Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(499,1050)]
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, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.499");
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.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 499.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.499 |
Dual form | 1050.2.o.f.949.1 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0.866025 | + | 2.50000i | 0.327327 | + | 0.944911i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | − | 4.00000i | − | 1.10940i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | 0.500000 | − | 2.59808i | 0.133631 | − | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 4.33013 | − | 2.50000i | 1.05021 | − | 0.606339i | 0.127502 | − | 0.991838i | \(-0.459304\pi\) |
0.922708 | + | 0.385499i | \(0.125971\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | −2.00000 | + | 3.46410i | −0.458831 | + | 0.794719i | −0.998899 | − | 0.0469020i | \(-0.985065\pi\) |
0.540068 | + | 0.841621i | \(0.318398\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | + | 1.73205i | 0.436436 | + | 0.377964i | ||||
\(22\) | − | 2.00000i | − | 0.426401i | ||||||
\(23\) | −4.33013 | − | 2.50000i | −0.902894 | − | 0.521286i | −0.0247559 | − | 0.999694i | \(-0.507881\pi\) |
−0.878138 | + | 0.478407i | \(0.841214\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.00000 | + | 3.46410i | −0.392232 | + | 0.679366i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −1.73205 | + | 2.00000i | −0.327327 | + | 0.377964i | ||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.50000 | + | 9.52628i | 0.987829 | + | 1.71097i | 0.628619 | + | 0.777714i | \(0.283621\pi\) |
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 1.73205 | + | 1.00000i | 0.301511 | + | 0.174078i | ||||
\(34\) | −5.00000 | −0.857493 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.92820 | + | 4.00000i | 1.13899 | + | 0.657596i | 0.946180 | − | 0.323640i | \(-0.104907\pi\) |
0.192809 | + | 0.981236i | \(0.438240\pi\) | |||||||
\(38\) | 3.46410 | − | 2.00000i | 0.561951 | − | 0.324443i | ||||
\(39\) | −2.00000 | − | 3.46410i | −0.320256 | − | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.00000 | 0.780869 | 0.390434 | − | 0.920631i | \(-0.372325\pi\) | ||||
0.390434 | + | 0.920631i | \(0.372325\pi\) | |||||||
\(42\) | −0.866025 | − | 2.50000i | −0.133631 | − | 0.385758i | ||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | −1.00000 | + | 1.73205i | −0.150756 | + | 0.261116i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.50000 | + | 4.33013i | 0.368605 | + | 0.638442i | ||||
\(47\) | −0.866025 | − | 0.500000i | −0.126323 | − | 0.0729325i | 0.435507 | − | 0.900185i | \(-0.356569\pi\) |
−0.561830 | + | 0.827253i | \(0.689902\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −5.50000 | + | 4.33013i | −0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.50000 | − | 4.33013i | 0.350070 | − | 0.606339i | ||||
\(52\) | 3.46410 | − | 2.00000i | 0.480384 | − | 0.277350i | ||||
\(53\) | 10.3923 | − | 6.00000i | 1.42749 | − | 0.824163i | 0.430570 | − | 0.902557i | \(-0.358312\pi\) |
0.996922 | + | 0.0783936i | \(0.0249791\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.50000 | − | 0.866025i | 0.334077 | − | 0.115728i | ||||
\(57\) | 4.00000i | 0.529813i | ||||||||
\(58\) | −5.19615 | − | 3.00000i | −0.682288 | − | 0.393919i | ||||
\(59\) | −1.00000 | − | 1.73205i | −0.130189 | − | 0.225494i | 0.793560 | − | 0.608492i | \(-0.208225\pi\) |
−0.923749 | + | 0.382998i | \(0.874892\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.00000 | + | 8.66025i | −0.640184 | + | 1.10883i | 0.345207 | + | 0.938527i | \(0.387809\pi\) |
−0.985391 | + | 0.170305i | \(0.945525\pi\) | |||||||
\(62\) | − | 11.0000i | − | 1.39700i | ||||||
\(63\) | 2.59808 | + | 0.500000i | 0.327327 | + | 0.0629941i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.00000 | − | 1.73205i | −0.123091 | − | 0.213201i | ||||
\(67\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | 4.33013 | + | 2.50000i | 0.525105 | + | 0.303170i | ||||
\(69\) | −5.00000 | −0.601929 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.00000 | −0.118678 | −0.0593391 | − | 0.998238i | \(-0.518899\pi\) | ||||
−0.0593391 | + | 0.998238i | \(0.518899\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 1.73205 | − | 1.00000i | 0.202721 | − | 0.117041i | −0.395203 | − | 0.918594i | \(-0.629326\pi\) |
0.597924 | + | 0.801553i | \(0.295992\pi\) | |||||||
\(74\) | −4.00000 | − | 6.92820i | −0.464991 | − | 0.805387i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | −3.46410 | + | 4.00000i | −0.394771 | + | 0.455842i | ||||
\(78\) | 4.00000i | 0.452911i | ||||||||
\(79\) | 4.50000 | − | 7.79423i | 0.506290 | − | 0.876919i | −0.493684 | − | 0.869641i | \(-0.664350\pi\) |
0.999974 | − | 0.00727784i | \(-0.00231663\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −4.33013 | − | 2.50000i | −0.478183 | − | 0.276079i | ||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | −0.500000 | + | 2.59808i | −0.0545545 | + | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.19615 | − | 3.00000i | 0.557086 | − | 0.321634i | ||||
\(88\) | 1.73205 | − | 1.00000i | 0.184637 | − | 0.106600i | ||||
\(89\) | 5.50000 | − | 9.52628i | 0.582999 | − | 1.00978i | −0.412123 | − | 0.911128i | \(-0.635213\pi\) |
0.995122 | − | 0.0986553i | \(-0.0314541\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.0000 | − | 3.46410i | 1.04828 | − | 0.363137i | ||||
\(92\) | − | 5.00000i | − | 0.521286i | ||||||
\(93\) | 9.52628 | + | 5.50000i | 0.987829 | + | 0.570323i | ||||
\(94\) | 0.500000 | + | 0.866025i | 0.0515711 | + | 0.0893237i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 1.00000i | 0.101535i | 0.998711 | + | 0.0507673i | \(0.0161667\pi\) | ||||
−0.998711 | + | 0.0507673i | \(0.983833\pi\) | |||||||
\(98\) | 6.92820 | − | 1.00000i | 0.699854 | − | 0.101015i | ||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | − | 10.3923i | −0.597022 | − | 1.03407i | −0.993258 | − | 0.115924i | \(-0.963017\pi\) |
0.396236 | − | 0.918149i | \(-0.370316\pi\) | |||||||
\(102\) | −4.33013 | + | 2.50000i | −0.428746 | + | 0.247537i | ||||
\(103\) | −11.2583 | − | 6.50000i | −1.10932 | − | 0.640464i | −0.170664 | − | 0.985329i | \(-0.554591\pi\) |
−0.938652 | + | 0.344865i | \(0.887925\pi\) | |||||||
\(104\) | −4.00000 | −0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0000 | −1.16554 | ||||||||
\(107\) | 1.73205 | + | 1.00000i | 0.167444 | + | 0.0966736i | 0.581380 | − | 0.813632i | \(-0.302513\pi\) |
−0.413936 | + | 0.910306i | \(0.635846\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 2.00000 | + | 3.46410i | 0.191565 | + | 0.331801i | 0.945769 | − | 0.324840i | \(-0.105310\pi\) |
−0.754204 | + | 0.656640i | \(0.771977\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | 0.759326 | ||||||||
\(112\) | −2.59808 | − | 0.500000i | −0.245495 | − | 0.0472456i | ||||
\(113\) | 5.00000i | 0.470360i | 0.971952 | + | 0.235180i | \(0.0755680\pi\) | ||||
−0.971952 | + | 0.235180i | \(0.924432\pi\) | |||||||
\(114\) | 2.00000 | − | 3.46410i | 0.187317 | − | 0.324443i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.00000 | + | 5.19615i | 0.278543 | + | 0.482451i | ||||
\(117\) | −3.46410 | − | 2.00000i | −0.320256 | − | 0.184900i | ||||
\(118\) | 2.00000i | 0.184115i | ||||||||
\(119\) | 10.0000 | + | 8.66025i | 0.916698 | + | 0.793884i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 8.66025 | − | 5.00000i | 0.784063 | − | 0.452679i | ||||
\(123\) | 4.33013 | − | 2.50000i | 0.390434 | − | 0.225417i | ||||
\(124\) | −5.50000 | + | 9.52628i | −0.493915 | + | 0.855485i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | − | 1.73205i | −0.178174 | − | 0.154303i | ||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00000 | + | 5.19615i | −0.262111 | + | 0.453990i | −0.966803 | − | 0.255524i | \(-0.917752\pi\) |
0.704692 | + | 0.709514i | \(0.251085\pi\) | |||||||
\(132\) | 2.00000i | 0.174078i | ||||||||
\(133\) | −10.3923 | − | 2.00000i | −0.901127 | − | 0.173422i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.50000 | − | 4.33013i | −0.214373 | − | 0.371305i | ||||
\(137\) | −19.9186 | + | 11.5000i | −1.70176 | + | 0.982511i | −0.757778 | + | 0.652512i | \(0.773715\pi\) |
