Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [798,2,Mod(457,798)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(798, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("798.457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 798.j (of order \(3\), 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: | \(6.37206208130\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.856615824.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 571.4 | ||
Root | \(-0.385731i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 798.571 |
Dual form | 798.2.j.l.457.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/798\mathbb{Z}\right)^\times\).
\(n\) | \(115\) | \(211\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.73065 | + | 2.99758i | 0.773971 | + | 1.34056i | 0.935371 | + | 0.353668i | \(0.115066\pi\) |
−0.161400 | + | 0.986889i | \(0.551601\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −2.36975 | + | 1.17656i | −0.895681 | + | 0.444696i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −1.73065 | + | 2.99758i | −0.547280 | + | 0.947917i | ||||
\(11\) | −0.139098 | + | 0.240925i | −0.0419397 | + | 0.0726418i | −0.886233 | − | 0.463239i | \(-0.846687\pi\) |
0.844294 | + | 0.535881i | \(0.180020\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 6.92261 | 1.91999 | 0.959993 | − | 0.280025i | \(-0.0903427\pi\) | ||||
0.959993 | + | 0.280025i | \(0.0903427\pi\) | |||||||
\(14\) | −2.20380 | − | 1.46399i | −0.588991 | − | 0.391267i | ||||
\(15\) | 3.46130 | 0.893705 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.89876 | + | 5.02079i | −0.703052 | + | 1.21772i | 0.264338 | + | 0.964430i | \(0.414846\pi\) |
−0.967390 | + | 0.253291i | \(0.918487\pi\) | |||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | −0.500000 | − | 0.866025i | −0.114708 | − | 0.198680i | ||||
\(20\) | −3.46130 | −0.773971 | ||||||||
\(21\) | −0.165947 | + | 2.64054i | −0.0362127 | + | 0.576213i | ||||
\(22\) | −0.278197 | −0.0593118 | ||||||||
\(23\) | −1.54617 | − | 2.67804i | −0.322398 | − | 0.558410i | 0.658584 | − | 0.752507i | \(-0.271156\pi\) |
−0.980982 | + | 0.194097i | \(0.937822\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | −3.49031 | + | 6.04539i | −0.698062 | + | 1.20908i | ||||
\(26\) | 3.46130 | + | 5.99515i | 0.678817 | + | 1.17575i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.165947 | − | 2.64054i | 0.0313611 | − | 0.499016i | ||||
\(29\) | −8.55364 | −1.58837 | −0.794185 | − | 0.607676i | \(-0.792102\pi\) | ||||
−0.794185 | + | 0.607676i | \(0.792102\pi\) | |||||||
\(30\) | 1.73065 | + | 2.99758i | 0.315972 | + | 0.547280i | ||||
\(31\) | −3.67480 | + | 6.36493i | −0.660013 | + | 1.14318i | 0.320599 | + | 0.947215i | \(0.396116\pi\) |
−0.980612 | + | 0.195961i | \(0.937218\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0.139098 | + | 0.240925i | 0.0242139 | + | 0.0419397i | ||||
\(34\) | −5.79751 | −0.994265 | ||||||||
\(35\) | −7.62803 | − | 5.06730i | −1.28937 | − | 0.856530i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.62056 | + | 4.53894i | 0.430817 | + | 0.746198i | 0.996944 | − | 0.0781207i | \(-0.0248920\pi\) |
−0.566126 | + | 0.824318i | \(0.691559\pi\) | |||||||
\(38\) | 0.500000 | − | 0.866025i | 0.0811107 | − | 0.140488i | ||||
\(39\) | 3.46130 | − | 5.99515i | 0.554252 | − | 0.959993i | ||||
\(40\) | −1.73065 | − | 2.99758i | −0.273640 | − | 0.473958i | ||||
\(41\) | 8.88553 | 1.38769 | 0.693843 | − | 0.720126i | \(-0.255916\pi\) | ||||
0.693843 | + | 0.720126i | \(0.255916\pi\) | |||||||
\(42\) | −2.36975 | + | 1.17656i | −0.365660 | + | 0.181547i | ||||
\(43\) | 10.3705 | 1.58149 | 0.790745 | − | 0.612145i | \(-0.209693\pi\) | ||||
0.790745 | + | 0.612145i | \(0.209693\pi\) | |||||||
\(44\) | −0.139098 | − | 0.240925i | −0.0209699 | − | 0.0363209i | ||||
\(45\) | 1.73065 | − | 2.99758i | 0.257990 | − | 0.446852i | ||||
\(46\) | 1.54617 | − | 2.67804i | 0.227970 | − | 0.394855i | ||||
\(47\) | 0.896599 | + | 1.55296i | 0.130782 | + | 0.226522i | 0.923978 | − | 0.382445i | \(-0.124918\pi\) |
−0.793196 | + | 0.608966i | \(0.791584\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 4.23143 | − | 5.57629i | 0.604490 | − | 0.796613i | ||||
\(50\) | −6.98062 | −0.987209 | ||||||||
\(51\) | 2.89876 | + | 5.02079i | 0.405907 | + | 0.703052i | ||||
\(52\) | −3.46130 | + | 5.99515i | −0.479996 | + | 0.831378i | ||||
\(53\) | −4.19411 | + | 7.26442i | −0.576106 | + | 0.997844i | 0.419815 | + | 0.907610i | \(0.362095\pi\) |
−0.995921 | + | 0.0902346i | \(0.971238\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | −0.962923 | −0.129841 | ||||||||
\(56\) | 2.36975 | − | 1.17656i | 0.316671 | − | 0.157224i | ||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | −4.27682 | − | 7.40767i | −0.561574 | − | 0.972674i | ||||
\(59\) | 3.89738 | − | 6.75046i | 0.507395 | − | 0.878835i | −0.492568 | − | 0.870274i | \(-0.663942\pi\) |
0.999963 | − | 0.00856059i | \(-0.00272495\pi\) | |||||||
\(60\) | −1.73065 | + | 2.99758i | −0.223426 | + | 0.386985i | ||||
\(61\) | −4.56470 | − | 7.90630i | −0.584450 | − | 1.01230i | −0.994944 | − | 0.100434i | \(-0.967977\pi\) |
0.410493 | − | 0.911864i | \(-0.365357\pi\) | |||||||
\(62\) | −7.34959 | −0.933399 | ||||||||
\(63\) | 2.20380 | + | 1.46399i | 0.277653 | + | 0.184445i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 11.9806 | + | 20.7510i | 1.48601 | + | 2.57385i | ||||
\(66\) | −0.139098 | + | 0.240925i | −0.0171218 | + | 0.0296559i | ||||
\(67\) | 6.86891 | − | 11.8973i | 0.839171 | − | 1.45349i | −0.0514182 | − | 0.998677i | \(-0.516374\pi\) |
0.890589 | − | 0.454809i | \(-0.150293\pi\) | |||||||
\(68\) | −2.89876 | − | 5.02079i | −0.351526 | − | 0.608861i | ||||
\(69\) | −3.09233 | −0.372273 | ||||||||
\(70\) | 0.574394 | − | 9.13972i | 0.0686532 | − | 1.09241i | ||||
\(71\) | 0.684727 | 0.0812621 | 0.0406311 | − | 0.999174i | \(-0.487063\pi\) | ||||
0.0406311 | + | 0.999174i | \(0.487063\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | 0.962682 | − | 1.66741i | 0.112673 | − | 0.195156i | −0.804174 | − | 0.594394i | \(-0.797392\pi\) |
0.916847 | + | 0.399238i | \(0.130725\pi\) | |||||||
\(74\) | −2.62056 | + | 4.53894i | −0.304634 | + | 0.527641i | ||||
\(75\) | 3.49031 | + | 6.04539i | 0.403026 | + | 0.698062i | ||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0.0461660 | − | 0.734590i | 0.00526111 | − | 0.0837143i | ||||
\(78\) | 6.92261 | 0.783831 | ||||||||
\(79\) | −0.703803 | − | 1.21902i | −0.0791840 | − | 0.137151i | 0.823714 | − | 0.567005i | \(-0.191898\pi\) |
−0.902898 | + | 0.429855i | \(0.858565\pi\) | |||||||
\(80\) | 1.73065 | − | 2.99758i | 0.193493 | − | 0.335139i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 4.44277 | + | 7.69509i | 0.490621 | + | 0.849781i | ||||
\(83\) | −0.146030 | −0.0160289 | −0.00801443 | − | 0.999968i | \(-0.502551\pi\) | ||||
−0.00801443 | + | 0.999968i | \(0.502551\pi\) | |||||||
\(84\) | −2.20380 | − | 1.46399i | −0.240455 | − | 0.159734i | ||||
\(85\) | −20.0670 | −2.17657 | ||||||||
\(86\) | 5.18526 | + | 8.98114i | 0.559141 | + | 0.968461i | ||||
\(87\) | −4.27682 | + | 7.40767i | −0.458523 | + | 0.794185i | ||||
\(88\) | 0.139098 | − | 0.240925i | 0.0148279 | − | 0.0256827i | ||||
\(89\) | 6.85037 | + | 11.8652i | 0.726138 | + | 1.25771i | 0.958504 | + | 0.285079i | \(0.0920199\pi\) |
−0.232366 | + | 0.972628i | \(0.574647\pi\) | |||||||
\(90\) | 3.46130 | 0.364853 | ||||||||
\(91\) | −16.4048 | + | 8.14484i | −1.71970 | + | 0.853811i | ||||
\(92\) | 3.09233 | 0.322398 | ||||||||
\(93\) | 3.67480 | + | 6.36493i | 0.381059 | + | 0.660013i | ||||
\(94\) | −0.896599 | + | 1.55296i | −0.0924771 | + | 0.160175i | ||||
\(95\) | 1.73065 | − | 2.99758i | 0.177561 | − | 0.307545i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | 4.09233 | 0.415513 | 0.207757 | − | 0.978181i | \(-0.433384\pi\) | ||||
0.207757 | + | 0.978181i | \(0.433384\pi\) | |||||||
\(98\) | 6.94492 | + | 0.876382i | 0.701543 | + | 0.0885279i | ||||
\(99\) | 0.278197 | 0.0279598 | ||||||||
\(100\) | −3.49031 | − | 6.04539i | −0.349031 | − | 0.604539i | ||||
\(101\) | 1.22849 | − | 2.12781i | 0.122240 | − | 0.211725i | −0.798411 | − | 0.602113i | \(-0.794326\pi\) |
0.920651 | + | 0.390388i | \(0.127659\pi\) | |||||||
\(102\) | −2.89876 | + | 5.02079i | −0.287020 | + | 0.497133i | ||||
\(103\) | −8.67342 | − | 15.0228i | −0.854617 | − | 1.48024i | −0.877000 | − | 0.480491i | \(-0.840459\pi\) |
0.0223826 | − | 0.999749i | \(-0.492875\pi\) | |||||||
\(104\) | −6.92261 | −0.678817 | ||||||||
\(105\) | −8.20242 | + | 4.07242i | −0.800475 | + | 0.397427i | ||||
\(106\) | −8.38823 | −0.814737 | ||||||||
\(107\) | 5.73896 | + | 9.94017i | 0.554806 | + | 0.960953i | 0.997919 | + | 0.0644867i | \(0.0205410\pi\) |
−0.443112 | + | 0.896466i | \(0.646126\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 9.34068 | − | 16.1785i | 0.894675 | − | 1.54962i | 0.0604685 | − | 0.998170i | \(-0.480741\pi\) |
0.834206 | − | 0.551452i | \(-0.185926\pi\) | |||||||
\(110\) | −0.481462 | − | 0.833916i | −0.0459056 | − | 0.0795108i | ||||
\(111\) | 5.24112 | 0.497465 | ||||||||
\(112\) | 2.20380 | + | 1.46399i | 0.208240 | + | 0.138334i | ||||
\(113\) | 3.29913 | 0.310356 | 0.155178 | − | 0.987886i | \(-0.450405\pi\) | ||||
0.155178 | + | 0.987886i | \(0.450405\pi\) | |||||||
\(114\) | −0.500000 | − | 0.866025i | −0.0468293 | − | 0.0811107i | ||||
\(115\) | 5.35175 | − | 9.26950i | 0.499053 | − | 0.864386i | ||||
\(116\) | 4.27682 | − | 7.40767i | 0.397093 | − | 0.687784i | ||||
\(117\) | −3.46130 | − | 5.99515i | −0.319998 | − | 0.554252i | ||||
