Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [286,2,Mod(23,286)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(286, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("286.23");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 286 = 2 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 286.j (of order \(6\), 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: | \(2.28372149781\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 44x^{14} + 784x^{12} + 7200x^{10} + 35724x^{8} + 90936x^{6} + 101124x^{4} + 42336x^{2} + 5184 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 23.1 | ||
Root | \(-3.23409i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 286.23 |
Dual form | 286.2.j.b.199.1 |
$q$-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 \(\left(\mathbb{Z}/286\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −1.61705 | − | 2.80080i | −0.933602 | − | 1.61705i | −0.777109 | − | 0.629366i | \(-0.783315\pi\) |
−0.156493 | − | 0.987679i | \(-0.550019\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 2.38822i | 1.06805i | 0.845470 | + | 0.534023i | \(0.179320\pi\) | ||||
−0.845470 | + | 0.534023i | \(0.820680\pi\) | |||||||
\(6\) | 2.80080 | + | 1.61705i | 1.14342 | + | 0.660156i | ||||
\(7\) | 3.39370 | + | 1.95936i | 1.28270 | + | 0.740567i | 0.977341 | − | 0.211671i | \(-0.0678905\pi\) |
0.305358 | + | 0.952238i | \(0.401224\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −3.72967 | + | 6.45998i | −1.24322 | + | 2.15333i | ||||
\(10\) | −1.19411 | − | 2.06826i | −0.377611 | − | 0.654041i | ||||
\(11\) | 0.866025 | − | 0.500000i | 0.261116 | − | 0.150756i | ||||
\(12\) | −3.23409 | −0.933602 | ||||||||
\(13\) | 0.581485 | − | 3.55835i | 0.161275 | − | 0.986910i | ||||
\(14\) | −3.91871 | −1.04732 | ||||||||
\(15\) | 6.68894 | − | 3.86186i | 1.72708 | − | 0.997129i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.577065 | − | 0.999507i | 0.139959 | − | 0.242416i | −0.787522 | − | 0.616287i | \(-0.788636\pi\) |
0.927481 | + | 0.373871i | \(0.121970\pi\) | |||||||
\(18\) | − | 7.45934i | − | 1.75818i | ||||||
\(19\) | 7.24916 | + | 4.18531i | 1.66307 | + | 0.960175i | 0.971236 | + | 0.238121i | \(0.0765314\pi\) |
0.691836 | + | 0.722054i | \(0.256802\pi\) | |||||||
\(20\) | 2.06826 | + | 1.19411i | 0.462477 | + | 0.267011i | ||||
\(21\) | − | 12.6735i | − | 2.76558i | ||||||
\(22\) | −0.500000 | + | 0.866025i | −0.106600 | + | 0.184637i | ||||
\(23\) | −0.535560 | − | 0.927618i | −0.111672 | − | 0.193422i | 0.804772 | − | 0.593583i | \(-0.202287\pi\) |
−0.916445 | + | 0.400162i | \(0.868954\pi\) | |||||||
\(24\) | 2.80080 | − | 1.61705i | 0.571712 | − | 0.330078i | ||||
\(25\) | −0.703602 | −0.140720 | ||||||||
\(26\) | 1.27560 | + | 3.37237i | 0.250165 | + | 0.661375i | ||||
\(27\) | 14.4219 | 2.77550 | ||||||||
\(28\) | 3.39370 | − | 1.95936i | 0.641349 | − | 0.370283i | ||||
\(29\) | −1.06063 | − | 1.83706i | −0.196954 | − | 0.341134i | 0.750585 | − | 0.660773i | \(-0.229772\pi\) |
−0.947539 | + | 0.319639i | \(0.896438\pi\) | |||||||
\(30\) | −3.86186 | + | 6.68894i | −0.705076 | + | 1.22123i | ||||
\(31\) | − | 2.61922i | − | 0.470426i | −0.971944 | − | 0.235213i | \(-0.924421\pi\) | ||
0.971944 | − | 0.235213i | \(-0.0755787\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −2.80080 | − | 1.61705i | −0.487558 | − | 0.281491i | ||||
\(34\) | 1.15413i | 0.197932i | ||||||||
\(35\) | −4.67937 | + | 8.10491i | −0.790959 | + | 1.36998i | ||||
\(36\) | 3.72967 | + | 6.45998i | 0.621612 | + | 1.07666i | ||||
\(37\) | 1.01461 | − | 0.585786i | 0.166801 | − | 0.0963027i | −0.414276 | − | 0.910152i | \(-0.635965\pi\) |
0.581077 | + | 0.813849i | \(0.302632\pi\) | |||||||
\(38\) | −8.37061 | −1.35789 | ||||||||
\(39\) | −10.9065 | + | 4.12539i | −1.74644 | + | 0.660591i | ||||
\(40\) | −2.38822 | −0.377611 | ||||||||
\(41\) | −4.75743 | + | 2.74670i | −0.742986 | + | 0.428963i | −0.823154 | − | 0.567818i | \(-0.807788\pi\) |
0.0801682 | + | 0.996781i | \(0.474454\pi\) | |||||||
\(42\) | 6.33673 | + | 10.9755i | 0.977779 | + | 1.69356i | ||||
\(43\) | 2.85415 | − | 4.94354i | 0.435254 | − | 0.753883i | −0.562062 | − | 0.827095i | \(-0.689992\pi\) |
0.997316 | + | 0.0732123i | \(0.0233251\pi\) | |||||||
\(44\) | − | 1.00000i | − | 0.150756i | ||||||
\(45\) | −15.4279 | − | 8.90728i | −2.29985 | − | 1.32782i | ||||
\(46\) | 0.927618 | + | 0.535560i | 0.136770 | + | 0.0789641i | ||||
\(47\) | 7.13295i | 1.04045i | 0.854030 | + | 0.520224i | \(0.174152\pi\) | ||||
−0.854030 | + | 0.520224i | \(0.825848\pi\) | |||||||
\(48\) | −1.61705 | + | 2.80080i | −0.233400 | + | 0.404261i | ||||
\(49\) | 4.17814 | + | 7.23676i | 0.596878 | + | 1.03382i | ||||
\(50\) | 0.609337 | − | 0.351801i | 0.0861733 | − | 0.0497522i | ||||
\(51\) | −3.73256 | −0.522663 | ||||||||
\(52\) | −2.79088 | − | 2.28276i | −0.387026 | − | 0.316561i | ||||
\(53\) | 10.5155 | 1.44441 | 0.722207 | − | 0.691677i | \(-0.243128\pi\) | ||||
0.722207 | + | 0.691677i | \(0.243128\pi\) | |||||||
\(54\) | −12.4897 | + | 7.21096i | −1.69964 | + | 0.981287i | ||||
\(55\) | 1.19411 | + | 2.06826i | 0.161014 | + | 0.278884i | ||||
\(56\) | −1.95936 | + | 3.39370i | −0.261830 | + | 0.453503i | ||||
\(57\) | − | 27.0713i | − | 3.58568i | ||||||
\(58\) | 1.83706 | + | 1.06063i | 0.241218 | + | 0.139267i | ||||
\(59\) | 5.58283 | + | 3.22325i | 0.726822 | + | 0.419631i | 0.817258 | − | 0.576271i | \(-0.195493\pi\) |
−0.0904364 | + | 0.995902i | \(0.528826\pi\) | |||||||
\(60\) | − | 7.72372i | − | 0.997129i | ||||||
\(61\) | −4.49730 | + | 7.78954i | −0.575820 | + | 0.997349i | 0.420132 | + | 0.907463i | \(0.361984\pi\) |
−0.995952 | + | 0.0898860i | \(0.971350\pi\) | |||||||
\(62\) | 1.30961 | + | 2.26831i | 0.166321 | + | 0.288076i | ||||
\(63\) | −25.3148 | + | 14.6155i | −3.18936 | + | 1.84138i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 8.49813 | + | 1.38871i | 1.05406 | + | 0.172249i | ||||
\(66\) | 3.23409 | 0.398089 | ||||||||
\(67\) | 7.43183 | − | 4.29077i | 0.907943 | − | 0.524201i | 0.0281741 | − | 0.999603i | \(-0.491031\pi\) |
0.879769 | + | 0.475402i | \(0.157697\pi\) | |||||||
\(68\) | −0.577065 | − | 0.999507i | −0.0699795 | − | 0.121208i | ||||
\(69\) | −1.73205 | + | 3.00000i | −0.208514 | + | 0.361158i | ||||
\(70\) | − | 9.35875i | − | 1.11858i | ||||||
\(71\) | 1.31292 | + | 0.758013i | 0.155815 | + | 0.0899596i | 0.575880 | − | 0.817534i | \(-0.304660\pi\) |
−0.420065 | + | 0.907494i | \(0.637993\pi\) | |||||||
\(72\) | −6.45998 | − | 3.72967i | −0.761316 | − | 0.439546i | ||||
\(73\) | 7.00309i | 0.819650i | 0.912164 | + | 0.409825i | \(0.134410\pi\) | ||||
−0.912164 | + | 0.409825i | \(0.865590\pi\) | |||||||
\(74\) | −0.585786 | + | 1.01461i | −0.0680963 | + | 0.117946i | ||||
\(75\) | 1.13776 | + | 1.97065i | 0.131377 | + | 0.227551i | ||||
\(76\) | 7.24916 | − | 4.18531i | 0.831536 | − | 0.480088i | ||||
\(77\) | 3.91871 | 0.446578 | ||||||||
\(78\) | 7.38264 | − | 9.02596i | 0.835920 | − | 1.02199i | ||||
\(79\) | −9.72593 | −1.09425 | −0.547126 | − | 0.837050i | \(-0.684278\pi\) | ||||
−0.547126 | + | 0.837050i | \(0.684278\pi\) | |||||||
\(80\) | 2.06826 | − | 1.19411i | 0.231239 | − | 0.133506i | ||||
\(81\) | −12.1319 | − | 21.0130i | −1.34799 | − | 2.33478i | ||||
\(82\) | 2.74670 | − | 4.75743i | 0.303323 | − | 0.525370i | ||||
\(83\) | − | 7.20240i | − | 0.790566i | −0.918559 | − | 0.395283i | \(-0.870647\pi\) | ||
0.918559 | − | 0.395283i | \(-0.129353\pi\) | |||||||
\(84\) | −10.9755 | − | 6.33673i | −1.19753 | − | 0.691394i | ||||
\(85\) | 2.38704 | + | 1.37816i | 0.258911 | + | 0.149482i | ||||
\(86\) | 5.70831i | 0.615543i | ||||||||
\(87\) | −3.43017 | + | 5.94123i | −0.367753 | + | 0.636967i | ||||
\(88\) | 0.500000 | + | 0.866025i | 0.0533002 | + | 0.0923186i | ||||
\(89\) | −11.0570 | + | 6.38373i | −1.17203 | + | 0.676674i | −0.954158 | − | 0.299302i | \(-0.903246\pi\) |
−0.217876 | + | 0.975976i | \(0.569913\pi\) | |||||||
\(90\) | 17.8146 | 1.87782 | ||||||||
\(91\) | 8.94546 | − | 10.9367i | 0.937739 | − | 1.14647i | ||||
\(92\) | −1.07112 | −0.111672 | ||||||||
\(93\) | −7.33592 | + | 4.23540i | −0.760700 | + | 0.439190i | ||||
\(94\) | −3.56648 | − | 6.17732i | −0.367854 | − | 0.637142i | ||||
\(95\) | −9.99544 | + | 17.3126i | −1.02551 | + | 1.77624i | ||||
\(96\) | − | 3.23409i | − | 0.330078i | ||||||
\(97\) | −14.5485 | − | 8.39957i | −1.47717 | − | 0.852847i | −0.477506 | − | 0.878628i | \(-0.658459\pi\) |
−0.999668 | + | 0.0257814i | \(0.991793\pi\) | |||||||
\(98\) | −7.23676 | − | 4.17814i | −0.731023 | − | 0.422056i | ||||
\(99\) | 7.45934i | 0.749692i | ||||||||
\(100\) | −0.351801 | + | 0.609337i | −0.0351801 | + | 0.0609337i | ||||
\(101\) | −7.56376 | − | 13.1008i | −0.752622 | − | 1.30358i | −0.946548 | − | 0.322564i | \(-0.895455\pi\) |
0.193926 | − | 0.981016i | \(-0.437878\pi\) | |||||||
\(102\) | 3.23250 | − | 1.86628i | 0.320065 | − | 0.184789i | ||||
\(103\) | 9.09330 | 0.895989 | 0.447995 | − | 0.894036i | \(-0.352138\pi\) | ||||
0.447995 | + | 0.894036i | \(0.352138\pi\) | |||||||
\(104\) | 3.55835 | + | 0.581485i | 0.348925 | + | 0.0570193i | ||||
\(105\) | 30.2670 | 2.95376 | ||||||||
\(106\) | −9.10668 | + | 5.25774i | −0.884519 | + | 0.510677i | ||||
\(107\) | 0.874109 | + | 1.51400i | 0.0845033 | + | 0.146364i | 0.905179 | − | 0.425030i | \(-0.139736\pi\) |
−0.820676 | + | 0.571394i | \(0.806403\pi\) | |||||||
\(108\) | 7.21096 | − | 12.4897i | 0.693875 | − | 1.20183i | ||||
\(109\) | 5.31756i | 0.509330i | 0.967029 | + | 0.254665i | \(0.0819651\pi\) | ||||
−0.967029 | + | 0.254665i | \(0.918035\pi\) | |||||||
\(110\) | −2.06826 | − | 1.19411i | −0.197201 | − | 0.113854i | ||||
