Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(407,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.407");
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.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 407.4 | ||
Root | \(-1.14412 - 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.407 |
Dual form | 1050.2.j.b.743.4 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.58114 | + | 0.707107i | 0.912871 | + | 0.408248i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.61803 | − | 0.618034i | 0.660560 | − | 0.252311i | ||||
\(7\) | −0.707107 | − | 0.707107i | −0.267261 | − | 0.267261i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 2.00000 | + | 2.23607i | 0.666667 | + | 0.745356i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.23607i | − | 0.975711i | −0.872924 | − | 0.487856i | \(-0.837779\pi\) | ||
0.872924 | − | 0.487856i | \(-0.162221\pi\) | |||||||
\(12\) | 0.707107 | − | 1.58114i | 0.204124 | − | 0.456435i | ||||
\(13\) | 4.57649 | − | 4.57649i | 1.26929 | − | 1.26929i | 0.322835 | − | 0.946455i | \(-0.395364\pi\) |
0.946455 | − | 0.322835i | \(-0.104636\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.41421 | + | 1.41421i | −0.342997 | + | 0.342997i | −0.857493 | − | 0.514496i | \(-0.827979\pi\) |
0.514496 | + | 0.857493i | \(0.327979\pi\) | |||||||
\(18\) | 2.99535 | + | 0.166925i | 0.706011 | + | 0.0393447i | ||||
\(19\) | − | 0.763932i | − | 0.175258i | −0.996153 | − | 0.0876290i | \(-0.972071\pi\) | ||
0.996153 | − | 0.0876290i | \(-0.0279290\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.618034 | − | 1.61803i | −0.134866 | − | 0.353084i | ||||
\(22\) | −2.28825 | − | 2.28825i | −0.487856 | − | 0.487856i | ||||
\(23\) | 1.74806 | + | 1.74806i | 0.364497 | + | 0.364497i | 0.865465 | − | 0.500969i | \(-0.167023\pi\) |
−0.500969 | + | 0.865465i | \(0.667023\pi\) | |||||||
\(24\) | −0.618034 | − | 1.61803i | −0.126156 | − | 0.330280i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 6.47214i | − | 1.26929i | ||||||
\(27\) | 1.58114 | + | 4.94975i | 0.304290 | + | 0.952579i | ||||
\(28\) | −0.707107 | + | 0.707107i | −0.133631 | + | 0.133631i | ||||
\(29\) | −0.763932 | −0.141859 | −0.0709293 | − | 0.997481i | \(-0.522596\pi\) | ||||
−0.0709293 | + | 0.997481i | \(0.522596\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.23607 | 0.940426 | 0.470213 | − | 0.882553i | \(-0.344177\pi\) | ||||
0.470213 | + | 0.882553i | \(0.344177\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 2.28825 | − | 5.11667i | 0.398332 | − | 0.890698i | ||||
\(34\) | 2.00000i | 0.342997i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.23607 | − | 2.00000i | 0.372678 | − | 0.333333i | ||||
\(37\) | −5.11667 | − | 5.11667i | −0.841176 | − | 0.841176i | 0.147836 | − | 0.989012i | \(-0.452769\pi\) |
−0.989012 | + | 0.147836i | \(0.952769\pi\) | |||||||
\(38\) | −0.540182 | − | 0.540182i | −0.0876290 | − | 0.0876290i | ||||
\(39\) | 10.4721 | − | 4.00000i | 1.67688 | − | 0.640513i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.23607i | 1.44243i | 0.692711 | + | 0.721216i | \(0.256416\pi\) | ||||
−0.692711 | + | 0.721216i | \(0.743584\pi\) | |||||||
\(42\) | −1.58114 | − | 0.707107i | −0.243975 | − | 0.109109i | ||||
\(43\) | 2.28825 | − | 2.28825i | 0.348954 | − | 0.348954i | −0.510766 | − | 0.859720i | \(-0.670638\pi\) |
0.859720 | + | 0.510766i | \(0.170638\pi\) | |||||||
\(44\) | −3.23607 | −0.487856 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.47214 | 0.364497 | ||||||||
\(47\) | 7.19859 | − | 7.19859i | 1.05002 | − | 1.05002i | 0.0513407 | − | 0.998681i | \(-0.483651\pi\) |
0.998681 | − | 0.0513407i | \(-0.0163494\pi\) | |||||||
\(48\) | −1.58114 | − | 0.707107i | −0.228218 | − | 0.102062i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.23607 | + | 1.23607i | −0.453140 | + | 0.173084i | ||||
\(52\) | −4.57649 | − | 4.57649i | −0.634645 | − | 0.634645i | ||||
\(53\) | 7.73877 | + | 7.73877i | 1.06300 | + | 1.06300i | 0.997877 | + | 0.0651245i | \(0.0207445\pi\) |
0.0651245 | + | 0.997877i | \(0.479256\pi\) | |||||||
\(54\) | 4.61803 | + | 2.38197i | 0.628435 | + | 0.324145i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000i | 0.133631i | ||||||||
\(57\) | 0.540182 | − | 1.20788i | 0.0715488 | − | 0.159988i | ||||
\(58\) | −0.540182 | + | 0.540182i | −0.0709293 | + | 0.0709293i | ||||
\(59\) | −0.291796 | −0.0379886 | −0.0189943 | − | 0.999820i | \(-0.506046\pi\) | ||||
−0.0189943 | + | 0.999820i | \(0.506046\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.9443 | −1.65734 | −0.828672 | − | 0.559734i | \(-0.810903\pi\) | ||||
−0.828672 | + | 0.559734i | \(0.810903\pi\) | |||||||
\(62\) | 3.70246 | − | 3.70246i | 0.470213 | − | 0.470213i | ||||
\(63\) | 0.166925 | − | 2.99535i | 0.0210306 | − | 0.377379i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.00000 | − | 5.23607i | −0.246183 | − | 0.644515i | ||||
\(67\) | −6.19704 | − | 6.19704i | −0.757088 | − | 0.757088i | 0.218703 | − | 0.975791i | \(-0.429817\pi\) |
−0.975791 | + | 0.218703i | \(0.929817\pi\) | |||||||
\(68\) | 1.41421 | + | 1.41421i | 0.171499 | + | 0.171499i | ||||
\(69\) | 1.52786 | + | 4.00000i | 0.183933 | + | 0.481543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4164i | 1.35488i | 0.735579 | + | 0.677439i | \(0.236910\pi\) | ||||
−0.735579 | + | 0.677439i | \(0.763090\pi\) | |||||||
\(72\) | 0.166925 | − | 2.99535i | 0.0196723 | − | 0.353006i | ||||
\(73\) | 2.62210 | − | 2.62210i | 0.306893 | − | 0.306893i | −0.536810 | − | 0.843703i | \(-0.680371\pi\) |
0.843703 | + | 0.536810i | \(0.180371\pi\) | |||||||
\(74\) | −7.23607 | −0.841176 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.763932 | −0.0876290 | ||||||||
\(77\) | −2.28825 | + | 2.28825i | −0.260770 | + | 0.260770i | ||||
\(78\) | 4.57649 | − | 10.2333i | 0.518186 | − | 1.15870i | ||||
\(79\) | 12.9443i | 1.45634i | 0.685394 | + | 0.728172i | \(0.259630\pi\) | ||||
−0.685394 | + | 0.728172i | \(0.740370\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | + | 8.94427i | −0.111111 | + | 0.993808i | ||||
\(82\) | 6.53089 | + | 6.53089i | 0.721216 | + | 0.721216i | ||||
\(83\) | −5.11667 | − | 5.11667i | −0.561628 | − | 0.561628i | 0.368142 | − | 0.929770i | \(-0.379994\pi\) |
−0.929770 | + | 0.368142i | \(0.879994\pi\) | |||||||
\(84\) | −1.61803 | + | 0.618034i | −0.176542 | + | 0.0674330i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 3.23607i | − | 0.348954i | ||||||
\(87\) | −1.20788 | − | 0.540182i | −0.129499 | − | 0.0579135i | ||||
\(88\) | −2.28825 | + | 2.28825i | −0.243928 | + | 0.243928i | ||||
\(89\) | −9.23607 | −0.979021 | −0.489511 | − | 0.871997i | \(-0.662825\pi\) | ||||
−0.489511 | + | 0.871997i | \(0.662825\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.47214 | −0.678464 | ||||||||
\(92\) | 1.74806 | − | 1.74806i | 0.182248 | − | 0.182248i | ||||
\(93\) | 8.27895 | + | 3.70246i | 0.858487 | + | 0.383927i | ||||
\(94\) | − | 10.1803i | − | 1.05002i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.61803 | + | 0.618034i | −0.165140 | + | 0.0630778i | ||||
\(97\) | −10.0270 | − | 10.0270i | −1.01809 | − | 1.01809i | −0.999833 | − | 0.0182557i | \(-0.994189\pi\) |
−0.0182557 | − | 0.999833i | \(-0.505811\pi\) | |||||||
\(98\) | 0.707107 | + | 0.707107i | 0.0714286 | + | 0.0714286i | ||||
\(99\) | 7.23607 | − | 6.47214i | 0.727252 | − | 0.650474i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.9443i | 1.68602i | 0.537899 | + | 0.843009i | \(0.319218\pi\) | ||||
−0.537899 | + | 0.843009i | \(0.680782\pi\) | |||||||
\(102\) | −1.41421 | + | 3.16228i | −0.140028 | + | 0.313112i | ||||
\(103\) | 3.90879 | − | 3.90879i | 0.385145 | − | 0.385145i | −0.487807 | − | 0.872952i | \(-0.662203\pi\) |
0.872952 | + | 0.487807i | \(0.162203\pi\) | |||||||
\(104\) | −6.47214 | −0.634645 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.9443 | 1.06300 | ||||||||
\(107\) | −11.9814 | + | 11.9814i | −1.15829 | + | 1.15829i | −0.173443 | + | 0.984844i | \(0.555489\pi\) |
−0.984844 | + | 0.173443i | \(0.944511\pi\) | |||||||
\(108\) | 4.94975 | − | 1.58114i | 0.476290 | − | 0.152145i | ||||
\(109\) | − | 2.94427i | − | 0.282010i | −0.990009 | − | 0.141005i | \(-0.954967\pi\) | ||
0.990009 | − | 0.141005i | \(-0.0450334\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.47214 | − | 11.7082i | −0.424476 | − | 1.11129i | ||||
\(112\) | 0.707107 | + | 0.707107i | 0.0668153 | + | 0.0668153i | ||||
\(113\) | 2.49458 | + | 2.49458i | 0.234670 | + | 0.234670i | 0.814639 | − | 0.579969i | \(-0.196935\pi\) |
−0.579969 | + | 0.814639i | \(0.696935\pi\) | |||||||
\(114\) | −0.472136 | − | 1.23607i | −0.0442196 | − | 0.115768i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.763932i | 0.0709293i | ||||||||
\(117\) | 19.3863 | + | 1.08036i | 1.79227 | + | 0.0998796i | ||||
