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: | no (minimal twist has level 210) |
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.g.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 | ||||||||
\(7\) | −1.73205 | − | 2.00000i | −0.654654 | − | 0.755929i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50000 | + | 4.33013i | 0.753778 | + | 1.30558i | 0.945979 | + | 0.324227i | \(0.105104\pi\) |
−0.192201 | + | 0.981356i | \(0.561563\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | 5.00000i | 1.38675i | 0.720577 | + | 0.693375i | \(0.243877\pi\) | ||||
−0.720577 | + | 0.693375i | \(0.756123\pi\) | |||||||
\(14\) | 0.500000 | + | 2.59808i | 0.133631 | + | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.46410 | + | 2.00000i | −0.840168 | + | 0.485071i | −0.857321 | − | 0.514782i | \(-0.827873\pi\) |
0.0171533 | + | 0.999853i | \(0.494540\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | −3.50000 | + | 6.06218i | −0.802955 | + | 1.39076i | 0.114708 | + | 0.993399i | \(0.463407\pi\) |
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.50000 | − | 0.866025i | −0.545545 | − | 0.188982i | ||||
\(22\) | − | 5.00000i | − | 1.06600i | ||||||
\(23\) | 0.866025 | + | 0.500000i | 0.180579 | + | 0.104257i | 0.587565 | − | 0.809177i | \(-0.300087\pi\) |
−0.406986 | + | 0.913434i | \(0.633420\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.50000 | − | 4.33013i | 0.490290 | − | 0.849208i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0.866025 | − | 2.50000i | 0.163663 | − | 0.472456i | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | + | 1.73205i | 0.179605 | + | 0.311086i | 0.941745 | − | 0.336327i | \(-0.109185\pi\) |
−0.762140 | + | 0.647412i | \(0.775851\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 4.33013 | + | 2.50000i | 0.753778 | + | 0.435194i | ||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.866025 | − | 0.500000i | −0.142374 | − | 0.0821995i | 0.427121 | − | 0.904194i | \(-0.359528\pi\) |
−0.569495 | + | 0.821995i | \(0.692861\pi\) | |||||||
\(38\) | 6.06218 | − | 3.50000i | 0.983415 | − | 0.567775i | ||||
\(39\) | 2.50000 | + | 4.33013i | 0.400320 | + | 0.693375i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.00000 | 0.780869 | 0.390434 | − | 0.920631i | \(-0.372325\pi\) | ||||
0.390434 | + | 0.920631i | \(0.372325\pi\) | |||||||
\(42\) | 1.73205 | + | 2.00000i | 0.267261 | + | 0.308607i | ||||
\(43\) | − | 12.0000i | − | 1.82998i | −0.403473 | − | 0.914991i | \(-0.632197\pi\) | ||
0.403473 | − | 0.914991i | \(-0.367803\pi\) | |||||||
\(44\) | −2.50000 | + | 4.33013i | −0.376889 | + | 0.652791i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.500000 | − | 0.866025i | −0.0737210 | − | 0.127688i | ||||
\(47\) | 9.52628 | + | 5.50000i | 1.38955 | + | 0.802257i | 0.993264 | − | 0.115870i | \(-0.0369655\pi\) |
0.396286 | + | 0.918127i | \(0.370299\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −1.00000 | + | 6.92820i | −0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | + | 3.46410i | −0.280056 | + | 0.485071i | ||||
\(52\) | −4.33013 | + | 2.50000i | −0.600481 | + | 0.346688i | ||||
\(53\) | 7.79423 | − | 4.50000i | 1.07062 | − | 0.618123i | 0.142269 | − | 0.989828i | \(-0.454560\pi\) |
0.928351 | + | 0.371706i | \(0.121227\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | + | 1.73205i | −0.267261 | + | 0.231455i | ||||
\(57\) | 7.00000i | 0.927173i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.00000 | + | 3.46410i | 0.260378 | + | 0.450988i | 0.966342 | − | 0.257260i | \(-0.0828195\pi\) |
−0.705965 | + | 0.708247i | \(0.749486\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | + | 3.46410i | −0.256074 | + | 0.443533i | −0.965187 | − | 0.261562i | \(-0.915762\pi\) |
0.709113 | + | 0.705095i | \(0.249096\pi\) | |||||||
\(62\) | − | 2.00000i | − | 0.254000i | ||||||
\(63\) | −2.59808 | + | 0.500000i | −0.327327 | + | 0.0629941i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.50000 | − | 4.33013i | −0.307729 | − | 0.533002i | ||||
\(67\) | −10.3923 | + | 6.00000i | −1.26962 | + | 0.733017i | −0.974916 | − | 0.222571i | \(-0.928555\pi\) |
−0.294706 | + | 0.955588i | \(0.595222\pi\) | |||||||
\(68\) | −3.46410 | − | 2.00000i | −0.420084 | − | 0.242536i | ||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | −8.66025 | + | 5.00000i | −1.01361 | + | 0.585206i | −0.912245 | − | 0.409644i | \(-0.865653\pi\) |
−0.101361 | + | 0.994850i | \(0.532320\pi\) | |||||||
\(74\) | 0.500000 | + | 0.866025i | 0.0581238 | + | 0.100673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.00000 | −0.802955 | ||||||||
\(77\) | 4.33013 | − | 12.5000i | 0.493464 | − | 1.42451i | ||||
\(78\) | − | 5.00000i | − | 0.566139i | ||||||
\(79\) | −6.00000 | + | 10.3923i | −0.675053 | + | 1.16923i | 0.301401 | + | 0.953498i | \(0.402546\pi\) |
−0.976453 | + | 0.215728i | \(0.930788\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −4.33013 | − | 2.50000i | −0.478183 | − | 0.276079i | ||||
\(83\) | 12.0000i | 1.31717i | 0.752506 | + | 0.658586i | \(0.228845\pi\) | ||||
−0.752506 | + | 0.658586i | \(0.771155\pi\) | |||||||
\(84\) | −0.500000 | − | 2.59808i | −0.0545545 | − | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.00000 | + | 10.3923i | −0.646997 | + | 1.12063i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.33013 | − | 2.50000i | 0.461593 | − | 0.266501i | ||||
\(89\) | 7.00000 | − | 12.1244i | 0.741999 | − | 1.28518i | −0.209585 | − | 0.977790i | \(-0.567211\pi\) |
0.951584 | − | 0.307389i | \(-0.0994552\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.0000 | − | 8.66025i | 1.04828 | − | 0.907841i | ||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | 1.73205 | + | 1.00000i | 0.179605 | + | 0.103695i | ||||
\(94\) | −5.50000 | − | 9.52628i | −0.567282 | − | 0.982561i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | − | 8.00000i | − | 0.812277i | −0.913812 | − | 0.406138i | \(-0.866875\pi\) | ||
0.913812 | − | 0.406138i | \(-0.133125\pi\) | |||||||
\(98\) | 4.33013 | − | 5.50000i | 0.437409 | − | 0.555584i | ||||
\(99\) | 5.00000 | 0.502519 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 3.46410 | − | 2.00000i | 0.342997 | − | 0.198030i | ||||
\(103\) | 6.92820 | + | 4.00000i | 0.682656 | + | 0.394132i | 0.800855 | − | 0.598858i | \(-0.204379\pi\) |
−0.118199 | + | 0.992990i | \(0.537712\pi\) | |||||||
\(104\) | 5.00000 | 0.490290 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.00000 | −0.874157 | ||||||||
\(107\) | 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 | ||||
\(109\) | −1.00000 | − | 1.73205i | −0.0957826 | − | 0.165900i | 0.814152 | − | 0.580651i | \(-0.197202\pi\) |
−0.909935 | + | 0.414751i | \(0.863869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.00000 | −0.0949158 | ||||||||
\(112\) | 2.59808 | − | 0.500000i | 0.245495 | − | 0.0472456i | ||||
\(113\) | 14.0000i | 1.31701i | 0.752577 | + | 0.658505i | \(0.228811\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 3.50000 | − | 6.06218i | 0.327805 | − | 0.567775i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.33013 | + | 2.50000i | 0.400320 | + | 0.231125i | ||||
\(118\) | − | 4.00000i | − | 0.368230i | ||||||
\(119\) | 10.0000 | + | 3.46410i | 0.916698 | + | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 3.46410 | − | 2.00000i | 0.313625 | − | 0.181071i | ||||
\(123\) | 4.33013 | − | 2.50000i | 0.390434 | − | 0.225417i | ||||
\(124\) | −1.00000 | + | 1.73205i | −0.0898027 | + | 0.155543i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.50000 | + | 0.866025i | 0.222718 | + | 0.0771517i | ||||
\(127\) | 9.00000i | 0.798621i | 0.916816 | + | 0.399310i | \(0.130750\pi\) | ||||
−0.916816 | + | 0.399310i | \(0.869250\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −6.00000 | − | 10.3923i | −0.528271 | − | 0.914991i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.50000 | − | 7.79423i | 0.393167 | − | 0.680985i | −0.599699 | − | 0.800226i | \(-0.704713\pi\) |
0.992865 | + | 0.119241i | \(0.0380462\pi\) | |||||||
\(132\) | 5.00000i | 0.435194i | ||||||||
\(133\) | 18.1865 | − | 3.50000i | 1.57697 | − | 0.303488i | ||||
\(134\) | 12.0000 | 1.03664 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.00000 | + | 3.46410i | 0.171499 | + | 0.297044i | ||||