\(111\) | −3.28135 | − | 1.89449i | −0.311452 | − | 0.179817i | ||||
\(112\) | − | 3.91871i | − | 0.370283i | ||||||
\(113\) | 0.475848 | − | 0.824192i | 0.0447640 | − | 0.0775335i | −0.842775 | − | 0.538266i | \(-0.819080\pi\) |
0.887539 | + | 0.460732i | \(0.152413\pi\) | |||||||
\(114\) | 13.5357 | + | 23.4444i | 1.26773 | + | 2.19577i | ||||
\(115\) | 2.21536 | − | 1.27904i | 0.206583 | − | 0.119271i | ||||
\(116\) | −2.12126 | −0.196954 | ||||||||
\(117\) | 20.8181 | + | 17.0279i | 1.92464 | + | 1.57423i | ||||
\(118\) | −6.44649 | −0.593448 | ||||||||
\(119\) | 3.91678 | − | 2.26135i | 0.359050 | − | 0.207298i | ||||
\(120\) | 3.86186 | + | 6.68894i | 0.352538 | + | 0.610614i | ||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | − | 8.99459i | − | 0.814332i | ||||||
\(123\) | 15.3860 | + | 8.88309i | 1.38731 | + | 0.800961i | ||||
\(124\) | −2.26831 | − | 1.30961i | −0.203700 | − | 0.117606i | ||||
\(125\) | 10.2608i | 0.917749i | ||||||||
\(126\) | 14.6155 | − | 25.3148i | 1.30205 | − | 2.25522i | ||||
\(127\) | −2.67520 | − | 4.63358i | −0.237385 | − | 0.411164i | 0.722578 | − | 0.691290i | \(-0.242957\pi\) |
−0.959963 | + | 0.280126i | \(0.909624\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −18.4612 | −1.62542 | ||||||||
\(130\) | −8.05396 | + | 3.04641i | −0.706379 | + | 0.267187i | ||||
\(131\) | −6.92979 | −0.605458 | −0.302729 | − | 0.953077i | \(-0.597898\pi\) | ||||
−0.302729 | + | 0.953077i | \(0.597898\pi\) | |||||||
\(132\) | −2.80080 | + | 1.61705i | −0.243779 | + | 0.140746i | ||||
\(133\) | 16.4010 | + | 28.4074i | 1.42215 | + | 2.46323i | ||||
\(134\) | −4.29077 | + | 7.43183i | −0.370666 | + | 0.642012i | ||||
\(135\) | 34.4427i | 2.96436i | ||||||||
\(136\) | 0.999507 | + | 0.577065i | 0.0857070 | + | 0.0494830i | ||||
\(137\) | 16.3343 | + | 9.43062i | 1.39553 | + | 0.805712i | 0.993921 | − | 0.110097i | \(-0.0351162\pi\) |
0.401613 | + | 0.915809i | \(0.368450\pi\) | |||||||
\(138\) | − | 3.46410i | − | 0.294884i | ||||||
\(139\) | 4.95718 | − | 8.58608i | 0.420462 | − | 0.728262i | −0.575522 | − | 0.817786i | \(-0.695201\pi\) |
0.995985 | + | 0.0895240i | \(0.0285346\pi\) | |||||||
\(140\) | 4.67937 | + | 8.10491i | 0.395479 | + | 0.684990i | ||||
\(141\) | 19.9780 | − | 11.5343i | 1.68245 | − | 0.971364i | ||||
\(142\) | −1.51603 | −0.127222 | ||||||||
\(143\) | −1.27560 | − | 3.37237i | −0.106671 | − | 0.282011i | ||||
\(144\) | 7.45934 | 0.621612 | ||||||||
\(145\) | 4.38732 | − | 2.53302i | 0.364347 | − | 0.210356i | ||||
\(146\) | −3.50155 | − | 6.06486i | −0.289790 | − | 0.501931i | ||||
\(147\) | 13.5125 | − | 23.4043i | 1.11449 | − | 1.93036i | ||||
\(148\) | − | 1.17157i | − | 0.0963027i | ||||||
\(149\) | −13.2403 | − | 7.64429i | −1.08469 | − | 0.626245i | −0.152531 | − | 0.988299i | \(-0.548742\pi\) |
−0.932157 | + | 0.362054i | \(0.882076\pi\) | |||||||
\(150\) | −1.97065 | − | 1.13776i | −0.160903 | − | 0.0928974i | ||||
\(151\) | − | 0.741721i | − | 0.0603604i | −0.999544 | − | 0.0301802i | \(-0.990392\pi\) | ||
0.999544 | − | 0.0301802i | \(-0.00960811\pi\) | |||||||
\(152\) | −4.18531 | + | 7.24916i | −0.339473 | + | 0.587985i | ||||
\(153\) | 4.30453 | + | 7.45566i | 0.348001 | + | 0.602755i | ||||
\(154\) | −3.39370 | + | 1.95936i | −0.273472 | + | 0.157889i | ||||
\(155\) | 6.25528 | 0.502436 | ||||||||
\(156\) | −1.88058 | + | 11.5080i | −0.150567 | + | 0.921380i | ||||
\(157\) | −23.2033 | −1.85182 | −0.925911 | − | 0.377742i | \(-0.876700\pi\) | ||||
−0.925911 | + | 0.377742i | \(0.876700\pi\) | |||||||
\(158\) | 8.42290 | − | 4.86297i | 0.670090 | − | 0.386877i | ||||
\(159\) | −17.0040 | − | 29.4518i | −1.34851 | − | 2.33568i | ||||
\(160\) | −1.19411 | + | 2.06826i | −0.0944027 | + | 0.163510i | ||||
\(161\) | − | 4.19741i | − | 0.330802i | ||||||
\(162\) | 21.0130 | + | 12.1319i | 1.65094 | + | 0.953171i | ||||
\(163\) | −16.2334 | − | 9.37237i | −1.27150 | − | 0.734101i | −0.296229 | − | 0.955117i | \(-0.595729\pi\) |
−0.975270 | + | 0.221016i | \(0.929063\pi\) | |||||||
\(164\) | 5.49341i | 0.428963i | ||||||||
\(165\) | 3.86186 | − | 6.68894i | 0.300646 | − | 0.520733i | ||||
\(166\) | 3.60120 | + | 6.23746i | 0.279507 | + | 0.484121i | ||||
\(167\) | −1.23326 | + | 0.712024i | −0.0954327 | + | 0.0550981i | −0.546957 | − | 0.837161i | \(-0.684214\pi\) |
0.451524 | + | 0.892259i | \(0.350880\pi\) | |||||||
\(168\) | 12.6735 | 0.977779 | ||||||||
\(169\) | −12.3238 | − | 4.13826i | −0.947981 | − | 0.318327i | ||||
\(170\) | −2.75632 | −0.211400 | ||||||||
\(171\) | −54.0740 | + | 31.2196i | −4.13514 | + | 2.38742i | ||||
\(172\) | −2.85415 | − | 4.94354i | −0.217627 | − | 0.376941i | ||||
\(173\) | 6.26263 | − | 10.8472i | 0.476139 | − | 0.824697i | −0.523487 | − | 0.852033i | \(-0.675369\pi\) |
0.999626 | + | 0.0273367i | \(0.00870262\pi\) | |||||||
\(174\) | − | 6.86034i | − | 0.520081i | ||||||
\(175\) | −2.38782 | − | 1.37861i | −0.180502 | − | 0.104213i | ||||
\(176\) | −0.866025 | − | 0.500000i | −0.0652791 | − | 0.0376889i | ||||
\(177\) | − | 20.8485i | − | 1.56707i | ||||||
\(178\) | 6.38373 | − | 11.0570i | 0.478481 | − | 0.828753i | ||||
\(179\) | −1.35506 | − | 2.34704i | −0.101282 | − | 0.175426i | 0.810931 | − | 0.585142i | \(-0.198961\pi\) |
−0.912213 | + | 0.409716i | \(0.865628\pi\) | |||||||
\(180\) | −15.4279 | + | 8.90728i | −1.14993 | + | 0.663910i | ||||
\(181\) | 2.96325 | 0.220257 | 0.110128 | − | 0.993917i | \(-0.464874\pi\) | ||||
0.110128 | + | 0.993917i | \(0.464874\pi\) | |||||||
\(182\) | −2.27867 | + | 13.9442i | −0.168906 | + | 1.03361i | ||||
\(183\) | 29.0893 | 2.15034 | ||||||||
\(184\) | 0.927618 | − | 0.535560i | 0.0683849 | − | 0.0394820i | ||||
\(185\) | 1.39899 | + | 2.42312i | 0.102856 | + | 0.178151i | ||||
\(186\) | 4.23540 | − | 7.33592i | 0.310554 | − | 0.537896i | ||||
\(187\) | − | 1.15413i | − | 0.0843984i | ||||||
\(188\) | 6.17732 | + | 3.56648i | 0.450527 | + | 0.260112i | ||||
\(189\) | 48.9437 | + | 28.2577i | 3.56013 | + | 2.05544i | ||||
\(190\) | − | 19.9909i | − | 1.45029i | ||||||
\(191\) | −5.38945 | + | 9.33480i | −0.389967 | + | 0.675443i | −0.992445 | − | 0.122693i | \(-0.960847\pi\) |
0.602478 | + | 0.798136i | \(0.294180\pi\) | |||||||
\(192\) | 1.61705 | + | 2.80080i | 0.116700 | + | 0.202131i | ||||
\(193\) | 18.1368 | − | 10.4713i | 1.30551 | − | 0.753739i | 0.324170 | − | 0.945999i | \(-0.394915\pi\) |
0.981344 | + | 0.192260i | \(0.0615815\pi\) | |||||||
\(194\) | 16.7991 | 1.20611 | ||||||||
\(195\) | −9.85235 | − | 26.0472i | −0.705541 | − | 1.86528i | ||||
\(196\) | 8.35629 | 0.596878 | ||||||||
\(197\) | −12.2126 | + | 7.05092i | −0.870109 | + | 0.502358i | −0.867384 | − | 0.497639i | \(-0.834201\pi\) |
−0.00272441 | + | 0.999996i | \(0.500867\pi\) | |||||||
\(198\) | −3.72967 | − | 6.45998i | −0.265056 | − | 0.459091i | ||||
\(199\) | −5.49270 | + | 9.51364i | −0.389367 | + | 0.674404i | −0.992365 | − | 0.123339i | \(-0.960640\pi\) |
0.602997 | + | 0.797743i | \(0.293973\pi\) | |||||||
\(200\) | − | 0.703602i | − | 0.0497522i | ||||||
\(201\) | −24.0352 | − | 13.8767i | −1.69531 | − | 0.978790i | ||||
\(202\) | 13.1008 | + | 7.56376i | 0.921770 | + | 0.532184i | ||||
\(203\) | − | 8.31260i | − | 0.583430i | ||||||
\(204\) | −1.86628 | + | 3.23250i | −0.130666 | + | 0.226320i | ||||
\(205\) | −6.55974 | − | 11.3618i | −0.458152 | − | 0.793542i | ||||
\(206\) | −7.87503 | + | 4.54665i | −0.548679 | + | 0.316780i | ||||
\(207\) | 7.98986 | 0.555333 | ||||||||
\(208\) | −3.37237 | + | 1.27560i | −0.233832 | + | 0.0884466i | ||||
\(209\) | 8.37061 | 0.579007 | ||||||||
\(210\) | −26.2120 | + | 15.1335i | −1.80880 | + | 1.04431i | ||||
\(211\) | −0.692499 | − | 1.19944i | −0.0476736 | − | 0.0825731i | 0.841204 | − | 0.540718i | \(-0.181847\pi\) |
−0.888878 | + | 0.458145i | \(0.848514\pi\) | |||||||
\(212\) | 5.25774 | − | 9.10668i | 0.361103 | − | 0.625449i | ||||
\(213\) | − | 4.90297i | − | 0.335946i | ||||||
\(214\) | −1.51400 | − | 0.874109i | −0.103495 | − | 0.0597528i | ||||
\(215\) | 11.8063 | + | 6.81635i | 0.805181 | + | 0.464871i | ||||
\(216\) | 14.4219i | 0.981287i | ||||||||
\(217\) | 5.13198 | − | 8.88885i | 0.348382 | − | 0.603414i | ||||
\(218\) | −2.65878 | − | 4.60514i | −0.180075 | − | 0.311899i | ||||
\(219\) | 19.6143 | − | 11.3243i | 1.32541 | − | 0.765227i | ||||
\(220\) | 2.38822 | 0.161014 | ||||||||
\(221\) | −3.22104 | − | 2.63460i | −0.216671 | − | 0.177222i | ||||
\(222\) | 3.78897 | 0.254299 | ||||||||
\(223\) | −7.24466 | + | 4.18271i | −0.485139 | + | 0.280095i | −0.722555 | − | 0.691313i | \(-0.757033\pi\) |
0.237417 | + | 0.971408i | \(0.423699\pi\) | |||||||
\(224\) | 1.95936 | + | 3.39370i | 0.130915 | + | 0.226751i | ||||
\(225\) | 2.62420 | − | 4.54526i | 0.174947 | − | 0.303017i | ||||
\(226\) | 0.951695i | 0.0633058i | ||||||||
\(227\) | 0.569919 | + | 0.329043i | 0.0378268 | + | 0.0218393i | 0.518794 | − | 0.854899i | \(-0.326381\pi\) |
−0.480967 | + | 0.876739i | \(0.659714\pi\) | |||||||
\(228\) | −23.4444 | − | 13.5357i | −1.55265 | − | 0.896421i | ||||
\(229\) | 5.21273i | 0.344467i | 0.985056 | + | 0.172233i | \(0.0550983\pi\) | ||||
−0.985056 | + | 0.172233i | \(0.944902\pi\) | |||||||
\(230\) | −1.27904 | + | 2.21536i | −0.0843372 | + | 0.146076i | ||||
\(231\) | −6.33673 | − | 10.9755i | −0.416926 | − | 0.722138i | ||||
\(232\) | 1.83706 | − | 1.06063i | 0.120609 | − | 0.0696337i | ||||
\(233\) | −8.82754 | −0.578311 | −0.289156 | − | 0.957282i | \(-0.593375\pi\) | ||||
−0.289156 | + | 0.957282i | \(0.593375\pi\) | |||||||
\(234\) | −26.5430 | − | 4.33750i | −1.73517 | − | 0.283551i | ||||
\(235\) | −17.0351 | −1.11125 | ||||||||
