Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(117,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.117");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.h (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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 253.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.253 |
Dual form | 370.2.h.c.117.1 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.41421 | + | 1.41421i | −0.816497 | + | 0.816497i | −0.985599 | − | 0.169102i | \(-0.945913\pi\) |
0.169102 | + | 0.985599i | \(0.445913\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.707107 | − | 2.12132i | −0.316228 | − | 0.948683i | ||||
\(6\) | −1.41421 | + | 1.41421i | −0.577350 | + | 0.577350i | ||||
\(7\) | 2.70711 | − | 2.70711i | 1.02319 | − | 1.02319i | 0.0234655 | − | 0.999725i | \(-0.492530\pi\) |
0.999725 | − | 0.0234655i | \(-0.00747000\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −0.707107 | − | 2.12132i | −0.223607 | − | 0.670820i | ||||
\(11\) | − | 3.82843i | − | 1.15431i | −0.816633 | − | 0.577157i | \(-0.804162\pi\) | ||
0.816633 | − | 0.577157i | \(-0.195838\pi\) | |||||||
\(12\) | −1.41421 | + | 1.41421i | −0.408248 | + | 0.408248i | ||||
\(13\) | 2.24264 | 0.621997 | 0.310998 | − | 0.950410i | \(-0.399337\pi\) | ||||
0.310998 | + | 0.950410i | \(0.399337\pi\) | |||||||
\(14\) | 2.70711 | − | 2.70711i | 0.723505 | − | 0.723505i | ||||
\(15\) | 4.00000 | + | 2.00000i | 1.03280 | + | 0.516398i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.82843i | 0.443459i | 0.975108 | + | 0.221729i | \(0.0711701\pi\) | ||||
−0.975108 | + | 0.221729i | \(0.928830\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 5.82843 | + | 5.82843i | 1.33713 | + | 1.33713i | 0.898825 | + | 0.438308i | \(0.144422\pi\) |
0.438308 | + | 0.898825i | \(0.355578\pi\) | |||||||
\(20\) | −0.707107 | − | 2.12132i | −0.158114 | − | 0.474342i | ||||
\(21\) | 7.65685i | 1.67086i | ||||||||
\(22\) | − | 3.82843i | − | 0.816223i | ||||||
\(23\) | −2.58579 | −0.539174 | −0.269587 | − | 0.962976i | \(-0.586887\pi\) | ||||
−0.269587 | + | 0.962976i | \(0.586887\pi\) | |||||||
\(24\) | −1.41421 | + | 1.41421i | −0.288675 | + | 0.288675i | ||||
\(25\) | −4.00000 | + | 3.00000i | −0.800000 | + | 0.600000i | ||||
\(26\) | 2.24264 | 0.439818 | ||||||||
\(27\) | −2.82843 | − | 2.82843i | −0.544331 | − | 0.544331i | ||||
\(28\) | 2.70711 | − | 2.70711i | 0.511595 | − | 0.511595i | ||||
\(29\) | 6.70711 | − | 6.70711i | 1.24548 | − | 1.24548i | 0.287783 | − | 0.957696i | \(-0.407082\pi\) |
0.957696 | − | 0.287783i | \(-0.0929181\pi\) | |||||||
\(30\) | 4.00000 | + | 2.00000i | 0.730297 | + | 0.365148i | ||||
\(31\) | −4.12132 | − | 4.12132i | −0.740211 | − | 0.740211i | 0.232408 | − | 0.972619i | \(-0.425340\pi\) |
−0.972619 | + | 0.232408i | \(0.925340\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.41421 | + | 5.41421i | 0.942494 | + | 0.942494i | ||||
\(34\) | 1.82843i | 0.313573i | ||||||||
\(35\) | −7.65685 | − | 3.82843i | −1.29424 | − | 0.647122i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | 3.53553 | + | 4.94975i | 0.581238 | + | 0.813733i | ||||
\(38\) | 5.82843 | + | 5.82843i | 0.945496 | + | 0.945496i | ||||
\(39\) | −3.17157 | + | 3.17157i | −0.507858 | + | 0.507858i | ||||
\(40\) | −0.707107 | − | 2.12132i | −0.111803 | − | 0.335410i | ||||
\(41\) | − | 7.00000i | − | 1.09322i | −0.837389 | − | 0.546608i | \(-0.815919\pi\) | ||
0.837389 | − | 0.546608i | \(-0.184081\pi\) | |||||||
\(42\) | 7.65685i | 1.18148i | ||||||||
\(43\) | −7.00000 | −1.06749 | −0.533745 | − | 0.845645i | \(-0.679216\pi\) | ||||
−0.533745 | + | 0.845645i | \(0.679216\pi\) | |||||||
\(44\) | − | 3.82843i | − | 0.577157i | ||||||
\(45\) | −2.12132 | + | 0.707107i | −0.316228 | + | 0.105409i | ||||
\(46\) | −2.58579 | −0.381253 | ||||||||
\(47\) | −8.24264 | + | 8.24264i | −1.20231 | + | 1.20231i | −0.228851 | + | 0.973461i | \(0.573497\pi\) |
−0.973461 | + | 0.228851i | \(0.926503\pi\) | |||||||
\(48\) | −1.41421 | + | 1.41421i | −0.204124 | + | 0.204124i | ||||
\(49\) | − | 7.65685i | − | 1.09384i | ||||||
\(50\) | −4.00000 | + | 3.00000i | −0.565685 | + | 0.424264i | ||||
\(51\) | −2.58579 | − | 2.58579i | −0.362083 | − | 0.362083i | ||||
\(52\) | 2.24264 | 0.310998 | ||||||||
\(53\) | 2.12132 | + | 2.12132i | 0.291386 | + | 0.291386i | 0.837628 | − | 0.546242i | \(-0.183942\pi\) |
−0.546242 | + | 0.837628i | \(0.683942\pi\) | |||||||
\(54\) | −2.82843 | − | 2.82843i | −0.384900 | − | 0.384900i | ||||
\(55\) | −8.12132 | + | 2.70711i | −1.09508 | + | 0.365026i | ||||
\(56\) | 2.70711 | − | 2.70711i | 0.361752 | − | 0.361752i | ||||
\(57\) | −16.4853 | −2.18353 | ||||||||
\(58\) | 6.70711 | − | 6.70711i | 0.880686 | − | 0.880686i | ||||
\(59\) | 1.17157 | + | 1.17157i | 0.152526 | + | 0.152526i | 0.779245 | − | 0.626719i | \(-0.215603\pi\) |
−0.626719 | + | 0.779245i | \(0.715603\pi\) | |||||||
\(60\) | 4.00000 | + | 2.00000i | 0.516398 | + | 0.258199i | ||||
\(61\) | 9.29289 | + | 9.29289i | 1.18983 | + | 1.18983i | 0.977113 | + | 0.212720i | \(0.0682322\pi\) |
0.212720 | + | 0.977113i | \(0.431768\pi\) | |||||||
\(62\) | −4.12132 | − | 4.12132i | −0.523408 | − | 0.523408i | ||||
\(63\) | −2.70711 | − | 2.70711i | −0.341063 | − | 0.341063i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.58579 | − | 4.75736i | −0.196693 | − | 0.590078i | ||||
\(66\) | 5.41421 | + | 5.41421i | 0.666444 | + | 0.666444i | ||||
\(67\) | −1.24264 | − | 1.24264i | −0.151813 | − | 0.151813i | 0.627114 | − | 0.778927i | \(-0.284236\pi\) |
−0.778927 | + | 0.627114i | \(0.784236\pi\) | |||||||
\(68\) | 1.82843i | 0.221729i | ||||||||
\(69\) | 3.65685 | − | 3.65685i | 0.440234 | − | 0.440234i | ||||
\(70\) | −7.65685 | − | 3.82843i | −0.915169 | − | 0.457585i | ||||
\(71\) | −0.343146 | −0.0407239 | −0.0203620 | − | 0.999793i | \(-0.506482\pi\) | ||||
−0.0203620 | + | 0.999793i | \(0.506482\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | −6.00000 | + | 6.00000i | −0.702247 | + | 0.702247i | −0.964892 | − | 0.262646i | \(-0.915405\pi\) |
0.262646 | + | 0.964892i | \(0.415405\pi\) | |||||||
\(74\) | 3.53553 | + | 4.94975i | 0.410997 | + | 0.575396i | ||||
\(75\) | 1.41421 | − | 9.89949i | 0.163299 | − | 1.14310i | ||||
\(76\) | 5.82843 | + | 5.82843i | 0.668566 | + | 0.668566i | ||||
\(77\) | −10.3640 | − | 10.3640i | −1.18108 | − | 1.18108i | ||||
\(78\) | −3.17157 | + | 3.17157i | −0.359110 | + | 0.359110i | ||||
\(79\) | −9.65685 | − | 9.65685i | −1.08648 | − | 1.08648i | −0.995888 | − | 0.0905930i | \(-0.971124\pi\) |
−0.0905930 | − | 0.995888i | \(-0.528876\pi\) | |||||||
\(80\) | −0.707107 | − | 2.12132i | −0.0790569 | − | 0.237171i | ||||
\(81\) | 11.0000 | 1.22222 | ||||||||
\(82\) | − | 7.00000i | − | 0.773021i | ||||||
\(83\) | −0.828427 | − | 0.828427i | −0.0909317 | − | 0.0909317i | 0.660178 | − | 0.751109i | \(-0.270481\pi\) |
−0.751109 | + | 0.660178i | \(0.770481\pi\) | |||||||
\(84\) | 7.65685i | 0.835431i | ||||||||
\(85\) | 3.87868 | − | 1.29289i | 0.420702 | − | 0.140234i | ||||
\(86\) | −7.00000 | −0.754829 | ||||||||
\(87\) | 18.9706i | 2.03386i | ||||||||
\(88\) | − | 3.82843i | − | 0.408112i | ||||||
\(89\) | −7.41421 | + | 7.41421i | −0.785905 | + | 0.785905i | −0.980820 | − | 0.194915i | \(-0.937557\pi\) |
0.194915 | + | 0.980820i | \(0.437557\pi\) | |||||||
\(90\) | −2.12132 | + | 0.707107i | −0.223607 | + | 0.0745356i | ||||
\(91\) | 6.07107 | − | 6.07107i | 0.636421 | − | 0.636421i | ||||
\(92\) | −2.58579 | −0.269587 | ||||||||
\(93\) | 11.6569 | 1.20876 | ||||||||
\(94\) | −8.24264 | + | 8.24264i | −0.850163 | + | 0.850163i | ||||
\(95\) | 8.24264 | − | 16.4853i | 0.845677 | − | 1.69135i | ||||
\(96\) | −1.41421 | + | 1.41421i | −0.144338 | + | 0.144338i | ||||
\(97\) | 7.00000i | 0.710742i | 0.934725 | + | 0.355371i | \(0.115646\pi\) | ||||
−0.934725 | + | 0.355371i | \(0.884354\pi\) | |||||||
\(98\) | − | 7.65685i | − | 0.773459i | ||||||
\(99\) | −3.82843 | −0.384771 | ||||||||
\(100\) | −4.00000 | + | 3.00000i | −0.400000 | + | 0.300000i | ||||
\(101\) | 11.0711i | 1.10161i | 0.834633 | + | 0.550806i | \(0.185680\pi\) | ||||
−0.834633 | + | 0.550806i | \(0.814320\pi\) | |||||||
\(102\) | −2.58579 | − | 2.58579i | −0.256031 | − | 0.256031i | ||||
\(103\) | 13.5563i | 1.33575i | 0.744275 | + | 0.667873i | \(0.232795\pi\) | ||||
−0.744275 | + | 0.667873i | \(0.767205\pi\) | |||||||
\(104\) | 2.24264 | 0.219909 | ||||||||
\(105\) | 16.2426 | − | 5.41421i | 1.58512 | − | 0.528373i | ||||
\(106\) | 2.12132 | + | 2.12132i | 0.206041 | + | 0.206041i | ||||
\(107\) | −9.07107 | + | 9.07107i | −0.876933 | + | 0.876933i | −0.993216 | − | 0.116283i | \(-0.962902\pi\) |
0.116283 | + | 0.993216i | \(0.462902\pi\) | |||||||
\(108\) | −2.82843 | − | 2.82843i | −0.272166 | − | 0.272166i | ||||
\(109\) | 0.949747 | + | 0.949747i | 0.0909693 | + | 0.0909693i | 0.751127 | − | 0.660158i | \(-0.229511\pi\) |
−0.660158 | + | 0.751127i | \(0.729511\pi\) | |||||||
\(110\) | −8.12132 | + | 2.70711i | −0.774338 | + | 0.258113i | ||||
\(111\) | −12.0000 | − | 2.00000i | −1.13899 | − | 0.189832i | ||||
\(112\) | 2.70711 | − | 2.70711i | 0.255798 | − | 0.255798i | ||||
\(113\) | − | 3.82843i | − | 0.360148i | −0.983653 | − | 0.180074i | \(-0.942366\pi\) | ||
0.983653 | − | 0.180074i | \(-0.0576337\pi\) | |||||||
\(114\) | −16.4853 | −1.54399 | ||||||||