\(118\) | 7.79476 | 0.717565 | ||||||||
\(119\) | 0.962082 | − | 15.3086i | 0.0881939 | − | 1.40334i | ||||
\(120\) | −3.46130 | −0.315972 | ||||||||
\(121\) | 5.46130 | + | 9.45925i | 0.496482 | + | 0.859932i | ||||
\(122\) | 4.56470 | − | 7.90630i | 0.413269 | − | 0.715803i | ||||
\(123\) | 4.44277 | − | 7.69509i | 0.400591 | − | 0.693843i | ||||
\(124\) | −3.67480 | − | 6.36493i | −0.330006 | − | 0.571588i | ||||
\(125\) | −6.85553 | −0.613177 | ||||||||
\(126\) | −0.165947 | + | 2.64054i | −0.0147838 | + | 0.235238i | ||||
\(127\) | −3.45699 | −0.306758 | −0.153379 | − | 0.988167i | \(-0.549016\pi\) | ||||
−0.153379 | + | 0.988167i | \(0.549016\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 5.18526 | − | 8.98114i | 0.456537 | − | 0.790745i | ||||
\(130\) | −11.9806 | + | 20.7510i | −1.05077 | + | 1.81999i | ||||
\(131\) | −9.24781 | − | 16.0177i | −0.807985 | − | 1.39947i | −0.914257 | − | 0.405134i | \(-0.867225\pi\) |
0.106272 | − | 0.994337i | \(-0.466108\pi\) | |||||||
\(132\) | −0.278197 | −0.0242139 | ||||||||
\(133\) | 2.20380 | + | 1.46399i | 0.191094 | + | 0.126944i | ||||
\(134\) | 13.7378 | 1.18677 | ||||||||
\(135\) | −1.73065 | − | 2.99758i | −0.148951 | − | 0.257990i | ||||
\(136\) | 2.89876 | − | 5.02079i | 0.248566 | − | 0.430530i | ||||
\(137\) | 6.08402 | − | 10.5378i | 0.519793 | − | 0.900308i | −0.479942 | − | 0.877300i | \(-0.659342\pi\) |
0.999735 | − | 0.0230078i | \(-0.00732427\pi\) | |||||||
\(138\) | −1.54617 | − | 2.67804i | −0.131618 | − | 0.227970i | ||||
\(139\) | −2.91829 | −0.247526 | −0.123763 | − | 0.992312i | \(-0.539496\pi\) | ||||
−0.123763 | + | 0.992312i | \(0.539496\pi\) | |||||||
\(140\) | 8.20242 | − | 4.07242i | 0.693231 | − | 0.344182i | ||||
\(141\) | 1.79320 | 0.151015 | ||||||||
\(142\) | 0.342363 | + | 0.592991i | 0.0287305 | + | 0.0497627i | ||||
\(143\) | −0.962923 | + | 1.66783i | −0.0805237 | + | 0.139471i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −14.8034 | − | 25.6402i | −1.22935 | − | 2.12930i | ||||
\(146\) | 1.92536 | 0.159344 | ||||||||
\(147\) | −2.71349 | − | 6.45267i | −0.223805 | − | 0.532207i | ||||
\(148\) | −5.24112 | −0.430817 | ||||||||
\(149\) | 2.08246 | + | 3.60693i | 0.170602 | + | 0.295491i | 0.938631 | − | 0.344924i | \(-0.112095\pi\) |
−0.768028 | + | 0.640416i | \(0.778762\pi\) | |||||||
\(150\) | −3.49031 | + | 6.04539i | −0.284983 | + | 0.493604i | ||||
\(151\) | −9.63772 | + | 16.6930i | −0.784306 | + | 1.35846i | 0.145106 | + | 0.989416i | \(0.453648\pi\) |
−0.929413 | + | 0.369043i | \(0.879686\pi\) | |||||||
\(152\) | 0.500000 | + | 0.866025i | 0.0405554 | + | 0.0702439i | ||||
\(153\) | 5.79751 | 0.468701 | ||||||||
\(154\) | 0.659257 | − | 0.327314i | 0.0531244 | − | 0.0263757i | ||||
\(155\) | −25.4392 | −2.04332 | ||||||||
\(156\) | 3.46130 | + | 5.99515i | 0.277126 | + | 0.479996i | ||||
\(157\) | 10.7284 | − | 18.5822i | 0.856222 | − | 1.48302i | −0.0192847 | − | 0.999814i | \(-0.506139\pi\) |
0.875507 | − | 0.483206i | \(-0.160528\pi\) | |||||||
\(158\) | 0.703803 | − | 1.21902i | 0.0559915 | − | 0.0969802i | ||||
\(159\) | 4.19411 | + | 7.26442i | 0.332615 | + | 0.576106i | ||||
\(160\) | 3.46130 | 0.273640 | ||||||||
\(161\) | 6.81489 | + | 4.52713i | 0.537089 | + | 0.356788i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −7.97231 | − | 13.8084i | −0.624439 | − | 1.08156i | −0.988649 | − | 0.150244i | \(-0.951994\pi\) |
0.364209 | − | 0.931317i | \(-0.381339\pi\) | |||||||
\(164\) | −4.44277 | + | 7.69509i | −0.346922 | + | 0.600886i | ||||
\(165\) | −0.481462 | + | 0.833916i | −0.0374817 | + | 0.0649203i | ||||
\(166\) | −0.0730150 | − | 0.126466i | −0.00566706 | − | 0.00981564i | ||||
\(167\) | 17.6073 | 1.36250 | 0.681248 | − | 0.732053i | \(-0.261437\pi\) | ||||
0.681248 | + | 0.732053i | \(0.261437\pi\) | |||||||
\(168\) | 0.165947 | − | 2.64054i | 0.0128031 | − | 0.203722i | ||||
\(169\) | 34.9225 | 2.68634 | ||||||||
\(170\) | −10.0335 | − | 17.3785i | −0.769533 | − | 1.33287i | ||||
\(171\) | −0.500000 | + | 0.866025i | −0.0382360 | + | 0.0662266i | ||||
\(172\) | −5.18526 | + | 8.98114i | −0.395373 | + | 0.684806i | ||||
\(173\) | −5.00531 | − | 8.66945i | −0.380547 | − | 0.659126i | 0.610594 | − | 0.791944i | \(-0.290931\pi\) |
−0.991140 | + | 0.132818i | \(0.957598\pi\) | |||||||
\(174\) | −8.55364 | −0.648449 | ||||||||
\(175\) | 1.15842 | − | 18.4326i | 0.0875680 | − | 1.39338i | ||||
\(176\) | 0.278197 | 0.0209699 | ||||||||
\(177\) | −3.89738 | − | 6.75046i | −0.292945 | − | 0.507395i | ||||
\(178\) | −6.85037 | + | 11.8652i | −0.513457 | + | 0.889334i | ||||
\(179\) | −3.12941 | + | 5.42029i | −0.233903 | + | 0.405132i | −0.958953 | − | 0.283564i | \(-0.908483\pi\) |
0.725050 | + | 0.688696i | \(0.241816\pi\) | |||||||
\(180\) | 1.73065 | + | 2.99758i | 0.128995 | + | 0.223426i | ||||
\(181\) | −4.25019 | −0.315914 | −0.157957 | − | 0.987446i | \(-0.550491\pi\) | ||||
−0.157957 | + | 0.987446i | \(0.550491\pi\) | |||||||
\(182\) | −15.2561 | − | 10.1346i | −1.13085 | − | 0.751226i | ||||
\(183\) | −9.12941 | −0.674865 | ||||||||
\(184\) | 1.54617 | + | 2.67804i | 0.113985 | + | 0.197428i | ||||
\(185\) | −9.07055 | + | 15.7107i | −0.666880 | + | 1.15507i | ||||
\(186\) | −3.67480 | + | 6.36493i | −0.269449 | + | 0.466700i | ||||
\(187\) | −0.806425 | − | 1.39677i | −0.0589716 | − | 0.102142i | ||||
\(188\) | −1.79320 | −0.130782 | ||||||||
\(189\) | 2.36975 | − | 1.17656i | 0.172374 | − | 0.0855819i | ||||
\(190\) | 3.46130 | 0.251109 | ||||||||
\(191\) | 5.47393 | + | 9.48112i | 0.396080 | + | 0.686030i | 0.993238 | − | 0.116093i | \(-0.0370371\pi\) |
−0.597159 | + | 0.802123i | \(0.703704\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −10.6449 | + | 18.4376i | −0.766240 | + | 1.32717i | 0.173348 | + | 0.984861i | \(0.444541\pi\) |
−0.939588 | + | 0.342306i | \(0.888792\pi\) | |||||||
\(194\) | 2.04617 | + | 3.54406i | 0.146906 | + | 0.254449i | ||||
\(195\) | 23.9612 | 1.71590 | ||||||||
\(196\) | 2.71349 | + | 6.45267i | 0.193821 | + | 0.460905i | ||||
\(197\) | −6.63103 | −0.472441 | −0.236221 | − | 0.971699i | \(-0.575909\pi\) | ||||
−0.236221 | + | 0.971699i | \(0.575909\pi\) | |||||||
\(198\) | 0.139098 | + | 0.240925i | 0.00988529 | + | 0.0171218i | ||||
\(199\) | 3.93523 | − | 6.81602i | 0.278961 | − | 0.483175i | −0.692166 | − | 0.721739i | \(-0.743343\pi\) |
0.971127 | + | 0.238564i | \(0.0766766\pi\) | |||||||
\(200\) | 3.49031 | − | 6.04539i | 0.246802 | − | 0.427474i | ||||
\(201\) | −6.86891 | − | 11.8973i | −0.484495 | − | 0.839171i | ||||
\(202\) | 2.45699 | 0.172873 | ||||||||
\(203\) | 20.2700 | − | 10.0638i | 1.42267 | − | 0.706343i | ||||
\(204\) | −5.79751 | −0.405907 | ||||||||
\(205\) | 15.3778 | + | 26.6351i | 1.07403 | + | 1.86027i | ||||
\(206\) | 8.67342 | − | 15.0228i | 0.604306 | − | 1.04669i | ||||
\(207\) | −1.54617 | + | 2.67804i | −0.107466 | + | 0.186137i | ||||
\(208\) | −3.46130 | − | 5.99515i | −0.239998 | − | 0.415689i | ||||
\(209\) | 0.278197 | 0.0192433 | ||||||||
\(210\) | −7.62803 | − | 5.06730i | −0.526384 | − | 0.349677i | ||||
\(211\) | 14.9123 | 1.02660 | 0.513302 | − | 0.858208i | \(-0.328422\pi\) | ||||
0.513302 | + | 0.858208i | \(0.328422\pi\) | |||||||
\(212\) | −4.19411 | − | 7.26442i | −0.288053 | − | 0.498922i | ||||
\(213\) | 0.342363 | − | 0.592991i | 0.0234583 | − | 0.0406311i | ||||
\(214\) | −5.73896 | + | 9.94017i | −0.392307 | + | 0.679496i | ||||
\(215\) | 17.9478 | + | 31.0865i | 1.22403 | + | 2.12008i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 1.21965 | − | 19.4069i | 0.0827949 | − | 1.31743i | ||||
\(218\) | 18.6814 | 1.26526 | ||||||||
\(219\) | −0.962682 | − | 1.66741i | −0.0650520 | − | 0.112673i | ||||
\(220\) | 0.481462 | − | 0.833916i | 0.0324601 | − | 0.0562226i | ||||
\(221\) | −20.0670 | + | 34.7570i | −1.34985 | + | 2.33801i | ||||
\(222\) | 2.62056 | + | 4.53894i | 0.175880 | + | 0.304634i | ||||
\(223\) | 3.92861 | 0.263079 | 0.131539 | − | 0.991311i | \(-0.458008\pi\) | ||||
0.131539 | + | 0.991311i | \(0.458008\pi\) | |||||||
\(224\) | −0.165947 | + | 2.64054i | −0.0110878 | + | 0.176429i | ||||
\(225\) | 6.98062 | 0.465375 | ||||||||
\(226\) | 1.64957 | + | 2.85713i | 0.109728 | + | 0.190054i | ||||
\(227\) | 3.51985 | − | 6.09657i | 0.233621 | − | 0.404643i | −0.725250 | − | 0.688486i | \(-0.758276\pi\) |
0.958871 | + | 0.283842i | \(0.0916092\pi\) | |||||||
\(228\) | 0.500000 | − | 0.866025i | 0.0331133 | − | 0.0573539i | ||||
\(229\) | −2.94199 | − | 5.09567i | −0.194412 | − | 0.336731i | 0.752296 | − | 0.658826i | \(-0.228947\pi\) |
−0.946708 | + | 0.322094i | \(0.895613\pi\) | |||||||
\(230\) | 10.7035 | 0.705768 | ||||||||
\(231\) | −0.613091 | − | 0.407276i | −0.0403384 | − | 0.0267968i | ||||
\(232\) | 8.55364 | 0.561574 | ||||||||
\(233\) | −1.40329 | − | 2.43057i | −0.0919326 | − | 0.159232i | 0.816392 | − | 0.577499i | \(-0.195971\pi\) |
−0.908324 | + | 0.418267i | \(0.862638\pi\) | |||||||
\(234\) | 3.46130 | − | 5.99515i | 0.226272 | − | 0.391915i | ||||
\(235\) | −3.10340 | + | 5.37525i | −0.202444 | + | 0.350643i | ||||
\(236\) | 3.89738 | + | 6.75046i | 0.253698 | + | 0.439417i | ||||
\(237\) | −1.40761 | −0.0914338 | ||||||||
\(238\) | 13.7387 | − | 6.82110i | 0.890545 | − | 0.442146i | ||||
\(239\) | −12.4016 | −0.802193 | −0.401097 | − | 0.916036i | \(-0.631371\pi\) | ||||
−0.401097 | + | 0.916036i | \(0.631371\pi\) | |||||||
\(240\) | −1.73065 | − | 2.99758i | −0.111713 | − | 0.193493i | ||||
\(241\) | 7.59824 | − | 13.1605i | 0.489446 | − | 0.847745i | −0.510480 | − | 0.859889i | \(-0.670532\pi\) |