\(137\) | −1.73205 | + | 1.00000i | −0.147979 | + | 0.0854358i | −0.572161 | − | 0.820141i | \(-0.693895\pi\) |
0.424182 | + | 0.905577i | \(0.360562\pi\) | |||||||
\(138\) | −0.866025 | − | 0.500000i | −0.0737210 | − | 0.0425628i | ||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.0000 | 0.926367 | ||||||||
\(142\) | −1.73205 | − | 1.00000i | −0.145350 | − | 0.0839181i | ||||
\(143\) | −21.6506 | + | 12.5000i | −1.81052 | + | 1.04530i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.0000 | 0.827606 | ||||||||
\(147\) | 2.59808 | + | 6.50000i | 0.214286 | + | 0.536111i | ||||
\(148\) | − | 1.00000i | − | 0.0821995i | ||||||
\(149\) | 6.00000 | − | 10.3923i | 0.491539 | − | 0.851371i | −0.508413 | − | 0.861113i | \(-0.669768\pi\) |
0.999953 | + | 0.00974235i | \(0.00310113\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.00000 | − | 12.1244i | −0.569652 | − | 0.986666i | −0.996600 | − | 0.0823900i | \(-0.973745\pi\) |
0.426948 | − | 0.904276i | \(-0.359589\pi\) | |||||||
\(152\) | 6.06218 | + | 3.50000i | 0.491708 | + | 0.283887i | ||||
\(153\) | 4.00000i | 0.323381i | ||||||||
\(154\) | −10.0000 | + | 8.66025i | −0.805823 | + | 0.697863i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.50000 | + | 4.33013i | −0.200160 | + | 0.346688i | ||||
\(157\) | 9.52628 | − | 5.50000i | 0.760280 | − | 0.438948i | −0.0691164 | − | 0.997609i | \(-0.522018\pi\) |
0.829396 | + | 0.558661i | \(0.188685\pi\) | |||||||
\(158\) | 10.3923 | − | 6.00000i | 0.826767 | − | 0.477334i | ||||
\(159\) | 4.50000 | − | 7.79423i | 0.356873 | − | 0.618123i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.500000 | − | 2.59808i | −0.0394055 | − | 0.204757i | ||||
\(162\) | 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 | ||||||||
\(166\) | 6.00000 | − | 10.3923i | 0.465690 | − | 0.806599i | ||||
\(167\) | 11.0000i | 0.851206i | 0.904910 | + | 0.425603i | \(0.139938\pi\) | ||||
−0.904910 | + | 0.425603i | \(0.860062\pi\) | |||||||
\(168\) | −0.866025 | + | 2.50000i | −0.0668153 | + | 0.192879i | ||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.50000 | + | 6.06218i | 0.267652 | + | 0.463586i | ||||
\(172\) | 10.3923 | − | 6.00000i | 0.792406 | − | 0.457496i | ||||
\(173\) | −11.2583 | − | 6.50000i | −0.855955 | − | 0.494186i | 0.00670064 | − | 0.999978i | \(-0.497867\pi\) |
−0.862656 | + | 0.505792i | \(0.831200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.00000 | −0.376889 | ||||||||
\(177\) | 3.46410 | + | 2.00000i | 0.260378 | + | 0.150329i | ||||
\(178\) | −12.1244 | + | 7.00000i | −0.908759 | + | 0.524672i | ||||
\(179\) | −11.5000 | − | 19.9186i | −0.859550 | − | 1.48878i | −0.872358 | − | 0.488867i | \(-0.837410\pi\) |
0.0128080 | − | 0.999918i | \(-0.495923\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.0000 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(182\) | −12.9904 | + | 2.50000i | −0.962911 | + | 0.185312i | ||||
\(183\) | 4.00000i | 0.295689i | ||||||||
\(184\) | 0.500000 | − | 0.866025i | 0.0368605 | − | 0.0638442i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.00000 | − | 1.73205i | −0.0733236 | − | 0.127000i | ||||
\(187\) | −17.3205 | − | 10.0000i | −1.26660 | − | 0.731272i | ||||
\(188\) | 11.0000i | 0.802257i | ||||||||
\(189\) | −2.00000 | + | 1.73205i | −0.145479 | + | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.00000 | + | 12.1244i | −0.506502 | + | 0.877288i | 0.493469 | + | 0.869763i | \(0.335728\pi\) |
−0.999972 | + | 0.00752447i | \(0.997605\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −8.66025 | + | 5.00000i | −0.623379 | + | 0.359908i | −0.778183 | − | 0.628037i | \(-0.783859\pi\) |
0.154805 | + | 0.987945i | \(0.450525\pi\) | |||||||
\(194\) | −4.00000 | + | 6.92820i | −0.287183 | + | 0.497416i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | + | 2.59808i | −0.464286 | + | 0.185577i | ||||
\(197\) | − | 3.00000i | − | 0.213741i | −0.994273 | − | 0.106871i | \(-0.965917\pi\) | ||
0.994273 | − | 0.106871i | \(-0.0340831\pi\) | |||||||
\(198\) | −4.33013 | − | 2.50000i | −0.307729 | − | 0.177667i | ||||
\(199\) | −2.00000 | − | 3.46410i | −0.141776 | − | 0.245564i | 0.786389 | − | 0.617731i | \(-0.211948\pi\) |
−0.928166 | + | 0.372168i | \(0.878615\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.00000 | + | 10.3923i | −0.423207 | + | 0.733017i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.00000 | − | 6.92820i | −0.278693 | − | 0.482711i | ||||
\(207\) | 0.866025 | − | 0.500000i | 0.0601929 | − | 0.0347524i | ||||
\(208\) | −4.33013 | − | 2.50000i | −0.300240 | − | 0.173344i | ||||
\(209\) | −35.0000 | −2.42100 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0000 | 1.17033 | 0.585164 | − | 0.810915i | \(-0.301030\pi\) | ||||
0.585164 | + | 0.810915i | \(0.301030\pi\) | |||||||
\(212\) | 7.79423 | + | 4.50000i | 0.535310 | + | 0.309061i | ||||
\(213\) | 1.73205 | − | 1.00000i | 0.118678 | − | 0.0685189i | ||||
\(214\) | −1.00000 | − | 1.73205i | −0.0683586 | − | 0.118401i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 1.73205 | − | 5.00000i | 0.117579 | − | 0.339422i | ||||
\(218\) | 2.00000i | 0.135457i | ||||||||
\(219\) | −5.00000 | + | 8.66025i | −0.337869 | + | 0.585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.0000 | − | 17.3205i | −0.672673 | − | 1.16510i | ||||
\(222\) | 0.866025 | + | 0.500000i | 0.0581238 | + | 0.0335578i | ||||
\(223\) | 12.0000i | 0.803579i | 0.915732 | + | 0.401790i | \(0.131612\pi\) | ||||
−0.915732 | + | 0.401790i | \(0.868388\pi\) | |||||||
\(224\) | −2.50000 | − | 0.866025i | −0.167038 | − | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.00000 | − | 12.1244i | 0.465633 | − | 0.806500i | ||||
\(227\) | −10.3923 | + | 6.00000i | −0.689761 | + | 0.398234i | −0.803523 | − | 0.595274i | \(-0.797043\pi\) |
0.113761 | + | 0.993508i | \(0.463710\pi\) | |||||||
\(228\) | −6.06218 | + | 3.50000i | −0.401478 | + | 0.231793i | ||||
\(229\) | 5.00000 | − | 8.66025i | 0.330409 | − | 0.572286i | −0.652183 | − | 0.758062i | \(-0.726147\pi\) |
0.982592 | + | 0.185776i | \(0.0594799\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.50000 | − | 12.9904i | −0.164488 | − | 0.854704i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.1244 | − | 7.00000i | −0.794293 | − | 0.458585i | 0.0471787 | − | 0.998886i | \(-0.484977\pi\) |
−0.841472 | + | 0.540301i | \(0.818310\pi\) | |||||||
\(234\) | −2.50000 | − | 4.33013i | −0.163430 | − | 0.283069i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.00000 | + | 3.46410i | −0.130189 | + | 0.225494i | ||||
\(237\) | 12.0000i | 0.779484i | ||||||||
\(238\) | −6.92820 | − | 8.00000i | −0.449089 | − | 0.518563i | ||||
\(239\) | 22.0000 | 1.42306 | 0.711531 | − | 0.702655i | \(-0.248002\pi\) | ||||
0.711531 | + | 0.702655i | \(0.248002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.50000 | − | 12.9904i | −0.483117 | − | 0.836784i | 0.516695 | − | 0.856170i | \(-0.327162\pi\) |
−0.999812 | + | 0.0193858i | \(0.993829\pi\) | |||||||
\(242\) | 12.1244 | − | 7.00000i | 0.779383 | − | 0.449977i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −4.00000 | −0.256074 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.00000 | −0.318788 | ||||||||
\(247\) | −30.3109 | − | 17.5000i | −1.92864 | − | 1.11350i | ||||
\(248\) | 1.73205 | − | 1.00000i | 0.109985 | − | 0.0635001i | ||||
\(249\) | 6.00000 | + | 10.3923i | 0.380235 | + | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | 0.0315597 | − | 0.999502i | \(-0.489953\pi\) | ||||
0.0315597 | + | 0.999502i | \(0.489953\pi\) | |||||||
\(252\) | −1.73205 | − | 2.00000i | −0.109109 | − | 0.125988i | ||||
\(253\) | 5.00000i | 0.314347i | ||||||||
\(254\) | 4.50000 | − | 7.79423i | 0.282355 | − | 0.489053i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 13.8564 | + | 8.00000i | 0.864339 | + | 0.499026i | 0.865463 | − | 0.500973i | \(-0.167024\pi\) |
−0.00112398 | + | 0.999999i | \(0.500358\pi\) | |||||||
\(258\) | 12.0000i | 0.747087i | ||||||||
\(259\) | 0.500000 | + | 2.59808i | 0.0310685 | + | 0.161437i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.79423 | + | 4.50000i | −0.481529 | + | 0.278011i | ||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 2.50000 | − | 4.33013i | 0.153864 | − | 0.266501i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −17.5000 | − | 6.06218i | −1.07299 | − | 0.371696i | ||||
