Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(151,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.i (of order \(3\), degree \(2\), 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: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 151.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.151 |
Dual form | 1050.2.i.q.751.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −2.50000 | − | 0.866025i | −0.944911 | − | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | + | 5.19615i | −0.904534 | + | 1.56670i | −0.0829925 | + | 0.996550i | \(0.526448\pi\) |
−0.821541 | + | 0.570149i | \(0.806886\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 4.00000 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | −0.500000 | − | 2.59808i | −0.133631 | − | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.50000 | + | 2.59808i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | 2.00000 | + | 3.46410i | 0.458831 | + | 0.794719i | 0.998899 | − | 0.0469020i | \(-0.0149348\pi\) |
−0.540068 | + | 0.841621i | \(0.681602\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | + | 1.73205i | −0.436436 | + | 0.377964i | ||||
\(22\) | −6.00000 | −1.27920 | ||||||||
\(23\) | 1.50000 | + | 2.59808i | 0.312772 | + | 0.541736i | 0.978961 | − | 0.204046i | \(-0.0654092\pi\) |
−0.666190 | + | 0.745782i | \(0.732076\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.00000 | + | 3.46410i | 0.392232 | + | 0.679366i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.00000 | − | 1.73205i | 0.377964 | − | 0.327327i | ||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50000 | + | 4.33013i | −0.449013 | + | 0.777714i | −0.998322 | − | 0.0579057i | \(-0.981558\pi\) |
0.549309 | + | 0.835619i | \(0.314891\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 3.00000 | + | 5.19615i | 0.522233 | + | 0.904534i | ||||
\(34\) | −3.00000 | −0.514496 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.00000 | + | 6.92820i | 0.657596 | + | 1.13899i | 0.981236 | + | 0.192809i | \(0.0617599\pi\) |
−0.323640 | + | 0.946180i | \(0.604907\pi\) | |||||||
\(38\) | −2.00000 | + | 3.46410i | −0.324443 | + | 0.561951i | ||||
\(39\) | 2.00000 | − | 3.46410i | 0.320256 | − | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | −2.50000 | − | 0.866025i | −0.385758 | − | 0.133631i | ||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | −3.00000 | − | 5.19615i | −0.452267 | − | 0.783349i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.50000 | + | 2.59808i | −0.221163 | + | 0.383065i | ||||
\(47\) | 4.50000 | + | 7.79423i | 0.656392 | + | 1.13691i | 0.981543 | + | 0.191243i | \(0.0612518\pi\) |
−0.325150 | + | 0.945662i | \(0.605415\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.50000 | + | 2.59808i | 0.210042 | + | 0.363803i | ||||
\(52\) | −2.00000 | + | 3.46410i | −0.277350 | + | 0.480384i | ||||
\(53\) | 6.00000 | − | 10.3923i | 0.824163 | − | 1.42749i | −0.0783936 | − | 0.996922i | \(-0.524979\pi\) |
0.902557 | − | 0.430570i | \(-0.141688\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.50000 | + | 0.866025i | 0.334077 | + | 0.115728i | ||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | −3.00000 | − | 5.19615i | −0.393919 | − | 0.682288i | ||||
\(59\) | −3.00000 | + | 5.19615i | −0.390567 | + | 0.676481i | −0.992524 | − | 0.122047i | \(-0.961054\pi\) |
0.601958 | + | 0.798528i | \(0.294388\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | − | 1.73205i | −0.128037 | − | 0.221766i | 0.794879 | − | 0.606768i | \(-0.207534\pi\) |
−0.922916 | + | 0.385002i | \(0.874201\pi\) | |||||||
\(62\) | −5.00000 | −0.635001 | ||||||||
\(63\) | 0.500000 | + | 2.59808i | 0.0629941 | + | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.00000 | + | 5.19615i | −0.369274 | + | 0.639602i | ||||
\(67\) | 4.00000 | − | 6.92820i | 0.488678 | − | 0.846415i | −0.511237 | − | 0.859440i | \(-0.670813\pi\) |
0.999915 | + | 0.0130248i | \(0.00414604\pi\) | |||||||
\(68\) | −1.50000 | − | 2.59808i | −0.181902 | − | 0.315063i | ||||
\(69\) | 3.00000 | 0.361158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.00000 | −1.06810 | −0.534052 | − | 0.845452i | \(-0.679331\pi\) | ||||
−0.534052 | + | 0.845452i | \(0.679331\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | 7.00000 | − | 12.1244i | 0.819288 | − | 1.41905i | −0.0869195 | − | 0.996215i | \(-0.527702\pi\) |
0.906208 | − | 0.422833i | \(-0.138964\pi\) | |||||||
\(74\) | −4.00000 | + | 6.92820i | −0.464991 | + | 0.805387i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | 12.0000 | − | 10.3923i | 1.36753 | − | 1.18431i | ||||
\(78\) | 4.00000 | 0.452911 | ||||||||
\(79\) | 3.50000 | + | 6.06218i | 0.393781 | + | 0.682048i | 0.992945 | − | 0.118578i | \(-0.0378336\pi\) |
−0.599164 | + | 0.800626i | \(0.704500\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.50000 | − | 2.59808i | −0.165647 | − | 0.286910i | ||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | −0.500000 | − | 2.59808i | −0.0545545 | − | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.00000 | − | 6.92820i | −0.431331 | − | 0.747087i | ||||
\(87\) | −3.00000 | + | 5.19615i | −0.321634 | + | 0.557086i | ||||
\(88\) | 3.00000 | − | 5.19615i | 0.319801 | − | 0.553912i | ||||
\(89\) | −1.50000 | − | 2.59808i | −0.159000 | − | 0.275396i | 0.775509 | − | 0.631337i | \(-0.217494\pi\) |
−0.934508 | + | 0.355942i | \(0.884160\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0000 | − | 3.46410i | −1.04828 | − | 0.363137i | ||||
\(92\) | −3.00000 | −0.312772 | ||||||||
\(93\) | 2.50000 | + | 4.33013i | 0.259238 | + | 0.449013i | ||||
\(94\) | −4.50000 | + | 7.79423i | −0.464140 | + | 0.803913i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | −17.0000 | −1.72609 | −0.863044 | − | 0.505128i | \(-0.831445\pi\) | ||||
−0.863044 | + | 0.505128i | \(0.831445\pi\) | |||||||
\(98\) | −1.00000 | + | 6.92820i | −0.101015 | + | 0.699854i | ||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | + | 10.3923i | −0.597022 | + | 1.03407i | 0.396236 | + | 0.918149i | \(0.370316\pi\) |
−0.993258 | + | 0.115924i | \(0.963017\pi\) | |||||||
\(102\) | −1.50000 | + | 2.59808i | −0.148522 | + | 0.257248i | ||||
\(103\) | −6.50000 | − | 11.2583i | −0.640464 | − | 1.10932i | −0.985329 | − | 0.170664i | \(-0.945409\pi\) |
0.344865 | − | 0.938652i | \(-0.387925\pi\) | |||||||
\(104\) | −4.00000 | −0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.0000 | 1.16554 | ||||||||
\(107\) | 3.00000 | + | 5.19615i | 0.290021 | + | 0.502331i | 0.973814 | − | 0.227345i | \(-0.0730044\pi\) |
−0.683793 | + | 0.729676i | \(0.739671\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 2.00000 | − | 3.46410i | 0.191565 | − | 0.331801i | −0.754204 | − | 0.656640i | \(-0.771977\pi\) |
0.945769 | + | 0.324840i | \(0.105310\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | 0.759326 | ||||||||
\(112\) | 0.500000 | + | 2.59808i | 0.0472456 | + | 0.245495i | ||||
\(113\) | −3.00000 | −0.282216 | −0.141108 | − | 0.989994i | \(-0.545067\pi\) | ||||
−0.141108 | + | 0.989994i | \(0.545067\pi\) | |||||||
\(114\) | 2.00000 | + | 3.46410i | 0.187317 | + | 0.324443i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.00000 | − | 5.19615i | 0.278543 | − | 0.482451i | ||||
\(117\) | −2.00000 | − | 3.46410i | −0.184900 | − | 0.320256i | ||||
\(118\) | −6.00000 | −0.552345 | ||||||||
\(119\) | 6.00000 | − | 5.19615i | 0.550019 | − | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | − | 21.6506i | −1.13636 | − | 1.96824i | ||||
\(122\) | 1.00000 | − | 1.73205i | 0.0905357 | − | 0.156813i | ||||
\(123\) | −1.50000 | + | 2.59808i | −0.135250 | + | 0.234261i | ||||
\(124\) | −2.50000 | − | 4.33013i | −0.224507 | − | 0.388857i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | + | 1.73205i | −0.178174 | + | 0.154303i | ||||
\(127\) | 16.0000 | 1.41977 | 0.709885 | − | 0.704317i | \(-0.248747\pi\) | ||||
0.709885 | + | 0.704317i | \(0.248747\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −4.00000 | + | 6.92820i | −0.352180 | + | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.00000 | + | 15.5885i | 0.786334 | + | 1.36197i | 0.928199 | + | 0.372084i | \(0.121357\pi\) |
−0.141865 | + | 0.989886i | \(0.545310\pi\) | |||||||
\(132\) | −6.00000 | −0.522233 | ||||||||