0.999926 | + | 0.0121442i | \(0.00386573\pi\) | |||||||
\(242\) | −5.46130 | + | 9.45925i | −0.351066 | + | 0.608064i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 9.12941 | 0.584450 | ||||||||
\(245\) | 24.0385 | + | 3.03342i | 1.53576 | + | 0.193798i | ||||
\(246\) | 8.88553 | 0.566521 | ||||||||
\(247\) | −3.46130 | − | 5.99515i | −0.220237 | − | 0.381462i | ||||
\(248\) | 3.67480 | − | 6.36493i | 0.233350 | − | 0.404174i | ||||
\(249\) | −0.0730150 | + | 0.126466i | −0.00462714 | + | 0.00801443i | ||||
\(250\) | −3.42776 | − | 5.93706i | −0.216791 | − | 0.375493i | ||||
\(251\) | 5.91198 | 0.373161 | 0.186581 | − | 0.982440i | \(-0.440259\pi\) | ||||
0.186581 | + | 0.982440i | \(0.440259\pi\) | |||||||
\(252\) | −2.36975 | + | 1.17656i | −0.149280 | + | 0.0741161i | ||||
\(253\) | 0.860277 | 0.0540851 | ||||||||
\(254\) | −1.72849 | − | 2.99384i | −0.108455 | − | 0.187850i | ||||
\(255\) | −10.0335 | + | 17.3785i | −0.628321 | + | 1.08828i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −0.702424 | − | 1.21663i | −0.0438160 | − | 0.0758915i | 0.843286 | − | 0.537466i | \(-0.180618\pi\) |
−0.887102 | + | 0.461574i | \(0.847285\pi\) | |||||||
\(258\) | 10.3705 | 0.645641 | ||||||||
\(259\) | −11.5504 | − | 7.67292i | −0.717707 | − | 0.476772i | ||||
\(260\) | −23.9612 | −1.48601 | ||||||||
\(261\) | 4.27682 | + | 7.40767i | 0.264728 | + | 0.458523i | ||||
\(262\) | 9.24781 | − | 16.0177i | 0.571332 | − | 0.989575i | ||||
\(263\) | 5.38907 | − | 9.33414i | 0.332304 | − | 0.575568i | −0.650659 | − | 0.759370i | \(-0.725507\pi\) |
0.982963 | + | 0.183802i | \(0.0588406\pi\) | |||||||
\(264\) | −0.139098 | − | 0.240925i | −0.00856091 | − | 0.0148279i | ||||
\(265\) | −29.0342 | −1.78356 | ||||||||
\(266\) | −0.165947 | + | 2.64054i | −0.0101749 | + | 0.161902i | ||||
\(267\) | 13.7007 | 0.838472 | ||||||||
\(268\) | 6.86891 | + | 11.8973i | 0.419585 | + | 0.726743i | ||||
\(269\) | −11.2231 | + | 19.4390i | −0.684286 | + | 1.18522i | 0.289375 | + | 0.957216i | \(0.406553\pi\) |
−0.973661 | + | 0.228002i | \(0.926781\pi\) | |||||||
\(270\) | 1.73065 | − | 2.99758i | 0.105324 | − | 0.182427i | ||||
\(271\) | 1.13826 | + | 1.97152i | 0.0691442 | + | 0.119761i | 0.898525 | − | 0.438923i | \(-0.144640\pi\) |
−0.829381 | + | 0.558684i | \(0.811306\pi\) | |||||||
\(272\) | 5.79751 | 0.351526 | ||||||||
\(273\) | −1.14879 | + | 18.2794i | −0.0695278 | + | 1.10632i | ||||
\(274\) | 12.1680 | 0.735098 | ||||||||
\(275\) | −0.970993 | − | 1.68181i | −0.0585531 | − | 0.101417i | ||||
\(276\) | 1.54617 | − | 2.67804i | 0.0930683 | − | 0.161199i | ||||
\(277\) | −13.7260 | + | 23.7742i | −0.824717 | + | 1.42845i | 0.0774178 | + | 0.996999i | \(0.475332\pi\) |
−0.902135 | + | 0.431454i | \(0.858001\pi\) | |||||||
\(278\) | −1.45915 | − | 2.52731i | −0.0875137 | − | 0.151578i | ||||
\(279\) | 7.34959 | 0.440009 | ||||||||
\(280\) | 7.62803 | + | 5.06730i | 0.455862 | + | 0.302829i | ||||
\(281\) | 8.14279 | 0.485758 | 0.242879 | − | 0.970057i | \(-0.421908\pi\) | ||||
0.242879 | + | 0.970057i | \(0.421908\pi\) | |||||||
\(282\) | 0.896599 | + | 1.55296i | 0.0533917 | + | 0.0924771i | ||||
\(283\) | 4.09293 | − | 7.08917i | 0.243300 | − | 0.421407i | −0.718353 | − | 0.695679i | \(-0.755104\pi\) |
0.961652 | + | 0.274272i | \(0.0884369\pi\) | |||||||
\(284\) | −0.342363 | + | 0.592991i | −0.0203155 | + | 0.0351875i | ||||
\(285\) | −1.73065 | − | 2.99758i | −0.102515 | − | 0.177561i | ||||
\(286\) | −1.92585 | −0.113878 | ||||||||
\(287\) | −21.0565 | + | 10.4543i | −1.24293 | + | 0.617099i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −8.30558 | − | 14.3857i | −0.488564 | − | 0.846217i | ||||
\(290\) | 14.8034 | − | 25.6402i | 0.869283 | − | 1.50564i | ||||
\(291\) | 2.04617 | − | 3.54406i | 0.119948 | − | 0.207757i | ||||
\(292\) | 0.962682 | + | 1.66741i | 0.0563367 | + | 0.0975781i | ||||
\(293\) | −19.3421 | −1.12998 | −0.564988 | − | 0.825099i | \(-0.691119\pi\) | ||||
−0.564988 | + | 0.825099i | \(0.691119\pi\) | |||||||
\(294\) | 4.23143 | − | 5.57629i | 0.246782 | − | 0.325216i | ||||
\(295\) | 26.9800 | 1.57084 | ||||||||
\(296\) | −2.62056 | − | 4.53894i | −0.152317 | − | 0.263821i | ||||
\(297\) | 0.139098 | − | 0.240925i | 0.00807131 | − | 0.0139799i | ||||
\(298\) | −2.08246 | + | 3.60693i | −0.120634 | + | 0.208944i | ||||
\(299\) | −10.7035 | − | 18.5390i | −0.618999 | − | 1.07214i | ||||
\(300\) | −6.98062 | −0.403026 | ||||||||
\(301\) | −24.5756 | + | 12.2015i | −1.41651 | + | 0.703283i | ||||
\(302\) | −19.2754 | −1.10918 | ||||||||
\(303\) | −1.22849 | − | 2.12781i | −0.0705751 | − | 0.122240i | ||||
\(304\) | −0.500000 | + | 0.866025i | −0.0286770 | + | 0.0496700i | ||||
\(305\) | 15.7998 | − | 27.3661i | 0.904695 | − | 1.56698i | ||||
\(306\) | 2.89876 | + | 5.02079i | 0.165711 | + | 0.287020i | ||||
\(307\) | −11.7007 | −0.667797 | −0.333898 | − | 0.942609i | \(-0.608364\pi\) | ||||
−0.333898 | + | 0.942609i | \(0.608364\pi\) | |||||||
\(308\) | 0.613091 | + | 0.407276i | 0.0349341 | + | 0.0232067i | ||||
\(309\) | −17.3468 | −0.986827 | ||||||||
\(310\) | −12.7196 | − | 22.0310i | −0.722424 | − | 1.25127i | ||||
\(311\) | −6.92776 | + | 11.9992i | −0.392837 | + | 0.680414i | −0.992823 | − | 0.119597i | \(-0.961840\pi\) |
0.599985 | + | 0.800011i | \(0.295173\pi\) | |||||||
\(312\) | −3.46130 | + | 5.99515i | −0.195958 | + | 0.339409i | ||||
\(313\) | 0.985994 | + | 1.70779i | 0.0557317 | + | 0.0965301i | 0.892545 | − | 0.450958i | \(-0.148918\pi\) |
−0.836814 | + | 0.547488i | \(0.815584\pi\) | |||||||
\(314\) | 21.4569 | 1.21088 | ||||||||
\(315\) | −0.574394 | + | 9.13972i | −0.0323634 | + | 0.514965i | ||||
\(316\) | 1.40761 | 0.0791840 | ||||||||
\(317\) | −9.95023 | − | 17.2343i | −0.558861 | − | 0.967975i | −0.997592 | − | 0.0693570i | \(-0.977905\pi\) |
0.438731 | − | 0.898618i | \(-0.355428\pi\) | |||||||
\(318\) | −4.19411 | + | 7.26442i | −0.235194 | + | 0.407368i | ||||
\(319\) | 1.18980 | − | 2.06079i | 0.0666158 | − | 0.115382i | ||||
\(320\) | 1.73065 | + | 2.99758i | 0.0967464 | + | 0.167570i | ||||
\(321\) | 11.4779 | 0.640635 | ||||||||
\(322\) | −0.513164 | + | 8.16543i | −0.0285975 | + | 0.455042i | ||||
\(323\) | 5.79751 | 0.322582 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −24.1620 | + | 41.8499i | −1.34027 | + | 2.32141i | ||||
\(326\) | 7.97231 | − | 13.8084i | 0.441545 | − | 0.764779i | ||||
\(327\) | −9.34068 | − | 16.1785i | −0.516541 | − | 0.894675i | ||||
\(328\) | −8.88553 | −0.490621 | ||||||||
\(329\) | −3.95185 | − | 2.62522i | −0.217873 | − | 0.144733i | ||||
\(330\) | −0.962923 | −0.0530072 | ||||||||
\(331\) | 2.33381 | + | 4.04228i | 0.128278 | + | 0.222184i | 0.923009 | − | 0.384777i | \(-0.125722\pi\) |
−0.794732 | + | 0.606961i | \(0.792388\pi\) | |||||||
\(332\) | 0.0730150 | − | 0.126466i | 0.00400722 | − | 0.00694070i | ||||
\(333\) | 2.62056 | − | 4.53894i | 0.143606 | − | 0.248733i | ||||
\(334\) | 8.80367 | + | 15.2484i | 0.481715 | + | 0.834355i | ||||
\(335\) | 47.5508 | 2.59798 | ||||||||
\(336\) | 2.36975 | − | 1.17656i | 0.129280 | − | 0.0641864i | ||||
\(337\) | −11.4639 | −0.624480 | −0.312240 | − | 0.950003i | \(-0.601079\pi\) | ||||
−0.312240 | + | 0.950003i | \(0.601079\pi\) | |||||||
\(338\) | 17.4612 | + | 30.2438i | 0.949766 | + | 1.64504i | ||||
\(339\) | 1.64957 | − | 2.85713i | 0.0895922 | − | 0.155178i | ||||
\(340\) | 10.0335 | − | 17.3785i | 0.544142 | − | 0.942481i | ||||
\(341\) | −1.02232 | − | 1.77070i | −0.0553615 | − | 0.0958890i | ||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | −3.46661 | + | 18.1929i | −0.187180 | + | 0.982326i | ||||
\(344\) | −10.3705 | −0.559141 | ||||||||
\(345\) | −5.35175 | − | 9.26950i | −0.288129 | − | 0.499053i | ||||
\(346\) | 5.00531 | − | 8.66945i | 0.269087 | − | 0.466073i | ||||
\(347\) | −3.92129 | + | 6.79187i | −0.210506 | + | 0.364607i | −0.951873 | − | 0.306493i | \(-0.900844\pi\) |
0.741367 | + | 0.671100i | \(0.234178\pi\) | |||||||
\(348\) | −4.27682 | − | 7.40767i | −0.229261 | − | 0.397093i | ||||
\(349\) | 21.2991 | 1.14012 | 0.570058 | − | 0.821604i | \(-0.306921\pi\) | ||||
0.570058 | + | 0.821604i | \(0.306921\pi\) | |||||||
\(350\) | 16.5423 | − | 8.21309i | 0.884224 | − | 0.439008i | ||||
\(351\) | −6.92261 | −0.369501 | ||||||||
\(352\) | 0.139098 | + | 0.240925i | 0.00741397 | + | 0.0128414i | ||||
\(353\) | −4.35850 | + | 7.54915i | −0.231980 | + | 0.401801i | −0.958391 | − | 0.285460i | \(-0.907854\pi\) |
0.726411 | + | 0.687261i | \(0.241187\pi\) | |||||||
\(354\) | 3.89738 | − | 6.75046i | 0.207143 | − | 0.358783i | ||||
\(355\) | 1.18502 | + | 2.05252i | 0.0628945 | + | 0.108936i | ||||
\(356\) | −13.7007 | −0.726138 | ||||||||
\(357\) | −12.7766 | − | 8.48748i | −0.676208 | − | 0.449205i | ||||
\(358\) | −6.25882 | −0.330789 | ||||||||
\(359\) | −0.585642 | − | 1.01436i | −0.0309090 | − | 0.0535359i | 0.850157 | − | 0.526529i | \(-0.176507\pi\) |
−0.881066 | + | 0.472993i | \(0.843174\pi\) | |||||||
\(360\) | −1.73065 | + | 2.99758i | −0.0912134 | + | 0.157986i | ||||
\(361\) | −0.500000 | + | 0.866025i | −0.0263158 | + | 0.0455803i | ||||
\(362\) | −2.12509 | − | 3.68077i | −0.111692 | − | 0.193457i | ||||
\(363\) | 10.9226 | 0.573288 | ||||||||
\(364\) | 1.14879 | − | 18.2794i | 0.0602129 | − | 0.958103i | ||||
\(365\) | 6.66427 | 0.348824 | ||||||||
\(366\) | −4.56470 | − | 7.90630i | −0.238601 | − | 0.413269i | ||||
\(367\) | −2.50647 | + | 4.34134i | −0.130837 | + | 0.226616i | −0.923999 | − | 0.382394i | \(-0.875100\pi\) |
0.793163 | + | 0.609010i | \(0.208433\pi\) | |||||||
