −1.09235 | ||||||||
\(677\) | −15.9782 | −0.614092 | −0.307046 | − | 0.951695i | \(-0.599341\pi\) | ||||
−0.307046 | + | 0.951695i | \(0.599341\pi\) | |||||||
\(678\) | 42.1615 | − | 6.48988i | 1.61920 | − | 0.249242i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.18673i | 0.0838571i | ||||||||
\(681\) | −40.1011 | + | 6.17273i | −1.53668 | + | 0.236539i | ||||
\(682\) | − | 22.6274i | − | 0.866447i | ||||||
\(683\) | 2.26463i | 0.0866535i | 0.999061 | + | 0.0433268i | \(0.0137957\pi\) | ||||
−0.999061 | + | 0.0433268i | \(0.986204\pi\) | |||||||
\(684\) | 1.82565 | + | 5.78965i | 0.0698053 | + | 0.221373i | ||||
\(685\) | − | 4.33830i | − | 0.165758i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.03646 | + | 13.2299i | 0.0776960 | + | 0.504752i | ||||
\(688\) | −10.7823 | −0.411071 | ||||||||
\(689\) | 1.44687 | 0.0551213 | ||||||||
\(690\) | 24.0291 | − | 3.69877i | 0.914771 | − | 0.140810i | ||||
\(691\) | − | 2.77178i | − | 0.105444i | −0.998609 | − | 0.0527218i | \(-0.983210\pi\) | ||
0.998609 | − | 0.0527218i | \(-0.0167897\pi\) | |||||||
\(692\) | 25.2256 | 0.958934 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 32.6582 | 1.23969 | ||||||||
\(695\) | 10.9631i | 0.415856i | ||||||||
\(696\) | −1.93738 | + | 0.298219i | −0.0734362 | + | 0.0113040i | ||||
\(697\) | −17.0378 | −0.645351 | ||||||||
\(698\) | 18.4838 | 0.699623 | ||||||||
\(699\) | 1.07507 | + | 6.98419i | 0.0406629 | + | 0.264166i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.1184i | 0.873169i | 0.899663 | + | 0.436585i | \(0.143812\pi\) | ||||
−0.899663 | + | 0.436585i | \(0.856188\pi\) | |||||||
\(702\) | −6.13998 | + | 3.02822i | −0.231738 | + | 0.114293i | ||||
\(703\) | 10.2120i | 0.385154i | ||||||||
\(704\) | 46.4359i | 1.75012i | ||||||||
\(705\) | −11.6570 | + | 1.79435i | −0.439027 | + | 0.0675791i | ||||
\(706\) | − | 27.7612i | − | 1.04481i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.96187 | + | 0.301989i | −0.0737317 | + | 0.0113495i | ||||
\(709\) | −36.0268 | −1.35302 | −0.676508 | − | 0.736435i | \(-0.736508\pi\) | ||||
−0.676508 | + | 0.736435i | \(0.736508\pi\) | |||||||
\(710\) | 2.53323 | 0.0950703 | ||||||||
\(711\) | 25.9822 | − | 8.19297i | 0.974410 | − | 0.307260i | ||||
\(712\) | − | 7.27357i | − | 0.272589i | ||||||
\(713\) | −15.9067 | −0.595710 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.99679 | 0.112074 | ||||||||
\(716\) | − | 0.558658i | − | 0.0208780i | ||||||
\(717\) | 1.51855 | + | 9.86529i | 0.0567114 | + | 0.368426i | ||||
\(718\) | 11.5724 | 0.431877 | ||||||||
\(719\) | −17.1420 | −0.639288 | −0.319644 | − | 0.947538i | \(-0.603563\pi\) | ||||
−0.319644 | + | 0.947538i | \(0.603563\pi\) | |||||||
\(720\) | 9.79586 | − | 3.08892i | 0.365070 | − | 0.115117i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 37.5343i | 1.39688i | ||||||||