\(267\) | − | 14.0000i | − | 0.856786i | ||||||
\(268\) | −10.3923 | − | 6.00000i | −0.634811 | − | 0.366508i | ||||
\(269\) | −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 | ||||||||
\(271\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(272\) | − | 4.00000i | − | 0.242536i | ||||||
\(273\) | 4.33013 | − | 12.5000i | 0.262071 | − | 0.756534i | ||||
\(274\) | 2.00000 | 0.120824 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.500000 | + | 0.866025i | 0.0300965 | + | 0.0521286i | ||||
\(277\) | 12.1244 | − | 7.00000i | 0.728482 | − | 0.420589i | −0.0893846 | − | 0.995997i | \(-0.528490\pi\) |
0.817867 | + | 0.575408i | \(0.195157\pi\) | |||||||
\(278\) | −3.46410 | − | 2.00000i | −0.207763 | − | 0.119952i | ||||
\(279\) | 2.00000 | 0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.00000 | 0.417585 | 0.208792 | − | 0.977960i | \(-0.433047\pi\) | ||||
0.208792 | + | 0.977960i | \(0.433047\pi\) | |||||||
\(282\) | −9.52628 | − | 5.50000i | −0.567282 | − | 0.327520i | ||||
\(283\) | 8.66025 | − | 5.00000i | 0.514799 | − | 0.297219i | −0.220005 | − | 0.975499i | \(-0.570607\pi\) |
0.734804 | + | 0.678280i | \(0.237274\pi\) | |||||||
\(284\) | 1.00000 | + | 1.73205i | 0.0593391 | + | 0.102778i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 25.0000 | 1.47828 | ||||||||
\(287\) | −8.66025 | − | 10.0000i | −0.511199 | − | 0.590281i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −0.500000 | + | 0.866025i | −0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.00000 | − | 6.92820i | −0.234484 | − | 0.406138i | ||||
\(292\) | −8.66025 | − | 5.00000i | −0.506803 | − | 0.292603i | ||||
\(293\) | − | 9.00000i | − | 0.525786i | −0.964825 | − | 0.262893i | \(-0.915323\pi\) | ||
0.964825 | − | 0.262893i | \(-0.0846766\pi\) | |||||||
\(294\) | 1.00000 | − | 6.92820i | 0.0583212 | − | 0.404061i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.500000 | + | 0.866025i | −0.0290619 | + | 0.0503367i | ||||
\(297\) | 4.33013 | − | 2.50000i | 0.251259 | − | 0.145065i | ||||
\(298\) | −10.3923 | + | 6.00000i | −0.602010 | + | 0.347571i | ||||
\(299\) | −2.50000 | + | 4.33013i | −0.144579 | + | 0.250418i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.0000 | + | 20.7846i | −1.38334 | + | 1.19800i | ||||
\(302\) | 14.0000i | 0.805609i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.50000 | − | 6.06218i | −0.200739 | − | 0.347690i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.00000 | − | 3.46410i | 0.114332 | − | 0.198030i | ||||
\(307\) | 8.00000i | 0.456584i | 0.973593 | + | 0.228292i | \(0.0733141\pi\) | ||||
−0.973593 | + | 0.228292i | \(0.926686\pi\) | |||||||
\(308\) | 12.9904 | − | 2.50000i | 0.740196 | − | 0.142451i | ||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.00000 | − | 6.92820i | −0.226819 | − | 0.392862i | 0.730044 | − | 0.683400i | \(-0.239499\pi\) |
−0.956864 | + | 0.290537i | \(0.906166\pi\) | |||||||
\(312\) | 4.33013 | − | 2.50000i | 0.245145 | − | 0.141535i | ||||
\(313\) | 13.8564 | + | 8.00000i | 0.783210 | + | 0.452187i | 0.837567 | − | 0.546335i | \(-0.183977\pi\) |
−0.0543564 | + | 0.998522i | \(0.517311\pi\) | |||||||
\(314\) | −11.0000 | −0.620766 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.0000 | −0.675053 | ||||||||
\(317\) | 19.0526 | + | 11.0000i | 1.07010 | + | 0.617822i | 0.928208 | − | 0.372061i | \(-0.121349\pi\) |
0.141890 | + | 0.989882i | \(0.454682\pi\) | |||||||
\(318\) | −7.79423 | + | 4.50000i | −0.437079 | + | 0.252347i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.00000 | 0.111629 | ||||||||
\(322\) | −0.866025 | + | 2.50000i | −0.0482617 | + | 0.139320i | ||||
\(323\) | − | 28.0000i | − | 1.55796i | ||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.0000 | + | 20.7846i | 0.664619 | + | 1.15115i | ||||
\(327\) | −1.73205 | − | 1.00000i | −0.0957826 | − | 0.0553001i | ||||
\(328\) | − | 5.00000i | − | 0.276079i | ||||||
\(329\) | −5.50000 | − | 28.5788i | −0.303225 | − | 1.57560i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.5000 | + | 26.8468i | −0.851957 | + | 1.47563i | 0.0274825 | + | 0.999622i | \(0.491251\pi\) |
−0.879440 | + | 0.476011i | \(0.842082\pi\) | |||||||
\(332\) | −10.3923 | + | 6.00000i | −0.570352 | + | 0.329293i | ||||
\(333\) | −0.866025 | + | 0.500000i | −0.0474579 | + | 0.0273998i | ||||
\(334\) | 5.50000 | − | 9.52628i | 0.300947 | − | 0.521255i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.00000 | − | 1.73205i | 0.109109 | − | 0.0944911i | ||||
\(337\) | − | 16.0000i | − | 0.871576i | −0.900049 | − | 0.435788i | \(-0.856470\pi\) | ||
0.900049 | − | 0.435788i | \(-0.143530\pi\) | |||||||
\(338\) | 10.3923 | + | 6.00000i | 0.565267 | + | 0.326357i | ||||
\(339\) | 7.00000 | + | 12.1244i | 0.380188 | + | 0.658505i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.00000 | + | 8.66025i | −0.270765 | + | 0.468979i | ||||
\(342\) | − | 7.00000i | − | 0.378517i | ||||||
\(343\) | 15.5885 | − | 10.0000i | 0.841698 | − | 0.539949i | ||||
\(344\) | −12.0000 | −0.646997 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.50000 | + | 11.2583i | 0.349442 | + | 0.605252i | ||||
\(347\) | −15.5885 | + | 9.00000i | −0.836832 | + | 0.483145i | −0.856186 | − | 0.516667i | \(-0.827172\pi\) |
0.0193540 | + | 0.999813i | \(0.493839\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.00000 | 0.214115 | 0.107058 | − | 0.994253i | \(-0.465857\pi\) | ||||
0.107058 | + | 0.994253i | \(0.465857\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.00000 | 0.266880 | ||||||||
\(352\) | 4.33013 | + | 2.50000i | 0.230797 | + | 0.133250i | ||||
\(353\) | −20.7846 | + | 12.0000i | −1.10625 | + | 0.638696i | −0.937856 | − | 0.347024i | \(-0.887192\pi\) |
−0.168397 | + | 0.985719i | \(0.553859\pi\) | |||||||
\(354\) | −2.00000 | − | 3.46410i | −0.106299 | − | 0.184115i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.0000 | 0.741999 | ||||||||
\(357\) | 10.3923 | − | 2.00000i | 0.550019 | − | 0.105851i | ||||
\(358\) | 23.0000i | 1.21559i | ||||||||
\(359\) | −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 | ||||||||
\(361\) | −15.0000 | − | 25.9808i | −0.789474 | − | 1.36741i | ||||
\(362\) | −17.3205 | − | 10.0000i | −0.910346 | − | 0.525588i | ||||
\(363\) | 14.0000i | 0.734809i | ||||||||
\(364\) | 12.5000 | + | 4.33013i | 0.655178 | + | 0.226960i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.00000 | − | 3.46410i | 0.104542 | − | 0.181071i | ||||
\(367\) | 6.06218 | − | 3.50000i | 0.316443 | − | 0.182699i | −0.333363 | − | 0.942799i | \(-0.608183\pi\) |
0.649806 | + | 0.760100i | \(0.274850\pi\) | |||||||
\(368\) | −0.866025 | + | 0.500000i | −0.0451447 | + | 0.0260643i | ||||
\(369\) | 2.50000 | − | 4.33013i | 0.130145 | − | 0.225417i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.5000 | − | 7.79423i | −1.16814 | − | 0.404656i | ||||
\(372\) | 2.00000i | 0.103695i | ||||||||
\(373\) | −19.0526 | − | 11.0000i | −0.986504 | − | 0.569558i | −0.0822766 | − | 0.996610i | \(-0.526219\pi\) |
−0.904227 | + | 0.427051i | \(0.859552\pi\) | |||||||
\(374\) | 10.0000 | + | 17.3205i | 0.517088 | + | 0.895622i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.50000 | − | 9.52628i | 0.283641 | − | 0.491280i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.59808 | − | 0.500000i | 0.133631 | − | 0.0257172i | ||||
\(379\) | −1.00000 | −0.0513665 | −0.0256833 | − | 0.999670i | \(-0.508176\pi\) | ||||
−0.0256833 | + | 0.999670i | \(0.508176\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.50000 | + | 7.79423i | 0.230542 | + | 0.399310i | ||||
\(382\) | 12.1244 | − | 7.00000i | 0.620336 | − | 0.358151i | ||||
\(383\) | 18.1865 | + | 10.5000i | 0.929288 | + | 0.536525i | 0.886586 | − | 0.462563i | \(-0.153070\pi\) |
0.0427020 | + | 0.999088i | \(0.486403\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.0000 | 0.508987 | ||||||||
\(387\) | −10.3923 | − | 6.00000i | −0.528271 | − | 0.304997i | ||||
\(388\) | 6.92820 | − | 4.00000i | 0.351726 | − | 0.203069i | ||||
\(389\) | 9.00000 | + | 15.5885i | 0.456318 | + | 0.790366i | 0.998763 | − | 0.0497253i | \(-0.0158346\pi\) |
−0.542445 | + | 0.840091i | \(0.682501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | 6.92820 | + | 1.00000i | 0.349927 | + | 0.0505076i | ||||
\(393\) | − | 9.00000i | − | 0.453990i | ||||||