\(368\) | −1.54617 | + | 2.67804i | −0.0805995 | + | 0.139602i | ||||
\(369\) | −4.44277 | − | 7.69509i | −0.231281 | − | 0.400591i | ||||
\(370\) | −18.1411 | −0.943111 | ||||||||
\(371\) | 1.39200 | − | 22.1495i | 0.0722692 | − | 1.14994i | ||||
\(372\) | −7.34959 | −0.381059 | ||||||||
\(373\) | −0.932921 | − | 1.61587i | −0.0483048 | − | 0.0836664i | 0.840862 | − | 0.541250i | \(-0.182049\pi\) |
−0.889167 | + | 0.457583i | \(0.848715\pi\) | |||||||
\(374\) | 0.806425 | − | 1.39677i | 0.0416992 | − | 0.0722252i | ||||
\(375\) | −3.42776 | + | 5.93706i | −0.177009 | + | 0.306589i | ||||
\(376\) | −0.896599 | − | 1.55296i | −0.0462386 | − | 0.0800875i | ||||
\(377\) | −59.2135 | −3.04965 | ||||||||
\(378\) | 2.20380 | + | 1.46399i | 0.113351 | + | 0.0752993i | ||||
\(379\) | −11.8065 | −0.606457 | −0.303228 | − | 0.952918i | \(-0.598065\pi\) | ||||
−0.303228 | + | 0.952918i | \(0.598065\pi\) | |||||||
\(380\) | 1.73065 | + | 2.99758i | 0.0887806 | + | 0.153772i | ||||
\(381\) | −1.72849 | + | 2.99384i | −0.0885534 | + | 0.153379i | ||||
\(382\) | −5.47393 | + | 9.48112i | −0.280071 | + | 0.485097i | ||||
\(383\) | −2.76320 | − | 4.78600i | −0.141193 | − | 0.244553i | 0.786753 | − | 0.617268i | \(-0.211760\pi\) |
−0.927946 | + | 0.372715i | \(0.878427\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 2.28189 | − | 1.13293i | 0.116296 | − | 0.0577396i | ||||
\(386\) | −21.2899 | −1.08363 | ||||||||
\(387\) | −5.18526 | − | 8.98114i | −0.263582 | − | 0.456537i | ||||
\(388\) | −2.04617 | + | 3.54406i | −0.103878 | + | 0.179923i | ||||
\(389\) | −0.632104 | + | 1.09484i | −0.0320490 | + | 0.0555104i | −0.881605 | − | 0.471988i | \(-0.843537\pi\) |
0.849556 | + | 0.527498i | \(0.176870\pi\) | |||||||
\(390\) | 11.9806 | + | 20.7510i | 0.606662 | + | 1.05077i | ||||
\(391\) | 17.9278 | 0.906650 | ||||||||
\(392\) | −4.23143 | + | 5.57629i | −0.213720 | + | 0.281645i | ||||
\(393\) | −18.4956 | −0.932981 | ||||||||
\(394\) | −3.31551 | − | 5.74264i | −0.167033 | − | 0.289310i | ||||
\(395\) | 2.43607 | − | 4.21940i | 0.122572 | − | 0.212301i | ||||
\(396\) | −0.139098 | + | 0.240925i | −0.00698996 | + | 0.0121070i | ||||
\(397\) | 0.702424 | + | 1.21663i | 0.0352536 | + | 0.0610611i | 0.883114 | − | 0.469159i | \(-0.155443\pi\) |
−0.847860 | + | 0.530220i | \(0.822109\pi\) | |||||||
\(398\) | 7.87047 | 0.394511 | ||||||||
\(399\) | 2.36975 | − | 1.17656i | 0.118636 | − | 0.0589015i | ||||
\(400\) | 6.98062 | 0.349031 | ||||||||
\(401\) | 2.38559 | + | 4.13197i | 0.119131 | + | 0.206341i | 0.919423 | − | 0.393269i | \(-0.128656\pi\) |
−0.800293 | + | 0.599610i | \(0.795323\pi\) | |||||||
\(402\) | 6.86891 | − | 11.8973i | 0.342590 | − | 0.593383i | ||||
\(403\) | −25.4392 | + | 44.0619i | −1.26722 | + | 2.19488i | ||||
\(404\) | 1.22849 | + | 2.12781i | 0.0611198 | + | 0.105863i | ||||
\(405\) | −3.46130 | −0.171994 | ||||||||
\(406\) | 18.8505 | + | 12.5224i | 0.935536 | + | 0.621476i | ||||
\(407\) | −1.45806 | −0.0722735 | ||||||||
\(408\) | −2.89876 | − | 5.02079i | −0.143510 | − | 0.248566i | ||||
\(409\) | 9.04448 | − | 15.6655i | 0.447221 | − | 0.774609i | −0.550983 | − | 0.834516i | \(-0.685747\pi\) |
0.998204 | + | 0.0599071i | \(0.0190804\pi\) | |||||||
\(410\) | −15.3778 | + | 26.6351i | −0.759453 | + | 1.31541i | ||||
\(411\) | −6.08402 | − | 10.5378i | −0.300103 | − | 0.519793i | ||||
\(412\) | 17.3468 | 0.854617 | ||||||||
\(413\) | −1.29352 | + | 20.5824i | −0.0636499 | + | 1.01279i | ||||
\(414\) | −3.09233 | −0.151980 | ||||||||
\(415\) | −0.252727 | − | 0.437736i | −0.0124059 | − | 0.0214876i | ||||
\(416\) | 3.46130 | − | 5.99515i | 0.169704 | − | 0.293937i | ||||
\(417\) | −1.45915 | + | 2.52731i | −0.0714547 | + | 0.123763i | ||||
\(418\) | 0.139098 | + | 0.240925i | 0.00680353 | + | 0.0117841i | ||||
\(419\) | 2.70518 | 0.132157 | 0.0660784 | − | 0.997814i | \(-0.478951\pi\) | ||||
0.0660784 | + | 0.997814i | \(0.478951\pi\) | |||||||
\(420\) | 0.574394 | − | 9.13972i | 0.0280276 | − | 0.445972i | ||||
\(421\) | 6.14064 | 0.299276 | 0.149638 | − | 0.988741i | \(-0.452189\pi\) | ||||
0.149638 | + | 0.988741i | \(0.452189\pi\) | |||||||
\(422\) | 7.45615 | + | 12.9144i | 0.362960 | + | 0.628664i | ||||
\(423\) | 0.896599 | − | 1.55296i | 0.0435941 | − | 0.0755073i | ||||
\(424\) | 4.19411 | − | 7.26442i | 0.203684 | − | 0.352791i | ||||
\(425\) | −20.2351 | − | 35.0483i | −0.981548 | − | 1.70009i | ||||
\(426\) | 0.684727 | 0.0331751 | ||||||||
\(427\) | 20.1194 | + | 13.3653i | 0.973647 | + | 0.646793i | ||||
\(428\) | −11.4779 | −0.554806 | ||||||||
\(429\) | 0.962923 | + | 1.66783i | 0.0464904 | + | 0.0805237i | ||||
\(430\) | −17.9478 | + | 31.0865i | −0.865518 | + | 1.49912i | ||||
\(431\) | −10.6383 | + | 18.4260i | −0.512427 | + | 0.887549i | 0.487469 | + | 0.873140i | \(0.337920\pi\) |
−0.999896 | + | 0.0144092i | \(0.995413\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −9.42099 | −0.452744 | −0.226372 | − | 0.974041i | \(-0.572686\pi\) | ||||
−0.226372 | + | 0.974041i | \(0.572686\pi\) | |||||||
\(434\) | 17.4167 | − | 8.64721i | 0.836028 | − | 0.415079i | ||||
\(435\) | −29.6067 | −1.41953 | ||||||||
\(436\) | 9.34068 | + | 16.1785i | 0.447337 | + | 0.774811i | ||||
\(437\) | −1.54617 | + | 2.67804i | −0.0739632 | + | 0.128108i | ||||
\(438\) | 0.962682 | − | 1.66741i | 0.0459987 | − | 0.0796722i | ||||
\(439\) | −6.29620 | − | 10.9053i | −0.300501 | − | 0.520483i | 0.675748 | − | 0.737132i | \(-0.263821\pi\) |
−0.976250 | + | 0.216649i | \(0.930487\pi\) | |||||||
\(440\) | 0.962923 | 0.0459056 | ||||||||
\(441\) | −6.94492 | − | 0.876382i | −0.330711 | − | 0.0417325i | ||||
\(442\) | −40.1339 | −1.90898 | ||||||||
\(443\) | 11.6473 | + | 20.1738i | 0.553382 | + | 0.958486i | 0.998027 | + | 0.0627792i | \(0.0199964\pi\) |
−0.444645 | + | 0.895707i | \(0.646670\pi\) | |||||||
\(444\) | −2.62056 | + | 4.53894i | −0.124366 | + | 0.215409i | ||||
\(445\) | −23.7112 | + | 41.0690i | −1.12402 | + | 1.94686i | ||||
\(446\) | 1.96430 | + | 3.40227i | 0.0930124 | + | 0.161102i | ||||
\(447\) | 4.16493 | 0.196994 | ||||||||
\(448\) | −2.36975 | + | 1.17656i | −0.111960 | + | 0.0555871i | ||||
\(449\) | −0.486074 | −0.0229393 | −0.0114696 | − | 0.999934i | \(-0.503651\pi\) | ||||
−0.0114696 | + | 0.999934i | \(0.503651\pi\) | |||||||
\(450\) | 3.49031 | + | 6.04539i | 0.164535 | + | 0.284983i | ||||
\(451\) | −1.23596 | + | 2.14075i | −0.0581992 | + | 0.100804i | ||||
\(452\) | −1.64957 | + | 2.85713i | −0.0775891 | + | 0.134388i | ||||
\(453\) | 9.63772 | + | 16.6930i | 0.452820 | + | 0.784306i | ||||
\(454\) | 7.03971 | 0.330390 | ||||||||
\(455\) | −52.8058 | − | 35.0789i | −2.47558 | − | 1.64452i | ||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | −7.22987 | − | 12.5225i | −0.338199 | − | 0.585778i | 0.645895 | − | 0.763426i | \(-0.276484\pi\) |
−0.984094 | + | 0.177648i | \(0.943151\pi\) | |||||||
\(458\) | 2.94199 | − | 5.09567i | 0.137470 | − | 0.238105i | ||||
\(459\) | 2.89876 | − | 5.02079i | 0.135302 | − | 0.234351i | ||||
\(460\) | 5.35175 | + | 9.26950i | 0.249527 | + | 0.432193i | ||||
\(461\) | 18.0188 | 0.839218 | 0.419609 | − | 0.907705i | \(-0.362167\pi\) | ||||
0.419609 | + | 0.907705i | \(0.362167\pi\) | |||||||
\(462\) | 0.0461660 | − | 0.734590i | 0.00214784 | − | 0.0341762i | ||||
\(463\) | 23.3408 | 1.08474 | 0.542370 | − | 0.840140i | \(-0.317527\pi\) | ||||
0.542370 | + | 0.840140i | \(0.317527\pi\) | |||||||
\(464\) | 4.27682 | + | 7.40767i | 0.198546 | + | 0.343892i | ||||
\(465\) | −12.7196 | + | 22.0310i | −0.589857 | + | 1.02166i | ||||
\(466\) | 1.40329 | − | 2.43057i | 0.0650061 | − | 0.112594i | ||||
\(467\) | 4.07439 | + | 7.05706i | 0.188540 | + | 0.326562i | 0.944764 | − | 0.327752i | \(-0.106291\pi\) |
−0.756223 | + | 0.654314i | \(0.772958\pi\) | |||||||
\(468\) | 6.92261 | 0.319998 | ||||||||
\(469\) | −2.27975 | + | 36.2753i | −0.105269 | + | 1.67504i | ||||
\(470\) | −6.20680 | −0.286298 | ||||||||
\(471\) | −10.7284 | − | 18.5822i | −0.494340 | − | 0.856222i | ||||
\(472\) | −3.89738 | + | 6.75046i | −0.179391 | + | 0.310715i | ||||
\(473\) | −1.44252 | + | 2.49852i | −0.0663273 | + | 0.114882i | ||||
\(474\) | −0.703803 | − | 1.21902i | −0.0323267 | − | 0.0559915i | ||||
\(475\) | 6.98062 | 0.320293 | ||||||||
\(476\) | 12.7766 | + | 8.48748i | 0.585613 | + | 0.389023i | ||||
\(477\) | 8.38823 | 0.384070 | ||||||||
\(478\) | −6.20080 | − | 10.7401i | −0.283618 | − | 0.491241i | ||||
\(479\) | −13.5813 | + | 23.5235i | −0.620547 | + | 1.07482i | 0.368837 | + | 0.929494i | \(0.379756\pi\) |
−0.989384 | + | 0.145324i | \(0.953577\pi\) | |||||||
\(480\) | 1.73065 | − | 2.99758i | 0.0789931 | − | 0.136820i | ||||
\(481\) | 18.1411 | + | 31.4213i | 0.827163 | + | 1.43269i | ||||
\(482\) | 15.1965 | 0.692181 | ||||||||
\(483\) | 7.32805 | − | 3.63830i | 0.333438 | − | 0.165549i | ||||
\(484\) | −10.9226 | −0.496482 | ||||||||
\(485\) | 7.08240 | + | 12.2671i | 0.321595 | + | 0.557019i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | 5.97117 | − | 10.3424i | 0.270580 | − | 0.468658i | −0.698431 | − | 0.715678i | \(-0.746118\pi\) |
0.969010 | + | 0.247020i | \(0.0794513\pi\) | |||||||
\(488\) | 4.56470 | + | 7.90630i | 0.206634 | + | 0.357901i | ||||
\(489\) | −15.9446 | −0.721041 | ||||||||
\(490\) | 9.39222 | + | 22.3346i | 0.424297 | + | 1.00898i | ||||
\(491\) | −7.00863 | −0.316295 | −0.158148 | − | 0.987415i | \(-0.550552\pi\) | ||||
−0.158148 | + | 0.987415i | \(0.550552\pi\) | |||||||
\(492\) | 4.44277 | + | 7.69509i | 0.200295 | + | 0.346922i | ||||
\(493\) | 24.7949 | − | 42.9460i | 1.11671 | − | 1.93419i | ||||