\(133\) | −2.00000 | − | 10.3923i | −0.173422 | − | 0.901127i | ||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.50000 | − | 2.59808i | 0.128624 | − | 0.222783i | ||||
\(137\) | −7.50000 | + | 12.9904i | −0.640768 | + | 1.10984i | 0.344493 | + | 0.938789i | \(0.388051\pi\) |
−0.985262 | + | 0.171054i | \(0.945283\pi\) | |||||||
\(138\) | 1.50000 | + | 2.59808i | 0.127688 | + | 0.221163i | ||||
\(139\) | 2.00000 | 0.169638 | 0.0848189 | − | 0.996396i | \(-0.472969\pi\) | ||||
0.0848189 | + | 0.996396i | \(0.472969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.00000 | 0.757937 | ||||||||
\(142\) | −4.50000 | − | 7.79423i | −0.377632 | − | 0.654077i | ||||
\(143\) | −12.0000 | + | 20.7846i | −1.00349 | + | 1.73810i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 14.0000 | 1.15865 | ||||||||
\(147\) | 6.50000 | − | 2.59808i | 0.536111 | − | 0.214286i | ||||
\(148\) | −8.00000 | −0.657596 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | − | 13.8564i | 0.651031 | − | 1.12762i | −0.331842 | − | 0.943335i | \(-0.607670\pi\) |
0.982873 | − | 0.184284i | \(-0.0589965\pi\) | |||||||
\(152\) | −2.00000 | − | 3.46410i | −0.162221 | − | 0.280976i | ||||
\(153\) | 3.00000 | 0.242536 | ||||||||
\(154\) | 15.0000 | + | 5.19615i | 1.20873 | + | 0.418718i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | + | 3.46410i | 0.160128 | + | 0.277350i | ||||
\(157\) | 7.00000 | − | 12.1244i | 0.558661 | − | 0.967629i | −0.438948 | − | 0.898513i | \(-0.644649\pi\) |
0.997609 | − | 0.0691164i | \(-0.0220180\pi\) | |||||||
\(158\) | −3.50000 | + | 6.06218i | −0.278445 | + | 0.482281i | ||||
\(159\) | −6.00000 | − | 10.3923i | −0.475831 | − | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.50000 | − | 7.79423i | −0.118217 | − | 0.614271i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 4.00000 | + | 6.92820i | 0.313304 | + | 0.542659i | 0.979076 | − | 0.203497i | \(-0.0652307\pi\) |
−0.665771 | + | 0.746156i | \(0.731897\pi\) | |||||||
\(164\) | 1.50000 | − | 2.59808i | 0.117130 | − | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.00000 | + | 5.19615i | 0.232845 | + | 0.403300i | ||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 2.00000 | − | 1.73205i | 0.154303 | − | 0.133631i | ||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | − | 3.46410i | 0.152944 | − | 0.264906i | ||||
\(172\) | 4.00000 | − | 6.92820i | 0.304997 | − | 0.528271i | ||||
\(173\) | −3.00000 | − | 5.19615i | −0.228086 | − | 0.395056i | 0.729155 | − | 0.684349i | \(-0.239913\pi\) |
−0.957241 | + | 0.289292i | \(0.906580\pi\) | |||||||
\(174\) | −6.00000 | −0.454859 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.00000 | 0.452267 | ||||||||
\(177\) | 3.00000 | + | 5.19615i | 0.225494 | + | 0.390567i | ||||
\(178\) | 1.50000 | − | 2.59808i | 0.112430 | − | 0.194734i | ||||
\(179\) | 9.00000 | − | 15.5885i | 0.672692 | − | 1.16514i | −0.304446 | − | 0.952529i | \(-0.598471\pi\) |
0.977138 | − | 0.212607i | \(-0.0681952\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | −2.00000 | − | 10.3923i | −0.148250 | − | 0.770329i | ||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | −1.50000 | − | 2.59808i | −0.110581 | − | 0.191533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.50000 | + | 4.33013i | −0.183309 | + | 0.317500i | ||||
\(187\) | −9.00000 | − | 15.5885i | −0.658145 | − | 1.13994i | ||||
\(188\) | −9.00000 | −0.656392 | ||||||||
\(189\) | 2.50000 | + | 0.866025i | 0.181848 | + | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.50000 | − | 12.9904i | −0.542681 | − | 0.939951i | −0.998749 | − | 0.0500060i | \(-0.984076\pi\) |
0.456068 | − | 0.889945i | \(-0.349257\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 2.50000 | − | 4.33013i | 0.179954 | − | 0.311689i | −0.761911 | − | 0.647682i | \(-0.775738\pi\) |
0.941865 | + | 0.335993i | \(0.109072\pi\) | |||||||
\(194\) | −8.50000 | − | 14.7224i | −0.610264 | − | 1.05701i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | + | 2.59808i | −0.464286 | + | 0.185577i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 3.00000 | + | 5.19615i | 0.213201 | + | 0.369274i | ||||
\(199\) | −2.50000 | + | 4.33013i | −0.177220 | + | 0.306955i | −0.940927 | − | 0.338608i | \(-0.890044\pi\) |
0.763707 | + | 0.645563i | \(0.223377\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00000 | − | 6.92820i | −0.282138 | − | 0.488678i | ||||
\(202\) | −12.0000 | −0.844317 | ||||||||
\(203\) | 15.0000 | + | 5.19615i | 1.05279 | + | 0.364698i | ||||
\(204\) | −3.00000 | −0.210042 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.50000 | − | 11.2583i | 0.452876 | − | 0.784405i | ||||
\(207\) | 1.50000 | − | 2.59808i | 0.104257 | − | 0.180579i | ||||
\(208\) | −2.00000 | − | 3.46410i | −0.138675 | − | 0.240192i | ||||
\(209\) | −24.0000 | −1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | 6.00000 | + | 10.3923i | 0.412082 | + | 0.713746i | ||||
\(213\) | −4.50000 | + | 7.79423i | −0.308335 | + | 0.534052i | ||||
\(214\) | −3.00000 | + | 5.19615i | −0.205076 | + | 0.355202i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 10.0000 | − | 8.66025i | 0.678844 | − | 0.587896i | ||||
\(218\) | 4.00000 | 0.270914 | ||||||||
\(219\) | −7.00000 | − | 12.1244i | −0.473016 | − | 0.819288i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | + | 10.3923i | −0.403604 | + | 0.699062i | ||||
\(222\) | 4.00000 | + | 6.92820i | 0.268462 | + | 0.464991i | ||||
\(223\) | −11.0000 | −0.736614 | −0.368307 | − | 0.929704i | \(-0.620063\pi\) | ||||
−0.368307 | + | 0.929704i | \(0.620063\pi\) | |||||||
\(224\) | −2.00000 | + | 1.73205i | −0.133631 | + | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.50000 | − | 2.59808i | −0.0997785 | − | 0.172821i | ||||
\(227\) | −9.00000 | + | 15.5885i | −0.597351 | + | 1.03464i | 0.395860 | + | 0.918311i | \(0.370447\pi\) |
−0.993210 | + | 0.116331i | \(0.962887\pi\) | |||||||
\(228\) | −2.00000 | + | 3.46410i | −0.132453 | + | 0.229416i | ||||
\(229\) | 11.0000 | + | 19.0526i | 0.726900 | + | 1.25903i | 0.958187 | + | 0.286143i | \(0.0923732\pi\) |
−0.231287 | + | 0.972886i | \(0.574293\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.00000 | − | 15.5885i | −0.197386 | − | 1.02565i | ||||
\(232\) | 6.00000 | 0.393919 | ||||||||
\(233\) | 3.00000 | + | 5.19615i | 0.196537 | + | 0.340411i | 0.947403 | − | 0.320043i | \(-0.103697\pi\) |
−0.750867 | + | 0.660454i | \(0.770364\pi\) | |||||||
\(234\) | 2.00000 | − | 3.46410i | 0.130744 | − | 0.226455i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.00000 | − | 5.19615i | −0.195283 | − | 0.338241i | ||||
\(237\) | 7.00000 | 0.454699 | ||||||||
\(238\) | 7.50000 | + | 2.59808i | 0.486153 | + | 0.168408i | ||||
\(239\) | 3.00000 | 0.194054 | 0.0970269 | − | 0.995282i | \(-0.469067\pi\) | ||||
0.0970269 | + | 0.995282i | \(0.469067\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0000 | − | 19.0526i | 0.708572 | − | 1.22728i | −0.256814 | − | 0.966461i | \(-0.582673\pi\) |
0.965387 | − | 0.260822i | \(-0.0839937\pi\) | |||||||
\(242\) | 12.5000 | − | 21.6506i | 0.803530 | − | 1.39176i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.00000 | −0.191273 | ||||||||
\(247\) | 8.00000 | + | 13.8564i | 0.509028 | + | 0.881662i | ||||
\(248\) | 2.50000 | − | 4.33013i | 0.158750 | − | 0.274963i | ||||
\(249\) | 3.00000 | − | 5.19615i | 0.190117 | − | 0.329293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | −2.50000 | − | 0.866025i | −0.157485 | − | 0.0545545i | ||||
\(253\) | −18.0000 | −1.13165 | ||||||||
\(254\) | 8.00000 | + | 13.8564i | 0.501965 | + | 0.869428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −9.00000 | − | 15.5885i | −0.561405 | − | 0.972381i | −0.997374 | − | 0.0724199i | \(-0.976928\pi\) |
0.435970 | − | 0.899961i | \(-0.356405\pi\) | |||||||
\(258\) | −8.00000 | −0.498058 | ||||||||
\(259\) | −4.00000 | − | 20.7846i | −0.248548 | − | 1.29149i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | + | 5.19615i | 0.185695 | + | 0.321634i | ||||
\(262\) | −9.00000 | + | 15.5885i | −0.556022 | + | 0.963058i | ||||
\(263\) | −1.50000 | + | 2.59808i | −0.0924940 | + | 0.160204i | −0.908560 | − | 0.417755i | \(-0.862817\pi\) |
0.816066 | + | 0.577959i | \(0.196151\pi\) | |||||||
\(264\) | −3.00000 | − | 5.19615i | −0.184637 | − | 0.319801i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.00000 | − | 6.92820i | 0.490511 | − | 0.424795i | ||||