\(115\) | 1.82843 | + | 5.48528i | 0.170502 | + | 0.511505i | ||||
\(116\) | 6.70711 | − | 6.70711i | 0.622739 | − | 0.622739i | ||||
\(117\) | − | 2.24264i | − | 0.207332i | ||||||
\(118\) | 1.17157 | + | 1.17157i | 0.107852 | + | 0.107852i | ||||
\(119\) | 4.94975 | + | 4.94975i | 0.453743 | + | 0.453743i | ||||
\(120\) | 4.00000 | + | 2.00000i | 0.365148 | + | 0.182574i | ||||
\(121\) | −3.65685 | −0.332441 | ||||||||
\(122\) | 9.29289 | + | 9.29289i | 0.841339 | + | 0.841339i | ||||
\(123\) | 9.89949 | + | 9.89949i | 0.892607 | + | 0.892607i | ||||
\(124\) | −4.12132 | − | 4.12132i | −0.370105 | − | 0.370105i | ||||
\(125\) | 9.19239 | + | 6.36396i | 0.822192 | + | 0.569210i | ||||
\(126\) | −2.70711 | − | 2.70711i | −0.241168 | − | 0.241168i | ||||
\(127\) | 2.58579 | − | 2.58579i | 0.229451 | − | 0.229451i | −0.583012 | − | 0.812464i | \(-0.698126\pi\) |
0.812464 | + | 0.583012i | \(0.198126\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 9.89949 | − | 9.89949i | 0.871602 | − | 0.871602i | ||||
\(130\) | −1.58579 | − | 4.75736i | −0.139083 | − | 0.417248i | ||||
\(131\) | 0.414214 | + | 0.414214i | 0.0361900 | + | 0.0361900i | 0.724970 | − | 0.688780i | \(-0.241853\pi\) |
−0.688780 | + | 0.724970i | \(0.741853\pi\) | |||||||
\(132\) | 5.41421 | + | 5.41421i | 0.471247 | + | 0.471247i | ||||
\(133\) | 31.5563 | 2.73628 | ||||||||
\(134\) | −1.24264 | − | 1.24264i | −0.107348 | − | 0.107348i | ||||
\(135\) | −4.00000 | + | 8.00000i | −0.344265 | + | 0.688530i | ||||
\(136\) | 1.82843i | 0.156786i | ||||||||
\(137\) | 8.41421 | − | 8.41421i | 0.718875 | − | 0.718875i | −0.249500 | − | 0.968375i | \(-0.580266\pi\) |
0.968375 | + | 0.249500i | \(0.0802663\pi\) | |||||||
\(138\) | 3.65685 | − | 3.65685i | 0.311292 | − | 0.311292i | ||||
\(139\) | 6.17157 | 0.523466 | 0.261733 | − | 0.965140i | \(-0.415706\pi\) | ||||
0.261733 | + | 0.965140i | \(0.415706\pi\) | |||||||
\(140\) | −7.65685 | − | 3.82843i | −0.647122 | − | 0.323561i | ||||
\(141\) | − | 23.3137i | − | 1.96337i | ||||||
\(142\) | −0.343146 | −0.0287962 | ||||||||
\(143\) | − | 8.58579i | − | 0.717980i | ||||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | −18.9706 | − | 9.48528i | −1.57542 | − | 0.787710i | ||||
\(146\) | −6.00000 | + | 6.00000i | −0.496564 | + | 0.496564i | ||||
\(147\) | 10.8284 | + | 10.8284i | 0.893114 | + | 0.893114i | ||||
\(148\) | 3.53553 | + | 4.94975i | 0.290619 | + | 0.406867i | ||||
\(149\) | 8.24264i | 0.675263i | 0.941278 | + | 0.337632i | \(0.109626\pi\) | ||||
−0.941278 | + | 0.337632i | \(0.890374\pi\) | |||||||
\(150\) | 1.41421 | − | 9.89949i | 0.115470 | − | 0.808290i | ||||
\(151\) | 12.0000i | 0.976546i | 0.872691 | + | 0.488273i | \(0.162373\pi\) | ||||
−0.872691 | + | 0.488273i | \(0.837627\pi\) | |||||||
\(152\) | 5.82843 | + | 5.82843i | 0.472748 | + | 0.472748i | ||||
\(153\) | 1.82843 | 0.147820 | ||||||||
\(154\) | −10.3640 | − | 10.3640i | −0.835152 | − | 0.835152i | ||||
\(155\) | −5.82843 | + | 11.6569i | −0.468151 | + | 0.936301i | ||||
\(156\) | −3.17157 | + | 3.17157i | −0.253929 | + | 0.253929i | ||||
\(157\) | 5.87868 | − | 5.87868i | 0.469170 | − | 0.469170i | −0.432476 | − | 0.901646i | \(-0.642360\pi\) |
0.901646 | + | 0.432476i | \(0.142360\pi\) | |||||||
\(158\) | −9.65685 | − | 9.65685i | −0.768258 | − | 0.768258i | ||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | −0.707107 | − | 2.12132i | −0.0559017 | − | 0.167705i | ||||
\(161\) | −7.00000 | + | 7.00000i | −0.551677 | + | 0.551677i | ||||
\(162\) | 11.0000 | 0.864242 | ||||||||
\(163\) | − | 14.6569i | − | 1.14801i | −0.818851 | − | 0.574007i | \(-0.805388\pi\) | ||
0.818851 | − | 0.574007i | \(-0.194612\pi\) | |||||||
\(164\) | − | 7.00000i | − | 0.546608i | ||||||
\(165\) | 7.65685 | − | 15.3137i | 0.596085 | − | 1.19217i | ||||
\(166\) | −0.828427 | − | 0.828427i | −0.0642984 | − | 0.0642984i | ||||
\(167\) | 1.17157i | 0.0906590i | 0.998972 | + | 0.0453295i | \(0.0144338\pi\) | ||||
−0.998972 | + | 0.0453295i | \(0.985566\pi\) | |||||||
\(168\) | 7.65685i | 0.590739i | ||||||||
\(169\) | −7.97056 | −0.613120 | ||||||||
\(170\) | 3.87868 | − | 1.29289i | 0.297481 | − | 0.0991604i | ||||
\(171\) | 5.82843 | − | 5.82843i | 0.445711 | − | 0.445711i | ||||
\(172\) | −7.00000 | −0.533745 | ||||||||
\(173\) | −6.02082 | + | 6.02082i | −0.457754 | + | 0.457754i | −0.897918 | − | 0.440164i | \(-0.854920\pi\) |
0.440164 | + | 0.897918i | \(0.354920\pi\) | |||||||
\(174\) | 18.9706i | 1.43815i | ||||||||
\(175\) | −2.70711 | + | 18.9497i | −0.204638 | + | 1.43247i | ||||
\(176\) | − | 3.82843i | − | 0.288579i | ||||||
\(177\) | −3.31371 | −0.249074 | ||||||||
\(178\) | −7.41421 | + | 7.41421i | −0.555719 | + | 0.555719i | ||||
\(179\) | 14.4853 | − | 14.4853i | 1.08268 | − | 1.08268i | 0.0864222 | − | 0.996259i | \(-0.472457\pi\) |
0.996259 | − | 0.0864222i | \(-0.0275434\pi\) | |||||||
\(180\) | −2.12132 | + | 0.707107i | −0.158114 | + | 0.0527046i | ||||
\(181\) | 7.65685 | 0.569129 | 0.284565 | − | 0.958657i | \(-0.408151\pi\) | ||||
0.284565 | + | 0.958657i | \(0.408151\pi\) | |||||||
\(182\) | 6.07107 | − | 6.07107i | 0.450017 | − | 0.450017i | ||||
\(183\) | −26.2843 | −1.94299 | ||||||||
\(184\) | −2.58579 | −0.190627 | ||||||||
\(185\) | 8.00000 | − | 11.0000i | 0.588172 | − | 0.808736i | ||||
\(186\) | 11.6569 | 0.854722 | ||||||||
\(187\) | 7.00000 | 0.511891 | ||||||||
\(188\) | −8.24264 | + | 8.24264i | −0.601156 | + | 0.601156i | ||||
\(189\) | −15.3137 | −1.11391 | ||||||||
\(190\) | 8.24264 | − | 16.4853i | 0.597984 | − | 1.19597i | ||||
\(191\) | 1.53553 | − | 1.53553i | 0.111107 | − | 0.111107i | −0.649367 | − | 0.760475i | \(-0.724966\pi\) |
0.760475 | + | 0.649367i | \(0.224966\pi\) | |||||||
\(192\) | −1.41421 | + | 1.41421i | −0.102062 | + | 0.102062i | ||||
\(193\) | −20.4853 | −1.47456 | −0.737281 | − | 0.675586i | \(-0.763891\pi\) | ||||
−0.737281 | + | 0.675586i | \(0.763891\pi\) | |||||||
\(194\) | 7.00000i | 0.502571i | ||||||||
\(195\) | 8.97056 | + | 4.48528i | 0.642395 | + | 0.321198i | ||||
\(196\) | − | 7.65685i | − | 0.546918i | ||||||
\(197\) | −2.00000 | + | 2.00000i | −0.142494 | + | 0.142494i | −0.774755 | − | 0.632261i | \(-0.782127\pi\) |
0.632261 | + | 0.774755i | \(0.282127\pi\) | |||||||
\(198\) | −3.82843 | −0.272074 | ||||||||
\(199\) | 3.89949 | − | 3.89949i | 0.276428 | − | 0.276428i | −0.555253 | − | 0.831681i | \(-0.687379\pi\) |
0.831681 | + | 0.555253i | \(0.187379\pi\) | |||||||
\(200\) | −4.00000 | + | 3.00000i | −0.282843 | + | 0.212132i | ||||
\(201\) | 3.51472 | 0.247909 | ||||||||
\(202\) | 11.0711i | 0.778958i | ||||||||
\(203\) | − | 36.3137i | − | 2.54872i | ||||||
\(204\) | −2.58579 | − | 2.58579i | −0.181041 | − | 0.181041i | ||||
\(205\) | −14.8492 | + | 4.94975i | −1.03712 | + | 0.345705i | ||||
\(206\) | 13.5563i | 0.944516i | ||||||||
\(207\) | 2.58579i | 0.179725i | ||||||||
\(208\) | 2.24264 | 0.155499 | ||||||||
\(209\) | 22.3137 | − | 22.3137i | 1.54347 | − | 1.54347i | ||||
\(210\) | 16.2426 | − | 5.41421i | 1.12085 | − | 0.373616i | ||||
\(211\) | −9.00000 | −0.619586 | −0.309793 | − | 0.950804i | \(-0.600260\pi\) | ||||
−0.309793 | + | 0.950804i | \(0.600260\pi\) | |||||||
\(212\) | 2.12132 | + | 2.12132i | 0.145693 | + | 0.145693i | ||||
\(213\) | 0.485281 | − | 0.485281i | 0.0332509 | − | 0.0332509i | ||||
\(214\) | −9.07107 | + | 9.07107i | −0.620085 | + | 0.620085i | ||||
\(215\) | 4.94975 | + | 14.8492i | 0.337570 | + | 1.01271i | ||||
\(216\) | −2.82843 | − | 2.82843i | −0.192450 | − | 0.192450i | ||||
\(217\) | −22.3137 | −1.51475 | ||||||||
\(218\) | 0.949747 | + | 0.949747i | 0.0643250 | + | 0.0643250i | ||||
\(219\) | − | 16.9706i | − | 1.14676i | ||||||
\(220\) | −8.12132 | + | 2.70711i | −0.547539 | + | 0.182513i | ||||
\(221\) | 4.10051i | 0.275830i | ||||||||
\(222\) | −12.0000 | − | 2.00000i | −0.805387 | − | 0.134231i | ||||
\(223\) | 13.8787 | + | 13.8787i | 0.929385 | + | 0.929385i | 0.997666 | − | 0.0682810i | \(-0.0217514\pi\) |
−0.0682810 | + | 0.997666i | \(0.521751\pi\) | |||||||
\(224\) | 2.70711 | − | 2.70711i | 0.180876 | − | 0.180876i | ||||
\(225\) | 3.00000 | + | 4.00000i | 0.200000 | + | 0.266667i | ||||
\(226\) | − | 3.82843i | − | 0.254663i | ||||||
\(227\) | 7.48528i | 0.496816i | 0.968656 | + | 0.248408i | \(0.0799073\pi\) | ||||
−0.968656 | + | 0.248408i | \(0.920093\pi\) | |||||||
\(228\) | −16.4853 | −1.09176 | ||||||||
\(229\) | − | 1.41421i | − | 0.0934539i | −0.998908 | − | 0.0467269i | \(-0.985121\pi\) | ||
0.998908 | − | 0.0467269i | \(-0.0148791\pi\) | |||||||
\(230\) | 1.82843 | + | 5.48528i | 0.120563 | + | 0.361689i | ||||
\(231\) | 29.3137 | 1.92870 | ||||||||
\(232\) | 6.70711 | − | 6.70711i | 0.440343 | − | 0.440343i | ||||
\(233\) | −0.0710678 | + | 0.0710678i | −0.00465581 | + | 0.00465581i | −0.709431 | − | 0.704775i | \(-0.751048\pi\) |
0.704775 | + | 0.709431i | \(0.251048\pi\) | |||||||
\(234\) | − | 2.24264i | − | 0.146606i | ||||||
\(235\) | 23.3137 | + | 11.6569i | 1.52082 | + | 0.760409i | ||||
\(236\) | 1.17157 | + | 1.17157i | 0.0762629 | + | 0.0762629i | ||||
\(237\) | 27.3137 | 1.77422 | ||||||||
\(238\) | 4.94975 | + | 4.94975i | 0.320844 | + | 0.320844i | ||||
\(239\) | −7.05025 | − | 7.05025i | −0.456043 | − | 0.456043i | 0.441311 | − | 0.897354i | \(-0.354513\pi\) |
−0.897354 | + | 0.441311i | \(0.854513\pi\) | |||||||
