Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(2155,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3234.2155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.e (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: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2155.8 | ||
Character | \(\chi\) | \(=\) | 3234.2155 |
Dual form | 3234.2.e.c.2155.17 |
$q$-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 \(\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(1079\) | \(2059\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.357203i | 0.159746i | 0.996805 | + | 0.0798729i | \(0.0254515\pi\) | ||||
−0.996805 | + | 0.0798729i | \(0.974549\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.357203 | 0.112957 | ||||||||
\(11\) | −3.31411 | − | 0.129255i | −0.999240 | − | 0.0389718i | ||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 4.33393 | 1.20202 | 0.601008 | − | 0.799243i | \(-0.294766\pi\) | ||||
0.601008 | + | 0.799243i | \(0.294766\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.357203 | 0.0922293 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.347231 | 0.0842160 | 0.0421080 | − | 0.999113i | \(-0.486593\pi\) | ||||
0.0421080 | + | 0.999113i | \(0.486593\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −7.81849 | −1.79369 | −0.896843 | − | 0.442349i | \(-0.854145\pi\) | ||||
−0.896843 | + | 0.442349i | \(0.854145\pi\) | |||||||
\(20\) | − | 0.357203i | − | 0.0798729i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.129255 | + | 3.31411i | −0.0275572 | + | 0.706570i | ||||
\(23\) | 6.36865 | 1.32795 | 0.663977 | − | 0.747753i | \(-0.268867\pi\) | ||||
0.663977 | + | 0.747753i | \(0.268867\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 4.87241 | 0.974481 | ||||||||
\(26\) | − | 4.33393i | − | 0.849954i | ||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.67778i | 1.42573i | 0.701302 | + | 0.712864i | \(0.252602\pi\) | ||||
−0.701302 | + | 0.712864i | \(0.747398\pi\) | |||||||
\(30\) | − | 0.357203i | − | 0.0652160i | ||||||
\(31\) | 6.20254i | 1.11401i | 0.830510 | + | 0.557004i | \(0.188049\pi\) | ||||
−0.830510 | + | 0.557004i | \(0.811951\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −0.129255 | + | 3.31411i | −0.0225004 | + | 0.576912i | ||||
\(34\) | − | 0.347231i | − | 0.0595497i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −8.95377 | −1.47199 | −0.735995 | − | 0.676987i | \(-0.763285\pi\) | ||||
−0.735995 | + | 0.676987i | \(0.763285\pi\) | |||||||
\(38\) | 7.81849i | 1.26833i | ||||||||
\(39\) | − | 4.33393i | − | 0.693985i | ||||||
\(40\) | −0.357203 | −0.0564787 | ||||||||
\(41\) | 5.43717 | 0.849143 | 0.424572 | − | 0.905394i | \(-0.360425\pi\) | ||||
0.424572 | + | 0.905394i | \(0.360425\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.91740i | − | 0.444899i | −0.974944 | − | 0.222450i | \(-0.928595\pi\) | ||
0.974944 | − | 0.222450i | \(-0.0714053\pi\) | |||||||
\(44\) | 3.31411 | + | 0.129255i | 0.499620 | + | 0.0194859i | ||||
\(45\) | − | 0.357203i | − | 0.0532486i | ||||||
\(46\) | − | 6.36865i | − | 0.939006i | ||||||
\(47\) | 3.84135i | 0.560318i | 0.959954 | + | 0.280159i | \(0.0903872\pi\) | ||||
−0.959954 | + | 0.280159i | \(0.909613\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 4.87241i | − | 0.689062i | ||||||
\(51\) | − | 0.347231i | − | 0.0486221i | ||||||
\(52\) | −4.33393 | −0.601008 | ||||||||
\(53\) | −2.73623 | −0.375850 | −0.187925 | − | 0.982183i | \(-0.560176\pi\) | ||||
−0.187925 | + | 0.982183i | \(0.560176\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.0461702 | − | 1.18381i | 0.00622558 | − | 0.159624i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.81849i | 1.03558i | ||||||||
\(58\) | 7.67778 | 1.00814 | ||||||||
\(59\) | 0.911386i | 0.118652i | 0.998239 | + | 0.0593261i | \(0.0188952\pi\) | ||||
−0.998239 | + | 0.0593261i | \(0.981105\pi\) | |||||||
\(60\) | −0.357203 | −0.0461147 | ||||||||
\(61\) | 12.4897 | 1.59914 | 0.799570 | − | 0.600572i | \(-0.205061\pi\) | ||||
0.799570 | + | 0.600572i | \(0.205061\pi\) | |||||||
\(62\) | 6.20254 | 0.787723 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.54809i | 0.192017i | ||||||||
\(66\) | 3.31411 | + | 0.129255i | 0.407938 | + | 0.0159102i | ||||
\(67\) | −13.6448 | −1.66697 | −0.833487 | − | 0.552538i | \(-0.813659\pi\) | ||||
−0.833487 | + | 0.552538i | \(0.813659\pi\) | |||||||
\(68\) | −0.347231 | −0.0421080 | ||||||||
\(69\) | − | 6.36865i | − | 0.766695i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.18162 | 0.733623 | 0.366812 | − | 0.930295i | \(-0.380449\pi\) | ||||
0.366812 | + | 0.930295i | \(0.380449\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | 11.4503 | 1.34015 | 0.670076 | − | 0.742292i | \(-0.266261\pi\) | ||||
0.670076 | + | 0.742292i | \(0.266261\pi\) | |||||||
\(74\) | 8.95377i | 1.04085i | ||||||||
\(75\) | − | 4.87241i | − | 0.562617i | ||||||
\(76\) | 7.81849 | 0.896843 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.33393 | −0.490721 | ||||||||
\(79\) | − | 6.65938i | − | 0.749238i | −0.927179 | − | 0.374619i | \(-0.877773\pi\) | ||
0.927179 | − | 0.374619i | \(-0.122227\pi\) | |||||||
\(80\) | 0.357203i | 0.0399365i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 5.43717i | − | 0.600435i | ||||||
\(83\) | 16.7247 | 1.83577 | 0.917886 | − | 0.396845i | \(-0.129895\pi\) | ||||
0.917886 | + | 0.396845i | \(0.129895\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.124032i | 0.0134531i | ||||||||
\(86\) | −2.91740 | −0.314591 | ||||||||
\(87\) | 7.67778 | 0.823145 | ||||||||
\(88\) | 0.129255 | − | 3.31411i | 0.0137786 | − | 0.353285i | ||||
\(89\) | 14.5026i | 1.53728i | 0.639684 | + | 0.768638i | \(0.279065\pi\) | ||||
−0.639684 | + | 0.768638i | \(0.720935\pi\) | |||||||
\(90\) | −0.357203 | −0.0376525 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.36865 | −0.663977 | ||||||||
\(93\) | 6.20254 | 0.643173 | ||||||||
\(94\) | 3.84135 | 0.396205 | ||||||||
\(95\) | − | 2.79279i | − | 0.286534i | ||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 18.1486i | 1.84271i | 0.388725 | + | 0.921354i | \(0.372915\pi\) | ||||
−0.388725 | + | 0.921354i | \(0.627085\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.31411 | + | 0.129255i | 0.333080 | + | 0.0129906i | ||||
\(100\) | −4.87241 | −0.487241 | ||||||||
\(101\) | −7.40672 | −0.736996 | −0.368498 | − | 0.929629i | \(-0.620128\pi\) | ||||
−0.368498 | + | 0.929629i | \(0.620128\pi\) | |||||||
\(102\) | −0.347231 | −0.0343810 | ||||||||
\(103\) | 0.972851i | 0.0958579i | 0.998851 | + | 0.0479289i | \(0.0152621\pi\) | ||||
−0.998851 | + | 0.0479289i | \(0.984738\pi\) | |||||||
\(104\) | 4.33393i | 0.424977i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.73623i | 0.265766i | ||||||||
\(107\) | − | 4.11580i | − | 0.397889i | −0.980011 | − | 0.198945i | \(-0.936249\pi\) | ||
0.980011 | − | 0.198945i | \(-0.0637514\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | − | 9.36206i | − | 0.896723i | −0.893852 | − | 0.448361i | \(-0.852008\pi\) | ||
0.893852 | − | 0.448361i | \(-0.147992\pi\) | |||||||
\(110\) | −1.18381 | − | 0.0461702i | −0.112872 | − | 0.00440215i | ||||
\(111\) | 8.95377i | 0.849854i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.9856 | 1.31566 | 0.657828 | − | 0.753168i | \(-0.271475\pi\) | ||||
0.657828 | + | 0.753168i | \(0.271475\pi\) | |||||||
\(114\) | 7.81849 | 0.732269 | ||||||||
\(115\) | 2.27490i | 0.212135i | ||||||||