\(267\) | −3.00000 | −0.183597 | ||||||||
\(268\) | 4.00000 | + | 6.92820i | 0.244339 | + | 0.423207i | ||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.5000 | + | 21.6506i | 0.759321 | + | 1.31518i | 0.943197 | + | 0.332233i | \(0.107802\pi\) |
−0.183876 | + | 0.982949i | \(0.558865\pi\) | |||||||
\(272\) | 3.00000 | 0.181902 | ||||||||
\(273\) | −8.00000 | + | 6.92820i | −0.484182 | + | 0.419314i | ||||
\(274\) | −15.0000 | −0.906183 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.50000 | + | 2.59808i | −0.0902894 | + | 0.156386i | ||||
\(277\) | 13.0000 | − | 22.5167i | 0.781094 | − | 1.35290i | −0.150210 | − | 0.988654i | \(-0.547995\pi\) |
0.931305 | − | 0.364241i | \(-0.118672\pi\) | |||||||
\(278\) | 1.00000 | + | 1.73205i | 0.0599760 | + | 0.103882i | ||||
\(279\) | 5.00000 | 0.299342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.0000 | 1.61068 | 0.805342 | − | 0.592810i | \(-0.201981\pi\) | ||||
0.805342 | + | 0.592810i | \(0.201981\pi\) | |||||||
\(282\) | 4.50000 | + | 7.79423i | 0.267971 | + | 0.464140i | ||||
\(283\) | −11.0000 | + | 19.0526i | −0.653882 | + | 1.13256i | 0.328291 | + | 0.944577i | \(0.393527\pi\) |
−0.982173 | + | 0.187980i | \(0.939806\pi\) | |||||||
\(284\) | 4.50000 | − | 7.79423i | 0.267026 | − | 0.462502i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −24.0000 | −1.41915 | ||||||||
\(287\) | 7.50000 | + | 2.59808i | 0.442711 | + | 0.153360i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.50000 | + | 14.7224i | −0.498279 | + | 0.863044i | ||||
\(292\) | 7.00000 | + | 12.1244i | 0.409644 | + | 0.709524i | ||||
\(293\) | 18.0000 | 1.05157 | 0.525786 | − | 0.850617i | \(-0.323771\pi\) | ||||
0.525786 | + | 0.850617i | \(0.323771\pi\) | |||||||
\(294\) | 5.50000 | + | 4.33013i | 0.320767 | + | 0.252538i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.00000 | − | 6.92820i | −0.232495 | − | 0.402694i | ||||
\(297\) | 3.00000 | − | 5.19615i | 0.174078 | − | 0.301511i | ||||
\(298\) | −3.00000 | + | 5.19615i | −0.173785 | + | 0.301005i | ||||
\(299\) | 6.00000 | + | 10.3923i | 0.346989 | + | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.0000 | + | 6.92820i | 1.15278 | + | 0.399335i | ||||
\(302\) | 16.0000 | 0.920697 | ||||||||
\(303\) | 6.00000 | + | 10.3923i | 0.344691 | + | 0.597022i | ||||
\(304\) | 2.00000 | − | 3.46410i | 0.114708 | − | 0.198680i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.50000 | + | 2.59808i | 0.0857493 | + | 0.148522i | ||||
\(307\) | −20.0000 | −1.14146 | −0.570730 | − | 0.821138i | \(-0.693340\pi\) | ||||
−0.570730 | + | 0.821138i | \(0.693340\pi\) | |||||||
\(308\) | 3.00000 | + | 15.5885i | 0.170941 | + | 0.888235i | ||||
\(309\) | −13.0000 | −0.739544 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.5000 | + | 18.1865i | −0.595400 | + | 1.03126i | 0.398090 | + | 0.917346i | \(0.369673\pi\) |
−0.993490 | + | 0.113917i | \(0.963660\pi\) | |||||||
\(312\) | −2.00000 | + | 3.46410i | −0.113228 | + | 0.196116i | ||||
\(313\) | 8.50000 | + | 14.7224i | 0.480448 | + | 0.832161i | 0.999748 | − | 0.0224310i | \(-0.00714060\pi\) |
−0.519300 | + | 0.854592i | \(0.673807\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.00000 | −0.393781 | ||||||||
\(317\) | 6.00000 | + | 10.3923i | 0.336994 | + | 0.583690i | 0.983866 | − | 0.178908i | \(-0.0572566\pi\) |
−0.646872 | + | 0.762598i | \(0.723923\pi\) | |||||||
\(318\) | 6.00000 | − | 10.3923i | 0.336463 | − | 0.582772i | ||||
\(319\) | 18.0000 | − | 31.1769i | 1.00781 | − | 1.74557i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.00000 | 0.334887 | ||||||||
\(322\) | 6.00000 | − | 5.19615i | 0.334367 | − | 0.289570i | ||||
\(323\) | −12.0000 | −0.667698 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.00000 | + | 6.92820i | −0.221540 | + | 0.383718i | ||||
\(327\) | −2.00000 | − | 3.46410i | −0.110600 | − | 0.191565i | ||||
\(328\) | 3.00000 | 0.165647 | ||||||||
\(329\) | −4.50000 | − | 23.3827i | −0.248093 | − | 1.28913i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0000 | − | 22.5167i | −0.714545 | − | 1.23763i | −0.963135 | − | 0.269019i | \(-0.913301\pi\) |
0.248590 | − | 0.968609i | \(-0.420033\pi\) | |||||||
\(332\) | −3.00000 | + | 5.19615i | −0.164646 | + | 0.285176i | ||||
\(333\) | 4.00000 | − | 6.92820i | 0.219199 | − | 0.379663i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.50000 | + | 0.866025i | 0.136386 | + | 0.0472456i | ||||
\(337\) | 13.0000 | 0.708155 | 0.354078 | − | 0.935216i | \(-0.384795\pi\) | ||||
0.354078 | + | 0.935216i | \(0.384795\pi\) | |||||||
\(338\) | 1.50000 | + | 2.59808i | 0.0815892 | + | 0.141317i | ||||
\(339\) | −1.50000 | + | 2.59808i | −0.0814688 | + | 0.141108i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.0000 | − | 25.9808i | −0.812296 | − | 1.40694i | ||||
\(342\) | 4.00000 | 0.216295 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 8.00000 | 0.431331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00000 | − | 5.19615i | 0.161281 | − | 0.279347i | ||||
\(347\) | 9.00000 | − | 15.5885i | 0.483145 | − | 0.836832i | −0.516667 | − | 0.856186i | \(-0.672828\pi\) |
0.999813 | + | 0.0193540i | \(0.00616095\pi\) | |||||||
\(348\) | −3.00000 | − | 5.19615i | −0.160817 | − | 0.278543i | ||||
\(349\) | −28.0000 | −1.49881 | −0.749403 | − | 0.662114i | \(-0.769659\pi\) | ||||
−0.749403 | + | 0.662114i | \(0.769659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | 3.00000 | + | 5.19615i | 0.159901 | + | 0.276956i | ||||
\(353\) | 7.50000 | − | 12.9904i | 0.399185 | − | 0.691408i | −0.594441 | − | 0.804139i | \(-0.702627\pi\) |
0.993626 | + | 0.112731i | \(0.0359599\pi\) | |||||||
\(354\) | −3.00000 | + | 5.19615i | −0.159448 | + | 0.276172i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.00000 | 0.159000 | ||||||||
\(357\) | −1.50000 | − | 7.79423i | −0.0793884 | − | 0.412514i | ||||
\(358\) | 18.0000 | 0.951330 | ||||||||
\(359\) | 18.0000 | + | 31.1769i | 0.950004 | + | 1.64545i | 0.745409 | + | 0.666608i | \(0.232254\pi\) |
0.204595 | + | 0.978847i | \(0.434412\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | − | 2.59808i | 0.0789474 | − | 0.136741i | ||||
\(362\) | 1.00000 | + | 1.73205i | 0.0525588 | + | 0.0910346i | ||||
\(363\) | −25.0000 | −1.31216 | ||||||||
\(364\) | 8.00000 | − | 6.92820i | 0.419314 | − | 0.363137i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.00000 | − | 1.73205i | −0.0522708 | − | 0.0905357i | ||||
\(367\) | −14.0000 | + | 24.2487i | −0.730794 | + | 1.26577i | 0.225750 | + | 0.974185i | \(0.427517\pi\) |
−0.956544 | + | 0.291587i | \(0.905817\pi\) | |||||||
\(368\) | 1.50000 | − | 2.59808i | 0.0781929 | − | 0.135434i | ||||
\(369\) | 1.50000 | + | 2.59808i | 0.0780869 | + | 0.135250i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.0000 | + | 20.7846i | −1.24602 | + | 1.07908i | ||||
\(372\) | −5.00000 | −0.259238 | ||||||||
\(373\) | 4.00000 | + | 6.92820i | 0.207112 | + | 0.358729i | 0.950804 | − | 0.309794i | \(-0.100260\pi\) |
−0.743691 | + | 0.668523i | \(0.766927\pi\) | |||||||
\(374\) | 9.00000 | − | 15.5885i | 0.465379 | − | 0.806060i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.50000 | − | 7.79423i | −0.232070 | − | 0.401957i | ||||
\(377\) | −24.0000 | −1.23606 | ||||||||
\(378\) | 0.500000 | + | 2.59808i | 0.0257172 | + | 0.133631i | ||||
\(379\) | −10.0000 | −0.513665 | −0.256833 | − | 0.966456i | \(-0.582679\pi\) | ||||
−0.256833 | + | 0.966456i | \(0.582679\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.00000 | − | 13.8564i | 0.409852 | − | 0.709885i | ||||
\(382\) | 7.50000 | − | 12.9904i | 0.383733 | − | 0.664646i | ||||
\(383\) | 10.5000 | + | 18.1865i | 0.536525 | + | 0.929288i | 0.999088 | + | 0.0427020i | \(0.0135966\pi\) |
−0.462563 | + | 0.886586i | \(0.653070\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.00000 | 0.254493 | ||||||||
\(387\) | 4.00000 | + | 6.92820i | 0.203331 | + | 0.352180i | ||||
\(388\) | 8.50000 | − | 14.7224i | 0.431522 | − | 0.747418i | ||||
\(389\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | −0.455150 | ||||||||
\(392\) | −5.50000 | − | 4.33013i | −0.277792 | − | 0.218704i | ||||
\(393\) | 18.0000 | 0.907980 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.00000 | + | 5.19615i | −0.150756 | + | 0.261116i | ||||