\(240\) | 4.00000 | + | 2.00000i | 0.258199 | + | 0.129099i | ||||
\(241\) | 0.757359 | − | 0.757359i | 0.0487858 | − | 0.0487858i | −0.682293 | − | 0.731079i | \(-0.739017\pi\) |
0.731079 | + | 0.682293i | \(0.239017\pi\) | |||||||
\(242\) | −3.65685 | −0.235071 | ||||||||
\(243\) | −7.07107 | + | 7.07107i | −0.453609 | + | 0.453609i | ||||
\(244\) | 9.29289 | + | 9.29289i | 0.594917 | + | 0.594917i | ||||
\(245\) | −16.2426 | + | 5.41421i | −1.03770 | + | 0.345901i | ||||
\(246\) | 9.89949 | + | 9.89949i | 0.631169 | + | 0.631169i | ||||
\(247\) | 13.0711 | + | 13.0711i | 0.831692 | + | 0.831692i | ||||
\(248\) | −4.12132 | − | 4.12132i | −0.261704 | − | 0.261704i | ||||
\(249\) | 2.34315 | 0.148491 | ||||||||
\(250\) | 9.19239 | + | 6.36396i | 0.581378 | + | 0.402492i | ||||
\(251\) | −17.8995 | − | 17.8995i | −1.12981 | − | 1.12981i | −0.990208 | − | 0.139598i | \(-0.955419\pi\) |
−0.139598 | − | 0.990208i | \(-0.544581\pi\) | |||||||
\(252\) | −2.70711 | − | 2.70711i | −0.170532 | − | 0.170532i | ||||
\(253\) | 9.89949i | 0.622376i | ||||||||
\(254\) | 2.58579 | − | 2.58579i | 0.162247 | − | 0.162247i | ||||
\(255\) | −3.65685 | + | 7.31371i | −0.229001 | + | 0.458002i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 18.8284i | − | 1.17449i | −0.809411 | − | 0.587243i | \(-0.800213\pi\) | ||
0.809411 | − | 0.587243i | \(-0.199787\pi\) | |||||||
\(258\) | 9.89949 | − | 9.89949i | 0.616316 | − | 0.616316i | ||||
\(259\) | 22.9706 | + | 3.82843i | 1.42732 | + | 0.237887i | ||||
\(260\) | −1.58579 | − | 4.75736i | −0.0983463 | − | 0.295039i | ||||
\(261\) | −6.70711 | − | 6.70711i | −0.415159 | − | 0.415159i | ||||
\(262\) | 0.414214 | + | 0.414214i | 0.0255902 | + | 0.0255902i | ||||
\(263\) | 14.6066 | − | 14.6066i | 0.900682 | − | 0.900682i | −0.0948134 | − | 0.995495i | \(-0.530225\pi\) |
0.995495 | + | 0.0948134i | \(0.0302254\pi\) | |||||||
\(264\) | 5.41421 | + | 5.41421i | 0.333222 | + | 0.333222i | ||||
\(265\) | 3.00000 | − | 6.00000i | 0.184289 | − | 0.368577i | ||||
\(266\) | 31.5563 | 1.93484 | ||||||||
\(267\) | − | 20.9706i | − | 1.28338i | ||||||
\(268\) | −1.24264 | − | 1.24264i | −0.0759064 | − | 0.0759064i | ||||
\(269\) | 17.7990i | 1.08522i | 0.839984 | + | 0.542612i | \(0.182565\pi\) | ||||
−0.839984 | + | 0.542612i | \(0.817435\pi\) | |||||||
\(270\) | −4.00000 | + | 8.00000i | −0.243432 | + | 0.486864i | ||||
\(271\) | −3.07107 | −0.186554 | −0.0932770 | − | 0.995640i | \(-0.529734\pi\) | ||||
−0.0932770 | + | 0.995640i | \(0.529734\pi\) | |||||||
\(272\) | 1.82843i | 0.110865i | ||||||||
\(273\) | 17.1716i | 1.03927i | ||||||||
\(274\) | 8.41421 | − | 8.41421i | 0.508321 | − | 0.508321i | ||||
\(275\) | 11.4853 | + | 15.3137i | 0.692589 | + | 0.923451i | ||||
\(276\) | 3.65685 | − | 3.65685i | 0.220117 | − | 0.220117i | ||||
\(277\) | 7.79899 | 0.468596 | 0.234298 | − | 0.972165i | \(-0.424721\pi\) | ||||
0.234298 | + | 0.972165i | \(0.424721\pi\) | |||||||
\(278\) | 6.17157 | 0.370146 | ||||||||
\(279\) | −4.12132 | + | 4.12132i | −0.246737 | + | 0.246737i | ||||
\(280\) | −7.65685 | − | 3.82843i | −0.457585 | − | 0.228792i | ||||
\(281\) | 4.00000 | − | 4.00000i | 0.238620 | − | 0.238620i | −0.577659 | − | 0.816279i | \(-0.696033\pi\) |
0.816279 | + | 0.577659i | \(0.196033\pi\) | |||||||
\(282\) | − | 23.3137i | − | 1.38831i | ||||||
\(283\) | 28.0000i | 1.66443i | 0.554455 | + | 0.832214i | \(0.312927\pi\) | ||||
−0.554455 | + | 0.832214i | \(0.687073\pi\) | |||||||
\(284\) | −0.343146 | −0.0203620 | ||||||||
\(285\) | 11.6569 | + | 34.9706i | 0.690492 | + | 2.07148i | ||||
\(286\) | − | 8.58579i | − | 0.507688i | ||||||
\(287\) | −18.9497 | − | 18.9497i | −1.11857 | − | 1.11857i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 13.6569 | 0.803344 | ||||||||
\(290\) | −18.9706 | − | 9.48528i | −1.11399 | − | 0.556995i | ||||
\(291\) | −9.89949 | − | 9.89949i | −0.580319 | − | 0.580319i | ||||
\(292\) | −6.00000 | + | 6.00000i | −0.351123 | + | 0.351123i | ||||
\(293\) | −1.77817 | − | 1.77817i | −0.103882 | − | 0.103882i | 0.653255 | − | 0.757138i | \(-0.273403\pi\) |
−0.757138 | + | 0.653255i | \(0.773403\pi\) | |||||||
\(294\) | 10.8284 | + | 10.8284i | 0.631527 | + | 0.631527i | ||||
\(295\) | 1.65685 | − | 3.31371i | 0.0964658 | − | 0.192932i | ||||
\(296\) | 3.53553 | + | 4.94975i | 0.205499 | + | 0.287698i | ||||
\(297\) | −10.8284 | + | 10.8284i | −0.628329 | + | 0.628329i | ||||
\(298\) | 8.24264i | 0.477483i | ||||||||
\(299\) | −5.79899 | −0.335364 | ||||||||
\(300\) | 1.41421 | − | 9.89949i | 0.0816497 | − | 0.571548i | ||||
\(301\) | −18.9497 | + | 18.9497i | −1.09225 | + | 1.09225i | ||||
\(302\) | 12.0000i | 0.690522i | ||||||||
\(303\) | −15.6569 | − | 15.6569i | −0.899463 | − | 0.899463i | ||||
\(304\) | 5.82843 | + | 5.82843i | 0.334283 | + | 0.334283i | ||||
\(305\) | 13.1421 | − | 26.2843i | 0.752516 | − | 1.50503i | ||||
\(306\) | 1.82843 | 0.104524 | ||||||||
\(307\) | 1.89949 | + | 1.89949i | 0.108410 | + | 0.108410i | 0.759231 | − | 0.650821i | \(-0.225575\pi\) |
−0.650821 | + | 0.759231i | \(0.725575\pi\) | |||||||
\(308\) | −10.3640 | − | 10.3640i | −0.590541 | − | 0.590541i | ||||
\(309\) | −19.1716 | − | 19.1716i | −1.09063 | − | 1.09063i | ||||
\(310\) | −5.82843 | + | 11.6569i | −0.331032 | + | 0.662065i | ||||
\(311\) | −11.7782 | − | 11.7782i | −0.667879 | − | 0.667879i | 0.289346 | − | 0.957225i | \(-0.406562\pi\) |
−0.957225 | + | 0.289346i | \(0.906562\pi\) | |||||||
\(312\) | −3.17157 | + | 3.17157i | −0.179555 | + | 0.179555i | ||||
\(313\) | −0.686292 | −0.0387915 | −0.0193957 | − | 0.999812i | \(-0.506174\pi\) | ||||
−0.0193957 | + | 0.999812i | \(0.506174\pi\) | |||||||
\(314\) | 5.87868 | − | 5.87868i | 0.331753 | − | 0.331753i | ||||
\(315\) | −3.82843 | + | 7.65685i | −0.215707 | + | 0.431415i | ||||
\(316\) | −9.65685 | − | 9.65685i | −0.543240 | − | 0.543240i | ||||
\(317\) | −15.5355 | − | 15.5355i | −0.872563 | − | 0.872563i | 0.120189 | − | 0.992751i | \(-0.461650\pi\) |
−0.992751 | + | 0.120189i | \(0.961650\pi\) | |||||||
\(318\) | −6.00000 | −0.336463 | ||||||||
\(319\) | −25.6777 | − | 25.6777i | −1.43767 | − | 1.43767i | ||||
\(320\) | −0.707107 | − | 2.12132i | −0.0395285 | − | 0.118585i | ||||
\(321\) | − | 25.6569i | − | 1.43203i | ||||||
\(322\) | −7.00000 | + | 7.00000i | −0.390095 | + | 0.390095i | ||||
\(323\) | −10.6569 | + | 10.6569i | −0.592963 | + | 0.592963i | ||||
\(324\) | 11.0000 | 0.611111 | ||||||||
\(325\) | −8.97056 | + | 6.72792i | −0.497597 | + | 0.373198i | ||||
\(326\) | − | 14.6569i | − | 0.811768i | ||||||
\(327\) | −2.68629 | −0.148552 | ||||||||
\(328\) | − | 7.00000i | − | 0.386510i | ||||||
\(329\) | 44.6274i | 2.46039i | ||||||||
\(330\) | 7.65685 | − | 15.3137i | 0.421496 | − | 0.842992i | ||||
\(331\) | 2.58579 | − | 2.58579i | 0.142128 | − | 0.142128i | −0.632463 | − | 0.774591i | \(-0.717956\pi\) |
0.774591 | + | 0.632463i | \(0.217956\pi\) | |||||||
\(332\) | −0.828427 | − | 0.828427i | −0.0454658 | − | 0.0454658i | ||||
\(333\) | 4.94975 | − | 3.53553i | 0.271244 | − | 0.193746i | ||||
\(334\) | 1.17157i | 0.0641056i | ||||||||
\(335\) | −1.75736 | + | 3.51472i | −0.0960148 | + | 0.192030i | ||||
\(336\) | 7.65685i | 0.417716i | ||||||||
\(337\) | −5.65685 | − | 5.65685i | −0.308148 | − | 0.308148i | 0.536043 | − | 0.844191i | \(-0.319919\pi\) |
−0.844191 | + | 0.536043i | \(0.819919\pi\) | |||||||
\(338\) | −7.97056 | −0.433541 | ||||||||
\(339\) | 5.41421 | + | 5.41421i | 0.294060 | + | 0.294060i | ||||
\(340\) | 3.87868 | − | 1.29289i | 0.210351 | − | 0.0701170i | ||||
\(341\) | −15.7782 | + | 15.7782i | −0.854436 | + | 0.854436i | ||||
\(342\) | 5.82843 | − | 5.82843i | 0.315165 | − | 0.315165i | ||||
\(343\) | −1.77817 | − | 1.77817i | −0.0960124 | − | 0.0960124i | ||||
\(344\) | −7.00000 | −0.377415 | ||||||||
\(345\) | −10.3431 | − | 5.17157i | −0.556856 | − | 0.278428i | ||||
\(346\) | −6.02082 | + | 6.02082i | −0.323681 | + | 0.323681i | ||||
\(347\) | −17.3137 | −0.929449 | −0.464724 | − | 0.885455i | \(-0.653847\pi\) | ||||
−0.464724 | + | 0.885455i | \(0.653847\pi\) | |||||||
\(348\) | 18.9706i | 1.01693i | ||||||||
\(349\) | − | 4.14214i | − | 0.221723i | −0.993836 | − | 0.110862i | \(-0.964639\pi\) | ||
0.993836 | − | 0.110862i | \(-0.0353611\pi\) | |||||||
\(350\) | −2.70711 | + | 18.9497i | −0.144701 | + | 1.01291i | ||||
\(351\) | −6.34315 | − | 6.34315i | −0.338572 | − | 0.338572i | ||||
\(352\) | − | 3.82843i | − | 0.204056i | ||||||
\(353\) | 7.34315i | 0.390836i | 0.980720 | + | 0.195418i | \(0.0626064\pi\) | ||||
−0.980720 | + | 0.195418i | \(0.937394\pi\) | |||||||
\(354\) | −3.31371 | −0.176122 | ||||||||
\(355\) | 0.242641 | + | 0.727922i | 0.0128780 | + | 0.0386341i | ||||
\(356\) | −7.41421 | + | 7.41421i | −0.392953 | + | 0.392953i | ||||
\(357\) | −14.0000 | −0.740959 | ||||||||
\(358\) | 14.4853 | − | 14.4853i | 0.765571 | − | 0.765571i | ||||
\(359\) | 30.5269i | 1.61115i | 0.592495 | + | 0.805574i | \(0.298143\pi\) | ||||
−0.592495 | + | 0.805574i | \(0.701857\pi\) | |||||||
\(360\) | −2.12132 | + | 0.707107i | −0.111803 | + | 0.0372678i | ||||
\(361\) | 48.9411i | 2.57585i | ||||||||
\(362\) | 7.65685 | 0.402435 | ||||||||
\(363\) | 5.17157 | − | 5.17157i | 0.271437 | − | 0.271437i | ||||
\(364\) | 6.07107 | − | 6.07107i | 0.318210 | − | 0.318210i | ||||