−0.943981 | + | 0.329999i | \(0.892952\pi\) | |||||||
\(138\) | 4.33013 | + | 2.50000i | 0.368605 | + | 0.212814i | ||||
\(139\) | −2.00000 | −0.169638 | −0.0848189 | − | 0.996396i | \(-0.527031\pi\) | ||||
−0.0848189 | + | 0.996396i | \(0.527031\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.00000 | −0.0842152 | ||||||||
\(142\) | 0.866025 | + | 0.500000i | 0.0726752 | + | 0.0419591i | ||||
\(143\) | 6.92820 | − | 4.00000i | 0.579365 | − | 0.334497i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | −2.59808 | + | 6.50000i | −0.214286 | + | 0.536111i | ||||
\(148\) | 8.00000i | 0.657596i | ||||||||
\(149\) | 9.00000 | − | 15.5885i | 0.737309 | − | 1.27706i | −0.216394 | − | 0.976306i | \(-0.569430\pi\) |
0.953703 | − | 0.300750i | \(-0.0972370\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | + | 13.8564i | 0.651031 | + | 1.12762i | 0.982873 | + | 0.184284i | \(0.0589965\pi\) |
−0.331842 | + | 0.943335i | \(0.607670\pi\) | |||||||
\(152\) | 3.46410 | + | 2.00000i | 0.280976 | + | 0.162221i | ||||
\(153\) | − | 5.00000i | − | 0.404226i | ||||||
\(154\) | 5.00000 | − | 1.73205i | 0.402911 | − | 0.139573i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | − | 3.46410i | 0.160128 | − | 0.277350i | ||||
\(157\) | 12.1244 | − | 7.00000i | 0.967629 | − | 0.558661i | 0.0691164 | − | 0.997609i | \(-0.477982\pi\) |
0.898513 | + | 0.438948i | \(0.144649\pi\) | |||||||
\(158\) | −7.79423 | + | 4.50000i | −0.620076 | + | 0.358001i | ||||
\(159\) | 6.00000 | − | 10.3923i | 0.475831 | − | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.50000 | − | 12.9904i | 0.197028 | − | 1.02379i | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | −20.7846 | − | 12.0000i | −1.62798 | − | 0.939913i | −0.984696 | − | 0.174282i | \(-0.944240\pi\) |
−0.643280 | − | 0.765631i | \(-0.722427\pi\) | |||||||
\(164\) | 2.50000 | + | 4.33013i | 0.195217 | + | 0.338126i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.00000 | − | 5.19615i | 0.232845 | − | 0.403300i | ||||
\(167\) | − | 16.0000i | − | 1.23812i | −0.785345 | − | 0.619059i | \(-0.787514\pi\) | ||
0.785345 | − | 0.619059i | \(-0.212486\pi\) | |||||||
\(168\) | 1.73205 | − | 2.00000i | 0.133631 | − | 0.154303i | ||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | + | 3.46410i | 0.152944 | + | 0.264906i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.73205 | + | 1.00000i | 0.131685 | + | 0.0760286i | 0.564396 | − | 0.825505i | \(-0.309109\pi\) |
−0.432710 | + | 0.901533i | \(0.642443\pi\) | |||||||
\(174\) | −6.00000 | −0.454859 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.00000 | −0.150756 | ||||||||
\(177\) | −1.73205 | − | 1.00000i | −0.130189 | − | 0.0751646i | ||||
\(178\) | −9.52628 | + | 5.50000i | −0.714025 | + | 0.412242i | ||||
\(179\) | 11.0000 | + | 19.0526i | 0.822179 | + | 1.42406i | 0.904057 | + | 0.427413i | \(0.140575\pi\) |
−0.0818780 | + | 0.996642i | \(0.526092\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | −10.3923 | − | 2.00000i | −0.770329 | − | 0.148250i | ||||
\(183\) | 10.0000i | 0.739221i | ||||||||
\(184\) | −2.50000 | + | 4.33013i | −0.184302 | + | 0.319221i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.50000 | − | 9.52628i | −0.403280 | − | 0.698501i | ||||
\(187\) | 8.66025 | + | 5.00000i | 0.633300 | + | 0.365636i | ||||
\(188\) | − | 1.00000i | − | 0.0729325i | ||||||
\(189\) | 2.50000 | − | 0.866025i | 0.181848 | − | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.5000 | − | 21.6506i | 0.904468 | − | 1.56658i | 0.0828388 | − | 0.996563i | \(-0.473601\pi\) |
0.821629 | − | 0.570022i | \(-0.193065\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 9.52628 | − | 5.50000i | 0.685717 | − | 0.395899i | −0.116289 | − | 0.993215i | \(-0.537100\pi\) |
0.802005 | + | 0.597317i | \(0.203766\pi\) | |||||||
\(194\) | 0.500000 | − | 0.866025i | 0.0358979 | − | 0.0621770i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | 24.0000i | 1.70993i | 0.518686 | + | 0.854965i | \(0.326421\pi\) | ||||
−0.518686 | + | 0.854965i | \(0.673579\pi\) | |||||||
\(198\) | −1.73205 | − | 1.00000i | −0.123091 | − | 0.0710669i | ||||
\(199\) | 2.50000 | + | 4.33013i | 0.177220 | + | 0.306955i | 0.940927 | − | 0.338608i | \(-0.109956\pi\) |
−0.763707 | + | 0.645563i | \(0.776623\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.0000i | 0.844317i | ||||||||
\(203\) | 5.19615 | + | 15.0000i | 0.364698 | + | 1.05279i | ||||
\(204\) | 5.00000 | 0.350070 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.50000 | + | 11.2583i | 0.452876 | + | 0.784405i | ||||
\(207\) | −4.33013 | + | 2.50000i | −0.300965 | + | 0.173762i | ||||
\(208\) | 3.46410 | + | 2.00000i | 0.240192 | + | 0.138675i | ||||
\(209\) | −8.00000 | −0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 10.3923 | + | 6.00000i | 0.713746 | + | 0.412082i | ||||
\(213\) | −0.866025 | + | 0.500000i | −0.0593391 | + | 0.0342594i | ||||
\(214\) | −1.00000 | − | 1.73205i | −0.0683586 | − | 0.118401i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −19.0526 | + | 22.0000i | −1.29337 | + | 1.49346i | ||||
\(218\) | − | 4.00000i | − | 0.270914i | ||||||
\(219\) | 1.00000 | − | 1.73205i | 0.0675737 | − | 0.117041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.0000 | − | 17.3205i | −0.672673 | − | 1.16510i | ||||
\(222\) | −6.92820 | − | 4.00000i | −0.464991 | − | 0.268462i | ||||
\(223\) | 21.0000i | 1.40626i | 0.711059 | + | 0.703132i | \(0.248216\pi\) | ||||
−0.711059 | + | 0.703132i | \(0.751784\pi\) | |||||||
\(224\) | 2.00000 | + | 1.73205i | 0.133631 | + | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.50000 | − | 4.33013i | 0.166298 | − | 0.288036i | ||||
\(227\) | −15.5885 | + | 9.00000i | −1.03464 | + | 0.597351i | −0.918311 | − | 0.395860i | \(-0.870447\pi\) |
−0.116331 | + | 0.993210i | \(0.537113\pi\) | |||||||
\(228\) | −3.46410 | + | 2.00000i | −0.229416 | + | 0.132453i | ||||
\(229\) | −7.00000 | + | 12.1244i | −0.462573 | + | 0.801200i | −0.999088 | − | 0.0426906i | \(-0.986407\pi\) |
0.536515 | + | 0.843891i | \(0.319740\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.00000 | + | 5.19615i | −0.0657952 | + | 0.341882i | ||||
\(232\) | − | 6.00000i | − | 0.393919i | ||||||
\(233\) | −22.5167 | − | 13.0000i | −1.47512 | − | 0.851658i | −0.475509 | − | 0.879711i | \(-0.657736\pi\) |
−0.999606 | + | 0.0280525i | \(0.991069\pi\) | |||||||
\(234\) | 2.00000 | + | 3.46410i | 0.130744 | + | 0.226455i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.00000 | − | 1.73205i | 0.0650945 | − | 0.112747i | ||||
\(237\) | − | 9.00000i | − | 0.584613i | ||||||
\(238\) | −4.33013 | − | 12.5000i | −0.280680 | − | 0.810255i | ||||
\(239\) | −11.0000 | −0.711531 | −0.355765 | − | 0.934575i | \(-0.615780\pi\) | ||||
−0.355765 | + | 0.934575i | \(0.615780\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.00000 | + | 5.19615i | 0.193247 | + | 0.334714i | 0.946324 | − | 0.323218i | \(-0.104765\pi\) |
−0.753077 | + | 0.657932i | \(0.771431\pi\) | |||||||
\(242\) | −6.06218 | + | 3.50000i | −0.389692 | + | 0.224989i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.00000 | −0.318788 | ||||||||
\(247\) | 13.8564 | + | 8.00000i | 0.881662 | + | 0.509028i | ||||
\(248\) | 9.52628 | − | 5.50000i | 0.604919 | − | 0.349250i | ||||
\(249\) | 3.00000 | + | 5.19615i | 0.190117 | + | 0.329293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.00000 | −0.504956 | −0.252478 | − | 0.967603i | \(-0.581245\pi\) | ||||
−0.252478 | + | 0.967603i | \(0.581245\pi\) | |||||||
\(252\) | 0.866025 | + | 2.50000i | 0.0545545 | + | 0.157485i | ||||
\(253\) | − | 10.0000i | − | 0.628695i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −12.1244 | − | 7.00000i | −0.756297 | − | 0.436648i | 0.0716680 | − | 0.997429i | \(-0.477168\pi\) |
−0.827964 | + | 0.560781i | \(0.810501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | + | 20.7846i | −0.248548 | + | 1.29149i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | 5.19615 | − | 3.00000i | 0.321019 | − | 0.185341i | ||||
\(263\) | −18.1865 | + | 10.5000i | −1.12143 | + | 0.647458i | −0.941766 | − | 0.336270i | \(-0.890834\pi\) |
−0.179664 | + | 0.983728i | \(0.557501\pi\) | |||||||