\(116\) | − | 7.67778i | − | 0.712864i | ||||||
\(117\) | −4.33393 | −0.400672 | ||||||||
\(118\) | 0.911386 | 0.0838998 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.357203i | 0.0326080i | ||||||||
\(121\) | 10.9666 | + | 0.856728i | 0.996962 | + | 0.0778844i | ||||
\(122\) | − | 12.4897i | − | 1.13076i | ||||||
\(123\) | − | 5.43717i | − | 0.490253i | ||||||
\(124\) | − | 6.20254i | − | 0.557004i | ||||||
\(125\) | 3.52645i | 0.315415i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.1853i | 1.34748i | 0.738970 | + | 0.673739i | \(0.235313\pi\) | ||||
−0.738970 | + | 0.673739i | \(0.764687\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −2.91740 | −0.256863 | ||||||||
\(130\) | 1.54809 | 0.135777 | ||||||||
\(131\) | 15.1562 | 1.32420 | 0.662100 | − | 0.749416i | \(-0.269665\pi\) | ||||
0.662100 | + | 0.749416i | \(0.269665\pi\) | |||||||
\(132\) | 0.129255 | − | 3.31411i | 0.0112502 | − | 0.288456i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.6448i | 1.17873i | ||||||||
\(135\) | −0.357203 | −0.0307431 | ||||||||
\(136\) | 0.347231i | 0.0297748i | ||||||||
\(137\) | 13.2508 | 1.13210 | 0.566048 | − | 0.824373i | \(-0.308472\pi\) | ||||
0.566048 | + | 0.824373i | \(0.308472\pi\) | |||||||
\(138\) | −6.36865 | −0.542135 | ||||||||
\(139\) | 2.10063 | 0.178173 | 0.0890866 | − | 0.996024i | \(-0.471605\pi\) | ||||
0.0890866 | + | 0.996024i | \(0.471605\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.84135 | 0.323500 | ||||||||
\(142\) | − | 6.18162i | − | 0.518750i | ||||||
\(143\) | −14.3631 | − | 0.560182i | −1.20110 | − | 0.0468448i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −2.74252 | −0.227754 | ||||||||
\(146\) | − | 11.4503i | − | 0.947631i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.95377 | 0.735995 | ||||||||
\(149\) | − | 21.4377i | − | 1.75624i | −0.478439 | − | 0.878121i | \(-0.658797\pi\) | ||
0.478439 | − | 0.878121i | \(-0.341203\pi\) | |||||||
\(150\) | −4.87241 | −0.397830 | ||||||||
\(151\) | − | 19.3147i | − | 1.57181i | −0.618347 | − | 0.785905i | \(-0.712197\pi\) | ||
0.618347 | − | 0.785905i | \(-0.287803\pi\) | |||||||
\(152\) | − | 7.81849i | − | 0.634164i | ||||||
\(153\) | −0.347231 | −0.0280720 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.21556 | −0.177958 | ||||||||
\(156\) | 4.33393i | 0.346992i | ||||||||
\(157\) | 17.5668i | 1.40198i | 0.713170 | + | 0.700991i | \(0.247259\pi\) | ||||
−0.713170 | + | 0.700991i | \(0.752741\pi\) | |||||||
\(158\) | −6.65938 | −0.529792 | ||||||||
\(159\) | 2.73623i | 0.216997i | ||||||||
\(160\) | 0.357203 | 0.0282393 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −13.7943 | −1.08046 | −0.540228 | − | 0.841519i | \(-0.681662\pi\) | ||||
−0.540228 | + | 0.841519i | \(0.681662\pi\) | |||||||
\(164\) | −5.43717 | −0.424572 | ||||||||
\(165\) | −1.18381 | − | 0.0461702i | −0.0921592 | − | 0.00359434i | ||||
\(166\) | − | 16.7247i | − | 1.29809i | ||||||
\(167\) | 8.30859 | 0.642938 | 0.321469 | − | 0.946920i | \(-0.395823\pi\) | ||||
0.321469 | + | 0.946920i | \(0.395823\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.78297 | 0.444844 | ||||||||
\(170\) | 0.124032 | 0.00951281 | ||||||||
\(171\) | 7.81849 | 0.597895 | ||||||||
\(172\) | 2.91740i | 0.222450i | ||||||||
\(173\) | 9.78367 | 0.743839 | 0.371920 | − | 0.928265i | \(-0.378700\pi\) | ||||
0.371920 | + | 0.928265i | \(0.378700\pi\) | |||||||
\(174\) | − | 7.67778i | − | 0.582051i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.31411 | − | 0.129255i | −0.249810 | − | 0.00974295i | ||||
\(177\) | 0.911386 | 0.0685039 | ||||||||
\(178\) | 14.5026 | 1.08702 | ||||||||
\(179\) | 5.65887 | 0.422964 | 0.211482 | − | 0.977382i | \(-0.432171\pi\) | ||||
0.211482 | + | 0.977382i | \(0.432171\pi\) | |||||||
\(180\) | 0.357203i | 0.0266243i | ||||||||
\(181\) | − | 13.6419i | − | 1.01399i | −0.861949 | − | 0.506995i | \(-0.830756\pi\) | ||
0.861949 | − | 0.506995i | \(-0.169244\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 12.4897i | − | 0.923264i | ||||||
\(184\) | 6.36865i | 0.469503i | ||||||||
\(185\) | − | 3.19831i | − | 0.235144i | ||||||
\(186\) | − | 6.20254i | − | 0.454792i | ||||||
\(187\) | −1.15076 | − | 0.0448813i | −0.0841520 | − | 0.00328205i | ||||
\(188\) | − | 3.84135i | − | 0.280159i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.79279 | −0.202610 | ||||||||
\(191\) | −4.61622 | −0.334018 | −0.167009 | − | 0.985955i | \(-0.553411\pi\) | ||||
−0.167009 | + | 0.985955i | \(0.553411\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | 5.24602i | 0.377617i | 0.982014 | + | 0.188809i | \(0.0604626\pi\) | ||||
−0.982014 | + | 0.188809i | \(0.939537\pi\) | |||||||
\(194\) | 18.1486 | 1.30299 | ||||||||
\(195\) | 1.54809 | 0.110861 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.35695i | − | 0.167926i | −0.996469 | − | 0.0839629i | \(-0.973242\pi\) | ||
0.996469 | − | 0.0839629i | \(-0.0267577\pi\) | |||||||
\(198\) | 0.129255 | − | 3.31411i | 0.00918574 | − | 0.235523i | ||||
\(199\) | − | 4.46393i | − | 0.316440i | −0.987404 | − | 0.158220i | \(-0.949424\pi\) | ||
0.987404 | − | 0.158220i | \(-0.0505755\pi\) | |||||||
\(200\) | 4.87241i | 0.344531i | ||||||||
\(201\) | 13.6448i | 0.962428i | ||||||||
\(202\) | 7.40672i | 0.521135i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.347231i | 0.0243111i | ||||||||
\(205\) | 1.94217i | 0.135647i | ||||||||
\(206\) | 0.972851 | 0.0677817 | ||||||||
\(207\) | −6.36865 | −0.442652 | ||||||||
\(208\) | 4.33393 | 0.300504 | ||||||||
\(209\) | 25.9113 | + | 1.01058i | 1.79232 | + | 0.0699032i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.7624i | 0.878602i | 0.898340 | + | 0.439301i | \(0.144774\pi\) | ||||
−0.898340 | + | 0.439301i | \(0.855226\pi\) | |||||||
\(212\) | 2.73623 | 0.187925 | ||||||||
\(213\) | − | 6.18162i | − | 0.423558i | ||||||
\(214\) | −4.11580 | −0.281350 | ||||||||
\(215\) | 1.04210 | 0.0710708 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.36206 | −0.634079 | ||||||||
\(219\) | − | 11.4503i | − | 0.773737i | ||||||
\(220\) | −0.0461702 | + | 1.18381i | −0.00311279 | + | 0.0798122i | ||||
\(221\) | 1.50488 | 0.101229 | ||||||||
\(222\) | 8.95377 | 0.600937 | ||||||||
\(223\) | 8.18197i | 0.547905i | 0.961743 | + | 0.273953i | \(0.0883311\pi\) | ||||
−0.961743 | + | 0.273953i | \(0.911669\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.87241 | −0.324827 | ||||||||
\(226\) | − | 13.9856i | − | 0.930310i | ||||||
\(227\) | −3.26368 | −0.216618 | −0.108309 | − | 0.994117i | \(-0.534544\pi\) | ||||
−0.108309 | + | 0.994117i | \(0.534544\pi\) | |||||||
\(228\) | − | 7.81849i | − | 0.517792i | ||||||
\(229\) | 21.9790i | 1.45241i | 0.687476 | + | 0.726207i | \(0.258719\pi\) | ||||
−0.687476 | + | 0.726207i | \(0.741281\pi\) | |||||||
\(230\) | 2.27490 | 0.150002 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.67778 | −0.504071 | ||||||||
\(233\) | 17.7061i | 1.15996i | 0.814630 | + | 0.579981i | \(0.196940\pi\) | ||||
−0.814630 | + | 0.579981i | \(0.803060\pi\) | |||||||
\(234\) | 4.33393i | 0.283318i | ||||||||
\(235\) | −1.37214 | −0.0895085 | ||||||||
\(236\) | − | 0.911386i | − | 0.0593261i | ||||||
\(237\) | −6.65938 | −0.432573 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.53011i | 0.163659i | 0.996646 | + | 0.0818296i | \(0.0260763\pi\) | ||||
−0.996646 | + | 0.0818296i | \(0.973924\pi\) | |||||||