\(365\) | 16.9706 | + | 8.48528i | 0.888280 | + | 0.444140i | ||||
\(366\) | −26.2843 | −1.37390 | ||||||||
\(367\) | 13.0919 | − | 13.0919i | 0.683391 | − | 0.683391i | −0.277372 | − | 0.960763i | \(-0.589463\pi\) |
0.960763 | + | 0.277372i | \(0.0894634\pi\) | |||||||
\(368\) | −2.58579 | −0.134793 | ||||||||
\(369\) | −7.00000 | −0.364405 | ||||||||
\(370\) | 8.00000 | − | 11.0000i | 0.415900 | − | 0.571863i | ||||
\(371\) | 11.4853 | 0.596286 | ||||||||
\(372\) | 11.6569 | 0.604380 | ||||||||
\(373\) | 10.8284 | − | 10.8284i | 0.560675 | − | 0.560675i | −0.368824 | − | 0.929499i | \(-0.620240\pi\) |
0.929499 | + | 0.368824i | \(0.120240\pi\) | |||||||
\(374\) | 7.00000 | 0.361961 | ||||||||
\(375\) | −22.0000 | + | 4.00000i | −1.13608 | + | 0.206559i | ||||
\(376\) | −8.24264 | + | 8.24264i | −0.425082 | + | 0.425082i | ||||
\(377\) | 15.0416 | − | 15.0416i | 0.774683 | − | 0.774683i | ||||
\(378\) | −15.3137 | −0.787652 | ||||||||
\(379\) | 18.0000i | 0.924598i | 0.886724 | + | 0.462299i | \(0.152975\pi\) | ||||
−0.886724 | + | 0.462299i | \(0.847025\pi\) | |||||||
\(380\) | 8.24264 | − | 16.4853i | 0.422839 | − | 0.845677i | ||||
\(381\) | 7.31371i | 0.374693i | ||||||||
\(382\) | 1.53553 | − | 1.53553i | 0.0785647 | − | 0.0785647i | ||||
\(383\) | −16.5858 | −0.847494 | −0.423747 | − | 0.905781i | \(-0.639285\pi\) | ||||
−0.423747 | + | 0.905781i | \(0.639285\pi\) | |||||||
\(384\) | −1.41421 | + | 1.41421i | −0.0721688 | + | 0.0721688i | ||||
\(385\) | −14.6569 | + | 29.3137i | −0.746982 | + | 1.49396i | ||||
\(386\) | −20.4853 | −1.04267 | ||||||||
\(387\) | 7.00000i | 0.355830i | ||||||||
\(388\) | 7.00000i | 0.355371i | ||||||||
\(389\) | 3.77817 | + | 3.77817i | 0.191561 | + | 0.191561i | 0.796370 | − | 0.604809i | \(-0.206751\pi\) |
−0.604809 | + | 0.796370i | \(0.706751\pi\) | |||||||
\(390\) | 8.97056 | + | 4.48528i | 0.454242 | + | 0.227121i | ||||
\(391\) | − | 4.72792i | − | 0.239101i | ||||||
\(392\) | − | 7.65685i | − | 0.386730i | ||||||
\(393\) | −1.17157 | −0.0590980 | ||||||||
\(394\) | −2.00000 | + | 2.00000i | −0.100759 | + | 0.100759i | ||||
\(395\) | −13.6569 | + | 27.3137i | −0.687151 | + | 1.37430i | ||||
\(396\) | −3.82843 | −0.192386 | ||||||||
\(397\) | −8.48528 | − | 8.48528i | −0.425864 | − | 0.425864i | 0.461353 | − | 0.887217i | \(-0.347364\pi\) |
−0.887217 | + | 0.461353i | \(0.847364\pi\) | |||||||
\(398\) | 3.89949 | − | 3.89949i | 0.195464 | − | 0.195464i | ||||
\(399\) | −44.6274 | + | 44.6274i | −2.23417 | + | 2.23417i | ||||
\(400\) | −4.00000 | + | 3.00000i | −0.200000 | + | 0.150000i | ||||
\(401\) | −7.07107 | − | 7.07107i | −0.353112 | − | 0.353112i | 0.508154 | − | 0.861266i | \(-0.330328\pi\) |
−0.861266 | + | 0.508154i | \(0.830328\pi\) | |||||||
\(402\) | 3.51472 | 0.175298 | ||||||||
\(403\) | −9.24264 | − | 9.24264i | −0.460409 | − | 0.460409i | ||||
\(404\) | 11.0711i | 0.550806i | ||||||||
\(405\) | −7.77817 | − | 23.3345i | −0.386501 | − | 1.15950i | ||||
\(406\) | − | 36.3137i | − | 1.80222i | ||||||
\(407\) | 18.9497 | − | 13.5355i | 0.939304 | − | 0.670932i | ||||
\(408\) | −2.58579 | − | 2.58579i | −0.128016 | − | 0.128016i | ||||
\(409\) | 19.7990 | − | 19.7990i | 0.978997 | − | 0.978997i | −0.0207869 | − | 0.999784i | \(-0.506617\pi\) |
0.999784 | + | 0.0207869i | \(0.00661715\pi\) | |||||||
\(410\) | −14.8492 | + | 4.94975i | −0.733352 | + | 0.244451i | ||||
\(411\) | 23.7990i | 1.17392i | ||||||||
\(412\) | 13.5563i | 0.667873i | ||||||||
\(413\) | 6.34315 | 0.312126 | ||||||||
\(414\) | 2.58579i | 0.127084i | ||||||||
\(415\) | −1.17157 | + | 2.34315i | −0.0575103 | + | 0.115021i | ||||
\(416\) | 2.24264 | 0.109955 | ||||||||
\(417\) | −8.72792 | + | 8.72792i | −0.427408 | + | 0.427408i | ||||
\(418\) | 22.3137 | − | 22.3137i | 1.09140 | − | 1.09140i | ||||
\(419\) | − | 26.9706i | − | 1.31760i | −0.752319 | − | 0.658799i | \(-0.771065\pi\) | ||
0.752319 | − | 0.658799i | \(-0.228935\pi\) | |||||||
\(420\) | 16.2426 | − | 5.41421i | 0.792560 | − | 0.264187i | ||||
\(421\) | −25.3137 | − | 25.3137i | −1.23371 | − | 1.23371i | −0.962526 | − | 0.271188i | \(-0.912583\pi\) |
−0.271188 | − | 0.962526i | \(-0.587417\pi\) | |||||||
\(422\) | −9.00000 | −0.438113 | ||||||||
\(423\) | 8.24264 | + | 8.24264i | 0.400771 | + | 0.400771i | ||||
\(424\) | 2.12132 | + | 2.12132i | 0.103020 | + | 0.103020i | ||||
\(425\) | −5.48528 | − | 7.31371i | −0.266075 | − | 0.354767i | ||||
\(426\) | 0.485281 | − | 0.485281i | 0.0235120 | − | 0.0235120i | ||||
\(427\) | 50.3137 | 2.43485 | ||||||||
\(428\) | −9.07107 | + | 9.07107i | −0.438467 | + | 0.438467i | ||||
\(429\) | 12.1421 | + | 12.1421i | 0.586228 | + | 0.586228i | ||||
\(430\) | 4.94975 | + | 14.8492i | 0.238698 | + | 0.716094i | ||||
\(431\) | −20.5061 | − | 20.5061i | −0.987744 | − | 0.987744i | 0.0121819 | − | 0.999926i | \(-0.496122\pi\) |
−0.999926 | + | 0.0121819i | \(0.996122\pi\) | |||||||
\(432\) | −2.82843 | − | 2.82843i | −0.136083 | − | 0.136083i | ||||
\(433\) | 5.14214 | + | 5.14214i | 0.247115 | + | 0.247115i | 0.819786 | − | 0.572670i | \(-0.194093\pi\) |
−0.572670 | + | 0.819786i | \(0.694093\pi\) | |||||||
\(434\) | −22.3137 | −1.07109 | ||||||||
\(435\) | 40.2426 | − | 13.4142i | 1.92949 | − | 0.643162i | ||||
\(436\) | 0.949747 | + | 0.949747i | 0.0454847 | + | 0.0454847i | ||||
\(437\) | −15.0711 | − | 15.0711i | −0.720947 | − | 0.720947i | ||||
\(438\) | − | 16.9706i | − | 0.810885i | ||||||
\(439\) | −2.22183 | + | 2.22183i | −0.106042 | + | 0.106042i | −0.758137 | − | 0.652095i | \(-0.773890\pi\) |
0.652095 | + | 0.758137i | \(0.273890\pi\) | |||||||
\(440\) | −8.12132 | + | 2.70711i | −0.387169 | + | 0.129056i | ||||
\(441\) | −7.65685 | −0.364612 | ||||||||
\(442\) | 4.10051i | 0.195041i | ||||||||
\(443\) | 5.34315 | − | 5.34315i | 0.253861 | − | 0.253861i | −0.568691 | − | 0.822551i | \(-0.692550\pi\) |
0.822551 | + | 0.568691i | \(0.192550\pi\) | |||||||
\(444\) | −12.0000 | − | 2.00000i | −0.569495 | − | 0.0949158i | ||||
\(445\) | 20.9706 | + | 10.4853i | 0.994100 | + | 0.497050i | ||||
\(446\) | 13.8787 | + | 13.8787i | 0.657175 | + | 0.657175i | ||||
\(447\) | −11.6569 | − | 11.6569i | −0.551350 | − | 0.551350i | ||||
\(448\) | 2.70711 | − | 2.70711i | 0.127899 | − | 0.127899i | ||||
\(449\) | 25.6274 | + | 25.6274i | 1.20943 | + | 1.20943i | 0.971211 | + | 0.238222i | \(0.0765645\pi\) |
0.238222 | + | 0.971211i | \(0.423435\pi\) | |||||||
\(450\) | 3.00000 | + | 4.00000i | 0.141421 | + | 0.188562i | ||||
\(451\) | −26.7990 | −1.26192 | ||||||||
\(452\) | − | 3.82843i | − | 0.180074i | ||||||
\(453\) | −16.9706 | − | 16.9706i | −0.797347 | − | 0.797347i | ||||
\(454\) | 7.48528i | 0.351302i | ||||||||
\(455\) | −17.1716 | − | 8.58579i | −0.805016 | − | 0.402508i | ||||
\(456\) | −16.4853 | −0.771994 | ||||||||
\(457\) | 3.68629i | 0.172437i | 0.996276 | + | 0.0862187i | \(0.0274784\pi\) | ||||
−0.996276 | + | 0.0862187i | \(0.972522\pi\) | |||||||
\(458\) | − | 1.41421i | − | 0.0660819i | ||||||
\(459\) | 5.17157 | − | 5.17157i | 0.241388 | − | 0.241388i | ||||
\(460\) | 1.82843 | + | 5.48528i | 0.0852509 | + | 0.255753i | ||||
\(461\) | 10.4645 | − | 10.4645i | 0.487379 | − | 0.487379i | −0.420099 | − | 0.907478i | \(-0.638005\pi\) |
0.907478 | + | 0.420099i | \(0.138005\pi\) | |||||||
\(462\) | 29.3137 | 1.36380 | ||||||||
\(463\) | 29.9411 | 1.39148 | 0.695741 | − | 0.718293i | \(-0.255076\pi\) | ||||
0.695741 | + | 0.718293i | \(0.255076\pi\) | |||||||
\(464\) | 6.70711 | − | 6.70711i | 0.311370 | − | 0.311370i | ||||
\(465\) | −8.24264 | − | 24.7279i | −0.382243 | − | 1.14673i | ||||
\(466\) | −0.0710678 | + | 0.0710678i | −0.00329215 | + | 0.00329215i | ||||
\(467\) | − | 2.31371i | − | 0.107066i | −0.998566 | − | 0.0535328i | \(-0.982952\pi\) | ||
0.998566 | − | 0.0535328i | \(-0.0170482\pi\) | |||||||
\(468\) | − | 2.24264i | − | 0.103666i | ||||||
\(469\) | −6.72792 | −0.310667 | ||||||||
\(470\) | 23.3137 | + | 11.6569i | 1.07538 | + | 0.537691i | ||||
\(471\) | 16.6274i | 0.766151i | ||||||||
\(472\) | 1.17157 | + | 1.17157i | 0.0539260 | + | 0.0539260i | ||||
\(473\) | 26.7990i | 1.23222i | ||||||||
\(474\) | 27.3137 | 1.25456 | ||||||||
\(475\) | −40.7990 | − | 5.82843i | −1.87199 | − | 0.267427i | ||||
\(476\) | 4.94975 | + | 4.94975i | 0.226871 | + | 0.226871i | ||||
\(477\) | 2.12132 | − | 2.12132i | 0.0971286 | − | 0.0971286i | ||||
\(478\) | −7.05025 | − | 7.05025i | −0.322471 | − | 0.322471i | ||||
\(479\) | −15.5563 | − | 15.5563i | −0.710788 | − | 0.710788i | 0.255912 | − | 0.966700i | \(-0.417624\pi\) |
−0.966700 | + | 0.255912i | \(0.917624\pi\) | |||||||
\(480\) | 4.00000 | + | 2.00000i | 0.182574 | + | 0.0912871i | ||||
\(481\) | 7.92893 | + | 11.1005i | 0.361528 | + | 0.506139i | ||||
\(482\) | 0.757359 | − | 0.757359i | 0.0344968 | − | 0.0344968i | ||||
\(483\) | − | 19.7990i | − | 0.900885i | ||||||
\(484\) | −3.65685 | −0.166221 | ||||||||
\(485\) | 14.8492 | − | 4.94975i | 0.674269 | − | 0.224756i | ||||
\(486\) | −7.07107 | + | 7.07107i | −0.320750 | + | 0.320750i | ||||
\(487\) | − | 26.9706i | − | 1.22215i | −0.791572 | − | 0.611076i | \(-0.790737\pi\) | ||
0.791572 | − | 0.611076i | \(-0.209263\pi\) | |||||||
\(488\) | 9.29289 | + | 9.29289i | 0.420670 | + | 0.420670i | ||||
\(489\) | 20.7279 | + | 20.7279i | 0.937349 | + | 0.937349i | ||||
\(490\) | −16.2426 | + | 5.41421i | −0.733768 | + | 0.244589i | ||||