\(723\) | 5.38078 | + | 34.9562i | 0.200113 | + | 1.30004i | ||||
\(724\) | 32.3403i | 1.20192i | ||||||||
\(725\) | − | 2.14740i | − | 0.0797524i | ||||||
\(726\) | −5.98809 | − | 38.9016i | −0.222239 | − | 1.44378i | ||||
\(727\) | − | 16.6832i | − | 0.618747i | −0.950941 | − | 0.309374i | \(-0.899881\pi\) | ||
0.950941 | − | 0.309374i | \(-0.100119\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.4348 | − | 21.4219i | 0.608695 | − | 0.793404i | ||||
\(730\) | −29.8221 | −1.10376 | ||||||||
\(731\) | 13.0669 | 0.483298 | ||||||||
\(732\) | −3.08104 | − | 20.0160i | −0.113879 | − | 0.739812i | ||||
\(733\) | 38.0836i | 1.40665i | 0.710868 | + | 0.703326i | \(0.248302\pi\) | ||||
−0.710868 | + | 0.703326i | \(0.751698\pi\) | |||||||
\(734\) | −4.07690 | −0.150481 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 55.2302 | 2.03581 | ||||||||
\(737\) | 22.6558i | 0.834537i | ||||||||
\(738\) | −7.64223 | − | 24.2357i | −0.281314 | − | 0.892128i | ||||
\(739\) | −22.4373 | −0.825368 | −0.412684 | − | 0.910874i | \(-0.635409\pi\) | ||||
−0.412684 | + | 0.910874i | \(0.635409\pi\) | |||||||
\(740\) | −25.6728 | −0.943752 | ||||||||
\(741\) | 0.980937 | − | 0.150995i | 0.0360356 | − | 0.00554693i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 6.39189i | − | 0.234496i | −0.993103 | − | 0.117248i | \(-0.962593\pi\) | ||
0.993103 | − | 0.117248i | \(-0.0374072\pi\) | |||||||
\(744\) | 2.10909 | − | 0.324649i | 0.0773228 | − | 0.0119022i | ||||
\(745\) | − | 8.66656i | − | 0.317518i | ||||||
\(746\) | − | 47.6389i | − | 1.74419i | ||||||
\(747\) | 7.90697 | − | 2.49330i | 0.289301 | − | 0.0912251i | ||||
\(748\) | − | 43.9111i | − | 1.60555i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.543588 | − | 3.53142i | −0.0198490 | − | 0.128949i | ||||
\(751\) | −10.9989 | −0.401355 | −0.200677 | − | 0.979657i | \(-0.564314\pi\) | ||||
−0.200677 | + | 0.979657i | \(0.564314\pi\) | |||||||
\(752\) | −23.3140 | −0.850173 | ||||||||
\(753\) | 7.57586 | − | 1.16614i | 0.276080 | − | 0.0424967i | ||||
\(754\) | 2.82928i | 0.103036i | ||||||||
\(755\) | −13.4604 | −0.489873 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.8216 | −1.01119 | −0.505597 | − | 0.862770i | \(-0.668728\pi\) | ||||
−0.505597 | + | 0.862770i | \(0.668728\pi\) | |||||||
\(758\) | − | 35.2021i | − | 1.27860i | ||||||
\(759\) | −54.6551 | + | 8.41300i | −1.98385 | + | 0.305373i | ||||
\(760\) | 0.472828 | 0.0171513 | ||||||||
\(761\) | 13.0953 | 0.474705 | 0.237352 | − | 0.971424i | \(-0.423720\pi\) | ||||
0.237352 | + | 0.971424i | \(0.423720\pi\) | |||||||
\(762\) | −9.15904 | − | 59.5017i | −0.331797 | − | 2.15552i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 38.4336i | − | 1.39048i | ||||||
\(765\) | −11.8715 | + | 3.74343i | −0.429215 | + | 0.135344i | ||||