\(240\) | 0.357203 | 0.0230573 | ||||||||
\(241\) | 1.93061 | 0.124362 | 0.0621809 | − | 0.998065i | \(-0.480194\pi\) | ||||
0.0621809 | + | 0.998065i | \(0.480194\pi\) | |||||||
\(242\) | 0.856728 | − | 10.9666i | 0.0550726 | − | 0.704959i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −12.4897 | −0.799570 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.43717 | −0.346661 | ||||||||
\(247\) | −33.8848 | −2.15604 | ||||||||
\(248\) | −6.20254 | −0.393862 | ||||||||
\(249\) | − | 16.7247i | − | 1.05988i | ||||||
\(250\) | 3.52645 | 0.223032 | ||||||||
\(251\) | − | 24.7683i | − | 1.56336i | −0.623678 | − | 0.781681i | \(-0.714362\pi\) | ||
0.623678 | − | 0.781681i | \(-0.285638\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.1064 | − | 0.823179i | −1.32695 | − | 0.0517528i | ||||
\(254\) | 15.1853 | 0.952810 | ||||||||
\(255\) | 0.124032 | 0.00776718 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 4.66839i | − | 0.291206i | −0.989343 | − | 0.145603i | \(-0.953488\pi\) | ||
0.989343 | − | 0.145603i | \(-0.0465123\pi\) | |||||||
\(258\) | 2.91740i | 0.181629i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 1.54809i | − | 0.0960086i | ||||||
\(261\) | − | 7.67778i | − | 0.475243i | ||||||
\(262\) | − | 15.1562i | − | 0.936351i | ||||||
\(263\) | 17.4163i | 1.07394i | 0.843602 | + | 0.536968i | \(0.180430\pi\) | ||||
−0.843602 | + | 0.536968i | \(0.819570\pi\) | |||||||
\(264\) | −3.31411 | − | 0.129255i | −0.203969 | − | 0.00795509i | ||||
\(265\) | − | 0.977388i | − | 0.0600405i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.5026 | 0.887547 | ||||||||
\(268\) | 13.6448 | 0.833487 | ||||||||
\(269\) | − | 9.65915i | − | 0.588929i | −0.955662 | − | 0.294464i | \(-0.904859\pi\) | ||
0.955662 | − | 0.294464i | \(-0.0951413\pi\) | |||||||
\(270\) | 0.357203i | 0.0217387i | ||||||||
\(271\) | 2.73625 | 0.166215 | 0.0831076 | − | 0.996541i | \(-0.473515\pi\) | ||||
0.0831076 | + | 0.996541i | \(0.473515\pi\) | |||||||
\(272\) | 0.347231 | 0.0210540 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 13.2508i | − | 0.800512i | ||||||
\(275\) | −16.1477 | − | 0.629782i | −0.973741 | − | 0.0379773i | ||||
\(276\) | 6.36865i | 0.383348i | ||||||||
\(277\) | − | 22.9739i | − | 1.38037i | −0.723634 | − | 0.690184i | \(-0.757530\pi\) | ||
0.723634 | − | 0.690184i | \(-0.242470\pi\) | |||||||
\(278\) | − | 2.10063i | − | 0.125987i | ||||||
\(279\) | − | 6.20254i | − | 0.371336i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.8340i | 0.705954i | 0.935632 | + | 0.352977i | \(0.114831\pi\) | ||||
−0.935632 | + | 0.352977i | \(0.885169\pi\) | |||||||
\(282\) | − | 3.84135i | − | 0.228749i | ||||||
\(283\) | −2.38857 | −0.141985 | −0.0709927 | − | 0.997477i | \(-0.522617\pi\) | ||||
−0.0709927 | + | 0.997477i | \(0.522617\pi\) | |||||||
\(284\) | −6.18162 | −0.366812 | ||||||||
\(285\) | −2.79279 | −0.165430 | ||||||||
\(286\) | −0.560182 | + | 14.3631i | −0.0331243 | + | 0.849308i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −16.8794 | −0.992908 | ||||||||
\(290\) | 2.74252i | 0.161047i | ||||||||
\(291\) | 18.1486 | 1.06389 | ||||||||
\(292\) | −11.4503 | −0.670076 | ||||||||
\(293\) | −21.8292 | −1.27528 | −0.637639 | − | 0.770335i | \(-0.720089\pi\) | ||||
−0.637639 | + | 0.770335i | \(0.720089\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.325549 | −0.0189542 | ||||||||
\(296\) | − | 8.95377i | − | 0.520427i | ||||||
\(297\) | 0.129255 | − | 3.31411i | 0.00750013 | − | 0.192304i | ||||
\(298\) | −21.4377 | −1.24185 | ||||||||
\(299\) | 27.6013 | 1.59622 | ||||||||
\(300\) | 4.87241i | 0.281309i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −19.3147 | −1.11144 | ||||||||
\(303\) | 7.40672i | 0.425505i | ||||||||
\(304\) | −7.81849 | −0.448421 | ||||||||
\(305\) | 4.46135i | 0.255456i | ||||||||
\(306\) | 0.347231i | 0.0198499i | ||||||||
\(307\) | 5.28799 | 0.301801 | 0.150901 | − | 0.988549i | \(-0.451783\pi\) | ||||
0.150901 | + | 0.988549i | \(0.451783\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.972851 | 0.0553436 | ||||||||
\(310\) | 2.21556i | 0.125836i | ||||||||
\(311\) | 7.26261i | 0.411825i | 0.978570 | + | 0.205912i | \(0.0660162\pi\) | ||||
−0.978570 | + | 0.205912i | \(0.933984\pi\) | |||||||
\(312\) | 4.33393 | 0.245361 | ||||||||
\(313\) | 4.59656i | 0.259813i | 0.991526 | + | 0.129906i | \(0.0414677\pi\) | ||||
−0.991526 | + | 0.129906i | \(0.958532\pi\) | |||||||
\(314\) | 17.5668 | 0.991351 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.65938i | 0.374619i | ||||||||
\(317\) | 13.4968 | 0.758059 | 0.379029 | − | 0.925385i | \(-0.376258\pi\) | ||||
0.379029 | + | 0.925385i | \(0.376258\pi\) | |||||||
\(318\) | 2.73623 | 0.153440 | ||||||||
\(319\) | 0.992391 | − | 25.4450i | 0.0555632 | − | 1.42465i | ||||
\(320\) | − | 0.357203i | − | 0.0199682i | ||||||
\(321\) | −4.11580 | −0.229721 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.71483 | −0.151057 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 21.1167 | 1.17134 | ||||||||
\(326\) | 13.7943i | 0.763998i | ||||||||
\(327\) | −9.36206 | −0.517723 | ||||||||
\(328\) | 5.43717i | 0.300217i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.0461702 | + | 1.18381i | −0.00254158 | + | 0.0651664i | ||||
\(331\) | −6.39942 | −0.351744 | −0.175872 | − | 0.984413i | \(-0.556275\pi\) | ||||
−0.175872 | + | 0.984413i | \(0.556275\pi\) | |||||||
\(332\) | −16.7247 | −0.917886 | ||||||||
\(333\) | 8.95377 | 0.490663 | ||||||||
\(334\) | − | 8.30859i | − | 0.454626i | ||||||
\(335\) | − | 4.87395i | − | 0.266292i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 13.2274i | − | 0.720544i | −0.932847 | − | 0.360272i | \(-0.882684\pi\) | ||
0.932847 | − | 0.360272i | \(-0.117316\pi\) | |||||||
\(338\) | − | 5.78297i | − | 0.314552i | ||||||
\(339\) | − | 13.9856i | − | 0.759595i | ||||||
\(340\) | − | 0.124032i | − | 0.00672657i | ||||||
\(341\) | 0.801708 | − | 20.5559i | 0.0434149 | − | 1.11316i | ||||
\(342\) | − | 7.81849i | − | 0.422776i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.91740 | 0.157296 | ||||||||
\(345\) | 2.27490 | 0.122476 | ||||||||
\(346\) | − | 9.78367i | − | 0.525974i | ||||||
\(347\) | 30.5044i | 1.63756i | 0.574105 | + | 0.818782i | \(0.305350\pi\) | ||||
−0.574105 | + | 0.818782i | \(0.694650\pi\) | |||||||
\(348\) | −7.67778 | −0.411572 | ||||||||
\(349\) | −0.480174 | −0.0257031 | −0.0128516 | − | 0.999917i | \(-0.504091\pi\) | ||||
−0.0128516 | + | 0.999917i | \(0.504091\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.33393i | 0.231328i | ||||||||
\(352\) | −0.129255 | + | 3.31411i | −0.00688931 | + | 0.176642i | ||||
\(353\) | − | 4.03853i | − | 0.214949i | −0.994208 | − | 0.107475i | \(-0.965724\pi\) | ||
0.994208 | − | 0.107475i | \(-0.0342764\pi\) | |||||||
\(354\) | − | 0.911386i | − | 0.0484396i | ||||||
\(355\) | 2.20809i | 0.117193i | ||||||||
\(356\) | − | 14.5026i | − | 0.768638i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 5.65887i | − | 0.299081i | ||||||
\(359\) | 6.57967i | 0.347262i | 0.984811 | + | 0.173631i | \(0.0555500\pi\) | ||||
−0.984811 | + | 0.173631i | \(0.944450\pi\) | |||||||
\(360\) | 0.357203 | 0.0188262 | ||||||||
\(361\) | 42.1289 | 2.21731 | ||||||||
\(362\) | −13.6419 | −0.717000 | ||||||||
\(363\) | 0.856728 | − | 10.9666i | 0.0449666 | − | 0.575597i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.09006i | 0.214084i | ||||||||