\(491\) | 17.7990 | 0.803257 | 0.401629 | − | 0.915803i | \(-0.368444\pi\) | ||||
0.401629 | + | 0.915803i | \(0.368444\pi\) | |||||||
\(492\) | 9.89949 | + | 9.89949i | 0.446304 | + | 0.446304i | ||||
\(493\) | 12.2635 | + | 12.2635i | 0.552318 | + | 0.552318i | ||||
\(494\) | 13.0711 | + | 13.0711i | 0.588095 | + | 0.588095i | ||||
\(495\) | 2.70711 | + | 8.12132i | 0.121675 | + | 0.365026i | ||||
\(496\) | −4.12132 | − | 4.12132i | −0.185053 | − | 0.185053i | ||||
\(497\) | −0.928932 | + | 0.928932i | −0.0416683 | + | 0.0416683i | ||||
\(498\) | 2.34315 | 0.104999 | ||||||||
\(499\) | 10.2426 | − | 10.2426i | 0.458524 | − | 0.458524i | −0.439647 | − | 0.898171i | \(-0.644896\pi\) |
0.898171 | + | 0.439647i | \(0.144896\pi\) | |||||||
\(500\) | 9.19239 | + | 6.36396i | 0.411096 | + | 0.284605i | ||||
\(501\) | −1.65685 | − | 1.65685i | −0.0740228 | − | 0.0740228i | ||||
\(502\) | −17.8995 | − | 17.8995i | −0.798894 | − | 0.798894i | ||||
\(503\) | −32.5858 | −1.45293 | −0.726464 | − | 0.687204i | \(-0.758838\pi\) | ||||
−0.726464 | + | 0.687204i | \(0.758838\pi\) | |||||||
\(504\) | −2.70711 | − | 2.70711i | −0.120584 | − | 0.120584i | ||||
\(505\) | 23.4853 | − | 7.82843i | 1.04508 | − | 0.348360i | ||||
\(506\) | 9.89949i | 0.440086i | ||||||||
\(507\) | 11.2721 | − | 11.2721i | 0.500611 | − | 0.500611i | ||||
\(508\) | 2.58579 | − | 2.58579i | 0.114726 | − | 0.114726i | ||||
\(509\) | −1.27208 | −0.0563839 | −0.0281919 | − | 0.999603i | \(-0.508975\pi\) | ||||
−0.0281919 | + | 0.999603i | \(0.508975\pi\) | |||||||
\(510\) | −3.65685 | + | 7.31371i | −0.161928 | + | 0.323856i | ||||
\(511\) | 32.4853i | 1.43706i | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | − | 32.9706i | − | 1.45569i | ||||||
\(514\) | − | 18.8284i | − | 0.830486i | ||||||
\(515\) | 28.7574 | − | 9.58579i | 1.26720 | − | 0.422400i | ||||
\(516\) | 9.89949 | − | 9.89949i | 0.435801 | − | 0.435801i | ||||
\(517\) | 31.5563 | + | 31.5563i | 1.38785 | + | 1.38785i | ||||
\(518\) | 22.9706 | + | 3.82843i | 1.00927 | + | 0.168211i | ||||
\(519\) | − | 17.0294i | − | 0.747509i | ||||||
\(520\) | −1.58579 | − | 4.75736i | −0.0695413 | − | 0.208624i | ||||
\(521\) | 27.6274i | 1.21038i | 0.796081 | + | 0.605190i | \(0.206903\pi\) | ||||
−0.796081 | + | 0.605190i | \(0.793097\pi\) | |||||||
\(522\) | −6.70711 | − | 6.70711i | −0.293562 | − | 0.293562i | ||||
\(523\) | 43.6569 | 1.90898 | 0.954490 | − | 0.298241i | \(-0.0964000\pi\) | ||||
0.954490 | + | 0.298241i | \(0.0964000\pi\) | |||||||
\(524\) | 0.414214 | + | 0.414214i | 0.0180950 | + | 0.0180950i | ||||
\(525\) | −22.9706 | − | 30.6274i | −1.00252 | − | 1.33669i | ||||
\(526\) | 14.6066 | − | 14.6066i | 0.636878 | − | 0.636878i | ||||
\(527\) | 7.53553 | − | 7.53553i | 0.328253 | − | 0.328253i | ||||
\(528\) | 5.41421 | + | 5.41421i | 0.235623 | + | 0.235623i | ||||
\(529\) | −16.3137 | −0.709292 | ||||||||
\(530\) | 3.00000 | − | 6.00000i | 0.130312 | − | 0.260623i | ||||
\(531\) | 1.17157 | − | 1.17157i | 0.0508419 | − | 0.0508419i | ||||
\(532\) | 31.5563 | 1.36814 | ||||||||
\(533\) | − | 15.6985i | − | 0.679977i | ||||||
\(534\) | − | 20.9706i | − | 0.907485i | ||||||
\(535\) | 25.6569 | + | 12.8284i | 1.10924 | + | 0.554621i | ||||
\(536\) | −1.24264 | − | 1.24264i | −0.0536739 | − | 0.0536739i | ||||
\(537\) | 40.9706i | 1.76801i | ||||||||
\(538\) | 17.7990i | 0.767369i | ||||||||
\(539\) | −29.3137 | −1.26263 | ||||||||
\(540\) | −4.00000 | + | 8.00000i | −0.172133 | + | 0.344265i | ||||
\(541\) | −27.7990 | + | 27.7990i | −1.19517 | + | 1.19517i | −0.219577 | + | 0.975595i | \(0.570468\pi\) |
−0.975595 | + | 0.219577i | \(0.929532\pi\) | |||||||
\(542\) | −3.07107 | −0.131914 | ||||||||
\(543\) | −10.8284 | + | 10.8284i | −0.464692 | + | 0.464692i | ||||
\(544\) | 1.82843i | 0.0783932i | ||||||||
\(545\) | 1.34315 | − | 2.68629i | 0.0575340 | − | 0.115068i | ||||
\(546\) | 17.1716i | 0.734875i | ||||||||
\(547\) | −27.8284 | −1.18986 | −0.594929 | − | 0.803778i | \(-0.702820\pi\) | ||||
−0.594929 | + | 0.803778i | \(0.702820\pi\) | |||||||
\(548\) | 8.41421 | − | 8.41421i | 0.359437 | − | 0.359437i | ||||
\(549\) | 9.29289 | − | 9.29289i | 0.396611 | − | 0.396611i | ||||
\(550\) | 11.4853 | + | 15.3137i | 0.489734 | + | 0.652979i | ||||
\(551\) | 78.1838 | 3.33074 | ||||||||
\(552\) | 3.65685 | − | 3.65685i | 0.155646 | − | 0.155646i | ||||
\(553\) | −52.2843 | −2.22335 | ||||||||
\(554\) | 7.79899 | 0.331347 | ||||||||
\(555\) | 4.24264 | + | 26.8701i | 0.180090 | + | 1.14057i | ||||
\(556\) | 6.17157 | 0.261733 | ||||||||
\(557\) | 23.2132 | 0.983575 | 0.491787 | − | 0.870715i | \(-0.336344\pi\) | ||||
0.491787 | + | 0.870715i | \(0.336344\pi\) | |||||||
\(558\) | −4.12132 | + | 4.12132i | −0.174469 | + | 0.174469i | ||||
\(559\) | −15.6985 | −0.663975 | ||||||||
\(560\) | −7.65685 | − | 3.82843i | −0.323561 | − | 0.161781i | ||||
\(561\) | −9.89949 | + | 9.89949i | −0.417957 | + | 0.417957i | ||||
\(562\) | 4.00000 | − | 4.00000i | 0.168730 | − | 0.168730i | ||||
\(563\) | −24.1127 | −1.01623 | −0.508115 | − | 0.861290i | \(-0.669657\pi\) | ||||
−0.508115 | + | 0.861290i | \(0.669657\pi\) | |||||||
\(564\) | − | 23.3137i | − | 0.981684i | ||||||
\(565\) | −8.12132 | + | 2.70711i | −0.341667 | + | 0.113889i | ||||
\(566\) | 28.0000i | 1.17693i | ||||||||
\(567\) | 29.7782 | − | 29.7782i | 1.25057 | − | 1.25057i | ||||
\(568\) | −0.343146 | −0.0143981 | ||||||||
\(569\) | 1.68629 | − | 1.68629i | 0.0706930 | − | 0.0706930i | −0.670876 | − | 0.741569i | \(-0.734082\pi\) |
0.741569 | + | 0.670876i | \(0.234082\pi\) | |||||||
\(570\) | 11.6569 | + | 34.9706i | 0.488252 | + | 1.46476i | ||||
\(571\) | 46.7990 | 1.95848 | 0.979238 | − | 0.202712i | \(-0.0649755\pi\) | ||||
0.979238 | + | 0.202712i | \(0.0649755\pi\) | |||||||
\(572\) | − | 8.58579i | − | 0.358990i | ||||||
\(573\) | 4.34315i | 0.181438i | ||||||||
\(574\) | −18.9497 | − | 18.9497i | −0.790947 | − | 0.790947i | ||||
\(575\) | 10.3431 | − | 7.75736i | 0.431339 | − | 0.323504i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | − | 21.6569i | − | 0.901587i | −0.892628 | − | 0.450793i | \(-0.851141\pi\) | ||
0.892628 | − | 0.450793i | \(-0.148859\pi\) | |||||||
\(578\) | 13.6569 | 0.568050 | ||||||||
\(579\) | 28.9706 | − | 28.9706i | 1.20398 | − | 1.20398i | ||||
\(580\) | −18.9706 | − | 9.48528i | −0.787710 | − | 0.393855i | ||||
\(581\) | −4.48528 | −0.186081 | ||||||||
\(582\) | −9.89949 | − | 9.89949i | −0.410347 | − | 0.410347i | ||||
\(583\) | 8.12132 | − | 8.12132i | 0.336351 | − | 0.336351i | ||||
\(584\) | −6.00000 | + | 6.00000i | −0.248282 | + | 0.248282i | ||||
\(585\) | −4.75736 | + | 1.58579i | −0.196693 | + | 0.0655642i | ||||
\(586\) | −1.77817 | − | 1.77817i | −0.0734557 | − | 0.0734557i | ||||
\(587\) | −4.45584 | −0.183912 | −0.0919562 | − | 0.995763i | \(-0.529312\pi\) | ||||
−0.0919562 | + | 0.995763i | \(0.529312\pi\) | |||||||
\(588\) | 10.8284 | + | 10.8284i | 0.446557 | + | 0.446557i | ||||
\(589\) | − | 48.0416i | − | 1.97952i | ||||||
\(590\) | 1.65685 | − | 3.31371i | 0.0682116 | − | 0.136423i | ||||
\(591\) | − | 5.65685i | − | 0.232692i | ||||||
\(592\) | 3.53553 | + | 4.94975i | 0.145310 | + | 0.203433i | ||||
\(593\) | −26.1421 | − | 26.1421i | −1.07353 | − | 1.07353i | −0.997073 | − | 0.0764559i | \(-0.975640\pi\) |
−0.0764559 | − | 0.997073i | \(-0.524360\pi\) | |||||||
\(594\) | −10.8284 | + | 10.8284i | −0.444296 | + | 0.444296i | ||||
\(595\) | 7.00000 | − | 14.0000i | 0.286972 | − | 0.573944i | ||||
\(596\) | 8.24264i | 0.337632i | ||||||||
\(597\) | 11.0294i | 0.451405i | ||||||||
\(598\) | −5.79899 | −0.237138 | ||||||||
\(599\) | 33.7574i | 1.37929i | 0.724148 | + | 0.689644i | \(0.242233\pi\) | ||||
−0.724148 | + | 0.689644i | \(0.757767\pi\) | |||||||
\(600\) | 1.41421 | − | 9.89949i | 0.0577350 | − | 0.404145i | ||||
\(601\) | −16.5147 | −0.673649 | −0.336825 | − | 0.941567i | \(-0.609353\pi\) | ||||
−0.336825 | + | 0.941567i | \(0.609353\pi\) | |||||||
\(602\) | −18.9497 | + | 18.9497i | −0.772334 | + | 0.772334i | ||||
\(603\) | −1.24264 | + | 1.24264i | −0.0506042 | + | 0.0506042i | ||||
\(604\) | 12.0000i | 0.488273i | ||||||||
\(605\) | 2.58579 | + | 7.75736i | 0.105127 | + | 0.315382i | ||||
\(606\) | −15.6569 | − | 15.6569i | −0.636016 | − | 0.636016i | ||||
\(607\) | −34.1838 | −1.38748 | −0.693738 | − | 0.720227i | \(-0.744037\pi\) | ||||
−0.693738 | + | 0.720227i | \(0.744037\pi\) | |||||||
\(608\) | 5.82843 | + | 5.82843i | 0.236374 | + | 0.236374i | ||||
\(609\) | 51.3553 | + | 51.3553i | 2.08102 | + | 2.08102i | ||||
\(610\) | 13.1421 | − | 26.2843i | 0.532110 | − | 1.06422i | ||||
\(611\) | −18.4853 | + | 18.4853i | −0.747834 | + | 0.747834i | ||||
\(612\) | 1.82843 | 0.0739098 | ||||||||
\(613\) | 12.1213 | − | 12.1213i | 0.489576 | − | 0.489576i | −0.418597 | − | 0.908172i | \(-0.637478\pi\) |
0.908172 | + | 0.418597i | \(0.137478\pi\) | |||||||
\(614\) | 1.89949 | + | 1.89949i | 0.0766574 | + | 0.0766574i | ||||
\(615\) | 14.0000 | − | 28.0000i | 0.564534 | − | 1.12907i | ||||
\(616\) | −10.3640 | − | 10.3640i | −0.417576 | − | 0.417576i | ||||
\(617\) | 27.7279 | + | 27.7279i | 1.11628 | + | 1.11628i | 0.992282 | + | 0.124002i | \(0.0395730\pi\) |
0.124002 | + | 0.992282i | \(0.460427\pi\) | |||||||
\(618\) | −19.1716 | − | 19.1716i | −0.771194 | − | 0.771194i | ||||