\(766\) | − | 54.8958i | − | 1.98347i | ||||||
\(767\) | 0.324523i | 0.0117179i | ||||||||
\(768\) | 19.1162 | − | 2.94254i | 0.689798 | − | 0.106180i | ||||
\(769\) | − | 7.74247i | − | 0.279201i | −0.990208 | − | 0.139600i | \(-0.955418\pi\) | ||
0.990208 | − | 0.139600i | \(-0.0445818\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.6664 | + | 6.72153i | −1.57261 | + | 0.242070i | ||||
\(772\) | −6.36861 | −0.229211 | ||||||||
\(773\) | −38.3465 | −1.37923 | −0.689614 | − | 0.724177i | \(-0.742220\pi\) | ||||
−0.689614 | + | 0.724177i | \(0.742220\pi\) | |||||||
\(774\) | 5.86113 | + | 18.5873i | 0.210674 | + | 0.668107i | ||||
\(775\) | 2.33772i | 0.0839734i | ||||||||
\(776\) | −6.80301 | −0.244214 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 19.5551 | 0.701086 | ||||||||
\(779\) | 3.68401i | 0.131993i | ||||||||
\(780\) | 0.379597 | + | 2.46605i | 0.0135918 | + | 0.0882989i | ||||
\(781\) | −5.76192 | −0.206178 | ||||||||
\(782\) | −58.2411 | −2.08270 | ||||||||
\(783\) | −4.93557 | − | 10.0073i | −0.176383 | − | 0.357632i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 7.81320i | − | 0.278865i | ||||||
\(786\) | −7.53928 | − | 48.9789i | −0.268917 | − | 1.74702i | ||||
\(787\) | 24.9621i | 0.889803i | 0.895580 | + | 0.444901i | \(0.146761\pi\) | ||||
−0.895580 | + | 0.444901i | \(0.853239\pi\) | |||||||
\(788\) | − | 21.6453i | − | 0.771080i | ||||||
\(789\) | −0.0943310 | − | 0.612822i | −0.00335827 | − | 0.0218170i | ||||
\(790\) | − | 18.7333i | − | 0.666500i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.07507 | − | 2.23098i | 0.251402 | − | 0.0792744i | ||||
\(793\) | −3.31094 | −0.117575 | ||||||||
\(794\) | −25.4976 | −0.904875 | ||||||||
\(795\) | 0.596948 | + | 3.87807i | 0.0211716 | + | 0.137541i | ||||
\(796\) | 27.5487i | 0.976436i | ||||||||
\(797\) | 5.81191 | 0.205868 | 0.102934 | − | 0.994688i | \(-0.467177\pi\) | ||||
0.102934 | + | 0.994688i | \(0.467177\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.2539 | 0.999552 | ||||||||
\(800\) | − | 8.11688i | − | 0.286975i | ||||||
\(801\) | 39.4874 | − | 12.4515i | 1.39522 | − | 0.439954i | ||||
\(802\) | −16.9479 | −0.598450 | ||||||||
\(803\) | 67.8315 | 2.39372 | ||||||||
\(804\) | −18.6434 | + | 2.86976i | −0.657502 | + | 0.101209i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 3.08003i | − | 0.108490i | ||||||
\(807\) | −14.6163 | + | 2.24987i | −0.514517 | + | 0.0791991i | ||||
\(808\) | − | 4.76414i | − | 0.167602i | ||||||
\(809\) | − | 1.75010i | − | 0.0615301i | −0.999527 | − | 0.0307650i | \(-0.990206\pi\) | ||
0.999527 | − | 0.0307650i | \(-0.00979436\pi\) | |||||||
\(810\) | −10.6498 | − | 15.2077i | −0.374197 | − | 0.534345i | ||||
\(811\) | 28.4479i | 0.998940i | 0.866331 | + | 0.499470i | \(0.166472\pi\) | ||||