\(397\) | 1.00000 | + | 1.73205i | 0.0501886 | + | 0.0869291i | 0.890028 | − | 0.455905i | \(-0.150684\pi\) |
−0.839840 | + | 0.542834i | \(0.817351\pi\) | |||||||
\(398\) | −5.00000 | −0.250627 | ||||||||
\(399\) | −10.0000 | − | 3.46410i | −0.500626 | − | 0.173422i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.00000 | + | 5.19615i | 0.149813 | + | 0.259483i | 0.931158 | − | 0.364615i | \(-0.118800\pi\) |
−0.781345 | + | 0.624099i | \(0.785466\pi\) | |||||||
\(402\) | 4.00000 | − | 6.92820i | 0.199502 | − | 0.345547i | ||||
\(403\) | −10.0000 | + | 17.3205i | −0.498135 | + | 0.862796i | ||||
\(404\) | −6.00000 | − | 10.3923i | −0.298511 | − | 0.517036i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.00000 | + | 15.5885i | 0.148888 | + | 0.773642i | ||||
\(407\) | −48.0000 | −2.37927 | ||||||||
\(408\) | −1.50000 | − | 2.59808i | −0.0742611 | − | 0.128624i | ||||
\(409\) | −14.5000 | + | 25.1147i | −0.716979 | + | 1.24184i | 0.245212 | + | 0.969469i | \(0.421142\pi\) |
−0.962191 | + | 0.272374i | \(0.912191\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.50000 | + | 12.9904i | 0.369948 | + | 0.640768i | ||||
\(412\) | 13.0000 | 0.640464 | ||||||||
\(413\) | 12.0000 | − | 10.3923i | 0.590481 | − | 0.511372i | ||||
\(414\) | 3.00000 | 0.147442 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.00000 | − | 3.46410i | 0.0980581 | − | 0.169842i | ||||
\(417\) | 1.00000 | − | 1.73205i | 0.0489702 | − | 0.0848189i | ||||
\(418\) | −12.0000 | − | 20.7846i | −0.586939 | − | 1.01661i | ||||
\(419\) | 24.0000 | 1.17248 | 0.586238 | − | 0.810139i | \(-0.300608\pi\) | ||||
0.586238 | + | 0.810139i | \(0.300608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00000 | −0.194948 | −0.0974740 | − | 0.995238i | \(-0.531076\pi\) | ||||
−0.0974740 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(422\) | 4.00000 | + | 6.92820i | 0.194717 | + | 0.337260i | ||||
\(423\) | 4.50000 | − | 7.79423i | 0.218797 | − | 0.378968i | ||||
\(424\) | −6.00000 | + | 10.3923i | −0.291386 | + | 0.504695i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.00000 | −0.436051 | ||||||||
\(427\) | 1.00000 | + | 5.19615i | 0.0483934 | + | 0.251459i | ||||
\(428\) | −6.00000 | −0.290021 | ||||||||
\(429\) | 12.0000 | + | 20.7846i | 0.579365 | + | 1.00349i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.5000 | + | 18.1865i | −0.505767 | + | 0.876014i | 0.494211 | + | 0.869342i | \(0.335457\pi\) |
−0.999978 | + | 0.00667224i | \(0.997876\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 7.00000 | 0.336399 | 0.168199 | − | 0.985753i | \(-0.446205\pi\) | ||||
0.168199 | + | 0.985753i | \(0.446205\pi\) | |||||||
\(434\) | 12.5000 | + | 4.33013i | 0.600019 | + | 0.207853i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | + | 3.46410i | 0.0957826 | + | 0.165900i | ||||
\(437\) | −6.00000 | + | 10.3923i | −0.287019 | + | 0.497131i | ||||
\(438\) | 7.00000 | − | 12.1244i | 0.334473 | − | 0.579324i | ||||
\(439\) | 6.50000 | + | 11.2583i | 0.310228 | + | 0.537331i | 0.978412 | − | 0.206666i | \(-0.0662612\pi\) |
−0.668184 | + | 0.743996i | \(0.732928\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | − | 6.92820i | 0.0476190 | − | 0.329914i | ||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | −12.0000 | − | 20.7846i | −0.570137 | − | 0.987507i | −0.996551 | − | 0.0829786i | \(-0.973557\pi\) |
0.426414 | − | 0.904528i | \(-0.359777\pi\) | |||||||
\(444\) | −4.00000 | + | 6.92820i | −0.189832 | + | 0.328798i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.50000 | − | 9.52628i | −0.260433 | − | 0.451082i | ||||
\(447\) | 6.00000 | 0.283790 | ||||||||
\(448\) | −2.50000 | − | 0.866025i | −0.118114 | − | 0.0409159i | ||||
\(449\) | −3.00000 | −0.141579 | −0.0707894 | − | 0.997491i | \(-0.522552\pi\) | ||||
−0.0707894 | + | 0.997491i | \(0.522552\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | − | 15.5885i | 0.423793 | − | 0.734032i | ||||
\(452\) | 1.50000 | − | 2.59808i | 0.0705541 | − | 0.122203i | ||||
\(453\) | −8.00000 | − | 13.8564i | −0.375873 | − | 0.651031i | ||||
\(454\) | −18.0000 | −0.844782 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.00000 | −0.187317 | ||||||||
\(457\) | 1.00000 | + | 1.73205i | 0.0467780 | + | 0.0810219i | 0.888466 | − | 0.458942i | \(-0.151771\pi\) |
−0.841688 | + | 0.539964i | \(0.818438\pi\) | |||||||
\(458\) | −11.0000 | + | 19.0526i | −0.513996 | + | 0.890268i | ||||
\(459\) | 1.50000 | − | 2.59808i | 0.0700140 | − | 0.121268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.0000 | 1.67669 | 0.838344 | − | 0.545142i | \(-0.183524\pi\) | ||||
0.838344 | + | 0.545142i | \(0.183524\pi\) | |||||||
\(462\) | 12.0000 | − | 10.3923i | 0.558291 | − | 0.483494i | ||||
\(463\) | 13.0000 | 0.604161 | 0.302081 | − | 0.953282i | \(-0.402319\pi\) | ||||
0.302081 | + | 0.953282i | \(0.402319\pi\) | |||||||
\(464\) | 3.00000 | + | 5.19615i | 0.139272 | + | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | + | 5.19615i | −0.138972 | + | 0.240707i | ||||
\(467\) | −15.0000 | − | 25.9808i | −0.694117 | − | 1.20225i | −0.970477 | − | 0.241192i | \(-0.922462\pi\) |
0.276360 | − | 0.961054i | \(-0.410872\pi\) | |||||||
\(468\) | 4.00000 | 0.184900 | ||||||||
\(469\) | −16.0000 | + | 13.8564i | −0.738811 | + | 0.639829i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.00000 | − | 12.1244i | −0.322543 | − | 0.558661i | ||||
\(472\) | 3.00000 | − | 5.19615i | 0.138086 | − | 0.239172i | ||||
\(473\) | 24.0000 | − | 41.5692i | 1.10352 | − | 1.91135i | ||||
\(474\) | 3.50000 | + | 6.06218i | 0.160760 | + | 0.278445i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.50000 | + | 7.79423i | 0.0687524 | + | 0.357248i | ||||
\(477\) | −12.0000 | −0.549442 | ||||||||
\(478\) | 1.50000 | + | 2.59808i | 0.0686084 | + | 0.118833i | ||||
\(479\) | −10.5000 | + | 18.1865i | −0.479757 | + | 0.830964i | −0.999730 | − | 0.0232187i | \(-0.992609\pi\) |
0.519973 | + | 0.854183i | \(0.325942\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0000 | + | 27.7128i | 0.729537 | + | 1.26360i | ||||
\(482\) | 22.0000 | 1.00207 | ||||||||
\(483\) | −7.50000 | − | 2.59808i | −0.341262 | − | 0.118217i | ||||
\(484\) | 25.0000 | 1.13636 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | −12.5000 | + | 21.6506i | −0.566429 | + | 0.981084i | 0.430486 | + | 0.902597i | \(0.358342\pi\) |
−0.996915 | + | 0.0784867i | \(0.974991\pi\) | |||||||
\(488\) | 1.00000 | + | 1.73205i | 0.0452679 | + | 0.0784063i | ||||
\(489\) | 8.00000 | 0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | −1.50000 | − | 2.59808i | −0.0676252 | − | 0.117130i | ||||
\(493\) | 9.00000 | − | 15.5885i | 0.405340 | − | 0.702069i | ||||
\(494\) | −8.00000 | + | 13.8564i | −0.359937 | + | 0.623429i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.00000 | 0.224507 | ||||||||
\(497\) | 22.5000 | + | 7.79423i | 1.00926 | + | 0.349619i | ||||
\(498\) | 6.00000 | 0.268866 | ||||||||
\(499\) | −19.0000 | − | 32.9090i | −0.850557 | − | 1.47321i | −0.880707 | − | 0.473662i | \(-0.842932\pi\) |
0.0301498 | − | 0.999545i | \(-0.490402\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0000 | + | 20.7846i | 0.535586 | + | 0.927663i | ||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | −0.500000 | − | 2.59808i | −0.0222718 | − | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.00000 | − | 15.5885i | −0.400099 | − | 0.692991i | ||||
\(507\) | 1.50000 | − | 2.59808i | 0.0666173 | − | 0.115385i | ||||
\(508\) | −8.00000 | + | 13.8564i | −0.354943 | + | 0.614779i | ||||
\(509\) | 3.00000 | + | 5.19615i | 0.132973 | + | 0.230315i | 0.924821 | − | 0.380402i | \(-0.124214\pi\) |
−0.791849 | + | 0.610718i | \(0.790881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.0000 | + | 24.2487i | −1.23865 | + | 1.07270i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.00000 | − | 3.46410i | −0.0883022 | − | 0.152944i | ||||
\(514\) | 9.00000 | − | 15.5885i | 0.396973 | − | 0.687577i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.00000 | − | 6.92820i | −0.176090 | − | 0.304997i | ||||
\(517\) | −54.0000 | −2.37492 | ||||||||
\(518\) | 16.0000 | − | 13.8564i | 0.703000 | − | 0.608816i | ||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.5000 | + | 18.1865i | −0.460013 | + | 0.796766i | −0.998961 | − | 0.0455727i | \(-0.985489\pi\) |