\(264\) | 1.00000 | − | 1.73205i | 0.0615457 | − | 0.106600i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.00000 | + | 6.92820i | 0.490511 | + | 0.424795i | ||||
\(267\) | − | 11.0000i | − | 0.673189i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.0000 | − | 20.7846i | −0.731653 | − | 1.26726i | −0.956176 | − | 0.292791i | \(-0.905416\pi\) |
0.224523 | − | 0.974469i | \(-0.427917\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.50000 | − | 7.79423i | 0.273356 | − | 0.473466i | −0.696363 | − | 0.717689i | \(-0.745200\pi\) |
0.969719 | + | 0.244224i | \(0.0785331\pi\) | |||||||
\(272\) | 5.00000i | 0.303170i | ||||||||
\(273\) | 6.92820 | − | 8.00000i | 0.419314 | − | 0.484182i | ||||
\(274\) | 23.0000 | 1.38948 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.50000 | − | 4.33013i | −0.150482 | − | 0.260643i | ||||
\(277\) | 1.73205 | − | 1.00000i | 0.104069 | − | 0.0600842i | −0.447062 | − | 0.894503i | \(-0.647530\pi\) |
0.551131 | + | 0.834419i | \(0.314196\pi\) | |||||||
\(278\) | 1.73205 | + | 1.00000i | 0.103882 | + | 0.0599760i | ||||
\(279\) | 11.0000 | 0.658553 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.0000 | −1.72999 | −0.864997 | − | 0.501776i | \(-0.832680\pi\) | ||||
−0.864997 | + | 0.501776i | \(0.832680\pi\) | |||||||
\(282\) | 0.866025 | + | 0.500000i | 0.0515711 | + | 0.0297746i | ||||
\(283\) | −22.5167 | + | 13.0000i | −1.33848 | + | 0.772770i | −0.986581 | − | 0.163270i | \(-0.947796\pi\) |
−0.351895 | + | 0.936039i | \(0.614463\pi\) | |||||||
\(284\) | −0.500000 | − | 0.866025i | −0.0296695 | − | 0.0513892i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.00000 | −0.473050 | ||||||||
\(287\) | 4.33013 | + | 12.5000i | 0.255599 | + | 0.737852i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.500000 | + | 0.866025i | 0.0293105 | + | 0.0507673i | ||||
\(292\) | 1.73205 | + | 1.00000i | 0.101361 | + | 0.0585206i | ||||
\(293\) | 18.0000i | 1.05157i | 0.850617 | + | 0.525786i | \(0.176229\pi\) | ||||
−0.850617 | + | 0.525786i | \(0.823771\pi\) | |||||||
\(294\) | 5.50000 | − | 4.33013i | 0.320767 | − | 0.252538i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.00000 | − | 6.92820i | 0.232495 | − | 0.402694i | ||||
\(297\) | 1.73205 | − | 1.00000i | 0.100504 | − | 0.0580259i | ||||
\(298\) | −15.5885 | + | 9.00000i | −0.903015 | + | 0.521356i | ||||
\(299\) | −10.0000 | + | 17.3205i | −0.578315 | + | 1.00167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 16.0000i | − | 0.920697i | ||||||
\(303\) | −10.3923 | − | 6.00000i | −0.597022 | − | 0.344691i | ||||
\(304\) | −2.00000 | − | 3.46410i | −0.114708 | − | 0.198680i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.50000 | + | 4.33013i | −0.142915 | + | 0.247537i | ||||
\(307\) | − | 28.0000i | − | 1.59804i | −0.601302 | − | 0.799022i | \(-0.705351\pi\) | ||
0.601302 | − | 0.799022i | \(-0.294649\pi\) | |||||||
\(308\) | −5.19615 | − | 1.00000i | −0.296078 | − | 0.0569803i | ||||
\(309\) | −13.0000 | −0.739544 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.5000 | − | 25.1147i | −0.822220 | − | 1.42413i | −0.904026 | − | 0.427478i | \(-0.859402\pi\) |
0.0818063 | − | 0.996648i | \(-0.473931\pi\) | |||||||
\(312\) | −3.46410 | + | 2.00000i | −0.196116 | + | 0.113228i | ||||
\(313\) | 0.866025 | + | 0.500000i | 0.0489506 | + | 0.0282617i | 0.524276 | − | 0.851549i | \(-0.324336\pi\) |
−0.475325 | + | 0.879810i | \(0.657669\pi\) | |||||||
\(314\) | −14.0000 | −0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.00000 | 0.506290 | ||||||||
\(317\) | 3.46410 | + | 2.00000i | 0.194563 | + | 0.112331i | 0.594117 | − | 0.804379i | \(-0.297502\pi\) |
−0.399554 | + | 0.916710i | \(0.630835\pi\) | |||||||
\(318\) | −10.3923 | + | 6.00000i | −0.582772 | + | 0.336463i | ||||
\(319\) | 6.00000 | + | 10.3923i | 0.335936 | + | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.00000 | 0.111629 | ||||||||
\(322\) | −8.66025 | + | 10.0000i | −0.482617 | + | 0.557278i | ||||
\(323\) | 20.0000i | 1.11283i | ||||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.0000 | + | 20.7846i | 0.664619 | + | 1.15115i | ||||
\(327\) | 3.46410 | + | 2.00000i | 0.191565 | + | 0.110600i | ||||
\(328\) | − | 5.00000i | − | 0.276079i | ||||||
\(329\) | 0.500000 | − | 2.59808i | 0.0275659 | − | 0.143237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.00000 | + | 8.66025i | −0.274825 | + | 0.476011i | −0.970091 | − | 0.242742i | \(-0.921953\pi\) |
0.695266 | + | 0.718752i | \(0.255287\pi\) | |||||||
\(332\) | −5.19615 | + | 3.00000i | −0.285176 | + | 0.164646i | ||||
\(333\) | 6.92820 | − | 4.00000i | 0.379663 | − | 0.219199i | ||||
\(334\) | −8.00000 | + | 13.8564i | −0.437741 | + | 0.758189i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.50000 | + | 0.866025i | −0.136386 | + | 0.0472456i | ||||
\(337\) | − | 13.0000i | − | 0.708155i | −0.935216 | − | 0.354078i | \(-0.884795\pi\) | ||
0.935216 | − | 0.354078i | \(-0.115205\pi\) | |||||||
\(338\) | 2.59808 | + | 1.50000i | 0.141317 | + | 0.0815892i | ||||
\(339\) | 2.50000 | + | 4.33013i | 0.135781 | + | 0.235180i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.0000 | + | 19.0526i | −0.595683 | + | 1.03175i | ||||
\(342\) | − | 4.00000i | − | 0.216295i | ||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.00000 | − | 1.73205i | −0.0537603 | − | 0.0931156i | ||||
\(347\) | 15.5885 | − | 9.00000i | 0.836832 | − | 0.483145i | −0.0193540 | − | 0.999813i | \(-0.506161\pi\) |
0.856186 | + | 0.516667i | \(0.172828\pi\) | |||||||
\(348\) | 5.19615 | + | 3.00000i | 0.278543 | + | 0.160817i | ||||
\(349\) | 4.00000 | 0.214115 | 0.107058 | − | 0.994253i | \(-0.465857\pi\) | ||||
0.107058 | + | 0.994253i | \(0.465857\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | 1.73205 | + | 1.00000i | 0.0923186 | + | 0.0533002i | ||||
\(353\) | 7.79423 | − | 4.50000i | 0.414845 | − | 0.239511i | −0.278024 | − | 0.960574i | \(-0.589680\pi\) |
0.692869 | + | 0.721063i | \(0.256346\pi\) | |||||||
\(354\) | 1.00000 | + | 1.73205i | 0.0531494 | + | 0.0920575i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.0000 | 0.582999 | ||||||||
\(357\) | 12.9904 | + | 2.50000i | 0.687524 | + | 0.132314i | ||||
\(358\) | − | 22.0000i | − | 1.16274i | ||||||
\(359\) | −10.0000 | + | 17.3205i | −0.527780 | + | 0.914141i | 0.471696 | + | 0.881761i | \(0.343642\pi\) |
−0.999476 | + | 0.0323801i | \(0.989691\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | + | 2.59808i | 0.0789474 | + | 0.136741i | ||||
\(362\) | 19.0526 | + | 11.0000i | 1.00138 | + | 0.578147i | ||||
\(363\) | − | 7.00000i | − | 0.367405i | ||||||
\(364\) | 8.00000 | + | 6.92820i | 0.419314 | + | 0.363137i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.00000 | − | 8.66025i | 0.261354 | − | 0.452679i | ||||
\(367\) | 3.46410 | − | 2.00000i | 0.180825 | − | 0.104399i | −0.406855 | − | 0.913493i | \(-0.633375\pi\) |
0.587680 | + | 0.809093i | \(0.300041\pi\) | |||||||
\(368\) | 4.33013 | − | 2.50000i | 0.225723 | − | 0.130322i | ||||
\(369\) | 2.50000 | − | 4.33013i | 0.130145 | − | 0.225417i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.0000 | + | 20.7846i | 1.24602 | + | 1.07908i | ||||
\(372\) | 11.0000i | 0.570323i | ||||||||
\(373\) | 27.7128 | + | 16.0000i | 1.43492 | + | 0.828449i | 0.997490 | − | 0.0708063i | \(-0.0225572\pi\) |
0.437425 | + | 0.899255i | \(0.355891\pi\) | |||||||
\(374\) | −5.00000 | − | 8.66025i | −0.258544 | − | 0.447811i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.500000 | + | 0.866025i | −0.0257855 | + | 0.0446619i | ||||
\(377\) | − | 24.0000i | − | 1.23606i | ||||||
\(378\) | −2.59808 | − | 0.500000i | −0.133631 | − | 0.0257172i | ||||
\(379\) | 2.00000 | 0.102733 | 0.0513665 | − | 0.998680i | \(-0.483642\pi\) | ||||
0.0513665 | + | 0.998680i | \(0.483642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.6506 | + | 12.5000i | −1.10774 | + | 0.639556i | ||||
\(383\) | −2.59808 | − | 1.50000i | −0.132755 | − | 0.0766464i | 0.432151 | − | 0.901801i | \(-0.357755\pi\) |
−0.564907 | + | 0.825155i | \(0.691088\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.0000 | −0.559885 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.866025 | + | 0.500000i | −0.0439658 | + | 0.0253837i | ||||