\(236\) | 5.58283 | − | 3.22325i | 0.363411 | − | 0.209815i | ||||
\(237\) | 15.7273 | + | 27.2404i | 1.02160 | + | 1.76946i | ||||
\(238\) | −2.26135 | + | 3.91678i | −0.146582 | + | 0.253887i | ||||
\(239\) | − | 7.30848i | − | 0.472746i | −0.971662 | − | 0.236373i | \(-0.924041\pi\) | ||
0.971662 | − | 0.236373i | \(-0.0759588\pi\) | |||||||
\(240\) | −6.68894 | − | 3.86186i | −0.431769 | − | 0.249282i | ||||
\(241\) | −13.4873 | − | 7.78691i | −0.868795 | − | 0.501599i | −0.00184744 | − | 0.999998i | \(-0.500588\pi\) |
−0.866948 | + | 0.498399i | \(0.833921\pi\) | |||||||
\(242\) | 1.00000i | 0.0642824i | ||||||||
\(243\) | −17.6027 | + | 30.4888i | −1.12922 | + | 1.95586i | ||||
\(244\) | 4.49730 | + | 7.78954i | 0.287910 | + | 0.498674i | ||||
\(245\) | −17.2830 | + | 9.97833i | −1.10417 | + | 0.637492i | ||||
\(246\) | −17.7662 | −1.13273 | ||||||||
\(247\) | 19.1081 | − | 23.3614i | 1.21582 | − | 1.48645i | ||||
\(248\) | 2.61922 | 0.166321 | ||||||||
\(249\) | −20.1725 | + | 11.6466i | −1.27838 | + | 0.738074i | ||||
\(250\) | −5.13038 | − | 8.88607i | −0.324473 | − | 0.562004i | ||||
\(251\) | 9.13700 | − | 15.8258i | 0.576723 | − | 0.998913i | −0.419130 | − | 0.907926i | \(-0.637665\pi\) |
0.995852 | − | 0.0909863i | \(-0.0290020\pi\) | |||||||
\(252\) | 29.2310i | 1.84138i | ||||||||
\(253\) | −0.927618 | − | 0.535560i | −0.0583188 | − | 0.0336704i | ||||
\(254\) | 4.63358 | + | 2.67520i | 0.290737 | + | 0.167857i | ||||
\(255\) | − | 8.91419i | − | 0.558228i | ||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.87233 | − | 6.70707i | −0.241549 | − | 0.418376i | 0.719606 | − | 0.694382i | \(-0.244322\pi\) |
−0.961156 | + | 0.276006i | \(0.910989\pi\) | |||||||
\(258\) | 15.9879 | − | 9.23059i | 0.995361 | − | 0.574672i | ||||
\(259\) | 4.59105 | 0.285274 | ||||||||
\(260\) | 5.45173 | − | 6.66524i | 0.338102 | − | 0.413361i | ||||
\(261\) | 15.8232 | 0.979431 | ||||||||
\(262\) | 6.00137 | − | 3.46489i | 0.370766 | − | 0.214062i | ||||
\(263\) | −1.56963 | − | 2.71869i | −0.0967878 | − | 0.167641i | 0.813566 | − | 0.581473i | \(-0.197523\pi\) |
−0.910353 | + | 0.413832i | \(0.864190\pi\) | |||||||
\(264\) | 1.61705 | − | 2.80080i | 0.0995223 | − | 0.172378i | ||||
\(265\) | 25.1133i | 1.54270i | ||||||||
\(266\) | −28.4074 | − | 16.4010i | −1.74177 | − | 1.00561i | ||||
\(267\) | 35.7592 | + | 20.6456i | 2.18843 | + | 1.26349i | ||||
\(268\) | − | 8.58154i | − | 0.524201i | ||||||
\(269\) | −1.98821 | + | 3.44369i | −0.121224 | + | 0.209965i | −0.920250 | − | 0.391330i | \(-0.872015\pi\) |
0.799027 | + | 0.601295i | \(0.205348\pi\) | |||||||
\(270\) | −17.2214 | − | 29.8283i | −1.04806 | − | 1.81529i | ||||
\(271\) | −9.92563 | + | 5.73056i | −0.602939 | + | 0.348107i | −0.770197 | − | 0.637806i | \(-0.779842\pi\) |
0.167258 | + | 0.985913i | \(0.446509\pi\) | |||||||
\(272\) | −1.15413 | −0.0699795 | ||||||||
\(273\) | −45.0967 | − | 7.36943i | −2.72937 | − | 0.446018i | ||||
\(274\) | −18.8612 | −1.13945 | ||||||||
\(275\) | −0.609337 | + | 0.351801i | −0.0367444 | + | 0.0212144i | ||||
\(276\) | 1.73205 | + | 3.00000i | 0.104257 | + | 0.180579i | ||||
\(277\) | −1.35793 | + | 2.35200i | −0.0815900 | + | 0.141318i | −0.903933 | − | 0.427674i | \(-0.859333\pi\) |
0.822343 | + | 0.568992i | \(0.192666\pi\) | |||||||
\(278\) | 9.91435i | 0.594623i | ||||||||
\(279\) | 16.9201 | + | 9.76883i | 1.01298 | + | 0.584844i | ||||
\(280\) | −8.10491 | − | 4.67937i | −0.484361 | − | 0.279646i | ||||
\(281\) | 9.61705i | 0.573705i | 0.957975 | + | 0.286853i | \(0.0926090\pi\) | ||||
−0.957975 | + | 0.286853i | \(0.907391\pi\) | |||||||
\(282\) | −11.5343 | + | 19.9780i | −0.686858 | + | 1.18967i | ||||
\(283\) | 4.64628 | + | 8.04759i | 0.276193 | + | 0.478380i | 0.970435 | − | 0.241361i | \(-0.0775939\pi\) |
−0.694243 | + | 0.719741i | \(0.744261\pi\) | |||||||
\(284\) | 1.31292 | − | 0.758013i | 0.0779073 | − | 0.0449798i | ||||
\(285\) | 64.6523 | 3.82967 | ||||||||
\(286\) | 2.79088 | + | 2.28276i | 0.165028 | + | 0.134982i | ||||
\(287\) | −21.5271 | −1.27070 | ||||||||
\(288\) | −6.45998 | + | 3.72967i | −0.380658 | + | 0.219773i | ||||
\(289\) | 7.83399 | + | 13.5689i | 0.460823 | + | 0.798169i | ||||
\(290\) | −2.53302 | + | 4.38732i | −0.148744 | + | 0.257632i | ||||
\(291\) | 54.3299i | 3.18488i | ||||||||
\(292\) | 6.06486 | + | 3.50155i | 0.354919 | + | 0.204913i | ||||
\(293\) | −29.2907 | − | 16.9110i | −1.71118 | − | 0.987950i | −0.932976 | − | 0.359938i | \(-0.882798\pi\) |
−0.778204 | − | 0.628012i | \(-0.783869\pi\) | |||||||
\(294\) | 27.0250i | 1.57613i | ||||||||
\(295\) | −7.69783 | + | 13.3330i | −0.448185 | + | 0.776279i | ||||
\(296\) | 0.585786 | + | 1.01461i | 0.0340481 | + | 0.0589731i | ||||
\(297\) | 12.4897 | − | 7.21096i | 0.724729 | − | 0.418422i | ||||
\(298\) | 15.2886 | 0.885644 | ||||||||
\(299\) | −3.61221 | + | 1.36632i | −0.208900 | + | 0.0790162i | ||||
\(300\) | 2.27551 | 0.131377 | ||||||||
\(301\) | 19.3723 | − | 11.1846i | 1.11660 | − | 0.644670i | ||||
\(302\) | 0.370860 | + | 0.642349i | 0.0213406 | + | 0.0369630i | ||||
\(303\) | −24.4619 | + | 42.3692i | −1.40530 | + | 2.43405i | ||||
\(304\) | − | 8.37061i | − | 0.480088i | ||||||
\(305\) | −18.6032 | − | 10.7405i | −1.06521 | − | 0.615001i | ||||
\(306\) | −7.45566 | − | 4.30453i | −0.426212 | − | 0.246074i | ||||
\(307\) | 6.77842i | 0.386865i | 0.981114 | + | 0.193432i | \(0.0619620\pi\) | ||||
−0.981114 | + | 0.193432i | \(0.938038\pi\) | |||||||
\(308\) | 1.95936 | − | 3.39370i | 0.111645 | − | 0.193374i | ||||
\(309\) | −14.7043 | − | 25.4685i | −0.836497 | − | 1.44885i | ||||
\(310\) | −5.41723 | + | 3.12764i | −0.307678 | + | 0.177638i | ||||
\(311\) | 12.4786 | 0.707598 | 0.353799 | − | 0.935322i | \(-0.384890\pi\) | ||||
0.353799 | + | 0.935322i | \(0.384890\pi\) | |||||||
\(312\) | −4.12539 | − | 10.9065i | −0.233554 | − | 0.617461i | ||||
\(313\) | −12.5453 | −0.709101 | −0.354550 | − | 0.935037i | \(-0.615366\pi\) | ||||
−0.354550 | + | 0.935037i | \(0.615366\pi\) | |||||||
\(314\) | 20.0946 | − | 11.6016i | 1.13400 | − | 0.654718i | ||||
\(315\) | −34.9051 | − | 60.4573i | −1.96668 | − | 3.40638i | ||||
\(316\) | −4.86297 | + | 8.42290i | −0.273563 | + | 0.473825i | ||||
\(317\) | − | 21.7954i | − | 1.22415i | −0.790800 | − | 0.612075i | \(-0.790335\pi\) | ||
0.790800 | − | 0.612075i | \(-0.209665\pi\) | |||||||
\(318\) | 29.4518 | + | 17.0040i | 1.65158 | + | 0.953538i | ||||
\(319\) | −1.83706 | − | 1.06063i | −0.102856 | − | 0.0593839i | ||||
\(320\) | − | 2.38822i | − | 0.133506i | ||||||
\(321\) | 2.82695 | − | 4.89641i | 0.157785 | − | 0.273291i | ||||
\(322\) | 2.09871 | + | 3.63507i | 0.116956 | + | 0.202574i | ||||
\(323\) | 8.36648 | − | 4.83039i | 0.465524 | − | 0.268770i | ||||
\(324\) | −24.2638 | −1.34799 | ||||||||
\(325\) | −0.409134 | + | 2.50366i | −0.0226947 | + | 0.138878i | ||||
\(326\) | 18.7447 | 1.03817 | ||||||||
\(327\) | 14.8934 | − | 8.59873i | 0.823609 | − | 0.475511i | ||||
\(328\) | −2.74670 | − | 4.75743i | −0.151661 | − | 0.262685i | ||||
\(329\) | −13.9760 | + | 24.2071i | −0.770521 | + | 1.33458i | ||||
\(330\) | 7.72372i | 0.425177i | ||||||||
\(331\) | 29.0919 | + | 16.7962i | 1.59903 | + | 0.923202i | 0.991674 | + | 0.128775i | \(0.0411043\pi\) |
0.607359 | + | 0.794428i | \(0.292229\pi\) | |||||||
\(332\) | −6.23746 | − | 3.60120i | −0.342325 | − | 0.197642i | ||||
\(333\) | 8.73916i | 0.478903i | ||||||||
\(334\) | 0.712024 | − | 1.23326i | 0.0389602 | − | 0.0674811i | ||||
\(335\) | 10.2473 | + | 17.7489i | 0.559870 | + | 0.969724i | ||||
\(336\) | −10.9755 | + | 6.33673i | −0.598765 | + | 0.345697i | ||||
\(337\) | −9.44785 | −0.514657 | −0.257329 | − | 0.966324i | \(-0.582842\pi\) | ||||
−0.257329 | + | 0.966324i | \(0.582842\pi\) | |||||||
\(338\) | 12.7418 | − | 2.57804i | 0.693063 | − | 0.140227i | ||||
\(339\) | −3.07787 | −0.167167 | ||||||||
\(340\) | 2.38704 | − | 1.37816i | 0.129456 | − | 0.0747412i | ||||
\(341\) | −1.30961 | − | 2.26831i | −0.0709193 | − | 0.122836i | ||||
\(342\) | 31.2196 | − | 54.0740i | 1.68816 | − | 2.92399i | ||||
\(343\) | 5.31490i | 0.286978i | ||||||||
\(344\) | 4.94354 | + | 2.85415i | 0.266538 | + | 0.153886i | ||||
\(345\) | −7.16466 | − | 4.13652i | −0.385733 | − | 0.222703i | ||||
\(346\) | 12.5253i | 0.673362i | ||||||||
\(347\) | 13.7611 | − | 23.8350i | 0.738737 | − | 1.27953i | −0.214328 | − | 0.976762i | \(-0.568756\pi\) |
0.953064 | − | 0.302768i | \(-0.0979106\pi\) | |||||||
\(348\) | 3.43017 | + | 5.94123i | 0.183877 | + | 0.318483i | ||||
\(349\) | −1.28701 | + | 0.743058i | −0.0688923 | + | 0.0397750i | −0.534050 | − | 0.845453i | \(-0.679331\pi\) |
0.465158 | + | 0.885228i | \(0.345997\pi\) | |||||||
\(350\) | 2.75721 | 0.147379 | ||||||||
\(351\) | 8.38613 | − | 51.3183i | 0.447618 | − | 2.73917i | ||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 27.6110 | − | 15.9412i | 1.46959 | − | 0.848466i | 0.470168 | − | 0.882577i | \(-0.344193\pi\) |
0.999418 | + | 0.0341110i | \(0.0108600\pi\) | |||||||
\(354\) | 10.4243 | + | 18.0554i | 0.554044 | + | 0.959632i | ||||
\(355\) | −1.81030 | + | 3.13554i | −0.0960809 | + | 0.166417i | ||||
\(356\) | 12.7675i | 0.676674i | ||||||||
\(357\) | −12.6672 | − | 7.31342i | −0.670420 | − | 0.387067i | ||||
\(358\) | 2.34704 | + | 1.35506i | 0.124045 | + | 0.0716173i | ||||
\(359\) | − | 18.3795i | − | 0.970034i | −0.874505 | − | 0.485017i | \(-0.838813\pi\) | ||
0.874505 | − | 0.485017i | \(-0.161187\pi\) | |||||||
\(360\) | 8.90728 | − | 15.4279i | 0.469455 | − | 0.813120i | ||||
\(361\) | 25.5336 | + | 44.2254i | 1.34387 | + | 2.32765i | ||||
\(362\) | −2.56625 | + | 1.48163i | −0.134879 | + | 0.0778725i | ||||