0.538948 | + | 0.842339i | \(0.318822\pi\) | |||||||
\(522\) | −3.00000 | + | 5.19615i | −0.131306 | + | 0.227429i | ||||
\(523\) | −17.0000 | − | 29.4449i | −0.743358 | − | 1.28753i | −0.950958 | − | 0.309320i | \(-0.899899\pi\) |
0.207600 | − | 0.978214i | \(-0.433435\pi\) | |||||||
\(524\) | −18.0000 | −0.786334 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.00000 | −0.130806 | ||||||||
\(527\) | −7.50000 | − | 12.9904i | −0.326705 | − | 0.565870i | ||||
\(528\) | 3.00000 | − | 5.19615i | 0.130558 | − | 0.226134i | ||||
\(529\) | 7.00000 | − | 12.1244i | 0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.00000 | 0.260378 | ||||||||
\(532\) | 10.0000 | + | 3.46410i | 0.433555 | + | 0.150188i | ||||
\(533\) | −12.0000 | −0.519778 | ||||||||
\(534\) | −1.50000 | − | 2.59808i | −0.0649113 | − | 0.112430i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.00000 | + | 6.92820i | −0.172774 | + | 0.299253i | ||||
\(537\) | −9.00000 | − | 15.5885i | −0.388379 | − | 0.672692i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −39.0000 | + | 15.5885i | −1.67985 | + | 0.671442i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.0000 | + | 24.2487i | 0.601907 | + | 1.04253i | 0.992532 | + | 0.121984i | \(0.0389256\pi\) |
−0.390625 | + | 0.920550i | \(0.627741\pi\) | |||||||
\(542\) | −12.5000 | + | 21.6506i | −0.536921 | + | 0.929974i | ||||
\(543\) | 1.00000 | − | 1.73205i | 0.0429141 | − | 0.0743294i | ||||
\(544\) | 1.50000 | + | 2.59808i | 0.0643120 | + | 0.111392i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −10.0000 | − | 3.46410i | −0.427960 | − | 0.148250i | ||||
\(547\) | −8.00000 | −0.342055 | −0.171028 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171028 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(548\) | −7.50000 | − | 12.9904i | −0.320384 | − | 0.554922i | ||||
\(549\) | −1.00000 | + | 1.73205i | −0.0426790 | + | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0000 | − | 20.7846i | −0.511217 | − | 0.885454i | ||||
\(552\) | −3.00000 | −0.127688 | ||||||||
\(553\) | −3.50000 | − | 18.1865i | −0.148835 | − | 0.773370i | ||||
\(554\) | 26.0000 | 1.10463 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.00000 | + | 1.73205i | −0.0424094 | + | 0.0734553i | ||||
\(557\) | −15.0000 | + | 25.9808i | −0.635570 | + | 1.10084i | 0.350824 | + | 0.936442i | \(0.385902\pi\) |
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(558\) | 2.50000 | + | 4.33013i | 0.105833 | + | 0.183309i | ||||
\(559\) | −32.0000 | −1.35346 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.0000 | −0.759961 | ||||||||
\(562\) | 13.5000 | + | 23.3827i | 0.569463 | + | 0.986339i | ||||
\(563\) | 6.00000 | − | 10.3923i | 0.252870 | − | 0.437983i | −0.711445 | − | 0.702742i | \(-0.751959\pi\) |
0.964315 | + | 0.264758i | \(0.0852922\pi\) | |||||||
\(564\) | −4.50000 | + | 7.79423i | −0.189484 | + | 0.328196i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −22.0000 | −0.924729 | ||||||||
\(567\) | 2.00000 | − | 1.73205i | 0.0839921 | − | 0.0727393i | ||||
\(568\) | 9.00000 | 0.377632 | ||||||||
\(569\) | 7.50000 | + | 12.9904i | 0.314416 | + | 0.544585i | 0.979313 | − | 0.202350i | \(-0.0648579\pi\) |
−0.664897 | + | 0.746935i | \(0.731525\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | −12.0000 | − | 20.7846i | −0.501745 | − | 0.869048i | ||||
\(573\) | −15.0000 | −0.626634 | ||||||||
\(574\) | 1.50000 | + | 7.79423i | 0.0626088 | + | 0.325325i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 1.00000 | − | 1.73205i | 0.0416305 | − | 0.0721062i | −0.844459 | − | 0.535620i | \(-0.820078\pi\) |
0.886090 | + | 0.463513i | \(0.153411\pi\) | |||||||
\(578\) | −4.00000 | + | 6.92820i | −0.166378 | + | 0.288175i | ||||
\(579\) | −2.50000 | − | 4.33013i | −0.103896 | − | 0.179954i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.0000 | − | 5.19615i | −0.622305 | − | 0.215573i | ||||
\(582\) | −17.0000 | −0.704673 | ||||||||
\(583\) | 36.0000 | + | 62.3538i | 1.49097 | + | 2.58243i | ||||
\(584\) | −7.00000 | + | 12.1244i | −0.289662 | + | 0.501709i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.00000 | + | 15.5885i | 0.371787 | + | 0.643953i | ||||
\(587\) | −18.0000 | −0.742940 | −0.371470 | − | 0.928445i | \(-0.621146\pi\) | ||||
−0.371470 | + | 0.928445i | \(0.621146\pi\) | |||||||
\(588\) | −1.00000 | + | 6.92820i | −0.0412393 | + | 0.285714i | ||||
\(589\) | −20.0000 | −0.824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.00000 | − | 6.92820i | 0.164399 | − | 0.284747i | ||||
\(593\) | −16.5000 | − | 28.5788i | −0.677574 | − | 1.17359i | −0.975709 | − | 0.219069i | \(-0.929698\pi\) |
0.298136 | − | 0.954524i | \(-0.403635\pi\) | |||||||
\(594\) | 6.00000 | 0.246183 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 2.50000 | + | 4.33013i | 0.102318 | + | 0.177220i | ||||
\(598\) | −6.00000 | + | 10.3923i | −0.245358 | + | 0.424973i | ||||
\(599\) | −4.50000 | + | 7.79423i | −0.183865 | + | 0.318464i | −0.943193 | − | 0.332244i | \(-0.892194\pi\) |
0.759328 | + | 0.650708i | \(0.225528\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.0000 | −1.38689 | −0.693444 | − | 0.720510i | \(-0.743908\pi\) | ||||
−0.693444 | + | 0.720510i | \(0.743908\pi\) | |||||||
\(602\) | 4.00000 | + | 20.7846i | 0.163028 | + | 0.847117i | ||||
\(603\) | −8.00000 | −0.325785 | ||||||||
\(604\) | 8.00000 | + | 13.8564i | 0.325515 | + | 0.563809i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.00000 | + | 10.3923i | −0.243733 | + | 0.422159i | ||||
\(607\) | 5.50000 | + | 9.52628i | 0.223238 | + | 0.386660i | 0.955789 | − | 0.294052i | \(-0.0950039\pi\) |
−0.732551 | + | 0.680712i | \(0.761671\pi\) | |||||||
\(608\) | 4.00000 | 0.162221 | ||||||||
\(609\) | 12.0000 | − | 10.3923i | 0.486265 | − | 0.421117i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.0000 | + | 31.1769i | 0.728202 | + | 1.26128i | ||||
\(612\) | −1.50000 | + | 2.59808i | −0.0606339 | + | 0.105021i | ||||
\(613\) | −17.0000 | + | 29.4449i | −0.686624 | + | 1.18927i | 0.286300 | + | 0.958140i | \(0.407575\pi\) |
−0.972924 | + | 0.231127i | \(0.925759\pi\) | |||||||
\(614\) | −10.0000 | − | 17.3205i | −0.403567 | − | 0.698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.0000 | + | 10.3923i | −0.483494 | + | 0.418718i | ||||
\(617\) | 21.0000 | 0.845428 | 0.422714 | − | 0.906263i | \(-0.361077\pi\) | ||||
0.422714 | + | 0.906263i | \(0.361077\pi\) | |||||||
\(618\) | −6.50000 | − | 11.2583i | −0.261468 | − | 0.452876i | ||||
\(619\) | 23.0000 | − | 39.8372i | 0.924448 | − | 1.60119i | 0.132002 | − | 0.991250i | \(-0.457860\pi\) |
0.792446 | − | 0.609941i | \(-0.208807\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.50000 | − | 2.59808i | −0.0601929 | − | 0.104257i | ||||
\(622\) | −21.0000 | −0.842023 | ||||||||
\(623\) | 1.50000 | + | 7.79423i | 0.0600962 | + | 0.312269i | ||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.50000 | + | 14.7224i | −0.339728 | + | 0.588427i | ||||
\(627\) | −12.0000 | + | 20.7846i | −0.479234 | + | 0.830057i | ||||
\(628\) | 7.00000 | + | 12.1244i | 0.279330 | + | 0.483814i | ||||
\(629\) | −24.0000 | −0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.0000 | 0.676759 | 0.338380 | − | 0.941010i | \(-0.390121\pi\) | ||||
0.338380 | + | 0.941010i | \(0.390121\pi\) | |||||||
\(632\) | −3.50000 | − | 6.06218i | −0.139223 | − | 0.241140i | ||||
\(633\) | 4.00000 | − | 6.92820i | 0.158986 | − | 0.275371i | ||||
\(634\) | −6.00000 | + | 10.3923i | −0.238290 | + | 0.412731i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 12.0000 | 0.475831 | ||||||||
\(637\) | 22.0000 | + | 17.3205i | 0.871672 | + | 0.686264i | ||||
\(638\) | 36.0000 | 1.42525 | ||||||||
\(639\) | 4.50000 | + | 7.79423i | 0.178017 | + | 0.308335i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.5000 | − | 33.7750i | 0.770204 | − | 1.33403i | −0.167247 | − | 0.985915i | \(-0.553488\pi\) |
0.937451 | − | 0.348117i | \(-0.113179\pi\) | |||||||
\(642\) | 3.00000 | + | 5.19615i | 0.118401 | + | 0.205076i | ||||
\(643\) | 34.0000 | 1.34083 | 0.670415 | − | 0.741987i | \(-0.266116\pi\) | ||||
0.670415 | + | 0.741987i | \(0.266116\pi\) | |||||||
\(644\) | 7.50000 | + | 2.59808i | 0.295541 | + | 0.102379i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | − | 10.3923i | −0.236067 | − | 0.408880i | ||||