\(394\) | −1.50000 | + | 2.59808i | −0.0755689 | + | 0.130889i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.50000 | + | 4.33013i | 0.125630 | + | 0.217597i | ||||
\(397\) | 12.1244 | + | 7.00000i | 0.608504 | + | 0.351320i | 0.772380 | − | 0.635161i | \(-0.219066\pi\) |
−0.163876 | + | 0.986481i | \(0.552400\pi\) | |||||||
\(398\) | 4.00000i | 0.200502i | ||||||||
\(399\) | 14.0000 | − | 12.1244i | 0.700877 | − | 0.606977i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.5000 | − | 18.1865i | 0.524345 | − | 0.908192i | −0.475253 | − | 0.879849i | \(-0.657644\pi\) |
0.999598 | − | 0.0283431i | \(-0.00902310\pi\) | |||||||
\(402\) | 10.3923 | − | 6.00000i | 0.518321 | − | 0.299253i | ||||
\(403\) | −8.66025 | + | 5.00000i | −0.431398 | + | 0.249068i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.00000i | − | 0.247841i | ||||||
\(408\) | 3.46410 | + | 2.00000i | 0.171499 | + | 0.0990148i | ||||
\(409\) | 5.00000 | + | 8.66025i | 0.247234 | + | 0.428222i | 0.962757 | − | 0.270367i | \(-0.0871450\pi\) |
−0.715523 | + | 0.698589i | \(0.753812\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.00000 | + | 1.73205i | −0.0493264 | + | 0.0854358i | ||||
\(412\) | 8.00000i | 0.394132i | ||||||||
\(413\) | 3.46410 | − | 10.0000i | 0.170457 | − | 0.492068i | ||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.50000 | + | 4.33013i | 0.122573 | + | 0.212302i | ||||
\(417\) | 3.46410 | − | 2.00000i | 0.169638 | − | 0.0979404i | ||||
\(418\) | 30.3109 | + | 17.5000i | 1.48255 | + | 0.855953i | ||||
\(419\) | −15.0000 | −0.732798 | −0.366399 | − | 0.930458i | \(-0.619409\pi\) | ||||
−0.366399 | + | 0.930458i | \(0.619409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | −14.7224 | − | 8.50000i | −0.716677 | − | 0.413774i | ||||
\(423\) | 9.52628 | − | 5.50000i | 0.463184 | − | 0.267419i | ||||
\(424\) | −4.50000 | − | 7.79423i | −0.218539 | − | 0.378521i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.00000 | −0.0969003 | ||||||||
\(427\) | 10.3923 | − | 2.00000i | 0.502919 | − | 0.0967868i | ||||
\(428\) | 2.00000i | 0.0966736i | ||||||||
\(429\) | −12.5000 | + | 21.6506i | −0.603506 | + | 1.04530i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.00000 | − | 10.3923i | −0.289010 | − | 0.500580i | 0.684564 | − | 0.728953i | \(-0.259993\pi\) |
−0.973574 | + | 0.228373i | \(0.926659\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 24.0000i | − | 1.15337i | −0.816968 | − | 0.576683i | \(-0.804347\pi\) | ||
0.816968 | − | 0.576683i | \(-0.195653\pi\) | |||||||
\(434\) | −4.00000 | + | 3.46410i | −0.192006 | + | 0.166282i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.00000 | − | 1.73205i | 0.0478913 | − | 0.0829502i | ||||
\(437\) | −6.06218 | + | 3.50000i | −0.289993 | + | 0.167428i | ||||
\(438\) | 8.66025 | − | 5.00000i | 0.413803 | − | 0.238909i | ||||
\(439\) | −20.0000 | + | 34.6410i | −0.954548 | + | 1.65333i | −0.219149 | + | 0.975691i | \(0.570328\pi\) |
−0.735399 | + | 0.677634i | \(0.763005\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.50000 | + | 4.33013i | 0.261905 | + | 0.206197i | ||||
\(442\) | 20.0000i | 0.951303i | ||||||||
\(443\) | −24.2487 | − | 14.0000i | −1.15209 | − | 0.665160i | −0.202695 | − | 0.979242i | \(-0.564970\pi\) |
−0.949396 | + | 0.314082i | \(0.898303\pi\) | |||||||
\(444\) | −0.500000 | − | 0.866025i | −0.0237289 | − | 0.0410997i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.00000 | − | 10.3923i | 0.284108 | − | 0.492090i | ||||
\(447\) | − | 12.0000i | − | 0.567581i | ||||||
\(448\) | 1.73205 | + | 2.00000i | 0.0818317 | + | 0.0944911i | ||||
\(449\) | 29.0000 | 1.36859 | 0.684297 | − | 0.729203i | \(-0.260109\pi\) | ||||
0.684297 | + | 0.729203i | \(0.260109\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.5000 | + | 21.6506i | 0.588602 | + | 1.01949i | ||||
\(452\) | −12.1244 | + | 7.00000i | −0.570282 | + | 0.329252i | ||||
\(453\) | −12.1244 | − | 7.00000i | −0.569652 | − | 0.328889i | ||||
\(454\) | 12.0000 | 0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.00000 | 0.327805 | ||||||||
\(457\) | 12.1244 | + | 7.00000i | 0.567153 | + | 0.327446i | 0.756012 | − | 0.654558i | \(-0.227145\pi\) |
−0.188858 | + | 0.982004i | \(0.560479\pi\) | |||||||
\(458\) | −8.66025 | + | 5.00000i | −0.404667 | + | 0.233635i | ||||
\(459\) | 2.00000 | + | 3.46410i | 0.0933520 | + | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.00000 | −0.186299 | −0.0931493 | − | 0.995652i | \(-0.529693\pi\) | ||||
−0.0931493 | + | 0.995652i | \(0.529693\pi\) | |||||||
\(462\) | −4.33013 | + | 12.5000i | −0.201456 | + | 0.581553i | ||||
\(463\) | 19.0000i | 0.883005i | 0.897260 | + | 0.441502i | \(0.145554\pi\) | ||||
−0.897260 | + | 0.441502i | \(0.854446\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.00000 | + | 12.1244i | 0.324269 | + | 0.561650i | ||||
\(467\) | 17.3205 | + | 10.0000i | 0.801498 | + | 0.462745i | 0.843995 | − | 0.536352i | \(-0.180198\pi\) |
−0.0424970 | + | 0.999097i | \(0.513531\pi\) | |||||||
\(468\) | 5.00000i | 0.231125i | ||||||||
\(469\) | 30.0000 | + | 10.3923i | 1.38527 | + | 0.479872i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.50000 | − | 9.52628i | 0.253427 | − | 0.438948i | ||||
\(472\) | 3.46410 | − | 2.00000i | 0.159448 | − | 0.0920575i | ||||
\(473\) | 51.9615 | − | 30.0000i | 2.38919 | − | 1.37940i | ||||
\(474\) | 6.00000 | − | 10.3923i | 0.275589 | − | 0.477334i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.00000 | + | 10.3923i | 0.0916698 | + | 0.476331i | ||||
\(477\) | − | 9.00000i | − | 0.412082i | ||||||
\(478\) | −19.0526 | − | 11.0000i | −0.871444 | − | 0.503128i | ||||
\(479\) | 9.00000 | + | 15.5885i | 0.411220 | + | 0.712255i | 0.995023 | − | 0.0996406i | \(-0.0317693\pi\) |
−0.583803 | + | 0.811895i | \(0.698436\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.50000 | − | 4.33013i | 0.113990 | − | 0.197437i | ||||
\(482\) | 15.0000i | 0.683231i | ||||||||
\(483\) | −1.73205 | − | 2.00000i | −0.0788110 | − | 0.0910032i | ||||
\(484\) | −14.0000 | −0.636364 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(488\) | 3.46410 | + | 2.00000i | 0.156813 | + | 0.0905357i | ||||
\(489\) | −24.0000 | −1.08532 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.0000 | −1.62466 | −0.812329 | − | 0.583200i | \(-0.801800\pi\) | ||||
−0.812329 | + | 0.583200i | \(0.801800\pi\) | |||||||
\(492\) | 4.33013 | + | 2.50000i | 0.195217 | + | 0.112709i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 17.5000 | + | 30.3109i | 0.787362 | + | 1.36375i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | −3.46410 | − | 4.00000i | −0.155386 | − | 0.179425i | ||||
\(498\) | − | 12.0000i | − | 0.537733i | ||||||
\(499\) | 20.0000 | − | 34.6410i | 0.895323 | − | 1.55074i | 0.0619186 | − | 0.998081i | \(-0.480278\pi\) |
0.833404 | − | 0.552664i | \(-0.186389\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.50000 | + | 9.52628i | 0.245722 | + | 0.425603i | ||||
\(502\) | −0.866025 | − | 0.500000i | −0.0386526 | − | 0.0223161i | ||||
\(503\) | 20.0000i | 0.891756i | 0.895094 | + | 0.445878i | \(0.147108\pi\) | ||||
−0.895094 | + | 0.445878i | \(0.852892\pi\) | |||||||
\(504\) | 0.500000 | + | 2.59808i | 0.0222718 | + | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.50000 | − | 4.33013i | 0.111139 | − | 0.192498i | ||||
\(507\) | −10.3923 | + | 6.00000i | −0.461538 | + | 0.266469i | ||||
\(508\) | −7.79423 | + | 4.50000i | −0.345813 | + | 0.199655i | ||||
\(509\) | −5.00000 | + | 8.66025i | −0.221621 | + | 0.383859i | −0.955300 | − | 0.295637i | \(-0.904468\pi\) |
0.733679 | + | 0.679496i | \(0.237801\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.0000 | + | 8.66025i | 1.10593 | + | 0.383107i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 6.06218 | + | 3.50000i | 0.267652 | + | 0.154529i | ||||
\(514\) | −8.00000 | − | 13.8564i | −0.352865 | − | 0.611180i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.00000 | − | 10.3923i | 0.264135 | − | 0.457496i | ||||
\(517\) | 55.0000i | 2.41890i | ||||||||
\(518\) | 0.866025 | − | 2.50000i | 0.0380510 | − | 0.109844i | ||||
\(519\) | −13.0000 | −0.570637 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.5000 | + | 28.5788i | 0.722878 | + | 1.25206i | 0.959841 | + | 0.280543i | \(0.0905145\pi\) |