\(389\) | 12.0000 | + | 20.7846i | 0.608424 | + | 1.05382i | 0.991500 | + | 0.130105i | \(0.0415314\pi\) |
−0.383076 | + | 0.923717i | \(0.625135\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.0000 | −1.26430 | ||||||||
\(392\) | 4.33013 | + | 5.50000i | 0.218704 | + | 0.277792i | ||||
\(393\) | 6.00000i | 0.302660i | ||||||||
\(394\) | 12.0000 | − | 20.7846i | 0.604551 | − | 1.04711i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.00000 | + | 1.73205i | 0.0502519 | + | 0.0870388i | ||||
\(397\) | −29.4449 | − | 17.0000i | −1.47780 | − | 0.853206i | −0.478110 | − | 0.878300i | \(-0.658678\pi\) |
−0.999685 | + | 0.0250943i | \(0.992011\pi\) | |||||||
\(398\) | − | 5.00000i | − | 0.250627i | ||||||
\(399\) | −10.0000 | + | 3.46410i | −0.500626 | + | 0.173422i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.00000 | − | 5.19615i | 0.149813 | − | 0.259483i | −0.781345 | − | 0.624099i | \(-0.785466\pi\) |
0.931158 | + | 0.364615i | \(0.118800\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.1051 | − | 22.0000i | 1.89815 | − | 1.09590i | ||||
\(404\) | 6.00000 | − | 10.3923i | 0.298511 | − | 0.517036i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.00000 | − | 15.5885i | 0.148888 | − | 0.773642i | ||||
\(407\) | 16.0000i | 0.793091i | ||||||||
\(408\) | −4.33013 | − | 2.50000i | −0.214373 | − | 0.123768i | ||||
\(409\) | −17.5000 | − | 30.3109i | −0.865319 | − | 1.49878i | −0.866730 | − | 0.498778i | \(-0.833782\pi\) |
0.00141047 | − | 0.999999i | \(-0.499551\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.5000 | + | 19.9186i | −0.567253 | + | 0.982511i | ||||
\(412\) | − | 13.0000i | − | 0.640464i | ||||||
\(413\) | 3.46410 | − | 4.00000i | 0.170457 | − | 0.196827i | ||||
\(414\) | 5.00000 | 0.245737 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.00000 | − | 3.46410i | −0.0980581 | − | 0.169842i | ||||
\(417\) | −1.73205 | + | 1.00000i | −0.0848189 | + | 0.0489702i | ||||
\(418\) | 6.92820 | + | 4.00000i | 0.338869 | + | 0.195646i | ||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.0000 | 1.36464 | 0.682318 | − | 0.731055i | \(-0.260972\pi\) | ||||
0.682318 | + | 0.731055i | \(0.260972\pi\) | |||||||
\(422\) | 13.8564 | + | 8.00000i | 0.674519 | + | 0.389434i | ||||
\(423\) | −0.866025 | + | 0.500000i | −0.0421076 | + | 0.0243108i | ||||
\(424\) | −6.00000 | − | 10.3923i | −0.291386 | − | 0.504695i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.00000 | 0.0484502 | ||||||||
\(427\) | −25.9808 | − | 5.00000i | −1.25730 | − | 0.241967i | ||||
\(428\) | 2.00000i | 0.0966736i | ||||||||
\(429\) | 4.00000 | − | 6.92820i | 0.193122 | − | 0.334497i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.50000 | + | 2.59808i | 0.0722525 | + | 0.125145i | 0.899888 | − | 0.436121i | \(-0.143648\pi\) |
−0.827636 | + | 0.561266i | \(0.810315\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 9.00000i | − | 0.432512i | −0.976337 | − | 0.216256i | \(-0.930615\pi\) | ||
0.976337 | − | 0.216256i | \(-0.0693846\pi\) | |||||||
\(434\) | 27.5000 | − | 9.52628i | 1.32004 | − | 0.457276i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.00000 | + | 3.46410i | −0.0957826 | + | 0.165900i | ||||
\(437\) | 17.3205 | − | 10.0000i | 0.828552 | − | 0.478365i | ||||
\(438\) | −1.73205 | + | 1.00000i | −0.0827606 | + | 0.0477818i | ||||
\(439\) | 17.5000 | − | 30.3109i | 0.835229 | − | 1.44666i | −0.0586141 | − | 0.998281i | \(-0.518668\pi\) |
0.893843 | − | 0.448379i | \(-0.147999\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | + | 6.92820i | 0.0476190 | + | 0.329914i | ||||
\(442\) | 20.0000i | 0.951303i | ||||||||
\(443\) | 6.92820 | + | 4.00000i | 0.329169 | + | 0.190046i | 0.655472 | − | 0.755219i | \(-0.272470\pi\) |
−0.326303 | + | 0.945265i | \(0.605803\pi\) | |||||||
\(444\) | 4.00000 | + | 6.92820i | 0.189832 | + | 0.328798i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.5000 | − | 18.1865i | 0.497189 | − | 0.861157i | ||||
\(447\) | − | 18.0000i | − | 0.851371i | ||||||
\(448\) | −0.866025 | − | 2.50000i | −0.0409159 | − | 0.118114i | ||||
\(449\) | −37.0000 | −1.74614 | −0.873069 | − | 0.487597i | \(-0.837874\pi\) | ||||
−0.873069 | + | 0.487597i | \(0.837874\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.00000 | + | 8.66025i | 0.235441 | + | 0.407795i | ||||
\(452\) | −4.33013 | + | 2.50000i | −0.203672 | + | 0.117590i | ||||
\(453\) | 13.8564 | + | 8.00000i | 0.651031 | + | 0.375873i | ||||
\(454\) | 18.0000 | 0.844782 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.00000 | 0.187317 | ||||||||
\(457\) | 12.1244 | + | 7.00000i | 0.567153 | + | 0.327446i | 0.756012 | − | 0.654558i | \(-0.227145\pi\) |
−0.188858 | + | 0.982004i | \(0.560479\pi\) | |||||||
\(458\) | 12.1244 | − | 7.00000i | 0.566534 | − | 0.327089i | ||||
\(459\) | −2.50000 | − | 4.33013i | −0.116690 | − | 0.202113i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.0000 | 0.931493 | 0.465746 | − | 0.884918i | \(-0.345786\pi\) | ||||
0.465746 | + | 0.884918i | \(0.345786\pi\) | |||||||
\(462\) | 3.46410 | − | 4.00000i | 0.161165 | − | 0.186097i | ||||
\(463\) | 13.0000i | 0.604161i | 0.953282 | + | 0.302081i | \(0.0976812\pi\) | ||||
−0.953282 | + | 0.302081i | \(0.902319\pi\) | |||||||
\(464\) | −3.00000 | + | 5.19615i | −0.139272 | + | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.0000 | + | 22.5167i | 0.602213 | + | 1.04306i | ||||
\(467\) | −29.4449 | − | 17.0000i | −1.36255 | − | 0.786666i | −0.372584 | − | 0.927999i | \(-0.621528\pi\) |
−0.989962 | + | 0.141332i | \(0.954861\pi\) | |||||||
\(468\) | − | 4.00000i | − | 0.184900i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.00000 | − | 12.1244i | 0.322543 | − | 0.558661i | ||||
\(472\) | −1.73205 | + | 1.00000i | −0.0797241 | + | 0.0460287i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −4.50000 | + | 7.79423i | −0.206692 | + | 0.358001i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.50000 | + | 12.9904i | −0.114587 | + | 0.595413i | ||||
\(477\) | − | 12.0000i | − | 0.549442i | ||||||
\(478\) | 9.52628 | + | 5.50000i | 0.435722 | + | 0.251564i | ||||
\(479\) | −1.50000 | − | 2.59808i | −0.0685367 | − | 0.118709i | 0.829721 | − | 0.558179i | \(-0.188500\pi\) |
−0.898257 | + | 0.439470i | \(0.855166\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0000 | − | 27.7128i | 0.729537 | − | 1.26360i | ||||
\(482\) | − | 6.00000i | − | 0.273293i | ||||||
\(483\) | −4.33013 | − | 12.5000i | −0.197028 | − | 0.568770i | ||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 33.7750 | − | 19.5000i | 1.53049 | − | 0.883629i | 0.531152 | − | 0.847277i | \(-0.321759\pi\) |
0.999339 | − | 0.0363527i | \(-0.0115740\pi\) | |||||||
\(488\) | 8.66025 | + | 5.00000i | 0.392031 | + | 0.226339i | ||||
\(489\) | −24.0000 | −1.08532 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | 4.33013 | + | 2.50000i | 0.195217 | + | 0.112709i | ||||
\(493\) | 25.9808 | − | 15.0000i | 1.17011 | − | 0.675566i | ||||
\(494\) | −8.00000 | − | 13.8564i | −0.359937 | − | 0.623429i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.0000 | −0.493915 | ||||||||
\(497\) | −0.866025 | − | 2.50000i | −0.0388465 | − | 0.112140i | ||||
\(498\) | − | 6.00000i | − | 0.268866i | ||||||
\(499\) | 11.0000 | − | 19.0526i | 0.492428 | − | 0.852910i | −0.507534 | − | 0.861632i | \(-0.669443\pi\) |
0.999962 | + | 0.00872186i | \(0.00277629\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.00000 | − | 13.8564i | −0.357414 | − | 0.619059i | ||||
\(502\) | 6.92820 | + | 4.00000i | 0.309221 | + | 0.178529i | ||||
\(503\) | 8.00000i | 0.356702i | 0.983967 | + | 0.178351i | \(0.0570763\pi\) | ||||
−0.983967 | + | 0.178351i | \(0.942924\pi\) | |||||||
\(504\) | 0.500000 | − | 2.59808i | 0.0222718 | − | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.00000 | + | 8.66025i | −0.222277 | + | 0.384995i | ||||
\(507\) | −2.59808 | + | 1.50000i | −0.115385 | + | 0.0666173i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.00000 | − | 1.73205i | 0.0443242 | − | 0.0767718i | −0.843012 | − | 0.537895i | \(-0.819220\pi\) |
0.887336 | + | 0.461123i | \(0.152553\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.00000 | + | 3.46410i | 0.176950 | + | 0.153243i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 3.46410 | + | 2.00000i | 0.152944 | + | 0.0883022i | ||||