\(494\) | 3.46130 | − | 5.99515i | 0.155731 | − | 0.269735i | ||||
\(495\) | 0.481462 | + | 0.833916i | 0.0216401 | + | 0.0374817i | ||||
\(496\) | 7.34959 | 0.330006 | ||||||||
\(497\) | −1.62263 | + | 0.805620i | −0.0727850 | + | 0.0361370i | ||||
\(498\) | −0.146030 | −0.00654376 | ||||||||
\(499\) | 4.56302 | + | 7.90339i | 0.204269 | + | 0.353804i | 0.949900 | − | 0.312555i | \(-0.101185\pi\) |
−0.745631 | + | 0.666359i | \(0.767852\pi\) | |||||||
\(500\) | 3.42776 | − | 5.93706i | 0.153294 | − | 0.265513i | ||||
\(501\) | 8.80367 | − | 15.2484i | 0.393319 | − | 0.681248i | ||||
\(502\) | 2.95599 | + | 5.11993i | 0.131932 | + | 0.228514i | ||||
\(503\) | −24.1190 | −1.07541 | −0.537706 | − | 0.843133i | \(-0.680709\pi\) | ||||
−0.537706 | + | 0.843133i | \(0.680709\pi\) | |||||||
\(504\) | −2.20380 | − | 1.46399i | −0.0981652 | − | 0.0652111i | ||||
\(505\) | 8.50438 | 0.378440 | ||||||||
\(506\) | 0.430138 | + | 0.745022i | 0.0191220 | + | 0.0331203i | ||||
\(507\) | 17.4612 | − | 30.2438i | 0.775481 | − | 1.34317i | ||||
\(508\) | 1.72849 | − | 2.99384i | 0.0766895 | − | 0.132830i | ||||
\(509\) | 18.7531 | + | 32.4813i | 0.831215 | + | 1.43971i | 0.897075 | + | 0.441877i | \(0.145687\pi\) |
−0.0658607 | + | 0.997829i | \(0.520979\pi\) | |||||||
\(510\) | −20.0670 | −0.888580 | ||||||||
\(511\) | −0.319509 | + | 5.08401i | −0.0141343 | + | 0.224903i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.500000 | + | 0.866025i | 0.0220755 | + | 0.0382360i | ||||
\(514\) | 0.702424 | − | 1.21663i | 0.0309826 | − | 0.0536634i | ||||
\(515\) | 30.0213 | − | 51.9985i | 1.32290 | − | 2.29133i | ||||
\(516\) | 5.18526 | + | 8.98114i | 0.228269 | + | 0.395373i | ||||
\(517\) | −0.498862 | −0.0219399 | ||||||||
\(518\) | 0.869750 | − | 13.8394i | 0.0382146 | − | 0.608068i | ||||
\(519\) | −10.0106 | −0.439418 | ||||||||
\(520\) | −11.9806 | − | 20.7510i | −0.525385 | − | 0.909993i | ||||
\(521\) | −21.1025 | + | 36.5506i | −0.924516 | + | 1.60131i | −0.132179 | + | 0.991226i | \(0.542197\pi\) |
−0.792338 | + | 0.610083i | \(0.791136\pi\) | |||||||
\(522\) | −4.27682 | + | 7.40767i | −0.187191 | + | 0.324225i | ||||
\(523\) | −9.54692 | − | 16.5358i | −0.417458 | − | 0.723058i | 0.578225 | − | 0.815877i | \(-0.303745\pi\) |
−0.995683 | + | 0.0928192i | \(0.970412\pi\) | |||||||
\(524\) | 18.4956 | 0.807985 | ||||||||
\(525\) | −15.3839 | − | 10.2195i | −0.671409 | − | 0.446017i | ||||
\(526\) | 10.7781 | 0.469949 | ||||||||
\(527\) | −21.3047 | − | 36.9008i | −0.928046 | − | 1.60742i | ||||
\(528\) | 0.139098 | − | 0.240925i | 0.00605348 | − | 0.0104849i | ||||
\(529\) | 6.71874 | − | 11.6372i | 0.292119 | − | 0.505965i | ||||
\(530\) | −14.5171 | − | 25.1443i | −0.630582 | − | 1.09220i | ||||
\(531\) | −7.79476 | −0.338264 | ||||||||
\(532\) | −2.36975 | + | 1.17656i | −0.102742 | + | 0.0510102i | ||||
\(533\) | 61.5110 | 2.66434 | ||||||||
\(534\) | 6.85037 | + | 11.8652i | 0.296445 | + | 0.513457i | ||||
\(535\) | −19.8643 | + | 34.4060i | −0.858808 | + | 1.48750i | ||||
\(536\) | −6.86891 | + | 11.8973i | −0.296692 | + | 0.513885i | ||||
\(537\) | 3.12941 | + | 5.42029i | 0.135044 | + | 0.233903i | ||||
\(538\) | −22.4462 | −0.967726 | ||||||||
\(539\) | 0.754885 | + | 1.79511i | 0.0325152 | + | 0.0773210i | ||||
\(540\) | 3.46130 | 0.148951 | ||||||||
\(541\) | −0.393062 | − | 0.680803i | −0.0168991 | − | 0.0292700i | 0.857452 | − | 0.514564i | \(-0.172046\pi\) |
−0.874351 | + | 0.485294i | \(0.838713\pi\) | |||||||
\(542\) | −1.13826 | + | 1.97152i | −0.0488923 | + | 0.0846840i | ||||
\(543\) | −2.12509 | + | 3.68077i | −0.0911965 | + | 0.157957i | ||||
\(544\) | 2.89876 | + | 5.02079i | 0.124283 | + | 0.215265i | ||||
\(545\) | 64.6619 | 2.76981 | ||||||||
\(546\) | −16.4048 | + | 8.14484i | −0.702063 | + | 0.348567i | ||||
\(547\) | 0.670738 | 0.0286787 | 0.0143394 | − | 0.999897i | \(-0.495435\pi\) | ||||
0.0143394 | + | 0.999897i | \(0.495435\pi\) | |||||||
\(548\) | 6.08402 | + | 10.5378i | 0.259897 | + | 0.450154i | ||||
\(549\) | −4.56470 | + | 7.90630i | −0.194817 | + | 0.337433i | ||||
\(550\) | 0.970993 | − | 1.68181i | 0.0414033 | − | 0.0717126i | ||||
\(551\) | 4.27682 | + | 7.40767i | 0.182199 | + | 0.315577i | ||||
\(552\) | 3.09233 | 0.131618 | ||||||||
\(553\) | 3.10208 | + | 2.06071i | 0.131914 | + | 0.0876305i | ||||
\(554\) | −27.4521 | −1.16633 | ||||||||
\(555\) | 9.07055 | + | 15.7107i | 0.385024 | + | 0.666880i | ||||
\(556\) | 1.45915 | − | 2.52731i | 0.0618815 | − | 0.107182i | ||||
\(557\) | −3.07649 | + | 5.32864i | −0.130355 | + | 0.225782i | −0.923813 | − | 0.382843i | \(-0.874945\pi\) |
0.793458 | + | 0.608624i | \(0.208278\pi\) | |||||||
\(558\) | 3.67480 | + | 6.36493i | 0.155567 | + | 0.269449i | ||||
\(559\) | 71.7911 | 3.03644 | ||||||||
\(560\) | −0.574394 | + | 9.13972i | −0.0242726 | + | 0.386224i | ||||
\(561\) | −1.61285 | −0.0680946 | ||||||||
\(562\) | 4.07139 | + | 7.05186i | 0.171741 | + | 0.297465i | ||||
\(563\) | 11.8377 | − | 20.5035i | 0.498899 | − | 0.864118i | −0.501100 | − | 0.865389i | \(-0.667071\pi\) |
0.999999 | + | 0.00127111i | \(0.000404608\pi\) | |||||||
\(564\) | −0.896599 | + | 1.55296i | −0.0377536 | + | 0.0653912i | ||||
\(565\) | 5.70965 | + | 9.88941i | 0.240207 | + | 0.416050i | ||||
\(566\) | 8.18586 | 0.344078 | ||||||||
\(567\) | 0.165947 | − | 2.64054i | 0.00696913 | − | 0.110892i | ||||
\(568\) | −0.684727 | −0.0287305 | ||||||||
\(569\) | −18.3345 | − | 31.7563i | −0.768623 | − | 1.33129i | −0.938309 | − | 0.345797i | \(-0.887609\pi\) |
0.169686 | − | 0.985498i | \(-0.445725\pi\) | |||||||
\(570\) | 1.73065 | − | 2.99758i | 0.0724890 | − | 0.125555i | ||||
\(571\) | 8.86399 | − | 15.3529i | 0.370947 | − | 0.642498i | −0.618765 | − | 0.785576i | \(-0.712367\pi\) |
0.989711 | + | 0.143078i | \(0.0457000\pi\) | |||||||
\(572\) | −0.962923 | − | 1.66783i | −0.0402619 | − | 0.0697356i | ||||
\(573\) | 10.9479 | 0.457353 | ||||||||
\(574\) | −19.5820 | − | 13.0083i | −0.817335 | − | 0.542955i | ||||
\(575\) | 21.5864 | 0.900215 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 0.616028 | − | 1.06699i | 0.0256456 | − | 0.0444194i | −0.852918 | − | 0.522045i | \(-0.825169\pi\) |
0.878563 | + | 0.477626i | \(0.158503\pi\) | |||||||
\(578\) | 8.30558 | − | 14.3857i | 0.345467 | − | 0.598366i | ||||
\(579\) | 10.6449 | + | 18.4376i | 0.442389 | + | 0.766240i | ||||
\(580\) | 29.6067 | 1.22935 | ||||||||
\(581\) | 0.346054 | − | 0.171812i | 0.0143568 | − | 0.00712798i | ||||
\(582\) | 4.09233 | 0.169633 | ||||||||
\(583\) | −1.16679 | − | 2.02094i | −0.0483235 | − | 0.0836987i | ||||
\(584\) | −0.962682 | + | 1.66741i | −0.0398361 | + | 0.0689981i | ||||
\(585\) | 11.9806 | − | 20.7510i | 0.495338 | − | 0.857950i | ||||
\(586\) | −9.67104 | − | 16.7507i | −0.399507 | − | 0.691967i | ||||
\(587\) | −10.0714 | −0.415691 | −0.207845 | − | 0.978162i | \(-0.566645\pi\) | ||||
−0.207845 | + | 0.978162i | \(0.566645\pi\) | |||||||
\(588\) | 6.94492 | + | 0.876382i | 0.286404 | + | 0.0361414i | ||||
\(589\) | 7.34959 | 0.302835 | ||||||||
\(590\) | 13.4900 | + | 23.3654i | 0.555375 | + | 0.961937i | ||||
\(591\) | −3.31551 | + | 5.74264i | −0.136382 | + | 0.236221i | ||||
\(592\) | 2.62056 | − | 4.53894i | 0.107704 | − | 0.186549i | ||||
\(593\) | −14.1317 | − | 24.4769i | −0.580320 | − | 1.00514i | −0.995441 | − | 0.0953778i | \(-0.969594\pi\) |
0.415121 | − | 0.909766i | \(-0.363739\pi\) | |||||||
\(594\) | 0.278197 | 0.0114146 | ||||||||
\(595\) | 47.5537 | − | 23.6099i | 1.94951 | − | 0.967912i | ||||
\(596\) | −4.16493 | −0.170602 | ||||||||
\(597\) | −3.93523 | − | 6.81602i | −0.161058 | − | 0.278961i | ||||
\(598\) | 10.7035 | − | 18.5390i | 0.437699 | − | 0.758116i | ||||
\(599\) | −2.13988 | + | 3.70638i | −0.0874330 | + | 0.151438i | −0.906425 | − | 0.422366i | \(-0.861200\pi\) |
0.818992 | + | 0.573804i | \(0.194533\pi\) | |||||||
\(600\) | −3.49031 | − | 6.04539i | −0.142491 | − | 0.246802i | ||||
\(601\) | −47.6366 | −1.94314 | −0.971569 | − | 0.236757i | \(-0.923915\pi\) | ||||
−0.971569 | + | 0.236757i | \(0.923915\pi\) | |||||||
\(602\) | −22.8546 | − | 15.1823i | −0.931484 | − | 0.618785i | ||||
\(603\) | −13.7378 | −0.559447 | ||||||||
\(604\) | −9.63772 | − | 16.6930i | −0.392153 | − | 0.679229i | ||||
\(605\) | −18.9032 | + | 32.7413i | −0.768525 | + | 1.33113i | ||||
\(606\) | 1.22849 | − | 2.12781i | 0.0499041 | − | 0.0864365i | ||||
\(607\) | 10.3465 | + | 17.9207i | 0.419953 | + | 0.727379i | 0.995934 | − | 0.0900833i | \(-0.0287133\pi\) |
−0.575982 | + | 0.817463i | \(0.695380\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 1.41945 | − | 22.5862i | 0.0575191 | − | 0.915240i | ||||
\(610\) | 31.5997 | 1.27943 | ||||||||
\(611\) | 6.20680 | + | 10.7505i | 0.251100 | + | 0.434919i | ||||
\(612\) | −2.89876 | + | 5.02079i | −0.117175 | + | 0.202954i | ||||
\(613\) | −0.836989 | + | 1.44971i | −0.0338057 | + | 0.0585532i | −0.882433 | − | 0.470438i | \(-0.844096\pi\) |
0.848628 | + | 0.528991i | \(0.177429\pi\) | |||||||
\(614\) | −5.85037 | − | 10.1331i | −0.236102 | − | 0.408940i | ||||
\(615\) | 30.7555 | 1.24018 | ||||||||
\(616\) | −0.0461660 | + | 0.734590i | −0.00186008 | + | 0.0295975i | ||||
\(617\) | −13.5252 | −0.544504 | −0.272252 | − | 0.962226i | \(-0.587768\pi\) | ||||
−0.272252 | + | 0.962226i | \(0.587768\pi\) | |||||||
\(618\) | −8.67342 | − | 15.0228i | −0.348896 | − | 0.604306i | ||||
\(619\) | −22.5780 | + | 39.1062i | −0.907485 | + | 1.57181i | −0.0899383 | + | 0.995947i | \(0.528667\pi\) |
−0.817547 | + | 0.575862i | \(0.804666\pi\) | |||||||