\(366\) | −12.4897 | −0.652846 | ||||||||
\(367\) | 11.0084i | 0.574632i | 0.957836 | + | 0.287316i | \(0.0927630\pi\) | ||||
−0.957836 | + | 0.287316i | \(0.907237\pi\) | |||||||
\(368\) | 6.36865 | 0.331989 | ||||||||
\(369\) | −5.43717 | −0.283048 | ||||||||
\(370\) | −3.19831 | −0.166272 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.20254 | −0.321587 | ||||||||
\(373\) | − | 25.8257i | − | 1.33720i | −0.743621 | − | 0.668601i | \(-0.766893\pi\) | ||
0.743621 | − | 0.668601i | \(-0.233107\pi\) | |||||||
\(374\) | −0.0448813 | + | 1.15076i | −0.00232076 | + | 0.0595044i | ||||
\(375\) | 3.52645 | 0.182105 | ||||||||
\(376\) | −3.84135 | −0.198102 | ||||||||
\(377\) | 33.2750i | 1.71375i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.0073 | 1.18180 | 0.590902 | − | 0.806743i | \(-0.298772\pi\) | ||||
0.590902 | + | 0.806743i | \(0.298772\pi\) | |||||||
\(380\) | 2.79279i | 0.143267i | ||||||||
\(381\) | 15.1853 | 0.777966 | ||||||||
\(382\) | 4.61622i | 0.236186i | ||||||||
\(383\) | 17.2499i | 0.881429i | 0.897647 | + | 0.440715i | \(0.145275\pi\) | ||||
−0.897647 | + | 0.440715i | \(0.854725\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.24602 | 0.267016 | ||||||||
\(387\) | 2.91740i | 0.148300i | ||||||||
\(388\) | − | 18.1486i | − | 0.921354i | ||||||
\(389\) | 18.5596 | 0.941011 | 0.470506 | − | 0.882397i | \(-0.344072\pi\) | ||||
0.470506 | + | 0.882397i | \(0.344072\pi\) | |||||||
\(390\) | − | 1.54809i | − | 0.0783907i | ||||||
\(391\) | 2.21139 | 0.111835 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 15.1562i | − | 0.764527i | ||||||
\(394\) | −2.35695 | −0.118741 | ||||||||
\(395\) | 2.37875 | 0.119688 | ||||||||
\(396\) | −3.31411 | − | 0.129255i | −0.166540 | − | 0.00649530i | ||||
\(397\) | − | 6.86138i | − | 0.344363i | −0.985065 | − | 0.172181i | \(-0.944918\pi\) | ||
0.985065 | − | 0.172181i | \(-0.0550815\pi\) | |||||||
\(398\) | −4.46393 | −0.223757 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.87241 | 0.243620 | ||||||||
\(401\) | 9.50963 | 0.474888 | 0.237444 | − | 0.971401i | \(-0.423690\pi\) | ||||
0.237444 | + | 0.971401i | \(0.423690\pi\) | |||||||
\(402\) | 13.6448 | 0.680540 | ||||||||
\(403\) | 26.8814i | 1.33906i | ||||||||
\(404\) | 7.40672 | 0.368498 | ||||||||
\(405\) | 0.357203i | 0.0177495i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.6737 | + | 1.15732i | 1.47087 | + | 0.0573661i | ||||
\(408\) | 0.347231 | 0.0171905 | ||||||||
\(409\) | −4.61520 | −0.228207 | −0.114103 | − | 0.993469i | \(-0.536400\pi\) | ||||
−0.114103 | + | 0.993469i | \(0.536400\pi\) | |||||||
\(410\) | 1.94217 | 0.0959170 | ||||||||
\(411\) | − | 13.2508i | − | 0.653615i | ||||||
\(412\) | − | 0.972851i | − | 0.0479289i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.36865i | 0.313002i | ||||||||
\(415\) | 5.97410i | 0.293257i | ||||||||
\(416\) | − | 4.33393i | − | 0.212489i | ||||||
\(417\) | − | 2.10063i | − | 0.102868i | ||||||
\(418\) | 1.01058 | − | 25.9113i | 0.0494290 | − | 1.26736i | ||||
\(419\) | 15.9343i | 0.778442i | 0.921144 | + | 0.389221i | \(0.127256\pi\) | ||||
−0.921144 | + | 0.389221i | \(0.872744\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.4154 | −0.946247 | −0.473123 | − | 0.880996i | \(-0.656873\pi\) | ||||
−0.473123 | + | 0.880996i | \(0.656873\pi\) | |||||||
\(422\) | 12.7624 | 0.621266 | ||||||||
\(423\) | − | 3.84135i | − | 0.186773i | ||||||
\(424\) | − | 2.73623i | − | 0.132883i | ||||||
\(425\) | 1.69185 | 0.0820669 | ||||||||
\(426\) | −6.18162 | −0.299501 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.11580i | 0.198945i | ||||||||
\(429\) | −0.560182 | + | 14.3631i | −0.0270458 | + | 0.693457i | ||||
\(430\) | − | 1.04210i | − | 0.0502547i | ||||||
\(431\) | 7.41070i | 0.356961i | 0.983943 | + | 0.178480i | \(0.0571181\pi\) | ||||
−0.983943 | + | 0.178480i | \(0.942882\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − | 19.3089i | − | 0.927928i | −0.885854 | − | 0.463964i | \(-0.846427\pi\) | ||
0.885854 | − | 0.463964i | \(-0.153573\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.74252i | 0.131494i | ||||||||
\(436\) | 9.36206i | 0.448361i | ||||||||
\(437\) | −49.7932 | −2.38193 | ||||||||
\(438\) | −11.4503 | −0.547115 | ||||||||
\(439\) | −32.5688 | −1.55442 | −0.777212 | − | 0.629238i | \(-0.783367\pi\) | ||||
−0.777212 | + | 0.629238i | \(0.783367\pi\) | |||||||
\(440\) | 1.18381 | + | 0.0461702i | 0.0564358 | + | 0.00220108i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 1.50488i | − | 0.0715797i | ||||||
\(443\) | −29.8320 | −1.41736 | −0.708681 | − | 0.705529i | \(-0.750710\pi\) | ||||
−0.708681 | + | 0.705529i | \(0.750710\pi\) | |||||||
\(444\) | − | 8.95377i | − | 0.424927i | ||||||
\(445\) | −5.18038 | −0.245573 | ||||||||
\(446\) | 8.18197 | 0.387427 | ||||||||
\(447\) | −21.4377 | −1.01397 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.45126 | −0.210068 | −0.105034 | − | 0.994469i | \(-0.533495\pi\) | ||||
−0.105034 | + | 0.994469i | \(0.533495\pi\) | |||||||
\(450\) | 4.87241i | 0.229687i | ||||||||
\(451\) | −18.0194 | − | 0.702781i | −0.848498 | − | 0.0330926i | ||||
\(452\) | −13.9856 | −0.657828 | ||||||||
\(453\) | −19.3147 | −0.907485 | ||||||||
\(454\) | 3.26368i | 0.153172i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.81849 | −0.366135 | ||||||||
\(457\) | − | 27.1160i | − | 1.26843i | −0.773156 | − | 0.634216i | \(-0.781323\pi\) | ||
0.773156 | − | 0.634216i | \(-0.218677\pi\) | |||||||
\(458\) | 21.9790 | 1.02701 | ||||||||
\(459\) | 0.347231i | 0.0162074i | ||||||||
\(460\) | − | 2.27490i | − | 0.106068i | ||||||
\(461\) | 12.7571 | 0.594158 | 0.297079 | − | 0.954853i | \(-0.403987\pi\) | ||||
0.297079 | + | 0.954853i | \(0.403987\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.8679 | −1.24866 | −0.624329 | − | 0.781162i | \(-0.714627\pi\) | ||||
−0.624329 | + | 0.781162i | \(0.714627\pi\) | |||||||
\(464\) | 7.67778i | 0.356432i | ||||||||
\(465\) | 2.21556i | 0.102744i | ||||||||
\(466\) | 17.7061 | 0.820217 | ||||||||
\(467\) | 35.2058i | 1.62913i | 0.580073 | + | 0.814565i | \(0.303024\pi\) | ||||
−0.580073 | + | 0.814565i | \(0.696976\pi\) | |||||||
\(468\) | 4.33393 | 0.200336 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.37214i | 0.0632920i | ||||||||
\(471\) | 17.5668 | 0.809434 | ||||||||
\(472\) | −0.911386 | −0.0419499 | ||||||||
\(473\) | −0.377088 | + | 9.66857i | −0.0173385 | + | 0.444561i | ||||
\(474\) | 6.65938i | 0.305875i | ||||||||
\(475\) | −38.0949 | −1.74791 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.73623 | 0.125283 | ||||||||
\(478\) | 2.53011 | 0.115724 | ||||||||
\(479\) | 31.8131 | 1.45358 | 0.726789 | − | 0.686861i | \(-0.241012\pi\) | ||||
0.726789 | + | 0.686861i | \(0.241012\pi\) | |||||||
\(480\) | − | 0.357203i | − | 0.0163040i | ||||||
\(481\) | −38.8050 | −1.76936 | ||||||||
\(482\) | − | 1.93061i | − | 0.0879370i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9666 | − | 0.856728i | −0.498481 | − | 0.0389422i | ||||
\(485\) | −6.48271 | −0.294365 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −28.4612 | −1.28970 | −0.644849 | − | 0.764310i | \(-0.723080\pi\) | ||||
−0.644849 | + | 0.764310i | \(0.723080\pi\) | |||||||
\(488\) | 12.4897i | 0.565382i | ||||||||
\(489\) | 13.7943i | 0.623802i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.2454i | 1.54547i | 0.634727 | + | 0.772737i | \(0.281113\pi\) | ||||