\(118\) | −0.206331 | + | 0.206331i | −0.0189943 | + | 0.0189943i | ||||
\(119\) | 2.00000 | 0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.527864 | 0.0479876 | ||||||||
\(122\) | −9.15298 | + | 9.15298i | −0.828672 | + | 0.828672i | ||||
\(123\) | −6.53089 | + | 14.6035i | −0.588870 | + | 1.31675i | ||||
\(124\) | − | 5.23607i | − | 0.470213i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | − | 2.23607i | −0.178174 | − | 0.199205i | ||||
\(127\) | 10.2333 | + | 10.2333i | 0.908063 | + | 0.908063i | 0.996116 | − | 0.0880532i | \(-0.0280646\pi\) |
−0.0880532 | + | 0.996116i | \(0.528065\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 5.23607 | − | 2.00000i | 0.461010 | − | 0.176090i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.29180i | 0.724458i | 0.932089 | + | 0.362229i | \(0.117984\pi\) | ||||
−0.932089 | + | 0.362229i | \(0.882016\pi\) | |||||||
\(132\) | −5.11667 | − | 2.28825i | −0.445349 | − | 0.199166i | ||||
\(133\) | −0.540182 | + | 0.540182i | −0.0468397 | + | 0.0468397i | ||||
\(134\) | −8.76393 | −0.757088 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.00000 | 0.171499 | ||||||||
\(137\) | 9.89949 | − | 9.89949i | 0.845771 | − | 0.845771i | −0.143831 | − | 0.989602i | \(-0.545942\pi\) |
0.989602 | + | 0.143831i | \(0.0459423\pi\) | |||||||
\(138\) | 3.90879 | + | 1.74806i | 0.332738 | + | 0.148805i | ||||
\(139\) | 1.70820i | 0.144888i | 0.997372 | + | 0.0724440i | \(0.0230799\pi\) | ||||
−0.997372 | + | 0.0724440i | \(0.976920\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.4721 | − | 6.29180i | 1.38720 | − | 0.529865i | ||||
\(142\) | 8.07262 | + | 8.07262i | 0.677439 | + | 0.677439i | ||||
\(143\) | −14.8098 | − | 14.8098i | −1.23846 | − | 1.23846i | ||||
\(144\) | −2.00000 | − | 2.23607i | −0.166667 | − | 0.186339i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 3.70820i | − | 0.306893i | ||||||
\(147\) | −0.707107 | + | 1.58114i | −0.0583212 | + | 0.130410i | ||||
\(148\) | −5.11667 | + | 5.11667i | −0.420588 | + | 0.420588i | ||||
\(149\) | −20.1803 | −1.65324 | −0.826619 | − | 0.562762i | \(-0.809739\pi\) | ||||
−0.826619 | + | 0.562762i | \(0.809739\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.52786 | 0.449851 | 0.224926 | − | 0.974376i | \(-0.427786\pi\) | ||||
0.224926 | + | 0.974376i | \(0.427786\pi\) | |||||||
\(152\) | −0.540182 | + | 0.540182i | −0.0438145 | + | 0.0438145i | ||||
\(153\) | −5.99070 | − | 0.333851i | −0.484320 | − | 0.0269902i | ||||
\(154\) | 3.23607i | 0.260770i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.00000 | − | 10.4721i | −0.320256 | − | 0.838442i | ||||
\(157\) | −3.90879 | − | 3.90879i | −0.311955 | − | 0.311955i | 0.533711 | − | 0.845667i | \(-0.320797\pi\) |
−0.845667 | + | 0.533711i | \(0.820797\pi\) | |||||||
\(158\) | 9.15298 | + | 9.15298i | 0.728172 | + | 0.728172i | ||||
\(159\) | 6.76393 | + | 17.7082i | 0.536415 | + | 1.40435i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2.47214i | − | 0.194832i | ||||||
\(162\) | 5.61745 | + | 7.03166i | 0.441348 | + | 0.552460i | ||||
\(163\) | −10.3609 | + | 10.3609i | −0.811526 | + | 0.811526i | −0.984863 | − | 0.173337i | \(-0.944545\pi\) |
0.173337 | + | 0.984863i | \(0.444545\pi\) | |||||||
\(164\) | 9.23607 | 0.721216 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.23607 | −0.561628 | ||||||||
\(167\) | 0.206331 | − | 0.206331i | 0.0159664 | − | 0.0159664i | −0.699079 | − | 0.715045i | \(-0.746406\pi\) |
0.715045 | + | 0.699079i | \(0.246406\pi\) | |||||||
\(168\) | −0.707107 | + | 1.58114i | −0.0545545 | + | 0.121988i | ||||
\(169\) | − | 28.8885i | − | 2.22220i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.70820 | − | 1.52786i | 0.130630 | − | 0.116839i | ||||
\(172\) | −2.28825 | − | 2.28825i | −0.174477 | − | 0.174477i | ||||
\(173\) | −6.32456 | − | 6.32456i | −0.480847 | − | 0.480847i | 0.424555 | − | 0.905402i | \(-0.360431\pi\) |
−0.905402 | + | 0.424555i | \(0.860431\pi\) | |||||||
\(174\) | −1.23607 | + | 0.472136i | −0.0937061 | + | 0.0357925i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.23607i | 0.243928i | ||||||||
\(177\) | −0.461370 | − | 0.206331i | −0.0346787 | − | 0.0155088i | ||||
\(178\) | −6.53089 | + | 6.53089i | −0.489511 | + | 0.489511i | ||||
\(179\) | −8.76393 | −0.655047 | −0.327524 | − | 0.944843i | \(-0.606214\pi\) | ||||
−0.327524 | + | 0.944843i | \(0.606214\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.8885 | −1.62696 | −0.813481 | − | 0.581591i | \(-0.802430\pi\) | ||||
−0.813481 | + | 0.581591i | \(0.802430\pi\) | |||||||
\(182\) | −4.57649 | + | 4.57649i | −0.339232 | + | 0.339232i | ||||
\(183\) | −20.4667 | − | 9.15298i | −1.51294 | − | 0.676608i | ||||
\(184\) | − | 2.47214i | − | 0.182248i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.47214 | − | 3.23607i | 0.621207 | − | 0.237280i | ||||
\(187\) | 4.57649 | + | 4.57649i | 0.334666 | + | 0.334666i | ||||
\(188\) | −7.19859 | − | 7.19859i | −0.525011 | − | 0.525011i | ||||
\(189\) | 2.38197 | − | 4.61803i | 0.173263 | − | 0.335913i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.05573i | 0.221105i | 0.993870 | + | 0.110552i | \(0.0352620\pi\) | ||||
−0.993870 | + | 0.110552i | \(0.964738\pi\) | |||||||
\(192\) | −0.707107 | + | 1.58114i | −0.0510310 | + | 0.114109i | ||||
\(193\) | −5.24419 | + | 5.24419i | −0.377485 | + | 0.377485i | −0.870194 | − | 0.492709i | \(-0.836007\pi\) |
0.492709 | + | 0.870194i | \(0.336007\pi\) | |||||||
\(194\) | −14.1803 | −1.01809 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 1.41421 | − | 1.41421i | 0.100759 | − | 0.100759i | −0.654931 | − | 0.755689i | \(-0.727302\pi\) |
0.755689 | + | 0.654931i | \(0.227302\pi\) | |||||||
\(198\) | 0.540182 | − | 9.69316i | 0.0383890 | − | 0.688863i | ||||
\(199\) | 2.18034i | 0.154560i | 0.997009 | + | 0.0772801i | \(0.0246236\pi\) | ||||
−0.997009 | + | 0.0772801i | \(0.975376\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.41641 | − | 14.1803i | −0.382044 | − | 1.00020i | ||||
\(202\) | 11.9814 | + | 11.9814i | 0.843009 | + | 0.843009i | ||||
\(203\) | 0.540182 | + | 0.540182i | 0.0379133 | + | 0.0379133i | ||||
\(204\) | 1.23607 | + | 3.23607i | 0.0865421 | + | 0.226570i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 5.52786i | − | 0.385145i | ||||||
\(207\) | −0.412662 | + | 7.40492i | −0.0286820 | + | 0.514677i | ||||
\(208\) | −4.57649 | + | 4.57649i | −0.317323 | + | 0.317323i | ||||
\(209\) | −2.47214 | −0.171001 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.8328 | 1.84725 | 0.923624 | − | 0.383301i | \(-0.125213\pi\) | ||||
0.923624 | + | 0.383301i | \(0.125213\pi\) | |||||||
\(212\) | 7.73877 | − | 7.73877i | 0.531501 | − | 0.531501i | ||||
\(213\) | −8.07262 | + | 18.0509i | −0.553127 | + | 1.23683i | ||||
\(214\) | 16.9443i | 1.15829i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.38197 | − | 4.61803i | 0.162072 | − | 0.314217i | ||||
\(217\) | −3.70246 | − | 3.70246i | −0.251339 | − | 0.251339i | ||||
\(218\) | −2.08191 | − | 2.08191i | −0.141005 | − | 0.141005i | ||||
\(219\) | 6.00000 | − | 2.29180i | 0.405442 | − | 0.154865i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.9443i | 0.870726i | ||||||||
\(222\) | −11.4412 | − | 5.11667i | −0.767885 | − | 0.343409i | ||||
\(223\) | −3.49613 | + | 3.49613i | −0.234118 | + | 0.234118i | −0.814409 | − | 0.580291i | \(-0.802939\pi\) |
0.580291 | + | 0.814409i | \(0.302939\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.52786 | 0.234670 | ||||||||
\(227\) | −2.28825 | + | 2.28825i | −0.151876 | + | 0.151876i | −0.778955 | − | 0.627079i | \(-0.784250\pi\) |
0.627079 | + | 0.778955i | \(0.284250\pi\) | |||||||
\(228\) | −1.20788 | − | 0.540182i | −0.0799940 | − | 0.0357744i | ||||
\(229\) | 8.94427i | 0.591054i | 0.955334 | + | 0.295527i | \(0.0954953\pi\) | ||||
−0.955334 | + | 0.295527i | \(0.904505\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.23607 | + | 2.00000i | −0.344508 | + | 0.131590i | ||||
\(232\) | 0.540182 | + | 0.540182i | 0.0354647 | + | 0.0354647i | ||||
\(233\) | 5.99070 | + | 5.99070i | 0.392464 | + | 0.392464i | 0.875565 | − | 0.483101i | \(-0.160489\pi\) |
−0.483101 | + | 0.875565i | \(0.660489\pi\) | |||||||
\(234\) | 14.4721 | − | 12.9443i | 0.946073 | − | 0.846194i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.291796i | 0.0189943i | ||||||||
\(237\) | −9.15298 | + | 20.4667i | −0.594550 | + | 1.32945i | ||||
\(238\) | 1.41421 | − | 1.41421i | 0.0916698 | − | 0.0916698i | ||||
\(239\) | 30.8328 | 1.99441 | 0.997205 | − | 0.0747204i | \(-0.0238064\pi\) | ||||
0.997205 | + | 0.0747204i | \(0.0238064\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.8885 | 1.79646 | 0.898230 | − | 0.439527i | \(-0.144854\pi\) | ||||
0.898230 | + | 0.439527i | \(0.144854\pi\) | |||||||
\(242\) | 0.373256 | − | 0.373256i | 0.0239938 | − | 0.0239938i | ||||