\(620\) | 12.7196 | − | 22.0310i | 0.510831 | − | 0.884785i | ||||
\(621\) | 1.54617 | + | 2.67804i | 0.0620455 | + | 0.107466i | ||||
\(622\) | −13.8555 | −0.555556 | ||||||||
\(623\) | −30.1937 | − | 20.0577i | −1.20969 | − | 0.803594i | ||||
\(624\) | −6.92261 | −0.277126 | ||||||||
\(625\) | 5.58702 | + | 9.67700i | 0.223481 | + | 0.387080i | ||||
\(626\) | −0.985994 | + | 1.70779i | −0.0394083 | + | 0.0682571i | ||||
\(627\) | 0.139098 | − | 0.240925i | 0.00555505 | − | 0.00962164i | ||||
\(628\) | 10.7284 | + | 18.5822i | 0.428111 | + | 0.741510i | ||||
\(629\) | −30.3855 | −1.21155 | ||||||||
\(630\) | −8.20242 | + | 4.07242i | −0.326792 | + | 0.162249i | ||||
\(631\) | −3.01542 | −0.120042 | −0.0600210 | − | 0.998197i | \(-0.519117\pi\) | ||||
−0.0600210 | + | 0.998197i | \(0.519117\pi\) | |||||||
\(632\) | 0.703803 | + | 1.21902i | 0.0279958 | + | 0.0484901i | ||||
\(633\) | 7.45615 | − | 12.9144i | 0.296355 | − | 0.513302i | ||||
\(634\) | 9.95023 | − | 17.2343i | 0.395174 | − | 0.684462i | ||||
\(635\) | −5.98284 | − | 10.3626i | −0.237422 | − | 0.411227i | ||||
\(636\) | −8.38823 | −0.332615 | ||||||||
\(637\) | 29.2925 | − | 38.6025i | 1.16061 | − | 1.52948i | ||||
\(638\) | 2.37959 | 0.0942090 | ||||||||
\(639\) | −0.342363 | − | 0.592991i | −0.0135437 | − | 0.0234583i | ||||
\(640\) | −1.73065 | + | 2.99758i | −0.0684100 | + | 0.118490i | ||||
\(641\) | −7.99808 | + | 13.8531i | −0.315905 | + | 0.547164i | −0.979630 | − | 0.200813i | \(-0.935642\pi\) |
0.663724 | + | 0.747977i | \(0.268975\pi\) | |||||||
\(642\) | 5.73896 | + | 9.94017i | 0.226499 | + | 0.392307i | ||||
\(643\) | −20.9315 | −0.825460 | −0.412730 | − | 0.910854i | \(-0.635425\pi\) | ||||
−0.412730 | + | 0.910854i | \(0.635425\pi\) | |||||||
\(644\) | −7.32805 | + | 3.63830i | −0.288766 | + | 0.143369i | ||||
\(645\) | 35.8955 | 1.41339 | ||||||||
\(646\) | 2.89876 | + | 5.02079i | 0.114050 | + | 0.197541i | ||||
\(647\) | −21.7099 | + | 37.6026i | −0.853504 | + | 1.47831i | 0.0245220 | + | 0.999699i | \(0.492194\pi\) |
−0.878026 | + | 0.478613i | \(0.841140\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 1.08424 | + | 1.87796i | 0.0425601 | + | 0.0737162i | ||||
\(650\) | −48.3241 | −1.89543 | ||||||||
\(651\) | −16.1970 | − | 10.7597i | −0.634812 | − | 0.421706i | ||||
\(652\) | 15.9446 | 0.624439 | ||||||||
\(653\) | 3.03110 | + | 5.25002i | 0.118616 | + | 0.205449i | 0.919220 | − | 0.393745i | \(-0.128821\pi\) |
−0.800603 | + | 0.599195i | \(0.795488\pi\) | |||||||
\(654\) | 9.34068 | − | 16.1785i | 0.365250 | − | 0.632631i | ||||
\(655\) | 32.0095 | − | 55.4420i | 1.25071 | − | 2.16630i | ||||
\(656\) | −4.44277 | − | 7.69509i | −0.173461 | − | 0.300443i | ||||
\(657\) | −1.92536 | −0.0751156 | ||||||||
\(658\) | 0.297576 | − | 4.73501i | 0.0116007 | − | 0.184590i | ||||
\(659\) | −0.570382 | −0.0222189 | −0.0111095 | − | 0.999938i | \(-0.503536\pi\) | ||||
−0.0111095 | + | 0.999938i | \(0.503536\pi\) | |||||||
\(660\) | −0.481462 | − | 0.833916i | −0.0187409 | − | 0.0324601i | ||||
\(661\) | 8.81981 | − | 15.2764i | 0.343051 | − | 0.594181i | −0.641947 | − | 0.766749i | \(-0.721873\pi\) |
0.984998 | + | 0.172568i | \(0.0552064\pi\) | |||||||
\(662\) | −2.33381 | + | 4.04228i | −0.0907062 | + | 0.157108i | ||||
\(663\) | 20.0670 | + | 34.7570i | 0.779336 | + | 1.34985i | ||||
\(664\) | 0.146030 | 0.00566706 | ||||||||
\(665\) | −0.574394 | + | 9.13972i | −0.0222740 | + | 0.354423i | ||||
\(666\) | 5.24112 | 0.203089 | ||||||||
\(667\) | 13.2253 | + | 22.9070i | 0.512087 | + | 0.886961i | ||||
\(668\) | −8.80367 | + | 15.2484i | −0.340624 | + | 0.589978i | ||||
\(669\) | 1.96430 | − | 3.40227i | 0.0759443 | − | 0.131539i | ||||
\(670\) | 23.7754 | + | 41.1802i | 0.918523 | + | 1.59093i | ||||
\(671\) | 2.53977 | 0.0980468 | ||||||||
\(672\) | 2.20380 | + | 1.46399i | 0.0850135 | + | 0.0564745i | ||||
\(673\) | −39.1296 | −1.50833 | −0.754167 | − | 0.656682i | \(-0.771959\pi\) | ||||
−0.754167 | + | 0.656682i | \(0.771959\pi\) | |||||||
\(674\) | −5.73197 | − | 9.92806i | −0.220787 | − | 0.382415i | ||||
\(675\) | 3.49031 | − | 6.04539i | 0.134342 | − | 0.232687i | ||||
\(676\) | −17.4612 | + | 30.2438i | −0.671586 | + | 1.16322i | ||||
\(677\) | −17.7074 | − | 30.6702i | −0.680552 | − | 1.17875i | −0.974813 | − | 0.223025i | \(-0.928407\pi\) |
0.294261 | − | 0.955725i | \(-0.404927\pi\) | |||||||
\(678\) | 3.29913 | 0.126702 | ||||||||
\(679\) | −9.69780 | + | 4.81486i | −0.372168 | + | 0.184777i | ||||
\(680\) | 20.0670 | 0.769533 | ||||||||
\(681\) | −3.51985 | − | 6.09657i | −0.134881 | − | 0.233621i | ||||
\(682\) | 1.02232 | − | 1.77070i | 0.0391465 | − | 0.0678038i | ||||
\(683\) | 18.1449 | − | 31.4279i | 0.694295 | − | 1.20255i | −0.276123 | − | 0.961122i | \(-0.589050\pi\) |
0.970418 | − | 0.241431i | \(-0.0776169\pi\) | |||||||
\(684\) | −0.500000 | − | 0.866025i | −0.0191180 | − | 0.0331133i | ||||
\(685\) | 42.1173 | 1.60922 | ||||||||
\(686\) | −17.4888 | + | 6.09429i | −0.667727 | + | 0.232681i | ||||
\(687\) | −5.88397 | −0.224488 | ||||||||
\(688\) | −5.18526 | − | 8.98114i | −0.197686 | − | 0.342403i | ||||
\(689\) | −29.0342 | + | 50.2887i | −1.10611 | + | 1.91585i | ||||
\(690\) | 5.35175 | − | 9.26950i | 0.203738 | − | 0.352884i | ||||
\(691\) | −16.8574 | − | 29.1978i | −0.641284 | − | 1.11074i | −0.985146 | − | 0.171717i | \(-0.945069\pi\) |
0.343862 | − | 0.939020i | \(-0.388265\pi\) | |||||||
\(692\) | 10.0106 | 0.380547 | ||||||||
\(693\) | −0.659257 | + | 0.327314i | −0.0250431 | + | 0.0124336i | ||||
\(694\) | −7.84258 | −0.297700 | ||||||||
\(695\) | −5.05054 | − | 8.74780i | −0.191578 | − | 0.331823i | ||||
\(696\) | 4.27682 | − | 7.40767i | 0.162112 | − | 0.280787i | ||||
\(697\) | −25.7570 | + | 44.6124i | −0.975616 | + | 1.68982i | ||||
\(698\) | 10.6496 | + | 18.4456i | 0.403092 | + | 0.698176i | ||||
\(699\) | −2.80658 | −0.106155 | ||||||||
\(700\) | 15.3839 | + | 10.2195i | 0.581457 | + | 0.386262i | ||||
\(701\) | 12.6976 | 0.479583 | 0.239791 | − | 0.970824i | \(-0.422921\pi\) | ||||
0.239791 | + | 0.970824i | \(0.422921\pi\) | |||||||
\(702\) | −3.46130 | − | 5.99515i | −0.130638 | − | 0.226272i | ||||
\(703\) | 2.62056 | − | 4.53894i | 0.0988363 | − | 0.171189i | ||||
\(704\) | −0.139098 | + | 0.240925i | −0.00524247 | + | 0.00908022i | ||||
\(705\) | 3.10340 | + | 5.37525i | 0.116881 | + | 0.202444i | ||||
\(706\) | −8.71701 | −0.328069 | ||||||||
\(707\) | −0.407731 | + | 6.48778i | −0.0153343 | + | 0.243998i | ||||
\(708\) | 7.79476 | 0.292945 | ||||||||
\(709\) | 10.6396 | + | 18.4283i | 0.399578 | + | 0.692089i | 0.993674 | − | 0.112305i | \(-0.0358235\pi\) |
−0.594096 | + | 0.804394i | \(0.702490\pi\) | |||||||
\(710\) | −1.18502 | + | 2.05252i | −0.0444731 | + | 0.0770297i | ||||
\(711\) | −0.703803 | + | 1.21902i | −0.0263947 | + | 0.0457169i | ||||
\(712\) | −6.85037 | − | 11.8652i | −0.256728 | − | 0.444667i | ||||
\(713\) | 22.7274 | 0.851147 | ||||||||
\(714\) | 0.962082 | − | 15.3086i | 0.0360050 | − | 0.572909i | ||||
\(715\) | −6.66594 | −0.249292 | ||||||||
\(716\) | −3.12941 | − | 5.42029i | −0.116951 | − | 0.202566i | ||||
\(717\) | −6.20080 | + | 10.7401i | −0.231573 | + | 0.401097i | ||||
\(718\) | 0.585642 | − | 1.01436i | 0.0218559 | − | 0.0378556i | ||||
\(719\) | −24.1116 | − | 41.7625i | −0.899210 | − | 1.55748i | −0.828506 | − | 0.559981i | \(-0.810808\pi\) |
−0.0707049 | − | 0.997497i | \(-0.522525\pi\) | |||||||
\(720\) | −3.46130 | −0.128995 | ||||||||
\(721\) | 38.2290 | + | 25.3955i | 1.42372 | + | 0.945778i | ||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −7.59824 | − | 13.1605i | −0.282582 | − | 0.489446i | ||||
\(724\) | 2.12509 | − | 3.68077i | 0.0789784 | − | 0.136795i | ||||
\(725\) | 29.8548 | − | 51.7101i | 1.10878 | − | 1.92046i | ||||
\(726\) | 5.46130 | + | 9.45925i | 0.202688 | + | 0.351066i | ||||
\(727\) | 49.2945 | 1.82823 | 0.914116 | − | 0.405452i | \(-0.132886\pi\) | ||||
0.914116 | + | 0.405452i | \(0.132886\pi\) | |||||||
\(728\) | 16.4048 | − | 8.14484i | 0.608004 | − | 0.301868i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.33214 | + | 5.77143i | 0.123328 | + | 0.213610i | ||||
\(731\) | −30.0616 | + | 52.0683i | −1.11187 | + | 1.92582i | ||||
\(732\) | 4.56470 | − | 7.90630i | 0.168716 | − | 0.292225i | ||||
\(733\) | 0.462145 | + | 0.800458i | 0.0170697 | + | 0.0295656i | 0.874434 | − | 0.485144i | \(-0.161233\pi\) |
−0.857364 | + | 0.514710i | \(0.827900\pi\) | |||||||
\(734\) | −5.01295 | −0.185031 | ||||||||
\(735\) | 14.6463 | − | 19.3012i | 0.540236 | − | 0.711936i | ||||
\(736\) | −3.09233 | −0.113985 | ||||||||
\(737\) | 1.91091 | + | 3.30979i | 0.0703892 | + | 0.121918i | ||||
\(738\) | 4.44277 | − | 7.69509i | 0.163540 | − | 0.283260i | ||||
\(739\) | −1.17588 | + | 2.03668i | −0.0432554 | + | 0.0749205i | −0.886843 | − | 0.462072i | \(-0.847106\pi\) |
0.843587 | + | 0.536992i | \(0.180440\pi\) | |||||||
\(740\) | −9.07055 | − | 15.7107i | −0.333440 | − | 0.577535i | ||||
\(741\) | −6.92261 | −0.254308 | ||||||||
\(742\) | 19.8780 | − | 9.86922i | 0.729744 | − | 0.362310i | ||||
\(743\) | −50.4616 | −1.85126 | −0.925628 | − | 0.378433i | \(-0.876463\pi\) | ||||
−0.925628 | + | 0.378433i | \(0.876463\pi\) | |||||||
\(744\) | −3.67480 | − | 6.36493i | −0.134725 | − | 0.233350i | ||||
\(745\) | −7.20804 | + | 12.4847i | −0.264082 | + | 0.457404i | ||||
\(746\) | 0.932921 | − | 1.61587i | 0.0341567 | − | 0.0591611i | ||||
\(747\) | 0.0730150 | + | 0.126466i | 0.00267148 | + | 0.00462714i | ||||
\(748\) | 1.61285 | 0.0589716 | ||||||||