\(514\) | 7.00000 | + | 12.1244i | 0.308757 | + | 0.534782i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.00000i | − | 0.0879599i | ||||||
\(518\) | 13.8564 | − | 16.0000i | 0.608816 | − | 0.703000i | ||||
\(519\) | 2.00000 | 0.0877903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.50000 | + | 2.59808i | 0.0657162 | + | 0.113824i | 0.897011 | − | 0.442007i | \(-0.145733\pi\) |
−0.831295 | + | 0.555831i | \(0.812400\pi\) | |||||||
\(522\) | −5.19615 | + | 3.00000i | −0.227429 | + | 0.131306i | ||||
\(523\) | 12.1244 | + | 7.00000i | 0.530161 | + | 0.306089i | 0.741082 | − | 0.671414i | \(-0.234313\pi\) |
−0.210921 | + | 0.977503i | \(0.567646\pi\) | |||||||
\(524\) | −6.00000 | −0.262111 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.0000 | 0.915644 | ||||||||
\(527\) | 47.6314 | + | 27.5000i | 2.07486 | + | 1.19792i | ||||
\(528\) | −1.73205 | + | 1.00000i | −0.0753778 | + | 0.0435194i | ||||
\(529\) | 1.00000 | + | 1.73205i | 0.0434783 | + | 0.0753066i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.00000 | −0.0867926 | ||||||||
\(532\) | −3.46410 | − | 10.0000i | −0.150188 | − | 0.433555i | ||||
\(533\) | − | 20.0000i | − | 0.866296i | ||||||
\(534\) | −5.50000 | + | 9.52628i | −0.238008 | + | 0.412242i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.0526 | + | 11.0000i | 0.822179 | + | 0.474685i | ||||
\(538\) | 24.0000i | 1.03471i | ||||||||
\(539\) | −13.0000 | − | 5.19615i | −0.559950 | − | 0.223814i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | − | 3.46410i | 0.0859867 | − | 0.148933i | −0.819825 | − | 0.572615i | \(-0.805929\pi\) |
0.905811 | + | 0.423681i | \(0.139262\pi\) | |||||||
\(542\) | −7.79423 | + | 4.50000i | −0.334791 | + | 0.193292i | ||||
\(543\) | −19.0526 | + | 11.0000i | −0.817624 | + | 0.472055i | ||||
\(544\) | 2.50000 | − | 4.33013i | 0.107187 | − | 0.185653i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −10.0000 | + | 3.46410i | −0.427960 | + | 0.148250i | ||||
\(547\) | − | 8.00000i | − | 0.342055i | −0.985266 | − | 0.171028i | \(-0.945291\pi\) | ||
0.985266 | − | 0.171028i | \(-0.0547087\pi\) | |||||||
\(548\) | −19.9186 | − | 11.5000i | −0.850880 | − | 0.491256i | ||||
\(549\) | 5.00000 | + | 8.66025i | 0.213395 | + | 0.369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0000 | + | 20.7846i | −0.511217 | + | 0.885454i | ||||
\(552\) | 5.00000i | 0.212814i | ||||||||
\(553\) | 23.3827 | + | 4.50000i | 0.994333 | + | 0.191359i | ||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.00000 | − | 1.73205i | −0.0424094 | − | 0.0734553i | ||||
\(557\) | −32.9090 | + | 19.0000i | −1.39440 | + | 0.805056i | −0.993798 | − | 0.111198i | \(-0.964531\pi\) |
−0.400599 | + | 0.916253i | \(0.631198\pi\) | |||||||
\(558\) | −9.52628 | − | 5.50000i | −0.403280 | − | 0.232834i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.0000 | 0.422200 | ||||||||
\(562\) | 25.1147 | + | 14.5000i | 1.05940 | + | 0.611646i | ||||
\(563\) | −31.1769 | + | 18.0000i | −1.31395 | + | 0.758610i | −0.982748 | − | 0.184950i | \(-0.940788\pi\) |
−0.331202 | + | 0.943560i | \(0.607454\pi\) | |||||||
\(564\) | −0.500000 | − | 0.866025i | −0.0210538 | − | 0.0364662i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 26.0000 | 1.09286 | ||||||||
\(567\) | 1.73205 | − | 2.00000i | 0.0727393 | − | 0.0839921i | ||||
\(568\) | 1.00000i | 0.0419591i | ||||||||
\(569\) | 4.50000 | − | 7.79423i | 0.188650 | − | 0.326751i | −0.756151 | − | 0.654398i | \(-0.772922\pi\) |
0.944800 | + | 0.327647i | \(0.106256\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.0000 | + | 38.1051i | 0.920671 | + | 1.59465i | 0.798379 | + | 0.602155i | \(0.205691\pi\) |
0.122292 | + | 0.992494i | \(0.460975\pi\) | |||||||
\(572\) | 6.92820 | + | 4.00000i | 0.289683 | + | 0.167248i | ||||
\(573\) | − | 25.0000i | − | 1.04439i | ||||||
\(574\) | 2.50000 | − | 12.9904i | 0.104348 | − | 0.542208i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 1.73205 | − | 1.00000i | 0.0721062 | − | 0.0416305i | −0.463513 | − | 0.886090i | \(-0.653411\pi\) |
0.535620 | + | 0.844459i | \(0.320078\pi\) | |||||||
\(578\) | −6.92820 | + | 4.00000i | −0.288175 | + | 0.166378i | ||||
\(579\) | 5.50000 | − | 9.52628i | 0.228572 | − | 0.395899i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.0000 | + | 5.19615i | −0.622305 | + | 0.215573i | ||||
\(582\) | − | 1.00000i | − | 0.0414513i | ||||||
\(583\) | 20.7846 | + | 12.0000i | 0.860811 | + | 0.496989i | ||||
\(584\) | −1.00000 | − | 1.73205i | −0.0413803 | − | 0.0716728i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.00000 | − | 15.5885i | 0.371787 | − | 0.643953i | ||||
\(587\) | − | 6.00000i | − | 0.247647i | −0.992304 | − | 0.123823i | \(-0.960484\pi\) | ||
0.992304 | − | 0.123823i | \(-0.0395156\pi\) | |||||||
\(588\) | −6.92820 | + | 1.00000i | −0.285714 | + | 0.0412393i | ||||
\(589\) | −44.0000 | −1.81299 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.0000 | + | 20.7846i | 0.493614 | + | 0.854965i | ||||
\(592\) | −6.92820 | + | 4.00000i | −0.284747 | + | 0.164399i | ||||
\(593\) | −7.79423 | − | 4.50000i | −0.320071 | − | 0.184793i | 0.331353 | − | 0.943507i | \(-0.392495\pi\) |
−0.651424 | + | 0.758714i | \(0.725828\pi\) | |||||||
\(594\) | −2.00000 | −0.0820610 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18.0000 | 0.737309 | ||||||||
\(597\) | 4.33013 | + | 2.50000i | 0.177220 | + | 0.102318i | ||||
\(598\) | 17.3205 | − | 10.0000i | 0.708288 | − | 0.408930i | ||||
\(599\) | 8.50000 | + | 14.7224i | 0.347301 | + | 0.601542i | 0.985769 | − | 0.168106i | \(-0.0537650\pi\) |
−0.638468 | + | 0.769648i | \(0.720432\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.0000 | −1.38689 | −0.693444 | − | 0.720510i | \(-0.743908\pi\) | ||||
−0.693444 | + | 0.720510i | \(0.743908\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.00000 | + | 13.8564i | −0.325515 | + | 0.563809i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.00000 | + | 10.3923i | 0.243733 | + | 0.422159i | ||||
\(607\) | −23.3827 | − | 13.5000i | −0.949074 | − | 0.547948i | −0.0562808 | − | 0.998415i | \(-0.517924\pi\) |
−0.892793 | + | 0.450467i | \(0.851258\pi\) | |||||||
\(608\) | 4.00000i | 0.162221i | ||||||||
\(609\) | 12.0000 | + | 10.3923i | 0.486265 | + | 0.421117i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.00000 | + | 3.46410i | −0.0809113 | + | 0.140143i | ||||
\(612\) | 4.33013 | − | 2.50000i | 0.175035 | − | 0.101057i | ||||
\(613\) | 29.4449 | − | 17.0000i | 1.18927 | − | 0.686624i | 0.231127 | − | 0.972924i | \(-0.425759\pi\) |
0.958140 | + | 0.286300i | \(0.0924254\pi\) | |||||||
\(614\) | −14.0000 | + | 24.2487i | −0.564994 | + | 0.978598i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.00000 | + | 3.46410i | 0.161165 | + | 0.139573i | ||||
\(617\) | − | 29.0000i | − | 1.16750i | −0.811935 | − | 0.583748i | \(-0.801586\pi\) | ||
0.811935 | − | 0.583748i | \(-0.198414\pi\) | |||||||
\(618\) | 11.2583 | + | 6.50000i | 0.452876 | + | 0.261468i | ||||
\(619\) | −7.00000 | − | 12.1244i | −0.281354 | − | 0.487319i | 0.690365 | − | 0.723462i | \(-0.257450\pi\) |
−0.971718 | + | 0.236143i | \(0.924117\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.50000 | + | 4.33013i | −0.100322 | + | 0.173762i | ||||
\(622\) | 29.0000i | 1.16279i | ||||||||
\(623\) | 28.5788 | + | 5.50000i | 1.14499 | + | 0.220353i | ||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.500000 | − | 0.866025i | −0.0199840 | − | 0.0346133i | ||||
\(627\) | −6.92820 | + | 4.00000i | −0.276686 | + | 0.159745i | ||||
\(628\) | 12.1244 | + | 7.00000i | 0.483814 | + | 0.279330i | ||||
\(629\) | 40.0000 | 1.59490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.0000 | 1.31371 | 0.656855 | − | 0.754017i | \(-0.271887\pi\) | ||||
0.656855 | + | 0.754017i | \(0.271887\pi\) | |||||||
\(632\) | −7.79423 | − | 4.50000i | −0.310038 | − | 0.179000i | ||||
\(633\) | −13.8564 | + | 8.00000i | −0.550743 | + | 0.317971i | ||||
\(634\) | −2.00000 | − | 3.46410i | −0.0794301 | − | 0.137577i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 12.0000 | 0.475831 | ||||||||
\(637\) | 17.3205 | + | 22.0000i | 0.686264 | + | 0.871672i | ||||
\(638\) | − | 12.0000i | − | 0.475085i | ||||||