\(647\) | 6.00000 | − | 10.3923i | 0.235884 | − | 0.408564i | −0.723645 | − | 0.690172i | \(-0.757535\pi\) |
0.959529 | + | 0.281609i | \(0.0908680\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | −18.0000 | − | 31.1769i | −0.706562 | − | 1.22380i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.50000 | − | 12.9904i | −0.0979827 | − | 0.509133i | ||||
\(652\) | −8.00000 | −0.313304 | ||||||||
\(653\) | −18.0000 | − | 31.1769i | −0.704394 | − | 1.22005i | −0.966910 | − | 0.255119i | \(-0.917885\pi\) |
0.262515 | − | 0.964928i | \(-0.415448\pi\) | |||||||
\(654\) | 2.00000 | − | 3.46410i | 0.0782062 | − | 0.135457i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.50000 | + | 2.59808i | 0.0585652 | + | 0.101438i | ||||
\(657\) | −14.0000 | −0.546192 | ||||||||
\(658\) | 18.0000 | − | 15.5885i | 0.701713 | − | 0.607701i | ||||
\(659\) | −30.0000 | −1.16863 | −0.584317 | − | 0.811525i | \(-0.698638\pi\) | ||||
−0.584317 | + | 0.811525i | \(0.698638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00000 | − | 8.66025i | 0.194477 | − | 0.336845i | −0.752252 | − | 0.658876i | \(-0.771032\pi\) |
0.946729 | + | 0.322031i | \(0.104366\pi\) | |||||||
\(662\) | 13.0000 | − | 22.5167i | 0.505259 | − | 0.875135i | ||||
\(663\) | 6.00000 | + | 10.3923i | 0.233021 | + | 0.403604i | ||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.00000 | 0.309994 | ||||||||
\(667\) | −9.00000 | − | 15.5885i | −0.348481 | − | 0.603587i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.50000 | + | 9.52628i | −0.212642 | + | 0.368307i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 0.500000 | + | 2.59808i | 0.0192879 | + | 0.100223i | ||||
\(673\) | 19.0000 | 0.732396 | 0.366198 | − | 0.930537i | \(-0.380659\pi\) | ||||
0.366198 | + | 0.930537i | \(0.380659\pi\) | |||||||
\(674\) | 6.50000 | + | 11.2583i | 0.250371 | + | 0.433655i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.50000 | + | 2.59808i | −0.0576923 | + | 0.0999260i | ||||
\(677\) | 9.00000 | + | 15.5885i | 0.345898 | + | 0.599113i | 0.985517 | − | 0.169580i | \(-0.0542410\pi\) |
−0.639618 | + | 0.768693i | \(0.720908\pi\) | |||||||
\(678\) | −3.00000 | −0.115214 | ||||||||
\(679\) | 42.5000 | + | 14.7224i | 1.63100 | + | 0.564995i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.00000 | + | 15.5885i | 0.344881 | + | 0.597351i | ||||
\(682\) | 15.0000 | − | 25.9808i | 0.574380 | − | 0.994855i | ||||
\(683\) | 9.00000 | − | 15.5885i | 0.344375 | − | 0.596476i | −0.640865 | − | 0.767654i | \(-0.721424\pi\) |
0.985240 | + | 0.171178i | \(0.0547574\pi\) | |||||||
\(684\) | 2.00000 | + | 3.46410i | 0.0764719 | + | 0.132453i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.50000 | − | 16.4545i | 0.324532 | − | 0.628235i | ||||
\(687\) | 22.0000 | 0.839352 | ||||||||
\(688\) | 4.00000 | + | 6.92820i | 0.152499 | + | 0.264135i | ||||
\(689\) | 24.0000 | − | 41.5692i | 0.914327 | − | 1.58366i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.0000 | + | 29.4449i | 0.646710 | + | 1.12014i | 0.983904 | + | 0.178700i | \(0.0571891\pi\) |
−0.337193 | + | 0.941435i | \(0.609478\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | −15.0000 | − | 5.19615i | −0.569803 | − | 0.197386i | ||||
\(694\) | 18.0000 | 0.683271 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.00000 | − | 5.19615i | 0.113715 | − | 0.196960i | ||||
\(697\) | 4.50000 | − | 7.79423i | 0.170450 | − | 0.295227i | ||||
\(698\) | −14.0000 | − | 24.2487i | −0.529908 | − | 0.917827i | ||||
\(699\) | 6.00000 | 0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.0000 | −1.81293 | −0.906467 | − | 0.422276i | \(-0.861231\pi\) | ||||
−0.906467 | + | 0.422276i | \(0.861231\pi\) | |||||||
\(702\) | −2.00000 | − | 3.46410i | −0.0754851 | − | 0.130744i | ||||
\(703\) | −16.0000 | + | 27.7128i | −0.603451 | + | 1.04521i | ||||
\(704\) | −3.00000 | + | 5.19615i | −0.113067 | + | 0.195837i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.0000 | 0.564532 | ||||||||
\(707\) | 24.0000 | − | 20.7846i | 0.902613 | − | 0.781686i | ||||
\(708\) | −6.00000 | −0.225494 | ||||||||
\(709\) | 23.0000 | + | 39.8372i | 0.863783 | + | 1.49612i | 0.868250 | + | 0.496126i | \(0.165245\pi\) |
−0.00446726 | + | 0.999990i | \(0.501422\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.50000 | − | 6.06218i | 0.131260 | − | 0.227349i | ||||
\(712\) | 1.50000 | + | 2.59808i | 0.0562149 | + | 0.0973670i | ||||
\(713\) | −15.0000 | −0.561754 | ||||||||
\(714\) | 6.00000 | − | 5.19615i | 0.224544 | − | 0.194461i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.00000 | + | 15.5885i | 0.336346 | + | 0.582568i | ||||
\(717\) | 1.50000 | − | 2.59808i | 0.0560185 | − | 0.0970269i | ||||
\(718\) | −18.0000 | + | 31.1769i | −0.671754 | + | 1.16351i | ||||
\(719\) | 13.5000 | + | 23.3827i | 0.503465 | + | 0.872027i | 0.999992 | + | 0.00400572i | \(0.00127506\pi\) |
−0.496527 | + | 0.868021i | \(0.665392\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.50000 | + | 33.7750i | 0.242073 | + | 1.25785i | ||||
\(722\) | 3.00000 | 0.111648 | ||||||||
\(723\) | −11.0000 | − | 19.0526i | −0.409094 | − | 0.708572i | ||||
\(724\) | −1.00000 | + | 1.73205i | −0.0371647 | + | 0.0643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −12.5000 | − | 21.6506i | −0.463919 | − | 0.803530i | ||||
\(727\) | 31.0000 | 1.14973 | 0.574863 | − | 0.818250i | \(-0.305055\pi\) | ||||
0.574863 | + | 0.818250i | \(0.305055\pi\) | |||||||
\(728\) | 10.0000 | + | 3.46410i | 0.370625 | + | 0.128388i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0000 | − | 20.7846i | 0.443836 | − | 0.768747i | ||||
\(732\) | 1.00000 | − | 1.73205i | 0.0369611 | − | 0.0640184i | ||||
\(733\) | 25.0000 | + | 43.3013i | 0.923396 | + | 1.59937i | 0.794121 | + | 0.607760i | \(0.207932\pi\) |
0.129275 | + | 0.991609i | \(0.458735\pi\) | |||||||
\(734\) | −28.0000 | −1.03350 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | 0.110581 | ||||||||
\(737\) | 24.0000 | + | 41.5692i | 0.884051 | + | 1.53122i | ||||
\(738\) | −1.50000 | + | 2.59808i | −0.0552158 | + | 0.0956365i | ||||
\(739\) | 8.00000 | − | 13.8564i | 0.294285 | − | 0.509716i | −0.680534 | − | 0.732717i | \(-0.738252\pi\) |
0.974818 | + | 0.223001i | \(0.0715853\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.0000 | 0.587775 | ||||||||
\(742\) | −30.0000 | − | 10.3923i | −1.10133 | − | 0.381514i | ||||
\(743\) | −9.00000 | −0.330178 | −0.165089 | − | 0.986279i | \(-0.552791\pi\) | ||||
−0.165089 | + | 0.986279i | \(0.552791\pi\) | |||||||
\(744\) | −2.50000 | − | 4.33013i | −0.0916544 | − | 0.158750i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.00000 | + | 6.92820i | −0.146450 | + | 0.253660i | ||||
\(747\) | −3.00000 | − | 5.19615i | −0.109764 | − | 0.190117i | ||||
\(748\) | 18.0000 | 0.658145 | ||||||||
\(749\) | −3.00000 | − | 15.5885i | −0.109618 | − | 0.569590i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | + | 13.8564i | 0.291924 | + | 0.505627i | 0.974265 | − | 0.225407i | \(-0.0723712\pi\) |
−0.682341 | + | 0.731034i | \(0.739038\pi\) | |||||||
\(752\) | 4.50000 | − | 7.79423i | 0.164098 | − | 0.284226i | ||||
\(753\) | 12.0000 | − | 20.7846i | 0.437304 | − | 0.757433i | ||||
\(754\) | −12.0000 | − | 20.7846i | −0.437014 | − | 0.756931i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.00000 | + | 1.73205i | −0.0727393 | + | 0.0629941i | ||||
\(757\) | 4.00000 | 0.145382 | 0.0726912 | − | 0.997354i | \(-0.476841\pi\) | ||||
0.0726912 | + | 0.997354i | \(0.476841\pi\) | |||||||
\(758\) | −5.00000 | − | 8.66025i | −0.181608 | − | 0.314555i | ||||
\(759\) | −9.00000 | + | 15.5885i | −0.326679 | + | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.50000 | − | 7.79423i | −0.163125 | − | 0.282541i | 0.772863 | − | 0.634573i | \(-0.218824\pi\) |
−0.935988 | + | 0.352032i | \(0.885491\pi\) | |||||||
\(762\) | 16.0000 | 0.579619 | ||||||||
\(763\) | −8.00000 | + | 6.92820i | −0.289619 | + | 0.250818i | ||||
\(764\) | 15.0000 | 0.542681 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.5000 | + | 18.1865i | −0.379380 | + | 0.657106i | ||||
\(767\) | −12.0000 | + | 20.7846i | −0.433295 | + | 0.750489i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | 50.0000 | 1.80305 | 0.901523 | − | 0.432731i | \(-0.142450\pi\) | ||||