\(749\) | −25.2951 | − | 16.8035i | −0.924262 | − | 0.613987i | ||||
\(750\) | −6.85553 | −0.250328 | ||||||||
\(751\) | 3.11141 | + | 5.38912i | 0.113537 | + | 0.196652i | 0.917194 | − | 0.398441i | \(-0.130449\pi\) |
−0.803657 | + | 0.595093i | \(0.797115\pi\) | |||||||
\(752\) | 0.896599 | − | 1.55296i | 0.0326956 | − | 0.0566304i | ||||
\(753\) | 2.95599 | − | 5.11993i | 0.107722 | − | 0.186581i | ||||
\(754\) | −29.6067 | − | 51.2804i | −1.07821 | − | 1.86752i | ||||
\(755\) | −66.7181 | −2.42812 | ||||||||
\(756\) | −0.165947 | + | 2.64054i | −0.00603545 | + | 0.0960356i | ||||
\(757\) | 19.9762 | 0.726047 | 0.363023 | − | 0.931780i | \(-0.381745\pi\) | ||||
0.363023 | + | 0.931780i | \(0.381745\pi\) | |||||||
\(758\) | −5.90323 | − | 10.2247i | −0.214415 | − | 0.371377i | ||||
\(759\) | 0.430138 | − | 0.745022i | 0.0156130 | − | 0.0270426i | ||||
\(760\) | −1.73065 | + | 2.99758i | −0.0627773 | + | 0.108734i | ||||
\(761\) | −7.65272 | − | 13.2549i | −0.277411 | − | 0.480490i | 0.693330 | − | 0.720621i | \(-0.256143\pi\) |
−0.970741 | + | 0.240131i | \(0.922810\pi\) | |||||||
\(762\) | −3.45699 | −0.125233 | ||||||||
\(763\) | −3.10012 | + | 49.3289i | −0.112232 | + | 1.78583i | ||||
\(764\) | −10.9479 | −0.396080 | ||||||||
\(765\) | 10.0335 | + | 17.3785i | 0.362761 | + | 0.628321i | ||||
\(766\) | 2.76320 | − | 4.78600i | 0.0998383 | − | 0.172925i | ||||
\(767\) | 26.9800 | − | 46.7308i | 0.974192 | − | 1.68735i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −18.0461 | −0.650761 | −0.325380 | − | 0.945583i | \(-0.605492\pi\) | ||||
−0.325380 | + | 0.945583i | \(0.605492\pi\) | |||||||
\(770\) | 2.12209 | + | 1.40971i | 0.0764749 | + | 0.0508023i | ||||
\(771\) | −1.40485 | −0.0505943 | ||||||||
\(772\) | −10.6449 | − | 18.4376i | −0.383120 | − | 0.663583i | ||||
\(773\) | 20.1390 | − | 34.8818i | 0.724351 | − | 1.25461i | −0.234890 | − | 0.972022i | \(-0.575473\pi\) |
0.959241 | − | 0.282590i | \(-0.0911937\pi\) | |||||||
\(774\) | 5.18526 | − | 8.98114i | 0.186380 | − | 0.322820i | ||||
\(775\) | −25.6524 | − | 44.4312i | −0.921460 | − | 1.59602i | ||||
\(776\) | −4.09233 | −0.146906 | ||||||||
\(777\) | −12.4201 | + | 6.16647i | −0.445570 | + | 0.221221i | ||||
\(778\) | −1.26421 | −0.0453241 | ||||||||
\(779\) | −4.44277 | − | 7.69509i | −0.159179 | − | 0.275705i | ||||
\(780\) | −11.9806 | + | 20.7510i | −0.428975 | + | 0.743007i | ||||
\(781\) | −0.0952444 | + | 0.164968i | −0.00340811 | + | 0.00590302i | ||||
\(782\) | 8.96392 | + | 15.5260i | 0.320549 | + | 0.555207i | ||||
\(783\) | 8.55364 | 0.305682 | ||||||||
\(784\) | −6.94492 | − | 0.876382i | −0.248033 | − | 0.0312994i | ||||
\(785\) | 74.2687 | 2.65076 | ||||||||
\(786\) | −9.24781 | − | 16.0177i | −0.329858 | − | 0.571332i | ||||
\(787\) | 11.1428 | − | 19.2999i | 0.397198 | − | 0.687966i | −0.596181 | − | 0.802850i | \(-0.703316\pi\) |
0.993379 | + | 0.114883i | \(0.0366494\pi\) | |||||||
\(788\) | 3.31551 | − | 5.74264i | 0.118110 | − | 0.204573i | ||||
\(789\) | −5.38907 | − | 9.33414i | −0.191856 | − | 0.332304i | ||||
\(790\) | 4.87215 | 0.173343 | ||||||||
\(791\) | −7.81812 | + | 3.88162i | −0.277980 | + | 0.138014i | ||||
\(792\) | −0.278197 | −0.00988529 | ||||||||
\(793\) | −31.5997 | − | 54.7322i | −1.12214 | − | 1.94360i | ||||
\(794\) | −0.702424 | + | 1.21663i | −0.0249281 | + | 0.0431767i | ||||
\(795\) | −14.5171 | + | 25.1443i | −0.514868 | + | 0.891778i | ||||
\(796\) | 3.93523 | + | 6.81602i | 0.139481 | + | 0.241588i | ||||
\(797\) | −11.6159 | −0.411457 | −0.205728 | − | 0.978609i | \(-0.565956\pi\) | ||||
−0.205728 | + | 0.978609i | \(0.565956\pi\) | |||||||
\(798\) | 2.20380 | + | 1.46399i | 0.0780138 | + | 0.0518245i | ||||
\(799\) | −10.3961 | −0.367787 | ||||||||
\(800\) | 3.49031 | + | 6.04539i | 0.123401 | + | 0.213737i | ||||
\(801\) | 6.85037 | − | 11.8652i | 0.242046 | − | 0.419236i | ||||
\(802\) | −2.38559 | + | 4.13197i | −0.0842382 | + | 0.145905i | ||||
\(803\) | 0.267815 | + | 0.463869i | 0.00945099 | + | 0.0163696i | ||||
\(804\) | 13.7378 | 0.484495 | ||||||||
\(805\) | −1.77622 | + | 28.2630i | −0.0626034 | + | 0.996141i | ||||
\(806\) | −50.8783 | −1.79211 | ||||||||
\(807\) | 11.2231 | + | 19.4390i | 0.395073 | + | 0.684286i | ||||
\(808\) | −1.22849 | + | 2.12781i | −0.0432183 | + | 0.0748562i | ||||
\(809\) | 10.9978 | − | 19.0488i | 0.386664 | − | 0.669721i | −0.605335 | − | 0.795971i | \(-0.706961\pi\) |
0.991998 | + | 0.126250i | \(0.0402941\pi\) | |||||||
\(810\) | −1.73065 | − | 2.99758i | −0.0608089 | − | 0.105324i | ||||
\(811\) | 24.2399 | 0.851177 | 0.425588 | − | 0.904917i | \(-0.360067\pi\) | ||||
0.425588 | + | 0.904917i | \(0.360067\pi\) | |||||||
\(812\) | −1.41945 | + | 22.5862i | −0.0498130 | + | 0.792621i | ||||
\(813\) | 2.27651 | 0.0798408 | ||||||||
\(814\) | −0.729031 | − | 1.26272i | −0.0255525 | − | 0.0442583i | ||||
\(815\) | 27.5946 | − | 47.7952i | 0.966596 | − | 1.67419i | ||||
\(816\) | 2.89876 | − | 5.02079i | 0.101477 | − | 0.175763i | ||||
\(817\) | −5.18526 | − | 8.98114i | −0.181409 | − | 0.314210i | ||||
\(818\) | 18.0890 | 0.632466 | ||||||||
\(819\) | 15.2561 | + | 10.1346i | 0.533090 | + | 0.354131i | ||||
\(820\) | −30.7555 | −1.07403 | ||||||||
\(821\) | 6.71658 | + | 11.6335i | 0.234410 | + | 0.406011i | 0.959101 | − | 0.283064i | \(-0.0913507\pi\) |
−0.724691 | + | 0.689074i | \(0.758017\pi\) | |||||||
\(822\) | 6.08402 | − | 10.5378i | 0.212205 | − | 0.367549i | ||||
\(823\) | −4.76827 | + | 8.25888i | −0.166211 | + | 0.287886i | −0.937085 | − | 0.349102i | \(-0.886487\pi\) |
0.770873 | + | 0.636988i | \(0.219820\pi\) | |||||||
\(824\) | 8.67342 | + | 15.0228i | 0.302153 | + | 0.523344i | ||||
\(825\) | −1.94199 | −0.0676113 | ||||||||
\(826\) | −18.4716 | + | 9.17097i | −0.642710 | + | 0.319099i | ||||
\(827\) | 46.7140 | 1.62440 | 0.812202 | − | 0.583376i | \(-0.198268\pi\) | ||||
0.812202 | + | 0.583376i | \(0.198268\pi\) | |||||||
\(828\) | −1.54617 | − | 2.67804i | −0.0537330 | − | 0.0930683i | ||||
\(829\) | −8.66379 | + | 15.0061i | −0.300906 | + | 0.521184i | −0.976341 | − | 0.216235i | \(-0.930622\pi\) |
0.675436 | + | 0.737419i | \(0.263956\pi\) | |||||||
\(830\) | 0.252727 | − | 0.437736i | 0.00877228 | − | 0.0151940i | ||||
\(831\) | 13.7260 | + | 23.7742i | 0.476151 | + | 0.824717i | ||||
\(832\) | 6.92261 | 0.239998 | ||||||||
\(833\) | 15.7315 | + | 37.4094i | 0.545065 | + | 1.29616i | ||||
\(834\) | −2.91829 | −0.101052 | ||||||||
\(835\) | 30.4722 | + | 52.7793i | 1.05453 | + | 1.82650i | ||||
\(836\) | −0.139098 | + | 0.240925i | −0.00481082 | + | 0.00833258i | ||||
\(837\) | 3.67480 | − | 6.36493i | 0.127020 | − | 0.220004i | ||||
\(838\) | 1.35259 | + | 2.34276i | 0.0467245 | + | 0.0809292i | ||||
\(839\) | −26.5740 | −0.917435 | −0.458718 | − | 0.888582i | \(-0.651691\pi\) | ||||
−0.458718 | + | 0.888582i | \(0.651691\pi\) | |||||||
\(840\) | 8.20242 | − | 4.07242i | 0.283010 | − | 0.140512i | ||||
\(841\) | 44.1647 | 1.52292 | ||||||||
\(842\) | 3.07032 | + | 5.31795i | 0.105810 | + | 0.183269i | ||||
\(843\) | 4.07139 | − | 7.05186i | 0.140226 | − | 0.242879i | ||||
\(844\) | −7.45615 | + | 12.9144i | −0.256651 | + | 0.444533i | ||||
\(845\) | 60.4386 | + | 104.683i | 2.07915 | + | 3.60120i | ||||
\(846\) | 1.79320 | 0.0616514 | ||||||||
\(847\) | −24.0713 | − | 15.9905i | −0.827099 | − | 0.549441i | ||||
\(848\) | 8.38823 | 0.288053 | ||||||||
\(849\) | −4.09293 | − | 7.08917i | −0.140469 | − | 0.243300i | ||||
\(850\) | 20.2351 | − | 35.0483i | 0.694059 | − | 1.20215i | ||||
\(851\) | 8.10364 | − | 14.0359i | 0.277789 | − | 0.481145i | ||||
\(852\) | 0.342363 | + | 0.592991i | 0.0117292 | + | 0.0203155i | ||||
\(853\) | −4.35464 | −0.149100 | −0.0745500 | − | 0.997217i | \(-0.523752\pi\) | ||||
−0.0745500 | + | 0.997217i | \(0.523752\pi\) | |||||||
\(854\) | −1.51500 | + | 24.1066i | −0.0518423 | + | 0.824910i | ||||
\(855\) | −3.46130 | −0.118374 | ||||||||
\(856\) | −5.73896 | − | 9.94017i | −0.196154 | − | 0.339748i | ||||
\(857\) | 22.3505 | − | 38.7123i | 0.763480 | − | 1.32239i | −0.177567 | − | 0.984109i | \(-0.556822\pi\) |
0.941046 | − | 0.338277i | \(-0.109844\pi\) | |||||||
\(858\) | −0.962923 | + | 1.66783i | −0.0328737 | + | 0.0569389i | ||||
\(859\) | −2.71025 | − | 4.69429i | −0.0924726 | − | 0.160167i | 0.816078 | − | 0.577941i | \(-0.196144\pi\) |
−0.908551 | + | 0.417774i | \(0.862810\pi\) | |||||||
\(860\) | −35.8955 | −1.22403 | ||||||||
\(861\) | −1.47453 | + | 23.4626i | −0.0502519 | + | 0.799604i | ||||
\(862\) | −21.2765 | −0.724681 | ||||||||
\(863\) | 20.8794 | + | 36.1641i | 0.710742 | + | 1.23104i | 0.964579 | + | 0.263795i | \(0.0849741\pi\) |
−0.253837 | + | 0.967247i | \(0.581693\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 17.3249 | − | 30.0076i | 0.589064 | − | 1.02029i | ||||
\(866\) | −4.71049 | − | 8.15881i | −0.160069 | − | 0.277248i | ||||
\(867\) | −16.6112 | −0.564145 | ||||||||
\(868\) | 16.1970 | + | 10.7597i | 0.549764 | + | 0.365208i | ||||
\(869\) | 0.391591 | 0.0132838 | ||||||||
\(870\) | −14.8034 | − | 25.6402i | −0.501881 | − | 0.869283i | ||||
\(871\) | 47.5508 | − | 82.3603i | 1.61120 | − | 2.79067i | ||||
\(872\) | −9.34068 | + | 16.1785i | −0.316315 | + | 0.547874i | ||||
\(873\) | −2.04617 | − | 3.54406i | −0.0692522 | − | 0.119948i | ||||
\(874\) | −3.09233 | −0.104600 | ||||||||
\(875\) | 16.2459 | − | 8.06591i | 0.549211 | − | 0.272678i | ||||
\(876\) | 1.92536 | 0.0650520 | ||||||||
\(877\) | −17.9700 | − | 31.1250i | −0.606805 | − | 1.05102i | −0.991763 | − | 0.128083i | \(-0.959118\pi\) |
0.384959 | − | 0.922934i | \(-0.374216\pi\) | |||||||