−0.866331 | + | 0.499470i | \(0.833528\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.22265 | − | 14.4394i | −0.0779516 | − | 0.506412i | ||||
\(814\) | 110.174 | 3.86158 | ||||||||
\(815\) | −16.6789 | −0.584236 | ||||||||
\(816\) | −24.3192 | + | 3.74343i | −0.851342 | + | 0.131046i | ||||
\(817\) | − | 2.82541i | − | 0.0988487i | ||||||
\(818\) | −42.7750 | −1.49559 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.26153 | −0.323427 | ||||||||
\(821\) | 29.9504i | 1.04528i | 0.852555 | + | 0.522638i | \(0.175052\pi\) | ||||
−0.852555 | + | 0.522638i | \(0.824948\pi\) | |||||||
\(822\) | −15.3204 | + | 2.35825i | −0.534360 | + | 0.0822535i | ||||
\(823\) | 16.1257 | 0.562105 | 0.281053 | − | 0.959692i | \(-0.409316\pi\) | ||||
0.281053 | + | 0.959692i | \(0.409316\pi\) | |||||||
\(824\) | −8.17965 | −0.284952 | ||||||||
\(825\) | 1.23641 | + | 8.03236i | 0.0430464 | + | 0.279651i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 15.9844i | − | 0.555831i | −0.960605 | − | 0.277916i | \(-0.910356\pi\) | ||
0.960605 | − | 0.277916i | \(-0.0896436\pi\) | |||||||
\(828\) | −13.8461 | − | 43.9099i | −0.481185 | − | 1.52597i | ||||
\(829\) | − | 20.8727i | − | 0.724938i | −0.931996 | − | 0.362469i | \(-0.881934\pi\) | ||
0.931996 | − | 0.362469i | \(-0.118066\pi\) | |||||||
\(830\) | − | 5.70095i | − | 0.197883i | ||||||
\(831\) | 17.3001 | − | 2.66299i | 0.600135 | − | 0.0923782i | ||||
\(832\) | 6.32084i | 0.219136i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 38.7155 | − | 5.95943i | 1.34061 | − | 0.206358i | ||||
\(835\) | −0.465112 | −0.0160959 | ||||||||
\(836\) | −9.49474 | −0.328382 | ||||||||
\(837\) | 5.37300 | + | 10.8942i | 0.185718 | + | 0.376559i | ||||
\(838\) | 14.3148i | 0.494497i | ||||||||
\(839\) | −14.2504 | −0.491977 | −0.245989 | − | 0.969273i | \(-0.579113\pi\) | ||||
−0.245989 | + | 0.969273i | \(0.579113\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.3887 | 0.840989 | ||||||||
\(842\) | − | 31.3893i | − | 1.08175i | ||||||
\(843\) | 3.99358 | + | 25.9443i | 0.137546 | + | 0.893570i | ||||
\(844\) | −12.7234 | −0.437959 | ||||||||
\(845\) | −12.5921 | −0.433181 | ||||||||
\(846\) | 12.6732 | + | 40.1903i | 0.435714 | + | 1.38177i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.75614i | 0.266347i | ||||||||
\(849\) | −6.30828 | − | 40.9817i | −0.216499 | − | 1.40649i | ||||
\(850\) | 8.55938i | 0.293584i | ||||||||
\(851\) | − | 77.4502i | − | 2.65496i | ||||||
\(852\) | −0.729851 | − | 4.74148i | −0.0250043 | − | 0.162440i | ||||
\(853\) | 49.6034i | 1.69839i | 0.528081 | + | 0.849194i | \(0.322912\pi\) | ||||
−0.528081 | + | 0.849194i | \(0.677088\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.809428 | + | 2.56693i | 0.0276819 | + | 0.0877871i | ||||
\(856\) | −2.82374 | −0.0965133 | ||||||||