−0.236963 | + | 0.971519i | \(0.576152\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.0526 | − | 11.0000i | −0.833110 | − | 0.480996i | 0.0218062 | − | 0.999762i | \(-0.493058\pi\) |
−0.854916 | + | 0.518766i | \(0.826392\pi\) | |||||||
\(524\) | 9.00000 | 0.393167 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.92820 | − | 4.00000i | −0.301797 | − | 0.174243i | ||||
\(528\) | −4.33013 | + | 2.50000i | −0.188445 | + | 0.108799i | ||||
\(529\) | −11.0000 | − | 19.0526i | −0.478261 | − | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 12.1244 | + | 14.0000i | 0.525657 | + | 0.606977i | ||||
\(533\) | 25.0000i | 1.08287i | ||||||||
\(534\) | −7.00000 | + | 12.1244i | −0.302920 | + | 0.524672i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.00000 | + | 10.3923i | 0.259161 | + | 0.448879i | ||||
\(537\) | −19.9186 | − | 11.5000i | −0.859550 | − | 0.496262i | ||||
\(538\) | 24.0000i | 1.03471i | ||||||||
\(539\) | −32.5000 | + | 12.9904i | −1.39987 | + | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.00000 | + | 1.73205i | −0.0429934 | + | 0.0744667i | −0.886721 | − | 0.462304i | \(-0.847023\pi\) |
0.843728 | + | 0.536771i | \(0.180356\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.3205 | − | 10.0000i | 0.743294 | − | 0.429141i | ||||
\(544\) | −2.00000 | + | 3.46410i | −0.0857493 | + | 0.148522i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −10.0000 | + | 8.66025i | −0.427960 | + | 0.370625i | ||||
\(547\) | 28.0000i | 1.19719i | 0.801050 | + | 0.598597i | \(0.204275\pi\) | ||||
−0.801050 | + | 0.598597i | \(0.795725\pi\) | |||||||
\(548\) | −1.73205 | − | 1.00000i | −0.0739895 | − | 0.0427179i | ||||
\(549\) | 2.00000 | + | 3.46410i | 0.0853579 | + | 0.147844i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | − | 1.00000i | − | 0.0425628i | ||||||
\(553\) | 31.1769 | − | 6.00000i | 1.32578 | − | 0.255146i | ||||
\(554\) | −14.0000 | −0.594803 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | 32.0429 | − | 18.5000i | 1.35770 | − | 0.783870i | 0.368389 | − | 0.929672i | \(-0.379909\pi\) |
0.989314 | + | 0.145802i | \(0.0465761\pi\) | |||||||
\(558\) | −1.73205 | − | 1.00000i | −0.0733236 | − | 0.0423334i | ||||
\(559\) | 60.0000 | 2.53773 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.0000 | −0.844401 | ||||||||
\(562\) | −6.06218 | − | 3.50000i | −0.255718 | − | 0.147639i | ||||
\(563\) | 15.5885 | − | 9.00000i | 0.656975 | − | 0.379305i | −0.134148 | − | 0.990961i | \(-0.542830\pi\) |
0.791123 | + | 0.611656i | \(0.209497\pi\) | |||||||
\(564\) | 5.50000 | + | 9.52628i | 0.231592 | + | 0.401129i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.0000 | −0.420331 | ||||||||
\(567\) | −0.866025 | + | 2.50000i | −0.0363696 | + | 0.104990i | ||||
\(568\) | − | 2.00000i | − | 0.0839181i | ||||||
\(569\) | 19.5000 | − | 33.7750i | 0.817483 | − | 1.41592i | −0.0900490 | − | 0.995937i | \(-0.528702\pi\) |
0.907532 | − | 0.419984i | \(-0.137964\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | − | 34.6410i | −0.836974 | − | 1.44968i | −0.892413 | − | 0.451219i | \(-0.850989\pi\) |
0.0554391 | − | 0.998462i | \(-0.482344\pi\) | |||||||
\(572\) | −21.6506 | − | 12.5000i | −0.905259 | − | 0.522651i | ||||
\(573\) | 14.0000i | 0.584858i | ||||||||
\(574\) | 2.50000 | + | 12.9904i | 0.104348 | + | 0.542208i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 22.5167 | − | 13.0000i | 0.937381 | − | 0.541197i | 0.0482425 | − | 0.998836i | \(-0.484638\pi\) |
0.889138 | + | 0.457639i | \(0.151305\pi\) | |||||||
\(578\) | 0.866025 | − | 0.500000i | 0.0360219 | − | 0.0207973i | ||||
\(579\) | −5.00000 | + | 8.66025i | −0.207793 | + | 0.359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.0000 | − | 20.7846i | 0.995688 | − | 0.862291i | ||||
\(582\) | 8.00000i | 0.331611i | ||||||||
\(583\) | 38.9711 | + | 22.5000i | 1.61402 | + | 0.931855i | ||||
\(584\) | 5.00000 | + | 8.66025i | 0.206901 | + | 0.358364i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.50000 | + | 7.79423i | −0.185893 | + | 0.321977i | ||||
\(587\) | − | 30.0000i | − | 1.23823i | −0.785299 | − | 0.619116i | \(-0.787491\pi\) | ||
0.785299 | − | 0.619116i | \(-0.212509\pi\) | |||||||
\(588\) | −4.33013 | + | 5.50000i | −0.178571 | + | 0.226816i | ||||
\(589\) | −14.0000 | −0.576860 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.50000 | − | 2.59808i | −0.0617018 | − | 0.106871i | ||||
\(592\) | 0.866025 | − | 0.500000i | 0.0355934 | − | 0.0205499i | ||||
\(593\) | 31.1769 | + | 18.0000i | 1.28028 | + | 0.739171i | 0.976900 | − | 0.213697i | \(-0.0685507\pi\) |
0.303383 | + | 0.952869i | \(0.401884\pi\) | |||||||
\(594\) | −5.00000 | −0.205152 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.0000 | 0.491539 | ||||||||
\(597\) | −3.46410 | − | 2.00000i | −0.141776 | − | 0.0818546i | ||||
\(598\) | 4.33013 | − | 2.50000i | 0.177072 | − | 0.102233i | ||||
\(599\) | −5.00000 | − | 8.66025i | −0.204294 | − | 0.353848i | 0.745613 | − | 0.666379i | \(-0.232157\pi\) |
−0.949908 | + | 0.312531i | \(0.898823\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 31.1769 | − | 6.00000i | 1.27068 | − | 0.244542i | ||||
\(603\) | 12.0000i | 0.488678i | ||||||||
\(604\) | 7.00000 | − | 12.1244i | 0.284826 | − | 0.493333i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.3827 | + | 13.5000i | 0.949074 | + | 0.547948i | 0.892793 | − | 0.450467i | \(-0.148742\pi\) |
0.0562808 | + | 0.998415i | \(0.482076\pi\) | |||||||
\(608\) | 7.00000i | 0.283887i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.5000 | + | 47.6314i | −1.11253 | + | 1.92696i | ||||
\(612\) | −3.46410 | + | 2.00000i | −0.140028 | + | 0.0808452i | ||||
\(613\) | 37.2391 | − | 21.5000i | 1.50407 | − | 0.868377i | 0.504084 | − | 0.863655i | \(-0.331830\pi\) |
0.999989 | − | 0.00472215i | \(-0.00150311\pi\) | |||||||
\(614\) | 4.00000 | − | 6.92820i | 0.161427 | − | 0.279600i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.5000 | − | 4.33013i | −0.503639 | − | 0.174466i | ||||
\(617\) | − | 8.00000i | − | 0.322068i | −0.986949 | − | 0.161034i | \(-0.948517\pi\) | ||
0.986949 | − | 0.161034i | \(-0.0514829\pi\) | |||||||
\(618\) | −6.92820 | − | 4.00000i | −0.278693 | − | 0.160904i | ||||
\(619\) | 12.5000 | + | 21.6506i | 0.502417 | + | 0.870212i | 0.999996 | + | 0.00279365i | \(0.000889247\pi\) |
−0.497579 | + | 0.867419i | \(0.665777\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.500000 | − | 0.866025i | 0.0200643 | − | 0.0347524i | ||||
\(622\) | 8.00000i | 0.320771i | ||||||||
\(623\) | −36.3731 | + | 7.00000i | −1.45726 | + | 0.280449i | ||||
\(624\) | −5.00000 | −0.200160 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.00000 | − | 13.8564i | −0.319744 | − | 0.553813i | ||||
\(627\) | −30.3109 | + | 17.5000i | −1.21050 | + | 0.698883i | ||||
\(628\) | 9.52628 | + | 5.50000i | 0.380140 | + | 0.219474i | ||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.00000 | 0.238856 | 0.119428 | − | 0.992843i | \(-0.461894\pi\) | ||||
0.119428 | + | 0.992843i | \(0.461894\pi\) | |||||||
\(632\) | 10.3923 | + | 6.00000i | 0.413384 | + | 0.238667i | ||||
\(633\) | 14.7224 | − | 8.50000i | 0.585164 | − | 0.337845i | ||||
\(634\) | −11.0000 | − | 19.0526i | −0.436866 | − | 0.756674i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.00000 | 0.356873 | ||||||||
\(637\) | −34.6410 | − | 5.00000i | −1.37253 | − | 0.198107i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.00000 | − | 1.73205i | 0.0395594 | − | 0.0685189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.5000 | − | 18.1865i | −0.414725 | − | 0.718325i | 0.580674 | − | 0.814136i | \(-0.302789\pi\) |
−0.995400 | + | 0.0958109i | \(0.969456\pi\) | |||||||
\(642\) | −1.73205 | − | 1.00000i | −0.0683586 | − | 0.0394669i | ||||
\(643\) | − | 34.0000i | − | 1.34083i | −0.741987 | − | 0.670415i | \(-0.766116\pi\) | ||
0.741987 | − | 0.670415i | \(-0.233884\pi\) | |||||||
\(644\) | 2.00000 | − | 1.73205i | 0.0788110 | − | 0.0682524i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.0000 | + | 24.2487i | −0.550823 | + | 0.954053i | ||||
\(647\) | −19.9186 | + | 11.5000i | −0.783080 | + | 0.452112i | −0.837521 | − | 0.546405i | \(-0.815996\pi\) |