−0.634727 | + | 0.772737i | \(0.718887\pi\) | |||||||
\(492\) | 5.43717i | 0.245127i | ||||||||
\(493\) | 2.66597i | 0.120069i | ||||||||
\(494\) | 33.8848i | 1.52455i | ||||||||
\(495\) | −0.0461702 | + | 1.18381i | −0.00207519 | + | 0.0532082i | ||||
\(496\) | 6.20254i | 0.278502i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −16.7247 | −0.749451 | ||||||||
\(499\) | −7.93504 | −0.355221 | −0.177611 | − | 0.984101i | \(-0.556837\pi\) | ||||
−0.177611 | + | 0.984101i | \(0.556837\pi\) | |||||||
\(500\) | − | 3.52645i | − | 0.157708i | ||||||
\(501\) | − | 8.30859i | − | 0.371200i | ||||||
\(502\) | −24.7683 | −1.10546 | ||||||||
\(503\) | −7.71704 | −0.344086 | −0.172043 | − | 0.985089i | \(-0.555037\pi\) | ||||
−0.172043 | + | 0.985089i | \(0.555037\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 2.64570i | − | 0.117732i | ||||||
\(506\) | −0.823179 | + | 21.1064i | −0.0365948 | + | 0.938293i | ||||
\(507\) | − | 5.78297i | − | 0.256831i | ||||||
\(508\) | − | 15.1853i | − | 0.673739i | ||||||
\(509\) | 33.2386i | 1.47328i | 0.676288 | + | 0.736638i | \(0.263588\pi\) | ||||
−0.676288 | + | 0.736638i | \(0.736412\pi\) | |||||||
\(510\) | − | 0.124032i | − | 0.00549222i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 7.81849i | − | 0.345195i | ||||||
\(514\) | −4.66839 | −0.205914 | ||||||||
\(515\) | −0.347505 | −0.0153129 | ||||||||
\(516\) | 2.91740 | 0.128431 | ||||||||
\(517\) | 0.496513 | − | 12.7306i | 0.0218366 | − | 0.559892i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 9.78367i | − | 0.429456i | ||||||
\(520\) | −1.54809 | −0.0678883 | ||||||||
\(521\) | − | 9.99903i | − | 0.438066i | −0.975717 | − | 0.219033i | \(-0.929710\pi\) | ||
0.975717 | − | 0.219033i | \(-0.0702902\pi\) | |||||||
\(522\) | −7.67778 | −0.336047 | ||||||||
\(523\) | 4.45341 | 0.194734 | 0.0973669 | − | 0.995249i | \(-0.468958\pi\) | ||||
0.0973669 | + | 0.995249i | \(0.468958\pi\) | |||||||
\(524\) | −15.1562 | −0.662100 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.4163 | 0.759388 | ||||||||
\(527\) | 2.15372i | 0.0938173i | ||||||||
\(528\) | −0.129255 | + | 3.31411i | −0.00562510 | + | 0.144228i | ||||
\(529\) | 17.5597 | 0.763464 | ||||||||
\(530\) | −0.977388 | −0.0424550 | ||||||||
\(531\) | − | 0.911386i | − | 0.0395508i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.5643 | 1.02068 | ||||||||
\(534\) | − | 14.5026i | − | 0.627590i | ||||||
\(535\) | 1.47017 | 0.0635611 | ||||||||
\(536\) | − | 13.6448i | − | 0.589365i | ||||||
\(537\) | − | 5.65887i | − | 0.244198i | ||||||
\(538\) | −9.65915 | −0.416436 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.357203 | 0.0153716 | ||||||||
\(541\) | 36.1740i | 1.55524i | 0.628732 | + | 0.777622i | \(0.283574\pi\) | ||||
−0.628732 | + | 0.777622i | \(0.716426\pi\) | |||||||
\(542\) | − | 2.73625i | − | 0.117532i | ||||||
\(543\) | −13.6419 | −0.585428 | ||||||||
\(544\) | − | 0.347231i | − | 0.0148874i | ||||||
\(545\) | 3.34415 | 0.143248 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 37.3673i | − | 1.59771i | −0.601523 | − | 0.798855i | \(-0.705439\pi\) | ||
0.601523 | − | 0.798855i | \(-0.294561\pi\) | |||||||
\(548\) | −13.2508 | −0.566048 | ||||||||
\(549\) | −12.4897 | −0.533047 | ||||||||
\(550\) | −0.629782 | + | 16.1477i | −0.0268540 | + | 0.688539i | ||||
\(551\) | − | 60.0287i | − | 2.55731i | ||||||
\(552\) | 6.36865 | 0.271068 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −22.9739 | −0.976068 | ||||||||
\(555\) | −3.19831 | −0.135761 | ||||||||
\(556\) | −2.10063 | −0.0890866 | ||||||||
\(557\) | 41.1608i | 1.74404i | 0.489470 | + | 0.872020i | \(0.337190\pi\) | ||||
−0.489470 | + | 0.872020i | \(0.662810\pi\) | |||||||
\(558\) | −6.20254 | −0.262574 | ||||||||
\(559\) | − | 12.6438i | − | 0.534776i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0448813 | + | 1.15076i | −0.00189489 | + | 0.0485852i | ||||
\(562\) | 11.8340 | 0.499185 | ||||||||
\(563\) | −19.1043 | −0.805151 | −0.402575 | − | 0.915387i | \(-0.631885\pi\) | ||||
−0.402575 | + | 0.915387i | \(0.631885\pi\) | |||||||
\(564\) | −3.84135 | −0.161750 | ||||||||
\(565\) | 4.99570i | 0.210171i | ||||||||
\(566\) | 2.38857i | 0.100399i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.18162i | 0.259375i | ||||||||
\(569\) | 42.6242i | 1.78690i | 0.449164 | + | 0.893449i | \(0.351722\pi\) | ||||
−0.449164 | + | 0.893449i | \(0.648278\pi\) | |||||||
\(570\) | 2.79279i | 0.116977i | ||||||||
\(571\) | 8.53860i | 0.357329i | 0.983910 | + | 0.178665i | \(0.0571777\pi\) | ||||
−0.983910 | + | 0.178665i | \(0.942822\pi\) | |||||||
\(572\) | 14.3631 | + | 0.560182i | 0.600552 | + | 0.0234224i | ||||
\(573\) | 4.61622i | 0.192845i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 31.0306 | 1.29407 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 31.5935i | 1.31525i | 0.753344 | + | 0.657627i | \(0.228440\pi\) | ||||
−0.753344 | + | 0.657627i | \(0.771560\pi\) | |||||||
\(578\) | 16.8794i | 0.702092i | ||||||||
\(579\) | 5.24602 | 0.218017 | ||||||||
\(580\) | 2.74252 | 0.113877 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 18.1486i | − | 0.752282i | ||||||
\(583\) | 9.06815 | + | 0.353671i | 0.375565 | + | 0.0146476i | ||||
\(584\) | 11.4503i | 0.473815i | ||||||||
\(585\) | − | 1.54809i | − | 0.0640057i | ||||||
\(586\) | 21.8292i | 0.901758i | ||||||||
\(587\) | − | 19.9085i | − | 0.821710i | −0.911701 | − | 0.410855i | \(-0.865230\pi\) | ||
0.911701 | − | 0.410855i | \(-0.134770\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 48.4945i | − | 1.99818i | ||||||
\(590\) | 0.325549i | 0.0134027i | ||||||||
\(591\) | −2.35695 | −0.0969520 | ||||||||
\(592\) | −8.95377 | −0.367998 | ||||||||
\(593\) | 34.5395 | 1.41837 | 0.709184 | − | 0.705023i | \(-0.249063\pi\) | ||||
0.709184 | + | 0.705023i | \(0.249063\pi\) | |||||||
\(594\) | −3.31411 | − | 0.129255i | −0.135979 | − | 0.00530339i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 21.4377i | 0.878121i | ||||||||
\(597\) | −4.46393 | −0.182697 | ||||||||
\(598\) | − | 27.6013i | − | 1.12870i | ||||||
\(599\) | −12.8576 | −0.525346 | −0.262673 | − | 0.964885i | \(-0.584604\pi\) | ||||
−0.262673 | + | 0.964885i | \(0.584604\pi\) | |||||||
\(600\) | 4.87241 | 0.198915 | ||||||||
\(601\) | 11.2038 | 0.457011 | 0.228505 | − | 0.973543i | \(-0.426616\pi\) | ||||
0.228505 | + | 0.973543i | \(0.426616\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.6448 | 0.555658 | ||||||||
\(604\) | 19.3147i | 0.785905i | ||||||||
\(605\) | −0.306026 | + | 3.91729i | −0.0124417 | + | 0.159261i | ||||
\(606\) | 7.40672 | 0.300877 | ||||||||
\(607\) | 3.49287 | 0.141771 | 0.0708857 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708857 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(608\) | 7.81849i | 0.317082i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.46135 | 0.180635 | ||||||||
\(611\) | 16.6481i | 0.673511i | ||||||||
\(612\) | 0.347231 | 0.0140360 | ||||||||
\(613\) | 31.2095i | 1.26054i | 0.776377 | + | 0.630269i | \(0.217056\pi\) | ||||
−0.776377 | + | 0.630269i | \(0.782944\pi\) | |||||||
\(614\) | − | 5.28799i | − | 0.213406i | ||||||
\(615\) | 1.94217 | 0.0783159 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.4070 | −1.42543 | −0.712717 | − | 0.701452i | \(-0.752536\pi\) | ||||
−0.712717 | + | 0.701452i | \(0.752536\pi\) | |||||||
\(618\) | − | 0.972851i | − | 0.0391338i | ||||||