\(857\) | −5.24503 | −0.179167 | −0.0895834 | − | 0.995979i | \(-0.528554\pi\) | ||||
−0.0895834 | + | 0.995979i | \(0.528554\pi\) | |||||||
\(858\) | −1.62902 | − | 10.5829i | −0.0556139 | − | 0.361295i | ||||
\(859\) | − | 11.7458i | − | 0.400763i | −0.979718 | − | 0.200382i | \(-0.935782\pi\) | ||
0.979718 | − | 0.200382i | \(-0.0642182\pi\) | |||||||
\(860\) | 7.10303 | 0.242211 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −64.0863 | −2.18279 | ||||||||
\(863\) | 35.0909i | 1.19451i | 0.802052 | + | 0.597254i | \(0.203741\pi\) | ||||
−0.802052 | + | 0.597254i | \(0.796259\pi\) | |||||||
\(864\) | −18.6558 | − | 37.8262i | −0.634683 | − | 1.28687i | ||||
\(865\) | 11.1842 | 0.380273 | ||||||||
\(866\) | 46.0194 | 1.56380 | ||||||||
\(867\) | 0.370054 | − | 0.0569621i | 0.0125677 | − | 0.00193454i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 42.6096i | 1.44543i | ||||||||
\(870\) | −7.58338 | + | 1.16730i | −0.257101 | + | 0.0395752i | ||||
\(871\) | 3.08390i | 0.104494i | ||||||||
\(872\) | − | 0.716151i | − | 0.0242519i | ||||||
\(873\) | −11.6460 | − | 36.9328i | −0.394157 | − | 1.24999i | ||||
\(874\) | 12.5933i | 0.425973i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.59208 | + | 55.8184i | 0.290299 | + | 1.88593i | ||||
\(877\) | −16.8532 | −0.569094 | −0.284547 | − | 0.958662i | \(-0.591843\pi\) | ||||
−0.284547 | + | 0.958662i | \(0.591843\pi\) | |||||||
\(878\) | 53.3871 | 1.80173 | ||||||||
\(879\) | −36.3302 | + | 5.59227i | −1.22539 | + | 0.188623i | ||||
\(880\) | 16.0647i | 0.541542i | ||||||||
\(881\) | −51.9437 | −1.75003 | −0.875015 | − | 0.484096i | \(-0.839148\pi\) | ||||
−0.875015 | + | 0.484096i | \(0.839148\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.9096 | 0.501748 | 0.250874 | − | 0.968020i | \(-0.419282\pi\) | ||||
0.250874 | + | 0.968020i | \(0.419282\pi\) | |||||||
\(884\) | − | 5.97717i | − | 0.201034i | ||||||
\(885\) | −0.869826 | + | 0.133892i | −0.0292389 | + | 0.00450071i | ||||
\(886\) | 63.8774 | 2.14600 | ||||||||
\(887\) | 13.1885 | 0.442828 | 0.221414 | − | 0.975180i | \(-0.428933\pi\) | ||||
0.221414 | + | 0.975180i | \(0.428933\pi\) | |||||||
\(888\) | 1.58073 | + | 10.2692i | 0.0530458 | + | 0.344612i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 28.4705i | − | 0.954335i | ||||||
\(891\) | 24.2235 | + | 34.5906i | 0.811517 | + | 1.15883i | ||||
\(892\) | 0.884999i | 0.0296319i | ||||||||
\(893\) | − | 6.10924i | − | 0.204438i | ||||||
\(894\) | −30.6053 | + | 4.71104i | −1.02359 | + | 0.157561i | ||||
\(895\) | − | 0.247690i | − | 0.00827935i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.43963 | + | 1.14518i | −0.248402 | + | 0.0382363i | ||||
\(898\) | 49.9283 | 1.66613 | ||||||||
\(899\) | 5.02002 | 0.167427 | ||||||||
\(900\) | −6.45320 | + | 2.03489i | −0.215107 | + | 0.0678295i | ||||