\(243\) | −7.90569 | + | 13.4350i | −0.507151 | + | 0.861858i | ||||
\(244\) | 12.9443i | 0.828672i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.70820 | + | 14.9443i | 0.363942 | + | 0.952812i | ||||
\(247\) | −3.49613 | − | 3.49613i | −0.222453 | − | 0.222453i | ||||
\(248\) | −3.70246 | − | 3.70246i | −0.235106 | − | 0.235106i | ||||
\(249\) | −4.47214 | − | 11.7082i | −0.283410 | − | 0.741977i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 27.1246i | − | 1.71209i | −0.516901 | − | 0.856045i | \(-0.672914\pi\) | ||
0.516901 | − | 0.856045i | \(-0.327086\pi\) | |||||||
\(252\) | −2.99535 | − | 0.166925i | −0.188689 | − | 0.0105153i | ||||
\(253\) | 5.65685 | − | 5.65685i | 0.355643 | − | 0.355643i | ||||
\(254\) | 14.4721 | 0.908063 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.41421 | − | 1.41421i | 0.0882162 | − | 0.0882162i | −0.661622 | − | 0.749838i | \(-0.730131\pi\) |
0.749838 | + | 0.661622i | \(0.230131\pi\) | |||||||
\(258\) | 2.28825 | − | 5.11667i | 0.142460 | − | 0.318550i | ||||
\(259\) | 7.23607i | 0.449627i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.52786 | − | 1.70820i | −0.0945724 | − | 0.105735i | ||||
\(262\) | 5.86319 | + | 5.86319i | 0.362229 | + | 0.362229i | ||||
\(263\) | 9.56564 | + | 9.56564i | 0.589843 | + | 0.589843i | 0.937589 | − | 0.347746i | \(-0.113053\pi\) |
−0.347746 | + | 0.937589i | \(0.613053\pi\) | |||||||
\(264\) | −5.23607 | + | 2.00000i | −0.322258 | + | 0.123091i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.763932i | 0.0468397i | ||||||||
\(267\) | −14.6035 | − | 6.53089i | −0.893720 | − | 0.399684i | ||||
\(268\) | −6.19704 | + | 6.19704i | −0.378544 | + | 0.378544i | ||||
\(269\) | −26.4721 | −1.61403 | −0.807017 | − | 0.590528i | \(-0.798920\pi\) | ||||
−0.807017 | + | 0.590528i | \(0.798920\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.7639 | −0.896845 | −0.448423 | − | 0.893822i | \(-0.648014\pi\) | ||||
−0.448423 | + | 0.893822i | \(0.648014\pi\) | |||||||
\(272\) | 1.41421 | − | 1.41421i | 0.0857493 | − | 0.0857493i | ||||
\(273\) | −10.2333 | − | 4.57649i | −0.619350 | − | 0.276982i | ||||
\(274\) | − | 14.0000i | − | 0.845771i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.00000 | − | 1.52786i | 0.240772 | − | 0.0919666i | ||||
\(277\) | 22.3423 | + | 22.3423i | 1.34242 | + | 1.34242i | 0.893647 | + | 0.448770i | \(0.148138\pi\) |
0.448770 | + | 0.893647i | \(0.351862\pi\) | |||||||
\(278\) | 1.20788 | + | 1.20788i | 0.0724440 | + | 0.0724440i | ||||
\(279\) | 10.4721 | + | 11.7082i | 0.626950 | + | 0.700952i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.3607i | 0.737376i | 0.929553 | + | 0.368688i | \(0.120193\pi\) | ||||
−0.929553 | + | 0.368688i | \(0.879807\pi\) | |||||||
\(282\) | 7.19859 | − | 16.0965i | 0.428670 | − | 0.958534i | ||||
\(283\) | 11.1074 | − | 11.1074i | 0.660265 | − | 0.660265i | −0.295177 | − | 0.955442i | \(-0.595379\pi\) |
0.955442 | + | 0.295177i | \(0.0953788\pi\) | |||||||
\(284\) | 11.4164 | 0.677439 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.9443 | −1.23846 | ||||||||
\(287\) | 6.53089 | − | 6.53089i | 0.385506 | − | 0.385506i | ||||
\(288\) | −2.99535 | − | 0.166925i | −0.176503 | − | 0.00983617i | ||||
\(289\) | 13.0000i | 0.764706i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.76393 | − | 22.9443i | −0.513751 | − | 1.34502i | ||||
\(292\) | −2.62210 | − | 2.62210i | −0.153447 | − | 0.153447i | ||||
\(293\) | 2.16073 | + | 2.16073i | 0.126231 | + | 0.126231i | 0.767400 | − | 0.641169i | \(-0.221550\pi\) |
−0.641169 | + | 0.767400i | \(0.721550\pi\) | |||||||
\(294\) | 0.618034 | + | 1.61803i | 0.0360445 | + | 0.0943657i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.23607i | 0.420588i | ||||||||
\(297\) | 16.0177 | − | 5.11667i | 0.929442 | − | 0.296899i | ||||
\(298\) | −14.2697 | + | 14.2697i | −0.826619 | + | 0.826619i | ||||
\(299\) | 16.0000 | 0.925304 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.23607 | −0.186524 | ||||||||
\(302\) | 3.90879 | − | 3.90879i | 0.224926 | − | 0.224926i | ||||
\(303\) | −11.9814 | + | 26.7912i | −0.688314 | + | 1.53912i | ||||
\(304\) | 0.763932i | 0.0438145i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.47214 | + | 4.00000i | −0.255655 | + | 0.228665i | ||||
\(307\) | 12.1877 | + | 12.1877i | 0.695591 | + | 0.695591i | 0.963456 | − | 0.267865i | \(-0.0863182\pi\) |
−0.267865 | + | 0.963456i | \(0.586318\pi\) | |||||||
\(308\) | 2.28825 | + | 2.28825i | 0.130385 | + | 0.130385i | ||||
\(309\) | 8.94427 | − | 3.41641i | 0.508822 | − | 0.194353i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8.00000i | − | 0.453638i | −0.973937 | − | 0.226819i | \(-0.927167\pi\) | ||
0.973937 | − | 0.226819i | \(-0.0728326\pi\) | |||||||
\(312\) | −10.2333 | − | 4.57649i | −0.579349 | − | 0.259093i | ||||
\(313\) | −6.53089 | + | 6.53089i | −0.369148 | + | 0.369148i | −0.867166 | − | 0.498019i | \(-0.834061\pi\) |
0.498019 | + | 0.867166i | \(0.334061\pi\) | |||||||
\(314\) | −5.52786 | −0.311955 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.9443 | 0.728172 | ||||||||
\(317\) | −19.0525 | + | 19.0525i | −1.07009 | + | 1.07009i | −0.0727430 | + | 0.997351i | \(0.523175\pi\) |
−0.997351 | + | 0.0727430i | \(0.976825\pi\) | |||||||
\(318\) | 17.3044 | + | 7.73877i | 0.970383 | + | 0.433969i | ||||
\(319\) | 2.47214i | 0.138413i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −27.4164 | + | 10.4721i | −1.53023 | + | 0.584498i | ||||
\(322\) | −1.74806 | − | 1.74806i | −0.0974158 | − | 0.0974158i | ||||
\(323\) | 1.08036 | + | 1.08036i | 0.0601130 | + | 0.0601130i | ||||
\(324\) | 8.94427 | + | 1.00000i | 0.496904 | + | 0.0555556i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.6525i | 0.811526i | ||||||||
\(327\) | 2.08191 | − | 4.65530i | 0.115130 | − | 0.257439i | ||||
\(328\) | 6.53089 | − | 6.53089i | 0.360608 | − | 0.360608i | ||||
\(329\) | −10.1803 | −0.561260 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.4721 | −1.45504 | −0.727520 | − | 0.686086i | \(-0.759327\pi\) | ||||
−0.727520 | + | 0.686086i | \(0.759327\pi\) | |||||||
\(332\) | −5.11667 | + | 5.11667i | −0.280814 | + | 0.280814i | ||||
\(333\) | 1.20788 | − | 21.6746i | 0.0661916 | − | 1.18776i | ||||
\(334\) | − | 0.291796i | − | 0.0159664i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.618034 | + | 1.61803i | 0.0337165 | + | 0.0882710i | ||||
\(337\) | −15.8902 | − | 15.8902i | −0.865594 | − | 0.865594i | 0.126387 | − | 0.991981i | \(-0.459662\pi\) |
−0.991981 | + | 0.126387i | \(0.959662\pi\) | |||||||
\(338\) | −20.4273 | − | 20.4273i | −1.11110 | − | 1.11110i | ||||
\(339\) | 2.18034 | + | 5.70820i | 0.118420 | + | 0.310027i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 16.9443i | − | 0.917584i | ||||||
\(342\) | 0.127520 | − | 2.28825i | 0.00689547 | − | 0.123734i | ||||
\(343\) | 0.707107 | − | 0.707107i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | −3.23607 | −0.174477 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.94427 | −0.480847 | ||||||||
\(347\) | 10.9010 | − | 10.9010i | 0.585199 | − | 0.585199i | −0.351128 | − | 0.936327i | \(-0.614202\pi\) |
0.936327 | + | 0.351128i | \(0.114202\pi\) | |||||||
\(348\) | −0.540182 | + | 1.20788i | −0.0289568 | + | 0.0647493i | ||||
\(349\) | 4.00000i | 0.214115i | 0.994253 | + | 0.107058i | \(0.0341429\pi\) | ||||
−0.994253 | + | 0.107058i | \(0.965857\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 29.8885 | + | 15.4164i | 1.59533 | + | 0.822867i | ||||
\(352\) | 2.28825 | + | 2.28825i | 0.121964 | + | 0.121964i | ||||
\(353\) | −24.0416 | − | 24.0416i | −1.27961 | − | 1.27961i | −0.940887 | − | 0.338719i | \(-0.890006\pi\) |
−0.338719 | − | 0.940887i | \(-0.609994\pi\) | |||||||
\(354\) | −0.472136 | + | 0.180340i | −0.0250937 | + | 0.00958496i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.23607i | 0.489511i | ||||||||
\(357\) | 3.16228 | + | 1.41421i | 0.167365 | + | 0.0748481i | ||||
\(358\) | −6.19704 | + | 6.19704i | −0.327524 | + | 0.327524i | ||||
\(359\) | 11.4164 | 0.602535 | 0.301267 | − | 0.953540i | \(-0.402590\pi\) | ||||
0.301267 | + | 0.953540i | \(0.402590\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.4164 | 0.969285 | ||||||||
\(362\) | −15.4775 | + | 15.4775i | −0.813481 | + | 0.813481i | ||||
\(363\) | 0.834626 | + | 0.373256i | 0.0438065 | + | 0.0195909i | ||||
\(364\) | 6.47214i | 0.339232i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −20.9443 | + | 8.00000i | −1.09477 | + | 0.418167i | ||||
\(367\) | 14.8098 | + | 14.8098i | 0.773067 | + | 0.773067i | 0.978642 | − | 0.205574i | \(-0.0659062\pi\) |
−0.205574 | + | 0.978642i | \(0.565906\pi\) | |||||||
\(368\) | −1.74806 | − | 1.74806i | −0.0911241 | − | 0.0911241i | ||||
\(369\) | −20.6525 | + | 18.4721i | −1.07512 | + | 0.961621i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 10.9443i | − | 0.568198i | ||||||