\(363\) | −3.23409 | −0.169746 | ||||||||
\(364\) | −4.99869 | − | 13.2153i | −0.262003 | − | 0.692671i | ||||
\(365\) | −16.7249 | −0.875423 | ||||||||
\(366\) | −25.1921 | + | 14.5447i | −1.31681 | + | 0.760262i | ||||
\(367\) | 11.0161 | + | 19.0805i | 0.575037 | + | 0.995994i | 0.996038 | + | 0.0889331i | \(0.0283457\pi\) |
−0.421000 | + | 0.907060i | \(0.638321\pi\) | |||||||
\(368\) | −0.535560 | + | 0.927618i | −0.0279180 | + | 0.0483554i | ||||
\(369\) | − | 40.9772i | − | 2.13319i | ||||||
\(370\) | −2.42312 | − | 1.39899i | −0.125972 | − | 0.0727299i | ||||
\(371\) | 35.6864 | + | 20.6036i | 1.85275 | + | 1.06968i | ||||
\(372\) | 8.47079i | 0.439190i | ||||||||
\(373\) | −6.25297 | + | 10.8305i | −0.323767 | + | 0.560780i | −0.981262 | − | 0.192678i | \(-0.938283\pi\) |
0.657495 | + | 0.753459i | \(0.271616\pi\) | |||||||
\(374\) | 0.577065 | + | 0.999507i | 0.0298393 | + | 0.0516833i | ||||
\(375\) | 28.7384 | − | 16.5921i | 1.48404 | − | 0.856812i | ||||
\(376\) | −7.13295 | −0.367854 | ||||||||
\(377\) | −7.15366 | + | 2.70587i | −0.368432 | + | 0.139359i | ||||
\(378\) | −56.5153 | −2.90683 | ||||||||
\(379\) | −1.85398 | + | 1.07040i | −0.0952326 | + | 0.0549826i | −0.546860 | − | 0.837224i | \(-0.684177\pi\) |
0.451627 | + | 0.892207i | \(0.350844\pi\) | |||||||
\(380\) | 9.99544 | + | 17.3126i | 0.512755 | + | 0.888118i | ||||
\(381\) | −8.65183 | + | 14.9854i | −0.443247 | + | 0.767726i | ||||
\(382\) | − | 10.7789i | − | 0.551497i | ||||||
\(383\) | −31.9266 | − | 18.4328i | −1.63137 | − | 0.941873i | −0.983670 | − | 0.179980i | \(-0.942397\pi\) |
−0.647702 | − | 0.761894i | \(-0.724270\pi\) | |||||||
\(384\) | −2.80080 | − | 1.61705i | −0.142928 | − | 0.0825195i | ||||
\(385\) | 9.35875i | 0.476966i | ||||||||
\(386\) | −10.4713 | + | 18.1368i | −0.532974 | + | 0.923138i | ||||
\(387\) | 21.2901 | + | 36.8756i | 1.08224 | + | 1.87449i | ||||
\(388\) | −14.5485 | + | 8.39957i | −0.738587 | + | 0.426423i | ||||
\(389\) | −3.62824 | −0.183959 | −0.0919794 | − | 0.995761i | \(-0.529319\pi\) | ||||
−0.0919794 | + | 0.995761i | \(0.529319\pi\) | |||||||
\(390\) | 21.5560 | + | 17.6314i | 1.09153 | + | 0.892800i | ||||
\(391\) | −1.23621 | −0.0625180 | ||||||||
\(392\) | −7.23676 | + | 4.17814i | −0.365511 | + | 0.211028i | ||||
\(393\) | 11.2058 | + | 19.4090i | 0.565257 | + | 0.979053i | ||||
\(394\) | 7.05092 | − | 12.2126i | 0.355220 | − | 0.615260i | ||||
\(395\) | − | 23.2277i | − | 1.16871i | ||||||
\(396\) | 6.45998 | + | 3.72967i | 0.324626 | + | 0.187423i | ||||
\(397\) | 11.5249 | + | 6.65393i | 0.578420 | + | 0.333951i | 0.760505 | − | 0.649332i | \(-0.224951\pi\) |
−0.182085 | + | 0.983283i | \(0.558285\pi\) | |||||||
\(398\) | − | 10.9854i | − | 0.550648i | ||||||
\(399\) | 53.0423 | − | 91.8720i | 2.65544 | − | 4.59935i | ||||
\(400\) | 0.351801 | + | 0.609337i | 0.0175901 | + | 0.0304669i | ||||
\(401\) | 9.01085 | − | 5.20242i | 0.449981 | − | 0.259796i | −0.257841 | − | 0.966187i | \(-0.583011\pi\) |
0.707822 | + | 0.706391i | \(0.249678\pi\) | |||||||
\(402\) | 27.7535 | 1.38422 | ||||||||
\(403\) | −9.32011 | − | 1.52304i | −0.464268 | − | 0.0758679i | ||||
\(404\) | −15.1275 | −0.752622 | ||||||||
\(405\) | 50.1838 | − | 28.9736i | 2.49365 | − | 1.43971i | ||||
\(406\) | 4.15630 | + | 7.19892i | 0.206274 | + | 0.357276i | ||||
\(407\) | 0.585786 | − | 1.01461i | 0.0290363 | − | 0.0502924i | ||||
\(408\) | − | 3.73256i | − | 0.184789i | ||||||
\(409\) | −16.8420 | − | 9.72376i | −0.832786 | − | 0.480809i | 0.0220198 | − | 0.999758i | \(-0.492990\pi\) |
−0.854806 | + | 0.518949i | \(0.826324\pi\) | |||||||
\(410\) | 11.3618 | + | 6.55974i | 0.561119 | + | 0.323962i | ||||
\(411\) | − | 60.9989i | − | 3.00886i | ||||||
\(412\) | 4.54665 | − | 7.87503i | 0.223997 | − | 0.387975i | ||||
\(413\) | 12.6310 | + | 21.8775i | 0.621529 | + | 1.07652i | ||||
\(414\) | −6.91942 | + | 3.99493i | −0.340071 | + | 0.196340i | ||||
\(415\) | 17.2009 | 0.844360 | ||||||||
\(416\) | 2.28276 | − | 2.79088i | 0.111921 | − | 0.136834i | ||||
\(417\) | −32.0639 | −1.57018 | ||||||||
\(418\) | −7.24916 | + | 4.18531i | −0.354568 | + | 0.204710i | ||||
\(419\) | 6.36864 | + | 11.0308i | 0.311129 | + | 0.538890i | 0.978607 | − | 0.205739i | \(-0.0659597\pi\) |
−0.667478 | + | 0.744629i | \(0.732626\pi\) | |||||||
\(420\) | 15.1335 | − | 26.2120i | 0.738440 | − | 1.27902i | ||||
\(421\) | 21.2899i | 1.03761i | 0.854894 | + | 0.518803i | \(0.173622\pi\) | ||||
−0.854894 | + | 0.518803i | \(0.826378\pi\) | |||||||
\(422\) | 1.19944 | + | 0.692499i | 0.0583880 | + | 0.0337103i | ||||
\(423\) | −46.0787 | − | 26.6036i | −2.24043 | − | 1.29351i | ||||
\(424\) | 10.5155i | 0.510677i | ||||||||
\(425\) | −0.406024 | + | 0.703255i | −0.0196951 | + | 0.0341129i | ||||
\(426\) | 2.45148 | + | 4.24609i | 0.118775 | + | 0.205724i | ||||
\(427\) | −30.5250 | + | 17.6236i | −1.47721 | + | 0.852866i | ||||
\(428\) | 1.74822 | 0.0845033 | ||||||||
\(429\) | −7.38264 | + | 9.02596i | −0.356437 | + | 0.435778i | ||||
\(430\) | −13.6327 | −0.657427 | ||||||||
\(431\) | 30.7867 | − | 17.7747i | 1.48294 | − | 0.856178i | 0.483132 | − | 0.875547i | \(-0.339499\pi\) |
0.999812 | + | 0.0193689i | \(0.00616571\pi\) | |||||||
\(432\) | −7.21096 | − | 12.4897i | −0.346937 | − | 0.600913i | ||||
\(433\) | −9.75895 | + | 16.9030i | −0.468985 | + | 0.812306i | −0.999371 | − | 0.0354498i | \(-0.988714\pi\) |
0.530386 | + | 0.847756i | \(0.322047\pi\) | |||||||
\(434\) | 10.2640i | 0.492686i | ||||||||
\(435\) | −14.1890 | − | 8.19201i | −0.680309 | − | 0.392777i | ||||
\(436\) | 4.60514 | + | 2.65878i | 0.220546 | + | 0.127332i | ||||
\(437\) | − | 8.96594i | − | 0.428899i | ||||||
\(438\) | −11.3243 | + | 19.6143i | −0.541097 | + | 0.937207i | ||||
\(439\) | −4.59965 | − | 7.96683i | −0.219529 | − | 0.380236i | 0.735135 | − | 0.677921i | \(-0.237119\pi\) |
−0.954664 | + | 0.297685i | \(0.903786\pi\) | |||||||
\(440\) | −2.06826 | + | 1.19411i | −0.0986005 | + | 0.0569270i | ||||
\(441\) | −62.3324 | −2.96821 | ||||||||
\(442\) | 4.10680 | + | 0.671110i | 0.195341 | + | 0.0319214i | ||||
\(443\) | −9.27465 | −0.440652 | −0.220326 | − | 0.975426i | \(-0.570712\pi\) | ||||
−0.220326 | + | 0.975426i | \(0.570712\pi\) | |||||||
\(444\) | −3.28135 | + | 1.89449i | −0.155726 | + | 0.0899083i | ||||
\(445\) | −15.2458 | − | 26.4064i | −0.722719 | − | 1.25179i | ||||
\(446\) | 4.18271 | − | 7.24466i | 0.198057 | − | 0.343045i | ||||
\(447\) | 49.4447i | 2.33865i | ||||||||
\(448\) | −3.39370 | − | 1.95936i | −0.160337 | − | 0.0925708i | ||||
\(449\) | 5.66250 | + | 3.26925i | 0.267230 | + | 0.154285i | 0.627628 | − | 0.778513i | \(-0.284026\pi\) |
−0.360398 | + | 0.932799i | \(0.617359\pi\) | |||||||
\(450\) | 5.24841i | 0.247412i | ||||||||
\(451\) | −2.74670 | + | 4.75743i | −0.129337 | + | 0.224019i | ||||
\(452\) | −0.475848 | − | 0.824192i | −0.0223820 | − | 0.0387668i | ||||
\(453\) | −2.07742 | + | 1.19940i | −0.0976055 | + | 0.0563526i | ||||
\(454\) | −0.658085 | −0.0308855 | ||||||||
\(455\) | 26.1192 | + | 21.3637i | 1.22448 | + | 1.00155i | ||||
\(456\) | 27.0713 | 1.26773 | ||||||||
\(457\) | 0.217086 | − | 0.125334i | 0.0101548 | − | 0.00586290i | −0.494914 | − | 0.868942i | \(-0.664800\pi\) |
0.505069 | + | 0.863079i | \(0.331467\pi\) | |||||||
\(458\) | −2.60636 | − | 4.51436i | −0.121787 | − | 0.210942i | ||||
\(459\) | 8.32239 | − | 14.4148i | 0.388456 | − | 0.672825i | ||||
\(460\) | − | 2.55807i | − | 0.119271i | ||||||
\(461\) | −16.8434 | − | 9.72457i | −0.784477 | − | 0.452918i | 0.0535374 | − | 0.998566i | \(-0.482950\pi\) |
−0.838015 | + | 0.545648i | \(0.816284\pi\) | |||||||
\(462\) | 10.9755 | + | 6.33673i | 0.510628 | + | 0.294811i | ||||
\(463\) | − | 12.1144i | − | 0.563005i | −0.959561 | − | 0.281502i | \(-0.909167\pi\) | ||
0.959561 | − | 0.281502i | \(-0.0908327\pi\) | |||||||
\(464\) | −1.06063 | + | 1.83706i | −0.0492385 | + | 0.0852836i | ||||
\(465\) | −10.1151 | − | 17.5198i | −0.469075 | − | 0.812462i | ||||
\(466\) | 7.64487 | − | 4.41377i | 0.354142 | − | 0.204464i | ||||
\(467\) | −7.68809 | −0.355762 | −0.177881 | − | 0.984052i | \(-0.556924\pi\) | ||||
−0.177881 | + | 0.984052i | \(0.556924\pi\) | |||||||
\(468\) | 25.1556 | − | 9.51511i | 1.16282 | − | 0.439836i | ||||
\(469\) | 33.6286 | 1.55282 | ||||||||
\(470\) | 14.7528 | − | 8.51754i | 0.680496 | − | 0.392885i | ||||
\(471\) | 37.5207 | + | 64.9878i | 1.72886 | + | 2.99448i | ||||
\(472\) | −3.22325 | + | 5.58283i | −0.148362 | + | 0.256970i | ||||
\(473\) | − | 5.70831i | − | 0.262468i | ||||||
\(474\) | −27.2404 | − | 15.7273i | −1.25119 | − | 0.722377i | ||||
\(475\) | −5.10053 | − | 2.94479i | −0.234028 | − | 0.135116i | ||||
\(476\) | − | 4.52270i | − | 0.207298i | ||||||
\(477\) | −39.2193 | + | 67.9299i | −1.79573 | + | 3.11029i | ||||
\(478\) | 3.65424 | + | 6.32933i | 0.167141 | + | 0.289497i | ||||
\(479\) | −11.8997 | + | 6.87030i | −0.543711 | + | 0.313912i | −0.746582 | − | 0.665294i | \(-0.768306\pi\) |
0.202870 | + | 0.979206i | \(0.434973\pi\) | |||||||
\(480\) | 7.72372 | 0.352538 | ||||||||
\(481\) | −1.49445 | − | 3.95097i | −0.0681412 | − | 0.180149i | ||||
\(482\) | 15.5738 | 0.709368 | ||||||||
\(483\) | −11.7561 | + | 6.78740i | −0.534922 | + | 0.308838i | ||||
\(484\) | −0.500000 | − | 0.866025i | −0.0227273 | − | 0.0393648i | ||||
\(485\) | 20.0600 | − | 34.7450i | 0.910879 | − | 1.57769i | ||||
\(486\) | − | 35.2054i | − | 1.59695i | ||||||
\(487\) | −3.81826 | − | 2.20447i | −0.173022 | − | 0.0998943i | 0.410988 | − | 0.911641i | \(-0.365184\pi\) |
−0.584010 | + | 0.811746i | \(0.698517\pi\) | |||||||