\(619\) | −46.5980 | −1.87293 | −0.936465 | − | 0.350760i | \(-0.885923\pi\) | ||||
−0.936465 | + | 0.350760i | \(0.885923\pi\) | |||||||
\(620\) | −5.82843 | + | 11.6569i | −0.234075 | + | 0.468151i | ||||
\(621\) | 7.31371 | + | 7.31371i | 0.293489 | + | 0.293489i | ||||
\(622\) | −11.7782 | − | 11.7782i | −0.472262 | − | 0.472262i | ||||
\(623\) | 40.1421i | 1.60826i | ||||||||
\(624\) | −3.17157 | + | 3.17157i | −0.126965 | + | 0.126965i | ||||
\(625\) | 7.00000 | − | 24.0000i | 0.280000 | − | 0.960000i | ||||
\(626\) | −0.686292 | −0.0274297 | ||||||||
\(627\) | 63.1127i | 2.52048i | ||||||||
\(628\) | 5.87868 | − | 5.87868i | 0.234585 | − | 0.234585i | ||||
\(629\) | −9.05025 | + | 6.46447i | −0.360857 | + | 0.257755i | ||||
\(630\) | −3.82843 | + | 7.65685i | −0.152528 | + | 0.305056i | ||||
\(631\) | −18.8492 | − | 18.8492i | −0.750376 | − | 0.750376i | 0.224173 | − | 0.974549i | \(-0.428032\pi\) |
−0.974549 | + | 0.224173i | \(0.928032\pi\) | |||||||
\(632\) | −9.65685 | − | 9.65685i | −0.384129 | − | 0.384129i | ||||
\(633\) | 12.7279 | − | 12.7279i | 0.505889 | − | 0.505889i | ||||
\(634\) | −15.5355 | − | 15.5355i | −0.616995 | − | 0.616995i | ||||
\(635\) | −7.31371 | − | 3.65685i | −0.290236 | − | 0.145118i | ||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | − | 17.1716i | − | 0.680362i | ||||||
\(638\) | −25.6777 | − | 25.6777i | −1.01659 | − | 1.01659i | ||||
\(639\) | 0.343146i | 0.0135746i | ||||||||
\(640\) | −0.707107 | − | 2.12132i | −0.0279508 | − | 0.0838525i | ||||
\(641\) | 25.2843 | 0.998669 | 0.499334 | − | 0.866409i | \(-0.333578\pi\) | ||||
0.499334 | + | 0.866409i | \(0.333578\pi\) | |||||||
\(642\) | − | 25.6569i | − | 1.01260i | ||||||
\(643\) | − | 24.5147i | − | 0.966766i | −0.875409 | − | 0.483383i | \(-0.839408\pi\) | ||
0.875409 | − | 0.483383i | \(-0.160592\pi\) | |||||||
\(644\) | −7.00000 | + | 7.00000i | −0.275839 | + | 0.275839i | ||||
\(645\) | −28.0000 | − | 14.0000i | −1.10250 | − | 0.551249i | ||||
\(646\) | −10.6569 | + | 10.6569i | −0.419288 | + | 0.419288i | ||||
\(647\) | 27.3137 | 1.07381 | 0.536906 | − | 0.843642i | \(-0.319593\pi\) | ||||
0.536906 | + | 0.843642i | \(0.319593\pi\) | |||||||
\(648\) | 11.0000 | 0.432121 | ||||||||
\(649\) | 4.48528 | − | 4.48528i | 0.176063 | − | 0.176063i | ||||
\(650\) | −8.97056 | + | 6.72792i | −0.351854 | + | 0.263891i | ||||
\(651\) | 31.5563 | − | 31.5563i | 1.23679 | − | 1.23679i | ||||
\(652\) | − | 14.6569i | − | 0.574007i | ||||||
\(653\) | − | 19.6569i | − | 0.769232i | −0.923077 | − | 0.384616i | \(-0.874334\pi\) | ||
0.923077 | − | 0.384616i | \(-0.125666\pi\) | |||||||
\(654\) | −2.68629 | −0.105042 | ||||||||
\(655\) | 0.585786 | − | 1.17157i | 0.0228886 | − | 0.0457771i | ||||
\(656\) | − | 7.00000i | − | 0.273304i | ||||||
\(657\) | 6.00000 | + | 6.00000i | 0.234082 | + | 0.234082i | ||||
\(658\) | 44.6274i | 1.73976i | ||||||||
\(659\) | 20.1421 | 0.784626 | 0.392313 | − | 0.919832i | \(-0.371675\pi\) | ||||
0.392313 | + | 0.919832i | \(0.371675\pi\) | |||||||
\(660\) | 7.65685 | − | 15.3137i | 0.298043 | − | 0.596085i | ||||
\(661\) | −20.2635 | − | 20.2635i | −0.788157 | − | 0.788157i | 0.193035 | − | 0.981192i | \(-0.438167\pi\) |
−0.981192 | + | 0.193035i | \(0.938167\pi\) | |||||||
\(662\) | 2.58579 | − | 2.58579i | 0.100499 | − | 0.100499i | ||||
\(663\) | −5.79899 | − | 5.79899i | −0.225214 | − | 0.225214i | ||||
\(664\) | −0.828427 | − | 0.828427i | −0.0321492 | − | 0.0321492i | ||||
\(665\) | −22.3137 | − | 66.9411i | −0.865289 | − | 2.59587i | ||||
\(666\) | 4.94975 | − | 3.53553i | 0.191799 | − | 0.136999i | ||||
\(667\) | −17.3431 | + | 17.3431i | −0.671529 | + | 0.671529i | ||||
\(668\) | 1.17157i | 0.0453295i | ||||||||
\(669\) | −39.2548 | −1.51768 | ||||||||
\(670\) | −1.75736 | + | 3.51472i | −0.0678927 | + | 0.135785i | ||||
\(671\) | 35.5772 | − | 35.5772i | 1.37344 | − | 1.37344i | ||||
\(672\) | 7.65685i | 0.295370i | ||||||||
\(673\) | −10.5147 | − | 10.5147i | −0.405313 | − | 0.405313i | 0.474788 | − | 0.880100i | \(-0.342525\pi\) |
−0.880100 | + | 0.474788i | \(0.842525\pi\) | |||||||
\(674\) | −5.65685 | − | 5.65685i | −0.217894 | − | 0.217894i | ||||
\(675\) | 19.7990 | + | 2.82843i | 0.762063 | + | 0.108866i | ||||
\(676\) | −7.97056 | −0.306560 | ||||||||
\(677\) | 13.5147 | + | 13.5147i | 0.519413 | + | 0.519413i | 0.917394 | − | 0.397981i | \(-0.130289\pi\) |
−0.397981 | + | 0.917394i | \(0.630289\pi\) | |||||||
\(678\) | 5.41421 | + | 5.41421i | 0.207932 | + | 0.207932i | ||||
\(679\) | 18.9497 | + | 18.9497i | 0.727225 | + | 0.727225i | ||||
\(680\) | 3.87868 | − | 1.29289i | 0.148741 | − | 0.0495802i | ||||
\(681\) | −10.5858 | − | 10.5858i | −0.405648 | − | 0.405648i | ||||
\(682\) | −15.7782 | + | 15.7782i | −0.604178 | + | 0.604178i | ||||
\(683\) | 12.3137 | 0.471171 | 0.235585 | − | 0.971854i | \(-0.424299\pi\) | ||||
0.235585 | + | 0.971854i | \(0.424299\pi\) | |||||||
\(684\) | 5.82843 | − | 5.82843i | 0.222855 | − | 0.222855i | ||||
\(685\) | −23.7990 | − | 11.8995i | −0.909313 | − | 0.454656i | ||||
\(686\) | −1.77817 | − | 1.77817i | −0.0678910 | − | 0.0678910i | ||||
\(687\) | 2.00000 | + | 2.00000i | 0.0763048 | + | 0.0763048i | ||||
\(688\) | −7.00000 | −0.266872 | ||||||||
\(689\) | 4.75736 | + | 4.75736i | 0.181241 | + | 0.181241i | ||||
\(690\) | −10.3431 | − | 5.17157i | −0.393757 | − | 0.196878i | ||||
\(691\) | − | 9.97056i | − | 0.379298i | −0.981852 | − | 0.189649i | \(-0.939265\pi\) | ||
0.981852 | − | 0.189649i | \(-0.0607350\pi\) | |||||||
\(692\) | −6.02082 | + | 6.02082i | −0.228877 | + | 0.228877i | ||||
\(693\) | −10.3640 | + | 10.3640i | −0.393694 | + | 0.393694i | ||||
\(694\) | −17.3137 | −0.657219 | ||||||||
\(695\) | −4.36396 | − | 13.0919i | −0.165534 | − | 0.496603i | ||||
\(696\) | 18.9706i | 0.719077i | ||||||||
\(697\) | 12.7990 | 0.484796 | ||||||||
\(698\) | − | 4.14214i | − | 0.156782i | ||||||
\(699\) | − | 0.201010i | − | 0.00760290i | ||||||
\(700\) | −2.70711 | + | 18.9497i | −0.102319 | + | 0.716233i | ||||
\(701\) | 4.34315 | − | 4.34315i | 0.164038 | − | 0.164038i | −0.620315 | − | 0.784353i | \(-0.712995\pi\) |
0.784353 | + | 0.620315i | \(0.212995\pi\) | |||||||
\(702\) | −6.34315 | − | 6.34315i | −0.239407 | − | 0.239407i | ||||
\(703\) | −8.24264 | + | 49.4558i | −0.310877 | + | 1.86526i | ||||
\(704\) | − | 3.82843i | − | 0.144289i | ||||||
\(705\) | −49.4558 | + | 16.4853i | −1.86261 | + | 0.620872i | ||||
\(706\) | 7.34315i | 0.276363i | ||||||||
\(707\) | 29.9706 | + | 29.9706i | 1.12716 | + | 1.12716i | ||||
\(708\) | −3.31371 | −0.124537 | ||||||||
\(709\) | −10.7071 | − | 10.7071i | −0.402114 | − | 0.402114i | 0.476864 | − | 0.878977i | \(-0.341774\pi\) |
−0.878977 | + | 0.476864i | \(0.841774\pi\) | |||||||
\(710\) | 0.242641 | + | 0.727922i | 0.00910614 | + | 0.0273184i | ||||
\(711\) | −9.65685 | + | 9.65685i | −0.362160 | + | 0.362160i | ||||
\(712\) | −7.41421 | + | 7.41421i | −0.277859 | + | 0.277859i | ||||
\(713\) | 10.6569 | + | 10.6569i | 0.399102 | + | 0.399102i | ||||
\(714\) | −14.0000 | −0.523937 | ||||||||
\(715\) | −18.2132 | + | 6.07107i | −0.681135 | + | 0.227045i | ||||
\(716\) | 14.4853 | − | 14.4853i | 0.541340 | − | 0.541340i | ||||
\(717\) | 19.9411 | 0.744715 | ||||||||
\(718\) | 30.5269i | 1.13925i | ||||||||
\(719\) | 24.1421i | 0.900350i | 0.892940 | + | 0.450175i | \(0.148638\pi\) | ||||
−0.892940 | + | 0.450175i | \(0.851362\pi\) | |||||||
\(720\) | −2.12132 | + | 0.707107i | −0.0790569 | + | 0.0263523i | ||||
\(721\) | 36.6985 | + | 36.6985i | 1.36672 | + | 1.36672i | ||||
\(722\) | 48.9411i | 1.82140i | ||||||||
\(723\) | 2.14214i | 0.0796669i | ||||||||
\(724\) | 7.65685 | 0.284565 | ||||||||
\(725\) | −6.70711 | + | 46.9497i | −0.249096 | + | 1.74367i | ||||
\(726\) | 5.17157 | − | 5.17157i | 0.191935 | − | 0.191935i | ||||
\(727\) | −13.8579 | −0.513960 | −0.256980 | − | 0.966417i | \(-0.582727\pi\) | ||||
−0.256980 | + | 0.966417i | \(0.582727\pi\) | |||||||
\(728\) | 6.07107 | − | 6.07107i | 0.225009 | − | 0.225009i | ||||
\(729\) | 13.0000i | 0.481481i | ||||||||
\(730\) | 16.9706 | + | 8.48528i | 0.628109 | + | 0.314054i | ||||
\(731\) | − | 12.7990i | − | 0.473388i | ||||||
\(732\) | −26.2843 | −0.971495 | ||||||||
\(733\) | 22.7487 | − | 22.7487i | 0.840244 | − | 0.840244i | −0.148647 | − | 0.988890i | \(-0.547492\pi\) |
0.988890 | + | 0.148647i | \(0.0474917\pi\) | |||||||
\(734\) | 13.0919 | − | 13.0919i | 0.483230 | − | 0.483230i | ||||
\(735\) | 15.3137 | − | 30.6274i | 0.564855 | − | 1.12971i | ||||
\(736\) | −2.58579 | −0.0953134 | ||||||||
\(737\) | −4.75736 | + | 4.75736i | −0.175240 | + | 0.175240i | ||||
\(738\) | −7.00000 | −0.257674 | ||||||||
\(739\) | 10.7990 | 0.397247 | 0.198624 | − | 0.980076i | \(-0.436353\pi\) | ||||
0.198624 | + | 0.980076i | \(0.436353\pi\) | |||||||
\(740\) | 8.00000 | − | 11.0000i | 0.294086 | − | 0.404368i | ||||
\(741\) | −36.9706 | −1.35815 | ||||||||
\(742\) | 11.4853 | 0.421638 | ||||||||
\(743\) | −5.05025 | + | 5.05025i | −0.185276 | + | 0.185276i | −0.793650 | − | 0.608374i | \(-0.791822\pi\) |
0.608374 | + | 0.793650i | \(0.291822\pi\) | |||||||
\(744\) | 11.6569 | 0.427361 | ||||||||
\(745\) | 17.4853 | − | 5.82843i | 0.640611 | − | 0.213537i | ||||
\(746\) | 10.8284 | − | 10.8284i | 0.396457 | − | 0.396457i | ||||
\(747\) | −0.828427 | + | 0.828427i | −0.0303106 | + | 0.0303106i | ||||