0.0544405 | + | 0.998517i | \(0.482662\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | −10.0000 | + | 17.3205i | −0.392534 | + | 0.679889i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.00000 | − | 5.19615i | −0.0391931 | − | 0.203653i | ||||
\(652\) | − | 24.0000i | − | 0.939913i | ||||||
\(653\) | −16.4545 | − | 9.50000i | −0.643914 | − | 0.371764i | 0.142207 | − | 0.989837i | \(-0.454580\pi\) |
−0.786121 | + | 0.618073i | \(0.787914\pi\) | |||||||
\(654\) | 1.00000 | + | 1.73205i | 0.0391031 | + | 0.0677285i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.50000 | + | 4.33013i | −0.0976086 | + | 0.169063i | ||||
\(657\) | 10.0000i | 0.390137i | ||||||||
\(658\) | −9.52628 | + | 27.5000i | −0.371373 | + | 1.07206i | ||||
\(659\) | 20.0000 | 0.779089 | 0.389545 | − | 0.921008i | \(-0.372632\pi\) | ||||
0.389545 | + | 0.921008i | \(0.372632\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.0000 | + | 34.6410i | 0.777910 | + | 1.34738i | 0.933144 | + | 0.359502i | \(0.117053\pi\) |
−0.155235 | + | 0.987878i | \(0.549613\pi\) | |||||||
\(662\) | 26.8468 | − | 15.5000i | 1.04343 | − | 0.602425i | ||||
\(663\) | −17.3205 | − | 10.0000i | −0.672673 | − | 0.388368i | ||||
\(664\) | 12.0000 | 0.465690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.00000 | 0.0387492 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −9.52628 | + | 5.50000i | −0.368583 | + | 0.212801i | ||||
\(669\) | 6.00000 | + | 10.3923i | 0.231973 | + | 0.401790i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.0000 | −0.772091 | ||||||||
\(672\) | −2.59808 | + | 0.500000i | −0.100223 | + | 0.0192879i | ||||
\(673\) | 4.00000i | 0.154189i | 0.997024 | + | 0.0770943i | \(0.0245643\pi\) | ||||
−0.997024 | + | 0.0770943i | \(0.975436\pi\) | |||||||
\(674\) | −8.00000 | + | 13.8564i | −0.308148 | + | 0.533729i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.00000 | − | 10.3923i | −0.230769 | − | 0.399704i | ||||
\(677\) | −28.5788 | − | 16.5000i | −1.09837 | − | 0.634147i | −0.162581 | − | 0.986695i | \(-0.551982\pi\) |
−0.935793 | + | 0.352549i | \(0.885315\pi\) | |||||||
\(678\) | − | 14.0000i | − | 0.537667i | ||||||
\(679\) | −16.0000 | + | 13.8564i | −0.614024 | + | 0.531760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.00000 | + | 10.3923i | −0.229920 | + | 0.398234i | ||||
\(682\) | 8.66025 | − | 5.00000i | 0.331618 | − | 0.191460i | ||||
\(683\) | 3.46410 | − | 2.00000i | 0.132550 | − | 0.0765279i | −0.432259 | − | 0.901750i | \(-0.642283\pi\) |
0.564809 | + | 0.825222i | \(0.308950\pi\) | |||||||
\(684\) | −3.50000 | + | 6.06218i | −0.133826 | + | 0.231793i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.5000 | + | 0.866025i | −0.706333 | + | 0.0330650i | ||||
\(687\) | − | 10.0000i | − | 0.381524i | ||||||
\(688\) | 10.3923 | + | 6.00000i | 0.396203 | + | 0.228748i | ||||
\(689\) | 22.5000 | + | 38.9711i | 0.857182 | + | 1.48468i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.0000 | + | 24.2487i | −0.532585 | + | 0.922464i | 0.466691 | + | 0.884420i | \(0.345446\pi\) |
−0.999276 | + | 0.0380440i | \(0.987887\pi\) | |||||||
\(692\) | − | 13.0000i | − | 0.494186i | ||||||
\(693\) | −8.66025 | − | 10.0000i | −0.328976 | − | 0.379869i | ||||
\(694\) | 18.0000 | 0.683271 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.3205 | + | 10.0000i | −0.656061 | + | 0.378777i | ||||
\(698\) | −3.46410 | − | 2.00000i | −0.131118 | − | 0.0757011i | ||||
\(699\) | −14.0000 | −0.529529 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | −4.33013 | − | 2.50000i | −0.163430 | − | 0.0943564i | ||||
\(703\) | 6.06218 | − | 3.50000i | 0.228639 | − | 0.132005i | ||||
\(704\) | −2.50000 | − | 4.33013i | −0.0942223 | − | 0.163198i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.0000 | 0.903252 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.00000i | 0.150329i | ||||||||
\(709\) | 14.0000 | − | 24.2487i | 0.525781 | − | 0.910679i | −0.473768 | − | 0.880650i | \(-0.657106\pi\) |
0.999549 | − | 0.0300298i | \(-0.00956021\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.00000 | + | 10.3923i | 0.225018 | + | 0.389742i | ||||
\(712\) | −12.1244 | − | 7.00000i | −0.454379 | − | 0.262336i | ||||
\(713\) | 2.00000i | 0.0749006i | ||||||||
\(714\) | −10.0000 | − | 3.46410i | −0.374241 | − | 0.129641i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.5000 | − | 19.9186i | 0.429775 | − | 0.744392i | ||||
\(717\) | 19.0526 | − | 11.0000i | 0.711531 | − | 0.410803i | ||||
\(718\) | 17.3205 | − | 10.0000i | 0.646396 | − | 0.373197i | ||||
\(719\) | −3.00000 | + | 5.19615i | −0.111881 | + | 0.193784i | −0.916529 | − | 0.399969i | \(-0.869021\pi\) |
0.804648 | + | 0.593753i | \(0.202354\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.00000 | − | 20.7846i | −0.148968 | − | 0.774059i | ||||
\(722\) | 30.0000i | 1.11648i | ||||||||
\(723\) | −12.9904 | − | 7.50000i | −0.483117 | − | 0.278928i | ||||
\(724\) | 10.0000 | + | 17.3205i | 0.371647 | + | 0.643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.00000 | − | 12.1244i | 0.259794 | − | 0.449977i | ||||
\(727\) | − | 3.00000i | − | 0.111264i | −0.998451 | − | 0.0556319i | \(-0.982283\pi\) | ||
0.998451 | − | 0.0556319i | \(-0.0177173\pi\) | |||||||
\(728\) | −8.66025 | − | 10.0000i | −0.320970 | − | 0.370625i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0000 | + | 41.5692i | 0.887672 | + | 1.53749i | ||||
\(732\) | −3.46410 | + | 2.00000i | −0.128037 | + | 0.0739221i | ||||
\(733\) | 7.79423 | + | 4.50000i | 0.287886 | + | 0.166211i | 0.636988 | − | 0.770873i | \(-0.280180\pi\) |
−0.349102 | + | 0.937085i | \(0.613513\pi\) | |||||||
\(734\) | −7.00000 | −0.258375 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −51.9615 | − | 30.0000i | −1.91403 | − | 1.10506i | ||||
\(738\) | −4.33013 | + | 2.50000i | −0.159394 | + | 0.0920263i | ||||
\(739\) | −7.50000 | − | 12.9904i | −0.275892 | − | 0.477859i | 0.694468 | − | 0.719524i | \(-0.255640\pi\) |
−0.970360 | + | 0.241665i | \(0.922307\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −35.0000 | −1.28576 | ||||||||
\(742\) | 15.5885 | + | 18.0000i | 0.572270 | + | 0.660801i | ||||
\(743\) | − | 15.0000i | − | 0.550297i | −0.961402 | − | 0.275148i | \(-0.911273\pi\) | ||
0.961402 | − | 0.275148i | \(-0.0887270\pi\) | |||||||
\(744\) | 1.00000 | − | 1.73205i | 0.0366618 | − | 0.0635001i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11.0000 | + | 19.0526i | 0.402739 | + | 0.697564i | ||||
\(747\) | 10.3923 | + | 6.00000i | 0.380235 | + | 0.219529i | ||||
\(748\) | − | 20.0000i | − | 0.731272i | ||||||
\(749\) | −1.00000 | − | 5.19615i | −0.0365392 | − | 0.189863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.0000 | − | 43.3013i | 0.912263 | − | 1.58009i | 0.101403 | − | 0.994845i | \(-0.467667\pi\) |
0.810860 | − | 0.585240i | \(-0.199000\pi\) | |||||||
\(752\) | −9.52628 | + | 5.50000i | −0.347388 | + | 0.200564i | ||||
\(753\) | 0.866025 | − | 0.500000i | 0.0315597 | − | 0.0182210i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.50000 | − | 0.866025i | −0.0909241 | − | 0.0314970i | ||||
\(757\) | − | 34.0000i | − | 1.23575i | −0.786276 | − | 0.617876i | \(-0.787994\pi\) | ||
0.786276 | − | 0.617876i | \(-0.212006\pi\) | |||||||
\(758\) | 0.866025 | + | 0.500000i | 0.0314555 | + | 0.0181608i | ||||
\(759\) | 2.50000 | + | 4.33013i | 0.0907443 | + | 0.157174i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.5000 | − | 32.0429i | 0.670624 | − | 1.16156i | −0.307103 | − | 0.951676i | \(-0.599360\pi\) |
0.977727 | − | 0.209879i | \(-0.0673071\pi\) | |||||||
\(762\) | − | 9.00000i | − | 0.326036i | ||||||
\(763\) | −1.73205 | + | 5.00000i | −0.0627044 | + | 0.181012i | ||||
\(764\) | −14.0000 | −0.506502 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.5000 | − | 18.1865i | −0.379380 | − | 0.657106i | ||||
\(767\) | −17.3205 | + | 10.0000i | −0.625407 | + | 0.361079i | ||||
\(768\) | −0.866025 | − | 0.500000i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | 5.00000 | 0.180305 | 0.0901523 | − | 0.995928i | \(-0.471265\pi\) | ||||
0.0901523 | + | 0.995928i | \(0.471265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.0000 | 0.576226 | ||||||||
\(772\) | −8.66025 | − | 5.00000i | −0.311689 | − | 0.179954i | ||||
\(773\) | 4.33013 | − | 2.50000i | 0.155744 | − | 0.0899188i | −0.420103 | − | 0.907477i | \(-0.638006\pi\) |