\(488\) | −7.78954 | − | 4.49730i | −0.352616 | − | 0.203583i | ||||
\(489\) | 60.6222i | 2.74143i | ||||||||
\(490\) | 9.97833 | − | 17.2830i | 0.450775 | − | 0.780766i | ||||
\(491\) | −9.46134 | − | 16.3875i | −0.426984 | − | 0.739558i | 0.569619 | − | 0.821909i | \(-0.307091\pi\) |
−0.996603 | + | 0.0823504i | \(0.973757\pi\) | |||||||
\(492\) | 15.3860 | − | 8.88309i | 0.693653 | − | 0.400481i | ||||
\(493\) | −2.44821 | −0.110262 | ||||||||
\(494\) | −4.86738 | + | 29.7856i | −0.218994 | + | 1.34012i | ||||
\(495\) | −17.8146 | −0.800705 | ||||||||
\(496\) | −2.26831 | + | 1.30961i | −0.101850 | + | 0.0588032i | ||||
\(497\) | 2.97043 | + | 5.14494i | 0.133242 | + | 0.230782i | ||||
\(498\) | 11.6466 | − | 20.1725i | 0.521897 | − | 0.903952i | ||||
\(499\) | − | 16.5285i | − | 0.739915i | −0.929049 | − | 0.369958i | \(-0.879372\pi\) | ||
0.929049 | − | 0.369958i | \(-0.120628\pi\) | |||||||
\(500\) | 8.88607 | + | 5.13038i | 0.397397 | + | 0.229437i | ||||
\(501\) | 3.98848 | + | 2.30275i | 0.178192 | + | 0.102879i | ||||
\(502\) | 18.2740i | 0.815609i | ||||||||
\(503\) | −14.0835 | + | 24.3933i | −0.627952 | + | 1.08764i | 0.360010 | + | 0.932948i | \(0.382773\pi\) |
−0.987962 | + | 0.154696i | \(0.950560\pi\) | |||||||
\(504\) | −14.6155 | − | 25.3148i | −0.651026 | − | 1.12761i | ||||
\(505\) | 31.2877 | − | 18.0639i | 1.39228 | − | 0.803834i | ||||
\(506\) | 1.07112 | 0.0476171 | ||||||||
\(507\) | 8.33761 | + | 41.2082i | 0.370286 | + | 1.83012i | ||||
\(508\) | −5.35040 | −0.237385 | ||||||||
\(509\) | 4.45335 | − | 2.57114i | 0.197391 | − | 0.113964i | −0.398047 | − | 0.917365i | \(-0.630312\pi\) |
0.595438 | + | 0.803401i | \(0.296978\pi\) | |||||||
\(510\) | 4.45709 | + | 7.71991i | 0.197363 | + | 0.341844i | ||||
\(511\) | −13.7215 | + | 23.7664i | −0.607005 | + | 1.05136i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 104.547 | + | 60.3601i | 4.61585 | + | 2.66497i | ||||
\(514\) | 6.70707 | + | 3.87233i | 0.295836 | + | 0.170801i | ||||
\(515\) | 21.7168i | 0.956957i | ||||||||
\(516\) | −9.23059 | + | 15.9879i | −0.406354 | + | 0.703826i | ||||
\(517\) | 3.56648 | + | 6.17732i | 0.156853 | + | 0.271678i | ||||
\(518\) | −3.97597 | + | 2.29553i | −0.174694 | + | 0.100860i | ||||
\(519\) | −40.5078 | −1.77810 | ||||||||
\(520\) | −1.38871 | + | 8.49813i | −0.0608992 | + | 0.372668i | ||||
\(521\) | 27.1371 | 1.18890 | 0.594449 | − | 0.804133i | \(-0.297370\pi\) | ||||
0.594449 | + | 0.804133i | \(0.297370\pi\) | |||||||
\(522\) | −13.7033 | + | 7.91160i | −0.599777 | + | 0.346281i | ||||
\(523\) | −6.51845 | − | 11.2903i | −0.285032 | − | 0.493690i | 0.687585 | − | 0.726104i | \(-0.258671\pi\) |
−0.972617 | + | 0.232414i | \(0.925337\pi\) | |||||||
\(524\) | −3.46489 | + | 6.00137i | −0.151365 | + | 0.262171i | ||||
\(525\) | 8.91708i | 0.389173i | ||||||||
\(526\) | 2.71869 | + | 1.56963i | 0.118540 | + | 0.0684393i | ||||
\(527\) | −2.61793 | − | 1.51146i | −0.114039 | − | 0.0658403i | ||||
\(528\) | 3.23409i | 0.140746i | ||||||||
\(529\) | 10.9264 | − | 18.9250i | 0.475059 | − | 0.822826i | ||||
\(530\) | −12.5567 | − | 21.7488i | −0.545426 | − | 0.944706i | ||||
\(531\) | −41.6442 | + | 24.0433i | −1.80720 | + | 1.04339i | ||||
\(532\) | 32.8020 | 1.42215 | ||||||||
\(533\) | 7.00737 | + | 18.5258i | 0.303523 | + | 0.802441i | ||||
\(534\) | −41.2911 | −1.78684 | ||||||||
\(535\) | −3.61577 | + | 2.08756i | −0.156323 | + | 0.0902533i | ||||
\(536\) | 4.29077 | + | 7.43183i | 0.185333 | + | 0.321006i | ||||
\(537\) | −4.38240 | + | 7.59054i | −0.189114 | + | 0.327556i | ||||
\(538\) | − | 3.97643i | − | 0.171436i | ||||||
\(539\) | 7.23676 | + | 4.17814i | 0.311709 | + | 0.179965i | ||||
\(540\) | 29.8283 | + | 17.2214i | 1.28360 | + | 0.741090i | ||||
\(541\) | 17.1543i | 0.737519i | 0.929525 | + | 0.368759i | \(0.120217\pi\) | ||||
−0.929525 | + | 0.368759i | \(0.879783\pi\) | |||||||
\(542\) | 5.73056 | − | 9.92563i | 0.246149 | − | 0.426342i | ||||
\(543\) | −4.79171 | − | 8.29949i | −0.205632 | − | 0.356165i | ||||
\(544\) | 0.999507 | − | 0.577065i | 0.0428535 | − | 0.0247415i | ||||
\(545\) | −12.6995 | −0.543987 | ||||||||
\(546\) | 42.7396 | − | 16.1662i | 1.82908 | − | 0.691850i | ||||
\(547\) | 5.19197 | 0.221992 | 0.110996 | − | 0.993821i | \(-0.464596\pi\) | ||||
0.110996 | + | 0.993821i | \(0.464596\pi\) | |||||||
\(548\) | 16.3343 | − | 9.43062i | 0.697767 | − | 0.402856i | ||||
\(549\) | −33.5469 | − | 58.1049i | −1.43175 | − | 2.47986i | ||||
\(550\) | 0.351801 | − | 0.609337i | 0.0150008 | − | 0.0259822i | ||||
\(551\) | − | 17.7562i | − | 0.756441i | ||||||
\(552\) | −3.00000 | − | 1.73205i | −0.127688 | − | 0.0737210i | ||||
\(553\) | −33.0069 | − | 19.0566i | −1.40360 | − | 0.810367i | ||||
\(554\) | − | 2.71586i | − | 0.115386i | ||||||
\(555\) | 4.52445 | − | 7.83658i | 0.192052 | − | 0.332644i | ||||
\(556\) | −4.95718 | − | 8.58608i | −0.210231 | − | 0.364131i | ||||
\(557\) | 21.7440 | − | 12.5539i | 0.921323 | − | 0.531926i | 0.0372661 | − | 0.999305i | \(-0.488135\pi\) |
0.884057 | + | 0.467379i | \(0.154802\pi\) | |||||||
\(558\) | −19.5377 | −0.827095 | ||||||||
\(559\) | −15.9312 | − | 13.0307i | −0.673819 | − | 0.551139i | ||||
\(560\) | 9.35875 | 0.395479 | ||||||||
\(561\) | −3.23250 | + | 1.86628i | −0.136476 | + | 0.0787945i | ||||
\(562\) | −4.80852 | − | 8.32861i | −0.202835 | − | 0.351321i | ||||
\(563\) | 17.1294 | − | 29.6689i | 0.721917 | − | 1.25040i | −0.238314 | − | 0.971188i | \(-0.576595\pi\) |
0.960231 | − | 0.279208i | \(-0.0900720\pi\) | |||||||
\(564\) | − | 23.0686i | − | 0.971364i | ||||||
\(565\) | 1.96835 | + | 1.13643i | 0.0828093 | + | 0.0478100i | ||||
\(566\) | −8.04759 | − | 4.64628i | −0.338266 | − | 0.195298i | ||||
\(567\) | − | 95.0826i | − | 3.99310i | ||||||
\(568\) | −0.758013 | + | 1.31292i | −0.0318055 | + | 0.0550888i | ||||
\(569\) | 15.9081 | + | 27.5536i | 0.666901 | + | 1.15511i | 0.978766 | + | 0.204980i | \(0.0657129\pi\) |
−0.311865 | + | 0.950126i | \(0.600954\pi\) | |||||||
\(570\) | −55.9905 | + | 32.3262i | −2.34519 | + | 1.35399i | ||||
\(571\) | −40.2689 | −1.68520 | −0.842600 | − | 0.538540i | \(-0.818976\pi\) | ||||
−0.842600 | + | 0.538540i | \(0.818976\pi\) | |||||||
\(572\) | −3.55835 | − | 0.581485i | −0.148782 | − | 0.0243131i | ||||
\(573\) | 34.8599 | 1.45630 | ||||||||
\(574\) | 18.6430 | − | 10.7635i | 0.778143 | − | 0.449261i | ||||
\(575\) | 0.376821 | + | 0.652674i | 0.0157145 | + | 0.0272184i | ||||
\(576\) | 3.72967 | − | 6.45998i | 0.155403 | − | 0.269166i | ||||
\(577\) | − | 10.4030i | − | 0.433081i | −0.976274 | − | 0.216540i | \(-0.930523\pi\) | ||
0.976274 | − | 0.216540i | \(-0.0694773\pi\) | |||||||
\(578\) | −13.5689 | − | 7.83399i | −0.564391 | − | 0.325851i | ||||
\(579\) | −58.6560 | − | 33.8651i | −2.43766 | − | 1.40738i | ||||
\(580\) | − | 5.06604i | − | 0.210356i | ||||||
\(581\) | 14.1121 | − | 24.4428i | 0.585467 | − | 1.01406i | ||||
\(582\) | −27.1650 | − | 47.0511i | −1.12602 | − | 1.95033i | ||||
\(583\) | 9.10668 | − | 5.25774i | 0.377160 | − | 0.217754i | ||||
\(584\) | −7.00309 | −0.289790 | ||||||||
\(585\) | −40.6663 | + | 49.7183i | −1.68135 | + | 2.05560i | ||||
\(586\) | 33.8220 | 1.39717 | ||||||||
\(587\) | −7.55694 | + | 4.36300i | −0.311908 | + | 0.180080i | −0.647780 | − | 0.761827i | \(-0.724302\pi\) |
0.335872 | + | 0.941908i | \(0.390969\pi\) | |||||||
\(588\) | −13.5125 | − | 23.4043i | −0.557246 | − | 0.965178i | ||||
\(589\) | 10.9622 | − | 18.9871i | 0.451691 | − | 0.782352i | ||||
\(590\) | − | 15.3957i | − | 0.633829i | ||||||
\(591\) | 39.4965 | + | 22.8033i | 1.62467 | + | 0.938004i | ||||
\(592\) | −1.01461 | − | 0.585786i | −0.0417003 | − | 0.0240757i | ||||
\(593\) | 6.48140i | 0.266159i | 0.991105 | + | 0.133080i | \(0.0424866\pi\) | ||||
−0.991105 | + | 0.133080i | \(0.957513\pi\) | |||||||
\(594\) | −7.21096 | + | 12.4897i | −0.295869 | + | 0.512461i | ||||
\(595\) | 5.40061 | + | 9.35413i | 0.221403 | + | 0.383482i | ||||
\(596\) | −13.2403 | + | 7.64429i | −0.542344 | + | 0.313122i | ||||
\(597\) | 35.5278 | 1.45406 | ||||||||
\(598\) | 2.44511 | − | 2.98937i | 0.0999879 | − | 0.122244i | ||||
\(599\) | 29.7830 | 1.21690 | 0.608450 | − | 0.793593i | \(-0.291792\pi\) | ||||
0.608450 | + | 0.793593i | \(0.291792\pi\) | |||||||
\(600\) | −1.97065 | + | 1.13776i | −0.0804515 | + | 0.0464487i | ||||
\(601\) | 6.54759 | + | 11.3408i | 0.267082 | + | 0.462600i | 0.968107 | − | 0.250537i | \(-0.0806072\pi\) |
−0.701025 | + | 0.713137i | \(0.747274\pi\) | |||||||
\(602\) | −11.1846 | + | 19.3723i | −0.455850 | + | 0.789556i | ||||
\(603\) | 64.0126i | 2.60680i | ||||||||
\(604\) | −0.642349 | − | 0.370860i | −0.0261368 | − | 0.0150901i | ||||
\(605\) | 2.06826 | + | 1.19411i | 0.0840867 | + | 0.0485475i | ||||
\(606\) | − | 48.9238i | − | 1.98739i | ||||||
\(607\) | −0.852879 | + | 1.47723i | −0.0346173 | + | 0.0599589i | −0.882815 | − | 0.469721i | \(-0.844355\pi\) |
0.848198 | + | 0.529680i | \(0.177688\pi\) | |||||||
\(608\) | 4.18531 | + | 7.24916i | 0.169737 | + | 0.293992i | ||||
\(609\) | −23.2820 | + | 13.4418i | −0.943433 | + | 0.544691i | ||||
\(610\) | 21.4811 | 0.869743 | ||||||||
\(611\) | 25.3816 | + | 4.14771i | 1.02683 | + | 0.167798i | ||||
\(612\) | 8.60906 | 0.348001 | ||||||||
\(613\) | −4.79886 | + | 2.77062i | −0.193824 | + | 0.111904i | −0.593771 | − | 0.804634i | \(-0.702362\pi\) |
0.399948 | + | 0.916538i | \(0.369028\pi\) | |||||||
\(614\) | −3.38921 | − | 5.87029i | −0.136777 | − | 0.236905i | ||||
\(615\) | −21.2148 | + | 36.7451i | −0.855463 | + | 1.48170i | ||||
\(616\) | 3.91871i | 0.157889i | ||||||||
\(617\) | −11.5081 | − | 6.64420i | −0.463298 | − | 0.267485i | 0.250132 | − | 0.968212i | \(-0.419526\pi\) |