\(878\) | 6.29620 | − | 10.9053i | 0.212486 | − | 0.368037i | ||||
\(879\) | −9.67104 | + | 16.7507i | −0.326196 | + | 0.564988i | ||||
\(880\) | 0.481462 | + | 0.833916i | 0.0162301 | + | 0.0281113i | ||||
\(881\) | 49.3541 | 1.66278 | 0.831391 | − | 0.555688i | \(-0.187545\pi\) | ||||
0.831391 | + | 0.555688i | \(0.187545\pi\) | |||||||
\(882\) | −2.71349 | − | 6.45267i | −0.0913680 | − | 0.217273i | ||||
\(883\) | 12.0927 | 0.406951 | 0.203476 | − | 0.979080i | \(-0.434776\pi\) | ||||
0.203476 | + | 0.979080i | \(0.434776\pi\) | |||||||
\(884\) | −20.0670 | − | 34.7570i | −0.674925 | − | 1.16900i | ||||
\(885\) | 13.4900 | − | 23.3654i | 0.453462 | − | 0.785419i | ||||
\(886\) | −11.6473 | + | 20.1738i | −0.391300 | + | 0.677752i | ||||
\(887\) | −13.7810 | − | 23.8695i | −0.462722 | − | 0.801458i | 0.536373 | − | 0.843981i | \(-0.319794\pi\) |
−0.999096 | + | 0.0425224i | \(0.986461\pi\) | |||||||
\(888\) | −5.24112 | −0.175880 | ||||||||
\(889\) | 8.19220 | − | 4.06734i | 0.274757 | − | 0.136414i | ||||
\(890\) | −47.4224 | −1.58960 | ||||||||
\(891\) | −0.139098 | − | 0.240925i | −0.00465997 | − | 0.00807131i | ||||
\(892\) | −1.96430 | + | 3.40227i | −0.0657697 | + | 0.113916i | ||||
\(893\) | 0.896599 | − | 1.55296i | 0.0300035 | − | 0.0519677i | ||||
\(894\) | 2.08246 | + | 3.60693i | 0.0696480 | + | 0.120634i | ||||
\(895\) | −21.6637 | −0.724136 | ||||||||
\(896\) | −2.20380 | − | 1.46399i | −0.0736239 | − | 0.0489083i | ||||
\(897\) | −21.4070 | −0.714759 | ||||||||
\(898\) | −0.243037 | − | 0.420953i | −0.00811025 | − | 0.0140474i | ||||
\(899\) | 31.4329 | − | 54.4433i | 1.04834 | − | 1.81579i | ||||
\(900\) | −3.49031 | + | 6.04539i | −0.116344 | + | 0.201513i | ||||
\(901\) | −24.3154 | − | 42.1156i | −0.810064 | − | 1.40307i | ||||
\(902\) | −2.47193 | −0.0823061 | ||||||||
\(903\) | −1.72096 | + | 27.3838i | −0.0572700 | + | 0.911276i | ||||
\(904\) | −3.29913 | −0.109728 | ||||||||
\(905\) | −7.35559 | − | 12.7403i | −0.244508 | − | 0.423500i | ||||
\(906\) | −9.63772 | + | 16.6930i | −0.320192 | + | 0.554588i | ||||
\(907\) | −20.1839 | + | 34.9596i | −0.670197 | + | 1.16082i | 0.307651 | + | 0.951499i | \(0.400457\pi\) |
−0.977848 | + | 0.209316i | \(0.932876\pi\) | |||||||
\(908\) | 3.51985 | + | 6.09657i | 0.116810 | + | 0.202322i | ||||
\(909\) | −2.45699 | −0.0814931 | ||||||||
\(910\) | 3.97630 | − | 63.2707i | 0.131813 | − | 2.09740i | ||||
\(911\) | −6.02988 | −0.199779 | −0.0998894 | − | 0.994999i | \(-0.531849\pi\) | ||||
−0.0998894 | + | 0.994999i | \(0.531849\pi\) | |||||||
\(912\) | 0.500000 | + | 0.866025i | 0.0165567 | + | 0.0286770i | ||||
\(913\) | 0.0203125 | − | 0.0351823i | 0.000672247 | − | 0.00116437i | ||||
\(914\) | 7.22987 | − | 12.5225i | 0.239143 | − | 0.414208i | ||||
\(915\) | −15.7998 | − | 27.3661i | −0.522326 | − | 0.904695i | ||||
\(916\) | 5.88397 | 0.194412 | ||||||||
\(917\) | 40.7607 | + | 27.0773i | 1.34604 | + | 0.894172i | ||||
\(918\) | 5.79751 | 0.191346 | ||||||||
\(919\) | −25.7574 | − | 44.6132i | −0.849659 | − | 1.47165i | −0.881512 | − | 0.472161i | \(-0.843474\pi\) |
0.0318529 | − | 0.999493i | \(-0.489859\pi\) | |||||||
\(920\) | −5.35175 | + | 9.26950i | −0.176442 | + | 0.305606i | ||||
\(921\) | −5.85037 | + | 10.1331i | −0.192776 | + | 0.333898i | ||||
\(922\) | 9.00939 | + | 15.6047i | 0.296708 | + | 0.513914i | ||||
\(923\) | 4.74009 | 0.156022 | ||||||||
\(924\) | 0.659257 | − | 0.327314i | 0.0216880 | − | 0.0107678i | ||||
\(925\) | −36.5863 | −1.20295 | ||||||||
\(926\) | 11.6704 | + | 20.2138i | 0.383514 | + | 0.664265i | ||||
\(927\) | −8.67342 | + | 15.0228i | −0.284872 | + | 0.493413i | ||||
\(928\) | −4.27682 | + | 7.40767i | −0.140393 | + | 0.243169i | ||||
\(929\) | 4.34268 | + | 7.52175i | 0.142479 | + | 0.246781i | 0.928430 | − | 0.371509i | \(-0.121159\pi\) |
−0.785951 | + | 0.618289i | \(0.787826\pi\) | |||||||
\(930\) | −25.4392 | −0.834183 | ||||||||
\(931\) | −6.94492 | − | 0.876382i | −0.227611 | − | 0.0287223i | ||||
\(932\) | 2.80658 | 0.0919326 | ||||||||
\(933\) | 6.92776 | + | 11.9992i | 0.226805 | + | 0.392837i | ||||
\(934\) | −4.07439 | + | 7.05706i | −0.133318 | + | 0.230914i | ||||
\(935\) | 2.79128 | − | 4.83464i | 0.0912847 | − | 0.158110i | ||||
\(936\) | 3.46130 | + | 5.99515i | 0.113136 | + | 0.195958i | ||||
\(937\) | −59.2801 | −1.93660 | −0.968298 | − | 0.249799i | \(-0.919635\pi\) | ||||
−0.968298 | + | 0.249799i | \(0.919635\pi\) | |||||||
\(938\) | −32.5552 | + | 16.1633i | −1.06296 | + | 0.527751i | ||||
\(939\) | 1.97199 | 0.0643534 | ||||||||
\(940\) | −3.10340 | − | 5.37525i | −0.101222 | − | 0.175321i | ||||
\(941\) | 7.11409 | − | 12.3220i | 0.231913 | − | 0.401684i | −0.726458 | − | 0.687211i | \(-0.758835\pi\) |
0.958371 | + | 0.285526i | \(0.0921683\pi\) | |||||||
\(942\) | 10.7284 | − | 18.5822i | 0.349551 | − | 0.605440i | ||||
\(943\) | −13.7385 | − | 23.7958i | −0.447387 | − | 0.774897i | ||||
\(944\) | −7.79476 | −0.253698 | ||||||||
\(945\) | 7.62803 | + | 5.06730i | 0.248140 | + | 0.164839i | ||||
\(946\) | −2.88505 | −0.0938010 | ||||||||
\(947\) | −7.80403 | − | 13.5170i | −0.253597 | − | 0.439242i | 0.710917 | − | 0.703276i | \(-0.248280\pi\) |
−0.964513 | + | 0.264034i | \(0.914947\pi\) | |||||||
\(948\) | 0.703803 | − | 1.21902i | 0.0228584 | − | 0.0395920i | ||||
\(949\) | 6.66427 | − | 11.5429i | 0.216331 | − | 0.374697i | ||||
\(950\) | 3.49031 | + | 6.04539i | 0.113241 | + | 0.196138i | ||||
\(951\) | −19.9005 | −0.645317 | ||||||||
\(952\) | −0.962082 | + | 15.3086i | −0.0311813 | + | 0.496154i | ||||
\(953\) | 9.11279 | 0.295192 | 0.147596 | − | 0.989048i | \(-0.452846\pi\) | ||||
0.147596 | + | 0.989048i | \(0.452846\pi\) | |||||||
\(954\) | 4.19411 | + | 7.26442i | 0.135789 | + | 0.235194i | ||||
\(955\) | −18.9469 | + | 32.8170i | −0.613108 | + | 1.06193i | ||||
\(956\) | 6.20080 | − | 10.7401i | 0.200548 | − | 0.347360i | ||||
\(957\) | −1.18980 | − | 2.06079i | −0.0384607 | − | 0.0666158i | ||||
\(958\) | −27.1627 | −0.877585 | ||||||||
\(959\) | −2.01925 | + | 32.1302i | −0.0652051 | + | 1.03754i | ||||
\(960\) | 3.46130 | 0.111713 | ||||||||
\(961\) | −11.5082 | − | 19.9329i | −0.371234 | − | 0.642996i | ||||
\(962\) | −18.1411 | + | 31.4213i | −0.584893 | + | 1.01306i | ||||
\(963\) | 5.73896 | − | 9.94017i | 0.184935 | − | 0.320318i | ||||
\(964\) | 7.59824 | + | 13.1605i | 0.244723 | + | 0.423873i | ||||
\(965\) | −73.6908 | −2.37219 | ||||||||
\(966\) | 6.81489 | + | 4.52713i | 0.219265 | + | 0.145658i | ||||
\(967\) | −4.04494 | −0.130077 | −0.0650383 | − | 0.997883i | \(-0.520717\pi\) | ||||
−0.0650383 | + | 0.997883i | \(0.520717\pi\) | |||||||
\(968\) | −5.46130 | − | 9.45925i | −0.175533 | − | 0.304032i | ||||
\(969\) | 2.89876 | − | 5.02079i | 0.0931215 | − | 0.161291i | ||||
\(970\) | −7.08240 | + | 12.2671i | −0.227402 | + | 0.393872i | ||||
\(971\) | −9.04293 | − | 15.6628i | −0.290201 | − | 0.502643i | 0.683656 | − | 0.729805i | \(-0.260389\pi\) |
−0.973857 | + | 0.227161i | \(0.927056\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 6.91562 | − | 3.43353i | 0.221705 | − | 0.110074i | ||||
\(974\) | 11.9423 | 0.382657 | ||||||||
\(975\) | 24.1620 | + | 41.8499i | 0.773805 | + | 1.34027i | ||||
\(976\) | −4.56470 | + | 7.90630i | −0.146113 | + | 0.253074i | ||||
\(977\) | 21.5756 | − | 37.3701i | 0.690266 | − | 1.19558i | −0.281484 | − | 0.959566i | \(-0.590827\pi\) |
0.971751 | − | 0.236010i | \(-0.0758399\pi\) | |||||||
\(978\) | −7.97231 | − | 13.8084i | −0.254926 | − | 0.441545i | ||||
\(979\) | −3.81150 | −0.121816 | ||||||||
\(980\) | −14.6463 | + | 19.3012i | −0.467858 | + | 0.616555i | ||||
\(981\) | −18.6814 | −0.596450 | ||||||||
\(982\) | −3.50432 | − | 6.06965i | −0.111827 | − | 0.193690i | ||||
\(983\) | 15.7958 | − | 27.3592i | 0.503809 | − | 0.872622i | −0.496182 | − | 0.868219i | \(-0.665265\pi\) |
0.999990 | − | 0.00440358i | \(-0.00140171\pi\) | |||||||
\(984\) | −4.44277 | + | 7.69509i | −0.141630 | + | 0.245311i | ||||
\(985\) | −11.4760 | − | 19.8770i | −0.365656 | − | 0.633334i | ||||
\(986\) | 49.5898 | 1.57926 | ||||||||
\(987\) | −4.24943 | + | 2.10980i | −0.135261 | + | 0.0671556i | ||||
\(988\) | 6.92261 | 0.220237 | ||||||||
\(989\) | −16.0346 | − | 27.7727i | −0.509869 | − | 0.883120i | ||||
\(990\) | −0.481462 | + | 0.833916i | −0.0153019 | + | 0.0265036i | ||||
\(991\) | −18.3975 | + | 31.8655i | −0.584417 | + | 1.01224i | 0.410530 | + | 0.911847i | \(0.365344\pi\) |
−0.994948 | + | 0.100394i | \(0.967990\pi\) | |||||||
\(992\) | 3.67480 | + | 6.36493i | 0.116675 | + | 0.202087i | ||||
\(993\) | 4.66762 | 0.148123 | ||||||||
\(994\) | −1.50900 | − | 1.00243i | −0.0478627 | − | 0.0317951i | ||||
\(995\) | 27.2421 | 0.863632 | ||||||||
\(996\) | −0.0730150 | − | 0.126466i | −0.00231357 | − | 0.00400722i | ||||
\(997\) | 21.1562 | − | 36.6436i | 0.670023 | − | 1.16051i | −0.307875 | − | 0.951427i | \(-0.599618\pi\) |
0.977897 | − | 0.209086i | \(-0.0670490\pi\) | |||||||
\(998\) | −4.56302 | + | 7.90339i | −0.144440 | + | 0.250177i | ||||
\(999\) | −2.62056 | − | 4.53894i | −0.0829109 | − | 0.143606i |
(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 | 798.2.j.l.571.4 | yes | 8 | |
7.2 | even | 3 | inner | 798.2.j.l.457.4 | ✓ | 8 | |
7.3 | odd | 6 | 5586.2.a.bz.1.4 | 4 | |||
7.4 | even | 3 | 5586.2.a.bw.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
798.2.j.l.457.4 | ✓ | 8 | 7.2 | even | 3 | inner | |
798.2.j.l.571.4 | yes | 8 | 1.1 | even | 1 | trivial | |
5586.2.a.bw.1.1 | 4 | 7.4 | even | 3 | |||
5586.2.a.bz.1.4 | 4 | 7.3 | odd | 6 |