\(639\) | −0.500000 | + | 0.866025i | −0.0197797 | + | 0.0342594i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.50000 | + | 12.9904i | 0.296232 | + | 0.513089i | 0.975271 | − | 0.221013i | \(-0.0709364\pi\) |
−0.679039 | + | 0.734103i | \(0.737603\pi\) | |||||||
\(642\) | −1.73205 | − | 1.00000i | −0.0683586 | − | 0.0394669i | ||||
\(643\) | 26.0000i | 1.02534i | 0.858586 | + | 0.512670i | \(0.171344\pi\) | ||||
−0.858586 | + | 0.512670i | \(0.828656\pi\) | |||||||
\(644\) | 12.5000 | − | 4.33013i | 0.492569 | − | 0.170631i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.0000 | − | 17.3205i | 0.393445 | − | 0.681466i | ||||
\(647\) | 24.2487 | − | 14.0000i | 0.953315 | − | 0.550397i | 0.0592060 | − | 0.998246i | \(-0.481143\pi\) |
0.894109 | + | 0.447849i | \(0.147810\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 2.00000 | − | 3.46410i | 0.0785069 | − | 0.135978i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.50000 | + | 28.5788i | −0.215562 | + | 1.12009i | ||||
\(652\) | − | 24.0000i | − | 0.939913i | ||||||
\(653\) | −24.2487 | − | 14.0000i | −0.948925 | − | 0.547862i | −0.0561784 | − | 0.998421i | \(-0.517892\pi\) |
−0.892747 | + | 0.450558i | \(0.851225\pi\) | |||||||
\(654\) | −2.00000 | − | 3.46410i | −0.0782062 | − | 0.135457i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.50000 | + | 4.33013i | −0.0976086 | + | 0.169063i | ||||
\(657\) | − | 2.00000i | − | 0.0780274i | ||||||
\(658\) | −1.73205 | + | 2.00000i | −0.0675224 | + | 0.0779681i | ||||
\(659\) | 14.0000 | 0.545363 | 0.272681 | − | 0.962104i | \(-0.412090\pi\) | ||||
0.272681 | + | 0.962104i | \(0.412090\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00000 | − | 12.1244i | −0.272268 | − | 0.471583i | 0.697174 | − | 0.716902i | \(-0.254441\pi\) |
−0.969442 | + | 0.245319i | \(0.921107\pi\) | |||||||
\(662\) | 8.66025 | − | 5.00000i | 0.336590 | − | 0.194331i | ||||
\(663\) | −17.3205 | − | 10.0000i | −0.672673 | − | 0.388368i | ||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.00000 | −0.309994 | ||||||||
\(667\) | −25.9808 | − | 15.0000i | −1.00598 | − | 0.580802i | ||||
\(668\) | 13.8564 | − | 8.00000i | 0.536120 | − | 0.309529i | ||||
\(669\) | 10.5000 | + | 18.1865i | 0.405953 | + | 0.703132i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.0000 | −0.772091 | ||||||||
\(672\) | 2.59808 | + | 0.500000i | 0.100223 | + | 0.0192879i | ||||
\(673\) | 19.0000i | 0.732396i | 0.930537 | + | 0.366198i | \(0.119341\pi\) | ||||
−0.930537 | + | 0.366198i | \(0.880659\pi\) | |||||||
\(674\) | −6.50000 | + | 11.2583i | −0.250371 | + | 0.433655i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.50000 | − | 2.59808i | −0.0576923 | − | 0.0999260i | ||||
\(677\) | −15.5885 | − | 9.00000i | −0.599113 | − | 0.345898i | 0.169580 | − | 0.985517i | \(-0.445759\pi\) |
−0.768693 | + | 0.639618i | \(0.779092\pi\) | |||||||
\(678\) | − | 5.00000i | − | 0.192024i | ||||||
\(679\) | −2.50000 | + | 0.866025i | −0.0959412 | + | 0.0332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.00000 | + | 15.5885i | −0.344881 | + | 0.597351i | ||||
\(682\) | 19.0526 | − | 11.0000i | 0.729560 | − | 0.421212i | ||||
\(683\) | −1.73205 | + | 1.00000i | −0.0662751 | + | 0.0382639i | −0.532771 | − | 0.846259i | \(-0.678849\pi\) |
0.466496 | + | 0.884523i | \(0.345516\pi\) | |||||||
\(684\) | −2.00000 | + | 3.46410i | −0.0764719 | + | 0.132453i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.50000 | + | 16.4545i | 0.324532 | + | 0.628235i | ||||
\(687\) | 14.0000i | 0.534133i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.0000 | − | 41.5692i | −0.914327 | − | 1.58366i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.00000 | − | 1.73205i | 0.0380418 | − | 0.0658903i | −0.846378 | − | 0.532583i | \(-0.821221\pi\) |
0.884419 | + | 0.466693i | \(0.154555\pi\) | |||||||
\(692\) | 2.00000i | 0.0760286i | ||||||||
\(693\) | 1.73205 | + | 5.00000i | 0.0657952 | + | 0.189934i | ||||
\(694\) | −18.0000 | −0.683271 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.00000 | − | 5.19615i | −0.113715 | − | 0.196960i | ||||
\(697\) | 21.6506 | − | 12.5000i | 0.820076 | − | 0.473471i | ||||
\(698\) | −3.46410 | − | 2.00000i | −0.131118 | − | 0.0757011i | ||||
\(699\) | −26.0000 | −0.983410 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 3.46410 | + | 2.00000i | 0.130744 | + | 0.0754851i | ||||
\(703\) | −27.7128 | + | 16.0000i | −1.04521 | + | 0.603451i | ||||
\(704\) | −1.00000 | − | 1.73205i | −0.0376889 | − | 0.0652791i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.00000 | −0.338719 | ||||||||
\(707\) | 20.7846 | − | 24.0000i | 0.781686 | − | 0.902613i | ||||
\(708\) | − | 2.00000i | − | 0.0751646i | ||||||
\(709\) | 5.00000 | − | 8.66025i | 0.187779 | − | 0.325243i | −0.756730 | − | 0.653727i | \(-0.773204\pi\) |
0.944509 | + | 0.328484i | \(0.106538\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.50000 | − | 7.79423i | −0.168763 | − | 0.292306i | ||||
\(712\) | −9.52628 | − | 5.50000i | −0.357012 | − | 0.206121i | ||||
\(713\) | − | 55.0000i | − | 2.05977i | ||||||
\(714\) | −10.0000 | − | 8.66025i | −0.374241 | − | 0.324102i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.0000 | + | 19.0526i | −0.411089 | + | 0.712028i | ||||
\(717\) | −9.52628 | + | 5.50000i | −0.355765 | + | 0.205401i | ||||
\(718\) | 17.3205 | − | 10.0000i | 0.646396 | − | 0.373197i | ||||
\(719\) | −1.50000 | + | 2.59808i | −0.0559406 | + | 0.0968919i | −0.892640 | − | 0.450771i | \(-0.851149\pi\) |
0.836699 | + | 0.547663i | \(0.184482\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.50000 | − | 33.7750i | 0.242073 | − | 1.25785i | ||||
\(722\) | − | 3.00000i | − | 0.111648i | ||||||
\(723\) | 5.19615 | + | 3.00000i | 0.193247 | + | 0.111571i | ||||
\(724\) | −11.0000 | − | 19.0526i | −0.408812 | − | 0.708083i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.50000 | + | 6.06218i | −0.129897 | + | 0.224989i | ||||
\(727\) | 33.0000i | 1.22390i | 0.790896 | + | 0.611951i | \(0.209615\pi\) | ||||
−0.790896 | + | 0.611951i | \(0.790385\pi\) | |||||||
\(728\) | −3.46410 | − | 10.0000i | −0.128388 | − | 0.370625i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −8.66025 | + | 5.00000i | −0.320092 | + | 0.184805i | ||||
\(733\) | −25.9808 | − | 15.0000i | −0.959621 | − | 0.554038i | −0.0635649 | − | 0.997978i | \(-0.520247\pi\) |
−0.896056 | + | 0.443940i | \(0.853580\pi\) | |||||||
\(734\) | −4.00000 | −0.147643 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.00000 | −0.184302 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −4.33013 | + | 2.50000i | −0.159394 | + | 0.0920263i | ||||
\(739\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.0000 | 0.587775 | ||||||||
\(742\) | −10.3923 | − | 30.0000i | −0.381514 | − | 1.10133i | ||||
\(743\) | − | 33.0000i | − | 1.21065i | −0.795977 | − | 0.605326i | \(-0.793043\pi\) | ||
0.795977 | − | 0.605326i | \(-0.206957\pi\) | |||||||
\(744\) | 5.50000 | − | 9.52628i | 0.201640 | − | 0.349250i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −16.0000 | − | 27.7128i | −0.585802 | − | 1.01464i | ||||
\(747\) | 5.19615 | + | 3.00000i | 0.190117 | + | 0.109764i | ||||
\(748\) | 10.0000i | 0.365636i | ||||||||
\(749\) | −1.00000 | + | 5.19615i | −0.0365392 | + | 0.189863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0000 | − | 27.7128i | 0.583848 | − | 1.01125i | −0.411170 | − | 0.911559i | \(-0.634880\pi\) |
0.995018 | − | 0.0996961i | \(-0.0317870\pi\) | |||||||
\(752\) | 0.866025 | − | 0.500000i | 0.0315807 | − | 0.0182331i | ||||
\(753\) | −6.92820 | + | 4.00000i | −0.252478 | + | 0.145768i | ||||
\(754\) | −12.0000 | + | 20.7846i | −0.437014 | + | 0.756931i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.00000 | + | 1.73205i | 0.0727393 | + | 0.0629941i | ||||
\(757\) | − | 28.0000i | − | 1.01768i | −0.860862 | − | 0.508839i | \(-0.830075\pi\) | ||
0.860862 | − | 0.508839i | \(-0.169925\pi\) | |||||||
\(758\) | −1.73205 | − | 1.00000i | −0.0629109 | − | 0.0363216i | ||||
\(759\) | −5.00000 | − | 8.66025i | −0.181489 | − | 0.314347i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.50000 | + | 14.7224i | −0.308125 | + | 0.533688i | −0.977952 | − | 0.208829i | \(-0.933035\pi\) |