\(619\) | − | 0.132999i | − | 0.00534570i | −0.999996 | − | 0.00267285i | \(-0.999149\pi\) | ||
0.999996 | − | 0.00267285i | \(-0.000850795\pi\) | |||||||
\(620\) | 2.21556 | 0.0889791 | ||||||||
\(621\) | 6.36865i | 0.255565i | ||||||||
\(622\) | 7.26261 | 0.291204 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 4.33393i | − | 0.173496i | ||||||
\(625\) | 23.1024 | 0.924095 | ||||||||
\(626\) | 4.59656 | 0.183715 | ||||||||
\(627\) | 1.01058 | − | 25.9113i | 0.0403586 | − | 1.03480i | ||||
\(628\) | − | 17.5668i | − | 0.700991i | ||||||
\(629\) | −3.10903 | −0.123965 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.18583 | 0.206445 | 0.103222 | − | 0.994658i | \(-0.467085\pi\) | ||||
0.103222 | + | 0.994658i | \(0.467085\pi\) | |||||||
\(632\) | 6.65938 | 0.264896 | ||||||||
\(633\) | 12.7624 | 0.507261 | ||||||||
\(634\) | − | 13.4968i | − | 0.536028i | ||||||
\(635\) | −5.42423 | −0.215254 | ||||||||
\(636\) | − | 2.73623i | − | 0.108499i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −25.4450 | − | 0.992391i | −1.00738 | − | 0.0392891i | ||||
\(639\) | −6.18162 | −0.244541 | ||||||||
\(640\) | −0.357203 | −0.0141197 | ||||||||
\(641\) | 13.0446 | 0.515232 | 0.257616 | − | 0.966247i | \(-0.417063\pi\) | ||||
0.257616 | + | 0.966247i | \(0.417063\pi\) | |||||||
\(642\) | 4.11580i | 0.162438i | ||||||||
\(643\) | 7.54506i | 0.297548i | 0.988871 | + | 0.148774i | \(0.0475327\pi\) | ||||
−0.988871 | + | 0.148774i | \(0.952467\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1.04210i | − | 0.0410328i | ||||||
\(646\) | 2.71483i | 0.106813i | ||||||||
\(647\) | 18.9501i | 0.745006i | 0.928031 | + | 0.372503i | \(0.121500\pi\) | ||||
−0.928031 | + | 0.372503i | \(0.878500\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 0.117801 | − | 3.02043i | 0.00462409 | − | 0.118562i | ||||
\(650\) | − | 21.1167i | − | 0.828264i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.7943 | 0.540228 | ||||||||
\(653\) | 16.3241 | 0.638810 | 0.319405 | − | 0.947618i | \(-0.396517\pi\) | ||||
0.319405 | + | 0.947618i | \(0.396517\pi\) | |||||||
\(654\) | 9.36206i | 0.366085i | ||||||||
\(655\) | 5.41382i | 0.211535i | ||||||||
\(656\) | 5.43717 | 0.212286 | ||||||||
\(657\) | −11.4503 | −0.446717 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 43.7066i | − | 1.70257i | −0.524706 | − | 0.851283i | \(-0.675825\pi\) | ||
0.524706 | − | 0.851283i | \(-0.324175\pi\) | |||||||
\(660\) | 1.18381 | + | 0.0461702i | 0.0460796 | + | 0.00179717i | ||||
\(661\) | 10.3498i | 0.402560i | 0.979534 | + | 0.201280i | \(0.0645101\pi\) | ||||
−0.979534 | + | 0.201280i | \(0.935490\pi\) | |||||||
\(662\) | 6.39942i | 0.248721i | ||||||||
\(663\) | − | 1.50488i | − | 0.0584446i | ||||||
\(664\) | 16.7247i | 0.649043i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 8.95377i | − | 0.346951i | ||||||
\(667\) | 48.8971i | 1.89330i | ||||||||
\(668\) | −8.30859 | −0.321469 | ||||||||
\(669\) | 8.18197 | 0.316333 | ||||||||
\(670\) | −4.87395 | −0.188297 | ||||||||
\(671\) | −41.3921 | − | 1.61435i | −1.59793 | − | 0.0623214i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.3241i | 1.32310i | 0.749902 | + | 0.661549i | \(0.230101\pi\) | ||||
−0.749902 | + | 0.661549i | \(0.769899\pi\) | |||||||
\(674\) | −13.2274 | −0.509502 | ||||||||
\(675\) | 4.87241i | 0.187539i | ||||||||
\(676\) | −5.78297 | −0.222422 | ||||||||
\(677\) | 18.1171 | 0.696298 | 0.348149 | − | 0.937439i | \(-0.386810\pi\) | ||||
0.348149 | + | 0.937439i | \(0.386810\pi\) | |||||||
\(678\) | −13.9856 | −0.537115 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.124032 | −0.00475641 | ||||||||
\(681\) | 3.26368i | 0.125064i | ||||||||
\(682\) | −20.5559 | − | 0.801708i | −0.787125 | − | 0.0306990i | ||||
\(683\) | 27.7424 | 1.06153 | 0.530767 | − | 0.847518i | \(-0.321904\pi\) | ||||
0.530767 | + | 0.847518i | \(0.321904\pi\) | |||||||
\(684\) | −7.81849 | −0.298948 | ||||||||
\(685\) | 4.73323i | 0.180848i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.9790 | 0.838552 | ||||||||
\(688\) | − | 2.91740i | − | 0.111225i | ||||||
\(689\) | −11.8586 | −0.451778 | ||||||||
\(690\) | − | 2.27490i | − | 0.0866039i | ||||||
\(691\) | 15.2646i | 0.580693i | 0.956922 | + | 0.290347i | \(0.0937706\pi\) | ||||
−0.956922 | + | 0.290347i | \(0.906229\pi\) | |||||||
\(692\) | −9.78367 | −0.371920 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.5044 | 1.15793 | ||||||||
\(695\) | 0.750351i | 0.0284624i | ||||||||
\(696\) | 7.67778i | 0.291026i | ||||||||
\(697\) | 1.88796 | 0.0715114 | ||||||||
\(698\) | 0.480174i | 0.0181749i | ||||||||
\(699\) | 17.7061 | 0.669704 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 7.78140i | − | 0.293900i | −0.989144 | − | 0.146950i | \(-0.953054\pi\) | ||
0.989144 | − | 0.146950i | \(-0.0469456\pi\) | |||||||
\(702\) | 4.33393 | 0.163574 | ||||||||
\(703\) | 70.0050 | 2.64029 | ||||||||
\(704\) | 3.31411 | + | 0.129255i | 0.124905 | + | 0.00487148i | ||||
\(705\) | 1.37214i | 0.0516777i | ||||||||
\(706\) | −4.03853 | −0.151992 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.911386 | −0.0342520 | ||||||||
\(709\) | −1.43232 | −0.0537919 | −0.0268960 | − | 0.999638i | \(-0.508562\pi\) | ||||
−0.0268960 | + | 0.999638i | \(0.508562\pi\) | |||||||
\(710\) | 2.20809 | 0.0828682 | ||||||||
\(711\) | 6.65938i | 0.249746i | ||||||||
\(712\) | −14.5026 | −0.543509 | ||||||||
\(713\) | 39.5018i | 1.47935i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.200098 | − | 5.13054i | 0.00748326 | − | 0.191871i | ||||
\(716\) | −5.65887 | −0.211482 | ||||||||
\(717\) | 2.53011 | 0.0944886 | ||||||||
\(718\) | 6.57967 | 0.245551 | ||||||||
\(719\) | − | 49.3021i | − | 1.83866i | −0.393491 | − | 0.919328i | \(-0.628733\pi\) | ||
0.393491 | − | 0.919328i | \(-0.371267\pi\) | |||||||
\(720\) | − | 0.357203i | − | 0.0133122i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 42.1289i | − | 1.56787i | ||||||
\(723\) | − | 1.93061i | − | 0.0718003i | ||||||
\(724\) | 13.6419i | 0.506995i | ||||||||
\(725\) | 37.4093i | 1.38935i | ||||||||
\(726\) | −10.9666 | − | 0.856728i | −0.407008 | − | 0.0317962i | ||||
\(727\) | − | 26.7798i | − | 0.993209i | −0.867977 | − | 0.496604i | \(-0.834580\pi\) | ||
0.867977 | − | 0.496604i | \(-0.165420\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 4.09006 | 0.151380 | ||||||||
\(731\) | − | 1.01301i | − | 0.0374676i | ||||||
\(732\) | 12.4897i | 0.461632i | ||||||||
\(733\) | −3.04403 | −0.112434 | −0.0562170 | − | 0.998419i | \(-0.517904\pi\) | ||||
−0.0562170 | + | 0.998419i | \(0.517904\pi\) | |||||||
\(734\) | 11.0084 | 0.406326 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 6.36865i | − | 0.234751i | ||||||
\(737\) | 45.2202 | + | 1.76365i | 1.66571 | + | 0.0649650i | ||||
\(738\) | 5.43717i | 0.200145i | ||||||||
\(739\) | − | 9.04683i | − | 0.332793i | −0.986059 | − | 0.166397i | \(-0.946787\pi\) | ||
0.986059 | − | 0.166397i | \(-0.0532132\pi\) | |||||||
\(740\) | 3.19831i | 0.117572i | ||||||||
\(741\) | 33.8848i | 1.24479i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 38.9413i | − | 1.42862i | −0.699830 | − | 0.714309i | \(-0.746741\pi\) | ||
0.699830 | − | 0.714309i | \(-0.253259\pi\) | |||||||
\(744\) | 6.20254i | 0.227396i | ||||||||
\(745\) | 7.65759 | 0.280552 | ||||||||
\(746\) | −25.8257 | −0.945545 | ||||||||
\(747\) | −16.7247 | −0.611924 | ||||||||