\(372\) | 3.70246 | − | 8.27895i | 0.191964 | − | 0.429244i | ||||
\(373\) | 16.4304 | − | 16.4304i | 0.850733 | − | 0.850733i | −0.139491 | − | 0.990223i | \(-0.544546\pi\) |
0.990223 | + | 0.139491i | \(0.0445465\pi\) | |||||||
\(374\) | 6.47214 | 0.334666 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.1803 | −0.525011 | ||||||||
\(377\) | −3.49613 | + | 3.49613i | −0.180060 | + | 0.180060i | ||||
\(378\) | −1.58114 | − | 4.94975i | −0.0813250 | − | 0.254588i | ||||
\(379\) | − | 28.3607i | − | 1.45679i | −0.685157 | − | 0.728395i | \(-0.740267\pi\) | ||
0.685157 | − | 0.728395i | \(-0.259733\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.94427 | + | 23.4164i | 0.458229 | + | 1.19966i | ||||
\(382\) | 2.16073 | + | 2.16073i | 0.110552 | + | 0.110552i | ||||
\(383\) | 8.94665 | + | 8.94665i | 0.457153 | + | 0.457153i | 0.897720 | − | 0.440567i | \(-0.145223\pi\) |
−0.440567 | + | 0.897720i | \(0.645223\pi\) | |||||||
\(384\) | 0.618034 | + | 1.61803i | 0.0315389 | + | 0.0825700i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.41641i | 0.377485i | ||||||||
\(387\) | 9.69316 | + | 0.540182i | 0.492731 | + | 0.0274590i | ||||
\(388\) | −10.0270 | + | 10.0270i | −0.509045 | + | 0.509045i | ||||
\(389\) | 23.2361 | 1.17812 | 0.589058 | − | 0.808091i | \(-0.299499\pi\) | ||||
0.589058 | + | 0.808091i | \(0.299499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.94427 | −0.250043 | ||||||||
\(392\) | 0.707107 | − | 0.707107i | 0.0357143 | − | 0.0357143i | ||||
\(393\) | −5.86319 | + | 13.1105i | −0.295759 | + | 0.661336i | ||||
\(394\) | − | 2.00000i | − | 0.100759i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.47214 | − | 7.23607i | −0.325237 | − | 0.363626i | ||||
\(397\) | −0.412662 | − | 0.412662i | −0.0207109 | − | 0.0207109i | 0.696675 | − | 0.717386i | \(-0.254662\pi\) |
−0.717386 | + | 0.696675i | \(0.754662\pi\) | |||||||
\(398\) | 1.54173 | + | 1.54173i | 0.0772801 | + | 0.0772801i | ||||
\(399\) | −1.23607 | + | 0.472136i | −0.0618808 | + | 0.0236364i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.05573i | 0.152596i | 0.997085 | + | 0.0762979i | \(0.0243100\pi\) | ||||
−0.997085 | + | 0.0762979i | \(0.975690\pi\) | |||||||
\(402\) | −13.8570 | − | 6.19704i | −0.691124 | − | 0.309080i | ||||
\(403\) | 23.9628 | − | 23.9628i | 1.19367 | − | 1.19367i | ||||
\(404\) | 16.9443 | 0.843009 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.763932 | 0.0379133 | ||||||||
\(407\) | −16.5579 | + | 16.5579i | −0.820745 | + | 0.820745i | ||||
\(408\) | 3.16228 | + | 1.41421i | 0.156556 | + | 0.0700140i | ||||
\(409\) | 4.11146i | 0.203298i | 0.994820 | + | 0.101649i | \(0.0324119\pi\) | ||||
−0.994820 | + | 0.101649i | \(0.967588\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.6525 | − | 8.65248i | 1.11736 | − | 0.426795i | ||||
\(412\) | −3.90879 | − | 3.90879i | −0.192572 | − | 0.192572i | ||||
\(413\) | 0.206331 | + | 0.206331i | 0.0101529 | + | 0.0101529i | ||||
\(414\) | 4.94427 | + | 5.52786i | 0.242998 | + | 0.271680i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.47214i | 0.317323i | ||||||||
\(417\) | −1.20788 | + | 2.70091i | −0.0591503 | + | 0.132264i | ||||
\(418\) | −1.74806 | + | 1.74806i | −0.0855006 | + | 0.0855006i | ||||
\(419\) | −19.1246 | −0.934298 | −0.467149 | − | 0.884178i | \(-0.654719\pi\) | ||||
−0.467149 | + | 0.884178i | \(0.654719\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.9443 | 0.533391 | 0.266696 | − | 0.963781i | \(-0.414068\pi\) | ||||
0.266696 | + | 0.963781i | \(0.414068\pi\) | |||||||
\(422\) | 18.9737 | − | 18.9737i | 0.923624 | − | 0.923624i | ||||
\(423\) | 30.4937 | + | 1.69936i | 1.48265 | + | 0.0826255i | ||||
\(424\) | − | 10.9443i | − | 0.531501i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.05573 | + | 18.4721i | 0.341851 | + | 0.894978i | ||||
\(427\) | 9.15298 | + | 9.15298i | 0.442944 | + | 0.442944i | ||||
\(428\) | 11.9814 | + | 11.9814i | 0.579143 | + | 0.579143i | ||||
\(429\) | −12.9443 | − | 33.8885i | −0.624955 | − | 1.63615i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 12.5836i | − | 0.606130i | −0.952970 | − | 0.303065i | \(-0.901990\pi\) | ||
0.952970 | − | 0.303065i | \(-0.0980100\pi\) | |||||||
\(432\) | −1.58114 | − | 4.94975i | −0.0760726 | − | 0.238145i | ||||
\(433\) | −4.78282 | + | 4.78282i | −0.229848 | + | 0.229848i | −0.812629 | − | 0.582781i | \(-0.801964\pi\) |
0.582781 | + | 0.812629i | \(0.301964\pi\) | |||||||
\(434\) | −5.23607 | −0.251339 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.94427 | −0.141005 | ||||||||
\(437\) | 1.33540 | − | 1.33540i | 0.0638809 | − | 0.0638809i | ||||
\(438\) | 2.62210 | − | 5.86319i | 0.125289 | − | 0.280154i | ||||
\(439\) | − | 9.81966i | − | 0.468667i | −0.972156 | − | 0.234333i | \(-0.924709\pi\) | ||
0.972156 | − | 0.234333i | \(-0.0752907\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.23607 | + | 2.00000i | −0.106479 | + | 0.0952381i | ||||
\(442\) | 9.15298 | + | 9.15298i | 0.435363 | + | 0.435363i | ||||
\(443\) | 6.32456 | + | 6.32456i | 0.300489 | + | 0.300489i | 0.841205 | − | 0.540716i | \(-0.181847\pi\) |
−0.540716 | + | 0.841205i | \(0.681847\pi\) | |||||||
\(444\) | −11.7082 | + | 4.47214i | −0.555647 | + | 0.212238i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.94427i | 0.234118i | ||||||||
\(447\) | −31.9079 | − | 14.2697i | −1.50919 | − | 0.674932i | ||||
\(448\) | 0.707107 | − | 0.707107i | 0.0334077 | − | 0.0334077i | ||||
\(449\) | −35.4164 | −1.67140 | −0.835702 | − | 0.549183i | \(-0.814939\pi\) | ||||
−0.835702 | + | 0.549183i | \(0.814939\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.8885 | 1.40740 | ||||||||
\(452\) | 2.49458 | − | 2.49458i | 0.117335 | − | 0.117335i | ||||
\(453\) | 8.74032 | + | 3.90879i | 0.410656 | + | 0.183651i | ||||
\(454\) | 3.23607i | 0.151876i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.23607 | + | 0.472136i | −0.0578842 | + | 0.0221098i | ||||
\(457\) | −3.08347 | − | 3.08347i | −0.144238 | − | 0.144238i | 0.631300 | − | 0.775539i | \(-0.282522\pi\) |
−0.775539 | + | 0.631300i | \(0.782522\pi\) | |||||||
\(458\) | 6.32456 | + | 6.32456i | 0.295527 | + | 0.295527i | ||||
\(459\) | −9.23607 | − | 4.76393i | −0.431103 | − | 0.222361i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 20.3607i | − | 0.948291i | −0.880446 | − | 0.474146i | \(-0.842757\pi\) | ||
0.880446 | − | 0.474146i | \(-0.157243\pi\) | |||||||
\(462\) | −2.28825 | + | 5.11667i | −0.106459 | + | 0.238049i | ||||
\(463\) | 14.8098 | − | 14.8098i | 0.688271 | − | 0.688271i | −0.273578 | − | 0.961850i | \(-0.588207\pi\) |
0.961850 | + | 0.273578i | \(0.0882073\pi\) | |||||||
\(464\) | 0.763932 | 0.0354647 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.47214 | 0.392464 | ||||||||
\(467\) | −5.11667 | + | 5.11667i | −0.236771 | + | 0.236771i | −0.815512 | − | 0.578740i | \(-0.803544\pi\) |
0.578740 | + | 0.815512i | \(0.303544\pi\) | |||||||
\(468\) | 1.08036 | − | 19.3863i | 0.0499398 | − | 0.896133i | ||||
\(469\) | 8.76393i | 0.404681i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.41641 | − | 8.94427i | −0.157420 | − | 0.412130i | ||||
\(472\) | 0.206331 | + | 0.206331i | 0.00949715 | + | 0.00949715i | ||||
\(473\) | −7.40492 | − | 7.40492i | −0.340479 | − | 0.340479i | ||||
\(474\) | 8.00000 | + | 20.9443i | 0.367452 | + | 0.962002i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 2.00000i | − | 0.0916698i | ||||||
\(477\) | −1.82688 | + | 32.7820i | −0.0836469 | + | 1.50098i | ||||
\(478\) | 21.8021 | − | 21.8021i | 0.997205 | − | 0.997205i | ||||
\(479\) | 5.52786 | 0.252575 | 0.126287 | − | 0.991994i | \(-0.459694\pi\) | ||||
0.126287 | + | 0.991994i | \(0.459694\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −46.8328 | −2.13539 | ||||||||
\(482\) | 19.7202 | − | 19.7202i | 0.898230 | − | 0.898230i | ||||
\(483\) | 1.74806 | − | 3.90879i | 0.0795397 | − | 0.177856i | ||||
\(484\) | − | 0.527864i | − | 0.0239938i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.90983 | + | 15.0902i | 0.177353 | + | 0.684504i | ||||
\(487\) | −11.5687 | − | 11.5687i | −0.524230 | − | 0.524230i | 0.394616 | − | 0.918846i | \(-0.370878\pi\) |
−0.918846 | + | 0.394616i | \(0.870878\pi\) | |||||||
\(488\) | 9.15298 | + | 9.15298i | 0.414336 | + | 0.414336i | ||||
\(489\) | −23.7082 | + | 9.05573i | −1.07212 | + | 0.409514i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 21.7082i | − | 0.979678i | −0.871813 | − | 0.489839i | \(-0.837056\pi\) | ||
0.871813 | − | 0.489839i | \(-0.162944\pi\) | |||||||
\(492\) | 14.6035 | + | 6.53089i | 0.658377 | + | 0.294435i | ||||
\(493\) | 1.08036 | − | 1.08036i | 0.0486571 | − | 0.0486571i | ||||
\(494\) | −4.94427 | −0.222453 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.23607 | −0.235106 | ||||||||