0.575846 | + | 0.817558i | \(0.304673\pi\) | |||||||
\(774\) | 6.00000 | + | 10.3923i | 0.215666 | + | 0.373544i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.00000 | −0.287183 | ||||||||
\(777\) | 1.73205 | + | 2.00000i | 0.0621370 | + | 0.0717496i | ||||
\(778\) | − | 18.0000i | − | 0.645331i | ||||||
\(779\) | −17.5000 | + | 30.3109i | −0.627003 | + | 1.08600i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.00000 | + | 8.66025i | 0.178914 | + | 0.309888i | ||||
\(782\) | 3.46410 | + | 2.00000i | 0.123876 | + | 0.0715199i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.50000 | − | 4.33013i | −0.196429 | − | 0.154647i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.50000 | + | 7.79423i | −0.160510 | + | 0.278011i | ||||
\(787\) | 1.73205 | − | 1.00000i | 0.0617409 | − | 0.0356462i | −0.468812 | − | 0.883298i | \(-0.655318\pi\) |
0.530553 | + | 0.847652i | \(0.321984\pi\) | |||||||
\(788\) | 2.59808 | − | 1.50000i | 0.0925526 | − | 0.0534353i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.0000 | − | 24.2487i | 0.995565 | − | 0.862185i | ||||
\(792\) | − | 5.00000i | − | 0.177667i | ||||||
\(793\) | −17.3205 | − | 10.0000i | −0.615069 | − | 0.355110i | ||||
\(794\) | −7.00000 | − | 12.1244i | −0.248421 | − | 0.430277i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.00000 | − | 3.46410i | 0.0708881 | − | 0.122782i | ||||
\(797\) | − | 54.0000i | − | 1.91278i | −0.292096 | − | 0.956389i | \(-0.594353\pi\) | ||
0.292096 | − | 0.956389i | \(-0.405647\pi\) | |||||||
\(798\) | −18.1865 | + | 3.50000i | −0.643796 | + | 0.123899i | ||||
\(799\) | −44.0000 | −1.55661 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.00000 | − | 12.1244i | −0.247333 | − | 0.428393i | ||||
\(802\) | −18.1865 | + | 10.5000i | −0.642189 | + | 0.370768i | ||||
\(803\) | −43.3013 | − | 25.0000i | −1.52807 | − | 0.882231i | ||||
\(804\) | −12.0000 | −0.423207 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.0000 | 0.352235 | ||||||||
\(807\) | −20.7846 | − | 12.0000i | −0.731653 | − | 0.422420i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.5000 | + | 21.6506i | 0.439477 | + | 0.761196i | 0.997649 | − | 0.0685291i | \(-0.0218306\pi\) |
−0.558173 | + | 0.829725i | \(0.688497\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.0000 | 0.737410 | 0.368705 | − | 0.929547i | \(-0.379801\pi\) | ||||
0.368705 | + | 0.929547i | \(0.379801\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.50000 | + | 4.33013i | −0.0876250 | + | 0.151771i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.00000 | − | 3.46410i | −0.0700140 | − | 0.121268i | ||||
\(817\) | 72.7461 | + | 42.0000i | 2.54507 | + | 1.46939i | ||||
\(818\) | − | 10.0000i | − | 0.349642i | ||||||
\(819\) | −2.50000 | − | 12.9904i | −0.0873571 | − | 0.453921i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.00000 | + | 8.66025i | −0.174501 | + | 0.302245i | −0.939989 | − | 0.341206i | \(-0.889165\pi\) |
0.765487 | + | 0.643451i | \(0.222498\pi\) | |||||||
\(822\) | 1.73205 | − | 1.00000i | 0.0604122 | − | 0.0348790i | ||||
\(823\) | −34.6410 | + | 20.0000i | −1.20751 | + | 0.697156i | −0.962215 | − | 0.272292i | \(-0.912218\pi\) |
−0.245295 | + | 0.969448i | \(0.578885\pi\) | |||||||
\(824\) | 4.00000 | − | 6.92820i | 0.139347 | − | 0.241355i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | + | 6.92820i | −0.278356 | + | 0.241063i | ||||
\(827\) | − | 6.00000i | − | 0.208640i | −0.994544 | − | 0.104320i | \(-0.966733\pi\) | ||
0.994544 | − | 0.104320i | \(-0.0332667\pi\) | |||||||
\(828\) | 0.866025 | + | 0.500000i | 0.0300965 | + | 0.0173762i | ||||
\(829\) | −26.0000 | − | 45.0333i | −0.903017 | − | 1.56407i | −0.823557 | − | 0.567234i | \(-0.808014\pi\) |
−0.0794606 | − | 0.996838i | \(-0.525320\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.00000 | − | 12.1244i | 0.242827 | − | 0.420589i | ||||
\(832\) | − | 5.00000i | − | 0.173344i | ||||||
\(833\) | −10.3923 | − | 26.0000i | −0.360072 | − | 0.900847i | ||||
\(834\) | −4.00000 | −0.138509 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −17.5000 | − | 30.3109i | −0.605250 | − | 1.04832i | ||||
\(837\) | 1.73205 | − | 1.00000i | 0.0598684 | − | 0.0345651i | ||||
\(838\) | 12.9904 | + | 7.50000i | 0.448745 | + | 0.259083i | ||||
\(839\) | −12.0000 | −0.414286 | −0.207143 | − | 0.978311i | \(-0.566417\pi\) | ||||
−0.207143 | + | 0.978311i | \(0.566417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | −8.66025 | − | 5.00000i | −0.298452 | − | 0.172311i | ||||
\(843\) | 6.06218 | − | 3.50000i | 0.208792 | − | 0.120546i | ||||
\(844\) | 8.50000 | + | 14.7224i | 0.292582 | + | 0.506767i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11.0000 | −0.378188 | ||||||||
\(847\) | 36.3731 | − | 7.00000i | 1.24979 | − | 0.240523i | ||||
\(848\) | 9.00000i | 0.309061i | ||||||||
\(849\) | 5.00000 | − | 8.66025i | 0.171600 | − | 0.297219i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.500000 | − | 0.866025i | −0.0171398 | − | 0.0296870i | ||||
\(852\) | 1.73205 | + | 1.00000i | 0.0593391 | + | 0.0342594i | ||||
\(853\) | 11.0000i | 0.376633i | 0.982108 | + | 0.188316i | \(0.0603030\pi\) | ||||
−0.982108 | + | 0.188316i | \(0.939697\pi\) | |||||||
\(854\) | −10.0000 | − | 3.46410i | −0.342193 | − | 0.118539i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.00000 | − | 1.73205i | 0.0341793 | − | 0.0592003i | ||||
\(857\) | 1.73205 | − | 1.00000i | 0.0591657 | − | 0.0341593i | −0.470125 | − | 0.882600i | \(-0.655791\pi\) |
0.529291 | + | 0.848440i | \(0.322458\pi\) | |||||||
\(858\) | 21.6506 | − | 12.5000i | 0.739140 | − | 0.426743i | ||||
\(859\) | −2.00000 | + | 3.46410i | −0.0682391 | + | 0.118194i | −0.898126 | − | 0.439738i | \(-0.855071\pi\) |
0.829887 | + | 0.557931i | \(0.188405\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.5000 | − | 4.33013i | −0.425999 | − | 0.147570i | ||||
\(862\) | 12.0000i | 0.408722i | ||||||||
\(863\) | 38.9711 | + | 22.5000i | 1.32659 | + | 0.765909i | 0.984771 | − | 0.173856i | \(-0.0556227\pi\) |
0.341822 | + | 0.939765i | \(0.388956\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −12.0000 | + | 20.7846i | −0.407777 | + | 0.706290i | ||||
\(867\) | 1.00000i | 0.0339618i | ||||||||
\(868\) | 5.19615 | − | 1.00000i | 0.176369 | − | 0.0339422i | ||||
\(869\) | −60.0000 | −2.03536 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.0000 | − | 51.9615i | −1.01651 | − | 1.76065i | ||||
\(872\) | −1.73205 | + | 1.00000i | −0.0586546 | + | 0.0338643i | ||||
\(873\) | −6.92820 | − | 4.00000i | −0.234484 | − | 0.135379i | ||||
\(874\) | 7.00000 | 0.236779 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.0000 | −0.337869 | ||||||||
\(877\) | 32.0429 | + | 18.5000i | 1.08201 | + | 0.624701i | 0.931439 | − | 0.363898i | \(-0.118554\pi\) |
0.150574 | + | 0.988599i | \(0.451888\pi\) | |||||||
\(878\) | 34.6410 | − | 20.0000i | 1.16908 | − | 0.674967i | ||||
\(879\) | −4.50000 | − | 7.79423i | −0.151781 | − | 0.262893i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.00000 | 0.101073 | 0.0505363 | − | 0.998722i | \(-0.483907\pi\) | ||||
0.0505363 | + | 0.998722i | \(0.483907\pi\) | |||||||
\(882\) | −2.59808 | − | 6.50000i | −0.0874818 | − | 0.218866i | ||||
\(883\) | 50.0000i | 1.68263i | 0.540542 | + | 0.841317i | \(0.318219\pi\) | ||||
−0.540542 | + | 0.841317i | \(0.681781\pi\) | |||||||
\(884\) | 10.0000 | − | 17.3205i | 0.336336 | − | 0.582552i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.0000 | + | 24.2487i | 0.470339 | + | 0.814651i | ||||
\(887\) | 38.1051 | + | 22.0000i | 1.27944 | + | 0.738688i | 0.976746 | − | 0.214399i | \(-0.0687792\pi\) |
0.302698 | + | 0.953086i | \(0.402113\pi\) | |||||||
\(888\) | 1.00000i | 0.0335578i | ||||||||
\(889\) | 18.0000 | − | 15.5885i | 0.603701 | − | 0.522820i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.50000 | − | 4.33013i | 0.0837532 | − | 0.145065i | ||||
\(892\) | −10.3923 | + | 6.00000i | −0.347960 | + | 0.200895i | ||||
\(893\) | −66.6840 | + | 38.5000i | −2.23149 | + | 1.28835i | ||||
\(894\) | −6.00000 | + | 10.3923i | −0.200670 | + | 0.347571i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.500000 | − | 2.59808i | −0.0167038 | − | 0.0867956i | ||||
\(897\) | 5.00000i | 0.166945i | ||||||||