−0.713430 | + | 0.700726i | \(0.752859\pi\) | |||||||
\(618\) | 25.4685 | + | 14.7043i | 1.02450 | + | 0.591493i | ||||
\(619\) | 7.12717i | 0.286465i | 0.989689 | + | 0.143233i | \(0.0457497\pi\) | ||||
−0.989689 | + | 0.143233i | \(0.954250\pi\) | |||||||
\(620\) | 3.12764 | − | 5.41723i | 0.125609 | − | 0.217561i | ||||
\(621\) | −7.72381 | − | 13.3780i | −0.309946 | − | 0.536842i | ||||
\(622\) | −10.8068 | + | 6.23931i | −0.433313 | + | 0.250174i | ||||
\(623\) | −50.0320 | −2.00449 | ||||||||
\(624\) | 9.02596 | + | 7.38264i | 0.361328 | + | 0.295542i | ||||
\(625\) | −28.0230 | −1.12092 | ||||||||
\(626\) | 10.8645 | − | 6.27264i | 0.434234 | − | 0.250705i | ||||
\(627\) | −13.5357 | − | 23.4444i | −0.540562 | − | 0.936281i | ||||
\(628\) | −11.6016 | + | 20.0946i | −0.462955 | + | 0.801862i | ||||
\(629\) | − | 1.35215i | − | 0.0539137i | ||||||
\(630\) | 60.4573 | + | 34.9051i | 2.40868 | + | 1.39065i | ||||
\(631\) | 35.2594 | + | 20.3570i | 1.40366 | + | 0.810401i | 0.994766 | − | 0.102183i | \(-0.0325827\pi\) |
0.408890 | + | 0.912584i | \(0.365916\pi\) | |||||||
\(632\) | − | 9.72593i | − | 0.386877i | ||||||
\(633\) | −2.23961 | + | 3.87911i | −0.0890163 | + | 0.154181i | ||||
\(634\) | 10.8977 | + | 18.8753i | 0.432802 | + | 0.749636i | ||||
\(635\) | 11.0660 | − | 6.38897i | 0.439141 | − | 0.253538i | ||||
\(636\) | −34.0080 | −1.34851 | ||||||||
\(637\) | 28.1805 | − | 10.6592i | 1.11655 | − | 0.422335i | ||||
\(638\) | 2.12126 | 0.0839814 | ||||||||
\(639\) | −9.79350 | + | 5.65428i | −0.387425 | + | 0.223680i | ||||
\(640\) | 1.19411 | + | 2.06826i | 0.0472014 | + | 0.0817552i | ||||
\(641\) | −21.4093 | + | 37.0819i | −0.845615 | + | 1.46465i | 0.0394712 | + | 0.999221i | \(0.487433\pi\) |
−0.885086 | + | 0.465427i | \(0.845901\pi\) | |||||||
\(642\) | 5.65389i | 0.223141i | ||||||||
\(643\) | −35.9494 | − | 20.7554i | −1.41771 | − | 0.818513i | −0.421609 | − | 0.906778i | \(-0.638534\pi\) |
−0.996097 | + | 0.0882649i | \(0.971868\pi\) | |||||||
\(644\) | −3.63507 | − | 2.09871i | −0.143242 | − | 0.0827006i | ||||
\(645\) | − | 44.0894i | − | 1.73602i | ||||||
\(646\) | −4.83039 | + | 8.36648i | −0.190049 | + | 0.329175i | ||||
\(647\) | 13.4542 | + | 23.3034i | 0.528941 | + | 0.916153i | 0.999430 | + | 0.0337470i | \(0.0107440\pi\) |
−0.470489 | + | 0.882406i | \(0.655923\pi\) | |||||||
\(648\) | 21.0130 | − | 12.1319i | 0.825470 | − | 0.476585i | ||||
\(649\) | 6.44649 | 0.253047 | ||||||||
\(650\) | −0.897512 | − | 2.37280i | −0.0352033 | − | 0.0930690i | ||||
\(651\) | −33.1946 | −1.30100 | ||||||||
\(652\) | −16.2334 | + | 9.37237i | −0.635750 | + | 0.367050i | ||||
\(653\) | 1.68437 | + | 2.91741i | 0.0659143 | + | 0.114167i | 0.897099 | − | 0.441829i | \(-0.145670\pi\) |
−0.831185 | + | 0.555996i | \(0.812337\pi\) | |||||||
\(654\) | −8.59873 | + | 14.8934i | −0.336237 | + | 0.582380i | ||||
\(655\) | − | 16.5499i | − | 0.646657i | ||||||
\(656\) | 4.75743 | + | 2.74670i | 0.185746 | + | 0.107241i | ||||
\(657\) | −45.2398 | − | 26.1192i | −1.76497 | − | 1.01901i | ||||
\(658\) | − | 27.9520i | − | 1.08968i | ||||||
\(659\) | 19.5994 | − | 33.9472i | 0.763484 | − | 1.32239i | −0.177560 | − | 0.984110i | \(-0.556820\pi\) |
0.941044 | − | 0.338284i | \(-0.109846\pi\) | |||||||
\(660\) | −3.86186 | − | 6.68894i | −0.150323 | − | 0.260367i | ||||
\(661\) | −15.0024 | + | 8.66166i | −0.583527 | + | 0.336899i | −0.762534 | − | 0.646948i | \(-0.776045\pi\) |
0.179007 | + | 0.983848i | \(0.442712\pi\) | |||||||
\(662\) | −33.5924 | −1.30560 | ||||||||
\(663\) | −2.17043 | + | 13.2818i | −0.0842925 | + | 0.515822i | ||||
\(664\) | 7.20240 | 0.279507 | ||||||||
\(665\) | −67.8431 | + | 39.1692i | −2.63084 | + | 1.51892i | ||||
\(666\) | −4.36958 | − | 7.56833i | −0.169318 | − | 0.293267i | ||||
\(667\) | −1.13606 | + | 1.96772i | −0.0439885 | + | 0.0761903i | ||||
\(668\) | 1.42405i | 0.0550981i | ||||||||
\(669\) | 23.4299 | + | 13.5273i | 0.905852 | + | 0.522994i | ||||
\(670\) | −17.7489 | − | 10.2473i | −0.685698 | − | 0.395888i | ||||
\(671\) | 8.99459i | 0.347232i | ||||||||
\(672\) | 6.33673 | − | 10.9755i | 0.244445 | − | 0.423391i | ||||
\(673\) | −19.8511 | − | 34.3831i | −0.765204 | − | 1.32537i | −0.940139 | − | 0.340792i | \(-0.889305\pi\) |
0.174935 | − | 0.984580i | \(-0.444028\pi\) | |||||||
\(674\) | 8.18208 | − | 4.72393i | 0.315162 | − | 0.181959i | ||||
\(675\) | −10.1473 | −0.390569 | ||||||||
\(676\) | −9.74571 | + | 8.60355i | −0.374835 | + | 0.330906i | ||||
\(677\) | 13.0488 | 0.501506 | 0.250753 | − | 0.968051i | \(-0.419322\pi\) | ||||
0.250753 | + | 0.968051i | \(0.419322\pi\) | |||||||
\(678\) | 2.66551 | − | 1.53893i | 0.102368 | − | 0.0591024i | ||||
\(679\) | −32.9155 | − | 57.0113i | −1.26318 | − | 2.18789i | ||||
\(680\) | −1.37816 | + | 2.38704i | −0.0528500 | + | 0.0915389i | ||||
\(681\) | − | 2.12831i | − | 0.0815569i | ||||||
\(682\) | 2.26831 | + | 1.30961i | 0.0868581 | + | 0.0501475i | ||||
\(683\) | −2.79663 | − | 1.61464i | −0.107010 | − | 0.0617823i | 0.445540 | − | 0.895262i | \(-0.353012\pi\) |
−0.552550 | + | 0.833480i | \(0.686345\pi\) | |||||||
\(684\) | 62.4393i | 2.38742i | ||||||||
\(685\) | −22.5224 | + | 39.0100i | −0.860537 | + | 1.49049i | ||||
\(686\) | −2.65745 | − | 4.60284i | −0.101462 | − | 0.175737i | ||||
\(687\) | 14.5998 | − | 8.42922i | 0.557018 | − | 0.321595i | ||||
\(688\) | −5.70831 | −0.217627 | ||||||||
\(689\) | 6.11460 | − | 37.4178i | 0.232948 | − | 1.42551i | ||||
\(690\) | 8.27304 | 0.314949 | ||||||||
\(691\) | 10.0044 | − | 5.77607i | 0.380587 | − | 0.219732i | −0.297487 | − | 0.954726i | \(-0.596148\pi\) |
0.678074 | + | 0.734994i | \(0.262815\pi\) | |||||||
\(692\) | −6.26263 | − | 10.8472i | −0.238069 | − | 0.412348i | ||||
\(693\) | −14.6155 | + | 25.3148i | −0.555197 | + | 0.961629i | ||||
\(694\) | 27.5223i | 1.04473i | ||||||||
\(695\) | 20.5055 | + | 11.8388i | 0.777817 | + | 0.449073i | ||||
\(696\) | −5.94123 | − | 3.43017i | −0.225202 | − | 0.130020i | ||||
\(697\) | 6.34011i | 0.240149i | ||||||||
\(698\) | 0.743058 | − | 1.28701i | 0.0281252 | − | 0.0487142i | ||||
\(699\) | 14.2745 | + | 24.7242i | 0.539912 | + | 0.935156i | ||||
\(700\) | −2.38782 | + | 1.37861i | −0.0902510 | + | 0.0521064i | ||||
\(701\) | −21.2257 | −0.801683 | −0.400841 | − | 0.916147i | \(-0.631282\pi\) | ||||
−0.400841 | + | 0.916147i | \(0.631282\pi\) | |||||||
\(702\) | 18.3965 | + | 48.6360i | 0.694332 | + | 1.83565i | ||||
\(703\) | 9.80678 | 0.369870 | ||||||||
\(704\) | −0.866025 | + | 0.500000i | −0.0326396 | + | 0.0188445i | ||||
\(705\) | 27.5465 | + | 47.7119i | 1.03746 | + | 1.79693i | ||||
\(706\) | −15.9412 | + | 27.6110i | −0.599956 | + | 1.03915i | ||||
\(707\) | − | 59.2804i | − | 2.22947i | ||||||
\(708\) | −18.0554 | − | 10.4243i | −0.678562 | − | 0.391768i | ||||
\(709\) | 28.7567 | + | 16.6027i | 1.07998 | + | 0.623526i | 0.930891 | − | 0.365297i | \(-0.119033\pi\) |
0.149089 | + | 0.988824i | \(0.452366\pi\) | |||||||
\(710\) | − | 3.62061i | − | 0.135879i | ||||||
\(711\) | 36.2745 | − | 62.8293i | 1.36040 | − | 2.35628i | ||||
\(712\) | −6.38373 | − | 11.0570i | −0.239241 | − | 0.414377i | ||||
\(713\) | −2.42963 | + | 1.40275i | −0.0909905 | + | 0.0525334i | ||||
\(714\) | 14.6268 | 0.547396 | ||||||||
\(715\) | 8.05396 | − | 3.04641i | 0.301201 | − | 0.113929i | ||||
\(716\) | −2.71013 | −0.101282 | ||||||||
\(717\) | −20.4696 | + | 11.8181i | −0.764452 | + | 0.441357i | ||||
\(718\) | 9.18976 | + | 15.9171i | 0.342959 | + | 0.594022i | ||||
\(719\) | −12.6104 | + | 21.8419i | −0.470289 | + | 0.814564i | −0.999423 | − | 0.0339741i | \(-0.989184\pi\) |
0.529134 | + | 0.848538i | \(0.322517\pi\) | |||||||
\(720\) | 17.8146i | 0.663910i | ||||||||
\(721\) | 30.8599 | + | 17.8170i | 1.14928 | + | 0.663540i | ||||
\(722\) | −44.2254 | − | 25.5336i | −1.64590 | − | 0.950261i | ||||
\(723\) | 50.3672i | 1.87317i | ||||||||
\(724\) | 1.48163 | − | 2.56625i | 0.0550642 | − | 0.0953740i | ||||
\(725\) | 0.746261 | + | 1.29256i | 0.0277154 | + | 0.0480046i | ||||
\(726\) | 2.80080 | − | 1.61705i | 0.103948 | − | 0.0600142i | ||||
\(727\) | −42.4070 | −1.57279 | −0.786394 | − | 0.617725i | \(-0.788054\pi\) | ||||
−0.786394 | + | 0.617725i | \(0.788054\pi\) | |||||||
\(728\) | 10.9367 | + | 8.94546i | 0.405339 | + | 0.331541i | ||||
\(729\) | 41.0663 | 1.52098 | ||||||||
\(730\) | 14.4842 | − | 8.36247i | 0.536085 | − | 0.309509i | ||||
\(731\) | −3.29407 | − | 5.70549i | −0.121835 | − | 0.211025i | ||||
\(732\) | 14.5447 | − | 25.1921i | 0.537586 | − | 0.931126i | ||||
\(733\) | 31.0453i | 1.14669i | 0.819316 | + | 0.573343i | \(0.194354\pi\) | ||||
−0.819316 | + | 0.573343i | \(0.805646\pi\) | |||||||
\(734\) | −19.0805 | − | 11.0161i | −0.704274 | − | 0.406613i | ||||
\(735\) | 55.8947 | + | 32.2708i | 2.06171 | + | 1.19033i | ||||
\(736\) | − | 1.07112i | − | 0.0394820i | ||||||
\(737\) | 4.29077 | − | 7.43183i | 0.158053 | − | 0.273755i | ||||
\(738\) | 20.4886 | + | 35.4873i | 0.754196 | + | 1.30631i | ||||
\(739\) | −7.27048 | + | 4.19761i | −0.267449 | + | 0.154412i | −0.627728 | − | 0.778433i | \(-0.716015\pi\) |
0.360279 | + | 0.932845i | \(0.382682\pi\) | |||||||
\(740\) | 2.79797 | 0.102856 | ||||||||
\(741\) | −96.3293 | − | 15.7416i | −3.53875 | − | 0.578281i | ||||
\(742\) | −41.2072 | −1.51276 | ||||||||
\(743\) | 22.2340 | − | 12.8368i | 0.815688 | − | 0.470937i | −0.0332395 | − | 0.999447i | \(-0.510582\pi\) |
0.848927 | + | 0.528510i | \(0.177249\pi\) | |||||||
\(744\) | −4.23540 | − | 7.33592i | −0.155277 | − | 0.268948i | ||||
\(745\) | 18.2563 | − | 31.6208i | 0.668858 | − | 1.15850i | ||||