\(748\) | 1.15076 | + | 0.0448813i | 0.0420760 | + | 0.00164102i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 3.52645i | − | 0.128768i | ||||||
\(751\) | −1.90337 | −0.0694549 | −0.0347274 | − | 0.999397i | \(-0.511056\pi\) | ||||
−0.0347274 | + | 0.999397i | \(0.511056\pi\) | |||||||
\(752\) | 3.84135i | 0.140079i | ||||||||
\(753\) | −24.7683 | −0.902608 | ||||||||
\(754\) | 33.2750 | 1.21180 | ||||||||
\(755\) | 6.89927 | 0.251090 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.1242 | 0.549697 | 0.274848 | − | 0.961488i | \(-0.411372\pi\) | ||||
0.274848 | + | 0.961488i | \(0.411372\pi\) | |||||||
\(758\) | − | 23.0073i | − | 0.835662i | ||||||
\(759\) | −0.823179 | + | 21.1064i | −0.0298795 | + | 0.766113i | ||||
\(760\) | 2.79279 | 0.101305 | ||||||||
\(761\) | −8.47032 | −0.307049 | −0.153524 | − | 0.988145i | \(-0.549062\pi\) | ||||
−0.153524 | + | 0.988145i | \(0.549062\pi\) | |||||||
\(762\) | − | 15.1853i | − | 0.550105i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.61622 | 0.167009 | ||||||||
\(765\) | − | 0.124032i | − | 0.00448438i | ||||||
\(766\) | 17.2499 | 0.623265 | ||||||||
\(767\) | 3.94988i | 0.142622i | ||||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | −40.4068 | −1.45711 | −0.728553 | − | 0.684990i | \(-0.759807\pi\) | ||||
−0.728553 | + | 0.684990i | \(0.759807\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.66839 | −0.168128 | ||||||||
\(772\) | − | 5.24602i | − | 0.188809i | ||||||
\(773\) | − | 36.4379i | − | 1.31058i | −0.755378 | − | 0.655290i | \(-0.772547\pi\) | ||
0.755378 | − | 0.655290i | \(-0.227453\pi\) | |||||||
\(774\) | 2.91740 | 0.104864 | ||||||||
\(775\) | 30.2213i | 1.08558i | ||||||||
\(776\) | −18.1486 | −0.651495 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 18.5596i | − | 0.665395i | ||||||
\(779\) | −42.5105 | −1.52310 | ||||||||
\(780\) | −1.54809 | −0.0554306 | ||||||||
\(781\) | −20.4865 | − | 0.799005i | −0.733066 | − | 0.0285906i | ||||
\(782\) | − | 2.21139i | − | 0.0790793i | ||||||
\(783\) | −7.67778 | −0.274382 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.27490 | −0.223961 | ||||||||
\(786\) | −15.1562 | −0.540602 | ||||||||
\(787\) | 12.6092 | 0.449470 | 0.224735 | − | 0.974420i | \(-0.427848\pi\) | ||||
0.224735 | + | 0.974420i | \(0.427848\pi\) | |||||||
\(788\) | 2.35695i | 0.0839629i | ||||||||
\(789\) | 17.4163 | 0.620037 | ||||||||
\(790\) | − | 2.37875i | − | 0.0846320i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.129255 | + | 3.31411i | −0.00459287 | + | 0.117762i | ||||
\(793\) | 54.1295 | 1.92219 | ||||||||
\(794\) | −6.86138 | −0.243501 | ||||||||
\(795\) | −0.977388 | −0.0346644 | ||||||||
\(796\) | 4.46393i | 0.158220i | ||||||||
\(797\) | − | 17.2558i | − | 0.611231i | −0.952155 | − | 0.305616i | \(-0.901138\pi\) | ||
0.952155 | − | 0.305616i | \(-0.0988622\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.33384i | 0.0471877i | ||||||||
\(800\) | − | 4.87241i | − | 0.172266i | ||||||
\(801\) | − | 14.5026i | − | 0.512425i | ||||||
\(802\) | − | 9.50963i | − | 0.335797i | ||||||
\(803\) | −37.9474 | − | 1.48000i | −1.33913 | − | 0.0522282i | ||||
\(804\) | − | 13.6448i | − | 0.481214i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26.8814 | 0.946856 | ||||||||
\(807\) | −9.65915 | −0.340018 | ||||||||
\(808\) | − | 7.40672i | − | 0.260567i | ||||||
\(809\) | 25.3566i | 0.891492i | 0.895160 | + | 0.445746i | \(0.147061\pi\) | ||||
−0.895160 | + | 0.445746i | \(0.852939\pi\) | |||||||
\(810\) | 0.357203 | 0.0125508 | ||||||||
\(811\) | −29.5935 | −1.03917 | −0.519583 | − | 0.854420i | \(-0.673913\pi\) | ||||
−0.519583 | + | 0.854420i | \(0.673913\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 2.73625i | − | 0.0959643i | ||||||
\(814\) | 1.15732 | − | 29.6737i | 0.0405640 | − | 1.04006i | ||||
\(815\) | − | 4.92738i | − | 0.172598i | ||||||
\(816\) | − | 0.347231i | − | 0.0121555i | ||||||
\(817\) | 22.8097i | 0.798009i | ||||||||
\(818\) | 4.61520i | 0.161367i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 1.94217i | − | 0.0678235i | ||||||
\(821\) | − | 3.66644i | − | 0.127960i | −0.997951 | − | 0.0639798i | \(-0.979621\pi\) | ||
0.997951 | − | 0.0639798i | \(-0.0203793\pi\) | |||||||
\(822\) | −13.2508 | −0.462176 | ||||||||
\(823\) | −40.4699 | −1.41069 | −0.705347 | − | 0.708862i | \(-0.749209\pi\) | ||||
−0.705347 | + | 0.708862i | \(0.749209\pi\) | |||||||
\(824\) | −0.972851 | −0.0338909 | ||||||||
\(825\) | −0.629782 | + | 16.1477i | −0.0219262 | + | 0.562190i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.6107i | 1.62081i | 0.585869 | + | 0.810406i | \(0.300753\pi\) | ||||
−0.585869 | + | 0.810406i | \(0.699247\pi\) | |||||||
\(828\) | 6.36865 | 0.221326 | ||||||||
\(829\) | 33.1897i | 1.15273i | 0.817194 | + | 0.576363i | \(0.195529\pi\) | ||||
−0.817194 | + | 0.576363i | \(0.804471\pi\) | |||||||
\(830\) | 5.97410 | 0.207364 | ||||||||
\(831\) | −22.9739 | −0.796956 | ||||||||
\(832\) | −4.33393 | −0.150252 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.10063 | −0.0727389 | ||||||||
\(835\) | 2.96785i | 0.102707i | ||||||||
\(836\) | −25.9113 | − | 1.01058i | −0.896161 | − | 0.0349516i | ||||
\(837\) | −6.20254 | −0.214391 | ||||||||
\(838\) | 15.9343 | 0.550442 | ||||||||
\(839\) | − | 5.48280i | − | 0.189287i | −0.995511 | − | 0.0946436i | \(-0.969829\pi\) | ||
0.995511 | − | 0.0946436i | \(-0.0301712\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.9484 | −1.03270 | ||||||||
\(842\) | 19.4154i | 0.669097i | ||||||||
\(843\) | 11.8340 | 0.407583 | ||||||||
\(844\) | − | 12.7624i | − | 0.439301i | ||||||
\(845\) | 2.06569i | 0.0710620i | ||||||||
\(846\) | −3.84135 | −0.132068 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.73623 | −0.0939625 | ||||||||
\(849\) | 2.38857i | 0.0819753i | ||||||||
\(850\) | − | 1.69185i | − | 0.0580300i | ||||||
\(851\) | −57.0234 | −1.95474 | ||||||||
\(852\) | 6.18162i | 0.211779i | ||||||||
\(853\) | −26.9597 | −0.923083 | −0.461541 | − | 0.887119i | \(-0.652703\pi\) | ||||
−0.461541 | + | 0.887119i | \(0.652703\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.79279i | 0.0955113i | ||||||||
\(856\) | 4.11580 | 0.140675 | ||||||||
\(857\) | −5.65832 | −0.193285 | −0.0966423 | − | 0.995319i | \(-0.530810\pi\) | ||||
−0.0966423 | + | 0.995319i | \(0.530810\pi\) | |||||||
\(858\) | 14.3631 | + | 0.560182i | 0.490348 | + | 0.0191243i | ||||
\(859\) | 19.7245i | 0.672992i | 0.941685 | + | 0.336496i | \(0.109242\pi\) | ||||
−0.941685 | + | 0.336496i | \(0.890758\pi\) | |||||||
\(860\) | −1.04210 | −0.0355354 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.41070 | 0.252409 | ||||||||
\(863\) | −2.24915 | −0.0765621 | −0.0382810 | − | 0.999267i | \(-0.512188\pi\) | ||||
−0.0382810 | + | 0.999267i | \(0.512188\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 3.49475i | 0.118825i | ||||||||
\(866\) | −19.3089 | −0.656144 | ||||||||
\(867\) | 16.8794i | 0.573256i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.860757 | + | 22.0699i | −0.0291992 | + | 0.748669i | ||||
\(870\) | 2.74252 | 0.0929803 | ||||||||
\(871\) | −59.1355 | −2.00373 | ||||||||
\(872\) | 9.36206 | 0.317039 | ||||||||
\(873\) | − | 18.1486i | − | 0.614236i | ||||||
\(874\) | 49.7932i | 1.68428i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.4503i | 0.386869i | ||||||||
\(877\) | 40.6162i | 1.37151i | 0.727831 | + | 0.685756i | \(0.240528\pi\) | ||||
−0.727831 | + | 0.685756i | \(0.759472\pi\) | |||||||