\(748\) | 7.00000 | 0.255945 | ||||||||
\(749\) | 49.1127i | 1.79454i | ||||||||
\(750\) | −22.0000 | + | 4.00000i | −0.803326 | + | 0.146059i | ||||
\(751\) | 16.0416i | 0.585367i | 0.956209 | + | 0.292684i | \(0.0945483\pi\) | ||||
−0.956209 | + | 0.292684i | \(0.905452\pi\) | |||||||
\(752\) | −8.24264 | + | 8.24264i | −0.300578 | + | 0.300578i | ||||
\(753\) | 50.6274 | 1.84497 | ||||||||
\(754\) | 15.0416 | − | 15.0416i | 0.547784 | − | 0.547784i | ||||
\(755\) | 25.4558 | − | 8.48528i | 0.926433 | − | 0.308811i | ||||
\(756\) | −15.3137 | −0.556954 | ||||||||
\(757\) | − | 27.6569i | − | 1.00521i | −0.864517 | − | 0.502603i | \(-0.832376\pi\) | ||
0.864517 | − | 0.502603i | \(-0.167624\pi\) | |||||||
\(758\) | 18.0000i | 0.653789i | ||||||||
\(759\) | −14.0000 | − | 14.0000i | −0.508168 | − | 0.508168i | ||||
\(760\) | 8.24264 | − | 16.4853i | 0.298992 | − | 0.597984i | ||||
\(761\) | 11.6863i | 0.423628i | 0.977310 | + | 0.211814i | \(0.0679371\pi\) | ||||
−0.977310 | + | 0.211814i | \(0.932063\pi\) | |||||||
\(762\) | 7.31371i | 0.264948i | ||||||||
\(763\) | 5.14214 | 0.186158 | ||||||||
\(764\) | 1.53553 | − | 1.53553i | 0.0555537 | − | 0.0555537i | ||||
\(765\) | −1.29289 | − | 3.87868i | −0.0467447 | − | 0.140234i | ||||
\(766\) | −16.5858 | −0.599269 | ||||||||
\(767\) | 2.62742 | + | 2.62742i | 0.0948705 | + | 0.0948705i | ||||
\(768\) | −1.41421 | + | 1.41421i | −0.0510310 | + | 0.0510310i | ||||
\(769\) | 19.1716 | − | 19.1716i | 0.691345 | − | 0.691345i | −0.271183 | − | 0.962528i | \(-0.587415\pi\) |
0.962528 | + | 0.271183i | \(0.0874149\pi\) | |||||||
\(770\) | −14.6569 | + | 29.3137i | −0.528196 | + | 1.05639i | ||||
\(771\) | 26.6274 | + | 26.6274i | 0.958963 | + | 0.958963i | ||||
\(772\) | −20.4853 | −0.737281 | ||||||||
\(773\) | 10.1213 | + | 10.1213i | 0.364039 | + | 0.364039i | 0.865297 | − | 0.501259i | \(-0.167130\pi\) |
−0.501259 | + | 0.865297i | \(0.667130\pi\) | |||||||
\(774\) | 7.00000i | 0.251610i | ||||||||
\(775\) | 28.8492 | + | 4.12132i | 1.03630 | + | 0.148042i | ||||
\(776\) | 7.00000i | 0.251285i | ||||||||
\(777\) | −37.8995 | + | 27.0711i | −1.35964 | + | 0.971169i | ||||
\(778\) | 3.77817 | + | 3.77817i | 0.135454 | + | 0.135454i | ||||
\(779\) | 40.7990 | − | 40.7990i | 1.46178 | − | 1.46178i | ||||
\(780\) | 8.97056 | + | 4.48528i | 0.321198 | + | 0.160599i | ||||
\(781\) | 1.31371i | 0.0470082i | ||||||||
\(782\) | − | 4.72792i | − | 0.169070i | ||||||
\(783\) | −37.9411 | −1.35591 | ||||||||
\(784\) | − | 7.65685i | − | 0.273459i | ||||||
\(785\) | −16.6274 | − | 8.31371i | −0.593458 | − | 0.296729i | ||||
\(786\) | −1.17157 | −0.0417886 | ||||||||
\(787\) | 16.2426 | − | 16.2426i | 0.578988 | − | 0.578988i | −0.355637 | − | 0.934624i | \(-0.615736\pi\) |
0.934624 | + | 0.355637i | \(0.115736\pi\) | |||||||
\(788\) | −2.00000 | + | 2.00000i | −0.0712470 | + | 0.0712470i | ||||
\(789\) | 41.3137i | 1.47081i | ||||||||
\(790\) | −13.6569 | + | 27.3137i | −0.485889 | + | 0.971778i | ||||
\(791\) | −10.3640 | − | 10.3640i | −0.368500 | − | 0.368500i | ||||
\(792\) | −3.82843 | −0.136037 | ||||||||
\(793\) | 20.8406 | + | 20.8406i | 0.740072 | + | 0.740072i | ||||
\(794\) | −8.48528 | − | 8.48528i | −0.301131 | − | 0.301131i | ||||
\(795\) | 4.24264 | + | 12.7279i | 0.150471 | + | 0.451413i | ||||
\(796\) | 3.89949 | − | 3.89949i | 0.138214 | − | 0.138214i | ||||
\(797\) | −51.2548 | −1.81554 | −0.907770 | − | 0.419469i | \(-0.862216\pi\) | ||||
−0.907770 | + | 0.419469i | \(0.862216\pi\) | |||||||
\(798\) | −44.6274 | + | 44.6274i | −1.57979 | + | 1.57979i | ||||
\(799\) | −15.0711 | − | 15.0711i | −0.533176 | − | 0.533176i | ||||
\(800\) | −4.00000 | + | 3.00000i | −0.141421 | + | 0.106066i | ||||
\(801\) | 7.41421 | + | 7.41421i | 0.261968 | + | 0.261968i | ||||
\(802\) | −7.07107 | − | 7.07107i | −0.249688 | − | 0.249688i | ||||
\(803\) | 22.9706 | + | 22.9706i | 0.810614 | + | 0.810614i | ||||
\(804\) | 3.51472 | 0.123955 | ||||||||
\(805\) | 19.7990 | + | 9.89949i | 0.697823 | + | 0.348911i | ||||
\(806\) | −9.24264 | − | 9.24264i | −0.325558 | − | 0.325558i | ||||
\(807\) | −25.1716 | − | 25.1716i | −0.886081 | − | 0.886081i | ||||
\(808\) | 11.0711i | 0.389479i | ||||||||
\(809\) | −39.9706 | + | 39.9706i | −1.40529 | + | 1.40529i | −0.623336 | + | 0.781954i | \(0.714223\pi\) |
−0.781954 | + | 0.623336i | \(0.785777\pi\) | |||||||
\(810\) | −7.77817 | − | 23.3345i | −0.273297 | − | 0.819892i | ||||
\(811\) | −24.9706 | −0.876835 | −0.438418 | − | 0.898771i | \(-0.644461\pi\) | ||||
−0.438418 | + | 0.898771i | \(0.644461\pi\) | |||||||
\(812\) | − | 36.3137i | − | 1.27436i | ||||||
\(813\) | 4.34315 | − | 4.34315i | 0.152321 | − | 0.152321i | ||||
\(814\) | 18.9497 | − | 13.5355i | 0.664188 | − | 0.474420i | ||||
\(815\) | −31.0919 | + | 10.3640i | −1.08910 | + | 0.363034i | ||||
\(816\) | −2.58579 | − | 2.58579i | −0.0905206 | − | 0.0905206i | ||||
\(817\) | −40.7990 | − | 40.7990i | −1.42738 | − | 1.42738i | ||||
\(818\) | 19.7990 | − | 19.7990i | 0.692255 | − | 0.692255i | ||||
\(819\) | −6.07107 | − | 6.07107i | −0.212140 | − | 0.212140i | ||||
\(820\) | −14.8492 | + | 4.94975i | −0.518558 | + | 0.172853i | ||||
\(821\) | −41.5563 | −1.45033 | −0.725163 | − | 0.688577i | \(-0.758236\pi\) | ||||
−0.725163 | + | 0.688577i | \(0.758236\pi\) | |||||||
\(822\) | 23.7990i | 0.830085i | ||||||||
\(823\) | −28.9706 | − | 28.9706i | −1.00985 | − | 1.00985i | −0.999951 | − | 0.00989933i | \(-0.996849\pi\) |
−0.00989933 | − | 0.999951i | \(-0.503151\pi\) | |||||||
\(824\) | 13.5563i | 0.472258i | ||||||||
\(825\) | −37.8995 | − | 5.41421i | −1.31949 | − | 0.188499i | ||||
\(826\) | 6.34315 | 0.220706 | ||||||||
\(827\) | − | 3.82843i | − | 0.133127i | −0.997782 | − | 0.0665637i | \(-0.978796\pi\) | ||
0.997782 | − | 0.0665637i | \(-0.0212036\pi\) | |||||||
\(828\) | 2.58579i | 0.0898623i | ||||||||
\(829\) | 24.7487 | − | 24.7487i | 0.859559 | − | 0.859559i | −0.131727 | − | 0.991286i | \(-0.542052\pi\) |
0.991286 | + | 0.131727i | \(0.0420522\pi\) | |||||||
\(830\) | −1.17157 | + | 2.34315i | −0.0406659 | + | 0.0813318i | ||||
\(831\) | −11.0294 | + | 11.0294i | −0.382607 | + | 0.382607i | ||||
\(832\) | 2.24264 | 0.0777496 | ||||||||
\(833\) | 14.0000 | 0.485071 | ||||||||
\(834\) | −8.72792 | + | 8.72792i | −0.302223 | + | 0.302223i | ||||
\(835\) | 2.48528 | − | 0.828427i | 0.0860067 | − | 0.0286689i | ||||
\(836\) | 22.3137 | − | 22.3137i | 0.771736 | − | 0.771736i | ||||
\(837\) | 23.3137i | 0.805840i | ||||||||
\(838\) | − | 26.9706i | − | 0.931683i | ||||||
\(839\) | −25.3553 | −0.875364 | −0.437682 | − | 0.899130i | \(-0.644200\pi\) | ||||
−0.437682 | + | 0.899130i | \(0.644200\pi\) | |||||||
\(840\) | 16.2426 | − | 5.41421i | 0.560424 | − | 0.186808i | ||||
\(841\) | − | 60.9706i | − | 2.10243i | ||||||
\(842\) | −25.3137 | − | 25.3137i | −0.872368 | − | 0.872368i | ||||
\(843\) | 11.3137i | 0.389665i | ||||||||
\(844\) | −9.00000 | −0.309793 | ||||||||
\(845\) | 5.63604 | + | 16.9081i | 0.193886 | + | 0.581657i | ||||
\(846\) | 8.24264 | + | 8.24264i | 0.283388 | + | 0.283388i | ||||
\(847\) | −9.89949 | + | 9.89949i | −0.340151 | + | 0.340151i | ||||
\(848\) | 2.12132 | + | 2.12132i | 0.0728464 | + | 0.0728464i | ||||
\(849\) | −39.5980 | − | 39.5980i | −1.35900 | − | 1.35900i | ||||
\(850\) | −5.48528 | − | 7.31371i | −0.188144 | − | 0.250858i | ||||
\(851\) | −9.14214 | − | 12.7990i | −0.313388 | − | 0.438744i | ||||
\(852\) | 0.485281 | − | 0.485281i | 0.0166255 | − | 0.0166255i | ||||
\(853\) | − | 27.1716i | − | 0.930337i | −0.885222 | − | 0.465168i | \(-0.845994\pi\) | ||
0.885222 | − | 0.465168i | \(-0.154006\pi\) | |||||||
\(854\) | 50.3137 | 1.72170 | ||||||||
\(855\) | −16.4853 | − | 8.24264i | −0.563785 | − | 0.281892i | ||||
\(856\) | −9.07107 | + | 9.07107i | −0.310043 | + | 0.310043i | ||||
\(857\) | − | 13.1421i | − | 0.448927i | −0.974483 | − | 0.224463i | \(-0.927937\pi\) | ||
0.974483 | − | 0.224463i | \(-0.0720629\pi\) | |||||||
\(858\) | 12.1421 | + | 12.1421i | 0.414526 | + | 0.414526i | ||||
\(859\) | 36.5563 | + | 36.5563i | 1.24729 | + | 1.24729i | 0.956914 | + | 0.290373i | \(0.0937794\pi\) |
0.290373 | + | 0.956914i | \(0.406221\pi\) | |||||||
\(860\) | 4.94975 | + | 14.8492i | 0.168785 | + | 0.506355i | ||||
\(861\) | 53.5980 | 1.82661 | ||||||||
\(862\) | −20.5061 | − | 20.5061i | −0.698440 | − | 0.698440i | ||||
\(863\) | 20.7071 | + | 20.7071i | 0.704878 | + | 0.704878i | 0.965454 | − | 0.260575i | \(-0.0839123\pi\) |
−0.260575 | + | 0.965454i | \(0.583912\pi\) | |||||||
\(864\) | −2.82843 | − | 2.82843i | −0.0962250 | − | 0.0962250i | ||||
\(865\) | 17.0294 | + | 8.51472i | 0.579018 | + | 0.289509i | ||||
\(866\) | 5.14214 | + | 5.14214i | 0.174737 | + | 0.174737i | ||||
\(867\) | −19.3137 | + | 19.3137i | −0.655928 | + | 0.655928i | ||||
\(868\) | −22.3137 | −0.757377 | ||||||||
\(869\) | −36.9706 | + | 36.9706i | −1.25414 | + | 1.25414i | ||||
\(870\) | 40.2426 | − | 13.4142i | 1.36435 | − | 0.454784i | ||||
\(871\) | −2.78680 | − | 2.78680i | −0.0944270 | − | 0.0944270i | ||||
\(872\) | 0.949747 | + | 0.949747i | 0.0321625 | + | 0.0321625i | ||||
\(873\) | 7.00000 | 0.236914 | ||||||||
\(874\) | −15.0711 | − | 15.0711i | −0.509786 | − | 0.509786i | ||||
\(875\) | 42.1127 | − | 7.65685i | 1.42367 | − | 0.258849i | ||||