\(901\) | − | 9.39958i | − | 0.313146i | ||||||
\(902\) | 39.7453 | 1.32338 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.29206 | −0.209271 | ||||||||
\(905\) | 14.3385i | 0.476629i | ||||||||
\(906\) | 7.31689 | + | 47.5342i | 0.243088 | + | 1.57922i | ||||
\(907\) | 46.9417 | 1.55867 | 0.779337 | − | 0.626605i | \(-0.215556\pi\) | ||||
0.779337 | + | 0.626605i | \(0.215556\pi\) | |||||||
\(908\) | 52.8347 | 1.75338 | ||||||||
\(909\) | 25.8640 | − | 8.15567i | 0.857854 | − | 0.270507i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 45.2977i | − | 1.50078i | −0.660996 | − | 0.750389i | \(-0.729866\pi\) | ||
0.660996 | − | 0.750389i | \(-0.270134\pi\) | |||||||
\(912\) | 0.809428 | + | 5.25845i | 0.0268028 | + | 0.174125i | ||||
\(913\) | 12.9670i | 0.429146i | ||||||||
\(914\) | − | 4.98086i | − | 0.164752i | ||||||
\(915\) | −1.36603 | − | 8.87439i | −0.0451594 | − | 0.293378i | ||||
\(916\) | − | 17.4309i | − | 0.575932i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 19.6728 | + | 39.8884i | 0.649300 | + | 1.31651i | ||||
\(919\) | 43.1822 | 1.42445 | 0.712225 | − | 0.701951i | \(-0.247687\pi\) | ||||
0.712225 | + | 0.701951i | \(0.247687\pi\) | |||||||
\(920\) | −3.58602 | −0.118228 | ||||||||
\(921\) | 6.39846 | + | 41.5676i | 0.210837 | + | 1.36970i | ||||
\(922\) | 15.3762i | 0.506389i | ||||||||
\(923\) | −0.784311 | −0.0258159 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.3824 | −0.374252 | ||||||||
\(926\) | 28.6455i | 0.941349i | ||||||||
\(927\) | −14.0026 | − | 44.4064i | −0.459907 | − | 1.45850i | ||||
\(928\) | −17.4302 | −0.572174 | ||||||||
\(929\) | 9.01140 | 0.295655 | 0.147827 | − | 0.989013i | \(-0.452772\pi\) | ||||
0.147827 | + | 0.989013i | \(0.452772\pi\) | |||||||
\(930\) | 8.25548 | − | 1.27076i | 0.270708 | − | 0.0416698i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 9.20194i | − | 0.301419i | ||||||
\(933\) | −12.1838 | + | 1.87544i | −0.398879 | + | 0.0613991i | ||||
\(934\) | 41.5432i | 1.35933i | ||||||||
\(935\) | − | 19.4687i | − | 0.636693i | ||||||
\(936\) | 0.963056 | − | 0.303680i | 0.0314785 | − | 0.00992610i | ||||
\(937\) | 21.9677i | 0.717654i | 0.933404 | + | 0.358827i | \(0.116823\pi\) | ||||
−0.933404 | + | 0.358827i | \(0.883177\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.934731 | + | 6.07248i | 0.0305038 | + | 0.198168i | ||||
\(940\) | 15.3585 | 0.500939 | ||||||||
\(941\) | −1.64772 | −0.0537142 | −0.0268571 | − | 0.999639i | \(-0.508550\pi\) | ||||
−0.0268571 | + | 0.999639i | \(0.508550\pi\) | |||||||
\(942\) | −27.5917 | + | 4.24717i | −0.898987 | + | 0.138380i | ||||
\(943\) | − | 27.9403i | − | 0.909862i | ||||||
\(944\) | −1.73965 | −0.0566209 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −30.4823 | −0.991064 | ||||||||