0.669827 | + | 0.742517i | \(0.266368\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.92820 | + | 8.00000i | −0.250818 | + | 0.289619i | ||||
\(764\) | 25.0000 | 0.904468 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.50000 | + | 2.59808i | 0.0541972 | + | 0.0938723i | ||||
\(767\) | −6.92820 | + | 4.00000i | −0.250163 | + | 0.144432i | ||||
\(768\) | −0.866025 | − | 0.500000i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.0000 | −0.504198 | ||||||||
\(772\) | 9.52628 | + | 5.50000i | 0.342858 | + | 0.197949i | ||||
\(773\) | −3.46410 | + | 2.00000i | −0.124595 | + | 0.0719350i | −0.561002 | − | 0.827814i | \(-0.689584\pi\) |
0.436407 | + | 0.899749i | \(0.356251\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.00000 | 0.0358979 | ||||||||
\(777\) | 6.92820 | + | 20.0000i | 0.248548 | + | 0.717496i | ||||
\(778\) | − | 24.0000i | − | 0.860442i | ||||||
\(779\) | −10.0000 | + | 17.3205i | −0.358287 | + | 0.620572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.00000 | − | 1.73205i | −0.0357828 | − | 0.0619777i | ||||
\(782\) | 21.6506 | + | 12.5000i | 0.774225 | + | 0.446999i | ||||
\(783\) | − | 6.00000i | − | 0.214423i | ||||||
\(784\) | −1.00000 | − | 6.92820i | −0.0357143 | − | 0.247436i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.00000 | − | 5.19615i | 0.107006 | − | 0.185341i | ||||
\(787\) | −34.6410 | + | 20.0000i | −1.23482 | + | 0.712923i | −0.968031 | − | 0.250832i | \(-0.919296\pi\) |
−0.266788 | + | 0.963755i | \(0.585962\pi\) | |||||||
\(788\) | −20.7846 | + | 12.0000i | −0.740421 | + | 0.427482i | ||||
\(789\) | −10.5000 | + | 18.1865i | −0.373810 | + | 0.647458i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.5000 | + | 4.33013i | −0.444449 | + | 0.153962i | ||||
\(792\) | − | 2.00000i | − | 0.0710669i | ||||||
\(793\) | 34.6410 | + | 20.0000i | 1.23014 | + | 0.710221i | ||||
\(794\) | 17.0000 | + | 29.4449i | 0.603307 | + | 1.04496i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.50000 | + | 4.33013i | −0.0886102 | + | 0.153477i | ||||
\(797\) | − | 42.0000i | − | 1.48772i | −0.668338 | − | 0.743858i | \(-0.732994\pi\) | ||
0.668338 | − | 0.743858i | \(-0.267006\pi\) | |||||||
\(798\) | 10.3923 | + | 2.00000i | 0.367884 | + | 0.0707992i | ||||
\(799\) | −5.00000 | −0.176887 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.50000 | − | 9.52628i | −0.194333 | − | 0.336595i | ||||
\(802\) | −5.19615 | + | 3.00000i | −0.183483 | + | 0.105934i | ||||
\(803\) | 3.46410 | + | 2.00000i | 0.122245 | + | 0.0705785i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −44.0000 | −1.54983 | ||||||||
\(807\) | −20.7846 | − | 12.0000i | −0.731653 | − | 0.422420i | ||||
\(808\) | −10.3923 | + | 6.00000i | −0.365600 | + | 0.211079i | ||||
\(809\) | 5.00000 | + | 8.66025i | 0.175791 | + | 0.304478i | 0.940435 | − | 0.339975i | \(-0.110418\pi\) |
−0.764644 | + | 0.644453i | \(0.777085\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.0000 | −1.68551 | −0.842754 | − | 0.538299i | \(-0.819067\pi\) | ||||
−0.842754 | + | 0.538299i | \(0.819067\pi\) | |||||||
\(812\) | −10.3923 | + | 12.0000i | −0.364698 | + | 0.421117i | ||||
\(813\) | − | 9.00000i | − | 0.315644i | ||||||
\(814\) | 8.00000 | − | 13.8564i | 0.280400 | − | 0.485667i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.50000 | + | 4.33013i | 0.0875175 | + | 0.151585i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 35.0000i | 1.22375i | ||||||||
\(819\) | 2.00000 | − | 10.3923i | 0.0698857 | − | 0.363137i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.0000 | + | 45.0333i | −0.907406 | + | 1.57167i | −0.0897520 | + | 0.995964i | \(0.528607\pi\) |
−0.817654 | + | 0.575710i | \(0.804726\pi\) | |||||||
\(822\) | 19.9186 | − | 11.5000i | 0.694740 | − | 0.401109i | ||||
\(823\) | 17.3205 | − | 10.0000i | 0.603755 | − | 0.348578i | −0.166762 | − | 0.985997i | \(-0.553331\pi\) |
0.770517 | + | 0.637419i | \(0.219998\pi\) | |||||||
\(824\) | −6.50000 | + | 11.2583i | −0.226438 | + | 0.392203i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.00000 | + | 1.73205i | −0.173972 | + | 0.0602658i | ||||
\(827\) | 30.0000i | 1.04320i | 0.853189 | + | 0.521601i | \(0.174665\pi\) | ||||
−0.853189 | + | 0.521601i | \(0.825335\pi\) | |||||||
\(828\) | −4.33013 | − | 2.50000i | −0.150482 | − | 0.0868810i | ||||
\(829\) | 13.0000 | + | 22.5167i | 0.451509 | + | 0.782036i | 0.998480 | − | 0.0551154i | \(-0.0175527\pi\) |
−0.546971 | + | 0.837151i | \(0.684219\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.00000 | − | 1.73205i | 0.0346896 | − | 0.0600842i | ||||
\(832\) | 4.00000i | 0.138675i | ||||||||
\(833\) | −12.9904 | + | 32.5000i | −0.450090 | + | 1.12606i | ||||
\(834\) | 2.00000 | 0.0692543 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.00000 | − | 6.92820i | −0.138343 | − | 0.239617i | ||||
\(837\) | 9.52628 | − | 5.50000i | 0.329276 | − | 0.190108i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.00000 | 0.310715 | 0.155357 | − | 0.987858i | \(-0.450347\pi\) | ||||
0.155357 | + | 0.987858i | \(0.450347\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | −24.2487 | − | 14.0000i | −0.835666 | − | 0.482472i | ||||
\(843\) | −25.1147 | + | 14.5000i | −0.864997 | + | 0.499407i | ||||
\(844\) | −8.00000 | − | 13.8564i | −0.275371 | − | 0.476957i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.00000 | 0.0343807 | ||||||||
\(847\) | 18.1865 | + | 3.50000i | 0.624897 | + | 0.120261i | ||||
\(848\) | 12.0000i | 0.412082i | ||||||||
\(849\) | −13.0000 | + | 22.5167i | −0.446159 | + | 0.772770i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.0000 | − | 34.6410i | −0.685591 | − | 1.18748i | ||||
\(852\) | −0.866025 | − | 0.500000i | −0.0296695 | − | 0.0171297i | ||||
\(853\) | 20.0000i | 0.684787i | 0.939557 | + | 0.342393i | \(0.111238\pi\) | ||||
−0.939557 | + | 0.342393i | \(0.888762\pi\) | |||||||
\(854\) | 20.0000 | + | 17.3205i | 0.684386 | + | 0.592696i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.00000 | − | 1.73205i | 0.0341793 | − | 0.0592003i | ||||
\(857\) | −50.2295 | + | 29.0000i | −1.71581 | + | 0.990621i | −0.789584 | + | 0.613642i | \(0.789704\pi\) |
−0.926222 | + | 0.376979i | \(0.876963\pi\) | |||||||
\(858\) | −6.92820 | + | 4.00000i | −0.236525 | + | 0.136558i | ||||
\(859\) | −5.00000 | + | 8.66025i | −0.170598 | + | 0.295484i | −0.938629 | − | 0.344928i | \(-0.887903\pi\) |
0.768031 | + | 0.640412i | \(0.221237\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.0000 | + | 8.66025i | 0.340799 | + | 0.295141i | ||||
\(862\) | − | 3.00000i | − | 0.102180i | ||||||
\(863\) | −44.1673 | − | 25.5000i | −1.50347 | − | 0.868030i | −0.999992 | − | 0.00402340i | \(-0.998719\pi\) |
−0.503480 | − | 0.864007i | \(-0.667947\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.50000 | + | 7.79423i | −0.152916 | + | 0.264859i | ||||
\(867\) | − | 8.00000i | − | 0.271694i | ||||||
\(868\) | −28.5788 | − | 5.50000i | −0.970029 | − | 0.186682i | ||||
\(869\) | 18.0000 | 0.610608 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 3.46410 | − | 2.00000i | 0.117309 | − | 0.0677285i | ||||
\(873\) | 0.866025 | + | 0.500000i | 0.0293105 | + | 0.0169224i | ||||
\(874\) | −20.0000 | −0.676510 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | 19.0526 | + | 11.0000i | 0.643359 | + | 0.371444i | 0.785907 | − | 0.618344i | \(-0.212196\pi\) |
−0.142548 | + | 0.989788i | \(0.545530\pi\) | |||||||
\(878\) | −30.3109 | + | 17.5000i | −1.02294 | + | 0.590596i | ||||
\(879\) | 9.00000 | + | 15.5885i | 0.303562 | + | 0.525786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.0000 | 1.31394 | 0.656972 | − | 0.753915i | \(-0.271837\pi\) | ||||
0.656972 | + | 0.753915i | \(0.271837\pi\) | |||||||
\(882\) | 2.59808 | − | 6.50000i | 0.0874818 | − | 0.218866i | ||||
\(883\) | 2.00000i | 0.0673054i | 0.999434 | + | 0.0336527i | \(0.0107140\pi\) | ||||
−0.999434 | + | 0.0336527i | \(0.989286\pi\) | |||||||
\(884\) | 10.0000 | − | 17.3205i | 0.336336 | − | 0.582552i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.00000 | − | 6.92820i | −0.134383 | − | 0.232758i | ||||
\(887\) | 48.4974 | + | 28.0000i | 1.62838 | + | 0.940148i | 0.984575 | + | 0.174962i | \(0.0559801\pi\) |
0.643809 | + | 0.765186i | \(0.277353\pi\) | |||||||