\(497\) | 8.07262 | − | 8.07262i | 0.362106 | − | 0.362106i | ||||
\(498\) | −11.4412 | − | 5.11667i | −0.512694 | − | 0.229284i | ||||
\(499\) | 12.0000i | 0.537194i | 0.963253 | + | 0.268597i | \(0.0865599\pi\) | ||||
−0.963253 | + | 0.268597i | \(0.913440\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.472136 | − | 0.180340i | 0.0210935 | − | 0.00805699i | ||||
\(502\) | −19.1800 | − | 19.1800i | −0.856045 | − | 0.856045i | ||||
\(503\) | 28.3330 | + | 28.3330i | 1.26331 | + | 1.26331i | 0.949481 | + | 0.313824i | \(0.101610\pi\) |
0.313824 | + | 0.949481i | \(0.398390\pi\) | |||||||
\(504\) | −2.23607 | + | 2.00000i | −0.0996024 | + | 0.0890871i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 8.00000i | − | 0.355643i | ||||||
\(507\) | 20.4273 | − | 45.6768i | 0.907208 | − | 2.02858i | ||||
\(508\) | 10.2333 | − | 10.2333i | 0.454031 | − | 0.454031i | ||||
\(509\) | −37.3050 | −1.65351 | −0.826756 | − | 0.562560i | \(-0.809817\pi\) | ||||
−0.826756 | + | 0.562560i | \(0.809817\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.70820 | −0.164041 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 3.78127 | − | 1.20788i | 0.166947 | − | 0.0533293i | ||||
\(514\) | − | 2.00000i | − | 0.0882162i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.00000 | − | 5.23607i | −0.0880451 | − | 0.230505i | ||||
\(517\) | −23.2951 | − | 23.2951i | −1.02452 | − | 1.02452i | ||||
\(518\) | 5.11667 | + | 5.11667i | 0.224814 | + | 0.224814i | ||||
\(519\) | −5.52786 | − | 14.4721i | −0.242646 | − | 0.635256i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 12.2918i | − | 0.538513i | −0.963068 | − | 0.269257i | \(-0.913222\pi\) | ||
0.963068 | − | 0.269257i | \(-0.0867780\pi\) | |||||||
\(522\) | −2.28825 | − | 0.127520i | −0.100154 | − | 0.00558138i | ||||
\(523\) | 19.8477 | − | 19.8477i | 0.867879 | − | 0.867879i | −0.124358 | − | 0.992237i | \(-0.539687\pi\) |
0.992237 | + | 0.124358i | \(0.0396872\pi\) | |||||||
\(524\) | 8.29180 | 0.362229 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.5279 | 0.589843 | ||||||||
\(527\) | −7.40492 | + | 7.40492i | −0.322563 | + | 0.322563i | ||||
\(528\) | −2.28825 | + | 5.11667i | −0.0995831 | + | 0.222675i | ||||
\(529\) | − | 16.8885i | − | 0.734285i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.583592 | − | 0.652476i | −0.0253257 | − | 0.0283150i | ||||
\(532\) | 0.540182 | + | 0.540182i | 0.0234198 | + | 0.0234198i | ||||
\(533\) | 42.2688 | + | 42.2688i | 1.83086 | + | 1.83086i | ||||
\(534\) | −14.9443 | + | 5.70820i | −0.646702 | + | 0.247018i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.76393i | 0.378544i | ||||||||
\(537\) | −13.8570 | − | 6.19704i | −0.597973 | − | 0.267422i | ||||
\(538\) | −18.7186 | + | 18.7186i | −0.807017 | + | 0.807017i | ||||
\(539\) | 3.23607 | 0.139387 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.00000 | 0.257960 | 0.128980 | − | 0.991647i | \(-0.458830\pi\) | ||||
0.128980 | + | 0.991647i | \(0.458830\pi\) | |||||||
\(542\) | −10.4397 | + | 10.4397i | −0.448423 | + | 0.448423i | ||||
\(543\) | −34.6088 | − | 15.4775i | −1.48521 | − | 0.664205i | ||||
\(544\) | − | 2.00000i | − | 0.0857493i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −10.4721 | + | 4.00000i | −0.448166 | + | 0.171184i | ||||
\(547\) | −18.4335 | − | 18.4335i | −0.788159 | − | 0.788159i | 0.193033 | − | 0.981192i | \(-0.438167\pi\) |
−0.981192 | + | 0.193033i | \(0.938167\pi\) | |||||||
\(548\) | −9.89949 | − | 9.89949i | −0.422885 | − | 0.422885i | ||||
\(549\) | −25.8885 | − | 28.9443i | −1.10490 | − | 1.23531i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.583592i | 0.0248619i | ||||||||
\(552\) | 1.74806 | − | 3.90879i | 0.0744025 | − | 0.166369i | ||||
\(553\) | 9.15298 | − | 9.15298i | 0.389224 | − | 0.389224i | ||||
\(554\) | 31.5967 | 1.34242 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.70820 | 0.0724440 | ||||||||
\(557\) | 26.0447 | − | 26.0447i | 1.10355 | − | 1.10355i | 0.109572 | − | 0.993979i | \(-0.465052\pi\) |
0.993979 | − | 0.109572i | \(-0.0349480\pi\) | |||||||
\(558\) | 15.6839 | + | 0.874032i | 0.663951 | + | 0.0370007i | ||||
\(559\) | − | 20.9443i | − | 0.885848i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.00000 | + | 10.4721i | 0.168880 | + | 0.442134i | ||||
\(562\) | 8.74032 | + | 8.74032i | 0.368688 | + | 0.368688i | ||||
\(563\) | −26.6637 | − | 26.6637i | −1.12374 | − | 1.12374i | −0.991174 | − | 0.132568i | \(-0.957678\pi\) |
−0.132568 | − | 0.991174i | \(-0.542322\pi\) | |||||||
\(564\) | −6.29180 | − | 16.4721i | −0.264932 | − | 0.693602i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 15.7082i | − | 0.660265i | ||||||
\(567\) | 7.03166 | − | 5.61745i | 0.295302 | − | 0.235911i | ||||
\(568\) | 8.07262 | − | 8.07262i | 0.338720 | − | 0.338720i | ||||
\(569\) | 11.0557 | 0.463480 | 0.231740 | − | 0.972778i | \(-0.425558\pi\) | ||||
0.231740 | + | 0.972778i | \(0.425558\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.4164 | 0.979946 | 0.489973 | − | 0.871738i | \(-0.337007\pi\) | ||||
0.489973 | + | 0.871738i | \(0.337007\pi\) | |||||||
\(572\) | −14.8098 | + | 14.8098i | −0.619230 | + | 0.619230i | ||||
\(573\) | −2.16073 | + | 4.83153i | −0.0902656 | + | 0.201840i | ||||
\(574\) | − | 9.23607i | − | 0.385506i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.23607 | + | 2.00000i | −0.0931695 | + | 0.0833333i | ||||
\(577\) | −10.4397 | − | 10.4397i | −0.434609 | − | 0.434609i | 0.455584 | − | 0.890193i | \(-0.349431\pi\) |
−0.890193 | + | 0.455584i | \(0.849431\pi\) | |||||||
\(578\) | 9.19239 | + | 9.19239i | 0.382353 | + | 0.382353i | ||||
\(579\) | −12.0000 | + | 4.58359i | −0.498703 | + | 0.190488i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.23607i | 0.300203i | ||||||||
\(582\) | −22.4211 | − | 10.0270i | −0.929384 | − | 0.415633i | ||||
\(583\) | 25.0432 | − | 25.0432i | 1.03718 | − | 1.03718i | ||||
\(584\) | −3.70820 | −0.153447 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.05573 | 0.126231 | ||||||||
\(587\) | 16.4304 | − | 16.4304i | 0.678154 | − | 0.678154i | −0.281428 | − | 0.959582i | \(-0.590808\pi\) |
0.959582 | + | 0.281428i | \(0.0908080\pi\) | |||||||
\(588\) | 1.58114 | + | 0.707107i | 0.0652051 | + | 0.0291606i | ||||
\(589\) | − | 4.00000i | − | 0.164817i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.23607 | − | 1.23607i | 0.133114 | − | 0.0508450i | ||||
\(592\) | 5.11667 | + | 5.11667i | 0.210294 | + | 0.210294i | ||||
\(593\) | −24.7093 | − | 24.7093i | −1.01469 | − | 1.01469i | −0.999890 | − | 0.0148002i | \(-0.995289\pi\) |
−0.0148002 | − | 0.999890i | \(-0.504711\pi\) | |||||||
\(594\) | 7.70820 | − | 14.9443i | 0.316271 | − | 0.613171i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.1803i | 0.826619i | ||||||||
\(597\) | −1.54173 | + | 3.44742i | −0.0630989 | + | 0.141094i | ||||
\(598\) | 11.3137 | − | 11.3137i | 0.462652 | − | 0.462652i | ||||
\(599\) | 20.9443 | 0.855760 | 0.427880 | − | 0.903836i | \(-0.359261\pi\) | ||||
0.427880 | + | 0.903836i | \(0.359261\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.0000 | 0.734235 | 0.367118 | − | 0.930175i | \(-0.380345\pi\) | ||||
0.367118 | + | 0.930175i | \(0.380345\pi\) | |||||||
\(602\) | −2.28825 | + | 2.28825i | −0.0932619 | + | 0.0932619i | ||||
\(603\) | 1.46292 | − | 26.2511i | 0.0595748 | − | 1.06903i | ||||
\(604\) | − | 5.52786i | − | 0.224926i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.4721 | + | 27.4164i | 0.425401 | + | 1.11372i | ||||
\(607\) | −22.6274 | − | 22.6274i | −0.918419 | − | 0.918419i | 0.0784959 | − | 0.996914i | \(-0.474988\pi\) |
−0.996914 | + | 0.0784959i | \(0.974988\pi\) | |||||||
\(608\) | 0.540182 | + | 0.540182i | 0.0219073 | + | 0.0219073i | ||||
\(609\) | 0.472136 | + | 1.23607i | 0.0191319 | + | 0.0500880i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 65.8885i | − | 2.66557i | ||||||
\(612\) | −0.333851 | + | 5.99070i | −0.0134951 | + | 0.242160i | ||||
\(613\) | −11.8539 | + | 11.8539i | −0.478774 | + | 0.478774i | −0.904739 | − | 0.425965i | \(-0.859935\pi\) |
0.425965 | + | 0.904739i | \(0.359935\pi\) | |||||||
\(614\) | 17.2361 | 0.695591 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.23607 | 0.130385 | ||||||||
\(617\) | 22.9613 | − | 22.9613i | 0.924386 | − | 0.924386i | −0.0729498 | − | 0.997336i | \(-0.523241\pi\) |
0.997336 | + | 0.0729498i | \(0.0232413\pi\) | |||||||
\(618\) | 3.90879 | − | 8.74032i | 0.157235 | − | 0.351587i | ||||
\(619\) | 7.23607i | 0.290842i | 0.989370 | + | 0.145421i | \(0.0464537\pi\) | ||||
−0.989370 | + | 0.145421i | \(0.953546\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.88854 | + | 11.4164i | −0.236299 | + | 0.458125i | ||||
\(622\) | −5.65685 | − | 5.65685i | −0.226819 | − | 0.226819i | ||||
\(623\) | 6.53089 | + | 6.53089i | 0.261654 | + | 0.261654i | ||||