\(947\) | − | 27.3254i | − | 0.887958i | −0.896037 | − | 0.443979i | \(-0.853567\pi\) | ||
0.896037 | − | 0.443979i | \(-0.146433\pi\) | |||||||
\(948\) | −35.0634 | + | 5.39727i | −1.13880 | + | 0.175295i | ||||
\(949\) | 9.23321 | 0.299723 | ||||||||
\(950\) | 1.85076 | 0.0600467 | ||||||||
\(951\) | −5.55384 | − | 36.0805i | −0.180095 | − | 1.16999i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.2380i | 1.78933i | 0.446734 | + | 0.894667i | \(0.352587\pi\) | ||||
−0.446734 | + | 0.894667i | \(0.647413\pi\) | |||||||
\(954\) | 13.3706 | − | 4.21615i | 0.432890 | − | 0.136503i | ||||
\(955\) | − | 17.0401i | − | 0.551405i | ||||||
\(956\) | − | 12.9979i | − | 0.420382i | ||||||
\(957\) | 17.2487 | − | 2.65508i | 0.557571 | − | 0.0858264i | ||||
\(958\) | 68.5654i | 2.21525i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −16.9419 | + | 2.60785i | −0.546797 | + | 0.0841679i | ||||
\(961\) | 25.5351 | 0.823712 | ||||||||
\(962\) | 14.9968 | 0.483516 | ||||||||
\(963\) | −4.83392 | − | 15.3297i | −0.155771 | − | 0.493994i | ||||
\(964\) | − | 46.0562i | − | 1.48337i | ||||||
\(965\) | −2.82362 | −0.0908956 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.5930 | −1.11244 | −0.556218 | − | 0.831036i | \(-0.687748\pi\) | ||||
−0.556218 | + | 0.831036i | \(0.687748\pi\) | |||||||
\(968\) | 5.80556i | 0.186598i | ||||||||
\(969\) | −0.980937 | − | 6.37266i | −0.0315122 | − | 0.204719i | ||||
\(970\) | −26.6287 | −0.854995 | ||||||||
\(971\) | −4.24492 | −0.136226 | −0.0681129 | − | 0.997678i | \(-0.521698\pi\) | ||||
−0.0681129 | + | 0.997678i | \(0.521698\pi\) | |||||||
\(972\) | −25.3962 | + | 24.3150i | −0.814583 | + | 0.779903i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 66.4407i | − | 2.12890i | ||||||
\(975\) | 0.168300 | + | 1.09336i | 0.00538992 | + | 0.0350156i | ||||
\(976\) | − | 17.7488i | − | 0.568125i | ||||||
\(977\) | 38.8911i | 1.24424i | 0.782924 | + | 0.622118i | \(0.213727\pi\) | ||||
−0.782924 | + | 0.622118i | \(0.786273\pi\) | |||||||
\(978\) | 9.06645 | + | 58.9002i | 0.289913 | + | 1.88342i | ||||
\(979\) | 64.7574i | 2.06966i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.88790 | − | 1.22597i | 0.124131 | − | 0.0391422i | ||||
\(982\) | −46.4155 | −1.48118 | ||||||||
\(983\) | 26.3768 | 0.841288 | 0.420644 | − | 0.907226i | \(-0.361804\pi\) | ||||
0.420644 | + | 0.907226i | \(0.361804\pi\) | |||||||
\(984\) | 0.570251 | + | 3.70464i | 0.0181790 | + | 0.118100i | ||||
\(985\) | − | 9.59675i | − | 0.305778i | ||||||
\(986\) | 18.3804 | 0.585352 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.29242 | −0.0411174 | ||||||||
\(989\) | 21.4285i | 0.681388i | ||||||||
\(990\) | 27.6936 | − | 8.73260i | 0.880159 | − | 0.277540i | ||||
\(991\) | −13.8167 | −0.438901 | −0.219450 | − | 0.975624i | \(-0.570426\pi\) | ||||