\(898\) | −25.1147 | − | 14.5000i | −0.838090 | − | 0.483871i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.0000 | + | 31.1769i | −0.599667 | + | 1.03865i | ||||
\(902\) | − | 25.0000i | − | 0.832409i | ||||||
\(903\) | −10.3923 | + | 30.0000i | −0.345834 | + | 0.998337i | ||||
\(904\) | 14.0000 | 0.465633 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.00000 | + | 12.1244i | 0.232559 | + | 0.402805i | ||||
\(907\) | −15.5885 | + | 9.00000i | −0.517606 | + | 0.298840i | −0.735955 | − | 0.677031i | \(-0.763266\pi\) |
0.218348 | + | 0.975871i | \(0.429933\pi\) | |||||||
\(908\) | −10.3923 | − | 6.00000i | −0.344881 | − | 0.199117i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | −6.06218 | − | 3.50000i | −0.200739 | − | 0.115897i | ||||
\(913\) | −51.9615 | + | 30.0000i | −1.71968 | + | 0.992855i | ||||
\(914\) | −7.00000 | − | 12.1244i | −0.231539 | − | 0.401038i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.0000 | 0.330409 | ||||||||
\(917\) | −23.3827 | + | 4.50000i | −0.772164 | + | 0.148603i | ||||
\(918\) | − | 4.00000i | − | 0.132020i | ||||||
\(919\) | 14.0000 | − | 24.2487i | 0.461817 | − | 0.799891i | −0.537234 | − | 0.843433i | \(-0.680531\pi\) |
0.999052 | + | 0.0435419i | \(0.0138642\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.00000 | + | 6.92820i | 0.131804 | + | 0.228292i | ||||
\(922\) | 3.46410 | + | 2.00000i | 0.114084 | + | 0.0658665i | ||||
\(923\) | 10.0000i | 0.329154i | ||||||||
\(924\) | 10.0000 | − | 8.66025i | 0.328976 | − | 0.284901i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.50000 | − | 16.4545i | 0.312189 | − | 0.540728i | ||||
\(927\) | 6.92820 | − | 4.00000i | 0.227552 | − | 0.131377i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.50000 | − | 16.4545i | 0.311685 | − | 0.539854i | −0.667042 | − | 0.745020i | \(-0.732440\pi\) |
0.978727 | + | 0.205166i | \(0.0657733\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38.5000 | − | 30.3109i | −1.26179 | − | 0.993399i | ||||
\(932\) | − | 14.0000i | − | 0.458585i | ||||||
\(933\) | −6.92820 | − | 4.00000i | −0.226819 | − | 0.130954i | ||||
\(934\) | −10.0000 | − | 17.3205i | −0.327210 | − | 0.566744i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.50000 | − | 4.33013i | 0.0817151 | − | 0.141535i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | −20.7846 | − | 24.0000i | −0.678642 | − | 0.783628i | ||||
\(939\) | 16.0000 | 0.522140 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.00000 | + | 5.19615i | 0.0977972 | + | 0.169390i | 0.910773 | − | 0.412908i | \(-0.135487\pi\) |
−0.812975 | + | 0.582298i | \(0.802154\pi\) | |||||||
\(942\) | −9.52628 | + | 5.50000i | −0.310383 | + | 0.179200i | ||||
\(943\) | 4.33013 | + | 2.50000i | 0.141008 | + | 0.0814112i | ||||
\(944\) | −4.00000 | −0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −60.0000 | −1.95077 | ||||||||
\(947\) | 36.3731 | + | 21.0000i | 1.18197 | + | 0.682408i | 0.956469 | − | 0.291835i | \(-0.0942660\pi\) |
0.225497 | + | 0.974244i | \(0.427599\pi\) | |||||||
\(948\) | −10.3923 | + | 6.00000i | −0.337526 | + | 0.194871i | ||||
\(949\) | −25.0000 | − | 43.3013i | −0.811534 | − | 1.40562i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.0000 | 0.713399 | ||||||||
\(952\) | 3.46410 | − | 10.0000i | 0.112272 | − | 0.324102i | ||||
\(953\) | − | 12.0000i | − | 0.388718i | −0.980930 | − | 0.194359i | \(-0.937737\pi\) | ||
0.980930 | − | 0.194359i | \(-0.0622627\pi\) | |||||||
\(954\) | −4.50000 | + | 7.79423i | −0.145693 | + | 0.252347i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.0000 | + | 19.0526i | 0.355765 | + | 0.616204i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 18.0000i | − | 0.581554i | ||||||
\(959\) | 5.00000 | + | 1.73205i | 0.161458 | + | 0.0559308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | −4.33013 | + | 2.50000i | −0.139609 | + | 0.0806032i | ||||
\(963\) | 1.73205 | − | 1.00000i | 0.0558146 | − | 0.0322245i | ||||
\(964\) | 7.50000 | − | 12.9904i | 0.241559 | − | 0.418392i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.500000 | + | 2.59808i | 0.0160872 | + | 0.0835917i | ||||
\(967\) | 4.00000i | 0.128631i | 0.997930 | + | 0.0643157i | \(0.0204865\pi\) | ||||
−0.997930 | + | 0.0643157i | \(0.979514\pi\) | |||||||
\(968\) | 12.1244 | + | 7.00000i | 0.389692 | + | 0.224989i | ||||
\(969\) | −14.0000 | − | 24.2487i | −0.449745 | − | 0.778981i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.50000 | + | 12.9904i | −0.240686 | + | 0.416881i | −0.960910 | − | 0.276861i | \(-0.910706\pi\) |
0.720224 | + | 0.693742i | \(0.244039\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | −6.92820 | − | 8.00000i | −0.222108 | − | 0.256468i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.00000 | − | 3.46410i | −0.0640184 | − | 0.110883i | ||||
\(977\) | −25.9808 | + | 15.0000i | −0.831198 | + | 0.479893i | −0.854263 | − | 0.519841i | \(-0.825991\pi\) |
0.0230645 | + | 0.999734i | \(0.492658\pi\) | |||||||
\(978\) | 20.7846 | + | 12.0000i | 0.664619 | + | 0.383718i | ||||
\(979\) | 70.0000 | 2.23721 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | 31.1769 | + | 18.0000i | 0.994895 | + | 0.574403i | ||||
\(983\) | 21.6506 | − | 12.5000i | 0.690548 | − | 0.398688i | −0.113269 | − | 0.993564i | \(-0.536132\pi\) |
0.803817 | + | 0.594876i | \(0.202799\pi\) | |||||||
\(984\) | −2.50000 | − | 4.33013i | −0.0796971 | − | 0.138039i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19.0526 | − | 22.0000i | −0.606450 | − | 0.700268i | ||||
\(988\) | − | 35.0000i | − | 1.11350i | ||||||
\(989\) | 6.00000 | − | 10.3923i | 0.190789 | − | 0.330456i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.0000 | + | 32.9090i | 0.603555 | + | 1.04539i | 0.992278 | + | 0.124033i | \(0.0395829\pi\) |
−0.388723 | + | 0.921355i | \(0.627084\pi\) | |||||||
\(992\) | 1.73205 | + | 1.00000i | 0.0549927 | + | 0.0317500i | ||||
\(993\) | 31.0000i | 0.983755i | ||||||||
\(994\) | 1.00000 | + | 5.19615i | 0.0317181 | + | 0.164812i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.00000 | + | 10.3923i | −0.190117 | + | 0.329293i | ||||
\(997\) | −19.0526 | + | 11.0000i | −0.603401 | + | 0.348373i | −0.770378 | − | 0.637587i | \(-0.779933\pi\) |
0.166978 | + | 0.985961i | \(0.446599\pi\) | |||||||
\(998\) | −34.6410 | + | 20.0000i | −1.09654 | + | 0.633089i | ||||
\(999\) | −0.500000 | + | 0.866025i | −0.0158193 | + | 0.0273998i |
(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.g.499.1 | 4 | ||
5.2 | odd | 4 | 1050.2.i.p.751.1 | 2 | |||
5.3 | odd | 4 | 210.2.i.b.121.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 1050.2.o.g.499.2 | 4 | ||
7.4 | even | 3 | inner | 1050.2.o.g.949.2 | 4 | ||
15.8 | even | 4 | 630.2.k.g.541.1 | 2 | |||
20.3 | even | 4 | 1680.2.bg.d.961.1 | 2 | |||
35.2 | odd | 12 | 7350.2.a.u.1.1 | 1 | |||
35.3 | even | 12 | 1470.2.i.e.361.1 | 2 | |||
35.4 | even | 6 | inner | 1050.2.o.g.949.1 | 4 | ||
35.12 | even | 12 | 7350.2.a.a.1.1 | 1 | |||
35.13 | even | 4 | 1470.2.i.e.961.1 | 2 | |||
35.18 | odd | 12 | 210.2.i.b.151.1 | yes | 2 | ||
35.23 | odd | 12 | 1470.2.a.l.1.1 | 1 | |||
35.32 | odd | 12 | 1050.2.i.p.151.1 | 2 | |||
35.33 | even | 12 | 1470.2.a.o.1.1 | 1 | |||
105.23 | even | 12 | 4410.2.a.j.1.1 | 1 | |||
105.53 | even | 12 | 630.2.k.g.361.1 | 2 | |||
105.68 | odd | 12 | 4410.2.a.u.1.1 | 1 | |||
140.123 | even | 12 | 1680.2.bg.d.1201.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.i.b.121.1 | ✓ | 2 | 5.3 | odd | 4 | ||
210.2.i.b.151.1 | yes | 2 | 35.18 | odd | 12 | ||
630.2.k.g.361.1 | 2 | 105.53 | even | 12 | |||
630.2.k.g.541.1 | 2 | 15.8 | even | 4 | |||
1050.2.i.p.151.1 | 2 | 35.32 | odd | 12 | |||
1050.2.i.p.751.1 | 2 | 5.2 | odd | 4 | |||
1050.2.o.g.499.1 | 4 | 1.1 | even | 1 | trivial | ||
1050.2.o.g.499.2 | 4 | 5.4 | even | 2 | inner | ||
1050.2.o.g.949.1 | 4 | 35.4 | even | 6 | inner | ||
1050.2.o.g.949.2 | 4 | 7.4 | even | 3 | inner | ||
1470.2.a.l.1.1 | 1 | 35.23 | odd | 12 | |||
1470.2.a.o.1.1 | 1 | 35.33 | even | 12 | |||
1470.2.i.e.361.1 | 2 | 35.3 | even | 12 | |||
1470.2.i.e.961.1 | 2 | 35.13 | even | 4 | |||
1680.2.bg.d.961.1 | 2 | 20.3 | even | 4 | |||
1680.2.bg.d.1201.1 | 2 | 140.123 | even | 12 | |||
4410.2.a.j.1.1 | 1 | 105.23 | even | 12 | |||
4410.2.a.u.1.1 | 1 | 105.68 | odd | 12 | |||
7350.2.a.a.1.1 | 1 | 35.12 | even | 12 | |||
7350.2.a.u.1.1 | 1 | 35.2 | odd | 12 |