0.901523 | + | 0.432731i | \(0.142450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0000 | −0.648254 | ||||||||
\(772\) | 2.50000 | + | 4.33013i | 0.0899770 | + | 0.155845i | ||||
\(773\) | −6.00000 | + | 10.3923i | −0.215805 | + | 0.373785i | −0.953521 | − | 0.301326i | \(-0.902571\pi\) |
0.737716 | + | 0.675111i | \(0.235904\pi\) | |||||||
\(774\) | −4.00000 | + | 6.92820i | −0.143777 | + | 0.249029i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.0000 | 0.610264 | ||||||||
\(777\) | −20.0000 | − | 6.92820i | −0.717496 | − | 0.248548i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.00000 | − | 10.3923i | −0.214972 | − | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.0000 | − | 46.7654i | 0.966136 | − | 1.67340i | ||||
\(782\) | −4.50000 | − | 7.79423i | −0.160920 | − | 0.278721i | ||||
\(783\) | 6.00000 | 0.214423 | ||||||||
\(784\) | 1.00000 | − | 6.92820i | 0.0357143 | − | 0.247436i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.00000 | + | 15.5885i | 0.321019 | + | 0.556022i | ||||
\(787\) | 4.00000 | − | 6.92820i | 0.142585 | − | 0.246964i | −0.785885 | − | 0.618373i | \(-0.787792\pi\) |
0.928469 | + | 0.371409i | \(0.121125\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.50000 | + | 2.59808i | 0.0534014 | + | 0.0924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.50000 | + | 2.59808i | 0.266669 | + | 0.0923770i | ||||
\(792\) | −6.00000 | −0.213201 | ||||||||
\(793\) | −4.00000 | − | 6.92820i | −0.142044 | − | 0.246028i | ||||
\(794\) | −1.00000 | + | 1.73205i | −0.0354887 | + | 0.0614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.50000 | − | 4.33013i | −0.0886102 | − | 0.153477i | ||||
\(797\) | 18.0000 | 0.637593 | 0.318796 | − | 0.947823i | \(-0.396721\pi\) | ||||
0.318796 | + | 0.947823i | \(0.396721\pi\) | |||||||
\(798\) | −2.00000 | − | 10.3923i | −0.0707992 | − | 0.367884i | ||||
\(799\) | −27.0000 | −0.955191 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.50000 | + | 2.59808i | −0.0529999 | + | 0.0917985i | ||||
\(802\) | −3.00000 | + | 5.19615i | −0.105934 | + | 0.183483i | ||||
\(803\) | 42.0000 | + | 72.7461i | 1.48215 | + | 2.56716i | ||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.0000 | −0.704470 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.00000 | − | 10.3923i | 0.211079 | − | 0.365600i | ||||
\(809\) | 3.00000 | − | 5.19615i | 0.105474 | − | 0.182687i | −0.808458 | − | 0.588555i | \(-0.799697\pi\) |
0.913932 | + | 0.405868i | \(0.133031\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.0000 | −1.40459 | −0.702295 | − | 0.711886i | \(-0.747841\pi\) | ||||
−0.702295 | + | 0.711886i | \(0.747841\pi\) | |||||||
\(812\) | −12.0000 | + | 10.3923i | −0.421117 | + | 0.364698i | ||||
\(813\) | 25.0000 | 0.876788 | ||||||||
\(814\) | −24.0000 | − | 41.5692i | −0.841200 | − | 1.45700i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.50000 | − | 2.59808i | 0.0525105 | − | 0.0909509i | ||||
\(817\) | −16.0000 | − | 27.7128i | −0.559769 | − | 0.969549i | ||||
\(818\) | −29.0000 | −1.01396 | ||||||||
\(819\) | 2.00000 | + | 10.3923i | 0.0698857 | + | 0.363137i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.0000 | − | 31.1769i | −0.628204 | − | 1.08808i | −0.987912 | − | 0.155017i | \(-0.950457\pi\) |
0.359708 | − | 0.933065i | \(-0.382876\pi\) | |||||||
\(822\) | −7.50000 | + | 12.9904i | −0.261593 | + | 0.453092i | ||||
\(823\) | 22.0000 | − | 38.1051i | 0.766872 | − | 1.32826i | −0.172379 | − | 0.985031i | \(-0.555146\pi\) |
0.939251 | − | 0.343230i | \(-0.111521\pi\) | |||||||
\(824\) | 6.50000 | + | 11.2583i | 0.226438 | + | 0.392203i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.0000 | + | 5.19615i | 0.521917 | + | 0.180797i | ||||
\(827\) | −30.0000 | −1.04320 | −0.521601 | − | 0.853189i | \(-0.674665\pi\) | ||||
−0.521601 | + | 0.853189i | \(0.674665\pi\) | |||||||
\(828\) | 1.50000 | + | 2.59808i | 0.0521286 | + | 0.0902894i | ||||
\(829\) | −1.00000 | + | 1.73205i | −0.0347314 | + | 0.0601566i | −0.882869 | − | 0.469620i | \(-0.844391\pi\) |
0.848137 | + | 0.529777i | \(0.177724\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.0000 | − | 22.5167i | −0.450965 | − | 0.781094i | ||||
\(832\) | 4.00000 | 0.138675 | ||||||||
\(833\) | −19.5000 | + | 7.79423i | −0.675635 | + | 0.270054i | ||||
\(834\) | 2.00000 | 0.0692543 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.0000 | − | 20.7846i | 0.415029 | − | 0.718851i | ||||
\(837\) | 2.50000 | − | 4.33013i | 0.0864126 | − | 0.149671i | ||||
\(838\) | 12.0000 | + | 20.7846i | 0.414533 | + | 0.717992i | ||||
\(839\) | 15.0000 | 0.517858 | 0.258929 | − | 0.965896i | \(-0.416631\pi\) | ||||
0.258929 | + | 0.965896i | \(0.416631\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | −2.00000 | − | 3.46410i | −0.0689246 | − | 0.119381i | ||||
\(843\) | 13.5000 | − | 23.3827i | 0.464965 | − | 0.805342i | ||||
\(844\) | −4.00000 | + | 6.92820i | −0.137686 | + | 0.238479i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.00000 | 0.309426 | ||||||||
\(847\) | 12.5000 | + | 64.9519i | 0.429505 | + | 2.23177i | ||||
\(848\) | −12.0000 | −0.412082 | ||||||||
\(849\) | 11.0000 | + | 19.0526i | 0.377519 | + | 0.653882i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.0000 | + | 20.7846i | −0.411355 | + | 0.712487i | ||||
\(852\) | −4.50000 | − | 7.79423i | −0.154167 | − | 0.267026i | ||||
\(853\) | 28.0000 | 0.958702 | 0.479351 | − | 0.877623i | \(-0.340872\pi\) | ||||
0.479351 | + | 0.877623i | \(0.340872\pi\) | |||||||
\(854\) | −4.00000 | + | 3.46410i | −0.136877 | + | 0.118539i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.00000 | − | 5.19615i | −0.102538 | − | 0.177601i | ||||
\(857\) | 3.00000 | − | 5.19615i | 0.102478 | − | 0.177497i | −0.810227 | − | 0.586116i | \(-0.800656\pi\) |
0.912705 | + | 0.408619i | \(0.133990\pi\) | |||||||
\(858\) | −12.0000 | + | 20.7846i | −0.409673 | + | 0.709575i | ||||
\(859\) | −7.00000 | − | 12.1244i | −0.238837 | − | 0.413678i | 0.721544 | − | 0.692369i | \(-0.243433\pi\) |
−0.960381 | + | 0.278691i | \(0.910099\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.00000 | − | 5.19615i | 0.204479 | − | 0.177084i | ||||
\(862\) | −21.0000 | −0.715263 | ||||||||
\(863\) | 10.5000 | + | 18.1865i | 0.357424 | + | 0.619077i | 0.987530 | − | 0.157433i | \(-0.0503217\pi\) |
−0.630106 | + | 0.776509i | \(0.716988\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.50000 | + | 6.06218i | 0.118935 | + | 0.206001i | ||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | 2.50000 | + | 12.9904i | 0.0848555 | + | 0.440922i | ||||
\(869\) | −42.0000 | −1.42475 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.0000 | − | 27.7128i | 0.542139 | − | 0.939013i | ||||
\(872\) | −2.00000 | + | 3.46410i | −0.0677285 | + | 0.117309i | ||||
\(873\) | 8.50000 | + | 14.7224i | 0.287681 | + | 0.498279i | ||||
\(874\) | −12.0000 | −0.405906 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.0000 | 0.473016 | ||||||||
\(877\) | 1.00000 | + | 1.73205i | 0.0337676 | + | 0.0584872i | 0.882415 | − | 0.470471i | \(-0.155916\pi\) |
−0.848648 | + | 0.528958i | \(0.822583\pi\) | |||||||
\(878\) | −6.50000 | + | 11.2583i | −0.219364 | + | 0.379950i | ||||
\(879\) | 9.00000 | − | 15.5885i | 0.303562 | − | 0.525786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.0000 | 0.505363 | 0.252681 | − | 0.967550i | \(-0.418688\pi\) | ||||
0.252681 | + | 0.967550i | \(0.418688\pi\) | |||||||
\(882\) | 6.50000 | − | 2.59808i | 0.218866 | − | 0.0874818i | ||||
\(883\) | −14.0000 | −0.471138 | −0.235569 | − | 0.971858i | \(-0.575695\pi\) | ||||
−0.235569 | + | 0.971858i | \(0.575695\pi\) | |||||||
\(884\) | −6.00000 | − | 10.3923i | −0.201802 | − | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.0000 | − | 20.7846i | 0.403148 | − | 0.698273i | ||||
\(887\) | 12.0000 | + | 20.7846i | 0.402921 | + | 0.697879i | 0.994077 | − | 0.108678i | \(-0.0346618\pi\) |
−0.591156 | + | 0.806557i | \(0.701328\pi\) | |||||||
\(888\) | −8.00000 | −0.268462 | ||||||||
\(889\) | −40.0000 | − | 13.8564i | −1.34156 | − | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.00000 | − | 5.19615i | −0.100504 | − | 0.174078i | ||||
\(892\) | 5.50000 | − | 9.52628i | 0.184154 | − | 0.318963i | ||||
\(893\) | −18.0000 | + | 31.1769i | −0.602347 | + | 1.04330i | ||||