\(746\) | − | 12.5059i | − | 0.457875i | ||||||
\(747\) | 46.5274 | + | 26.8626i | 1.70235 | + | 0.982851i | ||||
\(748\) | −0.999507 | − | 0.577065i | −0.0365456 | − | 0.0210996i | ||||
\(749\) | 6.85076i | 0.250321i | ||||||||
\(750\) | −16.5921 | + | 28.7384i | −0.605858 | + | 1.04938i | ||||
\(751\) | −12.1212 | − | 20.9946i | −0.442310 | − | 0.766103i | 0.555551 | − | 0.831483i | \(-0.312508\pi\) |
−0.997860 | + | 0.0653796i | \(0.979174\pi\) | |||||||
\(752\) | 6.17732 | − | 3.56648i | 0.225264 | − | 0.130056i | ||||
\(753\) | −59.0998 | −2.15372 | ||||||||
\(754\) | 4.84232 | − | 5.92018i | 0.176347 | − | 0.215600i | ||||
\(755\) | 1.77139 | 0.0644676 | ||||||||
\(756\) | 48.9437 | − | 28.2577i | 1.78007 | − | 1.02772i | ||||
\(757\) | 21.2536 | + | 36.8123i | 0.772474 | + | 1.33796i | 0.936203 | + | 0.351459i | \(0.114314\pi\) |
−0.163729 | + | 0.986505i | \(0.552352\pi\) | |||||||
\(758\) | 1.07040 | − | 1.85398i | 0.0388785 | − | 0.0673396i | ||||
\(759\) | 3.46410i | 0.125739i | ||||||||
\(760\) | −17.3126 | − | 9.99544i | −0.627994 | − | 0.362573i | ||||
\(761\) | 26.6585 | + | 15.3913i | 0.966371 | + | 0.557935i | 0.898128 | − | 0.439734i | \(-0.144927\pi\) |
0.0682432 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(762\) | − | 17.3037i | − | 0.626846i | ||||||
\(763\) | −10.4190 | + | 18.0462i | −0.377193 | + | 0.653317i | ||||
\(764\) | 5.38945 | + | 9.33480i | 0.194983 | + | 0.337721i | ||||
\(765\) | −17.8058 | + | 10.2802i | −0.643769 | + | 0.371680i | ||||
\(766\) | 36.8656 | 1.33201 | ||||||||
\(767\) | 14.7158 | − | 17.9914i | 0.531356 | − | 0.649632i | ||||
\(768\) | 3.23409 | 0.116700 | ||||||||
\(769\) | 44.9612 | − | 25.9584i | 1.62134 | − | 0.936083i | 0.634783 | − | 0.772691i | \(-0.281090\pi\) |
0.986561 | − | 0.163393i | \(-0.0522438\pi\) | |||||||
\(770\) | −4.67937 | − | 8.10491i | −0.168633 | − | 0.292081i | ||||
\(771\) | −12.5235 | + | 21.6913i | −0.451022 | + | 0.781193i | ||||
\(772\) | − | 20.9426i | − | 0.753739i | ||||||
\(773\) | −5.44613 | − | 3.14433i | −0.195884 | − | 0.113094i | 0.398850 | − | 0.917016i | \(-0.369409\pi\) |
−0.594734 | + | 0.803922i | \(0.702743\pi\) | |||||||
\(774\) | −36.8756 | − | 21.2901i | −1.32546 | − | 0.765257i | ||||
\(775\) | 1.84289i | 0.0661985i | ||||||||
\(776\) | 8.39957 | − | 14.5485i | 0.301527 | − | 0.522260i | ||||
\(777\) | −7.42394 | − | 12.8586i | −0.266332 | − | 0.461301i | ||||
\(778\) | 3.14215 | − | 1.81412i | 0.112651 | − | 0.0650393i | ||||
\(779\) | −45.9832 | −1.64752 | ||||||||
\(780\) | −27.4837 | − | 4.49123i | −0.984076 | − | 0.160812i | ||||
\(781\) | 1.51603 | 0.0542477 | ||||||||
\(782\) | 1.07059 | − | 0.618107i | 0.0382843 | − | 0.0221035i | ||||
\(783\) | −15.2963 | − | 26.4940i | −0.546646 | − | 0.946818i | ||||
\(784\) | 4.17814 | − | 7.23676i | 0.149219 | − | 0.258456i | ||||
\(785\) | − | 55.4145i | − | 1.97783i | ||||||
\(786\) | −19.4090 | − | 11.2058i | −0.692295 | − | 0.399697i | ||||
\(787\) | −11.3186 | − | 6.53482i | −0.403466 | − | 0.232941i | 0.284512 | − | 0.958672i | \(-0.408168\pi\) |
−0.687979 | + | 0.725731i | \(0.741502\pi\) | |||||||
\(788\) | 14.1018i | 0.502358i | ||||||||
\(789\) | −5.07634 | + | 8.79248i | −0.180723 | + | 0.313021i | ||||
\(790\) | 11.6138 | + | 20.1158i | 0.413202 | + | 0.715687i | ||||
\(791\) | 3.22977 | − | 1.86471i | 0.114837 | − | 0.0663014i | ||||
\(792\) | −7.45934 | −0.265056 | ||||||||
\(793\) | 25.1028 | + | 20.5325i | 0.891428 | + | 0.729129i | ||||
\(794\) | −13.3079 | −0.472278 | ||||||||
\(795\) | 70.3375 | − | 40.6094i | 2.49461 | − | 1.44027i | ||||
\(796\) | 5.49270 | + | 9.51364i | 0.194684 | + | 0.337202i | ||||
\(797\) | −7.78060 | + | 13.4764i | −0.275603 | + | 0.477358i | −0.970287 | − | 0.241957i | \(-0.922211\pi\) |
0.694684 | + | 0.719315i | \(0.255544\pi\) | |||||||
\(798\) | 106.085i | 3.75536i | ||||||||
\(799\) | 7.12944 | + | 4.11618i | 0.252221 | + | 0.145620i | ||||
\(800\) | −0.609337 | − | 0.351801i | −0.0215433 | − | 0.0124380i | ||||
\(801\) | − | 95.2369i | − | 3.36503i | ||||||
\(802\) | −5.20242 | + | 9.01085i | −0.183704 | + | 0.318184i | ||||
\(803\) | 3.50155 | + | 6.06486i | 0.123567 | + | 0.214024i | ||||
\(804\) | −24.0352 | + | 13.8767i | −0.847657 | + | 0.489395i | ||||
\(805\) | 10.0243 | 0.353312 | ||||||||
\(806\) | 8.83297 | − | 3.34106i | 0.311128 | − | 0.117684i | ||||
\(807\) | 12.8601 | 0.452698 | ||||||||
\(808\) | 13.1008 | − | 7.56376i | 0.460885 | − | 0.266092i | ||||
\(809\) | −22.7081 | − | 39.3316i | −0.798374 | − | 1.38282i | −0.920674 | − | 0.390331i | \(-0.872360\pi\) |
0.122300 | − | 0.992493i | \(-0.460973\pi\) | |||||||
\(810\) | −28.9736 | + | 50.1838i | −1.01803 | + | 1.76328i | ||||
\(811\) | 3.39071i | 0.119064i | 0.998226 | + | 0.0595320i | \(0.0189608\pi\) | ||||
−0.998226 | + | 0.0595320i | \(0.981039\pi\) | |||||||
\(812\) | −7.19892 | − | 4.15630i | −0.252633 | − | 0.145858i | ||||
\(813\) | 32.1004 | + | 18.5332i | 1.12581 | + | 0.649987i | ||||
\(814\) | 1.17157i | 0.0410636i | ||||||||
\(815\) | 22.3833 | − | 38.7690i | 0.784053 | − | 1.35802i | ||||
\(816\) | 1.86628 | + | 3.23250i | 0.0653329 | + | 0.113160i | ||||
\(817\) | 41.3805 | − | 23.8910i | 1.44772 | − | 0.835841i | ||||
\(818\) | 19.4475 | 0.679967 | ||||||||
\(819\) | 37.2869 | + | 98.5776i | 1.30291 | + | 3.44458i | ||||
\(820\) | −13.1195 | −0.458152 | ||||||||
\(821\) | 8.03450 | − | 4.63872i | 0.280406 | − | 0.161893i | −0.353201 | − | 0.935547i | \(-0.614907\pi\) |
0.633607 | + | 0.773655i | \(0.281574\pi\) | |||||||
\(822\) | 30.4995 | + | 52.8266i | 1.06379 | + | 1.84254i | ||||
\(823\) | 15.3830 | − | 26.6441i | 0.536217 | − | 0.928754i | −0.462887 | − | 0.886417i | \(-0.653186\pi\) |
0.999103 | − | 0.0423370i | \(-0.0134803\pi\) | |||||||
\(824\) | 9.09330i | 0.316780i | ||||||||
\(825\) | 1.97065 | + | 1.13776i | 0.0686093 | + | 0.0396116i | ||||
\(826\) | −21.8775 | − | 12.6310i | −0.761215 | − | 0.439488i | ||||
\(827\) | − | 13.0368i | − | 0.453333i | −0.973972 | − | 0.226666i | \(-0.927217\pi\) | ||
0.973972 | − | 0.226666i | \(-0.0727827\pi\) | |||||||
\(828\) | 3.99493 | − | 6.91942i | 0.138833 | − | 0.240466i | ||||
\(829\) | −14.5790 | − | 25.2515i | −0.506348 | − | 0.877021i | −0.999973 | − | 0.00734588i | \(-0.997662\pi\) |
0.493625 | − | 0.869675i | \(-0.335672\pi\) | |||||||
\(830\) | −14.8964 | + | 8.60046i | −0.517063 | + | 0.298526i | ||||
\(831\) | 8.78332 | 0.304690 | ||||||||
\(832\) | −0.581485 | + | 3.55835i | −0.0201594 | + | 0.123364i | ||||
\(833\) | 9.64425 | 0.334153 | ||||||||
\(834\) | 27.7682 | − | 16.0320i | 0.961533 | − | 0.555141i | ||||
\(835\) | −1.70047 | − | 2.94530i | −0.0588472 | − | 0.101926i | ||||
\(836\) | 4.18531 | − | 7.24916i | 0.144752 | − | 0.250718i | ||||
\(837\) | − | 37.7742i | − | 1.30567i | ||||||
\(838\) | −11.0308 | − | 6.36864i | −0.381053 | − | 0.220001i | ||||
\(839\) | −10.0023 | − | 5.77483i | −0.345318 | − | 0.199369i | 0.317303 | − | 0.948324i | \(-0.397223\pi\) |
−0.662621 | + | 0.748955i | \(0.730556\pi\) | |||||||
\(840\) | 30.2670i | 1.04431i | ||||||||
\(841\) | 12.2501 | − | 21.2178i | 0.422418 | − | 0.731650i | ||||
\(842\) | −10.6449 | − | 18.4376i | −0.366849 | − | 0.635401i | ||||
\(843\) | 26.9355 | − | 15.5512i | 0.927707 | − | 0.535612i | ||||
\(844\) | −1.38500 | −0.0476736 | ||||||||
\(845\) | 9.88308 | − | 29.4318i | 0.339988 | − | 1.01249i | ||||
\(846\) | 53.2071 | 1.82930 | ||||||||
\(847\) | 3.39370 | − | 1.95936i | 0.116609 | − | 0.0673242i | ||||
\(848\) | −5.25774 | − | 9.10668i | −0.180552 | − | 0.312725i | ||||
\(849\) | 15.0265 | − | 26.0266i | 0.515708 | − | 0.893232i | ||||
\(850\) | − | 0.812049i | − | 0.0278530i | ||||||
\(851\) | −1.08677 | − | 0.627448i | −0.0372540 | − | 0.0215086i | ||||
\(852\) | −4.24609 | − | 2.45148i | −0.145469 | − | 0.0839864i | ||||
\(853\) | 47.4969i | 1.62626i | 0.582079 | + | 0.813132i | \(0.302239\pi\) | ||||
−0.582079 | + | 0.813132i | \(0.697761\pi\) | |||||||
\(854\) | 17.6236 | − | 30.5250i | 0.603067 | − | 1.04454i | ||||
\(855\) | −74.5594 | − | 129.141i | −2.54988 | − | 4.41652i | ||||
\(856\) | −1.51400 | + | 0.874109i | −0.0517475 | + | 0.0298764i | ||||
\(857\) | −24.1917 | −0.826372 | −0.413186 | − | 0.910647i | \(-0.635584\pi\) | ||||
−0.413186 | + | 0.910647i | \(0.635584\pi\) | |||||||
\(858\) | 1.88058 | − | 11.5080i | 0.0642018 | − | 0.392878i | ||||
\(859\) | −41.4686 | −1.41489 | −0.707446 | − | 0.706768i | \(-0.750153\pi\) | ||||
−0.707446 | + | 0.706768i | \(0.750153\pi\) | |||||||
\(860\) | 11.8063 | − | 6.81635i | 0.402590 | − | 0.232436i | ||||
\(861\) | 34.8102 | + | 60.2931i | 1.18633 | + | 2.05478i | ||||
\(862\) | −17.7747 | + | 30.7867i | −0.605410 | + | 1.04860i | ||||
\(863\) | − | 20.3423i | − | 0.692460i | −0.938150 | − | 0.346230i | \(-0.887462\pi\) | ||
0.938150 | − | 0.346230i | \(-0.112538\pi\) | |||||||
\(864\) | 12.4897 | + | 7.21096i | 0.424910 | + | 0.245322i | ||||
\(865\) | 25.9055 | + | 14.9565i | 0.880813 | + | 0.508538i | ||||
\(866\) | − | 19.5179i | − | 0.663245i | ||||||
\(867\) | 25.3358 | − | 43.8830i | 0.860450 | − | 1.49034i | ||||
\(868\) | −5.13198 | − | 8.88885i | −0.174191 | − | 0.301707i | ||||
\(869\) | −8.42290 | + | 4.86297i | −0.285727 | + | 0.164965i | ||||
\(870\) | 16.3840 | 0.555470 | ||||||||
\(871\) | −10.9466 | − | 28.9401i | −0.370911 | − | 0.980598i | ||||
\(872\) | −5.31756 | −0.180075 | ||||||||
\(873\) | 108.522 | − | 62.6552i | 3.67292 | − | 2.12056i | ||||
\(874\) | 4.48297 | + | 7.76473i | 0.151639 | + | 0.262646i | ||||
\(875\) | −20.1045 | + | 34.8219i | −0.679655 | + | 1.17720i | ||||
\(876\) | − | 22.6486i | − | 0.765227i | ||||||