\(624\) | −10.4721 | + | 4.00000i | −0.419221 | + | 0.160128i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.23607i | 0.369148i | ||||||||
\(627\) | −3.90879 | − | 1.74806i | −0.156102 | − | 0.0698110i | ||||
\(628\) | −3.90879 | + | 3.90879i | −0.155978 | + | 0.155978i | ||||
\(629\) | 14.4721 | 0.577042 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.41641 | 0.295243 | 0.147621 | − | 0.989044i | \(-0.452838\pi\) | ||||
0.147621 | + | 0.989044i | \(0.452838\pi\) | |||||||
\(632\) | 9.15298 | − | 9.15298i | 0.364086 | − | 0.364086i | ||||
\(633\) | 42.4264 | + | 18.9737i | 1.68630 | + | 0.754136i | ||||
\(634\) | 26.9443i | 1.07009i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 17.7082 | − | 6.76393i | 0.702176 | − | 0.268207i | ||||
\(637\) | 4.57649 | + | 4.57649i | 0.181327 | + | 0.181327i | ||||
\(638\) | 1.74806 | + | 1.74806i | 0.0692065 | + | 0.0692065i | ||||
\(639\) | −25.5279 | + | 22.8328i | −1.00987 | + | 0.903252i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.0557i | 0.436675i | 0.975873 | + | 0.218338i | \(0.0700634\pi\) | ||||
−0.975873 | + | 0.218338i | \(0.929937\pi\) | |||||||
\(642\) | −11.9814 | + | 26.7912i | −0.472869 | + | 1.05737i | ||||
\(643\) | −1.12907 | + | 1.12907i | −0.0445262 | + | 0.0445262i | −0.729019 | − | 0.684493i | \(-0.760024\pi\) |
0.684493 | + | 0.729019i | \(0.260024\pi\) | |||||||
\(644\) | −2.47214 | −0.0974158 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.52786 | 0.0601130 | ||||||||
\(647\) | −0.618993 | + | 0.618993i | −0.0243351 | + | 0.0243351i | −0.719170 | − | 0.694835i | \(-0.755478\pi\) |
0.694835 | + | 0.719170i | \(0.255478\pi\) | |||||||
\(648\) | 7.03166 | − | 5.61745i | 0.276230 | − | 0.220674i | ||||
\(649\) | 0.944272i | 0.0370659i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.23607 | − | 8.47214i | −0.126832 | − | 0.332049i | ||||
\(652\) | 10.3609 | + | 10.3609i | 0.405763 | + | 0.405763i | ||||
\(653\) | −20.5455 | − | 20.5455i | −0.804008 | − | 0.804008i | 0.179712 | − | 0.983719i | \(-0.442484\pi\) |
−0.983719 | + | 0.179712i | \(0.942484\pi\) | |||||||
\(654\) | −1.81966 | − | 4.76393i | −0.0711543 | − | 0.186284i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 9.23607i | − | 0.360608i | ||||||
\(657\) | 11.1074 | + | 0.618993i | 0.433340 | + | 0.0241492i | ||||
\(658\) | −7.19859 | + | 7.19859i | −0.280630 | + | 0.280630i | ||||
\(659\) | 19.2361 | 0.749331 | 0.374665 | − | 0.927160i | \(-0.377758\pi\) | ||||
0.374665 | + | 0.927160i | \(0.377758\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.00000 | −0.311164 | −0.155582 | − | 0.987823i | \(-0.549725\pi\) | ||||
−0.155582 | + | 0.987823i | \(0.549725\pi\) | |||||||
\(662\) | −18.7186 | + | 18.7186i | −0.727520 | + | 0.727520i | ||||
\(663\) | −9.15298 | + | 20.4667i | −0.355472 | + | 0.794860i | ||||
\(664\) | 7.23607i | 0.280814i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.4721 | − | 16.1803i | −0.560784 | − | 0.626975i | ||||
\(667\) | −1.33540 | − | 1.33540i | −0.0517070 | − | 0.0517070i | ||||
\(668\) | −0.206331 | − | 0.206331i | −0.00798319 | − | 0.00798319i | ||||
\(669\) | −8.00000 | + | 3.05573i | −0.309298 | + | 0.118141i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.8885i | 1.61709i | ||||||||
\(672\) | 1.58114 | + | 0.707107i | 0.0609938 | + | 0.0272772i | ||||
\(673\) | −24.6305 | + | 24.6305i | −0.949437 | + | 0.949437i | −0.998782 | − | 0.0493450i | \(-0.984287\pi\) |
0.0493450 | + | 0.998782i | \(0.484287\pi\) | |||||||
\(674\) | −22.4721 | −0.865594 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28.8885 | −1.11110 | ||||||||
\(677\) | −21.1344 | + | 21.1344i | −0.812261 | + | 0.812261i | −0.984972 | − | 0.172712i | \(-0.944747\pi\) |
0.172712 | + | 0.984972i | \(0.444747\pi\) | |||||||
\(678\) | 5.57804 | + | 2.49458i | 0.214223 | + | 0.0958036i | ||||
\(679\) | 14.1803i | 0.544191i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.23607 | + | 2.00000i | −0.200647 | + | 0.0766402i | ||||
\(682\) | −11.9814 | − | 11.9814i | −0.458792 | − | 0.458792i | ||||
\(683\) | −13.3168 | − | 13.3168i | −0.509554 | − | 0.509554i | 0.404836 | − | 0.914389i | \(-0.367329\pi\) |
−0.914389 | + | 0.404836i | \(0.867329\pi\) | |||||||
\(684\) | −1.52786 | − | 1.70820i | −0.0584193 | − | 0.0653148i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 1.00000i | − | 0.0381802i | ||||||
\(687\) | −6.32456 | + | 14.1421i | −0.241297 | + | 0.539556i | ||||
\(688\) | −2.28825 | + | 2.28825i | −0.0872385 | + | 0.0872385i | ||||
\(689\) | 70.8328 | 2.69852 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.87539 | −0.109385 | −0.0546925 | − | 0.998503i | \(-0.517418\pi\) | ||||
−0.0546925 | + | 0.998503i | \(0.517418\pi\) | |||||||
\(692\) | −6.32456 | + | 6.32456i | −0.240424 | + | 0.240424i | ||||
\(693\) | −9.69316 | − | 0.540182i | −0.368213 | − | 0.0205198i | ||||
\(694\) | − | 15.4164i | − | 0.585199i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.472136 | + | 1.23607i | 0.0178963 | + | 0.0468530i | ||||
\(697\) | −13.0618 | − | 13.0618i | −0.494750 | − | 0.494750i | ||||
\(698\) | 2.82843 | + | 2.82843i | 0.107058 | + | 0.107058i | ||||
\(699\) | 5.23607 | + | 13.7082i | 0.198046 | + | 0.518492i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6.87539i | − | 0.259680i | −0.991535 | − | 0.129840i | \(-0.958554\pi\) | ||
0.991535 | − | 0.129840i | \(-0.0414463\pi\) | |||||||
\(702\) | 32.0354 | − | 10.2333i | 1.20910 | − | 0.386233i | ||||
\(703\) | −3.90879 | + | 3.90879i | −0.147423 | + | 0.147423i | ||||
\(704\) | 3.23607 | 0.121964 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −34.0000 | −1.27961 | ||||||||
\(707\) | 11.9814 | − | 11.9814i | 0.450607 | − | 0.450607i | ||||
\(708\) | −0.206331 | + | 0.461370i | −0.00775439 | + | 0.0173393i | ||||
\(709\) | 9.05573i | 0.340095i | 0.985436 | + | 0.170048i | \(0.0543921\pi\) | ||||
−0.985436 | + | 0.170048i | \(0.945608\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −28.9443 | + | 25.8885i | −1.08550 | + | 0.970896i | ||||
\(712\) | 6.53089 | + | 6.53089i | 0.244755 | + | 0.244755i | ||||
\(713\) | 9.15298 | + | 9.15298i | 0.342782 | + | 0.342782i | ||||
\(714\) | 3.23607 | − | 1.23607i | 0.121107 | − | 0.0462587i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.76393i | 0.327524i | ||||||||
\(717\) | 48.7510 | + | 21.8021i | 1.82064 | + | 0.814214i | ||||
\(718\) | 8.07262 | − | 8.07262i | 0.301267 | − | 0.301267i | ||||
\(719\) | 23.4164 | 0.873285 | 0.436642 | − | 0.899635i | \(-0.356168\pi\) | ||||
0.436642 | + | 0.899635i | \(0.356168\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.52786 | −0.205868 | ||||||||
\(722\) | 13.0224 | − | 13.0224i | 0.484642 | − | 0.484642i | ||||
\(723\) | 44.0957 | + | 19.7202i | 1.63994 | + | 0.733401i | ||||
\(724\) | 21.8885i | 0.813481i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.854102 | − | 0.326238i | 0.0316987 | − | 0.0121078i | ||||
\(727\) | 22.2148 | + | 22.2148i | 0.823900 | + | 0.823900i | 0.986665 | − | 0.162765i | \(-0.0520413\pi\) |
−0.162765 | + | 0.986665i | \(0.552041\pi\) | |||||||
\(728\) | 4.57649 | + | 4.57649i | 0.169616 | + | 0.169616i | ||||
\(729\) | −22.0000 | + | 15.6525i | −0.814815 | + | 0.579721i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.47214i | 0.239381i | ||||||||
\(732\) | −9.15298 | + | 20.4667i | −0.338304 | + | 0.756471i | ||||
\(733\) | −4.32145 | + | 4.32145i | −0.159616 | + | 0.159616i | −0.782397 | − | 0.622780i | \(-0.786003\pi\) |
0.622780 | + | 0.782397i | \(0.286003\pi\) | |||||||
\(734\) | 20.9443 | 0.773067 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.47214 | −0.0911241 | ||||||||
\(737\) | −20.0540 | + | 20.0540i | −0.738700 | + | 0.738700i | ||||
\(738\) | −1.54173 | + | 27.6653i | −0.0567520 | + | 1.01837i | ||||
\(739\) | 44.3607i | 1.63183i | 0.578169 | + | 0.815917i | \(0.303767\pi\) | ||||
−0.578169 | + | 0.815917i | \(0.696233\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.05573 | − | 8.00000i | −0.112255 | − | 0.293887i | ||||
\(742\) | −7.73877 | − | 7.73877i | −0.284099 | − | 0.284099i | ||||
\(743\) | 13.4744 | + | 13.4744i | 0.494329 | + | 0.494329i | 0.909667 | − | 0.415338i | \(-0.136337\pi\) |
−0.415338 | + | 0.909667i | \(0.636337\pi\) | |||||||
\(744\) | −3.23607 | − | 8.47214i | −0.118640 | − | 0.310604i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 23.2361i | − | 0.850733i | ||||||
\(747\) | 1.20788 | − | 21.6746i | 0.0441941 | − | 0.793031i | ||||
\(748\) | 4.57649 | − | 4.57649i | 0.167333 | − | 0.167333i | ||||
\(749\) | 16.9443 | 0.619130 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.4164 | −0.562553 | −0.281276 | − | 0.959627i | \(-0.590758\pi\) | ||||
−0.281276 | + | 0.959627i | \(0.590758\pi\) | |||||||
\(752\) | −7.19859 | + | 7.19859i | −0.262505 | + | 0.262505i | ||||