\(888\) | − | 8.00000i | − | 0.268462i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | − | 1.73205i | 0.0335013 | − | 0.0580259i | ||||
\(892\) | −18.1865 | + | 10.5000i | −0.608930 | + | 0.351566i | ||||
\(893\) | 3.46410 | − | 2.00000i | 0.115922 | − | 0.0669274i | ||||
\(894\) | −9.00000 | + | 15.5885i | −0.301005 | + | 0.521356i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.500000 | + | 2.59808i | −0.0167038 | + | 0.0867956i | ||||
\(897\) | 20.0000i | 0.667781i | ||||||||
\(898\) | 32.0429 | + | 18.5000i | 1.06929 | + | 0.617353i | ||||
\(899\) | 33.0000 | + | 57.1577i | 1.10061 | + | 1.90632i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.0000 | − | 51.9615i | 0.999445 | − | 1.73109i | ||||
\(902\) | − | 10.0000i | − | 0.332964i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.00000 | 0.166298 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.00000 | − | 13.8564i | −0.265782 | − | 0.460348i | ||||
\(907\) | −15.5885 | + | 9.00000i | −0.517606 | + | 0.298840i | −0.735955 | − | 0.677031i | \(-0.763266\pi\) |
0.218348 | + | 0.975871i | \(0.429933\pi\) | |||||||
\(908\) | −15.5885 | − | 9.00000i | −0.517321 | − | 0.298675i | ||||
\(909\) | −12.0000 | −0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.0000 | 1.68971 | 0.844853 | − | 0.534999i | \(-0.179688\pi\) | ||||
0.844853 | + | 0.534999i | \(0.179688\pi\) | |||||||
\(912\) | −3.46410 | − | 2.00000i | −0.114708 | − | 0.0662266i | ||||
\(913\) | −10.3923 | + | 6.00000i | −0.343935 | + | 0.198571i | ||||
\(914\) | −7.00000 | − | 12.1244i | −0.231539 | − | 0.401038i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.0000 | −0.462573 | ||||||||
\(917\) | −15.5885 | − | 3.00000i | −0.514776 | − | 0.0990687i | ||||
\(918\) | 5.00000i | 0.165025i | ||||||||
\(919\) | 21.5000 | − | 37.2391i | 0.709220 | − | 1.22840i | −0.255927 | − | 0.966696i | \(-0.582381\pi\) |
0.965147 | − | 0.261708i | \(-0.0842858\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.0000 | − | 24.2487i | −0.461316 | − | 0.799022i | ||||
\(922\) | −17.3205 | − | 10.0000i | −0.570421 | − | 0.329332i | ||||
\(923\) | 4.00000i | 0.131662i | ||||||||
\(924\) | −5.00000 | + | 1.73205i | −0.164488 | + | 0.0569803i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.50000 | − | 11.2583i | 0.213603 | − | 0.369972i | ||||
\(927\) | −11.2583 | + | 6.50000i | −0.369772 | + | 0.213488i | ||||
\(928\) | 5.19615 | − | 3.00000i | 0.170572 | − | 0.0984798i | ||||
\(929\) | 17.0000 | − | 29.4449i | 0.557752 | − | 0.966055i | −0.439932 | − | 0.898031i | \(-0.644997\pi\) |
0.997684 | − | 0.0680235i | \(-0.0216693\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.00000 | − | 27.7128i | −0.131095 | − | 0.908251i | ||||
\(932\) | − | 26.0000i | − | 0.851658i | ||||||
\(933\) | −25.1147 | − | 14.5000i | −0.822220 | − | 0.474709i | ||||
\(934\) | 17.0000 | + | 29.4449i | 0.556257 | + | 0.963465i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.00000 | + | 3.46410i | −0.0653720 | + | 0.113228i | ||||
\(937\) | 30.0000i | 0.980057i | 0.871706 | + | 0.490029i | \(0.163014\pi\) | ||||
−0.871706 | + | 0.490029i | \(0.836986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.00000 | 0.0326338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.0000 | − | 31.1769i | −0.586783 | − | 1.01634i | −0.994651 | − | 0.103297i | \(-0.967061\pi\) |
0.407867 | − | 0.913041i | \(-0.366273\pi\) | |||||||
\(942\) | −12.1244 | + | 7.00000i | −0.395033 | + | 0.228072i | ||||
\(943\) | −21.6506 | − | 12.5000i | −0.705042 | − | 0.407056i | ||||
\(944\) | 2.00000 | 0.0650945 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(948\) | 7.79423 | − | 4.50000i | 0.253145 | − | 0.146153i | ||||
\(949\) | −4.00000 | − | 6.92820i | −0.129845 | − | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.00000 | 0.129709 | ||||||||
\(952\) | 8.66025 | − | 10.0000i | 0.280680 | − | 0.324102i | ||||
\(953\) | − | 6.00000i | − | 0.194359i | −0.995267 | − | 0.0971795i | \(-0.969018\pi\) | ||
0.995267 | − | 0.0971795i | \(-0.0309821\pi\) | |||||||
\(954\) | −6.00000 | + | 10.3923i | −0.194257 | + | 0.336463i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.50000 | − | 9.52628i | −0.177883 | − | 0.308102i | ||||
\(957\) | 10.3923 | + | 6.00000i | 0.335936 | + | 0.193952i | ||||
\(958\) | 3.00000i | 0.0969256i | ||||||||
\(959\) | −46.0000 | − | 39.8372i | −1.48542 | − | 1.28641i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −45.0000 | + | 77.9423i | −1.45161 | + | 2.51427i | ||||
\(962\) | −27.7128 | + | 16.0000i | −0.893497 | + | 0.515861i | ||||
\(963\) | 1.73205 | − | 1.00000i | 0.0558146 | − | 0.0322245i | ||||
\(964\) | −3.00000 | + | 5.19615i | −0.0966235 | + | 0.167357i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.50000 | + | 12.9904i | −0.0804362 | + | 0.417959i | ||||
\(967\) | 1.00000i | 0.0321578i | 0.999871 | + | 0.0160789i | \(0.00511830\pi\) | ||||
−0.999871 | + | 0.0160789i | \(0.994882\pi\) | |||||||
\(968\) | −6.06218 | − | 3.50000i | −0.194846 | − | 0.112494i | ||||
\(969\) | 10.0000 | + | 17.3205i | 0.321246 | + | 0.556415i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.00000 | + | 5.19615i | −0.0962746 | + | 0.166752i | −0.910140 | − | 0.414301i | \(-0.864026\pi\) |
0.813865 | + | 0.581054i | \(0.197359\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | −1.73205 | − | 5.00000i | −0.0555270 | − | 0.160293i | ||||
\(974\) | −39.0000 | −1.24964 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.00000 | − | 8.66025i | −0.160046 | − | 0.277208i | ||||
\(977\) | 28.5788 | − | 16.5000i | 0.914318 | − | 0.527882i | 0.0325001 | − | 0.999472i | \(-0.489653\pi\) |
0.881818 | + | 0.471590i | \(0.156320\pi\) | |||||||
\(978\) | 20.7846 | + | 12.0000i | 0.664619 | + | 0.383718i | ||||
\(979\) | 22.0000 | 0.703123 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.00000 | 0.127710 | ||||||||
\(982\) | −10.3923 | − | 6.00000i | −0.331632 | − | 0.191468i | ||||
\(983\) | 13.8564 | − | 8.00000i | 0.441951 | − | 0.255160i | −0.262474 | − | 0.964939i | \(-0.584538\pi\) |
0.704425 | + | 0.709779i | \(0.251205\pi\) | |||||||
\(984\) | −2.50000 | − | 4.33013i | −0.0796971 | − | 0.138039i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −30.0000 | −0.955395 | ||||||||
\(987\) | −0.866025 | − | 2.50000i | −0.0275659 | − | 0.0795759i | ||||
\(988\) | 16.0000i | 0.509028i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.5000 | − | 32.0429i | −0.587672 | − | 1.01788i | −0.994537 | − | 0.104389i | \(-0.966711\pi\) |
0.406865 | − | 0.913488i | \(-0.366622\pi\) | |||||||
\(992\) | 9.52628 | + | 5.50000i | 0.302460 | + | 0.174625i | ||||
\(993\) | 10.0000i | 0.317340i | ||||||||
\(994\) | −0.500000 | + | 2.59808i | −0.0158590 | + | 0.0824060i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.00000 | + | 5.19615i | −0.0950586 | + | 0.164646i | ||||
\(997\) | −3.46410 | + | 2.00000i | −0.109709 | + | 0.0633406i | −0.553851 | − | 0.832616i | \(-0.686842\pi\) |
0.444141 | + | 0.895957i | \(0.353509\pi\) | |||||||
\(998\) | −19.0526 | + | 11.0000i | −0.603098 | + | 0.348199i | ||||
\(999\) | 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.o.f.499.1 | 4 | ||
5.2 | odd | 4 | 1050.2.i.k.751.1 | yes | 2 | ||
5.3 | odd | 4 | 1050.2.i.j.751.1 | yes | 2 | ||
5.4 | even | 2 | inner | 1050.2.o.f.499.2 | 4 | ||
7.4 | even | 3 | inner | 1050.2.o.f.949.2 | 4 | ||
35.2 | odd | 12 | 7350.2.a.z.1.1 | 1 | |||
35.4 | even | 6 | inner | 1050.2.o.f.949.1 | 4 | ||
35.12 | even | 12 | 7350.2.a.h.1.1 | 1 | |||
35.18 | odd | 12 | 1050.2.i.j.151.1 | ✓ | 2 | ||
35.23 | odd | 12 | 7350.2.a.bt.1.1 | 1 | |||
35.32 | odd | 12 | 1050.2.i.k.151.1 | yes | 2 | ||
35.33 | even | 12 | 7350.2.a.cn.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.i.j.151.1 | ✓ | 2 | 35.18 | odd | 12 | ||
1050.2.i.j.751.1 | yes | 2 | 5.3 | odd | 4 | ||
1050.2.i.k.151.1 | yes | 2 | 35.32 | odd | 12 | ||
1050.2.i.k.751.1 | yes | 2 | 5.2 | odd | 4 | ||
1050.2.o.f.499.1 | 4 | 1.1 | even | 1 | trivial | ||
1050.2.o.f.499.2 | 4 | 5.4 | even | 2 | inner | ||
1050.2.o.f.949.1 | 4 | 35.4 | even | 6 | inner | ||
1050.2.o.f.949.2 | 4 | 7.4 | even | 3 | inner | ||
7350.2.a.h.1.1 | 1 | 35.12 | even | 12 | |||
7350.2.a.z.1.1 | 1 | 35.2 | odd | 12 | |||
7350.2.a.bt.1.1 | 1 | 35.23 | odd | 12 | |||
7350.2.a.cn.1.1 | 1 | 35.33 | even | 12 |