\(877\) | 13.0950 | + | 7.56043i | 0.442188 | + | 0.255297i | 0.704525 | − | 0.709679i | \(-0.251160\pi\) |
−0.262337 | + | 0.964976i | \(0.584493\pi\) | |||||||
\(878\) | 7.96683 | + | 4.59965i | 0.268867 | + | 0.155231i | ||||
\(879\) | 109.383i | 3.68941i | ||||||||
\(880\) | 1.19411 | − | 2.06826i | 0.0402535 | − | 0.0697210i | ||||
\(881\) | 10.9581 | + | 18.9800i | 0.369188 | + | 0.639452i | 0.989439 | − | 0.144952i | \(-0.0463027\pi\) |
−0.620251 | + | 0.784403i | \(0.712969\pi\) | |||||||
\(882\) | 53.9815 | − | 31.1662i | 1.81765 | − | 1.04942i | ||||
\(883\) | 42.5451 | 1.43176 | 0.715878 | − | 0.698225i | \(-0.246027\pi\) | ||||
0.715878 | + | 0.698225i | \(0.246027\pi\) | |||||||
\(884\) | −3.89215 | + | 1.47220i | −0.130907 | + | 0.0495156i | ||||
\(885\) | 49.7909 | 1.67370 | ||||||||
\(886\) | 8.03208 | − | 4.63732i | 0.269843 | − | 0.155794i | ||||
\(887\) | −14.3781 | − | 24.9036i | −0.482769 | − | 0.836181i | 0.517035 | − | 0.855964i | \(-0.327036\pi\) |
−0.999804 | + | 0.0197834i | \(0.993702\pi\) | |||||||
\(888\) | 1.89449 | − | 3.28135i | 0.0635748 | − | 0.110115i | ||||
\(889\) | − | 20.9667i | − | 0.703199i | ||||||
\(890\) | 26.4064 | + | 15.2458i | 0.885146 | + | 0.511039i | ||||
\(891\) | −21.0130 | − | 12.1319i | −0.703963 | − | 0.406433i | ||||
\(892\) | 8.36542i | 0.280095i | ||||||||
\(893\) | −29.8536 | + | 51.7079i | −0.999012 | + | 1.73034i | ||||
\(894\) | −24.7223 | − | 42.8203i | −0.826839 | − | 1.43213i | ||||
\(895\) | 5.60525 | − | 3.23619i | 0.187363 | − | 0.108174i | ||||
\(896\) | 3.91871 | 0.130915 | ||||||||
\(897\) | 9.66790 | + | 7.90770i | 0.322802 | + | 0.264031i | ||||
\(898\) | −6.53849 | −0.218192 | ||||||||
\(899\) | −4.81167 | + | 2.77802i | −0.160478 | + | 0.0926522i | ||||
\(900\) | −2.62420 | − | 4.54526i | −0.0874735 | − | 0.151509i | ||||
\(901\) | 6.06813 | − | 10.5103i | 0.202159 | − | 0.350149i | ||||
\(902\) | − | 5.49341i | − | 0.182910i | ||||||
\(903\) | −62.6518 | − | 36.1720i | −2.08492 | − | 1.20373i | ||||
\(904\) | 0.824192 | + | 0.475848i | 0.0274122 | + | 0.0158265i | ||||
\(905\) | 7.07690i | 0.235244i | ||||||||
\(906\) | 1.19940 | − | 2.07742i | 0.0398473 | − | 0.0690175i | ||||
\(907\) | −21.7361 | − | 37.6480i | −0.721736 | − | 1.25008i | −0.960304 | − | 0.278957i | \(-0.910011\pi\) |
0.238568 | − | 0.971126i | \(-0.423322\pi\) | |||||||
\(908\) | 0.569919 | − | 0.329043i | 0.0189134 | − | 0.0109197i | ||||
\(909\) | 112.841 | 3.74271 | ||||||||
\(910\) | −33.3017 | − | 5.44197i | −1.10394 | − | 0.180400i | ||||
\(911\) | −20.1691 | −0.668232 | −0.334116 | − | 0.942532i | \(-0.608438\pi\) | ||||
−0.334116 | + | 0.942532i | \(0.608438\pi\) | |||||||
\(912\) | −23.4444 | + | 13.5357i | −0.776323 | + | 0.448210i | ||||
\(913\) | −3.60120 | − | 6.23746i | −0.119182 | − | 0.206430i | ||||
\(914\) | −0.125334 | + | 0.217086i | −0.00414570 | + | 0.00718056i | ||||
\(915\) | 69.4717i | 2.29666i | ||||||||
\(916\) | 4.51436 | + | 2.60636i | 0.149158 | + | 0.0861167i | ||||
\(917\) | −23.5176 | − | 13.5779i | −0.776621 | − | 0.448382i | ||||
\(918\) | 16.6448i | 0.549360i | ||||||||
\(919\) | 20.3495 | − | 35.2464i | 0.671269 | − | 1.16267i | −0.306276 | − | 0.951943i | \(-0.599083\pi\) |
0.977545 | − | 0.210729i | \(-0.0675837\pi\) | |||||||
\(920\) | 1.27904 | + | 2.21536i | 0.0421686 | + | 0.0730381i | ||||
\(921\) | 18.9850 | − | 10.9610i | 0.625578 | − | 0.361178i | ||||
\(922\) | 19.4491 | 0.640523 | ||||||||
\(923\) | 3.46072 | − | 4.23105i | 0.113911 | − | 0.139267i | ||||
\(924\) | −12.6735 | −0.416926 | ||||||||
\(925\) | −0.713883 | + | 0.412160i | −0.0234723 | + | 0.0135517i | ||||
\(926\) | 6.05721 | + | 10.4914i | 0.199052 | + | 0.344769i | ||||
\(927\) | −33.9150 | + | 58.7425i | −1.11391 | + | 1.92936i | ||||
\(928\) | − | 2.12126i | − | 0.0696337i | ||||||
\(929\) | 12.1067 | + | 6.98982i | 0.397209 | + | 0.229328i | 0.685279 | − | 0.728281i | \(-0.259680\pi\) |
−0.288070 | + | 0.957609i | \(0.593014\pi\) | |||||||
\(930\) | 17.5198 | + | 10.1151i | 0.574497 | + | 0.331686i | ||||
\(931\) | 69.9472i | 2.29243i | ||||||||
\(932\) | −4.41377 | + | 7.64487i | −0.144578 | + | 0.250416i | ||||
\(933\) | −20.1785 | − | 34.9502i | −0.660614 | − | 1.14422i | ||||
\(934\) | 6.65808 | − | 3.84404i | 0.217859 | − | 0.125781i | ||||
\(935\) | 2.75632 | 0.0901413 | ||||||||
\(936\) | −17.0279 | + | 20.8181i | −0.556573 | + | 0.680462i | ||||
\(937\) | −36.9852 | −1.20825 | −0.604126 | − | 0.796889i | \(-0.706478\pi\) | ||||
−0.604126 | + | 0.796889i | \(0.706478\pi\) | |||||||
\(938\) | −29.1232 | + | 16.8143i | −0.950906 | + | 0.549006i | ||||
\(939\) | 20.2863 | + | 35.1369i | 0.662018 | + | 1.14665i | ||||
\(940\) | −8.51754 | + | 14.7528i | −0.277811 | + | 0.481184i | ||||
\(941\) | 39.7092i | 1.29448i | 0.762286 | + | 0.647241i | \(0.224077\pi\) | ||||
−0.762286 | + | 0.647241i | \(0.775923\pi\) | |||||||
\(942\) | −64.9878 | − | 37.5207i | −2.11742 | − | 1.22249i | ||||
\(943\) | 5.09578 | + | 2.94205i | 0.165941 | + | 0.0958064i | ||||
\(944\) | − | 6.44649i | − | 0.209815i | ||||||
\(945\) | −67.4855 | + | 116.888i | −2.19530 | + | 3.80238i | ||||
\(946\) | 2.85415 | + | 4.94354i | 0.0927966 | + | 0.160728i | ||||
\(947\) | 42.8699 | − | 24.7510i | 1.39309 | − | 0.804298i | 0.399430 | − | 0.916764i | \(-0.369208\pi\) |
0.993656 | + | 0.112465i | \(0.0358747\pi\) | |||||||
\(948\) | 31.4545 | 1.02160 | ||||||||
\(949\) | 24.9195 | + | 4.07219i | 0.808920 | + | 0.132189i | ||||
\(950\) | 5.88958 | 0.191083 | ||||||||
\(951\) | −61.0446 | + | 35.2441i | −1.97951 | + | 1.14287i | ||||
\(952\) | 2.26135 | + | 3.91678i | 0.0732908 | + | 0.126943i | ||||
\(953\) | −16.8221 | + | 29.1367i | −0.544920 | + | 0.943829i | 0.453692 | + | 0.891159i | \(0.350107\pi\) |
−0.998612 | + | 0.0526704i | \(0.983227\pi\) | |||||||
\(954\) | − | 78.4386i | − | 2.53954i | ||||||
\(955\) | −22.2936 | − | 12.8712i | −0.721403 | − | 0.416502i | ||||
\(956\) | −6.32933 | − | 3.65424i | −0.204705 | − | 0.118187i | ||||
\(957\) | 6.86034i | 0.221763i | ||||||||
\(958\) | 6.87030 | − | 11.8997i | 0.221969 | − | 0.384462i | ||||
\(959\) | 36.9559 | + | 64.0094i | 1.19337 | + | 2.06697i | ||||
\(960\) | −6.68894 | + | 3.86186i | −0.215885 | + | 0.124641i | ||||
\(961\) | 24.1397 | 0.778700 | ||||||||
\(962\) | 3.26972 | + | 2.67442i | 0.105420 | + | 0.0862266i | ||||
\(963\) | −13.0405 | −0.420226 | ||||||||
\(964\) | −13.4873 | + | 7.78691i | −0.434398 | + | 0.250800i | ||||
\(965\) | 25.0077 | + | 43.3147i | 0.805027 | + | 1.39435i | ||||
\(966\) | 6.78740 | − | 11.7561i | 0.218381 | − | 0.378247i | ||||
\(967\) | 4.49705i | 0.144615i | 0.997382 | + | 0.0723077i | \(0.0230364\pi\) | ||||
−0.997382 | + | 0.0723077i | \(0.976964\pi\) | |||||||
\(968\) | 0.866025 | + | 0.500000i | 0.0278351 | + | 0.0160706i | ||||
\(969\) | −27.0580 | − | 15.6219i | −0.869227 | − | 0.501848i | ||||
\(970\) | 40.1201i | 1.28818i | ||||||||
\(971\) | −17.8306 | + | 30.8834i | −0.572210 | + | 0.991097i | 0.424129 | + | 0.905602i | \(0.360580\pi\) |
−0.996339 | + | 0.0854947i | \(0.972753\pi\) | |||||||
\(972\) | 17.6027 | + | 30.4888i | 0.564608 | + | 0.977929i | ||||
\(973\) | 33.6464 | − | 19.4257i | 1.07865 | − | 0.622761i | ||||
\(974\) | 4.40895 | 0.141272 | ||||||||
\(975\) | 7.67386 | − | 2.90263i | 0.245760 | − | 0.0929587i | ||||
\(976\) | 8.99459 | 0.287910 | ||||||||
\(977\) | −42.3506 | + | 24.4511i | −1.35492 | + | 0.782261i | −0.988933 | − | 0.148361i | \(-0.952600\pi\) |
−0.365982 | + | 0.930622i | \(0.619267\pi\) | |||||||
\(978\) | −30.3111 | − | 52.5003i | −0.969242 | − | 1.67878i | ||||
\(979\) | −6.38373 | + | 11.0570i | −0.204025 | + | 0.353382i | ||||
\(980\) | 19.9567i | 0.637492i | ||||||||
\(981\) | −34.3513 | − | 19.8327i | −1.09675 | − | 0.633211i | ||||
\(982\) | 16.3875 | + | 9.46134i | 0.522947 | + | 0.301923i | ||||
\(983\) | 48.2431i | 1.53872i | 0.638817 | + | 0.769359i | \(0.279424\pi\) | ||||
−0.638817 | + | 0.769359i | \(0.720576\pi\) | |||||||
\(984\) | −8.88309 | + | 15.3860i | −0.283183 | + | 0.490486i | ||||
\(985\) | −16.8392 | − | 29.1663i | −0.536541 | − | 0.929315i | ||||
\(986\) | 2.12021 | − | 1.22411i | 0.0675213 | − | 0.0389835i | ||||
\(987\) | 90.3992 | 2.87744 | ||||||||
\(988\) | −10.6775 | − | 28.2288i | −0.339697 | − | 0.898077i | ||||
\(989\) | −6.11429 | −0.194423 | ||||||||
\(990\) | 15.4279 | − | 8.90728i | 0.490330 | − | 0.283092i | ||||
\(991\) | 18.0962 | + | 31.3435i | 0.574844 | + | 0.995658i | 0.996059 | + | 0.0886976i | \(0.0282705\pi\) |
−0.421215 | + | 0.906961i | \(0.638396\pi\) | |||||||
\(992\) | 1.30961 | − | 2.26831i | 0.0415801 | − | 0.0720189i | ||||
\(993\) | − | 108.641i | − | 3.44761i | ||||||
\(994\) | −5.14494 | − | 2.97043i | −0.163188 | − | 0.0942165i | ||||
\(995\) | −22.7207 | − | 13.1178i | −0.720294 | − | 0.415862i | ||||
\(996\) | 23.2932i | 0.738074i | ||||||||
\(997\) | −10.5413 | + | 18.2580i | −0.333845 | + | 0.578236i | −0.983262 | − | 0.182196i | \(-0.941679\pi\) |
0.649417 | + | 0.760432i | \(0.275013\pi\) | |||||||
\(998\) | 8.26423 | + | 14.3141i | 0.261600 | + | 0.453104i | ||||
\(999\) | 14.6326 | − | 8.44816i | 0.462956 | − | 0.267288i |
(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 | 286.2.j.b.23.1 | ✓ | 16 | |
13.2 | odd | 12 | 3718.2.a.bn.1.8 | 8 | |||
13.4 | even | 6 | inner | 286.2.j.b.199.1 | yes | 16 | |
13.11 | odd | 12 | 3718.2.a.bo.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
286.2.j.b.23.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
286.2.j.b.199.1 | yes | 16 | 13.4 | even | 6 | inner | |
3718.2.a.bn.1.8 | 8 | 13.2 | odd | 12 | |||
3718.2.a.bo.1.8 | 8 | 13.11 | odd | 12 |