\(753\) | 19.1800 | − | 42.8878i | 0.698958 | − | 1.56292i | ||||
\(754\) | 4.94427i | 0.180060i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.61803 | − | 2.38197i | −0.167956 | − | 0.0866313i | ||||
\(757\) | −8.35776 | − | 8.35776i | −0.303768 | − | 0.303768i | 0.538718 | − | 0.842486i | \(-0.318909\pi\) |
−0.842486 | + | 0.538718i | \(0.818909\pi\) | |||||||
\(758\) | −20.0540 | − | 20.0540i | −0.728395 | − | 0.728395i | ||||
\(759\) | 12.9443 | − | 4.94427i | 0.469847 | − | 0.179466i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 14.7639i | − | 0.535192i | −0.963531 | − | 0.267596i | \(-0.913771\pi\) | ||
0.963531 | − | 0.267596i | \(-0.0862293\pi\) | |||||||
\(762\) | 22.8825 | + | 10.2333i | 0.828944 | + | 0.370715i | ||||
\(763\) | −2.08191 | + | 2.08191i | −0.0753704 | + | 0.0753704i | ||||
\(764\) | 3.05573 | 0.110552 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.6525 | 0.457153 | ||||||||
\(767\) | −1.33540 | + | 1.33540i | −0.0482186 | + | 0.0482186i | ||||
\(768\) | 1.58114 | + | 0.707107i | 0.0570544 | + | 0.0255155i | ||||
\(769\) | − | 29.0557i | − | 1.04778i | −0.851787 | − | 0.523888i | \(-0.824481\pi\) | ||
0.851787 | − | 0.523888i | \(-0.175519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.23607 | − | 1.23607i | 0.116544 | − | 0.0445159i | ||||
\(772\) | 5.24419 | + | 5.24419i | 0.188743 | + | 0.188743i | ||||
\(773\) | −2.16073 | − | 2.16073i | −0.0777159 | − | 0.0777159i | 0.667180 | − | 0.744896i | \(-0.267501\pi\) |
−0.744896 | + | 0.667180i | \(0.767501\pi\) | |||||||
\(774\) | 7.23607 | − | 6.47214i | 0.260095 | − | 0.232636i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.1803i | 0.509045i | ||||||||
\(777\) | −5.11667 | + | 11.4412i | −0.183560 | + | 0.410452i | ||||
\(778\) | 16.4304 | − | 16.4304i | 0.589058 | − | 0.589058i | ||||
\(779\) | 7.05573 | 0.252798 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.9443 | 1.32197 | ||||||||
\(782\) | −3.49613 | + | 3.49613i | −0.125021 | + | 0.125021i | ||||
\(783\) | −1.20788 | − | 3.78127i | −0.0431662 | − | 0.135132i | ||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.12461 | + | 13.4164i | 0.182789 | + | 0.478547i | ||||
\(787\) | 13.5231 | + | 13.5231i | 0.482048 | + | 0.482048i | 0.905785 | − | 0.423737i | \(-0.139282\pi\) |
−0.423737 | + | 0.905785i | \(0.639282\pi\) | |||||||
\(788\) | −1.41421 | − | 1.41421i | −0.0503793 | − | 0.0503793i | ||||
\(789\) | 8.36068 | + | 21.8885i | 0.297648 | + | 0.779253i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 3.52786i | − | 0.125436i | ||||||
\(792\) | −9.69316 | − | 0.540182i | −0.344432 | − | 0.0191945i | ||||
\(793\) | −59.2393 | + | 59.2393i | −2.10365 | + | 2.10365i | ||||
\(794\) | −0.583592 | −0.0207109 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.18034 | 0.0772801 | ||||||||
\(797\) | −32.4481 | + | 32.4481i | −1.14937 | + | 1.14937i | −0.162694 | + | 0.986677i | \(0.552018\pi\) |
−0.986677 | + | 0.162694i | \(0.947982\pi\) | |||||||
\(798\) | −0.540182 | + | 1.20788i | −0.0191222 | + | 0.0427586i | ||||
\(799\) | 20.3607i | 0.720309i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.4721 | − | 20.6525i | −0.652681 | − | 0.729719i | ||||
\(802\) | 2.16073 | + | 2.16073i | 0.0762979 | + | 0.0762979i | ||||
\(803\) | −8.48528 | − | 8.48528i | −0.299439 | − | 0.299439i | ||||
\(804\) | −14.1803 | + | 5.41641i | −0.500102 | + | 0.191022i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 33.8885i | − | 1.19367i | ||||||
\(807\) | −41.8561 | − | 18.7186i | −1.47341 | − | 0.658927i | ||||
\(808\) | 11.9814 | − | 11.9814i | 0.421505 | − | 0.421505i | ||||
\(809\) | −39.4164 | −1.38581 | −0.692904 | − | 0.721030i | \(-0.743669\pi\) | ||||
−0.692904 | + | 0.721030i | \(0.743669\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.5410 | 1.14267 | 0.571335 | − | 0.820717i | \(-0.306426\pi\) | ||||
0.571335 | + | 0.820717i | \(0.306426\pi\) | |||||||
\(812\) | 0.540182 | − | 0.540182i | 0.0189567 | − | 0.0189567i | ||||
\(813\) | −23.3438 | − | 10.4397i | −0.818704 | − | 0.366135i | ||||
\(814\) | 23.4164i | 0.820745i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.23607 | − | 1.23607i | 0.113285 | − | 0.0432710i | ||||
\(817\) | −1.74806 | − | 1.74806i | −0.0611570 | − | 0.0611570i | ||||
\(818\) | 2.90724 | + | 2.90724i | 0.101649 | + | 0.101649i | ||||
\(819\) | −12.9443 | − | 14.4721i | −0.452309 | − | 0.505697i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.5967i | 1.66114i | 0.556916 | + | 0.830569i | \(0.311985\pi\) | ||||
−0.556916 | + | 0.830569i | \(0.688015\pi\) | |||||||
\(822\) | 9.89949 | − | 22.1359i | 0.345285 | − | 0.772080i | ||||
\(823\) | 19.6414 | − | 19.6414i | 0.684655 | − | 0.684655i | −0.276390 | − | 0.961045i | \(-0.589138\pi\) |
0.961045 | + | 0.276390i | \(0.0891383\pi\) | |||||||
\(824\) | −5.52786 | −0.192572 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.291796 | 0.0101529 | ||||||||
\(827\) | 7.14988 | − | 7.14988i | 0.248626 | − | 0.248626i | −0.571781 | − | 0.820406i | \(-0.693747\pi\) |
0.820406 | + | 0.571781i | \(0.193747\pi\) | |||||||
\(828\) | 7.40492 | + | 0.412662i | 0.257339 | + | 0.0143410i | ||||
\(829\) | − | 25.8885i | − | 0.899146i | −0.893244 | − | 0.449573i | \(-0.851576\pi\) | ||
0.893244 | − | 0.449573i | \(-0.148424\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.5279 | + | 51.1246i | 0.677414 | + | 1.77349i | ||||
\(832\) | 4.57649 | + | 4.57649i | 0.158661 | + | 0.158661i | ||||
\(833\) | −1.41421 | − | 1.41421i | −0.0489996 | − | 0.0489996i | ||||
\(834\) | 1.05573 | + | 2.76393i | 0.0365569 | + | 0.0957071i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.47214i | 0.0855006i | ||||||||
\(837\) | 8.27895 | + | 25.9172i | 0.286162 | + | 0.895830i | ||||
\(838\) | −13.5231 | + | 13.5231i | −0.467149 | + | 0.467149i | ||||
\(839\) | 52.3607 | 1.80769 | 0.903846 | − | 0.427859i | \(-0.140732\pi\) | ||||
0.903846 | + | 0.427859i | \(0.140732\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4164 | −0.979876 | ||||||||
\(842\) | 7.73877 | − | 7.73877i | 0.266696 | − | 0.266696i | ||||
\(843\) | −8.74032 | + | 19.5440i | −0.301033 | + | 0.673129i | ||||
\(844\) | − | 26.8328i | − | 0.923624i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 22.7639 | − | 20.3607i | 0.782640 | − | 0.700015i | ||||
\(847\) | −0.373256 | − | 0.373256i | −0.0128252 | − | 0.0128252i | ||||
\(848\) | −7.73877 | − | 7.73877i | −0.265750 | − | 0.265750i | ||||
\(849\) | 25.4164 | − | 9.70820i | 0.872289 | − | 0.333185i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 17.8885i | − | 0.613211i | ||||||
\(852\) | 18.0509 | + | 8.07262i | 0.618415 | + | 0.276563i | ||||
\(853\) | 16.5579 | − | 16.5579i | 0.566932 | − | 0.566932i | −0.364336 | − | 0.931268i | \(-0.618704\pi\) |
0.931268 | + | 0.364336i | \(0.118704\pi\) | |||||||
\(854\) | 12.9443 | 0.442944 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.9443 | 0.579143 | ||||||||
\(857\) | 17.5595 | − | 17.5595i | 0.599819 | − | 0.599819i | −0.340445 | − | 0.940264i | \(-0.610578\pi\) |
0.940264 | + | 0.340445i | \(0.110578\pi\) | |||||||
\(858\) | −33.1158 | − | 14.8098i | −1.13055 | − | 0.505599i | ||||
\(859\) | − | 32.5410i | − | 1.11029i | −0.831755 | − | 0.555143i | \(-0.812664\pi\) | ||
0.831755 | − | 0.555143i | \(-0.187336\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.9443 | − | 5.70820i | 0.509299 | − | 0.194535i | ||||
\(862\) | −8.89794 | − | 8.89794i | −0.303065 | − | 0.303065i | ||||
\(863\) | −9.15298 | − | 9.15298i | −0.311571 | − | 0.311571i | 0.533947 | − | 0.845518i | \(-0.320708\pi\) |
−0.845518 | + | 0.533947i | \(0.820708\pi\) | |||||||
\(864\) | −4.61803 | − | 2.38197i | −0.157109 | − | 0.0810361i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.76393i | 0.229848i | ||||||||
\(867\) | −9.19239 | + | 20.5548i | −0.312190 | + | 0.698078i | ||||
\(868\) | −3.70246 | + | 3.70246i | −0.125670 | + | 0.125670i | ||||
\(869\) | 41.8885 | 1.42097 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −56.7214 | −1.92193 | ||||||||
\(872\) | −2.08191 | + | 2.08191i | −0.0705025 | + | 0.0705025i | ||||
\(873\) | 2.36706 | − | 42.4751i | 0.0801127 | − | 1.43756i | ||||
\(874\) | − | 1.88854i | − | 0.0638809i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.29180 | − | 6.00000i | −0.0774326 | − | 0.202721i | ||||
\(877\) | −16.4304 | − | 16.4304i | −0.554815 | − | 0.554815i | 0.373012 | − | 0.927827i | \(-0.378325\pi\) |
−0.927827 | + | 0.373012i | \(0.878325\pi\) | |||||||
\(878\) | −6.94355 | − | 6.94355i | −0.234333 | − | 0.234333i | ||||
\(879\) | 1.88854 | + | 4.94427i | 0.0636990 | + | 0.166766i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 36.2918i | − | 1.22270i | −0.791360 | − | 0.611351i | \(-0.790626\pi\) | ||
0.791360 | − | 0.611351i | \(-0.209374\pi\) | |||||||
\(882\) | −0.166925 | + | 2.99535i | −0.00562067 | + | 0.100859i | ||||