−0.219450 | + | 0.975624i | \(0.570426\pi\) | |||||||
\(992\) | 18.9750 | 0.602457 | ||||||||
\(993\) | −25.3501 | + | 3.90211i | −0.804460 | + | 0.123830i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.2141i | 0.387213i | ||||||||
\(996\) | −10.6706 | + | 1.64251i | −0.338109 | + | 0.0520449i | ||||
\(997\) | − | 61.3148i | − | 1.94186i | −0.239368 | − | 0.970929i | \(-0.576940\pi\) | ||
0.239368 | − | 0.970929i | \(-0.423060\pi\) | |||||||
\(998\) | 13.2314i | 0.418832i | ||||||||
\(999\) | −53.0444 | + | 26.1613i | −1.67825 | + | 0.827708i |
(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 | 735.2.b.d.146.7 | 8 | ||
3.2 | odd | 2 | 735.2.b.c.146.2 | 8 | |||
7.2 | even | 3 | 105.2.s.c.101.4 | yes | 8 | ||
7.3 | odd | 6 | 105.2.s.d.26.1 | yes | 8 | ||
7.4 | even | 3 | 735.2.s.l.656.1 | 8 | |||
7.5 | odd | 6 | 735.2.s.k.521.4 | 8 | |||
7.6 | odd | 2 | 735.2.b.c.146.7 | 8 | |||
21.2 | odd | 6 | 105.2.s.d.101.1 | yes | 8 | ||
21.5 | even | 6 | 735.2.s.l.521.1 | 8 | |||
21.11 | odd | 6 | 735.2.s.k.656.4 | 8 | |||
21.17 | even | 6 | 105.2.s.c.26.4 | ✓ | 8 | ||
21.20 | even | 2 | inner | 735.2.b.d.146.2 | 8 | ||
35.2 | odd | 12 | 525.2.q.f.374.7 | 16 | |||
35.3 | even | 12 | 525.2.q.e.299.2 | 16 | |||
35.9 | even | 6 | 525.2.t.g.101.1 | 8 | |||
35.17 | even | 12 | 525.2.q.e.299.7 | 16 | |||
35.23 | odd | 12 | 525.2.q.f.374.2 | 16 | |||
35.24 | odd | 6 | 525.2.t.f.26.4 | 8 | |||
105.2 | even | 12 | 525.2.q.e.374.2 | 16 | |||
105.17 | odd | 12 | 525.2.q.f.299.2 | 16 | |||
105.23 | even | 12 | 525.2.q.e.374.7 | 16 | |||
105.38 | odd | 12 | 525.2.q.f.299.7 | 16 | |||
105.44 | odd | 6 | 525.2.t.f.101.4 | 8 | |||
105.59 | even | 6 | 525.2.t.g.26.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.s.c.26.4 | ✓ | 8 | 21.17 | even | 6 | ||
105.2.s.c.101.4 | yes | 8 | 7.2 | even | 3 | ||
105.2.s.d.26.1 | yes | 8 | 7.3 | odd | 6 | ||
105.2.s.d.101.1 | yes | 8 | 21.2 | odd | 6 | ||
525.2.q.e.299.2 | 16 | 35.3 | even | 12 | |||
525.2.q.e.299.7 | 16 | 35.17 | even | 12 | |||
525.2.q.e.374.2 | 16 | 105.2 | even | 12 | |||
525.2.q.e.374.7 | 16 | 105.23 | even | 12 | |||
525.2.q.f.299.2 | 16 | 105.17 | odd | 12 | |||
525.2.q.f.299.7 | 16 | 105.38 | odd | 12 | |||
525.2.q.f.374.2 | 16 | 35.23 | odd | 12 | |||
525.2.q.f.374.7 | 16 | 35.2 | odd | 12 | |||
525.2.t.f.26.4 | 8 | 35.24 | odd | 6 | |||
525.2.t.f.101.4 | 8 | 105.44 | odd | 6 | |||
525.2.t.g.26.1 | 8 | 105.59 | even | 6 | |||
525.2.t.g.101.1 | 8 | 35.9 | even | 6 | |||
735.2.b.c.146.2 | 8 | 3.2 | odd | 2 | |||
735.2.b.c.146.7 | 8 | 7.6 | odd | 2 | |||
735.2.b.d.146.2 | 8 | 21.20 | even | 2 | inner | ||
735.2.b.d.146.7 | 8 | 1.1 | even | 1 | trivial | ||
735.2.s.k.521.4 | 8 | 7.5 | odd | 6 | |||
735.2.s.k.656.4 | 8 | 21.11 | odd | 6 | |||
735.2.s.l.521.1 | 8 | 21.5 | even | 6 | |||
735.2.s.l.656.1 | 8 | 7.4 | even | 3 |