\(878\) | 32.5688i | 1.09914i | ||||||||
\(879\) | 21.8292i | 0.736282i | ||||||||
\(880\) | 0.0461702 | − | 1.18381i | 0.00155640 | − | 0.0399061i | ||||
\(881\) | 16.7791i | 0.565302i | 0.959223 | + | 0.282651i | \(0.0912139\pi\) | ||||
−0.959223 | + | 0.282651i | \(0.908786\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.56752 | 0.0864041 | 0.0432020 | − | 0.999066i | \(-0.486244\pi\) | ||||
0.0432020 | + | 0.999066i | \(0.486244\pi\) | |||||||
\(884\) | −1.50488 | −0.0506145 | ||||||||
\(885\) | 0.325549i | 0.0109432i | ||||||||
\(886\) | 29.8320i | 1.00223i | ||||||||
\(887\) | 11.5185 | 0.386755 | 0.193377 | − | 0.981124i | \(-0.438056\pi\) | ||||
0.193377 | + | 0.981124i | \(0.438056\pi\) | |||||||
\(888\) | −8.95377 | −0.300469 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.18038i | 0.173647i | ||||||||
\(891\) | −3.31411 | − | 0.129255i | −0.111027 | − | 0.00433020i | ||||
\(892\) | − | 8.18197i | − | 0.273953i | ||||||
\(893\) | − | 30.0335i | − | 1.00503i | ||||||
\(894\) | 21.4377i | 0.716983i | ||||||||
\(895\) | 2.02136i | 0.0675667i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 27.6013i | − | 0.921580i | ||||||
\(898\) | 4.45126i | 0.148541i | ||||||||
\(899\) | −47.6217 | −1.58827 | ||||||||
\(900\) | 4.87241 | 0.162414 | ||||||||
\(901\) | −0.950105 | −0.0316526 | ||||||||
\(902\) | −0.702781 | + | 18.0194i | −0.0234000 | + | 0.599979i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.9856i | 0.465155i | ||||||||
\(905\) | 4.87290 | 0.161981 | ||||||||
\(906\) | 19.3147i | 0.641689i | ||||||||
\(907\) | 26.8783 | 0.892478 | 0.446239 | − | 0.894914i | \(-0.352763\pi\) | ||||
0.446239 | + | 0.894914i | \(0.352763\pi\) | |||||||
\(908\) | 3.26368 | 0.108309 | ||||||||
\(909\) | 7.40672 | 0.245665 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.9723 | −1.12555 | −0.562776 | − | 0.826609i | \(-0.690267\pi\) | ||||
−0.562776 | + | 0.826609i | \(0.690267\pi\) | |||||||
\(912\) | 7.81849i | 0.258896i | ||||||||
\(913\) | −55.4273 | − | 2.16175i | −1.83438 | − | 0.0715433i | ||||
\(914\) | −27.1160 | −0.896916 | ||||||||
\(915\) | 4.46135 | 0.147488 | ||||||||
\(916\) | − | 21.9790i | − | 0.726207i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.347231 | 0.0114603 | ||||||||
\(919\) | − | 49.8543i | − | 1.64454i | −0.569096 | − | 0.822271i | \(-0.692707\pi\) | ||
0.569096 | − | 0.822271i | \(-0.307293\pi\) | |||||||
\(920\) | −2.27490 | −0.0750012 | ||||||||
\(921\) | − | 5.28799i | − | 0.174245i | ||||||
\(922\) | − | 12.7571i | − | 0.420133i | ||||||
\(923\) | 26.7907 | 0.881828 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −43.6264 | −1.43443 | ||||||||
\(926\) | 26.8679i | 0.882934i | ||||||||
\(927\) | − | 0.972851i | − | 0.0319526i | ||||||
\(928\) | 7.67778 | 0.252036 | ||||||||
\(929\) | 7.49418i | 0.245876i | 0.992414 | + | 0.122938i | \(0.0392316\pi\) | ||||
−0.992414 | + | 0.122938i | \(0.960768\pi\) | |||||||
\(930\) | 2.21556 | 0.0726512 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 17.7061i | − | 0.579981i | ||||||
\(933\) | 7.26261 | 0.237767 | ||||||||
\(934\) | 35.2058 | 1.15197 | ||||||||
\(935\) | 0.0160317 | − | 0.411055i | 0.000524294 | − | 0.0134429i | ||||
\(936\) | − | 4.33393i | − | 0.141659i | ||||||
\(937\) | −51.6569 | −1.68756 | −0.843779 | − | 0.536690i | \(-0.819674\pi\) | ||||
−0.843779 | + | 0.536690i | \(0.819674\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.59656 | 0.150003 | ||||||||
\(940\) | 1.37214 | 0.0447542 | ||||||||
\(941\) | 46.4654 | 1.51473 | 0.757364 | − | 0.652993i | \(-0.226487\pi\) | ||||
0.757364 | + | 0.652993i | \(0.226487\pi\) | |||||||
\(942\) | − | 17.5668i | − | 0.572356i | ||||||
\(943\) | 34.6274 | 1.12762 | ||||||||
\(944\) | 0.911386i | 0.0296631i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.66857 | + | 0.377088i | 0.314352 | + | 0.0122602i | ||||
\(947\) | 39.3012 | 1.27712 | 0.638559 | − | 0.769573i | \(-0.279531\pi\) | ||||
0.638559 | + | 0.769573i | \(0.279531\pi\) | |||||||
\(948\) | 6.65938 | 0.216286 | ||||||||
\(949\) | 49.6247 | 1.61089 | ||||||||
\(950\) | 38.0949i | 1.23596i | ||||||||
\(951\) | − | 13.4968i | − | 0.437665i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 59.6687i | − | 1.93286i | −0.256931 | − | 0.966430i | \(-0.582711\pi\) | ||
0.256931 | − | 0.966430i | \(-0.417289\pi\) | |||||||
\(954\) | − | 2.73623i | − | 0.0885887i | ||||||
\(955\) | − | 1.64893i | − | 0.0533580i | ||||||
\(956\) | − | 2.53011i | − | 0.0818296i | ||||||
\(957\) | −25.4450 | − | 0.992391i | −0.822519 | − | 0.0320794i | ||||
\(958\) | − | 31.8131i | − | 1.02783i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.357203 | −0.0115287 | ||||||||
\(961\) | −7.47149 | −0.241016 | ||||||||
\(962\) | 38.8050i | 1.25112i | ||||||||
\(963\) | 4.11580i | 0.132630i | ||||||||
\(964\) | −1.93061 | −0.0621809 | ||||||||
\(965\) | −1.87389 | −0.0603228 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 40.0267i | − | 1.28717i | −0.765374 | − | 0.643586i | \(-0.777446\pi\) | ||
0.765374 | − | 0.643586i | \(-0.222554\pi\) | |||||||
\(968\) | −0.856728 | + | 10.9666i | −0.0275363 | + | 0.352479i | ||||
\(969\) | 2.71483i | 0.0872128i | ||||||||
\(970\) | 6.48271i | 0.208147i | ||||||||
\(971\) | − | 8.33112i | − | 0.267358i | −0.991025 | − | 0.133679i | \(-0.957321\pi\) | ||
0.991025 | − | 0.133679i | \(-0.0426791\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 28.4612i | 0.911954i | ||||||||
\(975\) | − | 21.1167i | − | 0.676275i | ||||||
\(976\) | 12.4897 | 0.399785 | ||||||||
\(977\) | 8.84048 | 0.282832 | 0.141416 | − | 0.989950i | \(-0.454834\pi\) | ||||
0.141416 | + | 0.989950i | \(0.454834\pi\) | |||||||
\(978\) | 13.7943 | 0.441095 | ||||||||
\(979\) | 1.87454 | − | 48.0632i | 0.0599104 | − | 1.53611i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.36206i | 0.298908i | ||||||||
\(982\) | 34.2454 | 1.09281 | ||||||||
\(983\) | 40.8291i | 1.30224i | 0.758973 | + | 0.651122i | \(0.225702\pi\) | ||||
−0.758973 | + | 0.651122i | \(0.774298\pi\) | |||||||
\(984\) | 5.43717 | 0.173331 | ||||||||
\(985\) | 0.841909 | 0.0268255 | ||||||||
\(986\) | 2.66597 | 0.0849017 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 33.8848 | 1.07802 | ||||||||
\(989\) | − | 18.5799i | − | 0.590806i | ||||||
\(990\) | 1.18381 | + | 0.0461702i | 0.0376239 | + | 0.00146738i | ||||
\(991\) | −17.4799 | −0.555266 | −0.277633 | − | 0.960687i | \(-0.589550\pi\) | ||||
−0.277633 | + | 0.960687i | \(0.589550\pi\) | |||||||
\(992\) | 6.20254 | 0.196931 | ||||||||
\(993\) | 6.39942i | 0.203080i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.59453 | 0.0505500 | ||||||||
\(996\) | 16.7247i | 0.529942i | ||||||||
\(997\) | 17.5927 | 0.557168 | 0.278584 | − | 0.960412i | \(-0.410135\pi\) | ||||
0.278584 | + | 0.960412i | \(0.410135\pi\) | |||||||
\(998\) | 7.93504i | 0.251179i | ||||||||
\(999\) | − | 8.95377i | − | 0.283285i |
(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 | 3234.2.e.c.2155.8 | ✓ | 24 | |
7.6 | odd | 2 | 3234.2.e.d.2155.5 | yes | 24 | ||
11.10 | odd | 2 | 3234.2.e.d.2155.20 | yes | 24 | ||
77.76 | even | 2 | inner | 3234.2.e.c.2155.17 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.e.c.2155.8 | ✓ | 24 | 1.1 | even | 1 | trivial | |
3234.2.e.c.2155.17 | yes | 24 | 77.76 | even | 2 | inner | |
3234.2.e.d.2155.5 | yes | 24 | 7.6 | odd | 2 | ||
3234.2.e.d.2155.20 | yes | 24 | 11.10 | odd | 2 |