\(894\) | 3.00000 | + | 5.19615i | 0.100335 | + | 0.173785i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.500000 | − | 2.59808i | −0.0167038 | − | 0.0867956i | ||||
\(897\) | 12.0000 | 0.400668 | ||||||||
\(898\) | −1.50000 | − | 2.59808i | −0.0500556 | − | 0.0866989i | ||||
\(899\) | 15.0000 | − | 25.9808i | 0.500278 | − | 0.866507i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.0000 | + | 31.1769i | 0.599667 | + | 1.03865i | ||||
\(902\) | 18.0000 | 0.599334 | ||||||||
\(903\) | 16.0000 | − | 13.8564i | 0.532447 | − | 0.461112i | ||||
\(904\) | 3.00000 | 0.0997785 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.00000 | − | 13.8564i | 0.265782 | − | 0.460348i | ||||
\(907\) | 19.0000 | − | 32.9090i | 0.630885 | − | 1.09272i | −0.356487 | − | 0.934300i | \(-0.616025\pi\) |
0.987371 | − | 0.158424i | \(-0.0506412\pi\) | |||||||
\(908\) | −9.00000 | − | 15.5885i | −0.298675 | − | 0.517321i | ||||
\(909\) | 12.0000 | 0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.0000 | −0.695761 | −0.347881 | − | 0.937539i | \(-0.613099\pi\) | ||||
−0.347881 | + | 0.937539i | \(0.613099\pi\) | |||||||
\(912\) | −2.00000 | − | 3.46410i | −0.0662266 | − | 0.114708i | ||||
\(913\) | −18.0000 | + | 31.1769i | −0.595713 | + | 1.03181i | ||||
\(914\) | −1.00000 | + | 1.73205i | −0.0330771 | + | 0.0572911i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.0000 | −0.726900 | ||||||||
\(917\) | −9.00000 | − | 46.7654i | −0.297206 | − | 1.54433i | ||||
\(918\) | 3.00000 | 0.0990148 | ||||||||
\(919\) | −5.50000 | − | 9.52628i | −0.181428 | − | 0.314243i | 0.760939 | − | 0.648824i | \(-0.224739\pi\) |
−0.942367 | + | 0.334581i | \(0.891405\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.0000 | + | 17.3205i | −0.329511 | + | 0.570730i | ||||
\(922\) | 18.0000 | + | 31.1769i | 0.592798 | + | 1.02676i | ||||
\(923\) | −36.0000 | −1.18495 | ||||||||
\(924\) | 15.0000 | + | 5.19615i | 0.493464 | + | 0.170941i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.50000 | + | 11.2583i | 0.213603 | + | 0.369972i | ||||
\(927\) | −6.50000 | + | 11.2583i | −0.213488 | + | 0.369772i | ||||
\(928\) | −3.00000 | + | 5.19615i | −0.0984798 | + | 0.170572i | ||||
\(929\) | 15.0000 | + | 25.9808i | 0.492134 | + | 0.852401i | 0.999959 | − | 0.00905914i | \(-0.00288365\pi\) |
−0.507825 | + | 0.861460i | \(0.669550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.00000 | + | 27.7128i | −0.131095 | + | 0.908251i | ||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | 10.5000 | + | 18.1865i | 0.343755 | + | 0.595400i | ||||
\(934\) | 15.0000 | − | 25.9808i | 0.490815 | − | 0.850117i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.00000 | + | 3.46410i | 0.0653720 | + | 0.113228i | ||||
\(937\) | 34.0000 | 1.11073 | 0.555366 | − | 0.831606i | \(-0.312578\pi\) | ||||
0.555366 | + | 0.831606i | \(0.312578\pi\) | |||||||
\(938\) | −20.0000 | − | 6.92820i | −0.653023 | − | 0.226214i | ||||
\(939\) | 17.0000 | 0.554774 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.00000 | + | 10.3923i | −0.195594 | + | 0.338779i | −0.947095 | − | 0.320953i | \(-0.895997\pi\) |
0.751501 | + | 0.659732i | \(0.229330\pi\) | |||||||
\(942\) | 7.00000 | − | 12.1244i | 0.228072 | − | 0.395033i | ||||
\(943\) | −4.50000 | − | 7.79423i | −0.146540 | − | 0.253815i | ||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 48.0000 | 1.56061 | ||||||||
\(947\) | −24.0000 | − | 41.5692i | −0.779895 | − | 1.35082i | −0.932002 | − | 0.362454i | \(-0.881939\pi\) |
0.152106 | − | 0.988364i | \(-0.451394\pi\) | |||||||
\(948\) | −3.50000 | + | 6.06218i | −0.113675 | + | 0.196890i | ||||
\(949\) | 28.0000 | − | 48.4974i | 0.908918 | − | 1.57429i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.0000 | 0.389127 | ||||||||
\(952\) | −6.00000 | + | 5.19615i | −0.194461 | + | 0.168408i | ||||
\(953\) | −6.00000 | −0.194359 | −0.0971795 | − | 0.995267i | \(-0.530982\pi\) | ||||
−0.0971795 | + | 0.995267i | \(0.530982\pi\) | |||||||
\(954\) | −6.00000 | − | 10.3923i | −0.194257 | − | 0.336463i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.50000 | + | 2.59808i | −0.0485135 | + | 0.0840278i | ||||
\(957\) | −18.0000 | − | 31.1769i | −0.581857 | − | 1.00781i | ||||
\(958\) | −21.0000 | −0.678479 | ||||||||
\(959\) | 30.0000 | − | 25.9808i | 0.968751 | − | 0.838963i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | + | 5.19615i | 0.0967742 | + | 0.167618i | ||||
\(962\) | −16.0000 | + | 27.7128i | −0.515861 | + | 0.893497i | ||||
\(963\) | 3.00000 | − | 5.19615i | 0.0966736 | − | 0.167444i | ||||
\(964\) | 11.0000 | + | 19.0526i | 0.354286 | + | 0.613642i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.50000 | − | 7.79423i | −0.0482617 | − | 0.250775i | ||||
\(967\) | 31.0000 | 0.996893 | 0.498446 | − | 0.866921i | \(-0.333904\pi\) | ||||
0.498446 | + | 0.866921i | \(0.333904\pi\) | |||||||
\(968\) | 12.5000 | + | 21.6506i | 0.401765 | + | 0.695878i | ||||
\(969\) | −6.00000 | + | 10.3923i | −0.192748 | + | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.00000 | − | 5.19615i | −0.0962746 | − | 0.166752i | 0.813865 | − | 0.581054i | \(-0.197359\pi\) |
−0.910140 | + | 0.414301i | \(0.864026\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −5.00000 | − | 1.73205i | −0.160293 | − | 0.0555270i | ||||
\(974\) | −25.0000 | −0.801052 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.00000 | + | 1.73205i | −0.0320092 | + | 0.0554416i | ||||
\(977\) | 28.5000 | − | 49.3634i | 0.911796 | − | 1.57928i | 0.100270 | − | 0.994960i | \(-0.468029\pi\) |
0.811526 | − | 0.584316i | \(-0.198637\pi\) | |||||||
\(978\) | 4.00000 | + | 6.92820i | 0.127906 | + | 0.221540i | ||||
\(979\) | 18.0000 | 0.575282 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.00000 | −0.127710 | ||||||||
\(982\) | −6.00000 | − | 10.3923i | −0.191468 | − | 0.331632i | ||||
\(983\) | −24.0000 | + | 41.5692i | −0.765481 | + | 1.32585i | 0.174511 | + | 0.984655i | \(0.444166\pi\) |
−0.939992 | + | 0.341197i | \(0.889168\pi\) | |||||||
\(984\) | 1.50000 | − | 2.59808i | 0.0478183 | − | 0.0828236i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 18.0000 | 0.573237 | ||||||||
\(987\) | −22.5000 | − | 7.79423i | −0.716183 | − | 0.248093i | ||||
\(988\) | −16.0000 | −0.509028 | ||||||||
\(989\) | −12.0000 | − | 20.7846i | −0.381578 | − | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.5000 | − | 37.2391i | 0.682970 | − | 1.18294i | −0.291100 | − | 0.956693i | \(-0.594021\pi\) |
0.974070 | − | 0.226246i | \(-0.0726454\pi\) | |||||||
\(992\) | 2.50000 | + | 4.33013i | 0.0793751 | + | 0.137482i | ||||
\(993\) | −26.0000 | −0.825085 | ||||||||
\(994\) | 4.50000 | + | 23.3827i | 0.142731 | + | 0.741654i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.00000 | + | 5.19615i | 0.0950586 | + | 0.164646i | ||||
\(997\) | −2.00000 | + | 3.46410i | −0.0633406 | + | 0.109709i | −0.895957 | − | 0.444141i | \(-0.853509\pi\) |
0.832616 | + | 0.553851i | \(0.186842\pi\) | |||||||
\(998\) | 19.0000 | − | 32.9090i | 0.601434 | − | 1.04172i | ||||
\(999\) | −4.00000 | − | 6.92820i | −0.126554 | − | 0.219199i |
(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 | 1050.2.i.q.151.1 | yes | 2 | |
5.2 | odd | 4 | 1050.2.o.h.949.1 | 4 | |||
5.3 | odd | 4 | 1050.2.o.h.949.2 | 4 | |||
5.4 | even | 2 | 1050.2.i.c.151.1 | ✓ | 2 | ||
7.2 | even | 3 | inner | 1050.2.i.q.751.1 | yes | 2 | |
7.3 | odd | 6 | 7350.2.a.bm.1.1 | 1 | |||
7.4 | even | 3 | 7350.2.a.s.1.1 | 1 | |||
35.2 | odd | 12 | 1050.2.o.h.499.2 | 4 | |||
35.4 | even | 6 | 7350.2.a.cy.1.1 | 1 | |||
35.9 | even | 6 | 1050.2.i.c.751.1 | yes | 2 | ||
35.23 | odd | 12 | 1050.2.o.h.499.1 | 4 | |||
35.24 | odd | 6 | 7350.2.a.cg.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.i.c.151.1 | ✓ | 2 | 5.4 | even | 2 | ||
1050.2.i.c.751.1 | yes | 2 | 35.9 | even | 6 | ||
1050.2.i.q.151.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1050.2.i.q.751.1 | yes | 2 | 7.2 | even | 3 | inner | |
1050.2.o.h.499.1 | 4 | 35.23 | odd | 12 | |||
1050.2.o.h.499.2 | 4 | 35.2 | odd | 12 | |||
1050.2.o.h.949.1 | 4 | 5.2 | odd | 4 | |||
1050.2.o.h.949.2 | 4 | 5.3 | odd | 4 | |||
7350.2.a.s.1.1 | 1 | 7.4 | even | 3 | |||
7350.2.a.bm.1.1 | 1 | 7.3 | odd | 6 | |||
7350.2.a.cg.1.1 | 1 | 35.24 | odd | 6 | |||
7350.2.a.cy.1.1 | 1 | 35.4 | even | 6 |