\(876\) | − | 16.9706i | − | 0.573382i | ||||||
\(877\) | −14.0208 | + | 14.0208i | −0.473449 | + | 0.473449i | −0.903029 | − | 0.429580i | \(-0.858662\pi\) |
0.429580 | + | 0.903029i | \(0.358662\pi\) | |||||||
\(878\) | −2.22183 | + | 2.22183i | −0.0749830 | + | 0.0749830i | ||||
\(879\) | 5.02944 | 0.169639 | ||||||||
\(880\) | −8.12132 | + | 2.70711i | −0.273770 | + | 0.0912566i | ||||
\(881\) | 9.48528i | 0.319567i | 0.987152 | + | 0.159784i | \(0.0510797\pi\) | ||||
−0.987152 | + | 0.159784i | \(0.948920\pi\) | |||||||
\(882\) | −7.65685 | −0.257820 | ||||||||
\(883\) | 8.37258i | 0.281760i | 0.990027 | + | 0.140880i | \(0.0449931\pi\) | ||||
−0.990027 | + | 0.140880i | \(0.955007\pi\) | |||||||
\(884\) | 4.10051i | 0.137915i | ||||||||
\(885\) | 2.34315 | + | 7.02944i | 0.0787640 | + | 0.236292i | ||||
\(886\) | 5.34315 | − | 5.34315i | 0.179506 | − | 0.179506i | ||||
\(887\) | 34.0624 | + | 34.0624i | 1.14370 | + | 1.14370i | 0.987767 | + | 0.155938i | \(0.0498401\pi\) |
0.155938 | + | 0.987767i | \(0.450160\pi\) | |||||||
\(888\) | −12.0000 | − | 2.00000i | −0.402694 | − | 0.0671156i | ||||
\(889\) | − | 14.0000i | − | 0.469545i | ||||||
\(890\) | 20.9706 | + | 10.4853i | 0.702935 | + | 0.351467i | ||||
\(891\) | − | 42.1127i | − | 1.41083i | ||||||
\(892\) | 13.8787 | + | 13.8787i | 0.464693 | + | 0.464693i | ||||
\(893\) | −96.0833 | −3.21530 | ||||||||
\(894\) | −11.6569 | − | 11.6569i | −0.389864 | − | 0.389864i | ||||
\(895\) | −40.9706 | − | 20.4853i | −1.36949 | − | 0.684747i | ||||
\(896\) | 2.70711 | − | 2.70711i | 0.0904381 | − | 0.0904381i | ||||
\(897\) | 8.20101 | − | 8.20101i | 0.273824 | − | 0.273824i | ||||
\(898\) | 25.6274 | + | 25.6274i | 0.855198 | + | 0.855198i | ||||
\(899\) | −55.2843 | −1.84383 | ||||||||
\(900\) | 3.00000 | + | 4.00000i | 0.100000 | + | 0.133333i | ||||
\(901\) | −3.87868 | + | 3.87868i | −0.129218 | + | 0.129218i | ||||
\(902\) | −26.7990 | −0.892309 | ||||||||
\(903\) | − | 53.5980i | − | 1.78363i | ||||||
\(904\) | − | 3.82843i | − | 0.127332i | ||||||
\(905\) | −5.41421 | − | 16.2426i | −0.179975 | − | 0.539924i | ||||
\(906\) | −16.9706 | − | 16.9706i | −0.563809 | − | 0.563809i | ||||
\(907\) | 14.0000i | 0.464862i | 0.972613 | + | 0.232431i | \(0.0746680\pi\) | ||||
−0.972613 | + | 0.232431i | \(0.925332\pi\) | |||||||
\(908\) | 7.48528i | 0.248408i | ||||||||
\(909\) | 11.0711 | 0.367204 | ||||||||
\(910\) | −17.1716 | − | 8.58579i | −0.569232 | − | 0.284616i | ||||
\(911\) | 24.5858 | − | 24.5858i | 0.814563 | − | 0.814563i | −0.170751 | − | 0.985314i | \(-0.554619\pi\) |
0.985314 | + | 0.170751i | \(0.0546193\pi\) | |||||||
\(912\) | −16.4853 | −0.545882 | ||||||||
\(913\) | −3.17157 | + | 3.17157i | −0.104964 | + | 0.104964i | ||||
\(914\) | 3.68629i | 0.121932i | ||||||||
\(915\) | 18.5858 | + | 55.7574i | 0.614427 | + | 1.84328i | ||||
\(916\) | − | 1.41421i | − | 0.0467269i | ||||||
\(917\) | 2.24264 | 0.0740585 | ||||||||
\(918\) | 5.17157 | − | 5.17157i | 0.170687 | − | 0.170687i | ||||
\(919\) | 34.6274 | − | 34.6274i | 1.14225 | − | 1.14225i | 0.154216 | − | 0.988037i | \(-0.450715\pi\) |
0.988037 | − | 0.154216i | \(-0.0492851\pi\) | |||||||
\(920\) | 1.82843 | + | 5.48528i | 0.0602815 | + | 0.180844i | ||||
\(921\) | −5.37258 | −0.177033 | ||||||||
\(922\) | 10.4645 | − | 10.4645i | 0.344629 | − | 0.344629i | ||||
\(923\) | −0.769553 | −0.0253301 | ||||||||
\(924\) | 29.3137 | 0.964350 | ||||||||
\(925\) | −28.9914 | − | 9.19239i | −0.953231 | − | 0.302244i | ||||
\(926\) | 29.9411 | 0.983926 | ||||||||
\(927\) | 13.5563 | 0.445249 | ||||||||
\(928\) | 6.70711 | − | 6.70711i | 0.220172 | − | 0.220172i | ||||
\(929\) | −9.34315 | −0.306539 | −0.153269 | − | 0.988184i | \(-0.548980\pi\) | ||||
−0.153269 | + | 0.988184i | \(0.548980\pi\) | |||||||
\(930\) | −8.24264 | − | 24.7279i | −0.270287 | − | 0.810861i | ||||
\(931\) | 44.6274 | − | 44.6274i | 1.46260 | − | 1.46260i | ||||
\(932\) | −0.0710678 | + | 0.0710678i | −0.00232790 | + | 0.00232790i | ||||
\(933\) | 33.3137 | 1.09064 | ||||||||
\(934\) | − | 2.31371i | − | 0.0757069i | ||||||
\(935\) | −4.94975 | − | 14.8492i | −0.161874 | − | 0.485622i | ||||
\(936\) | − | 2.24264i | − | 0.0733030i | ||||||
\(937\) | 4.58579 | − | 4.58579i | 0.149811 | − | 0.149811i | −0.628223 | − | 0.778034i | \(-0.716217\pi\) |
0.778034 | + | 0.628223i | \(0.216217\pi\) | |||||||
\(938\) | −6.72792 | −0.219674 | ||||||||
\(939\) | 0.970563 | − | 0.970563i | 0.0316731 | − | 0.0316731i | ||||
\(940\) | 23.3137 | + | 11.6569i | 0.760409 | + | 0.380205i | ||||
\(941\) | 20.9289 | 0.682264 | 0.341132 | − | 0.940015i | \(-0.389190\pi\) | ||||
0.341132 | + | 0.940015i | \(0.389190\pi\) | |||||||
\(942\) | 16.6274i | 0.541751i | ||||||||
\(943\) | 18.1005i | 0.589434i | ||||||||
\(944\) | 1.17157 | + | 1.17157i | 0.0381314 | + | 0.0381314i | ||||
\(945\) | 10.8284 | + | 32.4853i | 0.352249 | + | 1.05675i | ||||
\(946\) | 26.7990i | 0.871310i | ||||||||
\(947\) | 8.79899i | 0.285929i | 0.989728 | + | 0.142964i | \(0.0456634\pi\) | ||||
−0.989728 | + | 0.142964i | \(0.954337\pi\) | |||||||
\(948\) | 27.3137 | 0.887108 | ||||||||
\(949\) | −13.4558 | + | 13.4558i | −0.436795 | + | 0.436795i | ||||
\(950\) | −40.7990 | − | 5.82843i | −1.32369 | − | 0.189099i | ||||
\(951\) | 43.9411 | 1.42489 | ||||||||
\(952\) | 4.94975 | + | 4.94975i | 0.160422 | + | 0.160422i | ||||
\(953\) | −20.3431 | + | 20.3431i | −0.658979 | + | 0.658979i | −0.955139 | − | 0.296159i | \(-0.904294\pi\) |
0.296159 | + | 0.955139i | \(0.404294\pi\) | |||||||
\(954\) | 2.12132 | − | 2.12132i | 0.0686803 | − | 0.0686803i | ||||
\(955\) | −4.34315 | − | 2.17157i | −0.140541 | − | 0.0702704i | ||||
\(956\) | −7.05025 | − | 7.05025i | −0.228021 | − | 0.228021i | ||||
\(957\) | 72.6274 | 2.34771 | ||||||||
\(958\) | −15.5563 | − | 15.5563i | −0.502603 | − | 0.502603i | ||||
\(959\) | − | 45.5563i | − | 1.47109i | ||||||
\(960\) | 4.00000 | + | 2.00000i | 0.129099 | + | 0.0645497i | ||||
\(961\) | 2.97056i | 0.0958246i | ||||||||
\(962\) | 7.92893 | + | 11.1005i | 0.255639 | + | 0.357895i | ||||
\(963\) | 9.07107 | + | 9.07107i | 0.292311 | + | 0.292311i | ||||
\(964\) | 0.757359 | − | 0.757359i | 0.0243929 | − | 0.0243929i | ||||
\(965\) | 14.4853 | + | 43.4558i | 0.466298 | + | 1.39889i | ||||
\(966\) | − | 19.7990i | − | 0.637022i | ||||||
\(967\) | 53.9411i | 1.73463i | 0.497760 | + | 0.867315i | \(0.334156\pi\) | ||||
−0.497760 | + | 0.867315i | \(0.665844\pi\) | |||||||
\(968\) | −3.65685 | −0.117536 | ||||||||
\(969\) | − | 30.1421i | − | 0.968305i | ||||||
\(970\) | 14.8492 | − | 4.94975i | 0.476780 | − | 0.158927i | ||||
\(971\) | −53.7696 | −1.72555 | −0.862774 | − | 0.505591i | \(-0.831275\pi\) | ||||
−0.862774 | + | 0.505591i | \(0.831275\pi\) | |||||||
\(972\) | −7.07107 | + | 7.07107i | −0.226805 | + | 0.226805i | ||||
\(973\) | 16.7071 | − | 16.7071i | 0.535605 | − | 0.535605i | ||||
\(974\) | − | 26.9706i | − | 0.864193i | ||||||
\(975\) | 3.17157 | − | 22.2010i | 0.101572 | − | 0.711001i | ||||
\(976\) | 9.29289 | + | 9.29289i | 0.297458 | + | 0.297458i | ||||
\(977\) | 32.5147 | 1.04024 | 0.520119 | − | 0.854094i | \(-0.325888\pi\) | ||||
0.520119 | + | 0.854094i | \(0.325888\pi\) | |||||||
\(978\) | 20.7279 | + | 20.7279i | 0.662806 | + | 0.662806i | ||||
\(979\) | 28.3848 | + | 28.3848i | 0.907181 | + | 0.907181i | ||||
\(980\) | −16.2426 | + | 5.41421i | −0.518852 | + | 0.172951i | ||||
\(981\) | 0.949747 | − | 0.949747i | 0.0303231 | − | 0.0303231i | ||||
\(982\) | 17.7990 | 0.567989 | ||||||||
\(983\) | −30.6066 | + | 30.6066i | −0.976199 | + | 0.976199i | −0.999723 | − | 0.0235243i | \(-0.992511\pi\) |
0.0235243 | + | 0.999723i | \(0.492511\pi\) | |||||||
\(984\) | 9.89949 | + | 9.89949i | 0.315584 | + | 0.315584i | ||||
\(985\) | 5.65685 | + | 2.82843i | 0.180242 | + | 0.0901212i | ||||
\(986\) | 12.2635 | + | 12.2635i | 0.390548 | + | 0.390548i | ||||
\(987\) | −63.1127 | − | 63.1127i | −2.00890 | − | 2.00890i | ||||
\(988\) | 13.0711 | + | 13.0711i | 0.415846 | + | 0.415846i | ||||
\(989\) | 18.1005 | 0.575563 | ||||||||
\(990\) | 2.70711 | + | 8.12132i | 0.0860375 | + | 0.258113i | ||||
\(991\) | 38.8492 | + | 38.8492i | 1.23409 | + | 1.23409i | 0.962380 | + | 0.271707i | \(0.0875881\pi\) |
0.271707 | + | 0.962380i | \(0.412412\pi\) | |||||||
\(992\) | −4.12132 | − | 4.12132i | −0.130852 | − | 0.130852i | ||||
\(993\) | 7.31371i | 0.232094i | ||||||||
\(994\) | −0.928932 | + | 0.928932i | −0.0294639 | + | 0.0294639i | ||||
\(995\) | −11.0294 | − | 5.51472i | −0.349657 | − | 0.174828i | ||||
\(996\) | 2.34315 | 0.0742454 | ||||||||
\(997\) | − | 37.4558i | − | 1.18624i | −0.805115 | − | 0.593119i | \(-0.797896\pi\) | ||
0.805115 | − | 0.593119i | \(-0.202104\pi\) | |||||||
\(998\) | 10.2426 | − | 10.2426i | 0.324225 | − | 0.324225i | ||||
\(999\) | 4.00000 | − | 24.0000i | 0.126554 | − | 0.759326i |
(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 | 370.2.h.c.253.1 | yes | 4 | |
5.2 | odd | 4 | 370.2.g.c.327.2 | yes | 4 | ||
37.6 | odd | 4 | 370.2.g.c.43.2 | ✓ | 4 | ||
185.117 | even | 4 | inner | 370.2.h.c.117.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.g.c.43.2 | ✓ | 4 | 37.6 | odd | 4 | ||
370.2.g.c.327.2 | yes | 4 | 5.2 | odd | 4 | ||
370.2.h.c.117.1 | yes | 4 | 185.117 | even | 4 | inner | |
370.2.h.c.253.1 | yes | 4 | 1.1 | even | 1 | trivial |