\(883\) | −36.8971 | + | 36.8971i | −1.24169 | + | 1.24169i | −0.282384 | + | 0.959301i | \(0.591125\pi\) |
−0.959301 | + | 0.282384i | \(0.908875\pi\) | |||||||
\(884\) | 12.9443 | 0.435363 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.94427 | 0.300489 | ||||||||
\(887\) | 24.1692 | − | 24.1692i | 0.811521 | − | 0.811521i | −0.173341 | − | 0.984862i | \(-0.555456\pi\) |
0.984862 | + | 0.173341i | \(0.0554563\pi\) | |||||||
\(888\) | −5.11667 | + | 11.4412i | −0.171704 | + | 0.383942i | ||||
\(889\) | − | 14.4721i | − | 0.485380i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.9443 | + | 3.23607i | 0.969670 | + | 0.108412i | ||||
\(892\) | 3.49613 | + | 3.49613i | 0.117059 | + | 0.117059i | ||||
\(893\) | −5.49923 | − | 5.49923i | −0.184025 | − | 0.184025i | ||||
\(894\) | −32.6525 | + | 12.4721i | −1.09206 | + | 0.417131i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 1.00000i | − | 0.0334077i | ||||||
\(897\) | 25.2982 | + | 11.3137i | 0.844683 | + | 0.377754i | ||||
\(898\) | −25.0432 | + | 25.0432i | −0.835702 | + | 0.835702i | ||||
\(899\) | −4.00000 | −0.133407 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.8885 | −0.729213 | ||||||||
\(902\) | 21.1344 | − | 21.1344i | 0.703698 | − | 0.703698i | ||||
\(903\) | −5.11667 | − | 2.28825i | −0.170272 | − | 0.0761480i | ||||
\(904\) | − | 3.52786i | − | 0.117335i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.94427 | − | 3.41641i | 0.297154 | − | 0.113503i | ||||
\(907\) | 17.5107 | + | 17.5107i | 0.581435 | + | 0.581435i | 0.935297 | − | 0.353863i | \(-0.115132\pi\) |
−0.353863 | + | 0.935297i | \(0.615132\pi\) | |||||||
\(908\) | 2.28825 | + | 2.28825i | 0.0759381 | + | 0.0759381i | ||||
\(909\) | −37.8885 | + | 33.8885i | −1.25668 | + | 1.12401i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.0557i | 1.16145i | 0.814100 | + | 0.580724i | \(0.197230\pi\) | ||||
−0.814100 | + | 0.580724i | \(0.802770\pi\) | |||||||
\(912\) | −0.540182 | + | 1.20788i | −0.0178872 | + | 0.0399970i | ||||
\(913\) | −16.5579 | + | 16.5579i | −0.547987 | + | 0.547987i | ||||
\(914\) | −4.36068 | −0.144238 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.94427 | 0.295527 | ||||||||
\(917\) | 5.86319 | − | 5.86319i | 0.193619 | − | 0.193619i | ||||
\(918\) | −9.89949 | + | 3.16228i | −0.326732 | + | 0.104371i | ||||
\(919\) | 20.3607i | 0.671637i | 0.941927 | + | 0.335818i | \(0.109013\pi\) | ||||
−0.941927 | + | 0.335818i | \(0.890987\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.6525 | + | 27.8885i | 0.351011 | + | 0.918959i | ||||
\(922\) | −14.3972 | − | 14.3972i | −0.474146 | − | 0.474146i | ||||
\(923\) | 52.2471 | + | 52.2471i | 1.71973 | + | 1.71973i | ||||
\(924\) | 2.00000 | + | 5.23607i | 0.0657952 | + | 0.172254i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 20.9443i | − | 0.688271i | ||||||
\(927\) | 16.5579 | + | 0.922740i | 0.543833 | + | 0.0303068i | ||||
\(928\) | 0.540182 | − | 0.540182i | 0.0177323 | − | 0.0177323i | ||||
\(929\) | 14.1803 | 0.465242 | 0.232621 | − | 0.972567i | \(-0.425270\pi\) | ||||
0.232621 | + | 0.972567i | \(0.425270\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.763932 | 0.0250369 | ||||||||
\(932\) | 5.99070 | − | 5.99070i | 0.196232 | − | 0.196232i | ||||
\(933\) | 5.65685 | − | 12.6491i | 0.185197 | − | 0.414113i | ||||
\(934\) | 7.23607i | 0.236771i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.9443 | − | 14.4721i | −0.423097 | − | 0.473037i | ||||
\(937\) | 8.27895 | + | 8.27895i | 0.270462 | + | 0.270462i | 0.829286 | − | 0.558824i | \(-0.188747\pi\) |
−0.558824 | + | 0.829286i | \(0.688747\pi\) | |||||||
\(938\) | 6.19704 | + | 6.19704i | 0.202340 | + | 0.202340i | ||||
\(939\) | −14.9443 | + | 5.70820i | −0.487688 | + | 0.186280i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.05573i | 0.230010i | 0.993365 | + | 0.115005i | \(0.0366884\pi\) | ||||
−0.993365 | + | 0.115005i | \(0.963312\pi\) | |||||||
\(942\) | −8.74032 | − | 3.90879i | −0.284775 | − | 0.127355i | ||||
\(943\) | −16.1452 | + | 16.1452i | −0.525761 | + | 0.525761i | ||||
\(944\) | 0.291796 | 0.00949715 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.4721 | −0.340479 | ||||||||
\(947\) | −18.7186 | + | 18.7186i | −0.608274 | + | 0.608274i | −0.942495 | − | 0.334221i | \(-0.891527\pi\) |
0.334221 | + | 0.942495i | \(0.391527\pi\) | |||||||
\(948\) | 20.4667 | + | 9.15298i | 0.664727 | + | 0.297275i | ||||
\(949\) | − | 24.0000i | − | 0.779073i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −43.5967 | + | 16.6525i | −1.41372 | + | 0.539994i | ||||
\(952\) | −1.41421 | − | 1.41421i | −0.0458349 | − | 0.0458349i | ||||
\(953\) | 22.9613 | + | 22.9613i | 0.743788 | + | 0.743788i | 0.973305 | − | 0.229516i | \(-0.0737144\pi\) |
−0.229516 | + | 0.973305i | \(0.573714\pi\) | |||||||
\(954\) | 21.8885 | + | 24.4721i | 0.708668 | + | 0.792315i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 30.8328i | − | 0.997205i | ||||||
\(957\) | −1.74806 | + | 3.90879i | −0.0565069 | + | 0.126353i | ||||
\(958\) | 3.90879 | − | 3.90879i | 0.126287 | − | 0.126287i | ||||
\(959\) | −14.0000 | −0.452084 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.58359 | −0.115600 | ||||||||
\(962\) | −33.1158 | + | 33.1158i | −1.06770 | + | 1.06770i | ||||
\(963\) | −50.7541 | − | 2.82843i | −1.63553 | − | 0.0911448i | ||||
\(964\) | − | 27.8885i | − | 0.898230i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.52786 | − | 4.00000i | −0.0491582 | − | 0.128698i | ||||
\(967\) | 16.9706 | + | 16.9706i | 0.545737 | + | 0.545737i | 0.925205 | − | 0.379468i | \(-0.123893\pi\) |
−0.379468 | + | 0.925205i | \(0.623893\pi\) | |||||||
\(968\) | −0.373256 | − | 0.373256i | −0.0119969 | − | 0.0119969i | ||||
\(969\) | 0.944272 | + | 2.47214i | 0.0303344 | + | 0.0794164i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 48.6525i | − | 1.56133i | −0.624948 | − | 0.780666i | \(-0.714880\pi\) | ||
0.624948 | − | 0.780666i | \(-0.285120\pi\) | |||||||
\(972\) | 13.4350 | + | 7.90569i | 0.430929 | + | 0.253575i | ||||
\(973\) | 1.20788 | − | 1.20788i | 0.0387229 | − | 0.0387229i | ||||
\(974\) | −16.3607 | −0.524230 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.9443 | 0.414336 | ||||||||
\(977\) | −27.7928 | + | 27.7928i | −0.889170 | + | 0.889170i | −0.994443 | − | 0.105273i | \(-0.966428\pi\) |
0.105273 | + | 0.994443i | \(0.466428\pi\) | |||||||
\(978\) | −10.3609 | + | 23.1676i | −0.331304 | + | 0.740818i | ||||
\(979\) | 29.8885i | 0.955242i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.58359 | − | 5.88854i | 0.210198 | − | 0.188007i | ||||
\(982\) | −15.3500 | − | 15.3500i | −0.489839 | − | 0.489839i | ||||
\(983\) | −29.8260 | − | 29.8260i | −0.951302 | − | 0.951302i | 0.0475663 | − | 0.998868i | \(-0.484853\pi\) |
−0.998868 | + | 0.0475663i | \(0.984853\pi\) | |||||||
\(984\) | 14.9443 | − | 5.70820i | 0.476406 | − | 0.181971i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 1.52786i | − | 0.0486571i | ||||||
\(987\) | −16.0965 | − | 7.19859i | −0.512358 | − | 0.229134i | ||||
\(988\) | −3.49613 | + | 3.49613i | −0.111227 | + | 0.111227i | ||||
\(989\) | 8.00000 | 0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.1935 | −1.37209 | −0.686043 | − | 0.727561i | \(-0.740654\pi\) | ||||
−0.686043 | + | 0.727561i | \(0.740654\pi\) | |||||||
\(992\) | −3.70246 | + | 3.70246i | −0.117553 | + | 0.117553i | ||||
\(993\) | −41.8561 | − | 18.7186i | −1.32826 | − | 0.594018i | ||||
\(994\) | − | 11.4164i | − | 0.362106i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −11.7082 | + | 4.47214i | −0.370989 | + | 0.141705i | ||||
\(997\) | 6.99226 | + | 6.99226i | 0.221447 | + | 0.221447i | 0.809108 | − | 0.587661i | \(-0.199951\pi\) |
−0.587661 | + | 0.809108i | \(0.699951\pi\) | |||||||
\(998\) | 8.48528 | + | 8.48528i | 0.268597 | + | 0.268597i | ||||
\(999\) | 17.2361 | − | 33.4164i | 0.545325 | − | 1.05725i |
(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.j.b.407.4 | yes | 8 | |
3.2 | odd | 2 | 1050.2.j.a.407.1 | ✓ | 8 | ||
5.2 | odd | 4 | 1050.2.j.a.743.3 | yes | 8 | ||
5.3 | odd | 4 | 1050.2.j.a.743.2 | yes | 8 | ||
5.4 | even | 2 | inner | 1050.2.j.b.407.1 | yes | 8 | |
15.2 | even | 4 | inner | 1050.2.j.b.743.1 | yes | 8 | |
15.8 | even | 4 | inner | 1050.2.j.b.743.4 | yes | 8 | |
15.14 | odd | 2 | 1050.2.j.a.407.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.j.a.407.1 | ✓ | 8 | 3.2 | odd | 2 | ||
1050.2.j.a.407.4 | yes | 8 | 15.14 | odd | 2 | ||
1050.2.j.a.743.2 | yes | 8 | 5.3 | odd | 4 | ||
1050.2.j.a.743.3 | yes | 8 | 5.2 | odd | 4 | ||
1050.2.j.b.407.1 | yes | 8 | 5.4 | even | 2 | inner | |
1050.2.j.b.407.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1050.2.j.b.743.1 | yes | 8 | 15.2 | even | 4 | inner | |
1050.2.j.b.743.4 | yes | 8 | 15.8 | even | 4 | inner |